Subgroups — C₇×#60835 #13238051

Order 1792.

2040 conjugacy classes of subgroups.

The subgroup lattice has 1258 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×#3461	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×#3223	C₂	1	2	yes	maximal, complemented
6	C₇×#3222	C₂	1	2	yes	maximal, complemented
7	C₇×#3219	C₂	1	2	yes	maximal, complemented
8	C₇×#3215	C₂	1	2	yes	maximal, complemented
9	C₇×#3211	C₂	1	2	yes	maximal, complemented
10	C₇×#3210	C₂	1	2	yes	maximal, complemented
11	C₇×#3156	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×#3037	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#464	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×#3011	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#3009	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
27	C₂×C₇×#137	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₇×#137	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
30	C₂×C₇×#135	C₂²	1	1	yes	characteristic
31	C₂×C₇×#135	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₇×SD₁₆	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	1	no	—
38	C₇×#546	—	2	2	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×#541	—	2	1	no	—
44	C₇×#541	C₂²	1	2	yes	complemented
45	C₇×#539	—	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	—
49	C₇×#536	C₂²	1	1	yes	characteristic
50	C₇×#536	C₂²	1	1	yes	characteristic, complemented
51	C₇×#535	C₂²	1	2	yes	—
52	C₇×#535	C₂²	1	1	yes	characteristic
53	C₇×#533	—	2	1	no	—
54	C₇×#533	C₂²	1	2	yes	complemented
55	C₇×#532	C₂²	1	2	yes	—
56	C₇×#532	C₂²	1	1	yes	characteristic
57	C₇×#529	—	2	2	no	—
58	C₇×#529	—	2	1	no	—
59	C₇×#529	C₂²	1	2	yes	complemented
60	C₂×C₇×#124	C₂²	1	2	yes	—
61	C₂×C₇×#124	C₂²	1	1	yes	characteristic
62	C₄×C₇×#41	C₂²	1	1	yes	characteristic
63	C₄×C₇×#41	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
65	C₇×#497	C₂²	1	2	yes	complemented
66	C₇×#497	C₂²	1	2	yes	complemented
67	C₇×#497	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×#494	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	2	yes	complemented
84	C₇×#464	C₂²	1	2	yes	complemented
85	C₇×#464	C₂²	1	2	yes	complemented
86	C₇×#464	C₂²	1	1	yes	characteristic, complemented
87	C₇×#464	C₂²	1	2	yes	complemented
88	C₇×#464	C₂²	1	2	yes	complemented
89	C₇×#464	C₂²	1	2	yes	complemented
90	C₇×#464	C₂²	1	2	yes	complemented
91	C₇×#463	C₂²	1	1	yes	characteristic, complemented
92	C₇×#463	C₂²	1	2	yes	complemented
93	C₇×#463	C₂²	1	1	yes	characteristic, complemented
94	C₇×#463	C₂²	1	2	yes	complemented
95	C₇×#462	C₂²	1	1	yes	characteristic, complemented
96	C₇×#462	C₂²	1	2	yes	complemented
97	C₇×#461	C₂²	1	1	yes	characteristic, complemented
98	C₇×#460	C₂²	1	1	yes	characteristic, complemented
99	C₇×#460	C₂²	1	2	yes	complemented
100	C₇×#459	C₂²	1	1	yes	characteristic, complemented
101	C₇×#452	C₂²	1	2	yes	—
102	C₇×#452	C₂²	1	2	yes	—
103	C₇×#452	C₂²	1	2	yes	—
104	C₇×#452	C₂²	1	2	yes	complemented
105	C₇×#452	C₂²	1	2	yes	complemented
106	C₇×#452	C₂²	1	2	yes	complemented
107	C₇×#451	C₂²	1	2	yes	complemented
108	C₇×#451	C₂²	1	2	yes	complemented
109	C₇×#451	C₂²	1	2	yes	complemented
110	C₇×#450	C₂²	1	2	yes	—
111	C₇×#450	C₂²	1	2	yes	—
112	C₇×#450	C₂²	1	2	yes	—
113	C₇×#449	C₂²	1	2	yes	—
114	C₇×#449	C₂²	1	2	yes	complemented
115	C₇×#448	C₂²	1	2	yes	complemented
116	C₇×#447	C₂²	1	2	yes	—
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	#60835	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	C₂³	1	1	yes	characteristic
144	C₂×C₇×#41	C₂³	1	1	yes	characteristic
145	C₂×C₇×#41	C₂³	1	1	yes	characteristic
146	C₂×C₇×#41	C₂³	1	2	yes	—
147	C₂×C₇×#41	C₂³	1	2	yes	—
148	C₂×C₇×#41	C₂³	1	1	yes	characteristic
149	C₂²×C₇×Q₈	—	2	1	no	—
150	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
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	2	yes	—
157	C₇×#137	—	4	2	no	—
158	C₇×#137	—	4	2	no	—
159	C₇×#137	—	4	2	no	—
160	C₇×AGL(1,ℤ/8)	—	4	2	no	—
161	C₇×#135	—	4	2	no	—
162	C₇×#135	—	4	2	no	—
163	C₂×C₇×Q₁₆	—	4	2	no	—
164	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
166	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
167	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
168	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
169	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
170	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
171	C₂×C₇×SD₁₆	—	4	2	no	—
172	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
173	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
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	2	yes	—
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×D₈	C₂³	1	1	yes	characteristic
183	C₂×C₇×D₈	C₂³	1	2	yes	—
184	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
185	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
186	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
