Subgroups — C₇×#61184 #13238400

Order 1792.

2226 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3484	C₂	1	1	yes	maximal, characteristic
3	C₇×#3324	C₂	1	2	yes	maximal, complemented
4	C₇×#3323	C₂	1	2	yes	maximal, complemented
5	C₇×#3314	C₂	1	2	yes	maximal, complemented
6	C₇×#3311	C₂	1	2	yes	maximal, complemented
7	C₇×#3310	C₂	1	2	yes	maximal, complemented
8	C₇×#3310	C₂	1	2	yes	maximal, complemented
9	C₇×#3296	C₂	1	2	yes	maximal, complemented
10	C₇×#3295	C₂	1	2	yes	maximal, complemented
11	C₇×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3096	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×#3056	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3043	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3009	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₇×#450	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2949	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	C₂×C₇×#418	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
26	C₂×C₇×#137	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₇×#556	C₂²	1	2	yes	complemented
32	C₇×#554	C₂²	1	2	yes	complemented
33	C₇×#552	—	2	2	no	—
34	C₇×#552	C₂²	1	2	yes	complemented
35	C₇×#552	C₂²	1	2	yes	complemented
36	C₇×#551	—	2	2	no	—
37	C₇×#546	—	2	1	no	—
38	C₇×#546	—	2	1	no	—
39	C₇×#546	C₂²	1	2	yes	—
40	C₇×#546	C₂²	1	2	yes	—
41	C₇×D₄²	—	2	1	no	—
42	C₇×D₄²	—	2	1	no	—
43	C₇×D₄²	C₂²	1	2	yes	—
44	C₇×D₄²	C₂²	1	2	yes	—
45	C₇×#544	C₂²	1	1	yes	characteristic, complemented
46	C₇×#542	—	2	1	no	—
47	C₇×#541	—	2	1	no	—
48	C₇×#536	C₂²	1	1	yes	characteristic, complemented
49	C₇×#535	C₂²	1	1	yes	characteristic
50	C₇×#535	C₂²	1	1	yes	characteristic
51	C₇×#534	—	2	2	no	—
52	C₇×#533	—	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×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₇×#120	—	2	2	no	—
58	C₇×#520	C₂²	1	1	yes	characteristic, complemented
59	C₇×#519	C₂²	1	1	yes	characteristic, complemented
60	C₇×#518	C₂²	1	1	yes	characteristic
61	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
62	C₇×#490	C₂²	1	2	yes	complemented
63	C₇×#489	C₂²	1	2	yes	complemented
64	C₇×#488	C₂²	1	2	yes	complemented
65	C₇×#486	C₂²	1	2	yes	complemented
66	C₇×#485	C₂²	1	1	yes	characteristic, complemented
67	C₇×#485	C₂²	1	1	yes	characteristic, complemented
68	C₇×#484	C₂²	1	1	yes	characteristic, complemented
69	C₇×#483	C₂²	1	1	yes	characteristic, complemented
70	C₇×#482	C₂²	1	1	yes	characteristic, complemented
71	C₇×#482	C₂²	1	1	yes	characteristic, complemented
72	C₇×#482	C₂²	1	2	yes	complemented
73	C₇×#482	C₂²	1	2	yes	complemented
74	C₇×#481	C₂²	1	1	yes	characteristic, complemented
75	C₇×#481	C₂²	1	2	yes	complemented
76	C₇×#480	C₂²	1	1	yes	characteristic, complemented
77	C₇×#480	C₂²	1	2	yes	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×#470	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×#467	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×#464	C₂²	1	2	yes	complemented
91	C₇×#464	C₂²	1	2	yes	complemented
92	C₇×#460	C₂²	1	2	yes	complemented
93	C₇×#460	C₂²	1	2	yes	complemented
94	C₇×#452	C₂²	1	2	yes	complemented
95	C₇×#452	C₂²	1	2	yes	complemented
96	C₇×#450	C₂²	1	2	yes	complemented
97	C₇×#450	C₂²	1	2	yes	complemented
98	C₇×#450	C₂²	1	2	yes	complemented
99	C₇×#450	C₂²	1	2	yes	complemented
100	C₇×#450	C₂²	1	2	yes	complemented
101	C₇×#450	C₂²	1	2	yes	complemented
102	C₇×#440	C₂²	1	2	yes	complemented
103	C₇×#440	C₂²	1	2	yes	complemented
104	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
105	C₄×C₇×SD₁₆	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×#418	C₂²	1	1	yes	characteristic
116	C₇×#418	C₂²	1	1	yes	characteristic
117	C₇×#418	C₂²	1	1	yes	characteristic, complemented
118	C₇×#418	C₂²	1	2	yes	complemented
119	C₇×#418	C₂²	1	2	yes	complemented
120	C₇×#418	C₂²	1	1	yes	characteristic, complemented
121	C₇×#418	C₂²	1	2	yes	complemented
122	C₇×#417	C₂²	1	2	yes	complemented
123	C₇×#417	C₂²	1	1	yes	characteristic, complemented
124	C₇×#416	C₂²	1	2	yes	complemented
125	C₇×#416	C₂²	1	1	yes	characteristic, complemented
126	C₇×#416	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₇×#102	C₂²	1	1	yes	characteristic
128	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₇×#102	C₂²	1	2	yes	complemented
130	C₂×C₇×#102	C₂²	1	2	yes	complemented
131	C₂×C₇×#102	C₂²	1	2	yes	complemented
132	C₇×#408	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
134	C₇×#405	C₂²	1	1	yes	characteristic, complemented
135	#61184	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂⁵×C₇	—	2	1	no	—
137	C₇×H(5,𝔽₂)	—	2	4	no	—
138	C₇×H(5,𝔽₂)	—	4	2	no	—
139	C₂×C₇×#41	—	2	1	no	—
140	C₂×C₇×#41	C₂³	1	1	yes	characteristic
141	C₂×C₇×#41	C₂³	1	2	yes	—
142	C₂×C₇×#41	C₂³	1	1	yes	characteristic
143	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
144	C₂²×C₇×D₄	—	2	4	no	—
145	C₂²×C₇×D₄	—	2	2	no	—
146	C₂²×C₇×D₄	—	2	1	no	—
147	C₂²×C₇×D₄	—	2	2	no	—
148	C₂²×C₇×D₄	—	2	2	no	—
149	C₂²×C₇×D₄	—	2	1	no	—
150	C₂²×C₇×D₄	—	2	1	no	—
151	C₂²×C₇×D₄	—	2	1	no	—
152	C₂²×C₇×D₄	—	4	2	no	—
153	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
154	C₂²×C₇×D₄	C₂³	1	2	yes	—
155	C₂²×C₇×D₄	C₂³	1	2	yes	—
156	C₂²×C₇×D₄	C₂³	1	2	yes	—
157	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
158	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
159	C₇×#137	—	4	2	no	—
160	C₂×C₇×Q₁₆	C₂³	1	2	yes	complemented
161	C₂×C₇×SD₁₆	—	2	4	no	—
162	C₂×C₇×SD₁₆	—	4	2	no	—
163	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
165	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
