Subgroups — C₇×#60702 #13237918

Order 1792.

2008 conjugacy classes of subgroups.

The subgroup lattice has 1004 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×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3183	C₂	1	4	yes	maximal, complemented
4	C₇×#3181	C₂	1	2	yes	maximal, complemented
5	C₇×#3180	C₂	1	2	yes	maximal, complemented
6	C₇×#3172	C₂	1	2	yes	maximal, complemented
7	C₇×#3171	C₂	1	2	yes	maximal, complemented
8	C₇×#3168	C₂	1	4	yes	maximal, complemented
9	C₇×#3166	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3153	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3140	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3056	C₂	1	2	yes	maximal, complemented
14	C₇×#3055	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×#137	C₂	1	2	yes	maximal, complemented
16	C₄×C₇×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#137	C₂²	1	2	yes	—
19	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
21	C₇×#533	C₂²	1	1	yes	characteristic
22	C₇×#533	C₂²	1	1	yes	characteristic, complemented
23	C₇×#533	C₂²	1	1	yes	characteristic, complemented
24	C₇×#532	C₂²	1	1	yes	characteristic
25	C₇×#532	C₂²	1	1	yes	characteristic, complemented
26	C₇×#532	C₂²	1	1	yes	characteristic, complemented
27	C₇×#529	—	2	1	no	—
28	C₇×#529	—	2	1	no	—
29	C₇×#529	—	2	1	no	—
30	C₇×#529	—	2	1	no	—
31	C₇×#529	—	2	1	no	—
32	C₇×#529	—	2	1	no	—
33	C₇×#529	—	2	1	no	—
34	C₇×#529	—	2	1	no	—
35	C₇×#529	C₂²	1	2	yes	—
36	C₇×#529	C₂²	1	2	yes	—
37	C₇×#529	C₂²	1	2	yes	—
38	C₇×#529	C₂²	1	2	yes	—
39	C₇×#529	C₂²	1	2	yes	complemented
40	C₇×#529	C₂²	1	2	yes	complemented
41	C₂×C₇×#126	—	2	1	no	—
42	C₂×C₇×#125	C₂²	1	1	yes	characteristic
43	C₂×C₇×#124	C₂²	1	1	yes	characteristic
44	C₇×#525	—	2	1	no	—
45	C₇×#525	—	2	1	no	—
46	C₇×#525	C₂²	1	2	yes	—
47	C₂×C₇×#123	—	2	1	no	—
48	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₇×#121	C₂²	1	1	yes	characteristic
50	C₄×C₇×#41	—	2	1	no	—
51	C₄×C₇×#41	—	2	1	no	—
52	C₄×C₇×#41	C₂²	1	2	yes	—
53	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₇×D₄	—	2	1	no	—
55	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
56	C₂×C₇×#117	—	2	1	no	—
57	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
58	C₇×#501	C₂²	1	2	yes	complemented
59	C₇×#501	C₂²	1	2	yes	complemented
60	C₇×#499	C₂²	1	4	yes	complemented
61	C₇×#497	C₂²	1	2	yes	complemented
62	C₇×#496	C₂²	1	2	yes	complemented
63	C₇×#495	C₂²	1	4	yes	complemented
64	C₇×#491	C₂²	1	2	yes	complemented
65	C₇×#490	C₂²	1	2	yes	complemented
66	C₇×#489	C₂²	1	2	yes	complemented
67	C₇×#489	C₂²	1	2	yes	complemented
68	C₇×#488	C₂²	1	4	yes	complemented
69	C₇×#488	C₂²	1	4	yes	complemented
70	C₇×#470	C₂²	1	4	yes	complemented
71	C₇×#469	C₂²	1	4	yes	—
72	C₇×#468	C₂²	1	4	yes	—
73	C₇×#468	C₂²	1	4	yes	complemented
74	C₇×#467	C₂²	1	4	yes	complemented
75	C₇×#466	C₂²	1	4	yes	—
76	C₇×#465	C₂²	1	4	yes	—
77	C₇×#465	C₂²	1	4	yes	complemented
78	C₇×#442	C₂²	1	4	yes	complemented
79	C₇×#441	C₂²	1	4	yes	complemented
80	C₇×#440	C₂²	1	4	yes	complemented
81	C₇×#440	C₂²	1	4	yes	complemented
82	C₄×C₇×Q₁₆	C₂²	1	4	yes	complemented
83	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
84	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
85	C₄×C₇×D₈	C₂²	1	4	yes	complemented
86	C₇×#428	C₂²	1	2	yes	—
87	C₇×#428	C₂²	1	2	yes	—
88	C₇×#419	C₂²	1	2	yes	—
89	C₇×#418	C₂²	1	2	yes	—
90	C₇×#417	C₂²	1	2	yes	—
91	C₇×#417	C₂²	1	2	yes	—
92	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
93	C₄×C₇×M₁₆	C₂²	1	2	yes	—
94	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
95	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
96	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
97	C₂×C₇×#97	C₂²	1	2	yes	complemented
98	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
99	#60702	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂×C₇×#41	—	2	1	no	—
101	C₂×C₇×#41	—	2	1	no	—
102	C₂×C₇×#41	C₂³	1	2	yes	—
