Subgroups — C₇×#61003 #13238219

Order 1792.

1792 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3494	C₂	1	2	yes	maximal, complemented
2	C₇×#3256	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3253	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3251	C₂	1	2	yes	maximal, complemented
5	C₇×#3244	C₂	1	2	yes	maximal, complemented
6	C₇×#3241	C₂	1	2	yes	maximal, complemented
7	C₇×#3224	C₂	1	2	yes	maximal, complemented
8	C₇×#3220	C₂	1	2	yes	maximal, complemented
9	C₇×#3197	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3194	C₂	1	2	yes	maximal, complemented
11	C₇×#3192	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3184	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3183	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3171	C₂	1	2	yes	maximal, complemented
15	C₇×#3125	C₂	1	2	yes	maximal, complemented
16	C₇×#3122	C₂	1	2	yes	maximal, complemented
17	C₇×#3119	C₂	1	2	yes	maximal, complemented
18	C₇×#3118	C₂	1	2	yes	maximal, complemented
19	C₇×#2921	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#555	—	2	2	no	—
21	C₇×#553	—	2	2	no	—
22	C₇×#553	—	2	2	no	—
23	C₇×#551	—	2	2	no	—
24	C₇×#551	—	2	2	no	—
25	C₇×#547	—	2	2	no	—
26	C₇×#546	—	2	2	no	—
27	C₇×#546	—	2	2	no	—
28	C₇×#544	C₂²	1	2	yes	complemented
29	C₇×#542	C₂²	1	2	yes	—
30	C₇×#542	C₂²	1	2	yes	—
31	C₇×#540	C₂²	1	2	yes	—
32	C₇×#540	C₂²	1	2	yes	—
33	C₇×#535	C₂²	1	2	yes	complemented
34	C₇×#532	C₂²	1	2	yes	complemented
35	C₇×#532	C₂²	1	2	yes	complemented
36	C₇×#529	C₂²	1	2	yes	complemented
37	C₇×#529	C₂²	1	2	yes	complemented
38	C₇×#525	C₂²	1	2	yes	—
39	C₂×C₇×#121	C₂²	1	2	yes	—
40	C₇×#520	C₂²	1	2	yes	complemented
41	C₇×#518	C₂²	1	2	yes	complemented
42	C₂×C₇×#117	C₂²	1	1	yes	characteristic
43	C₇×#501	C₂²	1	2	yes	complemented
44	C₇×#499	C₂²	1	1	yes	characteristic, complemented
45	C₇×#498	C₂²	1	1	yes	characteristic, complemented
46	C₇×#496	C₂²	1	2	yes	complemented
47	C₇×#495	C₂²	1	1	yes	characteristic, complemented
48	C₇×#493	C₂²	1	1	yes	characteristic, complemented
49	C₇×#490	C₂²	1	2	yes	complemented
50	C₇×#489	C₂²	1	2	yes	complemented
51	C₇×#488	C₂²	1	2	yes	complemented
52	C₇×#486	C₂²	1	2	yes	complemented
53	C₇×#485	C₂²	1	2	yes	complemented
54	C₇×#483	C₂²	1	2	yes	complemented
55	C₇×#482	C₂²	1	2	yes	—
56	C₇×#482	C₂²	1	2	yes	—
57	C₇×#482	C₂²	1	2	yes	complemented
58	C₇×#481	C₂²	1	2	yes	—
59	C₇×#481	C₂²	1	2	yes	—
60	C₇×#480	C₂²	1	2	yes	complemented
61	C₇×#479	C₂²	1	2	yes	complemented
62	C₇×#478	C₂²	1	2	yes	complemented
63	C₇×#478	C₂²	1	2	yes	complemented
64	C₇×#478	C₂²	1	2	yes	complemented
65	C₇×#476	C₂²	1	2	yes	complemented
66	C₇×#476	C₂²	1	2	yes	complemented
67	C₇×#475	C₂²	1	2	yes	complemented
68	C₇×#474	C₂²	1	2	yes	complemented
69	C₇×#470	C₂²	1	1	yes	characteristic, complemented
70	C₇×#469	C₂²	1	2	yes	—
71	C₇×#469	C₂²	1	1	yes	characteristic
72	C₇×#469	C₂²	1	1	yes	characteristic
73	C₇×#469	C₂²	1	2	yes	complemented
74	C₇×#469	C₂²	1	2	yes	complemented
75	C₇×#469	C₂²	1	1	yes	characteristic, complemented
76	C₇×#468	C₂²	1	2	yes	complemented
77	C₇×#468	C₂²	1	2	yes	complemented
78	C₇×#468	C₂²	1	2	yes	complemented
79	C₇×#464	C₂²	1	2	yes	complemented
80	C₇×#463	C₂²	1	2	yes	complemented
81	C₇×#463	C₂²	1	2	yes	complemented
82	C₇×#463	C₂²	1	2	yes	complemented
83	C₇×#460	C₂²	1	2	yes	complemented
84	C₇×#459	C₂²	1	2	yes	complemented
85	C₇×#459	C₂²	1	2	yes	complemented
86	C₇×#459	C₂²	1	2	yes	complemented
87	C₇×#452	C₂²	1	2	yes	complemented
88	C₇×#450	C₂²	1	2	yes	complemented
89	C₇×#449	C₂²	1	2	yes	—
90	C₇×#449	C₂²	1	2	yes	—
91	C₇×#449	C₂²	1	2	yes	complemented
92	C₇×#447	C₂²	1	2	yes	—
93	C₇×#447	C₂²	1	2	yes	—
94	C₇×#447	C₂²	1	2	yes	complemented
95	C₇×#442	C₂²	1	1	yes	characteristic, complemented
96	C₇×#442	C₂²	1	1	yes	characteristic, complemented
97	C₇×#442	C₂²	1	1	yes	characteristic, complemented
98	C₇×#442	C₂²	1	2	yes	complemented
99	C₇×#441	C₂²	1	1	yes	characteristic, complemented
100	C₇×#440	C₂²	1	2	yes	complemented
101	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
