Subgroups — C₇×#61200 #13238416

Order 1792.

2152 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3331	C₂	1	2	yes	maximal, complemented
4	C₇×#3325	C₂	1	2	yes	maximal, complemented
5	C₇×#3311	C₂	1	4	yes	maximal, complemented
6	C₇×#3306	C₂	1	4	yes	maximal, complemented
7	C₇×#3303	C₂	1	2	yes	maximal, complemented
8	C₇×#3295	C₂	1	2	yes	maximal, complemented
9	C₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3099	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3060	C₂	1	2	yes	maximal, complemented
13	C₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3012	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	C₂×C₇×#135	C₂²	1	2	yes	complemented
21	C₂×C₇×#131	C₂²	1	2	yes	complemented
22	C₇×#556	C₂²	1	2	yes	complemented
23	C₇×#555	C₂²	1	2	yes	complemented
24	C₇×#554	C₂²	1	2	yes	complemented
25	C₇×#553	—	2	2	no	—
26	C₇×#548	—	2	2	no	—
27	C₇×#547	—	2	1	no	—
28	C₇×#547	C₂²	1	2	yes	—
29	C₇×#547	C₂²	1	2	yes	complemented
30	C₇×#546	—	2	2	no	—
31	C₇×#546	C₂²	1	4	yes	—
32	C₇×D₄²	—	2	1	no	—
33	C₇×D₄²	C₂²	1	2	yes	—
34	C₇×#542	—	2	2	no	—
35	C₇×#537	C₂²	1	2	yes	—
36	C₇×#537	C₂²	1	2	yes	complemented
37	C₇×#534	—	2	2	no	—
38	C₇×#533	—	2	1	no	—
39	C₇×#532	—	2	1	no	—
40	C₇×#532	C₂²	1	1	yes	characteristic
41	C₇×#532	C₂²	1	1	yes	characteristic
42	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₇×#121	—	2	2	no	—
44	C₇×#520	C₂²	1	2	yes	complemented
45	C₄×C₇×#41	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
47	C₇×#489	C₂²	1	4	yes	complemented
48	C₇×#487	C₂²	1	2	yes	complemented
49	C₇×#486	C₂²	1	2	yes	complemented
50	C₇×#485	C₂²	1	4	yes	complemented
51	C₇×#483	C₂²	1	4	yes	complemented
52	C₇×#482	C₂²	1	4	yes	complemented
53	C₇×#481	C₂²	1	4	yes	complemented
54	C₇×#476	C₂²	1	2	yes	complemented
55	C₇×#476	C₂²	1	4	yes	complemented
56	C₇×#476	C₂²	1	2	yes	complemented
57	C₇×#470	C₂²	1	4	yes	complemented
58	C₇×#469	C₂²	1	4	yes	complemented
59	C₇×#465	C₂²	1	4	yes	complemented
60	C₇×#465	C₂²	1	4	yes	complemented
61	C₇×#464	C₂²	1	2	yes	complemented
62	C₇×#463	C₂²	1	2	yes	complemented
63	C₇×#462	C₂²	1	1	yes	characteristic, complemented
64	C₇×#461	C₂²	1	1	yes	characteristic, complemented
65	C₇×#460	C₂²	1	1	yes	characteristic, complemented
66	C₇×#459	C₂²	1	1	yes	characteristic, complemented
67	C₇×#452	C₂²	1	4	yes	complemented
68	C₇×#450	C₂²	1	4	yes	complemented
69	C₇×#449	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	C₂×C₇×#106	C₂²	1	2	yes	complemented
80	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
81	C₇×#418	C₂²	1	1	yes	characteristic
82	C₇×#418	C₂²	1	4	yes	complemented
83	C₇×#417	C₂²	1	1	yes	characteristic, complemented
84	C₇×#417	C₂²	1	2	yes	complemented
85	C₇×#417	C₂²	1	4	yes	complemented
86	C₇×#417	C₂²	1	2	yes	complemented
87	C₇×#416	C₂²	1	2	yes	complemented
88	C₇×#416	C₂²	1	4	yes	complemented
89	C₂×C₇×#102	C₂²	1	2	yes	—
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	#61200	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	2	yes	—
99	C₂×C₇×#41	C₂³	1	1	yes	characteristic
100	C₂×C₇×#41	C₂³	1	4	yes	—
101	C₂×C₇×#41	C₂³	1	2	yes	—
102	C₂²×C₇×Q₈	—	2	1	no	—
103	C₂²×C₇×D₄	—	2	4	no	—
104	C₂²×C₇×D₄	—	2	2	no	—
105	C₂²×C₇×D₄	—	2	2	no	—
106	C₂²×C₇×D₄	C₂³	1	4	yes	—
107	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₇	—	2	1	no	—
109	C₇×AGL(1,ℤ/8)	—	2	4	no	—
110	C₇×#135	—	4	4	no	—
111	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
112	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
