Subgroups — C₇×#60834 #13238050

Order 1792.

2104 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3460	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×#3213	C₂	1	2	yes	maximal, complemented
9	C₇×#3211	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×#3040	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#463	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3012	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3010	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#3008	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₇×H(5,𝔽₂)	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, complemented
32	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
34	C₇×#548	—	2	1	no	—
35	C₇×#548	—	2	1	no	—
36	C₇×#546	—	2	2	no	—
37	C₇×#546	—	2	2	no	—
38	C₇×#546	—	2	1	no	—
39	C₇×#546	—	2	1	no	—
40	C₇×#544	C₂²	1	1	yes	characteristic, complemented
41	C₇×#542	—	2	1	no	—
42	C₇×#542	C₂²	1	2	yes	complemented
43	C₇×#540	—	2	1	no	—
44	C₇×#540	C₂²	1	2	yes	complemented
45	C₇×#538	—	2	2	no	—
46	C₇×#537	C₂²	1	1	yes	characteristic
47	C₇×#536	C₂²	1	1	yes	characteristic
48	C₇×#536	C₂²	1	2	yes	complemented
49	C₇×#535	C₂²	1	1	yes	characteristic
50	C₇×#535	C₂²	1	1	yes	characteristic
51	C₇×#535	C₂²	1	1	yes	characteristic, complemented
52	C₇×#535	C₂²	1	2	yes	complemented
53	C₇×#532	—	2	1	no	—
54	C₇×#532	C₂²	1	1	yes	characteristic
55	C₇×#532	C₂²	1	2	yes	complemented
56	C₇×#532	C₂²	1	2	yes	complemented
57	C₇×#529	—	2	1	no	—
58	C₇×#529	C₂²	1	2	yes	complemented
59	C₂×C₇×#124	C₂²	1	1	yes	characteristic
60	C₂×C₇×#124	C₂²	1	2	yes	complemented
61	C₇×#525	—	2	2	no	—
62	C₄×C₇×#41	C₂²	1	1	yes	characteristic
63	C₄×C₇×#41	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
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	1	yes	characteristic, complemented
82	C₇×#464	C₂²	1	2	yes	complemented
83	C₇×#464	C₂²	1	1	yes	characteristic, complemented
84	C₇×#464	C₂²	1	2	yes	complemented
85	C₇×#463	C₂²	1	1	yes	characteristic, 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×#463	C₂²	1	2	yes	complemented
90	C₇×#463	C₂²	1	1	yes	characteristic, complemented
91	C₇×#463	C₂²	1	2	yes	complemented
92	C₇×#463	C₂²	1	2	yes	complemented
93	C₇×#463	C₂²	1	2	yes	complemented
94	C₇×#463	C₂²	1	2	yes	complemented
95	C₇×#462	C₂²	1	1	yes	characteristic, complemented
96	C₇×#461	C₂²	1	1	yes	characteristic, complemented
97	C₇×#461	C₂²	1	2	yes	complemented
98	C₇×#460	C₂²	1	1	yes	characteristic, complemented
99	C₇×#459	C₂²	1	1	yes	characteristic, complemented
100	C₇×#459	C₂²	1	2	yes	complemented
101	C₇×#452	C₂²	1	2	yes	complemented
102	C₇×#452	C₂²	1	2	yes	complemented
103	C₇×#451	C₂²	1	2	yes	complemented
104	C₇×#450	C₂²	1	2	yes	complemented
105	C₇×#449	C₂²	1	2	yes	—
106	C₇×#449	C₂²	1	2	yes	—
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	2	yes	complemented
111	C₇×#448	C₂²	1	2	yes	complemented
112	C₇×#448	C₂²	1	2	yes	complemented
113	C₇×#448	C₂²	1	2	yes	complemented
114	C₇×#447	C₂²	1	2	yes	—
115	C₇×#447	C₂²	1	2	yes	—
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×#423	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
123	C₇×#419	C₂²	1	1	yes	characteristic, complemented
124	C₇×#418	C₂²	1	1	yes	characteristic
125	C₇×#417	C₂²	1	1	yes	characteristic
126	C₇×#417	C₂²	1	1	yes	characteristic, complemented
127	C₇×#416	C₂²	1	1	yes	characteristic
128	C₇×#416	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₇×#102	C₂²	1	1	yes	characteristic
131	C₇×#408	C₂²	1	1	yes	characteristic
132	C₇×#408	C₂²	1	1	yes	characteristic
133	C₇×#405	C₂²	1	1	yes	characteristic, complemented
134	C₇×#405	C₂²	1	1	yes	characteristic, complemented
135	#60834	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₇×2₋¹⁺⁴	—	4	2	no	—
137	C₇×2₋¹⁺⁴	—	4	2	no	—
138	C₇×H(5,𝔽₂)	—	4	2	no	—
139	C₇×H(5,𝔽₂)	—	4	2	no	—
140	C₂×C₇×#41	—	2	1	no	—
141	C₂×C₇×#41	—	2	2	no	—
142	C₂×C₇×#41	—	2	1	no	—
143	C₂×C₇×#41	—	2	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	2	yes	—
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	2	yes	—
153	C₂²×C₇×D₄	—	2	2	no	—
154	C₂²×C₇×D₄	—	2	1	no	—
155	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
156	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
157	C₂²×C₇×D₄	C₂³	1	2	yes	—
158	C₂³×C₄×C₇	—	2	1	no	—
159	C₇×#137	—	4	2	no	—
160	C₇×AGL(1,ℤ/8)	—	4	2	no	—
161	C₇×AGL(1,ℤ/8)	—	4	2	no	—
162	C₇×AGL(1,ℤ/8)	—	4	2	no	—
163	C₇×#135	—	4	2	no	—
164	C₇×#135	—	4	2	no	—
165	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
166	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
167	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
168	C₂×C₇×SD₁₆	—	4	2	no	—
169	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
170	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
171	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
172	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
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	1	yes	characteristic
177	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
178	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
179	C₂×C₇×D₈	—	4	2	no	—
180	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
181	C₂×C₇×D₈	C₂³	1	2	yes	—
182	C₂×C₇×D₈	C₂³	1	2	yes	—
183	C₂×C₇×D₈	C₂³	1	2	yes	—
184	C₂×C₇×D₈	C₂³	1	2	yes	—
185	C₂×C₇×D₈	C₂³	1	2	yes	—
