Subgroups — C₇×#61010 #13238226

Order 1792.

1700 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3258	C₂	1	2	yes	maximal, complemented
4	C₇×#3257	C₂	1	2	yes	maximal, complemented
5	C₇×#3233	C₂	1	2	yes	maximal, complemented
6	C₇×#3232	C₂	1	2	yes	maximal, complemented
7	C₇×#3212	C₂	1	2	yes	maximal, complemented
8	C₇×#3211	C₂	1	2	yes	maximal, complemented
9	C₇×#3201	C₂	1	2	yes	maximal, complemented
10	C₇×#3198	C₂	1	2	yes	maximal, complemented
11	C₇×#3183	C₂	1	2	yes	maximal, complemented
12	C₇×#3168	C₂	1	2	yes	maximal, complemented
13	C₇×#3127	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3126	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3125	C₂	1	2	yes	maximal, complemented
16	C₇×#3124	C₂	1	2	yes	maximal, complemented
17	C₇×#3123	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3122	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#559	—	2	2	no	—
21	C₇×#556	—	2	2	no	—
22	C₇×#553	—	2	2	no	—
23	C₇×#553	—	2	2	no	—
24	C₇×#553	—	2	2	no	—
25	C₇×#552	—	2	2	no	—
26	C₇×#551	—	2	2	no	—
27	C₇×#551	—	2	2	no	—
28	C₇×#542	C₂²	1	2	yes	—
29	C₇×#542	C₂²	1	2	yes	—
30	C₇×#541	C₂²	1	1	yes	characteristic
31	C₇×#541	C₂²	1	1	yes	characteristic, complemented
32	C₇×#540	C₂²	1	1	yes	characteristic
33	C₇×#540	C₂²	1	1	yes	characteristic, complemented
34	C₇×#537	C₂²	1	2	yes	—
35	C₇×#536	C₂²	1	1	yes	characteristic
36	C₇×#535	C₂²	1	1	yes	characteristic
37	C₇×#533	C₂²	1	1	yes	characteristic
38	C₇×#532	C₂²	1	1	yes	characteristic, complemented
39	C₇×#529	C₂²	1	2	yes	—
40	C₇×#529	C₂²	1	2	yes	—
41	C₇×#529	C₂²	1	2	yes	—
42	C₇×#529	C₂²	1	2	yes	complemented
43	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₇×#124	C₂²	1	1	yes	characteristic
45	C₇×#520	C₂²	1	2	yes	complemented
46	C₇×#519	C₂²	1	1	yes	characteristic
47	C₇×#518	C₂²	1	1	yes	characteristic
48	C₄×C₇×#41	C₂²	1	1	yes	characteristic
49	C₇×#499	C₂²	1	2	yes	complemented
50	C₇×#499	C₂²	1	2	yes	complemented
51	C₇×#495	C₂²	1	2	yes	—
52	C₇×#495	C₂²	1	2	yes	—
53	C₇×#488	C₂²	1	2	yes	—
54	C₇×#488	C₂²	1	2	yes	—
55	C₇×#488	C₂²	1	2	yes	complemented
56	C₇×#488	C₂²	1	2	yes	complemented
57	C₇×#485	C₂²	1	2	yes	—
58	C₇×#485	C₂²	1	2	yes	—
59	C₇×#484	C₂²	1	2	yes	complemented
60	C₇×#483	C₂²	1	2	yes	complemented
61	C₇×#482	C₂²	1	2	yes	—
62	C₇×#482	C₂²	1	2	yes	—
63	C₇×#481	C₂²	1	2	yes	—
64	C₇×#480	C₂²	1	2	yes	—
65	C₇×#479	C₂²	1	2	yes	complemented
66	C₇×#479	C₂²	1	2	yes	complemented
67	C₇×#478	C₂²	1	2	yes	—
68	C₇×#478	C₂²	1	2	yes	—
69	C₇×#477	C₂²	1	2	yes	complemented
70	C₇×#476	C₂²	1	2	yes	complemented
71	C₇×#475	C₂²	1	2	yes	complemented
72	C₇×#474	C₂²	1	2	yes	complemented
73	C₇×#470	C₂²	1	2	yes	complemented
74	C₇×#469	C₂²	1	2	yes	—
75	C₇×#468	C₂²	1	2	yes	—
76	C₇×#468	C₂²	1	2	yes	complemented
77	C₇×#467	C₂²	1	2	yes	complemented
78	C₇×#466	C₂²	1	2	yes	—
79	C₇×#465	C₂²	1	2	yes	—
80	C₇×#465	C₂²	1	2	yes	complemented
81	C₇×#464	C₂²	1	2	yes	—
82	C₇×#464	C₂²	1	2	yes	—
83	C₇×#463	C₂²	1	2	yes	—
84	C₇×#463	C₂²	1	2	yes	—
85	C₇×#462	C₂²	1	2	yes	complemented
86	C₇×#461	C₂²	1	2	yes	—
87	C₇×#460	C₂²	1	2	yes	complemented
88	C₇×#459	C₂²	1	2	yes	—
89	C₇×#452	C₂²	1	2	yes	complemented
90	C₇×#452	C₂²	1	2	yes	complemented
91	C₇×#451	C₂²	1	2	yes	—
92	C₇×#450	C₂²	1	2	yes	—
93	C₇×#449	C₂²	1	2	yes	—
94	C₇×#449	C₂²	1	2	yes	—
95	C₇×#448	C₂²	1	2	yes	—
96	C₇×#447	C₂²	1	2	yes	—
97	C₇×#442	C₂²	1	2	yes	—
98	C₇×#441	C₂²	1	2	yes	complemented
99	C₇×#440	C₂²	1	2	yes	—
100	C₇×#440	C₂²	1	2	yes	complemented
101	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
102	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
103	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
104	C₄×C₇×D₈	C₂²	1	2	yes	—
105	C₇×#433	C₂²	1	1	yes	characteristic
