Subgroups — C₇×#60816 #13238032

Order 1792.

2048 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#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×#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×#3216	C₂	1	2	yes	maximal, complemented
9	C₇×#3212	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×#3046	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3045	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3043	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3007	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×#452	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
27	C₂×C₇×#137	C₂²	1	1	yes	characteristic
28	C₂×C₇×#137	C₂²	1	1	yes	characteristic, complemented
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×Q₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₇×#556	—	2	1	no	—
35	C₇×#554	—	2	1	no	—
36	C₇×#552	—	2	2	no	—
37	C₇×#552	—	2	1	no	—
38	C₇×#552	—	2	1	no	—
39	C₇×#551	—	2	2	no	—
40	C₇×#544	C₂²	1	1	yes	characteristic, complemented
41	C₇×#542	C₂²	1	2	yes	complemented
42	C₇×#541	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	2	yes	—
47	C₇×#536	C₂²	1	1	yes	characteristic
48	C₇×#536	C₂²	1	1	yes	characteristic, complemented
49	C₇×#535	C₂²	1	2	yes	—
50	C₇×#535	C₂²	1	1	yes	characteristic
51	C₇×#535	C₂²	1	1	yes	characteristic
52	C₇×#534	—	2	2	no	—
53	C₇×#533	C₂²	1	2	yes	complemented
54	C₇×#532	C₂²	1	2	yes	—
55	C₇×#532	C₂²	1	2	yes	—
56	C₇×#529	C₂²	1	2	yes	complemented
57	C₇×#525	—	2	1	no	—
58	C₇×#525	—	2	2	no	—
59	C₇×#525	—	2	1	no	—
60	C₇×#525	C₂²	1	1	yes	characteristic
61	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
62	C₇×#520	C₂²	1	1	yes	characteristic, complemented
63	C₇×#519	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×#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	2	yes	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	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×#462	C₂²	1	2	yes	complemented
91	C₇×#462	C₂²	1	2	yes	complemented
92	C₇×#461	C₂²	1	2	yes	complemented
93	C₇×#460	C₂²	1	2	yes	complemented
94	C₇×#460	C₂²	1	2	yes	complemented
95	C₇×#460	C₂²	1	2	yes	complemented
96	C₇×#459	C₂²	1	2	yes	complemented
97	C₇×#452	C₂²	1	2	yes	—
98	C₇×#452	C₂²	1	2	yes	—
99	C₇×#452	C₂²	1	2	yes	—
100	C₇×#452	C₂²	1	1	yes	characteristic, complemented
101	C₇×#452	C₂²	1	2	yes	complemented
102	C₇×#452	C₂²	1	2	yes	complemented
103	C₇×#452	C₂²	1	2	yes	complemented
104	C₇×#452	C₂²	1	2	yes	complemented
105	C₇×#452	C₂²	1	1	yes	characteristic, complemented
106	C₇×#452	C₂²	1	2	yes	complemented
107	C₇×#451	C₂²	1	1	yes	characteristic, complemented
108	C₇×#451	C₂²	1	2	yes	complemented
109	C₇×#450	C₂²	1	1	yes	characteristic, complemented
110	C₇×#450	C₂²	1	2	yes	complemented
111	C₇×#449	C₂²	1	2	yes	—
112	C₇×#449	C₂²	1	1	yes	characteristic, complemented
113	C₇×#449	C₂²	1	2	yes	complemented
114	C₇×#449	C₂²	1	1	yes	characteristic, complemented
115	C₇×#448	C₂²	1	1	yes	characteristic, complemented
116	C₇×#447	C₂²	1	1	yes	characteristic, 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	#60816	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	—	4	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	C₂³	1	1	yes	characteristic
145	C₂×C₇×#41	C₂³	1	1	yes	characteristic
146	C₂×C₇×#41	C₂³	1	1	yes	characteristic
147	C₂×C₇×#41	C₂³	1	2	yes	—
148	C₂×C₇×#41	C₂³	1	1	yes	characteristic
149	C₂×C₇×#41	C₂³	1	1	yes	characteristic
150	C₂×C₇×#41	C₂³	1	2	yes	—
151	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
152	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
154	C₂²×C₇×D₄	—	2	1	no	—
155	C₂²×C₇×D₄	—	2	1	no	—
156	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
157	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
158	C₂³×C₄×C₇	—	2	1	no	—
159	C₂³×C₄×C₇	—	2	1	no	—
160	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
161	C₇×#137	—	4	2	no	—
162	C₇×#137	—	4	2	no	—
163	C₇×#137	—	4	2	no	—
164	C₇×AGL(1,ℤ/8)	—	4	2	no	—
165	C₇×#135	—	4	2	no	—
166	C₇×#135	—	4	2	no	—
167	C₂×C₇×Q₁₆	—	4	2	no	—
168	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
169	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
170	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
171	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
172	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
173	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
174	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
175	C₂×C₇×SD₁₆	—	4	2	no	—
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	2	yes	—
182	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
183	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
184	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
185	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
186	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
187	C₂×C₇×D₈	C₂³	1	2	yes	—