166	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
167	C₂×C₇×SD₁₆	C₂³	1	2	yes	complemented
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	complemented
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	complemented
178	C₇×C₄⋊Q₈	—	2	1	no	—
179	C₇×C₄⋊Q₈	—	2	1	no	—
180	C₇×C₄⋊Q₈	C₂³	1	2	yes	complemented
181	C₇×#127	—	2	1	no	—
182	C₇×#127	C₂³	1	2	yes	—
183	C₇×#126	—	2	2	no	—
184	C₇×#126	—	2	2	no	—
185	C₇×#126	—	2	2	no	—
186	C₇×#126	—	2	2	no	—
187	C₇×#125	—	2	1	no	—
188	C₇×#125	—	2	2	no	—
189	C₇×#125	—	2	2	no	—
190	C₇×#125	—	2	2	no	—
191	C₇×#125	C₂³	1	2	yes	complemented
192	C₇×#124	—	2	1	no	—
193	C₇×#124	—	2	1	no	—
194	C₇×#124	—	2	2	no	—
195	C₇×#124	C₂³	1	2	yes	—
196	C₇×#123	—	2	2	no	—
197	C₇×#123	—	2	2	no	—
198	C₇×#123	—	2	2	no	—
199	C₇×#123	—	2	1	no	—
200	C₇×#123	—	2	2	no	—
201	C₇×#123	—	2	2	no	—
202	C₇×#123	D₄	1	2	yes	—
203	C₇×C₂²⋊Q₈	—	2	1	no	—
204	C₇×C₂²⋊Q₈	—	2	1	no	—
205	C₇×C₂²⋊Q₈	—	2	2	no	—
206	C₇×C₂²⋊Q₈	—	2	2	no	—
207	C₇×C₂²⋊Q₈	—	2	2	no	—
208	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₇×C₂²⋊Q₈	C₂³	1	2	yes	complemented
215	C₇×C₂²⋊Q₈	C₂³	1	2	yes	complemented
216	C₇×#121	—	2	2	no	—
217	C₇×#121	—	2	2	no	—
218	C₇×#121	—	2	1	no	—
219	C₇×#121	—	2	1	no	—
220	C₇×#121	—	2	2	no	—
221	C₇×#121	—	2	2	no	—
222	C₇×#121	D₄	1	1	yes	characteristic
223	C₇×#121	D₄	1	1	yes	characteristic
224	C₇×#121	C₂³	1	1	yes	characteristic
225	C₇×#121	C₂³	1	2	yes	—
226	C₇×#121	C₂³	1	2	yes	—
227	C₇×#121	C₂³	1	1	yes	characteristic
228	C₇×#120	—	2	1	no	—
229	C₇×#120	—	2	2	no	—
230	C₇×#120	—	2	2	no	—
231	C₇×#120	—	2	2	no	—
232	C₇×#120	—	2	2	no	—
233	C₇×#120	—	2	2	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×Q₈	—	2	1	no	—
240	C₄×C₇×Q₈	—	2	1	no	—
241	C₄×C₇×Q₈	—	2	2	no	—
242	C₄×C₇×Q₈	C₂³	1	2	yes	complemented
243	C₄×C₇×Q₈	C₂³	1	2	yes	complemented
244	C₄×C₇×D₄	—	2	1	no	—
245	C₄×C₇×D₄	—	2	2	no	—
246	C₄×C₇×D₄	—	2	2	no	—
247	C₄×C₇×D₄	—	2	1	no	—
248	C₄×C₇×D₄	—	2	1	no	—
249	C₄×C₇×D₄	—	2	1	no	—
250	C₄×C₇×D₄	—	2	1	no	—
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	—	2	2	no	—
259	C₇×#117	—	2	2	no	—
260	C₇×#117	C₂³	1	1	yes	characteristic
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	C₇×#117	C₂³	1	1	yes	characteristic
266	C₇×#117	C₂³	1	2	yes	complemented
267	C₂×C₇×C₄⋊C₄	—	2	1	no	—
268	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	complemented
272	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₇×C₂²⋊C₄	—	2	1	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	complemented
279	C₇×#107	C₂³	1	1	yes	characteristic, complemented
280	C₇×#107	C₂³	1	1	yes	characteristic, complemented
281	C₇×#107	C₂³	1	1	yes	characteristic, complemented
282	C₇×#107	C₂³	1	1	yes	characteristic, complemented
283	C₇×#106	C₂³	1	2	yes	complemented
284	C₇×#106	C₂³	1	1	yes	characteristic, complemented
285	C₇×#106	C₂³	1	1	yes	characteristic, complemented
286	C₇×#106	C₂³	1	1	yes	characteristic, complemented
287	C₇×#106	C₂³	1	1	yes	characteristic, complemented
288	C₇×C₄⋊C₈	C₂³	1	2	yes	complemented
289	C₇×C₄⋊C₈	C₂³	1	2	yes	complemented
290	C₇×#103	C₂³	1	2	yes	complemented
291	C₇×#103	C₂³	1	2	yes	complemented
292	C₇×#103	C₂³	1	2	yes	complemented
293	C₇×#103	C₂³	1	1	yes	characteristic, complemented
294	C₇×#103	C₂³	1	1	yes	characteristic, complemented
295	C₇×#103	C₂³	1	1	yes	characteristic, complemented
296	C₇×#103	C₂³	1	1	yes	characteristic, complemented
297	C₇×#102	C₂³	1	2	yes	—
298	C₇×#102	C₂³	1	2	yes	—
299	C₇×#102	C₂³	1	2	yes	—
300	C₇×#102	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	2	yes	—
309	C₇×#102	C₂³	1	2	yes	complemented
310	C₇×#102	C₂³	1	1	yes	characteristic, complemented
311	C₇×#102	C₂³	1	1	yes	characteristic, complemented
312	C₇×#102	C₂³	1	1	yes	characteristic, complemented
313	C₇×#102	C₂³	1	1	yes	characteristic, complemented
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	complemented
319	C₇×C₂²⋊C₈	C₂³	1	2	yes	complemented
320	C₇×#97	C₂³	1	2	yes	complemented
321	C₄×C₇×C₈	C₂³	1	2	yes	complemented
322	#3495	C₂×C₇	1	1	yes	characteristic, complemented
323	#3484	C₂×C₇	1	1	yes	characteristic
324	#3324	C₂×C₇	1	2	yes	complemented
325	#3323	C₂×C₇	1	2	yes	complemented
326	#3314	C₂×C₇	1	2	yes	complemented
327	#3311	C₂×C₇	1	2	yes	complemented
328	#3310	C₂×C₇	1	2	yes	complemented
329	#3310	C₂×C₇	1	2	yes	complemented
330	#3296	C₂×C₇	1	2	yes	complemented
331	#3295	C₂×C₇	1	2	yes	complemented
332	#3136	C₂×C₇	1	1	yes	characteristic, complemented
333	#3096	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	#3056	C₂×C₇	1	1	yes	characteristic, complemented
338	#3043	C₂×C₇	1	1	yes	characteristic, complemented
339	#3009	C₂×C₇	1	1	yes	characteristic, complemented
340	C₂×#450	C₂×C₇	1	1	yes	characteristic, complemented
341	#2949	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	C₂×#418	C₂×C₇	1	1	yes	characteristic, complemented
345	C₂⁴×C₇	—	2	1	no	—
346	C₂⁴×C₇	—	2	2	no	—
347	C₂⁴×C₇	—	2	2	no	—
348	C₂⁴×C₇	—	2	1	no	—
349	C₂⁴×C₇	—	2	2	no	—
350	C₂⁴×C₇	—	4	4	no	—
351	C₂⁴×C₇	—	8	2	no	—
352	C₂⁴×C₇	—	8	2	no	—
353	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
354	C₇×#41	—	2	2	no	—
355	C₇×#41	—	2	2	no	—
356	C₇×#41	—	2	4	no	—
357	C₇×#41	—	2	2	no	—
358	C₇×#41	—	2	2	no	—
359	C₇×#41	—	4	2	no	—
360	C₇×#41	—	4	4	no	—
361	C₂×C₇×Q₈	—	2	1	no	—
362	C₂×C₇×Q₈	—	2	2	no	—
363	C₂×C₇×Q₈	—	2	2	no	—
364	C₂×C₇×Q₈	—	2	2	no	—
365	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
366	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
