Subgroups — C₇×#60976 #13238192

Order 1792.

1792 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#542	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3262	C₂	1	2	yes	maximal, complemented
4	C₇×#3257	C₂	1	2	yes	maximal, complemented
5	C₇×#3243	C₂	1	2	yes	maximal, complemented
6	C₇×#3238	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3224	C₂	1	2	yes	maximal, complemented
9	C₇×#3213	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3211	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3194	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3193	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3190	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3186	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3179	C₂	1	2	yes	maximal, complemented
16	C₇×#3175	C₂	1	2	yes	maximal, complemented
17	C₇×#3124	C₂	1	2	yes	maximal, complemented
18	C₇×#3118	C₂	1	2	yes	maximal, complemented
19	C₇×#3114	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#555	—	2	1	no	—
25	C₇×#553	—	2	1	no	—
26	C₇×#553	—	2	1	no	—
27	C₇×#551	—	2	1	no	—
28	C₇×#551	—	2	1	no	—
29	C₇×#547	—	2	1	no	—
30	C₇×#546	—	2	1	no	—
31	C₇×#546	—	2	1	no	—
32	C₇×#544	C₂²	1	1	yes	characteristic, complemented
33	C₇×#542	—	2	1	no	—
34	C₇×#542	—	2	1	no	—
35	C₇×#542	—	2	1	no	—
36	C₇×#542	—	2	1	no	—
37	C₇×#542	C₂²	1	2	yes	—
38	C₇×#542	C₂²	1	2	yes	—
39	C₇×#542	C₂²	1	1	yes	characteristic, complemented
40	C₇×#542	C₂²	1	2	yes	complemented
41	C₇×#542	C₂²	1	2	yes	complemented
42	C₇×#542	C₂²	1	1	yes	characteristic, complemented
43	C₇×#540	C₂²	1	1	yes	characteristic, complemented
44	C₇×#540	C₂²	1	1	yes	characteristic, complemented
45	C₇×#535	C₂²	1	1	yes	characteristic, complemented
46	C₇×#532	C₂²	1	1	yes	characteristic
47	C₇×#532	C₂²	1	1	yes	characteristic
48	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₇×#529	C₂²	1	1	yes	characteristic
50	C₇×#529	C₂²	1	1	yes	characteristic
51	C₂×C₇×#126	—	2	1	no	—
52	C₂×C₇×#124	—	2	1	no	—
53	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
54	C₇×#525	C₂²	1	1	yes	characteristic
55	C₂×C₇×#123	—	2	1	no	—
56	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
57	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₇×#121	C₂²	1	1	yes	characteristic
59	C₂×C₇×#121	C₂²	1	1	yes	characteristic
60	C₇×#520	C₂²	1	1	yes	characteristic, complemented
61	C₇×#518	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₇×#117	C₂²	1	1	yes	characteristic
65	C₇×#501	C₂²	1	2	yes	complemented
66	C₇×#500	C₂²	1	2	yes	complemented
67	C₇×#496	C₂²	1	2	yes	complemented
68	C₇×#495	C₂²	1	2	yes	complemented
69	C₇×#489	C₂²	1	2	yes	complemented
70	C₇×#489	C₂²	1	2	yes	complemented
71	C₇×#488	C₂²	1	2	yes	complemented
72	C₇×#486	C₂²	1	2	yes	complemented
73	C₇×#485	C₂²	1	2	yes	complemented
74	C₇×#484	C₂²	1	2	yes	complemented
75	C₇×#483	C₂²	1	1	yes	characteristic, complemented
76	C₇×#483	C₂²	1	1	yes	characteristic, complemented
77	C₇×#482	C₂²	1	2	yes	—
78	C₇×#480	C₂²	1	1	yes	characteristic
79	C₇×#480	C₂²	1	1	yes	characteristic
80	C₇×#480	C₂²	1	2	yes	—
81	C₇×#480	C₂²	1	1	yes	characteristic
82	C₇×#480	C₂²	1	1	yes	characteristic
83	C₇×#480	C₂²	1	1	yes	characteristic, complemented
84	C₇×#480	C₂²	1	1	yes	characteristic, complemented
85	C₇×#479	C₂²	1	2	yes	complemented
86	C₇×#478	C₂²	1	2	yes	complemented
87	C₇×#477	C₂²	1	2	yes	complemented
88	C₇×#477	C₂²	1	2	yes	complemented
89	C₇×#476	C₂²	1	2	yes	complemented
90	C₇×#474	C₂²	1	2	yes	complemented
91	C₇×#474	C₂²	1	2	yes	complemented
92	C₇×#474	C₂²	1	2	yes	complemented
93	C₇×#469	C₂²	1	2	yes	complemented
94	C₇×#468	C₂²	1	2	yes	complemented
95	C₇×#468	C₂²	1	2	yes	complemented
96	C₇×#468	C₂²	1	2	yes	complemented
97	C₇×#467	C₂²	1	2	yes	complemented
98	C₇×#466	C₂²	1	2	yes	—
99	C₇×#466	C₂²	1	2	yes	—
100	C₇×#465	C₂²	1	2	yes	complemented
101	C₇×#464	C₂²	1	2	yes	complemented
102	C₇×#464	C₂²	1	2	yes	complemented
103	C₇×#463	C₂²	1	2	yes	complemented
104	C₇×#463	C₂²	1	2	yes	complemented
105	C₇×#463	C₂²	1	2	yes	complemented
106	C₇×#463	C₂²	1	2	yes	complemented
107	C₇×#460	C₂²	1	2	yes	complemented
108	C₇×#459	C₂²	1	2	yes	complemented
109	C₇×#452	C₂²	1	2	yes	complemented
110	C₇×#451	C₂²	1	1	yes	characteristic, complemented
111	C₇×#450	C₂²	1	2	yes	complemented
112	C₇×#450	C₂²	1	1	yes	characteristic, complemented
113	C₇×#449	C₂²	1	2	yes	—
114	C₇×#448	C₂²	1	1	yes	characteristic
115	C₇×#448	C₂²	1	1	yes	characteristic
116	C₇×#448	C₂²	1	1	yes	characteristic, complemented
117	C₇×#447	C₂²	1	1	yes	characteristic
118	C₇×#447	C₂²	1	1	yes	characteristic
119	C₇×#447	C₂²	1	2	yes	—
120	C₇×#447	C₂²	1	1	yes	characteristic, complemented
121	C₇×#442	C₂²	1	2	yes	complemented
122	C₇×#440	C₂²	1	2	yes	complemented
123	C₇×#440	C₂²	1	2	yes	complemented
124	C₇×#440	C₂²	1	2	yes	complemented
125	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
126	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
127	C₄×C₇×D₈	C₂²	1	2	yes	complemented
128	C₄×C₇×D₈	C₂²	1	2	yes	complemented
129	C₇×#433	C₂²	1	2	yes	complemented
130	C₇×#433	C₂²	1	2	yes	complemented
131	C₇×#432	C₂²	1	1	yes	characteristic, complemented
132	C₇×#432	C₂²	1	1	yes	characteristic, complemented
133	C₇×#431	C₂²	1	1	yes	characteristic, complemented
134	C₇×#431	C₂²	1	1	yes	characteristic, complemented
135	C₇×#424	C₂²	1	2	yes	complemented
136	C₇×#407	C₂²	1	1	yes	characteristic
137	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
138	C₇×#405	C₂²	1	2	yes	complemented
139	#60976	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂×C₇×#41	—	2	1	no	—
141	C₂×C₇×#41	—	2	1	no	—
142	C₂×C₇×#41	C₂³	1	1	yes	characteristic
143	C₂²×C₇×Q₈	—	2	1	no	—
144	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
