Subgroups — C₆₁×#24230 #29527663

Order 15616.

1624 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#453	C₂	1	2	yes	maximal, complemented
4	C₄×AGL(1,ℤ/8)×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2541	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2037	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2002	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1980	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1965	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1806	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1792	C₂	1	2	yes	maximal, complemented
12	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	2	yes	—
13	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	complemented
15	C₆₁×#550	—	2	1	no	—
16	C₆₁×#550	—	2	1	no	—
17	D₄²×C₆₁	—	2	2	no	—
18	D₄²×C₆₁	—	2	2	no	—
19	D₄²×C₆₁	—	2	1	no	—
20	D₄²×C₆₁	—	2	1	no	—
21	C₆₁×#535	—	2	2	no	—
22	C₆₁×#535	C₂²	1	2	yes	—
23	C₆₁×#532	—	2	1	no	—
24	C₆₁×#532	C₂²	1	1	yes	characteristic
25	C₂×#127×C₆₁	—	2	1	no	—
26	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#127×C₆₁	C₂²	1	2	yes	complemented
28	C₂×#121×C₆₁	—	2	2	no	—
29	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
31	C₆₁×#463	—	2	2	no	—
32	C₆₁×#461	—	2	1	no	—
33	C₆₁×#459	—	2	1	no	—
34	C₆₁×#453	—	2	8	no	—
35	C₆₁×#442	—	2	1	no	—
36	C₆₁×#440	—	2	1	no	—
37	C₄×SD₁₆×C₆₁	—	2	1	no	—
38	C₄×D₈×C₆₁	—	2	1	no	—
39	C₆₁×#428	C₂²	1	1	yes	characteristic, complemented
40	C₆₁×#423	C₂²	1	1	yes	characteristic, complemented
41	C₂×#104×C₆₁	C₂²	1	2	yes	—
42	C₂×#104×C₆₁	C₂²	1	2	yes	complemented
43	C₂×#104×C₆₁	C₂²	1	2	yes	complemented
44	C₆₁×#418	C₂²	1	1	yes	characteristic, complemented
45	C₆₁×#417	C₂²	1	1	yes	characteristic
46	C₆₁×#417	C₂²	1	2	yes	complemented
47	C₂×#100×C₆₁	C₂²	1	2	yes	complemented
48	C₂×#100×C₆₁	C₂²	1	2	yes	complemented
49	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
50	C₆₁×#392	—	2	2	no	—
51	C₆₁×#390	C₂²	1	2	yes	complemented
52	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
53	C₆₁×#339	C₂²	1	2	yes	complemented
54	H(5,𝔽₂)×C₆₁	—	2	4	no	—
55	H(5,𝔽₂)×C₆₁	—	2	4	no	—
56	H(5,𝔽₂)×C₆₁	—	4	2	no	—
57	H(5,𝔽₂)×C₆₁	—	4	2	no	—
58	C₂×#41×C₆₁	—	2	2	no	—
59	C₂×#41×C₆₁	—	2	2	no	—
60	C₂×#41×C₆₁	C₂³	1	2	yes	—
61	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₆₁	—	2	4	no	—
63	C₂²×D₄×C₆₁	—	2	2	no	—
64	C₂²×D₄×C₆₁	—	2	2	no	—
65	C₂²×D₄×C₆₁	—	2	2	no	—
66	C₂²×D₄×C₆₁	—	2	2	no	—
67	C₂²×D₄×C₆₁	—	2	4	no	—
68	C₂²×D₄×C₆₁	D₄	1	2	yes	—
69	C₂²×D₄×C₆₁	D₄	1	2	yes	—
70	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
71	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₆₁	—	2	1	no	—
73	AGL(1,ℤ/8)×C₆₁	—	2	2	no	—
74	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
75	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
76	AGL(1,ℤ/8)×C₆₁	D₄	1	4	yes	complemented
77	C₂×SD₁₆×C₆₁	—	2	1	no	—
78	C₂×SD₁₆×C₆₁	—	2	2	no	—
79	C₂×D₈×C₆₁	—	2	1	no	—
80	C₂×D₈×C₆₁	—	2	2	no	—
81	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
82	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
