Subgroups — C₃×C₅×#3533 #14276567

Order 1920.

2120 conjugacy classes of subgroups.

The subgroup lattice has 1192 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	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#562	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#560	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#559	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#553	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#552	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#551	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#551	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#547	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#546	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#542	C₂	1	2	yes	maximal, complemented
12	C₃×C₅×#540	C₂	1	2	yes	maximal, complemented
13	C₃×C₅×#539	C₂	1	2	yes	maximal, complemented
14	C₃×C₅×#538	C₂	1	2	yes	maximal, complemented
15	C₃×C₅×#538	C₂	1	2	yes	maximal, complemented
16	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×C₅×#534	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×C₅×#525	C₂	1	2	yes	maximal, complemented
19	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#3533	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×D₄	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
25	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
27	C₃×C₅×#127	C₂²	1	1	yes	characteristic
28	C₃×C₅×#127	C₂²	1	1	yes	characteristic, 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×#124	C₂²	1	1	yes	characteristic
39	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₅×#124	C₂²	1	2	yes	complemented
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	1	yes	characteristic
46	C₃×C₅×#123	C₂²	1	1	yes	characteristic
47	C₃×C₅×#123	C₂²	1	2	yes	—
48	C₃×C₅×#123	C₂²	1	1	yes	characteristic
49	C₃×C₅×#123	C₂²	1	2	yes	—
50	C₃×C₅×#123	C₂²	1	1	yes	characteristic
51	C₃×C₅×#123	C₂²	1	2	yes	complemented
52	C₃×C₅×#123	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#123	C₂²	1	1	yes	characteristic, 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×#123	C₂²	1	2	yes	complemented
59	C₃×C₅×#123	C₂²	1	2	yes	complemented
60	C₃×C₅×#123	C₂²	1	2	yes	complemented
61	C₃×C₅×#123	C₂²	1	2	yes	complemented
62	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
64	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
65	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
66	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	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×#121	C₂²	1	2	yes	—
71	C₃×C₅×#121	C₂²	1	2	yes	—
72	C₃×C₅×#121	C₂²	1	2	yes	—
73	C₃×C₅×#121	C₂²	1	2	yes	—
74	C₃×C₅×#121	C₂²	1	2	yes	complemented
75	C₃×C₅×#121	C₂²	1	2	yes	complemented
76	C₃×C₅×#121	C₂²	1	2	yes	complemented
77	C₃×C₅×#121	C₂²	1	2	yes	complemented
78	C₃×C₅×#121	C₂²	1	2	yes	complemented
79	C₃×C₅×#121	C₂²	1	2	yes	complemented
80	C₃×C₅×#121	C₂²	1	2	yes	complemented
81	C₃×C₅×#121	C₂²	1	2	yes	complemented
82	C₃×C₅×#120	C₂²	1	2	yes	—
83	C₃×C₅×#120	C₂²	1	1	yes	characteristic
84	C₃×C₅×#120	C₂²	1	1	yes	characteristic
85	C₃×C₅×#120	C₂²	1	2	yes	—
86	C₃×C₅×#120	C₂²	1	2	yes	complemented
87	C₃×C₅×#120	C₂²	1	2	yes	complemented
88	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
89	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
90	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
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×C₄×C₅×D₄	C₂²	1	2	yes	complemented
95	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
96	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
97	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
98	C₃×C₅×#117	C₂²	1	2	yes	complemented
99	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
100	C₃×C₅×#117	C₂²	1	2	yes	complemented
101	C₃×C₅×#117	C₂²	1	2	yes	complemented
102	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
103	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
104	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
106	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
108	C₃×#3533	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
109	C₅×#563	C₂×C₃	1	1	yes	characteristic, complemented
110	C₅×#562	C₂×C₃	1	2	yes	complemented
111	C₅×#560	C₂×C₃	1	1	yes	characteristic, complemented
112	C₅×#559	C₂×C₃	1	1	yes	characteristic, complemented
113	C₅×#553	C₂×C₃	1	2	yes	complemented
114	C₅×#552	C₂×C₃	1	2	yes	complemented
115	C₅×#551	C₂×C₃	1	2	yes	complemented
116	C₅×#551	C₂×C₃	1	1	yes	characteristic, complemented
117	C₅×#547	C₂×C₃	1	2	yes	complemented
118	C₅×#546	C₂×C₃	1	2	yes	complemented
119	C₅×#542	C₂×C₃	1	2	yes	complemented
120	C₅×#540	C₂×C₃	1	2	yes	complemented
121	C₅×#539	C₂×C₃	1	2	yes	complemented
122	C₅×#538	C₂×C₃	1	2	yes	complemented
123	C₅×#538	C₂×C₃	1	2	yes	complemented
124	C₅×#535	C₂×C₃	1	1	yes	characteristic, complemented
125	C₅×#534	C₂×C₃	1	1	yes	characteristic, complemented
126	C₅×#525	C₂×C₃	1	2	yes	complemented
127	C₂×C₅×#123	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	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
131	C₃×C₅×#41	—	4	4	no	—
132	C₃×C₅×#41	—	4	2	no	—
133	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
134	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
135	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
136	C₂×C₃×C₅×D₄	—	4	2	no	—
137	C₂×C₃×C₅×D₄	—	4	2	no	—
138	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
139	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
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	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
149	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
150	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
152	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄×C₅	—	4	2	no	—
155	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
156	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
