Subgroups — C₆₁×#29959 #29533392

Order 15616.

958 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2628	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#2309	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2092	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2067	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2065	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2023	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1854	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1798	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1786	C₂	1	2	yes	maximal
10	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
12	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#107×C₆₁	C₂²	1	2	yes	complemented
15	C₂×#106×C₆₁	C₂²	1	2	yes	complemented
16	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
18	C₂×#102×C₆₁	C₂²	1	2	yes	—
19	C₂×#102×C₆₁	C₂²	1	2	yes	—
20	C₂×#102×C₆₁	C₂²	1	2	yes	—
21	C₂×#102×C₆₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
23	C₆₁×#400	—	2	1	no	—
24	C₆₁×#399	—	2	1	no	—
25	C₆₁×#395	—	2	1	no	—
26	C₆₁×#393	—	2	1	no	—
27	C₆₁×#390	—	2	1	no	—
28	C₆₁×#390	—	2	1	no	—
29	C₆₁×#390	C₂²	1	2	yes	—
30	C₆₁×#390	C₂²	1	2	yes	—
31	C₆₁×#389	C₂²	1	2	yes	complemented
32	C₆₁×#382	C₂²	1	1	yes	characteristic, complemented
33	C₆₁×#380	C₂²	1	2	yes	—
34	C₆₁×#379	—	2	1	no	—
35	C₆₁×#379	—	2	1	no	—
36	C₆₁×#340	C₂²	1	2	yes	complemented
37	C₆₁×#340	C₂²	1	2	yes	complemented
38	C₆₁×#336	C₂²	1	2	yes	complemented
39	C₂⁵×C₆₁	—	2	1	no	—
40	C₂²×Q₈×C₆₁	—	2	1	no	—
41	C₂²×D₄×C₆₁	—	2	1	no	—
42	C₂²×D₄×C₆₁	—	2	2	no	—
43	C₂²×D₄×C₆₁	—	4	1	no	—
44	C₂²×D₄×C₆₁	—	4	1	no	—
45	C₂²×D₄×C₆₁	—	4	1	no	—
46	C₂²×D₄×C₆₁	—	4	1	no	—
47	C₂²×D₄×C₆₁	Q₈	1	4	yes	complemented
48	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₆₁	—	4	1	no	—
53	C₄⋊Q₈×C₆₁	—	4	1	no	—
54	#117×C₆₁	—	4	1	no	—
55	#117×C₆₁	—	4	1	no	—
56	#117×C₆₁	—	4	1	no	—
57	#117×C₆₁	—	4	1	no	—
58	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₆₁	—	2	1	no	—
74	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
76	#107×C₆₁	—	4	2	no	—
77	#106×C₆₁	—	4	2	no	—
78	C₄⋊C₈×C₆₁	—	4	1	no	—
79	C₄⋊C₈×C₆₁	—	4	1	no	—
80	#102×C₆₁	—	4	2	no	—
81	#102×C₆₁	—	4	2	no	—
82	#102×C₆₁	—	4	2	no	—
83	#102×C₆₁	—	4	2	no	—
84	C₂²⋊C₈×C₆₁	—	2	4	no	—
85	#95×C₆₁	—	2	2	no	—
86	#95×C₆₁	—	2	1	no	—
87	#95×C₆₁	—	2	1	no	—
88	#95×C₆₁	—	2	2	no	—
89	C₂⁴×C₆₁	—	2	2	no	—
90	C₂⁴×C₆₁	—	2	4	no	—
91	C₂⁴×C₆₁	—	4	2	no	—
92	C₂⁴×C₆₁	—	4	2	no	—
93	C₂⁴×C₆₁	—	8	2	no	—
94	C₂⁴×C₆₁	—	8	2	no	—
95	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₆₁	—	4	2	no	—
97	C₂×Q₈×C₆₁	—	8	2	no	—
98	C₂×D₄×C₆₁	—	2	4	no	—
99	C₂×D₄×C₆₁	—	2	2	no	—
