Subgroups — C₇×#60815 #13238031

Order 1792.

2108 conjugacy classes of subgroups.

The subgroup lattice has 1320 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×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3225	C₂	1	2	yes	maximal, complemented
4	C₇×#3224	C₂	1	2	yes	maximal, complemented
5	C₇×#3221	C₂	1	2	yes	maximal, complemented
6	C₇×#3220	C₂	1	2	yes	maximal, complemented
7	C₇×#3219	C₂	1	2	yes	maximal, complemented
8	C₇×#3214	C₂	1	2	yes	maximal, complemented
9	C₇×#3212	C₂	1	2	yes	maximal, complemented
10	C₇×#3207	C₂	1	2	yes	maximal, complemented
11	C₇×#3155	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3154	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3045	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3042	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3041	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3006	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3005	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3002	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₇×#449	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
25	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
26	C₂×C₇×#137	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
29	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₇×#135	C₂²	1	1	yes	characteristic
31	C₂×C₇×#135	C₂²	1	1	yes	characteristic
32	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
34	C₇×#555	—	2	1	no	—
35	C₇×#553	—	2	1	no	—
36	C₇×#553	—	2	1	no	—
37	C₇×#551	—	2	2	no	—
38	C₇×#547	—	2	1	no	—
39	C₇×#546	—	2	2	no	—
40	C₇×#544	C₂²	1	1	yes	characteristic, complemented
41	C₇×#542	C₂²	1	2	yes	complemented
42	C₇×#540	C₂²	1	2	yes	complemented
43	C₇×#537	—	2	1	no	—
44	C₇×#537	—	2	1	no	—
45	C₇×#536	C₂²	1	1	yes	characteristic
46	C₇×#536	C₂²	1	1	yes	characteristic
47	C₇×#536	C₂²	1	2	yes	complemented
48	C₇×#535	C₂²	1	1	yes	characteristic
49	C₇×#535	C₂²	1	1	yes	characteristic
50	C₇×#535	C₂²	1	1	yes	characteristic, complemented
51	C₇×#535	C₂²	1	2	yes	complemented
52	C₇×#534	—	2	2	no	—
53	C₇×#532	C₂²	1	2	yes	complemented
54	C₇×#532	C₂²	1	2	yes	complemented
55	C₇×#532	C₂²	1	2	yes	complemented
56	C₇×#529	C₂²	1	2	yes	complemented
57	C₇×#525	—	2	2	no	—
58	C₇×#525	—	2	1	no	—
59	C₇×#525	—	2	1	no	—
60	C₇×#525	C₂²	1	1	yes	characteristic
61	C₂×C₇×#121	C₂²	1	1	yes	characteristic
62	C₇×#520	C₂²	1	1	yes	characteristic, complemented
63	C₇×#518	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₇×#117	C₂²	1	1	yes	characteristic
65	C₇×#497	C₂²	1	2	yes	complemented
66	C₇×#496	C₂²	1	2	yes	complemented
67	C₇×#496	C₂²	1	2	yes	complemented
68	C₇×#496	C₂²	1	2	yes	complemented
69	C₇×#495	C₂²	1	2	yes	complemented
70	C₇×#495	C₂²	1	2	yes	complemented
71	C₇×#493	C₂²	1	2	yes	complemented
72	C₇×#492	C₂²	1	2	yes	complemented
73	C₇×#491	C₂²	1	2	yes	complemented
74	C₇×#490	C₂²	1	2	yes	complemented
75	C₇×#489	C₂²	1	2	yes	complemented
76	C₇×#489	C₂²	1	2	yes	complemented
77	C₇×#488	C₂²	1	2	yes	complemented
78	C₇×#488	C₂²	1	2	yes	complemented
79	C₇×#487	C₂²	1	2	yes	complemented
80	C₇×#486	C₂²	1	2	yes	complemented
81	C₇×#464	C₂²	1	2	yes	complemented
82	C₇×#464	C₂²	1	2	yes	complemented
83	C₇×#463	C₂²	1	2	yes	complemented
84	C₇×#463	C₂²	1	2	yes	complemented
85	C₇×#463	C₂²	1	2	yes	complemented
86	C₇×#463	C₂²	1	2	yes	complemented
87	C₇×#463	C₂²	1	2	yes	complemented
88	C₇×#463	C₂²	1	2	yes	complemented
89	C₇×#462	C₂²	1	2	yes	complemented
90	C₇×#461	C₂²	1	2	yes	complemented
91	C₇×#461	C₂²	1	2	yes	complemented
92	C₇×#461	C₂²	1	2	yes	complemented
93	C₇×#460	C₂²	1	2	yes	complemented
94	C₇×#459	C₂²	1	2	yes	complemented
95	C₇×#459	C₂²	1	2	yes	complemented
96	C₇×#459	C₂²	1	2	yes	complemented
97	C₇×#452	C₂²	1	1	yes	characteristic, complemented
98	C₇×#452	C₂²	1	2	yes	complemented
99	C₇×#452	C₂²	1	1	yes	characteristic, complemented
100	C₇×#452	C₂²	1	2	yes	complemented
101	C₇×#451	C₂²	1	1	yes	characteristic, complemented
102	C₇×#450	C₂²	1	1	yes	characteristic, complemented
103	C₇×#449	C₂²	1	2	yes	—
104	C₇×#449	C₂²	1	2	yes	—
105	C₇×#449	C₂²	1	1	yes	characteristic, complemented
106	C₇×#449	C₂²	1	2	yes	complemented
107	C₇×#449	C₂²	1	2	yes	complemented
108	C₇×#449	C₂²	1	2	yes	complemented
109	C₇×#449	C₂²	1	2	yes	complemented
110	C₇×#449	C₂²	1	1	yes	characteristic, complemented
111	C₇×#449	C₂²	1	2	yes	complemented
112	C₇×#449	C₂²	1	2	yes	complemented
113	C₇×#448	C₂²	1	1	yes	characteristic, complemented
114	C₇×#448	C₂²	1	2	yes	complemented
115	C₇×#447	C₂²	1	1	yes	characteristic, complemented
116	C₇×#447	C₂²	1	2	yes	complemented
117	C₇×#433	C₂²	1	2	yes	complemented
118	C₇×#433	C₂²	1	2	yes	complemented
119	C₇×#432	C₂²	1	2	yes	complemented
120	C₇×#431	C₂²	1	2	yes	complemented
121	C₇×#424	C₂²	1	1	yes	characteristic, complemented
122	C₇×#424	C₂²	1	1	yes	characteristic, complemented
123	C₇×#419	C₂²	1	1	yes	characteristic, complemented
124	C₇×#418	C₂²	1	1	yes	characteristic, complemented
125	C₇×#417	C₂²	1	1	yes	characteristic
126	C₇×#417	C₂²	1	1	yes	characteristic
127	C₇×#416	C₂²	1	1	yes	characteristic
128	C₇×#416	C₂²	1	1	yes	characteristic
129	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
131	C₇×#407	C₂²	1	1	yes	characteristic
132	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
133	C₇×#405	C₂²	1	1	yes	characteristic, complemented
134	C₇×#405	C₂²	1	1	yes	characteristic, complemented
135	#60815	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	1	no	—
137	C₂×C₇×#41	—	2	1	no	—
138	C₂×C₇×#41	—	2	1	no	—
139	C₂×C₇×#41	—	2	1	no	—
140	C₂×C₇×#41	—	2	2	no	—
141	C₂×C₇×#41	—	4	2	no	—
142	C₂×C₇×#41	—	4	2	no	—
143	C₂×C₇×#41	—	4	2	no	—
144	C₂×C₇×#41	—	4	2	no	—
145	C₂×C₇×#41	C₂³	1	1	yes	characteristic
146	C₂×C₇×#41	C₂³	1	1	yes	characteristic
147	C₂×C₇×#41	C₂³	1	1	yes	characteristic
148	C₂×C₇×#41	C₂³	1	2	yes	—
149	C₂×C₇×#41	C₂³	1	1	yes	characteristic
150	C₂×C₇×#41	C₂³	1	1	yes	characteristic
151	C₂×C₇×#41	C₂³	1	2	yes	—
152	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
154	C₂²×C₇×D₄	—	2	1	no	—
155	C₂²×C₇×D₄	—	2	1	no	—
