Subgroups — C₇×#60811 #13238027

Order 1792.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3224	C₂	1	4	yes	maximal, complemented
4	C₇×#3220	C₂	1	4	yes	maximal, complemented
5	C₇×#3217	C₂	1	2	yes	maximal, complemented
6	C₇×#3213	C₂	1	2	yes	maximal, complemented
7	C₇×#3211	C₂	1	2	yes	maximal, complemented
8	C₇×#3205	C₂	1	2	yes	maximal, complemented
9	C₇×#3155	C₂	1	2	yes	maximal, complemented
10	C₇×#3136	C₂	1	2	yes	maximal, complemented
11	C₇×#3045	C₂	1	2	yes	maximal, complemented
12	C₇×#3041	C₂	1	2	yes	maximal, complemented
13	C₇×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3003	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3002	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#447	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
19	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
21	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂×C₇×#135	C₂²	1	2	yes	complemented
23	C₂²×C₇×D₈	C₂²	1	2	yes	complemented
24	C₇×#555	—	2	1	no	—
25	C₇×#553	—	2	1	no	—
26	C₇×#553	—	2	1	no	—
27	C₇×#551	—	2	2	no	—
28	C₇×#547	—	2	1	no	—
29	C₇×#546	—	2	2	no	—
30	C₇×#544	C₂²	1	1	yes	characteristic, complemented
31	C₇×#542	C₂²	1	2	yes	complemented
32	C₇×#540	C₂²	1	2	yes	complemented
33	C₇×#535	—	2	2	no	—
34	C₇×#535	—	2	1	no	—
35	C₇×#535	—	2	1	no	—
36	C₇×#535	C₂²	1	2	yes	—
37	C₇×#535	C₂²	1	2	yes	—
38	C₇×#535	C₂²	1	4	yes	complemented
39	C₇×#535	C₂²	1	1	yes	characteristic, complemented
40	C₇×#532	C₂²	1	2	yes	complemented
41	C₂×C₇×#127	C₂²	1	2	yes	complemented
42	C₇×#529	C₂²	1	2	yes	complemented
43	C₂×C₇×#124	C₂²	1	2	yes	complemented
44	C₇×#525	C₂²	1	1	yes	characteristic
45	C₂×C₇×#121	—	2	1	no	—
46	C₂×C₇×#121	—	2	1	no	—
47	C₂×C₇×#121	C₂²	1	1	yes	characteristic
48	C₂×C₇×#120	—	2	2	no	—
49	C₇×#520	C₂²	1	1	yes	characteristic, complemented
50	C₇×#518	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₇×#117	C₂²	1	1	yes	characteristic
52	C₇×#496	C₂²	1	4	yes	complemented
53	C₇×#496	C₂²	1	4	yes	complemented
54	C₇×#495	C₂²	1	4	yes	complemented
55	C₇×#493	C₂²	1	4	yes	complemented
56	C₇×#490	C₂²	1	4	yes	complemented
57	C₇×#489	C₂²	1	4	yes	complemented
58	C₇×#488	C₂²	1	4	yes	complemented
59	C₇×#486	C₂²	1	4	yes	complemented
60	C₇×#464	C₂²	1	4	yes	complemented
61	C₇×#463	C₂²	1	4	yes	complemented
62	C₇×#463	C₂²	1	4	yes	complemented
63	C₇×#463	C₂²	1	4	yes	complemented
64	C₇×#460	C₂²	1	4	yes	complemented
65	C₇×#459	C₂²	1	4	yes	complemented
66	C₇×#459	C₂²	1	4	yes	complemented
67	C₇×#459	C₂²	1	4	yes	complemented
68	C₇×#452	C₂²	1	2	yes	complemented
69	C₇×#451	C₂²	1	1	yes	characteristic, complemented
70	C₇×#450	C₂²	1	2	yes	complemented
71	C₇×#450	C₂²	1	2	yes	complemented
72	C₇×#450	C₂²	1	1	yes	characteristic, complemented
73	C₇×#449	C₂²	1	2	yes	complemented
74	C₇×#449	C₂²	1	4	yes	complemented
75	C₇×#448	C₂²	1	2	yes	complemented
76	C₇×#448	C₂²	1	1	yes	characteristic, complemented
77	C₇×#447	C₂²	1	2	yes	—
78	C₇×#447	C₂²	1	2	yes	—
79	C₇×#447	C₂²	1	2	yes	complemented
80	C₇×#447	C₂²	1	2	yes	complemented
81	C₇×#447	C₂²	1	4	yes	complemented
82	C₇×#447	C₂²	1	1	yes	characteristic, complemented
83	C₇×#447	C₂²	1	2	yes	complemented
84	C₇×#433	C₂²	1	4	yes	complemented
85	C₇×#432	C₂²	1	2	yes	complemented
86	C₇×#431	C₂²	1	2	yes	complemented
87	C₇×#424	C₂²	1	2	yes	complemented
88	C₇×#418	C₂²	1	2	yes	complemented
89	C₇×#417	C₂²	1	2	yes	complemented
90	C₇×#416	C₂²	1	2	yes	complemented
91	C₂×C₇×#102	C₂²	1	2	yes	complemented
92	C₇×#407	C₂²	1	1	yes	characteristic
93	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₇×#405	C₂²	1	2	yes	complemented
95	#60811	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁵×C₇	—	2	1	no	—
97	C₂×C₇×#41	—	2	1	no	—
98	C₂×C₇×#41	—	2	1	no	—
99	C₂×C₇×#41	—	2	2	no	—
100	C₂×C₇×#41	—	4	4	no	—
101	C₂×C₇×#41	C₂³	1	2	yes	—
102	C₂×C₇×#41	C₂³	1	1	yes	characteristic
103	C₂×C₇×#41	C₂³	1	2	yes	—
104	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
105	C₂²×C₇×D₄	—	2	1	no	—
106	C₂²×C₇×D₄	—	2	1	no	—
107	C₂²×C₇×D₄	—	2	1	no	—
108	C₂²×C₇×D₄	—	2	1	no	—
109	C₂²×C₇×D₄	—	2	1	no	—
110	C₂²×C₇×D₄	—	2	2	no	—
111	C₂²×C₇×D₄	—	2	2	no	—
112	C₂²×C₇×D₄	—	4	4	no	—
113	C₂²×C₇×D₄	C₂³	1	2	yes	—
114	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
115	C₂²×C₇×D₄	C₂³	1	2	yes	—
116	C₂²×C₇×D₄	C₂³	1	2	yes	—
117	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₇	—	2	1	no	—
119	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
120	C₇×AGL(1,ℤ/8)	—	4	4	no	—