84	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic, complemented
85	#127×C₆₁	—	2	2	no	—
86	#127×C₆₁	—	2	2	no	—
87	#127×C₆₁	—	2	2	no	—
88	#127×C₆₁	—	2	4	no	—
89	#127×C₆₁	—	2	1	no	—
90	#127×C₆₁	—	2	1	no	—
91	#127×C₆₁	—	2	1	no	—
92	#127×C₆₁	—	2	1	no	—
93	#127×C₆₁	—	4	2	no	—
94	#127×C₆₁	D₄	1	1	yes	characteristic, complemented
95	#124×C₆₁	—	2	2	no	—
96	#124×C₆₁	D₄	1	2	yes	complemented
97	#121×C₆₁	—	2	2	no	—
98	#121×C₆₁	—	2	2	no	—
99	#121×C₆₁	—	2	4	no	—
100	#121×C₆₁	—	2	4	no	—
101	#121×C₆₁	—	2	1	no	—
102	#121×C₆₁	—	2	1	no	—
103	#121×C₆₁	—	2	2	no	—
104	#121×C₆₁	—	2	2	no	—
105	#121×C₆₁	—	4	8	no	—
106	#120×C₆₁	—	2	4	no	—
107	#120×C₆₁	—	2	4	no	—
108	#120×C₆₁	—	2	4	no	—
109	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic, complemented
110	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic, complemented
111	C₄×D₄×C₆₁	—	2	2	no	—
112	C₄×D₄×C₆₁	—	2	2	no	—
113	C₄×D₄×C₆₁	—	2	1	no	—
114	C₄×D₄×C₆₁	—	2	1	no	—
115	C₄×D₄×C₆₁	—	2	1	no	—
116	C₄×D₄×C₆₁	—	2	1	no	—
117	C₄×D₄×C₆₁	—	2	1	no	—
118	C₄×D₄×C₆₁	—	2	1	no	—
119	C₄×D₄×C₆₁	—	2	1	no	—
120	C₄×D₄×C₆₁	—	2	1	no	—
121	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic, complemented
122	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic, complemented
123	#117×C₆₁	—	2	1	no	—
124	#117×C₆₁	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
126	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
128	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
129	C₂×C₄²×C₆₁	—	2	1	no	—
130	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
131	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
132	#107×C₆₁	—	2	1	no	—
133	#106×C₆₁	—	2	1	no	—
134	C₄⋊C₈×C₆₁	—	2	1	no	—
135	C₄⋊C₈×C₆₁	—	2	1	no	—
136	#104×C₆₁	—	2	4	no	—
137	#104×C₆₁	—	2	4	no	—
138	#104×C₆₁	—	4	2	no	—
139	#103×C₆₁	—	2	1	no	—
140	#103×C₆₁	—	2	2	no	—
141	#102×C₆₁	—	2	1	no	—
142	#102×C₆₁	—	2	2	no	—
143	#102×C₆₁	—	2	1	no	—
144	#102×C₆₁	—	2	1	no	—
145	#100×C₆₁	—	2	4	no	—
146	#100×C₆₁	—	4	2	no	—
147	#97×C₆₁	—	2	1	no	—
148	C₄×C₈×C₆₁	—	2	1	no	—
149	#95×C₆₁	—	2	1	no	—
150	C₂⁴×C₆₁	—	2	4	no	—
151	C₂⁴×C₆₁	—	2	1	no	—
152	C₂⁴×C₆₁	C₂×D₄	1	4	yes	—
153	#41×C₆₁	—	2	1	no	—
154	#41×C₆₁	—	2	1	no	—
155	#41×C₆₁	—	2	2	no	—
156	#41×C₆₁	—	2	2	no	—
157	#41×C₆₁	—	2	2	no	—
158	#41×C₆₁	—	2	2	no	—
159	#41×C₆₁	—	4	4	no	—
160	#41×C₆₁	—	4	4	no	—
161	#41×C₆₁	—	4	4	no	—
162	#41×C₆₁	—	4	4	no	—
163	#41×C₆₁	C₂×D₄	1	2	yes	—
164	#41×C₆₁	#41	1	2	yes	—
165	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
166	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₆₁	—	2	1	no	—
168	C₂×D₄×C₆₁	—	2	4	no	—
169	C₂×D₄×C₆₁	—	2	4	no	—
170	C₂×D₄×C₆₁	—	2	2	no	—
171	C₂×D₄×C₆₁	—	2	4	no	—
172	C₂×D₄×C₆₁	—	2	4	no	—
173	C₂×D₄×C₆₁	—	2	2	no	—
174	C₂×D₄×C₆₁	—	2	2	no	—
175	C₂×D₄×C₆₁	—	2	1	no	—
176	C₂×D₄×C₆₁	—	2	1	no	—
177	C₂×D₄×C₆₁	—	2	2	no	—
178	C₂×D₄×C₆₁	—	2	2	no	—
179	C₂×D₄×C₆₁	—	2	1	no	—
180	C₂×D₄×C₆₁	—	2	1	no	—
181	C₂×D₄×C₆₁	—	2	2	no	—
182	C₂×D₄×C₆₁	—	2	2	no	—
183	C₂×D₄×C₆₁	—	2	2	no	—
184	C₂×D₄×C₆₁	—	2	1	no	—
185	C₂×D₄×C₆₁	—	2	2	no	—
186	C₂×D₄×C₆₁	—	2	1	no	—
187	C₂×D₄×C₆₁	—	2	2	no	—
