Subgroups — C₃×C₅×#3535 #14276569

Order 1920.

2076 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#563	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#562	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#554	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#552	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#551	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#551	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#547	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#546	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#544	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#543	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#542	C₂	1	2	yes	maximal, complemented
12	C₃×C₅×#539	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#539	C₂	1	2	yes	maximal, complemented
14	C₃×C₅×#539	C₂	1	2	yes	maximal, complemented
15	C₃×C₅×#538	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×C₅×#536	C₂	1	2	yes	maximal, complemented
17	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#3535	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
22	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
25	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
26	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
27	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
28	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
29	C₃×C₅×#126	C₂²	1	2	yes	complemented
30	C₃×C₅×#126	C₂²	1	2	yes	complemented
31	C₃×C₅×#126	C₂²	1	2	yes	complemented
32	C₃×C₅×#126	C₂²	1	2	yes	complemented
33	C₃×C₅×#126	C₂²	1	2	yes	complemented
34	C₃×C₅×#126	C₂²	1	2	yes	complemented
35	C₃×C₅×#125	C₂²	1	2	yes	complemented
36	C₃×C₅×#125	C₂²	1	2	yes	complemented
37	C₃×C₅×#125	C₂²	1	2	yes	complemented
38	C₃×C₅×#125	C₂²	1	2	yes	complemented
39	C₃×C₅×#125	C₂²	1	2	yes	complemented
40	C₃×C₅×#124	C₂²	1	2	yes	—
41	C₃×C₅×#124	C₂²	1	2	yes	complemented
42	C₃×C₅×#124	C₂²	1	2	yes	complemented
43	C₃×C₅×#124	C₂²	1	2	yes	complemented
44	C₃×C₅×#123	C₂²	1	2	yes	—
45	C₃×C₅×#123	C₂²	1	2	yes	—
46	C₃×C₅×#123	C₂²	1	2	yes	—
47	C₃×C₅×#123	C₂²	1	2	yes	—
48	C₃×C₅×#123	C₂²	1	2	yes	—
49	C₃×C₅×#123	C₂²	1	2	yes	—
50	C₃×C₅×#123	C₂²	1	2	yes	—
51	C₃×C₅×#123	C₂²	1	2	yes	complemented
52	C₃×C₅×#123	C₂²	1	2	yes	complemented
53	C₃×C₅×#123	C₂²	1	2	yes	complemented
54	C₃×C₅×#123	C₂²	1	2	yes	complemented
55	C₃×C₅×#123	C₂²	1	2	yes	complemented
56	C₃×C₅×#123	C₂²	1	2	yes	complemented
57	C₃×C₅×#123	C₂²	1	2	yes	complemented
58	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
60	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
61	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
62	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
63	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
64	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
65	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
66	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
67	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
72	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
73	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
74	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
75	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
76	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
77	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
78	C₃×C₅×#121	C₂²	1	1	yes	characteristic
79	C₃×C₅×#121	C₂²	1	2	yes	—
80	C₃×C₅×#121	C₂²	1	2	yes	—
81	C₃×C₅×#121	C₂²	1	2	yes	—
82	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
83	C₃×C₅×#121	C₂²	1	2	yes	complemented
84	C₃×C₅×#120	C₂²	1	2	yes	—
85	C₃×C₅×#120	C₂²	1	2	yes	—
86	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
87	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
88	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
89	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
90	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
91	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
92	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
93	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
94	C₃×C₅×#117	C₂²	1	2	yes	—
95	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
96	C₃×C₅×#117	C₂²	1	2	yes	complemented
97	C₃×C₅×#117	C₂²	1	2	yes	complemented
98	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
100	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
102	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
103	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
106	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
107	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
108	C₃×#3535	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
109	C₅×#563	C₂×C₃	1	2	yes	complemented
110	C₅×#562	C₂×C₃	1	2	yes	complemented
111	C₅×#554	C₂×C₃	1	2	yes	complemented
112	C₅×#552	C₂×C₃	1	2	yes	complemented
113	C₅×#551	C₂×C₃	1	2	yes	complemented
114	C₅×#551	C₂×C₃	1	2	yes	complemented
115	C₅×#547	C₂×C₃	1	2	yes	complemented
116	C₅×#546	C₂×C₃	1	2	yes	complemented
117	C₅×#544	C₂×C₃	1	1	yes	characteristic, complemented
118	C₅×#543	C₂×C₃	1	1	yes	characteristic, complemented
119	C₅×#542	C₂×C₃	1	2	yes	complemented
120	C₅×#539	C₂×C₃	1	1	yes	characteristic, complemented
121	C₅×#539	C₂×C₃	1	2	yes	complemented
122	C₅×#539	C₂×C₃	1	2	yes	complemented
123	C₅×#538	C₂×C₃	1	1	yes	characteristic, complemented
124	C₅×#536	C₂×C₃	1	2	yes	complemented
125	C₅×#525	C₂×C₃	1	1	yes	characteristic, complemented
126	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
128	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
129	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
130	C₃×C₅×#41	—	4	4	no	—
131	C₃×C₅×#41	—	4	2	no	—
132	C₂×C₃×C₅×Q₈	—	4	2	no	—
133	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
134	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
135	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
136	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
137	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
138	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
139	C₂×C₃×C₅×D₄	—	4	2	no	—
140	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
141	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
142	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
143	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
144	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
145	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
146	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
147	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
148	C₂²×C₃×C₄×C₅	—	4	2	no	—
149	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
150	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
151	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
152	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
156	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
157	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
158	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
159	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
160	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
161	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
162	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
163	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
164	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
165	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
166	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
168	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
169	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
170	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
171	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
172	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
