Subgroups — C₇×#61194 #13238410

Order 1792.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3489	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3330	C₂	1	2	yes	maximal, complemented
4	C₇×#3327	C₂	1	2	yes	maximal, complemented
5	C₇×#3320	C₂	1	2	yes	maximal, complemented
6	C₇×#3315	C₂	1	2	yes	maximal, complemented
7	C₇×#3314	C₂	1	2	yes	maximal, complemented
8	C₇×#3308	C₂	1	2	yes	maximal, complemented
9	C₇×#3299	C₂	1	2	yes	maximal, complemented
10	C₇×#3297	C₂	1	2	yes	maximal, complemented
11	C₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#484	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3061	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3002	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₇×#417	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
26	C₂×C₇×#137	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₇×#135	C₂²	1	1	yes	characteristic
28	C₂×C₇×#135	C₂²	1	1	yes	characteristic
29	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
31	C₇×#554	—	2	1	no	—
32	C₇×#554	C₂²	1	2	yes	—
33	C₇×#553	—	2	1	no	—
34	C₇×#553	C₂²	1	2	yes	—
35	C₇×#552	—	2	1	no	—
36	C₇×#552	C₂²	1	2	yes	complemented
37	C₇×D₄×Q₈	C₂²	1	2	yes	—
38	C₇×#548	C₂²	1	2	yes	—
39	C₇×#547	—	2	2	no	—
40	C₇×#547	—	2	1	no	—
41	C₇×#547	C₂²	1	2	yes	—
42	C₇×#547	C₂²	1	2	yes	complemented
43	C₇×#546	—	2	2	no	—
44	C₇×#546	C₂²	1	2	yes	—
45	C₇×#544	C₂²	1	1	yes	characteristic, complemented
46	C₇×#539	—	2	2	no	—
47	C₇×#537	—	2	1	no	—
48	C₇×#537	C₂²	1	1	yes	characteristic
49	C₇×#537	C₂²	1	1	yes	characteristic, complemented
50	C₇×#536	—	2	1	no	—
51	C₇×#536	C₂²	1	1	yes	characteristic
52	C₇×#525	—	2	1	no	—
53	C₇×#525	—	2	2	no	—
54	C₇×#525	C₂²	1	1	yes	characteristic
55	C₇×#525	C₂²	1	1	yes	characteristic
56	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
57	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₇×#520	C₂²	1	1	yes	characteristic
59	C₇×#520	C₂²	1	1	yes	characteristic, complemented
60	C₇×#520	C₂²	1	1	yes	characteristic, complemented
61	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
62	C₇×#491	C₂²	1	2	yes	complemented
63	C₇×#489	C₂²	1	2	yes	complemented
64	C₇×#488	C₂²	1	2	yes	complemented
65	C₇×#487	C₂²	1	2	yes	complemented
66	C₇×#485	C₂²	1	2	yes	complemented
67	C₇×#484	C₂²	1	2	yes	—
68	C₇×#484	C₂²	1	2	yes	—
69	C₇×#484	C₂²	1	2	yes	complemented
70	C₇×#484	C₂²	1	2	yes	complemented
71	C₇×#484	C₂²	1	2	yes	complemented
72	C₇×#482	C₂²	1	2	yes	complemented
73	C₇×#480	C₂²	1	2	yes	complemented
74	C₇×#479	C₂²	1	2	yes	complemented
75	C₇×#478	C₂²	1	2	yes	complemented
76	C₇×#477	C₂²	1	2	yes	complemented
77	C₇×#474	C₂²	1	2	yes	complemented
78	C₇×#470	C₂²	1	2	yes	complemented
79	C₇×#468	C₂²	1	2	yes	complemented
80	C₇×#468	C₂²	1	2	yes	complemented
81	C₇×#468	C₂²	1	2	yes	complemented
82	C₇×#467	C₂²	1	2	yes	—
83	C₇×#467	C₂²	1	2	yes	complemented
84	C₇×#466	C₂²	1	2	yes	complemented
85	C₇×#465	C₂²	1	2	yes	—
86	C₇×#464	C₂²	1	2	yes	complemented
87	C₇×#463	C₂²	1	2	yes	complemented
88	C₇×#462	C₂²	1	2	yes	complemented
89	C₇×#461	C₂²	1	2	yes	complemented
90	C₇×#452	C₂²	1	1	yes	characteristic
91	C₇×#452	C₂²	1	1	yes	characteristic
92	C₇×#452	C₂²	1	2	yes	complemented
93	C₇×#451	C₂²	1	1	yes	characteristic
94	C₇×#451	C₂²	1	2	yes	complemented
95	C₇×#450	C₂²	1	1	yes	characteristic
96	C₇×#449	C₂²	1	1	yes	characteristic
97	C₇×#449	C₂²	1	1	yes	characteristic
98	C₇×#449	C₂²	1	2	yes	complemented
99	C₇×#448	C₂²	1	1	yes	characteristic
100	C₇×#448	C₂²	1	2	yes	complemented
101	C₇×#447	C₂²	1	1	yes	characteristic
102	C₇×#440	C₂²	1	2	yes	complemented
103	C₇×#440	C₂²	1	2	yes	complemented
104	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
105	C₄×C₇×D₈	C₂²	1	2	yes	complemented
106	C₇×#436	C₂²	1	2	yes	complemented
107	C₇×#435	C₂²	1	2	yes	—
108	C₇×#435	C₂²	1	2	yes	complemented
109	C₇×C₈×D₄	C₂²	1	2	yes	—
110	C₇×#428	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
113	C₇×#424	C₂²	1	1	yes	characteristic, complemented
114	C₇×#419	C₂²	1	1	yes	characteristic, complemented
115	C₇×#419	C₂²	1	2	yes	complemented
116	C₇×#417	C₂²	1	1	yes	characteristic
117	C₇×#417	C₂²	1	1	yes	characteristic
118	C₇×#417	C₂²	1	1	yes	characteristic
119	C₇×#417	C₂²	1	2	yes	—
120	C₇×#417	C₂²	1	2	yes	—
121	C₇×#417	C₂²	1	1	yes	characteristic
122	C₇×#417	C₂²	1	1	yes	characteristic, complemented
123	C₇×#417	C₂²	1	2	yes	complemented
124	C₇×#416	C₂²	1	1	yes	characteristic
125	C₇×#416	C₂²	1	1	yes	characteristic
126	C₇×#416	C₂²	1	2	yes	complemented
127	C₂×C₇×#103	C₂²	1	2	yes	—
128	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₇×#103	C₂²	1	2	yes	complemented
130	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₇×#102	C₂²	1	2	yes	—
132	C₇×#408	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
134	C₇×#405	C₂²	1	1	yes	characteristic, complemented
135	#61194	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₇×2₋¹⁺⁴	—	2	4	no	—
137	C₇×2₋¹⁺⁴	—	4	2	no	—
138	C₂×C₇×#41	—	2	1	no	—
139	C₂×C₇×#41	—	2	2	no	—
140	C₂×C₇×#41	—	2	2	no	—
141	C₂×C₇×#41	—	2	1	no	—
142	C₂×C₇×#41	—	2	1	no	—
143	C₂×C₇×#41	—	2	4	no	—
144	C₂×C₇×#41	—	4	2	no	—
145	C₂×C₇×#41	C₂³	1	1	yes	characteristic
146	C₂×C₇×#41	C₂³	1	1	yes	characteristic
147	C₂×C₇×#41	C₂³	1	1	yes	characteristic
148	C₂×C₇×#41	C₂³	1	1	yes	characteristic
149	C₂×C₇×#41	C₂³	1	2	yes	—
150	C₂×C₇×#41	C₂³	1	1	yes	characteristic
151	C₂×C₇×#41	C₂³	1	1	yes	characteristic
152	C₂²×C₇×Q₈	—	2	1	no	—
153	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
