Subgroups — C₆₁×#24898 #29528331

Order 15616.

1016 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#448	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2422	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2096	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2077	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2034	C₂	1	1	yes	maximal, characteristic
9	C₆₁×#1933	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1923	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1877	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1787	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×#123×C₆₁	—	2	1	no	—
20	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#448	—	2	4	no	—
25	C₄×SD₁₆×C₆₁	—	2	4	no	—
26	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#397	—	2	1	no	—
41	C₆₁×#394	—	2	1	no	—
42	C₆₁×#391	—	2	1	no	—
43	C₆₁×#391	—	2	1	no	—
44	C₆₁×#391	C₂²	1	1	yes	characteristic
45	C₆₁×#391	C₂²	1	1	yes	characteristic
46	C₆₁×#390	C₂²	1	1	yes	characteristic
47	C₆₁×#389	C₂²	1	1	yes	characteristic
48	C₆₁×#385	—	2	1	no	—
49	C₆₁×#384	C₂²	1	1	yes	characteristic
50	C₆₁×#380	—	2	1	no	—
51	C₆₁×#380	C₂²	1	1	yes	characteristic
52	C₆₁×#380	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
54	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
55	C₆₁×#340	C₂²	1	1	yes	characteristic
56	C₆₁×#340	C₂²	1	1	yes	characteristic
57	C₆₁×#340	C₂²	1	1	yes	characteristic
58	C₆₁×#340	C₂²	1	1	yes	characteristic
59	C₆₁×#336	C₂²	1	1	yes	characteristic
60	C₆₁×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₆₁	—	2	2	no	—
62	C₂²×Q₈×C₆₁	—	2	2	no	—
63	C₂²×Q₈×C₆₁	—	2	1	no	—
64	C₂²×Q₈×C₆₁	—	2	2	no	—
65	C₂²×Q₈×C₆₁	—	2	2	no	—
66	C₂²×Q₈×C₆₁	—	4	1	no	—
67	C₂²×Q₈×C₆₁	—	4	1	no	—
68	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₆₁	—	2	1	no	—
71	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₆₁	—	2	1	no	—
73	C₂³×C₄×C₆₁	—	2	1	no	—
74	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
75	C₂×SD₁₆×C₆₁	—	2	2	no	—
76	C₂×SD₁₆×C₆₁	—	2	2	no	—
77	C₂×SD₁₆×C₆₁	—	2	2	no	—
78	C₂×SD₁₆×C₆₁	—	2	2	no	—
79	C₂×SD₁₆×C₆₁	—	4	1	no	—
80	C₂×SD₁₆×C₆₁	D₄	1	4	yes	—
81	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
85	#123×C₆₁	—	4	4	no	—
86	#121×C₆₁	—	2	2	no	—
87	#121×C₆₁	—	4	1	no	—
88	C₄×Q₈×C₆₁	—	2	2	no	—
89	C₄×Q₈×C₆₁	—	2	2	no	—
90	C₄×Q₈×C₆₁	—	4	1	no	—
91	C₄×Q₈×C₆₁	—	4	1	no	—
92	C₄×D₄×C₆₁	—	2	2	no	—
93	C₄×D₄×C₆₁	—	4	1	no	—
94	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
95	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
96	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
97	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
98	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
99	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₆₁	—	2	1	no	—