121	C₇×AGL(1,ℤ/8)	—	4	4	no	—
122	C₇×#135	—	4	4	no	—
123	C₂×C₇×Q₁₆	C₂³	1	2	yes	complemented
124	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
125	C₂×C₇×SD₁₆	C₂³	1	4	yes	complemented
126	C₂×C₇×SD₁₆	C₂³	1	2	yes	complemented
127	C₂×C₇×SD₁₆	C₂³	1	2	yes	complemented
128	C₂×C₇×D₈	—	4	4	no	—
129	C₂×C₇×D₈	C₂³	1	4	yes	—
130	C₂×C₇×D₈	C₂³	1	4	yes	—
131	C₂×C₇×D₈	C₂³	1	4	yes	—
132	C₂×C₇×D₈	C₂³	1	2	yes	complemented
133	C₂×C₇×D₈	C₂³	1	4	yes	complemented
134	C₂×C₇×M₁₆	C₂³	1	2	yes	—
135	C₂²×C₇×C₈	C₂³	1	2	yes	—
136	C₇×C₄⋊Q₈	—	2	1	no	—
137	C₇×C₄⋊Q₈	C₂³	1	2	yes	complemented
138	C₇×#127	—	2	2	no	—
139	C₇×#127	—	2	2	no	—
140	C₇×#127	C₂³	1	4	yes	—
141	C₇×#127	C₂³	1	4	yes	—
142	C₇×#127	C₂³	1	2	yes	complemented
143	C₇×#126	—	2	2	no	—
144	C₇×#126	—	2	2	no	—
145	C₇×#125	—	2	1	no	—
146	C₇×#125	C₂³	1	2	yes	complemented
147	C₇×#124	—	2	2	no	—
148	C₇×#124	—	2	2	no	—
149	C₇×#124	—	2	2	no	—
150	C₇×#124	—	2	2	no	—
151	C₇×#124	C₂³	1	4	yes	—
152	C₇×#124	C₂³	1	4	yes	—
153	C₇×#124	C₂³	1	2	yes	complemented
154	C₇×#123	—	2	1	no	—
155	C₇×#123	—	2	2	no	—
156	C₇×#123	—	2	2	no	—
157	C₇×#123	—	2	2	no	—
158	C₇×#123	—	2	2	no	—
159	C₇×C₂²⋊Q₈	—	2	2	no	—
160	C₇×C₂²⋊Q₈	—	2	2	no	—
161	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
162	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
163	C₇×#121	—	2	1	no	—
164	C₇×#121	—	2	1	no	—
165	C₇×#121	—	2	2	no	—
166	C₇×#121	—	2	2	no	—
167	C₇×#121	—	2	2	no	—
168	C₇×#121	—	2	2	no	—
169	C₇×#121	—	2	2	no	—
170	C₇×#121	—	2	4	no	—
171	C₇×#121	—	2	4	no	—
172	C₇×#121	—	2	1	no	—
173	C₇×#121	—	2	1	no	—
174	C₇×#121	—	2	2	no	—
175	C₇×#121	—	2	2	no	—
176	C₇×#121	C₂³	1	2	yes	—
177	C₇×#121	C₂³	1	2	yes	—
178	C₇×#121	C₂³	1	1	yes	characteristic
179	C₇×#121	C₂³	1	1	yes	characteristic
180	C₇×#120	—	2	1	no	—
181	C₇×#120	—	2	4	no	—
182	C₇×#120	—	2	4	no	—
183	C₇×#120	—	2	4	no	—
184	C₇×#120	—	2	4	no	—
185	C₇×#120	—	2	2	no	—
186	C₄×C₇×Q₈	C₂³	1	2	yes	complemented
187	C₄×C₇×D₄	—	2	1	no	—
188	C₄×C₇×D₄	—	2	1	no	—
189	C₄×C₇×D₄	—	2	2	no	—
190	C₄×C₇×D₄	—	2	1	no	—
191	C₄×C₇×D₄	—	2	1	no	—
192	C₄×C₇×D₄	—	2	2	no	—
193	C₄×C₇×D₄	—	2	2	no	—
194	C₄×C₇×D₄	C₂³	1	2	yes	complemented
195	C₄×C₇×D₄	C₂³	1	2	yes	complemented
196	C₄×C₇×D₄	C₂³	1	2	yes	complemented
197	C₇×#117	—	2	1	no	—
198	C₇×#117	—	2	2	no	—
199	C₇×#117	D₄	1	2	yes	—
200	C₇×#117	D₄	1	1	yes	characteristic
201	C₇×#117	D₄	1	1	yes	characteristic
202	C₇×#117	C₂³	1	1	yes	characteristic
203	C₇×#117	C₂³	1	1	yes	characteristic
204	C₇×#117	C₂³	1	1	yes	characteristic
205	C₇×#117	C₂³	1	2	yes	—
206	C₂×C₇×C₄⋊C₄	—	2	1	no	—
207	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
208	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
209	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
211	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
212	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
213	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
214	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
215	C₂×C₄²×C₇	C₂³	1	2	yes	—
216	C₇×C₄⋊C₈	C₂³	1	4	yes	complemented
217	C₇×C₄⋊C₈	C₂³	1	4	yes	complemented
218	C₇×#103	C₂³	1	2	yes	complemented
219	C₇×#103	C₂³	1	4	yes	complemented
220	C₇×#103	C₂³	1	2	yes	complemented
221	C₇×#102	C₂³	1	4	yes	—
222	C₇×#102	C₂³	1	4	yes	—
223	C₇×#102	C₂³	1	4	yes	—
224	C₇×#102	C₂³	1	4	yes	—
225	C₇×#102	C₂³	1	2	yes	complemented
226	C₇×#102	C₂³	1	4	yes	complemented
227	C₇×#102	C₂³	1	2	yes	complemented
228	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
229	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
230	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
231	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
232	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
233	C₇×#97	C₂³	1	4	yes	complemented
234	C₄×C₇×C₈	C₂³	1	4	yes	complemented
235	#3494	C₂×C₇	1	1	yes	characteristic, complemented
236	C₂×#535	C₂×C₇	1	1	yes	characteristic, complemented
237	#3224	C₂×C₇	1	4	yes	complemented
238	#3220	C₂×C₇	1	4	yes	complemented
239	#3217	C₂×C₇	1	2	yes	complemented
240	#3213	C₂×C₇	1	2	yes	complemented
241	#3211	C₂×C₇	1	2	yes	complemented
242	#3205	C₂×C₇	1	2	yes	complemented
243	#3155	C₂×C₇	1	2	yes	complemented
244	#3136	C₂×C₇	1	2	yes	complemented
245	#3045	C₂×C₇	1	2	yes	complemented
246	#3041	C₂×C₇	1	2	yes	complemented
247	#3006	C₂×C₇	1	1	yes	characteristic, complemented
248	#3003	C₂×C₇	1	1	yes	characteristic, complemented
249	#3002	C₂×C₇	1	1	yes	characteristic, complemented
