Subgroups — C₇×#60955 #13238171

Order 1792.

1804 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3460	C₂	1	2	yes	maximal, complemented
2	C₇×#3262	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3259	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3257	C₂	1	2	yes	maximal, complemented
5	C₇×#3243	C₂	1	2	yes	maximal, complemented
6	C₇×#3241	C₂	1	2	yes	maximal, complemented
7	C₇×#3224	C₂	1	2	yes	maximal, complemented
8	C₇×#3220	C₂	1	2	yes	maximal, complemented
9	C₇×#3203	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3199	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3198	C₂	1	2	yes	maximal, complemented
12	C₇×#3171	C₂	1	2	yes	maximal, complemented
13	C₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3106	C₂	1	2	yes	maximal, complemented
16	C₇×#3105	C₂	1	2	yes	maximal, complemented
17	C₇×#3102	C₂	1	2	yes	maximal, complemented
18	C₇×#3100	C₂	1	2	yes	maximal, complemented
19	C₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#544	C₂²	1	2	yes	complemented
21	C₇×#542	—	2	2	no	—
22	C₇×#542	C₂²	1	2	yes	—
23	C₇×#542	C₂²	1	2	yes	complemented
24	C₇×#540	—	2	2	no	—
25	C₇×#540	C₂²	1	2	yes	—
26	C₇×#540	C₂²	1	2	yes	complemented
27	C₇×#538	—	2	2	no	—
28	C₇×#538	—	2	2	no	—
29	C₇×#537	C₂²	1	2	yes	—
30	C₇×#535	C₂²	1	2	yes	—
31	C₇×#535	C₂²	1	2	yes	complemented
32	C₇×#532	—	2	2	no	—
33	C₇×#532	C₂²	1	2	yes	—
34	C₇×#532	C₂²	1	2	yes	complemented
35	C₇×#529	—	2	2	no	—
36	C₇×#529	C₂²	1	2	yes	—
37	C₇×#529	C₂²	1	2	yes	complemented
38	C₇×#525	—	2	2	no	—
39	C₇×#525	—	2	2	no	—
40	C₄×C₇×#41	C₂²	1	1	yes	characteristic
41	C₄×C₇×#41	C₂²	1	2	yes	complemented
42	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
43	C₇×#501	C₂²	1	2	yes	complemented
44	C₇×#500	C₂²	1	1	yes	characteristic, complemented
45	C₇×#499	C₂²	1	1	yes	characteristic, complemented
46	C₇×#496	C₂²	1	2	yes	—
47	C₇×#495	C₂²	1	1	yes	characteristic
48	C₇×#493	C₂²	1	1	yes	characteristic
49	C₇×#490	C₂²	1	2	yes	complemented
50	C₇×#489	C₂²	1	2	yes	complemented
51	C₇×#488	C₂²	1	2	yes	complemented
52	C₇×#486	C₂²	1	2	yes	complemented
53	C₇×#485	C₂²	1	2	yes	complemented
54	C₇×#484	C₂²	1	2	yes	complemented
55	C₇×#482	C₂²	1	2	yes	—
56	C₇×#482	C₂²	1	2	yes	—
57	C₇×#482	C₂²	1	2	yes	complemented
58	C₇×#481	C₂²	1	2	yes	—
59	C₇×#480	C₂²	1	2	yes	—
60	C₇×#480	C₂²	1	2	yes	complemented
61	C₇×#479	C₂²	1	2	yes	complemented
62	C₇×#478	C₂²	1	2	yes	complemented
63	C₇×#478	C₂²	1	2	yes	complemented
64	C₇×#478	C₂²	1	2	yes	complemented
65	C₇×#477	C₂²	1	2	yes	complemented
66	C₇×#476	C₂²	1	2	yes	complemented
67	C₇×#474	C₂²	1	2	yes	complemented
68	C₇×#474	C₂²	1	2	yes	complemented
69	C₇×#469	C₂²	1	2	yes	—
70	C₇×#469	C₂²	1	2	yes	complemented
71	C₇×#468	C₂²	1	2	yes	complemented
72	C₇×#468	C₂²	1	2	yes	complemented
73	C₇×#467	C₂²	1	1	yes	characteristic, complemented
74	C₇×#466	C₂²	1	1	yes	characteristic
75	C₇×#466	C₂²	1	1	yes	characteristic
76	C₇×#466	C₂²	1	2	yes	complemented
77	C₇×#466	C₂²	1	1	yes	characteristic, complemented
78	C₇×#465	C₂²	1	2	yes	complemented
79	C₇×#464	C₂²	1	2	yes	complemented
80	C₇×#463	C₂²	1	2	yes	—
81	C₇×#463	C₂²	1	2	yes	—
82	C₇×#463	C₂²	1	2	yes	complemented
83	C₇×#460	C₂²	1	2	yes	complemented
84	C₇×#459	C₂²	1	2	yes	—
85	C₇×#459	C₂²	1	2	yes	—
86	C₇×#459	C₂²	1	2	yes	complemented
87	C₇×#452	C₂²	1	2	yes	complemented
88	C₇×#450	C₂²	1	2	yes	complemented
89	C₇×#449	C₂²	1	2	yes	—
90	C₇×#449	C₂²	1	2	yes	—
91	C₇×#449	C₂²	1	2	yes	complemented
92	C₇×#447	C₂²	1	2	yes	—
93	C₇×#447	C₂²	1	2	yes	—
94	C₇×#447	C₂²	1	2	yes	complemented
95	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
97	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
98	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
99	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
100	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
101	C₄×C₇×D₈	C₂²	1	2	yes	—
102	C₄×C₇×D₈	C₂²	1	2	yes	complemented
103	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₇×D₈	C₂²	1	2	yes	complemented
105	C₇×#433	C₂²	1	2	yes	complemented
106	C₇×#433	C₂²	1	2	yes	complemented
107	C₇×#431	C₂²	1	2	yes	complemented
108	C₇×#431	C₂²	1	2	yes	complemented
