Subgroups — C₇×#34902 #13212118

Order 1792.

1768 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2596	C₂	1	2	yes	maximal, complemented
2	C₇×#2594	C₂	1	2	yes	maximal, complemented
3	C₇×#2592	C₂	1	1	yes	maximal, characteristic
4	C₇×#2581	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2570	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2545	C₂	1	1	yes	maximal, characteristic
7	C₇×#2525	C₂	1	2	yes	maximal, complemented
8	C₇×#2514	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2512	C₂	1	1	yes	maximal, characteristic
10	C₇×#2469	C₂	1	2	yes	maximal, complemented
11	C₇×#2448	C₂	1	1	yes	maximal, characteristic
12	C₇×#2446	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2401	C₂	1	2	yes	maximal, complemented
14	C₇×#2396	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×#126	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×#124	C₂	1	1	yes	maximal, characteristic
18	C₄×C₇×#124	C₂	1	1	yes	maximal, characteristic
19	C₇×#2298	C₂	1	2	yes	maximal, complemented
20	C₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2293	C₂	1	1	yes	maximal, characteristic
22	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#126	C₂²	1	2	yes	—
26	C₂×C₇×#124	C₂²	1	1	yes	characteristic
27	C₂×C₇×#124	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₇×#117	C₂²	1	2	yes	—
37	C₇×#401	C₂²	1	2	yes	—
38	C₇×#400	C₂²	1	2	yes	—
39	C₇×#400	C₂²	1	2	yes	—
40	C₇×#400	C₂²	1	2	yes	—
41	C₇×#400	C₂²	1	2	yes	—
42	C₇×#399	C₂²	1	2	yes	—
43	C₇×#398	C₂²	1	2	yes	—
44	C₇×#398	C₂²	1	2	yes	—
45	C₇×#397	C₂²	1	2	yes	—
46	C₇×#397	C₂²	1	2	yes	—
47	C₇×#397	C₂²	1	2	yes	—
48	C₇×#396	C₂²	1	2	yes	—
49	C₇×#396	C₂²	1	2	yes	—
50	C₇×#396	C₂²	1	2	yes	—
51	C₇×#395	C₂²	1	2	yes	—
52	C₇×#393	C₂²	1	2	yes	—
53	C₇×#391	C₂²	1	1	yes	characteristic
54	C₇×#391	C₂²	1	1	yes	characteristic
55	C₇×#391	C₂²	1	1	yes	characteristic
56	C₇×#391	C₂²	1	1	yes	characteristic
57	C₇×#391	C₂²	1	1	yes	characteristic
58	C₇×#391	C₂²	1	1	yes	characteristic
59	C₇×#390	C₂²	1	1	yes	characteristic
60	C₇×#390	C₂²	1	1	yes	characteristic
61	C₇×#390	C₂²	1	1	yes	characteristic
62	C₇×#390	C₂²	1	1	yes	characteristic
63	C₇×#389	C₂²	1	1	yes	characteristic
64	C₇×#389	C₂²	1	1	yes	characteristic
65	C₇×#389	C₂²	1	2	yes	—
66	C₇×#389	C₂²	1	1	yes	characteristic
67	C₇×#389	C₂²	1	1	yes	characteristic
68	C₇×#389	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	—
75	C₇×#388	C₂²	1	2	yes	—
76	C₇×#388	C₂²	1	2	yes	—
77	C₇×#388	C₂²	1	2	yes	—
78	C₇×#388	C₂²	1	2	yes	—
79	C₇×#388	C₂²	1	2	yes	—
80	C₇×#388	C₂²	1	2	yes	—
81	C₇×#388	C₂²	1	2	yes	—
82	C₇×#387	C₂²	1	2	yes	—
