Subgroups — C₆₁×#61720 #29565153

Order 15616.

2078 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3354	C₂	1	8	yes	maximal, complemented
4	C₆₁×#3325	C₂	1	8	yes	maximal, complemented
5	C₆₁×#3227	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3192	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3100	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3094	C₂	1	4	yes	maximal, complemented
9	C₆₁×#2975	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×H(5,𝔽₂)×C₆₁	—	2	1	no	—
11	C₆₁×#555	—	2	4	no	—
12	C₆₁×#555	C₂²	1	8	yes	complemented
13	C₆₁×#547	C₂²	1	4	yes	complemented
14	C₆₁×#546	—	2	4	no	—
15	D₄²×C₆₁	C₂²	1	4	yes	complemented
16	C₆₁×#537	—	2	1	no	—
17	C₆₁×#534	—	2	2	no	—
18	C₆₁×#532	C₂²	1	2	yes	—
19	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
20	C₂×#124×C₆₁	—	2	2	no	—
21	C₂×#121×C₆₁	—	2	1	no	—
22	C₂×#121×C₆₁	C₂²	1	4	yes	—
23	C₂×#121×C₆₁	C₂²	1	2	yes	complemented
24	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
26	C₂×#117×C₆₁	—	2	1	no	—
27	C₂×#117×C₆₁	C₂²	1	2	yes	complemented
28	C₆₁×#498	C₂²	1	4	yes	complemented
29	C₆₁×#486	C₂²	1	4	yes	complemented
30	C₆₁×#482	C₂²	1	16	yes	complemented
31	C₆₁×#481	C₂²	1	8	yes	complemented
32	C₆₁×#481	C₂²	1	8	yes	complemented
33	C₆₁×#480	C₂²	1	4	yes	complemented
34	C₆₁×#476	C₂²	1	8	yes	complemented
35	C₆₁×#474	C₂²	1	4	yes	complemented
36	C₆₁×#469	C₂²	1	16	yes	complemented
37	C₆₁×#459	C₂²	1	4	yes	complemented
38	C₆₁×#447	C₂²	1	8	yes	complemented
39	C₆₁×#447	C₂²	1	4	yes	complemented
40	C₄×D₈×C₆₁	C₂²	1	8	yes	complemented
41	C₆₁×#436	C₂²	1	8	yes	complemented
42	C₆₁×#431	C₂²	1	2	yes	complemented
43	C₆₁×#428	C₂²	1	8	yes	complemented
44	C₆₁×#418	C₂²	1	8	yes	complemented
45	C₆₁×#407	C₂²	1	4	yes	complemented
46	H(5,𝔽₂)×C₆₁	—	4	8	no	—
47	C₂×#41×C₆₁	—	2	4	no	—
48	C₂×#41×C₆₁	—	2	2	no	—
49	C₂²×Q₈×C₆₁	—	2	1	no	—
50	C₂²×D₄×C₆₁	—	2	4	no	—
51	C₂²×D₄×C₆₁	—	2	2	no	—
52	C₂²×D₄×C₆₁	—	2	4	no	—
53	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
54	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
55	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₆₁	—	2	1	no	—
57	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
58	C₂×D₈×C₆₁	C₂³	1	8	yes	—
59	C₂×M₁₆×C₆₁	C₂³	1	8	yes	—
60	C₄⋊Q₈×C₆₁	—	2	2	no	—
61	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
62	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
63	#127×C₆₁	C₂³	1	2	yes	—
64	#124×C₆₁	—	2	16	no	—
65	#124×C₆₁	—	2	2	no	—
66	#123×C₆₁	—	2	8	no	—
67	C₂²⋊Q₈×C₆₁	—	2	4	no	—
68	#121×C₆₁	—	2	8	no	—
69	#121×C₆₁	—	2	2	no	—
70	#121×C₆₁	—	2	4	no	—
71	#121×C₆₁	—	2	4	no	—
72	#121×C₆₁	—	2	4	no	—
73	#121×C₆₁	—	2	4	no	—
74	#121×C₆₁	C₂³	1	4	yes	—
75	#121×C₆₁	C₂³	1	8	yes	—
