Subgroups — C₇×#61323 #13238539

Order 1792.

1814 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3377	C₂	1	4	yes	maximal, complemented
4	C₇×#3376	C₂	1	4	yes	maximal, complemented
5	C₇×#3369	C₂	1	2	yes	maximal, complemented
6	C₇×#3367	C₂	1	2	yes	maximal, complemented
7	C₇×#3364	C₂	1	2	yes	maximal, complemented
8	C₇×#3360	C₂	1	2	yes	maximal, complemented
9	C₇×#3140	C₂	1	2	yes	maximal, complemented
10	C₇×#3139	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3078	C₂	1	2	yes	maximal, complemented
12	C₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3040	C₂	1	2	yes	maximal
14	C₇×#3039	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×#137	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
18	C₂×C₇×#137	C₂²	1	2	yes	—
19	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₇×Q₈²	C₂²	1	1	yes	characteristic, complemented
21	C₇×#557	C₂²	1	1	yes	characteristic, complemented
22	C₇×#557	C₂²	1	2	yes	complemented
23	C₇×#556	—	2	1	no	—
24	C₇×#556	—	2	2	no	—
25	C₇×#556	—	2	1	no	—
26	C₇×#556	C₂²	1	2	yes	—
27	C₇×#556	C₂²	1	2	yes	—
28	C₇×#556	C₂²	1	4	yes	—
29	C₇×#554	—	2	1	no	—
30	C₇×#554	—	2	2	no	—
31	C₇×#554	C₂²	1	1	yes	characteristic, complemented
32	C₇×#554	C₂²	1	2	yes	complemented
33	C₇×D₄×Q₈	—	2	1	no	—
34	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₇×#533	—	2	1	no	—
36	C₇×#533	—	2	2	no	—
37	C₇×#533	C₂²	1	1	yes	characteristic
38	C₇×#533	C₂²	1	2	yes	—
39	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₇×#126	—	2	2	no	—
41	C₂×C₇×#124	C₂²	1	2	yes	—
42	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
43	C₄×C₇×#41	C₂²	1	1	yes	characteristic
44	C₄×C₇×#41	C₂²	1	2	yes	—
45	C₂×C₄×C₇×Q₈	—	2	1	no	—
46	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
47	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₇×#117	—	2	1	no	—
50	C₇×#491	C₂²	1	4	yes	complemented
51	C₇×#489	C₂²	1	4	yes	—
52	C₇×#489	C₂²	1	4	yes	—
53	C₇×#488	C₂²	1	4	yes	—
54	C₇×#488	C₂²	1	4	yes	—
55	C₇×#487	C₂²	1	2	yes	complemented
56	C₇×#487	C₂²	1	2	yes	complemented
57	C₇×#479	C₂²	1	4	yes	complemented
58	C₇×#479	C₂²	1	4	yes	complemented
59	C₇×#478	C₂²	1	4	yes	—
60	C₇×#477	C₂²	1	4	yes	complemented
61	C₇×#476	C₂²	1	2	yes	—
62	C₇×#475	C₂²	1	4	yes	complemented
63	C₇×#474	C₂²	1	2	yes	—
64	C₇×#464	C₂²	1	4	yes	—
65	C₇×#464	C₂²	1	4	yes	—
66	C₇×#463	C₂²	1	4	yes	—
67	C₇×#463	C₂²	1	4	yes	—
68	C₇×#462	C₂²	1	2	yes	complemented
69	C₇×#462	C₂²	1	2	yes	complemented
70	C₇×#461	C₂²	1	2	yes	complemented
71	C₇×#461	C₂²	1	2	yes	complemented
72	C₇×#446	C₂²	1	2	yes	complemented
73	C₇×#446	C₂²	1	4	yes	complemented
74	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
75	C₇×#442	C₂²	1	2	yes	—
76	C₇×#441	C₂²	1	4	yes	complemented
77	C₇×#440	C₂²	1	2	yes	—
78	C₇×#440	C₂²	1	4	yes	complemented
79	C₄×C₇×Q₁₆	C₂²	1	4	yes	complemented
80	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
81	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
82	C₄×C₇×D₈	C₂²	1	2	yes	—
83	C₇×#428	C₂²	1	1	yes	characteristic
84	C₇×#428	C₂²	1	2	yes	—
85	C₇×#423	C₂²	1	1	yes	characteristic
86	C₇×#423	C₂²	1	2	yes	—
87	C₇×#419	C₂²	1	2	yes	—
88	C₇×#419	C₂²	1	2	yes	—
89	C₇×#419	C₂²	1	2	yes	—
90	C₇×#418	C₂²	1	1	yes	characteristic
91	C₇×#418	C₂²	1	2	yes	—
92	C₇×#417	C₂²	1	1	yes	characteristic
93	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
94	C₄×C₇×M₁₆	C₂²	1	2	yes	—
95	#61323	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₇×#41	C₂³	1	1	yes	characteristic
