Subgroups — C₆₁×#21549 #29524982

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3054	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#443	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2930	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1975	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1946	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1937	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1896	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1811	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1772	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1765	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#131×C₆₁	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
16	C₆₁×#525	C₂²	1	2	yes	—
17	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#470	C₄	1	2	yes	complemented
19	C₆₁×#469	C₄	1	2	yes	complemented
20	C₆₁×#468	C₄	1	4	yes	complemented
21	C₆₁×#443	—	2	4	no	—
22	C₆₁×#436	—	2	4	no	—
23	C₆₁×#435	—	2	4	no	—
24	C₂×#108×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#108×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#427	C₂²	1	1	yes	characteristic
27	C₆₁×#424	C₂²	1	2	yes	—
28	C₂×#104×C₆₁	C₂²	1	2	yes	—
29	C₂×#104×C₆₁	C₂²	1	2	yes	—
30	C₆₁×#416	C₂²	1	2	yes	—
31	C₆₁×#408	C₂²	1	2	yes	—
32	C₆₁×#407	C₂²	1	2	yes	—
33	C₆₁×#405	C₂²	1	2	yes	—
34	C₄×M₁₆×C₆₁	—	2	4	no	—
35	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#341	C₂²	1	2	yes	—
40	C₆₁×#339	C₂²	1	2	yes	—
41	C₆₁×#339	C₂²	1	2	yes	—
42	C₂×#41×C₆₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₆₁	—	2	1	no	—
44	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
45	#135×C₆₁	—	2	2	no	—
46	#135×C₆₁	—	2	2	no	—
47	C₂×Q₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂×SD₁₆×C₆₁	C₂×C₄	1	2	yes	complemented
49	C₂×D₈×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
50	#131×C₆₁	—	2	4	no	—
51	#131×C₆₁	—	2	4	no	—
52	C₂×M₁₆×C₆₁	—	2	2	no	—
53	C₂×M₁₆×C₆₁	—	2	2	no	—
54	C₂×M₁₆×C₆₁	—	2	2	no	—
55	C₂×M₁₆×C₆₁	—	2	2	no	—
56	C₂×M₁₆×C₆₁	—	2	2	no	—
57	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
58	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
59	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
60	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
61	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
62	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
63	C₂²×C₈×C₆₁	—	2	2	no	—
64	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
68	#123×C₆₁	—	2	2	no	—
69	C₂²⋊Q₈×C₆₁	C₂×C₄	1	4	yes	—
70	#121×C₆₁	C₂×C₄	1	4	yes	—
71	#120×C₆₁	—	2	2	no	—
72	C₄×D₄×C₆₁	—	2	4	no	—
73	#117×C₆₁	C₂³	1	2	yes	—
74	C₂×C₄²×C₆₁	—	2	1	no	—
75	C₂×C₄²×C₆₁	—	2	2	no	—
76	C₂×C₄²×C₆₁	—	2	2	no	—
