Subgroups — C₇×#61205 #13238421

Order 1792.

2214 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3332	C₂	1	2	yes	maximal, complemented
4	C₇×#3325	C₂	1	2	yes	maximal, complemented
5	C₇×#3318	C₂	1	4	yes	maximal, complemented
6	C₇×#3309	C₂	1	4	yes	maximal, complemented
7	C₇×#3305	C₂	1	2	yes	maximal, complemented
8	C₇×#3294	C₂	1	2	yes	maximal, complemented
9	C₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3096	C₂	1	2	yes	maximal, complemented
11	C₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3058	C₂	1	2	yes	maximal, complemented
13	C₂×C₇×#459	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3008	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2897	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	—
19	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂²×C₇×D₈	C₂²	1	2	yes	complemented
21	C₂×C₇×#131	C₂²	1	2	yes	complemented
22	C₇×#559	—	2	2	no	—
23	C₇×#556	—	2	1	no	—
24	C₇×#555	C₂²	1	2	yes	complemented
25	C₇×#553	C₂²	1	4	yes	complemented
26	C₇×#550	—	2	1	no	—
27	C₇×#550	C₂²	1	2	yes	complemented
28	C₇×#550	C₂²	1	2	yes	complemented
29	C₇×#547	C₂²	1	2	yes	complemented
30	C₇×D₄²	—	2	2	no	—
31	C₇×D₄²	—	2	2	no	—
32	C₇×D₄²	C₂²	1	2	yes	complemented
33	C₇×D₄²	C₂²	1	2	yes	complemented
34	C₇×#538	—	2	2	no	—
35	C₇×#535	—	2	2	no	—
36	C₇×#535	C₂²	1	2	yes	—
37	C₇×#535	C₂²	1	2	yes	complemented
38	C₇×#533	C₂²	1	1	yes	characteristic, complemented
39	C₇×#532	—	2	1	no	—
40	C₇×#532	C₂²	1	1	yes	characteristic
41	C₂×C₇×#127	—	2	1	no	—
42	C₂×C₇×#127	C₂²	1	1	yes	characteristic
43	C₇×#525	—	2	2	no	—
44	C₇×#520	C₂²	1	2	yes	complemented
45	C₄×C₇×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
47	C₇×#490	C₂²	1	4	yes	complemented
48	C₇×#486	C₂²	1	2	yes	complemented
49	C₇×#486	C₂²	1	2	yes	complemented
50	C₇×#482	C₂²	1	4	yes	complemented
51	C₇×#482	C₂²	1	4	yes	complemented
52	C₇×#481	C₂²	1	4	yes	complemented
53	C₇×#480	C₂²	1	4	yes	complemented
54	C₇×#479	C₂²	1	2	yes	complemented
55	C₇×#478	C₂²	1	2	yes	complemented
56	C₇×#477	C₂²	1	1	yes	characteristic, complemented
57	C₇×#476	C₂²	1	1	yes	characteristic, complemented
58	C₇×#475	C₂²	1	1	yes	characteristic, complemented
59	C₇×#474	C₂²	1	1	yes	characteristic, complemented
60	C₇×#469	C₂²	1	4	yes	complemented
61	C₇×#469	C₂²	1	4	yes	complemented
62	C₇×#466	C₂²	1	4	yes	complemented
63	C₇×#466	C₂²	1	4	yes	complemented
64	C₇×#459	C₂²	1	2	yes	complemented
65	C₇×#459	C₂²	1	4	yes	complemented
66	C₇×#459	C₂²	1	2	yes	complemented
67	C₇×#449	C₂²	1	4	yes	complemented
68	C₇×#449	C₂²	1	4	yes	complemented
69	C₇×#447	C₂²	1	4	yes	complemented
70	C₇×#447	C₂²	1	4	yes	complemented
71	C₇×#442	C₂²	1	2	yes	complemented
72	C₇×#440	C₂²	1	2	yes	complemented
73	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
74	C₄×C₇×D₈	C₂²	1	2	yes	complemented
75	C₇×#436	C₂²	1	2	yes	complemented
76	C₇×#435	C₂²	1	4	yes	complemented
77	C₇×C₈×D₄	C₂²	1	2	yes	complemented
78	C₇×#428	C₂²	1	1	yes	characteristic, complemented
79	C₇×#427	C₂²	1	2	yes	complemented
80	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
81	C₇×#418	C₂²	1	1	yes	characteristic, complemented
82	C₇×#418	C₂²	1	2	yes	complemented
83	C₇×#418	C₂²	1	2	yes	complemented
84	C₇×#418	C₂²	1	4	yes	complemented
85	C₇×#417	C₂²	1	1	yes	characteristic
86	C₇×#417	C₂²	1	4	yes	complemented
87	C₇×#416	C₂²	1	2	yes	—
88	C₇×#416	C₂²	1	4	yes	complemented
89	C₂×C₇×#102	C₂²	1	2	yes	complemented
90	C₂×C₇×#102	C₂²	1	4	yes	complemented
91	C₇×#408	C₂²	1	2	yes	complemented
92	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
93	#61205	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₇×H(5,𝔽₂)	—	2	8	no	—
95	C₇×H(5,𝔽₂)	—	4	4	no	—
96	C₂×C₇×#41	—	2	2	no	—
97	C₂×C₇×#41	—	2	2	no	—
98	C₂×C₇×#41	C₂³	1	4	yes	—
99	C₂×C₇×#41	C₂³	1	1	yes	characteristic