174	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
176	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
177	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
179	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
180	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
183	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
184	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₃×C₄²×C₅	C₂³	1	2	yes	—
216	C₃×C₄²×C₅	C₂³	1	2	yes	—
217	C₃×C₄²×C₅	C₂³	1	2	yes	—
218	C₃×C₄²×C₅	C₂³	1	2	yes	—
219	C₃×C₄²×C₅	C₂³	1	2	yes	—
220	C₃×#563	C₂×C₅	1	2	yes	complemented
221	C₃×#562	C₂×C₅	1	2	yes	complemented
222	C₃×#554	C₂×C₅	1	2	yes	complemented
223	C₃×#552	C₂×C₅	1	2	yes	complemented
224	C₃×#551	C₂×C₅	1	2	yes	complemented
225	C₃×#551	C₂×C₅	1	2	yes	complemented
226	C₃×#547	C₂×C₅	1	2	yes	complemented
227	C₃×#546	C₂×C₅	1	2	yes	complemented
228	C₃×#544	C₂×C₅	1	1	yes	characteristic, complemented
229	C₃×#543	C₂×C₅	1	1	yes	characteristic, complemented
230	C₃×#542	C₂×C₅	1	2	yes	complemented
231	C₃×#539	C₂×C₅	1	1	yes	characteristic, complemented
232	C₃×#539	C₂×C₅	1	2	yes	complemented
233	C₃×#539	C₂×C₅	1	2	yes	complemented
234	C₃×#538	C₂×C₅	1	1	yes	characteristic, complemented
235	C₃×#536	C₂×C₅	1	2	yes	complemented
236	C₃×#525	C₂×C₅	1	1	yes	characteristic, complemented
237	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
238	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
239	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
240	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
241	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
242	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
243	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
244	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
245	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
246	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
247	C₅×#126	C₂²×C₃	1	2	yes	complemented
248	C₅×#126	C₂²×C₃	1	2	yes	complemented
249	C₅×#126	C₂²×C₃	1	2	yes	complemented
250	C₅×#126	C₂²×C₃	1	2	yes	complemented
251	C₅×#126	C₂²×C₃	1	2	yes	complemented
252	C₅×#126	C₂²×C₃	1	2	yes	complemented
253	C₅×#125	C₂²×C₃	1	2	yes	complemented
254	C₅×#125	C₂²×C₃	1	2	yes	complemented
255	C₅×#125	C₂²×C₃	1	2	yes	complemented
256	C₅×#125	C₂²×C₃	1	2	yes	complemented
257	C₅×#125	C₂²×C₃	1	2	yes	complemented
258	C₅×#124	C₂²×C₃	1	2	yes	—
259	C₅×#124	C₂²×C₃	1	2	yes	complemented
260	C₅×#124	C₂²×C₃	1	2	yes	complemented
261	C₅×#124	C₂²×C₃	1	2	yes	complemented
262	C₅×#123	C₂²×C₃	1	2	yes	—
263	C₅×#123	C₂²×C₃	1	2	yes	—
264	C₅×#123	C₂²×C₃	1	2	yes	—
265	C₅×#123	C₂²×C₃	1	2	yes	—
266	C₅×#123	C₂²×C₃	1	2	yes	—
267	C₅×#123	C₂²×C₃	1	2	yes	—
268	C₅×#123	C₂²×C₃	1	2	yes	—
269	C₅×#123	C₂²×C₃	1	2	yes	complemented
270	C₅×#123	C₂²×C₃	1	2	yes	complemented
271	C₅×#123	C₂²×C₃	1	2	yes	complemented
272	C₅×#123	C₂²×C₃	1	2	yes	complemented
273	C₅×#123	C₂²×C₃	1	2	yes	complemented
274	C₅×#123	C₂²×C₃	1	2	yes	complemented
275	C₅×#123	C₂²×C₃	1	2	yes	complemented
276	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
277	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
278	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
279	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
280	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
281	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
282	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
283	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
284	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
285	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
286	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
287	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
288	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
289	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
290	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
291	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
292	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
293	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
294	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
295	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
296	C₅×#121	C₂²×C₃	1	1	yes	characteristic
297	C₅×#121	C₂²×C₃	1	2	yes	—
298	C₅×#121	C₂²×C₃	1	2	yes	—
299	C₅×#121	C₂²×C₃	1	2	yes	—
300	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
301	C₅×#121	C₂²×C₃	1	2	yes	complemented
302	C₅×#120	C₂²×C₃	1	2	yes	—
303	C₅×#120	C₂²×C₃	1	2	yes	—
304	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
305	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
306	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
307	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
308	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
309	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
310	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
311	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
312	C₅×#117	C₂²×C₃	1	2	yes	—
313	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
314	C₅×#117	C₂²×C₃	1	2	yes	complemented
315	C₅×#117	C₂²×C₃	1	2	yes	complemented
316	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
317	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
318	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
319	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
320	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
321	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
322	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
323	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
324	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
325	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
326	#3535	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
327	C₂³×C₃×C₅	—	2	2	no	—
328	C₂³×C₃×C₅	—	2	2	no	—
329	C₂³×C₃×C₅	—	2	2	no	—
330	C₂³×C₃×C₅	—	4	1	no	—
331	C₂³×C₃×C₅	—	4	1	no	—
332	C₂³×C₃×C₅	—	4	1	no	—
333	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
334	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
335	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
336	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
337	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
338	C₃×C₅×Q₈	—	4	1	no	—
339	C₃×C₅×Q₈	—	4	2	no	—
340	C₃×C₅×Q₈	—	4	1	no	—
341	C₃×C₅×Q₈	—	4	2	no	—
342	C₃×C₅×Q₈	—	4	1	no	—
343	C₃×C₅×Q₈	—	4	2	no	—
344	C₃×C₅×D₄	—	2	4	no	—
345	C₃×C₅×D₄	—	2	4	no	—
346	C₃×C₅×D₄	—	2	4	no	—
347	C₃×C₅×D₄	—	4	2	no	—
348	C₃×C₅×D₄	—	4	2	no	—
349	C₃×C₅×D₄	—	4	2	no	—
350	C₃×C₅×D₄	—	4	1	no	—
351	C₃×C₅×D₄	—	4	2	no	—
352	C₂×C₃×C₄×C₅	—	2	2	no	—
353	C₂×C₃×C₄×C₅	—	2	2	no	—
354	C₂×C₃×C₄×C₅	—	2	4	no	—
355	C₂×C₃×C₄×C₅	—	2	2	no	—
356	C₂×C₃×C₄×C₅	—	4	1	no	—
357	C₂×C₃×C₄×C₅	—	4	1	no	—
358	C₂×C₃×C₄×C₅	—	4	1	no	—
359	C₂×C₃×C₄×C₅	—	4	1	no	—
360	C₂×C₃×C₄×C₅	—	4	2	no	—
361	C₂×C₃×C₄×C₅	—	4	2	no	—
362	C₂×C₃×C₄×C₅	—	4	1	no	—
363	C₂×C₃×C₄×C₅	—	4	2	no	—
364	C₂×C₃×C₄×C₅	—	4	1	no	—
365	C₂×C₃×C₄×C₅	—	4	2	no	—
366	C₂×C₃×C₄×C₅	—	4	2	no	—
367	C₂×C₃×C₄×C₅	—	4	2	no	—
368	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
369	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
370	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
371	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
372	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
373	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
374	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
375	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
376	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
377	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
378	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
379	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