77	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
79	#108×C₆₁	—	2	2	no	—
80	#108×C₆₁	—	2	2	no	—
81	#107×C₆₁	C₂×C₄	1	2	yes	complemented
82	#106×C₆₁	C₂×C₄	1	2	yes	complemented
83	C₄⋊C₈×C₆₁	—	2	4	no	—
84	#104×C₆₁	—	2	4	no	—
85	#104×C₆₁	—	2	4	no	—
86	#103×C₆₁	C₂×C₄	1	4	yes	complemented
87	#102×C₆₁	C₂×C₄	1	4	yes	complemented
88	C₂²⋊C₈×C₆₁	—	2	4	no	—
89	C₂²⋊C₈×C₆₁	—	2	4	no	—
90	#97×C₆₁	—	2	2	no	—
91	#97×C₆₁	—	2	2	no	—
92	#97×C₆₁	—	2	2	no	—
93	C₄×C₈×C₆₁	—	2	2	no	—
94	C₄×C₈×C₆₁	—	2	2	no	—
95	C₄×C₈×C₆₁	D₄	1	4	yes	complemented
96	C₂⁴×C₆₁	#41	1	1	yes	characteristic
97	#41×C₆₁	—	2	2	no	—
98	#41×C₆₁	—	2	2	no	—
99	#41×C₆₁	—	2	2	no	—
100	#41×C₆₁	—	2	2	no	—
101	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₆₁	—	2	2	no	—
103	C₂×D₄×C₆₁	—	2	4	no	—
104	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₆₁	—	2	1	no	—
106	C₂²×C₄×C₆₁	—	2	1	no	—
107	C₂²×C₄×C₆₁	—	2	1	no	—
108	C₂²×C₄×C₆₁	—	2	1	no	—
109	C₂²×C₄×C₆₁	—	2	1	no	—
110	C₂²×C₄×C₆₁	—	2	4	no	—
111	C₂²×C₄×C₆₁	—	2	1	no	—
112	C₂²×C₄×C₆₁	—	2	2	no	—
113	C₂²×C₄×C₆₁	—	4	4	no	—
114	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
117	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
118	Q₁₆×C₆₁	—	2	2	no	—
119	SD₁₆×C₆₁	—	2	4	no	—
120	D₈×C₆₁	—	2	2	no	—
121	M₁₆×C₆₁	—	2	4	no	—
122	M₁₆×C₆₁	—	2	4	no	—
123	M₁₆×C₆₁	—	2	4	no	—
124	M₁₆×C₆₁	—	2	4	no	—
125	M₁₆×C₆₁	—	2	2	no	—
126	M₁₆×C₆₁	—	2	2	no	—
127	M₁₆×C₆₁	—	2	2	no	—
128	M₁₆×C₆₁	—	2	2	no	—
129	M₁₆×C₆₁	—	4	4	no	—
130	C₂×C₈×C₆₁	—	2	1	no	—
131	C₂×C₈×C₆₁	—	2	1	no	—
132	C₂×C₈×C₆₁	—	2	1	no	—
133	C₂×C₈×C₆₁	—	2	1	no	—
134	C₂×C₈×C₆₁	—	2	2	no	—
135	C₂×C₈×C₆₁	—	2	2	no	—
136	C₂×C₈×C₆₁	—	4	4	no	—
137	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₆₁	#41	1	2	yes	—
146	C₂×C₈×C₆₁	#41	1	2	yes	—
147	C₄⋊C₄×C₆₁	—	2	4	no	—
148	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
149	C₂²⋊C₄×C₆₁	—	2	4	no	—
150	C₂²⋊C₄×C₆₁	—	2	2	no	—
151	C₂²⋊C₄×C₆₁	—	2	4	no	—
152	C₄²×C₆₁	—	2	4	no	—
153	C₄²×C₆₁	—	2	1	no	—
154	C₄²×C₆₁	—	2	2	no	—
155	C₄²×C₆₁	—	2	1	no	—
156	C₄²×C₆₁	C₂×D₄	1	2	yes	—
157	C₄²×C₆₁	#41	1	2	yes	—
158	C₂³×C₆₁	—	2	1	no	—
159	C₂³×C₆₁	—	2	1	no	—
160	C₂³×C₆₁	—	2	2	no	—
161	C₂³×C₆₁	—	4	2	no	—
162	C₂³×C₆₁	C₄×D₄	1	2	yes	—
163	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
164	Q₈×C₆₁	—	2	2	no	—
165	Q₈×C₆₁	—	2	2	no	—
166	D₄×C₆₁	—	2	2	no	—
167	D₄×C₆₁	—	2	2	no	—
168	D₄×C₆₁	—	4	2	no	—
169	D₄×C₆₁	—	4	2	no	—
170	D₄×C₆₁	—	8	4	no	—
171	C₂×C₄×C₆₁	—	2	4	no	—
172	C₂×C₄×C₆₁	—	2	1	no	—
173	C₂×C₄×C₆₁	—	2	2	no	—
174	C₂×C₄×C₆₁	—	2	1	no	—
175	C₂×C₄×C₆₁	—	2	2	no	—
176	C₂×C₄×C₆₁	—	2	2	no	—
177	C₂×C₄×C₆₁	—	2	2	no	—
178	C₂×C₄×C₆₁	—	2	2	no	—
179	C₂×C₄×C₆₁	—	2	4	no	—
180	C₂×C₄×C₆₁	—	2	2	no	—
181	C₂×C₄×C₆₁	—	2	2	no	—
182	C₂×C₄×C₆₁	—	4	8	no	—
183	C₂×C₄×C₆₁	—	4	2	no	—
184	C₂×C₄×C₆₁	—	4	2	no	—