154	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
155	C₂²×C₇×Q₈	C₂³	1	2	yes	—
156	C₂²×C₇×D₄	—	2	1	no	—
157	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
158	C₂³×C₄×C₇	—	2	1	no	—
159	C₂³×C₄×C₇	—	2	1	no	—
160	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
161	C₇×#137	—	4	2	no	—
162	C₇×#135	—	2	4	no	—
163	C₇×#135	—	4	2	no	—
164	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
166	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
167	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
168	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
169	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
170	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
171	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
172	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
173	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
174	C₇×#131	—	4	2	no	—
175	C₂×C₇×M₁₆	—	4	2	no	—
176	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
177	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
178	C₂×C₇×M₁₆	C₂³	1	2	yes	—
179	C₂×C₇×M₁₆	C₂³	1	2	yes	—
180	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
181	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
182	C₂²×C₇×C₈	C₂³	1	2	yes	—
183	C₂²×C₇×C₈	C₂³	1	2	yes	—
184	C₇×C₄⋊Q₈	—	2	2	no	—
185	C₇×C₄⋊Q₈	—	2	1	no	—
186	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
187	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
188	C₇×#126	—	2	2	no	—
189	C₇×#126	—	2	2	no	—
190	C₇×#125	—	2	2	no	—
191	C₇×#125	—	2	2	no	—
192	C₇×#125	—	2	1	no	—
193	C₇×#125	C₂³	1	2	yes	—
194	C₇×#124	—	2	2	no	—
195	C₇×#124	C₂³	1	2	yes	—
196	C₇×#123	—	2	2	no	—
197	C₇×#123	—	2	1	no	—
198	C₇×#123	—	2	2	no	—
199	C₇×#123	—	2	2	no	—
200	C₇×#123	—	2	2	no	—
201	C₇×#123	—	2	2	no	—
202	C₇×#123	—	2	2	no	—
203	C₇×#123	—	2	2	no	—
204	C₇×#123	—	2	2	no	—
205	C₇×#123	D₄	1	2	yes	—
206	C₇×C₂²⋊Q₈	—	2	1	no	—
207	C₇×C₂²⋊Q₈	—	2	1	no	—
208	C₇×C₂²⋊Q₈	—	2	1	no	—
209	C₇×C₂²⋊Q₈	—	2	1	no	—
210	C₇×C₂²⋊Q₈	—	2	1	no	—
211	C₇×C₂²⋊Q₈	—	2	2	no	—
212	C₇×C₂²⋊Q₈	—	2	1	no	—
213	C₇×C₂²⋊Q₈	—	2	2	no	—
214	C₇×C₂²⋊Q₈	—	2	2	no	—
215	C₇×C₂²⋊Q₈	—	2	2	no	—
216	C₇×C₂²⋊Q₈	—	2	2	no	—
217	C₇×C₂²⋊Q₈	—	2	2	no	—
218	C₇×C₂²⋊Q₈	—	2	2	no	—
219	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
220	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
221	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
226	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₇×#121	—	2	1	no	—
228	C₇×#121	—	2	2	no	—
229	C₇×#121	—	2	2	no	—
230	C₇×#121	—	2	2	no	—
231	C₇×#121	—	2	2	no	—
232	C₇×#121	—	2	2	no	—
233	C₇×#121	—	2	1	no	—
234	C₇×#121	—	2	2	no	—
235	C₇×#121	D₄	1	1	yes	characteristic
236	C₇×#121	D₄	1	1	yes	characteristic
237	C₇×#121	C₂³	1	2	yes	—
238	C₇×#121	C₂³	1	2	yes	—
239	C₇×#121	C₂³	1	1	yes	characteristic
240	C₇×#121	C₂³	1	1	yes	characteristic
241	C₇×#120	—	2	1	no	—
242	C₇×#120	—	2	2	no	—
243	C₇×#120	D₄	1	2	yes	—
244	C₄×C₇×Q₈	—	2	1	no	—
245	C₄×C₇×Q₈	C₂³	1	2	yes	—
246	C₄×C₇×Q₈	C₂³	1	2	yes	—
247	C₄×C₇×D₄	—	2	2	no	—
248	C₄×C₇×D₄	—	2	1	no	—
249	C₄×C₇×D₄	—	2	2	no	—
250	C₄×C₇×D₄	—	2	2	no	—
251	C₄×C₇×D₄	—	2	1	no	—
252	C₄×C₇×D₄	—	2	1	no	—
253	C₄×C₇×D₄	—	2	2	no	—
254	C₄×C₇×D₄	—	2	2	no	—
255	C₄×C₇×D₄	—	2	2	no	—
256	C₄×C₇×D₄	—	2	2	no	—
257	C₄×C₇×D₄	C₂³	1	2	yes	—
258	C₄×C₇×D₄	C₂³	1	2	yes	—
259	C₄×C₇×D₄	C₂³	1	2	yes	—
260	C₄×C₇×D₄	C₂³	1	2	yes	—
261	C₇×#117	—	2	1	no	—
262	C₇×#117	—	2	1	no	—
263	C₇×#117	—	2	2	no	—
264	C₇×#117	C₂³	1	2	yes	—
265	C₇×#117	C₂³	1	1	yes	characteristic
266	C₇×#117	C₂³	1	1	yes	characteristic
267	C₂×C₇×C₄⋊C₄	—	2	1	no	—
268	C₂×C₇×C₄⋊C₄	—	2	1	no	—
269	C₂×C₇×C₄⋊C₄	—	2	1	no	—
270	C₂×C₇×C₄⋊C₄	—	2	1	no	—
271	C₂×C₇×C₄⋊C₄	—	2	1	no	—
272	C₂×C₇×C₄⋊C₄	—	2	1	no	—
273	C₂×C₇×C₄⋊C₄	—	2	2	no	—
274	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
275	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
276	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
277	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
278	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
282	C₇×#107	C₂³	1	2	yes	—
283	C₇×#107	C₂³	1	2	yes	—
284	C₇×#107	C₂³	1	2	yes	—
285	C₇×#107	C₂³	1	2	yes	—
286	C₇×#107	C₂³	1	2	yes	—
287	C₇×#106	C₂³	1	2	yes	—
288	C₇×C₄⋊C₈	C₂³	1	2	yes	—
289	C₇×C₄⋊C₈	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	2	yes	—
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	1	yes	characteristic
295	C₇×#103	C₂³	1	2	yes	—
296	C₇×#103	C₂³	1	1	yes	characteristic
297	C₇×#103	C₂³	1	2	yes	—
298	C₇×#103	C₂³	1	2	yes	—
299	C₇×#103	C₂³	1	2	yes	—
300	C₇×#103	C₂³	1	2	yes	—
301	C₇×#103	C₂³	1	1	yes	characteristic
302	C₇×#103	C₂³	1	2	yes	—
303	C₇×#103	C₂³	1	1	yes	characteristic
304	C₇×#103	C₂³	1	2	yes	—
305	C₇×#102	C₂³	1	2	yes	—
306	C₇×#102	C₂³	1	2	yes	—
307	C₇×#102	C₂³	1	1	yes	characteristic
308	C₇×#102	C₂³	1	2	yes	—
309	C₇×#102	C₂³	1	1	yes	characteristic
310	C₇×#102	C₂³	1	1	yes	characteristic
311	C₇×#102	C₂³	1	2	yes	—
312	C₇×#102	C₂³	1	1	yes	characteristic
313	C₇×#102	C₂³	1	2	yes	—
314	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
317	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
318	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
319	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
320	C₇×#97	C₂³	1	2	yes	—
321	C₄×C₇×C₈	C₂³	1	2	yes	—
322	#3492	C₂×C₇	1	1	yes	characteristic, complemented
323	#3489	C₂×C₇	1	1	yes	characteristic, complemented
324	#3330	C₂×C₇	1	2	yes	complemented
325	#3327	C₂×C₇	1	2	yes	complemented
326	#3320	C₂×C₇	1	2	yes	complemented
