Subgroups — C₆₁×#24201 #29527634

Order 15616.

1068 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#556	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#440	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2581	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2042	C₂	1	2	yes	maximal
6	C₆₁×#2015	C₂	1	2	yes	maximal
7	C₆₁×#1985	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1960	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1878	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1863	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1804	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#556	—	2	4	no	—
15	C₆₁×#556	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#126×C₆₁	—	2	2	no	—
18	C₂×#124×C₆₁	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
20	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#117×C₆₁	—	2	1	no	—
25	C₆₁×#462	—	2	4	no	—
26	C₆₁×#440	—	2	4	no	—
27	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#103×C₆₁	C₂²	1	2	yes	—
30	C₂×#103×C₆₁	C₂²	1	2	yes	—
31	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#103×C₆₁	C₂²	1	2	yes	—
33	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#102×C₆₁	C₂²	1	2	yes	—
35	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
36	C₆₁×#400	—	2	1	no	—
37	C₆₁×#395	—	2	1	no	—
38	C₆₁×#391	C₂²	1	2	yes	—
39	C₆₁×#389	C₂²	1	2	yes	—
40	C₆₁×#387	—	2	2	no	—
41	C₆₁×#382	C₂²	1	1	yes	characteristic
42	C₆₁×#340	C₂²	1	2	yes	—
43	C₆₁×#336	C₂²	1	2	yes	—
44	C₆₁×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
47	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₆₁	—	2	1	no	—
50	C₂×Q₁₆×C₆₁	—	2	4	no	—
51	C₂×Q₁₆×C₆₁	—	2	4	no	—
52	C₂×Q₁₆×C₆₁	—	4	2	no	—
53	C₂×SD₁₆×C₆₁	—	2	2	no	—
54	C₂×SD₁₆×C₆₁	—	2	2	no	—
55	C₂×SD₁₆×C₆₁	—	2	2	no	—
56	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
57	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₆₁	—	2	2	no	—
60	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
61	#126×C₆₁	—	2	16	no	—
62	#124×C₆₁	—	2	4	no	—
63	#124×C₆₁	—	2	4	no	—
64	C₂²⋊Q₈×C₆₁	—	2	8	no	—
65	C₄×Q₈×C₆₁	—	2	4	no	—
66	C₄×Q₈×C₆₁	—	2	4	no	—
67	C₄×Q₈×C₆₁	—	2	2	no	—
68	C₄×Q₈×C₆₁	—	2	2	no	—
69	C₄×Q₈×C₆₁	—	2	2	no	—
70	C₄×Q₈×C₆₁	—	2	2	no	—
71	C₄×D₄×C₆₁	—	2	2	no	—
72	C₄×D₄×C₆₁	D₄	1	4	yes	—
73	#117×C₆₁	—	2	8	no	—
74	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
78	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
87	C₂×C₄²×C₆₁	—	2	2	no	—
88	C₂×C₄²×C₆₁	—	2	1	no	—
89	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
90	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
91	#107×C₆₁	—	2	2	no	—
92	C₄⋊C₈×C₆₁	—	2	2	no	—
93	#103×C₆₁	—	2	4	no	—
94	#103×C₆₁	—	2	4	no	—
95	#103×C₆₁	—	2	2	no	—
96	#103×C₆₁	—	4	2	no	—
97	#102×C₆₁	—	2	2	no	—
98	#102×C₆₁	—	4	2	no	—
99	#97×C₆₁	—	2	2	no	—
100	#95×C₆₁	—	2	1	no	—
101	#95×C₆₁	—	2	1	no	—
102	#95×C₆₁	—	2	2	no	—
103	#95×C₆₁	—	2	2	no	—
104	#95×C₆₁	—	2	2	no	—
105	C₂⁴×C₆₁	—	2	1	no	—
106	C₂×Q₈×C₆₁	—	2	2	no	—
107	C₂×Q₈×C₆₁	—	2	2	no	—
108	C₂×Q₈×C₆₁	—	2	1	no	—
109	C₂×Q₈×C₆₁	—	2	1	no	—
110	C₂×Q₈×C₆₁	—	2	1	no	—
111	C₂×Q₈×C₆₁	—	2	2	no	—
112	C₂×Q₈×C₆₁	—	2	1	no	—
113	C₂×Q₈×C₆₁	—	2	2	no	—
114	C₂×Q₈×C₆₁	—	2	2	no	—
115	C₂×Q₈×C₆₁	—	2	1	no	—
116	C₂×Q₈×C₆₁	—	2	2	no	—
