Subgroups — C₇×#61006 #13238222

Order 1792.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3257	C₂	1	4	yes	maximal, complemented
4	C₇×#3231	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3228	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3227	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3207	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3207	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3198	C₂	1	4	yes	maximal, complemented
13	C₇×#3184	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3182	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3119	C₂	1	4	yes	maximal, complemented
18	C₇×#3118	C₂	1	4	yes	maximal, complemented
19	C₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#559	—	2	1	no	—
21	C₇×#559	—	2	1	no	—
22	C₇×#556	—	2	1	no	—
23	C₇×#555	—	2	1	no	—
24	C₇×#554	—	2	1	no	—
25	C₇×#553	—	2	1	no	—
26	C₇×#553	—	2	1	no	—
27	C₇×#550	—	2	1	no	—
28	C₇×#550	—	2	1	no	—
29	C₇×#548	—	2	1	no	—
30	C₇×#548	—	2	1	no	—
31	C₇×#547	—	2	1	no	—
32	C₇×#546	—	2	1	no	—
33	C₇×#546	—	2	1	no	—
34	C₇×#546	—	2	1	no	—
35	C₇×#546	—	2	1	no	—
36	C₇×#542	C₂²	1	2	yes	—
37	C₇×#542	C₂²	1	2	yes	complemented
38	C₇×#540	C₂²	1	2	yes	—
39	C₇×#540	C₂²	1	2	yes	—
40	C₇×#537	C₂²	1	2	yes	—
41	C₇×#535	C₂²	1	2	yes	—
42	C₇×#533	C₂²	1	1	yes	characteristic
43	C₇×#533	C₂²	1	1	yes	characteristic
44	C₇×#533	C₂²	1	1	yes	characteristic, complemented
45	C₇×#532	C₂²	1	1	yes	characteristic
46	C₇×#532	C₂²	1	1	yes	characteristic
47	C₇×#532	C₂²	1	1	yes	characteristic
48	C₇×#532	C₂²	1	1	yes	characteristic
49	C₇×#532	C₂²	1	1	yes	characteristic
50	C₇×#532	C₂²	1	1	yes	characteristic, complemented
51	C₇×#532	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₇×#127	C₂²	1	1	yes	characteristic
54	C₇×#520	C₂²	1	2	yes	complemented
55	C₇×#518	C₂²	1	2	yes	—
56	C₄×C₇×#41	C₂²	1	1	yes	characteristic
57	C₇×#500	C₂²	1	1	yes	characteristic, complemented
58	C₇×#500	C₂²	1	1	yes	characteristic, complemented
59	C₇×#498	C₂²	1	1	yes	characteristic, complemented
60	C₇×#498	C₂²	1	1	yes	characteristic, complemented
61	C₇×#493	C₂²	1	1	yes	characteristic
62	C₇×#493	C₂²	1	1	yes	characteristic
63	C₇×#492	C₂²	1	1	yes	characteristic
64	C₇×#492	C₂²	1	1	yes	characteristic
65	C₇×#487	C₂²	1	1	yes	characteristic, complemented
66	C₇×#487	C₂²	1	1	yes	characteristic, complemented
67	C₇×#486	C₂²	1	1	yes	characteristic
68	C₇×#486	C₂²	1	1	yes	characteristic
69	C₇×#486	C₂²	1	1	yes	characteristic
70	C₇×#486	C₂²	1	1	yes	characteristic
71	C₇×#486	C₂²	1	1	yes	characteristic, complemented
72	C₇×#486	C₂²	1	1	yes	characteristic, complemented
73	C₇×#485	C₂²	1	4	yes	—
74	C₇×#482	C₂²	1	4	yes	—
75	C₇×#481	C₂²	1	4	yes	complemented
76	C₇×#480	C₂²	1	4	yes	complemented
77	C₇×#479	C₂²	1	4	yes	complemented
78	C₇×#478	C₂²	1	4	yes	complemented
79	C₇×#476	C₂²	1	4	yes	complemented
80	C₇×#474	C₂²	1	4	yes	complemented
81	C₇×#469	C₂²	1	4	yes	complemented
82	C₇×#468	C₂²	1	4	yes	complemented
83	C₇×#466	C₂²	1	4	yes	complemented
84	C₇×#465	C₂²	1	4	yes	complemented
85	C₇×#463	C₂²	1	4	yes	complemented
86	C₇×#463	C₂²	1	4	yes	complemented
87	C₇×#460	C₂²	1	4	yes	—
88	C₇×#459	C₂²	1	4	yes	—
89	C₇×#450	C₂²	1	4	yes	—
90	C₇×#449	C₂²	1	4	yes	complemented
91	C₇×#449	C₂²	1	4	yes	complemented
92	C₇×#447	C₂²	1	4	yes	—
93	C₇×#442	C₂²	1	4	yes	complemented
94	C₇×#440	C₂²	1	4	yes	complemented
95	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
96	C₄×C₇×D₈	C₂²	1	4	yes	complemented
97	C₇×#433	C₂²	1	2	yes	—
98	C₇×#433	C₂²	1	2	yes	complemented
99	C₇×#431	C₂²	1	1	yes	characteristic
100	C₇×#431	C₂²	1	1	yes	characteristic
101	C₇×#431	C₂²	1	1	yes	characteristic, complemented
102	C₇×#431	C₂²	1	1	yes	characteristic, complemented
103	C₇×#424	C₂²	1	2	yes	complemented
104	C₇×#408	C₂²	1	2	yes	—
105	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
107	#61006	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂×C₇×#41	—	2	1	no	—
109	C₂×C₇×#41	—	2	1	no	—
110	C₂×C₇×#41	—	2	1	no	—
111	C₂×C₇×#41	—	2	1	no	—
112	C₂×C₇×#41	—	2	1	no	—
113	C₂×C₇×#41	—	2	1	no	—
114	C₂×C₇×#41	C₂³	1	2	yes	—
115	C₂×C₇×#41	C₂³	1	1	yes	characteristic
116	C₂²×C₇×Q₈	—	2	1	no	—
117	C₂²×C₇×D₄	—	2	1	no	—
118	C₂²×C₇×D₄	—	2	1	no	—