164	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
165	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
166	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
167	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
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	2	yes	—
181	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
198	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²×C₅	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
219	C₃×C₄²×C₅	C₂³	1	2	yes	—
220	C₃×#563	C₂×C₅	1	1	yes	characteristic, complemented
221	C₃×#562	C₂×C₅	1	2	yes	complemented
222	C₃×#560	C₂×C₅	1	1	yes	characteristic, complemented
223	C₃×#559	C₂×C₅	1	1	yes	characteristic, complemented
224	C₃×#553	C₂×C₅	1	2	yes	complemented
225	C₃×#552	C₂×C₅	1	2	yes	complemented
226	C₃×#551	C₂×C₅	1	2	yes	complemented
227	C₃×#551	C₂×C₅	1	1	yes	characteristic, complemented
228	C₃×#547	C₂×C₅	1	2	yes	complemented
229	C₃×#546	C₂×C₅	1	2	yes	complemented
230	C₃×#542	C₂×C₅	1	2	yes	complemented
231	C₃×#540	C₂×C₅	1	2	yes	complemented
232	C₃×#539	C₂×C₅	1	2	yes	complemented
233	C₃×#538	C₂×C₅	1	2	yes	complemented
234	C₃×#538	C₂×C₅	1	2	yes	complemented
235	C₃×#535	C₂×C₅	1	1	yes	characteristic, complemented
236	C₃×#534	C₂×C₅	1	1	yes	characteristic, complemented
237	C₃×#525	C₂×C₅	1	2	yes	complemented
238	C₂×C₃×#123	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×D₄	C₂²×C₃	1	1	yes	characteristic
242	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
243	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
244	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
245	C₅×#127	C₂²×C₃	1	1	yes	characteristic
246	C₅×#127	C₂²×C₃	1	1	yes	characteristic, 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×#124	C₂²×C₃	1	1	yes	characteristic
257	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
258	C₅×#124	C₂²×C₃	1	2	yes	complemented
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	1	yes	characteristic
264	C₅×#123	C₂²×C₃	1	1	yes	characteristic
265	C₅×#123	C₂²×C₃	1	2	yes	—
266	C₅×#123	C₂²×C₃	1	1	yes	characteristic
267	C₅×#123	C₂²×C₃	1	2	yes	—
268	C₅×#123	C₂²×C₃	1	1	yes	characteristic
269	C₅×#123	C₂²×C₃	1	2	yes	complemented
270	C₅×#123	C₂²×C₃	1	1	yes	characteristic, complemented
271	C₅×#123	C₂²×C₃	1	1	yes	characteristic, 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×#123	C₂²×C₃	1	2	yes	complemented
277	C₅×#123	C₂²×C₃	1	2	yes	complemented
278	C₅×#123	C₂²×C₃	1	2	yes	complemented
279	C₅×#123	C₂²×C₃	1	2	yes	complemented
280	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
281	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
282	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
283	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
284	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
285	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
286	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
287	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
288	C₅×#121	C₂²×C₃	1	2	yes	—
289	C₅×#121	C₂²×C₃	1	2	yes	—
290	C₅×#121	C₂²×C₃	1	2	yes	—
291	C₅×#121	C₂²×C₃	1	2	yes	—
292	C₅×#121	C₂²×C₃	1	2	yes	complemented
293	C₅×#121	C₂²×C₃	1	2	yes	complemented
294	C₅×#121	C₂²×C₃	1	2	yes	complemented
295	C₅×#121	C₂²×C₃	1	2	yes	complemented
296	C₅×#121	C₂²×C₃	1	2	yes	complemented
297	C₅×#121	C₂²×C₃	1	2	yes	complemented
298	C₅×#121	C₂²×C₃	1	2	yes	complemented
299	C₅×#121	C₂²×C₃	1	2	yes	complemented
300	C₅×#120	C₂²×C₃	1	2	yes	—
301	C₅×#120	C₂²×C₃	1	1	yes	characteristic
302	C₅×#120	C₂²×C₃	1	1	yes	characteristic
303	C₅×#120	C₂²×C₃	1	2	yes	—
304	C₅×#120	C₂²×C₃	1	2	yes	complemented
305	C₅×#120	C₂²×C₃	1	2	yes	complemented
306	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
307	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
308	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
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	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
313	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
314	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
315	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
316	C₅×#117	C₂²×C₃	1	2	yes	complemented
317	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
318	C₅×#117	C₂²×C₃	1	2	yes	complemented
319	C₅×#117	C₂²×C₃	1	2	yes	complemented
320	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
321	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
322	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
323	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
324	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
325	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
326	#3533	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	—	4	2	no	—
330	C₂³×C₃×C₅	—	4	1	no	—
331	C₂³×C₃×C₅	—	4	2	no	—
332	C₂³×C₃×C₅	—	4	2	no	—
333	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
334	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
335	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
336	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
337	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
338	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
339	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
340	C₃×C₅×Q₈	—	4	2	no	—
341	C₃×C₅×Q₈	—	4	2	no	—
342	C₃×C₅×Q₈	—	4	1	no	—
343	C₃×C₅×D₄	—	2	4	no	—
344	C₃×C₅×D₄	—	2	4	no	—
345	C₃×C₅×D₄	—	4	1	no	—
346	C₃×C₅×D₄	—	4	1	no	—
347	C₃×C₅×D₄	—	4	1	no	—
348	C₃×C₅×D₄	—	4	1	no	—
349	C₃×C₅×D₄	—	4	2	no	—
350	C₃×C₅×D₄	—	4	2	no	—
351	C₃×C₅×D₄	—	4	2	no	—
352	C₃×C₅×D₄	—	4	2	no	—
353	C₃×C₅×D₄	—	4	2	no	—
354	C₃×C₅×D₄	—	4	2	no	—
355	C₃×C₅×D₄	—	4	2	no	—
356	C₃×C₅×D₄	—	4	2	no	—
357	C₃×C₅×D₄	—	4	2	no	—
358	C₃×C₅×D₄	—	4	1	no	—
359	C₂×C₃×C₄×C₅	—	2	4	no	—
360	C₂×C₃×C₄×C₅	—	2	2	no	—
361	C₂×C₃×C₄×C₅	—	4	1	no	—
362	C₂×C₃×C₄×C₅	—	4	2	no	—
363	C₂×C₃×C₄×C₅	—	4	1	no	—
364	C₂×C₃×C₄×C₅	—	4	2	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	—	4	1	no	—
369	C₂×C₃×C₄×C₅	—	4	2	no	—
