Subgroups — C₆₁×#20886 #29524319

Order 15616.

1326 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#568	C₂	1	1	yes	maximal, characteristic
2	C₂²×#108×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2905	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#421	C₂	1	1	yes	maximal, characteristic
5	C₂×C₆₁×#416	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#1866	C₂	1	8	yes	maximal, complemented
7	C₆₁×#1733	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1729	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
10	C₆₁×#568	—	2	4	no	—
11	C₆₁×#568	—	2	4	no	—
12	C₂×#131×C₆₁	—	2	2	no	—
13	C₂×#131×C₆₁	C₂²	1	4	yes	—
14	C₂²×M₁₆×C₆₁	—	2	2	no	—
15	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#108×C₆₁	—	2	4	no	—
22	C₂×#108×C₆₁	C₂²	1	4	yes	complemented
23	C₆₁×#424	—	2	2	no	—
24	C₆₁×#424	C₂²	1	4	yes	complemented
25	C₆₁×#423	—	2	2	no	—
26	C₆₁×#421	—	2	4	no	—
27	C₂×#104×C₆₁	C₂²	1	4	yes	—
28	C₆₁×#416	C₄	1	4	yes	complemented
29	C₆₁×#416	C₂²	1	4	yes	—
30	C₂×#103×C₆₁	C₄	1	2	yes	complemented
31	C₂×#102×C₆₁	C₄	1	2	yes	complemented
32	C₆₁×#339	C₂²	1	4	yes	complemented
33	C₆₁×#336	C₂²	1	4	yes	complemented
34	C₂×#41×C₆₁	—	2	1	no	—
35	C₂×#41×C₆₁	—	2	2	no	—
36	C₂×#41×C₆₁	—	2	1	no	—
37	C₂×#41×C₆₁	—	2	2	no	—
38	C₂×#41×C₆₁	C₂×C₄	1	2	yes	—
39	C₂×#41×C₆₁	D₄	1	4	yes	—
40	C₂×#41×C₆₁	Q₈	1	4	yes	—
41	C₂×#41×C₆₁	C₂³	1	2	yes	—
42	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
43	C₂²×D₄×C₆₁	—	2	1	no	—
44	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₁	—	2	1	no	—
46	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
47	#131×C₆₁	—	2	16	no	—
48	#131×C₆₁	—	2	8	no	—
49	#131×C₆₁	—	2	8	no	—
50	C₂×M₁₆×C₆₁	—	2	16	no	—
51	C₂×M₁₆×C₆₁	—	2	1	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	1	no	—
56	C₂×M₁₆×C₆₁	—	2	4	no	—
57	C₂×M₁₆×C₆₁	—	2	2	no	—
58	C₂×M₁₆×C₆₁	—	2	2	no	—
59	C₂×M₁₆×C₆₁	D₄	1	4	yes	—
60	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
61	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
62	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
63	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
64	C₂²×C₈×C₆₁	—	2	2	no	—
65	C₂²×C₈×C₆₁	—	2	1	no	—
66	C₂²×C₈×C₆₁	—	2	2	no	—
67	C₂²×C₈×C₆₁	—	2	4	no	—
68	C₂²×C₈×C₆₁	—	2	1	no	—
69	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
72	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
73	#117×C₆₁	—	2	1	no	—
74	#117×C₆₁	—	2	1	no	—
75	#117×C₆₁	—	2	2	no	—
76	#117×C₆₁	—	2	2	no	—
77	#117×C₆₁	C₂×C₄	1	2	yes	—
78	#117×C₆₁	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
81	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
83	C₂×C₄²×C₆₁	—	2	1	no	—
84	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
85	#108×C₆₁	—	2	8	no	—
86	C₄⋊C₈×C₆₁	—	2	8	no	—
87	#104×C₆₁	—	2	8	no	—
88	#103×C₆₁	C₂×C₄	1	8	yes	—
89	#102×C₆₁	C₂×C₄	1	8	yes	—
90	C₂⁴×C₆₁	—	2	1	no	—
91	C₂⁴×C₆₁	#41	1	1	yes	characteristic
92	#41×C₆₁	—	2	4	no	—
93	#41×C₆₁	—	2	4	no	—
94	#41×C₆₁	—	2	4	no	—