250	C₂×#447	C₂×C₇	1	1	yes	characteristic, complemented
251	#2924	C₂×C₇	1	1	yes	characteristic, complemented
252	C₂⁴×C₇	—	2	2	no	—
253	C₂⁴×C₇	—	2	1	no	—
254	C₂⁴×C₇	—	2	1	no	—
255	C₂⁴×C₇	—	2	2	no	—
256	C₂⁴×C₇	—	2	2	no	—
257	C₂⁴×C₇	—	4	4	no	—
258	C₂⁴×C₇	—	8	2	no	—
259	C₂⁴×C₇	—	8	2	no	—
260	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
261	C₇×#41	—	2	4	no	—
262	C₇×#41	—	2	4	no	—
263	C₇×#41	—	2	4	no	—
264	C₇×#41	—	4	2	no	—
265	C₇×#41	—	4	2	no	—
266	C₇×#41	—	4	4	no	—
267	C₇×#41	—	4	4	no	—
268	C₇×#41	—	8	4	no	—
269	C₂×C₇×Q₈	—	2	1	no	—
270	C₂×C₇×Q₈	—	2	2	no	—
271	C₂×C₇×Q₈	—	4	2	no	—
272	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
273	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
274	C₂×C₇×D₄	—	2	1	no	—
275	C₂×C₇×D₄	—	2	1	no	—
276	C₂×C₇×D₄	—	2	2	no	—
277	C₂×C₇×D₄	—	2	2	no	—
278	C₂×C₇×D₄	—	2	2	no	—
279	C₂×C₇×D₄	—	2	1	no	—
280	C₂×C₇×D₄	—	2	2	no	—
281	C₂×C₇×D₄	—	2	1	no	—
282	C₂×C₇×D₄	—	2	2	no	—
283	C₂×C₇×D₄	—	2	2	no	—
284	C₂×C₇×D₄	—	2	2	no	—
285	C₂×C₇×D₄	—	2	1	no	—
286	C₂×C₇×D₄	—	2	2	no	—
287	C₂×C₇×D₄	—	2	4	no	—
288	C₂×C₇×D₄	—	2	4	no	—
289	C₂×C₇×D₄	—	2	4	no	—
290	C₂×C₇×D₄	—	2	4	no	—
291	C₂×C₇×D₄	—	2	2	no	—
292	C₂×C₇×D₄	—	2	4	no	—
293	C₂×C₇×D₄	—	2	4	no	—
294	C₂×C₇×D₄	—	2	4	no	—
295	C₂×C₇×D₄	—	4	4	no	—
296	C₂×C₇×D₄	—	4	4	no	—
297	C₂×C₇×D₄	—	4	2	no	—
298	C₂×C₇×D₄	—	4	4	no	—
299	C₂×C₇×D₄	—	4	4	no	—
300	C₂×C₇×D₄	—	4	4	no	—
301	C₂×C₇×D₄	—	4	4	no	—
302	C₂×C₇×D₄	—	8	4	no	—
303	C₂×C₇×D₄	—	8	4	no	—
304	C₂×C₇×D₄	—	8	2	no	—
305	C₂×C₇×D₄	C₂⁴	1	4	yes	—
306	C₂×C₇×D₄	C₂⁴	1	2	yes	—
307	C₂×C₇×D₄	C₂⁴	1	2	yes	—
308	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₇	—	2	4	no	—
310	C₂²×C₄×C₇	—	2	1	no	—
311	C₂²×C₄×C₇	—	2	1	no	—
312	C₂²×C₄×C₇	—	2	1	no	—
313	C₂²×C₄×C₇	—	2	2	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	—	4	4	no	—
319	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
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	2	yes	—
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	—	4	2	no	—
328	C₇×SD₁₆	—	4	4	no	—
329	C₇×SD₁₆	—	4	2	no	—
330	C₇×SD₁₆	—	4	2	no	—
331	C₇×SD₁₆	—	4	4	no	—
332	C₇×D₈	—	4	4	no	—
333	C₇×D₈	—	4	4	no	—
334	C₇×D₈	—	4	4	no	—
335	C₇×D₈	—	4	2	no	—
336	C₇×D₈	—	4	4	no	—
337	C₇×M₁₆	—	2	4	no	—
338	C₂×C₇×C₈	—	2	4	no	—
339	C₂×C₇×C₈	C₂⁴	1	2	yes	—
340	C₂×C₇×C₈	C₂⁴	1	4	yes	—
341	C₂×C₇×C₈	C₂⁴	1	2	yes	—
342	C₇×C₄⋊C₄	—	2	1	no	—
343	C₇×C₄⋊C₄	—	2	2	no	—
344	C₇×C₄⋊C₄	—	2	1	no	—
345	C₇×C₄⋊C₄	—	2	2	no	—
346	C₇×C₄⋊C₄	—	2	2	no	—
347	C₇×C₄⋊C₄	—	2	2	no	—
348	C₇×C₄⋊C₄	—	2	1	no	—
349	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
350	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
351	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
352	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
353	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
354	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
355	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
356	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
357	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
358	C₇×C₂²⋊C₄	—	2	1	no	—
359	C₇×C₂²⋊C₄	—	2	1	no	—
360	C₇×C₂²⋊C₄	—	2	1	no	—
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	4	no	—
365	C₇×C₂²⋊C₄	—	2	4	no	—
366	C₇×C₂²⋊C₄	—	2	4	no	—
367	C₇×C₂²⋊C₄	—	2	4	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	1	no	—
372	C₇×C₂²⋊C₄	—	2	2	no	—
373	C₇×C₂²⋊C₄	—	2	1	no	—
374	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
375	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
376	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
377	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
378	C₄²×C₇	—	2	2	no	—
379	C₄²×C₇	—	2	1	no	—
380	C₄²×C₇	C₂×D₄	1	2	yes	—
381	C₄²×C₇	C₂×D₄	1	2	yes	—
382	C₄²×C₇	C₂⁴	1	2	yes	—
383	C₄²×C₇	C₂⁴	1	2	yes	—
384	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
385	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
386	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	complemented
387	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	complemented
388	C₂×#135	C₂²×C₇	1	2	yes	complemented
389	C₂²×D₈	C₂²×C₇	1	2	yes	complemented
390	#555	—	2	1	no	—
391	#553	—	2	1	no	—
392	#553	—	2	1	no	—
393	#551	—	2	2	no	—
394	#547	—	2	1	no	—
395	#546	—	2	2	no	—
396	#544	C₂²×C₇	1	1	yes	characteristic, complemented
397	#542	C₂²×C₇	1	2	yes	complemented
398	#540	C₂²×C₇	1	2	yes	complemented
399	#535	—	2	2	no	—
400	#535	—	2	1	no	—
401	#535	—	2	1	no	—
