Subgroups — C₇×#36816 #13214032

Order 1792.

1800 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2852	C₂	1	2	yes	maximal, complemented
2	C₇×#2797	C₂	1	2	yes	maximal, complemented
3	C₇×#2759	C₂	1	2	yes	maximal, complemented
4	C₇×#2746	C₂	1	2	yes	maximal, complemented
5	C₇×#2737	C₂	1	2	yes	maximal, complemented
6	C₇×#2716	C₂	1	2	yes	maximal, complemented
7	C₇×#2712	C₂	1	2	yes	maximal, complemented
8	C₇×#2685	C₂	1	2	yes	maximal, complemented
9	C₇×#2684	C₂	1	2	yes	maximal, complemented
10	C₇×#2653	C₂	1	2	yes	maximal, complemented
11	C₇×#2607	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2597	C₂	1	2	yes	maximal, complemented
13	C₇×#2561	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2474	C₂	1	2	yes	maximal, complemented
15	C₇×#2432	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2404	C₂	1	1	yes	maximal, characteristic
17	C₇×#2332	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2312	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2297	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₇×#126	C₂²	1	2	yes	—
23	C₂×C₇×#124	C₂²	1	2	yes	—
24	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×#120	C₂²	1	1	yes	characteristic
27	C₂×C₇×#120	C₂²	1	1	yes	characteristic
28	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
31	C₇×#401	C₂²	1	2	yes	complemented
32	C₇×#400	C₂²	1	2	yes	complemented
33	C₇×#399	C₂²	1	2	yes	—
34	C₇×#398	C₂²	1	2	yes	complemented
35	C₇×#397	C₂²	1	2	yes	—
36	C₇×#397	C₂²	1	2	yes	—
37	C₇×#397	C₂²	1	2	yes	—
38	C₇×#397	C₂²	1	2	yes	complemented
39	C₇×#397	C₂²	1	2	yes	complemented
40	C₇×#397	C₂²	1	2	yes	complemented
41	C₇×#396	C₂²	1	2	yes	—
42	C₇×#395	C₂²	1	2	yes	complemented
43	C₇×#394	C₂²	1	2	yes	—
44	C₇×#394	C₂²	1	2	yes	—
45	C₇×#394	C₂²	1	2	yes	—
46	C₇×#394	C₂²	1	2	yes	—
47	C₇×#394	C₂²	1	2	yes	—
48	C₇×#394	C₂²	1	2	yes	—
49	C₇×#393	C₂²	1	2	yes	—
50	C₇×#393	C₂²	1	2	yes	—
51	C₇×#393	C₂²	1	2	yes	—
52	C₇×#393	C₂²	1	2	yes	—
53	C₇×#393	C₂²	1	2	yes	complemented
54	C₇×#392	C₂²	1	2	yes	—
55	C₇×#391	C₂²	1	2	yes	complemented
56	C₇×#391	C₂²	1	1	yes	characteristic, complemented
57	C₇×#391	C₂²	1	2	yes	complemented
58	C₇×#391	C₂²	1	2	yes	complemented
59	C₇×#391	C₂²	1	2	yes	complemented
60	C₇×#390	C₂²	1	2	yes	—
61	C₇×#390	C₂²	1	2	yes	—
62	C₇×#390	C₂²	1	1	yes	characteristic, complemented
63	C₇×#388	C₂²	1	2	yes	—
64	C₇×#388	C₂²	1	2	yes	—
65	C₇×#388	C₂²	1	2	yes	—
66	C₇×#388	C₂²	1	2	yes	—
67	C₇×#388	C₂²	1	2	yes	—
68	C₇×#388	C₂²	1	2	yes	—
69	C₇×#388	C₂²	1	2	yes	—
70	C₇×#388	C₂²	1	2	yes	—
71	C₇×#388	C₂²	1	2	yes	—
72	C₇×#388	C₂²	1	2	yes	—
73	C₇×#388	C₂²	1	2	yes	—
74	C₇×#388	C₂²	1	2	yes	complemented
75	C₇×#388	C₂²	1	2	yes	complemented
76	C₇×#387	C₂²	1	2	yes	complemented
77	C₇×#387	C₂²	1	2	yes	complemented
78	C₇×#387	C₂²	1	2	yes	complemented
79	C₇×#387	C₂²	1	2	yes	complemented
80	C₇×#387	C₂²	1	2	yes	complemented
81	C₇×#387	C₂²	1	2	yes	complemented
82	C₇×#387	C₂²	1	2	yes	complemented
83	C₇×#386	C₂²	1	2	yes	—
84	C₇×#386	C₂²	1	2	yes	—