76	#121×C₆₁	C₂³	1	8	yes	—
77	#120×C₆₁	—	2	8	no	—
78	C₄×D₄×C₆₁	—	2	2	no	—
79	C₄×D₄×C₆₁	—	2	2	no	—
80	C₄×D₄×C₆₁	D₄	1	4	yes	—
81	C₄×D₄×C₆₁	C₂³	1	4	yes	—
82	C₄×D₄×C₆₁	C₂³	1	4	yes	—
83	C₄×D₄×C₆₁	C₂³	1	4	yes	—
84	#117×C₆₁	—	2	4	no	—
85	#117×C₆₁	—	2	8	no	—
86	#117×C₆₁	C₂³	1	8	yes	—
87	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
97	C₂×C₄²×C₆₁	—	2	2	no	—
98	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
99	#107×C₆₁	C₂³	1	8	yes	—
100	#106×C₆₁	C₂³	1	16	yes	—
101	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
102	#102×C₆₁	C₂³	1	8	yes	—
103	#102×C₆₁	C₂³	1	16	yes	—
104	#102×C₆₁	C₂³	1	8	yes	—
105	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
106	C₂²⋊C₈×C₆₁	C₂³	1	8	yes	—
107	C₄×C₈×C₆₁	C₂³	1	4	yes	—
108	C₂⁴×C₆₁	—	2	1	no	—
109	C₂⁴×C₆₁	—	2	4	no	—
110	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
111	#41×C₆₁	—	4	16	no	—
112	#41×C₆₁	—	4	8	no	—
113	C₂×Q₈×C₆₁	—	2	2	no	—
114	C₂×Q₈×C₆₁	—	2	4	no	—
115	C₂×Q₈×C₆₁	—	8	2	no	—
116	C₂×D₄×C₆₁	—	2	8	no	—
117	C₂×D₄×C₆₁	—	2	4	no	—
118	C₂×D₄×C₆₁	—	2	8	no	—
119	C₂×D₄×C₆₁	—	2	4	no	—
120	C₂×D₄×C₆₁	—	2	1	no	—
121	C₂×D₄×C₆₁	—	2	2	no	—
122	C₂×D₄×C₆₁	—	2	2	no	—
123	C₂×D₄×C₆₁	—	2	4	no	—
124	C₂×D₄×C₆₁	—	4	2	no	—
125	C₂×D₄×C₆₁	—	4	8	no	—
126	C₂×D₄×C₆₁	—	4	16	no	—
127	C₂×D₄×C₆₁	—	4	16	no	—
128	C₂×D₄×C₆₁	—	8	4	no	—
129	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
130	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
131	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₆₁	—	2	1	no	—
133	C₂²×C₄×C₆₁	—	2	2	no	—
134	C₂²×C₄×C₆₁	—	2	4	no	—
135	C₂²×C₄×C₆₁	—	2	4	no	—
136	C₂²×C₄×C₆₁	—	2	4	no	—
137	C₂²×C₄×C₆₁	—	4	4	no	—
138	C₂²×C₄×C₆₁	—	4	4	no	—
139	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
145	D₈×C₆₁	—	4	8	no	—
146	M₁₆×C₆₁	—	4	8	no	—
147	C₂×C₈×C₆₁	C₂⁴	1	8	yes	—
148	C₄⋊C₄×C₆₁	—	2	4	no	—
149	C₄⋊C₄×C₆₁	—	2	1	no	—
150	C₄⋊C₄×C₆₁	—	2	2	no	—
151	C₄⋊C₄×C₆₁	—	2	4	no	—
152	C₄⋊C₄×C₆₁	—	2	2	no	—
153	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
154	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
155	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
156	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
157	C₂²⋊C₄×C₆₁	—	2	8	no	—
158	C₂²⋊C₄×C₆₁	—	2	4	no	—
159	C₂²⋊C₄×C₆₁	—	2	8	no	—
160	C₂²⋊C₄×C₆₁	—	2	4	no	—
161	C₂²⋊C₄×C₆₁	—	2	8	no	—
162	C₂²⋊C₄×C₆₁	—	2	4	no	—
163	C₂²⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
164	C₄²×C₆₁	—	2	8	no	—
165	C₄²×C₆₁	C₂×D₄	1	2	yes	—
166	C₄²×C₆₁	C₂⁴	1	2	yes	—
167	C₂³×C₆₁	—	2	4	no	—
168	C₂³×C₆₁	—	2	2	no	—
169	C₂³×C₆₁	—	2	4	no	—
170	C₂³×C₆₁	—	4	2	no	—
171	C₂³×C₆₁	—	4	2	no	—
172	C₂³×C₆₁	—	4	2	no	—
173	C₂³×C₆₁	—	4	2	no	—
174	C₂³×C₆₁	—	4	8	no	—
175	C₂³×C₆₁	—	4	2	no	—
