Subgroups — C₇×#60559 #13237775

Order 1792.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1044 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×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3116	C₂	1	2	yes	maximal, complemented
4	C₇×#3115	C₂	1	2	yes	maximal, complemented
5	C₇×#3111	C₂	1	4	yes	maximal, complemented
6	C₇×#3107	C₂	1	2	yes	maximal, complemented
7	C₇×#3106	C₂	1	2	yes	maximal, complemented
8	C₇×#3102	C₂	1	4	yes	maximal, complemented
9	C₇×#3093	C₂	1	2	yes	maximal, complemented
10	C₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3005	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	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
19	C₂×C₇×#137	C₂²	1	2	yes	—
20	C₂×C₇×AGL(1,ℤ/8)	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	C₂²	1	2	yes	complemented
32	C₇×#529	C₂²	1	2	yes	complemented
33	C₇×#525	—	2	1	no	—
34	C₇×#525	—	2	1	no	—
35	C₇×#525	C₂²	1	2	yes	—
36	C₄×C₇×#41	—	2	1	no	—
37	C₄×C₇×#41	—	2	1	no	—
38	C₄×C₇×#41	—	2	1	no	—
39	C₄×C₇×#41	—	2	1	no	—
40	C₄×C₇×#41	—	2	1	no	—
41	C₄×C₇×#41	—	2	1	no	—
42	C₄×C₇×#41	C₂²	1	2	yes	—
43	C₄×C₇×#41	C₂²	1	2	yes	—
44	C₄×C₇×#41	C₂²	1	2	yes	—
45	C₄×C₇×#41	C₂²	1	2	yes	—
46	C₄×C₇×#41	C₂²	1	2	yes	—
47	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₇×D₄	—	2	1	no	—
50	C₂×C₄×C₇×D₄	—	2	1	no	—
51	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
53	C₂×C₇×#117	—	2	1	no	—
54	C₂×C₇×#117	C₂²	1	1	yes	characteristic
55	C₂²×C₄²×C₇	—	2	1	no	—
56	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
57	C₇×#485	C₂²	1	4	yes	complemented
58	C₇×#485	C₂²	1	4	yes	complemented
59	C₇×#482	C₂²	1	4	yes	complemented
60	C₇×#482	C₂²	1	4	yes	complemented
61	C₇×#479	C₂²	1	4	yes	complemented
62	C₇×#478	C₂²	1	4	yes	complemented
63	C₇×#477	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×#464	C₂²	1	4	yes	complemented
68	C₇×#463	C₂²	1	4	yes	complemented
69	C₇×#462	C₂²	1	2	yes	complemented
70	C₇×#461	C₂²	1	2	yes	complemented
71	C₇×#460	C₂²	1	2	yes	complemented
72	C₇×#459	C₂²	1	2	yes	complemented
73	C₇×#452	C₂²	1	4	yes	—
74	C₇×#452	C₂²	1	4	yes	—
75	C₇×#449	C₂²	1	4	yes	—
76	C₇×#449	C₂²	1	4	yes	—
77	C₇×#442	C₂²	1	4	yes	complemented
78	C₇×#441	C₂²	1	4	yes	complemented
79	C₇×#440	C₂²	1	4	yes	complemented
80	C₇×#440	C₂²	1	4	yes	complemented
81	C₄×C₇×Q₁₆	C₂²	1	4	yes	complemented
82	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
83	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
84	C₄×C₇×D₈	C₂²	1	4	yes	complemented
85	C₇×#432	C₂²	1	2	yes	complemented
86	C₇×#432	C₂²	1	2	yes	complemented
87	C₇×#431	C₂²	1	2	yes	complemented
88	C₇×#431	C₂²	1	2	yes	complemented
89	C₇×#428	C₂²	1	2	yes	—
90	C₇×#428	C₂²	1	2	yes	—
91	C₇×#423	C₂²	1	1	yes	characteristic
92	C₇×#423	C₂²	1	1	yes	characteristic
93	C₇×#419	C₂²	1	2	yes	—
94	C₇×#418	C₂²	1	2	yes	—
95	C₇×#417	C₂²	1	2	yes	—
96	C₇×#417	C₂²	1	2	yes	—
97	C₇×#407	C₂²	1	2	yes	—
98	C₄×C₇×M₁₆	C₂²	1	2	yes	—
99	#60559	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂×C₇×#41	—	2	4	no	—
101	C₂×C₇×#41	—	2	4	no	—
102	C₂×C₇×#41	—	2	1	no	—
103	C₂×C₇×#41	—	2	1	no	—
104	C₂×C₇×#41	—	2	1	no	—
105	C₂×C₇×#41	—	2	1	no	—
106	C₂×C₇×#41	C₂³	1	2	yes	—
107	C₂×C₇×#41	C₂³	1	2	yes	—
108	C₂×C₇×#41	C₂³	1	2	yes	—
109	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
110	C₂²×C₇×D₄	—	2	1	no	—
111	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₇	—	2	1	no	—
113	C₂³×C₄×C₇	—	2	1	no	—
114	C₂³×C₄×C₇	—	2	1	no	—
115	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
116	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
117	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
118	C₇×#137	—	2	8	no	—
119	C₇×AGL(1,ℤ/8)	—	2	8	no	—
120	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
121	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
122	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
123	C₂×C₇×D₈	C₂³	1	4	yes	—
124	C₂×C₇×M₁₆	C₂³	1	2	yes	—
