Subgroups — C₇×#61256 #13238472

Order 1792.

1892 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×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3357	C₂	1	2	yes	maximal, complemented
4	C₇×#3354	C₂	1	2	yes	maximal, complemented
5	C₇×#3348	C₂	1	4	yes	maximal, complemented
6	C₇×#3347	C₂	1	4	yes	maximal, complemented
7	C₇×#3341	C₂	1	2	yes	maximal, complemented
8	C₇×#3340	C₂	1	2	yes	maximal, complemented
9	C₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3094	C₂	1	2	yes	maximal, complemented
11	C₇×#3093	C₂	1	2	yes	maximal, complemented
12	C₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3055	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2911	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
20	C₇×#556	C₂²	1	1	yes	characteristic, complemented
21	C₇×#555	—	2	1	no	—
22	C₇×#555	—	2	2	no	—
23	C₇×#555	—	2	1	no	—
24	C₇×#555	C₂²	1	2	yes	—
25	C₇×#555	C₂²	1	4	yes	—
26	C₇×#555	C₂²	1	2	yes	—
27	C₇×#555	C₂²	1	1	yes	characteristic, complemented
28	C₇×#554	C₂²	1	1	yes	characteristic, complemented
29	C₇×#553	C₂²	1	2	yes	complemented
30	C₇×#552	—	2	1	no	—
31	C₇×#552	C₂²	1	2	yes	complemented
32	C₇×#551	—	2	2	no	—
33	C₇×#547	C₂²	1	1	yes	characteristic, complemented
34	C₇×#546	—	2	1	no	—
35	C₇×#533	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₇×#529	—	2	2	no	—
38	C₇×#529	—	2	1	no	—
39	C₂×C₇×#124	—	2	2	no	—
40	C₇×#525	C₂²	1	2	yes	—
41	C₂×C₇×#121	—	2	1	no	—
42	C₂×C₇×#121	C₂²	1	2	yes	—
43	C₄×C₇×#41	—	2	1	no	—
44	C₄×C₇×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₇×#117	—	2	1	no	—
48	C₂×C₇×#117	C₂²	1	2	yes	—
49	C₂×C₇×#117	C₂²	1	2	yes	—
50	C₇×#501	C₂²	1	4	yes	complemented
51	C₇×#500	C₂²	1	2	yes	complemented
52	C₇×#498	C₂²	1	2	yes	complemented
53	C₇×#485	C₂²	1	4	yes	complemented
54	C₇×#485	C₂²	1	4	yes	complemented
55	C₇×#482	C₂²	1	4	yes	complemented
56	C₇×#482	C₂²	1	4	yes	complemented
57	C₇×#482	C₂²	1	4	yes	complemented
58	C₇×#482	C₂²	1	4	yes	complemented
59	C₇×#481	C₂²	1	4	yes	complemented
60	C₇×#480	C₂²	1	4	yes	complemented
61	C₇×#478	C₂²	1	4	yes	complemented
62	C₇×#477	C₂²	1	2	yes	complemented
63	C₇×#476	C₂²	1	2	yes	complemented
64	C₇×#476	C₂²	1	2	yes	complemented
65	C₇×#475	C₂²	1	2	yes	complemented
66	C₇×#474	C₂²	1	2	yes	complemented
67	C₇×#474	C₂²	1	2	yes	complemented
68	C₇×#469	C₂²	1	4	yes	complemented
69	C₇×#468	C₂²	1	4	yes	complemented
70	C₇×#466	C₂²	1	4	yes	complemented
71	C₇×#465	C₂²	1	4	yes	complemented
72	C₇×#442	C₂²	1	2	yes	complemented
73	C₇×#440	C₂²	1	2	yes	complemented
74	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
75	C₄×C₇×D₈	C₂²	1	2	yes	complemented
76	C₇×#436	C₂²	1	2	yes	complemented
77	C₇×#435	C₂²	1	4	yes	complemented
78	C₇×C₈×D₄	C₂²	1	2	yes	complemented
79	C₇×#428	C₂²	1	2	yes	—
80	C₇×#428	C₂²	1	2	yes	—
81	C₇×#428	C₂²	1	1	yes	characteristic
82	C₇×#428	C₂²	1	2	yes	—
83	C₇×#428	C₂²	1	2	yes	—
84	C₇×#428	C₂²	1	4	yes	complemented
85	C₇×#428	C₂²	1	4	yes	complemented
86	C₇×#427	C₂²	1	4	yes	complemented
87	C₇×#427	C₂²	1	4	yes	complemented
88	C₇×#423	C₂²	1	1	yes	characteristic
89	C₇×#418	C₂²	1	1	yes	characteristic
90	C₇×#418	C₂²	1	2	yes	—
91	C₇×#417	C₂²	1	1	yes	characteristic
92	C₇×#417	C₂²	1	2	yes	—
93	C₇×#407	C₂²	1	2	yes	—
94	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
95	#61256	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₇×#41	—	2	1	no	—
97	C₂×C₇×#41	C₂³	1	1	yes	characteristic
98	C₂²×C₇×Q₈	—	2	1	no	—
99	C₂²×C₇×D₄	—	2	2	no	—
100	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
101	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₇	—	2	1	no	—
103	C₂³×C₄×C₇	C₂³	1	2	yes	—