85	C₇×#386	C₂²	1	1	yes	characteristic
86	C₇×#386	C₂²	1	1	yes	characteristic
87	C₇×#386	C₂²	1	2	yes	—
88	C₇×#386	C₂²	1	2	yes	—
89	C₇×#386	C₂²	1	2	yes	—
90	C₇×#386	C₂²	1	2	yes	complemented
91	C₇×#385	C₂²	1	2	yes	complemented
92	C₇×#385	C₂²	1	2	yes	complemented
93	C₇×#385	C₂²	1	2	yes	complemented
94	C₇×#385	C₂²	1	2	yes	complemented
95	C₇×#383	C₂²	1	2	yes	complemented
96	C₇×#381	C₂²	1	1	yes	characteristic
97	C₇×#381	C₂²	1	2	yes	—
98	C₇×#380	C₂²	1	2	yes	—
99	C₇×#379	C₂²	1	2	yes	—
100	C₇×#379	C₂²	1	2	yes	—
101	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
102	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
107	#36816	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁵×C₇	C₂³	1	1	yes	characteristic
109	C₂×C₇×#41	—	2	4	no	—
110	C₂×C₇×#41	—	4	2	no	—
111	C₂×C₇×#41	—	4	2	no	—
112	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
113	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
114	C₂²×C₇×Q₈	C₂³	1	2	yes	—
115	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
116	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
117	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
118	C₂²×C₇×D₄	C₂³	1	2	yes	—
119	C₂²×C₇×D₄	C₂³	1	2	yes	—
120	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₇	C₂³	1	2	yes	—
124	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
125	C₇×C₄⋊Q₈	—	4	2	no	—
126	C₇×#126	—	4	4	no	—
127	C₇×#124	—	4	4	no	—
128	C₇×#124	—	4	2	no	—
129	C₇×C₂²⋊Q₈	—	2	4	no	—
130	C₇×#120	—	4	2	no	—
131	C₇×#120	—	4	2	no	—
132	C₇×#117	—	4	2	no	—
133	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
146	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₄²×C₇	—	4	2	no	—
174	C₂×C₄²×C₇	C₂³	1	2	yes	—
175	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₇	C₂³	1	2	yes	—
182	C₂×C₄²×C₇	C₂³	1	2	yes	—
183	C₇×#95	C₂³	1	2	yes	—
184	C₇×#95	C₂³	1	2	yes	—
185	C₇×#95	C₂³	1	2	yes	—
186	C₇×#95	C₂³	1	2	yes	—
187	C₇×#95	C₂³	1	2	yes	—
188	C₇×#95	C₂³	1	2	yes	—
189	C₇×#95	C₂³	1	2	yes	—
190	C₇×#95	C₂³	1	2	yes	—
191	C₇×#95	C₂³	1	2	yes	—
192	C₇×#95	C₂³	1	2	yes	—
193	C₇×#95	C₂³	1	2	yes	—
194	C₇×#95	C₂³	1	2	yes	—
195	C₇×#95	C₂³	1	2	yes	—
196	C₇×#95	C₂³	1	2	yes	—
197	C₇×#95	C₂³	1	2	yes	—
198	C₇×#95	C₂³	1	2	yes	—
199	C₇×#95	C₂³	1	2	yes	—
200	C₇×#95	C₂³	1	2	yes	—
201	C₇×#95	C₂³	1	2	yes	—
202	C₇×#95	C₂³	1	2	yes	—
203	C₇×#95	C₂³	1	2	yes	—
204	C₇×#95	C₂³	1	2	yes	—
205	C₇×#95	C₂³	1	2	yes	—
206	C₇×#95	C₂³	1	2	yes	—
207	C₇×#95	C₂³	1	2	yes	—
208	#2852	C₂×C₇	1	2	yes	complemented
209	#2797	C₂×C₇	1	2	yes	complemented
210	#2759	C₂×C₇	1	2	yes	complemented
211	#2746	C₂×C₇	1	2	yes	complemented
212	#2737	C₂×C₇	1	2	yes	complemented
213	#2716	C₂×C₇	1	2	yes	complemented
214	#2712	C₂×C₇	1	2	yes	complemented
215	#2685	C₂×C₇	1	2	yes	complemented
216	#2684	C₂×C₇	1	2	yes	complemented
217	#2653	C₂×C₇	1	2	yes	complemented
218	#2607	C₂×C₇	1	1	yes	characteristic, complemented
219	#2597	C₂×C₇	1	2	yes	complemented
220	#2561	C₂×C₇	1	1	yes	characteristic, complemented
221	#2474	C₂×C₇	1	2	yes	complemented
