Subgroups — C₇×#62055 #13239271

Order 1792.

1890 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3543	C₂	1	1	yes	maximal, characteristic
2	C₇×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3324	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3310	C₂	1	2	yes	maximal, complemented
9	C₇×#3304	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3296	C₂	1	2	yes	maximal, complemented
11	C₇×D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×D₄×SD₁₆	C₂	1	2	yes	maximal, complemented
13	C₇×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3266	C₂	1	2	yes	maximal, complemented
15	C₇×#3260	C₂	1	2	yes	maximal, complemented
16	C₇×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3222	C₂	1	2	yes	maximal, complemented
18	C₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3126	C₂	1	2	yes	maximal, complemented
20	C₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3043	C₂	1	2	yes	maximal, complemented
22	C₂×C₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#137	C₂²	1	2	yes	complemented
25	C₂²×C₇×SD₁₆	C₂²	1	2	yes	complemented
26	C₂²×C₇×SD₁₆	C₂²	1	2	yes	complemented
27	C₇×#560	—	2	2	no	—
28	C₇×#559	C₂²	1	1	yes	characteristic
29	C₇×#557	—	2	1	no	—
30	C₇×#557	C₂²	1	1	yes	characteristic, complemented
31	C₇×#557	C₂²	1	1	yes	characteristic, complemented
32	C₇×#556	—	2	1	no	—
33	C₇×#556	C₂²	1	1	yes	characteristic, complemented
34	C₇×#552	—	2	2	no	—
35	C₇×#552	C₂²	1	2	yes	complemented
36	C₇×#550	C₂²	1	1	yes	characteristic
37	C₇×#550	C₂²	1	1	yes	characteristic
38	C₇×D₄×Q₈	C₂²	1	2	yes	complemented
39	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₇×#546	—	2	1	no	—
41	C₇×#546	C₂²	1	2	yes	—
42	C₇×D₄²	—	2	1	no	—
43	C₇×D₄²	C₂²	1	2	yes	—
44	C₇×D₄²	C₂²	1	1	yes	characteristic
45	C₇×#541	—	2	2	no	—
46	C₇×#541	C₂²	1	2	yes	complemented
47	C₇×#540	—	2	1	no	—
48	C₇×#540	C₂²	1	2	yes	—
49	C₇×#535	—	2	1	no	—
50	C₇×#535	C₂²	1	2	yes	—
51	C₇×#534	—	2	2	no	—
52	C₇×#533	—	2	1	no	—
53	C₇×#533	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₇×#127	C₂²	1	1	yes	characteristic
55	C₇×#529	—	2	1	no	—
56	C₇×#529	C₂²	1	1	yes	characteristic
57	C₇×#529	C₂²	1	1	yes	characteristic
58	C₇×#519	C₂²	1	2	yes	complemented
59	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
60	C₇×#497	C₂²	1	2	yes	complemented
61	C₇×#492	C₂²	1	1	yes	characteristic
62	C₇×#492	C₂²	1	1	yes	characteristic, complemented
63	C₇×#492	C₂²	1	2	yes	complemented
64	C₇×#490	C₂²	1	2	yes	complemented
65	C₇×#488	C₂²	1	2	yes	complemented
66	C₇×#486	C₂²	1	1	yes	characteristic
67	C₇×#486	C₂²	1	1	yes	characteristic, complemented
68	C₇×#483	C₂²	1	1	yes	characteristic, complemented
69	C₇×#482	C₂²	1	2	yes	complemented
70	C₇×#482	C₂²	1	2	yes	complemented
71	C₇×#480	C₂²	1	1	yes	characteristic
72	C₇×#479	C₂²	1	2	yes	complemented
73	C₇×#479	C₂²	1	1	yes	characteristic, complemented
74	C₇×#479	C₂²	1	1	yes	characteristic, complemented
75	C₇×#478	C₂²	1	2	yes	complemented
76	C₇×#478	C₂²	1	2	yes	complemented
77	C₇×#475	C₂²	1	1	yes	characteristic, complemented
78	C₇×#474	C₂²	1	1	yes	characteristic, complemented
79	C₇×#468	C₂²	1	2	yes	complemented
80	C₇×#468	C₂²	1	2	yes	complemented
81	C₇×#467	C₂²	1	2	yes	complemented
82	C₇×#465	C₂²	1	2	yes	—
83	C₇×#465	C₂²	1	2	yes	complemented
84	C₇×#465	C₂²	1	2	yes	complemented
85	C₇×#464	C₂²	1	1	yes	characteristic, complemented
86	C₇×#464	C₂²	1	2	yes	complemented
87	C₇×#464	C₂²	1	2	yes	complemented
88	C₇×#464	C₂²	1	2	yes	complemented
89	C₇×#464	C₂²	1	1	yes	characteristic, complemented
90	C₇×#462	C₂²	1	1	yes	characteristic, complemented
91	C₇×#461	C₂²	1	1	yes	characteristic, complemented
92	C₇×#461	C₂²	1	2	yes	complemented
93	C₇×#461	C₂²	1	2	yes	complemented
94	C₇×#460	C₂²	1	1	yes	characteristic
95	C₇×#460	C₂²	1	1	yes	characteristic
96	C₇×#460	C₂²	1	2	yes	complemented
97	C₇×#460	C₂²	1	2	yes	complemented
98	C₇×#460	C₂²	1	2	yes	complemented
99	C₇×#460	C₂²	1	1	yes	characteristic, complemented
100	C₇×#460	C₂²	1	2	yes	complemented
101	C₇×#460	C₂²	1	2	yes	complemented
102	C₇×#460	C₂²	1	1	yes	characteristic, complemented
103	C₇×#460	C₂²	1	2	yes	complemented
104	C₇×#452	C₂²	1	2	yes	complemented
105	C₇×#452	C₂²	1	2	yes	complemented
106	C₇×#451	C₂²	1	1	yes	characteristic, complemented
107	C₇×#450	C₂²	1	2	yes	complemented
108	C₇×#450	C₂²	1	2	yes	complemented
109	C₇×#450	C₂²	1	2	yes	complemented
110	C₇×#450	C₂²	1	2	yes	complemented
111	C₇×#448	C₂²	1	1	yes	characteristic
112	C₇×#448	C₂²	1	2	yes	complemented
113	C₇×#448	C₂²	1	2	yes	complemented
114	C₇×#446	C₂²	1	1	yes	characteristic, complemented
115	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
116	C₇×#440	C₂²	1	2	yes	complemented
117	C₇×#440	C₂²	1	2	yes	complemented
118	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
122	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
123	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
124	C₇×#436	C₂²	1	1	yes	characteristic, complemented
125	C₇×#435	C₂²	1	2	yes	complemented
126	C₇×C₈×D₄	C₂²	1	2	yes	complemented
127	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
128	C₇×#433	C₂²	1	2	yes	complemented
