Subgroups — C₇×#60700 #13237916

Order 1792.

2256 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3184	C₂	1	2	yes	maximal, complemented
4	C₇×#3182	C₂	1	2	yes	maximal, complemented
5	C₇×#3180	C₂	1	4	yes	maximal, complemented
6	C₇×#3171	C₂	1	4	yes	maximal, complemented
7	C₇×#3169	C₂	1	2	yes	maximal, complemented
8	C₇×#3167	C₂	1	2	yes	maximal, complemented
9	C₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3055	C₂	1	4	yes	maximal, complemented
14	C₄×C₇×AGL(1,ℤ/8)	C₂	1	4	yes	maximal, complemented
15	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#41	—	2	1	no	—
17	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	4	yes	—
18	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
19	C₇×#533	C₂²	1	1	yes	characteristic
20	C₇×#533	C₂²	1	1	yes	characteristic, complemented
21	C₇×#533	C₂²	1	1	yes	characteristic, complemented
22	C₇×#532	—	2	1	no	—
23	C₇×#532	—	2	1	no	—
24	C₇×#532	—	2	1	no	—
25	C₇×#532	—	2	1	no	—
26	C₇×#532	C₂²	1	1	yes	characteristic
27	C₇×#532	C₂²	1	2	yes	—
28	C₇×#532	C₂²	1	2	yes	—
29	C₇×#532	C₂²	1	2	yes	—
30	C₇×#532	C₂²	1	2	yes	—
31	C₇×#532	C₂²	1	1	yes	characteristic, complemented
32	C₇×#532	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×#127	C₂²	1	1	yes	characteristic
35	C₇×#529	—	2	1	no	—
36	C₇×#529	—	2	1	no	—
37	C₇×#529	—	2	1	no	—
38	C₇×#529	—	2	1	no	—
39	C₇×#529	C₂²	1	2	yes	complemented
40	C₇×#529	C₂²	1	2	yes	complemented
41	C₂×C₇×#124	—	2	1	no	—
42	C₇×#525	—	2	1	no	—
43	C₇×#525	—	2	1	no	—
44	C₇×#525	C₂²	1	2	yes	—
45	C₂×C₇×#121	—	2	1	no	—
46	C₂×C₇×#121	C₂²	1	2	yes	—
47	C₄×C₇×#41	—	2	1	no	—
48	C₄×C₇×#41	—	2	1	no	—
49	C₄×C₇×#41	C₂²	1	2	yes	—
50	C₂×C₄×C₇×D₄	—	2	1	no	—
51	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
52	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
53	C₇×#501	C₂²	1	4	yes	complemented
54	C₇×#500	C₂²	1	2	yes	complemented
55	C₇×#498	C₂²	1	2	yes	complemented
56	C₇×#496	C₂²	1	4	yes	complemented
57	C₇×#493	C₂²	1	2	yes	complemented
58	C₇×#492	C₂²	1	2	yes	complemented
59	C₇×#490	C₂²	1	4	yes	complemented
60	C₇×#489	C₂²	1	4	yes	complemented
61	C₇×#487	C₂²	1	2	yes	complemented
62	C₇×#486	C₂²	1	2	yes	complemented
63	C₇×#486	C₂²	1	2	yes	complemented
64	C₇×#486	C₂²	1	2	yes	complemented
65	C₇×#469	C₂²	1	8	yes	complemented
66	C₇×#468	C₂²	1	8	yes	complemented
67	C₇×#466	C₂²	1	8	yes	complemented
68	C₇×#465	C₂²	1	8	yes	complemented
69	C₇×#442	C₂²	1	8	yes	complemented
70	C₇×#440	C₂²	1	8	yes	complemented
71	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
72	C₄×C₇×D₈	C₂²	1	8	yes	complemented
73	C₇×#428	C₂²	1	4	yes	—
74	C₇×#418	C₂²	1	4	yes	—
75	C₇×#417	C₂²	1	4	yes	—
76	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
77	C₄×C₇×M₁₆	C₂²	1	2	yes	—
78	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
79	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
80	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
81	C₂×C₇×#97	C₂²	1	2	yes	complemented
82	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
83	#60700	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂×C₇×#41	—	2	2	no	—
85	C₂×C₇×#41	—	2	2	no	—
86	C₂×C₇×#41	—	2	2	no	—
87	C₂×C₇×#41	—	2	2	no	—
88	C₂×C₇×#41	—	2	1	no	—
89	C₂×C₇×#41	—	2	1	no	—
90	C₂×C₇×#41	—	4	8	no	—
91	C₂×C₇×#41	C₂³	1	2	yes	—
92	C₂²×C₇×Q₈	—	2	1	no	—
93	C₂²×C₇×D₄	—	2	2	no	—
94	C₂²×C₇×D₄	—	2	1	no	—
95	C₂²×C₇×D₄	—	2	1	no	—
96	C₂²×C₇×D₄	C₂³	1	2	yes	—