402	#535	C₂²×C₇	1	2	yes	—
403	#535	C₂²×C₇	1	2	yes	—
404	#535	C₂²×C₇	1	4	yes	complemented
405	#535	C₂²×C₇	1	1	yes	characteristic, complemented
406	#532	C₂²×C₇	1	2	yes	complemented
407	C₂×#127	C₂²×C₇	1	2	yes	complemented
408	#529	C₂²×C₇	1	2	yes	complemented
409	C₂×#124	C₂²×C₇	1	2	yes	complemented
410	#525	C₂²×C₇	1	1	yes	characteristic
411	C₂×#121	—	2	1	no	—
412	C₂×#121	—	2	1	no	—
413	C₂×#121	C₂²×C₇	1	1	yes	characteristic
414	C₂×#120	—	2	2	no	—
415	#520	C₂²×C₇	1	1	yes	characteristic, complemented
416	#518	C₂²×C₇	1	1	yes	characteristic, complemented
417	C₂×#117	C₂²×C₇	1	1	yes	characteristic
418	#496	C₂²×C₇	1	4	yes	complemented
419	#496	C₂²×C₇	1	4	yes	complemented
420	#495	C₂²×C₇	1	4	yes	complemented
421	#493	C₂²×C₇	1	4	yes	complemented
422	#490	C₂²×C₇	1	4	yes	complemented
423	#489	C₂²×C₇	1	4	yes	complemented
424	#488	C₂²×C₇	1	4	yes	complemented
425	#486	C₂²×C₇	1	4	yes	complemented
426	#464	C₂²×C₇	1	4	yes	complemented
427	#463	C₂²×C₇	1	4	yes	complemented
428	#463	C₂²×C₇	1	4	yes	complemented
429	#463	C₂²×C₇	1	4	yes	complemented
430	#460	C₂²×C₇	1	4	yes	complemented
431	#459	C₂²×C₇	1	4	yes	complemented
432	#459	C₂²×C₇	1	4	yes	complemented
433	#459	C₂²×C₇	1	4	yes	complemented
434	#452	C₂²×C₇	1	2	yes	complemented
435	#451	C₂²×C₇	1	1	yes	characteristic, complemented
436	#450	C₂²×C₇	1	2	yes	complemented
437	#450	C₂²×C₇	1	2	yes	complemented
438	#450	C₂²×C₇	1	1	yes	characteristic, complemented
439	#449	C₂²×C₇	1	2	yes	complemented
440	#449	C₂²×C₇	1	4	yes	complemented
441	#448	C₂²×C₇	1	2	yes	complemented
442	#448	C₂²×C₇	1	1	yes	characteristic, complemented
443	#447	C₂²×C₇	1	2	yes	—
444	#447	C₂²×C₇	1	2	yes	—
445	#447	C₂²×C₇	1	2	yes	complemented
446	#447	C₂²×C₇	1	2	yes	complemented
447	#447	C₂²×C₇	1	4	yes	complemented
448	#447	C₂²×C₇	1	1	yes	characteristic, complemented
449	#447	C₂²×C₇	1	2	yes	complemented
450	#433	C₂²×C₇	1	4	yes	complemented
451	#432	C₂²×C₇	1	2	yes	complemented
452	#431	C₂²×C₇	1	2	yes	complemented
453	#424	C₂²×C₇	1	2	yes	complemented
454	#418	C₂²×C₇	1	2	yes	complemented
455	#417	C₂²×C₇	1	2	yes	complemented
456	#416	C₂²×C₇	1	2	yes	complemented
457	C₂×#102	C₂²×C₇	1	2	yes	complemented
458	#407	C₂²×C₇	1	1	yes	characteristic
459	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
460	#405	C₂²×C₇	1	2	yes	complemented
461	C₂³×C₇	—	2	2	no	—
462	C₂³×C₇	—	2	2	no	—
463	C₂³×C₇	—	2	2	no	—
464	C₂³×C₇	—	2	1	no	—
465	C₂³×C₇	—	2	4	no	—
466	C₂³×C₇	—	2	2	no	—
467	C₂³×C₇	—	4	1	no	—
468	C₂³×C₇	—	4	2	no	—
469	C₂³×C₇	—	4	4	no	—
470	C₂³×C₇	—	4	4	no	—
471	C₂³×C₇	—	4	2	no	—
472	C₂³×C₇	—	4	4	no	—
473	C₂³×C₇	—	4	4	no	—
474	C₂³×C₇	—	4	2	no	—
475	C₂³×C₇	—	4	4	no	—
476	C₂³×C₇	—	4	2	no	—
477	C₂³×C₇	—	8	2	no	—
478	C₂³×C₇	—	8	2	no	—
479	C₂³×C₇	—	8	2	no	—
480	C₂³×C₇	—	8	2	no	—
481	C₂³×C₇	—	8	1	no	—
482	C₂³×C₇	—	8	1	no	—
483	C₂³×C₇	—	8	16	no	—
484	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
485	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
486	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
487	C₇×Q₈	—	2	2	no	—
488	C₇×Q₈	—	2	2	no	—
489	C₇×Q₈	—	2	2	no	—
490	C₇×Q₈	—	4	2	no	—
491	C₇×Q₈	—	8	2	no	—
492	C₇×D₄	—	2	4	no	—
493	C₇×D₄	—	2	2	no	—
494	C₇×D₄	—	2	4	no	—
495	C₇×D₄	—	2	2	no	—
496	C₇×D₄	—	2	4	no	—
497	C₇×D₄	—	2	2	no	—
498	C₇×D₄	—	4	4	no	—
499	C₇×D₄	—	4	4	no	—
500	C₇×D₄	—	4	2	no	—
501	C₇×D₄	—	4	4	no	—
502	C₇×D₄	—	4	4	no	—
503	C₇×D₄	—	4	2	no	—
504	C₇×D₄	—	4	4	no	—
505	C₇×D₄	—	4	2	no	—
506	C₇×D₄	—	4	2	no	—
507	C₇×D₄	—	4	4	no	—
508	C₇×D₄	—	8	2	no	—
509	C₇×D₄	—	8	4	no	—
510	C₇×D₄	—	8	4	no	—
511	C₇×D₄	—	8	4	no	—
512	C₇×D₄	—	8	4	no	—
513	C₇×D₄	—	8	2	no	—
514	C₇×D₄	—	8	1	no	—
515	C₇×D₄	—	8	2	no	—
516	C₂×C₄×C₇	—	2	2	no	—
517	C₂×C₄×C₇	—	2	4	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	1	no	—
523	C₂×C₄×C₇	—	2	1	no	—
524	C₂×C₄×C₇	—	2	1	no	—
525	C₂×C₄×C₇	—	2	2	no	—
526	C₂×C₄×C₇	—	2	2	no	—
527	C₂×C₄×C₇	—	4	2	no	—
528	C₂×C₄×C₇	—	4	4	no	—
529	C₂×C₄×C₇	—	4	2	no	—
530	C₂×C₄×C₇	—	4	4	no	—
531	C₂×C₄×C₇	—	4	2	no	—
532	C₂×C₄×C₇	—	8	2	no	—
533	C₂×C₄×C₇	—	8	2	no	—
534	C₂×C₄×C₇	—	8	2	no	—
535	C₂×C₄×C₇	—	8	1	no	—
536	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
539	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
544	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
545	C₇×C₈	—	2	2	no	—
546	C₇×C₈	—	2	2	no	—
547	C₇×C₈	—	2	4	no	—
548	C₂⁵	—	2	1	no	—
549	C₂×#41	—	2	1	no	—
550	C₂×#41	—	2	1	no	—
551	C₂×#41	—	2	2	no	—
552	C₂×#41	—	4	4	no	—