125	C₂×C₇×M₁₆	C₂³	1	2	yes	—
126	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
129	C₇×#127	C₂³	1	1	yes	characteristic
130	C₇×#126	—	2	2	no	—
131	C₇×#126	—	2	2	no	—
132	C₇×#125	—	2	1	no	—
133	C₇×#125	—	2	1	no	—
134	C₇×#125	C₂³	1	2	yes	—
135	C₇×#124	—	2	1	no	—
136	C₇×#124	—	2	1	no	—
137	C₇×#124	C₂³	1	2	yes	—
138	C₇×#123	—	2	2	no	—
139	C₇×#123	—	2	2	no	—
140	C₇×#123	—	2	2	no	—
141	C₇×C₂²⋊Q₈	—	2	1	no	—
142	C₇×C₂²⋊Q₈	—	2	1	no	—
143	C₇×C₂²⋊Q₈	—	2	1	no	—
144	C₇×C₂²⋊Q₈	—	2	1	no	—
145	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₇×#121	—	2	1	no	—
148	C₇×#121	—	2	1	no	—
149	C₇×#121	—	2	1	no	—
150	C₇×#121	—	2	1	no	—
151	C₇×#121	C₂³	1	2	yes	—
152	C₇×#121	C₂³	1	2	yes	—
153	C₇×#120	—	2	2	no	—
154	C₄×C₇×Q₈	—	2	1	no	—
155	C₄×C₇×Q₈	—	2	1	no	—
156	C₄×C₇×Q₈	—	2	1	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	—	2	1	no	—
162	C₄×C₇×Q₈	C₂³	1	2	yes	—
163	C₄×C₇×Q₈	C₂³	1	2	yes	—
164	C₄×C₇×Q₈	C₂³	1	2	yes	—
165	C₄×C₇×Q₈	C₂³	1	2	yes	—
166	C₄×C₇×Q₈	C₂³	1	2	yes	—
167	C₄×C₇×Q₈	C₂³	1	2	yes	—
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	2	no	—
176	C₄×C₇×D₄	—	2	2	no	—
177	C₄×C₇×D₄	—	2	2	no	—
178	C₄×C₇×D₄	—	2	2	no	—
179	C₄×C₇×D₄	—	2	2	no	—
180	C₄×C₇×D₄	—	2	2	no	—
181	C₄×C₇×D₄	—	2	2	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	1	no	—
186	C₄×C₇×D₄	—	2	1	no	—
187	C₄×C₇×D₄	—	2	1	no	—
188	C₄×C₇×D₄	—	2	1	no	—
189	C₄×C₇×D₄	—	2	1	no	—
190	C₄×C₇×D₄	C₂³	1	2	yes	—
191	C₄×C₇×D₄	C₂³	1	2	yes	—
192	C₄×C₇×D₄	C₂³	1	2	yes	—
193	C₄×C₇×D₄	C₂³	1	2	yes	—
194	C₄×C₇×D₄	C₂³	1	2	yes	—
195	C₄×C₇×D₄	C₂³	1	2	yes	—
196	C₇×#117	—	2	1	no	—
197	C₇×#117	—	2	1	no	—
198	C₇×#117	—	2	1	no	—
199	C₇×#117	—	2	1	no	—
200	C₇×#117	—	2	2	no	—
201	C₇×#117	—	2	2	no	—
202	C₇×#117	—	2	2	no	—
203	C₇×#117	—	2	2	no	—
204	C₇×#117	—	2	2	no	—
205	C₇×#117	—	2	2	no	—
206	C₇×#117	—	2	2	no	—
207	C₇×#117	C₂³	1	2	yes	—
208	C₇×#117	C₂³	1	2	yes	—
209	C₇×#117	C₂³	1	2	yes	—
210	C₂×C₇×C₄⋊C₄	—	2	1	no	—
211	C₂×C₇×C₄⋊C₄	—	2	1	no	—
212	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
215	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
216	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
217	C₂×C₄²×C₇	—	2	1	no	—
218	C₂×C₄²×C₇	—	2	1	no	—
219	C₂×C₄²×C₇	—	2	1	no	—
220	C₂×C₄²×C₇	—	2	2	no	—
221	C₂×C₄²×C₇	—	2	2	no	—
222	C₂×C₄²×C₇	—	2	2	no	—
223	C₂×C₄²×C₇	—	2	2	no	—
224	C₂×C₄²×C₇	—	2	2	no	—
225	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
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	C₂³	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	C₇×#107	C₂³	1	4	yes	—
238	C₇×#107	C₂³	1	4	yes	—
239	C₇×#106	C₂³	1	4	yes	—
240	C₇×#106	C₂³	1	4	yes	—
241	C₇×C₄⋊C₈	C₂³	1	2	yes	—
242	C₇×C₄⋊C₈	C₂³	1	2	yes	—
243	C₇×C₄⋊C₈	C₂³	1	2	yes	—
244	C₇×C₄⋊C₈	C₂³	1	2	yes	—
245	C₇×#103	C₂³	1	4	yes	—
246	C₇×#103	C₂³	1	4	yes	—
247	C₇×#103	C₂³	1	4	yes	—
248	C₇×#103	C₂³	1	4	yes	—
249	C₇×#102	C₂³	1	4	yes	—
250	C₇×#102	C₂³	1	4	yes	—
251	C₇×#102	C₂³	1	4	yes	—
252	C₇×#102	C₂³	1	4	yes	—
253	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
254	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
255	C₇×#97	C₂³	1	4	yes	—
256	C₄×C₇×C₈	C₂³	1	4	yes	—
257	#3444	C₂×C₇	1	1	yes	characteristic, complemented
258	C₂×C₄×#41	C₂×C₇	1	1	yes	characteristic, complemented
259	#3116	C₂×C₇	1	2	yes	complemented
260	#3115	C₂×C₇	1	2	yes	complemented
261	#3111	C₂×C₇	1	4	yes	complemented
262	#3107	C₂×C₇	1	2	yes	complemented
263	#3106	C₂×C₇	1	2	yes	complemented
264	#3102	C₂×C₇	1	4	yes	complemented
265	#3093	C₂×C₇	1	2	yes	complemented
266	#3078	C₂×C₇	1	1	yes	characteristic, complemented
267	#3077	C₂×C₇	1	1	yes	characteristic, complemented
268	#3037	C₂×C₇	1	1	yes	characteristic, complemented
269	#3036	C₂×C₇	1	1	yes	characteristic, complemented
270	#3005	C₂×C₇	1	2	yes	complemented
271	C₄×#137	C₂×C₇	1	2	yes	complemented
272	C₄×AGL(1,ℤ/8)	C₂×C₇	1	2	yes	complemented
273	#2920	C₂×C₇	1	1	yes	characteristic, complemented
