Subgroups — #11743525

Order 896.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#539	C₂	1	1	yes	maximal, characteristic, complemented
2	#90401	C₂	1	1	yes	maximal, characteristic, complemented
3	#90396	C₂	1	1	yes	maximal, characteristic, complemented
4	#90396	C₂	1	1	yes	maximal, characteristic, complemented
5	#90395	C₂	1	1	yes	maximal, characteristic, complemented
6	#90391	C₂	1	1	yes	maximal, characteristic, complemented
7	#90386	C₂	1	1	yes	maximal, characteristic, complemented
8	#90385	C₂	1	1	yes	maximal, characteristic, complemented
9	#90384	C₂	1	1	yes	maximal, characteristic, complemented
10	#90357	C₂	1	1	yes	maximal, characteristic, complemented
11	#90354	C₂	1	1	yes	maximal, characteristic, complemented
12	#90351	C₂	1	1	yes	maximal, characteristic, complemented
13	#90350	C₂	1	1	yes	maximal, characteristic, complemented
14	#90348	C₂	1	1	yes	maximal, characteristic, complemented
15	#90348	C₂	1	1	yes	maximal, characteristic, complemented
16	#90344	C₂	1	1	yes	maximal, characteristic, complemented
17	D₇×#123	C₂	1	1	yes	maximal, characteristic, complemented
18	#90338	C₂	1	1	yes	maximal, characteristic, complemented
19	#90337	C₂	1	1	yes	maximal, characteristic, complemented
20	#90331	C₂	1	1	yes	maximal, characteristic, complemented
21	#90322	C₂	1	1	yes	maximal, characteristic, complemented
22	#90321	C₂	1	1	yes	maximal, characteristic, complemented
23	#90318	C₂	1	1	yes	maximal, characteristic, complemented
24	#90304	C₂	1	1	yes	maximal, characteristic, complemented
25	#90298	C₂	1	1	yes	maximal, characteristic, complemented
26	#90253	C₂	1	1	yes	maximal, characteristic, complemented
27	#90250	C₂	1	1	yes	maximal, characteristic, complemented
28	#90241	C₂	1	1	yes	maximal, characteristic, complemented
29	#90238	C₂	1	1	yes	maximal, characteristic, complemented
30	#90205	C₂	1	1	yes	maximal, characteristic, complemented
31	#90198	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#1161	C₂²	1	1	yes	characteristic
33	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
34	C₂×#1157	C₂²	1	1	yes	characteristic
35	C₂×#1157	C₂²	1	1	yes	characteristic, complemented
36	C₂²×D₂₈	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
38	C₇×#126	C₂²	1	1	yes	characteristic, complemented
39	C₇×#126	C₂²	1	1	yes	characteristic, complemented
40	C₇×#125	C₂²	1	1	yes	characteristic, complemented
41	C₇×#125	C₂²	1	1	yes	characteristic, complemented
42	C₇×#123	C₂²	1	1	yes	characteristic
43	C₇×#123	C₂²	1	1	yes	characteristic
44	C₇×#123	C₂²	1	1	yes	characteristic, complemented
45	C₇×#123	C₂²	1	1	yes	characteristic, complemented
46	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
47	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₇×#121	C₂²	1	1	yes	characteristic
50	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
51	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	#6510	C₂²	1	1	yes	characteristic, complemented
54	#6509	C₂²	1	1	yes	characteristic, complemented
55	#6507	C₂²	1	1	yes	characteristic, complemented
56	#6503	C₂²	1	1	yes	characteristic
57	#6503	C₂²	1	1	yes	characteristic, complemented
58	#6502	C₂²	1	1	yes	characteristic, complemented
59	#6501	C₂²	1	1	yes	characteristic
60	#6501	C₂²	1	1	yes	characteristic, complemented
61	#6500	C₂²	1	1	yes	characteristic
62	#6500	C₂²	1	1	yes	characteristic
63	#6500	C₂²	1	1	yes	characteristic, complemented
64	#6500	C₂²	1	1	yes	characteristic, complemented
65	#6499	C₂²	1	1	yes	characteristic, complemented
66	#6498	C₂²	1	1	yes	characteristic
67	#6493	C₂²	1	1	yes	characteristic, complemented
68	#6493	C₂²	1	1	yes	characteristic, complemented
69	#6493	C₂²	1	1	yes	characteristic, complemented
70	#6493	C₂²	1	1	yes	characteristic, complemented
71	#6493	C₂²	1	1	yes	characteristic, complemented
72	#6492	C₂²	1	1	yes	characteristic
73	#6492	C₂²	1	1	yes	characteristic, complemented
74	#6492	C₂²	1	1	yes	characteristic, complemented
75	#6492	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
81	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
82	#6487	C₂²	1	1	yes	characteristic, complemented
83	#6461	C₂²	1	1	yes	characteristic, complemented
84	#6461	C₂²	1	1	yes	characteristic, complemented
85	#6461	C₂²	1	1	yes	characteristic, complemented
86	#6461	C₂²	1	1	yes	characteristic, complemented
87	#6461	C₂²	1	1	yes	characteristic, complemented
88	#6461	C₂²	1	1	yes	characteristic, complemented
