Subgroups — C₆₁×#29911 #29533344

Order 15616.

706 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2855	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2285	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2101	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2097	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2084	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2083	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2072	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2072	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1873	C₂	1	2	yes	maximal
10	C₆₁×#1854	C₂	1	2	yes	maximal
11	C₆₁×#1817	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#117×C₆₁	C₂²	1	2	yes	—
14	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#107×C₆₁	C₂²	1	2	yes	—
16	C₂×#106×C₆₁	C₂²	1	2	yes	—
17	C₂×#103×C₆₁	C₂²	1	2	yes	—
18	C₂×#103×C₆₁	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
20	C₆₁×#391	C₂²	1	1	yes	characteristic
21	C₆₁×#391	C₂²	1	1	yes	characteristic
22	C₆₁×#389	C₂²	1	1	yes	characteristic
23	C₆₁×#389	C₂²	1	1	yes	characteristic
24	C₆₁×#387	—	2	1	no	—
25	C₆₁×#387	—	2	1	no	—
26	C₆₁×#385	—	2	1	no	—
27	C₆₁×#384	C₂²	1	1	yes	characteristic
28	C₆₁×#384	C₂²	1	1	yes	characteristic
29	C₆₁×#382	C₂²	1	2	yes	—
30	C₆₁×#381	—	2	1	no	—
31	C₆₁×#380	—	2	1	no	—
32	C₆₁×#380	—	2	1	no	—
33	C₆₁×#380	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
35	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
36	C₆₁×#340	C₂²	1	2	yes	—
37	C₆₁×#340	C₂²	1	2	yes	—
38	C₆₁×#340	C₂²	1	2	yes	—
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#336	C₂²	1	1	yes	characteristic
41	C₆₁×#336	C₂²	1	1	yes	characteristic
42	C₆₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
49	C₂²⋊Q₈×C₆₁	—	2	4	no	—
50	#117×C₆₁	—	4	2	no	—
51	#117×C₆₁	—	4	2	no	—
52	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
67	C₂×C₄²×C₆₁	—	2	4	no	—
68	C₂×C₄²×C₆₁	—	2	2	no	—
69	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
73	#107×C₆₁	—	4	2	no	—
74	#106×C₆₁	—	4	2	no	—
75	#103×C₆₁	—	4	2	no	—
76	#103×C₆₁	—	4	2	no	—
77	C₂²⋊C₈×C₆₁	—	2	4	no	—
78	#95×C₆₁	—	2	2	no	—
79	#95×C₆₁	—	2	2	no	—
80	#95×C₆₁	—	2	1	no	—
81	#95×C₆₁	—	2	1	no	—
82	#95×C₆₁	—	2	1	no	—
83	#95×C₆₁	—	2	1	no	—
84	#95×C₆₁	—	2	1	no	—
85	#95×C₆₁	—	2	1	no	—
86	#95×C₆₁	—	2	1	no	—
87	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
88	C₂×Q₈×C₆₁	—	2	2	no	—
89	C₂×Q₈×C₆₁	—	2	1	no	—
90	C₂×Q₈×C₆₁	—	2	1	no	—
91	C₂×Q₈×C₆₁	—	2	2	no	—
92	C₂²×C₄×C₆₁	—	2	1	no	—
93	C₂²×C₄×C₆₁	—	2	1	no	—
94	C₂²×C₄×C₆₁	—	2	2	no	—
95	C₂²×C₄×C₆₁	—	2	2	no	—
96	C₂²×C₄×C₆₁	—	2	2	no	—
97	C₂²×C₄×C₆₁	—	2	2	no	—
98	C₂²×C₄×C₆₁	—	2	2	no	—
99	C₂²×C₄×C₆₁	—	2	1	no	—
100	C₂²×C₄×C₆₁	—	2	1	no	—
101	C₂²×C₄×C₆₁	—	2	1	no	—
102	C₂²×C₄×C₆₁	—	2	2	no	—
103	C₂²×C₄×C₆₁	—	2	2	no	—