274	C₂⁴×C₇	—	2	1	no	—
275	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
276	C₇×#41	—	2	8	no	—
277	C₇×#41	—	2	8	no	—
278	C₇×#41	—	2	4	no	—
279	C₇×#41	—	2	4	no	—
280	C₇×#41	—	2	4	no	—
281	C₇×#41	—	2	4	no	—
282	C₇×#41	—	2	4	no	—
283	C₇×#41	—	2	4	no	—
284	C₇×#41	—	4	4	no	—
285	C₇×#41	—	4	4	no	—
286	C₂×C₇×Q₈	—	2	1	no	—
287	C₂×C₇×Q₈	—	2	1	no	—
288	C₂×C₇×Q₈	—	2	1	no	—
289	C₂×C₇×Q₈	—	2	2	no	—
290	C₂×C₇×Q₈	#41	1	4	yes	complemented
291	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
292	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
293	C₂×C₇×D₄	—	2	8	no	—
294	C₂×C₇×D₄	—	2	2	no	—
295	C₂×C₇×D₄	—	2	2	no	—
296	C₂×C₇×D₄	—	2	2	no	—
297	C₂×C₇×D₄	—	2	2	no	—
298	C₂×C₇×D₄	—	2	2	no	—
299	C₂×C₇×D₄	—	2	1	no	—
300	C₂×C₇×D₄	—	2	1	no	—
301	C₂×C₇×D₄	—	2	1	no	—
302	C₂×C₇×D₄	—	2	2	no	—
303	C₂×C₇×D₄	#41	1	4	yes	complemented
304	C₂×C₇×D₄	C₂⁴	1	2	yes	—
305	C₂×C₇×D₄	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₇	—	2	8	no	—
307	C₂²×C₄×C₇	—	2	1	no	—
308	C₂²×C₄×C₇	—	2	2	no	—
309	C₂²×C₄×C₇	—	2	2	no	—
310	C₂²×C₄×C₇	—	2	2	no	—
311	C₂²×C₄×C₇	—	2	2	no	—
312	C₂²×C₄×C₇	—	2	1	no	—
313	C₂²×C₄×C₇	—	2	1	no	—
314	C₂²×C₄×C₇	—	2	2	no	—
315	C₂²×C₄×C₇	—	2	2	no	—
316	C₂²×C₄×C₇	—	2	2	no	—
317	C₂²×C₄×C₇	—	2	2	no	—
318	C₂²×C₄×C₇	—	2	2	no	—
319	C₂²×C₄×C₇	—	2	2	no	—
320	C₂²×C₄×C₇	—	2	2	no	—
321	C₂²×C₄×C₇	—	4	2	no	—
322	C₂²×C₄×C₇	—	4	2	no	—
323	C₂²×C₄×C₇	—	4	4	no	—
324	C₂²×C₄×C₇	—	4	4	no	—
325	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
343	C₇×Q₁₆	—	2	8	no	—
344	C₇×SD₁₆	—	2	8	no	—
345	C₇×SD₁₆	—	2	8	no	—
346	C₇×D₈	—	2	8	no	—
347	C₇×M₁₆	—	2	4	no	—
348	C₇×M₁₆	—	2	4	no	—
349	C₂×C₇×C₈	C₂⁴	1	4	yes	—
350	C₂×C₇×C₈	C₂⁴	1	4	yes	—
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	1	no	—
356	C₇×C₄⋊C₄	—	2	1	no	—
357	C₇×C₄⋊C₄	—	2	1	no	—
358	C₇×C₄⋊C₄	—	2	1	no	—
359	C₇×C₄⋊C₄	—	2	1	no	—
360	C₇×C₄⋊C₄	—	2	1	no	—
361	C₇×C₄⋊C₄	—	2	2	no	—
362	C₇×C₄⋊C₄	—	2	2	no	—
363	C₇×C₄⋊C₄	—	2	2	no	—
364	C₇×C₄⋊C₄	—	2	2	no	—
365	C₇×C₄⋊C₄	—	2	2	no	—
366	C₇×C₄⋊C₄	—	2	2	no	—
367	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
368	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
369	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
370	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
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	C₇×C₂²⋊C₄	—	2	2	no	—
381	C₇×C₂²⋊C₄	—	2	2	no	—
382	C₇×C₂²⋊C₄	—	2	2	no	—
383	C₇×C₂²⋊C₄	—	2	2	no	—
384	C₇×C₂²⋊C₄	—	2	2	no	—
385	C₇×C₂²⋊C₄	—	2	2	no	—
386	C₄²×C₇	—	2	2	no	—
387	C₄²×C₇	—	2	2	no	—
388	C₄²×C₇	—	2	2	no	—
389	C₄²×C₇	—	2	2	no	—
390	C₄²×C₇	—	2	2	no	—
391	C₄²×C₇	—	2	2	no	—
392	C₄²×C₇	—	2	2	no	—
393	C₄²×C₇	—	2	2	no	—
394	C₄²×C₇	—	2	2	no	—
395	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
403	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
404	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
405	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
406	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
407	C₄²×C₇	C₂⁴	1	1	yes	characteristic
408	C₄²×C₇	C₂⁴	1	1	yes	characteristic
409	C₄²×C₇	C₂⁴	1	1	yes	characteristic
410	C₄²×C₇	C₂⁴	1	1	yes	characteristic
411	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
412	C₂×#137	C₂²×C₇	1	2	yes	—
413	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
414	#533	C₂²×C₇	1	1	yes	characteristic
415	#533	C₂²×C₇	1	1	yes	characteristic, complemented
416	#533	C₂²×C₇	1	1	yes	characteristic, complemented
417	#532	C₂²×C₇	1	1	yes	characteristic
418	#532	C₂²×C₇	1	1	yes	characteristic, complemented
419	#532	C₂²×C₇	1	1	yes	characteristic, complemented
420	#529	—	2	1	no	—
421	#529	—	2	1	no	—
422	#529	—	2	1	no	—
423	#529	—	2	1	no	—
424	#529	C₂²×C₇	1	2	yes	complemented
425	#529	C₂²×C₇	1	2	yes	complemented
426	#525	—	2	1	no	—
427	#525	—	2	1	no	—
428	#525	C₂²×C₇	1	2	yes	—
429	C₄×#41	—	2	1	no	—
430	C₄×#41	—	2	1	no	—
431	C₄×#41	—	2	1	no	—
432	C₄×#41	—	2	1	no	—