119	C₂²×C₇×D₄	C₂³	1	2	yes	—
120	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
121	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
122	C₂×C₇×D₈	C₂³	1	4	yes	—
123	C₂×C₇×D₈	C₂³	1	4	yes	—
124	C₂×C₇×M₁₆	C₂³	1	2	yes	—
125	C₂²×C₇×C₈	C₂³	1	2	yes	—
126	C₇×C₄⋊Q₈	—	2	1	no	—
127	C₇×C₄⋊Q₈	—	2	1	no	—
128	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
129	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
131	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
132	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
133	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
134	C₇×#127	—	2	2	no	—
135	C₇×#127	—	2	1	no	—
136	C₇×#127	—	2	1	no	—
137	C₇×#127	C₂³	1	1	yes	characteristic
138	C₇×#127	C₂³	1	1	yes	characteristic
139	C₇×#127	C₂³	1	1	yes	characteristic
140	C₇×#127	C₂³	1	2	yes	—
141	C₇×#126	—	2	2	no	—
142	C₇×#126	—	2	2	no	—
143	C₇×#125	—	2	1	no	—
144	C₇×#125	—	2	1	no	—
145	C₇×#125	C₂³	1	2	yes	—
146	C₇×#124	—	2	2	no	—
147	C₇×#124	—	2	2	no	—
148	C₇×#124	—	2	2	no	—
149	C₇×#124	—	2	1	no	—
150	C₇×#124	—	2	1	no	—
151	C₇×#124	—	2	1	no	—
152	C₇×#124	—	2	1	no	—
153	C₇×#124	—	2	1	no	—
154	C₇×#124	—	2	1	no	—
155	C₇×#124	C₂³	1	2	yes	—
156	C₇×#123	—	2	2	no	—
157	C₇×#123	—	2	2	no	—
158	C₇×#123	—	2	2	no	—
159	C₇×#123	—	2	2	no	—
160	C₇×#123	—	2	2	no	—
161	C₇×#123	—	2	2	no	—
162	C₇×C₂²⋊Q₈	—	2	2	no	—
163	C₇×C₂²⋊Q₈	—	2	1	no	—
164	C₇×C₂²⋊Q₈	—	2	1	no	—
165	C₇×C₂²⋊Q₈	—	2	1	no	—
166	C₇×C₂²⋊Q₈	—	2	1	no	—
167	C₇×C₂²⋊Q₈	—	2	2	no	—
168	C₇×C₂²⋊Q₈	—	2	2	no	—
169	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
170	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
171	C₇×#121	—	2	2	no	—
172	C₇×#121	—	2	2	no	—
173	C₇×#121	—	2	2	no	—
174	C₇×#121	—	2	1	no	—
175	C₇×#121	—	2	1	no	—
176	C₇×#121	—	2	1	no	—
177	C₇×#121	—	2	1	no	—
178	C₇×#121	—	2	1	no	—
179	C₇×#121	—	2	1	no	—
180	C₇×#121	—	2	1	no	—
181	C₇×#121	—	2	1	no	—
182	C₇×#121	—	2	2	no	—
183	C₇×#121	—	2	2	no	—
184	C₇×#121	—	2	2	no	—
185	C₇×#121	—	2	2	no	—
186	C₇×#121	C₂³	1	2	yes	—
187	C₇×#121	C₂³	1	2	yes	—
188	C₇×#121	C₂³	1	2	yes	—
189	C₇×#121	C₂³	1	2	yes	—
190	C₇×#121	C₂³	1	2	yes	—
191	C₇×#121	C₂³	1	2	yes	—
192	C₇×#120	—	2	2	no	—
193	C₇×#120	—	2	2	no	—
194	C₄×C₇×Q₈	—	2	1	no	—
195	C₄×C₇×Q₈	—	2	1	no	—
196	C₄×C₇×Q₈	—	2	1	no	—
197	C₄×C₇×Q₈	—	2	1	no	—
198	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
199	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
200	C₄×C₇×Q₈	C₂³	1	2	yes	—
201	C₄×C₇×Q₈	C₂³	1	2	yes	—
202	C₄×C₇×D₄	—	2	2	no	—
203	C₄×C₇×D₄	—	2	2	no	—
204	C₄×C₇×D₄	—	2	2	no	—
205	C₄×C₇×D₄	—	2	2	no	—
206	C₄×C₇×D₄	—	2	1	no	—
207	C₄×C₇×D₄	—	2	1	no	—
208	C₄×C₇×D₄	—	2	1	no	—
209	C₄×C₇×D₄	—	2	1	no	—
210	C₄×C₇×D₄	—	2	1	no	—
211	C₄×C₇×D₄	—	2	1	no	—
212	C₄×C₇×D₄	—	2	1	no	—
213	C₄×C₇×D₄	—	2	1	no	—
214	C₄×C₇×D₄	D₄	1	1	yes	characteristic
215	C₄×C₇×D₄	D₄	1	1	yes	characteristic
216	C₄×C₇×D₄	D₄	1	1	yes	characteristic
217	C₄×C₇×D₄	D₄	1	1	yes	characteristic
218	C₄×C₇×D₄	D₄	1	1	yes	characteristic
219	C₄×C₇×D₄	D₄	1	1	yes	characteristic
220	C₄×C₇×D₄	C₂³	1	2	yes	—
221	C₄×C₇×D₄	C₂³	1	2	yes	—
222	C₄×C₇×D₄	C₂³	1	2	yes	—
223	C₄×C₇×D₄	C₂³	1	2	yes	—
224	C₄×C₇×D₄	C₂³	1	2	yes	—
225	C₄×C₇×D₄	C₂³	1	2	yes	—
226	C₇×#117	—	2	1	no	—
227	C₇×#117	—	2	1	no	—
228	C₇×#117	—	2	2	no	—
229	C₇×#117	C₂³	1	2	yes	—
230	C₇×#117	C₂³	1	1	yes	characteristic
231	C₇×#117	C₂³	1	1	yes	characteristic
232	C₇×#117	C₂³	1	1	yes	characteristic
233	C₂×C₇×C₄⋊C₄	—	2	1	no	—
234	C₂×C₇×C₄⋊C₄	—	2	2	no	—
235	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
236	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
240	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
241	C₇×#107	C₂³	1	4	yes	—
242	C₇×#107	C₂³	1	4	yes	—
243	C₇×#106	C₂³	1	4	yes	—
244	C₇×#106	C₂³	1	4	yes	—
245	C₇×C₄⋊C₈	C₂³	1	2	yes	—
246	C₇×C₄⋊C₈	C₂³	1	2	yes	—
247	C₇×C₄⋊C₈	C₂³	1	2	yes	—
248	C₇×C₄⋊C₈	C₂³	1	2	yes	—
249	C₇×#103	C₂³	1	4	yes	—
250	C₇×#103	C₂³	1	4	yes	—
251	C₇×#102	C₂³	1	4	yes	—
252	C₇×#102	C₂³	1	4	yes	—
253	C₇×#102	C₂³	1	4	yes	—
254	C₇×#102	C₂³	1	4	yes	—
255	C₇×#102	C₂³	1	4	yes	—
256	C₇×#102	C₂³	1	4	yes	—
257	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
260	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
261	C₇×#97	C₂³	1	2	yes	—