104	C₂²×C₄×C₆₁	—	2	1	no	—
105	C₂²×C₄×C₆₁	—	4	1	no	—
106	C₂²×C₄×C₆₁	—	4	1	no	—
107	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₁	#41	1	4	yes	—
113	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₆₁	—	2	2	no	—
115	C₂×C₈×C₆₁	—	2	2	no	—
116	C₂×C₈×C₆₁	—	2	2	no	—
117	C₂×C₈×C₆₁	—	2	2	no	—
118	C₂×C₈×C₆₁	—	2	2	no	—
119	C₂×C₈×C₆₁	—	2	2	no	—
120	C₄⋊C₄×C₆₁	—	2	2	no	—
121	C₄⋊C₄×C₆₁	—	2	2	no	—
122	C₄⋊C₄×C₆₁	—	2	2	no	—
123	C₄⋊C₄×C₆₁	—	2	1	no	—
124	C₄⋊C₄×C₆₁	—	2	2	no	—
125	C₄⋊C₄×C₆₁	—	2	1	no	—
126	C₄⋊C₄×C₆₁	—	2	2	no	—
127	C₄⋊C₄×C₆₁	—	2	2	no	—
128	C₄⋊C₄×C₆₁	—	4	2	no	—
129	C₄⋊C₄×C₆₁	—	4	2	no	—
130	C₄⋊C₄×C₆₁	—	4	2	no	—
131	C₄⋊C₄×C₆₁	—	4	2	no	—
132	C₄⋊C₄×C₆₁	—	4	2	no	—
133	C₄⋊C₄×C₆₁	—	4	2	no	—
134	C₄⋊C₄×C₆₁	—	4	2	no	—
135	C₂²⋊C₄×C₆₁	—	4	2	no	—
136	C₂²⋊C₄×C₆₁	—	4	4	no	—
137	C₂²⋊C₄×C₆₁	—	4	2	no	—
138	C₄²×C₆₁	—	2	2	no	—
139	C₄²×C₆₁	—	2	2	no	—
140	C₄²×C₆₁	—	2	2	no	—
141	C₄²×C₆₁	—	2	2	no	—
142	C₄²×C₆₁	—	4	4	no	—
143	C₂³×C₆₁	—	2	1	no	—
144	C₂³×C₆₁	—	2	1	no	—
145	C₂³×C₆₁	—	2	1	no	—
146	C₂³×C₆₁	—	2	1	no	—
147	C₂³×C₆₁	—	2	1	no	—
148	C₂³×C₆₁	—	2	1	no	—
149	C₂³×C₆₁	#123	1	2	yes	—
150	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₆₁	—	4	2	no	—
152	Q₈×C₆₁	—	4	2	no	—
153	C₂×C₄×C₆₁	—	2	1	no	—
154	C₂×C₄×C₆₁	—	2	1	no	—
155	C₂×C₄×C₆₁	—	2	1	no	—
156	C₂×C₄×C₆₁	—	2	1	no	—
157	C₂×C₄×C₆₁	—	2	1	no	—
158	C₂×C₄×C₆₁	—	2	1	no	—
159	C₂×C₄×C₆₁	—	2	4	no	—
160	C₂×C₄×C₆₁	—	2	4	no	—
161	C₂×C₄×C₆₁	—	2	1	no	—
162	C₂×C₄×C₆₁	—	2	1	no	—
163	C₂×C₄×C₆₁	—	2	1	no	—
164	C₂×C₄×C₆₁	—	2	1	no	—
165	C₂×C₄×C₆₁	—	2	1	no	—
166	C₂×C₄×C₆₁	—	2	1	no	—
167	C₂×C₄×C₆₁	—	4	4	no	—
168	C₂×C₄×C₆₁	—	4	4	no	—
169	C₂×C₄×C₆₁	—	4	1	no	—
170	C₂×C₄×C₆₁	—	4	1	no	—
171	C₂×C₄×C₆₁	—	4	2	no	—
172	C₂×C₄×C₆₁	—	4	2	no	—
173	C₂×C₄×C₆₁	—	4	1	no	—
174	C₂×C₄×C₆₁	—	4	1	no	—
175	C₂×C₄×C₆₁	—	4	1	no	—
176	C₂×C₄×C₆₁	—	4	1	no	—
177	C₂×C₄×C₆₁	—	4	1	no	—
178	C₂×C₄×C₆₁	—	4	1	no	—
179	C₂×C₄×C₆₁	—	4	2	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	4	1	no	—
182	C₂×C₄×C₆₁	—	4	1	no	—
183	C₂×C₄×C₆₁	—	4	1	no	—
184	C₂×C₄×C₆₁	—	4	2	no	—
185	C₂×C₄×C₆₁	—	4	2	no	—
186	C₂×C₄×C₆₁	—	4	1	no	—
187	C₂×C₄×C₆₁	#123	1	2	yes	—
188	C₂×C₄×C₆₁	#135	1	2	yes	—
189	C₂×C₄×C₆₁	#137	1	2	yes	—
190	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
191	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
194	C₈×C₆₁	—	4	2	no	—
195	C₈×C₆₁	—	4	2	no	—
196	#29911	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂²×C₆₁	—	2	2	no	—
198	C₂²×C₆₁	—	2	2	no	—
199	C₂²×C₆₁	—	2	2	no	—
200	C₂²×C₆₁	—	4	1	no	—
201	C₂²×C₆₁	—	4	1	no	—
202	C₂²×C₆₁	—	4	1	no	—
203	C₂²×C₆₁	—	4	1	no	—
204	C₂²×C₆₁	C₂×#123	1	1	yes	characteristic
205	C₂²×C₆₁	#535	1	1	yes	characteristic
206	C₂²×C₆₁	#536	1	1	yes	characteristic
207	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
208	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