129	C₇×#431	C₂²	1	1	yes	characteristic, complemented
130	C₇×#424	C₂²	1	2	yes	complemented
131	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	C₇×#418	C₂²	1	2	yes	complemented
133	C₇×#416	C₂²	1	2	yes	complemented
134	C₂×C₇×#102	C₂²	1	2	yes	complemented
135	#62055	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	1	no	—
137	C₂×C₇×#41	C₂³	1	2	yes	—
138	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
139	C₂²×C₇×Q₈	C₂³	1	2	yes	—
140	C₂²×C₇×D₄	—	2	2	no	—
141	C₂²×C₇×D₄	—	2	1	no	—
142	C₂²×C₇×D₄	—	2	1	no	—
143	C₂²×C₇×D₄	—	2	1	no	—
144	C₂²×C₇×D₄	C₂³	1	2	yes	—
145	C₂²×C₇×D₄	C₂³	1	2	yes	—
146	C₇×#137	—	4	4	no	—
147	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
149	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
150	C₂×C₇×SD₁₆	—	4	4	no	—
151	C₂×C₇×SD₁₆	—	4	4	no	—
152	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
158	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
159	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
160	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
161	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
162	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
163	C₂×C₇×M₁₆	C₂³	1	2	yes	—
164	C₂²×C₇×C₈	C₂³	1	2	yes	—
165	C₂²×C₇×C₈	C₂³	1	2	yes	—
166	C₇×C₄⋊Q₈	—	2	1	no	—
167	C₇×C₄⋊Q₈	—	2	1	no	—
168	C₇×C₄⋊Q₈	—	2	2	no	—
169	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₇×#127	—	2	1	no	—
173	C₇×#127	—	2	1	no	—
174	C₇×#127	—	2	1	no	—
175	C₇×#127	C₂³	1	1	yes	characteristic
176	C₇×#127	C₂³	1	1	yes	characteristic
177	C₇×#127	C₂³	1	2	yes	—
178	C₇×#127	C₂³	1	2	yes	—
179	C₇×#126	—	2	2	no	—
180	C₇×#126	—	2	2	no	—
181	C₇×#126	—	2	2	no	—
182	C₇×#126	—	2	2	no	—
183	C₇×#126	—	2	1	no	—
184	C₇×#126	D₄	1	2	yes	—
185	C₇×#125	—	2	1	no	—
186	C₇×#125	—	2	2	no	—
187	C₇×#125	—	2	2	no	—
188	C₇×#125	—	2	2	no	—
189	C₇×#125	—	2	2	no	—
190	C₇×#125	—	2	2	no	—
191	C₇×#125	—	2	1	no	—
192	C₇×#125	D₄	1	1	yes	characteristic
193	C₇×#125	C₂³	1	2	yes	—
194	C₇×#125	C₂³	1	1	yes	characteristic
195	C₇×#124	—	2	1	no	—
196	C₇×#124	—	2	1	no	—
197	C₇×#124	D₄	1	1	yes	characteristic
198	C₇×#124	C₂³	1	2	yes	—
199	C₇×#124	C₂³	1	1	yes	characteristic
200	C₇×#123	—	2	2	no	—
201	C₇×#123	—	2	1	no	—
202	C₇×#123	—	2	2	no	—
203	C₇×#123	—	2	2	no	—
204	C₇×#123	—	2	2	no	—
205	C₇×#123	—	2	2	no	—
206	C₇×#123	D₄	1	2	yes	—
207	C₇×C₂²⋊Q₈	—	2	1	no	—
208	C₇×C₂²⋊Q₈	—	2	2	no	—
209	C₇×C₂²⋊Q₈	—	2	2	no	—
210	C₇×C₂²⋊Q₈	—	2	2	no	—
211	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
212	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₇×#121	—	2	2	no	—
217	C₇×#121	—	2	2	no	—
218	C₇×#121	—	2	2	no	—
219	C₇×#121	—	2	1	no	—
220	C₇×#121	—	2	1	no	—
221	C₇×#121	—	2	2	no	—
222	C₇×#121	—	2	2	no	—
223	C₇×#121	—	2	2	no	—
224	C₇×#121	—	2	2	no	—
225	C₇×#121	—	2	2	no	—
226	C₇×#121	D₄	1	1	yes	characteristic
227	C₇×#121	C₂³	1	2	yes	—
228	C₇×#121	C₂³	1	2	yes	—
229	C₇×#121	C₂³	1	1	yes	characteristic
230	C₇×#120	—	2	2	no	—
231	C₇×#120	—	2	2	no	—
232	C₇×#120	—	2	2	no	—
233	C₇×#120	—	2	2	no	—
234	C₇×#120	—	2	2	no	—
235	C₇×#120	—	2	2	no	—
236	C₄×C₇×Q₈	—	2	1	no	—
237	C₄×C₇×Q₈	—	2	2	no	—
238	C₄×C₇×Q₈	—	2	2	no	—
239	C₄×C₇×Q₈	—	2	1	no	—
240	C₄×C₇×Q₈	—	2	1	no	—
241	C₄×C₇×Q₈	—	2	1	no	—
242	C₄×C₇×Q₈	—	2	1	no	—
243	C₄×C₇×Q₈	—	2	1	no	—
244	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
245	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
246	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
247	C₄×C₇×Q₈	C₂³	1	2	yes	—
248	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
249	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
250	C₄×C₇×Q₈	C₂³	1	2	yes	—
251	C₄×C₇×Q₈	C₂³	1	2	yes	—
252	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
253	C₄×C₇×D₄	—	2	2	no	—
254	C₄×C₇×D₄	—	2	1	no	—
255	C₄×C₇×D₄	—	2	1	no	—
256	C₄×C₇×D₄	—	2	1	no	—
257	C₄×C₇×D₄	—	2	1	no	—
258	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
259	C₄×C₇×D₄	C₂³	1	2	yes	—
260	C₄×C₇×D₄	C₂³	1	2	yes	—
261	C₄×C₇×D₄	C₂³	1	2	yes	—
262	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
263	C₇×#117	—	2	1	no	—
264	C₇×#117	—	2	2	no	—
265	C₇×#117	—	2	2	no	—
266	C₇×#117	—	2	2	no	—
267	C₇×#117	—	2	1	no	—
268	C₇×#117	C₂³	1	2	yes	—
269	C₇×#117	C₂³	1	2	yes	—
270	C₂×C₇×C₄⋊C₄	—	2	1	no	—
271	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²×C₇	—	2	1	no	—
274	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
275	C₇×#107	C₂³	1	2	yes	—
276	C₇×#107	C₂³	1	1	yes	characteristic
277	C₇×#107	C₂³	1	1	yes	characteristic
278	C₇×#106	C₂³	1	2	yes	—
279	C₇×#106	C₂³	1	1	yes	characteristic
280	C₇×#106	C₂³	1	1	yes	characteristic
281	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₇×C₄⋊C₈	C₂³	1	2	yes	—
284	C₇×C₄⋊C₈	C₂³	1	2	yes	—
285	C₇×C₄⋊C₈	C₂³	1	2	yes	—
286	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₇×#103	C₂³	1	2	yes	—
289	C₇×#103	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	1	yes	characteristic
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	1	yes	characteristic
293	C₇×#103	C₂³	1	1	yes	characteristic
294	C₇×#103	C₂³	1	1	yes	characteristic
295	C₇×#103	C₂³	1	1	yes	characteristic
296	C₇×#103	C₂³	1	1	yes	characteristic
297	C₇×#102	C₂³	1	2	yes	—