262	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
263	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
264	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
265	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
266	C₄×C₇×C₈	C₂³	1	2	yes	—
267	#3511	C₂×C₇	1	1	yes	characteristic, complemented
268	#3508	C₂×C₇	1	1	yes	characteristic, complemented
269	#3257	C₂×C₇	1	4	yes	complemented
270	#3231	C₂×C₇	1	1	yes	characteristic, complemented
271	#3228	C₂×C₇	1	1	yes	characteristic, complemented
272	#3227	C₂×C₇	1	1	yes	characteristic, complemented
273	#3226	C₂×C₇	1	1	yes	characteristic, complemented
274	#3208	C₂×C₇	1	1	yes	characteristic, complemented
275	#3207	C₂×C₇	1	1	yes	characteristic, complemented
276	#3207	C₂×C₇	1	1	yes	characteristic, complemented
277	#3205	C₂×C₇	1	1	yes	characteristic, complemented
278	#3198	C₂×C₇	1	4	yes	complemented
279	#3184	C₂×C₇	1	1	yes	characteristic, complemented
280	#3182	C₂×C₇	1	1	yes	characteristic, complemented
281	#3169	C₂×C₇	1	1	yes	characteristic, complemented
282	#3167	C₂×C₇	1	1	yes	characteristic, complemented
283	#3119	C₂×C₇	1	4	yes	complemented
284	#3118	C₂×C₇	1	4	yes	complemented
285	#2922	C₂×C₇	1	1	yes	characteristic, complemented
286	C₂⁴×C₇	—	2	2	no	—
287	C₇×#41	—	4	2	no	—
288	C₇×#41	—	4	4	no	—
289	C₇×#41	—	8	2	no	—
290	C₇×#41	—	8	2	no	—
291	C₇×#41	—	8	2	no	—
292	C₇×#41	—	8	2	no	—
293	C₇×#41	—	8	2	no	—
294	C₇×#41	—	8	2	no	—
295	C₂×C₇×Q₈	—	2	1	no	—
296	C₂×C₇×Q₈	—	2	1	no	—
297	C₂×C₇×Q₈	—	2	1	no	—
298	C₂×C₇×Q₈	—	2	1	no	—
299	C₂×C₇×Q₈	—	2	2	no	—
300	C₂×C₇×Q₈	—	8	2	no	—
301	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
302	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
303	C₂×C₇×D₄	—	2	2	no	—
304	C₂×C₇×D₄	—	2	2	no	—
305	C₂×C₇×D₄	—	2	2	no	—
306	C₂×C₇×D₄	—	2	2	no	—
307	C₂×C₇×D₄	—	2	2	no	—
308	C₂×C₇×D₄	—	2	2	no	—
309	C₂×C₇×D₄	—	2	2	no	—
310	C₂×C₇×D₄	—	2	1	no	—
311	C₂×C₇×D₄	—	2	2	no	—
312	C₂×C₇×D₄	—	2	1	no	—
313	C₂×C₇×D₄	—	2	1	no	—
314	C₂×C₇×D₄	—	2	1	no	—
315	C₂×C₇×D₄	—	2	1	no	—
316	C₂×C₇×D₄	—	2	1	no	—
317	C₂×C₇×D₄	—	2	2	no	—
318	C₂×C₇×D₄	—	2	2	no	—
319	C₂×C₇×D₄	—	4	4	no	—
320	C₂×C₇×D₄	—	8	2	no	—
321	C₂×C₇×D₄	—	8	2	no	—
322	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
323	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
324	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
325	C₂×C₇×D₄	C₂⁴	1	2	yes	—
326	C₂×C₇×D₄	C₂⁴	1	2	yes	—
327	C₂×C₇×D₄	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₇	—	2	2	no	—
329	C₂²×C₄×C₇	—	2	2	no	—
330	C₂²×C₄×C₇	—	2	2	no	—
331	C₂²×C₄×C₇	—	2	2	no	—
332	C₂²×C₄×C₇	—	2	2	no	—
333	C₂²×C₄×C₇	—	2	2	no	—
334	C₂²×C₄×C₇	—	2	2	no	—
335	C₂²×C₄×C₇	—	2	2	no	—
336	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
345	C₇×SD₁₆	—	4	4	no	—
346	C₇×SD₁₆	—	4	4	no	—
347	C₇×D₈	—	4	4	no	—
348	C₇×D₈	—	4	4	no	—
349	C₇×M₁₆	—	4	2	no	—
350	C₂×C₇×C₈	—	4	2	no	—
351	C₂×C₇×C₈	C₂⁴	1	2	yes	—
352	C₂×C₇×C₈	C₂⁴	1	2	yes	—
353	C₂×C₇×C₈	C₂⁴	1	2	yes	—
354	C₂×C₇×C₈	C₂⁴	1	2	yes	—
355	C₇×C₄⋊C₄	—	2	2	no	—
356	C₇×C₄⋊C₄	—	2	1	no	—
357	C₇×C₄⋊C₄	—	2	1	no	—
358	C₇×C₄⋊C₄	—	2	2	no	—
359	C₇×C₄⋊C₄	—	2	2	no	—
360	C₇×C₄⋊C₄	—	2	2	no	—
361	C₇×C₄⋊C₄	—	2	1	no	—
362	C₇×C₄⋊C₄	—	2	1	no	—
363	C₇×C₄⋊C₄	—	2	1	no	—
364	C₇×C₄⋊C₄	—	2	1	no	—
365	C₇×C₄⋊C₄	—	2	2	no	—
366	C₇×C₄⋊C₄	—	2	2	no	—
367	C₇×C₄⋊C₄	—	2	2	no	—
368	C₇×C₄⋊C₄	—	2	2	no	—
369	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
370	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
371	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
372	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
373	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
374	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
375	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
376	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
377	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
378	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
379	C₇×C₂²⋊C₄	—	2	2	no	—
380	C₇×C₂²⋊C₄	—	2	2	no	—
381	C₇×C₂²⋊C₄	—	2	2	no	—
382	C₇×C₂²⋊C₄	—	2	2	no	—
383	C₇×C₂²⋊C₄	—	2	2	no	—
384	C₇×C₂²⋊C₄	—	2	2	no	—
385	C₇×C₂²⋊C₄	—	2	2	no	—
386	C₇×C₂²⋊C₄	—	2	2	no	—
387	C₇×C₂²⋊C₄	—	2	2	no	—
388	C₇×C₂²⋊C₄	—	2	2	no	—