89	#6460	C₂²	1	1	yes	characteristic, complemented
90	#6460	C₂²	1	1	yes	characteristic, complemented
91	#6460	C₂²	1	1	yes	characteristic, complemented
92	#6459	C₂²	1	1	yes	characteristic, complemented
93	#6459	C₂²	1	1	yes	characteristic, complemented
94	#6459	C₂²	1	1	yes	characteristic, complemented
95	#6459	C₂²	1	1	yes	characteristic, complemented
96	#6459	C₂²	1	1	yes	characteristic, complemented
97	#6459	C₂²	1	1	yes	characteristic, complemented
98	#6459	C₂²	1	1	yes	characteristic, complemented
99	#6458	C₂²	1	1	yes	characteristic
100	#6458	C₂²	1	1	yes	characteristic
101	#6458	C₂²	1	1	yes	characteristic
102	#6458	C₂²	1	1	yes	characteristic, complemented
103	#6458	C₂²	1	1	yes	characteristic, complemented
104	#6458	C₂²	1	1	yes	characteristic, complemented
105	#6458	C₂²	1	1	yes	characteristic, complemented
106	#6458	C₂²	1	1	yes	characteristic, complemented
107	#6457	C₂²	1	1	yes	characteristic
108	#6457	C₂²	1	1	yes	characteristic
109	#6457	C₂²	1	1	yes	characteristic
110	#6457	C₂²	1	1	yes	characteristic
111	#6457	C₂²	1	1	yes	characteristic, complemented
112	#6457	C₂²	1	1	yes	characteristic, complemented
113	#6457	C₂²	1	1	yes	characteristic, complemented
114	#6457	C₂²	1	1	yes	characteristic, complemented
115	#6457	C₂²	1	1	yes	characteristic, complemented
116	#6457	C₂²	1	1	yes	characteristic, complemented
117	#6457	C₂²	1	1	yes	characteristic, complemented
118	#6457	C₂²	1	1	yes	characteristic, complemented
119	#6457	C₂²	1	1	yes	characteristic, complemented
120	#6456	C₂²	1	1	yes	characteristic
121	#6456	C₂²	1	1	yes	characteristic, complemented
122	#6456	C₂²	1	1	yes	characteristic, complemented
123	#6456	C₂²	1	1	yes	characteristic, complemented
124	#6456	C₂²	1	1	yes	characteristic, complemented
125	#6455	C₂²	1	1	yes	characteristic, complemented
126	#6455	C₂²	1	1	yes	characteristic, complemented
127	#6455	C₂²	1	1	yes	characteristic, complemented
128	#6455	C₂²	1	1	yes	characteristic, complemented
129	#6455	C₂²	1	1	yes	characteristic, complemented
130	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
131	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
132	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
133	#6453	C₂²	1	1	yes	characteristic, complemented
134	#6453	C₂²	1	1	yes	characteristic, complemented
135	#6452	C₂²	1	1	yes	characteristic, complemented
136	#6452	C₂²	1	1	yes	characteristic, complemented
137	#6451	C₂²	1	1	yes	characteristic, complemented
138	#6450	C₂²	1	1	yes	characteristic, complemented
139	#6449	C₂²	1	1	yes	characteristic, complemented
140	#6448	C₂²	1	1	yes	characteristic
141	#6448	C₂²	1	1	yes	characteristic, complemented
142	#6448	C₂²	1	1	yes	characteristic, complemented
143	#6448	C₂²	1	1	yes	characteristic, complemented
144	#6448	C₂²	1	1	yes	characteristic, complemented
145	#6448	C₂²	1	1	yes	characteristic, complemented
146	#6447	C₂²	1	1	yes	characteristic
147	#6447	C₂²	1	1	yes	characteristic
148	#6447	C₂²	1	1	yes	characteristic
149	#6447	C₂²	1	1	yes	characteristic, complemented
150	#6447	C₂²	1	1	yes	characteristic, complemented
151	#6447	C₂²	1	1	yes	characteristic, complemented
152	#6447	C₂²	1	1	yes	characteristic, complemented
153	#6446	C₂²	1	1	yes	characteristic
154	#6446	C₂²	1	1	yes	characteristic
155	#6446	C₂²	1	1	yes	characteristic, complemented
156	#6446	C₂²	1	1	yes	characteristic, complemented
157	#6446	C₂²	1	1	yes	characteristic, complemented
158	#6446	C₂²	1	1	yes	characteristic, complemented
159	#6446	C₂²	1	1	yes	characteristic, complemented
160	#6445	C₂²	1	1	yes	characteristic
161	#6445	C₂²	1	1	yes	characteristic
162	#6445	C₂²	1	1	yes	characteristic
163	#6445	C₂²	1	1	yes	characteristic
164	#6445	C₂²	1	1	yes	characteristic, complemented
165	#6445	C₂²	1	1	yes	characteristic, complemented
166	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
167	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
168	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
169	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
170	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
171	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
172	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
173	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
174	#6442	C₂²	1	1	yes	characteristic, complemented
175	#6442	C₂²	1	1	yes	characteristic, complemented
176	#6442	C₂²	1	1	yes	characteristic, complemented
