Subgroups — C₇×#35022 #13212238

Order 1792.

2070 conjugacy classes of subgroups.

The subgroup lattice has 948 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×#2849	C₂	1	2	yes	maximal, complemented
3	C₇×#2646	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2639	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2626	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2617	C₂	1	1	yes	maximal, characteristic
7	C₇×#2573	C₂	1	2	yes	maximal, complemented
8	C₇×#2572	C₂	1	2	yes	maximal, complemented
9	C₇×#2554	C₂	1	2	yes	maximal, complemented
10	C₇×#2553	C₂	1	2	yes	maximal, complemented
11	C₇×#2516	C₂	1	2	yes	maximal, complemented
12	C₇×#2515	C₂	1	2	yes	maximal, complemented
13	C₇×#2458	C₂	1	2	yes	maximal, complemented
14	C₇×#2457	C₂	1	2	yes	maximal, complemented
15	C₇×#2321	C₂	1	2	yes	maximal, complemented
16	C₇×#2318	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₄×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
21	C₂×C₇×#126	C₂²	1	2	yes	complemented
22	C₂×C₇×#123	C₂²	1	2	yes	—
23	C₂×C₇×#123	C₂²	1	2	yes	—
24	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#121	C₂²	1	1	yes	characteristic
26	C₂×C₇×#120	C₂²	1	2	yes	—
27	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
29	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
34	C₇×#400	C₂²	1	2	yes	complemented
35	C₇×#400	C₂²	1	2	yes	complemented
36	C₇×#400	C₂²	1	2	yes	complemented
37	C₇×#399	C₂²	1	2	yes	—
38	C₇×#398	C₂²	1	2	yes	complemented
39	C₇×#398	C₂²	1	2	yes	complemented
40	C₇×#397	C₂²	1	2	yes	—
41	C₇×#397	C₂²	1	2	yes	complemented
42	C₇×#396	C₂²	1	2	yes	—
43	C₇×#396	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	complemented
47	C₇×#393	C₂²	1	2	yes	—
48	C₇×#393	C₂²	1	2	yes	complemented
49	C₇×#392	C₂²	1	2	yes	—
50	C₇×#391	C₂²	1	1	yes	characteristic, complemented
51	C₇×#390	C₂²	1	2	yes	—
52	C₇×#390	C₂²	1	2	yes	—
53	C₇×#390	C₂²	1	1	yes	characteristic, complemented
54	C₇×#389	C₂²	1	1	yes	characteristic, complemented
55	C₇×#389	C₂²	1	1	yes	characteristic, complemented
56	C₇×#388	C₂²	1	2	yes	—
57	C₇×#388	C₂²	1	2	yes	—
58	C₇×#388	C₂²	1	2	yes	—
59	C₇×#388	C₂²	1	2	yes	—
60	C₇×#388	C₂²	1	2	yes	complemented
61	C₇×#388	C₂²	1	2	yes	complemented
62	C₇×#388	C₂²	1	2	yes	complemented
63	C₇×#388	C₂²	1	2	yes	complemented
64	C₇×#388	C₂²	1	2	yes	complemented
65	C₇×#388	C₂²	1	2	yes	complemented
66	C₇×#387	C₂²	1	2	yes	complemented
67	C₇×#387	C₂²	1	2	yes	complemented
68	C₇×#387	C₂²	1	2	yes	complemented
69	C₇×#387	C₂²	1	2	yes	complemented
70	C₇×#387	C₂²	1	2	yes	complemented
71	C₇×#387	C₂²	1	2	yes	complemented
72	C₇×#386	C₂²	1	2	yes	—
73	C₇×#386	C₂²	1	2	yes	—
74	C₇×#386	C₂²	1	2	yes	—
75	C₇×#386	C₂²	1	2	yes	—
76	C₇×#386	C₂²	1	2	yes	—
77	C₇×#386	C₂²	1	2	yes	—
78	C₇×#386	C₂²	1	2	yes	—
79	C₇×#386	C₂²	1	2	yes	—
80	C₇×#385	C₂²	1	2	yes	—
81	C₇×#385	C₂²	1	2	yes	—
82	C₇×#385	C₂²	1	2	yes	—
83	C₇×#385	C₂²	1	2	yes	—
84	C₇×#385	C₂²	1	2	yes	—
85	C₇×#385	C₂²	1	2	yes	—