380	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
381	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
382	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
383	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
384	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
385	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
386	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
387	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
388	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
389	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
390	C₃×#126	C₂²×C₅	1	2	yes	complemented
391	C₃×#126	C₂²×C₅	1	2	yes	complemented
392	C₃×#126	C₂²×C₅	1	2	yes	complemented
393	C₃×#126	C₂²×C₅	1	2	yes	complemented
394	C₃×#126	C₂²×C₅	1	2	yes	complemented
395	C₃×#126	C₂²×C₅	1	2	yes	complemented
396	C₃×#125	C₂²×C₅	1	2	yes	complemented
397	C₃×#125	C₂²×C₅	1	2	yes	complemented
398	C₃×#125	C₂²×C₅	1	2	yes	complemented
399	C₃×#125	C₂²×C₅	1	2	yes	complemented
400	C₃×#125	C₂²×C₅	1	2	yes	complemented
401	C₃×#124	C₂²×C₅	1	2	yes	—
402	C₃×#124	C₂²×C₅	1	2	yes	complemented
403	C₃×#124	C₂²×C₅	1	2	yes	complemented
404	C₃×#124	C₂²×C₅	1	2	yes	complemented
405	C₃×#123	C₂²×C₅	1	2	yes	—
406	C₃×#123	C₂²×C₅	1	2	yes	—
407	C₃×#123	C₂²×C₅	1	2	yes	—
408	C₃×#123	C₂²×C₅	1	2	yes	—
409	C₃×#123	C₂²×C₅	1	2	yes	—
410	C₃×#123	C₂²×C₅	1	2	yes	—
411	C₃×#123	C₂²×C₅	1	2	yes	—
412	C₃×#123	C₂²×C₅	1	2	yes	complemented
413	C₃×#123	C₂²×C₅	1	2	yes	complemented
414	C₃×#123	C₂²×C₅	1	2	yes	complemented
415	C₃×#123	C₂²×C₅	1	2	yes	complemented
416	C₃×#123	C₂²×C₅	1	2	yes	complemented
417	C₃×#123	C₂²×C₅	1	2	yes	complemented
418	C₃×#123	C₂²×C₅	1	2	yes	complemented
419	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
420	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
421	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
422	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
423	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
424	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
425	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
426	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
427	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
428	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
429	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
430	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
431	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
432	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
433	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
434	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
435	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
436	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
437	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
438	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
439	C₃×#121	C₂²×C₅	1	2	yes	—
440	C₃×#121	C₂²×C₅	1	2	yes	—
441	C₃×#121	C₂²×C₅	1	1	yes	characteristic
442	C₃×#121	C₂²×C₅	1	2	yes	—
443	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
444	C₃×#121	C₂²×C₅	1	2	yes	complemented
445	C₃×#120	C₂²×C₅	1	2	yes	—
446	C₃×#120	C₂²×C₅	1	2	yes	—
447	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
448	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
449	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
450	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
451	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
452	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
453	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
454	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
455	C₃×#117	C₂²×C₅	1	2	yes	—
456	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
457	C₃×#117	C₂²×C₅	1	2	yes	complemented
458	C₃×#117	C₂²×C₅	1	2	yes	complemented
459	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
460	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
461	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
462	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
463	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
464	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
465	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
466	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
467	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
468	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
469	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
470	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
471	C₅×#41	—	4	4	no	—
472	C₅×#41	—	4	2	no	—
473	C₂×C₅×Q₈	—	4	2	no	—
474	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
475	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
476	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
477	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
478	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
479	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
480	C₂×C₅×D₄	—	4	2	no	—
481	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
482	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
483	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
484	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
485	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
486	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
487	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
488	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
489	C₂²×C₄×C₅	—	4	2	no	—
490	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
491	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
492	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
493	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
494	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
495	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
496	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
497	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
498	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
499	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
500	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
501	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
502	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
503	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
504	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
505	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
506	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
507	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
508	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
509	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
510	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
511	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
512	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
513	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
514	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
515	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
516	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
517	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
518	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
519	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
520	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
521	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
522	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
523	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
524	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
525	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
526	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
527	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
528	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