553	C₂×#41	C₂³×C₇	1	1	yes	characteristic
554	C₂×#41	C₂³×C₇	1	2	yes	—
555	C₂×#41	C₂³×C₇	1	2	yes	—
556	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	—	2	1	no	—
559	C₂²×D₄	—	2	1	no	—
560	C₂²×D₄	—	2	1	no	—
561	C₂²×D₄	—	2	1	no	—
562	C₂²×D₄	—	2	2	no	—
563	C₂²×D₄	—	2	2	no	—
564	C₂²×D₄	—	4	4	no	—
565	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₇	1	2	yes	—
567	C₂²×D₄	C₂³×C₇	1	2	yes	—
568	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₇	1	2	yes	—
570	C₂³×C₄	—	2	1	no	—
571	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
572	AGL(1,ℤ/8)	—	4	4	no	—
573	AGL(1,ℤ/8)	—	4	4	no	—
574	#135	—	4	4	no	—
575	C₂×Q₁₆	C₂³×C₇	1	2	yes	complemented
576	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
577	C₂×SD₁₆	C₂³×C₇	1	2	yes	complemented
578	C₂×SD₁₆	C₂³×C₇	1	2	yes	complemented
579	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
580	C₂×D₈	—	4	4	no	—
581	C₂×D₈	C₂³×C₇	1	4	yes	—
582	C₂×D₈	C₂³×C₇	1	4	yes	—
583	C₂×D₈	C₂³×C₇	1	4	yes	—
584	C₂×D₈	C₂³×C₇	1	2	yes	complemented
585	C₂×D₈	C₂³×C₇	1	4	yes	complemented
586	C₂×M₁₆	C₂³×C₇	1	2	yes	—
587	C₂²×C₈	C₂³×C₇	1	2	yes	—
588	C₄⋊Q₈	—	2	1	no	—
589	C₄⋊Q₈	C₂³×C₇	1	2	yes	complemented
590	#127	—	2	2	no	—
591	#127	—	2	2	no	—
592	#127	C₂³×C₇	1	4	yes	—
593	#127	C₂³×C₇	1	4	yes	—
594	#127	C₂³×C₇	1	2	yes	complemented
595	#126	—	2	2	no	—
596	#126	—	2	2	no	—
597	#125	—	2	1	no	—
598	#125	C₂³×C₇	1	2	yes	complemented
599	#124	—	2	2	no	—
600	#124	—	2	2	no	—
601	#124	—	2	2	no	—
602	#124	—	2	2	no	—
603	#124	C₂³×C₇	1	4	yes	—
604	#124	C₂³×C₇	1	4	yes	—
605	#124	C₂³×C₇	1	2	yes	complemented
606	#123	—	2	1	no	—
607	#123	—	2	2	no	—
608	#123	—	2	2	no	—
609	#123	—	2	2	no	—
610	#123	—	2	2	no	—
611	C₂²⋊Q₈	—	2	2	no	—
612	C₂²⋊Q₈	—	2	2	no	—
613	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
614	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
615	#121	—	2	1	no	—
616	#121	—	2	1	no	—
617	#121	—	2	2	no	—
618	#121	—	2	2	no	—
619	#121	—	2	2	no	—
620	#121	—	2	2	no	—
621	#121	—	2	2	no	—
622	#121	—	2	4	no	—
623	#121	—	2	4	no	—
624	#121	—	2	1	no	—
625	#121	—	2	1	no	—
626	#121	—	2	2	no	—
627	#121	—	2	2	no	—
628	#121	C₂³×C₇	1	2	yes	—
629	#121	C₂³×C₇	1	2	yes	—
630	#121	C₂³×C₇	1	1	yes	characteristic
631	#121	C₂³×C₇	1	1	yes	characteristic
632	#120	—	2	1	no	—
633	#120	—	2	4	no	—
634	#120	—	2	4	no	—
635	#120	—	2	4	no	—
636	#120	—	2	4	no	—
637	#120	—	2	2	no	—
638	C₄×Q₈	C₂³×C₇	1	2	yes	complemented
639	C₄×D₄	—	2	1	no	—
640	C₄×D₄	—	2	1	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	C₂³×C₇	1	2	yes	complemented
647	C₄×D₄	C₂³×C₇	1	2	yes	complemented
648	C₄×D₄	C₂³×C₇	1	2	yes	complemented
649	#117	—	2	1	no	—
650	#117	—	2	2	no	—
651	#117	C₇×D₄	1	2	yes	—
652	#117	C₇×D₄	1	1	yes	characteristic
653	#117	C₇×D₄	1	1	yes	characteristic
654	#117	C₂³×C₇	1	1	yes	characteristic
655	#117	C₂³×C₇	1	1	yes	characteristic
656	#117	C₂³×C₇	1	1	yes	characteristic
657	#117	C₂³×C₇	1	2	yes	—
658	C₂×C₄⋊C₄	—	2	1	no	—
659	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
662	C₂×C₂²⋊C₄	—	2	2	no	—
663	C₂×C₂²⋊C₄	—	2	2	no	—
664	C₂×C₂²⋊C₄	—	2	1	no	—
665	C₂×C₂²⋊C₄	—	2	2	no	—
666	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
667	C₂×C₄²	C₂³×C₇	1	2	yes	—
668	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
669	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
670	#103	C₂³×C₇	1	2	yes	complemented
671	#103	C₂³×C₇	1	2	yes	complemented
672	#103	C₂³×C₇	1	4	yes	complemented
673	#102	C₂³×C₇	1	4	yes	—
674	#102	C₂³×C₇	1	4	yes	—
675	#102	C₂³×C₇	1	4	yes	—
676	#102	C₂³×C₇	1	4	yes	—
677	#102	C₂³×C₇	1	2	yes	complemented
678	#102	C₂³×C₇	1	2	yes	complemented
679	#102	C₂³×C₇	1	4	yes	complemented
680	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
681	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
682	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
683	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
684	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
685	#97	C₂³×C₇	1	4	yes	complemented
686	C₄×C₈	C₂³×C₇	1	4	yes	complemented
687	C₂²×C₇	—	2	1	no	—
688	C₂²×C₇	—	2	1	no	—
689	C₂²×C₇	—	2	1	no	—
690	C₂²×C₇	—	2	1	no	—
691	C₂²×C₇	—	2	1	no	—
692	C₂²×C₇	—	2	1	no	—
693	C₂²×C₇	—	2	1	no	—
694	C₂²×C₇	—	4	4	no	—
695	C₂²×C₇	—	4	2	no	—
696	C₂²×C₇	—	4	2	no	—
697	C₂²×C₇	—	4	1	no	—
698	C₂²×C₇	—	4	4	no	—
699	C₂²×C₇	—	4	2	no	—
700	C₂²×C₇	—	4	1	no	—
701	C₂²×C₇	—	4	4	no	—
702	C₂²×C₇	—	4	2	no	—
703	C₂²×C₇	—	4	1	no	—
704	C₂²×C₇	—	4	2	no	—
705	C₂²×C₇	—	4	2	no	—
