Subgroups — C₆₁×#29981 #29533414

Order 15616.

806 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2868	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#2293	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2100	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2094	C₂	1	2	yes	maximal
5	C₆₁×#2058	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2023	C₂	1	2	yes	maximal
7	C₆₁×#1948	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1831	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1802	C₂	1	2	yes	maximal
10	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
11	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
12	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#117×C₆₁	—	2	1	no	—
15	C₂×#106×C₆₁	C₂²	1	4	yes	—
16	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
17	C₂×#102×C₆₁	C₂²	1	4	yes	—
18	C₆₁×#390	C₂²	1	1	yes	characteristic
19	C₆₁×#390	C₂²	1	1	yes	characteristic
20	C₆₁×#389	C₂²	1	1	yes	characteristic
21	C₆₁×#389	C₂²	1	1	yes	characteristic
22	C₆₁×#388	—	2	1	no	—
23	C₆₁×#388	—	2	1	no	—
24	C₆₁×#384	—	2	1	no	—
25	C₆₁×#384	—	2	1	no	—
26	C₆₁×#384	C₂²	1	2	yes	—
27	C₆₁×#384	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
30	C₄³×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#340	C₂²	1	4	yes	—
32	C₆₁×#340	C₂²	1	4	yes	—
33	C₆₁×#336	C₂²	1	2	yes	—
34	C₆₁×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₆₁	—	2	2	no	—
36	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₆₁	—	2	1	no	—
38	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
39	C₄⋊Q₈×C₆₁	—	4	4	no	—
40	C₄⋊Q₈×C₆₁	—	4	4	no	—
41	C₄⋊Q₈×C₆₁	—	4	4	no	—
42	C₄×D₄×C₆₁	—	2	2	no	—
43	C₄×D₄×C₆₁	Q₈	1	4	yes	complemented
44	#117×C₆₁	—	4	4	no	—
45	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
46	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
47	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
48	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
49	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
51	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
53	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
61	C₂×C₄²×C₆₁	—	2	1	no	—
62	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
69	#106×C₆₁	—	4	4	no	—
70	C₄⋊C₈×C₆₁	—	2	4	no	—
71	#102×C₆₁	—	4	4	no	—
72	#95×C₆₁	—	2	1	no	—
73	#95×C₆₁	—	2	1	no	—
74	#95×C₆₁	—	2	1	no	—
75	C₂⁴×C₆₁	—	2	1	no	—
76	C₂×Q₈×C₆₁	—	4	4	no	—
77	C₂×Q₈×C₆₁	—	4	4	no	—
78	C₂×Q₈×C₆₁	—	4	4	no	—
79	C₂×D₄×C₆₁	—	2	1	no	—
80	C₂×D₄×C₆₁	—	2	2	no	—
81	C₂×D₄×C₆₁	—	2	2	no	—
82	C₂×D₄×C₆₁	C₂×Q₈	1	2	yes	—
83	C₂²×C₄×C₆₁	—	2	1	no	—
84	C₂²×C₄×C₆₁	—	2	4	no	—
85	C₂²×C₄×C₆₁	—	2	1	no	—
86	C₂²×C₄×C₆₁	—	2	1	no	—
87	C₂²×C₄×C₆₁	—	2	4	no	—
88	C₂²×C₄×C₆₁	—	4	2	no	—
89	C₂²×C₄×C₆₁	—	4	2	no	—
90	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
97	C₂×C₈×C₆₁	—	2	4	no	—
98	C₂×C₈×C₆₁	—	2	4	no	—
99	C₂×C₈×C₆₁	—	2	4	no	—
100	C₄⋊C₄×C₆₁	—	2	1	no	—
101	C₄⋊C₄×C₆₁	—	2	4	no	—
102	C₄⋊C₄×C₆₁	—	2	2	no	—
103	C₄⋊C₄×C₆₁	—	2	4	no	—
104	C₄⋊C₄×C₆₁	—	2	2	no	—
105	C₄⋊C₄×C₆₁	—	4	4	no	—
106	C₄⋊C₄×C₆₁	—	4	4	no	—
107	C₄⋊C₄×C₆₁	—	4	4	no	—
108	C₄⋊C₄×C₆₁	—	4	4	no	—
109	C₄⋊C₄×C₆₁	—	4	2	no	—
110	C₄⋊C₄×C₆₁	—	4	2	no	—
111	C₄⋊C₄×C₆₁	—	4	4	no	—
112	C₄⋊C₄×C₆₁	C₂×Q₈	1	2	yes	—
113	C₂²⋊C₄×C₆₁	—	2	4	no	—
114	C₂²⋊C₄×C₆₁	—	4	2	no	—
115	C₂²⋊C₄×C₆₁	—	4	2	no	—
116	C₂²⋊C₄×C₆₁	—	4	2	no	—
117	C₂²⋊C₄×C₆₁	—	4	2	no	—
118	C₄²×C₆₁	—	2	2	no	—
119	C₄²×C₆₁	—	2	2	no	—
120	C₄²×C₆₁	—	2	2	no	—
121	C₄²×C₆₁	—	2	2	no	—
122	C₄²×C₆₁	—	2	2	no	—
123	C₄²×C₆₁	—	4	2	no	—
124	C₄²×C₆₁	SD₁₆	1	4	yes	—
125	C₄²×C₆₁	C₂×Q₈	1	2	yes	—
126	C₄²×C₆₁	#41	1	2	yes	—
127	C₂³×C₆₁	—	2	2	no	—
128	C₂³×C₆₁	—	4	1	no	—
129	C₂³×C₆₁	—	4	1	no	—
130	C₂³×C₆₁	—	4	1	no	—
131	C₂³×C₆₁	—	4	1	no	—
132	C₂³×C₆₁	—	4	1	no	—
133	C₂³×C₆₁	—	4	1	no	—