109	C₇×#424	C₂²	1	1	yes	characteristic, complemented
110	C₇×#424	C₂²	1	1	yes	characteristic, complemented
111	C₇×#408	C₂²	1	1	yes	characteristic
112	C₇×#408	C₂²	1	1	yes	characteristic
113	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
115	#60955	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂×C₇×#41	—	2	2	no	—
117	C₂×C₇×#41	—	2	2	no	—
118	C₂×C₇×#41	C₂³	1	2	yes	—
119	C₂×C₇×#41	C₂³	1	1	yes	characteristic
120	C₂²×C₇×D₄	C₂³	1	2	yes	—
121	C₂³×C₄×C₇	—	2	2	no	—
122	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
123	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
124	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
125	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
127	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
128	C₂×C₇×D₈	C₂³	1	2	yes	—
129	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
130	C₂×C₇×D₈	C₂³	1	2	yes	—
131	C₂×C₇×D₈	C₂³	1	2	yes	—
132	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
133	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
134	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
135	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
136	C₇×C₄⋊Q₈	—	2	2	no	—
137	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₇×#127	—	2	2	no	—
140	C₇×#127	C₂³	1	2	yes	—
141	C₇×#127	C₂³	1	2	yes	—
142	C₇×#126	—	2	2	no	—
143	C₇×#126	—	2	2	no	—
144	C₇×#126	—	2	2	no	—
145	C₇×#126	—	2	2	no	—
146	C₇×#125	—	2	2	no	—
147	C₇×#125	C₂³	1	2	yes	—
148	C₇×#125	C₂³	1	2	yes	—
149	C₇×#124	—	2	2	no	—
150	C₇×#124	—	2	2	no	—
151	C₇×#124	—	2	2	no	—
152	C₇×#124	—	2	2	no	—
153	C₇×#124	—	2	2	no	—
154	C₇×#124	C₂³	1	2	yes	—
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×#123	—	2	2	no	—
163	C₇×#123	—	2	2	no	—
164	C₇×C₂²⋊Q₈	—	2	2	no	—
165	C₇×C₂²⋊Q₈	—	2	2	no	—
166	C₇×C₂²⋊Q₈	—	2	2	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	2	no	—
175	C₇×#121	—	2	2	no	—
176	C₇×#121	—	2	2	no	—
177	C₇×#121	—	2	2	no	—
178	C₇×#121	—	2	2	no	—
179	C₇×#121	—	2	2	no	—
180	C₇×#121	—	2	2	no	—
181	C₇×#121	—	2	2	no	—
182	C₇×#121	C₂³	1	2	yes	—
183	C₇×#121	C₂³	1	2	yes	—
184	C₇×#121	C₂³	1	2	yes	—
185	C₇×#121	C₂³	1	2	yes	—
186	C₇×#121	C₂³	1	2	yes	—
187	C₇×#121	C₂³	1	2	yes	—
188	C₇×#120	—	2	2	no	—
189	C₇×#120	—	2	2	no	—
190	C₇×#120	—	2	2	no	—
191	C₇×#120	—	2	2	no	—
192	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
193	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
194	C₄×C₇×Q₈	C₂³	1	2	yes	—
195	C₄×C₇×Q₈	C₂³	1	2	yes	—
196	C₄×C₇×D₄	—	2	2	no	—
197	C₄×C₇×D₄	—	2	2	no	—
198	C₄×C₇×D₄	—	2	2	no	—
199	C₄×C₇×D₄	—	2	2	no	—
200	C₄×C₇×D₄	—	2	2	no	—
201	C₄×C₇×D₄	—	2	2	no	—
202	C₄×C₇×D₄	—	2	2	no	—
203	C₄×C₇×D₄	—	2	2	no	—
204	C₄×C₇×D₄	D₄	1	1	yes	characteristic
205	C₄×C₇×D₄	D₄	1	2	yes	—
206	C₄×C₇×D₄	D₄	1	1	yes	characteristic
207	C₄×C₇×D₄	D₄	1	2	yes	—
208	C₄×C₇×D₄	C₂³	1	2	yes	—
209	C₄×C₇×D₄	C₂³	1	2	yes	—
210	C₄×C₇×D₄	C₂³	1	2	yes	—
211	C₄×C₇×D₄	C₂³	1	2	yes	—
212	C₄×C₇×D₄	C₂³	1	2	yes	—
213	C₄×C₇×D₄	C₂³	1	2	yes	—
214	C₇×#117	—	2	2	no	—
215	C₇×#117	—	2	2	no	—
216	C₇×#117	—	2	2	no	—
217	C₇×#117	C₂³	1	2	yes	—
218	C₇×#117	C₂³	1	2	yes	—
219	C₇×#117	C₂³	1	1	yes	characteristic
220	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
221	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
222	C₂×C₄²×C₇	—	2	2	no	—
223	C₂×C₄²×C₇	C₂³	1	2	yes	—
224	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
225	C₇×#107	C₂³	1	1	yes	characteristic
226	C₇×#107	C₂³	1	1	yes	characteristic
227	C₇×#107	C₂³	1	2	yes	—
228	C₇×#107	C₂³	1	1	yes	characteristic
229	C₇×#107	C₂³	1	1	yes	characteristic
230	C₇×#107	C₂³	1	2	yes	—
231	C₇×#107	C₂³	1	2	yes	—
232	C₇×#106	C₂³	1	2	yes	—
233	C₇×#106	C₂³	1	2	yes	—
234	C₇×#106	C₂³	1	2	yes	—
235	C₇×C₄⋊C₈	C₂³	1	2	yes	—
236	C₇×C₄⋊C₈	C₂³	1	2	yes	—
237	C₇×C₄⋊C₈	C₂³	1	2	yes	—
238	C₇×C₄⋊C₈	C₂³	1	2	yes	—
239	C₇×#103	C₂³	1	2	yes	—
240	C₇×#103	C₂³	1	2	yes	—
241	C₇×#103	C₂³	1	2	yes	—
242	C₇×#103	C₂³	1	2	yes	—
243	C₇×#102	C₂³	1	2	yes	—
244	C₇×#102	C₂³	1	2	yes	—
245	C₇×#102	C₂³	1	2	yes	—
246	C₇×#102	C₂³	1	2	yes	—
247	C₇×#102	C₂³	1	2	yes	—
248	C₇×#102	C₂³	1	2	yes	—
249	C₇×#102	C₂³	1	2	yes	—
250	C₇×#102	C₂³	1	2	yes	—
