Subgroups — C₇×#60558 #13237774

Order 1792.

2570 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3114	C₂	1	4	yes	maximal, complemented
4	C₇×#3110	C₂	1	2	yes	maximal, complemented
5	C₇×#3109	C₂	1	2	yes	maximal, complemented
6	C₇×#3105	C₂	1	4	yes	maximal, complemented
7	C₇×#3101	C₂	1	2	yes	maximal, complemented
8	C₇×#3100	C₂	1	2	yes	maximal, complemented
9	C₇×#3092	C₂	1	2	yes	maximal, complemented
10	C₇×#3077	C₂	1	2	yes	maximal, complemented
11	C₇×#3036	C₂	1	2	yes	maximal, complemented
12	C₇×#3003	C₂	1	2	yes	maximal, complemented
13	C₄×C₇×AGL(1,ℤ/8)	C₂	1	4	yes	maximal, complemented
14	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₇	—	2	1	no	—
17	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	4	yes	—
18	C₇×#533	C₂²	1	1	yes	characteristic, complemented
19	C₇×#533	C₂²	1	1	yes	characteristic, complemented
20	C₇×#533	C₂²	1	1	yes	characteristic, complemented
21	C₇×#532	C₂²	1	1	yes	characteristic, complemented
22	C₇×#532	C₂²	1	1	yes	characteristic, complemented
23	C₇×#532	C₂²	1	1	yes	characteristic, complemented
24	C₇×#529	—	2	1	no	—
25	C₇×#529	—	2	1	no	—
26	C₇×#529	—	2	1	no	—
27	C₇×#529	—	2	1	no	—
28	C₇×#529	C₂²	1	2	yes	complemented
29	C₇×#529	C₂²	1	2	yes	complemented
30	C₇×#525	—	2	1	no	—
31	C₇×#525	—	2	1	no	—
32	C₇×#525	C₂²	1	2	yes	—
33	C₄×C₇×#41	—	2	1	no	—
34	C₄×C₇×#41	—	2	1	no	—
35	C₄×C₇×#41	C₂²	1	2	yes	complemented
36	C₂×C₄×C₇×D₄	—	2	1	no	—
37	C₂×C₄×C₇×D₄	—	2	1	no	—
38	C₂×C₄×C₇×D₄	—	2	1	no	—
39	C₂×C₄×C₇×D₄	—	2	1	no	—
40	C₂×C₄×C₇×D₄	—	2	1	no	—
41	C₂×C₄×C₇×D₄	—	2	1	no	—
42	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
43	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
44	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
45	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
46	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
47	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
48	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
50	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
51	C₇×#484	C₂²	1	4	yes	complemented
52	C₇×#483	C₂²	1	4	yes	complemented
53	C₇×#481	C₂²	1	4	yes	complemented
54	C₇×#480	C₂²	1	4	yes	complemented
55	C₇×#478	C₂²	1	8	yes	complemented
56	C₇×#476	C₂²	1	4	yes	complemented
57	C₇×#474	C₂²	1	4	yes	complemented
58	C₇×#463	C₂²	1	8	yes	complemented
59	C₇×#461	C₂²	1	4	yes	complemented
60	C₇×#459	C₂²	1	4	yes	complemented
61	C₇×#450	C₂²	1	4	yes	—
62	C₇×#450	C₂²	1	4	yes	—
63	C₇×#447	C₂²	1	4	yes	—
64	C₇×#447	C₂²	1	4	yes	—
65	C₇×#442	C₂²	1	8	yes	complemented
66	C₇×#440	C₂²	1	8	yes	complemented
67	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
68	C₄×C₇×D₈	C₂²	1	8	yes	complemented
69	C₇×#432	C₂²	1	2	yes	complemented
70	C₇×#432	C₂²	1	2	yes	complemented
71	C₇×#431	C₂²	1	2	yes	complemented
72	C₇×#431	C₂²	1	2	yes	complemented
73	C₇×#428	C₂²	1	4	yes	complemented
74	C₇×#423	C₂²	1	2	yes	complemented
75	C₇×#418	C₂²	1	4	yes	—
76	C₇×#417	C₂²	1	4	yes	complemented
77	C₇×#407	C₂²	1	2	yes	—
78	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
79	#60558	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂⁵×C₇	—	2	1	no	—
81	C₂×C₇×#41	—	2	1	no	—
82	C₂×C₇×#41	—	2	1	no	—
83	C₂×C₇×#41	C₂³	1	2	yes	—
84	C₂²×C₇×D₄	—	2	8	no	—
85	C₂²×C₇×D₄	—	2	1	no	—
86	C₂²×C₇×D₄	—	2	1	no	—
87	C₂²×C₇×D₄	—	2	1	no	—
88	C₂²×C₇×D₄	C₂³	1	2	yes	—
89	C₂²×C₇×D₄	C₂³	1	2	yes	—
90	C₂²×C₇×D₄	C₂³	1	2	yes	—
91	C₂³×C₄×C₇	—	2	1	no	—
92	C₂³×C₄×C₇	—	2	2	no	—
93	C₂³×C₄×C₇	—	2	2	no	—
94	C₂³×C₄×C₇	—	2	2	no	—
95	C₂³×C₄×C₇	—	2	2	no	—
96	C₂³×C₄×C₇	—	2	2	no	—
97	C₂³×C₄×C₇	—	2	2	no	—
98	C₂³×C₄×C₇	—	4	8	no	—
99	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