95	#41×C₆₁	—	2	4	no	—
96	#41×C₆₁	—	2	4	no	—
97	#41×C₆₁	—	2	2	no	—
98	#41×C₆₁	—	2	2	no	—
99	#41×C₆₁	C₄⋊C₄	1	8	yes	—
100	#41×C₆₁	C₂×D₄	1	4	yes	—
101	#41×C₆₁	C₂×Q₈	1	4	yes	—
102	C₂×Q₈×C₆₁	—	2	1	no	—
103	C₂×Q₈×C₆₁	—	2	2	no	—
104	C₂×Q₈×C₆₁	C₄⋊C₄	1	4	yes	—
105	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₆₁	—	2	2	no	—
107	C₂×D₄×C₆₁	—	2	4	no	—
108	C₂×D₄×C₆₁	—	2	4	no	—
109	C₂×D₄×C₆₁	—	2	2	no	—
110	C₂×D₄×C₆₁	—	2	2	no	—
111	C₂×D₄×C₆₁	—	2	1	no	—
112	C₂×D₄×C₆₁	C₄⋊C₄	1	4	yes	—
113	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₆₁	—	2	1	no	—
115	C₂²×C₄×C₆₁	—	2	2	no	—
116	C₂²×C₄×C₆₁	—	2	4	no	—
117	C₂²×C₄×C₆₁	—	2	4	no	—
118	C₂²×C₄×C₆₁	—	2	2	no	—
119	C₂²×C₄×C₆₁	—	2	2	no	—
120	C₂²×C₄×C₆₁	—	2	2	no	—
121	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
128	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
129	C₂²×C₄×C₆₁	#41	1	2	yes	—
130	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
131	M₁₆×C₆₁	—	2	16	no	—
132	M₁₆×C₆₁	—	2	4	no	—
133	M₁₆×C₆₁	—	2	4	no	—
134	M₁₆×C₆₁	—	2	4	no	—
135	M₁₆×C₆₁	—	2	2	no	—
136	M₁₆×C₆₁	—	2	2	no	—
137	M₁₆×C₆₁	—	2	2	no	—
138	M₁₆×C₆₁	—	4	2	no	—
139	M₁₆×C₆₁	C₂×D₄	1	4	yes	—
140	C₂×C₈×C₆₁	—	2	16	no	—
141	C₂×C₈×C₆₁	—	2	4	no	—
142	C₂×C₈×C₆₁	—	2	4	no	—
143	C₂×C₈×C₆₁	—	2	4	no	—
144	C₂×C₈×C₆₁	—	2	2	no	—
145	C₂×C₈×C₆₁	—	2	2	no	—
146	C₂×C₈×C₆₁	—	2	2	no	—
147	C₂×C₈×C₆₁	—	2	2	no	—
148	C₂×C₈×C₆₁	—	2	2	no	—
149	C₂×C₈×C₆₁	—	2	2	no	—
150	C₂×C₈×C₆₁	—	4	2	no	—
151	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
152	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
153	C₄⋊C₄×C₆₁	—	2	2	no	—
154	C₄⋊C₄×C₆₁	—	4	2	no	—
155	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
156	C₂²⋊C₄×C₆₁	—	2	2	no	—
157	C₂²⋊C₄×C₆₁	—	2	2	no	—
158	C₂²⋊C₄×C₆₁	—	4	2	no	—
159	C₄²×C₆₁	—	2	2	no	—
160	C₄²×C₆₁	—	2	2	no	—
161	C₄²×C₆₁	—	2	2	no	—
162	C₄²×C₆₁	—	2	2	no	—
163	C₂³×C₆₁	—	2	2	no	—
164	C₂³×C₆₁	—	2	4	no	—
165	C₂³×C₆₁	—	4	2	no	—
166	C₂³×C₆₁	—	8	2	no	—
167	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
168	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
169	C₂³×C₆₁	C₂²⋊Q₈	1	2	yes	—
170	C₂³×C₆₁	#123	1	2	yes	—
171	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
172	Q₈×C₆₁	—	2	2	no	—
173	Q₈×C₆₁	—	2	4	no	—
174	Q₈×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
175	D₄×C₆₁	—	2	4	no	—
176	D₄×C₆₁	—	2	4	no	—
177	D₄×C₆₁	—	2	8	no	—
178	D₄×C₆₁	—	2	2	no	—
179	D₄×C₆₁	—	2	4	no	—
180	D₄×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
181	C₂×C₄×C₆₁	—	2	2	no	—
182	C₂×C₄×C₆₁	—	2	4	no	—
183	C₂×C₄×C₆₁	—	2	4	no	—
184	C₂×C₄×C₆₁	—	2	4	no	—
185	C₂×C₄×C₆₁	—	2	8	no	—
186	C₂×C₄×C₆₁	—	2	4	no	—
187	C₂×C₄×C₆₁	—	4	4	no	—
188	C₂×C₄×C₆₁	—	4	2	no	—
189	C₂×C₄×C₆₁	—	8	2	no	—
190	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
191	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
192	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
193	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₆₁	#120	1	2	yes	—
