Subgroups — C₆₁×#60176 #29563609

Order 15616.

2818 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#576	C₂	1	1	yes	maximal, characteristic
2	C₄×H(5,𝔽₂)×C₆₁	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2952	C₂	1	3	yes	maximal, complemented
4	C₆₁×#2948	C₂	1	3	yes	maximal, complemented
5	C₆₁×#2946	C₂	1	6	yes	maximal, complemented
6	C₄×AGL(1,ℤ/8)×C₆₁	C₂	1	6	yes	maximal, complemented
7	C₆₁×#2943	C₂	1	3	yes	maximal, complemented
8	C₂×C₆₁×#442	C₂	1	3	yes	maximal, complemented
9	C₆₁×#2912	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2897	C₂	1	2	yes	maximal, complemented
11	C₆₁×#2875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	2	yes	—
13	C₆₁×#576	C₄	1	16	yes	complemented
14	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	6	yes	—
15	C₂×#135×C₆₁	C₂²	1	3	yes	—
16	C₂²×D₈×C₆₁	C₂²	1	3	yes	—
17	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#520	—	2	2	no	—
20	C₆₁×#520	C₂²	1	2	yes	—
21	C₆₁×#520	C₂²	1	6	yes	complemented
22	C₆₁×#518	—	2	6	no	—
23	C₆₁×#518	C₂²	1	6	yes	complemented
24	C₄×#41×C₆₁	—	2	2	no	—
25	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
26	C₄×#41×C₆₁	C₂²	1	6	yes	complemented
27	C₂×C₄×D₄×C₆₁	—	2	6	no	—
28	C₂×C₄×D₄×C₆₁	C₂²	1	6	yes	complemented
29	C₆₁×#442	C₂²	1	3	yes	complemented
30	C₆₁×#442	C₂²	1	6	yes	complemented
31	C₆₁×#442	C₂²	1	6	yes	complemented
32	C₆₁×#442	C₂²	1	6	yes	complemented
33	C₆₁×#442	C₂²	1	3	yes	complemented
34	C₆₁×#441	C₂²	1	1	yes	characteristic, complemented
35	C₆₁×#441	C₂²	1	3	yes	complemented
36	C₆₁×#440	C₂²	1	6	yes	complemented
37	C₆₁×#440	C₂²	1	6	yes	complemented
38	C₄×SD₁₆×C₆₁	C₂²	1	12	yes	complemented
39	C₄×D₈×C₆₁	C₂²	1	12	yes	complemented
40	C₆₁×#428	C₂²	1	6	yes	complemented
41	C₆₁×#427	C₂²	1	3	yes	complemented
42	C₂×#106×C₆₁	C₂²	1	3	yes	complemented
43	C₆₁×#418	C₂²	1	6	yes	complemented
44	C₆₁×#417	C₂²	1	6	yes	complemented
45	C₆₁×#416	C₂²	1	6	yes	complemented
46	C₂×#102×C₆₁	C₂²	1	6	yes	complemented
47	C₆₁×#405	C₂²	1	3	yes	complemented
48	C₆₁×#405	C₂²	1	3	yes	complemented
49	C₄×M₁₆×C₆₁	C₂²	1	3	yes	complemented
50	C₂×#97×C₆₁	C₂²	1	3	yes	complemented
51	H(5,𝔽₂)×C₆₁	—	2	8	no	—
52	H(5,𝔽₂)×C₆₁	C₂×C₄	1	16	yes	complemented
53	C₂×#41×C₆₁	—	2	2	no	—
54	C₂×#41×C₆₁	C₂³	1	6	yes	—
55	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₆₁	—	2	6	no	—