367	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
368	C₂×C₇×D₄	—	2	4	no	—
369	C₂×C₇×D₄	—	2	4	no	—
370	C₂×C₇×D₄	—	2	4	no	—
371	C₂×C₇×D₄	—	2	1	no	—
372	C₂×C₇×D₄	—	2	1	no	—
373	C₂×C₇×D₄	—	2	1	no	—
374	C₂×C₇×D₄	—	2	2	no	—
375	C₂×C₇×D₄	—	2	2	no	—
376	C₂×C₇×D₄	—	2	2	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	2	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	2	no	—
389	C₂×C₇×D₄	—	4	2	no	—
390	C₂×C₇×D₄	—	4	4	no	—
391	C₂×C₇×D₄	—	4	4	no	—
392	C₂×C₇×D₄	—	4	4	no	—
393	C₂×C₇×D₄	—	4	4	no	—
394	C₂×C₇×D₄	—	4	8	no	—
395	C₂×C₇×D₄	—	8	4	no	—
396	C₂×C₇×D₄	—	8	4	no	—
397	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
398	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
399	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
400	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
401	C₂×C₇×D₄	#41	1	4	yes	—
402	C₂×C₇×D₄	C₂⁴	1	2	yes	—
403	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
404	C₂×C₇×D₄	C₂⁴	1	2	yes	—
405	C₂²×C₄×C₇	—	2	2	no	—
406	C₂²×C₄×C₇	—	2	2	no	—
407	C₂²×C₄×C₇	—	2	1	no	—
408	C₂²×C₄×C₇	—	2	1	no	—
409	C₂²×C₄×C₇	—	2	1	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	1	no	—
414	C₂²×C₄×C₇	—	2	2	no	—
415	C₂²×C₄×C₇	—	2	2	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	1	yes	characteristic
421	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
422	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
423	C₇×Q₁₆	—	4	2	no	—
424	C₇×SD₁₆	—	2	4	no	—
425	C₇×SD₁₆	—	2	4	no	—
426	C₇×SD₁₆	—	4	2	no	—
427	C₇×SD₁₆	—	4	2	no	—
428	C₇×SD₁₆	—	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	2	no	—
444	C₇×C₄⋊C₄	—	2	2	no	—
445	C₇×C₄⋊C₄	—	2	1	no	—
446	C₇×C₄⋊C₄	—	2	1	no	—
447	C₇×C₄⋊C₄	—	2	1	no	—
448	C₇×C₄⋊C₄	—	2	2	no	—
449	C₇×C₄⋊C₄	—	2	2	no	—
450	C₇×C₄⋊C₄	—	2	2	no	—
451	C₇×C₄⋊C₄	—	2	2	no	—
452	C₇×C₄⋊C₄	—	2	2	no	—
453	C₇×C₄⋊C₄	—	2	2	no	—
454	C₇×C₄⋊C₄	—	2	1	no	—
455	C₇×C₄⋊C₄	—	2	1	no	—
456	C₇×C₄⋊C₄	—	2	2	no	—
457	C₇×C₄⋊C₄	—	2	2	no	—
458	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
459	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
460	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
461	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
462	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
463	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
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×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
468	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	1	no	—
473	C₇×C₂²⋊C₄	—	2	1	no	—
474	C₇×C₂²⋊C₄	—	2	1	no	—
475	C₇×C₂²⋊C₄	—	2	1	no	—
476	C₇×C₂²⋊C₄	—	2	2	no	—
477	C₇×C₂²⋊C₄	—	2	2	no	—
478	C₇×C₂²⋊C₄	—	2	2	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	1	no	—
488	C₇×C₂²⋊C₄	—	2	1	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	2	no	—
500	C₄²×C₇	—	2	2	no	—
501	C₄²×C₇	—	2	1	no	—
502	C₄²×C₇	C₂⁴	1	2	yes	—
503	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
504	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
505	C₂×#137	C₂²×C₇	1	1	yes	characteristic, complemented
506	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
507	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
508	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
509	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
510	#556	C₂²×C₇	1	2	yes	complemented
511	#554	C₂²×C₇	1	2	yes	complemented
512	#552	—	2	2	no	—
513	#552	C₂²×C₇	1	2	yes	complemented
514	#552	C₂²×C₇	1	2	yes	complemented
515	#551	—	2	2	no	—
516	#546	—	2	1	no	—
517	#546	—	2	1	no	—
518	#546	C₂²×C₇	1	2	yes	—
519	#546	C₂²×C₇	1	2	yes	—
520	D₄²	—	2	1	no	—
521	D₄²	—	2	1	no	—
522	D₄²	C₂²×C₇	1	2	yes	—
523	D₄²	C₂²×C₇	1	2	yes	—
524	#544	C₂²×C₇	1	1	yes	characteristic, complemented
525	#542	—	2	1	no	—
526	#541	—	2	1	no	—
527	#536	C₂²×C₇	1	1	yes	characteristic, complemented
528	#535	C₂²×C₇	1	1	yes	characteristic
529	#535	C₂²×C₇	1	1	yes	characteristic
530	#534	—	2	2	no	—
531	#533	—	2	1	no	—
532	#529	—	2	1	no	—
533	#525	C₂²×C₇	1	1	yes	characteristic
534	#525	C₂²×C₇	1	1	yes	characteristic
535	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
536	C₂×#120	—	2	2	no	—
537	#520	C₂²×C₇	1	1	yes	characteristic, complemented
538	#519	C₂²×C₇	1	1	yes	characteristic, complemented
539	#518	C₂²×C₇	1	1	yes	characteristic
540	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
541	#490	C₂²×C₇	1	2	yes	complemented
542	#489	C₂²×C₇	1	2	yes	complemented
543	#488	C₂²×C₇	1	2	yes	complemented
544	#486	C₂²×C₇	1	2	yes	complemented
545	#485	C₂²×C₇	1	1	yes	characteristic, complemented
546	#485	C₂²×C₇	1	1	yes	characteristic, complemented
547	#484	C₂²×C₇	1	1	yes	characteristic, complemented
548	#483	C₂²×C₇	1	1	yes	characteristic, complemented
549	#482	C₂²×C₇	1	1	yes	characteristic, complemented
550	#482	C₂²×C₇	1	1	yes	characteristic, complemented
551	#482	C₂²×C₇	1	2	yes	complemented
552	#482	C₂²×C₇	1	2	yes	complemented
553	#481	C₂²×C₇	1	1	yes	characteristic, complemented
554	#481	C₂²×C₇	1	2	yes	complemented
555	#480	C₂²×C₇	1	1	yes	characteristic, complemented
556	#480	C₂²×C₇	1	2	yes	complemented
557	#478	C₂²×C₇	1	2	yes	complemented
558	#478	C₂²×C₇	1	2	yes	complemented
559	#476	C₂²×C₇	1	2	yes	complemented
560	#474	C₂²×C₇	1	2	yes	complemented
561	#470	C₂²×C₇	1	2	yes	complemented
562	#468	C₂²×C₇	1	2	yes	complemented
563	#468	C₂²×C₇	1	2	yes	complemented
564	#468	C₂²×C₇	1	2	yes	complemented
565	#467	C₂²×C₇	1	2	yes	complemented
566	#465	C₂²×C₇	1	2	yes	complemented
567	#465	C₂²×C₇	1	2	yes	complemented
568	#465	C₂²×C₇	1	2	yes	complemented
569	#464	C₂²×C₇	1	2	yes	complemented