104	C₇×AGL(1,ℤ/8)	—	2	4	no	—
105	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
106	C₂×C₇×D₈	C₂³	1	2	yes	—
107	C₂×C₇×M₁₆	—	2	8	no	—
108	C₂×C₇×M₁₆	C₂³	1	4	yes	—
109	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
110	C₂×C₇×M₁₆	C₂³	1	2	yes	—
111	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
112	C₂²×C₇×C₈	C₂³	1	4	yes	—
113	C₇×C₄⋊Q₈	—	2	1	no	—
114	C₇×C₄⋊Q₈	—	2	1	no	—
115	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₇×#126	—	2	2	no	—
120	C₇×#126	—	2	2	no	—
121	C₇×#126	—	2	2	no	—
122	C₇×#125	—	2	2	no	—
123	C₇×#125	—	2	1	no	—
124	C₇×#125	C₂³	1	2	yes	—
125	C₇×#124	—	2	1	no	—
126	C₇×#124	—	2	4	no	—
127	C₇×#124	—	2	4	no	—
128	C₇×#124	—	2	4	no	—
129	C₇×#124	—	2	4	no	—
130	C₇×#124	—	2	2	no	—
131	C₇×#123	—	2	2	no	—
132	C₇×#123	—	2	2	no	—
133	C₇×#123	—	2	2	no	—
134	C₇×#123	—	2	2	no	—
135	C₇×C₂²⋊Q₈	—	2	1	no	—
136	C₇×C₂²⋊Q₈	—	2	1	no	—
137	C₇×C₂²⋊Q₈	—	2	1	no	—
138	C₇×C₂²⋊Q₈	—	2	2	no	—
139	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
140	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
141	C₇×#121	—	2	2	no	—
142	C₇×#121	—	2	2	no	—
143	C₇×#121	—	2	4	no	—
144	C₇×#121	—	2	2	no	—
145	C₇×#121	—	2	1	no	—
146	C₇×#121	—	2	2	no	—
147	C₇×#121	—	2	2	no	—
148	C₇×#121	C₂³	1	2	yes	—
149	C₇×#121	C₂³	1	4	yes	—
150	C₇×#121	C₂³	1	4	yes	—
151	C₇×#121	C₂³	1	2	yes	—
152	C₇×#120	—	2	2	no	—
153	C₄×C₇×Q₈	—	2	1	no	—
154	C₄×C₇×Q₈	—	2	1	no	—
155	C₄×C₇×Q₈	—	2	1	no	—
156	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
157	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
158	C₄×C₇×D₄	—	2	1	no	—
159	C₄×C₇×D₄	—	2	2	no	—
160	C₄×C₇×D₄	—	2	1	no	—
161	C₄×C₇×D₄	—	2	1	no	—
162	C₄×C₇×D₄	—	2	2	no	—
163	C₄×C₇×D₄	—	2	2	no	—
164	C₄×C₇×D₄	—	2	1	no	—
165	C₄×C₇×D₄	—	2	1	no	—
166	C₄×C₇×D₄	D₄	1	1	yes	characteristic
167	C₄×C₇×D₄	D₄	1	1	yes	characteristic
168	C₄×C₇×D₄	D₄	1	2	yes	—
169	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
170	C₄×C₇×D₄	C₂³	1	2	yes	—
171	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
172	C₄×C₇×D₄	C₂³	1	2	yes	—
173	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
174	C₄×C₇×D₄	C₂³	1	2	yes	—
175	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
176	C₇×#117	—	2	2	no	—
177	C₇×#117	—	2	2	no	—
178	C₇×#117	—	2	2	no	—
179	C₇×#117	—	2	2	no	—
180	C₇×#117	—	2	2	no	—
181	C₇×#117	—	2	2	no	—
182	C₇×#117	—	2	4	no	—
183	C₇×#117	—	2	1	no	—
184	C₇×#117	—	2	2	no	—
185	C₇×#117	—	2	1	no	—
186	C₇×#117	C₂³	1	2	yes	—
187	C₇×#117	C₂³	1	2	yes	—
188	C₇×#117	C₂³	1	4	yes	—
189	C₇×#117	C₂³	1	4	yes	—
190	C₇×#117	C₂³	1	1	yes	characteristic
191	C₇×#117	C₂³	1	2	yes	—
192	C₂×C₇×C₄⋊C₄	—	2	1	no	—
193	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
194	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
202	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
203	C₂×C₄²×C₇	—	2	2	no	—
204	C₂×C₄²×C₇	—	2	2	no	—
205	C₂×C₄²×C₇	—	2	1	no	—
206	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
207	C₇×#107	C₂³	1	4	yes	—
208	C₇×#107	C₂³	1	4	yes	—
209	C₇×#107	C₂³	1	4	yes	—
210	C₇×#107	C₂³	1	4	yes	—
211	C₇×#107	C₂³	1	2	yes	—
212	C₇×#106	C₂³	1	4	yes	—
213	C₇×#106	C₂³	1	4	yes	—
214	C₇×#106	C₂³	1	4	yes	—
215	C₇×#106	C₂³	1	4	yes	—
216	C₇×#106	C₂³	1	2	yes	—
217	C₇×C₄⋊C₈	C₂³	1	2	yes	—
218	C₇×C₄⋊C₈	C₂³	1	2	yes	—
219	C₇×#103	C₂³	1	4	yes	—
220	C₇×#103	C₂³	1	2	yes	—
221	C₇×#102	C₂³	1	4	yes	—
222	C₇×#102	C₂³	1	4	yes	—
223	C₇×#102	C₂³	1	4	yes	—
224	C₇×#102	C₂³	1	2	yes	—
225	C₇×#102	C₂³	1	2	yes	—
226	C₇×#102	C₂³	1	2	yes	—
227	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₇×#97	C₂³	1	2	yes	—
230	C₄×C₇×C₈	C₂³	1	2	yes	—
231	#3475	C₂×C₇	1	1	yes	characteristic, complemented
