Subgroups — C₆₁×#29726 #29533159

Order 15616.

970 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#452	C₂	1	2	yes	maximal
2	C₆₁×#2621	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2311	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2074	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2073	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2056	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2055	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2016	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2013	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1872	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
17	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#452	—	2	8	no	—
20	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
21	C₂×#103×C₆₁	C₂²	1	2	yes	—
22	C₂×#103×C₆₁	C₂²	1	2	yes	—
23	C₂×#103×C₆₁	C₂²	1	2	yes	—
24	C₂×#102×C₆₁	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
26	C₆₁×#398	—	2	2	no	—
27	C₆₁×#397	—	2	2	no	—
28	C₆₁×#391	C₂²	1	1	yes	characteristic
29	C₆₁×#391	C₂²	1	2	yes	—
30	C₆₁×#391	C₂²	1	1	yes	characteristic
31	C₆₁×#390	C₂²	1	1	yes	characteristic
32	C₆₁×#390	C₂²	1	1	yes	characteristic
33	C₆₁×#386	—	2	2	no	—
34	C₆₁×#382	C₂²	1	1	yes	characteristic
35	C₆₁×#380	—	2	2	no	—
36	C₆₁×#340	C₂²	1	2	yes	—
37	C₆₁×#340	C₂²	1	2	yes	—
38	C₆₁×#336	C₂²	1	1	yes	characteristic
39	C₆₁×#336	C₂²	1	1	yes	characteristic
40	C₂×#41×C₆₁	—	2	2	no	—
41	C₂×#41×C₆₁	—	4	2	no	—
42	C₂×#41×C₆₁	—	4	2	no	—
43	C₂×#41×C₆₁	D₄	1	4	yes	—
44	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
45	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₆₁	—	2	1	no	—
47	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₆₁	—	2	1	no	—
49	C₂³×C₄×C₆₁	—	2	1	no	—
50	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
51	C₂×Q₁₆×C₆₁	—	2	4	no	—
52	C₂×Q₁₆×C₆₁	—	4	2	no	—
53	C₂×Q₁₆×C₆₁	—	4	2	no	—
54	C₂×SD₁₆×C₆₁	—	2	4	no	—
55	C₂×SD₁₆×C₆₁	—	4	2	no	—
56	C₂×SD₁₆×C₆₁	—	4	2	no	—
57	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₆₁	—	4	2	no	—
60	C₂²⋊Q₈×C₆₁	—	2	4	no	—
61	C₂²⋊Q₈×C₆₁	—	2	4	no	—
62	#117×C₆₁	—	4	2	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₆₁	—	4	2	no	—
67	C₂×C₄⋊C₄×C₆₁	D₄	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	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
75	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₆₁	—	4	2	no	—
78	#103×C₆₁	—	2	4	no	—
79	#103×C₆₁	—	4	2	no	—
80	#103×C₆₁	—	4	2	no	—
81	#102×C₆₁	—	2	4	no	—
82	C₂²⋊C₈×C₆₁	—	2	4	no	—
83	#95×C₆₁	—	2	2	no	—
84	#95×C₆₁	—	2	2	no	—
85	#95×C₆₁	—	2	2	no	—
86	#95×C₆₁	—	2	4	no	—
87	C₂⁴×C₆₁	—	2	1	no	—
88	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
89	#41×C₆₁	—	4	8	no	—
90	#41×C₆₁	—	4	8	no	—
91	C₂×Q₈×C₆₁	—	2	1	no	—
92	C₂×Q₈×C₆₁	—	2	2	no	—
93	C₂×Q₈×C₆₁	—	2	2	no	—
94	C₂×Q₈×C₆₁	—	2	2	no	—
95	C₂×Q₈×C₆₁	—	2	2	no	—
96	C₂×Q₈×C₆₁	—	2	2	no	—
97	C₂×Q₈×C₆₁	—	2	2	no	—
98	C₂×Q₈×C₆₁	—	2	2	no	—
99	C₂×Q₈×C₆₁	—	2	2	no	—
100	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
101	C₂×D₄×C₆₁	—	2	4	no	—
102	C₂×D₄×C₆₁	—	2	1	no	—
