Subgroups — C₃×C₅×#3521 #14276555

Order 1920.

2084 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#553	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#553	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#552	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#552	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#551	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#551	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#546	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#539	C₂	1	2	yes	maximal, complemented
16	C₃×C₅×#538	C₂	1	2	yes	maximal, complemented
17	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×C₅×#529	C₂	1	2	yes	maximal, complemented
19	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃×C₅×#126	C₂	1	2	yes	maximal, complemented
21	C₃×C₅×#520	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×C₅×#518	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#3521	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₅×#126	C₂²	1	1	yes	characteristic
31	C₃×C₅×#126	C₂²	1	2	yes	—
32	C₃×C₅×#126	C₂²	1	2	yes	—
33	C₃×C₅×#126	C₂²	1	2	yes	—
34	C₃×C₅×#126	C₂²	1	2	yes	—
35	C₃×C₅×#126	C₂²	1	2	yes	complemented
36	C₃×C₅×#126	C₂²	1	2	yes	complemented
37	C₃×C₅×#126	C₂²	1	2	yes	complemented
38	C₃×C₅×#126	C₂²	1	2	yes	complemented
39	C₃×C₅×#126	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₅×#126	C₂²	1	2	yes	complemented
41	C₃×C₅×#126	C₂²	1	2	yes	complemented
42	C₃×C₅×#125	C₂²	1	2	yes	complemented
43	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#125	C₂²	1	2	yes	complemented
46	C₃×C₅×#125	C₂²	1	2	yes	complemented
47	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₅×#124	C₂²	1	1	yes	characteristic
49	C₃×C₅×#124	C₂²	1	1	yes	characteristic
50	C₃×C₅×#124	C₂²	1	2	yes	—
51	C₃×C₅×#124	C₂²	1	1	yes	characteristic
52	C₃×C₅×#124	C₂²	1	2	yes	complemented
53	C₃×C₅×#123	C₂²	1	2	yes	—
54	C₃×C₅×#123	C₂²	1	1	yes	characteristic
55	C₃×C₅×#123	C₂²	1	2	yes	—
56	C₃×C₅×#123	C₂²	1	2	yes	—
57	C₃×C₅×#123	C₂²	1	2	yes	complemented
58	C₃×C₅×#123	C₂²	1	2	yes	complemented
59	C₃×C₅×#123	C₂²	1	1	yes	characteristic, complemented
60	C₃×C₅×#123	C₂²	1	2	yes	complemented
61	C₃×C₅×#123	C₂²	1	2	yes	complemented
62	C₃×C₅×#123	C₂²	1	2	yes	complemented
63	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
64	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
65	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
66	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
67	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
68	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
69	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
70	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
71	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
72	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
73	C₃×C₅×#121	C₂²	1	1	yes	characteristic
74	C₃×C₅×#121	C₂²	1	1	yes	characteristic
75	C₃×C₅×#121	C₂²	1	2	yes	—
76	C₃×C₅×#121	C₂²	1	2	yes	—
77	C₃×C₅×#121	C₂²	1	1	yes	characteristic
78	C₃×C₅×#121	C₂²	1	2	yes	complemented
79	C₃×C₅×#121	C₂²	1	2	yes	complemented
80	C₃×C₅×#120	C₂²	1	2	yes	—
81	C₃×C₅×#120	C₂²	1	2	yes	—
82	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
83	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
84	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
85	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
86	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
87	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
88	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
89	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
90	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
91	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
92	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
93	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
94	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
95	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
96	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
97	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
98	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
99	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
100	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
101	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
102	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
103	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
104	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
105	C₃×C₅×#117	C₂²	1	1	yes	characteristic
106	C₃×C₅×#117	C₂²	1	1	yes	characteristic
107	C₃×C₅×#117	C₂²	1	2	yes	complemented
108	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
109	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
110	C₃×C₅×#117	C₂²	1	2	yes	complemented
111	C₃×C₅×#117	C₂²	1	2	yes	complemented
112	C₃×C₅×#117	C₂²	1	2	yes	complemented
113	C₃×C₅×#117	C₂²	1	2	yes	complemented
114	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
115	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
117	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
118	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
123	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
124	C₃×#3521	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
125	C₅×#556	C₂×C₃	1	1	yes	characteristic, complemented
126	C₅×#556	C₂×C₃	1	1	yes	characteristic, complemented
127	C₅×#554	C₂×C₃	1	1	yes	characteristic, complemented
128	C₅×#553	C₂×C₃	1	1	yes	characteristic, complemented
129	C₅×#553	C₂×C₃	1	2	yes	complemented
130	C₅×#552	C₂×C₃	1	1	yes	characteristic, complemented
131	C₅×#552	C₂×C₃	1	2	yes	complemented
132	C₅×#551	C₂×C₃	1	2	yes	complemented
133	C₅×#551	C₂×C₃	1	2	yes	complemented
134	C₅×#547	C₂×C₃	1	1	yes	characteristic, complemented
135	C₅×#546	C₂×C₃	1	1	yes	characteristic, complemented
136	C₅×#546	C₂×C₃	1	1	yes	characteristic, complemented
137	C₅×#542	C₂×C₃	1	1	yes	characteristic, complemented
138	C₅×#541	C₂×C₃	1	1	yes	characteristic, complemented
139	C₅×#539	C₂×C₃	1	2	yes	complemented
140	C₅×#538	C₂×C₃	1	2	yes	complemented
141	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
142	C₅×#529	C₂×C₃	1	2	yes	complemented
143	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
144	C₂×C₅×#126	C₂×C₃	1	2	yes	complemented
145	C₅×#520	C₂×C₃	1	1	yes	characteristic, complemented
146	C₅×#518	C₂×C₃	1	1	yes	characteristic, complemented
147	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
149	C₃×C₅×#41	—	2	4	no	—
150	C₃×C₅×#41	—	2	4	no	—
151	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
152	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
154	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
155	C₂×C₃×C₅×D₄	—	2	4	no	—
156	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
157	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
158	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
159	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
160	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
161	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
163	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
164	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
165	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
166	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
167	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
168	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
169	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
170	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
171	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
172	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
173	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
174	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
175	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
176	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
177	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
178	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
179	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
180	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
182	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
186	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
187	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
189	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
191	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
192	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
201	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
202	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
203	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
204	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