222	#2432	C₂×C₇	1	1	yes	characteristic, complemented
223	#2404	C₂×C₇	1	1	yes	characteristic
224	#2332	C₂×C₇	1	1	yes	characteristic, complemented
225	#2312	C₂×C₇	1	1	yes	characteristic, complemented
226	#2297	C₂×C₇	1	1	yes	characteristic, complemented
227	C₂⁴×C₇	—	2	2	no	—
228	C₂⁴×C₇	—	4	2	no	—
229	C₂⁴×C₇	—	4	1	no	—
230	C₂⁴×C₇	—	4	1	no	—
231	C₂⁴×C₇	—	4	2	no	—
232	C₂⁴×C₇	C₂⁴	1	2	yes	—
233	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
234	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
235	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
236	C₇×#41	—	4	16	no	—
237	C₂×C₇×Q₈	—	2	2	no	—
238	C₂×C₇×Q₈	—	2	2	no	—
239	C₂×C₇×Q₈	—	2	2	no	—
240	C₂×C₇×Q₈	—	4	1	no	—
241	C₂×C₇×Q₈	—	4	1	no	—
242	C₂×C₇×Q₈	—	4	2	no	—
243	C₂×C₇×Q₈	—	4	1	no	—
244	C₂×C₇×Q₈	—	4	2	no	—
245	C₂×C₇×Q₈	—	4	2	no	—
246	C₂×C₇×D₄	—	2	2	no	—
247	C₂×C₇×D₄	—	2	2	no	—
248	C₂×C₇×D₄	—	2	2	no	—
249	C₂×C₇×D₄	—	2	2	no	—
250	C₂×C₇×D₄	—	2	4	no	—
251	C₂×C₇×D₄	—	2	2	no	—
252	C₂×C₇×D₄	—	2	2	no	—
253	C₂×C₇×D₄	—	4	1	no	—
254	C₂×C₇×D₄	—	4	1	no	—
255	C₂×C₇×D₄	—	4	1	no	—
256	C₂×C₇×D₄	—	4	2	no	—
257	C₂×C₇×D₄	—	4	2	no	—
258	C₂×C₇×D₄	—	4	2	no	—
259	C₂×C₇×D₄	—	4	2	no	—
260	C₂×C₇×D₄	—	4	2	no	—
261	C₂²×C₄×C₇	—	2	2	no	—
262	C₂²×C₄×C₇	—	2	2	no	—
263	C₂²×C₄×C₇	—	2	2	no	—
264	C₂²×C₄×C₇	—	2	2	no	—
265	C₂²×C₄×C₇	—	2	2	no	—
266	C₂²×C₄×C₇	—	4	2	no	—
267	C₂²×C₄×C₇	—	4	2	no	—
268	C₂²×C₄×C₇	—	4	2	no	—
269	C₂²×C₄×C₇	—	4	1	no	—
270	C₂²×C₄×C₇	—	4	1	no	—
271	C₂²×C₄×C₇	—	4	1	no	—
272	C₂²×C₄×C₇	—	4	1	no	—
273	C₂²×C₄×C₇	—	4	2	no	—
274	C₂²×C₄×C₇	#41	1	4	yes	—
275	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
290	C₇×C₄⋊C₄	—	2	2	no	—
291	C₇×C₄⋊C₄	—	2	4	no	—
292	C₇×C₄⋊C₄	—	2	4	no	—
293	C₇×C₄⋊C₄	—	4	2	no	—
294	C₇×C₄⋊C₄	—	4	2	no	—
295	C₇×C₄⋊C₄	—	4	2	no	—
296	C₇×C₄⋊C₄	—	4	2	no	—
297	C₇×C₄⋊C₄	—	4	2	no	—
298	C₇×C₄⋊C₄	—	4	2	no	—
299	C₇×C₄⋊C₄	—	4	2	no	—
300	C₇×C₄⋊C₄	—	4	2	no	—
301	C₇×C₄⋊C₄	—	4	2	no	—
302	C₇×C₂²⋊C₄	—	2	4	no	—
303	C₇×C₂²⋊C₄	—	2	4	no	—
304	C₇×C₂²⋊C₄	—	2	4	no	—
305	C₇×C₂²⋊C₄	—	2	4	no	—
306	C₇×C₂²⋊C₄	—	2	4	no	—
307	C₇×C₂²⋊C₄	—	2	4	no	—
308	C₇×C₂²⋊C₄	—	4	2	no	—
309	C₇×C₂²⋊C₄	—	4	2	no	—
310	C₇×C₂²⋊C₄	—	4	2	no	—
311	C₇×C₂²⋊C₄	—	4	2	no	—
312	C₇×C₂²⋊C₄	—	4	2	no	—
313	C₇×C₂²⋊C₄	—	4	2	no	—
314	C₇×C₂²⋊C₄	—	4	2	no	—
315	C₇×C₂²⋊C₄	—	4	2	no	—
316	C₇×C₂²⋊C₄	—	4	2	no	—
317	C₇×C₂²⋊C₄	—	4	2	no	—
318	C₇×C₂²⋊C₄	—	4	2	no	—
319	C₇×C₂²⋊C₄	—	4	2	no	—
320	C₇×C₂²⋊C₄	—	4	2	no	—
321	C₇×C₂²⋊C₄	—	4	1	no	—
322	C₇×C₂²⋊C₄	—	4	2	no	—
323	C₇×C₂²⋊C₄	—	4	1	no	—
324	C₇×C₂²⋊C₄	—	4	2	no	—
325	C₇×C₂²⋊C₄	—	4	2	no	—
326	C₇×C₂²⋊C₄	—	4	2	no	—
327	C₇×C₂²⋊C₄	—	4	2	no	—
328	C₇×C₂²⋊C₄	—	4	2	no	—
329	C₄²×C₇	—	2	4	no	—
330	C₄²×C₇	—	4	1	no	—
331	C₄²×C₇	—	4	1	no	—
332	C₄²×C₇	—	4	2	no	—
333	C₄²×C₇	—	4	1	no	—
334	C₄²×C₇	—	4	1	no	—
335	C₄²×C₇	—	4	1	no	—
336	C₄²×C₇	—	4	2	no	—
337	C₄²×C₇	—	4	1	no	—
338	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
339	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
340	C₂×#126	C₂²×C₇	1	2	yes	—
341	C₂×#124	C₂²×C₇	1	2	yes	—