570	#464	C₂²×C₇	1	2	yes	complemented
571	#460	C₂²×C₇	1	2	yes	complemented
572	#460	C₂²×C₇	1	2	yes	complemented
573	#452	C₂²×C₇	1	2	yes	complemented
574	#452	C₂²×C₇	1	2	yes	complemented
575	#450	C₂²×C₇	1	2	yes	complemented
576	#450	C₂²×C₇	1	2	yes	complemented
577	#450	C₂²×C₇	1	2	yes	complemented
578	#450	C₂²×C₇	1	2	yes	complemented
579	#450	C₂²×C₇	1	2	yes	complemented
580	#450	C₂²×C₇	1	2	yes	complemented
581	#440	C₂²×C₇	1	2	yes	complemented
582	#440	C₂²×C₇	1	2	yes	complemented
583	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
584	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
585	#436	C₂²×C₇	1	2	yes	complemented
586	#435	C₂²×C₇	1	2	yes	complemented
587	#435	C₂²×C₇	1	2	yes	complemented
588	C₈×D₄	C₂²×C₇	1	2	yes	complemented
589	#428	C₂²×C₇	1	1	yes	characteristic, complemented
590	#427	C₂²×C₇	1	1	yes	characteristic, complemented
591	#427	C₂²×C₇	1	1	yes	characteristic, complemented
592	#424	C₂²×C₇	1	1	yes	characteristic, complemented
593	#419	C₂²×C₇	1	1	yes	characteristic, complemented
594	#418	C₂²×C₇	1	1	yes	characteristic
595	#418	C₂²×C₇	1	1	yes	characteristic
596	#418	C₂²×C₇	1	1	yes	characteristic, complemented
597	#418	C₂²×C₇	1	1	yes	characteristic, complemented
598	#418	C₂²×C₇	1	2	yes	complemented
599	#418	C₂²×C₇	1	2	yes	complemented
600	#418	C₂²×C₇	1	2	yes	complemented
601	#417	C₂²×C₇	1	2	yes	complemented
602	#417	C₂²×C₇	1	1	yes	characteristic, complemented
603	#416	C₂²×C₇	1	2	yes	complemented
604	#416	C₂²×C₇	1	1	yes	characteristic, complemented
605	#416	C₂²×C₇	1	1	yes	characteristic, complemented
606	C₂×#102	C₂²×C₇	1	1	yes	characteristic
607	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
608	C₂×#102	C₂²×C₇	1	2	yes	complemented
609	C₂×#102	C₂²×C₇	1	2	yes	complemented
610	C₂×#102	C₂²×C₇	1	2	yes	complemented
611	#408	C₂²×C₇	1	1	yes	characteristic, complemented
612	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
613	#405	C₂²×C₇	1	1	yes	characteristic, complemented
614	C₂³×C₇	—	2	2	no	—
615	C₂³×C₇	—	2	2	no	—
616	C₂³×C₇	—	2	2	no	—
617	C₂³×C₇	—	2	4	no	—
618	C₂³×C₇	—	2	2	no	—
619	C₂³×C₇	—	2	1	no	—
620	C₂³×C₇	—	4	1	no	—
621	C₂³×C₇	—	4	4	no	—
622	C₂³×C₇	—	4	4	no	—
623	C₂³×C₇	—	4	4	no	—
624	C₂³×C₇	—	4	4	no	—
625	C₂³×C₇	—	4	2	no	—
626	C₂³×C₇	—	4	4	no	—
627	C₂³×C₇	—	8	1	no	—
628	C₂³×C₇	—	8	2	no	—
629	C₂³×C₇	—	8	1	no	—
630	C₂³×C₇	—	8	1	no	—
631	C₂³×C₇	—	8	1	no	—
632	C₂³×C₇	—	8	2	no	—
633	C₂³×C₇	—	8	2	no	—
634	C₂³×C₇	—	8	2	no	—
635	C₂³×C₇	—	8	16	no	—
636	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
637	C₂³×C₇	C₂²×D₄	1	2	yes	—
638	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
639	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
640	C₇×Q₈	—	2	2	no	—
641	C₇×Q₈	—	2	2	no	—
642	C₇×Q₈	—	2	1	no	—
643	C₇×Q₈	—	2	2	no	—
644	C₇×Q₈	—	2	1	no	—
645	C₇×Q₈	—	4	2	no	—
646	C₇×Q₈	—	8	2	no	—
647	C₇×D₄	—	2	4	no	—
648	C₇×D₄	—	2	4	no	—
649	C₇×D₄	—	2	4	no	—
650	C₇×D₄	—	2	2	no	—
651	C₇×D₄	—	2	2	no	—
652	C₇×D₄	—	2	1	no	—
653	C₇×D₄	—	2	2	no	—
654	C₇×D₄	—	2	2	no	—
655	C₇×D₄	—	2	1	no	—
656	C₇×D₄	—	4	2	no	—
657	C₇×D₄	—	4	4	no	—
658	C₇×D₄	—	4	4	no	—
659	C₇×D₄	—	4	4	no	—
660	C₇×D₄	—	4	4	no	—
661	C₇×D₄	—	4	2	no	—
662	C₇×D₄	—	4	2	no	—
663	C₇×D₄	—	4	2	no	—
664	C₇×D₄	—	4	2	no	—
665	C₇×D₄	—	8	2	no	—
666	C₇×D₄	—	8	2	no	—
667	C₇×D₄	—	8	2	no	—
668	C₇×D₄	—	8	2	no	—
669	C₇×D₄	C₂×#41	1	4	yes	—
670	C₂×C₄×C₇	—	2	2	no	—
671	C₂×C₄×C₇	—	2	2	no	—
672	C₂×C₄×C₇	—	2	2	no	—
673	C₂×C₄×C₇	—	2	1	no	—
674	C₂×C₄×C₇	—	2	1	no	—
675	C₂×C₄×C₇	—	2	2	no	—
676	C₂×C₄×C₇	—	2	1	no	—
677	C₂×C₄×C₇	—	2	2	no	—
678	C₂×C₄×C₇	—	2	1	no	—
679	C₂×C₄×C₇	—	2	1	no	—
680	C₂×C₄×C₇	—	2	1	no	—
681	C₂×C₄×C₇	—	2	1	no	—
682	C₂×C₄×C₇	—	2	2	no	—
683	C₂×C₄×C₇	—	2	1	no	—
684	C₂×C₄×C₇	—	2	1	no	—
685	C₂×C₄×C₇	—	2	1	no	—
686	C₂×C₄×C₇	—	2	2	no	—
687	C₂×C₄×C₇	—	2	1	no	—
688	C₂×C₄×C₇	—	4	4	no	—
689	C₂×C₄×C₇	—	4	2	no	—
690	C₂×C₄×C₇	—	4	2	no	—
691	C₂×C₄×C₇	—	4	2	no	—
692	C₂×C₄×C₇	—	8	2	no	—
693	C₂×C₄×C₇	—	8	2	no	—
694	C₂×C₄×C₇	—	8	2	no	—
695	C₂×C₄×C₇	—	8	1	no	—
696	C₂×C₄×C₇	—	8	1	no	—
697	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
698	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
699	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
700	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
701	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
702	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
703	C₂×C₄×C₇	C₂×#41	1	2	yes	—
704	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
705	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
706	C₇×C₈	—	2	1	no	—
707	C₇×C₈	—	2	1	no	—
708	C₇×C₈	—	2	1	no	—
709	C₇×C₈	—	2	1	no	—
710	C₇×C₈	—	2	2	no	—
711	C₇×C₈	—	2	2	no	—
712	C₂⁵	—	2	1	no	—
713	H(5,𝔽₂)	—	2	4	no	—
714	H(5,𝔽₂)	—	4	2	no	—
715	C₂×#41	—	2	1	no	—
716	C₂×#41	C₂³×C₇	1	1	yes	characteristic
717	C₂×#41	C₂³×C₇	1	2	yes	—
718	C₂×#41	C₂³×C₇	1	1	yes	characteristic
719	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
720	C₂²×D₄	—	2	4	no	—
721	C₂²×D₄	—	2	2	no	—
722	C₂²×D₄	—	2	1	no	—
723	C₂²×D₄	—	2	2	no	—
724	C₂²×D₄	—	2	2	no	—
725	C₂²×D₄	—	2	1	no	—
726	C₂²×D₄	—	2	1	no	—
727	C₂²×D₄	—	2	1	no	—
728	C₂²×D₄	—	4	2	no	—
729	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
730	C₂²×D₄	C₂³×C₇	1	2	yes	—
731	C₂²×D₄	C₂³×C₇	1	2	yes	—
732	C₂²×D₄	C₂³×C₇	1	2	yes	—
733	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
734	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
735	#137	—	4	2	no	—
736	C₂×Q₁₆	C₂³×C₇	1	2	yes	complemented
737	C₂×SD₁₆	—	2	4	no	—
738	C₂×SD₁₆	—	4	2	no	—
