Subgroups — C₇×#62051 #13239267

Order 1792.

2020 conjugacy classes of subgroups.

The subgroup lattice has 1244 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, complemented
2	C₇×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3325	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3318	C₂	1	2	yes	maximal, complemented
9	C₇×#3305	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3297	C₂	1	2	yes	maximal, complemented
11	C₇×D₄×D₈	C₂	1	2	yes	maximal, complemented
12	C₇×D₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3264	C₂	1	2	yes	maximal, complemented
15	C₇×#3259	C₂	1	2	yes	maximal, complemented
16	C₇×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3220	C₂	1	2	yes	maximal, complemented
18	C₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3122	C₂	1	2	yes	maximal, complemented
20	C₇×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3041	C₂	1	2	yes	maximal, complemented
22	C₂×C₇×#459	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂²×C₇×D₈	C₂²	1	2	yes	complemented
26	C₂²×C₇×D₈	C₂²	1	2	yes	complemented
27	C₇×#560	—	2	2	no	—
28	C₇×#559	C₂²	1	1	yes	characteristic, complemented
29	C₇×#555	C₂²	1	1	yes	characteristic, complemented
30	C₇×#554	C₂²	1	1	yes	characteristic, complemented
31	C₇×#553	—	2	1	no	—
32	C₇×#553	C₂²	1	2	yes	complemented
33	C₇×#550	C₂²	1	1	yes	characteristic, complemented
34	C₇×#550	C₂²	1	1	yes	characteristic, complemented
35	C₇×#550	C₂²	1	1	yes	characteristic, complemented
36	C₇×#546	—	2	1	no	—
37	C₇×#546	—	2	2	no	—
38	C₇×#546	—	2	1	no	—
39	C₇×#546	C₂²	1	2	yes	complemented
40	C₇×D₄²	—	2	1	no	—
41	C₇×D₄²	C₂²	1	2	yes	complemented
42	C₇×D₄²	C₂²	1	1	yes	characteristic, complemented
43	C₇×D₄²	C₂²	1	2	yes	complemented
44	C₇×D₄²	C₂²	1	1	yes	characteristic, complemented
45	C₇×#540	—	2	1	no	—
46	C₇×#540	C₂²	1	2	yes	complemented
47	C₇×#540	C₂²	1	2	yes	complemented
48	C₇×#538	—	2	2	no	—
49	C₇×#535	—	2	1	no	—
50	C₇×#535	C₂²	1	2	yes	complemented
51	C₇×#534	—	2	2	no	—
52	C₇×#532	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₇×#127	C₂²	1	1	yes	characteristic, complemented
54	C₇×#529	C₂²	1	1	yes	characteristic
55	C₇×#529	C₂²	1	1	yes	characteristic, complemented
56	C₇×#525	—	2	1	no	—
57	C₂×C₇×#121	—	2	1	no	—
58	C₇×#518	C₂²	1	2	yes	complemented
59	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
60	C₇×#496	C₂²	1	2	yes	complemented
61	C₇×#493	C₂²	1	1	yes	characteristic, complemented
62	C₇×#493	C₂²	1	1	yes	characteristic, complemented
63	C₇×#493	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, complemented
67	C₇×#486	C₂²	1	1	yes	characteristic, complemented
68	C₇×#484	C₂²	1	1	yes	characteristic, complemented
69	C₇×#482	C₂²	1	2	yes	complemented
70	C₇×#482	C₂²	1	2	yes	complemented
71	C₇×#481	C₂²	1	1	yes	characteristic, complemented
72	C₇×#478	C₂²	1	2	yes	complemented
73	C₇×#478	C₂²	1	1	yes	characteristic, complemented
74	C₇×#478	C₂²	1	2	yes	complemented
75	C₇×#478	C₂²	1	2	yes	complemented
76	C₇×#478	C₂²	1	1	yes	characteristic, complemented
77	C₇×#477	C₂²	1	1	yes	characteristic, complemented
78	C₇×#476	C₂²	1	1	yes	characteristic, complemented
79	C₇×#469	C₂²	1	2	yes	complemented
80	C₇×#469	C₂²	1	2	yes	complemented
81	C₇×#466	C₂²	1	2	yes	complemented
82	C₇×#466	C₂²	1	2	yes	complemented
83	C₇×#466	C₂²	1	2	yes	complemented
84	C₇×#465	C₂²	1	2	yes	complemented
85	C₇×#463	C₂²	1	1	yes	characteristic, complemented
86	C₇×#463	C₂²	1	2	yes	complemented
87	C₇×#463	C₂²	1	2	yes	complemented
88	C₇×#463	C₂²	1	1	yes	characteristic, complemented
89	C₇×#463	C₂²	1	2	yes	complemented
90	C₇×#460	C₂²	1	1	yes	characteristic, complemented
91	C₇×#459	C₂²	1	1	yes	characteristic
92	C₇×#459	C₂²	1	2	yes	complemented
93	C₇×#459	C₂²	1	2	yes	complemented
94	C₇×#459	C₂²	1	2	yes	complemented
95	C₇×#459	C₂²	1	1	yes	characteristic, complemented
96	C₇×#459	C₂²	1	2	yes	complemented
97	C₇×#459	C₂²	1	2	yes	complemented
98	C₇×#459	C₂²	1	1	yes	characteristic, complemented
99	C₇×#459	C₂²	1	2	yes	complemented
100	C₇×#459	C₂²	1	2	yes	complemented
101	C₇×#459	C₂²	1	1	yes	characteristic, complemented
102	C₇×#459	C₂²	1	1	yes	characteristic, complemented
103	C₇×#459	C₂²	1	2	yes	complemented
104	C₇×#450	C₂²	1	1	yes	characteristic, complemented
105	C₇×#449	C₂²	1	2	yes	complemented
106	C₇×#449	C₂²	1	2	yes	complemented
107	C₇×#447	C₂²	1	1	yes	characteristic
108	C₇×#447	C₂²	1	2	yes	complemented
109	C₇×#447	C₂²	1	2	yes	complemented
110	C₇×#447	C₂²	1	2	yes	complemented
111	C₇×#447	C₂²	1	2	yes	complemented
112	C₇×#447	C₂²	1	2	yes	complemented
113	C₇×#447	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×#442	C₂²	1	2	yes	complemented
117	C₇×#442	C₂²	1	2	yes	complemented
118	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₇×D₈	C₂²	1	2	yes	complemented
122	C₄×C₇×D₈	C₂²	1	2	yes	complemented
123	C₄×C₇×D₈	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	#62051	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	1	no	—
137	C₂×C₇×#41	—	2	1	no	—
138	C₂×C₇×#41	—	2	1	no	—
139	C₂×C₇×#41	C₂³	1	2	yes	—
140	C₂²×C₇×D₄	—	2	1	no	—
141	C₂²×C₇×D₄	—	2	2	no	—
142	C₂²×C₇×D₄	—	2	2	no	—
143	C₂²×C₇×D₄	—	2	1	no	—
144	C₂²×C₇×D₄	—	2	1	no	—
145	C₂²×C₇×D₄	—	2	1	no	—
146	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
147	C₂²×C₇×D₄	C₂³	1	2	yes	—
148	C₂²×C₇×D₄	C₂³	1	2	yes	—
149	C₂²×C₇×D₄	C₂³	1	2	yes	—
150	C₂³×C₄×C₇	—	2	1	no	—