529	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
530	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
531	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
532	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
533	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
534	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
535	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
536	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
537	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
538	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
539	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
540	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
541	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
542	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
543	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
544	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
545	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
546	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
547	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
548	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
549	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
550	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
551	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
552	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
553	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
554	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
555	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
556	C₄²×C₅	C₂³×C₃	1	2	yes	—
557	C₄²×C₅	C₂³×C₃	1	2	yes	—
558	C₄²×C₅	C₂³×C₃	1	2	yes	—
559	C₄²×C₅	C₂³×C₃	1	2	yes	—
560	C₄²×C₅	C₂³×C₃	1	2	yes	—
561	#563	C₂×C₃×C₅	1	2	yes	complemented
562	#562	C₂×C₃×C₅	1	2	yes	complemented
563	#554	C₂×C₃×C₅	1	2	yes	complemented
564	#552	C₂×C₃×C₅	1	2	yes	complemented
565	#551	C₂×C₃×C₅	1	2	yes	complemented
566	#551	C₂×C₃×C₅	1	2	yes	complemented
567	#547	C₂×C₃×C₅	1	2	yes	complemented
568	#546	C₂×C₃×C₅	1	2	yes	complemented
569	#544	C₂×C₃×C₅	1	1	yes	characteristic, complemented
570	#543	C₂×C₃×C₅	1	1	yes	characteristic, complemented
571	#542	C₂×C₃×C₅	1	2	yes	complemented
572	#539	C₂×C₃×C₅	1	1	yes	characteristic, complemented
573	#539	C₂×C₃×C₅	1	2	yes	complemented
574	#539	C₂×C₃×C₅	1	2	yes	complemented
575	#538	C₂×C₃×C₅	1	1	yes	characteristic, complemented
576	#536	C₂×C₃×C₅	1	2	yes	complemented
577	#525	C₂×C₃×C₅	1	1	yes	characteristic, complemented
578	C₂×#123	C₂×C₃×C₅	1	1	yes	characteristic, complemented
579	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
580	C₂²×C₃×C₅	—	2	1	no	—
581	C₂²×C₃×C₅	—	2	1	no	—
582	C₂²×C₃×C₅	—	2	1	no	—
583	C₂²×C₃×C₅	—	2	1	no	—
584	C₂²×C₃×C₅	—	2	2	no	—
585	C₂²×C₃×C₅	—	2	1	no	—
586	C₂²×C₃×C₅	—	2	2	no	—
587	C₂²×C₃×C₅	—	2	2	no	—
588	C₂²×C₃×C₅	—	2	1	no	—
589	C₂²×C₃×C₅	—	2	2	no	—
590	C₂²×C₃×C₅	—	2	2	no	—
591	C₂²×C₃×C₅	—	2	2	no	—
592	C₂²×C₃×C₅	—	2	1	no	—
593	C₂²×C₃×C₅	—	4	4	no	—
594	C₂²×C₃×C₅	—	8	2	no	—
595	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
596	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
597	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
598	C₃×C₄×C₅	—	2	1	no	—
599	C₃×C₄×C₅	—	2	1	no	—
600	C₃×C₄×C₅	—	2	1	no	—
601	C₃×C₄×C₅	—	2	1	no	—
602	C₃×C₄×C₅	—	2	2	no	—
603	C₃×C₄×C₅	—	2	2	no	—
604	C₃×C₄×C₅	—	2	2	no	—
605	C₃×C₄×C₅	—	2	2	no	—
606	C₃×C₄×C₅	—	2	2	no	—
607	C₃×C₄×C₅	—	2	2	no	—
608	C₃×C₄×C₅	—	2	2	no	—
609	C₃×C₄×C₅	—	2	2	no	—
610	C₃×C₄×C₅	—	2	2	no	—
611	C₃×C₄×C₅	—	2	2	no	—
612	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
613	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
614	C₃×#41	—	4	4	no	—
615	C₃×#41	—	4	2	no	—
616	C₂×C₃×Q₈	—	4	2	no	—
617	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
618	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
619	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
620	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
621	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
622	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
623	C₂×C₃×D₄	—	4	2	no	—
624	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
625	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
626	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
627	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
628	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
629	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
630	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
631	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
632	C₂²×C₃×C₄	—	4	2	no	—
633	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
634	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
635	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
636	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
637	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
638	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
639	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
640	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
641	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
642	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
643	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
644	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
645	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
646	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
647	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
648	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
649	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
650	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
651	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
652	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
653	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
654	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
655	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
656	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
657	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
658	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
659	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
660	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
661	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
662	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
663	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
664	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
665	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
666	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
667	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
668	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
669	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
670	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
671	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
672	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
673	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
674	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
675	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
676	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
677	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
678	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
679	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
680	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
681	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
682	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
683	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
684	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
685	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
