Subgroups — C₇×#61209 #13238425

Order 1792.

2078 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3330	C₂	1	2	yes	maximal, complemented
4	C₇×#3329	C₂	1	2	yes	maximal, complemented
5	C₇×#3320	C₂	1	4	yes	maximal, complemented
6	C₇×#3307	C₂	1	4	yes	maximal, complemented
7	C₇×#3303	C₂	1	2	yes	maximal, complemented
8	C₇×#3298	C₂	1	2	yes	maximal, complemented
9	C₇×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3097	C₂	1	2	yes	maximal, complemented
11	C₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3057	C₂	1	2	yes	maximal, complemented
13	C₂×C₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3010	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2898	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×2₋¹⁺⁴	C₂²	1	2	yes	—
19	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
21	C₂×C₇×#131	C₂²	1	2	yes	—
22	C₇×#559	—	2	2	no	—
23	C₇×#556	—	2	1	no	—
24	C₇×#555	C₂²	1	2	yes	—
25	C₇×#553	C₂²	1	4	yes	—
26	C₇×#550	—	2	1	no	—
27	C₇×D₄×Q₈	C₂²	1	2	yes	complemented
28	C₇×D₄×Q₈	C₂²	1	2	yes	complemented
29	C₇×#547	—	2	2	no	—
30	C₇×#547	—	2	2	no	—
31	C₇×#547	C₂²	1	2	yes	—
32	C₇×#547	C₂²	1	2	yes	complemented
33	C₇×#547	C₂²	1	2	yes	complemented
34	C₇×#538	—	2	2	no	—
35	C₇×#536	—	2	2	no	—
36	C₇×#536	C₂²	1	2	yes	—
37	C₇×#535	C₂²	1	2	yes	—
38	C₇×#533	C₂²	1	1	yes	characteristic
39	C₇×#532	—	2	1	no	—
40	C₇×#532	C₂²	1	1	yes	characteristic
41	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
42	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
43	C₇×#525	—	2	2	no	—
44	C₇×#520	C₂²	1	2	yes	—
45	C₄×C₇×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
47	C₇×#491	C₂²	1	4	yes	complemented
48	C₇×#487	C₂²	1	2	yes	complemented
49	C₇×#487	C₂²	1	2	yes	complemented
50	C₇×#485	C₂²	1	4	yes	complemented
51	C₇×#485	C₂²	1	4	yes	complemented
52	C₇×#484	C₂²	1	4	yes	complemented
53	C₇×#483	C₂²	1	4	yes	complemented
54	C₇×#479	C₂²	1	2	yes	complemented
55	C₇×#478	C₂²	1	2	yes	complemented
56	C₇×#477	C₂²	1	1	yes	characteristic, complemented
57	C₇×#476	C₂²	1	1	yes	characteristic, complemented
58	C₇×#475	C₂²	1	1	yes	characteristic, complemented
59	C₇×#474	C₂²	1	1	yes	characteristic, complemented
60	C₇×#468	C₂²	1	4	yes	—
61	C₇×#468	C₂²	1	4	yes	—
62	C₇×#465	C₂²	1	4	yes	—
63	C₇×#465	C₂²	1	4	yes	—
64	C₇×#461	C₂²	1	2	yes	—
65	C₇×#461	C₂²	1	4	yes	—
66	C₇×#461	C₂²	1	2	yes	—
67	C₇×#449	C₂²	1	4	yes	—
68	C₇×#449	C₂²	1	4	yes	—
69	C₇×#448	C₂²	1	4	yes	—
70	C₇×#448	C₂²	1	4	yes	—
71	C₇×#442	C₂²	1	2	yes	—
72	C₇×#440	C₂²	1	2	yes	—
73	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
74	C₄×C₇×D₈	C₂²	1	2	yes	—
75	C₇×#436	C₂²	1	2	yes	complemented
76	C₇×#435	C₂²	1	4	yes	complemented
77	C₇×C₈×D₄	C₂²	1	2	yes	complemented
78	C₇×#428	C₂²	1	1	yes	characteristic
79	C₇×#427	C₂²	1	2	yes	—
80	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
81	C₇×#419	C₂²	1	2	yes	—
82	C₇×#419	C₂²	1	2	yes	—
83	C₇×#419	C₂²	1	4	yes	complemented
84	C₇×#418	C₂²	1	1	yes	characteristic
85	C₇×#417	C₂²	1	1	yes	characteristic
86	C₇×#417	C₂²	1	4	yes	complemented
87	C₇×#416	C₂²	1	2	yes	—
88	C₇×#416	C₂²	1	4	yes	complemented
89	C₂×C₇×#103	C₂²	1	2	yes	—
90	C₂×C₇×#103	C₂²	1	4	yes	complemented
91	C₇×#408	C₂²	1	2	yes	—
92	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
93	#61209	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₇×2₋¹⁺⁴	—	2	8	no	—
95	C₇×2₋¹⁺⁴	—	4	4	no	—
96	C₂×C₇×#41	—	2	2	no	—
97	C₂×C₇×#41	—	2	4	no	—
98	C₂×C₇×#41	—	2	2	no	—