342	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
343	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
344	C₂×#120	C₂²×C₇	1	1	yes	characteristic
345	C₂×#120	C₂²×C₇	1	1	yes	characteristic
346	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
347	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
348	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
349	#401	C₂²×C₇	1	2	yes	complemented
350	#400	C₂²×C₇	1	2	yes	complemented
351	#399	C₂²×C₇	1	2	yes	—
352	#398	C₂²×C₇	1	2	yes	complemented
353	#397	C₂²×C₇	1	2	yes	—
354	#397	C₂²×C₇	1	2	yes	—
355	#397	C₂²×C₇	1	2	yes	—
356	#397	C₂²×C₇	1	2	yes	complemented
357	#397	C₂²×C₇	1	2	yes	complemented
358	#397	C₂²×C₇	1	2	yes	complemented
359	#396	C₂²×C₇	1	2	yes	—
360	#395	C₂²×C₇	1	2	yes	complemented
361	#394	C₂²×C₇	1	2	yes	—
362	#394	C₂²×C₇	1	2	yes	—
363	#394	C₂²×C₇	1	2	yes	—
364	#394	C₂²×C₇	1	2	yes	—
365	#394	C₂²×C₇	1	2	yes	—
366	#394	C₂²×C₇	1	2	yes	—
367	#393	C₂²×C₇	1	2	yes	—
368	#393	C₂²×C₇	1	2	yes	—
369	#393	C₂²×C₇	1	2	yes	—
370	#393	C₂²×C₇	1	2	yes	—
371	#393	C₂²×C₇	1	2	yes	complemented
372	#392	C₂²×C₇	1	2	yes	—
373	#391	C₂²×C₇	1	2	yes	complemented
374	#391	C₂²×C₇	1	2	yes	complemented
375	#391	C₂²×C₇	1	2	yes	complemented
376	#391	C₂²×C₇	1	1	yes	characteristic, complemented
377	#391	C₂²×C₇	1	2	yes	complemented
378	#390	C₂²×C₇	1	2	yes	—
379	#390	C₂²×C₇	1	2	yes	—
380	#390	C₂²×C₇	1	1	yes	characteristic, complemented
381	#388	C₂²×C₇	1	2	yes	—
382	#388	C₂²×C₇	1	2	yes	—
383	#388	C₂²×C₇	1	2	yes	—
384	#388	C₂²×C₇	1	2	yes	—
385	#388	C₂²×C₇	1	2	yes	—
386	#388	C₂²×C₇	1	2	yes	—
387	#388	C₂²×C₇	1	2	yes	—
388	#388	C₂²×C₇	1	2	yes	—
389	#388	C₂²×C₇	1	2	yes	—
390	#388	C₂²×C₇	1	2	yes	—
391	#388	C₂²×C₇	1	2	yes	—
392	#388	C₂²×C₇	1	2	yes	complemented
393	#388	C₂²×C₇	1	2	yes	complemented
394	#387	C₂²×C₇	1	2	yes	complemented
395	#387	C₂²×C₇	1	2	yes	complemented
396	#387	C₂²×C₇	1	2	yes	complemented
397	#387	C₂²×C₇	1	2	yes	complemented
398	#387	C₂²×C₇	1	2	yes	complemented
399	#387	C₂²×C₇	1	2	yes	complemented
400	#387	C₂²×C₇	1	2	yes	complemented
401	#386	C₂²×C₇	1	2	yes	—
402	#386	C₂²×C₇	1	2	yes	—
403	#386	C₂²×C₇	1	2	yes	—
404	#386	C₂²×C₇	1	2	yes	—
405	#386	C₂²×C₇	1	1	yes	characteristic
406	#386	C₂²×C₇	1	1	yes	characteristic
407	#386	C₂²×C₇	1	2	yes	—
408	#386	C₂²×C₇	1	2	yes	complemented
409	#385	C₂²×C₇	1	2	yes	complemented
410	#385	C₂²×C₇	1	2	yes	complemented
411	#385	C₂²×C₇	1	2	yes	complemented
412	#385	C₂²×C₇	1	2	yes	complemented
413	#383	C₂²×C₇	1	2	yes	complemented
414	#381	C₂²×C₇	1	2	yes	—
415	#381	C₂²×C₇	1	1	yes	characteristic
416	#380	C₂²×C₇	1	2	yes	—
417	#379	C₂²×C₇	1	2	yes	—
418	#379	C₂²×C₇	1	2	yes	—
419	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
420	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
421	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
422	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
423	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