106	C₇×#433	C₂²	1	1	yes	characteristic
107	C₇×#433	C₂²	1	1	yes	characteristic, complemented
108	C₇×#433	C₂²	1	1	yes	characteristic, complemented
109	C₇×#431	C₂²	1	2	yes	—
110	C₇×#431	C₂²	1	2	yes	complemented
111	C₇×#424	C₂²	1	2	yes	complemented
112	C₇×#408	C₂²	1	2	yes	—
113	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
115	#61010	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂×C₇×#41	C₂³	1	2	yes	—
117	C₂×C₇×#41	C₂³	1	1	yes	characteristic
118	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
119	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
120	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
121	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
122	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
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	2	yes	—
127	C₂×C₇×D₈	C₂³	1	2	yes	—
128	C₂×C₇×M₁₆	C₂³	1	2	yes	—
129	C₂²×C₇×C₈	C₂³	1	2	yes	—
130	C₇×C₄⋊Q₈	—	2	1	no	—
131	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
132	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
133	C₇×#127	—	2	1	no	—
134	C₇×#127	C₂³	1	1	yes	characteristic
135	C₇×#126	—	2	2	no	—
136	C₇×#126	—	2	2	no	—
137	C₇×#126	—	2	2	no	—
138	C₇×#126	—	2	2	no	—
139	C₇×#126	—	2	2	no	—
140	C₇×#126	—	2	2	no	—
141	C₇×#126	—	2	2	no	—
142	C₇×#126	—	2	2	no	—
143	C₇×#125	—	2	2	no	—
144	C₇×#125	—	2	2	no	—
145	C₇×#125	—	2	2	no	—
146	C₇×#125	C₂³	1	1	yes	characteristic
147	C₇×#125	C₂³	1	1	yes	characteristic
148	C₇×#125	C₂³	1	2	yes	—
149	C₇×#125	C₂³	1	2	yes	—
150	C₇×#124	—	2	1	no	—
151	C₇×#124	—	2	1	no	—
152	C₇×#124	—	2	2	no	—
153	C₇×#124	—	2	2	no	—
154	C₇×#124	—	2	2	no	—
155	C₇×#124	C₂³	1	2	yes	—
156	C₇×#124	C₂³	1	2	yes	—
157	C₇×#124	C₂³	1	2	yes	—
158	C₇×#123	—	2	1	no	—
159	C₇×#123	—	2	1	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×#123	—	2	2	no	—
165	C₇×#123	—	2	2	no	—
166	C₇×#123	—	2	2	no	—
167	C₇×#123	—	2	2	no	—
168	C₇×C₂²⋊Q₈	—	2	2	no	—
169	C₇×C₂²⋊Q₈	—	2	2	no	—
170	C₇×C₂²⋊Q₈	—	2	2	no	—
171	C₇×C₂²⋊Q₈	—	2	2	no	—
172	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
173	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
174	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
175	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
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×#120	—	2	1	no	—
187	C₇×#120	—	2	1	no	—
188	C₄×C₇×Q₈	—	2	2	no	—
189	C₄×C₇×Q₈	—	2	2	no	—
190	C₄×C₇×Q₈	D₄	1	2	yes	—
191	C₄×C₇×Q₈	C₂³	1	2	yes	—
192	C₄×C₇×Q₈	C₂³	1	2	yes	—
193	C₄×C₇×Q₈	C₂³	1	2	yes	—
194	C₄×C₇×Q₈	C₂³	1	2	yes	—
195	C₄×C₇×D₄	—	2	2	no	—
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	D₄	1	2	yes	—
204	C₄×C₇×D₄	D₄	1	2	yes	—
205	C₄×C₇×D₄	D₄	1	2	yes	—
206	C₄×C₇×D₄	C₂³	1	2	yes	—
207	C₄×C₇×D₄	C₂³	1	2	yes	—
208	C₄×C₇×D₄	C₂³	1	2	yes	—
209	C₄×C₇×D₄	C₂³	1	2	yes	—
210	C₇×#117	—	2	2	no	—
211	C₇×#117	—	2	2	no	—
212	C₇×#117	—	2	2	no	—
213	C₇×#117	—	2	2	no	—
214	C₇×#117	—	2	2	no	—
215	C₇×#117	—	2	2	no	—
216	C₇×#117	C₂³	1	1	yes	characteristic
217	C₇×#117	C₂³	1	1	yes	characteristic
218	C₇×#117	C₂³	1	1	yes	characteristic
219	C₇×#117	C₂³	1	1	yes	characteristic
220	C₇×#117	C₂³	1	1	yes	characteristic
221	C₂×C₇×C₄⋊C₄	—	2	2	no	—
222	C₂×C₇×C₄⋊C₄	—	2	2	no	—
223	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
224	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
225	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
226	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
229	C₇×#107	C₂³	1	2	yes	—
230	C₇×#107	C₂³	1	2	yes	—
231	C₇×#107	C₂³	1	2	yes	—
232	C₇×#107	C₂³	1	2	yes	—
233	C₇×#106	C₂³	1	2	yes	—
234	C₇×#106	C₂³	1	2	yes	—
235	C₇×#106	C₂³	1	2	yes	—
236	C₇×#106	C₂³	1	2	yes	—
237	C₇×C₄⋊C₈	C₂³	1	2	yes	—