156	C₂²×C₇×D₄	—	2	1	no	—
157	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
158	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
159	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
160	C₂³×C₄×C₇	—	2	1	no	—
161	C₂³×C₄×C₇	—	2	1	no	—
162	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
163	C₇×#137	—	4	2	no	—
164	C₇×AGL(1,ℤ/8)	—	4	2	no	—
165	C₇×AGL(1,ℤ/8)	—	4	2	no	—
166	C₇×AGL(1,ℤ/8)	—	4	2	no	—
167	C₇×#135	—	4	2	no	—
168	C₇×#135	—	4	2	no	—
169	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
170	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
171	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
172	C₂×C₇×SD₁₆	—	4	2	no	—
173	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
174	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
175	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
176	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
177	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
178	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
179	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
180	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
181	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
182	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
183	C₂×C₇×D₈	—	4	2	no	—
184	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
185	C₂×C₇×D₈	C₂³	1	2	yes	—
186	C₂×C₇×D₈	C₂³	1	2	yes	—
187	C₂×C₇×D₈	C₂³	1	2	yes	—
188	C₂×C₇×D₈	C₂³	1	2	yes	—
189	C₂×C₇×D₈	C₂³	1	2	yes	—
190	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
191	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
192	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
193	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
194	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
195	C₇×C₄⋊Q₈	—	2	1	no	—
196	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
197	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
198	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
199	C₇×#127	C₂³	1	2	yes	—
200	C₇×#127	C₂³	1	2	yes	—
201	C₇×#127	C₂³	1	2	yes	—
202	C₇×#126	—	2	2	no	—
203	C₇×#126	—	2	2	no	—
204	C₇×#125	—	2	1	no	—
205	C₇×#125	C₂³	1	2	yes	—
206	C₇×#124	—	2	2	no	—
207	C₇×#124	—	2	2	no	—
208	C₇×#124	C₂³	1	2	yes	—
209	C₇×#124	C₂³	1	2	yes	—
210	C₇×#124	C₂³	1	2	yes	—
211	C₇×#124	C₂³	1	2	yes	—
212	C₇×#124	C₂³	1	2	yes	—
213	C₇×#123	—	2	1	no	—
214	C₇×#123	—	2	2	no	—
215	C₇×#123	—	2	2	no	—
216	C₇×#123	—	2	2	no	—
217	C₇×#123	—	2	2	no	—
218	C₇×#123	—	2	2	no	—
219	C₇×#123	—	2	2	no	—
220	C₇×#123	—	2	2	no	—
221	C₇×#123	—	2	2	no	—
222	C₇×C₂²⋊Q₈	—	2	1	no	—
223	C₇×C₂²⋊Q₈	—	2	1	no	—
224	C₇×C₂²⋊Q₈	—	2	1	no	—
225	C₇×C₂²⋊Q₈	—	2	1	no	—
226	C₇×C₂²⋊Q₈	—	2	2	no	—
227	C₇×C₂²⋊Q₈	—	2	2	no	—
228	C₇×C₂²⋊Q₈	—	2	2	no	—
229	C₇×C₂²⋊Q₈	—	2	2	no	—
230	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
231	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
232	C₇×#121	—	2	1	no	—
233	C₇×#121	—	2	1	no	—
234	C₇×#121	—	2	2	no	—
235	C₇×#121	—	2	2	no	—
236	C₇×#121	—	2	2	no	—
237	C₇×#121	—	2	2	no	—
238	C₇×#121	—	2	2	no	—
239	C₇×#121	—	2	1	no	—
240	C₇×#121	—	2	1	no	—
241	C₇×#121	—	2	1	no	—
242	C₇×#121	—	2	1	no	—
243	C₇×#121	—	2	2	no	—
244	C₇×#121	—	2	2	no	—
245	C₇×#121	—	2	1	no	—
246	C₇×#121	—	2	1	no	—
247	C₇×#121	—	2	2	no	—
248	C₇×#121	—	2	2	no	—
249	C₇×#121	C₂³	1	2	yes	—
250	C₇×#121	C₂³	1	2	yes	—
251	C₇×#121	C₂³	1	1	yes	characteristic
252	C₇×#121	C₂³	1	1	yes	characteristic
253	C₇×#120	—	2	1	no	—
254	C₇×#120	—	2	2	no	—
255	C₇×#120	—	2	2	no	—
256	C₇×#120	—	2	2	no	—
257	C₇×#120	—	2	2	no	—
258	C₇×#120	—	2	2	no	—
259	C₄×C₇×Q₈	C₂³	1	2	yes	—
260	C₄×C₇×D₄	—	2	1	no	—
261	C₄×C₇×D₄	—	2	1	no	—
262	C₄×C₇×D₄	—	2	2	no	—
263	C₄×C₇×D₄	—	2	1	no	—
264	C₄×C₇×D₄	—	2	1	no	—
265	C₄×C₇×D₄	—	2	2	no	—
266	C₄×C₇×D₄	—	2	2	no	—
267	C₄×C₇×D₄	—	2	2	no	—
268	C₄×C₇×D₄	—	2	2	no	—
269	C₄×C₇×D₄	—	2	2	no	—
270	C₄×C₇×D₄	—	2	2	no	—
271	C₄×C₇×D₄	C₂³	1	2	yes	—
272	C₄×C₇×D₄	C₂³	1	2	yes	—
273	C₄×C₇×D₄	C₂³	1	2	yes	—
274	C₇×#117	—	2	1	no	—
275	C₇×#117	—	2	2	no	—
276	C₇×#117	D₄	1	2	yes	—
277	C₇×#117	D₄	1	1	yes	characteristic
278	C₇×#117	D₄	1	1	yes	characteristic
279	C₇×#117	C₂³	1	1	yes	characteristic
280	C₇×#117	C₂³	1	1	yes	characteristic
281	C₇×#117	C₂³	1	1	yes	characteristic
282	C₇×#117	C₂³	1	2	yes	—
283	C₂×C₇×C₄⋊C₄	—	2	1	no	—
284	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
285	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
286	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
287	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
290	C₂×C₄²×C₇	C₂³	1	2	yes	—
291	C₇×C₄⋊C₈	C₂³	1	2	yes	—
292	C₇×C₄⋊C₈	C₂³	1	2	yes	—
293	C₇×C₄⋊C₈	C₂³	1	2	yes	—
294	C₇×C₄⋊C₈	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	1	yes	characteristic
296	C₇×#103	C₂³	1	2	yes	—
297	C₇×#103	C₂³	1	2	yes	—
298	C₇×#103	C₂³	1	2	yes	—
299	C₇×#103	C₂³	1	1	yes	characteristic
300	C₇×#103	C₂³	1	2	yes	—
301	C₇×#103	C₂³	1	2	yes	—
302	C₇×#103	C₂³	1	1	yes	characteristic
303	C₇×#103	C₂³	1	2	yes	—
304	C₇×#103	C₂³	1	1	yes	characteristic
305	C₇×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
310	C₇×#102	C₂³	1	2	yes	—
311	C₇×#102	C₂³	1	2	yes	—
312	C₇×#102	C₂³	1	1	yes	characteristic
313	C₇×#102	C₂³	1	2	yes	—
314	C₇×#102	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	1	yes	characteristic
319	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
320	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
321	C₇×#97	C₂³	1	2	yes	—
322	C₇×#97	C₂³	1	2	yes	—
323	C₄×C₇×C₈	C₂³	1	2	yes	—
324	C₄×C₇×C₈	C₂³	1	2	yes	—
325	#3494	C₂×C₇	1	1	yes	characteristic, complemented
326	#3449	C₂×C₇	1	1	yes	characteristic, complemented
327	#3225	C₂×C₇	1	2	yes	complemented
328	#3224	C₂×C₇	1	2	yes	complemented
329	#3221	C₂×C₇	1	2	yes	complemented
330	#3220	C₂×C₇	1	2	yes	complemented
331	#3219	C₂×C₇	1	2	yes	complemented
332	#3214	C₂×C₇	1	2	yes	complemented
333	#3212	C₂×C₇	1	2	yes	complemented
334	#3207	C₂×C₇	1	2	yes	complemented
335	#3155	C₂×C₇	1	1	yes	characteristic, complemented
336	#3154	C₂×C₇	1	1	yes	characteristic, complemented
