Subgroups — C₇×#61215 #13238431

Order 1792.

2200 conjugacy classes of subgroups.

The subgroup lattice has 932 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×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3333	C₂	1	2	yes	maximal, complemented
4	C₇×#3332	C₂	1	2	yes	maximal, complemented
5	C₇×#3325	C₂	1	2	yes	maximal, complemented
6	C₇×#3324	C₂	1	2	yes	maximal, complemented
7	C₇×#3305	C₂	1	2	yes	maximal, complemented
8	C₇×#3304	C₂	1	2	yes	maximal, complemented
9	C₇×#3295	C₂	1	2	yes	maximal, complemented
10	C₇×#3294	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#486	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3096	C₂	1	2	yes	maximal, complemented
13	C₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3062	C₂	1	2	yes	maximal, complemented
15	C₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3012	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2897	C₂	1	2	yes	maximal, complemented
20	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	—
21	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂×C₇×#135	C₂²	1	1	yes	characteristic
23	C₂×C₇×#131	C₂²	1	2	yes	complemented
24	C₇×#556	C₂²	1	2	yes	complemented
25	C₇×#555	C₂²	1	2	yes	complemented
26	C₇×#554	C₂²	1	2	yes	complemented
27	C₇×#553	—	2	2	no	—
28	C₇×#550	C₂²	1	2	yes	—
29	C₇×#550	C₂²	1	2	yes	—
30	C₇×#548	—	2	2	no	—
31	C₇×#547	C₂²	1	2	yes	complemented
32	C₇×D₄²	—	2	2	no	—
33	C₇×D₄²	—	2	2	no	—
34	C₇×D₄²	C₂²	1	2	yes	—
35	C₇×D₄²	C₂²	1	2	yes	—
36	C₇×#542	—	2	2	no	—
37	C₇×#537	C₂²	1	2	yes	complemented
38	C₇×#535	—	2	2	no	—
39	C₇×#535	C₂²	1	2	yes	—
40	C₇×#533	—	2	1	no	—
41	C₇×#532	—	2	1	no	—
42	C₇×#532	—	2	1	no	—
43	C₇×#532	C₂²	1	1	yes	characteristic
44	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₇×#127	—	2	1	no	—
46	C₂×C₇×#127	C₂²	1	1	yes	characteristic
47	C₇×#520	C₂²	1	2	yes	complemented
48	C₄×C₇×#41	C₂²	1	1	yes	characteristic
49	C₄×C₇×#41	C₂²	1	1	yes	characteristic, complemented
50	C₇×#486	C₂²	1	2	yes	complemented
51	C₇×#486	C₂²	1	2	yes	complemented
52	C₇×#486	C₂²	1	2	yes	complemented
53	C₇×#486	C₂²	1	2	yes	complemented
54	C₇×#482	C₂²	1	4	yes	complemented
55	C₇×#482	C₂²	1	4	yes	complemented
56	C₇×#481	C₂²	1	4	yes	complemented
57	C₇×#480	C₂²	1	4	yes	complemented
58	C₇×#477	C₂²	1	2	yes	complemented
59	C₇×#476	C₂²	1	2	yes	complemented
60	C₇×#475	C₂²	1	2	yes	complemented
61	C₇×#474	C₂²	1	2	yes	complemented
62	C₇×#469	C₂²	1	4	yes	complemented
63	C₇×#468	C₂²	1	4	yes	complemented
64	C₇×#466	C₂²	1	4	yes	complemented
65	C₇×#465	C₂²	1	4	yes	complemented
66	C₇×#460	C₂²	1	2	yes	complemented
67	C₇×#460	C₂²	1	2	yes	complemented
68	C₇×#459	C₂²	1	2	yes	complemented
69	C₇×#459	C₂²	1	2	yes	complemented
70	C₇×#452	C₂²	1	4	yes	complemented
71	C₇×#450	C₂²	1	4	yes	complemented
72	C₇×#449	C₂²	1	4	yes	complemented
73	C₇×#447	C₂²	1	4	yes	complemented
74	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
75	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
81	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
82	C₇×#436	C₂²	1	2	yes	complemented
83	C₇×#436	C₂²	1	2	yes	complemented
84	C₇×C₈×D₄	C₂²	1	2	yes	complemented
85	C₇×C₈×D₄	C₂²	1	2	yes	complemented
86	C₇×#428	C₂²	1	2	yes	complemented
87	C₇×#427	C₂²	1	1	yes	characteristic, complemented
88	C₇×#423	C₂²	1	1	yes	characteristic, complemented
89	C₇×#418	C₂²	1	2	yes	complemented
90	C₇×#418	C₂²	1	4	yes	complemented
91	C₇×#417	C₂²	1	2	yes	—
92	C₇×#417	C₂²	1	4	yes	complemented
93	C₇×#416	C₂²	1	1	yes	characteristic
94	C₇×#416	C₂²	1	1	yes	characteristic, complemented
95	C₇×#416	C₂²	1	4	yes	complemented
96	C₂×C₇×#102	C₂²	1	2	yes	complemented
97	C₂×C₇×#102	C₂²	1	4	yes	complemented
98	C₂×C₇×#102	C₂²	1	2	yes	complemented
99	C₇×#408	C₂²	1	2	yes	complemented
100	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
101	#61215	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₇×H(5,𝔽₂)	—	2	8	no	—
103	C₇×H(5,𝔽₂)	—	4	4	no	—
104	C₂×C₇×#41	—	2	2	no	—
105	C₂×C₇×#41	—	2	2	no	—
106	C₂×C₇×#41	C₂³	1	1	yes	characteristic
107	C₂×C₇×#41	C₂³	1	4	yes	—
108	C₂×C₇×#41	C₂³	1	1	yes	characteristic
109	C₂×C₇×#41	C₂³	1	2	yes	—
110	C₂²×C₇×Q₈	—	2	1	no	—
111	C₂²×C₇×D₄	—	2	2	no	—
112	C₂²×C₇×D₄	—	2	4	no	—
113	C₂²×C₇×D₄	—	2	2	no	—