113	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
114	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
115	C₂×C₇×D₈	C₂³	1	2	yes	—
116	C₂×C₇×D₈	C₂³	1	2	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	—	2	1	no	—
124	C₇×C₄⋊Q₈	—	2	1	no	—
125	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
126	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
128	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₇×#127	D₄	1	1	yes	characteristic
130	C₇×#127	C₂³	1	1	yes	characteristic
131	C₇×#126	—	2	4	no	—
132	C₇×#125	—	2	2	no	—
133	C₇×#124	—	2	2	no	—
134	C₇×#124	—	2	4	no	—
135	C₇×#124	D₄	1	2	yes	—
136	C₇×#124	C₂³	1	2	yes	—
137	C₇×#123	—	2	4	no	—
138	C₇×#123	—	2	4	no	—
139	C₇×#123	—	2	4	no	—
140	C₇×C₂²⋊Q₈	—	2	2	no	—
141	C₇×C₂²⋊Q₈	—	2	2	no	—
142	C₇×C₂²⋊Q₈	—	2	2	no	—
143	C₇×C₂²⋊Q₈	—	2	4	no	—
144	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
145	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
146	C₇×#121	—	2	4	no	—
147	C₇×#121	—	2	2	no	—
148	C₇×#121	—	2	2	no	—
149	C₇×#121	—	2	2	no	—
150	C₇×#121	—	2	2	no	—
151	C₇×#121	—	2	4	no	—
152	C₇×#121	—	2	1	no	—
153	C₇×#121	—	2	1	no	—
154	C₇×#121	—	2	2	no	—
155	C₇×#121	—	2	4	no	—
156	C₇×#121	D₄	1	2	yes	—
157	C₇×#121	D₄	1	2	yes	—
158	C₇×#121	C₂³	1	4	yes	—
159	C₇×#121	C₂³	1	4	yes	—
160	C₇×#120	—	2	4	no	—
161	C₇×#120	—	2	4	no	—
162	C₄×C₇×Q₈	—	2	2	no	—
163	C₄×C₇×Q₈	—	2	2	no	—
164	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
165	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
166	C₄×C₇×D₄	—	2	2	no	—
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	1	no	—
172	C₄×C₇×D₄	—	2	1	no	—
173	C₄×C₇×D₄	—	2	1	no	—
174	C₄×C₇×D₄	—	2	1	no	—
175	C₄×C₇×D₄	C₂³	1	2	yes	—
176	C₄×C₇×D₄	C₂³	1	2	yes	—
177	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
178	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
179	C₄×C₇×D₄	C₂³	1	2	yes	—
180	C₄×C₇×D₄	C₂³	1	2	yes	—
181	C₇×#117	—	2	2	no	—
182	C₇×#117	—	2	1	no	—
183	C₇×#117	C₂³	1	4	yes	—
184	C₇×#117	C₂³	1	1	yes	characteristic
185	C₂×C₇×C₄⋊C₄	—	2	1	no	—
186	C₂×C₇×C₄⋊C₄	—	2	2	no	—
187	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
188	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
191	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
192	C₂×C₄²×C₇	—	2	1	no	—
193	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
194	C₇×#107	C₂³	1	2	yes	—
195	C₇×#106	C₂³	1	4	yes	—
196	C₇×#106	C₂³	1	4	yes	—
197	C₇×#106	C₂³	1	2	yes	—
198	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
199	C₇×C₄⋊C₈	C₂³	1	2	yes	—
200	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
201	C₇×#103	C₂³	1	2	yes	—
202	C₇×#103	C₂³	1	4	yes	—
203	C₇×#103	C₂³	1	2	yes	—
204	C₇×#103	C₂³	1	4	yes	—
205	C₇×#103	C₂³	1	2	yes	—
206	C₇×#102	C₂³	1	2	yes	—
207	C₇×#102	C₂³	1	4	yes	—
208	C₇×#102	C₂³	1	4	yes	—
209	C₇×#102	C₂³	1	4	yes	—
210	C₇×#102	C₂³	1	2	yes	—
211	C₇×#102	C₂³	1	4	yes	—
212	C₇×#102	C₂³	1	2	yes	—
213	C₇×#102	C₂³	1	2	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	#3511	C₂×C₇	1	1	yes	characteristic, complemented
220	#3496	C₂×C₇	1	1	yes	characteristic, complemented
221	#3331	C₂×C₇	1	2	yes	complemented
222	#3325	C₂×C₇	1	2	yes	complemented
223	#3311	C₂×C₇	1	4	yes	complemented
224	#3306	C₂×C₇	1	4	yes	complemented
225	#3303	C₂×C₇	1	2	yes	complemented
226	#3295	C₂×C₇	1	2	yes	complemented
227	#3141	C₂×C₇	1	1	yes	characteristic, complemented
228	#3099	C₂×C₇	1	2	yes	complemented
229	C₂×#476	C₂×C₇	1	1	yes	characteristic, complemented
