Subgroups — C₇×#61181 #13238397

Order 1792.

2032 conjugacy classes of subgroups.

The subgroup lattice has 1240 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×#3489	C₂	1	1	yes	maximal, characteristic
3	C₇×#3331	C₂	1	2	yes	maximal, complemented
4	C₇×#3328	C₂	1	2	yes	maximal, complemented
5	C₇×#3327	C₂	1	2	yes	maximal, complemented
6	C₇×#3323	C₂	1	2	yes	maximal, complemented
7	C₇×#3316	C₂	1	2	yes	maximal, complemented
8	C₇×#3315	C₂	1	2	yes	maximal, complemented
9	C₇×#3312	C₂	1	2	yes	maximal, complemented
10	C₇×#3311	C₂	1	2	yes	maximal, complemented
11	C₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3095	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#470	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3011	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2896	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
27	C₂×C₇×#137	C₂²	1	1	yes	characteristic
28	C₂²×C₇×Q₁₆	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
31	C₇×#556	C₂²	1	2	yes	—
32	C₇×#554	C₂²	1	2	yes	complemented
33	C₇×#552	—	2	2	no	—
34	C₇×#552	C₂²	1	2	yes	—
35	C₇×#552	C₂²	1	2	yes	complemented
36	C₇×#551	—	2	2	no	—
37	C₇×D₄×Q₈	C₂²	1	2	yes	—
38	C₇×#548	C₂²	1	2	yes	—
39	C₇×#547	—	2	2	no	—
40	C₇×#547	C₂²	1	2	yes	—
41	C₇×#546	—	2	2	no	—
42	C₇×#546	C₂²	1	2	yes	—
43	C₇×#544	C₂²	1	1	yes	characteristic, complemented
44	C₇×#542	—	2	1	no	—
45	C₇×#541	—	2	1	no	—
46	C₇×#537	—	2	1	no	—
47	C₇×#537	C₂²	1	1	yes	characteristic
48	C₇×#536	—	2	1	no	—
49	C₇×#536	C₂²	1	1	yes	characteristic
50	C₇×#536	C₂²	1	1	yes	characteristic, complemented
51	C₇×#533	—	2	1	no	—
52	C₇×#529	—	2	1	no	—
53	C₇×#525	—	2	1	no	—
54	C₇×#525	C₂²	1	1	yes	characteristic
55	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
56	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
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×#519	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₇×#117	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	—
67	C₇×#485	C₂²	1	2	yes	—
68	C₇×#485	C₂²	1	2	yes	complemented
69	C₇×#484	C₂²	1	2	yes	complemented
70	C₇×#483	C₂²	1	2	yes	complemented
71	C₇×#483	C₂²	1	2	yes	complemented
72	C₇×#482	C₂²	1	2	yes	complemented
73	C₇×#481	C₂²	1	2	yes	complemented
74	C₇×#479	C₂²	1	2	yes	complemented
75	C₇×#478	C₂²	1	2	yes	complemented
76	C₇×#476	C₂²	1	2	yes	complemented
77	C₇×#475	C₂²	1	2	yes	complemented
78	C₇×#470	C₂²	1	2	yes	—
79	C₇×#470	C₂²	1	2	yes	—
80	C₇×#470	C₂²	1	2	yes	complemented
81	C₇×#470	C₂²	1	2	yes	complemented
82	C₇×#470	C₂²	1	2	yes	complemented
83	C₇×#468	C₂²	1	2	yes	complemented
84	C₇×#467	C₂²	1	2	yes	complemented
85	C₇×#465	C₂²	1	2	yes	complemented
86	C₇×#464	C₂²	1	2	yes	complemented
87	C₇×#464	C₂²	1	2	yes	complemented
88	C₇×#462	C₂²	1	2	yes	complemented
89	C₇×#462	C₂²	1	2	yes	complemented
90	C₇×#452	C₂²	1	2	yes	—
91	C₇×#452	C₂²	1	2	yes	—
92	C₇×#452	C₂²	1	2	yes	complemented
93	C₇×#452	C₂²	1	2	yes	complemented
94	C₇×#451	C₂²	1	2	yes	—
95	C₇×#451	C₂²	1	2	yes	complemented
96	C₇×#451	C₂²	1	2	yes	complemented
97	C₇×#450	C₂²	1	2	yes	—
98	C₇×#441	C₂²	1	2	yes	complemented
99	C₇×#440	C₂²	1	2	yes	complemented
100	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
101	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
102	C₇×#436	C₂²	1	2	yes	—
103	C₇×#436	C₂²	1	2	yes	complemented
104	C₇×#435	C₂²	1	2	yes	—
105	C₇×#435	C₂²	1	2	yes	complemented
106	C₇×#428	C₂²	1	1	yes	characteristic, complemented
107	C₇×#428	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₇×#106	C₂²	1	1	yes	characteristic, complemented
109	C₇×#424	C₂²	1	1	yes	characteristic, complemented
110	C₇×#419	C₂²	1	1	yes	characteristic
111	C₇×#419	C₂²	1	1	yes	characteristic
112	C₇×#419	C₂²	1	1	yes	characteristic, complemented
113	C₇×#419	C₂²	1	1	yes	characteristic, complemented
114	C₇×#419	C₂²	1	2	yes	complemented
115	C₇×#418	C₂²	1	1	yes	characteristic
116	C₇×#418	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	1	yes	characteristic
120	C₇×#417	C₂²	1	1	yes	characteristic
121	C₇×#417	C₂²	1	1	yes	characteristic
122	C₇×#417	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
127	C₇×#416	C₂²	1	1	yes	characteristic
128	C₇×#416	C₂²	1	2	yes	complemented
129	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₇×#103	C₂²	1	2	yes	complemented
132	C₇×#408	C₂²	1	1	yes	characteristic, complemented
133	C₇×#407	C₂²	1	1	yes	characteristic
134	C₇×#405	C₂²	1	1	yes	characteristic, complemented
135	#61181	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	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	1	yes	characteristic
146	C₂×C₇×#41	C₂³	1	1	yes	characteristic