187	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
188	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
189	C₇×C₄⋊Q₈	—	2	1	no	—
190	C₇×C₄⋊Q₈	—	2	1	no	—
191	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
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	C₂³	1	2	yes	—
196	C₇×#127	C₂³	1	1	yes	characteristic
197	C₇×#126	—	2	2	no	—
198	C₇×#126	—	2	2	no	—
199	C₇×#126	—	2	2	no	—
200	C₇×#126	—	2	2	no	—
201	C₇×#125	—	2	2	no	—
202	C₇×#125	—	2	1	no	—
203	C₇×#125	—	2	2	no	—
204	C₇×#125	—	2	2	no	—
205	C₇×#125	C₂³	1	2	yes	—
206	C₇×#124	—	2	1	no	—
207	C₇×#124	—	2	2	no	—
208	C₇×#124	—	2	1	no	—
209	C₇×#124	—	2	2	no	—
210	C₇×#124	—	2	1	no	—
211	C₇×#124	—	2	2	no	—
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	2	yes	—
217	C₇×#124	C₂³	1	2	yes	—
218	C₇×#124	C₂³	1	1	yes	characteristic
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×#123	—	2	2	no	—
225	C₇×#123	—	2	2	no	—
226	C₇×C₂²⋊Q₈	—	2	1	no	—
227	C₇×C₂²⋊Q₈	—	2	2	no	—
228	C₇×C₂²⋊Q₈	—	2	1	no	—
229	C₇×C₂²⋊Q₈	—	2	1	no	—
230	C₇×C₂²⋊Q₈	—	2	2	no	—
231	C₇×C₂²⋊Q₈	—	2	1	no	—
232	C₇×C₂²⋊Q₈	—	2	2	no	—
233	C₇×C₂²⋊Q₈	—	2	1	no	—
234	C₇×C₂²⋊Q₈	—	2	2	no	—
235	C₇×C₂²⋊Q₈	—	2	2	no	—
236	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
237	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
238	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
239	C₇×#121	—	2	2	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	1	no	—
247	C₇×#121	—	2	1	no	—
248	C₇×#121	—	2	2	no	—
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	C₄×C₇×Q₈	—	2	1	no	—
254	C₄×C₇×Q₈	—	2	1	no	—
255	C₄×C₇×Q₈	—	2	2	no	—
256	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
257	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
258	C₄×C₇×Q₈	C₂³	1	2	yes	—
259	C₄×C₇×Q₈	C₂³	1	2	yes	—
260	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
261	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
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	2	no	—
267	C₄×C₇×D₄	—	2	1	no	—
268	C₄×C₇×D₄	—	2	2	no	—
269	C₄×C₇×D₄	D₄	1	1	yes	characteristic
270	C₄×C₇×D₄	D₄	1	2	yes	—
271	C₄×C₇×D₄	D₄	1	2	yes	—
272	C₄×C₇×D₄	D₄	1	1	yes	characteristic
273	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
274	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
275	C₇×#117	—	2	2	no	—
276	C₇×#117	—	2	1	no	—
277	C₇×#117	—	2	2	no	—
278	C₇×#117	C₂³	1	1	yes	characteristic
279	C₇×#117	C₂³	1	1	yes	characteristic
280	C₇×#117	C₂³	1	2	yes	—
281	C₂×C₇×C₄⋊C₄	—	2	1	no	—
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	2	no	—
286	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₄²×C₇	—	2	1	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	#3461	C₂×C₇	1	1	yes	characteristic, complemented
327	#3225	C₂×C₇	1	2	yes	complemented
328	#3224	C₂×C₇	1	2	yes	complemented
329	#3223	C₂×C₇	1	2	yes	complemented
330	#3222	C₂×C₇	1	2	yes	complemented
331	#3219	C₂×C₇	1	2	yes	complemented
332	#3215	C₂×C₇	1	2	yes	complemented
333	#3211	C₂×C₇	1	2	yes	complemented
334	#3210	C₂×C₇	1	2	yes	complemented
335	#3156	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	#3037	C₂×C₇	1	1	yes	characteristic, complemented
341	#3035	C₂×C₇	1	1	yes	characteristic, complemented
342	C₂×#464	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	#3011	C₂×C₇	1	1	yes	characteristic, complemented
346	#3009	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	C₇×#41	—	2	2	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	—	4	2	no	—
359	C₇×#41	—	4	2	no	—
360	C₇×#41	—	4	2	no	—
361	C₇×#41	—	4	2	no	—
362	C₇×#41	—	4	8	no	—
363	C₇×#41	—	4	4	no	—
364	C₇×#41	—	4	4	no	—
365	C₂×C₇×Q₈	—	2	1	no	—
366	C₂×C₇×Q₈	—	2	2	no	—
367	C₂×C₇×Q₈	—	2	1	no	—
368	C₂×C₇×Q₈	—	2	2	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	—	2	2	no	—
373	C₂×C₇×Q₈	—	4	2	no	—
374	C₂×C₇×Q₈	—	4	2	no	—
375	C₂×C₇×Q₈	—	4	4	no	—
376	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
377	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
378	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
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	1	no	—
385	C₂×C₇×D₄	—	2	2	no	—
386	C₂×C₇×D₄	—	2	1	no	—
387	C₂×C₇×D₄	—	2	2	no	—
388	C₂×C₇×D₄	—	2	2	no	—
389	C₂×C₇×D₄	—	2	1	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	2	no	—
394	C₂×C₇×D₄	—	2	2	no	—
395	C₂×C₇×D₄	—	2	2	no	—
396	C₂×C₇×D₄	—	4	2	no	—
397	C₂×C₇×D₄	—	4	2	no	—
398	C₂×C₇×D₄	—	4	8	no	—
399	C₂×C₇×D₄	—	4	4	no	—
400	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
401	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
402	C₂×C₇×D₄	C₂⁴	1	2	yes	—
403	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
404	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
405	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₇	—	2	1	no	—
407	C₂²×C₄×C₇	—	2	2	no	—
408	C₂²×C₄×C₇	—	2	1	no	—
409	C₂²×C₄×C₇	—	2	1	no	—
410	C₂²×C₄×C₇	—	2	1	no	—
411	C₂²×C₄×C₇	—	2	1	no	—
412	C₂²×C₄×C₇	—	2	2	no	—
413	C₂²×C₄×C₇	—	2	1	no	—
