Subgroups — C₇×#60819 #13238035

Order 1792.

2058 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3225	C₂	1	4	yes	maximal, complemented
4	C₇×#3224	C₂	1	4	yes	maximal, complemented
5	C₇×#3212	C₂	1	4	yes	maximal, complemented
6	C₇×#3211	C₂	1	4	yes	maximal, complemented
7	C₇×#3153	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#495	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3044	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3043	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3042	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3041	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3011	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3010	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3009	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
21	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
22	C₂×C₇×#137	C₂²	1	1	yes	characteristic
23	C₂×C₇×#137	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
30	C₇×#559	—	2	2	no	—
31	C₇×#556	—	2	2	no	—
32	C₇×#551	—	2	4	no	—
33	C₇×#548	—	2	2	no	—
34	C₇×#546	—	2	4	no	—
35	C₇×#546	—	2	2	no	—
36	C₇×#542	C₂²	1	4	yes	complemented
37	C₇×#536	C₂²	1	1	yes	characteristic
38	C₇×#536	C₂²	1	1	yes	characteristic
39	C₇×#536	C₂²	1	2	yes	complemented
40	C₇×#535	C₂²	1	1	yes	characteristic
41	C₇×#535	C₂²	1	1	yes	characteristic
42	C₇×#535	C₂²	1	2	yes	complemented
43	C₇×#533	C₂²	1	1	yes	characteristic, complemented
44	C₇×#532	C₂²	1	1	yes	characteristic
45	C₇×#532	C₂²	1	2	yes	complemented
46	C₇×#529	C₂²	1	4	yes	complemented
47	C₂×C₇×#124	C₂²	1	1	yes	characteristic
48	C₂×C₇×#124	C₂²	1	2	yes	complemented
49	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
50	C₇×#519	C₂²	1	1	yes	characteristic, complemented
51	C₇×#518	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₇×#41	C₂²	1	1	yes	characteristic
53	C₇×#497	C₂²	1	2	yes	complemented
54	C₇×#496	C₂²	1	2	yes	complemented
55	C₇×#495	C₂²	1	2	yes	complemented
56	C₇×#495	C₂²	1	4	yes	complemented
57	C₇×#495	C₂²	1	2	yes	complemented
58	C₇×#495	C₂²	1	4	yes	complemented
59	C₇×#489	C₂²	1	4	yes	complemented
60	C₇×#488	C₂²	1	2	yes	complemented
61	C₇×#488	C₂²	1	4	yes	complemented
62	C₇×#488	C₂²	1	2	yes	complemented
63	C₇×#487	C₂²	1	2	yes	complemented
64	C₇×#486	C₂²	1	2	yes	complemented
65	C₇×#464	C₂²	1	4	yes	complemented
66	C₇×#464	C₂²	1	4	yes	complemented
67	C₇×#463	C₂²	1	4	yes	complemented
68	C₇×#463	C₂²	1	4	yes	complemented
69	C₇×#462	C₂²	1	4	yes	complemented
70	C₇×#461	C₂²	1	4	yes	complemented
71	C₇×#460	C₂²	1	4	yes	complemented
72	C₇×#459	C₂²	1	4	yes	complemented
73	C₇×#452	C₂²	1	4	yes	complemented
74	C₇×#452	C₂²	1	4	yes	complemented
75	C₇×#451	C₂²	1	4	yes	complemented
76	C₇×#450	C₂²	1	4	yes	complemented
77	C₇×#449	C₂²	1	4	yes	—
78	C₇×#449	C₂²	1	4	yes	complemented
79	C₇×#448	C₂²	1	4	yes	complemented
80	C₇×#447	C₂²	1	4	yes	—
81	C₇×#433	C₂²	1	4	yes	complemented
82	C₇×#431	C₂²	1	4	yes	complemented
83	C₇×#424	C₂²	1	1	yes	characteristic, complemented
84	C₇×#424	C₂²	1	1	yes	characteristic, complemented
85	C₇×#419	C₂²	1	1	yes	characteristic, complemented
86	C₇×#419	C₂²	1	1	yes	characteristic, complemented
87	C₇×#418	C₂²	1	1	yes	characteristic
88	C₇×#418	C₂²	1	1	yes	characteristic
89	C₇×#416	C₂²	1	1	yes	characteristic
90	C₇×#416	C₂²	1	1	yes	characteristic
91	C₇×#416	C₂²	1	1	yes	characteristic, complemented
92	C₇×#416	C₂²	1	1	yes	characteristic, complemented
93	C₇×#408	C₂²	1	1	yes	characteristic
94	C₇×#408	C₂²	1	1	yes	characteristic
95	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
96	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
97	#60819	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₇×2₋¹⁺⁴	—	4	2	no	—
99	C₇×2₋¹⁺⁴	—	4	2	no	—
100	C₇×H(5,𝔽₂)	—	4	2	no	—
101	C₇×H(5,𝔽₂)	—	4	2	no	—
102	C₂×C₇×#41	—	2	1	no	—
103	C₂×C₇×#41	—	2	2	no	—
104	C₂×C₇×#41	—	2	1	no	—
105	C₂×C₇×#41	C₂³	1	1	yes	characteristic
106	C₂×C₇×#41	C₂³	1	1	yes	characteristic
107	C₂×C₇×#41	C₂³	1	2	yes	—
108	C₂×C₇×#41	C₂³	1	2	yes	—
109	C₂×C₇×#41	C₂³	1	1	yes	characteristic