176	C₂³×C₆₁	—	8	4	no	—
177	C₂³×C₆₁	—	8	4	no	—
178	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
179	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₆₁	—	4	4	no	—
181	Q₈×C₆₁	—	8	4	no	—
182	D₄×C₆₁	—	2	8	no	—
183	D₄×C₆₁	—	2	4	no	—
184	D₄×C₆₁	—	2	8	no	—
185	D₄×C₆₁	—	4	2	no	—
186	D₄×C₆₁	—	4	16	no	—
187	D₄×C₆₁	—	4	8	no	—
188	D₄×C₆₁	—	4	4	no	—
189	D₄×C₆₁	—	8	2	no	—
190	D₄×C₆₁	—	8	4	no	—
191	D₄×C₆₁	—	8	8	no	—
192	C₂×C₄×C₆₁	—	2	8	no	—
193	C₂×C₄×C₆₁	—	2	2	no	—
194	C₂×C₄×C₆₁	—	2	2	no	—
195	C₂×C₄×C₆₁	—	2	4	no	—
196	C₂×C₄×C₆₁	—	2	4	no	—
197	C₂×C₄×C₆₁	—	4	4	no	—
198	C₂×C₄×C₆₁	—	4	2	no	—
199	C₂×C₄×C₆₁	—	4	1	no	—
200	C₂×C₄×C₆₁	—	4	8	no	—
201	C₂×C₄×C₆₁	—	4	4	no	—
202	C₂×C₄×C₆₁	—	4	2	no	—
203	C₂×C₄×C₆₁	—	4	8	no	—
204	C₂×C₄×C₆₁	—	4	8	no	—
205	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
206	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
207	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
211	C₈×C₆₁	—	2	8	no	—
212	#61720	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂²×C₆₁	—	2	1	no	—
214	C₂²×C₆₁	—	2	1	no	—
215	C₂²×C₆₁	—	2	4	no	—
216	C₂²×C₆₁	—	2	4	no	—
217	C₂²×C₆₁	—	2	4	no	—
218	C₂²×C₆₁	—	4	2	no	—
219	C₂²×C₆₁	—	4	4	no	—
220	C₂²×C₆₁	—	4	2	no	—
221	C₂²×C₆₁	—	4	4	no	—
222	C₂²×C₆₁	—	4	2	no	—
223	C₂²×C₆₁	—	4	4	no	—
224	C₂²×C₆₁	—	8	4	no	—
225	C₂²×C₆₁	—	8	4	no	—
226	C₂²×C₆₁	—	16	8	no	—
227	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
228	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
229	C₄×C₆₁	—	2	2	no	—
230	C₄×C₆₁	—	2	1	no	—
231	C₄×C₆₁	—	2	4	no	—
232	C₄×C₆₁	—	4	4	no	—
233	C₄×C₆₁	—	4	2	no	—
234	C₄×C₆₁	—	4	4	no	—
235	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
236	C₄×C₆₁	#585	1	2	yes	—
237	#3496	C₂×C₆₁	1	1	yes	characteristic, complemented
238	C₂×#555	C₂×C₆₁	1	1	yes	characteristic, complemented
239	#3354	C₂×C₆₁	1	8	yes	complemented
240	#3325	C₂×C₆₁	1	8	yes	complemented
241	#3227	C₂×C₆₁	1	2	yes	complemented
242	#3192	C₂×C₆₁	1	4	yes	complemented
243	#3100	C₂×C₆₁	1	2	yes	complemented
244	#3094	C₂×C₆₁	1	4	yes	complemented
245	#2975	C₂×C₆₁	1	1	yes	characteristic, complemented
246	C₂×C₆₁	—	2	2	no	—
247	C₂×C₆₁	—	4	4	no	—
248	C₂×C₆₁	—	8	2	no	—
249	C₂×C₆₁	—	8	4	no	—
250	C₂×C₆₁	#3485	1	1	yes	characteristic
251	C₂×C₆₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
252	C₂×C₆₁	#3585	1	1	yes	characteristic
253	C₂×H(5,𝔽₂)	—	2	1	no	—
254	#555	—	2	4	no	—
255	#555	C₂²×C₆₁	1	8	yes	complemented
256	#547	C₂²×C₆₁	1	4	yes	complemented
257	#546	—	2	4	no	—
258	D₄²	C₂²×C₆₁	1	4	yes	complemented
259	#537	—	2	1	no	—
260	#534	—	2	2	no	—
261	#532	C₂²×C₆₁	1	2	yes	—
262	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
263	C₂×#124	—	2	2	no	—
264	C₂×#121	—	2	1	no	—