102	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
103	C₄×C₇×D₈	C₂²	1	2	yes	complemented
104	C₄×C₇×D₈	C₂²	1	2	yes	complemented
105	C₇×#433	C₂²	1	2	yes	complemented
106	C₇×#433	C₂²	1	2	yes	complemented
107	C₇×#433	C₂²	1	2	yes	complemented
108	C₇×#433	C₂²	1	2	yes	complemented
109	C₇×#423	C₂²	1	1	yes	characteristic, complemented
110	C₇×#423	C₂²	1	1	yes	characteristic, complemented
111	C₇×#407	C₂²	1	1	yes	characteristic
112	C₇×#407	C₂²	1	1	yes	characteristic
113	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
115	#61003	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂×C₇×#41	—	2	2	no	—
117	C₂×C₇×#41	—	2	2	no	—
118	C₂×C₇×#41	C₂³	1	2	yes	—
119	C₂²×C₇×D₄	—	2	2	no	—
120	C₂²×C₇×D₄	C₂³	1	2	yes	—
121	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
122	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
123	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
124	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
125	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
127	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
128	C₂×C₇×D₈	C₂³	1	2	yes	—
129	C₂×C₇×D₈	C₂³	1	2	yes	—
130	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
131	C₂×C₇×D₈	C₂³	1	2	yes	—
132	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
133	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
134	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
135	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
136	C₇×C₄⋊Q₈	—	2	2	no	—
137	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₇×#127	C₂³	1	2	yes	—
140	C₇×#127	C₂³	1	2	yes	—
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×#125	—	2	2	no	—
146	C₇×#125	C₂³	1	2	yes	—
147	C₇×#125	C₂³	1	2	yes	—
148	C₇×#124	—	2	2	no	—
149	C₇×#124	—	2	2	no	—
150	C₇×#124	—	2	2	no	—
151	C₇×#124	—	2	2	no	—
152	C₇×#124	C₂³	1	2	yes	—
153	C₇×#124	C₂³	1	2	yes	—
154	C₇×#123	—	2	2	no	—
155	C₇×#123	—	2	2	no	—
156	C₇×#123	—	2	2	no	—
157	C₇×#123	—	2	2	no	—
158	C₇×#123	—	2	2	no	—
159	C₇×#123	—	2	2	no	—
160	C₇×#123	—	2	2	no	—
161	C₇×#123	—	2	2	no	—
162	C₇×#123	—	2	2	no	—
163	C₇×C₂²⋊Q₈	—	2	2	no	—
164	C₇×C₂²⋊Q₈	—	2	2	no	—
165	C₇×C₂²⋊Q₈	—	2	2	no	—
166	C₇×C₂²⋊Q₈	—	2	2	no	—
167	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₇×#121	—	2	2	no	—
170	C₇×#121	—	2	2	no	—
171	C₇×#121	—	2	2	no	—
172	C₇×#121	—	2	2	no	—
173	C₇×#121	—	2	2	no	—
174	C₇×#121	—	2	2	no	—
175	C₇×#121	—	2	2	no	—
176	C₇×#121	—	2	2	no	—
177	C₇×#121	—	2	2	no	—
178	C₇×#121	—	2	2	no	—
179	C₇×#121	C₂³	1	2	yes	—
180	C₇×#121	C₂³	1	2	yes	—
181	C₇×#121	C₂³	1	2	yes	—
182	C₇×#121	C₂³	1	2	yes	—
183	C₇×#121	C₂³	1	2	yes	—
184	C₇×#121	C₂³	1	2	yes	—
185	C₇×#120	—	2	2	no	—
186	C₇×#120	—	2	2	no	—
187	C₇×#120	—	2	2	no	—
188	C₄×C₇×Q₈	C₂³	1	2	yes	—
189	C₄×C₇×Q₈	C₂³	1	2	yes	—
190	C₄×C₇×D₄	—	2	2	no	—
191	C₄×C₇×D₄	—	2	2	no	—
192	C₄×C₇×D₄	—	2	2	no	—
193	C₄×C₇×D₄	—	2	2	no	—
194	C₄×C₇×D₄	—	2	2	no	—
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	C₂³	1	2	yes	—
201	C₄×C₇×D₄	C₂³	1	2	yes	—
202	C₄×C₇×D₄	C₂³	1	2	yes	—
203	C₄×C₇×D₄	C₂³	1	2	yes	—
204	C₄×C₇×D₄	C₂³	1	2	yes	—
205	C₄×C₇×D₄	C₂³	1	2	yes	—
206	C₇×#117	—	2	2	no	—
207	C₇×#117	—	2	2	no	—
208	C₇×#117	—	2	2	no	—
209	C₇×#117	D₄	1	2	yes	—
210	C₇×#117	D₄	1	2	yes	—
211	C₇×#117	C₂³	1	2	yes	—
212	C₇×#117	C₂³	1	2	yes	—
213	C₇×#117	C₂³	1	2	yes	—
214	C₂×C₇×C₄⋊C₄	—	2	2	no	—
215	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
216	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
217	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
218	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
219	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
220	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
221	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
223	C₇×#107	C₂³	1	2	yes	—
224	C₇×#107	C₂³	1	2	yes	—
225	C₇×#107	C₂³	1	2	yes	—
226	C₇×#106	C₂³	1	2	yes	—
227	C₇×#106	C₂³	1	1	yes	characteristic
228	C₇×#106	C₂³	1	1	yes	characteristic
229	C₇×#106	C₂³	1	2	yes	—
230	C₇×#106	C₂³	1	2	yes	—
231	C₇×#106	C₂³	1	1	yes	characteristic