97	C₂³×C₄×C₇	—	2	2	no	—
98	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
99	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
100	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
101	C₇×AGL(1,ℤ/8)	—	2	16	no	—
102	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
103	C₂×C₇×D₈	C₂³	1	8	yes	—
104	C₂×C₇×M₁₆	—	2	8	no	—
105	C₂×C₇×M₁₆	C₂³	1	4	yes	—
106	C₂×C₇×M₁₆	C₂³	1	2	yes	—
107	C₂×C₇×M₁₆	C₂³	1	2	yes	—
108	C₂²×C₇×C₈	C₂³	1	4	yes	—
109	C₇×C₄⋊Q₈	—	2	1	no	—
110	C₇×C₄⋊Q₈	—	2	1	no	—
111	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₇×#127	—	2	1	no	—
117	C₇×#127	—	2	1	no	—
118	C₇×#127	C₂³	1	2	yes	—
119	C₇×#127	C₂³	1	1	yes	characteristic
120	C₇×#127	C₂³	1	2	yes	—
121	C₇×#126	—	2	2	no	—
122	C₇×#126	—	2	2	no	—
123	C₇×#125	—	2	1	no	—
124	C₇×#125	—	2	1	no	—
125	C₇×#125	C₂³	1	2	yes	—
126	C₇×#124	—	2	2	no	—
127	C₇×#124	—	2	2	no	—
128	C₇×#124	—	2	2	no	—
129	C₇×#124	—	2	2	no	—
130	C₇×#124	—	2	1	no	—
131	C₇×#124	—	2	1	no	—
132	C₇×#124	C₂³	1	2	yes	—
133	C₇×#123	—	2	2	no	—
134	C₇×#123	—	2	2	no	—
135	C₇×#123	—	2	2	no	—
136	C₇×C₂²⋊Q₈	—	2	1	no	—
137	C₇×C₂²⋊Q₈	—	2	1	no	—
138	C₇×C₂²⋊Q₈	—	2	1	no	—
139	C₇×C₂²⋊Q₈	—	2	1	no	—
140	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
141	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₇×#121	—	2	2	no	—
143	C₇×#121	—	2	2	no	—
144	C₇×#121	—	2	2	no	—
145	C₇×#121	—	2	2	no	—
146	C₇×#121	—	2	2	no	—
147	C₇×#121	—	2	2	no	—
148	C₇×#121	—	2	1	no	—
149	C₇×#121	—	2	1	no	—
150	C₇×#121	—	2	1	no	—
151	C₇×#121	—	2	1	no	—
152	C₇×#121	C₂³	1	2	yes	—
153	C₇×#121	C₂³	1	4	yes	—
154	C₇×#121	C₂³	1	4	yes	—
155	C₇×#121	C₂³	1	2	yes	—
156	C₇×#120	—	2	2	no	—
157	C₄×C₇×Q₈	—	2	1	no	—
158	C₄×C₇×Q₈	—	2	1	no	—
159	C₄×C₇×Q₈	—	2	1	no	—
160	C₄×C₇×Q₈	—	2	1	no	—
161	C₄×C₇×Q₈	C₂³	1	2	yes	—
162	C₄×C₇×Q₈	C₂³	1	2	yes	—
163	C₄×C₇×D₄	—	2	2	no	—
164	C₄×C₇×D₄	—	2	2	no	—
165	C₄×C₇×D₄	—	2	2	no	—
166	C₄×C₇×D₄	—	2	2	no	—
167	C₄×C₇×D₄	—	2	2	no	—
168	C₄×C₇×D₄	—	2	2	no	—
169	C₄×C₇×D₄	—	2	2	no	—
170	C₄×C₇×D₄	—	2	2	no	—
171	C₄×C₇×D₄	—	2	2	no	—
172	C₄×C₇×D₄	—	2	2	no	—
173	C₄×C₇×D₄	—	2	2	no	—
174	C₄×C₇×D₄	—	2	2	no	—
175	C₄×C₇×D₄	—	2	1	no	—
176	C₄×C₇×D₄	—	2	1	no	—
177	C₄×C₇×D₄	—	2	1	no	—
178	C₄×C₇×D₄	—	2	1	no	—
179	C₄×C₇×D₄	C₂³	1	4	yes	—
180	C₄×C₇×D₄	C₂³	1	4	yes	—
181	C₄×C₇×D₄	C₂³	1	2	yes	—
182	C₄×C₇×D₄	C₂³	1	2	yes	—
183	C₇×#117	—	2	1	no	—
184	C₇×#117	—	2	1	no	—
185	C₇×#117	—	2	2	no	—
186	C₇×#117	—	2	2	no	—
187	C₇×#117	—	2	2	no	—
188	C₇×#117	C₂³	1	2	yes	—
189	C₂×C₇×C₄⋊C₄	—	2	1	no	—
190	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
192	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
193	C₂×C₄²×C₇	—	2	2	no	—
194	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
195	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
196	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
197	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
199	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
200	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
206	C₇×#107	C₂³	1	8	yes	—
207	C₇×#106	C₂³	1	8	yes	—
208	C₇×#103	C₂³	1	8	yes	—
209	C₇×#102	C₂³	1	8	yes	—
210	C₇×#102	C₂³	1	8	yes	—
211	C₇×#102	C₂³	1	8	yes	—
212	C₇×#97	C₂³	1	2	yes	—
213	C₇×#97	C₂³	1	2	yes	—
214	C₇×#97	C₂³	1	4	yes	—
215	C₄×C₇×C₈	C₂³	1	2	yes	—
216	C₄×C₇×C₈	C₂³	1	2	yes	—
217	C₄×C₇×C₈	C₂³	1	4	yes	—
218	#3444	C₂×C₇	1	1	yes	characteristic, complemented
219	C₂×#532	C₂×C₇	1	1	yes	characteristic, complemented