232	C₂×#555	C₂×C₇	1	1	yes	characteristic, complemented
233	#3357	C₂×C₇	1	2	yes	complemented
234	#3354	C₂×C₇	1	2	yes	complemented
235	#3348	C₂×C₇	1	4	yes	complemented
236	#3347	C₂×C₇	1	4	yes	complemented
237	#3341	C₂×C₇	1	2	yes	complemented
238	#3340	C₂×C₇	1	2	yes	complemented
239	#3165	C₂×C₇	1	1	yes	characteristic, complemented
240	#3094	C₂×C₇	1	2	yes	complemented
241	#3093	C₂×C₇	1	2	yes	complemented
242	#3079	C₂×C₇	1	1	yes	characteristic, complemented
243	#3077	C₂×C₇	1	1	yes	characteristic, complemented
244	#3055	C₂×C₇	1	2	yes	complemented
245	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic, complemented
246	D₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
247	#2911	C₂×C₇	1	2	yes	complemented
248	C₂⁴×C₇	—	2	1	no	—
249	C₂⁴×C₇	C₂×D₄	1	2	yes	—
250	C₇×#41	—	2	2	no	—
251	C₇×#41	—	2	2	no	—
252	C₇×#41	—	4	4	no	—
253	C₂×C₇×Q₈	—	2	1	no	—
254	C₂×C₇×Q₈	—	2	1	no	—
255	C₂×C₇×Q₈	—	2	2	no	—
256	C₂×C₇×Q₈	—	2	2	no	—
257	C₂×C₇×Q₈	—	8	2	no	—
258	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
259	C₂×C₇×D₄	—	2	1	no	—
260	C₂×C₇×D₄	—	2	2	no	—
261	C₂×C₇×D₄	—	2	2	no	—
262	C₂×C₇×D₄	—	2	4	no	—
263	C₂×C₇×D₄	—	2	4	no	—
264	C₂×C₇×D₄	—	2	1	no	—
265	C₂×C₇×D₄	—	2	2	no	—
266	C₂×C₇×D₄	—	2	2	no	—
267	C₂×C₇×D₄	—	4	2	no	—
268	C₂×C₇×D₄	—	8	4	no	—
269	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
270	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
271	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
272	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
273	C₂×C₇×D₄	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₇	—	2	4	no	—
275	C₂²×C₄×C₇	—	2	4	no	—
276	C₂²×C₄×C₇	—	2	1	no	—
277	C₂²×C₄×C₇	—	2	2	no	—
278	C₂²×C₄×C₇	—	2	2	no	—
279	C₂²×C₄×C₇	—	2	2	no	—
280	C₂²×C₄×C₇	—	2	1	no	—
281	C₂²×C₄×C₇	—	2	1	no	—
282	C₂²×C₄×C₇	—	2	2	no	—
283	C₂²×C₄×C₇	—	2	2	no	—
284	C₂²×C₄×C₇	—	2	1	no	—
285	C₂²×C₄×C₇	—	4	4	no	—
286	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
290	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
294	C₇×SD₁₆	—	2	4	no	—
295	C₇×D₈	—	2	4	no	—
296	C₇×M₁₆	—	2	4	no	—
297	C₇×M₁₆	—	2	2	no	—
298	C₇×M₁₆	—	2	8	no	—
299	C₇×M₁₆	#41	1	4	yes	complemented
300	C₂×C₇×C₈	—	2	8	no	—
301	C₂×C₇×C₈	C₂⁴	1	2	yes	—
302	C₂×C₇×C₈	C₂⁴	1	4	yes	—
303	C₂×C₇×C₈	C₂⁴	1	2	yes	—
304	C₇×C₄⋊C₄	—	2	2	no	—
305	C₇×C₄⋊C₄	—	2	2	no	—
306	C₇×C₄⋊C₄	—	2	1	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	—	2	1	no	—
311	C₇×C₄⋊C₄	—	2	2	no	—
312	C₇×C₄⋊C₄	—	2	2	no	—
313	C₇×C₄⋊C₄	—	2	1	no	—
314	C₇×C₄⋊C₄	—	2	1	no	—
315	C₇×C₄⋊C₄	—	2	2	no	—
316	C₇×C₄⋊C₄	—	2	2	no	—
317	C₇×C₄⋊C₄	—	2	1	no	—
318	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
319	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
320	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
321	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
322	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
323	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
324	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
325	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
326	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
327	C₇×C₂²⋊C₄	—	2	1	no	—
328	C₇×C₂²⋊C₄	—	2	2	no	—
329	C₇×C₂²⋊C₄	—	2	4	no	—
330	C₇×C₂²⋊C₄	—	2	4	no	—
331	C₇×C₂²⋊C₄	—	2	2	no	—
332	C₇×C₂²⋊C₄	—	2	2	no	—
333	C₇×C₂²⋊C₄	—	2	2	no	—
334	C₇×C₂²⋊C₄	—	2	2	no	—
335	C₇×C₂²⋊C₄	—	2	4	no	—
336	C₇×C₂²⋊C₄	—	2	4	no	—
337	C₇×C₂²⋊C₄	—	2	2	no	—
338	C₇×C₂²⋊C₄	—	2	2	no	—
339	C₇×C₂²⋊C₄	—	2	2	no	—
340	C₇×C₂²⋊C₄	—	2	1	no	—
341	C₇×C₂²⋊C₄	—	2	1	no	—
342	C₇×C₂²⋊C₄	—	2	2	no	—
343	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