232	C₇×#106	C₂³	1	1	yes	characteristic
233	C₇×C₄⋊C₈	C₂³	1	2	yes	—
234	C₇×C₄⋊C₈	C₂³	1	2	yes	—
235	C₇×C₄⋊C₈	C₂³	1	2	yes	—
236	C₇×C₄⋊C₈	C₂³	1	2	yes	—
237	C₇×#103	C₂³	1	2	yes	—
238	C₇×#103	C₂³	1	2	yes	—
239	C₇×#103	C₂³	1	2	yes	—
240	C₇×#103	C₂³	1	2	yes	—
241	C₇×#102	C₂³	1	2	yes	—
242	C₇×#102	C₂³	1	2	yes	—
243	C₇×#102	C₂³	1	2	yes	—
244	C₇×#102	C₂³	1	2	yes	—
245	C₇×#102	C₂³	1	2	yes	—
246	C₇×#102	C₂³	1	2	yes	—
247	C₇×#102	C₂³	1	2	yes	—
248	C₇×#102	C₂³	1	2	yes	—
249	C₇×#102	C₂³	1	2	yes	—
250	C₇×#102	C₂³	1	2	yes	—
251	C₇×#102	C₂³	1	2	yes	—
252	C₇×#102	C₂³	1	2	yes	—
253	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
254	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₇×#97	C₂³	1	2	yes	—
258	C₇×#97	C₂³	1	1	yes	characteristic
259	C₇×#97	C₂³	1	1	yes	characteristic
260	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
261	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
262	C₄×C₇×C₈	C₂³	1	2	yes	—
263	#3494	C₂×C₇	1	2	yes	complemented
264	#3256	C₂×C₇	1	1	yes	characteristic, complemented
265	#3253	C₂×C₇	1	1	yes	characteristic, complemented
266	#3251	C₂×C₇	1	2	yes	complemented
267	#3244	C₂×C₇	1	2	yes	complemented
268	#3241	C₂×C₇	1	2	yes	complemented
269	#3224	C₂×C₇	1	2	yes	complemented
270	#3220	C₂×C₇	1	2	yes	complemented
271	#3197	C₂×C₇	1	1	yes	characteristic, complemented
272	#3194	C₂×C₇	1	2	yes	complemented
273	#3192	C₂×C₇	1	1	yes	characteristic, complemented
274	#3184	C₂×C₇	1	1	yes	characteristic, complemented
275	#3183	C₂×C₇	1	1	yes	characteristic, complemented
276	#3171	C₂×C₇	1	2	yes	complemented
277	#3125	C₂×C₇	1	2	yes	complemented
278	#3122	C₂×C₇	1	2	yes	complemented
279	#3119	C₂×C₇	1	2	yes	complemented
280	#3118	C₂×C₇	1	2	yes	complemented
281	#2921	C₂×C₇	1	1	yes	characteristic, complemented
282	C₂⁴×C₇	—	2	2	no	—
283	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
284	C₇×#41	—	4	2	no	—
285	C₇×#41	—	4	2	no	—
286	C₇×#41	—	8	4	no	—
287	C₇×#41	—	8	4	no	—
288	C₂×C₇×Q₈	—	2	2	no	—
289	C₂×C₇×Q₈	—	2	2	no	—
290	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
291	C₂×C₇×D₄	—	2	2	no	—
292	C₂×C₇×D₄	—	2	2	no	—
293	C₂×C₇×D₄	—	2	2	no	—
294	C₂×C₇×D₄	—	2	2	no	—
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	—	2	2	no	—
299	C₂×C₇×D₄	—	2	2	no	—
300	C₂×C₇×D₄	—	2	2	no	—
301	C₂×C₇×D₄	—	2	2	no	—
302	C₂×C₇×D₄	—	2	2	no	—
303	C₂×C₇×D₄	—	4	2	no	—
304	C₂×C₇×D₄	—	4	2	no	—
305	C₂×C₇×D₄	—	8	4	no	—
306	C₂×C₇×D₄	C₂⁴	1	2	yes	—
307	C₂×C₇×D₄	C₂⁴	1	2	yes	—
308	C₂×C₇×D₄	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₇	—	2	2	no	—
310	C₂²×C₄×C₇	—	2	2	no	—
311	C₂²×C₄×C₇	—	2	2	no	—
312	C₂²×C₄×C₇	—	2	2	no	—
313	C₂²×C₄×C₇	—	2	2	no	—
314	C₂²×C₄×C₇	—	2	2	no	—
315	C₂²×C₄×C₇	—	2	2	no	—
316	C₂²×C₄×C₇	—	2	2	no	—
317	C₂²×C₄×C₇	—	4	1	no	—
318	C₂²×C₄×C₇	—	4	1	no	—
319	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
320	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
321	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
322	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
325	C₇×Q₁₆	—	4	1	no	—
326	C₇×SD₁₆	—	4	2	no	—
327	C₇×SD₁₆	—	4	2	no	—
328	C₇×SD₁₆	—	4	2	no	—
329	C₇×D₈	—	4	2	no	—
330	C₇×D₈	—	4	1	no	—
331	C₇×D₈	—	4	1	no	—
332	C₇×D₈	—	4	2	no	—
333	C₇×D₈	—	4	2	no	—
334	C₇×D₈	—	4	1	no	—
335	C₇×M₁₆	—	4	1	no	—
336	C₇×M₁₆	—	4	1	no	—
337	C₇×M₁₆	—	4	1	no	—
338	C₇×M₁₆	—	4	1	no	—
339	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
340	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
341	C₂×C₇×C₈	C₂⁴	1	2	yes	—
342	C₂×C₇×C₈	C₂⁴	1	2	yes	—
343	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
344	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
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	C₂⁴	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×C₂²⋊C₄	—	2	2	no	—
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	—	2	2	no	—
381	C₇×C₂²⋊C₄	—	2	2	no	—
382	C₇×C₂²⋊C₄	—	2	2	no	—
383	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
384	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
385	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
