Subgroups — C₇×#61187 #13238403

Order 1792.

2116 conjugacy classes of subgroups.

The subgroup lattice has 1252 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	1	yes	maximal, characteristic, complemented
2	C₇×#3485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3330	C₂	1	2	yes	maximal, complemented
4	C₇×#3322	C₂	1	2	yes	maximal, complemented
5	C₇×#3319	C₂	1	2	yes	maximal, complemented
6	C₇×#3307	C₂	1	2	yes	maximal, complemented
7	C₇×#3307	C₂	1	2	yes	maximal, complemented
8	C₇×#3306	C₂	1	2	yes	maximal, complemented
9	C₇×#3303	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×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3057	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3055	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3042	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₇×#449	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2948	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
26	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×#131	C₂²	1	1	yes	characteristic
30	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₇×#555	C₂²	1	2	yes	complemented
32	C₇×#553	C₂²	1	2	yes	complemented
33	C₇×#553	C₂²	1	2	yes	complemented
34	C₇×#551	—	2	2	no	—
35	C₇×#547	—	2	1	no	—
36	C₇×#547	—	2	1	no	—
37	C₇×#547	C₂²	1	2	yes	complemented
38	C₇×#547	C₂²	1	2	yes	complemented
39	C₇×#547	C₂²	1	2	yes	complemented
40	C₇×#546	—	2	1	no	—
41	C₇×#546	—	2	1	no	—
42	C₇×#546	—	2	2	no	—
43	C₇×#546	C₂²	1	2	yes	complemented
44	C₇×#546	C₂²	1	2	yes	complemented
45	C₇×#544	C₂²	1	1	yes	characteristic, complemented
46	C₇×#542	—	2	1	no	—
47	C₇×#540	—	2	1	no	—
48	C₇×#536	C₂²	1	1	yes	characteristic
49	C₇×#536	C₂²	1	1	yes	characteristic
50	C₇×#535	C₂²	1	1	yes	characteristic
51	C₇×#534	—	2	2	no	—
52	C₇×#532	—	2	1	no	—
53	C₇×#529	—	2	1	no	—
54	C₇×#525	C₂²	1	1	yes	characteristic
55	C₇×#525	C₂²	1	1	yes	characteristic
56	C₂×C₇×#123	—	2	2	no	—
57	C₂×C₇×#121	C₂²	1	1	yes	characteristic, complemented
58	C₇×#520	C₂²	1	1	yes	characteristic
59	C₇×#518	C₂²	1	1	yes	characteristic
60	C₇×#518	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
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	1	yes	characteristic, complemented
67	C₇×#485	C₂²	1	2	yes	complemented
68	C₇×#485	C₂²	1	1	yes	characteristic, complemented
69	C₇×#485	C₂²	1	2	yes	complemented
70	C₇×#484	C₂²	1	2	yes	complemented
71	C₇×#484	C₂²	1	1	yes	characteristic, complemented
72	C₇×#483	C₂²	1	2	yes	complemented
73	C₇×#483	C₂²	1	1	yes	characteristic, complemented
74	C₇×#482	C₂²	1	1	yes	characteristic, complemented
75	C₇×#482	C₂²	1	1	yes	characteristic, complemented
76	C₇×#481	C₂²	1	1	yes	characteristic, complemented
77	C₇×#480	C₂²	1	1	yes	characteristic, complemented
78	C₇×#478	C₂²	1	2	yes	complemented
79	C₇×#478	C₂²	1	2	yes	complemented
80	C₇×#476	C₂²	1	2	yes	complemented
81	C₇×#474	C₂²	1	2	yes	complemented
82	C₇×#469	C₂²	1	2	yes	complemented
83	C₇×#468	C₂²	1	2	yes	complemented
84	C₇×#468	C₂²	1	2	yes	complemented
85	C₇×#468	C₂²	1	2	yes	complemented
86	C₇×#466	C₂²	1	2	yes	complemented
87	C₇×#465	C₂²	1	2	yes	complemented
88	C₇×#465	C₂²	1	2	yes	complemented
89	C₇×#465	C₂²	1	2	yes	complemented
90	C₇×#463	C₂²	1	2	yes	complemented
91	C₇×#463	C₂²	1	2	yes	complemented
92	C₇×#461	C₂²	1	2	yes	complemented
93	C₇×#461	C₂²	1	2	yes	complemented
94	C₇×#449	C₂²	1	2	yes	complemented
95	C₇×#449	C₂²	1	2	yes	complemented
96	C₇×#449	C₂²	1	2	yes	complemented
97	C₇×#449	C₂²	1	2	yes	complemented
98	C₇×#449	C₂²	1	2	yes	complemented
99	C₇×#449	C₂²	1	2	yes	complemented
100	C₇×#447	C₂²	1	2	yes	complemented
101	C₇×#447	C₂²	1	2	yes	complemented
102	C₇×#442	C₂²	1	2	yes	complemented
103	C₇×#442	C₂²	1	2	yes	complemented
104	C₄×C₇×D₈	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	complemented
108	C₇×#435	C₂²	1	2	yes	complemented
109	C₇×C₈×D₄	C₂²	1	2	yes	complemented
110	C₇×#428	C₂²	1	1	yes	characteristic, complemented
111	C₇×#427	C₂²	1	1	yes	characteristic, complemented
112	C₇×#427	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	1	yes	characteristic, complemented
116	C₇×#418	C₂²	1	1	yes	characteristic
117	C₇×#418	C₂²	1	1	yes	characteristic
118	C₇×#418	C₂²	1	1	yes	characteristic, complemented
119	C₇×#418	C₂²	1	2	yes	complemented
120	C₇×#417	C₂²	1	1	yes	characteristic
121	C₇×#417	C₂²	1	2	yes	complemented
122	C₇×#417	C₂²	1	2	yes	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	C₇×#416	C₂²	1	2	yes	complemented
128	C₇×#416	C₂²	1	2	yes	complemented
129	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₇×#102	C₂²	1	1	yes	characteristic
131	C₂×C₇×#102	C₂²	1	2	yes	complemented
132	C₇×#408	C₂²	1	1	yes	characteristic
133	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
134	C₇×#405	C₂²	1	1	yes	characteristic, complemented
135	#61187	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₇×H(5,𝔽₂)	—	2	4	no	—
137	C₇×H(5,𝔽₂)	—	4	2	no	—
138	C₂×C₇×#41	—	2	1	no	—
139	C₂×C₇×#41	—	2	2	no	—
140	C₂×C₇×#41	—	2	1	no	—
141	C₂×C₇×#41	—	2	1	no	—
142	C₂×C₇×#41	—	2	4	no	—
143	C₂×C₇×#41	—	4	2	no	—
144	C₂×C₇×#41	C₂³	1	1	yes	characteristic
145	C₂×C₇×#41	C₂³	1	2	yes	—
146	C₂×C₇×#41	C₂³	1	2	yes	—
147	C₂×C₇×#41	C₂³	1	2	yes	—
148	C₂×C₇×#41	C₂³	1	1	yes	characteristic
149	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
150	C₂²×C₇×D₄	—	2	1	no	—
151	C₂²×C₇×D₄	—	2	1	no	—
152	C₂²×C₇×D₄	—	2	2	no	—
153	C₂²×C₇×D₄	—	2	1	no	—
