Subgroups — C₆₁×#20884 #29524317

Order 15616.

1342 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#430	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#421	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2896	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	C₂×#131×C₆₁	—	2	4	no	—
11	C₂×#131×C₆₁	—	2	4	no	—
12	C₂×#131×C₆₁	—	2	2	no	—
13	C₂×#131×C₆₁	C₂²	1	4	yes	—
14	C₂²×M₁₆×C₆₁	—	2	1	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	—	2	1	no	—
19	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
22	C₆₁×#430	—	2	4	no	—
23	C₂×#108×C₆₁	C₂²	1	4	yes	complemented
24	C₆₁×#424	—	2	1	no	—
25	C₆₁×#424	—	2	1	no	—
26	C₆₁×#424	C₂²	1	4	yes	complemented
27	C₂×C₄⋊C₈×C₆₁	—	2	2	no	—
28	C₆₁×#421	—	2	4	no	—
29	C₂×#104×C₆₁	C₂²	1	4	yes	—
30	C₆₁×#419	C₄	1	2	yes	complemented
31	C₆₁×#418	C₄	1	2	yes	complemented
32	C₆₁×#417	C₄	1	4	yes	complemented
33	C₆₁×#416	C₂²	1	4	yes	—
34	C₆₁×#339	C₂²	1	4	yes	complemented
35	C₆₁×#336	C₂²	1	4	yes	complemented
36	C₂×#41×C₆₁	—	2	2	no	—
37	C₂×#41×C₆₁	—	2	1	no	—
38	C₂×#41×C₆₁	—	2	1	no	—
39	C₂×#41×C₆₁	—	2	2	no	—
40	C₂×#41×C₆₁	C₂×C₄	1	2	yes	—
41	C₂×#41×C₆₁	D₄	1	4	yes	—
42	C₂×#41×C₆₁	Q₈	1	4	yes	—
43	C₂×#41×C₆₁	C₂³	1	2	yes	—
44	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₆₁	—	2	1	no	—
46	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₆₁	—	2	1	no	—
48	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
49	#131×C₆₁	—	2	16	no	—
50	#131×C₆₁	—	2	8	no	—
51	#131×C₆₁	—	2	8	no	—
52	C₂×M₁₆×C₆₁	—	2	8	no	—
53	C₂×M₁₆×C₆₁	—	2	2	no	—
54	C₂×M₁₆×C₆₁	—	2	1	no	—
55	C₂×M₁₆×C₆₁	—	2	2	no	—
56	C₂×M₁₆×C₆₁	—	2	2	no	—
57	C₂×M₁₆×C₆₁	—	2	1	no	—
58	C₂×M₁₆×C₆₁	—	2	4	no	—
59	C₂×M₁₆×C₆₁	—	2	2	no	—
60	C₂×M₁₆×C₆₁	—	2	2	no	—
61	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
62	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
63	C₂×M₁₆×C₆₁	D₄	1	4	yes	—
64	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
65	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
66	C₂²×C₈×C₆₁	—	2	8	no	—
67	C₂²×C₈×C₆₁	—	2	1	no	—
68	C₂²×C₈×C₆₁	—	2	2	no	—
69	C₂²×C₈×C₆₁	—	2	2	no	—
70	C₂²×C₈×C₆₁	—	2	4	no	—
71	C₂²×C₈×C₆₁	—	2	1	no	—
72	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₆₁	D₄	1	2	yes	—
75	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
76	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
77	#117×C₆₁	—	2	1	no	—
78	#117×C₆₁	—	2	1	no	—
79	#117×C₆₁	—	2	2	no	—
80	#117×C₆₁	—	2	2	no	—
81	#117×C₆₁	C₂×C₄	1	2	yes	—
82	#117×C₆₁	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
84	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
87	C₂×C₄²×C₆₁	—	2	1	no	—
88	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
89	#108×C₆₁	—	2	8	no	—
90	C₄⋊C₈×C₆₁	—	2	4	no	—
91	C₄⋊C₈×C₆₁	—	2	4	no	—
92	#104×C₆₁	—	2	8	no	—
93	#103×C₆₁	C₂×C₄	1	8	yes	—
94	#102×C₆₁	C₂×C₄	1	8	yes	—
95	C₂⁴×C₆₁	—	2	1	no	—
96	C₂⁴×C₆₁	#41	1	1	yes	characteristic
97	#41×C₆₁	—	2	4	no	—
98	#41×C₆₁	—	2	4	no	—
99	#41×C₆₁	—	2	4	no	—
100	#41×C₆₁	—	2	4	no	—
101	#41×C₆₁	—	2	4	no	—