110	C₂²×C₇×Q₈	—	2	1	no	—
111	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
112	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
113	C₂²×C₇×Q₈	C₂³	1	2	yes	—
114	C₂²×C₇×D₄	—	2	2	no	—
115	C₂²×C₇×D₄	—	2	1	no	—
116	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
117	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
118	C₂²×C₇×D₄	C₂³	1	2	yes	—
119	C₇×#137	—	4	2	no	—
120	C₇×#137	—	4	2	no	—
121	C₇×AGL(1,ℤ/8)	—	4	2	no	—
122	C₇×AGL(1,ℤ/8)	—	4	2	no	—
123	C₂×C₇×Q₁₆	—	4	2	no	—
124	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
125	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
126	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
127	C₂×C₇×SD₁₆	—	4	2	no	—
128	C₂×C₇×SD₁₆	—	4	2	no	—
129	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
130	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
131	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
132	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
133	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
134	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
135	C₂×C₇×D₈	—	4	2	no	—
136	C₂×C₇×D₈	C₂³	1	4	yes	—
137	C₂×C₇×D₈	C₂³	1	2	yes	—
138	C₂×C₇×D₈	C₂³	1	2	yes	—
139	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
141	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
142	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
143	C₇×C₄⋊Q₈	—	2	1	no	—
144	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
145	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
146	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
147	C₇×#127	—	2	1	no	—
148	C₇×#127	C₂³	1	1	yes	characteristic
149	C₇×#127	C₂³	1	2	yes	—
150	C₇×#126	—	2	4	no	—
151	C₇×#126	—	2	4	no	—
152	C₇×#125	C₂³	1	2	yes	—
153	C₇×#124	—	2	1	no	—
154	C₇×#124	—	2	1	no	—
155	C₇×#124	—	2	4	no	—
156	C₇×#124	—	2	2	no	—
157	C₇×#124	—	2	4	no	—
158	C₇×#124	—	2	2	no	—
159	C₇×#124	C₂³	1	2	yes	—
160	C₇×#124	C₂³	1	1	yes	characteristic
161	C₇×#124	C₂³	1	1	yes	characteristic
162	C₇×#124	C₂³	1	2	yes	—
163	C₇×#124	C₂³	1	2	yes	—
164	C₇×#124	C₂³	1	2	yes	—
165	C₇×#124	C₂³	1	2	yes	—
166	C₇×#124	C₂³	1	2	yes	—
167	C₇×#123	—	2	2	no	—
168	C₇×#123	—	2	4	no	—
169	C₇×#123	—	2	2	no	—
170	C₇×#123	—	2	4	no	—
171	C₇×#123	—	2	4	no	—
172	C₇×C₂²⋊Q₈	—	2	2	no	—
173	C₇×C₂²⋊Q₈	—	2	2	no	—
174	C₇×C₂²⋊Q₈	—	2	4	no	—
175	C₇×C₂²⋊Q₈	—	2	4	no	—
176	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
177	C₇×#121	—	2	2	no	—
178	C₇×#121	—	2	4	no	—
179	C₇×#121	—	2	2	no	—
180	C₇×#121	—	2	4	no	—
181	C₇×#121	C₂³	1	4	yes	—
182	C₇×#120	—	2	2	no	—
183	C₇×#120	—	2	2	no	—
184	C₇×#120	—	2	4	no	—
185	C₄×C₇×Q₈	—	2	2	no	—
186	C₄×C₇×Q₈	—	2	2	no	—
187	C₄×C₇×Q₈	D₄	1	2	yes	—
188	C₄×C₇×Q₈	C₂³	1	4	yes	—
189	C₄×C₇×D₄	—	2	4	no	—
190	C₄×C₇×D₄	—	2	2	no	—
191	C₄×C₇×D₄	—	2	2	no	—
192	C₄×C₇×D₄	—	2	4	no	—
193	C₄×C₇×D₄	D₄	1	4	yes	—
194	C₄×C₇×D₄	D₄	1	2	yes	—
195	C₄×C₇×D₄	C₂³	1	4	yes	—
196	C₇×#117	—	2	2	no	—
197	C₇×#117	—	2	4	no	—
198	C₇×#117	C₂³	1	1	yes	characteristic
199	C₇×#117	C₂³	1	1	yes	characteristic
200	C₇×#117	C₂³	1	1	yes	characteristic
201	C₇×#117	C₂³	1	2	yes	—
202	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
203	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
204	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
206	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₇	C₂³	1	2	yes	—
208	C₇×C₄⋊C₈	C₂³	1	4	yes	—
209	C₇×C₄⋊C₈	C₂³	1	4	yes	—
210	C₇×#103	C₂³	1	2	yes	—
211	C₇×#103	C₂³	1	2	yes	—
212	C₇×#103	C₂³	1	2	yes	—
213	C₇×#103	C₂³	1	2	yes	—
214	C₇×#103	C₂³	1	4	yes	—
215	C₇×#103	C₂³	1	4	yes	—
216	C₇×#102	C₂³	1	2	yes	—
217	C₇×#102	C₂³	1	2	yes	—
218	C₇×#102	C₂³	1	2	yes	—
219	C₇×#102	C₂³	1	2	yes	—
220	C₇×#102	C₂³	1	4	yes	—
221	C₇×#102	C₂³	1	4	yes	—
222	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
223	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
224	C₇×#97	C₂³	1	2	yes	—
225	C₄×C₇×C₈	C₂³	1	2	yes	—
226	C₄×C₇×C₈	C₂³	1	2	yes	—
227	C₄×C₇×C₈	C₂³	1	2	yes	—
228	#3510	C₂×C₇	1	1	yes	characteristic, complemented