99	C₂×C₇×#41	C₂³	1	4	yes	—
100	C₂×C₇×#41	C₂³	1	1	yes	characteristic
101	C₂×C₇×#41	C₂³	1	2	yes	—
102	C₂²×C₇×Q₈	—	2	2	no	—
103	C₂²×C₇×Q₈	C₂³	1	2	yes	—
104	C₂²×C₇×Q₈	C₂³	1	4	yes	—
105	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₇	—	2	1	no	—
107	C₇×AGL(1,ℤ/8)	—	2	4	no	—
108	C₂×C₇×SD₁₆	—	4	4	no	—
109	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
110	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
111	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₇×D₈	C₂³	1	2	yes	—
113	C₇×#131	—	4	4	no	—
114	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
115	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
116	C₂×C₇×M₁₆	C₂³	1	4	yes	—
117	C₂²×C₇×C₈	C₂³	1	2	yes	—
118	C₂²×C₇×C₈	C₂³	1	4	yes	—
119	C₇×C₄⋊Q₈	—	2	2	no	—
120	C₇×C₄⋊Q₈	—	2	2	no	—
121	C₇×C₄⋊Q₈	—	2	2	no	—
122	C₇×C₄⋊Q₈	—	2	1	no	—
123	C₇×C₄⋊Q₈	—	2	1	no	—
124	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
125	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
127	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
129	C₇×#127	—	2	2	no	—
130	C₇×#127	D₄	1	1	yes	characteristic
131	C₇×#126	—	2	4	no	—
132	C₇×#125	C₂³	1	2	yes	—
133	C₇×#124	—	2	2	no	—
134	C₇×#124	—	2	2	no	—
135	C₇×#124	—	2	4	no	—
136	C₇×#124	D₄	1	2	yes	—
137	C₇×#123	—	2	4	no	—
138	C₇×#123	—	2	4	no	—
139	C₇×#123	—	2	4	no	—
140	C₇×#123	—	2	4	no	—
141	C₇×#123	—	2	4	no	—
142	C₇×C₂²⋊Q₈	—	2	1	no	—
143	C₇×C₂²⋊Q₈	—	2	1	no	—
144	C₇×C₂²⋊Q₈	—	2	2	no	—
145	C₇×C₂²⋊Q₈	—	2	4	no	—
146	C₇×C₂²⋊Q₈	—	2	4	no	—
147	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
149	C₇×#121	—	2	2	no	—
150	C₇×#121	—	2	2	no	—
151	C₇×#121	—	2	2	no	—
152	C₇×#121	—	2	4	no	—
153	C₇×#121	D₄	1	2	yes	—
154	C₇×#121	D₄	1	2	yes	—
155	C₇×#121	C₂³	1	4	yes	—
156	C₇×#121	C₂³	1	4	yes	—
157	C₇×#120	—	2	4	no	—
158	C₄×C₇×Q₈	—	2	2	no	—
159	C₄×C₇×Q₈	—	2	1	no	—
160	C₄×C₇×Q₈	—	2	1	no	—
161	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
162	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
163	C₄×C₇×D₄	—	2	4	no	—
164	C₄×C₇×D₄	—	2	2	no	—
165	C₄×C₇×D₄	—	2	2	no	—
166	C₄×C₇×D₄	—	2	2	no	—
167	C₄×C₇×D₄	—	2	1	no	—
168	C₄×C₇×D₄	—	2	1	no	—
169	C₄×C₇×D₄	—	2	4	no	—
170	C₄×C₇×D₄	—	2	1	no	—
171	C₄×C₇×D₄	—	2	1	no	—
172	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
173	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
174	C₄×C₇×D₄	C₂³	1	2	yes	—
175	C₄×C₇×D₄	C₂³	1	2	yes	—
176	C₄×C₇×D₄	C₂³	1	2	yes	—
177	C₄×C₇×D₄	C₂³	1	2	yes	—
178	C₇×#117	—	2	2	no	—
179	C₇×#117	—	2	1	no	—
180	C₇×#117	C₂³	1	4	yes	—
181	C₇×#117	C₂³	1	1	yes	characteristic
182	C₇×#117	C₂³	1	2	yes	—
183	C₂×C₇×C₄⋊C₄	—	2	1	no	—
184	C₂×C₇×C₄⋊C₄	—	2	1	no	—
185	C₂×C₇×C₄⋊C₄	—	2	2	no	—
186	C₂×C₇×C₄⋊C₄	—	2	2	no	—
187	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
188	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
190	C₂×C₄²×C₇	—	2	1	no	—
191	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
192	C₇×#107	C₂³	1	2	yes	—
193	C₇×#107	C₂³	1	2	yes	—
194	C₇×#107	C₂³	1	2	yes	—
195	C₇×#106	C₂³	1	2	yes	—
196	C₇×#106	C₂³	1	2	yes	—
197	C₇×#106	C₂³	1	2	yes	—
198	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
199	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
200	C₇×C₄⋊C₈	C₂³	1	2	yes	—
201	C₇×#103	C₂³	1	4	yes	—
202	C₇×#103	C₂³	1	4	yes	—
203	C₇×#103	C₂³	1	2	yes	—
204	C₇×#103	C₂³	1	2	yes	—
205	C₇×#103	C₂³	1	4	yes	—
206	C₇×#103	C₂³	1	4	yes	—
207	C₇×#103	C₂³	1	4	yes	—
208	C₇×#103	C₂³	1	4	yes	—
209	C₇×#103	C₂³	1	2	yes	—
210	C₇×#102	C₂³	1	2	yes	—