205	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
208	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
209	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
215	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
229	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
231	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
235	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
236	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
238	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
239	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
240	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
241	C₃×C₄²×C₅	C₂³	1	2	yes	—
242	C₃×C₄²×C₅	C₂³	1	2	yes	—
243	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
244	C₃×C₄²×C₅	C₂³	1	2	yes	—
245	C₃×C₄²×C₅	C₂³	1	2	yes	—
246	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
247	C₃×C₄²×C₅	C₂³	1	2	yes	—
248	C₃×C₄²×C₅	C₂³	1	2	yes	—
249	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
250	C₃×#556	C₂×C₅	1	1	yes	characteristic, complemented
251	C₃×#556	C₂×C₅	1	1	yes	characteristic, complemented
252	C₃×#554	C₂×C₅	1	1	yes	characteristic, complemented
253	C₃×#553	C₂×C₅	1	1	yes	characteristic, complemented
254	C₃×#553	C₂×C₅	1	2	yes	complemented
255	C₃×#552	C₂×C₅	1	1	yes	characteristic, complemented
256	C₃×#552	C₂×C₅	1	2	yes	complemented
257	C₃×#551	C₂×C₅	1	2	yes	complemented
258	C₃×#551	C₂×C₅	1	2	yes	complemented
259	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
260	C₃×#546	C₂×C₅	1	1	yes	characteristic, complemented
261	C₃×#546	C₂×C₅	1	1	yes	characteristic, complemented
262	C₃×#542	C₂×C₅	1	1	yes	characteristic, complemented
263	C₃×#541	C₂×C₅	1	1	yes	characteristic, complemented
264	C₃×#539	C₂×C₅	1	2	yes	complemented
265	C₃×#538	C₂×C₅	1	2	yes	complemented
266	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
267	C₃×#529	C₂×C₅	1	2	yes	complemented
268	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
269	C₂×C₃×#126	C₂×C₅	1	2	yes	complemented
270	C₃×#520	C₂×C₅	1	1	yes	characteristic, complemented
271	C₃×#518	C₂×C₅	1	1	yes	characteristic, complemented
272	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
273	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
274	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
275	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
276	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
277	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
278	C₅×#126	C₂²×C₃	1	1	yes	characteristic
279	C₅×#126	C₂²×C₃	1	2	yes	—
280	C₅×#126	C₂²×C₃	1	2	yes	—
281	C₅×#126	C₂²×C₃	1	2	yes	—
282	C₅×#126	C₂²×C₃	1	2	yes	—
283	C₅×#126	C₂²×C₃	1	2	yes	complemented
284	C₅×#126	C₂²×C₃	1	2	yes	complemented
285	C₅×#126	C₂²×C₃	1	2	yes	complemented
286	C₅×#126	C₂²×C₃	1	2	yes	complemented
287	C₅×#126	C₂²×C₃	1	1	yes	characteristic, complemented
288	C₅×#126	C₂²×C₃	1	2	yes	complemented
289	C₅×#126	C₂²×C₃	1	2	yes	complemented
290	C₅×#125	C₂²×C₃	1	2	yes	complemented
291	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
292	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
293	C₅×#125	C₂²×C₃	1	2	yes	complemented
294	C₅×#125	C₂²×C₃	1	2	yes	complemented
295	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
296	C₅×#124	C₂²×C₃	1	1	yes	characteristic
297	C₅×#124	C₂²×C₃	1	1	yes	characteristic
298	C₅×#124	C₂²×C₃	1	2	yes	—
299	C₅×#124	C₂²×C₃	1	1	yes	characteristic
300	C₅×#124	C₂²×C₃	1	2	yes	complemented
301	C₅×#123	C₂²×C₃	1	2	yes	—
302	C₅×#123	C₂²×C₃	1	1	yes	characteristic
303	C₅×#123	C₂²×C₃	1	2	yes	—
304	C₅×#123	C₂²×C₃	1	2	yes	—
305	C₅×#123	C₂²×C₃	1	2	yes	complemented
306	C₅×#123	C₂²×C₃	1	2	yes	complemented
307	C₅×#123	C₂²×C₃	1	1	yes	characteristic, complemented
308	C₅×#123	C₂²×C₃	1	2	yes	complemented
309	C₅×#123	C₂²×C₃	1	2	yes	complemented
310	C₅×#123	C₂²×C₃	1	2	yes	complemented
311	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
312	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
313	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
314	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
315	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
316	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
317	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
318	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
319	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
320	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
321	C₅×#121	C₂²×C₃	1	1	yes	characteristic
322	C₅×#121	C₂²×C₃	1	1	yes	characteristic
323	C₅×#121	C₂²×C₃	1	2	yes	—
324	C₅×#121	C₂²×C₃	1	2	yes	—
325	C₅×#121	C₂²×C₃	1	1	yes	characteristic
326	C₅×#121	C₂²×C₃	1	2	yes	complemented
327	C₅×#121	C₂²×C₃	1	2	yes	complemented
328	C₅×#120	C₂²×C₃	1	2	yes	—
329	C₅×#120	C₂²×C₃	1	2	yes	—
330	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
331	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
332	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
333	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
334	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
335	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
336	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
337	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
338	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
339	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
340	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
341	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
342	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
343	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
344	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
345	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
346	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
347	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
348	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
349	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
350	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
351	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
352	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
353	C₅×#117	C₂²×C₃	1	1	yes	characteristic
354	C₅×#117	C₂²×C₃	1	1	yes	characteristic
355	C₅×#117	C₂²×C₃	1	2	yes	complemented
356	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
357	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
358	C₅×#117	C₂²×C₃	1	2	yes	complemented
359	C₅×#117	C₂²×C₃	1	2	yes	complemented
360	C₅×#117	C₂²×C₃	1	2	yes	complemented
361	C₅×#117	C₂²×C₃	1	2	yes	complemented
362	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
363	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
364	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
365	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
366	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
367	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
368	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
369	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
370	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	complemented
371	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
372	#3521	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
373	C₂³×C₃×C₅	—	2	4	no	—
374	C₂³×C₃×C₅	—	4	2	no	—
375	C₂³×C₃×C₅	—	4	2	no	—
376	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
377	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
378	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
379	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
380	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
381	C₃×C₅×Q₈	—	2	2	no	—
382	C₃×C₅×Q₈	—	2	2	no	—
383	C₃×C₅×Q₈	—	4	1	no	—
384	C₃×C₅×Q₈	—	4	2	no	—
385	C₃×C₅×D₄	—	2	4	no	—
386	C₃×C₅×D₄	—	2	4	no	—
387	C₃×C₅×D₄	—	2	4	no	—
388	C₃×C₅×D₄	—	2	2	no	—
389	C₃×C₅×D₄	—	4	2	no	—
390	C₃×C₅×D₄	—	4	1	no	—
391	C₃×C₅×D₄	—	4	1	no	—
392	C₃×C₅×D₄	—	4	2	no	—
393	C₃×C₅×D₄	—	4	1	no	—
394	C₃×C₅×D₄	#41	1	4	yes	—
395	C₂×C₃×C₄×C₅	—	2	4	no	—
396	C₂×C₃×C₄×C₅	—	2	4	no	—
397	C₂×C₃×C₄×C₅	—	2	2	no	—
398	C₂×C₃×C₄×C₅	—	2	2	no	—
399	C₂×C₃×C₄×C₅	—	2	2	no	—
400	C₂×C₃×C₄×C₅	—	4	2	no	—
401	C₂×C₃×C₄×C₅	—	4	1	no	—
402	C₂×C₃×C₄×C₅	—	4	2	no	—
403	C₂×C₃×C₄×C₅	—	4	2	no	—
404	C₂×C₃×C₄×C₅	—	4	2	no	—
405	C₂×C₃×C₄×C₅	—	4	2	no	—
406	C₂×C₃×C₄×C₅	—	4	1	no	—
407	C₂×C₃×C₄×C₅	—	4	2	no	—
408	C₂×C₃×C₄×C₅	—	4	2	no	—
409	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
410	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
411	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
412	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
413	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
414	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
415	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