57	C₂²×D₄×C₆₁	C₂³	1	6	yes	—
58	C₂³×C₄×C₆₁	—	2	6	no	—
59	AGL(1,ℤ/8)×C₆₁	C₂×C₄	1	48	yes	complemented
60	#135×C₆₁	C₂×C₄	1	24	yes	complemented
61	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
62	C₂×SD₁₆×C₆₁	C₂³	1	6	yes	—
63	C₂×D₈×C₆₁	C₂×C₄	1	24	yes	complemented
64	C₂×D₈×C₆₁	C₂³	1	3	yes	—
65	C₂×D₈×C₆₁	C₂³	1	6	yes	—
66	#131×C₆₁	—	2	4	no	—
67	#131×C₆₁	C₂×C₄	1	8	yes	complemented
68	C₂×M₁₆×C₆₁	C₂³	1	3	yes	—
69	C₂×M₁₆×C₆₁	C₂³	1	3	yes	—
70	C₂²×C₈×C₆₁	C₂³	1	3	yes	—
71	C₂²×C₈×C₆₁	C₂³	1	3	yes	—
72	C₄×Q₈×C₆₁	—	2	2	no	—
73	C₄×Q₈×C₆₁	D₄	1	2	yes	—
74	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
75	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
76	C₄×D₄×C₆₁	—	2	6	no	—
77	C₄×D₄×C₆₁	—	2	6	no	—
78	C₄×D₄×C₆₁	—	2	6	no	—
79	C₄×D₄×C₆₁	—	2	6	no	—
80	C₄×D₄×C₆₁	—	2	6	no	—
81	C₄×D₄×C₆₁	—	2	12	no	—
82	C₄×D₄×C₆₁	—	2	6	no	—
83	C₄×D₄×C₆₁	—	2	6	no	—
84	C₄×D₄×C₆₁	D₄	1	6	yes	—
85	C₄×D₄×C₆₁	C₂³	1	6	yes	—
86	C₄×D₄×C₆₁	C₂³	1	12	yes	—
87	C₄×D₄×C₆₁	C₂³	1	6	yes	—
88	#117×C₆₁	—	2	6	no	—
89	#117×C₆₁	—	2	6	no	—
90	#117×C₆₁	C₂³	1	6	yes	—
91	#117×C₆₁	C₂³	1	3	yes	—
92	C₂×C₄⋊C₄×C₆₁	—	2	6	no	—
93	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
94	C₂×C₂²⋊C₄×C₆₁	—	2	6	no	—
95	C₂×C₂²⋊C₄×C₆₁	—	2	12	no	—
96	C₂×C₄²×C₆₁	—	2	6	no	—
97	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
98	#107×C₆₁	C₂³	1	6	yes	—
99	#106×C₆₁	C₂³	1	3	yes	—
100	#106×C₆₁	C₂³	1	6	yes	—
101	#106×C₆₁	C₂³	1	1	yes	characteristic
102	#103×C₆₁	C₂³	1	2	yes	—
103	#103×C₆₁	C₂³	1	6	yes	—
104	#102×C₆₁	C₂³	1	6	yes	—
105	#102×C₆₁	C₂³	1	12	yes	—
106	#102×C₆₁	C₂³	1	6	yes	—
107	#97×C₆₁	C₂³	1	1	yes	characteristic
108	#97×C₆₁	C₂³	1	3	yes	—
109	#97×C₆₁	C₂³	1	3	yes	—
110	#97×C₆₁	C₂³	1	3	yes	—
111	C₄×C₈×C₆₁	C₂³	1	6	yes	—
112	C₂⁴×C₆₁	—	2	6	no	—
113	#41×C₆₁	—	2	16	no	—
114	#41×C₆₁	—	2	12	no	—
115	#41×C₆₁	C₂²×C₄	1	4	yes	—
116	#41×C₆₁	C₂²×C₄	1	24	yes	complemented
117	#41×C₆₁	#41	1	4	yes	—
118	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
119	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
120	C₂×D₄×C₆₁	—	2	6	no	—
121	C₂×D₄×C₆₁	—	2	48	no	—
122	C₂×D₄×C₆₁	—	2	6	no	—
123	C₂×D₄×C₆₁	—	2	12	no	—
124	C₂×D₄×C₆₁	C₂²×C₄	1	24	yes	complemented
125	C₂×D₄×C₆₁	C₂×D₄	1	3	yes	—
126	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
127	C₂²×C₄×C₆₁	—	2	6	no	—