211	C₇×#102	C₂³	1	2	yes	—
212	C₇×#102	C₂³	1	2	yes	—
213	C₇×#102	C₂³	1	2	yes	—
214	C₇×#102	C₂³	1	2	yes	—
215	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
216	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
217	C₇×#97	C₂³	1	2	yes	—
218	C₄×C₇×C₈	C₂³	1	2	yes	—
219	#3506	C₂×C₇	1	1	yes	characteristic, complemented
220	#3499	C₂×C₇	1	1	yes	characteristic, complemented
221	#3330	C₂×C₇	1	2	yes	complemented
222	#3329	C₂×C₇	1	2	yes	complemented
223	#3320	C₂×C₇	1	4	yes	complemented
224	#3307	C₂×C₇	1	4	yes	complemented
225	#3303	C₂×C₇	1	2	yes	complemented
226	#3298	C₂×C₇	1	2	yes	complemented
227	#3139	C₂×C₇	1	1	yes	characteristic, complemented
228	#3097	C₂×C₇	1	2	yes	complemented
229	#3076	C₂×C₇	1	1	yes	characteristic, complemented
230	#3057	C₂×C₇	1	2	yes	complemented
231	C₂×#461	C₂×C₇	1	1	yes	characteristic, complemented
232	#3010	C₂×C₇	1	2	yes	complemented
233	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic, complemented
234	#2935	C₂×C₇	1	1	yes	characteristic, complemented
235	#2898	C₂×C₇	1	2	yes	complemented
236	C₂⁴×C₇	—	2	1	no	—
237	C₇×#41	—	2	4	no	—
238	C₇×#41	—	2	4	no	—
239	C₇×#41	—	2	2	no	—
240	C₇×#41	—	2	8	no	—
241	C₇×#41	—	4	4	no	—
242	C₇×#41	—	4	8	no	—
243	C₇×#41	—	4	16	no	—
244	C₇×#41	—	8	4	no	—
245	C₇×#41	#41	1	4	yes	complemented
246	C₂×C₇×Q₈	—	2	1	no	—
247	C₂×C₇×Q₈	—	2	4	no	—
248	C₂×C₇×Q₈	—	2	2	no	—
249	C₂×C₇×Q₈	—	2	1	no	—
250	C₂×C₇×Q₈	—	2	8	no	—
251	C₂×C₇×Q₈	—	2	4	no	—
252	C₂×C₇×Q₈	—	2	4	no	—
253	C₂×C₇×Q₈	—	4	4	no	—
254	C₂×C₇×Q₈	—	4	8	no	—
255	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
256	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
257	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
258	C₂×C₇×D₄	—	2	1	no	—
259	C₂×C₇×D₄	—	2	4	no	—
260	C₂×C₇×D₄	—	2	4	no	—
261	C₂×C₇×D₄	—	2	4	no	—
262	C₂×C₇×D₄	—	2	1	no	—
263	C₂×C₇×D₄	—	2	2	no	—
264	C₂×C₇×D₄	—	2	2	no	—
265	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
266	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
267	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
268	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
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	2	no	—
273	C₂²×C₄×C₇	—	2	4	no	—
274	C₂²×C₄×C₇	—	2	1	no	—
275	C₂²×C₄×C₇	—	2	4	no	—
276	C₂²×C₄×C₇	—	2	1	no	—
277	C₂²×C₄×C₇	—	2	1	no	—
278	C₂²×C₄×C₇	—	2	4	no	—
279	C₂²×C₄×C₇	—	2	2	no	—
280	C₂²×C₄×C₇	—	2	2	no	—
281	C₂²×C₄×C₇	—	8	2	no	—
282	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
285	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
286	C₇×SD₁₆	—	2	4	no	—
287	C₇×SD₁₆	—	4	4	no	—
288	C₇×SD₁₆	—	4	4	no	—
289	C₇×D₈	—	2	4	no	—
290	C₇×M₁₆	—	2	2	no	—
291	C₇×M₁₆	—	2	2	no	—
292	C₇×M₁₆	—	4	4	no	—
293	C₂×C₇×C₈	—	2	4	no	—
294	C₂×C₇×C₈	—	4	4	no	—
295	C₂×C₇×C₈	C₂⁴	1	2	yes	—
296	C₂×C₇×C₈	C₂⁴	1	2	yes	—
297	C₂×C₇×C₈	C₂⁴	1	2	yes	—
298	C₂×C₇×C₈	C₂⁴	1	2	yes	—
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	2	no	—
303	C₇×C₄⋊C₄	—	2	4	no	—
304	C₇×C₄⋊C₄	—	2	4	no	—
305	C₇×C₄⋊C₄	—	2	1	no	—
306	C₇×C₄⋊C₄	—	2	4	no	—
307	C₇×C₄⋊C₄	—	2	1	no	—
308	C₇×C₄⋊C₄	—	2	1	no	—
309	C₇×C₄⋊C₄	—	2	1	no	—
310	C₇×C₄⋊C₄	—	2	2	no	—
311	C₇×C₄⋊C₄	—	2	2	no	—
312	C₇×C₄⋊C₄	—	2	1	no	—
313	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
314	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
315	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
316	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