251	C₇×#102	C₂³	1	2	yes	—
252	C₇×#102	C₂³	1	2	yes	—
253	C₇×#102	C₂³	1	2	yes	—
254	C₇×#102	C₂³	1	2	yes	—
255	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₇×#97	C₂³	1	2	yes	—
260	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
261	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
262	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
263	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
264	C₄×C₇×C₈	C₂³	1	2	yes	—
265	#3460	C₂×C₇	1	2	yes	complemented
266	#3262	C₂×C₇	1	1	yes	characteristic, complemented
267	#3259	C₂×C₇	1	1	yes	characteristic, complemented
268	#3257	C₂×C₇	1	2	yes	complemented
269	#3243	C₂×C₇	1	2	yes	complemented
270	#3241	C₂×C₇	1	2	yes	complemented
271	#3224	C₂×C₇	1	2	yes	complemented
272	#3220	C₂×C₇	1	2	yes	complemented
273	#3203	C₂×C₇	1	1	yes	characteristic, complemented
274	#3199	C₂×C₇	1	1	yes	characteristic, complemented
275	#3198	C₂×C₇	1	2	yes	complemented
276	#3171	C₂×C₇	1	2	yes	complemented
277	#3169	C₂×C₇	1	1	yes	characteristic, complemented
278	#3168	C₂×C₇	1	1	yes	characteristic, complemented
279	#3106	C₂×C₇	1	2	yes	complemented
280	#3105	C₂×C₇	1	2	yes	complemented
281	#3102	C₂×C₇	1	2	yes	complemented
282	#3100	C₂×C₇	1	2	yes	complemented
283	#2922	C₂×C₇	1	1	yes	characteristic, complemented
284	C₂⁴×C₇	—	2	2	no	—
285	C₇×#41	—	4	1	no	—
286	C₇×#41	—	4	1	no	—
287	C₇×#41	—	4	2	no	—
288	C₇×#41	—	4	2	no	—
289	C₇×#41	—	8	4	no	—
290	C₇×#41	—	8	4	no	—
291	C₂×C₇×Q₈	—	2	2	no	—
292	C₂×C₇×Q₈	—	2	2	no	—
293	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
294	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
295	C₂×C₇×D₄	—	2	2	no	—
296	C₂×C₇×D₄	—	2	2	no	—
297	C₂×C₇×D₄	—	2	2	no	—
298	C₂×C₇×D₄	—	2	2	no	—
299	C₂×C₇×D₄	—	2	2	no	—
300	C₂×C₇×D₄	—	2	2	no	—
301	C₂×C₇×D₄	—	2	2	no	—
302	C₂×C₇×D₄	—	2	2	no	—
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	—	4	2	no	—
308	C₂×C₇×D₄	—	4	2	no	—
309	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
310	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
311	C₂×C₇×D₄	C₂⁴	1	2	yes	—
312	C₂×C₇×D₄	C₂⁴	1	2	yes	—
313	C₂×C₇×D₄	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₇	—	2	2	no	—
315	C₂²×C₄×C₇	—	2	2	no	—
316	C₂²×C₄×C₇	—	2	2	no	—
317	C₂²×C₄×C₇	—	2	2	no	—
318	C₂²×C₄×C₇	—	2	2	no	—
319	C₂²×C₄×C₇	—	2	2	no	—
320	C₂²×C₄×C₇	—	2	2	no	—
321	C₂²×C₄×C₇	—	2	2	no	—
322	C₂²×C₄×C₇	—	8	4	no	—
323	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
324	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
326	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
329	C₇×Q₁₆	—	4	1	no	—
330	C₇×SD₁₆	—	4	2	no	—
331	C₇×SD₁₆	—	4	2	no	—
332	C₇×SD₁₆	—	4	2	no	—
333	C₇×D₈	—	4	2	no	—
334	C₇×D₈	—	4	1	no	—
335	C₇×D₈	—	4	1	no	—
336	C₇×D₈	—	4	1	no	—
337	C₇×D₈	—	4	2	no	—
338	C₇×D₈	—	4	2	no	—
339	C₇×M₁₆	—	4	1	no	—
340	C₇×M₁₆	—	4	1	no	—
341	C₂×C₇×C₈	—	4	1	no	—
342	C₂×C₇×C₈	—	4	1	no	—
343	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
344	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
345	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
346	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
347	C₂×C₇×C₈	C₂⁴	1	2	yes	—
348	C₂×C₇×C₈	C₂⁴	1	2	yes	—
349	C₇×C₄⋊C₄	—	2	2	no	—
350	C₇×C₄⋊C₄	—	2	2	no	—
351	C₇×C₄⋊C₄	—	2	2	no	—
352	C₇×C₄⋊C₄	—	2	2	no	—
353	C₇×C₄⋊C₄	—	2	2	no	—
354	C₇×C₄⋊C₄	—	2	2	no	—
355	C₇×C₄⋊C₄	—	2	2	no	—
356	C₇×C₄⋊C₄	—	2	2	no	—
357	C₇×C₄⋊C₄	—	2	2	no	—
358	C₇×C₄⋊C₄	—	2	2	no	—
359	C₇×C₄⋊C₄	—	2	2	no	—
360	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
361	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
362	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
363	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
364	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
365	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
366	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
367	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
368	C₇×C₂²⋊C₄	—	2	2	no	—
369	C₇×C₂²⋊C₄	—	2	2	no	—
370	C₇×C₂²⋊C₄	—	2	2	no	—
371	C₇×C₂²⋊C₄	—	2	2	no	—
372	C₇×C₂²⋊C₄	—	2	2	no	—
373	C₇×C₂²⋊C₄	—	2	2	no	—
374	C₇×C₂²⋊C₄	—	2	2	no	—
375	C₇×C₂²⋊C₄	—	2	2	no	—
376	C₇×C₂²⋊C₄	—	2	2	no	—