414	C₂²×C₄×C₇	—	2	2	no	—
415	C₂²×C₄×C₇	—	2	1	no	—
416	C₂²×C₄×C₇	—	2	1	no	—
417	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
418	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
419	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
420	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
421	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
422	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
423	C₇×Q₁₆	—	4	2	no	—
424	C₇×Q₁₆	—	4	2	no	—
425	C₇×Q₁₆	—	4	1	no	—
426	C₇×Q₁₆	—	4	1	no	—
427	C₇×Q₁₆	—	4	2	no	—
428	C₇×Q₁₆	—	4	2	no	—
429	C₇×Q₁₆	—	4	2	no	—
430	C₇×SD₁₆	—	4	2	no	—
431	C₇×SD₁₆	—	4	2	no	—
432	C₇×SD₁₆	—	4	1	no	—
433	C₇×SD₁₆	—	4	1	no	—
434	C₇×SD₁₆	—	4	1	no	—
435	C₇×SD₁₆	—	4	1	no	—
436	C₇×SD₁₆	—	4	2	no	—
437	C₇×SD₁₆	—	4	2	no	—
438	C₇×SD₁₆	—	4	2	no	—
439	C₇×SD₁₆	—	4	2	no	—
440	C₇×D₈	—	4	1	no	—
441	C₇×D₈	—	4	1	no	—
442	C₇×D₈	—	4	2	no	—
443	C₇×M₁₆	—	2	2	no	—
444	C₇×M₁₆	—	2	2	no	—
445	C₂×C₇×C₈	—	2	2	no	—
446	C₂×C₇×C₈	—	2	2	no	—
447	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
448	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
449	C₂×C₇×C₈	C₂⁴	1	2	yes	—
450	C₂×C₇×C₈	C₂⁴	1	2	yes	—
451	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
452	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
453	C₇×C₄⋊C₄	—	2	2	no	—
454	C₇×C₄⋊C₄	—	2	2	no	—
455	C₇×C₄⋊C₄	—	2	1	no	—
456	C₇×C₄⋊C₄	—	2	1	no	—
457	C₇×C₄⋊C₄	—	2	1	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	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	2	no	—
467	C₇×C₄⋊C₄	—	2	2	no	—
468	C₇×C₄⋊C₄	—	2	2	no	—
469	C₇×C₄⋊C₄	—	2	2	no	—
470	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
471	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
472	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
473	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
474	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
475	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
476	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
477	C₇×C₂²⋊C₄	—	2	2	no	—
478	C₇×C₂²⋊C₄	—	2	2	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	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	1	no	—
492	C₇×C₂²⋊C₄	—	2	1	no	—
493	C₇×C₂²⋊C₄	—	2	2	no	—
494	C₇×C₂²⋊C₄	—	2	2	no	—
495	C₇×C₂²⋊C₄	—	2	1	no	—
496	C₇×C₂²⋊C₄	—	2	1	no	—
497	C₇×C₂²⋊C₄	—	2	2	no	—
498	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
499	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
500	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
501	C₄²×C₇	—	2	2	no	—
502	C₄²×C₇	—	2	1	no	—
503	C₄²×C₇	—	2	1	no	—
504	C₄²×C₇	—	2	1	no	—
505	C₄²×C₇	—	2	2	no	—
506	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
507	C₄²×C₇	C₂×D₄	1	2	yes	—
508	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
509	C₄²×C₇	C₂×D₄	1	2	yes	—
510	C₄²×C₇	C₂⁴	1	2	yes	—
511	C₄²×C₇	C₂⁴	1	1	yes	characteristic
512	C₄²×C₇	C₂⁴	1	1	yes	characteristic
513	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
514	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
515	C₂×#137	C₂²×C₇	1	1	yes	characteristic
516	C₂×#137	C₂²×C₇	1	1	yes	characteristic, complemented
517	C₂×#137	C₂²×C₇	1	1	yes	characteristic, complemented
518	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
519	C₂×#135	C₂²×C₇	1	1	yes	characteristic
520	C₂×#135	C₂²×C₇	1	1	yes	characteristic, complemented
521	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
522	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
523	#548	—	2	1	no	—
524	#548	—	2	1	no	—
525	#546	—	2	2	no	—
526	#546	—	2	1	no	—
527	#546	—	2	2	no	—
528	#546	—	2	1	no	—
529	#544	C₂²×C₇	1	1	yes	characteristic, complemented
530	#542	—	2	1	no	—
531	#542	C₂²×C₇	1	2	yes	complemented
532	#541	—	2	1	no	—
533	#541	C₂²×C₇	1	2	yes	complemented
534	#539	—	2	2	no	—
535	#537	C₂²×C₇	1	1	yes	characteristic
536	#536	C₂²×C₇	1	1	yes	characteristic
537	#536	C₂²×C₇	1	2	yes	—
538	#536	C₂²×C₇	1	1	yes	characteristic
539	#536	C₂²×C₇	1	1	yes	characteristic, complemented
540	#535	C₂²×C₇	1	1	yes	characteristic
541	#535	C₂²×C₇	1	2	yes	—
542	#533	—	2	1	no	—
543	#533	C₂²×C₇	1	2	yes	complemented
544	#532	C₂²×C₇	1	2	yes	—
545	#532	C₂²×C₇	1	1	yes	characteristic
546	#529	—	2	2	no	—
547	#529	—	2	1	no	—
548	#529	C₂²×C₇	1	2	yes	complemented
549	C₂×#124	C₂²×C₇	1	2	yes	—
550	C₂×#124	C₂²×C₇	1	1	yes	characteristic
551	C₄×#41	C₂²×C₇	1	1	yes	characteristic
552	C₄×#41	C₂²×C₇	1	1	yes	characteristic, complemented
553	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
554	#497	C₂²×C₇	1	2	yes	complemented
555	#497	C₂²×C₇	1	2	yes	complemented
556	#497	C₂²×C₇	1	2	yes	complemented
557	#496	C₂²×C₇	1	2	yes	complemented
558	#495	C₂²×C₇	1	2	yes	complemented
559	#495	C₂²×C₇	1	2	yes	complemented
560	#494	C₂²×C₇	1	2	yes	complemented
561	#492	C₂²×C₇	1	2	yes	complemented
562	#491	C₂²×C₇	1	2	yes	complemented
563	#490	C₂²×C₇	1	2	yes	complemented
564	#489	C₂²×C₇	1	2	yes	complemented