197	C₂×C₄×C₆₁	#120	1	2	yes	—
198	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
199	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
200	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
201	C₂×C₄×C₆₁	#123	1	2	yes	—
202	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
207	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
208	C₈×C₆₁	—	2	4	no	—
209	C₈×C₆₁	—	2	4	no	—
210	C₈×C₆₁	—	2	4	no	—
211	C₈×C₆₁	—	4	2	no	—
212	#20886	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂²×C₆₁	—	2	2	no	—
214	C₂²×C₆₁	—	2	2	no	—
215	C₂²×C₆₁	—	2	2	no	—
216	C₂²×C₆₁	—	2	4	no	—
217	C₂²×C₆₁	—	4	2	no	—
218	C₂²×C₆₁	—	4	2	no	—
219	C₂²×C₆₁	—	4	4	no	—
220	C₂²×C₆₁	—	8	4	no	—
221	C₂²×C₆₁	#385	1	2	yes	—
222	C₂²×C₆₁	#385	1	2	yes	—
223	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
224	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
225	C₂²×C₆₁	C₂×#123	1	1	yes	characteristic
226	C₄×C₆₁	—	2	4	no	—
227	C₄×C₆₁	—	4	4	no	—
228	C₄×C₆₁	—	8	2	no	—
229	C₄×C₆₁	#385	1	2	yes	—
230	C₄×C₆₁	#385	1	2	yes	—
231	C₄×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
232	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
233	C₄×C₆₁	C₂×#120	1	1	yes	characteristic
234	C₄×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
235	C₂×#568	C₂×C₆₁	1	1	yes	characteristic
236	C₂²×#108	C₂×C₆₁	1	1	yes	characteristic, complemented
237	#2905	C₂×C₆₁	1	1	yes	characteristic, complemented
238	C₂×#421	C₂×C₆₁	1	1	yes	characteristic
239	C₂×#416	C₂×C₆₁	1	1	yes	characteristic
240	#1866	C₂×C₆₁	1	8	yes	complemented
241	#1733	C₂×C₆₁	1	1	yes	characteristic, complemented
242	#1729	C₂×C₆₁	1	1	yes	characteristic, complemented
243	C₂×C₆₁	—	2	1	no	—
244	C₂×C₆₁	—	2	2	no	—
245	C₂×C₆₁	—	2	1	no	—
246	C₂×C₆₁	—	2	2	no	—
247	C₂×C₆₁	—	4	4	no	—
248	C₂×C₆₁	C₂×#385	1	1	yes	characteristic
249	C₂×C₆₁	#2957	1	2	yes	—
250	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
251	#568	—	2	4	no	—
252	#568	—	2	4	no	—
253	C₂×#131	—	2	2	no	—
254	C₂×#131	C₂²×C₆₁	1	4	yes	—
255	C₂²×M₁₆	—	2	2	no	—
256	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
257	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
258	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
259	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
260	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
261	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
262	C₂×#108	—	2	4	no	—
263	C₂×#108	C₂²×C₆₁	1	4	yes	complemented
264	#424	—	2	2	no	—
265	#424	C₂²×C₆₁	1	4	yes	complemented
266	#423	—	2	2	no	—
267	#421	—	2	4	no	—
268	C₂×#104	C₂²×C₆₁	1	4	yes	—
269	#416	C₄×C₆₁	1	4	yes	complemented
270	#416	C₂²×C₆₁	1	4	yes	—
271	C₂×#103	C₄×C₆₁	1	2	yes	complemented
272	C₂×#102	C₄×C₆₁	1	2	yes	complemented
273	#339	C₂²×C₆₁	1	4	yes	complemented
274	#336	C₂²×C₆₁	1	4	yes	complemented
275	C₆₁	#20886	1	1	yes	characteristic, direct product factor, Sylow
276	C₂×#41	—	2	1	no	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	—	2	1	no	—