177	#6442	C₂²	1	1	yes	characteristic, complemented
178	#6441	C₂²	1	1	yes	characteristic, complemented
179	#6438	C₂²	1	1	yes	characteristic, complemented
180	#6438	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₂₈	C₂²	1	1	yes	characteristic
182	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
183	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
184	#6435	C₂²	1	1	yes	characteristic, complemented
185	#6435	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
187	#3533	—	7	1	no	maximal, Sylow
188	C₂³×D₇	C₂³	1	1	yes	characteristic
189	C₂³×D₇	C₂³	1	1	yes	characteristic
190	C₂³×D₇	C₂³	1	1	yes	characteristic
191	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
192	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
193	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
194	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
212	C₂²×Dic₇	C₂³	1	1	yes	characteristic
213	#1161	—	4	2	no	—
214	D₄×D₇	—	4	2	no	—
215	#1157	—	4	2	no	—
216	#1157	—	4	2	no	—
217	C₂×D₂₈	—	4	2	no	—
218	C₂×D₂₈	C₂³	1	1	yes	characteristic
219	C₂×D₂₈	C₂³	1	1	yes	characteristic
220	C₂×D₂₈	C₂³	1	1	yes	characteristic
221	C₂×D₂₈	C₂³	1	1	yes	characteristic
222	C₂×D₂₈	C₂³	1	1	yes	characteristic
223	C₂×D₂₈	C₂³	1	1	yes	characteristic
224	C₂×D₂₈	C₂³	1	1	yes	characteristic
225	C₂×D₂₈	C₂³	1	1	yes	characteristic
226	C₂×D₂₈	C₂³	1	1	yes	characteristic
227	C₂×D₂₈	C₂³	1	1	yes	characteristic
228	C₂×D₂₈	C₂³	1	1	yes	characteristic
229	C₂×D₂₈	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₇	—	4	2	no	—
231	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
247	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
248	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
249	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
250	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
251	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
266	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
272	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
273	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
274	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
275	C₄²×C₇	C₂³	1	1	yes	characteristic
276	C₄²×C₇	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
285	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
304	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
305	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
306	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
307	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
308	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
309	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
310	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
311	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
312	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
313	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
314	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
315	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
316	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
317	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
318	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
319	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
320	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
321	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
322	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
323	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
324	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
325	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
326	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
327	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
328	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
329	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
330	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
331	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
332	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
333	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
334	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
335	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
336	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
337	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
338	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
339	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