114	C₂²×C₇×D₄	—	2	2	no	—
115	C₂²×C₇×D₄	—	2	1	no	—
116	C₂²×C₇×D₄	—	2	1	no	—
117	C₂²×C₇×D₄	C₂³	1	2	yes	—
118	C₂²×C₇×D₄	C₂³	1	4	yes	—
119	C₇×AGL(1,ℤ/8)	—	4	4	no	—
120	C₇×#135	—	2	4	no	—
121	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
123	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
124	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
125	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
126	C₂×C₇×D₈	C₂³	1	4	yes	—
127	C₇×#131	—	4	4	no	—
128	C₂×C₇×M₁₆	C₂³	1	2	yes	—
129	C₂×C₇×M₁₆	C₂³	1	4	yes	—
130	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
131	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
132	C₂²×C₇×C₈	C₂³	1	4	yes	—
133	C₇×C₄⋊Q₈	—	2	1	no	—
134	C₇×C₄⋊Q₈	—	2	1	no	—
135	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
136	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₇×#127	—	2	2	no	—
139	C₇×#127	—	2	2	no	—
140	C₇×#127	—	2	2	no	—
141	C₇×#127	—	2	1	no	—
142	C₇×#127	—	2	1	no	—
143	C₇×#127	D₄	1	1	yes	characteristic
144	C₇×#127	C₂³	1	2	yes	—
145	C₇×#127	C₂³	1	2	yes	—
146	C₇×#126	—	2	4	no	—
147	C₇×#125	—	2	2	no	—
148	C₇×#124	—	2	2	no	—
149	C₇×#124	—	2	2	no	—
150	C₇×#124	—	2	4	no	—
151	C₇×#124	D₄	1	2	yes	—
152	C₇×#123	—	2	4	no	—
153	C₇×C₂²⋊Q₈	—	2	2	no	—
154	C₇×C₂²⋊Q₈	—	2	2	no	—
155	C₇×C₂²⋊Q₈	—	2	4	no	—
156	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
157	C₇×#121	—	2	2	no	—
158	C₇×#121	—	2	2	no	—
159	C₇×#121	—	2	4	no	—
160	C₇×#121	—	2	2	no	—
161	C₇×#121	—	2	2	no	—
162	C₇×#121	—	2	4	no	—
163	C₇×#121	—	2	4	no	—
164	C₇×#121	D₄	1	2	yes	—
165	C₇×#121	D₄	1	2	yes	—
166	C₇×#121	C₂³	1	4	yes	—
167	C₇×#121	C₂³	1	4	yes	—
168	C₇×#121	C₂³	1	4	yes	—
169	C₇×#120	—	2	4	no	—
170	C₇×#120	—	2	4	no	—
171	C₇×#120	—	2	4	no	—
172	C₄×C₇×Q₈	—	2	2	no	—
173	C₄×C₇×Q₈	—	2	2	no	—
174	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
175	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
176	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
177	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
178	C₄×C₇×D₄	—	2	2	no	—
179	C₄×C₇×D₄	—	2	4	no	—
180	C₄×C₇×D₄	—	2	2	no	—
181	C₄×C₇×D₄	—	2	1	no	—
182	C₄×C₇×D₄	—	2	1	no	—
183	C₄×C₇×D₄	—	2	1	no	—
184	C₄×C₇×D₄	—	2	1	no	—
185	C₄×C₇×D₄	—	2	2	no	—
186	C₄×C₇×D₄	—	2	2	no	—
187	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
188	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
189	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
190	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
191	C₄×C₇×D₄	C₂³	1	2	yes	—
192	C₄×C₇×D₄	C₂³	1	2	yes	—
193	C₇×#117	—	2	2	no	—
194	C₇×#117	—	2	1	no	—
195	C₇×#117	—	2	1	no	—
196	C₇×#117	C₂³	1	4	yes	—
197	C₇×#117	C₂³	1	1	yes	characteristic
198	C₇×#117	C₂³	1	1	yes	characteristic
199	C₂×C₇×C₄⋊C₄	—	2	1	no	—
200	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
201	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₄²×C₇	—	2	1	no	—
203	C₂×C₄²×C₇	—	2	1	no	—
204	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
205	C₇×#107	C₂³	1	4	yes	—
206	C₇×#107	C₂³	1	1	yes	characteristic
207	C₇×#107	C₂³	1	1	yes	characteristic
208	C₇×#106	C₂³	1	4	yes	—
209	C₇×#106	C₂³	1	1	yes	characteristic
210	C₇×#106	C₂³	1	1	yes	characteristic
211	C₇×C₄⋊C₈	C₂³	1	2	yes	—
212	C₇×C₄⋊C₈	C₂³	1	2	yes	—
213	C₇×#103	C₂³	1	1	yes	characteristic
214	C₇×#103	C₂³	1	4	yes	—
215	C₇×#103	C₂³	1	1	yes	characteristic
216	C₇×#103	C₂³	1	1	yes	characteristic
217	C₇×#103	C₂³	1	1	yes	characteristic
218	C₇×#102	C₂³	1	1	yes	characteristic
219	C₇×#102	C₂³	1	4	yes	—
220	C₇×#102	C₂³	1	4	yes	—
221	C₇×#102	C₂³	1	1	yes	characteristic
222	C₇×#102	C₂³	1	4	yes	—
223	C₇×#102	C₂³	1	4	yes	—
224	C₇×#102	C₂³	1	4	yes	—
225	C₇×#102	C₂³	1	4	yes	—
226	C₇×#102	C₂³	1	4	yes	—
227	C₇×#102	C₂³	1	1	yes	characteristic
228	C₇×#102	C₂³	1	1	yes	characteristic
229	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
232	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
233	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
234	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
235	#3511	C₂×C₇	1	1	yes	characteristic, complemented
236	#3498	C₂×C₇	1	1	yes	characteristic, complemented
237	#3333	C₂×C₇	1	2	yes	complemented
238	#3332	C₂×C₇	1	2	yes	complemented
239	#3325	C₂×C₇	1	2	yes	complemented