220	#3184	C₂×C₇	1	2	yes	complemented
221	#3182	C₂×C₇	1	2	yes	complemented
222	#3180	C₂×C₇	1	4	yes	complemented
223	#3171	C₂×C₇	1	4	yes	complemented
224	#3169	C₂×C₇	1	2	yes	complemented
225	#3167	C₂×C₇	1	2	yes	complemented
226	#3165	C₂×C₇	1	1	yes	characteristic, complemented
227	#3151	C₂×C₇	1	1	yes	characteristic, complemented
228	#3141	C₂×C₇	1	1	yes	characteristic, complemented
229	#3138	C₂×C₇	1	1	yes	characteristic, complemented
230	#3055	C₂×C₇	1	4	yes	complemented
231	C₄×AGL(1,ℤ/8)	C₂×C₇	1	4	yes	complemented
232	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
233	C₂⁴×C₇	—	2	2	no	—
234	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
235	C₇×#41	—	2	8	no	—
236	C₇×#41	—	4	4	no	—
237	C₇×#41	—	4	8	no	—
238	C₇×#41	—	4	8	no	—
239	C₇×#41	—	4	8	no	—
240	C₇×#41	—	4	4	no	—
241	C₇×#41	—	4	8	no	—
242	C₂×C₇×Q₈	—	2	1	no	—
243	C₂×C₇×Q₈	—	2	1	no	—
244	C₂×C₇×Q₈	—	2	2	no	—
245	C₂×C₇×Q₈	—	2	2	no	—
246	C₂×C₇×Q₈	—	4	4	no	—
247	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
248	C₂×C₇×D₄	—	2	2	no	—
249	C₂×C₇×D₄	—	2	2	no	—
250	C₂×C₇×D₄	—	2	2	no	—
251	C₂×C₇×D₄	—	2	4	no	—
252	C₂×C₇×D₄	—	2	4	no	—
253	C₂×C₇×D₄	—	2	1	no	—
254	C₂×C₇×D₄	—	2	1	no	—
255	C₂×C₇×D₄	—	2	2	no	—
256	C₂×C₇×D₄	—	2	2	no	—
257	C₂×C₇×D₄	—	2	2	no	—
258	C₂×C₇×D₄	—	2	2	no	—
259	C₂×C₇×D₄	—	2	2	no	—
260	C₂×C₇×D₄	—	2	8	no	—
261	C₂×C₇×D₄	—	4	4	no	—
262	C₂×C₇×D₄	—	4	4	no	—
263	C₂×C₇×D₄	—	4	8	no	—
264	C₂×C₇×D₄	C₂⁴	1	2	yes	—
265	C₂×C₇×D₄	C₂⁴	1	4	yes	—
266	C₂²×C₄×C₇	—	2	4	no	—
267	C₂²×C₄×C₇	—	2	4	no	—
268	C₂²×C₄×C₇	—	2	2	no	—
269	C₂²×C₄×C₇	—	2	2	no	—
270	C₂²×C₄×C₇	—	2	2	no	—
271	C₂²×C₄×C₇	—	2	4	no	—
272	C₂²×C₄×C₇	—	2	2	no	—
273	C₂²×C₄×C₇	—	2	4	no	—
274	C₂²×C₄×C₇	—	4	2	no	—
275	C₂²×C₄×C₇	—	4	8	no	—
276	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
294	C₇×SD₁₆	—	2	16	no	—
295	C₇×D₈	—	2	16	no	—
296	C₇×M₁₆	—	2	4	no	—
297	C₇×M₁₆	—	2	8	no	—
298	C₇×M₁₆	#41	1	8	yes	complemented
299	C₂×C₇×C₈	—	2	8	no	—
300	C₂×C₇×C₈	C₂⁴	1	4	yes	—
301	C₂×C₇×C₈	C₂⁴	1	4	yes	—
302	C₇×C₄⋊C₄	—	2	2	no	—
303	C₇×C₄⋊C₄	—	2	2	no	—
304	C₇×C₄⋊C₄	—	2	2	no	—
305	C₇×C₄⋊C₄	—	2	1	no	—
306	C₇×C₄⋊C₄	—	2	1	no	—
307	C₇×C₄⋊C₄	—	2	1	no	—
308	C₇×C₄⋊C₄	—	2	1	no	—
309	C₇×C₄⋊C₄	—	2	2	no	—
310	C₇×C₄⋊C₄	—	2	2	no	—
311	C₇×C₄⋊C₄	—	2	2	no	—
312	C₇×C₄⋊C₄	—	2	2	no	—
313	C₇×C₄⋊C₄	—	2	2	no	—
314	C₇×C₄⋊C₄	—	2	2	no	—
315	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
316	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
317	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
318	C₇×C₂²⋊C₄	—	2	2	no	—
319	C₇×C₂²⋊C₄	—	2	2	no	—
320	C₇×C₂²⋊C₄	—	2	2	no	—
321	C₇×C₂²⋊C₄	—	2	4	no	—
322	C₇×C₂²⋊C₄	—	2	4	no	—
323	C₇×C₂²⋊C₄	—	2	4	no	—
324	C₇×C₂²⋊C₄	—	2	4	no	—
325	C₇×C₂²⋊C₄	—	2	2	no	—
326	C₇×C₂²⋊C₄	—	2	2	no	—
327	C₇×C₂²⋊C₄	—	2	2	no	—
328	C₇×C₂²⋊C₄	—	2	2	no	—
329	C₇×C₂²⋊C₄	—	2	2	no	—
330	C₇×C₂²⋊C₄	—	2	2	no	—
331	C₄²×C₇	—	2	2	no	—
332	C₄²×C₇	—	2	2	no	—
333	C₄²×C₇	—	2	2	no	—
334	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
344	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
345	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
346	C₄²×C₇	C₂⁴	1	1	yes	characteristic
347	C₄²×C₇	C₂⁴	1	1	yes	characteristic
348	C₄²×C₇	C₂⁴	1	1	yes	characteristic
349	C₄²×C₇	C₂⁴	1	1	yes	characteristic
350	C₂²×#41	—	2	1	no	—
351	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	4	yes	—
352	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