265	C₂×#121	C₂²×C₆₁	1	4	yes	—
266	C₂×#121	C₂²×C₆₁	1	2	yes	complemented
267	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
268	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
269	C₂×#117	—	2	1	no	—
270	C₂×#117	C₂²×C₆₁	1	2	yes	complemented
271	#498	C₂²×C₆₁	1	4	yes	complemented
272	#486	C₂²×C₆₁	1	4	yes	complemented
273	#482	C₂²×C₆₁	1	16	yes	complemented
274	#481	C₂²×C₆₁	1	8	yes	complemented
275	#481	C₂²×C₆₁	1	8	yes	complemented
276	#480	C₂²×C₆₁	1	4	yes	complemented
277	#476	C₂²×C₆₁	1	8	yes	complemented
278	#474	C₂²×C₆₁	1	4	yes	complemented
279	#469	C₂²×C₆₁	1	16	yes	complemented
280	#459	C₂²×C₆₁	1	4	yes	complemented
281	#447	C₂²×C₆₁	1	4	yes	complemented
282	#447	C₂²×C₆₁	1	8	yes	complemented
283	C₄×D₈	C₂²×C₆₁	1	8	yes	complemented
284	#436	C₂²×C₆₁	1	8	yes	complemented
285	#431	C₂²×C₆₁	1	2	yes	complemented
286	#428	C₂²×C₆₁	1	8	yes	complemented
287	#418	C₂²×C₆₁	1	8	yes	complemented
288	#407	C₂²×C₆₁	1	4	yes	complemented
289	C₆₁	#61720	1	1	yes	characteristic, direct product factor, Sylow
290	H(5,𝔽₂)	—	4	8	no	—
291	C₂×#41	—	2	4	no	—
292	C₂×#41	—	2	2	no	—
293	C₂²×Q₈	—	2	1	no	—
294	C₂²×D₄	—	2	4	no	—
295	C₂²×D₄	—	2	2	no	—
296	C₂²×D₄	—	2	4	no	—
297	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
298	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
299	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
300	C₂³×C₄	—	2	1	no	—
301	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
302	C₂×D₈	C₂³×C₆₁	1	8	yes	—
303	C₂×M₁₆	C₂³×C₆₁	1	8	yes	—
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
306	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
307	#127	C₂³×C₆₁	1	2	yes	—
308	#124	—	2	16	no	—
309	#124	—	2	2	no	—
310	#123	—	2	8	no	—
311	C₂²⋊Q₈	—	2	4	no	—
312	#121	—	2	8	no	—
313	#121	—	2	4	no	—
314	#121	—	2	4	no	—
315	#121	—	2	4	no	—
316	#121	—	2	2	no	—
317	#121	—	2	4	no	—
318	#121	C₂³×C₆₁	1	4	yes	—
319	#121	C₂³×C₆₁	1	8	yes	—
320	#121	C₂³×C₆₁	1	8	yes	—
321	#120	—	2	8	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	D₄×C₆₁	1	4	yes	—
325	C₄×D₄	C₂³×C₆₁	1	4	yes	—
326	C₄×D₄	C₂³×C₆₁	1	4	yes	—
327	C₄×D₄	C₂³×C₆₁	1	4	yes	—
328	#117	—	2	4	no	—
329	#117	—	2	8	no	—
330	#117	C₂³×C₆₁	1	8	yes	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
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	4	yes	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	4	no	—
340	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
341	C₂×C₄²	—	2	2	no	—
342	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
343	#107	C₂³×C₆₁	1	8	yes	—
344	#106	C₂³×C₆₁	1	16	yes	—
345	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
346	#102	C₂³×C₆₁	1	8	yes	—
347	#102	C₂³×C₆₁	1	16	yes	—