151	C₇×AGL(1,ℤ/8)	—	4	4	no	—
152	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
154	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₇×D₈	—	4	4	no	—
156	C₂×C₇×D₈	—	4	4	no	—
157	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
158	C₂×C₇×D₈	C₂³	1	2	yes	—
159	C₂×C₇×D₈	C₂³	1	2	yes	—
160	C₂×C₇×D₈	C₂³	1	2	yes	—
161	C₂×C₇×D₈	C₂³	1	2	yes	—
162	C₂×C₇×D₈	C₂³	1	2	yes	—
163	C₂×C₇×D₈	C₂³	1	2	yes	—
164	C₂×C₇×D₈	C₂³	1	2	yes	—
165	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
166	C₂×C₇×D₈	C₂³	1	2	yes	—
167	C₂×C₇×D₈	C₂³	1	2	yes	—
168	C₂×C₇×M₁₆	C₂³	1	2	yes	—
169	C₂²×C₇×C₈	C₂³	1	2	yes	—
170	C₂²×C₇×C₈	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	1	yes	characteristic
179	C₇×#127	C₂³	1	2	yes	—
180	C₇×#127	C₂³	1	2	yes	—
181	C₇×#126	—	2	2	no	—
182	C₇×#126	—	2	1	no	—
183	C₇×#126	D₄	1	2	yes	—
184	C₇×#125	D₄	1	1	yes	characteristic
185	C₇×#125	C₂³	1	1	yes	characteristic
186	C₇×#125	C₂³	1	2	yes	—
187	C₇×#124	—	2	1	no	—
188	C₇×#124	—	2	2	no	—
189	C₇×#124	—	2	1	no	—
190	C₇×#124	D₄	1	1	yes	characteristic
191	C₇×#124	C₂³	1	2	yes	—
192	C₇×#124	C₂³	1	1	yes	characteristic
193	C₇×#123	—	2	1	no	—
194	C₇×#123	—	2	2	no	—
195	C₇×#123	—	2	2	no	—
196	C₇×#123	—	2	2	no	—
197	C₇×#123	—	2	2	no	—
198	C₇×#123	—	2	2	no	—
199	C₇×#123	—	2	2	no	—
200	C₇×#123	—	2	2	no	—
201	C₇×#123	D₄	1	2	yes	—
202	C₇×C₂²⋊Q₈	—	2	1	no	—
203	C₇×C₂²⋊Q₈	—	2	2	no	—
204	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
205	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
206	C₇×#121	—	2	2	no	—
207	C₇×#121	—	2	1	no	—
208	C₇×#121	—	2	1	no	—
209	C₇×#121	—	2	1	no	—
210	C₇×#121	—	2	1	no	—
211	C₇×#121	—	2	2	no	—
212	C₇×#121	—	2	2	no	—
213	C₇×#121	—	2	2	no	—
214	C₇×#121	—	2	2	no	—
215	C₇×#121	—	2	2	no	—
216	C₇×#121	—	2	1	no	—
217	C₇×#121	—	2	1	no	—
218	C₇×#121	—	2	2	no	—
219	C₇×#121	—	2	2	no	—
220	C₇×#121	—	2	2	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	D₄	1	1	yes	characteristic
226	C₇×#121	C₂³	1	1	yes	characteristic
227	C₇×#121	C₂³	1	2	yes	—
228	C₇×#121	C₂³	1	2	yes	—
229	C₇×#121	C₂³	1	2	yes	—
230	C₇×#121	C₂³	1	2	yes	—
231	C₇×#121	C₂³	1	2	yes	—
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	C₇×#120	—	2	2	no	—
237	C₇×#120	—	2	2	no	—
238	C₇×#120	—	2	2	no	—
239	C₇×#120	—	2	2	no	—
240	C₇×#120	—	2	2	no	—
241	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
242	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
243	C₄×C₇×D₄	—	2	1	no	—
244	C₄×C₇×D₄	—	2	2	no	—
245	C₄×C₇×D₄	—	2	2	no	—
246	C₄×C₇×D₄	—	2	1	no	—
247	C₄×C₇×D₄	—	2	1	no	—
248	C₄×C₇×D₄	—	2	2	no	—
249	C₄×C₇×D₄	—	2	1	no	—
250	C₄×C₇×D₄	—	2	1	no	—
251	C₄×C₇×D₄	—	2	1	no	—
252	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
253	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
254	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
255	C₄×C₇×D₄	C₂³	1	2	yes	—
256	C₄×C₇×D₄	C₂³	1	2	yes	—
257	C₄×C₇×D₄	C₂³	1	2	yes	—
258	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
259	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
260	C₄×C₇×D₄	C₂³	1	2	yes	—
261	C₄×C₇×D₄	C₂³	1	2	yes	—
262	C₄×C₇×D₄	C₂³	1	2	yes	—
263	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
264	C₇×#117	—	2	1	no	—
265	C₇×#117	—	2	1	no	—
266	C₇×#117	C₂³	1	2	yes	—
267	C₇×#117	C₂³	1	2	yes	—
268	C₂×C₇×C₄⋊C₄	—	2	1	no	—
269	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₇×C₂²⋊C₄	—	2	2	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	1	yes	characteristic
279	C₇×#106	C₂³	1	2	yes	—
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	1	yes	characteristic
285	C₇×C₄⋊C₈	C₂³	1	2	yes	—
286	C₇×C₄⋊C₈	C₂³	1	2	yes	—
287	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₇×#103	C₂³	1	2	yes	—
289	C₇×#103	C₂³	1	1	yes	characteristic
290	C₇×#103	C₂³	1	1	yes	characteristic
291	C₇×#102	C₂³	1	1	yes	characteristic
292	C₇×#102	C₂³	1	2	yes	—
293	C₇×#102	C₂³	1	2	yes	—
294	C₇×#102	C₂³	1	2	yes	—
295	C₇×#102	C₂³	1	2	yes	—
296	C₇×#102	C₂³	1	2	yes	—
297	C₇×#102	C₂³	1	1	yes	characteristic
298	C₇×#102	C₂³	1	2	yes	—
299	C₇×#102	C₂³	1	2	yes	—
300	C₇×#102	C₂³	1	1	yes	characteristic
301	C₇×#102	C₂³	1	1	yes	characteristic
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, complemented
317	#3519	C₂×C₇	1	1	yes	characteristic, complemented
318	#3399	C₂×C₇	1	1	yes	characteristic, complemented
319	#3391	C₂×C₇	1	1	yes	characteristic, complemented
320	#3366	C₂×C₇	1	1	yes	characteristic, complemented
321	#3361	C₂×C₇	1	1	yes	characteristic, complemented
322	#3325	C₂×C₇	1	1	yes	characteristic, complemented
323	#3318	C₂×C₇	1	2	yes	complemented
324	#3305	C₂×C₇	1	1	yes	characteristic, complemented
325	#3297	C₂×C₇	1	2	yes	complemented
326	D₄×D₈	C₂×C₇	1	2	yes	complemented
327	D₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
328	#3274	C₂×C₇	1	1	yes	characteristic, complemented
329	#3264	C₂×C₇	1	2	yes	complemented
330	#3259	C₂×C₇	1	2	yes	complemented
331	#3247	C₂×C₇	1	1	yes	characteristic, complemented
332	#3220	C₂×C₇	1	2	yes	complemented
333	#3205	C₂×C₇	1	1	yes	characteristic, complemented
334	#3122	C₂×C₇	1	2	yes	complemented
335	#3105	C₂×C₇	1	1	yes	characteristic, complemented
336	#3041	C₂×C₇	1	2	yes	complemented
337	C₂×#459	C₂×C₇	1	1	yes	characteristic, complemented
338	#2994	C₂×C₇	1	1	yes	characteristic, complemented
339	C₂⁴×C₇	—	2	1	no	—
340	C₂⁴×C₇	—	2	2	no	—
341	C₂⁴×C₇	—	2	2	no	—
342	C₂⁴×C₇	—	2	2	no	—
343	C₇×#41	—	4	2	no	—
344	C₇×#41	—	4	2	no	—