337	#3137	C₂×C₇	1	1	yes	characteristic, complemented
338	#3136	C₂×C₇	1	1	yes	characteristic, complemented
339	#3046	C₂×C₇	1	1	yes	characteristic, complemented
340	#3045	C₂×C₇	1	1	yes	characteristic, complemented
341	#3042	C₂×C₇	1	1	yes	characteristic, complemented
342	#3041	C₂×C₇	1	1	yes	characteristic, complemented
343	#3006	C₂×C₇	1	1	yes	characteristic, complemented
344	#3005	C₂×C₇	1	1	yes	characteristic, complemented
345	#3002	C₂×C₇	1	1	yes	characteristic, complemented
346	C₂×#449	C₂×C₇	1	1	yes	characteristic, complemented
347	#2924	C₂×C₇	1	1	yes	characteristic, complemented
348	C₂⁴×C₇	—	2	1	no	—
349	C₂⁴×C₇	—	2	1	no	—
350	C₂⁴×C₇	—	2	1	no	—
351	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
352	C₇×#41	—	2	2	no	—
353	C₇×#41	—	2	2	no	—
354	C₇×#41	—	2	2	no	—
355	C₇×#41	—	2	2	no	—
356	C₇×#41	—	2	2	no	—
357	C₇×#41	—	2	2	no	—
358	C₇×#41	—	4	2	no	—
359	C₇×#41	—	4	2	no	—
360	C₇×#41	—	4	2	no	—
361	C₇×#41	—	4	1	no	—
362	C₇×#41	—	4	1	no	—
363	C₇×#41	—	4	2	no	—
364	C₇×#41	—	4	1	no	—
365	C₇×#41	—	4	1	no	—
366	C₇×#41	—	4	4	no	—
367	C₇×#41	—	4	4	no	—
368	C₇×#41	—	4	4	no	—
369	C₇×#41	—	4	4	no	—
370	C₇×#41	—	8	4	no	—
371	C₂×C₇×Q₈	—	2	1	no	—
372	C₂×C₇×Q₈	—	2	1	no	—
373	C₂×C₇×Q₈	—	2	2	no	—
374	C₂×C₇×Q₈	—	2	2	no	—
375	C₂×C₇×Q₈	—	2	2	no	—
376	C₂×C₇×Q₈	—	4	1	no	—
377	C₂×C₇×Q₈	—	4	1	no	—
378	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
379	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
380	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
382	C₂×C₇×D₄	—	2	1	no	—
383	C₂×C₇×D₄	—	2	1	no	—
384	C₂×C₇×D₄	—	2	2	no	—
385	C₂×C₇×D₄	—	2	2	no	—
386	C₂×C₇×D₄	—	2	1	no	—
387	C₂×C₇×D₄	—	2	1	no	—
388	C₂×C₇×D₄	—	2	1	no	—
389	C₂×C₇×D₄	—	2	2	no	—
390	C₂×C₇×D₄	—	2	1	no	—
391	C₂×C₇×D₄	—	2	1	no	—
392	C₂×C₇×D₄	—	2	2	no	—
393	C₂×C₇×D₄	—	2	1	no	—
394	C₂×C₇×D₄	—	2	1	no	—
395	C₂×C₇×D₄	—	2	1	no	—
396	C₂×C₇×D₄	—	2	2	no	—
397	C₂×C₇×D₄	—	2	2	no	—
398	C₂×C₇×D₄	—	2	2	no	—
399	C₂×C₇×D₄	—	2	2	no	—
400	C₂×C₇×D₄	—	2	2	no	—
401	C₂×C₇×D₄	—	2	2	no	—
402	C₂×C₇×D₄	—	2	2	no	—
403	C₂×C₇×D₄	—	2	2	no	—
404	C₂×C₇×D₄	—	2	2	no	—
405	C₂×C₇×D₄	—	2	2	no	—
406	C₂×C₇×D₄	—	4	1	no	—
407	C₂×C₇×D₄	—	4	1	no	—
408	C₂×C₇×D₄	—	4	4	no	—
409	C₂×C₇×D₄	—	4	4	no	—
410	C₂×C₇×D₄	—	8	2	no	—
411	C₂×C₇×D₄	C₂⁴	1	2	yes	—
412	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
413	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
414	C₂×C₇×D₄	C₂⁴	1	2	yes	—
415	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₇	—	2	2	no	—
417	C₂²×C₄×C₇	—	2	2	no	—
418	C₂²×C₄×C₇	—	2	1	no	—
419	C₂²×C₄×C₇	—	2	1	no	—
420	C₂²×C₄×C₇	—	2	1	no	—
421	C₂²×C₄×C₇	—	2	1	no	—
422	C₂²×C₄×C₇	—	2	1	no	—
423	C₂²×C₄×C₇	—	2	2	no	—
424	C₂²×C₄×C₇	—	2	1	no	—
425	C₂²×C₄×C₇	—	2	2	no	—
426	C₂²×C₄×C₇	—	2	1	no	—
427	C₂²×C₄×C₇	—	2	1	no	—
428	C₂²×C₄×C₇	—	2	2	no	—
429	C₂²×C₄×C₇	—	2	2	no	—
430	C₂²×C₄×C₇	—	2	2	no	—
431	C₂²×C₄×C₇	—	4	4	no	—
432	C₂²×C₄×C₇	—	4	4	no	—
433	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
434	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
435	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
436	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
437	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
438	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
439	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
440	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
441	C₇×Q₁₆	—	4	1	no	—
442	C₇×Q₁₆	—	4	1	no	—
443	C₇×Q₁₆	—	4	2	no	—
444	C₇×SD₁₆	—	4	2	no	—
445	C₇×SD₁₆	—	4	2	no	—
446	C₇×SD₁₆	—	4	1	no	—
447	C₇×SD₁₆	—	4	1	no	—
448	C₇×SD₁₆	—	4	1	no	—
449	C₇×SD₁₆	—	4	1	no	—
450	C₇×SD₁₆	—	4	2	no	—
451	C₇×SD₁₆	—	4	2	no	—
452	C₇×SD₁₆	—	4	2	no	—
453	C₇×SD₁₆	—	4	2	no	—
454	C₇×D₈	—	4	2	no	—
455	C₇×D₈	—	4	2	no	—
456	C₇×D₈	—	4	1	no	—
457	C₇×D₈	—	4	1	no	—
458	C₇×D₈	—	4	2	no	—
459	C₇×D₈	—	4	2	no	—
460	C₇×D₈	—	4	2	no	—
461	C₇×M₁₆	—	2	2	no	—
462	C₇×M₁₆	—	2	2	no	—
463	C₂×C₇×C₈	—	2	2	no	—
464	C₂×C₇×C₈	—	2	2	no	—
465	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
466	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
467	C₂×C₇×C₈	C₂⁴	1	2	yes	—
468	C₂×C₇×C₈	C₂⁴	1	2	yes	—
469	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
470	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
471	C₇×C₄⋊C₄	—	2	1	no	—
472	C₇×C₄⋊C₄	—	2	2	no	—
473	C₇×C₄⋊C₄	—	2	1	no	—
474	C₇×C₄⋊C₄	—	2	2	no	—
475	C₇×C₄⋊C₄	—	2	2	no	—
476	C₇×C₄⋊C₄	—	2	2	no	—
477	C₇×C₄⋊C₄	—	2	2	no	—
478	C₇×C₄⋊C₄	—	2	2	no	—
479	C₇×C₄⋊C₄	—	2	2	no	—
480	C₇×C₄⋊C₄	—	2	2	no	—
481	C₇×C₄⋊C₄	—	2	1	no	—
482	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
483	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
484	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
485	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
486	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
487	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
488	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
489	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
490	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
491	C₇×C₂²⋊C₄	—	2	1	no	—
492	C₇×C₂²⋊C₄	—	2	1	no	—
493	C₇×C₂²⋊C₄	—	2	1	no	—
494	C₇×C₂²⋊C₄	—	2	2	no	—
495	C₇×C₂²⋊C₄	—	2	2	no	—
496	C₇×C₂²⋊C₄	—	2	2	no	—
497	C₇×C₂²⋊C₄	—	2	2	no	—
498	C₇×C₂²⋊C₄	—	2	2	no	—
499	C₇×C₂²⋊C₄	—	2	2	no	—
500	C₇×C₂²⋊C₄	—	2	1	no	—
501	C₇×C₂²⋊C₄	—	2	2	no	—
502	C₇×C₂²⋊C₄	—	2	2	no	—
503	C₇×C₂²⋊C₄	—	2	2	no	—
504	C₇×C₂²⋊C₄	—	2	2	no	—
505	C₇×C₂²⋊C₄	—	2	2	no	—
506	C₇×C₂²⋊C₄	—	2	2	no	—
507	C₇×C₂²⋊C₄	—	2	2	no	—
508	C₇×C₂²⋊C₄	—	2	2	no	—
509	C₇×C₂²⋊C₄	—	2	2	no	—
510	C₇×C₂²⋊C₄	—	2	1	no	—
511	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
512	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
513	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
514	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
515	C₄²×C₇	—	2	2	no	—
516	C₄²×C₇	—	2	1	no	—
517	C₄²×C₇	C₂×D₄	1	2	yes	—
518	C₄²×C₇	C₂×D₄	1	2	yes	—
519	C₄²×C₇	C₂⁴	1	2	yes	—
520	C₄²×C₇	C₂⁴	1	2	yes	—
521	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
522	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
