Subgroups — C₇×#61875 #13239091

Order 1792.

1598 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3555	C₂	1	1	yes	maximal, characteristic
2	C₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3390	C₂	1	2	yes	maximal, complemented
4	C₇×#3388	C₂	1	2	yes	maximal, complemented
5	C₇×#3387	C₂	1	2	yes	maximal, complemented
6	C₇×#3387	C₂	1	2	yes	maximal, complemented
7	C₇×#3377	C₂	1	2	yes	maximal, complemented
8	C₇×#3377	C₂	1	2	yes	maximal, complemented
9	C₇×#3374	C₂	1	2	yes	maximal, complemented
10	C₇×#3369	C₂	1	2	yes	maximal, complemented
11	C₇×#3244	C₂	1	2	yes	maximal
12	C₇×#3242	C₂	1	2	yes	maximal, complemented
13	C₇×#3240	C₂	1	1	yes	maximal, characteristic
14	C₇×#3237	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3127	C₂	1	2	yes	maximal, complemented
16	C₇×#3121	C₂	1	2	yes	maximal
17	C₇×#3117	C₂	1	1	yes	maximal, characteristic
18	C₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#563	—	2	2	no	—
21	C₇×Q₈²	—	2	1	no	—
22	C₇×Q₈²	C₂²	1	2	yes	—
23	C₇×Q₈²	C₂²	1	1	yes	characteristic
24	C₇×#557	—	2	1	no	—
25	C₇×#557	—	2	2	no	—
26	C₇×#557	C₂²	1	1	yes	characteristic
27	C₇×#557	C₂²	1	2	yes	—
28	C₇×#557	C₂²	1	2	yes	—
29	C₇×#557	C₂²	1	2	yes	—
30	C₇×#557	C₂²	1	2	yes	—
31	C₇×#556	—	2	1	no	—
32	C₇×#556	C₂²	1	2	yes	—
33	C₇×#556	C₂²	1	1	yes	characteristic
34	C₇×#554	C₂²	1	1	yes	characteristic
35	C₇×#552	—	2	1	no	—
36	C₇×#544	—	2	1	no	—
37	C₇×#544	—	2	1	no	—
38	C₇×#544	—	2	1	no	—
39	C₇×#544	C₂²	1	2	yes	—
40	C₇×#542	C₂²	1	2	yes	—
41	C₇×#541	—	2	1	no	—
42	C₇×#541	—	2	2	no	—
43	C₇×#541	C₂²	1	2	yes	—
44	C₇×#533	—	2	2	no	—
45	C₇×#533	C₂²	1	1	yes	characteristic
46	C₇×#533	C₂²	1	1	yes	characteristic
47	C₇×#533	C₂²	1	1	yes	characteristic
48	C₇×#529	C₂²	1	1	yes	characteristic
49	C₇×#519	C₂²	1	2	yes	—
50	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
51	C₇×#501	C₂²	1	2	yes	—
52	C₇×#501	C₂²	1	1	yes	characteristic
53	C₇×#501	C₂²	1	1	yes	characteristic
54	C₇×#501	C₂²	1	2	yes	—
55	C₇×#501	C₂²	1	2	yes	—
56	C₇×#499	C₂²	1	2	yes	—
57	C₇×#498	C₂²	1	2	yes	—
58	C₇×#491	C₂²	1	2	yes	—
59	C₇×#491	C₂²	1	2	yes	—
60	C₇×#489	C₂²	1	1	yes	characteristic
61	C₇×#489	C₂²	1	1	yes	characteristic
62	C₇×#489	C₂²	1	2	yes	—
63	C₇×#488	C₂²	1	2	yes	—
64	C₇×#487	C₂²	1	2	yes	—
65	C₇×#485	C₂²	1	2	yes	—
66	C₇×#485	C₂²	1	2	yes	—
67	C₇×#485	C₂²	1	2	yes	—
68	C₇×#484	C₂²	1	1	yes	characteristic
69	C₇×#483	C₂²	1	2	yes	—
70	C₇×#482	C₂²	1	2	yes	—
71	C₇×#481	C₂²	1	1	yes	characteristic
72	C₇×#479	C₂²	1	2	yes	—
73	C₇×#479	C₂²	1	2	yes	—
74	C₇×#479	C₂²	1	2	yes	—
75	C₇×#479	C₂²	1	2	yes	—
76	C₇×#479	C₂²	1	2	yes	—
77	C₇×#479	C₂²	1	2	yes	—
78	C₇×#479	C₂²	1	2	yes	—
79	C₇×#478	C₂²	1	2	yes	—
80	C₇×#478	C₂²	1	2	yes	—
81	C₇×#477	C₂²	1	2	yes	—
82	C₇×#477	C₂²	1	2	yes	—
83	C₇×#477	C₂²	1	2	yes	—
84	C₇×#476	C₂²	1	2	yes	—
85	C₇×#475	C₂²	1	2	yes	—
86	C₇×#475	C₂²	1	2	yes	—
87	C₇×#475	C₂²	1	2	yes	—
88	C₇×#475	C₂²	1	2	yes	—
89	C₇×#475	C₂²	1	2	yes	—
90	C₇×#464	C₂²	1	2	yes	—
91	C₇×#464	C₂²	1	2	yes	—
92	C₇×#464	C₂²	1	2	yes	—
93	C₇×#462	C₂²	1	2	yes	—
94	C₇×#462	C₂²	1	2	yes	—
95	C₇×#462	C₂²	1	2	yes	—
96	C₇×#451	C₂²	1	2	yes	—
97	C₇×#451	C₂²	1	1	yes	characteristic
98	C₇×#448	C₂²	1	1	yes	characteristic
99	C₇×#446	C₂²	1	2	yes	—
100	C₇×#446	C₂²	1	2	yes	—
101	C₇×#446	C₂²	1	2	yes	—
102	C₇×#446	C₂²	1	2	yes	—
103	C₇×#441	C₂²	1	2	yes	—
104	C₇×#441	C₂²	1	2	yes	—
105	C₇×#441	C₂²	1	2	yes	—
106	C₇×#441	C₂²	1	2	yes	—
107	C₇×#441	C₂²	1	2	yes	—
108	C₇×#441	C₂²	1	2	yes	—
109	C₇×#440	C₂²	1	2	yes	—
110	C₇×#440	C₂²	1	2	yes	—
111	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