100	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
101	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
102	C₇×AGL(1,ℤ/8)	—	2	16	no	—
103	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
104	C₂×C₇×D₈	C₂³	1	8	yes	—
105	C₂×C₇×M₁₆	C₂³	1	4	yes	—
106	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
107	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
108	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
109	C₇×#127	C₂³	1	1	yes	characteristic, complemented
110	C₇×#126	—	2	2	no	—
111	C₇×#126	—	2	2	no	—
112	C₇×#125	—	2	1	no	—
113	C₇×#125	—	2	1	no	—
114	C₇×#125	C₂³	1	2	yes	complemented
115	C₇×#124	—	2	1	no	—
116	C₇×#124	—	2	1	no	—
117	C₇×#124	C₂³	1	2	yes	complemented
118	C₇×#123	—	2	2	no	—
119	C₇×#123	—	2	2	no	—
120	C₇×#123	—	2	2	no	—
121	C₇×C₂²⋊Q₈	—	2	1	no	—
122	C₇×C₂²⋊Q₈	—	2	1	no	—
123	C₇×C₂²⋊Q₈	—	2	1	no	—
124	C₇×C₂²⋊Q₈	—	2	1	no	—
125	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
126	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
127	C₇×#121	—	2	1	no	—
128	C₇×#121	—	2	1	no	—
129	C₇×#121	—	2	1	no	—
130	C₇×#121	—	2	1	no	—
131	C₇×#121	C₂³	1	2	yes	—
132	C₇×#121	C₂³	1	2	yes	—
133	C₇×#120	—	2	2	no	—
134	C₄×C₇×Q₈	—	2	1	no	—
135	C₄×C₇×Q₈	—	2	1	no	—
136	C₄×C₇×Q₈	—	2	1	no	—
137	C₄×C₇×Q₈	—	2	1	no	—
138	C₄×C₇×Q₈	C₂³	1	2	yes	complemented
139	C₄×C₇×Q₈	C₂³	1	2	yes	complemented
140	C₄×C₇×D₄	—	2	2	no	—
141	C₄×C₇×D₄	—	2	2	no	—
142	C₄×C₇×D₄	—	2	2	no	—
143	C₄×C₇×D₄	—	2	2	no	—
144	C₄×C₇×D₄	—	2	2	no	—
145	C₄×C₇×D₄	—	2	2	no	—
146	C₄×C₇×D₄	—	2	2	no	—
147	C₄×C₇×D₄	—	2	2	no	—
148	C₄×C₇×D₄	—	2	2	no	—
149	C₄×C₇×D₄	—	2	2	no	—
150	C₄×C₇×D₄	—	2	2	no	—
151	C₄×C₇×D₄	—	2	2	no	—
152	C₄×C₇×D₄	—	2	2	no	—
153	C₄×C₇×D₄	—	2	2	no	—
154	C₄×C₇×D₄	—	2	2	no	—
155	C₄×C₇×D₄	—	2	2	no	—
156	C₄×C₇×D₄	—	2	2	no	—
157	C₄×C₇×D₄	—	2	2	no	—
158	C₄×C₇×D₄	—	2	1	no	—
159	C₄×C₇×D₄	—	2	1	no	—
160	C₄×C₇×D₄	—	2	1	no	—
161	C₄×C₇×D₄	—	2	1	no	—
162	C₄×C₇×D₄	C₂³	1	4	yes	—
163	C₄×C₇×D₄	C₂³	1	4	yes	—
164	C₄×C₇×D₄	C₂³	1	4	yes	—
165	C₄×C₇×D₄	C₂³	1	4	yes	—
166	C₄×C₇×D₄	C₂³	1	2	yes	complemented
167	C₄×C₇×D₄	C₂³	1	2	yes	complemented
168	C₇×#117	—	2	1	no	—
169	C₇×#117	—	2	1	no	—
170	C₇×#117	—	2	2	no	—
171	C₇×#117	—	2	2	no	—
172	C₇×#117	—	2	2	no	—
173	C₇×#117	C₂³	1	2	yes	—
174	C₂×C₇×C₄⋊C₄	—	2	1	no	—
175	C₂×C₇×C₄⋊C₄	—	2	1	no	—
176	C₂×C₇×C₄⋊C₄	—	2	1	no	—
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×C₂²⋊C₄	—	2	2	no	—
181	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
182	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
183	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
184	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
185	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
186	C₂×C₄²×C₇	—	2	2	no	—
187	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
199	C₇×#107	C₂³	1	8	yes	complemented
200	C₇×#106	C₂³	1	8	yes	complemented
201	C₇×C₄⋊C₈	C₂³	1	4	yes	complemented
202	C₇×C₄⋊C₈	C₂³	1	4	yes	complemented
203	C₇×#103	C₂³	1	8	yes	complemented
204	C₇×#102	C₂³	1	8	yes	—
205	C₇×#102	C₂³	1	8	yes	—
206	C₇×#102	C₂³	1	8	yes	complemented
207	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
208	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
209	C₇×#97	C₂³	1	4	yes	complemented
210	C₄×C₇×C₈	C₂³	1	4	yes	complemented
211	#3444	C₂×C₇	1	1	yes	characteristic, complemented
212	C₂²×C₄×D₄	C₂×C₇	1	1	yes	characteristic, complemented
213	#3114	C₂×C₇	1	4	yes	complemented
214	#3110	C₂×C₇	1	2	yes	complemented
215	#3109	C₂×C₇	1	2	yes	complemented
216	#3105	C₂×C₇	1	4	yes	complemented
217	#3101	C₂×C₇	1	2	yes	complemented
218	#3100	C₂×C₇	1	2	yes	complemented