386	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
387	C₄²×C₇	—	2	2	no	—
388	C₄²×C₇	—	2	2	no	—
389	C₄²×C₇	—	2	2	no	—
390	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₇	C₂×D₄	1	2	yes	—
392	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₇	C₂⁴	1	1	yes	characteristic
394	C₄²×C₇	C₂⁴	1	1	yes	characteristic
395	C₄²×C₇	C₂⁴	1	2	yes	—
396	#555	—	2	2	no	—
397	#553	—	2	2	no	—
398	#553	—	2	2	no	—
399	#551	—	2	2	no	—
400	#551	—	2	2	no	—
401	#547	—	2	2	no	—
402	#546	—	2	2	no	—
403	#546	—	2	2	no	—
404	#544	C₂²×C₇	1	2	yes	complemented
405	#542	C₂²×C₇	1	2	yes	—
406	#542	C₂²×C₇	1	2	yes	—
407	#540	C₂²×C₇	1	2	yes	—
408	#540	C₂²×C₇	1	2	yes	—
409	#535	C₂²×C₇	1	2	yes	complemented
410	#532	C₂²×C₇	1	2	yes	complemented
411	#532	C₂²×C₇	1	2	yes	complemented
412	#529	C₂²×C₇	1	2	yes	complemented
413	#529	C₂²×C₇	1	2	yes	complemented
414	#525	C₂²×C₇	1	2	yes	—
415	C₂×#121	C₂²×C₇	1	2	yes	—
416	#520	C₂²×C₇	1	2	yes	complemented
417	#518	C₂²×C₇	1	2	yes	complemented
418	C₂×#117	C₂²×C₇	1	1	yes	characteristic
419	#501	C₂²×C₇	1	2	yes	complemented
420	#499	C₂²×C₇	1	1	yes	characteristic, complemented
421	#498	C₂²×C₇	1	1	yes	characteristic, complemented
422	#496	C₂²×C₇	1	2	yes	complemented
423	#495	C₂²×C₇	1	1	yes	characteristic, complemented
424	#493	C₂²×C₇	1	1	yes	characteristic, complemented
425	#490	C₂²×C₇	1	2	yes	complemented
426	#489	C₂²×C₇	1	2	yes	complemented
427	#488	C₂²×C₇	1	2	yes	complemented
428	#486	C₂²×C₇	1	2	yes	complemented
429	#485	C₂²×C₇	1	2	yes	complemented
430	#483	C₂²×C₇	1	2	yes	complemented
431	#482	C₂²×C₇	1	2	yes	—
432	#482	C₂²×C₇	1	2	yes	—
433	#482	C₂²×C₇	1	2	yes	complemented
434	#481	C₂²×C₇	1	2	yes	—
435	#481	C₂²×C₇	1	2	yes	—
436	#480	C₂²×C₇	1	2	yes	complemented
437	#479	C₂²×C₇	1	2	yes	complemented
438	#478	C₂²×C₇	1	2	yes	complemented
439	#478	C₂²×C₇	1	2	yes	complemented
440	#478	C₂²×C₇	1	2	yes	complemented
441	#476	C₂²×C₇	1	2	yes	complemented
442	#476	C₂²×C₇	1	2	yes	complemented
443	#475	C₂²×C₇	1	2	yes	complemented
444	#474	C₂²×C₇	1	2	yes	complemented
445	#470	C₂²×C₇	1	1	yes	characteristic, complemented
446	#469	C₂²×C₇	1	2	yes	—
447	#469	C₂²×C₇	1	1	yes	characteristic
448	#469	C₂²×C₇	1	1	yes	characteristic
449	#469	C₂²×C₇	1	2	yes	complemented
450	#469	C₂²×C₇	1	2	yes	complemented
451	#469	C₂²×C₇	1	1	yes	characteristic, complemented
452	#468	C₂²×C₇	1	2	yes	complemented
453	#468	C₂²×C₇	1	2	yes	complemented
454	#468	C₂²×C₇	1	2	yes	complemented
455	#464	C₂²×C₇	1	2	yes	complemented
456	#463	C₂²×C₇	1	2	yes	complemented
457	#463	C₂²×C₇	1	2	yes	complemented
458	#463	C₂²×C₇	1	2	yes	complemented
459	#460	C₂²×C₇	1	2	yes	complemented
460	#459	C₂²×C₇	1	2	yes	complemented
461	#459	C₂²×C₇	1	2	yes	complemented
462	#459	C₂²×C₇	1	2	yes	complemented
463	#452	C₂²×C₇	1	2	yes	complemented
464	#450	C₂²×C₇	1	2	yes	complemented
465	#449	C₂²×C₇	1	2	yes	—
466	#449	C₂²×C₇	1	2	yes	—
467	#449	C₂²×C₇	1	2	yes	complemented
468	#447	C₂²×C₇	1	2	yes	—
469	#447	C₂²×C₇	1	2	yes	—
470	#447	C₂²×C₇	1	2	yes	complemented
471	#442	C₂²×C₇	1	1	yes	characteristic, complemented
472	#442	C₂²×C₇	1	1	yes	characteristic, complemented
473	#442	C₂²×C₇	1	1	yes	characteristic, complemented
474	#442	C₂²×C₇	1	2	yes	complemented
475	#441	C₂²×C₇	1	1	yes	characteristic, complemented
476	#440	C₂²×C₇	1	2	yes	complemented
477	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
478	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
479	C₄×D₈	C₂²×C₇	1	2	yes	complemented
480	C₄×D₈	C₂²×C₇	1	2	yes	complemented
481	#433	C₂²×C₇	1	2	yes	complemented
482	#433	C₂²×C₇	1	2	yes	complemented
483	#433	C₂²×C₇	1	2	yes	complemented
484	#433	C₂²×C₇	1	2	yes	complemented
485	#423	C₂²×C₇	1	1	yes	characteristic, complemented
486	#423	C₂²×C₇	1	1	yes	characteristic, complemented
487	#407	C₂²×C₇	1	1	yes	characteristic
488	#407	C₂²×C₇	1	1	yes	characteristic
489	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
490	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
491	C₂³×C₇	—	2	2	no	—
492	C₂³×C₇	—	2	2	no	—
493	C₂³×C₇	—	2	2	no	—