103	C₂×D₄×C₆₁	—	2	2	no	—
104	C₂×D₄×C₆₁	—	2	2	no	—
105	C₂×D₄×C₆₁	—	4	2	no	—
106	C₂×D₄×C₆₁	—	4	2	no	—
107	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₆₁	—	2	2	no	—
109	C₂²×C₄×C₆₁	—	2	2	no	—
110	C₂²×C₄×C₆₁	—	2	1	no	—
111	C₂²×C₄×C₆₁	—	2	4	no	—
112	C₂²×C₄×C₆₁	—	2	2	no	—
113	C₂²×C₄×C₆₁	—	2	1	no	—
114	C₂²×C₄×C₆₁	—	2	1	no	—
115	C₂²×C₄×C₆₁	—	2	2	no	—
116	C₂²×C₄×C₆₁	—	4	2	no	—
117	C₂²×C₄×C₆₁	—	4	2	no	—
118	C₂²×C₄×C₆₁	—	4	2	no	—
119	C₂²×C₄×C₆₁	—	8	2	no	—
120	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₆₁	#41	1	2	yes	—
125	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
126	Q₁₆×C₆₁	—	4	8	no	—
127	SD₁₆×C₆₁	—	4	8	no	—
128	C₂×C₈×C₆₁	—	2	2	no	—
129	C₂×C₈×C₆₁	—	2	2	no	—
130	C₂×C₈×C₆₁	—	2	2	no	—
131	C₂×C₈×C₆₁	—	2	2	no	—
132	C₂×C₈×C₆₁	—	2	2	no	—
133	C₂×C₈×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	2	2	no	—
135	C₄⋊C₄×C₆₁	—	2	2	no	—
136	C₄⋊C₄×C₆₁	—	2	2	no	—
137	C₄⋊C₄×C₆₁	—	2	2	no	—
138	C₄⋊C₄×C₆₁	—	4	2	no	—
139	C₄⋊C₄×C₆₁	—	4	2	no	—
140	C₄⋊C₄×C₆₁	—	4	4	no	—
141	C₄⋊C₄×C₆₁	—	4	4	no	—
142	C₂²⋊C₄×C₆₁	—	4	2	no	—
143	C₂²⋊C₄×C₆₁	—	4	4	no	—
144	C₂²⋊C₄×C₆₁	—	8	2	no	—
145	C₂²⋊C₄×C₆₁	—	8	2	no	—
146	C₄²×C₆₁	—	2	2	no	—
147	C₄²×C₆₁	—	2	2	no	—
148	C₂³×C₆₁	—	2	1	no	—
149	C₂³×C₆₁	—	2	1	no	—
150	C₂³×C₆₁	—	2	2	no	—
151	C₂³×C₆₁	—	2	2	no	—
152	C₂³×C₆₁	—	2	2	no	—
153	C₂³×C₆₁	—	4	1	no	—
154	C₂³×C₆₁	—	4	1	no	—
155	C₂³×C₆₁	—	4	2	no	—
156	C₂³×C₆₁	—	4	2	no	—
157	C₂³×C₆₁	#121	1	2	yes	—
158	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₆₁	—	2	4	no	—
160	Q₈×C₆₁	—	4	2	no	—
161	Q₈×C₆₁	—	4	2	no	—
162	Q₈×C₆₁	—	4	2	no	—
163	Q₈×C₆₁	—	4	2	no	—
164	Q₈×C₆₁	—	4	2	no	—
165	D₄×C₆₁	—	2	4	no	—
166	D₄×C₆₁	—	4	8	no	—
167	D₄×C₆₁	—	4	2	no	—
168	C₂×C₄×C₆₁	—	2	1	no	—
169	C₂×C₄×C₆₁	—	2	1	no	—
170	C₂×C₄×C₆₁	—	2	4	no	—
171	C₂×C₄×C₆₁	—	2	4	no	—
172	C₂×C₄×C₆₁	—	2	2	no	—
173	C₂×C₄×C₆₁	—	2	2	no	—
174	C₂×C₄×C₆₁	—	2	2	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	—	4	8	no	—
180	C₂×C₄×C₆₁	—	4	1	no	—
181	C₂×C₄×C₆₁	—	4	1	no	—
182	C₂×C₄×C₆₁	—	4	2	no	—
183	C₂×C₄×C₆₁	—	4	2	no	—
184	C₂×C₄×C₆₁	—	4	2	no	—
185	C₂×C₄×C₆₁	—	4	1	no	—
186	C₂×C₄×C₆₁	—	4	1	no	—
187	C₂×C₄×C₆₁	—	4	2	no	—
188	C₂×C₄×C₆₁	—	4	2	no	—
189	C₂×C₄×C₆₁	—	4	2	no	—
190	C₂×C₄×C₆₁	—	4	2	no	—
191	C₂×C₄×C₆₁	—	4	2	no	—
192	C₂×C₄×C₆₁	—	8	4	no	—
193	C₂×C₄×C₆₁	#121	1	2	yes	—
194	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
197	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
198	C₈×C₆₁	—	4	2	no	—
199	C₈×C₆₁	—	4	2	no	—
200	#29726	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂²×C₆₁	—	2	2	no	—
202	C₂²×C₆₁	—	2	4	no	—
203	C₂²×C₆₁	—	4	2	no	—
204	C₂²×C₆₁	—	4	1	no	—
205	C₂²×C₆₁	—	4	1	no	—
206	C₂²×C₆₁	—	4	2	no	—
207	C₂²×C₆₁	—	4	4	no	—
208	C₂²×C₆₁	—	8	2	no	—
209	C₂²×C₆₁	—	8	1	no	—
210	C₂²×C₆₁	—	8	1	no	—
211	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
212	C₂²×C₆₁	#534	1	1	yes	characteristic
213	C₂²×C₆₁	#535	1	1	yes	characteristic
214	C₂²×C₆₁	#577	1	2	yes	—
215	C₂²×C₆₁	#578	1	2	yes	—
216	C₄×C₆₁	—	2	2	no	—
217	C₄×C₆₁	—	4	2	no	—
218	C₄×C₆₁	—	4	2	no	—
219	C₄×C₆₁	—	4	2	no	—