154	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
155	C₂²×C₇×D₄	C₂³	1	2	yes	—
156	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₇	—	2	1	no	—
158	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
159	C₇×AGL(1,ℤ/8)	—	4	2	no	—
160	C₂×C₇×SD₁₆	—	4	2	no	—
161	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
162	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
163	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₇×D₈	—	2	4	no	—
165	C₂×C₇×D₈	C₂³	1	2	yes	—
166	C₂×C₇×D₈	C₂³	1	2	yes	—
167	C₂×C₇×D₈	C₂³	1	2	yes	—
168	C₇×#131	—	4	2	no	—
169	C₂×C₇×M₁₆	—	4	2	no	—
170	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
171	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
172	C₂×C₇×M₁₆	C₂³	1	2	yes	—
173	C₂×C₇×M₁₆	C₂³	1	2	yes	—
174	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
175	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
176	C₂²×C₇×C₈	C₂³	1	2	yes	—
177	C₂²×C₇×C₈	C₂³	1	2	yes	—
178	C₇×C₄⋊Q₈	—	2	1	no	—
179	C₇×C₄⋊Q₈	—	2	1	no	—
180	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
181	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
182	C₇×#127	—	2	1	no	—
183	C₇×#126	—	2	2	no	—
184	C₇×#126	—	2	2	no	—
185	C₇×#125	—	2	1	no	—
186	C₇×#125	C₂³	1	2	yes	—
187	C₇×#124	—	2	1	no	—
188	C₇×#124	—	2	1	no	—
189	C₇×#124	—	2	2	no	—
190	C₇×#124	—	2	2	no	—
191	C₇×#124	C₂³	1	2	yes	—
192	C₇×#123	—	2	2	no	—
193	C₇×#123	—	2	1	no	—
194	C₇×#123	—	2	2	no	—
195	C₇×#123	—	2	2	no	—
196	C₇×#123	—	2	2	no	—
197	C₇×#123	—	2	2	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	2	no	—
209	C₇×C₂²⋊Q₈	—	2	2	no	—
210	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
211	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
212	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₇×#121	—	2	2	no	—
217	C₇×#121	—	2	2	no	—
218	C₇×#121	—	2	2	no	—
219	C₇×#121	—	2	2	no	—
220	C₇×#121	—	2	2	no	—
221	C₇×#121	—	2	1	no	—
222	C₇×#121	—	2	1	no	—
223	C₇×#121	—	2	2	no	—
224	C₇×#121	—	2	2	no	—
225	C₇×#121	D₄	1	1	yes	characteristic
226	C₇×#121	D₄	1	1	yes	characteristic
227	C₇×#121	C₂³	1	1	yes	characteristic
228	C₇×#121	C₂³	1	2	yes	—
229	C₇×#121	C₂³	1	2	yes	—
230	C₇×#121	C₂³	1	2	yes	—
231	C₇×#121	C₂³	1	2	yes	—
232	C₇×#121	C₂³	1	1	yes	characteristic
233	C₇×#120	—	2	1	no	—
234	C₇×#120	—	2	2	no	—
235	C₇×#120	—	2	2	no	—
236	C₇×#120	—	2	2	no	—
237	C₇×#120	D₄	1	2	yes	—
238	C₄×C₇×Q₈	—	2	1	no	—
239	C₄×C₇×D₄	—	2	1	no	—
240	C₄×C₇×D₄	—	2	2	no	—
241	C₄×C₇×D₄	—	2	1	no	—
242	C₄×C₇×D₄	—	2	1	no	—
243	C₄×C₇×D₄	—	2	1	no	—
244	C₄×C₇×D₄	—	2	1	no	—
245	C₄×C₇×D₄	—	2	1	no	—
246	C₄×C₇×D₄	—	2	1	no	—
247	C₄×C₇×D₄	—	2	2	no	—
248	C₄×C₇×D₄	—	2	2	no	—
249	C₄×C₇×D₄	C₂³	1	2	yes	—
250	C₄×C₇×D₄	C₂³	1	2	yes	—
251	C₄×C₇×D₄	C₂³	1	2	yes	—
252	C₄×C₇×D₄	C₂³	1	2	yes	—
253	C₄×C₇×D₄	C₂³	1	2	yes	—
254	C₄×C₇×D₄	C₂³	1	2	yes	—
255	C₇×#117	—	2	1	no	—
256	C₇×#117	—	2	1	no	—
257	C₇×#117	—	2	2	no	—
258	C₇×#117	C₂³	1	1	yes	characteristic
259	C₇×#117	C₂³	1	1	yes	characteristic
260	C₇×#117	C₂³	1	2	yes	—
261	C₇×#117	C₂³	1	1	yes	characteristic
262	C₇×#117	C₂³	1	1	yes	characteristic
263	C₇×#117	C₂³	1	1	yes	characteristic
264	C₇×#117	C₂³	1	1	yes	characteristic
265	C₂×C₇×C₄⋊C₄	—	2	2	no	—
266	C₂×C₇×C₄⋊C₄	—	2	2	no	—
267	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
270	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²×C₇	—	2	1	no	—
278	C₇×#107	C₂³	1	2	yes	—
279	C₇×#107	C₂³	1	1	yes	characteristic
280	C₇×#107	C₂³	1	1	yes	characteristic
281	C₇×#107	C₂³	1	1	yes	characteristic
282	C₇×#107	C₂³	1	1	yes	characteristic
283	C₇×#106	C₂³	1	2	yes	—
284	C₇×#106	C₂³	1	1	yes	characteristic
285	C₇×#106	C₂³	1	1	yes	characteristic
286	C₇×#106	C₂³	1	1	yes	characteristic
287	C₇×#106	C₂³	1	1	yes	characteristic
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	2	yes	—
295	C₇×#103	C₂³	1	1	yes	characteristic
296	C₇×#103	C₂³	1	1	yes	characteristic
297	C₇×#103	C₂³	1	1	yes	characteristic
298	C₇×#103	C₂³	1	2	yes	—
299	C₇×#103	C₂³	1	1	yes	characteristic
300	C₇×#103	C₂³	1	2	yes	—
301	C₇×#102	C₂³	1	2	yes	—
302	C₇×#102	C₂³	1	2	yes	—
303	C₇×#102	C₂³	1	2	yes	—
304	C₇×#102	C₂³	1	2	yes	—
305	C₇×#102	C₂³	1	2	yes	—
306	C₇×#102	C₂³	1	2	yes	—
307	C₇×#102	C₂³	1	2	yes	—
308	C₇×#102	C₂³	1	1	yes	characteristic
309	C₇×#102	C₂³	1	1	yes	characteristic
310	C₇×#102	C₂³	1	1	yes	characteristic
311	C₇×#102	C₂³	1	1	yes	characteristic
312	C₇×#102	C₂³	1	2	yes	—
313	C₇×#102	C₂³	1	2	yes	—
314	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
315	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
316	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
317	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
318	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
320	C₇×#97	C₂³	1	2	yes	—
321	C₄×C₇×C₈	C₂³	1	2	yes	—
322	#3494	C₂×C₇	1	1	yes	characteristic, complemented
323	#3485	C₂×C₇	1	1	yes	characteristic, complemented
324	#3330	C₂×C₇	1	2	yes	complemented
325	#3322	C₂×C₇	1	2	yes	complemented
326	#3319	C₂×C₇	1	2	yes	complemented
327	#3307	C₂×C₇	1	2	yes	complemented
328	#3307	C₂×C₇	1	2	yes	complemented
329	#3306	C₂×C₇	1	2	yes	complemented
330	#3303	C₂×C₇	1	2	yes	complemented
331	#3297	C₂×C₇	1	2	yes	complemented
332	#3137	C₂×C₇	1	1	yes	characteristic, complemented
333	#3097	C₂×C₇	1	1	yes	characteristic, complemented
334	#3091	C₂×C₇	1	1	yes	characteristic, complemented
335	#3081	C₂×C₇	1	1	yes	characteristic, complemented