370	C₂×C₃×C₄×C₅	—	4	2	no	—
371	C₂×C₃×C₄×C₅	—	4	2	no	—
372	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
380	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
381	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
382	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
383	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
384	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
385	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
386	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
387	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
388	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
389	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
390	C₃×#127	C₂²×C₅	1	1	yes	characteristic
391	C₃×#127	C₂²×C₅	1	1	yes	characteristic, 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×#126	C₂²×C₅	1	2	yes	complemented
397	C₃×#126	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	1	yes	characteristic
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×#124	C₂²×C₅	1	1	yes	characteristic, complemented
406	C₃×#124	C₂²×C₅	1	2	yes	complemented
407	C₃×#123	C₂²×C₅	1	1	yes	characteristic
408	C₃×#123	C₂²×C₅	1	1	yes	characteristic
409	C₃×#123	C₂²×C₅	1	1	yes	characteristic
410	C₃×#123	C₂²×C₅	1	2	yes	—
411	C₃×#123	C₂²×C₅	1	2	yes	—
412	C₃×#123	C₂²×C₅	1	1	yes	characteristic
413	C₃×#123	C₂²×C₅	1	2	yes	—
414	C₃×#123	C₂²×C₅	1	2	yes	complemented
415	C₃×#123	C₂²×C₅	1	2	yes	complemented
416	C₃×#123	C₂²×C₅	1	1	yes	characteristic, complemented
417	C₃×#123	C₂²×C₅	1	2	yes	complemented
418	C₃×#123	C₂²×C₅	1	2	yes	complemented
419	C₃×#123	C₂²×C₅	1	2	yes	complemented
420	C₃×#123	C₂²×C₅	1	2	yes	complemented
421	C₃×#123	C₂²×C₅	1	1	yes	characteristic, complemented
422	C₃×#123	C₂²×C₅	1	2	yes	complemented
423	C₃×#123	C₂²×C₅	1	2	yes	complemented
424	C₃×#123	C₂²×C₅	1	2	yes	complemented
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	2	yes	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	2	yes	complemented
433	C₃×#121	C₂²×C₅	1	2	yes	—
434	C₃×#121	C₂²×C₅	1	2	yes	—
435	C₃×#121	C₂²×C₅	1	2	yes	—
436	C₃×#121	C₂²×C₅	1	2	yes	—
437	C₃×#121	C₂²×C₅	1	2	yes	complemented
438	C₃×#121	C₂²×C₅	1	2	yes	complemented
439	C₃×#121	C₂²×C₅	1	2	yes	complemented
440	C₃×#121	C₂²×C₅	1	2	yes	complemented
441	C₃×#121	C₂²×C₅	1	2	yes	complemented
442	C₃×#121	C₂²×C₅	1	2	yes	complemented
443	C₃×#121	C₂²×C₅	1	2	yes	complemented
444	C₃×#121	C₂²×C₅	1	2	yes	complemented
445	C₃×#120	C₂²×C₅	1	1	yes	characteristic
446	C₃×#120	C₂²×C₅	1	2	yes	—
447	C₃×#120	C₂²×C₅	1	1	yes	characteristic
448	C₃×#120	C₂²×C₅	1	2	yes	—
449	C₃×#120	C₂²×C₅	1	2	yes	complemented
450	C₃×#120	C₂²×C₅	1	2	yes	complemented
451	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
452	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
453	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
454	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
455	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
456	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
457	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
458	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
459	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
460	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
461	C₃×#117	C₂²×C₅	1	2	yes	complemented
462	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
463	C₃×#117	C₂²×C₅	1	2	yes	complemented
464	C₃×#117	C₂²×C₅	1	2	yes	complemented
465	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
466	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
467	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
468	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
469	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
470	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
471	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
472	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
473	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
474	C₅×#41	—	4	4	no	—
475	C₅×#41	—	4	2	no	—
476	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
477	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
478	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
479	C₂×C₅×D₄	—	4	2	no	—
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	2	yes	—
489	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
490	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
491	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
492	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
493	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
494	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
495	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
496	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
497	C₂²×C₄×C₅	—	4	2	no	—
498	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
499	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
500	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
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	2	yes	—
505	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
506	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
507	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
508	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
509	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
510	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
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	2	yes	—
522	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
531	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
532	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
533	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
534	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
541	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
542	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
557	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
