Subgroups — C₇×#60983 #13238199

Order 1792.

1668 conjugacy classes of subgroups.

The subgroup lattice has 1220 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
2	C₂×C₇×#541	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3261	C₂	1	2	yes	maximal, complemented
4	C₇×#3258	C₂	1	2	yes	maximal, complemented
5	C₇×#3242	C₂	1	2	yes	maximal, complemented
6	C₇×#3236	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3232	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3223	C₂	1	2	yes	maximal, complemented
9	C₇×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3209	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3196	C₂	1	1	yes	maximal, characteristic
12	C₇×#3195	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3190	C₂	1	1	yes	maximal, characteristic
14	C₇×#3189	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3178	C₂	1	2	yes	maximal, complemented
16	C₇×#3177	C₂	1	2	yes	maximal, complemented
17	C₇×#3127	C₂	1	2	yes	maximal, complemented
18	C₇×#3120	C₂	1	2	yes	maximal, complemented
19	C₇×#3117	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#556	—	2	1	no	—
25	C₇×#554	—	2	1	no	—
26	C₇×#552	—	2	1	no	—
27	C₇×#552	—	2	1	no	—
28	C₇×#552	—	2	1	no	—
29	C₇×#552	—	2	1	no	—
30	C₇×#551	—	2	1	no	—
31	C₇×#551	—	2	1	no	—
32	C₇×#544	C₂²	1	1	yes	characteristic
33	C₇×#542	C₂²	1	1	yes	characteristic
34	C₇×#542	C₂²	1	1	yes	characteristic
35	C₇×#541	—	2	1	no	—
36	C₇×#541	—	2	1	no	—
37	C₇×#541	—	2	1	no	—
38	C₇×#541	—	2	1	no	—
39	C₇×#541	C₂²	1	1	yes	characteristic
40	C₇×#541	C₂²	1	2	yes	—
41	C₇×#541	C₂²	1	2	yes	—
42	C₇×#541	C₂²	1	2	yes	—
43	C₇×#541	C₂²	1	1	yes	characteristic
44	C₇×#541	C₂²	1	2	yes	—
45	C₇×#536	C₂²	1	1	yes	characteristic
46	C₇×#533	C₂²	1	1	yes	characteristic
47	C₇×#533	C₂²	1	1	yes	characteristic
48	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
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×#126	—	2	1	no	—
53	C₂×C₇×#125	—	2	1	no	—
54	C₂×C₇×#125	—	2	1	no	—
55	C₂×C₇×#125	C₂²	1	1	yes	characteristic
56	C₇×#525	C₂²	1	1	yes	characteristic
57	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
60	C₇×#520	C₂²	1	1	yes	characteristic
61	C₇×#519	C₂²	1	1	yes	characteristic
62	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
63	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
64	C₂×C₇×#117	C₂²	1	1	yes	characteristic
65	C₇×#501	C₂²	1	2	yes	complemented
66	C₇×#499	C₂²	1	2	yes	complemented
67	C₇×#497	C₂²	1	2	yes	complemented
68	C₇×#494	C₂²	1	2	yes	complemented
69	C₇×#491	C₂²	1	2	yes	complemented
70	C₇×#491	C₂²	1	2	yes	complemented
71	C₇×#488	C₂²	1	2	yes	complemented
72	C₇×#487	C₂²	1	2	yes	complemented
73	C₇×#485	C₂²	1	2	yes	—
74	C₇×#485	C₂²	1	2	yes	—
75	C₇×#484	C₂²	1	1	yes	characteristic
76	C₇×#484	C₂²	1	1	yes	characteristic
77	C₇×#484	C₂²	1	2	yes	—
78	C₇×#484	C₂²	1	1	yes	characteristic
79	C₇×#483	C₂²	1	1	yes	characteristic
80	C₇×#483	C₂²	1	1	yes	characteristic
81	C₇×#483	C₂²	1	1	yes	characteristic
82	C₇×#483	C₂²	1	2	yes	—
83	C₇×#481	C₂²	1	1	yes	characteristic
84	C₇×#480	C₂²	1	1	yes	characteristic
85	C₇×#479	C₂²	1	2	yes	complemented
86	C₇×#479	C₂²	1	2	yes	complemented
87	C₇×#479	C₂²	1	2	yes	complemented
88	C₇×#479	C₂²	1	2	yes	complemented
89	C₇×#479	C₂²	1	2	yes	complemented
90	C₇×#478	C₂²	1	2	yes	complemented
91	C₇×#477	C₂²	1	2	yes	complemented
92	C₇×#475	C₂²	1	2	yes	complemented
93	C₇×#470	C₂²	1	2	yes	—
94	C₇×#470	C₂²	1	2	yes	—
95	C₇×#470	C₂²	1	2	yes	—
96	C₇×#468	C₂²	1	2	yes	—
97	C₇×#467	C₂²	1	2	yes	—
98	C₇×#467	C₂²	1	2	yes	—
99	C₇×#467	C₂²	1	2	yes	—
100	C₇×#465	C₂²	1	2	yes	—
101	C₇×#464	C₂²	1	2	yes	complemented
102	C₇×#464	C₂²	1	2	yes	complemented
103	C₇×#462	C₂²	1	2	yes	complemented
104	C₇×#462	C₂²	1	2	yes	complemented
105	C₇×#462	C₂²	1	2	yes	complemented
106	C₇×#462	C₂²	1	2	yes	complemented
107	C₇×#462	C₂²	1	2	yes	complemented
108	C₇×#461	C₂²	1	2	yes	complemented
109	C₇×#452	C₂²	1	2	yes	—
110	C₇×#452	C₂²	1	2	yes	—
111	C₇×#451	C₂²	1	1	yes	characteristic
112	C₇×#451	C₂²	1	1	yes	characteristic
113	C₇×#451	C₂²	1	2	yes	—
114	C₇×#451	C₂²	1	1	yes	characteristic
115	C₇×#451	C₂²	1	1	yes	characteristic
116	C₇×#451	C₂²	1	1	yes	characteristic
117	C₇×#451	C₂²	1	2	yes	—
118	C₇×#451	C₂²	1	1	yes	characteristic
119	C₇×#448	C₂²	1	1	yes	characteristic
120	C₇×#448	C₂²	1	1	yes	characteristic
121	C₇×#441	C₂²	1	2	yes	complemented
122	C₇×#441	C₂²	1	2	yes	complemented
123	C₇×#441	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×Q₁₆	C₂²	1	2	yes	complemented
127	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
128	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
129	C₇×#433	C₂²	1	2	yes	—
130	C₇×#433	C₂²	1	2	yes	—
131	C₇×#432	C₂²	1	1	yes	characteristic