230	#3060	C₂×C₇	1	2	yes	complemented
231	#3035	C₂×C₇	1	1	yes	characteristic, complemented
232	#3012	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	C₇×#41	—	2	4	no	—
239	C₇×#41	—	2	4	no	—
240	C₇×#41	—	2	8	no	—
241	C₇×#41	—	2	2	no	—
242	C₇×#41	—	2	4	no	—
243	C₇×#41	—	2	2	no	—
244	C₇×#41	—	2	4	no	—
245	C₇×#41	—	4	4	no	—
246	C₇×#41	—	4	8	no	—
247	C₇×#41	—	8	4	no	—
248	C₂×C₇×Q₈	—	2	2	no	—
249	C₂×C₇×Q₈	—	2	2	no	—
250	C₂×C₇×Q₈	—	8	2	no	—
251	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
252	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
253	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
254	C₂×C₇×D₄	—	2	8	no	—
255	C₂×C₇×D₄	—	2	1	no	—
256	C₂×C₇×D₄	—	2	4	no	—
257	C₂×C₇×D₄	—	2	2	no	—
258	C₂×C₇×D₄	—	2	4	no	—
259	C₂×C₇×D₄	—	2	4	no	—
260	C₂×C₇×D₄	—	2	1	no	—
261	C₂×C₇×D₄	—	2	1	no	—
262	C₂×C₇×D₄	—	2	4	no	—
263	C₂×C₇×D₄	—	2	1	no	—
264	C₂×C₇×D₄	—	2	2	no	—
265	C₂×C₇×D₄	—	4	4	no	—
266	C₂×C₇×D₄	—	4	8	no	—
267	C₂×C₇×D₄	—	4	16	no	—
268	C₂×C₇×D₄	—	8	4	no	—
269	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
270	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
271	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
272	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
273	C₂×C₇×D₄	#41	1	4	yes	complemented
274	C₂×C₇×D₄	C₂⁴	1	2	yes	—
275	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
276	C₂×C₇×D₄	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₇	—	2	1	no	—
278	C₂²×C₄×C₇	—	2	2	no	—
279	C₂²×C₄×C₇	—	2	4	no	—
280	C₂²×C₄×C₇	—	2	1	no	—
281	C₂²×C₄×C₇	—	2	1	no	—
282	C₂²×C₄×C₇	—	2	1	no	—
283	C₂²×C₄×C₇	—	2	4	no	—
284	C₂²×C₄×C₇	—	2	2	no	—
285	C₂²×C₄×C₇	—	2	2	no	—
286	C₂²×C₄×C₇	—	2	2	no	—
287	C₂²×C₄×C₇	—	8	2	no	—
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	4	yes	—
291	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
292	C₇×Q₁₆	—	4	2	no	—
293	C₇×SD₁₆	—	2	4	no	—
294	C₇×SD₁₆	—	4	2	no	—
295	C₇×SD₁₆	—	4	2	no	—
296	C₇×D₈	—	2	4	no	—
297	C₇×D₈	—	4	2	no	—
298	C₇×M₁₆	—	2	2	no	—
299	C₇×M₁₆	—	2	2	no	—
300	C₇×M₁₆	—	4	4	no	—
301	C₂×C₇×C₈	—	2	4	no	—
302	C₂×C₇×C₈	—	4	4	no	—
303	C₂×C₇×C₈	C₂⁴	1	2	yes	—
304	C₂×C₇×C₈	C₂⁴	1	2	yes	—
305	C₂×C₇×C₈	C₂⁴	1	2	yes	—
306	C₂×C₇×C₈	C₂⁴	1	2	yes	—
307	C₇×C₄⋊C₄	—	2	1	no	—
308	C₇×C₄⋊C₄	—	2	2	no	—
309	C₇×C₄⋊C₄	—	2	4	no	—
310	C₇×C₄⋊C₄	—	2	2	no	—
311	C₇×C₄⋊C₄	—	2	1	no	—
312	C₇×C₄⋊C₄	—	2	2	no	—
313	C₇×C₄⋊C₄	—	2	4	no	—
314	C₇×C₄⋊C₄	—	2	1	no	—
315	C₇×C₄⋊C₄	—	2	1	no	—
316	C₇×C₄⋊C₄	—	2	1	no	—
317	C₇×C₄⋊C₄	—	2	4	no	—
318	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
319	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
320	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
321	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
322	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
323	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
324	C₇×C₂²⋊C₄	—	2	4	no	—
325	C₇×C₂²⋊C₄	—	2	1	no	—
326	C₇×C₂²⋊C₄	—	2	4	no	—
327	C₇×C₂²⋊C₄	—	2	4	no	—
328	C₇×C₂²⋊C₄	—	2	2	no	—
329	C₇×C₂²⋊C₄	—	2	2	no	—
330	C₇×C₂²⋊C₄	—	2	2	no	—
331	C₇×C₂²⋊C₄	—	2	4	no	—
332	C₇×C₂²⋊C₄	—	2	1	no	—
333	C₇×C₂²⋊C₄	—	2	1	no	—
334	C₇×C₂²⋊C₄	—	2	4	no	—
335	C₇×C₂²⋊C₄	—	2	2	no	—
336	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
337	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
338	C₄²×C₇	—	2	1	no	—
339	C₄²×C₇	—	2	1	no	—
340	C₄²×C₇	—	2	1	no	—
341	C₄²×C₇	—	2	4	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	C₂×#135	C₂²×C₇	1	2	yes	complemented
349	C₂×#131	C₂²×C₇	1	2	yes	complemented