102	#41×C₆₁	—	2	2	no	—
103	#41×C₆₁	—	2	2	no	—
104	#41×C₆₁	C₄⋊C₄	1	8	yes	—
105	#41×C₆₁	C₂×D₄	1	4	yes	—
106	#41×C₆₁	C₂×Q₈	1	4	yes	—
107	C₂×Q₈×C₆₁	—	2	1	no	—
108	C₂×Q₈×C₆₁	—	2	2	no	—
109	C₂×Q₈×C₆₁	C₄⋊C₄	1	4	yes	—
110	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
111	C₂×D₄×C₆₁	—	2	2	no	—
112	C₂×D₄×C₆₁	—	2	4	no	—
113	C₂×D₄×C₆₁	—	2	4	no	—
114	C₂×D₄×C₆₁	—	2	2	no	—
115	C₂×D₄×C₆₁	—	2	2	no	—
116	C₂×D₄×C₆₁	—	2	1	no	—
117	C₂×D₄×C₆₁	C₄⋊C₄	1	4	yes	—
118	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₆₁	—	2	1	no	—
120	C₂²×C₄×C₆₁	—	2	2	no	—
121	C₂²×C₄×C₆₁	—	2	4	no	—
122	C₂²×C₄×C₆₁	—	2	4	no	—
123	C₂²×C₄×C₆₁	—	2	2	no	—
124	C₂²×C₄×C₆₁	—	2	2	no	—
125	C₂²×C₄×C₆₁	—	2	2	no	—
126	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
133	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
134	C₂²×C₄×C₆₁	#41	1	2	yes	—
135	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
136	M₁₆×C₆₁	—	2	16	no	—
137	M₁₆×C₆₁	—	2	4	no	—
138	M₁₆×C₆₁	—	2	4	no	—
139	M₁₆×C₆₁	—	2	4	no	—
140	M₁₆×C₆₁	—	2	2	no	—
141	M₁₆×C₆₁	—	2	2	no	—
142	M₁₆×C₆₁	—	2	2	no	—
143	M₁₆×C₆₁	—	4	2	no	—
144	M₁₆×C₆₁	C₂×D₄	1	4	yes	—
145	C₂×C₈×C₆₁	—	2	16	no	—
146	C₂×C₈×C₆₁	—	2	2	no	—
147	C₂×C₈×C₆₁	—	2	4	no	—
148	C₂×C₈×C₆₁	—	2	2	no	—
149	C₂×C₈×C₆₁	—	2	4	no	—
150	C₂×C₈×C₆₁	—	2	2	no	—
151	C₂×C₈×C₆₁	—	2	2	no	—
152	C₂×C₈×C₆₁	—	2	2	no	—
153	C₂×C₈×C₆₁	—	2	2	no	—
154	C₂×C₈×C₆₁	—	2	2	no	—
155	C₂×C₈×C₆₁	—	2	2	no	—
156	C₂×C₈×C₆₁	—	4	2	no	—
157	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
158	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₆₁	—	2	2	no	—
161	C₄⋊C₄×C₆₁	—	4	2	no	—
162	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
163	C₂²⋊C₄×C₆₁	—	2	2	no	—
164	C₂²⋊C₄×C₆₁	—	2	2	no	—
165	C₂²⋊C₄×C₆₁	—	4	2	no	—
166	C₄²×C₆₁	—	2	2	no	—
167	C₄²×C₆₁	—	2	2	no	—
168	C₄²×C₆₁	—	2	2	no	—
169	C₄²×C₆₁	—	2	2	no	—
170	C₂³×C₆₁	—	2	2	no	—
171	C₂³×C₆₁	—	2	4	no	—
172	C₂³×C₆₁	—	4	2	no	—
173	C₂³×C₆₁	—	4	4	no	—
174	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
175	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
176	C₂³×C₆₁	C₂²⋊Q₈	1	2	yes	—
177	C₂³×C₆₁	#123	1	2	yes	—
178	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
179	Q₈×C₆₁	—	2	2	no	—
180	Q₈×C₆₁	—	2	4	no	—
181	Q₈×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
182	D₄×C₆₁	—	2	4	no	—
183	D₄×C₆₁	—	2	4	no	—
184	D₄×C₆₁	—	2	8	no	—
185	D₄×C₆₁	—	2	2	no	—
186	D₄×C₆₁	—	2	4	no	—
187	D₄×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
188	C₂×C₄×C₆₁	—	2	2	no	—
189	C₂×C₄×C₆₁	—	2	4	no	—
190	C₂×C₄×C₆₁	—	2	4	no	—
191	C₂×C₄×C₆₁	—	2	4	no	—
192	C₂×C₄×C₆₁	—	2	8	no	—
193	C₂×C₄×C₆₁	—	2	4	no	—
194	C₂×C₄×C₆₁	—	4	4	no	—
195	C₂×C₄×C₆₁	—	4	4	no	—
196	C₂×C₄×C₆₁	—	4	2	no	—
197	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
198	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
199	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
201	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₆₁	#120	1	2	yes	—
204	C₂×C₄×C₆₁	#120	1	2	yes	—
205	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