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	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
562	C₄²×C₅	C₂³×C₃	1	2	yes	—
563	#563	C₂×C₃×C₅	1	1	yes	characteristic, complemented
564	#562	C₂×C₃×C₅	1	2	yes	complemented
565	#560	C₂×C₃×C₅	1	1	yes	characteristic, complemented
566	#559	C₂×C₃×C₅	1	1	yes	characteristic, complemented
567	#553	C₂×C₃×C₅	1	2	yes	complemented
568	#552	C₂×C₃×C₅	1	2	yes	complemented
569	#551	C₂×C₃×C₅	1	2	yes	complemented
570	#551	C₂×C₃×C₅	1	1	yes	characteristic, complemented
571	#547	C₂×C₃×C₅	1	2	yes	complemented
572	#546	C₂×C₃×C₅	1	2	yes	complemented
573	#542	C₂×C₃×C₅	1	2	yes	complemented
574	#540	C₂×C₃×C₅	1	2	yes	complemented
575	#539	C₂×C₃×C₅	1	2	yes	complemented
576	#538	C₂×C₃×C₅	1	2	yes	complemented
577	#538	C₂×C₃×C₅	1	2	yes	complemented
578	#535	C₂×C₃×C₅	1	1	yes	characteristic, complemented
579	#534	C₂×C₃×C₅	1	1	yes	characteristic, complemented
580	#525	C₂×C₃×C₅	1	2	yes	complemented
581	C₂×#123	C₂×C₃×C₅	1	1	yes	characteristic, complemented
582	C₂²×C₃×C₅	—	2	2	no	—
583	C₂²×C₃×C₅	—	2	2	no	—
584	C₂²×C₃×C₅	—	2	1	no	—
585	C₂²×C₃×C₅	—	2	1	no	—
586	C₂²×C₃×C₅	—	2	2	no	—
587	C₂²×C₃×C₅	—	2	1	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	2	no	—
593	C₂²×C₃×C₅	—	2	2	no	—
594	C₂²×C₃×C₅	—	2	2	no	—
595	C₂²×C₃×C₅	—	2	2	no	—
596	C₂²×C₃×C₅	—	2	2	no	—
597	C₂²×C₃×C₅	—	4	4	no	—
598	C₂²×C₃×C₅	—	8	2	no	—
599	C₂²×C₃×C₅	—	8	2	no	—
600	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
601	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
602	C₃×C₄×C₅	—	2	2	no	—
603	C₃×C₄×C₅	—	2	1	no	—
604	C₃×C₄×C₅	—	2	2	no	—
605	C₃×C₄×C₅	—	2	1	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	C₃×C₄×C₅	—	2	2	no	—
613	C₃×C₄×C₅	—	2	2	no	—
614	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
615	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
616	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
617	C₃×#41	—	4	4	no	—
618	C₃×#41	—	4	2	no	—
619	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
620	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
621	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
622	C₂×C₃×D₄	—	4	2	no	—
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	2	yes	—
632	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
633	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
634	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
635	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
636	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
637	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
638	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
639	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
640	C₂²×C₃×C₄	—	4	2	no	—
641	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
642	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
643	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
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	2	yes	—
648	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
649	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
650	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
651	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
652	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
653	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
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	2	yes	—
665	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
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×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
674	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
675	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
676	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
677	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	1	yes	characteristic
684	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
685	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
700	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
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	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
705	C₃×C₄²	C₂³×C₅	1	2	yes	—
706	C₂³×C₅	—	2	2	no	—
707	C₂³×C₅	—	2	2	no	—
708	C₂³×C₅	—	4	2	no	—
709	C₂³×C₅	—	4	1	no	—
710	C₂³×C₅	—	4	2	no	—
711	C₂³×C₅	—	4	2	no	—
712	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
713	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
714	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
715	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
716	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
717	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
718	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
719	C₅×Q₈	—	4	2	no	—
720	C₅×Q₈	—	4	2	no	—
721	C₅×Q₈	—	4	1	no	—
722	C₅×D₄	—	2	4	no	—
723	C₅×D₄	—	2	4	no	—
724	C₅×D₄	—	4	1	no	—
725	C₅×D₄	—	4	1	no	—
726	C₅×D₄	—	4	1	no	—
727	C₅×D₄	—	4	1	no	—
728	C₅×D₄	—	4	2	no	—
729	C₅×D₄	—	4	2	no	—
730	C₅×D₄	—	4	2	no	—
731	C₅×D₄	—	4	2	no	—
732	C₅×D₄	—	4	2	no	—
733	C₅×D₄	—	4	2	no	—
734	C₅×D₄	—	4	2	no	—
735	C₅×D₄	—	4	2	no	—
736	C₅×D₄	—	4	2	no	—
737	C₅×D₄	—	4	1	no	—
738	C₂×C₄×C₅	—	2	4	no	—
739	C₂×C₄×C₅	—	2	2	no	—
740	C₂×C₄×C₅	—	4	1	no	—
741	C₂×C₄×C₅	—	4	2	no	—
742	C₂×C₄×C₅	—	4	1	no	—
743	C₂×C₄×C₅	—	4	2	no	—
744	C₂×C₄×C₅	—	4	2	no	—
745	C₂×C₄×C₅	—	4	2	no	—
746	C₂×C₄×C₅	—	4	2	no	—
747	C₂×C₄×C₅	—	4	1	no	—
748	C₂×C₄×C₅	—	4	2	no	—
749	C₂×C₄×C₅	—	4	2	no	—
750	C₂×C₄×C₅	—	4	2	no	—
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	1	yes	characteristic
756	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
757	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
758	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
759	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
760	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
761	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
762	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