240	#3324	C₂×C₇	1	2	yes	complemented
241	#3305	C₂×C₇	1	2	yes	complemented
242	#3304	C₂×C₇	1	2	yes	complemented
243	#3295	C₂×C₇	1	2	yes	complemented
244	#3294	C₂×C₇	1	2	yes	complemented
245	C₂×#486	C₂×C₇	1	1	yes	characteristic, complemented
246	#3096	C₂×C₇	1	2	yes	complemented
247	#3079	C₂×C₇	1	1	yes	characteristic, complemented
248	#3062	C₂×C₇	1	2	yes	complemented
249	#3038	C₂×C₇	1	1	yes	characteristic, complemented
250	#3012	C₂×C₇	1	2	yes	complemented
251	C₄×#135	C₂×C₇	1	1	yes	characteristic, complemented
252	#2931	C₂×C₇	1	1	yes	characteristic, complemented
253	#2897	C₂×C₇	1	2	yes	complemented
254	C₂⁴×C₇	—	2	4	no	—
255	C₂⁴×C₇	—	2	2	no	—
256	C₇×#41	—	2	4	no	—
257	C₇×#41	—	2	4	no	—
258	C₇×#41	—	2	2	no	—
259	C₇×#41	—	2	8	no	—
260	C₇×#41	—	2	2	no	—
261	C₇×#41	—	2	2	no	—
262	C₇×#41	—	4	4	no	—
263	C₇×#41	—	4	8	no	—
264	C₇×#41	—	8	4	no	—
265	C₇×#41	#41	1	4	yes	complemented
266	C₂×C₇×Q₈	—	2	2	no	—
267	C₂×C₇×Q₈	—	2	2	no	—
268	C₂×C₇×Q₈	—	8	2	no	—
269	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
270	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
271	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
272	C₂×C₇×D₄	—	2	1	no	—
273	C₂×C₇×D₄	—	2	8	no	—
274	C₂×C₇×D₄	—	2	1	no	—
275	C₂×C₇×D₄	—	2	4	no	—
276	C₂×C₇×D₄	—	2	4	no	—
277	C₂×C₇×D₄	—	2	4	no	—
278	C₂×C₇×D₄	—	2	4	no	—
279	C₂×C₇×D₄	—	2	2	no	—
280	C₂×C₇×D₄	—	2	2	no	—
281	C₂×C₇×D₄	—	2	4	no	—
282	C₂×C₇×D₄	—	2	2	no	—
283	C₂×C₇×D₄	—	2	2	no	—
284	C₂×C₇×D₄	—	2	2	no	—
285	C₂×C₇×D₄	—	2	4	no	—
286	C₂×C₇×D₄	—	2	4	no	—
287	C₂×C₇×D₄	—	4	4	no	—
288	C₂×C₇×D₄	—	4	8	no	—
289	C₂×C₇×D₄	—	4	16	no	—
290	C₂×C₇×D₄	—	8	2	no	—
291	C₂×C₇×D₄	—	8	2	no	—
292	C₂×C₇×D₄	—	8	4	no	—
293	C₂×C₇×D₄	—	8	4	no	—
294	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
295	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
296	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
297	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
298	C₂×C₇×D₄	C₂⁴	1	4	yes	—
299	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
300	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₇	—	2	1	no	—
302	C₂²×C₄×C₇	—	2	2	no	—
303	C₂²×C₄×C₇	—	2	4	no	—
304	C₂²×C₄×C₇	—	2	1	no	—
305	C₂²×C₄×C₇	—	2	1	no	—
306	C₂²×C₄×C₇	—	2	1	no	—
307	C₂²×C₄×C₇	—	2	1	no	—
308	C₂²×C₄×C₇	—	2	1	no	—
309	C₂²×C₄×C₇	—	2	4	no	—
310	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
313	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
314	C₇×Q₁₆	—	2	2	no	—
315	C₇×SD₁₆	—	2	2	no	—
316	C₇×SD₁₆	—	2	2	no	—
317	C₇×SD₁₆	—	4	4	no	—
318	C₇×D₈	—	2	2	no	—
319	C₇×D₈	—	4	4	no	—
320	C₇×M₁₆	—	2	4	no	—
321	C₇×M₁₆	—	4	4	no	—
322	C₂×C₇×C₈	—	2	2	no	—
323	C₂×C₇×C₈	—	2	2	no	—
324	C₂×C₇×C₈	—	4	4	no	—
325	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
326	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
327	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
328	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
329	C₂×C₇×C₈	C₂⁴	1	4	yes	—
330	C₇×C₄⋊C₄	—	2	2	no	—
331	C₇×C₄⋊C₄	—	2	2	no	—
332	C₇×C₄⋊C₄	—	2	2	no	—
333	C₇×C₄⋊C₄	—	2	4	no	—
334	C₇×C₄⋊C₄	—	2	1	no	—
335	C₇×C₄⋊C₄	—	2	1	no	—
336	C₇×C₄⋊C₄	—	2	1	no	—
337	C₇×C₄⋊C₄	—	2	1	no	—
338	C₇×C₄⋊C₄	—	2	4	no	—
339	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
340	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
341	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
342	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
343	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
344	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
345	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
346	C₇×C₂²⋊C₄	—	2	1	no	—
347	C₇×C₂²⋊C₄	—	2	1	no	—
348	C₇×C₂²⋊C₄	—	2	4	no	—
349	C₇×C₂²⋊C₄	—	2	4	no	—
350	C₇×C₂²⋊C₄	—	2	1	no	—
351	C₇×C₂²⋊C₄	—	2	1	no	—
352	C₇×C₂²⋊C₄	—	2	1	no	—
353	C₇×C₂²⋊C₄	—	2	1	no	—
354	C₇×C₂²⋊C₄	—	2	4	no	—
355	C₇×C₂²⋊C₄	—	2	4	no	—
356	C₇×C₂²⋊C₄	—	2	4	no	—
357	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
358	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
359	C₄²×C₇	—	2	1	no	—
360	C₄²×C₇	—	2	1	no	—
361	C₄²×C₇	—	2	1	no	—
362	C₄²×C₇	—	2	1	no	—
363	C₄²×C₇	—	2	1	no	—
364	C₄²×C₇	—	2	1	no	—
365	C₄²×C₇	—	2	4	no	—
366	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