117	C₂×Q₈×C₆₁	—	4	2	no	—
118	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
119	C₂×Q₈×C₆₁	#41	1	2	yes	—
120	C₂×D₄×C₆₁	—	2	1	no	—
121	C₂×D₄×C₆₁	—	2	1	no	—
122	C₂×D₄×C₆₁	—	2	1	no	—
123	C₂×D₄×C₆₁	—	2	1	no	—
124	C₂×D₄×C₆₁	—	2	1	no	—
125	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₆₁	—	2	1	no	—
127	C₂²×C₄×C₆₁	—	2	1	no	—
128	C₂²×C₄×C₆₁	—	2	2	no	—
129	C₂²×C₄×C₆₁	—	2	4	no	—
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	2	1	no	—
132	C₂²×C₄×C₆₁	—	4	4	no	—
133	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
138	Q₁₆×C₆₁	—	4	8	no	—
139	SD₁₆×C₆₁	—	2	8	no	—
140	C₂×C₈×C₆₁	—	2	1	no	—
141	C₂×C₈×C₆₁	—	2	1	no	—
142	C₂×C₈×C₆₁	—	2	1	no	—
143	C₂×C₈×C₆₁	—	2	2	no	—
144	C₂×C₈×C₆₁	—	2	2	no	—
145	C₂×C₈×C₆₁	—	2	2	no	—
146	C₂×C₈×C₆₁	—	2	1	no	—
147	C₂×C₈×C₆₁	—	2	1	no	—
148	C₂×C₈×C₆₁	#41	1	2	yes	—
149	C₄⋊C₄×C₆₁	—	2	8	no	—
150	C₄⋊C₄×C₆₁	—	2	4	no	—
151	C₄⋊C₄×C₆₁	—	2	4	no	—
152	C₄⋊C₄×C₆₁	—	2	2	no	—
153	C₄⋊C₄×C₆₁	—	2	4	no	—
154	C₄⋊C₄×C₆₁	—	2	1	no	—
155	C₄⋊C₄×C₆₁	—	2	1	no	—
156	C₄⋊C₄×C₆₁	—	2	1	no	—
157	C₄⋊C₄×C₆₁	—	2	2	no	—
158	C₄⋊C₄×C₆₁	—	2	2	no	—
159	C₄⋊C₄×C₆₁	—	4	4	no	—
160	C₄⋊C₄×C₆₁	—	4	2	no	—
161	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
162	C₂²⋊C₄×C₆₁	—	2	8	no	—
163	C₂²⋊C₄×C₆₁	—	2	8	no	—
164	C₂²⋊C₄×C₆₁	—	2	4	no	—
165	C₄²×C₆₁	—	2	8	no	—
166	C₄²×C₆₁	—	2	2	no	—
167	C₄²×C₆₁	—	2	2	no	—
168	C₄²×C₆₁	—	4	2	no	—
169	C₄²×C₆₁	C₂×D₄	1	2	yes	—
170	C₄²×C₆₁	C₂×D₄	1	2	yes	—
171	C₂³×C₆₁	—	2	2	no	—
172	C₂³×C₆₁	—	4	1	no	—
173	C₂³×C₆₁	—	4	1	no	—
174	C₂³×C₆₁	—	4	2	no	—
175	C₂³×C₆₁	—	4	2	no	—
176	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
177	Q₈×C₆₁	—	2	2	no	—
178	Q₈×C₆₁	—	2	2	no	—
179	Q₈×C₆₁	—	2	4	no	—
180	Q₈×C₆₁	—	2	4	no	—
181	Q₈×C₆₁	—	4	4	no	—
182	Q₈×C₆₁	—	4	2	no	—
183	Q₈×C₆₁	—	4	2	no	—
184	Q₈×C₆₁	—	4	1	no	—
185	Q₈×C₆₁	—	4	1	no	—
186	D₄×C₆₁	—	2	2	no	—
187	D₄×C₆₁	—	2	2	no	—
188	D₄×C₆₁	—	4	1	no	—
189	D₄×C₆₁	—	4	1	no	—
190	C₂×C₄×C₆₁	—	2	2	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	2	2	no	—
193	C₂×C₄×C₆₁	—	2	2	no	—
194	C₂×C₄×C₆₁	—	2	4	no	—
195	C₂×C₄×C₆₁	—	2	2	no	—
196	C₂×C₄×C₆₁	—	2	2	no	—
197	C₂×C₄×C₆₁	—	2	2	no	—
198	C₂×C₄×C₆₁	—	2	2	no	—
199	C₂×C₄×C₆₁	—	2	4	no	—
200	C₂×C₄×C₆₁	—	4	8	no	—
201	C₂×C₄×C₆₁	—	4	1	no	—
202	C₂×C₄×C₆₁	—	4	2	no	—
203	C₂×C₄×C₆₁	—	4	1	no	—
204	C₂×C₄×C₆₁	—	4	2	no	—
205	C₂×C₄×C₆₁	—	4	2	no	—
206	C₂×C₄×C₆₁	—	4	1	no	—
207	C₂×C₄×C₆₁	—	4	2	no	—
208	C₂×C₄×C₆₁	—	4	2	no	—
209	C₂×C₄×C₆₁	—	4	2	no	—
210	C₂×C₄×C₆₁	—	4	2	no	—
211	C₂×C₄×C₆₁	#120	1	2	yes	—
212	C₂×C₄×C₆₁	#120	1	2	yes	—
213	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
219	C₈×C₆₁	—	2	2	no	—
220	C₈×C₆₁	—	4	1	no	—
221	C₈×C₆₁	—	4	2	no	—
222	#24201	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂²×C₆₁	—	4	2	no	—
224	C₂²×C₆₁	—	4	2	no	—
225	C₂²×C₆₁	—	4	2	no	—
226	C₂²×C₆₁	—	8	2	no	—
227	C₂²×C₆₁	—	8	2	no	—
228	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
229	C₂²×C₆₁	#548	1	1	yes	characteristic
230	C₂²×C₆₁	#550	1	1	yes	characteristic
231	C₂²×C₆₁	#575	1	2	yes	—
232	C₂²×C₆₁	#578	1	2	yes	—
233	C₄×C₆₁	—	2	2	no	—
234	C₄×C₆₁	—	2	2	no	—
235	C₄×C₆₁	—	4	4	no	—
236	C₄×C₆₁	—	4	2	no	—
237	C₄×C₆₁	—	4	2	no	—
238	C₄×C₆₁	—	4	2	no	—
239	C₄×C₆₁	—	4	2	no	—
240	C₄×C₆₁	—	8	2	no	—
