Subgroups — C₆₁×#61415 #29564848

Order 15616.

1914 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3403	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3402	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3400	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3397	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3154	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3150	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3046	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3045	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#2951	C₂	1	2	yes	maximal, complemented
15	C₂×C₆₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#137×C₆₁	C₂²	1	2	yes	—
17	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
18	C₂×#135×C₆₁	C₂²	1	2	yes	—
19	C₂×#135×C₆₁	C₂²	1	2	yes	—
20	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
21	C₆₁×#559	C₂²	1	4	yes	—
22	C₆₁×#559	C₂²	1	2	yes	complemented
23	C₆₁×#557	C₂²	1	2	yes	complemented
24	C₆₁×#556	—	2	1	no	—
25	C₆₁×#556	C₂²	1	2	yes	—
26	C₆₁×#556	C₂²	1	4	yes	complemented
27	C₆₁×#555	—	2	1	no	—
28	C₆₁×#554	—	2	1	no	—
29	C₆₁×#553	—	2	2	no	—
30	C₆₁×#552	—	2	2	no	—
31	C₆₁×#550	C₂²	1	2	yes	—
32	C₆₁×#547	—	2	1	no	—
33	C₆₁×#539	—	2	2	no	—
34	C₆₁×#538	—	2	2	no	—
35	C₆₁×#536	C₂²	1	2	yes	—
36	C₆₁×#535	C₂²	1	2	yes	—
37	C₆₁×#533	C₂²	1	1	yes	characteristic
38	C₆₁×#532	C₂²	1	1	yes	characteristic
39	C₆₁×#532	C₂²	1	1	yes	characteristic
40	C₆₁×#529	—	2	2	no	—
41	C₆₁×#525	—	2	2	no	—
42	C₆₁×#520	C₂²	1	2	yes	—
43	C₆₁×#520	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
46	C₆₁×#497	C₂²	1	4	yes	—
47	C₆₁×#497	C₂²	1	2	yes	complemented
48	C₆₁×#497	C₂²	1	2	yes	complemented
49	C₆₁×#496	C₂²	1	4	yes	—
50	C₆₁×#496	C₂²	1	2	yes	complemented
51	C₆₁×#496	C₂²	1	2	yes	complemented
52	C₆₁×#495	C₂²	1	4	yes	—
53	C₆₁×#492	C₂²	1	4	yes	—
54	C₆₁×#464	C₂²	1	4	yes	—
55	C₆₁×#464	C₂²	1	4	yes	complemented
56	C₆₁×#464	C₂²	1	4	yes	complemented
57	C₆₁×#463	C₂²	1	4	yes	—
58	C₆₁×#463	C₂²	1	4	yes	—
59	C₆₁×#463	C₂²	1	4	yes	complemented
60	C₆₁×#462	C₂²	1	2	yes	complemented
61	C₆₁×#462	C₂²	1	4	yes	complemented
62	C₆₁×#461	C₂²	1	2	yes	—
63	C₆₁×#461	C₂²	1	4	yes	complemented
64	C₆₁×#460	C₂²	1	4	yes	—
65	C₆₁×#460	C₂²	1	2	yes	complemented
66	C₆₁×#459	C₂²	1	2	yes	—
67	C₆₁×#459	C₂²	1	4	yes	—
68	C₆₁×#446	C₂²	1	4	yes	complemented
69	C₆₁×#446	C₂²	1	4	yes	complemented
70	C₆₁×#440	C₂²	1	4	yes	—
71	C₆₁×#440	C₂²	1	4	yes	—
72	C₆₁×#440	C₂²	1	4	yes	complemented
73	C₆₁×#440	C₂²	1	4	yes	complemented
74	C₄×Q₁₆×C₆₁	C₂²	1	4	yes	complemented
75	C₄×D₈×C₆₁	C₂²	1	4	yes	complemented
76	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
77	C₆₁×#424	C₂²	1	2	yes	—
78	C₆₁×#423	C₂²	1	1	yes	characteristic
79	C₆₁×#417	C₂²	1	2	yes	—
80	C₆₁×#417	C₂²	1	2	yes	—
81	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
82	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
83	C₆₁×#405	C₂²	1	2	yes	—
84	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
85	C₂×#41×C₆₁	—	2	2	no	—
86	C₂×#41×C₆₁	C₂³	1	2	yes	—
87	C₂×#41×C₆₁	C₂³	1	2	yes	—
88	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₆₁	—	2	1	no	—
