Subgroups — C₇×#61002 #13238218

Order 1792.

1682 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3495	C₂	1	2	yes	maximal, complemented
2	C₇×#3250	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3249	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3248	C₂	1	2	yes	maximal, complemented
5	C₇×#3243	C₂	1	2	yes	maximal, complemented
6	C₇×#3242	C₂	1	2	yes	maximal, complemented
7	C₇×#3225	C₂	1	2	yes	maximal, complemented
8	C₇×#3223	C₂	1	2	yes	maximal, complemented
9	C₇×#3191	C₂	1	1	yes	maximal, characteristic
10	C₇×#3190	C₂	1	2	yes	maximal, complemented
11	C₇×#3189	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3181	C₂	1	2	yes	maximal, complemented
13	C₇×#3170	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3127	C₂	1	2	yes	maximal, complemented
16	C₇×#3124	C₂	1	2	yes	maximal, complemented
17	C₇×#3121	C₂	1	2	yes	maximal, complemented
18	C₇×#3120	C₂	1	2	yes	maximal, complemented
19	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#556	—	2	2	no	—
21	C₇×#554	—	2	2	no	—
22	C₇×#552	—	2	2	no	—
23	C₇×#552	—	2	2	no	—
24	C₇×#552	—	2	2	no	—
25	C₇×#552	—	2	2	no	—
26	C₇×#551	—	2	2	no	—
27	C₇×#551	—	2	2	no	—
28	C₇×#544	C₂²	1	2	yes	—
29	C₇×#542	C₂²	1	2	yes	—
30	C₇×#542	C₂²	1	2	yes	—
31	C₇×#541	C₂²	1	2	yes	—
32	C₇×#541	C₂²	1	2	yes	—
33	C₇×#536	C₂²	1	2	yes	—
34	C₇×#533	C₂²	1	2	yes	—
35	C₇×#533	C₂²	1	2	yes	—
36	C₇×#529	C₂²	1	2	yes	—
37	C₇×#529	C₂²	1	2	yes	—
38	C₇×#525	C₂²	1	2	yes	—
39	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
40	C₇×#520	C₂²	1	2	yes	—
41	C₇×#519	C₂²	1	2	yes	—
42	C₂×C₇×#117	C₂²	1	1	yes	characteristic
43	C₇×#501	C₂²	1	2	yes	complemented
44	C₇×#500	C₂²	1	1	yes	characteristic, complemented
45	C₇×#499	C₂²	1	1	yes	characteristic, complemented
46	C₇×#497	C₂²	1	2	yes	complemented
47	C₇×#495	C₂²	1	1	yes	characteristic, complemented
48	C₇×#494	C₂²	1	1	yes	characteristic, complemented
49	C₇×#491	C₂²	1	2	yes	complemented
50	C₇×#489	C₂²	1	2	yes	complemented
51	C₇×#488	C₂²	1	2	yes	complemented
52	C₇×#487	C₂²	1	2	yes	complemented
53	C₇×#485	C₂²	1	2	yes	—
54	C₇×#485	C₂²	1	2	yes	—
55	C₇×#485	C₂²	1	2	yes	—
56	C₇×#484	C₂²	1	2	yes	—
57	C₇×#484	C₂²	1	2	yes	—
58	C₇×#483	C₂²	1	2	yes	—
59	C₇×#482	C₂²	1	2	yes	—
60	C₇×#480	C₂²	1	2	yes	—
61	C₇×#479	C₂²	1	2	yes	complemented
62	C₇×#479	C₂²	1	2	yes	complemented
63	C₇×#479	C₂²	1	2	yes	complemented
64	C₇×#478	C₂²	1	2	yes	complemented
65	C₇×#477	C₂²	1	2	yes	complemented
66	C₇×#477	C₂²	1	2	yes	complemented
67	C₇×#475	C₂²	1	2	yes	complemented
68	C₇×#474	C₂²	1	2	yes	complemented
69	C₇×#467	C₂²	1	1	yes	characteristic
70	C₇×#467	C₂²	1	1	yes	characteristic
71	C₇×#467	C₂²	1	2	yes	—
72	C₇×#467	C₂²	1	1	yes	characteristic
73	C₇×#467	C₂²	1	2	yes	—
74	C₇×#467	C₂²	1	2	yes	—
75	C₇×#466	C₂²	1	1	yes	characteristic
76	C₇×#465	C₂²	1	2	yes	—
77	C₇×#465	C₂²	1	2	yes	—
78	C₇×#465	C₂²	1	2	yes	—
79	C₇×#464	C₂²	1	2	yes	complemented
80	C₇×#464	C₂²	1	2	yes	complemented
81	C₇×#464	C₂²	1	2	yes	complemented
82	C₇×#463	C₂²	1	2	yes	complemented
83	C₇×#462	C₂²	1	2	yes	complemented
84	C₇×#462	C₂²	1	2	yes	complemented
85	C₇×#462	C₂²	1	2	yes	complemented
86	C₇×#461	C₂²	1	2	yes	complemented
87	C₇×#452	C₂²	1	2	yes	—
88	C₇×#452	C₂²	1	2	yes	—
89	C₇×#452	C₂²	1	2	yes	—
90	C₇×#451	C₂²	1	2	yes	—
91	C₇×#451	C₂²	1	2	yes	—
92	C₇×#451	C₂²	1	2	yes	—
93	C₇×#449	C₂²	1	2	yes	—
94	C₇×#448	C₂²	1	2	yes	—
95	C₇×#441	C₂²	1	2	yes	complemented
96	C₇×#441	C₂²	1	2	yes	complemented
97	C₇×#440	C₂²	1	2	yes	complemented
98	C₇×#440	C₂²	1	2	yes	complemented
99	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
103	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
104	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
105	C₇×#433	C₂²	1	2	yes	—
106	C₇×#433	C₂²	1	2	yes	—
107	C₇×#433	C₂²	1	2	yes	—
108	C₇×#433	C₂²	1	2	yes	—
109	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
110	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