97	C₂²×C₇×Q₈	—	2	1	no	—
98	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
99	C₂²×C₇×Q₈	C₂³	1	2	yes	—
100	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₇	—	2	1	no	—
102	C₇×#137	—	2	8	no	—
103	C₇×AGL(1,ℤ/8)	—	2	4	no	—
104	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
105	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
106	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₇×D₈	C₂³	1	2	yes	—
108	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
109	C₂×C₇×M₁₆	C₂³	1	2	yes	—
110	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
111	C₇×C₄⋊Q₈	—	2	1	no	—
112	C₇×C₄⋊Q₈	—	2	2	no	—
113	C₇×C₄⋊Q₈	—	2	1	no	—
114	C₇×C₄⋊Q₈	—	2	2	no	—
115	C₇×C₄⋊Q₈	—	2	1	no	—
116	C₇×C₄⋊Q₈	—	2	1	no	—
117	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
123	C₇×#126	—	2	4	no	—
124	C₇×#126	—	2	4	no	—
125	C₇×#126	—	2	4	no	—
126	C₇×#126	—	2	4	no	—
127	C₇×#125	—	2	2	no	—
128	C₇×#125	—	2	2	no	—
129	C₇×#125	—	2	2	no	—
130	C₇×#125	C₂³	1	2	yes	—
131	C₇×#125	C₂³	1	2	yes	—
132	C₇×#125	C₂³	1	2	yes	—
133	C₇×#124	—	2	2	no	—
134	C₇×#124	—	2	2	no	—
135	C₇×#124	C₂³	1	4	yes	—
136	C₇×#124	C₂³	1	4	yes	—
137	C₇×C₂²⋊Q₈	—	2	2	no	—
138	C₇×C₂²⋊Q₈	—	2	2	no	—
139	C₇×C₂²⋊Q₈	—	2	4	no	—
140	C₇×C₂²⋊Q₈	—	2	1	no	—
141	C₇×C₂²⋊Q₈	—	2	2	no	—
142	C₇×C₂²⋊Q₈	—	2	1	no	—
143	C₇×C₂²⋊Q₈	—	2	2	no	—
144	C₇×C₂²⋊Q₈	—	2	2	no	—
145	C₇×C₂²⋊Q₈	—	2	1	no	—
146	C₇×C₂²⋊Q₈	—	2	1	no	—
147	C₇×C₂²⋊Q₈	—	2	2	no	—
148	C₇×C₂²⋊Q₈	—	2	2	no	—
149	C₇×C₂²⋊Q₈	—	2	2	no	—
150	C₇×C₂²⋊Q₈	—	2	2	no	—
151	C₄×C₇×Q₈	—	2	1	no	—
152	C₄×C₇×Q₈	—	2	1	no	—
153	C₄×C₇×Q₈	—	2	2	no	—
154	C₄×C₇×Q₈	—	2	1	no	—
155	C₄×C₇×Q₈	—	2	2	no	—
156	C₄×C₇×Q₈	—	2	2	no	—
157	C₄×C₇×Q₈	—	2	2	no	—
158	C₄×C₇×Q₈	—	2	1	no	—
159	C₄×C₇×Q₈	—	2	2	no	—
160	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
161	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
162	C₄×C₇×Q₈	D₄	1	2	yes	—
163	C₄×C₇×Q₈	C₂³	1	4	yes	—
164	C₄×C₇×Q₈	C₂³	1	4	yes	—
165	C₄×C₇×Q₈	C₂³	1	2	yes	—
166	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
167	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
168	C₄×C₇×Q₈	C₂³	1	2	yes	—
169	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
170	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
171	C₄×C₇×Q₈	C₂³	1	2	yes	—
172	C₄×C₇×D₄	—	2	1	no	—
173	C₄×C₇×D₄	—	2	2	no	—
174	C₄×C₇×D₄	—	2	2	no	—
175	C₄×C₇×D₄	—	2	1	no	—
176	C₄×C₇×D₄	—	2	1	no	—
177	C₄×C₇×D₄	—	2	1	no	—
178	C₄×C₇×D₄	C₂³	1	2	yes	—
179	C₄×C₇×D₄	C₂³	1	2	yes	—
180	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
181	C₄×C₇×D₄	C₂³	1	2	yes	—
182	C₄×C₇×D₄	C₂³	1	2	yes	—
183	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
184	C₇×#117	—	2	2	no	—
185	C₇×#117	—	2	4	no	—
186	C₇×#117	—	2	2	no	—
187	C₇×#117	—	2	1	no	—
188	C₇×#117	—	2	2	no	—
189	C₇×#117	C₂³	1	1	yes	characteristic
190	C₇×#117	C₂³	1	2	yes	—
191	C₂×C₇×C₄⋊C₄	—	2	1	no	—
192	C₂×C₇×C₄⋊C₄	—	2	2	no	—
193	C₂×C₇×C₄⋊C₄	—	2	1	no	—
194	C₂×C₇×C₄⋊C₄	—	2	1	no	—
195	C₂×C₇×C₄⋊C₄	—	2	2	no	—
196	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
197	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
198	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
201	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
202	C₂×C₄²×C₇	—	2	2	no	—
203	C₂×C₄²×C₇	—	2	1	no	—
204	C₂×C₄²×C₇	—	2	2	no	—
205	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₇	C₂³	1	2	yes	—
207	C₇×#107	C₂³	1	4	yes	—
208	C₇×#107	C₂³	1	2	yes	—
209	C₇×#106	C₂³	1	2	yes	—