416	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
417	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
418	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
419	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
420	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
421	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
422	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
423	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
424	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
425	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
426	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
427	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
428	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
429	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
430	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
431	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
432	C₃×#126	C₂²×C₅	1	1	yes	characteristic
433	C₃×#126	C₂²×C₅	1	2	yes	—
434	C₃×#126	C₂²×C₅	1	2	yes	—
435	C₃×#126	C₂²×C₅	1	2	yes	—
436	C₃×#126	C₂²×C₅	1	2	yes	—
437	C₃×#126	C₂²×C₅	1	2	yes	complemented
438	C₃×#126	C₂²×C₅	1	2	yes	complemented
439	C₃×#126	C₂²×C₅	1	2	yes	complemented
440	C₃×#126	C₂²×C₅	1	2	yes	complemented
441	C₃×#126	C₂²×C₅	1	1	yes	characteristic, complemented
442	C₃×#126	C₂²×C₅	1	2	yes	complemented
443	C₃×#126	C₂²×C₅	1	2	yes	complemented
444	C₃×#125	C₂²×C₅	1	2	yes	complemented
445	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
446	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
447	C₃×#125	C₂²×C₅	1	2	yes	complemented
448	C₃×#125	C₂²×C₅	1	2	yes	complemented
449	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
450	C₃×#124	C₂²×C₅	1	1	yes	characteristic
451	C₃×#124	C₂²×C₅	1	1	yes	characteristic
452	C₃×#124	C₂²×C₅	1	2	yes	—
453	C₃×#124	C₂²×C₅	1	1	yes	characteristic
454	C₃×#124	C₂²×C₅	1	2	yes	complemented
455	C₃×#123	C₂²×C₅	1	2	yes	—
456	C₃×#123	C₂²×C₅	1	1	yes	characteristic
457	C₃×#123	C₂²×C₅	1	2	yes	—
458	C₃×#123	C₂²×C₅	1	2	yes	—
459	C₃×#123	C₂²×C₅	1	2	yes	complemented
460	C₃×#123	C₂²×C₅	1	2	yes	complemented
461	C₃×#123	C₂²×C₅	1	1	yes	characteristic, complemented
462	C₃×#123	C₂²×C₅	1	2	yes	complemented
463	C₃×#123	C₂²×C₅	1	2	yes	complemented
464	C₃×#123	C₂²×C₅	1	2	yes	complemented
465	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
466	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
467	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
468	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
469	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
470	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
471	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
472	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
473	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
474	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
475	C₃×#121	C₂²×C₅	1	1	yes	characteristic
476	C₃×#121	C₂²×C₅	1	1	yes	characteristic
477	C₃×#121	C₂²×C₅	1	2	yes	—
478	C₃×#121	C₂²×C₅	1	2	yes	—
479	C₃×#121	C₂²×C₅	1	1	yes	characteristic
480	C₃×#121	C₂²×C₅	1	2	yes	complemented
481	C₃×#121	C₂²×C₅	1	2	yes	complemented
482	C₃×#120	C₂²×C₅	1	2	yes	—
483	C₃×#120	C₂²×C₅	1	2	yes	—
484	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
485	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
486	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
487	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
488	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
489	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
490	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
491	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
492	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
493	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
494	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
495	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
496	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
497	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
498	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
499	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
500	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
501	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
502	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
503	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
504	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
505	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
506	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
507	C₃×#117	C₂²×C₅	1	1	yes	characteristic
508	C₃×#117	C₂²×C₅	1	1	yes	characteristic
509	C₃×#117	C₂²×C₅	1	2	yes	complemented
510	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
511	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
512	C₃×#117	C₂²×C₅	1	2	yes	complemented
513	C₃×#117	C₂²×C₅	1	2	yes	complemented
514	C₃×#117	C₂²×C₅	1	2	yes	complemented
515	C₃×#117	C₂²×C₅	1	2	yes	complemented
516	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
517	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
518	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
519	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
520	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
521	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
522	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
523	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
524	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
525	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
526	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
527	C₅×#41	—	2	4	no	—
528	C₅×#41	—	2	4	no	—
529	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
530	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
531	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
532	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
533	C₂×C₅×D₄	—	2	4	no	—
534	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
535	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
536	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
537	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
538	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
539	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
540	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
541	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
542	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
543	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
544	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
545	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
546	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
547	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
548	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
549	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
550	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
551	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
552	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
553	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
554	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
555	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
556	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
557	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
558	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
559	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
560	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
561	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
562	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
563	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
564	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
565	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
566	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
567	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
568	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
569	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
570	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
571	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
572	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
573	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
574	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
575	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
576	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
577	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
578	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
579	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