111	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
112	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
113	C₂×C₇×#97	C₂²	1	1	yes	characteristic
114	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
115	#61002	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂×C₇×#41	C₂³	1	2	yes	—
117	C₂²×C₇×Q₈	C₂³	1	2	yes	—
118	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
119	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
120	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
121	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
123	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
124	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
125	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
129	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
130	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
131	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
132	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
133	C₇×C₄⋊Q₈	—	2	2	no	—
134	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₇×#126	—	2	2	no	—
139	C₇×#126	—	2	2	no	—
140	C₇×#126	—	2	2	no	—
141	C₇×#126	—	2	2	no	—
142	C₇×#126	—	2	2	no	—
143	C₇×#126	—	2	2	no	—
144	C₇×#126	—	2	2	no	—
145	C₇×#126	—	2	2	no	—
146	C₇×#125	—	2	2	no	—
147	C₇×#125	—	2	2	no	—
148	C₇×#125	—	2	2	no	—
149	C₇×#125	—	2	2	no	—
150	C₇×#125	—	2	2	no	—
151	C₇×#125	—	2	2	no	—
152	C₇×#125	—	2	2	no	—
153	C₇×#125	C₂³	1	2	yes	—
154	C₇×#125	C₂³	1	2	yes	—
155	C₇×#124	—	2	2	no	—
156	C₇×#124	—	2	2	no	—
157	C₇×#124	C₂³	1	2	yes	—
158	C₇×#124	C₂³	1	2	yes	—
159	C₇×#123	—	2	2	no	—
160	C₇×#123	—	2	2	no	—
161	C₇×#123	—	2	2	no	—
162	C₇×#123	—	2	2	no	—
163	C₇×#123	—	2	2	no	—
164	C₇×#123	—	2	2	no	—
165	C₇×#123	—	2	2	no	—
166	C₇×C₂²⋊Q₈	—	2	2	no	—
167	C₇×C₂²⋊Q₈	—	2	2	no	—
168	C₇×C₂²⋊Q₈	—	2	2	no	—
169	C₇×C₂²⋊Q₈	—	2	2	no	—
170	C₇×C₂²⋊Q₈	—	2	2	no	—
171	C₇×C₂²⋊Q₈	—	2	2	no	—
172	C₇×C₂²⋊Q₈	—	2	2	no	—
173	C₇×C₂²⋊Q₈	—	2	2	no	—
174	C₇×C₂²⋊Q₈	—	2	2	no	—
175	C₇×C₂²⋊Q₈	—	2	2	no	—
176	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
179	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
180	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
181	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
182	C₇×#121	C₂³	1	2	yes	—
183	C₇×#121	C₂³	1	2	yes	—
184	C₇×#120	—	2	2	no	—
185	C₄×C₇×Q₈	—	2	2	no	—
186	C₄×C₇×Q₈	—	2	2	no	—
187	C₄×C₇×Q₈	—	2	2	no	—
188	C₄×C₇×Q₈	—	2	2	no	—
189	C₄×C₇×Q₈	C₂³	1	2	yes	—
190	C₄×C₇×Q₈	C₂³	1	2	yes	—
191	C₄×C₇×Q₈	C₂³	1	2	yes	—
192	C₄×C₇×Q₈	C₂³	1	2	yes	—
193	C₄×C₇×Q₈	C₂³	1	2	yes	—
194	C₄×C₇×Q₈	C₂³	1	2	yes	—
195	C₄×C₇×D₄	—	2	2	no	—
196	C₄×C₇×D₄	—	2	2	no	—
197	C₄×C₇×D₄	—	2	2	no	—
198	C₄×C₇×D₄	—	2	2	no	—
199	C₄×C₇×D₄	—	2	2	no	—
200	C₄×C₇×D₄	—	2	2	no	—
201	C₄×C₇×D₄	C₂³	1	2	yes	—
202	C₄×C₇×D₄	C₂³	1	2	yes	—
203	C₇×#117	—	2	2	no	—
204	C₇×#117	—	2	2	no	—
205	C₇×#117	—	2	2	no	—
206	C₇×#117	—	2	2	no	—
207	C₇×#117	—	2	2	no	—
208	C₇×#117	—	2	2	no	—
209	C₇×#117	—	2	2	no	—
210	C₇×#117	D₄	1	2	yes	—
211	C₇×#117	D₄	1	2	yes	—
212	C₇×#117	C₂³	1	2	yes	—
213	C₇×#117	C₂³	1	2	yes	—
214	C₇×#117	C₂³	1	2	yes	—
215	C₂×C₇×C₄⋊C₄	—	2	2	no	—
216	C₂×C₇×C₄⋊C₄	—	2	2	no	—
217	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
218	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
219	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
220	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
221	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
222	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
223	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
225	C₇×#107	C₂³	1	1	yes	characteristic
226	C₇×#107	C₂³	1	2	yes	—
227	C₇×#107	C₂³	1	2	yes	—
228	C₇×#107	C₂³	1	2	yes	—
229	C₇×#107	C₂³	1	1	yes	characteristic
230	C₇×#107	C₂³	1	1	yes	characteristic
231	C₇×#107	C₂³	1	1	yes	characteristic
232	C₇×#106	C₂³	1	2	yes	—
233	C₇×#106	C₂³	1	2	yes	—