83	C₇×#387	C₂²	1	2	yes	—
84	C₇×#387	C₂²	1	2	yes	—
85	C₇×#387	C₂²	1	2	yes	—
86	C₇×#387	C₂²	1	2	yes	—
87	C₇×#387	C₂²	1	2	yes	—
88	C₇×#387	C₂²	1	2	yes	—
89	C₇×#387	C₂²	1	2	yes	—
90	C₇×#387	C₂²	1	2	yes	—
91	C₇×#384	C₂²	1	1	yes	characteristic
92	C₇×#383	C₂²	1	2	yes	—
93	C₇×#382	C₂²	1	1	yes	characteristic
94	C₇×#382	C₂²	1	1	yes	characteristic
95	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
97	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
100	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
103	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
112	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
115	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₇×#376	C₂²	1	2	yes	—
119	C₄³×C₇	C₂²	1	1	yes	characteristic
120	C₄³×C₇	C₂²	1	1	yes	characteristic
121	C₄³×C₇	C₂²	1	1	yes	characteristic
122	C₄³×C₇	C₂²	1	2	yes	—
123	#34902	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
125	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
127	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₇	C₂³	1	2	yes	—
129	C₇×C₄⋊Q₈	—	2	4	no	—
130	C₇×#126	—	2	8	no	—
131	C₇×#124	—	2	4	no	—
132	C₇×#124	—	2	4	no	—
133	C₄×C₇×Q₈	—	2	4	no	—
134	C₄×C₇×Q₈	—	2	4	no	—
135	C₄×C₇×Q₈	—	2	4	no	—
136	C₄×C₇×Q₈	—	2	4	no	—
137	C₄×C₇×Q₈	—	2	4	no	—
138	C₄×C₇×Q₈	—	2	4	no	—
139	C₄×C₇×Q₈	—	2	4	no	—
140	C₄×C₇×D₄	—	2	4	no	—
141	C₇×#117	—	2	8	no	—
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	1	yes	characteristic
145	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
186	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₇	C₂³	1	2	yes	—
189	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇	C₂³	1	2	yes	—
195	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇	C₂³	1	2	yes	—
199	C₂×C₄²×C₇	C₂³	1	2	yes	—
200	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
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	C₇×#95	C₂³	1	2	yes	—
212	C₇×#95	C₂³	1	2	yes	—
213	C₇×#95	C₂³	1	2	yes	—
214	C₇×#95	C₂³	1	2	yes	—
215	C₇×#95	C₂³	1	2	yes	—
216	C₇×#95	C₂³	1	2	yes	—
217	C₇×#95	C₂³	1	2	yes	—
218	C₇×#95	C₂³	1	2	yes	—
219	C₇×#95	C₂³	1	2	yes	—
220	C₇×#95	C₂³	1	2	yes	—
221	C₇×#95	C₂³	1	1	yes	characteristic
222	C₇×#95	C₂³	1	1	yes	characteristic
223	C₇×#95	C₂³	1	1	yes	characteristic
224	C₇×#95	C₂³	1	2	yes	—
225	C₇×#95	C₂³	1	1	yes	characteristic
226	C₇×#95	C₂³	1	2	yes	—
227	C₇×#95	C₂³	1	2	yes	—
228	C₇×#95	C₂³	1	1	yes	characteristic
229	C₇×#95	C₂³	1	1	yes	characteristic
230	C₇×#95	C₂³	1	2	yes	—
231	C₇×#95	C₂³	1	2	yes	—
232	C₇×#95	C₂³	1	2	yes	—
233	C₇×#95	C₂³	1	2	yes	—
234	C₇×#95	C₂³	1	2	yes	—
235	C₇×#95	C₂³	1	2	yes	—
