Subgroups — C₆₁×#24212 #29527645

Order 15616.

1430 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#462	C₂	1	2	yes	maximal, complemented
3	C₂×C₆₁×#451	C₂	1	2	yes	maximal
4	C₄×C₂²⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2043	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2016	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1981	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1797	C₂	1	1	yes	maximal, characteristic
9	C₆₁×#1787	C₂	1	2	yes	maximal
10	C₂³×Q₈×C₆₁	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₆₁	C₂²	1	4	yes	—
12	C₂×C₄⋊Q₈×C₆₁	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
14	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
20	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
21	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
22	C₆₁×#462	—	2	8	no	—
23	C₆₁×#451	—	2	8	no	—
24	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
25	C₂×#103×C₆₁	C₂²	1	4	yes	—
26	C₂×#103×C₆₁	C₂²	1	4	yes	—
27	C₂×#103×C₆₁	C₂²	1	4	yes	—
28	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
29	C₆₁×#391	C₂²	1	1	yes	characteristic
30	C₆₁×#389	C₂²	1	1	yes	characteristic
31	C₆₁×#387	—	2	1	no	—
32	C₆₁×#385	—	2	1	no	—
33	C₆₁×#380	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
35	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
37	C₆₁×#336	C₂²	1	2	yes	—
38	C₂²×Q₈×C₆₁	—	2	8	no	—
39	C₂²×Q₈×C₆₁	—	2	2	no	—
40	C₂²×Q₈×C₆₁	—	2	4	no	—
41	C₂²×Q₈×C₆₁	—	2	4	no	—
42	C₂²×Q₈×C₆₁	—	4	4	no	—
43	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
44	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₆₁	—	2	2	no	—
46	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
49	C₂×Q₁₆×C₆₁	—	2	8	no	—
50	C₂×Q₁₆×C₆₁	—	2	8	no	—
51	C₂×Q₁₆×C₆₁	—	4	4	no	—
52	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
53	C₄⋊Q₈×C₆₁	—	2	8	no	—
54	C₄⋊Q₈×C₆₁	—	2	8	no	—
55	C₄⋊Q₈×C₆₁	—	2	8	no	—
56	C₄⋊Q₈×C₆₁	—	2	4	no	—
57	C₄⋊Q₈×C₆₁	D₄	1	8	yes	—
58	C₂²⋊Q₈×C₆₁	—	2	2	no	—
59	C₂²⋊Q₈×C₆₁	D₄	1	4	yes	—
60	C₄×Q₈×C₆₁	—	2	4	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
75	C₂×C₄²×C₆₁	—	2	4	no	—
76	C₂×C₄²×C₆₁	—	2	1	no	—
77	C₂×C₄²×C₆₁	—	2	1	no	—
78	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₆₁	—	2	4	no	—
83	#103×C₆₁	—	2	8	no	—
84	#103×C₆₁	—	2	8	no	—
85	#103×C₆₁	—	4	4	no	—
86	C₂²⋊C₈×C₆₁	—	2	4	no	—
87	#95×C₆₁	—	2	1	no	—
88	#95×C₆₁	—	2	1	no	—
89	#95×C₆₁	—	2	1	no	—
90	#95×C₆₁	—	2	1	no	—
91	#95×C₆₁	—	2	1	no	—
92	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
93	C₂×Q₈×C₆₁	—	2	8	no	—
94	C₂×Q₈×C₆₁	—	2	4	no	—
95	C₂×Q₈×C₆₁	—	2	1	no	—
96	C₂×Q₈×C₆₁	—	2	4	no	—
97	C₂×Q₈×C₆₁	—	2	2	no	—
98	C₂×Q₈×C₆₁	—	2	4	no	—
99	C₂×Q₈×C₆₁	—	2	4	no	—
100	C₂×Q₈×C₆₁	—	2	2	no	—
101	C₂×Q₈×C₆₁	—	2	4	no	—
102	C₂×Q₈×C₆₁	—	4	16	no	—