229	#3500	C₂×C₇	1	1	yes	characteristic, complemented
230	#3225	C₂×C₇	1	4	yes	complemented
231	#3224	C₂×C₇	1	4	yes	complemented
232	#3212	C₂×C₇	1	4	yes	complemented
233	#3211	C₂×C₇	1	4	yes	complemented
234	#3153	C₂×C₇	1	1	yes	characteristic, complemented
235	C₂×#495	C₂×C₇	1	1	yes	characteristic, complemented
236	#3140	C₂×C₇	1	1	yes	characteristic, complemented
237	#3131	C₂×C₇	1	1	yes	characteristic, complemented
238	#3044	C₂×C₇	1	1	yes	characteristic, complemented
239	#3043	C₂×C₇	1	1	yes	characteristic, complemented
240	#3042	C₂×C₇	1	1	yes	characteristic, complemented
241	#3041	C₂×C₇	1	1	yes	characteristic, complemented
242	#3011	C₂×C₇	1	1	yes	characteristic, complemented
243	#3010	C₂×C₇	1	1	yes	characteristic, complemented
244	#3009	C₂×C₇	1	1	yes	characteristic, complemented
245	#3008	C₂×C₇	1	1	yes	characteristic, complemented
246	#2922	C₂×C₇	1	1	yes	characteristic, complemented
247	C₂⁴×C₇	—	2	1	no	—
248	C₂⁴×C₇	—	2	2	no	—
249	C₂⁴×C₇	—	2	1	no	—
250	C₇×#41	—	2	2	no	—
251	C₇×#41	—	2	2	no	—
252	C₇×#41	—	2	2	no	—
253	C₇×#41	—	2	2	no	—
254	C₇×#41	—	2	2	no	—
255	C₇×#41	—	2	2	no	—
256	C₇×#41	—	4	2	no	—
257	C₇×#41	—	4	2	no	—
258	C₇×#41	—	4	2	no	—
259	C₇×#41	—	4	2	no	—
260	C₇×#41	—	4	8	no	—
261	C₇×#41	—	4	4	no	—
262	C₇×#41	—	4	4	no	—
263	C₂×C₇×Q₈	—	2	1	no	—
264	C₂×C₇×Q₈	—	2	2	no	—
265	C₂×C₇×Q₈	—	2	1	no	—
266	C₂×C₇×Q₈	—	2	2	no	—
267	C₂×C₇×Q₈	—	2	2	no	—
268	C₂×C₇×Q₈	—	2	2	no	—
269	C₂×C₇×Q₈	—	2	2	no	—
270	C₂×C₇×Q₈	—	2	2	no	—
271	C₂×C₇×Q₈	—	4	2	no	—
272	C₂×C₇×Q₈	—	4	2	no	—
273	C₂×C₇×Q₈	—	4	4	no	—
274	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
275	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
276	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
277	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
278	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
279	C₂×C₇×D₄	—	2	2	no	—
280	C₂×C₇×D₄	—	2	1	no	—
281	C₂×C₇×D₄	—	2	2	no	—
282	C₂×C₇×D₄	—	2	1	no	—
283	C₂×C₇×D₄	—	2	4	no	—
284	C₂×C₇×D₄	—	2	1	no	—
285	C₂×C₇×D₄	—	2	2	no	—
286	C₂×C₇×D₄	—	2	1	no	—
287	C₂×C₇×D₄	—	2	4	no	—
288	C₂×C₇×D₄	—	2	2	no	—
289	C₂×C₇×D₄	—	2	2	no	—
290	C₂×C₇×D₄	—	2	2	no	—
291	C₂×C₇×D₄	—	2	2	no	—
292	C₂×C₇×D₄	—	2	2	no	—
293	C₂×C₇×D₄	—	4	2	no	—
294	C₂×C₇×D₄	—	4	2	no	—
295	C₂×C₇×D₄	—	4	8	no	—
296	C₂×C₇×D₄	—	4	4	no	—
297	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
298	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
299	C₂×C₇×D₄	C₂⁴	1	2	yes	—
300	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
301	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
302	C₂×C₇×D₄	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₇	—	2	1	no	—
304	C₂²×C₄×C₇	—	2	2	no	—
305	C₂²×C₄×C₇	—	2	1	no	—
306	C₂²×C₄×C₇	—	2	2	no	—
307	C₂²×C₄×C₇	—	2	1	no	—
308	C₂²×C₄×C₇	—	2	2	no	—
309	C₂²×C₄×C₇	—	2	1	no	—
310	C₂²×C₄×C₇	—	2	4	no	—
311	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
312	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
313	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
315	C₇×Q₁₆	—	4	4	no	—
316	C₇×Q₁₆	—	4	2	no	—
317	C₇×Q₁₆	—	4	2	no	—
318	C₇×SD₁₆	—	4	4	no	—
319	C₇×SD₁₆	—	4	4	no	—
320	C₇×SD₁₆	—	4	2	no	—
321	C₇×SD₁₆	—	4	2	no	—
322	C₇×SD₁₆	—	4	2	no	—
323	C₇×SD₁₆	—	4	2	no	—
324	C₇×D₈	—	4	4	no	—
325	C₇×D₈	—	4	2	no	—
326	C₇×D₈	—	4	2	no	—
327	C₇×M₁₆	—	2	2	no	—
328	C₇×M₁₆	—	2	2	no	—
329	C₂×C₇×C₈	—	2	2	no	—
330	C₂×C₇×C₈	—	2	2	no	—
331	C₂×C₇×C₈	C₂⁴	1	2	yes	—
332	C₂×C₇×C₈	C₂⁴	1	2	yes	—
333	C₂×C₇×C₈	C₂⁴	1	2	yes	—
334	C₂×C₇×C₈	C₂⁴	1	2	yes	—
335	C₇×C₄⋊C₄	—	2	2	no	—
336	C₇×C₄⋊C₄	—	2	4	no	—
337	C₇×C₄⋊C₄	—	2	4	no	—
338	C₇×C₄⋊C₄	—	2	2	no	—
339	C₇×C₄⋊C₄	—	2	4	no	—
340	C₇×C₄⋊C₄	—	2	2	no	—
341	C₇×C₄⋊C₄	—	2	2	no	—
342	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
343	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
344	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
345	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
346	C₇×C₂²⋊C₄	—	2	1	no	—
347	C₇×C₂²⋊C₄	—	2	1	no	—
348	C₇×C₂²⋊C₄	—	2	4	no	—
349	C₇×C₂²⋊C₄	—	2	4	no	—
350	C₇×C₂²⋊C₄	—	2	2	no	—
351	C₇×C₂²⋊C₄	—	2	4	no	—
352	C₇×C₂²⋊C₄	—	2	4	no	—