100	C₂×C₇×#41	C₂³	1	2	yes	—
101	C₂²×C₇×D₄	—	2	2	no	—
102	C₂²×C₇×D₄	—	2	4	no	—
103	C₂²×C₇×D₄	—	2	2	no	—
104	C₂²×C₇×D₄	—	2	2	no	—
105	C₂²×C₇×D₄	—	2	1	no	—
106	C₂²×C₇×D₄	—	2	1	no	—
107	C₂²×C₇×D₄	C₂³	1	2	yes	—
108	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
109	C₂²×C₇×D₄	C₂³	1	4	yes	—
110	C₂³×C₄×C₇	—	2	1	no	—
111	C₇×AGL(1,ℤ/8)	—	2	4	no	—
112	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
113	C₂×C₇×D₈	—	4	4	no	—
114	C₂×C₇×D₈	C₂³	1	2	yes	—
115	C₂×C₇×D₈	C₂³	1	4	yes	—
116	C₂×C₇×D₈	C₂³	1	4	yes	—
117	C₇×#131	—	4	4	no	—
118	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
119	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
120	C₂×C₇×M₁₆	C₂³	1	4	yes	—
121	C₂²×C₇×C₈	C₂³	1	2	yes	—
122	C₂²×C₇×C₈	C₂³	1	4	yes	—
123	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
124	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₇×#127	—	2	2	no	—
127	C₇×#127	—	2	2	no	—
128	C₇×#127	—	2	2	no	—
129	C₇×#127	—	2	2	no	—
130	C₇×#127	—	2	1	no	—
131	C₇×#127	—	2	1	no	—
132	C₇×#127	D₄	1	1	yes	characteristic
133	C₇×#127	C₂³	1	2	yes	—
134	C₇×#127	C₂³	1	2	yes	—
135	C₇×#126	—	2	4	no	—
136	C₇×#125	C₂³	1	2	yes	—
137	C₇×#124	—	2	2	no	—
138	C₇×#124	—	2	2	no	—
139	C₇×#124	—	2	4	no	—
140	C₇×#124	D₄	1	2	yes	—
141	C₇×#123	—	2	4	no	—
142	C₇×#123	—	2	4	no	—
143	C₇×C₂²⋊Q₈	—	2	1	no	—
144	C₇×C₂²⋊Q₈	—	2	1	no	—
145	C₇×C₂²⋊Q₈	—	2	2	no	—
146	C₇×#121	—	2	2	no	—
147	C₇×#121	—	2	4	no	—
148	C₇×#121	—	2	2	no	—
149	C₇×#121	—	2	2	no	—
150	C₇×#121	—	2	4	no	—
151	C₇×#121	—	2	4	no	—
152	C₇×#121	D₄	1	2	yes	—
153	C₇×#121	D₄	1	2	yes	—
154	C₇×#121	C₂³	1	4	yes	—
155	C₇×#121	C₂³	1	4	yes	—
156	C₇×#121	C₂³	1	4	yes	—
157	C₇×#121	C₂³	1	4	yes	—
158	C₇×#120	—	2	4	no	—
159	C₇×#120	—	2	4	no	—
160	C₇×#120	—	2	4	no	—
161	C₇×#120	—	2	4	no	—
162	C₄×C₇×Q₈	—	2	2	no	—
163	C₄×C₇×Q₈	—	2	1	no	—
164	C₄×C₇×Q₈	—	2	1	no	—
165	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
166	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
167	C₄×C₇×D₄	—	2	4	no	—
168	C₄×C₇×D₄	—	2	2	no	—
169	C₄×C₇×D₄	—	2	1	no	—
170	C₄×C₇×D₄	—	2	1	no	—
171	C₄×C₇×D₄	—	2	2	no	—
172	C₄×C₇×D₄	—	2	2	no	—
173	C₄×C₇×D₄	—	2	4	no	—
174	C₄×C₇×D₄	—	2	1	no	—
175	C₄×C₇×D₄	—	2	1	no	—
176	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
177	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
178	C₄×C₇×D₄	C₂³	1	2	yes	—
179	C₄×C₇×D₄	C₂³	1	2	yes	—
180	C₄×C₇×D₄	C₂³	1	2	yes	—
181	C₄×C₇×D₄	C₂³	1	2	yes	—
182	C₇×#117	—	2	2	no	—
183	C₇×#117	—	2	1	no	—
184	C₇×#117	C₂³	1	4	yes	—
185	C₇×#117	C₂³	1	1	yes	characteristic
186	C₇×#117	C₂³	1	2	yes	—
187	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
188	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
190	C₂×C₄²×C₇	—	2	1	no	—
191	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
192	C₇×#107	C₂³	1	2	yes	—
193	C₇×#107	C₂³	1	2	yes	—
194	C₇×#107	C₂³	1	2	yes	—
195	C₇×#106	C₂³	1	2	yes	—
196	C₇×#106	C₂³	1	2	yes	—
197	C₇×#106	C₂³	1	2	yes	—
198	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
199	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
200	C₇×C₄⋊C₈	C₂³	1	2	yes	—
201	C₇×#103	C₂³	1	2	yes	—
202	C₇×#103	C₂³	1	2	yes	—
203	C₇×#103	C₂³	1	2	yes	—
204	C₇×#102	C₂³	1	2	yes	—
205	C₇×#102	C₂³	1	2	yes	—
206	C₇×#102	C₂³	1	4	yes	—
207	C₇×#102	C₂³	1	4	yes	—
208	C₇×#102	C₂³	1	2	yes	—
209	C₇×#102	C₂³	1	2	yes	—
210	C₇×#102	C₂³	1	4	yes	—
211	C₇×#102	C₂³	1	4	yes	—
212	C₇×#102	C₂³	1	4	yes	—
213	C₇×#102	C₂³	1	4	yes	—
214	C₇×#102	C₂³	1	2	yes	—
215	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
216	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
217	C₇×#97	C₂³	1	2	yes	—
218	C₄×C₇×C₈	C₂³	1	2	yes	—
219	#3506	C₂×C₇	1	1	yes	characteristic, complemented
220	#3498	C₂×C₇	1	1	yes	characteristic, complemented
221	#3332	C₂×C₇	1	2	yes	complemented
222	#3325	C₂×C₇	1	2	yes	complemented
