Subgroups — C₇×#34476 #13211692

Order 1792.

2736 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#546	C₂	1	1	yes	maximal, characteristic
2	C₇×#2377	C₂	1	2	yes	maximal, complemented
3	C₇×#2376	C₂	1	2	yes	maximal, complemented
4	C₇×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2358	C₂	1	2	yes	maximal, complemented
8	C₇×#2354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2342	C₂	1	2	yes	maximal, complemented
11	C₇×#2341	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2335	C₂	1	2	yes	maximal, complemented
14	C₇×#2326	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2324	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2324	C₂	1	2	yes	maximal, complemented
17	C₇×#2321	C₂	1	2	yes	maximal, complemented
18	C₇×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2315	C₂	1	2	yes	maximal, complemented
20	C₇×#2311	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₇×#390	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
25	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
26	C₇×#546	C₄	1	16	yes	complemented
27	C₂×C₇×#124	C₂²	1	1	yes	characteristic
28	C₂×C₇×#123	C₂²	1	2	yes	—
29	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×#121	C₂²	1	1	yes	characteristic
31	C₂×C₇×#121	C₂²	1	2	yes	—
32	C₂×C₇×#120	C₂²	1	2	yes	—
33	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
36	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
41	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₇×#117	C₂²	1	2	yes	complemented
43	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
46	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
47	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
48	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
49	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
50	C₇×#391	C₂²	1	1	yes	characteristic, complemented
51	C₇×#391	C₂²	1	1	yes	characteristic, complemented
52	C₇×#390	C₂²	1	1	yes	characteristic
53	C₇×#390	C₂²	1	1	yes	characteristic
54	C₇×#390	C₂²	1	2	yes	—
55	C₇×#390	C₂²	1	1	yes	characteristic
56	C₇×#390	C₂²	1	1	yes	characteristic
57	C₇×#390	C₂²	1	2	yes	—
58	C₇×#390	C₂²	1	1	yes	characteristic
59	C₇×#390	C₂²	1	1	yes	characteristic
60	C₇×#390	C₂²	1	2	yes	complemented
61	C₇×#390	C₂²	1	2	yes	complemented
62	C₇×#390	C₂²	1	2	yes	complemented
63	C₇×#389	C₂²	1	1	yes	characteristic, complemented
64	C₇×#389	C₂²	1	1	yes	characteristic, complemented
65	C₇×#389	C₂²	1	2	yes	complemented
66	C₇×#389	C₂²	1	2	yes	complemented
67	C₇×#388	C₂²	1	1	yes	characteristic, complemented
68	C₇×#388	C₂²	1	1	yes	characteristic, complemented
69	C₇×#388	C₂²	1	2	yes	complemented
70	C₇×#388	C₂²	1	2	yes	complemented
71	C₇×#388	C₂²	1	2	yes	complemented
72	C₇×#388	C₂²	1	2	yes	complemented
73	C₇×#388	C₂²	1	2	yes	complemented
74	C₇×#388	C₂²	1	2	yes	complemented
75	C₇×#388	C₂²	1	2	yes	complemented
76	C₇×#388	C₂²	1	2	yes	complemented
77	C₇×#388	C₂²	1	2	yes	complemented
78	C₇×#388	C₂²	1	2	yes	complemented
79	C₇×#387	C₂²	1	1	yes	characteristic, complemented
80	C₇×#387	C₂²	1	1	yes	characteristic, complemented
81	C₇×#387	C₂²	1	2	yes	complemented
82	C₇×#387	C₂²	1	2	yes	complemented
83	C₇×#386	C₂²	1	1	yes	characteristic
84	C₇×#386	C₂²	1	1	yes	characteristic
85	C₇×#386	C₂²	1	2	yes	—
86	C₇×#386	C₂²	1	2	yes	—
87	C₇×#386	C₂²	1	2	yes	complemented
88	C₇×#386	C₂²	1	2	yes	complemented
89	C₇×#386	C₂²	1	2	yes	complemented
90	C₇×#386	C₂²	1	2	yes	complemented
91	C₇×#385	C₂²	1	1	yes	characteristic
92	C₇×#385	C₂²	1	1	yes	characteristic
93	C₇×#385	C₂²	1	2	yes	—
94	C₇×#385	C₂²	1	2	yes	—
95	C₇×#385	C₂²	1	2	yes	—
96	C₇×#385	C₂²	1	2	yes	complemented
97	C₇×#385	C₂²	1	2	yes	complemented
98	C₇×#385	C₂²	1	2	yes	complemented
99	C₇×#385	C₂²	1	2	yes	complemented
100	C₇×#385	C₂²	1	2	yes	complemented
101	C₇×#385	C₂²	1	2	yes	complemented
102	C₇×#384	C₂²	1	1	yes	characteristic, complemented
103	C₇×#381	C₂²	1	2	yes	complemented
104	C₇×#380	C₂²	1	1	yes	characteristic
105	C₇×#380	C₂²	1	2	yes	complemented
106	C₇×#380	C₂²	1	2	yes	complemented
107	C₇×#380	C₂²	1	2	yes	complemented
108	C₇×#380	C₂²	1	2	yes	complemented
109	C₇×#380	C₂²	1	2	yes	complemented
110	C₇×#380	C₂²	1	1	yes	characteristic, complemented
111	C₇×#379	C₂²	1	2	yes	—
112	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
114	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₇×#376	C₂²	1	1	yes	characteristic, complemented
124	#34476	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁵×C₇	C₂³	1	2	yes	—
126	C₂×C₇×#41	—	4	2	no	—
127	C₂×C₇×#41	—	4	2	no	—
128	C₂×C₇×#41	C₂×C₄	1	8	yes	complemented
129	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
130	C₂²×C₇×D₄	—	4	2	no	—
131	C₂²×C₇×D₄	—	4	2	no	—
132	C₂²×C₇×D₄	C₂×C₄	1	8	yes	complemented
133	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