336	#3057	C₂×C₇	1	1	yes	characteristic, complemented
337	#3055	C₂×C₇	1	1	yes	characteristic, complemented
338	#3042	C₂×C₇	1	1	yes	characteristic, complemented
339	#3008	C₂×C₇	1	1	yes	characteristic, complemented
340	C₂×#449	C₂×C₇	1	1	yes	characteristic, complemented
341	#2948	C₂×C₇	1	1	yes	characteristic, complemented
342	#2933	C₂×C₇	1	1	yes	characteristic, complemented
343	#2897	C₂×C₇	1	1	yes	characteristic, complemented
344	#2896	C₂×C₇	1	1	yes	characteristic, complemented
345	C₂⁴×C₇	—	2	1	no	—
346	C₂⁴×C₇	—	2	1	no	—
347	C₂⁴×C₇	—	2	2	no	—
348	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
349	C₇×#41	—	2	2	no	—
350	C₇×#41	—	2	2	no	—
351	C₇×#41	—	2	4	no	—
352	C₇×#41	—	2	4	no	—
353	C₇×#41	—	2	4	no	—
354	C₇×#41	—	2	2	no	—
355	C₇×#41	—	2	2	no	—
356	C₇×#41	—	4	2	no	—
357	C₇×#41	—	4	2	no	—
358	C₇×#41	—	4	2	no	—
359	C₇×#41	—	4	4	no	—
360	C₇×#41	—	4	4	no	—
361	C₇×#41	—	4	4	no	—
362	C₇×#41	—	8	4	no	—
363	C₂×C₇×Q₈	—	2	1	no	—
364	C₂×C₇×Q₈	—	2	2	no	—
365	C₂×C₇×Q₈	—	2	2	no	—
366	C₂×C₇×Q₈	—	2	2	no	—
367	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
368	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
369	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
370	C₂×C₇×D₄	—	2	4	no	—
371	C₂×C₇×D₄	—	2	2	no	—
372	C₂×C₇×D₄	—	2	2	no	—
373	C₂×C₇×D₄	—	2	2	no	—
374	C₂×C₇×D₄	—	2	1	no	—
375	C₂×C₇×D₄	—	2	2	no	—
376	C₂×C₇×D₄	—	2	1	no	—
377	C₂×C₇×D₄	—	2	1	no	—
378	C₂×C₇×D₄	—	2	2	no	—
379	C₂×C₇×D₄	—	2	2	no	—
380	C₂×C₇×D₄	—	2	2	no	—
381	C₂×C₇×D₄	—	2	1	no	—
382	C₂×C₇×D₄	—	2	1	no	—
383	C₂×C₇×D₄	—	2	2	no	—
384	C₂×C₇×D₄	—	2	2	no	—
385	C₂×C₇×D₄	—	2	2	no	—
386	C₂×C₇×D₄	—	2	2	no	—
387	C₂×C₇×D₄	—	4	2	no	—
388	C₂×C₇×D₄	—	4	4	no	—
389	C₂×C₇×D₄	—	4	8	no	—
390	C₂×C₇×D₄	—	4	4	no	—
391	C₂×C₇×D₄	—	8	2	no	—
392	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
393	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
394	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
395	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
396	C₂×C₇×D₄	#41	1	4	yes	complemented
397	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
398	C₂×C₇×D₄	C₂⁴	1	2	yes	—
399	C₂×C₇×D₄	C₂⁴	1	2	yes	—
400	C₂²×C₄×C₇	—	2	2	no	—
401	C₂²×C₄×C₇	—	2	2	no	—
402	C₂²×C₄×C₇	—	2	1	no	—
403	C₂²×C₄×C₇	—	2	1	no	—
404	C₂²×C₄×C₇	—	2	1	no	—
405	C₂²×C₄×C₇	—	2	1	no	—
406	C₂²×C₄×C₇	—	2	2	no	—
407	C₂²×C₄×C₇	—	2	2	no	—
408	C₂²×C₄×C₇	—	2	2	no	—
409	C₂²×C₄×C₇	—	2	2	no	—
410	C₂²×C₄×C₇	—	2	1	no	—
411	C₂²×C₄×C₇	—	2	2	no	—
412	C₂²×C₄×C₇	—	2	2	no	—
413	C₂²×C₄×C₇	—	2	2	no	—
414	C₂²×C₄×C₇	—	2	2	no	—
415	C₂²×C₄×C₇	—	4	4	no	—
416	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
417	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
418	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
419	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
421	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
423	C₇×SD₁₆	—	4	2	no	—
424	C₇×SD₁₆	—	4	2	no	—
425	C₇×SD₁₆	—	4	2	no	—
426	C₇×D₈	—	2	4	no	—
427	C₇×D₈	—	2	4	no	—
428	C₇×D₈	—	4	2	no	—
429	C₇×M₁₆	—	2	2	no	—
430	C₇×M₁₆	—	2	2	no	—
431	C₇×M₁₆	—	4	2	no	—
432	C₇×M₁₆	—	4	2	no	—
433	C₂×C₇×C₈	—	2	2	no	—
434	C₂×C₇×C₈	—	2	2	no	—
435	C₂×C₇×C₈	—	4	2	no	—
436	C₂×C₇×C₈	—	4	2	no	—
437	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
438	C₂×C₇×C₈	C₂⁴	1	2	yes	—
439	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
440	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
441	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
442	C₂×C₇×C₈	C₂⁴	1	2	yes	—
443	C₇×C₄⋊C₄	—	2	1	no	—
444	C₇×C₄⋊C₄	—	2	1	no	—
445	C₇×C₄⋊C₄	—	2	2	no	—
446	C₇×C₄⋊C₄	—	2	2	no	—
447	C₇×C₄⋊C₄	—	2	2	no	—
448	C₇×C₄⋊C₄	—	2	2	no	—
449	C₇×C₄⋊C₄	—	2	1	no	—
450	C₇×C₄⋊C₄	—	2	1	no	—
451	C₇×C₄⋊C₄	—	2	1	no	—
452	C₇×C₄⋊C₄	—	2	2	no	—
453	C₇×C₄⋊C₄	—	2	2	no	—
454	C₇×C₄⋊C₄	—	2	2	no	—
455	C₇×C₄⋊C₄	—	2	2	no	—
456	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
457	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
458	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
459	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
460	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
461	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
462	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
463	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
464	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
465	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
466	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
467	C₇×C₂²⋊C₄	—	2	1	no	—
468	C₇×C₂²⋊C₄	—	2	1	no	—
469	C₇×C₂²⋊C₄	—	2	1	no	—
470	C₇×C₂²⋊C₄	—	2	1	no	—
471	C₇×C₂²⋊C₄	—	2	1	no	—
472	C₇×C₂²⋊C₄	—	2	2	no	—
473	C₇×C₂²⋊C₄	—	2	2	no	—
474	C₇×C₂²⋊C₄	—	2	2	no	—
475	C₇×C₂²⋊C₄	—	2	1	no	—
476	C₇×C₂²⋊C₄	—	2	1	no	—
477	C₇×C₂²⋊C₄	—	2	1	no	—
478	C₇×C₂²⋊C₄	—	2	1	no	—
479	C₇×C₂²⋊C₄	—	2	2	no	—
480	C₇×C₂²⋊C₄	—	2	2	no	—
481	C₇×C₂²⋊C₄	—	2	2	no	—
482	C₇×C₂²⋊C₄	—	2	2	no	—
483	C₇×C₂²⋊C₄	—	2	2	no	—
484	C₇×C₂²⋊C₄	—	2	2	no	—
485	C₇×C₂²⋊C₄	—	2	2	no	—
486	C₇×C₂²⋊C₄	—	2	2	no	—
487	C₇×C₂²⋊C₄	—	2	2	no	—
488	C₇×C₂²⋊C₄	—	2	2	no	—
489	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
490	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
491	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
492	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
493	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
494	C₄²×C₇	—	2	1	no	—
495	C₄²×C₇	—	2	1	no	—
