Subgroups — C₆₁×#22893 #29526326

Order 15616.

1012 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#454	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2946	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2898	C₂	1	2	yes	maximal, complemented
4	C₆₁×#1959	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1930	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1907	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1885	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1859	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1765	C₂	1	2	yes	maximal, complemented
10	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
12	C₂×#131×C₆₁	C₂²	1	2	yes	—
13	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#520	C₂²	1	2	yes	—
15	C₆₁×#518	C₂²	1	1	yes	characteristic
16	C₆₁×#454	C₄	1	8	yes	complemented
17	C₆₁×#442	—	2	2	no	—
18	C₆₁×#440	—	2	2	no	—
19	C₄×SD₁₆×C₆₁	—	2	2	no	—
20	C₄×D₈×C₆₁	—	2	2	no	—
21	C₆₁×#428	C₂²	1	2	yes	—
22	C₂×#104×C₆₁	C₂²	1	2	yes	—
23	C₆₁×#419	—	2	2	no	—
24	C₆₁×#419	C₂²	1	2	yes	—
25	C₆₁×#417	—	2	2	no	—
26	C₆₁×#417	C₂²	1	2	yes	—
27	C₆₁×#416	—	2	2	no	—
28	C₆₁×#416	C₂²	1	2	yes	—
29	C₂×#103×C₆₁	—	2	2	no	—
30	C₂×#103×C₆₁	C₂²	1	2	yes	—
31	C₂×#102×C₆₁	C₂²	1	2	yes	—
32	C₂×#101×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#100×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#405	C₂²	1	2	yes	—
35	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
36	C₆₁×#384	C₂²	1	1	yes	characteristic
37	C₆₁×#343	C₂²	1	2	yes	—
38	C₆₁×#341	C₂²	1	2	yes	—
39	C₆₁×#339	C₂²	1	2	yes	—
40	2₋¹⁺⁴×C₆₁	—	2	4	no	—
41	2₋¹⁺⁴×C₆₁	—	4	1	no	—
42	2₋¹⁺⁴×C₆₁	C₂×C₄	1	4	yes	complemented
43	C₂×#41×C₆₁	—	2	2	no	—
44	C₂×#41×C₆₁	—	4	1	no	—
45	C₂×#41×C₆₁	C₂³	1	2	yes	—
46	C₂²×Q₈×C₆₁	—	2	2	no	—
47	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
49	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
50	AGL(1,ℤ/8)×C₆₁	C₂×C₄	1	8	yes	complemented
51	C₂×SD₁₆×C₆₁	—	2	2	no	—
52	C₂×D₈×C₆₁	—	2	2	no	—
53	#131×C₆₁	—	2	4	no	—
54	#131×C₆₁	—	4	2	no	—
55	C₂×M₁₆×C₆₁	—	2	2	no	—
56	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
57	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₆₁	—	2	2	no	—
59	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
60	#124×C₆₁	—	4	1	no	—
61	#124×C₆₁	C₂×C₄	1	4	yes	complemented
62	C₄×Q₈×C₆₁	—	2	2	no	—
63	C₄×D₄×C₆₁	—	2	2	no	—
64	C₄×D₄×C₆₁	—	2	2	no	—
65	C₄×D₄×C₆₁	—	2	2	no	—
66	C₄×D₄×C₆₁	—	4	2	no	—
67	#117×C₆₁	—	2	2	no	—
68	#117×C₆₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₁	—	4	1	no	—
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₆₁	—	4	1	no	—
73	C₂×C₂²⋊C₄×C₆₁	—	4	1	no	—
74	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
75	#107×C₆₁	—	2	2	no	—