523	C₂×#137	C₂²×C₇	1	1	yes	characteristic, complemented
524	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
525	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
526	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic, complemented
527	C₂×#135	C₂²×C₇	1	1	yes	characteristic
528	C₂×#135	C₂²×C₇	1	1	yes	characteristic
529	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
530	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
531	#555	—	2	1	no	—
532	#553	—	2	1	no	—
533	#553	—	2	1	no	—
534	#551	—	2	2	no	—
535	#547	—	2	1	no	—
536	#546	—	2	2	no	—
537	#544	C₂²×C₇	1	1	yes	characteristic, complemented
538	#542	C₂²×C₇	1	2	yes	complemented
539	#540	C₂²×C₇	1	2	yes	complemented
540	#537	—	2	1	no	—
541	#537	—	2	1	no	—
542	#536	C₂²×C₇	1	1	yes	characteristic
543	#536	C₂²×C₇	1	1	yes	characteristic
544	#536	C₂²×C₇	1	2	yes	complemented
545	#535	C₂²×C₇	1	1	yes	characteristic
546	#535	C₂²×C₇	1	1	yes	characteristic
547	#535	C₂²×C₇	1	1	yes	characteristic, complemented
548	#535	C₂²×C₇	1	2	yes	complemented
549	#534	—	2	2	no	—
550	#532	C₂²×C₇	1	2	yes	complemented
551	#532	C₂²×C₇	1	2	yes	complemented
552	#532	C₂²×C₇	1	2	yes	complemented
553	#529	C₂²×C₇	1	2	yes	complemented
554	#525	—	2	2	no	—
555	#525	—	2	1	no	—
556	#525	—	2	1	no	—
557	#525	C₂²×C₇	1	1	yes	characteristic
558	C₂×#121	C₂²×C₇	1	1	yes	characteristic
559	#520	C₂²×C₇	1	1	yes	characteristic, complemented
560	#518	C₂²×C₇	1	1	yes	characteristic, complemented
561	C₂×#117	C₂²×C₇	1	1	yes	characteristic
562	#497	C₂²×C₇	1	2	yes	complemented
563	#496	C₂²×C₇	1	2	yes	complemented
564	#496	C₂²×C₇	1	2	yes	complemented
565	#496	C₂²×C₇	1	2	yes	complemented
566	#495	C₂²×C₇	1	2	yes	complemented
567	#495	C₂²×C₇	1	2	yes	complemented
568	#493	C₂²×C₇	1	2	yes	complemented
569	#492	C₂²×C₇	1	2	yes	complemented
570	#491	C₂²×C₇	1	2	yes	complemented
571	#490	C₂²×C₇	1	2	yes	complemented
572	#489	C₂²×C₇	1	2	yes	complemented
573	#489	C₂²×C₇	1	2	yes	complemented
574	#488	C₂²×C₇	1	2	yes	complemented
575	#488	C₂²×C₇	1	2	yes	complemented
576	#487	C₂²×C₇	1	2	yes	complemented
577	#486	C₂²×C₇	1	2	yes	complemented
578	#464	C₂²×C₇	1	2	yes	complemented
579	#464	C₂²×C₇	1	2	yes	complemented
580	#463	C₂²×C₇	1	2	yes	complemented
581	#463	C₂²×C₇	1	2	yes	complemented
582	#463	C₂²×C₇	1	2	yes	complemented
583	#463	C₂²×C₇	1	2	yes	complemented
584	#463	C₂²×C₇	1	2	yes	complemented
585	#463	C₂²×C₇	1	2	yes	complemented
586	#462	C₂²×C₇	1	2	yes	complemented
587	#461	C₂²×C₇	1	2	yes	complemented
588	#461	C₂²×C₇	1	2	yes	complemented
589	#461	C₂²×C₇	1	2	yes	complemented
590	#460	C₂²×C₇	1	2	yes	complemented
591	#459	C₂²×C₇	1	2	yes	complemented
592	#459	C₂²×C₇	1	2	yes	complemented
593	#459	C₂²×C₇	1	2	yes	complemented
594	#452	C₂²×C₇	1	1	yes	characteristic, complemented
595	#452	C₂²×C₇	1	2	yes	complemented
596	#452	C₂²×C₇	1	1	yes	characteristic, complemented
597	#452	C₂²×C₇	1	2	yes	complemented
598	#451	C₂²×C₇	1	1	yes	characteristic, complemented
599	#450	C₂²×C₇	1	1	yes	characteristic, complemented
600	#449	C₂²×C₇	1	2	yes	—
601	#449	C₂²×C₇	1	2	yes	—
602	#449	C₂²×C₇	1	1	yes	characteristic, complemented
603	#449	C₂²×C₇	1	2	yes	complemented
604	#449	C₂²×C₇	1	2	yes	complemented
605	#449	C₂²×C₇	1	2	yes	complemented
606	#449	C₂²×C₇	1	2	yes	complemented
607	#449	C₂²×C₇	1	1	yes	characteristic, complemented
608	#449	C₂²×C₇	1	2	yes	complemented
609	#449	C₂²×C₇	1	2	yes	complemented
610	#448	C₂²×C₇	1	1	yes	characteristic, complemented
611	#448	C₂²×C₇	1	2	yes	complemented
612	#447	C₂²×C₇	1	1	yes	characteristic, complemented
613	#447	C₂²×C₇	1	2	yes	complemented
614	#433	C₂²×C₇	1	2	yes	complemented
615	#433	C₂²×C₇	1	2	yes	complemented
616	#432	C₂²×C₇	1	2	yes	complemented
617	#431	C₂²×C₇	1	2	yes	complemented
618	#424	C₂²×C₇	1	1	yes	characteristic, complemented
619	#424	C₂²×C₇	1	1	yes	characteristic, complemented
620	#419	C₂²×C₇	1	1	yes	characteristic, complemented
621	#418	C₂²×C₇	1	1	yes	characteristic, complemented
622	#417	C₂²×C₇	1	1	yes	characteristic
623	#417	C₂²×C₇	1	1	yes	characteristic
624	#416	C₂²×C₇	1	1	yes	characteristic
625	#416	C₂²×C₇	1	1	yes	characteristic
626	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
627	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
628	#407	C₂²×C₇	1	1	yes	characteristic
629	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
630	#405	C₂²×C₇	1	1	yes	characteristic, complemented
631	#405	C₂²×C₇	1	1	yes	characteristic, complemented
632	C₂³×C₇	—	2	2	no	—
633	C₂³×C₇	—	2	2	no	—
634	C₂³×C₇	—	2	1	no	—
635	C₂³×C₇	—	2	2	no	—
636	C₂³×C₇	—	2	1	no	—
637	C₂³×C₇	—	2	1	no	—
638	C₂³×C₇	—	4	1	no	—
639	C₂³×C₇	—	4	1	no	—
640	C₂³×C₇	—	4	2	no	—
641	C₂³×C₇	—	4	2	no	—
642	C₂³×C₇	—	4	2	no	—
643	C₂³×C₇	—	8	1	no	—
644	C₂³×C₇	—	8	1	no	—
645	C₂³×C₇	—	8	1	no	—
646	C₂³×C₇	—	8	1	no	—
647	C₂³×C₇	—	8	1	no	—
648	C₂³×C₇	—	8	1	no	—
649	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
650	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
651	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
652	C₇×Q₈	—	2	1	no	—
653	C₇×Q₈	—	2	2	no	—
654	C₇×Q₈	—	2	1	no	—
655	C₇×Q₈	—	2	1	no	—
656	C₇×Q₈	—	2	1	no	—
657	C₇×Q₈	—	2	2	no	—
658	C₇×Q₈	—	2	1	no	—
659	C₇×Q₈	—	2	1	no	—
660	C₇×Q₈	—	4	2	no	—
661	C₇×Q₈	—	4	2	no	—
662	C₇×Q₈	—	8	2	no	—
663	C₇×D₄	—	2	2	no	—
664	C₇×D₄	—	2	1	no	—
665	C₇×D₄	—	2	2	no	—
666	C₇×D₄	—	2	1	no	—
667	C₇×D₄	—	2	1	no	—
668	C₇×D₄	—	2	2	no	—
669	C₇×D₄	—	2	1	no	—
670	C₇×D₄	—	2	2	no	—
671	C₇×D₄	—	2	1	no	—
672	C₇×D₄	—	2	1	no	—
673	C₇×D₄	—	4	2	no	—
674	C₇×D₄	—	4	4	no	—
675	C₇×D₄	—	4	4	no	—
676	C₇×D₄	—	4	2	no	—
677	C₇×D₄	—	4	2	no	—
678	C₇×D₄	—	4	4	no	—
679	C₇×D₄	—	4	2	no	—
680	C₇×D₄	—	4	2	no	—
681	C₇×D₄	—	4	2	no	—
682	C₇×D₄	—	4	2	no	—
683	C₇×D₄	—	4	2	no	—
684	C₇×D₄	—	4	2	no	—
685	C₇×D₄	—	8	2	no	—
686	C₇×D₄	—	8	2	no	—
687	C₇×D₄	—	8	2	no	—
688	C₇×D₄	—	8	2	no	—
689	C₇×D₄	—	8	2	no	—
690	C₇×D₄	—	8	2	no	—
691	C₇×D₄	—	8	1	no	—
692	C₇×D₄	—	8	2	no	—
693	C₂×C₄×C₇	—	2	2	no	—
694	C₂×C₄×C₇	—	2	2	no	—
695	C₂×C₄×C₇	—	2	2	no	—
696	C₂×C₄×C₇	—	2	1	no	—
697	C₂×C₄×C₇	—	2	1	no	—
698	C₂×C₄×C₇	—	2	1	no	—