132	C₇×#432	C₂²	1	1	yes	characteristic
133	C₇×#431	C₂²	1	1	yes	characteristic
134	C₇×#431	C₂²	1	1	yes	characteristic
135	C₇×#424	C₂²	1	2	yes	—
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	—
139	#60983	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂×C₇×#41	C₂³	1	1	yes	characteristic
141	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
142	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
143	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
145	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
146	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
147	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
149	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
150	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
151	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₇×M₁₆	C₂³	1	2	yes	—
154	C₂²×C₇×C₈	C₂³	1	2	yes	—
155	C₇×C₄⋊Q₈	—	2	1	no	—
156	C₇×C₄⋊Q₈	—	2	1	no	—
157	C₇×C₄⋊Q₈	—	2	1	no	—
158	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₇×#126	—	2	1	no	—
165	C₇×#126	—	2	1	no	—
166	C₇×#126	—	2	2	no	—
167	C₇×#126	—	2	2	no	—
168	C₇×#126	—	2	2	no	—
169	C₇×#126	—	2	2	no	—
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×#126	—	2	1	no	—
179	C₇×#126	—	2	1	no	—
180	C₇×#125	—	2	2	no	—
181	C₇×#125	—	2	2	no	—
182	C₇×#125	—	2	2	no	—
183	C₇×#125	—	2	2	no	—
184	C₇×#125	—	2	2	no	—
185	C₇×#125	—	2	2	no	—
186	C₇×#125	—	2	2	no	—
187	C₇×#125	—	2	2	no	—
188	C₇×#125	—	2	1	no	—
189	C₇×#125	—	2	1	no	—
190	C₇×#125	—	2	1	no	—
191	C₇×#125	—	2	1	no	—
192	C₇×#125	—	2	1	no	—
193	C₇×#125	—	2	1	no	—
194	C₇×#125	—	2	1	no	—
195	C₇×#125	—	2	1	no	—
196	C₇×#125	—	2	1	no	—
197	C₇×#125	C₂³	1	2	yes	—
198	C₇×#125	C₂³	1	1	yes	characteristic
199	C₇×#125	C₂³	1	2	yes	—
200	C₇×#125	C₂³	1	1	yes	characteristic
201	C₇×#124	—	2	1	no	—
202	C₇×#124	—	2	1	no	—
203	C₇×#124	C₂³	1	1	yes	characteristic
204	C₇×#124	C₂³	1	1	yes	characteristic
205	C₇×#123	—	2	1	no	—
206	C₇×#123	—	2	1	no	—
207	C₇×#123	—	2	1	no	—
208	C₇×#123	—	2	1	no	—
209	C₇×#123	—	2	1	no	—
210	C₇×#123	—	2	1	no	—
211	C₇×#123	—	2	1	no	—
212	C₇×C₂²⋊Q₈	—	2	1	no	—
213	C₇×C₂²⋊Q₈	—	2	1	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	—	2	1	no	—
219	C₇×C₂²⋊Q₈	—	2	1	no	—
220	C₇×C₂²⋊Q₈	—	2	1	no	—
221	C₇×C₂²⋊Q₈	—	2	1	no	—
222	C₇×C₂²⋊Q₈	—	2	1	no	—
223	C₇×C₂²⋊Q₈	—	2	1	no	—
224	C₇×C₂²⋊Q₈	—	2	1	no	—
225	C₇×C₂²⋊Q₈	—	2	1	no	—
226	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
227	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
228	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
229	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
230	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
231	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
232	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
233	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
234	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
235	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
236	C₇×#121	C₂³	1	1	yes	characteristic
237	C₇×#121	C₂³	1	1	yes	characteristic
238	C₇×#120	—	2	1	no	—
239	C₄×C₇×Q₈	—	2	1	no	—
240	C₄×C₇×Q₈	—	2	1	no	—
241	C₄×C₇×Q₈	—	2	1	no	—
242	C₄×C₇×Q₈	—	2	1	no	—
243	C₄×C₇×Q₈	—	2	1	no	—
244	C₄×C₇×Q₈	—	2	1	no	—
245	C₄×C₇×Q₈	—	2	1	no	—
246	C₄×C₇×Q₈	—	2	1	no	—
247	C₄×C₇×Q₈	C₂³	1	2	yes	—
248	C₄×C₇×Q₈	C₂³	1	2	yes	—
249	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
250	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
251	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
252	C₄×C₇×Q₈	C₂³	1	2	yes	—
253	C₄×C₇×Q₈	C₂³	1	2	yes	—
254	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
255	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
256	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
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	C₇×#117	—	2	1	no	—
266	C₇×#117	—	2	1	no	—
267	C₇×#117	—	2	1	no	—
268	C₇×#117	—	2	1	no	—
269	C₇×#117	—	2	1	no	—
270	C₇×#117	—	2	1	no	—
271	C₇×#117	—	2	1	no	—
272	C₇×#117	D₄	1	1	yes	characteristic
273	C₇×#117	D₄	1	1	yes	characteristic
274	C₇×#117	D₄	1	1	yes	characteristic
275	C₇×#117	D₄	1	1	yes	characteristic
276	C₇×#117	C₂³	1	1	yes	characteristic
277	C₇×#117	C₂³	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	C₂×C₇×C₄⋊C₄	—	2	1	no	—
282	C₂×C₇×C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
288	C₂×C₇×C₄⋊C₄	—	2	1	no	—
289	C₂×C₇×C₄⋊C₄	—	2	1	no	—
290	C₂×C₇×C₄⋊C₄	—	2	1	no	—
291	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
292	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
293	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
294	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
295	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