298	C₇×#102	C₂³	1	2	yes	—
299	C₇×#102	C₂³	1	2	yes	—
300	C₇×#102	C₂³	1	2	yes	—
301	C₇×#102	C₂³	1	2	yes	—
302	C₇×#102	C₂³	1	1	yes	characteristic
303	C₇×#102	C₂³	1	1	yes	characteristic
304	C₇×#102	C₂³	1	2	yes	—
305	C₇×#102	C₂³	1	2	yes	—
306	C₇×#102	C₂³	1	2	yes	—
307	C₇×#102	C₂³	1	2	yes	—
308	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
312	C₇×#97	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
315	C₄×C₇×C₈	C₂³	1	2	yes	—
316	#3543	C₂×C₇	1	1	yes	characteristic
317	#3523	C₂×C₇	1	1	yes	characteristic, complemented
318	#3400	C₂×C₇	1	1	yes	characteristic, complemented
319	#3392	C₂×C₇	1	1	yes	characteristic, complemented
320	#3368	C₂×C₇	1	1	yes	characteristic, complemented
321	#3365	C₂×C₇	1	1	yes	characteristic, complemented
322	#3324	C₂×C₇	1	1	yes	characteristic, complemented
323	#3310	C₂×C₇	1	2	yes	complemented
324	#3304	C₂×C₇	1	1	yes	characteristic, complemented
325	#3296	C₂×C₇	1	2	yes	complemented
326	D₄×SD₁₆	C₂×C₇	1	2	yes	complemented
327	D₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
328	#3278	C₂×C₇	1	1	yes	characteristic, complemented
329	#3266	C₂×C₇	1	2	yes	complemented
330	#3260	C₂×C₇	1	2	yes	complemented
331	#3248	C₂×C₇	1	1	yes	characteristic, complemented
332	#3222	C₂×C₇	1	2	yes	complemented
333	#3208	C₂×C₇	1	1	yes	characteristic, complemented
334	#3126	C₂×C₇	1	2	yes	complemented
335	#3108	C₂×C₇	1	1	yes	characteristic, complemented
336	#3043	C₂×C₇	1	2	yes	complemented
337	C₂×#460	C₂×C₇	1	1	yes	characteristic, complemented
338	#2994	C₂×C₇	1	1	yes	characteristic, complemented
339	C₂⁴×C₇	—	2	2	no	—
340	C₂⁴×C₇	—	2	2	no	—
341	C₇×#41	—	4	2	no	—
342	C₇×#41	—	4	2	no	—
343	C₇×#41	—	8	2	no	—
344	C₂×C₇×Q₈	—	2	1	no	—
345	C₂×C₇×Q₈	—	2	2	no	—
346	C₂×C₇×Q₈	—	2	1	no	—
347	C₂×C₇×Q₈	—	2	2	no	—
348	C₂×C₇×Q₈	—	2	4	no	—
349	C₂×C₇×Q₈	—	4	1	no	—
350	C₂×C₇×Q₈	—	4	2	no	—
351	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
352	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
353	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
354	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
355	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
356	C₂×C₇×D₄	—	2	1	no	—
357	C₂×C₇×D₄	—	2	2	no	—
358	C₂×C₇×D₄	—	2	2	no	—
359	C₂×C₇×D₄	—	2	2	no	—
360	C₂×C₇×D₄	—	2	1	no	—
361	C₂×C₇×D₄	—	2	1	no	—
362	C₂×C₇×D₄	—	2	2	no	—
363	C₂×C₇×D₄	—	2	2	no	—
364	C₂×C₇×D₄	—	2	1	no	—
365	C₂×C₇×D₄	—	2	2	no	—
366	C₂×C₇×D₄	—	2	2	no	—
367	C₂×C₇×D₄	—	2	2	no	—
368	C₂×C₇×D₄	—	2	2	no	—
369	C₂×C₇×D₄	—	2	1	no	—
370	C₂×C₇×D₄	—	4	2	no	—
371	C₂×C₇×D₄	—	4	2	no	—
372	C₂×C₇×D₄	—	4	2	no	—
373	C₂×C₇×D₄	—	4	2	no	—
374	C₂×C₇×D₄	—	8	2	no	—
375	C₂×C₇×D₄	—	8	2	no	—
376	C₂×C₇×D₄	—	8	2	no	—
377	C₂×C₇×D₄	—	8	4	no	—
378	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
379	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
380	C₂×C₇×D₄	C₂⁴	1	2	yes	—
381	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
382	C₂×C₇×D₄	C₂⁴	1	2	yes	—
383	C₂²×C₄×C₇	—	2	1	no	—
384	C₂²×C₄×C₇	—	2	1	no	—
385	C₂²×C₄×C₇	—	2	2	no	—
386	C₂²×C₄×C₇	—	2	1	no	—
387	C₂²×C₄×C₇	—	2	2	no	—
388	C₂²×C₄×C₇	—	2	2	no	—
389	C₂²×C₄×C₇	—	2	2	no	—
390	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
394	C₇×Q₁₆	—	2	2	no	—
395	C₇×Q₁₆	—	4	1	no	—
396	C₇×Q₁₆	—	4	2	no	—
397	C₇×SD₁₆	—	2	2	no	—
398	C₇×SD₁₆	—	2	4	no	—
399	C₇×SD₁₆	—	2	4	no	—
400	C₇×SD₁₆	—	4	2	no	—
401	C₇×SD₁₆	—	4	2	no	—
402	C₇×SD₁₆	—	4	2	no	—
403	C₇×SD₁₆	—	4	2	no	—
404	C₇×SD₁₆	—	4	1	no	—
405	C₇×SD₁₆	—	4	2	no	—
406	C₇×SD₁₆	—	4	2	no	—
407	C₇×SD₁₆	—	4	2	no	—
408	C₇×M₁₆	—	4	2	no	—
409	C₂×C₇×C₈	—	4	2	no	—
410	C₂×C₇×C₈	—	4	2	no	—
411	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
412	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
413	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
414	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
415	C₂×C₇×C₈	C₂⁴	1	2	yes	—
416	C₂×C₇×C₈	C₂⁴	1	2	yes	—
417	C₇×C₄⋊C₄	—	2	1	no	—
418	C₇×C₄⋊C₄	—	2	1	no	—
419	C₇×C₄⋊C₄	—	2	1	no	—
420	C₇×C₄⋊C₄	—	2	1	no	—
421	C₇×C₄⋊C₄	—	2	1	no	—
422	C₇×C₄⋊C₄	—	2	2	no	—
423	C₇×C₄⋊C₄	—	2	2	no	—
424	C₇×C₄⋊C₄	—	2	2	no	—
425	C₇×C₄⋊C₄	—	2	1	no	—
426	C₇×C₄⋊C₄	—	2	1	no	—
427	C₇×C₄⋊C₄	—	2	1	no	—
428	C₇×C₄⋊C₄	—	2	2	no	—
429	C₇×C₄⋊C₄	—	2	1	no	—
430	C₇×C₄⋊C₄	—	2	2	no	—
431	C₇×C₄⋊C₄	—	2	1	no	—
432	C₇×C₄⋊C₄	—	2	1	no	—
433	C₇×C₄⋊C₄	—	2	2	no	—
434	C₇×C₄⋊C₄	—	2	2	no	—
435	C₇×C₄⋊C₄	—	2	2	no	—
436	C₇×C₄⋊C₄	—	2	2	no	—
437	C₇×C₄⋊C₄	—	2	2	no	—
438	C₇×C₄⋊C₄	—	2	1	no	—
439	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
440	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
441	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
442	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
443	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
444	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
445	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
446	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
447	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
448	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
449	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
450	C₇×C₂²⋊C₄	—	2	1	no	—
451	C₇×C₂²⋊C₄	—	2	2	no	—