344	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
345	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
346	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
347	C₄²×C₇	—	2	1	no	—
348	C₄²×C₇	—	2	4	no	—
349	C₄²×C₇	—	2	4	no	—
350	C₄²×C₇	—	2	2	no	—
351	C₄²×C₇	—	2	1	no	—
352	C₄²×C₇	—	2	2	no	—
353	C₄²×C₇	—	2	2	no	—
354	C₄²×C₇	—	2	1	no	—
355	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
356	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
357	C₄²×C₇	C₂⁴	1	1	yes	characteristic
358	C₄²×C₇	C₂⁴	1	1	yes	characteristic
359	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
360	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
361	#556	C₂²×C₇	1	1	yes	characteristic, complemented
362	#555	—	2	1	no	—
363	#555	—	2	2	no	—
364	#555	—	2	1	no	—
365	#555	C₂²×C₇	1	2	yes	—
366	#555	C₂²×C₇	1	4	yes	—
367	#555	C₂²×C₇	1	2	yes	—
368	#555	C₂²×C₇	1	1	yes	characteristic, complemented
369	#554	C₂²×C₇	1	1	yes	characteristic, complemented
370	#553	C₂²×C₇	1	2	yes	complemented
371	#552	—	2	1	no	—
372	#552	C₂²×C₇	1	2	yes	complemented
373	#551	—	2	2	no	—
374	#547	C₂²×C₇	1	1	yes	characteristic, complemented
375	#546	—	2	1	no	—
376	#533	C₂²×C₇	1	1	yes	characteristic
377	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
378	#529	—	2	2	no	—
379	#529	—	2	1	no	—
380	C₂×#124	—	2	2	no	—
381	#525	C₂²×C₇	1	2	yes	—
382	C₂×#121	—	2	1	no	—
383	C₂×#121	C₂²×C₇	1	2	yes	—
384	C₄×#41	—	2	1	no	—
385	C₄×#41	C₂²×C₇	1	1	yes	characteristic
386	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
387	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
388	C₂×#117	—	2	1	no	—
389	C₂×#117	C₂²×C₇	1	2	yes	—
390	C₂×#117	C₂²×C₇	1	2	yes	—
391	#501	C₂²×C₇	1	4	yes	complemented
392	#500	C₂²×C₇	1	2	yes	complemented
393	#498	C₂²×C₇	1	2	yes	complemented
394	#485	C₂²×C₇	1	4	yes	complemented
395	#485	C₂²×C₇	1	4	yes	complemented
396	#482	C₂²×C₇	1	4	yes	complemented
397	#482	C₂²×C₇	1	4	yes	complemented
398	#482	C₂²×C₇	1	4	yes	complemented
399	#482	C₂²×C₇	1	4	yes	complemented
400	#481	C₂²×C₇	1	4	yes	complemented
401	#480	C₂²×C₇	1	4	yes	complemented
402	#478	C₂²×C₇	1	4	yes	complemented
403	#477	C₂²×C₇	1	2	yes	complemented
404	#476	C₂²×C₇	1	2	yes	complemented
405	#476	C₂²×C₇	1	2	yes	complemented
406	#475	C₂²×C₇	1	2	yes	complemented
407	#474	C₂²×C₇	1	2	yes	complemented
408	#474	C₂²×C₇	1	2	yes	complemented
409	#469	C₂²×C₇	1	4	yes	complemented
410	#468	C₂²×C₇	1	4	yes	complemented
411	#466	C₂²×C₇	1	4	yes	complemented
412	#465	C₂²×C₇	1	4	yes	complemented
413	#442	C₂²×C₇	1	2	yes	complemented
414	#440	C₂²×C₇	1	2	yes	complemented
415	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
416	C₄×D₈	C₂²×C₇	1	2	yes	complemented
417	#436	C₂²×C₇	1	2	yes	complemented
418	#435	C₂²×C₇	1	4	yes	complemented
419	C₈×D₄	C₂²×C₇	1	2	yes	complemented
420	#428	C₂²×C₇	1	2	yes	—
421	#428	C₂²×C₇	1	2	yes	—
422	#428	C₂²×C₇	1	2	yes	—
423	#428	C₂²×C₇	1	2	yes	—
424	#428	C₂²×C₇	1	1	yes	characteristic
425	#428	C₂²×C₇	1	4	yes	complemented
426	#428	C₂²×C₇	1	4	yes	complemented
427	#427	C₂²×C₇	1	4	yes	complemented
428	#427	C₂²×C₇	1	4	yes	complemented
429	#423	C₂²×C₇	1	1	yes	characteristic
430	#418	C₂²×C₇	1	2	yes	—
431	#418	C₂²×C₇	1	1	yes	characteristic
432	#417	C₂²×C₇	1	2	yes	—
433	#417	C₂²×C₇	1	1	yes	characteristic
434	#407	C₂²×C₇	1	2	yes	—
435	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
436	C₂³×C₇	—	2	4	no	—
437	C₂³×C₇	—	2	1	no	—
438	C₂³×C₇	—	2	2	no	—
439	C₂³×C₇	—	4	2	no	—
440	C₂³×C₇	—	4	2	no	—
441	C₂³×C₇	—	4	2	no	—
442	C₂³×C₇	—	4	2	no	—
443	C₂³×C₇	—	4	2	no	—
444	C₂³×C₇	C₂²×D₄	1	2	yes	—
445	C₂³×C₇	C₂²×D₄	1	2	yes	—