353	#533	C₂²×C₇	1	1	yes	characteristic
354	#533	C₂²×C₇	1	1	yes	characteristic, complemented
355	#533	C₂²×C₇	1	1	yes	characteristic, complemented
356	#532	—	2	1	no	—
357	#532	—	2	1	no	—
358	#532	—	2	1	no	—
359	#532	—	2	1	no	—
360	#532	C₂²×C₇	1	1	yes	characteristic
361	#532	C₂²×C₇	1	2	yes	—
362	#532	C₂²×C₇	1	2	yes	—
363	#532	C₂²×C₇	1	2	yes	—
364	#532	C₂²×C₇	1	2	yes	—
365	#532	C₂²×C₇	1	1	yes	characteristic, complemented
366	#532	C₂²×C₇	1	1	yes	characteristic, complemented
367	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
368	C₂×#127	C₂²×C₇	1	1	yes	characteristic
369	#529	—	2	1	no	—
370	#529	—	2	1	no	—
371	#529	—	2	1	no	—
372	#529	—	2	1	no	—
373	#529	C₂²×C₇	1	2	yes	complemented
374	#529	C₂²×C₇	1	2	yes	complemented
375	C₂×#124	—	2	1	no	—
376	#525	—	2	1	no	—
377	#525	—	2	1	no	—
378	#525	C₂²×C₇	1	2	yes	—
379	C₂×#121	—	2	1	no	—
380	C₂×#121	C₂²×C₇	1	2	yes	—
381	C₄×#41	—	2	1	no	—
382	C₄×#41	—	2	1	no	—
383	C₄×#41	C₂²×C₇	1	2	yes	—
384	C₂×C₄×D₄	—	2	1	no	—
385	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
386	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
387	#501	C₂²×C₇	1	4	yes	complemented
388	#500	C₂²×C₇	1	2	yes	complemented
389	#498	C₂²×C₇	1	2	yes	complemented
390	#496	C₂²×C₇	1	4	yes	complemented
391	#493	C₂²×C₇	1	2	yes	complemented
392	#492	C₂²×C₇	1	2	yes	complemented
393	#490	C₂²×C₇	1	4	yes	complemented
394	#489	C₂²×C₇	1	4	yes	complemented
395	#487	C₂²×C₇	1	2	yes	complemented
396	#486	C₂²×C₇	1	2	yes	complemented
397	#486	C₂²×C₇	1	2	yes	complemented
398	#486	C₂²×C₇	1	2	yes	complemented
399	#469	C₂²×C₇	1	8	yes	complemented
400	#468	C₂²×C₇	1	8	yes	complemented
401	#466	C₂²×C₇	1	8	yes	complemented
402	#465	C₂²×C₇	1	8	yes	complemented
403	#442	C₂²×C₇	1	8	yes	complemented
404	#440	C₂²×C₇	1	8	yes	complemented
405	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
406	C₄×D₈	C₂²×C₇	1	8	yes	complemented
407	#428	C₂²×C₇	1	4	yes	—
408	#418	C₂²×C₇	1	4	yes	—
409	#417	C₂²×C₇	1	4	yes	—
410	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
411	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
412	C₄×M₁₆	C₂²×C₇	1	2	yes	—
413	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
414	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
415	C₂×#97	C₂²×C₇	1	2	yes	complemented
416	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
417	C₂³×C₇	—	2	2	no	—
418	C₂³×C₇	—	2	2	no	—
419	C₂³×C₇	—	2	2	no	—
420	C₂³×C₇	—	2	4	no	—
421	C₂³×C₇	—	4	1	no	—
422	C₂³×C₇	—	4	4	no	—
423	C₂³×C₇	—	4	4	no	—
424	C₂³×C₇	—	4	4	no	—
425	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
426	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
427	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
428	C₇×Q₈	—	2	4	no	—
429	C₇×Q₈	—	4	4	no	—
430	C₇×Q₈	—	4	4	no	—
431	C₇×Q₈	—	4	2	no	—
432	C₇×Q₈	—	4	2	no	—
433	C₇×D₄	—	2	4	no	—
434	C₇×D₄	—	2	8	no	—
435	C₇×D₄	—	4	4	no	—
436	C₇×D₄	—	4	4	no	—
437	C₇×D₄	—	4	8	no	—
438	C₇×D₄	—	4	4	no	—
439	C₇×D₄	—	4	4	no	—
440	C₇×D₄	—	4	8	no	—
441	C₇×D₄	—	4	4	no	—
442	C₇×D₄	—	4	4	no	—
443	C₇×D₄	—	4	4	no	—
444	C₇×D₄	—	4	2	no	—
445	C₇×D₄	—	4	4	no	—
446	C₇×D₄	—	4	2	no	—
447	C₂×C₄×C₇	—	2	2	no	—
448	C₂×C₄×C₇	—	2	2	no	—
449	C₂×C₄×C₇	—	2	2	no	—
450	C₂×C₄×C₇	—	2	2	no	—
451	C₂×C₄×C₇	—	2	2	no	—
452	C₂×C₄×C₇	—	2	2	no	—
453	C₂×C₄×C₇	—	2	2	no	—
454	C₂×C₄×C₇	—	2	2	no	—
455	C₂×C₄×C₇	—	2	2	no	—
456	C₂×C₄×C₇	—	2	2	no	—
457	C₂×C₄×C₇	—	2	2	no	—
