Subgroups — C₆₁×#25839 #29529272

Order 15616.

1062 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#476	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2567	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2059	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1984	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1862	C₂	1	4	yes	maximal
9	C₄×#102×C₆₁	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#554	—	2	4	no	—
11	C₆₁×#554	—	2	4	no	—
12	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#125×C₆₁	C₂²	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
17	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
21	C₆₁×#500	—	2	4	no	—
22	C₆₁×#476	—	2	4	no	—
23	C₂×#107×C₆₁	C₂²	1	4	yes	—
24	C₂×#106×C₆₁	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#102×C₆₁	C₂²	1	2	yes	—
27	C₂×#102×C₆₁	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₆₁×#395	—	2	2	no	—
30	C₆₁×#391	—	2	1	no	—
31	C₆₁×#389	C₂²	1	4	yes	—
32	C₆₁×#384	—	2	1	no	—
33	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#340	C₂²	1	2	yes	—
35	C₆₁×#340	C₂²	1	4	yes	—
36	C₆₁×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₆₁	—	2	1	no	—
38	C₂²×Q₈×C₆₁	—	2	1	no	—
39	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
40	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₆₁	—	2	1	no	—
42	C₂³×C₄×C₆₁	—	2	2	no	—
43	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
45	C₄⋊Q₈×C₆₁	—	2	2	no	—
46	C₄⋊Q₈×C₆₁	—	2	2	no	—
47	C₄⋊Q₈×C₆₁	—	2	2	no	—
48	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
49	#125×C₆₁	—	2	4	no	—
50	#125×C₆₁	—	2	4	no	—
51	C₂²⋊Q₈×C₆₁	—	2	8	no	—
52	C₂²⋊Q₈×C₆₁	—	2	16	no	—
53	C₄×Q₈×C₆₁	—	2	2	no	—
54	C₄×Q₈×C₆₁	—	2	2	no	—
55	C₄×D₄×C₆₁	—	2	4	no	—
56	C₄×D₄×C₆₁	—	2	4	no	—
57	C₄×D₄×C₆₁	—	2	2	no	—
58	C₄×D₄×C₆₁	D₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
65	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
73	C₂×C₄²×C₆₁	—	2	1	no	—
74	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
75	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
76	#107×C₆₁	—	2	8	no	—
77	#106×C₆₁	—	2	4	no	—
78	C₄⋊C₈×C₆₁	—	2	2	no	—
79	#102×C₆₁	—	2	4	no	—
80	#102×C₆₁	Q₈	1	8	yes	complemented
81	C₄×C₈×C₆₁	—	2	2	no	—
82	#95×C₆₁	—	2	1	no	—
83	#95×C₆₁	—	2	4	no	—
84	C₂⁴×C₆₁	—	2	1	no	—
85	C₂×Q₈×C₆₁	—	2	2	no	—
86	C₂×Q₈×C₆₁	—	2	4	no	—
87	C₂×Q₈×C₆₁	—	2	2	no	—
88	C₂×Q₈×C₆₁	—	2	2	no	—
89	C₂×Q₈×C₆₁	—	4	2	no	—
90	C₂×Q₈×C₆₁	—	8	2	no	—
91	C₂×Q₈×C₆₁	—	8	2	no	—
92	C₂×D₄×C₆₁	—	2	1	no	—
93	C₂×D₄×C₆₁	—	2	2	no	—
94	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
95	C₂×D₄×C₆₁	C₂×Q₈	1	4	yes	—
96	C₂²×C₄×C₆₁	—	2	2	no	—
97	C₂²×C₄×C₆₁	—	2	1	no	—
98	C₂²×C₄×C₆₁	—	2	2	no	—
99	C₂²×C₄×C₆₁	—	2	8	no	—