147	C₂×C₇×#41	C₂³	1	2	yes	—
148	C₂×C₇×#41	C₂³	1	1	yes	characteristic
149	C₂×C₇×#41	C₂³	1	1	yes	characteristic
150	C₂²×C₇×Q₈	—	2	1	no	—
151	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
152	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
154	C₂²×C₇×Q₈	C₂³	1	2	yes	—
155	C₂²×C₇×D₄	—	2	1	no	—
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×#137	—	2	4	no	—
160	C₇×#137	—	4	2	no	—
161	C₂×C₇×Q₁₆	—	4	2	no	—
162	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
163	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
164	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
165	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
166	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
167	C₂×C₇×SD₁₆	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	1	yes	characteristic
174	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
175	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
176	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
177	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
178	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
179	C₂²×C₇×C₈	C₂³	1	2	yes	—
180	C₇×C₄⋊Q₈	—	2	1	no	—
181	C₇×C₄⋊Q₈	—	2	1	no	—
182	C₇×C₄⋊Q₈	—	2	2	no	—
183	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
184	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
185	C₇×#126	—	2	2	no	—
186	C₇×#126	—	2	2	no	—
187	C₇×#126	—	2	2	no	—
188	C₇×#126	—	2	2	no	—
189	C₇×#125	—	2	1	no	—
190	C₇×#125	—	2	2	no	—
191	C₇×#125	—	2	2	no	—
192	C₇×#125	—	2	2	no	—
193	C₇×#125	C₂³	1	2	yes	—
194	C₇×#124	—	2	1	no	—
195	C₇×#124	—	2	2	no	—
196	C₇×#124	—	2	2	no	—
197	C₇×#124	C₂³	1	2	yes	—
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	1	no	—
212	C₇×C₂²⋊Q₈	—	2	2	no	—
213	C₇×C₂²⋊Q₈	—	2	1	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	2	yes	—
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	2	yes	—
227	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
228	C₇×#121	—	2	1	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	D₄	1	1	yes	characteristic
234	C₇×#121	D₄	1	1	yes	characteristic
235	C₇×#121	C₂³	1	2	yes	—
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	—
243	C₄×C₇×Q₈	C₂³	1	2	yes	—
244	C₄×C₇×Q₈	C₂³	1	2	yes	—
245	C₄×C₇×D₄	—	2	1	no	—
246	C₄×C₇×D₄	—	2	2	no	—
247	C₄×C₇×D₄	—	2	2	no	—
248	C₄×C₇×D₄	—	2	2	no	—
249	C₄×C₇×D₄	—	2	2	no	—
250	C₄×C₇×D₄	—	2	2	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	C₇×#117	—	2	1	no	—
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	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	C₇×#117	C₂³	1	1	yes	characteristic
266	C₂×C₇×C₄⋊C₄	—	2	1	no	—
267	C₂×C₇×C₄⋊C₄	—	2	1	no	—
268	C₂×C₇×C₄⋊C₄	—	2	1	no	—
269	C₂×C₇×C₄⋊C₄	—	2	2	no	—
270	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
271	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₄²×C₇	—	2	1	no	—
280	C₇×#107	C₂³	1	2	yes	—
281	C₇×#107	C₂³	1	2	yes	—
282	C₇×#106	C₂³	1	2	yes	—
283	C₇×#106	C₂³	1	2	yes	—
284	C₇×#106	C₂³	1	2	yes	—
285	C₇×#106	C₂³	1	2	yes	—
286	C₇×C₄⋊C₈	C₂³	1	2	yes	—
287	C₇×C₄⋊C₈	C₂³	1	2	yes	—
288	C₇×#103	C₂³	1	1	yes	characteristic
289	C₇×#103	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	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
302	C₇×#103	C₂³	1	2	yes	—
303	C₇×#103	C₂³	1	1	yes	characteristic
304	C₇×#103	C₂³	1	1	yes	characteristic
305	C₇×#103	C₂³	1	1	yes	characteristic
306	C₇×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
314	C₇×#102	C₂³	1	1	yes	characteristic
315	C₇×#102	C₂³	1	1	yes	characteristic
316	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
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	#3495	C₂×C₇	1	1	yes	characteristic, complemented
323	#3489	C₂×C₇	1	1	yes	characteristic
324	#3331	C₂×C₇	1	2	yes	complemented
325	#3328	C₂×C₇	1	2	yes	complemented
326	#3327	C₂×C₇	1	2	yes	complemented
327	#3323	C₂×C₇	1	2	yes	complemented
328	#3316	C₂×C₇	1	2	yes	complemented
329	#3315	C₂×C₇	1	2	yes	complemented
330	#3312	C₂×C₇	1	2	yes	complemented
331	#3311	C₂×C₇	1	2	yes	complemented
332	#3137	C₂×C₇	1	1	yes	characteristic, complemented
333	#3099	C₂×C₇	1	1	yes	characteristic, complemented
334	#3095	C₂×C₇	1	1	yes	characteristic, complemented
335	#3084	C₂×C₇	1	1	yes	characteristic, complemented
336	#3063	C₂×C₇	1	1	yes	characteristic, complemented
337	C₂×#470	C₂×C₇	1	1	yes	characteristic, complemented
338	#3044	C₂×C₇	1	1	yes	characteristic, complemented
339	#3011	C₂×C₇	1	1	yes	characteristic, complemented
340	#3007	C₂×C₇	1	1	yes	characteristic, complemented
341	#2947	C₂×C₇	1	1	yes	characteristic, complemented
342	#2930	C₂×C₇	1	1	yes	characteristic, complemented