763	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
764	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
765	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
766	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
767	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
768	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
769	#127	C₂²×C₃×C₅	1	1	yes	characteristic
770	#127	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
771	#126	C₂²×C₃×C₅	1	2	yes	complemented
772	#126	C₂²×C₃×C₅	1	2	yes	complemented
773	#126	C₂²×C₃×C₅	1	2	yes	complemented
774	#126	C₂²×C₃×C₅	1	2	yes	complemented
775	#126	C₂²×C₃×C₅	1	2	yes	complemented
776	#126	C₂²×C₃×C₅	1	2	yes	complemented
777	#125	C₂²×C₃×C₅	1	2	yes	complemented
778	#125	C₂²×C₃×C₅	1	2	yes	complemented
779	#125	C₂²×C₃×C₅	1	2	yes	complemented
780	#124	C₂²×C₃×C₅	1	1	yes	characteristic
781	#124	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
782	#124	C₂²×C₃×C₅	1	2	yes	complemented
783	#124	C₂²×C₃×C₅	1	2	yes	complemented
784	#124	C₂²×C₃×C₅	1	2	yes	complemented
785	#124	C₂²×C₃×C₅	1	2	yes	complemented
786	#123	C₂²×C₃×C₅	1	2	yes	—
787	#123	C₂²×C₃×C₅	1	1	yes	characteristic
788	#123	C₂²×C₃×C₅	1	1	yes	characteristic
789	#123	C₂²×C₃×C₅	1	2	yes	—
790	#123	C₂²×C₃×C₅	1	1	yes	characteristic
791	#123	C₂²×C₃×C₅	1	2	yes	—
792	#123	C₂²×C₃×C₅	1	1	yes	characteristic
793	#123	C₂²×C₃×C₅	1	2	yes	complemented
794	#123	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
795	#123	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
796	#123	C₂²×C₃×C₅	1	2	yes	complemented
797	#123	C₂²×C₃×C₅	1	2	yes	complemented
798	#123	C₂²×C₃×C₅	1	2	yes	complemented
799	#123	C₂²×C₃×C₅	1	2	yes	complemented
800	#123	C₂²×C₃×C₅	1	2	yes	complemented
801	#123	C₂²×C₃×C₅	1	2	yes	complemented
802	#123	C₂²×C₃×C₅	1	2	yes	complemented
803	#123	C₂²×C₃×C₅	1	2	yes	complemented
804	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
805	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	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	#121	C₂²×C₃×C₅	1	2	yes	—
813	#121	C₂²×C₃×C₅	1	2	yes	—
814	#121	C₂²×C₃×C₅	1	2	yes	—
815	#121	C₂²×C₃×C₅	1	2	yes	—
816	#121	C₂²×C₃×C₅	1	2	yes	complemented
817	#121	C₂²×C₃×C₅	1	2	yes	complemented
818	#121	C₂²×C₃×C₅	1	2	yes	complemented
819	#121	C₂²×C₃×C₅	1	2	yes	complemented
820	#121	C₂²×C₃×C₅	1	2	yes	complemented
821	#121	C₂²×C₃×C₅	1	2	yes	complemented
822	#121	C₂²×C₃×C₅	1	2	yes	complemented
823	#121	C₂²×C₃×C₅	1	2	yes	complemented
824	#120	C₂²×C₃×C₅	1	2	yes	—
825	#120	C₂²×C₃×C₅	1	1	yes	characteristic
826	#120	C₂²×C₃×C₅	1	1	yes	characteristic
827	#120	C₂²×C₃×C₅	1	2	yes	—
828	#120	C₂²×C₃×C₅	1	2	yes	complemented
829	#120	C₂²×C₃×C₅	1	2	yes	complemented
830	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
831	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
832	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
833	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
834	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
835	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
836	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
837	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
838	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
839	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
840	#117	C₂²×C₃×C₅	1	2	yes	complemented
841	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
842	#117	C₂²×C₃×C₅	1	2	yes	complemented
843	#117	C₂²×C₃×C₅	1	2	yes	complemented
844	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
845	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
846	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
847	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
848	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
849	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
850	C₂×C₃×C₅	—	2	2	no	—
851	C₂×C₃×C₅	—	4	2	no	—
852	C₂×C₃×C₅	—	4	1	no	—
853	C₂×C₃×C₅	—	4	1	no	—
854	C₂×C₃×C₅	—	4	2	no	—
855	C₂×C₃×C₅	—	4	1	no	—
856	C₂×C₃×C₅	—	4	1	no	—
857	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
858	C₂×C₃×C₅	#585	1	2	yes	—
859	C₂³×C₃	—	2	2	no	—
860	C₂³×C₃	—	2	2	no	—
861	C₂³×C₃	—	4	2	no	—
862	C₂³×C₃	—	4	1	no	—
863	C₂³×C₃	—	4	2	no	—
864	C₂³×C₃	—	4	2	no	—
865	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
866	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
867	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
868	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
869	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
870	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
871	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
872	C₃×Q₈	—	4	2	no	—
873	C₃×Q₈	—	4	2	no	—
874	C₃×Q₈	—	4	1	no	—
875	C₃×D₄	—	2	4	no	—
876	C₃×D₄	—	2	4	no	—
877	C₃×D₄	—	4	1	no	—
878	C₃×D₄	—	4	1	no	—
879	C₃×D₄	—	4	1	no	—
880	C₃×D₄	—	4	1	no	—
881	C₃×D₄	—	4	2	no	—
882	C₃×D₄	—	4	2	no	—
883	C₃×D₄	—	4	2	no	—
884	C₃×D₄	—	4	2	no	—
885	C₃×D₄	—	4	2	no	—
886	C₃×D₄	—	4	2	no	—
887	C₃×D₄	—	4	2	no	—
888	C₃×D₄	—	4	2	no	—
889	C₃×D₄	—	4	2	no	—
890	C₃×D₄	—	4	1	no	—
891	C₂×C₃×C₄	—	2	4	no	—
892	C₂×C₃×C₄	—	2	2	no	—
893	C₂×C₃×C₄	—	4	1	no	—
894	C₂×C₃×C₄	—	4	2	no	—
895	C₂×C₃×C₄	—	4	1	no	—
896	C₂×C₃×C₄	—	4	2	no	—
897	C₂×C₃×C₄	—	4	2	no	—
898	C₂×C₃×C₄	—	4	2	no	—
899	C₂×C₃×C₄	—	4	2	no	—
900	C₂×C₃×C₄	—	4	1	no	—
901	C₂×C₃×C₄	—	4	2	no	—
902	C₂×C₃×C₄	—	4	2	no	—
903	C₂×C₃×C₄	—	4	2	no	—
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	2	yes	—
907	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
908	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
909	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
910	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
911	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
912	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
913	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
914	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