345	C₇×#41	—	8	2	no	—
346	C₇×#41	—	8	2	no	—
347	C₇×#41	—	8	2	no	—
348	C₂×C₇×Q₈	—	2	1	no	—
349	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
350	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
351	C₂×C₇×D₄	—	2	2	no	—
352	C₂×C₇×D₄	—	2	4	no	—
353	C₂×C₇×D₄	—	2	1	no	—
354	C₂×C₇×D₄	—	2	2	no	—
355	C₂×C₇×D₄	—	2	2	no	—
356	C₂×C₇×D₄	—	2	2	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	2	no	—
361	C₂×C₇×D₄	—	2	1	no	—
362	C₂×C₇×D₄	—	2	1	no	—
363	C₂×C₇×D₄	—	2	1	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	1	no	—
369	C₂×C₇×D₄	—	2	1	no	—
370	C₂×C₇×D₄	—	2	2	no	—
371	C₂×C₇×D₄	—	2	2	no	—
372	C₂×C₇×D₄	—	2	2	no	—
373	C₂×C₇×D₄	—	2	2	no	—
374	C₂×C₇×D₄	—	2	2	no	—
375	C₂×C₇×D₄	—	2	1	no	—
376	C₂×C₇×D₄	—	4	1	no	—
377	C₂×C₇×D₄	—	4	2	no	—
378	C₂×C₇×D₄	—	4	2	no	—
379	C₂×C₇×D₄	—	4	2	no	—
380	C₂×C₇×D₄	—	4	2	no	—
381	C₂×C₇×D₄	—	4	2	no	—
382	C₂×C₇×D₄	—	8	2	no	—
383	C₂×C₇×D₄	—	8	2	no	—
384	C₂×C₇×D₄	—	8	2	no	—
385	C₂×C₇×D₄	—	8	2	no	—
386	C₂×C₇×D₄	—	8	4	no	—
387	C₂×C₇×D₄	—	8	4	no	—
388	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
389	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
390	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
391	C₂×C₇×D₄	C₂⁴	1	2	yes	—
392	C₂×C₇×D₄	C₂⁴	1	2	yes	—
393	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
394	C₂×C₇×D₄	C₂⁴	1	2	yes	—
395	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₇	—	2	1	no	—
397	C₂²×C₄×C₇	—	2	1	no	—
398	C₂²×C₄×C₇	—	2	1	no	—
399	C₂²×C₄×C₇	—	2	1	no	—
400	C₂²×C₄×C₇	—	2	1	no	—
401	C₂²×C₄×C₇	—	2	2	no	—
402	C₂²×C₄×C₇	—	2	2	no	—
403	C₂²×C₄×C₇	—	2	2	no	—
404	C₂²×C₄×C₇	—	2	2	no	—
405	C₂²×C₄×C₇	—	2	2	no	—
406	C₂²×C₄×C₇	—	2	1	no	—
407	C₂²×C₄×C₇	—	2	2	no	—
408	C₂²×C₄×C₇	—	8	2	no	—
409	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
410	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
413	C₇×SD₁₆	—	2	2	no	—
414	C₇×SD₁₆	—	4	1	no	—
415	C₇×SD₁₆	—	4	2	no	—
416	C₇×D₈	—	2	2	no	—
417	C₇×D₈	—	2	4	no	—
418	C₇×D₈	—	2	4	no	—
419	C₇×D₈	—	4	2	no	—
420	C₇×D₈	—	4	2	no	—
421	C₇×D₈	—	4	2	no	—
422	C₇×D₈	—	4	2	no	—
423	C₇×D₈	—	4	2	no	—
424	C₇×D₈	—	4	1	no	—
425	C₇×D₈	—	4	2	no	—
426	C₇×D₈	—	4	2	no	—
427	C₇×M₁₆	—	4	2	no	—
428	C₂×C₇×C₈	—	4	2	no	—
429	C₂×C₇×C₈	—	4	2	no	—
430	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
431	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
432	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
433	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
434	C₂×C₇×C₈	C₂⁴	1	2	yes	—
435	C₂×C₇×C₈	C₂⁴	1	2	yes	—
436	C₇×C₄⋊C₄	—	2	1	no	—
437	C₇×C₄⋊C₄	—	2	2	no	—
438	C₇×C₄⋊C₄	—	2	1	no	—
439	C₇×C₄⋊C₄	—	2	1	no	—
440	C₇×C₄⋊C₄	—	2	1	no	—
441	C₇×C₄⋊C₄	—	2	1	no	—
442	C₇×C₄⋊C₄	—	2	2	no	—
443	C₇×C₄⋊C₄	—	2	1	no	—
444	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
445	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
446	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
447	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
448	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
449	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
450	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
451	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
453	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
454	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
455	C₇×C₂²⋊C₄	—	2	2	no	—
456	C₇×C₂²⋊C₄	—	2	1	no	—
457	C₇×C₂²⋊C₄	—	2	1	no	—
458	C₇×C₂²⋊C₄	—	2	2	no	—
459	C₇×C₂²⋊C₄	—	2	1	no	—
460	C₇×C₂²⋊C₄	—	2	2	no	—
461	C₇×C₂²⋊C₄	—	2	1	no	—
462	C₇×C₂²⋊C₄	—	2	2	no	—
463	C₇×C₂²⋊C₄	—	2	1	no	—
464	C₇×C₂²⋊C₄	—	2	2	no	—
465	C₇×C₂²⋊C₄	—	2	2	no	—
466	C₇×C₂²⋊C₄	—	2	1	no	—
467	C₇×C₂²⋊C₄	—	2	1	no	—
468	C₇×C₂²⋊C₄	—	2	2	no	—
469	C₇×C₂²⋊C₄	—	2	1	no	—
470	C₇×C₂²⋊C₄	—	2	2	no	—
471	C₇×C₂²⋊C₄	—	2	2	no	—
472	C₇×C₂²⋊C₄	—	2	2	no	—
473	C₇×C₂²⋊C₄	—	2	2	no	—
474	C₇×C₂²⋊C₄	—	2	1	no	—
475	C₇×C₂²⋊C₄	—	2	2	no	—
476	C₇×C₂²⋊C₄	—	2	2	no	—
477	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
478	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
479	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
480	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
481	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
482	C₄²×C₇	—	2	2	no	—
483	C₄²×C₇	—	2	1	no	—
484	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
485	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
486	C₄²×C₇	C₂⁴	1	1	yes	characteristic
487	C₄²×C₇	C₂⁴	1	2	yes	—
488	C₄²×C₇	C₂⁴	1	1	yes	characteristic
489	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	complemented
490	C₂²×D₈	C₂²×C₇	1	2	yes	complemented
491	C₂²×D₈	C₂²×C₇	1	2	yes	complemented
492	#560	—	2	2	no	—
493	#559	C₂²×C₇	1	1	yes	characteristic, complemented
494	#555	C₂²×C₇	1	1	yes	characteristic, complemented
495	#554	C₂²×C₇	1	1	yes	characteristic, complemented
496	#553	—	2	1	no	—
497	#553	C₂²×C₇	1	2	yes	complemented
498	#550	C₂²×C₇	1	1	yes	characteristic, complemented
499	#550	C₂²×C₇	1	1	yes	characteristic, complemented
500	#550	C₂²×C₇	1	1	yes	characteristic, complemented
501	#546	—	2	1	no	—
502	#546	—	2	2	no	—
503	#546	—	2	1	no	—
504	#546	C₂²×C₇	1	2	yes	complemented
505	D₄²	—	2	1	no	—
506	D₄²	C₂²×C₇	1	2	yes	complemented
507	D₄²	C₂²×C₇	1	1	yes	characteristic, complemented
508	D₄²	C₂²×C₇	1	2	yes	complemented
509	D₄²	C₂²×C₇	1	1	yes	characteristic, complemented
510	#540	—	2	1	no	—
511	#540	C₂²×C₇	1	2	yes	complemented