494	C₂³×C₇	—	4	1	no	—
495	C₂³×C₇	—	4	2	no	—
496	C₂³×C₇	—	4	4	no	—
497	C₂³×C₇	—	8	2	no	—
498	C₂³×C₇	—	8	2	no	—
499	C₂³×C₇	C₂²×D₄	1	2	yes	—
500	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
501	C₇×Q₈	—	2	2	no	—
502	C₇×Q₈	—	2	2	no	—
503	C₇×Q₈	—	8	2	no	—
504	C₇×Q₈	—	8	2	no	—
505	C₇×D₄	—	2	2	no	—
506	C₇×D₄	—	2	2	no	—
507	C₇×D₄	—	2	2	no	—
508	C₇×D₄	—	2	2	no	—
509	C₇×D₄	—	2	2	no	—
510	C₇×D₄	—	2	2	no	—
511	C₇×D₄	—	4	4	no	—
512	C₇×D₄	—	4	4	no	—
513	C₇×D₄	—	4	4	no	—
514	C₇×D₄	—	4	4	no	—
515	C₇×D₄	—	4	4	no	—
516	C₇×D₄	—	8	2	no	—
517	C₇×D₄	—	8	2	no	—
518	C₇×D₄	—	8	2	no	—
519	C₇×D₄	—	8	2	no	—
520	C₇×D₄	—	8	2	no	—
521	C₇×D₄	—	8	2	no	—
522	C₇×D₄	—	8	2	no	—
523	C₂×C₄×C₇	—	2	1	no	—
524	C₂×C₄×C₇	—	2	1	no	—
525	C₂×C₄×C₇	—	2	2	no	—
526	C₂×C₄×C₇	—	2	2	no	—
527	C₂×C₄×C₇	—	2	2	no	—
528	C₂×C₄×C₇	—	2	2	no	—
529	C₂×C₄×C₇	—	2	2	no	—
530	C₂×C₄×C₇	—	2	2	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	4	1	no	—
533	C₂×C₄×C₇	—	4	2	no	—
534	C₂×C₄×C₇	—	4	2	no	—
535	C₂×C₄×C₇	—	4	2	no	—
536	C₂×C₄×C₇	—	4	4	no	—
537	C₂×C₄×C₇	—	8	2	no	—
538	C₂×C₄×C₇	—	8	2	no	—
539	C₂×C₄×C₇	—	8	2	no	—
540	C₂×C₄×C₇	—	8	2	no	—
541	C₂×C₄×C₇	—	8	2	no	—
542	C₂×C₄×C₇	—	8	2	no	—
543	C₂×C₄×C₇	—	8	2	no	—
544	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
545	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
546	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
547	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
550	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
551	C₇×C₈	—	2	1	no	—
552	C₇×C₈	—	2	1	no	—
553	C₇×C₈	—	2	2	no	—
554	C₇×C₈	—	2	2	no	—
555	C₇×C₈	—	2	1	no	—
556	C₇×C₈	—	2	1	no	—
557	C₂×#41	—	2	2	no	—
558	C₂×#41	—	2	2	no	—
559	C₂×#41	C₂³×C₇	1	2	yes	—
560	C₂²×D₄	—	2	2	no	—
561	C₂²×D₄	C₂³×C₇	1	2	yes	—
562	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
563	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
564	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
565	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
566	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
567	C₂×D₈	C₂³×C₇	1	2	yes	—
568	C₂×D₈	C₂³×C₇	1	2	yes	—
569	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
570	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
571	C₂×D₈	C₂³×C₇	1	2	yes	—
572	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
573	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
574	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
575	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
576	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
577	C₄⋊Q₈	—	2	2	no	—
578	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
579	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
580	#127	C₂³×C₇	1	2	yes	—
581	#127	C₂³×C₇	1	2	yes	—
582	#126	—	2	2	no	—
583	#126	—	2	2	no	—
584	#126	—	2	2	no	—
585	#126	—	2	2	no	—
586	#125	—	2	2	no	—
587	#125	C₂³×C₇	1	2	yes	—
588	#125	C₂³×C₇	1	2	yes	—
589	#124	—	2	2	no	—
590	#124	—	2	2	no	—
591	#124	—	2	2	no	—
592	#124	—	2	2	no	—
593	#124	C₂³×C₇	1	2	yes	—
594	#124	C₂³×C₇	1	2	yes	—
595	#123	—	2	2	no	—
596	#123	—	2	2	no	—
597	#123	—	2	2	no	—
598	#123	—	2	2	no	—
599	#123	—	2	2	no	—
600	#123	—	2	2	no	—
601	#123	—	2	2	no	—
602	#123	—	2	2	no	—
603	#123	—	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	C₂³×C₇	1	2	yes	—
609	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
610	#121	—	2	2	no	—
611	#121	—	2	2	no	—
612	#121	—	2	2	no	—
613	#121	—	2	2	no	—
614	#121	—	2	2	no	—
615	#121	—	2	2	no	—
616	#121	—	2	2	no	—
617	#121	—	2	2	no	—
618	#121	—	2	2	no	—
619	#121	—	2	2	no	—
620	#121	C₂³×C₇	1	2	yes	—
621	#121	C₂³×C₇	1	2	yes	—
622	#121	C₂³×C₇	1	2	yes	—
623	#121	C₂³×C₇	1	2	yes	—
624	#121	C₂³×C₇	1	2	yes	—
625	#121	C₂³×C₇	1	2	yes	—
626	#120	—	2	2	no	—
627	#120	—	2	2	no	—
628	#120	—	2	2	no	—
629	C₄×Q₈	C₂³×C₇	1	2	yes	—
630	C₄×Q₈	C₂³×C₇	1	2	yes	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	C₂³×C₇	1	2	yes	—
642	C₄×D₄	C₂³×C₇	1	2	yes	—
643	C₄×D₄	C₂³×C₇	1	2	yes	—
644	C₄×D₄	C₂³×C₇	1	2	yes	—
645	C₄×D₄	C₂³×C₇	1	2	yes	—
646	C₄×D₄	C₂³×C₇	1	2	yes	—
