Subgroups — C₆₁×#26024 #29529457

Order 15616.

786 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	C₆₁×#2551	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#2354	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2065	C₂	1	2	yes	maximal
4	C₆₁×#2023	C₂	1	2	yes	maximal
5	C₆₁×#1987	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1920	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1834	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1802	C₂	1	1	yes	maximal, characteristic
11	C₄×#102×C₆₁	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
13	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#117×C₆₁	—	2	1	no	—
16	C₂×#106×C₆₁	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
19	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#102×C₆₁	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#395	—	2	2	no	—
24	C₆₁×#390	C₂²	1	2	yes	—
25	C₆₁×#389	—	2	1	no	—
26	C₆₁×#389	C₂²	1	2	yes	—
27	C₆₁×#388	—	2	2	no	—
28	C₆₁×#384	C₂²	1	1	yes	characteristic
29	C₆₁×#384	C₂²	1	1	yes	characteristic
30	C₆₁×#380	—	2	1	no	—
31	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#340	C₂²	1	1	yes	characteristic
35	C₆₁×#340	C₂²	1	1	yes	characteristic
36	C₆₁×#340	C₂²	1	2	yes	—
37	C₆₁×#340	C₂²	1	2	yes	—
38	C₆₁×#340	C₂²	1	2	yes	—
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₆₁	—	2	2	no	—
42	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₆₁	—	2	1	no	—
44	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
47	C₄⋊Q₈×C₆₁	—	2	4	no	—
48	C₄⋊Q₈×C₆₁	—	4	2	no	—
49	C₄⋊Q₈×C₆₁	—	4	4	no	—
50	C₄×D₄×C₆₁	—	2	2	no	—
51	C₄×D₄×C₆₁	Q₈	1	4	yes	complemented
52	#117×C₆₁	—	4	4	no	—
53	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₄²×C₆₁	—	2	1	no	—
70	C₂×C₄²×C₆₁	—	2	2	no	—
71	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
72	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
73	#106×C₆₁	—	2	4	no	—
74	C₄⋊C₈×C₆₁	—	2	2	no	—
75	C₄⋊C₈×C₆₁	—	4	2	no	—
76	#102×C₆₁	—	2	2	no	—
77	#102×C₆₁	—	2	2	no	—
78	#102×C₆₁	—	4	2	no	—
79	C₄×C₈×C₆₁	—	2	2	no	—
80	#95×C₆₁	—	2	2	no	—
81	#95×C₆₁	—	2	1	no	—
82	#95×C₆₁	—	2	2	no	—
83	#95×C₆₁	D₄	1	2	yes	—
84	C₂⁴×C₆₁	—	2	1	no	—
85	C₂×Q₈×C₆₁	—	4	4	no	—
86	C₂×Q₈×C₆₁	—	4	4	no	—
87	C₂×Q₈×C₆₁	—	8	2	no	—
88	C₂×D₄×C₆₁	—	2	1	no	—
89	C₂×D₄×C₆₁	—	2	1	no	—
90	C₂×D₄×C₆₁	—	2	1	no	—
91	C₂×D₄×C₆₁	—	2	1	no	—
92	C₂×D₄×C₆₁	—	2	1	no	—
93	C₂×D₄×C₆₁	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₆₁	—	2	1	no	—
95	C₂²×C₄×C₆₁	—	2	1	no	—
96	C₂²×C₄×C₆₁	—	2	1	no	—
97	C₂²×C₄×C₆₁	—	2	4	no	—
98	C₂²×C₄×C₆₁	—	2	2	no	—
99	C₂²×C₄×C₆₁	—	2	2	no	—
100	C₂²×C₄×C₆₁	—	4	2	no	—
101	C₂²×C₄×C₆₁	—	4	2	no	—
102	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₆₁	—	2	1	no	—
108	C₂×C₈×C₆₁	—	2	1	no	—
109	C₂×C₈×C₆₁	—	2	1	no	—
110	C₂×C₈×C₆₁	—	2	1	no	—
111	C₂×C₈×C₆₁	—	2	2	no	—
112	C₂×C₈×C₆₁	—	2	2	no	—
113	C₂×C₈×C₆₁	—	2	2	no	—
114	C₂×C₈×C₆₁	—	2	1	no	—
115	C₂×C₈×C₆₁	—	2	1	no	—
116	C₄⋊C₄×C₆₁	—	2	2	no	—