512	#540	C₂²×C₇	1	2	yes	complemented
513	#538	—	2	2	no	—
514	#535	—	2	1	no	—
515	#535	C₂²×C₇	1	2	yes	complemented
516	#534	—	2	2	no	—
517	#532	C₂²×C₇	1	1	yes	characteristic, complemented
518	C₂×#127	C₂²×C₇	1	1	yes	characteristic, complemented
519	#529	C₂²×C₇	1	1	yes	characteristic
520	#529	C₂²×C₇	1	1	yes	characteristic, complemented
521	#525	—	2	1	no	—
522	C₂×#121	—	2	1	no	—
523	#518	C₂²×C₇	1	2	yes	complemented
524	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
525	#496	C₂²×C₇	1	2	yes	complemented
526	#493	C₂²×C₇	1	1	yes	characteristic, complemented
527	#493	C₂²×C₇	1	2	yes	complemented
528	#493	C₂²×C₇	1	1	yes	characteristic, complemented
529	#490	C₂²×C₇	1	2	yes	complemented
530	#488	C₂²×C₇	1	2	yes	complemented
531	#486	C₂²×C₇	1	1	yes	characteristic, complemented
532	#486	C₂²×C₇	1	1	yes	characteristic, complemented
533	#484	C₂²×C₇	1	1	yes	characteristic, complemented
534	#482	C₂²×C₇	1	2	yes	complemented
535	#482	C₂²×C₇	1	2	yes	complemented
536	#481	C₂²×C₇	1	1	yes	characteristic, complemented
537	#478	C₂²×C₇	1	1	yes	characteristic, complemented
538	#478	C₂²×C₇	1	1	yes	characteristic, complemented
539	#478	C₂²×C₇	1	2	yes	complemented
540	#478	C₂²×C₇	1	2	yes	complemented
541	#478	C₂²×C₇	1	2	yes	complemented
542	#477	C₂²×C₇	1	1	yes	characteristic, complemented
543	#476	C₂²×C₇	1	1	yes	characteristic, complemented
544	#469	C₂²×C₇	1	2	yes	complemented
545	#469	C₂²×C₇	1	2	yes	complemented
546	#466	C₂²×C₇	1	2	yes	complemented
547	#466	C₂²×C₇	1	2	yes	complemented
548	#466	C₂²×C₇	1	2	yes	complemented
549	#465	C₂²×C₇	1	2	yes	complemented
550	#463	C₂²×C₇	1	1	yes	characteristic, complemented
551	#463	C₂²×C₇	1	1	yes	characteristic, complemented
552	#463	C₂²×C₇	1	2	yes	complemented
553	#463	C₂²×C₇	1	2	yes	complemented
554	#463	C₂²×C₇	1	2	yes	complemented
555	#460	C₂²×C₇	1	1	yes	characteristic, complemented
556	#459	C₂²×C₇	1	1	yes	characteristic
557	#459	C₂²×C₇	1	1	yes	characteristic, complemented
558	#459	C₂²×C₇	1	2	yes	complemented
559	#459	C₂²×C₇	1	2	yes	complemented
560	#459	C₂²×C₇	1	2	yes	complemented
561	#459	C₂²×C₇	1	1	yes	characteristic, complemented
562	#459	C₂²×C₇	1	2	yes	complemented
563	#459	C₂²×C₇	1	1	yes	characteristic, complemented
564	#459	C₂²×C₇	1	2	yes	complemented
565	#459	C₂²×C₇	1	2	yes	complemented
566	#459	C₂²×C₇	1	1	yes	characteristic, complemented
567	#459	C₂²×C₇	1	2	yes	complemented
568	#459	C₂²×C₇	1	2	yes	complemented
569	#450	C₂²×C₇	1	1	yes	characteristic, complemented
570	#449	C₂²×C₇	1	2	yes	complemented
571	#449	C₂²×C₇	1	2	yes	complemented
572	#447	C₂²×C₇	1	1	yes	characteristic
573	#447	C₂²×C₇	1	2	yes	complemented
574	#447	C₂²×C₇	1	2	yes	complemented
575	#447	C₂²×C₇	1	2	yes	complemented
576	#447	C₂²×C₇	1	2	yes	complemented
577	#447	C₂²×C₇	1	2	yes	complemented
578	#447	C₂²×C₇	1	2	yes	complemented
579	#446	C₂²×C₇	1	1	yes	characteristic, complemented
580	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
581	#442	C₂²×C₇	1	2	yes	complemented
582	#442	C₂²×C₇	1	2	yes	complemented
583	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
584	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
585	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
586	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
587	C₄×D₈	C₂²×C₇	1	2	yes	complemented
588	C₄×D₈	C₂²×C₇	1	2	yes	complemented
589	#436	C₂²×C₇	1	1	yes	characteristic, complemented
590	#435	C₂²×C₇	1	2	yes	complemented
591	C₈×D₄	C₂²×C₇	1	2	yes	complemented
592	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
593	#433	C₂²×C₇	1	2	yes	complemented
594	#431	C₂²×C₇	1	1	yes	characteristic, complemented
595	#424	C₂²×C₇	1	2	yes	complemented
596	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
597	#418	C₂²×C₇	1	2	yes	complemented
598	#416	C₂²×C₇	1	2	yes	complemented
599	C₂×#102	C₂²×C₇	1	2	yes	complemented
600	C₂³×C₇	—	2	1	no	—
601	C₂³×C₇	—	2	1	no	—
602	C₂³×C₇	—	2	2	no	—
603	C₂³×C₇	—	2	1	no	—
604	C₂³×C₇	—	2	2	no	—
605	C₂³×C₇	—	2	2	no	—
606	C₂³×C₇	—	4	2	no	—
607	C₂³×C₇	—	4	4	no	—
608	C₂³×C₇	—	4	2	no	—
609	C₂³×C₇	—	4	4	no	—
610	C₂³×C₇	—	8	1	no	—
611	C₂³×C₇	—	8	2	no	—
612	C₂³×C₇	—	8	2	no	—
613	C₂³×C₇	—	8	2	no	—
614	C₂³×C₇	—	8	2	no	—
615	C₂³×C₇	—	8	2	no	—
616	C₂³×C₇	—	8	2	no	—
617	C₂³×C₇	—	8	2	no	—
618	C₂³×C₇	C₂²×D₄	1	2	yes	—
619	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
620	C₇×Q₈	—	2	2	no	—
621	C₇×Q₈	—	2	1	no	—
622	C₇×Q₈	—	2	1	no	—
623	C₇×Q₈	—	8	1	no	—
624	C₇×D₄	—	2	4	no	—
625	C₇×D₄	—	2	2	no	—
626	C₇×D₄	—	2	1	no	—
627	C₇×D₄	—	2	2	no	—
628	C₇×D₄	—	2	2	no	—
629	C₇×D₄	—	2	1	no	—
630	C₇×D₄	—	2	2	no	—
631	C₇×D₄	—	2	1	no	—
632	C₇×D₄	—	2	2	no	—
633	C₇×D₄	—	2	1	no	—
634	C₇×D₄	—	2	1	no	—
635	C₇×D₄	—	2	2	no	—
636	C₇×D₄	—	2	2	no	—
637	C₇×D₄	—	4	4	no	—
638	C₇×D₄	—	4	2	no	—
639	C₇×D₄	—	4	2	no	—
640	C₇×D₄	—	4	4	no	—
641	C₇×D₄	—	4	2	no	—
642	C₇×D₄	—	4	2	no	—
643	C₇×D₄	—	4	2	no	—
644	C₇×D₄	—	8	2	no	—
645	C₇×D₄	—	8	2	no	—
646	C₇×D₄	—	8	2	no	—
647	C₇×D₄	—	8	2	no	—
648	C₇×D₄	—	8	1	no	—
649	C₇×D₄	—	8	1	no	—
650	C₇×D₄	—	8	2	no	—
651	C₇×D₄	—	8	2	no	—
652	C₇×D₄	—	8	1	no	—
653	C₇×D₄	—	8	2	no	—
654	C₇×D₄	—	8	2	no	—
655	C₇×D₄	—	8	2	no	—
656	C₇×D₄	—	8	2	no	—
657	C₇×D₄	—	8	2	no	—
658	C₇×D₄	—	8	2	no	—
659	C₇×D₄	—	8	2	no	—
660	C₇×D₄	H(5,𝔽₂)	1	2	yes	—
661	C₂×C₄×C₇	—	2	2	no	—
662	C₂×C₄×C₇	—	2	2	no	—
663	C₂×C₄×C₇	—	2	1	no	—
664	C₂×C₄×C₇	—	2	2	no	—
665	C₂×C₄×C₇	—	2	1	no	—