219	#3092	C₂×C₇	1	2	yes	complemented
220	#3077	C₂×C₇	1	2	yes	complemented
221	#3036	C₂×C₇	1	2	yes	complemented
222	#3003	C₂×C₇	1	2	yes	complemented
223	C₄×AGL(1,ℤ/8)	C₂×C₇	1	4	yes	complemented
224	#2920	C₂×C₇	1	1	yes	characteristic, complemented
225	C₂⁴×C₇	—	2	8	no	—
226	C₂⁴×C₇	—	2	2	no	—
227	C₂⁴×C₇	—	2	2	no	—
228	C₂⁴×C₇	—	2	2	no	—
229	C₂⁴×C₇	—	4	4	no	—
230	C₂⁴×C₇	—	4	4	no	—
231	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
232	C₇×#41	—	2	8	no	—
233	C₇×#41	—	4	4	no	—
234	C₇×#41	—	4	4	no	—
235	C₂×C₇×Q₈	—	2	1	no	—
236	C₂×C₇×Q₈	—	2	1	no	—
237	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
238	C₂×C₇×D₄	—	2	8	no	—
239	C₂×C₇×D₄	—	2	8	no	—
240	C₂×C₇×D₄	—	2	8	no	—
241	C₂×C₇×D₄	—	2	8	no	—
242	C₂×C₇×D₄	—	2	8	no	—
243	C₂×C₇×D₄	—	2	2	no	—
244	C₂×C₇×D₄	—	2	2	no	—
245	C₂×C₇×D₄	—	2	2	no	—
246	C₂×C₇×D₄	—	2	2	no	—
247	C₂×C₇×D₄	—	2	2	no	—
248	C₂×C₇×D₄	—	2	2	no	—
249	C₂×C₇×D₄	—	2	1	no	—
250	C₂×C₇×D₄	—	2	1	no	—
251	C₂×C₇×D₄	—	2	4	no	—
252	C₂×C₇×D₄	#41	1	8	yes	complemented
253	C₂×C₇×D₄	C₂⁴	1	2	yes	—
254	C₂×C₇×D₄	C₂⁴	1	4	yes	—
255	C₂²×C₄×C₇	—	2	4	no	—
256	C₂²×C₄×C₇	—	2	4	no	—
257	C₂²×C₄×C₇	—	2	2	no	—
258	C₂²×C₄×C₇	—	2	2	no	—
259	C₂²×C₄×C₇	—	2	2	no	—
260	C₂²×C₄×C₇	—	2	2	no	—
261	C₂²×C₄×C₇	—	2	2	no	—
262	C₂²×C₄×C₇	—	2	4	no	—
263	C₂²×C₄×C₇	—	2	4	no	—
264	C₂²×C₄×C₇	—	2	4	no	—
265	C₂²×C₄×C₇	—	2	2	no	—
266	C₂²×C₄×C₇	—	2	4	no	—
267	C₂²×C₄×C₇	—	4	2	no	—
268	C₂²×C₄×C₇	—	4	8	no	—
269	C₂²×C₄×C₇	—	4	8	no	—
270	C₂²×C₄×C₇	—	4	8	no	—
271	C₂²×C₄×C₇	—	4	8	no	—
272	C₂²×C₄×C₇	—	4	8	no	—
273	C₂²×C₄×C₇	—	4	4	no	—
274	C₂²×C₄×C₇	—	4	8	no	—
275	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
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	C₇×SD₁₆	—	2	16	no	—
294	C₇×D₈	—	2	16	no	—
295	C₇×M₁₆	—	2	8	no	—
296	C₂×C₇×C₈	C₂⁴	1	8	yes	—
297	C₇×C₄⋊C₄	—	2	2	no	—
298	C₇×C₄⋊C₄	—	2	2	no	—
299	C₇×C₄⋊C₄	—	2	2	no	—
300	C₇×C₄⋊C₄	—	2	1	no	—
301	C₇×C₄⋊C₄	—	2	1	no	—
302	C₇×C₄⋊C₄	—	2	1	no	—
303	C₇×C₄⋊C₄	—	2	1	no	—
304	C₇×C₄⋊C₄	—	2	2	no	—
305	C₇×C₄⋊C₄	—	2	2	no	—
306	C₇×C₄⋊C₄	—	2	2	no	—
307	C₇×C₄⋊C₄	—	2	2	no	—
308	C₇×C₄⋊C₄	—	2	2	no	—
309	C₇×C₄⋊C₄	—	2	2	no	—
310	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
311	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
312	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
313	C₇×C₂²⋊C₄	—	2	2	no	—
314	C₇×C₂²⋊C₄	—	2	2	no	—
315	C₇×C₂²⋊C₄	—	2	2	no	—
316	C₇×C₂²⋊C₄	—	2	4	no	—
317	C₇×C₂²⋊C₄	—	2	4	no	—
318	C₇×C₂²⋊C₄	—	2	4	no	—
319	C₇×C₂²⋊C₄	—	2	4	no	—
320	C₇×C₂²⋊C₄	—	2	2	no	—
321	C₇×C₂²⋊C₄	—	2	2	no	—
322	C₇×C₂²⋊C₄	—	2	2	no	—
323	C₇×C₂²⋊C₄	—	2	2	no	—
324	C₇×C₂²⋊C₄	—	2	2	no	—
325	C₇×C₂²⋊C₄	—	2	2	no	—
326	C₄²×C₇	—	2	2	no	—
327	C₄²×C₇	—	2	2	no	—
328	C₄²×C₇	—	2	2	no	—
329	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₇	C₂⁴	1	1	yes	characteristic
342	C₄²×C₇	C₂⁴	1	1	yes	characteristic
343	C₄²×C₇	C₂⁴	1	1	yes	characteristic
344	C₄²×C₇	C₂⁴	1	1	yes	characteristic
345	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
346	C₂⁴×C₄	—	2	1	no	—
347	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	4	yes	—
348	#533	C₂²×C₇	1	1	yes	characteristic, complemented
349	#533	C₂²×C₇	1	1	yes	characteristic, complemented
350	#533	C₂²×C₇	1	1	yes	characteristic, complemented
351	#532	C₂²×C₇	1	1	yes	characteristic, complemented
352	#532	C₂²×C₇	1	1	yes	characteristic, complemented
353	#532	C₂²×C₇	1	1	yes	characteristic, complemented
354	#529	—	2	1	no	—
355	#529	—	2	1	no	—
356	#529	—	2	1	no	—
357	#529	—	2	1	no	—
358	#529	C₂²×C₇	1	2	yes	complemented
359	#529	C₂²×C₇	1	2	yes	complemented
360	#525	—	2	1	no	—
361	#525	—	2	1	no	—
362	#525	C₂²×C₇	1	2	yes	—