145	C₂²×C₇×D₄	—	2	1	no	—
146	C₂²×C₇×D₄	—	2	1	no	—
147	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
148	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₇	—	2	1	no	—
150	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
151	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
152	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₇×D₈	C₂³	1	2	yes	—
157	C₂×C₇×D₈	C₂³	1	2	yes	—
158	C₂×C₇×D₈	C₂³	1	2	yes	—
159	C₂×C₇×M₁₆	C₂³	1	2	yes	—
160	C₂²×C₇×C₈	C₂³	1	2	yes	—
161	C₇×C₄⋊Q₈	—	2	1	no	—
162	C₇×C₄⋊Q₈	—	2	1	no	—
163	C₇×C₄⋊Q₈	—	2	1	no	—
164	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₇×#127	C₂³	1	1	yes	characteristic
169	C₇×#127	C₂³	1	1	yes	characteristic
170	C₇×#126	—	2	2	no	—
171	C₇×#126	—	2	2	no	—
172	C₇×#126	—	2	2	no	—
173	C₇×#126	—	2	2	no	—
174	C₇×#126	—	2	1	no	—
175	C₇×#126	—	2	1	no	—
176	C₇×#126	—	2	1	no	—
177	C₇×#126	—	2	1	no	—
178	C₇×#125	—	2	1	no	—
179	C₇×#125	C₂³	1	1	yes	characteristic
180	C₇×#125	C₂³	1	1	yes	characteristic
181	C₇×#124	—	2	2	no	—
182	C₇×#124	—	2	2	no	—
183	C₇×#124	—	2	2	no	—
184	C₇×#124	—	2	2	no	—
185	C₇×#124	—	2	1	no	—
186	C₇×#124	—	2	1	no	—
187	C₇×#124	—	2	1	no	—
188	C₇×#124	—	2	1	no	—
189	C₇×#124	—	2	1	no	—
190	C₇×#124	—	2	1	no	—
191	C₇×#124	C₂³	1	2	yes	—
192	C₇×#124	C₂³	1	1	yes	characteristic
193	C₇×#124	C₂³	1	2	yes	—
194	C₇×#124	C₂³	1	1	yes	characteristic
195	C₇×#123	—	2	1	no	—
196	C₇×#123	—	2	1	no	—
197	C₇×#123	—	2	1	no	—
198	C₇×#123	—	2	1	no	—
199	C₇×#123	—	2	1	no	—
200	C₇×#123	—	2	1	no	—
201	C₇×#123	—	2	1	no	—
202	C₇×#123	—	2	2	no	—
203	C₇×#123	—	2	2	no	—
204	C₇×#123	—	2	2	no	—
205	C₇×#123	—	2	2	no	—
206	C₇×#123	—	2	1	no	—
207	C₇×#123	—	2	1	no	—
208	C₇×C₂²⋊Q₈	—	2	1	no	—
209	C₇×C₂²⋊Q₈	—	2	1	no	—
210	C₇×C₂²⋊Q₈	—	2	2	no	—
211	C₇×C₂²⋊Q₈	—	2	2	no	—
212	C₇×C₂²⋊Q₈	—	2	2	no	—
213	C₇×C₂²⋊Q₈	—	2	2	no	—
214	C₇×C₂²⋊Q₈	—	2	1	no	—
215	C₇×C₂²⋊Q₈	—	2	1	no	—
216	C₇×C₂²⋊Q₈	—	2	1	no	—
217	C₇×C₂²⋊Q₈	—	2	1	no	—
218	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₇×#121	—	2	1	no	—
223	C₇×#121	—	2	1	no	—
224	C₇×#121	—	2	1	no	—
225	C₇×#121	—	2	1	no	—
226	C₇×#121	—	2	1	no	—
227	C₇×#121	—	2	1	no	—
228	C₇×#121	—	2	1	no	—
229	C₇×#121	—	2	1	no	—
230	C₇×#121	—	2	1	no	—
231	C₇×#121	—	2	1	no	—
232	C₇×#121	—	2	1	no	—
233	C₇×#121	—	2	1	no	—
234	C₇×#121	C₂³	1	1	yes	characteristic
235	C₇×#121	C₂³	1	1	yes	characteristic
236	C₇×#121	C₂³	1	2	yes	—
237	C₇×#121	C₂³	1	1	yes	characteristic
238	C₇×#121	C₂³	1	1	yes	characteristic
239	C₇×#121	C₂³	1	1	yes	characteristic
240	C₇×#121	C₂³	1	2	yes	—
241	C₇×#121	C₂³	1	1	yes	characteristic
242	C₇×#120	—	2	1	no	—
243	C₇×#120	—	2	1	no	—
244	C₇×#120	—	2	1	no	—
245	C₄×C₇×Q₈	—	2	1	no	—
246	C₄×C₇×Q₈	—	2	1	no	—
247	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
248	C₄×C₇×Q₈	C₂³	1	2	yes	—
249	C₄×C₇×Q₈	C₂³	1	2	yes	—
250	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
251	C₄×C₇×D₄	—	2	1	no	—
252	C₄×C₇×D₄	—	2	1	no	—
253	C₄×C₇×D₄	—	2	1	no	—
254	C₄×C₇×D₄	—	2	1	no	—
255	C₄×C₇×D₄	—	2	1	no	—
256	C₄×C₇×D₄	—	2	1	no	—
257	C₄×C₇×D₄	—	2	1	no	—
258	C₄×C₇×D₄	—	2	1	no	—
259	C₄×C₇×D₄	—	2	1	no	—
260	C₄×C₇×D₄	—	2	1	no	—
261	C₄×C₇×D₄	—	2	1	no	—
262	C₄×C₇×D₄	—	2	1	no	—
263	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
264	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
265	C₄×C₇×D₄	C₂³	1	2	yes	—
266	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
267	C₄×C₇×D₄	C₂³	1	2	yes	—
268	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
269	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
270	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
271	C₇×#117	—	2	1	no	—
272	C₇×#117	—	2	1	no	—
273	C₇×#117	—	2	1	no	—
274	C₇×#117	D₄	1	1	yes	characteristic
275	C₇×#117	D₄	1	1	yes	characteristic
276	C₇×#117	D₄	1	1	yes	characteristic
277	C₇×#117	D₄	1	1	yes	characteristic
278	C₇×#117	C₂³	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	1	yes	characteristic
283	C₂×C₇×C₄⋊C₄	—	2	1	no	—
284	C₂×C₇×C₄⋊C₄	—	2	1	no	—
285	C₂×C₇×C₄⋊C₄	—	2	1	no	—
286	C₂×C₇×C₄⋊C₄	—	2	1	no	—
287	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
288	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
289	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
292	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
301	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
302	C₂×C₄²×C₇	—	2	1	no	—
303	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
304	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
305	C₇×#107	C₂³	1	2	yes	—
306	C₇×#107	C₂³	1	2	yes	—
307	C₇×#107	C₂³	1	2	yes	—
308	C₇×#107	C₂³	1	2	yes	—
309	C₇×#107	C₂³	1	2	yes	—
310	C₇×#107	C₂³	1	2	yes	—
311	C₇×#106	C₂³	1	2	yes	—
312	C₇×#106	C₂³	1	2	yes	—
313	C₇×C₄⋊C₈	C₂³	1	2	yes	—
314	C₇×C₄⋊C₈	C₂³	1	2	yes	—
315	C₇×C₄⋊C₈	C₂³	1	2	yes	—
316	C₇×C₄⋊C₈	C₂³	1	2	yes	—
317	C₇×#103	C₂³	1	2	yes	—
318	C₇×#103	C₂³	1	2	yes	—
319	C₇×#103	C₂³	1	2	yes	—
320	C₇×#103	C₂³	1	2	yes	—
321	C₇×#103	C₂³	1	2	yes	—
322	C₇×#103	C₂³	1	2	yes	—
323	C₇×#102	C₂³	1	2	yes	—
324	C₇×#102	C₂³	1	2	yes	—
325	C₇×#102	C₂³	1	2	yes	—
326	C₇×#102	C₂³	1	2	yes	—
327	C₇×#102	C₂³	1	2	yes	—
328	C₇×#102	C₂³	1	2	yes	—
329	C₇×#102	C₂³	1	2	yes	—
330	C₇×#102	C₂³	1	2	yes	—
331	C₇×#102	C₂³	1	2	yes	—
332	C₇×#102	C₂³	1	2	yes	—
333	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
334	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
335	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
336	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
337	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
339	C₇×#97	C₂³	1	2	yes	—
340	C₇×#97	C₂³	1	2	yes	—
341	C₄×C₇×C₈	C₂³	1	2	yes	—
342	C₄×C₇×C₈	C₂³	1	2	yes	—
343	#3494	C₂×C₇	1	1	yes	characteristic, complemented