496	C₄²×C₇	—	2	1	no	—
497	C₄²×C₇	—	2	1	no	—
498	C₄²×C₇	—	2	2	no	—
499	C₄²×C₇	—	2	1	no	—
500	C₄²×C₇	C₂⁴	1	2	yes	—
501	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
502	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
503	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
504	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
505	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
506	C₂×#131	C₂²×C₇	1	1	yes	characteristic
507	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
508	#555	C₂²×C₇	1	2	yes	complemented
509	#553	C₂²×C₇	1	2	yes	complemented
510	#553	C₂²×C₇	1	2	yes	complemented
511	#551	—	2	2	no	—
512	#547	—	2	1	no	—
513	#547	—	2	1	no	—
514	#547	C₂²×C₇	1	2	yes	complemented
515	#547	C₂²×C₇	1	2	yes	complemented
516	#547	C₂²×C₇	1	2	yes	complemented
517	#546	—	2	1	no	—
518	#546	—	2	1	no	—
519	#546	—	2	2	no	—
520	#546	C₂²×C₇	1	2	yes	complemented
521	#546	C₂²×C₇	1	2	yes	complemented
522	#544	C₂²×C₇	1	1	yes	characteristic, complemented
523	#542	—	2	1	no	—
524	#540	—	2	1	no	—
525	#536	C₂²×C₇	1	1	yes	characteristic
526	#536	C₂²×C₇	1	1	yes	characteristic
527	#535	C₂²×C₇	1	1	yes	characteristic
528	#534	—	2	2	no	—
529	#532	—	2	1	no	—
530	#529	—	2	1	no	—
531	#525	C₂²×C₇	1	1	yes	characteristic
532	#525	C₂²×C₇	1	1	yes	characteristic
533	C₂×#123	—	2	2	no	—
534	C₂×#121	C₂²×C₇	1	1	yes	characteristic, complemented
535	#520	C₂²×C₇	1	1	yes	characteristic
536	#518	C₂²×C₇	1	1	yes	characteristic
537	#518	C₂²×C₇	1	1	yes	characteristic, complemented
538	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
539	#491	C₂²×C₇	1	2	yes	complemented
540	#489	C₂²×C₇	1	2	yes	complemented
541	#488	C₂²×C₇	1	2	yes	complemented
542	#487	C₂²×C₇	1	2	yes	complemented
543	#485	C₂²×C₇	1	1	yes	characteristic, complemented
544	#485	C₂²×C₇	1	1	yes	characteristic, complemented
545	#485	C₂²×C₇	1	2	yes	complemented
546	#485	C₂²×C₇	1	2	yes	complemented
547	#484	C₂²×C₇	1	1	yes	characteristic, complemented
548	#484	C₂²×C₇	1	2	yes	complemented
549	#483	C₂²×C₇	1	1	yes	characteristic, complemented
550	#483	C₂²×C₇	1	2	yes	complemented
551	#482	C₂²×C₇	1	1	yes	characteristic, complemented
552	#482	C₂²×C₇	1	1	yes	characteristic, complemented
553	#481	C₂²×C₇	1	1	yes	characteristic, complemented
554	#480	C₂²×C₇	1	1	yes	characteristic, complemented
555	#478	C₂²×C₇	1	2	yes	complemented
556	#478	C₂²×C₇	1	2	yes	complemented
557	#476	C₂²×C₇	1	2	yes	complemented
558	#474	C₂²×C₇	1	2	yes	complemented
559	#469	C₂²×C₇	1	2	yes	complemented
560	#468	C₂²×C₇	1	2	yes	complemented
561	#468	C₂²×C₇	1	2	yes	complemented
562	#468	C₂²×C₇	1	2	yes	complemented
563	#466	C₂²×C₇	1	2	yes	complemented
564	#465	C₂²×C₇	1	2	yes	complemented
565	#465	C₂²×C₇	1	2	yes	complemented
566	#465	C₂²×C₇	1	2	yes	complemented
567	#463	C₂²×C₇	1	2	yes	complemented
568	#463	C₂²×C₇	1	2	yes	complemented
569	#461	C₂²×C₇	1	2	yes	complemented
570	#461	C₂²×C₇	1	2	yes	complemented
571	#449	C₂²×C₇	1	2	yes	complemented
572	#449	C₂²×C₇	1	2	yes	complemented
573	#449	C₂²×C₇	1	2	yes	complemented
574	#449	C₂²×C₇	1	2	yes	complemented
575	#449	C₂²×C₇	1	2	yes	complemented
576	#449	C₂²×C₇	1	2	yes	complemented
577	#447	C₂²×C₇	1	2	yes	complemented
578	#447	C₂²×C₇	1	2	yes	complemented
579	#442	C₂²×C₇	1	2	yes	complemented
580	#442	C₂²×C₇	1	2	yes	complemented
581	C₄×D₈	C₂²×C₇	1	2	yes	complemented
582	C₄×D₈	C₂²×C₇	1	2	yes	complemented
583	#436	C₂²×C₇	1	2	yes	complemented
584	#435	C₂²×C₇	1	2	yes	complemented
585	#435	C₂²×C₇	1	2	yes	complemented
586	C₈×D₄	C₂²×C₇	1	2	yes	complemented
587	#428	C₂²×C₇	1	1	yes	characteristic, complemented
588	#427	C₂²×C₇	1	1	yes	characteristic, complemented
589	#427	C₂²×C₇	1	1	yes	characteristic, complemented
590	#424	C₂²×C₇	1	1	yes	characteristic, complemented
591	#419	C₂²×C₇	1	1	yes	characteristic, complemented
592	#419	C₂²×C₇	1	1	yes	characteristic, complemented
593	#418	C₂²×C₇	1	1	yes	characteristic
594	#418	C₂²×C₇	1	1	yes	characteristic
595	#418	C₂²×C₇	1	2	yes	complemented
596	#418	C₂²×C₇	1	1	yes	characteristic, complemented
597	#417	C₂²×C₇	1	1	yes	characteristic
598	#417	C₂²×C₇	1	2	yes	complemented
599	#417	C₂²×C₇	1	2	yes	complemented
600	#417	C₂²×C₇	1	2	yes	complemented
601	#416	C₂²×C₇	1	1	yes	characteristic
602	#416	C₂²×C₇	1	1	yes	characteristic
603	#416	C₂²×C₇	1	2	yes	complemented
604	#416	C₂²×C₇	1	2	yes	complemented
605	#416	C₂²×C₇	1	2	yes	complemented
606	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
607	C₂×#102	C₂²×C₇	1	1	yes	characteristic
608	C₂×#102	C₂²×C₇	1	2	yes	complemented
609	#408	C₂²×C₇	1	1	yes	characteristic
610	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
611	#405	C₂²×C₇	1	1	yes	characteristic, complemented
612	C₂³×C₇	—	2	2	no	—
613	C₂³×C₇	—	2	2	no	—
614	C₂³×C₇	—	2	4	no	—
615	C₂³×C₇	—	2	2	no	—
616	C₂³×C₇	—	2	1	no	—
617	C₂³×C₇	—	4	1	no	—
618	C₂³×C₇	—	4	1	no	—
619	C₂³×C₇	—	4	4	no	—
620	C₂³×C₇	—	4	2	no	—
621	C₂³×C₇	—	8	1	no	—
622	C₂³×C₇	—	8	1	no	—
623	C₂³×C₇	—	8	1	no	—
624	C₂³×C₇	—	8	1	no	—
625	C₂³×C₇	—	8	2	no	—
626	C₂³×C₇	—	8	2	no	—
627	C₂³×C₇	C₂²×D₄	1	2	yes	—
628	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
629	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
630	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
631	C₇×Q₈	—	2	2	no	—
632	C₇×Q₈	—	2	2	no	—
633	C₇×Q₈	—	2	1	no	—
634	C₇×Q₈	—	2	2	no	—
635	C₇×Q₈	—	2	1	no	—
636	C₇×Q₈	—	4	2	no	—