363	C₄×#41	—	2	1	no	—
364	C₄×#41	—	2	1	no	—
365	C₄×#41	C₂²×C₇	1	2	yes	complemented
366	C₂×C₄×D₄	—	2	1	no	—
367	C₂×C₄×D₄	—	2	1	no	—
368	C₂×C₄×D₄	—	2	1	no	—
369	C₂×C₄×D₄	—	2	1	no	—
370	C₂×C₄×D₄	—	2	1	no	—
371	C₂×C₄×D₄	—	2	1	no	—
372	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
373	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
374	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
375	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
376	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
377	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
378	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
379	C₂²×C₂²⋊C₄	—	2	1	no	—
380	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
381	#484	C₂²×C₇	1	4	yes	complemented
382	#483	C₂²×C₇	1	4	yes	complemented
383	#481	C₂²×C₇	1	4	yes	complemented
384	#480	C₂²×C₇	1	4	yes	complemented
385	#478	C₂²×C₇	1	8	yes	complemented
386	#476	C₂²×C₇	1	4	yes	complemented
387	#474	C₂²×C₇	1	4	yes	complemented
388	#463	C₂²×C₇	1	8	yes	complemented
389	#461	C₂²×C₇	1	4	yes	complemented
390	#459	C₂²×C₇	1	4	yes	complemented
391	#450	C₂²×C₇	1	4	yes	—
392	#450	C₂²×C₇	1	4	yes	—
393	#447	C₂²×C₇	1	4	yes	—
394	#447	C₂²×C₇	1	4	yes	—
395	#442	C₂²×C₇	1	8	yes	complemented
396	#440	C₂²×C₇	1	8	yes	complemented
397	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
398	C₄×D₈	C₂²×C₇	1	8	yes	complemented
399	#432	C₂²×C₇	1	2	yes	complemented
400	#432	C₂²×C₇	1	2	yes	complemented
401	#431	C₂²×C₇	1	2	yes	complemented
402	#431	C₂²×C₇	1	2	yes	complemented
403	#428	C₂²×C₇	1	4	yes	complemented
404	#423	C₂²×C₇	1	2	yes	complemented
405	#418	C₂²×C₇	1	4	yes	—
406	#417	C₂²×C₇	1	4	yes	complemented
407	#407	C₂²×C₇	1	2	yes	—
408	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
409	C₂³×C₇	—	2	2	no	—
410	C₂³×C₇	—	2	2	no	—
411	C₂³×C₇	—	2	2	no	—
412	C₂³×C₇	—	2	8	no	—
413	C₂³×C₇	—	2	8	no	—
414	C₂³×C₇	—	2	8	no	—
415	C₂³×C₇	—	2	4	no	—
416	C₂³×C₇	—	2	2	no	—
417	C₂³×C₇	—	4	4	no	—
418	C₂³×C₇	—	4	4	no	—
419	C₂³×C₇	—	4	32	no	—
420	C₂³×C₇	—	4	4	no	—
421	C₂³×C₇	—	4	4	no	—
422	C₂³×C₇	—	4	4	no	—
423	C₂³×C₇	—	4	4	no	—
424	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
425	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
426	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
427	C₇×Q₈	—	2	4	no	—
428	C₇×Q₈	—	4	2	no	—
429	C₇×Q₈	—	4	2	no	—
430	C₇×D₄	—	2	8	no	—
431	C₇×D₄	—	2	8	no	—
432	C₇×D₄	—	2	8	no	—
433	C₇×D₄	—	2	4	no	—
434	C₇×D₄	—	2	4	no	—
435	C₇×D₄	—	4	2	no	—
436	C₇×D₄	—	4	4	no	—
437	C₇×D₄	—	4	4	no	—
438	C₇×D₄	—	4	4	no	—
439	C₇×D₄	—	4	2	no	—
440	C₇×D₄	C₂×#41	1	8	yes	—
441	C₂×C₄×C₇	—	2	2	no	—
442	C₂×C₄×C₇	—	2	2	no	—
443	C₂×C₄×C₇	—	2	2	no	—
444	C₂×C₄×C₇	—	2	2	no	—
445	C₂×C₄×C₇	—	2	2	no	—
446	C₂×C₄×C₇	—	2	2	no	—
447	C₂×C₄×C₇	—	2	2	no	—
448	C₂×C₄×C₇	—	2	2	no	—
449	C₂×C₄×C₇	—	2	2	no	—
450	C₂×C₄×C₇	—	2	2	no	—
451	C₂×C₄×C₇	—	2	2	no	—
452	C₂×C₄×C₇	—	2	2	no	—
453	C₂×C₄×C₇	—	2	2	no	—
454	C₂×C₄×C₇	—	2	2	no	—
455	C₂×C₄×C₇	—	2	2	no	—
456	C₂×C₄×C₇	—	2	4	no	—
457	C₂×C₄×C₇	—	4	1	no	—
458	C₂×C₄×C₇	—	4	1	no	—
459	C₂×C₄×C₇	—	4	1	no	—
460	C₂×C₄×C₇	—	4	1	no	—
461	C₂×C₄×C₇	—	4	8	no	—
462	C₂×C₄×C₇	—	4	8	no	—
463	C₂×C₄×C₇	—	4	4	no	—
464	C₂×C₄×C₇	—	4	4	no	—
465	C₂×C₄×C₇	—	4	4	no	—
466	C₂×C₄×C₇	—	4	4	no	—
467	C₂×C₄×C₇	—	4	4	no	—
468	C₂×C₄×C₇	—	4	8	no	—
469	C₂×C₄×C₇	—	4	8	no	—
470	C₂×C₄×C₇	—	4	4	no	—
471	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	complemented
472	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₇	C₂×#41	1	4	yes	—
484	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
485	C₇×C₈	—	2	8	no	—
486	C₂⁵	—	2	1	no	—
487	C₂×#41	—	2	1	no	—
