Subgroups — C₇×#34700 #13211916

Order 1792.

2992 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2480	C₂	1	2	yes	maximal, complemented
4	C₇×#2468	C₂	1	2	yes	maximal, complemented
5	C₇×#2457	C₂	1	2	yes	maximal, complemented
6	C₇×#2454	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2447	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2442	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2435	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2427	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2420	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2418	C₂	1	2	yes	maximal, complemented
13	C₇×#2417	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2408	C₂	1	1	yes	maximal, characteristic
15	C₇×#2395	C₂	1	2	yes	maximal, complemented
16	C₇×#2392	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₇×#120	C₂	1	2	yes	maximal, complemented
21	C₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2280	C₂	1	2	yes	maximal, complemented
23	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
26	C₇×#529	—	2	8	no	—
27	C₂×C₇×#126	C₂²	1	2	yes	complemented
28	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₇×#124	C₂²	1	1	yes	characteristic
30	C₂×C₇×#124	C₂²	1	1	yes	characteristic
31	C₂×C₇×#123	C₂²	1	2	yes	complemented
32	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₇×#121	C₂²	1	1	yes	characteristic
35	C₂×C₇×#121	C₂²	1	1	yes	characteristic
36	C₂×C₇×#120	C₂²	1	2	yes	—
37	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×C₇×D₄	—	2	8	no	—
39	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
40	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
45	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
49	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
50	C₂×C₇×#117	C₂²	1	2	yes	complemented
51	C₂×C₇×#117	C₂²	1	2	yes	complemented
52	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
54	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
55	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
56	C₇×#400	C₂²	1	2	yes	complemented
57	C₇×#399	C₂²	1	2	yes	complemented
58	C₇×#398	C₂²	1	2	yes	complemented
59	C₇×#398	C₂²	1	2	yes	complemented
60	C₇×#397	C₂²	1	2	yes	complemented
61	C₇×#397	C₂²	1	2	yes	complemented
62	C₇×#397	C₂²	1	2	yes	complemented
63	C₇×#397	C₂²	1	2	yes	complemented
64	C₇×#396	C₂²	1	2	yes	complemented
65	C₇×#396	C₂²	1	2	yes	complemented
66	C₇×#394	C₂²	1	2	yes	—
67	C₇×#394	C₂²	1	2	yes	—
68	C₇×#394	C₂²	1	2	yes	—
69	C₇×#394	C₂²	1	2	yes	complemented
70	C₇×#394	C₂²	1	2	yes	complemented
71	C₇×#392	C₂²	1	2	yes	—
72	C₇×#391	C₂²	1	1	yes	characteristic, complemented
73	C₇×#391	C₂²	1	1	yes	characteristic, complemented
74	C₇×#390	C₂²	1	1	yes	characteristic
75	C₇×#390	C₂²	1	1	yes	characteristic
76	C₇×#390	C₂²	1	1	yes	characteristic
77	C₇×#390	C₂²	1	1	yes	characteristic
78	C₇×#389	C₂²	1	1	yes	characteristic, complemented
79	C₇×#389	C₂²	1	1	yes	characteristic, complemented
80	C₇×#389	C₂²	1	1	yes	characteristic, complemented
81	C₇×#389	C₂²	1	1	yes	characteristic, complemented
82	C₇×#388	C₂²	1	2	yes	complemented
83	C₇×#388	C₂²	1	2	yes	complemented
84	C₇×#388	C₂²	1	2	yes	complemented
85	C₇×#388	C₂²	1	2	yes	complemented
86	C₇×#388	C₂²	1	2	yes	complemented
87	C₇×#387	C₂²	1	2	yes	complemented
88	C₇×#386	C₂²	1	2	yes	—
89	C₇×#386	C₂²	1	2	yes	complemented
90	C₇×#386	C₂²	1	2	yes	complemented
91	C₇×#386	C₂²	1	2	yes	complemented
92	C₇×#385	C₂²	1	2	yes	—
93	C₇×#385	C₂²	1	2	yes	—
94	C₇×#385	C₂²	1	2	yes	complemented
95	C₇×#385	C₂²	1	2	yes	complemented
96	C₇×#382	C₂²	1	1	yes	characteristic, complemented
97	C₇×#381	C₂²	1	2	yes	complemented
98	C₇×#381	C₂²	1	2	yes	complemented
99	C₇×#380	C₂²	1	1	yes	characteristic
100	C₇×#380	C₂²	1	2	yes	—
101	C₇×#380	C₂²	1	2	yes	—
102	C₇×#380	C₂²	1	1	yes	characteristic, complemented
103	C₇×#380	C₂²	1	2	yes	complemented
104	C₇×#380	C₂²	1	2	yes	complemented
105	C₇×#379	C₂²	1	2	yes	—
106	C₇×#379	C₂²	1	2	yes	—
107	C₇×#379	C₂²	1	2	yes	—
108	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
109	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
110	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
119	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
120	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
124	C₄³×C₇	C₂²	1	1	yes	characteristic, complemented
125	#34700	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁵×C₇	C₂³	1	2	yes	—
127	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
128	C₂²×C₇×D₄	—	2	4	no	—
129	C₂²×C₇×D₄	—	2	4	no	—
130	C₂²×C₇×D₄	—	2	4	no	—
131	C₂²×C₇×D₄	C₂³	1	2	yes	—
132	C₂²×C₇×D₄	C₂³	1	2	yes	—
133	C₂²×C₇×D₄	C₂³	1	2	yes	—