424	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
425	C₂³×C₇	—	2	1	no	—
426	C₂³×C₇	—	2	1	no	—
427	C₂³×C₇	—	2	1	no	—
428	C₂³×C₇	—	2	1	no	—
429	C₂³×C₇	—	2	2	no	—
430	C₂³×C₇	—	2	2	no	—
431	C₂³×C₇	—	2	2	no	—
432	C₂³×C₇	—	2	2	no	—
433	C₂³×C₇	—	2	2	no	—
434	C₂³×C₇	—	2	1	no	—
435	C₂³×C₇	—	2	2	no	—
436	C₂³×C₇	—	2	2	no	—
437	C₂³×C₇	—	2	1	no	—
438	C₂³×C₇	—	2	1	no	—
439	C₂³×C₇	—	2	2	no	—
440	C₂³×C₇	—	2	2	no	—
441	C₂³×C₇	—	2	2	no	—
442	C₂³×C₇	—	2	2	no	—
443	C₂³×C₇	—	2	2	no	—
444	C₂³×C₇	—	2	2	no	—
445	C₂³×C₇	—	4	4	no	—
446	C₂³×C₇	—	8	2	no	—
447	C₂³×C₇	—	8	2	no	—
448	C₂³×C₇	—	8	4	no	—
449	C₂³×C₇	—	8	4	no	—
450	C₂³×C₇	C₂×#41	1	2	yes	—
451	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
452	C₂³×C₇	C₂⁵	1	1	yes	characteristic
453	C₇×Q₈	—	4	4	no	—
454	C₇×Q₈	—	8	2	no	—
455	C₇×Q₈	—	8	4	no	—
456	C₇×D₄	—	4	4	no	—
457	C₇×D₄	—	4	4	no	—
458	C₇×D₄	—	4	4	no	—
459	C₇×D₄	—	8	4	no	—
460	C₇×D₄	—	8	4	no	—
461	C₂×C₄×C₇	—	2	8	no	—
462	C₂×C₄×C₇	—	2	1	no	—
463	C₂×C₄×C₇	—	2	1	no	—
464	C₂×C₄×C₇	—	2	1	no	—
465	C₂×C₄×C₇	—	2	1	no	—
466	C₂×C₄×C₇	—	2	1	no	—
467	C₂×C₄×C₇	—	2	1	no	—
468	C₂×C₄×C₇	—	2	2	no	—
469	C₂×C₄×C₇	—	2	2	no	—
470	C₂×C₄×C₇	—	2	2	no	—
471	C₂×C₄×C₇	—	2	1	no	—
472	C₂×C₄×C₇	—	2	2	no	—
473	C₂×C₄×C₇	—	2	2	no	—
474	C₂×C₄×C₇	—	2	2	no	—
475	C₂×C₄×C₇	—	2	2	no	—
476	C₂×C₄×C₇	—	2	2	no	—
477	C₂×C₄×C₇	—	2	2	no	—
478	C₂×C₄×C₇	—	2	2	no	—
479	C₂×C₄×C₇	—	2	2	no	—
480	C₂×C₄×C₇	—	2	2	no	—
481	C₂×C₄×C₇	—	2	1	no	—
482	C₂×C₄×C₇	—	2	2	no	—
483	C₂×C₄×C₇	—	2	1	no	—
484	C₂×C₄×C₇	—	2	2	no	—
485	C₂×C₄×C₇	—	2	2	no	—
486	C₂×C₄×C₇	—	2	2	no	—
487	C₂×C₄×C₇	—	2	2	no	—
488	C₂×C₄×C₇	—	2	2	no	—
489	C₂×C₄×C₇	—	2	2	no	—
490	C₂×C₄×C₇	—	2	2	no	—
491	C₂×C₄×C₇	—	2	2	no	—
492	C₂×C₄×C₇	—	2	2	no	—
493	C₂×C₄×C₇	—	2	2	no	—
494	C₂×C₄×C₇	—	2	2	no	—
495	C₂×C₄×C₇	—	2	2	no	—
496	C₂×C₄×C₇	—	2	2	no	—
497	C₂×C₄×C₇	—	2	2	no	—
498	C₂×C₄×C₇	—	2	2	no	—
499	C₂×C₄×C₇	—	2	2	no	—
500	C₂×C₄×C₇	—	2	2	no	—
501	C₂×C₄×C₇	—	2	2	no	—
502	C₂×C₄×C₇	—	2	2	no	—
503	C₂×C₄×C₇	—	2	2	no	—
504	C₂×C₄×C₇	—	4	4	no	—
505	C₂×C₄×C₇	—	4	4	no	—
506	C₂×C₄×C₇	—	4	8	no	—
507	C₂×C₄×C₇	—	8	2	no	—
508	C₂×C₄×C₇	C₂×#41	1	2	yes	—
509	C₂×C₄×C₇	C₂×#41	1	2	yes	—
510	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
511	C₂⁵	C₂³×C₇	1	1	yes	characteristic
512	C₂×#41	—	2	4	no	—
513	C₂×#41	—	4	2	no	—
514	C₂×#41	—	4	2	no	—
515	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
516	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
517	C₂²×Q₈	C₂³×C₇	1	2	yes	—
518	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
519	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
520	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
521	C₂²×D₄	C₂³×C₇	1	2	yes	—
522	C₂²×D₄	C₂³×C₇	1	2	yes	—
523	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
525	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₇	1	2	yes	—
527	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
528	C₄⋊Q₈	—	4	2	no	—
529	#126	—	4	4	no	—
530	#124	—	4	4	no	—
531	#124	—	4	2	no	—
532	C₂²⋊Q₈	—	2	4	no	—
533	#120	—	4	2	no	—