234	C₇×#106	C₂³	1	2	yes	—
235	C₇×C₄⋊C₈	C₂³	1	2	yes	—
236	C₇×C₄⋊C₈	C₂³	1	2	yes	—
237	C₇×C₄⋊C₈	C₂³	1	2	yes	—
238	C₇×C₄⋊C₈	C₂³	1	2	yes	—
239	C₇×#103	C₂³	1	2	yes	—
240	C₇×#103	C₂³	1	2	yes	—
241	C₇×#103	C₂³	1	2	yes	—
242	C₇×#103	C₂³	1	2	yes	—
243	C₇×#103	C₂³	1	2	yes	—
244	C₇×#103	C₂³	1	2	yes	—
245	C₇×#103	C₂³	1	2	yes	—
246	C₇×#103	C₂³	1	2	yes	—
247	C₇×#103	C₂³	1	2	yes	—
248	C₇×#103	C₂³	1	2	yes	—
249	C₇×#103	C₂³	1	2	yes	—
250	C₇×#103	C₂³	1	2	yes	—
251	C₇×#102	C₂³	1	2	yes	—
252	C₇×#102	C₂³	1	2	yes	—
253	C₇×#102	C₂³	1	2	yes	—
254	C₇×#102	C₂³	1	2	yes	—
255	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₇×#97	C₂³	1	2	yes	—
260	C₇×#97	C₂³	1	2	yes	—
261	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
262	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
263	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
264	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
265	#3495	C₂×C₇	1	2	yes	complemented
266	#3250	C₂×C₇	1	1	yes	characteristic, complemented
267	#3249	C₂×C₇	1	1	yes	characteristic, complemented
268	#3248	C₂×C₇	1	2	yes	complemented
269	#3243	C₂×C₇	1	2	yes	complemented
270	#3242	C₂×C₇	1	2	yes	complemented
271	#3225	C₂×C₇	1	2	yes	complemented
272	#3223	C₂×C₇	1	2	yes	complemented
273	#3191	C₂×C₇	1	1	yes	characteristic
274	#3190	C₂×C₇	1	2	yes	complemented
275	#3189	C₂×C₇	1	1	yes	characteristic, complemented
276	#3181	C₂×C₇	1	2	yes	complemented
277	#3170	C₂×C₇	1	1	yes	characteristic, complemented
278	#3168	C₂×C₇	1	1	yes	characteristic, complemented
279	#3127	C₂×C₇	1	2	yes	complemented
280	#3124	C₂×C₇	1	2	yes	complemented
281	#3121	C₂×C₇	1	2	yes	complemented
282	#3120	C₂×C₇	1	2	yes	complemented
283	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
284	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
285	C₇×#41	—	4	2	no	—
286	C₇×#41	—	4	2	no	—
287	C₂×C₇×Q₈	—	2	2	no	—
288	C₂×C₇×Q₈	—	2	2	no	—
289	C₂×C₇×Q₈	—	2	2	no	—
290	C₂×C₇×Q₈	—	4	2	no	—
291	C₂×C₇×Q₈	—	4	2	no	—
292	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
293	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
294	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
295	C₂×C₇×D₄	—	2	2	no	—
296	C₂×C₇×D₄	—	2	2	no	—
297	C₂×C₇×D₄	—	2	2	no	—
298	C₂×C₇×D₄	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₇	—	2	2	no	—
300	C₂²×C₄×C₇	—	2	2	no	—
301	C₂²×C₄×C₇	—	2	2	no	—
302	C₂²×C₄×C₇	—	2	2	no	—
303	C₂²×C₄×C₇	—	2	2	no	—
304	C₂²×C₄×C₇	—	4	1	no	—
305	C₂²×C₄×C₇	—	4	1	no	—
306	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
311	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
314	C₇×Q₁₆	—	4	1	no	—
315	C₇×Q₁₆	—	4	2	no	—
316	C₇×Q₁₆	—	4	2	no	—
317	C₇×Q₁₆	—	4	1	no	—
318	C₇×Q₁₆	—	4	2	no	—
319	C₇×Q₁₆	—	4	1	no	—
320	C₇×SD₁₆	—	4	2	no	—
321	C₇×SD₁₆	—	4	2	no	—
322	C₇×SD₁₆	—	4	2	no	—
323	C₇×D₈	—	4	1	no	—
324	C₂×C₇×C₈	—	4	1	no	—
325	C₂×C₇×C₈	—	4	1	no	—
326	C₂×C₇×C₈	—	4	1	no	—
327	C₂×C₇×C₈	—	4	1	no	—
328	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
329	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
330	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
331	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
332	C₂×C₇×C₈	C₂⁴	1	2	yes	—
333	C₂×C₇×C₈	C₂⁴	1	2	yes	—
334	C₇×C₄⋊C₄	—	2	2	no	—
335	C₇×C₄⋊C₄	—	2	2	no	—
336	C₇×C₄⋊C₄	—	2	2	no	—
337	C₇×C₄⋊C₄	—	2	2	no	—
338	C₇×C₄⋊C₄	—	2	2	no	—
339	C₇×C₄⋊C₄	—	2	2	no	—
340	C₇×C₄⋊C₄	—	2	2	no	—
341	C₇×C₄⋊C₄	—	2	2	no	—
342	C₇×C₄⋊C₄	—	2	2	no	—
343	C₇×C₄⋊C₄	—	2	2	no	—
344	C₇×C₄⋊C₄	—	2	2	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	2	no	—
349	C₇×C₄⋊C₄	—	2	2	no	—
350	C₇×C₄⋊C₄	—	2	2	no	—
351	C₇×C₄⋊C₄	—	2	2	no	—
352	C₇×C₄⋊C₄	—	2	2	no	—
353	C₇×C₄⋊C₄	—	2	2	no	—
354	C₇×C₄⋊C₄	—	2	2	no	—
355	C₇×C₄⋊C₄	—	2	2	no	—
356	C₇×C₄⋊C₄	—	2	2	no	—
357	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
358	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
359	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