103	C₂×Q₈×C₆₁	—	4	16	no	—
104	C₂×Q₈×C₆₁	—	4	4	no	—
105	C₂×Q₈×C₆₁	—	4	4	no	—
106	C₂×Q₈×C₆₁	C₂×D₄	1	8	yes	—
107	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₆₁	—	2	2	no	—
109	C₂²×C₄×C₆₁	—	2	2	no	—
110	C₂²×C₄×C₆₁	—	2	2	no	—
111	C₂²×C₄×C₆₁	—	2	2	no	—
112	C₂²×C₄×C₆₁	—	2	2	no	—
113	C₂²×C₄×C₆₁	—	2	2	no	—
114	C₂²×C₄×C₆₁	—	2	2	no	—
115	C₂²×C₄×C₆₁	—	2	8	no	—
116	C₂²×C₄×C₆₁	—	2	1	no	—
117	C₂²×C₄×C₆₁	—	2	1	no	—
118	C₂²×C₄×C₆₁	—	2	4	no	—
119	C₂²×C₄×C₆₁	—	2	1	no	—
120	C₂²×C₄×C₆₁	—	2	1	no	—
121	C₂²×C₄×C₆₁	—	4	4	no	—
122	C₂²×C₄×C₆₁	—	4	4	no	—
123	C₂²×C₄×C₆₁	Q₁₆	1	4	yes	complemented
124	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₆₁	#41	1	2	yes	—
131	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
132	Q₁₆×C₆₁	—	4	16	no	—
133	C₂×C₈×C₆₁	—	2	4	no	—
134	C₂×C₈×C₆₁	—	2	4	no	—
135	C₂×C₈×C₆₁	—	2	4	no	—
136	C₄⋊C₄×C₆₁	—	2	8	no	—
137	C₄⋊C₄×C₆₁	—	2	8	no	—
138	C₄⋊C₄×C₆₁	—	2	8	no	—
139	C₄⋊C₄×C₆₁	—	2	8	no	—
140	C₄⋊C₄×C₆₁	—	2	4	no	—
141	C₄⋊C₄×C₆₁	—	2	1	no	—
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	—	4	2	no	—
146	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
147	C₂²⋊C₄×C₆₁	—	2	4	no	—
148	C₂²⋊C₄×C₆₁	—	4	2	no	—
149	C₄²×C₆₁	—	2	2	no	—
150	C₄²×C₆₁	—	2	2	no	—
151	C₄²×C₆₁	—	2	2	no	—
152	C₄²×C₆₁	—	4	2	no	—
153	C₄²×C₆₁	—	4	2	no	—
154	C₄²×C₆₁	C₂×D₄	1	4	yes	—
155	C₂³×C₆₁	—	2	1	no	—
156	C₂³×C₆₁	—	2	1	no	—
157	C₂³×C₆₁	—	2	1	no	—
158	C₂³×C₆₁	—	2	1	no	—
159	C₂³×C₆₁	#121	1	2	yes	—
160	C₂³×C₆₁	C₂×Q₁₆	1	2	yes	—
161	C₂³×C₆₁	#137	1	2	yes	—
162	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₆₁	—	2	4	no	—
164	Q₈×C₆₁	—	2	8	no	—
165	Q₈×C₆₁	—	2	8	no	—
166	Q₈×C₆₁	—	4	16	no	—
167	Q₈×C₆₁	—	4	4	no	—
168	Q₈×C₆₁	—	4	2	no	—
169	Q₈×C₆₁	—	4	4	no	—
170	C₂×C₄×C₆₁	—	2	8	no	—
171	C₂×C₄×C₆₁	—	2	1	no	—
172	C₂×C₄×C₆₁	—	2	1	no	—
173	C₂×C₄×C₆₁	—	2	1	no	—
174	C₂×C₄×C₆₁	—	2	1	no	—
175	C₂×C₄×C₆₁	—	2	1	no	—
176	C₂×C₄×C₆₁	—	2	1	no	—
177	C₂×C₄×C₆₁	—	2	1	no	—
178	C₂×C₄×C₆₁	—	2	1	no	—
179	C₂×C₄×C₆₁	—	2	4	no	—
180	C₂×C₄×C₆₁	—	2	4	no	—
181	C₂×C₄×C₆₁	—	2	8	no	—
182	C₂×C₄×C₆₁	—	2	8	no	—
183	C₂×C₄×C₆₁	—	2	2	no	—
184	C₂×C₄×C₆₁	—	2	2	no	—
185	C₂×C₄×C₆₁	—	4	16	no	—
186	C₂×C₄×C₆₁	—	4	1	no	—
187	C₂×C₄×C₆₁	—	4	4	no	—
188	C₂×C₄×C₆₁	—	4	4	no	—
189	C₂×C₄×C₆₁	—	4	1	no	—
190	C₂×C₄×C₆₁	—	4	1	no	—
191	C₂×C₄×C₆₁	—	4	1	no	—
192	C₂×C₄×C₆₁	—	4	1	no	—
193	C₂×C₄×C₆₁	—	4	1	no	—
194	C₂×C₄×C₆₁	—	4	1	no	—
195	C₂×C₄×C₆₁	—	4	1	no	—
196	C₂×C₄×C₆₁	—	4	1	no	—
197	C₂×C₄×C₆₁	—	4	1	no	—
198	C₂×C₄×C₆₁	#120	1	2	yes	—
199	C₂×C₄×C₆₁	#120	1	2	yes	—
200	C₂×C₄×C₆₁	#121	1	2	yes	—
201	C₂×C₄×C₆₁	C₂×Q₁₆	1	2	yes	—
202	C₂×C₄×C₆₁	C₂×Q₁₆	1	2	yes	—
203	C₂×C₄×C₆₁	#137	1	2	yes	—
204	C₂×C₄×C₆₁	#137	1	2	yes	—
205	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
209	C₈×C₆₁	—	4	4	no	—