458	C₂×C₄×C₇	—	2	2	no	—
459	C₂×C₄×C₇	—	2	2	no	—
460	C₂×C₄×C₇	—	2	2	no	—
461	C₂×C₄×C₇	—	2	2	no	—
462	C₂×C₄×C₇	—	2	2	no	—
463	C₂×C₄×C₇	—	2	4	no	—
464	C₂×C₄×C₇	—	4	1	no	—
465	C₂×C₄×C₇	—	4	1	no	—
466	C₂×C₄×C₇	—	4	1	no	—
467	C₂×C₄×C₇	—	4	8	no	—
468	C₂×C₄×C₇	—	4	4	no	—
469	C₂×C₄×C₇	—	4	4	no	—
470	C₂×C₄×C₇	—	4	4	no	—
471	C₂×C₄×C₇	—	4	8	no	—
472	C₂×C₄×C₇	—	4	4	no	—
473	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	complemented
474	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₇	C₂×#41	1	4	yes	—
486	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
487	C₇×C₈	—	2	4	no	—
488	C₇×C₈	C₂×#41	1	8	yes	complemented
489	C₂×#41	—	2	1	no	—
490	C₂×#41	—	2	1	no	—
491	C₂×#41	—	2	2	no	—
492	C₂×#41	—	2	2	no	—
493	C₂×#41	—	2	2	no	—
494	C₂×#41	—	2	2	no	—
495	C₂×#41	—	4	8	no	—
496	C₂×#41	C₂³×C₇	1	2	yes	—
497	C₂²×Q₈	—	2	1	no	—
498	C₂²×D₄	—	2	2	no	—
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	C₂³×C₇	1	2	yes	—
502	C₂³×C₄	—	2	2	no	—
503	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
504	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
506	AGL(1,ℤ/8)	—	2	16	no	—
507	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
508	C₂×D₈	C₂³×C₇	1	8	yes	—
509	C₂×M₁₆	—	2	8	no	—
510	C₂×M₁₆	C₂³×C₇	1	2	yes	—
511	C₂×M₁₆	C₂³×C₇	1	4	yes	—
512	C₂×M₁₆	C₂³×C₇	1	2	yes	—
513	C₂²×C₈	C₂³×C₇	1	4	yes	—
514	C₄⋊Q₈	—	2	1	no	—
515	C₄⋊Q₈	—	2	1	no	—
516	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
517	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
518	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
519	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
520	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
521	#127	—	2	1	no	—
522	#127	—	2	1	no	—
523	#127	C₂³×C₇	1	2	yes	—
524	#127	C₂³×C₇	1	2	yes	—
525	#127	C₂³×C₇	1	1	yes	characteristic
526	#126	—	2	2	no	—
527	#126	—	2	2	no	—
528	#125	—	2	1	no	—
529	#125	—	2	1	no	—
530	#125	C₂³×C₇	1	2	yes	—
531	#124	—	2	2	no	—
532	#124	—	2	2	no	—
533	#124	—	2	2	no	—
534	#124	—	2	2	no	—
535	#124	—	2	1	no	—
536	#124	—	2	1	no	—
537	#124	C₂³×C₇	1	2	yes	—
538	#123	—	2	2	no	—
539	#123	—	2	2	no	—
540	#123	—	2	2	no	—
541	C₂²⋊Q₈	—	2	1	no	—
542	C₂²⋊Q₈	—	2	1	no	—
543	C₂²⋊Q₈	—	2	1	no	—
544	C₂²⋊Q₈	—	2	1	no	—
545	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
546	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
547	#121	—	2	2	no	—
548	#121	—	2	2	no	—
549	#121	—	2	2	no	—
550	#121	—	2	2	no	—
551	#121	—	2	2	no	—
552	#121	—	2	2	no	—
553	#121	—	2	1	no	—
554	#121	—	2	1	no	—
555	#121	—	2	1	no	—
556	#121	—	2	1	no	—
557	#121	C₂³×C₇	1	4	yes	—
558	#121	C₂³×C₇	1	4	yes	—
559	#121	C₂³×C₇	1	2	yes	—
560	#121	C₂³×C₇	1	2	yes	—
561	#120	—	2	2	no	—
562	C₄×Q₈	—	2	1	no	—
563	C₄×Q₈	—	2	1	no	—
564	C₄×Q₈	—	2	1	no	—
565	C₄×Q₈	—	2	1	no	—
566	C₄×Q₈	C₂³×C₇	1	2	yes	—
567	C₄×Q₈	C₂³×C₇	1	2	yes	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	—	2	1	no	—
584	C₄×D₄	C₂³×C₇	1	4	yes	—
585	C₄×D₄	C₂³×C₇	1	4	yes	—
586	C₄×D₄	C₂³×C₇	1	2	yes	—
587	C₄×D₄	C₂³×C₇	1	2	yes	—
588	#117	—	2	1	no	—
589	#117	—	2	1	no	—
590	#117	—	2	2	no	—
591	#117	—	2	2	no	—
592	#117	—	2	2	no	—
593	#117	C₂³×C₇	1	2	yes	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
596	C₂×C₂²⋊C₄	—	2	2	no	—
597	C₂×C₂²⋊C₄	—	2	2	no	—
598	C₂×C₄²	—	2	2	no	—
599	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
600	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
