Subgroups — C₇×#61217 #13238433

Order 1792.

2064 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3331	C₂	1	2	yes	maximal, complemented
4	C₇×#3330	C₂	1	2	yes	maximal, complemented
5	C₇×#3329	C₂	1	2	yes	maximal, complemented
6	C₇×#3328	C₂	1	2	yes	maximal, complemented
7	C₇×#3303	C₂	1	2	yes	maximal, complemented
8	C₇×#3302	C₂	1	2	yes	maximal, complemented
9	C₇×#3299	C₂	1	2	yes	maximal, complemented
10	C₇×#3298	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3097	C₂	1	2	yes	maximal, complemented
13	C₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3063	C₂	1	2	yes	maximal, complemented
15	C₇×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3013	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2898	C₂	1	2	yes	maximal, complemented
20	C₂×C₇×2₋¹⁺⁴	C₂²	1	2	yes	—
21	C₂×C₇×#137	C₂²	1	2	yes	—
22	C₂×C₇×#135	C₂²	1	1	yes	characteristic
23	C₂×C₇×#131	C₂²	1	2	yes	—
24	C₇×#556	C₂²	1	2	yes	—
25	C₇×#555	C₂²	1	2	yes	—
26	C₇×#554	C₂²	1	2	yes	—
27	C₇×#553	—	2	2	no	—
28	C₇×D₄×Q₈	C₂²	1	2	yes	—
29	C₇×D₄×Q₈	C₂²	1	2	yes	—
30	C₇×#548	—	2	2	no	—
31	C₇×#547	—	2	2	no	—
32	C₇×#547	—	2	2	no	—
33	C₇×#547	C₂²	1	2	yes	—
34	C₇×#547	C₂²	1	2	yes	—
35	C₇×#547	C₂²	1	2	yes	—
36	C₇×#542	—	2	2	no	—
37	C₇×#537	C₂²	1	2	yes	—
38	C₇×#536	—	2	2	no	—
39	C₇×#536	C₂²	1	2	yes	—
40	C₇×#533	—	2	1	no	—
41	C₇×#532	—	2	1	no	—
42	C₇×#532	—	2	1	no	—
43	C₇×#532	C₂²	1	1	yes	characteristic
44	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
45	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
47	C₇×#520	C₂²	1	2	yes	—
48	C₄×C₇×#41	C₂²	1	1	yes	characteristic
49	C₄×C₇×#41	C₂²	1	1	yes	characteristic
50	C₇×#487	C₂²	1	2	yes	—
51	C₇×#487	C₂²	1	2	yes	—
52	C₇×#487	C₂²	1	2	yes	—
53	C₇×#487	C₂²	1	2	yes	—
54	C₇×#485	C₂²	1	4	yes	—
55	C₇×#485	C₂²	1	4	yes	—
56	C₇×#484	C₂²	1	4	yes	—
57	C₇×#483	C₂²	1	4	yes	—
58	C₇×#477	C₂²	1	2	yes	—
59	C₇×#476	C₂²	1	2	yes	—
60	C₇×#475	C₂²	1	2	yes	—
61	C₇×#474	C₂²	1	2	yes	—
62	C₇×#470	C₂²	1	4	yes	—
63	C₇×#468	C₂²	1	4	yes	—
64	C₇×#467	C₂²	1	4	yes	—
65	C₇×#465	C₂²	1	4	yes	—
66	C₇×#462	C₂²	1	2	yes	—
67	C₇×#462	C₂²	1	2	yes	—
68	C₇×#461	C₂²	1	2	yes	—
69	C₇×#461	C₂²	1	2	yes	—
70	C₇×#452	C₂²	1	4	yes	—
71	C₇×#451	C₂²	1	4	yes	—
72	C₇×#449	C₂²	1	4	yes	—
73	C₇×#448	C₂²	1	4	yes	—
74	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
75	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
76	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
77	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
78	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
79	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
80	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
81	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
82	C₇×#436	C₂²	1	2	yes	—
83	C₇×#436	C₂²	1	2	yes	—
84	C₇×C₈×D₄	C₂²	1	2	yes	—
85	C₇×C₈×D₄	C₂²	1	2	yes	—
86	C₇×#428	C₂²	1	2	yes	—
87	C₇×#427	C₂²	1	1	yes	characteristic
88	C₇×#423	C₂²	1	1	yes	characteristic
89	C₇×#419	C₂²	1	2	yes	—
90	C₇×#419	C₂²	1	4	yes	—
91	C₇×#417	C₂²	1	2	yes	—
92	C₇×#417	C₂²	1	4	yes	—
93	C₇×#416	C₂²	1	1	yes	characteristic
94	C₇×#416	C₂²	1	1	yes	characteristic
95	C₇×#416	C₂²	1	4	yes	—
96	C₂×C₇×#103	C₂²	1	2	yes	—
97	C₂×C₇×#103	C₂²	1	4	yes	—
98	C₂×C₇×#103	C₂²	1	2	yes	—
99	C₇×#408	C₂²	1	2	yes	—
100	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
101	#61217	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₇×2₋¹⁺⁴	—	2	8	no	—
103	C₇×2₋¹⁺⁴	—	4	4	no	—
104	C₂×C₇×#41	—	2	2	no	—
105	C₂×C₇×#41	—	2	4	no	—