128	C₂²×C₄×C₆₁	—	2	6	no	—
129	C₂²×C₄×C₆₁	—	2	6	no	—
130	C₂²×C₄×C₆₁	—	2	6	no	—
131	C₂²×C₄×C₆₁	—	2	12	no	—
132	C₂²×C₄×C₆₁	—	8	12	no	—
133	C₂²×C₄×C₆₁	C₂×D₄	1	6	yes	—
134	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
135	Q₁₆×C₆₁	C₂²×C₄	1	4	yes	complemented
136	SD₁₆×C₆₁	C₂²×C₄	1	24	yes	complemented
137	D₈×C₆₁	C₂²×C₄	1	12	yes	complemented
138	D₈×C₆₁	C₂²×C₄	1	24	yes	complemented
139	M₁₆×C₆₁	—	2	6	no	—
140	M₁₆×C₆₁	C₂²×C₄	1	12	yes	complemented
141	C₂×C₈×C₆₁	—	2	6	no	—
142	C₂×C₈×C₆₁	C₂²×C₄	1	12	yes	complemented
143	C₂×C₈×C₆₁	C₂⁴	1	3	yes	—
144	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
145	C₂×C₈×C₆₁	C₂⁴	1	3	yes	—
146	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
147	C₄⋊C₄×C₆₁	—	2	6	no	—
148	C₄⋊C₄×C₆₁	—	2	6	no	—
149	C₄⋊C₄×C₆₁	—	2	2	no	—
150	C₄⋊C₄×C₆₁	C₂×D₄	1	6	yes	—
151	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
152	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
153	C₂²⋊C₄×C₆₁	—	2	6	no	—
154	C₂²⋊C₄×C₆₁	—	2	6	no	—
155	C₂²⋊C₄×C₆₁	—	2	6	no	—
156	C₂²⋊C₄×C₆₁	—	2	12	no	—
157	C₂²⋊C₄×C₆₁	C₂×D₄	1	6	yes	—
158	C₄²×C₆₁	—	2	2	no	—
159	C₄²×C₆₁	—	2	6	no	—
160	C₄²×C₆₁	—	2	6	no	—
161	C₄²×C₆₁	C₂×D₄	1	6	yes	—
162	C₄²×C₆₁	C₂⁴	1	3	yes	—
163	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
164	C₂³×C₆₁	—	2	6	no	—
165	C₂³×C₆₁	—	2	24	no	—
166	C₂³×C₆₁	—	8	6	no	—
167	C₂³×C₆₁	—	8	6	no	—
168	C₂³×C₆₁	C₂²×D₄	1	3	yes	—
169	Q₈×C₆₁	—	2	2	no	—
170	Q₈×C₆₁	C₄×D₄	1	4	yes	—
171	Q₈×C₆₁	C₂³×C₄	1	4	yes	—
172	D₄×C₆₁	—	2	24	no	—
173	D₄×C₆₁	—	2	24	no	—
174	D₄×C₆₁	—	2	6	no	—
175	D₄×C₆₁	C₄×D₄	1	12	yes	—
176	D₄×C₆₁	C₂³×C₄	1	12	yes	—
177	C₂×C₄×C₆₁	—	2	2	no	—
178	C₂×C₄×C₆₁	—	2	24	no	—
179	C₂×C₄×C₆₁	—	2	2	no	—
180	C₂×C₄×C₆₁	—	2	6	no	—
181	C₂×C₄×C₆₁	—	4	6	no	—
182	C₂×C₄×C₆₁	—	4	12	no	—
183	C₂×C₄×C₆₁	—	8	6	no	—
184	C₂×C₄×C₆₁	—	8	12	no	—
185	C₂×C₄×C₆₁	—	8	6	no	—
186	C₂×C₄×C₆₁	C₂³×C₄	1	6	yes	—
187	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₆₁	C₂²×D₄	1	6	yes	—
189	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
190	C₂×C₄×C₆₁	C₂×#41	1	6	yes	—
191	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
192	C₈×C₆₁	—	2	1	no	—
193	C₈×C₆₁	—	2	3	no	—
194	C₈×C₆₁	C₂³×C₄	1	2	yes	—
195	C₈×C₆₁	C₂³×C₄	1	6	yes	—
196	#60176	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂²×C₆₁	—	2	6	no	—
198	C₂²×C₆₁	—	2	12	no	—