367	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
368	C₄²×C₇	C₂⁴	1	1	yes	characteristic
369	C₄²×C₇	C₂⁴	1	1	yes	characteristic
370	C₂×H(5,𝔽₂)	C₂²×C₇	1	2	yes	—
371	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	complemented
372	C₂×#135	C₂²×C₇	1	1	yes	characteristic
373	C₂×#131	C₂²×C₇	1	2	yes	complemented
374	#556	C₂²×C₇	1	2	yes	complemented
375	#555	C₂²×C₇	1	2	yes	complemented
376	#554	C₂²×C₇	1	2	yes	complemented
377	#553	—	2	2	no	—
378	#550	C₂²×C₇	1	2	yes	—
379	#550	C₂²×C₇	1	2	yes	—
380	#548	—	2	2	no	—
381	#547	C₂²×C₇	1	2	yes	complemented
382	D₄²	—	2	2	no	—
383	D₄²	—	2	2	no	—
384	D₄²	C₂²×C₇	1	2	yes	—
385	D₄²	C₂²×C₇	1	2	yes	—
386	#542	—	2	2	no	—
387	#537	C₂²×C₇	1	2	yes	complemented
388	#535	—	2	2	no	—
389	#535	C₂²×C₇	1	2	yes	—
390	#533	—	2	1	no	—
391	#532	—	2	1	no	—
392	#532	—	2	1	no	—
393	#532	C₂²×C₇	1	1	yes	characteristic
394	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
395	C₂×#127	—	2	1	no	—
396	C₂×#127	C₂²×C₇	1	1	yes	characteristic
397	#520	C₂²×C₇	1	2	yes	complemented
398	C₄×#41	C₂²×C₇	1	1	yes	characteristic
399	C₄×#41	C₂²×C₇	1	1	yes	characteristic, complemented
400	#486	C₂²×C₇	1	2	yes	complemented
401	#486	C₂²×C₇	1	2	yes	complemented
402	#486	C₂²×C₇	1	2	yes	complemented
403	#486	C₂²×C₇	1	2	yes	complemented
404	#482	C₂²×C₇	1	4	yes	complemented
405	#482	C₂²×C₇	1	4	yes	complemented
406	#481	C₂²×C₇	1	4	yes	complemented
407	#480	C₂²×C₇	1	4	yes	complemented
408	#477	C₂²×C₇	1	2	yes	complemented
409	#476	C₂²×C₇	1	2	yes	complemented
410	#475	C₂²×C₇	1	2	yes	complemented
411	#474	C₂²×C₇	1	2	yes	complemented
412	#469	C₂²×C₇	1	4	yes	complemented
413	#468	C₂²×C₇	1	4	yes	complemented
414	#466	C₂²×C₇	1	4	yes	complemented
415	#465	C₂²×C₇	1	4	yes	complemented
416	#460	C₂²×C₇	1	2	yes	complemented
417	#460	C₂²×C₇	1	2	yes	complemented
418	#459	C₂²×C₇	1	2	yes	complemented
419	#459	C₂²×C₇	1	2	yes	complemented
420	#452	C₂²×C₇	1	4	yes	complemented
421	#450	C₂²×C₇	1	4	yes	complemented
422	#449	C₂²×C₇	1	4	yes	complemented
423	#447	C₂²×C₇	1	4	yes	complemented
424	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
425	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
426	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
427	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
428	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
429	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
430	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
431	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
432	#436	C₂²×C₇	1	2	yes	complemented
433	#436	C₂²×C₇	1	2	yes	complemented
434	C₈×D₄	C₂²×C₇	1	2	yes	complemented
435	C₈×D₄	C₂²×C₇	1	2	yes	complemented
436	#428	C₂²×C₇	1	2	yes	complemented
437	#427	C₂²×C₇	1	1	yes	characteristic, complemented
438	#423	C₂²×C₇	1	1	yes	characteristic, complemented
439	#418	C₂²×C₇	1	2	yes	complemented
440	#418	C₂²×C₇	1	4	yes	complemented
441	#417	C₂²×C₇	1	2	yes	—
442	#417	C₂²×C₇	1	4	yes	complemented
443	#416	C₂²×C₇	1	1	yes	characteristic
444	#416	C₂²×C₇	1	4	yes	complemented
445	#416	C₂²×C₇	1	1	yes	characteristic, complemented
446	C₂×#102	C₂²×C₇	1	2	yes	complemented
447	C₂×#102	C₂²×C₇	1	2	yes	complemented
448	C₂×#102	C₂²×C₇	1	4	yes	complemented
449	#408	C₂²×C₇	1	2	yes	complemented
450	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
451	C₂³×C₇	—	2	1	no	—
452	C₂³×C₇	—	2	1	no	—
453	C₂³×C₇	—	2	4	no	—
454	C₂³×C₇	—	4	8	no	—
455	C₂³×C₇	—	4	4	no	—
456	C₂³×C₇	—	8	2	no	—
457	C₂³×C₇	—	8	2	no	—
458	C₂³×C₇	—	8	4	no	—
459	C₂³×C₇	—	8	4	no	—
460	C₂³×C₇	C₂²×D₄	1	4	yes	—
461	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
462	C₇×Q₈	—	2	4	no	—
463	C₇×Q₈	—	2	1	no	—
464	C₇×Q₈	—	2	1	no	—
465	C₇×Q₈	—	2	1	no	—
466	C₇×Q₈	—	4	4	no	—
467	C₇×Q₈	—	8	2	no	—
468	C₇×Q₈	C₂×#41	1	2	yes	—
469	C₇×D₄	—	2	4	no	—
470	C₇×D₄	—	2	8	no	—
471	C₇×D₄	—	2	4	no	—
472	C₇×D₄	—	2	4	no	—
473	C₇×D₄	—	2	4	no	—
474	C₇×D₄	—	2	1	no	—
475	C₇×D₄	—	2	4	no	—
476	C₇×D₄	—	2	1	no	—
477	C₇×D₄	—	2	1	no	—
478	C₇×D₄	—	2	4	no	—
479	C₇×D₄	—	4	8	no	—
480	C₇×D₄	—	4	8	no	—
481	C₇×D₄	—	4	2	no	—
482	C₇×D₄	—	4	4	no	—
483	C₇×D₄	—	4	4	no	—
484	C₇×D₄	—	4	4	no	—
485	C₇×D₄	—	8	2	no	—
486	C₇×D₄	—	8	2	no	—
487	C₇×D₄	—	8	4	no	—
488	C₇×D₄	—	8	4	no	—