86	C₇×#383	C₂²	1	2	yes	complemented
87	C₇×#383	C₂²	1	2	yes	complemented
88	C₇×#382	C₂²	1	2	yes	complemented
89	C₇×#381	C₂²	1	2	yes	—
90	C₇×#381	C₂²	1	2	yes	—
91	C₇×#381	C₂²	1	2	yes	complemented
92	C₇×#380	C₂²	1	1	yes	characteristic
93	C₇×#380	C₂²	1	1	yes	characteristic
94	C₇×#380	C₂²	1	2	yes	complemented
95	C₇×#379	C₂²	1	2	yes	—
96	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
97	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
99	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
105	C₂×C₇×#95	C₂²	1	1	yes	characteristic
106	C₂×C₇×#95	C₂²	1	1	yes	characteristic
107	#35022	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁵×C₇	C₂³	1	1	yes	characteristic
109	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
110	C₂²×C₇×D₄	C₂³	1	2	yes	—
111	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
112	C₂²×C₇×D₄	C₂³	1	2	yes	—
113	C₂²×C₇×D₄	C₂³	1	2	yes	—
114	C₂³×C₄×C₇	—	2	4	no	—
115	C₂³×C₄×C₇	—	4	2	no	—
116	C₂³×C₄×C₇	—	4	2	no	—
117	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₇	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	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
126	C₇×#126	—	4	4	no	—
127	C₇×#123	—	4	4	no	—
128	C₇×#123	—	4	4	no	—
129	C₇×C₂²⋊Q₈	—	2	4	no	—
130	C₇×#121	—	2	4	no	—
131	C₇×#120	—	2	8	no	—
132	C₄×C₇×Q₈	—	4	2	no	—
133	C₄×C₇×D₄	—	2	8	no	—
134	C₄×C₇×D₄	—	4	2	no	—
135	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
142	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
152	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
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	2	yes	—
166	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₄²×C₇	—	4	2	no	—
177	C₂×C₄²×C₇	—	4	2	no	—
178	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₇	C₂³	1	2	yes	—
181	C₂×C₄²×C₇	C₂³	1	2	yes	—
182	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₇	C₂³	1	2	yes	—
185	C₂×C₄²×C₇	C₂³	1	2	yes	—
186	C₂×C₄²×C₇	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	C₇×#95	C₂³	1	2	yes	—
209	C₇×#95	C₂³	1	2	yes	—
210	C₇×#95	C₂³	1	2	yes	—
211	#2852	C₂×C₇	1	2	yes	complemented
212	#2849	C₂×C₇	1	2	yes	complemented
213	#2646	C₂×C₇	1	1	yes	characteristic, complemented
214	#2639	C₂×C₇	1	1	yes	characteristic, complemented
215	#2626	C₂×C₇	1	1	yes	characteristic, complemented
216	#2617	C₂×C₇	1	1	yes	characteristic
217	#2573	C₂×C₇	1	2	yes	complemented
218	#2572	C₂×C₇	1	2	yes	complemented
219	#2554	C₂×C₇	1	2	yes	complemented
220	#2553	C₂×C₇	1	2	yes	complemented
221	#2516	C₂×C₇	1	2	yes	complemented
222	#2515	C₂×C₇	1	2	yes	complemented
223	#2458	C₂×C₇	1	2	yes	complemented
224	#2457	C₂×C₇	1	2	yes	complemented
225	#2321	C₂×C₇	1	2	yes	complemented
226	#2318	C₂×C₇	1	2	yes	complemented
227	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
228	C₄×#121	C₂×C₇	1	1	yes	characteristic, complemented
229	C₂×C₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
230	C₂⁴×C₇	—	2	2	no	—
231	C₂⁴×C₇	—	2	2	no	—