210	C₇×#106	C₂³	1	4	yes	—
211	C₇×C₄⋊C₈	C₂³	1	2	yes	—
212	C₇×C₄⋊C₈	C₂³	1	4	yes	—
213	C₇×C₄⋊C₈	C₂³	1	2	yes	—
214	C₇×C₄⋊C₈	C₂³	1	4	yes	—
215	C₇×#103	C₂³	1	4	yes	—
216	C₇×#103	C₂³	1	4	yes	—
217	C₇×#103	C₂³	1	4	yes	—
218	C₇×#103	C₂³	1	4	yes	—
219	C₇×#103	C₂³	1	4	yes	—
220	C₇×#103	C₂³	1	4	yes	—
221	C₇×#103	C₂³	1	2	yes	—
222	C₇×#102	C₂³	1	4	yes	—
223	C₇×#102	C₂³	1	4	yes	—
224	C₇×#102	C₂³	1	2	yes	—
225	C₇×#102	C₂³	1	2	yes	—
226	C₇×#102	C₂³	1	2	yes	—
227	C₇×#97	C₂³	1	4	yes	—
228	C₇×#97	C₂³	1	2	yes	—
229	C₄×C₇×C₈	C₂³	1	2	yes	—
230	C₄×C₇×C₈	C₂³	1	4	yes	—
231	Q₈×#41	C₂×C₇	1	1	yes	characteristic, complemented
232	C₂×#556	C₂×C₇	1	1	yes	characteristic, complemented
233	#3377	C₂×C₇	1	4	yes	complemented
234	#3376	C₂×C₇	1	4	yes	complemented
235	#3369	C₂×C₇	1	2	yes	complemented
236	#3367	C₂×C₇	1	2	yes	complemented
237	#3364	C₂×C₇	1	2	yes	complemented
238	#3360	C₂×C₇	1	2	yes	complemented
239	#3140	C₂×C₇	1	2	yes	complemented
240	#3139	C₂×C₇	1	1	yes	characteristic, complemented
241	#3078	C₂×C₇	1	2	yes	complemented
242	#3077	C₂×C₇	1	1	yes	characteristic, complemented
243	#3040	C₂×C₇	1	2	yes	—
244	#3039	C₂×C₇	1	1	yes	characteristic, complemented
245	Q₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
246	C₄×#137	C₂×C₇	1	2	yes	complemented
247	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic
248	C₂⁴×C₇	—	2	1	no	—
249	C₇×#41	—	2	2	no	—
250	C₇×#41	#41	1	4	yes	—
251	C₂×C₇×Q₈	—	2	2	no	—
252	C₂×C₇×Q₈	—	2	1	no	—
253	C₂×C₇×Q₈	—	2	2	no	—
254	C₂×C₇×Q₈	—	2	2	no	—
255	C₂×C₇×Q₈	—	2	1	no	—
256	C₂×C₇×Q₈	—	2	4	no	—
257	C₂×C₇×Q₈	—	2	4	no	—
258	C₂×C₇×Q₈	—	4	2	no	—
259	C₂×C₇×Q₈	—	4	4	no	—
260	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
261	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
262	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
263	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
264	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
265	C₂×C₇×D₄	—	2	1	no	—
266	C₂×C₇×D₄	—	2	1	no	—
267	C₂×C₇×D₄	—	2	2	no	—
268	C₂×C₇×D₄	—	2	2	no	—
269	C₂×C₇×D₄	C₂⁴	1	2	yes	—
270	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₇	—	2	1	no	—
272	C₂²×C₄×C₇	—	2	1	no	—
273	C₂²×C₄×C₇	—	2	2	no	—
274	C₂²×C₄×C₇	—	2	2	no	—
275	C₂²×C₄×C₇	—	2	1	no	—
276	C₂²×C₄×C₇	—	2	2	no	—
277	C₂²×C₄×C₇	—	2	2	no	—
278	C₂²×C₄×C₇	—	2	2	no	—
279	C₂²×C₄×C₇	—	2	1	no	—
280	C₂²×C₄×C₇	—	4	4	no	—
281	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
286	C₇×Q₁₆	—	2	8	no	—
287	C₇×SD₁₆	—	2	4	no	—
288	C₇×SD₁₆	—	2	8	no	—
289	C₇×D₈	—	2	4	no	—
290	C₇×M₁₆	—	2	2	no	—
291	C₇×M₁₆	—	2	4	no	—
292	C₇×M₁₆	—	2	2	no	—
293	C₂×C₇×C₈	C₂⁴	1	2	yes	—
294	C₂×C₇×C₈	C₂⁴	1	4	yes	—
295	C₂×C₇×C₈	C₂⁴	1	2	yes	—
296	C₇×C₄⋊C₄	—	2	2	no	—
297	C₇×C₄⋊C₄	—	2	2	no	—
298	C₇×C₄⋊C₄	—	2	2	no	—
299	C₇×C₄⋊C₄	—	2	2	no	—
300	C₇×C₄⋊C₄	—	2	2	no	—
301	C₇×C₄⋊C₄	—	2	2	no	—
302	C₇×C₄⋊C₄	—	2	1	no	—
303	C₇×C₄⋊C₄	—	2	4	no	—
304	C₇×C₄⋊C₄	—	2	4	no	—
305	C₇×C₄⋊C₄	—	2	2	no	—
306	C₇×C₄⋊C₄	—	2	2	no	—
307	C₇×C₄⋊C₄	—	2	1	no	—
308	C₇×C₄⋊C₄	—	2	2	no	—
309	C₇×C₄⋊C₄	—	2	2	no	—
310	C₇×C₄⋊C₄	—	2	1	no	—
311	C₇×C₄⋊C₄	—	2	1	no	—
312	C₇×C₄⋊C₄	—	2	2	no	—
313	C₇×C₄⋊C₄	—	2	1	no	—
314	C₇×C₄⋊C₄	—	2	2	no	—
315	C₇×C₄⋊C₄	—	2	2	no	—
316	C₇×C₄⋊C₄	—	2	2	no	—
317	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
318	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
319	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
320	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