389	C₇×C₂²⋊C₄	—	2	2	no	—
390	C₇×C₂²⋊C₄	—	2	2	no	—
391	C₇×C₂²⋊C₄	—	2	2	no	—
392	C₇×C₂²⋊C₄	—	2	2	no	—
393	C₇×C₂²⋊C₄	—	2	2	no	—
394	C₇×C₂²⋊C₄	—	2	2	no	—
395	C₇×C₂²⋊C₄	—	2	2	no	—
396	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
397	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
398	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
400	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
401	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₇	—	2	2	no	—
403	C₄²×C₇	—	2	2	no	—
404	C₄²×C₇	—	2	2	no	—
405	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
406	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
407	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
408	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
409	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
410	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
411	C₄²×C₇	C₂⁴	1	1	yes	characteristic
412	C₄²×C₇	C₂⁴	1	1	yes	characteristic
413	C₄²×C₇	C₂⁴	1	1	yes	characteristic
414	C₄²×C₇	C₂⁴	1	1	yes	characteristic
415	#559	—	2	1	no	—
416	#559	—	2	1	no	—
417	#556	—	2	1	no	—
418	#555	—	2	1	no	—
419	#554	—	2	1	no	—
420	#553	—	2	1	no	—
421	#553	—	2	1	no	—
422	#550	—	2	1	no	—
423	#550	—	2	1	no	—
424	#548	—	2	1	no	—
425	#548	—	2	1	no	—
426	#547	—	2	1	no	—
427	#546	—	2	1	no	—
428	#546	—	2	1	no	—
429	#546	—	2	1	no	—
430	#546	—	2	1	no	—
431	#542	C₂²×C₇	1	2	yes	—
432	#542	C₂²×C₇	1	2	yes	complemented
433	#540	C₂²×C₇	1	2	yes	—
434	#540	C₂²×C₇	1	2	yes	—
435	#537	C₂²×C₇	1	2	yes	—
436	#535	C₂²×C₇	1	2	yes	—
437	#533	C₂²×C₇	1	1	yes	characteristic
438	#533	C₂²×C₇	1	1	yes	characteristic
439	#533	C₂²×C₇	1	1	yes	characteristic, complemented
440	#532	C₂²×C₇	1	1	yes	characteristic
441	#532	C₂²×C₇	1	1	yes	characteristic
442	#532	C₂²×C₇	1	1	yes	characteristic
443	#532	C₂²×C₇	1	1	yes	characteristic
444	#532	C₂²×C₇	1	1	yes	characteristic
445	#532	C₂²×C₇	1	1	yes	characteristic, complemented
446	#532	C₂²×C₇	1	1	yes	characteristic, complemented
447	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
448	C₂×#127	C₂²×C₇	1	1	yes	characteristic
449	#520	C₂²×C₇	1	2	yes	complemented
450	#518	C₂²×C₇	1	2	yes	—
451	C₄×#41	C₂²×C₇	1	1	yes	characteristic
452	#500	C₂²×C₇	1	1	yes	characteristic, complemented
453	#500	C₂²×C₇	1	1	yes	characteristic, complemented
454	#498	C₂²×C₇	1	1	yes	characteristic, complemented
455	#498	C₂²×C₇	1	1	yes	characteristic, complemented
456	#493	C₂²×C₇	1	1	yes	characteristic
457	#493	C₂²×C₇	1	1	yes	characteristic
458	#492	C₂²×C₇	1	1	yes	characteristic
459	#492	C₂²×C₇	1	1	yes	characteristic
460	#487	C₂²×C₇	1	1	yes	characteristic, complemented
461	#487	C₂²×C₇	1	1	yes	characteristic, complemented
462	#486	C₂²×C₇	1	1	yes	characteristic
463	#486	C₂²×C₇	1	1	yes	characteristic
464	#486	C₂²×C₇	1	1	yes	characteristic
465	#486	C₂²×C₇	1	1	yes	characteristic
466	#486	C₂²×C₇	1	1	yes	characteristic, complemented
467	#486	C₂²×C₇	1	1	yes	characteristic, complemented
468	#485	C₂²×C₇	1	4	yes	—
469	#482	C₂²×C₇	1	4	yes	—
470	#481	C₂²×C₇	1	4	yes	complemented
471	#480	C₂²×C₇	1	4	yes	complemented
472	#479	C₂²×C₇	1	4	yes	complemented
473	#478	C₂²×C₇	1	4	yes	complemented
474	#476	C₂²×C₇	1	4	yes	complemented
475	#474	C₂²×C₇	1	4	yes	complemented
476	#469	C₂²×C₇	1	4	yes	complemented
477	#468	C₂²×C₇	1	4	yes	complemented
478	#466	C₂²×C₇	1	4	yes	complemented
479	#465	C₂²×C₇	1	4	yes	complemented
480	#463	C₂²×C₇	1	4	yes	complemented
481	#463	C₂²×C₇	1	4	yes	complemented
482	#460	C₂²×C₇	1	4	yes	—
483	#459	C₂²×C₇	1	4	yes	—
484	#450	C₂²×C₇	1	4	yes	—
485	#449	C₂²×C₇	1	4	yes	complemented
486	#449	C₂²×C₇	1	4	yes	complemented
487	#447	C₂²×C₇	1	4	yes	—
488	#442	C₂²×C₇	1	4	yes	complemented
489	#440	C₂²×C₇	1	4	yes	complemented
490	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
491	C₄×D₈	C₂²×C₇	1	4	yes	complemented
492	#433	C₂²×C₇	1	2	yes	—
493	#433	C₂²×C₇	1	2	yes	complemented
494	#431	C₂²×C₇	1	1	yes	characteristic
495	#431	C₂²×C₇	1	1	yes	characteristic
496	#431	C₂²×C₇	1	1	yes	characteristic, complemented
497	#431	C₂²×C₇	1	1	yes	characteristic, complemented
498	#424	C₂²×C₇	1	2	yes	complemented
499	#408	C₂²×C₇	1	2	yes	—
500	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