91	#137×C₆₁	—	4	4	no	—
92	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
93	#135×C₆₁	—	2	8	no	—
94	#135×C₆₁	—	4	4	no	—
95	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
96	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₆₁	—	2	4	no	—
99	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
101	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
106	C₂×D₈×C₆₁	C₂³	1	2	yes	—
107	C₂×D₈×C₆₁	C₂³	1	2	yes	—
108	C₂×D₈×C₆₁	C₂³	1	4	yes	—
109	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
110	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
117	#127×C₆₁	C₂³	1	1	yes	characteristic
118	#127×C₆₁	C₂³	1	1	yes	characteristic
119	#127×C₆₁	C₂³	1	4	yes	—
120	#126×C₆₁	—	2	4	no	—
121	#126×C₆₁	—	2	4	no	—
122	#126×C₆₁	—	2	4	no	—
123	#125×C₆₁	—	2	4	no	—
124	#125×C₆₁	—	2	2	no	—
125	#125×C₆₁	D₄	1	2	yes	—
126	#124×C₆₁	—	2	4	no	—
127	#124×C₆₁	—	2	2	no	—
128	#124×C₆₁	C₂³	1	2	yes	—
129	#124×C₆₁	C₂³	1	2	yes	—
130	#124×C₆₁	C₂³	1	4	yes	—
131	#124×C₆₁	C₂³	1	4	yes	—
132	#123×C₆₁	—	2	4	no	—
133	#123×C₆₁	—	2	4	no	—
134	#123×C₆₁	—	2	4	no	—
135	#123×C₆₁	—	2	4	no	—
136	C₂²⋊Q₈×C₆₁	—	2	4	no	—
137	C₂²⋊Q₈×C₆₁	—	2	2	no	—
138	C₂²⋊Q₈×C₆₁	—	2	2	no	—
139	C₂²⋊Q₈×C₆₁	—	2	2	no	—
140	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
141	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
142	#121×C₆₁	—	2	1	no	—
143	#121×C₆₁	—	2	1	no	—
144	#121×C₆₁	—	2	1	no	—
145	#121×C₆₁	—	2	1	no	—
146	#121×C₆₁	—	2	2	no	—
147	#121×C₆₁	—	2	2	no	—
148	#121×C₆₁	—	2	4	no	—
149	#121×C₆₁	—	2	2	no	—
150	#120×C₆₁	—	2	4	no	—
151	C₄×Q₈×C₆₁	—	2	2	no	—
152	C₄×Q₈×C₆₁	—	2	1	no	—
153	C₄×Q₈×C₆₁	—	2	1	no	—
154	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
155	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
156	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
157	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
158	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
159	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
160	C₄×D₄×C₆₁	—	2	4	no	—
161	C₄×D₄×C₆₁	—	2	2	no	—
162	C₄×D₄×C₆₁	—	2	4	no	—
163	C₄×D₄×C₆₁	—	2	4	no	—
164	C₄×D₄×C₆₁	—	2	1	no	—
165	C₄×D₄×C₆₁	—	2	1	no	—
166	C₄×D₄×C₆₁	—	2	1	no	—
167	C₄×D₄×C₆₁	—	2	1	no	—
168	C₄×D₄×C₆₁	—	2	1	no	—
169	C₄×D₄×C₆₁	—	2	1	no	—
170	C₄×D₄×C₆₁	C₂³	1	2	yes	—
171	C₄×D₄×C₆₁	C₂³	1	4	yes	—
172	C₄×D₄×C₆₁	C₂³	1	4	yes	—
173	C₄×D₄×C₆₁	C₂³	1	2	yes	—
174	#117×C₆₁	—	2	2	no	—
175	#117×C₆₁	—	2	4	no	—
176	#117×C₆₁	—	2	2	no	—
177	#117×C₆₁	—	2	2	no	—
178	#117×C₆₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
180	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
181	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
182	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
185	C₂×C₄²×C₆₁	—	2	1	no	—
186	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
187	#107×C₆₁	C₂³	1	4	yes	—
188	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
189	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
190	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
191	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
192	#103×C₆₁	C₂³	1	4	yes	—
193	#103×C₆₁	C₂³	1	4	yes	—
194	#103×C₆₁	C₂³	1	4	yes	—