321	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
322	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
323	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
324	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
325	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
326	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
327	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
328	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
329	C₇×C₂²⋊C₄	—	2	1	no	—
330	C₇×C₂²⋊C₄	—	2	2	no	—
331	C₇×C₂²⋊C₄	—	2	4	no	—
332	C₇×C₂²⋊C₄	—	2	4	no	—
333	C₇×C₂²⋊C₄	—	2	2	no	—
334	C₇×C₂²⋊C₄	—	2	2	no	—
335	C₇×C₂²⋊C₄	—	2	4	no	—
336	C₇×C₂²⋊C₄	—	2	4	no	—
337	C₇×C₂²⋊C₄	—	2	2	no	—
338	C₇×C₂²⋊C₄	—	2	2	no	—
339	C₇×C₂²⋊C₄	—	2	1	no	—
340	C₇×C₂²⋊C₄	—	2	1	no	—
341	C₄²×C₇	—	2	4	no	—
342	C₄²×C₇	—	2	4	no	—
343	C₄²×C₇	—	2	1	no	—
344	C₄²×C₇	—	2	2	no	—
345	C₄²×C₇	—	2	2	no	—
346	C₄²×C₇	—	2	1	no	—
347	C₄²×C₇	—	2	2	no	—
348	C₄²×C₇	—	2	1	no	—
349	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
350	C₄²×C₇	C₂×D₄	1	2	yes	—
351	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
352	C₄²×C₇	C₂×D₄	1	2	yes	—
353	C₄²×C₇	C₂⁴	1	1	yes	characteristic
354	C₄²×C₇	C₂⁴	1	2	yes	—
355	C₄²×C₇	C₂⁴	1	1	yes	characteristic
356	C₄²×C₇	C₂⁴	1	2	yes	—
357	C₂×#137	C₂²×C₇	1	2	yes	—
358	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
359	Q₈²	C₂²×C₇	1	1	yes	characteristic, complemented
360	#557	C₂²×C₇	1	1	yes	characteristic, complemented
361	#557	C₂²×C₇	1	2	yes	complemented
362	#556	—	2	1	no	—
363	#556	—	2	2	no	—
364	#556	—	2	1	no	—
365	#556	C₂²×C₇	1	2	yes	—
366	#556	C₂²×C₇	1	2	yes	—
367	#556	C₂²×C₇	1	4	yes	—
368	#554	—	2	1	no	—
369	#554	—	2	2	no	—
370	#554	C₂²×C₇	1	1	yes	characteristic, complemented
371	#554	C₂²×C₇	1	2	yes	complemented
372	D₄×Q₈	—	2	1	no	—
373	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
374	#533	—	2	1	no	—
375	#533	—	2	2	no	—
376	#533	C₂²×C₇	1	1	yes	characteristic
377	#533	C₂²×C₇	1	2	yes	—
378	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
379	C₂×#126	—	2	2	no	—
380	C₂×#124	C₂²×C₇	1	2	yes	—
381	C₂×C₂²⋊Q₈	—	2	1	no	—
382	C₄×#41	C₂²×C₇	1	1	yes	characteristic
383	C₄×#41	C₂²×C₇	1	2	yes	—
384	C₂×C₄×Q₈	—	2	1	no	—
385	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
386	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
387	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
388	C₂×#117	—	2	1	no	—
389	#491	C₂²×C₇	1	4	yes	complemented
390	#489	C₂²×C₇	1	4	yes	—
391	#489	C₂²×C₇	1	4	yes	—
392	#488	C₂²×C₇	1	4	yes	—
393	#488	C₂²×C₇	1	4	yes	—
394	#487	C₂²×C₇	1	2	yes	complemented
395	#487	C₂²×C₇	1	2	yes	complemented
396	#479	C₂²×C₇	1	4	yes	complemented
397	#479	C₂²×C₇	1	4	yes	complemented
398	#478	C₂²×C₇	1	4	yes	—
399	#477	C₂²×C₇	1	4	yes	complemented
400	#476	C₂²×C₇	1	2	yes	—
401	#475	C₂²×C₇	1	4	yes	complemented
402	#474	C₂²×C₇	1	2	yes	—
403	#464	C₂²×C₇	1	4	yes	—
404	#464	C₂²×C₇	1	4	yes	—
405	#463	C₂²×C₇	1	4	yes	—
406	#463	C₂²×C₇	1	4	yes	—
407	#462	C₂²×C₇	1	2	yes	complemented
408	#462	C₂²×C₇	1	2	yes	complemented
409	#461	C₂²×C₇	1	2	yes	complemented
410	#461	C₂²×C₇	1	2	yes	complemented
411	#446	C₂²×C₇	1	2	yes	complemented
412	#446	C₂²×C₇	1	4	yes	complemented
413	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
414	#442	C₂²×C₇	1	2	yes	—
415	#441	C₂²×C₇	1	4	yes	complemented
416	#440	C₂²×C₇	1	2	yes	—
417	#440	C₂²×C₇	1	4	yes	complemented
418	C₄×Q₁₆	C₂²×C₇	1	4	yes	complemented