699	C₂×C₄×C₇	—	2	1	no	—
700	C₂×C₄×C₇	—	2	1	no	—
701	C₂×C₄×C₇	—	2	1	no	—
702	C₂×C₄×C₇	—	2	1	no	—
703	C₂×C₄×C₇	—	2	2	no	—
704	C₂×C₄×C₇	—	2	2	no	—
705	C₂×C₄×C₇	—	2	1	no	—
706	C₂×C₄×C₇	—	2	1	no	—
707	C₂×C₄×C₇	—	4	2	no	—
708	C₂×C₄×C₇	—	4	2	no	—
709	C₂×C₄×C₇	—	4	4	no	—
710	C₂×C₄×C₇	—	4	2	no	—
711	C₂×C₄×C₇	—	4	2	no	—
712	C₂×C₄×C₇	—	4	4	no	—
713	C₂×C₄×C₇	—	4	2	no	—
714	C₂×C₄×C₇	—	4	2	no	—
715	C₂×C₄×C₇	—	4	2	no	—
716	C₂×C₄×C₇	—	4	2	no	—
717	C₂×C₄×C₇	—	4	2	no	—
718	C₂×C₄×C₇	—	8	2	no	—
719	C₂×C₄×C₇	—	8	2	no	—
720	C₂×C₄×C₇	—	8	2	no	—
721	C₂×C₄×C₇	—	8	1	no	—
722	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
723	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
724	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
725	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
726	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
727	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
728	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
729	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
730	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
731	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
732	C₇×C₈	—	2	1	no	—
733	C₇×C₈	—	2	1	no	—
734	C₇×C₈	—	2	1	no	—
735	C₇×C₈	—	2	1	no	—
736	C₇×C₈	—	2	2	no	—
737	C₇×C₈	—	2	2	no	—
738	C₂×#41	—	2	1	no	—
739	C₂×#41	—	2	1	no	—
740	C₂×#41	—	2	1	no	—
741	C₂×#41	—	2	1	no	—
742	C₂×#41	—	2	2	no	—
743	C₂×#41	—	4	2	no	—
744	C₂×#41	—	4	2	no	—
745	C₂×#41	—	4	2	no	—
746	C₂×#41	—	4	2	no	—
747	C₂×#41	C₂³×C₇	1	1	yes	characteristic
748	C₂×#41	C₂³×C₇	1	1	yes	characteristic
749	C₂×#41	C₂³×C₇	1	1	yes	characteristic
750	C₂×#41	C₂³×C₇	1	1	yes	characteristic
751	C₂×#41	C₂³×C₇	1	2	yes	—
752	C₂×#41	C₂³×C₇	1	1	yes	characteristic
753	C₂×#41	C₂³×C₇	1	2	yes	—
754	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
755	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
756	C₂²×D₄	—	2	1	no	—
757	C₂²×D₄	—	2	1	no	—
758	C₂²×D₄	—	2	1	no	—
759	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
760	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
761	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
762	C₂³×C₄	—	2	1	no	—
763	C₂³×C₄	—	2	1	no	—
764	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
765	#137	—	4	2	no	—
766	AGL(1,ℤ/8)	—	4	2	no	—
767	AGL(1,ℤ/8)	—	4	2	no	—
768	AGL(1,ℤ/8)	—	4	2	no	—
769	#135	—	4	2	no	—
770	#135	—	4	2	no	—
771	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
772	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
773	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
774	C₂×SD₁₆	—	4	2	no	—
775	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
778	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
779	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
780	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
781	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
782	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
783	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
785	C₂×D₈	—	4	2	no	—
786	C₂×D₈	C₂³×C₇	1	2	yes	—
787	C₂×D₈	C₂³×C₇	1	2	yes	—
788	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
789	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
790	C₂×D₈	C₂³×C₇	1	2	yes	—
791	C₂×D₈	C₂³×C₇	1	2	yes	—
792	C₂×D₈	C₂³×C₇	1	2	yes	—
793	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
794	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
795	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
796	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
797	C₄⋊Q₈	—	2	1	no	—
798	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
799	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
800	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
801	#127	C₂³×C₇	1	2	yes	—
802	#127	C₂³×C₇	1	2	yes	—
803	#127	C₂³×C₇	1	2	yes	—
804	#126	—	2	2	no	—
805	#126	—	2	2	no	—
806	#125	—	2	1	no	—
807	#125	C₂³×C₇	1	2	yes	—
808	#124	—	2	2	no	—
809	#124	—	2	2	no	—
810	#124	C₂³×C₇	1	2	yes	—
811	#124	C₂³×C₇	1	2	yes	—
812	#124	C₂³×C₇	1	2	yes	—
813	#124	C₂³×C₇	1	2	yes	—
814	#124	C₂³×C₇	1	2	yes	—
815	#123	—	2	1	no	—
816	#123	—	2	2	no	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	2	no	—
822	#123	—	2	2	no	—
823	#123	—	2	2	no	—
824	C₂²⋊Q₈	—	2	1	no	—
825	C₂²⋊Q₈	—	2	1	no	—
826	C₂²⋊Q₈	—	2	1	no	—
827	C₂²⋊Q₈	—	2	1	no	—
828	C₂²⋊Q₈	—	2	2	no	—
829	C₂²⋊Q₈	—	2	2	no	—
830	C₂²⋊Q₈	—	2	2	no	—
831	C₂²⋊Q₈	—	2	2	no	—
832	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
833	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
834	#121	—	2	1	no	—
835	#121	—	2	1	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	2	no	—
841	#121	—	2	1	no	—
842	#121	—	2	1	no	—
843	#121	—	2	1	no	—
844	#121	—	2	1	no	—
845	#121	—	2	2	no	—
846	#121	—	2	2	no	—
847	#121	—	2	1	no	—
848	#121	—	2	1	no	—
849	#121	—	2	2	no	—
850	#121	—	2	2	no	—
851	#121	C₂³×C₇	1	2	yes	—
852	#121	C₂³×C₇	1	2	yes	—
853	#121	C₂³×C₇	1	1	yes	characteristic
854	#121	C₂³×C₇	1	1	yes	characteristic
855	#120	—	2	1	no	—
856	#120	—	2	2	no	—
857	#120	—	2	2	no	—
858	#120	—	2	2	no	—
859	#120	—	2	2	no	—
860	#120	—	2	2	no	—
861	C₄×Q₈	C₂³×C₇	1	2	yes	—
862	C₄×D₄	—	2	1	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	2	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	2	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	—	2	2	no	—
871	C₄×D₄	—	2	2	no	—
872	C₄×D₄	—	2	2	no	—
873	C₄×D₄	C₂³×C₇	1	2	yes	—
874	C₄×D₄	C₂³×C₇	1	2	yes	—
875	C₄×D₄	C₂³×C₇	1	2	yes	—
876	#117	—	2	1	no	—
877	#117	—	2	2	no	—
878	#117	C₇×D₄	1	2	yes	—
879	#117	C₇×D₄	1	1	yes	characteristic
880	#117	C₇×D₄	1	1	yes	characteristic
881	#117	C₂³×C₇	1	1	yes	characteristic
882	#117	C₂³×C₇	1	1	yes	characteristic
883	#117	C₂³×C₇	1	1	yes	characteristic
884	#117	C₂³×C₇	1	2	yes	—
885	C₂×C₄⋊C₄	—	2	1	no	—
886	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
887	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
888	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
889	C₂×C₂²⋊C₄	—	2	1	no	—
890	C₂×C₂²⋊C₄	—	2	2	no	—
891	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
892	C₂×C₄²	C₂³×C₇	1	2	yes	—