195	#102×C₆₁	C₂³	1	4	yes	—
196	#102×C₆₁	C₂³	1	4	yes	—
197	#102×C₆₁	C₂³	1	4	yes	—
198	#97×C₆₁	C₂³	1	2	yes	—
199	#97×C₆₁	C₂³	1	2	yes	—
200	#97×C₆₁	C₂³	1	4	yes	—
201	C₄×C₈×C₆₁	C₂³	1	4	yes	—
202	C₂⁴×C₆₁	—	2	1	no	—
203	#41×C₆₁	—	2	4	no	—
204	#41×C₆₁	—	2	4	no	—
205	#41×C₆₁	—	2	4	no	—
206	#41×C₆₁	—	2	4	no	—
207	#41×C₆₁	—	8	4	no	—
208	C₂×Q₈×C₆₁	—	2	1	no	—
209	C₂×Q₈×C₆₁	—	2	2	no	—
210	C₂×Q₈×C₆₁	—	2	2	no	—
211	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
212	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
213	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
214	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
216	C₂×D₄×C₆₁	—	2	2	no	—
217	C₂×D₄×C₆₁	—	2	2	no	—
218	C₂×D₄×C₆₁	—	2	1	no	—
219	C₂×D₄×C₆₁	—	2	1	no	—
220	C₂×D₄×C₆₁	—	2	1	no	—
221	C₂×D₄×C₆₁	—	2	4	no	—
222	C₂×D₄×C₆₁	—	2	1	no	—
223	C₂×D₄×C₆₁	—	2	1	no	—
224	C₂×D₄×C₆₁	—	2	4	no	—
225	C₂×D₄×C₆₁	—	2	2	no	—
226	C₂×D₄×C₆₁	—	2	2	no	—
227	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
228	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
229	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₆₁	—	2	1	no	—
231	C₂²×C₄×C₆₁	—	2	1	no	—
232	C₂²×C₄×C₆₁	—	2	1	no	—
233	C₂²×C₄×C₆₁	—	2	2	no	—
234	C₂²×C₄×C₆₁	—	2	2	no	—
235	C₂²×C₄×C₆₁	—	2	2	no	—
236	C₂²×C₄×C₆₁	—	2	4	no	—
237	C₂²×C₄×C₆₁	—	2	4	no	—
238	C₂²×C₄×C₆₁	—	2	2	no	—
239	C₂²×C₄×C₆₁	—	8	2	no	—
240	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
243	Q₁₆×C₆₁	—	2	4	no	—
244	Q₁₆×C₆₁	—	4	2	no	—
245	Q₁₆×C₆₁	—	4	4	no	—
246	SD₁₆×C₆₁	—	2	8	no	—
247	SD₁₆×C₆₁	—	2	4	no	—
248	SD₁₆×C₆₁	—	2	4	no	—
249	SD₁₆×C₆₁	—	4	2	no	—
250	SD₁₆×C₆₁	—	4	2	no	—
251	SD₁₆×C₆₁	—	4	4	no	—
252	SD₁₆×C₆₁	—	4	4	no	—
253	D₈×C₆₁	—	2	4	no	—
254	D₈×C₆₁	—	4	2	no	—
255	D₈×C₆₁	—	4	4	no	—
256	M₁₆×C₆₁	—	2	4	no	—
257	C₂×C₈×C₆₁	—	2	2	no	—
258	C₂×C₈×C₆₁	#41	1	4	yes	complemented
259	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
260	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
261	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₆₁	—	2	1	no	—
263	C₄⋊C₄×C₆₁	—	2	1	no	—
264	C₄⋊C₄×C₆₁	—	2	4	no	—
265	C₄⋊C₄×C₆₁	—	2	4	no	—
266	C₄⋊C₄×C₆₁	—	2	2	no	—
267	C₄⋊C₄×C₆₁	—	2	2	no	—
268	C₄⋊C₄×C₆₁	—	2	1	no	—
269	C₄⋊C₄×C₆₁	—	2	4	no	—
270	C₄⋊C₄×C₆₁	—	2	1	no	—
271	C₄⋊C₄×C₆₁	—	2	1	no	—
272	C₄⋊C₄×C₆₁	—	2	1	no	—
273	C₄⋊C₄×C₆₁	—	2	4	no	—
274	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
277	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
279	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
282	C₂²⋊C₄×C₆₁	—	2	2	no	—
283	C₂²⋊C₄×C₆₁	—	2	2	no	—
284	C₂²⋊C₄×C₆₁	—	2	2	no	—
285	C₂²⋊C₄×C₆₁	—	2	4	no	—
286	C₂²⋊C₄×C₆₁	—	2	4	no	—
287	C₂²⋊C₄×C₆₁	—	2	4	no	—
288	C₂²⋊C₄×C₆₁	—	2	4	no	—
289	C₂²⋊C₄×C₆₁	—	2	2	no	—
290	C₂²⋊C₄×C₆₁	—	2	4	no	—
291	C₂²⋊C₄×C₆₁	—	2	2	no	—
292	C₂²⋊C₄×C₆₁	—	2	2	no	—
293	C₂²⋊C₄×C₆₁	—	2	4	no	—
294	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
295	C₄²×C₆₁	—	2	2	no	—
296	C₄²×C₆₁	—	2	2	no	—
297	C₄²×C₆₁	—	2	4	no	—
298	C₄²×C₆₁	—	2	4	no	—
299	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₆₁	C₂⁴	1	4	yes	—
302	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
303	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