565	#489	C₂²×C₇	1	2	yes	complemented
566	#488	C₂²×C₇	1	2	yes	complemented
567	#488	C₂²×C₇	1	2	yes	complemented
568	#487	C₂²×C₇	1	2	yes	complemented
569	#486	C₂²×C₇	1	2	yes	complemented
570	#464	C₂²×C₇	1	1	yes	characteristic, complemented
571	#464	C₂²×C₇	1	2	yes	complemented
572	#464	C₂²×C₇	1	2	yes	complemented
573	#464	C₂²×C₇	1	2	yes	complemented
574	#464	C₂²×C₇	1	2	yes	complemented
575	#464	C₂²×C₇	1	1	yes	characteristic, complemented
576	#464	C₂²×C₇	1	2	yes	complemented
577	#464	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	1	yes	characteristic, complemented
581	#463	C₂²×C₇	1	2	yes	complemented
582	#463	C₂²×C₇	1	1	yes	characteristic, complemented
583	#463	C₂²×C₇	1	2	yes	complemented
584	#462	C₂²×C₇	1	1	yes	characteristic, complemented
585	#462	C₂²×C₇	1	2	yes	complemented
586	#461	C₂²×C₇	1	1	yes	characteristic, complemented
587	#460	C₂²×C₇	1	1	yes	characteristic, complemented
588	#460	C₂²×C₇	1	2	yes	complemented
589	#459	C₂²×C₇	1	1	yes	characteristic, complemented
590	#452	C₂²×C₇	1	2	yes	—
591	#452	C₂²×C₇	1	2	yes	—
592	#452	C₂²×C₇	1	2	yes	—
593	#452	C₂²×C₇	1	2	yes	complemented
594	#452	C₂²×C₇	1	2	yes	complemented
595	#452	C₂²×C₇	1	2	yes	complemented
596	#451	C₂²×C₇	1	2	yes	complemented
597	#451	C₂²×C₇	1	2	yes	complemented
598	#451	C₂²×C₇	1	2	yes	complemented
599	#450	C₂²×C₇	1	2	yes	—
600	#450	C₂²×C₇	1	2	yes	—
601	#450	C₂²×C₇	1	2	yes	—
602	#449	C₂²×C₇	1	2	yes	—
603	#449	C₂²×C₇	1	2	yes	complemented
604	#448	C₂²×C₇	1	2	yes	complemented
605	#447	C₂²×C₇	1	2	yes	—
606	#433	C₂²×C₇	1	2	yes	complemented
607	#433	C₂²×C₇	1	2	yes	complemented
608	#432	C₂²×C₇	1	2	yes	complemented
609	#431	C₂²×C₇	1	2	yes	complemented
610	#423	C₂²×C₇	1	1	yes	characteristic, complemented
611	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
612	#419	C₂²×C₇	1	1	yes	characteristic, complemented
613	#418	C₂²×C₇	1	1	yes	characteristic
614	#417	C₂²×C₇	1	1	yes	characteristic
615	#417	C₂²×C₇	1	1	yes	characteristic, complemented
616	#416	C₂²×C₇	1	1	yes	characteristic
617	#416	C₂²×C₇	1	1	yes	characteristic, complemented
618	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
619	C₂×#102	C₂²×C₇	1	1	yes	characteristic
620	#408	C₂²×C₇	1	1	yes	characteristic
621	#408	C₂²×C₇	1	1	yes	characteristic
622	#405	C₂²×C₇	1	1	yes	characteristic, complemented
623	#405	C₂²×C₇	1	1	yes	characteristic, complemented
624	C₂³×C₇	—	2	1	no	—
625	C₂³×C₇	—	2	2	no	—
626	C₂³×C₇	—	2	1	no	—
627	C₂³×C₇	—	2	1	no	—
628	C₂³×C₇	—	4	4	no	—
629	C₂³×C₇	—	4	2	no	—
630	C₂³×C₇	—	8	1	no	—
631	C₂³×C₇	—	8	1	no	—
632	C₂³×C₇	—	8	2	no	—
633	C₂³×C₇	—	8	2	no	—
634	C₂³×C₇	C₂²×D₄	1	2	yes	—
635	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
636	C₇×Q₈	—	2	2	no	—
637	C₇×Q₈	—	2	2	no	—
638	C₇×Q₈	—	2	2	no	—
639	C₇×Q₈	—	2	1	no	—
640	C₇×Q₈	—	2	1	no	—
641	C₇×Q₈	—	2	2	no	—
642	C₇×Q₈	—	2	1	no	—
643	C₇×Q₈	—	2	1	no	—
644	C₇×Q₈	—	2	2	no	—
645	C₇×Q₈	—	2	1	no	—
646	C₇×Q₈	—	2	1	no	—
647	C₇×Q₈	—	4	4	no	—
648	C₇×Q₈	—	4	2	no	—
649	C₇×Q₈	—	4	2	no	—
650	C₇×Q₈	—	8	2	no	—
651	C₇×D₄	—	2	4	no	—
652	C₇×D₄	—	2	2	no	—
653	C₇×D₄	—	2	1	no	—
654	C₇×D₄	—	2	1	no	—
655	C₇×D₄	—	2	2	no	—
656	C₇×D₄	—	2	1	no	—
657	C₇×D₄	—	2	1	no	—
658	C₇×D₄	—	2	2	no	—
659	C₇×D₄	—	2	1	no	—
660	C₇×D₄	—	2	1	no	—
661	C₇×D₄	—	4	4	no	—
662	C₇×D₄	—	4	4	no	—
663	C₇×D₄	—	4	4	no	—
664	C₇×D₄	—	4	2	no	—
665	C₇×D₄	—	4	2	no	—
666	C₇×D₄	—	4	2	no	—
667	C₇×D₄	—	4	2	no	—
668	C₇×D₄	—	8	1	no	—
669	C₇×D₄	—	8	2	no	—
670	C₇×D₄	—	8	1	no	—
671	C₇×D₄	—	8	2	no	—
672	C₇×D₄	—	8	2	no	—
673	C₂×C₄×C₇	—	2	2	no	—
674	C₂×C₄×C₇	—	2	2	no	—
675	C₂×C₄×C₇	—	2	1	no	—
676	C₂×C₄×C₇	—	2	2	no	—
677	C₂×C₄×C₇	—	2	1	no	—
678	C₂×C₄×C₇	—	2	1	no	—
679	C₂×C₄×C₇	—	2	2	no	—
680	C₂×C₄×C₇	—	2	2	no	—
681	C₂×C₄×C₇	—	2	1	no	—
682	C₂×C₄×C₇	—	2	1	no	—
683	C₂×C₄×C₇	—	4	1	no	—
684	C₂×C₄×C₇	—	4	2	no	—
685	C₂×C₄×C₇	—	4	1	no	—
686	C₂×C₄×C₇	—	4	2	no	—
687	C₂×C₄×C₇	—	4	2	no	—
688	C₂×C₄×C₇	—	4	4	no	—
689	C₂×C₄×C₇	—	4	4	no	—
690	C₂×C₄×C₇	—	4	4	no	—
691	C₂×C₄×C₇	—	4	2	no	—
692	C₂×C₄×C₇	—	4	2	no	—
693	C₂×C₄×C₇	—	4	2	no	—
694	C₂×C₄×C₇	—	4	2	no	—
695	C₂×C₄×C₇	—	4	2	no	—
696	C₂×C₄×C₇	—	8	1	no	—
697	C₂×C₄×C₇	—	8	1	no	—
698	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
699	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
700	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
701	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
702	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
703	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
704	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
705	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
706	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
707	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
708	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
709	C₇×C₈	—	2	1	no	—
710	C₇×C₈	—	2	1	no	—
711	C₇×C₈	—	2	1	no	—
712	C₇×C₈	—	2	1	no	—
713	C₇×C₈	—	2	2	no	—
714	C₇×C₈	—	2	2	no	—