117	C₄⋊C₄×C₆₁	—	2	1	no	—
118	C₄⋊C₄×C₆₁	—	2	1	no	—
119	C₄⋊C₄×C₆₁	—	2	1	no	—
120	C₄⋊C₄×C₆₁	—	2	2	no	—
121	C₄⋊C₄×C₆₁	—	2	2	no	—
122	C₄⋊C₄×C₆₁	—	2	2	no	—
123	C₄⋊C₄×C₆₁	—	2	2	no	—
124	C₄⋊C₄×C₆₁	—	4	4	no	—
125	C₄⋊C₄×C₆₁	—	4	4	no	—
126	C₄⋊C₄×C₆₁	—	4	2	no	—
127	C₄⋊C₄×C₆₁	—	4	2	no	—
128	C₄⋊C₄×C₆₁	—	8	1	no	—
129	C₄⋊C₄×C₆₁	—	8	1	no	—
130	C₄⋊C₄×C₆₁	SD₁₆	1	4	yes	—
131	C₄⋊C₄×C₆₁	C₂×Q₈	1	2	yes	—
132	C₄⋊C₄×C₆₁	#41	1	2	yes	—
133	C₄⋊C₄×C₆₁	#41	1	2	yes	—
134	C₂²⋊C₄×C₆₁	—	2	4	no	—
135	C₂²⋊C₄×C₆₁	—	4	4	no	—
136	C₂²⋊C₄×C₆₁	—	8	2	no	—
137	C₄²×C₆₁	—	2	2	no	—
138	C₄²×C₆₁	—	2	2	no	—
139	C₄²×C₆₁	—	4	4	no	—
140	C₄²×C₆₁	—	4	2	no	—
141	C₄²×C₆₁	C₂×Q₈	1	2	yes	—
142	C₄²×C₆₁	#41	1	2	yes	—
143	C₂³×C₆₁	—	2	2	no	—
144	C₂³×C₆₁	—	4	1	no	—
145	C₂³×C₆₁	—	4	1	no	—
146	C₂³×C₆₁	—	4	1	no	—
147	C₂³×C₆₁	—	4	1	no	—
148	C₂³×C₆₁	—	4	1	no	—
149	C₂³×C₆₁	—	4	1	no	—
150	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₆₁	—	8	8	no	—
152	D₄×C₆₁	—	2	2	no	—
153	D₄×C₆₁	—	2	2	no	—
154	D₄×C₆₁	—	4	1	no	—
155	D₄×C₆₁	—	4	1	no	—
156	C₂×C₄×C₆₁	—	2	2	no	—
157	C₂×C₄×C₆₁	—	2	1	no	—
158	C₂×C₄×C₆₁	—	2	1	no	—
159	C₂×C₄×C₆₁	—	2	2	no	—
160	C₂×C₄×C₆₁	—	2	2	no	—
161	C₂×C₄×C₆₁	—	2	2	no	—
162	C₂×C₄×C₆₁	—	2	2	no	—
163	C₂×C₄×C₆₁	—	2	2	no	—
164	C₂×C₄×C₆₁	—	2	2	no	—
165	C₂×C₄×C₆₁	—	2	2	no	—
166	C₂×C₄×C₆₁	—	4	1	no	—
167	C₂×C₄×C₆₁	—	4	1	no	—
168	C₂×C₄×C₆₁	—	4	1	no	—
169	C₂×C₄×C₆₁	—	4	1	no	—
170	C₂×C₄×C₆₁	—	4	1	no	—
171	C₂×C₄×C₆₁	—	4	1	no	—
172	C₂×C₄×C₆₁	—	4	8	no	—
173	C₂×C₄×C₆₁	—	4	2	no	—
174	C₂×C₄×C₆₁	—	4	2	no	—
175	C₂×C₄×C₆₁	—	4	2	no	—
176	C₂×C₄×C₆₁	—	4	2	no	—
177	C₂×C₄×C₆₁	—	4	2	no	—
178	C₂×C₄×C₆₁	—	4	2	no	—
179	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
180	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
181	C₂×C₄×C₆₁	C₂×SD₁₆	1	4	yes	—
182	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
183	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
184	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
189	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
190	C₈×C₆₁	—	4	1	no	—
191	C₈×C₆₁	—	4	2	no	—
192	C₈×C₆₁	—	4	1	no	—
193	#26024	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂²×C₆₁	—	4	2	no	—
195	C₂²×C₆₁	—	4	2	no	—
196	C₂²×C₆₁	—	4	2	no	—
197	C₂²×C₆₁	—	8	1	no	—
198	C₂²×C₆₁	—	8	1	no	—
199	C₂²×C₆₁	—	8	1	no	—
200	C₂²×C₆₁	—	8	1	no	—
201	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
202	C₂²×C₆₁	#546	1	1	yes	characteristic
203	C₂²×C₆₁	#548	1	1	yes	characteristic
204	C₂²×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
205	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₂²×C₆₁	#576	1	1	yes	characteristic
207	C₂²×C₆₁	#578	1	1	yes	characteristic
208	C₄×C₆₁	—	2	2	no	—
209	C₄×C₆₁	—	2	4	no	—
210	C₄×C₆₁	—	4	2	no	—
211	C₄×C₆₁	—	4	2	no	—
212	C₄×C₆₁	—	4	2	no	—
213	C₄×C₆₁	—	4	2	no	—
214	C₄×C₆₁	—	8	2	no	—
215	C₄×C₆₁	—	8	2	no	—
216	C₄×C₆₁	#476	1	4	yes	—
217	C₄×C₆₁	#533	1	1	yes	characteristic
218	C₄×C₆₁	#544	1	1	yes	characteristic