100	C₂²×C₄×C₆₁	—	2	4	no	—
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	—	4	2	no	—
103	C₂²×C₄×C₆₁	—	4	2	no	—
104	C₂²×C₄×C₆₁	—	8	4	no	—
105	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₆₁	—	2	2	no	—
111	C₂×C₈×C₆₁	—	2	2	no	—
112	C₂×C₈×C₆₁	—	2	2	no	—
113	C₂×C₈×C₆₁	—	2	4	no	—
114	C₂×C₈×C₆₁	C₂×Q₈	1	4	yes	—
115	C₄⋊C₄×C₆₁	—	2	8	no	—
116	C₄⋊C₄×C₆₁	—	2	8	no	—
117	C₄⋊C₄×C₆₁	—	2	2	no	—
118	C₄⋊C₄×C₆₁	—	2	4	no	—
119	C₄⋊C₄×C₆₁	—	2	4	no	—
120	C₄⋊C₄×C₆₁	—	2	1	no	—
121	C₄⋊C₄×C₆₁	—	2	2	no	—
122	C₄⋊C₄×C₆₁	—	2	2	no	—
123	C₄⋊C₄×C₆₁	—	2	2	no	—
124	C₄⋊C₄×C₆₁	—	2	2	no	—
125	C₄⋊C₄×C₆₁	—	4	2	no	—
126	C₄⋊C₄×C₆₁	—	8	4	no	—
127	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
129	C₄⋊C₄×C₆₁	C₂×Q₈	1	4	yes	—
130	C₂²⋊C₄×C₆₁	—	2	8	no	—
131	C₂²⋊C₄×C₆₁	—	2	4	no	—
132	C₄²×C₆₁	—	2	2	no	—
133	C₄²×C₆₁	—	2	2	no	—
134	C₄²×C₆₁	—	4	2	no	—
135	C₄²×C₆₁	C₂×D₄	1	2	yes	—
136	C₄²×C₆₁	C₂×D₄	1	2	yes	—
137	C₂³×C₆₁	—	2	2	no	—
138	C₂³×C₆₁	—	2	4	no	—
139	C₂³×C₆₁	—	4	1	no	—
140	C₂³×C₆₁	—	4	1	no	—
141	C₂³×C₆₁	—	4	2	no	—
142	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₆₁	—	4	4	no	—
144	Q₈×C₆₁	—	8	4	no	—
145	Q₈×C₆₁	—	8	4	no	—
146	D₄×C₆₁	—	2	2	no	—
147	D₄×C₆₁	—	2	4	no	—
148	D₄×C₆₁	C₄⋊Q₈	1	4	yes	—
149	C₂×C₄×C₆₁	—	2	2	no	—
150	C₂×C₄×C₆₁	—	2	2	no	—
151	C₂×C₄×C₆₁	—	2	2	no	—
152	C₂×C₄×C₆₁	—	2	2	no	—
153	C₂×C₄×C₆₁	—	2	4	no	—
154	C₂×C₄×C₆₁	—	2	4	no	—
155	C₂×C₄×C₆₁	—	2	2	no	—
156	C₂×C₄×C₆₁	—	2	2	no	—
157	C₂×C₄×C₆₁	—	2	4	no	—
158	C₂×C₄×C₆₁	—	4	2	no	—
159	C₂×C₄×C₆₁	—	4	1	no	—
160	C₂×C₄×C₆₁	—	4	1	no	—
161	C₂×C₄×C₆₁	—	4	2	no	—
162	C₂×C₄×C₆₁	—	4	4	no	—
163	C₂×C₄×C₆₁	—	4	8	no	—
164	C₂×C₄×C₆₁	—	4	2	no	—
165	C₂×C₄×C₆₁	—	4	4	no	—
166	C₂×C₄×C₆₁	—	8	8	no	—
167	C₂×C₄×C₆₁	#120	1	2	yes	—
168	C₂×C₄×C₆₁	#120	1	2	yes	—
169	C₂×C₄×C₆₁	#135	1	2	yes	—
170	C₂×C₄×C₆₁	#137	1	2	yes	—
171	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
174	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
175	C₈×C₆₁	—	2	4	no	—
176	C₈×C₆₁	—	4	2	no	—
177	#25839	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂²×C₆₁	—	2	4	no	—
179	C₂²×C₆₁	—	4	4	no	—
180	C₂²×C₆₁	—	4	4	no	—
181	C₂²×C₆₁	—	4	2	no	—
182	C₂²×C₆₁	—	4	2	no	—
183	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
184	C₂²×C₆₁	D₄×Q₈	1	2	yes	—
185	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
186	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
187	C₂²×C₆₁	#576	1	2	yes	—
188	C₄×C₆₁	—	2	2	no	—
189	C₄×C₆₁	—	4	4	no	—
190	C₄×C₆₁	—	4	2	no	—
191	C₄×C₆₁	—	4	2	no	—
192	C₄×C₆₁	—	4	2	no	—
193	C₄×C₆₁	—	4	4	no	—
194	C₄×C₆₁	—	8	2	no	—
195	C₄×C₆₁	#452	1	4	yes	—
196	C₄×C₆₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
197	C₄×C₆₁	#536	1	1	yes	characteristic
198	C₄×C₆₁	D₄×Q₈	1	2	yes	—