647	#117	—	2	2	no	—
648	#117	—	2	2	no	—
649	#117	—	2	2	no	—
650	#117	C₇×D₄	1	2	yes	—
651	#117	C₇×D₄	1	2	yes	—
652	#117	C₂³×C₇	1	2	yes	—
653	#117	C₂³×C₇	1	2	yes	—
654	#117	C₂³×C₇	1	2	yes	—
655	C₂×C₄⋊C₄	—	2	2	no	—
656	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
658	C₂×C₂²⋊C₄	—	2	2	no	—
659	C₂×C₂²⋊C₄	—	2	2	no	—
660	C₂×C₂²⋊C₄	—	2	2	no	—
661	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
662	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
664	#107	C₂³×C₇	1	2	yes	—
665	#107	C₂³×C₇	1	2	yes	—
666	#107	C₂³×C₇	1	2	yes	—
667	#106	C₂³×C₇	1	2	yes	—
668	#106	C₂³×C₇	1	2	yes	—
669	#106	C₂³×C₇	1	1	yes	characteristic
670	#106	C₂³×C₇	1	1	yes	characteristic
671	#106	C₂³×C₇	1	2	yes	—
672	#106	C₂³×C₇	1	1	yes	characteristic
673	#106	C₂³×C₇	1	1	yes	characteristic
674	C₄⋊C₈	C₂³×C₇	1	2	yes	—
675	C₄⋊C₈	C₂³×C₇	1	2	yes	—
676	C₄⋊C₈	C₂³×C₇	1	2	yes	—
677	C₄⋊C₈	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	#102	C₂³×C₇	1	2	yes	—
683	#102	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	#102	C₂³×C₇	1	2	yes	—
689	#102	C₂³×C₇	1	2	yes	—
690	#102	C₂³×C₇	1	2	yes	—
691	#102	C₂³×C₇	1	2	yes	—
692	#102	C₂³×C₇	1	2	yes	—
693	#102	C₂³×C₇	1	2	yes	—
694	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
695	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
696	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
697	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
698	#97	C₂³×C₇	1	1	yes	characteristic
699	#97	C₂³×C₇	1	1	yes	characteristic
700	#97	C₂³×C₇	1	2	yes	—
701	C₄×C₈	C₂³×C₇	1	2	yes	—
702	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
703	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
704	C₂²×C₇	—	2	2	no	—
705	C₂²×C₇	—	2	2	no	—
706	C₂²×C₇	—	2	2	no	—
707	C₂²×C₇	—	2	2	no	—
708	C₂²×C₇	—	2	1	no	—
709	C₂²×C₇	—	4	2	no	—
710	C₂²×C₇	—	4	2	no	—
711	C₂²×C₇	—	4	2	no	—
712	C₂²×C₇	—	4	2	no	—
713	C₂²×C₇	—	4	2	no	—
714	C₂²×C₇	—	4	2	no	—
715	C₂²×C₇	—	4	2	no	—
716	C₂²×C₇	—	4	2	no	—
717	C₂²×C₇	—	4	2	no	—
718	C₂²×C₇	—	8	2	no	—
719	C₂²×C₇	—	16	4	no	—
720	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
721	C₄×C₇	—	2	2	no	—
722	C₄×C₇	—	2	2	no	—
723	C₄×C₇	—	2	2	no	—
724	C₄×C₇	—	2	2	no	—
725	C₄×C₇	—	2	2	no	—
726	C₄×C₇	—	2	1	no	—
727	C₄×C₇	—	4	2	no	—
728	C₄×C₇	—	4	2	no	—
729	C₄×C₇	—	4	2	no	—
730	C₄×C₇	—	4	2	no	—
731	C₄×C₇	—	4	2	no	—
732	C₄×C₇	#585	1	1	yes	characteristic
733	C₄×C₇	#585	1	1	yes	characteristic
734	C₂⁴	—	2	2	no	—
735	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
736	#41	—	4	2	no	—
737	#41	—	4	2	no	—
738	#41	—	8	4	no	—
739	#41	—	8	4	no	—
740	C₂×Q₈	—	2	2	no	—
741	C₂×Q₈	—	2	2	no	—
742	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	8	4	no	—
758	C₂×D₄	C₂⁴×C₇	1	2	yes	—
759	C₂×D₄	C₂⁴×C₇	1	2	yes	—
760	C₂×D₄	C₂⁴×C₇	1	2	yes	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	4	1	no	—
770	C₂²×C₄	—	4	1	no	—
771	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
772	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
773	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
774	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
777	Q₁₆	—	4	1	no	—
778	SD₁₆	—	4	2	no	—
779	SD₁₆	—	4	2	no	—
780	SD₁₆	—	4	2	no	—
781	D₈	—	4	2	no	—
782	D₈	—	4	1	no	—
783	D₈	—	4	1	no	—
784	D₈	—	4	2	no	—
785	D₈	—	4	2	no	—
786	D₈	—	4	1	no	—
787	M₁₆	—	4	1	no	—
788	M₁₆	—	4	1	no	—
789	M₁₆	—	4	1	no	—
790	M₁₆	—	4	1	no	—
791	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
792	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
793	C₂×C₈	C₂⁴×C₇	1	2	yes	—
794	C₂×C₈	C₂⁴×C₇	1	2	yes	—
795	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
796	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
809	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
810	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
811	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
812	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
813	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
814	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