706	C₂²×C₇	—	4	4	no	—
707	C₂²×C₇	—	8	4	no	—
708	C₂²×C₇	—	8	8	no	—
709	C₂²×C₇	—	8	8	no	—
710	C₂²×C₇	—	8	8	no	—
711	C₂²×C₇	—	16	2	no	—
712	C₂²×C₇	#535	1	2	yes	—
713	C₂²×C₇	#576	1	2	yes	—
714	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
715	C₄×C₇	—	2	2	no	—
716	C₄×C₇	—	2	2	no	—
717	C₄×C₇	—	2	1	no	—
718	C₄×C₇	—	2	1	no	—
719	C₄×C₇	—	2	2	no	—
720	C₄×C₇	—	2	2	no	—
721	C₄×C₇	—	4	1	no	—
722	C₄×C₇	—	4	2	no	—
723	C₄×C₇	—	4	1	no	—
724	C₄×C₇	—	4	2	no	—
725	C₄×C₇	—	4	1	no	—
726	C₄×C₇	#535	1	2	yes	—
727	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
728	C₂⁴	—	2	2	no	—
729	C₂⁴	—	2	1	no	—
730	C₂⁴	—	2	1	no	—
731	C₂⁴	—	2	2	no	—
732	C₂⁴	—	2	2	no	—
733	C₂⁴	—	4	4	no	—
734	C₂⁴	—	8	2	no	—
735	C₂⁴	—	8	2	no	—
736	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
737	#41	—	2	4	no	—
738	#41	—	2	4	no	—
739	#41	—	2	4	no	—
740	#41	—	4	2	no	—
741	#41	—	4	2	no	—
742	#41	—	4	4	no	—
743	#41	—	4	4	no	—
744	#41	—	8	4	no	—
745	C₂×Q₈	—	2	1	no	—
746	C₂×Q₈	—	2	2	no	—
747	C₂×Q₈	—	4	2	no	—
748	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
749	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
750	C₂×D₄	—	2	1	no	—
751	C₂×D₄	—	2	1	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	1	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	1	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	1	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	4	no	—
764	C₂×D₄	—	2	4	no	—
765	C₂×D₄	—	2	4	no	—
766	C₂×D₄	—	2	4	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	4	no	—
769	C₂×D₄	—	2	4	no	—
770	C₂×D₄	—	2	4	no	—
771	C₂×D₄	—	4	4	no	—
772	C₂×D₄	—	4	4	no	—
773	C₂×D₄	—	4	2	no	—
774	C₂×D₄	—	4	4	no	—
775	C₂×D₄	—	4	4	no	—
776	C₂×D₄	—	4	4	no	—
777	C₂×D₄	—	4	4	no	—
778	C₂×D₄	—	8	4	no	—
779	C₂×D₄	—	8	4	no	—
780	C₂×D₄	—	8	2	no	—
781	C₂×D₄	C₂⁴×C₇	1	4	yes	—
782	C₂×D₄	C₂⁴×C₇	1	2	yes	—
783	C₂×D₄	C₂⁴×C₇	1	2	yes	—
784	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
785	C₂²×C₄	—	2	4	no	—
786	C₂²×C₄	—	2	1	no	—
787	C₂²×C₄	—	2	1	no	—
788	C₂²×C₄	—	2	1	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	4	4	no	—
795	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
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	C₂×C₇×D₄	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
801	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
803	Q₁₆	—	4	2	no	—
804	SD₁₆	—	4	4	no	—
805	SD₁₆	—	4	2	no	—
806	SD₁₆	—	4	2	no	—
807	SD₁₆	—	4	4	no	—
808	D₈	—	4	4	no	—
809	D₈	—	4	4	no	—
810	D₈	—	4	4	no	—
811	D₈	—	4	2	no	—
812	D₈	—	4	4	no	—
813	M₁₆	—	2	4	no	—
814	C₂×C₈	—	2	4	no	—
815	C₂×C₈	C₂⁴×C₇	1	2	yes	—
816	C₂×C₈	C₂⁴×C₇	1	4	yes	—
817	C₂×C₈	C₂⁴×C₇	1	2	yes	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	1	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
826	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
827	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
828	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
829	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
830	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
831	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
832	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
833	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
834	C₂²⋊C₄	—	2	1	no	—
835	C₂²⋊C₄	—	2	1	no	—
836	C₂²⋊C₄	—	2	1	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	4	no	—
841	C₂²⋊C₄	—	2	4	no	—
842	C₂²⋊C₄	—	2	4	no	—
843	C₂²⋊C₄	—	2	4	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	1	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	1	no	—
850	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
851	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
852	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
853	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
854	C₄²	—	2	2	no	—
855	C₄²	—	2	1	no	—
856	C₄²	C₂×C₇×D₄	1	2	yes	—
857	C₄²	C₂×C₇×D₄	1	2	yes	—
858	C₄²	C₂⁴×C₇	1	2	yes	—
859	C₄²	C₂⁴×C₇	1	2	yes	—
860	C₂×C₇	—	2	2	no	—
861	C₂×C₇	—	2	2	no	—
862	C₂×C₇	—	4	1	no	—
863	C₂×C₇	—	8	1	no	—
864	C₂×C₇	—	8	2	no	—
865	C₂×C₇	—	8	4	no	—
866	C₂×C₇	—	8	2	no	—
867	C₂×C₇	C₂×#535	1	1	yes	characteristic
868	C₂×C₇	C₂×#576	1	1	yes	characteristic
869	C₂×C₇	#3585	1	1	yes	characteristic
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	4	no	—
875	C₂³	—	2	2	no	—
876	C₂³	—	4	1	no	—
877	C₂³	—	4	2	no	—
878	C₂³	—	4	4	no	—
879	C₂³	—	4	4	no	—
880	C₂³	—	4	2	no	—
881	C₂³	—	4	4	no	—
882	C₂³	—	4	4	no	—
883	C₂³	—	4	2	no	—