666	C₂×C₄×C₇	—	2	2	no	—
667	C₂×C₄×C₇	—	2	1	no	—
668	C₂×C₄×C₇	—	2	1	no	—
669	C₂×C₄×C₇	—	2	1	no	—
670	C₂×C₄×C₇	—	2	2	no	—
671	C₂×C₄×C₇	—	2	1	no	—
672	C₂×C₄×C₇	—	2	1	no	—
673	C₂×C₄×C₇	—	4	2	no	—
674	C₂×C₄×C₇	—	4	2	no	—
675	C₂×C₄×C₇	—	4	2	no	—
676	C₂×C₄×C₇	—	8	1	no	—
677	C₂×C₄×C₇	—	8	1	no	—
678	C₂×C₄×C₇	—	8	2	no	—
679	C₂×C₄×C₇	—	8	2	no	—
680	C₂×C₄×C₇	—	8	2	no	—
681	C₂×C₄×C₇	—	8	2	no	—
682	C₂×C₄×C₇	—	8	2	no	—
683	C₂×C₄×C₇	—	8	2	no	—
684	C₂×C₄×C₇	—	8	1	no	—
685	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
686	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
687	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
688	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
689	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
690	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
691	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
692	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
693	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
694	C₇×C₈	—	2	1	no	—
695	C₇×C₈	—	2	2	no	—
696	C₇×C₈	—	2	2	no	—
697	C₇×C₈	—	2	1	no	—
698	C₇×C₈	—	2	1	no	—
699	C₇×C₈	—	2	1	no	—
700	C₂×#41	—	2	1	no	—
701	C₂×#41	—	2	1	no	—
702	C₂×#41	—	2	1	no	—
703	C₂×#41	C₂³×C₇	1	2	yes	—
704	C₂²×D₄	—	2	1	no	—
705	C₂²×D₄	—	2	2	no	—
706	C₂²×D₄	—	2	2	no	—
707	C₂²×D₄	—	2	1	no	—
708	C₂²×D₄	—	2	1	no	—
709	C₂²×D₄	—	2	1	no	—
710	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
711	C₂²×D₄	C₂³×C₇	1	2	yes	—
712	C₂²×D₄	C₂³×C₇	1	2	yes	—
713	C₂²×D₄	C₂³×C₇	1	2	yes	—
714	C₂³×C₄	—	2	1	no	—
715	AGL(1,ℤ/8)	—	4	4	no	—
716	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
717	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
719	C₂×D₈	—	4	4	no	—
720	C₂×D₈	—	4	4	no	—
721	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
722	C₂×D₈	C₂³×C₇	1	2	yes	—
723	C₂×D₈	C₂³×C₇	1	2	yes	—
724	C₂×D₈	C₂³×C₇	1	2	yes	—
725	C₂×D₈	C₂³×C₇	1	2	yes	—
726	C₂×D₈	C₂³×C₇	1	2	yes	—
727	C₂×D₈	C₂³×C₇	1	2	yes	—
728	C₂×D₈	C₂³×C₇	1	2	yes	—
729	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
730	C₂×D₈	C₂³×C₇	1	2	yes	—
731	C₂×D₈	C₂³×C₇	1	2	yes	—
732	C₂×M₁₆	C₂³×C₇	1	2	yes	—
733	C₂²×C₈	C₂³×C₇	1	2	yes	—
734	C₂²×C₈	C₂³×C₇	1	2	yes	—
735	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
736	#127	—	2	1	no	—
737	#127	—	2	1	no	—
738	#127	—	2	1	no	—
739	#127	C₂³×C₇	1	2	yes	—
740	#127	C₂³×C₇	1	1	yes	characteristic
741	#127	C₂³×C₇	1	1	yes	characteristic
742	#127	C₂³×C₇	1	1	yes	characteristic
743	#127	C₂³×C₇	1	2	yes	—
744	#127	C₂³×C₇	1	2	yes	—
745	#126	—	2	2	no	—
746	#126	—	2	1	no	—
747	#126	C₇×D₄	1	2	yes	—
748	#125	C₇×D₄	1	1	yes	characteristic
749	#125	C₂³×C₇	1	1	yes	characteristic
750	#125	C₂³×C₇	1	2	yes	—
751	#124	—	2	1	no	—
752	#124	—	2	2	no	—
753	#124	—	2	1	no	—
754	#124	C₇×D₄	1	1	yes	characteristic
755	#124	C₂³×C₇	1	1	yes	characteristic
756	#124	C₂³×C₇	1	2	yes	—
757	#123	—	2	1	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	C₇×D₄	1	2	yes	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
769	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
770	#121	—	2	2	no	—
771	#121	—	2	1	no	—
772	#121	—	2	1	no	—
773	#121	—	2	1	no	—
774	#121	—	2	1	no	—
775	#121	—	2	2	no	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	—	2	2	no	—
779	#121	—	2	2	no	—
780	#121	—	2	1	no	—
781	#121	—	2	1	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	C₇×D₄	1	1	yes	characteristic
790	#121	C₂³×C₇	1	1	yes	characteristic
791	#121	C₂³×C₇	1	2	yes	—
792	#121	C₂³×C₇	1	2	yes	—
793	#121	C₂³×C₇	1	2	yes	—
794	#121	C₂³×C₇	1	2	yes	—
795	#121	C₂³×C₇	1	2	yes	—
796	#120	—	2	2	no	—
797	#120	—	2	2	no	—
798	#120	—	2	2	no	—
799	#120	—	2	2	no	—
800	#120	—	2	2	no	—
801	#120	—	2	2	no	—
802	#120	—	2	2	no	—
803	#120	—	2	2	no	—
804	#120	—	2	2	no	—
805	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₇	1	2	yes	—
821	C₄×D₄	C₂³×C₇	1	2	yes	—
822	C₄×D₄	C₂³×C₇	1	2	yes	—
823	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₇	1	2	yes	—
825	C₄×D₄	C₂³×C₇	1	2	yes	—
826	C₄×D₄	C₂³×C₇	1	2	yes	—
827	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
828	#117	—	2	1	no	—
829	#117	—	2	1	no	—
830	#117	C₂³×C₇	1	2	yes	—
831	#117	C₂³×C₇	1	2	yes	—
832	C₂×C₄⋊C₄	—	2	1	no	—
833	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
834	C₂×C₂²⋊C₄	—	2	1	no	—
835	C₂×C₂²⋊C₄	—	2	2	no	—
836	C₂×C₂²⋊C₄	—	2	2	no	—
837	C₂×C₂²⋊C₄	—	2	2	no	—
838	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
839	#107	C₂³×C₇	1	1	yes	characteristic
840	#107	C₂³×C₇	1	2	yes	—
841	#107	C₂³×C₇	1	1	yes	characteristic
842	#106	C₂³×C₇	1	1	yes	characteristic
843	#106	C₂³×C₇	1	1	yes	characteristic
844	#106	C₂³×C₇	1	2	yes	—
845	C₄⋊C₈	C₂³×C₇	1	2	yes	—
846	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
849	C₄⋊C₈	C₂³×C₇	1	2	yes	—
850	C₄⋊C₈	C₂³×C₇	1	2	yes	—
851	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
852	#103	C₂³×C₇	1	1	yes	characteristic
853	#103	C₂³×C₇	1	2	yes	—
854	#103	C₂³×C₇	1	1	yes	characteristic
855	#102	C₂³×C₇	1	2	yes	—
856	#102	C₂³×C₇	1	2	yes	—
857	#102	C₂³×C₇	1	2	yes	—
858	#102	C₂³×C₇	1	2	yes	—
859	#102	C₂³×C₇	1	2	yes	—
860	#102	C₂³×C₇	1	1	yes	characteristic
861	#102	C₂³×C₇	1	2	yes	—
862	#102	C₂³×C₇	1	2	yes	—
863	#102	C₂³×C₇	1	1	yes	characteristic
864	#102	C₂³×C₇	1	1	yes	characteristic
865	#102	C₂³×C₇	1	2	yes	—
866	#102	C₂³×C₇	1	1	yes	characteristic
867	#102	C₂³×C₇	1	2	yes	—
868	#102	C₂³×C₇	1	1	yes	characteristic