915	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
916	C₂²×C₅	—	2	2	no	—
917	C₂²×C₅	—	2	2	no	—
918	C₂²×C₅	—	2	1	no	—
919	C₂²×C₅	—	2	1	no	—
920	C₂²×C₅	—	2	2	no	—
921	C₂²×C₅	—	2	1	no	—
922	C₂²×C₅	—	2	1	no	—
923	C₂²×C₅	—	2	2	no	—
924	C₂²×C₅	—	2	2	no	—
925	C₂²×C₅	—	2	2	no	—
926	C₂²×C₅	—	2	2	no	—
927	C₂²×C₅	—	2	2	no	—
928	C₂²×C₅	—	2	2	no	—
929	C₂²×C₅	—	2	2	no	—
930	C₂²×C₅	—	2	2	no	—
931	C₂²×C₅	—	4	4	no	—
932	C₂²×C₅	—	8	2	no	—
933	C₂²×C₅	—	8	2	no	—
934	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
935	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
936	C₄×C₅	—	2	2	no	—
937	C₄×C₅	—	2	1	no	—
938	C₄×C₅	—	2	2	no	—
939	C₄×C₅	—	2	1	no	—
940	C₄×C₅	—	2	2	no	—
941	C₄×C₅	—	2	2	no	—
942	C₄×C₅	—	2	2	no	—
943	C₄×C₅	—	2	2	no	—
944	C₄×C₅	—	2	2	no	—
945	C₄×C₅	—	2	2	no	—
946	C₄×C₅	—	2	2	no	—
947	C₄×C₅	—	2	2	no	—
948	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
949	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
950	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
951	#41	—	4	4	no	—
952	#41	—	4	2	no	—
953	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
954	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
955	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
956	C₂×D₄	—	4	2	no	—
957	C₂×D₄	—	4	2	no	—
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	2	yes	—
961	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
962	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
963	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
964	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
965	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
966	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
967	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
968	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
969	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
970	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
971	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
972	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
973	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
974	C₂²×C₄	—	4	2	no	—
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	2	yes	—
978	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
979	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
980	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
981	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
982	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
983	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
984	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
985	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
986	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
987	C₂²×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	2	yes	—
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	2	yes	—
994	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
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	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1006	C₄⋊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	1	yes	characteristic
1011	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
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	1	yes	characteristic
1018	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1019	C₂²⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
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	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1029	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1030	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1031	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1032	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1033	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1034	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1035	C₄²	C₂³×C₃×C₅	1	2	yes	—
1036	C₄²	C₂³×C₃×C₅	1	2	yes	—
1037	C₄²	C₂³×C₃×C₅	1	2	yes	—
1038	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
1039	C₄²	C₂³×C₃×C₅	1	2	yes	—
1040	C₃×C₅	#3533	1	1	yes	characteristic, direct product factor, Hall
1041	C₂²×C₃	—	2	2	no	—
1042	C₂²×C₃	—	2	2	no	—
1043	C₂²×C₃	—	2	1	no	—
1044	C₂²×C₃	—	2	1	no	—
1045	C₂²×C₃	—	2	2	no	—
1046	C₂²×C₃	—	2	1	no	—
1047	C₂²×C₃	—	2	1	no	—
1048	C₂²×C₃	—	2	2	no	—
1049	C₂²×C₃	—	2	2	no	—
1050	C₂²×C₃	—	2	2	no	—
1051	C₂²×C₃	—	2	2	no	—
1052	C₂²×C₃	—	2	2	no	—
1053	C₂²×C₃	—	2	2	no	—
1054	C₂²×C₃	—	2	2	no	—
1055	C₂²×C₃	—	2	2	no	—
1056	C₂²×C₃	—	4	4	no	—
1057	C₂²×C₃	—	8	2	no	—
1058	C₂²×C₃	—	8	2	no	—
1059	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
1060	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1061	C₃×C₄	—	2	2	no	—
1062	C₃×C₄	—	2	1	no	—
1063	C₃×C₄	—	2	2	no	—
1064	C₃×C₄	—	2	1	no	—
1065	C₃×C₄	—	2	2	no	—
1066	C₃×C₄	—	2	2	no	—
1067	C₃×C₄	—	2	2	no	—
1068	C₃×C₄	—	2	2	no	—
1069	C₃×C₄	—	2	2	no	—
1070	C₃×C₄	—	2	2	no	—
1071	C₃×C₄	—	2	2	no	—
1072	C₃×C₄	—	2	2	no	—
1073	C₂×C₅	—	2	2	no	—
1074	C₂×C₅	—	4	1	no	—
1075	C₂×C₅	—	4	1	no	—
1076	C₂×C₅	—	4	1	no	—
1077	C₂×C₅	—	4	2	no	—
1078	C₂×C₅	—	4	1	no	—
1079	C₂×C₅	—	4	2	no	—
1080	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1081	C₂×C₅	C₃×#585	1	2	yes	—
1082	C₂³	—	2	2	no	—
1083	C₂³	—	2	2	no	—
1084	C₂³	—	4	2	no	—
1085	C₂³	—	4	1	no	—
1086	C₂³	—	4	2	no	—
1087	C₂³	—	4	2	no	—
1088	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1089	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1090	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1091	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1092	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1093	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1094	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1095	Q₈	—	4	2	no	—
1096	Q₈	—	4	1	no	—
1097	Q₈	—	4	2	no	—
1098	D₄	—	2	4	no	—
1099	D₄	—	2	4	no	—
1100	D₄	—	4	1	no	—
1101	D₄	—	4	1	no	—
1102	D₄	—	4	1	no	—
1103	D₄	—	4	1	no	—
1104	D₄	—	4	2	no	—
1105	D₄	—	4	2	no	—