360	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
361	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
362	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
363	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
364	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
365	C₇×C₂²⋊C₄	—	2	2	no	—
366	C₇×C₂²⋊C₄	—	2	2	no	—
367	C₇×C₂²⋊C₄	—	2	2	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	2	no	—
372	C₇×C₂²⋊C₄	—	2	2	no	—
373	C₇×C₂²⋊C₄	—	2	2	no	—
374	C₇×C₂²⋊C₄	—	2	2	no	—
375	C₇×C₂²⋊C₄	—	2	2	no	—
376	C₇×C₂²⋊C₄	—	2	2	no	—
377	C₇×C₂²⋊C₄	—	2	2	no	—
378	C₇×C₂²⋊C₄	—	2	2	no	—
379	C₇×C₂²⋊C₄	—	2	2	no	—
380	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
381	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
382	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
383	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
384	C₄²×C₇	—	2	2	no	—
385	C₄²×C₇	—	2	2	no	—
386	C₄²×C₇	—	2	2	no	—
387	C₄²×C₇	—	2	2	no	—
388	C₄²×C₇	—	2	2	no	—
389	C₄²×C₇	—	2	2	no	—
390	C₄²×C₇	—	2	2	no	—
391	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
392	C₄²×C₇	C₂×D₄	1	2	yes	—
393	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₇	C₂⁴	1	1	yes	characteristic
395	C₄²×C₇	C₂⁴	1	1	yes	characteristic
396	C₄²×C₇	C₂⁴	1	2	yes	—
397	#556	—	2	2	no	—
398	#554	—	2	2	no	—
399	#552	—	2	2	no	—
400	#552	—	2	2	no	—
401	#552	—	2	2	no	—
402	#552	—	2	2	no	—
403	#551	—	2	2	no	—
404	#551	—	2	2	no	—
405	#544	C₂²×C₇	1	2	yes	—
406	#542	C₂²×C₇	1	2	yes	—
407	#542	C₂²×C₇	1	2	yes	—
408	#541	C₂²×C₇	1	2	yes	—
409	#541	C₂²×C₇	1	2	yes	—
410	#536	C₂²×C₇	1	2	yes	—
411	#533	C₂²×C₇	1	2	yes	—
412	#533	C₂²×C₇	1	2	yes	—
413	#529	C₂²×C₇	1	2	yes	—
414	#529	C₂²×C₇	1	2	yes	—
415	#525	C₂²×C₇	1	2	yes	—
416	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
417	#520	C₂²×C₇	1	2	yes	—
418	#519	C₂²×C₇	1	2	yes	—
419	C₂×#117	C₂²×C₇	1	1	yes	characteristic
420	#501	C₂²×C₇	1	2	yes	complemented
421	#500	C₂²×C₇	1	1	yes	characteristic, complemented
422	#499	C₂²×C₇	1	1	yes	characteristic, complemented
423	#497	C₂²×C₇	1	2	yes	complemented
424	#495	C₂²×C₇	1	1	yes	characteristic, complemented
425	#494	C₂²×C₇	1	1	yes	characteristic, complemented
426	#491	C₂²×C₇	1	2	yes	complemented
427	#489	C₂²×C₇	1	2	yes	complemented
428	#488	C₂²×C₇	1	2	yes	complemented
429	#487	C₂²×C₇	1	2	yes	complemented
430	#485	C₂²×C₇	1	2	yes	—
431	#485	C₂²×C₇	1	2	yes	—
432	#485	C₂²×C₇	1	2	yes	—
433	#484	C₂²×C₇	1	2	yes	—
434	#484	C₂²×C₇	1	2	yes	—
435	#483	C₂²×C₇	1	2	yes	—
436	#482	C₂²×C₇	1	2	yes	—
437	#480	C₂²×C₇	1	2	yes	—
438	#479	C₂²×C₇	1	2	yes	complemented
439	#479	C₂²×C₇	1	2	yes	complemented
440	#479	C₂²×C₇	1	2	yes	complemented
441	#478	C₂²×C₇	1	2	yes	complemented
442	#477	C₂²×C₇	1	2	yes	complemented
443	#477	C₂²×C₇	1	2	yes	complemented
444	#475	C₂²×C₇	1	2	yes	complemented
445	#474	C₂²×C₇	1	2	yes	complemented
446	#467	C₂²×C₇	1	1	yes	characteristic
447	#467	C₂²×C₇	1	1	yes	characteristic
448	#467	C₂²×C₇	1	2	yes	—
449	#467	C₂²×C₇	1	1	yes	characteristic
450	#467	C₂²×C₇	1	2	yes	—
451	#467	C₂²×C₇	1	2	yes	—
452	#466	C₂²×C₇	1	1	yes	characteristic
453	#465	C₂²×C₇	1	2	yes	—
454	#465	C₂²×C₇	1	2	yes	—
455	#465	C₂²×C₇	1	2	yes	—
456	#464	C₂²×C₇	1	2	yes	complemented
457	#464	C₂²×C₇	1	2	yes	complemented
458	#464	C₂²×C₇	1	2	yes	complemented
459	#463	C₂²×C₇	1	2	yes	complemented
460	#462	C₂²×C₇	1	2	yes	complemented
461	#462	C₂²×C₇	1	2	yes	complemented
462	#462	C₂²×C₇	1	2	yes	complemented
463	#461	C₂²×C₇	1	2	yes	complemented
464	#452	C₂²×C₇	1	2	yes	—
465	#452	C₂²×C₇	1	2	yes	—
466	#452	C₂²×C₇	1	2	yes	—
467	#451	C₂²×C₇	1	2	yes	—
468	#451	C₂²×C₇	1	2	yes	—
469	#451	C₂²×C₇	1	2	yes	—
470	#449	C₂²×C₇	1	2	yes	—
471	#448	C₂²×C₇	1	2	yes	—
472	#441	C₂²×C₇	1	2	yes	complemented
473	#441	C₂²×C₇	1	2	yes	complemented
474	#440	C₂²×C₇	1	2	yes	complemented
475	#440	C₂²×C₇	1	2	yes	complemented