446	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
447	C₇×Q₈	—	2	1	no	—
448	C₇×Q₈	—	2	1	no	—
449	C₇×Q₈	—	4	2	no	—
450	C₇×Q₈	—	8	1	no	—
451	C₇×Q₈	—	8	2	no	—
452	C₇×Q₈	—	8	2	no	—
453	C₇×D₄	—	2	2	no	—
454	C₇×D₄	—	2	2	no	—
455	C₇×D₄	—	2	1	no	—
456	C₇×D₄	—	2	2	no	—
457	C₇×D₄	—	2	2	no	—
458	C₇×D₄	—	2	1	no	—
459	C₇×D₄	—	4	2	no	—
460	C₇×D₄	—	4	4	no	—
461	C₇×D₄	—	4	2	no	—
462	C₇×D₄	—	4	2	no	—
463	C₇×D₄	—	8	2	no	—
464	C₇×D₄	—	8	4	no	—
465	C₇×D₄	—	8	4	no	—
466	C₂×C₄×C₇	—	2	4	no	—
467	C₂×C₄×C₇	—	2	4	no	—
468	C₂×C₄×C₇	—	2	4	no	—
469	C₂×C₄×C₇	—	2	2	no	—
470	C₂×C₄×C₇	—	2	2	no	—
471	C₂×C₄×C₇	—	2	2	no	—
472	C₂×C₄×C₇	—	2	2	no	—
473	C₂×C₄×C₇	—	2	2	no	—
474	C₂×C₄×C₇	—	2	2	no	—
475	C₂×C₄×C₇	—	2	1	no	—
476	C₂×C₄×C₇	—	2	1	no	—
477	C₂×C₄×C₇	—	2	1	no	—
478	C₂×C₄×C₇	—	2	2	no	—
479	C₂×C₄×C₇	—	2	2	no	—
480	C₂×C₄×C₇	—	2	4	no	—
481	C₂×C₄×C₇	—	4	1	no	—
482	C₂×C₄×C₇	—	4	4	no	—
483	C₂×C₄×C₇	—	4	2	no	—
484	C₂×C₄×C₇	—	4	4	no	—
485	C₂×C₄×C₇	—	4	4	no	—
486	C₂×C₄×C₇	—	4	2	no	—
487	C₂×C₄×C₇	—	4	4	no	—
488	C₂×C₄×C₇	—	4	2	no	—
489	C₂×C₄×C₇	—	8	1	no	—
490	C₂×C₄×C₇	—	8	2	no	—
491	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₇	C₂×#41	1	2	yes	—
499	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
500	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
501	C₇×C₈	—	2	4	no	—
502	C₇×C₈	—	2	2	no	—
503	C₇×C₈	C₂×#41	1	4	yes	—
504	C₂×#41	—	2	1	no	—
505	C₂×#41	C₂³×C₇	1	1	yes	characteristic
506	C₂²×Q₈	—	2	1	no	—
507	C₂²×D₄	—	2	2	no	—
508	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
509	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
510	C₂³×C₄	—	2	1	no	—
511	C₂³×C₄	C₂³×C₇	1	2	yes	—
512	AGL(1,ℤ/8)	—	2	4	no	—
513	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
514	C₂×D₈	C₂³×C₇	1	2	yes	—
515	C₂×M₁₆	—	2	8	no	—
516	C₂×M₁₆	C₂³×C₇	1	2	yes	—
517	C₂×M₁₆	C₂³×C₇	1	4	yes	—
518	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
519	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
520	C₂²×C₈	C₂³×C₇	1	4	yes	—
521	C₄⋊Q₈	—	2	1	no	—
522	C₄⋊Q₈	—	2	1	no	—
523	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
524	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
525	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
526	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
527	#126	—	2	2	no	—
528	#126	—	2	2	no	—
529	#126	—	2	2	no	—
530	#125	—	2	2	no	—
531	#125	—	2	1	no	—
532	#125	C₂³×C₇	1	2	yes	—
533	#124	—	2	1	no	—
534	#124	—	2	4	no	—
535	#124	—	2	4	no	—
536	#124	—	2	4	no	—
537	#124	—	2	4	no	—
538	#124	—	2	2	no	—
539	#123	—	2	2	no	—
540	#123	—	2	2	no	—
541	#123	—	2	2	no	—
542	#123	—	2	2	no	—
543	C₂²⋊Q₈	—	2	1	no	—
544	C₂²⋊Q₈	—	2	1	no	—
545	C₂²⋊Q₈	—	2	1	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
548	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
549	#121	—	2	2	no	—
550	#121	—	2	2	no	—
551	#121	—	2	4	no	—
552	#121	—	2	2	no	—
553	#121	—	2	1	no	—
554	#121	—	2	2	no	—
555	#121	—	2	2	no	—
556	#121	C₂³×C₇	1	4	yes	—
557	#121	C₂³×C₇	1	4	yes	—
558	#121	C₂³×C₇	1	2	yes	—
559	#121	C₂³×C₇	1	2	yes	—
560	#120	—	2	2	no	—
561	C₄×Q₈	—	2	1	no	—
562	C₄×Q₈	—	2	1	no	—
563	C₄×Q₈	—	2	1	no	—
564	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
565	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	C₇×D₄	1	1	yes	characteristic
575	C₄×D₄	C₇×D₄	1	1	yes	characteristic
576	C₄×D₄	C₇×D₄	1	2	yes	—
577	C₄×D₄	C₂³×C₇	1	2	yes	—
578	C₄×D₄	C₂³×C₇	1	2	yes	—
579	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
580	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
581	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
582	C₄×D₄	C₂³×C₇	1	2	yes	—