1106	D₄	—	4	1	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	4	2	no	—
1109	D₄	—	4	2	no	—
1110	D₄	—	4	2	no	—
1111	D₄	—	4	2	no	—
1112	D₄	—	4	2	no	—
1113	D₄	—	4	2	no	—
1114	C₂×C₄	—	2	4	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	4	1	no	—
1117	C₂×C₄	—	4	2	no	—
1118	C₂×C₄	—	4	1	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	4	2	no	—
1122	C₂×C₄	—	4	2	no	—
1123	C₂×C₄	—	4	2	no	—
1124	C₂×C₄	—	4	2	no	—
1125	C₂×C₄	—	4	2	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1128	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1129	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1130	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1131	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1132	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1133	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1134	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1135	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1136	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1137	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1138	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1139	C₂×C₃	—	2	2	no	—
1140	C₂×C₃	—	4	1	no	—
1141	C₂×C₃	—	4	1	no	—
1142	C₂×C₃	—	4	1	no	—
1143	C₂×C₃	—	4	2	no	—
1144	C₂×C₃	—	4	1	no	—
1145	C₂×C₃	—	4	2	no	—
1146	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1147	C₂×C₃	C₅×#585	1	2	yes	—
1148	C₅	C₃×#3533	1	1	yes	characteristic, direct product factor, Sylow
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	1	no	—
1152	C₂²	—	2	1	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	1	no	—
1155	C₂²	—	2	1	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	2	2	no	—
1160	C₂²	—	2	2	no	—
1161	C₂²	—	2	2	no	—
1162	C₂²	—	2	2	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	4	4	no	—
1165	C₂²	—	8	2	no	—
1166	C₂²	—	8	2	no	—
1167	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
1168	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
1169	C₄	—	2	2	no	—
1170	C₄	—	2	1	no	—
1171	C₄	—	2	2	no	—
1172	C₄	—	2	1	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	2	2	no	—
1175	C₄	—	2	2	no	—
1176	C₄	—	2	2	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	2	no	—
1179	C₄	—	2	2	no	—
1180	C₄	—	2	2	no	—
1181	C₃	C₅×#3533	1	1	yes	characteristic, direct product factor, Sylow
1182	C₂	—	2	2	no	—
1183	C₂	—	4	1	no	—
1184	C₂	—	4	1	no	—
1185	C₂	—	4	1	no	—
1186	C₂	—	4	2	no	—
1187	C₂	—	4	1	no	—
1188	C₂	—	4	2	no	—
1189	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1190	C₂	C₃×C₅×#585	1	2	yes	—

	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×#560	C₂	semidirect
4. C₃×C₅×#559	C₂	semidirect
5. C₃×C₅×#553	C₂	semidirect
6. C₃×C₅×#552	C₂	semidirect
7. C₃×C₅×#551	C₂	semidirect
8. C₃×C₅×#551	C₂	semidirect
9. C₃×C₅×#547	C₂	semidirect
10. C₃×C₅×#546	C₂	semidirect
11. C₃×C₅×#542	C₂	semidirect
12. C₃×C₅×#540	C₂	semidirect
13. C₃×C₅×#539	C₂	semidirect
14. C₃×C₅×#538	C₂	semidirect
15. C₃×C₅×#538	C₂	semidirect
16. C₃×C₅×#535	C₂	semidirect
17. C₃×C₅×#534	C₂	semidirect
18. C₃×C₅×#525	C₂	semidirect
19. C₂×C₃×C₅×#123	C₂	semidirect
20. C₅×#3533	C₃	direct (N × H)
22. C₂×C₃×C₅×#41	C₂²	semidirect
25. C₂³×C₃×C₄×C₅	C₂²	semidirect
26. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
28. C₃×C₅×#127	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
39. C₃×C₅×#124	C₂²	semidirect
40. C₃×C₅×#124	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
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×C₂²⋊Q₈	C₂²	semidirect
63. C₃×C₅×C₂²⋊Q₈	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
74. C₃×C₅×#121	C₂²	semidirect
75. C₃×C₅×#121	C₂²	semidirect
76. C₃×C₅×#121	C₂²	semidirect
77. C₃×C₅×#121	C₂²	semidirect
78. C₃×C₅×#121	C₂²	semidirect
79. C₃×C₅×#121	C₂²	semidirect
80. C₃×C₅×#121	C₂²	semidirect
81. C₃×C₅×#121	C₂²	semidirect
86. C₃×C₅×#120	C₂²	semidirect
87. C₃×C₅×#120	C₂²	semidirect
88. C₃×C₄×C₅×Q₈	C₂²	semidirect
90. C₃×C₄×C₅×D₄	C₂²	semidirect
91. C₃×C₄×C₅×D₄	C₂²	semidirect
92. C₃×C₄×C₅×D₄	C₂²	semidirect
93. C₃×C₄×C₅×D₄	C₂²	semidirect
94. C₃×C₄×C₅×D₄	C₂²	semidirect
95. C₃×C₄×C₅×D₄	C₂²	semidirect
96. C₃×C₄×C₅×D₄	C₂²	semidirect
97. C₃×C₄×C₅×D₄	C₂²	semidirect
98. C₃×C₅×#117	C₂²	semidirect
99. C₃×C₅×#117	C₂²	semidirect
100. C₃×C₅×#117	C₂²	semidirect
101. C₃×C₅×#117	C₂²	semidirect
102. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
103. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
106. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
107. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
108. C₃×#3533	C₅	direct (N × H)
109. C₅×#563	C₂×C₃	semidirect
110. C₅×#562	C₂×C₃	semidirect
111. C₅×#560	C₂×C₃	semidirect
112. C₅×#559	C₂×C₃	semidirect
113. C₅×#553	C₂×C₃	semidirect
114. C₅×#552	C₂×C₃	semidirect
115. C₅×#551	C₂×C₃	semidirect
116. C₅×#551	C₂×C₃	semidirect
117. C₅×#547	C₂×C₃	semidirect
118. C₅×#546	C₂×C₃	semidirect
119. C₅×#542	C₂×C₃	semidirect
120. C₅×#540	C₂×C₃	semidirect
121. C₅×#539	C₂×C₃	semidirect
122. C₅×#538	C₂×C₃	semidirect
123. C₅×#538	C₂×C₃	semidirect
124. C₅×#535	C₂×C₃	semidirect
125. C₅×#534	C₂×C₃	semidirect
126. C₅×#525	C₂×C₃	semidirect
127. C₂×C₅×#123	C₂×C₃	semidirect
220. C₃×#563	C₂×C₅	semidirect
221. C₃×#562	C₂×C₅	semidirect
222. C₃×#560	C₂×C₅	semidirect
223. C₃×#559	C₂×C₅	semidirect
224. C₃×#553	C₂×C₅	semidirect
225. C₃×#552	C₂×C₅	semidirect
226. C₃×#551	C₂×C₅	semidirect
227. C₃×#551	C₂×C₅	semidirect
228. C₃×#547	C₂×C₅	semidirect
229. C₃×#546	C₂×C₅	semidirect
230. C₃×#542	C₂×C₅	semidirect
231. C₃×#540	C₂×C₅	semidirect
232. C₃×#539	C₂×C₅	semidirect
233. C₃×#538	C₂×C₅	semidirect
234. C₃×#538	C₂×C₅	semidirect
235. C₃×#535	C₂×C₅	semidirect
236. C₃×#534	C₂×C₅	semidirect
237. C₃×#525	C₂×C₅	semidirect
238. C₂×C₃×#123	C₂×C₅	semidirect
240. C₂×C₅×#41	C₂²×C₃	semidirect
243. C₂³×C₄×C₅	C₂²×C₃	semidirect
244. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
246. C₅×#127	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