327	#3315	C₂×C₇	1	2	yes	complemented
328	#3314	C₂×C₇	1	2	yes	complemented
329	#3308	C₂×C₇	1	2	yes	complemented
330	#3299	C₂×C₇	1	2	yes	complemented
331	#3297	C₂×C₇	1	2	yes	complemented
332	#3137	C₂×C₇	1	1	yes	characteristic, complemented
333	#3098	C₂×C₇	1	1	yes	characteristic, complemented
334	C₂×#484	C₂×C₇	1	1	yes	characteristic, complemented
335	#3083	C₂×C₇	1	1	yes	characteristic, complemented
336	#3061	C₂×C₇	1	1	yes	characteristic, complemented
337	#3056	C₂×C₇	1	1	yes	characteristic, complemented
338	#3046	C₂×C₇	1	1	yes	characteristic, complemented
339	#3013	C₂×C₇	1	1	yes	characteristic, complemented
340	#3002	C₂×C₇	1	1	yes	characteristic, complemented
341	#2951	C₂×C₇	1	1	yes	characteristic, complemented
342	#2933	C₂×C₇	1	1	yes	characteristic, complemented
343	#2898	C₂×C₇	1	1	yes	characteristic, complemented
344	C₂×#417	C₂×C₇	1	1	yes	characteristic, complemented
345	C₂⁴×C₇	—	2	1	no	—
346	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
347	C₇×#41	—	2	2	no	—
348	C₇×#41	—	2	2	no	—
349	C₇×#41	—	2	2	no	—
350	C₇×#41	—	2	2	no	—
351	C₇×#41	—	2	2	no	—
352	C₇×#41	—	2	4	no	—
353	C₇×#41	—	2	2	no	—
354	C₇×#41	—	2	2	no	—
355	C₇×#41	—	2	2	no	—
356	C₇×#41	—	2	2	no	—
357	C₇×#41	—	4	4	no	—
358	C₇×#41	—	4	1	no	—
359	C₇×#41	—	4	1	no	—
360	C₇×#41	—	4	2	no	—
361	C₇×#41	—	4	4	no	—
362	C₇×#41	—	4	4	no	—
363	C₇×#41	—	4	8	no	—
364	C₇×#41	—	8	4	no	—
365	C₇×#41	#41	1	4	yes	complemented
366	C₂×C₇×Q₈	—	2	1	no	—
367	C₂×C₇×Q₈	—	2	2	no	—
368	C₂×C₇×Q₈	—	2	1	no	—
369	C₂×C₇×Q₈	—	2	2	no	—
370	C₂×C₇×Q₈	—	2	2	no	—
371	C₂×C₇×Q₈	—	2	4	no	—
372	C₂×C₇×Q₈	—	2	2	no	—
373	C₂×C₇×Q₈	—	2	2	no	—
374	C₂×C₇×Q₈	—	4	1	no	—
375	C₂×C₇×Q₈	—	4	2	no	—
376	C₂×C₇×Q₈	—	4	4	no	—
377	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
378	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
379	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
380	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
382	C₂×C₇×D₄	—	2	1	no	—
383	C₂×C₇×D₄	—	2	2	no	—
384	C₂×C₇×D₄	—	2	1	no	—
385	C₂×C₇×D₄	—	2	1	no	—
386	C₂×C₇×D₄	—	2	1	no	—
387	C₂×C₇×D₄	—	2	2	no	—
388	C₂×C₇×D₄	—	2	1	no	—
389	C₂×C₇×D₄	—	2	1	no	—
390	C₂×C₇×D₄	—	2	1	no	—
391	C₂×C₇×D₄	—	2	2	no	—
392	C₂×C₇×D₄	—	2	2	no	—
393	C₂×C₇×D₄	—	2	1	no	—
394	C₂×C₇×D₄	—	4	1	no	—
395	C₂×C₇×D₄	—	4	4	no	—
396	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
397	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
398	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
399	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
400	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
401	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
402	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₇	—	2	1	no	—
404	C₂²×C₄×C₇	—	2	2	no	—
405	C₂²×C₄×C₇	—	2	2	no	—
406	C₂²×C₄×C₇	—	2	1	no	—
407	C₂²×C₄×C₇	—	2	2	no	—
408	C₂²×C₄×C₇	—	2	2	no	—
409	C₂²×C₄×C₇	—	2	1	no	—
410	C₂²×C₄×C₇	—	2	1	no	—
411	C₂²×C₄×C₇	—	2	1	no	—
412	C₂²×C₄×C₇	—	2	2	no	—
413	C₂²×C₄×C₇	—	2	1	no	—
414	C₂²×C₄×C₇	—	2	2	no	—
415	C₂²×C₄×C₇	—	2	2	no	—
416	C₂²×C₄×C₇	—	2	1	no	—
417	C₂²×C₄×C₇	—	2	1	no	—
418	C₂²×C₄×C₇	—	2	1	no	—
419	C₂²×C₄×C₇	—	2	1	no	—
420	C₂²×C₄×C₇	—	2	2	no	—
421	C₂²×C₄×C₇	—	2	2	no	—
422	C₂²×C₄×C₇	—	4	4	no	—
423	C₂²×C₄×C₇	—	8	2	no	—
424	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
425	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
426	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
427	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
429	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
430	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
431	C₇×Q₁₆	—	2	2	no	—
432	C₇×Q₁₆	—	4	1	no	—
433	C₇×Q₁₆	—	4	2	no	—
434	C₇×SD₁₆	—	2	2	no	—
435	C₇×SD₁₆	—	2	2	no	—
436	C₇×SD₁₆	—	4	1	no	—
437	C₇×SD₁₆	—	4	1	no	—
438	C₇×SD₁₆	—	4	2	no	—
439	C₇×D₈	—	2	2	no	—
440	C₇×D₈	—	4	1	no	—
441	C₇×M₁₆	—	2	2	no	—
442	C₇×M₁₆	—	2	2	no	—
443	C₇×M₁₆	—	4	2	no	—
444	C₇×M₁₆	—	4	2	no	—
445	C₂×C₇×C₈	—	2	2	no	—
446	C₂×C₇×C₈	—	2	2	no	—
447	C₂×C₇×C₈	—	4	2	no	—
448	C₂×C₇×C₈	—	4	2	no	—
449	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
450	C₂×C₇×C₈	C₂⁴	1	2	yes	—
451	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
452	C₂×C₇×C₈	C₂⁴	1	2	yes	—
453	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
454	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
455	C₇×C₄⋊C₄	—	2	1	no	—
456	C₇×C₄⋊C₄	—	2	1	no	—
457	C₇×C₄⋊C₄	—	2	2	no	—
458	C₇×C₄⋊C₄	—	2	2	no	—
459	C₇×C₄⋊C₄	—	2	2	no	—
460	C₇×C₄⋊C₄	—	2	1	no	—
461	C₇×C₄⋊C₄	—	2	2	no	—
462	C₇×C₄⋊C₄	—	2	2	no	—
463	C₇×C₄⋊C₄	—	2	2	no	—
464	C₇×C₄⋊C₄	—	2	2	no	—
465	C₇×C₄⋊C₄	—	2	2	no	—
466	C₇×C₄⋊C₄	—	2	2	no	—
467	C₇×C₄⋊C₄	—	2	2	no	—
468	C₇×C₄⋊C₄	—	2	2	no	—
469	C₇×C₄⋊C₄	—	2	1	no	—
470	C₇×C₄⋊C₄	—	2	2	no	—
471	C₇×C₄⋊C₄	—	2	2	no	—
472	C₇×C₄⋊C₄	—	2	2	no	—
473	C₇×C₄⋊C₄	—	2	1	no	—
474	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
475	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
476	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
477	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
478	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
479	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
480	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
481	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
482	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
483	C₇×C₂²⋊C₄	—	2	2	no	—
484	C₇×C₂²⋊C₄	—	2	2	no	—
485	C₇×C₂²⋊C₄	—	2	1	no	—
486	C₇×C₂²⋊C₄	—	2	1	no	—
487	C₇×C₂²⋊C₄	—	2	2	no	—
488	C₇×C₂²⋊C₄	—	2	1	no	—