134	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₆₁	—	8	8	no	—
136	D₄×C₆₁	—	2	4	no	—
137	D₄×C₆₁	—	4	2	no	—
138	C₂×C₄×C₆₁	—	2	1	no	—
139	C₂×C₄×C₆₁	—	2	1	no	—
140	C₂×C₄×C₆₁	—	2	1	no	—
141	C₂×C₄×C₆₁	—	2	1	no	—
142	C₂×C₄×C₆₁	—	2	1	no	—
143	C₂×C₄×C₆₁	—	2	1	no	—
144	C₂×C₄×C₆₁	—	2	1	no	—
145	C₂×C₄×C₆₁	—	2	1	no	—
146	C₂×C₄×C₆₁	—	2	1	no	—
147	C₂×C₄×C₆₁	—	2	1	no	—
148	C₂×C₄×C₆₁	—	2	2	no	—
149	C₂×C₄×C₆₁	—	4	1	no	—
150	C₂×C₄×C₆₁	—	4	1	no	—
151	C₂×C₄×C₆₁	—	4	8	no	—
152	C₂×C₄×C₆₁	—	4	4	no	—
153	C₂×C₄×C₆₁	—	4	1	no	—
154	C₂×C₄×C₆₁	—	4	1	no	—
155	C₂×C₄×C₆₁	—	4	1	no	—
156	C₂×C₄×C₆₁	—	4	1	no	—
157	C₂×C₄×C₆₁	—	4	1	no	—
158	C₂×C₄×C₆₁	—	4	4	no	—
159	C₂×C₄×C₆₁	—	4	4	no	—
160	C₂×C₄×C₆₁	—	4	1	no	—
161	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
162	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
163	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
164	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
165	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
166	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
167	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
168	C₂×C₄×C₆₁	#137	1	2	yes	—
169	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
172	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
173	C₈×C₆₁	—	4	4	no	—
174	#29981	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₆₁	—	4	2	no	—
176	C₂²×C₆₁	—	4	2	no	—
177	C₂²×C₆₁	—	4	2	no	—
178	C₂²×C₆₁	—	8	1	no	—
179	C₂²×C₆₁	—	8	1	no	—
180	C₂²×C₆₁	—	8	1	no	—
181	C₂²×C₆₁	—	8	1	no	—
182	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
183	C₂²×C₆₁	#535	1	1	yes	characteristic
184	C₂²×C₆₁	#536	1	1	yes	characteristic
185	C₂²×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
186	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
189	C₄×C₆₁	—	2	2	no	—
190	C₄×C₆₁	—	2	2	no	—
191	C₄×C₆₁	—	2	2	no	—
192	C₄×C₆₁	—	2	2	no	—
193	C₄×C₆₁	—	2	2	no	—
194	C₄×C₆₁	—	4	2	no	—
195	C₄×C₆₁	—	8	1	no	—
196	C₄×C₆₁	—	8	4	no	—
197	C₄×C₆₁	—	8	1	no	—
198	C₄×C₆₁	#476	1	4	yes	—
199	C₄×C₆₁	#542	1	2	yes	—
200	C₄×C₆₁	#544	1	2	yes	—
201	#2868	C₂×C₆₁	1	1	yes	characteristic, complemented
202	#2293	C₂×C₆₁	1	1	yes	characteristic
203	#2100	C₂×C₆₁	1	2	yes	complemented
204	#2094	C₂×C₆₁	1	2	yes	—
205	#2058	C₂×C₆₁	1	2	yes	complemented
206	#2023	C₂×C₆₁	1	2	yes	—
207	#1948	C₂×C₆₁	1	2	yes	complemented
208	#1831	C₂×C₆₁	1	1	yes	characteristic, complemented
209	#1802	C₂×C₆₁	1	2	yes	—
210	C₂×C₆₁	—	8	2	no	—
211	C₂×C₆₁	#2628	1	1	yes	characteristic
212	C₂×C₆₁	C₂×#476	1	1	yes	characteristic
213	C₂×C₆₁	#3079	1	1	yes	characteristic
214	C₂×C₆₁	#3206	1	1	yes	characteristic
215	C₂×C₆₁	#3217	1	1	yes	characteristic
216	C₂×C₆₁	#3227	1	1	yes	characteristic
217	C₂×C₆₁	#3239	1	1	yes	characteristic
218	C₂×C₄⋊Q₈	—	2	1	no	—
219	C₂×C₄⋊Q₈	—	2	1	no	—
220	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
221	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
222	C₂×#117	—	2	1	no	—
223	C₂×#106	C₂²×C₆₁	1	4	yes	—
224	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
225	C₂×#102	C₂²×C₆₁	1	4	yes	—
226	#390	C₂²×C₆₁	1	1	yes	characteristic
227	#390	C₂²×C₆₁	1	1	yes	characteristic
228	#389	C₂²×C₆₁	1	1	yes	characteristic
229	#389	C₂²×C₆₁	1	1	yes	characteristic
230	#388	—	2	1	no	—
231	#388	—	2	1	no	—
232	#384	—	2	1	no	—
233	#384	—	2	1	no	—
234	#384	C₂²×C₆₁	1	2	yes	—
235	#384	C₂²×C₆₁	1	2	yes	—
236	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
237	C₄×C₂²⋊C₄	—	2	1	no	—
238	C₄³	C₂²×C₆₁	1	1	yes	characteristic
239	#340	C₂²×C₆₁	1	4	yes	—
240	#340	C₂²×C₆₁	1	4	yes	—
241	#336	C₂²×C₆₁	1	2	yes	—
242	#336	C₂²×C₆₁	1	2	yes	—
243	C₆₁	#29981	1	1	yes	characteristic, direct product factor, Sylow
244	C₂²×Q₈	—	2	2	no	—
245	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