209	C₂²×C₆₁	#575	1	1	yes	characteristic
210	C₂²×C₆₁	#575	1	1	yes	characteristic
211	C₄×C₆₁	—	2	2	no	—
212	C₄×C₆₁	—	2	2	no	—
213	C₄×C₆₁	—	2	2	no	—
214	C₄×C₆₁	—	4	1	no	—
215	C₄×C₆₁	—	4	1	no	—
216	C₄×C₆₁	—	8	1	no	—
217	C₄×C₆₁	—	8	1	no	—
218	C₄×C₆₁	—	8	2	no	—
219	C₄×C₆₁	—	8	1	no	—
220	C₄×C₆₁	—	8	2	no	—
221	C₄×C₆₁	—	8	1	no	—
222	C₄×C₆₁	#539	1	2	yes	—
223	C₄×C₆₁	#539	1	2	yes	—
224	#2855	C₂×C₆₁	1	1	yes	characteristic
225	#2285	C₂×C₆₁	1	1	yes	characteristic
226	#2101	C₂×C₆₁	1	2	yes	complemented
227	#2097	C₂×C₆₁	1	2	yes	complemented
228	#2084	C₂×C₆₁	1	1	yes	characteristic, complemented
229	#2083	C₂×C₆₁	1	1	yes	characteristic, complemented
230	#2072	C₂×C₆₁	1	1	yes	characteristic, complemented
231	#2072	C₂×C₆₁	1	1	yes	characteristic, complemented
232	#1873	C₂×C₆₁	1	2	yes	—
233	#1854	C₂×C₆₁	1	2	yes	—
234	#1817	C₂×C₆₁	1	1	yes	characteristic
235	C₂×C₆₁	—	4	2	no	—
236	C₂×C₆₁	#2623	1	1	yes	characteristic
237	C₂×C₆₁	#3091	1	1	yes	characteristic
238	C₂×C₆₁	#3095	1	1	yes	characteristic
239	C₂×C₆₁	#3212	1	1	yes	characteristic
240	C₂×C₆₁	#3216	1	1	yes	characteristic
241	C₂×C₆₁	#3231	1	1	yes	characteristic
242	C₂×C₆₁	#3240	1	1	yes	characteristic
243	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
244	C₂×#117	C₂²×C₆₁	1	2	yes	—
245	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
246	C₂×#107	C₂²×C₆₁	1	2	yes	—
247	C₂×#106	C₂²×C₆₁	1	2	yes	—
248	C₂×#103	C₂²×C₆₁	1	2	yes	—
249	C₂×#103	C₂²×C₆₁	1	2	yes	—
250	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
251	#391	C₂²×C₆₁	1	1	yes	characteristic
252	#391	C₂²×C₆₁	1	1	yes	characteristic
253	#389	C₂²×C₆₁	1	1	yes	characteristic
254	#389	C₂²×C₆₁	1	1	yes	characteristic
255	#387	—	2	1	no	—
256	#387	—	2	1	no	—
257	#385	—	2	1	no	—
258	#384	C₂²×C₆₁	1	1	yes	characteristic
259	#384	C₂²×C₆₁	1	1	yes	characteristic
260	#382	C₂²×C₆₁	1	2	yes	—
261	#381	—	2	1	no	—
262	#380	—	2	1	no	—
263	#380	—	2	1	no	—
264	#380	C₂²×C₆₁	1	1	yes	characteristic
265	C₄×C₄⋊C₄	—	2	1	no	—
266	C₄×C₄⋊C₄	—	2	1	no	—
267	#340	C₂²×C₆₁	1	2	yes	—
268	#340	C₂²×C₆₁	1	2	yes	—
269	#340	C₂²×C₆₁	1	2	yes	—
270	#340	C₂²×C₆₁	1	2	yes	—
271	#336	C₂²×C₆₁	1	1	yes	characteristic
272	#336	C₂²×C₆₁	1	1	yes	characteristic
273	#336	C₂²×C₆₁	1	2	yes	—
274	C₆₁	#29911	1	1	yes	characteristic, direct product factor, Sylow
275	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
276	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
277	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
280	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
281	C₂²⋊Q₈	—	2	4	no	—
282	#117	—	4	2	no	—
283	#117	—	4	2	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₄²	—	2	4	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
302	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
305	#107	—	4	2	no	—