350	#556	C₂²×C₇	1	2	yes	complemented
351	#555	C₂²×C₇	1	2	yes	complemented
352	#554	C₂²×C₇	1	2	yes	complemented
353	#553	—	2	2	no	—
354	#548	—	2	2	no	—
355	#547	—	2	1	no	—
356	#547	C₂²×C₇	1	2	yes	—
357	#547	C₂²×C₇	1	2	yes	complemented
358	#546	—	2	2	no	—
359	#546	C₂²×C₇	1	4	yes	—
360	D₄²	—	2	1	no	—
361	D₄²	C₂²×C₇	1	2	yes	—
362	#542	—	2	2	no	—
363	#537	C₂²×C₇	1	2	yes	—
364	#537	C₂²×C₇	1	2	yes	complemented
365	#534	—	2	2	no	—
366	#533	—	2	1	no	—
367	#532	—	2	1	no	—
368	#532	C₂²×C₇	1	1	yes	characteristic
369	#532	C₂²×C₇	1	1	yes	characteristic
370	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
371	C₂×#121	—	2	2	no	—
372	#520	C₂²×C₇	1	2	yes	complemented
373	C₄×#41	C₂²×C₇	1	1	yes	characteristic, complemented
374	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
375	#489	C₂²×C₇	1	4	yes	complemented
376	#487	C₂²×C₇	1	2	yes	complemented
377	#486	C₂²×C₇	1	2	yes	complemented
378	#485	C₂²×C₇	1	4	yes	complemented
379	#483	C₂²×C₇	1	4	yes	complemented
380	#482	C₂²×C₇	1	4	yes	complemented
381	#481	C₂²×C₇	1	4	yes	complemented
382	#476	C₂²×C₇	1	2	yes	complemented
383	#476	C₂²×C₇	1	2	yes	complemented
384	#476	C₂²×C₇	1	4	yes	complemented
385	#470	C₂²×C₇	1	4	yes	complemented
386	#469	C₂²×C₇	1	4	yes	complemented
387	#465	C₂²×C₇	1	4	yes	complemented
388	#465	C₂²×C₇	1	4	yes	complemented
389	#464	C₂²×C₇	1	2	yes	complemented
390	#463	C₂²×C₇	1	2	yes	complemented
391	#462	C₂²×C₇	1	1	yes	characteristic, complemented
392	#461	C₂²×C₇	1	1	yes	characteristic, complemented
393	#460	C₂²×C₇	1	1	yes	characteristic, complemented
394	#459	C₂²×C₇	1	1	yes	characteristic, complemented
395	#452	C₂²×C₇	1	4	yes	complemented
396	#450	C₂²×C₇	1	4	yes	complemented
397	#449	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	C₂×#106	C₂²×C₇	1	2	yes	complemented
408	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
409	#418	C₂²×C₇	1	1	yes	characteristic
410	#418	C₂²×C₇	1	4	yes	complemented
411	#417	C₂²×C₇	1	4	yes	complemented
412	#417	C₂²×C₇	1	2	yes	complemented
413	#417	C₂²×C₇	1	2	yes	complemented
414	#417	C₂²×C₇	1	1	yes	characteristic, complemented
415	#416	C₂²×C₇	1	2	yes	complemented
416	#416	C₂²×C₇	1	4	yes	complemented
417	C₂×#102	C₂²×C₇	1	2	yes	—
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	2	no	—
422	C₂³×C₇	—	2	4	no	—
423	C₂³×C₇	—	2	1	no	—
424	C₂³×C₇	—	2	2	no	—
425	C₂³×C₇	—	4	8	no	—
426	C₂³×C₇	—	8	1	no	—
427	C₂³×C₇	—	8	1	no	—
428	C₂³×C₇	—	8	4	no	—
429	C₂³×C₇	—	8	4	no	—
430	C₂³×C₇	C₂²×D₄	1	4	yes	—
431	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
432	C₇×Q₈	—	2	4	no	—
433	C₇×Q₈	—	2	1	no	—
434	C₇×Q₈	—	2	2	no	—
435	C₇×Q₈	—	2	1	no	—
436	C₇×Q₈	—	2	2	no	—
437	C₇×Q₈	—	4	4	no	—
438	C₇×Q₈	—	8	2	no	—
439	C₇×D₄	—	2	8	no	—
440	C₇×D₄	—	2	4	no	—
441	C₇×D₄	—	2	4	no	—
442	C₇×D₄	—	2	4	no	—
443	C₇×D₄	—	2	1	no	—
444	C₇×D₄	—	2	2	no	—
445	C₇×D₄	—	2	2	no	—
446	C₇×D₄	—	2	1	no	—
447	C₇×D₄	—	2	2	no	—
448	C₇×D₄	—	4	2	no	—
449	C₇×D₄	—	4	8	no	—
450	C₇×D₄	—	4	8	no	—
451	C₇×D₄	—	4	4	no	—
452	C₇×D₄	—	4	2	no	—
453	C₇×D₄	—	4	2	no	—
454	C₇×D₄	—	8	1	no	—
455	C₇×D₄	—	8	4	no	—
456	C₇×D₄	—	8	4	no	—
457	C₇×D₄	C₂×#41	1	4	yes	—
458	C₂×C₄×C₇	—	2	2	no	—
459	C₂×C₄×C₇	—	2	4	no	—
460	C₂×C₄×C₇	—	2	4	no	—
461	C₂×C₄×C₇	—	2	1	no	—
462	C₂×C₄×C₇	—	2	1	no	—
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	2	no	—
467	C₂×C₄×C₇	—	4	1	no	—
468	C₂×C₄×C₇	—	4	8	no	—
469	C₂×C₄×C₇	—	4	2	no	—
470	C₂×C₄×C₇	—	4	4	no	—
471	C₂×C₄×C₇	—	4	2	no	—
472	C₂×C₄×C₇	—	4	2	no	—
473	C₂×C₄×C₇	—	4	4	no	—