343	#2898	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	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	—	4	4	no	—
356	C₇×#41	—	4	1	no	—
357	C₇×#41	—	4	1	no	—
358	C₇×#41	—	4	2	no	—
359	C₇×#41	—	4	4	no	—
360	C₇×#41	—	4	4	no	—
361	C₇×#41	—	4	8	no	—
362	C₇×#41	#41	1	4	yes	—
363	C₂×C₇×Q₈	—	2	1	no	—
364	C₂×C₇×Q₈	—	2	1	no	—
365	C₂×C₇×Q₈	—	2	2	no	—
366	C₂×C₇×Q₈	—	2	1	no	—
367	C₂×C₇×Q₈	—	2	2	no	—
368	C₂×C₇×Q₈	—	2	2	no	—
369	C₂×C₇×Q₈	—	2	4	no	—
370	C₂×C₇×Q₈	—	2	2	no	—
371	C₂×C₇×Q₈	—	2	2	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	2	yes	—
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	2	no	—
385	C₂×C₇×D₄	—	2	1	no	—
386	C₂×C₇×D₄	—	2	1	no	—
387	C₂×C₇×D₄	—	2	1	no	—
388	C₂×C₇×D₄	—	2	2	no	—
389	C₂×C₇×D₄	—	2	1	no	—
390	C₂×C₇×D₄	—	4	1	no	—
391	C₂×C₇×D₄	—	4	4	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	C₂⁴	1	1	yes	characteristic
397	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₇	—	2	1	no	—
399	C₂²×C₄×C₇	—	2	2	no	—
400	C₂²×C₄×C₇	—	2	2	no	—
401	C₂²×C₄×C₇	—	2	1	no	—
402	C₂²×C₄×C₇	—	2	1	no	—
403	C₂²×C₄×C₇	—	2	1	no	—
404	C₂²×C₄×C₇	—	2	2	no	—
405	C₂²×C₄×C₇	—	2	1	no	—
406	C₂²×C₄×C₇	—	2	1	no	—
407	C₂²×C₄×C₇	—	2	1	no	—
408	C₂²×C₄×C₇	—	2	1	no	—
409	C₂²×C₄×C₇	—	2	2	no	—
410	C₂²×C₄×C₇	—	2	2	no	—
411	C₂²×C₄×C₇	—	2	1	no	—
412	C₂²×C₄×C₇	—	2	1	no	—
413	C₂²×C₄×C₇	—	2	1	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×Q₁₆	—	2	4	no	—
424	C₇×Q₁₆	—	4	2	no	—
425	C₇×Q₁₆	—	4	2	no	—
426	C₇×Q₁₆	—	4	2	no	—
427	C₇×SD₁₆	—	2	4	no	—
428	C₇×SD₁₆	—	4	2	no	—
429	C₇×M₁₆	—	2	2	no	—
430	C₇×M₁₆	—	2	2	no	—
431	C₇×M₁₆	—	4	1	no	—
432	C₇×M₁₆	—	4	1	no	—
433	C₇×M₁₆	—	4	1	no	—
434	C₇×M₁₆	—	4	1	no	—
435	C₇×M₁₆	—	4	2	no	—
436	C₂×C₇×C₈	—	2	2	no	—
437	C₂×C₇×C₈	—	2	2	no	—
438	C₂×C₇×C₈	—	4	2	no	—
439	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
440	C₂×C₇×C₈	C₂⁴	1	2	yes	—
441	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
442	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
443	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
444	C₂×C₇×C₈	C₂⁴	1	2	yes	—
445	C₇×C₄⋊C₄	—	2	2	no	—
446	C₇×C₄⋊C₄	—	2	1	no	—
447	C₇×C₄⋊C₄	—	2	2	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	1	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	—	2	2	no	—
459	C₇×C₄⋊C₄	—	2	2	no	—
460	C₇×C₄⋊C₄	—	2	2	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	C₂×D₄	1	1	yes	characteristic
466	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
467	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
468	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
469	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
470	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
471	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
472	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
473	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
474	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
475	C₇×C₂²⋊C₄	—	2	2	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	1	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	—	2	2	no	—
490	C₇×C₂²⋊C₄	—	2	2	no	—
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	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
495	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
496	C₄²×C₇	—	2	1	no	—
497	C₄²×C₇	—	2	1	no	—
498	C₄²×C₇	—	2	1	no	—
499	C₄²×C₇	—	2	1	no	—
500	C₄²×C₇	—	2	2	no	—
501	C₄²×C₇	—	2	2	no	—
502	C₄²×C₇	—	2	2	no	—
503	C₄²×C₇	—	2	2	no	—
504	C₄²×C₇	C₂⁴	1	2	yes	—
505	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
506	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
507	C₂×#137	C₂²×C₇	1	1	yes	characteristic
508	C₂×#137	C₂²×C₇	1	1	yes	characteristic
509	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
510	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
511	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
512	#556	C₂²×C₇	1	2	yes	—
513	#554	C₂²×C₇	1	2	yes	complemented
514	#552	—	2	2	no	—
515	#552	C₂²×C₇	1	2	yes	—
516	#552	C₂²×C₇	1	2	yes	complemented
517	#551	—	2	2	no	—
518	D₄×Q₈	C₂²×C₇	1	2	yes	—
519	#548	C₂²×C₇	1	2	yes	—
520	#547	—	2	2	no	—
521	#547	C₂²×C₇	1	2	yes	—
522	#546	—	2	2	no	—
523	#546	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	#537	—	2	1	no	—
528	#537	C₂²×C₇	1	1	yes	characteristic
529	#536	—	2	1	no	—
530	#536	C₂²×C₇	1	1	yes	characteristic
531	#536	C₂²×C₇	1	1	yes	characteristic, complemented
532	#533	—	2	1	no	—
533	#529	—	2	1	no	—
534	#525	—	2	1	no	—
535	#525	C₂²×C₇	1	1	yes	characteristic
536	C₂×C₂²⋊Q₈	—	2	1	no	—
537	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
538	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