489	C₇×D₄	—	8	4	no	—
490	C₇×D₄	C₂×#41	1	2	yes	—
491	C₂×C₄×C₇	—	2	1	no	—
492	C₂×C₄×C₇	—	2	4	no	—
493	C₂×C₄×C₇	—	2	2	no	—
494	C₂×C₄×C₇	—	2	2	no	—
495	C₂×C₄×C₇	—	2	4	no	—
496	C₂×C₄×C₇	—	2	4	no	—
497	C₂×C₄×C₇	—	2	1	no	—
498	C₂×C₄×C₇	—	2	1	no	—
499	C₂×C₄×C₇	—	2	1	no	—
500	C₂×C₄×C₇	—	2	1	no	—
501	C₂×C₄×C₇	—	2	1	no	—
502	C₂×C₄×C₇	—	2	4	no	—
503	C₂×C₄×C₇	—	4	8	no	—
504	C₂×C₄×C₇	—	4	2	no	—
505	C₂×C₄×C₇	—	4	2	no	—
506	C₂×C₄×C₇	—	4	2	no	—
507	C₂×C₄×C₇	—	4	2	no	—
508	C₂×C₄×C₇	—	4	2	no	—
509	C₂×C₄×C₇	—	8	2	no	—
510	C₂×C₄×C₇	—	8	4	no	—
511	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
512	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₇	C₂×#41	1	2	yes	—
518	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
519	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
520	C₇×C₈	—	2	1	no	—
521	C₇×C₈	—	2	1	no	—
522	C₇×C₈	—	2	1	no	—
523	C₇×C₈	—	2	1	no	—
524	C₇×C₈	—	2	4	no	—
525	H(5,𝔽₂)	—	2	8	no	—
526	H(5,𝔽₂)	—	4	4	no	—
527	C₂×#41	—	2	2	no	—
528	C₂×#41	—	2	2	no	—
529	C₂×#41	C₂³×C₇	1	1	yes	characteristic
530	C₂×#41	C₂³×C₇	1	4	yes	—
531	C₂×#41	C₂³×C₇	1	1	yes	characteristic
532	C₂×#41	C₂³×C₇	1	2	yes	—
533	C₂²×Q₈	—	2	1	no	—
534	C₂²×D₄	—	2	2	no	—
535	C₂²×D₄	—	2	4	no	—
536	C₂²×D₄	—	2	2	no	—
537	C₂²×D₄	—	2	2	no	—
538	C₂²×D₄	—	2	1	no	—
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	C₂³×C₇	1	2	yes	—
541	C₂²×D₄	C₂³×C₇	1	4	yes	—
542	AGL(1,ℤ/8)	—	4	4	no	—
543	#135	—	2	4	no	—
544	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
545	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
546	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
547	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
548	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
549	C₂×D₈	C₂³×C₇	1	4	yes	—
550	#131	—	4	4	no	—
551	C₂×M₁₆	C₂³×C₇	1	2	yes	—
552	C₂×M₁₆	C₂³×C₇	1	4	yes	—
553	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
554	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
555	C₂²×C₈	C₂³×C₇	1	4	yes	—
556	C₄⋊Q₈	—	2	1	no	—
557	C₄⋊Q₈	—	2	1	no	—
558	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
559	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
560	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
561	#127	—	2	2	no	—
562	#127	—	2	2	no	—
563	#127	—	2	2	no	—
564	#127	—	2	1	no	—
565	#127	—	2	1	no	—
566	#127	C₇×D₄	1	1	yes	characteristic
567	#127	C₂³×C₇	1	2	yes	—
568	#127	C₂³×C₇	1	2	yes	—
569	#126	—	2	4	no	—
570	#125	—	2	2	no	—
571	#124	—	2	2	no	—
572	#124	—	2	2	no	—
573	#124	—	2	4	no	—
574	#124	C₇×D₄	1	2	yes	—
575	#123	—	2	4	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	4	no	—
579	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
580	#121	—	2	2	no	—
581	#121	—	2	2	no	—
582	#121	—	2	4	no	—
583	#121	—	2	2	no	—
584	#121	—	2	2	no	—
585	#121	—	2	4	no	—
586	#121	—	2	4	no	—
587	#121	C₇×D₄	1	2	yes	—
588	#121	C₇×D₄	1	2	yes	—
589	#121	C₂³×C₇	1	4	yes	—
590	#121	C₂³×C₇	1	4	yes	—
591	#121	C₂³×C₇	1	4	yes	—
592	#120	—	2	4	no	—
593	#120	—	2	4	no	—
594	#120	—	2	4	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
598	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	4	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
611	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
612	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
613	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
614	C₄×D₄	C₂³×C₇	1	2	yes	—
615	C₄×D₄	C₂³×C₇	1	2	yes	—
616	#117	—	2	2	no	—
617	#117	—	2	1	no	—
618	#117	—	2	1	no	—
619	#117	C₂³×C₇	1	1	yes	characteristic
620	#117	C₂³×C₇	1	1	yes	characteristic
621	#117	C₂³×C₇	1	4	yes	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
625	C₂×C₄²	—	2	1	no	—
626	C₂×C₄²	—	2	1	no	—
627	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
628	#107	C₂³×C₇	1	1	yes	characteristic
629	#107	C₂³×C₇	1	1	yes	characteristic
630	#107	C₂³×C₇	1	4	yes	—
631	#106	C₂³×C₇	1	1	yes	characteristic
632	#106	C₂³×C₇	1	1	yes	characteristic
633	#106	C₂³×C₇	1	4	yes	—
634	C₄⋊C₈	C₂³×C₇	1	2	yes	—
635	C₄⋊C₈	C₂³×C₇	1	2	yes	—
636	#103	C₂³×C₇	1	1	yes	characteristic
637	#103	C₂³×C₇	1	1	yes	characteristic
638	#103	C₂³×C₇	1	4	yes	—
639	#103	C₂³×C₇	1	1	yes	characteristic
640	#103	C₂³×C₇	1	1	yes	characteristic
641	#102	C₂³×C₇	1	1	yes	characteristic