474	C₂×C₄×C₇	—	8	2	no	—
475	C₂×C₄×C₇	—	8	1	no	—
476	C₂×C₄×C₇	—	8	2	no	—
477	C₂×C₄×C₇	—	8	4	no	—
478	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
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	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₇	C₂×#41	1	2	yes	—
485	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
486	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
487	C₇×C₈	—	2	2	no	—
488	C₇×C₈	—	2	2	no	—
489	C₇×C₈	—	2	2	no	—
490	C₇×C₈	—	2	2	no	—
491	H(5,𝔽₂)	—	2	8	no	—
492	H(5,𝔽₂)	—	4	4	no	—
493	C₂×#41	—	2	2	no	—
494	C₂×#41	—	2	2	no	—
495	C₂×#41	C₂³×C₇	1	1	yes	characteristic
496	C₂×#41	C₂³×C₇	1	2	yes	—
497	C₂×#41	C₂³×C₇	1	4	yes	—
498	C₂×#41	C₂³×C₇	1	2	yes	—
499	C₂²×Q₈	—	2	1	no	—
500	C₂²×D₄	—	2	4	no	—
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	—	2	2	no	—
503	C₂²×D₄	C₂³×C₇	1	4	yes	—
504	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
505	C₂³×C₄	—	2	1	no	—
506	AGL(1,ℤ/8)	—	2	4	no	—
507	#135	—	4	4	no	—
508	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
509	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
510	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
511	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
512	C₂×D₈	C₂³×C₇	1	2	yes	—
513	C₂×D₈	C₂³×C₇	1	2	yes	—
514	#131	—	4	4	no	—
515	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
516	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
517	C₂×M₁₆	C₂³×C₇	1	4	yes	—
518	C₂²×C₈	C₂³×C₇	1	2	yes	—
519	C₂²×C₈	C₂³×C₇	1	4	yes	—
520	C₄⋊Q₈	—	2	1	no	—
521	C₄⋊Q₈	—	2	1	no	—
522	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
523	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
524	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
525	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
526	#127	C₇×D₄	1	1	yes	characteristic
527	#127	C₂³×C₇	1	1	yes	characteristic
528	#126	—	2	4	no	—
529	#125	—	2	2	no	—
530	#124	—	2	2	no	—
531	#124	—	2	4	no	—
532	#124	C₇×D₄	1	2	yes	—
533	#124	C₂³×C₇	1	2	yes	—
534	#123	—	2	4	no	—
535	#123	—	2	4	no	—
536	#123	—	2	4	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
542	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
543	#121	—	2	4	no	—
544	#121	—	2	2	no	—
545	#121	—	2	2	no	—
546	#121	—	2	2	no	—
547	#121	—	2	2	no	—
548	#121	—	2	4	no	—
549	#121	—	2	1	no	—
550	#121	—	2	1	no	—
551	#121	—	2	2	no	—
552	#121	—	2	4	no	—
553	#121	C₇×D₄	1	2	yes	—
554	#121	C₇×D₄	1	2	yes	—
555	#121	C₂³×C₇	1	4	yes	—
556	#121	C₂³×C₇	1	4	yes	—
557	#120	—	2	4	no	—
558	#120	—	2	4	no	—
559	C₄×Q₈	—	2	2	no	—
560	C₄×Q₈	—	2	2	no	—
561	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
562	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	4	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	C₂³×C₇	1	2	yes	—
573	C₄×D₄	C₂³×C₇	1	2	yes	—
574	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
575	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
576	C₄×D₄	C₂³×C₇	1	2	yes	—
577	C₄×D₄	C₂³×C₇	1	2	yes	—
578	#117	—	2	2	no	—
579	#117	—	2	1	no	—
580	#117	C₂³×C₇	1	1	yes	characteristic
581	#117	C₂³×C₇	1	4	yes	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	2	no	—
584	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	4	no	—
589	C₂×C₄²	—	2	1	no	—
590	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
591	#107	C₂³×C₇	1	2	yes	—
592	#106	C₂³×C₇	1	4	yes	—
593	#106	C₂³×C₇	1	4	yes	—
594	#106	C₂³×C₇	1	2	yes	—
595	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
596	C₄⋊C₈	C₂³×C₇	1	2	yes	—