236	#2596	C₂×C₇	1	2	yes	complemented
237	#2594	C₂×C₇	1	2	yes	complemented
238	#2592	C₂×C₇	1	1	yes	characteristic
239	#2581	C₂×C₇	1	1	yes	characteristic, complemented
240	#2570	C₂×C₇	1	1	yes	characteristic, complemented
241	#2545	C₂×C₇	1	1	yes	characteristic
242	#2525	C₂×C₇	1	2	yes	complemented
243	#2514	C₂×C₇	1	1	yes	characteristic, complemented
244	#2512	C₂×C₇	1	1	yes	characteristic
245	#2469	C₂×C₇	1	2	yes	complemented
246	#2448	C₂×C₇	1	1	yes	characteristic
247	#2446	C₂×C₇	1	1	yes	characteristic, complemented
248	#2401	C₂×C₇	1	2	yes	complemented
249	#2396	C₂×C₇	1	2	yes	complemented
250	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
251	C₄×#126	C₂×C₇	1	2	yes	complemented
252	C₄×#124	C₂×C₇	1	1	yes	characteristic
253	C₄×#124	C₂×C₇	1	1	yes	characteristic
254	#2298	C₂×C₇	1	2	yes	complemented
255	#2295	C₂×C₇	1	1	yes	characteristic, complemented
256	#2293	C₂×C₇	1	1	yes	characteristic
257	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
258	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
259	C₂⁴×C₇	C₂⁴	1	2	yes	—
260	C₂×C₇×Q₈	—	2	2	no	—
261	C₂×C₇×Q₈	—	2	2	no	—
262	C₂×C₇×Q₈	—	2	2	no	—
263	C₂×C₇×Q₈	—	2	2	no	—
264	C₂×C₇×Q₈	—	2	2	no	—
265	C₂×C₇×Q₈	—	2	2	no	—
266	C₂×C₇×Q₈	—	2	2	no	—
267	C₂×C₇×Q₈	—	2	2	no	—
268	C₂×C₇×Q₈	#41	1	4	yes	—
269	C₂×C₇×D₄	—	2	2	no	—
270	C₂×C₇×D₄	—	2	2	no	—
271	C₂×C₇×D₄	—	2	2	no	—
272	C₂²×C₄×C₇	—	2	4	no	—
273	C₂²×C₄×C₇	—	2	4	no	—
274	C₂²×C₄×C₇	—	2	4	no	—
275	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
285	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	C₇×C₄⋊C₄	—	2	4	no	—
298	C₇×C₄⋊C₄	—	2	4	no	—
299	C₇×C₄⋊C₄	—	2	2	no	—
300	C₇×C₄⋊C₄	—	2	2	no	—
301	C₇×C₄⋊C₄	—	2	2	no	—
302	C₇×C₄⋊C₄	—	2	2	no	—
303	C₇×C₄⋊C₄	—	2	2	no	—
304	C₇×C₄⋊C₄	—	2	4	no	—
305	C₇×C₄⋊C₄	—	2	2	no	—
306	C₇×C₄⋊C₄	—	2	2	no	—
307	C₇×C₄⋊C₄	—	2	4	no	—
308	C₇×C₄⋊C₄	—	2	4	no	—
309	C₇×C₄⋊C₄	—	2	2	no	—
310	C₇×C₄⋊C₄	—	2	2	no	—
311	C₇×C₄⋊C₄	—	2	2	no	—
312	C₇×C₄⋊C₄	—	2	2	no	—
313	C₇×C₄⋊C₄	—	2	2	no	—
314	C₇×C₄⋊C₄	—	2	2	no	—
315	C₇×C₄⋊C₄	—	2	4	no	—
316	C₇×C₄⋊C₄	—	2	4	no	—
317	C₇×C₄⋊C₄	—	2	4	no	—
318	C₇×C₄⋊C₄	—	2	4	no	—
319	C₇×C₄⋊C₄	—	2	4	no	—
320	C₇×C₄⋊C₄	—	4	2	no	—
321	C₇×C₄⋊C₄	—	4	2	no	—
322	C₇×C₄⋊C₄	#41	1	4	yes	—
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	—	2	4	no	—
329	C₇×C₂²⋊C₄	—	2	4	no	—
330	C₇×C₂²⋊C₄	—	2	4	no	—
331	C₇×C₂²⋊C₄	—	2	4	no	—
332	C₇×C₂²⋊C₄	—	2	4	no	—
333	C₇×C₂²⋊C₄	—	4	2	no	—
334	C₇×C₂²⋊C₄	—	4	2	no	—
335	C₇×C₂²⋊C₄	—	4	2	no	—
336	C₄²×C₇	—	2	4	no	—
337	C₄²×C₇	—	2	2	no	—
338	C₄²×C₇	—	2	2	no	—
339	C₄²×C₇	—	2	4	no	—
340	C₄²×C₇	—	2	2	no	—
341	C₄²×C₇	—	2	2	no	—
342	C₄²×C₇	—	2	4	no	—