893	C₄⋊C₈	C₂³×C₇	1	2	yes	—
894	C₄⋊C₈	C₂³×C₇	1	2	yes	—
895	C₄⋊C₈	C₂³×C₇	1	2	yes	—
896	C₄⋊C₈	C₂³×C₇	1	2	yes	—
897	#103	C₂³×C₇	1	2	yes	—
898	#103	C₂³×C₇	1	2	yes	—
899	#103	C₂³×C₇	1	1	yes	characteristic
900	#103	C₂³×C₇	1	1	yes	characteristic
901	#103	C₂³×C₇	1	1	yes	characteristic
902	#103	C₂³×C₇	1	1	yes	characteristic
903	#103	C₂³×C₇	1	2	yes	—
904	#103	C₂³×C₇	1	2	yes	—
905	#103	C₂³×C₇	1	2	yes	—
906	#103	C₂³×C₇	1	2	yes	—
907	#102	C₂³×C₇	1	2	yes	—
908	#102	C₂³×C₇	1	2	yes	—
909	#102	C₂³×C₇	1	1	yes	characteristic
910	#102	C₂³×C₇	1	1	yes	characteristic
911	#102	C₂³×C₇	1	1	yes	characteristic
912	#102	C₂³×C₇	1	1	yes	characteristic
913	#102	C₂³×C₇	1	2	yes	—
914	#102	C₂³×C₇	1	2	yes	—
915	#102	C₂³×C₇	1	2	yes	—
916	#102	C₂³×C₇	1	2	yes	—
917	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
918	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
919	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
920	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
921	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
922	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
923	#97	C₂³×C₇	1	2	yes	—
924	#97	C₂³×C₇	1	2	yes	—
925	C₄×C₈	C₂³×C₇	1	2	yes	—
926	C₄×C₈	C₂³×C₇	1	2	yes	—
927	C₂²×C₇	—	2	1	no	—
928	C₂²×C₇	—	2	1	no	—
929	C₂²×C₇	—	2	1	no	—
930	C₂²×C₇	—	2	1	no	—
931	C₂²×C₇	—	2	1	no	—
932	C₂²×C₇	—	2	1	no	—
933	C₂²×C₇	—	2	1	no	—
934	C₂²×C₇	—	2	1	no	—
935	C₂²×C₇	—	4	2	no	—
936	C₂²×C₇	—	4	1	no	—
937	C₂²×C₇	—	4	2	no	—
938	C₂²×C₇	—	4	1	no	—
939	C₂²×C₇	—	4	1	no	—
940	C₂²×C₇	—	4	1	no	—
941	C₂²×C₇	—	4	2	no	—
942	C₂²×C₇	—	4	2	no	—
943	C₂²×C₇	—	4	1	no	—
944	C₂²×C₇	—	4	1	no	—
945	C₂²×C₇	—	4	2	no	—
946	C₂²×C₇	—	4	1	no	—
947	C₂²×C₇	—	4	1	no	—
948	C₂²×C₇	—	4	1	no	—
949	C₂²×C₇	—	4	2	no	—
950	C₂²×C₇	—	8	2	no	—
951	C₂²×C₇	—	8	4	no	—
952	C₂²×C₇	—	8	4	no	—
953	C₂²×C₇	—	16	2	no	—
954	C₂²×C₇	#535	1	2	yes	—
955	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
956	C₄×C₇	—	2	2	no	—
957	C₄×C₇	—	2	2	no	—
958	C₄×C₇	—	2	2	no	—
959	C₄×C₇	—	2	2	no	—
960	C₄×C₇	—	2	1	no	—
961	C₄×C₇	—	2	1	no	—
962	C₄×C₇	—	4	1	no	—
963	C₄×C₇	—	4	2	no	—
964	C₄×C₇	—	4	1	no	—
965	C₄×C₇	—	4	2	no	—
966	C₄×C₇	—	4	1	no	—
967	C₄×C₇	—	4	1	no	—
968	C₄×C₇	—	4	1	no	—
969	C₄×C₇	#535	1	2	yes	—
970	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
971	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
972	C₂⁴	—	2	1	no	—
973	C₂⁴	—	2	1	no	—
974	C₂⁴	—	2	1	no	—
975	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
976	#41	—	2	2	no	—
977	#41	—	2	2	no	—
978	#41	—	2	2	no	—
979	#41	—	2	2	no	—
980	#41	—	2	2	no	—
981	#41	—	2	2	no	—
982	#41	—	4	2	no	—
983	#41	—	4	2	no	—
984	#41	—	4	2	no	—
985	#41	—	4	1	no	—
986	#41	—	4	1	no	—
987	#41	—	4	2	no	—
988	#41	—	4	1	no	—
989	#41	—	4	1	no	—
990	#41	—	4	4	no	—
991	#41	—	4	4	no	—
992	#41	—	4	4	no	—
993	#41	—	4	4	no	—
994	#41	—	8	4	no	—
995	C₂×Q₈	—	2	1	no	—
996	C₂×Q₈	—	2	1	no	—
997	C₂×Q₈	—	2	2	no	—
998	C₂×Q₈	—	2	2	no	—
999	C₂×Q₈	—	2	2	no	—
1000	C₂×Q₈	—	4	1	no	—
1001	C₂×Q₈	—	4	1	no	—
1002	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
1003	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
1004	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
1005	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	2	2	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	1	no	—
1012	C₂×D₄	—	2	1	no	—
1013	C₂×D₄	—	2	2	no	—
1014	C₂×D₄	—	2	1	no	—
1015	C₂×D₄	—	2	1	no	—
1016	C₂×D₄	—	2	2	no	—
1017	C₂×D₄	—	2	1	no	—
1018	C₂×D₄	—	2	1	no	—
1019	C₂×D₄	—	2	1	no	—
1020	C₂×D₄	—	2	2	no	—
1021	C₂×D₄	—	2	2	no	—
1022	C₂×D₄	—	2	2	no	—
1023	C₂×D₄	—	2	2	no	—
1024	C₂×D₄	—	2	2	no	—
1025	C₂×D₄	—	2	2	no	—
1026	C₂×D₄	—	2	2	no	—
1027	C₂×D₄	—	2	2	no	—
1028	C₂×D₄	—	2	2	no	—
1029	C₂×D₄	—	2	2	no	—
1030	C₂×D₄	—	4	1	no	—
1031	C₂×D₄	—	4	1	no	—
1032	C₂×D₄	—	4	4	no	—
1033	C₂×D₄	—	4	4	no	—
1034	C₂×D₄	—	8	2	no	—
1035	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1036	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1037	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1038	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1039	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1040	C₂²×C₄	—	2	2	no	—
1041	C₂²×C₄	—	2	2	no	—
1042	C₂²×C₄	—	2	1	no	—
1043	C₂²×C₄	—	2	1	no	—
1044	C₂²×C₄	—	2	1	no	—
1045	C₂²×C₄	—	2	1	no	—
1046	C₂²×C₄	—	2	1	no	—
1047	C₂²×C₄	—	2	2	no	—
1048	C₂²×C₄	—	2	1	no	—
1049	C₂²×C₄	—	2	2	no	—
1050	C₂²×C₄	—	2	1	no	—
1051	C₂²×C₄	—	2	1	no	—
1052	C₂²×C₄	—	2	2	no	—
1053	C₂²×C₄	—	2	2	no	—
1054	C₂²×C₄	—	2	2	no	—
1055	C₂²×C₄	—	4	4	no	—
1056	C₂²×C₄	—	4	4	no	—
1057	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1058	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1059	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1060	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
1061	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
1062	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1063	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1064	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1065	Q₁₆	—	4	1	no	—
1066	Q₁₆	—	4	1	no	—
1067	Q₁₆	—	4	2	no	—
1068	SD₁₆	—	4	2	no	—
1069	SD₁₆	—	4	2	no	—
1070	SD₁₆	—	4	1	no	—
1071	SD₁₆	—	4	1	no	—
1072	SD₁₆	—	4	1	no	—
1073	SD₁₆	—	4	1	no	—
1074	SD₁₆	—	4	2	no	—
1075	SD₁₆	—	4	2	no	—
1076	SD₁₆	—	4	2	no	—
1077	SD₁₆	—	4	2	no	—
1078	D₈	—	4	2	no	—
1079	D₈	—	4	2	no	—
1080	D₈	—	4	1	no	—
1081	D₈	—	4	1	no	—
1082	D₈	—	4	2	no	—
1083	D₈	—	4	2	no	—
1084	D₈	—	4	2	no	—
1085	M₁₆	—	2	2	no	—
1086	M₁₆	—	2	2	no	—
1087	C₂×C₈	—	2	2	no	—
1088	C₂×C₈	—	2	2	no	—
1089	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1090	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1091	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1092	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1093	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1094	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1095	C₄⋊C₄	—	2	1	no	—
1096	C₄⋊C₄	—	2	2	no	—
1097	C₄⋊C₄	—	2	1	no	—
1098	C₄⋊C₄	—	2	2	no	—
1099	C₄⋊C₄	—	2	2	no	—
1100	C₄⋊C₄	—	2	2	no	—
1101	C₄⋊C₄	—	2	2	no	—
1102	C₄⋊C₄	—	2	2	no	—