340	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
341	C₄×Dic₇	C₂³	1	1	yes	characteristic
342	C₄×Dic₇	C₂³	1	1	yes	characteristic
343	C₄×Dic₇	C₂³	1	1	yes	characteristic
344	C₄×Dic₇	C₂³	1	1	yes	characteristic
345	C₄×Dic₇	C₂³	1	1	yes	characteristic
346	C₄×Dic₇	C₂³	1	1	yes	characteristic
347	C₄×Dic₇	C₂³	1	1	yes	characteristic
348	C₄×Dic₇	C₂³	1	1	yes	characteristic
349	#563	—	7	1	no	—
350	#562	—	7	1	no	—
351	#562	—	7	1	no	—
352	#560	—	7	1	no	—
353	#559	—	7	1	no	—
354	#553	—	7	1	no	—
355	#553	—	7	1	no	—
356	#552	—	7	1	no	—
357	#552	—	7	1	no	—
358	#551	—	7	1	no	—
359	#551	—	7	1	no	—
360	#551	—	7	1	no	—
361	#547	—	7	1	no	—
362	#547	—	7	1	no	—
363	#546	—	7	1	no	—
364	#546	—	7	1	no	—
365	#542	—	7	1	no	—
366	#542	—	7	1	no	—
367	#540	—	7	1	no	—
368	#540	—	7	1	no	—
369	#539	—	7	1	no	—
370	#539	D₇	1	1	yes	characteristic, complemented
371	#538	—	7	1	no	—
372	#538	—	7	1	no	—
373	#538	—	7	1	no	—
374	#538	—	7	1	no	—
375	#535	—	7	1	no	—
376	#534	—	7	1	no	—
377	#525	—	7	1	no	—
378	#525	—	7	1	no	—
379	C₂×#123	—	7	1	no	—
380	C₂³×C₇	C₂⁴	1	1	yes	characteristic
381	C₂³×C₇	C₂⁴	1	1	yes	characteristic
382	C₂³×C₇	C₂⁴	1	1	yes	characteristic
383	C₂²×D₇	—	2	2	no	—
384	C₂²×D₇	—	2	2	no	—
385	C₂²×D₇	—	4	1	no	—
386	C₂²×D₇	—	4	1	no	—
387	C₂²×D₇	—	4	1	no	—
388	C₂²×D₇	—	4	1	no	—
389	C₂²×D₇	—	4	1	no	—
390	C₂²×D₇	—	4	1	no	—
391	C₂²×D₇	—	4	1	no	—
392	C₂²×D₇	C₂⁴	1	1	yes	characteristic
393	C₂²×D₇	C₂⁴	1	1	yes	characteristic
394	C₂²×D₇	C₂⁴	1	1	yes	characteristic
395	C₂²×D₇	C₂⁴	1	1	yes	characteristic
396	C₂²×D₇	C₂⁴	1	1	yes	characteristic
397	C₂²×D₇	C₂⁴	1	1	yes	characteristic
398	C₇×Q₈	—	4	1	no	—
399	C₇×D₄	—	4	1	no	—
400	C₇×D₄	—	4	1	no	—
401	C₇×D₄	—	4	1	no	—
402	C₂×C₄×C₇	—	4	1	no	—
403	C₂×C₄×C₇	—	4	1	no	—
404	C₂×C₄×C₇	—	4	1	no	—
405	C₂×C₄×C₇	—	4	1	no	—
406	C₂×C₄×C₇	—	4	1	no	—
407	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
408	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
409	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
410	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
411	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
412	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
413	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
414	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
415	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
416	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
417	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
418	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
419	C₂²⋊D₇	—	2	2	no	—
420	C₂²⋊D₇	—	4	1	no	—
421	C₂²⋊D₇	—	4	1	no	—
422	C₂²⋊D₇	—	4	1	no	—
423	C₂²⋊D₇	—	4	1	no	—
424	C₂²⋊D₇	—	4	1	no	—
425	C₂²⋊D₇	—	4	1	no	—
426	C₂²⋊D₇	—	4	1	no	—
427	C₂²⋊D₇	—	4	1	no	—
428	C₂²⋊D₇	—	4	1	no	—
429	C₂²⋊D₇	—	4	1	no	—
430	C₂²⋊D₇	—	4	1	no	—
431	C₂×Dic₇	—	4	1	no	—
432	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
433	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
434	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
435	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
436	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
437	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
438	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
439	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
440	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
441	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
442	D₂₈	—	2	2	no	—
443	D₂₈	—	2	2	no	—
444	D₂₈	—	2	2	no	—
445	D₂₈	—	4	1	no	—
446	D₂₈	—	4	1	no	—
447	D₂₈	—	4	1	no	—
448	D₂₈	—	4	1	no	—
449	D₂₈	—	4	1	no	—
450	D₂₈	—	4	1	no	—
451	D₂₈	—	4	1	no	—
452	D₂₈	—	4	1	no	—
453	D₂₈	—	4	1	no	—
454	C₄×D₇	—	2	2	no	—
455	C₄×D₇	—	2	2	no	—
456	C₄×D₇	—	2	2	no	—
457	C₄×D₇	—	4	1	no	—
458	C₄×D₇	—	4	1	no	—
459	C₄×D₇	—	4	1	no	—
460	C₄×D₇	—	4	1	no	—
461	C₄×D₇	—	4	1	no	—
462	C₄×D₇	—	4	1	no	—
463	C₄×D₇	—	4	1	no	—
464	C₄×D₇	—	4	1	no	—
465	C₄×D₇	—	4	1	no	—
466	C₄×D₇	—	4	1	no	—
467	C₄×D₇	—	4	1	no	—
468	C₄×D₇	—	4	1	no	—
469	C₄×D₇	—	4	1	no	—
470	Dic₁₄	—	4	1	no	—
471	Dic₁₄	—	4	1	no	—
472	Dic₁₄	—	4	1	no	—
473	Dic₁₄	—	4	1	no	—
474	C₂×#41	—	7	1	no	—
475	C₂×#41	—	7	1	no	—
476	C₂×#41	—	7	1	no	—
477	C₂²×D₄	—	7	1	no	—
478	C₂²×D₄	—	7	1	no	—
479	C₂³×C₄	—	7	1	no	—
480	C₄⋊Q₈	—	7	1	no	—
481	C₄⋊Q₈	—	7	1	no	—
482	#127	—	7	1	no	—
483	#127	—	7	1	no	—
484	#126	—	7	1	no	—
485	#126	—	7	1	no	—
486	#126	—	7	1	no	—
487	#126	—	7	1	no	—