76	#106×C₆₁	—	2	2	no	—
77	#104×C₆₁	C₂×C₄	1	8	yes	complemented
78	#103×C₆₁	—	2	2	no	—
79	#103×C₆₁	—	2	2	no	—
80	#103×C₆₁	—	2	2	no	—
81	#103×C₆₁	—	2	2	no	—
82	#103×C₆₁	—	2	2	no	—
83	#103×C₆₁	D₄	1	2	yes	—
84	#103×C₆₁	D₄	1	2	yes	—
85	#102×C₆₁	—	2	2	no	—
86	#102×C₆₁	—	2	2	no	—
87	#102×C₆₁	—	2	2	no	—
88	#102×C₆₁	D₄	1	2	yes	—
89	#102×C₆₁	D₄	1	2	yes	—
90	#101×C₆₁	C₂×C₄	1	4	yes	complemented
91	#100×C₆₁	—	4	1	no	—
92	#97×C₆₁	—	2	2	no	—
93	#97×C₆₁	—	4	1	no	—
94	C₄×C₈×C₆₁	—	2	2	no	—
95	C₂⁴×C₆₁	—	2	1	no	—
96	#41×C₆₁	—	2	2	no	—
97	#41×C₆₁	—	2	2	no	—
98	#41×C₆₁	—	2	8	no	—
99	#41×C₆₁	—	4	4	no	—
100	#41×C₆₁	—	4	4	no	—
101	#41×C₆₁	—	4	4	no	—
102	#41×C₆₁	C₂²×C₄	1	4	yes	—
103	#41×C₆₁	#41	1	4	yes	—
104	C₂×Q₈×C₆₁	—	2	1	no	—
105	C₂×Q₈×C₆₁	—	2	8	no	—
106	C₂×Q₈×C₆₁	—	2	2	no	—
107	C₂×Q₈×C₆₁	—	2	2	no	—
108	C₂×Q₈×C₆₁	—	4	1	no	—
109	C₂×Q₈×C₆₁	—	4	4	no	—
110	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
111	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
112	C₂×D₄×C₆₁	—	2	2	no	—
113	C₂×D₄×C₆₁	—	2	2	no	—
114	C₂×D₄×C₆₁	—	2	2	no	—
115	C₂×D₄×C₆₁	—	2	1	no	—
116	C₂×D₄×C₆₁	—	4	1	no	—
117	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
118	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₆₁	—	2	2	no	—
120	C₂²×C₄×C₆₁	—	2	1	no	—
121	C₂²×C₄×C₆₁	—	2	1	no	—
122	C₂²×C₄×C₆₁	—	2	2	no	—
123	C₂²×C₄×C₆₁	—	4	1	no	—
124	C₂²×C₄×C₆₁	—	4	1	no	—
125	C₂²×C₄×C₆₁	—	4	2	no	—
126	C₂²×C₄×C₆₁	—	4	2	no	—
127	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
128	SD₁₆×C₆₁	—	2	8	no	—
129	D₈×C₆₁	—	2	8	no	—
130	M₁₆×C₆₁	—	2	2	no	—
131	M₁₆×C₆₁	—	2	2	no	—
132	M₁₆×C₆₁	—	2	2	no	—
133	M₁₆×C₆₁	—	4	4	no	—
134	M₁₆×C₆₁	C₂²×C₄	1	4	yes	—
135	C₂×C₈×C₆₁	—	2	2	no	—
136	C₂×C₈×C₆₁	—	2	2	no	—
137	C₂×C₈×C₆₁	—	2	2	no	—
138	C₂×C₈×C₆₁	—	2	2	no	—
139	C₂×C₈×C₆₁	—	4	4	no	—
140	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
142	C₄⋊C₄×C₆₁	—	2	2	no	—
143	C₄⋊C₄×C₆₁	—	2	2	no	—
144	C₄⋊C₄×C₆₁	—	4	2	no	—
145	C₄⋊C₄×C₆₁	—	8	2	no	—
146	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
148	C₂²⋊C₄×C₆₁	—	2	2	no	—
149	C₂²⋊C₄×C₆₁	—	4	4	no	—
150	C₂²⋊C₄×C₆₁	—	4	2	no	—
151	C₂²⋊C₄×C₆₁	—	4	2	no	—
152	C₄²×C₆₁	—	2	2	no	—
153	C₄²×C₆₁	—	2	1	no	—
154	C₄²×C₆₁	—	4	2	no	—
155	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
156	C₂³×C₆₁	—	2	2	no	—
157	C₂³×C₆₁	—	2	2	no	—
158	C₂³×C₆₁	—	4	1	no	—
159	C₂³×C₆₁	—	4	1	no	—
160	C₂³×C₆₁	—	8	1	no	—
161	C₂³×C₆₁	—	8	1	no	—
162	C₂³×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
163	Q₈×C₆₁	—	2	2	no	—
164	Q₈×C₆₁	—	2	4	no	—
165	Q₈×C₆₁	—	4	4	no	—
166	Q₈×C₆₁	—	4	2	no	—
167	Q₈×C₆₁	C₄×D₄	1	4	yes	—
168	D₄×C₆₁	—	2	4	no	—
169	D₄×C₆₁	—	2	4	no	—
170	D₄×C₆₁	—	2	4	no	—
171	D₄×C₆₁	—	2	2	no	—
172	D₄×C₆₁	—	4	4	no	—
173	D₄×C₆₁	—	4	2	no	—
174	D₄×C₆₁	C₄×D₄	1	4	yes	—