476	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
477	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
478	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
479	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
480	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
481	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
482	#433	C₂²×C₇	1	2	yes	—
483	#433	C₂²×C₇	1	2	yes	—
484	#433	C₂²×C₇	1	2	yes	—
485	#433	C₂²×C₇	1	2	yes	—
486	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
487	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
488	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
489	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
490	C₂×#97	C₂²×C₇	1	1	yes	characteristic
491	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
492	C₂³×C₇	—	2	2	no	—
493	C₂³×C₇	—	2	2	no	—
494	C₂³×C₇	—	4	1	no	—
495	C₂³×C₇	—	4	1	no	—
496	C₂³×C₇	C₂²×D₄	1	2	yes	—
497	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
498	C₇×Q₈	—	2	2	no	—
499	C₇×Q₈	—	2	2	no	—
500	C₇×Q₈	—	2	2	no	—
501	C₇×Q₈	—	2	2	no	—
502	C₇×Q₈	—	2	2	no	—
503	C₇×Q₈	—	2	2	no	—
504	C₇×Q₈	—	4	4	no	—
505	C₇×Q₈	—	8	2	no	—
506	C₇×Q₈	—	8	2	no	—
507	C₇×D₄	—	2	2	no	—
508	C₇×D₄	—	2	2	no	—
509	C₇×D₄	—	4	4	no	—
510	C₇×D₄	—	4	4	no	—
511	C₇×D₄	—	8	2	no	—
512	C₂×C₄×C₇	—	2	2	no	—
513	C₂×C₄×C₇	—	2	2	no	—
514	C₂×C₄×C₇	—	2	1	no	—
515	C₂×C₄×C₇	—	2	1	no	—
516	C₂×C₄×C₇	—	2	2	no	—
517	C₂×C₄×C₇	—	2	2	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	2	no	—
523	C₂×C₄×C₇	—	2	2	no	—
524	C₂×C₄×C₇	—	2	2	no	—
525	C₂×C₄×C₇	—	4	1	no	—
526	C₂×C₄×C₇	—	4	2	no	—
527	C₂×C₄×C₇	—	4	1	no	—
528	C₂×C₄×C₇	—	4	1	no	—
529	C₂×C₄×C₇	—	4	4	no	—
530	C₂×C₄×C₇	—	4	4	no	—
531	C₂×C₄×C₇	—	8	2	no	—
532	C₂×C₄×C₇	—	8	2	no	—
533	C₂×C₄×C₇	—	8	2	no	—
534	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
538	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
539	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
543	C₇×C₈	—	2	1	no	—
544	C₇×C₈	—	2	1	no	—
545	C₇×C₈	—	2	2	no	—
546	C₇×C₈	—	2	2	no	—
547	C₇×C₈	—	2	1	no	—
548	C₇×C₈	—	2	1	no	—
549	C₂×#41	C₂³×C₇	1	2	yes	—
550	C₂²×Q₈	C₂³×C₇	1	2	yes	—
551	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
552	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
553	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
554	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
555	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
556	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
557	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
558	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
559	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
560	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
561	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
562	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
563	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
564	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
565	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
566	C₄⋊Q₈	—	2	2	no	—
567	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
568	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
569	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
570	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
571	#126	—	2	2	no	—
572	#126	—	2	2	no	—
573	#126	—	2	2	no	—
574	#126	—	2	2	no	—
575	#126	—	2	2	no	—
576	#126	—	2	2	no	—
577	#126	—	2	2	no	—
578	#126	—	2	2	no	—
579	#125	—	2	2	no	—
580	#125	—	2	2	no	—
581	#125	—	2	2	no	—
582	#125	—	2	2	no	—
583	#125	—	2	2	no	—
584	#125	—	2	2	no	—
585	#125	—	2	2	no	—
586	#125	C₂³×C₇	1	2	yes	—
587	#125	C₂³×C₇	1	2	yes	—
588	#124	—	2	2	no	—
589	#124	—	2	2	no	—
590	#124	C₂³×C₇	1	2	yes	—
591	#124	C₂³×C₇	1	2	yes	—
592	#123	—	2	2	no	—
593	#123	—	2	2	no	—
594	#123	—	2	2	no	—
595	#123	—	2	2	no	—
596	#123	—	2	2	no	—
597	#123	—	2	2	no	—
598	#123	—	2	2	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	C₂²⋊Q₈	—	2	2	no	—