488	C₂×#41	—	2	1	no	—
489	C₂×#41	C₂³×C₇	1	2	yes	—
490	C₂²×D₄	—	2	8	no	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	C₂³×C₇	1	2	yes	—
495	C₂²×D₄	C₂³×C₇	1	2	yes	—
496	C₂²×D₄	C₂³×C₇	1	2	yes	—
497	C₂³×C₄	—	2	1	no	—
498	C₂³×C₄	—	2	2	no	—
499	C₂³×C₄	—	2	2	no	—
500	C₂³×C₄	—	2	2	no	—
501	C₂³×C₄	—	2	2	no	—
502	C₂³×C₄	—	2	2	no	—
503	C₂³×C₄	—	2	2	no	—
504	C₂³×C₄	—	4	8	no	—
505	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
506	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
508	AGL(1,ℤ/8)	—	2	16	no	—
509	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
510	C₂×D₈	C₂³×C₇	1	8	yes	—
511	C₂×M₁₆	C₂³×C₇	1	4	yes	—
512	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic, complemented
513	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic, complemented
514	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic, complemented
515	#127	C₂³×C₇	1	1	yes	characteristic, complemented
516	#126	—	2	2	no	—
517	#126	—	2	2	no	—
518	#125	—	2	1	no	—
519	#125	—	2	1	no	—
520	#125	C₂³×C₇	1	2	yes	complemented
521	#124	—	2	1	no	—
522	#124	—	2	1	no	—
523	#124	C₂³×C₇	1	2	yes	complemented
524	#123	—	2	2	no	—
525	#123	—	2	2	no	—
526	#123	—	2	2	no	—
527	C₂²⋊Q₈	—	2	1	no	—
528	C₂²⋊Q₈	—	2	1	no	—
529	C₂²⋊Q₈	—	2	1	no	—
530	C₂²⋊Q₈	—	2	1	no	—
531	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
532	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
533	#121	—	2	1	no	—
534	#121	—	2	1	no	—
535	#121	—	2	1	no	—
536	#121	—	2	1	no	—
537	#121	C₂³×C₇	1	2	yes	—
538	#121	C₂³×C₇	1	2	yes	—
539	#120	—	2	2	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	—	2	1	no	—
543	C₄×Q₈	—	2	1	no	—
544	C₄×Q₈	C₂³×C₇	1	2	yes	complemented
545	C₄×Q₈	C₂³×C₇	1	2	yes	complemented
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	2	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	C₂³×C₇	1	4	yes	—
569	C₄×D₄	C₂³×C₇	1	4	yes	—
570	C₄×D₄	C₂³×C₇	1	4	yes	—
571	C₄×D₄	C₂³×C₇	1	4	yes	—
572	C₄×D₄	C₂³×C₇	1	2	yes	complemented
573	C₄×D₄	C₂³×C₇	1	2	yes	complemented
574	#117	—	2	1	no	—
575	#117	—	2	1	no	—
576	#117	—	2	2	no	—
577	#117	—	2	2	no	—
578	#117	—	2	2	no	—
579	#117	C₂³×C₇	1	2	yes	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
586	C₂×C₂²⋊C₄	—	2	2	no	—
587	C₂×C₂²⋊C₄	—	2	2	no	—
588	C₂×C₂²⋊C₄	—	2	2	no	—
589	C₂×C₂²⋊C₄	—	2	2	no	—
590	C₂×C₂²⋊C₄	—	2	2	no	—
591	C₂×C₂²⋊C₄	—	2	2	no	—
592	C₂×C₄²	—	2	2	no	—
593	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
594	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
595	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
596	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
597	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
598	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
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	1	yes	characteristic
605	#107	C₂³×C₇	1	8	yes	complemented
606	#106	C₂³×C₇	1	8	yes	complemented
607	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
608	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
609	#103	C₂³×C₇	1	8	yes	complemented
610	#102	C₂³×C₇	1	8	yes	—
611	#102	C₂³×C₇	1	8	yes	—
612	#102	C₂³×C₇	1	8	yes	complemented
613	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
614	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
615	#97	C₂³×C₇	1	4	yes	complemented
616	C₄×C₈	C₂³×C₇	1	4	yes	complemented
617	C₂²×C₇	—	2	8	no	—
618	C₂²×C₇	—	2	1	no	—
619	C₂²×C₇	—	2	1	no	—
620	C₂²×C₇	—	2	1	no	—
621	C₂²×C₇	—	2	1	no	—
622	C₂²×C₇	—	2	1	no	—
623	C₂²×C₇	—	2	1	no	—
624	C₂²×C₇	—	2	8	no	—
625	C₂²×C₇	—	4	16	no	—
626	C₂²×C₇	—	4	16	no	—
627	C₂²×C₇	—	4	16	no	—
628	C₂²×C₇	—	4	4	no	—
629	C₂²×C₇	—	4	4	no	—