583	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
584	#117	—	2	2	no	—
585	#117	—	2	2	no	—
586	#117	—	2	2	no	—
587	#117	—	2	2	no	—
588	#117	—	2	2	no	—
589	#117	—	2	2	no	—
590	#117	—	2	4	no	—
591	#117	—	2	1	no	—
592	#117	—	2	2	no	—
593	#117	—	2	1	no	—
594	#117	C₂³×C₇	1	1	yes	characteristic
595	#117	C₂³×C₇	1	2	yes	—
596	#117	C₂³×C₇	1	2	yes	—
597	#117	C₂³×C₇	1	2	yes	—
598	#117	C₂³×C₇	1	4	yes	—
599	#117	C₂³×C₇	1	4	yes	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
606	C₂×C₂²⋊C₄	—	2	2	no	—
607	C₂×C₂²⋊C₄	—	2	2	no	—
608	C₂×C₂²⋊C₄	—	2	2	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
611	C₂×C₄²	—	2	2	no	—
612	C₂×C₄²	—	2	2	no	—
613	C₂×C₄²	—	2	1	no	—
614	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
615	#107	C₂³×C₇	1	2	yes	—
616	#107	C₂³×C₇	1	4	yes	—
617	#107	C₂³×C₇	1	4	yes	—
618	#107	C₂³×C₇	1	4	yes	—
619	#107	C₂³×C₇	1	4	yes	—
620	#106	C₂³×C₇	1	2	yes	—
621	#106	C₂³×C₇	1	4	yes	—
622	#106	C₂³×C₇	1	4	yes	—
623	#106	C₂³×C₇	1	4	yes	—
624	#106	C₂³×C₇	1	4	yes	—
625	C₄⋊C₈	C₂³×C₇	1	2	yes	—
626	C₄⋊C₈	C₂³×C₇	1	2	yes	—
627	#103	C₂³×C₇	1	2	yes	—
628	#103	C₂³×C₇	1	4	yes	—
629	#102	C₂³×C₇	1	2	yes	—
630	#102	C₂³×C₇	1	4	yes	—
631	#102	C₂³×C₇	1	2	yes	—
632	#102	C₂³×C₇	1	2	yes	—
633	#102	C₂³×C₇	1	4	yes	—
634	#102	C₂³×C₇	1	4	yes	—
635	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
636	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
637	#97	C₂³×C₇	1	2	yes	—
638	C₄×C₈	C₂³×C₇	1	2	yes	—
639	C₂²×C₇	—	2	1	no	—
640	C₂²×C₇	—	2	1	no	—
641	C₂²×C₇	—	2	2	no	—
642	C₂²×C₇	—	2	2	no	—
643	C₂²×C₇	—	2	2	no	—
644	C₂²×C₇	—	2	2	no	—
645	C₂²×C₇	—	2	2	no	—
646	C₂²×C₇	—	2	2	no	—
647	C₂²×C₇	—	4	1	no	—
648	C₂²×C₇	—	4	2	no	—
649	C₂²×C₇	—	4	1	no	—
650	C₂²×C₇	—	4	2	no	—
651	C₂²×C₇	—	4	2	no	—
652	C₂²×C₇	—	4	1	no	—
653	C₂²×C₇	—	8	4	no	—
654	C₂²×C₇	—	8	4	no	—
655	C₂²×C₇	#547	1	2	yes	—
656	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
657	C₄×C₇	—	2	1	no	—
658	C₄×C₇	—	2	1	no	—
659	C₄×C₇	—	2	2	no	—
660	C₄×C₇	—	2	2	no	—
661	C₄×C₇	—	2	1	no	—
662	C₄×C₇	—	4	4	no	—
663	C₄×C₇	—	4	1	no	—
664	C₄×C₇	—	4	2	no	—
665	C₄×C₇	—	4	1	no	—
666	C₄×C₇	—	4	2	no	—
667	C₄×C₇	—	4	1	no	—
668	C₄×C₇	—	4	2	no	—
669	C₄×C₇	#547	1	2	yes	—
670	C₄×C₇	#575	1	2	yes	—
671	C₄×C₇	C₂²×#41	1	1	yes	characteristic
672	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
673	C₂⁴	—	2	1	no	—
674	C₂⁴	C₂×C₇×D₄	1	2	yes	—
675	#41	—	2	2	no	—
676	#41	—	2	2	no	—
677	#41	—	4	4	no	—
678	C₂×Q₈	—	2	1	no	—
679	C₂×Q₈	—	2	1	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	8	2	no	—
683	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	8	4	no	—
694	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
695	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
696	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
697	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
698	C₂×D₄	C₂⁴×C₇	1	2	yes	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	4	4	no	—
711	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
712	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
713	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
714	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
715	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
719	SD₁₆	—	2	4	no	—
720	D₈	—	2	4	no	—
721	M₁₆	—	2	4	no	—
722	M₁₆	—	2	2	no	—
723	M₁₆	—	2	8	no	—
724	M₁₆	C₇×#41	1	4	yes	complemented
725	C₂×C₈	—	2	8	no	—
726	C₂×C₈	C₂⁴×C₇	1	2	yes	—
727	C₂×C₈	C₂⁴×C₇	1	4	yes	—
728	C₂×C₈	C₂⁴×C₇	1	2	yes	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	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	1	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