433	C₄×#41	—	2	1	no	—
434	C₄×#41	—	2	1	no	—
435	C₄×#41	C₂²×C₇	1	2	yes	—
436	C₄×#41	C₂²×C₇	1	2	yes	—
437	C₄×#41	C₂²×C₇	1	2	yes	—
438	C₄×#41	C₂²×C₇	1	2	yes	—
439	C₄×#41	C₂²×C₇	1	2	yes	—
440	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
441	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
442	C₂×C₄×D₄	—	2	1	no	—
443	C₂×C₄×D₄	—	2	1	no	—
444	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
445	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
446	C₂×#117	—	2	1	no	—
447	C₂×#117	C₂²×C₇	1	1	yes	characteristic
448	C₂²×C₄²	—	2	1	no	—
449	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
450	#485	C₂²×C₇	1	4	yes	complemented
451	#485	C₂²×C₇	1	4	yes	complemented
452	#482	C₂²×C₇	1	4	yes	complemented
453	#482	C₂²×C₇	1	4	yes	complemented
454	#479	C₂²×C₇	1	4	yes	complemented
455	#478	C₂²×C₇	1	4	yes	complemented
456	#477	C₂²×C₇	1	2	yes	complemented
457	#476	C₂²×C₇	1	2	yes	complemented
458	#475	C₂²×C₇	1	2	yes	complemented
459	#474	C₂²×C₇	1	2	yes	complemented
460	#464	C₂²×C₇	1	4	yes	complemented
461	#463	C₂²×C₇	1	4	yes	complemented
462	#462	C₂²×C₇	1	2	yes	complemented
463	#461	C₂²×C₇	1	2	yes	complemented
464	#460	C₂²×C₇	1	2	yes	complemented
465	#459	C₂²×C₇	1	2	yes	complemented
466	#452	C₂²×C₇	1	4	yes	—
467	#452	C₂²×C₇	1	4	yes	—
468	#449	C₂²×C₇	1	4	yes	—
469	#449	C₂²×C₇	1	4	yes	—
470	#442	C₂²×C₇	1	4	yes	complemented
471	#441	C₂²×C₇	1	4	yes	complemented
472	#440	C₂²×C₇	1	4	yes	complemented
473	#440	C₂²×C₇	1	4	yes	complemented
474	C₄×Q₁₆	C₂²×C₇	1	4	yes	complemented
475	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
476	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
477	C₄×D₈	C₂²×C₇	1	4	yes	complemented
478	#432	C₂²×C₇	1	2	yes	complemented
479	#432	C₂²×C₇	1	2	yes	complemented
480	#431	C₂²×C₇	1	2	yes	complemented
481	#431	C₂²×C₇	1	2	yes	complemented
482	#428	C₂²×C₇	1	2	yes	—
483	#428	C₂²×C₇	1	2	yes	—
484	#423	C₂²×C₇	1	1	yes	characteristic
485	#423	C₂²×C₇	1	1	yes	characteristic
486	#419	C₂²×C₇	1	2	yes	—
487	#418	C₂²×C₇	1	2	yes	—
488	#417	C₂²×C₇	1	2	yes	—
489	#417	C₂²×C₇	1	2	yes	—
490	#407	C₂²×C₇	1	2	yes	—
491	C₄×M₁₆	C₂²×C₇	1	2	yes	—
492	C₂³×C₇	—	2	2	no	—
493	C₂³×C₇	—	2	4	no	—
494	C₂³×C₇	—	2	2	no	—
495	C₂³×C₇	—	2	2	no	—
496	C₂³×C₇	—	4	1	no	—
497	C₂³×C₇	—	4	1	no	—
498	C₂³×C₇	—	4	2	no	—
499	C₂³×C₇	—	4	2	no	—
500	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
501	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
502	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
503	C₇×Q₈	—	2	4	no	—
504	C₇×Q₈	—	2	2	no	—
505	C₇×Q₈	—	2	2	no	—
506	C₇×Q₈	—	2	2	no	—
507	C₇×Q₈	—	4	2	no	—
508	C₇×Q₈	—	4	2	no	—
509	C₇×Q₈	C₂×#41	1	4	yes	—
510	C₇×D₄	—	2	8	no	—
511	C₇×D₄	—	2	8	no	—
512	C₇×D₄	—	2	4	no	—
513	C₇×D₄	—	2	2	no	—
514	C₇×D₄	—	2	2	no	—
515	C₇×D₄	—	2	2	no	—
516	C₇×D₄	—	4	2	no	—
517	C₇×D₄	—	4	4	no	—
518	C₇×D₄	—	4	4	no	—
519	C₇×D₄	—	4	4	no	—
520	C₇×D₄	—	4	2	no	—
521	C₇×D₄	C₂×#41	1	4	yes	—
522	C₂×C₄×C₇	—	2	8	no	—
523	C₂×C₄×C₇	—	2	8	no	—
524	C₂×C₄×C₇	—	2	2	no	—
525	C₂×C₄×C₇	—	2	4	no	—
526	C₂×C₄×C₇	—	2	2	no	—
527	C₂×C₄×C₇	—	2	2	no	—
528	C₂×C₄×C₇	—	2	2	no	—
529	C₂×C₄×C₇	—	2	2	no	—
530	C₂×C₄×C₇	—	2	2	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	2	2	no	—
533	C₂×C₄×C₇	—	2	2	no	—
534	C₂×C₄×C₇	—	2	2	no	—
535	C₂×C₄×C₇	—	2	1	no	—
536	C₂×C₄×C₇	—	2	1	no	—
537	C₂×C₄×C₇	—	2	1	no	—
538	C₂×C₄×C₇	—	2	1	no	—
539	C₂×C₄×C₇	—	2	2	no	—
540	C₂×C₄×C₇	—	2	2	no	—
541	C₂×C₄×C₇	—	2	2	no	—
542	C₂×C₄×C₇	—	2	2	no	—
543	C₂×C₄×C₇	—	2	2	no	—
544	C₂×C₄×C₇	—	4	1	no	—
545	C₂×C₄×C₇	—	4	1	no	—
546	C₂×C₄×C₇	—	4	1	no	—
547	C₂×C₄×C₇	—	4	1	no	—
548	C₂×C₄×C₇	—	4	1	no	—
549	C₂×C₄×C₇	—	4	1	no	—
550	C₂×C₄×C₇	—	4	4	no	—
551	C₂×C₄×C₇	—	4	4	no	—
552	C₂×C₄×C₇	—	4	4	no	—
553	C₂×C₄×C₇	—	4	2	no	—
554	C₂×C₄×C₇	—	4	2	no	—
555	C₂×C₄×C₇	—	4	4	no	—
556	C₂×C₄×C₇	—	4	4	no	—
557	C₂×C₄×C₇	—	4	4	no	—
558	C₂×C₄×C₇	—	4	4	no	—