630	C₂²×C₇	—	4	2	no	—
631	C₂²×C₇	—	4	2	no	—
632	C₂²×C₇	—	4	2	no	—
633	C₂²×C₇	#525	1	2	yes	—
634	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
635	C₂²×C₇	#575	1	2	yes	—
636	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
637	C₄×C₇	—	2	1	no	—
638	C₄×C₇	—	2	1	no	—
639	C₄×C₇	—	2	1	no	—
640	C₄×C₇	—	2	1	no	—
641	C₄×C₇	—	2	1	no	—
642	C₄×C₇	—	2	1	no	—
643	C₄×C₇	—	2	1	no	—
644	C₄×C₇	—	2	1	no	—
645	C₄×C₇	—	4	2	no	—
646	C₄×C₇	—	4	4	no	—
647	C₄×C₇	—	4	2	no	—
648	C₄×C₇	—	4	2	no	—
649	C₄×C₇	#525	1	2	yes	—
650	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
651	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
652	C₄×C₇	C₂²×#41	1	2	yes	—
653	C₂⁴	—	2	8	no	—
654	C₂⁴	—	2	2	no	—
655	C₂⁴	—	2	2	no	—
656	C₂⁴	—	2	2	no	—
657	C₂⁴	—	4	4	no	—
658	C₂⁴	—	4	4	no	—
659	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
660	#41	—	2	8	no	—
661	#41	—	4	4	no	—
662	#41	—	4	4	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
666	C₂×D₄	—	2	8	no	—
667	C₂×D₄	—	2	8	no	—
668	C₂×D₄	—	2	8	no	—
669	C₂×D₄	—	2	8	no	—
670	C₂×D₄	—	2	8	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	C₇×#41	1	8	yes	complemented
681	C₂×D₄	C₂⁴×C₇	1	2	yes	—
682	C₂×D₄	C₂⁴×C₇	1	4	yes	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	—	4	8	no	—
697	C₂²×C₄	—	4	8	no	—
698	C₂²×C₄	—	4	8	no	—
699	C₂²×C₄	—	4	8	no	—
700	C₂²×C₄	—	4	8	no	—
701	C₂²×C₄	—	4	4	no	—
702	C₂²×C₄	—	4	8	no	—
703	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
704	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
705	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
706	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
707	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
708	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
709	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
710	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
711	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
712	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
713	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
714	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
715	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
716	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
717	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
721	SD₁₆	—	2	16	no	—
722	D₈	—	2	16	no	—
723	M₁₆	—	2	8	no	—
724	C₂×C₈	C₂⁴×C₇	1	8	yes	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
740	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
758	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
759	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
760	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
761	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
762	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
763	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
764	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
765	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
766	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
767	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
768	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
769	C₄²	C₂⁴×C₇	1	1	yes	characteristic
770	C₄²	C₂⁴×C₇	1	1	yes	characteristic
771	C₄²	C₂⁴×C₇	1	1	yes	characteristic
772	C₄²	C₂⁴×C₇	1	1	yes	characteristic
773	C₂×C₇	—	2	2	no	—
774	C₂×C₇	—	2	2	no	—
775	C₂×C₇	—	2	2	no	—
776	C₂×C₇	—	4	8	no	—
777	C₂×C₇	—	8	2	no	—
778	C₂×C₇	C₂×#525	1	1	yes	characteristic
779	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
780	C₂×C₇	C₂×#575	1	1	yes	characteristic
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	8	no	—