223	#3318	C₂×C₇	1	4	yes	complemented
224	#3309	C₂×C₇	1	4	yes	complemented
225	#3305	C₂×C₇	1	2	yes	complemented
226	#3294	C₂×C₇	1	2	yes	complemented
227	#3138	C₂×C₇	1	1	yes	characteristic, complemented
228	#3096	C₂×C₇	1	2	yes	complemented
229	#3076	C₂×C₇	1	1	yes	characteristic, complemented
230	#3058	C₂×C₇	1	2	yes	complemented
231	C₂×#459	C₂×C₇	1	1	yes	characteristic, complemented
232	#3008	C₂×C₇	1	2	yes	complemented
233	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic, complemented
234	#2935	C₂×C₇	1	1	yes	characteristic, complemented
235	#2897	C₂×C₇	1	2	yes	complemented
236	C₂⁴×C₇	—	2	1	no	—
237	C₂⁴×C₇	—	2	4	no	—
238	C₂⁴×C₇	—	2	2	no	—
239	C₇×#41	—	2	4	no	—
240	C₇×#41	—	2	4	no	—
241	C₇×#41	—	2	2	no	—
242	C₇×#41	—	2	8	no	—
243	C₇×#41	—	4	4	no	—
244	C₇×#41	—	4	8	no	—
245	C₇×#41	—	8	4	no	—
246	C₇×#41	#41	1	4	yes	complemented
247	C₂×C₇×Q₈	—	2	1	no	—
248	C₂×C₇×Q₈	—	2	1	no	—
249	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
250	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
251	C₂×C₇×D₄	—	2	1	no	—
252	C₂×C₇×D₄	—	2	8	no	—
253	C₂×C₇×D₄	—	2	4	no	—
254	C₂×C₇×D₄	—	2	4	no	—
255	C₂×C₇×D₄	—	2	4	no	—
256	C₂×C₇×D₄	—	2	4	no	—
257	C₂×C₇×D₄	—	2	4	no	—
258	C₂×C₇×D₄	—	2	1	no	—
259	C₂×C₇×D₄	—	2	2	no	—
260	C₂×C₇×D₄	—	2	2	no	—
261	C₂×C₇×D₄	—	2	4	no	—
262	C₂×C₇×D₄	—	2	2	no	—
263	C₂×C₇×D₄	—	2	2	no	—
264	C₂×C₇×D₄	—	2	2	no	—
265	C₂×C₇×D₄	—	2	2	no	—
266	C₂×C₇×D₄	—	2	4	no	—
267	C₂×C₇×D₄	—	2	2	no	—
268	C₂×C₇×D₄	—	2	4	no	—
269	C₂×C₇×D₄	—	4	4	no	—
270	C₂×C₇×D₄	—	4	8	no	—
271	C₂×C₇×D₄	—	4	16	no	—
272	C₂×C₇×D₄	—	8	2	no	—
273	C₂×C₇×D₄	—	8	4	no	—
274	C₂×C₇×D₄	—	8	2	no	—
275	C₂×C₇×D₄	—	8	4	no	—
276	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
277	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
278	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
279	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
280	C₂×C₇×D₄	C₂⁴	1	4	yes	—
281	C₂×C₇×D₄	C₂⁴	1	2	yes	—
282	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₇	—	2	1	no	—
284	C₂²×C₄×C₇	—	2	1	no	—
285	C₂²×C₄×C₇	—	2	4	no	—
286	C₂²×C₄×C₇	—	2	1	no	—
287	C₂²×C₄×C₇	—	2	1	no	—
288	C₂²×C₄×C₇	—	2	2	no	—
289	C₂²×C₄×C₇	—	2	4	no	—
290	C₂²×C₄×C₇	—	2	2	no	—
291	C₂²×C₄×C₇	—	8	2	no	—
292	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
295	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
296	C₇×SD₁₆	—	2	4	no	—
297	C₇×D₈	—	2	4	no	—
298	C₇×D₈	—	4	4	no	—
299	C₇×D₈	—	4	4	no	—
300	C₇×M₁₆	—	2	2	no	—
301	C₇×M₁₆	—	2	2	no	—
302	C₇×M₁₆	—	4	4	no	—
303	C₂×C₇×C₈	—	2	4	no	—
304	C₂×C₇×C₈	—	4	4	no	—
305	C₂×C₇×C₈	C₂⁴	1	2	yes	—
306	C₂×C₇×C₈	C₂⁴	1	2	yes	—
307	C₂×C₇×C₈	C₂⁴	1	2	yes	—
308	C₂×C₇×C₈	C₂⁴	1	2	yes	—
309	C₇×C₄⋊C₄	—	2	1	no	—
310	C₇×C₄⋊C₄	—	2	4	no	—
311	C₇×C₄⋊C₄	—	2	1	no	—
312	C₇×C₄⋊C₄	—	2	1	no	—
313	C₇×C₄⋊C₄	—	2	1	no	—
314	C₇×C₄⋊C₄	—	2	2	no	—
315	C₇×C₄⋊C₄	—	2	2	no	—
316	C₇×C₄⋊C₄	—	2	1	no	—
317	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
318	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
319	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
320	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
321	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
322	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
323	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
324	C₇×C₂²⋊C₄	—	2	1	no	—
325	C₇×C₂²⋊C₄	—	2	2	no	—
326	C₇×C₂²⋊C₄	—	2	4	no	—
327	C₇×C₂²⋊C₄	—	2	2	no	—
328	C₇×C₂²⋊C₄	—	2	2	no	—
329	C₇×C₂²⋊C₄	—	2	1	no	—
330	C₇×C₂²⋊C₄	—	2	1	no	—
331	C₇×C₂²⋊C₄	—	2	4	no	—
332	C₇×C₂²⋊C₄	—	2	4	no	—
333	C₇×C₂²⋊C₄	—	2	4	no	—
334	C₇×C₂²⋊C₄	—	2	4	no	—
335	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
336	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
337	C₄²×C₇	—	2	1	no	—
338	C₄²×C₇	—	2	1	no	—
339	C₄²×C₇	—	2	1	no	—
340	C₄²×C₇	—	2	4	no	—