501	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
502	C₂³×C₇	—	2	2	no	—
503	C₂³×C₇	—	2	2	no	—
504	C₂³×C₇	—	2	2	no	—
505	C₂³×C₇	—	4	4	no	—
506	C₂³×C₇	—	8	2	no	—
507	C₂³×C₇	—	8	2	no	—
508	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
509	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
510	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
511	C₇×Q₈	—	2	4	no	—
512	C₇×Q₈	—	4	1	no	—
513	C₇×Q₈	—	4	2	no	—
514	C₇×Q₈	—	4	2	no	—
515	C₇×Q₈	—	4	2	no	—
516	C₇×Q₈	—	4	2	no	—
517	C₇×Q₈	—	8	2	no	—
518	C₇×D₄	—	2	4	no	—
519	C₇×D₄	—	2	4	no	—
520	C₇×D₄	—	2	4	no	—
521	C₇×D₄	—	4	1	no	—
522	C₇×D₄	—	4	1	no	—
523	C₇×D₄	—	4	1	no	—
524	C₇×D₄	—	4	4	no	—
525	C₇×D₄	—	4	4	no	—
526	C₇×D₄	—	4	2	no	—
527	C₇×D₄	—	4	2	no	—
528	C₇×D₄	—	4	2	no	—
529	C₇×D₄	—	4	2	no	—
530	C₇×D₄	—	4	2	no	—
531	C₇×D₄	—	4	2	no	—
532	C₇×D₄	—	8	2	no	—
533	C₇×D₄	—	8	2	no	—
534	C₇×D₄	—	8	2	no	—
535	C₇×D₄	—	8	2	no	—
536	C₇×D₄	—	8	2	no	—
537	C₇×D₄	—	8	2	no	—
538	C₇×D₄	—	8	2	no	—
539	C₇×D₄	—	8	2	no	—
540	C₂×C₄×C₇	—	2	2	no	—
541	C₂×C₄×C₇	—	2	2	no	—
542	C₂×C₄×C₇	—	2	2	no	—
543	C₂×C₄×C₇	—	2	2	no	—
544	C₂×C₄×C₇	—	2	2	no	—
545	C₂×C₄×C₇	—	2	2	no	—
546	C₂×C₄×C₇	—	2	2	no	—
547	C₂×C₄×C₇	—	2	2	no	—
548	C₂×C₄×C₇	—	2	2	no	—
549	C₂×C₄×C₇	—	2	2	no	—
550	C₂×C₄×C₇	—	2	2	no	—
551	C₂×C₄×C₇	—	2	2	no	—
552	C₂×C₄×C₇	—	2	2	no	—
553	C₂×C₄×C₇	—	2	2	no	—
554	C₂×C₄×C₇	—	4	4	no	—
555	C₂×C₄×C₇	—	8	2	no	—
556	C₂×C₄×C₇	—	8	2	no	—
557	C₂×C₄×C₇	—	8	2	no	—
558	C₂×C₄×C₇	—	8	2	no	—
559	C₂×C₄×C₇	—	8	2	no	—
560	C₂×C₄×C₇	—	8	2	no	—
561	C₂×C₄×C₇	—	8	2	no	—
562	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
574	C₇×C₈	—	2	2	no	—
575	C₇×C₈	—	2	2	no	—
576	C₇×C₈	—	2	2	no	—
577	C₇×C₈	—	2	2	no	—
578	C₂×#41	—	2	1	no	—
579	C₂×#41	—	2	1	no	—
580	C₂×#41	—	2	1	no	—
581	C₂×#41	—	2	1	no	—
582	C₂×#41	—	2	1	no	—
583	C₂×#41	—	2	1	no	—
584	C₂×#41	C₂³×C₇	1	2	yes	—
585	C₂×#41	C₂³×C₇	1	1	yes	characteristic
586	C₂²×Q₈	—	2	1	no	—
587	C₂²×D₄	—	2	1	no	—
588	C₂²×D₄	—	2	1	no	—
589	C₂²×D₄	C₂³×C₇	1	2	yes	—
590	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
591	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
592	C₂×D₈	C₂³×C₇	1	4	yes	—
593	C₂×D₈	C₂³×C₇	1	4	yes	—
594	C₂×M₁₆	C₂³×C₇	1	2	yes	—
595	C₂²×C₈	C₂³×C₇	1	2	yes	—
596	C₄⋊Q₈	—	2	1	no	—
597	C₄⋊Q₈	—	2	1	no	—
598	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
599	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
600	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
601	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
602	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
603	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
604	#127	—	2	2	no	—
605	#127	—	2	1	no	—
606	#127	—	2	1	no	—
607	#127	C₂³×C₇	1	1	yes	characteristic
608	#127	C₂³×C₇	1	1	yes	characteristic
609	#127	C₂³×C₇	1	2	yes	—
610	#127	C₂³×C₇	1	1	yes	characteristic
611	#126	—	2	2	no	—
612	#126	—	2	2	no	—
613	#125	—	2	1	no	—
614	#125	—	2	1	no	—
615	#125	C₂³×C₇	1	2	yes	—
616	#124	—	2	2	no	—
617	#124	—	2	2	no	—
618	#124	—	2	2	no	—
619	#124	—	2	1	no	—
620	#124	—	2	1	no	—
621	#124	—	2	1	no	—
622	#124	—	2	1	no	—
623	#124	—	2	1	no	—
624	#124	—	2	1	no	—
625	#124	C₂³×C₇	1	2	yes	—
626	#123	—	2	2	no	—
627	#123	—	2	2	no	—
628	#123	—	2	2	no	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	1	no	—
634	C₂²⋊Q₈	—	2	1	no	—
635	C₂²⋊Q₈	—	2	1	no	—
636	C₂²⋊Q₈	—	2	1	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
640	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
641	#121	—	2	2	no	—
642	#121	—	2	2	no	—
643	#121	—	2	2	no	—
644	#121	—	2	1	no	—
645	#121	—	2	1	no	—
646	#121	—	2	1	no	—
647	#121	—	2	1	no	—
648	#121	—	2	1	no	—
649	#121	—	2	1	no	—
650	#121	—	2	1	no	—
651	#121	—	2	1	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	—	2	2	no	—
656	#121	C₂³×C₇	1	2	yes	—
657	#121	C₂³×C₇	1	2	yes	—
658	#121	C₂³×C₇	1	2	yes	—
659	#121	C₂³×C₇	1	2	yes	—
660	#121	C₂³×C₇	1	2	yes	—
661	#121	C₂³×C₇	1	2	yes	—
662	#120	—	2	2	no	—
663	#120	—	2	2	no	—
664	C₄×Q₈	—	2	1	no	—
665	C₄×Q₈	—	2	1	no	—
666	C₄×Q₈	—	2	1	no	—
667	C₄×Q₈	—	2	1	no	—
668	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
669	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
670	C₄×Q₈	C₂³×C₇	1	2	yes	—
