Subgroups — C₆₁×#60919 #29564352

Order 15616.

1822 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3263	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3262	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3258	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3257	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3079	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3056	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3055	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3040	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2905	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	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
19	C₆₁×#542	—	2	2	no	—
20	C₆₁×#542	—	2	2	no	—
21	C₆₁×#542	C₂²	1	4	yes	—
22	C₆₁×#542	C₂²	1	4	yes	—
23	C₆₁×#542	C₂²	1	2	yes	complemented
24	C₆₁×#542	C₂²	1	2	yes	complemented
25	C₆₁×#541	C₂²	1	2	yes	complemented
26	C₆₁×#540	C₂²	1	2	yes	complemented
27	C₆₁×#539	—	2	1	no	—
28	C₆₁×#539	—	2	1	no	—
29	C₆₁×#538	—	2	1	no	—
30	C₆₁×#538	—	2	1	no	—
31	C₆₁×#533	C₂²	1	1	yes	characteristic
32	C₆₁×#532	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#529	—	2	2	no	—
35	C₆₁×#529	—	2	2	no	—
36	C₂×#126×C₆₁	—	2	1	no	—
37	C₂×#124×C₆₁	—	2	1	no	—
38	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#525	C₂²	1	2	yes	—
40	C₂×#123×C₆₁	—	2	1	no	—
41	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
42	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
44	C₄×#41×C₆₁	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
48	C₆₁×#479	C₂²	1	4	yes	complemented
49	C₆₁×#478	C₂²	1	4	yes	complemented
50	C₆₁×#477	C₂²	1	2	yes	complemented
51	C₆₁×#477	C₂²	1	4	yes	complemented
52	C₆₁×#476	C₂²	1	2	yes	complemented
53	C₆₁×#476	C₂²	1	4	yes	complemented
54	C₆₁×#475	C₂²	1	2	yes	complemented
55	C₆₁×#475	C₂²	1	4	yes	complemented
56	C₆₁×#474	C₂²	1	2	yes	complemented
57	C₆₁×#474	C₂²	1	4	yes	complemented
58	C₆₁×#470	C₂²	1	4	yes	complemented
59	C₆₁×#469	C₂²	1	4	yes	—
60	C₆₁×#468	C₂²	1	4	yes	—
61	C₆₁×#468	C₂²	1	4	yes	complemented
62	C₆₁×#467	C₂²	1	4	yes	complemented
63	C₆₁×#466	C₂²	1	4	yes	—
64	C₆₁×#465	C₂²	1	4	yes	—
65	C₆₁×#465	C₂²	1	4	yes	complemented
66	C₆₁×#464	C₂²	1	4	yes	complemented
67	C₆₁×#464	C₂²	1	4	yes	complemented
68	C₆₁×#464	C₂²	1	4	yes	complemented
69	C₆₁×#463	C₂²	1	4	yes	complemented
70	C₆₁×#463	C₂²	1	4	yes	complemented
71	C₆₁×#463	C₂²	1	4	yes	complemented
72	C₆₁×#462	C₂²	1	2	yes	complemented
73	C₆₁×#461	C₂²	1	2	yes	complemented
74	C₆₁×#460	C₂²	1	2	yes	complemented
75	C₆₁×#459	C₂²	1	2	yes	complemented
76	C₆₁×#428	C₂²	1	2	yes	—
77	C₆₁×#428	C₂²	1	2	yes	—
78	C₆₁×#424	C₂²	1	4	yes	complemented
79	C₆₁×#424	C₂²	1	4	yes	complemented
80	C₆₁×#423	C₂²	1	1	yes	characteristic
81	C₆₁×#423	C₂²	1	1	yes	characteristic
82	C₆₁×#423	C₂²	1	2	yes	—
83	C₆₁×#419	C₂²	1	2	yes	—
84	C₆₁×#418	C₂²	1	2	yes	—
85	C₆₁×#417	C₂²	1	2	yes	—
86	C₆₁×#417	C₂²	1	2	yes	—
87	C₂×#41×C₆₁	C₂³	1	2	yes	—
88	C₂²×Q₈×C₆₁	—	2	1	no	—
89	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₆₁	—	2	1	no	—
91	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₆₁	—	2	1	no	—
93	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
94	#137×C₆₁	—	4	4	no	—
95	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
96	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