559	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₇	C₂×#41	1	2	yes	—
571	C₂×C₄×C₇	C₂×#41	1	2	yes	—
572	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
573	C₇×C₈	—	2	4	no	—
574	C₇×C₈	—	2	4	no	—
575	C₂×#41	—	2	4	no	—
576	C₂×#41	—	2	4	no	—
577	C₂×#41	—	2	1	no	—
578	C₂×#41	—	2	1	no	—
579	C₂×#41	—	2	1	no	—
580	C₂×#41	—	2	1	no	—
581	C₂×#41	C₂³×C₇	1	2	yes	—
582	C₂×#41	C₂³×C₇	1	2	yes	—
583	C₂×#41	C₂³×C₇	1	2	yes	—
584	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
585	C₂²×D₄	—	2	1	no	—
586	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
587	C₂³×C₄	—	2	1	no	—
588	C₂³×C₄	—	2	1	no	—
589	C₂³×C₄	—	2	1	no	—
590	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
591	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
592	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
593	#137	—	2	8	no	—
594	AGL(1,ℤ/8)	—	2	8	no	—
595	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
596	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
597	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
598	C₂×D₈	C₂³×C₇	1	4	yes	—
599	C₂×M₁₆	C₂³×C₇	1	2	yes	—
600	C₂×M₁₆	C₂³×C₇	1	2	yes	—
601	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
602	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
603	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
604	#127	C₂³×C₇	1	1	yes	characteristic
605	#126	—	2	2	no	—
606	#126	—	2	2	no	—
607	#125	—	2	1	no	—
608	#125	—	2	1	no	—
609	#125	C₂³×C₇	1	2	yes	—
610	#124	—	2	1	no	—
611	#124	—	2	1	no	—
612	#124	C₂³×C₇	1	2	yes	—
613	#123	—	2	2	no	—
614	#123	—	2	2	no	—
615	#123	—	2	2	no	—
616	C₂²⋊Q₈	—	2	1	no	—
617	C₂²⋊Q₈	—	2	1	no	—
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	—	2	1	no	—
620	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
621	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
622	#121	—	2	1	no	—
623	#121	—	2	1	no	—
624	#121	—	2	1	no	—
625	#121	—	2	1	no	—
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	—	2	1	no	—
636	C₄×Q₈	—	2	1	no	—
637	C₄×Q₈	C₂³×C₇	1	2	yes	—
638	C₄×Q₈	C₂³×C₇	1	2	yes	—
639	C₄×Q₈	C₂³×C₇	1	2	yes	—
640	C₄×Q₈	C₂³×C₇	1	2	yes	—
641	C₄×Q₈	C₂³×C₇	1	2	yes	—
642	C₄×Q₈	C₂³×C₇	1	2	yes	—
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	2	no	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	2	no	—
654	C₄×D₄	—	2	2	no	—
655	C₄×D₄	—	2	2	no	—
656	C₄×D₄	—	2	2	no	—
657	C₄×D₄	—	2	1	no	—
658	C₄×D₄	—	2	1	no	—
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	—	2	1	no	—
661	C₄×D₄	—	2	1	no	—
662	C₄×D₄	—	2	1	no	—
663	C₄×D₄	—	2	1	no	—
664	C₄×D₄	—	2	1	no	—
665	C₄×D₄	C₂³×C₇	1	2	yes	—
666	C₄×D₄	C₂³×C₇	1	2	yes	—
667	C₄×D₄	C₂³×C₇	1	2	yes	—
668	C₄×D₄	C₂³×C₇	1	2	yes	—
669	C₄×D₄	C₂³×C₇	1	2	yes	—
670	C₄×D₄	C₂³×C₇	1	2	yes	—
671	#117	—	2	1	no	—
672	#117	—	2	1	no	—
673	#117	—	2	1	no	—
674	#117	—	2	1	no	—
675	#117	—	2	2	no	—
676	#117	—	2	2	no	—
677	#117	—	2	2	no	—
678	#117	—	2	2	no	—
679	#117	—	2	2	no	—
680	#117	—	2	2	no	—
681	#117	—	2	2	no	—
682	#117	C₂³×C₇	1	2	yes	—
683	#117	C₂³×C₇	1	2	yes	—
684	#117	C₂³×C₇	1	2	yes	—
685	C₂×C₄⋊C₄	—	2	1	no	—
686	C₂×C₄⋊C₄	—	2	1	no	—
687	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
689	C₂×C₂²⋊C₄	—	2	1	no	—
690	C₂×C₂²⋊C₄	—	2	1	no	—
691	C₂×C₂²⋊C₄	—	2	1	no	—
692	C₂×C₄²	—	2	1	no	—
693	C₂×C₄²	—	2	1	no	—
694	C₂×C₄²	—	2	1	no	—
695	C₂×C₄²	—	2	2	no	—
696	C₂×C₄²	—	2	2	no	—
697	C₂×C₄²	—	2	2	no	—
698	C₂×C₄²	—	2	2	no	—
699	C₂×C₄²	—	2	2	no	—
700	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
701	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
702	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
703	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
704	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
705	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
708	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
709	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
710	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