199	C₂²×C₆₁	—	4	6	no	—
200	C₂²×C₆₁	—	4	6	no	—
201	C₂²×C₆₁	—	8	24	no	—
202	C₂²×C₆₁	C₂×C₄×D₄	1	6	yes	—
203	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
204	C₄×C₆₁	—	2	2	no	—
205	C₄×C₆₁	—	2	6	no	—
206	C₄×C₆₁	—	2	4	no	—
207	C₄×C₆₁	—	4	6	no	—
208	C₄×C₆₁	—	4	2	no	—
209	C₄×C₆₁	C₂×C₄×D₄	1	6	yes	—
210	C₄×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
211	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
212	C₂×#576	C₂×C₆₁	1	1	yes	characteristic
213	C₄×H(5,𝔽₂)	C₂×C₆₁	1	2	yes	complemented
214	#2952	C₂×C₆₁	1	3	yes	complemented
215	#2948	C₂×C₆₁	1	3	yes	complemented
216	#2946	C₂×C₆₁	1	6	yes	complemented
217	C₄×AGL(1,ℤ/8)	C₂×C₆₁	1	6	yes	complemented
218	#2943	C₂×C₆₁	1	3	yes	complemented
219	C₂×#442	C₂×C₆₁	1	3	yes	complemented
220	#2912	C₂×C₆₁	1	1	yes	characteristic, complemented
221	#2897	C₂×C₆₁	1	2	yes	complemented
222	#2875	C₂×C₆₁	1	1	yes	characteristic, complemented
223	C₂×C₆₁	—	2	6	no	—
224	C₂×C₆₁	—	4	12	no	—
225	C₂×C₆₁	C₂²×C₄×D₄	1	1	yes	characteristic
226	C₂×C₆₁	#3585	1	2	yes	—
227	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	2	yes	—
228	#576	C₄×C₆₁	1	16	yes	complemented
229	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	6	yes	—
230	C₂×#135	C₂²×C₆₁	1	3	yes	—
231	C₂²×D₈	C₂²×C₆₁	1	3	yes	—
232	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
233	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
234	#520	—	2	2	no	—
235	#520	C₂²×C₆₁	1	2	yes	—
236	#520	C₂²×C₆₁	1	6	yes	complemented
237	#518	—	2	6	no	—
238	#518	C₂²×C₆₁	1	6	yes	complemented
239	C₄×#41	—	2	2	no	—
240	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
241	C₄×#41	C₂²×C₆₁	1	6	yes	complemented
242	C₂×C₄×D₄	—	2	6	no	—
243	C₂×C₄×D₄	C₂²×C₆₁	1	6	yes	complemented
244	#442	C₂²×C₆₁	1	3	yes	complemented
245	#442	C₂²×C₆₁	1	6	yes	complemented
246	#442	C₂²×C₆₁	1	6	yes	complemented
247	#442	C₂²×C₆₁	1	6	yes	complemented
248	#442	C₂²×C₆₁	1	3	yes	complemented
249	#441	C₂²×C₆₁	1	1	yes	characteristic, complemented
250	#441	C₂²×C₆₁	1	3	yes	complemented
251	#440	C₂²×C₆₁	1	6	yes	complemented
252	#440	C₂²×C₆₁	1	6	yes	complemented
253	C₄×SD₁₆	C₂²×C₆₁	1	12	yes	complemented
254	C₄×D₈	C₂²×C₆₁	1	12	yes	complemented
255	#428	C₂²×C₆₁	1	6	yes	complemented
256	#427	C₂²×C₆₁	1	3	yes	complemented
257	C₂×#106	C₂²×C₆₁	1	3	yes	complemented