869	#102	C₂³×C₇	1	1	yes	characteristic
870	#102	C₂³×C₇	1	2	yes	—
871	#102	C₂³×C₇	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
874	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
876	#97	C₂³×C₇	1	2	yes	—
877	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
878	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
879	C₄×C₈	C₂³×C₇	1	2	yes	—
880	C₂²×C₇	—	2	1	no	—
881	C₂²×C₇	—	2	1	no	—
882	C₂²×C₇	—	2	2	no	—
883	C₂²×C₇	—	2	2	no	—
884	C₂²×C₇	—	2	2	no	—
885	C₂²×C₇	—	2	2	no	—
886	C₂²×C₇	—	4	1	no	—
887	C₂²×C₇	—	4	1	no	—
888	C₂²×C₇	—	4	2	no	—
889	C₂²×C₇	—	4	1	no	—
890	C₂²×C₇	—	4	2	no	—
891	C₂²×C₇	—	4	1	no	—
892	C₂²×C₇	—	4	2	no	—
893	C₂²×C₇	—	4	1	no	—
894	C₂²×C₇	—	4	1	no	—
895	C₂²×C₇	—	4	2	no	—
896	C₂²×C₇	—	4	2	no	—
897	C₂²×C₇	—	4	2	no	—
898	C₂²×C₇	—	4	2	no	—
899	C₂²×C₇	—	4	1	no	—
900	C₂²×C₇	—	4	2	no	—
901	C₂²×C₇	—	4	1	no	—
902	C₂²×C₇	—	4	2	no	—
903	C₂²×C₇	—	8	4	no	—
904	C₂²×C₇	—	16	4	no	—
905	C₂²×C₇	—	16	4	no	—
906	C₂²×C₇	—	16	4	no	—
907	C₂²×C₇	#576	1	2	yes	—
908	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
909	C₄×C₇	—	2	2	no	—
910	C₄×C₇	—	2	1	no	—
911	C₄×C₇	—	2	1	no	—
912	C₄×C₇	—	2	1	no	—
913	C₄×C₇	—	2	1	no	—
914	C₄×C₇	—	2	2	no	—
915	C₄×C₇	—	2	2	no	—
916	C₄×C₇	—	4	1	no	—
917	C₄×C₇	—	4	1	no	—
918	C₄×C₇	—	4	1	no	—
919	C₄×C₇	—	4	1	no	—
920	C₄×C₇	—	4	1	no	—
921	C₄×C₇	—	4	2	no	—
922	C₄×C₇	#576	1	2	yes	—
923	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
924	C₄×C₇	#585	1	1	yes	characteristic
925	C₂⁴	—	2	1	no	—
926	C₂⁴	—	2	2	no	—
927	C₂⁴	—	2	2	no	—
928	C₂⁴	—	2	2	no	—
929	#41	—	4	2	no	—
930	#41	—	4	2	no	—
931	#41	—	8	2	no	—
932	#41	—	8	2	no	—
933	#41	—	8	2	no	—
934	C₂×Q₈	—	2	1	no	—
935	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
936	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	4	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	1	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	1	no	—
950	C₂×D₄	—	2	1	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	1	no	—
955	C₂×D₄	—	2	1	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	4	1	no	—
963	C₂×D₄	—	4	2	no	—
964	C₂×D₄	—	4	2	no	—
965	C₂×D₄	—	4	2	no	—
966	C₂×D₄	—	4	2	no	—
967	C₂×D₄	—	4	2	no	—
968	C₂×D₄	—	8	2	no	—
969	C₂×D₄	—	8	2	no	—
970	C₂×D₄	—	8	2	no	—
971	C₂×D₄	—	8	2	no	—
972	C₂×D₄	—	8	4	no	—
973	C₂×D₄	—	8	4	no	—
974	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
975	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
976	C₂×D₄	C₂⁴×C₇	1	2	yes	—
977	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
978	C₂×D₄	C₂⁴×C₇	1	2	yes	—
979	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
980	C₂×D₄	C₂⁴×C₇	1	2	yes	—
981	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
982	C₂²×C₄	—	2	1	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	1	no	—
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	8	2	no	—
995	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
996	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
997	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
998	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
999	SD₁₆	—	2	2	no	—
1000	SD₁₆	—	4	1	no	—
1001	SD₁₆	—	4	2	no	—
1002	D₈	—	2	2	no	—
1003	D₈	—	2	4	no	—
1004	D₈	—	2	4	no	—
1005	D₈	—	4	2	no	—
1006	D₈	—	4	2	no	—
1007	D₈	—	4	2	no	—
1008	D₈	—	4	2	no	—
1009	D₈	—	4	2	no	—
1010	D₈	—	4	1	no	—
1011	D₈	—	4	2	no	—
1012	D₈	—	4	2	no	—
1013	M₁₆	—	4	2	no	—
1014	C₂×C₈	—	4	2	no	—
1015	C₂×C₈	—	4	2	no	—
1016	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1017	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1018	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1019	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1020	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1021	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	2	1	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1031	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1032	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1033	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1034	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1035	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1036	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1037	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1038	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1039	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1040	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	1	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	1	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1064	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1065	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1066	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1067	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1068	C₄²	—	2	2	no	—
1069	C₄²	—	2	1	no	—
1070	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1071	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1072	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1073	C₄²	C₂⁴×C₇	1	2	yes	—
1074	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1075	C₂×C₇	—	2	2	no	—
1076	C₂×C₇	—	4	2	no	—
1077	C₂×C₇	—	4	2	no	—
1078	C₂×C₇	—	8	1	no	—
1079	C₂×C₇	—	8	2	no	—
1080	C₂×C₇	—	8	2	no	—
1081	C₂×C₇	—	8	1	no	—
1082	C₂×C₇	—	8	2	no	—
1083	C₂×C₇	#3488	1	1	yes	characteristic
1084	C₂×C₇	C₂×#576	1	1	yes	characteristic