715	2₋¹⁺⁴	—	4	2	no	—
716	2₋¹⁺⁴	—	4	2	no	—
717	H(5,𝔽₂)	—	4	2	no	—
718	H(5,𝔽₂)	—	4	2	no	—
719	C₂×#41	—	2	1	no	—
720	C₂×#41	—	2	2	no	—
721	C₂×#41	—	2	1	no	—
722	C₂×#41	C₂³×C₇	1	1	yes	characteristic
723	C₂×#41	C₂³×C₇	1	1	yes	characteristic
724	C₂×#41	C₂³×C₇	1	1	yes	characteristic
725	C₂×#41	C₂³×C₇	1	2	yes	—
726	C₂×#41	C₂³×C₇	1	2	yes	—
727	C₂×#41	C₂³×C₇	1	1	yes	characteristic
728	C₂²×Q₈	—	2	1	no	—
729	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
730	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
731	C₂²×Q₈	C₂³×C₇	1	2	yes	—
732	C₂²×D₄	—	2	2	no	—
733	C₂²×D₄	—	2	1	no	—
734	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
735	C₂²×D₄	C₂³×C₇	1	2	yes	—
736	#137	—	4	2	no	—
737	#137	—	4	2	no	—
738	#137	—	4	2	no	—
739	AGL(1,ℤ/8)	—	4	2	no	—
740	#135	—	4	2	no	—
741	#135	—	4	2	no	—
742	C₂×Q₁₆	—	4	2	no	—
743	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
744	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
745	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
746	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
747	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
748	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
749	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
750	C₂×SD₁₆	—	4	2	no	—
751	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
752	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
753	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
754	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
755	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
756	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
757	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
758	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
759	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
760	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
761	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
762	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
763	C₂×D₈	C₂³×C₇	1	2	yes	—
764	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
765	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
766	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
767	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
768	C₄⋊Q₈	—	2	1	no	—
769	C₄⋊Q₈	—	2	1	no	—
770	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
771	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
772	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
773	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
774	#127	C₂³×C₇	1	1	yes	characteristic
775	#127	C₂³×C₇	1	2	yes	—
776	#126	—	2	2	no	—
777	#126	—	2	2	no	—
778	#126	—	2	2	no	—
779	#126	—	2	2	no	—
780	#125	—	2	2	no	—
781	#125	—	2	1	no	—
782	#125	—	2	2	no	—
783	#125	—	2	2	no	—
784	#125	C₂³×C₇	1	2	yes	—
785	#124	—	2	1	no	—
786	#124	—	2	2	no	—
787	#124	—	2	1	no	—
788	#124	—	2	2	no	—
789	#124	—	2	1	no	—
790	#124	—	2	2	no	—
791	#124	C₂³×C₇	1	1	yes	characteristic
792	#124	C₂³×C₇	1	2	yes	—
793	#124	C₂³×C₇	1	2	yes	—
794	#124	C₂³×C₇	1	2	yes	—
795	#124	C₂³×C₇	1	2	yes	—
796	#124	C₂³×C₇	1	2	yes	—
797	#124	C₂³×C₇	1	1	yes	characteristic
798	#123	—	2	2	no	—
799	#123	—	2	2	no	—
800	#123	—	2	2	no	—
801	#123	—	2	2	no	—
802	#123	—	2	2	no	—
803	#123	—	2	2	no	—
804	#123	—	2	2	no	—
805	C₂²⋊Q₈	—	2	1	no	—
806	C₂²⋊Q₈	—	2	2	no	—
807	C₂²⋊Q₈	—	2	1	no	—
808	C₂²⋊Q₈	—	2	1	no	—
809	C₂²⋊Q₈	—	2	2	no	—
810	C₂²⋊Q₈	—	2	1	no	—
811	C₂²⋊Q₈	—	2	2	no	—
812	C₂²⋊Q₈	—	2	1	no	—
813	C₂²⋊Q₈	—	2	2	no	—
814	C₂²⋊Q₈	—	2	2	no	—
815	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
816	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
817	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
818	#121	—	2	2	no	—
819	#121	—	2	1	no	—
820	#121	—	2	1	no	—
821	#121	—	2	1	no	—
822	#121	—	2	2	no	—
823	#121	—	2	2	no	—
824	#121	—	2	1	no	—
825	#121	—	2	2	no	—
826	#121	—	2	1	no	—
827	#121	—	2	2	no	—
828	#121	C₂³×C₇	1	2	yes	—
829	#120	—	2	2	no	—
830	#120	—	2	2	no	—
831	#120	—	2	2	no	—
832	C₄×Q₈	—	2	1	no	—
833	C₄×Q₈	—	2	1	no	—
834	C₄×Q₈	—	2	2	no	—
835	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
836	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
837	C₄×Q₈	C₂³×C₇	1	2	yes	—
838	C₄×Q₈	C₂³×C₇	1	2	yes	—
839	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
840	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	—	2	2	no	—
844	C₄×D₄	—	2	1	no	—
845	C₄×D₄	—	2	2	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	2	no	—
848	C₄×D₄	C₇×D₄	1	1	yes	characteristic
849	C₄×D₄	C₇×D₄	1	2	yes	—
850	C₄×D₄	C₇×D₄	1	2	yes	—
851	C₄×D₄	C₇×D₄	1	1	yes	characteristic
852	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
853	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
854	#117	—	2	2	no	—
855	#117	—	2	1	no	—
856	#117	—	2	2	no	—
857	#117	C₂³×C₇	1	1	yes	characteristic
858	#117	C₂³×C₇	1	1	yes	characteristic
859	#117	C₂³×C₇	1	2	yes	—
860	C₂×C₄⋊C₄	—	2	1	no	—