185	C₂×C₄×C₆₁	—	4	2	no	—
186	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
193	C₈×C₆₁	—	2	2	no	—
194	C₈×C₆₁	—	2	2	no	—
195	C₈×C₆₁	—	4	2	no	—
196	C₈×C₆₁	—	4	2	no	—
197	C₈×C₆₁	C₄×D₄	1	2	yes	—
198	C₈×C₆₁	C₄×D₄	1	2	yes	—
199	C₈×C₆₁	#121	1	2	yes	—
200	C₈×C₆₁	#121	1	2	yes	—
201	#21549	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₆₁	—	2	2	no	—
203	C₂²×C₆₁	—	2	4	no	—
204	C₂²×C₆₁	—	2	2	no	—
205	C₂²×C₆₁	—	4	2	no	—
206	C₂²×C₆₁	—	4	2	no	—
207	C₂²×C₆₁	—	4	4	no	—
208	C₂²×C₆₁	—	4	2	no	—
209	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
210	C₂²×C₆₁	#525	1	1	yes	characteristic
211	C₂²×C₆₁	#529	1	1	yes	characteristic
212	C₄×C₆₁	—	2	4	no	—
213	C₄×C₆₁	—	2	2	no	—
214	C₄×C₆₁	—	4	2	no	—
215	C₄×C₆₁	—	4	4	no	—
216	C₄×C₆₁	—	4	2	no	—
217	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
218	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
219	C₄×C₆₁	C₂×#121	1	1	yes	characteristic
220	C₄×C₆₁	#532	1	1	yes	characteristic
221	#3054	C₂×C₆₁	1	1	yes	characteristic
222	C₂×#443	C₂×C₆₁	1	1	yes	characteristic, complemented
223	#2930	C₂×C₆₁	1	2	yes	complemented
224	C₂×C₄×M₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
225	#1975	C₂×C₆₁	1	1	yes	characteristic, complemented
226	#1946	C₂×C₆₁	1	1	yes	characteristic, complemented
227	#1937	C₂×C₆₁	1	2	yes	complemented
228	#1896	C₂×C₆₁	1	2	yes	complemented
229	#1811	C₂×C₆₁	1	1	yes	characteristic, complemented
230	#1772	C₂×C₆₁	1	1	yes	characteristic, complemented
231	#1765	C₂×C₆₁	1	2	yes	complemented
232	C₂×C₆₁	—	2	1	no	—
233	C₂×C₆₁	—	2	1	no	—
234	C₂×C₆₁	—	4	2	no	—
235	C₂×C₆₁	—	8	2	no	—
236	C₂×C₆₁	C₄×#121	1	1	yes	characteristic
237	C₂×C₆₁	#2956	1	2	yes	—
238	C₂×#135	C₂²×C₆₁	1	1	yes	characteristic
239	C₂×#131	C₂²×C₆₁	1	2	yes	—
240	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
241	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
242	#525	C₂²×C₆₁	1	2	yes	—
243	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
244	#470	C₄×C₆₁	1	2	yes	complemented
245	#469	C₄×C₆₁	1	2	yes	complemented
246	#468	C₄×C₆₁	1	4	yes	complemented
247	#443	—	2	4	no	—
248	#436	—	2	4	no	—
249	#435	—	2	4	no	—
250	C₂×#108	C₂²×C₆₁	1	1	yes	characteristic
251	C₂×#108	C₂²×C₆₁	1	1	yes	characteristic
252	#427	C₂²×C₆₁	1	1	yes	characteristic
253	#424	C₂²×C₆₁	1	2	yes	—
254	C₂×#104	C₂²×C₆₁	1	2	yes	—
255	C₂×#104	C₂²×C₆₁	1	2	yes	—
256	#416	C₂²×C₆₁	1	2	yes	—
257	#408	C₂²×C₆₁	1	2	yes	—
258	#407	C₂²×C₆₁	1	2	yes	—
259	#405	C₂²×C₆₁	1	2	yes	—
260	C₄×M₁₆	—	2	4	no	—
261	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
262	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
265	#341	C₂²×C₆₁	1	2	yes	—
266	#339	C₂²×C₆₁	1	2	yes	—
267	#339	C₂²×C₆₁	1	2	yes	—
268	C₆₁	#21549	1	1	yes	characteristic, direct product factor, Sylow