113	C₂×C₄²×C₆₁	—	2	1	no	—
114	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
116	#106×C₆₁	—	2	2	no	—
117	#106×C₆₁	—	4	1	no	—
118	C₄⋊C₈×C₆₁	—	4	1	no	—
119	#103×C₆₁	—	2	2	no	—
120	#103×C₆₁	—	2	2	no	—
121	#103×C₆₁	—	2	2	no	—
122	#103×C₆₁	—	2	2	no	—
123	#103×C₆₁	—	2	2	no	—
124	#103×C₆₁	—	4	1	no	—
125	#102×C₆₁	—	2	2	no	—
126	#102×C₆₁	—	4	1	no	—
127	C₂²⋊C₈×C₆₁	—	2	2	no	—
128	C₂²⋊C₈×C₆₁	—	4	1	no	—
129	C₄×C₈×C₆₁	—	2	2	no	—
130	#95×C₆₁	—	2	1	no	—
131	#95×C₆₁	—	2	1	no	—
132	#95×C₆₁	—	2	1	no	—
133	#95×C₆₁	—	2	1	no	—
134	#95×C₆₁	—	2	1	no	—
135	#95×C₆₁	—	2	1	no	—
136	#95×C₆₁	—	2	1	no	—
137	#95×C₆₁	D₄	1	1	yes	characteristic
138	#95×C₆₁	D₄	1	1	yes	characteristic
139	C₂⁴×C₆₁	—	2	1	no	—
140	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
141	C₂×Q₈×C₆₁	—	2	4	no	—
142	C₂×Q₈×C₆₁	—	2	1	no	—
143	C₂×Q₈×C₆₁	—	2	1	no	—
144	C₂×Q₈×C₆₁	—	2	1	no	—
145	C₂×Q₈×C₆₁	—	2	1	no	—
146	C₂×Q₈×C₆₁	—	2	1	no	—
147	C₂×Q₈×C₆₁	—	2	1	no	—
148	C₂×Q₈×C₆₁	—	2	1	no	—
149	C₂×Q₈×C₆₁	—	2	1	no	—
150	C₂×Q₈×C₆₁	—	4	2	no	—
151	C₂×Q₈×C₆₁	—	4	2	no	—
152	C₂×Q₈×C₆₁	—	4	4	no	—
153	C₂×Q₈×C₆₁	—	4	4	no	—
154	C₂×Q₈×C₆₁	—	4	4	no	—
155	C₂×Q₈×C₆₁	—	4	4	no	—
156	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
157	C₂×Q₈×C₆₁	#41	1	2	yes	—
158	C₂×Q₈×C₆₁	#41	1	2	yes	—
159	C₂×Q₈×C₆₁	#41	1	2	yes	—
160	C₂×D₄×C₆₁	—	2	1	no	—
161	C₂×D₄×C₆₁	—	2	1	no	—
162	C₂×D₄×C₆₁	—	2	1	no	—
163	C₂×D₄×C₆₁	—	2	1	no	—
164	C₂×D₄×C₆₁	—	2	1	no	—
165	C₂×D₄×C₆₁	—	4	2	no	—
166	C₂×D₄×C₆₁	—	4	2	no	—
167	C₂×D₄×C₆₁	—	8	1	no	—
168	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₆₁	—	2	1	no	—
170	C₂²×C₄×C₆₁	—	2	4	no	—
171	C₂²×C₄×C₆₁	—	2	1	no	—
172	C₂²×C₄×C₆₁	—	2	1	no	—
173	C₂²×C₄×C₆₁	—	2	1	no	—
174	C₂²×C₄×C₆₁	—	2	1	no	—
175	C₂²×C₄×C₆₁	—	2	1	no	—
176	C₂²×C₄×C₆₁	—	2	1	no	—
177	C₂²×C₄×C₆₁	—	2	1	no	—
178	C₂²×C₄×C₆₁	—	2	1	no	—
179	C₂²×C₄×C₆₁	—	2	1	no	—
180	C₂²×C₄×C₆₁	—	2	1	no	—
181	C₂²×C₄×C₆₁	—	2	1	no	—
182	C₂²×C₄×C₆₁	—	2	1	no	—
183	C₂²×C₄×C₆₁	—	4	2	no	—
184	C₂²×C₄×C₆₁	—	4	2	no	—
185	C₂²×C₄×C₆₁	—	4	2	no	—
186	C₂²×C₄×C₆₁	—	4	2	no	—
187	C₂²×C₄×C₆₁	—	8	1	no	—
188	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
194	SD₁₆×C₆₁	—	2	8	no	—
195	SD₁₆×C₆₁	—	4	4	no	—
196	C₂×C₈×C₆₁	—	2	1	no	—
197	C₂×C₈×C₆₁	—	2	1	no	—
198	C₂×C₈×C₆₁	—	2	1	no	—
199	C₂×C₈×C₆₁	—	2	1	no	—
200	C₂×C₈×C₆₁	—	2	1	no	—
201	C₂×C₈×C₆₁	—	2	1	no	—
202	C₂×C₈×C₆₁	—	2	1	no	—
203	C₂×C₈×C₆₁	—	2	1	no	—
204	C₂×C₈×C₆₁	—	2	1	no	—
205	C₂×C₈×C₆₁	—	2	1	no	—
206	C₂×C₈×C₆₁	—	2	1	no	—
207	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
208	C₄⋊C₄×C₆₁	—	2	1	no	—
209	C₄⋊C₄×C₆₁	—	2	1	no	—
210	C₄⋊C₄×C₆₁	—	2	1	no	—
211	C₄⋊C₄×C₆₁	—	2	1	no	—
212	C₄⋊C₄×C₆₁	—	2	1	no	—
213	C₄⋊C₄×C₆₁	—	2	1	no	—
214	C₄⋊C₄×C₆₁	—	2	1	no	—
215	C₄⋊C₄×C₆₁	—	2	1	no	—
216	C₄⋊C₄×C₆₁	—	2	1	no	—
217	C₄⋊C₄×C₆₁	—	2	1	no	—
218	C₄⋊C₄×C₆₁	—	4	2	no	—