343	C₄²×C₇	—	2	2	no	—
344	C₄²×C₇	—	2	2	no	—
345	C₄²×C₇	—	2	4	no	—
346	C₄²×C₇	—	2	2	no	—
347	C₄²×C₇	—	2	2	no	—
348	C₄²×C₇	—	2	4	no	—
349	C₄²×C₇	—	2	2	no	—
350	C₄²×C₇	—	2	4	no	—
351	C₄²×C₇	—	2	2	no	—
352	C₄²×C₇	—	2	2	no	—
353	C₄²×C₇	—	2	2	no	—
354	C₄²×C₇	—	2	2	no	—
355	C₄²×C₇	—	4	1	no	—
356	C₄²×C₇	—	4	1	no	—
357	C₄²×C₇	—	4	1	no	—
358	C₄²×C₇	—	4	2	no	—
359	C₄²×C₇	#41	1	4	yes	—
360	C₄²×C₇	#41	1	4	yes	—
361	C₄²×C₇	#41	1	4	yes	—
362	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
363	C₂×#126	C₂²×C₇	1	2	yes	—
364	C₂×#124	C₂²×C₇	1	1	yes	characteristic
365	C₂×#124	C₂²×C₇	1	1	yes	characteristic
366	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
367	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
368	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
369	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
370	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
371	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
372	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
373	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
374	C₂×#117	C₂²×C₇	1	2	yes	—
375	#401	C₂²×C₇	1	2	yes	—
376	#400	C₂²×C₇	1	2	yes	—
377	#400	C₂²×C₇	1	2	yes	—
378	#400	C₂²×C₇	1	2	yes	—
379	#400	C₂²×C₇	1	2	yes	—
380	#399	C₂²×C₇	1	2	yes	—
381	#398	C₂²×C₇	1	2	yes	—
382	#398	C₂²×C₇	1	2	yes	—
383	#397	C₂²×C₇	1	2	yes	—
384	#397	C₂²×C₇	1	2	yes	—
385	#397	C₂²×C₇	1	2	yes	—
386	#396	C₂²×C₇	1	2	yes	—
387	#396	C₂²×C₇	1	2	yes	—
388	#396	C₂²×C₇	1	2	yes	—
389	#395	C₂²×C₇	1	2	yes	—
390	#393	C₂²×C₇	1	2	yes	—
391	#391	C₂²×C₇	1	1	yes	characteristic
392	#391	C₂²×C₇	1	1	yes	characteristic
393	#391	C₂²×C₇	1	1	yes	characteristic
394	#391	C₂²×C₇	1	1	yes	characteristic
395	#391	C₂²×C₇	1	1	yes	characteristic
396	#391	C₂²×C₇	1	1	yes	characteristic
397	#390	C₂²×C₇	1	1	yes	characteristic
398	#390	C₂²×C₇	1	1	yes	characteristic
399	#390	C₂²×C₇	1	1	yes	characteristic
400	#390	C₂²×C₇	1	1	yes	characteristic
401	#389	C₂²×C₇	1	2	yes	—
402	#389	C₂²×C₇	1	2	yes	—
403	#389	C₂²×C₇	1	1	yes	characteristic
404	#389	C₂²×C₇	1	1	yes	characteristic
405	#389	C₂²×C₇	1	1	yes	characteristic
406	#389	C₂²×C₇	1	1	yes	characteristic
407	#388	C₂²×C₇	1	2	yes	—
408	#388	C₂²×C₇	1	2	yes	—
409	#388	C₂²×C₇	1	2	yes	—
410	#388	C₂²×C₇	1	2	yes	—
411	#388	C₂²×C₇	1	2	yes	—
412	#388	C₂²×C₇	1	2	yes	—
413	#388	C₂²×C₇	1	2	yes	—
414	#388	C₂²×C₇	1	2	yes	—
415	#388	C₂²×C₇	1	2	yes	—
416	#388	C₂²×C₇	1	2	yes	—
417	#388	C₂²×C₇	1	2	yes	—
418	#388	C₂²×C₇	1	2	yes	—
419	#388	C₂²×C₇	1	2	yes	—
420	#387	C₂²×C₇	1	2	yes	—
421	#387	C₂²×C₇	1	2	yes	—
422	#387	C₂²×C₇	1	2	yes	—