300	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
301	C₂×C₄²×C₇	—	2	1	no	—
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×#106	C₂³	1	2	yes	—
310	C₇×#106	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×#103	C₂³	1	2	yes	—
324	C₇×#103	C₂³	1	2	yes	—
325	C₇×#103	C₂³	1	2	yes	—
326	C₇×#103	C₂³	1	2	yes	—
327	C₇×#103	C₂³	1	2	yes	—
328	C₇×#103	C₂³	1	2	yes	—
329	C₇×#103	C₂³	1	2	yes	—
330	C₇×#103	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	#3495	C₂×C₇	1	1	yes	characteristic
344	C₂×#541	C₂×C₇	1	1	yes	characteristic, complemented
345	#3261	C₂×C₇	1	2	yes	complemented
346	#3258	C₂×C₇	1	2	yes	complemented
347	#3242	C₂×C₇	1	2	yes	complemented
348	#3236	C₂×C₇	1	1	yes	characteristic, complemented
349	#3232	C₂×C₇	1	1	yes	characteristic, complemented
350	#3223	C₂×C₇	1	2	yes	complemented
351	#3218	C₂×C₇	1	1	yes	characteristic, complemented
352	#3209	C₂×C₇	1	1	yes	characteristic, complemented
353	#3196	C₂×C₇	1	1	yes	characteristic
354	#3195	C₂×C₇	1	1	yes	characteristic, complemented
355	#3190	C₂×C₇	1	1	yes	characteristic
356	#3189	C₂×C₇	1	1	yes	characteristic, complemented
357	#3178	C₂×C₇	1	2	yes	complemented
358	#3177	C₂×C₇	1	2	yes	complemented
359	#3127	C₂×C₇	1	2	yes	complemented
360	#3120	C₂×C₇	1	2	yes	complemented
361	#3117	C₂×C₇	1	1	yes	characteristic, complemented
362	#3113	C₂×C₇	1	1	yes	characteristic, complemented
363	#3108	C₂×C₇	1	1	yes	characteristic, complemented
364	#3104	C₂×C₇	1	1	yes	characteristic, complemented
365	#2924	C₂×C₇	1	1	yes	characteristic, complemented
366	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
367	C₇×#41	—	4	2	no	—
368	C₂×C₇×Q₈	—	2	1	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	1	no	—
373	C₂×C₇×Q₈	—	4	2	no	—
374	C₂×C₇×Q₈	—	4	2	no	—
375	C₂×C₇×Q₈	—	4	2	no	—
376	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
377	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
378	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₇	—	2	1	no	—
386	C₂²×C₄×C₇	—	2	1	no	—
387	C₂²×C₄×C₇	—	2	1	no	—
388	C₂²×C₄×C₇	—	2	1	no	—
389	C₂²×C₄×C₇	—	2	1	no	—
390	C₂²×C₄×C₇	—	2	1	no	—
391	C₂²×C₄×C₇	—	2	1	no	—
392	C₂²×C₄×C₇	—	2	1	no	—
393	C₂²×C₄×C₇	—	2	1	no	—
394	C₂²×C₄×C₇	—	4	2	no	—
395	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
405	C₇×Q₁₆	—	4	2	no	—
406	C₇×Q₁₆	—	4	2	no	—
407	C₇×Q₁₆	—	4	2	no	—
408	C₇×Q₁₆	—	4	2	no	—
409	C₇×Q₁₆	—	4	2	no	—
410	C₇×Q₁₆	—	4	2	no	—
411	C₇×SD₁₆	—	4	2	no	—
412	C₇×SD₁₆	—	4	2	no	—
413	C₇×M₁₆	—	4	2	no	—
414	C₂×C₇×C₈	—	4	2	no	—
415	C₂×C₇×C₈	C₂⁴	1	2	yes	—
416	C₂×C₇×C₈	C₂⁴	1	2	yes	—
417	C₂×C₇×C₈	C₂⁴	1	2	yes	—
418	C₂×C₇×C₈	C₂⁴	1	2	yes	—
419	C₇×C₄⋊C₄	—	2	1	no	—
420	C₇×C₄⋊C₄	—	2	1	no	—
421	C₇×C₄⋊C₄	—	2	1	no	—
422	C₇×C₄⋊C₄	—	2	1	no	—
423	C₇×C₄⋊C₄	—	2	1	no	—
424	C₇×C₄⋊C₄	—	2	2	no	—
425	C₇×C₄⋊C₄	—	2	2	no	—
426	C₇×C₄⋊C₄	—	2	2	no	—
427	C₇×C₄⋊C₄	—	2	2	no	—
428	C₇×C₄⋊C₄	—	2	1	no	—
429	C₇×C₄⋊C₄	—	2	1	no	—
430	C₇×C₄⋊C₄	—	2	2	no	—
431	C₇×C₄⋊C₄	—	2	2	no	—
432	C₇×C₄⋊C₄	—	2	2	no	—
433	C₇×C₄⋊C₄	—	2	2	no	—
434	C₇×C₄⋊C₄	—	2	2	no	—
435	C₇×C₄⋊C₄	—	2	2	no	—
436	C₇×C₄⋊C₄	—	2	2	no	—
437	C₇×C₄⋊C₄	—	2	2	no	—
438	C₇×C₄⋊C₄	—	2	2	no	—
439	C₇×C₄⋊C₄	—	2	2	no	—
440	C₇×C₄⋊C₄	—	2	2	no	—
441	C₇×C₄⋊C₄	—	2	2	no	—
442	C₇×C₄⋊C₄	—	2	1	no	—
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	1	no	—
447	C₇×C₄⋊C₄	—	2	1	no	—
448	C₇×C₄⋊C₄	—	2	1	no	—
449	C₇×C₄⋊C₄	—	2	1	no	—
450	C₇×C₄⋊C₄	—	2	1	no	—
451	C₇×C₄⋊C₄	—	2	1	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	C₂×D₄	1	1	yes	characteristic
461	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	2	yes	—
469	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
470	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
471	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
472	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
473	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
474	C₇×C₂²⋊C₄	—	2	1	no	—
475	C₇×C₂²⋊C₄	—	2	1	no	—
476	C₇×C₂²⋊C₄	—	2	1	no	—
477	C₇×C₂²⋊C₄	—	2	1	no	—
478	C₇×C₂²⋊C₄	—	2	2	no	—
479	C₇×C₂²⋊C₄	—	2	2	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	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	1	no	—
488	C₇×C₂²⋊C₄	—	2	1	no	—
489	C₇×C₂²⋊C₄	—	2	1	no	—
490	C₇×C₂²⋊C₄	—	2	1	no	—
491	C₇×C₂²⋊C₄	—	2	1	no	—
492	C₇×C₂²⋊C₄	—	2	1	no	—
493	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
494	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
495	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
496	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
497	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
498	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
499	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