175	C₂×C₄×C₆₁	—	2	2	no	—
176	C₂×C₄×C₆₁	—	2	4	no	—
177	C₂×C₄×C₆₁	—	2	4	no	—
178	C₂×C₄×C₆₁	—	2	2	no	—
179	C₂×C₄×C₆₁	—	2	2	no	—
180	C₂×C₄×C₆₁	—	2	2	no	—
181	C₂×C₄×C₆₁	—	2	2	no	—
182	C₂×C₄×C₆₁	—	4	8	no	—
183	C₂×C₄×C₆₁	—	4	1	no	—
184	C₂×C₄×C₆₁	—	4	1	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	—	8	2	no	—
189	C₂×C₄×C₆₁	—	16	1	no	—
190	C₂×C₄×C₆₁	—	16	1	no	—
191	C₂×C₄×C₆₁	—	16	2	no	—
192	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
195	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
196	C₈×C₆₁	—	2	4	no	—
197	C₈×C₆₁	—	2	2	no	—
198	C₈×C₆₁	—	2	2	no	—
199	C₈×C₆₁	—	4	2	no	—
200	#22893	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂²×C₆₁	—	2	1	no	—
202	C₂²×C₆₁	—	2	1	no	—
203	C₂²×C₆₁	—	2	4	no	—
204	C₂²×C₆₁	—	4	2	no	—
205	C₂²×C₆₁	—	4	2	no	—
206	C₂²×C₆₁	—	4	2	no	—
207	C₂²×C₆₁	—	8	2	no	—
208	C₂²×C₆₁	—	8	1	no	—
209	C₂²×C₆₁	—	8	1	no	—
210	C₂²×C₆₁	—	16	1	no	—
211	C₂²×C₆₁	#518	1	1	yes	characteristic
212	C₂²×C₆₁	D₄²	1	1	yes	characteristic
213	C₂²×C₆₁	#551	1	1	yes	characteristic
214	C₄×C₆₁	—	2	4	no	—
215	C₄×C₆₁	—	4	2	no	—
216	C₄×C₆₁	—	4	2	no	—
217	C₄×C₆₁	—	4	2	no	—
218	C₄×C₆₁	—	4	2	no	—
219	C₄×C₆₁	—	8	2	no	—
220	C₄×C₆₁	C₂×C₄×D₄	1	2	yes	—
221	C₄×C₆₁	#546	1	2	yes	—
222	C₂×#454	C₂×C₆₁	1	1	yes	characteristic
223	#2946	C₂×C₆₁	1	2	yes	complemented
224	#2898	C₂×C₆₁	1	2	yes	complemented
225	#1959	C₂×C₆₁	1	1	yes	characteristic, complemented
226	#1930	C₂×C₆₁	1	2	yes	complemented
227	#1907	C₂×C₆₁	1	2	yes	complemented
228	#1885	C₂×C₆₁	1	1	yes	characteristic, complemented
229	#1859	C₂×C₆₁	1	2	yes	complemented
230	#1765	C₂×C₆₁	1	2	yes	complemented
231	C₂×C₆₁	—	2	1	no	—
232	C₂×C₆₁	—	2	1	no	—
233	C₂×C₆₁	—	4	4	no	—
234	C₂×C₆₁	—	8	2	no	—
235	C₂×C₆₁	#2358	1	1	yes	characteristic
236	C₂×C₆₁	#3288	1	1	yes	characteristic
237	C₂×C₆₁	#3289	1	1	yes	characteristic
238	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	1	yes	characteristic
239	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
240	C₂×#131	C₂²×C₆₁	1	2	yes	—
241	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
242	#520	C₂²×C₆₁	1	2	yes	—
243	#518	C₂²×C₆₁	1	1	yes	characteristic
244	#454	C₄×C₆₁	1	8	yes	complemented
245	#442	—	2	2	no	—
246	#440	—	2	2	no	—
247	C₄×SD₁₆	—	2	2	no	—
248	C₄×D₈	—	2	2	no	—
249	#428	C₂²×C₆₁	1	2	yes	—
250	C₂×#104	C₂²×C₆₁	1	2	yes	—
251	#419	—	2	2	no	—
252	#419	C₂²×C₆₁	1	2	yes	—
253	#417	—	2	2	no	—
254	#417	C₂²×C₆₁	1	2	yes	—
255	#416	—	2	2	no	—
256	#416	C₂²×C₆₁	1	2	yes	—
257	C₂×#103	—	2	2	no	—
258	C₂×#103	C₂²×C₆₁	1	2	yes	—
259	C₂×#102	C₂²×C₆₁	1	2	yes	—
260	C₂×#101	C₂²×C₆₁	1	1	yes	characteristic
261	C₂×#100	C₂²×C₆₁	1	1	yes	characteristic
262	#405	C₂²×C₆₁	1	2	yes	—
263	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