112	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
113	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
114	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
115	C₇×#433	C₂²	1	2	yes	—
116	C₇×#433	C₂²	1	2	yes	—
117	C₇×#432	C₂²	1	1	yes	characteristic
118	C₇×#432	C₂²	1	1	yes	characteristic
119	#61875	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
121	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
122	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
123	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
124	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
125	C₇×C₄⋊Q₈	—	2	2	no	—
126	C₇×C₄⋊Q₈	—	2	2	no	—
127	C₇×C₄⋊Q₈	—	2	2	no	—
128	C₇×C₄⋊Q₈	—	2	2	no	—
129	C₇×C₄⋊Q₈	—	2	2	no	—
130	C₇×C₄⋊Q₈	—	2	2	no	—
131	C₇×C₄⋊Q₈	—	2	1	no	—
132	C₇×C₄⋊Q₈	—	2	2	no	—
133	C₇×C₄⋊Q₈	—	2	2	no	—
134	C₇×C₄⋊Q₈	—	2	2	no	—
135	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
136	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
137	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
142	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
143	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
144	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
145	C₇×#126	—	2	2	no	—
146	C₇×#126	—	2	2	no	—
147	C₇×#126	—	2	2	no	—
148	C₇×#126	—	2	2	no	—
149	C₇×#126	—	2	2	no	—
150	C₇×#126	—	2	2	no	—
151	C₇×#126	—	2	1	no	—
152	C₇×#125	—	2	2	no	—
153	C₇×#125	—	2	2	no	—
154	C₇×#125	—	2	2	no	—
155	C₇×#125	—	2	2	no	—
156	C₇×#125	—	2	2	no	—
157	C₇×#125	—	2	2	no	—
158	C₇×#125	—	2	2	no	—
159	C₇×#125	—	2	1	no	—
160	C₇×#125	—	2	2	no	—
161	C₇×#125	—	2	2	no	—
162	C₇×#125	—	2	2	no	—
163	C₇×#125	—	2	2	no	—
164	C₇×#125	—	2	2	no	—
165	C₇×#125	—	2	1	no	—
166	C₇×#125	D₄	1	2	yes	—
167	C₇×#125	C₂³	1	2	yes	—
168	C₇×#125	C₂³	1	2	yes	—
169	C₇×#125	C₂³	1	2	yes	—
170	C₇×#125	C₂³	1	2	yes	—
171	C₇×#125	C₂³	1	1	yes	characteristic
172	C₇×#124	—	2	2	no	—
173	C₇×#124	C₂³	1	2	yes	—
174	C₇×#124	C₂³	1	1	yes	characteristic
175	C₇×#123	—	2	1	no	—
176	C₇×#123	—	2	2	no	—
177	C₇×C₂²⋊Q₈	—	2	1	no	—
178	C₇×C₂²⋊Q₈	—	2	1	no	—
179	C₇×C₂²⋊Q₈	—	2	2	no	—
180	C₇×C₂²⋊Q₈	—	2	1	no	—
181	C₇×C₂²⋊Q₈	—	2	1	no	—
182	C₇×C₂²⋊Q₈	—	2	1	no	—
183	C₇×C₂²⋊Q₈	—	2	2	no	—
184	C₇×C₂²⋊Q₈	—	2	2	no	—
185	C₇×C₂²⋊Q₈	—	2	2	no	—
186	C₇×C₂²⋊Q₈	—	2	2	no	—
187	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
188	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
189	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
190	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
192	C₇×#121	C₂³	1	1	yes	characteristic
193	C₄×C₇×Q₈	—	2	2	no	—
194	C₄×C₇×Q₈	—	2	1	no	—
195	C₄×C₇×Q₈	—	2	1	no	—
196	C₄×C₇×Q₈	—	2	2	no	—
197	C₄×C₇×Q₈	—	2	2	no	—
198	C₄×C₇×Q₈	—	2	2	no	—
199	C₄×C₇×Q₈	—	2	2	no	—
200	C₄×C₇×Q₈	—	2	2	no	—
201	C₄×C₇×Q₈	—	2	2	no	—
202	C₄×C₇×Q₈	—	2	1	no	—
203	C₄×C₇×Q₈	—	2	1	no	—
204	C₄×C₇×Q₈	—	2	1	no	—
205	C₄×C₇×Q₈	—	2	1	no	—
206	C₄×C₇×Q₈	—	2	1	no	—
207	C₄×C₇×Q₈	C₂³	1	2	yes	—
208	C₄×C₇×Q₈	C₂³	1	2	yes	—
209	C₄×C₇×Q₈	C₂³	1	2	yes	—
210	C₄×C₇×Q₈	C₂³	1	2	yes	—
211	C₄×C₇×Q₈	C₂³	1	2	yes	—
212	C₄×C₇×Q₈	C₂³	1	2	yes	—
213	C₄×C₇×Q₈	C₂³	1	2	yes	—
214	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
215	C₄×C₇×Q₈	C₂³	1	2	yes	—
216	C₄×C₇×Q₈	C₂³	1	2	yes	—
217	C₄×C₇×Q₈	C₂³	1	2	yes	—
218	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
219	C₄×C₇×Q₈	C₂³	1	2	yes	—
220	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
221	C₄×C₇×D₄	—	2	1	no	—
222	C₄×C₇×D₄	C₂³	1	2	yes	—
223	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
224	C₇×#117	—	2	1	no	—
225	C₇×#117	—	2	2	no	—
226	C₇×#117	—	2	1	no	—