103	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
104	C₂²×C₇×D₄	—	2	1	no	—
105	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₇	—	2	1	no	—
107	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
108	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
109	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
110	C₇×#137	—	2	8	no	—
111	C₇×AGL(1,ℤ/8)	—	2	8	no	—
112	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
113	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
115	C₂×C₇×D₈	C₂³	1	4	yes	—
116	C₂×C₇×M₁₆	—	2	8	no	—
117	C₂×C₇×M₁₆	C₂³	1	4	yes	—
118	C₂×C₇×M₁₆	C₂³	1	2	yes	—
119	C₂×C₇×M₁₆	C₂³	1	2	yes	—
120	C₂²×C₇×C₈	C₂³	1	4	yes	—
121	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₇×#127	C₂³	1	1	yes	characteristic
125	C₇×#126	—	2	2	no	—
126	C₇×#126	—	2	2	no	—
127	C₇×#126	—	2	2	no	—
128	C₇×#126	—	2	2	no	—
129	C₇×#126	—	2	2	no	—
130	C₇×#126	—	2	2	no	—
131	C₇×#125	—	2	1	no	—
132	C₇×#125	—	2	1	no	—
133	C₇×#125	—	2	1	no	—
134	C₇×#125	—	2	1	no	—
135	C₇×#125	C₂³	1	2	yes	—
136	C₇×#125	C₂³	1	2	yes	—
137	C₇×#125	C₂³	1	2	yes	—
138	C₇×#124	—	2	1	no	—
139	C₇×#124	—	2	1	no	—
140	C₇×#124	—	2	1	no	—
141	C₇×#124	—	2	1	no	—
142	C₇×#124	C₂³	1	2	yes	—
143	C₇×#124	C₂³	1	2	yes	—
144	C₇×#124	C₂³	1	2	yes	—
145	C₇×#123	—	2	2	no	—
146	C₇×#123	—	2	2	no	—
147	C₇×#123	—	2	2	no	—
148	C₇×#123	—	2	2	no	—
149	C₇×#123	—	2	2	no	—
150	C₇×#123	—	2	2	no	—
151	C₇×#123	—	2	2	no	—
152	C₇×C₂²⋊Q₈	—	2	1	no	—
153	C₇×C₂²⋊Q₈	—	2	1	no	—
154	C₇×C₂²⋊Q₈	—	2	1	no	—
155	C₇×C₂²⋊Q₈	—	2	1	no	—
156	C₇×C₂²⋊Q₈	—	2	1	no	—
157	C₇×C₂²⋊Q₈	—	2	1	no	—
158	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
159	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
160	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
161	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
162	C₇×#121	—	2	1	no	—
163	C₇×#121	—	2	1	no	—
164	C₇×#121	—	2	1	no	—
165	C₇×#121	—	2	1	no	—
166	C₇×#121	—	2	1	no	—
167	C₇×#121	—	2	1	no	—
168	C₇×#121	C₂³	1	2	yes	—
169	C₇×#121	C₂³	1	2	yes	—
170	C₇×#121	C₂³	1	2	yes	—
171	C₇×#121	C₂³	1	2	yes	—
172	C₇×#120	—	2	2	no	—
173	C₄×C₇×Q₈	—	2	1	no	—
174	C₄×C₇×Q₈	—	2	1	no	—
175	C₄×C₇×Q₈	—	2	1	no	—
176	C₄×C₇×Q₈	—	2	1	no	—
177	C₄×C₇×Q₈	—	2	1	no	—
178	C₄×C₇×Q₈	—	2	1	no	—
179	C₄×C₇×Q₈	C₂³	1	2	yes	—
180	C₄×C₇×Q₈	C₂³	1	2	yes	—
181	C₄×C₇×Q₈	C₂³	1	2	yes	—
182	C₄×C₇×Q₈	C₂³	1	2	yes	—
183	C₄×C₇×D₄	—	2	2	no	—
184	C₄×C₇×D₄	—	2	2	no	—
185	C₄×C₇×D₄	—	2	2	no	—
186	C₄×C₇×D₄	—	2	2	no	—
187	C₄×C₇×D₄	—	2	2	no	—
188	C₄×C₇×D₄	—	2	2	no	—
189	C₄×C₇×D₄	—	2	2	no	—
190	C₄×C₇×D₄	—	2	2	no	—
191	C₄×C₇×D₄	—	2	2	no	—
192	C₄×C₇×D₄	—	2	2	no	—
193	C₄×C₇×D₄	—	2	1	no	—
194	C₄×C₇×D₄	—	2	1	no	—
195	C₄×C₇×D₄	—	2	1	no	—
196	C₄×C₇×D₄	—	2	1	no	—
197	C₄×C₇×D₄	—	2	1	no	—
198	C₄×C₇×D₄	—	2	1	no	—
199	C₄×C₇×D₄	C₂³	1	2	yes	—
200	C₄×C₇×D₄	C₂³	1	2	yes	—
201	C₄×C₇×D₄	C₂³	1	2	yes	—
202	C₄×C₇×D₄	C₂³	1	2	yes	—
203	C₇×#117	—	2	1	no	—
204	C₇×#117	—	2	1	no	—
205	C₇×#117	—	2	2	no	—
206	C₇×#117	—	2	2	no	—
207	C₇×#117	—	2	2	no	—
208	C₇×#117	—	2	2	no	—
209	C₇×#117	—	2	2	no	—
210	C₇×#117	—	2	2	no	—
211	C₇×#117	—	2	2	no	—
212	C₇×#117	C₂³	1	2	yes	—
213	C₂×C₇×C₄⋊C₄	—	2	1	no	—
214	C₂×C₇×C₄⋊C₄	—	2	1	no	—
215	C₂×C₇×C₄⋊C₄	—	2	1	no	—
216	C₂×C₇×C₄⋊C₄	—	2	1	no	—
217	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
219	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
220	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
221	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
222	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
223	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
224	C₂×C₄²×C₇	—	2	1	no	—
225	C₂×C₄²×C₇	—	2	2	no	—
226	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
227	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
228	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
229	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
230	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