597	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
598	#103	C₂³×C₇	1	2	yes	—
599	#103	C₂³×C₇	1	2	yes	—
600	#103	C₂³×C₇	1	4	yes	—
601	#103	C₂³×C₇	1	2	yes	—
602	#103	C₂³×C₇	1	4	yes	—
603	#102	C₂³×C₇	1	4	yes	—
604	#102	C₂³×C₇	1	4	yes	—
605	#102	C₂³×C₇	1	2	yes	—
606	#102	C₂³×C₇	1	2	yes	—
607	#102	C₂³×C₇	1	4	yes	—
608	#102	C₂³×C₇	1	2	yes	—
609	#102	C₂³×C₇	1	2	yes	—
610	#102	C₂³×C₇	1	2	yes	—
611	#102	C₂³×C₇	1	4	yes	—
612	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
613	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
614	#97	C₂³×C₇	1	2	yes	—
615	C₄×C₈	C₂³×C₇	1	2	yes	—
616	C₂²×C₇	—	2	1	no	—
617	C₂²×C₇	—	2	1	no	—
618	C₂²×C₇	—	2	4	no	—
619	C₂²×C₇	—	2	4	no	—
620	C₂²×C₇	—	2	4	no	—
621	C₂²×C₇	—	2	4	no	—
622	C₂²×C₇	—	4	2	no	—
623	C₂²×C₇	—	4	2	no	—
624	C₂²×C₇	—	4	1	no	—
625	C₂²×C₇	—	4	2	no	—
626	C₂²×C₇	—	4	2	no	—
627	C₂²×C₇	—	4	1	no	—
628	C₂²×C₇	—	4	1	no	—
629	C₂²×C₇	—	4	2	no	—
630	C₂²×C₇	—	8	4	no	—
631	C₂²×C₇	—	16	8	no	—
632	C₂²×C₇	#546	1	2	yes	—
633	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
634	C₄×C₇	—	2	1	no	—
635	C₄×C₇	—	2	1	no	—
636	C₄×C₇	—	2	4	no	—
637	C₄×C₇	—	2	1	no	—
638	C₄×C₇	—	4	1	no	—
639	C₄×C₇	—	4	4	no	—
640	C₄×C₇	—	4	2	no	—
641	C₄×C₇	—	4	1	no	—
642	C₄×C₇	—	4	1	no	—
643	C₄×C₇	—	4	2	no	—
644	C₄×C₇	#546	1	2	yes	—
645	C₄×C₇	#577	1	2	yes	—
646	C₄×C₇	C₂²×#41	1	1	yes	characteristic
647	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
648	C₂⁴	—	2	1	no	—
649	C₂⁴	—	2	4	no	—
650	#41	—	2	4	no	—
651	#41	—	2	4	no	—
652	#41	—	2	8	no	—
653	#41	—	2	2	no	—
654	#41	—	2	4	no	—
655	#41	—	2	2	no	—
656	#41	—	2	4	no	—
657	#41	—	4	4	no	—
658	#41	—	4	8	no	—
659	#41	—	8	4	no	—
660	C₂×Q₈	—	2	2	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	8	2	no	—
663	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
664	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
665	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
666	C₂×D₄	—	2	8	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	4	4	no	—
678	C₂×D₄	—	4	8	no	—
679	C₂×D₄	—	4	16	no	—
680	C₂×D₄	—	8	4	no	—
681	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
682	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
683	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
684	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
685	C₂×D₄	C₇×#41	1	4	yes	complemented
686	C₂×D₄	C₂⁴×C₇	1	2	yes	—
687	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
688	C₂×D₄	C₂⁴×C₇	1	2	yes	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	8	2	no	—
700	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
701	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
703	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
704	Q₁₆	—	4	2	no	—
705	SD₁₆	—	2	4	no	—
706	SD₁₆	—	4	2	no	—
707	SD₁₆	—	4	2	no	—
708	D₈	—	2	4	no	—
709	D₈	—	4	2	no	—
710	M₁₆	—	2	2	no	—
711	M₁₆	—	2	2	no	—
712	M₁₆	—	4	4	no	—
713	C₂×C₈	—	2	4	no	—
714	C₂×C₈	—	4	4	no	—
715	C₂×C₈	C₂⁴×C₇	1	2	yes	—
716	C₂×C₈	C₂⁴×C₇	1	2	yes	—
717	C₂×C₈	C₂⁴×C₇	1	2	yes	—
718	C₂×C₈	C₂⁴×C₇	1	2	yes	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
731	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
732	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
733	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
734	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
735	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
749	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
750	C₄²	—	2	1	no	—
751	C₄²	—	2	1	no	—