227	C₇×#117	—	2	2	no	—
228	C₇×#117	—	2	2	no	—
229	C₇×#117	—	2	1	no	—
230	C₇×#117	C₂³	1	2	yes	—
231	C₇×#117	C₂³	1	2	yes	—
232	C₂×C₇×C₄⋊C₄	—	2	1	no	—
233	C₂×C₇×C₄⋊C₄	—	2	1	no	—
234	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₇	—	2	1	no	—
236	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
237	C₇×#107	C₂³	1	2	yes	—
238	C₇×#107	C₂³	1	2	yes	—
239	C₇×#107	C₂³	1	2	yes	—
240	C₇×#107	C₂³	1	2	yes	—
241	C₇×#107	C₂³	1	2	yes	—
242	C₇×#106	C₂³	1	2	yes	—
243	C₇×#106	C₂³	1	2	yes	—
244	C₇×#106	C₂³	1	2	yes	—
245	C₇×#106	C₂³	1	2	yes	—
246	C₇×#106	C₂³	1	2	yes	—
247	C₇×#106	C₂³	1	2	yes	—
248	C₇×#106	C₂³	1	2	yes	—
249	C₇×C₄⋊C₈	C₂³	1	2	yes	—
250	C₇×C₄⋊C₈	C₂³	1	2	yes	—
251	C₇×C₄⋊C₈	C₂³	1	2	yes	—
252	C₇×C₄⋊C₈	C₂³	1	2	yes	—
253	C₇×C₄⋊C₈	C₂³	1	2	yes	—
254	C₇×C₄⋊C₈	C₂³	1	2	yes	—
255	C₇×#103	C₂³	1	2	yes	—
256	C₇×#103	C₂³	1	2	yes	—
257	C₇×#103	C₂³	1	2	yes	—
258	C₇×#103	C₂³	1	2	yes	—
259	C₇×#103	C₂³	1	2	yes	—
260	C₇×#103	C₂³	1	2	yes	—
261	C₇×#103	C₂³	1	2	yes	—
262	C₇×#103	C₂³	1	2	yes	—
263	C₇×#103	C₂³	1	2	yes	—
264	C₇×#103	C₂³	1	2	yes	—
265	C₇×#103	C₂³	1	2	yes	—
266	C₇×#103	C₂³	1	2	yes	—
267	C₇×#103	C₂³	1	2	yes	—
268	C₇×#102	C₂³	1	2	yes	—
269	C₇×#102	C₂³	1	2	yes	—
270	C₇×#102	C₂³	1	2	yes	—
271	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₇×#97	C₂³	1	1	yes	characteristic
275	C₇×#97	C₂³	1	1	yes	characteristic
276	C₇×#97	C₂³	1	2	yes	—
277	C₇×#97	C₂³	1	2	yes	—
278	C₇×#97	C₂³	1	2	yes	—
279	C₄×C₇×C₈	C₂³	1	2	yes	—
280	C₄×C₇×C₈	C₂³	1	2	yes	—
281	#3555	C₂×C₇	1	1	yes	characteristic
282	#3502	C₂×C₇	1	1	yes	characteristic, complemented
283	#3390	C₂×C₇	1	2	yes	complemented
284	#3388	C₂×C₇	1	2	yes	complemented
285	#3387	C₂×C₇	1	2	yes	complemented
286	#3387	C₂×C₇	1	2	yes	complemented
287	#3377	C₂×C₇	1	2	yes	complemented
288	#3377	C₂×C₇	1	2	yes	complemented
289	#3374	C₂×C₇	1	2	yes	complemented
290	#3369	C₂×C₇	1	2	yes	complemented
291	#3244	C₂×C₇	1	2	yes	—
292	#3242	C₂×C₇	1	2	yes	complemented
293	#3240	C₂×C₇	1	1	yes	characteristic
294	#3237	C₂×C₇	1	1	yes	characteristic, complemented
295	#3127	C₂×C₇	1	2	yes	complemented
296	#3121	C₂×C₇	1	2	yes	—
297	#3117	C₂×C₇	1	1	yes	characteristic
298	#3113	C₂×C₇	1	1	yes	characteristic, complemented
299	#2987	C₂×C₇	1	1	yes	characteristic, complemented
300	C₂×C₇×Q₈	—	2	4	no	—
301	C₂×C₇×Q₈	—	2	1	no	—
302	C₂×C₇×Q₈	—	2	1	no	—
303	C₂×C₇×Q₈	—	2	1	no	—
304	C₂×C₇×Q₈	—	2	2	no	—
305	C₂×C₇×Q₈	—	2	1	no	—
306	C₂×C₇×Q₈	—	2	2	no	—
307	C₂×C₇×Q₈	—	2	2	no	—
308	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
309	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
310	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
311	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
312	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
313	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
314	C₂×C₇×D₄	—	2	1	no	—
315	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₇	—	2	1	no	—
317	C₂²×C₄×C₇	—	2	1	no	—
318	C₂²×C₄×C₇	—	2	1	no	—
319	C₂²×C₄×C₇	—	2	2	no	—
320	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
323	C₇×Q₁₆	—	2	4	no	—
324	C₇×Q₁₆	—	2	4	no	—
325	C₇×Q₁₆	—	2	4	no	—
326	C₇×SD₁₆	—	2	4	no	—
327	C₂×C₇×C₈	C₂⁴	1	2	yes	—
328	C₂×C₇×C₈	C₂⁴	1	2	yes	—
329	C₂×C₇×C₈	C₂⁴	1	2	yes	—
330	C₂×C₇×C₈	C₂⁴	1	2	yes	—
331	C₇×C₄⋊C₄	—	2	1	no	—
332	C₇×C₄⋊C₄	—	2	2	no	—
333	C₇×C₄⋊C₄	—	2	2	no	—
334	C₇×C₄⋊C₄	—	2	2	no	—
335	C₇×C₄⋊C₄	—	2	1	no	—
336	C₇×C₄⋊C₄	—	2	1	no	—
337	C₇×C₄⋊C₄	—	2	2	no	—
338	C₇×C₄⋊C₄	—	2	2	no	—
339	C₇×C₄⋊C₄	—	2	2	no	—
340	C₇×C₄⋊C₄	—	2	2	no	—
341	C₇×C₄⋊C₄	—	2	2	no	—
342	C₇×C₄⋊C₄	—	2	1	no	—