500	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
501	C₄²×C₇	—	2	2	no	—
502	C₄²×C₇	—	2	2	no	—
503	C₄²×C₇	—	2	2	no	—
504	C₄²×C₇	—	2	2	no	—
505	C₄²×C₇	—	2	1	no	—
506	C₄²×C₇	—	2	1	no	—
507	C₄²×C₇	—	2	1	no	—
508	C₄²×C₇	—	2	1	no	—
509	C₄²×C₇	—	2	1	no	—
510	C₄²×C₇	—	2	1	no	—
511	C₄²×C₇	—	2	1	no	—
512	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
513	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
514	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
515	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
516	C₄²×C₇	C₂⁴	1	1	yes	characteristic
517	C₄²×C₇	C₂⁴	1	1	yes	characteristic
518	C₄²×C₇	C₂⁴	1	1	yes	characteristic
519	C₄²×C₇	C₂⁴	1	1	yes	characteristic
520	#556	—	2	1	no	—
521	#554	—	2	1	no	—
522	#552	—	2	1	no	—
523	#552	—	2	1	no	—
524	#552	—	2	1	no	—
525	#552	—	2	1	no	—
526	#551	—	2	1	no	—
527	#551	—	2	1	no	—
528	#544	C₂²×C₇	1	1	yes	characteristic
529	#542	C₂²×C₇	1	1	yes	characteristic
530	#542	C₂²×C₇	1	1	yes	characteristic
531	#541	—	2	1	no	—
532	#541	—	2	1	no	—
533	#541	—	2	1	no	—
534	#541	—	2	1	no	—
535	#541	C₂²×C₇	1	2	yes	—
536	#541	C₂²×C₇	1	1	yes	characteristic
537	#541	C₂²×C₇	1	2	yes	—
538	#541	C₂²×C₇	1	2	yes	—
539	#541	C₂²×C₇	1	2	yes	—
540	#541	C₂²×C₇	1	1	yes	characteristic
541	#536	C₂²×C₇	1	1	yes	characteristic
542	#533	C₂²×C₇	1	1	yes	characteristic
543	#533	C₂²×C₇	1	1	yes	characteristic
544	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
545	#529	C₂²×C₇	1	1	yes	characteristic
546	#529	C₂²×C₇	1	1	yes	characteristic
547	C₂×#126	—	2	1	no	—
548	C₂×#126	—	2	1	no	—
549	C₂×#125	—	2	1	no	—
550	C₂×#125	—	2	1	no	—
551	C₂×#125	C₂²×C₇	1	1	yes	characteristic
552	#525	C₂²×C₇	1	1	yes	characteristic
553	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
554	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
555	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
556	#520	C₂²×C₇	1	1	yes	characteristic
557	#519	C₂²×C₇	1	1	yes	characteristic
558	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
559	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
560	C₂×#117	C₂²×C₇	1	1	yes	characteristic
561	#501	C₂²×C₇	1	2	yes	complemented
562	#499	C₂²×C₇	1	2	yes	complemented
563	#497	C₂²×C₇	1	2	yes	complemented
564	#494	C₂²×C₇	1	2	yes	complemented
565	#491	C₂²×C₇	1	2	yes	complemented
566	#491	C₂²×C₇	1	2	yes	complemented
567	#488	C₂²×C₇	1	2	yes	complemented
568	#487	C₂²×C₇	1	2	yes	complemented
569	#485	C₂²×C₇	1	2	yes	—
570	#485	C₂²×C₇	1	2	yes	—
571	#484	C₂²×C₇	1	1	yes	characteristic
572	#484	C₂²×C₇	1	1	yes	characteristic
573	#484	C₂²×C₇	1	1	yes	characteristic
574	#484	C₂²×C₇	1	2	yes	—
575	#483	C₂²×C₇	1	1	yes	characteristic
576	#483	C₂²×C₇	1	1	yes	characteristic
577	#483	C₂²×C₇	1	1	yes	characteristic
578	#483	C₂²×C₇	1	2	yes	—
579	#481	C₂²×C₇	1	1	yes	characteristic
580	#480	C₂²×C₇	1	1	yes	characteristic
581	#479	C₂²×C₇	1	2	yes	complemented
582	#479	C₂²×C₇	1	2	yes	complemented
583	#479	C₂²×C₇	1	2	yes	complemented
584	#479	C₂²×C₇	1	2	yes	complemented
585	#479	C₂²×C₇	1	2	yes	complemented
586	#478	C₂²×C₇	1	2	yes	complemented
587	#477	C₂²×C₇	1	2	yes	complemented
588	#475	C₂²×C₇	1	2	yes	complemented
589	#470	C₂²×C₇	1	2	yes	—
590	#470	C₂²×C₇	1	2	yes	—
591	#470	C₂²×C₇	1	2	yes	—
592	#468	C₂²×C₇	1	2	yes	—
593	#467	C₂²×C₇	1	2	yes	—
594	#467	C₂²×C₇	1	2	yes	—
595	#467	C₂²×C₇	1	2	yes	—
596	#465	C₂²×C₇	1	2	yes	—
597	#464	C₂²×C₇	1	2	yes	complemented
598	#464	C₂²×C₇	1	2	yes	complemented
599	#462	C₂²×C₇	1	2	yes	complemented
600	#462	C₂²×C₇	1	2	yes	complemented
601	#462	C₂²×C₇	1	2	yes	complemented
602	#462	C₂²×C₇	1	2	yes	complemented
603	#462	C₂²×C₇	1	2	yes	complemented
604	#461	C₂²×C₇	1	2	yes	complemented
605	#452	C₂²×C₇	1	2	yes	—
606	#452	C₂²×C₇	1	2	yes	—
607	#451	C₂²×C₇	1	1	yes	characteristic
608	#451	C₂²×C₇	1	1	yes	characteristic
609	#451	C₂²×C₇	1	1	yes	characteristic
610	#451	C₂²×C₇	1	1	yes	characteristic
611	#451	C₂²×C₇	1	1	yes	characteristic
612	#451	C₂²×C₇	1	1	yes	characteristic
613	#451	C₂²×C₇	1	2	yes	—
614	#451	C₂²×C₇	1	2	yes	—
615	#448	C₂²×C₇	1	1	yes	characteristic
616	#448	C₂²×C₇	1	1	yes	characteristic
617	#441	C₂²×C₇	1	2	yes	complemented
618	#441	C₂²×C₇	1	2	yes	complemented
619	#441	C₂²×C₇	1	2	yes	complemented
620	#440	C₂²×C₇	1	2	yes	complemented
621	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
622	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
623	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
624	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
625	#433	C₂²×C₇	1	2	yes	—
626	#433	C₂²×C₇	1	2	yes	—
627	#432	C₂²×C₇	1	1	yes	characteristic
628	#432	C₂²×C₇	1	1	yes	characteristic
629	#431	C₂²×C₇	1	1	yes	characteristic