134	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
135	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
136	C₂²×C₇×D₄	C₂³	1	2	yes	—
137	C₂²×C₇×D₄	C₂³	1	2	yes	—
138	C₂²×C₇×D₄	C₂³	1	2	yes	—
139	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₇	C₂³	1	2	yes	—
144	C₂³×C₄×C₇	C₂³	1	2	yes	—
145	C₂³×C₄×C₇	C₂³	1	2	yes	—
146	C₂³×C₄×C₇	C₂³	1	2	yes	—
147	C₂³×C₄×C₇	C₂³	1	2	yes	—
148	C₂³×C₄×C₇	C₂³	1	2	yes	—
149	C₇×#124	C₂×C₄	1	8	yes	complemented
150	C₇×#123	C₂×C₄	1	16	yes	complemented
151	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
152	C₇×#121	C₂×C₄	1	8	yes	complemented
153	C₇×#121	C₂×C₄	1	16	yes	complemented
154	C₇×#120	C₂×C₄	1	16	yes	complemented
155	C₄×C₇×Q₈	—	4	2	no	—
156	C₄×C₇×Q₈	—	4	2	no	—
157	C₄×C₇×D₄	—	4	4	no	—
158	C₄×C₇×D₄	—	4	2	no	—
159	C₄×C₇×D₄	—	4	2	no	—
160	C₄×C₇×D₄	—	4	4	no	—
161	C₄×C₇×D₄	C₂×C₄	1	8	yes	complemented
162	C₄×C₇×D₄	C₂×C₄	1	8	yes	complemented
163	C₇×#117	—	4	2	no	—
164	C₇×#117	—	4	4	no	—
165	C₂×C₇×C₄⋊C₄	—	4	2	no	—
166	C₂×C₇×C₄⋊C₄	—	4	2	no	—
167	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
187	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
188	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
189	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
190	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₇	—	4	2	no	—
220	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₇	C₂³	1	2	yes	—
225	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₇	C₂³	1	2	yes	—
228	C₂×C₄²×C₇	C₂³	1	2	yes	—
229	C₂×C₄²×C₇	C₂³	1	2	yes	—
230	C₂×C₄²×C₇	C₂³	1	2	yes	—
231	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
232	C₇×#95	C₂³	1	1	yes	characteristic
233	C₇×#95	C₂³	1	1	yes	characteristic
234	C₇×#95	C₂³	1	1	yes	characteristic
235	C₇×#95	C₂³	1	1	yes	characteristic
236	C₇×#95	C₂³	1	2	yes	—
237	C₇×#95	C₂³	1	2	yes	—
238	C₇×#95	C₂³	1	2	yes	—
239	C₇×#95	C₂³	1	2	yes	—
240	C₇×#95	C₂³	1	1	yes	characteristic
241	C₇×#95	C₂³	1	1	yes	characteristic
242	C₇×#95	C₂³	1	1	yes	characteristic
243	C₇×#95	C₂³	1	1	yes	characteristic
244	C₇×#95	C₂³	1	1	yes	characteristic
245	C₇×#95	C₂³	1	2	yes	—
246	C₇×#95	C₂³	1	2	yes	—
247	C₇×#95	C₂³	1	2	yes	—
248	C₇×#95	C₂³	1	2	yes	—
249	C₇×#95	C₂³	1	2	yes	—
250	C₇×#95	C₂³	1	2	yes	—
251	C₇×#95	C₂³	1	2	yes	—
252	C₇×#95	C₂³	1	1	yes	characteristic
253	C₂×#546	C₂×C₇	1	1	yes	characteristic
254	#2377	C₂×C₇	1	2	yes	complemented
255	#2376	C₂×C₇	1	2	yes	complemented
256	#2367	C₂×C₇	1	1	yes	characteristic, complemented
257	#2361	C₂×C₇	1	1	yes	characteristic, complemented
258	#2360	C₂×C₇	1	1	yes	characteristic, complemented
259	#2358	C₂×C₇	1	2	yes	complemented
260	#2354	C₂×C₇	1	1	yes	characteristic, complemented
261	D₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
262	#2342	C₂×C₇	1	2	yes	complemented
263	#2341	C₂×C₇	1	1	yes	characteristic, complemented
264	D₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
265	#2335	C₂×C₇	1	2	yes	complemented
266	#2326	C₂×C₇	1	1	yes	characteristic, complemented
267	#2324	C₂×C₇	1	1	yes	characteristic, complemented
268	#2324	C₂×C₇	1	2	yes	complemented
269	#2321	C₂×C₇	1	2	yes	complemented
270	#2319	C₂×C₇	1	1	yes	characteristic, complemented
271	#2315	C₂×C₇	1	2	yes	complemented
272	#2311	C₂×C₇	1	1	yes	characteristic, complemented
273	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
274	C₂×#390	C₂×C₇	1	1	yes	characteristic, complemented
275	#2290	C₂×C₇	1	1	yes	characteristic, complemented
276	C₂⁴×C₇	—	2	4	no	—
277	C₂⁴×C₇	—	2	4	no	—
278	C₂⁴×C₇	—	4	2	no	—
279	C₂⁴×C₇	—	4	2	no	—
280	C₂⁴×C₇	—	4	2	no	—
281	C₂⁴×C₇	—	4	2	no	—
282	C₂⁴×C₇	C₂²×C₄	1	8	yes	—
283	C₂⁴×C₇	C₂⁴	1	2	yes	—
284	C₂⁴×C₇	C₂⁴	1	2	yes	—
285	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
286	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
287	C₇×#41	—	4	16	no	—
288	C₂×C₇×Q₈	—	2	2	no	—
289	C₂×C₇×Q₈	—	2	2	no	—
290	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
291	C₂×C₇×D₄	—	2	2	no	—
292	C₂×C₇×D₄	—	2	2	no	—
293	C₂×C₇×D₄	—	2	2	no	—
294	C₂×C₇×D₄	—	2	2	no	—
295	C₂×C₇×D₄	—	2	2	no	—
296	C₂×C₇×D₄	—	2	2	no	—
297	C₂×C₇×D₄	—	4	16	no	—
298	C₂×C₇×D₄	—	4	2	no	—
299	C₂×C₇×D₄	—	4	2	no	—
300	C₂×C₇×D₄	—	4	2	no	—
301	C₂×C₇×D₄	—	4	2	no	—
302	C₂×C₇×D₄	—	4	2	no	—
303	C₂×C₇×D₄	—	4	2	no	—
304	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
305	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
306	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
307	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
308	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
309	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
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	—	2	4	no	—
317	C₂²×C₄×C₇	—	2	2	no	—
318	C₂²×C₄×C₇	—	4	1	no	—
319	C₂²×C₄×C₇	—	4	1	no	—