257. C₅×#124	C₂²×C₃	semidirect
258. C₅×#124	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
276. C₅×#123	C₂²×C₃	semidirect
277. C₅×#123	C₂²×C₃	semidirect
278. C₅×#123	C₂²×C₃	semidirect
279. C₅×#123	C₂²×C₃	semidirect
280. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
281. C₅×C₂²⋊Q₈	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
292. C₅×#121	C₂²×C₃	semidirect
293. C₅×#121	C₂²×C₃	semidirect
294. C₅×#121	C₂²×C₃	semidirect
295. C₅×#121	C₂²×C₃	semidirect
296. C₅×#121	C₂²×C₃	semidirect
297. C₅×#121	C₂²×C₃	semidirect
298. C₅×#121	C₂²×C₃	semidirect
299. C₅×#121	C₂²×C₃	semidirect
304. C₅×#120	C₂²×C₃	semidirect
305. C₅×#120	C₂²×C₃	semidirect
306. C₄×C₅×Q₈	C₂²×C₃	semidirect
308. C₄×C₅×D₄	C₂²×C₃	semidirect
309. C₄×C₅×D₄	C₂²×C₃	semidirect
310. C₄×C₅×D₄	C₂²×C₃	semidirect
311. C₄×C₅×D₄	C₂²×C₃	semidirect
312. C₄×C₅×D₄	C₂²×C₃	semidirect
313. C₄×C₅×D₄	C₂²×C₃	semidirect
314. C₄×C₅×D₄	C₂²×C₃	semidirect
315. C₄×C₅×D₄	C₂²×C₃	semidirect
316. C₅×#117	C₂²×C₃	semidirect
317. C₅×#117	C₂²×C₃	semidirect
318. C₅×#117	C₂²×C₃	semidirect
319. C₅×#117	C₂²×C₃	semidirect
320. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
321. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
324. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
325. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
326. #3533	C₃×C₅	direct (N × H)
385. C₂×C₃×#41	C₂²×C₅	semidirect
388. C₂³×C₃×C₄	C₂²×C₅	semidirect
389. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
391. C₃×#127	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×#126	C₂²×C₅	semidirect
397. C₃×#126	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
405. C₃×#124	C₂²×C₅	semidirect
406. C₃×#124	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
419. C₃×#123	C₂²×C₅	semidirect
420. C₃×#123	C₂²×C₅	semidirect
421. C₃×#123	C₂²×C₅	semidirect
422. C₃×#123	C₂²×C₅	semidirect
423. C₃×#123	C₂²×C₅	semidirect
424. 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
437. C₃×#121	C₂²×C₅	semidirect
438. C₃×#121	C₂²×C₅	semidirect
439. C₃×#121	C₂²×C₅	semidirect
440. C₃×#121	C₂²×C₅	semidirect
441. C₃×#121	C₂²×C₅	semidirect
442. C₃×#121	C₂²×C₅	semidirect
443. C₃×#121	C₂²×C₅	semidirect
444. C₃×#121	C₂²×C₅	semidirect
449. C₃×#120	C₂²×C₅	semidirect
450. C₃×#120	C₂²×C₅	semidirect
451. C₃×C₄×Q₈	C₂²×C₅	semidirect
453. C₃×C₄×D₄	C₂²×C₅	semidirect
454. C₃×C₄×D₄	C₂²×C₅	semidirect
455. C₃×C₄×D₄	C₂²×C₅	semidirect
456. C₃×C₄×D₄	C₂²×C₅	semidirect
457. C₃×C₄×D₄	C₂²×C₅	semidirect
458. C₃×C₄×D₄	C₂²×C₅	semidirect
459. C₃×C₄×D₄	C₂²×C₅	semidirect
460. C₃×C₄×D₄	C₂²×C₅	semidirect
461. C₃×#117	C₂²×C₅	semidirect
462. C₃×#117	C₂²×C₅	semidirect
463. C₃×#117	C₂²×C₅	semidirect
464. C₃×#117	C₂²×C₅	semidirect
465. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
466. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
469. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
470. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
563. #563	C₂×C₃×C₅	semidirect
564. #562	C₂×C₃×C₅	semidirect
565. #560	C₂×C₃×C₅	semidirect
566. #559	C₂×C₃×C₅	semidirect
567. #553	C₂×C₃×C₅	semidirect
568. #552	C₂×C₃×C₅	semidirect
569. #551	C₂×C₃×C₅	semidirect
570. #551	C₂×C₃×C₅	semidirect
571. #547	C₂×C₃×C₅	semidirect
572. #546	C₂×C₃×C₅	semidirect
573. #542	C₂×C₃×C₅	semidirect
574. #540	C₂×C₃×C₅	semidirect
575. #539	C₂×C₃×C₅	semidirect
576. #538	C₂×C₃×C₅	semidirect
577. #538	C₂×C₃×C₅	semidirect
578. #535	C₂×C₃×C₅	semidirect
579. #534	C₂×C₃×C₅	semidirect
580. #525	C₂×C₃×C₅	semidirect
581. C₂×#123	C₂×C₃×C₅	semidirect
764. C₂×#41	C₂²×C₃×C₅	semidirect
767. C₂³×C₄	C₂²×C₃×C₅	semidirect
768. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
770. #127	C₂²×C₃×C₅	semidirect
771. #126	C₂²×C₃×C₅	semidirect
772. #126	C₂²×C₃×C₅	semidirect
773. #126	C₂²×C₃×C₅	semidirect
774. #126	C₂²×C₃×C₅	semidirect
775. #126	C₂²×C₃×C₅	semidirect
776. #126	C₂²×C₃×C₅	semidirect
777. #125	C₂²×C₃×C₅	semidirect
778. #125	C₂²×C₃×C₅	semidirect
779. #125	C₂²×C₃×C₅	semidirect
781. #124	C₂²×C₃×C₅	semidirect
782. #124	C₂²×C₃×C₅	semidirect
783. #124	C₂²×C₃×C₅	semidirect
784. #124	C₂²×C₃×C₅	semidirect
785. #124	C₂²×C₃×C₅	semidirect
793. #123	C₂²×C₃×C₅	semidirect
794. #123	C₂²×C₃×C₅	semidirect
795. #123	C₂²×C₃×C₅	semidirect
796. #123	C₂²×C₃×C₅	semidirect
797. #123	C₂²×C₃×C₅	semidirect
798. #123	C₂²×C₃×C₅	semidirect
799. #123	C₂²×C₃×C₅	semidirect
800. #123	C₂²×C₃×C₅	semidirect
801. #123	C₂²×C₃×C₅	semidirect
802. #123	C₂²×C₃×C₅	semidirect
803. #123	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
816. #121	C₂²×C₃×C₅	semidirect
817. #121	C₂²×C₃×C₅	semidirect
818. #121	C₂²×C₃×C₅	semidirect
819. #121	C₂²×C₃×C₅	semidirect
820. #121	C₂²×C₃×C₅	semidirect
821. #121	C₂²×C₃×C₅	semidirect
822. #121	C₂²×C₃×C₅	semidirect
823. #121	C₂²×C₃×C₅	semidirect
828. #120	C₂²×C₃×C₅	semidirect
829. #120	C₂²×C₃×C₅	semidirect
830. C₄×Q₈	C₂²×C₃×C₅	semidirect
832. C₄×D₄	C₂²×C₃×C₅	semidirect
833. C₄×D₄	C₂²×C₃×C₅	semidirect
834. C₄×D₄	C₂²×C₃×C₅	semidirect
835. C₄×D₄	C₂²×C₃×C₅	semidirect
836. C₄×D₄	C₂²×C₃×C₅	semidirect
837. C₄×D₄	C₂²×C₃×C₅	semidirect
838. C₄×D₄	C₂²×C₃×C₅	semidirect
839. C₄×D₄	C₂²×C₃×C₅	semidirect
840. #117	C₂²×C₃×C₅	semidirect
841. #117	C₂²×C₃×C₅	semidirect
842. #117	C₂²×C₃×C₅	semidirect
843. #117	C₂²×C₃×C₅	semidirect
844. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
845. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
848. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
849. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
1040. C₃×C₅	#3533	direct (N × H)
1148. C₅	C₃×#3533	direct (N × H)
1181. C₃	C₅×#3533	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×#560	2
C₃×C₅×#559	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×#540	2
C₃×C₅×#539	2
C₃×C₅×#538	2
C₃×C₅×#535	2
C₃×C₅×#534	2
C₃×C₅×#525	2
C₂×C₃×C₅×#123	2
C₅×#3533	3
C₃×#3533	5

Subgroups — C3×C5×#3533 #14276567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3533 #14276567