601	C₂²⋊Q₈	—	2	2	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	—	2	2	no	—
604	C₂²⋊Q₈	—	2	2	no	—
605	C₂²⋊Q₈	—	2	2	no	—
606	C₂²⋊Q₈	—	2	2	no	—
607	C₂²⋊Q₈	—	2	2	no	—
608	C₂²⋊Q₈	—	2	2	no	—
609	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
610	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
611	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
612	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
613	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
614	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
615	#121	C₂³×C₇	1	2	yes	—
616	#121	C₂³×C₇	1	2	yes	—
617	#120	—	2	2	no	—
618	C₄×Q₈	—	2	2	no	—
619	C₄×Q₈	—	2	2	no	—
620	C₄×Q₈	—	2	2	no	—
621	C₄×Q₈	—	2	2	no	—
622	C₄×Q₈	C₂³×C₇	1	2	yes	—
623	C₄×Q₈	C₂³×C₇	1	2	yes	—
624	C₄×Q₈	C₂³×C₇	1	2	yes	—
625	C₄×Q₈	C₂³×C₇	1	2	yes	—
626	C₄×Q₈	C₂³×C₇	1	2	yes	—
627	C₄×Q₈	C₂³×C₇	1	2	yes	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	C₂³×C₇	1	2	yes	—
635	C₄×D₄	C₂³×C₇	1	2	yes	—
636	#117	—	2	2	no	—
637	#117	—	2	2	no	—
638	#117	—	2	2	no	—
639	#117	—	2	2	no	—
640	#117	—	2	2	no	—
641	#117	—	2	2	no	—
642	#117	—	2	2	no	—
643	#117	C₇×D₄	1	2	yes	—
644	#117	C₇×D₄	1	2	yes	—
645	#117	C₂³×C₇	1	2	yes	—
646	#117	C₂³×C₇	1	2	yes	—
647	#117	C₂³×C₇	1	2	yes	—
648	C₂×C₄⋊C₄	—	2	2	no	—
649	C₂×C₄⋊C₄	—	2	2	no	—
650	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
653	C₂×C₂²⋊C₄	—	2	2	no	—
654	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
658	#107	C₂³×C₇	1	1	yes	characteristic
659	#107	C₂³×C₇	1	1	yes	characteristic
660	#107	C₂³×C₇	1	2	yes	—
661	#107	C₂³×C₇	1	1	yes	characteristic
662	#107	C₂³×C₇	1	1	yes	characteristic
663	#107	C₂³×C₇	1	2	yes	—
664	#107	C₂³×C₇	1	2	yes	—
665	#106	C₂³×C₇	1	2	yes	—
666	#106	C₂³×C₇	1	2	yes	—
667	#106	C₂³×C₇	1	2	yes	—
668	C₄⋊C₈	C₂³×C₇	1	2	yes	—
669	C₄⋊C₈	C₂³×C₇	1	2	yes	—
670	C₄⋊C₈	C₂³×C₇	1	2	yes	—
671	C₄⋊C₈	C₂³×C₇	1	2	yes	—
672	#103	C₂³×C₇	1	2	yes	—
673	#103	C₂³×C₇	1	2	yes	—
674	#103	C₂³×C₇	1	2	yes	—
675	#103	C₂³×C₇	1	2	yes	—
676	#103	C₂³×C₇	1	2	yes	—
677	#103	C₂³×C₇	1	2	yes	—
678	#103	C₂³×C₇	1	2	yes	—
679	#103	C₂³×C₇	1	2	yes	—
680	#103	C₂³×C₇	1	2	yes	—
681	#103	C₂³×C₇	1	2	yes	—
682	#103	C₂³×C₇	1	2	yes	—
683	#103	C₂³×C₇	1	2	yes	—
684	#102	C₂³×C₇	1	2	yes	—
685	#102	C₂³×C₇	1	2	yes	—
686	#102	C₂³×C₇	1	2	yes	—
687	#102	C₂³×C₇	1	2	yes	—
688	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
689	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
690	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
691	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
692	#97	C₂³×C₇	1	2	yes	—
693	#97	C₂³×C₇	1	2	yes	—
694	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
695	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
696	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
697	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
698	C₂²×C₇	—	2	1	no	—
699	C₂²×C₇	—	2	1	no	—
700	C₂²×C₇	—	2	2	no	—
701	C₂²×C₇	—	2	2	no	—
702	C₂²×C₇	—	2	2	no	—
703	C₂²×C₇	—	4	2	no	—
704	C₂²×C₇	—	4	2	no	—
705	C₂²×C₇	—	4	2	no	—
706	C₂²×C₇	—	8	2	no	—
707	C₂²×C₇	#578	1	2	yes	—
708	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
709	C₄×C₇	—	2	1	no	—
710	C₄×C₇	—	2	2	no	—
711	C₄×C₇	—	2	1	no	—
712	C₄×C₇	—	2	2	no	—
713	C₄×C₇	—	2	1	no	—
714	C₄×C₇	—	2	1	no	—
715	C₄×C₇	—	2	2	no	—
716	C₄×C₇	—	2	1	no	—
717	C₄×C₇	—	4	2	no	—
718	C₄×C₇	—	4	2	no	—
719	C₄×C₇	—	4	2	no	—
720	C₄×C₇	—	4	2	no	—
721	C₄×C₇	—	4	2	no	—
722	C₄×C₇	—	4	2	no	—
723	C₄×C₇	—	4	2	no	—
724	C₄×C₇	#585	1	1	yes	characteristic
725	C₄×C₇	#585	1	1	yes	characteristic
726	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
727	#41	—	4	2	no	—
728	#41	—	4	2	no	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	—	2	2	no	—
731	C₂×Q₈	—	2	2	no	—
732	C₂×Q₈	—	4	2	no	—
733	C₂×Q₈	—	4	2	no	—
734	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