642	#102	C₂³×C₇	1	4	yes	—
643	#102	C₂³×C₇	1	4	yes	—
644	#102	C₂³×C₇	1	4	yes	—
645	#102	C₂³×C₇	1	4	yes	—
646	#102	C₂³×C₇	1	4	yes	—
647	#102	C₂³×C₇	1	4	yes	—
648	#102	C₂³×C₇	1	1	yes	characteristic
649	#102	C₂³×C₇	1	4	yes	—
650	#102	C₂³×C₇	1	1	yes	characteristic
651	#102	C₂³×C₇	1	1	yes	characteristic
652	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
653	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
654	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
655	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
656	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
657	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
658	C₂²×C₇	—	2	1	no	—
659	C₂²×C₇	—	2	1	no	—
660	C₂²×C₇	—	2	4	no	—
661	C₂²×C₇	—	2	2	no	—
662	C₂²×C₇	—	2	4	no	—
663	C₂²×C₇	—	2	4	no	—
664	C₂²×C₇	—	4	1	no	—
665	C₂²×C₇	—	4	1	no	—
666	C₂²×C₇	—	4	4	no	—
667	C₂²×C₇	—	4	1	no	—
668	C₂²×C₇	—	4	1	no	—
669	C₂²×C₇	—	4	4	no	—
670	C₂²×C₇	—	4	1	no	—
671	C₂²×C₇	—	4	4	no	—
672	C₂²×C₇	—	16	4	no	—
673	C₂²×C₇	—	16	8	no	—
674	C₂²×C₇	#546	1	2	yes	—
675	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
676	C₄×C₇	—	2	2	no	—
677	C₄×C₇	—	2	4	no	—
678	C₄×C₇	—	2	1	no	—
679	C₄×C₇	—	2	1	no	—
680	C₄×C₇	—	4	1	no	—
681	C₄×C₇	—	4	1	no	—
682	C₄×C₇	—	4	1	no	—
683	C₄×C₇	—	4	4	no	—
684	C₄×C₇	—	4	1	no	—
685	C₄×C₇	—	4	1	no	—
686	C₄×C₇	#546	1	2	yes	—
687	C₄×C₇	#576	1	2	yes	—
688	C₄×C₇	#577	1	2	yes	—
689	C₄×C₇	C₂²×#41	1	1	yes	characteristic
690	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
691	C₂⁴	—	2	4	no	—
692	C₂⁴	—	2	2	no	—
693	#41	—	2	4	no	—
694	#41	—	2	4	no	—
695	#41	—	2	2	no	—
696	#41	—	2	8	no	—
697	#41	—	2	2	no	—
698	#41	—	2	2	no	—
699	#41	—	4	4	no	—
700	#41	—	4	8	no	—
701	#41	—	8	4	no	—
702	#41	C₇×#41	1	4	yes	complemented
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	—	8	2	no	—
706	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
707	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
708	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	8	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	4	no	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	4	4	no	—
725	C₂×D₄	—	4	8	no	—
726	C₂×D₄	—	4	16	no	—
727	C₂×D₄	—	8	2	no	—
728	C₂×D₄	—	8	2	no	—
729	C₂×D₄	—	8	4	no	—
730	C₂×D₄	—	8	4	no	—
731	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
732	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
733	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
734	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
735	C₂×D₄	C₂⁴×C₇	1	4	yes	—
736	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
737	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	4	no	—
747	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
748	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
750	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
751	Q₁₆	—	2	2	no	—
752	SD₁₆	—	2	2	no	—
753	SD₁₆	—	2	2	no	—
754	SD₁₆	—	4	4	no	—
755	D₈	—	2	2	no	—
756	D₈	—	4	4	no	—
757	M₁₆	—	2	4	no	—
758	M₁₆	—	4	4	no	—
759	C₂×C₈	—	2	2	no	—
760	C₂×C₈	—	2	2	no	—
761	C₂×C₈	—	4	4	no	—
762	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
763	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
764	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
765	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
766	C₂×C₈	C₂⁴×C₇	1	4	yes	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	1	no	—
773	C₄⋊C₄	—	2	1	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	—	2	4	no	—
776	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
777	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
778	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
779	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
780	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
781	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
782	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	1	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	1	no	—
788	C₂²⋊C₄	—	2	1	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
795	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
796	C₄²	—	2	1	no	—
797	C₄²	—	2	1	no	—
798	C₄²	—	2	1	no	—
799	C₄²	—	2	1	no	—
800	C₄²	—	2	1	no	—
801	C₄²	—	2	1	no	—