353	C₇×C₂²⋊C₄	—	2	4	no	—
354	C₇×C₂²⋊C₄	—	2	4	no	—
355	C₇×C₂²⋊C₄	—	2	4	no	—
356	C₇×C₂²⋊C₄	—	2	4	no	—
357	C₇×C₂²⋊C₄	—	2	4	no	—
358	C₇×C₂²⋊C₄	—	2	2	no	—
359	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
360	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
361	C₄²×C₇	—	2	4	no	—
362	C₄²×C₇	—	2	1	no	—
363	C₄²×C₇	—	2	1	no	—
364	C₄²×C₇	C₂×D₄	1	4	yes	—
365	C₄²×C₇	C₂×D₄	1	2	yes	—
366	C₄²×C₇	C₂⁴	1	1	yes	characteristic
367	C₄²×C₇	C₂⁴	1	1	yes	characteristic
368	C₄²×C₇	C₂⁴	1	2	yes	—
369	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
370	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
371	C₂×#137	C₂²×C₇	1	1	yes	characteristic
372	C₂×#137	C₂²×C₇	1	1	yes	characteristic, complemented
373	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
374	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic, complemented
375	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
376	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
377	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
378	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
379	#559	—	2	2	no	—
380	#556	—	2	2	no	—
381	#551	—	2	4	no	—
382	#548	—	2	2	no	—
383	#546	—	2	4	no	—
384	#546	—	2	2	no	—
385	#542	C₂²×C₇	1	4	yes	complemented
386	#536	C₂²×C₇	1	1	yes	characteristic
387	#536	C₂²×C₇	1	1	yes	characteristic
388	#536	C₂²×C₇	1	2	yes	complemented
389	#535	C₂²×C₇	1	1	yes	characteristic
390	#535	C₂²×C₇	1	1	yes	characteristic
391	#535	C₂²×C₇	1	2	yes	complemented
392	#533	C₂²×C₇	1	1	yes	characteristic, complemented
393	#532	C₂²×C₇	1	1	yes	characteristic
394	#532	C₂²×C₇	1	2	yes	complemented
395	#529	C₂²×C₇	1	4	yes	complemented
396	C₂×#124	C₂²×C₇	1	1	yes	characteristic
397	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
398	C₂×#124	C₂²×C₇	1	2	yes	complemented
399	#519	C₂²×C₇	1	1	yes	characteristic, complemented
400	#518	C₂²×C₇	1	1	yes	characteristic, complemented
401	C₄×#41	C₂²×C₇	1	1	yes	characteristic
402	#497	C₂²×C₇	1	2	yes	complemented
403	#496	C₂²×C₇	1	2	yes	complemented
404	#495	C₂²×C₇	1	4	yes	complemented
405	#495	C₂²×C₇	1	4	yes	complemented
406	#495	C₂²×C₇	1	2	yes	complemented
407	#495	C₂²×C₇	1	2	yes	complemented
408	#489	C₂²×C₇	1	4	yes	complemented
409	#488	C₂²×C₇	1	2	yes	complemented
410	#488	C₂²×C₇	1	2	yes	complemented
411	#488	C₂²×C₇	1	4	yes	complemented
412	#487	C₂²×C₇	1	2	yes	complemented
413	#486	C₂²×C₇	1	2	yes	complemented
414	#464	C₂²×C₇	1	4	yes	complemented
415	#464	C₂²×C₇	1	4	yes	complemented
416	#463	C₂²×C₇	1	4	yes	complemented
417	#463	C₂²×C₇	1	4	yes	complemented
418	#462	C₂²×C₇	1	4	yes	complemented
419	#461	C₂²×C₇	1	4	yes	complemented
420	#460	C₂²×C₇	1	4	yes	complemented
421	#459	C₂²×C₇	1	4	yes	complemented
422	#452	C₂²×C₇	1	4	yes	complemented
423	#452	C₂²×C₇	1	4	yes	complemented
424	#451	C₂²×C₇	1	4	yes	complemented
425	#450	C₂²×C₇	1	4	yes	complemented
426	#449	C₂²×C₇	1	4	yes	—
427	#449	C₂²×C₇	1	4	yes	complemented
428	#448	C₂²×C₇	1	4	yes	complemented
429	#447	C₂²×C₇	1	4	yes	—
430	#433	C₂²×C₇	1	4	yes	complemented
431	#431	C₂²×C₇	1	4	yes	complemented
432	#424	C₂²×C₇	1	1	yes	characteristic, complemented
433	#424	C₂²×C₇	1	1	yes	characteristic, complemented
434	#419	C₂²×C₇	1	1	yes	characteristic, complemented
435	#419	C₂²×C₇	1	1	yes	characteristic, complemented
436	#418	C₂²×C₇	1	1	yes	characteristic
437	#418	C₂²×C₇	1	1	yes	characteristic
438	#416	C₂²×C₇	1	1	yes	characteristic
439	#416	C₂²×C₇	1	1	yes	characteristic
440	#416	C₂²×C₇	1	1	yes	characteristic, complemented
441	#416	C₂²×C₇	1	1	yes	characteristic, complemented
442	#408	C₂²×C₇	1	1	yes	characteristic
443	#408	C₂²×C₇	1	1	yes	characteristic
444	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
445	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
446	C₂³×C₇	—	2	2	no	—
447	C₂³×C₇	—	2	2	no	—
448	C₂³×C₇	—	2	1	no	—
449	C₂³×C₇	—	2	1	no	—
450	C₂³×C₇	—	4	4	no	—
451	C₂³×C₇	—	4	2	no	—
452	C₂³×C₇	—	4	2	no	—
453	C₂³×C₇	—	8	2	no	—
454	C₂³×C₇	—	8	2	no	—
455	C₂³×C₇	—	8	4	no	—
456	C₂³×C₇	C₂²×D₄	1	2	yes	—