232	C₂⁴×C₇	—	4	1	no	—
233	C₂⁴×C₇	—	4	1	no	—
234	C₂⁴×C₇	—	4	1	no	—
235	C₂⁴×C₇	—	4	1	no	—
236	C₂⁴×C₇	#41	1	4	yes	—
237	C₂⁴×C₇	C₂⁴	1	2	yes	—
238	C₂⁴×C₇	C₂⁴	1	2	yes	—
239	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
240	C₂×C₇×Q₈	—	2	2	no	—
241	C₂×C₇×Q₈	—	4	1	no	—
242	C₂×C₇×Q₈	—	4	1	no	—
243	C₂×C₇×D₄	—	2	4	no	—
244	C₂×C₇×D₄	—	2	4	no	—
245	C₂×C₇×D₄	—	2	4	no	—
246	C₂×C₇×D₄	—	2	4	no	—
247	C₂×C₇×D₄	—	2	4	no	—
248	C₂×C₇×D₄	—	2	2	no	—
249	C₂×C₇×D₄	—	4	1	no	—
250	C₂×C₇×D₄	—	4	1	no	—
251	C₂×C₇×D₄	—	4	2	no	—
252	C₂×C₇×D₄	—	4	2	no	—
253	C₂×C₇×D₄	—	4	2	no	—
254	C₂×C₇×D₄	—	4	2	no	—
255	C₂²×C₄×C₇	—	2	2	no	—
256	C₂²×C₄×C₇	—	2	2	no	—
257	C₂²×C₄×C₇	—	2	2	no	—
258	C₂²×C₄×C₇	—	2	2	no	—
259	C₂²×C₄×C₇	—	2	2	no	—
260	C₂²×C₄×C₇	—	2	4	no	—
261	C₂²×C₄×C₇	—	2	4	no	—
262	C₂²×C₄×C₇	—	2	2	no	—
263	C₂²×C₄×C₇	—	2	4	no	—
264	C₂²×C₄×C₇	—	2	4	no	—
265	C₂²×C₄×C₇	—	2	4	no	—
266	C₂²×C₄×C₇	—	4	1	no	—
267	C₂²×C₄×C₇	—	4	1	no	—
268	C₂²×C₄×C₇	—	4	1	no	—
269	C₂²×C₄×C₇	—	4	1	no	—
270	C₂²×C₄×C₇	—	4	2	no	—
271	C₂²×C₄×C₇	—	4	2	no	—
272	C₂²×C₄×C₇	—	4	1	no	—
273	C₂²×C₄×C₇	—	4	1	no	—
274	C₂²×C₄×C₇	—	4	1	no	—
275	C₂²×C₄×C₇	—	4	1	no	—
276	C₂²×C₄×C₇	—	4	1	no	—
277	C₂²×C₄×C₇	—	4	1	no	—
278	C₂²×C₄×C₇	—	4	2	no	—
279	C₂²×C₄×C₇	—	4	2	no	—
280	C₂²×C₄×C₇	—	4	16	no	—
281	C₂²×C₄×C₇	#41	1	4	yes	—
282	C₂²×C₄×C₇	#41	1	4	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	2	yes	—
288	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
299	C₇×C₄⋊C₄	—	2	4	no	—
300	C₇×C₄⋊C₄	—	2	2	no	—
301	C₇×C₄⋊C₄	—	2	2	no	—
302	C₇×C₄⋊C₄	—	2	4	no	—
303	C₇×C₄⋊C₄	—	2	4	no	—
304	C₇×C₄⋊C₄	—	2	4	no	—
305	C₇×C₄⋊C₄	—	4	1	no	—
306	C₇×C₄⋊C₄	—	4	1	no	—
307	C₇×C₄⋊C₄	—	4	2	no	—
308	C₇×C₄⋊C₄	—	4	2	no	—
309	C₇×C₄⋊C₄	—	4	1	no	—
310	C₇×C₄⋊C₄	—	4	1	no	—
311	C₇×C₄⋊C₄	—	4	2	no	—
312	C₇×C₄⋊C₄	—	4	2	no	—
313	C₇×C₄⋊C₄	—	4	2	no	—
314	C₇×C₄⋊C₄	—	4	2	no	—
315	C₇×C₂²⋊C₄	—	2	4	no	—
316	C₇×C₂²⋊C₄	—	2	4	no	—
317	C₇×C₂²⋊C₄	—	2	4	no	—
318	C₇×C₂²⋊C₄	—	2	4	no	—
319	C₇×C₂²⋊C₄	—	2	4	no	—
320	C₇×C₂²⋊C₄	—	2	4	no	—
321	C₇×C₂²⋊C₄	—	2	4	no	—
322	C₇×C₂²⋊C₄	—	2	4	no	—
323	C₇×C₂²⋊C₄	—	2	4	no	—
324	C₇×C₂²⋊C₄	—	2	4	no	—
325	C₇×C₂²⋊C₄	—	2	4	no	—
326	C₇×C₂²⋊C₄	—	2	4	no	—
327	C₇×C₂²⋊C₄	—	2	4	no	—
328	C₇×C₂²⋊C₄	—	4	2	no	—
329	C₇×C₂²⋊C₄	—	4	2	no	—
330	C₇×C₂²⋊C₄	—	4	2	no	—
331	C₇×C₂²⋊C₄	—	4	2	no	—
332	C₇×C₂²⋊C₄	—	4	2	no	—
333	C₇×C₂²⋊C₄	—	4	2	no	—
334	C₇×C₂²⋊C₄	—	4	2	no	—
335	C₇×C₂²⋊C₄	—	4	2	no	—
336	C₇×C₂²⋊C₄	—	4	2	no	—
337	C₇×C₂²⋊C₄	—	4	2	no	—
338	C₄²×C₇	—	2	4	no	—
339	C₄²×C₇	—	2	2	no	—
340	C₄²×C₇	—	2	2	no	—
341	C₄²×C₇	—	2	4	no	—
342	C₄²×C₇	—	4	1	no	—
343	C₄²×C₇	—	4	1	no	—
344	C₄²×C₇	—	4	2	no	—
345	C₄²×C₇	—	4	2	no	—
346	C₄²×C₇	—	4	2	no	—
347	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
348	C₂×#126	C₂²×C₇	1	2	yes	complemented
349	C₂×#123	C₂²×C₇	1	2	yes	—
350	C₂×#123	C₂²×C₇	1	2	yes	—
351	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
352	C₂×#121	C₂²×C₇	1	1	yes	characteristic
353	C₂×#120	C₂²×C₇	1	2	yes	—
354	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