188	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
189	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
190	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
191	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
192	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
193	C₇×C₄⋊Q₈	—	2	1	no	—
194	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
195	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
196	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
197	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
198	C₇×#127	C₂³	1	2	yes	—
199	C₇×#127	C₂³	1	2	yes	—
200	C₇×#126	—	2	2	no	—
201	C₇×#126	—	2	2	no	—
202	C₇×#126	—	2	2	no	—
203	C₇×#126	—	2	2	no	—
204	C₇×#125	—	2	2	no	—
205	C₇×#125	—	2	2	no	—
206	C₇×#125	—	2	1	no	—
207	C₇×#125	—	2	2	no	—
208	C₇×#125	C₂³	1	2	yes	—
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×#123	—	2	1	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×#123	—	2	2	no	—
223	C₇×C₂²⋊Q₈	—	2	1	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	1	no	—
229	C₇×C₂²⋊Q₈	—	2	2	no	—
230	C₇×C₂²⋊Q₈	—	2	1	no	—
231	C₇×C₂²⋊Q₈	—	2	2	no	—
232	C₇×C₂²⋊Q₈	—	2	1	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	1	yes	characteristic
239	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
240	C₇×#121	—	2	2	no	—
241	C₇×#121	—	2	2	no	—
242	C₇×#121	—	2	2	no	—
243	C₇×#121	—	2	2	no	—
244	C₇×#121	—	2	1	no	—
245	C₇×#121	—	2	1	no	—
246	C₇×#121	—	2	2	no	—
247	C₇×#121	—	2	1	no	—
248	C₇×#121	—	2	1	no	—
249	C₇×#121	—	2	2	no	—
250	C₇×#121	C₂³	1	1	yes	characteristic
251	C₇×#121	C₂³	1	1	yes	characteristic
252	C₇×#120	—	2	1	no	—
253	C₇×#120	—	2	2	no	—
254	C₇×#120	—	2	2	no	—
255	C₇×#120	—	2	2	no	—
256	C₇×#120	—	2	2	no	—
257	C₄×C₇×Q₈	—	2	1	no	—
258	C₄×C₇×Q₈	—	2	1	no	—
259	C₄×C₇×Q₈	—	2	2	no	—
260	C₄×C₇×Q₈	C₂³	1	2	yes	—
261	C₄×C₇×Q₈	C₂³	1	2	yes	—
262	C₄×C₇×Q₈	C₂³	1	2	yes	—
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	C₇×#117	—	2	2	no	—
273	C₇×#117	—	2	1	no	—
274	C₇×#117	—	2	2	no	—
275	C₇×#117	—	2	2	no	—
276	C₇×#117	D₄	1	1	yes	characteristic
277	C₇×#117	D₄	1	2	yes	—
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	—	2	1	no	—
285	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
286	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
287	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×C₇×C₂²⋊C₄	—	2	1	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	#3495	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	#3223	C₂×C₇	1	2	yes	complemented
330	#3222	C₂×C₇	1	2	yes	complemented
331	#3219	C₂×C₇	1	2	yes	complemented
332	#3216	C₂×C₇	1	2	yes	complemented
333	#3212	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	#3046	C₂×C₇	1	1	yes	characteristic, complemented
340	#3045	C₂×C₇	1	1	yes	characteristic, complemented
341	#3044	C₂×C₇	1	1	yes	characteristic, complemented
342	#3043	C₂×C₇	1	1	yes	characteristic, complemented
343	#3007	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×#452	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	C₂×D₄	1	1	yes	characteristic
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	—	4	2	no	—
358	C₇×#41	—	4	2	no	—
359	C₇×#41	—	4	2	no	—
360	C₇×#41	—	4	1	no	—
361	C₇×#41	—	4	1	no	—
362	C₇×#41	—	4	2	no	—
363	C₇×#41	—	4	1	no	—
364	C₇×#41	—	4	1	no	—
365	C₇×#41	—	4	4	no	—
366	C₇×#41	—	4	4	no	—
367	C₇×#41	—	4	4	no	—
368	C₇×#41	—	4	4	no	—
369	C₂×C₇×Q₈	—	2	1	no	—
370	C₂×C₇×Q₈	—	2	1	no	—
371	C₂×C₇×Q₈	—	2	1	no	—
372	C₂×C₇×Q₈	—	2	2	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	—	2	2	no	—
377	C₂×C₇×Q₈	—	4	1	no	—
378	C₂×C₇×Q₈	—	4	1	no	—
379	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
380	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
382	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
383	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
384	C₂×C₇×D₄	—	2	1	no	—
385	C₂×C₇×D₄	—	2	1	no	—
386	C₂×C₇×D₄	—	2	2	no	—
387	C₂×C₇×D₄	—	2	1	no	—
388	C₂×C₇×D₄	—	2	1	no	—
389	C₂×C₇×D₄	—	2	1	no	—
390	C₂×C₇×D₄	—	2	2	no	—
391	C₂×C₇×D₄	—	2	1	no	—
392	C₂×C₇×D₄	—	2	1	no	—
393	C₂×C₇×D₄	—	2	1	no	—
394	C₂×C₇×D₄	—	2	1	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	1	no	—
402	C₂×C₇×D₄	—	4	1	no	—
403	C₂×C₇×D₄	—	4	4	no	—
404	C₂×C₇×D₄	—	4	4	no	—
405	C₂×C₇×D₄	C₂⁴	1	2	yes	—
406	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
407	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
408	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₇	—	2	2	no	—
410	C₂²×C₄×C₇	—	2	2	no	—
411	C₂²×C₄×C₇	—	2	1	no	—
412	C₂²×C₄×C₇	—	2	1	no	—
413	C₂²×C₄×C₇	—	2	1	no	—
414	C₂²×C₄×C₇	—	2	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	1	no	—
419	C₂²×C₄×C₇	—	2	2	no	—
420	C₂²×C₄×C₇	—	2	1	no	—
421	C₂²×C₄×C₇	—	2	1	no	—
422	C₂²×C₄×C₇	—	2	2	no	—
423	C₂²×C₄×C₇	—	4	4	no	—
424	C₂²×C₄×C₇	—	4	4	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	1	yes	characteristic