377	C₇×C₂²⋊C₄	—	2	2	no	—
378	C₇×C₂²⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
388	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
389	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
390	C₄²×C₇	—	2	2	no	—
391	C₄²×C₇	—	2	2	no	—
392	C₄²×C₇	—	2	2	no	—
393	C₄²×C₇	C₂×D₄	1	2	yes	—
394	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₇	C₂×D₄	1	2	yes	—
396	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₇	C₂⁴	1	1	yes	characteristic
398	C₄²×C₇	C₂⁴	1	2	yes	—
399	C₄²×C₇	C₂⁴	1	1	yes	characteristic
400	#544	C₂²×C₇	1	2	yes	complemented
401	#542	—	2	2	no	—
402	#542	C₂²×C₇	1	2	yes	—
403	#542	C₂²×C₇	1	2	yes	complemented
404	#540	—	2	2	no	—
405	#540	C₂²×C₇	1	2	yes	—
406	#540	C₂²×C₇	1	2	yes	complemented
407	#538	—	2	2	no	—
408	#538	—	2	2	no	—
409	#537	C₂²×C₇	1	2	yes	—
410	#535	C₂²×C₇	1	2	yes	—
411	#535	C₂²×C₇	1	2	yes	complemented
412	#532	—	2	2	no	—
413	#532	C₂²×C₇	1	2	yes	—
414	#532	C₂²×C₇	1	2	yes	complemented
415	#529	—	2	2	no	—
416	#529	C₂²×C₇	1	2	yes	—
417	#529	C₂²×C₇	1	2	yes	complemented
418	#525	—	2	2	no	—
419	#525	—	2	2	no	—
420	C₄×#41	C₂²×C₇	1	1	yes	characteristic
421	C₄×#41	C₂²×C₇	1	2	yes	complemented
422	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
423	#501	C₂²×C₇	1	2	yes	complemented
424	#500	C₂²×C₇	1	1	yes	characteristic, complemented
425	#499	C₂²×C₇	1	1	yes	characteristic, complemented
426	#496	C₂²×C₇	1	2	yes	—
427	#495	C₂²×C₇	1	1	yes	characteristic
428	#493	C₂²×C₇	1	1	yes	characteristic
429	#490	C₂²×C₇	1	2	yes	complemented
430	#489	C₂²×C₇	1	2	yes	complemented
431	#488	C₂²×C₇	1	2	yes	complemented
432	#486	C₂²×C₇	1	2	yes	complemented
433	#485	C₂²×C₇	1	2	yes	complemented
434	#484	C₂²×C₇	1	2	yes	complemented
435	#482	C₂²×C₇	1	2	yes	—
436	#482	C₂²×C₇	1	2	yes	—
437	#482	C₂²×C₇	1	2	yes	complemented
438	#481	C₂²×C₇	1	2	yes	—
439	#480	C₂²×C₇	1	2	yes	—
440	#480	C₂²×C₇	1	2	yes	complemented
441	#479	C₂²×C₇	1	2	yes	complemented
442	#478	C₂²×C₇	1	2	yes	complemented
443	#478	C₂²×C₇	1	2	yes	complemented
444	#478	C₂²×C₇	1	2	yes	complemented
445	#477	C₂²×C₇	1	2	yes	complemented
446	#476	C₂²×C₇	1	2	yes	complemented
447	#474	C₂²×C₇	1	2	yes	complemented
448	#474	C₂²×C₇	1	2	yes	complemented
449	#469	C₂²×C₇	1	2	yes	—
450	#469	C₂²×C₇	1	2	yes	complemented
451	#468	C₂²×C₇	1	2	yes	complemented
452	#468	C₂²×C₇	1	2	yes	complemented
453	#467	C₂²×C₇	1	1	yes	characteristic, complemented
454	#466	C₂²×C₇	1	1	yes	characteristic
455	#466	C₂²×C₇	1	1	yes	characteristic
456	#466	C₂²×C₇	1	2	yes	complemented
457	#466	C₂²×C₇	1	1	yes	characteristic, complemented
458	#465	C₂²×C₇	1	2	yes	complemented
459	#464	C₂²×C₇	1	2	yes	complemented
460	#463	C₂²×C₇	1	2	yes	—
461	#463	C₂²×C₇	1	2	yes	—
462	#463	C₂²×C₇	1	2	yes	complemented
463	#460	C₂²×C₇	1	2	yes	complemented
464	#459	C₂²×C₇	1	2	yes	—
465	#459	C₂²×C₇	1	2	yes	—
466	#459	C₂²×C₇	1	2	yes	complemented
467	#452	C₂²×C₇	1	2	yes	complemented
468	#450	C₂²×C₇	1	2	yes	complemented
469	#449	C₂²×C₇	1	2	yes	—
470	#449	C₂²×C₇	1	2	yes	—
471	#449	C₂²×C₇	1	2	yes	complemented
472	#447	C₂²×C₇	1	2	yes	—
473	#447	C₂²×C₇	1	2	yes	—
474	#447	C₂²×C₇	1	2	yes	complemented
475	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
476	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
477	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
478	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
479	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
480	C₄×D₈	C₂²×C₇	1	2	yes	—
481	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
482	C₄×D₈	C₂²×C₇	1	2	yes	complemented
483	C₄×D₈	C₂²×C₇	1	2	yes	complemented
484	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
485	#433	C₂²×C₇	1	2	yes	complemented
486	#433	C₂²×C₇	1	2	yes	complemented
487	#431	C₂²×C₇	1	2	yes	complemented
488	#431	C₂²×C₇	1	2	yes	complemented
489	#424	C₂²×C₇	1	1	yes	characteristic, complemented
490	#424	C₂²×C₇	1	1	yes	characteristic, complemented
491	#408	C₂²×C₇	1	1	yes	characteristic
492	#408	C₂²×C₇	1	1	yes	characteristic
493	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
494	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