884	C₂³	—	4	4	no	—
885	C₂³	—	4	2	no	—
886	C₂³	—	8	2	no	—
887	C₂³	—	8	2	no	—
888	C₂³	—	8	2	no	—
889	C₂³	—	8	2	no	—
890	C₂³	—	8	1	no	—
891	C₂³	—	8	1	no	—
892	C₂³	—	8	16	no	—
893	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
894	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
895	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
896	Q₈	—	2	2	no	—
897	Q₈	—	2	2	no	—
898	Q₈	—	2	2	no	—
899	Q₈	—	4	2	no	—
900	Q₈	—	8	2	no	—
901	D₄	—	2	4	no	—
902	D₄	—	2	2	no	—
903	D₄	—	2	4	no	—
904	D₄	—	2	2	no	—
905	D₄	—	2	4	no	—
906	D₄	—	2	2	no	—
907	D₄	—	4	4	no	—
908	D₄	—	4	4	no	—
909	D₄	—	4	2	no	—
910	D₄	—	4	4	no	—
911	D₄	—	4	4	no	—
912	D₄	—	4	2	no	—
913	D₄	—	4	4	no	—
914	D₄	—	4	2	no	—
915	D₄	—	4	2	no	—
916	D₄	—	4	4	no	—
917	D₄	—	8	2	no	—
918	D₄	—	8	4	no	—
919	D₄	—	8	4	no	—
920	D₄	—	8	4	no	—
921	D₄	—	8	4	no	—
922	D₄	—	8	2	no	—
923	D₄	—	8	1	no	—
924	D₄	—	8	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	4	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	4	2	no	—
937	C₂×C₄	—	4	4	no	—
938	C₂×C₄	—	4	2	no	—
939	C₂×C₄	—	4	4	no	—
940	C₂×C₄	—	4	2	no	—
941	C₂×C₄	—	8	2	no	—
942	C₂×C₄	—	8	2	no	—
943	C₂×C₄	—	8	2	no	—
944	C₂×C₄	—	8	1	no	—
945	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
946	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
947	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
948	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
949	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
950	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
951	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
952	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
953	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
954	C₈	—	2	2	no	—
955	C₈	—	2	2	no	—
956	C₈	—	2	4	no	—
957	C₇	#60811	1	1	yes	characteristic, direct product factor, Sylow
958	C₂²	—	2	1	no	—
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	—	4	4	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	4	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	1	no	—
973	C₂²	—	4	4	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	4	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	8	8	no	—
979	C₂²	—	8	4	no	—
980	C₂²	—	8	8	no	—
981	C₂²	—	8	8	no	—
982	C₂²	—	16	2	no	—
983	C₂²	C₇×#535	1	2	yes	—
984	C₂²	C₇×#576	1	2	yes	—
985	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
986	C₄	—	2	2	no	—
987	C₄	—	2	2	no	—
988	C₄	—	2	2	no	—
989	C₄	—	2	2	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	1	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	1	no	—
997	C₄	C₇×#535	1	2	yes	—
998	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
999	C₂	—	2	2	no	—
1000	C₂	—	2	2	no	—
1001	C₂	—	4	1	no	—
1002	C₂	—	8	4	no	—
1003	C₂	—	8	2	no	—
1004	C₂	—	8	2	no	—
1005	C₂	—	8	1	no	—
1006	C₂	C₂×C₇×#535	1	1	yes	characteristic
1007	C₂	C₂×C₇×#576	1	1	yes	characteristic
1008	C₂	C₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3494	C₂	semidirect
2. C₂×C₇×#535	C₂	semidirect
3. C₇×#3224	C₂	semidirect
4. C₇×#3220	C₂	semidirect
5. C₇×#3217	C₂	semidirect
6. C₇×#3213	C₂	semidirect
7. C₇×#3211	C₂	semidirect
8. C₇×#3205	C₂	semidirect
9. C₇×#3155	C₂	semidirect
10. C₇×#3136	C₂	semidirect
11. C₇×#3045	C₂	semidirect
12. C₇×#3041	C₂	semidirect
13. C₇×#3006	C₂	semidirect
14. C₇×#3003	C₂	semidirect
15. C₇×#3002	C₂	semidirect
16. C₂×C₇×#447	C₂	semidirect
17. C₇×#2924	C₂	semidirect
20. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₇×#135	C₂²	semidirect
23. C₂²×C₇×D₈	C₂²	semidirect
30. C₇×#544	C₂²	semidirect
31. C₇×#542	C₂²	semidirect
32. C₇×#540	C₂²	semidirect
38. C₇×#535	C₂²	semidirect
39. C₇×#535	C₂²	semidirect
40. C₇×#532	C₂²	semidirect
41. C₂×C₇×#127	C₂²	semidirect
42. C₇×#529	C₂²	semidirect
43. C₂×C₇×#124	C₂²	semidirect
49. C₇×#520	C₂²	semidirect
50. C₇×#518	C₂²	semidirect
52. C₇×#496	C₂²	semidirect
53. C₇×#496	C₂²	semidirect
54. C₇×#495	C₂²	semidirect
55. C₇×#493	C₂²	semidirect
56. C₇×#490	C₂²	semidirect
57. C₇×#489	C₂²	semidirect
58. C₇×#488	C₂²	semidirect
59. C₇×#486	C₂²	semidirect
60. C₇×#464	C₂²	semidirect
61. C₇×#463	C₂²	semidirect
62. C₇×#463	C₂²	semidirect
63. C₇×#463	C₂²	semidirect
64. C₇×#460	C₂²	semidirect
65. C₇×#459	C₂²	semidirect
66. C₇×#459	C₂²	semidirect
67. C₇×#459	C₂²	semidirect
68. C₇×#452	C₂²	semidirect
69. C₇×#451	C₂²	semidirect
70. C₇×#450	C₂²	semidirect
71. C₇×#450	C₂²	semidirect
72. C₇×#450	C₂²	semidirect
73. C₇×#449	C₂²	semidirect