258	#418	C₂²×C₆₁	1	6	yes	complemented
259	#417	C₂²×C₆₁	1	6	yes	complemented
260	#416	C₂²×C₆₁	1	6	yes	complemented
261	C₂×#102	C₂²×C₆₁	1	6	yes	complemented
262	#405	C₂²×C₆₁	1	3	yes	complemented
263	#405	C₂²×C₆₁	1	3	yes	complemented
264	C₄×M₁₆	C₂²×C₆₁	1	3	yes	complemented
265	C₂×#97	C₂²×C₆₁	1	3	yes	complemented
266	C₆₁	#60176	1	1	yes	characteristic, direct product factor, Sylow
267	H(5,𝔽₂)	—	2	8	no	—
268	H(5,𝔽₂)	C₂×C₄×C₆₁	1	16	yes	complemented
269	C₂×#41	—	2	2	no	—
270	C₂×#41	C₂³×C₆₁	1	6	yes	—
271	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
272	C₂²×D₄	—	2	6	no	—
273	C₂²×D₄	C₂³×C₆₁	1	6	yes	—
274	C₂³×C₄	—	2	6	no	—
275	AGL(1,ℤ/8)	C₂×C₄×C₆₁	1	48	yes	complemented
276	#135	C₂×C₄×C₆₁	1	24	yes	complemented
277	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
278	C₂×SD₁₆	C₂³×C₆₁	1	6	yes	—
279	C₂×D₈	C₂×C₄×C₆₁	1	24	yes	complemented
280	C₂×D₈	C₂³×C₆₁	1	3	yes	—
281	C₂×D₈	C₂³×C₆₁	1	6	yes	—
282	#131	—	2	4	no	—
283	#131	C₂×C₄×C₆₁	1	8	yes	complemented
284	C₂×M₁₆	C₂³×C₆₁	1	3	yes	—
285	C₂×M₁₆	C₂³×C₆₁	1	3	yes	—
286	C₂²×C₈	C₂³×C₆₁	1	3	yes	—
287	C₂²×C₈	C₂³×C₆₁	1	3	yes	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	D₄×C₆₁	1	2	yes	—
290	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
291	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
292	C₄×D₄	—	2	6	no	—
293	C₄×D₄	—	2	6	no	—
294	C₄×D₄	—	2	6	no	—
295	C₄×D₄	—	2	6	no	—
296	C₄×D₄	—	2	6	no	—
297	C₄×D₄	—	2	12	no	—
298	C₄×D₄	—	2	6	no	—
299	C₄×D₄	—	2	6	no	—
300	C₄×D₄	D₄×C₆₁	1	6	yes	—
301	C₄×D₄	C₂³×C₆₁	1	6	yes	—
302	C₄×D₄	C₂³×C₆₁	1	12	yes	—
303	C₄×D₄	C₂³×C₆₁	1	6	yes	—
304	#117	—	2	6	no	—
305	#117	—	2	6	no	—
306	#117	C₂³×C₆₁	1	6	yes	—
307	#117	C₂³×C₆₁	1	3	yes	—
308	C₂×C₄⋊C₄	—	2	6	no	—
309	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
310	C₂×C₂²⋊C₄	—	2	6	no	—
311	C₂×C₂²⋊C₄	—	2	12	no	—
312	C₂×C₄²	—	2	6	no	—
313	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
314	#107	C₂³×C₆₁	1	6	yes	—
315	#106	C₂³×C₆₁	1	3	yes	—
316	#106	C₂³×C₆₁	1	6	yes	—
317	#106	C₂³×C₆₁	1	1	yes	characteristic
318	#103	C₂³×C₆₁	1	2	yes	—
319	#103	C₂³×C₆₁	1	6	yes	—
320	#102	C₂³×C₆₁	1	6	yes	—
321	#102	C₂³×C₆₁	1	12	yes	—
322	#102	C₂³×C₆₁	1	6	yes	—
323	#97	C₂³×C₆₁	1	1	yes	characteristic
324	#97	C₂³×C₆₁	1	3	yes	—
325	#97	C₂³×C₆₁	1	3	yes	—
326	#97	C₂³×C₆₁	1	3	yes	—