495	C₂³×C₇	—	2	2	no	—
496	C₂³×C₇	—	2	2	no	—
497	C₂³×C₇	—	2	2	no	—
498	C₂³×C₇	—	4	4	no	—
499	C₂³×C₇	—	8	2	no	—
500	C₂³×C₇	—	8	2	no	—
501	C₂³×C₇	C₂²×D₄	1	2	yes	—
502	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
503	C₇×Q₈	—	2	2	no	—
504	C₇×Q₈	—	2	2	no	—
505	C₇×Q₈	—	4	1	no	—
506	C₇×Q₈	—	8	2	no	—
507	C₇×Q₈	—	8	2	no	—
508	C₇×D₄	—	2	2	no	—
509	C₇×D₄	—	2	2	no	—
510	C₇×D₄	—	2	2	no	—
511	C₇×D₄	—	2	2	no	—
512	C₇×D₄	—	2	2	no	—
513	C₇×D₄	—	2	2	no	—
514	C₇×D₄	—	4	2	no	—
515	C₇×D₄	—	4	1	no	—
516	C₇×D₄	—	4	4	no	—
517	C₇×D₄	—	4	4	no	—
518	C₇×D₄	—	8	2	no	—
519	C₇×D₄	—	8	2	no	—
520	C₇×D₄	—	8	2	no	—
521	C₇×D₄	—	8	2	no	—
522	C₇×D₄	—	8	2	no	—
523	C₇×D₄	—	8	2	no	—
524	C₇×D₄	—	8	2	no	—
525	C₇×D₄	—	8	2	no	—
526	C₇×D₄	—	8	2	no	—
527	C₇×D₄	—	8	2	no	—
528	C₂×C₄×C₇	—	2	4	no	—
529	C₂×C₄×C₇	—	2	2	no	—
530	C₂×C₄×C₇	—	2	1	no	—
531	C₂×C₄×C₇	—	2	1	no	—
532	C₂×C₄×C₇	—	2	2	no	—
533	C₂×C₄×C₇	—	2	2	no	—
534	C₂×C₄×C₇	—	2	2	no	—
535	C₂×C₄×C₇	—	2	2	no	—
536	C₂×C₄×C₇	—	2	2	no	—
537	C₂×C₄×C₇	—	2	2	no	—
538	C₂×C₄×C₇	—	2	2	no	—
539	C₂×C₄×C₇	—	4	2	no	—
540	C₂×C₄×C₇	—	4	1	no	—
541	C₂×C₄×C₇	—	4	4	no	—
542	C₂×C₄×C₇	—	4	4	no	—
543	C₂×C₄×C₇	—	4	4	no	—
544	C₂×C₄×C₇	—	4	4	no	—
545	C₂×C₄×C₇	—	8	2	no	—
546	C₂×C₄×C₇	—	8	2	no	—
547	C₂×C₄×C₇	—	8	2	no	—
548	C₂×C₄×C₇	—	8	2	no	—
549	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
550	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
551	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
558	C₇×C₈	—	2	1	no	—
559	C₇×C₈	—	2	1	no	—
560	C₇×C₈	—	2	1	no	—
561	C₇×C₈	—	2	1	no	—
562	C₇×C₈	—	2	2	no	—
563	C₇×C₈	—	2	2	no	—
564	C₂×#41	—	2	2	no	—
565	C₂×#41	—	2	2	no	—
566	C₂×#41	C₂³×C₇	1	2	yes	—
567	C₂×#41	C₂³×C₇	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₇	1	2	yes	—
569	C₂³×C₄	—	2	2	no	—
570	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
571	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
572	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
573	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
574	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
575	C₂×D₈	C₂³×C₇	1	2	yes	—
576	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
577	C₂×D₈	C₂³×C₇	1	2	yes	—
578	C₂×D₈	C₂³×C₇	1	2	yes	—
579	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
580	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
581	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
582	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
583	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
584	C₄⋊Q₈	—	2	2	no	—
585	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
586	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
587	#127	—	2	2	no	—
588	#127	C₂³×C₇	1	2	yes	—
589	#127	C₂³×C₇	1	2	yes	—
590	#126	—	2	2	no	—
591	#126	—	2	2	no	—
592	#126	—	2	2	no	—
593	#126	—	2	2	no	—
594	#125	—	2	2	no	—
595	#125	C₂³×C₇	1	2	yes	—
596	#125	C₂³×C₇	1	2	yes	—
597	#124	—	2	2	no	—
598	#124	—	2	2	no	—
599	#124	—	2	2	no	—
600	#124	—	2	2	no	—
601	#124	—	2	2	no	—
602	#124	C₂³×C₇	1	2	yes	—
603	#124	C₂³×C₇	1	2	yes	—
604	#123	—	2	2	no	—
605	#123	—	2	2	no	—
606	#123	—	2	2	no	—
607	#123	—	2	2	no	—
608	#123	—	2	2	no	—
609	#123	—	2	2	no	—
610	#123	—	2	2	no	—
611	#123	—	2	2	no	—
612	C₂²⋊Q₈	—	2	2	no	—
613	C₂²⋊Q₈	—	2	2	no	—
614	C₂²⋊Q₈	—	2	2	no	—
615	C₂²⋊Q₈	—	2	2	no	—
616	C₂²⋊Q₈	—	2	2	no	—
617	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
618	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
619	#121	—	2	2	no	—
620	#121	—	2	2	no	—
621	#121	—	2	2	no	—
622	#121	—	2	2	no	—
623	#121	—	2	2	no	—
624	#121	—	2	2	no	—
625	#121	—	2	2	no	—
626	#121	—	2	2	no	—
627	#121	—	2	2	no	—
628	#121	—	2	2	no	—
629	#121	—	2	2	no	—
630	#121	C₂³×C₇	1	2	yes	—
631	#121	C₂³×C₇	1	2	yes	—
632	#121	C₂³×C₇	1	2	yes	—
633	#121	C₂³×C₇	1	2	yes	—
634	#121	C₂³×C₇	1	2	yes	—
635	#121	C₂³×C₇	1	2	yes	—
636	#120	—	2	2	no	—
637	#120	—	2	2	no	—
638	#120	—	2	2	no	—
639	#120	—	2	2	no	—
640	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
641	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
642	C₄×Q₈	C₂³×C₇	1	2	yes	—