241	C₄×C₆₁	—	8	1	no	—
242	C₄×C₆₁	#525	1	1	yes	characteristic
243	C₄×C₆₁	#537	1	1	yes	characteristic
244	C₄×C₆₁	#546	1	1	yes	characteristic
245	C₄×C₆₁	#547	1	1	yes	characteristic
246	C₂×#556	C₂×C₆₁	1	1	yes	characteristic
247	C₂×#462	C₂×C₆₁	1	1	yes	characteristic, complemented
248	C₂×#440	C₂×C₆₁	1	1	yes	characteristic
249	#2581	C₂×C₆₁	1	1	yes	characteristic, complemented
250	#2042	C₂×C₆₁	1	2	yes	—
251	#2015	C₂×C₆₁	1	2	yes	—
252	#1985	C₂×C₆₁	1	1	yes	characteristic, complemented
253	#1960	C₂×C₆₁	1	1	yes	characteristic, complemented
254	#1878	C₂×C₆₁	1	2	yes	complemented
255	#1863	C₂×C₆₁	1	2	yes	complemented
256	#1804	C₂×C₆₁	1	1	yes	characteristic
257	C₂×C₆₁	—	8	2	no	—
258	C₂×C₆₁	#2407	1	1	yes	characteristic
259	C₂×C₆₁	#3005	1	1	yes	characteristic
260	C₂×C₆₁	#3011	1	1	yes	characteristic
261	C₂×C₆₁	#3377	1	2	yes	—
262	C₂×C₆₁	#3402	1	2	yes	—
263	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
264	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
265	#556	—	2	4	no	—
266	#556	—	2	4	no	—
267	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
268	C₂×#126	—	2	2	no	—
269	C₂×#124	C₂²×C₆₁	1	2	yes	—
270	C₂×C₂²⋊Q₈	—	2	1	no	—
271	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
272	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
273	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
275	C₂×#117	—	2	1	no	—
276	#462	—	2	4	no	—
277	#440	—	2	4	no	—
278	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
279	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
280	C₂×#103	C₂²×C₆₁	1	2	yes	—
281	C₂×#103	C₂²×C₆₁	1	2	yes	—
282	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
283	C₂×#103	C₂²×C₆₁	1	2	yes	—
284	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
285	C₂×#102	C₂²×C₆₁	1	2	yes	—
286	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
287	#400	—	2	1	no	—
288	#395	—	2	1	no	—
289	#391	C₂²×C₆₁	1	2	yes	—
290	#389	C₂²×C₆₁	1	2	yes	—
291	#387	—	2	2	no	—
292	#382	C₂²×C₆₁	1	1	yes	characteristic
293	#340	C₂²×C₆₁	1	2	yes	—
294	#336	C₂²×C₆₁	1	2	yes	—
295	#336	C₂²×C₆₁	1	2	yes	—
296	C₆₁	#24201	1	1	yes	characteristic, direct product factor, Sylow
297	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
298	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
299	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
300	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
301	C₂³×C₄	—	2	1	no	—
302	C₂×Q₁₆	—	2	4	no	—
303	C₂×Q₁₆	—	2	4	no	—
304	C₂×Q₁₆	—	4	2	no	—
305	C₂×SD₁₆	—	2	2	no	—
306	C₂×SD₁₆	—	2	2	no	—
307	C₂×SD₁₆	—	2	2	no	—
308	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
309	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
313	#126	—	2	16	no	—
314	#124	—	2	4	no	—
315	#124	—	2	4	no	—
316	C₂²⋊Q₈	—	2	8	no	—
317	C₄×Q₈	—	2	4	no	—
318	C₄×Q₈	—	2	4	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	D₄×C₆₁	1	4	yes	—
325	#117	—	2	8	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
332	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₄²	—	2	2	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
342	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
343	#107	—	2	2	no	—
344	C₄⋊C₈	—	2	2	no	—
345	#103	—	2	4	no	—
346	#103	—	2	4	no	—
347	#103	—	2	2	no	—