428	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
429	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
430	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
432	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
433	C₇×Q₁₆	—	4	2	no	—
434	C₇×Q₁₆	—	4	2	no	—
435	C₇×Q₁₆	—	4	1	no	—
436	C₇×Q₁₆	—	4	1	no	—
437	C₇×Q₁₆	—	4	2	no	—
438	C₇×Q₁₆	—	4	2	no	—
439	C₇×Q₁₆	—	4	2	no	—
440	C₇×SD₁₆	—	4	2	no	—
441	C₇×SD₁₆	—	4	2	no	—
442	C₇×SD₁₆	—	4	1	no	—
443	C₇×SD₁₆	—	4	1	no	—
444	C₇×SD₁₆	—	4	1	no	—
445	C₇×SD₁₆	—	4	1	no	—
446	C₇×SD₁₆	—	4	2	no	—
447	C₇×SD₁₆	—	4	2	no	—
448	C₇×SD₁₆	—	4	2	no	—
449	C₇×SD₁₆	—	4	2	no	—
450	C₇×D₈	—	4	1	no	—
451	C₇×D₈	—	4	1	no	—
452	C₇×D₈	—	4	2	no	—
453	C₇×M₁₆	—	2	2	no	—
454	C₇×M₁₆	—	2	2	no	—
455	C₂×C₇×C₈	—	2	2	no	—
456	C₂×C₇×C₈	—	2	2	no	—
457	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
458	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
459	C₂×C₇×C₈	C₂⁴	1	2	yes	—
460	C₂×C₇×C₈	C₂⁴	1	2	yes	—
461	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
462	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
471	C₇×C₄⋊C₄	—	2	2	no	—
472	C₇×C₄⋊C₄	—	2	1	no	—
473	C₇×C₄⋊C₄	—	2	2	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	1	no	—
479	C₇×C₄⋊C₄	—	2	2	no	—
480	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
481	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
482	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
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	2	yes	—
486	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
487	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
488	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	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	2	no	—
498	C₇×C₂²⋊C₄	—	2	2	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	—	2	2	no	—
503	C₇×C₂²⋊C₄	—	2	2	no	—
504	C₇×C₂²⋊C₄	—	2	2	no	—
505	C₇×C₂²⋊C₄	—	2	1	no	—
506	C₇×C₂²⋊C₄	—	2	2	no	—
507	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
508	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
509	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
510	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
511	C₄²×C₇	—	2	2	no	—
512	C₄²×C₇	—	2	2	no	—
513	C₄²×C₇	—	2	2	no	—
514	C₄²×C₇	—	2	1	no	—
515	C₄²×C₇	C₂×D₄	1	2	yes	—
516	C₄²×C₇	C₂×D₄	1	2	yes	—
517	C₄²×C₇	C₂⁴	1	2	yes	—
518	C₄²×C₇	C₂⁴	1	2	yes	—
519	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
520	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
521	C₂×#137	C₂²×C₇	1	1	yes	characteristic
522	C₂×#137	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, complemented
525	C₂×#135	C₂²×C₇	1	1	yes	characteristic
526	C₂×#135	C₂²×C₇	1	1	yes	characteristic
527	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
528	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
529	#556	—	2	1	no	—
530	#554	—	2	1	no	—
531	#552	—	2	2	no	—
532	#552	—	2	1	no	—
533	#552	—	2	1	no	—
534	#551	—	2	2	no	—
535	#544	C₂²×C₇	1	1	yes	characteristic, complemented
536	#542	C₂²×C₇	1	2	yes	complemented
537	#541	C₂²×C₇	1	2	yes	complemented
538	#537	—	2	1	no	—
539	#537	—	2	1	no	—
540	#536	C₂²×C₇	1	1	yes	characteristic
541	#536	C₂²×C₇	1	2	yes	—
542	#536	C₂²×C₇	1	1	yes	characteristic
543	#536	C₂²×C₇	1	1	yes	characteristic, complemented
544	#535	C₂²×C₇	1	1	yes	characteristic
545	#535	C₂²×C₇	1	2	yes	—
546	#535	C₂²×C₇	1	1	yes	characteristic
547	#534	—	2	2	no	—
548	#533	C₂²×C₇	1	2	yes	complemented
549	#532	C₂²×C₇	1	2	yes	—
550	#532	C₂²×C₇	1	2	yes	—
551	#529	C₂²×C₇	1	2	yes	complemented
552	#525	—	2	1	no	—
553	#525	—	2	2	no	—
554	#525	—	2	1	no	—
555	#525	C₂²×C₇	1	1	yes	characteristic
556	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
557	#520	C₂²×C₇	1	1	yes	characteristic, complemented
558	#519	C₂²×C₇	1	1	yes	characteristic, complemented
559	C₂×#117	C₂²×C₇	1	1	yes	characteristic
560	#497	C₂²×C₇	1	2	yes	complemented
561	#497	C₂²×C₇	1	2	yes	complemented
562	#497	C₂²×C₇	1	2	yes	complemented
563	#496	C₂²×C₇	1	2	yes	complemented
564	#495	C₂²×C₇	1	2	yes	complemented
565	#495	C₂²×C₇	1	2	yes	complemented
566	#494	C₂²×C₇	1	2	yes	complemented
567	#492	C₂²×C₇	1	2	yes	complemented
568	#491	C₂²×C₇	1	2	yes	complemented
569	#490	C₂²×C₇	1	2	yes	complemented
570	#489	C₂²×C₇	1	2	yes	complemented
571	#489	C₂²×C₇	1	2	yes	complemented
572	#488	C₂²×C₇	1	2	yes	complemented
573	#488	C₂²×C₇	1	2	yes	complemented
574	#487	C₂²×C₇	1	2	yes	complemented
575	#486	C₂²×C₇	1	2	yes	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	#464	C₂²×C₇	1	2	yes	complemented
581	#464	C₂²×C₇	1	2	yes	complemented
582	#463	C₂²×C₇	1	2	yes	complemented
583	#463	C₂²×C₇	1	2	yes	complemented
584	#462	C₂²×C₇	1	2	yes	complemented
585	#462	C₂²×C₇	1	2	yes	complemented
586	#462	C₂²×C₇	1	2	yes	complemented
587	#461	C₂²×C₇	1	2	yes	complemented
588	#460	C₂²×C₇	1	2	yes	complemented
589	#460	C₂²×C₇	1	2	yes	complemented
590	#460	C₂²×C₇	1	2	yes	complemented