488	#126	—	7	1	no	—
489	#126	—	7	1	no	—
490	#126	—	7	1	no	—
491	#126	—	7	1	no	—
492	#126	—	7	1	no	—
493	#126	—	7	1	no	—
494	#126	C₂×D₇	1	1	yes	characteristic, complemented
495	#126	C₂×D₇	1	1	yes	characteristic, complemented
496	#125	—	7	1	no	—
497	#125	—	7	1	no	—
498	#125	—	7	1	no	—
499	#125	—	7	1	no	—
500	#125	C₂×D₇	1	1	yes	characteristic, complemented
501	#125	C₂×D₇	1	1	yes	characteristic, complemented
502	#124	—	7	1	no	—
503	#124	—	7	1	no	—
504	#124	—	7	1	no	—
505	#124	—	7	1	no	—
506	#124	—	7	1	no	—
507	#124	—	7	1	no	—
508	#124	—	7	1	no	—
509	#124	—	7	1	no	—
510	#124	—	7	1	no	—
511	#124	—	7	1	no	—
512	#123	—	7	1	no	—
513	#123	—	7	1	no	—
514	#123	—	7	1	no	—
515	#123	—	7	1	no	—
516	#123	—	7	1	no	—
517	#123	—	7	1	no	—
518	#123	—	7	1	no	—
519	#123	—	7	1	no	—
520	#123	—	7	1	no	—
521	#123	—	7	1	no	—
522	#123	—	7	1	no	—
523	#123	—	7	1	no	—
524	#123	—	7	1	no	—
525	#123	—	7	1	no	—
526	#123	—	7	1	no	—
527	#123	—	7	1	no	—
528	#123	—	7	1	no	—
529	#123	—	7	1	no	—
530	#123	—	7	1	no	—
531	#123	—	7	1	no	—
532	#123	—	7	1	no	—
533	#123	—	7	1	no	—
534	#123	—	7	1	no	—
535	#123	—	7	1	no	—
536	#123	—	7	1	no	—
537	#123	—	7	1	no	—
538	#123	C₂×D₇	1	1	yes	characteristic
539	#123	C₂×D₇	1	1	yes	characteristic
540	#123	C₂×D₇	1	1	yes	characteristic, complemented
541	#123	C₂×D₇	1	1	yes	characteristic, complemented
542	C₂²⋊Q₈	—	7	1	no	—
543	C₂²⋊Q₈	—	7	1	no	—
544	C₂²⋊Q₈	—	7	1	no	—
545	C₂²⋊Q₈	—	7	1	no	—
546	C₂²⋊Q₈	—	7	1	no	—
547	C₂²⋊Q₈	—	7	1	no	—
548	C₂²⋊Q₈	—	7	1	no	—
549	C₂²⋊Q₈	—	7	1	no	—
550	C₂²⋊Q₈	—	7	1	no	—
551	C₂²⋊Q₈	—	7	1	no	—
552	C₂²⋊Q₈	—	7	1	no	—
553	C₂²⋊Q₈	—	7	1	no	—
554	C₂²⋊Q₈	—	7	1	no	—
555	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
556	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
557	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
558	#121	—	7	1	no	—
559	#121	—	7	1	no	—
560	#121	—	7	1	no	—
561	#121	—	7	1	no	—
562	#121	—	7	1	no	—
563	#121	—	7	1	no	—
564	#121	—	7	1	no	—
565	#121	—	7	1	no	—
566	#121	—	7	1	no	—
567	#121	—	7	1	no	—
568	#121	—	7	1	no	—
569	#121	—	7	1	no	—
570	#121	—	7	1	no	—
571	#121	—	7	1	no	—
572	#121	—	7	1	no	—
573	#121	—	7	1	no	—
574	#121	—	7	1	no	—
575	#121	—	7	1	no	—
576	#121	—	7	1	no	—
577	#121	—	7	1	no	—
578	#121	—	7	1	no	—
579	#121	—	7	1	no	—
580	#121	—	7	1	no	—
581	#121	C₂×D₇	1	1	yes	characteristic
582	#120	—	7	1	no	—
583	#120	—	7	1	no	—
584	#120	—	7	1	no	—
585	#120	—	7	1	no	—
586	#120	—	7	1	no	—
587	#120	—	7	1	no	—
588	#120	—	7	1	no	—
589	#120	—	7	1	no	—
590	#120	—	7	1	no	—
591	#120	—	7	1	no	—
592	C₄×Q₈	—	7	1	no	—
593	C₄×Q₈	—	7	1	no	—
594	C₄×D₄	—	7	1	no	—
595	C₄×D₄	—	7	1	no	—
596	C₄×D₄	—	7	1	no	—
597	C₄×D₄	—	7	1	no	—
598	C₄×D₄	—	7	1	no	—
599	C₄×D₄	—	7	1	no	—
600	C₄×D₄	—	7	1	no	—
601	C₄×D₄	—	7	1	no	—
602	C₄×D₄	—	7	1	no	—
603	C₄×D₄	—	7	1	no	—
604	C₄×D₄	—	7	1	no	—
605	C₄×D₄	—	7	1	no	—
606	C₄×D₄	—	7	1	no	—
607	C₄×D₄	—	7	1	no	—
608	C₄×D₄	—	7	1	no	—
609	C₄×D₄	—	7	1	no	—
610	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
611	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
612	#117	—	7	1	no	—
613	#117	—	7	1	no	—
614	#117	—	7	1	no	—
615	#117	—	7	1	no	—
616	#117	—	7	1	no	—
617	#117	—	7	1	no	—
618	#117	—	7	1	no	—
619	C₂×C₄⋊C₄	—	7	1	no	—
620	C₂×C₄⋊C₄	—	7	1	no	—
621	C₂×C₄⋊C₄	—	7	1	no	—
622	C₂×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
623	C₂×C₂²⋊C₄	—	7	1	no	—
624	C₂×C₂²⋊C₄	—	7	1	no	—
625	C₂×C₂²⋊C₄	—	7	1	no	—
626	C₂×C₂²⋊C₄	—	7	1	no	—
627	C₂×C₂²⋊C₄	—	7	1	no	—
628	C₂×C₂²⋊C₄	—	7	1	no	—
629	C₂²×C₇	—	2	1	no	—
630	C₂²×C₇	—	2	1	no	—
631	C₂²×C₇	—	2	1	no	—
632	C₂²×C₇	—	2	1	no	—
633	C₂²×C₇	—	2	1	no	—
634	C₂²×C₇	—	2	1	no	—
635	C₂²×C₇	—	2	1	no	—
636	C₂²×C₇	—	2	1	no	—
637	C₂²×C₇	—	2	1	no	—
638	C₂²×C₇	C₂⁵	1	1	yes	characteristic
639	C₂×D₇	—	2	1	no	—
640	C₂×D₇	—	2	1	no	—
641	C₂×D₇	—	2	1	no	—
642	C₂×D₇	—	2	1	no	—
643	C₂×D₇	—	2	1	no	—
644	C₂×D₇	—	2	1	no	—
645	C₂×D₇	—	2	1	no	—
646	C₂×D₇	—	2	1	no	—
647	C₂×D₇	—	2	1	no	—
648	C₂×D₇	—	2	1	no	—
649	C₂×D₇	—	2	1	no	—
650	C₂×D₇	—	2	1	no	—
651	C₂×D₇	—	2	1	no	—
652	C₂×D₇	—	2	1	no	—
653	C₂×D₇	—	2	1	no	—
654	C₂×D₇	—	2	1	no	—
655	C₂×D₇	—	2	1	no	—
656	C₂×D₇	—	4	4	no	—
657	C₂×D₇	—	8	2	no	—
658	C₂×D₇	—	8	2	no	—
659	C₂×D₇	H(5,𝔽₂)	1	2	yes	—
660	C₄×C₇	—	2	1	no	—
661	C₄×C₇	—	2	1	no	—
662	C₄×C₇	—	2	1	no	—
663	C₄×C₇	—	2	1	no	—
664	C₄×C₇	—	2	1	no	—
665	C₄×C₇	—	2	1	no	—
666	C₄×C₇	—	2	1	no	—
667	C₄×C₇	—	2	1	no	—
668	C₄×C₇	—	2	1	no	—
669	C₄×C₇	—	2	1	no	—
670	C₄×C₇	—	2	1	no	—