355	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
356	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
357	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
358	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
359	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
360	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
361	#400	C₂²×C₇	1	2	yes	complemented
362	#400	C₂²×C₇	1	2	yes	complemented
363	#400	C₂²×C₇	1	2	yes	complemented
364	#399	C₂²×C₇	1	2	yes	—
365	#398	C₂²×C₇	1	2	yes	complemented
366	#398	C₂²×C₇	1	2	yes	complemented
367	#397	C₂²×C₇	1	2	yes	—
368	#397	C₂²×C₇	1	2	yes	complemented
369	#396	C₂²×C₇	1	2	yes	—
370	#396	C₂²×C₇	1	2	yes	—
371	#394	C₂²×C₇	1	2	yes	—
372	#394	C₂²×C₇	1	2	yes	—
373	#394	C₂²×C₇	1	2	yes	complemented
374	#393	C₂²×C₇	1	2	yes	—
375	#393	C₂²×C₇	1	2	yes	complemented
376	#392	C₂²×C₇	1	2	yes	—
377	#391	C₂²×C₇	1	1	yes	characteristic, 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	#389	C₂²×C₇	1	1	yes	characteristic, complemented
382	#389	C₂²×C₇	1	1	yes	characteristic, complemented
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	complemented
388	#388	C₂²×C₇	1	2	yes	complemented
389	#388	C₂²×C₇	1	2	yes	complemented
390	#388	C₂²×C₇	1	2	yes	complemented
391	#388	C₂²×C₇	1	2	yes	complemented
392	#388	C₂²×C₇	1	2	yes	complemented
393	#387	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	#386	C₂²×C₇	1	2	yes	—
400	#386	C₂²×C₇	1	2	yes	—
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	2	yes	—
406	#386	C₂²×C₇	1	2	yes	—
407	#385	C₂²×C₇	1	2	yes	—
408	#385	C₂²×C₇	1	2	yes	—
409	#385	C₂²×C₇	1	2	yes	—
410	#385	C₂²×C₇	1	2	yes	—
411	#385	C₂²×C₇	1	2	yes	—
412	#385	C₂²×C₇	1	2	yes	—
413	#383	C₂²×C₇	1	2	yes	complemented
414	#383	C₂²×C₇	1	2	yes	complemented
415	#382	C₂²×C₇	1	2	yes	complemented
416	#381	C₂²×C₇	1	2	yes	—
417	#381	C₂²×C₇	1	2	yes	—
418	#381	C₂²×C₇	1	2	yes	complemented
419	#380	C₂²×C₇	1	1	yes	characteristic
420	#380	C₂²×C₇	1	1	yes	characteristic
421	#380	C₂²×C₇	1	2	yes	complemented
422	#379	C₂²×C₇	1	2	yes	—
423	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
424	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
425	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
426	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
427	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
428	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
429	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
430	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
431	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
432	C₂×#95	C₂²×C₇	1	1	yes	characteristic
433	C₂×#95	C₂²×C₇	1	1	yes	characteristic
434	C₂³×C₇	—	2	1	no	—
435	C₂³×C₇	—	2	1	no	—
436	C₂³×C₇	—	2	1	no	—
437	C₂³×C₇	—	2	1	no	—
438	C₂³×C₇	—	2	8	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	—	2	2	no	—
446	C₂³×C₇	—	2	2	no	—
447	C₂³×C₇	—	2	2	no	—
448	C₂³×C₇	—	2	2	no	—
449	C₂³×C₇	—	2	2	no	—