238	C₇×C₄⋊C₈	C₂³	1	2	yes	—
239	C₇×C₄⋊C₈	C₂³	1	2	yes	—
240	C₇×C₄⋊C₈	C₂³	1	2	yes	—
241	C₇×#103	C₂³	1	2	yes	—
242	C₇×#103	C₂³	1	2	yes	—
243	C₇×#103	C₂³	1	2	yes	—
244	C₇×#103	C₂³	1	2	yes	—
245	C₇×#103	C₂³	1	2	yes	—
246	C₇×#103	C₂³	1	2	yes	—
247	C₇×#103	C₂³	1	2	yes	—
248	C₇×#103	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×#102	C₂³	1	2	yes	—
256	C₇×#102	C₂³	1	2	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	1	yes	characteristic
262	C₇×#97	C₂³	1	1	yes	characteristic
263	C₄×C₇×C₈	C₂³	1	2	yes	—
264	C₄×C₇×C₈	C₂³	1	2	yes	—
265	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
266	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
267	#3512	C₂×C₇	1	1	yes	characteristic, complemented
268	#3510	C₂×C₇	1	1	yes	characteristic, complemented
269	#3258	C₂×C₇	1	2	yes	complemented
270	#3257	C₂×C₇	1	2	yes	complemented
271	#3233	C₂×C₇	1	2	yes	complemented
272	#3232	C₂×C₇	1	2	yes	complemented
273	#3212	C₂×C₇	1	2	yes	complemented
274	#3211	C₂×C₇	1	2	yes	complemented
275	#3201	C₂×C₇	1	2	yes	complemented
276	#3198	C₂×C₇	1	2	yes	complemented
277	#3183	C₂×C₇	1	2	yes	complemented
278	#3168	C₂×C₇	1	2	yes	complemented
279	#3127	C₂×C₇	1	1	yes	characteristic, complemented
280	#3126	C₂×C₇	1	1	yes	characteristic, complemented
281	#3125	C₂×C₇	1	2	yes	complemented
282	#3124	C₂×C₇	1	2	yes	complemented
283	#3123	C₂×C₇	1	1	yes	characteristic, complemented
284	#3122	C₂×C₇	1	1	yes	characteristic, complemented
285	#2922	C₂×C₇	1	1	yes	characteristic, complemented
286	C₂⁴×C₇	—	2	1	no	—
287	C₇×#41	—	4	2	no	—
288	C₇×#41	—	4	2	no	—
289	C₇×#41	—	4	2	no	—
290	C₂×C₇×Q₈	—	2	1	no	—
291	C₂×C₇×Q₈	—	2	2	no	—
292	C₂×C₇×Q₈	—	4	2	no	—
293	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
294	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
295	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
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	1	no	—
302	C₂×C₇×D₄	—	2	2	no	—
303	C₂×C₇×D₄	—	4	2	no	—
304	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
305	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
306	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
307	C₂×C₇×D₄	C₂⁴	1	2	yes	—
308	C₂×C₇×D₄	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₇	—	2	1	no	—
310	C₂²×C₄×C₇	—	2	2	no	—
311	C₂²×C₄×C₇	—	2	2	no	—
312	C₂²×C₄×C₇	—	2	2	no	—
313	C₂²×C₄×C₇	—	2	2	no	—
314	C₂²×C₄×C₇	—	2	2	no	—
315	C₂²×C₄×C₇	—	2	2	no	—
316	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
317	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
318	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
319	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
322	C₇×Q₁₆	—	4	2	no	—
323	C₇×Q₁₆	—	4	2	no	—
324	C₇×SD₁₆	—	4	2	no	—
325	C₇×SD₁₆	—	4	2	no	—
326	C₇×SD₁₆	—	4	2	no	—
327	C₇×SD₁₆	—	4	2	no	—
328	C₇×D₈	—	4	2	no	—
329	C₇×D₈	—	4	2	no	—
330	C₇×M₁₆	—	4	2	no	—
331	C₂×C₇×C₈	—	4	2	no	—
332	C₂×C₇×C₈	C₂⁴	1	2	yes	—
333	C₂×C₇×C₈	C₂⁴	1	2	yes	—
334	C₂×C₇×C₈	C₂⁴	1	2	yes	—
335	C₂×C₇×C₈	C₂⁴	1	2	yes	—
336	C₇×C₄⋊C₄	—	2	2	no	—
337	C₇×C₄⋊C₄	—	2	2	no	—
338	C₇×C₄⋊C₄	—	2	2	no	—
339	C₇×C₄⋊C₄	—	2	2	no	—
340	C₇×C₄⋊C₄	—	2	2	no	—
341	C₇×C₄⋊C₄	—	2	2	no	—
342	C₇×C₄⋊C₄	—	2	2	no	—
343	C₇×C₄⋊C₄	—	2	2	no	—
344	C₇×C₄⋊C₄	—	2	2	no	—
345	C₇×C₄⋊C₄	—	2	2	no	—
346	C₇×C₄⋊C₄	—	2	2	no	—
347	C₇×C₄⋊C₄	—	2	2	no	—
348	C₇×C₄⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
354	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
355	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
356	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
357	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
358	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
359	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