220	C₄×C₆₁	—	8	2	no	—
221	C₄×C₆₁	—	8	1	no	—
222	C₄×C₆₁	—	8	1	no	—
223	C₄×C₆₁	—	8	2	no	—
224	C₄×C₆₁	#534	1	2	yes	—
225	C₄×C₆₁	#538	1	2	yes	—
226	C₂×#452	C₂×C₆₁	1	2	yes	—
227	#2621	C₂×C₆₁	1	1	yes	characteristic, complemented
228	#2311	C₂×C₆₁	1	1	yes	characteristic
229	#2074	C₂×C₆₁	1	1	yes	characteristic, complemented
230	#2073	C₂×C₆₁	1	1	yes	characteristic, complemented
231	#2056	C₂×C₆₁	1	2	yes	complemented
232	#2055	C₂×C₆₁	1	2	yes	complemented
233	#2016	C₂×C₆₁	1	1	yes	characteristic, complemented
234	#2013	C₂×C₆₁	1	1	yes	characteristic, complemented
235	#1872	C₂×C₆₁	1	2	yes	complemented
236	#1798	C₂×C₆₁	1	1	yes	characteristic, complemented
237	C₂×C₆₁	—	4	2	no	—
238	C₂×C₆₁	—	8	2	no	—
239	C₂×C₆₁	#2617	1	1	yes	characteristic
240	C₂×C₆₁	#3046	1	2	yes	—
241	C₂×C₆₁	#3201	1	2	yes	—
242	C₂×C₆₁	#3222	1	1	yes	characteristic
243	C₂×C₆₁	#3223	1	1	yes	characteristic
244	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
245	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
246	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
247	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
248	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
249	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
250	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
251	#452	—	2	8	no	—
252	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
253	C₂×#103	C₂²×C₆₁	1	2	yes	—
254	C₂×#103	C₂²×C₆₁	1	2	yes	—
255	C₂×#103	C₂²×C₆₁	1	2	yes	—
256	C₂×#102	C₂²×C₆₁	1	2	yes	—
257	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
258	#398	—	2	2	no	—
259	#397	—	2	2	no	—
260	#391	C₂²×C₆₁	1	2	yes	—
261	#391	C₂²×C₆₁	1	1	yes	characteristic
262	#391	C₂²×C₆₁	1	1	yes	characteristic
263	#390	C₂²×C₆₁	1	1	yes	characteristic
264	#390	C₂²×C₆₁	1	1	yes	characteristic
265	#386	—	2	2	no	—
266	#382	C₂²×C₆₁	1	1	yes	characteristic
267	#380	—	2	2	no	—
268	#340	C₂²×C₆₁	1	2	yes	—
269	#340	C₂²×C₆₁	1	2	yes	—
270	#336	C₂²×C₆₁	1	1	yes	characteristic
271	#336	C₂²×C₆₁	1	1	yes	characteristic
272	C₆₁	#29726	1	1	yes	characteristic, direct product factor, Sylow
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	4	2	no	—
275	C₂×#41	—	4	2	no	—
276	C₂×#41	D₄×C₆₁	1	4	yes	—
277	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
278	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
279	C₂²×D₄	—	2	1	no	—
280	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
281	C₂³×C₄	—	2	1	no	—
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
284	C₂×Q₁₆	—	2	4	no	—
285	C₂×Q₁₆	—	4	2	no	—
286	C₂×Q₁₆	—	4	2	no	—
287	C₂×SD₁₆	—	2	4	no	—
288	C₂×SD₁₆	—	4	2	no	—
289	C₂×SD₁₆	—	4	2	no	—
290	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
291	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
292	C₄⋊Q₈	—	4	2	no	—
293	C₂²⋊Q₈	—	2	4	no	—
294	C₂²⋊Q₈	—	2	4	no	—
295	#117	—	4	2	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	4	2	no	—
300	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
308	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
310	C₄⋊C₈	—	4	2	no	—