601	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
602	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
603	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
604	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
611	#107	C₂³×C₇	1	8	yes	—
612	#106	C₂³×C₇	1	8	yes	—
613	#103	C₂³×C₇	1	8	yes	—
614	#102	C₂³×C₇	1	8	yes	—
615	#102	C₂³×C₇	1	8	yes	—
616	#102	C₂³×C₇	1	8	yes	—
617	#97	C₂³×C₇	1	4	yes	—
618	#97	C₂³×C₇	1	2	yes	—
619	#97	C₂³×C₇	1	2	yes	—
620	C₄×C₈	C₂³×C₇	1	4	yes	—
621	C₄×C₈	C₂³×C₇	1	2	yes	—
622	C₄×C₈	C₂³×C₇	1	2	yes	—
623	C₂²×C₇	—	2	1	no	—
624	C₂²×C₇	—	2	1	no	—
625	C₂²×C₇	—	2	1	no	—
626	C₂²×C₇	—	2	1	no	—
627	C₂²×C₇	—	2	1	no	—
628	C₂²×C₇	—	2	1	no	—
629	C₂²×C₇	—	2	1	no	—
630	C₂²×C₇	—	4	4	no	—
631	C₂²×C₇	—	4	2	no	—
632	C₂²×C₇	—	4	4	no	—
633	C₂²×C₇	—	4	4	no	—
634	C₂²×C₇	—	4	2	no	—
635	C₂²×C₇	—	4	2	no	—
636	C₂²×C₇	—	4	4	no	—
637	C₂²×C₇	—	8	8	no	—
638	C₂²×C₇	#532	1	2	yes	—
639	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
640	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
641	C₄×C₇	—	2	1	no	—
642	C₄×C₇	—	2	1	no	—
643	C₄×C₇	—	2	1	no	—
644	C₄×C₇	—	2	1	no	—
645	C₄×C₇	—	2	1	no	—
646	C₄×C₇	—	2	1	no	—
647	C₄×C₇	—	2	1	no	—
648	C₄×C₇	—	4	2	no	—
649	C₄×C₇	—	4	4	no	—
650	C₄×C₇	—	4	2	no	—
651	C₄×C₇	—	4	2	no	—
652	C₄×C₇	#532	1	2	yes	—
653	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
654	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
655	C₄×C₇	#575	1	2	yes	—
656	C₄×C₇	C₂²×#41	1	2	yes	—
657	C₂⁴	—	2	2	no	—
658	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
659	#41	—	2	8	no	—
660	#41	—	4	8	no	—
661	#41	—	4	8	no	—
662	#41	—	4	8	no	—
663	#41	—	4	4	no	—
664	#41	—	4	8	no	—
665	#41	—	4	4	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	4	4	no	—
671	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	8	no	—
685	C₂×D₄	—	4	4	no	—
686	C₂×D₄	—	4	4	no	—
687	C₂×D₄	—	4	8	no	—
688	C₂×D₄	C₂⁴×C₇	1	2	yes	—
689	C₂×D₄	C₂⁴×C₇	1	4	yes	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	8	no	—
700	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
701	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
702	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
703	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
704	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
705	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
706	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
707	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
708	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
709	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
710	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
711	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
712	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
713	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
714	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
718	SD₁₆	—	2	16	no	—
719	D₈	—	2	16	no	—
720	M₁₆	—	2	4	no	—
721	M₁₆	—	2	8	no	—
722	M₁₆	C₇×#41	1	8	yes	complemented
723	C₂×C₈	—	2	8	no	—
724	C₂×C₈	C₂⁴×C₇	1	4	yes	—
725	C₂×C₈	C₂⁴×C₇	1	4	yes	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
740	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	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	C₂×C₇×D₄	1	1	yes	characteristic
761	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
762	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