219	C₄⋊C₄×C₆₁	—	4	2	no	—
220	C₄⋊C₄×C₆₁	—	4	2	no	—
221	C₄⋊C₄×C₆₁	—	4	2	no	—
222	C₄⋊C₄×C₆₁	—	8	1	no	—
223	C₂²⋊C₄×C₆₁	—	4	1	no	—
224	C₂²⋊C₄×C₆₁	—	4	2	no	—
225	C₂²⋊C₄×C₆₁	—	4	2	no	—
226	C₂²⋊C₄×C₆₁	—	4	2	no	—
227	C₂²⋊C₄×C₆₁	—	4	2	no	—
228	C₂²⋊C₄×C₆₁	—	4	2	no	—
229	C₂²⋊C₄×C₆₁	—	4	2	no	—
230	C₂²⋊C₄×C₆₁	SD₁₆	1	4	yes	complemented
231	C₄²×C₆₁	—	2	1	no	—
232	C₄²×C₆₁	—	2	1	no	—
233	C₄²×C₆₁	—	2	1	no	—
234	C₄²×C₆₁	—	2	1	no	—
235	C₄²×C₆₁	—	4	2	no	—
236	C₄²×C₆₁	—	4	2	no	—
237	C₂³×C₆₁	—	2	1	no	—
238	C₂³×C₆₁	—	2	1	no	—
239	C₂³×C₆₁	—	2	1	no	—
240	C₂³×C₆₁	—	2	1	no	—
241	C₂³×C₆₁	—	2	1	no	—
242	C₂³×C₆₁	—	2	1	no	—
243	C₂³×C₆₁	—	2	2	no	—
244	C₂³×C₆₁	—	4	1	no	—
245	C₂³×C₆₁	—	4	1	no	—
246	C₂³×C₆₁	—	4	1	no	—
247	C₂³×C₆₁	—	4	1	no	—
248	C₂³×C₆₁	—	4	1	no	—
249	C₂³×C₆₁	—	4	1	no	—
250	C₂³×C₆₁	C₂×SD₁₆	1	2	yes	—
251	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
252	Q₈×C₆₁	—	2	2	no	—
253	Q₈×C₆₁	—	2	2	no	—
254	Q₈×C₆₁	—	2	2	no	—
255	Q₈×C₆₁	—	2	2	no	—
256	Q₈×C₆₁	—	2	2	no	—
257	Q₈×C₆₁	—	4	8	no	—
258	Q₈×C₆₁	—	4	1	no	—
259	Q₈×C₆₁	—	4	1	no	—
260	Q₈×C₆₁	#123	1	4	yes	complemented
261	D₄×C₆₁	—	2	2	no	—
262	D₄×C₆₁	—	2	2	no	—
263	D₄×C₆₁	—	4	1	no	—
264	D₄×C₆₁	—	4	1	no	—
265	D₄×C₆₁	—	8	4	no	—
266	C₂×C₄×C₆₁	—	2	2	no	—
267	C₂×C₄×C₆₁	—	2	1	no	—
268	C₂×C₄×C₆₁	—	2	2	no	—
269	C₂×C₄×C₆₁	—	2	1	no	—
270	C₂×C₄×C₆₁	—	2	2	no	—
271	C₂×C₄×C₆₁	—	2	1	no	—
272	C₂×C₄×C₆₁	—	2	1	no	—
273	C₂×C₄×C₆₁	—	2	2	no	—
274	C₂×C₄×C₆₁	—	2	1	no	—
275	C₂×C₄×C₆₁	—	2	1	no	—
276	C₂×C₄×C₆₁	—	2	1	no	—
277	C₂×C₄×C₆₁	—	2	1	no	—
278	C₂×C₄×C₆₁	—	2	1	no	—
279	C₂×C₄×C₆₁	—	2	1	no	—
280	C₂×C₄×C₆₁	—	2	1	no	—
281	C₂×C₄×C₆₁	—	2	1	no	—
282	C₂×C₄×C₆₁	—	2	1	no	—
283	C₂×C₄×C₆₁	—	4	8	no	—
284	C₂×C₄×C₆₁	—	4	1	no	—
285	C₂×C₄×C₆₁	—	4	1	no	—
286	C₂×C₄×C₆₁	—	4	1	no	—
287	C₂×C₄×C₆₁	—	4	1	no	—
288	C₂×C₄×C₆₁	—	4	1	no	—
289	C₂×C₄×C₆₁	—	4	1	no	—
290	C₂×C₄×C₆₁	—	4	1	no	—
291	C₂×C₄×C₆₁	—	4	1	no	—
292	C₂×C₄×C₆₁	—	4	1	no	—
293	C₂×C₄×C₆₁	—	4	1	no	—
294	C₂×C₄×C₆₁	—	4	1	no	—
295	C₂×C₄×C₆₁	—	4	1	no	—
296	C₂×C₄×C₆₁	—	4	1	no	—
297	C₂×C₄×C₆₁	—	4	1	no	—
298	C₂×C₄×C₆₁	—	4	1	no	—
299	C₂×C₄×C₆₁	—	4	1	no	—
300	C₂×C₄×C₆₁	—	4	1	no	—
301	C₂×C₄×C₆₁	—	4	1	no	—
302	C₂×C₄×C₆₁	—	4	1	no	—
303	C₂×C₄×C₆₁	—	4	1	no	—
304	C₂×C₄×C₆₁	—	4	1	no	—
305	C₂×C₄×C₆₁	—	8	4	no	—
306	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
307	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
308	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
310	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
311	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
312	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
314	C₈×C₆₁	—	2	2	no	—
315	C₈×C₆₁	—	4	1	no	—
316	C₈×C₆₁	—	4	1	no	—
317	C₈×C₆₁	—	4	1	no	—
318	#24898	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₂²×C₆₁	—	2	2	no	—