320	C₂²×C₄×C₇	—	4	2	no	—
321	C₂²×C₄×C₇	—	4	2	no	—
322	C₂²×C₄×C₇	—	4	1	no	—
323	C₂²×C₄×C₇	—	4	2	no	—
324	C₂²×C₄×C₇	—	4	2	no	—
325	C₂²×C₄×C₇	—	4	2	no	—
326	C₂²×C₄×C₇	—	4	2	no	—
327	C₂²×C₄×C₇	—	4	2	no	—
328	C₂²×C₄×C₇	—	4	2	no	—
329	C₂²×C₄×C₇	—	4	2	no	—
330	C₂²×C₄×C₇	—	4	2	no	—
331	C₂²×C₄×C₇	—	4	2	no	—
332	C₂²×C₄×C₇	—	4	2	no	—
333	C₂²×C₄×C₇	—	4	2	no	—
334	C₂²×C₄×C₇	—	4	2	no	—
335	C₂²×C₄×C₇	—	4	2	no	—
336	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
337	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
338	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
339	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
340	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
359	C₇×C₄⋊C₄	—	2	2	no	—
360	C₇×C₄⋊C₄	—	2	2	no	—
361	C₇×C₄⋊C₄	—	2	2	no	—
362	C₇×C₄⋊C₄	—	2	2	no	—
363	C₇×C₄⋊C₄	—	2	2	no	—
364	C₇×C₄⋊C₄	—	4	2	no	—
365	C₇×C₄⋊C₄	—	4	2	no	—
366	C₇×C₄⋊C₄	—	4	1	no	—
367	C₇×C₄⋊C₄	—	4	2	no	—
368	C₇×C₄⋊C₄	—	4	2	no	—
369	C₇×C₄⋊C₄	—	4	1	no	—
370	C₇×C₄⋊C₄	—	4	1	no	—
371	C₇×C₄⋊C₄	—	4	2	no	—
372	C₇×C₄⋊C₄	—	4	2	no	—
373	C₇×C₄⋊C₄	—	4	2	no	—
374	C₇×C₄⋊C₄	—	4	2	no	—
375	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
376	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
377	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
378	C₇×C₂²⋊C₄	—	2	2	no	—
379	C₇×C₂²⋊C₄	—	2	4	no	—
380	C₇×C₂²⋊C₄	—	2	2	no	—
381	C₇×C₂²⋊C₄	—	2	4	no	—
382	C₇×C₂²⋊C₄	—	2	4	no	—
383	C₇×C₂²⋊C₄	—	2	2	no	—
384	C₇×C₂²⋊C₄	—	4	2	no	—
385	C₇×C₂²⋊C₄	—	4	2	no	—
386	C₇×C₂²⋊C₄	—	4	2	no	—
387	C₇×C₂²⋊C₄	—	4	2	no	—
388	C₇×C₂²⋊C₄	—	4	2	no	—
389	C₇×C₂²⋊C₄	—	4	2	no	—
390	C₇×C₂²⋊C₄	—	4	2	no	—
391	C₇×C₂²⋊C₄	—	4	2	no	—
392	C₇×C₂²⋊C₄	—	4	2	no	—
393	C₇×C₂²⋊C₄	—	4	1	no	—
394	C₇×C₂²⋊C₄	—	4	1	no	—
395	C₇×C₂²⋊C₄	—	4	1	no	—
396	C₇×C₂²⋊C₄	—	4	2	no	—
397	C₇×C₂²⋊C₄	—	4	2	no	—
398	C₇×C₂²⋊C₄	—	4	2	no	—
399	C₇×C₂²⋊C₄	—	4	2	no	—
400	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
401	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
402	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
403	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
404	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
405	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
406	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
407	C₄²×C₇	—	2	2	no	—
408	C₄²×C₇	—	2	2	no	—
409	C₄²×C₇	—	2	4	no	—
410	C₄²×C₇	—	2	2	no	—
411	C₄²×C₇	—	2	2	no	—
412	C₄²×C₇	—	4	1	no	—
413	C₄²×C₇	—	4	1	no	—
414	C₄²×C₇	—	4	2	no	—
415	C₄²×C₇	—	4	2	no	—
416	C₄²×C₇	—	4	2	no	—
417	C₄²×C₇	—	4	2	no	—
418	C₄²×C₇	C₂²×C₄	1	4	yes	—
419	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
420	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
421	#546	C₄×C₇	1	16	yes	complemented
422	C₂×#124	C₂²×C₇	1	1	yes	characteristic
423	C₂×#123	C₂²×C₇	1	2	yes	—
424	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
425	C₂×#121	C₂²×C₇	1	1	yes	characteristic
426	C₂×#121	C₂²×C₇	1	2	yes	—
427	C₂×#120	C₂²×C₇	1	2	yes	—
428	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
429	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
430	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
431	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
432	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
434	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
435	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
436	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
437	C₂×#117	C₂²×C₇	1	2	yes	complemented
438	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
439	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
440	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
441	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
442	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
443	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
444	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
445	#391	C₂²×C₇	1	1	yes	characteristic, complemented
446	#391	C₂²×C₇	1	1	yes	characteristic, complemented
447	#390	C₂²×C₇	1	1	yes	characteristic
448	#390	C₂²×C₇	1	1	yes	characteristic
449	#390	C₂²×C₇	1	1	yes	characteristic
450	#390	C₂²×C₇	1	1	yes	characteristic
451	#390	C₂²×C₇	1	2	yes	—
452	#390	C₂²×C₇	1	1	yes	characteristic
453	#390	C₂²×C₇	1	1	yes	characteristic
454	#390	C₂²×C₇	1	2	yes	—
455	#390	C₂²×C₇	1	2	yes	complemented
456	#390	C₂²×C₇	1	2	yes	complemented
457	#390	C₂²×C₇	1	2	yes	complemented
458	#389	C₂²×C₇	1	1	yes	characteristic, complemented
459	#389	C₂²×C₇	1	1	yes	characteristic, complemented
460	#389	C₂²×C₇	1	2	yes	complemented
461	#389	C₂²×C₇	1	2	yes	complemented
462	#388	C₂²×C₇	1	2	yes	complemented
463	#388	C₂²×C₇	1	2	yes	complemented
464	#388	C₂²×C₇	1	2	yes	complemented
465	#388	C₂²×C₇	1	2	yes	complemented