861	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
862	C₂×C₂²⋊C₄	—	2	1	no	—
863	C₂×C₂²⋊C₄	—	2	1	no	—
864	C₂×C₂²⋊C₄	—	2	2	no	—
865	C₂×C₂²⋊C₄	—	2	2	no	—
866	C₂×C₄²	—	2	1	no	—
867	C₂×C₄²	—	2	1	no	—
868	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
869	C₂×C₄²	C₂³×C₇	1	2	yes	—
870	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
871	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
872	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
873	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
874	C₄⋊C₈	C₂³×C₇	1	2	yes	—
875	C₄⋊C₈	C₂³×C₇	1	2	yes	—
876	#103	C₂³×C₇	1	2	yes	—
877	#103	C₂³×C₇	1	2	yes	—
878	#103	C₂³×C₇	1	1	yes	characteristic
879	#103	C₂³×C₇	1	1	yes	characteristic
880	#103	C₂³×C₇	1	1	yes	characteristic
881	#103	C₂³×C₇	1	1	yes	characteristic
882	#103	C₂³×C₇	1	2	yes	—
883	#103	C₂³×C₇	1	2	yes	—
884	#103	C₂³×C₇	1	2	yes	—
885	#103	C₂³×C₇	1	2	yes	—
886	#102	C₂³×C₇	1	2	yes	—
887	#102	C₂³×C₇	1	2	yes	—
888	#102	C₂³×C₇	1	1	yes	characteristic
889	#102	C₂³×C₇	1	1	yes	characteristic
890	#102	C₂³×C₇	1	1	yes	characteristic
891	#102	C₂³×C₇	1	1	yes	characteristic
892	#102	C₂³×C₇	1	2	yes	—
893	#102	C₂³×C₇	1	2	yes	—
894	#102	C₂³×C₇	1	2	yes	—
895	#102	C₂³×C₇	1	2	yes	—
896	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
897	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
898	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
899	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
900	#97	C₂³×C₇	1	2	yes	—
901	#97	C₂³×C₇	1	2	yes	—
902	C₄×C₈	C₂³×C₇	1	2	yes	—
903	C₄×C₈	C₂³×C₇	1	2	yes	—
904	C₂²×C₇	—	2	1	no	—
905	C₂²×C₇	—	2	1	no	—
906	C₂²×C₇	—	2	2	no	—
907	C₂²×C₇	—	2	2	no	—
908	C₂²×C₇	—	2	2	no	—
909	C₂²×C₇	—	4	1	no	—
910	C₂²×C₇	—	4	1	no	—
911	C₂²×C₇	—	4	2	no	—
912	C₂²×C₇	—	4	1	no	—
913	C₂²×C₇	—	4	1	no	—
914	C₂²×C₇	—	4	1	no	—
915	C₂²×C₇	—	4	2	no	—
916	C₂²×C₇	—	4	1	no	—
917	C₂²×C₇	—	4	1	no	—
918	C₂²×C₇	—	4	2	no	—
919	C₂²×C₇	—	4	1	no	—
920	C₂²×C₇	—	4	1	no	—
921	C₂²×C₇	—	16	2	no	—
922	C₂²×C₇	—	16	4	no	—
923	C₂²×C₇	#535	1	2	yes	—
924	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
925	C₄×C₇	—	2	1	no	—
926	C₄×C₇	—	2	1	no	—
927	C₄×C₇	—	2	2	no	—
928	C₄×C₇	—	2	1	no	—
929	C₄×C₇	—	2	1	no	—
930	C₄×C₇	—	2	2	no	—
931	C₄×C₇	—	2	2	no	—
932	C₄×C₇	—	4	2	no	—
933	C₄×C₇	—	4	1	no	—
934	C₄×C₇	—	4	1	no	—
935	C₄×C₇	—	4	1	no	—
936	C₄×C₇	—	4	2	no	—
937	C₄×C₇	—	4	1	no	—
938	C₄×C₇	—	4	1	no	—
939	C₄×C₇	—	4	2	no	—
940	C₄×C₇	#535	1	2	yes	—
941	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
942	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
943	C₂⁴	—	2	2	no	—
944	C₂⁴	—	2	1	no	—
945	#41	—	2	2	no	—
946	#41	—	2	2	no	—
947	#41	—	2	2	no	—
948	#41	—	2	2	no	—
949	#41	—	2	2	no	—
950	#41	—	2	2	no	—
951	#41	—	2	2	no	—
952	#41	—	2	2	no	—
953	#41	—	4	2	no	—
954	#41	—	4	2	no	—
955	#41	—	4	2	no	—
956	#41	—	4	2	no	—
957	#41	—	4	8	no	—
958	#41	—	4	4	no	—
959	#41	—	4	4	no	—
960	C₂×Q₈	—	2	1	no	—
961	C₂×Q₈	—	2	2	no	—
962	C₂×Q₈	—	2	1	no	—
963	C₂×Q₈	—	2	2	no	—
964	C₂×Q₈	—	2	2	no	—
965	C₂×Q₈	—	2	2	no	—
966	C₂×Q₈	—	2	2	no	—
967	C₂×Q₈	—	2	2	no	—
968	C₂×Q₈	—	4	2	no	—
969	C₂×Q₈	—	4	2	no	—
970	C₂×Q₈	—	4	4	no	—
971	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
972	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
973	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
974	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
975	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
976	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
977	C₂×D₄	—	2	1	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	1	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	2	2	no	—
991	C₂×D₄	—	4	2	no	—
992	C₂×D₄	—	4	2	no	—
993	C₂×D₄	—	4	8	no	—
994	C₂×D₄	—	4	4	no	—
995	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
996	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
997	C₂×D₄	C₂⁴×C₇	1	2	yes	—
998	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
999	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1000	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1013	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1014	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
1015	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
1016	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
1017	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1018	Q₁₆	—	4	2	no	—
1019	Q₁₆	—	4	2	no	—
1020	Q₁₆	—	4	1	no	—
1021	Q₁₆	—	4	1	no	—
1022	Q₁₆	—	4	2	no	—
1023	Q₁₆	—	4	2	no	—
1024	Q₁₆	—	4	2	no	—
1025	SD₁₆	—	4	2	no	—
1026	SD₁₆	—	4	2	no	—
1027	SD₁₆	—	4	1	no	—
1028	SD₁₆	—	4	1	no	—
1029	SD₁₆	—	4	1	no	—
1030	SD₁₆	—	4	1	no	—
1031	SD₁₆	—	4	2	no	—
1032	SD₁₆	—	4	2	no	—
1033	SD₁₆	—	4	2	no	—
1034	SD₁₆	—	4	2	no	—
1035	D₈	—	4	1	no	—
1036	D₈	—	4	1	no	—
1037	D₈	—	4	2	no	—
1038	M₁₆	—	2	2	no	—
1039	M₁₆	—	2	2	no	—
1040	C₂×C₈	—	2	2	no	—
1041	C₂×C₈	—	2	2	no	—