815	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
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	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
836	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
837	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
838	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
843	C₄²	C₂×C₇×D₄	1	2	yes	—
844	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
845	C₄²	C₂⁴×C₇	1	1	yes	characteristic
846	C₄²	C₂⁴×C₇	1	1	yes	characteristic
847	C₄²	C₂⁴×C₇	1	2	yes	—
848	C₂×C₇	—	4	1	no	—
849	C₂×C₇	—	4	2	no	—
850	C₂×C₇	—	8	2	no	—
851	C₂×C₇	—	8	2	no	—
852	C₂×C₇	—	8	2	no	—
853	C₂×C₇	#3449	1	1	yes	characteristic
854	C₂×C₇	#3585	1	2	yes	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	4	1	no	—
859	C₂³	—	4	2	no	—
860	C₂³	—	4	4	no	—
861	C₂³	—	8	2	no	—
862	C₂³	—	8	2	no	—
863	C₂³	C₂²×C₇×D₄	1	2	yes	—
864	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
865	Q₈	—	2	2	no	—
866	Q₈	—	2	2	no	—
867	Q₈	—	8	2	no	—
868	Q₈	—	8	2	no	—
869	D₄	—	2	2	no	—
870	D₄	—	2	2	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	2	no	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	4	no	—
877	D₄	—	4	4	no	—
878	D₄	—	4	4	no	—
879	D₄	—	4	4	no	—
880	D₄	—	8	2	no	—
881	D₄	—	8	2	no	—
882	D₄	—	8	2	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	2	no	—
885	D₄	—	8	2	no	—
886	D₄	—	8	2	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	4	1	no	—
897	C₂×C₄	—	4	2	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	8	2	no	—
902	C₂×C₄	—	8	2	no	—
903	C₂×C₄	—	8	2	no	—
904	C₂×C₄	—	8	2	no	—
905	C₂×C₄	—	8	2	no	—
906	C₂×C₄	—	8	2	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
909	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
910	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
911	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
912	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
913	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
914	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
915	C₈	—	2	1	no	—
916	C₈	—	2	1	no	—
917	C₈	—	2	2	no	—
918	C₈	—	2	2	no	—
919	C₈	—	2	1	no	—
920	C₈	—	2	1	no	—
921	C₇	#61003	1	1	yes	characteristic, direct product factor, Sylow
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	8	2	no	—
937	C₂²	—	16	4	no	—
938	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	2	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	2	no	—
944	C₄	—	2	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	C₇×#585	1	1	yes	characteristic
951	C₄	C₇×#585	1	1	yes	characteristic
952	C₂	—	4	2	no	—
953	C₂	—	4	1	no	—
954	C₂	—	8	2	no	—
955	C₂	—	8	2	no	—
956	C₂	—	8	2	no	—
957	C₂	C₇×#3449	1	1	yes	characteristic
958	C₂	C₇×#3585	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₇×#3494	C₂	semidirect
2. C₇×#3256	C₂	semidirect
3. C₇×#3253	C₂	semidirect
4. C₇×#3251	C₂	semidirect
5. C₇×#3244	C₂	semidirect
6. C₇×#3241	C₂	semidirect
7. C₇×#3224	C₂	semidirect
8. C₇×#3220	C₂	semidirect
9. C₇×#3197	C₂	semidirect
10. C₇×#3194	C₂	semidirect
11. C₇×#3192	C₂	semidirect
12. C₇×#3184	C₂	semidirect
13. C₇×#3183	C₂	semidirect
14. C₇×#3171	C₂	semidirect
15. C₇×#3125	C₂	semidirect
16. C₇×#3122	C₂	semidirect
17. C₇×#3119	C₂	semidirect
18. C₇×#3118	C₂	semidirect
19. C₇×#2921	C₂	semidirect
28. C₇×#544	C₂²	semidirect
33. C₇×#535	C₂²	semidirect
34. C₇×#532	C₂²	semidirect
35. C₇×#532	C₂²	semidirect
36. C₇×#529	C₂²	semidirect
37. C₇×#529	C₂²	semidirect
40. C₇×#520	C₂²	semidirect
41. C₇×#518	C₂²	semidirect
43. C₇×#501	C₂²	semidirect
44. C₇×#499	C₂²	semidirect
45. C₇×#498	C₂²	semidirect
46. C₇×#496	C₂²	semidirect
47. C₇×#495	C₂²	semidirect
48. C₇×#493	C₂²	semidirect
49. C₇×#490	C₂²	semidirect
50. C₇×#489	C₂²	semidirect
51. C₇×#488	C₂²	semidirect
52. C₇×#486	C₂²	semidirect
53. C₇×#485	C₂²	semidirect
54. C₇×#483	C₂²	semidirect
57. C₇×#482	C₂²	semidirect
60. C₇×#480	C₂²	semidirect
61. C₇×#479	C₂²	semidirect
62. C₇×#478	C₂²	semidirect
63. C₇×#478	C₂²	semidirect
64. C₇×#478	C₂²	semidirect
65. C₇×#476	C₂²	semidirect
66. C₇×#476	C₂²	semidirect