320	C₂²×C₆₁	—	2	2	no	—
321	C₂²×C₆₁	—	2	2	no	—
322	C₂²×C₆₁	—	4	1	no	—
323	C₂²×C₆₁	—	4	1	no	—
324	C₂²×C₆₁	—	4	1	no	—
325	C₂²×C₆₁	—	4	1	no	—
326	C₂²×C₆₁	—	4	2	no	—
327	C₂²×C₆₁	—	4	2	no	—
328	C₂²×C₆₁	—	4	2	no	—
329	C₂²×C₆₁	—	8	1	no	—
330	C₂²×C₆₁	—	8	1	no	—
331	C₂²×C₆₁	—	8	1	no	—
332	C₂²×C₆₁	—	8	1	no	—
333	C₂²×C₆₁	#525	1	1	yes	characteristic
334	C₂²×C₆₁	D₄²	1	1	yes	characteristic
335	C₂²×C₆₁	#546	1	1	yes	characteristic
336	C₂²×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
337	C₂²×C₆₁	#575	1	1	yes	characteristic
338	C₂²×C₆₁	#577	1	1	yes	characteristic
339	C₂²×C₆₁	#578	1	1	yes	characteristic
340	C₄×C₆₁	—	2	4	no	—
341	C₄×C₆₁	—	2	2	no	—
342	C₄×C₆₁	—	2	2	no	—
343	C₄×C₆₁	—	4	1	no	—
344	C₄×C₆₁	—	4	2	no	—
345	C₄×C₆₁	—	4	1	no	—
346	C₄×C₆₁	—	4	1	no	—
347	C₄×C₆₁	—	8	1	no	—
348	C₄×C₆₁	—	8	1	no	—
349	C₄×C₆₁	—	8	1	no	—
350	C₄×C₆₁	—	8	1	no	—
351	C₄×C₆₁	—	8	1	no	—
352	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
353	C₄×C₆₁	#538	1	1	yes	characteristic
354	C₄×C₆₁	#546	1	1	yes	characteristic
355	C₄×C₆₁	#551	1	1	yes	characteristic
356	C₂×#448	C₂×C₆₁	1	1	yes	characteristic
357	C₂×C₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
358	#2422	C₂×C₆₁	1	1	yes	characteristic
359	Q₈×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
360	#2096	C₂×C₆₁	1	1	yes	characteristic, complemented
361	#2077	C₂×C₆₁	1	1	yes	characteristic, complemented
362	#2055	C₂×C₆₁	1	1	yes	characteristic, complemented
363	#2034	C₂×C₆₁	1	1	yes	characteristic
364	#1933	C₂×C₆₁	1	1	yes	characteristic, complemented
365	#1923	C₂×C₆₁	1	1	yes	characteristic, complemented
366	#1880	C₂×C₆₁	1	1	yes	characteristic, complemented
367	#1877	C₂×C₆₁	1	1	yes	characteristic, complemented
368	#1865	C₂×C₆₁	1	1	yes	characteristic, complemented
369	#1803	C₂×C₆₁	1	1	yes	characteristic, complemented
370	#1787	C₂×C₆₁	1	1	yes	characteristic, complemented
371	C₂×C₆₁	—	4	2	no	—
372	C₂×C₆₁	—	8	2	no	—
373	C₂×C₆₁	#2418	1	1	yes	characteristic
374	C₂×C₆₁	#3103	1	1	yes	characteristic
375	C₂×C₆₁	#3121	1	1	yes	characteristic
376	C₂×C₆₁	#3269	1	1	yes	characteristic
377	C₂×C₆₁	D₄×SD₁₆	1	1	yes	characteristic
378	C₂×C₆₁	#3298	1	1	yes	characteristic
379	C₂×C₆₁	#3326	1	1	yes	characteristic
380	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
381	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
382	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
383	C₂×#123	—	2	1	no	—
384	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
385	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
386	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
387	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
388	#448	—	2	4	no	—
389	C₄×SD₁₆	—	2	4	no	—
390	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