74. C₇×#449	C₂²	semidirect
75. C₇×#448	C₂²	semidirect
76. C₇×#448	C₂²	semidirect
79. C₇×#447	C₂²	semidirect
80. C₇×#447	C₂²	semidirect
81. C₇×#447	C₂²	semidirect
82. C₇×#447	C₂²	semidirect
83. C₇×#447	C₂²	semidirect
84. C₇×#433	C₂²	semidirect
85. C₇×#432	C₂²	semidirect
86. C₇×#431	C₂²	semidirect
87. C₇×#424	C₂²	semidirect
88. C₇×#418	C₂²	semidirect
89. C₇×#417	C₂²	semidirect
90. C₇×#416	C₂²	semidirect
91. C₂×C₇×#102	C₂²	semidirect
94. C₇×#405	C₂²	semidirect
95. #60811	C₇	direct (N × H)
123. C₂×C₇×Q₁₆	C₂³	semidirect
125. C₂×C₇×SD₁₆	C₂³	semidirect
126. C₂×C₇×SD₁₆	C₂³	semidirect
127. C₂×C₇×SD₁₆	C₂³	semidirect
132. C₂×C₇×D₈	C₂³	semidirect
133. C₂×C₇×D₈	C₂³	semidirect
137. C₇×C₄⋊Q₈	C₂³	semidirect
142. C₇×#127	C₂³	semidirect
146. C₇×#125	C₂³	semidirect
153. C₇×#124	C₂³	semidirect
186. C₄×C₇×Q₈	C₂³	semidirect
194. C₄×C₇×D₄	C₂³	semidirect
195. C₄×C₇×D₄	C₂³	semidirect
196. C₄×C₇×D₄	C₂³	semidirect
216. C₇×C₄⋊C₈	C₂³	semidirect
217. C₇×C₄⋊C₈	C₂³	semidirect
218. C₇×#103	C₂³	semidirect
219. C₇×#103	C₂³	semidirect
220. C₇×#103	C₂³	semidirect
225. C₇×#102	C₂³	semidirect
226. C₇×#102	C₂³	semidirect
227. C₇×#102	C₂³	semidirect
233. C₇×#97	C₂³	semidirect
234. C₄×C₇×C₈	C₂³	semidirect
235. #3494	C₂×C₇	semidirect
236. C₂×#535	C₂×C₇	semidirect
237. #3224	C₂×C₇	semidirect
238. #3220	C₂×C₇	semidirect
239. #3217	C₂×C₇	semidirect
240. #3213	C₂×C₇	semidirect
241. #3211	C₂×C₇	semidirect
242. #3205	C₂×C₇	semidirect
243. #3155	C₂×C₇	semidirect
244. #3136	C₂×C₇	semidirect
245. #3045	C₂×C₇	semidirect
246. #3041	C₂×C₇	semidirect
247. #3006	C₂×C₇	semidirect
248. #3003	C₂×C₇	semidirect
249. #3002	C₂×C₇	semidirect
250. C₂×#447	C₂×C₇	semidirect
251. #2924	C₂×C₇	semidirect
386. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
387. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
388. C₂×#135	C₂²×C₇	semidirect
389. C₂²×D₈	C₂²×C₇	semidirect
396. #544	C₂²×C₇	semidirect
397. #542	C₂²×C₇	semidirect
398. #540	C₂²×C₇	semidirect
404. #535	C₂²×C₇	semidirect
405. #535	C₂²×C₇	semidirect
406. #532	C₂²×C₇	semidirect
407. C₂×#127	C₂²×C₇	semidirect
408. #529	C₂²×C₇	semidirect
409. C₂×#124	C₂²×C₇	semidirect
415. #520	C₂²×C₇	semidirect
416. #518	C₂²×C₇	semidirect
418. #496	C₂²×C₇	semidirect
419. #496	C₂²×C₇	semidirect
420. #495	C₂²×C₇	semidirect
421. #493	C₂²×C₇	semidirect
422. #490	C₂²×C₇	semidirect
423. #489	C₂²×C₇	semidirect
424. #488	C₂²×C₇	semidirect
425. #486	C₂²×C₇	semidirect
426. #464	C₂²×C₇	semidirect
427. #463	C₂²×C₇	semidirect
428. #463	C₂²×C₇	semidirect
429. #463	C₂²×C₇	semidirect
430. #460	C₂²×C₇	semidirect
431. #459	C₂²×C₇	semidirect
432. #459	C₂²×C₇	semidirect
433. #459	C₂²×C₇	semidirect
434. #452	C₂²×C₇	semidirect
435. #451	C₂²×C₇	semidirect
436. #450	C₂²×C₇	semidirect
437. #450	C₂²×C₇	semidirect
438. #450	C₂²×C₇	semidirect
439. #449	C₂²×C₇	semidirect
440. #449	C₂²×C₇	semidirect
441. #448	C₂²×C₇	semidirect
442. #448	C₂²×C₇	semidirect
445. #447	C₂²×C₇	semidirect
446. #447	C₂²×C₇	semidirect
447. #447	C₂²×C₇	semidirect
448. #447	C₂²×C₇	semidirect
449. #447	C₂²×C₇	semidirect
450. #433	C₂²×C₇	semidirect
451. #432	C₂²×C₇	semidirect
452. #431	C₂²×C₇	semidirect
453. #424	C₂²×C₇	semidirect
454. #418	C₂²×C₇	semidirect
455. #417	C₂²×C₇	semidirect
456. #416	C₂²×C₇	semidirect
457. C₂×#102	C₂²×C₇	semidirect
460. #405	C₂²×C₇	semidirect
575. C₂×Q₁₆	C₂³×C₇	semidirect
577. C₂×SD₁₆	C₂³×C₇	semidirect
578. C₂×SD₁₆	C₂³×C₇	semidirect
579. C₂×SD₁₆	C₂³×C₇	semidirect
584. C₂×D₈	C₂³×C₇	semidirect
585. C₂×D₈	C₂³×C₇	semidirect
589. C₄⋊Q₈	C₂³×C₇	semidirect
594. #127	C₂³×C₇	semidirect
598. #125	C₂³×C₇	semidirect
605. #124	C₂³×C₇	semidirect
638. C₄×Q₈	C₂³×C₇	semidirect
646. C₄×D₄	C₂³×C₇	semidirect
647. C₄×D₄	C₂³×C₇	semidirect
648. C₄×D₄	C₂³×C₇	semidirect
668. C₄⋊C₈	C₂³×C₇	semidirect
669. C₄⋊C₈	C₂³×C₇	semidirect
670. #103	C₂³×C₇	semidirect
671. #103	C₂³×C₇	semidirect
672. #103	C₂³×C₇	semidirect
677. #102	C₂³×C₇	semidirect
678. #102	C₂³×C₇	semidirect
679. #102	C₂³×C₇	semidirect
685. #97	C₂³×C₇	semidirect
686. C₄×C₈	C₂³×C₇	semidirect
957. C₇	#60811	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×#3494	2
C₂×C₇×#535	2
C₇×#3224	2
C₇×#3220	2
C₇×#3217	2
C₇×#3213	2
C₇×#3211	2
C₇×#3205	2
C₇×#3155	2
C₇×#3136	2
C₇×#3045	2
C₇×#3041	2
C₇×#3006	2
C₇×#3003	2
C₇×#3002	2
C₂×C₇×#447	2
C₇×#2924	2
#60811	7

Subgroups — C7×#60811 #13238027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60811 #13238027