643	C₄×Q₈	C₂³×C₇	1	2	yes	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	—	2	2	no	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	C₇×D₄	1	1	yes	characteristic
653	C₄×D₄	C₇×D₄	1	2	yes	—
654	C₄×D₄	C₇×D₄	1	1	yes	characteristic
655	C₄×D₄	C₇×D₄	1	2	yes	—
656	C₄×D₄	C₂³×C₇	1	2	yes	—
657	C₄×D₄	C₂³×C₇	1	2	yes	—
658	C₄×D₄	C₂³×C₇	1	2	yes	—
659	C₄×D₄	C₂³×C₇	1	2	yes	—
660	C₄×D₄	C₂³×C₇	1	2	yes	—
661	C₄×D₄	C₂³×C₇	1	2	yes	—
662	#117	—	2	2	no	—
663	#117	—	2	2	no	—
664	#117	—	2	2	no	—
665	#117	C₂³×C₇	1	2	yes	—
666	#117	C₂³×C₇	1	2	yes	—
667	#117	C₂³×C₇	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
669	C₂×C₂²⋊C₄	—	2	2	no	—
670	C₂×C₄²	—	2	2	no	—
671	C₂×C₄²	C₂³×C₇	1	2	yes	—
672	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
673	#107	C₂³×C₇	1	1	yes	characteristic
674	#107	C₂³×C₇	1	1	yes	characteristic
675	#107	C₂³×C₇	1	2	yes	—
676	#107	C₂³×C₇	1	1	yes	characteristic
677	#107	C₂³×C₇	1	2	yes	—
678	#107	C₂³×C₇	1	2	yes	—
679	#107	C₂³×C₇	1	1	yes	characteristic
680	#106	C₂³×C₇	1	2	yes	—
681	#106	C₂³×C₇	1	2	yes	—
682	#106	C₂³×C₇	1	2	yes	—
683	C₄⋊C₈	C₂³×C₇	1	2	yes	—
684	C₄⋊C₈	C₂³×C₇	1	2	yes	—
685	C₄⋊C₈	C₂³×C₇	1	2	yes	—
686	C₄⋊C₈	C₂³×C₇	1	2	yes	—
687	#103	C₂³×C₇	1	2	yes	—
688	#103	C₂³×C₇	1	2	yes	—
689	#103	C₂³×C₇	1	2	yes	—
690	#103	C₂³×C₇	1	2	yes	—
691	#102	C₂³×C₇	1	2	yes	—
692	#102	C₂³×C₇	1	2	yes	—
693	#102	C₂³×C₇	1	2	yes	—
694	#102	C₂³×C₇	1	2	yes	—
695	#102	C₂³×C₇	1	2	yes	—
696	#102	C₂³×C₇	1	2	yes	—
697	#102	C₂³×C₇	1	2	yes	—
698	#102	C₂³×C₇	1	2	yes	—
699	#102	C₂³×C₇	1	2	yes	—
700	#102	C₂³×C₇	1	2	yes	—
701	#102	C₂³×C₇	1	2	yes	—
702	#102	C₂³×C₇	1	2	yes	—
703	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
704	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
705	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
706	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
707	#97	C₂³×C₇	1	2	yes	—
708	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
709	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
710	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
711	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
712	C₄×C₈	C₂³×C₇	1	2	yes	—
713	C₂²×C₇	—	2	1	no	—
714	C₂²×C₇	—	2	2	no	—
715	C₂²×C₇	—	2	2	no	—
716	C₂²×C₇	—	2	1	no	—
717	C₂²×C₇	—	2	2	no	—
718	C₂²×C₇	—	2	1	no	—
719	C₂²×C₇	—	4	2	no	—
720	C₂²×C₇	—	4	2	no	—
721	C₂²×C₇	—	4	2	no	—
722	C₂²×C₇	—	4	2	no	—
723	C₂²×C₇	—	4	2	no	—
724	C₂²×C₇	—	4	2	no	—
725	C₂²×C₇	—	4	2	no	—
726	C₂²×C₇	—	4	2	no	—
727	C₂²×C₇	—	4	2	no	—
728	C₂²×C₇	—	8	8	no	—
729	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
730	C₄×C₇	—	2	1	no	—
731	C₄×C₇	—	2	2	no	—
732	C₄×C₇	—	2	1	no	—
733	C₄×C₇	—	2	2	no	—
734	C₄×C₇	—	2	1	no	—
735	C₄×C₇	—	2	2	no	—
736	C₄×C₇	—	2	1	no	—
737	C₄×C₇	—	4	2	no	—
738	C₄×C₇	—	4	2	no	—
739	C₄×C₇	—	4	2	no	—
740	C₄×C₇	—	4	2	no	—
741	C₄×C₇	—	4	2	no	—
742	C₄×C₇	#576	1	2	yes	—
743	C₄×C₇	#585	1	1	yes	characteristic
744	C₄×C₇	#585	1	1	yes	characteristic
745	C₂⁴	—	2	2	no	—
746	#41	—	4	1	no	—
747	#41	—	4	1	no	—
748	#41	—	4	2	no	—
749	#41	—	4	2	no	—
750	#41	—	8	4	no	—
751	#41	—	8	4	no	—
752	C₂×Q₈	—	2	2	no	—
753	C₂×Q₈	—	2	2	no	—
754	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
755	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	4	2	no	—
769	C₂×D₄	—	4	2	no	—
770	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
771	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
772	C₂×D₄	C₂⁴×C₇	1	2	yes	—
773	C₂×D₄	C₂⁴×C₇	1	2	yes	—
774	C₂×D₄	C₂⁴×C₇	1	2	yes	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	8	4	no	—
784	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
785	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
786	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
787	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
790	Q₁₆	—	4	1	no	—
791	SD₁₆	—	4	2	no	—
792	SD₁₆	—	4	2	no	—
793	SD₁₆	—	4	2	no	—
794	D₈	—	4	2	no	—
795	D₈	—	4	1	no	—
796	D₈	—	4	1	no	—
797	D₈	—	4	1	no	—
798	D₈	—	4	2	no	—
799	D₈	—	4	2	no	—
800	M₁₆	—	4	1	no	—
801	M₁₆	—	4	1	no	—
802	C₂×C₈	—	4	1	no	—
803	C₂×C₈	—	4	1	no	—
804	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
805	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
806	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