134	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
135	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
136	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₇	—	2	8	no	—
138	C₂³×C₄×C₇	—	2	8	no	—
139	C₂³×C₄×C₇	—	4	4	no	—
140	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
151	C₇×#126	—	2	8	no	—
152	C₇×#125	—	2	4	no	—
153	C₇×#124	—	2	4	no	—
154	C₇×#124	—	2	4	no	—
155	C₇×#123	—	2	8	no	—
156	C₇×C₂²⋊Q₈	—	2	4	no	—
157	C₇×C₂²⋊Q₈	—	2	4	no	—
158	C₇×#121	—	2	4	no	—
159	C₇×#121	—	2	4	no	—
160	C₇×#120	—	2	8	no	—
161	C₄×C₇×Q₈	—	2	4	no	—
162	C₄×C₇×D₄	—	2	4	no	—
163	C₄×C₇×D₄	—	2	4	no	—
164	C₄×C₇×D₄	—	2	8	no	—
165	C₄×C₇×D₄	—	2	8	no	—
166	C₄×C₇×D₄	—	2	4	no	—
167	C₄×C₇×D₄	—	2	4	no	—
168	C₄×C₇×D₄	—	2	4	no	—
169	C₄×C₇×D₄	—	2	8	no	—
170	C₄×C₇×D₄	—	2	4	no	—
171	C₄×C₇×D₄	—	4	4	no	—
172	C₄×C₇×D₄	D₄	1	8	yes	complemented
173	C₇×#117	—	2	8	no	—
174	C₇×#117	—	4	4	no	—
175	C₂×C₇×C₄⋊C₄	—	2	4	no	—
176	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
181	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
195	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
199	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
204	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
208	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
219	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₄²×C₇	—	2	4	no	—
224	C₂×C₄²×C₇	—	2	4	no	—
225	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₇	C₂³	1	2	yes	—
237	C₂×C₄²×C₇	C₂³	1	2	yes	—
238	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
253	C₇×#95	C₂³	1	2	yes	—
254	C₇×#95	C₂³	1	2	yes	—
255	C₇×#95	C₂³	1	2	yes	—
256	C₇×#95	C₂³	1	2	yes	—
257	C₇×#95	C₂³	1	2	yes	—
258	C₇×#95	C₂³	1	2	yes	—
259	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
260	C₂²×C₄×D₄	C₂×C₇	1	1	yes	characteristic, complemented
261	#2480	C₂×C₇	1	2	yes	complemented
262	#2468	C₂×C₇	1	2	yes	complemented
263	#2457	C₂×C₇	1	2	yes	complemented
264	#2454	C₂×C₇	1	1	yes	characteristic, complemented
265	#2447	C₂×C₇	1	1	yes	characteristic, complemented
266	#2442	C₂×C₇	1	1	yes	characteristic, complemented
267	#2435	C₂×C₇	1	1	yes	characteristic, complemented
268	#2427	C₂×C₇	1	1	yes	characteristic, complemented
269	#2420	C₂×C₇	1	1	yes	characteristic, complemented
270	#2418	C₂×C₇	1	2	yes	complemented
271	#2417	C₂×C₇	1	1	yes	characteristic, complemented
272	#2408	C₂×C₇	1	1	yes	characteristic
273	#2395	C₂×C₇	1	2	yes	complemented
274	#2392	C₂×C₇	1	2	yes	complemented
275	C₄×#124	C₂×C₇	1	1	yes	characteristic, complemented
276	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
277	C₄×#121	C₂×C₇	1	1	yes	characteristic, complemented
278	C₄×#120	C₂×C₇	1	2	yes	complemented
279	#2293	C₂×C₇	1	1	yes	characteristic, complemented
280	#2280	C₂×C₇	1	2	yes	complemented
281	C₄²×D₄	C₂×C₇	1	1	yes	characteristic, complemented
282	C₂⁴×C₇	—	2	4	no	—
283	C₂⁴×C₇	—	2	4	no	—
284	C₂⁴×C₇	—	2	4	no	—
285	C₂⁴×C₇	—	2	4	no	—
286	C₂⁴×C₇	—	2	4	no	—
287	C₂⁴×C₇	—	4	2	no	—
288	C₂⁴×C₇	—	4	2	no	—
289	C₂⁴×C₇	C₂⁴	1	2	yes	—
290	C₂⁴×C₇	C₂⁴	1	2	yes	—
291	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
292	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
293	C₂×C₇×Q₈	—	2	2	no	—
294	C₂×C₇×Q₈	—	2	2	no	—
295	C₂×C₇×Q₈	—	2	2	no	—
296	C₂×C₇×D₄	—	2	32	no	—
297	C₂×C₇×D₄	—	2	4	no	—
298	C₂×C₇×D₄	—	2	2	no	—
299	C₂×C₇×D₄	—	2	2	no	—
300	C₂×C₇×D₄	—	2	4	no	—
301	C₂×C₇×D₄	—	2	4	no	—
302	C₂×C₇×D₄	—	2	4	no	—
303	C₂×C₇×D₄	—	2	4	no	—
304	C₂×C₇×D₄	—	2	4	no	—
305	C₂×C₇×D₄	—	2	2	no	—
306	C₂×C₇×D₄	—	2	4	no	—
307	C₂×C₇×D₄	—	2	2	no	—
308	C₂×C₇×D₄	—	2	2	no	—
309	C₂×C₇×D₄	—	2	2	no	—
310	C₂×C₇×D₄	—	4	2	no	—
311	C₂×C₇×D₄	—	4	2	no	—
312	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
313	C₂×C₇×D₄	#41	1	4	yes	—
314	C₂×C₇×D₄	#41	1	4	yes	—
315	C₂²×C₄×C₇	—	2	2	no	—
316	C₂²×C₄×C₇	—	2	2	no	—
317	C₂²×C₄×C₇	—	2	4	no	—
318	C₂²×C₄×C₇	—	2	2	no	—
319	C₂²×C₄×C₇	—	2	4	no	—
320	C₂²×C₄×C₇	—	2	2	no	—
321	C₂²×C₄×C₇	—	2	4	no	—
322	C₂²×C₄×C₇	—	2	2	no	—
323	C₂²×C₄×C₇	—	2	2	no	—
324	C₂²×C₄×C₇	—	2	4	no	—
325	C₂²×C₄×C₇	—	2	2	no	—
326	C₂²×C₄×C₇	—	2	2	no	—
327	C₂²×C₄×C₇	—	2	2	no	—
328	C₂²×C₄×C₇	—	2	2	no	—
329	C₂²×C₄×C₇	—	2	4	no	—
330	C₂²×C₄×C₇	—	2	4	no	—
331	C₂²×C₄×C₇	—	2	4	no	—
332	C₂²×C₄×C₇	—	2	2	no	—
333	C₂²×C₄×C₇	—	2	2	no	—
334	C₂²×C₄×C₇	—	2	2	no	—
335	C₂²×C₄×C₇	—	2	4	no	—
336	C₂²×C₄×C₇	—	2	4	no	—
337	C₂²×C₄×C₇	—	2	4	no	—
338	C₂²×C₄×C₇	—	2	2	no	—
339	C₂²×C₄×C₇	—	2	4	no	—
340	C₂²×C₄×C₇	—	4	2	no	—
341	C₂²×C₄×C₇	—	4	2	no	—
342	C₂²×C₄×C₇	—	4	2	no	—
343	C₂²×C₄×C₇	—	4	1	no	—
344	C₂²×C₄×C₇	—	4	1	no	—
345	C₂²×C₄×C₇	—	4	32	no	—
346	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
347	C₂²×C₄×C₇	#41	1	4	yes	—
348	C₂²×C₄×C₇	#41	1	4	yes	—