637	C₇×Q₈	—	8	2	no	—
638	C₇×D₄	—	2	4	no	—
639	C₇×D₄	—	2	4	no	—
640	C₇×D₄	—	2	2	no	—
641	C₇×D₄	—	2	2	no	—
642	C₇×D₄	—	2	1	no	—
643	C₇×D₄	—	2	2	no	—
644	C₇×D₄	—	2	1	no	—
645	C₇×D₄	—	2	2	no	—
646	C₇×D₄	—	4	2	no	—
647	C₇×D₄	—	4	2	no	—
648	C₇×D₄	—	4	4	no	—
649	C₇×D₄	—	4	4	no	—
650	C₇×D₄	—	4	4	no	—
651	C₇×D₄	—	4	4	no	—
652	C₇×D₄	—	4	4	no	—
653	C₇×D₄	—	4	2	no	—
654	C₇×D₄	—	4	2	no	—
655	C₇×D₄	—	8	1	no	—
656	C₇×D₄	—	8	2	no	—
657	C₇×D₄	—	8	1	no	—
658	C₇×D₄	—	8	2	no	—
659	C₇×D₄	—	8	2	no	—
660	C₇×D₄	C₂×#41	1	4	yes	—
661	C₂×C₄×C₇	—	2	2	no	—
662	C₂×C₄×C₇	—	2	2	no	—
663	C₂×C₄×C₇	—	2	2	no	—
664	C₂×C₄×C₇	—	2	1	no	—
665	C₂×C₄×C₇	—	2	1	no	—
666	C₂×C₄×C₇	—	2	2	no	—
667	C₂×C₄×C₇	—	2	1	no	—
668	C₂×C₄×C₇	—	2	2	no	—
669	C₂×C₄×C₇	—	2	1	no	—
670	C₂×C₄×C₇	—	2	1	no	—
671	C₂×C₄×C₇	—	2	1	no	—
672	C₂×C₄×C₇	—	2	1	no	—
673	C₂×C₄×C₇	—	2	1	no	—
674	C₂×C₄×C₇	—	2	1	no	—
675	C₂×C₄×C₇	—	2	1	no	—
676	C₂×C₄×C₇	—	2	2	no	—
677	C₂×C₄×C₇	—	2	2	no	—
678	C₂×C₄×C₇	—	2	1	no	—
679	C₂×C₄×C₇	—	4	4	no	—
680	C₂×C₄×C₇	—	4	4	no	—
681	C₂×C₄×C₇	—	4	4	no	—
682	C₂×C₄×C₇	—	4	2	no	—
683	C₂×C₄×C₇	—	4	2	no	—
684	C₂×C₄×C₇	—	4	2	no	—
685	C₂×C₄×C₇	—	8	2	no	—
686	C₂×C₄×C₇	—	8	2	no	—
687	C₂×C₄×C₇	—	8	2	no	—
688	C₂×C₄×C₇	—	8	2	no	—
689	C₂×C₄×C₇	—	8	1	no	—
690	C₂×C₄×C₇	—	8	1	no	—
691	C₂×C₄×C₇	—	8	2	no	—
692	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
693	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
694	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
695	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
696	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
697	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
698	C₂×C₄×C₇	C₂×#41	1	2	yes	—
699	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
700	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
701	C₇×C₈	—	2	1	no	—
702	C₇×C₈	—	2	1	no	—
703	C₇×C₈	—	2	1	no	—
704	C₇×C₈	—	2	1	no	—
705	C₇×C₈	—	2	2	no	—
706	C₇×C₈	—	2	2	no	—
707	H(5,𝔽₂)	—	2	4	no	—
708	H(5,𝔽₂)	—	4	2	no	—
709	C₂×#41	—	2	1	no	—
710	C₂×#41	—	2	2	no	—
711	C₂×#41	—	2	1	no	—
712	C₂×#41	—	2	1	no	—
713	C₂×#41	—	2	4	no	—
714	C₂×#41	—	4	2	no	—
715	C₂×#41	C₂³×C₇	1	1	yes	characteristic
716	C₂×#41	C₂³×C₇	1	2	yes	—
717	C₂×#41	C₂³×C₇	1	2	yes	—
718	C₂×#41	C₂³×C₇	1	2	yes	—
719	C₂×#41	C₂³×C₇	1	1	yes	characteristic
720	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
721	C₂²×D₄	—	2	1	no	—
722	C₂²×D₄	—	2	1	no	—
723	C₂²×D₄	—	2	2	no	—
724	C₂²×D₄	—	2	1	no	—
725	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
726	C₂²×D₄	C₂³×C₇	1	2	yes	—
727	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
728	C₂³×C₄	—	2	1	no	—
729	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
730	AGL(1,ℤ/8)	—	4	2	no	—
731	C₂×SD₁₆	—	4	2	no	—
732	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
735	C₂×D₈	—	2	4	no	—
736	C₂×D₈	C₂³×C₇	1	2	yes	—
737	C₂×D₈	C₂³×C₇	1	2	yes	—
738	C₂×D₈	C₂³×C₇	1	2	yes	—
739	#131	—	4	2	no	—
740	C₂×M₁₆	—	4	2	no	—
741	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
742	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
743	C₂×M₁₆	C₂³×C₇	1	2	yes	—
744	C₂×M₁₆	C₂³×C₇	1	2	yes	—
745	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
746	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
747	C₂²×C₈	C₂³×C₇	1	2	yes	—
748	C₂²×C₈	C₂³×C₇	1	2	yes	—
749	C₄⋊Q₈	—	2	1	no	—
750	C₄⋊Q₈	—	2	1	no	—
751	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
752	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
753	#127	—	2	1	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#125	—	2	1	no	—
757	#125	C₂³×C₇	1	2	yes	—
758	#124	—	2	1	no	—
759	#124	—	2	1	no	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	C₂³×C₇	1	2	yes	—
763	#123	—	2	2	no	—
764	#123	—	2	1	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	C₇×D₄	1	2	yes	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
782	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
784	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	C₇×D₄	1	1	yes	characteristic
797	#121	C₇×D₄	1	1	yes	characteristic
798	#121	C₂³×C₇	1	2	yes	—
799	#121	C₂³×C₇	1	2	yes	—
800	#121	C₂³×C₇	1	1	yes	characteristic
801	#121	C₂³×C₇	1	1	yes	characteristic
802	#121	C₂³×C₇	1	2	yes	—
803	#121	C₂³×C₇	1	2	yes	—
804	#120	—	2	1	no	—
805	#120	—	2	2	no	—
806	#120	—	2	2	no	—
807	#120	—	2	2	no	—
808	#120	C₇×D₄	1	2	yes	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	C₂³×C₇	1	2	yes	—
821	C₄×D₄	C₂³×C₇	1	2	yes	—
822	C₄×D₄	C₂³×C₇	1	2	yes	—
823	C₄×D₄	C₂³×C₇	1	2	yes	—
824	C₄×D₄	C₂³×C₇	1	2	yes	—
825	C₄×D₄	C₂³×C₇	1	2	yes	—
826	#117	—	2	1	no	—
827	#117	—	2	1	no	—
828	#117	—	2	2	no	—
829	#117	C₂³×C₇	1	1	yes	characteristic
830	#117	C₂³×C₇	1	1	yes	characteristic
831	#117	C₂³×C₇	1	1	yes	characteristic
832	#117	C₂³×C₇	1	1	yes	characteristic
833	#117	C₂³×C₇	1	1	yes	characteristic
834	#117	C₂³×C₇	1	2	yes	—
835	#117	C₂³×C₇	1	1	yes	characteristic
836	C₂×C₄⋊C₄	—	2	2	no	—
837	C₂×C₄⋊C₄	—	2	2	no	—
838	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
839	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
842	C₂×C₂²⋊C₄	—	2	1	no	—
843	C₂×C₂²⋊C₄	—	2	1	no	—
844	C₂×C₂²⋊C₄	—	2	2	no	—
845	C₂×C₂²⋊C₄	—	2	2	no	—
846	C₂×C₂²⋊C₄	—	2	2	no	—
847	C₂×C₂²⋊C₄	—	2	2	no	—
848	C₂×C₄²	—	2	1	no	—
849	#107	C₂³×C₇	1	1	yes	characteristic
850	#107	C₂³×C₇	1	1	yes	characteristic
851	#107	C₂³×C₇	1	1	yes	characteristic
852	#107	C₂³×C₇	1	1	yes	characteristic
853	#107	C₂³×C₇	1	2	yes	—