97	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
99	C₂×D₈×C₆₁	C₂³	1	4	yes	—
100	C₂×M₁₆×C₆₁	—	4	4	no	—
101	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
102	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
103	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
104	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
105	C₄⋊Q₈×C₆₁	—	2	2	no	—
106	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
108	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
109	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
110	#127×C₆₁	C₂³	1	1	yes	characteristic
111	#126×C₆₁	—	2	2	no	—
112	#126×C₆₁	—	2	2	no	—
113	#126×C₆₁	—	2	4	no	—
114	#126×C₆₁	—	2	4	no	—
115	#126×C₆₁	—	2	2	no	—
116	#126×C₆₁	—	2	2	no	—
117	#125×C₆₁	—	2	2	no	—
118	#125×C₆₁	—	2	2	no	—
119	#125×C₆₁	C₂³	1	2	yes	—
120	#124×C₆₁	—	2	2	no	—
121	#124×C₆₁	—	2	2	no	—
122	#124×C₆₁	—	2	4	no	—
123	#124×C₆₁	—	2	4	no	—
124	#124×C₆₁	—	2	2	no	—
125	#124×C₆₁	C₂³	1	2	yes	—
126	#124×C₆₁	C₂³	1	4	yes	—
127	#123×C₆₁	—	2	2	no	—
128	#123×C₆₁	—	2	2	no	—
129	#123×C₆₁	—	2	2	no	—
130	#123×C₆₁	—	2	2	no	—
131	#123×C₆₁	—	2	2	no	—
132	#123×C₆₁	—	2	4	no	—
133	#123×C₆₁	—	2	4	no	—
134	C₂²⋊Q₈×C₆₁	—	2	1	no	—
135	C₂²⋊Q₈×C₆₁	—	2	1	no	—
136	C₂²⋊Q₈×C₆₁	—	2	2	no	—
137	C₂²⋊Q₈×C₆₁	—	2	2	no	—
138	C₂²⋊Q₈×C₆₁	—	2	2	no	—
139	C₂²⋊Q₈×C₆₁	—	2	4	no	—
140	C₂²⋊Q₈×C₆₁	—	2	4	no	—
141	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
142	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
143	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
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	2	no	—
149	#121×C₆₁	C₂³	1	2	yes	—
150	#121×C₆₁	C₂³	1	2	yes	—
151	#121×C₆₁	C₂³	1	4	yes	—
152	#120×C₆₁	—	2	2	no	—
153	C₄×Q₈×C₆₁	—	2	1	no	—
154	C₄×Q₈×C₆₁	—	2	1	no	—
155	C₄×Q₈×C₆₁	—	2	1	no	—
156	C₄×Q₈×C₆₁	—	2	1	no	—
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×Q₈×C₆₁	C₂³	1	2	yes	—
161	C₄×D₄×C₆₁	—	2	2	no	—
162	C₄×D₄×C₆₁	—	2	2	no	—
163	C₄×D₄×C₆₁	—	2	2	no	—
164	C₄×D₄×C₆₁	—	2	2	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	C₂³	1	2	yes	—
170	C₄×D₄×C₆₁	C₂³	1	2	yes	—
171	C₄×D₄×C₆₁	C₂³	1	2	yes	—
172	C₄×D₄×C₆₁	C₂³	1	2	yes	—
173	#117×C₆₁	—	2	2	no	—
174	#117×C₆₁	D₄	1	2	yes	—
175	#117×C₆₁	D₄	1	2	yes	—
176	#117×C₆₁	C₂³	1	2	yes	—
177	#117×C₆₁	C₂³	1	2	yes	—
178	#117×C₆₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
180	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
181	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
182	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
187	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
188	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
189	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
191	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₆₁	—	2	1	no	—
194	C₂×C₄²×C₆₁	—	2	2	no	—
195	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
197	#107×C₆₁	C₂³	1	4	yes	—
198	#107×C₆₁	C₂³	1	4	yes	—
199	#106×C₆₁	C₂³	1	4	yes	—
200	#106×C₆₁	C₂³	1	4	yes	—
201	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
202	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
203	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
204	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
205	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
206	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