348	#103	—	4	2	no	—
349	#102	—	2	2	no	—
350	#102	—	4	2	no	—
351	#97	—	2	2	no	—
352	#95	—	2	1	no	—
353	#95	—	2	1	no	—
354	#95	—	2	2	no	—
355	#95	—	2	2	no	—
356	#95	—	2	2	no	—
357	C₂⁴	—	2	1	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	4	2	no	—
370	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
371	C₂×Q₈	#41×C₆₁	1	2	yes	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
386	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
390	Q₁₆	—	4	8	no	—
391	SD₁₆	—	2	8	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	#41×C₆₁	1	2	yes	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	4	4	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	2	8	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₄²	—	2	8	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	4	2	no	—
421	C₄²	C₂×D₄×C₆₁	1	2	yes	—
422	C₄²	C₂×D₄×C₆₁	1	2	yes	—
423	C₂³	—	2	2	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
429	Q₈	—	2	2	no	—
430	Q₈	—	2	4	no	—
431	Q₈	—	2	4	no	—
432	Q₈	—	2	2	no	—
433	Q₈	—	4	4	no	—
434	Q₈	—	4	2	no	—
435	Q₈	—	4	1	no	—
436	Q₈	—	4	1	no	—
437	Q₈	—	4	2	no	—
438	D₄	—	2	2	no	—
439	D₄	—	2	2	no	—
440	D₄	—	4	1	no	—
441	D₄	—	4	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	4	8	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	#120×C₆₁	1	2	yes	—
464	C₂×C₄	#120×C₆₁	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
466	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
467	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
468	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
469	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
470	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
471	C₈	—	2	2	no	—
472	C₈	—	4	1	no	—
473	C₈	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
480	C₂²	C₆₁×#548	1	1	yes	characteristic
481	C₂²	C₆₁×#550	1	1	yes	characteristic
482	C₂²	C₆₁×#575	1	2	yes	—
483	C₂²	C₆₁×#578	1	2	yes	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	4	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	8	2	no	—
492	C₄	—	8	1	no	—
493	C₄	C₆₁×#525	1	1	yes	characteristic
494	C₄	C₆₁×#537	1	1	yes	characteristic
495	C₄	C₆₁×#546	1	1	yes	characteristic
496	C₄	C₆₁×#547	1	1	yes	characteristic
497	C₂	—	8	2	no	—
498	C₂	C₆₁×#2407	1	1	yes	characteristic
499	C₂	C₆₁×#3005	1	1	yes	characteristic
500	C₂	C₆₁×#3011	1	1	yes	characteristic
501	C₂	C₆₁×#3377	1	2	yes	—
502	C₂	C₆₁×#3402	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×D₄×C₆₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#462	C₂	semidirect
4. C₆₁×#2581	C₂	semidirect
7. C₆₁×#1985	C₂	semidirect
8. C₆₁×#1960	C₂	semidirect
9. C₆₁×#1878	C₂	semidirect
10. C₆₁×#1863	C₂	semidirect
222. #24201	C₆₁	direct (N × H)
247. C₂×#462	C₂×C₆₁	semidirect
249. #2581	C₂×C₆₁	semidirect
252. #1985	C₂×C₆₁	semidirect
253. #1960	C₂×C₆₁	semidirect
254. #1878	C₂×C₆₁	semidirect
255. #1863	C₂×C₆₁	semidirect
296. C₆₁	#24201	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×#556	2
C₂×C₆₁×#462	2
C₂×C₆₁×#440	2
C₆₁×#2581	2
C₆₁×#2042	2
C₆₁×#2015	2
C₆₁×#1985	2
C₆₁×#1960	2
C₆₁×#1878	2
C₆₁×#1863	2
C₆₁×#1804	2
#24201	61

Subgroups — C61×#24201 #29527634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24201 #29527634