735	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
736	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	C₂⁴×C₇	1	2	yes	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	4	1	no	—
747	C₂²×C₄	—	4	1	no	—
748	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
749	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
750	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
751	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
752	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
753	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
756	Q₁₆	—	4	1	no	—
757	Q₁₆	—	4	2	no	—
758	Q₁₆	—	4	2	no	—
759	Q₁₆	—	4	1	no	—
760	Q₁₆	—	4	2	no	—
761	Q₁₆	—	4	1	no	—
762	SD₁₆	—	4	2	no	—
763	SD₁₆	—	4	2	no	—
764	SD₁₆	—	4	2	no	—
765	D₈	—	4	1	no	—
766	C₂×C₈	—	4	1	no	—
767	C₂×C₈	—	4	1	no	—
768	C₂×C₈	—	4	1	no	—
769	C₂×C₈	—	4	1	no	—
770	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
771	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
772	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
773	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
774	C₂×C₈	C₂⁴×C₇	1	2	yes	—
775	C₂×C₈	C₂⁴×C₇	1	2	yes	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
800	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
801	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
802	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
803	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
804	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
805	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
806	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
823	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
824	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
825	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
826	C₄²	—	2	2	no	—
827	C₄²	—	2	2	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
834	C₄²	C₂×C₇×D₄	1	2	yes	—
835	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
836	C₄²	C₂⁴×C₇	1	1	yes	characteristic
837	C₄²	C₂⁴×C₇	1	1	yes	characteristic
838	C₄²	C₂⁴×C₇	1	2	yes	—
839	C₂×C₇	—	2	2	no	—
840	C₂×C₇	—	4	2	no	—
841	C₂×C₇	—	8	2	no	—
842	C₂×C₇	#3449	1	1	yes	characteristic
843	C₂×C₇	C₂×#578	1	1	yes	characteristic
844	C₂×C₇	#3584	1	1	yes	characteristic
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	4	1	no	—
848	C₂³	—	4	1	no	—
849	C₂³	C₂²×C₇×D₄	1	2	yes	—
850	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
851	Q₈	—	2	2	no	—
852	Q₈	—	2	2	no	—
853	Q₈	—	2	2	no	—
854	Q₈	—	2	2	no	—
855	Q₈	—	2	2	no	—
856	Q₈	—	2	2	no	—
857	Q₈	—	4	4	no	—
858	Q₈	—	8	2	no	—
859	Q₈	—	8	2	no	—
860	D₄	—	2	2	no	—
861	D₄	—	2	2	no	—
862	D₄	—	4	4	no	—
863	D₄	—	4	4	no	—
864	D₄	—	8	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	2	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	4	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	8	2	no	—
885	C₂×C₄	—	8	2	no	—
886	C₂×C₄	—	8	2	no	—
887	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
888	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
889	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
890	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
891	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
892	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
893	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
894	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
895	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
896	C₈	—	2	1	no	—
897	C₈	—	2	1	no	—
898	C₈	—	2	2	no	—
899	C₈	—	2	2	no	—
900	C₈	—	2	1	no	—
901	C₈	—	2	1	no	—
902	C₇	#61002	1	1	yes	characteristic, direct product factor, Sylow
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	8	2	no	—
912	C₂²	C₇×#578	1	2	yes	—
913	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
914	C₄	—	2	1	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	2	no	—