450	C₂³×C₇	—	2	2	no	—
451	C₂³×C₇	—	2	2	no	—
452	C₂³×C₇	—	4	4	no	—
453	C₂³×C₇	—	4	4	no	—
454	C₂³×C₇	—	4	4	no	—
455	C₂³×C₇	—	4	4	no	—
456	C₂³×C₇	—	4	4	no	—
457	C₂³×C₇	—	4	4	no	—
458	C₂³×C₇	C₂×#41	1	4	yes	—
459	C₂³×C₇	C₂×#41	1	2	yes	—
460	C₂³×C₇	C₂×#41	1	2	yes	—
461	C₂³×C₇	C₂×#41	1	2	yes	—
462	C₂³×C₇	C₂⁵	1	1	yes	characteristic
463	C₇×Q₈	—	4	4	no	—
464	C₇×D₄	—	4	4	no	—
465	C₇×D₄	—	4	8	no	—
466	C₇×D₄	—	8	4	no	—
467	C₇×D₄	—	8	4	no	—
468	C₂×C₄×C₇	—	2	8	no	—
469	C₂×C₄×C₇	—	2	1	no	—
470	C₂×C₄×C₇	—	2	1	no	—
471	C₂×C₄×C₇	—	2	1	no	—
472	C₂×C₄×C₇	—	2	1	no	—
473	C₂×C₄×C₇	—	2	1	no	—
474	C₂×C₄×C₇	—	2	1	no	—
475	C₂×C₄×C₇	—	2	1	no	—
476	C₂×C₄×C₇	—	2	1	no	—
477	C₂×C₄×C₇	—	2	1	no	—
478	C₂×C₄×C₇	—	2	1	no	—
479	C₂×C₄×C₇	—	2	1	no	—
480	C₂×C₄×C₇	—	2	1	no	—
481	C₂×C₄×C₇	—	2	2	no	—
482	C₂×C₄×C₇	—	2	2	no	—
483	C₂×C₄×C₇	—	2	2	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	—	2	2	no	—
505	C₂×C₄×C₇	—	2	2	no	—
506	C₂×C₄×C₇	—	2	2	no	—
507	C₂×C₄×C₇	—	2	2	no	—
508	C₂×C₄×C₇	—	2	2	no	—
509	C₂×C₄×C₇	—	2	2	no	—
510	C₂×C₄×C₇	—	2	2	no	—
511	C₂×C₄×C₇	—	4	4	no	—
512	C₂×C₄×C₇	—	4	4	no	—
513	C₂×C₄×C₇	—	4	8	no	—
514	C₂×C₄×C₇	—	4	8	no	—
515	C₂×C₄×C₇	—	4	4	no	—
516	C₂×C₄×C₇	—	4	4	no	—
517	C₂×C₄×C₇	—	4	4	no	—
518	C₂×C₄×C₇	—	8	4	no	—
519	C₂×C₄×C₇	C₂×#41	1	2	yes	—
520	C₂×C₄×C₇	C₂×#41	1	2	yes	—
521	C₂×C₄×C₇	C₂×#41	1	2	yes	—
522	C₂×C₄×C₇	C₂×#41	1	2	yes	—
523	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
524	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
525	C₂⁵	C₂³×C₇	1	1	yes	characteristic
526	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₇	1	2	yes	—
528	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
529	C₂²×D₄	C₂³×C₇	1	2	yes	—
530	C₂²×D₄	C₂³×C₇	1	2	yes	—
531	C₂³×C₄	—	2	4	no	—
532	C₂³×C₄	—	4	2	no	—
533	C₂³×C₄	—	4	2	no	—
534	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₇	1	2	yes	—
536	C₂³×C₄	C₂³×C₇	1	2	yes	—
537	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₇	1	2	yes	—
540	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
543	#126	—	4	4	no	—
544	#123	—	4	4	no	—
545	#123	—	4	4	no	—
546	C₂²⋊Q₈	—	2	4	no	—
547	#121	—	2	4	no	—
548	#120	—	2	8	no	—
549	C₄×Q₈	—	4	2	no	—
550	C₄×D₄	—	2	8	no	—
551	C₄×D₄	—	4	2	no	—
552	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
568	C₂×C₂²⋊C₄	—	2	4	no	—
569	C₂×C₂²⋊C₄	—	2	4	no	—
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×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
593	C₂×C₄²	—	4	2	no	—
594	C₂×C₄²	—	4	2	no	—
595	C₂×C₄²	C₂³×C₇	1	2	yes	—
596	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₇	1	2	yes	—
599	C₂×C₄²	C₂³×C₇	1	2	yes	—
600	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₇	1	2	yes	—
603	C₂×C₄²	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	#95	C₂³×C₇	1	2	yes	—
612	#95	C₂³×C₇	1	2	yes	—
613	#95	C₂³×C₇	1	2	yes	—
614	#95	C₂³×C₇	1	2	yes	—
615	#95	C₂³×C₇	1	2	yes	—
616	#95	C₂³×C₇	1	2	yes	—
617	#95	C₂³×C₇	1	2	yes	—
618	#95	C₂³×C₇	1	2	yes	—