317	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
318	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
319	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
320	C₇×C₂²⋊C₄	—	2	2	no	—
321	C₇×C₂²⋊C₄	—	2	4	no	—
322	C₇×C₂²⋊C₄	—	2	1	no	—
323	C₇×C₂²⋊C₄	—	2	4	no	—
324	C₇×C₂²⋊C₄	—	2	4	no	—
325	C₇×C₂²⋊C₄	—	2	2	no	—
326	C₇×C₂²⋊C₄	—	2	2	no	—
327	C₇×C₂²⋊C₄	—	2	1	no	—
328	C₇×C₂²⋊C₄	—	2	1	no	—
329	C₇×C₂²⋊C₄	—	2	4	no	—
330	C₇×C₂²⋊C₄	—	2	4	no	—
331	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
332	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
333	C₄²×C₇	—	2	1	no	—
334	C₄²×C₇	—	2	1	no	—
335	C₄²×C₇	—	2	1	no	—
336	C₄²×C₇	—	2	4	no	—
337	C₄²×C₇	—	2	2	no	—
338	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₇	C₂⁴	1	1	yes	characteristic
341	C₄²×C₇	C₂⁴	1	1	yes	characteristic
342	C₂×2₋¹⁺⁴	C₂²×C₇	1	2	yes	—
343	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
344	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
345	C₂×#131	C₂²×C₇	1	2	yes	—
346	#559	—	2	2	no	—
347	#556	—	2	1	no	—
348	#555	C₂²×C₇	1	2	yes	—
349	#553	C₂²×C₇	1	4	yes	—
350	#550	—	2	1	no	—
351	D₄×Q₈	C₂²×C₇	1	2	yes	complemented
352	D₄×Q₈	C₂²×C₇	1	2	yes	complemented
353	#547	—	2	2	no	—
354	#547	—	2	2	no	—
355	#547	C₂²×C₇	1	2	yes	—
356	#547	C₂²×C₇	1	2	yes	complemented
357	#547	C₂²×C₇	1	2	yes	complemented
358	#538	—	2	2	no	—
359	#536	—	2	2	no	—
360	#536	C₂²×C₇	1	2	yes	—
361	#535	C₂²×C₇	1	2	yes	—
362	#533	C₂²×C₇	1	1	yes	characteristic
363	#532	—	2	1	no	—
364	#532	C₂²×C₇	1	1	yes	characteristic
365	C₂×C₄⋊Q₈	—	2	1	no	—
366	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
367	#525	—	2	2	no	—
368	#520	C₂²×C₇	1	2	yes	—
369	C₄×#41	C₂²×C₇	1	1	yes	characteristic
370	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
371	#491	C₂²×C₇	1	4	yes	complemented
372	#487	C₂²×C₇	1	2	yes	complemented
373	#487	C₂²×C₇	1	2	yes	complemented
374	#485	C₂²×C₇	1	4	yes	complemented
375	#485	C₂²×C₇	1	4	yes	complemented
376	#484	C₂²×C₇	1	4	yes	complemented
377	#483	C₂²×C₇	1	4	yes	complemented
378	#479	C₂²×C₇	1	2	yes	complemented
379	#478	C₂²×C₇	1	2	yes	complemented
380	#477	C₂²×C₇	1	1	yes	characteristic, complemented
381	#476	C₂²×C₇	1	1	yes	characteristic, complemented
382	#475	C₂²×C₇	1	1	yes	characteristic, complemented
383	#474	C₂²×C₇	1	1	yes	characteristic, complemented
384	#468	C₂²×C₇	1	4	yes	—
385	#468	C₂²×C₇	1	4	yes	—
386	#465	C₂²×C₇	1	4	yes	—
387	#465	C₂²×C₇	1	4	yes	—
388	#461	C₂²×C₇	1	2	yes	—
389	#461	C₂²×C₇	1	2	yes	—
390	#461	C₂²×C₇	1	4	yes	—
391	#449	C₂²×C₇	1	4	yes	—
392	#449	C₂²×C₇	1	4	yes	—
393	#448	C₂²×C₇	1	4	yes	—
394	#448	C₂²×C₇	1	4	yes	—
395	#442	C₂²×C₇	1	2	yes	—
396	#440	C₂²×C₇	1	2	yes	—
397	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
398	C₄×D₈	C₂²×C₇	1	2	yes	—
399	#436	C₂²×C₇	1	2	yes	complemented
400	#435	C₂²×C₇	1	4	yes	complemented
401	C₈×D₄	C₂²×C₇	1	2	yes	complemented
402	#428	C₂²×C₇	1	1	yes	characteristic
403	#427	C₂²×C₇	1	2	yes	—
404	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
405	#419	C₂²×C₇	1	2	yes	—
406	#419	C₂²×C₇	1	2	yes	—
407	#419	C₂²×C₇	1	4	yes	complemented
408	#418	C₂²×C₇	1	1	yes	characteristic
409	#417	C₂²×C₇	1	1	yes	characteristic
410	#417	C₂²×C₇	1	4	yes	complemented
411	#416	C₂²×C₇	1	2	yes	—
412	#416	C₂²×C₇	1	4	yes	complemented
413	C₂×#103	C₂²×C₇	1	2	yes	—
414	C₂×#103	C₂²×C₇	1	4	yes	complemented
415	#408	C₂²×C₇	1	2	yes	—
416	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
417	C₂³×C₇	—	2	1	no	—