106	C₂×C₇×#41	—	2	2	no	—
107	C₂×C₇×#41	C₂³	1	1	yes	characteristic
108	C₂×C₇×#41	C₂³	1	4	yes	—
109	C₂×C₇×#41	C₂³	1	1	yes	characteristic
110	C₂×C₇×#41	C₂³	1	2	yes	—
111	C₂²×C₇×Q₈	—	2	2	no	—
112	C₂²×C₇×Q₈	—	2	1	no	—
113	C₂²×C₇×Q₈	C₂³	1	2	yes	—
114	C₂²×C₇×Q₈	C₂³	1	4	yes	—
115	C₇×#137	—	4	4	no	—
116	C₇×#135	—	2	4	no	—
117	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
119	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
120	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
122	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
123	C₇×#131	—	4	4	no	—
124	C₂×C₇×M₁₆	C₂³	1	2	yes	—
125	C₂×C₇×M₁₆	C₂³	1	4	yes	—
126	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
127	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
128	C₂²×C₇×C₈	C₂³	1	4	yes	—
129	C₇×C₄⋊Q₈	—	2	2	no	—
130	C₇×C₄⋊Q₈	—	2	2	no	—
131	C₇×C₄⋊Q₈	—	2	2	no	—
132	C₇×C₄⋊Q₈	—	2	1	no	—
133	C₇×C₄⋊Q₈	—	2	1	no	—
134	C₇×C₄⋊Q₈	—	2	1	no	—
135	C₇×C₄⋊Q₈	—	2	1	no	—
136	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
137	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₇×#127	D₄	1	1	yes	characteristic
142	C₇×#126	—	2	4	no	—
143	C₇×#125	—	2	2	no	—
144	C₇×#124	—	2	2	no	—
145	C₇×#124	—	2	2	no	—
146	C₇×#124	—	2	4	no	—
147	C₇×#124	D₄	1	2	yes	—
148	C₇×#123	—	2	4	no	—
149	C₇×#123	—	2	4	no	—
150	C₇×#123	—	2	4	no	—
151	C₇×#123	—	2	4	no	—
152	C₇×C₂²⋊Q₈	—	2	2	no	—
153	C₇×C₂²⋊Q₈	—	2	2	no	—
154	C₇×C₂²⋊Q₈	—	2	4	no	—
155	C₇×C₂²⋊Q₈	—	2	4	no	—
156	C₇×C₂²⋊Q₈	—	2	4	no	—
157	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
158	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
159	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
160	C₇×#121	—	2	2	no	—
161	C₇×#121	—	2	2	no	—
162	C₇×#121	—	2	2	no	—
163	C₇×#121	—	2	2	no	—
164	C₇×#121	—	2	4	no	—
165	C₇×#121	D₄	1	2	yes	—
166	C₇×#121	D₄	1	2	yes	—
167	C₇×#121	C₂³	1	4	yes	—
168	C₄×C₇×Q₈	—	2	2	no	—
169	C₄×C₇×Q₈	—	2	2	no	—
170	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
171	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
172	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
173	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
174	C₄×C₇×D₄	—	2	2	no	—
175	C₄×C₇×D₄	—	2	4	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	1	no	—
180	C₄×C₇×D₄	—	2	1	no	—
181	C₄×C₇×D₄	—	2	1	no	—
182	C₄×C₇×D₄	—	2	1	no	—
183	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
184	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
185	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
186	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
187	C₄×C₇×D₄	C₂³	1	2	yes	—
188	C₄×C₇×D₄	C₂³	1	2	yes	—
189	C₇×#117	—	2	2	no	—
190	C₇×#117	—	2	1	no	—
191	C₇×#117	—	2	1	no	—
192	C₇×#117	C₂³	1	4	yes	—
193	C₇×#117	C₂³	1	1	yes	characteristic
194	C₇×#117	C₂³	1	1	yes	characteristic
195	C₂×C₇×C₄⋊C₄	—	2	1	no	—
196	C₂×C₇×C₄⋊C₄	—	2	1	no	—
197	C₂×C₇×C₄⋊C₄	—	2	1	no	—
198	C₂×C₇×C₄⋊C₄	—	2	2	no	—
199	C₂×C₇×C₄⋊C₄	—	2	2	no	—
200	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
201	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₄²×C₇	—	2	1	no	—
203	C₂×C₄²×C₇	—	2	1	no	—
204	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
205	C₇×#107	C₂³	1	4	yes	—
206	C₇×#107	C₂³	1	1	yes	characteristic
207	C₇×#107	C₂³	1	1	yes	characteristic
208	C₇×#106	C₂³	1	4	yes	—
209	C₇×#106	C₂³	1	1	yes	characteristic
210	C₇×#106	C₂³	1	1	yes	characteristic
211	C₇×C₄⋊C₈	C₂³	1	2	yes	—
212	C₇×C₄⋊C₈	C₂³	1	2	yes	—
213	C₇×#103	C₂³	1	1	yes	characteristic
214	C₇×#103	C₂³	1	4	yes	—