67. C₇×#475	C₂²	semidirect
68. C₇×#474	C₂²	semidirect
69. C₇×#470	C₂²	semidirect
73. C₇×#469	C₂²	semidirect
74. C₇×#469	C₂²	semidirect
75. C₇×#469	C₂²	semidirect
76. C₇×#468	C₂²	semidirect
77. C₇×#468	C₂²	semidirect
78. C₇×#468	C₂²	semidirect
79. C₇×#464	C₂²	semidirect
80. C₇×#463	C₂²	semidirect
81. C₇×#463	C₂²	semidirect
82. C₇×#463	C₂²	semidirect
83. C₇×#460	C₂²	semidirect
84. C₇×#459	C₂²	semidirect
85. C₇×#459	C₂²	semidirect
86. C₇×#459	C₂²	semidirect
87. C₇×#452	C₂²	semidirect
88. C₇×#450	C₂²	semidirect
91. C₇×#449	C₂²	semidirect
94. C₇×#447	C₂²	semidirect
95. C₇×#442	C₂²	semidirect
96. C₇×#442	C₂²	semidirect
97. C₇×#442	C₂²	semidirect
98. C₇×#442	C₂²	semidirect
99. C₇×#441	C₂²	semidirect
100. C₇×#440	C₂²	semidirect
101. C₄×C₇×SD₁₆	C₂²	semidirect
102. C₄×C₇×SD₁₆	C₂²	semidirect
103. C₄×C₇×D₈	C₂²	semidirect
104. C₄×C₇×D₈	C₂²	semidirect
105. C₇×#433	C₂²	semidirect
106. C₇×#433	C₂²	semidirect
107. C₇×#433	C₂²	semidirect
108. C₇×#433	C₂²	semidirect
109. C₇×#423	C₂²	semidirect
110. C₇×#423	C₂²	semidirect
113. C₄×C₇×M₁₆	C₂²	semidirect
114. C₄×C₇×M₁₆	C₂²	semidirect
115. #61003	C₇	direct (N × H)
263. #3494	C₂×C₇	semidirect
264. #3256	C₂×C₇	semidirect
265. #3253	C₂×C₇	semidirect
266. #3251	C₂×C₇	semidirect
267. #3244	C₂×C₇	semidirect
268. #3241	C₂×C₇	semidirect
269. #3224	C₂×C₇	semidirect
270. #3220	C₂×C₇	semidirect
271. #3197	C₂×C₇	semidirect
272. #3194	C₂×C₇	semidirect
273. #3192	C₂×C₇	semidirect
274. #3184	C₂×C₇	semidirect
275. #3183	C₂×C₇	semidirect
276. #3171	C₂×C₇	semidirect
277. #3125	C₂×C₇	semidirect
278. #3122	C₂×C₇	semidirect
279. #3119	C₂×C₇	semidirect
280. #3118	C₂×C₇	semidirect
281. #2921	C₂×C₇	semidirect
404. #544	C₂²×C₇	semidirect
409. #535	C₂²×C₇	semidirect
410. #532	C₂²×C₇	semidirect
411. #532	C₂²×C₇	semidirect
412. #529	C₂²×C₇	semidirect
413. #529	C₂²×C₇	semidirect
416. #520	C₂²×C₇	semidirect
417. #518	C₂²×C₇	semidirect
419. #501	C₂²×C₇	semidirect
420. #499	C₂²×C₇	semidirect
421. #498	C₂²×C₇	semidirect
422. #496	C₂²×C₇	semidirect
423. #495	C₂²×C₇	semidirect
424. #493	C₂²×C₇	semidirect
425. #490	C₂²×C₇	semidirect
426. #489	C₂²×C₇	semidirect
427. #488	C₂²×C₇	semidirect
428. #486	C₂²×C₇	semidirect
429. #485	C₂²×C₇	semidirect
430. #483	C₂²×C₇	semidirect
433. #482	C₂²×C₇	semidirect
436. #480	C₂²×C₇	semidirect
437. #479	C₂²×C₇	semidirect
438. #478	C₂²×C₇	semidirect
439. #478	C₂²×C₇	semidirect
440. #478	C₂²×C₇	semidirect
441. #476	C₂²×C₇	semidirect
442. #476	C₂²×C₇	semidirect
443. #475	C₂²×C₇	semidirect
444. #474	C₂²×C₇	semidirect
445. #470	C₂²×C₇	semidirect
449. #469	C₂²×C₇	semidirect
450. #469	C₂²×C₇	semidirect
451. #469	C₂²×C₇	semidirect
452. #468	C₂²×C₇	semidirect
453. #468	C₂²×C₇	semidirect
454. #468	C₂²×C₇	semidirect
455. #464	C₂²×C₇	semidirect
456. #463	C₂²×C₇	semidirect
457. #463	C₂²×C₇	semidirect
458. #463	C₂²×C₇	semidirect
459. #460	C₂²×C₇	semidirect
460. #459	C₂²×C₇	semidirect
461. #459	C₂²×C₇	semidirect
462. #459	C₂²×C₇	semidirect
463. #452	C₂²×C₇	semidirect
464. #450	C₂²×C₇	semidirect
467. #449	C₂²×C₇	semidirect
470. #447	C₂²×C₇	semidirect
471. #442	C₂²×C₇	semidirect
472. #442	C₂²×C₇	semidirect
473. #442	C₂²×C₇	semidirect
474. #442	C₂²×C₇	semidirect
475. #441	C₂²×C₇	semidirect
476. #440	C₂²×C₇	semidirect
477. C₄×SD₁₆	C₂²×C₇	semidirect
478. C₄×SD₁₆	C₂²×C₇	semidirect
479. C₄×D₈	C₂²×C₇	semidirect
480. C₄×D₈	C₂²×C₇	semidirect
481. #433	C₂²×C₇	semidirect
482. #433	C₂²×C₇	semidirect
483. #433	C₂²×C₇	semidirect
484. #433	C₂²×C₇	semidirect
485. #423	C₂²×C₇	semidirect
486. #423	C₂²×C₇	semidirect
489. C₄×M₁₆	C₂²×C₇	semidirect
490. C₄×M₁₆	C₂²×C₇	semidirect
921. C₇	#61003	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#3494	2
C₇×#3256	2
C₇×#3253	2
C₇×#3251	2
C₇×#3244	2
C₇×#3241	2
C₇×#3224	2
C₇×#3220	2
C₇×#3197	2
C₇×#3194	2
C₇×#3192	2
C₇×#3184	2
C₇×#3183	2
C₇×#3171	2
C₇×#3125	2
C₇×#3122	2
C₇×#3119	2
C₇×#3118	2
C₇×#2921	2
#61003	7

Subgroups — C7×#61003 #13238219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61003 #13238219