188	C₂×D₄×C₆₁	—	2	1	no	—
189	C₂×D₄×C₆₁	—	2	2	no	—
190	C₂×D₄×C₆₁	—	4	4	no	—
191	C₂×D₄×C₆₁	—	4	4	no	—
192	C₂×D₄×C₆₁	—	4	4	no	—
193	C₂×D₄×C₆₁	—	4	8	no	—
194	C₂×D₄×C₆₁	—	4	8	no	—
195	C₂×D₄×C₆₁	—	4	8	no	—
196	C₂×D₄×C₆₁	—	4	4	no	—
197	C₂×D₄×C₆₁	—	4	4	no	—
198	C₂×D₄×C₆₁	—	4	8	no	—
199	C₂×D₄×C₆₁	—	8	4	no	—
200	C₂×D₄×C₆₁	—	8	4	no	—
201	C₂×D₄×C₆₁	—	8	2	no	—
202	C₂×D₄×C₆₁	—	8	4	no	—
203	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
204	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
205	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	complemented
206	C₂²×C₄×C₆₁	—	2	1	no	—
207	C₂²×C₄×C₆₁	—	2	4	no	—
208	C₂²×C₄×C₆₁	—	2	2	no	—
209	C₂²×C₄×C₆₁	—	2	1	no	—
210	C₂²×C₄×C₆₁	—	2	1	no	—
211	C₂²×C₄×C₆₁	—	2	2	no	—
212	C₂²×C₄×C₆₁	—	2	1	no	—
213	C₂²×C₄×C₆₁	—	4	4	no	—
214	C₂²×C₄×C₆₁	—	4	1	no	—
215	C₂²×C₄×C₆₁	—	4	1	no	—
216	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
219	SD₁₆×C₆₁	—	2	4	no	—
220	SD₁₆×C₆₁	—	4	4	no	—
221	D₈×C₆₁	—	2	4	no	—
222	D₈×C₆₁	—	4	4	no	—
223	M₁₆×C₆₁	—	2	1	no	—
224	M₁₆×C₆₁	—	2	2	no	—
225	M₁₆×C₆₁	—	2	1	no	—
226	M₁₆×C₆₁	—	2	2	no	—
227	M₁₆×C₆₁	—	2	1	no	—
228	M₁₆×C₆₁	C₂×D₄	1	2	yes	complemented
229	C₂×C₈×C₆₁	—	2	1	no	—
230	C₂×C₈×C₆₁	—	2	1	no	—
231	C₂×C₈×C₆₁	—	2	2	no	—
232	C₄⋊C₄×C₆₁	—	2	4	no	—
233	C₄⋊C₄×C₆₁	—	2	1	no	—
234	C₄⋊C₄×C₆₁	—	2	1	no	—
235	C₄⋊C₄×C₆₁	—	2	1	no	—
236	C₄⋊C₄×C₆₁	—	2	1	no	—
237	C₄⋊C₄×C₆₁	—	2	1	no	—
238	C₄⋊C₄×C₆₁	—	2	1	no	—
239	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
240	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
241	C₂²⋊C₄×C₆₁	—	2	4	no	—
242	C₂²⋊C₄×C₆₁	—	2	4	no	—
243	C₂²⋊C₄×C₆₁	—	2	1	no	—
244	C₂²⋊C₄×C₆₁	—	2	1	no	—
245	C₂²⋊C₄×C₆₁	—	2	1	no	—
246	C₂²⋊C₄×C₆₁	—	2	2	no	—
247	C₂²⋊C₄×C₆₁	—	2	2	no	—
248	C₂²⋊C₄×C₆₁	—	4	8	no	—
249	C₂²⋊C₄×C₆₁	—	4	1	no	—
250	C₂²⋊C₄×C₆₁	—	4	1	no	—
251	C₄²×C₆₁	—	2	1	no	—
252	C₄²×C₆₁	—	2	1	no	—
253	C₄²×C₆₁	—	2	1	no	—
254	C₄²×C₆₁	—	2	2	no	—
255	C₄²×C₆₁	—	2	2	no	—
256	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
257	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
258	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
259	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
260	C₂³×C₆₁	—	2	1	no	—
261	C₂³×C₆₁	—	2	4	no	—
262	C₂³×C₆₁	—	2	2	no	—
263	C₂³×C₆₁	—	2	2	no	—
264	C₂³×C₆₁	—	2	4	no	—
265	C₂³×C₆₁	—	2	4	no	—
266	C₂³×C₆₁	—	4	2	no	—
267	C₂³×C₆₁	—	4	2	no	—
268	C₂³×C₆₁	—	4	8	no	—
269	C₂³×C₆₁	—	4	4	no	—
270	C₂³×C₆₁	—	4	4	no	—
271	C₂³×C₆₁	—	4	1	no	—
272	C₂³×C₆₁	—	4	1	no	—
273	C₂³×C₆₁	—	8	4	no	—
274	C₂³×C₆₁	—	8	4	no	—
275	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
276	Q₈×C₆₁	—	2	1	no	—
277	Q₈×C₆₁	—	2	2	no	—
278	Q₈×C₆₁	—	2	2	no	—
279	Q₈×C₆₁	#121	1	2	yes	complemented
280	D₄×C₆₁	—	2	2	no	—
281	D₄×C₆₁	—	2	2	no	—
282	D₄×C₆₁	—	2	2	no	—
283	D₄×C₆₁	—	2	1	no	—
284	D₄×C₆₁	—	2	2	no	—
285	D₄×C₆₁	—	2	2	no	—
286	D₄×C₆₁	—	2	2	no	—
287	D₄×C₆₁	—	4	8	no	—
288	D₄×C₆₁	—	4	4	no	—
289	D₄×C₆₁	—	4	2	no	—
290	D₄×C₆₁	—	4	8	no	—
291	D₄×C₆₁	—	4	2	no	—
292	D₄×C₆₁	—	4	2	no	—
293	D₄×C₆₁	—	4	2	no	—
294	D₄×C₆₁	—	4	1	no	—
295	D₄×C₆₁	—	4	2	no	—
296	D₄×C₆₁	—	4	2	no	—