539	#520	C₂²×C₇	1	1	yes	characteristic
540	#520	C₂²×C₇	1	1	yes	characteristic, complemented
541	#519	C₂²×C₇	1	1	yes	characteristic, complemented
542	C₂×#117	C₂²×C₇	1	1	yes	characteristic
543	#491	C₂²×C₇	1	2	yes	complemented
544	#489	C₂²×C₇	1	2	yes	complemented
545	#488	C₂²×C₇	1	2	yes	complemented
546	#487	C₂²×C₇	1	2	yes	complemented
547	#485	C₂²×C₇	1	2	yes	—
548	#485	C₂²×C₇	1	2	yes	—
549	#485	C₂²×C₇	1	2	yes	complemented
550	#484	C₂²×C₇	1	2	yes	complemented
551	#483	C₂²×C₇	1	2	yes	complemented
552	#483	C₂²×C₇	1	2	yes	complemented
553	#482	C₂²×C₇	1	2	yes	complemented
554	#481	C₂²×C₇	1	2	yes	complemented
555	#479	C₂²×C₇	1	2	yes	complemented
556	#478	C₂²×C₇	1	2	yes	complemented
557	#476	C₂²×C₇	1	2	yes	complemented
558	#475	C₂²×C₇	1	2	yes	complemented
559	#470	C₂²×C₇	1	2	yes	—
560	#470	C₂²×C₇	1	2	yes	—
561	#470	C₂²×C₇	1	2	yes	complemented
562	#470	C₂²×C₇	1	2	yes	complemented
563	#470	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	#464	C₂²×C₇	1	2	yes	complemented
568	#464	C₂²×C₇	1	2	yes	complemented
569	#462	C₂²×C₇	1	2	yes	complemented
570	#462	C₂²×C₇	1	2	yes	complemented
571	#452	C₂²×C₇	1	2	yes	—
572	#452	C₂²×C₇	1	2	yes	—
573	#452	C₂²×C₇	1	2	yes	complemented
574	#452	C₂²×C₇	1	2	yes	complemented
575	#451	C₂²×C₇	1	2	yes	—
576	#451	C₂²×C₇	1	2	yes	complemented
577	#451	C₂²×C₇	1	2	yes	complemented
578	#450	C₂²×C₇	1	2	yes	—
579	#441	C₂²×C₇	1	2	yes	complemented
580	#440	C₂²×C₇	1	2	yes	complemented
581	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
582	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
583	#436	C₂²×C₇	1	2	yes	—
584	#436	C₂²×C₇	1	2	yes	complemented
585	#435	C₂²×C₇	1	2	yes	—
586	#435	C₂²×C₇	1	2	yes	complemented
587	#428	C₂²×C₇	1	1	yes	characteristic, complemented
588	#428	C₂²×C₇	1	1	yes	characteristic, complemented
589	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
590	#424	C₂²×C₇	1	1	yes	characteristic, complemented
591	#419	C₂²×C₇	1	1	yes	characteristic
592	#419	C₂²×C₇	1	1	yes	characteristic
593	#419	C₂²×C₇	1	2	yes	complemented
594	#419	C₂²×C₇	1	1	yes	characteristic, complemented
595	#419	C₂²×C₇	1	1	yes	characteristic, complemented
596	#418	C₂²×C₇	1	1	yes	characteristic
597	#418	C₂²×C₇	1	1	yes	characteristic
598	#417	C₂²×C₇	1	1	yes	characteristic
599	#417	C₂²×C₇	1	1	yes	characteristic
600	#417	C₂²×C₇	1	1	yes	characteristic
601	#417	C₂²×C₇	1	1	yes	characteristic
602	#417	C₂²×C₇	1	1	yes	characteristic
603	#417	C₂²×C₇	1	1	yes	characteristic
604	#417	C₂²×C₇	1	2	yes	complemented
605	#416	C₂²×C₇	1	1	yes	characteristic
606	#416	C₂²×C₇	1	1	yes	characteristic
607	#416	C₂²×C₇	1	1	yes	characteristic
608	#416	C₂²×C₇	1	1	yes	characteristic
609	#416	C₂²×C₇	1	2	yes	complemented
610	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
611	C₂×#103	C₂²×C₇	1	2	yes	complemented
612	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
613	#408	C₂²×C₇	1	1	yes	characteristic, complemented
614	#407	C₂²×C₇	1	1	yes	characteristic
615	#405	C₂²×C₇	1	1	yes	characteristic, complemented
616	C₂³×C₇	—	2	1	no	—
617	C₂³×C₇	—	2	2	no	—
618	C₂³×C₇	—	2	1	no	—
619	C₂³×C₇	—	4	1	no	—
620	C₂³×C₇	—	4	1	no	—
621	C₂³×C₇	—	4	2	no	—
622	C₂³×C₇	—	4	2	no	—
623	C₂³×C₇	—	8	1	no	—
624	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
625	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
626	C₂³×C₇	C₂²×D₄	1	2	yes	—
627	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
628	C₇×Q₈	—	2	2	no	—
629	C₇×Q₈	—	2	1	no	—
630	C₇×Q₈	—	2	2	no	—
631	C₇×Q₈	—	2	2	no	—
632	C₇×Q₈	—	2	1	no	—
633	C₇×Q₈	—	2	2	no	—
634	C₇×Q₈	—	2	2	no	—
635	C₇×Q₈	—	2	1	no	—
636	C₇×Q₈	—	4	4	no	—
637	C₇×Q₈	—	4	2	no	—
638	C₇×Q₈	—	4	2	no	—
639	C₇×Q₈	—	4	2	no	—
640	C₇×Q₈	—	8	2	no	—
641	C₇×Q₈	C₂×#41	1	2	yes	—
642	C₇×D₄	—	2	4	no	—
643	C₇×D₄	—	2	4	no	—
644	C₇×D₄	—	2	2	no	—
645	C₇×D₄	—	2	1	no	—
646	C₇×D₄	—	2	1	no	—
647	C₇×D₄	—	2	1	no	—
648	C₇×D₄	—	4	2	no	—
649	C₇×D₄	—	4	2	no	—
650	C₇×D₄	—	4	2	no	—
651	C₇×D₄	—	4	2	no	—
652	C₇×D₄	—	4	2	no	—
653	C₇×D₄	—	4	4	no	—
654	C₇×D₄	—	4	2	no	—
655	C₇×D₄	—	8	2	no	—
656	C₇×D₄	C₂×#41	1	2	yes	—
657	C₂×C₄×C₇	—	2	2	no	—
658	C₂×C₄×C₇	—	2	1	no	—
659	C₂×C₄×C₇	—	2	2	no	—
660	C₂×C₄×C₇	—	2	2	no	—
661	C₂×C₄×C₇	—	2	4	no	—
662	C₂×C₄×C₇	—	2	1	no	—
663	C₂×C₄×C₇	—	2	1	no	—
664	C₂×C₄×C₇	—	2	2	no	—
665	C₂×C₄×C₇	—	2	2	no	—
666	C₂×C₄×C₇	—	2	1	no	—
667	C₂×C₄×C₇	—	2	1	no	—
668	C₂×C₄×C₇	—	2	1	no	—
669	C₂×C₄×C₇	—	2	1	no	—
670	C₂×C₄×C₇	—	2	1	no	—
671	C₂×C₄×C₇	—	2	2	no	—
672	C₂×C₄×C₇	—	2	1	no	—
673	C₂×C₄×C₇	—	2	2	no	—
674	C₂×C₄×C₇	—	2	2	no	—
675	C₂×C₄×C₇	—	2	2	no	—
676	C₂×C₄×C₇	—	2	1	no	—
677	C₂×C₄×C₇	—	4	2	no	—
678	C₂×C₄×C₇	—	4	2	no	—
679	C₂×C₄×C₇	—	4	2	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	—	4	2	no	—