807	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
808	C₂×C₈	C₂⁴×C₇	1	2	yes	—
809	C₂×C₈	C₂⁴×C₇	1	2	yes	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
822	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
823	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
824	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
825	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
827	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
828	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
849	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
850	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	C₂×C₇×D₄	1	2	yes	—
855	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
856	C₄²	C₂×C₇×D₄	1	2	yes	—
857	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
858	C₄²	C₂⁴×C₇	1	1	yes	characteristic
859	C₄²	C₂⁴×C₇	1	1	yes	characteristic
860	C₄²	C₂⁴×C₇	1	2	yes	—
861	C₂×C₇	—	4	1	no	—
862	C₂×C₇	—	4	2	no	—
863	C₂×C₇	—	8	2	no	—
864	C₂×C₇	—	8	2	no	—
865	C₂×C₇	—	8	2	no	—
866	C₂×C₇	#3449	1	1	yes	characteristic
867	C₂×C₇	C₂×#576	1	1	yes	characteristic
868	C₂×C₇	#3584	1	1	yes	characteristic
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	4	4	no	—
873	C₂³	—	8	2	no	—
874	C₂³	—	8	2	no	—
875	C₂³	C₂²×C₇×D₄	1	2	yes	—
876	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
877	Q₈	—	2	2	no	—
878	Q₈	—	2	2	no	—
879	Q₈	—	4	1	no	—
880	Q₈	—	8	2	no	—
881	Q₈	—	8	2	no	—
882	D₄	—	2	2	no	—
883	D₄	—	2	2	no	—
884	D₄	—	2	2	no	—
885	D₄	—	2	2	no	—
886	D₄	—	2	2	no	—
887	D₄	—	2	2	no	—
888	D₄	—	4	2	no	—
889	D₄	—	4	1	no	—
890	D₄	—	4	4	no	—
891	D₄	—	4	4	no	—
892	D₄	—	8	2	no	—
893	D₄	—	8	2	no	—
894	D₄	—	8	2	no	—
895	D₄	—	8	2	no	—
896	D₄	—	8	2	no	—
897	D₄	—	8	2	no	—
898	D₄	—	8	2	no	—
899	D₄	—	8	2	no	—
900	D₄	—	8	2	no	—
901	D₄	—	8	2	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	4	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	4	2	no	—
914	C₂×C₄	—	4	1	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	—	4	4	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	—	8	2	no	—
922	C₂×C₄	—	8	2	no	—
923	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
924	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
925	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
926	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
927	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
928	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
929	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
930	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
931	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
932	C₈	—	2	1	no	—
933	C₈	—	2	1	no	—
934	C₈	—	2	1	no	—
935	C₈	—	2	1	no	—
936	C₈	—	2	2	no	—
937	C₈	—	2	2	no	—
938	C₇	#60955	1	1	yes	characteristic, direct product factor, Sylow
939	C₂²	—	2	2	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	8	8	no	—
955	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
956	C₄	—	2	2	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	1	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	1	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	C₇×#576	1	2	yes	—
969	C₄	C₇×#585	1	1	yes	characteristic
970	C₄	C₇×#585	1	1	yes	characteristic
971	C₂	—	4	2	no	—
972	C₂	—	4	1	no	—
973	C₂	—	8	2	no	—
974	C₂	—	8	2	no	—
975	C₂	—	8	2	no	—
976	C₂	C₇×#3449	1	1	yes	characteristic
977	C₂	C₂×C₇×#576	1	1	yes	characteristic
978	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3460	C₂	semidirect
2. C₇×#3262	C₂	semidirect
3. C₇×#3259	C₂	semidirect
4. C₇×#3257	C₂	semidirect
5. C₇×#3243	C₂	semidirect
6. C₇×#3241	C₂	semidirect
7. C₇×#3224	C₂	semidirect
8. C₇×#3220	C₂	semidirect
9. C₇×#3203	C₂	semidirect
10. C₇×#3199	C₂	semidirect
11. C₇×#3198	C₂	semidirect
12. C₇×#3171	C₂	semidirect
13. C₇×#3169	C₂	semidirect
14. C₇×#3168	C₂	semidirect
15. C₇×#3106	C₂	semidirect
16. C₇×#3105	C₂	semidirect
17. C₇×#3102	C₂	semidirect
18. C₇×#3100	C₂	semidirect
19. C₇×#2922	C₂	semidirect
20. C₇×#544	C₂²	semidirect
23. C₇×#542	C₂²	semidirect
26. C₇×#540	C₂²	semidirect
31. C₇×#535	C₂²	semidirect
34. C₇×#532	C₂²	semidirect