231	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
232	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
238	C₇×#107	C₂³	1	4	yes	—
239	C₇×#107	C₂³	1	4	yes	—
240	C₇×#106	C₂³	1	4	yes	—
241	C₇×#106	C₂³	1	4	yes	—
242	C₇×#103	C₂³	1	4	yes	—
243	C₇×#103	C₂³	1	4	yes	—
244	C₇×#103	C₂³	1	4	yes	—
245	C₇×#103	C₂³	1	4	yes	—
246	C₇×#102	C₂³	1	4	yes	—
247	C₇×#102	C₂³	1	4	yes	—
248	C₇×#102	C₂³	1	4	yes	—
249	C₇×#102	C₂³	1	4	yes	—
250	C₇×#97	C₂³	1	2	yes	—
251	C₇×#97	C₂³	1	2	yes	—
252	C₇×#97	C₂³	1	4	yes	—
253	C₄×C₇×C₈	C₂³	1	2	yes	—
254	C₄×C₇×C₈	C₂³	1	2	yes	—
255	C₄×C₇×C₈	C₂³	1	4	yes	—
256	#3444	C₂×C₇	1	1	yes	characteristic, complemented
257	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
258	#3183	C₂×C₇	1	4	yes	complemented
259	#3181	C₂×C₇	1	2	yes	complemented
260	#3180	C₂×C₇	1	2	yes	complemented
261	#3172	C₂×C₇	1	2	yes	complemented
262	#3171	C₂×C₇	1	2	yes	complemented
263	#3168	C₂×C₇	1	4	yes	complemented
264	#3166	C₂×C₇	1	1	yes	characteristic, complemented
265	#3153	C₂×C₇	1	1	yes	characteristic, complemented
266	#3142	C₂×C₇	1	1	yes	characteristic, complemented
267	#3140	C₂×C₇	1	1	yes	characteristic, complemented
268	#3056	C₂×C₇	1	2	yes	complemented
269	#3055	C₂×C₇	1	2	yes	complemented
270	C₄×#137	C₂×C₇	1	2	yes	complemented
271	C₄×AGL(1,ℤ/8)	C₂×C₇	1	2	yes	complemented
272	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
273	C₂⁴×C₇	—	2	1	no	—
274	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
275	C₇×#41	—	2	4	no	—
276	C₇×#41	—	2	4	no	—
277	C₇×#41	—	4	4	no	—
278	C₇×#41	—	4	4	no	—
279	C₂×C₇×Q₈	—	2	1	no	—
280	C₂×C₇×Q₈	—	2	1	no	—
281	C₂×C₇×Q₈	—	2	1	no	—
282	C₂×C₇×Q₈	—	2	4	no	—
283	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
284	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
285	C₂×C₇×D₄	—	2	2	no	—
286	C₂×C₇×D₄	—	2	2	no	—
287	C₂×C₇×D₄	—	2	2	no	—
288	C₂×C₇×D₄	—	2	2	no	—
289	C₂×C₇×D₄	—	2	2	no	—
290	C₂×C₇×D₄	—	2	1	no	—
291	C₂×C₇×D₄	—	2	1	no	—
292	C₂×C₇×D₄	—	2	1	no	—
293	C₂×C₇×D₄	—	2	4	no	—
294	C₂×C₇×D₄	—	4	4	no	—
295	C₂×C₇×D₄	C₂⁴	1	2	yes	—
296	C₂×C₇×D₄	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₇	—	2	4	no	—
298	C₂²×C₄×C₇	—	2	1	no	—
299	C₂²×C₄×C₇	—	2	1	no	—
300	C₂²×C₄×C₇	—	2	1	no	—
301	C₂²×C₄×C₇	—	2	2	no	—
302	C₂²×C₄×C₇	—	2	2	no	—
303	C₂²×C₄×C₇	—	2	2	no	—
304	C₂²×C₄×C₇	—	2	2	no	—
305	C₂²×C₄×C₇	—	2	2	no	—
306	C₂²×C₄×C₇	—	4	2	no	—
307	C₂²×C₄×C₇	—	4	2	no	—
308	C₂²×C₄×C₇	—	4	4	no	—
309	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
327	C₇×Q₁₆	—	2	8	no	—
328	C₇×SD₁₆	—	2	8	no	—
329	C₇×SD₁₆	—	2	8	no	—
330	C₇×D₈	—	2	8	no	—
331	C₇×M₁₆	—	2	4	no	—
332	C₇×M₁₆	—	2	8	no	—
333	C₇×M₁₆	#41	1	8	yes	complemented
334	C₂×C₇×C₈	—	2	8	no	—
335	C₂×C₇×C₈	C₂⁴	1	4	yes	—
336	C₂×C₇×C₈	C₂⁴	1	4	yes	—
337	C₇×C₄⋊C₄	—	2	2	no	—
338	C₇×C₄⋊C₄	—	2	2	no	—
339	C₇×C₄⋊C₄	—	2	2	no	—
340	C₇×C₄⋊C₄	—	2	2	no	—
341	C₇×C₄⋊C₄	—	2	2	no	—
342	C₇×C₄⋊C₄	—	2	2	no	—
343	C₇×C₄⋊C₄	—	2	2	no	—
344	C₇×C₄⋊C₄	—	2	2	no	—
345	C₇×C₄⋊C₄	—	2	1	no	—
346	C₇×C₄⋊C₄	—	2	1	no	—
347	C₇×C₄⋊C₄	—	2	1	no	—
348	C₇×C₄⋊C₄	—	2	1	no	—
349	C₇×C₄⋊C₄	—	2	1	no	—
350	C₇×C₄⋊C₄	—	2	1	no	—
351	C₇×C₄⋊C₄	—	2	2	no	—
352	C₇×C₄⋊C₄	—	2	2	no	—
353	C₇×C₄⋊C₄	—	2	2	no	—
354	C₇×C₄⋊C₄	—	2	2	no	—
355	C₇×C₄⋊C₄	—	2	2	no	—
356	C₇×C₄⋊C₄	—	2	2	no	—
357	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
358	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
359	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
360	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
361	C₇×C₂²⋊C₄	—	2	2	no	—
362	C₇×C₂²⋊C₄	—	2	2	no	—
363	C₇×C₂²⋊C₄	—	2	2	no	—
364	C₇×C₂²⋊C₄	—	2	2	no	—
365	C₇×C₂²⋊C₄	—	2	2	no	—
366	C₇×C₂²⋊C₄	—	2	2	no	—
367	C₇×C₂²⋊C₄	—	2	2	no	—
368	C₇×C₂²⋊C₄	—	2	2	no	—
369	C₇×C₂²⋊C₄	—	2	2	no	—
370	C₇×C₂²⋊C₄	—	2	2	no	—
371	C₇×C₂²⋊C₄	—	2	2	no	—
372	C₇×C₂²⋊C₄	—	2	2	no	—
373	C₇×C₂²⋊C₄	—	2	2	no	—
374	C₇×C₂²⋊C₄	—	2	2	no	—
375	C₇×C₂²⋊C₄	—	2	2	no	—
376	C₇×C₂²⋊C₄	—	2	2	no	—
377	C₇×C₂²⋊C₄	—	2	2	no	—
378	C₇×C₂²⋊C₄	—	2	2	no	—
379	C₇×C₂²⋊C₄	—	2	2	no	—