100	C₂×D₄×C₆₁	—	2	2	no	—
101	C₂×D₄×C₆₁	—	2	2	no	—
102	C₂×D₄×C₆₁	—	2	2	no	—
103	C₂×D₄×C₆₁	—	2	2	no	—
104	C₂×D₄×C₆₁	—	4	4	no	—
105	C₂×D₄×C₆₁	—	4	4	no	—
106	C₂×D₄×C₆₁	—	4	2	no	—
107	C₂×D₄×C₆₁	—	4	2	no	—
108	C₂×D₄×C₆₁	—	4	4	no	—
109	C₂×D₄×C₆₁	—	4	4	no	—
110	C₂×D₄×C₆₁	C₂×Q₈	1	4	yes	—
111	C₂²×C₄×C₆₁	—	2	1	no	—
112	C₂²×C₄×C₆₁	—	2	1	no	—
113	C₂²×C₄×C₆₁	—	2	1	no	—
114	C₂²×C₄×C₆₁	—	2	1	no	—
115	C₂²×C₄×C₆₁	—	2	2	no	—
116	C₂²×C₄×C₆₁	—	2	2	no	—
117	C₂²×C₄×C₆₁	—	2	2	no	—
118	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
124	C₂²×C₄×C₆₁	#41	1	2	yes	—
125	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
126	C₂×C₈×C₆₁	—	2	2	no	—
127	C₂×C₈×C₆₁	—	2	2	no	—
128	C₂×C₈×C₆₁	—	2	2	no	—
129	C₂×C₈×C₆₁	—	2	2	no	—
130	C₂×C₈×C₆₁	—	2	2	no	—
131	C₂×C₈×C₆₁	—	2	2	no	—
132	C₄⋊C₄×C₆₁	—	2	2	no	—
133	C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	2	2	no	—
135	C₄⋊C₄×C₆₁	—	2	2	no	—
136	C₄⋊C₄×C₆₁	—	2	2	no	—
137	C₄⋊C₄×C₆₁	—	2	2	no	—
138	C₄⋊C₄×C₆₁	—	4	1	no	—
139	C₄⋊C₄×C₆₁	—	4	1	no	—
140	C₄⋊C₄×C₆₁	—	4	2	no	—
141	C₄⋊C₄×C₆₁	—	8	2	no	—
142	C₂²⋊C₄×C₆₁	—	4	1	no	—
143	C₂²⋊C₄×C₆₁	—	4	1	no	—
144	C₂²⋊C₄×C₆₁	—	4	2	no	—
145	C₂²⋊C₄×C₆₁	—	8	2	no	—
146	C₂²⋊C₄×C₆₁	—	8	2	no	—
147	C₂²⋊C₄×C₆₁	—	8	2	no	—
148	C₂²⋊C₄×C₆₁	—	8	2	no	—
149	C₂²⋊C₄×C₆₁	—	8	2	no	—
150	C₄²×C₆₁	—	2	1	no	—
151	C₄²×C₆₁	—	2	1	no	—
152	C₄²×C₆₁	—	2	1	no	—
153	C₄²×C₆₁	—	2	1	no	—
154	C₄²×C₆₁	—	4	2	no	—
155	C₂³×C₆₁	—	2	1	no	—
156	C₂³×C₆₁	—	2	1	no	—
157	C₂³×C₆₁	—	2	2	no	—
158	C₂³×C₆₁	—	2	2	no	—
159	C₂³×C₆₁	—	2	4	no	—
160	C₂³×C₆₁	—	4	8	no	—
161	C₂³×C₆₁	—	4	2	no	—
162	C₂³×C₆₁	—	4	2	no	—
163	C₂³×C₆₁	—	4	2	no	—
164	C₂³×C₆₁	—	4	2	no	—
165	C₂³×C₆₁	—	4	2	no	—
166	C₂³×C₆₁	—	4	2	no	—
167	C₂³×C₆₁	—	8	8	no	—
168	C₂³×C₆₁	—	8	4	no	—
169	C₂³×C₆₁	—	8	4	no	—
170	C₂³×C₆₁	—	8	8	no	—
171	C₂³×C₆₁	C₂²⋊Q₈	1	2	yes	—
172	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₆₁	—	8	4	no	—
174	D₄×C₆₁	—	2	4	no	—
175	D₄×C₆₁	—	2	4	no	—
176	D₄×C₆₁	—	4	8	no	—
177	D₄×C₆₁	—	4	2	no	—
178	D₄×C₆₁	—	4	2	no	—
179	C₂×C₄×C₆₁	—	2	1	no	—
180	C₂×C₄×C₆₁	—	2	1	no	—
181	C₂×C₄×C₆₁	—	2	2	no	—
182	C₂×C₄×C₆₁	—	2	2	no	—
183	C₂×C₄×C₆₁	—	2	2	no	—
184	C₂×C₄×C₆₁	—	2	2	no	—
185	C₂×C₄×C₆₁	—	2	1	no	—
186	C₂×C₄×C₆₁	—	2	1	no	—
187	C₂×C₄×C₆₁	—	2	1	no	—
188	C₂×C₄×C₆₁	—	2	1	no	—
189	C₂×C₄×C₆₁	—	2	2	no	—
190	C₂×C₄×C₆₁	—	2	2	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	2	2	no	—
193	C₂×C₄×C₆₁	—	4	2	no	—
194	C₂×C₄×C₆₁	—	4	2	no	—
195	C₂×C₄×C₆₁	—	4	2	no	—
196	C₂×C₄×C₆₁	—	4	2	no	—
197	C₂×C₄×C₆₁	—	4	2	no	—
198	C₂×C₄×C₆₁	—	4	2	no	—
199	C₂×C₄×C₆₁	—	4	2	no	—
200	C₂×C₄×C₆₁	—	4	2	no	—
201	C₂×C₄×C₆₁	—	4	2	no	—
202	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
203	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