489	C₇×C₂²⋊C₄	—	2	2	no	—
490	C₇×C₂²⋊C₄	—	2	2	no	—
491	C₇×C₂²⋊C₄	—	2	2	no	—
492	C₇×C₂²⋊C₄	—	2	2	no	—
493	C₇×C₂²⋊C₄	—	2	2	no	—
494	C₇×C₂²⋊C₄	—	2	2	no	—
495	C₇×C₂²⋊C₄	—	2	2	no	—
496	C₇×C₂²⋊C₄	—	2	2	no	—
497	C₇×C₂²⋊C₄	—	2	1	no	—
498	C₇×C₂²⋊C₄	—	2	1	no	—
499	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
500	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
501	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
502	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
503	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
504	C₄²×C₇	—	2	2	no	—
505	C₄²×C₇	—	2	2	no	—
506	C₄²×C₇	—	2	2	no	—
507	C₄²×C₇	—	2	1	no	—
508	C₄²×C₇	C₂⁴	1	2	yes	—
509	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
510	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
511	C₂×#137	C₂²×C₇	1	1	yes	characteristic, complemented
512	C₂×#135	C₂²×C₇	1	1	yes	characteristic
513	C₂×#135	C₂²×C₇	1	1	yes	characteristic
514	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
515	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
516	#554	—	2	1	no	—
517	#554	C₂²×C₇	1	2	yes	—
518	#553	—	2	1	no	—
519	#553	C₂²×C₇	1	2	yes	—
520	#552	—	2	1	no	—
521	#552	C₂²×C₇	1	2	yes	complemented
522	D₄×Q₈	C₂²×C₇	1	2	yes	—
523	#548	C₂²×C₇	1	2	yes	—
524	#547	—	2	2	no	—
525	#547	—	2	1	no	—
526	#547	C₂²×C₇	1	2	yes	—
527	#547	C₂²×C₇	1	2	yes	complemented
528	#546	—	2	2	no	—
529	#546	C₂²×C₇	1	2	yes	—
530	#544	C₂²×C₇	1	1	yes	characteristic, complemented
531	#539	—	2	2	no	—
532	#537	—	2	1	no	—
533	#537	C₂²×C₇	1	1	yes	characteristic
534	#537	C₂²×C₇	1	1	yes	characteristic, complemented
535	#536	—	2	1	no	—
536	#536	C₂²×C₇	1	1	yes	characteristic
537	#525	—	2	1	no	—
538	#525	—	2	2	no	—
539	#525	C₂²×C₇	1	1	yes	characteristic
540	#525	C₂²×C₇	1	1	yes	characteristic
541	C₂×C₂²⋊Q₈	—	2	1	no	—
542	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
543	#520	C₂²×C₇	1	1	yes	characteristic
544	#520	C₂²×C₇	1	1	yes	characteristic, complemented
545	#520	C₂²×C₇	1	1	yes	characteristic, complemented
546	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
547	#491	C₂²×C₇	1	2	yes	complemented
548	#489	C₂²×C₇	1	2	yes	complemented
549	#488	C₂²×C₇	1	2	yes	complemented
550	#487	C₂²×C₇	1	2	yes	complemented
551	#485	C₂²×C₇	1	2	yes	complemented
552	#484	C₂²×C₇	1	2	yes	—
553	#484	C₂²×C₇	1	2	yes	—
554	#484	C₂²×C₇	1	2	yes	complemented
555	#484	C₂²×C₇	1	2	yes	complemented
556	#484	C₂²×C₇	1	2	yes	complemented
557	#482	C₂²×C₇	1	2	yes	complemented
558	#480	C₂²×C₇	1	2	yes	complemented
559	#479	C₂²×C₇	1	2	yes	complemented
560	#478	C₂²×C₇	1	2	yes	complemented
561	#477	C₂²×C₇	1	2	yes	complemented
562	#474	C₂²×C₇	1	2	yes	complemented
563	#470	C₂²×C₇	1	2	yes	complemented
564	#468	C₂²×C₇	1	2	yes	complemented
565	#468	C₂²×C₇	1	2	yes	complemented
566	#468	C₂²×C₇	1	2	yes	complemented
567	#467	C₂²×C₇	1	2	yes	—
568	#467	C₂²×C₇	1	2	yes	complemented
569	#466	C₂²×C₇	1	2	yes	complemented
570	#465	C₂²×C₇	1	2	yes	—
571	#464	C₂²×C₇	1	2	yes	complemented
572	#463	C₂²×C₇	1	2	yes	complemented
573	#462	C₂²×C₇	1	2	yes	complemented
574	#461	C₂²×C₇	1	2	yes	complemented
575	#452	C₂²×C₇	1	1	yes	characteristic
576	#452	C₂²×C₇	1	1	yes	characteristic
577	#452	C₂²×C₇	1	2	yes	complemented
578	#451	C₂²×C₇	1	1	yes	characteristic
579	#451	C₂²×C₇	1	2	yes	complemented
580	#450	C₂²×C₇	1	1	yes	characteristic
581	#449	C₂²×C₇	1	1	yes	characteristic
582	#449	C₂²×C₇	1	1	yes	characteristic
583	#449	C₂²×C₇	1	2	yes	complemented
584	#448	C₂²×C₇	1	1	yes	characteristic
585	#448	C₂²×C₇	1	2	yes	complemented
586	#447	C₂²×C₇	1	1	yes	characteristic
587	#440	C₂²×C₇	1	2	yes	complemented
588	#440	C₂²×C₇	1	2	yes	complemented
589	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
590	C₄×D₈	C₂²×C₇	1	2	yes	complemented
591	#436	C₂²×C₇	1	2	yes	complemented
592	#435	C₂²×C₇	1	2	yes	—
593	#435	C₂²×C₇	1	2	yes	complemented
594	C₈×D₄	C₂²×C₇	1	2	yes	—
595	#428	C₂²×C₇	1	1	yes	characteristic, complemented
596	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
597	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
598	#424	C₂²×C₇	1	1	yes	characteristic, complemented
599	#419	C₂²×C₇	1	1	yes	characteristic, complemented
600	#419	C₂²×C₇	1	2	yes	complemented
601	#417	C₂²×C₇	1	2	yes	—
602	#417	C₂²×C₇	1	1	yes	characteristic
603	#417	C₂²×C₇	1	1	yes	characteristic
604	#417	C₂²×C₇	1	1	yes	characteristic
605	#417	C₂²×C₇	1	1	yes	characteristic
606	#417	C₂²×C₇	1	2	yes	—
607	#417	C₂²×C₇	1	2	yes	complemented
608	#417	C₂²×C₇	1	1	yes	characteristic, complemented
609	#416	C₂²×C₇	1	1	yes	characteristic
610	#416	C₂²×C₇	1	1	yes	characteristic
611	#416	C₂²×C₇	1	2	yes	complemented
612	C₂×#103	C₂²×C₇	1	2	yes	—
613	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
614	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
615	C₂×#103	C₂²×C₇	1	2	yes	complemented
616	C₂×#102	C₂²×C₇	1	2	yes	—
617	#408	C₂²×C₇	1	1	yes	characteristic, complemented
618	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
619	#405	C₂²×C₇	1	1	yes	characteristic, complemented
620	C₂³×C₇	—	2	2	no	—
621	C₂³×C₇	—	2	2	no	—
622	C₂³×C₇	—	2	1	no	—
623	C₂³×C₇	—	2	1	no	—
624	C₂³×C₇	—	2	1	no	—
625	C₂³×C₇	—	4	1	no	—
626	C₂³×C₇	—	4	2	no	—
627	C₂³×C₇	—	4	2	no	—
628	C₂³×C₇	—	8	1	no	—
629	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
630	C₂³×C₇	C₂²×D₄	1	2	yes	—
631	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
632	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
633	C₇×Q₈	—	2	2	no	—
634	C₇×Q₈	—	2	1	no	—