419	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
420	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
421	C₄×D₈	C₂²×C₇	1	2	yes	—
422	#428	C₂²×C₇	1	2	yes	—
423	#428	C₂²×C₇	1	1	yes	characteristic
424	#423	C₂²×C₇	1	1	yes	characteristic
425	#423	C₂²×C₇	1	2	yes	—
426	#419	C₂²×C₇	1	2	yes	—
427	#419	C₂²×C₇	1	2	yes	—
428	#419	C₂²×C₇	1	2	yes	—
429	#418	C₂²×C₇	1	2	yes	—
430	#418	C₂²×C₇	1	1	yes	characteristic
431	#417	C₂²×C₇	1	1	yes	characteristic
432	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
433	C₄×M₁₆	C₂²×C₇	1	2	yes	—
434	C₂³×C₇	—	2	1	no	—
435	C₂³×C₇	—	2	2	no	—
436	C₂³×C₇	—	4	2	no	—
437	C₂³×C₇	—	4	2	no	—
438	C₂³×C₇	—	4	2	no	—
439	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
440	C₇×Q₈	—	2	2	no	—
441	C₇×Q₈	—	2	2	no	—
442	C₇×Q₈	—	2	1	no	—
443	C₇×Q₈	—	2	4	no	—
444	C₇×Q₈	—	2	4	no	—
445	C₇×Q₈	—	4	2	no	—
446	C₇×Q₈	—	4	4	no	—
447	C₇×Q₈	—	4	4	no	—
448	C₇×Q₈	—	4	2	no	—
449	C₇×Q₈	—	8	2	no	—
450	C₇×Q₈	—	8	1	no	—
451	C₇×Q₈	C₂×#41	1	2	yes	—
452	C₇×D₄	—	2	4	no	—
453	C₇×D₄	—	2	2	no	—
454	C₇×D₄	—	2	1	no	—
455	C₇×D₄	—	2	2	no	—
456	C₇×D₄	—	4	2	no	—
457	C₇×D₄	C₂×#41	1	2	yes	—
458	C₂×C₄×C₇	—	2	1	no	—
459	C₂×C₄×C₇	—	2	4	no	—
460	C₂×C₄×C₇	—	2	2	no	—
461	C₂×C₄×C₇	—	2	2	no	—
462	C₂×C₄×C₇	—	2	4	no	—
463	C₂×C₄×C₇	—	2	2	no	—
464	C₂×C₄×C₇	—	2	1	no	—
465	C₂×C₄×C₇	—	2	2	no	—
466	C₂×C₄×C₇	—	2	1	no	—
467	C₂×C₄×C₇	—	4	2	no	—
468	C₂×C₄×C₇	—	4	1	no	—
469	C₂×C₄×C₇	—	4	2	no	—
470	C₂×C₄×C₇	—	4	4	no	—
471	C₂×C₄×C₇	—	4	4	no	—
472	C₂×C₄×C₇	—	4	2	no	—
473	C₂×C₄×C₇	—	4	4	no	—
474	C₂×C₄×C₇	—	4	4	no	—
475	C₂×C₄×C₇	—	4	2	no	—
476	C₂×C₄×C₇	—	8	2	no	—
477	C₂×C₄×C₇	—	8	1	no	—
478	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
479	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₇	C₂×#41	1	2	yes	—
488	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
489	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
490	C₇×C₈	—	2	2	no	—
491	C₇×C₈	—	2	4	no	—
492	C₇×C₈	—	2	2	no	—
493	C₂×#41	C₂³×C₇	1	1	yes	characteristic
494	C₂²×Q₈	—	2	1	no	—
495	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
496	C₂²×Q₈	C₂³×C₇	1	2	yes	—
497	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
498	C₂³×C₄	—	2	1	no	—
499	#137	—	2	8	no	—
500	AGL(1,ℤ/8)	—	2	4	no	—
501	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
502	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
503	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
504	C₂×D₈	C₂³×C₇	1	2	yes	—
505	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
506	C₂×M₁₆	C₂³×C₇	1	2	yes	—
507	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
508	C₄⋊Q₈	—	2	1	no	—
509	C₄⋊Q₈	—	2	2	no	—
510	C₄⋊Q₈	—	2	1	no	—
511	C₄⋊Q₈	—	2	2	no	—
512	C₄⋊Q₈	—	2	1	no	—
513	C₄⋊Q₈	—	2	1	no	—
514	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
515	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
516	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
517	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
518	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
519	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
520	#126	—	2	4	no	—
521	#126	—	2	4	no	—
522	#126	—	2	4	no	—
523	#126	—	2	4	no	—
524	#125	—	2	2	no	—
525	#125	—	2	2	no	—
526	#125	—	2	2	no	—
527	#125	C₂³×C₇	1	2	yes	—
528	#125	C₂³×C₇	1	2	yes	—
529	#125	C₂³×C₇	1	2	yes	—
530	#124	—	2	2	no	—
531	#124	—	2	2	no	—
532	#124	C₂³×C₇	1	4	yes	—
533	#124	C₂³×C₇	1	4	yes	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	—	2	1	no	—