206	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
207	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
208	C₂×C₄×C₆₁	#123	1	2	yes	—
209	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
215	C₈×C₆₁	—	2	4	no	—
216	C₈×C₆₁	—	2	2	no	—
217	C₈×C₆₁	—	2	4	no	—
218	C₈×C₆₁	—	2	2	no	—
219	C₈×C₆₁	—	4	2	no	—
220	#20884	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂²×C₆₁	—	2	2	no	—
222	C₂²×C₆₁	—	2	2	no	—
223	C₂²×C₆₁	—	2	2	no	—
224	C₂²×C₆₁	—	2	4	no	—
225	C₂²×C₆₁	—	4	2	no	—
226	C₂²×C₆₁	—	4	2	no	—
227	C₂²×C₆₁	—	4	8	no	—
228	C₂²×C₆₁	—	4	4	no	—
229	C₂²×C₆₁	#385	1	2	yes	—
230	C₂²×C₆₁	#385	1	2	yes	—
231	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
232	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
233	C₂²×C₆₁	C₂×#123	1	1	yes	characteristic
234	C₄×C₆₁	—	2	4	no	—
235	C₄×C₆₁	—	4	4	no	—
236	C₄×C₆₁	—	8	2	no	—
237	C₄×C₆₁	#385	1	2	yes	—
238	C₄×C₆₁	#385	1	2	yes	—
239	C₄×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
240	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
241	C₄×C₆₁	C₂×#120	1	1	yes	characteristic
242	C₄×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
243	C₂²×#131	C₂×C₆₁	1	1	yes	characteristic
244	C₂×#430	C₂×C₆₁	1	1	yes	characteristic, complemented
245	C₂×#424	C₂×C₆₁	1	1	yes	characteristic, complemented
246	C₂×#421	C₂×C₆₁	1	1	yes	characteristic
247	#2896	C₂×C₆₁	1	1	yes	characteristic
248	#1866	C₂×C₆₁	1	8	yes	complemented
249	#1733	C₂×C₆₁	1	1	yes	characteristic, complemented
250	#1729	C₂×C₆₁	1	1	yes	characteristic, complemented
251	C₂×C₆₁	—	2	1	no	—
252	C₂×C₆₁	—	2	2	no	—
253	C₂×C₆₁	—	2	1	no	—
254	C₂×C₆₁	—	2	2	no	—
255	C₂×C₆₁	—	4	4	no	—
256	C₂×C₆₁	C₂×#385	1	1	yes	characteristic
257	C₂×C₆₁	#2955	1	2	yes	—
258	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
259	C₂×#131	—	2	4	no	—
260	C₂×#131	—	2	4	no	—
261	C₂×#131	—	2	2	no	—
262	C₂×#131	C₂²×C₆₁	1	4	yes	—
263	C₂²×M₁₆	—	2	1	no	—
264	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
265	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
266	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
267	C₂³×C₈	—	2	1	no	—
268	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
269	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
270	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
271	#430	—	2	4	no	—
272	C₂×#108	C₂²×C₆₁	1	4	yes	complemented
273	#424	—	2	1	no	—
274	#424	—	2	1	no	—
275	#424	C₂²×C₆₁	1	4	yes	complemented
276	C₂×C₄⋊C₈	—	2	2	no	—
277	#421	—	2	4	no	—
278	C₂×#104	C₂²×C₆₁	1	4	yes	—
279	#419	C₄×C₆₁	1	2	yes	complemented
280	#418	C₄×C₆₁	1	2	yes	complemented
281	#417	C₄×C₆₁	1	4	yes	complemented
282	#416	C₂²×C₆₁	1	4	yes	—
283	#339	C₂²×C₆₁	1	4	yes	complemented
284	#336	C₂²×C₆₁	1	4	yes	complemented
285	C₆₁	#20884	1	1	yes	characteristic, direct product factor, Sylow
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	1	no	—
288	C₂×#41	—	2	1	no	—
289	C₂×#41	—	2	2	no	—
290	C₂×#41	C₂×C₄×C₆₁	1	2	yes	—
291	C₂×#41	D₄×C₆₁	1	4	yes	—
292	C₂×#41	Q₈×C₆₁	1	4	yes	—