215	C₇×#103	C₂³	1	4	yes	—
216	C₇×#103	C₂³	1	1	yes	characteristic
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	4	yes	—
222	C₇×#103	C₂³	1	1	yes	characteristic
223	C₇×#103	C₂³	1	1	yes	characteristic
224	C₇×#102	C₂³	1	1	yes	characteristic
225	C₇×#102	C₂³	1	4	yes	—
226	C₇×#102	C₂³	1	1	yes	characteristic
227	C₇×#102	C₂³	1	1	yes	characteristic
228	C₇×#102	C₂³	1	1	yes	characteristic
229	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
232	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
233	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
234	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
235	#3511	C₂×C₇	1	1	yes	characteristic, complemented
236	#3499	C₂×C₇	1	1	yes	characteristic, complemented
237	#3331	C₂×C₇	1	2	yes	complemented
238	#3330	C₂×C₇	1	2	yes	complemented
239	#3329	C₂×C₇	1	2	yes	complemented
240	#3328	C₂×C₇	1	2	yes	complemented
241	#3303	C₂×C₇	1	2	yes	complemented
242	#3302	C₂×C₇	1	2	yes	complemented
243	#3299	C₂×C₇	1	2	yes	complemented
244	#3298	C₂×C₇	1	2	yes	complemented
245	C₂×#487	C₂×C₇	1	1	yes	characteristic, complemented
246	#3097	C₂×C₇	1	2	yes	complemented
247	#3079	C₂×C₇	1	1	yes	characteristic, complemented
248	#3063	C₂×C₇	1	2	yes	complemented
249	#3039	C₂×C₇	1	1	yes	characteristic, complemented
250	#3013	C₂×C₇	1	2	yes	complemented
251	C₄×#135	C₂×C₇	1	1	yes	characteristic, complemented
252	#2931	C₂×C₇	1	1	yes	characteristic, complemented
253	#2898	C₂×C₇	1	2	yes	complemented
254	C₇×#41	—	2	4	no	—
255	C₇×#41	—	2	4	no	—
256	C₇×#41	—	2	2	no	—
257	C₇×#41	—	2	8	no	—
258	C₇×#41	—	2	2	no	—
259	C₇×#41	—	2	2	no	—
260	C₇×#41	—	4	4	no	—
261	C₇×#41	—	4	8	no	—
262	C₇×#41	—	4	16	no	—
263	C₇×#41	—	8	4	no	—
264	C₇×#41	#41	1	4	yes	complemented
265	C₂×C₇×Q₈	—	2	2	no	—
266	C₂×C₇×Q₈	—	2	4	no	—
267	C₂×C₇×Q₈	—	2	2	no	—
268	C₂×C₇×Q₈	—	2	2	no	—
269	C₂×C₇×Q₈	—	2	8	no	—
270	C₂×C₇×Q₈	—	2	4	no	—
271	C₂×C₇×Q₈	—	2	4	no	—
272	C₂×C₇×Q₈	—	4	4	no	—
273	C₂×C₇×Q₈	—	4	8	no	—
274	C₂×C₇×Q₈	—	8	2	no	—
275	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
276	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
277	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
278	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
279	C₂×C₇×D₄	—	2	1	no	—
280	C₂×C₇×D₄	—	2	1	no	—
281	C₂×C₇×D₄	—	2	4	no	—
282	C₂×C₇×D₄	—	2	4	no	—
283	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
284	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
285	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
286	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
287	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
288	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₇	—	2	1	no	—
290	C₂²×C₄×C₇	—	2	2	no	—
291	C₂²×C₄×C₇	—	2	4	no	—
292	C₂²×C₄×C₇	—	2	2	no	—
293	C₂²×C₄×C₇	—	2	4	no	—
294	C₂²×C₄×C₇	—	2	1	no	—
295	C₂²×C₄×C₇	—	2	1	no	—
296	C₂²×C₄×C₇	—	2	1	no	—
297	C₂²×C₄×C₇	—	2	1	no	—
298	C₂²×C₄×C₇	—	2	1	no	—
299	C₂²×C₄×C₇	—	2	4	no	—
300	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
304	C₇×Q₁₆	—	2	2	no	—
305	C₇×Q₁₆	—	4	4	no	—
306	C₇×SD₁₆	—	2	2	no	—
307	C₇×SD₁₆	—	2	2	no	—
308	C₇×SD₁₆	—	4	4	no	—
309	C₇×D₈	—	2	2	no	—
310	C₇×M₁₆	—	2	4	no	—
311	C₇×M₁₆	—	4	4	no	—
312	C₂×C₇×C₈	—	2	2	no	—
313	C₂×C₇×C₈	—	2	2	no	—
314	C₂×C₇×C₈	—	4	4	no	—
315	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
316	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
317	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