543	C₂²⋊Q₈	—	2	1	no	—
544	C₂²⋊Q₈	—	2	2	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	—	2	1	no	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	1	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	2	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	2	no	—
557	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
558	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
559	C₄×Q₈	C₇×D₄	1	2	yes	—
560	C₄×Q₈	C₂³×C₇	1	4	yes	—
561	C₄×Q₈	C₂³×C₇	1	4	yes	—
562	C₄×Q₈	C₂³×C₇	1	2	yes	—
563	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
564	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
565	C₄×Q₈	C₂³×C₇	1	2	yes	—
566	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
567	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
568	C₄×Q₈	C₂³×C₇	1	2	yes	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	—	2	1	no	—
575	C₄×D₄	C₂³×C₇	1	2	yes	—
576	C₄×D₄	C₂³×C₇	1	2	yes	—
577	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
578	C₄×D₄	C₂³×C₇	1	2	yes	—
579	C₄×D₄	C₂³×C₇	1	2	yes	—
580	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
581	#117	—	2	2	no	—
582	#117	—	2	4	no	—
583	#117	—	2	2	no	—
584	#117	—	2	1	no	—
585	#117	—	2	2	no	—
586	#117	C₂³×C₇	1	1	yes	characteristic
587	#117	C₂³×C₇	1	2	yes	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	2	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	2	no	—
593	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	—	2	2	no	—
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₂²⋊C₄	—	2	2	no	—
599	C₂×C₄²	—	2	2	no	—
600	C₂×C₄²	—	2	1	no	—
601	C₂×C₄²	—	2	2	no	—
602	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₇	1	2	yes	—
604	#107	C₂³×C₇	1	2	yes	—
605	#107	C₂³×C₇	1	4	yes	—
606	#106	C₂³×C₇	1	2	yes	—
607	#106	C₂³×C₇	1	4	yes	—
608	C₄⋊C₈	C₂³×C₇	1	2	yes	—
609	C₄⋊C₈	C₂³×C₇	1	4	yes	—
610	C₄⋊C₈	C₂³×C₇	1	2	yes	—
611	C₄⋊C₈	C₂³×C₇	1	4	yes	—
612	#103	C₂³×C₇	1	2	yes	—
613	#103	C₂³×C₇	1	4	yes	—
614	#103	C₂³×C₇	1	4	yes	—
615	#103	C₂³×C₇	1	4	yes	—
616	#103	C₂³×C₇	1	4	yes	—
617	#103	C₂³×C₇	1	4	yes	—
618	#103	C₂³×C₇	1	4	yes	—
619	#102	C₂³×C₇	1	2	yes	—
620	#102	C₂³×C₇	1	2	yes	—
621	#102	C₂³×C₇	1	2	yes	—
622	#102	C₂³×C₇	1	4	yes	—
623	#102	C₂³×C₇	1	4	yes	—
624	#97	C₂³×C₇	1	2	yes	—
625	#97	C₂³×C₇	1	4	yes	—
626	C₄×C₈	C₂³×C₇	1	2	yes	—
627	C₄×C₈	C₂³×C₇	1	4	yes	—
628	C₂²×C₇	—	2	1	no	—
629	C₂²×C₇	—	2	1	no	—
630	C₂²×C₇	—	2	2	no	—
631	C₂²×C₇	—	4	1	no	—
632	C₂²×C₇	—	4	1	no	—
633	C₂²×C₇	—	4	2	no	—
634	C₂²×C₇	—	4	2	no	—
635	C₂²×C₇	—	4	2	no	—
636	C₂²×C₇	—	8	4	no	—
637	C₂²×C₇	#548	1	2	yes	—
638	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
639	C₄×C₇	—	2	2	no	—
640	C₄×C₇	—	2	1	no	—
641	C₄×C₇	—	2	2	no	—
642	C₄×C₇	—	2	1	no	—
643	C₄×C₇	—	2	2	no	—
644	C₄×C₇	—	2	1	no	—
645	C₄×C₇	—	2	2	no	—
646	C₄×C₇	—	2	2	no	—
647	C₄×C₇	—	4	2	no	—
648	C₄×C₇	—	4	1	no	—
649	C₄×C₇	—	4	4	no	—
650	C₄×C₇	—	4	2	no	—
651	C₄×C₇	—	4	2	no	—
652	C₄×C₇	—	4	1	no	—
653	C₄×C₇	#548	1	2	yes	—
654	C₄×C₇	#575	1	2	yes	—
655	C₄×C₇	C₂²×#41	1	1	yes	characteristic
656	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
657	C₂⁴	—	2	1	no	—
658	#41	—	2	2	no	—
659	#41	C₇×#41	1	4	yes	—
660	C₂×Q₈	—	2	2	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	—	2	2	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	4	no	—
666	C₂×Q₈	—	2	4	no	—
667	C₂×Q₈	—	4	2	no	—
668	C₂×Q₈	—	4	4	no	—
669	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