279	C₂×#41	—	2	2	no	—
280	C₂×#41	C₂×C₄×C₆₁	1	2	yes	—
281	C₂×#41	D₄×C₆₁	1	4	yes	—
282	C₂×#41	Q₈×C₆₁	1	4	yes	—
283	C₂×#41	C₂³×C₆₁	1	2	yes	—
284	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
287	C₂³×C₄	—	2	1	no	—
288	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
289	#131	—	2	16	no	—
290	#131	—	2	8	no	—
291	#131	—	2	8	no	—
292	C₂×M₁₆	—	2	16	no	—
293	C₂×M₁₆	—	2	1	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	1	no	—
298	C₂×M₁₆	—	2	4	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	D₄×C₆₁	1	4	yes	—
302	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
303	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
304	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
305	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	2	2	no	—
309	C₂²×C₈	—	2	4	no	—
310	C₂²×C₈	—	2	1	no	—
311	C₂²×C₈	C₂×C₄×C₆₁	1	2	yes	—
312	C₂²×C₈	C₂×C₄×C₆₁	1	2	yes	—
313	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
314	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
315	#117	—	2	1	no	—
316	#117	—	2	1	no	—
317	#117	—	2	2	no	—
318	#117	—	2	2	no	—
319	#117	C₂×C₄×C₆₁	1	2	yes	—
320	#117	C₂³×C₆₁	1	2	yes	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
327	#108	—	2	8	no	—
328	C₄⋊C₈	—	2	8	no	—
329	#104	—	2	8	no	—
330	#103	C₂×C₄×C₆₁	1	8	yes	—
331	#102	C₂×C₄×C₆₁	1	8	yes	—
332	C₂⁴	—	2	1	no	—
333	C₂⁴	#41×C₆₁	1	1	yes	characteristic
334	#41	—	2	4	no	—
335	#41	—	2	4	no	—
336	#41	—	2	4	no	—
337	#41	—	2	4	no	—
338	#41	—	2	4	no	—
339	#41	—	2	2	no	—
340	#41	—	2	2	no	—
341	#41	C₄⋊C₄×C₆₁	1	8	yes	—
342	#41	C₂×D₄×C₆₁	1	4	yes	—
343	#41	C₂×Q₈×C₆₁	1	4	yes	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	C₄⋊C₄×C₆₁	1	4	yes	—
347	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	C₄⋊C₄×C₆₁	1	4	yes	—
355	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
364	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
369	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
370	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
371	C₂²×C₄	#41×C₆₁	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
373	M₁₆	—	2	16	no	—
374	M₁₆	—	2	4	no	—
375	M₁₆	—	2	4	no	—
376	M₁₆	—	2	4	no	—
377	M₁₆	—	2	2	no	—
378	M₁₆	—	2	2	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	4	2	no	—
381	M₁₆	C₂×D₄×C₆₁	1	4	yes	—
382	C₂×C₈	—	2	16	no	—
383	C₂×C₈	—	2	4	no	—
384	C₂×C₈	—	2	4	no	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	4	2	no	—
393	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
394	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	4	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	4	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	8	2	no	—
409	C₂³	C₄×D₄×C₆₁	1	1	yes	characteristic
410	C₂³	C₄×D₄×C₆₁	1	1	yes	characteristic
411	C₂³	C₂²⋊Q₈×C₆₁	1	2	yes	—
412	C₂³	#123×C₆₁	1	2	yes	—
413	C₂³	C₂×#41×C₆₁	1	1	yes	characteristic
414	Q₈	—	2	4	no	—
415	Q₈	—	2	2	no	—
416	Q₈	C₂×C₄⋊C₄×C₆₁	1	4	yes	—
417	D₄	—	2	8	no	—