264	#384	C₂²×C₆₁	1	1	yes	characteristic
265	#343	C₂²×C₆₁	1	2	yes	—
266	#341	C₂²×C₆₁	1	2	yes	—
267	#339	C₂²×C₆₁	1	2	yes	—
268	C₆₁	#22893	1	1	yes	characteristic, direct product factor, Sylow
269	2₋¹⁺⁴	—	2	4	no	—
270	2₋¹⁺⁴	—	4	1	no	—
271	2₋¹⁺⁴	C₂×C₄×C₆₁	1	4	yes	complemented
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	4	1	no	—
274	C₂×#41	C₂³×C₆₁	1	2	yes	—
275	C₂²×Q₈	—	2	2	no	—
276	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
277	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
278	AGL(1,ℤ/8)	—	2	4	no	—
279	AGL(1,ℤ/8)	C₂×C₄×C₆₁	1	8	yes	complemented
280	C₂×SD₁₆	—	2	2	no	—
281	C₂×D₈	—	2	2	no	—
282	#131	—	2	4	no	—
283	#131	—	4	2	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
286	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
289	#124	—	4	1	no	—
290	#124	C₂×C₄×C₆₁	1	4	yes	complemented
291	C₄×Q₈	—	2	2	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	4	2	no	—
296	#117	—	2	2	no	—
297	#117	C₂³×C₆₁	1	2	yes	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	4	1	no	—
300	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
301	C₂×C₂²⋊C₄	—	4	1	no	—
302	C₂×C₂²⋊C₄	—	4	1	no	—
303	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
304	#107	—	2	2	no	—
305	#106	—	2	2	no	—
306	#104	C₂×C₄×C₆₁	1	8	yes	complemented
307	#103	—	2	2	no	—
308	#103	—	2	2	no	—
309	#103	—	2	2	no	—
310	#103	—	2	2	no	—
311	#103	—	2	2	no	—
312	#103	D₄×C₆₁	1	2	yes	—
313	#103	D₄×C₆₁	1	2	yes	—
314	#102	—	2	2	no	—
315	#102	—	2	2	no	—
316	#102	—	2	2	no	—
317	#102	D₄×C₆₁	1	2	yes	—
318	#102	D₄×C₆₁	1	2	yes	—
319	#101	C₂×C₄×C₆₁	1	4	yes	complemented
320	#100	—	4	1	no	—
321	#97	—	2	2	no	—
322	#97	—	4	1	no	—
323	C₄×C₈	—	2	2	no	—
324	C₂⁴	—	2	1	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	8	no	—
328	#41	—	4	4	no	—
329	#41	—	4	4	no	—
330	#41	—	4	4	no	—
331	#41	C₂²×C₄×C₆₁	1	4	yes	—
332	#41	#41×C₆₁	1	4	yes	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	8	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	4	1	no	—
338	C₂×Q₈	—	4	4	no	—
339	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
340	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
347	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
357	SD₁₆	—	2	8	no	—
358	D₈	—	2	8	no	—
359	M₁₆	—	2	2	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	4	4	no	—
363	M₁₆	C₂²×C₄×C₆₁	1	4	yes	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	4	4	no	—
369	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
370	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	8	2	no	—
375	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
376	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	4	2	no	—
384	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	8	1	no	—