619	#95	C₂³×C₇	1	2	yes	—
620	#95	C₂³×C₇	1	2	yes	—
621	#95	C₂³×C₇	1	2	yes	—
622	#95	C₂³×C₇	1	2	yes	—
623	#95	C₂³×C₇	1	2	yes	—
624	#95	C₂³×C₇	1	2	yes	—
625	#95	C₂³×C₇	1	2	yes	—
626	#95	C₂³×C₇	1	2	yes	—
627	#95	C₂³×C₇	1	2	yes	—
628	C₂²×C₇	—	2	2	no	—
629	C₂²×C₇	—	2	2	no	—
630	C₂²×C₇	—	2	2	no	—
631	C₂²×C₇	—	2	2	no	—
632	C₂²×C₇	—	2	2	no	—
633	C₂²×C₇	—	2	2	no	—
634	C₂²×C₇	—	2	4	no	—
635	C₂²×C₇	—	2	4	no	—
636	C₂²×C₇	—	2	4	no	—
637	C₂²×C₇	—	4	16	no	—
638	C₂²×C₇	—	4	2	no	—
639	C₂²×C₇	—	4	2	no	—
640	C₂²×C₇	—	4	2	no	—
641	C₂²×C₇	—	4	2	no	—
642	C₂²×C₇	—	4	2	no	—
643	C₂²×C₇	—	4	2	no	—
644	C₂²×C₇	—	4	2	no	—
645	C₂²×C₇	—	4	2	no	—
646	C₂²×C₇	—	4	2	no	—
647	C₂²×C₇	—	4	2	no	—
648	C₂²×C₇	—	4	2	no	—
649	C₂²×C₇	#529	1	4	yes	—
650	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
651	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
652	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
653	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
654	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
655	C₂²×C₇	#585	1	1	yes	characteristic
656	C₂²×C₇	#585	1	1	yes	characteristic
657	C₄×C₇	—	2	2	no	—
658	C₄×C₇	—	2	2	no	—
659	C₄×C₇	—	2	2	no	—
660	C₄×C₇	—	2	2	no	—
661	C₄×C₇	—	2	2	no	—
662	C₄×C₇	—	2	2	no	—
663	C₄×C₇	—	4	2	no	—
664	C₄×C₇	—	4	2	no	—
665	C₄×C₇	—	4	2	no	—
666	C₄×C₇	—	4	2	no	—
667	C₄×C₇	—	4	2	no	—
668	C₄×C₇	—	4	2	no	—
669	C₄×C₇	—	4	2	no	—
670	C₄×C₇	—	4	2	no	—
671	C₄×C₇	—	4	2	no	—
672	C₄×C₇	—	4	2	no	—
673	C₂⁴	—	2	2	no	—
674	C₂⁴	—	2	2	no	—
675	C₂⁴	—	4	1	no	—
676	C₂⁴	—	4	1	no	—
677	C₂⁴	—	4	1	no	—
678	C₂⁴	—	4	1	no	—
679	C₂⁴	C₇×#41	1	4	yes	—
680	C₂⁴	C₂⁴×C₇	1	2	yes	—
681	C₂⁴	C₂⁴×C₇	1	2	yes	—
682	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	4	1	no	—
685	C₂×Q₈	—	4	1	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	4	1	no	—
693	C₂×D₄	—	4	1	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	4	1	no	—
710	C₂²×C₄	—	4	1	no	—
711	C₂²×C₄	—	4	1	no	—
712	C₂²×C₄	—	4	1	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	1	no	—
716	C₂²×C₄	—	4	1	no	—
717	C₂²×C₄	—	4	1	no	—
718	C₂²×C₄	—	4	1	no	—
719	C₂²×C₄	—	4	1	no	—
720	C₂²×C₄	—	4	1	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	16	no	—
724	C₂²×C₄	C₇×#41	1	4	yes	—
725	C₂²×C₄	C₇×#41	1	4	yes	—
726	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	4	1	no	—
749	C₄⋊C₄	—	4	1	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₄⋊C₄	—	4	1	no	—
753	C₄⋊C₄	—	4	1	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₂²⋊C₄	—	4	2	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₄²	—	2	4	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	4	no	—
785	C₄²	—	4	1	no	—
786	C₄²	—	4	1	no	—
787	C₄²	—	4	2	no	—
788	C₄²	—	4	2	no	—
789	C₄²	—	4	2	no	—
790	C₂×C₇	—	2	4	no	—
791	C₂×C₇	—	4	4	no	—
792	C₂×C₇	—	8	2	no	—
793	C₂×C₇	C₂×#529	1	1	yes	characteristic
794	C₂×C₇	#3459	1	1	yes	characteristic
795	C₂×C₇	#3460	1	1	yes	characteristic
796	C₂×C₇	#3490	1	1	yes	characteristic
797	C₂×C₇	#3491	1	1	yes	characteristic