293	C₂×#41	C₂³×C₆₁	1	2	yes	—
294	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
297	C₂³×C₄	—	2	1	no	—
298	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
299	#131	—	2	16	no	—
300	#131	—	2	8	no	—
301	#131	—	2	8	no	—
302	C₂×M₁₆	—	2	8	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	—	2	1	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	2	2	no	—
307	C₂×M₁₆	—	2	1	no	—
308	C₂×M₁₆	—	2	4	no	—
309	C₂×M₁₆	—	2	2	no	—
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	C₂×C₄×C₆₁	1	2	yes	—
312	C₂×M₁₆	C₂×C₄×C₆₁	1	2	yes	—
313	C₂×M₁₆	D₄×C₆₁	1	4	yes	—
314	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
315	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
316	C₂²×C₈	—	2	8	no	—
317	C₂²×C₈	—	2	1	no	—
318	C₂²×C₈	—	2	2	no	—
319	C₂²×C₈	—	2	2	no	—
320	C₂²×C₈	—	2	4	no	—
321	C₂²×C₈	—	2	1	no	—
322	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
323	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
324	C₂²×C₈	D₄×C₆₁	1	2	yes	—
325	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
326	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
327	#117	—	2	1	no	—
328	#117	—	2	1	no	—
329	#117	—	2	2	no	—
330	#117	—	2	2	no	—
331	#117	C₂×C₄×C₆₁	1	2	yes	—
332	#117	C₂³×C₆₁	1	2	yes	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
339	#108	—	2	8	no	—
340	C₄⋊C₈	—	2	4	no	—
341	C₄⋊C₈	—	2	4	no	—
342	#104	—	2	8	no	—
343	#103	C₂×C₄×C₆₁	1	8	yes	—
344	#102	C₂×C₄×C₆₁	1	8	yes	—
345	C₂⁴	—	2	1	no	—
346	C₂⁴	#41×C₆₁	1	1	yes	characteristic
347	#41	—	2	4	no	—
348	#41	—	2	4	no	—
349	#41	—	2	4	no	—
350	#41	—	2	4	no	—
351	#41	—	2	4	no	—
352	#41	—	2	2	no	—
353	#41	—	2	2	no	—
354	#41	C₄⋊C₄×C₆₁	1	8	yes	—
355	#41	C₂×D₄×C₆₁	1	4	yes	—
356	#41	C₂×Q₈×C₆₁	1	4	yes	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	C₄⋊C₄×C₆₁	1	4	yes	—
360	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	C₄⋊C₄×C₆₁	1	4	yes	—
368	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
377	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
382	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
383	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
384	C₂²×C₄	#41×C₆₁	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
386	M₁₆	—	2	16	no	—
387	M₁₆	—	2	4	no	—
388	M₁₆	—	2	4	no	—
389	M₁₆	—	2	4	no	—
390	M₁₆	—	2	2	no	—
391	M₁₆	—	2	2	no	—
392	M₁₆	—	2	2	no	—
393	M₁₆	—	4	2	no	—
394	M₁₆	C₂×D₄×C₆₁	1	4	yes	—
395	C₂×C₈	—	2	16	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	4	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	4	2	no	—
407	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
408	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
409	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	4	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	4	no	—
424	C₂³	C₄×D₄×C₆₁	1	1	yes	characteristic
425	C₂³	C₄×D₄×C₆₁	1	1	yes	characteristic
426	C₂³	C₂²⋊Q₈×C₆₁	1	2	yes	—
427	C₂³	#123×C₆₁	1	2	yes	—
428	C₂³	C₂×#41×C₆₁	1	1	yes	characteristic
429	Q₈	—	2	4	no	—
430	Q₈	—	2	2	no	—