204	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
206	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
209	C₈×C₆₁	—	4	2	no	—
210	C₈×C₆₁	—	4	2	no	—
211	#29959	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂²×C₆₁	—	2	4	no	—
213	C₂²×C₆₁	—	2	2	no	—
214	C₂²×C₆₁	—	4	1	no	—
215	C₂²×C₆₁	—	4	1	no	—
216	C₂²×C₆₁	—	4	2	no	—
217	C₂²×C₆₁	—	4	4	no	—
218	C₂²×C₆₁	—	4	4	no	—
219	C₂²×C₆₁	—	4	4	no	—
220	C₂²×C₆₁	—	8	16	no	—
221	C₂²×C₆₁	—	8	2	no	—
222	C₂²×C₆₁	—	8	2	no	—
223	C₂²×C₆₁	—	8	2	no	—
224	C₂²×C₆₁	—	8	2	no	—
225	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
226	C₂²×C₆₁	#534	1	1	yes	characteristic
227	C₂²×C₆₁	#535	1	1	yes	characteristic
228	C₂²×C₆₁	#576	1	2	yes	—
229	C₂²×C₆₁	#577	1	2	yes	—
230	C₄×C₆₁	—	2	2	no	—
231	C₄×C₆₁	—	4	1	no	—
232	C₄×C₆₁	—	4	1	no	—
233	C₄×C₆₁	—	4	1	no	—
234	C₄×C₆₁	—	4	1	no	—
235	C₄×C₆₁	—	8	2	no	—
236	C₄×C₆₁	—	8	2	no	—
237	C₄×C₆₁	—	8	2	no	—
238	C₄×C₆₁	#538	1	1	yes	characteristic
239	C₄×C₆₁	#538	1	1	yes	characteristic
240	C₄×C₆₁	#543	1	1	yes	characteristic
241	C₄×C₆₁	#543	1	1	yes	characteristic
242	#2628	C₂×C₆₁	1	1	yes	characteristic, complemented
243	#2309	C₂×C₆₁	1	1	yes	characteristic
244	#2092	C₂×C₆₁	1	2	yes	complemented
245	#2067	C₂×C₆₁	1	2	yes	complemented
246	#2065	C₂×C₆₁	1	2	yes	complemented
247	#2023	C₂×C₆₁	1	2	yes	complemented
248	#1854	C₂×C₆₁	1	2	yes	complemented
249	#1798	C₂×C₆₁	1	1	yes	characteristic, complemented
250	#1786	C₂×C₆₁	1	2	yes	—
251	C₂×C₆₁	—	4	2	no	—
252	C₂×C₆₁	—	8	4	no	—
253	C₂×C₆₁	#2626	1	1	yes	characteristic
254	C₂×C₆₁	#3081	1	2	yes	—
255	C₂×C₆₁	#3199	1	1	yes	characteristic
256	C₂×C₆₁	#3200	1	1	yes	characteristic
257	C₂×C₆₁	#3224	1	2	yes	—
258	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
259	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
260	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
261	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
262	C₂×#107	C₂²×C₆₁	1	2	yes	complemented
263	C₂×#106	C₂²×C₆₁	1	2	yes	complemented
264	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
265	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
266	C₂×#102	C₂²×C₆₁	1	2	yes	—
267	C₂×#102	C₂²×C₆₁	1	2	yes	—
268	C₂×#102	C₂²×C₆₁	1	2	yes	—
269	C₂×#102	C₂²×C₆₁	1	2	yes	—
270	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
271	#400	—	2	1	no	—
272	#399	—	2	1	no	—
273	#395	—	2	1	no	—
274	#393	—	2	1	no	—
275	#390	—	2	1	no	—
276	#390	—	2	1	no	—
277	#390	C₂²×C₆₁	1	2	yes	—
278	#390	C₂²×C₆₁	1	2	yes	—
279	#389	C₂²×C₆₁	1	2	yes	complemented
280	#382	C₂²×C₆₁	1	1	yes	characteristic, complemented
281	#380	C₂²×C₆₁	1	2	yes	—
282	#379	—	2	1	no	—
283	#379	—	2	1	no	—