207	#103×C₆₁	C₂³	1	4	yes	—
208	#103×C₆₁	C₂³	1	4	yes	—
209	#103×C₆₁	C₂³	1	4	yes	—
210	#103×C₆₁	C₂³	1	4	yes	—
211	#102×C₆₁	C₂³	1	4	yes	—
212	#102×C₆₁	C₂³	1	4	yes	—
213	#102×C₆₁	C₂³	1	4	yes	—
214	#102×C₆₁	C₂³	1	4	yes	—
215	C₂⁴×C₆₁	—	2	1	no	—
216	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
217	#41×C₆₁	—	2	4	no	—
218	#41×C₆₁	—	2	4	no	—
219	C₂×Q₈×C₆₁	—	2	1	no	—
220	C₂×Q₈×C₆₁	—	2	1	no	—
221	C₂×Q₈×C₆₁	—	2	1	no	—
222	C₂×Q₈×C₆₁	—	2	4	no	—
223	C₂×Q₈×C₆₁	—	2	2	no	—
224	C₂×Q₈×C₆₁	—	2	2	no	—
225	C₂×Q₈×C₆₁	—	8	2	no	—
226	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
227	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
228	C₂×D₄×C₆₁	—	2	2	no	—
229	C₂×D₄×C₆₁	—	2	2	no	—
230	C₂×D₄×C₆₁	—	2	2	no	—
231	C₂×D₄×C₆₁	—	2	4	no	—
232	C₂×D₄×C₆₁	—	2	1	no	—
233	C₂×D₄×C₆₁	—	2	1	no	—
234	C₂×D₄×C₆₁	—	2	1	no	—
235	C₂×D₄×C₆₁	—	2	2	no	—
236	C₂×D₄×C₆₁	—	2	2	no	—
237	C₂×D₄×C₆₁	—	8	2	no	—
238	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
239	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₆₁	—	2	2	no	—
241	C₂²×C₄×C₆₁	—	2	2	no	—
242	C₂²×C₄×C₆₁	—	2	1	no	—
243	C₂²×C₄×C₆₁	—	2	1	no	—
244	C₂²×C₄×C₆₁	—	2	1	no	—
245	C₂²×C₄×C₆₁	—	2	2	no	—
246	C₂²×C₄×C₆₁	—	2	2	no	—
247	C₂²×C₄×C₆₁	—	2	2	no	—
248	C₂²×C₄×C₆₁	—	2	2	no	—
249	C₂²×C₄×C₆₁	—	2	2	no	—
250	C₂²×C₄×C₆₁	—	8	2	no	—
251	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
253	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
259	Q₁₆×C₆₁	—	4	4	no	—
260	SD₁₆×C₆₁	—	4	4	no	—
261	SD₁₆×C₆₁	—	4	4	no	—
262	D₈×C₆₁	—	4	4	no	—
263	M₁₆×C₆₁	—	2	4	no	—
264	M₁₆×C₆₁	—	2	4	no	—
265	M₁₆×C₆₁	—	4	4	no	—
266	C₂×C₈×C₆₁	—	4	4	no	—
267	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
268	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
269	C₄⋊C₄×C₆₁	—	2	2	no	—
270	C₄⋊C₄×C₆₁	—	2	2	no	—
271	C₄⋊C₄×C₆₁	—	2	4	no	—
272	C₄⋊C₄×C₆₁	—	2	4	no	—
273	C₄⋊C₄×C₆₁	—	2	1	no	—
274	C₄⋊C₄×C₆₁	—	2	1	no	—
275	C₄⋊C₄×C₆₁	—	2	2	no	—
276	C₄⋊C₄×C₆₁	—	2	2	no	—
277	C₄⋊C₄×C₆₁	—	2	1	no	—
278	C₄⋊C₄×C₆₁	—	2	1	no	—
279	C₄⋊C₄×C₆₁	—	2	2	no	—
280	C₄⋊C₄×C₆₁	—	2	2	no	—
281	C₄⋊C₄×C₆₁	—	2	2	no	—
282	C₄⋊C₄×C₆₁	—	2	2	no	—
283	C₄⋊C₄×C₆₁	—	2	1	no	—
284	C₄⋊C₄×C₆₁	—	2	1	no	—
285	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
286	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
287	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
288	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
289	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
290	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
291	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
292	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
293	C₂²⋊C₄×C₆₁	—	2	4	no	—
294	C₂²⋊C₄×C₆₁	—	2	2	no	—
295	C₂²⋊C₄×C₆₁	—	2	2	no	—
296	C₂²⋊C₄×C₆₁	—	2	2	no	—
297	C₂²⋊C₄×C₆₁	—	2	2	no	—
298	C₂²⋊C₄×C₆₁	—	2	2	no	—
299	C₂²⋊C₄×C₆₁	—	2	4	no	—
300	C₂²⋊C₄×C₆₁	—	2	4	no	—
301	C₂²⋊C₄×C₆₁	—	2	4	no	—
302	C₂²⋊C₄×C₆₁	—	2	2	no	—
303	C₂²⋊C₄×C₆₁	—	2	2	no	—
304	C₂²⋊C₄×C₆₁	—	2	2	no	—
305	C₂²⋊C₄×C₆₁	—	2	2	no	—
306	C₂²⋊C₄×C₆₁	—	2	2	no	—
307	C₂²⋊C₄×C₆₁	—	2	2	no	—
308	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
309	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
310	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
311	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
312	C₄²×C₆₁	—	2	2	no	—