744	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
745	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
746	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
747	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
748	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
749	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	1	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
769	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
770	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
771	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
772	C₄²	—	2	1	no	—
773	C₄²	—	2	4	no	—
774	C₄²	—	2	4	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	1	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	1	no	—
780	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
781	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
782	C₄²	C₂⁴×C₇	1	1	yes	characteristic
783	C₄²	C₂⁴×C₇	1	1	yes	characteristic
784	C₂×C₇	—	2	2	no	—
785	C₂×C₇	—	4	2	no	—
786	C₂×C₇	—	4	2	no	—
787	C₂×C₇	—	8	1	no	—
788	C₂×C₇	—	8	2	no	—
789	C₂×C₇	C₂×#547	1	1	yes	characteristic
790	C₂×C₇	C₂×#575	1	1	yes	characteristic
791	C₂×C₇	#3585	1	1	yes	characteristic
792	C₂³	—	2	4	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	4	2	no	—
796	C₂³	—	4	2	no	—
797	C₂³	—	4	2	no	—
798	C₂³	—	4	2	no	—
799	C₂³	—	4	2	no	—
800	C₂³	C₂²×C₇×D₄	1	2	yes	—
801	C₂³	C₂²×C₇×D₄	1	2	yes	—
802	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
803	Q₈	—	2	1	no	—
804	Q₈	—	2	1	no	—
805	Q₈	—	4	2	no	—
806	Q₈	—	8	1	no	—
807	Q₈	—	8	2	no	—
808	Q₈	—	8	2	no	—
809	D₄	—	2	1	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	2	no	—
812	D₄	—	2	1	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	2	no	—
815	D₄	—	4	2	no	—
816	D₄	—	4	4	no	—
817	D₄	—	4	2	no	—
818	D₄	—	4	2	no	—
819	D₄	—	8	2	no	—
820	D₄	—	8	4	no	—
821	D₄	—	8	4	no	—
822	C₂×C₄	—	2	4	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	4	no	—
828	C₂×C₄	—	2	4	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	4	no	—
837	C₂×C₄	—	4	1	no	—
838	C₂×C₄	—	4	4	no	—
839	C₂×C₄	—	4	2	no	—
840	C₂×C₄	—	4	4	no	—
841	C₂×C₄	—	4	4	no	—
842	C₂×C₄	—	4	2	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	—	4	2	no	—
845	C₂×C₄	—	8	1	no	—
846	C₂×C₄	—	8	2	no	—
847	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
848	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
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	C₂×C₇×#41	1	2	yes	—
855	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
856	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
857	C₈	—	2	4	no	—
858	C₈	—	2	2	no	—
859	C₈	C₂×C₇×#41	1	4	yes	—
860	C₇	#61256	1	1	yes	characteristic, direct product factor, Sylow
861	C₂²	—	2	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	8	4	no	—
876	C₂²	—	8	4	no	—
877	C₂²	C₇×#547	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	2	no	—
883	C₄	—	2	2	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	2	no	—
887	C₄	—	4	4	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	1	no	—
891	C₄	C₇×#547	1	2	yes	—
892	C₄	C₇×#575	1	2	yes	—
893	C₄	C₂²×C₇×#41	1	1	yes	characteristic
894	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
895	C₂	—	2	2	no	—
896	C₂	—	4	2	no	—
897	C₂	—	4	2	no	—
898	C₂	—	8	2	no	—
899	C₂	—	8	1	no	—
900	C₂	C₂×C₇×#547	1	1	yes	characteristic
901	C₂	C₂×C₇×#575	1	1	yes	characteristic
902	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 ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3475	C₂	semidirect
2. C₂×C₇×#555	C₂	semidirect
3. C₇×#3357	C₂	semidirect
4. C₇×#3354	C₂	semidirect