457	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
458	C₇×Q₈	—	2	2	no	—
459	C₇×Q₈	—	2	2	no	—
460	C₇×Q₈	—	2	2	no	—
461	C₇×Q₈	—	2	1	no	—
462	C₇×Q₈	—	2	1	no	—
463	C₇×Q₈	—	2	2	no	—
464	C₇×Q₈	—	2	2	no	—
465	C₇×Q₈	—	2	1	no	—
466	C₇×Q₈	—	2	1	no	—
467	C₇×Q₈	—	4	4	no	—
468	C₇×Q₈	—	4	2	no	—
469	C₇×Q₈	—	4	2	no	—
470	C₇×Q₈	—	8	2	no	—
471	C₇×D₄	—	2	4	no	—
472	C₇×D₄	—	2	2	no	—
473	C₇×D₄	—	2	2	no	—
474	C₇×D₄	—	2	2	no	—
475	C₇×D₄	—	2	1	no	—
476	C₇×D₄	—	2	1	no	—
477	C₇×D₄	—	2	2	no	—
478	C₇×D₄	—	2	2	no	—
479	C₇×D₄	—	2	1	no	—
480	C₇×D₄	—	2	1	no	—
481	C₇×D₄	—	4	4	no	—
482	C₇×D₄	—	4	4	no	—
483	C₇×D₄	—	4	4	no	—
484	C₇×D₄	—	4	2	no	—
485	C₇×D₄	—	4	2	no	—
486	C₇×D₄	—	4	2	no	—
487	C₇×D₄	—	4	2	no	—
488	C₇×D₄	—	8	4	no	—
489	C₇×D₄	—	8	2	no	—
490	C₇×D₄	—	8	4	no	—
491	C₂×C₄×C₇	—	2	2	no	—
492	C₂×C₄×C₇	—	2	2	no	—
493	C₂×C₄×C₇	—	2	2	no	—
494	C₂×C₄×C₇	—	2	2	no	—
495	C₂×C₄×C₇	—	2	2	no	—
496	C₂×C₄×C₇	—	2	2	no	—
497	C₂×C₄×C₇	—	2	1	no	—
498	C₂×C₄×C₇	—	2	1	no	—
499	C₂×C₄×C₇	—	4	4	no	—
500	C₂×C₄×C₇	—	4	2	no	—
501	C₂×C₄×C₇	—	4	4	no	—
502	C₂×C₄×C₇	—	4	4	no	—
503	C₂×C₄×C₇	—	4	4	no	—
504	C₂×C₄×C₇	—	4	2	no	—
505	C₂×C₄×C₇	—	4	2	no	—
506	C₂×C₄×C₇	—	4	2	no	—
507	C₂×C₄×C₇	—	4	2	no	—
508	C₂×C₄×C₇	—	8	4	no	—
509	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
510	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
515	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
516	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
517	C₇×C₈	—	2	2	no	—
518	C₇×C₈	—	2	2	no	—
519	C₇×C₈	—	2	2	no	—
520	C₇×C₈	—	2	2	no	—
521	2₋¹⁺⁴	—	4	2	no	—
522	2₋¹⁺⁴	—	4	2	no	—
523	H(5,𝔽₂)	—	4	2	no	—
524	H(5,𝔽₂)	—	4	2	no	—
525	C₂×#41	—	2	1	no	—
526	C₂×#41	—	2	2	no	—
527	C₂×#41	—	2	1	no	—
528	C₂×#41	C₂³×C₇	1	1	yes	characteristic
529	C₂×#41	C₂³×C₇	1	1	yes	characteristic
530	C₂×#41	C₂³×C₇	1	2	yes	—
531	C₂×#41	C₂³×C₇	1	2	yes	—
532	C₂×#41	C₂³×C₇	1	1	yes	characteristic
533	C₂²×Q₈	—	2	1	no	—
534	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
535	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
536	C₂²×Q₈	C₂³×C₇	1	2	yes	—
537	C₂²×D₄	—	2	2	no	—
538	C₂²×D₄	—	2	1	no	—
539	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
540	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
541	C₂²×D₄	C₂³×C₇	1	2	yes	—
542	#137	—	4	2	no	—
543	#137	—	4	2	no	—
544	AGL(1,ℤ/8)	—	4	2	no	—
545	AGL(1,ℤ/8)	—	4	2	no	—
546	C₂×Q₁₆	—	4	2	no	—
547	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
548	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
549	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
550	C₂×SD₁₆	—	4	2	no	—
551	C₂×SD₁₆	—	4	2	no	—
552	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
553	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
554	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
555	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
556	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
557	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
558	C₂×D₈	—	4	2	no	—
559	C₂×D₈	C₂³×C₇	1	4	yes	—
560	C₂×D₈	C₂³×C₇	1	2	yes	—
561	C₂×D₈	C₂³×C₇	1	2	yes	—
562	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
563	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
564	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
565	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
566	C₄⋊Q₈	—	2	1	no	—
567	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
568	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
569	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
570	#127	—	2	1	no	—
571	#127	C₂³×C₇	1	1	yes	characteristic
572	#127	C₂³×C₇	1	2	yes	—
573	#126	—	2	4	no	—
574	#126	—	2	4	no	—
575	#125	C₂³×C₇	1	2	yes	—
576	#124	—	2	1	no	—
577	#124	—	2	1	no	—
578	#124	—	2	4	no	—
579	#124	—	2	2	no	—
580	#124	—	2	4	no	—
581	#124	—	2	2	no	—
582	#124	C₂³×C₇	1	2	yes	—
583	#124	C₂³×C₇	1	2	yes	—
584	#124	C₂³×C₇	1	1	yes	characteristic
585	#124	C₂³×C₇	1	2	yes	—
586	#124	C₂³×C₇	1	2	yes	—
587	#124	C₂³×C₇	1	2	yes	—
588	#124	C₂³×C₇	1	2	yes	—
589	#124	C₂³×C₇	1	1	yes	characteristic
590	#123	—	2	2	no	—