246	C₂³×C₄	—	2	1	no	—
247	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
248	C₄⋊Q₈	—	4	4	no	—
249	C₄⋊Q₈	—	4	4	no	—
250	C₄⋊Q₈	—	4	4	no	—
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	Q₈×C₆₁	1	4	yes	complemented
253	#117	—	4	4	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
262	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
272	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
273	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
274	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
278	#106	—	4	4	no	—
279	C₄⋊C₈	—	2	4	no	—
280	#102	—	4	4	no	—
281	#95	—	2	1	no	—
282	#95	—	2	1	no	—
283	#95	—	2	1	no	—
284	C₂⁴	—	2	1	no	—
285	C₂×Q₈	—	4	4	no	—
286	C₂×Q₈	—	4	4	no	—
287	C₂×Q₈	—	4	4	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	C₂×Q₈×C₆₁	1	2	yes	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
305	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	2	4	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	4	4	no	—
316	C₄⋊C₄	—	4	4	no	—
317	C₄⋊C₄	—	4	4	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	C₂×Q₈×C₆₁	1	2	yes	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	4	2	no	—
333	C₄²	SD₁₆×C₆₁	1	4	yes	—
334	C₄²	C₂×Q₈×C₆₁	1	2	yes	—
335	C₄²	#41×C₆₁	1	2	yes	—
336	C₂³	—	2	2	no	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
344	Q₈	—	8	8	no	—
345	D₄	—	2	4	no	—
346	D₄	—	4	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
371	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
372	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
373	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
374	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
375	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
376	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
377	C₂×C₄	#137×C₆₁	1	2	yes	—
378	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
379	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
380	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
381	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
382	C₈	—	4	4	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	8	1	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
391	C₂²	C₆₁×#535	1	1	yes	characteristic
392	C₂²	C₆₁×#536	1	1	yes	characteristic
393	C₂²	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
394	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
395	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
396	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	8	1	no	—
404	C₄	—	8	4	no	—
405	C₄	—	8	1	no	—
406	C₄	C₆₁×#476	1	4	yes	—
407	C₄	C₆₁×#542	1	2	yes	—
408	C₄	C₆₁×#544	1	2	yes	—
409	C₂	—	8	2	no	—
410	C₂	C₆₁×#2628	1	1	yes	characteristic
411	C₂	C₂×C₆₁×#476	1	1	yes	characteristic
412	C₂	C₆₁×#3079	1	1	yes	characteristic
413	C₂	C₆₁×#3206	1	1	yes	characteristic
414	C₂	C₆₁×#3217	1	1	yes	characteristic
415	C₂	C₆₁×#3227	1	1	yes	characteristic
416	C₂	C₆₁×#3239	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 ◁ C₄³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#2868	C₂	semidirect
3. C₆₁×#2100	C₂	semidirect
5. C₆₁×#2058	C₂	semidirect
7. C₆₁×#1948	C₂	semidirect
8. C₆₁×#1831	C₂	semidirect
43. C₄×D₄×C₆₁	Q₈	semidirect
174. #29981	C₆₁	direct (N × H)
201. #2868	C₂×C₆₁	semidirect
203. #2100	C₂×C₆₁	semidirect
205. #2058	C₂×C₆₁	semidirect
207. #1948	C₂×C₆₁	semidirect
208. #1831	C₂×C₆₁	semidirect
243. C₆₁	#29981	direct (N × H)
252. 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×#2868	2
C₆₁×#2293	2
C₆₁×#2100	2
C₆₁×#2094	2
C₆₁×#2058	2
C₆₁×#2023	2
C₆₁×#1948	2
C₆₁×#1831	2
C₆₁×#1802	2
#29981	61

Subgroups — C61×#29981 #29533414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#29981 #29533414