671	C₄×C₇	—	2	1	no	—
672	Dic₇	—	2	1	no	—
673	Dic₇	—	2	1	no	—
674	Dic₇	—	2	1	no	—
675	Dic₇	—	2	1	no	—
676	Dic₇	—	2	1	no	—
677	Dic₇	—	2	1	no	—
678	Dic₇	—	2	1	no	—
679	Dic₇	—	2	1	no	—
680	Dic₇	—	2	1	no	—
681	Dic₇	—	2	1	no	—
682	C₂⁴	—	7	1	no	—
683	C₂⁴	—	7	1	no	—
684	C₂⁴	—	7	1	no	—
685	#41	—	28	2	no	—
686	#41	—	28	2	no	—
687	#41	—	28	2	no	—
688	C₂×Q₈	—	7	1	no	—
689	C₂×Q₈	—	7	1	no	—
690	C₂×Q₈	—	7	1	no	—
691	C₂×Q₈	—	7	1	no	—
692	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
693	C₂×D₄	—	7	1	no	—
694	C₂×D₄	—	7	1	no	—
695	C₂×D₄	—	7	1	no	—
696	C₂×D₄	—	7	1	no	—
697	C₂×D₄	—	7	1	no	—
698	C₂×D₄	—	7	1	no	—
699	C₂×D₄	—	7	1	no	—
700	C₂×D₄	—	7	1	no	—
701	C₂×D₄	—	7	1	no	—
702	C₂×D₄	—	7	1	no	—
703	C₂×D₄	—	7	1	no	—
704	C₂×D₄	—	7	1	no	—
705	C₂×D₄	—	7	1	no	—
706	C₂×D₄	—	7	1	no	—
707	C₂×D₄	—	7	1	no	—
708	C₂×D₄	—	7	1	no	—
709	C₂×D₄	—	7	1	no	—
710	C₂×D₄	—	7	1	no	—
711	C₂×D₄	—	7	1	no	—
712	C₂×D₄	—	7	1	no	—
713	C₂×D₄	—	7	1	no	—
714	C₂×D₄	—	7	1	no	—
715	C₂×D₄	—	7	1	no	—
716	C₂×D₄	—	7	1	no	—
717	C₂×D₄	—	28	2	no	—
718	C₂×D₄	—	28	2	no	—
719	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
720	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
721	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
722	C₂²×C₄	—	7	1	no	—
723	C₂²×C₄	—	7	1	no	—
724	C₂²×C₄	—	7	1	no	—
725	C₂²×C₄	—	7	1	no	—
726	C₂²×C₄	—	7	1	no	—
727	C₂²×C₄	—	7	1	no	—
728	C₂²×C₄	—	7	1	no	—
729	C₂²×C₄	—	7	1	no	—
730	C₂²×C₄	—	7	1	no	—
731	C₂²×C₄	—	7	1	no	—
732	C₂²×C₄	—	7	1	no	—
733	C₂²×C₄	—	7	1	no	—
734	C₂²×C₄	—	7	1	no	—
735	C₂²×C₄	—	7	1	no	—
736	C₂²×C₄	—	7	1	no	—
737	C₂²×C₄	—	7	1	no	—
738	C₂²×C₄	—	7	1	no	—
739	C₂²×C₄	—	28	2	no	—
740	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
741	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
742	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
743	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
744	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
745	C₄⋊C₄	—	7	1	no	—
746	C₄⋊C₄	—	7	1	no	—
747	C₄⋊C₄	—	7	1	no	—
748	C₄⋊C₄	—	7	1	no	—
749	C₄⋊C₄	—	7	1	no	—
750	C₄⋊C₄	—	7	1	no	—
751	C₄⋊C₄	—	7	1	no	—
752	C₄⋊C₄	—	7	1	no	—
753	C₄⋊C₄	—	7	1	no	—
754	C₄⋊C₄	—	7	1	no	—
755	C₄⋊C₄	—	7	1	no	—
756	C₄⋊C₄	—	7	1	no	—
757	C₄⋊C₄	—	7	1	no	—
758	C₄⋊C₄	—	7	1	no	—
759	C₄⋊C₄	—	7	1	no	—
760	C₄⋊C₄	—	7	1	no	—
761	C₄⋊C₄	—	7	1	no	—
762	C₄⋊C₄	—	7	1	no	—
763	C₄⋊C₄	—	7	1	no	—
764	C₄⋊C₄	—	7	1	no	—
765	C₄⋊C₄	—	7	1	no	—
766	C₄⋊C₄	—	7	1	no	—
767	C₄⋊C₄	—	7	1	no	—
768	C₄⋊C₄	—	7	1	no	—
769	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
770	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
772	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
774	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
775	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
776	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
777	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
782	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
783	C₂²⋊C₄	—	7	1	no	—
784	C₂²⋊C₄	—	7	1	no	—
785	C₂²⋊C₄	—	7	1	no	—
786	C₂²⋊C₄	—	7	1	no	—
787	C₂²⋊C₄	—	7	1	no	—
788	C₂²⋊C₄	—	7	1	no	—
789	C₂²⋊C₄	—	7	1	no	—
790	C₂²⋊C₄	—	7	1	no	—
791	C₂²⋊C₄	—	7	1	no	—
792	C₂²⋊C₄	—	7	1	no	—
793	C₂²⋊C₄	—	7	1	no	—
794	C₂²⋊C₄	—	7	1	no	—
795	C₂²⋊C₄	—	7	1	no	—
796	C₂²⋊C₄	—	7	1	no	—
797	C₂²⋊C₄	—	7	1	no	—
798	C₂²⋊C₄	—	7	1	no	—
799	C₂²⋊C₄	—	7	1	no	—
800	C₂²⋊C₄	—	7	1	no	—
801	C₂²⋊C₄	—	7	1	no	—
802	C₂²⋊C₄	—	7	1	no	—
803	C₂²⋊C₄	—	7	1	no	—
804	C₂²⋊C₄	—	7	1	no	—
805	C₂²⋊C₄	—	7	1	no	—
806	C₂²⋊C₄	—	7	1	no	—
807	C₂²⋊C₄	—	7	1	no	—
808	C₂²⋊C₄	—	7	1	no	—
809	C₂²⋊C₄	—	7	1	no	—
810	C₂²⋊C₄	—	7	1	no	—
811	C₂²⋊C₄	—	7	1	no	—
812	C₂²⋊C₄	—	7	1	no	—
813	C₂²⋊C₄	—	7	1	no	—
814	C₂²⋊C₄	—	7	1	no	—
815	C₂²⋊C₄	—	7	1	no	—
816	C₂²⋊C₄	—	7	1	no	—
817	C₂²⋊C₄	—	7	1	no	—
818	C₂²⋊C₄	—	7	1	no	—
819	C₂²⋊C₄	—	7	1	no	—
820	C₂²⋊C₄	—	7	1	no	—
821	C₂²⋊C₄	—	7	1	no	—
822	C₂²⋊C₄	—	7	1	no	—
823	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
824	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
825	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
826	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
827	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
828	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
829	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
830	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
831	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
832	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