671	C₄×Q₈	C₂³×C₇	1	2	yes	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	1	no	—
677	C₄×D₄	—	2	1	no	—
678	C₄×D₄	—	2	1	no	—
679	C₄×D₄	—	2	1	no	—
680	C₄×D₄	—	2	1	no	—
681	C₄×D₄	—	2	1	no	—
682	C₄×D₄	—	2	1	no	—
683	C₄×D₄	—	2	1	no	—
684	C₄×D₄	C₇×D₄	1	1	yes	characteristic
685	C₄×D₄	C₇×D₄	1	1	yes	characteristic
686	C₄×D₄	C₇×D₄	1	1	yes	characteristic
687	C₄×D₄	C₇×D₄	1	1	yes	characteristic
688	C₄×D₄	C₇×D₄	1	1	yes	characteristic
689	C₄×D₄	C₇×D₄	1	1	yes	characteristic
690	C₄×D₄	C₂³×C₇	1	2	yes	—
691	C₄×D₄	C₂³×C₇	1	2	yes	—
692	C₄×D₄	C₂³×C₇	1	2	yes	—
693	C₄×D₄	C₂³×C₇	1	2	yes	—
694	C₄×D₄	C₂³×C₇	1	2	yes	—
695	C₄×D₄	C₂³×C₇	1	2	yes	—
696	#117	—	2	1	no	—
697	#117	—	2	1	no	—
698	#117	—	2	2	no	—
699	#117	C₂³×C₇	1	2	yes	—
700	#117	C₂³×C₇	1	1	yes	characteristic
701	#117	C₂³×C₇	1	1	yes	characteristic
702	#117	C₂³×C₇	1	1	yes	characteristic
703	C₂×C₄⋊C₄	—	2	1	no	—
704	C₂×C₄⋊C₄	—	2	2	no	—
705	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
706	C₂×C₂²⋊C₄	—	2	2	no	—
707	C₂×C₂²⋊C₄	—	2	2	no	—
708	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
709	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
710	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
711	#107	C₂³×C₇	1	4	yes	—
712	#107	C₂³×C₇	1	4	yes	—
713	#106	C₂³×C₇	1	4	yes	—
714	#106	C₂³×C₇	1	4	yes	—
715	C₄⋊C₈	C₂³×C₇	1	2	yes	—
716	C₄⋊C₈	C₂³×C₇	1	2	yes	—
717	C₄⋊C₈	C₂³×C₇	1	2	yes	—
718	C₄⋊C₈	C₂³×C₇	1	2	yes	—
719	#103	C₂³×C₇	1	4	yes	—
720	#103	C₂³×C₇	1	4	yes	—
721	#102	C₂³×C₇	1	4	yes	—
722	#102	C₂³×C₇	1	4	yes	—
723	#102	C₂³×C₇	1	4	yes	—
724	#102	C₂³×C₇	1	4	yes	—
725	#102	C₂³×C₇	1	4	yes	—
726	#102	C₂³×C₇	1	4	yes	—
727	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
728	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
729	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
730	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
731	#97	C₂³×C₇	1	2	yes	—
732	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
733	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
734	C₄×C₈	C₂³×C₇	1	2	yes	—
735	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
736	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
737	C₂²×C₇	—	2	1	no	—
738	C₂²×C₇	—	2	1	no	—
739	C₂²×C₇	—	2	1	no	—
740	C₂²×C₇	—	2	1	no	—
741	C₂²×C₇	—	2	1	no	—
742	C₂²×C₇	—	2	1	no	—
743	C₂²×C₇	—	2	1	no	—
744	C₂²×C₇	—	2	1	no	—
745	C₂²×C₇	—	2	1	no	—
746	C₂²×C₇	—	4	2	no	—
747	C₂²×C₇	—	4	2	no	—
748	C₂²×C₇	—	4	2	no	—
749	C₂²×C₇	—	4	2	no	—
750	C₂²×C₇	—	4	2	no	—
751	C₂²×C₇	—	4	2	no	—
752	C₂²×C₇	—	4	2	no	—
753	C₂²×C₇	—	4	2	no	—
754	C₂²×C₇	—	4	2	no	—
755	C₂²×C₇	—	16	4	no	—
756	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
757	C₄×C₇	—	2	1	no	—
758	C₄×C₇	—	2	1	no	—
759	C₄×C₇	—	2	1	no	—
760	C₄×C₇	—	2	1	no	—
761	C₄×C₇	—	2	1	no	—
762	C₄×C₇	—	2	1	no	—
763	C₄×C₇	—	2	1	no	—
764	C₄×C₇	—	2	1	no	—
765	C₄×C₇	—	2	1	no	—
766	C₄×C₇	—	4	2	no	—
767	C₄×C₇	—	4	2	no	—
768	C₄×C₇	—	4	2	no	—
769	C₄×C₇	—	4	2	no	—
770	C₄×C₇	—	4	2	no	—
771	C₄×C₇	#576	1	2	yes	—
772	C₄×C₇	#577	1	2	yes	—
773	C₄×C₇	#585	1	2	yes	—
774	C₂⁴	—	2	2	no	—
775	#41	—	4	2	no	—
776	#41	—	4	4	no	—
777	#41	—	8	2	no	—
778	#41	—	8	2	no	—
779	#41	—	8	2	no	—
780	#41	—	8	2	no	—
781	#41	—	8	2	no	—
782	#41	—	8	2	no	—
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	2	no	—
788	C₂×Q₈	—	8	2	no	—
789	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
790	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	2	no	—
800	C₂×D₄	—	2	1	no	—
801	C₂×D₄	—	2	1	no	—
802	C₂×D₄	—	2	1	no	—
803	C₂×D₄	—	2	1	no	—
804	C₂×D₄	—	2	1	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	4	4	no	—
808	C₂×D₄	—	8	2	no	—
809	C₂×D₄	—	8	2	no	—
810	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
811	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
812	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
813	C₂×D₄	C₂⁴×C₇	1	2	yes	—
814	C₂×D₄	C₂⁴×C₇	1	2	yes	—
815	C₂×D₄	C₂⁴×C₇	1	2	yes	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
825	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
826	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
827	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
828	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