534	#120	—	4	2	no	—
535	#117	—	4	2	no	—
536	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
548	C₂×C₂²⋊C₄	—	2	4	no	—
549	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
576	C₂×C₄²	—	4	2	no	—
577	C₂×C₄²	C₂³×C₇	1	2	yes	—
578	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
579	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
580	C₂×C₄²	C₂³×C₇	1	2	yes	—
581	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₇	1	2	yes	—
586	#95	C₂³×C₇	1	2	yes	—
587	#95	C₂³×C₇	1	2	yes	—
588	#95	C₂³×C₇	1	2	yes	—
589	#95	C₂³×C₇	1	2	yes	—
590	#95	C₂³×C₇	1	2	yes	—
591	#95	C₂³×C₇	1	2	yes	—
592	#95	C₂³×C₇	1	2	yes	—
593	#95	C₂³×C₇	1	2	yes	—
594	#95	C₂³×C₇	1	2	yes	—
595	#95	C₂³×C₇	1	2	yes	—
596	#95	C₂³×C₇	1	2	yes	—
597	#95	C₂³×C₇	1	2	yes	—
598	#95	C₂³×C₇	1	2	yes	—
599	#95	C₂³×C₇	1	2	yes	—
600	#95	C₂³×C₇	1	2	yes	—
601	#95	C₂³×C₇	1	2	yes	—
602	#95	C₂³×C₇	1	2	yes	—
603	#95	C₂³×C₇	1	2	yes	—
604	#95	C₂³×C₇	1	2	yes	—
605	#95	C₂³×C₇	1	2	yes	—
606	#95	C₂³×C₇	1	2	yes	—
607	#95	C₂³×C₇	1	2	yes	—
608	#95	C₂³×C₇	1	2	yes	—
609	#95	C₂³×C₇	1	2	yes	—
610	#95	C₂³×C₇	1	2	yes	—
611	C₂²×C₇	—	2	2	no	—
612	C₂²×C₇	—	2	2	no	—
613	C₂²×C₇	—	2	2	no	—
614	C₂²×C₇	—	2	2	no	—
615	C₂²×C₇	—	2	4	no	—
616	C₂²×C₇	—	4	1	no	—
617	C₂²×C₇	—	4	1	no	—
618	C₂²×C₇	—	4	2	no	—
619	C₂²×C₇	—	4	2	no	—
620	C₂²×C₇	—	4	2	no	—
621	C₂²×C₇	—	4	1	no	—
622	C₂²×C₇	—	4	2	no	—
623	C₂²×C₇	—	4	1	no	—
624	C₂²×C₇	—	4	2	no	—
625	C₂²×C₇	—	4	1	no	—
626	C₂²×C₇	—	4	2	no	—
627	C₂²×C₇	—	4	2	no	—
628	C₂²×C₇	—	4	2	no	—
629	C₂²×C₇	—	4	2	no	—
630	C₂²×C₇	—	4	2	no	—
631	C₂²×C₇	—	4	2	no	—
632	C₂²×C₇	—	4	2	no	—
633	C₂²×C₇	—	8	8	no	—
634	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
635	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
636	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
637	C₂²×C₇	#585	1	2	yes	—
638	C₂²×C₇	#585	1	2	yes	—
639	C₄×C₇	—	2	2	no	—
640	C₄×C₇	—	2	2	no	—
641	C₄×C₇	—	2	2	no	—
642	C₄×C₇	—	4	2	no	—
643	C₄×C₇	—	4	1	no	—
644	C₄×C₇	—	4	2	no	—
645	C₄×C₇	—	4	2	no	—
646	C₄×C₇	—	4	2	no	—
647	C₄×C₇	—	4	2	no	—
648	C₄×C₇	—	4	2	no	—
649	C₄×C₇	—	4	2	no	—
650	C₄×C₇	—	4	2	no	—
651	C₄×C₇	—	4	2	no	—
652	C₄×C₇	—	4	2	no	—
653	C₄×C₇	—	4	2	no	—
654	C₂⁴	—	2	2	no	—
655	C₂⁴	—	4	2	no	—
656	C₂⁴	—	4	1	no	—
657	C₂⁴	—	4	1	no	—
658	C₂⁴	—	4	2	no	—
659	C₂⁴	C₂⁴×C₇	1	2	yes	—
660	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
661	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
662	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
663	#41	—	4	16	no	—
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	4	1	no	—
668	C₂×Q₈	—	4	1	no	—
669	C₂×Q₈	—	4	2	no	—
670	C₂×Q₈	—	4	1	no	—
671	C₂×Q₈	—	4	2	no	—
672	C₂×Q₈	—	4	2	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	4	1	no	—
681	C₂×D₄	—	4	1	no	—
682	C₂×D₄	—	4	1	no	—
683	C₂×D₄	—	4	2	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	—	4	2	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂×D₄	—	4	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	—	4	1	no	—