635	C₇×Q₈	—	2	1	no	—
636	C₇×Q₈	—	2	2	no	—
637	C₇×Q₈	—	2	1	no	—
638	C₇×Q₈	—	2	1	no	—
639	C₇×Q₈	—	2	2	no	—
640	C₇×Q₈	—	2	1	no	—
641	C₇×Q₈	—	4	4	no	—
642	C₇×Q₈	—	4	2	no	—
643	C₇×Q₈	—	4	2	no	—
644	C₇×Q₈	—	8	2	no	—
645	C₇×Q₈	C₂×#41	1	2	yes	—
646	C₇×D₄	—	2	4	no	—
647	C₇×D₄	—	2	4	no	—
648	C₇×D₄	—	2	4	no	—
649	C₇×D₄	—	2	2	no	—
650	C₇×D₄	—	2	1	no	—
651	C₇×D₄	—	2	1	no	—
652	C₇×D₄	—	2	1	no	—
653	C₇×D₄	—	2	1	no	—
654	C₇×D₄	—	2	1	no	—
655	C₇×D₄	—	4	2	no	—
656	C₇×D₄	—	4	2	no	—
657	C₇×D₄	—	4	2	no	—
658	C₇×D₄	—	4	2	no	—
659	C₇×D₄	—	4	4	no	—
660	C₇×D₄	—	4	2	no	—
661	C₇×D₄	—	4	2	no	—
662	C₇×D₄	—	4	2	no	—
663	C₇×D₄	—	4	2	no	—
664	C₇×D₄	—	8	2	no	—
665	C₇×D₄	—	8	2	no	—
666	C₇×D₄	C₂×#41	1	2	yes	—
667	C₂×C₄×C₇	—	2	2	no	—
668	C₂×C₄×C₇	—	2	1	no	—
669	C₂×C₄×C₇	—	2	2	no	—
670	C₂×C₄×C₇	—	2	2	no	—
671	C₂×C₄×C₇	—	2	4	no	—
672	C₂×C₄×C₇	—	2	1	no	—
673	C₂×C₄×C₇	—	2	1	no	—
674	C₂×C₄×C₇	—	2	2	no	—
675	C₂×C₄×C₇	—	2	1	no	—
676	C₂×C₄×C₇	—	2	2	no	—
677	C₂×C₄×C₇	—	2	1	no	—
678	C₂×C₄×C₇	—	2	1	no	—
679	C₂×C₄×C₇	—	2	1	no	—
680	C₂×C₄×C₇	—	2	2	no	—
681	C₂×C₄×C₇	—	2	2	no	—
682	C₂×C₄×C₇	—	2	1	no	—
683	C₂×C₄×C₇	—	2	2	no	—
684	C₂×C₄×C₇	—	2	2	no	—
685	C₂×C₄×C₇	—	2	1	no	—
686	C₂×C₄×C₇	—	4	2	no	—
687	C₂×C₄×C₇	—	4	2	no	—
688	C₂×C₄×C₇	—	4	2	no	—
689	C₂×C₄×C₇	—	4	4	no	—
690	C₂×C₄×C₇	—	4	4	no	—
691	C₂×C₄×C₇	—	4	4	no	—
692	C₂×C₄×C₇	—	4	2	no	—
693	C₂×C₄×C₇	—	4	2	no	—
694	C₂×C₄×C₇	—	4	2	no	—
695	C₂×C₄×C₇	—	8	2	no	—
696	C₂×C₄×C₇	—	8	2	no	—
697	C₂×C₄×C₇	—	8	1	no	—
698	C₂×C₄×C₇	—	8	1	no	—
699	C₂×C₄×C₇	—	8	2	no	—
700	C₂×C₄×C₇	—	8	1	no	—
701	C₂×C₄×C₇	—	8	2	no	—
702	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
703	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
704	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
705	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
706	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
707	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
708	C₂×C₄×C₇	C₂×#41	1	2	yes	—
709	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
710	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
711	C₇×C₈	—	2	1	no	—
712	C₇×C₈	—	2	1	no	—
713	C₇×C₈	—	2	1	no	—
714	C₇×C₈	—	2	1	no	—
715	C₇×C₈	—	2	2	no	—
716	C₇×C₈	—	2	2	no	—
717	2₋¹⁺⁴	—	2	4	no	—
718	2₋¹⁺⁴	—	4	2	no	—
719	C₂×#41	—	2	1	no	—
720	C₂×#41	—	2	2	no	—
721	C₂×#41	—	2	2	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	—	2	1	no	—
724	C₂×#41	—	2	4	no	—
725	C₂×#41	—	4	2	no	—
726	C₂×#41	C₂³×C₇	1	1	yes	characteristic
727	C₂×#41	C₂³×C₇	1	1	yes	characteristic
728	C₂×#41	C₂³×C₇	1	2	yes	—
729	C₂×#41	C₂³×C₇	1	1	yes	characteristic
730	C₂×#41	C₂³×C₇	1	1	yes	characteristic
731	C₂×#41	C₂³×C₇	1	1	yes	characteristic
732	C₂×#41	C₂³×C₇	1	1	yes	characteristic
733	C₂²×Q₈	—	2	1	no	—
734	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
735	C₂²×Q₈	C₂³×C₇	1	2	yes	—
736	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
737	C₂²×D₄	—	2	1	no	—
738	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
739	C₂³×C₄	—	2	1	no	—
740	C₂³×C₄	—	2	1	no	—
741	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
742	#137	—	4	2	no	—
743	#135	—	2	4	no	—
744	#135	—	4	2	no	—
745	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
746	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
747	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
749	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
750	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
751	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
752	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
753	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
754	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
755	#131	—	4	2	no	—
756	C₂×M₁₆	—	4	2	no	—
757	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
758	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
759	C₂×M₁₆	C₂³×C₇	1	2	yes	—
760	C₂×M₁₆	C₂³×C₇	1	2	yes	—
761	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
762	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
763	C₂²×C₈	C₂³×C₇	1	2	yes	—
764	C₂²×C₈	C₂³×C₇	1	2	yes	—
765	C₄⋊Q₈	—	2	2	no	—
766	C₄⋊Q₈	—	2	1	no	—
767	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
768	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
769	#126	—	2	2	no	—
770	#126	—	2	2	no	—
771	#125	—	2	2	no	—
772	#125	—	2	2	no	—
773	#125	—	2	1	no	—
774	#125	C₂³×C₇	1	2	yes	—
775	#124	—	2	2	no	—
776	#124	C₂³×C₇	1	2	yes	—
777	#123	—	2	2	no	—
778	#123	—	2	1	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	C₇×D₄	1	2	yes	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
801	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
802	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
803	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
804	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
805	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
806	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
807	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
808	#121	—	2	1	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	—	2	2	no	—
814	#121	—	2	1	no	—
815	#121	—	2	2	no	—
816	#121	C₇×D₄	1	1	yes	characteristic
817	#121	C₇×D₄	1	1	yes	characteristic
818	#121	C₂³×C₇	1	1	yes	characteristic
819	#121	C₂³×C₇	1	1	yes	characteristic
820	#121	C₂³×C₇	1	2	yes	—
821	#121	C₂³×C₇	1	2	yes	—
822	#120	—	2	1	no	—
823	#120	—	2	2	no	—
824	#120	C₇×D₄	1	2	yes	—
825	C₄×Q₈	—	2	1	no	—
826	C₄×Q₈	C₂³×C₇	1	2	yes	—
827	C₄×Q₈	C₂³×C₇	1	2	yes	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	C₂³×C₇	1	2	yes	—