349	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
358	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
359	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
360	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
368	C₇×C₄⋊C₄	—	2	4	no	—
369	C₇×C₄⋊C₄	—	2	2	no	—
370	C₇×C₄⋊C₄	—	2	4	no	—
371	C₇×C₄⋊C₄	—	2	4	no	—
372	C₇×C₄⋊C₄	—	2	4	no	—
373	C₇×C₄⋊C₄	—	2	2	no	—
374	C₇×C₄⋊C₄	—	2	4	no	—
375	C₇×C₄⋊C₄	—	2	2	no	—
376	C₇×C₄⋊C₄	—	2	2	no	—
377	C₇×C₄⋊C₄	—	2	2	no	—
378	C₇×C₄⋊C₄	—	2	2	no	—
379	C₇×C₄⋊C₄	—	2	2	no	—
380	C₇×C₄⋊C₄	—	2	4	no	—
381	C₇×C₄⋊C₄	—	4	2	no	—
382	C₇×C₄⋊C₄	—	4	2	no	—
383	C₇×C₄⋊C₄	—	4	2	no	—
384	C₇×C₄⋊C₄	—	4	2	no	—
385	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
386	C₇×C₂²⋊C₄	—	2	4	no	—
387	C₇×C₂²⋊C₄	—	2	4	no	—
388	C₇×C₂²⋊C₄	—	2	4	no	—
389	C₇×C₂²⋊C₄	—	2	4	no	—
390	C₇×C₂²⋊C₄	—	2	2	no	—
391	C₇×C₂²⋊C₄	—	2	2	no	—
392	C₇×C₂²⋊C₄	—	2	2	no	—
393	C₇×C₂²⋊C₄	—	2	2	no	—
394	C₇×C₂²⋊C₄	—	2	4	no	—
395	C₇×C₂²⋊C₄	—	2	4	no	—
396	C₇×C₂²⋊C₄	—	2	4	no	—
397	C₇×C₂²⋊C₄	—	2	4	no	—
398	C₇×C₂²⋊C₄	—	2	4	no	—
399	C₇×C₂²⋊C₄	—	2	4	no	—
400	C₇×C₂²⋊C₄	—	2	4	no	—
401	C₇×C₂²⋊C₄	—	2	4	no	—
402	C₇×C₂²⋊C₄	—	2	2	no	—
403	C₇×C₂²⋊C₄	—	2	2	no	—
404	C₇×C₂²⋊C₄	—	2	4	no	—
405	C₇×C₂²⋊C₄	—	2	4	no	—
406	C₇×C₂²⋊C₄	—	4	2	no	—
407	C₇×C₂²⋊C₄	—	4	2	no	—
408	C₇×C₂²⋊C₄	—	4	2	no	—
409	C₇×C₂²⋊C₄	—	4	2	no	—
410	C₇×C₂²⋊C₄	—	4	2	no	—
411	C₇×C₂²⋊C₄	—	4	2	no	—
412	C₇×C₂²⋊C₄	—	4	2	no	—
413	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
414	C₄²×C₇	—	2	2	no	—
415	C₄²×C₇	—	2	2	no	—
416	C₄²×C₇	—	2	2	no	—
417	C₄²×C₇	—	2	2	no	—
418	C₄²×C₇	—	2	2	no	—
419	C₄²×C₇	—	2	2	no	—
420	C₄²×C₇	—	2	4	no	—
421	C₄²×C₇	—	2	2	no	—
422	C₄²×C₇	—	2	2	no	—
423	C₄²×C₇	—	2	2	no	—
424	C₄²×C₇	—	2	2	no	—
425	C₄²×C₇	—	2	2	no	—
426	C₄²×C₇	—	2	4	no	—
427	C₄²×C₇	—	4	1	no	—
428	C₄²×C₇	C₂×D₄	1	4	yes	—
429	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
430	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
431	#529	—	2	8	no	—
432	C₂×#126	C₂²×C₇	1	2	yes	complemented
433	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
434	C₂×#124	C₂²×C₇	1	1	yes	characteristic
435	C₂×#124	C₂²×C₇	1	1	yes	characteristic
436	C₂×#123	C₂²×C₇	1	2	yes	complemented
437	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
438	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
439	C₂×#121	C₂²×C₇	1	1	yes	characteristic
440	C₂×#121	C₂²×C₇	1	1	yes	characteristic
441	C₂×#120	C₂²×C₇	1	2	yes	—
442	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
443	C₂×C₄×D₄	—	2	8	no	—
444	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
445	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
446	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
447	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
448	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
449	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
450	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
451	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
452	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
454	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
455	C₂×#117	C₂²×C₇	1	2	yes	complemented
456	C₂×#117	C₂²×C₇	1	2	yes	complemented
457	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
458	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
459	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
460	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
461	#400	C₂²×C₇	1	2	yes	complemented
462	#399	C₂²×C₇	1	2	yes	complemented
463	#398	C₂²×C₇	1	2	yes	complemented
464	#398	C₂²×C₇	1	2	yes	complemented
465	#397	C₂²×C₇	1	2	yes	complemented
466	#397	C₂²×C₇	1	2	yes	complemented
467	#397	C₂²×C₇	1	2	yes	complemented
468	#397	C₂²×C₇	1	2	yes	complemented
469	#396	C₂²×C₇	1	2	yes	complemented
470	#396	C₂²×C₇	1	2	yes	complemented
471	#394	C₂²×C₇	1	2	yes	—
472	#394	C₂²×C₇	1	2	yes	—
473	#394	C₂²×C₇	1	2	yes	—
474	#394	C₂²×C₇	1	2	yes	complemented
475	#394	C₂²×C₇	1	2	yes	complemented
476	#392	C₂²×C₇	1	2	yes	—
477	#391	C₂²×C₇	1	1	yes	characteristic, complemented
478	#391	C₂²×C₇	1	1	yes	characteristic, complemented
479	#390	C₂²×C₇	1	1	yes	characteristic
480	#390	C₂²×C₇	1	1	yes	characteristic
481	#390	C₂²×C₇	1	1	yes	characteristic
482	#390	C₂²×C₇	1	1	yes	characteristic
483	#389	C₂²×C₇	1	1	yes	characteristic, complemented
484	#389	C₂²×C₇	1	1	yes	characteristic, complemented
485	#389	C₂²×C₇	1	1	yes	characteristic, complemented
486	#389	C₂²×C₇	1	1	yes	characteristic, complemented
487	#388	C₂²×C₇	1	2	yes	complemented
488	#388	C₂²×C₇	1	2	yes	complemented
489	#388	C₂²×C₇	1	2	yes	complemented
490	#388	C₂²×C₇	1	2	yes	complemented
491	#388	C₂²×C₇	1	2	yes	complemented