304	C₂³×C₆₁	—	2	2	no	—
305	C₂³×C₆₁	—	2	2	no	—
306	C₂³×C₆₁	—	2	2	no	—
307	C₂³×C₆₁	—	4	2	no	—
308	C₂³×C₆₁	—	8	1	no	—
309	C₂³×C₆₁	—	8	1	no	—
310	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
311	Q₈×C₆₁	—	2	2	no	—
312	Q₈×C₆₁	—	2	2	no	—
313	Q₈×C₆₁	—	2	2	no	—
314	Q₈×C₆₁	—	2	2	no	—
315	Q₈×C₆₁	—	2	2	no	—
316	Q₈×C₆₁	—	2	2	no	—
317	Q₈×C₆₁	—	4	2	no	—
318	Q₈×C₆₁	—	4	2	no	—
319	Q₈×C₆₁	—	4	2	no	—
320	D₄×C₆₁	—	2	2	no	—
321	D₄×C₆₁	—	2	2	no	—
322	D₄×C₆₁	—	2	2	no	—
323	D₄×C₆₁	—	2	2	no	—
324	D₄×C₆₁	—	2	2	no	—
325	D₄×C₆₁	—	2	2	no	—
326	D₄×C₆₁	—	4	2	no	—
327	D₄×C₆₁	—	4	2	no	—
328	D₄×C₆₁	—	4	4	no	—
329	D₄×C₆₁	—	4	4	no	—
330	D₄×C₆₁	—	4	2	no	—
331	D₄×C₆₁	—	8	1	no	—
332	D₄×C₆₁	—	8	1	no	—
333	D₄×C₆₁	—	8	4	no	—
334	D₄×C₆₁	—	8	4	no	—
335	C₂×C₄×C₆₁	—	2	2	no	—
336	C₂×C₄×C₆₁	—	2	2	no	—
337	C₂×C₄×C₆₁	—	2	2	no	—
338	C₂×C₄×C₆₁	—	2	2	no	—
339	C₂×C₄×C₆₁	—	2	2	no	—
340	C₂×C₄×C₆₁	—	4	1	no	—
341	C₂×C₄×C₆₁	—	4	1	no	—
342	C₂×C₄×C₆₁	—	4	4	no	—
343	C₂×C₄×C₆₁	—	4	2	no	—
344	C₂×C₄×C₆₁	—	4	4	no	—
345	C₂×C₄×C₆₁	—	4	4	no	—
346	C₂×C₄×C₆₁	—	8	4	no	—
347	C₂×C₄×C₆₁	—	8	2	no	—
348	C₂×C₄×C₆₁	—	8	4	no	—
349	C₂×C₄×C₆₁	—	8	1	no	—
350	C₂×C₄×C₆₁	—	8	1	no	—
351	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
354	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
359	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
360	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
361	C₈×C₆₁	—	2	2	no	—
362	C₈×C₆₁	—	2	4	no	—
363	C₈×C₆₁	C₂×#41	1	4	yes	—
364	#61415	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
365	C₂²×C₆₁	—	2	1	no	—
366	C₂²×C₆₁	—	2	1	no	—
367	C₂²×C₆₁	—	4	2	no	—
368	C₂²×C₆₁	—	4	2	no	—
369	C₂²×C₆₁	—	4	2	no	—
370	C₂²×C₆₁	—	4	2	no	—
371	C₂²×C₆₁	—	4	2	no	—
372	C₂²×C₆₁	—	4	2	no	—
373	C₂²×C₆₁	—	4	2	no	—
374	C₂²×C₆₁	—	4	2	no	—
375	C₂²×C₆₁	—	4	2	no	—
376	C₂²×C₆₁	—	8	4	no	—
377	C₂²×C₆₁	#550	1	2	yes	—
378	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
379	C₄×C₆₁	—	2	1	no	—
380	C₄×C₆₁	—	2	1	no	—
381	C₄×C₆₁	—	2	4	no	—
382	C₄×C₆₁	—	2	1	no	—
383	C₄×C₆₁	—	2	1	no	—
384	C₄×C₆₁	—	2	4	no	—
385	C₄×C₆₁	—	4	2	no	—
386	C₄×C₆₁	—	4	2	no	—
387	C₄×C₆₁	—	4	2	no	—
388	C₄×C₆₁	—	4	2	no	—
389	C₄×C₆₁	—	4	2	no	—
390	C₄×C₆₁	#550	1	2	yes	—
391	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
392	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
393	#3507	C₂×C₆₁	1	1	yes	characteristic, complemented
394	#3506	C₂×C₆₁	1	1	yes	characteristic, complemented
395	#3403	C₂×C₆₁	1	4	yes	complemented
396	#3402	C₂×C₆₁	1	4	yes	complemented
397	#3400	C₂×C₆₁	1	4	yes	complemented
398	#3397	C₂×C₆₁	1	4	yes	complemented
399	#3154	C₂×C₆₁	1	2	yes	complemented
400	#3150	C₂×C₆₁	1	1	yes	characteristic, complemented
401	#3046	C₂×C₆₁	1	2	yes	complemented
402	#3045	C₂×C₆₁	1	2	yes	complemented
403	#3037	C₂×C₆₁	1	1	yes	characteristic, complemented
404	#3036	C₂×C₆₁	1	1	yes	characteristic, complemented
405	#2961	C₂×C₆₁	1	1	yes	characteristic, complemented
406	#2951	C₂×C₆₁	1	2	yes	complemented
407	C₂×#440	C₂×C₆₁	1	1	yes	characteristic, complemented
408	C₂×C₆₁	—	2	2	no	—
409	C₂×C₆₁	—	8	2	no	—
410	C₂×C₆₁	—	8	2	no	—
411	C₂×C₆₁	—	8	2	no	—