318	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
319	C₂×C₇×C₈	C₂⁴	1	4	yes	—
320	C₇×C₄⋊C₄	—	2	2	no	—
321	C₇×C₄⋊C₄	—	2	2	no	—
322	C₇×C₄⋊C₄	—	2	2	no	—
323	C₇×C₄⋊C₄	—	2	2	no	—
324	C₇×C₄⋊C₄	—	2	2	no	—
325	C₇×C₄⋊C₄	—	2	4	no	—
326	C₇×C₄⋊C₄	—	2	4	no	—
327	C₇×C₄⋊C₄	—	2	2	no	—
328	C₇×C₄⋊C₄	—	2	2	no	—
329	C₇×C₄⋊C₄	—	2	4	no	—
330	C₇×C₄⋊C₄	—	2	1	no	—
331	C₇×C₄⋊C₄	—	2	1	no	—
332	C₇×C₄⋊C₄	—	2	1	no	—
333	C₇×C₄⋊C₄	—	2	1	no	—
334	C₇×C₄⋊C₄	—	2	4	no	—
335	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
336	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
337	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
338	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
339	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
340	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
341	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
342	C₇×C₂²⋊C₄	—	2	1	no	—
343	C₇×C₂²⋊C₄	—	2	4	no	—
344	C₇×C₂²⋊C₄	—	2	1	no	—
345	C₇×C₂²⋊C₄	—	2	4	no	—
346	C₇×C₂²⋊C₄	—	2	4	no	—
347	C₇×C₂²⋊C₄	—	2	4	no	—
348	C₇×C₂²⋊C₄	—	2	1	no	—
349	C₇×C₂²⋊C₄	—	2	1	no	—
350	C₇×C₂²⋊C₄	—	2	1	no	—
351	C₇×C₂²⋊C₄	—	2	1	no	—
352	C₇×C₂²⋊C₄	—	2	4	no	—
353	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
354	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
355	C₄²×C₇	—	2	1	no	—
356	C₄²×C₇	—	2	1	no	—
357	C₄²×C₇	—	2	1	no	—
358	C₄²×C₇	—	2	1	no	—
359	C₄²×C₇	—	2	1	no	—
360	C₄²×C₇	—	2	1	no	—
361	C₄²×C₇	—	2	4	no	—
362	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
363	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
364	C₄²×C₇	C₂⁴	1	1	yes	characteristic
365	C₄²×C₇	C₂⁴	1	1	yes	characteristic
366	C₂×2₋¹⁺⁴	C₂²×C₇	1	2	yes	—
367	C₂×#137	C₂²×C₇	1	2	yes	—
368	C₂×#135	C₂²×C₇	1	1	yes	characteristic
369	C₂×#131	C₂²×C₇	1	2	yes	—
370	#556	C₂²×C₇	1	2	yes	—
371	#555	C₂²×C₇	1	2	yes	—
372	#554	C₂²×C₇	1	2	yes	—
373	#553	—	2	2	no	—
374	D₄×Q₈	C₂²×C₇	1	2	yes	—
375	D₄×Q₈	C₂²×C₇	1	2	yes	—
376	#548	—	2	2	no	—
377	#547	—	2	2	no	—
378	#547	—	2	2	no	—
379	#547	C₂²×C₇	1	2	yes	—
380	#547	C₂²×C₇	1	2	yes	—
381	#547	C₂²×C₇	1	2	yes	—
382	#542	—	2	2	no	—
383	#537	C₂²×C₇	1	2	yes	—
384	#536	—	2	2	no	—
385	#536	C₂²×C₇	1	2	yes	—
386	#533	—	2	1	no	—
387	#532	—	2	1	no	—
388	#532	—	2	1	no	—
389	#532	C₂²×C₇	1	1	yes	characteristic
390	C₂×C₄⋊Q₈	—	2	1	no	—
391	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
392	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
393	#520	C₂²×C₇	1	2	yes	—
394	C₄×#41	C₂²×C₇	1	1	yes	characteristic
395	C₄×#41	C₂²×C₇	1	1	yes	characteristic
396	#487	C₂²×C₇	1	2	yes	—
397	#487	C₂²×C₇	1	2	yes	—
398	#487	C₂²×C₇	1	2	yes	—
399	#487	C₂²×C₇	1	2	yes	—
400	#485	C₂²×C₇	1	4	yes	—
401	#485	C₂²×C₇	1	4	yes	—
402	#484	C₂²×C₇	1	4	yes	—
403	#483	C₂²×C₇	1	4	yes	—
404	#477	C₂²×C₇	1	2	yes	—
405	#476	C₂²×C₇	1	2	yes	—
406	#475	C₂²×C₇	1	2	yes	—
407	#474	C₂²×C₇	1	2	yes	—
408	#470	C₂²×C₇	1	4	yes	—
409	#468	C₂²×C₇	1	4	yes	—
410	#467	C₂²×C₇	1	4	yes	—
411	#465	C₂²×C₇	1	4	yes	—
412	#462	C₂²×C₇	1	2	yes	—
413	#462	C₂²×C₇	1	2	yes	—
414	#461	C₂²×C₇	1	2	yes	—
415	#461	C₂²×C₇	1	2	yes	—
416	#452	C₂²×C₇	1	4	yes	—
417	#451	C₂²×C₇	1	4	yes	—
418	#449	C₂²×C₇	1	4	yes	—
419	#448	C₂²×C₇	1	4	yes	—
420	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
421	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
422	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
423	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
424	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
425	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