686	C₂×C₄×C₇	—	8	2	no	—
687	C₂×C₄×C₇	—	8	2	no	—
688	C₂×C₄×C₇	—	8	1	no	—
689	C₂×C₄×C₇	—	8	1	no	—
690	C₂×C₄×C₇	—	8	1	no	—
691	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
696	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
697	C₂×C₄×C₇	C₂×#41	1	2	yes	—
698	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
699	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
700	C₇×C₈	—	2	2	no	—
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	2₋¹⁺⁴	—	2	4	no	—
707	2₋¹⁺⁴	—	4	2	no	—
708	C₂×#41	—	2	1	no	—
709	C₂×#41	—	2	2	no	—
710	C₂×#41	—	2	1	no	—
711	C₂×#41	—	2	1	no	—
712	C₂×#41	—	2	4	no	—
713	C₂×#41	—	4	2	no	—
714	C₂×#41	C₂³×C₇	1	1	yes	characteristic
715	C₂×#41	C₂³×C₇	1	2	yes	—
716	C₂×#41	C₂³×C₇	1	1	yes	characteristic
717	C₂×#41	C₂³×C₇	1	1	yes	characteristic
718	C₂×#41	C₂³×C₇	1	1	yes	characteristic
719	C₂×#41	C₂³×C₇	1	1	yes	characteristic
720	C₂²×Q₈	—	2	1	no	—
721	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
722	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
723	C₂²×Q₈	C₂³×C₇	1	2	yes	—
724	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
725	C₂²×D₄	—	2	1	no	—
726	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
727	C₂³×C₄	—	2	1	no	—
728	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
729	#137	—	2	4	no	—
730	#137	—	4	2	no	—
731	C₂×Q₁₆	—	4	2	no	—
732	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
733	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
734	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
735	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
738	#131	—	4	2	no	—
739	C₂×M₁₆	—	4	2	no	—
740	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
741	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
742	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
743	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
744	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
745	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
746	C₂×M₁₆	C₂³×C₇	1	2	yes	—
747	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
748	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
749	C₂²×C₈	C₂³×C₇	1	2	yes	—
750	C₄⋊Q₈	—	2	1	no	—
751	C₄⋊Q₈	—	2	1	no	—
752	C₄⋊Q₈	—	2	2	no	—
753	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
754	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#125	—	2	1	no	—
760	#125	—	2	2	no	—
761	#125	—	2	2	no	—
762	#125	—	2	2	no	—
763	#125	C₂³×C₇	1	2	yes	—
764	#124	—	2	1	no	—
765	#124	—	2	2	no	—
766	#124	—	2	2	no	—
767	#124	C₂³×C₇	1	2	yes	—
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	C₇×D₄	1	2	yes	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
790	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
791	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
792	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
795	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
796	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
797	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
798	#121	—	2	1	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	C₇×D₄	1	1	yes	characteristic
804	#121	C₇×D₄	1	1	yes	characteristic
805	#121	C₂³×C₇	1	2	yes	—
806	#120	—	2	2	no	—
807	#120	C₇×D₄	1	2	yes	—
808	C₄×Q₈	—	2	1	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	—	2	1	no	—
811	C₄×Q₈	—	2	2	no	—
812	C₄×Q₈	C₂³×C₇	1	2	yes	—
813	C₄×Q₈	C₂³×C₇	1	2	yes	—
814	C₄×Q₈	C₂³×C₇	1	2	yes	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
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	#117	—	2	1	no	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	—	2	2	no	—
828	#117	—	2	2	no	—
829	#117	—	2	2	no	—
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	1	no	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	—	2	1	no	—
839	C₂×C₄⋊C₄	—	2	2	no	—
840	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
842	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
843	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
844	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
845	C₂×C₂²⋊C₄	—	2	1	no	—
846	C₂×C₂²⋊C₄	—	2	1	no	—
847	C₂×C₂²⋊C₄	—	2	1	no	—
848	C₂×C₂²⋊C₄	—	2	2	no	—
849	C₂×C₄²	—	2	1	no	—
850	#107	C₂³×C₇	1	2	yes	—
851	#107	C₂³×C₇	1	2	yes	—
852	#106	C₂³×C₇	1	2	yes	—
853	#106	C₂³×C₇	1	2	yes	—
854	#106	C₂³×C₇	1	2	yes	—
855	#106	C₂³×C₇	1	2	yes	—
856	C₄⋊C₈	C₂³×C₇	1	2	yes	—
857	C₄⋊C₈	C₂³×C₇	1	2	yes	—
858	#103	C₂³×C₇	1	1	yes	characteristic
859	#103	C₂³×C₇	1	2	yes	—
860	#103	C₂³×C₇	1	2	yes	—
861	#103	C₂³×C₇	1	2	yes	—
862	#103	C₂³×C₇	1	2	yes	—
863	#103	C₂³×C₇	1	2	yes	—
864	#103	C₂³×C₇	1	2	yes	—