466	#388	C₂²×C₇	1	2	yes	complemented
467	#388	C₂²×C₇	1	1	yes	characteristic, complemented
468	#388	C₂²×C₇	1	2	yes	complemented
469	#388	C₂²×C₇	1	2	yes	complemented
470	#388	C₂²×C₇	1	2	yes	complemented
471	#388	C₂²×C₇	1	2	yes	complemented
472	#388	C₂²×C₇	1	2	yes	complemented
473	#388	C₂²×C₇	1	1	yes	characteristic, complemented
474	#387	C₂²×C₇	1	1	yes	characteristic, complemented
475	#387	C₂²×C₇	1	2	yes	complemented
476	#387	C₂²×C₇	1	1	yes	characteristic, complemented
477	#387	C₂²×C₇	1	2	yes	complemented
478	#386	C₂²×C₇	1	1	yes	characteristic
479	#386	C₂²×C₇	1	2	yes	—
480	#386	C₂²×C₇	1	2	yes	—
481	#386	C₂²×C₇	1	1	yes	characteristic
482	#386	C₂²×C₇	1	2	yes	complemented
483	#386	C₂²×C₇	1	2	yes	complemented
484	#386	C₂²×C₇	1	2	yes	complemented
485	#386	C₂²×C₇	1	2	yes	complemented
486	#385	C₂²×C₇	1	1	yes	characteristic
487	#385	C₂²×C₇	1	2	yes	—
488	#385	C₂²×C₇	1	2	yes	—
489	#385	C₂²×C₇	1	2	yes	—
490	#385	C₂²×C₇	1	1	yes	characteristic
491	#385	C₂²×C₇	1	2	yes	complemented
492	#385	C₂²×C₇	1	2	yes	complemented
493	#385	C₂²×C₇	1	2	yes	complemented
494	#385	C₂²×C₇	1	2	yes	complemented
495	#385	C₂²×C₇	1	2	yes	complemented
496	#385	C₂²×C₇	1	2	yes	complemented
497	#384	C₂²×C₇	1	1	yes	characteristic, complemented
498	#381	C₂²×C₇	1	2	yes	complemented
499	#380	C₂²×C₇	1	1	yes	characteristic
500	#380	C₂²×C₇	1	2	yes	complemented
501	#380	C₂²×C₇	1	2	yes	complemented
502	#380	C₂²×C₇	1	2	yes	complemented
503	#380	C₂²×C₇	1	2	yes	complemented
504	#380	C₂²×C₇	1	2	yes	complemented
505	#380	C₂²×C₇	1	1	yes	characteristic, complemented
506	#379	C₂²×C₇	1	2	yes	—
507	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
508	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
509	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
510	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
511	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
512	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
513	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
514	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
515	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
516	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
517	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
518	#376	C₂²×C₇	1	1	yes	characteristic, complemented
519	C₂³×C₇	—	2	1	no	—
520	C₂³×C₇	—	2	1	no	—
521	C₂³×C₇	—	2	1	no	—
522	C₂³×C₇	—	2	1	no	—
523	C₂³×C₇	—	2	2	no	—
524	C₂³×C₇	—	2	2	no	—
525	C₂³×C₇	—	2	1	no	—
526	C₂³×C₇	—	2	2	no	—
527	C₂³×C₇	—	2	1	no	—
528	C₂³×C₇	—	2	1	no	—
529	C₂³×C₇	—	2	2	no	—
530	C₂³×C₇	—	2	2	no	—
531	C₂³×C₇	—	2	2	no	—
532	C₂³×C₇	—	2	1	no	—
533	C₂³×C₇	—	2	2	no	—
534	C₂³×C₇	—	2	2	no	—
535	C₂³×C₇	—	2	1	no	—
536	C₂³×C₇	—	2	2	no	—
537	C₂³×C₇	—	2	2	no	—
538	C₂³×C₇	—	2	2	no	—
539	C₂³×C₇	—	2	1	no	—
540	C₂³×C₇	—	2	2	no	—
541	C₂³×C₇	—	2	16	no	—
542	C₂³×C₇	—	4	8	no	—
543	C₂³×C₇	—	4	8	no	—
544	C₂³×C₇	—	8	4	no	—
545	C₂³×C₇	—	8	4	no	—
546	C₂³×C₇	—	8	4	no	—
547	C₂³×C₇	—	8	4	no	—
548	C₂³×C₇	C₂³×C₄	1	4	yes	—
549	C₂³×C₇	C₂³×C₄	1	4	yes	—
550	C₂³×C₇	C₂³×C₄	1	2	yes	—
551	C₂³×C₇	C₂³×C₄	1	2	yes	—
552	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
553	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
554	C₂³×C₇	C₂⁵	1	1	yes	characteristic
555	C₇×Q₈	—	2	8	no	—
556	C₇×D₄	—	2	8	no	—
557	C₇×D₄	—	2	8	no	—
558	C₇×D₄	—	2	8	no	—
559	C₇×D₄	—	4	8	no	—
560	C₇×D₄	—	4	8	no	—
561	C₇×D₄	—	4	8	no	—
562	C₂×C₄×C₇	—	2	1	no	—
563	C₂×C₄×C₇	—	2	2	no	—
564	C₂×C₄×C₇	—	2	1	no	—
565	C₂×C₄×C₇	—	2	1	no	—
566	C₂×C₄×C₇	—	2	2	no	—
567	C₂×C₄×C₇	—	2	2	no	—
568	C₂×C₄×C₇	—	2	1	no	—
569	C₂×C₄×C₇	—	2	1	no	—
570	C₂×C₄×C₇	—	2	1	no	—
571	C₂×C₄×C₇	—	2	1	no	—
572	C₂×C₄×C₇	—	2	1	no	—
573	C₂×C₄×C₇	—	2	1	no	—
574	C₂×C₄×C₇	—	2	1	no	—
575	C₂×C₄×C₇	—	2	2	no	—
576	C₂×C₄×C₇	—	2	8	no	—
577	C₂×C₄×C₇	—	2	8	no	—
578	C₂×C₄×C₇	—	2	1	no	—
579	C₂×C₄×C₇	—	2	1	no	—
580	C₂×C₄×C₇	—	2	1	no	—
581	C₂×C₄×C₇	—	2	1	no	—
582	C₂×C₄×C₇	—	2	1	no	—
583	C₂×C₄×C₇	—	2	1	no	—
584	C₂×C₄×C₇	—	2	2	no	—
585	C₂×C₄×C₇	—	2	1	no	—
586	C₂×C₄×C₇	—	2	1	no	—
587	C₂×C₄×C₇	—	2	2	no	—
588	C₂×C₄×C₇	—	2	2	no	—
589	C₂×C₄×C₇	—	2	2	no	—
590	C₂×C₄×C₇	—	2	2	no	—
591	C₂×C₄×C₇	—	2	2	no	—
592	C₂×C₄×C₇	—	2	1	no	—
593	C₂×C₄×C₇	—	2	1	no	—
594	C₂×C₄×C₇	—	2	2	no	—
595	C₂×C₄×C₇	—	2	2	no	—
596	C₂×C₄×C₇	—	2	1	no	—
597	C₂×C₄×C₇	—	2	1	no	—
598	C₂×C₄×C₇	—	2	1	no	—
599	C₂×C₄×C₇	—	2	1	no	—
600	C₂×C₄×C₇	—	2	2	no	—
601	C₂×C₄×C₇	—	2	2	no	—
602	C₂×C₄×C₇	—	2	2	no	—
603	C₂×C₄×C₇	—	2	1	no	—
604	C₂×C₄×C₇	—	2	1	no	—
605	C₂×C₄×C₇	—	2	1	no	—
606	C₂×C₄×C₇	—	2	1	no	—
607	C₂×C₄×C₇	—	2	1	no	—
608	C₂×C₄×C₇	—	2	2	no	—
609	C₂×C₄×C₇	—	2	1	no	—
610	C₂×C₄×C₇	—	2	1	no	—
611	C₂×C₄×C₇	—	4	8	no	—
612	C₂×C₄×C₇	—	4	8	no	—
613	C₂×C₄×C₇	—	4	4	no	—
614	C₂×C₄×C₇	—	4	4	no	—
615	C₂×C₄×C₇	—	8	4	no	—
616	C₂×C₄×C₇	—	8	4	no	—