763	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
764	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
765	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
766	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
767	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
768	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
769	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
770	C₄²	C₂⁴×C₇	1	1	yes	characteristic
771	C₄²	C₂⁴×C₇	1	1	yes	characteristic
772	C₄²	C₂⁴×C₇	1	1	yes	characteristic
773	C₄²	C₂⁴×C₇	1	1	yes	characteristic
774	C₂×C₇	—	2	2	no	—
775	C₂×C₇	—	2	2	no	—
776	C₂×C₇	—	4	1	no	—
777	C₂×C₇	—	8	2	no	—
778	C₂×C₇	—	8	4	no	—
779	C₂×C₇	C₂×#532	1	1	yes	characteristic
780	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
781	C₂×C₇	C₂×#575	1	1	yes	characteristic
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	4	no	—
786	C₂³	—	4	1	no	—
787	C₂³	—	4	4	no	—
788	C₂³	—	4	4	no	—
789	C₂³	—	4	4	no	—
790	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
791	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
792	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
793	Q₈	—	2	4	no	—
794	Q₈	—	4	4	no	—
795	Q₈	—	4	4	no	—
796	Q₈	—	4	2	no	—
797	Q₈	—	4	2	no	—
798	D₄	—	2	4	no	—
799	D₄	—	2	8	no	—
800	D₄	—	4	4	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	8	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	4	no	—
805	D₄	—	4	8	no	—
806	D₄	—	4	4	no	—
807	D₄	—	4	4	no	—
808	D₄	—	4	4	no	—
809	D₄	—	4	2	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	4	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	8	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	4	8	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	complemented
839	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
840	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
841	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
842	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
843	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
844	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
845	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
846	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
847	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
848	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
849	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
850	C₂×C₄	C₂×C₇×#41	1	4	yes	—
851	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
852	C₈	—	2	4	no	—
853	C₈	C₂×C₇×#41	1	8	yes	complemented
854	C₇	#60700	1	1	yes	characteristic, direct product factor, Sylow
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	4	4	no	—
863	C₂²	—	4	4	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	4	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	4	no	—
869	C₂²	—	8	8	no	—
870	C₂²	C₇×#532	1	2	yes	—
871	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
872	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	1	no	—
878	C₄	—	2	1	no	—
879	C₄	—	2	1	no	—
880	C₄	—	4	4	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₄	C₇×#532	1	2	yes	—
885	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
886	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
887	C₄	C₇×#575	1	2	yes	—
888	C₄	C₂²×C₇×#41	1	2	yes	—
889	C₂	—	2	2	no	—
890	C₂	—	2	2	no	—
891	C₂	—	4	1	no	—
892	C₂	—	8	4	no	—
893	C₂	—	8	2	no	—