380	C₄²×C₇	—	2	2	no	—
381	C₄²×C₇	—	2	2	no	—
382	C₄²×C₇	—	2	2	no	—
383	C₄²×C₇	—	2	2	no	—
384	C₄²×C₇	—	2	2	no	—
385	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
386	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
387	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
388	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
392	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₇	C₂⁴	1	1	yes	characteristic
398	C₄²×C₇	C₂⁴	1	1	yes	characteristic
399	C₄²×C₇	C₂⁴	1	1	yes	characteristic
400	C₄²×C₇	C₂⁴	1	1	yes	characteristic
401	C₂×#137	C₂²×C₇	1	2	yes	—
402	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
403	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
404	#533	C₂²×C₇	1	1	yes	characteristic
405	#533	C₂²×C₇	1	1	yes	characteristic, complemented
406	#533	C₂²×C₇	1	1	yes	characteristic, complemented
407	#532	C₂²×C₇	1	1	yes	characteristic
408	#532	C₂²×C₇	1	1	yes	characteristic, complemented
409	#532	C₂²×C₇	1	1	yes	characteristic, complemented
410	#529	—	2	1	no	—
411	#529	—	2	1	no	—
412	#529	—	2	1	no	—
413	#529	—	2	1	no	—
414	#529	—	2	1	no	—
415	#529	—	2	1	no	—
416	#529	—	2	1	no	—
417	#529	—	2	1	no	—
418	#529	C₂²×C₇	1	2	yes	—
419	#529	C₂²×C₇	1	2	yes	—
420	#529	C₂²×C₇	1	2	yes	—
421	#529	C₂²×C₇	1	2	yes	—
422	#529	C₂²×C₇	1	2	yes	complemented
423	#529	C₂²×C₇	1	2	yes	complemented
424	C₂×#126	—	2	1	no	—
425	C₂×#125	C₂²×C₇	1	1	yes	characteristic
426	C₂×#124	C₂²×C₇	1	1	yes	characteristic
427	#525	—	2	1	no	—
428	#525	—	2	1	no	—
429	#525	C₂²×C₇	1	2	yes	—
430	C₂×#123	—	2	1	no	—
431	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
432	C₂×#121	C₂²×C₇	1	1	yes	characteristic
433	C₄×#41	—	2	1	no	—
434	C₄×#41	—	2	1	no	—
435	C₄×#41	C₂²×C₇	1	2	yes	—
436	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
437	C₂×C₄×D₄	—	2	1	no	—
438	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
439	C₂×#117	—	2	1	no	—
440	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
441	#501	C₂²×C₇	1	2	yes	complemented
442	#501	C₂²×C₇	1	2	yes	complemented
443	#499	C₂²×C₇	1	4	yes	complemented
444	#497	C₂²×C₇	1	2	yes	complemented
445	#496	C₂²×C₇	1	2	yes	complemented
446	#495	C₂²×C₇	1	4	yes	complemented
447	#491	C₂²×C₇	1	2	yes	complemented
448	#490	C₂²×C₇	1	2	yes	complemented
449	#489	C₂²×C₇	1	2	yes	complemented
450	#489	C₂²×C₇	1	2	yes	complemented
451	#488	C₂²×C₇	1	4	yes	complemented
452	#488	C₂²×C₇	1	4	yes	complemented
453	#470	C₂²×C₇	1	4	yes	complemented
454	#469	C₂²×C₇	1	4	yes	—
455	#468	C₂²×C₇	1	4	yes	—
456	#468	C₂²×C₇	1	4	yes	complemented
457	#467	C₂²×C₇	1	4	yes	complemented
458	#466	C₂²×C₇	1	4	yes	—
459	#465	C₂²×C₇	1	4	yes	—
460	#465	C₂²×C₇	1	4	yes	complemented
461	#442	C₂²×C₇	1	4	yes	complemented
462	#441	C₂²×C₇	1	4	yes	complemented
463	#440	C₂²×C₇	1	4	yes	complemented
464	#440	C₂²×C₇	1	4	yes	complemented
465	C₄×Q₁₆	C₂²×C₇	1	4	yes	complemented
466	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
467	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
468	C₄×D₈	C₂²×C₇	1	4	yes	complemented
469	#428	C₂²×C₇	1	2	yes	—
470	#428	C₂²×C₇	1	2	yes	—
471	#419	C₂²×C₇	1	2	yes	—
472	#418	C₂²×C₇	1	2	yes	—
473	#417	C₂²×C₇	1	2	yes	—
474	#417	C₂²×C₇	1	2	yes	—
475	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
476	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
477	C₄×M₁₆	C₂²×C₇	1	2	yes	—
478	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
479	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
480	C₂×#97	C₂²×C₇	1	2	yes	complemented
481	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
482	C₂³×C₇	—	2	2	no	—
483	C₂³×C₇	—	2	2	no	—
484	C₂³×C₇	—	2	2	no	—
485	C₂³×C₇	—	2	2	no	—
486	C₂³×C₇	—	4	1	no	—
487	C₂³×C₇	—	4	2	no	—
488	C₂³×C₇	—	4	2	no	—
489	C₂³×C₇	—	4	2	no	—
490	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
491	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
492	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