591	#123	—	2	4	no	—
592	#123	—	2	2	no	—
593	#123	—	2	4	no	—
594	#123	—	2	4	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	4	no	—
598	C₂²⋊Q₈	—	2	4	no	—
599	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
600	#121	—	2	2	no	—
601	#121	—	2	4	no	—
602	#121	—	2	2	no	—
603	#121	—	2	4	no	—
604	#121	C₂³×C₇	1	4	yes	—
605	#120	—	2	2	no	—
606	#120	—	2	2	no	—
607	#120	—	2	4	no	—
608	C₄×Q₈	—	2	2	no	—
609	C₄×Q₈	—	2	2	no	—
610	C₄×Q₈	C₇×D₄	1	2	yes	—
611	C₄×Q₈	C₂³×C₇	1	4	yes	—
612	C₄×D₄	—	2	4	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	4	no	—
616	C₄×D₄	C₇×D₄	1	4	yes	—
617	C₄×D₄	C₇×D₄	1	2	yes	—
618	C₄×D₄	C₂³×C₇	1	4	yes	—
619	#117	—	2	2	no	—
620	#117	—	2	4	no	—
621	#117	C₂³×C₇	1	1	yes	characteristic
622	#117	C₂³×C₇	1	1	yes	characteristic
623	#117	C₂³×C₇	1	1	yes	characteristic
624	#117	C₂³×C₇	1	2	yes	—
625	C₂×C₂²⋊C₄	—	2	2	no	—
626	C₂×C₂²⋊C₄	—	2	4	no	—
627	C₂×C₂²⋊C₄	—	2	2	no	—
628	C₂×C₂²⋊C₄	—	2	2	no	—
629	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₇	1	2	yes	—
631	C₄⋊C₈	C₂³×C₇	1	4	yes	—
632	C₄⋊C₈	C₂³×C₇	1	4	yes	—
633	#103	C₂³×C₇	1	2	yes	—
634	#103	C₂³×C₇	1	2	yes	—
635	#103	C₂³×C₇	1	2	yes	—
636	#103	C₂³×C₇	1	2	yes	—
637	#103	C₂³×C₇	1	4	yes	—
638	#103	C₂³×C₇	1	4	yes	—
639	#102	C₂³×C₇	1	2	yes	—
640	#102	C₂³×C₇	1	2	yes	—
641	#102	C₂³×C₇	1	2	yes	—
642	#102	C₂³×C₇	1	2	yes	—
643	#102	C₂³×C₇	1	4	yes	—
644	#102	C₂³×C₇	1	4	yes	—
645	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
646	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
647	#97	C₂³×C₇	1	2	yes	—
648	C₄×C₈	C₂³×C₇	1	2	yes	—
649	C₄×C₈	C₂³×C₇	1	2	yes	—
650	C₄×C₈	C₂³×C₇	1	2	yes	—
651	C₂²×C₇	—	2	2	no	—
652	C₂²×C₇	—	2	4	no	—
653	C₂²×C₇	—	2	2	no	—
654	C₂²×C₇	—	4	4	no	—
655	C₂²×C₇	—	4	2	no	—
656	C₂²×C₇	—	4	4	no	—
657	C₂²×C₇	—	4	2	no	—
658	C₂²×C₇	—	4	1	no	—
659	C₂²×C₇	—	4	2	no	—
660	C₂²×C₇	—	4	1	no	—
661	C₂²×C₇	—	4	2	no	—
662	C₂²×C₇	—	16	2	no	—
663	C₂²×C₇	—	16	2	no	—
664	C₂²×C₇	—	16	4	no	—
665	C₂²×C₇	#535	1	2	yes	—
666	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
667	C₄×C₇	—	2	2	no	—
668	C₄×C₇	—	2	4	no	—
669	C₄×C₇	—	2	2	no	—
670	C₄×C₇	—	2	2	no	—
671	C₄×C₇	—	4	2	no	—
672	C₄×C₇	—	4	2	no	—
673	C₄×C₇	—	4	1	no	—
674	C₄×C₇	—	4	2	no	—
675	C₄×C₇	—	4	1	no	—
676	C₄×C₇	—	4	2	no	—
677	C₄×C₇	#535	1	2	yes	—
678	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
679	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂⁴	—	2	1	no	—
681	C₂⁴	—	2	2	no	—
682	C₂⁴	—	2	1	no	—
683	#41	—	2	2	no	—
684	#41	—	2	2	no	—
685	#41	—	2	2	no	—
686	#41	—	2	2	no	—
687	#41	—	2	2	no	—
688	#41	—	2	2	no	—
689	#41	—	4	2	no	—
690	#41	—	4	2	no	—
691	#41	—	4	2	no	—
692	#41	—	4	2	no	—
693	#41	—	4	8	no	—
694	#41	—	4	4	no	—
695	#41	—	4	4	no	—
696	C₂×Q₈	—	2	1	no	—
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	—	2	1	no	—
699	C₂×Q₈	—	2	2	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	—	4	2	no	—
705	C₂×Q₈	—	4	2	no	—
706	C₂×Q₈	—	4	4	no	—
707	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
708	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
709	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
710	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
711	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	4	2	no	—
727	C₂×D₄	—	4	2	no	—
728	C₂×D₄	—	4	8	no	—
729	C₂×D₄	—	4	4	no	—
730	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
731	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
732	C₂×D₄	C₂⁴×C₇	1	2	yes	—
733	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
734	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
735	C₂×D₄	C₂⁴×C₇	1	2	yes	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	1	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
745	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
746	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
748	Q₁₆	—	4	4	no	—
749	Q₁₆	—	4	2	no	—
750	Q₁₆	—	4	2	no	—
751	SD₁₆	—	4	4	no	—
752	SD₁₆	—	4	4	no	—
753	SD₁₆	—	4	2	no	—
754	SD₁₆	—	4	2	no	—
755	SD₁₆	—	4	2	no	—
756	SD₁₆	—	4	2	no	—
757	D₈	—	4	4	no	—
758	D₈	—	4	2	no	—
759	D₈	—	4	2	no	—