785	C₂³	—	2	8	no	—
786	C₂³	—	2	4	no	—
787	C₂³	—	2	8	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	4	4	no	—
790	C₂³	—	4	4	no	—
791	C₂³	—	4	32	no	—
792	C₂³	—	4	4	no	—
793	C₂³	—	4	4	no	—
794	C₂³	—	4	4	no	—
795	C₂³	—	4	4	no	—
796	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
797	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
798	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
799	Q₈	—	2	4	no	—
800	Q₈	—	4	2	no	—
801	Q₈	—	4	2	no	—
802	D₄	—	2	8	no	—
803	D₄	—	2	8	no	—
804	D₄	—	2	4	no	—
805	D₄	—	2	4	no	—
806	D₄	—	2	8	no	—
807	D₄	—	4	2	no	—
808	D₄	—	4	4	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	2	no	—
812	D₄	C₂×C₇×#41	1	8	yes	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	4	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	8	no	—
834	C₂×C₄	—	4	8	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	—	4	4	no	—
839	C₂×C₄	—	4	4	no	—
840	C₂×C₄	—	4	8	no	—
841	C₂×C₄	—	4	8	no	—
842	C₂×C₄	—	4	4	no	—
843	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	complemented
844	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
845	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
846	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
847	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
848	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
849	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
850	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
851	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
852	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
853	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
854	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
855	C₂×C₄	C₂×C₇×#41	1	4	yes	—
856	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
857	C₈	—	2	8	no	—
858	C₇	#60558	1	1	yes	characteristic, direct product factor, Sylow
859	C₂²	—	2	8	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	2	1	no	—
866	C₂²	—	2	8	no	—
867	C₂²	—	4	16	no	—
868	C₂²	—	4	16	no	—
869	C₂²	—	4	16	no	—
870	C₂²	—	4	4	no	—
871	C₂²	—	4	4	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	C₇×#525	1	2	yes	—
876	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
877	C₂²	C₇×#575	1	2	yes	—
878	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
879	C₄	—	2	1	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	1	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	1	no	—
884	C₄	—	2	1	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	4	4	no	—
888	C₄	—	4	2	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	2	no	—
891	C₄	C₇×#525	1	2	yes	—
892	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
893	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
894	C₄	C₂²×C₇×#41	1	2	yes	—
895	C₂	—	2	2	no	—
896	C₂	—	2	2	no	—
897	C₂	—	2	2	no	—
898	C₂	—	4	8	no	—
899	C₂	—	8	2	no	—
900	C₂	C₂×C₇×#525	1	1	yes	characteristic
901	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
902	C₂	C₂×C₇×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3444	C₂	semidirect
2. C₂²×C₄×C₇×D₄	C₂	semidirect
3. C₇×#3114	C₂	semidirect
4. C₇×#3110	C₂	semidirect
5. C₇×#3109	C₂	semidirect
6. C₇×#3105	C₂	semidirect
7. C₇×#3101	C₂	semidirect
8. C₇×#3100	C₂	semidirect
9. C₇×#3092	C₂	semidirect
10. C₇×#3077	C₂	semidirect
11. C₇×#3036	C₂	semidirect
12. C₇×#3003	C₂	semidirect
13. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
14. C₇×#2920	C₂	semidirect
18. C₇×#533	C₂²	semidirect
19. C₇×#533	C₂²	semidirect
20. C₇×#533	C₂²	semidirect
21. C₇×#532	C₂²	semidirect
22. C₇×#532	C₂²	semidirect
23. C₇×#532	C₂²	semidirect