1103	C₄⋊C₄	—	2	2	no	—
1104	C₄⋊C₄	—	2	2	no	—
1105	C₄⋊C₄	—	2	1	no	—
1106	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1107	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1108	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1109	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1110	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1111	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1112	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1113	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1114	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	2	no	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	1	no	—
1125	C₂²⋊C₄	—	2	2	no	—
1126	C₂²⋊C₄	—	2	2	no	—
1127	C₂²⋊C₄	—	2	2	no	—
1128	C₂²⋊C₄	—	2	2	no	—
1129	C₂²⋊C₄	—	2	2	no	—
1130	C₂²⋊C₄	—	2	2	no	—
1131	C₂²⋊C₄	—	2	2	no	—
1132	C₂²⋊C₄	—	2	2	no	—
1133	C₂²⋊C₄	—	2	2	no	—
1134	C₂²⋊C₄	—	2	1	no	—
1135	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1136	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1137	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1138	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1139	C₄²	—	2	2	no	—
1140	C₄²	—	2	1	no	—
1141	C₄²	C₂×C₇×D₄	1	2	yes	—
1142	C₄²	C₂×C₇×D₄	1	2	yes	—
1143	C₄²	C₂⁴×C₇	1	2	yes	—
1144	C₄²	C₂⁴×C₇	1	2	yes	—
1145	C₂×C₇	—	2	2	no	—
1146	C₂×C₇	—	4	1	no	—
1147	C₂×C₇	—	4	1	no	—
1148	C₂×C₇	—	8	1	no	—
1149	C₂×C₇	—	8	2	no	—
1150	C₂×C₇	—	8	1	no	—
1151	C₂×C₇	—	8	1	no	—
1152	C₂×C₇	—	8	2	no	—
1153	C₂×C₇	C₂×#535	1	1	yes	characteristic
1154	C₂×C₇	#3584	1	1	yes	characteristic
1155	C₂×C₇	#3585	1	1	yes	characteristic
1156	C₂³	—	2	2	no	—
1157	C₂³	—	2	2	no	—
1158	C₂³	—	2	1	no	—
1159	C₂³	—	2	2	no	—
1160	C₂³	—	2	1	no	—
1161	C₂³	—	2	1	no	—
1162	C₂³	—	4	1	no	—
1163	C₂³	—	4	1	no	—
1164	C₂³	—	4	2	no	—
1165	C₂³	—	4	2	no	—
1166	C₂³	—	4	2	no	—
1167	C₂³	—	8	1	no	—
1168	C₂³	—	8	1	no	—
1169	C₂³	—	8	1	no	—
1170	C₂³	—	8	1	no	—
1171	C₂³	—	8	1	no	—
1172	C₂³	—	8	1	no	—
1173	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1174	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1175	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1176	Q₈	—	2	1	no	—
1177	Q₈	—	2	2	no	—
1178	Q₈	—	2	1	no	—
1179	Q₈	—	2	1	no	—
1180	Q₈	—	2	1	no	—
1181	Q₈	—	2	2	no	—
1182	Q₈	—	2	1	no	—
1183	Q₈	—	2	1	no	—
1184	Q₈	—	4	2	no	—
1185	Q₈	—	4	2	no	—
1186	Q₈	—	8	2	no	—
1187	D₄	—	2	2	no	—
1188	D₄	—	2	1	no	—
1189	D₄	—	2	2	no	—
1190	D₄	—	2	1	no	—
1191	D₄	—	2	1	no	—
1192	D₄	—	2	2	no	—
1193	D₄	—	2	1	no	—
1194	D₄	—	2	2	no	—
1195	D₄	—	2	1	no	—
1196	D₄	—	2	1	no	—
1197	D₄	—	4	2	no	—
1198	D₄	—	4	4	no	—
1199	D₄	—	4	4	no	—
1200	D₄	—	4	2	no	—
1201	D₄	—	4	2	no	—
1202	D₄	—	4	4	no	—
1203	D₄	—	4	2	no	—
1204	D₄	—	4	2	no	—
1205	D₄	—	4	2	no	—
1206	D₄	—	4	2	no	—
1207	D₄	—	4	2	no	—
1208	D₄	—	4	2	no	—
1209	D₄	—	8	2	no	—
1210	D₄	—	8	2	no	—
1211	D₄	—	8	2	no	—
1212	D₄	—	8	2	no	—
1213	D₄	—	8	2	no	—
1214	D₄	—	8	2	no	—
1215	D₄	—	8	1	no	—
1216	D₄	—	8	2	no	—
1217	C₂×C₄	—	2	2	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	1	no	—
1220	C₂×C₄	—	2	1	no	—
1221	C₂×C₄	—	2	1	no	—
1222	C₂×C₄	—	2	2	no	—
1223	C₂×C₄	—	2	2	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	1	no	—
1226	C₂×C₄	—	2	1	no	—
1227	C₂×C₄	—	2	2	no	—
1228	C₂×C₄	—	2	2	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	4	2	no	—
1232	C₂×C₄	—	4	2	no	—
1233	C₂×C₄	—	4	4	no	—
1234	C₂×C₄	—	4	2	no	—
1235	C₂×C₄	—	4	2	no	—
1236	C₂×C₄	—	4	4	no	—
1237	C₂×C₄	—	4	2	no	—
1238	C₂×C₄	—	4	2	no	—
1239	C₂×C₄	—	4	2	no	—
1240	C₂×C₄	—	4	2	no	—
1241	C₂×C₄	—	4	2	no	—
1242	C₂×C₄	—	8	2	no	—
1243	C₂×C₄	—	8	2	no	—
1244	C₂×C₄	—	8	2	no	—
1245	C₂×C₄	—	8	1	no	—
1246	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1247	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1248	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1249	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1250	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1251	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1252	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1253	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1254	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1255	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1256	C₈	—	2	1	no	—
1257	C₈	—	2	1	no	—
1258	C₈	—	2	1	no	—
1259	C₈	—	2	1	no	—
1260	C₈	—	2	2	no	—
1261	C₈	—	2	2	no	—
1262	C₇	#60815	1	1	yes	characteristic, direct product factor, Sylow
1263	C₂²	—	2	1	no	—
1264	C₂²	—	2	1	no	—
1265	C₂²	—	2	1	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	1	no	—
1269	C₂²	—	2	1	no	—
1270	C₂²	—	2	1	no	—
1271	C₂²	—	4	2	no	—
1272	C₂²	—	4	1	no	—
1273	C₂²	—	4	2	no	—
1274	C₂²	—	4	1	no	—
1275	C₂²	—	4	1	no	—
1276	C₂²	—	4	1	no	—
1277	C₂²	—	4	2	no	—
1278	C₂²	—	4	2	no	—
1279	C₂²	—	4	1	no	—
1280	C₂²	—	4	1	no	—
1281	C₂²	—	4	2	no	—
1282	C₂²	—	4	1	no	—
1283	C₂²	—	4	1	no	—
1284	C₂²	—	4	1	no	—
1285	C₂²	—	4	2	no	—
1286	C₂²	—	8	2	no	—
1287	C₂²	—	8	4	no	—
1288	C₂²	—	8	4	no	—
1289	C₂²	—	16	2	no	—
1290	C₂²	C₇×#535	1	2	yes	—
1291	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1292	C₄	—	2	2	no	—
1293	C₄	—	2	2	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	2	2	no	—
1296	C₄	—	2	1	no	—
1297	C₄	—	2	1	no	—
1298	C₄	—	4	1	no	—
1299	C₄	—	4	2	no	—
1300	C₄	—	4	1	no	—
1301	C₄	—	4	2	no	—
1302	C₄	—	4	1	no	—
1303	C₄	—	4	1	no	—
1304	C₄	—	4	1	no	—
1305	C₄	C₇×#535	1	2	yes	—
1306	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1307	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1308	C₂	—	2	2	no	—
1309	C₂	—	4	1	no	—
1310	C₂	—	4	1	no	—
1311	C₂	—	8	2	no	—
1312	C₂	—	8	1	no	—
1313	C₂	—	8	1	no	—
1314	C₂	—	8	2	no	—
1315	C₂	—	8	1	no	—
1316	C₂	C₂×C₇×#535	1	1	yes	characteristic
1317	C₂	C₇×#3584	1	1	yes	characteristic
1318	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 ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3494	C₂	semidirect
2. C₇×#3449	C₂	semidirect
3. C₇×#3225	C₂	semidirect
4. C₇×#3224	C₂	semidirect
5. C₇×#3221	C₂	semidirect
6. C₇×#3220	C₂	semidirect
7. C₇×#3219	C₂	semidirect
8. C₇×#3214	C₂	semidirect
9. C₇×#3212	C₂	semidirect