306	#106	—	4	2	no	—
307	#103	—	4	2	no	—
308	#103	—	4	2	no	—
309	C₂²⋊C₈	—	2	4	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	1	no	—
313	#95	—	2	1	no	—
314	#95	—	2	1	no	—
315	#95	—	2	1	no	—
316	#95	—	2	1	no	—
317	#95	—	2	1	no	—
318	#95	—	2	1	no	—
319	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
344	C₂²×C₄	#41×C₆₁	1	4	yes	—
345	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	4	4	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₂²⋊C₄	—	4	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	4	4	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	#123×C₆₁	1	2	yes	—
382	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
383	Q₈	—	4	2	no	—
384	Q₈	—	4	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	#123×C₆₁	1	2	yes	—
420	C₂×C₄	#135×C₆₁	1	2	yes	—
421	C₂×C₄	#137×C₆₁	1	2	yes	—
422	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
423	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
424	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
425	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
426	C₈	—	4	2	no	—
427	C₈	—	4	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	C₂×#123×C₆₁	1	1	yes	characteristic
436	C₂²	C₆₁×#535	1	1	yes	characteristic
437	C₂²	C₆₁×#536	1	1	yes	characteristic
438	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
439	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
440	C₂²	C₆₁×#575	1	1	yes	characteristic
441	C₂²	C₆₁×#575	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	1	no	—
447	C₄	—	8	1	no	—
448	C₄	—	8	1	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	1	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	1	no	—
453	C₄	C₆₁×#539	1	2	yes	—
454	C₄	C₆₁×#539	1	2	yes	—
455	C₂	—	4	2	no	—
456	C₂	C₆₁×#2623	1	1	yes	characteristic
457	C₂	C₆₁×#3091	1	1	yes	characteristic
458	C₂	C₆₁×#3095	1	1	yes	characteristic
459	C₂	C₆₁×#3212	1	1	yes	characteristic
460	C₂	C₆₁×#3216	1	1	yes	characteristic
461	C₂	C₆₁×#3231	1	1	yes	characteristic
462	C₂	C₆₁×#3240	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂⁴×C₆₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₆₁×#2101	C₂	semidirect
4. C₆₁×#2097	C₂	semidirect
5. C₆₁×#2084	C₂	semidirect
6. C₆₁×#2083	C₂	semidirect
7. C₆₁×#2072	C₂	semidirect
8. C₆₁×#2072	C₂	semidirect
196. #29911	C₆₁	direct (N × H)
226. #2101	C₂×C₆₁	semidirect
227. #2097	C₂×C₆₁	semidirect
228. #2084	C₂×C₆₁	semidirect
229. #2083	C₂×C₆₁	semidirect
230. #2072	C₂×C₆₁	semidirect
231. #2072	C₂×C₆₁	semidirect
274. C₆₁	#29911	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×#2855	2
C₆₁×#2285	2
C₆₁×#2101	2
C₆₁×#2097	2
C₆₁×#2084	2
C₆₁×#2083	2
C₆₁×#2072	2
C₆₁×#1873	2
C₆₁×#1854	2
C₆₁×#1817	2
#29911	61

Subgroups — C61×#29911 #29533344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#29911 #29533344