630	#431	C₂²×C₇	1	1	yes	characteristic
631	#424	C₂²×C₇	1	2	yes	—
632	#407	C₂²×C₇	1	1	yes	characteristic
633	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
634	#405	C₂²×C₇	1	2	yes	—
635	C₂³×C₇	—	2	2	no	—
636	C₂³×C₇	—	2	1	no	—
637	C₂³×C₇	—	4	1	no	—
638	C₂³×C₇	—	4	1	no	—
639	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
640	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
641	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
642	C₇×Q₈	—	2	2	no	—
643	C₇×Q₈	—	2	2	no	—
644	C₇×Q₈	—	2	2	no	—
645	C₇×Q₈	—	2	2	no	—
646	C₇×Q₈	—	2	2	no	—
647	C₇×Q₈	—	2	2	no	—
648	C₇×Q₈	—	2	2	no	—
649	C₇×Q₈	—	4	2	no	—
650	C₇×Q₈	—	4	2	no	—
651	C₇×Q₈	—	4	2	no	—
652	C₇×Q₈	—	8	1	no	—
653	C₇×Q₈	—	8	1	no	—
654	C₇×D₄	—	2	2	no	—
655	C₇×D₄	—	4	2	no	—
656	C₇×D₄	—	4	2	no	—
657	C₇×D₄	—	8	1	no	—
658	C₂×C₄×C₇	—	2	2	no	—
659	C₂×C₄×C₇	—	2	2	no	—
660	C₂×C₄×C₇	—	2	2	no	—
661	C₂×C₄×C₇	—	2	2	no	—
662	C₂×C₄×C₇	—	2	2	no	—
663	C₂×C₄×C₇	—	2	1	no	—
664	C₂×C₄×C₇	—	2	1	no	—
665	C₂×C₄×C₇	—	2	1	no	—
666	C₂×C₄×C₇	—	2	1	no	—
667	C₂×C₄×C₇	—	2	2	no	—
668	C₂×C₄×C₇	—	2	2	no	—
669	C₂×C₄×C₇	—	2	1	no	—
670	C₂×C₄×C₇	—	2	2	no	—
671	C₂×C₄×C₇	—	2	2	no	—
672	C₂×C₄×C₇	—	2	1	no	—
673	C₂×C₄×C₇	—	2	1	no	—
674	C₂×C₄×C₇	—	4	1	no	—
675	C₂×C₄×C₇	—	4	1	no	—
676	C₂×C₄×C₇	—	4	1	no	—
677	C₂×C₄×C₇	—	4	1	no	—
678	C₂×C₄×C₇	—	4	1	no	—
679	C₂×C₄×C₇	—	4	2	no	—
680	C₂×C₄×C₇	—	4	2	no	—
681	C₂×C₄×C₇	—	4	2	no	—
682	C₂×C₄×C₇	—	4	2	no	—
683	C₂×C₄×C₇	—	4	2	no	—
684	C₂×C₄×C₇	—	4	2	no	—
685	C₂×C₄×C₇	—	8	1	no	—
686	C₂×C₄×C₇	—	8	1	no	—
687	C₂×C₄×C₇	—	8	1	no	—
688	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
689	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
690	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
691	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
692	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
693	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
694	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
695	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
696	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
697	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
698	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
699	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
700	C₇×C₈	—	2	2	no	—
701	C₇×C₈	—	2	2	no	—
702	C₇×C₈	—	2	2	no	—
703	C₇×C₈	—	2	2	no	—
704	C₂×#41	C₂³×C₇	1	1	yes	characteristic
705	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
706	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
707	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
708	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
709	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
710	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
711	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
712	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
713	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
714	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
716	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
717	C₂×M₁₆	C₂³×C₇	1	2	yes	—
718	C₂²×C₈	C₂³×C₇	1	2	yes	—
719	C₄⋊Q₈	—	2	1	no	—
720	C₄⋊Q₈	—	2	1	no	—
721	C₄⋊Q₈	—	2	1	no	—
722	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
723	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
724	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
728	#126	—	2	1	no	—
729	#126	—	2	1	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	1	no	—
739	#126	—	2	1	no	—
740	#126	—	2	1	no	—
741	#126	—	2	1	no	—
742	#126	—	2	1	no	—
743	#126	—	2	1	no	—
744	#125	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	—	2	2	no	—
747	#125	—	2	2	no	—
748	#125	—	2	2	no	—
749	#125	—	2	2	no	—
750	#125	—	2	2	no	—
751	#125	—	2	2	no	—
752	#125	—	2	1	no	—
753	#125	—	2	1	no	—
754	#125	—	2	1	no	—
755	#125	—	2	1	no	—
756	#125	—	2	1	no	—
757	#125	—	2	1	no	—
758	#125	—	2	1	no	—
759	#125	—	2	1	no	—
760	#125	—	2	1	no	—
761	#125	C₂³×C₇	1	2	yes	—
762	#125	C₂³×C₇	1	2	yes	—
763	#125	C₂³×C₇	1	1	yes	characteristic
764	#125	C₂³×C₇	1	1	yes	characteristic
765	#124	—	2	1	no	—
766	#124	—	2	1	no	—
767	#124	C₂³×C₇	1	1	yes	characteristic
768	#124	C₂³×C₇	1	1	yes	characteristic
769	#123	—	2	1	no	—
770	#123	—	2	1	no	—
771	#123	—	2	1	no	—
772	#123	—	2	1	no	—
773	#123	—	2	1	no	—
774	#123	—	2	1	no	—
775	#123	—	2	1	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
791	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
792	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
795	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
796	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
797	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
798	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