752	C₄²	—	2	1	no	—
753	C₄²	—	2	4	no	—
754	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
755	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
756	C₄²	C₂⁴×C₇	1	1	yes	characteristic
757	C₄²	C₂⁴×C₇	1	1	yes	characteristic
758	C₂×C₇	—	2	2	no	—
759	C₂×C₇	—	4	4	no	—
760	C₂×C₇	—	4	4	no	—
761	C₂×C₇	—	8	1	no	—
762	C₂×C₇	—	8	2	no	—
763	C₂×C₇	C₂×#546	1	1	yes	characteristic
764	C₂×C₇	C₂×#577	1	1	yes	characteristic
765	C₂×C₇	#3585	1	1	yes	characteristic
766	C₂³	—	2	2	no	—
767	C₂³	—	2	4	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	4	8	no	—
771	C₂³	—	8	1	no	—
772	C₂³	—	8	1	no	—
773	C₂³	—	8	4	no	—
774	C₂³	—	8	4	no	—
775	C₂³	C₂²×C₇×D₄	1	4	yes	—
776	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
777	Q₈	—	2	4	no	—
778	Q₈	—	2	1	no	—
779	Q₈	—	2	2	no	—
780	Q₈	—	2	1	no	—
781	Q₈	—	2	2	no	—
782	Q₈	—	4	4	no	—
783	Q₈	—	8	2	no	—
784	D₄	—	2	8	no	—
785	D₄	—	2	1	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	2	no	—
788	D₄	—	2	1	no	—
789	D₄	—	2	2	no	—
790	D₄	—	2	4	no	—
791	D₄	—	2	4	no	—
792	D₄	—	2	4	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	8	no	—
795	D₄	—	4	8	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	2	no	—
799	D₄	—	8	1	no	—
800	D₄	—	8	4	no	—
801	D₄	—	8	4	no	—
802	D₄	C₂×C₇×#41	1	4	yes	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	8	2	no	—
820	C₂×C₄	—	8	1	no	—
821	C₂×C₄	—	8	2	no	—
822	C₂×C₄	—	8	4	no	—
823	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
824	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
825	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
826	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
827	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
828	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
829	C₂×C₄	C₂×C₇×#41	1	2	yes	—
830	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
831	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
832	C₈	—	2	2	no	—
833	C₈	—	2	2	no	—
834	C₈	—	2	2	no	—
835	C₈	—	2	2	no	—
836	C₇	#61200	1	1	yes	characteristic, direct product factor, Sylow
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	8	4	no	—
852	C₂²	—	16	8	no	—
853	C₂²	C₇×#546	1	2	yes	—
854	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	4	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	4	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	1	no	—
865	C₄	C₇×#546	1	2	yes	—
866	C₄	C₇×#577	1	2	yes	—
867	C₄	C₂²×C₇×#41	1	1	yes	characteristic
868	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
869	C₂	—	2	2	no	—
870	C₂	—	4	4	no	—
871	C₂	—	4	4	no	—
872	C₂	—	8	2	no	—
873	C₂	—	8	1	no	—
874	C₂	C₂×C₇×#546	1	1	yes	characteristic
875	C₂	C₂×C₇×#577	1	1	yes	characteristic
876	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×#3511	C₂	semidirect
2. C₇×#3496	C₂	semidirect
3. C₇×#3331	C₂	semidirect
4. C₇×#3325	C₂	semidirect
5. C₇×#3311	C₂	semidirect
6. C₇×#3306	C₂	semidirect
7. C₇×#3303	C₂	semidirect
8. C₇×#3295	C₂	semidirect
9. C₇×#3141	C₂	semidirect
10. C₇×#3099	C₂	semidirect
11. C₂×C₇×#476	C₂	semidirect
12. C₇×#3060	C₂	semidirect
13. C₇×#3035	C₂	semidirect
14. C₇×#3012	C₂	semidirect
15. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
16. C₇×#2935	C₂	semidirect
17. C₇×#2897	C₂	semidirect
20. C₂×C₇×#135	C₂²	semidirect
21. C₂×C₇×#131	C₂²	semidirect
22. C₇×#556	C₂²	semidirect
23. C₇×#555	C₂²	semidirect
24. C₇×#554	C₂²	semidirect
29. C₇×#547	C₂²	semidirect
36. C₇×#537	C₂²	semidirect
42. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