829	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
833	SD₁₆	—	4	4	no	—
834	SD₁₆	—	4	4	no	—
835	D₈	—	4	4	no	—
836	D₈	—	4	4	no	—
837	M₁₆	—	4	2	no	—
838	C₂×C₈	—	4	2	no	—
839	C₂×C₈	C₂⁴×C₇	1	2	yes	—
840	C₂×C₈	C₂⁴×C₇	1	2	yes	—
841	C₂×C₈	C₂⁴×C₇	1	2	yes	—
842	C₂×C₈	C₂⁴×C₇	1	2	yes	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
858	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
859	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
860	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
861	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
862	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
863	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
864	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
865	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
866	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
885	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
886	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
887	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
888	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
889	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
890	C₄²	—	2	2	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
894	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
895	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
896	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
897	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
898	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
899	C₄²	C₂⁴×C₇	1	1	yes	characteristic
900	C₄²	C₂⁴×C₇	1	1	yes	characteristic
901	C₄²	C₂⁴×C₇	1	1	yes	characteristic
902	C₄²	C₂⁴×C₇	1	1	yes	characteristic
903	C₂×C₇	—	4	1	no	—
904	C₂×C₇	—	4	1	no	—
905	C₂×C₇	—	4	1	no	—
906	C₂×C₇	—	8	2	no	—
907	C₂×C₇	—	8	2	no	—
908	C₂×C₇	—	8	2	no	—
909	C₂×C₇	#3449	1	1	yes	characteristic
910	C₂×C₇	C₂×#576	1	1	yes	characteristic
911	C₂×C₇	C₂×#577	1	1	yes	characteristic
912	C₂³	—	2	2	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	4	4	no	—
916	C₂³	—	8	2	no	—
917	C₂³	—	8	2	no	—
918	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
919	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
920	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
921	Q₈	—	2	4	no	—
922	Q₈	—	4	1	no	—
923	Q₈	—	4	2	no	—
924	Q₈	—	4	2	no	—
925	Q₈	—	4	2	no	—
926	Q₈	—	4	2	no	—
927	Q₈	—	8	2	no	—
928	D₄	—	2	4	no	—
929	D₄	—	2	4	no	—
930	D₄	—	2	4	no	—
931	D₄	—	4	1	no	—
932	D₄	—	4	1	no	—
933	D₄	—	4	1	no	—
934	D₄	—	4	4	no	—
935	D₄	—	4	4	no	—
936	D₄	—	4	2	no	—
937	D₄	—	4	2	no	—
938	D₄	—	4	2	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	2	no	—
942	D₄	—	8	2	no	—
943	D₄	—	8	2	no	—
944	D₄	—	8	2	no	—
945	D₄	—	8	2	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	2	no	—
948	D₄	—	8	2	no	—
949	D₄	—	8	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	4	4	no	—
965	C₂×C₄	—	8	2	no	—
966	C₂×C₄	—	8	2	no	—
967	C₂×C₄	—	8	2	no	—
968	C₂×C₄	—	8	2	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	2	no	—
972	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
973	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
974	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
975	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
976	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
977	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
978	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
979	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
980	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
981	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
982	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
983	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
984	C₈	—	2	2	no	—
985	C₈	—	2	2	no	—
986	C₈	—	2	2	no	—
987	C₈	—	2	2	no	—
988	C₇	#61006	1	1	yes	characteristic, direct product factor, Sylow
989	C₂²	—	2	1	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	2	1	no	—
993	C₂²	—	2	1	no	—
994	C₂²	—	2	1	no	—
995	C₂²	—	2	1	no	—
996	C₂²	—	2	1	no	—
997	C₂²	—	2	1	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	16	4	no	—
1008	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1009	C₄	—	2	1	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	2	no	—