493	C₇×Q₈	—	2	2	no	—
494	C₇×Q₈	—	2	4	no	—
495	C₇×Q₈	—	2	2	no	—
496	C₇×Q₈	—	4	2	no	—
497	C₇×Q₈	—	4	2	no	—
498	C₇×Q₈	—	4	2	no	—
499	C₇×D₄	—	2	2	no	—
500	C₇×D₄	—	2	4	no	—
501	C₇×D₄	—	2	2	no	—
502	C₇×D₄	—	4	2	no	—
503	C₇×D₄	—	4	2	no	—
504	C₇×D₄	—	4	4	no	—
505	C₇×D₄	—	4	4	no	—
506	C₇×D₄	—	4	4	no	—
507	C₇×D₄	—	4	4	no	—
508	C₇×D₄	—	4	4	no	—
509	C₇×D₄	—	4	2	no	—
510	C₂×C₄×C₇	—	2	2	no	—
511	C₂×C₄×C₇	—	2	2	no	—
512	C₂×C₄×C₇	—	2	2	no	—
513	C₂×C₄×C₇	—	2	2	no	—
514	C₂×C₄×C₇	—	2	2	no	—
515	C₂×C₄×C₇	—	2	2	no	—
516	C₂×C₄×C₇	—	2	2	no	—
517	C₂×C₄×C₇	—	2	2	no	—
518	C₂×C₄×C₇	—	2	2	no	—
519	C₂×C₄×C₇	—	2	2	no	—
520	C₂×C₄×C₇	—	2	2	no	—
521	C₂×C₄×C₇	—	2	2	no	—
522	C₂×C₄×C₇	—	2	2	no	—
523	C₂×C₄×C₇	—	2	2	no	—
524	C₂×C₄×C₇	—	2	2	no	—
525	C₂×C₄×C₇	—	2	2	no	—
526	C₂×C₄×C₇	—	4	1	no	—
527	C₂×C₄×C₇	—	4	1	no	—
528	C₂×C₄×C₇	—	4	1	no	—
529	C₂×C₄×C₇	—	4	1	no	—
530	C₂×C₄×C₇	—	4	1	no	—
531	C₂×C₄×C₇	—	4	1	no	—
532	C₂×C₄×C₇	—	4	1	no	—
533	C₂×C₄×C₇	—	4	4	no	—
534	C₂×C₄×C₇	—	4	4	no	—
535	C₂×C₄×C₇	—	4	2	no	—
536	C₂×C₄×C₇	—	4	2	no	—
537	C₂×C₄×C₇	—	4	2	no	—
538	C₂×C₄×C₇	—	4	4	no	—
539	C₂×C₄×C₇	—	4	4	no	—
540	C₂×C₄×C₇	—	4	4	no	—
541	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₇	C₂×#41	1	4	yes	—
553	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
554	C₇×C₈	—	2	4	no	—
555	C₇×C₈	C₂×#41	1	8	yes	—
556	C₂×#41	—	2	1	no	—
557	C₂×#41	—	2	1	no	—
558	C₂×#41	C₂³×C₇	1	2	yes	—
559	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
560	C₂²×D₄	—	2	1	no	—
561	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
562	C₂³×C₄	—	2	1	no	—
563	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
564	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
566	#137	—	2	8	no	—
567	AGL(1,ℤ/8)	—	2	8	no	—
568	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
569	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
570	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
571	C₂×D₈	C₂³×C₇	1	4	yes	—
572	C₂×M₁₆	—	2	8	no	—
573	C₂×M₁₆	C₂³×C₇	1	2	yes	—
574	C₂×M₁₆	C₂³×C₇	1	4	yes	—
575	C₂×M₁₆	C₂³×C₇	1	2	yes	—
576	C₂²×C₈	C₂³×C₇	1	4	yes	—
577	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
578	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
579	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
580	#127	C₂³×C₇	1	1	yes	characteristic
581	#126	—	2	2	no	—
582	#126	—	2	2	no	—
583	#126	—	2	2	no	—
584	#126	—	2	2	no	—
585	#126	—	2	2	no	—
586	#126	—	2	2	no	—
587	#125	—	2	1	no	—
588	#125	—	2	1	no	—
589	#125	—	2	1	no	—
590	#125	—	2	1	no	—
591	#125	C₂³×C₇	1	2	yes	—
592	#125	C₂³×C₇	1	2	yes	—
593	#125	C₂³×C₇	1	2	yes	—
594	#124	—	2	1	no	—
595	#124	—	2	1	no	—
596	#124	—	2	1	no	—
597	#124	—	2	1	no	—
598	#124	C₂³×C₇	1	2	yes	—
599	#124	C₂³×C₇	1	2	yes	—
600	#124	C₂³×C₇	1	2	yes	—
601	#123	—	2	2	no	—
602	#123	—	2	2	no	—
603	#123	—	2	2	no	—
604	#123	—	2	2	no	—
605	#123	—	2	2	no	—
606	#123	—	2	2	no	—
607	#123	—	2	2	no	—
608	C₂²⋊Q₈	—	2	1	no	—
609	C₂²⋊Q₈	—	2	1	no	—
610	C₂²⋊Q₈	—	2	1	no	—
611	C₂²⋊Q₈	—	2	1	no	—
612	C₂²⋊Q₈	—	2	1	no	—
613	C₂²⋊Q₈	—	2	1	no	—
614	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
615	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
616	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
617	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
618	#121	—	2	1	no	—
619	#121	—	2	1	no	—
620	#121	—	2	1	no	—
621	#121	—	2	1	no	—
622	#121	—	2	1	no	—
623	#121	—	2	1	no	—
624	#121	C₂³×C₇	1	2	yes	—
625	#121	C₂³×C₇	1	2	yes	—
626	#121	C₂³×C₇	1	2	yes	—
627	#121	C₂³×C₇	1	2	yes	—
628	#120	—	2	2	no	—
629	C₄×Q₈	—	2	1	no	—
630	C₄×Q₈	—	2	1	no	—
631	C₄×Q₈	—	2	1	no	—
632	C₄×Q₈	—	2	1	no	—
633	C₄×Q₈	—	2	1	no	—
634	C₄×Q₈	—	2	1	no	—
635	C₄×Q₈	C₂³×C₇	1	2	yes	—
636	C₄×Q₈	C₂³×C₇	1	2	yes	—
637	C₄×Q₈	C₂³×C₇	1	2	yes	—
638	C₄×Q₈	C₂³×C₇	1	2	yes	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	—	2	1	no	—
651	C₄×D₄	—	2	1	no	—
652	C₄×D₄	—	2	1	no	—
653	C₄×D₄	—	2	1	no	—
654	C₄×D₄	—	2	1	no	—
655	C₄×D₄	C₂³×C₇	1	2	yes	—