343	C₇×C₄⋊C₄	—	2	1	no	—
344	C₇×C₄⋊C₄	—	2	1	no	—
345	C₇×C₄⋊C₄	—	2	2	no	—
346	C₇×C₄⋊C₄	—	2	1	no	—
347	C₇×C₄⋊C₄	—	2	2	no	—
348	C₇×C₄⋊C₄	—	2	2	no	—
349	C₇×C₄⋊C₄	—	2	1	no	—
350	C₇×C₄⋊C₄	—	2	2	no	—
351	C₇×C₄⋊C₄	—	2	2	no	—
352	C₇×C₄⋊C₄	—	2	2	no	—
353	C₇×C₄⋊C₄	—	2	2	no	—
354	C₇×C₄⋊C₄	—	2	2	no	—
355	C₇×C₄⋊C₄	—	2	2	no	—
356	C₇×C₄⋊C₄	—	2	2	no	—
357	C₇×C₄⋊C₄	—	2	1	no	—
358	C₇×C₄⋊C₄	—	2	2	no	—
359	C₇×C₄⋊C₄	—	2	2	no	—
360	C₇×C₄⋊C₄	—	2	2	no	—
361	C₇×C₄⋊C₄	—	2	2	no	—
362	C₇×C₄⋊C₄	—	2	2	no	—
363	C₇×C₄⋊C₄	—	2	2	no	—
364	C₇×C₄⋊C₄	—	2	1	no	—
365	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
366	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
367	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
368	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
369	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
370	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
371	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
372	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
373	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
374	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
375	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
376	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
377	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
378	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
379	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
380	C₇×C₂²⋊C₄	—	2	2	no	—
381	C₇×C₂²⋊C₄	—	2	2	no	—
382	C₇×C₂²⋊C₄	—	2	1	no	—
383	C₇×C₂²⋊C₄	—	2	1	no	—
384	C₇×C₂²⋊C₄	—	2	1	no	—
385	C₇×C₂²⋊C₄	—	2	1	no	—
386	C₇×C₂²⋊C₄	—	2	2	no	—
387	C₇×C₂²⋊C₄	—	2	2	no	—
388	C₇×C₂²⋊C₄	—	2	1	no	—
389	C₇×C₂²⋊C₄	—	2	2	no	—
390	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
391	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
392	C₄²×C₇	—	2	2	no	—
393	C₄²×C₇	—	2	2	no	—
394	C₄²×C₇	—	2	2	no	—
395	C₄²×C₇	—	2	1	no	—
396	C₄²×C₇	—	2	2	no	—
397	C₄²×C₇	—	2	2	no	—
398	C₄²×C₇	—	2	2	no	—
399	C₄²×C₇	—	2	2	no	—
400	C₄²×C₇	—	2	2	no	—
401	C₄²×C₇	—	2	2	no	—
402	C₄²×C₇	—	2	2	no	—
403	C₄²×C₇	—	2	2	no	—
404	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
405	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
406	C₄²×C₇	C₂⁴	1	2	yes	—
407	C₄²×C₇	C₂⁴	1	2	yes	—
408	C₄²×C₇	C₂⁴	1	1	yes	characteristic
409	C₄²×C₇	C₂⁴	1	1	yes	characteristic
410	#563	—	2	2	no	—
411	Q₈²	—	2	1	no	—
412	Q₈²	C₂²×C₇	1	2	yes	—
413	Q₈²	C₂²×C₇	1	1	yes	characteristic
414	#557	—	2	1	no	—
415	#557	—	2	2	no	—
416	#557	C₂²×C₇	1	1	yes	characteristic
417	#557	C₂²×C₇	1	2	yes	—
418	#557	C₂²×C₇	1	2	yes	—
419	#557	C₂²×C₇	1	2	yes	—
420	#557	C₂²×C₇	1	2	yes	—
421	#556	—	2	1	no	—
422	#556	C₂²×C₇	1	2	yes	—
423	#556	C₂²×C₇	1	1	yes	characteristic
424	#554	C₂²×C₇	1	1	yes	characteristic
425	#552	—	2	1	no	—
426	#544	—	2	1	no	—
427	#544	—	2	1	no	—
428	#544	—	2	1	no	—
429	#544	C₂²×C₇	1	2	yes	—
430	#542	C₂²×C₇	1	2	yes	—
431	#541	—	2	1	no	—
432	#541	—	2	2	no	—
433	#541	C₂²×C₇	1	2	yes	—
434	#533	—	2	2	no	—
435	#533	C₂²×C₇	1	1	yes	characteristic
436	#533	C₂²×C₇	1	1	yes	characteristic
437	#533	C₂²×C₇	1	1	yes	characteristic
438	#529	C₂²×C₇	1	1	yes	characteristic
439	#519	C₂²×C₇	1	2	yes	—
440	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
441	#501	C₂²×C₇	1	1	yes	characteristic
442	#501	C₂²×C₇	1	2	yes	—
443	#501	C₂²×C₇	1	2	yes	—
444	#501	C₂²×C₇	1	2	yes	—
445	#501	C₂²×C₇	1	1	yes	characteristic
446	#499	C₂²×C₇	1	2	yes	—
447	#498	C₂²×C₇	1	2	yes	—
448	#491	C₂²×C₇	1	2	yes	—
449	#491	C₂²×C₇	1	2	yes	—
450	#489	C₂²×C₇	1	1	yes	characteristic
451	#489	C₂²×C₇	1	2	yes	—