431	Q₈	C₂×C₄⋊C₄×C₆₁	1	4	yes	—
432	D₄	—	2	8	no	—
433	D₄	—	2	4	no	—
434	D₄	—	2	4	no	—
435	D₄	—	2	4	no	—
436	D₄	—	2	2	no	—
437	D₄	C₂×C₄⋊C₄×C₆₁	1	4	yes	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
448	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
449	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
450	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
451	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
452	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
453	C₂×C₄	#120×C₆₁	1	2	yes	—
454	C₂×C₄	#120×C₆₁	1	2	yes	—
455	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
456	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
457	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
458	C₂×C₄	#123×C₆₁	1	2	yes	—
459	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
463	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
464	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
465	C₈	—	2	4	no	—
466	C₈	—	2	2	no	—
467	C₈	—	2	4	no	—
468	C₈	—	2	2	no	—
469	C₈	—	4	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	4	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	8	no	—
477	C₂²	—	4	4	no	—
478	C₂²	C₆₁×#385	1	2	yes	—
479	C₂²	C₆₁×#385	1	2	yes	—
480	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
481	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
482	C₂²	C₂×#123×C₆₁	1	1	yes	characteristic
483	C₄	—	2	4	no	—
484	C₄	—	4	4	no	—
485	C₄	—	8	2	no	—
486	C₄	C₆₁×#385	1	2	yes	—
487	C₄	C₆₁×#385	1	2	yes	—
488	C₄	C₂²×C₄⋊C₄×C₆₁	1	1	yes	characteristic
489	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
490	C₄	C₂×#120×C₆₁	1	1	yes	characteristic
491	C₄	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
492	C₂	—	2	1	no	—
493	C₂	—	2	2	no	—
494	C₂	—	2	2	no	—
495	C₂	—	2	1	no	—
496	C₂	—	4	4	no	—
497	C₂	C₂×C₆₁×#385	1	1	yes	characteristic
498	C₂	C₆₁×#2955	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 ◁ C₂³×C₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#430	C₂	semidirect
3. C₂×C₆₁×#424	C₂	semidirect
6. C₆₁×#1866	C₂	semidirect
7. C₆₁×#1733	C₂	semidirect
8. C₆₁×#1729	C₂	semidirect
23. C₂×#108×C₆₁	C₂²	semidirect
26. C₆₁×#424	C₂²	semidirect
30. C₆₁×#419	C₄	semidirect
31. C₆₁×#418	C₄	semidirect
32. C₆₁×#417	C₄	semidirect
34. C₆₁×#339	C₂²	semidirect
35. C₆₁×#336	C₂²	semidirect
220. #20884	C₆₁	direct (N × H)
244. C₂×#430	C₂×C₆₁	semidirect
245. C₂×#424	C₂×C₆₁	semidirect
248. #1866	C₂×C₆₁	semidirect
249. #1733	C₂×C₆₁	semidirect
250. #1729	C₂×C₆₁	semidirect
272. C₂×#108	C₂²×C₆₁	semidirect
275. #424	C₂²×C₆₁	semidirect
279. #419	C₄×C₆₁	semidirect
280. #418	C₄×C₆₁	semidirect
281. #417	C₄×C₆₁	semidirect
283. #339	C₂²×C₆₁	semidirect
284. #336	C₂²×C₆₁	semidirect
285. C₆₁	#20884	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#131×C₆₁	2
C₂×C₆₁×#430	2
C₂×C₆₁×#424	2
C₂×C₆₁×#421	2
C₆₁×#2896	2
C₆₁×#1866	2
C₆₁×#1733	2
C₆₁×#1729	2
#20884	61

Subgroups — C61×#20884 #29524317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#20884 #29524317