390	C₂³	—	8	1	no	—
391	C₂³	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	2	4	no	—
394	Q₈	—	4	4	no	—
395	Q₈	—	4	2	no	—
396	Q₈	C₄×D₄×C₆₁	1	4	yes	—
397	D₄	—	2	4	no	—
398	D₄	—	2	4	no	—
399	D₄	—	2	2	no	—
400	D₄	—	2	4	no	—
401	D₄	—	4	4	no	—
402	D₄	—	4	2	no	—
403	D₄	C₄×D₄×C₆₁	1	4	yes	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	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	—	4	8	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	8	2	no	—
418	C₂×C₄	—	16	1	no	—
419	C₂×C₄	—	16	1	no	—
420	C₂×C₄	—	16	2	no	—
421	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
422	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
423	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
424	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	2	2	no	—
427	C₈	—	2	4	no	—
428	C₈	—	4	2	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	16	1	no	—
439	C₂²	C₆₁×#518	1	1	yes	characteristic
440	C₂²	D₄²×C₆₁	1	1	yes	characteristic
441	C₂²	C₆₁×#551	1	1	yes	characteristic
442	C₄	—	2	4	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	8	2	no	—
448	C₄	C₂×C₄×D₄×C₆₁	1	2	yes	—
449	C₄	C₆₁×#546	1	2	yes	—
450	C₂	—	2	1	no	—
451	C₂	—	2	1	no	—
452	C₂	—	4	4	no	—
453	C₂	—	8	2	no	—
454	C₂	C₆₁×#2358	1	1	yes	characteristic
455	C₂	C₆₁×#3288	1	1	yes	characteristic
456	C₂	C₆₁×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	D₄²
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×C₆₁×#454	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂²×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2946	C₂	semidirect
3. C₆₁×#2898	C₂	semidirect
4. C₆₁×#1959	C₂	semidirect
5. C₆₁×#1930	C₂	semidirect
6. C₆₁×#1907	C₂	semidirect
7. C₆₁×#1885	C₂	semidirect
8. C₆₁×#1859	C₂	semidirect
9. C₆₁×#1765	C₂	semidirect
16. C₆₁×#454	C₄	semidirect
42. 2₋¹⁺⁴×C₆₁	C₂×C₄	semidirect
50. AGL(1,ℤ/8)×C₆₁	C₂×C₄	semidirect
61. #124×C₆₁	C₂×C₄	semidirect
77. #104×C₆₁	C₂×C₄	semidirect
90. #101×C₆₁	C₂×C₄	semidirect
200. #22893	C₆₁	direct (N × H)
223. #2946	C₂×C₆₁	semidirect
224. #2898	C₂×C₆₁	semidirect
225. #1959	C₂×C₆₁	semidirect
226. #1930	C₂×C₆₁	semidirect
227. #1907	C₂×C₆₁	semidirect
228. #1885	C₂×C₆₁	semidirect
229. #1859	C₂×C₆₁	semidirect
230. #1765	C₂×C₆₁	semidirect
244. #454	C₄×C₆₁	semidirect
268. C₆₁	#22893	direct (N × H)
271. 2₋¹⁺⁴	C₂×C₄×C₆₁	semidirect
279. AGL(1,ℤ/8)	C₂×C₄×C₆₁	semidirect
290. #124	C₂×C₄×C₆₁	semidirect
306. #104	C₂×C₄×C₆₁	semidirect
319. #101	C₂×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×#454	2
C₆₁×#2946	2
C₆₁×#2898	2
C₆₁×#1959	2
C₆₁×#1930	2
C₆₁×#1907	2
C₆₁×#1885	2
C₆₁×#1859	2
C₆₁×#1765	2
#22893	61

Subgroups — C61×#22893 #29526326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#22893 #29526326