452	#489	C₂²×C₇	1	1	yes	characteristic
453	#488	C₂²×C₇	1	2	yes	—
454	#487	C₂²×C₇	1	2	yes	—
455	#485	C₂²×C₇	1	2	yes	—
456	#485	C₂²×C₇	1	2	yes	—
457	#485	C₂²×C₇	1	2	yes	—
458	#484	C₂²×C₇	1	1	yes	characteristic
459	#483	C₂²×C₇	1	2	yes	—
460	#482	C₂²×C₇	1	2	yes	—
461	#481	C₂²×C₇	1	1	yes	characteristic
462	#479	C₂²×C₇	1	2	yes	—
463	#479	C₂²×C₇	1	2	yes	—
464	#479	C₂²×C₇	1	2	yes	—
465	#479	C₂²×C₇	1	2	yes	—
466	#479	C₂²×C₇	1	2	yes	—
467	#479	C₂²×C₇	1	2	yes	—
468	#479	C₂²×C₇	1	2	yes	—
469	#478	C₂²×C₇	1	2	yes	—
470	#478	C₂²×C₇	1	2	yes	—
471	#477	C₂²×C₇	1	2	yes	—
472	#477	C₂²×C₇	1	2	yes	—
473	#477	C₂²×C₇	1	2	yes	—
474	#476	C₂²×C₇	1	2	yes	—
475	#475	C₂²×C₇	1	2	yes	—
476	#475	C₂²×C₇	1	2	yes	—
477	#475	C₂²×C₇	1	2	yes	—
478	#475	C₂²×C₇	1	2	yes	—
479	#475	C₂²×C₇	1	2	yes	—
480	#464	C₂²×C₇	1	2	yes	—
481	#464	C₂²×C₇	1	2	yes	—
482	#464	C₂²×C₇	1	2	yes	—
483	#462	C₂²×C₇	1	2	yes	—
484	#462	C₂²×C₇	1	2	yes	—
485	#462	C₂²×C₇	1	2	yes	—
486	#451	C₂²×C₇	1	2	yes	—
487	#451	C₂²×C₇	1	1	yes	characteristic
488	#448	C₂²×C₇	1	1	yes	characteristic
489	#446	C₂²×C₇	1	2	yes	—
490	#446	C₂²×C₇	1	2	yes	—
491	#446	C₂²×C₇	1	2	yes	—
492	#446	C₂²×C₇	1	2	yes	—
493	#441	C₂²×C₇	1	2	yes	—
494	#441	C₂²×C₇	1	2	yes	—
495	#441	C₂²×C₇	1	2	yes	—
496	#441	C₂²×C₇	1	2	yes	—
497	#441	C₂²×C₇	1	2	yes	—
498	#441	C₂²×C₇	1	2	yes	—
499	#440	C₂²×C₇	1	2	yes	—
500	#440	C₂²×C₇	1	2	yes	—
501	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
502	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
503	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
504	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
505	#433	C₂²×C₇	1	2	yes	—
506	#433	C₂²×C₇	1	2	yes	—
507	#432	C₂²×C₇	1	1	yes	characteristic
508	#432	C₂²×C₇	1	1	yes	characteristic
509	C₂³×C₇	—	2	1	no	—
510	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
511	C₇×Q₈	—	2	4	no	—
512	C₇×Q₈	—	2	2	no	—
513	C₇×Q₈	—	2	2	no	—
514	C₇×Q₈	—	2	2	no	—
515	C₇×Q₈	—	2	2	no	—
516	C₇×Q₈	—	4	1	no	—
517	C₇×Q₈	—	4	1	no	—
518	C₇×Q₈	—	4	2	no	—
519	C₇×Q₈	—	4	2	no	—
520	C₇×Q₈	—	8	1	no	—
521	C₇×Q₈	—	8	1	no	—
522	C₇×Q₈	—	8	2	no	—
523	C₇×Q₈	—	8	2	no	—
524	C₇×Q₈	—	8	2	no	—
525	C₇×Q₈	2₋¹⁺⁴	1	4	yes	—
526	C₇×D₄	—	2	2	no	—
527	C₇×D₄	—	8	1	no	—
528	C₂×C₄×C₇	—	2	4	no	—
529	C₂×C₄×C₇	—	2	2	no	—
530	C₂×C₄×C₇	—	2	2	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	2	1	no	—
533	C₂×C₄×C₇	—	2	2	no	—
534	C₂×C₄×C₇	—	2	1	no	—
535	C₂×C₄×C₇	—	2	2	no	—
536	C₂×C₄×C₇	—	2	1	no	—
537	C₂×C₄×C₇	—	2	2	no	—
538	C₂×C₄×C₇	—	2	2	no	—
539	C₂×C₄×C₇	—	4	1	no	—
540	C₂×C₄×C₇	—	4	1	no	—
541	C₂×C₄×C₇	—	4	2	no	—
542	C₂×C₄×C₇	—	8	2	no	—
543	C₂×C₄×C₇	—	8	1	no	—
544	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
550	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
551	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
553	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
554	C₇×C₈	—	2	2	no	—
555	C₇×C₈	—	2	2	no	—
556	C₇×C₈	—	2	2	no	—
557	C₇×C₈	—	2	2	no	—
558	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
559	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
560	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
561	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
562	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
563	C₄⋊Q₈	—	2	2	no	—
564	C₄⋊Q₈	—	2	2	no	—
565	C₄⋊Q₈	—	2	2	no	—
566	C₄⋊Q₈	—	2	2	no	—
567	C₄⋊Q₈	—	2	2	no	—
568	C₄⋊Q₈	—	2	2	no	—
569	C₄⋊Q₈	—	2	1	no	—
570	C₄⋊Q₈	—	2	2	no	—
571	C₄⋊Q₈	—	2	2	no	—
572	C₄⋊Q₈	—	2	2	no	—
573	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
574	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