341	C₄²×C₇	—	2	2	no	—
342	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
344	C₄²×C₇	C₂⁴	1	1	yes	characteristic
345	C₄²×C₇	C₂⁴	1	1	yes	characteristic
346	C₂×H(5,𝔽₂)	C₂²×C₇	1	2	yes	—
347	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
348	C₂²×D₈	C₂²×C₇	1	2	yes	complemented
349	C₂×#131	C₂²×C₇	1	2	yes	complemented
350	#559	—	2	2	no	—
351	#556	—	2	1	no	—
352	#555	C₂²×C₇	1	2	yes	complemented
353	#553	C₂²×C₇	1	4	yes	complemented
354	#550	—	2	1	no	—
355	#550	C₂²×C₇	1	2	yes	complemented
356	#550	C₂²×C₇	1	2	yes	complemented
357	#547	C₂²×C₇	1	2	yes	complemented
358	D₄²	—	2	2	no	—
359	D₄²	—	2	2	no	—
360	D₄²	C₂²×C₇	1	2	yes	complemented
361	D₄²	C₂²×C₇	1	2	yes	complemented
362	#538	—	2	2	no	—
363	#535	—	2	2	no	—
364	#535	C₂²×C₇	1	2	yes	—
365	#535	C₂²×C₇	1	2	yes	complemented
366	#533	C₂²×C₇	1	1	yes	characteristic, complemented
367	#532	—	2	1	no	—
368	#532	C₂²×C₇	1	1	yes	characteristic
369	C₂×#127	—	2	1	no	—
370	C₂×#127	C₂²×C₇	1	1	yes	characteristic
371	#525	—	2	2	no	—
372	#520	C₂²×C₇	1	2	yes	complemented
373	C₄×#41	C₂²×C₇	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
375	#490	C₂²×C₇	1	4	yes	complemented
376	#486	C₂²×C₇	1	2	yes	complemented
377	#486	C₂²×C₇	1	2	yes	complemented
378	#482	C₂²×C₇	1	4	yes	complemented
379	#482	C₂²×C₇	1	4	yes	complemented
380	#481	C₂²×C₇	1	4	yes	complemented
381	#480	C₂²×C₇	1	4	yes	complemented
382	#479	C₂²×C₇	1	2	yes	complemented
383	#478	C₂²×C₇	1	2	yes	complemented
384	#477	C₂²×C₇	1	1	yes	characteristic, complemented
385	#476	C₂²×C₇	1	1	yes	characteristic, complemented
386	#475	C₂²×C₇	1	1	yes	characteristic, complemented
387	#474	C₂²×C₇	1	1	yes	characteristic, complemented
388	#469	C₂²×C₇	1	4	yes	complemented
389	#469	C₂²×C₇	1	4	yes	complemented
390	#466	C₂²×C₇	1	4	yes	complemented
391	#466	C₂²×C₇	1	4	yes	complemented
392	#459	C₂²×C₇	1	2	yes	complemented
393	#459	C₂²×C₇	1	2	yes	complemented
394	#459	C₂²×C₇	1	4	yes	complemented
395	#449	C₂²×C₇	1	4	yes	complemented
396	#449	C₂²×C₇	1	4	yes	complemented
397	#447	C₂²×C₇	1	4	yes	complemented
398	#447	C₂²×C₇	1	4	yes	complemented
399	#442	C₂²×C₇	1	2	yes	complemented
400	#440	C₂²×C₇	1	2	yes	complemented
401	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
402	C₄×D₈	C₂²×C₇	1	2	yes	complemented
403	#436	C₂²×C₇	1	2	yes	complemented
404	#435	C₂²×C₇	1	4	yes	complemented
405	C₈×D₄	C₂²×C₇	1	2	yes	complemented
406	#428	C₂²×C₇	1	1	yes	characteristic, complemented
407	#427	C₂²×C₇	1	2	yes	complemented
408	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
409	#418	C₂²×C₇	1	2	yes	complemented
410	#418	C₂²×C₇	1	2	yes	complemented
411	#418	C₂²×C₇	1	4	yes	complemented
412	#418	C₂²×C₇	1	1	yes	characteristic, complemented
413	#417	C₂²×C₇	1	1	yes	characteristic
414	#417	C₂²×C₇	1	4	yes	complemented
415	#416	C₂²×C₇	1	2	yes	—
416	#416	C₂²×C₇	1	4	yes	complemented
417	C₂×#102	C₂²×C₇	1	2	yes	complemented
418	C₂×#102	C₂²×C₇	1	4	yes	complemented
419	#408	C₂²×C₇	1	2	yes	complemented
420	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
421	C₂³×C₇	—	2	1	no	—
422	C₂³×C₇	—	2	2	no	—
423	C₂³×C₇	—	2	4	no	—
424	C₂³×C₇	—	4	8	no	—
425	C₂³×C₇	—	4	2	no	—
426	C₂³×C₇	—	4	4	no	—
427	C₂³×C₇	—	8	1	no	—
428	C₂³×C₇	—	8	1	no	—
429	C₂³×C₇	—	8	2	no	—
430	C₂³×C₇	—	8	2	no	—
431	C₂³×C₇	—	8	4	no	—
432	C₂³×C₇	—	8	4	no	—
433	C₂³×C₇	C₂²×D₄	1	4	yes	—
434	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
435	C₇×Q₈	—	2	4	no	—
436	C₇×Q₈	—	2	1	no	—
437	C₇×Q₈	—	4	2	no	—
438	C₇×Q₈	—	8	1	no	—
439	C₇×Q₈	C₂×#41	1	2	yes	—
440	C₇×D₄	—	2	4	no	—
441	C₇×D₄	—	2	8	no	—
442	C₇×D₄	—	2	4	no	—
443	C₇×D₄	—	2	4	no	—
444	C₇×D₄	—	2	2	no	—
445	C₇×D₄	—	2	4	no	—
446	C₇×D₄	—	2	1	no	—
447	C₇×D₄	—	2	2	no	—
448	C₇×D₄	—	2	4	no	—
449	C₇×D₄	—	4	2	no	—
450	C₇×D₄	—	4	8	no	—
451	C₇×D₄	—	4	8	no	—