656	C₄×D₄	C₂³×C₇	1	2	yes	—
657	C₄×D₄	C₂³×C₇	1	2	yes	—
658	C₄×D₄	C₂³×C₇	1	2	yes	—
659	#117	—	2	1	no	—
660	#117	—	2	1	no	—
661	#117	—	2	2	no	—
662	#117	—	2	2	no	—
663	#117	—	2	2	no	—
664	#117	—	2	2	no	—
665	#117	—	2	2	no	—
666	#117	—	2	2	no	—
667	#117	—	2	2	no	—
668	#117	C₂³×C₇	1	2	yes	—
669	C₂×C₄⋊C₄	—	2	1	no	—
670	C₂×C₄⋊C₄	—	2	1	no	—
671	C₂×C₄⋊C₄	—	2	1	no	—
672	C₂×C₄⋊C₄	—	2	1	no	—
673	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	—	2	1	no	—
676	C₂×C₂²⋊C₄	—	2	1	no	—
677	C₂×C₂²⋊C₄	—	2	1	no	—
678	C₂×C₂²⋊C₄	—	2	1	no	—
679	C₂×C₂²⋊C₄	—	2	1	no	—
680	C₂×C₄²	—	2	1	no	—
681	C₂×C₄²	—	2	2	no	—
682	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
683	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
684	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
685	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
686	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
687	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
694	#107	C₂³×C₇	1	4	yes	—
695	#107	C₂³×C₇	1	4	yes	—
696	#106	C₂³×C₇	1	4	yes	—
697	#106	C₂³×C₇	1	4	yes	—
698	#103	C₂³×C₇	1	4	yes	—
699	#103	C₂³×C₇	1	4	yes	—
700	#103	C₂³×C₇	1	4	yes	—
701	#103	C₂³×C₇	1	4	yes	—
702	#102	C₂³×C₇	1	4	yes	—
703	#102	C₂³×C₇	1	4	yes	—
704	#102	C₂³×C₇	1	4	yes	—
705	#102	C₂³×C₇	1	4	yes	—
706	#97	C₂³×C₇	1	4	yes	—
707	#97	C₂³×C₇	1	2	yes	—
708	#97	C₂³×C₇	1	2	yes	—
709	C₄×C₈	C₂³×C₇	1	4	yes	—
710	C₄×C₈	C₂³×C₇	1	2	yes	—
711	C₄×C₈	C₂³×C₇	1	2	yes	—
712	C₂²×C₇	—	2	1	no	—
713	C₂²×C₇	—	2	1	no	—
714	C₂²×C₇	—	2	1	no	—
715	C₂²×C₇	—	2	1	no	—
716	C₂²×C₇	—	2	1	no	—
717	C₂²×C₇	—	2	1	no	—
718	C₂²×C₇	—	2	1	no	—
719	C₂²×C₇	—	4	4	no	—
720	C₂²×C₇	—	4	2	no	—
721	C₂²×C₇	—	4	2	no	—
722	C₂²×C₇	—	4	2	no	—
723	C₂²×C₇	—	4	2	no	—
724	C₂²×C₇	—	4	2	no	—
725	C₂²×C₇	—	4	2	no	—
726	C₂²×C₇	—	8	4	no	—
727	C₂²×C₇	#532	1	2	yes	—
728	C₂²×C₇	#575	1	2	yes	—
729	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
730	C₄×C₇	—	2	1	no	—
731	C₄×C₇	—	2	1	no	—
732	C₄×C₇	—	2	1	no	—
733	C₄×C₇	—	2	1	no	—
734	C₄×C₇	—	2	1	no	—
735	C₄×C₇	—	2	1	no	—
736	C₄×C₇	—	2	1	no	—
737	C₄×C₇	—	2	1	no	—
738	C₄×C₇	—	2	1	no	—
739	C₄×C₇	—	4	2	no	—
740	C₄×C₇	—	4	2	no	—
741	C₄×C₇	—	4	2	no	—
742	C₄×C₇	—	4	2	no	—
743	C₄×C₇	—	4	2	no	—
744	C₄×C₇	—	4	2	no	—
745	C₄×C₇	#532	1	2	yes	—
746	C₄×C₇	#575	1	2	yes	—
747	C₄×C₇	C₂²×#41	1	2	yes	—
748	C₂⁴	—	2	1	no	—
749	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
750	#41	—	2	4	no	—
751	#41	—	2	4	no	—
752	#41	—	4	4	no	—
753	#41	—	4	4	no	—
754	C₂×Q₈	—	2	1	no	—
755	C₂×Q₈	—	2	1	no	—
756	C₂×Q₈	—	2	1	no	—
757	C₂×Q₈	—	2	4	no	—
758	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
759	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	—	2	1	no	—
767	C₂×D₄	—	2	1	no	—
768	C₂×D₄	—	2	4	no	—
769	C₂×D₄	—	4	4	no	—
770	C₂×D₄	C₂⁴×C₇	1	2	yes	—
771	C₂×D₄	C₂⁴×C₇	1	2	yes	—
772	C₂²×C₄	—	2	4	no	—
773	C₂²×C₄	—	2	1	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	2	1	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	4	2	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	—	4	4	no	—
784	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
785	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
786	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
787	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
788	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
789	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
790	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
791	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
792	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
793	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
794	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
795	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
796	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
797	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
798	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