344	C₂×#542	C₂×C₇	1	1	yes	characteristic, complemented
345	#3262	C₂×C₇	1	2	yes	complemented
346	#3257	C₂×C₇	1	2	yes	complemented
347	#3243	C₂×C₇	1	2	yes	complemented
348	#3238	C₂×C₇	1	1	yes	characteristic, complemented
349	#3226	C₂×C₇	1	1	yes	characteristic, complemented
350	#3224	C₂×C₇	1	2	yes	complemented
351	#3213	C₂×C₇	1	1	yes	characteristic, complemented
352	#3211	C₂×C₇	1	1	yes	characteristic, complemented
353	#3194	C₂×C₇	1	1	yes	characteristic, complemented
354	#3193	C₂×C₇	1	1	yes	characteristic, complemented
355	#3190	C₂×C₇	1	1	yes	characteristic, complemented
356	#3186	C₂×C₇	1	1	yes	characteristic, complemented
357	#3179	C₂×C₇	1	2	yes	complemented
358	#3175	C₂×C₇	1	2	yes	complemented
359	#3124	C₂×C₇	1	2	yes	complemented
360	#3118	C₂×C₇	1	2	yes	complemented
361	#3114	C₂×C₇	1	1	yes	characteristic, complemented
362	#3112	C₂×C₇	1	1	yes	characteristic, complemented
363	#3108	C₂×C₇	1	1	yes	characteristic, complemented
364	#3100	C₂×C₇	1	1	yes	characteristic, complemented
365	#2924	C₂×C₇	1	1	yes	characteristic, complemented
366	C₂⁴×C₇	—	2	1	no	—
367	C₂⁴×C₇	—	2	1	no	—
368	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
369	C₇×#41	—	4	2	no	—
370	C₇×#41	—	8	2	no	—
371	C₇×#41	—	8	2	no	—
372	C₂×C₇×Q₈	—	2	1	no	—
373	C₂×C₇×Q₈	—	2	2	no	—
374	C₂×C₇×Q₈	—	2	2	no	—
375	C₂×C₇×Q₈	—	2	1	no	—
376	C₂×C₇×Q₈	—	2	1	no	—
377	C₂×C₇×Q₈	—	4	2	no	—
378	C₂×C₇×Q₈	—	8	2	no	—
379	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
380	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₇×D₄	—	2	1	no	—
382	C₂×C₇×D₄	—	2	1	no	—
383	C₂×C₇×D₄	—	2	1	no	—
384	C₂×C₇×D₄	—	2	1	no	—
385	C₂×C₇×D₄	—	2	1	no	—
386	C₂×C₇×D₄	—	2	1	no	—
387	C₂×C₇×D₄	—	2	1	no	—
388	C₂×C₇×D₄	—	2	2	no	—
389	C₂×C₇×D₄	—	2	2	no	—
390	C₂×C₇×D₄	—	2	1	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	1	no	—
396	C₂×C₇×D₄	—	4	2	no	—
397	C₂×C₇×D₄	—	4	2	no	—
398	C₂×C₇×D₄	—	8	2	no	—
399	C₂×C₇×D₄	—	8	2	no	—
400	C₂×C₇×D₄	C₂⁴	1	2	yes	—
401	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
402	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
403	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₇	—	2	1	no	—
405	C₂²×C₄×C₇	—	2	1	no	—
406	C₂²×C₄×C₇	—	2	1	no	—
407	C₂²×C₄×C₇	—	2	1	no	—
408	C₂²×C₄×C₇	—	2	1	no	—
409	C₂²×C₄×C₇	—	2	1	no	—
410	C₂²×C₄×C₇	—	2	1	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	2	no	—
416	C₂²×C₄×C₇	—	2	2	no	—
417	C₂²×C₄×C₇	—	4	2	no	—
418	C₂²×C₄×C₇	—	8	2	no	—
419	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
420	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
421	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
422	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
423	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
424	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
425	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
426	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
429	C₇×Q₁₆	—	4	2	no	—
430	C₇×SD₁₆	—	4	2	no	—
431	C₇×SD₁₆	—	4	2	no	—
432	C₇×SD₁₆	—	4	2	no	—
433	C₇×SD₁₆	—	4	2	no	—
434	C₇×D₈	—	4	2	no	—
435	C₇×D₈	—	4	2	no	—
436	C₇×D₈	—	4	2	no	—
437	C₇×M₁₆	—	4	2	no	—
438	C₂×C₇×C₈	—	4	2	no	—
439	C₂×C₇×C₈	C₂⁴	1	2	yes	—
440	C₂×C₇×C₈	C₂⁴	1	2	yes	—
441	C₂×C₇×C₈	C₂⁴	1	2	yes	—
442	C₂×C₇×C₈	C₂⁴	1	2	yes	—
443	C₇×C₄⋊C₄	—	2	1	no	—
444	C₇×C₄⋊C₄	—	2	1	no	—
445	C₇×C₄⋊C₄	—	2	1	no	—
446	C₇×C₄⋊C₄	—	2	2	no	—
447	C₇×C₄⋊C₄	—	2	2	no	—
448	C₇×C₄⋊C₄	—	2	2	no	—
449	C₇×C₄⋊C₄	—	2	2	no	—
450	C₇×C₄⋊C₄	—	2	2	no	—
451	C₇×C₄⋊C₄	—	2	2	no	—
452	C₇×C₄⋊C₄	—	2	1	no	—
453	C₇×C₄⋊C₄	—	2	1	no	—
454	C₇×C₄⋊C₄	—	2	1	no	—
455	C₇×C₄⋊C₄	—	2	1	no	—
456	C₇×C₄⋊C₄	—	2	1	no	—
457	C₇×C₄⋊C₄	—	2	1	no	—
458	C₇×C₄⋊C₄	—	2	1	no	—
459	C₇×C₄⋊C₄	—	2	1	no	—
460	C₇×C₄⋊C₄	—	2	1	no	—
461	C₇×C₄⋊C₄	—	2	1	no	—
462	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
463	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
464	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
465	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
466	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
467	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
468	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
469	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
470	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
471	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
472	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
473	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
474	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
475	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
476	C₇×C₂²⋊C₄	—	2	1	no	—
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	1	no	—
481	C₇×C₂²⋊C₄	—	2	1	no	—
482	C₇×C₂²⋊C₄	—	2	1	no	—
483	C₇×C₂²⋊C₄	—	2	1	no	—
484	C₇×C₂²⋊C₄	—	2	1	no	—
485	C₇×C₂²⋊C₄	—	2	1	no	—
486	C₇×C₂²⋊C₄	—	2	1	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	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	1	no	—
500	C₇×C₂²⋊C₄	—	2	1	no	—
501	C₇×C₂²⋊C₄	—	2	1	no	—
502	C₇×C₂²⋊C₄	—	2	1	no	—
503	C₇×C₂²⋊C₄	—	2	1	no	—
504	C₇×C₂²⋊C₄	—	2	1	no	—
505	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
506	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
507	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
508	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
509	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
510	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
511	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
512	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
513	C₄²×C₇	—	2	2	no	—
514	C₄²×C₇	—	2	2	no	—
515	C₄²×C₇	—	2	1	no	—
516	C₄²×C₇	—	2	1	no	—
517	C₄²×C₇	—	2	1	no	—