575	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
576	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
577	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
578	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
579	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
580	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
581	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
582	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
583	#126	—	2	2	no	—
584	#126	—	2	2	no	—
585	#126	—	2	2	no	—
586	#126	—	2	2	no	—
587	#126	—	2	2	no	—
588	#126	—	2	2	no	—
589	#126	—	2	1	no	—
590	#125	—	2	2	no	—
591	#125	—	2	2	no	—
592	#125	—	2	2	no	—
593	#125	—	2	2	no	—
594	#125	—	2	2	no	—
595	#125	—	2	2	no	—
596	#125	—	2	2	no	—
597	#125	—	2	1	no	—
598	#125	—	2	2	no	—
599	#125	—	2	2	no	—
600	#125	—	2	2	no	—
601	#125	—	2	2	no	—
602	#125	—	2	2	no	—
603	#125	—	2	1	no	—
604	#125	C₇×D₄	1	2	yes	—
605	#125	C₂³×C₇	1	1	yes	characteristic
606	#125	C₂³×C₇	1	2	yes	—
607	#125	C₂³×C₇	1	2	yes	—
608	#125	C₂³×C₇	1	2	yes	—
609	#125	C₂³×C₇	1	2	yes	—
610	#124	—	2	2	no	—
611	#124	C₂³×C₇	1	1	yes	characteristic
612	#124	C₂³×C₇	1	2	yes	—
613	#123	—	2	1	no	—
614	#123	—	2	2	no	—
615	C₂²⋊Q₈	—	2	1	no	—
616	C₂²⋊Q₈	—	2	1	no	—
617	C₂²⋊Q₈	—	2	2	no	—
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	—	2	1	no	—
620	C₂²⋊Q₈	—	2	1	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	—	2	2	no	—
624	C₂²⋊Q₈	—	2	2	no	—
625	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
626	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
627	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
628	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
629	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
630	#121	C₂³×C₇	1	1	yes	characteristic
631	C₄×Q₈	—	2	2	no	—
632	C₄×Q₈	—	2	1	no	—
633	C₄×Q₈	—	2	1	no	—
634	C₄×Q₈	—	2	2	no	—
635	C₄×Q₈	—	2	2	no	—
636	C₄×Q₈	—	2	2	no	—
637	C₄×Q₈	—	2	2	no	—
638	C₄×Q₈	—	2	2	no	—
639	C₄×Q₈	—	2	2	no	—
640	C₄×Q₈	—	2	1	no	—
641	C₄×Q₈	—	2	1	no	—
642	C₄×Q₈	—	2	1	no	—
643	C₄×Q₈	—	2	1	no	—
644	C₄×Q₈	—	2	1	no	—
645	C₄×Q₈	C₂³×C₇	1	2	yes	—
646	C₄×Q₈	C₂³×C₇	1	2	yes	—
647	C₄×Q₈	C₂³×C₇	1	2	yes	—
648	C₄×Q₈	C₂³×C₇	1	2	yes	—
649	C₄×Q₈	C₂³×C₇	1	2	yes	—
650	C₄×Q₈	C₂³×C₇	1	2	yes	—
651	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
652	C₄×Q₈	C₂³×C₇	1	2	yes	—
653	C₄×Q₈	C₂³×C₇	1	2	yes	—
654	C₄×Q₈	C₂³×C₇	1	2	yes	—
655	C₄×Q₈	C₂³×C₇	1	2	yes	—
656	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
657	C₄×Q₈	C₂³×C₇	1	2	yes	—
658	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
661	C₄×D₄	C₂³×C₇	1	2	yes	—
662	#117	—	2	1	no	—
663	#117	—	2	2	no	—
664	#117	—	2	1	no	—
665	#117	—	2	2	no	—
666	#117	—	2	2	no	—
667	#117	—	2	1	no	—
668	#117	C₂³×C₇	1	2	yes	—
669	#117	C₂³×C₇	1	2	yes	—
670	C₂×C₄⋊C₄	—	2	1	no	—
671	C₂×C₄⋊C₄	—	2	1	no	—
672	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
673	C₂×C₄²	—	2	1	no	—
674	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
675	#107	C₂³×C₇	1	2	yes	—
676	#107	C₂³×C₇	1	2	yes	—
677	#107	C₂³×C₇	1	2	yes	—
678	#107	C₂³×C₇	1	2	yes	—
679	#107	C₂³×C₇	1	2	yes	—
680	#106	C₂³×C₇	1	2	yes	—
681	#106	C₂³×C₇	1	2	yes	—
682	#106	C₂³×C₇	1	2	yes	—
683	#106	C₂³×C₇	1	2	yes	—
684	#106	C₂³×C₇	1	2	yes	—
685	#106	C₂³×C₇	1	2	yes	—
686	#106	C₂³×C₇	1	2	yes	—
687	C₄⋊C₈	C₂³×C₇	1	2	yes	—
688	C₄⋊C₈	C₂³×C₇	1	2	yes	—
689	C₄⋊C₈	C₂³×C₇	1	2	yes	—
690	C₄⋊C₈	C₂³×C₇	1	2	yes	—
691	C₄⋊C₈	C₂³×C₇	1	2	yes	—
692	C₄⋊C₈	C₂³×C₇	1	2	yes	—
693	#103	C₂³×C₇	1	2	yes	—
694	#103	C₂³×C₇	1	2	yes	—
695	#103	C₂³×C₇	1	2	yes	—