839	C₄×D₄	C₂³×C₇	1	2	yes	—
840	C₄×D₄	C₂³×C₇	1	2	yes	—
841	C₄×D₄	C₂³×C₇	1	2	yes	—
842	#117	—	2	1	no	—
843	#117	—	2	1	no	—
844	#117	—	2	2	no	—
845	#117	C₂³×C₇	1	1	yes	characteristic
846	#117	C₂³×C₇	1	2	yes	—
847	#117	C₂³×C₇	1	1	yes	characteristic
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	—	2	1	no	—
850	C₂×C₄⋊C₄	—	2	1	no	—
851	C₂×C₄⋊C₄	—	2	1	no	—
852	C₂×C₄⋊C₄	—	2	1	no	—
853	C₂×C₄⋊C₄	—	2	1	no	—
854	C₂×C₄⋊C₄	—	2	2	no	—
855	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
856	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
857	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
858	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
859	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
860	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
861	C₂×C₂²⋊C₄	—	2	1	no	—
862	C₂×C₂²⋊C₄	—	2	2	no	—
863	#107	C₂³×C₇	1	2	yes	—
864	#107	C₂³×C₇	1	2	yes	—
865	#107	C₂³×C₇	1	2	yes	—
866	#107	C₂³×C₇	1	2	yes	—
867	#107	C₂³×C₇	1	2	yes	—
868	#106	C₂³×C₇	1	2	yes	—
869	C₄⋊C₈	C₂³×C₇	1	2	yes	—
870	C₄⋊C₈	C₂³×C₇	1	2	yes	—
871	#103	C₂³×C₇	1	2	yes	—
872	#103	C₂³×C₇	1	2	yes	—
873	#103	C₂³×C₇	1	2	yes	—
874	#103	C₂³×C₇	1	2	yes	—
875	#103	C₂³×C₇	1	1	yes	characteristic
876	#103	C₂³×C₇	1	2	yes	—
877	#103	C₂³×C₇	1	2	yes	—
878	#103	C₂³×C₇	1	2	yes	—
879	#103	C₂³×C₇	1	2	yes	—
880	#103	C₂³×C₇	1	2	yes	—
881	#103	C₂³×C₇	1	1	yes	characteristic
882	#103	C₂³×C₇	1	1	yes	characteristic
883	#103	C₂³×C₇	1	1	yes	characteristic
884	#103	C₂³×C₇	1	2	yes	—
885	#103	C₂³×C₇	1	2	yes	—
886	#102	C₂³×C₇	1	2	yes	—
887	#102	C₂³×C₇	1	2	yes	—
888	#102	C₂³×C₇	1	2	yes	—
889	#102	C₂³×C₇	1	2	yes	—
890	#102	C₂³×C₇	1	1	yes	characteristic
891	#102	C₂³×C₇	1	1	yes	characteristic
892	#102	C₂³×C₇	1	1	yes	characteristic
893	#102	C₂³×C₇	1	1	yes	characteristic
894	#102	C₂³×C₇	1	2	yes	—
895	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
896	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
897	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
898	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
899	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
900	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
901	#97	C₂³×C₇	1	2	yes	—
902	C₄×C₈	C₂³×C₇	1	2	yes	—
903	C₂²×C₇	—	2	1	no	—
904	C₂²×C₇	—	2	1	no	—
905	C₂²×C₇	—	2	1	no	—
906	C₂²×C₇	—	2	1	no	—
907	C₂²×C₇	—	2	1	no	—
908	C₂²×C₇	—	2	2	no	—
909	C₂²×C₇	—	2	1	no	—
910	C₂²×C₇	—	2	2	no	—
911	C₂²×C₇	—	2	2	no	—
912	C₂²×C₇	—	2	2	no	—
913	C₂²×C₇	—	2	1	no	—
914	C₂²×C₇	—	4	4	no	—
915	C₂²×C₇	—	4	1	no	—
916	C₂²×C₇	—	4	1	no	—
917	C₂²×C₇	—	4	1	no	—
918	C₂²×C₇	—	4	1	no	—
919	C₂²×C₇	—	4	1	no	—
920	C₂²×C₇	—	4	1	no	—
921	C₂²×C₇	—	4	1	no	—
922	C₂²×C₇	—	4	1	no	—
923	C₂²×C₇	—	8	4	no	—
924	C₂²×C₇	#546	1	2	yes	—
925	C₂²×C₇	#578	1	2	yes	—
926	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
927	C₄×C₇	—	2	2	no	—
928	C₄×C₇	—	2	1	no	—
929	C₄×C₇	—	2	1	no	—
930	C₄×C₇	—	2	2	no	—
931	C₄×C₇	—	2	2	no	—
932	C₄×C₇	—	2	2	no	—
933	C₄×C₇	—	4	2	no	—
934	C₄×C₇	—	4	2	no	—
935	C₄×C₇	—	4	1	no	—
936	C₄×C₇	—	4	2	no	—
937	C₄×C₇	—	4	1	no	—
938	C₄×C₇	—	4	2	no	—
939	C₄×C₇	—	4	1	no	—
940	C₄×C₇	—	4	1	no	—
941	C₄×C₇	#546	1	2	yes	—
942	C₄×C₇	C₂²×#41	1	1	yes	characteristic
943	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
944	C₂⁴	—	2	1	no	—
945	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
946	#41	—	2	2	no	—
947	#41	—	2	2	no	—
948	#41	—	2	2	no	—
949	#41	—	2	2	no	—
950	#41	—	2	2	no	—
951	#41	—	2	4	no	—
952	#41	—	2	2	no	—
953	#41	—	2	2	no	—
954	#41	—	2	2	no	—
955	#41	—	2	2	no	—
956	#41	—	4	4	no	—
957	#41	—	4	1	no	—
958	#41	—	4	1	no	—
959	#41	—	4	2	no	—
960	#41	—	4	4	no	—
961	#41	—	4	4	no	—
962	#41	—	4	8	no	—
963	#41	—	8	4	no	—
964	#41	C₇×#41	1	4	yes	complemented
965	C₂×Q₈	—	2	1	no	—
966	C₂×Q₈	—	2	2	no	—
967	C₂×Q₈	—	2	1	no	—
968	C₂×Q₈	—	2	2	no	—
969	C₂×Q₈	—	2	2	no	—
970	C₂×Q₈	—	2	4	no	—
971	C₂×Q₈	—	2	2	no	—
972	C₂×Q₈	—	2	2	no	—
973	C₂×Q₈	—	4	1	no	—
974	C₂×Q₈	—	4	2	no	—
975	C₂×Q₈	—	4	4	no	—
976	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
977	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
978	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
979	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
980	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	1	no	—
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	—	2	1	no	—
990	C₂×D₄	—	2	2	no	—
991	C₂×D₄	—	2	2	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	4	1	no	—
994	C₂×D₄	—	4	4	no	—
995	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
996	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
997	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
998	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
999	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1000	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1001	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	2	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	2	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	2	no	—
1014	C₂²×C₄	—	2	2	no	—
1015	C₂²×C₄	—	2	1	no	—
1016	C₂²×C₄	—	2	1	no	—
1017	C₂²×C₄	—	2	1	no	—
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	—	2	2	no	—
1020	C₂²×C₄	—	2	2	no	—
1021	C₂²×C₄	—	4	4	no	—
1022	C₂²×C₄	—	8	2	no	—
1023	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1024	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1025	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1026	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1027	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1028	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