580	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
581	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
582	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
583	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
584	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
585	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
586	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
587	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
588	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
589	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
590	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
591	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
592	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
593	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
594	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
595	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
596	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
597	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
598	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
599	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
600	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
601	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
602	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
603	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
604	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
605	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
606	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
607	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
608	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
609	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
610	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
611	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
612	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
613	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
614	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
615	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
616	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
617	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
618	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
619	C₄²×C₅	C₂³×C₃	1	2	yes	—
620	C₄²×C₅	C₂³×C₃	1	2	yes	—
621	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
622	C₄²×C₅	C₂³×C₃	1	2	yes	—
623	C₄²×C₅	C₂³×C₃	1	2	yes	—
624	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
625	C₄²×C₅	C₂³×C₃	1	2	yes	—
626	C₄²×C₅	C₂³×C₃	1	2	yes	—
627	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
628	#556	C₂×C₃×C₅	1	1	yes	characteristic, complemented
629	#556	C₂×C₃×C₅	1	1	yes	characteristic, complemented
630	#554	C₂×C₃×C₅	1	1	yes	characteristic, complemented
631	#553	C₂×C₃×C₅	1	1	yes	characteristic, complemented
632	#553	C₂×C₃×C₅	1	2	yes	complemented
633	#552	C₂×C₃×C₅	1	1	yes	characteristic, complemented
634	#552	C₂×C₃×C₅	1	2	yes	complemented
635	#551	C₂×C₃×C₅	1	2	yes	complemented
636	#551	C₂×C₃×C₅	1	2	yes	complemented
637	#547	C₂×C₃×C₅	1	1	yes	characteristic, complemented
638	#546	C₂×C₃×C₅	1	1	yes	characteristic, complemented
639	#546	C₂×C₃×C₅	1	1	yes	characteristic, complemented
640	#542	C₂×C₃×C₅	1	1	yes	characteristic, complemented
641	#541	C₂×C₃×C₅	1	1	yes	characteristic, complemented
642	#539	C₂×C₃×C₅	1	2	yes	complemented
643	#538	C₂×C₃×C₅	1	2	yes	complemented
644	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
645	#529	C₂×C₃×C₅	1	2	yes	complemented
646	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
647	C₂×#126	C₂×C₃×C₅	1	2	yes	complemented
648	#520	C₂×C₃×C₅	1	1	yes	characteristic, complemented
649	#518	C₂×C₃×C₅	1	1	yes	characteristic, complemented
650	C₄×#41	C₂×C₃×C₅	1	1	yes	characteristic, complemented
651	C₂²×C₃×C₅	—	2	2	no	—
652	C₂²×C₃×C₅	—	2	2	no	—
653	C₂²×C₃×C₅	—	2	1	no	—
654	C₂²×C₃×C₅	—	2	1	no	—
655	C₂²×C₃×C₅	—	2	1	no	—
656	C₂²×C₃×C₅	—	2	2	no	—
657	C₂²×C₃×C₅	—	2	1	no	—
658	C₂²×C₃×C₅	—	2	1	no	—
659	C₂²×C₃×C₅	—	2	1	no	—
660	C₂²×C₃×C₅	—	2	2	no	—
661	C₂²×C₃×C₅	—	2	2	no	—
662	C₂²×C₃×C₅	—	2	1	no	—
663	C₂²×C₃×C₅	—	2	1	no	—
664	C₂²×C₃×C₅	—	2	1	no	—
665	C₂²×C₃×C₅	—	8	4	no	—
666	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
667	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
668	C₃×C₄×C₅	—	2	1	no	—
669	C₃×C₄×C₅	—	2	1	no	—
670	C₃×C₄×C₅	—	2	1	no	—
671	C₃×C₄×C₅	—	2	2	no	—
672	C₃×C₄×C₅	—	2	2	no	—
673	C₃×C₄×C₅	—	2	1	no	—
674	C₃×C₄×C₅	—	2	2	no	—
675	C₃×C₄×C₅	—	2	1	no	—
676	C₃×C₄×C₅	—	2	1	no	—
677	C₃×C₄×C₅	—	2	2	no	—
678	C₃×C₄×C₅	—	2	1	no	—
679	C₃×C₄×C₅	—	2	1	no	—
680	C₃×C₄×C₅	—	2	1	no	—
681	C₃×C₄×C₅	—	2	2	no	—
682	C₃×C₄×C₅	—	2	1	no	—
683	C₃×C₄×C₅	—	2	2	no	—
684	C₃×C₄×C₅	—	2	1	no	—
685	C₃×C₄×C₅	C₂×#41	1	2	yes	—
686	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
687	C₃×#41	—	2	4	no	—
688	C₃×#41	—	2	4	no	—
689	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
690	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
691	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
692	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
693	C₂×C₃×D₄	—	2	4	no	—
694	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
695	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
696	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
697	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
698	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
699	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
700	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
701	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
702	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
703	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
704	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
705	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
706	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
707	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
708	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
709	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
710	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
711	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
712	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
713	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
714	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
715	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
716	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
717	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
718	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
719	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
720	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
721	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
722	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
723	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
724	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
725	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
726	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
727	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
728	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
729	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
730	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
731	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
732	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
733	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
734	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
735	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
736	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
737	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
738	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
739	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
740	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
741	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
742	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
743	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
744	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
745	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
746	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
747	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
748	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
749	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
750	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
751	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
752	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
753	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