739	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
740	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₇	1	2	yes	complemented
744	#131	—	4	2	no	—
745	C₂×M₁₆	—	4	2	no	—
746	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
747	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
748	C₂×M₁₆	C₂³×C₇	1	2	yes	—
749	C₂×M₁₆	C₂³×C₇	1	2	yes	complemented
750	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
751	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
752	C₂²×C₈	C₂³×C₇	1	2	yes	—
753	C₂²×C₈	C₂³×C₇	1	2	yes	complemented
754	C₄⋊Q₈	—	2	1	no	—
755	C₄⋊Q₈	—	2	1	no	—
756	C₄⋊Q₈	C₂³×C₇	1	2	yes	complemented
757	#127	—	2	1	no	—
758	#127	C₂³×C₇	1	2	yes	—
759	#126	—	2	2	no	—
760	#126	—	2	2	no	—
761	#126	—	2	2	no	—
762	#126	—	2	2	no	—
763	#125	—	2	1	no	—
764	#125	—	2	2	no	—
765	#125	—	2	2	no	—
766	#125	—	2	2	no	—
767	#125	C₂³×C₇	1	2	yes	complemented
768	#124	—	2	1	no	—
769	#124	—	2	1	no	—
770	#124	—	2	2	no	—
771	#124	C₂³×C₇	1	2	yes	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	1	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	C₇×D₄	1	2	yes	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
785	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
786	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
788	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
789	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
790	C₂²⋊Q₈	C₂³×C₇	1	2	yes	complemented
791	C₂²⋊Q₈	C₂³×C₇	1	2	yes	complemented
792	#121	—	2	2	no	—
793	#121	—	2	2	no	—
794	#121	—	2	1	no	—
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	C₇×D₄	1	1	yes	characteristic
799	#121	C₇×D₄	1	1	yes	characteristic
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	—	2	2	no	—
809	#120	—	2	2	no	—
810	#120	—	2	2	no	—
811	#120	—	2	2	no	—
812	#120	—	2	2	no	—
813	#120	C₇×D₄	1	2	yes	—
814	C₄×Q₈	—	2	1	no	—
815	C₄×Q₈	—	2	1	no	—
816	C₄×Q₈	—	2	1	no	—
817	C₄×Q₈	—	2	2	no	—
818	C₄×Q₈	C₂³×C₇	1	2	yes	complemented
819	C₄×Q₈	C₂³×C₇	1	2	yes	complemented
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	C₂³×C₇	1	2	yes	—
828	C₄×D₄	C₂³×C₇	1	2	yes	—
829	C₄×D₄	C₂³×C₇	1	2	yes	—
830	C₄×D₄	C₂³×C₇	1	2	yes	—
831	#117	—	2	1	no	—
832	#117	—	2	1	no	—
833	#117	—	2	2	no	—
834	#117	—	2	2	no	—
835	#117	—	2	2	no	—
836	#117	C₂³×C₇	1	1	yes	characteristic
837	#117	C₂³×C₇	1	1	yes	characteristic
838	#117	C₂³×C₇	1	1	yes	characteristic
839	#117	C₂³×C₇	1	1	yes	characteristic
840	#117	C₂³×C₇	1	1	yes	characteristic
841	#117	C₂³×C₇	1	1	yes	characteristic
842	#117	C₂³×C₇	1	2	yes	complemented
843	C₂×C₄⋊C₄	—	2	1	no	—
844	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
845	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
846	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
847	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	complemented
848	C₂×C₂²⋊C₄	—	2	1	no	—
849	C₂×C₂²⋊C₄	—	2	1	no	—
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₂²⋊C₄	—	2	2	no	—
853	C₂×C₄²	—	2	1	no	—
854	#107	C₂³×C₇	1	1	yes	characteristic, complemented
855	#107	C₂³×C₇	1	1	yes	characteristic, complemented
856	#107	C₂³×C₇	1	1	yes	characteristic, complemented
857	#107	C₂³×C₇	1	1	yes	characteristic, complemented
858	#107	C₂³×C₇	1	2	yes	complemented
859	#106	C₂³×C₇	1	1	yes	characteristic, complemented
860	#106	C₂³×C₇	1	1	yes	characteristic, complemented
861	#106	C₂³×C₇	1	1	yes	characteristic, complemented
862	#106	C₂³×C₇	1	1	yes	characteristic, complemented
863	#106	C₂³×C₇	1	2	yes	complemented
864	C₄⋊C₈	C₂³×C₇	1	2	yes	complemented
865	C₄⋊C₈	C₂³×C₇	1	2	yes	complemented
866	#103	C₂³×C₇	1	1	yes	characteristic, complemented
867	#103	C₂³×C₇	1	1	yes	characteristic, complemented
868	#103	C₂³×C₇	1	2	yes	complemented
869	#103	C₂³×C₇	1	1	yes	characteristic, complemented
870	#103	C₂³×C₇	1	1	yes	characteristic, complemented
871	#103	C₂³×C₇	1	2	yes	complemented
872	#103	C₂³×C₇	1	2	yes	complemented
873	#102	C₂³×C₇	1	2	yes	—
874	#102	C₂³×C₇	1	2	yes	—
875	#102	C₂³×C₇	1	2	yes	—
876	#102	C₂³×C₇	1	2	yes	—
877	#102	C₂³×C₇	1	2	yes	—
878	#102	C₂³×C₇	1	2	yes	—
879	#102	C₂³×C₇	1	2	yes	—
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	#102	C₂³×C₇	1	1	yes	characteristic, complemented
886	#102	C₂³×C₇	1	2	yes	complemented
887	#102	C₂³×C₇	1	1	yes	characteristic, complemented
888	#102	C₂³×C₇	1	1	yes	characteristic, complemented
889	#102	C₂³×C₇	1	1	yes	characteristic, complemented
890	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
891	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
892	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
893	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
894	C₂²⋊C₈	C₂³×C₇	1	2	yes	complemented
895	C₂²⋊C₈	C₂³×C₇	1	2	yes	complemented
896	#97	C₂³×C₇	1	2	yes	complemented
897	C₄×C₈	C₂³×C₇	1	2	yes	complemented
898	C₂²×C₇	—	2	1	no	—
899	C₂²×C₇	—	2	1	no	—
900	C₂²×C₇	—	2	1	no	—
901	C₂²×C₇	—	2	1	no	—
902	C₂²×C₇	—	2	2	no	—
903	C₂²×C₇	—	2	1	no	—
904	C₂²×C₇	—	2	1	no	—
905	C₂²×C₇	—	2	2	no	—
906	C₂²×C₇	—	2	4	no	—
907	C₂²×C₇	—	2	2	no	—
908	C₂²×C₇	—	2	1	no	—
909	C₂²×C₇	—	4	4	no	—
910	C₂²×C₇	—	4	2	no	—
911	C₂²×C₇	—	4	2	no	—
912	C₂²×C₇	—	4	1	no	—
913	C₂²×C₇	—	4	2	no	—
914	C₂²×C₇	—	4	1	no	—
915	C₂²×C₇	—	4	2	no	—
916	C₂²×C₇	—	4	1	no	—
917	C₂²×C₇	—	4	2	no	—
918	C₂²×C₇	—	8	4	no	—
919	C₂²×C₇	—	8	8	no	—
920	C₂²×C₇	—	8	4	no	—
921	C₂²×C₇	—	8	8	no	—
922	C₂²×C₇	—	16	4	no	—
923	C₂²×C₇	#546	1	2	yes	—
924	C₂²×C₇	#577	1	2	yes	—
925	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
926	C₄×C₇	—	2	2	no	—
927	C₄×C₇	—	2	1	no	—
928	C₄×C₇	—	2	1	no	—