418	C₂³×C₇	—	2	2	no	—
419	C₂³×C₇	—	4	2	no	—
420	C₂³×C₇	—	8	1	no	—
421	C₂³×C₇	—	8	1	no	—
422	C₂³×C₇	C₂²×D₄	1	4	yes	—
423	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
424	C₇×Q₈	—	2	4	no	—
425	C₇×Q₈	—	2	1	no	—
426	C₇×Q₈	—	2	4	no	—
427	C₇×Q₈	—	2	4	no	—
428	C₇×Q₈	—	4	8	no	—
429	C₇×Q₈	—	4	4	no	—
430	C₇×Q₈	—	4	2	no	—
431	C₇×Q₈	—	8	1	no	—
432	C₇×Q₈	C₂×#41	1	2	yes	—
433	C₇×D₄	—	2	4	no	—
434	C₇×D₄	—	2	8	no	—
435	C₇×D₄	—	2	4	no	—
436	C₇×D₄	—	2	4	no	—
437	C₇×D₄	—	2	2	no	—
438	C₇×D₄	—	2	1	no	—
439	C₇×D₄	—	2	2	no	—
440	C₇×D₄	—	4	2	no	—
441	C₇×D₄	—	4	8	no	—
442	C₇×D₄	—	4	2	no	—
443	C₇×D₄	—	8	4	no	—
444	C₇×D₄	—	8	4	no	—
445	C₇×D₄	C₂×#41	1	2	yes	—
446	C₂×C₄×C₇	—	2	1	no	—
447	C₂×C₄×C₇	—	2	4	no	—
448	C₂×C₄×C₇	—	2	2	no	—
449	C₂×C₄×C₇	—	2	4	no	—
450	C₂×C₄×C₇	—	2	4	no	—
451	C₂×C₄×C₇	—	2	2	no	—
452	C₂×C₄×C₇	—	2	1	no	—
453	C₂×C₄×C₇	—	2	1	no	—
454	C₂×C₄×C₇	—	2	2	no	—
455	C₂×C₄×C₇	—	2	2	no	—
456	C₂×C₄×C₇	—	2	4	no	—
457	C₂×C₄×C₇	—	4	1	no	—
458	C₂×C₄×C₇	—	4	8	no	—
459	C₂×C₄×C₇	—	4	8	no	—
460	C₂×C₄×C₇	—	4	2	no	—
461	C₂×C₄×C₇	—	4	4	no	—
462	C₂×C₄×C₇	—	4	2	no	—
463	C₂×C₄×C₇	—	4	4	no	—
464	C₂×C₄×C₇	—	8	2	no	—
465	C₂×C₄×C₇	—	8	1	no	—
466	C₂×C₄×C₇	—	8	4	no	—
467	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
469	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₇	C₂×#41	1	2	yes	—
474	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
475	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
476	C₇×C₈	—	2	2	no	—
477	C₇×C₈	—	2	2	no	—
478	C₇×C₈	—	2	2	no	—
479	C₇×C₈	—	2	2	no	—
480	2₋¹⁺⁴	—	2	8	no	—
481	2₋¹⁺⁴	—	4	4	no	—
482	C₂×#41	—	2	2	no	—
483	C₂×#41	—	2	4	no	—
484	C₂×#41	—	2	2	no	—
485	C₂×#41	C₂³×C₇	1	4	yes	—
486	C₂×#41	C₂³×C₇	1	1	yes	characteristic
487	C₂×#41	C₂³×C₇	1	2	yes	—
488	C₂²×Q₈	—	2	2	no	—
489	C₂²×Q₈	C₂³×C₇	1	2	yes	—
490	C₂²×Q₈	C₂³×C₇	1	4	yes	—
491	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
492	C₂³×C₄	—	2	1	no	—
493	AGL(1,ℤ/8)	—	2	4	no	—
494	C₂×SD₁₆	—	4	4	no	—
495	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
496	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
497	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
498	C₂×D₈	C₂³×C₇	1	2	yes	—
499	#131	—	4	4	no	—
500	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
501	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
502	C₂×M₁₆	C₂³×C₇	1	4	yes	—
503	C₂²×C₈	C₂³×C₇	1	2	yes	—
504	C₂²×C₈	C₂³×C₇	1	4	yes	—
505	C₄⋊Q₈	—	2	2	no	—
506	C₄⋊Q₈	—	2	2	no	—
507	C₄⋊Q₈	—	2	2	no	—
508	C₄⋊Q₈	—	2	1	no	—
509	C₄⋊Q₈	—	2	1	no	—
510	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
511	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
512	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
513	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
515	#127	—	2	2	no	—
516	#127	C₇×D₄	1	1	yes	characteristic
517	#126	—	2	4	no	—
518	#125	C₂³×C₇	1	2	yes	—
519	#124	—	2	2	no	—
520	#124	—	2	2	no	—
521	#124	—	2	4	no	—
522	#124	C₇×D₄	1	2	yes	—
523	#123	—	2	4	no	—
524	#123	—	2	4	no	—
525	#123	—	2	4	no	—
526	#123	—	2	4	no	—
527	#123	—	2	4	no	—
528	C₂²⋊Q₈	—	2	1	no	—
529	C₂²⋊Q₈	—	2	1	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	4	no	—
532	C₂²⋊Q₈	—	2	4	no	—
533	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
534	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
535	#121	—	2	2	no	—
536	#121	—	2	2	no	—
537	#121	—	2	2	no	—
538	#121	—	2	4	no	—
539	#121	C₇×D₄	1	2	yes	—
540	#121	C₇×D₄	1	2	yes	—
541	#121	C₂³×C₇	1	4	yes	—