452	C₇×C₂²⋊C₄	—	2	2	no	—
453	C₇×C₂²⋊C₄	—	2	2	no	—
454	C₇×C₂²⋊C₄	—	2	2	no	—
455	C₇×C₂²⋊C₄	—	2	2	no	—
456	C₇×C₂²⋊C₄	—	2	2	no	—
457	C₇×C₂²⋊C₄	—	2	1	no	—
458	C₇×C₂²⋊C₄	—	2	1	no	—
459	C₇×C₂²⋊C₄	—	2	1	no	—
460	C₇×C₂²⋊C₄	—	2	2	no	—
461	C₇×C₂²⋊C₄	—	2	2	no	—
462	C₇×C₂²⋊C₄	—	2	1	no	—
463	C₇×C₂²⋊C₄	—	2	2	no	—
464	C₇×C₂²⋊C₄	—	2	2	no	—
465	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
466	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
467	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
468	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
469	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
470	C₄²×C₇	—	2	1	no	—
471	C₄²×C₇	—	2	1	no	—
472	C₄²×C₇	—	2	1	no	—
473	C₄²×C₇	—	2	1	no	—
474	C₄²×C₇	—	2	2	no	—
475	C₄²×C₇	—	2	2	no	—
476	C₄²×C₇	—	2	2	no	—
477	C₄²×C₇	—	2	1	no	—
478	C₄²×C₇	—	2	2	no	—
479	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
480	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
481	C₄²×C₇	C₂⁴	1	1	yes	characteristic
482	C₄²×C₇	C₂⁴	1	2	yes	—
483	C₄²×C₇	C₂⁴	1	1	yes	characteristic
484	C₂×#137	C₂²×C₇	1	2	yes	complemented
485	C₂²×SD₁₆	C₂²×C₇	1	2	yes	complemented
486	C₂²×SD₁₆	C₂²×C₇	1	2	yes	complemented
487	#560	—	2	2	no	—
488	#559	C₂²×C₇	1	1	yes	characteristic
489	#557	—	2	1	no	—
490	#557	C₂²×C₇	1	1	yes	characteristic, complemented
491	#557	C₂²×C₇	1	1	yes	characteristic, complemented
492	#556	—	2	1	no	—
493	#556	C₂²×C₇	1	1	yes	characteristic, complemented
494	#552	—	2	2	no	—
495	#552	C₂²×C₇	1	2	yes	complemented
496	#550	C₂²×C₇	1	1	yes	characteristic
497	#550	C₂²×C₇	1	1	yes	characteristic
498	D₄×Q₈	C₂²×C₇	1	2	yes	complemented
499	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
500	#546	—	2	1	no	—
501	#546	C₂²×C₇	1	2	yes	—
502	D₄²	—	2	1	no	—
503	D₄²	C₂²×C₇	1	2	yes	—
504	D₄²	C₂²×C₇	1	1	yes	characteristic
505	#541	—	2	2	no	—
506	#541	C₂²×C₇	1	2	yes	complemented
507	#540	—	2	1	no	—
508	#540	C₂²×C₇	1	2	yes	—
509	#535	—	2	1	no	—
510	#535	C₂²×C₇	1	2	yes	—
511	#534	—	2	2	no	—
512	#533	—	2	1	no	—
513	#533	C₂²×C₇	1	1	yes	characteristic, complemented
514	C₂×#127	C₂²×C₇	1	1	yes	characteristic
515	#529	—	2	1	no	—
516	#529	C₂²×C₇	1	1	yes	characteristic
517	#529	C₂²×C₇	1	1	yes	characteristic
518	#519	C₂²×C₇	1	2	yes	complemented
519	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
520	#497	C₂²×C₇	1	2	yes	complemented
521	#492	C₂²×C₇	1	1	yes	characteristic
522	#492	C₂²×C₇	1	1	yes	characteristic, complemented
523	#492	C₂²×C₇	1	2	yes	complemented
524	#490	C₂²×C₇	1	2	yes	complemented
525	#488	C₂²×C₇	1	2	yes	complemented
526	#486	C₂²×C₇	1	1	yes	characteristic
527	#486	C₂²×C₇	1	1	yes	characteristic, complemented
528	#483	C₂²×C₇	1	1	yes	characteristic, complemented
529	#482	C₂²×C₇	1	2	yes	complemented
530	#482	C₂²×C₇	1	2	yes	complemented
531	#480	C₂²×C₇	1	1	yes	characteristic
532	#479	C₂²×C₇	1	1	yes	characteristic, complemented
533	#479	C₂²×C₇	1	1	yes	characteristic, complemented
534	#479	C₂²×C₇	1	2	yes	complemented
535	#478	C₂²×C₇	1	2	yes	complemented
536	#478	C₂²×C₇	1	2	yes	complemented
537	#475	C₂²×C₇	1	1	yes	characteristic, complemented
538	#474	C₂²×C₇	1	1	yes	characteristic, complemented
539	#468	C₂²×C₇	1	2	yes	complemented
540	#468	C₂²×C₇	1	2	yes	complemented
541	#467	C₂²×C₇	1	2	yes	complemented
542	#465	C₂²×C₇	1	2	yes	—
543	#465	C₂²×C₇	1	2	yes	complemented
544	#465	C₂²×C₇	1	2	yes	complemented
545	#464	C₂²×C₇	1	1	yes	characteristic, complemented
546	#464	C₂²×C₇	1	1	yes	characteristic, complemented
547	#464	C₂²×C₇	1	2	yes	complemented
548	#464	C₂²×C₇	1	2	yes	complemented
549	#464	C₂²×C₇	1	2	yes	complemented
550	#462	C₂²×C₇	1	1	yes	characteristic, complemented
551	#461	C₂²×C₇	1	1	yes	characteristic, complemented
552	#461	C₂²×C₇	1	2	yes	complemented
553	#461	C₂²×C₇	1	2	yes	complemented
554	#460	C₂²×C₇	1	1	yes	characteristic
555	#460	C₂²×C₇	1	1	yes	characteristic
556	#460	C₂²×C₇	1	1	yes	characteristic, complemented
557	#460	C₂²×C₇	1	2	yes	complemented
558	#460	C₂²×C₇	1	2	yes	complemented
559	#460	C₂²×C₇	1	2	yes	complemented
560	#460	C₂²×C₇	1	1	yes	characteristic, complemented
561	#460	C₂²×C₇	1	2	yes	complemented
562	#460	C₂²×C₇	1	2	yes	complemented
563	#460	C₂²×C₇	1	2	yes	complemented
564	#452	C₂²×C₇	1	2	yes	complemented
565	#452	C₂²×C₇	1	2	yes	complemented
566	#451	C₂²×C₇	1	1	yes	characteristic, complemented
567	#450	C₂²×C₇	1	2	yes	complemented
568	#450	C₂²×C₇	1	2	yes	complemented
569	#450	C₂²×C₇	1	2	yes	complemented
570	#450	C₂²×C₇	1	2	yes	complemented
571	#448	C₂²×C₇	1	1	yes	characteristic
572	#448	C₂²×C₇	1	2	yes	complemented
573	#448	C₂²×C₇	1	2	yes	complemented
574	#446	C₂²×C₇	1	1	yes	characteristic, complemented
575	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
576	#440	C₂²×C₇	1	2	yes	complemented
577	#440	C₂²×C₇	1	2	yes	complemented
578	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
579	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
580	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
581	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
582	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