754	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
755	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
756	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
757	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
758	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
759	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
760	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
761	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
762	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
763	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
764	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
765	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
766	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
767	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
768	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
769	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
770	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
771	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
772	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
773	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
774	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
775	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
776	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
777	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
778	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
779	C₃×C₄²	C₂³×C₅	1	2	yes	—
780	C₃×C₄²	C₂³×C₅	1	2	yes	—
781	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
782	C₃×C₄²	C₂³×C₅	1	2	yes	—
783	C₃×C₄²	C₂³×C₅	1	2	yes	—
784	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
785	C₃×C₄²	C₂³×C₅	1	2	yes	—
786	C₃×C₄²	C₂³×C₅	1	2	yes	—
787	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
788	C₂³×C₅	—	2	4	no	—
789	C₂³×C₅	—	4	2	no	—
790	C₂³×C₅	—	4	2	no	—
791	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
792	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
793	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
794	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
795	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
796	C₅×Q₈	—	2	2	no	—
797	C₅×Q₈	—	2	2	no	—
798	C₅×Q₈	—	4	1	no	—
799	C₅×Q₈	—	4	2	no	—
800	C₅×D₄	—	2	4	no	—
801	C₅×D₄	—	2	4	no	—
802	C₅×D₄	—	2	4	no	—
803	C₅×D₄	—	2	2	no	—
804	C₅×D₄	—	4	2	no	—
805	C₅×D₄	—	4	1	no	—
806	C₅×D₄	—	4	1	no	—
807	C₅×D₄	—	4	2	no	—
808	C₅×D₄	—	4	1	no	—
809	C₅×D₄	C₃×#41	1	4	yes	—
810	C₂×C₄×C₅	—	2	4	no	—
811	C₂×C₄×C₅	—	2	4	no	—
812	C₂×C₄×C₅	—	2	2	no	—
813	C₂×C₄×C₅	—	2	2	no	—
814	C₂×C₄×C₅	—	2	2	no	—
815	C₂×C₄×C₅	—	4	2	no	—
816	C₂×C₄×C₅	—	4	1	no	—
817	C₂×C₄×C₅	—	4	2	no	—
818	C₂×C₄×C₅	—	4	2	no	—
819	C₂×C₄×C₅	—	4	2	no	—
820	C₂×C₄×C₅	—	4	2	no	—
821	C₂×C₄×C₅	—	4	1	no	—
822	C₂×C₄×C₅	—	4	2	no	—
823	C₂×C₄×C₅	—	4	2	no	—
824	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
825	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
826	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
827	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
828	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
829	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
830	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
831	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
832	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
833	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
834	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
835	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
836	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
837	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
838	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
839	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
840	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
841	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
842	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
843	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
844	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
845	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
846	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
847	#126	C₂²×C₃×C₅	1	1	yes	characteristic
848	#126	C₂²×C₃×C₅	1	2	yes	—
849	#126	C₂²×C₃×C₅	1	2	yes	—
850	#126	C₂²×C₃×C₅	1	2	yes	—
851	#126	C₂²×C₃×C₅	1	2	yes	—
852	#126	C₂²×C₃×C₅	1	2	yes	complemented
853	#126	C₂²×C₃×C₅	1	2	yes	complemented
854	#126	C₂²×C₃×C₅	1	2	yes	complemented
855	#126	C₂²×C₃×C₅	1	2	yes	complemented
856	#126	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
857	#126	C₂²×C₃×C₅	1	2	yes	complemented
858	#126	C₂²×C₃×C₅	1	2	yes	complemented
859	#125	C₂²×C₃×C₅	1	2	yes	complemented
860	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
861	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
862	#125	C₂²×C₃×C₅	1	2	yes	complemented
863	#125	C₂²×C₃×C₅	1	2	yes	complemented
864	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
865	#124	C₂²×C₃×C₅	1	1	yes	characteristic
866	#124	C₂²×C₃×C₅	1	1	yes	characteristic
867	#124	C₂²×C₃×C₅	1	2	yes	—
868	#124	C₂²×C₃×C₅	1	1	yes	characteristic
869	#124	C₂²×C₃×C₅	1	2	yes	complemented
870	#123	C₂²×C₃×C₅	1	2	yes	—
871	#123	C₂²×C₃×C₅	1	1	yes	characteristic
872	#123	C₂²×C₃×C₅	1	2	yes	—
873	#123	C₂²×C₃×C₅	1	2	yes	—
874	#123	C₂²×C₃×C₅	1	2	yes	complemented
875	#123	C₂²×C₃×C₅	1	2	yes	complemented
876	#123	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
877	#123	C₂²×C₃×C₅	1	2	yes	complemented
878	#123	C₂²×C₃×C₅	1	2	yes	complemented
879	#123	C₂²×C₃×C₅	1	2	yes	complemented
880	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
881	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
882	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
883	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
884	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
885	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
886	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
887	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
888	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
889	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
890	#121	C₂²×C₃×C₅	1	1	yes	characteristic
891	#121	C₂²×C₃×C₅	1	1	yes	characteristic
892	#121	C₂²×C₃×C₅	1	2	yes	—
893	#121	C₂²×C₃×C₅	1	2	yes	—
894	#121	C₂²×C₃×C₅	1	1	yes	characteristic
895	#121	C₂²×C₃×C₅	1	2	yes	complemented
896	#121	C₂²×C₃×C₅	1	2	yes	complemented
897	#120	C₂²×C₃×C₅	1	2	yes	—
898	#120	C₂²×C₃×C₅	1	2	yes	—
899	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
900	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
901	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
902	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
903	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
904	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
905	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
906	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
907	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
908	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
909	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
910	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
911	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
912	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
913	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
914	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
915	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
916	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
917	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
918	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
919	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
920	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
921	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
922	#117	C₂²×C₃×C₅	1	1	yes	characteristic
923	#117	C₂²×C₃×C₅	1	1	yes	characteristic
924	#117	C₂²×C₃×C₅	1	2	yes	complemented
925	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
926	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
927	#117	C₂²×C₃×C₅	1	2	yes	complemented
928	#117	C₂²×C₃×C₅	1	2	yes	complemented
929	#117	C₂²×C₃×C₅	1	2	yes	complemented
930	#117	C₂²×C₃×C₅	1	2	yes	complemented
931	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
932	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
933	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
934	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
935	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
936	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
937	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