854	#106	C₂³×C₇	1	1	yes	characteristic
855	#106	C₂³×C₇	1	1	yes	characteristic
856	#106	C₂³×C₇	1	1	yes	characteristic
857	#106	C₂³×C₇	1	1	yes	characteristic
858	#106	C₂³×C₇	1	2	yes	—
859	C₄⋊C₈	C₂³×C₇	1	2	yes	—
860	C₄⋊C₈	C₂³×C₇	1	2	yes	—
861	#103	C₂³×C₇	1	2	yes	—
862	#103	C₂³×C₇	1	2	yes	—
863	#103	C₂³×C₇	1	1	yes	characteristic
864	#103	C₂³×C₇	1	1	yes	characteristic
865	#103	C₂³×C₇	1	1	yes	characteristic
866	#103	C₂³×C₇	1	1	yes	characteristic
867	#103	C₂³×C₇	1	2	yes	—
868	#103	C₂³×C₇	1	2	yes	—
869	#103	C₂³×C₇	1	2	yes	—
870	#103	C₂³×C₇	1	2	yes	—
871	#103	C₂³×C₇	1	2	yes	—
872	#102	C₂³×C₇	1	2	yes	—
873	#102	C₂³×C₇	1	2	yes	—
874	#102	C₂³×C₇	1	1	yes	characteristic
875	#102	C₂³×C₇	1	2	yes	—
876	#102	C₂³×C₇	1	2	yes	—
877	#102	C₂³×C₇	1	1	yes	characteristic
878	#102	C₂³×C₇	1	1	yes	characteristic
879	#102	C₂³×C₇	1	1	yes	characteristic
880	#102	C₂³×C₇	1	2	yes	—
881	#102	C₂³×C₇	1	2	yes	—
882	#102	C₂³×C₇	1	2	yes	—
883	#102	C₂³×C₇	1	2	yes	—
884	#102	C₂³×C₇	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
886	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
888	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
889	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
891	#97	C₂³×C₇	1	2	yes	—
892	C₄×C₈	C₂³×C₇	1	2	yes	—
893	C₂²×C₇	—	2	1	no	—
894	C₂²×C₇	—	2	1	no	—
895	C₂²×C₇	—	2	1	no	—
896	C₂²×C₇	—	2	1	no	—
897	C₂²×C₇	—	2	2	no	—
898	C₂²×C₇	—	2	1	no	—
899	C₂²×C₇	—	2	2	no	—
900	C₂²×C₇	—	2	1	no	—
901	C₂²×C₇	—	2	1	no	—
902	C₂²×C₇	—	2	1	no	—
903	C₂²×C₇	—	2	2	no	—
904	C₂²×C₇	—	2	4	no	—
905	C₂²×C₇	—	4	2	no	—
906	C₂²×C₇	—	4	2	no	—
907	C₂²×C₇	—	4	2	no	—
908	C₂²×C₇	—	4	1	no	—
909	C₂²×C₇	—	4	2	no	—
910	C₂²×C₇	—	4	1	no	—
911	C₂²×C₇	—	4	1	no	—
912	C₂²×C₇	—	4	2	no	—
913	C₂²×C₇	—	8	2	no	—
914	C₂²×C₇	—	8	4	no	—
915	C₂²×C₇	—	16	2	no	—
916	C₂²×C₇	—	16	4	no	—
917	C₂²×C₇	#546	1	2	yes	—
918	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
919	C₄×C₇	—	2	2	no	—
920	C₄×C₇	—	2	2	no	—
921	C₄×C₇	—	2	1	no	—
922	C₄×C₇	—	2	1	no	—
923	C₄×C₇	—	2	2	no	—
924	C₄×C₇	—	4	1	no	—
925	C₄×C₇	—	4	1	no	—
926	C₄×C₇	—	4	1	no	—
927	C₄×C₇	—	4	1	no	—
928	C₄×C₇	—	4	1	no	—
929	C₄×C₇	—	4	2	no	—
930	C₄×C₇	—	4	1	no	—
931	C₄×C₇	—	4	1	no	—
932	C₄×C₇	—	4	2	no	—
933	C₄×C₇	#546	1	2	yes	—
934	C₄×C₇	C₂²×#41	1	1	yes	characteristic
935	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
936	C₂⁴	—	2	1	no	—
937	C₂⁴	—	2	1	no	—
938	C₂⁴	—	2	2	no	—
939	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
940	#41	—	2	2	no	—
941	#41	—	2	2	no	—
942	#41	—	2	4	no	—
943	#41	—	2	4	no	—
944	#41	—	2	4	no	—
945	#41	—	2	2	no	—
946	#41	—	2	2	no	—
947	#41	—	4	2	no	—
948	#41	—	4	2	no	—
949	#41	—	4	2	no	—
950	#41	—	4	4	no	—
951	#41	—	4	4	no	—
952	#41	—	4	4	no	—
953	#41	—	8	4	no	—
954	C₂×Q₈	—	2	1	no	—
955	C₂×Q₈	—	2	2	no	—
956	C₂×Q₈	—	2	2	no	—
957	C₂×Q₈	—	2	2	no	—
958	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
959	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
960	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
961	C₂×D₄	—	2	4	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	1	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	1	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	1	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	4	2	no	—
979	C₂×D₄	—	4	4	no	—
980	C₂×D₄	—	4	8	no	—
981	C₂×D₄	—	4	4	no	—
982	C₂×D₄	—	8	2	no	—
983	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
984	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
985	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
986	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
987	C₂×D₄	C₇×#41	1	4	yes	complemented
988	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
989	C₂×D₄	C₂⁴×C₇	1	2	yes	—
990	C₂×D₄	C₂⁴×C₇	1	2	yes	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	2	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	1	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	2	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	4	4	no	—
1007	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1008	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1009	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1010	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1011	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
1012	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1014	SD₁₆	—	4	2	no	—
1015	SD₁₆	—	4	2	no	—
1016	SD₁₆	—	4	2	no	—
1017	D₈	—	2	4	no	—
1018	D₈	—	2	4	no	—
1019	D₈	—	4	2	no	—
1020	M₁₆	—	2	2	no	—
1021	M₁₆	—	2	2	no	—
1022	M₁₆	—	4	2	no	—
1023	M₁₆	—	4	2	no	—
1024	C₂×C₈	—	2	2	no	—
1025	C₂×C₈	—	2	2	no	—
1026	C₂×C₈	—	4	2	no	—
1027	C₂×C₈	—	4	2	no	—
1028	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1029	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1030	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1031	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1032	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1033	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1048	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1049	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1050	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1051	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1052	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1053	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1054	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1055	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1056	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1057	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	1	no	—