670	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
671	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
672	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
673	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	C₂⁴×C₇	1	2	yes	—
679	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	4	4	no	—
690	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
691	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
692	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
693	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
695	Q₁₆	—	2	8	no	—
696	SD₁₆	—	2	4	no	—
697	SD₁₆	—	2	8	no	—
698	D₈	—	2	4	no	—
699	M₁₆	—	2	2	no	—
700	M₁₆	—	2	4	no	—
701	M₁₆	—	2	2	no	—
702	C₂×C₈	C₂⁴×C₇	1	2	yes	—
703	C₂×C₈	C₂⁴×C₇	1	4	yes	—
704	C₂×C₈	C₂⁴×C₇	1	2	yes	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
727	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
728	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
729	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
730	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
731	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
732	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
734	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
736	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
738	C₂²⋊C₄	—	2	1	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₄²	—	2	4	no	—
751	C₄²	—	2	4	no	—
752	C₄²	—	2	1	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	1	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	1	no	—
758	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
759	C₄²	C₂×C₇×D₄	1	2	yes	—
760	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
761	C₄²	C₂×C₇×D₄	1	2	yes	—
762	C₄²	C₂⁴×C₇	1	1	yes	characteristic
763	C₄²	C₂⁴×C₇	1	2	yes	—
764	C₄²	C₂⁴×C₇	1	1	yes	characteristic
765	C₄²	C₂⁴×C₇	1	2	yes	—
766	C₂×C₇	—	2	2	no	—
767	C₂×C₇	—	4	2	no	—
768	C₂×C₇	—	8	2	no	—
769	C₂×C₇	C₂×#548	1	1	yes	characteristic
770	C₂×C₇	C₂×#575	1	1	yes	characteristic
771	C₂×C₇	#3586	1	1	yes	characteristic
772	C₂³	—	2	1	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	4	2	no	—
775	C₂³	—	4	2	no	—
776	C₂³	—	4	2	no	—
777	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
778	Q₈	—	2	1	no	—
779	Q₈	—	2	2	no	—
780	Q₈	—	2	2	no	—
781	Q₈	—	2	4	no	—
782	Q₈	—	2	4	no	—
783	Q₈	—	4	2	no	—
784	Q₈	—	4	4	no	—
785	Q₈	—	4	4	no	—
786	Q₈	—	4	2	no	—
787	Q₈	—	8	2	no	—
788	Q₈	—	8	1	no	—
789	Q₈	C₂×C₇×#41	1	2	yes	—
790	D₄	—	2	4	no	—
791	D₄	—	2	2	no	—
792	D₄	—	2	1	no	—
793	D₄	—	2	2	no	—
794	D₄	—	4	2	no	—
795	D₄	C₂×C₇×#41	1	2	yes	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	4	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	4	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	8	2	no	—
815	C₂×C₄	—	8	1	no	—
816	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
817	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
818	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
819	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
820	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
821	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
822	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
823	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
824	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
825	C₂×C₄	C₂×C₇×#41	1	2	yes	—
826	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
827	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