894	C₂	C₂×C₇×#532	1	1	yes	characteristic
895	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
896	C₂	C₂×C₇×#575	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₇×#3444	C₂	semidirect
2. C₂×C₇×#532	C₂	semidirect
3. C₇×#3184	C₂	semidirect
4. C₇×#3182	C₂	semidirect
5. C₇×#3180	C₂	semidirect
6. C₇×#3171	C₂	semidirect
7. C₇×#3169	C₂	semidirect
8. C₇×#3167	C₂	semidirect
9. C₇×#3165	C₂	semidirect
10. C₇×#3151	C₂	semidirect
11. C₇×#3141	C₂	semidirect
12. C₇×#3138	C₂	semidirect
13. C₇×#3055	C₂	semidirect
14. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
15. C₂×C₄×C₇×M₁₆	C₂	semidirect
20. C₇×#533	C₂²	semidirect
21. C₇×#533	C₂²	semidirect
31. C₇×#532	C₂²	semidirect
32. C₇×#532	C₂²	semidirect
39. C₇×#529	C₂²	semidirect
40. C₇×#529	C₂²	semidirect
53. C₇×#501	C₂²	semidirect
54. C₇×#500	C₂²	semidirect
55. C₇×#498	C₂²	semidirect
56. C₇×#496	C₂²	semidirect
57. C₇×#493	C₂²	semidirect
58. C₇×#492	C₂²	semidirect
59. C₇×#490	C₂²	semidirect
60. C₇×#489	C₂²	semidirect
61. C₇×#487	C₂²	semidirect
62. C₇×#486	C₂²	semidirect
63. C₇×#486	C₂²	semidirect
64. C₇×#486	C₂²	semidirect
65. C₇×#469	C₂²	semidirect
66. C₇×#468	C₂²	semidirect
67. C₇×#466	C₂²	semidirect
68. C₇×#465	C₂²	semidirect
69. C₇×#442	C₂²	semidirect
70. C₇×#440	C₂²	semidirect
71. C₄×C₇×SD₁₆	C₂²	semidirect
72. C₄×C₇×D₈	C₂²	semidirect
79. C₄×C₇×M₁₆	C₂²	semidirect
80. C₄×C₇×M₁₆	C₂²	semidirect
81. C₂×C₇×#97	C₂²	semidirect
82. C₂×C₄×C₇×C₈	C₂²	semidirect
83. #60700	C₇	direct (N × H)
218. #3444	C₂×C₇	semidirect
219. C₂×#532	C₂×C₇	semidirect
220. #3184	C₂×C₇	semidirect
221. #3182	C₂×C₇	semidirect
222. #3180	C₂×C₇	semidirect
223. #3171	C₂×C₇	semidirect
224. #3169	C₂×C₇	semidirect
225. #3167	C₂×C₇	semidirect
226. #3165	C₂×C₇	semidirect
227. #3151	C₂×C₇	semidirect
228. #3141	C₂×C₇	semidirect
229. #3138	C₂×C₇	semidirect
230. #3055	C₂×C₇	semidirect
231. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
232. C₂×C₄×M₁₆	C₂×C₇	semidirect
298. C₇×M₁₆	#41	semidirect
354. #533	C₂²×C₇	semidirect
355. #533	C₂²×C₇	semidirect
365. #532	C₂²×C₇	semidirect
366. #532	C₂²×C₇	semidirect
373. #529	C₂²×C₇	semidirect
374. #529	C₂²×C₇	semidirect
387. #501	C₂²×C₇	semidirect
388. #500	C₂²×C₇	semidirect
389. #498	C₂²×C₇	semidirect
390. #496	C₂²×C₇	semidirect
391. #493	C₂²×C₇	semidirect
392. #492	C₂²×C₇	semidirect
393. #490	C₂²×C₇	semidirect
394. #489	C₂²×C₇	semidirect
395. #487	C₂²×C₇	semidirect
396. #486	C₂²×C₇	semidirect
397. #486	C₂²×C₇	semidirect
398. #486	C₂²×C₇	semidirect
399. #469	C₂²×C₇	semidirect
400. #468	C₂²×C₇	semidirect
401. #466	C₂²×C₇	semidirect
402. #465	C₂²×C₇	semidirect
403. #442	C₂²×C₇	semidirect
404. #440	C₂²×C₇	semidirect
405. C₄×SD₁₆	C₂²×C₇	semidirect
406. C₄×D₈	C₂²×C₇	semidirect
413. C₄×M₁₆	C₂²×C₇	semidirect
414. C₄×M₁₆	C₂²×C₇	semidirect
415. C₂×#97	C₂²×C₇	semidirect
416. C₂×C₄×C₈	C₂²×C₇	semidirect
473. C₂×C₄×C₇	AGL(1,ℤ/8)	semidirect
488. C₇×C₈	C₂×#41	semidirect
722. M₁₆	C₇×#41	semidirect
838. C₂×C₄	C₇×AGL(1,ℤ/8)	semidirect
853. C₈	C₂×C₇×#41	semidirect
854. C₇	#60700	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#3444	2
C₂×C₇×#532	2
C₇×#3184	2
C₇×#3182	2
C₇×#3180	2
C₇×#3171	2
C₇×#3169	2
C₇×#3167	2
C₇×#3165	2
C₇×#3151	2
C₇×#3141	2
C₇×#3138	2
C₇×#3055	2
C₄×C₇×AGL(1,ℤ/8)	2
C₂×C₄×C₇×M₁₆	2
#60700	7

Subgroups — C7×#60700 #13237916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60700 #13237916