760	M₁₆	—	2	2	no	—
761	M₁₆	—	2	2	no	—
762	C₂×C₈	—	2	2	no	—
763	C₂×C₈	—	2	2	no	—
764	C₂×C₈	C₂⁴×C₇	1	2	yes	—
765	C₂×C₈	C₂⁴×C₇	1	2	yes	—
766	C₂×C₈	C₂⁴×C₇	1	2	yes	—
767	C₂×C₈	C₂⁴×C₇	1	2	yes	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	4	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
776	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
777	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
778	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	1	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
793	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
794	C₄²	—	2	4	no	—
795	C₄²	—	2	1	no	—
796	C₄²	—	2	1	no	—
797	C₄²	C₂×C₇×D₄	1	4	yes	—
798	C₄²	C₂×C₇×D₄	1	2	yes	—
799	C₄²	C₂⁴×C₇	1	1	yes	characteristic
800	C₄²	C₂⁴×C₇	1	1	yes	characteristic
801	C₄²	C₂⁴×C₇	1	2	yes	—
802	C₂×C₇	—	2	2	no	—
803	C₂×C₇	—	4	2	no	—
804	C₂×C₇	—	8	1	no	—
805	C₂×C₇	—	8	2	no	—
806	C₂×C₇	—	8	2	no	—
807	C₂×C₇	—	8	1	no	—
808	C₂×C₇	C₂×#535	1	1	yes	characteristic
809	C₂×C₇	#3584	1	2	yes	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	1	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	4	4	no	—
815	C₂³	—	4	2	no	—
816	C₂³	—	4	2	no	—
817	C₂³	—	8	2	no	—
818	C₂³	—	8	2	no	—
819	C₂³	—	8	4	no	—
820	C₂³	C₂²×C₇×D₄	1	2	yes	—
821	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
822	Q₈	—	2	2	no	—
823	Q₈	—	2	2	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	2	1	no	—
826	Q₈	—	2	1	no	—
827	Q₈	—	2	2	no	—
828	Q₈	—	2	2	no	—
829	Q₈	—	2	1	no	—
830	Q₈	—	2	1	no	—
831	Q₈	—	4	4	no	—
832	Q₈	—	4	2	no	—
833	Q₈	—	4	2	no	—
834	Q₈	—	8	2	no	—
835	D₄	—	2	4	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	2	no	—
838	D₄	—	2	1	no	—
839	D₄	—	2	1	no	—
840	D₄	—	2	2	no	—
841	D₄	—	2	2	no	—
842	D₄	—	2	1	no	—
843	D₄	—	2	1	no	—
844	D₄	—	2	2	no	—
845	D₄	—	4	4	no	—
846	D₄	—	4	4	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	2	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	2	no	—
851	D₄	—	4	2	no	—
852	D₄	—	8	4	no	—
853	D₄	—	8	2	no	—
854	D₄	—	8	4	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	4	4	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	4	no	—
866	C₂×C₄	—	4	4	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	4	2	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	8	4	no	—
873	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
874	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
875	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
876	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
877	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
878	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
879	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
880	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
881	C₈	—	2	2	no	—
882	C₈	—	2	2	no	—
883	C₈	—	2	2	no	—
884	C₈	—	2	2	no	—
885	C₇	#60819	1	1	yes	characteristic, direct product factor, Sylow
886	C₂²	—	2	2	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	4	4	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	4	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	16	2	no	—
898	C₂²	—	16	2	no	—
899	C₂²	—	16	4	no	—
900	C₂²	C₇×#535	1	2	yes	—
901	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
902	C₄	—	2	2	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	C₇×#535	1	2	yes	—
913	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
914	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
915	C₂	—	2	2	no	—
916	C₂	—	4	2	no	—
917	C₂	—	8	2	no	—
918	C₂	—	8	1	no	—
919	C₂	—	8	2	no	—
920	C₂	—	8	1	no	—
921	C₂	C₂×C₇×#535	1	1	yes	characteristic
922	C₂	C₇×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3510	C₂	semidirect
2. C₇×#3500	C₂	semidirect
3. C₇×#3225	C₂	semidirect
4. C₇×#3224	C₂	semidirect
5. C₇×#3212	C₂	semidirect
6. C₇×#3211	C₂	semidirect
7. C₇×#3153	C₂	semidirect
8. C₂×C₇×#495	C₂	semidirect
9. C₇×#3140	C₂	semidirect
10. C₇×#3131	C₂	semidirect
11. C₇×#3044	C₂	semidirect
12. C₇×#3043	C₂	semidirect
13. C₇×#3042	C₂	semidirect
14. C₇×#3041	C₂	semidirect