865	#103	C₂³×C₇	1	1	yes	characteristic
866	#103	C₂³×C₇	1	1	yes	characteristic
867	#103	C₂³×C₇	1	1	yes	characteristic
868	#103	C₂³×C₇	1	1	yes	characteristic
869	#103	C₂³×C₇	1	1	yes	characteristic
870	#103	C₂³×C₇	1	1	yes	characteristic
871	#103	C₂³×C₇	1	1	yes	characteristic
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	2	yes	—
876	#102	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
881	#102	C₂³×C₇	1	1	yes	characteristic
882	#102	C₂³×C₇	1	1	yes	characteristic
883	#102	C₂³×C₇	1	1	yes	characteristic
884	#102	C₂³×C₇	1	2	yes	—
885	#102	C₂³×C₇	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
890	#97	C₂³×C₇	1	2	yes	—
891	C₄×C₈	C₂³×C₇	1	2	yes	—
892	C₂²×C₇	—	2	1	no	—
893	C₂²×C₇	—	2	1	no	—
894	C₂²×C₇	—	2	1	no	—
895	C₂²×C₇	—	2	2	no	—
896	C₂²×C₇	—	2	1	no	—
897	C₂²×C₇	—	2	1	no	—
898	C₂²×C₇	—	2	2	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	2	no	—
904	C₂²×C₇	—	4	1	no	—
905	C₂²×C₇	—	4	1	no	—
906	C₂²×C₇	—	4	1	no	—
907	C₂²×C₇	—	4	1	no	—
908	C₂²×C₇	—	4	1	no	—
909	C₂²×C₇	—	8	2	no	—
910	C₂²×C₇	—	8	4	no	—
911	C₂²×C₇	#546	1	2	yes	—
912	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
913	C₄×C₇	—	2	2	no	—
914	C₄×C₇	—	2	2	no	—
915	C₄×C₇	—	2	1	no	—
916	C₄×C₇	—	2	1	no	—
917	C₄×C₇	—	2	2	no	—
918	C₄×C₇	—	2	2	no	—
919	C₄×C₇	—	4	1	no	—
920	C₄×C₇	—	4	1	no	—
921	C₄×C₇	—	4	1	no	—
922	C₄×C₇	—	4	2	no	—
923	C₄×C₇	—	4	2	no	—
924	C₄×C₇	—	4	1	no	—
925	C₄×C₇	—	4	1	no	—
926	C₄×C₇	—	4	2	no	—
927	C₄×C₇	—	4	2	no	—
928	C₄×C₇	#546	1	2	yes	—
929	C₄×C₇	C₂²×#41	1	1	yes	characteristic
930	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
931	C₂⁴	—	2	1	no	—
932	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
933	#41	—	2	2	no	—
934	#41	—	2	2	no	—
935	#41	—	2	2	no	—
936	#41	—	2	2	no	—
937	#41	—	2	2	no	—
938	#41	—	2	4	no	—
939	#41	—	2	2	no	—
940	#41	—	2	2	no	—
941	#41	—	4	4	no	—
942	#41	—	4	1	no	—
943	#41	—	4	1	no	—
944	#41	—	4	2	no	—
945	#41	—	4	4	no	—
946	#41	—	4	4	no	—
947	#41	—	4	8	no	—
948	#41	C₇×#41	1	4	yes	—
949	C₂×Q₈	—	2	1	no	—
950	C₂×Q₈	—	2	1	no	—
951	C₂×Q₈	—	2	2	no	—
952	C₂×Q₈	—	2	1	no	—
953	C₂×Q₈	—	2	2	no	—
954	C₂×Q₈	—	2	2	no	—
955	C₂×Q₈	—	2	4	no	—
956	C₂×Q₈	—	2	2	no	—
957	C₂×Q₈	—	2	2	no	—
958	C₂×Q₈	—	2	2	no	—
959	C₂×Q₈	—	2	2	no	—
960	C₂×Q₈	—	4	1	no	—
961	C₂×Q₈	—	4	2	no	—
962	C₂×Q₈	—	4	4	no	—
963	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
964	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
965	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
966	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
967	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
968	C₂×D₄	—	2	1	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	1	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	1	no	—
976	C₂×D₄	—	4	1	no	—
977	C₂×D₄	—	4	4	no	—
978	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
979	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
980	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
981	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
982	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
983	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	1	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	4	4	no	—
1002	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1003	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1004	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1005	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1006	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
1007	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1008	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1009	Q₁₆	—	2	4	no	—
1010	Q₁₆	—	4	2	no	—
1011	Q₁₆	—	4	2	no	—
1012	Q₁₆	—	4	2	no	—
1013	SD₁₆	—	2	4	no	—
1014	SD₁₆	—	4	2	no	—
1015	M₁₆	—	2	2	no	—
1016	M₁₆	—	2	2	no	—
1017	M₁₆	—	4	1	no	—
1018	M₁₆	—	4	1	no	—
1019	M₁₆	—	4	1	no	—
1020	M₁₆	—	4	1	no	—
1021	M₁₆	—	4	2	no	—
1022	C₂×C₈	—	2	2	no	—
1023	C₂×C₈	—	2	2	no	—
1024	C₂×C₈	—	4	2	no	—
1025	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1026	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1027	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1028	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1029	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1030	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	2	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	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1052	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1053	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1054	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1055	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1056	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1057	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1058	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1059	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1060	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	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	C₂×C₇×D₄	1	2	yes	—