391	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
392	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
393	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
394	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
395	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
396	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
397	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
398	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
399	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
400	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
401	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
402	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
403	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
404	#397	—	2	1	no	—
405	#394	—	2	1	no	—
406	#391	—	2	1	no	—
407	#391	—	2	1	no	—
408	#391	C₂²×C₆₁	1	1	yes	characteristic
409	#391	C₂²×C₆₁	1	1	yes	characteristic
410	#390	C₂²×C₆₁	1	1	yes	characteristic
411	#389	C₂²×C₆₁	1	1	yes	characteristic
412	#385	—	2	1	no	—
413	#384	C₂²×C₆₁	1	1	yes	characteristic
414	#380	—	2	1	no	—
415	#380	C₂²×C₆₁	1	1	yes	characteristic
416	#380	C₂²×C₆₁	1	1	yes	characteristic
417	C₄×C₂²⋊C₄	—	2	1	no	—
418	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
419	#340	C₂²×C₆₁	1	1	yes	characteristic
420	#340	C₂²×C₆₁	1	1	yes	characteristic
421	#340	C₂²×C₆₁	1	1	yes	characteristic
422	#340	C₂²×C₆₁	1	1	yes	characteristic
423	#336	C₂²×C₆₁	1	1	yes	characteristic
424	#336	C₂²×C₆₁	1	1	yes	characteristic
425	C₆₁	#24898	1	1	yes	characteristic, direct product factor, Sylow
426	C₂²×Q₈	—	2	2	no	—
427	C₂²×Q₈	—	2	2	no	—
428	C₂²×Q₈	—	2	1	no	—
429	C₂²×Q₈	—	2	2	no	—
430	C₂²×Q₈	—	2	2	no	—
431	C₂²×Q₈	—	4	1	no	—
432	C₂²×Q₈	—	4	1	no	—
433	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
434	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
435	C₂²×D₄	—	2	1	no	—
436	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
437	C₂³×C₄	—	2	1	no	—
438	C₂³×C₄	—	2	1	no	—
439	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
440	C₂×SD₁₆	—	2	2	no	—
441	C₂×SD₁₆	—	2	2	no	—
442	C₂×SD₁₆	—	2	2	no	—
443	C₂×SD₁₆	—	2	2	no	—
444	C₂×SD₁₆	—	4	1	no	—
445	C₂×SD₁₆	D₄×C₆₁	1	4	yes	—
446	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
450	#123	—	4	4	no	—
451	#121	—	2	2	no	—
452	#121	—	4	1	no	—
453	C₄×Q₈	—	2	2	no	—
454	C₄×Q₈	—	2	2	no	—
455	C₄×Q₈	—	4	1	no	—
456	C₄×Q₈	—	4	1	no	—
457	C₄×D₄	—	2	2	no	—
458	C₄×D₄	—	4	1	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄⋊C₄	—	2	1	no	—
462	C₂×C₄⋊C₄	—	2	1	no	—
463	C₂×C₄⋊C₄	—	2	1	no	—
464	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	—	2	1	no	—
472	C₂×C₂²⋊C₄	—	2	1	no	—
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
476	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
477	C₂×C₄²	—	2	1	no	—