711	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
712	#107	C₂³×C₇	1	4	yes	—
713	#107	C₂³×C₇	1	4	yes	—
714	#106	C₂³×C₇	1	4	yes	—
715	#106	C₂³×C₇	1	4	yes	—
716	C₄⋊C₈	C₂³×C₇	1	2	yes	—
717	C₄⋊C₈	C₂³×C₇	1	2	yes	—
718	C₄⋊C₈	C₂³×C₇	1	2	yes	—
719	C₄⋊C₈	C₂³×C₇	1	2	yes	—
720	#103	C₂³×C₇	1	4	yes	—
721	#103	C₂³×C₇	1	4	yes	—
722	#103	C₂³×C₇	1	4	yes	—
723	#103	C₂³×C₇	1	4	yes	—
724	#102	C₂³×C₇	1	4	yes	—
725	#102	C₂³×C₇	1	4	yes	—
726	#102	C₂³×C₇	1	4	yes	—
727	#102	C₂³×C₇	1	4	yes	—
728	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
729	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
730	#97	C₂³×C₇	1	4	yes	—
731	C₄×C₈	C₂³×C₇	1	4	yes	—
732	C₂²×C₇	—	2	1	no	—
733	C₂²×C₇	—	2	1	no	—
734	C₂²×C₇	—	2	1	no	—
735	C₂²×C₇	—	2	1	no	—
736	C₂²×C₇	—	2	4	no	—
737	C₂²×C₇	—	2	1	no	—
738	C₂²×C₇	—	2	1	no	—
739	C₂²×C₇	—	2	1	no	—
740	C₂²×C₇	—	2	1	no	—
741	C₂²×C₇	—	4	4	no	—
742	C₂²×C₇	—	4	8	no	—
743	C₂²×C₇	—	4	2	no	—
744	C₂²×C₇	—	4	2	no	—
745	C₂²×C₇	—	4	2	no	—
746	C₂²×C₇	—	4	2	no	—
747	C₂²×C₇	—	4	2	no	—
748	C₂²×C₇	#525	1	2	yes	—
749	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
750	C₄×C₇	—	2	1	no	—
751	C₄×C₇	—	2	1	no	—
752	C₄×C₇	—	2	4	no	—
753	C₄×C₇	—	2	1	no	—
754	C₄×C₇	—	2	1	no	—
755	C₄×C₇	—	2	1	no	—
756	C₄×C₇	—	2	1	no	—
757	C₄×C₇	—	2	1	no	—
758	C₄×C₇	—	2	1	no	—
759	C₄×C₇	—	4	2	no	—
760	C₄×C₇	—	4	2	no	—
761	C₄×C₇	—	4	2	no	—
762	C₄×C₇	—	4	2	no	—
763	C₄×C₇	—	4	2	no	—
764	C₄×C₇	#525	1	2	yes	—
765	C₄×C₇	#575	1	2	yes	—
766	C₄×C₇	#575	1	2	yes	—
767	C₄×C₇	C₂²×#41	1	1	yes	characteristic
768	C₄×C₇	C₂²×#41	1	1	yes	characteristic
769	C₂⁴	—	2	1	no	—
770	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
771	#41	—	2	8	no	—
772	#41	—	2	8	no	—
773	#41	—	2	4	no	—
774	#41	—	2	4	no	—
775	#41	—	2	4	no	—
776	#41	—	2	4	no	—
777	#41	—	2	4	no	—
778	#41	—	2	4	no	—
779	#41	—	4	4	no	—
780	#41	—	4	4	no	—
781	C₂×Q₈	—	2	1	no	—
782	C₂×Q₈	—	2	1	no	—
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	2	no	—
785	C₂×Q₈	C₇×#41	1	4	yes	complemented
786	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
787	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
788	C₂×D₄	—	2	8	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	2	1	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	C₇×#41	1	4	yes	complemented
799	C₂×D₄	C₂⁴×C₇	1	2	yes	—
800	C₂×D₄	C₂⁴×C₇	1	2	yes	—
801	C₂²×C₄	—	2	8	no	—
802	C₂²×C₄	—	2	1	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	4	no	—
819	C₂²×C₄	—	4	4	no	—
820	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
821	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
822	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
823	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
824	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
825	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
826	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
827	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
828	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
829	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
830	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
831	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
832	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
833	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
834	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
838	Q₁₆	—	2	8	no	—
839	SD₁₆	—	2	8	no	—
840	SD₁₆	—	2	8	no	—
841	D₈	—	2	8	no	—
842	M₁₆	—	2	4	no	—
843	M₁₆	—	2	4	no	—
844	C₂×C₈	C₂⁴×C₇	1	4	yes	—
845	C₂×C₈	C₂⁴×C₇	1	4	yes	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	2	1	no	—
855	C₄⋊C₄	—	2	1	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
863	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
864	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
865	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₄²	—	2	2	no	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	2	no	—