297	D₄×C₆₁	—	4	1	no	—
298	D₄×C₆₁	—	4	2	no	—
299	D₄×C₆₁	—	4	4	no	—
300	D₄×C₆₁	—	4	2	no	—
301	D₄×C₆₁	—	8	2	no	—
302	D₄×C₆₁	—	8	2	no	—
303	D₄×C₆₁	—	8	4	no	—
304	D₄×C₆₁	—	8	4	no	—
305	D₄×C₆₁	—	8	16	no	—
306	D₄×C₆₁	#121	1	2	yes	complemented
307	C₂×C₄×C₆₁	—	2	1	no	—
308	C₂×C₄×C₆₁	—	2	2	no	—
309	C₂×C₄×C₆₁	—	2	2	no	—
310	C₂×C₄×C₆₁	—	2	2	no	—
311	C₂×C₄×C₆₁	—	2	4	no	—
312	C₂×C₄×C₆₁	—	2	1	no	—
313	C₂×C₄×C₆₁	—	2	1	no	—
314	C₂×C₄×C₆₁	—	2	2	no	—
315	C₂×C₄×C₆₁	—	4	1	no	—
316	C₂×C₄×C₆₁	—	4	8	no	—
317	C₂×C₄×C₆₁	—	4	2	no	—
318	C₂×C₄×C₆₁	—	4	2	no	—
319	C₂×C₄×C₆₁	—	4	2	no	—
320	C₂×C₄×C₆₁	—	4	2	no	—
321	C₂×C₄×C₆₁	—	4	2	no	—
322	C₂×C₄×C₆₁	—	4	2	no	—
323	C₂×C₄×C₆₁	—	4	2	no	—
324	C₂×C₄×C₆₁	—	4	1	no	—
325	C₂×C₄×C₆₁	—	8	2	no	—
326	C₂×C₄×C₆₁	—	8	2	no	—
327	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
328	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
329	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
330	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
331	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
335	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
336	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
337	C₈×C₆₁	—	2	2	no	—
338	C₈×C₆₁	—	4	1	no	—
339	C₈×C₆₁	—	4	2	no	—
340	#24230	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
341	C₂²×C₆₁	—	2	1	no	—
342	C₂²×C₆₁	—	2	1	no	—
343	C₂²×C₆₁	—	2	2	no	—
344	C₂²×C₆₁	—	4	4	no	—
345	C₂²×C₆₁	—	4	1	no	—
346	C₂²×C₆₁	—	4	1	no	—
347	C₂²×C₆₁	—	4	2	no	—
348	C₂²×C₆₁	—	4	4	no	—
349	C₂²×C₆₁	—	4	2	no	—
350	C₂²×C₆₁	—	4	4	no	—
351	C₂²×C₆₁	—	4	2	no	—
352	C₂²×C₆₁	—	4	4	no	—
353	C₂²×C₆₁	—	4	2	no	—
354	C₂²×C₆₁	—	8	4	no	—
355	C₂²×C₆₁	—	8	4	no	—
356	C₂²×C₆₁	—	8	2	no	—
357	C₂²×C₆₁	—	8	1	no	—
358	C₂²×C₆₁	—	8	1	no	—
359	C₂²×C₆₁	—	16	8	no	—
360	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
361	C₂²×C₆₁	D₄²	1	1	yes	characteristic
362	C₂²×C₆₁	#546	1	1	yes	characteristic
363	C₄×C₆₁	—	2	2	no	—
364	C₄×C₆₁	—	2	1	no	—
365	C₄×C₆₁	—	2	1	no	—
366	C₄×C₆₁	—	2	1	no	—
367	C₄×C₆₁	—	4	4	no	—
368	C₄×C₆₁	—	4	2	no	—
369	C₄×C₆₁	—	4	1	no	—
370	C₄×C₆₁	—	4	1	no	—
371	C₄×C₆₁	—	8	1	no	—
372	C₄×C₆₁	#453	1	2	yes	complemented
373	C₄×C₆₁	C₂×#121	1	1	yes	characteristic
374	C₄×C₆₁	#535	1	1	yes	characteristic
375	C₄×C₆₁	D₄²	1	1	yes	characteristic
376	C₄×C₆₁	#546	1	1	yes	characteristic
377	#3498	C₂×C₆₁	1	1	yes	characteristic, complemented
378	#3036	C₂×C₆₁	1	1	yes	characteristic, complemented
379	C₂×#453	C₂×C₆₁	1	2	yes	complemented
380	C₄×AGL(1,ℤ/8)	C₂×C₆₁	1	1	yes	characteristic, complemented
381	#2541	C₂×C₆₁	1	1	yes	characteristic, complemented
382	#2037	C₂×C₆₁	1	2	yes	complemented
383	#2002	C₂×C₆₁	1	2	yes	complemented
384	#1980	C₂×C₆₁	1	1	yes	characteristic, complemented
385	#1965	C₂×C₆₁	1	1	yes	characteristic, complemented
386	#1806	C₂×C₆₁	1	1	yes	characteristic, complemented
387	#1792	C₂×C₆₁	1	2	yes	complemented
388	C₂×C₆₁	—	2	1	no	—
389	C₂×C₆₁	—	2	1	no	—
390	C₂×C₆₁	—	4	2	no	—
391	C₂×C₆₁	—	8	2	no	—
392	C₂×C₆₁	—	8	4	no	—
393	C₂×C₆₁	—	8	2	no	—
394	C₂×C₆₁	#2408	1	1	yes	characteristic