799	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
800	#121	C₂³×C₇	1	1	yes	characteristic
801	#121	C₂³×C₇	1	1	yes	characteristic
802	#120	—	2	1	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	—	2	1	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	—	2	1	no	—
811	C₄×Q₈	C₂³×C₇	1	2	yes	—
812	C₄×Q₈	C₂³×C₇	1	2	yes	—
813	C₄×Q₈	C₂³×C₇	1	2	yes	—
814	C₄×Q₈	C₂³×C₇	1	2	yes	—
815	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
816	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
817	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
818	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
819	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
820	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
829	#117	—	2	1	no	—
830	#117	—	2	1	no	—
831	#117	—	2	1	no	—
832	#117	—	2	1	no	—
833	#117	—	2	1	no	—
834	#117	—	2	1	no	—
835	#117	—	2	1	no	—
836	#117	C₇×D₄	1	1	yes	characteristic
837	#117	C₇×D₄	1	1	yes	characteristic
838	#117	C₇×D₄	1	1	yes	characteristic
839	#117	C₇×D₄	1	1	yes	characteristic
840	#117	C₂³×C₇	1	1	yes	characteristic
841	#117	C₂³×C₇	1	1	yes	characteristic
842	#117	C₂³×C₇	1	1	yes	characteristic
843	#117	C₂³×C₇	1	1	yes	characteristic
844	#117	C₂³×C₇	1	1	yes	characteristic
845	C₂×C₄⋊C₄	—	2	1	no	—
846	C₂×C₄⋊C₄	—	2	1	no	—
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	—	2	1	no	—
850	C₂×C₄⋊C₄	—	2	1	no	—
851	C₂×C₄⋊C₄	—	2	1	no	—
852	C₂×C₄⋊C₄	—	2	1	no	—
853	C₂×C₄⋊C₄	—	2	1	no	—
854	C₂×C₄⋊C₄	—	2	1	no	—
855	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
856	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
857	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
858	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
859	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
860	C₂×C₂²⋊C₄	—	2	1	no	—
861	C₂×C₂²⋊C₄	—	2	1	no	—
862	C₂×C₂²⋊C₄	—	2	1	no	—
863	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
864	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
865	C₂×C₄²	—	2	1	no	—
866	C₂×C₄²	—	2	1	no	—
867	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
868	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
869	#107	C₂³×C₇	1	2	yes	—
870	#107	C₂³×C₇	1	2	yes	—
871	#107	C₂³×C₇	1	2	yes	—
872	#107	C₂³×C₇	1	2	yes	—
873	#106	C₂³×C₇	1	2	yes	—
874	#106	C₂³×C₇	1	2	yes	—
875	#106	C₂³×C₇	1	2	yes	—
876	#106	C₂³×C₇	1	2	yes	—
877	C₄⋊C₈	C₂³×C₇	1	2	yes	—
878	C₄⋊C₈	C₂³×C₇	1	2	yes	—
879	C₄⋊C₈	C₂³×C₇	1	2	yes	—
880	C₄⋊C₈	C₂³×C₇	1	2	yes	—
881	#103	C₂³×C₇	1	2	yes	—
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	#103	C₂³×C₇	1	2	yes	—
887	#103	C₂³×C₇	1	2	yes	—
888	#103	C₂³×C₇	1	2	yes	—
889	#103	C₂³×C₇	1	2	yes	—
890	#103	C₂³×C₇	1	2	yes	—
891	#103	C₂³×C₇	1	2	yes	—
892	#103	C₂³×C₇	1	2	yes	—
893	#103	C₂³×C₇	1	2	yes	—
894	#103	C₂³×C₇	1	2	yes	—
895	#102	C₂³×C₇	1	2	yes	—
896	#102	C₂³×C₇	1	2	yes	—
897	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
898	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
899	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
900	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
901	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
902	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
903	#97	C₂³×C₇	1	2	yes	—
904	#97	C₂³×C₇	1	2	yes	—
905	C₄×C₈	C₂³×C₇	1	2	yes	—
906	C₄×C₈	C₂³×C₇	1	2	yes	—
907	C₂²×C₇	—	2	1	no	—
908	C₂²×C₇	—	2	1	no	—
909	C₂²×C₇	—	2	1	no	—
910	C₂²×C₇	—	2	1	no	—
911	C₂²×C₇	—	2	1	no	—
912	C₂²×C₇	—	2	1	no	—
913	C₂²×C₇	—	2	1	no	—
914	C₂²×C₇	—	2	1	no	—
915	C₂²×C₇	—	4	1	no	—
916	C₂²×C₇	—	4	1	no	—
917	C₂²×C₇	—	4	1	no	—
918	C₂²×C₇	—	8	2	no	—
919	C₂²×C₇	#578	1	2	yes	—
920	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
921	C₄×C₇	—	2	1	no	—
922	C₄×C₇	—	2	1	no	—
923	C₄×C₇	—	2	1	no	—
924	C₄×C₇	—	2	1	no	—
925	C₄×C₇	—	2	1	no	—
926	C₄×C₇	—	2	1	no	—
927	C₄×C₇	—	2	1	no	—
928	C₄×C₇	—	2	1	no	—
929	C₄×C₇	—	2	1	no	—
930	C₄×C₇	—	2	1	no	—
931	C₄×C₇	—	2	1	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	1	no	—
937	C₄×C₇	—	4	1	no	—
938	C₄×C₇	—	4	1	no	—
939	C₄×C₇	—	4	2	no	—
940	C₄×C₇	—	4	2	no	—
941	C₄×C₇	—	4	2	no	—
942	C₄×C₇	—	4	1	no	—
943	C₄×C₇	#585	1	2	yes	—
944	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
945	#41	—	4	2	no	—
946	C₂×Q₈	—	2	1	no	—
947	C₂×Q₈	—	2	1	no	—
948	C₂×Q₈	—	2	1	no	—
949	C₂×Q₈	—	2	1	no	—
950	C₂×Q₈	—	2	1	no	—
951	C₂×Q₈	—	4	2	no	—
952	C₂×Q₈	—	4	2	no	—
953	C₂×Q₈	—	4	2	no	—
954	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
955	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
956	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
957	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