542	#121	C₂³×C₇	1	4	yes	—
543	#120	—	2	4	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	1	no	—
546	C₄×Q₈	—	2	1	no	—
547	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
548	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
549	C₄×D₄	—	2	4	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	—	2	4	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	C₂³×C₇	1	2	yes	—
559	C₄×D₄	C₂³×C₇	1	2	yes	—
560	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
561	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
562	C₄×D₄	C₂³×C₇	1	2	yes	—
563	C₄×D₄	C₂³×C₇	1	2	yes	—
564	#117	—	2	2	no	—
565	#117	—	2	1	no	—
566	#117	C₂³×C₇	1	1	yes	characteristic
567	#117	C₂³×C₇	1	2	yes	—
568	#117	C₂³×C₇	1	4	yes	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	2	no	—
572	C₂×C₄⋊C₄	—	2	2	no	—
573	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
575	C₂×C₂²⋊C₄	—	2	1	no	—
576	C₂×C₄²	—	2	1	no	—
577	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
578	#107	C₂³×C₇	1	2	yes	—
579	#107	C₂³×C₇	1	2	yes	—
580	#107	C₂³×C₇	1	2	yes	—
581	#106	C₂³×C₇	1	2	yes	—
582	#106	C₂³×C₇	1	2	yes	—
583	#106	C₂³×C₇	1	2	yes	—
584	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
585	C₄⋊C₈	C₂³×C₇	1	2	yes	—
586	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
587	#103	C₂³×C₇	1	4	yes	—
588	#103	C₂³×C₇	1	4	yes	—
589	#103	C₂³×C₇	1	2	yes	—
590	#103	C₂³×C₇	1	2	yes	—
591	#103	C₂³×C₇	1	4	yes	—
592	#103	C₂³×C₇	1	2	yes	—
593	#103	C₂³×C₇	1	4	yes	—
594	#103	C₂³×C₇	1	4	yes	—
595	#103	C₂³×C₇	1	4	yes	—
596	#102	C₂³×C₇	1	2	yes	—
597	#102	C₂³×C₇	1	2	yes	—
598	#102	C₂³×C₇	1	2	yes	—
599	#102	C₂³×C₇	1	2	yes	—
600	#102	C₂³×C₇	1	2	yes	—
601	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
602	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
603	#97	C₂³×C₇	1	2	yes	—
604	C₄×C₈	C₂³×C₇	1	2	yes	—
605	C₂²×C₇	—	2	1	no	—
606	C₂²×C₇	—	2	1	no	—
607	C₂²×C₇	—	2	4	no	—
608	C₂²×C₇	—	2	2	no	—
609	C₂²×C₇	—	2	4	no	—
610	C₂²×C₇	—	2	4	no	—
611	C₂²×C₇	—	4	1	no	—
612	C₂²×C₇	—	4	1	no	—
613	C₂²×C₇	—	4	2	no	—
614	C₂²×C₇	—	4	2	no	—
615	C₂²×C₇	—	4	2	no	—
616	C₂²×C₇	—	8	4	no	—
617	C₂²×C₇	#546	1	2	yes	—
618	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
619	C₄×C₇	—	2	1	no	—
620	C₄×C₇	—	2	1	no	—
621	C₄×C₇	—	2	2	no	—
622	C₄×C₇	—	2	4	no	—
623	C₄×C₇	—	2	1	no	—
624	C₄×C₇	—	4	1	no	—
625	C₄×C₇	—	4	2	no	—
626	C₄×C₇	—	4	4	no	—
627	C₄×C₇	—	4	1	no	—
628	C₄×C₇	—	4	2	no	—
629	C₄×C₇	—	4	2	no	—
630	C₄×C₇	#546	1	2	yes	—
631	C₄×C₇	#577	1	2	yes	—
632	C₄×C₇	C₂²×#41	1	1	yes	characteristic
633	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
634	C₂⁴	—	2	1	no	—
635	#41	—	2	4	no	—
636	#41	—	2	4	no	—
637	#41	—	2	2	no	—
638	#41	—	2	8	no	—
639	#41	—	4	4	no	—
640	#41	—	4	8	no	—
641	#41	—	4	16	no	—
642	#41	—	8	4	no	—
643	#41	C₇×#41	1	4	yes	complemented
644	C₂×Q₈	—	2	1	no	—
645	C₂×Q₈	—	2	4	no	—
646	C₂×Q₈	—	2	2	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	8	no	—
649	C₂×Q₈	—	2	4	no	—
650	C₂×Q₈	—	2	4	no	—
651	C₂×Q₈	—	4	4	no	—
652	C₂×Q₈	—	4	8	no	—
653	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
654	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
655	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	4	no	—
658	C₂×D₄	—	2	4	no	—
659	C₂×D₄	—	2	4	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
664	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
665	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
666	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