395	C₂×C₆₁	C₂×#453	1	1	yes	characteristic
396	C₂×C₆₁	#3019	1	1	yes	characteristic
397	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	2	yes	—
398	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
399	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	complemented
400	#550	—	2	1	no	—
401	#550	—	2	1	no	—
402	D₄²	—	2	2	no	—
403	D₄²	—	2	2	no	—
404	D₄²	—	2	1	no	—
405	D₄²	—	2	1	no	—
406	#535	—	2	2	no	—
407	#535	C₂²×C₆₁	1	2	yes	—
408	#532	—	2	1	no	—
409	#532	C₂²×C₆₁	1	1	yes	characteristic
410	C₂×#127	—	2	1	no	—
411	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
412	C₂×#127	C₂²×C₆₁	1	2	yes	complemented
413	C₂×#121	—	2	2	no	—
414	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
415	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
416	#463	—	2	2	no	—
417	#461	—	2	1	no	—
418	#459	—	2	1	no	—
419	#453	—	2	8	no	—
420	#442	—	2	1	no	—
421	#440	—	2	1	no	—
422	C₄×SD₁₆	—	2	1	no	—
423	C₄×D₈	—	2	1	no	—
424	#428	C₂²×C₆₁	1	1	yes	characteristic, complemented
425	#423	C₂²×C₆₁	1	1	yes	characteristic, complemented
426	C₂×#104	C₂²×C₆₁	1	2	yes	—
427	C₂×#104	C₂²×C₆₁	1	2	yes	complemented
428	C₂×#104	C₂²×C₆₁	1	2	yes	complemented
429	#418	C₂²×C₆₁	1	1	yes	characteristic, complemented
430	#417	C₂²×C₆₁	1	1	yes	characteristic
431	#417	C₂²×C₆₁	1	2	yes	complemented
432	C₂×#100	C₂²×C₆₁	1	2	yes	complemented
433	C₂×#100	C₂²×C₆₁	1	2	yes	complemented
434	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
435	#392	—	2	2	no	—
436	#390	C₂²×C₆₁	1	2	yes	complemented
437	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
438	#339	C₂²×C₆₁	1	2	yes	complemented
439	C₆₁	#24230	1	1	yes	characteristic, direct product factor, Sylow
440	H(5,𝔽₂)	—	2	4	no	—
441	H(5,𝔽₂)	—	2	4	no	—
442	H(5,𝔽₂)	—	4	2	no	—
443	H(5,𝔽₂)	—	4	2	no	—
444	C₂×#41	—	2	2	no	—
445	C₂×#41	—	2	2	no	—
446	C₂×#41	C₂³×C₆₁	1	2	yes	—
447	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
448	C₂²×D₄	—	2	4	no	—
449	C₂²×D₄	—	2	2	no	—
450	C₂²×D₄	—	2	2	no	—
451	C₂²×D₄	—	2	2	no	—
452	C₂²×D₄	—	2	2	no	—
453	C₂²×D₄	—	2	4	no	—
454	C₂²×D₄	D₄×C₆₁	1	2	yes	—
455	C₂²×D₄	D₄×C₆₁	1	2	yes	—
456	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
457	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
458	C₂³×C₄	—	2	1	no	—
459	AGL(1,ℤ/8)	—	2	2	no	—
460	AGL(1,ℤ/8)	—	2	4	no	—
461	AGL(1,ℤ/8)	—	4	2	no	—
462	AGL(1,ℤ/8)	D₄×C₆₁	1	4	yes	complemented
463	C₂×SD₁₆	—	2	1	no	—
464	C₂×SD₁₆	—	2	2	no	—
465	C₂×D₈	—	2	1	no	—
466	C₂×D₈	—	2	2	no	—
467	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
468	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
469	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
470	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic, complemented
471	#127	—	2	2	no	—
472	#127	—	2	2	no	—
473	#127	—	2	2	no	—
474	#127	—	2	4	no	—
475	#127	—	2	1	no	—
476	#127	—	2	1	no	—
477	#127	—	2	1	no	—
478	#127	—	2	1	no	—
479	#127	—	4	2	no	—
480	#127	D₄×C₆₁	1	1	yes	characteristic, complemented
481	#124	—	2	2	no	—
482	#124	D₄×C₆₁	1	2	yes	complemented
483	#121	—	2	2	no	—
484	#121	—	2	2	no	—