929	C₄×C₇	—	2	2	no	—
930	C₄×C₇	—	2	2	no	—
931	C₄×C₇	—	4	1	no	—
932	C₄×C₇	—	4	1	no	—
933	C₄×C₇	—	4	2	no	—
934	C₄×C₇	—	4	1	no	—
935	C₄×C₇	—	4	1	no	—
936	C₄×C₇	—	4	2	no	—
937	C₄×C₇	—	4	1	no	—
938	C₄×C₇	—	4	1	no	—
939	C₄×C₇	—	4	1	no	—
940	C₄×C₇	#546	1	2	yes	—
941	C₄×C₇	C₂²×#41	1	1	yes	characteristic
942	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
943	C₂⁴	—	2	1	no	—
944	C₂⁴	—	2	2	no	—
945	C₂⁴	—	2	2	no	—
946	C₂⁴	—	2	1	no	—
947	C₂⁴	—	2	2	no	—
948	C₂⁴	—	4	4	no	—
949	C₂⁴	—	8	2	no	—
950	C₂⁴	—	8	2	no	—
951	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
952	#41	—	2	2	no	—
953	#41	—	2	2	no	—
954	#41	—	2	4	no	—
955	#41	—	2	2	no	—
956	#41	—	2	2	no	—
957	#41	—	4	2	no	—
958	#41	—	4	4	no	—
959	C₂×Q₈	—	2	1	no	—
960	C₂×Q₈	—	2	2	no	—
961	C₂×Q₈	—	2	2	no	—
962	C₂×Q₈	—	2	2	no	—
963	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
964	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
965	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
966	C₂×D₄	—	2	4	no	—
967	C₂×D₄	—	2	4	no	—
968	C₂×D₄	—	2	4	no	—
969	C₂×D₄	—	2	1	no	—
970	C₂×D₄	—	2	1	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	1	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	2	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	4	2	no	—
986	C₂×D₄	—	4	2	no	—
987	C₂×D₄	—	4	2	no	—
988	C₂×D₄	—	4	4	no	—
989	C₂×D₄	—	4	4	no	—
990	C₂×D₄	—	4	4	no	—
991	C₂×D₄	—	4	4	no	—
992	C₂×D₄	—	4	8	no	—
993	C₂×D₄	—	8	4	no	—
994	C₂×D₄	—	8	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	C₇×#41	1	4	yes	—
1000	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1001	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1002	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	2	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	2	no	—
1013	C₂²×C₄	—	2	2	no	—
1014	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1015	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1016	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1017	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1019	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
1020	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1021	Q₁₆	—	4	2	no	—
1022	SD₁₆	—	2	4	no	—
1023	SD₁₆	—	2	4	no	—
1024	SD₁₆	—	4	2	no	—
1025	SD₁₆	—	4	2	no	—
1026	SD₁₆	—	4	2	no	—
1027	M₁₆	—	2	2	no	—
1028	M₁₆	—	2	2	no	—
1029	M₁₆	—	4	2	no	—
1030	M₁₆	—	4	2	no	—
1031	C₂×C₈	—	2	2	no	—
1032	C₂×C₈	—	2	2	no	—
1033	C₂×C₈	—	4	2	no	—
1034	C₂×C₈	—	4	2	no	—
1035	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1036	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1037	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1038	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1039	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1040	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1057	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1058	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1059	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1060	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1061	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1062	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1063	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1064	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1065	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1067	C₂²⋊C₄	—	2	1	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	1	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	—	2	2	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1088	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1089	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1090	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1091	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1092	C₄²	—	2	1	no	—
1093	C₄²	—	2	1	no	—
1094	C₄²	—	2	1	no	—
1095	C₄²	—	2	1	no	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	2	no	—
1098	C₄²	—	2	2	no	—
1099	C₄²	—	2	1	no	—
1100	C₄²	C₂⁴×C₇	1	2	yes	—
1101	C₂×C₇	—	2	2	no	—
1102	C₂×C₇	—	2	2	no	—
1103	C₂×C₇	—	4	1	no	—
1104	C₂×C₇	—	4	2	no	—
1105	C₂×C₇	—	4	4	no	—
1106	C₂×C₇	—	8	2	no	—
1107	C₂×C₇	—	8	1	no	—
1108	C₂×C₇	C₂×#546	1	1	yes	characteristic
1109	C₂×C₇	C₂×#577	1	1	yes	characteristic
1110	C₂×C₇	#3585	1	1	yes	characteristic
1111	C₂³	—	2	2	no	—
1112	C₂³	—	2	2	no	—
1113	C₂³	—	2	2	no	—
1114	C₂³	—	2	4	no	—
1115	C₂³	—	2	2	no	—
1116	C₂³	—	2	1	no	—
1117	C₂³	—	4	1	no	—
1118	C₂³	—	4	4	no	—
1119	C₂³	—	4	4	no	—
1120	C₂³	—	4	4	no	—
1121	C₂³	—	4	4	no	—
1122	C₂³	—	4	2	no	—
1123	C₂³	—	4	4	no	—
1124	C₂³	—	8	1	no	—
1125	C₂³	—	8	1	no	—
1126	C₂³	—	8	1	no	—
1127	C₂³	—	8	2	no	—
1128	C₂³	—	8	1	no	—
1129	C₂³	—	8	2	no	—
1130	C₂³	—	8	2	no	—
1131	C₂³	—	8	2	no	—
1132	C₂³	—	8	16	no	—
1133	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1134	C₂³	C₂²×C₇×D₄	1	2	yes	—
1135	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1136	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1137	Q₈	—	2	2	no	—
1138	Q₈	—	2	2	no	—
1139	Q₈	—	2	1	no	—
1140	Q₈	—	2	2	no	—
1141	Q₈	—	2	1	no	—
1142	Q₈	—	4	2	no	—
1143	Q₈	—	8	2	no	—
1144	D₄	—	2	4	no	—
1145	D₄	—	2	4	no	—
1146	D₄	—	2	2	no	—
1147	D₄	—	2	1	no	—
1148	D₄	—	2	2	no	—
1149	D₄	—	2	2	no	—
1150	D₄	—	2	1	no	—
1151	D₄	—	2	4	no	—
1152	D₄	—	2	2	no	—
1153	D₄	—	4	2	no	—
1154	D₄	—	4	4	no	—
1155	D₄	—	4	4	no	—
1156	D₄	—	4	4	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	—	8	2	no	—
1165	D₄	—	8	2	no	—
1166	D₄	C₂×C₇×#41	1	4	yes	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	4	4	no	—