412	C₂×C₆₁	C₂×#550	1	1	yes	characteristic
413	C₂×C₆₁	#3585	1	1	yes	characteristic
414	C₂×C₆₁	#3586	1	1	yes	characteristic
415	C₂×#137	C₂²×C₆₁	1	2	yes	—
416	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
417	C₂×#135	C₂²×C₆₁	1	2	yes	—
418	C₂×#135	C₂²×C₆₁	1	2	yes	—
419	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
420	#559	C₂²×C₆₁	1	4	yes	—
421	#559	C₂²×C₆₁	1	2	yes	complemented
422	#557	C₂²×C₆₁	1	2	yes	complemented
423	#556	—	2	1	no	—
424	#556	C₂²×C₆₁	1	2	yes	—
425	#556	C₂²×C₆₁	1	4	yes	complemented
426	#555	—	2	1	no	—
427	#554	—	2	1	no	—
428	#553	—	2	2	no	—
429	#552	—	2	2	no	—
430	#550	C₂²×C₆₁	1	2	yes	—
431	#547	—	2	1	no	—
432	#539	—	2	2	no	—
433	#538	—	2	2	no	—
434	#536	C₂²×C₆₁	1	2	yes	—
435	#535	C₂²×C₆₁	1	2	yes	—
436	#533	C₂²×C₆₁	1	1	yes	characteristic
437	#532	C₂²×C₆₁	1	1	yes	characteristic
438	#532	C₂²×C₆₁	1	1	yes	characteristic
439	#529	—	2	2	no	—
440	#525	—	2	2	no	—
441	#520	C₂²×C₆₁	1	2	yes	—
442	#520	C₂²×C₆₁	1	2	yes	—
443	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
444	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
445	#497	C₂²×C₆₁	1	4	yes	—
446	#497	C₂²×C₆₁	1	2	yes	complemented
447	#497	C₂²×C₆₁	1	2	yes	complemented
448	#496	C₂²×C₆₁	1	4	yes	—
449	#496	C₂²×C₆₁	1	2	yes	complemented
450	#496	C₂²×C₆₁	1	2	yes	complemented
451	#495	C₂²×C₆₁	1	4	yes	—
452	#492	C₂²×C₆₁	1	4	yes	—
453	#464	C₂²×C₆₁	1	4	yes	—
454	#464	C₂²×C₆₁	1	4	yes	complemented
455	#464	C₂²×C₆₁	1	4	yes	complemented
456	#463	C₂²×C₆₁	1	4	yes	—
457	#463	C₂²×C₆₁	1	4	yes	—
458	#463	C₂²×C₆₁	1	4	yes	complemented
459	#462	C₂²×C₆₁	1	4	yes	complemented
460	#462	C₂²×C₆₁	1	2	yes	complemented
461	#461	C₂²×C₆₁	1	2	yes	—
462	#461	C₂²×C₆₁	1	4	yes	complemented
463	#460	C₂²×C₆₁	1	4	yes	—
464	#460	C₂²×C₆₁	1	2	yes	complemented
465	#459	C₂²×C₆₁	1	4	yes	—
466	#459	C₂²×C₆₁	1	2	yes	—
467	#446	C₂²×C₆₁	1	4	yes	complemented
468	#446	C₂²×C₆₁	1	4	yes	complemented
469	#440	C₂²×C₆₁	1	4	yes	—
470	#440	C₂²×C₆₁	1	4	yes	—
471	#440	C₂²×C₆₁	1	4	yes	complemented
472	#440	C₂²×C₆₁	1	4	yes	complemented
473	C₄×Q₁₆	C₂²×C₆₁	1	4	yes	complemented
474	C₄×D₈	C₂²×C₆₁	1	4	yes	complemented
475	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
476	#424	C₂²×C₆₁	1	2	yes	—
477	#423	C₂²×C₆₁	1	1	yes	characteristic
478	#417	C₂²×C₆₁	1	2	yes	—
479	#417	C₂²×C₆₁	1	2	yes	—
480	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
481	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
482	#405	C₂²×C₆₁	1	2	yes	—
483	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
484	C₆₁	#61415	1	1	yes	characteristic, direct product factor, Sylow
485	C₂×#41	—	2	2	no	—
486	C₂×#41	C₂³×C₆₁	1	2	yes	—
487	C₂×#41	C₂³×C₆₁	1	2	yes	—
488	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
489	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
490	C₂³×C₄	—	2	1	no	—
491	#137	—	4	4	no	—
492	AGL(1,ℤ/8)	—	4	4	no	—
493	#135	—	2	8	no	—
494	#135	—	4	4	no	—
495	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
496	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
497	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
498	C₂×SD₁₆	—	2	4	no	—
499	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