890	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
891	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
892	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
893	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
894	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
895	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
896	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
897	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
898	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
899	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
900	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
901	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
902	C₄²	C₂⁴×C₇	1	1	yes	characteristic
903	C₄²	C₂⁴×C₇	1	1	yes	characteristic
904	C₄²	C₂⁴×C₇	1	1	yes	characteristic
905	C₄²	C₂⁴×C₇	1	1	yes	characteristic
906	C₂×C₇	—	2	2	no	—
907	C₂×C₇	—	4	1	no	—
908	C₂×C₇	—	4	1	no	—
909	C₂×C₇	—	4	4	no	—
910	C₂×C₇	—	8	2	no	—
911	C₂×C₇	C₂×#525	1	1	yes	characteristic
912	C₂×C₇	C₂×#575	1	1	yes	characteristic
913	C₂×C₇	C₂×#575	1	1	yes	characteristic
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	4	no	—
917	C₂³	—	2	2	no	—
918	C₂³	—	4	1	no	—
919	C₂³	—	4	1	no	—
920	C₂³	—	4	2	no	—
921	C₂³	—	4	2	no	—
922	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
923	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
924	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
925	Q₈	—	2	2	no	—
926	Q₈	—	2	4	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	2	2	no	—
929	Q₈	—	4	2	no	—
930	Q₈	—	4	2	no	—
931	Q₈	C₂×C₇×#41	1	4	yes	—
932	D₄	—	2	8	no	—
933	D₄	—	2	8	no	—
934	D₄	—	2	2	no	—
935	D₄	—	2	2	no	—
936	D₄	—	2	2	no	—
937	D₄	—	2	4	no	—
938	D₄	—	4	2	no	—
939	D₄	—	4	4	no	—
940	D₄	—	4	4	no	—
941	D₄	—	4	4	no	—
942	D₄	—	4	2	no	—
943	D₄	C₂×C₇×#41	1	4	yes	—
944	C₂×C₄	—	2	8	no	—
945	C₂×C₄	—	2	8	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	4	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	4	1	no	—
970	C₂×C₄	—	4	1	no	—
971	C₂×C₄	—	4	1	no	—
972	C₂×C₄	—	4	4	no	—
973	C₂×C₄	—	4	4	no	—
974	C₂×C₄	—	4	4	no	—
975	C₂×C₄	—	4	2	no	—
976	C₂×C₄	—	4	2	no	—
977	C₂×C₄	—	4	4	no	—
978	C₂×C₄	—	4	4	no	—
979	C₂×C₄	—	4	4	no	—
980	C₂×C₄	—	4	4	no	—
981	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
982	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
983	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
984	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
985	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
986	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
987	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
988	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
989	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
990	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
991	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
992	C₂×C₄	C₂×C₇×#41	1	2	yes	—
993	C₂×C₄	C₂×C₇×#41	1	2	yes	—
994	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
995	C₈	—	2	4	no	—
996	C₈	—	2	4	no	—
997	C₇	#60559	1	1	yes	characteristic, direct product factor, Sylow
998	C₂²	—	2	1	no	—
999	C₂²	—	2	1	no	—
1000	C₂²	—	2	1	no	—
1001	C₂²	—	2	1	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	2	1	no	—
1004	C₂²	—	2	1	no	—
1005	C₂²	—	2	1	no	—
1006	C₂²	—	2	4	no	—
1007	C₂²	—	4	4	no	—
1008	C₂²	—	4	8	no	—
1009	C₂²	—	4	2	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	2	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	C₇×#525	1	2	yes	—
1015	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1016	C₄	—	2	1	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	1	no	—
1021	C₄	—	2	1	no	—
1022	C₄	—	2	1	no	—
1023	C₄	—	2	1	no	—
1024	C₄	—	2	4	no	—
1025	C₄	—	4	2	no	—
1026	C₄	—	4	2	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	2	no	—
1029	C₄	—	4	2	no	—
1030	C₄	C₇×#525	1	2	yes	—