199	C₂×#554	C₂×C₆₁	1	1	yes	characteristic
200	C₂×#500	C₂×C₆₁	1	1	yes	characteristic, complemented
201	C₂×#476	C₂×C₆₁	1	1	yes	characteristic
202	#2567	C₂×C₆₁	1	1	yes	characteristic, complemented
203	#2059	C₂×C₆₁	1	4	yes	complemented
204	#1987	C₂×C₆₁	1	1	yes	characteristic, complemented
205	#1984	C₂×C₆₁	1	1	yes	characteristic, complemented
206	#1862	C₂×C₆₁	1	4	yes	—
207	C₄×#102	C₂×C₆₁	1	1	yes	characteristic
208	C₂×C₆₁	—	4	4	no	—
209	C₂×C₆₁	#2434	1	1	yes	characteristic
210	C₂×C₆₁	C₂×#452	1	1	yes	characteristic
211	C₂×C₆₁	#3008	1	1	yes	characteristic
212	C₂×C₆₁	#3380	1	2	yes	—
213	C₂×C₆₁	#3385	1	2	yes	—
214	#554	—	2	4	no	—
215	#554	—	2	4	no	—
216	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
217	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
218	C₂×#125	C₂²×C₆₁	1	2	yes	—
219	C₂×C₂²⋊Q₈	—	2	1	no	—
220	C₂×C₂²⋊Q₈	—	2	2	no	—
221	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
222	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
223	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
224	C₂²×C₄⋊C₄	—	2	1	no	—
225	#500	—	2	4	no	—
226	#476	—	2	4	no	—
227	C₂×#107	C₂²×C₆₁	1	4	yes	—
228	C₂×#106	C₂²×C₆₁	1	2	yes	—
229	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
230	C₂×#102	C₂²×C₆₁	1	2	yes	—
231	C₂×#102	C₂²×C₆₁	1	2	yes	—
232	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
233	#395	—	2	2	no	—
234	#391	—	2	1	no	—
235	#389	C₂²×C₆₁	1	4	yes	—
236	#384	—	2	1	no	—
237	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
238	#340	C₂²×C₆₁	1	2	yes	—
239	#340	C₂²×C₆₁	1	4	yes	—
240	#336	C₂²×C₆₁	1	4	yes	—
241	C₆₁	#25839	1	1	yes	characteristic, direct product factor, Sylow
242	C₂²×Q₈	—	2	1	no	—
243	C₂²×Q₈	—	2	1	no	—
244	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
245	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	—	2	2	no	—
248	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
249	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
250	C₄⋊Q₈	—	2	2	no	—
251	C₄⋊Q₈	—	2	2	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
254	#125	—	2	4	no	—
255	#125	—	2	4	no	—
256	C₂²⋊Q₈	—	2	8	no	—
257	C₂²⋊Q₈	—	2	16	no	—
258	C₄×Q₈	—	2	2	no	—
259	C₄×Q₈	—	2	2	no	—
260	C₄×D₄	—	2	4	no	—
261	C₄×D₄	—	2	4	no	—
262	C₄×D₄	—	2	2	no	—
263	C₄×D₄	D₄×C₆₁	1	4	yes	—
264	C₂×C₄⋊C₄	—	2	8	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	4	no	—
270	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
271	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
280	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
281	#107	—	2	8	no	—
282	#106	—	2	4	no	—
283	C₄⋊C₈	—	2	2	no	—
284	#102	—	2	4	no	—
285	#102	Q₈×C₆₁	1	8	yes	complemented
286	C₄×C₈	—	2	2	no	—
287	#95	—	2	1	no	—