938	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
939	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	complemented
940	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
941	C₂×C₃×C₅	—	2	4	no	—
942	C₂×C₃×C₅	—	4	1	no	—
943	C₂×C₃×C₅	—	4	1	no	—
944	C₂×C₃×C₅	—	4	2	no	—
945	C₂×C₃×C₅	—	4	1	no	—
946	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
947	C₂×C₃×C₅	#585	1	1	yes	characteristic
948	C₂×C₃×C₅	#585	1	1	yes	characteristic
949	C₂³×C₃	—	2	4	no	—
950	C₂³×C₃	—	4	2	no	—
951	C₂³×C₃	—	4	2	no	—
952	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
953	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
954	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
955	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
956	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
957	C₃×Q₈	—	2	2	no	—
958	C₃×Q₈	—	2	2	no	—
959	C₃×Q₈	—	4	1	no	—
960	C₃×Q₈	—	4	2	no	—
961	C₃×D₄	—	2	4	no	—
962	C₃×D₄	—	2	4	no	—
963	C₃×D₄	—	2	4	no	—
964	C₃×D₄	—	2	2	no	—
965	C₃×D₄	—	4	2	no	—
966	C₃×D₄	—	4	1	no	—
967	C₃×D₄	—	4	1	no	—
968	C₃×D₄	—	4	2	no	—
969	C₃×D₄	—	4	1	no	—
970	C₃×D₄	C₅×#41	1	4	yes	—
971	C₂×C₃×C₄	—	2	4	no	—
972	C₂×C₃×C₄	—	2	4	no	—
973	C₂×C₃×C₄	—	2	2	no	—
974	C₂×C₃×C₄	—	2	2	no	—
975	C₂×C₃×C₄	—	2	2	no	—
976	C₂×C₃×C₄	—	4	2	no	—
977	C₂×C₃×C₄	—	4	1	no	—
978	C₂×C₃×C₄	—	4	2	no	—
979	C₂×C₃×C₄	—	4	2	no	—
980	C₂×C₃×C₄	—	4	2	no	—
981	C₂×C₃×C₄	—	4	2	no	—
982	C₂×C₃×C₄	—	4	1	no	—
983	C₂×C₃×C₄	—	4	2	no	—
984	C₂×C₃×C₄	—	4	2	no	—
985	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
986	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
987	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
988	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
989	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
990	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
991	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
992	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
993	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
994	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
995	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
996	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
997	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
998	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
999	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1000	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
1001	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1002	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1003	C₂²×C₅	—	2	2	no	—
1004	C₂²×C₅	—	2	2	no	—
1005	C₂²×C₅	—	2	1	no	—
1006	C₂²×C₅	—	2	1	no	—
1007	C₂²×C₅	—	2	1	no	—
1008	C₂²×C₅	—	2	2	no	—
1009	C₂²×C₅	—	2	1	no	—
1010	C₂²×C₅	—	2	1	no	—
1011	C₂²×C₅	—	2	1	no	—
1012	C₂²×C₅	—	2	2	no	—
1013	C₂²×C₅	—	2	2	no	—
1014	C₂²×C₅	—	2	1	no	—
1015	C₂²×C₅	—	2	1	no	—
1016	C₂²×C₅	—	2	1	no	—
1017	C₂²×C₅	—	8	4	no	—
1018	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
1019	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
1020	C₄×C₅	—	2	1	no	—
1021	C₄×C₅	—	2	1	no	—
1022	C₄×C₅	—	2	1	no	—
1023	C₄×C₅	—	2	2	no	—
1024	C₄×C₅	—	2	2	no	—
1025	C₄×C₅	—	2	1	no	—
1026	C₄×C₅	—	2	2	no	—
1027	C₄×C₅	—	2	1	no	—
1028	C₄×C₅	—	2	1	no	—
1029	C₄×C₅	—	2	2	no	—
1030	C₄×C₅	—	2	1	no	—
1031	C₄×C₅	—	2	1	no	—
1032	C₄×C₅	—	2	1	no	—
1033	C₄×C₅	—	2	2	no	—
1034	C₄×C₅	—	2	1	no	—
1035	C₄×C₅	—	2	2	no	—
1036	C₄×C₅	—	2	1	no	—
1037	C₄×C₅	C₂×C₃×#41	1	2	yes	—
1038	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
1039	#41	—	2	4	no	—
1040	#41	—	2	4	no	—
1041	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
1042	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
1043	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
1044	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
1045	C₂×D₄	—	2	4	no	—
1046	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1047	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1048	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1049	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1050	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1051	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1052	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1053	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1054	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1055	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1056	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1057	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1058	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1059	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1060	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1061	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1062	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1063	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1064	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1065	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1066	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1067	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1068	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1069	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1070	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1071	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1072	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1073	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1074	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1075	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1076	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1077	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1078	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1079	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1080	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1081	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1082	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1083	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1084	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1085	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1086	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1087	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1088	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1089	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1090	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1091	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1092	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1093	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1094	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1095	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1096	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1097	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1098	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1099	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1100	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1101	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1102	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1103	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1104	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1105	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1106	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1107	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1108	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1109	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1110	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1111	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1112	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1113	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1114	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1115	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1116	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1117	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1118	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1119	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1120	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1121	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1122	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1123	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1124	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1125	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1126	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1127	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1128	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1129	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1130	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1131	C₄²	C₂³×C₃×C₅	1	2	yes	—