500	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
501	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
502	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
503	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
504	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
505	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
506	C₂×D₈	C₂³×C₆₁	1	2	yes	—
507	C₂×D₈	C₂³×C₆₁	1	2	yes	—
508	C₂×D₈	C₂³×C₆₁	1	4	yes	—
509	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
510	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
511	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
512	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
513	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
517	#127	C₂³×C₆₁	1	1	yes	characteristic
518	#127	C₂³×C₆₁	1	1	yes	characteristic
519	#127	C₂³×C₆₁	1	4	yes	—
520	#126	—	2	4	no	—
521	#126	—	2	4	no	—
522	#126	—	2	4	no	—
523	#125	—	2	2	no	—
524	#125	—	2	4	no	—
525	#125	D₄×C₆₁	1	2	yes	—
526	#124	—	2	2	no	—
527	#124	—	2	4	no	—
528	#124	C₂³×C₆₁	1	2	yes	—
529	#124	C₂³×C₆₁	1	2	yes	—
530	#124	C₂³×C₆₁	1	4	yes	—
531	#124	C₂³×C₆₁	1	4	yes	—
532	#123	—	2	4	no	—
533	#123	—	2	4	no	—
534	#123	—	2	4	no	—
535	#123	—	2	4	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
541	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
542	#121	—	2	1	no	—
543	#121	—	2	1	no	—
544	#121	—	2	1	no	—
545	#121	—	2	1	no	—
546	#121	—	2	2	no	—
547	#121	—	2	2	no	—
548	#121	—	2	2	no	—
549	#121	—	2	4	no	—
550	#120	—	2	4	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	1	no	—
553	C₄×Q₈	—	2	1	no	—
554	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
555	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
556	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
557	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
558	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
559	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
560	C₄×D₄	—	2	4	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	4	no	—
563	C₄×D₄	—	2	4	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	C₂³×C₆₁	1	2	yes	—
571	C₄×D₄	C₂³×C₆₁	1	2	yes	—
572	C₄×D₄	C₂³×C₆₁	1	4	yes	—
573	C₄×D₄	C₂³×C₆₁	1	4	yes	—
574	#117	—	2	2	no	—
575	#117	—	2	2	no	—
576	#117	—	2	2	no	—
577	#117	—	2	4	no	—
578	#117	C₂³×C₆₁	1	2	yes	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	2	no	—
581	C₂×C₄⋊C₄	—	2	2	no	—
582	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₄²	—	2	1	no	—
586	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
587	#107	C₂³×C₆₁	1	4	yes	—
588	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
589	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
590	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
591	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
592	#103	C₂³×C₆₁	1	4	yes	—
593	#103	C₂³×C₆₁	1	4	yes	—
594	#103	C₂³×C₆₁	1	4	yes	—
595	#102	C₂³×C₆₁	1	4	yes	—
596	#102	C₂³×C₆₁	1	4	yes	—
597	#102	C₂³×C₆₁	1	4	yes	—
598	#97	C₂³×C₆₁	1	2	yes	—
599	#97	C₂³×C₆₁	1	2	yes	—
600	#97	C₂³×C₆₁	1	4	yes	—
601	C₄×C₈	C₂³×C₆₁	1	4	yes	—
602	C₂⁴	—	2	1	no	—
603	#41	—	2	4	no	—