802	C₄²	—	2	4	no	—
803	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
804	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
805	C₄²	C₂⁴×C₇	1	1	yes	characteristic
806	C₄²	C₂⁴×C₇	1	1	yes	characteristic
807	C₂×C₇	—	2	2	no	—
808	C₂×C₇	—	4	4	no	—
809	C₂×C₇	—	4	2	no	—
810	C₂×C₇	—	8	1	no	—
811	C₂×C₇	—	8	4	no	—
812	C₂×C₇	C₂×#546	1	1	yes	characteristic
813	C₂×C₇	C₂×#576	1	1	yes	characteristic
814	C₂×C₇	C₂×#577	1	1	yes	characteristic
815	C₂³	—	2	1	no	—
816	C₂³	—	2	1	no	—
817	C₂³	—	2	4	no	—
818	C₂³	—	4	8	no	—
819	C₂³	—	4	4	no	—
820	C₂³	—	8	2	no	—
821	C₂³	—	8	2	no	—
822	C₂³	—	8	4	no	—
823	C₂³	—	8	4	no	—
824	C₂³	C₂²×C₇×D₄	1	4	yes	—
825	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
826	Q₈	—	2	1	no	—
827	Q₈	—	2	4	no	—
828	Q₈	—	2	1	no	—
829	Q₈	—	2	1	no	—
830	Q₈	—	4	4	no	—
831	Q₈	—	8	2	no	—
832	Q₈	C₂×C₇×#41	1	2	yes	—
833	D₄	—	2	4	no	—
834	D₄	—	2	8	no	—
835	D₄	—	2	1	no	—
836	D₄	—	2	4	no	—
837	D₄	—	2	1	no	—
838	D₄	—	2	1	no	—
839	D₄	—	2	4	no	—
840	D₄	—	2	4	no	—
841	D₄	—	2	4	no	—
842	D₄	—	2	4	no	—
843	D₄	—	4	8	no	—
844	D₄	—	4	8	no	—
845	D₄	—	4	2	no	—
846	D₄	—	4	4	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	4	no	—
849	D₄	—	8	2	no	—
850	D₄	—	8	2	no	—
851	D₄	—	8	4	no	—
852	D₄	—	8	4	no	—
853	D₄	—	8	4	no	—
854	D₄	C₂×C₇×#41	1	2	yes	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	4	no	—
857	C₂×C₄	—	2	4	no	—
858	C₂×C₄	—	2	4	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	4	no	—
867	C₂×C₄	—	4	8	no	—
868	C₂×C₄	—	4	2	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	4	2	no	—
873	C₂×C₄	—	8	2	no	—
874	C₂×C₄	—	8	4	no	—
875	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
876	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
877	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
878	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
879	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
880	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
881	C₂×C₄	C₂×C₇×#41	1	2	yes	—
882	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
883	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
884	C₈	—	2	1	no	—
885	C₈	—	2	1	no	—
886	C₈	—	2	1	no	—
887	C₈	—	2	1	no	—
888	C₈	—	2	4	no	—
889	C₇	#61215	1	1	yes	characteristic, direct product factor, Sylow
890	C₂²	—	2	1	no	—
891	C₂²	—	2	1	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	2	4	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	1	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	4	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	4	no	—
902	C₂²	—	4	4	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	16	4	no	—
905	C₂²	—	16	8	no	—
906	C₂²	C₇×#546	1	2	yes	—
907	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
908	C₄	—	2	1	no	—
909	C₄	—	2	1	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	4	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	1	no	—
914	C₄	—	4	4	no	—
915	C₄	—	4	1	no	—
916	C₄	—	4	1	no	—
917	C₄	—	4	1	no	—
918	C₄	C₇×#546	1	2	yes	—
919	C₄	C₇×#576	1	2	yes	—
920	C₄	C₇×#577	1	2	yes	—
921	C₄	C₂²×C₇×#41	1	1	yes	characteristic
922	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
923	C₂	—	2	2	no	—
924	C₂	—	4	4	no	—
925	C₂	—	4	2	no	—
926	C₂	—	8	4	no	—
927	C₂	—	8	1	no	—
928	C₂	C₂×C₇×#546	1	1	yes	characteristic
929	C₂	C₂×C₇×#576	1	1	yes	characteristic
930	C₂	C₂×C₇×#577	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×#3498	C₂	semidirect
3. C₇×#3333	C₂	semidirect
4. C₇×#3332	C₂	semidirect
5. C₇×#3325	C₂	semidirect
6. C₇×#3324	C₂	semidirect
7. C₇×#3305	C₂	semidirect
8. C₇×#3304	C₂	semidirect
9. C₇×#3295	C₂	semidirect
10. C₇×#3294	C₂	semidirect
11. C₂×C₇×#486	C₂	semidirect
12. C₇×#3096	C₂	semidirect
13. C₇×#3079	C₂	semidirect
14. C₇×#3062	C₂	semidirect
15. C₇×#3038	C₂	semidirect
16. C₇×#3012	C₂	semidirect
17. C₄×C₇×#135	C₂	semidirect
18. C₇×#2931	C₂	semidirect
19. C₇×#2897	C₂	semidirect
21. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₇×#131	C₂²	semidirect
24. C₇×#556	C₂²	semidirect
25. C₇×#555	C₂²	semidirect
26. C₇×#554	C₂²	semidirect
31. C₇×#547	C₂²	semidirect
37. C₇×#537	C₂²	semidirect
44. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
47. C₇×#520	C₂²	semidirect
49. C₄×C₇×#41	C₂²	semidirect