518	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
519	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
520	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
521	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
522	C₄²×C₇	C₂⁴	1	1	yes	characteristic
523	C₄²×C₇	C₂⁴	1	1	yes	characteristic
524	C₄²×C₇	C₂⁴	1	1	yes	characteristic
525	C₄²×C₇	C₂⁴	1	1	yes	characteristic
526	#555	—	2	1	no	—
527	#553	—	2	1	no	—
528	#553	—	2	1	no	—
529	#551	—	2	1	no	—
530	#551	—	2	1	no	—
531	#547	—	2	1	no	—
532	#546	—	2	1	no	—
533	#546	—	2	1	no	—
534	#544	C₂²×C₇	1	1	yes	characteristic, complemented
535	#542	—	2	1	no	—
536	#542	—	2	1	no	—
537	#542	—	2	1	no	—
538	#542	—	2	1	no	—
539	#542	C₂²×C₇	1	2	yes	—
540	#542	C₂²×C₇	1	2	yes	—
541	#542	C₂²×C₇	1	1	yes	characteristic, complemented
542	#542	C₂²×C₇	1	2	yes	complemented
543	#542	C₂²×C₇	1	2	yes	complemented
544	#542	C₂²×C₇	1	1	yes	characteristic, complemented
545	#540	C₂²×C₇	1	1	yes	characteristic, complemented
546	#540	C₂²×C₇	1	1	yes	characteristic, complemented
547	#535	C₂²×C₇	1	1	yes	characteristic, complemented
548	#532	C₂²×C₇	1	1	yes	characteristic
549	#532	C₂²×C₇	1	1	yes	characteristic
550	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
551	#529	C₂²×C₇	1	1	yes	characteristic
552	#529	C₂²×C₇	1	1	yes	characteristic
553	C₂×#126	—	2	1	no	—
554	C₂×#124	—	2	1	no	—
555	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
556	#525	C₂²×C₇	1	1	yes	characteristic
557	C₂×#123	—	2	1	no	—
558	C₂×C₂²⋊Q₈	—	2	1	no	—
559	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
560	C₂×#121	C₂²×C₇	1	1	yes	characteristic
561	C₂×#121	C₂²×C₇	1	1	yes	characteristic
562	#520	C₂²×C₇	1	1	yes	characteristic, complemented
563	#518	C₂²×C₇	1	1	yes	characteristic, complemented
564	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
565	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
566	C₂×#117	C₂²×C₇	1	1	yes	characteristic
567	#501	C₂²×C₇	1	2	yes	complemented
568	#500	C₂²×C₇	1	2	yes	complemented
569	#496	C₂²×C₇	1	2	yes	complemented
570	#495	C₂²×C₇	1	2	yes	complemented
571	#489	C₂²×C₇	1	2	yes	complemented
572	#489	C₂²×C₇	1	2	yes	complemented
573	#488	C₂²×C₇	1	2	yes	complemented
574	#486	C₂²×C₇	1	2	yes	complemented
575	#485	C₂²×C₇	1	2	yes	complemented
576	#484	C₂²×C₇	1	2	yes	complemented
577	#483	C₂²×C₇	1	1	yes	characteristic, complemented
578	#483	C₂²×C₇	1	1	yes	characteristic, complemented
579	#482	C₂²×C₇	1	2	yes	—
580	#480	C₂²×C₇	1	1	yes	characteristic
581	#480	C₂²×C₇	1	1	yes	characteristic
582	#480	C₂²×C₇	1	1	yes	characteristic
583	#480	C₂²×C₇	1	1	yes	characteristic
584	#480	C₂²×C₇	1	2	yes	—
585	#480	C₂²×C₇	1	1	yes	characteristic, complemented
586	#480	C₂²×C₇	1	1	yes	characteristic, complemented
587	#479	C₂²×C₇	1	2	yes	complemented
588	#478	C₂²×C₇	1	2	yes	complemented
589	#477	C₂²×C₇	1	2	yes	complemented
590	#477	C₂²×C₇	1	2	yes	complemented
591	#476	C₂²×C₇	1	2	yes	complemented
592	#474	C₂²×C₇	1	2	yes	complemented
593	#474	C₂²×C₇	1	2	yes	complemented
594	#474	C₂²×C₇	1	2	yes	complemented
595	#469	C₂²×C₇	1	2	yes	complemented
596	#468	C₂²×C₇	1	2	yes	complemented
597	#468	C₂²×C₇	1	2	yes	complemented
598	#468	C₂²×C₇	1	2	yes	complemented
599	#467	C₂²×C₇	1	2	yes	complemented
600	#466	C₂²×C₇	1	2	yes	—
601	#466	C₂²×C₇	1	2	yes	—
602	#465	C₂²×C₇	1	2	yes	complemented
603	#464	C₂²×C₇	1	2	yes	complemented
604	#464	C₂²×C₇	1	2	yes	complemented
605	#463	C₂²×C₇	1	2	yes	complemented
606	#463	C₂²×C₇	1	2	yes	complemented
607	#463	C₂²×C₇	1	2	yes	complemented
608	#463	C₂²×C₇	1	2	yes	complemented
609	#460	C₂²×C₇	1	2	yes	complemented
610	#459	C₂²×C₇	1	2	yes	complemented
611	#452	C₂²×C₇	1	2	yes	complemented
612	#451	C₂²×C₇	1	1	yes	characteristic, complemented
613	#450	C₂²×C₇	1	1	yes	characteristic, complemented
614	#450	C₂²×C₇	1	2	yes	complemented
615	#449	C₂²×C₇	1	2	yes	—
616	#448	C₂²×C₇	1	1	yes	characteristic
617	#448	C₂²×C₇	1	1	yes	characteristic
618	#448	C₂²×C₇	1	1	yes	characteristic, complemented
619	#447	C₂²×C₇	1	1	yes	characteristic
620	#447	C₂²×C₇	1	1	yes	characteristic
621	#447	C₂²×C₇	1	2	yes	—
622	#447	C₂²×C₇	1	1	yes	characteristic, complemented
623	#442	C₂²×C₇	1	2	yes	complemented
624	#440	C₂²×C₇	1	2	yes	complemented
625	#440	C₂²×C₇	1	2	yes	complemented
626	#440	C₂²×C₇	1	2	yes	complemented
627	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
628	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
629	C₄×D₈	C₂²×C₇	1	2	yes	complemented
630	C₄×D₈	C₂²×C₇	1	2	yes	complemented
631	#433	C₂²×C₇	1	2	yes	complemented
632	#433	C₂²×C₇	1	2	yes	complemented
633	#432	C₂²×C₇	1	1	yes	characteristic, complemented
634	#432	C₂²×C₇	1	1	yes	characteristic, complemented
635	#431	C₂²×C₇	1	1	yes	characteristic, complemented
636	#431	C₂²×C₇	1	1	yes	characteristic, complemented
637	#424	C₂²×C₇	1	2	yes	complemented
638	#407	C₂²×C₇	1	1	yes	characteristic
639	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
640	#405	C₂²×C₇	1	2	yes	complemented
641	C₂³×C₇	—	2	2	no	—
642	C₂³×C₇	—	2	2	no	—
643	C₂³×C₇	—	2	1	no	—
644	C₂³×C₇	—	2	1	no	—
645	C₂³×C₇	—	2	1	no	—
646	C₂³×C₇	—	4	1	no	—
647	C₂³×C₇	—	4	1	no	—
648	C₂³×C₇	—	4	2	no	—
649	C₂³×C₇	—	4	2	no	—
650	C₂³×C₇	—	4	2	no	—
651	C₂³×C₇	—	4	2	no	—
652	C₂³×C₇	—	8	1	no	—
653	C₂³×C₇	—	8	1	no	—
654	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
655	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
656	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
657	C₇×Q₈	—	2	2	no	—
658	C₇×Q₈	—	2	2	no	—
659	C₇×Q₈	—	2	2	no	—
660	C₇×Q₈	—	4	2	no	—
661	C₇×Q₈	—	8	2	no	—
662	C₇×Q₈	—	8	2	no	—
663	C₇×Q₈	—	8	1	no	—
664	C₇×Q₈	—	8	1	no	—
665	C₇×D₄	—	2	2	no	—
666	C₇×D₄	—	2	2	no	—
667	C₇×D₄	—	2	2	no	—