186	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
187	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
188	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
189	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
190	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
191	C₇×C₄⋊Q₈	—	2	1	no	—
192	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
193	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
194	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
195	C₇×#127	—	2	1	no	—
196	C₇×#127	C₂³	1	2	yes	—
197	C₇×#127	C₂³	1	2	yes	—
198	C₇×#127	C₂³	1	1	yes	characteristic
199	C₇×#126	—	2	2	no	—
200	C₇×#126	—	2	2	no	—
201	C₇×#125	—	2	1	no	—
202	C₇×#125	C₂³	1	2	yes	—
203	C₇×#124	—	2	1	no	—
204	C₇×#124	—	2	2	no	—
205	C₇×#124	—	2	1	no	—
206	C₇×#124	—	2	1	no	—
207	C₇×#124	—	2	2	no	—
208	C₇×#124	—	2	2	no	—
209	C₇×#124	—	2	2	no	—
210	C₇×#124	C₂³	1	2	yes	—
211	C₇×#124	C₂³	1	2	yes	—
212	C₇×#124	C₂³	1	2	yes	—
213	C₇×#124	C₂³	1	2	yes	—
214	C₇×#124	C₂³	1	2	yes	—
215	C₇×#124	C₂³	1	1	yes	characteristic
216	C₇×#124	C₂³	1	1	yes	characteristic
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×#123	—	2	2	no	—
223	C₇×#123	—	2	2	no	—
224	C₇×C₂²⋊Q₈	—	2	1	no	—
225	C₇×C₂²⋊Q₈	—	2	2	no	—
226	C₇×C₂²⋊Q₈	—	2	1	no	—
227	C₇×C₂²⋊Q₈	—	2	1	no	—
228	C₇×C₂²⋊Q₈	—	2	2	no	—
229	C₇×C₂²⋊Q₈	—	2	2	no	—
230	C₇×C₂²⋊Q₈	—	2	2	no	—
231	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
232	C₇×#121	—	2	2	no	—
233	C₇×#121	—	2	1	no	—
234	C₇×#121	—	2	1	no	—
235	C₇×#121	—	2	1	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	2	no	—
246	C₇×#121	—	2	2	no	—
247	C₇×#121	C₂³	1	2	yes	—
248	C₇×#121	C₂³	1	2	yes	—
249	C₇×#121	C₂³	1	2	yes	—
250	C₇×#120	—	2	2	no	—
251	C₇×#120	—	2	2	no	—
252	C₇×#120	—	2	2	no	—
253	C₇×#120	—	2	2	no	—
254	C₇×#120	—	2	2	no	—
255	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
256	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
257	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
258	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
259	C₄×C₇×D₄	—	2	1	no	—
260	C₄×C₇×D₄	—	2	1	no	—
261	C₄×C₇×D₄	—	2	2	no	—
262	C₄×C₇×D₄	—	2	1	no	—
263	C₄×C₇×D₄	—	2	1	no	—
264	C₄×C₇×D₄	—	2	2	no	—
265	C₄×C₇×D₄	—	2	1	no	—
266	C₄×C₇×D₄	—	2	1	no	—
267	C₄×C₇×D₄	—	2	2	no	—
268	C₄×C₇×D₄	—	2	2	no	—
269	C₄×C₇×D₄	D₄	1	2	yes	—
270	C₄×C₇×D₄	D₄	1	1	yes	characteristic
271	C₄×C₇×D₄	D₄	1	2	yes	—
272	C₄×C₇×D₄	D₄	1	1	yes	characteristic
273	C₄×C₇×D₄	C₂³	1	2	yes	—
274	C₄×C₇×D₄	C₂³	1	2	yes	—
275	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
276	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
277	C₇×#117	—	2	1	no	—
278	C₇×#117	—	2	2	no	—
279	C₇×#117	C₂³	1	1	yes	characteristic
280	C₇×#117	C₂³	1	1	yes	characteristic
281	C₇×#117	C₂³	1	2	yes	—
282	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
283	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₄²×C₇	—	2	1	no	—
289	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
290	C₂×C₄²×C₇	C₂³	1	2	yes	—
291	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
293	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
294	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
295	C₇×C₄⋊C₈	C₂³	1	2	yes	—
296	C₇×C₄⋊C₈	C₂³	1	2	yes	—
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	1	yes	characteristic
302	C₇×#103	C₂³	1	2	yes	—
303	C₇×#103	C₂³	1	2	yes	—
304	C₇×#103	C₂³	1	1	yes	characteristic
305	C₇×#103	C₂³	1	2	yes	—
306	C₇×#103	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	2	yes	—
310	C₇×#102	C₂³	1	2	yes	—
311	C₇×#102	C₂³	1	1	yes	characteristic
312	C₇×#102	C₂³	1	2	yes	—
313	C₇×#102	C₂³	1	2	yes	—
314	C₇×#102	C₂³	1	1	yes	characteristic
315	C₇×#102	C₂³	1	2	yes	—
316	C₇×#102	C₂³	1	1	yes	characteristic
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×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	#3500	C₂×C₇	1	1	yes	characteristic, complemented
326	#3460	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	#3213	C₂×C₇	1	2	yes	complemented
333	#3211	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	#3040	C₂×C₇	1	1	yes	characteristic, complemented
340	#3036	C₂×C₇	1	1	yes	characteristic, complemented
341	#3035	C₂×C₇	1	1	yes	characteristic, complemented
342	C₂×#463	C₂×C₇	1	1	yes	characteristic, complemented
343	#3013	C₂×C₇	1	1	yes	characteristic, complemented
344	#3012	C₂×C₇	1	1	yes	characteristic, complemented
345	#3010	C₂×C₇	1	1	yes	characteristic, complemented
346	#3008	C₂×C₇	1	1	yes	characteristic, complemented
347	#2925	C₂×C₇	1	1	yes	characteristic, complemented
348	C₂⁴×C₇	—	2	2	no	—
349	C₂⁴×C₇	—	2	1	no	—
350	C₂⁴×C₇	—	2	1	no	—
351	C₇×#41	—	2	2	no	—
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	—	2	2	no	—
359	C₇×#41	—	4	2	no	—
360	C₇×#41	—	4	2	no	—
361	C₇×#41	—	4	2	no	—
362	C₇×#41	—	4	2	no	—
363	C₇×#41	—	4	8	no	—
364	C₇×#41	—	4	4	no	—
365	C₇×#41	—	4	4	no	—
366	C₇×#41	—	8	4	no	—
367	C₂×C₇×Q₈	—	2	2	no	—
368	C₂×C₇×Q₈	—	2	1	no	—
369	C₂×C₇×Q₈	—	2	2	no	—
370	C₂×C₇×Q₈	—	2	2	no	—
371	C₂×C₇×Q₈	—	2	2	no	—
372	C₂×C₇×Q₈	—	4	2	no	—
373	C₂×C₇×Q₈	—	4	2	no	—
374	C₂×C₇×Q₈	—	4	4	no	—
375	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
376	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
377	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