583	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
584	#436	C₂²×C₇	1	1	yes	characteristic, complemented
585	#435	C₂²×C₇	1	2	yes	complemented
586	C₈×D₄	C₂²×C₇	1	2	yes	complemented
587	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
588	#433	C₂²×C₇	1	2	yes	complemented
589	#431	C₂²×C₇	1	1	yes	characteristic, complemented
590	#424	C₂²×C₇	1	2	yes	complemented
591	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
592	#418	C₂²×C₇	1	2	yes	complemented
593	#416	C₂²×C₇	1	2	yes	complemented
594	C₂×#102	C₂²×C₇	1	2	yes	complemented
595	C₂³×C₇	—	2	1	no	—
596	C₂³×C₇	—	2	2	no	—
597	C₂³×C₇	—	2	2	no	—
598	C₂³×C₇	—	4	4	no	—
599	C₂³×C₇	—	8	2	no	—
600	C₂³×C₇	—	8	2	no	—
601	C₂³×C₇	—	8	2	no	—
602	C₂³×C₇	—	8	2	no	—
603	C₂³×C₇	—	8	2	no	—
604	C₂³×C₇	C₂²×D₄	1	2	yes	—
605	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
606	C₇×Q₈	—	2	2	no	—
607	C₇×Q₈	—	2	1	no	—
608	C₇×Q₈	—	2	1	no	—
609	C₇×Q₈	—	2	2	no	—
610	C₇×Q₈	—	2	1	no	—
611	C₇×Q₈	—	2	2	no	—
612	C₇×Q₈	—	2	1	no	—
613	C₇×Q₈	—	2	1	no	—
614	C₇×Q₈	—	4	4	no	—
615	C₇×Q₈	—	4	2	no	—
616	C₇×Q₈	—	4	2	no	—
617	C₇×Q₈	H(5,𝔽₂)	1	2	yes	—
618	C₇×D₄	—	2	4	no	—
619	C₇×D₄	—	2	2	no	—
620	C₇×D₄	—	2	1	no	—
621	C₇×D₄	—	2	2	no	—
622	C₇×D₄	—	2	2	no	—
623	C₇×D₄	—	2	1	no	—
624	C₇×D₄	—	2	2	no	—
625	C₇×D₄	—	2	2	no	—
626	C₇×D₄	—	4	2	no	—
627	C₇×D₄	—	4	2	no	—
628	C₇×D₄	—	4	2	no	—
629	C₇×D₄	—	8	2	no	—
630	C₇×D₄	—	8	2	no	—
631	C₇×D₄	—	8	2	no	—
632	C₇×D₄	—	8	1	no	—
633	C₇×D₄	—	8	2	no	—
634	C₇×D₄	—	8	1	no	—
635	C₇×D₄	—	8	2	no	—
636	C₇×D₄	—	8	2	no	—
637	C₇×D₄	—	8	2	no	—
638	C₇×D₄	—	8	2	no	—
639	C₇×D₄	—	8	2	no	—
640	C₂×C₄×C₇	—	2	2	no	—
641	C₂×C₄×C₇	—	2	1	no	—
642	C₂×C₄×C₇	—	2	2	no	—
643	C₂×C₄×C₇	—	2	1	no	—
644	C₂×C₄×C₇	—	2	2	no	—
645	C₂×C₄×C₇	—	2	1	no	—
646	C₂×C₄×C₇	—	2	2	no	—
647	C₂×C₄×C₇	—	2	1	no	—
648	C₂×C₄×C₇	—	2	2	no	—
649	C₂×C₄×C₇	—	2	1	no	—
650	C₂×C₄×C₇	—	2	1	no	—
651	C₂×C₄×C₇	—	2	2	no	—
652	C₂×C₄×C₇	—	2	1	no	—
653	C₂×C₄×C₇	—	2	1	no	—
654	C₂×C₄×C₇	—	2	1	no	—
655	C₂×C₄×C₇	—	4	2	no	—
656	C₂×C₄×C₇	—	4	4	no	—
657	C₂×C₄×C₇	—	4	2	no	—
658	C₂×C₄×C₇	—	4	2	no	—
659	C₂×C₄×C₇	—	8	2	no	—
660	C₂×C₄×C₇	—	8	2	no	—
661	C₂×C₄×C₇	—	8	2	no	—
662	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
663	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
664	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
665	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
666	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
667	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
668	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
669	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
670	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
671	C₇×C₈	—	2	1	no	—
672	C₇×C₈	—	2	2	no	—
673	C₇×C₈	—	2	2	no	—
674	C₇×C₈	—	2	1	no	—
675	C₇×C₈	—	2	1	no	—
676	C₇×C₈	—	2	1	no	—
677	C₂×#41	—	2	1	no	—
678	C₂×#41	C₂³×C₇	1	2	yes	—
679	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
680	C₂²×Q₈	C₂³×C₇	1	2	yes	—
681	C₂²×D₄	—	2	2	no	—
682	C₂²×D₄	—	2	1	no	—
683	C₂²×D₄	—	2	1	no	—
684	C₂²×D₄	—	2	1	no	—
685	C₂²×D₄	C₂³×C₇	1	2	yes	—
686	C₂²×D₄	C₂³×C₇	1	2	yes	—
687	#137	—	4	4	no	—
688	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
689	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
690	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
691	C₂×SD₁₆	—	4	4	no	—
692	C₂×SD₁₆	—	4	4	no	—
693	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
694	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
695	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
696	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
697	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
698	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
699	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
700	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
701	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
702	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
703	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
704	C₂×M₁₆	C₂³×C₇	1	2	yes	—
705	C₂²×C₈	C₂³×C₇	1	2	yes	—
706	C₂²×C₈	C₂³×C₇	1	2	yes	—
707	C₄⋊Q₈	—	2	1	no	—
708	C₄⋊Q₈	—	2	1	no	—
709	C₄⋊Q₈	—	2	2	no	—
710	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
712	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
713	#127	—	2	1	no	—
714	#127	—	2	1	no	—
715	#127	—	2	1	no	—
716	#127	C₂³×C₇	1	2	yes	—
717	#127	C₂³×C₇	1	1	yes	characteristic
718	#127	C₂³×C₇	1	1	yes	characteristic
719	#127	C₂³×C₇	1	2	yes	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#126	—	2	2	no	—
724	#126	—	2	1	no	—
725	#126	C₇×D₄	1	2	yes	—
726	#125	—	2	1	no	—
727	#125	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	2	2	no	—
731	#125	—	2	2	no	—
732	#125	—	2	1	no	—
733	#125	C₇×D₄	1	1	yes	characteristic
734	#125	C₂³×C₇	1	1	yes	characteristic
735	#125	C₂³×C₇	1	2	yes	—
736	#124	—	2	1	no	—
737	#124	—	2	1	no	—
738	#124	C₇×D₄	1	1	yes	characteristic
739	#124	C₂³×C₇	1	1	yes	characteristic
740	#124	C₂³×C₇	1	2	yes	—
741	#123	—	2	2	no	—
742	#123	—	2	1	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	C₇×D₄	1	2	yes	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