492	#387	C₂²×C₇	1	2	yes	complemented
493	#386	C₂²×C₇	1	2	yes	—
494	#386	C₂²×C₇	1	2	yes	complemented
495	#386	C₂²×C₇	1	2	yes	complemented
496	#386	C₂²×C₇	1	2	yes	complemented
497	#385	C₂²×C₇	1	2	yes	—
498	#385	C₂²×C₇	1	2	yes	—
499	#385	C₂²×C₇	1	2	yes	complemented
500	#385	C₂²×C₇	1	2	yes	complemented
501	#382	C₂²×C₇	1	1	yes	characteristic, complemented
502	#381	C₂²×C₇	1	2	yes	complemented
503	#381	C₂²×C₇	1	2	yes	complemented
504	#380	C₂²×C₇	1	1	yes	characteristic
505	#380	C₂²×C₇	1	2	yes	—
506	#380	C₂²×C₇	1	2	yes	—
507	#380	C₂²×C₇	1	1	yes	characteristic, complemented
508	#380	C₂²×C₇	1	2	yes	complemented
509	#380	C₂²×C₇	1	2	yes	complemented
510	#379	C₂²×C₇	1	2	yes	—
511	#379	C₂²×C₇	1	2	yes	—
512	#379	C₂²×C₇	1	2	yes	—
513	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
514	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
515	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
516	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
517	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
518	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
519	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
520	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
521	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
522	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
523	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
524	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
525	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
526	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
527	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
528	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
529	C₄³	C₂²×C₇	1	1	yes	characteristic, complemented
530	C₂³×C₇	—	2	1	no	—
531	C₂³×C₇	—	2	1	no	—
532	C₂³×C₇	—	2	1	no	—
533	C₂³×C₇	—	2	1	no	—
534	C₂³×C₇	—	2	16	no	—
535	C₂³×C₇	—	2	1	no	—
536	C₂³×C₇	—	2	2	no	—
537	C₂³×C₇	—	2	1	no	—
538	C₂³×C₇	—	2	1	no	—
539	C₂³×C₇	—	2	2	no	—
540	C₂³×C₇	—	2	2	no	—
541	C₂³×C₇	—	2	2	no	—
542	C₂³×C₇	—	2	2	no	—
543	C₂³×C₇	—	2	1	no	—
544	C₂³×C₇	—	2	2	no	—
545	C₂³×C₇	—	2	2	no	—
546	C₂³×C₇	—	2	2	no	—
547	C₂³×C₇	—	2	2	no	—
548	C₂³×C₇	—	2	1	no	—
549	C₂³×C₇	—	2	2	no	—
550	C₂³×C₇	—	2	2	no	—
551	C₂³×C₇	—	2	2	no	—
552	C₂³×C₇	—	2	1	no	—
553	C₂³×C₇	—	4	8	no	—
554	C₂³×C₇	—	4	8	no	—
555	C₂³×C₇	—	4	8	no	—
556	C₂³×C₇	—	4	8	no	—
557	C₂³×C₇	—	4	8	no	—
558	C₂³×C₇	—	4	8	no	—
559	C₂³×C₇	C₂²×D₄	1	4	yes	—
560	C₂³×C₇	C₂×#41	1	4	yes	—
561	C₂³×C₇	C₂×#41	1	2	yes	—
562	C₂³×C₇	C₂×#41	1	2	yes	—
563	C₂³×C₇	C₂×#41	1	2	yes	—
564	C₂³×C₇	C₂×#41	1	2	yes	—
565	C₂³×C₇	C₂⁵	1	1	yes	characteristic
566	C₇×Q₈	—	4	4	no	—
567	C₇×D₄	—	2	16	no	—
568	C₇×D₄	—	2	8	no	—
569	C₇×D₄	—	2	8	no	—
570	C₇×D₄	—	2	8	no	—
571	C₇×D₄	—	4	8	no	—
572	C₇×D₄	—	4	8	no	—
573	C₂×C₄×C₇	—	2	1	no	—
574	C₂×C₄×C₇	—	2	1	no	—
575	C₂×C₄×C₇	—	2	1	no	—
576	C₂×C₄×C₇	—	2	1	no	—
577	C₂×C₄×C₇	—	2	1	no	—
578	C₂×C₄×C₇	—	2	2	no	—
579	C₂×C₄×C₇	—	2	1	no	—
580	C₂×C₄×C₇	—	2	2	no	—
581	C₂×C₄×C₇	—	2	1	no	—
582	C₂×C₄×C₇	—	2	1	no	—
583	C₂×C₄×C₇	—	2	8	no	—
584	C₂×C₄×C₇	—	2	8	no	—
585	C₂×C₄×C₇	—	2	16	no	—
586	C₂×C₄×C₇	—	2	1	no	—
587	C₂×C₄×C₇	—	2	1	no	—
588	C₂×C₄×C₇	—	2	1	no	—
589	C₂×C₄×C₇	—	2	1	no	—
590	C₂×C₄×C₇	—	2	2	no	—
591	C₂×C₄×C₇	—	2	2	no	—
592	C₂×C₄×C₇	—	2	2	no	—
593	C₂×C₄×C₇	—	2	1	no	—
594	C₂×C₄×C₇	—	2	1	no	—
595	C₂×C₄×C₇	—	2	1	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	2	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	2	no	—
608	C₂×C₄×C₇	—	2	2	no	—
609	C₂×C₄×C₇	—	2	2	no	—
610	C₂×C₄×C₇	—	2	2	no	—
611	C₂×C₄×C₇	—	2	1	no	—
612	C₂×C₄×C₇	—	2	1	no	—
613	C₂×C₄×C₇	—	2	2	no	—
614	C₂×C₄×C₇	—	2	1	no	—
615	C₂×C₄×C₇	—	2	2	no	—
616	C₂×C₄×C₇	—	2	1	no	—
617	C₂×C₄×C₇	—	2	1	no	—
618	C₂×C₄×C₇	—	2	2	no	—
619	C₂×C₄×C₇	—	2	1	no	—
620	C₂×C₄×C₇	—	2	2	no	—
621	C₂×C₄×C₇	—	2	1	no	—
622	C₂×C₄×C₇	—	4	8	no	—
623	C₂×C₄×C₇	—	4	4	no	—
624	C₂×C₄×C₇	—	4	4	no	—
625	C₂×C₄×C₇	—	4	8	no	—
626	C₂×C₄×C₇	—	4	8	no	—
627	C₂×C₄×C₇	—	4	4	no	—
628	C₂×C₄×C₇	—	4	4	no	—
629	C₂×C₄×C₇	—	4	8	no	—
630	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
631	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
632	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
633	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
634	C₂×C₄×C₇	C₂×#41	1	2	yes	—
635	C₂×C₄×C₇	C₂×#41	1	2	yes	—
636	C₂×C₄×C₇	C₂×#41	1	2	yes	—
637	C₂×C₄×C₇	C₂×#41	1	2	yes	—
638	C₂×C₄×C₇	C₂×#41	1	2	yes	—
639	C₂×C₄×C₇	C₂×#41	1	2	yes	—
640	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
641	C₂⁵	C₂³×C₇	1	2	yes	—
642	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
643	C₂²×D₄	—	2	4	no	—
644	C₂²×D₄	—	2	4	no	—
645	C₂²×D₄	—	2	4	no	—