423	#387	C₂²×C₇	1	2	yes	—
424	#387	C₂²×C₇	1	2	yes	—
425	#387	C₂²×C₇	1	2	yes	—
426	#387	C₂²×C₇	1	2	yes	—
427	#387	C₂²×C₇	1	2	yes	—
428	#387	C₂²×C₇	1	2	yes	—
429	#384	C₂²×C₇	1	1	yes	characteristic
430	#383	C₂²×C₇	1	2	yes	—
431	#382	C₂²×C₇	1	1	yes	characteristic
432	#382	C₂²×C₇	1	1	yes	characteristic
433	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
434	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
435	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
436	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
437	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
441	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
443	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
447	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
450	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
451	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
452	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
453	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
454	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
455	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
456	#376	C₂²×C₇	1	2	yes	—
457	C₄³	C₂²×C₇	1	2	yes	—
458	C₄³	C₂²×C₇	1	1	yes	characteristic
459	C₄³	C₂²×C₇	1	1	yes	characteristic
460	C₄³	C₂²×C₇	1	1	yes	characteristic
461	C₂³×C₇	—	2	2	no	—
462	C₂³×C₇	—	2	2	no	—
463	C₂³×C₇	—	2	2	no	—
464	C₂³×C₇	—	2	2	no	—
465	C₂³×C₇	—	2	2	no	—
466	C₂³×C₇	—	2	2	no	—
467	C₂³×C₇	—	2	2	no	—
468	C₂³×C₇	C₂⁵	1	1	yes	characteristic
469	C₇×Q₈	—	2	8	no	—
470	C₇×Q₈	—	2	8	no	—
471	C₇×Q₈	—	4	4	no	—
472	C₇×D₄	—	4	4	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	2	no	—
478	C₂×C₄×C₇	—	2	2	no	—
479	C₂×C₄×C₇	—	2	1	no	—
480	C₂×C₄×C₇	—	2	1	no	—
481	C₂×C₄×C₇	—	2	1	no	—
482	C₂×C₄×C₇	—	2	1	no	—
483	C₂×C₄×C₇	—	2	1	no	—
484	C₂×C₄×C₇	—	2	1	no	—
485	C₂×C₄×C₇	—	2	1	no	—
486	C₂×C₄×C₇	—	2	1	no	—
487	C₂×C₄×C₇	—	2	1	no	—
488	C₂×C₄×C₇	—	2	1	no	—
489	C₂×C₄×C₇	—	2	1	no	—
490	C₂×C₄×C₇	—	2	1	no	—
491	C₂×C₄×C₇	—	2	1	no	—
492	C₂×C₄×C₇	—	2	1	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	1	no	—
499	C₂×C₄×C₇	—	2	1	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	1	no	—
504	C₂×C₄×C₇	—	2	1	no	—
505	C₂×C₄×C₇	—	2	1	no	—
506	C₂×C₄×C₇	—	2	1	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	—	2	2	no	—
512	C₂×C₄×C₇	—	2	2	no	—
513	C₂×C₄×C₇	—	2	1	no	—
514	C₂×C₄×C₇	—	2	1	no	—
515	C₂×C₄×C₇	—	2	1	no	—
516	C₂×C₄×C₇	—	2	2	no	—
517	C₂×C₄×C₇	—	2	1	no	—
518	C₂×C₄×C₇	—	2	1	no	—
519	C₂×C₄×C₇	—	2	1	no	—
520	C₂×C₄×C₇	—	2	2	no	—
521	C₂×C₄×C₇	—	2	2	no	—
522	C₂×C₄×C₇	—	2	1	no	—
523	C₂×C₄×C₇	—	2	2	no	—
524	C₂×C₄×C₇	—	4	8	no	—