360	C₇×C₂²⋊C₄	—	2	1	no	—
361	C₇×C₂²⋊C₄	—	2	1	no	—
362	C₇×C₂²⋊C₄	—	2	2	no	—
363	C₇×C₂²⋊C₄	—	2	2	no	—
364	C₇×C₂²⋊C₄	—	2	2	no	—
365	C₇×C₂²⋊C₄	—	2	2	no	—
366	C₇×C₂²⋊C₄	—	2	2	no	—
367	C₇×C₂²⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
381	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
382	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
383	C₄²×C₇	—	2	2	no	—
384	C₄²×C₇	—	2	2	no	—
385	C₄²×C₇	—	2	2	no	—
386	C₄²×C₇	—	2	2	no	—
387	C₄²×C₇	—	2	1	no	—
388	C₄²×C₇	—	2	1	no	—
389	C₄²×C₇	C₂×D₄	1	2	yes	—
390	C₄²×C₇	C₂×D₄	1	2	yes	—
391	C₄²×C₇	C₂×D₄	1	2	yes	—
392	C₄²×C₇	C₂⁴	1	1	yes	characteristic
393	C₄²×C₇	C₂⁴	1	1	yes	characteristic
394	C₄²×C₇	C₂⁴	1	1	yes	characteristic
395	C₄²×C₇	C₂⁴	1	1	yes	characteristic
396	#559	—	2	2	no	—
397	#556	—	2	2	no	—
398	#553	—	2	2	no	—
399	#553	—	2	2	no	—
400	#553	—	2	2	no	—
401	#552	—	2	2	no	—
402	#551	—	2	2	no	—
403	#551	—	2	2	no	—
404	#542	C₂²×C₇	1	2	yes	—
405	#542	C₂²×C₇	1	2	yes	—
406	#541	C₂²×C₇	1	1	yes	characteristic
407	#541	C₂²×C₇	1	1	yes	characteristic, complemented
408	#540	C₂²×C₇	1	1	yes	characteristic
409	#540	C₂²×C₇	1	1	yes	characteristic, complemented
410	#537	C₂²×C₇	1	2	yes	—
411	#536	C₂²×C₇	1	1	yes	characteristic
412	#535	C₂²×C₇	1	1	yes	characteristic
413	#533	C₂²×C₇	1	1	yes	characteristic
414	#532	C₂²×C₇	1	1	yes	characteristic, complemented
415	#529	C₂²×C₇	1	2	yes	—
416	#529	C₂²×C₇	1	2	yes	—
417	#529	C₂²×C₇	1	2	yes	—
418	#529	C₂²×C₇	1	2	yes	complemented
419	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
420	C₂×#124	C₂²×C₇	1	1	yes	characteristic
421	#520	C₂²×C₇	1	2	yes	complemented
422	#519	C₂²×C₇	1	1	yes	characteristic
423	#518	C₂²×C₇	1	1	yes	characteristic
424	C₄×#41	C₂²×C₇	1	1	yes	characteristic
425	#499	C₂²×C₇	1	2	yes	complemented
426	#499	C₂²×C₇	1	2	yes	complemented
427	#495	C₂²×C₇	1	2	yes	—
428	#495	C₂²×C₇	1	2	yes	—
429	#488	C₂²×C₇	1	2	yes	—
430	#488	C₂²×C₇	1	2	yes	—
431	#488	C₂²×C₇	1	2	yes	complemented
432	#488	C₂²×C₇	1	2	yes	complemented
433	#485	C₂²×C₇	1	2	yes	—
434	#485	C₂²×C₇	1	2	yes	—
435	#484	C₂²×C₇	1	2	yes	complemented
436	#483	C₂²×C₇	1	2	yes	complemented
437	#482	C₂²×C₇	1	2	yes	—
438	#482	C₂²×C₇	1	2	yes	—
439	#481	C₂²×C₇	1	2	yes	—
440	#480	C₂²×C₇	1	2	yes	—
441	#479	C₂²×C₇	1	2	yes	complemented
442	#479	C₂²×C₇	1	2	yes	complemented
443	#478	C₂²×C₇	1	2	yes	—
444	#478	C₂²×C₇	1	2	yes	—
445	#477	C₂²×C₇	1	2	yes	complemented
446	#476	C₂²×C₇	1	2	yes	complemented
447	#475	C₂²×C₇	1	2	yes	complemented
448	#474	C₂²×C₇	1	2	yes	complemented
449	#470	C₂²×C₇	1	2	yes	complemented
450	#469	C₂²×C₇	1	2	yes	—
451	#468	C₂²×C₇	1	2	yes	—
452	#468	C₂²×C₇	1	2	yes	complemented
453	#467	C₂²×C₇	1	2	yes	complemented
454	#466	C₂²×C₇	1	2	yes	—
455	#465	C₂²×C₇	1	2	yes	—
456	#465	C₂²×C₇	1	2	yes	complemented
457	#464	C₂²×C₇	1	2	yes	—
458	#464	C₂²×C₇	1	2	yes	—
459	#463	C₂²×C₇	1	2	yes	—
460	#463	C₂²×C₇	1	2	yes	—
461	#462	C₂²×C₇	1	2	yes	complemented
462	#461	C₂²×C₇	1	2	yes	—
463	#460	C₂²×C₇	1	2	yes	complemented
464	#459	C₂²×C₇	1	2	yes	—
465	#452	C₂²×C₇	1	2	yes	complemented
466	#452	C₂²×C₇	1	2	yes	complemented
467	#451	C₂²×C₇	1	2	yes	—
468	#450	C₂²×C₇	1	2	yes	—
469	#449	C₂²×C₇	1	2	yes	—
470	#449	C₂²×C₇	1	2	yes	—
471	#448	C₂²×C₇	1	2	yes	—
472	#447	C₂²×C₇	1	2	yes	—
473	#442	C₂²×C₇	1	2	yes	—
474	#441	C₂²×C₇	1	2	yes	complemented
475	#440	C₂²×C₇	1	2	yes	—
476	#440	C₂²×C₇	1	2	yes	complemented
477	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
478	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
479	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
480	C₄×D₈	C₂²×C₇	1	2	yes	—
481	#433	C₂²×C₇	1	1	yes	characteristic
482	#433	C₂²×C₇	1	1	yes	characteristic