1042	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1043	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1044	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1045	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1046	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1047	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	2	no	—
1065	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1066	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1067	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1068	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1069	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1070	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1071	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	1	no	—
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	1	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1094	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1095	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	1	no	—
1098	C₄²	—	2	1	no	—
1099	C₄²	—	2	1	no	—
1100	C₄²	—	2	2	no	—
1101	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1102	C₄²	C₂×C₇×D₄	1	2	yes	—
1103	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1104	C₄²	C₂×C₇×D₄	1	2	yes	—
1105	C₄²	C₂⁴×C₇	1	2	yes	—
1106	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1107	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1108	C₂×C₇	—	2	2	no	—
1109	C₂×C₇	—	4	2	no	—
1110	C₂×C₇	—	8	1	no	—
1111	C₂×C₇	—	8	1	no	—
1112	C₂×C₇	—	8	2	no	—
1113	C₂×C₇	—	8	1	no	—
1114	C₂×C₇	C₂×#535	1	1	yes	characteristic
1115	C₂×C₇	#3584	1	1	yes	characteristic
1116	C₂×C₇	#3586	1	1	yes	characteristic
1117	C₂³	—	2	1	no	—
1118	C₂³	—	2	2	no	—
1119	C₂³	—	2	1	no	—
1120	C₂³	—	2	1	no	—
1121	C₂³	—	4	4	no	—
1122	C₂³	—	4	2	no	—
1123	C₂³	—	8	1	no	—
1124	C₂³	—	8	1	no	—
1125	C₂³	—	8	2	no	—
1126	C₂³	—	8	2	no	—
1127	C₂³	C₂²×C₇×D₄	1	2	yes	—
1128	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1129	Q₈	—	2	2	no	—
1130	Q₈	—	2	2	no	—
1131	Q₈	—	2	2	no	—
1132	Q₈	—	2	1	no	—
1133	Q₈	—	2	1	no	—
1134	Q₈	—	2	2	no	—
1135	Q₈	—	2	1	no	—
1136	Q₈	—	2	1	no	—
1137	Q₈	—	2	2	no	—
1138	Q₈	—	2	1	no	—
1139	Q₈	—	2	1	no	—
1140	Q₈	—	4	4	no	—
1141	Q₈	—	4	2	no	—
1142	Q₈	—	4	2	no	—
1143	Q₈	—	8	2	no	—
1144	D₄	—	2	4	no	—
1145	D₄	—	2	1	no	—
1146	D₄	—	2	1	no	—
1147	D₄	—	2	2	no	—
1148	D₄	—	2	1	no	—
1149	D₄	—	2	1	no	—
1150	D₄	—	2	2	no	—
1151	D₄	—	2	1	no	—
1152	D₄	—	2	1	no	—
1153	D₄	—	2	2	no	—
1154	D₄	—	4	4	no	—
1155	D₄	—	4	4	no	—
1156	D₄	—	4	4	no	—
1157	D₄	—	4	2	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	8	1	no	—
1162	D₄	—	8	2	no	—
1163	D₄	—	8	1	no	—
1164	D₄	—	8	2	no	—
1165	D₄	—	8	2	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	2	no	—
1178	C₂×C₄	—	4	1	no	—
1179	C₂×C₄	—	4	2	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	4	4	no	—
1182	C₂×C₄	—	4	4	no	—
1183	C₂×C₄	—	4	4	no	—
1184	C₂×C₄	—	4	2	no	—
1185	C₂×C₄	—	4	2	no	—
1186	C₂×C₄	—	4	2	no	—
1187	C₂×C₄	—	4	2	no	—
1188	C₂×C₄	—	4	2	no	—
1189	C₂×C₄	—	8	1	no	—
1190	C₂×C₄	—	8	1	no	—
1191	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1192	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1193	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1194	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1195	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1196	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1197	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1198	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1199	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1200	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1201	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1202	C₈	—	2	1	no	—
1203	C₈	—	2	1	no	—
1204	C₈	—	2	1	no	—
1205	C₈	—	2	1	no	—
1206	C₈	—	2	2	no	—
1207	C₈	—	2	2	no	—
1208	C₇	#60835	1	1	yes	characteristic, direct product factor, Sylow
1209	C₂²	—	2	1	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	2	no	—
1212	C₂²	—	2	2	no	—
1213	C₂²	—	2	2	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	2	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	2	no	—
1221	C₂²	—	4	1	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	2	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	16	2	no	—
1227	C₂²	—	16	4	no	—
1228	C₂²	C₇×#535	1	2	yes	—
1229	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1230	C₄	—	2	1	no	—
1231	C₄	—	2	1	no	—
1232	C₄	—	2	2	no	—
1233	C₄	—	2	1	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	2	no	—
1236	C₄	—	2	2	no	—
1237	C₄	—	4	2	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	2	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	2	no	—
1245	C₄	C₇×#535	1	2	yes	—
1246	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1247	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1248	C₂	—	2	2	no	—
1249	C₂	—	4	2	no	—
1250	C₂	—	8	2	no	—
1251	C₂	—	8	1	no	—
1252	C₂	—	8	1	no	—
1253	C₂	—	8	1	no	—