1029	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1030	Q₁₆	—	2	2	no	—
1031	Q₁₆	—	4	1	no	—
1032	Q₁₆	—	4	2	no	—
1033	SD₁₆	—	2	2	no	—
1034	SD₁₆	—	2	2	no	—
1035	SD₁₆	—	4	1	no	—
1036	SD₁₆	—	4	1	no	—
1037	SD₁₆	—	4	2	no	—
1038	D₈	—	2	2	no	—
1039	D₈	—	4	1	no	—
1040	M₁₆	—	2	2	no	—
1041	M₁₆	—	2	2	no	—
1042	M₁₆	—	4	2	no	—
1043	M₁₆	—	4	2	no	—
1044	C₂×C₈	—	2	2	no	—
1045	C₂×C₈	—	2	2	no	—
1046	C₂×C₈	—	4	2	no	—
1047	C₂×C₈	—	4	2	no	—
1048	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1049	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1050	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1051	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1052	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1053	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	2	no	—
1065	C₄⋊C₄	—	2	2	no	—
1066	C₄⋊C₄	—	2	2	no	—
1067	C₄⋊C₄	—	2	2	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	2	2	no	—
1071	C₄⋊C₄	—	2	2	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1074	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1075	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1076	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1077	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1078	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1079	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1080	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1081	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1099	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1100	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1101	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1102	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1103	C₄²	—	2	2	no	—
1104	C₄²	—	2	2	no	—
1105	C₄²	—	2	2	no	—
1106	C₄²	—	2	1	no	—
1107	C₄²	C₂⁴×C₇	1	2	yes	—
1108	C₂×C₇	—	2	2	no	—
1109	C₂×C₇	—	2	2	no	—
1110	C₂×C₇	—	4	2	no	—
1111	C₂×C₇	—	4	1	no	—
1112	C₂×C₇	—	4	2	no	—
1113	C₂×C₇	—	8	1	no	—
1114	C₂×C₇	—	8	1	no	—
1115	C₂×C₇	C₂×#546	1	1	yes	characteristic
1116	C₂×C₇	C₂×#578	1	1	yes	characteristic
1117	C₂×C₇	#3585	1	1	yes	characteristic
1118	C₂³	—	2	1	no	—
1119	C₂³	—	2	2	no	—
1120	C₂³	—	2	2	no	—
1121	C₂³	—	2	1	no	—
1122	C₂³	—	2	1	no	—
1123	C₂³	—	4	1	no	—
1124	C₂³	—	4	2	no	—
1125	C₂³	—	4	2	no	—
1126	C₂³	—	8	1	no	—
1127	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1128	C₂³	C₂²×C₇×D₄	1	2	yes	—
1129	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1130	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1131	Q₈	—	2	1	no	—
1132	Q₈	—	2	2	no	—
1133	Q₈	—	2	1	no	—
1134	Q₈	—	2	2	no	—
1135	Q₈	—	2	1	no	—
1136	Q₈	—	2	1	no	—
1137	Q₈	—	2	2	no	—
1138	Q₈	—	2	1	no	—
1139	Q₈	—	4	4	no	—
1140	Q₈	—	4	2	no	—
1141	Q₈	—	4	2	no	—
1142	Q₈	—	8	2	no	—
1143	Q₈	C₂×C₇×#41	1	2	yes	—
1144	D₄	—	2	4	no	—
1145	D₄	—	2	4	no	—
1146	D₄	—	2	4	no	—
1147	D₄	—	2	1	no	—
1148	D₄	—	2	1	no	—
1149	D₄	—	2	1	no	—
1150	D₄	—	2	1	no	—
1151	D₄	—	2	1	no	—
1152	D₄	—	2	2	no	—
1153	D₄	—	4	2	no	—
1154	D₄	—	4	2	no	—
1155	D₄	—	4	2	no	—
1156	D₄	—	4	2	no	—
1157	D₄	—	4	4	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	8	2	no	—
1163	D₄	—	8	2	no	—
1164	D₄	C₂×C₇×#41	1	2	yes	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	4	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	2	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	2	no	—
1182	C₂×C₄	—	2	2	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	4	2	no	—
1185	C₂×C₄	—	4	2	no	—
1186	C₂×C₄	—	4	2	no	—
1187	C₂×C₄	—	4	4	no	—
1188	C₂×C₄	—	4	4	no	—
1189	C₂×C₄	—	4	4	no	—
1190	C₂×C₄	—	4	2	no	—
1191	C₂×C₄	—	4	2	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	8	2	no	—
1194	C₂×C₄	—	8	2	no	—
1195	C₂×C₄	—	8	1	no	—
1196	C₂×C₄	—	8	1	no	—
1197	C₂×C₄	—	8	2	no	—
1198	C₂×C₄	—	8	1	no	—
1199	C₂×C₄	—	8	2	no	—
1200	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1201	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1202	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1203	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1204	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1205	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1206	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1207	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1208	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1209	C₈	—	2	1	no	—
1210	C₈	—	2	1	no	—
1211	C₈	—	2	1	no	—
1212	C₈	—	2	1	no	—
1213	C₈	—	2	2	no	—
1214	C₈	—	2	2	no	—
1215	C₇	#61194	1	1	yes	characteristic, direct product factor, Sylow
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	2	2	no	—
1221	C₂²	—	2	1	no	—
1222	C₂²	—	2	1	no	—
1223	C₂²	—	2	2	no	—
1224	C₂²	—	2	1	no	—
1225	C₂²	—	2	2	no	—
1226	C₂²	—	2	2	no	—
1227	C₂²	—	4	4	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	4	1	no	—
1232	C₂²	—	4	1	no	—
1233	C₂²	—	4	1	no	—
1234	C₂²	—	4	1	no	—
1235	C₂²	—	4	1	no	—
1236	C₂²	—	8	4	no	—
1237	C₂²	C₇×#546	1	2	yes	—
1238	C₂²	C₇×#578	1	2	yes	—
1239	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1240	C₄	—	2	2	no	—
1241	C₄	—	2	2	no	—
1242	C₄	—	2	1	no	—
1243	C₄	—	2	1	no	—
1244	C₄	—	2	2	no	—
1245	C₄	—	2	2	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	2	no	—
1248	C₄	—	4	2	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	2	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	2	no	—
1253	C₄	—	4	1	no	—
1254	C₄	C₇×#546	1	2	yes	—