798	C₂×C₇	#3505	1	1	yes	characteristic
799	C₂×C₇	#3506	1	1	yes	characteristic
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	8	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	4	4	no	—
819	C₂³	—	4	4	no	—
820	C₂³	—	4	4	no	—
821	C₂³	—	4	4	no	—
822	C₂³	—	4	4	no	—
823	C₂³	—	4	4	no	—
824	C₂³	C₂×C₇×#41	1	4	yes	—
825	C₂³	C₂×C₇×#41	1	2	yes	—
826	C₂³	C₂×C₇×#41	1	2	yes	—
827	C₂³	C₂×C₇×#41	1	2	yes	—
828	C₂³	C₂⁵×C₇	1	1	yes	characteristic
829	Q₈	—	4	4	no	—
830	D₄	—	4	4	no	—
831	D₄	—	4	8	no	—
832	D₄	—	8	4	no	—
833	D₄	—	8	4	no	—
834	C₂×C₄	—	2	8	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	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	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	4	4	no	—
878	C₂×C₄	—	4	4	no	—
879	C₂×C₄	—	4	8	no	—
880	C₂×C₄	—	4	8	no	—
881	C₂×C₄	—	4	4	no	—
882	C₂×C₄	—	4	4	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	8	4	no	—
885	C₂×C₄	C₂×C₇×#41	1	2	yes	—
886	C₂×C₄	C₂×C₇×#41	1	2	yes	—
887	C₂×C₄	C₂×C₇×#41	1	2	yes	—
888	C₂×C₄	C₂×C₇×#41	1	2	yes	—
889	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
890	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
891	C₇	#35022	1	1	yes	characteristic, direct product factor, Sylow
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	2	4	no	—
900	C₂²	—	2	4	no	—
901	C₂²	—	4	16	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	C₇×#529	1	4	yes	—
914	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
915	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
916	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
917	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
918	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
919	C₂²	C₇×#585	1	1	yes	characteristic
920	C₂²	C₇×#585	1	1	yes	characteristic
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	2	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	—	4	2	no	—
934	C₄	—	4	2	no	—
935	C₄	—	4	2	no	—
936	C₄	—	4	2	no	—
937	C₂	—	2	4	no	—
938	C₂	—	4	4	no	—
939	C₂	—	8	2	no	—
940	C₂	C₂×C₇×#529	1	1	yes	characteristic
941	C₂	C₇×#3459	1	1	yes	characteristic
942	C₂	C₇×#3460	1	1	yes	characteristic
943	C₂	C₇×#3490	1	1	yes	characteristic
944	C₂	C₇×#3491	1	1	yes	characteristic
945	C₂	C₇×#3505	1	1	yes	characteristic
946	C₂	C₇×#3506	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₇×#2617	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×#2849	C₂	semidirect
3. C₇×#2646	C₂	semidirect
4. C₇×#2639	C₂	semidirect
5. C₇×#2626	C₂	semidirect
7. C₇×#2573	C₂	semidirect
8. C₇×#2572	C₂	semidirect
9. C₇×#2554	C₂	semidirect
10. C₇×#2553	C₂	semidirect
11. C₇×#2516	C₂	semidirect
12. C₇×#2515	C₂	semidirect
13. C₇×#2458	C₂	semidirect
14. C₇×#2457	C₂	semidirect
15. C₇×#2321	C₂	semidirect
16. C₇×#2318	C₂	semidirect
17. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₇×#121	C₂	semidirect
19. C₂×C₄×C₇×C₂²⋊C₄	C₂	semidirect
21. C₂×C₇×#126	C₂²	semidirect
27. C₂×C₄×C₇×Q₈	C₂²	semidirect