452	C₇×D₄	—	4	4	no	—
453	C₇×D₄	—	4	2	no	—
454	C₇×D₄	—	4	4	no	—
455	C₇×D₄	—	4	4	no	—
456	C₇×D₄	—	8	2	no	—
457	C₇×D₄	—	8	2	no	—
458	C₇×D₄	—	8	4	no	—
459	C₇×D₄	—	8	4	no	—
460	C₇×D₄	—	8	4	no	—
461	C₇×D₄	—	8	4	no	—
462	C₇×D₄	C₂×#41	1	2	yes	—
463	C₂×C₄×C₇	—	2	1	no	—
464	C₂×C₄×C₇	—	2	4	no	—
465	C₂×C₄×C₇	—	2	2	no	—
466	C₂×C₄×C₇	—	2	4	no	—
467	C₂×C₄×C₇	—	2	4	no	—
468	C₂×C₄×C₇	—	2	2	no	—
469	C₂×C₄×C₇	—	2	1	no	—
470	C₂×C₄×C₇	—	2	1	no	—
471	C₂×C₄×C₇	—	2	2	no	—
472	C₂×C₄×C₇	—	2	2	no	—
473	C₂×C₄×C₇	—	4	1	no	—
474	C₂×C₄×C₇	—	4	8	no	—
475	C₂×C₄×C₇	—	4	2	no	—
476	C₂×C₄×C₇	—	4	4	no	—
477	C₂×C₄×C₇	—	4	2	no	—
478	C₂×C₄×C₇	—	8	2	no	—
479	C₂×C₄×C₇	—	8	1	no	—
480	C₂×C₄×C₇	—	8	4	no	—
481	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
483	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₇	C₂×#41	1	2	yes	—
488	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
489	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
490	C₇×C₈	—	2	2	no	—
491	C₇×C₈	—	2	2	no	—
492	C₇×C₈	—	2	2	no	—
493	C₇×C₈	—	2	2	no	—
494	H(5,𝔽₂)	—	2	8	no	—
495	H(5,𝔽₂)	—	4	4	no	—
496	C₂×#41	—	2	2	no	—
497	C₂×#41	—	2	2	no	—
498	C₂×#41	C₂³×C₇	1	4	yes	—
499	C₂×#41	C₂³×C₇	1	1	yes	characteristic
500	C₂×#41	C₂³×C₇	1	2	yes	—
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	—	2	4	no	—
503	C₂²×D₄	—	2	2	no	—
504	C₂²×D₄	—	2	2	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
508	C₂²×D₄	C₂³×C₇	1	2	yes	—
509	C₂²×D₄	C₂³×C₇	1	4	yes	—
510	C₂³×C₄	—	2	1	no	—
511	AGL(1,ℤ/8)	—	2	4	no	—
512	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
513	C₂×D₈	—	4	4	no	—
514	C₂×D₈	C₂³×C₇	1	2	yes	—
515	C₂×D₈	C₂³×C₇	1	4	yes	—
516	C₂×D₈	C₂³×C₇	1	4	yes	—
517	#131	—	4	4	no	—
518	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
519	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
520	C₂×M₁₆	C₂³×C₇	1	4	yes	—
521	C₂²×C₈	C₂³×C₇	1	2	yes	—
522	C₂²×C₈	C₂³×C₇	1	4	yes	—
523	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
524	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
525	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
526	#127	—	2	2	no	—
527	#127	—	2	2	no	—
528	#127	—	2	2	no	—
529	#127	—	2	2	no	—
530	#127	—	2	1	no	—
531	#127	—	2	1	no	—
532	#127	C₇×D₄	1	1	yes	characteristic
533	#127	C₂³×C₇	1	2	yes	—
534	#127	C₂³×C₇	1	2	yes	—
535	#126	—	2	4	no	—
536	#125	C₂³×C₇	1	2	yes	—
537	#124	—	2	2	no	—
538	#124	—	2	2	no	—
539	#124	—	2	4	no	—
540	#124	C₇×D₄	1	2	yes	—
541	#123	—	2	4	no	—
542	#123	—	2	4	no	—
543	C₂²⋊Q₈	—	2	1	no	—
544	C₂²⋊Q₈	—	2	1	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	#121	—	2	2	no	—
547	#121	—	2	4	no	—
548	#121	—	2	2	no	—
549	#121	—	2	2	no	—
550	#121	—	2	4	no	—
551	#121	—	2	4	no	—
552	#121	C₇×D₄	1	2	yes	—
553	#121	C₇×D₄	1	2	yes	—
554	#121	C₂³×C₇	1	4	yes	—
555	#121	C₂³×C₇	1	4	yes	—
556	#121	C₂³×C₇	1	4	yes	—
557	#121	C₂³×C₇	1	4	yes	—
558	#120	—	2	4	no	—
559	#120	—	2	4	no	—
560	#120	—	2	4	no	—
561	#120	—	2	4	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	—	2	1	no	—
564	C₄×Q₈	—	2	1	no	—
565	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
566	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
567	C₄×D₄	—	2	4	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	4	no	—
574	C₄×D₄	—	2	1	no	—
575	C₄×D₄	—	2	1	no	—
576	C₄×D₄	C₂³×C₇	1	2	yes	—
577	C₄×D₄	C₂³×C₇	1	2	yes	—
578	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
579	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
580	C₄×D₄	C₂³×C₇	1	2	yes	—
581	C₄×D₄	C₂³×C₇	1	2	yes	—
582	#117	—	2	2	no	—
583	#117	—	2	1	no	—
584	#117	C₂³×C₇	1	1	yes	characteristic
585	#117	C₂³×C₇	1	2	yes	—
586	#117	C₂³×C₇	1	4	yes	—
587	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₄²	—	2	1	no	—
591	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
592	#107	C₂³×C₇	1	2	yes	—
593	#107	C₂³×C₇	1	2	yes	—