1031	C₄	C₇×#575	1	2	yes	—
1032	C₄	C₇×#575	1	2	yes	—
1033	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1034	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1035	C₂	—	2	2	no	—
1036	C₂	—	4	1	no	—
1037	C₂	—	4	1	no	—
1038	C₂	—	4	4	no	—
1039	C₂	—	8	2	no	—
1040	C₂	C₂×C₇×#525	1	1	yes	characteristic
1041	C₂	C₂×C₇×#575	1	1	yes	characteristic
1042	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×C₄×C₇×#41	C₂	semidirect
3. C₇×#3116	C₂	semidirect
4. C₇×#3115	C₂	semidirect
5. C₇×#3111	C₂	semidirect
6. C₇×#3107	C₂	semidirect
7. C₇×#3106	C₂	semidirect
8. C₇×#3102	C₂	semidirect
9. C₇×#3093	C₂	semidirect
10. C₇×#3078	C₂	semidirect
11. C₇×#3077	C₂	semidirect
12. C₇×#3037	C₂	semidirect
13. C₇×#3036	C₂	semidirect
14. C₇×#3005	C₂	semidirect
15. C₄×C₇×#137	C₂	semidirect
16. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
17. C₇×#2920	C₂	semidirect
22. C₇×#533	C₂²	semidirect
23. C₇×#533	C₂²	semidirect
25. C₇×#532	C₂²	semidirect
26. C₇×#532	C₂²	semidirect
31. C₇×#529	C₂²	semidirect
32. C₇×#529	C₂²	semidirect
57. C₇×#485	C₂²	semidirect
58. C₇×#485	C₂²	semidirect
59. C₇×#482	C₂²	semidirect
60. C₇×#482	C₂²	semidirect
61. C₇×#479	C₂²	semidirect
62. C₇×#478	C₂²	semidirect
63. C₇×#477	C₂²	semidirect
64. C₇×#476	C₂²	semidirect
65. C₇×#475	C₂²	semidirect
66. C₇×#474	C₂²	semidirect
67. C₇×#464	C₂²	semidirect
68. C₇×#463	C₂²	semidirect
69. C₇×#462	C₂²	semidirect
70. C₇×#461	C₂²	semidirect
71. C₇×#460	C₂²	semidirect
72. C₇×#459	C₂²	semidirect
77. C₇×#442	C₂²	semidirect
78. C₇×#441	C₂²	semidirect
79. C₇×#440	C₂²	semidirect
80. C₇×#440	C₂²	semidirect
81. C₄×C₇×Q₁₆	C₂²	semidirect
82. C₄×C₇×SD₁₆	C₂²	semidirect
83. C₄×C₇×SD₁₆	C₂²	semidirect
84. C₄×C₇×D₈	C₂²	semidirect
85. C₇×#432	C₂²	semidirect
86. C₇×#432	C₂²	semidirect
87. C₇×#431	C₂²	semidirect
88. C₇×#431	C₂²	semidirect
99. #60559	C₇	direct (N × H)
257. #3444	C₂×C₇	semidirect
258. C₂×C₄×#41	C₂×C₇	semidirect
259. #3116	C₂×C₇	semidirect
260. #3115	C₂×C₇	semidirect
261. #3111	C₂×C₇	semidirect
262. #3107	C₂×C₇	semidirect
263. #3106	C₂×C₇	semidirect
264. #3102	C₂×C₇	semidirect
265. #3093	C₂×C₇	semidirect
266. #3078	C₂×C₇	semidirect
267. #3077	C₂×C₇	semidirect
268. #3037	C₂×C₇	semidirect
269. #3036	C₂×C₇	semidirect
270. #3005	C₂×C₇	semidirect
271. C₄×#137	C₂×C₇	semidirect
272. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
273. #2920	C₂×C₇	semidirect
290. C₂×C₇×Q₈	#41	semidirect
303. C₂×C₇×D₄	#41	semidirect
415. #533	C₂²×C₇	semidirect
416. #533	C₂²×C₇	semidirect
418. #532	C₂²×C₇	semidirect
419. #532	C₂²×C₇	semidirect
424. #529	C₂²×C₇	semidirect
425. #529	C₂²×C₇	semidirect
450. #485	C₂²×C₇	semidirect
451. #485	C₂²×C₇	semidirect
452. #482	C₂²×C₇	semidirect
453. #482	C₂²×C₇	semidirect
454. #479	C₂²×C₇	semidirect
455. #478	C₂²×C₇	semidirect
456. #477	C₂²×C₇	semidirect
457. #476	C₂²×C₇	semidirect
458. #475	C₂²×C₇	semidirect
459. #474	C₂²×C₇	semidirect
460. #464	C₂²×C₇	semidirect
461. #463	C₂²×C₇	semidirect
462. #462	C₂²×C₇	semidirect
463. #461	C₂²×C₇	semidirect
464. #460	C₂²×C₇	semidirect
465. #459	C₂²×C₇	semidirect
470. #442	C₂²×C₇	semidirect
471. #441	C₂²×C₇	semidirect
472. #440	C₂²×C₇	semidirect
473. #440	C₂²×C₇	semidirect
474. C₄×Q₁₆	C₂²×C₇	semidirect
475. C₄×SD₁₆	C₂²×C₇	semidirect
476. C₄×SD₁₆	C₂²×C₇	semidirect
477. C₄×D₈	C₂²×C₇	semidirect
478. #432	C₂²×C₇	semidirect
479. #432	C₂²×C₇	semidirect
480. #431	C₂²×C₇	semidirect
481. #431	C₂²×C₇	semidirect
785. C₂×Q₈	C₇×#41	semidirect
798. C₂×D₄	C₇×#41	semidirect
997. C₇	#60559	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×C₄×C₇×#41	2
C₇×#3116	2
C₇×#3115	2
C₇×#3111	2
C₇×#3107	2
C₇×#3106	2
C₇×#3102	2
C₇×#3093	2
C₇×#3078	2
C₇×#3077	2
C₇×#3037	2
C₇×#3036	2
C₇×#3005	2
C₄×C₇×#137	2
C₄×C₇×AGL(1,ℤ/8)	2
C₇×#2920	2
#60559	7

Subgroups — C7×#60559 #13237775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60559 #13237775