426	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
427	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
428	#436	C₂²×C₇	1	2	yes	—
429	#436	C₂²×C₇	1	2	yes	—
430	C₈×D₄	C₂²×C₇	1	2	yes	—
431	C₈×D₄	C₂²×C₇	1	2	yes	—
432	#428	C₂²×C₇	1	2	yes	—
433	#427	C₂²×C₇	1	1	yes	characteristic
434	#423	C₂²×C₇	1	1	yes	characteristic
435	#419	C₂²×C₇	1	4	yes	—
436	#419	C₂²×C₇	1	2	yes	—
437	#417	C₂²×C₇	1	4	yes	—
438	#417	C₂²×C₇	1	2	yes	—
439	#416	C₂²×C₇	1	1	yes	characteristic
440	#416	C₂²×C₇	1	4	yes	—
441	#416	C₂²×C₇	1	1	yes	characteristic
442	C₂×#103	C₂²×C₇	1	2	yes	—
443	C₂×#103	C₂²×C₇	1	2	yes	—
444	C₂×#103	C₂²×C₇	1	4	yes	—
445	#408	C₂²×C₇	1	2	yes	—
446	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
447	C₂³×C₇	—	2	1	no	—
448	C₂³×C₇	—	2	1	no	—
449	C₂³×C₇	C₂²×D₄	1	4	yes	—
450	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
451	C₇×Q₈	—	2	4	no	—
452	C₇×Q₈	—	2	1	no	—
453	C₇×Q₈	—	2	1	no	—
454	C₇×Q₈	—	2	4	no	—
455	C₇×Q₈	—	2	4	no	—
456	C₇×Q₈	—	2	1	no	—
457	C₇×Q₈	—	4	8	no	—
458	C₇×Q₈	—	4	4	no	—
459	C₇×Q₈	—	4	4	no	—
460	C₇×Q₈	—	8	2	no	—
461	C₇×Q₈	C₂×#41	1	2	yes	—
462	C₇×D₄	—	2	4	no	—
463	C₇×D₄	—	2	8	no	—
464	C₇×D₄	—	2	4	no	—
465	C₇×D₄	—	2	4	no	—
466	C₇×D₄	—	2	4	no	—
467	C₇×D₄	—	2	1	no	—
468	C₇×D₄	—	2	1	no	—
469	C₇×D₄	—	2	1	no	—
470	C₇×D₄	—	4	8	no	—
471	C₇×D₄	—	4	2	no	—
472	C₇×D₄	—	8	4	no	—
473	C₇×D₄	C₂×#41	1	2	yes	—
474	C₂×C₄×C₇	—	2	1	no	—
475	C₂×C₄×C₇	—	2	4	no	—
476	C₂×C₄×C₇	—	2	2	no	—
477	C₂×C₄×C₇	—	2	2	no	—
478	C₂×C₄×C₇	—	2	4	no	—
479	C₂×C₄×C₇	—	2	4	no	—
480	C₂×C₄×C₇	—	2	1	no	—
481	C₂×C₄×C₇	—	2	1	no	—
482	C₂×C₄×C₇	—	2	1	no	—
483	C₂×C₄×C₇	—	2	1	no	—
484	C₂×C₄×C₇	—	2	1	no	—
485	C₂×C₄×C₇	—	2	4	no	—
486	C₂×C₄×C₇	—	2	4	no	—
487	C₂×C₄×C₇	—	4	8	no	—
488	C₂×C₄×C₇	—	4	8	no	—
489	C₂×C₄×C₇	—	4	4	no	—
490	C₂×C₄×C₇	—	4	2	no	—
491	C₂×C₄×C₇	—	4	2	no	—
492	C₂×C₄×C₇	—	4	2	no	—
493	C₂×C₄×C₇	—	4	2	no	—
494	C₂×C₄×C₇	—	4	2	no	—
495	C₂×C₄×C₇	—	8	2	no	—
496	C₂×C₄×C₇	—	8	4	no	—
497	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
498	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₇	C₂×#41	1	2	yes	—
504	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
505	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
506	C₇×C₈	—	2	1	no	—
507	C₇×C₈	—	2	1	no	—
508	C₇×C₈	—	2	1	no	—
509	C₇×C₈	—	2	1	no	—
510	C₇×C₈	—	2	4	no	—
511	2₋¹⁺⁴	—	2	8	no	—
512	2₋¹⁺⁴	—	4	4	no	—
513	C₂×#41	—	2	2	no	—
514	C₂×#41	—	2	4	no	—
515	C₂×#41	—	2	2	no	—
516	C₂×#41	C₂³×C₇	1	1	yes	characteristic
517	C₂×#41	C₂³×C₇	1	4	yes	—
518	C₂×#41	C₂³×C₇	1	1	yes	characteristic
519	C₂×#41	C₂³×C₇	1	2	yes	—
520	C₂²×Q₈	—	2	2	no	—
521	C₂²×Q₈	—	2	1	no	—
522	C₂²×Q₈	C₂³×C₇	1	2	yes	—
523	C₂²×Q₈	C₂³×C₇	1	4	yes	—
524	#137	—	4	4	no	—
525	#135	—	2	4	no	—
526	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
527	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
528	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
529	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
530	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
531	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
532	#131	—	4	4	no	—
533	C₂×M₁₆	C₂³×C₇	1	2	yes	—
534	C₂×M₁₆	C₂³×C₇	1	4	yes	—
535	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
536	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
537	C₂²×C₈	C₂³×C₇	1	4	yes	—
538	C₄⋊Q₈	—	2	2	no	—
539	C₄⋊Q₈	—	2	2	no	—
540	C₄⋊Q₈	—	2	2	no	—
541	C₄⋊Q₈	—	2	1	no	—
542	C₄⋊Q₈	—	2	1	no	—
543	C₄⋊Q₈	—	2	1	no	—
544	C₄⋊Q₈	—	2	1	no	—