686	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
687	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
688	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
689	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
690	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
691	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
692	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
693	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
694	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
695	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
696	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
697	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
698	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
699	C₃×C₄²	C₂³×C₅	1	2	yes	—
700	C₃×C₄²	C₂³×C₅	1	2	yes	—
701	C₃×C₄²	C₂³×C₅	1	2	yes	—
702	C₃×C₄²	C₂³×C₅	1	2	yes	—
703	C₃×C₄²	C₂³×C₅	1	2	yes	—
704	C₂³×C₅	—	2	2	no	—
705	C₂³×C₅	—	2	2	no	—
706	C₂³×C₅	—	2	2	no	—
707	C₂³×C₅	—	4	1	no	—
708	C₂³×C₅	—	4	1	no	—
709	C₂³×C₅	—	4	1	no	—
710	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
711	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
712	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
713	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
714	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
715	C₅×Q₈	—	4	1	no	—
716	C₅×Q₈	—	4	2	no	—
717	C₅×Q₈	—	4	1	no	—
718	C₅×Q₈	—	4	2	no	—
719	C₅×Q₈	—	4	1	no	—
720	C₅×Q₈	—	4	2	no	—
721	C₅×D₄	—	2	4	no	—
722	C₅×D₄	—	2	4	no	—
723	C₅×D₄	—	2	4	no	—
724	C₅×D₄	—	4	2	no	—
725	C₅×D₄	—	4	2	no	—
726	C₅×D₄	—	4	2	no	—
727	C₅×D₄	—	4	1	no	—
728	C₅×D₄	—	4	2	no	—
729	C₂×C₄×C₅	—	2	2	no	—
730	C₂×C₄×C₅	—	2	2	no	—
731	C₂×C₄×C₅	—	2	4	no	—
732	C₂×C₄×C₅	—	2	2	no	—
733	C₂×C₄×C₅	—	4	1	no	—
734	C₂×C₄×C₅	—	4	1	no	—
735	C₂×C₄×C₅	—	4	1	no	—
736	C₂×C₄×C₅	—	4	1	no	—
737	C₂×C₄×C₅	—	4	2	no	—
738	C₂×C₄×C₅	—	4	2	no	—
739	C₂×C₄×C₅	—	4	1	no	—
740	C₂×C₄×C₅	—	4	2	no	—
741	C₂×C₄×C₅	—	4	1	no	—
742	C₂×C₄×C₅	—	4	2	no	—
743	C₂×C₄×C₅	—	4	2	no	—
744	C₂×C₄×C₅	—	4	2	no	—
745	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
746	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
747	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
748	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
749	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
750	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
751	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
752	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
753	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
754	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
755	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
756	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
757	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
758	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
759	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
760	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
761	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
762	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
763	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
764	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
765	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
766	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
767	#126	C₂²×C₃×C₅	1	2	yes	complemented
768	#126	C₂²×C₃×C₅	1	2	yes	complemented
769	#126	C₂²×C₃×C₅	1	2	yes	complemented
770	#126	C₂²×C₃×C₅	1	2	yes	complemented
771	#126	C₂²×C₃×C₅	1	2	yes	complemented
772	#126	C₂²×C₃×C₅	1	2	yes	complemented
773	#125	C₂²×C₃×C₅	1	2	yes	complemented
774	#125	C₂²×C₃×C₅	1	2	yes	complemented
775	#125	C₂²×C₃×C₅	1	2	yes	complemented
776	#125	C₂²×C₃×C₅	1	2	yes	complemented
777	#125	C₂²×C₃×C₅	1	2	yes	complemented
778	#124	C₂²×C₃×C₅	1	2	yes	—
779	#124	C₂²×C₃×C₅	1	2	yes	complemented
780	#124	C₂²×C₃×C₅	1	2	yes	complemented
781	#124	C₂²×C₃×C₅	1	2	yes	complemented
782	#123	C₂²×C₃×C₅	1	2	yes	—
783	#123	C₂²×C₃×C₅	1	2	yes	—
784	#123	C₂²×C₃×C₅	1	2	yes	—
785	#123	C₂²×C₃×C₅	1	2	yes	—
786	#123	C₂²×C₃×C₅	1	2	yes	—
787	#123	C₂²×C₃×C₅	1	2	yes	—
788	#123	C₂²×C₃×C₅	1	2	yes	—
789	#123	C₂²×C₃×C₅	1	2	yes	complemented
790	#123	C₂²×C₃×C₅	1	2	yes	complemented
791	#123	C₂²×C₃×C₅	1	2	yes	complemented
792	#123	C₂²×C₃×C₅	1	2	yes	complemented
793	#123	C₂²×C₃×C₅	1	2	yes	complemented
794	#123	C₂²×C₃×C₅	1	2	yes	complemented
795	#123	C₂²×C₃×C₅	1	2	yes	complemented
796	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
797	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
798	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
799	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
800	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
801	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
802	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
803	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
804	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
805	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
806	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
807	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
808	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
809	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
810	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
811	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
812	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
813	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
814	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
815	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
816	#121	C₂²×C₃×C₅	1	1	yes	characteristic
817	#121	C₂²×C₃×C₅	1	2	yes	—
818	#121	C₂²×C₃×C₅	1	2	yes	—
819	#121	C₂²×C₃×C₅	1	2	yes	—
820	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
821	#121	C₂²×C₃×C₅	1	2	yes	complemented
822	#120	C₂²×C₃×C₅	1	2	yes	—
823	#120	C₂²×C₃×C₅	1	2	yes	—
824	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
825	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
826	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
827	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
828	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
829	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
830	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
831	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
832	#117	C₂²×C₃×C₅	1	2	yes	—
833	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
834	#117	C₂²×C₃×C₅	1	2	yes	complemented
835	#117	C₂²×C₃×C₅	1	2	yes	complemented
836	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
837	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
838	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
839	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
840	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
841	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
842	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
843	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
844	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
845	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
846	C₂×C₃×C₅	—	2	2	no	—
847	C₂×C₃×C₅	—	2	2	no	—
848	C₂×C₃×C₅	—	4	2	no	—
849	C₂×C₃×C₅	—	4	1	no	—
850	C₂×C₃×C₅	—	4	2	no	—
851	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
852	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
853	C₂×C₃×C₅	#585	1	1	yes	characteristic
854	C₂³×C₃	—	2	2	no	—
855	C₂³×C₃	—	2	2	no	—
856	C₂³×C₃	—	2	2	no	—
857	C₂³×C₃	—	4	1	no	—
858	C₂³×C₃	—	4	1	no	—
859	C₂³×C₃	—	4	1	no	—
860	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
861	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
862	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