801	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
802	Q₁₆	—	2	8	no	—
803	SD₁₆	—	2	8	no	—
804	SD₁₆	—	2	8	no	—
805	D₈	—	2	8	no	—
806	M₁₆	—	2	4	no	—
807	M₁₆	—	2	8	no	—
808	M₁₆	C₇×#41	1	8	yes	complemented
809	C₂×C₈	—	2	8	no	—
810	C₂×C₈	C₂⁴×C₇	1	4	yes	—
811	C₂×C₈	C₂⁴×C₇	1	4	yes	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	1	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
833	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
834	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
835	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₄²	—	2	2	no	—
856	C₄²	—	2	2	no	—
857	C₄²	—	2	2	no	—
858	C₄²	—	2	2	no	—
859	C₄²	—	2	2	no	—
860	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
861	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
862	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
863	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
864	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
865	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
866	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
867	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
868	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
869	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
870	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
871	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
872	C₄²	C₂⁴×C₇	1	1	yes	characteristic
873	C₄²	C₂⁴×C₇	1	1	yes	characteristic
874	C₄²	C₂⁴×C₇	1	1	yes	characteristic
875	C₄²	C₂⁴×C₇	1	1	yes	characteristic
876	C₂×C₇	—	2	2	no	—
877	C₂×C₇	—	2	2	no	—
878	C₂×C₇	—	4	1	no	—
879	C₂×C₇	—	8	2	no	—
880	C₂×C₇	—	8	2	no	—
881	C₂×C₇	C₂×#532	1	1	yes	characteristic
882	C₂×C₇	C₂×#575	1	1	yes	characteristic
883	C₂×C₇	C₂×#575	1	1	yes	characteristic
884	C₂³	—	2	2	no	—
885	C₂³	—	2	2	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	4	1	no	—
889	C₂³	—	4	2	no	—
890	C₂³	—	4	2	no	—
891	C₂³	—	4	2	no	—
892	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
893	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
894	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
895	Q₈	—	2	2	no	—
896	Q₈	—	2	4	no	—
897	Q₈	—	2	2	no	—
898	Q₈	—	4	2	no	—
899	Q₈	—	4	2	no	—
900	Q₈	—	4	2	no	—
901	D₄	—	2	2	no	—
902	D₄	—	2	4	no	—
903	D₄	—	2	2	no	—
904	D₄	—	4	2	no	—
905	D₄	—	4	2	no	—
906	D₄	—	4	4	no	—
907	D₄	—	4	4	no	—
908	D₄	—	4	4	no	—
909	D₄	—	4	4	no	—
910	D₄	—	4	4	no	—
911	D₄	—	4	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	4	1	no	—
929	C₂×C₄	—	4	1	no	—
930	C₂×C₄	—	4	1	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	1	no	—
935	C₂×C₄	—	4	4	no	—
936	C₂×C₄	—	4	4	no	—
937	C₂×C₄	—	4	2	no	—
938	C₂×C₄	—	4	2	no	—
939	C₂×C₄	—	4	2	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	4	4	no	—
942	C₂×C₄	—	4	4	no	—
943	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
944	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
945	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
946	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
947	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
948	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
949	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
950	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
951	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
952	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
953	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
954	C₂×C₄	C₂×C₇×#41	1	4	yes	—
955	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
956	C₈	—	2	4	no	—
957	C₈	C₂×C₇×#41	1	8	yes	—
958	C₇	#60702	1	1	yes	characteristic, direct product factor, Sylow
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	1	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	1	no	—
965	C₂²	—	2	1	no	—
966	C₂²	—	4	4	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	8	4	no	—
974	C₂²	C₇×#532	1	2	yes	—
975	C₂²	C₇×#575	1	2	yes	—