483	#433	C₂²×C₇	1	1	yes	characteristic, complemented
484	#433	C₂²×C₇	1	1	yes	characteristic, complemented
485	#431	C₂²×C₇	1	2	yes	—
486	#431	C₂²×C₇	1	2	yes	complemented
487	#424	C₂²×C₇	1	2	yes	complemented
488	#408	C₂²×C₇	1	2	yes	—
489	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
490	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
491	C₂³×C₇	—	2	2	no	—
492	C₂³×C₇	—	2	2	no	—
493	C₂³×C₇	—	4	2	no	—
494	C₂³×C₇	—	8	2	no	—
495	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
496	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
497	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
498	C₇×Q₈	—	2	2	no	—
499	C₇×Q₈	—	2	2	no	—
500	C₇×Q₈	—	2	2	no	—
501	C₇×Q₈	—	2	2	no	—
502	C₇×Q₈	—	4	1	no	—
503	C₇×Q₈	—	4	2	no	—
504	C₇×Q₈	—	8	2	no	—
505	C₇×D₄	—	2	2	no	—
506	C₇×D₄	—	2	2	no	—
507	C₇×D₄	—	2	2	no	—
508	C₇×D₄	—	2	2	no	—
509	C₇×D₄	—	4	1	no	—
510	C₇×D₄	—	4	1	no	—
511	C₇×D₄	—	4	1	no	—
512	C₇×D₄	—	4	2	no	—
513	C₇×D₄	—	4	4	no	—
514	C₇×D₄	—	8	2	no	—
515	C₇×D₄	—	8	2	no	—
516	C₇×D₄	—	8	2	no	—
517	C₇×D₄	—	8	2	no	—
518	C₇×D₄	—	8	2	no	—
519	C₂×C₄×C₇	—	2	2	no	—
520	C₂×C₄×C₇	—	2	2	no	—
521	C₂×C₄×C₇	—	2	2	no	—
522	C₂×C₄×C₇	—	2	2	no	—
523	C₂×C₄×C₇	—	2	2	no	—
524	C₂×C₄×C₇	—	2	2	no	—
525	C₂×C₄×C₇	—	2	2	no	—
526	C₂×C₄×C₇	—	2	2	no	—
527	C₂×C₄×C₇	—	2	2	no	—
528	C₂×C₄×C₇	—	4	2	no	—
529	C₂×C₄×C₇	—	4	2	no	—
530	C₂×C₄×C₇	—	4	2	no	—
531	C₂×C₄×C₇	—	4	4	no	—
532	C₂×C₄×C₇	—	4	2	no	—
533	C₂×C₄×C₇	—	8	2	no	—
534	C₂×C₄×C₇	—	8	2	no	—
535	C₂×C₄×C₇	—	8	2	no	—
536	C₂×C₄×C₇	—	8	2	no	—
537	C₂×C₄×C₇	—	8	2	no	—
538	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
542	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
546	C₇×C₈	—	2	2	no	—
547	C₇×C₈	—	2	2	no	—
548	C₇×C₈	—	2	2	no	—
549	C₇×C₈	—	2	2	no	—
550	C₂×#41	C₂³×C₇	1	2	yes	—
551	C₂×#41	C₂³×C₇	1	1	yes	characteristic
552	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
553	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
554	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
555	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
556	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
557	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
558	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
559	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
560	C₂×D₈	C₂³×C₇	1	2	yes	—
561	C₂×D₈	C₂³×C₇	1	2	yes	—
562	C₂×M₁₆	C₂³×C₇	1	2	yes	—
563	C₂²×C₈	C₂³×C₇	1	2	yes	—
564	C₄⋊Q₈	—	2	1	no	—
565	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
566	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
567	#127	—	2	1	no	—
568	#127	C₂³×C₇	1	1	yes	characteristic
569	#126	—	2	2	no	—
570	#126	—	2	2	no	—
571	#126	—	2	2	no	—
572	#126	—	2	2	no	—
573	#126	—	2	2	no	—
574	#126	—	2	2	no	—
575	#126	—	2	2	no	—
576	#126	—	2	2	no	—
577	#125	—	2	2	no	—
578	#125	—	2	2	no	—
579	#125	—	2	2	no	—
580	#125	C₂³×C₇	1	2	yes	—
581	#125	C₂³×C₇	1	1	yes	characteristic
582	#125	C₂³×C₇	1	1	yes	characteristic
583	#125	C₂³×C₇	1	2	yes	—
584	#124	—	2	1	no	—
585	#124	—	2	1	no	—
586	#124	—	2	2	no	—
587	#124	—	2	2	no	—
588	#124	—	2	2	no	—
589	#124	C₂³×C₇	1	2	yes	—
590	#124	C₂³×C₇	1	2	yes	—
591	#124	C₂³×C₇	1	2	yes	—
592	#123	—	2	1	no	—
593	#123	—	2	1	no	—
594	#123	—	2	2	no	—
595	#123	—	2	2	no	—
596	#123	—	2	2	no	—
597	#123	—	2	2	no	—
598	#123	—	2	2	no	—
599	#123	—	2	2	no	—
600	#123	—	2	2	no	—
601	#123	—	2	2	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	—	2	2	no	—
604	C₂²⋊Q₈	—	2	2	no	—
605	C₂²⋊Q₈	—	2	2	no	—
606	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
607	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
608	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
609	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