545	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
546	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
547	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
548	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
550	#127	C₇×D₄	1	1	yes	characteristic
551	#126	—	2	4	no	—
552	#125	—	2	2	no	—
553	#124	—	2	2	no	—
554	#124	—	2	2	no	—
555	#124	—	2	4	no	—
556	#124	C₇×D₄	1	2	yes	—
557	#123	—	2	4	no	—
558	#123	—	2	4	no	—
559	#123	—	2	4	no	—
560	#123	—	2	4	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	4	no	—
564	C₂²⋊Q₈	—	2	4	no	—
565	C₂²⋊Q₈	—	2	4	no	—
566	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
567	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
568	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
569	#121	—	2	2	no	—
570	#121	—	2	2	no	—
571	#121	—	2	2	no	—
572	#121	—	2	2	no	—
573	#121	—	2	4	no	—
574	#121	C₇×D₄	1	2	yes	—
575	#121	C₇×D₄	1	2	yes	—
576	#121	C₂³×C₇	1	4	yes	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
580	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
581	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
582	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	4	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
593	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
594	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
595	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
596	C₄×D₄	C₂³×C₇	1	2	yes	—
597	C₄×D₄	C₂³×C₇	1	2	yes	—
598	#117	—	2	2	no	—
599	#117	—	2	1	no	—
600	#117	—	2	1	no	—
601	#117	C₂³×C₇	1	1	yes	characteristic
602	#117	C₂³×C₇	1	1	yes	characteristic
603	#117	C₂³×C₇	1	4	yes	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	2	no	—
608	C₂×C₄⋊C₄	—	2	2	no	—
609	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
611	C₂×C₄²	—	2	1	no	—
612	C₂×C₄²	—	2	1	no	—
613	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
614	#107	C₂³×C₇	1	1	yes	characteristic
615	#107	C₂³×C₇	1	1	yes	characteristic
616	#107	C₂³×C₇	1	4	yes	—
617	#106	C₂³×C₇	1	1	yes	characteristic
618	#106	C₂³×C₇	1	1	yes	characteristic
619	#106	C₂³×C₇	1	4	yes	—
620	C₄⋊C₈	C₂³×C₇	1	2	yes	—
621	C₄⋊C₈	C₂³×C₇	1	2	yes	—
622	#103	C₂³×C₇	1	1	yes	characteristic
623	#103	C₂³×C₇	1	4	yes	—
624	#103	C₂³×C₇	1	4	yes	—
625	#103	C₂³×C₇	1	4	yes	—
626	#103	C₂³×C₇	1	4	yes	—
627	#103	C₂³×C₇	1	4	yes	—
628	#103	C₂³×C₇	1	4	yes	—
629	#103	C₂³×C₇	1	1	yes	characteristic
630	#103	C₂³×C₇	1	4	yes	—
631	#103	C₂³×C₇	1	1	yes	characteristic
632	#103	C₂³×C₇	1	1	yes	characteristic
633	#102	C₂³×C₇	1	1	yes	characteristic
634	#102	C₂³×C₇	1	1	yes	characteristic
635	#102	C₂³×C₇	1	4	yes	—
636	#102	C₂³×C₇	1	1	yes	characteristic
637	#102	C₂³×C₇	1	1	yes	characteristic
638	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
639	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
640	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
641	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
642	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
643	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
644	C₂²×C₇	—	2	1	no	—
645	C₂²×C₇	—	2	1	no	—
646	C₂²×C₇	—	2	2	no	—
647	C₂²×C₇	—	2	4	no	—
648	C₂²×C₇	—	2	4	no	—
649	C₂²×C₇	—	2	4	no	—
650	C₂²×C₇	—	4	1	no	—
651	C₂²×C₇	—	4	1	no	—
652	C₂²×C₇	—	4	1	no	—
653	C₂²×C₇	—	4	1	no	—
654	C₂²×C₇	—	4	1	no	—
655	C₂²×C₇	#546	1	2	yes	—
656	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
657	C₄×C₇	—	2	2	no	—
658	C₄×C₇	—	2	4	no	—
659	C₄×C₇	—	2	1	no	—
660	C₄×C₇	—	2	1	no	—
661	C₄×C₇	—	4	4	no	—