646	C₂²×D₄	C₂³×C₇	1	2	yes	—
647	C₂²×D₄	C₂³×C₇	1	2	yes	—
648	C₂²×D₄	C₂³×C₇	1	2	yes	—
649	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
650	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
651	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
652	C₂³×C₄	—	2	8	no	—
653	C₂³×C₄	—	2	8	no	—
654	C₂³×C₄	—	4	4	no	—
655	C₂³×C₄	C₂³×C₇	1	2	yes	—
656	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
657	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
658	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
659	C₂³×C₄	C₂³×C₇	1	2	yes	—
660	C₂³×C₄	C₂³×C₇	1	2	yes	—
661	C₂³×C₄	C₂³×C₇	1	2	yes	—
662	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
663	C₂³×C₄	C₂³×C₇	1	2	yes	—
664	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
665	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
666	#126	—	2	8	no	—
667	#125	—	2	4	no	—
668	#124	—	2	4	no	—
669	#124	—	2	4	no	—
670	#123	—	2	8	no	—
671	C₂²⋊Q₈	—	2	4	no	—
672	C₂²⋊Q₈	—	2	4	no	—
673	#121	—	2	4	no	—
674	#121	—	2	4	no	—
675	#120	—	2	8	no	—
676	C₄×Q₈	—	2	4	no	—
677	C₄×D₄	—	2	4	no	—
678	C₄×D₄	—	2	4	no	—
679	C₄×D₄	—	2	8	no	—
680	C₄×D₄	—	2	8	no	—
681	C₄×D₄	—	2	4	no	—
682	C₄×D₄	—	2	4	no	—
683	C₄×D₄	—	2	4	no	—
684	C₄×D₄	—	2	8	no	—
685	C₄×D₄	—	2	4	no	—
686	C₄×D₄	—	4	4	no	—
687	C₄×D₄	C₇×D₄	1	8	yes	complemented
688	#117	—	2	8	no	—
689	#117	—	4	4	no	—
690	C₂×C₄⋊C₄	—	2	4	no	—
691	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
693	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
696	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
697	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
701	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
702	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
705	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
706	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
707	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
708	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
709	C₂×C₂²⋊C₄	—	2	8	no	—
710	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
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	1	yes	characteristic
718	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
719	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
720	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
721	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
738	C₂×C₄²	—	2	4	no	—
739	C₂×C₄²	—	2	4	no	—
740	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
741	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
742	C₂×C₄²	C₂³×C₇	1	2	yes	—
743	C₂×C₄²	C₂³×C₇	1	2	yes	—
744	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
745	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
746	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
747	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
748	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
749	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
750	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
751	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
753	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
754	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
755	#95	C₂³×C₇	1	1	yes	characteristic
756	#95	C₂³×C₇	1	1	yes	characteristic
757	#95	C₂³×C₇	1	1	yes	characteristic
758	#95	C₂³×C₇	1	1	yes	characteristic
759	#95	C₂³×C₇	1	1	yes	characteristic
760	#95	C₂³×C₇	1	1	yes	characteristic
761	#95	C₂³×C₇	1	2	yes	—
762	#95	C₂³×C₇	1	2	yes	—
763	#95	C₂³×C₇	1	2	yes	—
764	#95	C₂³×C₇	1	2	yes	—
765	#95	C₂³×C₇	1	2	yes	—
766	#95	C₂³×C₇	1	2	yes	—
767	#95	C₂³×C₇	1	2	yes	—
768	#95	C₂³×C₇	1	2	yes	—
769	#95	C₂³×C₇	1	2	yes	—
770	#95	C₂³×C₇	1	2	yes	—
771	#95	C₂³×C₇	1	2	yes	—
772	#95	C₂³×C₇	1	2	yes	—
773	#95	C₂³×C₇	1	2	yes	—
774	C₂²×C₇	—	2	2	no	—
775	C₂²×C₇	—	2	2	no	—
776	C₂²×C₇	—	2	2	no	—
777	C₂²×C₇	—	2	2	no	—
778	C₂²×C₇	—	2	2	no	—
779	C₂²×C₇	—	2	2	no	—
780	C₂²×C₇	—	2	4	no	—
781	C₂²×C₇	—	2	4	no	—
782	C₂²×C₇	—	2	2	no	—
783	C₂²×C₇	—	2	4	no	—
784	C₂²×C₇	—	2	2	no	—
785	C₂²×C₇	—	2	4	no	—
786	C₂²×C₇	—	2	4	no	—
787	C₂²×C₇	—	2	2	no	—
788	C₂²×C₇	—	2	4	no	—
789	C₂²×C₇	—	4	32	no	—
790	C₂²×C₇	—	4	1	no	—
791	C₂²×C₇	—	4	2	no	—
792	C₂²×C₇	—	4	2	no	—
793	C₂²×C₇	—	4	1	no	—
794	C₂²×C₇	—	4	2	no	—
795	C₂²×C₇	—	4	2	no	—
796	C₂²×C₇	—	4	2	no	—
797	C₂²×C₇	—	4	1	no	—
798	C₂²×C₇	—	4	2	no	—
799	C₂²×C₇	—	4	1	no	—
800	C₂²×C₇	—	4	2	no	—
801	C₂²×C₇	—	4	2	no	—
802	C₂²×C₇	#529	1	4	yes	complemented
803	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
804	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
805	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