378	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
379	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
380	C₂×C₇×D₄	—	2	1	no	—
381	C₂×C₇×D₄	—	2	2	no	—
382	C₂×C₇×D₄	—	2	1	no	—
383	C₂×C₇×D₄	—	2	2	no	—
384	C₂×C₇×D₄	—	2	1	no	—
385	C₂×C₇×D₄	—	2	2	no	—
386	C₂×C₇×D₄	—	2	2	no	—
387	C₂×C₇×D₄	—	2	2	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	2	no	—
395	C₂×C₇×D₄	—	2	2	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	—	4	2	no	—
402	C₂×C₇×D₄	—	4	2	no	—
403	C₂×C₇×D₄	—	4	8	no	—
404	C₂×C₇×D₄	—	4	4	no	—
405	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
406	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
407	C₂×C₇×D₄	C₂⁴	1	2	yes	—
408	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
409	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
410	C₂×C₇×D₄	C₂⁴	1	2	yes	—
411	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₇	—	2	2	no	—
413	C₂²×C₄×C₇	—	2	1	no	—
414	C₂²×C₄×C₇	—	2	1	no	—
415	C₂²×C₄×C₇	—	2	1	no	—
416	C₂²×C₄×C₇	—	2	1	no	—
417	C₂²×C₄×C₇	—	2	2	no	—
418	C₂²×C₄×C₇	—	2	2	no	—
419	C₂²×C₄×C₇	—	2	1	no	—
420	C₂²×C₄×C₇	—	2	2	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	—	8	2	no	—
425	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
426	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
427	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
428	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
429	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
430	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
431	C₇×Q₁₆	—	4	1	no	—
432	C₇×Q₁₆	—	4	1	no	—
433	C₇×Q₁₆	—	4	2	no	—
434	C₇×SD₁₆	—	4	2	no	—
435	C₇×SD₁₆	—	4	2	no	—
436	C₇×SD₁₆	—	4	1	no	—
437	C₇×SD₁₆	—	4	1	no	—
438	C₇×SD₁₆	—	4	1	no	—
439	C₇×SD₁₆	—	4	1	no	—
440	C₇×SD₁₆	—	4	2	no	—
441	C₇×SD₁₆	—	4	2	no	—
442	C₇×SD₁₆	—	4	2	no	—
443	C₇×SD₁₆	—	4	2	no	—
444	C₇×D₈	—	4	2	no	—
445	C₇×D₈	—	4	2	no	—
446	C₇×D₈	—	4	1	no	—
447	C₇×D₈	—	4	1	no	—
448	C₇×D₈	—	4	2	no	—
449	C₇×D₈	—	4	2	no	—
450	C₇×D₈	—	4	2	no	—
451	C₇×M₁₆	—	2	2	no	—
452	C₇×M₁₆	—	2	2	no	—
453	C₂×C₇×C₈	—	2	2	no	—
454	C₂×C₇×C₈	—	2	2	no	—
455	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
456	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
457	C₂×C₇×C₈	C₂⁴	1	2	yes	—
458	C₂×C₇×C₈	C₂⁴	1	2	yes	—
459	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
460	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
461	C₇×C₄⋊C₄	—	2	1	no	—
462	C₇×C₄⋊C₄	—	2	1	no	—
463	C₇×C₄⋊C₄	—	2	1	no	—
464	C₇×C₄⋊C₄	—	2	2	no	—
465	C₇×C₄⋊C₄	—	2	2	no	—
466	C₇×C₄⋊C₄	—	2	1	no	—
467	C₇×C₄⋊C₄	—	2	2	no	—
468	C₇×C₄⋊C₄	—	2	1	no	—
469	C₇×C₄⋊C₄	—	2	2	no	—
470	C₇×C₄⋊C₄	—	2	2	no	—
471	C₇×C₄⋊C₄	—	2	2	no	—
472	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
473	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
474	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
475	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
476	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
477	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
478	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	1	no	—
483	C₇×C₂²⋊C₄	—	2	2	no	—
484	C₇×C₂²⋊C₄	—	2	1	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	—	2	2	no	—
492	C₇×C₂²⋊C₄	—	2	2	no	—
493	C₇×C₂²⋊C₄	—	2	1	no	—
494	C₇×C₂²⋊C₄	—	2	1	no	—
495	C₇×C₂²⋊C₄	—	2	2	no	—
496	C₇×C₂²⋊C₄	—	2	2	no	—
497	C₇×C₂²⋊C₄	—	2	1	no	—
498	C₇×C₂²⋊C₄	—	2	1	no	—
499	C₇×C₂²⋊C₄	—	2	2	no	—
500	C₇×C₂²⋊C₄	—	2	2	no	—
501	C₇×C₂²⋊C₄	—	2	2	no	—
502	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
503	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
504	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
505	C₄²×C₇	—	2	1	no	—
506	C₄²×C₇	—	2	1	no	—
507	C₄²×C₇	—	2	1	no	—
508	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
509	C₄²×C₇	C₂×D₄	1	2	yes	—
510	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
511	C₄²×C₇	C₂×D₄	1	2	yes	—
512	C₄²×C₇	C₂⁴	1	2	yes	—
513	C₄²×C₇	C₂⁴	1	1	yes	characteristic
514	C₄²×C₇	C₂⁴	1	1	yes	characteristic
515	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
516	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
517	C₂×#137	C₂²×C₇	1	1	yes	characteristic, complemented
518	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
519	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
520	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic, complemented
521	C₂×#135	C₂²×C₇	1	1	yes	characteristic
522	C₂×#135	C₂²×C₇	1	1	yes	characteristic, complemented
523	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
524	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
525	#548	—	2	1	no	—
526	#548	—	2	1	no	—
527	#546	—	2	2	no	—
528	#546	—	2	2	no	—
529	#546	—	2	1	no	—
530	#546	—	2	1	no	—
531	#544	C₂²×C₇	1	1	yes	characteristic, complemented
532	#542	—	2	1	no	—
533	#542	C₂²×C₇	1	2	yes	complemented
534	#540	—	2	1	no	—
535	#540	C₂²×C₇	1	2	yes	complemented
536	#538	—	2	2	no	—
537	#537	C₂²×C₇	1	1	yes	characteristic
538	#536	C₂²×C₇	1	1	yes	characteristic
539	#536	C₂²×C₇	1	2	yes	complemented
540	#535	C₂²×C₇	1	1	yes	characteristic
541	#535	C₂²×C₇	1	1	yes	characteristic
542	#535	C₂²×C₇	1	1	yes	characteristic, complemented
543	#535	C₂²×C₇	1	2	yes	complemented
544	#532	—	2	1	no	—
545	#532	C₂²×C₇	1	1	yes	characteristic
546	#532	C₂²×C₇	1	2	yes	complemented
547	#532	C₂²×C₇	1	2	yes	complemented
548	#529	—	2	1	no	—