617	C₂×C₄×C₇	—	8	4	no	—
618	C₂×C₄×C₇	—	8	4	no	—
619	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
620	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
621	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
622	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
623	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
624	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
625	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
626	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
627	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
628	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
629	C₂⁵	C₂³×C₇	1	2	yes	—
630	C₂×#41	—	4	2	no	—
631	C₂×#41	—	4	2	no	—
632	C₂×#41	C₂×C₄×C₇	1	8	yes	complemented
633	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
634	C₂²×D₄	—	4	2	no	—
635	C₂²×D₄	—	4	2	no	—
636	C₂²×D₄	C₂×C₄×C₇	1	8	yes	complemented
637	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
638	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
639	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
640	C₂²×D₄	C₂³×C₇	1	2	yes	—
641	C₂²×D₄	C₂³×C₇	1	2	yes	—
642	C₂²×D₄	C₂³×C₇	1	2	yes	—
643	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
644	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
645	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
646	C₂³×C₄	C₂³×C₇	1	2	yes	—
647	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
648	C₂³×C₄	C₂³×C₇	1	2	yes	—
649	C₂³×C₄	C₂³×C₇	1	2	yes	—
650	C₂³×C₄	C₂³×C₇	1	2	yes	—
651	C₂³×C₄	C₂³×C₇	1	2	yes	—
652	C₂³×C₄	C₂³×C₇	1	2	yes	—
653	#124	C₂×C₄×C₇	1	8	yes	complemented
654	#123	C₂×C₄×C₇	1	16	yes	complemented
655	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	complemented
656	#121	C₂×C₄×C₇	1	8	yes	complemented
657	#121	C₂×C₄×C₇	1	16	yes	complemented
658	#120	C₂×C₄×C₇	1	16	yes	complemented
659	C₄×Q₈	—	4	2	no	—
660	C₄×Q₈	—	4	2	no	—
661	C₄×D₄	—	4	4	no	—
662	C₄×D₄	—	4	2	no	—
663	C₄×D₄	—	4	2	no	—
664	C₄×D₄	—	4	4	no	—
665	C₄×D₄	C₂×C₄×C₇	1	8	yes	complemented
666	C₄×D₄	C₂×C₄×C₇	1	8	yes	complemented
667	#117	—	4	2	no	—
668	#117	—	4	4	no	—
669	C₂×C₄⋊C₄	—	4	2	no	—
670	C₂×C₄⋊C₄	—	4	2	no	—
671	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
682	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
683	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
686	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
690	C₂×C₂²⋊C₄	—	4	4	no	—
691	C₂×C₂²⋊C₄	—	4	4	no	—
692	C₂×C₂²⋊C₄	—	4	4	no	—
693	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	16	yes	complemented
694	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
695	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
710	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
711	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
716	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
717	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
722	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
723	C₂×C₄²	—	4	2	no	—
724	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
725	C₂×C₄²	C₂³×C₇	1	2	yes	—
726	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
727	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
728	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
729	C₂×C₄²	C₂³×C₇	1	2	yes	—
730	C₂×C₄²	C₂³×C₇	1	2	yes	—
731	C₂×C₄²	C₂³×C₇	1	2	yes	—
732	C₂×C₄²	C₂³×C₇	1	2	yes	—
733	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
734	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
735	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
736	#95	C₂³×C₇	1	1	yes	characteristic
737	#95	C₂³×C₇	1	1	yes	characteristic
738	#95	C₂³×C₇	1	1	yes	characteristic
739	#95	C₂³×C₇	1	1	yes	characteristic
740	#95	C₂³×C₇	1	2	yes	—
741	#95	C₂³×C₇	1	2	yes	—
742	#95	C₂³×C₇	1	2	yes	—
743	#95	C₂³×C₇	1	2	yes	—
744	#95	C₂³×C₇	1	1	yes	characteristic
745	#95	C₂³×C₇	1	1	yes	characteristic
746	#95	C₂³×C₇	1	1	yes	characteristic
747	#95	C₂³×C₇	1	1	yes	characteristic
748	#95	C₂³×C₇	1	1	yes	characteristic
749	#95	C₂³×C₇	1	2	yes	—
750	#95	C₂³×C₇	1	2	yes	—
751	#95	C₂³×C₇	1	2	yes	—
752	#95	C₂³×C₇	1	2	yes	—
753	#95	C₂³×C₇	1	2	yes	—
754	#95	C₂³×C₇	1	2	yes	—
755	#95	C₂³×C₇	1	2	yes	—
756	#95	C₂³×C₇	1	1	yes	characteristic
757	C₂²×C₇	—	2	2	no	—
758	C₂²×C₇	—	2	2	no	—
759	C₂²×C₇	—	2	2	no	—
760	C₂²×C₇	—	2	2	no	—
761	C₂²×C₇	—	2	2	no	—
762	C₂²×C₇	—	2	2	no	—
763	C₂²×C₇	—	2	2	no	—
764	C₂²×C₇	—	2	4	no	—
765	C₂²×C₇	—	2	4	no	—
766	C₂²×C₇	—	2	2	no	—
767	C₂²×C₇	—	2	4	no	—
768	C₂²×C₇	—	2	4	no	—
769	C₂²×C₇	—	2	4	no	—
770	C₂²×C₇	—	2	2	no	—
771	C₂²×C₇	—	2	4	no	—
772	C₂²×C₇	—	4	1	no	—
773	C₂²×C₇	—	4	2	no	—
774	C₂²×C₇	—	4	2	no	—
775	C₂²×C₇	—	4	2	no	—
776	C₂²×C₇	—	4	1	no	—
777	C₂²×C₇	—	4	2	no	—
778	C₂²×C₇	—	4	1	no	—