1186	C₂×C₄	—	4	2	no	—
1187	C₂×C₄	—	4	2	no	—
1188	C₂×C₄	—	4	2	no	—
1189	C₂×C₄	—	8	2	no	—
1190	C₂×C₄	—	8	2	no	—
1191	C₂×C₄	—	8	2	no	—
1192	C₂×C₄	—	8	1	no	—
1193	C₂×C₄	—	8	1	no	—
1194	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1195	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1196	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1197	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1198	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1199	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1200	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1201	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1202	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1203	C₈	—	2	1	no	—
1204	C₈	—	2	1	no	—
1205	C₈	—	2	1	no	—
1206	C₈	—	2	1	no	—
1207	C₈	—	2	2	no	—
1208	C₈	—	2	2	no	—
1209	C₇	#61184	1	1	yes	characteristic, direct product factor, Sylow
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	1	no	—
1212	C₂²	—	2	1	no	—
1213	C₂²	—	2	1	no	—
1214	C₂²	—	2	2	no	—
1215	C₂²	—	2	1	no	—
1216	C₂²	—	2	2	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	2	no	—
1220	C₂²	—	2	4	no	—
1221	C₂²	—	4	4	no	—
1222	C₂²	—	4	2	no	—
1223	C₂²	—	4	2	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	2	no	—
1226	C₂²	—	4	1	no	—
1227	C₂²	—	4	2	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	2	no	—
1230	C₂²	—	8	4	no	—
1231	C₂²	—	8	8	no	—
1232	C₂²	—	8	4	no	—
1233	C₂²	—	8	8	no	—
1234	C₂²	—	16	4	no	—
1235	C₂²	C₇×#546	1	2	yes	—
1236	C₂²	C₇×#577	1	2	yes	—
1237	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1238	C₄	—	2	2	no	—
1239	C₄	—	2	2	no	—
1240	C₄	—	2	1	no	—
1241	C₄	—	2	1	no	—
1242	C₄	—	2	2	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	2	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	2	no	—
1252	C₄	C₇×#546	1	2	yes	—
1253	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1254	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1255	C₂	—	2	2	no	—
1256	C₂	—	2	2	no	—
1257	C₂	—	4	1	no	—
1258	C₂	—	4	2	no	—
1259	C₂	—	4	4	no	—
1260	C₂	—	8	2	no	—
1261	C₂	—	8	1	no	—
1262	C₂	C₂×C₇×#546	1	1	yes	characteristic
1263	C₂	C₂×C₇×#577	1	1	yes	characteristic
1264	C₂	C₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3484	C₂
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×#3495	C₂	semidirect
3. C₇×#3324	C₂	semidirect
4. C₇×#3323	C₂	semidirect
5. C₇×#3314	C₂	semidirect
6. C₇×#3311	C₂	semidirect
7. C₇×#3310	C₂	semidirect
8. C₇×#3310	C₂	semidirect
9. C₇×#3296	C₂	semidirect
10. C₇×#3295	C₂	semidirect
11. C₇×#3136	C₂	semidirect
12. C₇×#3096	C₂	semidirect
13. C₇×#3091	C₂	semidirect
14. C₇×#3081	C₂	semidirect
15. C₇×#3057	C₂	semidirect
16. C₇×#3056	C₂	semidirect
17. C₇×#3043	C₂	semidirect
18. C₇×#3009	C₂	semidirect
19. C₂×C₇×#450	C₂	semidirect
20. C₇×#2949	C₂	semidirect
21. C₇×#2933	C₂	semidirect
22. C₇×#2897	C₂	semidirect
23. C₂×C₇×#418	C₂	semidirect
26. C₂×C₇×#137	C₂²	semidirect
28. C₂²×C₇×SD₁₆	C₂²	semidirect
29. C₂×C₇×#131	C₂²	semidirect
30. C₂²×C₇×M₁₆	C₂²	semidirect
31. C₇×#556	C₂²	semidirect
32. C₇×#554	C₂²	semidirect
34. C₇×#552	C₂²	semidirect
35. C₇×#552	C₂²	semidirect
45. C₇×#544	C₂²	semidirect
48. C₇×#536	C₂²	semidirect
56. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
58. C₇×#520	C₂²	semidirect
59. C₇×#519	C₂²	semidirect
61. C₂×C₇×#117	C₂²	semidirect
62. C₇×#490	C₂²	semidirect
63. C₇×#489	C₂²	semidirect
64. C₇×#488	C₂²	semidirect
65. C₇×#486	C₂²	semidirect
66. C₇×#485	C₂²	semidirect
67. C₇×#485	C₂²	semidirect
68. C₇×#484	C₂²	semidirect
69. C₇×#483	C₂²	semidirect
70. C₇×#482	C₂²	semidirect
71. C₇×#482	C₂²	semidirect
72. C₇×#482	C₂²	semidirect
73. C₇×#482	C₂²	semidirect
74. C₇×#481	C₂²	semidirect
75. C₇×#481	C₂²	semidirect
76. C₇×#480	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×#470	C₂²	semidirect
83. C₇×#468	C₂²	semidirect
84. C₇×#468	C₂²	semidirect
85. C₇×#468	C₂²	semidirect
86. C₇×#467	C₂²	semidirect
87. C₇×#465	C₂²	semidirect
88. C₇×#465	C₂²	semidirect
89. C₇×#465	C₂²	semidirect
90. C₇×#464	C₂²	semidirect
91. C₇×#464	C₂²	semidirect
92. C₇×#460	C₂²	semidirect
93. C₇×#460	C₂²	semidirect
94. C₇×#452	C₂²	semidirect
95. C₇×#452	C₂²	semidirect
96. C₇×#450	C₂²	semidirect
97. C₇×#450	C₂²	semidirect
98. C₇×#450	C₂²	semidirect
99. C₇×#450	C₂²	semidirect
100. C₇×#450	C₂²	semidirect
101. C₇×#450	C₂²	semidirect
102. C₇×#440	C₂²	semidirect
103. C₇×#440	C₂²	semidirect
104. C₄×C₇×SD₁₆	C₂²	semidirect
105. C₄×C₇×SD₁₆	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
117. C₇×#418	C₂²	semidirect
118. C₇×#418	C₂²	semidirect
119. C₇×#418	C₂²	semidirect
120. C₇×#418	C₂²	semidirect
121. C₇×#418	C₂²	semidirect
122. C₇×#417	C₂²	semidirect
123. C₇×#417	C₂²	semidirect
124. C₇×#416	C₂²	semidirect
125. C₇×#416	C₂²	semidirect
126. C₇×#416	C₂²	semidirect
128. C₂×C₇×#102	C₂²	semidirect
129. C₂×C₇×#102	C₂²	semidirect
130. C₂×C₇×#102	C₂²	semidirect
131. C₂×C₇×#102	C₂²	semidirect
132. C₇×#408	C₂²	semidirect
133. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
134. C₇×#405	C₂²	semidirect
135. #61184	C₇	direct (N × H)
160. C₂×C₇×Q₁₆	C₂³	semidirect
167. C₂×C₇×SD₁₆	C₂³	semidirect
173. C₂×C₇×M₁₆	C₂³	semidirect
177. C₂²×C₇×C₈	C₂³	semidirect
180. C₇×C₄⋊Q₈	C₂³	semidirect
191. C₇×#125	C₂³	semidirect
214. C₇×C₂²⋊Q₈	C₂³	semidirect
215. C₇×C₂²⋊Q₈	C₂³	semidirect
242. C₄×C₇×Q₈	C₂³	semidirect
243. C₄×C₇×Q₈	C₂³	semidirect
266. C₇×#117	C₂³	semidirect
271. C₂×C₇×C₄⋊C₄	C₂³	semidirect
278. C₇×#107	C₂³	semidirect
279. C₇×#107	C₂³	semidirect
280. C₇×#107	C₂³	semidirect