313	C₄²×C₆₁	—	2	2	no	—
314	C₄²×C₆₁	—	2	2	no	—
315	C₄²×C₆₁	—	2	2	no	—
316	C₄²×C₆₁	—	2	2	no	—
317	C₄²×C₆₁	C₂×D₄	1	2	yes	—
318	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
321	C₄²×C₆₁	C₂⁴	1	2	yes	—
322	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
323	C₂³×C₆₁	—	2	2	no	—
324	C₂³×C₆₁	—	2	2	no	—
325	C₂³×C₆₁	—	2	2	no	—
326	C₂³×C₆₁	—	4	1	no	—
327	C₂³×C₆₁	—	4	1	no	—
328	C₂³×C₆₁	—	4	2	no	—
329	C₂³×C₆₁	—	4	2	no	—
330	C₂³×C₆₁	—	4	2	no	—
331	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
332	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
333	Q₈×C₆₁	—	2	2	no	—
334	Q₈×C₆₁	—	2	2	no	—
335	Q₈×C₆₁	—	2	2	no	—
336	Q₈×C₆₁	—	2	2	no	—
337	Q₈×C₆₁	—	4	2	no	—
338	Q₈×C₆₁	—	8	1	no	—
339	Q₈×C₆₁	—	8	1	no	—
340	Q₈×C₆₁	—	8	4	no	—
341	D₄×C₆₁	—	2	2	no	—
342	D₄×C₆₁	—	2	2	no	—
343	D₄×C₆₁	—	2	2	no	—
344	D₄×C₆₁	—	2	2	no	—
345	D₄×C₆₁	—	4	4	no	—
346	D₄×C₆₁	—	4	2	no	—
347	D₄×C₆₁	—	8	1	no	—
348	D₄×C₆₁	—	8	1	no	—
349	D₄×C₆₁	—	8	2	no	—
350	D₄×C₆₁	—	8	2	no	—
351	D₄×C₆₁	—	8	4	no	—
352	C₂×C₄×C₆₁	—	2	2	no	—
353	C₂×C₄×C₆₁	—	2	4	no	—
354	C₂×C₄×C₆₁	—	2	2	no	—
355	C₂×C₄×C₆₁	—	2	2	no	—
356	C₂×C₄×C₆₁	—	2	2	no	—
357	C₂×C₄×C₆₁	—	2	2	no	—
358	C₂×C₄×C₆₁	—	2	2	no	—
359	C₂×C₄×C₆₁	—	2	2	no	—
360	C₂×C₄×C₆₁	—	2	2	no	—
361	C₂×C₄×C₆₁	—	2	2	no	—
362	C₂×C₄×C₆₁	—	4	1	no	—
363	C₂×C₄×C₆₁	—	4	1	no	—
364	C₂×C₄×C₆₁	—	4	1	no	—
365	C₂×C₄×C₆₁	—	4	1	no	—
366	C₂×C₄×C₆₁	—	4	2	no	—
367	C₂×C₄×C₆₁	—	4	2	no	—
368	C₂×C₄×C₆₁	—	4	2	no	—
369	C₂×C₄×C₆₁	—	4	4	no	—
370	C₂×C₄×C₆₁	—	8	2	no	—
371	C₂×C₄×C₆₁	—	8	2	no	—
372	C₂×C₄×C₆₁	—	8	2	no	—
373	C₂×C₄×C₆₁	—	8	2	no	—
374	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
383	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
384	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
385	C₈×C₆₁	—	2	4	no	—
386	C₈×C₆₁	—	2	4	no	—
387	#60919	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₂²×C₆₁	—	2	1	no	—
389	C₂²×C₆₁	—	2	1	no	—
390	C₂²×C₆₁	—	2	2	no	—
391	C₂²×C₆₁	—	2	2	no	—
392	C₂²×C₆₁	—	2	2	no	—
393	C₂²×C₆₁	—	4	2	no	—
394	C₂²×C₆₁	—	4	2	no	—
395	C₂²×C₆₁	—	4	2	no	—
396	C₂²×C₆₁	—	4	2	no	—
397	C₂²×C₆₁	—	4	2	no	—
398	C₂²×C₆₁	—	4	2	no	—
399	C₂²×C₆₁	—	8	2	no	—
400	C₂²×C₆₁	—	8	4	no	—
401	C₂²×C₆₁	#537	1	2	yes	—
402	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
403	C₄×C₆₁	—	2	1	no	—
404	C₄×C₆₁	—	2	1	no	—
405	C₄×C₆₁	—	2	2	no	—
406	C₄×C₆₁	—	2	2	no	—
407	C₄×C₆₁	—	2	1	no	—
408	C₄×C₆₁	—	2	1	no	—
409	C₄×C₆₁	—	2	2	no	—
410	C₄×C₆₁	—	4	2	no	—
411	C₄×C₆₁	—	4	2	no	—
412	C₄×C₆₁	—	4	2	no	—
413	C₄×C₆₁	—	4	2	no	—
414	C₄×C₆₁	—	4	2	no	—
415	C₄×C₆₁	—	4	2	no	—
416	C₄×C₆₁	#537	1	2	yes	—
417	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
418	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
419	#3455	C₂×C₆₁	1	1	yes	characteristic, complemented
420	C₂×#542	C₂×C₆₁	1	1	yes	characteristic, complemented
421	#3263	C₂×C₆₁	1	4	yes	complemented
422	#3262	C₂×C₆₁	1	4	yes	complemented
423	#3258	C₂×C₆₁	1	4	yes	complemented
424	#3257	C₂×C₆₁	1	4	yes	complemented
425	#3079	C₂×C₆₁	1	2	yes	complemented
426	#3078	C₂×C₆₁	1	1	yes	characteristic, complemented
427	#3077	C₂×C₆₁	1	1	yes	characteristic, complemented
428	#3056	C₂×C₆₁	1	2	yes	complemented
429	#3055	C₂×C₆₁	1	2	yes	complemented
430	#3040	C₂×C₆₁	1	2	yes	complemented
431	#3037	C₂×C₆₁	1	1	yes	characteristic, complemented