1132	C₄²	C₂³×C₃×C₅	1	2	yes	—
1133	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1134	C₄²	C₂³×C₃×C₅	1	2	yes	—
1135	C₄²	C₂³×C₃×C₅	1	2	yes	—
1136	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1137	C₄²	C₂³×C₃×C₅	1	2	yes	—
1138	C₄²	C₂³×C₃×C₅	1	2	yes	—
1139	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1140	C₃×C₅	#3521	1	1	yes	characteristic, direct product factor, Hall
1141	C₂²×C₃	—	2	2	no	—
1142	C₂²×C₃	—	2	2	no	—
1143	C₂²×C₃	—	2	1	no	—
1144	C₂²×C₃	—	2	1	no	—
1145	C₂²×C₃	—	2	1	no	—
1146	C₂²×C₃	—	2	2	no	—
1147	C₂²×C₃	—	2	1	no	—
1148	C₂²×C₃	—	2	1	no	—
1149	C₂²×C₃	—	2	1	no	—
1150	C₂²×C₃	—	2	2	no	—
1151	C₂²×C₃	—	2	2	no	—
1152	C₂²×C₃	—	2	1	no	—
1153	C₂²×C₃	—	2	1	no	—
1154	C₂²×C₃	—	2	1	no	—
1155	C₂²×C₃	—	8	4	no	—
1156	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
1157	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1158	C₃×C₄	—	2	1	no	—
1159	C₃×C₄	—	2	1	no	—
1160	C₃×C₄	—	2	1	no	—
1161	C₃×C₄	—	2	2	no	—
1162	C₃×C₄	—	2	2	no	—
1163	C₃×C₄	—	2	1	no	—
1164	C₃×C₄	—	2	2	no	—
1165	C₃×C₄	—	2	1	no	—
1166	C₃×C₄	—	2	1	no	—
1167	C₃×C₄	—	2	2	no	—
1168	C₃×C₄	—	2	1	no	—
1169	C₃×C₄	—	2	1	no	—
1170	C₃×C₄	—	2	1	no	—
1171	C₃×C₄	—	2	2	no	—
1172	C₃×C₄	—	2	1	no	—
1173	C₃×C₄	—	2	2	no	—
1174	C₃×C₄	—	2	1	no	—
1175	C₃×C₄	C₂×C₅×#41	1	2	yes	—
1176	C₂×C₅	—	2	4	no	—
1177	C₂×C₅	—	4	1	no	—
1178	C₂×C₅	—	4	2	no	—
1179	C₂×C₅	—	4	1	no	—
1180	C₂×C₅	—	4	1	no	—
1181	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
1182	C₂×C₅	C₃×#585	1	1	yes	characteristic
1183	C₂×C₅	C₃×#585	1	1	yes	characteristic
1184	C₂³	—	2	4	no	—
1185	C₂³	—	4	2	no	—
1186	C₂³	—	4	2	no	—
1187	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1188	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1189	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1190	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1191	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1192	Q₈	—	2	2	no	—
1193	Q₈	—	2	2	no	—
1194	Q₈	—	4	1	no	—
1195	Q₈	—	4	2	no	—
1196	D₄	—	2	4	no	—
1197	D₄	—	2	4	no	—
1198	D₄	—	2	4	no	—
1199	D₄	—	2	2	no	—
1200	D₄	—	4	2	no	—
1201	D₄	—	4	1	no	—
1202	D₄	—	4	1	no	—
1203	D₄	—	4	2	no	—
1204	D₄	—	4	1	no	—
1205	D₄	C₃×C₅×#41	1	4	yes	—
1206	C₂×C₄	—	2	4	no	—
1207	C₂×C₄	—	2	4	no	—
1208	C₂×C₄	—	2	2	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	2	no	—
1211	C₂×C₄	—	4	2	no	—
1212	C₂×C₄	—	4	1	no	—
1213	C₂×C₄	—	4	2	no	—
1214	C₂×C₄	—	4	2	no	—
1215	C₂×C₄	—	4	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	1	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1221	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1222	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1223	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1224	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1225	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1226	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1227	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1228	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1229	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1230	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1231	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1232	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1233	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1234	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1235	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1236	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1237	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1238	C₂×C₃	—	2	4	no	—
1239	C₂×C₃	—	4	1	no	—
1240	C₂×C₃	—	4	2	no	—
1241	C₂×C₃	—	4	1	no	—
1242	C₂×C₃	—	4	1	no	—
1243	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
1244	C₂×C₃	C₅×#585	1	1	yes	characteristic
1245	C₂×C₃	C₅×#585	1	1	yes	characteristic
1246	C₅	C₃×#3521	1	1	yes	characteristic, direct product factor, Sylow
1247	C₂²	—	2	2	no	—
1248	C₂²	—	2	2	no	—
1249	C₂²	—	2	1	no	—
1250	C₂²	—	2	1	no	—
1251	C₂²	—	2	1	no	—
1252	C₂²	—	2	2	no	—
1253	C₂²	—	2	1	no	—
1254	C₂²	—	2	1	no	—
1255	C₂²	—	2	1	no	—
1256	C₂²	—	2	2	no	—
1257	C₂²	—	2	2	no	—
1258	C₂²	—	2	1	no	—
1259	C₂²	—	2	1	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	8	4	no	—
1262	C₂²	C₂×C₃×C₅×#41	1	4	yes	—
1263	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
1264	C₄	—	2	1	no	—
1265	C₄	—	2	1	no	—
1266	C₄	—	2	1	no	—
1267	C₄	—	2	2	no	—
1268	C₄	—	2	2	no	—
1269	C₄	—	2	1	no	—
1270	C₄	—	2	2	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	2	1	no	—
1273	C₄	—	2	2	no	—
1274	C₄	—	2	1	no	—
1275	C₄	—	2	1	no	—
1276	C₄	—	2	1	no	—
1277	C₄	—	2	2	no	—
1278	C₄	—	2	1	no	—
1279	C₄	—	2	2	no	—
1280	C₄	—	2	1	no	—
1281	C₄	C₂×C₃×C₅×#41	1	2	yes	—
1282	C₃	C₅×#3521	1	1	yes	characteristic, direct product factor, Sylow
1283	C₂	—	2	4	no	—
1284	C₂	—	4	1	no	—
1285	C₂	—	4	2	no	—
1286	C₂	—	4	1	no	—
1287	C₂	—	4	1	no	—
1288	C₂	C₂²×C₃×C₅×#41	1	1	yes	characteristic
1289	C₂	C₃×C₅×#585	1	1	yes	characteristic
1290	C₂	C₃×C₅×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₅×#556	C₂	semidirect
2. C₃×C₅×#556	C₂	semidirect
3. C₃×C₅×#554	C₂	semidirect
4. C₃×C₅×#553	C₂	semidirect
5. C₃×C₅×#553	C₂	semidirect
6. C₃×C₅×#552	C₂	semidirect
7. C₃×C₅×#552	C₂	semidirect
8. C₃×C₅×#551	C₂	semidirect
9. C₃×C₅×#551	C₂	semidirect
10. C₃×C₅×#547	C₂	semidirect
11. C₃×C₅×#546	C₂	semidirect
12. C₃×C₅×#546	C₂	semidirect
13. C₃×C₅×#542	C₂	semidirect
14. C₃×C₅×#541	C₂	semidirect
15. C₃×C₅×#539	C₂	semidirect
16. C₃×C₅×#538	C₂	semidirect
17. C₃×C₅×#529	C₂	semidirect
18. C₃×C₅×#529	C₂	semidirect
19. C₃×C₅×#529	C₂	semidirect
20. C₂×C₃×C₅×#126	C₂	semidirect
21. C₃×C₅×#520	C₂	semidirect
22. C₃×C₅×#518	C₂	semidirect
23. C₃×C₄×C₅×#41	C₂	semidirect
24. C₅×#3521	C₃	direct (N × H)
28. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
29. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
35. C₃×C₅×#126	C₂²	semidirect
36. C₃×C₅×#126	C₂²	semidirect
37. C₃×C₅×#126	C₂²	semidirect
38. C₃×C₅×#126	C₂²	semidirect
39. C₃×C₅×#126	C₂²	semidirect
40. C₃×C₅×#126	C₂²	semidirect
41. C₃×C₅×#126	C₂²	semidirect
42. C₃×C₅×#125	C₂²	semidirect
43. C₃×C₅×#125	C₂²	semidirect
44. C₃×C₅×#125	C₂²	semidirect
45. C₃×C₅×#125	C₂²	semidirect
46. C₃×C₅×#125	C₂²	semidirect
47. C₃×C₅×#125	C₂²	semidirect
52. C₃×C₅×#124	C₂²	semidirect
57. C₃×C₅×#123	C₂²	semidirect
58. C₃×C₅×#123	C₂²	semidirect
59. C₃×C₅×#123	C₂²	semidirect
60. C₃×C₅×#123	C₂²	semidirect
61. C₃×C₅×#123	C₂²	semidirect
62. C₃×C₅×#123	C₂²	semidirect
65. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
66. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
67. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
68. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
69. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
70. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
71. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
72. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
78. C₃×C₅×#121	C₂²	semidirect
79. C₃×C₅×#121	C₂²	semidirect
82. C₃×C₄×C₅×Q₈	C₂²	semidirect
83. C₃×C₄×C₅×Q₈	C₂²	semidirect
84. C₃×C₄×C₅×Q₈	C₂²	semidirect
85. C₃×C₄×C₅×Q₈	C₂²	semidirect
86. C₃×C₄×C₅×Q₈	C₂²	semidirect
87. C₃×C₄×C₅×Q₈	C₂²	semidirect
98. C₃×C₄×C₅×D₄	C₂²	semidirect
99. C₃×C₄×C₅×D₄	C₂²	semidirect
100. C₃×C₄×C₅×D₄	C₂²	semidirect
101. C₃×C₄×C₅×D₄	C₂²	semidirect
102. C₃×C₄×C₅×D₄	C₂²	semidirect
103. C₃×C₄×C₅×D₄	C₂²	semidirect
104. C₃×C₄×C₅×D₄	C₂²	semidirect
107. C₃×C₅×#117	C₂²	semidirect
108. C₃×C₅×#117	C₂²	semidirect
109. C₃×C₅×#117	C₂²	semidirect
110. C₃×C₅×#117	C₂²	semidirect
111. C₃×C₅×#117	C₂²	semidirect
112. C₃×C₅×#117	C₂²	semidirect
113. C₃×C₅×#117	C₂²	semidirect
114. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
115. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
116. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
117. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
122. C₂×C₃×C₄²×C₅	C₂²	semidirect
123. C₂×C₃×C₄²×C₅	C₂²	semidirect
124. C₃×#3521	C₅	direct (N × H)
125. C₅×#556	C₂×C₃	semidirect
126. C₅×#556	C₂×C₃	semidirect
127. C₅×#554	C₂×C₃	semidirect
128. C₅×#553	C₂×C₃	semidirect
129. C₅×#553	C₂×C₃	semidirect
130. C₅×#552	C₂×C₃	semidirect
131. C₅×#552	C₂×C₃	semidirect
132. C₅×#551	C₂×C₃	semidirect
133. C₅×#551	C₂×C₃	semidirect
134. C₅×#547	C₂×C₃	semidirect
135. C₅×#546	C₂×C₃	semidirect
136. C₅×#546	C₂×C₃	semidirect
137. C₅×#542	C₂×C₃	semidirect
138. C₅×#541	C₂×C₃	semidirect
139. C₅×#539	C₂×C₃	semidirect
140. C₅×#538	C₂×C₃	semidirect
141. C₅×#529	C₂×C₃	semidirect
142. C₅×#529	C₂×C₃	semidirect
143. C₅×#529	C₂×C₃	semidirect
144. C₂×C₅×#126	C₂×C₃	semidirect
145. C₅×#520	C₂×C₃	semidirect