37. C₇×#529	C₂²	semidirect
41. C₄×C₇×#41	C₂²	semidirect
42. C₂×C₄×C₇×D₄	C₂²	semidirect
43. C₇×#501	C₂²	semidirect
44. C₇×#500	C₂²	semidirect
45. C₇×#499	C₂²	semidirect
49. C₇×#490	C₂²	semidirect
50. C₇×#489	C₂²	semidirect
51. C₇×#488	C₂²	semidirect
52. C₇×#486	C₂²	semidirect
53. C₇×#485	C₂²	semidirect
54. C₇×#484	C₂²	semidirect
57. C₇×#482	C₂²	semidirect
60. C₇×#480	C₂²	semidirect
61. C₇×#479	C₂²	semidirect
62. C₇×#478	C₂²	semidirect
63. C₇×#478	C₂²	semidirect
64. C₇×#478	C₂²	semidirect
65. C₇×#477	C₂²	semidirect
66. C₇×#476	C₂²	semidirect
67. C₇×#474	C₂²	semidirect
68. C₇×#474	C₂²	semidirect
70. C₇×#469	C₂²	semidirect
71. C₇×#468	C₂²	semidirect
72. C₇×#468	C₂²	semidirect
73. C₇×#467	C₂²	semidirect
76. C₇×#466	C₂²	semidirect
77. C₇×#466	C₂²	semidirect
78. C₇×#465	C₂²	semidirect
79. C₇×#464	C₂²	semidirect
82. C₇×#463	C₂²	semidirect
83. C₇×#460	C₂²	semidirect
86. C₇×#459	C₂²	semidirect
87. C₇×#452	C₂²	semidirect
88. C₇×#450	C₂²	semidirect
91. C₇×#449	C₂²	semidirect
94. C₇×#447	C₂²	semidirect
95. C₄×C₇×Q₁₆	C₂²	semidirect
96. C₄×C₇×SD₁₆	C₂²	semidirect
97. C₄×C₇×SD₁₆	C₂²	semidirect
98. C₄×C₇×SD₁₆	C₂²	semidirect
102. C₄×C₇×D₈	C₂²	semidirect
103. C₄×C₇×D₈	C₂²	semidirect
104. C₄×C₇×D₈	C₂²	semidirect
105. C₇×#433	C₂²	semidirect
106. C₇×#433	C₂²	semidirect
107. C₇×#431	C₂²	semidirect
108. C₇×#431	C₂²	semidirect
109. C₇×#424	C₂²	semidirect
110. C₇×#424	C₂²	semidirect
113. C₄×C₇×M₁₆	C₂²	semidirect
114. C₂×C₄×C₇×C₈	C₂²	semidirect
115. #60955	C₇	direct (N × H)
265. #3460	C₂×C₇	semidirect
266. #3262	C₂×C₇	semidirect
267. #3259	C₂×C₇	semidirect
268. #3257	C₂×C₇	semidirect
269. #3243	C₂×C₇	semidirect
270. #3241	C₂×C₇	semidirect
271. #3224	C₂×C₇	semidirect
272. #3220	C₂×C₇	semidirect
273. #3203	C₂×C₇	semidirect
274. #3199	C₂×C₇	semidirect
275. #3198	C₂×C₇	semidirect
276. #3171	C₂×C₇	semidirect
277. #3169	C₂×C₇	semidirect
278. #3168	C₂×C₇	semidirect
279. #3106	C₂×C₇	semidirect
280. #3105	C₂×C₇	semidirect
281. #3102	C₂×C₇	semidirect
282. #3100	C₂×C₇	semidirect
283. #2922	C₂×C₇	semidirect
400. #544	C₂²×C₇	semidirect
403. #542	C₂²×C₇	semidirect
406. #540	C₂²×C₇	semidirect
411. #535	C₂²×C₇	semidirect
414. #532	C₂²×C₇	semidirect
417. #529	C₂²×C₇	semidirect
421. C₄×#41	C₂²×C₇	semidirect
422. C₂×C₄×D₄	C₂²×C₇	semidirect
423. #501	C₂²×C₇	semidirect
424. #500	C₂²×C₇	semidirect
425. #499	C₂²×C₇	semidirect
429. #490	C₂²×C₇	semidirect
430. #489	C₂²×C₇	semidirect
431. #488	C₂²×C₇	semidirect
432. #486	C₂²×C₇	semidirect
433. #485	C₂²×C₇	semidirect
434. #484	C₂²×C₇	semidirect
437. #482	C₂²×C₇	semidirect
440. #480	C₂²×C₇	semidirect
441. #479	C₂²×C₇	semidirect
442. #478	C₂²×C₇	semidirect
443. #478	C₂²×C₇	semidirect
444. #478	C₂²×C₇	semidirect
445. #477	C₂²×C₇	semidirect
446. #476	C₂²×C₇	semidirect
447. #474	C₂²×C₇	semidirect
448. #474	C₂²×C₇	semidirect
450. #469	C₂²×C₇	semidirect
451. #468	C₂²×C₇	semidirect
452. #468	C₂²×C₇	semidirect
453. #467	C₂²×C₇	semidirect
456. #466	C₂²×C₇	semidirect
457. #466	C₂²×C₇	semidirect
458. #465	C₂²×C₇	semidirect
459. #464	C₂²×C₇	semidirect
462. #463	C₂²×C₇	semidirect
463. #460	C₂²×C₇	semidirect
466. #459	C₂²×C₇	semidirect
467. #452	C₂²×C₇	semidirect
468. #450	C₂²×C₇	semidirect
471. #449	C₂²×C₇	semidirect
474. #447	C₂²×C₇	semidirect
475. C₄×Q₁₆	C₂²×C₇	semidirect
476. C₄×SD₁₆	C₂²×C₇	semidirect
477. C₄×SD₁₆	C₂²×C₇	semidirect
478. C₄×SD₁₆	C₂²×C₇	semidirect
482. C₄×D₈	C₂²×C₇	semidirect
483. C₄×D₈	C₂²×C₇	semidirect
484. C₄×D₈	C₂²×C₇	semidirect
485. #433	C₂²×C₇	semidirect
486. #433	C₂²×C₇	semidirect
487. #431	C₂²×C₇	semidirect
488. #431	C₂²×C₇	semidirect
489. #424	C₂²×C₇	semidirect
490. #424	C₂²×C₇	semidirect
493. C₄×M₁₆	C₂²×C₇	semidirect
494. C₂×C₄×C₈	C₂²×C₇	semidirect
938. C₇	#60955	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×#3460	2
C₇×#3262	2
C₇×#3259	2
C₇×#3257	2
C₇×#3243	2
C₇×#3241	2
C₇×#3224	2
C₇×#3220	2
C₇×#3203	2
C₇×#3199	2
C₇×#3198	2
C₇×#3171	2
C₇×#3169	2
C₇×#3168	2
C₇×#3106	2
C₇×#3105	2
C₇×#3102	2
C₇×#3100	2
C₇×#2922	2
#60955	7

Subgroups — C7×#60955 #13238171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60955 #13238171