269	C₂×#41	C₂³×C₆₁	1	2	yes	—
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
272	#135	—	2	2	no	—
273	#135	—	2	2	no	—
274	C₂×Q₁₆	C₂×C₄×C₆₁	1	1	yes	characteristic, complemented
275	C₂×SD₁₆	C₂×C₄×C₆₁	1	2	yes	complemented
276	C₂×D₈	C₂×C₄×C₆₁	1	1	yes	characteristic, complemented
277	#131	—	2	4	no	—
278	#131	—	2	4	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	C₂×C₄×C₆₁	1	2	yes	—
285	C₂×M₁₆	C₂×C₄×C₆₁	1	2	yes	—
286	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
287	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
288	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
289	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
295	#123	—	2	2	no	—
296	C₂²⋊Q₈	C₂×C₄×C₆₁	1	4	yes	—
297	#121	C₂×C₄×C₆₁	1	4	yes	—
298	#120	—	2	2	no	—
299	C₄×D₄	—	2	4	no	—
300	#117	C₂³×C₆₁	1	2	yes	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
306	#108	—	2	2	no	—
307	#108	—	2	2	no	—
308	#107	C₂×C₄×C₆₁	1	2	yes	complemented
309	#106	C₂×C₄×C₆₁	1	2	yes	complemented
310	C₄⋊C₈	—	2	4	no	—
311	#104	—	2	4	no	—
312	#104	—	2	4	no	—
313	#103	C₂×C₄×C₆₁	1	4	yes	complemented
314	#102	C₂×C₄×C₆₁	1	4	yes	complemented
315	C₂²⋊C₈	—	2	4	no	—
316	C₂²⋊C₈	—	2	4	no	—
317	#97	—	2	2	no	—
318	#97	—	2	2	no	—
319	#97	—	2	2	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	D₄×C₆₁	1	4	yes	complemented
323	C₂⁴	#41×C₆₁	1	1	yes	characteristic
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	4	4	no	—
341	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
343	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
345	Q₁₆	—	2	2	no	—
346	SD₁₆	—	2	4	no	—
347	D₈	—	2	2	no	—
348	M₁₆	—	2	4	no	—
349	M₁₆	—	2	4	no	—
350	M₁₆	—	2	4	no	—
351	M₁₆	—	2	4	no	—
352	M₁₆	—	2	2	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	4	4	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	4	no	—
364	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
365	C₂×C₈	C₂²×C₄×C₆₁	1	1	yes	characteristic
366	C₂×C₈	C₂²×C₄×C₆₁	1	1	yes	characteristic
367	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
368	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
369	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
370	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
371	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
372	C₂×C₈	#41×C₆₁	1	2	yes	—
373	C₂×C₈	#41×C₆₁	1	2	yes	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₄²	—	2	4	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	C₂×D₄×C₆₁	1	2	yes	—
384	C₄²	#41×C₆₁	1	2	yes	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	C₄×D₄×C₆₁	1	2	yes	—
390	C₂³	C₂×#41×C₆₁	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	8	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	8	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