668	C₇×D₄	—	2	2	no	—
669	C₇×D₄	—	2	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	—	4	2	no	—
675	C₇×D₄	—	4	2	no	—
676	C₇×D₄	—	8	1	no	—
677	C₇×D₄	—	8	1	no	—
678	C₇×D₄	—	8	1	no	—
679	C₇×D₄	—	8	1	no	—
680	C₇×D₄	—	8	1	no	—
681	C₇×D₄	—	8	2	no	—
682	C₇×D₄	—	8	2	no	—
683	C₇×D₄	—	8	1	no	—
684	C₇×D₄	—	8	1	no	—
685	C₂×C₄×C₇	—	2	2	no	—
686	C₂×C₄×C₇	—	2	2	no	—
687	C₂×C₄×C₇	—	2	2	no	—
688	C₂×C₄×C₇	—	2	2	no	—
689	C₂×C₄×C₇	—	2	2	no	—
690	C₂×C₄×C₇	—	2	1	no	—
691	C₂×C₄×C₇	—	2	2	no	—
692	C₂×C₄×C₇	—	2	2	no	—
693	C₂×C₄×C₇	—	2	1	no	—
694	C₂×C₄×C₇	—	2	1	no	—
695	C₂×C₄×C₇	—	2	1	no	—
696	C₂×C₄×C₇	—	2	1	no	—
697	C₂×C₄×C₇	—	2	2	no	—
698	C₂×C₄×C₇	—	4	1	no	—
699	C₂×C₄×C₇	—	4	1	no	—
700	C₂×C₄×C₇	—	4	1	no	—
701	C₂×C₄×C₇	—	4	1	no	—
702	C₂×C₄×C₇	—	4	1	no	—
703	C₂×C₄×C₇	—	4	2	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	—	8	1	no	—
708	C₂×C₄×C₇	—	8	1	no	—
709	C₂×C₄×C₇	—	8	2	no	—
710	C₂×C₄×C₇	—	8	2	no	—
711	C₂×C₄×C₇	—	8	1	no	—
712	C₂×C₄×C₇	—	8	1	no	—
713	C₂×C₄×C₇	—	8	1	no	—
714	C₂×C₄×C₇	—	8	1	no	—
715	C₂×C₄×C₇	—	8	1	no	—
716	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
717	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
718	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
719	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
720	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
721	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
722	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
723	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
724	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
725	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
726	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
727	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
728	C₇×C₈	—	2	2	no	—
729	C₇×C₈	—	2	2	no	—
730	C₇×C₈	—	2	2	no	—
731	C₇×C₈	—	2	2	no	—
732	C₂×#41	—	2	1	no	—
733	C₂×#41	—	2	1	no	—
734	C₂×#41	C₂³×C₇	1	1	yes	characteristic
735	C₂²×Q₈	—	2	1	no	—
736	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
737	C₂²×D₄	—	2	1	no	—
738	C₂²×D₄	—	2	1	no	—
739	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
740	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
741	C₂³×C₄	—	2	1	no	—
742	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
743	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
748	C₂×D₈	C₂³×C₇	1	2	yes	—
749	C₂×D₈	C₂³×C₇	1	2	yes	—
750	C₂×D₈	C₂³×C₇	1	2	yes	—
751	C₂×M₁₆	C₂³×C₇	1	2	yes	—
752	C₂²×C₈	C₂³×C₇	1	2	yes	—
753	C₄⋊Q₈	—	2	1	no	—
754	C₄⋊Q₈	—	2	1	no	—
755	C₄⋊Q₈	—	2	1	no	—
756	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
757	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
758	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
759	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
760	#127	C₂³×C₇	1	1	yes	characteristic
761	#127	C₂³×C₇	1	1	yes	characteristic
762	#126	—	2	2	no	—
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#126	—	2	2	no	—
766	#126	—	2	1	no	—
767	#126	—	2	1	no	—
768	#126	—	2	1	no	—
769	#126	—	2	1	no	—
770	#125	—	2	1	no	—
771	#125	C₂³×C₇	1	1	yes	characteristic
772	#125	C₂³×C₇	1	1	yes	characteristic
773	#124	—	2	2	no	—
774	#124	—	2	2	no	—
775	#124	—	2	2	no	—
776	#124	—	2	2	no	—
777	#124	—	2	1	no	—
778	#124	—	2	1	no	—
779	#124	—	2	1	no	—
780	#124	—	2	1	no	—
781	#124	—	2	1	no	—
782	#124	—	2	1	no	—
783	#124	C₂³×C₇	1	2	yes	—
784	#124	C₂³×C₇	1	2	yes	—
785	#124	C₂³×C₇	1	1	yes	characteristic
786	#124	C₂³×C₇	1	1	yes	characteristic
787	#123	—	2	1	no	—
788	#123	—	2	1	no	—
789	#123	—	2	1	no	—
790	#123	—	2	1	no	—
791	#123	—	2	1	no	—
792	#123	—	2	1	no	—
793	#123	—	2	1	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	#123	—	2	1	no	—
799	#123	—	2	1	no	—
800	C₂²⋊Q₈	—	2	1	no	—
801	C₂²⋊Q₈	—	2	1	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	—	2	2	no	—
804	C₂²⋊Q₈	—	2	2	no	—
805	C₂²⋊Q₈	—	2	2	no	—
806	C₂²⋊Q₈	—	2	1	no	—
807	C₂²⋊Q₈	—	2	1	no	—
808	C₂²⋊Q₈	—	2	1	no	—
809	C₂²⋊Q₈	—	2	1	no	—
810	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
811	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
812	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
813	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
814	#121	—	2	1	no	—
815	#121	—	2	1	no	—
816	#121	—	2	1	no	—
817	#121	—	2	1	no	—
818	#121	—	2	1	no	—
819	#121	—	2	1	no	—
820	#121	—	2	1	no	—
821	#121	—	2	1	no	—
822	#121	—	2	1	no	—
823	#121	—	2	1	no	—
824	#121	—	2	1	no	—
825	#121	—	2	1	no	—
826	#121	C₂³×C₇	1	1	yes	characteristic
827	#121	C₂³×C₇	1	1	yes	characteristic
828	#121	C₂³×C₇	1	1	yes	characteristic
829	#121	C₂³×C₇	1	1	yes	characteristic
830	#121	C₂³×C₇	1	2	yes	—
831	#121	C₂³×C₇	1	2	yes	—
832	#121	C₂³×C₇	1	1	yes	characteristic
833	#121	C₂³×C₇	1	1	yes	characteristic
834	#120	—	2	1	no	—
835	#120	—	2	1	no	—
836	#120	—	2	1	no	—
837	C₄×Q₈	—	2	1	no	—
838	C₄×Q₈	—	2	1	no	—
839	C₄×Q₈	C₂³×C₇	1	2	yes	—
840	C₄×Q₈	C₂³×C₇	1	2	yes	—
841	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
842	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
843	C₄×D₄	—	2	1	no	—
844	C₄×D₄	—	2	1	no	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	1	no	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	C₂³×C₇	1	2	yes	—
856	C₄×D₄	C₂³×C₇	1	2	yes	—
857	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
858	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
859	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
860	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
861	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
862	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
863	#117	—	2	1	no	—
864	#117	—	2	1	no	—
865	#117	—	2	1	no	—
866	#117	C₇×D₄	1	1	yes	characteristic