219	C₄×C₆₁	#555	1	1	yes	characteristic
220	C₄×C₆₁	#556	1	1	yes	characteristic
221	#2551	C₂×C₆₁	1	1	yes	characteristic, complemented
222	#2354	C₂×C₆₁	1	1	yes	characteristic
223	#2065	C₂×C₆₁	1	2	yes	—
224	#2023	C₂×C₆₁	1	2	yes	—
225	#1987	C₂×C₆₁	1	2	yes	complemented
226	#1948	C₂×C₆₁	1	1	yes	characteristic, complemented
227	#1939	C₂×C₆₁	1	1	yes	characteristic, complemented
228	#1920	C₂×C₆₁	1	2	yes	complemented
229	#1834	C₂×C₆₁	1	1	yes	characteristic, complemented
230	#1802	C₂×C₆₁	1	1	yes	characteristic
231	C₄×#102	C₂×C₆₁	1	1	yes	characteristic
232	C₂×C₆₁	—	8	2	no	—
233	C₂×C₆₁	#2439	1	1	yes	characteristic
234	C₂×C₆₁	C₂×#476	1	1	yes	characteristic
235	C₂×C₆₁	#3083	1	1	yes	characteristic
236	C₂×C₆₁	#3298	1	1	yes	characteristic
237	C₂×C₆₁	#3325	1	1	yes	characteristic
238	C₂×C₆₁	#3362	1	1	yes	characteristic
239	C₂×C₆₁	#3367	1	1	yes	characteristic
240	C₂×C₄⋊Q₈	—	2	1	no	—
241	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
242	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
243	C₂×#117	—	2	1	no	—
244	C₂×#106	C₂²×C₆₁	1	2	yes	—
245	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
247	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
248	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
249	C₂×#102	C₂²×C₆₁	1	2	yes	—
250	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
251	#395	—	2	2	no	—
252	#390	C₂²×C₆₁	1	2	yes	—
253	#389	—	2	1	no	—
254	#389	C₂²×C₆₁	1	2	yes	—
255	#388	—	2	2	no	—
256	#384	C₂²×C₆₁	1	1	yes	characteristic
257	#384	C₂²×C₆₁	1	1	yes	characteristic
258	#380	—	2	1	no	—
259	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
260	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
261	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
262	#340	C₂²×C₆₁	1	2	yes	—
263	#340	C₂²×C₆₁	1	2	yes	—
264	#340	C₂²×C₆₁	1	2	yes	—
265	#340	C₂²×C₆₁	1	1	yes	characteristic
266	#340	C₂²×C₆₁	1	2	yes	—
267	#340	C₂²×C₆₁	1	1	yes	characteristic
268	#336	C₂²×C₆₁	1	2	yes	—
269	C₆₁	#26024	1	1	yes	characteristic, direct product factor, Sylow
270	C₂²×Q₈	—	2	2	no	—
271	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
272	C₂³×C₄	—	2	1	no	—
273	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
275	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
276	C₄⋊Q₈	—	2	4	no	—
277	C₄⋊Q₈	—	4	2	no	—
278	C₄⋊Q₈	—	4	4	no	—
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	Q₈×C₆₁	1	4	yes	complemented
281	#117	—	4	4	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
289	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
301	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
302	#106	—	2	4	no	—
303	C₄⋊C₈	—	2	2	no	—
304	C₄⋊C₈	—	4	2	no	—
305	#102	—	2	2	no	—
306	#102	—	2	2	no	—
307	#102	—	4	2	no	—
308	C₄×C₈	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	1	no	—
311	#95	—	2	2	no	—
312	#95	D₄×C₆₁	1	2	yes	—
313	C₂⁴	—	2	1	no	—
314	C₂×Q₈	—	4	4	no	—
315	C₂×Q₈	—	4	4	no	—