284	#340	C₂²×C₆₁	1	2	yes	complemented
285	#340	C₂²×C₆₁	1	2	yes	complemented
286	#336	C₂²×C₆₁	1	2	yes	complemented
287	C₆₁	#29959	1	1	yes	characteristic, direct product factor, Sylow
288	C₂⁵	—	2	1	no	—
289	C₂²×Q₈	—	2	1	no	—
290	C₂²×D₄	—	2	1	no	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	—	4	1	no	—
293	C₂²×D₄	—	4	1	no	—
294	C₂²×D₄	—	4	1	no	—
295	C₂²×D₄	—	4	1	no	—
296	C₂²×D₄	Q₈×C₆₁	1	4	yes	complemented
297	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
298	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
300	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
301	C₄⋊Q₈	—	4	1	no	—
302	C₄⋊Q₈	—	4	1	no	—
303	#117	—	4	1	no	—
304	#117	—	4	1	no	—
305	#117	—	4	1	no	—
306	#117	—	4	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
310	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
325	#107	—	4	2	no	—
326	#106	—	4	2	no	—
327	C₄⋊C₈	—	4	1	no	—
328	C₄⋊C₈	—	4	1	no	—
329	#102	—	4	2	no	—
330	#102	—	4	2	no	—
331	#102	—	4	2	no	—
332	#102	—	4	2	no	—
333	C₂²⋊C₈	—	2	4	no	—
334	#95	—	2	2	no	—
335	#95	—	2	1	no	—
336	#95	—	2	1	no	—
337	#95	—	2	2	no	—
338	C₂⁴	—	2	2	no	—
339	C₂⁴	—	2	4	no	—
340	C₂⁴	—	4	2	no	—
341	C₂⁴	—	4	2	no	—
342	C₂⁴	—	8	2	no	—
343	C₂⁴	—	8	2	no	—
344	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	—	8	2	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	4	4	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	—	4	2	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	—	4	4	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	C₂×Q₈×C₆₁	1	4	yes	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
372	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
373	C₂²×C₄	#41×C₆₁	1	2	yes	—
374	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	8	2	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	8	2	no	—
395	C₂²⋊C₄	—	8	2	no	—
396	C₂²⋊C₄	—	8	2	no	—
397	C₂²⋊C₄	—	8	2	no	—
398	C₂²⋊C₄	—	8	2	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	4	2	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	4	no	—
409	C₂³	—	4	8	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	8	8	no	—
417	C₂³	—	8	4	no	—
418	C₂³	—	8	4	no	—
419	C₂³	—	8	8	no	—
420	C₂³	C₂²⋊Q₈×C₆₁	1	2	yes	—
421	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
422	Q₈	—	8	4	no	—
423	D₄	—	2	4	no	—
424	D₄	—	2	4	no	—
425	D₄	—	4	8	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
452	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
454	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
455	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
456	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
457	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