348	#102	C₂³×C₆₁	1	8	yes	—
349	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
350	C₂²⋊C₈	C₂³×C₆₁	1	8	yes	—
351	C₄×C₈	C₂³×C₆₁	1	4	yes	—
352	C₂⁴	—	2	1	no	—
353	C₂⁴	—	2	4	no	—
354	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
355	#41	—	4	16	no	—
356	#41	—	4	8	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	4	no	—
359	C₂×Q₈	—	8	2	no	—
360	C₂×D₄	—	2	8	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	—	4	8	no	—
370	C₂×D₄	—	4	16	no	—
371	C₂×D₄	—	4	16	no	—
372	C₂×D₄	—	8	4	no	—
373	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
374	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
375	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	4	4	no	—
382	C₂²×C₄	—	4	4	no	—
383	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
386	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
388	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
389	D₈	—	4	8	no	—
390	M₁₆	—	4	8	no	—
391	C₂×C₈	C₂⁴×C₆₁	1	8	yes	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
398	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
399	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
400	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
401	C₂²⋊C₄	—	2	8	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
408	C₄²	—	2	8	no	—
409	C₄²	C₂×D₄×C₆₁	1	2	yes	—
410	C₄²	C₂⁴×C₆₁	1	2	yes	—
411	C₂³	—	2	4	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	8	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	8	4	no	—
421	C₂³	—	8	4	no	—
422	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
423	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
424	Q₈	—	4	4	no	—
425	Q₈	—	8	4	no	—
426	D₄	—	2	8	no	—
427	D₄	—	2	4	no	—
428	D₄	—	2	8	no	—
429	D₄	—	4	2	no	—
430	D₄	—	4	16	no	—
431	D₄	—	4	8	no	—
432	D₄	—	4	4	no	—
433	D₄	—	8	2	no	—
434	D₄	—	8	4	no	—
435	D₄	—	8	8	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	8	no	—
448	C₂×C₄	—	4	8	no	—
449	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
450	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
451	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
453	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
454	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
455	C₈	—	2	8	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	4	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	8	4	no	—
468	C₂²	—	8	4	no	—
469	C₂²	—	16	8	no	—
470	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
471	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	4	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	4	no	—
477	C₄	—	4	4	no	—
478	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	4	yes	—
479	C₄	C₆₁×#585	1	2	yes	—