604	#41	—	2	4	no	—
605	#41	—	2	4	no	—
606	#41	—	2	4	no	—
607	#41	—	8	4	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
612	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
613	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
614	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
615	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
628	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
629	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	8	2	no	—
640	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
643	Q₁₆	—	2	4	no	—
644	Q₁₆	—	4	2	no	—
645	Q₁₆	—	4	4	no	—
646	SD₁₆	—	2	8	no	—
647	SD₁₆	—	2	4	no	—
648	SD₁₆	—	2	4	no	—
649	SD₁₆	—	4	2	no	—
650	SD₁₆	—	4	2	no	—
651	SD₁₆	—	4	4	no	—
652	SD₁₆	—	4	4	no	—
653	D₈	—	2	4	no	—
654	D₈	—	4	2	no	—
655	D₈	—	4	4	no	—
656	M₁₆	—	2	4	no	—
657	C₂×C₈	—	2	2	no	—
658	C₂×C₈	#41×C₆₁	1	4	yes	complemented
659	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
660	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
661	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
675	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
676	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
677	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
678	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
679	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
681	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
682	C₂²⋊C₄	—	2	2	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
695	C₄²	—	2	2	no	—
696	C₄²	—	2	2	no	—
697	C₄²	—	2	4	no	—
698	C₄²	—	2	4	no	—
699	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
700	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
701	C₄²	C₂⁴×C₆₁	1	4	yes	—
702	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
703	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	4	2	no	—
708	C₂³	—	8	1	no	—
709	C₂³	—	8	1	no	—
710	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
711	Q₈	—	2	2	no	—
712	Q₈	—	2	2	no	—
713	Q₈	—	2	2	no	—
714	Q₈	—	2	2	no	—
715	Q₈	—	2	2	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	4	2	no	—
718	Q₈	—	4	2	no	—
719	Q₈	—	4	2	no	—
720	D₄	—	2	2	no	—
721	D₄	—	2	2	no	—
722	D₄	—	2	2	no	—
723	D₄	—	2	2	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	4	2	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	4	no	—
729	D₄	—	4	4	no	—
730	D₄	—	4	2	no	—
731	D₄	—	8	1	no	—
732	D₄	—	8	1	no	—
733	D₄	—	8	4	no	—
734	D₄	—	8	4	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	4	4	no	—
745	C₂×C₄	—	4	4	no	—
746	C₂×C₄	—	8	4	no	—
747	C₂×C₄	—	8	2	no	—
748	C₂×C₄	—	8	4	no	—
749	C₂×C₄	—	8	1	no	—
750	C₂×C₄	—	8	1	no	—
751	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
754	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
757	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
758	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
759	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
760	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
761	C₈	—	2	2	no	—
762	C₈	—	2	4	no	—
763	C₈	C₂×#41×C₆₁	1	4	yes	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	8	4	no	—