779	C₂²×C₇	—	4	2	no	—
780	C₂²×C₇	—	4	2	no	—
781	C₂²×C₇	—	4	1	no	—
782	C₂²×C₇	—	4	2	no	—
783	C₂²×C₇	—	4	2	no	—
784	C₂²×C₇	—	8	16	no	—
785	C₂²×C₇	#520	1	4	yes	—
786	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
787	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
788	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
789	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
790	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
791	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
792	C₂²×C₇	#585	1	1	yes	characteristic
793	C₄×C₇	—	2	2	no	—
794	C₄×C₇	—	2	2	no	—
795	C₄×C₇	—	2	4	no	—
796	C₄×C₇	—	2	2	no	—
797	C₄×C₇	—	2	2	no	—
798	C₄×C₇	—	2	4	no	—
799	C₄×C₇	—	2	2	no	—
800	C₄×C₇	—	4	1	no	—
801	C₄×C₇	—	4	1	no	—
802	C₄×C₇	—	4	1	no	—
803	C₄×C₇	—	4	1	no	—
804	C₄×C₇	—	4	2	no	—
805	C₄×C₇	—	4	1	no	—
806	C₄×C₇	—	4	2	no	—
807	C₄×C₇	—	4	2	no	—
808	C₄×C₇	—	4	1	no	—
809	C₄×C₇	—	4	2	no	—
810	C₄×C₇	—	4	1	no	—
811	C₄×C₇	#518	1	4	yes	—
812	C₂⁴	—	2	4	no	—
813	C₂⁴	—	2	4	no	—
814	C₂⁴	—	4	2	no	—
815	C₂⁴	—	4	2	no	—
816	C₂⁴	—	4	2	no	—
817	C₂⁴	—	4	2	no	—
818	C₂⁴	C₂²×C₄×C₇	1	8	yes	—
819	C₂⁴	C₂⁴×C₇	1	2	yes	—
820	C₂⁴	C₂⁴×C₇	1	2	yes	—
821	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
822	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
823	#41	—	4	16	no	—
824	C₂×Q₈	—	2	2	no	—
825	C₂×Q₈	—	2	2	no	—
826	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	4	16	no	—
834	C₂×D₄	—	4	2	no	—
835	C₂×D₄	—	4	2	no	—
836	C₂×D₄	—	4	2	no	—
837	C₂×D₄	—	4	2	no	—
838	C₂×D₄	—	4	2	no	—
839	C₂×D₄	—	4	2	no	—
840	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
841	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
842	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
843	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
844	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
845	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	4	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	4	1	no	—
855	C₂²×C₄	—	4	1	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	1	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	4	2	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
873	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
874	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
875	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
876	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
883	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
884	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
886	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
889	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
890	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
894	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	4	2	no	—
901	C₄⋊C₄	—	4	2	no	—
902	C₄⋊C₄	—	4	2	no	—
903	C₄⋊C₄	—	4	1	no	—
904	C₄⋊C₄	—	4	1	no	—
905	C₄⋊C₄	—	4	2	no	—
906	C₄⋊C₄	—	4	2	no	—
907	C₄⋊C₄	—	4	2	no	—
908	C₄⋊C₄	—	4	2	no	—
909	C₄⋊C₄	—	4	1	no	—
910	C₄⋊C₄	—	4	2	no	—
911	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
912	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
913	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	4	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	4	2	no	—
921	C₂²⋊C₄	—	4	2	no	—
922	C₂²⋊C₄	—	4	2	no	—
923	C₂²⋊C₄	—	4	2	no	—
924	C₂²⋊C₄	—	4	2	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	—	4	2	no	—
927	C₂²⋊C₄	—	4	2	no	—
928	C₂²⋊C₄	—	4	1	no	—
929	C₂²⋊C₄	—	4	1	no	—
930	C₂²⋊C₄	—	4	2	no	—
931	C₂²⋊C₄	—	4	2	no	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	4	2	no	—
935	C₂²⋊C₄	—	4	1	no	—
936	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
937	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
938	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
939	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
940	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
941	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
942	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	4	no	—
946	C₄²	—	2	2	no	—
947	C₄²	—	2	2	no	—
948	C₄²	—	4	1	no	—
949	C₄²	—	4	1	no	—
950	C₄²	—	4	2	no	—
951	C₄²	—	4	2	no	—
952	C₄²	—	4	2	no	—
953	C₄²	—	4	2	no	—
954	C₄²	C₂²×C₄×C₇	1	4	yes	—
955	C₂×C₇	—	2	4	no	—
956	C₂×C₇	—	4	2	no	—
957	C₂×C₇	—	4	4	no	—
958	C₂×C₇	—	4	4	no	—
959	C₂×C₇	C₂×#518	1	1	yes	characteristic
960	C₂×C₇	C₂×#520	1	1	yes	characteristic
961	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
962	C₂×C₇	#3536	1	1	yes	characteristic
963	C₂×C₇	#3542	1	1	yes	characteristic
964	C₂×C₇	#3543	1	1	yes	characteristic
965	C₂×C₇	#3561	1	1	yes	characteristic
966	C₂³	—	2	1	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	1	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	1	no	—
975	C₂³	—	2	1	no	—
976	C₂³	—	2	2	no	—