610	#121	—	2	2	no	—
611	#121	—	2	2	no	—
612	#121	—	2	2	no	—
613	#121	—	2	2	no	—
614	#121	—	2	2	no	—
615	#121	—	2	2	no	—
616	#121	C₂³×C₇	1	2	yes	—
617	#121	C₂³×C₇	1	2	yes	—
618	#121	C₂³×C₇	1	2	yes	—
619	#121	C₂³×C₇	1	2	yes	—
620	#120	—	2	1	no	—
621	#120	—	2	1	no	—
622	C₄×Q₈	—	2	2	no	—
623	C₄×Q₈	—	2	2	no	—
624	C₄×Q₈	C₇×D₄	1	2	yes	—
625	C₄×Q₈	C₂³×C₇	1	2	yes	—
626	C₄×Q₈	C₂³×C₇	1	2	yes	—
627	C₄×Q₈	C₂³×C₇	1	2	yes	—
628	C₄×Q₈	C₂³×C₇	1	2	yes	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	C₇×D₄	1	2	yes	—
638	C₄×D₄	C₇×D₄	1	2	yes	—
639	C₄×D₄	C₇×D₄	1	2	yes	—
640	C₄×D₄	C₂³×C₇	1	2	yes	—
641	C₄×D₄	C₂³×C₇	1	2	yes	—
642	C₄×D₄	C₂³×C₇	1	2	yes	—
643	C₄×D₄	C₂³×C₇	1	2	yes	—
644	#117	—	2	2	no	—
645	#117	—	2	2	no	—
646	#117	—	2	2	no	—
647	#117	—	2	2	no	—
648	#117	—	2	2	no	—
649	#117	—	2	2	no	—
650	#117	C₂³×C₇	1	1	yes	characteristic
651	#117	C₂³×C₇	1	1	yes	characteristic
652	#117	C₂³×C₇	1	1	yes	characteristic
653	#117	C₂³×C₇	1	1	yes	characteristic
654	#117	C₂³×C₇	1	1	yes	characteristic
655	C₂×C₄⋊C₄	—	2	2	no	—
656	C₂×C₄⋊C₄	—	2	2	no	—
657	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
658	C₂×C₂²⋊C₄	—	2	2	no	—
659	C₂×C₂²⋊C₄	—	2	2	no	—
660	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
663	#107	C₂³×C₇	1	2	yes	—
664	#107	C₂³×C₇	1	2	yes	—
665	#107	C₂³×C₇	1	2	yes	—
666	#107	C₂³×C₇	1	2	yes	—
667	#106	C₂³×C₇	1	2	yes	—
668	#106	C₂³×C₇	1	2	yes	—
669	#106	C₂³×C₇	1	2	yes	—
670	#106	C₂³×C₇	1	2	yes	—
671	C₄⋊C₈	C₂³×C₇	1	2	yes	—
672	C₄⋊C₈	C₂³×C₇	1	2	yes	—
673	C₄⋊C₈	C₂³×C₇	1	2	yes	—
674	C₄⋊C₈	C₂³×C₇	1	2	yes	—
675	#103	C₂³×C₇	1	2	yes	—
676	#103	C₂³×C₇	1	2	yes	—
677	#103	C₂³×C₇	1	2	yes	—
678	#103	C₂³×C₇	1	2	yes	—
679	#103	C₂³×C₇	1	2	yes	—
680	#103	C₂³×C₇	1	2	yes	—
681	#103	C₂³×C₇	1	2	yes	—
682	#103	C₂³×C₇	1	2	yes	—
683	#102	C₂³×C₇	1	2	yes	—
684	#102	C₂³×C₇	1	2	yes	—
685	#102	C₂³×C₇	1	2	yes	—
686	#102	C₂³×C₇	1	2	yes	—
687	#102	C₂³×C₇	1	2	yes	—
688	#102	C₂³×C₇	1	2	yes	—
689	#102	C₂³×C₇	1	2	yes	—
690	#102	C₂³×C₇	1	2	yes	—
691	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
692	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
693	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
694	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
695	#97	C₂³×C₇	1	1	yes	characteristic
696	#97	C₂³×C₇	1	1	yes	characteristic
697	C₄×C₈	C₂³×C₇	1	2	yes	—
698	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
699	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
700	C₄×C₈	C₂³×C₇	1	2	yes	—
701	C₂²×C₇	—	2	2	no	—
702	C₂²×C₇	—	2	2	no	—
703	C₂²×C₇	—	2	2	no	—
704	C₂²×C₇	—	2	1	no	—
705	C₂²×C₇	—	2	1	no	—
706	C₂²×C₇	—	2	1	no	—
707	C₂²×C₇	—	4	2	no	—
708	C₂²×C₇	—	4	2	no	—
709	C₂²×C₇	—	4	2	no	—
710	C₂²×C₇	—	4	2	no	—
711	C₂²×C₇	—	4	2	no	—
712	C₂²×C₇	—	4	2	no	—
713	C₂²×C₇	—	16	2	no	—
714	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
715	C₄×C₇	—	2	2	no	—
716	C₄×C₇	—	2	2	no	—
717	C₄×C₇	—	2	2	no	—
718	C₄×C₇	—	2	2	no	—
719	C₄×C₇	—	2	1	no	—
720	C₄×C₇	—	2	1	no	—
721	C₄×C₇	—	2	1	no	—
722	C₄×C₇	—	4	2	no	—
723	C₄×C₇	—	4	2	no	—
724	C₄×C₇	—	4	2	no	—
725	C₄×C₇	—	4	2	no	—
726	C₄×C₇	—	4	2	no	—
727	C₄×C₇	—	4	2	no	—
728	C₄×C₇	#585	1	2	yes	—
729	C₂⁴	—	2	1	no	—
730	#41	—	4	2	no	—
731	#41	—	4	2	no	—
732	#41	—	4	2	no	—
733	C₂×Q₈	—	2	1	no	—
734	C₂×Q₈	—	2	2	no	—
735	C₂×Q₈	—	4	2	no	—
736	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
737	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
738	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	1	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	4	2	no	—
747	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
748	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
749	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