591	#459	C₂²×C₇	1	2	yes	complemented
592	#452	C₂²×C₇	1	2	yes	—
593	#452	C₂²×C₇	1	2	yes	—
594	#452	C₂²×C₇	1	2	yes	—
595	#452	C₂²×C₇	1	1	yes	characteristic, complemented
596	#452	C₂²×C₇	1	2	yes	complemented
597	#452	C₂²×C₇	1	2	yes	complemented
598	#452	C₂²×C₇	1	2	yes	complemented
599	#452	C₂²×C₇	1	2	yes	complemented
600	#452	C₂²×C₇	1	1	yes	characteristic, complemented
601	#452	C₂²×C₇	1	2	yes	complemented
602	#451	C₂²×C₇	1	1	yes	characteristic, complemented
603	#451	C₂²×C₇	1	2	yes	complemented
604	#450	C₂²×C₇	1	1	yes	characteristic, complemented
605	#450	C₂²×C₇	1	2	yes	complemented
606	#449	C₂²×C₇	1	2	yes	—
607	#449	C₂²×C₇	1	1	yes	characteristic, complemented
608	#449	C₂²×C₇	1	2	yes	complemented
609	#449	C₂²×C₇	1	1	yes	characteristic, complemented
610	#448	C₂²×C₇	1	1	yes	characteristic, complemented
611	#447	C₂²×C₇	1	1	yes	characteristic, complemented
612	#433	C₂²×C₇	1	2	yes	complemented
613	#433	C₂²×C₇	1	2	yes	complemented
614	#432	C₂²×C₇	1	2	yes	complemented
615	#431	C₂²×C₇	1	2	yes	complemented
616	#424	C₂²×C₇	1	1	yes	characteristic, complemented
617	#424	C₂²×C₇	1	1	yes	characteristic, complemented
618	#419	C₂²×C₇	1	1	yes	characteristic, complemented
619	#418	C₂²×C₇	1	1	yes	characteristic, complemented
620	#417	C₂²×C₇	1	1	yes	characteristic
621	#417	C₂²×C₇	1	1	yes	characteristic
622	#416	C₂²×C₇	1	1	yes	characteristic
623	#416	C₂²×C₇	1	1	yes	characteristic
624	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
625	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
626	#407	C₂²×C₇	1	1	yes	characteristic
627	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
628	#405	C₂²×C₇	1	1	yes	characteristic, complemented
629	#405	C₂²×C₇	1	1	yes	characteristic, complemented
630	C₂³×C₇	—	2	2	no	—
631	C₂³×C₇	—	2	1	no	—
632	C₂³×C₇	—	2	2	no	—
633	C₂³×C₇	—	2	1	no	—
634	C₂³×C₇	—	2	1	no	—
635	C₂³×C₇	—	4	1	no	—
636	C₂³×C₇	—	4	1	no	—
637	C₂³×C₇	—	4	2	no	—
638	C₂³×C₇	—	4	2	no	—
639	C₂³×C₇	—	8	1	no	—
640	C₂³×C₇	—	8	1	no	—
641	C₂³×C₇	—	8	1	no	—
642	C₂³×C₇	—	8	1	no	—
643	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
644	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
645	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
646	C₇×Q₈	—	2	2	no	—
647	C₇×Q₈	—	2	1	no	—
648	C₇×Q₈	—	2	2	no	—
649	C₇×Q₈	—	2	1	no	—
650	C₇×Q₈	—	2	2	no	—
651	C₇×Q₈	—	2	1	no	—
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	—	4	2	no	—
657	C₇×Q₈	—	4	2	no	—
658	C₇×Q₈	—	4	2	no	—
659	C₇×Q₈	—	8	2	no	—
660	C₇×D₄	—	2	1	no	—
661	C₇×D₄	—	2	1	no	—
662	C₇×D₄	—	2	2	no	—
663	C₇×D₄	—	2	1	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	—	4	2	no	—
669	C₇×D₄	—	4	2	no	—
670	C₇×D₄	—	4	4	no	—
671	C₇×D₄	—	4	4	no	—
672	C₇×D₄	—	4	2	no	—
673	C₇×D₄	—	4	2	no	—
674	C₇×D₄	—	4	2	no	—
675	C₇×D₄	—	4	2	no	—
676	C₇×D₄	—	4	2	no	—
677	C₇×D₄	—	4	2	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	1	no	—
683	C₂×C₄×C₇	—	2	2	no	—
684	C₂×C₄×C₇	—	2	2	no	—
685	C₂×C₄×C₇	—	2	2	no	—
686	C₂×C₄×C₇	—	2	1	no	—
687	C₂×C₄×C₇	—	2	1	no	—
688	C₂×C₄×C₇	—	2	1	no	—
689	C₂×C₄×C₇	—	2	1	no	—
690	C₂×C₄×C₇	—	2	1	no	—
691	C₂×C₄×C₇	—	2	1	no	—
692	C₂×C₄×C₇	—	2	2	no	—
693	C₂×C₄×C₇	—	2	1	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	—	4	2	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	4	no	—
704	C₂×C₄×C₇	—	4	2	no	—
705	C₂×C₄×C₇	—	4	2	no	—
706	C₂×C₄×C₇	—	4	2	no	—
707	C₂×C₄×C₇	—	4	2	no	—
708	C₂×C₄×C₇	—	4	2	no	—
709	C₂×C₄×C₇	—	4	2	no	—
710	C₂×C₄×C₇	—	8	2	no	—
711	C₂×C₄×C₇	—	8	1	no	—
712	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
713	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
714	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
715	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
716	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
717	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
718	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
719	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
720	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
721	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
722	C₇×C₈	—	2	1	no	—
723	C₇×C₈	—	2	1	no	—
724	C₇×C₈	—	2	1	no	—
725	C₇×C₈	—	2	1	no	—
726	C₇×C₈	—	2	2	no	—
727	C₇×C₈	—	2	2	no	—
728	C₂×#41	—	2	1	no	—
729	C₂×#41	—	2	1	no	—
730	C₂×#41	—	2	1	no	—
731	C₂×#41	—	2	1	no	—
732	C₂×#41	—	4	2	no	—
733	C₂×#41	—	4	2	no	—
734	C₂×#41	—	4	2	no	—
735	C₂×#41	—	4	2	no	—
736	C₂×#41	C₂³×C₇	1	1	yes	characteristic
737	C₂×#41	C₂³×C₇	1	1	yes	characteristic
738	C₂×#41	C₂³×C₇	1	1	yes	characteristic
739	C₂×#41	C₂³×C₇	1	1	yes	characteristic
740	C₂×#41	C₂³×C₇	1	2	yes	—
741	C₂×#41	C₂³×C₇	1	1	yes	characteristic
742	C₂×#41	C₂³×C₇	1	2	yes	—
743	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
744	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
745	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
746	C₂²×D₄	—	2	1	no	—
747	C₂²×D₄	—	2	1	no	—