863	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
864	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
865	C₃×Q₈	—	4	1	no	—
866	C₃×Q₈	—	4	2	no	—
867	C₃×Q₈	—	4	1	no	—
868	C₃×Q₈	—	4	2	no	—
869	C₃×Q₈	—	4	1	no	—
870	C₃×Q₈	—	4	2	no	—
871	C₃×D₄	—	2	4	no	—
872	C₃×D₄	—	2	4	no	—
873	C₃×D₄	—	2	4	no	—
874	C₃×D₄	—	4	2	no	—
875	C₃×D₄	—	4	2	no	—
876	C₃×D₄	—	4	2	no	—
877	C₃×D₄	—	4	1	no	—
878	C₃×D₄	—	4	2	no	—
879	C₂×C₃×C₄	—	2	2	no	—
880	C₂×C₃×C₄	—	2	2	no	—
881	C₂×C₃×C₄	—	2	4	no	—
882	C₂×C₃×C₄	—	2	2	no	—
883	C₂×C₃×C₄	—	4	1	no	—
884	C₂×C₃×C₄	—	4	1	no	—
885	C₂×C₃×C₄	—	4	1	no	—
886	C₂×C₃×C₄	—	4	1	no	—
887	C₂×C₃×C₄	—	4	2	no	—
888	C₂×C₃×C₄	—	4	2	no	—
889	C₂×C₃×C₄	—	4	1	no	—
890	C₂×C₃×C₄	—	4	2	no	—
891	C₂×C₃×C₄	—	4	1	no	—
892	C₂×C₃×C₄	—	4	2	no	—
893	C₂×C₃×C₄	—	4	2	no	—
894	C₂×C₃×C₄	—	4	2	no	—
895	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
896	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
897	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
898	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
899	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
900	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
901	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
902	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
903	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
904	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
905	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
906	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
907	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
908	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
909	C₂²×C₅	—	2	1	no	—
910	C₂²×C₅	—	2	1	no	—
911	C₂²×C₅	—	2	1	no	—
912	C₂²×C₅	—	2	1	no	—
913	C₂²×C₅	—	2	2	no	—
914	C₂²×C₅	—	2	1	no	—
915	C₂²×C₅	—	2	2	no	—
916	C₂²×C₅	—	2	2	no	—
917	C₂²×C₅	—	2	1	no	—
918	C₂²×C₅	—	2	2	no	—
919	C₂²×C₅	—	2	2	no	—
920	C₂²×C₅	—	2	2	no	—
921	C₂²×C₅	—	2	1	no	—
922	C₂²×C₅	—	4	4	no	—
923	C₂²×C₅	—	8	2	no	—
924	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
925	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
926	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
927	C₄×C₅	—	2	1	no	—
928	C₄×C₅	—	2	1	no	—
929	C₄×C₅	—	2	1	no	—
930	C₄×C₅	—	2	1	no	—
931	C₄×C₅	—	2	2	no	—
932	C₄×C₅	—	2	2	no	—
933	C₄×C₅	—	2	2	no	—
934	C₄×C₅	—	2	2	no	—
935	C₄×C₅	—	2	2	no	—
936	C₄×C₅	—	2	2	no	—
937	C₄×C₅	—	2	2	no	—
938	C₄×C₅	—	2	2	no	—
939	C₄×C₅	—	2	2	no	—
940	C₄×C₅	—	2	2	no	—
941	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
942	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
943	#41	—	4	4	no	—
944	#41	—	4	2	no	—
945	C₂×Q₈	—	4	2	no	—
946	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
947	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
948	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
949	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
950	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
951	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
952	C₂×D₄	—	4	2	no	—
953	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
954	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
955	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
956	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
957	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
958	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
959	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
960	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
961	C₂²×C₄	—	4	2	no	—
962	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
963	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
964	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
965	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
966	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
967	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
968	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
969	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
970	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
971	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
972	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
973	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
974	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
975	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
976	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
977	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
978	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
979	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
980	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
981	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
982	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
983	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
984	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
985	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
986	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
987	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
988	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
989	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
990	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
991	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
992	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
993	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
994	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
995	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
996	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
997	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
998	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
999	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1000	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1001	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1002	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1003	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1004	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1005	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1006	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1007	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1008	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1009	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1010	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1011	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1012	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1013	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1014	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1015	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1016	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1017	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1018	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1019	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1020	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1021	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1022	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1023	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1024	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1025	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1026	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1027	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1028	C₄²	C₂³×C₃×C₅	1	2	yes	—
1029	C₄²	C₂³×C₃×C₅	1	2	yes	—
1030	C₄²	C₂³×C₃×C₅	1	2	yes	—
1031	C₄²	C₂³×C₃×C₅	1	2	yes	—
1032	C₄²	C₂³×C₃×C₅	1	2	yes	—
1033	C₃×C₅	#3535	1	1	yes	characteristic, direct product factor, Hall
1034	C₂²×C₃	—	2	1	no	—
1035	C₂²×C₃	—	2	1	no	—
1036	C₂²×C₃	—	2	1	no	—
1037	C₂²×C₃	—	2	1	no	—
1038	C₂²×C₃	—	2	2	no	—