750	C₂×D₄	C₂⁴×C₇	1	2	yes	—
751	C₂×D₄	C₂⁴×C₇	1	2	yes	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
760	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
761	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
765	Q₁₆	—	4	2	no	—
766	Q₁₆	—	4	2	no	—
767	SD₁₆	—	4	2	no	—
768	SD₁₆	—	4	2	no	—
769	SD₁₆	—	4	2	no	—
770	SD₁₆	—	4	2	no	—
771	D₈	—	4	2	no	—
772	D₈	—	4	2	no	—
773	M₁₆	—	4	2	no	—
774	C₂×C₈	—	4	2	no	—
775	C₂×C₈	C₂⁴×C₇	1	2	yes	—
776	C₂×C₈	C₂⁴×C₇	1	2	yes	—
777	C₂×C₈	C₂⁴×C₇	1	2	yes	—
778	C₂×C₈	C₂⁴×C₇	1	2	yes	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
797	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
798	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
799	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
800	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
801	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
802	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
803	C₂²⋊C₄	—	2	1	no	—
804	C₂²⋊C₄	—	2	1	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
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	C₂×C₇×D₄	1	2	yes	—
824	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
825	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
826	C₄²	—	2	2	no	—
827	C₄²	—	2	2	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	1	no	—
831	C₄²	—	2	1	no	—
832	C₄²	C₂×C₇×D₄	1	2	yes	—
833	C₄²	C₂×C₇×D₄	1	2	yes	—
834	C₄²	C₂×C₇×D₄	1	2	yes	—
835	C₄²	C₂⁴×C₇	1	1	yes	characteristic
836	C₄²	C₂⁴×C₇	1	1	yes	characteristic
837	C₄²	C₂⁴×C₇	1	1	yes	characteristic
838	C₄²	C₂⁴×C₇	1	1	yes	characteristic
839	C₂×C₇	—	4	1	no	—
840	C₂×C₇	—	4	1	no	—
841	C₂×C₇	—	4	1	no	—
842	C₂×C₇	—	8	2	no	—
843	C₂×C₇	—	8	2	no	—
844	C₂×C₇	#3449	1	1	yes	characteristic
845	C₂×C₇	#3584	1	2	yes	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	4	2	no	—
849	C₂³	—	8	2	no	—
850	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
851	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
852	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
853	Q₈	—	2	2	no	—
854	Q₈	—	2	2	no	—
855	Q₈	—	2	2	no	—
856	Q₈	—	2	2	no	—
857	Q₈	—	4	1	no	—
858	Q₈	—	4	2	no	—
859	Q₈	—	8	2	no	—
860	D₄	—	2	2	no	—
861	D₄	—	2	2	no	—
862	D₄	—	2	2	no	—
863	D₄	—	2	2	no	—
864	D₄	—	4	1	no	—
865	D₄	—	4	1	no	—
866	D₄	—	4	1	no	—
867	D₄	—	4	2	no	—
868	D₄	—	4	4	no	—
869	D₄	—	8	2	no	—
870	D₄	—	8	2	no	—
871	D₄	—	8	2	no	—
872	D₄	—	8	2	no	—
873	D₄	—	8	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	4	2	no	—
884	C₂×C₄	—	4	2	no	—
885	C₂×C₄	—	4	2	no	—
886	C₂×C₄	—	4	4	no	—
887	C₂×C₄	—	4	2	no	—
888	C₂×C₄	—	8	2	no	—
889	C₂×C₄	—	8	2	no	—
890	C₂×C₄	—	8	2	no	—
891	C₂×C₄	—	8	2	no	—
892	C₂×C₄	—	8	2	no	—
893	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
894	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
895	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
896	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
897	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
898	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
899	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
900	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
901	C₈	—	2	2	no	—
902	C₈	—	2	2	no	—
903	C₈	—	2	2	no	—
904	C₈	—	2	2	no	—
905	C₇	#61010	1	1	yes	characteristic, direct product factor, Sylow
906	C₂²	—	2	2	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	16	2	no	—
919	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
920	C₄	—	2	2	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	1	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	C₇×#585	1	2	yes	—
934	C₂	—	4	1	no	—
935	C₂	—	4	1	no	—
936	C₂	—	4	1	no	—
937	C₂	—	8	2	no	—
938	C₂	—	8	2	no	—