327	C₄×C₈	C₂³×C₆₁	1	6	yes	—
328	C₂⁴	—	2	6	no	—
329	#41	—	2	16	no	—
330	#41	—	2	12	no	—
331	#41	C₂²×C₄×C₆₁	1	4	yes	—
332	#41	C₂²×C₄×C₆₁	1	24	yes	complemented
333	#41	#41×C₆₁	1	4	yes	—
334	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
335	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
336	C₂×D₄	—	2	6	no	—
337	C₂×D₄	—	2	48	no	—
338	C₂×D₄	—	2	6	no	—
339	C₂×D₄	—	2	12	no	—
340	C₂×D₄	C₂²×C₄×C₆₁	1	24	yes	complemented
341	C₂×D₄	C₂×D₄×C₆₁	1	3	yes	—
342	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
343	C₂²×C₄	—	2	6	no	—
344	C₂²×C₄	—	2	6	no	—
345	C₂²×C₄	—	2	6	no	—
346	C₂²×C₄	—	2	6	no	—
347	C₂²×C₄	—	2	12	no	—
348	C₂²×C₄	—	8	12	no	—
349	C₂²×C₄	C₂×D₄×C₆₁	1	6	yes	—
350	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
351	Q₁₆	C₂²×C₄×C₆₁	1	4	yes	complemented
352	SD₁₆	C₂²×C₄×C₆₁	1	24	yes	complemented
353	D₈	C₂²×C₄×C₆₁	1	12	yes	complemented
354	D₈	C₂²×C₄×C₆₁	1	24	yes	complemented
355	M₁₆	—	2	6	no	—
356	M₁₆	C₂²×C₄×C₆₁	1	12	yes	complemented
357	C₂×C₈	—	2	6	no	—
358	C₂×C₈	C₂²×C₄×C₆₁	1	12	yes	complemented
359	C₂×C₈	C₂⁴×C₆₁	1	3	yes	—
360	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
361	C₂×C₈	C₂⁴×C₆₁	1	3	yes	—
362	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
363	C₄⋊C₄	—	2	6	no	—
364	C₄⋊C₄	—	2	6	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	C₂×D₄×C₆₁	1	6	yes	—
367	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
368	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
369	C₂²⋊C₄	—	2	6	no	—
370	C₂²⋊C₄	—	2	6	no	—
371	C₂²⋊C₄	—	2	6	no	—
372	C₂²⋊C₄	—	2	12	no	—
373	C₂²⋊C₄	C₂×D₄×C₆₁	1	6	yes	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	6	no	—
376	C₄²	—	2	6	no	—
377	C₄²	C₂×D₄×C₆₁	1	6	yes	—
378	C₄²	C₂⁴×C₆₁	1	3	yes	—
379	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
380	C₂³	—	2	6	no	—
381	C₂³	—	2	24	no	—
382	C₂³	—	8	6	no	—
383	C₂³	—	8	6	no	—
384	C₂³	C₂²×D₄×C₆₁	1	3	yes	—
385	Q₈	—	2	2	no	—
386	Q₈	C₄×D₄×C₆₁	1	4	yes	—
387	Q₈	C₂³×C₄×C₆₁	1	4	yes	—
388	D₄	—	2	24	no	—
389	D₄	—	2	6	no	—
390	D₄	—	2	24	no	—
391	D₄	C₄×D₄×C₆₁	1	12	yes	—
392	D₄	C₂³×C₄×C₆₁	1	12	yes	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	24	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	6	no	—
397	C₂×C₄	—	4	6	no	—
398	C₂×C₄	—	4	12	no	—
399	C₂×C₄	—	8	6	no	—
400	C₂×C₄	—	8	12	no	—
401	C₂×C₄	—	8	6	no	—