414	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
418	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	2	2	no	—
422	C₈	—	4	2	no	—
423	C₈	—	4	2	no	—
424	C₈	C₄×D₄×C₆₁	1	2	yes	—
425	C₈	C₄×D₄×C₆₁	1	2	yes	—
426	C₈	#121×C₆₁	1	2	yes	—
427	C₈	#121×C₆₁	1	2	yes	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	4	no	—
435	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
436	C₂²	C₆₁×#525	1	1	yes	characteristic
437	C₂²	C₆₁×#529	1	1	yes	characteristic
438	C₄	—	2	4	no	—
439	C₄	—	2	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	4	no	—
443	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
444	C₄	C₄×#41×C₆₁	1	1	yes	characteristic
445	C₄	C₂×#121×C₆₁	1	1	yes	characteristic
446	C₄	C₆₁×#532	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	4	2	no	—
450	C₂	—	8	2	no	—
451	C₂	C₄×#121×C₆₁	1	1	yes	characteristic
452	C₂	C₆₁×#2956	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
socle	C₂²×C₆₁	C₂×C₄×D₄
prime radical	C₆₁×#3054	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₂²×M₁₆×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#443	C₂	semidirect
3. C₆₁×#2930	C₂	semidirect
4. C₂×C₄×M₁₆×C₆₁	C₂	semidirect
5. C₆₁×#1975	C₂	semidirect
6. C₆₁×#1946	C₂	semidirect
7. C₆₁×#1937	C₂	semidirect
8. C₆₁×#1896	C₂	semidirect
9. C₆₁×#1811	C₂	semidirect
10. C₆₁×#1772	C₂	semidirect
11. C₆₁×#1765	C₂	semidirect
18. C₆₁×#470	C₄	semidirect
19. C₆₁×#469	C₄	semidirect
20. C₆₁×#468	C₄	semidirect
47. C₂×Q₁₆×C₆₁	C₂×C₄	semidirect
48. C₂×SD₁₆×C₆₁	C₂×C₄	semidirect
49. C₂×D₈×C₆₁	C₂×C₄	semidirect
81. #107×C₆₁	C₂×C₄	semidirect
82. #106×C₆₁	C₂×C₄	semidirect
86. #103×C₆₁	C₂×C₄	semidirect
87. #102×C₆₁	C₂×C₄	semidirect
95. C₄×C₈×C₆₁	D₄	semidirect
201. #21549	C₆₁	direct (N × H)
222. C₂×#443	C₂×C₆₁	semidirect
223. #2930	C₂×C₆₁	semidirect
224. C₂×C₄×M₁₆	C₂×C₆₁	semidirect
225. #1975	C₂×C₆₁	semidirect
226. #1946	C₂×C₆₁	semidirect
227. #1937	C₂×C₆₁	semidirect
228. #1896	C₂×C₆₁	semidirect
229. #1811	C₂×C₆₁	semidirect
230. #1772	C₂×C₆₁	semidirect
231. #1765	C₂×C₆₁	semidirect
244. #470	C₄×C₆₁	semidirect
245. #469	C₄×C₆₁	semidirect
246. #468	C₄×C₆₁	semidirect
268. C₆₁	#21549	direct (N × H)
274. C₂×Q₁₆	C₂×C₄×C₆₁	semidirect
275. C₂×SD₁₆	C₂×C₄×C₆₁	semidirect
276. C₂×D₈	C₂×C₄×C₆₁	semidirect
308. #107	C₂×C₄×C₆₁	semidirect
309. #106	C₂×C₄×C₆₁	semidirect
313. #103	C₂×C₄×C₆₁	semidirect
314. #102	C₂×C₄×C₆₁	semidirect
322. C₄×C₈	D₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3054	2
C₂×C₆₁×#443	2
C₆₁×#2930	2
C₂×C₄×M₁₆×C₆₁	2
C₆₁×#1975	2
C₆₁×#1946	2
C₆₁×#1937	2
C₆₁×#1896	2
C₆₁×#1811	2
C₆₁×#1772	2
C₆₁×#1765	2
#21549	61

Subgroups — C61×#21549 #29524982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21549 #29524982