485	#121	—	2	4	no	—
486	#121	—	2	4	no	—
487	#121	—	2	1	no	—
488	#121	—	2	1	no	—
489	#121	—	2	2	no	—
490	#121	—	2	2	no	—
491	#121	—	4	8	no	—
492	#120	—	2	4	no	—
493	#120	—	2	4	no	—
494	#120	—	2	4	no	—
495	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic, complemented
496	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic, complemented
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	1	no	—
500	C₄×D₄	—	2	1	no	—
501	C₄×D₄	—	2	1	no	—
502	C₄×D₄	—	2	1	no	—
503	C₄×D₄	—	2	1	no	—
504	C₄×D₄	—	2	1	no	—
505	C₄×D₄	—	2	1	no	—
506	C₄×D₄	—	2	1	no	—
507	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic, complemented
508	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic, complemented
509	#117	—	2	1	no	—
510	#117	C₂³×C₆₁	1	1	yes	characteristic
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	—	2	4	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₄²	—	2	1	no	—
516	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
517	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
518	#107	—	2	1	no	—
519	#106	—	2	1	no	—
520	C₄⋊C₈	—	2	1	no	—
521	C₄⋊C₈	—	2	1	no	—
522	#104	—	2	4	no	—
523	#104	—	2	4	no	—
524	#104	—	4	2	no	—
525	#103	—	2	1	no	—
526	#103	—	2	2	no	—
527	#102	—	2	1	no	—
528	#102	—	2	2	no	—
529	#102	—	2	1	no	—
530	#102	—	2	1	no	—
531	#100	—	2	4	no	—
532	#100	—	4	2	no	—
533	#97	—	2	1	no	—
534	C₄×C₈	—	2	1	no	—
535	#95	—	2	1	no	—
536	C₂⁴	—	2	4	no	—
537	C₂⁴	—	2	1	no	—
538	C₂⁴	C₂×D₄×C₆₁	1	4	yes	—
539	#41	—	2	1	no	—
540	#41	—	2	1	no	—
541	#41	—	2	2	no	—
542	#41	—	2	2	no	—
543	#41	—	2	2	no	—
544	#41	—	2	2	no	—
545	#41	—	4	4	no	—
546	#41	—	4	4	no	—
547	#41	—	4	4	no	—
548	#41	—	4	4	no	—
549	#41	C₂×D₄×C₆₁	1	2	yes	—
550	#41	#41×C₆₁	1	2	yes	—
551	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
552	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	4	4	no	—
577	C₂×D₄	—	4	4	no	—
578	C₂×D₄	—	4	4	no	—
579	C₂×D₄	—	4	8	no	—
580	C₂×D₄	—	4	8	no	—
581	C₂×D₄	—	4	8	no	—
582	C₂×D₄	—	4	4	no	—
583	C₂×D₄	—	4	4	no	—
584	C₂×D₄	—	4	8	no	—
585	C₂×D₄	—	8	4	no	—
586	C₂×D₄	—	8	4	no	—
587	C₂×D₄	—	8	2	no	—
588	C₂×D₄	—	8	4	no	—
589	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
590	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
591	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	complemented
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	4	4	no	—
600	C₂²×C₄	—	4	1	no	—
601	C₂²×C₄	—	4	1	no	—
602	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
605	SD₁₆	—	2	4	no	—
606	SD₁₆	—	4	4	no	—
607	D₈	—	2	4	no	—
608	D₈	—	4	4	no	—
609	M₁₆	—	2	1	no	—
610	M₁₆	—	2	2	no	—
611	M₁₆	—	2	1	no	—
612	M₁₆	—	2	2	no	—
613	M₁₆	—	2	1	no	—
614	M₁₆	C₂×D₄×C₆₁	1	2	yes	complemented
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	2	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
626	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	4	8	no	—
635	C₂²⋊C₄	—	4	1	no	—
636	C₂²⋊C₄	—	4	1	no	—
637	C₄²	—	2	1	no	—
638	C₄²	—	2	1	no	—
639	C₄²	—	2	1	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	2	no	—