281. C₇×#107	C₂³	semidirect
282. C₇×#107	C₂³	semidirect
283. C₇×#106	C₂³	semidirect
284. C₇×#106	C₂³	semidirect
285. C₇×#106	C₂³	semidirect
286. C₇×#106	C₂³	semidirect
287. C₇×#106	C₂³	semidirect
288. C₇×C₄⋊C₈	C₂³	semidirect
289. C₇×C₄⋊C₈	C₂³	semidirect
290. C₇×#103	C₂³	semidirect
291. C₇×#103	C₂³	semidirect
292. C₇×#103	C₂³	semidirect
293. C₇×#103	C₂³	semidirect
294. C₇×#103	C₂³	semidirect
295. C₇×#103	C₂³	semidirect
296. C₇×#103	C₂³	semidirect
309. C₇×#102	C₂³	semidirect
310. C₇×#102	C₂³	semidirect
311. C₇×#102	C₂³	semidirect
312. C₇×#102	C₂³	semidirect
313. C₇×#102	C₂³	semidirect
318. C₇×C₂²⋊C₈	C₂³	semidirect
319. C₇×C₂²⋊C₈	C₂³	semidirect
320. C₇×#97	C₂³	semidirect
321. C₄×C₇×C₈	C₂³	semidirect
322. #3495	C₂×C₇	semidirect
324. #3324	C₂×C₇	semidirect
325. #3323	C₂×C₇	semidirect
326. #3314	C₂×C₇	semidirect
327. #3311	C₂×C₇	semidirect
328. #3310	C₂×C₇	semidirect
329. #3310	C₂×C₇	semidirect
330. #3296	C₂×C₇	semidirect
331. #3295	C₂×C₇	semidirect
332. #3136	C₂×C₇	semidirect
333. #3096	C₂×C₇	semidirect
334. #3091	C₂×C₇	semidirect
335. #3081	C₂×C₇	semidirect
336. #3057	C₂×C₇	semidirect
337. #3056	C₂×C₇	semidirect
338. #3043	C₂×C₇	semidirect
339. #3009	C₂×C₇	semidirect
340. C₂×#450	C₂×C₇	semidirect
341. #2949	C₂×C₇	semidirect
342. #2933	C₂×C₇	semidirect
343. #2897	C₂×C₇	semidirect
344. C₂×#418	C₂×C₇	semidirect
505. C₂×#137	C₂²×C₇	semidirect
507. C₂²×SD₁₆	C₂²×C₇	semidirect
508. C₂×#131	C₂²×C₇	semidirect
509. C₂²×M₁₆	C₂²×C₇	semidirect
510. #556	C₂²×C₇	semidirect
511. #554	C₂²×C₇	semidirect
513. #552	C₂²×C₇	semidirect
514. #552	C₂²×C₇	semidirect
524. #544	C₂²×C₇	semidirect
527. #536	C₂²×C₇	semidirect
535. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
537. #520	C₂²×C₇	semidirect
538. #519	C₂²×C₇	semidirect
540. C₂×#117	C₂²×C₇	semidirect
541. #490	C₂²×C₇	semidirect
542. #489	C₂²×C₇	semidirect
543. #488	C₂²×C₇	semidirect
544. #486	C₂²×C₇	semidirect
545. #485	C₂²×C₇	semidirect
546. #485	C₂²×C₇	semidirect
547. #484	C₂²×C₇	semidirect
548. #483	C₂²×C₇	semidirect
549. #482	C₂²×C₇	semidirect
550. #482	C₂²×C₇	semidirect
551. #482	C₂²×C₇	semidirect
552. #482	C₂²×C₇	semidirect
553. #481	C₂²×C₇	semidirect
554. #481	C₂²×C₇	semidirect
555. #480	C₂²×C₇	semidirect
556. #480	C₂²×C₇	semidirect
557. #478	C₂²×C₇	semidirect
558. #478	C₂²×C₇	semidirect
559. #476	C₂²×C₇	semidirect
560. #474	C₂²×C₇	semidirect
561. #470	C₂²×C₇	semidirect
562. #468	C₂²×C₇	semidirect
563. #468	C₂²×C₇	semidirect
564. #468	C₂²×C₇	semidirect
565. #467	C₂²×C₇	semidirect
566. #465	C₂²×C₇	semidirect
567. #465	C₂²×C₇	semidirect
568. #465	C₂²×C₇	semidirect
569. #464	C₂²×C₇	semidirect
570. #464	C₂²×C₇	semidirect
571. #460	C₂²×C₇	semidirect
572. #460	C₂²×C₇	semidirect
573. #452	C₂²×C₇	semidirect
574. #452	C₂²×C₇	semidirect
575. #450	C₂²×C₇	semidirect
576. #450	C₂²×C₇	semidirect
577. #450	C₂²×C₇	semidirect
578. #450	C₂²×C₇	semidirect
579. #450	C₂²×C₇	semidirect
580. #450	C₂²×C₇	semidirect
581. #440	C₂²×C₇	semidirect
582. #440	C₂²×C₇	semidirect
583. C₄×SD₁₆	C₂²×C₇	semidirect
584. C₄×SD₁₆	C₂²×C₇	semidirect
585. #436	C₂²×C₇	semidirect
586. #435	C₂²×C₇	semidirect
587. #435	C₂²×C₇	semidirect
588. C₈×D₄	C₂²×C₇	semidirect
589. #428	C₂²×C₇	semidirect
590. #427	C₂²×C₇	semidirect
591. #427	C₂²×C₇	semidirect
592. #424	C₂²×C₇	semidirect
593. #419	C₂²×C₇	semidirect
596. #418	C₂²×C₇	semidirect
597. #418	C₂²×C₇	semidirect
598. #418	C₂²×C₇	semidirect
599. #418	C₂²×C₇	semidirect
600. #418	C₂²×C₇	semidirect
601. #417	C₂²×C₇	semidirect
602. #417	C₂²×C₇	semidirect
603. #416	C₂²×C₇	semidirect
604. #416	C₂²×C₇	semidirect
605. #416	C₂²×C₇	semidirect
607. C₂×#102	C₂²×C₇	semidirect
608. C₂×#102	C₂²×C₇	semidirect
609. C₂×#102	C₂²×C₇	semidirect
610. C₂×#102	C₂²×C₇	semidirect
611. #408	C₂²×C₇	semidirect
612. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
613. #405	C₂²×C₇	semidirect
736. C₂×Q₁₆	C₂³×C₇	semidirect
743. C₂×SD₁₆	C₂³×C₇	semidirect
749. C₂×M₁₆	C₂³×C₇	semidirect
753. C₂²×C₈	C₂³×C₇	semidirect
756. C₄⋊Q₈	C₂³×C₇	semidirect
767. #125	C₂³×C₇	semidirect
790. C₂²⋊Q₈	C₂³×C₇	semidirect
791. C₂²⋊Q₈	C₂³×C₇	semidirect
818. C₄×Q₈	C₂³×C₇	semidirect
819. C₄×Q₈	C₂³×C₇	semidirect
842. #117	C₂³×C₇	semidirect
847. C₂×C₄⋊C₄	C₂³×C₇	semidirect
854. #107	C₂³×C₇	semidirect
855. #107	C₂³×C₇	semidirect
856. #107	C₂³×C₇	semidirect
857. #107	C₂³×C₇	semidirect
858. #107	C₂³×C₇	semidirect
859. #106	C₂³×C₇	semidirect
860. #106	C₂³×C₇	semidirect
861. #106	C₂³×C₇	semidirect
862. #106	C₂³×C₇	semidirect
863. #106	C₂³×C₇	semidirect
864. C₄⋊C₈	C₂³×C₇	semidirect
865. C₄⋊C₈	C₂³×C₇	semidirect
866. #103	C₂³×C₇	semidirect
867. #103	C₂³×C₇	semidirect
868. #103	C₂³×C₇	semidirect
869. #103	C₂³×C₇	semidirect
870. #103	C₂³×C₇	semidirect
871. #103	C₂³×C₇	semidirect
872. #103	C₂³×C₇	semidirect
885. #102	C₂³×C₇	semidirect
886. #102	C₂³×C₇	semidirect
887. #102	C₂³×C₇	semidirect
888. #102	C₂³×C₇	semidirect
889. #102	C₂³×C₇	semidirect
894. C₂²⋊C₈	C₂³×C₇	semidirect
895. C₂²⋊C₈	C₂³×C₇	semidirect
896. #97	C₂³×C₇	semidirect
897. C₄×C₈	C₂³×C₇	semidirect
1209. C₇	#61184	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3495	2
C₇×#3484	2
C₇×#3324	2
C₇×#3323	2
C₇×#3314	2
C₇×#3311	2
C₇×#3310	2
C₇×#3296	2
C₇×#3295	2
C₇×#3136	2
C₇×#3096	2
C₇×#3091	2
C₇×#3081	2
C₇×#3057	2
C₇×#3056	2
C₇×#3043	2
C₇×#3009	2
C₂×C₇×#450	2
C₇×#2949	2
C₇×#2933	2
C₇×#2897	2
C₂×C₇×#418	2
#61184	7

Subgroups — C7×#61184 #13238400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61184 #13238400