977	C₂³	—	2	2	no	—
978	C₂³	—	2	2	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	2	2	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	1	no	—
983	C₂³	—	2	2	no	—
984	C₂³	—	2	2	no	—
985	C₂³	—	2	2	no	—
986	C₂³	—	2	1	no	—
987	C₂³	—	2	2	no	—
988	C₂³	—	2	16	no	—
989	C₂³	—	4	8	no	—
990	C₂³	—	4	8	no	—
991	C₂³	—	8	4	no	—
992	C₂³	—	8	4	no	—
993	C₂³	—	8	4	no	—
994	C₂³	—	8	4	no	—
995	C₂³	C₂³×C₄×C₇	1	4	yes	—
996	C₂³	C₂³×C₄×C₇	1	4	yes	—
997	C₂³	C₂³×C₄×C₇	1	2	yes	—
998	C₂³	C₂³×C₄×C₇	1	2	yes	—
999	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
1000	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
1001	C₂³	C₂⁵×C₇	1	1	yes	characteristic
1002	Q₈	—	2	8	no	—
1003	D₄	—	2	8	no	—
1004	D₄	—	2	8	no	—
1005	D₄	—	2	8	no	—
1006	D₄	—	4	8	no	—
1007	D₄	—	4	8	no	—
1008	D₄	—	4	8	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	8	no	—
1024	C₂×C₄	—	2	8	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	4	8	no	—
1059	C₂×C₄	—	4	8	no	—
1060	C₂×C₄	—	4	4	no	—
1061	C₂×C₄	—	4	4	no	—
1062	C₂×C₄	—	8	4	no	—
1063	C₂×C₄	—	8	4	no	—
1064	C₂×C₄	—	8	4	no	—
1065	C₂×C₄	—	8	4	no	—
1066	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1067	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1068	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
1069	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1070	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
1071	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1072	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1073	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1074	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1075	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1076	C₇	#34476	1	1	yes	characteristic, direct product factor, Sylow
1077	C₂²	—	2	2	no	—
1078	C₂²	—	2	2	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	4	no	—
1085	C₂²	—	2	4	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	4	no	—
1088	C₂²	—	2	4	no	—
1089	C₂²	—	2	4	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	4	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	2	no	—
1104	C₂²	—	8	16	no	—
1105	C₂²	C₇×#520	1	4	yes	—
1106	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
1107	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1108	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1109	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1110	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1111	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1112	C₂²	C₇×#585	1	1	yes	characteristic
1113	C₄	—	2	2	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	4	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	4	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	2	no	—
1131	C₄	C₇×#518	1	4	yes	—
1132	C₂	—	2	4	no	—
1133	C₂	—	4	4	no	—
1134	C₂	—	4	4	no	—
1135	C₂	—	4	2	no	—
1136	C₂	C₂×C₇×#518	1	1	yes	characteristic
1137	C₂	C₂×C₇×#520	1	1	yes	characteristic
1138	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1139	C₂	C₇×#3536	1	1	yes	characteristic
1140	C₂	C₇×#3542	1	1	yes	characteristic
1141	C₂	C₇×#3543	1	1	yes	characteristic
1142	C₂	C₇×#3561	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂×C₇×#546	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2377	C₂	semidirect
3. C₇×#2376	C₂	semidirect
4. C₇×#2367	C₂	semidirect
5. C₇×#2361	C₂	semidirect
6. C₇×#2360	C₂	semidirect
7. C₇×#2358	C₂	semidirect
8. C₇×#2354	C₂	semidirect
9. C₇×D₄×C₄⋊C₄	C₂	semidirect
10. C₇×#2342	C₂	semidirect
11. C₇×#2341	C₂	semidirect
12. C₇×D₄×C₂²⋊C₄	C₂	semidirect
13. C₇×#2335	C₂	semidirect
14. C₇×#2326	C₂	semidirect
15. C₇×#2324	C₂	semidirect
16. C₇×#2324	C₂	semidirect
17. C₇×#2321	C₂	semidirect
18. C₇×#2319	C₂	semidirect
19. C₇×#2315	C₂	semidirect
20. C₇×#2311	C₂	semidirect
21. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
22. C₂×C₇×#390	C₂	semidirect
23. C₇×#2290	C₂	semidirect
26. C₇×#546	C₄	semidirect
33. C₂×C₄×C₇×Q₈	C₂²	semidirect
34. C₂×C₄×C₇×Q₈	C₂²	semidirect
40. C₂×C₄×C₇×D₄	C₂²	semidirect
41. C₂×C₇×#117	C₂²	semidirect
42. C₂×C₇×#117	C₂²	semidirect
44. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
50. C₇×#391	C₂²	semidirect
51. C₇×#391	C₂²	semidirect
60. C₇×#390	C₂²	semidirect
61. C₇×#390	C₂²	semidirect
62. C₇×#390	C₂²	semidirect
63. C₇×#389	C₂²	semidirect
64. C₇×#389	C₂²	semidirect
65. C₇×#389	C₂²	semidirect
66. C₇×#389	C₂²	semidirect
67. C₇×#388	C₂²	semidirect
68. C₇×#388	C₂²	semidirect
69. C₇×#388	C₂²	semidirect
70. C₇×#388	C₂²	semidirect
71. C₇×#388	C₂²	semidirect
72. C₇×#388	C₂²	semidirect
73. C₇×#388	C₂²	semidirect
74. C₇×#388	C₂²	semidirect
75. C₇×#388	C₂²	semidirect
76. C₇×#388	C₂²	semidirect
77. C₇×#388	C₂²	semidirect
78. C₇×#388	C₂²	semidirect
79. C₇×#387	C₂²	semidirect