753	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
754	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
755	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
756	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
757	#121	—	2	2	no	—
758	#121	—	2	2	no	—
759	#121	—	2	2	no	—
760	#121	—	2	1	no	—
761	#121	—	2	1	no	—
762	#121	—	2	2	no	—
763	#121	—	2	2	no	—
764	#121	—	2	2	no	—
765	#121	—	2	2	no	—
766	#121	—	2	2	no	—
767	#121	C₇×D₄	1	1	yes	characteristic
768	#121	C₂³×C₇	1	1	yes	characteristic
769	#121	C₂³×C₇	1	2	yes	—
770	#121	C₂³×C₇	1	2	yes	—
771	#120	—	2	2	no	—
772	#120	—	2	2	no	—
773	#120	—	2	2	no	—
774	#120	—	2	2	no	—
775	#120	—	2	2	no	—
776	#120	—	2	2	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	2	no	—
779	C₄×Q₈	—	2	2	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₇	1	2	yes	—
790	C₄×Q₈	C₂³×C₇	1	2	yes	—
791	C₄×Q₈	C₂³×C₇	1	2	yes	—
792	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
793	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₇	1	2	yes	—
801	C₄×D₄	C₂³×C₇	1	2	yes	—
802	C₄×D₄	C₂³×C₇	1	2	yes	—
803	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
804	#117	—	2	1	no	—
805	#117	—	2	2	no	—
806	#117	—	2	2	no	—
807	#117	—	2	2	no	—
808	#117	—	2	1	no	—
809	#117	C₂³×C₇	1	2	yes	—
810	#117	C₂³×C₇	1	2	yes	—
811	C₂×C₄⋊C₄	—	2	1	no	—
812	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
813	C₂×C₂²⋊C₄	—	2	2	no	—
814	C₂×C₄²	—	2	1	no	—
815	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
816	#107	C₂³×C₇	1	1	yes	characteristic
817	#107	C₂³×C₇	1	1	yes	characteristic
818	#107	C₂³×C₇	1	2	yes	—
819	#106	C₂³×C₇	1	1	yes	characteristic
820	#106	C₂³×C₇	1	2	yes	—
821	#106	C₂³×C₇	1	1	yes	characteristic
822	C₄⋊C₈	C₂³×C₇	1	2	yes	—
823	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
825	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₇	1	2	yes	—
827	C₄⋊C₈	C₂³×C₇	1	2	yes	—
828	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
829	#103	C₂³×C₇	1	1	yes	characteristic
830	#103	C₂³×C₇	1	2	yes	—
831	#103	C₂³×C₇	1	1	yes	characteristic
832	#103	C₂³×C₇	1	1	yes	characteristic
833	#103	C₂³×C₇	1	2	yes	—
834	#103	C₂³×C₇	1	1	yes	characteristic
835	#103	C₂³×C₇	1	1	yes	characteristic
836	#103	C₂³×C₇	1	1	yes	characteristic
837	#103	C₂³×C₇	1	2	yes	—
838	#102	C₂³×C₇	1	2	yes	—
839	#102	C₂³×C₇	1	2	yes	—
840	#102	C₂³×C₇	1	2	yes	—
841	#102	C₂³×C₇	1	2	yes	—
842	#102	C₂³×C₇	1	2	yes	—
843	#102	C₂³×C₇	1	1	yes	characteristic
844	#102	C₂³×C₇	1	2	yes	—
845	#102	C₂³×C₇	1	2	yes	—
846	#102	C₂³×C₇	1	2	yes	—
847	#102	C₂³×C₇	1	1	yes	characteristic
848	#102	C₂³×C₇	1	2	yes	—
849	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
850	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
851	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
852	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
853	#97	C₂³×C₇	1	2	yes	—
854	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
855	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
856	C₄×C₈	C₂³×C₇	1	2	yes	—
857	C₂²×C₇	—	2	1	no	—
858	C₂²×C₇	—	2	1	no	—
859	C₂²×C₇	—	2	2	no	—
860	C₂²×C₇	—	2	2	no	—
861	C₂²×C₇	—	2	2	no	—
862	C₂²×C₇	—	4	2	no	—
863	C₂²×C₇	—	4	1	no	—
864	C₂²×C₇	—	4	2	no	—
865	C₂²×C₇	—	4	1	no	—
866	C₂²×C₇	—	4	2	no	—
867	C₂²×C₇	—	4	2	no	—
868	C₂²×C₇	—	4	1	no	—
869	C₂²×C₇	—	4	2	no	—
870	C₂²×C₇	—	4	2	no	—
871	C₂²×C₇	—	16	4	no	—
872	C₂²×C₇	—	16	4	no	—
873	C₂²×C₇	#577	1	2	yes	—
874	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
875	C₄×C₇	—	2	2	no	—
876	C₄×C₇	—	2	1	no	—
877	C₄×C₇	—	2	2	no	—
878	C₄×C₇	—	2	1	no	—
879	C₄×C₇	—	2	1	no	—
880	C₄×C₇	—	2	1	no	—
881	C₄×C₇	—	2	2	no	—
882	C₄×C₇	—	2	2	no	—
883	C₄×C₇	—	4	1	no	—
884	C₄×C₇	—	4	2	no	—
885	C₄×C₇	—	4	1	no	—
886	C₄×C₇	—	4	1	no	—
887	C₄×C₇	—	4	1	no	—
888	C₄×C₇	—	4	1	no	—
889	C₄×C₇	—	4	1	no	—
890	C₄×C₇	—	4	2	no	—
891	C₄×C₇	#577	1	2	yes	—
892	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
893	C₄×C₇	#585	1	1	yes	characteristic
894	C₂⁴	—	2	2	no	—
895	C₂⁴	—	2	2	no	—
896	#41	—	4	2	no	—
897	#41	—	4	2	no	—
898	#41	—	8	2	no	—
899	C₂×Q₈	—	2	1	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	4	no	—
904	C₂×Q₈	—	4	1	no	—
905	C₂×Q₈	—	4	2	no	—
906	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
907	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
908	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
909	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
910	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	4	2	no	—
926	C₂×D₄	—	4	2	no	—
927	C₂×D₄	—	4	2	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	8	2	no	—
930	C₂×D₄	—	8	2	no	—
931	C₂×D₄	—	8	2	no	—
932	C₂×D₄	—	8	4	no	—
933	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
934	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
935	C₂×D₄	C₂⁴×C₇	1	2	yes	—
936	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
937	C₂×D₄	C₂⁴×C₇	1	2	yes	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
946	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
949	Q₁₆	—	2	2	no	—
950	Q₁₆	—	4	1	no	—
951	Q₁₆	—	4	2	no	—
952	SD₁₆	—	2	2	no	—
953	SD₁₆	—	2	4	no	—
954	SD₁₆	—	2	4	no	—
955	SD₁₆	—	4	2	no	—
956	SD₁₆	—	4	2	no	—
957	SD₁₆	—	4	2	no	—