748	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
749	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
750	C₂³×C₄	—	2	1	no	—
751	C₂³×C₄	—	2	1	no	—
752	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
753	#137	—	4	2	no	—
754	#137	—	4	2	no	—
755	#137	—	4	2	no	—
756	AGL(1,ℤ/8)	—	4	2	no	—
757	#135	—	4	2	no	—
758	#135	—	4	2	no	—
759	C₂×Q₁₆	—	4	2	no	—
760	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
761	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
762	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
763	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
764	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
765	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
766	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
767	C₂×SD₁₆	—	4	2	no	—
768	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
769	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
770	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
771	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
772	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
773	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
774	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
778	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
779	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
780	C₂×D₈	C₂³×C₇	1	2	yes	—
781	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
782	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
783	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
784	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
785	C₄⋊Q₈	—	2	1	no	—
786	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
787	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
788	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
789	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
790	#127	C₂³×C₇	1	2	yes	—
791	#127	C₂³×C₇	1	2	yes	—
792	#126	—	2	2	no	—
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#126	—	2	2	no	—
796	#125	—	2	2	no	—
797	#125	—	2	2	no	—
798	#125	—	2	1	no	—
799	#125	—	2	2	no	—
800	#125	C₂³×C₇	1	2	yes	—
801	#124	—	2	2	no	—
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	2	yes	—
806	#124	C₂³×C₇	1	2	yes	—
807	#123	—	2	1	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	#123	—	2	2	no	—
814	#123	—	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	1	no	—
819	C₂²⋊Q₈	—	2	1	no	—
820	C₂²⋊Q₈	—	2	1	no	—
821	C₂²⋊Q₈	—	2	2	no	—
822	C₂²⋊Q₈	—	2	1	no	—
823	C₂²⋊Q₈	—	2	2	no	—
824	C₂²⋊Q₈	—	2	1	no	—
825	C₂²⋊Q₈	—	2	1	no	—
826	C₂²⋊Q₈	—	2	2	no	—
827	C₂²⋊Q₈	—	2	2	no	—
828	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
829	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
830	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
831	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	1	no	—
837	#121	—	2	1	no	—
838	#121	—	2	1	no	—
839	#121	—	2	2	no	—
840	#121	—	2	1	no	—
841	#121	—	2	2	no	—
842	#121	C₂³×C₇	1	1	yes	characteristic
843	#121	C₂³×C₇	1	1	yes	characteristic
844	#120	—	2	1	no	—
845	#120	—	2	2	no	—
846	#120	—	2	2	no	—
847	#120	—	2	2	no	—
848	#120	—	2	2	no	—
849	C₄×Q₈	—	2	1	no	—
850	C₄×Q₈	—	2	1	no	—
851	C₄×Q₈	—	2	2	no	—
852	C₄×Q₈	C₂³×C₇	1	2	yes	—
853	C₄×Q₈	C₂³×C₇	1	2	yes	—
854	C₄×Q₈	C₂³×C₇	1	2	yes	—
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	—	2	2	no	—
858	C₄×D₄	—	2	2	no	—
859	C₄×D₄	—	2	2	no	—
860	C₄×D₄	—	2	2	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	C₂³×C₇	1	2	yes	—
864	#117	—	2	2	no	—
865	#117	—	2	1	no	—
866	#117	—	2	2	no	—
867	#117	—	2	2	no	—
868	#117	C₇×D₄	1	1	yes	characteristic
869	#117	C₇×D₄	1	2	yes	—
870	#117	C₇×D₄	1	1	yes	characteristic
871	#117	C₂³×C₇	1	1	yes	characteristic
872	#117	C₂³×C₇	1	1	yes	characteristic
873	#117	C₂³×C₇	1	1	yes	characteristic
874	#117	C₂³×C₇	1	2	yes	—
875	C₂×C₄⋊C₄	—	2	1	no	—
876	C₂×C₄⋊C₄	—	2	1	no	—
877	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
878	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
879	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
880	C₂×C₂²⋊C₄	—	2	1	no	—
881	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
882	C₂×C₄²	C₂³×C₇	1	2	yes	—
883	C₄⋊C₈	C₂³×C₇	1	2	yes	—
884	C₄⋊C₈	C₂³×C₇	1	2	yes	—
885	C₄⋊C₈	C₂³×C₇	1	2	yes	—
886	C₄⋊C₈	C₂³×C₇	1	2	yes	—
887	#103	C₂³×C₇	1	2	yes	—
888	#103	C₂³×C₇	1	2	yes	—
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	1	yes	characteristic
893	#103	C₂³×C₇	1	2	yes	—
894	#103	C₂³×C₇	1	2	yes	—
895	#103	C₂³×C₇	1	2	yes	—
896	#103	C₂³×C₇	1	2	yes	—
897	#102	C₂³×C₇	1	2	yes	—
898	#102	C₂³×C₇	1	2	yes	—
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	1	yes	characteristic
903	#102	C₂³×C₇	1	2	yes	—
904	#102	C₂³×C₇	1	2	yes	—
905	#102	C₂³×C₇	1	2	yes	—
906	#102	C₂³×C₇	1	2	yes	—
907	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
908	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