1254	C₂	C₂×C₇×#535	1	1	yes	characteristic
1255	C₂	C₇×#3584	1	1	yes	characteristic
1256	C₂	C₇×#3586	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×#3461	C₂	semidirect
3. C₇×#3225	C₂	semidirect
4. C₇×#3224	C₂	semidirect
5. C₇×#3223	C₂	semidirect
6. C₇×#3222	C₂	semidirect
7. C₇×#3219	C₂	semidirect
8. C₇×#3215	C₂	semidirect
9. C₇×#3211	C₂	semidirect
10. C₇×#3210	C₂	semidirect
11. C₇×#3156	C₂	semidirect
12. C₇×#3154	C₂	semidirect
13. C₇×#3137	C₂	semidirect
14. C₇×#3136	C₂	semidirect
15. C₇×#3040	C₂	semidirect
16. C₇×#3037	C₂	semidirect
17. C₇×#3035	C₂	semidirect
18. C₂×C₇×#464	C₂	semidirect
19. C₇×#3013	C₂	semidirect
20. C₇×#3012	C₂	semidirect
21. C₇×#3011	C₂	semidirect
22. C₇×#3009	C₂	semidirect
23. C₇×#2925	C₂	semidirect
27. C₂×C₇×#137	C₂²	semidirect
28. C₂×C₇×#137	C₂²	semidirect
31. C₂×C₇×#135	C₂²	semidirect
32. C₂²×C₇×Q₁₆	C₂²	semidirect
40. C₇×#544	C₂²	semidirect
42. C₇×#542	C₂²	semidirect
44. C₇×#541	C₂²	semidirect
50. C₇×#536	C₂²	semidirect
54. C₇×#533	C₂²	semidirect
59. C₇×#529	C₂²	semidirect
63. C₄×C₇×#41	C₂²	semidirect
64. C₂×C₄×C₇×Q₈	C₂²	semidirect
65. C₇×#497	C₂²	semidirect
66. C₇×#497	C₂²	semidirect
67. C₇×#497	C₂²	semidirect
68. C₇×#496	C₂²	semidirect
69. C₇×#495	C₂²	semidirect
70. C₇×#495	C₂²	semidirect
71. C₇×#494	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×#464	C₂²	semidirect
86. C₇×#464	C₂²	semidirect
87. C₇×#464	C₂²	semidirect
88. C₇×#464	C₂²	semidirect
89. C₇×#464	C₂²	semidirect
90. C₇×#464	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×#462	C₂²	semidirect
97. C₇×#461	C₂²	semidirect
98. C₇×#460	C₂²	semidirect
99. C₇×#460	C₂²	semidirect
100. C₇×#459	C₂²	semidirect
104. C₇×#452	C₂²	semidirect
105. C₇×#452	C₂²	semidirect
106. C₇×#452	C₂²	semidirect
107. C₇×#451	C₂²	semidirect
108. C₇×#451	C₂²	semidirect
109. C₇×#451	C₂²	semidirect
114. C₇×#449	C₂²	semidirect
115. C₇×#448	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. #60835	C₇	direct (N × H)
325. #3500	C₂×C₇	semidirect
326. #3461	C₂×C₇	semidirect
327. #3225	C₂×C₇	semidirect
328. #3224	C₂×C₇	semidirect
329. #3223	C₂×C₇	semidirect
330. #3222	C₂×C₇	semidirect
331. #3219	C₂×C₇	semidirect
332. #3215	C₂×C₇	semidirect
333. #3211	C₂×C₇	semidirect
334. #3210	C₂×C₇	semidirect
335. #3156	C₂×C₇	semidirect
336. #3154	C₂×C₇	semidirect
337. #3137	C₂×C₇	semidirect
338. #3136	C₂×C₇	semidirect
339. #3040	C₂×C₇	semidirect
340. #3037	C₂×C₇	semidirect
341. #3035	C₂×C₇	semidirect
342. C₂×#464	C₂×C₇	semidirect
343. #3013	C₂×C₇	semidirect
344. #3012	C₂×C₇	semidirect
345. #3011	C₂×C₇	semidirect
346. #3009	C₂×C₇	semidirect
347. #2925	C₂×C₇	semidirect
516. C₂×#137	C₂²×C₇	semidirect
517. C₂×#137	C₂²×C₇	semidirect
520. C₂×#135	C₂²×C₇	semidirect
521. C₂²×Q₁₆	C₂²×C₇	semidirect
529. #544	C₂²×C₇	semidirect
531. #542	C₂²×C₇	semidirect
533. #541	C₂²×C₇	semidirect
539. #536	C₂²×C₇	semidirect
543. #533	C₂²×C₇	semidirect
548. #529	C₂²×C₇	semidirect
552. C₄×#41	C₂²×C₇	semidirect
553. C₂×C₄×Q₈	C₂²×C₇	semidirect
554. #497	C₂²×C₇	semidirect
555. #497	C₂²×C₇	semidirect
556. #497	C₂²×C₇	semidirect
557. #496	C₂²×C₇	semidirect
558. #495	C₂²×C₇	semidirect
559. #495	C₂²×C₇	semidirect
560. #494	C₂²×C₇	semidirect
561. #492	C₂²×C₇	semidirect
562. #491	C₂²×C₇	semidirect
563. #490	C₂²×C₇	semidirect
564. #489	C₂²×C₇	semidirect
565. #489	C₂²×C₇	semidirect
566. #488	C₂²×C₇	semidirect
567. #488	C₂²×C₇	semidirect
568. #487	C₂²×C₇	semidirect
569. #486	C₂²×C₇	semidirect
570. #464	C₂²×C₇	semidirect
571. #464	C₂²×C₇	semidirect
572. #464	C₂²×C₇	semidirect
573. #464	C₂²×C₇	semidirect
574. #464	C₂²×C₇	semidirect
575. #464	C₂²×C₇	semidirect
576. #464	C₂²×C₇	semidirect
577. #464	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. #462	C₂²×C₇	semidirect
585. #462	C₂²×C₇	semidirect
586. #461	C₂²×C₇	semidirect
587. #460	C₂²×C₇	semidirect
588. #460	C₂²×C₇	semidirect
589. #459	C₂²×C₇	semidirect
593. #452	C₂²×C₇	semidirect
594. #452	C₂²×C₇	semidirect
595. #452	C₂²×C₇	semidirect
596. #451	C₂²×C₇	semidirect
597. #451	C₂²×C₇	semidirect
598. #451	C₂²×C₇	semidirect
603. #449	C₂²×C₇	semidirect
604. #448	C₂²×C₇	semidirect
606. #433	C₂²×C₇	semidirect
607. #433	C₂²×C₇	semidirect
608. #432	C₂²×C₇	semidirect
609. #431	C₂²×C₇	semidirect
610. #423	C₂²×C₇	semidirect
611. C₂×C₄⋊C₈	C₂²×C₇	semidirect
612. #419	C₂²×C₇	semidirect
615. #417	C₂²×C₇	semidirect
617. #416	C₂²×C₇	semidirect
618. C₂×#103	C₂²×C₇	semidirect
622. #405	C₂²×C₇	semidirect
623. #405	C₂²×C₇	semidirect
1208. C₇	#60835	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×#3461	2
C₇×#3225	2
C₇×#3224	2
C₇×#3223	2
C₇×#3222	2
C₇×#3219	2
C₇×#3215	2
C₇×#3211	2
C₇×#3210	2
C₇×#3156	2
C₇×#3154	2
C₇×#3137	2
C₇×#3136	2
C₇×#3040	2
C₇×#3037	2
C₇×#3035	2
C₂×C₇×#464	2
C₇×#3013	2
C₇×#3012	2
C₇×#3011	2
C₇×#3009	2
C₇×#2925	2
#60835	7

Subgroups — C7×#60835 #13238051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60835 #13238051