549	#529	C₂²×C₇	1	2	yes	complemented
550	C₂×#124	C₂²×C₇	1	1	yes	characteristic
551	C₂×#124	C₂²×C₇	1	2	yes	complemented
552	#525	—	2	2	no	—
553	C₄×#41	C₂²×C₇	1	1	yes	characteristic
554	C₄×#41	C₂²×C₇	1	1	yes	characteristic, complemented
555	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
556	#497	C₂²×C₇	1	2	yes	complemented
557	#496	C₂²×C₇	1	2	yes	complemented
558	#496	C₂²×C₇	1	2	yes	complemented
559	#496	C₂²×C₇	1	2	yes	complemented
560	#495	C₂²×C₇	1	2	yes	complemented
561	#495	C₂²×C₇	1	2	yes	complemented
562	#493	C₂²×C₇	1	2	yes	complemented
563	#492	C₂²×C₇	1	2	yes	complemented
564	#491	C₂²×C₇	1	2	yes	complemented
565	#490	C₂²×C₇	1	2	yes	complemented
566	#489	C₂²×C₇	1	2	yes	complemented
567	#489	C₂²×C₇	1	2	yes	complemented
568	#488	C₂²×C₇	1	2	yes	complemented
569	#488	C₂²×C₇	1	2	yes	complemented
570	#487	C₂²×C₇	1	2	yes	complemented
571	#486	C₂²×C₇	1	2	yes	complemented
572	#464	C₂²×C₇	1	1	yes	characteristic, complemented
573	#464	C₂²×C₇	1	2	yes	complemented
574	#464	C₂²×C₇	1	1	yes	characteristic, complemented
575	#464	C₂²×C₇	1	2	yes	complemented
576	#463	C₂²×C₇	1	1	yes	characteristic, complemented
577	#463	C₂²×C₇	1	2	yes	complemented
578	#463	C₂²×C₇	1	2	yes	complemented
579	#463	C₂²×C₇	1	2	yes	complemented
580	#463	C₂²×C₇	1	2	yes	complemented
581	#463	C₂²×C₇	1	1	yes	characteristic, 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	1	yes	characteristic, complemented
587	#461	C₂²×C₇	1	1	yes	characteristic, complemented
588	#461	C₂²×C₇	1	2	yes	complemented
589	#460	C₂²×C₇	1	1	yes	characteristic, complemented
590	#459	C₂²×C₇	1	1	yes	characteristic, complemented
591	#459	C₂²×C₇	1	2	yes	complemented
592	#452	C₂²×C₇	1	2	yes	complemented
593	#452	C₂²×C₇	1	2	yes	complemented
594	#451	C₂²×C₇	1	2	yes	complemented
595	#450	C₂²×C₇	1	2	yes	complemented
596	#449	C₂²×C₇	1	2	yes	—
597	#449	C₂²×C₇	1	2	yes	—
598	#449	C₂²×C₇	1	2	yes	complemented
599	#449	C₂²×C₇	1	2	yes	complemented
600	#449	C₂²×C₇	1	2	yes	complemented
601	#449	C₂²×C₇	1	2	yes	complemented
602	#448	C₂²×C₇	1	2	yes	complemented
603	#448	C₂²×C₇	1	2	yes	complemented
604	#448	C₂²×C₇	1	2	yes	complemented
605	#447	C₂²×C₇	1	2	yes	—
606	#447	C₂²×C₇	1	2	yes	—
607	#447	C₂²×C₇	1	2	yes	complemented
608	#433	C₂²×C₇	1	2	yes	complemented
609	#433	C₂²×C₇	1	2	yes	complemented
610	#432	C₂²×C₇	1	2	yes	complemented
611	#431	C₂²×C₇	1	2	yes	complemented
612	#423	C₂²×C₇	1	1	yes	characteristic, complemented
613	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
614	#419	C₂²×C₇	1	1	yes	characteristic, complemented
615	#418	C₂²×C₇	1	1	yes	characteristic
616	#417	C₂²×C₇	1	1	yes	characteristic
617	#417	C₂²×C₇	1	1	yes	characteristic, complemented
618	#416	C₂²×C₇	1	1	yes	characteristic
619	#416	C₂²×C₇	1	1	yes	characteristic, complemented
620	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
621	C₂×#102	C₂²×C₇	1	1	yes	characteristic
622	#408	C₂²×C₇	1	1	yes	characteristic
623	#408	C₂²×C₇	1	1	yes	characteristic
624	#405	C₂²×C₇	1	1	yes	characteristic, complemented
625	#405	C₂²×C₇	1	1	yes	characteristic, complemented
626	C₂³×C₇	—	2	2	no	—
627	C₂³×C₇	—	2	2	no	—
628	C₂³×C₇	—	2	1	no	—
629	C₂³×C₇	—	2	1	no	—
630	C₂³×C₇	—	2	1	no	—
631	C₂³×C₇	—	4	4	no	—
632	C₂³×C₇	—	4	2	no	—
633	C₂³×C₇	—	4	2	no	—
634	C₂³×C₇	—	8	1	no	—
635	C₂³×C₇	—	8	1	no	—
636	C₂³×C₇	—	8	1	no	—
637	C₂³×C₇	—	8	1	no	—
638	C₂³×C₇	—	8	2	no	—
639	C₂³×C₇	—	8	2	no	—
640	C₂³×C₇	C₂²×D₄	1	2	yes	—
641	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
642	C₇×Q₈	—	2	2	no	—
643	C₇×Q₈	—	2	1	no	—
644	C₇×Q₈	—	2	1	no	—
645	C₇×Q₈	—	2	2	no	—
646	C₇×Q₈	—	2	1	no	—
647	C₇×Q₈	—	2	1	no	—
648	C₇×Q₈	—	2	2	no	—
649	C₇×Q₈	—	2	1	no	—
650	C₇×Q₈	—	2	1	no	—
651	C₇×Q₈	—	4	4	no	—
652	C₇×Q₈	—	4	2	no	—
653	C₇×Q₈	—	8	2	no	—
654	C₇×D₄	—	2	4	no	—
655	C₇×D₄	—	2	2	no	—
656	C₇×D₄	—	2	2	no	—
657	C₇×D₄	—	2	2	no	—
658	C₇×D₄	—	2	1	no	—
659	C₇×D₄	—	2	1	no	—
660	C₇×D₄	—	2	2	no	—
661	C₇×D₄	—	2	1	no	—
662	C₇×D₄	—	2	1	no	—
663	C₇×D₄	—	2	2	no	—
664	C₇×D₄	—	2	1	no	—
665	C₇×D₄	—	2	1	no	—
666	C₇×D₄	—	4	4	no	—
667	C₇×D₄	—	4	4	no	—
668	C₇×D₄	—	4	4	no	—
669	C₇×D₄	—	4	2	no	—
670	C₇×D₄	—	4	2	no	—
671	C₇×D₄	—	4	2	no	—
672	C₇×D₄	—	4	2	no	—
673	C₇×D₄	—	4	2	no	—
674	C₇×D₄	—	8	1	no	—
675	C₇×D₄	—	8	2	no	—
676	C₇×D₄	—	8	2	no	—
677	C₇×D₄	—	8	1	no	—
678	C₇×D₄	—	8	2	no	—
679	C₇×D₄	—	8	2	no	—
680	C₇×D₄	—	8	2	no	—
681	C₇×D₄	—	8	2	no	—
682	C₇×D₄	—	8	2	no	—
683	C₂×C₄×C₇	—	2	2	no	—
684	C₂×C₄×C₇	—	2	2	no	—
685	C₂×C₄×C₇	—	2	1	no	—
686	C₂×C₄×C₇	—	2	1	no	—
687	C₂×C₄×C₇	—	2	1	no	—
688	C₂×C₄×C₇	—	2	2	no	—
689	C₂×C₄×C₇	—	2	1	no	—
690	C₂×C₄×C₇	—	2	2	no	—
691	C₂×C₄×C₇	—	2	1	no	—
692	C₂×C₄×C₇	—	4	1	no	—
693	C₂×C₄×C₇	—	4	1	no	—
694	C₂×C₄×C₇	—	4	2	no	—
695	C₂×C₄×C₇	—	4	2	no	—
696	C₂×C₄×C₇	—	4	4	no	—
697	C₂×C₄×C₇	—	4	4	no	—
698	C₂×C₄×C₇	—	4	4	no	—
699	C₂×C₄×C₇	—	4	2	no	—
700	C₂×C₄×C₇	—	4	4	no	—
701	C₂×C₄×C₇	—	4	2	no	—
702	C₂×C₄×C₇	—	4	2	no	—
703	C₂×C₄×C₇	—	4	2	no	—
704	C₂×C₄×C₇	—	4	2	no	—
705	C₂×C₄×C₇	—	8	1	no	—
706	C₂×C₄×C₇	—	8	2	no	—
707	C₂×C₄×C₇	—	8	1	no	—
708	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
709	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
710	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
711	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
712	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