29. C₂×C₄×C₇×D₄	C₂²	semidirect
34. C₇×#400	C₂²	semidirect
35. C₇×#400	C₂²	semidirect
36. C₇×#400	C₂²	semidirect
38. C₇×#398	C₂²	semidirect
39. C₇×#398	C₂²	semidirect
41. C₇×#397	C₂²	semidirect
46. C₇×#394	C₂²	semidirect
48. C₇×#393	C₂²	semidirect
50. C₇×#391	C₂²	semidirect
53. C₇×#390	C₂²	semidirect
54. C₇×#389	C₂²	semidirect
55. C₇×#389	C₂²	semidirect
60. C₇×#388	C₂²	semidirect
61. C₇×#388	C₂²	semidirect
62. C₇×#388	C₂²	semidirect
63. C₇×#388	C₂²	semidirect
64. C₇×#388	C₂²	semidirect
65. C₇×#388	C₂²	semidirect
66. C₇×#387	C₂²	semidirect
67. C₇×#387	C₂²	semidirect
68. C₇×#387	C₂²	semidirect
69. C₇×#387	C₂²	semidirect
70. C₇×#387	C₂²	semidirect
71. C₇×#387	C₂²	semidirect
86. C₇×#383	C₂²	semidirect
87. C₇×#383	C₂²	semidirect
88. C₇×#382	C₂²	semidirect
91. C₇×#381	C₂²	semidirect
94. C₇×#380	C₂²	semidirect
96. C₄×C₇×C₄⋊C₄	C₂²	semidirect
97. C₄×C₇×C₄⋊C₄	C₂²	semidirect
98. C₄×C₇×C₄⋊C₄	C₂²	semidirect
104. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
107. #35022	C₇	direct (N × H)
211. #2852	C₂×C₇	semidirect
212. #2849	C₂×C₇	semidirect
213. #2646	C₂×C₇	semidirect
214. #2639	C₂×C₇	semidirect
215. #2626	C₂×C₇	semidirect
217. #2573	C₂×C₇	semidirect
218. #2572	C₂×C₇	semidirect
219. #2554	C₂×C₇	semidirect
220. #2553	C₂×C₇	semidirect
221. #2516	C₂×C₇	semidirect
222. #2515	C₂×C₇	semidirect
223. #2458	C₂×C₇	semidirect
224. #2457	C₂×C₇	semidirect
225. #2321	C₂×C₇	semidirect
226. #2318	C₂×C₇	semidirect
227. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
228. C₄×#121	C₂×C₇	semidirect
229. C₂×C₄×C₂²⋊C₄	C₂×C₇	semidirect
348. C₂×#126	C₂²×C₇	semidirect
354. C₂×C₄×Q₈	C₂²×C₇	semidirect
356. C₂×C₄×D₄	C₂²×C₇	semidirect
361. #400	C₂²×C₇	semidirect
362. #400	C₂²×C₇	semidirect
363. #400	C₂²×C₇	semidirect
365. #398	C₂²×C₇	semidirect
366. #398	C₂²×C₇	semidirect
368. #397	C₂²×C₇	semidirect
373. #394	C₂²×C₇	semidirect
375. #393	C₂²×C₇	semidirect
377. #391	C₂²×C₇	semidirect
380. #390	C₂²×C₇	semidirect
381. #389	C₂²×C₇	semidirect
382. #389	C₂²×C₇	semidirect
387. #388	C₂²×C₇	semidirect
388. #388	C₂²×C₇	semidirect
389. #388	C₂²×C₇	semidirect
390. #388	C₂²×C₇	semidirect
391. #388	C₂²×C₇	semidirect
392. #388	C₂²×C₇	semidirect
393. #387	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
413. #383	C₂²×C₇	semidirect
414. #383	C₂²×C₇	semidirect
415. #382	C₂²×C₇	semidirect
418. #381	C₂²×C₇	semidirect
421. #380	C₂²×C₇	semidirect
423. C₄×C₄⋊C₄	C₂²×C₇	semidirect
424. C₄×C₄⋊C₄	C₂²×C₇	semidirect
425. C₄×C₄⋊C₄	C₂²×C₇	semidirect
431. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
891. C₇	#35022	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×#2849	2
C₇×#2646	2
C₇×#2639	2
C₇×#2626	2
C₇×#2617	2
C₇×#2573	2
C₇×#2572	2
C₇×#2554	2
C₇×#2553	2
C₇×#2516	2
C₇×#2515	2
C₇×#2458	2
C₇×#2457	2
C₇×#2321	2
C₇×#2318	2
C₄×C₇×C₂²⋊Q₈	2
C₄×C₇×#121	2
C₂×C₄×C₇×C₂²⋊C₄	2
#35022	7

Subgroups — C7×#35022 #13212238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#35022 #13212238