958	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	1	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	4	2	no	—
973	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
974	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
975	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
976	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
977	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
978	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
979	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
980	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
981	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
982	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
983	Q₁₆	—	4	2	no	—
984	Q₁₆	—	4	2	no	—
985	Q₁₆	—	4	2	no	—
986	Q₁₆	—	4	2	no	—
987	Q₁₆	—	4	2	no	—
988	Q₁₆	—	4	2	no	—
989	SD₁₆	—	4	2	no	—
990	SD₁₆	—	4	2	no	—
991	M₁₆	—	4	2	no	—
992	C₂×C₈	—	4	2	no	—
993	C₂×C₈	C₂⁴×C₇	1	2	yes	—
994	C₂×C₈	C₂⁴×C₇	1	2	yes	—
995	C₂×C₈	C₂⁴×C₇	1	2	yes	—
996	C₂×C₈	C₂⁴×C₇	1	2	yes	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	1	no	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	2	1	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1039	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1040	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1041	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1042	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1043	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1044	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1045	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1046	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1047	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1048	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1049	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1051	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	1	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	1	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	1	no	—
1067	C₂²⋊C₄	—	2	1	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1072	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1073	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1074	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1075	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1076	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1077	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1078	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1079	C₄²	—	2	2	no	—
1080	C₄²	—	2	2	no	—
1081	C₄²	—	2	2	no	—
1082	C₄²	—	2	2	no	—
1083	C₄²	—	2	1	no	—
1084	C₄²	—	2	1	no	—
1085	C₄²	—	2	1	no	—
1086	C₄²	—	2	1	no	—
1087	C₄²	—	2	1	no	—
1088	C₄²	—	2	1	no	—
1089	C₄²	—	2	1	no	—
1090	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1091	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1092	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1093	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1094	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1095	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1096	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1097	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1098	C₂×C₇	—	2	2	no	—
1099	C₂×C₇	—	4	1	no	—
1100	C₂×C₇	—	4	1	no	—
1101	C₂×C₇	—	8	1	no	—
1102	C₂×C₇	#3449	1	1	yes	characteristic
1103	C₂×C₇	C₂×#578	1	1	yes	characteristic
1104	C₂×C₇	#3586	1	1	yes	characteristic
1105	C₂³	—	2	2	no	—
1106	C₂³	—	2	1	no	—
1107	C₂³	—	4	1	no	—
1108	C₂³	—	4	1	no	—
1109	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1110	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1111	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1112	Q₈	—	2	2	no	—
1113	Q₈	—	2	2	no	—
1114	Q₈	—	2	2	no	—
1115	Q₈	—	2	2	no	—
1116	Q₈	—	2	2	no	—
1117	Q₈	—	2	2	no	—
1118	Q₈	—	2	2	no	—
1119	Q₈	—	4	2	no	—
1120	Q₈	—	4	2	no	—
1121	Q₈	—	4	2	no	—
1122	Q₈	—	8	1	no	—
1123	Q₈	—	8	1	no	—
1124	D₄	—	2	2	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	8	1	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	2	no	—
1150	C₂×C₄	—	4	2	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	4	2	no	—
1155	C₂×C₄	—	8	1	no	—
1156	C₂×C₄	—	8	1	no	—
1157	C₂×C₄	—	8	1	no	—
1158	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1159	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1160	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1161	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1162	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1163	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1164	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1165	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1166	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1167	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1168	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1169	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1170	C₈	—	2	2	no	—