146. C₅×#518	C₂×C₃	semidirect
147. C₄×C₅×#41	C₂×C₃	semidirect
250. C₃×#556	C₂×C₅	semidirect
251. C₃×#556	C₂×C₅	semidirect
252. C₃×#554	C₂×C₅	semidirect
253. C₃×#553	C₂×C₅	semidirect
254. C₃×#553	C₂×C₅	semidirect
255. C₃×#552	C₂×C₅	semidirect
256. C₃×#552	C₂×C₅	semidirect
257. C₃×#551	C₂×C₅	semidirect
258. C₃×#551	C₂×C₅	semidirect
259. C₃×#547	C₂×C₅	semidirect
260. C₃×#546	C₂×C₅	semidirect
261. C₃×#546	C₂×C₅	semidirect
262. C₃×#542	C₂×C₅	semidirect
263. C₃×#541	C₂×C₅	semidirect
264. C₃×#539	C₂×C₅	semidirect
265. C₃×#538	C₂×C₅	semidirect
266. C₃×#529	C₂×C₅	semidirect
267. C₃×#529	C₂×C₅	semidirect
268. C₃×#529	C₂×C₅	semidirect
269. C₂×C₃×#126	C₂×C₅	semidirect
270. C₃×#520	C₂×C₅	semidirect
271. C₃×#518	C₂×C₅	semidirect
272. C₃×C₄×#41	C₂×C₅	semidirect
276. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
277. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
283. C₅×#126	C₂²×C₃	semidirect
284. C₅×#126	C₂²×C₃	semidirect
285. C₅×#126	C₂²×C₃	semidirect
286. C₅×#126	C₂²×C₃	semidirect
287. C₅×#126	C₂²×C₃	semidirect
288. C₅×#126	C₂²×C₃	semidirect
289. C₅×#126	C₂²×C₃	semidirect
290. C₅×#125	C₂²×C₃	semidirect
291. C₅×#125	C₂²×C₃	semidirect
292. C₅×#125	C₂²×C₃	semidirect
293. C₅×#125	C₂²×C₃	semidirect
294. C₅×#125	C₂²×C₃	semidirect
295. C₅×#125	C₂²×C₃	semidirect
300. C₅×#124	C₂²×C₃	semidirect
305. C₅×#123	C₂²×C₃	semidirect
306. C₅×#123	C₂²×C₃	semidirect
307. C₅×#123	C₂²×C₃	semidirect
308. C₅×#123	C₂²×C₃	semidirect
309. C₅×#123	C₂²×C₃	semidirect
310. C₅×#123	C₂²×C₃	semidirect
313. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
314. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
315. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
316. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
317. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
318. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
319. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
320. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
326. C₅×#121	C₂²×C₃	semidirect
327. C₅×#121	C₂²×C₃	semidirect
330. C₄×C₅×Q₈	C₂²×C₃	semidirect
331. C₄×C₅×Q₈	C₂²×C₃	semidirect
332. C₄×C₅×Q₈	C₂²×C₃	semidirect
333. C₄×C₅×Q₈	C₂²×C₃	semidirect
334. C₄×C₅×Q₈	C₂²×C₃	semidirect
335. C₄×C₅×Q₈	C₂²×C₃	semidirect
346. C₄×C₅×D₄	C₂²×C₃	semidirect
347. C₄×C₅×D₄	C₂²×C₃	semidirect
348. C₄×C₅×D₄	C₂²×C₃	semidirect
349. C₄×C₅×D₄	C₂²×C₃	semidirect
350. C₄×C₅×D₄	C₂²×C₃	semidirect
351. C₄×C₅×D₄	C₂²×C₃	semidirect
352. C₄×C₅×D₄	C₂²×C₃	semidirect
355. C₅×#117	C₂²×C₃	semidirect
356. C₅×#117	C₂²×C₃	semidirect
357. C₅×#117	C₂²×C₃	semidirect
358. C₅×#117	C₂²×C₃	semidirect
359. C₅×#117	C₂²×C₃	semidirect
360. C₅×#117	C₂²×C₃	semidirect
361. C₅×#117	C₂²×C₃	semidirect
362. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
363. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
364. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
365. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
370. C₂×C₄²×C₅	C₂²×C₃	semidirect
371. C₂×C₄²×C₅	C₂²×C₃	semidirect
372. #3521	C₃×C₅	direct (N × H)
430. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
431. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
437. C₃×#126	C₂²×C₅	semidirect
438. C₃×#126	C₂²×C₅	semidirect
439. C₃×#126	C₂²×C₅	semidirect
440. C₃×#126	C₂²×C₅	semidirect
441. C₃×#126	C₂²×C₅	semidirect
442. C₃×#126	C₂²×C₅	semidirect
443. C₃×#126	C₂²×C₅	semidirect
444. C₃×#125	C₂²×C₅	semidirect
445. C₃×#125	C₂²×C₅	semidirect
446. C₃×#125	C₂²×C₅	semidirect
447. C₃×#125	C₂²×C₅	semidirect
448. C₃×#125	C₂²×C₅	semidirect
449. C₃×#125	C₂²×C₅	semidirect
454. C₃×#124	C₂²×C₅	semidirect
459. C₃×#123	C₂²×C₅	semidirect
460. C₃×#123	C₂²×C₅	semidirect
461. C₃×#123	C₂²×C₅	semidirect
462. C₃×#123	C₂²×C₅	semidirect
463. C₃×#123	C₂²×C₅	semidirect
464. C₃×#123	C₂²×C₅	semidirect
467. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
468. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
469. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
470. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
471. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
472. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
473. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
474. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
480. C₃×#121	C₂²×C₅	semidirect
481. C₃×#121	C₂²×C₅	semidirect
484. C₃×C₄×Q₈	C₂²×C₅	semidirect
485. C₃×C₄×Q₈	C₂²×C₅	semidirect
486. C₃×C₄×Q₈	C₂²×C₅	semidirect
487. C₃×C₄×Q₈	C₂²×C₅	semidirect
488. C₃×C₄×Q₈	C₂²×C₅	semidirect
489. C₃×C₄×Q₈	C₂²×C₅	semidirect
500. C₃×C₄×D₄	C₂²×C₅	semidirect
501. C₃×C₄×D₄	C₂²×C₅	semidirect
502. C₃×C₄×D₄	C₂²×C₅	semidirect
503. C₃×C₄×D₄	C₂²×C₅	semidirect
504. C₃×C₄×D₄	C₂²×C₅	semidirect
505. C₃×C₄×D₄	C₂²×C₅	semidirect
506. C₃×C₄×D₄	C₂²×C₅	semidirect
509. C₃×#117	C₂²×C₅	semidirect
510. C₃×#117	C₂²×C₅	semidirect
511. C₃×#117	C₂²×C₅	semidirect
512. C₃×#117	C₂²×C₅	semidirect
513. C₃×#117	C₂²×C₅	semidirect
514. C₃×#117	C₂²×C₅	semidirect
515. C₃×#117	C₂²×C₅	semidirect
516. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
517. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
518. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
519. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
524. C₂×C₃×C₄²	C₂²×C₅	semidirect
525. C₂×C₃×C₄²	C₂²×C₅	semidirect
628. #556	C₂×C₃×C₅	semidirect
629. #556	C₂×C₃×C₅	semidirect
630. #554	C₂×C₃×C₅	semidirect
631. #553	C₂×C₃×C₅	semidirect
632. #553	C₂×C₃×C₅	semidirect
633. #552	C₂×C₃×C₅	semidirect
634. #552	C₂×C₃×C₅	semidirect
635. #551	C₂×C₃×C₅	semidirect
636. #551	C₂×C₃×C₅	semidirect
637. #547	C₂×C₃×C₅	semidirect
638. #546	C₂×C₃×C₅	semidirect
639. #546	C₂×C₃×C₅	semidirect
640. #542	C₂×C₃×C₅	semidirect
641. #541	C₂×C₃×C₅	semidirect
642. #539	C₂×C₃×C₅	semidirect
643. #538	C₂×C₃×C₅	semidirect
644. #529	C₂×C₃×C₅	semidirect
645. #529	C₂×C₃×C₅	semidirect
646. #529	C₂×C₃×C₅	semidirect
647. C₂×#126	C₂×C₃×C₅	semidirect
648. #520	C₂×C₃×C₅	semidirect
649. #518	C₂×C₃×C₅	semidirect
650. C₄×#41	C₂×C₃×C₅	semidirect
845. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
846. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
852. #126	C₂²×C₃×C₅	semidirect
853. #126	C₂²×C₃×C₅	semidirect
854. #126	C₂²×C₃×C₅	semidirect
855. #126	C₂²×C₃×C₅	semidirect
856. #126	C₂²×C₃×C₅	semidirect
857. #126	C₂²×C₃×C₅	semidirect
858. #126	C₂²×C₃×C₅	semidirect
859. #125	C₂²×C₃×C₅	semidirect
860. #125	C₂²×C₃×C₅	semidirect
861. #125	C₂²×C₃×C₅	semidirect
862. #125	C₂²×C₃×C₅	semidirect
863. #125	C₂²×C₃×C₅	semidirect
864. #125	C₂²×C₃×C₅	semidirect
869. #124	C₂²×C₃×C₅	semidirect
874. #123	C₂²×C₃×C₅	semidirect
875. #123	C₂²×C₃×C₅	semidirect
876. #123	C₂²×C₃×C₅	semidirect
877. #123	C₂²×C₃×C₅	semidirect
878. #123	C₂²×C₃×C₅	semidirect
879. #123	C₂²×C₃×C₅	semidirect
882. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
883. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
884. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
885. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
886. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
887. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
888. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
889. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
895. #121	C₂²×C₃×C₅	semidirect
896. #121	C₂²×C₃×C₅	semidirect
899. C₄×Q₈	C₂²×C₃×C₅	semidirect
900. C₄×Q₈	C₂²×C₃×C₅	semidirect
901. C₄×Q₈	C₂²×C₃×C₅	semidirect
902. C₄×Q₈	C₂²×C₃×C₅	semidirect
903. C₄×Q₈	C₂²×C₃×C₅	semidirect
904. C₄×Q₈	C₂²×C₃×C₅	semidirect
915. C₄×D₄	C₂²×C₃×C₅	semidirect
916. C₄×D₄	C₂²×C₃×C₅	semidirect
917. C₄×D₄	C₂²×C₃×C₅	semidirect
918. C₄×D₄	C₂²×C₃×C₅	semidirect
919. C₄×D₄	C₂²×C₃×C₅	semidirect
920. C₄×D₄	C₂²×C₃×C₅	semidirect
921. C₄×D₄	C₂²×C₃×C₅	semidirect
924. #117	C₂²×C₃×C₅	semidirect
925. #117	C₂²×C₃×C₅	semidirect
926. #117	C₂²×C₃×C₅	semidirect
927. #117	C₂²×C₃×C₅	semidirect
928. #117	C₂²×C₃×C₅	semidirect
929. #117	C₂²×C₃×C₅	semidirect
930. #117	C₂²×C₃×C₅	semidirect
931. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
932. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
933. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
934. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
939. C₂×C₄²	C₂²×C₃×C₅	semidirect
940. C₂×C₄²	C₂²×C₃×C₅	semidirect
1140. C₃×C₅	#3521	direct (N × H)
1246. C₅	C₃×#3521	direct (N × H)
1282. C₃	C₅×#3521	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×#556	2
C₃×C₅×#554	2
C₃×C₅×#553	2
C₃×C₅×#552	2
C₃×C₅×#551	2
C₃×C₅×#547	2
C₃×C₅×#546	2
C₃×C₅×#542	2
C₃×C₅×#541	2
C₃×C₅×#539	2
C₃×C₅×#538	2
C₃×C₅×#529	2
C₂×C₃×C₅×#126	2
C₃×C₅×#520	2
C₃×C₅×#518	2
C₃×C₄×C₅×#41	2
C₅×#3521	3
C₃×#3521	5

Subgroups — C3×C5×#3521 #14276555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3521 #14276555