939	C₂	C₇×#3449	1	1	yes	characteristic
940	C₂	C₇×#3584	1	2	yes	—

	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×#3512	C₂	semidirect
2. C₇×#3510	C₂	semidirect
3. C₇×#3258	C₂	semidirect
4. C₇×#3257	C₂	semidirect
5. C₇×#3233	C₂	semidirect
6. C₇×#3232	C₂	semidirect
7. C₇×#3212	C₂	semidirect
8. C₇×#3211	C₂	semidirect
9. C₇×#3201	C₂	semidirect
10. C₇×#3198	C₂	semidirect
11. C₇×#3183	C₂	semidirect
12. C₇×#3168	C₂	semidirect
13. C₇×#3127	C₂	semidirect
14. C₇×#3126	C₂	semidirect
15. C₇×#3125	C₂	semidirect
16. C₇×#3124	C₂	semidirect
17. C₇×#3123	C₂	semidirect
18. C₇×#3122	C₂	semidirect
19. C₇×#2922	C₂	semidirect
31. C₇×#541	C₂²	semidirect
33. C₇×#540	C₂²	semidirect
38. C₇×#532	C₂²	semidirect
42. C₇×#529	C₂²	semidirect
43. C₂×C₇×#125	C₂²	semidirect
45. C₇×#520	C₂²	semidirect
49. C₇×#499	C₂²	semidirect
50. C₇×#499	C₂²	semidirect
55. C₇×#488	C₂²	semidirect
56. C₇×#488	C₂²	semidirect
59. C₇×#484	C₂²	semidirect
60. C₇×#483	C₂²	semidirect
65. C₇×#479	C₂²	semidirect
66. C₇×#479	C₂²	semidirect
69. C₇×#477	C₂²	semidirect
70. C₇×#476	C₂²	semidirect
71. C₇×#475	C₂²	semidirect
72. C₇×#474	C₂²	semidirect
73. C₇×#470	C₂²	semidirect
76. C₇×#468	C₂²	semidirect
77. C₇×#467	C₂²	semidirect
80. C₇×#465	C₂²	semidirect
85. C₇×#462	C₂²	semidirect
87. C₇×#460	C₂²	semidirect
89. C₇×#452	C₂²	semidirect
90. C₇×#452	C₂²	semidirect
98. C₇×#441	C₂²	semidirect
100. C₇×#440	C₂²	semidirect
101. C₄×C₇×Q₁₆	C₂²	semidirect
103. C₄×C₇×SD₁₆	C₂²	semidirect
107. C₇×#433	C₂²	semidirect
108. C₇×#433	C₂²	semidirect
110. C₇×#431	C₂²	semidirect
111. C₇×#424	C₂²	semidirect
113. C₄×C₇×M₁₆	C₂²	semidirect
114. C₂×C₄×C₇×C₈	C₂²	semidirect
115. #61010	C₇	direct (N × H)
267. #3512	C₂×C₇	semidirect
268. #3510	C₂×C₇	semidirect
269. #3258	C₂×C₇	semidirect
270. #3257	C₂×C₇	semidirect
271. #3233	C₂×C₇	semidirect
272. #3232	C₂×C₇	semidirect
273. #3212	C₂×C₇	semidirect
274. #3211	C₂×C₇	semidirect
275. #3201	C₂×C₇	semidirect
276. #3198	C₂×C₇	semidirect
277. #3183	C₂×C₇	semidirect
278. #3168	C₂×C₇	semidirect
279. #3127	C₂×C₇	semidirect
280. #3126	C₂×C₇	semidirect
281. #3125	C₂×C₇	semidirect
282. #3124	C₂×C₇	semidirect
283. #3123	C₂×C₇	semidirect
284. #3122	C₂×C₇	semidirect
285. #2922	C₂×C₇	semidirect
407. #541	C₂²×C₇	semidirect
409. #540	C₂²×C₇	semidirect
414. #532	C₂²×C₇	semidirect
418. #529	C₂²×C₇	semidirect
419. C₂×#125	C₂²×C₇	semidirect
421. #520	C₂²×C₇	semidirect
425. #499	C₂²×C₇	semidirect
426. #499	C₂²×C₇	semidirect
431. #488	C₂²×C₇	semidirect
432. #488	C₂²×C₇	semidirect
435. #484	C₂²×C₇	semidirect
436. #483	C₂²×C₇	semidirect
441. #479	C₂²×C₇	semidirect
442. #479	C₂²×C₇	semidirect
445. #477	C₂²×C₇	semidirect
446. #476	C₂²×C₇	semidirect
447. #475	C₂²×C₇	semidirect
448. #474	C₂²×C₇	semidirect
449. #470	C₂²×C₇	semidirect
452. #468	C₂²×C₇	semidirect
453. #467	C₂²×C₇	semidirect
456. #465	C₂²×C₇	semidirect
461. #462	C₂²×C₇	semidirect
463. #460	C₂²×C₇	semidirect
465. #452	C₂²×C₇	semidirect
466. #452	C₂²×C₇	semidirect
474. #441	C₂²×C₇	semidirect
476. #440	C₂²×C₇	semidirect
477. C₄×Q₁₆	C₂²×C₇	semidirect
479. C₄×SD₁₆	C₂²×C₇	semidirect
483. #433	C₂²×C₇	semidirect
484. #433	C₂²×C₇	semidirect
486. #431	C₂²×C₇	semidirect
487. #424	C₂²×C₇	semidirect
489. C₄×M₁₆	C₂²×C₇	semidirect
490. C₂×C₄×C₈	C₂²×C₇	semidirect
905. C₇	#61010	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×#3512	2
C₇×#3510	2
C₇×#3258	2
C₇×#3257	2
C₇×#3233	2
C₇×#3232	2
C₇×#3212	2
C₇×#3211	2
C₇×#3201	2
C₇×#3198	2
C₇×#3183	2
C₇×#3168	2
C₇×#3127	2
C₇×#3126	2
C₇×#3125	2
C₇×#3124	2
C₇×#3123	2
C₇×#3122	2
C₇×#2922	2
#61010	7

Subgroups — C7×#61010 #13238226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61010 #13238226