1085	C₂×C₇	C₂×#576	1	1	yes	characteristic
1086	C₂³	—	2	1	no	—
1087	C₂³	—	2	1	no	—
1088	C₂³	—	2	2	no	—
1089	C₂³	—	2	1	no	—
1090	C₂³	—	2	2	no	—
1091	C₂³	—	2	2	no	—
1092	C₂³	—	4	2	no	—
1093	C₂³	—	4	4	no	—
1094	C₂³	—	4	2	no	—
1095	C₂³	—	4	4	no	—
1096	C₂³	—	8	1	no	—
1097	C₂³	—	8	2	no	—
1098	C₂³	—	8	2	no	—
1099	C₂³	—	8	2	no	—
1100	C₂³	—	8	2	no	—
1101	C₂³	—	8	2	no	—
1102	C₂³	—	8	2	no	—
1103	C₂³	—	8	2	no	—
1104	C₂³	C₂²×C₇×D₄	1	2	yes	—
1105	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1106	Q₈	—	2	2	no	—
1107	Q₈	—	2	1	no	—
1108	Q₈	—	2	1	no	—
1109	Q₈	—	8	1	no	—
1110	D₄	—	2	4	no	—
1111	D₄	—	2	1	no	—
1112	D₄	—	2	2	no	—
1113	D₄	—	2	2	no	—
1114	D₄	—	2	1	no	—
1115	D₄	—	2	2	no	—
1116	D₄	—	2	1	no	—
1117	D₄	—	2	2	no	—
1118	D₄	—	2	1	no	—
1119	D₄	—	2	1	no	—
1120	D₄	—	2	2	no	—
1121	D₄	—	2	2	no	—
1122	D₄	—	2	2	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	4	4	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	4	2	no	—
1129	D₄	—	4	2	no	—
1130	D₄	—	8	2	no	—
1131	D₄	—	8	2	no	—
1132	D₄	—	8	2	no	—
1133	D₄	—	8	2	no	—
1134	D₄	—	8	1	no	—
1135	D₄	—	8	1	no	—
1136	D₄	—	8	2	no	—
1137	D₄	—	8	2	no	—
1138	D₄	—	8	1	no	—
1139	D₄	—	8	2	no	—
1140	D₄	—	8	2	no	—
1141	D₄	—	8	2	no	—
1142	D₄	—	8	2	no	—
1143	D₄	—	8	2	no	—
1144	D₄	—	8	2	no	—
1145	D₄	—	8	2	no	—
1146	D₄	C₇×H(5,𝔽₂)	1	2	yes	—
1147	C₂×C₄	—	2	2	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	4	2	no	—
1160	C₂×C₄	—	4	2	no	—
1161	C₂×C₄	—	4	2	no	—
1162	C₂×C₄	—	8	1	no	—
1163	C₂×C₄	—	8	1	no	—
1164	C₂×C₄	—	8	2	no	—
1165	C₂×C₄	—	8	2	no	—
1166	C₂×C₄	—	8	2	no	—
1167	C₂×C₄	—	8	2	no	—
1168	C₂×C₄	—	8	2	no	—
1169	C₂×C₄	—	8	2	no	—
1170	C₂×C₄	—	8	1	no	—
1171	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1172	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1173	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1174	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1175	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1176	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1177	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1178	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1179	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1180	C₈	—	2	1	no	—
1181	C₈	—	2	2	no	—
1182	C₈	—	2	2	no	—
1183	C₈	—	2	1	no	—
1184	C₈	—	2	1	no	—
1185	C₈	—	2	1	no	—
1186	C₇	#62051	1	1	yes	characteristic, direct product factor, Sylow
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	2	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	2	no	—
1198	C₂²	—	4	2	no	—
1199	C₂²	—	4	2	no	—
1200	C₂²	—	4	2	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	2	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	2	no	—
1205	C₂²	—	4	2	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	2	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	2	no	—
1210	C₂²	—	8	4	no	—
1211	C₂²	—	16	4	no	—
1212	C₂²	—	16	4	no	—
1213	C₂²	—	16	4	no	—
1214	C₂²	C₇×#576	1	2	yes	—
1215	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1216	C₄	—	2	1	no	—
1217	C₄	—	2	1	no	—
1218	C₄	—	2	1	no	—
1219	C₄	—	2	2	no	—
1220	C₄	—	2	2	no	—
1221	C₄	—	2	2	no	—
1222	C₄	—	2	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	1	no	—
1227	C₄	—	4	2	no	—
1228	C₄	—	4	1	no	—
1229	C₄	C₇×#576	1	2	yes	—
1230	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1231	C₄	C₇×#585	1	1	yes	characteristic
1232	C₂	—	2	2	no	—
1233	C₂	—	4	2	no	—
1234	C₂	—	4	2	no	—
1235	C₂	—	8	1	no	—
1236	C₂	—	8	1	no	—
1237	C₂	—	8	2	no	—
1238	C₂	—	8	2	no	—
1239	C₂	—	8	2	no	—
1240	C₂	C₇×#3488	1	1	yes	characteristic
1241	C₂	C₂×C₇×#576	1	1	yes	characteristic
1242	C₂	C₂×C₇×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
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
1. C₇×#3543	C₂	semidirect
2. C₇×#3519	C₂	semidirect
3. C₇×#3399	C₂	semidirect
4. C₇×#3391	C₂	semidirect
5. C₇×#3366	C₂	semidirect
6. C₇×#3361	C₂	semidirect
7. C₇×#3325	C₂	semidirect
8. C₇×#3318	C₂	semidirect
9. C₇×#3305	C₂	semidirect
10. C₇×#3297	C₂	semidirect
11. C₇×D₄×D₈	C₂	semidirect
12. C₇×D₄×D₈	C₂	semidirect
13. C₇×#3274	C₂	semidirect
14. C₇×#3264	C₂	semidirect
15. C₇×#3259	C₂	semidirect
16. C₇×#3247	C₂	semidirect
17. C₇×#3220	C₂	semidirect
18. C₇×#3205	C₂	semidirect
19. C₇×#3122	C₂	semidirect
20. C₇×#3105	C₂	semidirect
21. C₇×#3041	C₂	semidirect
22. C₂×C₇×#459	C₂	semidirect
23. C₇×#2994	C₂	semidirect
24. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂²×C₇×D₈	C₂²	semidirect
26. C₂²×C₇×D₈	C₂²	semidirect
28. C₇×#559	C₂²	semidirect
29. C₇×#555	C₂²	semidirect
30. C₇×#554	C₂²	semidirect
32. C₇×#553	C₂²	semidirect
33. C₇×#550	C₂²	semidirect
34. C₇×#550	C₂²	semidirect
35. C₇×#550	C₂²	semidirect
39. C₇×#546	C₂²	semidirect
41. C₇×D₄²	C₂²	semidirect
42. C₇×D₄²	C₂²	semidirect
43. C₇×D₄²	C₂²	semidirect
44. C₇×D₄²	C₂²	semidirect
46. C₇×#540	C₂²	semidirect
47. C₇×#540	C₂²	semidirect
50. C₇×#535	C₂²	semidirect
52. C₇×#532	C₂²	semidirect
53. C₂×C₇×#127	C₂²	semidirect
55. C₇×#529	C₂²	semidirect
58. C₇×#518	C₂²	semidirect
59. C₂×C₄×C₇×D₄	C₂²	semidirect
60. C₇×#496	C₂²	semidirect
61. C₇×#493	C₂²	semidirect
62. C₇×#493	C₂²	semidirect
63. C₇×#493	C₂²	semidirect
64. C₇×#490	C₂²	semidirect
65. C₇×#488	C₂²	semidirect
66. C₇×#486	C₂²	semidirect
67. C₇×#486	C₂²	semidirect
68. C₇×#484	C₂²	semidirect
69. C₇×#482	C₂²	semidirect
70. C₇×#482	C₂²	semidirect
71. C₇×#481	C₂²	semidirect
72. C₇×#478	C₂²	semidirect