525	C₂×C₄×C₇	C₂×#41	1	2	yes	—
526	C₂×C₄×C₇	C₂×#41	1	2	yes	—
527	C₂×C₄×C₇	C₂×#41	1	2	yes	—
528	C₂×C₄×C₇	C₂×#41	1	4	yes	—
529	C₂×C₄×C₇	C₂×#41	1	2	yes	—
530	C₂×C₄×C₇	C₂×#41	1	2	yes	—
531	C₂×C₄×C₇	C₂×#41	1	2	yes	—
532	C₂×C₄×C₇	C₂×#41	1	2	yes	—
533	C₂×C₄×C₇	C₂×#41	1	2	yes	—
534	C₂×C₄×C₇	C₂×#41	1	2	yes	—
535	C₂×C₄×C₇	C₂×#41	1	2	yes	—
536	C₂×C₄×C₇	C₂×#41	1	2	yes	—
537	C₂×C₄×C₇	C₂×#41	1	2	yes	—
538	C₂×C₄×C₇	C₂×#41	1	2	yes	—
539	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
540	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
541	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
542	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₇	1	2	yes	—
545	C₄⋊Q₈	—	2	4	no	—
546	#126	—	2	8	no	—
547	#124	—	2	4	no	—
548	#124	—	2	4	no	—
549	C₄×Q₈	—	2	4	no	—
550	C₄×Q₈	—	2	4	no	—
551	C₄×Q₈	—	2	4	no	—
552	C₄×Q₈	—	2	4	no	—
553	C₄×Q₈	—	2	4	no	—
554	C₄×Q₈	—	2	4	no	—
555	C₄×Q₈	—	2	4	no	—
556	C₄×D₄	—	2	4	no	—
557	#117	—	2	8	no	—
558	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
597	C₂×C₄²	C₂³×C₇	1	2	yes	—
598	C₂×C₄²	C₂³×C₇	1	2	yes	—
599	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₇	1	2	yes	—
605	C₂×C₄²	C₂³×C₇	1	2	yes	—
606	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₇	1	2	yes	—
610	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₇	1	2	yes	—
612	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₇	1	2	yes	—
619	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
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	#95	C₂³×C₇	1	2	yes	—
629	#95	C₂³×C₇	1	2	yes	—
630	#95	C₂³×C₇	1	2	yes	—
631	#95	C₂³×C₇	1	2	yes	—
632	#95	C₂³×C₇	1	2	yes	—
633	#95	C₂³×C₇	1	2	yes	—
634	#95	C₂³×C₇	1	2	yes	—
635	#95	C₂³×C₇	1	2	yes	—
636	#95	C₂³×C₇	1	2	yes	—
637	#95	C₂³×C₇	1	1	yes	characteristic
638	#95	C₂³×C₇	1	1	yes	characteristic
639	#95	C₂³×C₇	1	1	yes	characteristic
640	#95	C₂³×C₇	1	2	yes	—
641	#95	C₂³×C₇	1	1	yes	characteristic
642	#95	C₂³×C₇	1	2	yes	—
643	#95	C₂³×C₇	1	2	yes	—
644	#95	C₂³×C₇	1	1	yes	characteristic
645	#95	C₂³×C₇	1	1	yes	characteristic
646	#95	C₂³×C₇	1	2	yes	—
647	#95	C₂³×C₇	1	2	yes	—
648	#95	C₂³×C₇	1	2	yes	—
649	#95	C₂³×C₇	1	2	yes	—
650	#95	C₂³×C₇	1	2	yes	—
651	#95	C₂³×C₇	1	2	yes	—
652	C₂²×C₇	—	4	2	no	—
653	C₂²×C₇	—	4	2	no	—
654	C₂²×C₇	—	4	2	no	—
655	C₂²×C₇	—	4	2	no	—
656	C₂²×C₇	—	4	2	no	—
657	C₂²×C₇	—	4	2	no	—
658	C₂²×C₇	—	4	2	no	—
659	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
660	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
661	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
662	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