713	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
714	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
715	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
716	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
717	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
718	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
719	C₇×C₈	—	2	1	no	—
720	C₇×C₈	—	2	1	no	—
721	C₇×C₈	—	2	1	no	—
722	C₇×C₈	—	2	1	no	—
723	C₇×C₈	—	2	2	no	—
724	C₇×C₈	—	2	2	no	—
725	2₋¹⁺⁴	—	4	2	no	—
726	2₋¹⁺⁴	—	4	2	no	—
727	H(5,𝔽₂)	—	4	2	no	—
728	H(5,𝔽₂)	—	4	2	no	—
729	C₂×#41	—	2	1	no	—
730	C₂×#41	—	2	2	no	—
731	C₂×#41	—	2	1	no	—
732	C₂×#41	—	2	2	no	—
733	C₂×#41	C₂³×C₇	1	1	yes	characteristic
734	C₂×#41	C₂³×C₇	1	1	yes	characteristic
735	C₂×#41	C₂³×C₇	1	1	yes	characteristic
736	C₂×#41	C₂³×C₇	1	2	yes	—
737	C₂×#41	C₂³×C₇	1	2	yes	—
738	C₂×#41	C₂³×C₇	1	1	yes	characteristic
739	C₂²×Q₈	—	2	1	no	—
740	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
741	C₂²×Q₈	C₂³×C₇	1	2	yes	—
742	C₂²×D₄	—	2	2	no	—
743	C₂²×D₄	—	2	1	no	—
744	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
745	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
746	C₂²×D₄	C₂³×C₇	1	2	yes	—
747	C₂³×C₄	—	2	1	no	—
748	#137	—	4	2	no	—
749	AGL(1,ℤ/8)	—	4	2	no	—
750	AGL(1,ℤ/8)	—	4	2	no	—
751	AGL(1,ℤ/8)	—	4	2	no	—
752	#135	—	4	2	no	—
753	#135	—	4	2	no	—
754	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
755	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
756	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
757	C₂×SD₁₆	—	4	2	no	—
758	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
759	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
760	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
761	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
762	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
763	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
764	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
765	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
766	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
767	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
768	C₂×D₈	—	4	2	no	—
769	C₂×D₈	C₂³×C₇	1	2	yes	—
770	C₂×D₈	C₂³×C₇	1	2	yes	—
771	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
772	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
773	C₂×D₈	C₂³×C₇	1	2	yes	—
774	C₂×D₈	C₂³×C₇	1	2	yes	—
775	C₂×D₈	C₂³×C₇	1	2	yes	—
776	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
777	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
778	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
779	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
780	C₄⋊Q₈	—	2	1	no	—
781	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
782	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
783	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
784	#127	—	2	1	no	—
785	#127	C₂³×C₇	1	1	yes	characteristic
786	#127	C₂³×C₇	1	2	yes	—
787	#127	C₂³×C₇	1	2	yes	—
788	#126	—	2	2	no	—
789	#126	—	2	2	no	—
790	#125	—	2	1	no	—
791	#125	C₂³×C₇	1	2	yes	—
792	#124	—	2	1	no	—
793	#124	—	2	2	no	—
794	#124	—	2	1	no	—
795	#124	—	2	1	no	—
796	#124	—	2	2	no	—
797	#124	—	2	2	no	—
798	#124	—	2	2	no	—
799	#124	C₂³×C₇	1	2	yes	—
800	#124	C₂³×C₇	1	2	yes	—
801	#124	C₂³×C₇	1	1	yes	characteristic
802	#124	C₂³×C₇	1	2	yes	—
803	#124	C₂³×C₇	1	2	yes	—
804	#124	C₂³×C₇	1	2	yes	—
805	#124	C₂³×C₇	1	1	yes	characteristic
806	#123	—	2	2	no	—
807	#123	—	2	2	no	—
808	#123	—	2	2	no	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	C₂²⋊Q₈	—	2	1	no	—
814	C₂²⋊Q₈	—	2	2	no	—
815	C₂²⋊Q₈	—	2	1	no	—
816	C₂²⋊Q₈	—	2	1	no	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	—	2	2	no	—
819	C₂²⋊Q₈	—	2	2	no	—
820	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
821	#121	—	2	2	no	—
822	#121	—	2	1	no	—
823	#121	—	2	1	no	—
824	#121	—	2	1	no	—
825	#121	—	2	2	no	—
826	#121	—	2	2	no	—
827	#121	—	2	2	no	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	C₂³×C₇	1	2	yes	—
837	#121	C₂³×C₇	1	2	yes	—
838	#121	C₂³×C₇	1	2	yes	—
839	#120	—	2	2	no	—
840	#120	—	2	2	no	—
841	#120	—	2	2	no	—
842	#120	—	2	2	no	—
843	#120	—	2	2	no	—
844	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
845	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
846	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
847	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	2	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	2	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	—	2	2	no	—
857	C₄×D₄	—	2	2	no	—
858	C₄×D₄	C₇×D₄	1	2	yes	—
859	C₄×D₄	C₇×D₄	1	1	yes	characteristic
860	C₄×D₄	C₇×D₄	1	2	yes	—
861	C₄×D₄	C₇×D₄	1	1	yes	characteristic
862	C₄×D₄	C₂³×C₇	1	2	yes	—
863	C₄×D₄	C₂³×C₇	1	2	yes	—
864	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
865	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
866	#117	—	2	1	no	—
867	#117	—	2	2	no	—
868	#117	C₂³×C₇	1	1	yes	characteristic
869	#117	C₂³×C₇	1	1	yes	characteristic
870	#117	C₂³×C₇	1	2	yes	—
871	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
872	C₂×C₂²⋊C₄	—	2	1	no	—
873	C₂×C₂²⋊C₄	—	2	1	no	—
874	C₂×C₂²⋊C₄	—	2	1	no	—
875	C₂×C₂²⋊C₄	—	2	2	no	—
876	C₂×C₂²⋊C₄	—	2	2	no	—
877	C₂×C₄²	—	2	1	no	—
878	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