418	D₄	—	2	4	no	—
419	D₄	—	2	4	no	—
420	D₄	—	2	4	no	—
421	D₄	—	2	2	no	—
422	D₄	C₂×C₄⋊C₄×C₆₁	1	4	yes	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	8	2	no	—
432	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
433	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
434	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
435	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
436	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
437	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
438	C₂×C₄	#120×C₆₁	1	2	yes	—
439	C₂×C₄	#120×C₆₁	1	2	yes	—
440	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
441	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
442	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
443	C₂×C₄	#123×C₆₁	1	2	yes	—
444	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
448	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
449	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
450	C₈	—	2	4	no	—
451	C₈	—	2	4	no	—
452	C₈	—	2	4	no	—
453	C₈	—	4	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	8	4	no	—
462	C₂²	C₆₁×#385	1	2	yes	—
463	C₂²	C₆₁×#385	1	2	yes	—
464	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
465	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
466	C₂²	C₂×#123×C₆₁	1	1	yes	characteristic
467	C₄	—	2	4	no	—
468	C₄	—	4	4	no	—
469	C₄	—	8	2	no	—
470	C₄	C₆₁×#385	1	2	yes	—
471	C₄	C₆₁×#385	1	2	yes	—
472	C₄	C₂²×C₄⋊C₄×C₆₁	1	1	yes	characteristic
473	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
474	C₄	C₂×#120×C₆₁	1	1	yes	characteristic
475	C₄	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
476	C₂	—	2	1	no	—
477	C₂	—	2	2	no	—
478	C₂	—	2	2	no	—
479	C₂	—	2	1	no	—
480	C₂	—	4	4	no	—
481	C₂	C₂×C₆₁×#385	1	1	yes	characteristic
482	C₂	C₆₁×#2957	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	C₂²×#41×C₆₁	C₂²
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. C₂²×#108×C₆₁	C₂	semidirect
3. C₆₁×#2905	C₂	semidirect
6. C₆₁×#1866	C₂	semidirect
7. C₆₁×#1733	C₂	semidirect
8. C₆₁×#1729	C₂	semidirect
22. C₂×#108×C₆₁	C₂²	semidirect
24. C₆₁×#424	C₂²	semidirect
28. C₆₁×#416	C₄	semidirect
30. C₂×#103×C₆₁	C₄	semidirect
31. C₂×#102×C₆₁	C₄	semidirect
32. C₆₁×#339	C₂²	semidirect
33. C₆₁×#336	C₂²	semidirect
212. #20886	C₆₁	direct (N × H)
236. C₂²×#108	C₂×C₆₁	semidirect
237. #2905	C₂×C₆₁	semidirect
240. #1866	C₂×C₆₁	semidirect
241. #1733	C₂×C₆₁	semidirect
242. #1729	C₂×C₆₁	semidirect
263. C₂×#108	C₂²×C₆₁	semidirect
265. #424	C₂²×C₆₁	semidirect
269. #416	C₄×C₆₁	semidirect
271. C₂×#103	C₄×C₆₁	semidirect
272. C₂×#102	C₄×C₆₁	semidirect
273. #339	C₂²×C₆₁	semidirect
274. #336	C₂²×C₆₁	semidirect
275. C₆₁	#20886	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#568	2
C₂²×#108×C₆₁	2
C₆₁×#2905	2
C₂×C₆₁×#421	2
C₂×C₆₁×#416	2
C₆₁×#1866	2
C₆₁×#1733	2
C₆₁×#1729	2
#20886	61

Subgroups — C61×#20886 #29524319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#20886 #29524319