696	#103	C₂³×C₇	1	2	yes	—
697	#103	C₂³×C₇	1	2	yes	—
698	#103	C₂³×C₇	1	2	yes	—
699	#103	C₂³×C₇	1	2	yes	—
700	#103	C₂³×C₇	1	2	yes	—
701	#103	C₂³×C₇	1	2	yes	—
702	#103	C₂³×C₇	1	2	yes	—
703	#103	C₂³×C₇	1	2	yes	—
704	#103	C₂³×C₇	1	2	yes	—
705	#103	C₂³×C₇	1	2	yes	—
706	#102	C₂³×C₇	1	2	yes	—
707	#102	C₂³×C₇	1	2	yes	—
708	#102	C₂³×C₇	1	2	yes	—
709	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
710	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
711	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
712	#97	C₂³×C₇	1	2	yes	—
713	#97	C₂³×C₇	1	1	yes	characteristic
714	#97	C₂³×C₇	1	1	yes	characteristic
715	#97	C₂³×C₇	1	2	yes	—
716	#97	C₂³×C₇	1	2	yes	—
717	C₄×C₈	C₂³×C₇	1	2	yes	—
718	C₄×C₈	C₂³×C₇	1	2	yes	—
719	C₂²×C₇	—	2	1	no	—
720	C₂²×C₇	—	2	1	no	—
721	C₂²×C₇	—	2	1	no	—
722	C₂²×C₇	—	4	1	no	—
723	C₂²×C₇	—	4	1	no	—
724	C₂²×C₇	—	4	1	no	—
725	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
726	C₄×C₇	—	2	1	no	—
727	C₄×C₇	—	2	1	no	—
728	C₄×C₇	—	2	1	no	—
729	C₄×C₇	—	2	1	no	—
730	C₄×C₇	—	2	2	no	—
731	C₄×C₇	—	2	2	no	—
732	C₄×C₇	—	2	2	no	—
733	C₄×C₇	—	2	2	no	—
734	C₄×C₇	—	2	4	no	—
735	C₄×C₇	—	2	1	no	—
736	C₄×C₇	—	4	1	no	—
737	C₄×C₇	—	4	2	no	—
738	C₄×C₇	—	4	2	no	—
739	C₄×C₇	—	4	1	no	—
740	C₄×C₇	—	4	2	no	—
741	C₄×C₇	—	4	2	no	—
742	C₄×C₇	—	4	2	no	—
743	C₄×C₇	—	4	1	no	—
744	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
745	C₂×Q₈	—	2	4	no	—
746	C₂×Q₈	—	2	1	no	—
747	C₂×Q₈	—	2	1	no	—
748	C₂×Q₈	—	2	1	no	—
749	C₂×Q₈	—	2	2	no	—
750	C₂×Q₈	—	2	1	no	—
751	C₂×Q₈	—	2	2	no	—
752	C₂×Q₈	—	2	2	no	—
753	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
754	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
755	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
756	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
757	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
758	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
759	C₂×D₄	—	2	1	no	—
760	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
761	C₂²×C₄	—	2	1	no	—
762	C₂²×C₄	—	2	1	no	—
763	C₂²×C₄	—	2	1	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
766	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
768	Q₁₆	—	2	4	no	—
769	Q₁₆	—	2	4	no	—
770	Q₁₆	—	2	4	no	—
771	SD₁₆	—	2	4	no	—
772	C₂×C₈	C₂⁴×C₇	1	2	yes	—
773	C₂×C₈	C₂⁴×C₇	1	2	yes	—
774	C₂×C₈	C₂⁴×C₇	1	2	yes	—
775	C₂×C₈	C₂⁴×C₇	1	2	yes	—
776	C₄⋊C₄	—	2	1	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	1	no	—
788	C₄⋊C₄	—	2	1	no	—
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	1	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	1	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	1	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
811	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
812	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
813	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
814	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
815	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
816	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
817	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
818	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
819	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
820	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
821	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
822	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
823	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
824	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	1	no	—
828	C₂²⋊C₄	—	2	1	no	—
829	C₂²⋊C₄	—	2	1	no	—