806	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
807	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
808	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
809	C₂²×C₇	#585	1	1	yes	characteristic
810	C₄×C₇	—	2	2	no	—
811	C₄×C₇	—	2	2	no	—
812	C₄×C₇	—	2	2	no	—
813	C₄×C₇	—	2	4	no	—
814	C₄×C₇	—	2	2	no	—
815	C₄×C₇	—	4	1	no	—
816	C₄×C₇	—	4	2	no	—
817	C₄×C₇	—	4	1	no	—
818	C₄×C₇	—	4	2	no	—
819	C₄×C₇	—	4	1	no	—
820	C₄×C₇	—	4	2	no	—
821	C₄×C₇	—	4	1	no	—
822	C₄×C₇	—	4	1	no	—
823	C₄×C₇	—	4	2	no	—
824	C₄×C₇	—	4	1	no	—
825	C₄×C₇	—	4	1	no	—
826	C₄×C₇	—	4	2	no	—
827	C₄×C₇	#525	1	4	yes	—
828	C₄×C₇	#546	1	4	yes	—
829	C₂⁴	—	2	4	no	—
830	C₂⁴	—	2	4	no	—
831	C₂⁴	—	2	4	no	—
832	C₂⁴	—	2	4	no	—
833	C₂⁴	—	2	4	no	—
834	C₂⁴	—	4	2	no	—
835	C₂⁴	—	4	2	no	—
836	C₂⁴	C₂⁴×C₇	1	2	yes	—
837	C₂⁴	C₂⁴×C₇	1	2	yes	—
838	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
839	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
840	C₂×Q₈	—	2	2	no	—
841	C₂×Q₈	—	2	2	no	—
842	C₂×Q₈	—	2	2	no	—
843	C₂×D₄	—	2	32	no	—
844	C₂×D₄	—	2	4	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	4	no	—
848	C₂×D₄	—	2	4	no	—
849	C₂×D₄	—	2	4	no	—
850	C₂×D₄	—	2	4	no	—
851	C₂×D₄	—	2	4	no	—
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	2	4	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	2	2	no	—
857	C₂×D₄	—	4	2	no	—
858	C₂×D₄	—	4	2	no	—
859	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
860	C₂×D₄	C₇×#41	1	4	yes	—
861	C₂×D₄	C₇×#41	1	4	yes	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	2	4	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	4	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	—	2	4	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	4	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	2	no	—
875	C₂²×C₄	—	2	2	no	—
876	C₂²×C₄	—	2	4	no	—
877	C₂²×C₄	—	2	4	no	—
878	C₂²×C₄	—	2	4	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	4	no	—
883	C₂²×C₄	—	2	4	no	—
884	C₂²×C₄	—	2	4	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	4	no	—
887	C₂²×C₄	—	4	2	no	—
888	C₂²×C₄	—	4	2	no	—
889	C₂²×C₄	—	4	2	no	—
890	C₂²×C₄	—	4	1	no	—
891	C₂²×C₄	—	4	1	no	—
892	C₂²×C₄	—	4	32	no	—
893	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
894	C₂²×C₄	C₇×#41	1	4	yes	—
895	C₂²×C₄	C₇×#41	1	4	yes	—
896	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
898	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
899	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
905	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
906	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
907	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
908	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
909	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
910	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
913	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
914	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
915	C₄⋊C₄	—	2	4	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	4	no	—
918	C₄⋊C₄	—	2	4	no	—
919	C₄⋊C₄	—	2	4	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	4	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	4	no	—
928	C₄⋊C₄	—	4	2	no	—
929	C₄⋊C₄	—	4	2	no	—
930	C₄⋊C₄	—	4	2	no	—
931	C₄⋊C₄	—	4	2	no	—
932	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
933	C₂²⋊C₄	—	2	4	no	—
934	C₂²⋊C₄	—	2	4	no	—
935	C₂²⋊C₄	—	2	4	no	—
936	C₂²⋊C₄	—	2	4	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	4	no	—
942	C₂²⋊C₄	—	2	4	no	—
943	C₂²⋊C₄	—	2	4	no	—
944	C₂²⋊C₄	—	2	4	no	—
945	C₂²⋊C₄	—	2	4	no	—
946	C₂²⋊C₄	—	2	4	no	—
947	C₂²⋊C₄	—	2	4	no	—
948	C₂²⋊C₄	—	2	4	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	4	no	—
952	C₂²⋊C₄	—	2	4	no	—
953	C₂²⋊C₄	—	4	2	no	—
954	C₂²⋊C₄	—	4	2	no	—
955	C₂²⋊C₄	—	4	2	no	—
956	C₂²⋊C₄	—	4	2	no	—
957	C₂²⋊C₄	—	4	2	no	—
958	C₂²⋊C₄	—	4	2	no	—
959	C₂²⋊C₄	—	4	2	no	—
960	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
961	C₄²	—	2	2	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	2	no	—
967	C₄²	—	2	4	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	2	no	—
970	C₄²	—	2	2	no	—
971	C₄²	—	2	2	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	4	no	—
974	C₄²	—	4	1	no	—
975	C₄²	C₂×C₇×D₄	1	4	yes	—
976	C₂×C₇	—	2	4	no	—
977	C₂×C₇	—	4	2	no	—
978	C₂×C₇	—	4	4	no	—
979	C₂×C₇	—	4	4	no	—
980	C₂×C₇	C₂×#525	1	1	yes	characteristic
981	C₂×C₇	C₂×#529	1	1	yes	characteristic
982	C₂×C₇	#3460	1	1	yes	characteristic
983	C₂×C₇	C₂×#546	1	1	yes	characteristic
984	C₂×C₇	D₄×#41	1	1	yes	characteristic
985	C₂×C₇	#3475	1	1	yes	characteristic
986	C₂×C₇	#3481	1	1	yes	characteristic
987	C₂³	—	2	1	no	—
988	C₂³	—	2	1	no	—
989	C₂³	—	2	1	no	—
990	C₂³	—	2	1	no	—