663	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
664	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
665	C₂²×C₇	#585	1	1	yes	characteristic
666	C₄×C₇	—	2	4	no	—
667	C₄×C₇	—	2	2	no	—
668	C₄×C₇	—	2	2	no	—
669	C₄×C₇	—	2	2	no	—
670	C₄×C₇	—	2	2	no	—
671	C₄×C₇	—	2	2	no	—
672	C₄×C₇	—	2	2	no	—
673	C₄×C₇	—	2	2	no	—
674	C₄×C₇	—	2	2	no	—
675	C₄×C₇	—	4	2	no	—
676	C₄×C₇	—	4	2	no	—
677	C₄×C₇	—	4	1	no	—
678	C₄×C₇	—	4	1	no	—
679	C₄×C₇	—	4	2	no	—
680	C₄×C₇	—	4	1	no	—
681	C₄×C₇	—	4	2	no	—
682	C₄×C₇	—	4	2	no	—
683	C₄×C₇	—	4	1	no	—
684	C₄×C₇	—	4	2	no	—
685	C₄×C₇	—	4	1	no	—
686	C₄×C₇	#529	1	4	yes	—
687	C₄×C₇	#556	1	4	yes	—
688	C₂⁴	C₂⁴×C₇	1	2	yes	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	2	2	no	—
692	C₂×Q₈	—	2	2	no	—
693	C₂×Q₈	—	2	2	no	—
694	C₂×Q₈	—	2	2	no	—
695	C₂×Q₈	—	2	2	no	—
696	C₂×Q₈	—	2	2	no	—
697	C₂×Q₈	C₇×#41	1	4	yes	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
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	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₄⋊C₄	C₇×#41	1	4	yes	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	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	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₄²	—	2	4	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	4	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	4	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	4	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	4	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	4	1	no	—
785	C₄²	—	4	1	no	—
786	C₄²	—	4	1	no	—
787	C₄²	—	4	2	no	—
788	C₄²	C₇×#41	1	4	yes	—
789	C₄²	C₇×#41	1	4	yes	—
790	C₄²	C₇×#41	1	4	yes	—
791	C₂×C₇	—	8	2	no	—
792	C₂×C₇	C₂×#529	1	1	yes	characteristic
793	C₂×C₇	#3444	1	1	yes	characteristic
794	C₂×C₇	#3461	1	1	yes	characteristic
795	C₂×C₇	C₂×#556	1	1	yes	characteristic
796	C₂×C₇	#3480	1	1	yes	characteristic
797	C₂×C₇	#3480	1	1	yes	characteristic
798	C₂×C₇	#3482	1	1	yes	characteristic
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	C₂⁵×C₇	1	1	yes	characteristic
807	Q₈	—	2	8	no	—
808	Q₈	—	2	8	no	—
809	Q₈	—	4	4	no	—
810	D₄	—	4	4	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	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	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	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	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	4	8	no	—
863	C₂×C₄	C₂×C₇×#41	1	2	yes	—
864	C₂×C₄	C₂×C₇×#41	1	2	yes	—
865	C₂×C₄	C₂×C₇×#41	1	2	yes	—
866	C₂×C₄	C₂×C₇×#41	1	4	yes	—
867	C₂×C₄	C₂×C₇×#41	1	2	yes	—
868	C₂×C₄	C₂×C₇×#41	1	2	yes	—
869	C₂×C₄	C₂×C₇×#41	1	2	yes	—