830	C₂²⋊C₄	—	2	1	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	1	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
836	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	1	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
850	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
851	C₄²	C₂⁴×C₇	1	2	yes	—
852	C₄²	C₂⁴×C₇	1	2	yes	—
853	C₄²	C₂⁴×C₇	1	1	yes	characteristic
854	C₄²	C₂⁴×C₇	1	1	yes	characteristic
855	C₂×C₇	—	4	1	no	—
856	C₂×C₇	—	8	1	no	—
857	C₂×C₇	#3486	1	1	yes	characteristic
858	C₂×C₇	#3586	1	1	yes	characteristic
859	C₂×C₇	#3586	1	1	yes	characteristic
860	C₂³	—	2	1	no	—
861	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
862	Q₈	—	2	4	no	—
863	Q₈	—	2	2	no	—
864	Q₈	—	2	2	no	—
865	Q₈	—	2	2	no	—
866	Q₈	—	2	2	no	—
867	Q₈	—	4	1	no	—
868	Q₈	—	4	1	no	—
869	Q₈	—	4	2	no	—
870	Q₈	—	4	2	no	—
871	Q₈	—	8	1	no	—
872	Q₈	—	8	1	no	—
873	Q₈	—	8	2	no	—
874	Q₈	—	8	2	no	—
875	Q₈	—	8	2	no	—
876	Q₈	C₇×2₋¹⁺⁴	1	4	yes	—
877	D₄	—	2	2	no	—
878	D₄	—	8	1	no	—
879	C₂×C₄	—	2	4	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	2	no	—
893	C₂×C₄	—	8	2	no	—
894	C₂×C₄	—	8	1	no	—
895	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
896	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
897	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
898	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
899	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
900	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
901	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
902	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
903	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
904	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
905	C₈	—	2	2	no	—
906	C₈	—	2	2	no	—
907	C₈	—	2	2	no	—
908	C₈	—	2	2	no	—
909	C₇	#61875	1	1	yes	characteristic, direct product factor, Sylow
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	4	no	—
926	C₄	—	2	1	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	1	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	2	no	—
934	C₄	—	4	1	no	—
935	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
936	C₂	—	4	1	no	—
937	C₂	—	8	1	no	—
938	C₂	C₇×#3486	1	1	yes	characteristic
939	C₂	C₇×#3586	1	1	yes	characteristic
940	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×#121	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3502	C₂	semidirect
3. C₇×#3390	C₂	semidirect
4. C₇×#3388	C₂	semidirect
5. C₇×#3387	C₂	semidirect
6. C₇×#3387	C₂	semidirect
7. C₇×#3377	C₂	semidirect
8. C₇×#3377	C₂	semidirect
9. C₇×#3374	C₂	semidirect
10. C₇×#3369	C₂	semidirect
12. C₇×#3242	C₂	semidirect
14. C₇×#3237	C₂	semidirect
15. C₇×#3127	C₂	semidirect
18. C₇×#3113	C₂	semidirect
19. C₇×#2987	C₂	semidirect
119. #61875	C₇	direct (N × H)
282. #3502	C₂×C₇	semidirect
283. #3390	C₂×C₇	semidirect
284. #3388	C₂×C₇	semidirect
285. #3387	C₂×C₇	semidirect
286. #3387	C₂×C₇	semidirect
287. #3377	C₂×C₇	semidirect
288. #3377	C₂×C₇	semidirect
289. #3374	C₂×C₇	semidirect
290. #3369	C₂×C₇	semidirect
292. #3242	C₂×C₇	semidirect
294. #3237	C₂×C₇	semidirect
295. #3127	C₂×C₇	semidirect
298. #3113	C₂×C₇	semidirect
299. #2987	C₂×C₇	semidirect
909. C₇	#61875	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×#3555	2
C₇×#3502	2
C₇×#3390	2
C₇×#3388	2
C₇×#3387	2
C₇×#3377	2
C₇×#3374	2
C₇×#3369	2
C₇×#3244	2
C₇×#3242	2
C₇×#3240	2
C₇×#3237	2
C₇×#3127	2
C₇×#3121	2
C₇×#3117	2
C₇×#3113	2
C₇×#2987	2
#61875	7

Subgroups — C7×#61875 #13239091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61875 #13239091