776	C₂²	C₆₁×#550	1	2	yes	—
777	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
778	C₄	—	2	1	no	—
779	C₄	—	2	1	no	—
780	C₄	—	2	4	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	1	no	—
783	C₄	—	2	4	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	C₆₁×#550	1	2	yes	—
790	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
791	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
792	C₂	—	2	2	no	—
793	C₂	—	8	2	no	—
794	C₂	—	8	2	no	—
795	C₂	—	8	2	no	—
796	C₂	C₂×C₆₁×#550	1	1	yes	characteristic
797	C₂	C₆₁×#3585	1	1	yes	characteristic
798	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3507	C₂	semidirect
2. C₆₁×#3506	C₂	semidirect
3. C₆₁×#3403	C₂	semidirect
4. C₆₁×#3402	C₂	semidirect
5. C₆₁×#3400	C₂	semidirect
6. C₆₁×#3397	C₂	semidirect
7. C₆₁×#3154	C₂	semidirect
8. C₆₁×#3150	C₂	semidirect
9. C₆₁×#3046	C₂	semidirect
10. C₆₁×#3045	C₂	semidirect
11. C₆₁×#3037	C₂	semidirect
12. C₆₁×#3036	C₂	semidirect
13. C₆₁×#2961	C₂	semidirect
14. C₆₁×#2951	C₂	semidirect
15. C₂×C₆₁×#440	C₂	semidirect
22. C₆₁×#559	C₂²	semidirect
23. C₆₁×#557	C₂²	semidirect
26. C₆₁×#556	C₂²	semidirect
47. C₆₁×#497	C₂²	semidirect
48. C₆₁×#497	C₂²	semidirect
50. C₆₁×#496	C₂²	semidirect
51. C₆₁×#496	C₂²	semidirect
55. C₆₁×#464	C₂²	semidirect
56. C₆₁×#464	C₂²	semidirect
59. C₆₁×#463	C₂²	semidirect
60. C₆₁×#462	C₂²	semidirect
61. C₆₁×#462	C₂²	semidirect
63. C₆₁×#461	C₂²	semidirect
65. C₆₁×#460	C₂²	semidirect
68. C₆₁×#446	C₂²	semidirect
69. C₆₁×#446	C₂²	semidirect
72. C₆₁×#440	C₂²	semidirect
73. C₆₁×#440	C₂²	semidirect
74. C₄×Q₁₆×C₆₁	C₂²	semidirect
75. C₄×D₈×C₆₁	C₂²	semidirect
258. C₂×C₈×C₆₁	#41	semidirect
364. #61415	C₆₁	direct (N × H)
393. #3507	C₂×C₆₁	semidirect
394. #3506	C₂×C₆₁	semidirect
395. #3403	C₂×C₆₁	semidirect
396. #3402	C₂×C₆₁	semidirect
397. #3400	C₂×C₆₁	semidirect
398. #3397	C₂×C₆₁	semidirect
399. #3154	C₂×C₆₁	semidirect
400. #3150	C₂×C₆₁	semidirect
401. #3046	C₂×C₆₁	semidirect
402. #3045	C₂×C₆₁	semidirect
403. #3037	C₂×C₆₁	semidirect
404. #3036	C₂×C₆₁	semidirect
405. #2961	C₂×C₆₁	semidirect
406. #2951	C₂×C₆₁	semidirect
407. C₂×#440	C₂×C₆₁	semidirect
421. #559	C₂²×C₆₁	semidirect
422. #557	C₂²×C₆₁	semidirect
425. #556	C₂²×C₆₁	semidirect
446. #497	C₂²×C₆₁	semidirect
447. #497	C₂²×C₆₁	semidirect
449. #496	C₂²×C₆₁	semidirect
450. #496	C₂²×C₆₁	semidirect
454. #464	C₂²×C₆₁	semidirect
455. #464	C₂²×C₆₁	semidirect
458. #463	C₂²×C₆₁	semidirect
459. #462	C₂²×C₆₁	semidirect
460. #462	C₂²×C₆₁	semidirect
462. #461	C₂²×C₆₁	semidirect
464. #460	C₂²×C₆₁	semidirect
467. #446	C₂²×C₆₁	semidirect
468. #446	C₂²×C₆₁	semidirect
471. #440	C₂²×C₆₁	semidirect
472. #440	C₂²×C₆₁	semidirect
473. C₄×Q₁₆	C₂²×C₆₁	semidirect
474. C₄×D₈	C₂²×C₆₁	semidirect
484. C₆₁	#61415	direct (N × H)
658. C₂×C₈	#41×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3507	2
C₆₁×#3506	2
C₆₁×#3403	2
C₆₁×#3402	2
C₆₁×#3400	2
C₆₁×#3397	2
C₆₁×#3154	2
C₆₁×#3150	2
C₆₁×#3046	2
C₆₁×#3045	2
C₆₁×#3037	2
C₆₁×#3036	2
C₆₁×#2961	2
C₆₁×#2951	2
C₂×C₆₁×#440	2
#61415	61

Subgroups — C61×#61415 #29564848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61415 #29564848