1078	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1079	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1080	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1081	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1082	C₄²	—	2	1	no	—
1083	C₄²	—	2	1	no	—
1084	C₄²	—	2	1	no	—
1085	C₄²	—	2	1	no	—
1086	C₄²	—	2	2	no	—
1087	C₄²	—	2	2	no	—
1088	C₄²	—	2	2	no	—
1089	C₄²	—	2	2	no	—
1090	C₄²	C₂⁴×C₇	1	2	yes	—
1091	C₂×C₇	—	2	2	no	—
1092	C₂×C₇	—	4	2	no	—
1093	C₂×C₇	—	4	1	no	—
1094	C₂×C₇	—	4	1	no	—
1095	C₂×C₇	—	4	2	no	—
1096	C₂×C₇	—	8	1	no	—
1097	C₂×C₇	C₂×#546	1	1	yes	characteristic
1098	C₂×C₇	#3586	1	1	yes	characteristic
1099	C₂×C₇	#3586	1	1	yes	characteristic
1100	C₂³	—	2	1	no	—
1101	C₂³	—	2	2	no	—
1102	C₂³	—	2	1	no	—
1103	C₂³	—	4	1	no	—
1104	C₂³	—	4	1	no	—
1105	C₂³	—	4	2	no	—
1106	C₂³	—	4	2	no	—
1107	C₂³	—	8	1	no	—
1108	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1109	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1110	C₂³	C₂²×C₇×D₄	1	2	yes	—
1111	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1112	Q₈	—	2	1	no	—
1113	Q₈	—	2	2	no	—
1114	Q₈	—	2	2	no	—
1115	Q₈	—	2	2	no	—
1116	Q₈	—	2	1	no	—
1117	Q₈	—	2	2	no	—
1118	Q₈	—	2	2	no	—
1119	Q₈	—	2	1	no	—
1120	Q₈	—	4	4	no	—
1121	Q₈	—	4	2	no	—
1122	Q₈	—	4	2	no	—
1123	Q₈	—	4	2	no	—
1124	Q₈	—	8	2	no	—
1125	Q₈	C₂×C₇×#41	1	2	yes	—
1126	D₄	—	2	4	no	—
1127	D₄	—	2	4	no	—
1128	D₄	—	2	1	no	—
1129	D₄	—	2	1	no	—
1130	D₄	—	2	1	no	—
1131	D₄	—	2	2	no	—
1132	D₄	—	4	2	no	—
1133	D₄	—	4	2	no	—
1134	D₄	—	4	2	no	—
1135	D₄	—	4	2	no	—
1136	D₄	—	4	2	no	—
1137	D₄	—	4	4	no	—
1138	D₄	—	4	2	no	—
1139	D₄	—	8	2	no	—
1140	D₄	C₂×C₇×#41	1	2	yes	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	4	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	4	2	no	—
1162	C₂×C₄	—	4	2	no	—
1163	C₂×C₄	—	4	2	no	—
1164	C₂×C₄	—	4	4	no	—
1165	C₂×C₄	—	4	4	no	—
1166	C₂×C₄	—	4	2	no	—
1167	C₂×C₄	—	4	2	no	—
1168	C₂×C₄	—	4	2	no	—
1169	C₂×C₄	—	4	2	no	—
1170	C₂×C₄	—	8	2	no	—
1171	C₂×C₄	—	8	2	no	—
1172	C₂×C₄	—	8	1	no	—
1173	C₂×C₄	—	8	1	no	—
1174	C₂×C₄	—	8	1	no	—
1175	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1176	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1177	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1178	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1179	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1180	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1181	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1182	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1183	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1184	C₈	—	2	2	no	—
1185	C₈	—	2	1	no	—
1186	C₈	—	2	1	no	—
1187	C₈	—	2	1	no	—
1188	C₈	—	2	1	no	—
1189	C₈	—	2	2	no	—
1190	C₇	#61181	1	1	yes	characteristic, direct product factor, Sylow
1191	C₂²	—	2	1	no	—
1192	C₂²	—	2	1	no	—
1193	C₂²	—	2	1	no	—
1194	C₂²	—	2	2	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	1	no	—
1197	C₂²	—	2	2	no	—
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	1	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	8	2	no	—
1209	C₂²	—	8	4	no	—
1210	C₂²	C₇×#546	1	2	yes	—
1211	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1212	C₄	—	2	2	no	—
1213	C₄	—	2	2	no	—
1214	C₄	—	2	1	no	—
1215	C₄	—	2	1	no	—
1216	C₄	—	2	2	no	—
1217	C₄	—	2	2	no	—
1218	C₄	—	4	1	no	—
1219	C₄	—	4	1	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	2	no	—
1222	C₄	—	4	2	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	2	no	—
1226	C₄	—	4	2	no	—
1227	C₄	C₇×#546	1	2	yes	—
1228	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1229	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1230	C₂	—	2	2	no	—
1231	C₂	—	4	1	no	—
1232	C₂	—	4	1	no	—
1233	C₂	—	4	2	no	—
1234	C₂	—	4	2	no	—
1235	C₂	—	8	1	no	—
1236	C₂	C₂×C₇×#546	1	1	yes	characteristic
1237	C₂	C₇×#3586	1	1	yes	characteristic
1238	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3489	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×#3331	C₂	semidirect
4. C₇×#3328	C₂	semidirect
5. C₇×#3327	C₂	semidirect
6. C₇×#3323	C₂	semidirect
7. C₇×#3316	C₂	semidirect
8. C₇×#3315	C₂	semidirect
9. C₇×#3312	C₂	semidirect
10. C₇×#3311	C₂	semidirect
11. C₇×#3137	C₂	semidirect
12. C₇×#3099	C₂	semidirect