50. C₇×#486	C₂²	semidirect
51. C₇×#486	C₂²	semidirect
52. C₇×#486	C₂²	semidirect
53. C₇×#486	C₂²	semidirect
54. C₇×#482	C₂²	semidirect
55. C₇×#482	C₂²	semidirect
56. C₇×#481	C₂²	semidirect
57. C₇×#480	C₂²	semidirect
58. C₇×#477	C₂²	semidirect
59. C₇×#476	C₂²	semidirect
60. C₇×#475	C₂²	semidirect
61. C₇×#474	C₂²	semidirect
62. C₇×#469	C₂²	semidirect
63. C₇×#468	C₂²	semidirect
64. C₇×#466	C₂²	semidirect
65. C₇×#465	C₂²	semidirect
66. C₇×#460	C₂²	semidirect
67. C₇×#460	C₂²	semidirect
68. C₇×#459	C₂²	semidirect
69. C₇×#459	C₂²	semidirect
70. C₇×#452	C₂²	semidirect
71. C₇×#450	C₂²	semidirect
72. C₇×#449	C₂²	semidirect
73. C₇×#447	C₂²	semidirect
74. C₄×C₇×Q₁₆	C₂²	semidirect
75. C₄×C₇×Q₁₆	C₂²	semidirect
76. C₄×C₇×SD₁₆	C₂²	semidirect
77. C₄×C₇×SD₁₆	C₂²	semidirect
78. C₄×C₇×SD₁₆	C₂²	semidirect
79. C₄×C₇×SD₁₆	C₂²	semidirect
80. C₄×C₇×D₈	C₂²	semidirect
81. C₄×C₇×D₈	C₂²	semidirect
82. C₇×#436	C₂²	semidirect
83. C₇×#436	C₂²	semidirect
84. C₇×C₈×D₄	C₂²	semidirect
85. C₇×C₈×D₄	C₂²	semidirect
86. C₇×#428	C₂²	semidirect
87. C₇×#427	C₂²	semidirect
88. C₇×#423	C₂²	semidirect
89. C₇×#418	C₂²	semidirect
90. C₇×#418	C₂²	semidirect
92. C₇×#417	C₂²	semidirect
94. C₇×#416	C₂²	semidirect
95. C₇×#416	C₂²	semidirect
96. C₂×C₇×#102	C₂²	semidirect
97. C₂×C₇×#102	C₂²	semidirect
98. C₂×C₇×#102	C₂²	semidirect
99. C₇×#408	C₂²	semidirect
100. C₂×C₄×C₇×C₈	C₂²	semidirect
101. #61215	C₇	direct (N × H)
235. #3511	C₂×C₇	semidirect
236. #3498	C₂×C₇	semidirect
237. #3333	C₂×C₇	semidirect
238. #3332	C₂×C₇	semidirect
239. #3325	C₂×C₇	semidirect
240. #3324	C₂×C₇	semidirect
241. #3305	C₂×C₇	semidirect
242. #3304	C₂×C₇	semidirect
243. #3295	C₂×C₇	semidirect
244. #3294	C₂×C₇	semidirect
245. C₂×#486	C₂×C₇	semidirect
246. #3096	C₂×C₇	semidirect
247. #3079	C₂×C₇	semidirect
248. #3062	C₂×C₇	semidirect
249. #3038	C₂×C₇	semidirect
250. #3012	C₂×C₇	semidirect
251. C₄×#135	C₂×C₇	semidirect
252. #2931	C₂×C₇	semidirect
253. #2897	C₂×C₇	semidirect
265. C₇×#41	#41	semidirect
371. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
373. C₂×#131	C₂²×C₇	semidirect
374. #556	C₂²×C₇	semidirect
375. #555	C₂²×C₇	semidirect
376. #554	C₂²×C₇	semidirect
381. #547	C₂²×C₇	semidirect
387. #537	C₂²×C₇	semidirect
394. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
397. #520	C₂²×C₇	semidirect
399. C₄×#41	C₂²×C₇	semidirect
400. #486	C₂²×C₇	semidirect
401. #486	C₂²×C₇	semidirect
402. #486	C₂²×C₇	semidirect
403. #486	C₂²×C₇	semidirect
404. #482	C₂²×C₇	semidirect
405. #482	C₂²×C₇	semidirect
406. #481	C₂²×C₇	semidirect
407. #480	C₂²×C₇	semidirect
408. #477	C₂²×C₇	semidirect
409. #476	C₂²×C₇	semidirect
410. #475	C₂²×C₇	semidirect
411. #474	C₂²×C₇	semidirect
412. #469	C₂²×C₇	semidirect
413. #468	C₂²×C₇	semidirect
414. #466	C₂²×C₇	semidirect
415. #465	C₂²×C₇	semidirect
416. #460	C₂²×C₇	semidirect
417. #460	C₂²×C₇	semidirect
418. #459	C₂²×C₇	semidirect
419. #459	C₂²×C₇	semidirect
420. #452	C₂²×C₇	semidirect
421. #450	C₂²×C₇	semidirect
422. #449	C₂²×C₇	semidirect
423. #447	C₂²×C₇	semidirect
424. C₄×Q₁₆	C₂²×C₇	semidirect
425. C₄×Q₁₆	C₂²×C₇	semidirect
426. C₄×SD₁₆	C₂²×C₇	semidirect
427. C₄×SD₁₆	C₂²×C₇	semidirect
428. C₄×SD₁₆	C₂²×C₇	semidirect
429. C₄×SD₁₆	C₂²×C₇	semidirect
430. C₄×D₈	C₂²×C₇	semidirect
431. C₄×D₈	C₂²×C₇	semidirect
432. #436	C₂²×C₇	semidirect
433. #436	C₂²×C₇	semidirect
434. C₈×D₄	C₂²×C₇	semidirect
435. C₈×D₄	C₂²×C₇	semidirect
436. #428	C₂²×C₇	semidirect
437. #427	C₂²×C₇	semidirect
438. #423	C₂²×C₇	semidirect
439. #418	C₂²×C₇	semidirect
440. #418	C₂²×C₇	semidirect
442. #417	C₂²×C₇	semidirect
444. #416	C₂²×C₇	semidirect
445. #416	C₂²×C₇	semidirect
446. C₂×#102	C₂²×C₇	semidirect
447. C₂×#102	C₂²×C₇	semidirect
448. C₂×#102	C₂²×C₇	semidirect
449. #408	C₂²×C₇	semidirect
450. C₂×C₄×C₈	C₂²×C₇	semidirect
702. #41	C₇×#41	semidirect
889. C₇	#61215	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×#3498	2
C₇×#3333	2
C₇×#3332	2
C₇×#3325	2
C₇×#3324	2
C₇×#3305	2
C₇×#3304	2
C₇×#3295	2
C₇×#3294	2
C₂×C₇×#486	2
C₇×#3096	2
C₇×#3079	2
C₇×#3062	2
C₇×#3038	2
C₇×#3012	2
C₄×C₇×#135	2
C₇×#2931	2
C₇×#2897	2
#61215	7

Subgroups — C7×#61215 #13238431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61215 #13238431