909	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
910	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
911	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
912	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
913	#97	C₂³×C₇	1	2	yes	—
914	#97	C₂³×C₇	1	2	yes	—
915	C₄×C₈	C₂³×C₇	1	2	yes	—
916	C₄×C₈	C₂³×C₇	1	2	yes	—
917	C₂²×C₇	—	2	1	no	—
918	C₂²×C₇	—	2	1	no	—
919	C₂²×C₇	—	2	1	no	—
920	C₂²×C₇	—	2	1	no	—
921	C₂²×C₇	—	2	1	no	—
922	C₂²×C₇	—	2	1	no	—
923	C₂²×C₇	—	2	1	no	—
924	C₂²×C₇	—	2	1	no	—
925	C₂²×C₇	—	4	1	no	—
926	C₂²×C₇	—	4	2	no	—
927	C₂²×C₇	—	4	1	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	—	4	1	no	—
935	C₂²×C₇	—	4	1	no	—
936	C₂²×C₇	—	4	1	no	—
937	C₂²×C₇	—	8	2	no	—
938	C₂²×C₇	—	8	4	no	—
939	C₂²×C₇	—	8	4	no	—
940	C₂²×C₇	#535	1	2	yes	—
941	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
942	C₄×C₇	—	2	2	no	—
943	C₄×C₇	—	2	2	no	—
944	C₄×C₇	—	2	2	no	—
945	C₄×C₇	—	2	2	no	—
946	C₄×C₇	—	2	1	no	—
947	C₄×C₇	—	2	1	no	—
948	C₄×C₇	—	4	2	no	—
949	C₄×C₇	—	4	1	no	—
950	C₄×C₇	—	4	1	no	—
951	C₄×C₇	—	4	2	no	—
952	C₄×C₇	—	4	1	no	—
953	C₄×C₇	—	4	1	no	—
954	C₄×C₇	—	4	1	no	—
955	C₄×C₇	—	4	2	no	—
956	C₄×C₇	#535	1	2	yes	—
957	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
958	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
959	C₂⁴	—	2	1	no	—
960	C₂⁴	—	2	1	no	—
961	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
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	—	2	2	no	—
968	#41	—	4	2	no	—
969	#41	—	4	2	no	—
970	#41	—	4	2	no	—
971	#41	—	4	1	no	—
972	#41	—	4	1	no	—
973	#41	—	4	2	no	—
974	#41	—	4	1	no	—
975	#41	—	4	1	no	—
976	#41	—	4	4	no	—
977	#41	—	4	4	no	—
978	#41	—	4	4	no	—
979	#41	—	4	4	no	—
980	C₂×Q₈	—	2	1	no	—
981	C₂×Q₈	—	2	1	no	—
982	C₂×Q₈	—	2	1	no	—
983	C₂×Q₈	—	2	2	no	—
984	C₂×Q₈	—	2	2	no	—
985	C₂×Q₈	—	2	2	no	—
986	C₂×Q₈	—	2	2	no	—
987	C₂×Q₈	—	2	2	no	—
988	C₂×Q₈	—	4	1	no	—
989	C₂×Q₈	—	4	1	no	—
990	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
991	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
992	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
993	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
994	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
995	C₂×D₄	—	2	1	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	1	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	1	no	—
1006	C₂×D₄	—	2	2	no	—
1007	C₂×D₄	—	2	2	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	2	2	no	—
1010	C₂×D₄	—	2	2	no	—
1011	C₂×D₄	—	2	2	no	—
1012	C₂×D₄	—	4	1	no	—
1013	C₂×D₄	—	4	1	no	—
1014	C₂×D₄	—	4	4	no	—
1015	C₂×D₄	—	4	4	no	—
1016	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1017	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1018	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1019	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1020	C₂²×C₄	—	2	2	no	—
1021	C₂²×C₄	—	2	2	no	—
1022	C₂²×C₄	—	2	1	no	—
1023	C₂²×C₄	—	2	1	no	—
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	1	no	—
1026	C₂²×C₄	—	2	1	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	2	no	—
1029	C₂²×C₄	—	2	1	no	—
1030	C₂²×C₄	—	2	2	no	—
1031	C₂²×C₄	—	2	1	no	—
1032	C₂²×C₄	—	2	1	no	—
1033	C₂²×C₄	—	2	2	no	—
1034	C₂²×C₄	—	4	4	no	—
1035	C₂²×C₄	—	4	4	no	—
1036	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1037	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1038	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1039	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
1040	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
1041	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1042	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1043	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1044	Q₁₆	—	4	2	no	—
1045	Q₁₆	—	4	2	no	—
1046	Q₁₆	—	4	1	no	—
1047	Q₁₆	—	4	1	no	—
1048	Q₁₆	—	4	2	no	—
1049	Q₁₆	—	4	2	no	—
1050	Q₁₆	—	4	2	no	—
1051	SD₁₆	—	4	2	no	—
1052	SD₁₆	—	4	2	no	—
1053	SD₁₆	—	4	1	no	—
1054	SD₁₆	—	4	1	no	—
1055	SD₁₆	—	4	1	no	—
1056	SD₁₆	—	4	1	no	—
1057	SD₁₆	—	4	2	no	—
1058	SD₁₆	—	4	2	no	—
1059	SD₁₆	—	4	2	no	—
1060	SD₁₆	—	4	2	no	—
1061	D₈	—	4	1	no	—
1062	D₈	—	4	1	no	—
1063	D₈	—	4	2	no	—
1064	M₁₆	—	2	2	no	—
1065	M₁₆	—	2	2	no	—
1066	C₂×C₈	—	2	2	no	—
1067	C₂×C₈	—	2	2	no	—
1068	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1069	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1070	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1071	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1072	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1073	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	2	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	2	no	—
1079	C₄⋊C₄	—	2	2	no	—
1080	C₄⋊C₄	—	2	2	no	—
1081	C₄⋊C₄	—	2	2	no	—
1082	C₄⋊C₄	—	2	2	no	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	2	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	1	no	—
1090	C₄⋊C₄	—	2	2	no	—