432	#3036	C₂×C₆₁	1	1	yes	characteristic, complemented
433	#2905	C₂×C₆₁	1	1	yes	characteristic, complemented
434	C₂×C₆₁	—	2	2	no	—
435	C₂×C₆₁	—	4	2	no	—
436	C₂×C₆₁	—	8	2	no	—
437	C₂×C₆₁	—	8	2	no	—
438	C₂×C₆₁	C₂×#537	1	1	yes	characteristic
439	C₂×C₆₁	#3585	1	1	yes	characteristic
440	C₂×C₆₁	#3586	1	1	yes	characteristic
441	C₂×#137	C₂²×C₆₁	1	2	yes	—
442	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
443	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
444	#542	—	2	2	no	—
445	#542	—	2	2	no	—
446	#542	C₂²×C₆₁	1	4	yes	—
447	#542	C₂²×C₆₁	1	4	yes	—
448	#542	C₂²×C₆₁	1	2	yes	complemented
449	#542	C₂²×C₆₁	1	2	yes	complemented
450	#541	C₂²×C₆₁	1	2	yes	complemented
451	#540	C₂²×C₆₁	1	2	yes	complemented
452	#539	—	2	1	no	—
453	#539	—	2	1	no	—
454	#538	—	2	1	no	—
455	#538	—	2	1	no	—
456	#533	C₂²×C₆₁	1	1	yes	characteristic
457	#532	C₂²×C₆₁	1	1	yes	characteristic
458	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
459	#529	—	2	2	no	—
460	#529	—	2	2	no	—
461	C₂×#126	—	2	1	no	—
462	C₂×#124	—	2	1	no	—
463	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
464	#525	C₂²×C₆₁	1	2	yes	—
465	C₂×#123	—	2	1	no	—
466	C₂×C₂²⋊Q₈	—	2	1	no	—
467	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
468	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
469	C₄×#41	C₂²×C₆₁	1	2	yes	—
470	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
471	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
472	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
473	#479	C₂²×C₆₁	1	4	yes	complemented
474	#478	C₂²×C₆₁	1	4	yes	complemented
475	#477	C₂²×C₆₁	1	2	yes	complemented
476	#477	C₂²×C₆₁	1	4	yes	complemented
477	#476	C₂²×C₆₁	1	2	yes	complemented
478	#476	C₂²×C₆₁	1	4	yes	complemented
479	#475	C₂²×C₆₁	1	2	yes	complemented
480	#475	C₂²×C₆₁	1	4	yes	complemented
481	#474	C₂²×C₆₁	1	2	yes	complemented
482	#474	C₂²×C₆₁	1	4	yes	complemented
483	#470	C₂²×C₆₁	1	4	yes	complemented
484	#469	C₂²×C₆₁	1	4	yes	—
485	#468	C₂²×C₆₁	1	4	yes	—
486	#468	C₂²×C₆₁	1	4	yes	complemented
487	#467	C₂²×C₆₁	1	4	yes	complemented
488	#466	C₂²×C₆₁	1	4	yes	—
489	#465	C₂²×C₆₁	1	4	yes	—
490	#465	C₂²×C₆₁	1	4	yes	complemented
491	#464	C₂²×C₆₁	1	4	yes	complemented
492	#464	C₂²×C₆₁	1	4	yes	complemented
493	#464	C₂²×C₆₁	1	4	yes	complemented
494	#463	C₂²×C₆₁	1	4	yes	complemented
495	#463	C₂²×C₆₁	1	4	yes	complemented
496	#463	C₂²×C₆₁	1	4	yes	complemented
497	#462	C₂²×C₆₁	1	2	yes	complemented
498	#461	C₂²×C₆₁	1	2	yes	complemented
499	#460	C₂²×C₆₁	1	2	yes	complemented
500	#459	C₂²×C₆₁	1	2	yes	complemented
501	#428	C₂²×C₆₁	1	2	yes	—
502	#428	C₂²×C₆₁	1	2	yes	—
503	#424	C₂²×C₆₁	1	4	yes	complemented
504	#424	C₂²×C₆₁	1	4	yes	complemented
505	#423	C₂²×C₆₁	1	1	yes	characteristic
506	#423	C₂²×C₆₁	1	1	yes	characteristic
507	#423	C₂²×C₆₁	1	2	yes	—
508	#419	C₂²×C₆₁	1	2	yes	—
509	#418	C₂²×C₆₁	1	2	yes	—
510	#417	C₂²×C₆₁	1	2	yes	—
511	#417	C₂²×C₆₁	1	2	yes	—
512	C₆₁	#60919	1	1	yes	characteristic, direct product factor, Sylow
513	C₂×#41	C₂³×C₆₁	1	2	yes	—
514	C₂²×Q₈	—	2	1	no	—
515	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
516	C₂²×D₄	—	2	1	no	—
517	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
520	#137	—	4	4	no	—
521	AGL(1,ℤ/8)	—	4	4	no	—
522	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
523	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