642	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
643	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
644	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
645	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
646	C₂³	—	2	1	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	4	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	4	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	4	2	no	—
653	C₂³	—	4	2	no	—
654	C₂³	—	4	8	no	—
655	C₂³	—	4	4	no	—
656	C₂³	—	4	4	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	8	4	no	—
660	C₂³	—	8	4	no	—
661	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
662	Q₈	—	2	1	no	—
663	Q₈	—	2	2	no	—
664	Q₈	—	2	2	no	—
665	Q₈	#121×C₆₁	1	2	yes	complemented
666	D₄	—	2	2	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	1	no	—
669	D₄	—	2	2	no	—
670	D₄	—	2	2	no	—
671	D₄	—	2	2	no	—
672	D₄	—	2	2	no	—
673	D₄	—	4	8	no	—
674	D₄	—	4	4	no	—
675	D₄	—	4	2	no	—
676	D₄	—	4	8	no	—
677	D₄	—	4	2	no	—
678	D₄	—	4	2	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	2	no	—
681	D₄	—	4	2	no	—
682	D₄	—	4	1	no	—
683	D₄	—	4	2	no	—
684	D₄	—	4	4	no	—
685	D₄	—	4	2	no	—
686	D₄	—	4	2	no	—
687	D₄	—	8	2	no	—
688	D₄	—	8	2	no	—
689	D₄	—	8	4	no	—
690	D₄	—	8	4	no	—
691	D₄	—	8	16	no	—
692	D₄	#121×C₆₁	1	2	yes	complemented
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	8	no	—
703	C₂×C₄	—	4	2	no	—
704	C₂×C₄	—	4	2	no	—
705	C₂×C₄	—	4	2	no	—
706	C₂×C₄	—	4	2	no	—
707	C₂×C₄	—	4	2	no	—
708	C₂×C₄	—	4	2	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	8	2	no	—
712	C₂×C₄	—	8	2	no	—
713	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
714	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
715	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
716	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
718	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
719	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
720	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
721	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
722	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
723	C₈	—	2	2	no	—
724	C₈	—	4	1	no	—
725	C₈	—	4	2	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	4	4	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	4	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	4	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	8	4	no	—
740	C₂²	—	8	4	no	—
741	C₂²	—	8	2	no	—
742	C₂²	—	8	1	no	—
743	C₂²	—	8	1	no	—
744	C₂²	—	16	8	no	—
745	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
746	C₂²	D₄²×C₆₁	1	1	yes	characteristic
747	C₂²	C₆₁×#546	1	1	yes	characteristic
748	C₄	—	2	2	no	—
749	C₄	—	2	1	no	—
750	C₄	—	2	1	no	—
751	C₄	—	2	1	no	—
752	C₄	—	4	4	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	8	1	no	—
757	C₄	C₆₁×#453	1	2	yes	complemented
758	C₄	C₂×#121×C₆₁	1	1	yes	characteristic
759	C₄	C₆₁×#535	1	1	yes	characteristic
760	C₄	D₄²×C₆₁	1	1	yes	characteristic
761	C₄	C₆₁×#546	1	1	yes	characteristic
762	C₂	—	2	1	no	—
763	C₂	—	2	1	no	—
764	C₂	—	4	2	no	—
765	C₂	—	8	2	no	—
766	C₂	—	8	4	no	—