1023	C₄	C₇×#576	1	2	yes	—
1024	C₄	C₇×#577	1	2	yes	—
1025	C₄	C₇×#585	1	2	yes	—
1026	C₂	—	4	1	no	—
1027	C₂	—	4	1	no	—
1028	C₂	—	4	1	no	—
1029	C₂	—	8	2	no	—
1030	C₂	—	8	2	no	—
1031	C₂	—	8	2	no	—
1032	C₂	C₇×#3449	1	1	yes	characteristic
1033	C₂	C₂×C₇×#576	1	1	yes	characteristic
1034	C₂	C₂×C₇×#577	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 ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3511	C₂	semidirect
2. C₇×#3508	C₂	semidirect
3. C₇×#3257	C₂	semidirect
4. C₇×#3231	C₂	semidirect
5. C₇×#3228	C₂	semidirect
6. C₇×#3227	C₂	semidirect
7. C₇×#3226	C₂	semidirect
8. C₇×#3208	C₂	semidirect
9. C₇×#3207	C₂	semidirect
10. C₇×#3207	C₂	semidirect
11. C₇×#3205	C₂	semidirect
12. C₇×#3198	C₂	semidirect
13. C₇×#3184	C₂	semidirect
14. C₇×#3182	C₂	semidirect
15. C₇×#3169	C₂	semidirect
16. C₇×#3167	C₂	semidirect
17. C₇×#3119	C₂	semidirect
18. C₇×#3118	C₂	semidirect
19. C₇×#2922	C₂	semidirect
37. C₇×#542	C₂²	semidirect
44. C₇×#533	C₂²	semidirect
50. C₇×#532	C₂²	semidirect
51. C₇×#532	C₂²	semidirect
52. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
54. C₇×#520	C₂²	semidirect
57. C₇×#500	C₂²	semidirect
58. C₇×#500	C₂²	semidirect
59. C₇×#498	C₂²	semidirect
60. C₇×#498	C₂²	semidirect
65. C₇×#487	C₂²	semidirect
66. C₇×#487	C₂²	semidirect
71. C₇×#486	C₂²	semidirect
72. C₇×#486	C₂²	semidirect
75. C₇×#481	C₂²	semidirect
76. C₇×#480	C₂²	semidirect
77. C₇×#479	C₂²	semidirect
78. C₇×#478	C₂²	semidirect
79. C₇×#476	C₂²	semidirect
80. C₇×#474	C₂²	semidirect
81. C₇×#469	C₂²	semidirect
82. C₇×#468	C₂²	semidirect
83. C₇×#466	C₂²	semidirect
84. C₇×#465	C₂²	semidirect
85. C₇×#463	C₂²	semidirect
86. C₇×#463	C₂²	semidirect
90. C₇×#449	C₂²	semidirect
91. C₇×#449	C₂²	semidirect
93. C₇×#442	C₂²	semidirect
94. C₇×#440	C₂²	semidirect
95. C₄×C₇×SD₁₆	C₂²	semidirect
96. C₄×C₇×D₈	C₂²	semidirect
98. C₇×#433	C₂²	semidirect
101. C₇×#431	C₂²	semidirect
102. C₇×#431	C₂²	semidirect
103. C₇×#424	C₂²	semidirect
105. C₄×C₇×M₁₆	C₂²	semidirect
106. C₂×C₄×C₇×C₈	C₂²	semidirect
107. #61006	C₇	direct (N × H)
267. #3511	C₂×C₇	semidirect
268. #3508	C₂×C₇	semidirect
269. #3257	C₂×C₇	semidirect
270. #3231	C₂×C₇	semidirect
271. #3228	C₂×C₇	semidirect
272. #3227	C₂×C₇	semidirect
273. #3226	C₂×C₇	semidirect
274. #3208	C₂×C₇	semidirect
275. #3207	C₂×C₇	semidirect
276. #3207	C₂×C₇	semidirect
277. #3205	C₂×C₇	semidirect
278. #3198	C₂×C₇	semidirect
279. #3184	C₂×C₇	semidirect
280. #3182	C₂×C₇	semidirect
281. #3169	C₂×C₇	semidirect
282. #3167	C₂×C₇	semidirect
283. #3119	C₂×C₇	semidirect
284. #3118	C₂×C₇	semidirect
285. #2922	C₂×C₇	semidirect
432. #542	C₂²×C₇	semidirect
439. #533	C₂²×C₇	semidirect
445. #532	C₂²×C₇	semidirect
446. #532	C₂²×C₇	semidirect
447. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
449. #520	C₂²×C₇	semidirect
452. #500	C₂²×C₇	semidirect
453. #500	C₂²×C₇	semidirect
454. #498	C₂²×C₇	semidirect
455. #498	C₂²×C₇	semidirect
460. #487	C₂²×C₇	semidirect
461. #487	C₂²×C₇	semidirect
466. #486	C₂²×C₇	semidirect
467. #486	C₂²×C₇	semidirect
470. #481	C₂²×C₇	semidirect
471. #480	C₂²×C₇	semidirect
472. #479	C₂²×C₇	semidirect
473. #478	C₂²×C₇	semidirect
474. #476	C₂²×C₇	semidirect
475. #474	C₂²×C₇	semidirect
476. #469	C₂²×C₇	semidirect
477. #468	C₂²×C₇	semidirect
478. #466	C₂²×C₇	semidirect
479. #465	C₂²×C₇	semidirect
480. #463	C₂²×C₇	semidirect
481. #463	C₂²×C₇	semidirect
485. #449	C₂²×C₇	semidirect
486. #449	C₂²×C₇	semidirect
488. #442	C₂²×C₇	semidirect
489. #440	C₂²×C₇	semidirect
490. C₄×SD₁₆	C₂²×C₇	semidirect
491. C₄×D₈	C₂²×C₇	semidirect
493. #433	C₂²×C₇	semidirect
496. #431	C₂²×C₇	semidirect
497. #431	C₂²×C₇	semidirect
498. #424	C₂²×C₇	semidirect
500. C₄×M₁₆	C₂²×C₇	semidirect
501. C₂×C₄×C₈	C₂²×C₇	semidirect
988. C₇	#61006	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×#3511	2
C₇×#3508	2
C₇×#3257	2
C₇×#3231	2
C₇×#3228	2
C₇×#3227	2
C₇×#3226	2
C₇×#3208	2
C₇×#3207	2
C₇×#3205	2
C₇×#3198	2
C₇×#3184	2
C₇×#3182	2
C₇×#3169	2
C₇×#3167	2
C₇×#3119	2
C₇×#3118	2
C₇×#2922	2
#61006	7

Subgroups — C7×#61006 #13238222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61006 #13238222