867	#117	C₇×D₄	1	1	yes	characteristic
868	#117	C₇×D₄	1	1	yes	characteristic
869	#117	C₇×D₄	1	1	yes	characteristic
870	#117	C₂³×C₇	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	1	yes	characteristic
875	C₂×C₄⋊C₄	—	2	1	no	—
876	C₂×C₄⋊C₄	—	2	1	no	—
877	C₂×C₄⋊C₄	—	2	1	no	—
878	C₂×C₄⋊C₄	—	2	1	no	—
879	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
880	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
884	C₂×C₂²⋊C₄	—	2	1	no	—
885	C₂×C₂²⋊C₄	—	2	1	no	—
886	C₂×C₂²⋊C₄	—	2	1	no	—
887	C₂×C₂²⋊C₄	—	2	1	no	—
888	C₂×C₂²⋊C₄	—	2	1	no	—
889	C₂×C₂²⋊C₄	—	2	1	no	—
890	C₂×C₂²⋊C₄	—	2	1	no	—
891	C₂×C₂²⋊C₄	—	2	1	no	—
892	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
893	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
894	C₂×C₄²	—	2	1	no	—
895	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
896	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
897	#107	C₂³×C₇	1	2	yes	—
898	#107	C₂³×C₇	1	2	yes	—
899	#107	C₂³×C₇	1	2	yes	—
900	#107	C₂³×C₇	1	2	yes	—
901	#107	C₂³×C₇	1	2	yes	—
902	#107	C₂³×C₇	1	2	yes	—
903	#106	C₂³×C₇	1	2	yes	—
904	#106	C₂³×C₇	1	2	yes	—
905	C₄⋊C₈	C₂³×C₇	1	2	yes	—
906	C₄⋊C₈	C₂³×C₇	1	2	yes	—
907	C₄⋊C₈	C₂³×C₇	1	2	yes	—
908	C₄⋊C₈	C₂³×C₇	1	2	yes	—
909	#103	C₂³×C₇	1	2	yes	—
910	#103	C₂³×C₇	1	2	yes	—
911	#103	C₂³×C₇	1	2	yes	—
912	#103	C₂³×C₇	1	2	yes	—
913	#103	C₂³×C₇	1	2	yes	—
914	#103	C₂³×C₇	1	2	yes	—
915	#102	C₂³×C₇	1	2	yes	—
916	#102	C₂³×C₇	1	2	yes	—
917	#102	C₂³×C₇	1	2	yes	—
918	#102	C₂³×C₇	1	2	yes	—
919	#102	C₂³×C₇	1	2	yes	—
920	#102	C₂³×C₇	1	2	yes	—
921	#102	C₂³×C₇	1	2	yes	—
922	#102	C₂³×C₇	1	2	yes	—
923	#102	C₂³×C₇	1	2	yes	—
924	#102	C₂³×C₇	1	2	yes	—
925	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
926	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
927	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
928	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
929	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
930	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
931	#97	C₂³×C₇	1	2	yes	—
932	#97	C₂³×C₇	1	2	yes	—
933	C₄×C₈	C₂³×C₇	1	2	yes	—
934	C₄×C₈	C₂³×C₇	1	2	yes	—
935	C₂²×C₇	—	2	1	no	—
936	C₂²×C₇	—	2	1	no	—
937	C₂²×C₇	—	2	1	no	—
938	C₂²×C₇	—	2	1	no	—
939	C₂²×C₇	—	2	1	no	—
940	C₂²×C₇	—	2	1	no	—
941	C₂²×C₇	—	2	1	no	—
942	C₂²×C₇	—	2	1	no	—
943	C₂²×C₇	—	4	1	no	—
944	C₂²×C₇	—	4	1	no	—
945	C₂²×C₇	—	4	1	no	—
946	C₂²×C₇	—	4	2	no	—
947	C₂²×C₇	—	4	1	no	—
948	C₂²×C₇	—	4	2	no	—
949	C₂²×C₇	—	4	1	no	—
950	C₂²×C₇	—	4	1	no	—
951	C₂²×C₇	—	4	1	no	—
952	C₂²×C₇	—	4	2	no	—
953	C₂²×C₇	—	4	1	no	—
954	C₂²×C₇	—	4	1	no	—
955	C₂²×C₇	—	8	2	no	—
956	C₂²×C₇	—	8	4	no	—
957	C₂²×C₇	—	16	2	no	—
958	C₂²×C₇	#576	1	2	yes	—
959	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
960	C₄×C₇	—	2	1	no	—
961	C₄×C₇	—	2	1	no	—
962	C₄×C₇	—	2	1	no	—
963	C₄×C₇	—	2	1	no	—
964	C₄×C₇	—	2	1	no	—
965	C₄×C₇	—	2	1	no	—
966	C₄×C₇	—	2	1	no	—
967	C₄×C₇	—	2	1	no	—
968	C₄×C₇	—	2	1	no	—
969	C₄×C₇	—	2	1	no	—
970	C₄×C₇	—	2	1	no	—
971	C₄×C₇	—	4	1	no	—
972	C₄×C₇	—	4	1	no	—
973	C₄×C₇	—	4	2	no	—
974	C₄×C₇	—	4	2	no	—
975	C₄×C₇	—	4	2	no	—
976	C₄×C₇	—	4	1	no	—
977	C₄×C₇	—	4	1	no	—
978	C₄×C₇	—	4	1	no	—
979	C₄×C₇	#585	1	2	yes	—
980	C₂⁴	—	2	1	no	—
981	C₂⁴	—	2	1	no	—
982	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
983	#41	—	4	2	no	—
984	#41	—	8	2	no	—
985	#41	—	8	2	no	—
986	C₂×Q₈	—	2	1	no	—
987	C₂×Q₈	—	2	2	no	—
988	C₂×Q₈	—	2	2	no	—
989	C₂×Q₈	—	2	1	no	—
990	C₂×Q₈	—	2	1	no	—
991	C₂×Q₈	—	4	2	no	—
992	C₂×Q₈	—	8	2	no	—
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	1	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	1	no	—
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	2	2	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	1	no	—
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	1	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	4	2	no	—
1011	C₂×D₄	—	4	2	no	—
1012	C₂×D₄	—	8	2	no	—
1013	C₂×D₄	—	8	2	no	—
1014	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1015	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1016	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1017	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	—	2	1	no	—
1020	C₂²×C₄	—	2	1	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	1	no	—
1026	C₂²×C₄	—	2	1	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	1	no	—
1029	C₂²×C₄	—	2	2	no	—
1030	C₂²×C₄	—	2	2	no	—
1031	C₂²×C₄	—	4	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	1	yes	characteristic
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	1	yes	characteristic
1040	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1041	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1042	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1043	Q₁₆	—	4	2	no	—
1044	SD₁₆	—	4	2	no	—
1045	SD₁₆	—	4	2	no	—
1046	SD₁₆	—	4	2	no	—
1047	SD₁₆	—	4	2	no	—
1048	D₈	—	4	2	no	—
1049	D₈	—	4	2	no	—
1050	D₈	—	4	2	no	—
1051	M₁₆	—	4	2	no	—
1052	C₂×C₈	—	4	2	no	—
1053	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1054	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1055	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1056	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	1	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	—	2	2	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1077	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1078	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1079	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
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	1	yes	characteristic