594	#107	C₂³×C₇	1	2	yes	—
595	#106	C₂³×C₇	1	2	yes	—
596	#106	C₂³×C₇	1	2	yes	—
597	#106	C₂³×C₇	1	2	yes	—
598	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
599	C₄⋊C₈	C₂³×C₇	1	2	yes	—
600	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
601	#103	C₂³×C₇	1	2	yes	—
602	#103	C₂³×C₇	1	2	yes	—
603	#103	C₂³×C₇	1	2	yes	—
604	#102	C₂³×C₇	1	2	yes	—
605	#102	C₂³×C₇	1	4	yes	—
606	#102	C₂³×C₇	1	2	yes	—
607	#102	C₂³×C₇	1	4	yes	—
608	#102	C₂³×C₇	1	4	yes	—
609	#102	C₂³×C₇	1	2	yes	—
610	#102	C₂³×C₇	1	4	yes	—
611	#102	C₂³×C₇	1	2	yes	—
612	#102	C₂³×C₇	1	2	yes	—
613	#102	C₂³×C₇	1	4	yes	—
614	#102	C₂³×C₇	1	4	yes	—
615	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
616	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
617	#97	C₂³×C₇	1	2	yes	—
618	C₄×C₈	C₂³×C₇	1	2	yes	—
619	C₂²×C₇	—	2	1	no	—
620	C₂²×C₇	—	2	1	no	—
621	C₂²×C₇	—	2	4	no	—
622	C₂²×C₇	—	2	4	no	—
623	C₂²×C₇	—	2	2	no	—
624	C₂²×C₇	—	2	4	no	—
625	C₂²×C₇	—	4	1	no	—
626	C₂²×C₇	—	4	1	no	—
627	C₂²×C₇	—	4	4	no	—
628	C₂²×C₇	—	4	2	no	—
629	C₂²×C₇	—	4	4	no	—
630	C₂²×C₇	—	4	2	no	—
631	C₂²×C₇	—	4	2	no	—
632	C₂²×C₇	—	4	4	no	—
633	C₂²×C₇	—	8	4	no	—
634	C₂²×C₇	—	16	4	no	—
635	C₂²×C₇	—	16	8	no	—
636	C₂²×C₇	#546	1	2	yes	—
637	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
638	C₄×C₇	—	2	1	no	—
639	C₄×C₇	—	2	1	no	—
640	C₄×C₇	—	2	2	no	—
641	C₄×C₇	—	2	4	no	—
642	C₄×C₇	—	2	1	no	—
643	C₄×C₇	—	4	1	no	—
644	C₄×C₇	—	4	2	no	—
645	C₄×C₇	—	4	2	no	—
646	C₄×C₇	—	4	1	no	—
647	C₄×C₇	—	4	2	no	—
648	C₄×C₇	#546	1	2	yes	—
649	C₄×C₇	#576	1	2	yes	—
650	C₄×C₇	C₂²×#41	1	1	yes	characteristic
651	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
652	C₂⁴	—	2	1	no	—
653	C₂⁴	—	2	4	no	—
654	C₂⁴	—	2	2	no	—
655	#41	—	2	4	no	—
656	#41	—	2	4	no	—
657	#41	—	2	2	no	—
658	#41	—	2	8	no	—
659	#41	—	4	4	no	—
660	#41	—	4	8	no	—
661	#41	—	8	4	no	—
662	#41	C₇×#41	1	4	yes	complemented
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
666	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	8	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	4	4	no	—
686	C₂×D₄	—	4	8	no	—
687	C₂×D₄	—	4	16	no	—
688	C₂×D₄	—	8	2	no	—
689	C₂×D₄	—	8	4	no	—
690	C₂×D₄	—	8	2	no	—
691	C₂×D₄	—	8	4	no	—
692	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
693	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
694	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
695	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
696	C₂×D₄	C₂⁴×C₇	1	4	yes	—
697	C₂×D₄	C₂⁴×C₇	1	2	yes	—
698	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	8	2	no	—
708	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
709	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
711	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
712	SD₁₆	—	2	4	no	—
713	D₈	—	2	4	no	—
714	D₈	—	4	4	no	—
715	D₈	—	4	4	no	—
716	M₁₆	—	2	2	no	—
717	M₁₆	—	2	2	no	—
718	M₁₆	—	4	4	no	—
719	C₂×C₈	—	2	4	no	—
720	C₂×C₈	—	4	4	no	—
721	C₂×C₈	C₂⁴×C₇	1	2	yes	—
722	C₂×C₈	C₂⁴×C₇	1	2	yes	—
723	C₂×C₈	C₂⁴×C₇	1	2	yes	—
724	C₂×C₈	C₂⁴×C₇	1	2	yes	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
734	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
739	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
752	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
753	C₄²	—	2	1	no	—
754	C₄²	—	2	1	no	—
755	C₄²	—	2	1	no	—
756	C₄²	—	2	4	no	—
757	C₄²	—	2	2	no	—
758	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
759	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
760	C₄²	C₂⁴×C₇	1	1	yes	characteristic
761	C₄²	C₂⁴×C₇	1	1	yes	characteristic
762	C₂×C₇	—	2	2	no	—
763	C₂×C₇	—	4	4	no	—
764	C₂×C₇	—	4	2	no	—
765	C₂×C₇	—	8	2	no	—
766	C₂×C₇	—	8	4	no	—
767	C₂×C₇	C₂×#546	1	1	yes	characteristic
768	C₂×C₇	C₂×#576	1	1	yes	characteristic
769	C₂×C₇	#3585	1	1	yes	characteristic