1067	C₂²⋊C₄	—	2	1	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1081	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1082	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1083	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1084	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1085	C₄²	—	2	1	no	—
1086	C₄²	—	2	1	no	—
1087	C₄²	—	2	1	no	—
1088	C₄²	—	2	1	no	—
1089	C₄²	—	2	2	no	—
1090	C₄²	—	2	1	no	—
1091	C₄²	C₂⁴×C₇	1	2	yes	—
1092	C₂×C₇	—	2	2	no	—
1093	C₂×C₇	—	4	1	no	—
1094	C₂×C₇	—	4	1	no	—
1095	C₂×C₇	—	4	2	no	—
1096	C₂×C₇	—	4	4	no	—
1097	C₂×C₇	—	8	2	no	—
1098	C₂×C₇	—	8	1	no	—
1099	C₂×C₇	C₂×#546	1	1	yes	characteristic
1100	C₂×C₇	#3584	1	1	yes	characteristic
1101	C₂×C₇	#3585	1	1	yes	characteristic
1102	C₂³	—	2	2	no	—
1103	C₂³	—	2	2	no	—
1104	C₂³	—	2	4	no	—
1105	C₂³	—	2	2	no	—
1106	C₂³	—	2	1	no	—
1107	C₂³	—	4	1	no	—
1108	C₂³	—	4	1	no	—
1109	C₂³	—	4	4	no	—
1110	C₂³	—	4	2	no	—
1111	C₂³	—	8	1	no	—
1112	C₂³	—	8	1	no	—
1113	C₂³	—	8	1	no	—
1114	C₂³	—	8	1	no	—
1115	C₂³	—	8	2	no	—
1116	C₂³	—	8	2	no	—
1117	C₂³	C₂²×C₇×D₄	1	2	yes	—
1118	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1119	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1120	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1121	Q₈	—	2	2	no	—
1122	Q₈	—	2	2	no	—
1123	Q₈	—	2	1	no	—
1124	Q₈	—	2	2	no	—
1125	Q₈	—	2	1	no	—
1126	Q₈	—	4	2	no	—
1127	Q₈	—	8	2	no	—
1128	D₄	—	2	4	no	—
1129	D₄	—	2	2	no	—
1130	D₄	—	2	1	no	—
1131	D₄	—	2	2	no	—
1132	D₄	—	2	1	no	—
1133	D₄	—	2	2	no	—
1134	D₄	—	2	4	no	—
1135	D₄	—	2	2	no	—
1136	D₄	—	4	2	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	4	no	—
1139	D₄	—	4	4	no	—
1140	D₄	—	4	4	no	—
1141	D₄	—	4	4	no	—
1142	D₄	—	4	4	no	—
1143	D₄	—	4	2	no	—
1144	D₄	—	4	2	no	—
1145	D₄	—	8	1	no	—
1146	D₄	—	8	2	no	—
1147	D₄	—	8	1	no	—
1148	D₄	—	8	2	no	—
1149	D₄	—	8	2	no	—
1150	D₄	C₂×C₇×#41	1	4	yes	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	2	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	4	4	no	—
1170	C₂×C₄	—	4	4	no	—
1171	C₂×C₄	—	4	4	no	—
1172	C₂×C₄	—	4	2	no	—
1173	C₂×C₄	—	4	2	no	—
1174	C₂×C₄	—	4	2	no	—
1175	C₂×C₄	—	8	2	no	—
1176	C₂×C₄	—	8	2	no	—
1177	C₂×C₄	—	8	2	no	—
1178	C₂×C₄	—	8	2	no	—
1179	C₂×C₄	—	8	1	no	—
1180	C₂×C₄	—	8	1	no	—
1181	C₂×C₄	—	8	2	no	—
1182	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1183	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1184	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1185	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1186	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1187	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1188	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1189	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1190	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1191	C₈	—	2	1	no	—
1192	C₈	—	2	1	no	—
1193	C₈	—	2	1	no	—
1194	C₈	—	2	1	no	—
1195	C₈	—	2	2	no	—
1196	C₈	—	2	2	no	—
1197	C₇	#61187	1	1	yes	characteristic, direct product factor, Sylow
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	1	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	1	no	—
1207	C₂²	—	2	1	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	2	4	no	—
1210	C₂²	—	4	2	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	2	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	2	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	8	2	no	—
1219	C₂²	—	8	4	no	—
1220	C₂²	—	16	2	no	—
1221	C₂²	—	16	4	no	—
1222	C₂²	C₇×#546	1	2	yes	—
1223	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1224	C₄	—	2	2	no	—
1225	C₄	—	2	2	no	—
1226	C₄	—	2	1	no	—
1227	C₄	—	2	1	no	—
1228	C₄	—	2	2	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	2	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	2	no	—
1238	C₄	C₇×#546	1	2	yes	—
1239	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1240	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1241	C₂	—	2	2	no	—
1242	C₂	—	4	1	no	—
1243	C₂	—	4	1	no	—
1244	C₂	—	4	2	no	—
1245	C₂	—	4	4	no	—
1246	C₂	—	8	1	no	—
1247	C₂	—	8	2	no	—
1248	C₂	C₂×C₇×#546	1	1	yes	characteristic
1249	C₂	C₇×#3584	1	1	yes	characteristic
1250	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×#3494	C₂	semidirect
2. C₇×#3485	C₂	semidirect
3. C₇×#3330	C₂	semidirect
4. C₇×#3322	C₂	semidirect
5. C₇×#3319	C₂	semidirect
6. C₇×#3307	C₂	semidirect
7. C₇×#3307	C₂	semidirect
8. C₇×#3306	C₂	semidirect
9. C₇×#3303	C₂	semidirect
10. C₇×#3297	C₂	semidirect
11. C₇×#3137	C₂	semidirect
12. C₇×#3097	C₂	semidirect
13. C₇×#3091	C₂	semidirect
14. C₇×#3081	C₂	semidirect
15. C₇×#3057	C₂	semidirect
16. C₇×#3055	C₂	semidirect
17. C₇×#3042	C₂	semidirect
18. C₇×#3008	C₂	semidirect
19. C₂×C₇×#449	C₂	semidirect
20. C₇×#2948	C₂	semidirect
21. C₇×#2933	C₂	semidirect
22. C₇×#2897	C₂	semidirect
23. C₇×#2896	C₂	semidirect
27. C₂²×C₇×SD₁₆	C₂²	semidirect
30. C₂²×C₇×M₁₆	C₂²	semidirect
31. C₇×#555	C₂²	semidirect
32. C₇×#553	C₂²	semidirect
33. C₇×#553	C₂²	semidirect
37. C₇×#547	C₂²	semidirect
38. C₇×#547	C₂²	semidirect
39. C₇×#547	C₂²	semidirect
43. C₇×#546	C₂²	semidirect
44. C₇×#546	C₂²	semidirect
45. C₇×#544	C₂²	semidirect
57. C₂×C₇×#121	C₂²	semidirect
60. C₇×#518	C₂²	semidirect