402	C₂×C₄	C₂³×C₄×C₆₁	1	6	yes	—
403	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
404	C₂×C₄	C₂²×D₄×C₆₁	1	6	yes	—
405	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
406	C₂×C₄	C₂×#41×C₆₁	1	6	yes	—
407	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
408	C₈	—	2	1	no	—
409	C₈	—	2	3	no	—
410	C₈	C₂³×C₄×C₆₁	1	2	yes	—
411	C₈	C₂³×C₄×C₆₁	1	6	yes	—
412	C₂²	—	2	6	no	—
413	C₂²	—	2	12	no	—
414	C₂²	—	4	6	no	—
415	C₂²	—	4	6	no	—
416	C₂²	—	8	24	no	—
417	C₂²	C₂×C₄×D₄×C₆₁	1	6	yes	—
418	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
419	C₄	—	2	2	no	—
420	C₄	—	2	6	no	—
421	C₄	—	2	4	no	—
422	C₄	—	4	6	no	—
423	C₄	—	4	2	no	—
424	C₄	C₂×C₄×D₄×C₆₁	1	6	yes	—
425	C₄	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
426	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
427	C₂	—	2	6	no	—
428	C₂	—	4	12	no	—
429	C₂	C₂²×C₄×D₄×C₆₁	1	1	yes	characteristic
430	C₂	C₆₁×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator	C₄	C₂⁴×C₄×C₆₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂×C₆₁×#576	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×H(5,𝔽₂)×C₆₁	C₂	semidirect
3. C₆₁×#2952	C₂	semidirect
4. C₆₁×#2948	C₂	semidirect
5. C₆₁×#2946	C₂	semidirect
6. C₄×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
7. C₆₁×#2943	C₂	semidirect
8. C₂×C₆₁×#442	C₂	semidirect
9. C₆₁×#2912	C₂	semidirect
10. C₆₁×#2897	C₂	semidirect
11. C₆₁×#2875	C₂	semidirect
13. C₆₁×#576	C₄	semidirect
21. C₆₁×#520	C₂²	semidirect
23. C₆₁×#518	C₂²	semidirect
26. C₄×#41×C₆₁	C₂²	semidirect
28. C₂×C₄×D₄×C₆₁	C₂²	semidirect
29. C₆₁×#442	C₂²	semidirect
30. C₆₁×#442	C₂²	semidirect
31. C₆₁×#442	C₂²	semidirect
32. C₆₁×#442	C₂²	semidirect
33. C₆₁×#442	C₂²	semidirect
34. C₆₁×#441	C₂²	semidirect
35. C₆₁×#441	C₂²	semidirect
36. C₆₁×#440	C₂²	semidirect
37. C₆₁×#440	C₂²	semidirect
38. C₄×SD₁₆×C₆₁	C₂²	semidirect
39. C₄×D₈×C₆₁	C₂²	semidirect
40. C₆₁×#428	C₂²	semidirect
41. C₆₁×#427	C₂²	semidirect
42. C₂×#106×C₆₁	C₂²	semidirect
43. C₆₁×#418	C₂²	semidirect
44. C₆₁×#417	C₂²	semidirect
45. C₆₁×#416	C₂²	semidirect
46. C₂×#102×C₆₁	C₂²	semidirect
47. C₆₁×#405	C₂²	semidirect
48. C₆₁×#405	C₂²	semidirect
49. C₄×M₁₆×C₆₁	C₂²	semidirect
50. C₂×#97×C₆₁	C₂²	semidirect
52. H(5,𝔽₂)×C₆₁	C₂×C₄	semidirect
59. AGL(1,ℤ/8)×C₆₁	C₂×C₄	semidirect