28. C₇×#529	C₂²	semidirect
29. C₇×#529	C₂²	semidirect
35. C₄×C₇×#41	C₂²	semidirect
51. C₇×#484	C₂²	semidirect
52. C₇×#483	C₂²	semidirect
53. C₇×#481	C₂²	semidirect
54. C₇×#480	C₂²	semidirect
55. C₇×#478	C₂²	semidirect
56. C₇×#476	C₂²	semidirect
57. C₇×#474	C₂²	semidirect
58. C₇×#463	C₂²	semidirect
59. C₇×#461	C₂²	semidirect
60. C₇×#459	C₂²	semidirect
65. C₇×#442	C₂²	semidirect
66. C₇×#440	C₂²	semidirect
67. C₄×C₇×SD₁₆	C₂²	semidirect
68. C₄×C₇×D₈	C₂²	semidirect
69. C₇×#432	C₂²	semidirect
70. C₇×#432	C₂²	semidirect
71. C₇×#431	C₂²	semidirect
72. C₇×#431	C₂²	semidirect
73. C₇×#428	C₂²	semidirect
74. C₇×#423	C₂²	semidirect
76. C₇×#417	C₂²	semidirect
78. C₄×C₇×M₁₆	C₂²	semidirect
79. #60558	C₇	direct (N × H)
106. C₇×C₄⋊Q₈	C₂³	semidirect
107. C₇×C₄⋊Q₈	C₂³	semidirect
108. C₇×C₄⋊Q₈	C₂³	semidirect
109. C₇×#127	C₂³	semidirect
114. C₇×#125	C₂³	semidirect
117. C₇×#124	C₂³	semidirect
138. C₄×C₇×Q₈	C₂³	semidirect
139. C₄×C₇×Q₈	C₂³	semidirect
166. C₄×C₇×D₄	C₂³	semidirect
167. C₄×C₇×D₄	C₂³	semidirect
199. C₇×#107	C₂³	semidirect
200. C₇×#106	C₂³	semidirect
201. C₇×C₄⋊C₈	C₂³	semidirect
202. C₇×C₄⋊C₈	C₂³	semidirect
203. C₇×#103	C₂³	semidirect
206. C₇×#102	C₂³	semidirect
209. C₇×#97	C₂³	semidirect
210. C₄×C₇×C₈	C₂³	semidirect
211. #3444	C₂×C₇	semidirect
212. C₂²×C₄×D₄	C₂×C₇	semidirect
213. #3114	C₂×C₇	semidirect
214. #3110	C₂×C₇	semidirect
215. #3109	C₂×C₇	semidirect
216. #3105	C₂×C₇	semidirect
217. #3101	C₂×C₇	semidirect
218. #3100	C₂×C₇	semidirect
219. #3092	C₂×C₇	semidirect
220. #3077	C₂×C₇	semidirect
221. #3036	C₂×C₇	semidirect
222. #3003	C₂×C₇	semidirect
223. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
224. #2920	C₂×C₇	semidirect
252. C₂×C₇×D₄	#41	semidirect
348. #533	C₂²×C₇	semidirect
349. #533	C₂²×C₇	semidirect
350. #533	C₂²×C₇	semidirect
351. #532	C₂²×C₇	semidirect
352. #532	C₂²×C₇	semidirect
353. #532	C₂²×C₇	semidirect
358. #529	C₂²×C₇	semidirect
359. #529	C₂²×C₇	semidirect
365. C₄×#41	C₂²×C₇	semidirect
381. #484	C₂²×C₇	semidirect
382. #483	C₂²×C₇	semidirect
383. #481	C₂²×C₇	semidirect
384. #480	C₂²×C₇	semidirect
385. #478	C₂²×C₇	semidirect
386. #476	C₂²×C₇	semidirect
387. #474	C₂²×C₇	semidirect
388. #463	C₂²×C₇	semidirect
389. #461	C₂²×C₇	semidirect
390. #459	C₂²×C₇	semidirect
395. #442	C₂²×C₇	semidirect
396. #440	C₂²×C₇	semidirect
397. C₄×SD₁₆	C₂²×C₇	semidirect
398. C₄×D₈	C₂²×C₇	semidirect
399. #432	C₂²×C₇	semidirect
400. #432	C₂²×C₇	semidirect
401. #431	C₂²×C₇	semidirect
402. #431	C₂²×C₇	semidirect
403. #428	C₂²×C₇	semidirect
404. #423	C₂²×C₇	semidirect
406. #417	C₂²×C₇	semidirect
408. C₄×M₁₆	C₂²×C₇	semidirect
471. C₂×C₄×C₇	AGL(1,ℤ/8)	semidirect
512. C₄⋊Q₈	C₂³×C₇	semidirect
513. C₄⋊Q₈	C₂³×C₇	semidirect
514. C₄⋊Q₈	C₂³×C₇	semidirect
515. #127	C₂³×C₇	semidirect
520. #125	C₂³×C₇	semidirect
523. #124	C₂³×C₇	semidirect
544. C₄×Q₈	C₂³×C₇	semidirect
545. C₄×Q₈	C₂³×C₇	semidirect
572. C₄×D₄	C₂³×C₇	semidirect
573. C₄×D₄	C₂³×C₇	semidirect
605. #107	C₂³×C₇	semidirect
606. #106	C₂³×C₇	semidirect
607. C₄⋊C₈	C₂³×C₇	semidirect
608. C₄⋊C₈	C₂³×C₇	semidirect
609. #103	C₂³×C₇	semidirect
612. #102	C₂³×C₇	semidirect
615. #97	C₂³×C₇	semidirect
616. C₄×C₈	C₂³×C₇	semidirect
680. C₂×D₄	C₇×#41	semidirect
843. C₂×C₄	C₇×AGL(1,ℤ/8)	semidirect
858. C₇	#60558	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×#3444	2
C₂²×C₄×C₇×D₄	2
C₇×#3114	2
C₇×#3110	2
C₇×#3109	2
C₇×#3105	2
C₇×#3101	2
C₇×#3100	2
C₇×#3092	2
C₇×#3077	2
C₇×#3036	2
C₇×#3003	2
C₄×C₇×AGL(1,ℤ/8)	2
C₇×#2920	2
#60558	7

Subgroups — C7×#60558 #13237774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60558 #13237774