478	C₂×C₄²	—	2	1	no	—
479	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
481	#106	—	2	2	no	—
482	#106	—	4	1	no	—
483	C₄⋊C₈	—	4	1	no	—
484	#103	—	2	2	no	—
485	#103	—	2	2	no	—
486	#103	—	2	2	no	—
487	#103	—	2	2	no	—
488	#103	—	2	2	no	—
489	#103	—	4	1	no	—
490	#102	—	2	2	no	—
491	#102	—	4	1	no	—
492	C₂²⋊C₈	—	2	2	no	—
493	C₂²⋊C₈	—	4	1	no	—
494	C₄×C₈	—	2	2	no	—
495	#95	—	2	1	no	—
496	#95	—	2	1	no	—
497	#95	—	2	1	no	—
498	#95	—	2	1	no	—
499	#95	—	2	1	no	—
500	#95	—	2	1	no	—
501	#95	—	2	1	no	—
502	#95	D₄×C₆₁	1	1	yes	characteristic
503	#95	D₄×C₆₁	1	1	yes	characteristic
504	C₂⁴	—	2	1	no	—
505	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
506	C₂×Q₈	—	2	4	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	4	2	no	—
516	C₂×Q₈	—	4	2	no	—
517	C₂×Q₈	—	4	4	no	—
518	C₂×Q₈	—	4	4	no	—
519	C₂×Q₈	—	4	4	no	—
520	C₂×Q₈	—	4	4	no	—
521	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
522	C₂×Q₈	#41×C₆₁	1	2	yes	—
523	C₂×Q₈	#41×C₆₁	1	2	yes	—
524	C₂×Q₈	#41×C₆₁	1	2	yes	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	4	2	no	—
531	C₂×D₄	—	4	2	no	—
532	C₂×D₄	—	8	1	no	—
533	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	4	2	no	—
549	C₂²×C₄	—	4	2	no	—
550	C₂²×C₄	—	4	2	no	—
551	C₂²×C₄	—	4	2	no	—
552	C₂²×C₄	—	8	1	no	—
553	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
556	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
557	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
559	SD₁₆	—	2	8	no	—
560	SD₁₆	—	4	4	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	4	2	no	—
584	C₄⋊C₄	—	4	2	no	—
585	C₄⋊C₄	—	4	2	no	—
586	C₄⋊C₄	—	4	2	no	—
587	C₄⋊C₄	—	8	1	no	—
588	C₂²⋊C₄	—	4	1	no	—
589	C₂²⋊C₄	—	4	2	no	—
590	C₂²⋊C₄	—	4	2	no	—
591	C₂²⋊C₄	—	4	2	no	—
592	C₂²⋊C₄	—	4	2	no	—
593	C₂²⋊C₄	—	4	2	no	—
594	C₂²⋊C₄	—	4	2	no	—
595	C₂²⋊C₄	SD₁₆×C₆₁	1	4	yes	complemented
596	C₄²	—	2	1	no	—
597	C₄²	—	2	1	no	—
598	C₄²	—	2	1	no	—
599	C₄²	—	2	1	no	—
600	C₄²	—	4	2	no	—
601	C₄²	—	4	2	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	C₂×SD₁₆×C₆₁	1	2	yes	—
616	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
617	Q₈	—	2	2	no	—
618	Q₈	—	2	2	no	—
619	Q₈	—	2	2	no	—
620	Q₈	—	2	2	no	—
621	Q₈	—	2	2	no	—
622	Q₈	—	4	8	no	—
623	Q₈	—	4	1	no	—
624	Q₈	—	4	1	no	—
625	Q₈	#123×C₆₁	1	4	yes	complemented
626	D₄	—	2	2	no	—
627	D₄	—	2	2	no	—
628	D₄	—	4	1	no	—
629	D₄	—	4	1	no	—
630	D₄	—	8	4	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	4	8	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	8	4	no	—
671	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
672	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
673	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
674	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
675	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