80. C₇×#387	C₂²	semidirect
81. C₇×#387	C₂²	semidirect
82. C₇×#387	C₂²	semidirect
87. C₇×#386	C₂²	semidirect
88. C₇×#386	C₂²	semidirect
89. C₇×#386	C₂²	semidirect
90. C₇×#386	C₂²	semidirect
96. C₇×#385	C₂²	semidirect
97. C₇×#385	C₂²	semidirect
98. C₇×#385	C₂²	semidirect
99. C₇×#385	C₂²	semidirect
100. C₇×#385	C₂²	semidirect
101. C₇×#385	C₂²	semidirect
102. C₇×#384	C₂²	semidirect
103. C₇×#381	C₂²	semidirect
105. C₇×#380	C₂²	semidirect
106. C₇×#380	C₂²	semidirect
107. C₇×#380	C₂²	semidirect
108. C₇×#380	C₂²	semidirect
109. C₇×#380	C₂²	semidirect
110. C₇×#380	C₂²	semidirect
112. C₄×C₇×C₄⋊C₄	C₂²	semidirect
113. C₄×C₇×C₄⋊C₄	C₂²	semidirect
114. C₄×C₇×C₄⋊C₄	C₂²	semidirect
115. C₄×C₇×C₄⋊C₄	C₂²	semidirect
116. C₄×C₇×C₄⋊C₄	C₂²	semidirect
120. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
121. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
122. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
123. C₇×#376	C₂²	semidirect
124. #34476	C₇	direct (N × H)
128. C₂×C₇×#41	C₂×C₄	semidirect
132. C₂²×C₇×D₄	C₂×C₄	semidirect
149. C₇×#124	C₂×C₄	semidirect
150. C₇×#123	C₂×C₄	semidirect
151. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
152. C₇×#121	C₂×C₄	semidirect
153. C₇×#121	C₂×C₄	semidirect
154. C₇×#120	C₂×C₄	semidirect
161. C₄×C₇×D₄	C₂×C₄	semidirect
162. C₄×C₇×D₄	C₂×C₄	semidirect
189. C₂×C₇×C₂²⋊C₄	C₂×C₄	semidirect
254. #2377	C₂×C₇	semidirect
255. #2376	C₂×C₇	semidirect
256. #2367	C₂×C₇	semidirect
257. #2361	C₂×C₇	semidirect
258. #2360	C₂×C₇	semidirect
259. #2358	C₂×C₇	semidirect
260. #2354	C₂×C₇	semidirect
261. D₄×C₄⋊C₄	C₂×C₇	semidirect
262. #2342	C₂×C₇	semidirect
263. #2341	C₂×C₇	semidirect
264. D₄×C₂²⋊C₄	C₂×C₇	semidirect
265. #2335	C₂×C₇	semidirect
266. #2326	C₂×C₇	semidirect
267. #2324	C₂×C₇	semidirect
268. #2324	C₂×C₇	semidirect
269. #2321	C₂×C₇	semidirect
270. #2319	C₂×C₇	semidirect
271. #2315	C₂×C₇	semidirect
272. #2311	C₂×C₇	semidirect
273. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
274. C₂×#390	C₂×C₇	semidirect
275. #2290	C₂×C₇	semidirect
421. #546	C₄×C₇	semidirect
428. C₂×C₄×Q₈	C₂²×C₇	semidirect
429. C₂×C₄×Q₈	C₂²×C₇	semidirect
435. C₂×C₄×D₄	C₂²×C₇	semidirect
436. C₂×#117	C₂²×C₇	semidirect
437. C₂×#117	C₂²×C₇	semidirect
439. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
445. #391	C₂²×C₇	semidirect
446. #391	C₂²×C₇	semidirect
455. #390	C₂²×C₇	semidirect
456. #390	C₂²×C₇	semidirect
457. #390	C₂²×C₇	semidirect
458. #389	C₂²×C₇	semidirect
459. #389	C₂²×C₇	semidirect
460. #389	C₂²×C₇	semidirect
461. #389	C₂²×C₇	semidirect
462. #388	C₂²×C₇	semidirect
463. #388	C₂²×C₇	semidirect
464. #388	C₂²×C₇	semidirect
465. #388	C₂²×C₇	semidirect
466. #388	C₂²×C₇	semidirect
467. #388	C₂²×C₇	semidirect
468. #388	C₂²×C₇	semidirect
469. #388	C₂²×C₇	semidirect
470. #388	C₂²×C₇	semidirect
471. #388	C₂²×C₇	semidirect
472. #388	C₂²×C₇	semidirect
473. #388	C₂²×C₇	semidirect
474. #387	C₂²×C₇	semidirect
475. #387	C₂²×C₇	semidirect
476. #387	C₂²×C₇	semidirect
477. #387	C₂²×C₇	semidirect
482. #386	C₂²×C₇	semidirect
483. #386	C₂²×C₇	semidirect
484. #386	C₂²×C₇	semidirect
485. #386	C₂²×C₇	semidirect
491. #385	C₂²×C₇	semidirect
492. #385	C₂²×C₇	semidirect
493. #385	C₂²×C₇	semidirect
494. #385	C₂²×C₇	semidirect
495. #385	C₂²×C₇	semidirect
496. #385	C₂²×C₇	semidirect
497. #384	C₂²×C₇	semidirect
498. #381	C₂²×C₇	semidirect
500. #380	C₂²×C₇	semidirect
501. #380	C₂²×C₇	semidirect
502. #380	C₂²×C₇	semidirect
503. #380	C₂²×C₇	semidirect
504. #380	C₂²×C₇	semidirect
505. #380	C₂²×C₇	semidirect
507. C₄×C₄⋊C₄	C₂²×C₇	semidirect
508. C₄×C₄⋊C₄	C₂²×C₇	semidirect
509. C₄×C₄⋊C₄	C₂²×C₇	semidirect
510. C₄×C₄⋊C₄	C₂²×C₇	semidirect
511. C₄×C₄⋊C₄	C₂²×C₇	semidirect
515. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
516. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
517. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
518. #376	C₂²×C₇	semidirect
632. C₂×#41	C₂×C₄×C₇	semidirect
636. C₂²×D₄	C₂×C₄×C₇	semidirect
653. #124	C₂×C₄×C₇	semidirect
654. #123	C₂×C₄×C₇	semidirect
655. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
656. #121	C₂×C₄×C₇	semidirect
657. #121	C₂×C₄×C₇	semidirect
658. #120	C₂×C₄×C₇	semidirect
665. C₄×D₄	C₂×C₄×C₇	semidirect
666. C₄×D₄	C₂×C₄×C₇	semidirect
693. C₂×C₂²⋊C₄	C₂×C₄×C₇	semidirect
1076. C₇	#34476	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#546	2
C₇×#2377	2
C₇×#2376	2
C₇×#2367	2
C₇×#2361	2
C₇×#2360	2
C₇×#2358	2
C₇×#2354	2
C₇×D₄×C₄⋊C₄	2
C₇×#2342	2
C₇×#2341	2
C₇×D₄×C₂²⋊C₄	2
C₇×#2335	2
C₇×#2326	2
C₇×#2324	2
C₇×#2321	2
C₇×#2319	2
C₇×#2315	2
C₇×#2311	2
C₄×C₇×C₂²⋊Q₈	2
C₂×C₇×#390	2
C₇×#2290	2
#34476	7

Subgroups — C7×#34476 #13211692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34476 #13211692