480	C₂	—	2	2	no	—
481	C₂	—	4	4	no	—
482	C₂	—	8	2	no	—
483	C₂	—	8	4	no	—
484	C₂	C₆₁×#3485	1	1	yes	characteristic
485	C₂	C₂²×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
486	C₂	C₆₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄×D₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3496	C₂	semidirect
2. C₂×C₆₁×#555	C₂	semidirect
3. C₆₁×#3354	C₂	semidirect
4. C₆₁×#3325	C₂	semidirect
5. C₆₁×#3227	C₂	semidirect
6. C₆₁×#3192	C₂	semidirect
7. C₆₁×#3100	C₂	semidirect
8. C₆₁×#3094	C₂	semidirect
9. C₆₁×#2975	C₂	semidirect
12. C₆₁×#555	C₂²	semidirect
13. C₆₁×#547	C₂²	semidirect
15. D₄²×C₆₁	C₂²	semidirect
19. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
23. C₂×#121×C₆₁	C₂²	semidirect
25. C₂×C₄×D₄×C₆₁	C₂²	semidirect
27. C₂×#117×C₆₁	C₂²	semidirect
28. C₆₁×#498	C₂²	semidirect
29. C₆₁×#486	C₂²	semidirect
30. C₆₁×#482	C₂²	semidirect
31. C₆₁×#481	C₂²	semidirect
32. C₆₁×#481	C₂²	semidirect
33. C₆₁×#480	C₂²	semidirect
34. C₆₁×#476	C₂²	semidirect
35. C₆₁×#474	C₂²	semidirect
36. C₆₁×#469	C₂²	semidirect
37. C₆₁×#459	C₂²	semidirect
38. C₆₁×#447	C₂²	semidirect
39. C₆₁×#447	C₂²	semidirect
40. C₄×D₈×C₆₁	C₂²	semidirect
41. C₆₁×#436	C₂²	semidirect
42. C₆₁×#431	C₂²	semidirect
43. C₆₁×#428	C₂²	semidirect
44. C₆₁×#418	C₂²	semidirect
45. C₆₁×#407	C₂²	semidirect
212. #61720	C₆₁	direct (N × H)
237. #3496	C₂×C₆₁	semidirect
238. C₂×#555	C₂×C₆₁	semidirect
239. #3354	C₂×C₆₁	semidirect
240. #3325	C₂×C₆₁	semidirect
241. #3227	C₂×C₆₁	semidirect
242. #3192	C₂×C₆₁	semidirect
243. #3100	C₂×C₆₁	semidirect
244. #3094	C₂×C₆₁	semidirect
245. #2975	C₂×C₆₁	semidirect
255. #555	C₂²×C₆₁	semidirect
256. #547	C₂²×C₆₁	semidirect
258. D₄²	C₂²×C₆₁	semidirect
262. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
266. C₂×#121	C₂²×C₆₁	semidirect
268. C₂×C₄×D₄	C₂²×C₆₁	semidirect
270. C₂×#117	C₂²×C₆₁	semidirect
271. #498	C₂²×C₆₁	semidirect
272. #486	C₂²×C₆₁	semidirect
273. #482	C₂²×C₆₁	semidirect
274. #481	C₂²×C₆₁	semidirect
275. #481	C₂²×C₆₁	semidirect
276. #480	C₂²×C₆₁	semidirect
277. #476	C₂²×C₆₁	semidirect
278. #474	C₂²×C₆₁	semidirect
279. #469	C₂²×C₆₁	semidirect
280. #459	C₂²×C₆₁	semidirect
281. #447	C₂²×C₆₁	semidirect
282. #447	C₂²×C₆₁	semidirect
283. C₄×D₈	C₂²×C₆₁	semidirect
284. #436	C₂²×C₆₁	semidirect
285. #431	C₂²×C₆₁	semidirect
286. #428	C₂²×C₆₁	semidirect
287. #418	C₂²×C₆₁	semidirect
288. #407	C₂²×C₆₁	semidirect
289. C₆₁	#61720	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#3496	2
C₂×C₆₁×#555	2
C₆₁×#3354	2
C₆₁×#3325	2
C₆₁×#3227	2
C₆₁×#3192	2
C₆₁×#3100	2
C₆₁×#3094	2
C₆₁×#2975	2
#61720	61

Subgroups — C61×#61720 #29565153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61720 #29565153