524	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
525	C₂×D₈	C₂³×C₆₁	1	4	yes	—
526	C₂×M₁₆	—	4	4	no	—
527	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
528	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
529	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
530	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
531	C₄⋊Q₈	—	2	2	no	—
532	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
533	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
534	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
535	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
536	#127	C₂³×C₆₁	1	1	yes	characteristic
537	#126	—	2	4	no	—
538	#126	—	2	4	no	—
539	#126	—	2	2	no	—
540	#126	—	2	2	no	—
541	#126	—	2	2	no	—
542	#126	—	2	2	no	—
543	#125	—	2	2	no	—
544	#125	—	2	2	no	—
545	#125	C₂³×C₆₁	1	2	yes	—
546	#124	—	2	4	no	—
547	#124	—	2	4	no	—
548	#124	—	2	2	no	—
549	#124	—	2	2	no	—
550	#124	—	2	2	no	—
551	#124	C₂³×C₆₁	1	4	yes	—
552	#124	C₂³×C₆₁	1	2	yes	—
553	#123	—	2	2	no	—
554	#123	—	2	2	no	—
555	#123	—	2	2	no	—
556	#123	—	2	4	no	—
557	#123	—	2	4	no	—
558	#123	—	2	2	no	—
559	#123	—	2	2	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	1	no	—
562	C₂²⋊Q₈	—	2	1	no	—
563	C₂²⋊Q₈	—	2	4	no	—
564	C₂²⋊Q₈	—	2	4	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
568	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
569	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
570	#121	—	2	2	no	—
571	#121	—	2	1	no	—
572	#121	—	2	1	no	—
573	#121	—	2	2	no	—
574	#121	—	2	2	no	—
575	#121	C₂³×C₆₁	1	4	yes	—
576	#121	C₂³×C₆₁	1	2	yes	—
577	#121	C₂³×C₆₁	1	2	yes	—
578	#120	—	2	2	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	—	2	1	no	—
582	C₄×Q₈	—	2	1	no	—
583	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
584	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
585	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
586	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	C₂³×C₆₁	1	2	yes	—
596	C₄×D₄	C₂³×C₆₁	1	2	yes	—
597	C₄×D₄	C₂³×C₆₁	1	2	yes	—
598	C₄×D₄	C₂³×C₆₁	1	2	yes	—
599	#117	—	2	2	no	—
600	#117	D₄×C₆₁	1	2	yes	—
601	#117	D₄×C₆₁	1	2	yes	—
602	#117	C₂³×C₆₁	1	2	yes	—
603	#117	C₂³×C₆₁	1	2	yes	—
604	#117	C₂³×C₆₁	1	2	yes	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
609	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
619	C₂×C₄²	—	2	1	no	—
620	C₂×C₄²	—	2	2	no	—
621	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
623	#107	C₂³×C₆₁	1	4	yes	—
624	#107	C₂³×C₆₁	1	4	yes	—
625	#106	C₂³×C₆₁	1	4	yes	—
626	#106	C₂³×C₆₁	1	4	yes	—
627	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
628	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
629	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
630	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
631	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
632	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
633	#103	C₂³×C₆₁	1	4	yes	—
634	#103	C₂³×C₆₁	1	4	yes	—
635	#103	C₂³×C₆₁	1	4	yes	—
636	#103	C₂³×C₆₁	1	4	yes	—
637	#102	C₂³×C₆₁	1	4	yes	—
638	#102	C₂³×C₆₁	1	4	yes	—
639	#102	C₂³×C₆₁	1	4	yes	—
640	#102	C₂³×C₆₁	1	4	yes	—
641	C₂⁴	—	2	1	no	—
642	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
643	#41	—	2	4	no	—