676	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
677	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
678	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
679	C₈	—	2	2	no	—
680	C₈	—	4	1	no	—
681	C₈	—	4	1	no	—
682	C₈	—	4	1	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	8	1	no	—
694	C₂²	—	8	1	no	—
695	C₂²	—	8	1	no	—
696	C₂²	—	8	1	no	—
697	C₂²	C₆₁×#525	1	1	yes	characteristic
698	C₂²	D₄²×C₆₁	1	1	yes	characteristic
699	C₂²	C₆₁×#546	1	1	yes	characteristic
700	C₂²	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
701	C₂²	C₆₁×#575	1	1	yes	characteristic
702	C₂²	C₆₁×#577	1	1	yes	characteristic
703	C₂²	C₆₁×#578	1	1	yes	characteristic
704	C₄	—	2	2	no	—
705	C₄	—	2	4	no	—
706	C₄	—	2	2	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	1	no	—
711	C₄	—	8	1	no	—
712	C₄	—	8	1	no	—
713	C₄	—	8	1	no	—
714	C₄	—	8	1	no	—
715	C₄	—	8	1	no	—
716	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
717	C₄	C₆₁×#538	1	1	yes	characteristic
718	C₄	C₆₁×#546	1	1	yes	characteristic
719	C₄	C₆₁×#551	1	1	yes	characteristic
720	C₂	—	4	2	no	—
721	C₂	—	8	2	no	—
722	C₂	C₆₁×#2418	1	1	yes	characteristic
723	C₂	C₆₁×#3103	1	1	yes	characteristic
724	C₂	C₆₁×#3121	1	1	yes	characteristic
725	C₂	C₆₁×#3269	1	1	yes	characteristic
726	C₂	D₄×SD₁₆×C₆₁	1	1	yes	characteristic
727	C₂	C₆₁×#3298	1	1	yes	characteristic
728	C₂	C₆₁×#3326	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#121×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₄×C₂²⋊C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×SD₁₆×C₆₁	C₂	semidirect
4. Q₈×C₂²⋊C₄×C₆₁	C₂	semidirect
5. C₆₁×#2096	C₂	semidirect
6. C₆₁×#2077	C₂	semidirect
7. C₆₁×#2055	C₂	semidirect
9. C₆₁×#1933	C₂	semidirect
10. C₆₁×#1923	C₂	semidirect
11. C₆₁×#1880	C₂	semidirect
12. C₆₁×#1877	C₂	semidirect
13. C₆₁×#1865	C₂	semidirect
14. C₆₁×#1803	C₂	semidirect
15. C₆₁×#1787	C₂	semidirect
230. C₂²⋊C₄×C₆₁	SD₁₆	semidirect
260. Q₈×C₆₁	#123	semidirect
318. #24898	C₆₁	direct (N × H)
357. C₂×C₄×SD₁₆	C₂×C₆₁	semidirect
359. Q₈×C₂²⋊C₄	C₂×C₆₁	semidirect
360. #2096	C₂×C₆₁	semidirect
361. #2077	C₂×C₆₁	semidirect
362. #2055	C₂×C₆₁	semidirect
364. #1933	C₂×C₆₁	semidirect
365. #1923	C₂×C₆₁	semidirect
366. #1880	C₂×C₆₁	semidirect
367. #1877	C₂×C₆₁	semidirect
368. #1865	C₂×C₆₁	semidirect
369. #1803	C₂×C₆₁	semidirect
370. #1787	C₂×C₆₁	semidirect
425. C₆₁	#24898	direct (N × H)
595. C₂²⋊C₄	SD₁₆×C₆₁	semidirect
625. Q₈	#123×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#448	2
C₂×C₄×SD₁₆×C₆₁	2
C₆₁×#2422	2
Q₈×C₂²⋊C₄×C₆₁	2
C₆₁×#2096	2
C₆₁×#2077	2
C₆₁×#2055	2
C₆₁×#2034	2
C₆₁×#1933	2
C₆₁×#1923	2
C₆₁×#1880	2
C₆₁×#1877	2
C₆₁×#1865	2
C₆₁×#1803	2
C₆₁×#1787	2
#24898	61

Subgroups — C61×#24898 #29528331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24898 #29528331