976	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
977	C₄	—	2	1	no	—
978	C₄	—	2	1	no	—
979	C₄	—	2	1	no	—
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	2	no	—
992	C₄	C₇×#532	1	2	yes	—
993	C₄	C₇×#575	1	2	yes	—
994	C₄	C₂²×C₇×#41	1	2	yes	—
995	C₂	—	2	2	no	—
996	C₂	—	2	2	no	—
997	C₂	—	4	1	no	—
998	C₂	—	8	2	no	—
999	C₂	—	8	2	no	—
1000	C₂	C₂×C₇×#532	1	1	yes	characteristic
1001	C₂	C₂×C₇×#575	1	1	yes	characteristic
1002	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×#529	C₂	semidirect
3. C₇×#3183	C₂	semidirect
4. C₇×#3181	C₂	semidirect
5. C₇×#3180	C₂	semidirect
6. C₇×#3172	C₂	semidirect
7. C₇×#3171	C₂	semidirect
8. C₇×#3168	C₂	semidirect
9. C₇×#3166	C₂	semidirect
10. C₇×#3153	C₂	semidirect
11. C₇×#3142	C₂	semidirect
12. C₇×#3140	C₂	semidirect
13. C₇×#3056	C₂	semidirect
14. C₇×#3055	C₂	semidirect
15. C₄×C₇×#137	C₂	semidirect
16. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
17. C₂×C₄×C₇×M₁₆	C₂	semidirect
22. C₇×#533	C₂²	semidirect
23. C₇×#533	C₂²	semidirect
25. C₇×#532	C₂²	semidirect
26. C₇×#532	C₂²	semidirect
39. C₇×#529	C₂²	semidirect
40. C₇×#529	C₂²	semidirect
58. C₇×#501	C₂²	semidirect
59. C₇×#501	C₂²	semidirect
60. C₇×#499	C₂²	semidirect
61. C₇×#497	C₂²	semidirect
62. C₇×#496	C₂²	semidirect
63. C₇×#495	C₂²	semidirect
64. C₇×#491	C₂²	semidirect
65. C₇×#490	C₂²	semidirect
66. C₇×#489	C₂²	semidirect
67. C₇×#489	C₂²	semidirect
68. C₇×#488	C₂²	semidirect
69. C₇×#488	C₂²	semidirect
70. C₇×#470	C₂²	semidirect
73. C₇×#468	C₂²	semidirect
74. C₇×#467	C₂²	semidirect
77. C₇×#465	C₂²	semidirect
78. C₇×#442	C₂²	semidirect
79. C₇×#441	C₂²	semidirect
80. C₇×#440	C₂²	semidirect
81. C₇×#440	C₂²	semidirect
82. C₄×C₇×Q₁₆	C₂²	semidirect
83. C₄×C₇×SD₁₆	C₂²	semidirect
84. C₄×C₇×SD₁₆	C₂²	semidirect
85. C₄×C₇×D₈	C₂²	semidirect
95. C₄×C₇×M₁₆	C₂²	semidirect
96. C₄×C₇×M₁₆	C₂²	semidirect
97. C₂×C₇×#97	C₂²	semidirect
98. C₂×C₄×C₇×C₈	C₂²	semidirect
99. #60702	C₇	direct (N × H)
256. #3444	C₂×C₇	semidirect
257. C₂×#529	C₂×C₇	semidirect
258. #3183	C₂×C₇	semidirect
259. #3181	C₂×C₇	semidirect
260. #3180	C₂×C₇	semidirect
261. #3172	C₂×C₇	semidirect
262. #3171	C₂×C₇	semidirect
263. #3168	C₂×C₇	semidirect
264. #3166	C₂×C₇	semidirect
265. #3153	C₂×C₇	semidirect
266. #3142	C₂×C₇	semidirect
267. #3140	C₂×C₇	semidirect
268. #3056	C₂×C₇	semidirect
269. #3055	C₂×C₇	semidirect
270. C₄×#137	C₂×C₇	semidirect
271. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
272. C₂×C₄×M₁₆	C₂×C₇	semidirect
333. C₇×M₁₆	#41	semidirect
405. #533	C₂²×C₇	semidirect
406. #533	C₂²×C₇	semidirect
408. #532	C₂²×C₇	semidirect
409. #532	C₂²×C₇	semidirect
422. #529	C₂²×C₇	semidirect
423. #529	C₂²×C₇	semidirect
441. #501	C₂²×C₇	semidirect
442. #501	C₂²×C₇	semidirect
443. #499	C₂²×C₇	semidirect
444. #497	C₂²×C₇	semidirect
445. #496	C₂²×C₇	semidirect
446. #495	C₂²×C₇	semidirect
447. #491	C₂²×C₇	semidirect
448. #490	C₂²×C₇	semidirect
449. #489	C₂²×C₇	semidirect
450. #489	C₂²×C₇	semidirect
451. #488	C₂²×C₇	semidirect
452. #488	C₂²×C₇	semidirect
453. #470	C₂²×C₇	semidirect
456. #468	C₂²×C₇	semidirect
457. #467	C₂²×C₇	semidirect
460. #465	C₂²×C₇	semidirect
461. #442	C₂²×C₇	semidirect
462. #441	C₂²×C₇	semidirect
463. #440	C₂²×C₇	semidirect
464. #440	C₂²×C₇	semidirect
465. C₄×Q₁₆	C₂²×C₇	semidirect
466. C₄×SD₁₆	C₂²×C₇	semidirect
467. C₄×SD₁₆	C₂²×C₇	semidirect
468. C₄×D₈	C₂²×C₇	semidirect
478. C₄×M₁₆	C₂²×C₇	semidirect
479. C₄×M₁₆	C₂²×C₇	semidirect
480. C₂×#97	C₂²×C₇	semidirect
481. C₂×C₄×C₈	C₂²×C₇	semidirect
808. M₁₆	C₇×#41	semidirect
958. C₇	#60702	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×#529	2
C₇×#3183	2
C₇×#3181	2
C₇×#3180	2
C₇×#3172	2
C₇×#3171	2
C₇×#3168	2
C₇×#3166	2
C₇×#3153	2
C₇×#3142	2
C₇×#3140	2
C₇×#3056	2
C₇×#3055	2
C₄×C₇×#137	2
C₄×C₇×AGL(1,ℤ/8)	2
C₂×C₄×C₇×M₁₆	2
#60702	7

Subgroups — C7×#60702 #13237918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60702 #13237918