879	C₂×C₄²	C₂³×C₇	1	2	yes	—
880	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
881	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
882	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
883	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₇	1	2	yes	—
885	C₄⋊C₈	C₂³×C₇	1	2	yes	—
886	#103	C₂³×C₇	1	2	yes	—
887	#103	C₂³×C₇	1	2	yes	—
888	#103	C₂³×C₇	1	1	yes	characteristic
889	#103	C₂³×C₇	1	1	yes	characteristic
890	#103	C₂³×C₇	1	1	yes	characteristic
891	#103	C₂³×C₇	1	1	yes	characteristic
892	#103	C₂³×C₇	1	2	yes	—
893	#103	C₂³×C₇	1	2	yes	—
894	#103	C₂³×C₇	1	2	yes	—
895	#103	C₂³×C₇	1	2	yes	—
896	#102	C₂³×C₇	1	2	yes	—
897	#102	C₂³×C₇	1	2	yes	—
898	#102	C₂³×C₇	1	1	yes	characteristic
899	#102	C₂³×C₇	1	1	yes	characteristic
900	#102	C₂³×C₇	1	1	yes	characteristic
901	#102	C₂³×C₇	1	1	yes	characteristic
902	#102	C₂³×C₇	1	2	yes	—
903	#102	C₂³×C₇	1	2	yes	—
904	#102	C₂³×C₇	1	2	yes	—
905	#102	C₂³×C₇	1	2	yes	—
906	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
907	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
908	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
909	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
910	#97	C₂³×C₇	1	2	yes	—
911	#97	C₂³×C₇	1	2	yes	—
912	C₄×C₈	C₂³×C₇	1	2	yes	—
913	C₄×C₈	C₂³×C₇	1	2	yes	—
914	C₂²×C₇	—	2	1	no	—
915	C₂²×C₇	—	2	1	no	—
916	C₂²×C₇	—	2	2	no	—
917	C₂²×C₇	—	2	2	no	—
918	C₂²×C₇	—	2	2	no	—
919	C₂²×C₇	—	4	1	no	—
920	C₂²×C₇	—	4	1	no	—
921	C₂²×C₇	—	4	2	no	—
922	C₂²×C₇	—	4	2	no	—
923	C₂²×C₇	—	4	1	no	—
924	C₂²×C₇	—	4	2	no	—
925	C₂²×C₇	—	4	1	no	—
926	C₂²×C₇	—	4	1	no	—
927	C₂²×C₇	—	4	2	no	—
928	C₂²×C₇	—	4	1	no	—
929	C₂²×C₇	—	4	1	no	—
930	C₂²×C₇	—	4	2	no	—
931	C₂²×C₇	—	4	1	no	—
932	C₂²×C₇	—	4	1	no	—
933	C₂²×C₇	—	4	2	no	—
934	C₂²×C₇	—	8	4	no	—
935	C₂²×C₇	—	16	2	no	—
936	C₂²×C₇	—	16	4	no	—
937	C₂²×C₇	#535	1	2	yes	—
938	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
939	C₄×C₇	—	2	1	no	—
940	C₄×C₇	—	2	1	no	—
941	C₄×C₇	—	2	2	no	—
942	C₄×C₇	—	2	1	no	—
943	C₄×C₇	—	2	1	no	—
944	C₄×C₇	—	2	2	no	—
945	C₄×C₇	—	2	2	no	—
946	C₄×C₇	—	4	1	no	—
947	C₄×C₇	—	4	2	no	—
948	C₄×C₇	—	4	1	no	—
949	C₄×C₇	—	4	1	no	—
950	C₄×C₇	—	4	2	no	—
951	C₄×C₇	—	4	1	no	—
952	C₄×C₇	—	4	1	no	—
953	C₄×C₇	#535	1	2	yes	—
954	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
955	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
956	C₂⁴	—	2	2	no	—
957	C₂⁴	—	2	1	no	—
958	C₂⁴	—	2	1	no	—
959	#41	—	2	2	no	—
960	#41	—	2	2	no	—
961	#41	—	2	2	no	—
962	#41	—	2	2	no	—
963	#41	—	2	2	no	—
964	#41	—	2	2	no	—
965	#41	—	2	2	no	—
966	#41	—	2	2	no	—
967	#41	—	4	2	no	—
968	#41	—	4	2	no	—
969	#41	—	4	2	no	—
970	#41	—	4	2	no	—
971	#41	—	4	8	no	—
972	#41	—	4	4	no	—
973	#41	—	4	4	no	—
974	#41	—	8	4	no	—
975	C₂×Q₈	—	2	2	no	—
976	C₂×Q₈	—	2	1	no	—
977	C₂×Q₈	—	2	2	no	—
978	C₂×Q₈	—	2	2	no	—
979	C₂×Q₈	—	2	2	no	—
980	C₂×Q₈	—	4	2	no	—
981	C₂×Q₈	—	4	2	no	—
982	C₂×Q₈	—	4	4	no	—
983	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
984	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
985	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
986	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
987	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	2	1	no	—
991	C₂×D₄	—	2	2	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	2	no	—
994	C₂×D₄	—	2	2	no	—
995	C₂×D₄	—	2	2	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	1	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	2	2	no	—
1004	C₂×D₄	—	2	2	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	2	no	—
1007	C₂×D₄	—	2	2	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	4	2	no	—
1010	C₂×D₄	—	4	2	no	—
1011	C₂×D₄	—	4	8	no	—
1012	C₂×D₄	—	4	4	no	—
1013	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
1014	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
1015	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1016	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1017	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1018	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1019	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1020	C₂²×C₄	—	2	2	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	1	no	—
1023	C₂²×C₄	—	2	1	no	—
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	2	no	—
1026	C₂²×C₄	—	2	2	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	2	no	—
1029	C₂²×C₄	—	2	1	no	—
1030	C₂²×C₄	—	2	1	no	—
1031	C₂²×C₄	—	2	2	no	—
1032	C₂²×C₄	—	8	2	no	—
1033	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1034	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1035	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
1036	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
1037	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
1038	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1039	Q₁₆	—	4	1	no	—
1040	Q₁₆	—	4	1	no	—
1041	Q₁₆	—	4	2	no	—
1042	SD₁₆	—	4	2	no	—
1043	SD₁₆	—	4	2	no	—
1044	SD₁₆	—	4	1	no	—
1045	SD₁₆	—	4	1	no	—
1046	SD₁₆	—	4	1	no	—
1047	SD₁₆	—	4	1	no	—
1048	SD₁₆	—	4	2	no	—
1049	SD₁₆	—	4	2	no	—
1050	SD₁₆	—	4	2	no	—
1051	SD₁₆	—	4	2	no	—
1052	D₈	—	4	2	no	—
1053	D₈	—	4	2	no	—
1054	D₈	—	4	1	no	—
1055	D₈	—	4	1	no	—
1056	D₈	—	4	2	no	—
1057	D₈	—	4	2	no	—
1058	D₈	—	4	2	no	—
1059	M₁₆	—	2	2	no	—
1060	M₁₆	—	2	2	no	—
1061	C₂×C₈	—	2	2	no	—