958	SD₁₆	—	4	2	no	—
959	SD₁₆	—	4	1	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	—	4	2	no	—
962	SD₁₆	—	4	2	no	—
963	M₁₆	—	4	2	no	—
964	C₂×C₈	—	4	2	no	—
965	C₂×C₈	—	4	2	no	—
966	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₇	1	2	yes	—
971	C₂×C₈	C₂⁴×C₇	1	2	yes	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
995	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
996	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
997	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
998	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
999	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1000	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1003	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1004	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1021	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1022	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1023	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1024	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1035	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₇	1	2	yes	—
1038	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1039	C₂×C₇	—	2	2	no	—
1040	C₂×C₇	—	4	2	no	—
1041	C₂×C₇	—	8	2	no	—
1042	C₂×C₇	—	8	1	no	—
1043	C₂×C₇	—	8	2	no	—
1044	C₂×C₇	#3488	1	1	yes	characteristic
1045	C₂×C₇	C₂×#577	1	1	yes	characteristic
1046	C₂×C₇	C₂×#577	1	1	yes	characteristic
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	4	4	no	—
1051	C₂³	—	8	2	no	—
1052	C₂³	—	8	2	no	—
1053	C₂³	—	8	2	no	—
1054	C₂³	—	8	2	no	—
1055	C₂³	—	8	2	no	—
1056	C₂³	C₂²×C₇×D₄	1	2	yes	—
1057	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1058	Q₈	—	2	1	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	1	no	—
1061	Q₈	—	2	2	no	—
1062	Q₈	—	2	1	no	—
1063	Q₈	—	2	2	no	—
1064	Q₈	—	2	1	no	—
1065	Q₈	—	2	1	no	—
1066	Q₈	—	4	4	no	—
1067	Q₈	—	4	2	no	—
1068	Q₈	—	4	2	no	—
1069	Q₈	C₇×H(5,𝔽₂)	1	2	yes	—
1070	D₄	—	2	4	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	2	no	—
1074	D₄	—	2	1	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	4	2	no	—
1079	D₄	—	4	2	no	—
1080	D₄	—	4	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	1	no	—
1085	D₄	—	8	2	no	—
1086	D₄	—	8	1	no	—
1087	D₄	—	8	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	4	2	no	—
1108	C₂×C₄	—	4	4	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	—	8	2	no	—
1114	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1115	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1116	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1117	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1118	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1119	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1120	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1121	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1122	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1123	C₈	—	2	1	no	—
1124	C₈	—	2	2	no	—
1125	C₈	—	2	2	no	—
1126	C₈	—	2	1	no	—
1127	C₈	—	2	1	no	—
1128	C₈	—	2	1	no	—
1129	C₇	#62055	1	1	yes	characteristic, direct product factor, Sylow
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	16	4	no	—
1145	C₂²	—	16	4	no	—
1146	C₂²	C₇×#577	1	2	yes	—
1147	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	2	no	—
1163	C₄	—	4	1	no	—
1164	C₄	C₇×#577	1	2	yes	—
1165	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1166	C₄	C₇×#585	1	1	yes	characteristic
1167	C₂	—	2	2	no	—
1168	C₂	—	4	2	no	—
1169	C₂	—	8	1	no	—
1170	C₂	—	8	2	no	—
1171	C₂	—	8	2	no	—
1172	C₂	C₇×#3488	1	1	yes	characteristic
1173	C₂	C₂×C₇×#577	1	1	yes	characteristic
1174	C₂	C₂×C₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3543	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#529 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3523	C₂	semidirect
3. C₇×#3400	C₂	semidirect
4. C₇×#3392	C₂	semidirect
5. C₇×#3368	C₂	semidirect
6. C₇×#3365	C₂	semidirect
7. C₇×#3324	C₂	semidirect
8. C₇×#3310	C₂	semidirect
9. C₇×#3304	C₂	semidirect
10. C₇×#3296	C₂	semidirect
11. C₇×D₄×SD₁₆	C₂	semidirect
12. C₇×D₄×SD₁₆	C₂	semidirect
13. C₇×#3278	C₂	semidirect
14. C₇×#3266	C₂	semidirect
15. C₇×#3260	C₂	semidirect
16. C₇×#3248	C₂	semidirect
17. C₇×#3222	C₂	semidirect
18. C₇×#3208	C₂	semidirect
19. C₇×#3126	C₂	semidirect
20. C₇×#3108	C₂	semidirect
21. C₇×#3043	C₂	semidirect
22. C₂×C₇×#460	C₂	semidirect
23. C₇×#2994	C₂	semidirect
24. C₂×C₇×#137	C₂²	semidirect
25. C₂²×C₇×SD₁₆	C₂²	semidirect
26. C₂²×C₇×SD₁₆	C₂²	semidirect
30. C₇×#557	C₂²	semidirect
31. C₇×#557	C₂²	semidirect
33. C₇×#556	C₂²	semidirect
35. C₇×#552	C₂²	semidirect
38. C₇×D₄×Q₈	C₂²	semidirect
39. C₇×D₄×Q₈	C₂²	semidirect
46. C₇×#541	C₂²	semidirect
53. C₇×#533	C₂²	semidirect
58. C₇×#519	C₂²	semidirect
59. C₂×C₄×C₇×Q₈	C₂²	semidirect
60. C₇×#497	C₂²	semidirect
62. C₇×#492	C₂²	semidirect
63. C₇×#492	C₂²	semidirect
64. C₇×#490	C₂²	semidirect
65. C₇×#488	C₂²	semidirect
67. C₇×#486	C₂²	semidirect
68. C₇×#483	C₂²	semidirect
69. C₇×#482	C₂²	semidirect
70. C₇×#482	C₂²	semidirect
72. C₇×#479	C₂²	semidirect
73. C₇×#479	C₂²	semidirect