73. C₇×#478	C₂²	semidirect
74. C₇×#478	C₂²	semidirect
75. C₇×#478	C₂²	semidirect
76. C₇×#478	C₂²	semidirect
77. C₇×#477	C₂²	semidirect
78. C₇×#476	C₂²	semidirect
79. C₇×#469	C₂²	semidirect
80. C₇×#469	C₂²	semidirect
81. C₇×#466	C₂²	semidirect
82. C₇×#466	C₂²	semidirect
83. C₇×#466	C₂²	semidirect
84. C₇×#465	C₂²	semidirect
85. C₇×#463	C₂²	semidirect
86. C₇×#463	C₂²	semidirect
87. C₇×#463	C₂²	semidirect
88. C₇×#463	C₂²	semidirect
89. C₇×#463	C₂²	semidirect
90. C₇×#460	C₂²	semidirect
92. C₇×#459	C₂²	semidirect
93. C₇×#459	C₂²	semidirect
94. C₇×#459	C₂²	semidirect
95. C₇×#459	C₂²	semidirect
96. C₇×#459	C₂²	semidirect
97. C₇×#459	C₂²	semidirect
98. C₇×#459	C₂²	semidirect
99. C₇×#459	C₂²	semidirect
100. C₇×#459	C₂²	semidirect
101. C₇×#459	C₂²	semidirect
102. C₇×#459	C₂²	semidirect
103. C₇×#459	C₂²	semidirect
104. C₇×#450	C₂²	semidirect
105. C₇×#449	C₂²	semidirect
106. C₇×#449	C₂²	semidirect
108. C₇×#447	C₂²	semidirect
109. C₇×#447	C₂²	semidirect
110. C₇×#447	C₂²	semidirect
111. C₇×#447	C₂²	semidirect
112. C₇×#447	C₂²	semidirect
113. C₇×#447	C₂²	semidirect
114. C₇×#446	C₂²	semidirect
115. C₇×C₈×Q₈	C₂²	semidirect
116. C₇×#442	C₂²	semidirect
117. C₇×#442	C₂²	semidirect
118. C₄×C₇×SD₁₆	C₂²	semidirect
119. C₄×C₇×SD₁₆	C₂²	semidirect
120. C₄×C₇×D₈	C₂²	semidirect
121. C₄×C₇×D₈	C₂²	semidirect
122. C₄×C₇×D₈	C₂²	semidirect
123. C₄×C₇×D₈	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. #62051	C₇	direct (N × H)
316. #3543	C₂×C₇	semidirect
317. #3519	C₂×C₇	semidirect
318. #3399	C₂×C₇	semidirect
319. #3391	C₂×C₇	semidirect
320. #3366	C₂×C₇	semidirect
321. #3361	C₂×C₇	semidirect
322. #3325	C₂×C₇	semidirect
323. #3318	C₂×C₇	semidirect
324. #3305	C₂×C₇	semidirect
325. #3297	C₂×C₇	semidirect
326. D₄×D₈	C₂×C₇	semidirect
327. D₄×D₈	C₂×C₇	semidirect
328. #3274	C₂×C₇	semidirect
329. #3264	C₂×C₇	semidirect
330. #3259	C₂×C₇	semidirect
331. #3247	C₂×C₇	semidirect
332. #3220	C₂×C₇	semidirect
333. #3205	C₂×C₇	semidirect
334. #3122	C₂×C₇	semidirect
335. #3105	C₂×C₇	semidirect
336. #3041	C₂×C₇	semidirect
337. C₂×#459	C₂×C₇	semidirect
338. #2994	C₂×C₇	semidirect
489. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
490. C₂²×D₈	C₂²×C₇	semidirect
491. C₂²×D₈	C₂²×C₇	semidirect
493. #559	C₂²×C₇	semidirect
494. #555	C₂²×C₇	semidirect
495. #554	C₂²×C₇	semidirect
497. #553	C₂²×C₇	semidirect
498. #550	C₂²×C₇	semidirect
499. #550	C₂²×C₇	semidirect
500. #550	C₂²×C₇	semidirect
504. #546	C₂²×C₇	semidirect
506. D₄²	C₂²×C₇	semidirect
507. D₄²	C₂²×C₇	semidirect
508. D₄²	C₂²×C₇	semidirect
509. D₄²	C₂²×C₇	semidirect
511. #540	C₂²×C₇	semidirect
512. #540	C₂²×C₇	semidirect
515. #535	C₂²×C₇	semidirect
517. #532	C₂²×C₇	semidirect
518. C₂×#127	C₂²×C₇	semidirect
520. #529	C₂²×C₇	semidirect
523. #518	C₂²×C₇	semidirect
524. C₂×C₄×D₄	C₂²×C₇	semidirect
525. #496	C₂²×C₇	semidirect
526. #493	C₂²×C₇	semidirect
527. #493	C₂²×C₇	semidirect
528. #493	C₂²×C₇	semidirect
529. #490	C₂²×C₇	semidirect
530. #488	C₂²×C₇	semidirect
531. #486	C₂²×C₇	semidirect
532. #486	C₂²×C₇	semidirect
533. #484	C₂²×C₇	semidirect
534. #482	C₂²×C₇	semidirect
535. #482	C₂²×C₇	semidirect
536. #481	C₂²×C₇	semidirect
537. #478	C₂²×C₇	semidirect
538. #478	C₂²×C₇	semidirect
539. #478	C₂²×C₇	semidirect
540. #478	C₂²×C₇	semidirect
541. #478	C₂²×C₇	semidirect
542. #477	C₂²×C₇	semidirect
543. #476	C₂²×C₇	semidirect
544. #469	C₂²×C₇	semidirect
545. #469	C₂²×C₇	semidirect
546. #466	C₂²×C₇	semidirect
547. #466	C₂²×C₇	semidirect
548. #466	C₂²×C₇	semidirect
549. #465	C₂²×C₇	semidirect
550. #463	C₂²×C₇	semidirect
551. #463	C₂²×C₇	semidirect
552. #463	C₂²×C₇	semidirect
553. #463	C₂²×C₇	semidirect
554. #463	C₂²×C₇	semidirect
555. #460	C₂²×C₇	semidirect
557. #459	C₂²×C₇	semidirect
558. #459	C₂²×C₇	semidirect
559. #459	C₂²×C₇	semidirect
560. #459	C₂²×C₇	semidirect
561. #459	C₂²×C₇	semidirect
562. #459	C₂²×C₇	semidirect
563. #459	C₂²×C₇	semidirect
564. #459	C₂²×C₇	semidirect
565. #459	C₂²×C₇	semidirect
566. #459	C₂²×C₇	semidirect
567. #459	C₂²×C₇	semidirect
568. #459	C₂²×C₇	semidirect
569. #450	C₂²×C₇	semidirect
570. #449	C₂²×C₇	semidirect
571. #449	C₂²×C₇	semidirect
573. #447	C₂²×C₇	semidirect
574. #447	C₂²×C₇	semidirect
575. #447	C₂²×C₇	semidirect
576. #447	C₂²×C₇	semidirect
577. #447	C₂²×C₇	semidirect
578. #447	C₂²×C₇	semidirect
579. #446	C₂²×C₇	semidirect
580. C₈×Q₈	C₂²×C₇	semidirect
581. #442	C₂²×C₇	semidirect
582. #442	C₂²×C₇	semidirect
583. C₄×SD₁₆	C₂²×C₇	semidirect
584. C₄×SD₁₆	C₂²×C₇	semidirect
585. C₄×D₈	C₂²×C₇	semidirect
586. C₄×D₈	C₂²×C₇	semidirect
587. C₄×D₈	C₂²×C₇	semidirect
588. C₄×D₈	C₂²×C₇	semidirect
589. #436	C₂²×C₇	semidirect
590. #435	C₂²×C₇	semidirect
591. C₈×D₄	C₂²×C₇	semidirect
592. C₈×D₄	C₂²×C₇	semidirect
593. #433	C₂²×C₇	semidirect
594. #431	C₂²×C₇	semidirect
595. #424	C₂²×C₇	semidirect
596. C₂×C₄⋊C₈	C₂²×C₇	semidirect
597. #418	C₂²×C₇	semidirect
598. #416	C₂²×C₇	semidirect
599. C₂×#102	C₂²×C₇	semidirect
1186. C₇	#62051	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×#3519	2
C₇×#3399	2
C₇×#3391	2
C₇×#3366	2
C₇×#3361	2
C₇×#3325	2
C₇×#3318	2
C₇×#3305	2
C₇×#3297	2
C₇×D₄×D₈	2
C₇×#3274	2
C₇×#3264	2
C₇×#3259	2
C₇×#3247	2
C₇×#3220	2
C₇×#3205	2
C₇×#3122	2
C₇×#3105	2
C₇×#3041	2
C₂×C₇×#459	2
C₇×#2994	2
#62051	7

Subgroups — C7×#62051 #13239267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62051 #13239267