833	C₄²	—	7	1	no	—
834	C₄²	—	7	1	no	—
835	C₄²	—	7	1	no	—
836	C₄²	—	7	1	no	—
837	C₄²	—	7	1	no	—
838	C₄²	—	7	1	no	—
839	C₄²	—	7	1	no	—
840	C₄²	—	7	1	no	—
841	C₄²	C₂²×D₇	1	1	yes	characteristic
842	C₄²	C₂²×D₇	1	1	yes	characteristic
843	C₂×C₇	—	4	1	no	—
844	C₂×C₇	—	4	1	no	—
845	C₂×C₇	—	4	1	no	—
846	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
847	C₂×C₇	#585	1	1	yes	characteristic
848	C₂×C₇	#585	1	1	yes	characteristic
849	D₇	—	2	2	no	—
850	D₇	—	4	1	no	—
851	D₇	—	4	1	no	—
852	D₇	—	4	1	no	—
853	D₇	—	4	1	no	—
854	D₇	—	4	1	no	—
855	C₂³	—	7	1	no	—
856	C₂³	—	7	1	no	—
857	C₂³	—	7	1	no	—
858	C₂³	—	7	1	no	—
859	C₂³	—	7	1	no	—
860	C₂³	—	7	1	no	—
861	C₂³	—	14	2	no	—
862	C₂³	—	14	2	no	—
863	C₂³	—	28	1	no	—
864	C₂³	—	28	1	no	—
865	C₂³	—	28	1	no	—
866	C₂³	—	28	1	no	—
867	C₂³	—	28	1	no	—
868	C₂³	—	28	1	no	—
869	C₂³	—	28	1	no	—
870	C₂³	C₂³×D₇	1	1	yes	characteristic
871	C₂³	C₂³×D₇	1	1	yes	characteristic
872	C₂³	C₂³×D₇	1	1	yes	characteristic
873	Q₈	—	4	1	no	—
874	Q₈	—	28	1	no	—
875	Q₈	—	28	1	no	—
876	Q₈	—	28	1	no	—
877	Q₈	—	28	1	no	—
878	D₄	—	4	1	no	—
879	D₄	—	4	1	no	—
880	D₄	—	4	1	no	—
881	D₄	—	14	2	no	—
882	D₄	—	14	2	no	—
883	D₄	—	14	2	no	—
884	D₄	—	14	2	no	—
885	D₄	—	28	1	no	—
886	D₄	—	28	1	no	—
887	D₄	—	28	1	no	—
888	D₄	—	28	1	no	—
889	D₄	—	28	1	no	—
890	D₄	—	28	1	no	—
891	D₄	—	28	1	no	—
892	D₄	—	28	1	no	—
893	D₄	—	28	1	no	—
894	D₄	—	28	1	no	—
895	D₄	—	28	1	no	—
896	D₄	—	28	1	no	—
897	D₄	—	28	1	no	—
898	D₄	—	28	1	no	—
899	D₄	—	28	1	no	—
900	D₄	—	28	1	no	—
901	D₄	—	28	1	no	—
902	D₄	—	28	1	no	—
903	D₄	—	28	1	no	—
904	D₄	—	28	1	no	—
905	C₂×C₄	—	4	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	7	1	no	—
911	C₂×C₄	—	7	1	no	—
912	C₂×C₄	—	7	1	no	—
913	C₂×C₄	—	7	1	no	—
914	C₂×C₄	—	7	1	no	—
915	C₂×C₄	—	7	1	no	—
916	C₂×C₄	—	7	1	no	—
917	C₂×C₄	—	7	1	no	—
918	C₂×C₄	—	7	1	no	—
919	C₂×C₄	—	7	1	no	—
920	C₂×C₄	—	14	2	no	—
921	C₂×C₄	—	14	2	no	—
922	C₂×C₄	—	14	2	no	—
923	C₂×C₄	—	28	1	no	—
924	C₂×C₄	—	28	1	no	—
925	C₂×C₄	—	28	1	no	—
926	C₂×C₄	—	28	1	no	—
927	C₂×C₄	—	28	1	no	—
928	C₂×C₄	—	28	1	no	—
929	C₂×C₄	—	28	1	no	—
930	C₂×C₄	—	28	1	no	—
931	C₂×C₄	—	28	1	no	—
932	C₂×C₄	—	28	1	no	—
933	C₂×C₄	—	28	1	no	—
934	C₂×C₄	—	28	1	no	—
935	C₂×C₄	—	28	1	no	—
936	C₂×C₄	—	28	1	no	—
937	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
938	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
939	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
940	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
941	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
942	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
948	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
949	C₇	#3533	1	1	yes	characteristic, complemented, Sylow
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	7	2	no	—
960	C₂²	—	14	1	no	—
961	C₂²	—	14	1	no	—
962	C₂²	—	14	1	no	—
963	C₂²	—	14	1	no	—
964	C₂²	—	14	1	no	—
965	C₂²	—	14	1	no	—
966	C₂²	—	14	1	no	—
967	C₂²	—	14	1	no	—
968	C₂²	—	14	1	no	—
969	C₂²	—	14	1	no	—
970	C₂²	—	14	1	no	—
971	C₂²	—	14	1	no	—
972	C₂²	—	14	1	no	—
973	C₂²	—	14	1	no	—
974	C₂²	—	14	1	no	—
975	C₂²	—	14	1	no	—
976	C₂²	—	14	1	no	—
977	C₂²	—	28	4	no	—
978	C₂²	—	56	2	no	—
979	C₂²	—	56	2	no	—
980	C₂²	C₂⁴×D₇	1	1	yes	characteristic
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	2	1	no	—
993	C₄	—	14	1	no	—
994	C₄	—	14	1	no	—
995	C₄	—	14	1	no	—
996	C₄	—	14	1	no	—
997	C₄	—	14	1	no	—
998	C₄	—	14	1	no	—
999	C₄	—	14	1	no	—
1000	C₄	—	14	1	no	—
1001	C₄	—	14	1	no	—
1002	C₄	—	14	1	no	—
1003	C₂	—	4	1	no	—
1004	C₂	—	4	1	no	—
1005	C₂	—	4	1	no	—
1006	C₂	—	14	2	no	—
1007	C₂	—	28	1	no	—
1008	C₂	—	28	1	no	—
1009	C₂	—	28	1	no	—
1010	C₂	—	28	1	no	—
1011	C₂	—	28	1	no	—
1012	C₂	#90616	1	1	yes	characteristic
1013	C₂	D₇×H(5,𝔽₂)	1	1	yes	characteristic
1014	C₂	#90620	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#539	C₂
hypercenter	#539	D₇
hypocenter	C₇	#3533
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. C₇×#539	C₂	semidirect
2. #90401	C₂	semidirect
3. #90396	C₂	semidirect
4. #90396	C₂	semidirect
5. #90395	C₂	semidirect
6. #90391	C₂	semidirect
7. #90386	C₂	semidirect
8. #90385	C₂	semidirect
9. #90384	C₂	semidirect
10. #90357	C₂	semidirect
11. #90354	C₂	semidirect
12. #90351	C₂	semidirect
13. #90350	C₂	semidirect
14. #90348	C₂	semidirect
15. #90348	C₂	semidirect
16. #90344	C₂	semidirect
17. D₇×#123	C₂	semidirect
18. #90338	C₂	semidirect