288	#95	—	2	4	no	—
289	C₂⁴	—	2	1	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	8	2	no	—
296	C₂×Q₈	—	8	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
300	C₂×D₄	C₂×Q₈×C₆₁	1	4	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	8	4	no	—
310	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	C₂×Q₈×C₆₁	1	4	yes	—
320	C₄⋊C₄	—	2	8	no	—
321	C₄⋊C₄	—	2	8	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	8	4	no	—
332	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
333	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
334	C₄⋊C₄	C₂×Q₈×C₆₁	1	4	yes	—
335	C₂²⋊C₄	—	2	8	no	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	4	2	no	—
340	C₄²	C₂×D₄×C₆₁	1	2	yes	—
341	C₄²	C₂×D₄×C₆₁	1	2	yes	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
348	Q₈	—	4	4	no	—
349	Q₈	—	8	4	no	—
350	Q₈	—	8	4	no	—
351	D₄	—	2	2	no	—
352	D₄	—	2	4	no	—
353	D₄	C₄⋊Q₈×C₆₁	1	4	yes	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	8	8	no	—
372	C₂×C₄	#120×C₆₁	1	2	yes	—
373	C₂×C₄	#120×C₆₁	1	2	yes	—
374	C₂×C₄	#135×C₆₁	1	2	yes	—
375	C₂×C₄	#137×C₆₁	1	2	yes	—
376	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
378	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
379	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
380	C₈	—	2	4	no	—
381	C₈	—	4	2	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
388	C₂²	D₄×Q₈×C₆₁	1	2	yes	—
389	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
390	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
391	C₂²	C₆₁×#576	1	2	yes	—
392	C₄	—	2	2	no	—
393	C₄	—	4	4	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	4	no	—
398	C₄	—	8	2	no	—
399	C₄	C₆₁×#452	1	4	yes	—
400	C₄	C₂×C₄⋊Q₈×C₆₁	1	1	yes	characteristic
401	C₄	C₆₁×#536	1	1	yes	characteristic
402	C₄	D₄×Q₈×C₆₁	1	2	yes	—
403	C₂	—	4	4	no	—
404	C₂	C₆₁×#2434	1	1	yes	characteristic
405	C₂	C₂×C₆₁×#452	1	1	yes	characteristic
406	C₂	C₆₁×#3008	1	1	yes	characteristic
407	C₂	C₆₁×#3380	1	2	yes	—
408	C₂	C₆₁×#3385	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×#500	C₂	semidirect
4. C₆₁×#2567	C₂	semidirect
5. C₆₁×#2059	C₂	semidirect
6. C₆₁×#1987	C₂	semidirect
7. C₆₁×#1984	C₂	semidirect
80. #102×C₆₁	Q₈	semidirect
177. #25839	C₆₁	direct (N × H)
200. C₂×#500	C₂×C₆₁	semidirect
202. #2567	C₂×C₆₁	semidirect
203. #2059	C₂×C₆₁	semidirect
204. #1987	C₂×C₆₁	semidirect
205. #1984	C₂×C₆₁	semidirect
241. C₆₁	#25839	direct (N × H)
285. #102	Q₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#554	2
C₂×C₆₁×#500	2
C₂×C₆₁×#476	2
C₆₁×#2567	2
C₆₁×#2059	2
C₆₁×#1987	2
C₆₁×#1984	2
C₆₁×#1862	2
C₄×#102×C₆₁	2
#25839	61

Subgroups — C61×#25839 #29529272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25839 #29529272