1091	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1092	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1093	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1094	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1095	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1096	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1097	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1098	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1099	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	1	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	2	no	—
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	2	no	—
1118	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1119	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1120	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1121	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1122	C₄²	—	2	2	no	—
1123	C₄²	—	2	2	no	—
1124	C₄²	—	2	2	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	C₂×C₇×D₄	1	2	yes	—
1127	C₄²	C₂×C₇×D₄	1	2	yes	—
1128	C₄²	C₂⁴×C₇	1	2	yes	—
1129	C₄²	C₂⁴×C₇	1	2	yes	—
1130	C₂×C₇	—	2	2	no	—
1131	C₂×C₇	—	4	1	no	—
1132	C₂×C₇	—	4	1	no	—
1133	C₂×C₇	—	8	1	no	—
1134	C₂×C₇	—	8	2	no	—
1135	C₂×C₇	—	8	1	no	—
1136	C₂×C₇	—	8	1	no	—
1137	C₂×C₇	C₂×#535	1	1	yes	characteristic
1138	C₂×C₇	#3584	1	1	yes	characteristic
1139	C₂×C₇	#3586	1	1	yes	characteristic
1140	C₂³	—	2	2	no	—
1141	C₂³	—	2	1	no	—
1142	C₂³	—	2	2	no	—
1143	C₂³	—	2	1	no	—
1144	C₂³	—	2	1	no	—
1145	C₂³	—	4	1	no	—
1146	C₂³	—	4	1	no	—
1147	C₂³	—	4	2	no	—
1148	C₂³	—	4	2	no	—
1149	C₂³	—	8	1	no	—
1150	C₂³	—	8	1	no	—
1151	C₂³	—	8	1	no	—
1152	C₂³	—	8	1	no	—
1153	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1154	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1155	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1156	Q₈	—	2	2	no	—
1157	Q₈	—	2	1	no	—
1158	Q₈	—	2	2	no	—
1159	Q₈	—	2	1	no	—
1160	Q₈	—	2	2	no	—
1161	Q₈	—	2	1	no	—
1162	Q₈	—	2	1	no	—
1163	Q₈	—	2	2	no	—
1164	Q₈	—	2	1	no	—
1165	Q₈	—	2	1	no	—
1166	Q₈	—	4	2	no	—
1167	Q₈	—	4	2	no	—
1168	Q₈	—	4	2	no	—
1169	Q₈	—	8	2	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	2	1	no	—
1172	D₄	—	2	2	no	—
1173	D₄	—	2	1	no	—
1174	D₄	—	2	1	no	—
1175	D₄	—	2	2	no	—
1176	D₄	—	2	1	no	—
1177	D₄	—	2	1	no	—
1178	D₄	—	4	2	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	4	no	—
1181	D₄	—	4	4	no	—
1182	D₄	—	4	2	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	2	no	—
1186	D₄	—	4	2	no	—
1187	D₄	—	4	2	no	—
1188	D₄	—	8	2	no	—
1189	D₄	—	8	2	no	—
1190	D₄	—	8	2	no	—
1191	D₄	—	8	2	no	—
1192	D₄	—	8	1	no	—
1193	C₂×C₄	—	2	2	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	2	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	2	no	—
1205	C₂×C₄	—	2	2	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	4	2	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	4	4	no	—
1211	C₂×C₄	—	4	2	no	—
1212	C₂×C₄	—	4	2	no	—
1213	C₂×C₄	—	4	4	no	—
1214	C₂×C₄	—	4	2	no	—
1215	C₂×C₄	—	4	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	—	8	2	no	—
1221	C₂×C₄	—	8	1	no	—
1222	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1223	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1224	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1225	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1226	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1227	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1228	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1229	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1230	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1231	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1232	C₈	—	2	1	no	—
1233	C₈	—	2	1	no	—
1234	C₈	—	2	1	no	—
1235	C₈	—	2	1	no	—
1236	C₈	—	2	2	no	—
1237	C₈	—	2	2	no	—
1238	C₇	#60816	1	1	yes	characteristic, direct product factor, Sylow
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	1	no	—
1241	C₂²	—	2	1	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	1	no	—
1246	C₂²	—	2	1	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	2	no	—
1249	C₂²	—	4	1	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	1	no	—
1255	C₂²	—	4	2	no	—
1256	C₂²	—	4	1	no	—
1257	C₂²	—	4	1	no	—
1258	C₂²	—	4	1	no	—
1259	C₂²	—	8	2	no	—
1260	C₂²	—	8	4	no	—
1261	C₂²	—	8	4	no	—
1262	C₂²	C₇×#535	1	2	yes	—
1263	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1264	C₄	—	2	2	no	—
1265	C₄	—	2	2	no	—
1266	C₄	—	2	2	no	—
1267	C₄	—	2	2	no	—
1268	C₄	—	2	1	no	—
1269	C₄	—	2	1	no	—
1270	C₄	—	4	2	no	—
1271	C₄	—	4	1	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	2	no	—
1274	C₄	—	4	1	no	—
1275	C₄	—	4	1	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	2	no	—
1278	C₄	C₇×#535	1	2	yes	—
1279	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1280	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1281	C₂	—	2	2	no	—