667	C₂×D₄	C₂⁴×C₇	1	2	yes	—
668	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	8	2	no	—
680	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
681	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
683	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
684	SD₁₆	—	2	4	no	—
685	SD₁₆	—	4	4	no	—
686	SD₁₆	—	4	4	no	—
687	D₈	—	2	4	no	—
688	M₁₆	—	2	2	no	—
689	M₁₆	—	2	2	no	—
690	M₁₆	—	4	4	no	—
691	C₂×C₈	—	2	4	no	—
692	C₂×C₈	—	4	4	no	—
693	C₂×C₈	C₂⁴×C₇	1	2	yes	—
694	C₂×C₈	C₂⁴×C₇	1	2	yes	—
695	C₂×C₈	C₂⁴×C₇	1	2	yes	—
696	C₂×C₈	C₂⁴×C₇	1	2	yes	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
712	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
713	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
714	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
715	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
716	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
717	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	1	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	1	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
730	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
731	C₄²	—	2	1	no	—
732	C₄²	—	2	1	no	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	4	no	—
735	C₄²	—	2	2	no	—
736	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
737	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
738	C₄²	C₂⁴×C₇	1	1	yes	characteristic
739	C₄²	C₂⁴×C₇	1	1	yes	characteristic
740	C₂×C₇	—	2	2	no	—
741	C₂×C₇	—	4	4	no	—
742	C₂×C₇	—	4	2	no	—
743	C₂×C₇	—	8	2	no	—
744	C₂×C₇	C₂×#546	1	1	yes	characteristic
745	C₂×C₇	C₂×#577	1	1	yes	characteristic
746	C₂×C₇	#3586	1	1	yes	characteristic
747	C₂³	—	2	1	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	4	2	no	—
750	C₂³	—	8	1	no	—
751	C₂³	—	8	1	no	—
752	C₂³	C₂²×C₇×D₄	1	4	yes	—
753	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
754	Q₈	—	2	1	no	—
755	Q₈	—	2	4	no	—
756	Q₈	—	2	4	no	—
757	Q₈	—	2	4	no	—
758	Q₈	—	4	8	no	—
759	Q₈	—	4	4	no	—
760	Q₈	—	4	2	no	—
761	Q₈	—	8	1	no	—
762	Q₈	C₂×C₇×#41	1	2	yes	—
763	D₄	—	2	4	no	—
764	D₄	—	2	8	no	—
765	D₄	—	2	2	no	—
766	D₄	—	2	1	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	4	no	—
769	D₄	—	2	4	no	—
770	D₄	—	4	2	no	—
771	D₄	—	4	8	no	—
772	D₄	—	4	2	no	—
773	D₄	—	8	4	no	—
774	D₄	—	8	4	no	—
775	D₄	C₂×C₇×#41	1	2	yes	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	8	no	—
789	C₂×C₄	—	4	8	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	8	2	no	—
795	C₂×C₄	—	8	1	no	—
796	C₂×C₄	—	8	4	no	—
797	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
798	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
799	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
800	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
801	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
802	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
803	C₂×C₄	C₂×C₇×#41	1	2	yes	—
804	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
805	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
806	C₈	—	2	2	no	—
807	C₈	—	2	2	no	—
808	C₈	—	2	2	no	—
809	C₈	—	2	2	no	—
810	C₇	#61209	1	1	yes	characteristic, direct product factor, Sylow
811	C₂²	—	2	1	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	2	4	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	8	4	no	—
823	C₂²	C₇×#546	1	2	yes	—
824	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
825	C₄	—	2	1	no	—