697	C₂²×C₄	—	4	1	no	—
698	C₂²×C₄	—	4	1	no	—
699	C₂²×C₄	—	4	1	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	C₇×#41	1	4	yes	—
702	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	4	1	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	1	no	—
738	C₂²⋊C₄	—	4	2	no	—
739	C₂²⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	4	2	no	—
743	C₂²⋊C₄	—	4	2	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₄²	—	2	4	no	—
757	C₄²	—	4	1	no	—
758	C₄²	—	4	1	no	—
759	C₄²	—	4	1	no	—
760	C₄²	—	4	1	no	—
761	C₄²	—	4	2	no	—
762	C₄²	—	4	1	no	—
763	C₄²	—	4	2	no	—
764	C₄²	—	4	1	no	—
765	C₂×C₇	—	4	2	no	—
766	C₂×C₇	—	4	2	no	—
767	C₂×C₇	—	8	1	no	—
768	C₂×C₇	—	8	2	no	—
769	C₂×C₇	#3455	1	1	yes	characteristic
770	C₂×C₇	#3490	1	1	yes	characteristic
771	C₂×C₇	#3510	1	1	yes	characteristic
772	C₂×C₇	#3540	1	2	yes	—
773	C₂×C₇	#3560	1	2	yes	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	1	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	4	4	no	—
795	C₂³	—	8	2	no	—
796	C₂³	—	8	2	no	—
797	C₂³	—	8	4	no	—
798	C₂³	—	8	4	no	—
799	C₂³	C₂×C₇×#41	1	2	yes	—
800	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
801	C₂³	C₂⁵×C₇	1	1	yes	characteristic
802	Q₈	—	4	4	no	—
803	Q₈	—	8	2	no	—
804	Q₈	—	8	4	no	—
805	D₄	—	4	4	no	—
806	D₄	—	4	4	no	—
807	D₄	—	4	4	no	—
808	D₄	—	8	4	no	—
809	D₄	—	8	4	no	—
810	C₂×C₄	—	2	8	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	8	2	no	—
857	C₂×C₄	C₂×C₇×#41	1	2	yes	—
858	C₂×C₄	C₂×C₇×#41	1	2	yes	—
859	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
860	C₇	#36816	1	1	yes	characteristic, direct product factor, Sylow
861	C₂²	—	2	4	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	8	8	no	—
884	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
885	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
886	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
887	C₂²	C₇×#585	1	2	yes	—
888	C₂²	C₇×#585	1	2	yes	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₂	—	4	2	no	—
905	C₂	—	4	2	no	—
906	C₂	—	8	2	no	—
907	C₂	—	8	1	no	—
908	C₂	C₇×#3455	1	1	yes	characteristic
909	C₂	C₇×#3490	1	1	yes	characteristic
910	C₂	C₇×#3510	1	1	yes	characteristic
911	C₂	C₇×#3540	1	2	yes	—
912	C₂	C₇×#3560	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₇×#2404	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2852	C₂	semidirect
2. C₇×#2797	C₂	semidirect
3. C₇×#2759	C₂	semidirect
4. C₇×#2746	C₂	semidirect
5. C₇×#2737	C₂	semidirect
6. C₇×#2716	C₂	semidirect
7. C₇×#2712	C₂	semidirect
8. C₇×#2685	C₂	semidirect
9. C₇×#2684	C₂	semidirect
10. C₇×#2653	C₂	semidirect
11. C₇×#2607	C₂	semidirect
12. C₇×#2597	C₂	semidirect
13. C₇×#2561	C₂	semidirect
14. C₇×#2474	C₂	semidirect
15. C₇×#2432	C₂	semidirect
17. C₇×#2332	C₂	semidirect
18. C₇×#2312	C₂	semidirect
19. C₇×#2297	C₂	semidirect
21. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₇×#124	C₂²	semidirect
28. C₂×C₇×#117	C₂²	semidirect
30. C₂²×C₄²×C₇	C₂²	semidirect
31. C₇×#401	C₂²	semidirect
32. C₇×#400	C₂²	semidirect