828	C₈	—	2	2	no	—
829	C₈	—	2	4	no	—
830	C₈	—	2	2	no	—
831	C₇	#61323	1	1	yes	characteristic, direct product factor, Sylow
832	C₂²	—	2	1	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	8	4	no	—
841	C₂²	C₇×#548	1	2	yes	—
842	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
843	C₄	—	2	1	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	1	no	—
850	C₄	—	2	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	4	no	—
857	C₄	C₇×#548	1	2	yes	—
858	C₄	C₇×#575	1	2	yes	—
859	C₄	C₂²×C₇×#41	1	1	yes	characteristic
860	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
861	C₂	—	2	2	no	—
862	C₂	—	4	2	no	—
863	C₂	—	8	2	no	—
864	C₂	C₂×C₇×#548	1	1	yes	characteristic
865	C₂	C₂×C₇×#575	1	1	yes	characteristic
866	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×Q₈×#41	C₂	semidirect
2. C₂×C₇×#556	C₂	semidirect
3. C₇×#3377	C₂	semidirect
4. C₇×#3376	C₂	semidirect
5. C₇×#3369	C₂	semidirect
6. C₇×#3367	C₂	semidirect
7. C₇×#3364	C₂	semidirect
8. C₇×#3360	C₂	semidirect
9. C₇×#3140	C₂	semidirect
10. C₇×#3139	C₂	semidirect
11. C₇×#3078	C₂	semidirect
12. C₇×#3077	C₂	semidirect
14. C₇×#3039	C₂	semidirect
15. C₇×Q₈×M₁₆	C₂	semidirect
16. C₄×C₇×#137	C₂	semidirect
20. C₇×Q₈²	C₂²	semidirect
21. C₇×#557	C₂²	semidirect
22. C₇×#557	C₂²	semidirect
31. C₇×#554	C₂²	semidirect
32. C₇×#554	C₂²	semidirect
34. C₇×D₄×Q₈	C₂²	semidirect
50. C₇×#491	C₂²	semidirect
55. C₇×#487	C₂²	semidirect
56. C₇×#487	C₂²	semidirect
57. C₇×#479	C₂²	semidirect
58. C₇×#479	C₂²	semidirect
60. C₇×#477	C₂²	semidirect
62. C₇×#475	C₂²	semidirect
68. C₇×#462	C₂²	semidirect
69. C₇×#462	C₂²	semidirect
70. C₇×#461	C₂²	semidirect
71. C₇×#461	C₂²	semidirect
72. C₇×#446	C₂²	semidirect
73. C₇×#446	C₂²	semidirect
74. C₇×C₈×Q₈	C₂²	semidirect
76. C₇×#441	C₂²	semidirect
78. C₇×#440	C₂²	semidirect
79. C₄×C₇×Q₁₆	C₂²	semidirect
81. C₄×C₇×SD₁₆	C₂²	semidirect
95. #61323	C₇	direct (N × H)
231. Q₈×#41	C₂×C₇	semidirect
232. C₂×#556	C₂×C₇	semidirect
233. #3377	C₂×C₇	semidirect
234. #3376	C₂×C₇	semidirect
235. #3369	C₂×C₇	semidirect
236. #3367	C₂×C₇	semidirect
237. #3364	C₂×C₇	semidirect
238. #3360	C₂×C₇	semidirect
239. #3140	C₂×C₇	semidirect
240. #3139	C₂×C₇	semidirect
241. #3078	C₂×C₇	semidirect
242. #3077	C₂×C₇	semidirect
244. #3039	C₂×C₇	semidirect
245. Q₈×M₁₆	C₂×C₇	semidirect
246. C₄×#137	C₂×C₇	semidirect
359. Q₈²	C₂²×C₇	semidirect
360. #557	C₂²×C₇	semidirect
361. #557	C₂²×C₇	semidirect
370. #554	C₂²×C₇	semidirect
371. #554	C₂²×C₇	semidirect
373. D₄×Q₈	C₂²×C₇	semidirect
389. #491	C₂²×C₇	semidirect
394. #487	C₂²×C₇	semidirect
395. #487	C₂²×C₇	semidirect
396. #479	C₂²×C₇	semidirect
397. #479	C₂²×C₇	semidirect
399. #477	C₂²×C₇	semidirect
401. #475	C₂²×C₇	semidirect
407. #462	C₂²×C₇	semidirect
408. #462	C₂²×C₇	semidirect
409. #461	C₂²×C₇	semidirect
410. #461	C₂²×C₇	semidirect
411. #446	C₂²×C₇	semidirect
412. #446	C₂²×C₇	semidirect
413. C₈×Q₈	C₂²×C₇	semidirect
415. #441	C₂²×C₇	semidirect
417. #440	C₂²×C₇	semidirect
418. C₄×Q₁₆	C₂²×C₇	semidirect
420. C₄×SD₁₆	C₂²×C₇	semidirect
831. C₇	#61323	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×Q₈×#41	2
C₂×C₇×#556	2
C₇×#3377	2
C₇×#3376	2
C₇×#3369	2
C₇×#3367	2
C₇×#3364	2
C₇×#3360	2
C₇×#3140	2
C₇×#3139	2
C₇×#3078	2
C₇×#3077	2
C₇×#3040	2
C₇×#3039	2
C₇×Q₈×M₁₆	2
C₄×C₇×#137	2
C₄×C₇×AGL(1,ℤ/8)	2
#61323	7

Subgroups — C7×#61323 #13238539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61323 #13238539