1083	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1084	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1085	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1086	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1087	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1088	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1089	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	1	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	2	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	—	2	2	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1120	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1121	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1122	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1123	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1124	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1125	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1126	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1127	C₄²	—	2	2	no	—
1128	C₄²	—	2	2	no	—
1129	C₄²	—	2	1	no	—
1130	C₄²	—	2	1	no	—
1131	C₄²	—	2	1	no	—
1132	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1133	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1134	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1135	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1136	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1137	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1138	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1139	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1140	C₂×C₇	—	2	2	no	—
1141	C₂×C₇	—	4	1	no	—
1142	C₂×C₇	—	4	1	no	—
1143	C₂×C₇	—	8	1	no	—
1144	C₂×C₇	—	8	2	no	—
1145	C₂×C₇	—	8	1	no	—
1146	C₂×C₇	—	8	1	no	—
1147	C₂×C₇	#3449	1	1	yes	characteristic
1148	C₂×C₇	C₂×#576	1	1	yes	characteristic
1149	C₂×C₇	#3586	1	1	yes	characteristic
1150	C₂³	—	2	2	no	—
1151	C₂³	—	2	2	no	—
1152	C₂³	—	2	1	no	—
1153	C₂³	—	2	1	no	—
1154	C₂³	—	2	1	no	—
1155	C₂³	—	4	1	no	—
1156	C₂³	—	4	1	no	—
1157	C₂³	—	4	2	no	—
1158	C₂³	—	4	2	no	—
1159	C₂³	—	4	2	no	—
1160	C₂³	—	4	2	no	—
1161	C₂³	—	8	1	no	—
1162	C₂³	—	8	1	no	—
1163	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1164	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1165	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1166	Q₈	—	2	2	no	—
1167	Q₈	—	2	2	no	—
1168	Q₈	—	2	2	no	—
1169	Q₈	—	4	2	no	—
1170	Q₈	—	8	2	no	—
1171	Q₈	—	8	2	no	—
1172	Q₈	—	8	1	no	—
1173	Q₈	—	8	1	no	—
1174	D₄	—	2	2	no	—
1175	D₄	—	2	2	no	—
1176	D₄	—	2	2	no	—
1177	D₄	—	2	2	no	—
1178	D₄	—	2	2	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	2	no	—
1182	D₄	—	4	2	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	8	1	no	—
1186	D₄	—	8	1	no	—
1187	D₄	—	8	1	no	—
1188	D₄	—	8	1	no	—
1189	D₄	—	8	1	no	—
1190	D₄	—	8	2	no	—
1191	D₄	—	8	2	no	—
1192	D₄	—	8	1	no	—
1193	D₄	—	8	1	no	—
1194	C₂×C₄	—	2	2	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	2	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	4	1	no	—
1208	C₂×C₄	—	4	1	no	—
1209	C₂×C₄	—	4	1	no	—
1210	C₂×C₄	—	4	1	no	—
1211	C₂×C₄	—	4	1	no	—
1212	C₂×C₄	—	4	2	no	—
1213	C₂×C₄	—	4	2	no	—
1214	C₂×C₄	—	4	2	no	—
1215	C₂×C₄	—	4	2	no	—
1216	C₂×C₄	—	8	1	no	—
1217	C₂×C₄	—	8	1	no	—
1218	C₂×C₄	—	8	2	no	—
1219	C₂×C₄	—	8	2	no	—
1220	C₂×C₄	—	8	1	no	—
1221	C₂×C₄	—	8	1	no	—
1222	C₂×C₄	—	8	1	no	—
1223	C₂×C₄	—	8	1	no	—
1224	C₂×C₄	—	8	1	no	—
1225	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1226	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1227	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1228	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1229	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1230	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1231	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1232	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1233	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1234	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1235	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1236	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1237	C₈	—	2	2	no	—
1238	C₈	—	2	2	no	—
1239	C₈	—	2	2	no	—
1240	C₈	—	2	2	no	—
1241	C₇	#60976	1	1	yes	characteristic, direct product factor, Sylow
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	—	2	1	no	—
1248	C₂²	—	2	1	no	—
1249	C₂²	—	2	1	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	2	no	—
1252	C₂²	—	4	1	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	1	no	—
1255	C₂²	—	4	1	no	—
1256	C₂²	—	4	1	no	—
1257	C₂²	—	4	2	no	—
1258	C₂²	—	4	1	no	—
1259	C₂²	—	4	2	no	—
1260	C₂²	—	4	1	no	—
1261	C₂²	—	4	1	no	—
1262	C₂²	—	8	2	no	—
1263	C₂²	—	8	4	no	—
1264	C₂²	—	16	2	no	—
1265	C₂²	C₇×#576	1	2	yes	—
1266	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1267	C₄	—	2	1	no	—
1268	C₄	—	2	1	no	—
1269	C₄	—	2	1	no	—
1270	C₄	—	2	1	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	2	1	no	—
1273	C₄	—	2	1	no	—
1274	C₄	—	2	1	no	—
1275	C₄	—	2	1	no	—
1276	C₄	—	2	1	no	—
1277	C₄	—	2	1	no	—
1278	C₄	—	4	2	no	—
1279	C₄	—	4	2	no	—
1280	C₄	—	4	1	no	—
1281	C₄	—	4	1	no	—
1282	C₄	—	4	1	no	—
1283	C₄	—	4	1	no	—
1284	C₄	—	4	1	no	—
1285	C₄	—	4	2	no	—
1286	C₄	C₇×#585	1	2	yes	—
1287	C₂	—	2	2	no	—
1288	C₂	—	4	1	no	—
1289	C₂	—	4	1	no	—
1290	C₂	—	8	2	no	—
1291	C₂	—	8	1	no	—
1292	C₂	—	8	1	no	—
1293	C₂	—	8	1	no	—
1294	C₂	C₇×#3449	1	1	yes	characteristic
1295	C₂	C₂×C₇×#576	1	1	yes	characteristic
1296	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×#3494	C₂	semidirect
2. C₂×C₇×#542	C₂	semidirect
3. C₇×#3262	C₂	semidirect
4. C₇×#3257	C₂	semidirect
5. C₇×#3243	C₂	semidirect
6. C₇×#3238	C₂	semidirect
7. C₇×#3226	C₂	semidirect
8. C₇×#3224	C₂	semidirect
9. C₇×#3213	C₂	semidirect
10. C₇×#3211	C₂	semidirect
11. C₇×#3194	C₂	semidirect