10. C₇×#3207	C₂	semidirect
11. C₇×#3155	C₂	semidirect
12. C₇×#3154	C₂	semidirect
13. C₇×#3137	C₂	semidirect
14. C₇×#3136	C₂	semidirect
15. C₇×#3046	C₂	semidirect
16. C₇×#3045	C₂	semidirect
17. C₇×#3042	C₂	semidirect
18. C₇×#3041	C₂	semidirect
19. C₇×#3006	C₂	semidirect
20. C₇×#3005	C₂	semidirect
21. C₇×#3002	C₂	semidirect
22. C₂×C₇×#449	C₂	semidirect
23. C₇×#2924	C₂	semidirect
26. C₂×C₇×#137	C₂²	semidirect
29. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
32. C₂²×C₇×SD₁₆	C₂²	semidirect
33. C₂²×C₇×D₈	C₂²	semidirect
40. C₇×#544	C₂²	semidirect
41. C₇×#542	C₂²	semidirect
42. C₇×#540	C₂²	semidirect
47. C₇×#536	C₂²	semidirect
50. C₇×#535	C₂²	semidirect
51. C₇×#535	C₂²	semidirect
53. C₇×#532	C₂²	semidirect
54. C₇×#532	C₂²	semidirect
55. C₇×#532	C₂²	semidirect
56. C₇×#529	C₂²	semidirect
62. C₇×#520	C₂²	semidirect
63. C₇×#518	C₂²	semidirect
65. C₇×#497	C₂²	semidirect
66. C₇×#496	C₂²	semidirect
67. C₇×#496	C₂²	semidirect
68. C₇×#496	C₂²	semidirect
69. C₇×#495	C₂²	semidirect
70. C₇×#495	C₂²	semidirect
71. C₇×#493	C₂²	semidirect
72. C₇×#492	C₂²	semidirect
73. C₇×#491	C₂²	semidirect
74. C₇×#490	C₂²	semidirect
75. C₇×#489	C₂²	semidirect
76. C₇×#489	C₂²	semidirect
77. C₇×#488	C₂²	semidirect
78. C₇×#488	C₂²	semidirect
79. C₇×#487	C₂²	semidirect
80. C₇×#486	C₂²	semidirect
81. C₇×#464	C₂²	semidirect
82. C₇×#464	C₂²	semidirect
83. C₇×#463	C₂²	semidirect
84. C₇×#463	C₂²	semidirect
85. C₇×#463	C₂²	semidirect
86. C₇×#463	C₂²	semidirect
87. C₇×#463	C₂²	semidirect
88. C₇×#463	C₂²	semidirect
89. C₇×#462	C₂²	semidirect
90. C₇×#461	C₂²	semidirect
91. C₇×#461	C₂²	semidirect
92. C₇×#461	C₂²	semidirect
93. C₇×#460	C₂²	semidirect
94. C₇×#459	C₂²	semidirect
95. C₇×#459	C₂²	semidirect
96. C₇×#459	C₂²	semidirect
97. C₇×#452	C₂²	semidirect
98. C₇×#452	C₂²	semidirect
99. C₇×#452	C₂²	semidirect
100. C₇×#452	C₂²	semidirect
101. C₇×#451	C₂²	semidirect
102. C₇×#450	C₂²	semidirect
105. C₇×#449	C₂²	semidirect
106. C₇×#449	C₂²	semidirect
107. C₇×#449	C₂²	semidirect
108. C₇×#449	C₂²	semidirect
109. C₇×#449	C₂²	semidirect
110. C₇×#449	C₂²	semidirect
111. C₇×#449	C₂²	semidirect
112. C₇×#449	C₂²	semidirect
113. C₇×#448	C₂²	semidirect
114. C₇×#448	C₂²	semidirect
115. C₇×#447	C₂²	semidirect
116. C₇×#447	C₂²	semidirect
117. C₇×#433	C₂²	semidirect
118. C₇×#433	C₂²	semidirect
119. C₇×#432	C₂²	semidirect
120. C₇×#431	C₂²	semidirect
121. C₇×#424	C₂²	semidirect
122. C₇×#424	C₂²	semidirect
123. C₇×#419	C₂²	semidirect
124. C₇×#418	C₂²	semidirect
129. C₂×C₇×#103	C₂²	semidirect
130. C₂×C₇×#102	C₂²	semidirect
133. C₇×#405	C₂²	semidirect
134. C₇×#405	C₂²	semidirect
135. #60815	C₇	direct (N × H)
325. #3494	C₂×C₇	semidirect
326. #3449	C₂×C₇	semidirect
327. #3225	C₂×C₇	semidirect
328. #3224	C₂×C₇	semidirect
329. #3221	C₂×C₇	semidirect
330. #3220	C₂×C₇	semidirect
331. #3219	C₂×C₇	semidirect
332. #3214	C₂×C₇	semidirect
333. #3212	C₂×C₇	semidirect
334. #3207	C₂×C₇	semidirect
335. #3155	C₂×C₇	semidirect
336. #3154	C₂×C₇	semidirect
337. #3137	C₂×C₇	semidirect
338. #3136	C₂×C₇	semidirect
339. #3046	C₂×C₇	semidirect
340. #3045	C₂×C₇	semidirect
341. #3042	C₂×C₇	semidirect
342. #3041	C₂×C₇	semidirect
343. #3006	C₂×C₇	semidirect
344. #3005	C₂×C₇	semidirect
345. #3002	C₂×C₇	semidirect
346. C₂×#449	C₂×C₇	semidirect
347. #2924	C₂×C₇	semidirect
523. C₂×#137	C₂²×C₇	semidirect
526. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
529. C₂²×SD₁₆	C₂²×C₇	semidirect
530. C₂²×D₈	C₂²×C₇	semidirect
537. #544	C₂²×C₇	semidirect
538. #542	C₂²×C₇	semidirect
539. #540	C₂²×C₇	semidirect
544. #536	C₂²×C₇	semidirect
547. #535	C₂²×C₇	semidirect
548. #535	C₂²×C₇	semidirect
550. #532	C₂²×C₇	semidirect
551. #532	C₂²×C₇	semidirect
552. #532	C₂²×C₇	semidirect
553. #529	C₂²×C₇	semidirect
559. #520	C₂²×C₇	semidirect
560. #518	C₂²×C₇	semidirect
562. #497	C₂²×C₇	semidirect
563. #496	C₂²×C₇	semidirect
564. #496	C₂²×C₇	semidirect
565. #496	C₂²×C₇	semidirect
566. #495	C₂²×C₇	semidirect
567. #495	C₂²×C₇	semidirect
568. #493	C₂²×C₇	semidirect
569. #492	C₂²×C₇	semidirect
570. #491	C₂²×C₇	semidirect
571. #490	C₂²×C₇	semidirect
572. #489	C₂²×C₇	semidirect
573. #489	C₂²×C₇	semidirect
574. #488	C₂²×C₇	semidirect
575. #488	C₂²×C₇	semidirect
576. #487	C₂²×C₇	semidirect
577. #486	C₂²×C₇	semidirect
578. #464	C₂²×C₇	semidirect
579. #464	C₂²×C₇	semidirect
580. #463	C₂²×C₇	semidirect
581. #463	C₂²×C₇	semidirect
582. #463	C₂²×C₇	semidirect
583. #463	C₂²×C₇	semidirect
584. #463	C₂²×C₇	semidirect
585. #463	C₂²×C₇	semidirect
586. #462	C₂²×C₇	semidirect
587. #461	C₂²×C₇	semidirect
588. #461	C₂²×C₇	semidirect
589. #461	C₂²×C₇	semidirect
590. #460	C₂²×C₇	semidirect
591. #459	C₂²×C₇	semidirect
592. #459	C₂²×C₇	semidirect
593. #459	C₂²×C₇	semidirect
594. #452	C₂²×C₇	semidirect
595. #452	C₂²×C₇	semidirect
596. #452	C₂²×C₇	semidirect
597. #452	C₂²×C₇	semidirect
598. #451	C₂²×C₇	semidirect
599. #450	C₂²×C₇	semidirect
602. #449	C₂²×C₇	semidirect
603. #449	C₂²×C₇	semidirect
604. #449	C₂²×C₇	semidirect
605. #449	C₂²×C₇	semidirect
606. #449	C₂²×C₇	semidirect
607. #449	C₂²×C₇	semidirect
608. #449	C₂²×C₇	semidirect
609. #449	C₂²×C₇	semidirect
610. #448	C₂²×C₇	semidirect
611. #448	C₂²×C₇	semidirect
612. #447	C₂²×C₇	semidirect
613. #447	C₂²×C₇	semidirect
614. #433	C₂²×C₇	semidirect
615. #433	C₂²×C₇	semidirect
616. #432	C₂²×C₇	semidirect
617. #431	C₂²×C₇	semidirect
618. #424	C₂²×C₇	semidirect
619. #424	C₂²×C₇	semidirect
620. #419	C₂²×C₇	semidirect
621. #418	C₂²×C₇	semidirect
626. C₂×#103	C₂²×C₇	semidirect
627. C₂×#102	C₂²×C₇	semidirect
630. #405	C₂²×C₇	semidirect
631. #405	C₂²×C₇	semidirect
1262. C₇	#60815	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×#3449	2
C₇×#3225	2
C₇×#3224	2
C₇×#3221	2
C₇×#3220	2
C₇×#3219	2
C₇×#3214	2
C₇×#3212	2
C₇×#3207	2
C₇×#3155	2
C₇×#3154	2
C₇×#3137	2
C₇×#3136	2
C₇×#3046	2
C₇×#3045	2
C₇×#3042	2
C₇×#3041	2
C₇×#3006	2
C₇×#3005	2
C₇×#3002	2
C₂×C₇×#449	2
C₇×#2924	2
#60815	7

Subgroups — C7×#60815 #13238031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60815 #13238031