1255	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1256	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1257	C₂	—	2	2	no	—
1258	C₂	—	2	2	no	—
1259	C₂	—	4	1	no	—
1260	C₂	—	4	2	no	—
1261	C₂	—	4	2	no	—
1262	C₂	—	8	1	no	—
1263	C₂	—	8	1	no	—
1264	C₂	C₂×C₇×#546	1	1	yes	characteristic
1265	C₂	C₂×C₇×#578	1	1	yes	characteristic
1266	C₂	C₇×#3585	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3492	C₂	semidirect
2. C₇×#3489	C₂	semidirect
3. C₇×#3330	C₂	semidirect
4. C₇×#3327	C₂	semidirect
5. C₇×#3320	C₂	semidirect
6. C₇×#3315	C₂	semidirect
7. C₇×#3314	C₂	semidirect
8. C₇×#3308	C₂	semidirect
9. C₇×#3299	C₂	semidirect
10. C₇×#3297	C₂	semidirect
11. C₇×#3137	C₂	semidirect
12. C₇×#3098	C₂	semidirect
13. C₂×C₇×#484	C₂	semidirect
14. C₇×#3083	C₂	semidirect
15. C₇×#3061	C₂	semidirect
16. C₇×#3056	C₂	semidirect
17. C₇×#3046	C₂	semidirect
18. C₇×#3013	C₂	semidirect
19. C₇×#3002	C₂	semidirect
20. C₇×#2951	C₂	semidirect
21. C₇×#2933	C₂	semidirect
22. C₇×#2898	C₂	semidirect
23. C₂×C₇×#417	C₂	semidirect
26. C₂×C₇×#137	C₂²	semidirect
29. C₂×C₇×#131	C₂²	semidirect
36. C₇×#552	C₂²	semidirect
42. C₇×#547	C₂²	semidirect
45. C₇×#544	C₂²	semidirect
49. C₇×#537	C₂²	semidirect
59. C₇×#520	C₂²	semidirect
60. C₇×#520	C₂²	semidirect
62. C₇×#491	C₂²	semidirect
63. C₇×#489	C₂²	semidirect
64. C₇×#488	C₂²	semidirect
65. C₇×#487	C₂²	semidirect
66. C₇×#485	C₂²	semidirect
69. C₇×#484	C₂²	semidirect
70. C₇×#484	C₂²	semidirect
71. C₇×#484	C₂²	semidirect
72. C₇×#482	C₂²	semidirect
73. C₇×#480	C₂²	semidirect
74. C₇×#479	C₂²	semidirect
75. C₇×#478	C₂²	semidirect
76. C₇×#477	C₂²	semidirect
77. C₇×#474	C₂²	semidirect
78. C₇×#470	C₂²	semidirect
79. C₇×#468	C₂²	semidirect
80. C₇×#468	C₂²	semidirect
81. C₇×#468	C₂²	semidirect
83. C₇×#467	C₂²	semidirect
84. C₇×#466	C₂²	semidirect
86. C₇×#464	C₂²	semidirect
87. C₇×#463	C₂²	semidirect
88. C₇×#462	C₂²	semidirect
89. C₇×#461	C₂²	semidirect
92. C₇×#452	C₂²	semidirect
94. C₇×#451	C₂²	semidirect
98. C₇×#449	C₂²	semidirect
100. C₇×#448	C₂²	semidirect
102. C₇×#440	C₂²	semidirect
103. C₇×#440	C₂²	semidirect
104. C₄×C₇×Q₁₆	C₂²	semidirect
105. C₄×C₇×D₈	C₂²	semidirect
106. C₇×#436	C₂²	semidirect
108. C₇×#435	C₂²	semidirect
110. C₇×#428	C₂²	semidirect
111. C₂×C₇×#107	C₂²	semidirect
112. C₂×C₇×#107	C₂²	semidirect
113. C₇×#424	C₂²	semidirect
114. C₇×#419	C₂²	semidirect
115. C₇×#419	C₂²	semidirect
122. C₇×#417	C₂²	semidirect
123. C₇×#417	C₂²	semidirect
126. C₇×#416	C₂²	semidirect
128. C₂×C₇×#103	C₂²	semidirect
129. C₂×C₇×#103	C₂²	semidirect
130. C₂×C₇×#103	C₂²	semidirect
132. C₇×#408	C₂²	semidirect
134. C₇×#405	C₂²	semidirect
135. #61194	C₇	direct (N × H)
322. #3492	C₂×C₇	semidirect
323. #3489	C₂×C₇	semidirect
324. #3330	C₂×C₇	semidirect
325. #3327	C₂×C₇	semidirect
326. #3320	C₂×C₇	semidirect
327. #3315	C₂×C₇	semidirect
328. #3314	C₂×C₇	semidirect
329. #3308	C₂×C₇	semidirect
330. #3299	C₂×C₇	semidirect
331. #3297	C₂×C₇	semidirect
332. #3137	C₂×C₇	semidirect
333. #3098	C₂×C₇	semidirect
334. C₂×#484	C₂×C₇	semidirect
335. #3083	C₂×C₇	semidirect
336. #3061	C₂×C₇	semidirect
337. #3056	C₂×C₇	semidirect
338. #3046	C₂×C₇	semidirect
339. #3013	C₂×C₇	semidirect
340. #3002	C₂×C₇	semidirect
341. #2951	C₂×C₇	semidirect
342. #2933	C₂×C₇	semidirect
343. #2898	C₂×C₇	semidirect
344. C₂×#417	C₂×C₇	semidirect
365. C₇×#41	#41	semidirect
511. C₂×#137	C₂²×C₇	semidirect
514. C₂×#131	C₂²×C₇	semidirect
521. #552	C₂²×C₇	semidirect
527. #547	C₂²×C₇	semidirect
530. #544	C₂²×C₇	semidirect
534. #537	C₂²×C₇	semidirect
544. #520	C₂²×C₇	semidirect
545. #520	C₂²×C₇	semidirect
547. #491	C₂²×C₇	semidirect
548. #489	C₂²×C₇	semidirect
549. #488	C₂²×C₇	semidirect
550. #487	C₂²×C₇	semidirect
551. #485	C₂²×C₇	semidirect
554. #484	C₂²×C₇	semidirect
555. #484	C₂²×C₇	semidirect
556. #484	C₂²×C₇	semidirect
557. #482	C₂²×C₇	semidirect
558. #480	C₂²×C₇	semidirect
559. #479	C₂²×C₇	semidirect
560. #478	C₂²×C₇	semidirect
561. #477	C₂²×C₇	semidirect
562. #474	C₂²×C₇	semidirect
563. #470	C₂²×C₇	semidirect
564. #468	C₂²×C₇	semidirect
565. #468	C₂²×C₇	semidirect
566. #468	C₂²×C₇	semidirect
568. #467	C₂²×C₇	semidirect
569. #466	C₂²×C₇	semidirect
571. #464	C₂²×C₇	semidirect
572. #463	C₂²×C₇	semidirect
573. #462	C₂²×C₇	semidirect
574. #461	C₂²×C₇	semidirect
577. #452	C₂²×C₇	semidirect
579. #451	C₂²×C₇	semidirect
583. #449	C₂²×C₇	semidirect
585. #448	C₂²×C₇	semidirect
587. #440	C₂²×C₇	semidirect
588. #440	C₂²×C₇	semidirect
589. C₄×Q₁₆	C₂²×C₇	semidirect
590. C₄×D₈	C₂²×C₇	semidirect
591. #436	C₂²×C₇	semidirect
593. #435	C₂²×C₇	semidirect
595. #428	C₂²×C₇	semidirect
596. C₂×#107	C₂²×C₇	semidirect
597. C₂×#107	C₂²×C₇	semidirect
598. #424	C₂²×C₇	semidirect
599. #419	C₂²×C₇	semidirect
600. #419	C₂²×C₇	semidirect
607. #417	C₂²×C₇	semidirect
608. #417	C₂²×C₇	semidirect
611. #416	C₂²×C₇	semidirect
613. C₂×#103	C₂²×C₇	semidirect
614. C₂×#103	C₂²×C₇	semidirect
615. C₂×#103	C₂²×C₇	semidirect
617. #408	C₂²×C₇	semidirect
619. #405	C₂²×C₇	semidirect
964. #41	C₇×#41	semidirect
1215. C₇	#61194	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×#3492	2
C₇×#3489	2
C₇×#3330	2
C₇×#3327	2
C₇×#3320	2
C₇×#3315	2
C₇×#3314	2
C₇×#3308	2
C₇×#3299	2
C₇×#3297	2
C₇×#3137	2
C₇×#3098	2
C₂×C₇×#484	2
C₇×#3083	2
C₇×#3061	2
C₇×#3056	2
C₇×#3046	2
C₇×#3013	2
C₇×#3002	2
C₇×#2951	2
C₇×#2933	2
C₇×#2898	2
C₂×C₇×#417	2
#61194	7

Subgroups — C7×#61194 #13238410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61194 #13238410