1171	C₈	—	2	2	no	—
1172	C₈	—	2	2	no	—
1173	C₈	—	2	2	no	—
1174	C₇	#60983	1	1	yes	characteristic, direct product factor, Sylow
1175	C₂²	—	2	1	no	—
1176	C₂²	—	2	1	no	—
1177	C₂²	—	2	1	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	8	2	no	—
1187	C₂²	C₇×#578	1	2	yes	—
1188	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1189	C₄	—	2	1	no	—
1190	C₄	—	2	1	no	—
1191	C₄	—	2	1	no	—
1192	C₄	—	2	1	no	—
1193	C₄	—	2	1	no	—
1194	C₄	—	2	1	no	—
1195	C₄	—	2	1	no	—
1196	C₄	—	2	1	no	—
1197	C₄	—	2	1	no	—
1198	C₄	—	2	1	no	—
1199	C₄	—	2	1	no	—
1200	C₄	—	4	2	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	2	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	2	no	—
1211	C₄	C₇×#585	1	2	yes	—
1212	C₂	—	2	2	no	—
1213	C₂	—	4	1	no	—
1214	C₂	—	4	1	no	—
1215	C₂	—	8	1	no	—
1216	C₂	C₇×#3449	1	1	yes	characteristic
1217	C₂	C₂×C₇×#578	1	1	yes	characteristic
1218	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#525	C₂²
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
2. C₂×C₇×#541	C₂	semidirect
3. C₇×#3261	C₂	semidirect
4. C₇×#3258	C₂	semidirect
5. C₇×#3242	C₂	semidirect
6. C₇×#3236	C₂	semidirect
7. C₇×#3232	C₂	semidirect
8. C₇×#3223	C₂	semidirect
9. C₇×#3218	C₂	semidirect
10. C₇×#3209	C₂	semidirect
12. C₇×#3195	C₂	semidirect
14. C₇×#3189	C₂	semidirect
15. C₇×#3178	C₂	semidirect
16. C₇×#3177	C₂	semidirect
17. C₇×#3127	C₂	semidirect
18. C₇×#3120	C₂	semidirect
19. C₇×#3117	C₂	semidirect
20. C₇×#3113	C₂	semidirect
21. C₇×#3108	C₂	semidirect
22. C₇×#3104	C₂	semidirect
23. C₇×#2924	C₂	semidirect
65. C₇×#501	C₂²	semidirect
66. C₇×#499	C₂²	semidirect
67. C₇×#497	C₂²	semidirect
68. C₇×#494	C₂²	semidirect
69. C₇×#491	C₂²	semidirect
70. C₇×#491	C₂²	semidirect
71. C₇×#488	C₂²	semidirect
72. C₇×#487	C₂²	semidirect
85. C₇×#479	C₂²	semidirect
86. C₇×#479	C₂²	semidirect
87. C₇×#479	C₂²	semidirect
88. C₇×#479	C₂²	semidirect
89. C₇×#479	C₂²	semidirect
90. C₇×#478	C₂²	semidirect
91. C₇×#477	C₂²	semidirect
92. C₇×#475	C₂²	semidirect
101. C₇×#464	C₂²	semidirect
102. C₇×#464	C₂²	semidirect
103. C₇×#462	C₂²	semidirect
104. C₇×#462	C₂²	semidirect
105. C₇×#462	C₂²	semidirect
106. C₇×#462	C₂²	semidirect
107. C₇×#462	C₂²	semidirect
108. C₇×#461	C₂²	semidirect
121. C₇×#441	C₂²	semidirect
122. C₇×#441	C₂²	semidirect
123. C₇×#441	C₂²	semidirect
124. C₇×#440	C₂²	semidirect
125. C₄×C₇×Q₁₆	C₂²	semidirect
126. C₄×C₇×Q₁₆	C₂²	semidirect
127. C₄×C₇×Q₁₆	C₂²	semidirect
128. C₄×C₇×SD₁₆	C₂²	semidirect
139. #60983	C₇	direct (N × H)
344. C₂×#541	C₂×C₇	semidirect
345. #3261	C₂×C₇	semidirect
346. #3258	C₂×C₇	semidirect
347. #3242	C₂×C₇	semidirect
348. #3236	C₂×C₇	semidirect
349. #3232	C₂×C₇	semidirect
350. #3223	C₂×C₇	semidirect
351. #3218	C₂×C₇	semidirect
352. #3209	C₂×C₇	semidirect
354. #3195	C₂×C₇	semidirect
356. #3189	C₂×C₇	semidirect
357. #3178	C₂×C₇	semidirect
358. #3177	C₂×C₇	semidirect
359. #3127	C₂×C₇	semidirect
360. #3120	C₂×C₇	semidirect
361. #3117	C₂×C₇	semidirect
362. #3113	C₂×C₇	semidirect
363. #3108	C₂×C₇	semidirect
364. #3104	C₂×C₇	semidirect
365. #2924	C₂×C₇	semidirect
561. #501	C₂²×C₇	semidirect
562. #499	C₂²×C₇	semidirect
563. #497	C₂²×C₇	semidirect
564. #494	C₂²×C₇	semidirect
565. #491	C₂²×C₇	semidirect
566. #491	C₂²×C₇	semidirect
567. #488	C₂²×C₇	semidirect
568. #487	C₂²×C₇	semidirect
581. #479	C₂²×C₇	semidirect
582. #479	C₂²×C₇	semidirect
583. #479	C₂²×C₇	semidirect
584. #479	C₂²×C₇	semidirect
585. #479	C₂²×C₇	semidirect
586. #478	C₂²×C₇	semidirect
587. #477	C₂²×C₇	semidirect
588. #475	C₂²×C₇	semidirect
597. #464	C₂²×C₇	semidirect
598. #464	C₂²×C₇	semidirect
599. #462	C₂²×C₇	semidirect
600. #462	C₂²×C₇	semidirect
601. #462	C₂²×C₇	semidirect
602. #462	C₂²×C₇	semidirect
603. #462	C₂²×C₇	semidirect
604. #461	C₂²×C₇	semidirect
617. #441	C₂²×C₇	semidirect
618. #441	C₂²×C₇	semidirect
619. #441	C₂²×C₇	semidirect
620. #440	C₂²×C₇	semidirect
621. C₄×Q₁₆	C₂²×C₇	semidirect
622. C₄×Q₁₆	C₂²×C₇	semidirect
623. C₄×Q₁₆	C₂²×C₇	semidirect
624. C₄×SD₁₆	C₂²×C₇	semidirect
1174. C₇	#60983	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
C₂×C₇×#541	2
C₇×#3261	2
C₇×#3258	2
C₇×#3242	2
C₇×#3236	2
C₇×#3232	2
C₇×#3223	2
C₇×#3218	2
C₇×#3209	2
C₇×#3196	2
C₇×#3195	2
C₇×#3190	2
C₇×#3189	2
C₇×#3178	2
C₇×#3177	2
C₇×#3127	2
C₇×#3120	2
C₇×#3117	2
C₇×#3113	2
C₇×#3108	2
C₇×#3104	2
C₇×#2924	2
#60983	7

Subgroups — C7×#60983 #13238199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60983 #13238199