5. C₇×#3348	C₂	semidirect
6. C₇×#3347	C₂	semidirect
7. C₇×#3341	C₂	semidirect
8. C₇×#3340	C₂	semidirect
9. C₇×#3165	C₂	semidirect
10. C₇×#3094	C₂	semidirect
11. C₇×#3093	C₂	semidirect
12. C₇×#3079	C₂	semidirect
13. C₇×#3077	C₂	semidirect
14. C₇×#3055	C₂	semidirect
15. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
16. C₇×D₄×M₁₆	C₂	semidirect
17. C₇×#2911	C₂	semidirect
20. C₇×#556	C₂²	semidirect
27. C₇×#555	C₂²	semidirect
28. C₇×#554	C₂²	semidirect
29. C₇×#553	C₂²	semidirect
31. C₇×#552	C₂²	semidirect
33. C₇×#547	C₂²	semidirect
50. C₇×#501	C₂²	semidirect
51. C₇×#500	C₂²	semidirect
52. C₇×#498	C₂²	semidirect
53. C₇×#485	C₂²	semidirect
54. C₇×#485	C₂²	semidirect
55. C₇×#482	C₂²	semidirect
56. C₇×#482	C₂²	semidirect
57. C₇×#482	C₂²	semidirect
58. C₇×#482	C₂²	semidirect
59. C₇×#481	C₂²	semidirect
60. C₇×#480	C₂²	semidirect
61. C₇×#478	C₂²	semidirect
62. C₇×#477	C₂²	semidirect
63. C₇×#476	C₂²	semidirect
64. C₇×#476	C₂²	semidirect
65. C₇×#475	C₂²	semidirect
66. C₇×#474	C₂²	semidirect
67. C₇×#474	C₂²	semidirect
68. C₇×#469	C₂²	semidirect
69. C₇×#468	C₂²	semidirect
70. C₇×#466	C₂²	semidirect
71. C₇×#465	C₂²	semidirect
72. C₇×#442	C₂²	semidirect
73. C₇×#440	C₂²	semidirect
74. C₄×C₇×SD₁₆	C₂²	semidirect
75. C₄×C₇×D₈	C₂²	semidirect
76. C₇×#436	C₂²	semidirect
77. C₇×#435	C₂²	semidirect
78. C₇×C₈×D₄	C₂²	semidirect
84. C₇×#428	C₂²	semidirect
85. C₇×#428	C₂²	semidirect
86. C₇×#427	C₂²	semidirect
87. C₇×#427	C₂²	semidirect
95. #61256	C₇	direct (N × H)
231. #3475	C₂×C₇	semidirect
232. C₂×#555	C₂×C₇	semidirect
233. #3357	C₂×C₇	semidirect
234. #3354	C₂×C₇	semidirect
235. #3348	C₂×C₇	semidirect
236. #3347	C₂×C₇	semidirect
237. #3341	C₂×C₇	semidirect
238. #3340	C₂×C₇	semidirect
239. #3165	C₂×C₇	semidirect
240. #3094	C₂×C₇	semidirect
241. #3093	C₂×C₇	semidirect
242. #3079	C₂×C₇	semidirect
243. #3077	C₂×C₇	semidirect
244. #3055	C₂×C₇	semidirect
245. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
246. D₄×M₁₆	C₂×C₇	semidirect
247. #2911	C₂×C₇	semidirect
299. C₇×M₁₆	#41	semidirect
361. #556	C₂²×C₇	semidirect
368. #555	C₂²×C₇	semidirect
369. #554	C₂²×C₇	semidirect
370. #553	C₂²×C₇	semidirect
372. #552	C₂²×C₇	semidirect
374. #547	C₂²×C₇	semidirect
391. #501	C₂²×C₇	semidirect
392. #500	C₂²×C₇	semidirect
393. #498	C₂²×C₇	semidirect
394. #485	C₂²×C₇	semidirect
395. #485	C₂²×C₇	semidirect
396. #482	C₂²×C₇	semidirect
397. #482	C₂²×C₇	semidirect
398. #482	C₂²×C₇	semidirect
399. #482	C₂²×C₇	semidirect
400. #481	C₂²×C₇	semidirect
401. #480	C₂²×C₇	semidirect
402. #478	C₂²×C₇	semidirect
403. #477	C₂²×C₇	semidirect
404. #476	C₂²×C₇	semidirect
405. #476	C₂²×C₇	semidirect
406. #475	C₂²×C₇	semidirect
407. #474	C₂²×C₇	semidirect
408. #474	C₂²×C₇	semidirect
409. #469	C₂²×C₇	semidirect
410. #468	C₂²×C₇	semidirect
411. #466	C₂²×C₇	semidirect
412. #465	C₂²×C₇	semidirect
413. #442	C₂²×C₇	semidirect
414. #440	C₂²×C₇	semidirect
415. C₄×SD₁₆	C₂²×C₇	semidirect
416. C₄×D₈	C₂²×C₇	semidirect
417. #436	C₂²×C₇	semidirect
418. #435	C₂²×C₇	semidirect
419. C₈×D₄	C₂²×C₇	semidirect
425. #428	C₂²×C₇	semidirect
426. #428	C₂²×C₇	semidirect
427. #427	C₂²×C₇	semidirect
428. #427	C₂²×C₇	semidirect
724. M₁₆	C₇×#41	semidirect
860. C₇	#61256	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×#3475	2
C₂×C₇×#555	2
C₇×#3357	2
C₇×#3354	2
C₇×#3348	2
C₇×#3347	2
C₇×#3341	2
C₇×#3340	2
C₇×#3165	2
C₇×#3094	2
C₇×#3093	2
C₇×#3079	2
C₇×#3077	2
C₇×#3055	2
C₄×C₇×AGL(1,ℤ/8)	2
C₇×D₄×M₁₆	2
C₇×#2911	2
#61256	7

Subgroups — C7×#61256 #13238472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61256 #13238472