770	C₂³	—	2	1	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	4	no	—
773	C₂³	—	4	8	no	—
774	C₂³	—	4	2	no	—
775	C₂³	—	4	4	no	—
776	C₂³	—	8	1	no	—
777	C₂³	—	8	1	no	—
778	C₂³	—	8	2	no	—
779	C₂³	—	8	2	no	—
780	C₂³	—	8	4	no	—
781	C₂³	—	8	4	no	—
782	C₂³	C₂²×C₇×D₄	1	4	yes	—
783	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
784	Q₈	—	2	1	no	—
785	Q₈	—	2	4	no	—
786	Q₈	—	4	2	no	—
787	Q₈	—	8	1	no	—
788	Q₈	C₂×C₇×#41	1	2	yes	—
789	D₄	—	2	4	no	—
790	D₄	—	2	8	no	—
791	D₄	—	2	2	no	—
792	D₄	—	2	4	no	—
793	D₄	—	2	1	no	—
794	D₄	—	2	2	no	—
795	D₄	—	2	4	no	—
796	D₄	—	2	4	no	—
797	D₄	—	2	4	no	—
798	D₄	—	4	2	no	—
799	D₄	—	4	8	no	—
800	D₄	—	4	8	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	2	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	4	no	—
805	D₄	—	8	2	no	—
806	D₄	—	8	2	no	—
807	D₄	—	8	4	no	—
808	D₄	—	8	4	no	—
809	D₄	—	8	4	no	—
810	D₄	—	8	4	no	—
811	D₄	C₂×C₇×#41	1	2	yes	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	4	no	—
814	C₂×C₄	—	2	4	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	8	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	8	2	no	—
828	C₂×C₄	—	8	1	no	—
829	C₂×C₄	—	8	4	no	—
830	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
831	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
832	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
833	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
834	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
835	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
836	C₂×C₄	C₂×C₇×#41	1	2	yes	—
837	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
838	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
839	C₈	—	2	2	no	—
840	C₈	—	2	2	no	—
841	C₈	—	2	2	no	—
842	C₈	—	2	2	no	—
843	C₇	#61205	1	1	yes	characteristic, direct product factor, Sylow
844	C₂²	—	2	1	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	4	no	—
848	C₂²	—	2	4	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	4	no	—
854	C₂²	—	4	4	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	4	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	8	4	no	—
859	C₂²	—	16	4	no	—
860	C₂²	—	16	8	no	—
861	C₂²	C₇×#546	1	2	yes	—
862	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
863	C₄	—	2	1	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	1	no	—
866	C₄	—	2	2	no	—
867	C₄	—	2	4	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	2	no	—
873	C₄	C₇×#546	1	2	yes	—
874	C₄	C₇×#576	1	2	yes	—
875	C₄	C₂²×C₇×#41	1	1	yes	characteristic
876	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
877	C₂	—	2	2	no	—
878	C₂	—	4	4	no	—
879	C₂	—	4	2	no	—
880	C₂	—	8	2	no	—
881	C₂	—	8	4	no	—
882	C₂	C₂×C₇×#546	1	1	yes	characteristic
883	C₂	C₂×C₇×#576	1	1	yes	characteristic
884	C₂	C₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3506	C₂	semidirect
2. C₇×#3498	C₂	semidirect
3. C₇×#3332	C₂	semidirect
4. C₇×#3325	C₂	semidirect
5. C₇×#3318	C₂	semidirect
6. C₇×#3309	C₂	semidirect
7. C₇×#3305	C₂	semidirect
8. C₇×#3294	C₂	semidirect
9. C₇×#3138	C₂	semidirect
10. C₇×#3096	C₂	semidirect
11. C₇×#3076	C₂	semidirect
12. C₇×#3058	C₂	semidirect
13. C₂×C₇×#459	C₂	semidirect
14. C₇×#3008	C₂	semidirect
15. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
16. C₇×#2935	C₂	semidirect
17. C₇×#2897	C₂	semidirect
20. C₂²×C₇×D₈	C₂²	semidirect
21. C₂×C₇×#131	C₂²	semidirect
24. C₇×#555	C₂²	semidirect
25. C₇×#553	C₂²	semidirect
27. C₇×#550	C₂²	semidirect
28. C₇×#550	C₂²	semidirect
29. C₇×#547	C₂²	semidirect
32. C₇×D₄²	C₂²	semidirect
33. C₇×D₄²	C₂²	semidirect
37. C₇×#535	C₂²	semidirect
38. C₇×#533	C₂²	semidirect
44. C₇×#520	C₂²	semidirect
46. C₂×C₄×C₇×D₄	C₂²	semidirect
47. C₇×#490	C₂²	semidirect
48. C₇×#486	C₂²	semidirect
49. C₇×#486	C₂²	semidirect
50. C₇×#482	C₂²	semidirect