34. C₇×#398	C₂²	semidirect
38. C₇×#397	C₂²	semidirect
39. C₇×#397	C₂²	semidirect
40. C₇×#397	C₂²	semidirect
42. C₇×#395	C₂²	semidirect
53. C₇×#393	C₂²	semidirect
55. C₇×#391	C₂²	semidirect
56. C₇×#391	C₂²	semidirect
57. C₇×#391	C₂²	semidirect
58. C₇×#391	C₂²	semidirect
59. C₇×#391	C₂²	semidirect
62. C₇×#390	C₂²	semidirect
74. C₇×#388	C₂²	semidirect
75. C₇×#388	C₂²	semidirect
76. C₇×#387	C₂²	semidirect
77. C₇×#387	C₂²	semidirect
78. C₇×#387	C₂²	semidirect
79. C₇×#387	C₂²	semidirect
80. C₇×#387	C₂²	semidirect
81. C₇×#387	C₂²	semidirect
82. C₇×#387	C₂²	semidirect
90. C₇×#386	C₂²	semidirect
91. C₇×#385	C₂²	semidirect
92. C₇×#385	C₂²	semidirect
93. C₇×#385	C₂²	semidirect
94. C₇×#385	C₂²	semidirect
95. C₇×#383	C₂²	semidirect
101. C₄×C₇×C₄⋊C₄	C₂²	semidirect
105. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
106. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
107. #36816	C₇	direct (N × H)
208. #2852	C₂×C₇	semidirect
209. #2797	C₂×C₇	semidirect
210. #2759	C₂×C₇	semidirect
211. #2746	C₂×C₇	semidirect
212. #2737	C₂×C₇	semidirect
213. #2716	C₂×C₇	semidirect
214. #2712	C₂×C₇	semidirect
215. #2685	C₂×C₇	semidirect
216. #2684	C₂×C₇	semidirect
217. #2653	C₂×C₇	semidirect
218. #2607	C₂×C₇	semidirect
219. #2597	C₂×C₇	semidirect
220. #2561	C₂×C₇	semidirect
221. #2474	C₂×C₇	semidirect
222. #2432	C₂×C₇	semidirect
224. #2332	C₂×C₇	semidirect
225. #2312	C₂×C₇	semidirect
226. #2297	C₂×C₇	semidirect
339. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
342. C₂×#124	C₂²×C₇	semidirect
346. C₂×#117	C₂²×C₇	semidirect
348. C₂²×C₄²	C₂²×C₇	semidirect
349. #401	C₂²×C₇	semidirect
350. #400	C₂²×C₇	semidirect
352. #398	C₂²×C₇	semidirect
356. #397	C₂²×C₇	semidirect
357. #397	C₂²×C₇	semidirect
358. #397	C₂²×C₇	semidirect
360. #395	C₂²×C₇	semidirect
371. #393	C₂²×C₇	semidirect
373. #391	C₂²×C₇	semidirect
374. #391	C₂²×C₇	semidirect
375. #391	C₂²×C₇	semidirect
376. #391	C₂²×C₇	semidirect
377. #391	C₂²×C₇	semidirect
380. #390	C₂²×C₇	semidirect
392. #388	C₂²×C₇	semidirect
393. #388	C₂²×C₇	semidirect
394. #387	C₂²×C₇	semidirect
395. #387	C₂²×C₇	semidirect
396. #387	C₂²×C₇	semidirect
397. #387	C₂²×C₇	semidirect
398. #387	C₂²×C₇	semidirect
399. #387	C₂²×C₇	semidirect
400. #387	C₂²×C₇	semidirect
408. #386	C₂²×C₇	semidirect
409. #385	C₂²×C₇	semidirect
410. #385	C₂²×C₇	semidirect
411. #385	C₂²×C₇	semidirect
412. #385	C₂²×C₇	semidirect
413. #383	C₂²×C₇	semidirect
419. C₄×C₄⋊C₄	C₂²×C₇	semidirect
423. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
424. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
860. C₇	#36816	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×#2852	2
C₇×#2797	2
C₇×#2759	2
C₇×#2746	2
C₇×#2737	2
C₇×#2716	2
C₇×#2712	2
C₇×#2685	2
C₇×#2684	2
C₇×#2653	2
C₇×#2607	2
C₇×#2597	2
C₇×#2561	2
C₇×#2474	2
C₇×#2432	2
C₇×#2404	2
C₇×#2332	2
C₇×#2312	2
C₇×#2297	2
#36816	7

Subgroups — C7×#36816 #13214032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#36816 #13214032