1039	C₂²×C₃	—	2	1	no	—
1040	C₂²×C₃	—	2	2	no	—
1041	C₂²×C₃	—	2	2	no	—
1042	C₂²×C₃	—	2	1	no	—
1043	C₂²×C₃	—	2	2	no	—
1044	C₂²×C₃	—	2	2	no	—
1045	C₂²×C₃	—	2	2	no	—
1046	C₂²×C₃	—	2	1	no	—
1047	C₂²×C₃	—	4	4	no	—
1048	C₂²×C₃	—	8	2	no	—
1049	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
1050	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
1051	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1052	C₃×C₄	—	2	1	no	—
1053	C₃×C₄	—	2	1	no	—
1054	C₃×C₄	—	2	1	no	—
1055	C₃×C₄	—	2	1	no	—
1056	C₃×C₄	—	2	2	no	—
1057	C₃×C₄	—	2	2	no	—
1058	C₃×C₄	—	2	2	no	—
1059	C₃×C₄	—	2	2	no	—
1060	C₃×C₄	—	2	2	no	—
1061	C₃×C₄	—	2	2	no	—
1062	C₃×C₄	—	2	2	no	—
1063	C₃×C₄	—	2	2	no	—
1064	C₃×C₄	—	2	2	no	—
1065	C₃×C₄	—	2	2	no	—
1066	C₂×C₅	—	2	2	no	—
1067	C₂×C₅	—	2	2	no	—
1068	C₂×C₅	—	4	1	no	—
1069	C₂×C₅	—	4	2	no	—
1070	C₂×C₅	—	4	2	no	—
1071	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1072	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1073	C₂×C₅	C₃×#585	1	1	yes	characteristic
1074	C₂³	—	2	2	no	—
1075	C₂³	—	2	2	no	—
1076	C₂³	—	2	2	no	—
1077	C₂³	—	4	1	no	—
1078	C₂³	—	4	1	no	—
1079	C₂³	—	4	1	no	—
1080	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1081	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1082	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1083	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1084	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1085	Q₈	—	4	1	no	—
1086	Q₈	—	4	2	no	—
1087	Q₈	—	4	1	no	—
1088	Q₈	—	4	1	no	—
1089	Q₈	—	4	2	no	—
1090	Q₈	—	4	2	no	—
1091	D₄	—	2	4	no	—
1092	D₄	—	2	4	no	—
1093	D₄	—	2	4	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	1	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	4	2	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	4	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	4	1	no	—
1104	C₂×C₄	—	4	1	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	1	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	2	no	—
1115	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1116	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1117	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1118	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1119	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1120	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1121	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1122	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1123	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1124	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1125	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1126	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1127	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1128	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1129	C₂×C₃	—	2	2	no	—
1130	C₂×C₃	—	2	2	no	—
1131	C₂×C₃	—	4	1	no	—
1132	C₂×C₃	—	4	2	no	—
1133	C₂×C₃	—	4	2	no	—
1134	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1135	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1136	C₂×C₃	C₅×#585	1	1	yes	characteristic
1137	C₅	C₃×#3535	1	1	yes	characteristic, direct product factor, Sylow
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	1	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	1	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	2	2	no	—
1146	C₂²	—	2	1	no	—
1147	C₂²	—	2	2	no	—
1148	C₂²	—	2	2	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	1	no	—
1151	C₂²	—	4	4	no	—
1152	C₂²	—	8	2	no	—
1153	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
1154	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
1155	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
1156	C₄	—	2	1	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	2	2	no	—
1167	C₄	—	2	2	no	—
1168	C₄	—	2	2	no	—
1169	C₄	—	2	2	no	—
1170	C₃	C₅×#3535	1	1	yes	characteristic, direct product factor, Sylow
1171	C₂	—	2	2	no	—
1172	C₂	—	2	2	no	—
1173	C₂	—	4	1	no	—
1174	C₂	—	4	2	no	—
1175	C₂	—	4	2	no	—
1176	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1177	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1178	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×#563	C₂	semidirect
2. C₃×C₅×#562	C₂	semidirect
3. C₃×C₅×#554	C₂	semidirect
4. C₃×C₅×#552	C₂	semidirect
5. C₃×C₅×#551	C₂	semidirect
6. C₃×C₅×#551	C₂	semidirect
7. C₃×C₅×#547	C₂	semidirect
8. C₃×C₅×#546	C₂	semidirect
9. C₃×C₅×#544	C₂	semidirect
10. C₃×C₅×#543	C₂	semidirect
11. C₃×C₅×#542	C₂	semidirect
12. C₃×C₅×#539	C₂	semidirect
13. C₃×C₅×#539	C₂	semidirect
14. C₃×C₅×#539	C₂	semidirect
15. C₃×C₅×#538	C₂	semidirect
16. C₃×C₅×#536	C₂	semidirect
17. C₃×C₅×#525	C₂	semidirect
18. C₂×C₃×C₅×#123	C₂	semidirect
19. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
20. C₅×#3535	C₃	direct (N × H)
22. C₂×C₃×C₅×#41	C₂²	semidirect
23. C₂²×C₃×C₅×Q₈	C₂²	semidirect
26. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
27. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
28. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
29. C₃×C₅×#126	C₂²	semidirect
30. C₃×C₅×#126	C₂²	semidirect
31. C₃×C₅×#126	C₂²	semidirect
32. C₃×C₅×#126	C₂²	semidirect
33. C₃×C₅×#126	C₂²	semidirect
34. C₃×C₅×#126	C₂²	semidirect
35. C₃×C₅×#125	C₂²	semidirect
36. C₃×C₅×#125	C₂²	semidirect
37. C₃×C₅×#125	C₂²	semidirect
38. C₃×C₅×#125	C₂²	semidirect
39. C₃×C₅×#125	C₂²	semidirect
41. C₃×C₅×#124	C₂²	semidirect
42. C₃×C₅×#124	C₂²	semidirect
43. C₃×C₅×#124	C₂²	semidirect
51. C₃×C₅×#123	C₂²	semidirect
52. C₃×C₅×#123	C₂²	semidirect
53. C₃×C₅×#123	C₂²	semidirect
54. C₃×C₅×#123	C₂²	semidirect
55. C₃×C₅×#123	C₂²	semidirect
56. C₃×C₅×#123	C₂²	semidirect
57. C₃×C₅×#123	C₂²	semidirect
64. C₃×C₅×C₂²⋊Q₈	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
73. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
74. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
75. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
76. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
77. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
82. C₃×C₅×#121	C₂²	semidirect
83. C₃×C₅×#121	C₂²	semidirect
86. C₃×C₄×C₅×Q₈	C₂²	semidirect
91. C₃×C₄×C₅×D₄	C₂²	semidirect
92. C₃×C₄×C₅×D₄	C₂²	semidirect
93. C₃×C₄×C₅×D₄	C₂²	semidirect
95. C₃×C₅×#117	C₂²	semidirect
96. C₃×C₅×#117	C₂²	semidirect
97. C₃×C₅×#117	C₂²	semidirect
100. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
101. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
102. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
108. C₃×#3535	C₅	direct (N × H)
109. C₅×#563	C₂×C₃	semidirect
110. C₅×#562	C₂×C₃	semidirect
111. C₅×#554	C₂×C₃	semidirect
112. C₅×#552	C₂×C₃	semidirect
113. C₅×#551	C₂×C₃	semidirect
114. C₅×#551	C₂×C₃	semidirect
115. C₅×#547	C₂×C₃	semidirect
116. C₅×#546	C₂×C₃	semidirect
117. C₅×#544	C₂×C₃	semidirect
118. C₅×#543	C₂×C₃	semidirect
119. C₅×#542	C₂×C₃	semidirect
120. C₅×#539	C₂×C₃	semidirect
121. C₅×#539	C₂×C₃	semidirect
122. C₅×#539	C₂×C₃	semidirect
123. C₅×#538	C₂×C₃	semidirect
124. C₅×#536	C₂×C₃	semidirect
125. C₅×#525	C₂×C₃	semidirect
126. C₂×C₅×#123	C₂×C₃	semidirect
127. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
220. C₃×#563	C₂×C₅	semidirect
221. C₃×#562	C₂×C₅	semidirect
222. C₃×#554	C₂×C₅	semidirect
223. C₃×#552	C₂×C₅	semidirect
224. C₃×#551	C₂×C₅	semidirect
225. C₃×#551	C₂×C₅	semidirect
226. C₃×#547	C₂×C₅	semidirect
227. C₃×#546	C₂×C₅	semidirect
228. C₃×#544	C₂×C₅	semidirect
229. C₃×#543	C₂×C₅	semidirect
230. C₃×#542	C₂×C₅	semidirect
231. C₃×#539	C₂×C₅	semidirect
232. C₃×#539	C₂×C₅	semidirect
233. C₃×#539	C₂×C₅	semidirect
234. C₃×#538	C₂×C₅	semidirect
235. C₃×#536	C₂×C₅	semidirect
236. C₃×#525	C₂×C₅	semidirect
237. C₂×C₃×#123	C₂×C₅	semidirect
238. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
240. C₂×C₅×#41	C₂²×C₃	semidirect