12. C₇×#3193	C₂	semidirect
13. C₇×#3190	C₂	semidirect
14. C₇×#3186	C₂	semidirect
15. C₇×#3179	C₂	semidirect
16. C₇×#3175	C₂	semidirect
17. C₇×#3124	C₂	semidirect
18. C₇×#3118	C₂	semidirect
19. C₇×#3114	C₂	semidirect
20. C₇×#3112	C₂	semidirect
21. C₇×#3108	C₂	semidirect
22. C₇×#3100	C₂	semidirect
23. C₇×#2924	C₂	semidirect
32. C₇×#544	C₂²	semidirect
39. C₇×#542	C₂²	semidirect
40. C₇×#542	C₂²	semidirect
41. C₇×#542	C₂²	semidirect
42. C₇×#542	C₂²	semidirect
43. C₇×#540	C₂²	semidirect
44. C₇×#540	C₂²	semidirect
45. C₇×#535	C₂²	semidirect
48. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
53. C₂×C₇×#124	C₂²	semidirect
60. C₇×#520	C₂²	semidirect
61. C₇×#518	C₂²	semidirect
62. C₂×C₄×C₇×Q₈	C₂²	semidirect
63. C₂×C₄×C₇×D₄	C₂²	semidirect
65. C₇×#501	C₂²	semidirect
66. C₇×#500	C₂²	semidirect
67. C₇×#496	C₂²	semidirect
68. C₇×#495	C₂²	semidirect
69. C₇×#489	C₂²	semidirect
70. C₇×#489	C₂²	semidirect
71. C₇×#488	C₂²	semidirect
72. C₇×#486	C₂²	semidirect
73. C₇×#485	C₂²	semidirect
74. C₇×#484	C₂²	semidirect
75. C₇×#483	C₂²	semidirect
76. C₇×#483	C₂²	semidirect
83. C₇×#480	C₂²	semidirect
84. C₇×#480	C₂²	semidirect
85. C₇×#479	C₂²	semidirect
86. C₇×#478	C₂²	semidirect
87. C₇×#477	C₂²	semidirect
88. C₇×#477	C₂²	semidirect
89. C₇×#476	C₂²	semidirect
90. C₇×#474	C₂²	semidirect
91. C₇×#474	C₂²	semidirect
92. C₇×#474	C₂²	semidirect
93. C₇×#469	C₂²	semidirect
94. C₇×#468	C₂²	semidirect
95. C₇×#468	C₂²	semidirect
96. C₇×#468	C₂²	semidirect
97. C₇×#467	C₂²	semidirect
100. C₇×#465	C₂²	semidirect
101. C₇×#464	C₂²	semidirect
102. C₇×#464	C₂²	semidirect
103. C₇×#463	C₂²	semidirect
104. C₇×#463	C₂²	semidirect
105. C₇×#463	C₂²	semidirect
106. C₇×#463	C₂²	semidirect
107. C₇×#460	C₂²	semidirect
108. C₇×#459	C₂²	semidirect
109. C₇×#452	C₂²	semidirect
110. C₇×#451	C₂²	semidirect
111. C₇×#450	C₂²	semidirect
112. C₇×#450	C₂²	semidirect
116. C₇×#448	C₂²	semidirect
120. C₇×#447	C₂²	semidirect
121. C₇×#442	C₂²	semidirect
122. C₇×#440	C₂²	semidirect
123. C₇×#440	C₂²	semidirect
124. C₇×#440	C₂²	semidirect
125. C₄×C₇×Q₁₆	C₂²	semidirect
126. C₄×C₇×SD₁₆	C₂²	semidirect
127. C₄×C₇×D₈	C₂²	semidirect
128. C₄×C₇×D₈	C₂²	semidirect
129. C₇×#433	C₂²	semidirect
130. C₇×#433	C₂²	semidirect
131. C₇×#432	C₂²	semidirect
132. C₇×#432	C₂²	semidirect
133. C₇×#431	C₂²	semidirect
134. C₇×#431	C₂²	semidirect
135. C₇×#424	C₂²	semidirect
138. C₇×#405	C₂²	semidirect
139. #60976	C₇	direct (N × H)
343. #3494	C₂×C₇	semidirect
344. C₂×#542	C₂×C₇	semidirect
345. #3262	C₂×C₇	semidirect
346. #3257	C₂×C₇	semidirect
347. #3243	C₂×C₇	semidirect
348. #3238	C₂×C₇	semidirect
349. #3226	C₂×C₇	semidirect
350. #3224	C₂×C₇	semidirect
351. #3213	C₂×C₇	semidirect
352. #3211	C₂×C₇	semidirect
353. #3194	C₂×C₇	semidirect
354. #3193	C₂×C₇	semidirect
355. #3190	C₂×C₇	semidirect
356. #3186	C₂×C₇	semidirect
357. #3179	C₂×C₇	semidirect
358. #3175	C₂×C₇	semidirect
359. #3124	C₂×C₇	semidirect
360. #3118	C₂×C₇	semidirect
361. #3114	C₂×C₇	semidirect
362. #3112	C₂×C₇	semidirect
363. #3108	C₂×C₇	semidirect
364. #3100	C₂×C₇	semidirect
365. #2924	C₂×C₇	semidirect
534. #544	C₂²×C₇	semidirect
541. #542	C₂²×C₇	semidirect
542. #542	C₂²×C₇	semidirect
543. #542	C₂²×C₇	semidirect
544. #542	C₂²×C₇	semidirect
545. #540	C₂²×C₇	semidirect
546. #540	C₂²×C₇	semidirect
547. #535	C₂²×C₇	semidirect
550. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
555. C₂×#124	C₂²×C₇	semidirect
562. #520	C₂²×C₇	semidirect
563. #518	C₂²×C₇	semidirect
564. C₂×C₄×Q₈	C₂²×C₇	semidirect
565. C₂×C₄×D₄	C₂²×C₇	semidirect
567. #501	C₂²×C₇	semidirect
568. #500	C₂²×C₇	semidirect
569. #496	C₂²×C₇	semidirect
570. #495	C₂²×C₇	semidirect
571. #489	C₂²×C₇	semidirect
572. #489	C₂²×C₇	semidirect
573. #488	C₂²×C₇	semidirect
574. #486	C₂²×C₇	semidirect
575. #485	C₂²×C₇	semidirect
576. #484	C₂²×C₇	semidirect
577. #483	C₂²×C₇	semidirect
578. #483	C₂²×C₇	semidirect
585. #480	C₂²×C₇	semidirect
586. #480	C₂²×C₇	semidirect
587. #479	C₂²×C₇	semidirect
588. #478	C₂²×C₇	semidirect
589. #477	C₂²×C₇	semidirect
590. #477	C₂²×C₇	semidirect
591. #476	C₂²×C₇	semidirect
592. #474	C₂²×C₇	semidirect
593. #474	C₂²×C₇	semidirect
594. #474	C₂²×C₇	semidirect
595. #469	C₂²×C₇	semidirect
596. #468	C₂²×C₇	semidirect
597. #468	C₂²×C₇	semidirect
598. #468	C₂²×C₇	semidirect
599. #467	C₂²×C₇	semidirect
602. #465	C₂²×C₇	semidirect
603. #464	C₂²×C₇	semidirect
604. #464	C₂²×C₇	semidirect
605. #463	C₂²×C₇	semidirect
606. #463	C₂²×C₇	semidirect
607. #463	C₂²×C₇	semidirect
608. #463	C₂²×C₇	semidirect
609. #460	C₂²×C₇	semidirect
610. #459	C₂²×C₇	semidirect
611. #452	C₂²×C₇	semidirect
612. #451	C₂²×C₇	semidirect
613. #450	C₂²×C₇	semidirect
614. #450	C₂²×C₇	semidirect
618. #448	C₂²×C₇	semidirect
622. #447	C₂²×C₇	semidirect
623. #442	C₂²×C₇	semidirect
624. #440	C₂²×C₇	semidirect
625. #440	C₂²×C₇	semidirect
626. #440	C₂²×C₇	semidirect
627. C₄×Q₁₆	C₂²×C₇	semidirect
628. C₄×SD₁₆	C₂²×C₇	semidirect
629. C₄×D₈	C₂²×C₇	semidirect
630. C₄×D₈	C₂²×C₇	semidirect
631. #433	C₂²×C₇	semidirect
632. #433	C₂²×C₇	semidirect
633. #432	C₂²×C₇	semidirect
634. #432	C₂²×C₇	semidirect
635. #431	C₂²×C₇	semidirect
636. #431	C₂²×C₇	semidirect
637. #424	C₂²×C₇	semidirect
640. #405	C₂²×C₇	semidirect
1241. C₇	#60976	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3494	2
C₂×C₇×#542	2
C₇×#3262	2
C₇×#3257	2
C₇×#3243	2
C₇×#3238	2
C₇×#3226	2
C₇×#3224	2
C₇×#3213	2
C₇×#3211	2
C₇×#3194	2
C₇×#3193	2
C₇×#3190	2
C₇×#3186	2
C₇×#3179	2
C₇×#3175	2
C₇×#3124	2
C₇×#3118	2
C₇×#3114	2
C₇×#3112	2
C₇×#3108	2
C₇×#3100	2
C₇×#2924	2
#60976	7

Subgroups — C7×#60976 #13238192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60976 #13238192