662	C₄×C₇	—	4	1	no	—
663	C₄×C₇	—	4	1	no	—
664	C₄×C₇	—	4	1	no	—
665	C₄×C₇	—	4	4	no	—
666	C₄×C₇	—	4	1	no	—
667	C₄×C₇	—	4	1	no	—
668	C₄×C₇	#546	1	2	yes	—
669	C₄×C₇	#577	1	2	yes	—
670	C₄×C₇	#578	1	2	yes	—
671	C₄×C₇	C₂²×#41	1	1	yes	characteristic
672	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
673	#41	—	2	4	no	—
674	#41	—	2	4	no	—
675	#41	—	2	2	no	—
676	#41	—	2	8	no	—
677	#41	—	2	2	no	—
678	#41	—	2	2	no	—
679	#41	—	4	4	no	—
680	#41	—	4	8	no	—
681	#41	—	4	16	no	—
682	#41	—	8	4	no	—
683	#41	C₇×#41	1	4	yes	complemented
684	C₂×Q₈	—	2	2	no	—
685	C₂×Q₈	—	2	4	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	2	2	no	—
688	C₂×Q₈	—	2	8	no	—
689	C₂×Q₈	—	2	4	no	—
690	C₂×Q₈	—	2	4	no	—
691	C₂×Q₈	—	4	4	no	—
692	C₂×Q₈	—	4	8	no	—
693	C₂×Q₈	—	8	2	no	—
694	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
695	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
696	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
697	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
703	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
704	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
705	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
706	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
707	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
720	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
722	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
723	Q₁₆	—	2	2	no	—
724	Q₁₆	—	4	4	no	—
725	SD₁₆	—	2	2	no	—
726	SD₁₆	—	2	2	no	—
727	SD₁₆	—	4	4	no	—
728	D₈	—	2	2	no	—
729	M₁₆	—	2	4	no	—
730	M₁₆	—	4	4	no	—
731	C₂×C₈	—	2	2	no	—
732	C₂×C₈	—	2	2	no	—
733	C₂×C₈	—	4	4	no	—
734	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
735	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
736	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
737	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
738	C₂×C₈	C₂⁴×C₇	1	4	yes	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
755	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
756	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
757	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
758	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
759	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
760	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	1	no	—
768	C₂²⋊C₄	—	2	1	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	1	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
773	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	1	no	—
777	C₄²	—	2	1	no	—
778	C₄²	—	2	1	no	—
779	C₄²	—	2	1	no	—
780	C₄²	—	2	4	no	—
781	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
782	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
783	C₄²	C₂⁴×C₇	1	1	yes	characteristic
784	C₄²	C₂⁴×C₇	1	1	yes	characteristic
785	C₂×C₇	—	2	2	no	—
786	C₂×C₇	—	4	4	no	—
787	C₂×C₇	—	4	2	no	—
788	C₂×C₇	—	8	1	no	—
789	C₂×C₇	C₂×#546	1	1	yes	characteristic
790	C₂×C₇	C₂×#577	1	1	yes	characteristic
791	C₂×C₇	C₂×#578	1	1	yes	characteristic
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	C₂²×C₇×D₄	1	4	yes	—
795	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
796	Q₈	—	2	1	no	—
797	Q₈	—	2	4	no	—
798	Q₈	—	2	1	no	—
799	Q₈	—	2	4	no	—
800	Q₈	—	2	4	no	—
801	Q₈	—	2	1	no	—
802	Q₈	—	4	8	no	—
803	Q₈	—	4	4	no	—
804	Q₈	—	4	4	no	—
805	Q₈	—	8	2	no	—
806	Q₈	C₂×C₇×#41	1	2	yes	—
807	D₄	—	2	4	no	—
808	D₄	—	2	8	no	—
809	D₄	—	2	1	no	—
810	D₄	—	2	1	no	—
811	D₄	—	2	1	no	—
812	D₄	—	2	4	no	—