51. C₇×#482	C₂²	semidirect
52. C₇×#481	C₂²	semidirect
53. C₇×#480	C₂²	semidirect
54. C₇×#479	C₂²	semidirect
55. C₇×#478	C₂²	semidirect
56. C₇×#477	C₂²	semidirect
57. C₇×#476	C₂²	semidirect
58. C₇×#475	C₂²	semidirect
59. C₇×#474	C₂²	semidirect
60. C₇×#469	C₂²	semidirect
61. C₇×#469	C₂²	semidirect
62. C₇×#466	C₂²	semidirect
63. C₇×#466	C₂²	semidirect
64. C₇×#459	C₂²	semidirect
65. C₇×#459	C₂²	semidirect
66. C₇×#459	C₂²	semidirect
67. C₇×#449	C₂²	semidirect
68. C₇×#449	C₂²	semidirect
69. C₇×#447	C₂²	semidirect
70. C₇×#447	C₂²	semidirect
71. C₇×#442	C₂²	semidirect
72. C₇×#440	C₂²	semidirect
73. C₄×C₇×SD₁₆	C₂²	semidirect
74. C₄×C₇×D₈	C₂²	semidirect
75. C₇×#436	C₂²	semidirect
76. C₇×#435	C₂²	semidirect
77. C₇×C₈×D₄	C₂²	semidirect
78. C₇×#428	C₂²	semidirect
79. C₇×#427	C₂²	semidirect
80. C₂×C₇×C₄⋊C₈	C₂²	semidirect
81. C₇×#418	C₂²	semidirect
82. C₇×#418	C₂²	semidirect
83. C₇×#418	C₂²	semidirect
84. C₇×#418	C₂²	semidirect
86. C₇×#417	C₂²	semidirect
88. C₇×#416	C₂²	semidirect
89. C₂×C₇×#102	C₂²	semidirect
90. C₂×C₇×#102	C₂²	semidirect
91. C₇×#408	C₂²	semidirect
92. C₄×C₇×M₁₆	C₂²	semidirect
93. #61205	C₇	direct (N × H)
219. #3506	C₂×C₇	semidirect
220. #3498	C₂×C₇	semidirect
221. #3332	C₂×C₇	semidirect
222. #3325	C₂×C₇	semidirect
223. #3318	C₂×C₇	semidirect
224. #3309	C₂×C₇	semidirect
225. #3305	C₂×C₇	semidirect
226. #3294	C₂×C₇	semidirect
227. #3138	C₂×C₇	semidirect
228. #3096	C₂×C₇	semidirect
229. #3076	C₂×C₇	semidirect
230. #3058	C₂×C₇	semidirect
231. C₂×#459	C₂×C₇	semidirect
232. #3008	C₂×C₇	semidirect
233. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
234. #2935	C₂×C₇	semidirect
235. #2897	C₂×C₇	semidirect
246. C₇×#41	#41	semidirect
348. C₂²×D₈	C₂²×C₇	semidirect
349. C₂×#131	C₂²×C₇	semidirect
352. #555	C₂²×C₇	semidirect
353. #553	C₂²×C₇	semidirect
355. #550	C₂²×C₇	semidirect
356. #550	C₂²×C₇	semidirect
357. #547	C₂²×C₇	semidirect
360. D₄²	C₂²×C₇	semidirect
361. D₄²	C₂²×C₇	semidirect
365. #535	C₂²×C₇	semidirect
366. #533	C₂²×C₇	semidirect
372. #520	C₂²×C₇	semidirect
374. C₂×C₄×D₄	C₂²×C₇	semidirect
375. #490	C₂²×C₇	semidirect
376. #486	C₂²×C₇	semidirect
377. #486	C₂²×C₇	semidirect
378. #482	C₂²×C₇	semidirect
379. #482	C₂²×C₇	semidirect
380. #481	C₂²×C₇	semidirect
381. #480	C₂²×C₇	semidirect
382. #479	C₂²×C₇	semidirect
383. #478	C₂²×C₇	semidirect
384. #477	C₂²×C₇	semidirect
385. #476	C₂²×C₇	semidirect
386. #475	C₂²×C₇	semidirect
387. #474	C₂²×C₇	semidirect
388. #469	C₂²×C₇	semidirect
389. #469	C₂²×C₇	semidirect
390. #466	C₂²×C₇	semidirect
391. #466	C₂²×C₇	semidirect
392. #459	C₂²×C₇	semidirect
393. #459	C₂²×C₇	semidirect
394. #459	C₂²×C₇	semidirect
395. #449	C₂²×C₇	semidirect
396. #449	C₂²×C₇	semidirect
397. #447	C₂²×C₇	semidirect
398. #447	C₂²×C₇	semidirect
399. #442	C₂²×C₇	semidirect
400. #440	C₂²×C₇	semidirect
401. C₄×SD₁₆	C₂²×C₇	semidirect
402. C₄×D₈	C₂²×C₇	semidirect
403. #436	C₂²×C₇	semidirect
404. #435	C₂²×C₇	semidirect
405. C₈×D₄	C₂²×C₇	semidirect
406. #428	C₂²×C₇	semidirect
407. #427	C₂²×C₇	semidirect
408. C₂×C₄⋊C₈	C₂²×C₇	semidirect
409. #418	C₂²×C₇	semidirect
410. #418	C₂²×C₇	semidirect
411. #418	C₂²×C₇	semidirect
412. #418	C₂²×C₇	semidirect
414. #417	C₂²×C₇	semidirect
416. #416	C₂²×C₇	semidirect
417. C₂×#102	C₂²×C₇	semidirect
418. C₂×#102	C₂²×C₇	semidirect
419. #408	C₂²×C₇	semidirect
420. C₄×M₁₆	C₂²×C₇	semidirect
662. #41	C₇×#41	semidirect
843. C₇	#61205	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×#3506	2
C₇×#3498	2
C₇×#3332	2
C₇×#3325	2
C₇×#3318	2
C₇×#3309	2
C₇×#3305	2
C₇×#3294	2
C₇×#3138	2
C₇×#3096	2
C₇×#3076	2
C₇×#3058	2
C₂×C₇×#459	2
C₇×#3008	2
C₄×C₇×AGL(1,ℤ/8)	2
C₇×#2935	2
C₇×#2897	2
#61205	7

Subgroups — C7×#61205 #13238421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61205 #13238421