44. C₇×#520	C₂²	semidirect
45. C₄×C₇×#41	C₂²	semidirect
47. C₇×#489	C₂²	semidirect
48. C₇×#487	C₂²	semidirect
49. C₇×#486	C₂²	semidirect
50. C₇×#485	C₂²	semidirect
51. C₇×#483	C₂²	semidirect
52. C₇×#482	C₂²	semidirect
53. C₇×#481	C₂²	semidirect
54. C₇×#476	C₂²	semidirect
55. C₇×#476	C₂²	semidirect
56. C₇×#476	C₂²	semidirect
57. C₇×#470	C₂²	semidirect
58. C₇×#469	C₂²	semidirect
59. C₇×#465	C₂²	semidirect
60. C₇×#465	C₂²	semidirect
61. C₇×#464	C₂²	semidirect
62. C₇×#463	C₂²	semidirect
63. C₇×#462	C₂²	semidirect
64. C₇×#461	C₂²	semidirect
65. C₇×#460	C₂²	semidirect
66. C₇×#459	C₂²	semidirect
67. C₇×#452	C₂²	semidirect
68. C₇×#450	C₂²	semidirect
69. C₇×#449	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. C₂×C₇×#106	C₂²	semidirect
80. C₂×C₇×C₄⋊C₈	C₂²	semidirect
82. C₇×#418	C₂²	semidirect
83. C₇×#417	C₂²	semidirect
84. C₇×#417	C₂²	semidirect
85. C₇×#417	C₂²	semidirect
86. C₇×#417	C₂²	semidirect
87. C₇×#416	C₂²	semidirect
88. C₇×#416	C₂²	semidirect
90. C₂×C₇×#102	C₂²	semidirect
91. C₇×#408	C₂²	semidirect
92. C₄×C₇×M₁₆	C₂²	semidirect
93. #61200	C₇	direct (N × H)
219. #3511	C₂×C₇	semidirect
220. #3496	C₂×C₇	semidirect
221. #3331	C₂×C₇	semidirect
222. #3325	C₂×C₇	semidirect
223. #3311	C₂×C₇	semidirect
224. #3306	C₂×C₇	semidirect
225. #3303	C₂×C₇	semidirect
226. #3295	C₂×C₇	semidirect
227. #3141	C₂×C₇	semidirect
228. #3099	C₂×C₇	semidirect
229. C₂×#476	C₂×C₇	semidirect
230. #3060	C₂×C₇	semidirect
231. #3035	C₂×C₇	semidirect
232. #3012	C₂×C₇	semidirect
233. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
234. #2935	C₂×C₇	semidirect
235. #2897	C₂×C₇	semidirect
273. C₂×C₇×D₄	#41	semidirect
348. C₂×#135	C₂²×C₇	semidirect
349. C₂×#131	C₂²×C₇	semidirect
350. #556	C₂²×C₇	semidirect
351. #555	C₂²×C₇	semidirect
352. #554	C₂²×C₇	semidirect
357. #547	C₂²×C₇	semidirect
364. #537	C₂²×C₇	semidirect
370. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
372. #520	C₂²×C₇	semidirect
373. C₄×#41	C₂²×C₇	semidirect
375. #489	C₂²×C₇	semidirect
376. #487	C₂²×C₇	semidirect
377. #486	C₂²×C₇	semidirect
378. #485	C₂²×C₇	semidirect
379. #483	C₂²×C₇	semidirect
380. #482	C₂²×C₇	semidirect
381. #481	C₂²×C₇	semidirect
382. #476	C₂²×C₇	semidirect
383. #476	C₂²×C₇	semidirect
384. #476	C₂²×C₇	semidirect
385. #470	C₂²×C₇	semidirect
386. #469	C₂²×C₇	semidirect
387. #465	C₂²×C₇	semidirect
388. #465	C₂²×C₇	semidirect
389. #464	C₂²×C₇	semidirect
390. #463	C₂²×C₇	semidirect
391. #462	C₂²×C₇	semidirect
392. #461	C₂²×C₇	semidirect
393. #460	C₂²×C₇	semidirect
394. #459	C₂²×C₇	semidirect
395. #452	C₂²×C₇	semidirect
396. #450	C₂²×C₇	semidirect
397. #449	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. C₂×#106	C₂²×C₇	semidirect
408. C₂×C₄⋊C₈	C₂²×C₇	semidirect
410. #418	C₂²×C₇	semidirect
411. #417	C₂²×C₇	semidirect
412. #417	C₂²×C₇	semidirect
413. #417	C₂²×C₇	semidirect
414. #417	C₂²×C₇	semidirect
415. #416	C₂²×C₇	semidirect
416. #416	C₂²×C₇	semidirect
418. C₂×#102	C₂²×C₇	semidirect
419. #408	C₂²×C₇	semidirect
420. C₄×M₁₆	C₂²×C₇	semidirect
685. C₂×D₄	C₇×#41	semidirect
836. C₇	#61200	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×#3511	2
C₇×#3496	2
C₇×#3331	2
C₇×#3325	2
C₇×#3311	2
C₇×#3306	2
C₇×#3303	2
C₇×#3295	2
C₇×#3141	2
C₇×#3099	2
C₂×C₇×#476	2
C₇×#3060	2
C₇×#3035	2
C₇×#3012	2
C₄×C₇×AGL(1,ℤ/8)	2
C₇×#2935	2
C₇×#2897	2
#61200	7

Subgroups — C7×#61200 #13238416

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61200 #13238416