991	C₂³	—	2	16	no	—
992	C₂³	—	2	1	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	2	1	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	2	2	no	—
997	C₂³	—	2	2	no	—
998	C₂³	—	2	2	no	—
999	C₂³	—	2	2	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	2	no	—
1002	C₂³	—	2	2	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	2	2	no	—
1005	C₂³	—	2	1	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	2	2	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	4	8	no	—
1011	C₂³	—	4	8	no	—
1012	C₂³	—	4	8	no	—
1013	C₂³	—	4	8	no	—
1014	C₂³	—	4	8	no	—
1015	C₂³	—	4	8	no	—
1016	C₂³	C₂²×C₇×D₄	1	4	yes	—
1017	C₂³	C₂×C₇×#41	1	4	yes	—
1018	C₂³	C₂×C₇×#41	1	2	yes	—
1019	C₂³	C₂×C₇×#41	1	2	yes	—
1020	C₂³	C₂×C₇×#41	1	2	yes	—
1021	C₂³	C₂×C₇×#41	1	2	yes	—
1022	C₂³	C₂⁵×C₇	1	1	yes	characteristic
1023	Q₈	—	4	4	no	—
1024	D₄	—	2	16	no	—
1025	D₄	—	2	8	no	—
1026	D₄	—	2	8	no	—
1027	D₄	—	2	8	no	—
1028	D₄	—	4	8	no	—
1029	D₄	—	4	8	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	8	no	—
1041	C₂×C₄	—	2	8	no	—
1042	C₂×C₄	—	2	16	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	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	4	8	no	—
1080	C₂×C₄	—	4	4	no	—
1081	C₂×C₄	—	4	4	no	—
1082	C₂×C₄	—	4	8	no	—
1083	C₂×C₄	—	4	8	no	—
1084	C₂×C₄	—	4	4	no	—
1085	C₂×C₄	—	4	4	no	—
1086	C₂×C₄	—	4	8	no	—
1087	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1088	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
1089	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1090	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1091	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1092	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1093	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1094	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1095	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1096	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1097	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1098	C₇	#34700	1	1	yes	characteristic, direct product factor, Sylow
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	4	no	—
1106	C₂²	—	2	4	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	4	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	4	no	—
1111	C₂²	—	2	4	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	4	no	—
1114	C₂²	—	4	32	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	C₇×#529	1	4	yes	complemented
1128	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1129	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1130	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1131	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1132	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1133	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1134	C₂²	C₇×#585	1	1	yes	characteristic
1135	C₄	—	2	2	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	4	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	2	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	2	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	2	no	—
1151	C₄	—	4	1	no	—
1152	C₄	C₇×#525	1	4	yes	—
1153	C₄	C₇×#546	1	4	yes	—
1154	C₂	—	2	4	no	—
1155	C₂	—	4	4	no	—
1156	C₂	—	4	4	no	—
1157	C₂	—	4	2	no	—
1158	C₂	C₂×C₇×#525	1	1	yes	characteristic
1159	C₂	C₂×C₇×#529	1	1	yes	characteristic
1160	C₂	C₇×#3460	1	1	yes	characteristic
1161	C₂	C₂×C₇×#546	1	1	yes	characteristic
1162	C₂	C₇×D₄×#41	1	1	yes	characteristic
1163	C₂	C₇×#3475	1	1	yes	characteristic
1164	C₂	C₇×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
prime radical	C₇×#2408	C₂
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. C₂×C₇×#529	C₂	semidirect
2. C₂²×C₄×C₇×D₄	C₂	semidirect
3. C₇×#2480	C₂	semidirect
4. C₇×#2468	C₂	semidirect
5. C₇×#2457	C₂	semidirect
6. C₇×#2454	C₂	semidirect
7. C₇×#2447	C₂	semidirect
8. C₇×#2442	C₂	semidirect
9. C₇×#2435	C₂	semidirect
10. C₇×#2427	C₂	semidirect
11. C₇×#2420	C₂	semidirect
12. C₇×#2418	C₂	semidirect
13. C₇×#2417	C₂	semidirect
15. C₇×#2395	C₂	semidirect
16. C₇×#2392	C₂	semidirect
17. C₄×C₇×#124	C₂	semidirect
18. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
19. C₄×C₇×#121	C₂	semidirect
20. C₄×C₇×#120	C₂	semidirect
21. C₇×#2293	C₂	semidirect
22. C₇×#2280	C₂	semidirect
23. C₄²×C₇×D₄	C₂	semidirect
27. C₂×C₇×#126	C₂²	semidirect
28. C₂×C₇×#125	C₂²	semidirect
31. C₂×C₇×#123	C₂²	semidirect
33. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
37. C₂×C₄×C₇×Q₈	C₂²	semidirect
48. C₂×C₄×C₇×D₄	C₂²	semidirect
49. C₂×C₄×C₇×D₄	C₂²	semidirect
50. C₂×C₇×#117	C₂²	semidirect
51. C₂×C₇×#117	C₂²	semidirect
55. C₂²×C₄²×C₇	C₂²	semidirect
56. C₇×#400	C₂²	semidirect