60. #135×C₆₁	C₂×C₄	semidirect
63. C₂×D₈×C₆₁	C₂×C₄	semidirect
67. #131×C₆₁	C₂×C₄	semidirect
116. #41×C₆₁	C₂²×C₄	semidirect
124. C₂×D₄×C₆₁	C₂²×C₄	semidirect
135. Q₁₆×C₆₁	C₂²×C₄	semidirect
136. SD₁₆×C₆₁	C₂²×C₄	semidirect
137. D₈×C₆₁	C₂²×C₄	semidirect
138. D₈×C₆₁	C₂²×C₄	semidirect
140. M₁₆×C₆₁	C₂²×C₄	semidirect
142. C₂×C₈×C₆₁	C₂²×C₄	semidirect
196. #60176	C₆₁	direct (N × H)
213. C₄×H(5,𝔽₂)	C₂×C₆₁	semidirect
214. #2952	C₂×C₆₁	semidirect
215. #2948	C₂×C₆₁	semidirect
216. #2946	C₂×C₆₁	semidirect
217. C₄×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
218. #2943	C₂×C₆₁	semidirect
219. C₂×#442	C₂×C₆₁	semidirect
220. #2912	C₂×C₆₁	semidirect
221. #2897	C₂×C₆₁	semidirect
222. #2875	C₂×C₆₁	semidirect
228. #576	C₄×C₆₁	semidirect
236. #520	C₂²×C₆₁	semidirect
238. #518	C₂²×C₆₁	semidirect
241. C₄×#41	C₂²×C₆₁	semidirect
243. C₂×C₄×D₄	C₂²×C₆₁	semidirect
244. #442	C₂²×C₆₁	semidirect
245. #442	C₂²×C₆₁	semidirect
246. #442	C₂²×C₆₁	semidirect
247. #442	C₂²×C₆₁	semidirect
248. #442	C₂²×C₆₁	semidirect
249. #441	C₂²×C₆₁	semidirect
250. #441	C₂²×C₆₁	semidirect
251. #440	C₂²×C₆₁	semidirect
252. #440	C₂²×C₆₁	semidirect
253. C₄×SD₁₆	C₂²×C₆₁	semidirect
254. C₄×D₈	C₂²×C₆₁	semidirect
255. #428	C₂²×C₆₁	semidirect
256. #427	C₂²×C₆₁	semidirect
257. C₂×#106	C₂²×C₆₁	semidirect
258. #418	C₂²×C₆₁	semidirect
259. #417	C₂²×C₆₁	semidirect
260. #416	C₂²×C₆₁	semidirect
261. C₂×#102	C₂²×C₆₁	semidirect
262. #405	C₂²×C₆₁	semidirect
263. #405	C₂²×C₆₁	semidirect
264. C₄×M₁₆	C₂²×C₆₁	semidirect
265. C₂×#97	C₂²×C₆₁	semidirect
266. C₆₁	#60176	direct (N × H)
268. H(5,𝔽₂)	C₂×C₄×C₆₁	semidirect
275. AGL(1,ℤ/8)	C₂×C₄×C₆₁	semidirect
276. #135	C₂×C₄×C₆₁	semidirect
279. C₂×D₈	C₂×C₄×C₆₁	semidirect
283. #131	C₂×C₄×C₆₁	semidirect
332. #41	C₂²×C₄×C₆₁	semidirect
340. C₂×D₄	C₂²×C₄×C₆₁	semidirect
351. Q₁₆	C₂²×C₄×C₆₁	semidirect
352. SD₁₆	C₂²×C₄×C₆₁	semidirect
353. D₈	C₂²×C₄×C₆₁	semidirect
354. D₈	C₂²×C₄×C₆₁	semidirect
356. M₁₆	C₂²×C₄×C₆₁	semidirect
358. C₂×C₈	C₂²×C₄×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×#576	2
C₄×H(5,𝔽₂)×C₆₁	2
C₆₁×#2952	2
C₆₁×#2948	2
C₆₁×#2946	2
C₄×AGL(1,ℤ/8)×C₆₁	2
C₆₁×#2943	2
C₂×C₆₁×#442	2
C₆₁×#2912	2
C₆₁×#2897	2
C₆₁×#2875	2
#60176	61

Subgroups — C61×#60176 #29563609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60176 #29563609