241. C₂²×C₅×Q₈	C₂²×C₃	semidirect
244. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
245. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
246. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
247. C₅×#126	C₂²×C₃	semidirect
248. C₅×#126	C₂²×C₃	semidirect
249. C₅×#126	C₂²×C₃	semidirect
250. C₅×#126	C₂²×C₃	semidirect
251. C₅×#126	C₂²×C₃	semidirect
252. C₅×#126	C₂²×C₃	semidirect
253. C₅×#125	C₂²×C₃	semidirect
254. C₅×#125	C₂²×C₃	semidirect
255. C₅×#125	C₂²×C₃	semidirect
256. C₅×#125	C₂²×C₃	semidirect
257. C₅×#125	C₂²×C₃	semidirect
259. C₅×#124	C₂²×C₃	semidirect
260. C₅×#124	C₂²×C₃	semidirect
261. C₅×#124	C₂²×C₃	semidirect
269. C₅×#123	C₂²×C₃	semidirect
270. C₅×#123	C₂²×C₃	semidirect
271. C₅×#123	C₂²×C₃	semidirect
272. C₅×#123	C₂²×C₃	semidirect
273. C₅×#123	C₂²×C₃	semidirect
274. C₅×#123	C₂²×C₃	semidirect
275. C₅×#123	C₂²×C₃	semidirect
282. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
283. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
284. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
285. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
286. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
287. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
288. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
289. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
290. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
291. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
292. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
293. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
294. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
295. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
300. C₅×#121	C₂²×C₃	semidirect
301. C₅×#121	C₂²×C₃	semidirect
304. C₄×C₅×Q₈	C₂²×C₃	semidirect
309. C₄×C₅×D₄	C₂²×C₃	semidirect
310. C₄×C₅×D₄	C₂²×C₃	semidirect
311. C₄×C₅×D₄	C₂²×C₃	semidirect
313. C₅×#117	C₂²×C₃	semidirect
314. C₅×#117	C₂²×C₃	semidirect
315. C₅×#117	C₂²×C₃	semidirect
318. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
319. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
320. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
326. #3535	C₃×C₅	direct (N × H)
383. C₂×C₃×#41	C₂²×C₅	semidirect
384. C₂²×C₃×Q₈	C₂²×C₅	semidirect
387. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
388. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
389. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
390. C₃×#126	C₂²×C₅	semidirect
391. C₃×#126	C₂²×C₅	semidirect
392. C₃×#126	C₂²×C₅	semidirect
393. C₃×#126	C₂²×C₅	semidirect
394. C₃×#126	C₂²×C₅	semidirect
395. C₃×#126	C₂²×C₅	semidirect
396. C₃×#125	C₂²×C₅	semidirect
397. C₃×#125	C₂²×C₅	semidirect
398. C₃×#125	C₂²×C₅	semidirect
399. C₃×#125	C₂²×C₅	semidirect
400. C₃×#125	C₂²×C₅	semidirect
402. C₃×#124	C₂²×C₅	semidirect
403. C₃×#124	C₂²×C₅	semidirect
404. C₃×#124	C₂²×C₅	semidirect
412. C₃×#123	C₂²×C₅	semidirect
413. C₃×#123	C₂²×C₅	semidirect
414. C₃×#123	C₂²×C₅	semidirect
415. C₃×#123	C₂²×C₅	semidirect
416. C₃×#123	C₂²×C₅	semidirect
417. C₃×#123	C₂²×C₅	semidirect
418. C₃×#123	C₂²×C₅	semidirect
425. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
426. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
427. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
428. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
429. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
430. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
431. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
432. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
433. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
434. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
435. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
436. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
437. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
438. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
443. C₃×#121	C₂²×C₅	semidirect
444. C₃×#121	C₂²×C₅	semidirect
447. C₃×C₄×Q₈	C₂²×C₅	semidirect
452. C₃×C₄×D₄	C₂²×C₅	semidirect
453. C₃×C₄×D₄	C₂²×C₅	semidirect
454. C₃×C₄×D₄	C₂²×C₅	semidirect
456. C₃×#117	C₂²×C₅	semidirect
457. C₃×#117	C₂²×C₅	semidirect
458. C₃×#117	C₂²×C₅	semidirect
461. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
462. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
463. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
561. #563	C₂×C₃×C₅	semidirect
562. #562	C₂×C₃×C₅	semidirect
563. #554	C₂×C₃×C₅	semidirect
564. #552	C₂×C₃×C₅	semidirect
565. #551	C₂×C₃×C₅	semidirect
566. #551	C₂×C₃×C₅	semidirect
567. #547	C₂×C₃×C₅	semidirect
568. #546	C₂×C₃×C₅	semidirect
569. #544	C₂×C₃×C₅	semidirect
570. #543	C₂×C₃×C₅	semidirect
571. #542	C₂×C₃×C₅	semidirect
572. #539	C₂×C₃×C₅	semidirect
573. #539	C₂×C₃×C₅	semidirect
574. #539	C₂×C₃×C₅	semidirect
575. #538	C₂×C₃×C₅	semidirect
576. #536	C₂×C₃×C₅	semidirect
577. #525	C₂×C₃×C₅	semidirect
578. C₂×#123	C₂×C₃×C₅	semidirect
579. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
760. C₂×#41	C₂²×C₃×C₅	semidirect
761. C₂²×Q₈	C₂²×C₃×C₅	semidirect
764. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
765. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
766. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
767. #126	C₂²×C₃×C₅	semidirect
768. #126	C₂²×C₃×C₅	semidirect
769. #126	C₂²×C₃×C₅	semidirect
770. #126	C₂²×C₃×C₅	semidirect
771. #126	C₂²×C₃×C₅	semidirect
772. #126	C₂²×C₃×C₅	semidirect
773. #125	C₂²×C₃×C₅	semidirect
774. #125	C₂²×C₃×C₅	semidirect
775. #125	C₂²×C₃×C₅	semidirect
776. #125	C₂²×C₃×C₅	semidirect
777. #125	C₂²×C₃×C₅	semidirect
779. #124	C₂²×C₃×C₅	semidirect
780. #124	C₂²×C₃×C₅	semidirect
781. #124	C₂²×C₃×C₅	semidirect
789. #123	C₂²×C₃×C₅	semidirect
790. #123	C₂²×C₃×C₅	semidirect
791. #123	C₂²×C₃×C₅	semidirect
792. #123	C₂²×C₃×C₅	semidirect
793. #123	C₂²×C₃×C₅	semidirect
794. #123	C₂²×C₃×C₅	semidirect
795. #123	C₂²×C₃×C₅	semidirect
802. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
803. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
804. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
805. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
806. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
807. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
808. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
809. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
810. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
811. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
812. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
813. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
814. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
815. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
820. #121	C₂²×C₃×C₅	semidirect
821. #121	C₂²×C₃×C₅	semidirect
824. C₄×Q₈	C₂²×C₃×C₅	semidirect
829. C₄×D₄	C₂²×C₃×C₅	semidirect
830. C₄×D₄	C₂²×C₃×C₅	semidirect
831. C₄×D₄	C₂²×C₃×C₅	semidirect
833. #117	C₂²×C₃×C₅	semidirect
834. #117	C₂²×C₃×C₅	semidirect
835. #117	C₂²×C₃×C₅	semidirect
838. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
839. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
840. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
1033. C₃×C₅	#3535	direct (N × H)
1137. C₅	C₃×#3535	direct (N × H)
1170. C₃	C₅×#3535	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×#563	2
C₃×C₅×#562	2
C₃×C₅×#554	2
C₃×C₅×#552	2
C₃×C₅×#551	2
C₃×C₅×#547	2
C₃×C₅×#546	2
C₃×C₅×#544	2
C₃×C₅×#543	2
C₃×C₅×#542	2
C₃×C₅×#539	2
C₃×C₅×#538	2
C₃×C₅×#536	2
C₃×C₅×#525	2
C₂×C₃×C₅×#123	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₅×#3535	3
C₃×#3535	5

Subgroups — C3×C5×#3535 #14276569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3535 #14276569