870	C₂×C₄	C₂×C₇×#41	1	2	yes	—
871	C₂×C₄	C₂×C₇×#41	1	2	yes	—
872	C₂×C₄	C₂×C₇×#41	1	2	yes	—
873	C₂×C₄	C₂×C₇×#41	1	2	yes	—
874	C₂×C₄	C₂×C₇×#41	1	2	yes	—
875	C₂×C₄	C₂×C₇×#41	1	2	yes	—
876	C₂×C₄	C₂×C₇×#41	1	2	yes	—
877	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
878	C₇	#34902	1	1	yes	characteristic, direct product factor, Sylow
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
887	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
888	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
889	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
890	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
891	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
892	C₂²	C₇×#585	1	1	yes	characteristic
893	C₄	—	2	4	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	1	no	—
913	C₄	C₇×#529	1	4	yes	—
914	C₄	C₇×#556	1	4	yes	—
915	C₂	—	8	2	no	—
916	C₂	C₂×C₇×#529	1	1	yes	characteristic
917	C₂	C₇×#3444	1	1	yes	characteristic
918	C₂	C₇×#3461	1	1	yes	characteristic
919	C₂	C₂×C₇×#556	1	1	yes	characteristic
920	C₂	C₇×#3480	1	1	yes	characteristic
921	C₂	C₇×#3480	1	1	yes	characteristic
922	C₂	C₇×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2596	C₂	semidirect
2. C₇×#2594	C₂	semidirect
4. C₇×#2581	C₂	semidirect
5. C₇×#2570	C₂	semidirect
7. C₇×#2525	C₂	semidirect
8. C₇×#2514	C₂	semidirect
10. C₇×#2469	C₂	semidirect
12. C₇×#2446	C₂	semidirect
13. C₇×#2401	C₂	semidirect
14. C₇×#2396	C₂	semidirect
15. C₄×C₇×C₄⋊Q₈	C₂	semidirect
16. C₄×C₇×#126	C₂	semidirect
19. C₇×#2298	C₂	semidirect
20. C₇×#2295	C₂	semidirect
22. C₄²×C₇×Q₈	C₂	semidirect
23. C₄²×C₇×Q₈	C₂	semidirect
123. #34902	C₇	direct (N × H)
236. #2596	C₂×C₇	semidirect
237. #2594	C₂×C₇	semidirect
239. #2581	C₂×C₇	semidirect
240. #2570	C₂×C₇	semidirect
242. #2525	C₂×C₇	semidirect
243. #2514	C₂×C₇	semidirect
245. #2469	C₂×C₇	semidirect
247. #2446	C₂×C₇	semidirect
248. #2401	C₂×C₇	semidirect
249. #2396	C₂×C₇	semidirect
250. C₄×C₄⋊Q₈	C₂×C₇	semidirect
251. C₄×#126	C₂×C₇	semidirect
254. #2298	C₂×C₇	semidirect
255. #2295	C₂×C₇	semidirect
257. C₄²×Q₈	C₂×C₇	semidirect
258. C₄²×Q₈	C₂×C₇	semidirect
878. C₇	#34902	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×#2596	2
C₇×#2594	2
C₇×#2592	2
C₇×#2581	2
C₇×#2570	2
C₇×#2545	2
C₇×#2525	2
C₇×#2514	2
C₇×#2512	2
C₇×#2469	2
C₇×#2448	2
C₇×#2446	2
C₇×#2401	2
C₇×#2396	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×#126	2
C₄×C₇×#124	2
C₇×#2298	2
C₇×#2295	2
C₇×#2293	2
C₄²×C₇×Q₈	2
#34902	7

Subgroups — C7×#34902 #13212118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34902 #13212118