458	C₈	—	4	2	no	—
459	C₈	—	4	2	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	4	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	8	16	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	2	no	—
471	C₂²	—	8	2	no	—
472	C₂²	—	8	2	no	—
473	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
474	C₂²	C₆₁×#534	1	1	yes	characteristic
475	C₂²	C₆₁×#535	1	1	yes	characteristic
476	C₂²	C₆₁×#576	1	2	yes	—
477	C₂²	C₆₁×#577	1	2	yes	—
478	C₄	—	2	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	4	1	no	—
482	C₄	—	4	1	no	—
483	C₄	—	8	2	no	—
484	C₄	—	8	2	no	—
485	C₄	—	8	2	no	—
486	C₄	C₆₁×#538	1	1	yes	characteristic
487	C₄	C₆₁×#538	1	1	yes	characteristic
488	C₄	C₆₁×#543	1	1	yes	characteristic
489	C₄	C₆₁×#543	1	1	yes	characteristic
490	C₂	—	4	2	no	—
491	C₂	—	8	4	no	—
492	C₂	C₆₁×#2626	1	1	yes	characteristic
493	C₂	C₆₁×#3081	1	2	yes	—
494	C₂	C₆₁×#3199	1	1	yes	characteristic
495	C₂	C₆₁×#3200	1	1	yes	characteristic
496	C₂	C₆₁×#3224	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂³×D₄×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#2628	C₂	semidirect
3. C₆₁×#2092	C₂	semidirect
4. C₆₁×#2067	C₂	semidirect
5. C₆₁×#2065	C₂	semidirect
6. C₆₁×#2023	C₂	semidirect
7. C₆₁×#1854	C₂	semidirect
8. C₆₁×#1798	C₂	semidirect
11. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
14. C₂×#107×C₆₁	C₂²	semidirect
15. C₂×#106×C₆₁	C₂²	semidirect
16. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
17. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
31. C₆₁×#389	C₂²	semidirect
32. C₆₁×#382	C₂²	semidirect
36. C₆₁×#340	C₂²	semidirect
37. C₆₁×#340	C₂²	semidirect
38. C₆₁×#336	C₂²	semidirect
47. C₂²×D₄×C₆₁	Q₈	semidirect
211. #29959	C₆₁	direct (N × H)
242. #2628	C₂×C₆₁	semidirect
244. #2092	C₂×C₆₁	semidirect
245. #2067	C₂×C₆₁	semidirect
246. #2065	C₂×C₆₁	semidirect
247. #2023	C₂×C₆₁	semidirect
248. #1854	C₂×C₆₁	semidirect
249. #1798	C₂×C₆₁	semidirect
259. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
262. C₂×#107	C₂²×C₆₁	semidirect
263. C₂×#106	C₂²×C₆₁	semidirect
264. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
265. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
279. #389	C₂²×C₆₁	semidirect
280. #382	C₂²×C₆₁	semidirect
284. #340	C₂²×C₆₁	semidirect
285. #340	C₂²×C₆₁	semidirect
286. #336	C₂²×C₆₁	semidirect
287. C₆₁	#29959	direct (N × H)
296. C₂²×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×#2628	2
C₆₁×#2309	2
C₆₁×#2092	2
C₆₁×#2067	2
C₆₁×#2065	2
C₆₁×#2023	2
C₆₁×#1854	2
C₆₁×#1798	2
C₆₁×#1786	2
#29959	61

Subgroups — C61×#29959 #29533392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#29959 #29533392