311	#103	—	2	4	no	—
312	#103	—	4	2	no	—
313	#103	—	4	2	no	—
314	#102	—	2	4	no	—
315	C₂²⋊C₈	—	2	4	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	—	2	4	no	—
320	C₂⁴	—	2	1	no	—
321	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
322	#41	—	4	8	no	—
323	#41	—	4	8	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	8	2	no	—
353	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
357	C₂²×C₄	#41×C₆₁	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
359	Q₁₆	—	4	8	no	—
360	SD₁₆	—	4	8	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₄⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	2	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₂²⋊C₄	—	8	2	no	—
378	C₂²⋊C₄	—	8	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	#121×C₆₁	1	2	yes	—
391	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
392	Q₈	—	2	4	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	4	2	no	—
398	D₄	—	2	4	no	—
399	D₄	—	4	8	no	—
400	D₄	—	4	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	8	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	8	4	no	—
426	C₂×C₄	#121×C₆₁	1	2	yes	—
427	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
428	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
429	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
430	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
431	C₈	—	4	2	no	—
432	C₈	—	4	2	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	8	2	no	—
441	C₂²	—	8	1	no	—
442	C₂²	—	8	1	no	—
443	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
444	C₂²	C₆₁×#534	1	1	yes	characteristic
445	C₂²	C₆₁×#535	1	1	yes	characteristic
446	C₂²	C₆₁×#577	1	2	yes	—
447	C₂²	C₆₁×#578	1	2	yes	—
448	C₄	—	2	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	8	2	no	—
453	C₄	—	8	2	no	—
454	C₄	—	8	1	no	—
455	C₄	—	8	1	no	—
456	C₄	C₆₁×#534	1	2	yes	—
457	C₄	C₆₁×#538	1	2	yes	—
458	C₂	—	4	2	no	—
459	C₂	—	8	2	no	—
460	C₂	C₆₁×#2617	1	1	yes	characteristic
461	C₂	C₆₁×#3046	1	2	yes	—
462	C₂	C₆₁×#3201	1	2	yes	—
463	C₂	C₆₁×#3222	1	1	yes	characteristic
464	C₂	C₆₁×#3223	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×#41×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2621	C₂	semidirect
4. C₆₁×#2074	C₂	semidirect
5. C₆₁×#2073	C₂	semidirect
6. C₆₁×#2056	C₂	semidirect
7. C₆₁×#2055	C₂	semidirect
8. C₆₁×#2016	C₂	semidirect
9. C₆₁×#2013	C₂	semidirect
10. C₆₁×#1872	C₂	semidirect
11. C₆₁×#1798	C₂	semidirect
200. #29726	C₆₁	direct (N × H)
227. #2621	C₂×C₆₁	semidirect
229. #2074	C₂×C₆₁	semidirect
230. #2073	C₂×C₆₁	semidirect
231. #2056	C₂×C₆₁	semidirect
232. #2055	C₂×C₆₁	semidirect
233. #2016	C₂×C₆₁	semidirect
234. #2013	C₂×C₆₁	semidirect
235. #1872	C₂×C₆₁	semidirect
236. #1798	C₂×C₆₁	semidirect
272. C₆₁	#29726	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×#452	2
C₆₁×#2621	2
C₆₁×#2311	2
C₆₁×#2074	2
C₆₁×#2073	2
C₆₁×#2056	2
C₆₁×#2055	2
C₆₁×#2016	2
C₆₁×#2013	2
C₆₁×#1872	2
C₆₁×#1798	2
#29726	61

Subgroups — C61×#29726 #29533159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#29726 #29533159