921	C₄	—	2	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	C₇×#585	1	1	yes	characteristic
930	C₄	C₇×#585	1	1	yes	characteristic
931	C₂	—	2	2	no	—
932	C₂	—	4	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₇×#3449	1	1	yes	characteristic
935	C₂	C₂×C₇×#578	1	1	yes	characteristic
936	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3191	C₂
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×#3495	C₂	semidirect
2. C₇×#3250	C₂	semidirect
3. C₇×#3249	C₂	semidirect
4. C₇×#3248	C₂	semidirect
5. C₇×#3243	C₂	semidirect
6. C₇×#3242	C₂	semidirect
7. C₇×#3225	C₂	semidirect
8. C₇×#3223	C₂	semidirect
10. C₇×#3190	C₂	semidirect
11. C₇×#3189	C₂	semidirect
12. C₇×#3181	C₂	semidirect
13. C₇×#3170	C₂	semidirect
14. C₇×#3168	C₂	semidirect
15. C₇×#3127	C₂	semidirect
16. C₇×#3124	C₂	semidirect
17. C₇×#3121	C₂	semidirect
18. C₇×#3120	C₂	semidirect
19. C₂×C₇×#433	C₂	semidirect
43. C₇×#501	C₂²	semidirect
44. C₇×#500	C₂²	semidirect
45. C₇×#499	C₂²	semidirect
46. C₇×#497	C₂²	semidirect
47. C₇×#495	C₂²	semidirect
48. C₇×#494	C₂²	semidirect
49. C₇×#491	C₂²	semidirect
50. C₇×#489	C₂²	semidirect
51. C₇×#488	C₂²	semidirect
52. C₇×#487	C₂²	semidirect
61. C₇×#479	C₂²	semidirect
62. C₇×#479	C₂²	semidirect
63. C₇×#479	C₂²	semidirect
64. C₇×#478	C₂²	semidirect
65. C₇×#477	C₂²	semidirect
66. C₇×#477	C₂²	semidirect
67. C₇×#475	C₂²	semidirect
68. C₇×#474	C₂²	semidirect
79. C₇×#464	C₂²	semidirect
80. C₇×#464	C₂²	semidirect
81. C₇×#464	C₂²	semidirect
82. C₇×#463	C₂²	semidirect
83. C₇×#462	C₂²	semidirect
84. C₇×#462	C₂²	semidirect
85. C₇×#462	C₂²	semidirect
86. C₇×#461	C₂²	semidirect
95. C₇×#441	C₂²	semidirect
96. C₇×#441	C₂²	semidirect
97. C₇×#440	C₂²	semidirect
98. C₇×#440	C₂²	semidirect
99. C₄×C₇×Q₁₆	C₂²	semidirect
100. C₄×C₇×Q₁₆	C₂²	semidirect
101. C₄×C₇×Q₁₆	C₂²	semidirect
102. C₄×C₇×Q₁₆	C₂²	semidirect
103. C₄×C₇×SD₁₆	C₂²	semidirect
104. C₄×C₇×D₈	C₂²	semidirect
115. #61002	C₇	direct (N × H)
265. #3495	C₂×C₇	semidirect
266. #3250	C₂×C₇	semidirect
267. #3249	C₂×C₇	semidirect
268. #3248	C₂×C₇	semidirect
269. #3243	C₂×C₇	semidirect
270. #3242	C₂×C₇	semidirect
271. #3225	C₂×C₇	semidirect
272. #3223	C₂×C₇	semidirect
274. #3190	C₂×C₇	semidirect
275. #3189	C₂×C₇	semidirect
276. #3181	C₂×C₇	semidirect
277. #3170	C₂×C₇	semidirect
278. #3168	C₂×C₇	semidirect
279. #3127	C₂×C₇	semidirect
280. #3124	C₂×C₇	semidirect
281. #3121	C₂×C₇	semidirect
282. #3120	C₂×C₇	semidirect
283. C₂×#433	C₂×C₇	semidirect
420. #501	C₂²×C₇	semidirect
421. #500	C₂²×C₇	semidirect
422. #499	C₂²×C₇	semidirect
423. #497	C₂²×C₇	semidirect
424. #495	C₂²×C₇	semidirect
425. #494	C₂²×C₇	semidirect
426. #491	C₂²×C₇	semidirect
427. #489	C₂²×C₇	semidirect
428. #488	C₂²×C₇	semidirect
429. #487	C₂²×C₇	semidirect
438. #479	C₂²×C₇	semidirect
439. #479	C₂²×C₇	semidirect
440. #479	C₂²×C₇	semidirect
441. #478	C₂²×C₇	semidirect
442. #477	C₂²×C₇	semidirect
443. #477	C₂²×C₇	semidirect
444. #475	C₂²×C₇	semidirect
445. #474	C₂²×C₇	semidirect
456. #464	C₂²×C₇	semidirect
457. #464	C₂²×C₇	semidirect
458. #464	C₂²×C₇	semidirect
459. #463	C₂²×C₇	semidirect
460. #462	C₂²×C₇	semidirect
461. #462	C₂²×C₇	semidirect
462. #462	C₂²×C₇	semidirect
463. #461	C₂²×C₇	semidirect
472. #441	C₂²×C₇	semidirect
473. #441	C₂²×C₇	semidirect
474. #440	C₂²×C₇	semidirect
475. #440	C₂²×C₇	semidirect
476. C₄×Q₁₆	C₂²×C₇	semidirect
477. C₄×Q₁₆	C₂²×C₇	semidirect
478. C₄×Q₁₆	C₂²×C₇	semidirect
479. C₄×Q₁₆	C₂²×C₇	semidirect
480. C₄×SD₁₆	C₂²×C₇	semidirect
481. C₄×D₈	C₂²×C₇	semidirect
902. C₇	#61002	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×#3495	2
C₇×#3250	2
C₇×#3249	2
C₇×#3248	2
C₇×#3243	2
C₇×#3242	2
C₇×#3225	2
C₇×#3223	2
C₇×#3191	2
C₇×#3190	2
C₇×#3189	2
C₇×#3181	2
C₇×#3170	2
C₇×#3168	2
C₇×#3127	2
C₇×#3124	2
C₇×#3121	2
C₇×#3120	2
C₂×C₇×#433	2
#61002	7

Subgroups — C7×#61002 #13238218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61002 #13238218