13. C₇×#3095	C₂	semidirect
14. C₇×#3084	C₂	semidirect
15. C₇×#3063	C₂	semidirect
16. C₂×C₇×#470	C₂	semidirect
17. C₇×#3044	C₂	semidirect
18. C₇×#3011	C₂	semidirect
19. C₇×#3007	C₂	semidirect
20. C₇×#2947	C₂	semidirect
21. C₇×#2930	C₂	semidirect
22. C₇×#2898	C₂	semidirect
23. C₇×#2896	C₂	semidirect
28. C₂²×C₇×Q₁₆	C₂²	semidirect
29. C₂×C₇×#131	C₂²	semidirect
32. C₇×#554	C₂²	semidirect
35. C₇×#552	C₂²	semidirect
43. C₇×#544	C₂²	semidirect
50. C₇×#536	C₂²	semidirect
59. C₇×#520	C₂²	semidirect
60. C₇×#519	C₂²	semidirect
62. C₇×#491	C₂²	semidirect
63. C₇×#489	C₂²	semidirect
64. C₇×#488	C₂²	semidirect
65. C₇×#487	C₂²	semidirect
68. C₇×#485	C₂²	semidirect
69. C₇×#484	C₂²	semidirect
70. C₇×#483	C₂²	semidirect
71. C₇×#483	C₂²	semidirect
72. C₇×#482	C₂²	semidirect
73. C₇×#481	C₂²	semidirect
74. C₇×#479	C₂²	semidirect
75. C₇×#478	C₂²	semidirect
76. C₇×#476	C₂²	semidirect
77. C₇×#475	C₂²	semidirect
80. C₇×#470	C₂²	semidirect
81. C₇×#470	C₂²	semidirect
82. C₇×#470	C₂²	semidirect
83. C₇×#468	C₂²	semidirect
84. C₇×#467	C₂²	semidirect
85. C₇×#465	C₂²	semidirect
86. C₇×#464	C₂²	semidirect
87. C₇×#464	C₂²	semidirect
88. C₇×#462	C₂²	semidirect
89. C₇×#462	C₂²	semidirect
92. C₇×#452	C₂²	semidirect
93. C₇×#452	C₂²	semidirect
95. C₇×#451	C₂²	semidirect
96. C₇×#451	C₂²	semidirect
98. C₇×#441	C₂²	semidirect
99. C₇×#440	C₂²	semidirect
100. C₄×C₇×Q₁₆	C₂²	semidirect
101. C₄×C₇×SD₁₆	C₂²	semidirect
103. C₇×#436	C₂²	semidirect
105. C₇×#435	C₂²	semidirect
106. C₇×#428	C₂²	semidirect
107. C₇×#428	C₂²	semidirect
108. C₂×C₇×#106	C₂²	semidirect
109. C₇×#424	C₂²	semidirect
112. C₇×#419	C₂²	semidirect
113. C₇×#419	C₂²	semidirect
114. C₇×#419	C₂²	semidirect
123. C₇×#417	C₂²	semidirect
128. C₇×#416	C₂²	semidirect
129. C₂×C₇×#103	C₂²	semidirect
130. C₂×C₇×#103	C₂²	semidirect
131. C₂×C₇×#103	C₂²	semidirect
132. C₇×#408	C₂²	semidirect
134. C₇×#405	C₂²	semidirect
135. #61181	C₇	direct (N × H)
322. #3495	C₂×C₇	semidirect
324. #3331	C₂×C₇	semidirect
325. #3328	C₂×C₇	semidirect
326. #3327	C₂×C₇	semidirect
327. #3323	C₂×C₇	semidirect
328. #3316	C₂×C₇	semidirect
329. #3315	C₂×C₇	semidirect
330. #3312	C₂×C₇	semidirect
331. #3311	C₂×C₇	semidirect
332. #3137	C₂×C₇	semidirect
333. #3099	C₂×C₇	semidirect
334. #3095	C₂×C₇	semidirect
335. #3084	C₂×C₇	semidirect
336. #3063	C₂×C₇	semidirect
337. C₂×#470	C₂×C₇	semidirect
338. #3044	C₂×C₇	semidirect
339. #3011	C₂×C₇	semidirect
340. #3007	C₂×C₇	semidirect
341. #2947	C₂×C₇	semidirect
342. #2930	C₂×C₇	semidirect
343. #2898	C₂×C₇	semidirect
344. #2896	C₂×C₇	semidirect
509. C₂²×Q₁₆	C₂²×C₇	semidirect
510. C₂×#131	C₂²×C₇	semidirect
513. #554	C₂²×C₇	semidirect
516. #552	C₂²×C₇	semidirect
524. #544	C₂²×C₇	semidirect
531. #536	C₂²×C₇	semidirect
540. #520	C₂²×C₇	semidirect
541. #519	C₂²×C₇	semidirect
543. #491	C₂²×C₇	semidirect
544. #489	C₂²×C₇	semidirect
545. #488	C₂²×C₇	semidirect
546. #487	C₂²×C₇	semidirect
549. #485	C₂²×C₇	semidirect
550. #484	C₂²×C₇	semidirect
551. #483	C₂²×C₇	semidirect
552. #483	C₂²×C₇	semidirect
553. #482	C₂²×C₇	semidirect
554. #481	C₂²×C₇	semidirect
555. #479	C₂²×C₇	semidirect
556. #478	C₂²×C₇	semidirect
557. #476	C₂²×C₇	semidirect
558. #475	C₂²×C₇	semidirect
561. #470	C₂²×C₇	semidirect
562. #470	C₂²×C₇	semidirect
563. #470	C₂²×C₇	semidirect
564. #468	C₂²×C₇	semidirect
565. #467	C₂²×C₇	semidirect
566. #465	C₂²×C₇	semidirect
567. #464	C₂²×C₇	semidirect
568. #464	C₂²×C₇	semidirect
569. #462	C₂²×C₇	semidirect
570. #462	C₂²×C₇	semidirect
573. #452	C₂²×C₇	semidirect
574. #452	C₂²×C₇	semidirect
576. #451	C₂²×C₇	semidirect
577. #451	C₂²×C₇	semidirect
579. #441	C₂²×C₇	semidirect
580. #440	C₂²×C₇	semidirect
581. C₄×Q₁₆	C₂²×C₇	semidirect
582. C₄×SD₁₆	C₂²×C₇	semidirect
584. #436	C₂²×C₇	semidirect
586. #435	C₂²×C₇	semidirect
587. #428	C₂²×C₇	semidirect
588. #428	C₂²×C₇	semidirect
589. C₂×#106	C₂²×C₇	semidirect
590. #424	C₂²×C₇	semidirect
593. #419	C₂²×C₇	semidirect
594. #419	C₂²×C₇	semidirect
595. #419	C₂²×C₇	semidirect
604. #417	C₂²×C₇	semidirect
609. #416	C₂²×C₇	semidirect
610. C₂×#103	C₂²×C₇	semidirect
611. C₂×#103	C₂²×C₇	semidirect
612. C₂×#103	C₂²×C₇	semidirect
613. #408	C₂²×C₇	semidirect
615. #405	C₂²×C₇	semidirect
1190. C₇	#61181	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×#3489	2
C₇×#3331	2
C₇×#3328	2
C₇×#3327	2
C₇×#3323	2
C₇×#3316	2
C₇×#3315	2
C₇×#3312	2
C₇×#3311	2
C₇×#3137	2
C₇×#3099	2
C₇×#3095	2
C₇×#3084	2
C₇×#3063	2
C₂×C₇×#470	2
C₇×#3044	2
C₇×#3011	2
C₇×#3007	2
C₇×#2947	2
C₇×#2930	2
C₇×#2898	2
C₇×#2896	2
#61181	7

Subgroups — C7×#61181 #13238397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61181 #13238397