19. #90337	C₂	semidirect
20. #90331	C₂	semidirect
21. #90322	C₂	semidirect
22. #90321	C₂	semidirect
23. #90318	C₂	semidirect
24. #90304	C₂	semidirect
25. #90298	C₂	semidirect
26. #90253	C₂	semidirect
27. #90250	C₂	semidirect
28. #90241	C₂	semidirect
29. #90238	C₂	semidirect
30. #90205	C₂	semidirect
31. #90198	C₂	semidirect
35. C₂×#1157	C₂²	semidirect
37. C₂²×C₄×D₇	C₂²	semidirect
38. C₇×#126	C₂²	semidirect
39. C₇×#126	C₂²	semidirect
40. C₇×#125	C₂²	semidirect
41. C₇×#125	C₂²	semidirect
44. C₇×#123	C₂²	semidirect
45. C₇×#123	C₂²	semidirect
46. C₇×C₂²⋊Q₈	C₂²	semidirect
47. C₇×C₂²⋊Q₈	C₂²	semidirect
48. C₇×C₂²⋊Q₈	C₂²	semidirect
50. C₄×C₇×D₄	C₂²	semidirect
51. C₄×C₇×D₄	C₂²	semidirect
52. C₂×C₇×C₄⋊C₄	C₂²	semidirect
53. #6510	C₂²	semidirect
54. #6509	C₂²	semidirect
55. #6507	C₂²	semidirect
57. #6503	C₂²	semidirect
58. #6502	C₂²	semidirect
60. #6501	C₂²	semidirect
63. #6500	C₂²	semidirect
64. #6500	C₂²	semidirect
65. #6499	C₂²	semidirect
67. #6493	C₂²	semidirect
68. #6493	C₂²	semidirect
69. #6493	C₂²	semidirect
70. #6493	C₂²	semidirect
71. #6493	C₂²	semidirect
73. #6492	C₂²	semidirect
74. #6492	C₂²	semidirect
75. #6492	C₂²	semidirect
76. C₄×C₂²⋊D₇	C₂²	semidirect
77. C₄×C₂²⋊D₇	C₂²	semidirect
78. C₄×C₂²⋊D₇	C₂²	semidirect
79. C₄×C₂²⋊D₇	C₂²	semidirect
80. C₄×C₂²⋊D₇	C₂²	semidirect
81. C₄×C₂²⋊D₇	C₂²	semidirect
82. #6487	C₂²	semidirect
83. #6461	C₂²	semidirect
84. #6461	C₂²	semidirect
85. #6461	C₂²	semidirect
86. #6461	C₂²	semidirect
87. #6461	C₂²	semidirect
88. #6461	C₂²	semidirect
89. #6460	C₂²	semidirect
90. #6460	C₂²	semidirect
91. #6460	C₂²	semidirect
92. #6459	C₂²	semidirect
93. #6459	C₂²	semidirect
94. #6459	C₂²	semidirect
95. #6459	C₂²	semidirect
96. #6459	C₂²	semidirect
97. #6459	C₂²	semidirect
98. #6459	C₂²	semidirect
102. #6458	C₂²	semidirect
103. #6458	C₂²	semidirect
104. #6458	C₂²	semidirect
105. #6458	C₂²	semidirect
106. #6458	C₂²	semidirect
111. #6457	C₂²	semidirect
112. #6457	C₂²	semidirect
113. #6457	C₂²	semidirect
114. #6457	C₂²	semidirect
115. #6457	C₂²	semidirect
116. #6457	C₂²	semidirect
117. #6457	C₂²	semidirect
118. #6457	C₂²	semidirect
119. #6457	C₂²	semidirect
121. #6456	C₂²	semidirect
122. #6456	C₂²	semidirect
123. #6456	C₂²	semidirect
124. #6456	C₂²	semidirect
125. #6455	C₂²	semidirect
126. #6455	C₂²	semidirect
127. #6455	C₂²	semidirect
128. #6455	C₂²	semidirect
129. #6455	C₂²	semidirect
130. D₇×C₄⋊C₄	C₂²	semidirect
131. D₇×C₄⋊C₄	C₂²	semidirect
132. D₇×C₄⋊C₄	C₂²	semidirect
133. #6453	C₂²	semidirect
134. #6453	C₂²	semidirect
135. #6452	C₂²	semidirect
136. #6452	C₂²	semidirect
137. #6451	C₂²	semidirect
138. #6450	C₂²	semidirect
139. #6449	C₂²	semidirect
141. #6448	C₂²	semidirect
142. #6448	C₂²	semidirect
143. #6448	C₂²	semidirect
144. #6448	C₂²	semidirect
145. #6448	C₂²	semidirect
149. #6447	C₂²	semidirect
150. #6447	C₂²	semidirect
151. #6447	C₂²	semidirect
152. #6447	C₂²	semidirect
155. #6446	C₂²	semidirect
156. #6446	C₂²	semidirect
157. #6446	C₂²	semidirect
158. #6446	C₂²	semidirect
159. #6446	C₂²	semidirect
164. #6445	C₂²	semidirect
165. #6445	C₂²	semidirect
166. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
167. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
171. D₇×C₂²⋊C₄	C₂²	semidirect
172. D₇×C₂²⋊C₄	C₂²	semidirect
173. D₇×C₂²⋊C₄	C₂²	semidirect
174. #6442	C₂²	semidirect
175. #6442	C₂²	semidirect
176. #6442	C₂²	semidirect
177. #6442	C₂²	semidirect
178. #6441	C₂²	semidirect
179. #6438	C₂²	semidirect
180. #6438	C₂²	semidirect
182. C₄×D₂₈	C₂²	semidirect
183. C₄×D₂₈	C₂²	semidirect
184. #6435	C₂²	semidirect
185. #6435	C₂²	semidirect
186. C₄×Dic₁₄	C₂²	semidirect
370. #539	D₇	semidirect
494. #126	C₂×D₇	semidirect
495. #126	C₂×D₇	semidirect
500. #125	C₂×D₇	semidirect
501. #125	C₂×D₇	semidirect
540. #123	C₂×D₇	semidirect
541. #123	C₂×D₇	semidirect
555. C₂²⋊Q₈	C₂×D₇	semidirect
556. C₂²⋊Q₈	C₂×D₇	semidirect
557. C₂²⋊Q₈	C₂×D₇	semidirect
610. C₄×D₄	C₂×D₇	semidirect
611. C₄×D₄	C₂×D₇	semidirect
622. C₂×C₄⋊C₄	C₂×D₇	semidirect
949. C₇	#3533	semidirect

Maximal subgroups

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

subgroup	index
C₇×#539	2
#90401	2
#90396	2
#90395	2
#90391	2
#90386	2
#90385	2
#90384	2
#90357	2
#90354	2
#90351	2
#90350	2
#90348	2
#90344	2
D₇×#123	2
#90338	2
#90337	2
#90331	2
#90322	2
#90321	2
#90318	2
#90304	2
#90298	2
#90253	2
#90250	2
#90241	2
#90238	2
#90205	2
#90198	2
#3533	7