1282	C₂	—	4	1	no	—
1283	C₂	—	4	1	no	—
1284	C₂	—	8	2	no	—
1285	C₂	—	8	1	no	—
1286	C₂	—	8	1	no	—
1287	C₂	—	8	1	no	—
1288	C₂	C₂×C₇×#535	1	1	yes	characteristic
1289	C₂	C₇×#3584	1	1	yes	characteristic
1290	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 ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3495	C₂	semidirect
2. C₇×#3449	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×#3216	C₂	semidirect
9. C₇×#3212	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×#3046	C₂	semidirect
16. C₇×#3045	C₂	semidirect
17. C₇×#3044	C₂	semidirect
18. C₇×#3043	C₂	semidirect
19. C₇×#3007	C₂	semidirect
20. C₇×#3005	C₂	semidirect
21. C₇×#3002	C₂	semidirect
22. C₂×C₇×#452	C₂	semidirect
23. C₇×#2924	C₂	semidirect
28. C₂×C₇×#137	C₂²	semidirect
29. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
32. C₂²×C₇×Q₁₆	C₂²	semidirect
33. C₂²×C₇×SD₁₆	C₂²	semidirect
40. C₇×#544	C₂²	semidirect
41. C₇×#542	C₂²	semidirect
42. C₇×#541	C₂²	semidirect
48. C₇×#536	C₂²	semidirect
53. C₇×#533	C₂²	semidirect
56. C₇×#529	C₂²	semidirect
62. C₇×#520	C₂²	semidirect
63. C₇×#519	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×#463	C₂²	semidirect
88. C₇×#463	C₂²	semidirect
89. C₇×#462	C₂²	semidirect
90. C₇×#462	C₂²	semidirect
91. C₇×#462	C₂²	semidirect
92. C₇×#461	C₂²	semidirect
93. C₇×#460	C₂²	semidirect
94. C₇×#460	C₂²	semidirect
95. C₇×#460	C₂²	semidirect
96. C₇×#459	C₂²	semidirect
100. C₇×#452	C₂²	semidirect
101. C₇×#452	C₂²	semidirect
102. C₇×#452	C₂²	semidirect
103. C₇×#452	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×#450	C₂²	semidirect
110. C₇×#450	C₂²	semidirect
112. C₇×#449	C₂²	semidirect
113. C₇×#449	C₂²	semidirect
114. C₇×#449	C₂²	semidirect
115. 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×#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. #60816	C₇	direct (N × H)
325. #3495	C₂×C₇	semidirect
326. #3449	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. #3216	C₂×C₇	semidirect
333. #3212	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. #3046	C₂×C₇	semidirect
340. #3045	C₂×C₇	semidirect
341. #3044	C₂×C₇	semidirect
342. #3043	C₂×C₇	semidirect
343. #3007	C₂×C₇	semidirect
344. #3005	C₂×C₇	semidirect
345. #3002	C₂×C₇	semidirect
346. C₂×#452	C₂×C₇	semidirect
347. #2924	C₂×C₇	semidirect
523. C₂×#137	C₂²×C₇	semidirect
524. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
527. C₂²×Q₁₆	C₂²×C₇	semidirect
528. C₂²×SD₁₆	C₂²×C₇	semidirect
535. #544	C₂²×C₇	semidirect
536. #542	C₂²×C₇	semidirect
537. #541	C₂²×C₇	semidirect
543. #536	C₂²×C₇	semidirect
548. #533	C₂²×C₇	semidirect
551. #529	C₂²×C₇	semidirect
557. #520	C₂²×C₇	semidirect
558. #519	C₂²×C₇	semidirect
560. #497	C₂²×C₇	semidirect
561. #497	C₂²×C₇	semidirect
562. #497	C₂²×C₇	semidirect
563. #496	C₂²×C₇	semidirect
564. #495	C₂²×C₇	semidirect
565. #495	C₂²×C₇	semidirect
566. #494	C₂²×C₇	semidirect
567. #492	C₂²×C₇	semidirect
568. #491	C₂²×C₇	semidirect
569. #490	C₂²×C₇	semidirect
570. #489	C₂²×C₇	semidirect
571. #489	C₂²×C₇	semidirect
572. #488	C₂²×C₇	semidirect
573. #488	C₂²×C₇	semidirect
574. #487	C₂²×C₇	semidirect
575. #486	C₂²×C₇	semidirect
576. #464	C₂²×C₇	semidirect
577. #464	C₂²×C₇	semidirect
578. #464	C₂²×C₇	semidirect
579. #464	C₂²×C₇	semidirect
580. #464	C₂²×C₇	semidirect
581. #464	C₂²×C₇	semidirect
582. #463	C₂²×C₇	semidirect
583. #463	C₂²×C₇	semidirect
584. #462	C₂²×C₇	semidirect
585. #462	C₂²×C₇	semidirect
586. #462	C₂²×C₇	semidirect
587. #461	C₂²×C₇	semidirect
588. #460	C₂²×C₇	semidirect
589. #460	C₂²×C₇	semidirect
590. #460	C₂²×C₇	semidirect
591. #459	C₂²×C₇	semidirect
595. #452	C₂²×C₇	semidirect
596. #452	C₂²×C₇	semidirect
597. #452	C₂²×C₇	semidirect
598. #452	C₂²×C₇	semidirect
599. #452	C₂²×C₇	semidirect
600. #452	C₂²×C₇	semidirect
601. #452	C₂²×C₇	semidirect
602. #451	C₂²×C₇	semidirect
603. #451	C₂²×C₇	semidirect
604. #450	C₂²×C₇	semidirect
605. #450	C₂²×C₇	semidirect
607. #449	C₂²×C₇	semidirect
608. #449	C₂²×C₇	semidirect
609. #449	C₂²×C₇	semidirect
610. #448	C₂²×C₇	semidirect
611. #447	C₂²×C₇	semidirect
612. #433	C₂²×C₇	semidirect
613. #433	C₂²×C₇	semidirect
614. #432	C₂²×C₇	semidirect
615. #431	C₂²×C₇	semidirect
616. #424	C₂²×C₇	semidirect
617. #424	C₂²×C₇	semidirect
618. #419	C₂²×C₇	semidirect
619. #418	C₂²×C₇	semidirect
624. C₂×#103	C₂²×C₇	semidirect
625. C₂×#102	C₂²×C₇	semidirect
628. #405	C₂²×C₇	semidirect
629. #405	C₂²×C₇	semidirect
1238. C₇	#60816	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3495	2
C₇×#3449	2
C₇×#3225	2
C₇×#3224	2
C₇×#3223	2
C₇×#3222	2
C₇×#3219	2
C₇×#3216	2
C₇×#3212	2
C₇×#3210	2
C₇×#3156	2
C₇×#3154	2
C₇×#3137	2
C₇×#3136	2
C₇×#3046	2
C₇×#3045	2
C₇×#3044	2
C₇×#3043	2
C₇×#3007	2
C₇×#3005	2
C₇×#3002	2
C₂×C₇×#452	2
C₇×#2924	2
#60816	7

Subgroups — C7×#60816 #13238032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60816 #13238032