1062	C₂×C₈	—	2	2	no	—
1063	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1064	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1065	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1066	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1067	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1068	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	2	no	—
1073	C₄⋊C₄	—	2	2	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	2	no	—
1079	C₄⋊C₄	—	2	2	no	—
1080	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1081	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1082	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1083	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1084	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1085	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1086	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	—	2	2	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1111	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1112	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1113	C₄²	—	2	1	no	—
1114	C₄²	—	2	1	no	—
1115	C₄²	—	2	1	no	—
1116	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1117	C₄²	C₂×C₇×D₄	1	2	yes	—
1118	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1119	C₄²	C₂×C₇×D₄	1	2	yes	—
1120	C₄²	C₂⁴×C₇	1	2	yes	—
1121	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1122	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1123	C₂×C₇	—	2	2	no	—
1124	C₂×C₇	—	4	2	no	—
1125	C₂×C₇	—	8	1	no	—
1126	C₂×C₇	—	8	1	no	—
1127	C₂×C₇	—	8	2	no	—
1128	C₂×C₇	—	8	2	no	—
1129	C₂×C₇	—	8	1	no	—
1130	C₂×C₇	C₂×#535	1	1	yes	characteristic
1131	C₂×C₇	#3584	1	1	yes	characteristic
1132	C₂×C₇	#3585	1	1	yes	characteristic
1133	C₂³	—	2	2	no	—
1134	C₂³	—	2	2	no	—
1135	C₂³	—	2	1	no	—
1136	C₂³	—	2	1	no	—
1137	C₂³	—	2	1	no	—
1138	C₂³	—	4	4	no	—
1139	C₂³	—	4	2	no	—
1140	C₂³	—	4	2	no	—
1141	C₂³	—	8	1	no	—
1142	C₂³	—	8	1	no	—
1143	C₂³	—	8	1	no	—
1144	C₂³	—	8	1	no	—
1145	C₂³	—	8	2	no	—
1146	C₂³	—	8	2	no	—
1147	C₂³	C₂²×C₇×D₄	1	2	yes	—
1148	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1149	Q₈	—	2	2	no	—
1150	Q₈	—	2	1	no	—
1151	Q₈	—	2	1	no	—
1152	Q₈	—	2	2	no	—
1153	Q₈	—	2	1	no	—
1154	Q₈	—	2	1	no	—
1155	Q₈	—	2	2	no	—
1156	Q₈	—	2	1	no	—
1157	Q₈	—	2	1	no	—
1158	Q₈	—	4	4	no	—
1159	Q₈	—	4	2	no	—
1160	Q₈	—	8	2	no	—
1161	D₄	—	2	4	no	—
1162	D₄	—	2	2	no	—
1163	D₄	—	2	2	no	—
1164	D₄	—	2	1	no	—
1165	D₄	—	2	1	no	—
1166	D₄	—	2	2	no	—
1167	D₄	—	2	1	no	—
1168	D₄	—	2	1	no	—
1169	D₄	—	2	2	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	2	1	no	—
1172	D₄	—	2	2	no	—
1173	D₄	—	4	4	no	—
1174	D₄	—	4	4	no	—
1175	D₄	—	4	4	no	—
1176	D₄	—	4	2	no	—
1177	D₄	—	4	2	no	—
1178	D₄	—	4	2	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	8	1	no	—
1182	D₄	—	8	2	no	—
1183	D₄	—	8	2	no	—
1184	D₄	—	8	1	no	—
1185	D₄	—	8	2	no	—
1186	D₄	—	8	2	no	—
1187	D₄	—	8	2	no	—
1188	D₄	—	8	2	no	—
1189	D₄	—	8	2	no	—
1190	C₂×C₄	—	2	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	1	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	4	1	no	—
1200	C₂×C₄	—	4	1	no	—
1201	C₂×C₄	—	4	2	no	—
1202	C₂×C₄	—	4	2	no	—
1203	C₂×C₄	—	4	4	no	—
1204	C₂×C₄	—	4	4	no	—
1205	C₂×C₄	—	4	4	no	—
1206	C₂×C₄	—	4	2	no	—
1207	C₂×C₄	—	4	4	no	—
1208	C₂×C₄	—	4	2	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	2	no	—
1212	C₂×C₄	—	8	1	no	—
1213	C₂×C₄	—	8	2	no	—
1214	C₂×C₄	—	8	1	no	—
1215	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1216	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1217	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1218	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1219	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1220	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1221	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1222	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1223	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1224	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1225	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1226	C₈	—	2	1	no	—
1227	C₈	—	2	1	no	—
1228	C₈	—	2	1	no	—
1229	C₈	—	2	1	no	—
1230	C₈	—	2	2	no	—
1231	C₈	—	2	2	no	—
1232	C₇	#60834	1	1	yes	characteristic, direct product factor, Sylow
1233	C₂²	—	2	1	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	2	2	no	—
1236	C₂²	—	2	2	no	—
1237	C₂²	—	2	2	no	—
1238	C₂²	—	4	1	no	—
1239	C₂²	—	4	1	no	—
1240	C₂²	—	4	2	no	—
1241	C₂²	—	4	2	no	—
1242	C₂²	—	4	1	no	—
1243	C₂²	—	4	2	no	—
1244	C₂²	—	4	1	no	—
1245	C₂²	—	4	1	no	—
1246	C₂²	—	4	2	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	1	no	—
1249	C₂²	—	4	2	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	8	4	no	—
1254	C₂²	—	16	2	no	—
1255	C₂²	—	16	4	no	—
1256	C₂²	C₇×#535	1	2	yes	—
1257	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1258	C₄	—	2	1	no	—
1259	C₄	—	2	1	no	—
1260	C₄	—	2	2	no	—
1261	C₄	—	2	1	no	—
1262	C₄	—	2	1	no	—
1263	C₄	—	2	2	no	—
1264	C₄	—	2	2	no	—
1265	C₄	—	4	1	no	—
1266	C₄	—	4	2	no	—
1267	C₄	—	4	1	no	—
1268	C₄	—	4	1	no	—
1269	C₄	—	4	2	no	—
1270	C₄	—	4	1	no	—
1271	C₄	—	4	1	no	—
1272	C₄	C₇×#535	1	2	yes	—
1273	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1274	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1275	C₂	—	2	2	no	—