826	C₄	—	2	1	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	2	no	—
829	C₄	—	2	4	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	4	no	—
836	C₄	C₇×#546	1	2	yes	—
837	C₄	C₇×#577	1	2	yes	—
838	C₄	C₂²×C₇×#41	1	1	yes	characteristic
839	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
840	C₂	—	2	2	no	—
841	C₂	—	4	4	no	—
842	C₂	—	4	2	no	—
843	C₂	—	8	2	no	—
844	C₂	C₂×C₇×#546	1	1	yes	characteristic
845	C₂	C₂×C₇×#577	1	1	yes	characteristic
846	C₂	C₇×#3586	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 ◁ C₇×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3506	C₂	semidirect
2. C₇×#3499	C₂	semidirect
3. C₇×#3330	C₂	semidirect
4. C₇×#3329	C₂	semidirect
5. C₇×#3320	C₂	semidirect
6. C₇×#3307	C₂	semidirect
7. C₇×#3303	C₂	semidirect
8. C₇×#3298	C₂	semidirect
9. C₇×#3139	C₂	semidirect
10. C₇×#3097	C₂	semidirect
11. C₇×#3076	C₂	semidirect
12. C₇×#3057	C₂	semidirect
13. C₂×C₇×#461	C₂	semidirect
14. C₇×#3010	C₂	semidirect
15. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
16. C₇×#2935	C₂	semidirect
17. C₇×#2898	C₂	semidirect
27. C₇×D₄×Q₈	C₂²	semidirect
28. C₇×D₄×Q₈	C₂²	semidirect
32. C₇×#547	C₂²	semidirect
33. C₇×#547	C₂²	semidirect
47. C₇×#491	C₂²	semidirect
48. C₇×#487	C₂²	semidirect
49. C₇×#487	C₂²	semidirect
50. C₇×#485	C₂²	semidirect
51. C₇×#485	C₂²	semidirect
52. C₇×#484	C₂²	semidirect
53. C₇×#483	C₂²	semidirect
54. C₇×#479	C₂²	semidirect
55. C₇×#478	C₂²	semidirect
56. C₇×#477	C₂²	semidirect
57. C₇×#476	C₂²	semidirect
58. C₇×#475	C₂²	semidirect
59. C₇×#474	C₂²	semidirect
75. C₇×#436	C₂²	semidirect
76. C₇×#435	C₂²	semidirect
77. C₇×C₈×D₄	C₂²	semidirect
83. C₇×#419	C₂²	semidirect
86. C₇×#417	C₂²	semidirect
88. C₇×#416	C₂²	semidirect
90. C₂×C₇×#103	C₂²	semidirect
93. #61209	C₇	direct (N × H)
219. #3506	C₂×C₇	semidirect
220. #3499	C₂×C₇	semidirect
221. #3330	C₂×C₇	semidirect
222. #3329	C₂×C₇	semidirect
223. #3320	C₂×C₇	semidirect
224. #3307	C₂×C₇	semidirect
225. #3303	C₂×C₇	semidirect
226. #3298	C₂×C₇	semidirect
227. #3139	C₂×C₇	semidirect
228. #3097	C₂×C₇	semidirect
229. #3076	C₂×C₇	semidirect
230. #3057	C₂×C₇	semidirect
231. C₂×#461	C₂×C₇	semidirect
232. #3010	C₂×C₇	semidirect
233. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
234. #2935	C₂×C₇	semidirect
235. #2898	C₂×C₇	semidirect
245. C₇×#41	#41	semidirect
351. D₄×Q₈	C₂²×C₇	semidirect
352. D₄×Q₈	C₂²×C₇	semidirect
356. #547	C₂²×C₇	semidirect
357. #547	C₂²×C₇	semidirect
371. #491	C₂²×C₇	semidirect
372. #487	C₂²×C₇	semidirect
373. #487	C₂²×C₇	semidirect
374. #485	C₂²×C₇	semidirect
375. #485	C₂²×C₇	semidirect
376. #484	C₂²×C₇	semidirect
377. #483	C₂²×C₇	semidirect
378. #479	C₂²×C₇	semidirect
379. #478	C₂²×C₇	semidirect
380. #477	C₂²×C₇	semidirect
381. #476	C₂²×C₇	semidirect
382. #475	C₂²×C₇	semidirect
383. #474	C₂²×C₇	semidirect
399. #436	C₂²×C₇	semidirect
400. #435	C₂²×C₇	semidirect
401. C₈×D₄	C₂²×C₇	semidirect
407. #419	C₂²×C₇	semidirect
410. #417	C₂²×C₇	semidirect
412. #416	C₂²×C₇	semidirect
414. C₂×#103	C₂²×C₇	semidirect
643. #41	C₇×#41	semidirect
810. C₇	#61209	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×#3506	2
C₇×#3499	2
C₇×#3330	2
C₇×#3329	2
C₇×#3320	2
C₇×#3307	2
C₇×#3303	2
C₇×#3298	2
C₇×#3139	2
C₇×#3097	2
C₇×#3076	2
C₇×#3057	2
C₂×C₇×#461	2
C₇×#3010	2
C₄×C₇×AGL(1,ℤ/8)	2
C₇×#2935	2
C₇×#2898	2
#61209	7

Subgroups — C7×#61209 #13238425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61209 #13238425