57. C₇×#399	C₂²	semidirect
58. C₇×#398	C₂²	semidirect
59. C₇×#398	C₂²	semidirect
60. C₇×#397	C₂²	semidirect
61. C₇×#397	C₂²	semidirect
62. C₇×#397	C₂²	semidirect
63. C₇×#397	C₂²	semidirect
64. C₇×#396	C₂²	semidirect
65. C₇×#396	C₂²	semidirect
69. C₇×#394	C₂²	semidirect
70. C₇×#394	C₂²	semidirect
72. C₇×#391	C₂²	semidirect
73. C₇×#391	C₂²	semidirect
78. C₇×#389	C₂²	semidirect
79. C₇×#389	C₂²	semidirect
80. C₇×#389	C₂²	semidirect
81. C₇×#389	C₂²	semidirect
82. C₇×#388	C₂²	semidirect
83. C₇×#388	C₂²	semidirect
84. C₇×#388	C₂²	semidirect
85. C₇×#388	C₂²	semidirect
86. C₇×#388	C₂²	semidirect
87. C₇×#387	C₂²	semidirect
89. C₇×#386	C₂²	semidirect
90. C₇×#386	C₂²	semidirect
91. C₇×#386	C₂²	semidirect
94. C₇×#385	C₂²	semidirect
95. C₇×#385	C₂²	semidirect
96. C₇×#382	C₂²	semidirect
97. C₇×#381	C₂²	semidirect
98. C₇×#381	C₂²	semidirect
102. C₇×#380	C₂²	semidirect
103. C₇×#380	C₂²	semidirect
104. C₇×#380	C₂²	semidirect
108. C₄×C₇×C₄⋊C₄	C₂²	semidirect
109. C₄×C₇×C₄⋊C₄	C₂²	semidirect
110. C₄×C₇×C₄⋊C₄	C₂²	semidirect
111. C₄×C₇×C₄⋊C₄	C₂²	semidirect
112. C₄×C₇×C₄⋊C₄	C₂²	semidirect
117. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
118. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
119. C₄×C₇×C₂²⋊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. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
124. C₄³×C₇	C₂²	semidirect
125. #34700	C₇	direct (N × H)
172. C₄×C₇×D₄	D₄	semidirect
259. C₂×#529	C₂×C₇	semidirect
260. C₂²×C₄×D₄	C₂×C₇	semidirect
261. #2480	C₂×C₇	semidirect
262. #2468	C₂×C₇	semidirect
263. #2457	C₂×C₇	semidirect
264. #2454	C₂×C₇	semidirect
265. #2447	C₂×C₇	semidirect
266. #2442	C₂×C₇	semidirect
267. #2435	C₂×C₇	semidirect
268. #2427	C₂×C₇	semidirect
269. #2420	C₂×C₇	semidirect
270. #2418	C₂×C₇	semidirect
271. #2417	C₂×C₇	semidirect
273. #2395	C₂×C₇	semidirect
274. #2392	C₂×C₇	semidirect
275. C₄×#124	C₂×C₇	semidirect
276. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
277. C₄×#121	C₂×C₇	semidirect
278. C₄×#120	C₂×C₇	semidirect
279. #2293	C₂×C₇	semidirect
280. #2280	C₂×C₇	semidirect
281. C₄²×D₄	C₂×C₇	semidirect
432. C₂×#126	C₂²×C₇	semidirect
433. C₂×#125	C₂²×C₇	semidirect
436. C₂×#123	C₂²×C₇	semidirect
438. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
442. C₂×C₄×Q₈	C₂²×C₇	semidirect
453. C₂×C₄×D₄	C₂²×C₇	semidirect
454. C₂×C₄×D₄	C₂²×C₇	semidirect
455. C₂×#117	C₂²×C₇	semidirect
456. C₂×#117	C₂²×C₇	semidirect
460. C₂²×C₄²	C₂²×C₇	semidirect
461. #400	C₂²×C₇	semidirect
462. #399	C₂²×C₇	semidirect
463. #398	C₂²×C₇	semidirect
464. #398	C₂²×C₇	semidirect
465. #397	C₂²×C₇	semidirect
466. #397	C₂²×C₇	semidirect
467. #397	C₂²×C₇	semidirect
468. #397	C₂²×C₇	semidirect
469. #396	C₂²×C₇	semidirect
470. #396	C₂²×C₇	semidirect
474. #394	C₂²×C₇	semidirect
475. #394	C₂²×C₇	semidirect
477. #391	C₂²×C₇	semidirect
478. #391	C₂²×C₇	semidirect
483. #389	C₂²×C₇	semidirect
484. #389	C₂²×C₇	semidirect
485. #389	C₂²×C₇	semidirect
486. #389	C₂²×C₇	semidirect
487. #388	C₂²×C₇	semidirect
488. #388	C₂²×C₇	semidirect
489. #388	C₂²×C₇	semidirect
490. #388	C₂²×C₇	semidirect
491. #388	C₂²×C₇	semidirect
492. #387	C₂²×C₇	semidirect
494. #386	C₂²×C₇	semidirect
495. #386	C₂²×C₇	semidirect
496. #386	C₂²×C₇	semidirect
499. #385	C₂²×C₇	semidirect
500. #385	C₂²×C₇	semidirect
501. #382	C₂²×C₇	semidirect
502. #381	C₂²×C₇	semidirect
503. #381	C₂²×C₇	semidirect
507. #380	C₂²×C₇	semidirect
508. #380	C₂²×C₇	semidirect
509. #380	C₂²×C₇	semidirect
513. C₄×C₄⋊C₄	C₂²×C₇	semidirect
514. C₄×C₄⋊C₄	C₂²×C₇	semidirect
515. C₄×C₄⋊C₄	C₂²×C₇	semidirect
516. C₄×C₄⋊C₄	C₂²×C₇	semidirect
517. C₄×C₄⋊C₄	C₂²×C₇	semidirect
522. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
523. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
524. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
525. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
526. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
527. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
528. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
529. C₄³	C₂²×C₇	semidirect
687. C₄×D₄	C₇×D₄	semidirect
802. C₂²×C₇	#529	semidirect
1098. C₇	#34700	direct (N × H)
1127. C₂²	C₇×#529	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#529	2
C₂²×C₄×C₇×D₄	2
C₇×#2480	2
C₇×#2468	2
C₇×#2457	2
C₇×#2454	2
C₇×#2447	2
C₇×#2442	2
C₇×#2435	2
C₇×#2427	2
C₇×#2420	2
C₇×#2418	2
C₇×#2417	2
C₇×#2408	2
C₇×#2395	2
C₇×#2392	2
C₄×C₇×#124	2
C₄×C₇×C₂²⋊Q₈	2
C₄×C₇×#121	2
C₄×C₇×#120	2
C₇×#2293	2
C₇×#2280	2
C₄²×C₇×D₄	2
#34700	7

Subgroups — C7×#34700 #13211916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34700 #13211916