1276	C₂	—	4	2	no	—
1277	C₂	—	8	2	no	—
1278	C₂	—	8	2	no	—
1279	C₂	—	8	1	no	—
1280	C₂	—	8	1	no	—
1281	C₂	—	8	1	no	—
1282	C₂	C₂×C₇×#535	1	1	yes	characteristic
1283	C₂	C₇×#3584	1	1	yes	characteristic
1284	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 ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3500	C₂	semidirect
2. C₇×#3460	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×#3213	C₂	semidirect
9. C₇×#3211	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×#3040	C₂	semidirect
16. C₇×#3036	C₂	semidirect
17. C₇×#3035	C₂	semidirect
18. C₂×C₇×#463	C₂	semidirect
19. C₇×#3013	C₂	semidirect
20. C₇×#3012	C₂	semidirect
21. C₇×#3010	C₂	semidirect
22. C₇×#3008	C₂	semidirect
23. C₇×#2925	C₂	semidirect
26. C₂×C₇×#137	C₂²	semidirect
29. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
31. C₂×C₇×#135	C₂²	semidirect
32. C₂²×C₇×SD₁₆	C₂²	semidirect
40. C₇×#544	C₂²	semidirect
42. C₇×#542	C₂²	semidirect
44. C₇×#540	C₂²	semidirect
48. C₇×#536	C₂²	semidirect
51. C₇×#535	C₂²	semidirect
52. C₇×#535	C₂²	semidirect
55. C₇×#532	C₂²	semidirect
56. C₇×#532	C₂²	semidirect
58. C₇×#529	C₂²	semidirect
60. C₂×C₇×#124	C₂²	semidirect
63. C₄×C₇×#41	C₂²	semidirect
64. C₂×C₄×C₇×D₄	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×#464	C₂²	semidirect
84. C₇×#464	C₂²	semidirect
85. C₇×#463	C₂²	semidirect
86. C₇×#463	C₂²	semidirect
87. C₇×#463	C₂²	semidirect
88. C₇×#463	C₂²	semidirect
89. C₇×#463	C₂²	semidirect
90. C₇×#463	C₂²	semidirect
91. C₇×#463	C₂²	semidirect
92. C₇×#463	C₂²	semidirect
93. C₇×#463	C₂²	semidirect
94. C₇×#463	C₂²	semidirect
95. C₇×#462	C₂²	semidirect
96. C₇×#461	C₂²	semidirect
97. C₇×#461	C₂²	semidirect
98. C₇×#460	C₂²	semidirect
99. C₇×#459	C₂²	semidirect
100. C₇×#459	C₂²	semidirect
101. C₇×#452	C₂²	semidirect
102. C₇×#452	C₂²	semidirect
103. C₇×#451	C₂²	semidirect
104. C₇×#450	C₂²	semidirect
107. C₇×#449	C₂²	semidirect
108. C₇×#449	C₂²	semidirect
109. C₇×#449	C₂²	semidirect
110. C₇×#449	C₂²	semidirect
111. C₇×#448	C₂²	semidirect
112. C₇×#448	C₂²	semidirect
113. C₇×#448	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×#423	C₂²	semidirect
122. C₂×C₇×C₄⋊C₈	C₂²	semidirect
123. C₇×#419	C₂²	semidirect
126. C₇×#417	C₂²	semidirect
128. C₇×#416	C₂²	semidirect
129. C₂×C₇×#103	C₂²	semidirect
133. C₇×#405	C₂²	semidirect
134. C₇×#405	C₂²	semidirect
135. #60834	C₇	direct (N × H)
325. #3500	C₂×C₇	semidirect
326. #3460	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. #3213	C₂×C₇	semidirect
333. #3211	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. #3040	C₂×C₇	semidirect
340. #3036	C₂×C₇	semidirect
341. #3035	C₂×C₇	semidirect
342. C₂×#463	C₂×C₇	semidirect
343. #3013	C₂×C₇	semidirect
344. #3012	C₂×C₇	semidirect
345. #3010	C₂×C₇	semidirect
346. #3008	C₂×C₇	semidirect
347. #2925	C₂×C₇	semidirect
517. C₂×#137	C₂²×C₇	semidirect
520. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
522. C₂×#135	C₂²×C₇	semidirect
523. C₂²×SD₁₆	C₂²×C₇	semidirect
531. #544	C₂²×C₇	semidirect
533. #542	C₂²×C₇	semidirect
535. #540	C₂²×C₇	semidirect
539. #536	C₂²×C₇	semidirect
542. #535	C₂²×C₇	semidirect
543. #535	C₂²×C₇	semidirect
546. #532	C₂²×C₇	semidirect
547. #532	C₂²×C₇	semidirect
549. #529	C₂²×C₇	semidirect
551. C₂×#124	C₂²×C₇	semidirect
554. C₄×#41	C₂²×C₇	semidirect
555. C₂×C₄×D₄	C₂²×C₇	semidirect
556. #497	C₂²×C₇	semidirect
557. #496	C₂²×C₇	semidirect
558. #496	C₂²×C₇	semidirect
559. #496	C₂²×C₇	semidirect
560. #495	C₂²×C₇	semidirect
561. #495	C₂²×C₇	semidirect
562. #493	C₂²×C₇	semidirect
563. #492	C₂²×C₇	semidirect
564. #491	C₂²×C₇	semidirect
565. #490	C₂²×C₇	semidirect
566. #489	C₂²×C₇	semidirect
567. #489	C₂²×C₇	semidirect
568. #488	C₂²×C₇	semidirect
569. #488	C₂²×C₇	semidirect
570. #487	C₂²×C₇	semidirect
571. #486	C₂²×C₇	semidirect
572. #464	C₂²×C₇	semidirect
573. #464	C₂²×C₇	semidirect
574. #464	C₂²×C₇	semidirect
575. #464	C₂²×C₇	semidirect
576. #463	C₂²×C₇	semidirect
577. #463	C₂²×C₇	semidirect
578. #463	C₂²×C₇	semidirect
579. #463	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. #460	C₂²×C₇	semidirect
590. #459	C₂²×C₇	semidirect
591. #459	C₂²×C₇	semidirect
592. #452	C₂²×C₇	semidirect
593. #452	C₂²×C₇	semidirect
594. #451	C₂²×C₇	semidirect
595. #450	C₂²×C₇	semidirect
598. #449	C₂²×C₇	semidirect
599. #449	C₂²×C₇	semidirect
600. #449	C₂²×C₇	semidirect
601. #449	C₂²×C₇	semidirect
602. #448	C₂²×C₇	semidirect
603. #448	C₂²×C₇	semidirect
604. #448	C₂²×C₇	semidirect
607. #447	C₂²×C₇	semidirect
608. #433	C₂²×C₇	semidirect
609. #433	C₂²×C₇	semidirect
610. #432	C₂²×C₇	semidirect
611. #431	C₂²×C₇	semidirect
612. #423	C₂²×C₇	semidirect
613. C₂×C₄⋊C₈	C₂²×C₇	semidirect
614. #419	C₂²×C₇	semidirect
617. #417	C₂²×C₇	semidirect
619. #416	C₂²×C₇	semidirect
620. C₂×#103	C₂²×C₇	semidirect
624. #405	C₂²×C₇	semidirect
625. #405	C₂²×C₇	semidirect
1232. C₇	#60834	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×#3500	2
C₇×#3460	2
C₇×#3225	2
C₇×#3224	2
C₇×#3221	2
C₇×#3220	2
C₇×#3219	2
C₇×#3213	2
C₇×#3211	2
C₇×#3207	2
C₇×#3155	2
C₇×#3154	2
C₇×#3137	2
C₇×#3136	2
C₇×#3040	2
C₇×#3036	2
C₇×#3035	2
C₂×C₇×#463	2
C₇×#3013	2
C₇×#3012	2
C₇×#3010	2
C₇×#3008	2
C₇×#2925	2
#60834	7

Subgroups — C7×#60834 #13238050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60834 #13238050