316	C₂×Q₈	—	8	2	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	C₂×Q₈×C₆₁	1	2	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	8	1	no	—
358	C₄⋊C₄	—	8	1	no	—
359	C₄⋊C₄	SD₁₆×C₆₁	1	4	yes	—
360	C₄⋊C₄	C₂×Q₈×C₆₁	1	2	yes	—
361	C₄⋊C₄	#41×C₆₁	1	2	yes	—
362	C₄⋊C₄	#41×C₆₁	1	2	yes	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	4	4	no	—
365	C₂²⋊C₄	—	8	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	4	no	—
369	C₄²	—	4	2	no	—
370	C₄²	C₂×Q₈×C₆₁	1	2	yes	—
371	C₄²	#41×C₆₁	1	2	yes	—
372	C₂³	—	2	2	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
380	Q₈	—	8	8	no	—
381	D₄	—	2	2	no	—
382	D₄	—	2	2	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	8	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
409	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
410	C₂×C₄	C₂×SD₁₆×C₆₁	1	4	yes	—
411	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
412	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
413	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
414	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
417	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
418	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
419	C₈	—	4	1	no	—
420	C₈	—	4	2	no	—
421	C₈	—	4	1	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
430	C₂²	C₆₁×#546	1	1	yes	characteristic
431	C₂²	C₆₁×#548	1	1	yes	characteristic
432	C₂²	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
433	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
434	C₂²	C₆₁×#576	1	1	yes	characteristic
435	C₂²	C₆₁×#578	1	1	yes	characteristic
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	8	2	no	—
443	C₄	—	8	2	no	—
444	C₄	C₆₁×#476	1	4	yes	—
445	C₄	C₆₁×#533	1	1	yes	characteristic
446	C₄	C₆₁×#544	1	1	yes	characteristic
447	C₄	C₆₁×#555	1	1	yes	characteristic
448	C₄	C₆₁×#556	1	1	yes	characteristic
449	C₂	—	8	2	no	—
450	C₂	C₆₁×#2439	1	1	yes	characteristic
451	C₂	C₂×C₆₁×#476	1	1	yes	characteristic
452	C₂	C₆₁×#3083	1	1	yes	characteristic
453	C₂	C₆₁×#3298	1	1	yes	characteristic
454	C₂	C₆₁×#3325	1	1	yes	characteristic
455	C₂	C₆₁×#3362	1	1	yes	characteristic
456	C₂	C₆₁×#3367	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₆₁×#2551	C₂	semidirect
5. C₆₁×#1987	C₂	semidirect
6. C₆₁×#1948	C₂	semidirect
7. C₆₁×#1939	C₂	semidirect
8. C₆₁×#1920	C₂	semidirect
9. C₆₁×#1834	C₂	semidirect
51. C₄×D₄×C₆₁	Q₈	semidirect
193. #26024	C₆₁	direct (N × H)
221. #2551	C₂×C₆₁	semidirect
225. #1987	C₂×C₆₁	semidirect
226. #1948	C₂×C₆₁	semidirect
227. #1939	C₂×C₆₁	semidirect
228. #1920	C₂×C₆₁	semidirect
229. #1834	C₂×C₆₁	semidirect
269. C₆₁	#26024	direct (N × H)
280. C₄×D₄	Q₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#2551	2
C₆₁×#2354	2
C₆₁×#2065	2
C₆₁×#2023	2
C₆₁×#1987	2
C₆₁×#1948	2
C₆₁×#1939	2
C₆₁×#1920	2
C₆₁×#1834	2
C₆₁×#1802	2
C₄×#102×C₆₁	2
#26024	61

Subgroups — C61×#26024 #29529457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#26024 #29529457