767	C₂	—	8	2	no	—
768	C₂	C₆₁×#2408	1	1	yes	characteristic
769	C₂	C₂×C₆₁×#453	1	1	yes	characteristic
770	C₂	C₆₁×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3498	C₂	semidirect
2. C₆₁×#3036	C₂	semidirect
3. C₂×C₆₁×#453	C₂	semidirect
4. C₄×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
5. C₆₁×#2541	C₂	semidirect
6. C₆₁×#2037	C₂	semidirect
7. C₆₁×#2002	C₂	semidirect
8. C₆₁×#1980	C₂	semidirect
9. C₆₁×#1965	C₂	semidirect
10. C₆₁×#1806	C₂	semidirect
11. C₆₁×#1792	C₂	semidirect
14. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
27. C₂×#127×C₆₁	C₂²	semidirect
30. C₂×C₄×D₄×C₆₁	C₂²	semidirect
39. C₆₁×#428	C₂²	semidirect
40. C₆₁×#423	C₂²	semidirect
42. C₂×#104×C₆₁	C₂²	semidirect
43. C₂×#104×C₆₁	C₂²	semidirect
44. C₆₁×#418	C₂²	semidirect
46. C₆₁×#417	C₂²	semidirect
47. C₂×#100×C₆₁	C₂²	semidirect
48. C₂×#100×C₆₁	C₂²	semidirect
49. C₄×M₁₆×C₆₁	C₂²	semidirect
51. C₆₁×#390	C₂²	semidirect
52. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
53. C₆₁×#339	C₂²	semidirect
76. AGL(1,ℤ/8)×C₆₁	D₄	semidirect
84. C₄⋊Q₈×C₆₁	D₄	semidirect
94. #127×C₆₁	D₄	semidirect
96. #124×C₆₁	D₄	semidirect
109. C₄×Q₈×C₆₁	D₄	semidirect
110. C₄×Q₈×C₆₁	D₄	semidirect
121. C₄×D₄×C₆₁	D₄	semidirect
122. C₄×D₄×C₆₁	D₄	semidirect
205. C₂×D₄×C₆₁	C₂×D₄	semidirect
228. M₁₆×C₆₁	C₂×D₄	semidirect
279. Q₈×C₆₁	#121	semidirect
306. D₄×C₆₁	#121	semidirect
340. #24230	C₆₁	direct (N × H)
372. C₄×C₆₁	#453	semidirect
377. #3498	C₂×C₆₁	semidirect
378. #3036	C₂×C₆₁	semidirect
379. C₂×#453	C₂×C₆₁	semidirect
380. C₄×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
381. #2541	C₂×C₆₁	semidirect
382. #2037	C₂×C₆₁	semidirect
383. #2002	C₂×C₆₁	semidirect
384. #1980	C₂×C₆₁	semidirect
385. #1965	C₂×C₆₁	semidirect
386. #1806	C₂×C₆₁	semidirect
387. #1792	C₂×C₆₁	semidirect
399. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
412. C₂×#127	C₂²×C₆₁	semidirect
415. C₂×C₄×D₄	C₂²×C₆₁	semidirect
424. #428	C₂²×C₆₁	semidirect
425. #423	C₂²×C₆₁	semidirect
427. C₂×#104	C₂²×C₆₁	semidirect
428. C₂×#104	C₂²×C₆₁	semidirect
429. #418	C₂²×C₆₁	semidirect
431. #417	C₂²×C₆₁	semidirect
432. C₂×#100	C₂²×C₆₁	semidirect
433. C₂×#100	C₂²×C₆₁	semidirect
434. C₄×M₁₆	C₂²×C₆₁	semidirect
436. #390	C₂²×C₆₁	semidirect
437. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
438. #339	C₂²×C₆₁	semidirect
439. C₆₁	#24230	direct (N × H)
462. AGL(1,ℤ/8)	D₄×C₆₁	semidirect
470. C₄⋊Q₈	D₄×C₆₁	semidirect
480. #127	D₄×C₆₁	semidirect
482. #124	D₄×C₆₁	semidirect
495. C₄×Q₈	D₄×C₆₁	semidirect
496. C₄×Q₈	D₄×C₆₁	semidirect
507. C₄×D₄	D₄×C₆₁	semidirect
508. C₄×D₄	D₄×C₆₁	semidirect
591. C₂×D₄	C₂×D₄×C₆₁	semidirect
614. M₁₆	C₂×D₄×C₆₁	semidirect
665. Q₈	#121×C₆₁	semidirect
692. D₄	#121×C₆₁	semidirect
757. C₄	C₆₁×#453	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3498	2
C₆₁×#3036	2
C₂×C₆₁×#453	2
C₄×AGL(1,ℤ/8)×C₆₁	2
C₆₁×#2541	2
C₆₁×#2037	2
C₆₁×#2002	2
C₆₁×#1980	2
C₆₁×#1965	2
C₆₁×#1806	2
C₆₁×#1792	2
#24230	61

Subgroups — C61×#24230 #29527663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24230 #29527663