644	#41	—	2	4	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	—	2	1	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	4	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	8	2	no	—
652	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
653	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	4	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	8	2	no	—
664	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
665	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	8	2	no	—
677	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
679	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
685	Q₁₆	—	4	4	no	—
686	SD₁₆	—	4	4	no	—
687	SD₁₆	—	4	4	no	—
688	D₈	—	4	4	no	—
689	M₁₆	—	2	4	no	—
690	M₁₆	—	2	4	no	—
691	M₁₆	—	4	4	no	—
692	C₂×C₈	—	4	4	no	—
693	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
694	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
712	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
713	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
714	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
715	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
716	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
717	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
735	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
736	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
737	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	2	no	—
743	C₄²	C₂×D₄×C₆₁	1	2	yes	—
744	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
745	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
746	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
747	C₄²	C₂⁴×C₆₁	1	2	yes	—
748	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	4	1	no	—
753	C₂³	—	4	1	no	—
754	C₂³	—	4	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	2	no	—
757	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
758	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
759	Q₈	—	2	2	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	2	2	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	4	2	no	—
764	Q₈	—	8	1	no	—
765	Q₈	—	8	1	no	—
766	Q₈	—	8	4	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	2	no	—
771	D₄	—	4	4	no	—
772	D₄	—	4	2	no	—
773	D₄	—	8	1	no	—
774	D₄	—	8	1	no	—
775	D₄	—	8	2	no	—
776	D₄	—	8	2	no	—
777	D₄	—	8	4	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	8	2	no	—
797	C₂×C₄	—	8	2	no	—
798	C₂×C₄	—	8	2	no	—
799	C₂×C₄	—	8	2	no	—
800	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
803	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
804	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
807	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
808	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
809	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
810	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
811	C₈	—	2	4	no	—
812	C₈	—	2	4	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	8	2	no	—
825	C₂²	—	8	4	no	—
826	C₂²	C₆₁×#537	1	2	yes	—
827	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	2	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	1	no	—
834	C₄	—	2	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	C₆₁×#537	1	2	yes	—
842	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
843	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