15. C₇×#3011	C₂	semidirect
16. C₇×#3010	C₂	semidirect
17. C₇×#3009	C₂	semidirect
18. C₇×#3008	C₂	semidirect
19. C₇×#2922	C₂	semidirect
23. C₂×C₇×#137	C₂²	semidirect
25. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂²×C₇×Q₁₆	C₂²	semidirect
28. C₂²×C₇×SD₁₆	C₂²	semidirect
36. C₇×#542	C₂²	semidirect
39. C₇×#536	C₂²	semidirect
42. C₇×#535	C₂²	semidirect
43. C₇×#533	C₂²	semidirect
45. C₇×#532	C₂²	semidirect
46. C₇×#529	C₂²	semidirect
48. C₂×C₇×#124	C₂²	semidirect
49. C₂×C₇×#124	C₂²	semidirect
50. C₇×#519	C₂²	semidirect
51. C₇×#518	C₂²	semidirect
53. C₇×#497	C₂²	semidirect
54. C₇×#496	C₂²	semidirect
55. C₇×#495	C₂²	semidirect
56. C₇×#495	C₂²	semidirect
57. C₇×#495	C₂²	semidirect
58. C₇×#495	C₂²	semidirect
59. C₇×#489	C₂²	semidirect
60. C₇×#488	C₂²	semidirect
61. C₇×#488	C₂²	semidirect
62. C₇×#488	C₂²	semidirect
63. C₇×#487	C₂²	semidirect
64. C₇×#486	C₂²	semidirect
65. C₇×#464	C₂²	semidirect
66. C₇×#464	C₂²	semidirect
67. C₇×#463	C₂²	semidirect
68. C₇×#463	C₂²	semidirect
69. C₇×#462	C₂²	semidirect
70. C₇×#461	C₂²	semidirect
71. C₇×#460	C₂²	semidirect
72. C₇×#459	C₂²	semidirect
73. C₇×#452	C₂²	semidirect
74. C₇×#452	C₂²	semidirect
75. C₇×#451	C₂²	semidirect
76. C₇×#450	C₂²	semidirect
78. C₇×#449	C₂²	semidirect
79. C₇×#448	C₂²	semidirect
81. C₇×#433	C₂²	semidirect
82. C₇×#431	C₂²	semidirect
83. C₇×#424	C₂²	semidirect
84. C₇×#424	C₂²	semidirect
85. C₇×#419	C₂²	semidirect
86. C₇×#419	C₂²	semidirect
91. C₇×#416	C₂²	semidirect
92. C₇×#416	C₂²	semidirect
95. C₄×C₇×M₁₆	C₂²	semidirect
96. C₂×C₄×C₇×C₈	C₂²	semidirect
97. #60819	C₇	direct (N × H)
228. #3510	C₂×C₇	semidirect
229. #3500	C₂×C₇	semidirect
230. #3225	C₂×C₇	semidirect
231. #3224	C₂×C₇	semidirect
232. #3212	C₂×C₇	semidirect
233. #3211	C₂×C₇	semidirect
234. #3153	C₂×C₇	semidirect
235. C₂×#495	C₂×C₇	semidirect
236. #3140	C₂×C₇	semidirect
237. #3131	C₂×C₇	semidirect
238. #3044	C₂×C₇	semidirect
239. #3043	C₂×C₇	semidirect
240. #3042	C₂×C₇	semidirect
241. #3041	C₂×C₇	semidirect
242. #3011	C₂×C₇	semidirect
243. #3010	C₂×C₇	semidirect
244. #3009	C₂×C₇	semidirect
245. #3008	C₂×C₇	semidirect
246. #2922	C₂×C₇	semidirect
372. C₂×#137	C₂²×C₇	semidirect
374. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
375. C₂²×Q₁₆	C₂²×C₇	semidirect
377. C₂²×SD₁₆	C₂²×C₇	semidirect
385. #542	C₂²×C₇	semidirect
388. #536	C₂²×C₇	semidirect
391. #535	C₂²×C₇	semidirect
392. #533	C₂²×C₇	semidirect
394. #532	C₂²×C₇	semidirect
395. #529	C₂²×C₇	semidirect
397. C₂×#124	C₂²×C₇	semidirect
398. C₂×#124	C₂²×C₇	semidirect
399. #519	C₂²×C₇	semidirect
400. #518	C₂²×C₇	semidirect
402. #497	C₂²×C₇	semidirect
403. #496	C₂²×C₇	semidirect
404. #495	C₂²×C₇	semidirect
405. #495	C₂²×C₇	semidirect
406. #495	C₂²×C₇	semidirect
407. #495	C₂²×C₇	semidirect
408. #489	C₂²×C₇	semidirect
409. #488	C₂²×C₇	semidirect
410. #488	C₂²×C₇	semidirect
411. #488	C₂²×C₇	semidirect
412. #487	C₂²×C₇	semidirect
413. #486	C₂²×C₇	semidirect
414. #464	C₂²×C₇	semidirect
415. #464	C₂²×C₇	semidirect
416. #463	C₂²×C₇	semidirect
417. #463	C₂²×C₇	semidirect
418. #462	C₂²×C₇	semidirect
419. #461	C₂²×C₇	semidirect
420. #460	C₂²×C₇	semidirect
421. #459	C₂²×C₇	semidirect
422. #452	C₂²×C₇	semidirect
423. #452	C₂²×C₇	semidirect
424. #451	C₂²×C₇	semidirect
425. #450	C₂²×C₇	semidirect
427. #449	C₂²×C₇	semidirect
428. #448	C₂²×C₇	semidirect
430. #433	C₂²×C₇	semidirect
431. #431	C₂²×C₇	semidirect
432. #424	C₂²×C₇	semidirect
433. #424	C₂²×C₇	semidirect
434. #419	C₂²×C₇	semidirect
435. #419	C₂²×C₇	semidirect
440. #416	C₂²×C₇	semidirect
441. #416	C₂²×C₇	semidirect
444. C₄×M₁₆	C₂²×C₇	semidirect
445. C₂×C₄×C₈	C₂²×C₇	semidirect
885. C₇	#60819	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×#3510	2
C₇×#3500	2
C₇×#3225	2
C₇×#3224	2
C₇×#3212	2
C₇×#3211	2
C₇×#3153	2
C₂×C₇×#495	2
C₇×#3140	2
C₇×#3131	2
C₇×#3044	2
C₇×#3043	2
C₇×#3042	2
C₇×#3041	2
C₇×#3011	2
C₇×#3010	2
C₇×#3009	2
C₇×#3008	2
C₇×#2922	2
#60819	7

Subgroups — C7×#60819 #13238035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60819 #13238035