813	D₄	—	2	4	no	—
814	D₄	—	2	4	no	—
815	D₄	—	4	8	no	—
816	D₄	—	4	2	no	—
817	D₄	—	8	4	no	—
818	D₄	C₂×C₇×#41	1	2	yes	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	4	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	4	8	no	—
833	C₂×C₄	—	4	8	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	2	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	4	2	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	—	8	4	no	—
842	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
843	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
844	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
845	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
846	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
847	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
848	C₂×C₄	C₂×C₇×#41	1	2	yes	—
849	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
850	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
851	C₈	—	2	1	no	—
852	C₈	—	2	1	no	—
853	C₈	—	2	1	no	—
854	C₈	—	2	1	no	—
855	C₈	—	2	4	no	—
856	C₇	#61217	1	1	yes	characteristic, direct product factor, Sylow
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	4	no	—
860	C₂²	—	2	4	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	4	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	C₇×#546	1	2	yes	—
869	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	4	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	4	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	4	no	—
880	C₄	—	4	1	no	—
881	C₄	C₇×#546	1	2	yes	—
882	C₄	C₇×#577	1	2	yes	—
883	C₄	C₇×#578	1	2	yes	—
884	C₄	C₂²×C₇×#41	1	1	yes	characteristic
885	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
886	C₂	—	2	2	no	—
887	C₂	—	4	4	no	—
888	C₂	—	4	2	no	—
889	C₂	—	8	1	no	—
890	C₂	C₂×C₇×#546	1	1	yes	characteristic
891	C₂	C₂×C₇×#577	1	1	yes	characteristic
892	C₂	C₂×C₇×#578	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×#3511	C₂	semidirect
2. C₇×#3499	C₂	semidirect
3. C₇×#3331	C₂	semidirect
4. C₇×#3330	C₂	semidirect
5. C₇×#3329	C₂	semidirect
6. C₇×#3328	C₂	semidirect
7. C₇×#3303	C₂	semidirect
8. C₇×#3302	C₂	semidirect
9. C₇×#3299	C₂	semidirect
10. C₇×#3298	C₂	semidirect
11. C₂×C₇×#487	C₂	semidirect
12. C₇×#3097	C₂	semidirect
13. C₇×#3079	C₂	semidirect
14. C₇×#3063	C₂	semidirect
15. C₇×#3039	C₂	semidirect
16. C₇×#3013	C₂	semidirect
17. C₄×C₇×#135	C₂	semidirect
18. C₇×#2931	C₂	semidirect
19. C₇×#2898	C₂	semidirect
101. #61217	C₇	direct (N × H)
235. #3511	C₂×C₇	semidirect
236. #3499	C₂×C₇	semidirect
237. #3331	C₂×C₇	semidirect
238. #3330	C₂×C₇	semidirect
239. #3329	C₂×C₇	semidirect
240. #3328	C₂×C₇	semidirect
241. #3303	C₂×C₇	semidirect
242. #3302	C₂×C₇	semidirect
243. #3299	C₂×C₇	semidirect
244. #3298	C₂×C₇	semidirect
245. C₂×#487	C₂×C₇	semidirect
246. #3097	C₂×C₇	semidirect
247. #3079	C₂×C₇	semidirect
248. #3063	C₂×C₇	semidirect
249. #3039	C₂×C₇	semidirect
250. #3013	C₂×C₇	semidirect
251. C₄×#135	C₂×C₇	semidirect
252. #2931	C₂×C₇	semidirect
253. #2898	C₂×C₇	semidirect
264. C₇×#41	#41	semidirect
683. #41	C₇×#41	semidirect
856. C₇	#61217	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×#3511	2
C₇×#3499	2
C₇×#3331	2
C₇×#3330	2
C₇×#3329	2
C₇×#3328	2
C₇×#3303	2
C₇×#3302	2
C₇×#3299	2
C₇×#3298	2
C₂×C₇×#487	2
C₇×#3097	2
C₇×#3079	2
C₇×#3063	2
C₇×#3039	2
C₇×#3013	2
C₄×C₇×#135	2
C₇×#2931	2
C₇×#2898	2
#61217	7

Subgroups — C7×#61217 #13238433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61217 #13238433