844	C₂	—	2	2	no	—
845	C₂	—	4	2	no	—
846	C₂	—	8	2	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×C₆₁×#537	1	1	yes	characteristic
849	C₂	C₆₁×#3585	1	1	yes	characteristic
850	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 ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3455	C₂	semidirect
2. C₂×C₆₁×#542	C₂	semidirect
3. C₆₁×#3263	C₂	semidirect
4. C₆₁×#3262	C₂	semidirect
5. C₆₁×#3258	C₂	semidirect
6. C₆₁×#3257	C₂	semidirect
7. C₆₁×#3079	C₂	semidirect
8. C₆₁×#3078	C₂	semidirect
9. C₆₁×#3077	C₂	semidirect
10. C₆₁×#3056	C₂	semidirect
11. C₆₁×#3055	C₂	semidirect
12. C₆₁×#3040	C₂	semidirect
13. C₆₁×#3037	C₂	semidirect
14. C₆₁×#3036	C₂	semidirect
15. C₆₁×#2905	C₂	semidirect
23. C₆₁×#542	C₂²	semidirect
24. C₆₁×#542	C₂²	semidirect
25. C₆₁×#541	C₂²	semidirect
26. C₆₁×#540	C₂²	semidirect
48. C₆₁×#479	C₂²	semidirect
49. C₆₁×#478	C₂²	semidirect
50. C₆₁×#477	C₂²	semidirect
51. C₆₁×#477	C₂²	semidirect
52. C₆₁×#476	C₂²	semidirect
53. C₆₁×#476	C₂²	semidirect
54. C₆₁×#475	C₂²	semidirect
55. C₆₁×#475	C₂²	semidirect
56. C₆₁×#474	C₂²	semidirect
57. C₆₁×#474	C₂²	semidirect
58. C₆₁×#470	C₂²	semidirect
61. C₆₁×#468	C₂²	semidirect
62. C₆₁×#467	C₂²	semidirect
65. C₆₁×#465	C₂²	semidirect
66. C₆₁×#464	C₂²	semidirect
67. C₆₁×#464	C₂²	semidirect
68. C₆₁×#464	C₂²	semidirect
69. C₆₁×#463	C₂²	semidirect
70. C₆₁×#463	C₂²	semidirect
71. C₆₁×#463	C₂²	semidirect
72. C₆₁×#462	C₂²	semidirect
73. C₆₁×#461	C₂²	semidirect
74. C₆₁×#460	C₂²	semidirect
75. C₆₁×#459	C₂²	semidirect
78. C₆₁×#424	C₂²	semidirect
79. C₆₁×#424	C₂²	semidirect
387. #60919	C₆₁	direct (N × H)
419. #3455	C₂×C₆₁	semidirect
420. C₂×#542	C₂×C₆₁	semidirect
421. #3263	C₂×C₆₁	semidirect
422. #3262	C₂×C₆₁	semidirect
423. #3258	C₂×C₆₁	semidirect
424. #3257	C₂×C₆₁	semidirect
425. #3079	C₂×C₆₁	semidirect
426. #3078	C₂×C₆₁	semidirect
427. #3077	C₂×C₆₁	semidirect
428. #3056	C₂×C₆₁	semidirect
429. #3055	C₂×C₆₁	semidirect
430. #3040	C₂×C₆₁	semidirect
431. #3037	C₂×C₆₁	semidirect
432. #3036	C₂×C₆₁	semidirect
433. #2905	C₂×C₆₁	semidirect
448. #542	C₂²×C₆₁	semidirect
449. #542	C₂²×C₆₁	semidirect
450. #541	C₂²×C₆₁	semidirect
451. #540	C₂²×C₆₁	semidirect
473. #479	C₂²×C₆₁	semidirect
474. #478	C₂²×C₆₁	semidirect
475. #477	C₂²×C₆₁	semidirect
476. #477	C₂²×C₆₁	semidirect
477. #476	C₂²×C₆₁	semidirect
478. #476	C₂²×C₆₁	semidirect
479. #475	C₂²×C₆₁	semidirect
480. #475	C₂²×C₆₁	semidirect
481. #474	C₂²×C₆₁	semidirect
482. #474	C₂²×C₆₁	semidirect
483. #470	C₂²×C₆₁	semidirect
486. #468	C₂²×C₆₁	semidirect
487. #467	C₂²×C₆₁	semidirect
490. #465	C₂²×C₆₁	semidirect
491. #464	C₂²×C₆₁	semidirect
492. #464	C₂²×C₆₁	semidirect
493. #464	C₂²×C₆₁	semidirect
494. #463	C₂²×C₆₁	semidirect
495. #463	C₂²×C₆₁	semidirect
496. #463	C₂²×C₆₁	semidirect
497. #462	C₂²×C₆₁	semidirect
498. #461	C₂²×C₆₁	semidirect
499. #460	C₂²×C₆₁	semidirect
500. #459	C₂²×C₆₁	semidirect
503. #424	C₂²×C₆₁	semidirect
504. #424	C₂²×C₆₁	semidirect
512. C₆₁	#60919	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#3455	2
C₂×C₆₁×#542	2
C₆₁×#3263	2
C₆₁×#3262	2
C₆₁×#3258	2
C₆₁×#3257	2
C₆₁×#3079	2
C₆₁×#3078	2
C₆₁×#3077	2
C₆₁×#3056	2
C₆₁×#3055	2
C₆₁×#3040	2
C₆₁×#3037	2
C₆₁×#3036	2
C₆₁×#2905	2
#60919	61

Subgroups — C61×#60919 #29564352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60919 #29564352