61. C₂×C₇×#117	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
67. C₇×#485	C₂²	semidirect
68. C₇×#485	C₂²	semidirect
69. C₇×#485	C₂²	semidirect
70. C₇×#484	C₂²	semidirect
71. C₇×#484	C₂²	semidirect
72. C₇×#483	C₂²	semidirect
73. C₇×#483	C₂²	semidirect
74. C₇×#482	C₂²	semidirect
75. C₇×#482	C₂²	semidirect
76. C₇×#481	C₂²	semidirect
77. C₇×#480	C₂²	semidirect
78. C₇×#478	C₂²	semidirect
79. C₇×#478	C₂²	semidirect
80. C₇×#476	C₂²	semidirect
81. C₇×#474	C₂²	semidirect
82. C₇×#469	C₂²	semidirect
83. C₇×#468	C₂²	semidirect
84. C₇×#468	C₂²	semidirect
85. C₇×#468	C₂²	semidirect
86. C₇×#466	C₂²	semidirect
87. C₇×#465	C₂²	semidirect
88. C₇×#465	C₂²	semidirect
89. C₇×#465	C₂²	semidirect
90. C₇×#463	C₂²	semidirect
91. C₇×#463	C₂²	semidirect
92. C₇×#461	C₂²	semidirect
93. C₇×#461	C₂²	semidirect
94. C₇×#449	C₂²	semidirect
95. C₇×#449	C₂²	semidirect
96. C₇×#449	C₂²	semidirect
97. C₇×#449	C₂²	semidirect
98. C₇×#449	C₂²	semidirect
99. C₇×#449	C₂²	semidirect
100. C₇×#447	C₂²	semidirect
101. C₇×#447	C₂²	semidirect
102. C₇×#442	C₂²	semidirect
103. C₇×#442	C₂²	semidirect
104. C₄×C₇×D₈	C₂²	semidirect
105. C₄×C₇×D₈	C₂²	semidirect
106. C₇×#436	C₂²	semidirect
107. C₇×#435	C₂²	semidirect
108. C₇×#435	C₂²	semidirect
109. C₇×C₈×D₄	C₂²	semidirect
110. C₇×#428	C₂²	semidirect
111. C₇×#427	C₂²	semidirect
112. C₇×#427	C₂²	semidirect
113. C₇×#424	C₂²	semidirect
114. C₇×#419	C₂²	semidirect
115. C₇×#419	C₂²	semidirect
118. C₇×#418	C₂²	semidirect
119. C₇×#418	C₂²	semidirect
121. C₇×#417	C₂²	semidirect
122. C₇×#417	C₂²	semidirect
123. C₇×#417	C₂²	semidirect
126. C₇×#416	C₂²	semidirect
127. C₇×#416	C₂²	semidirect
128. C₇×#416	C₂²	semidirect
129. C₂×C₇×#103	C₂²	semidirect
131. C₂×C₇×#102	C₂²	semidirect
133. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
134. C₇×#405	C₂²	semidirect
135. #61187	C₇	direct (N × H)
322. #3494	C₂×C₇	semidirect
323. #3485	C₂×C₇	semidirect
324. #3330	C₂×C₇	semidirect
325. #3322	C₂×C₇	semidirect
326. #3319	C₂×C₇	semidirect
327. #3307	C₂×C₇	semidirect
328. #3307	C₂×C₇	semidirect
329. #3306	C₂×C₇	semidirect
330. #3303	C₂×C₇	semidirect
331. #3297	C₂×C₇	semidirect
332. #3137	C₂×C₇	semidirect
333. #3097	C₂×C₇	semidirect
334. #3091	C₂×C₇	semidirect
335. #3081	C₂×C₇	semidirect
336. #3057	C₂×C₇	semidirect
337. #3055	C₂×C₇	semidirect
338. #3042	C₂×C₇	semidirect
339. #3008	C₂×C₇	semidirect
340. C₂×#449	C₂×C₇	semidirect
341. #2948	C₂×C₇	semidirect
342. #2933	C₂×C₇	semidirect
343. #2897	C₂×C₇	semidirect
344. #2896	C₂×C₇	semidirect
396. C₂×C₇×D₄	#41	semidirect
504. C₂²×SD₁₆	C₂²×C₇	semidirect
507. C₂²×M₁₆	C₂²×C₇	semidirect
508. #555	C₂²×C₇	semidirect
509. #553	C₂²×C₇	semidirect
510. #553	C₂²×C₇	semidirect
514. #547	C₂²×C₇	semidirect
515. #547	C₂²×C₇	semidirect
516. #547	C₂²×C₇	semidirect
520. #546	C₂²×C₇	semidirect
521. #546	C₂²×C₇	semidirect
522. #544	C₂²×C₇	semidirect
534. C₂×#121	C₂²×C₇	semidirect
537. #518	C₂²×C₇	semidirect
538. C₂×#117	C₂²×C₇	semidirect
539. #491	C₂²×C₇	semidirect
540. #489	C₂²×C₇	semidirect
541. #488	C₂²×C₇	semidirect
542. #487	C₂²×C₇	semidirect
543. #485	C₂²×C₇	semidirect
544. #485	C₂²×C₇	semidirect
545. #485	C₂²×C₇	semidirect
546. #485	C₂²×C₇	semidirect
547. #484	C₂²×C₇	semidirect
548. #484	C₂²×C₇	semidirect
549. #483	C₂²×C₇	semidirect
550. #483	C₂²×C₇	semidirect
551. #482	C₂²×C₇	semidirect
552. #482	C₂²×C₇	semidirect
553. #481	C₂²×C₇	semidirect
554. #480	C₂²×C₇	semidirect
555. #478	C₂²×C₇	semidirect
556. #478	C₂²×C₇	semidirect
557. #476	C₂²×C₇	semidirect
558. #474	C₂²×C₇	semidirect
559. #469	C₂²×C₇	semidirect
560. #468	C₂²×C₇	semidirect
561. #468	C₂²×C₇	semidirect
562. #468	C₂²×C₇	semidirect
563. #466	C₂²×C₇	semidirect
564. #465	C₂²×C₇	semidirect
565. #465	C₂²×C₇	semidirect
566. #465	C₂²×C₇	semidirect
567. #463	C₂²×C₇	semidirect
568. #463	C₂²×C₇	semidirect
569. #461	C₂²×C₇	semidirect
570. #461	C₂²×C₇	semidirect
571. #449	C₂²×C₇	semidirect
572. #449	C₂²×C₇	semidirect
573. #449	C₂²×C₇	semidirect
574. #449	C₂²×C₇	semidirect
575. #449	C₂²×C₇	semidirect
576. #449	C₂²×C₇	semidirect
577. #447	C₂²×C₇	semidirect
578. #447	C₂²×C₇	semidirect
579. #442	C₂²×C₇	semidirect
580. #442	C₂²×C₇	semidirect
581. C₄×D₈	C₂²×C₇	semidirect
582. C₄×D₈	C₂²×C₇	semidirect
583. #436	C₂²×C₇	semidirect
584. #435	C₂²×C₇	semidirect
585. #435	C₂²×C₇	semidirect
586. C₈×D₄	C₂²×C₇	semidirect
587. #428	C₂²×C₇	semidirect
588. #427	C₂²×C₇	semidirect
589. #427	C₂²×C₇	semidirect
590. #424	C₂²×C₇	semidirect
591. #419	C₂²×C₇	semidirect
592. #419	C₂²×C₇	semidirect
595. #418	C₂²×C₇	semidirect
596. #418	C₂²×C₇	semidirect
598. #417	C₂²×C₇	semidirect
599. #417	C₂²×C₇	semidirect
600. #417	C₂²×C₇	semidirect
603. #416	C₂²×C₇	semidirect
604. #416	C₂²×C₇	semidirect
605. #416	C₂²×C₇	semidirect
606. C₂×#103	C₂²×C₇	semidirect
608. C₂×#102	C₂²×C₇	semidirect
610. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
611. #405	C₂²×C₇	semidirect
987. C₂×D₄	C₇×#41	semidirect
1197. C₇	#61187	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×#3485	2
C₇×#3330	2
C₇×#3322	2
C₇×#3319	2
C₇×#3307	2
C₇×#3306	2
C₇×#3303	2
C₇×#3297	2
C₇×#3137	2
C₇×#3097	2
C₇×#3091	2
C₇×#3081	2
C₇×#3057	2
C₇×#3055	2
C₇×#3042	2
C₇×#3008	2
C₂×C₇×#449	2
C₇×#2948	2
C₇×#2933	2
C₇×#2897	2
C₇×#2896	2
#61187	7

Subgroups — C7×#61187 #13238403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61187 #13238403