74. C₇×#479	C₂²	semidirect
75. C₇×#478	C₂²	semidirect
76. C₇×#478	C₂²	semidirect
77. C₇×#475	C₂²	semidirect
78. C₇×#474	C₂²	semidirect
79. C₇×#468	C₂²	semidirect
80. C₇×#468	C₂²	semidirect
81. C₇×#467	C₂²	semidirect
83. C₇×#465	C₂²	semidirect
84. C₇×#465	C₂²	semidirect
85. C₇×#464	C₂²	semidirect
86. C₇×#464	C₂²	semidirect
87. C₇×#464	C₂²	semidirect
88. C₇×#464	C₂²	semidirect
89. C₇×#464	C₂²	semidirect
90. C₇×#462	C₂²	semidirect
91. C₇×#461	C₂²	semidirect
92. C₇×#461	C₂²	semidirect
93. C₇×#461	C₂²	semidirect
96. C₇×#460	C₂²	semidirect
97. C₇×#460	C₂²	semidirect
98. C₇×#460	C₂²	semidirect
99. C₇×#460	C₂²	semidirect
100. C₇×#460	C₂²	semidirect
101. C₇×#460	C₂²	semidirect
102. C₇×#460	C₂²	semidirect
103. C₇×#460	C₂²	semidirect
104. C₇×#452	C₂²	semidirect
105. C₇×#452	C₂²	semidirect
106. C₇×#451	C₂²	semidirect
107. C₇×#450	C₂²	semidirect
108. C₇×#450	C₂²	semidirect
109. C₇×#450	C₂²	semidirect
110. C₇×#450	C₂²	semidirect
112. C₇×#448	C₂²	semidirect
113. C₇×#448	C₂²	semidirect
114. C₇×#446	C₂²	semidirect
115. C₇×C₈×Q₈	C₂²	semidirect
116. C₇×#440	C₂²	semidirect
117. C₇×#440	C₂²	semidirect
118. C₄×C₇×Q₁₆	C₂²	semidirect
119. C₄×C₇×Q₁₆	C₂²	semidirect
120. C₄×C₇×SD₁₆	C₂²	semidirect
121. C₄×C₇×SD₁₆	C₂²	semidirect
122. C₄×C₇×SD₁₆	C₂²	semidirect
123. C₄×C₇×SD₁₆	C₂²	semidirect
124. C₇×#436	C₂²	semidirect
125. C₇×#435	C₂²	semidirect
126. C₇×C₈×D₄	C₂²	semidirect
127. C₇×C₈×D₄	C₂²	semidirect
128. C₇×#433	C₂²	semidirect
129. C₇×#431	C₂²	semidirect
130. C₇×#424	C₂²	semidirect
131. C₂×C₇×C₄⋊C₈	C₂²	semidirect
132. C₇×#418	C₂²	semidirect
133. C₇×#416	C₂²	semidirect
134. C₂×C₇×#102	C₂²	semidirect
135. #62055	C₇	direct (N × H)
317. #3523	C₂×C₇	semidirect
318. #3400	C₂×C₇	semidirect
319. #3392	C₂×C₇	semidirect
320. #3368	C₂×C₇	semidirect
321. #3365	C₂×C₇	semidirect
322. #3324	C₂×C₇	semidirect
323. #3310	C₂×C₇	semidirect
324. #3304	C₂×C₇	semidirect
325. #3296	C₂×C₇	semidirect
326. D₄×SD₁₆	C₂×C₇	semidirect
327. D₄×SD₁₆	C₂×C₇	semidirect
328. #3278	C₂×C₇	semidirect
329. #3266	C₂×C₇	semidirect
330. #3260	C₂×C₇	semidirect
331. #3248	C₂×C₇	semidirect
332. #3222	C₂×C₇	semidirect
333. #3208	C₂×C₇	semidirect
334. #3126	C₂×C₇	semidirect
335. #3108	C₂×C₇	semidirect
336. #3043	C₂×C₇	semidirect
337. C₂×#460	C₂×C₇	semidirect
338. #2994	C₂×C₇	semidirect
484. C₂×#137	C₂²×C₇	semidirect
485. C₂²×SD₁₆	C₂²×C₇	semidirect
486. C₂²×SD₁₆	C₂²×C₇	semidirect
490. #557	C₂²×C₇	semidirect
491. #557	C₂²×C₇	semidirect
493. #556	C₂²×C₇	semidirect
495. #552	C₂²×C₇	semidirect
498. D₄×Q₈	C₂²×C₇	semidirect
499. D₄×Q₈	C₂²×C₇	semidirect
506. #541	C₂²×C₇	semidirect
513. #533	C₂²×C₇	semidirect
518. #519	C₂²×C₇	semidirect
519. C₂×C₄×Q₈	C₂²×C₇	semidirect
520. #497	C₂²×C₇	semidirect
522. #492	C₂²×C₇	semidirect
523. #492	C₂²×C₇	semidirect
524. #490	C₂²×C₇	semidirect
525. #488	C₂²×C₇	semidirect
527. #486	C₂²×C₇	semidirect
528. #483	C₂²×C₇	semidirect
529. #482	C₂²×C₇	semidirect
530. #482	C₂²×C₇	semidirect
532. #479	C₂²×C₇	semidirect
533. #479	C₂²×C₇	semidirect
534. #479	C₂²×C₇	semidirect
535. #478	C₂²×C₇	semidirect
536. #478	C₂²×C₇	semidirect
537. #475	C₂²×C₇	semidirect
538. #474	C₂²×C₇	semidirect
539. #468	C₂²×C₇	semidirect
540. #468	C₂²×C₇	semidirect
541. #467	C₂²×C₇	semidirect
543. #465	C₂²×C₇	semidirect
544. #465	C₂²×C₇	semidirect
545. #464	C₂²×C₇	semidirect
546. #464	C₂²×C₇	semidirect
547. #464	C₂²×C₇	semidirect
548. #464	C₂²×C₇	semidirect
549. #464	C₂²×C₇	semidirect
550. #462	C₂²×C₇	semidirect
551. #461	C₂²×C₇	semidirect
552. #461	C₂²×C₇	semidirect
553. #461	C₂²×C₇	semidirect
556. #460	C₂²×C₇	semidirect
557. #460	C₂²×C₇	semidirect
558. #460	C₂²×C₇	semidirect
559. #460	C₂²×C₇	semidirect
560. #460	C₂²×C₇	semidirect
561. #460	C₂²×C₇	semidirect
562. #460	C₂²×C₇	semidirect
563. #460	C₂²×C₇	semidirect
564. #452	C₂²×C₇	semidirect
565. #452	C₂²×C₇	semidirect
566. #451	C₂²×C₇	semidirect
567. #450	C₂²×C₇	semidirect
568. #450	C₂²×C₇	semidirect
569. #450	C₂²×C₇	semidirect
570. #450	C₂²×C₇	semidirect
572. #448	C₂²×C₇	semidirect
573. #448	C₂²×C₇	semidirect
574. #446	C₂²×C₇	semidirect
575. C₈×Q₈	C₂²×C₇	semidirect
576. #440	C₂²×C₇	semidirect
577. #440	C₂²×C₇	semidirect
578. C₄×Q₁₆	C₂²×C₇	semidirect
579. C₄×Q₁₆	C₂²×C₇	semidirect
580. C₄×SD₁₆	C₂²×C₇	semidirect
581. C₄×SD₁₆	C₂²×C₇	semidirect
582. C₄×SD₁₆	C₂²×C₇	semidirect
583. C₄×SD₁₆	C₂²×C₇	semidirect
584. #436	C₂²×C₇	semidirect
585. #435	C₂²×C₇	semidirect
586. C₈×D₄	C₂²×C₇	semidirect
587. C₈×D₄	C₂²×C₇	semidirect
588. #433	C₂²×C₇	semidirect
589. #431	C₂²×C₇	semidirect
590. #424	C₂²×C₇	semidirect
591. C₂×C₄⋊C₈	C₂²×C₇	semidirect
592. #418	C₂²×C₇	semidirect
593. #416	C₂²×C₇	semidirect
594. C₂×#102	C₂²×C₇	semidirect
1129. C₇	#62055	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3543	2
C₇×#3523	2
C₇×#3400	2
C₇×#3392	2
C₇×#3368	2
C₇×#3365	2
C₇×#3324	2
C₇×#3310	2
C₇×#3304	2
C₇×#3296	2
C₇×D₄×SD₁₆	2
C₇×#3278	2
C₇×#3266	2
C₇×#3260	2
C₇×#3248	2
C₇×#3222	2
C₇×#3208	2
C₇×#3126	2
C₇×#3108	2
C₇×#3043	2
C₂×C₇×#460	2
C₇×#2994	2
#62055	7

Subgroups — C7×#62055 #13239271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62055 #13239271