210	#24212	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂²×C₆₁	—	2	2	no	—
212	C₂²×C₆₁	—	2	2	no	—
213	C₂²×C₆₁	—	2	2	no	—
214	C₂²×C₆₁	—	2	2	no	—
215	C₂²×C₆₁	—	2	2	no	—
216	C₂²×C₆₁	—	2	2	no	—
217	C₂²×C₆₁	#462	1	4	yes	complemented
218	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
219	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
220	C₂²×C₆₁	#535	1	1	yes	characteristic
221	C₂²×C₆₁	C₂²×Q₁₆	1	1	yes	characteristic
222	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
223	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
224	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
225	C₄×C₆₁	—	2	2	no	—
226	C₄×C₆₁	—	2	2	no	—
227	C₄×C₆₁	—	2	2	no	—
228	C₄×C₆₁	—	2	2	no	—
229	C₄×C₆₁	—	4	8	no	—
230	C₄×C₆₁	—	4	2	no	—
231	C₄×C₆₁	—	4	2	no	—
232	C₄×C₆₁	—	8	1	no	—
233	C₄×C₆₁	—	8	1	no	—
234	C₄×C₆₁	#451	1	4	yes	complemented
235	C₄×C₆₁	D₄²	1	2	yes	—
236	C₄×C₆₁	#546	1	2	yes	—
237	C₂²×C₄⋊Q₈	C₂×C₆₁	1	1	yes	characteristic
238	C₂×#462	C₂×C₆₁	1	2	yes	complemented
239	C₂×#451	C₂×C₆₁	1	2	yes	—
240	C₄×C₂²⋊Q₈	C₂×C₆₁	1	1	yes	characteristic
241	#2043	C₂×C₆₁	1	2	yes	complemented
242	#2016	C₂×C₆₁	1	2	yes	complemented
243	#1981	C₂×C₆₁	1	2	yes	complemented
244	#1797	C₂×C₆₁	1	1	yes	characteristic
245	#1787	C₂×C₆₁	1	2	yes	—
246	C₂×C₆₁	—	2	4	no	—
247	C₂×C₆₁	#2408	1	1	yes	characteristic
248	C₂×C₆₁	C₂×#451	1	1	yes	characteristic
249	C₂×C₆₁	#3004	1	1	yes	characteristic
250	C₂×C₆₁	C₂×#462	1	1	yes	characteristic
251	C₂×C₆₁	#3039	1	1	yes	characteristic
252	C₂×C₆₁	#3209	1	1	yes	characteristic
253	C₂×C₆₁	#3218	1	1	yes	characteristic
254	C₂³×Q₈	C₂²×C₆₁	1	2	yes	—
255	C₂²×Q₁₆	C₂²×C₆₁	1	4	yes	—
256	C₂×C₄⋊Q₈	—	2	8	no	—
257	C₂×C₄⋊Q₈	—	2	1	no	—
258	C₂×C₄⋊Q₈	—	2	1	no	—
259	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
260	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
261	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
263	C₂²×C₄⋊C₄	—	2	1	no	—
264	C₂²×C₄⋊C₄	—	2	1	no	—
265	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
266	#462	—	2	8	no	—
267	#451	—	2	8	no	—
268	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
269	C₂×#103	C₂²×C₆₁	1	4	yes	—
270	C₂×#103	C₂²×C₆₁	1	4	yes	—
271	C₂×#103	C₂²×C₆₁	1	4	yes	—
272	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
273	#391	C₂²×C₆₁	1	1	yes	characteristic
274	#389	C₂²×C₆₁	1	1	yes	characteristic
275	#387	—	2	1	no	—
276	#385	—	2	1	no	—
277	#380	C₂²×C₆₁	1	1	yes	characteristic
278	C₄×C₄⋊C₄	—	2	1	no	—
279	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
280	C₄×C₂²⋊C₄	—	2	1	no	—
281	#336	C₂²×C₆₁	1	2	yes	—
282	C₆₁	#24212	1	1	yes	characteristic, direct product factor, Sylow
283	C₂²×Q₈	—	2	8	no	—
284	C₂²×Q₈	—	2	2	no	—
285	C₂²×Q₈	—	2	4	no	—
286	C₂²×Q₈	—	2	4	no	—
287	C₂²×Q₈	—	4	4	no	—
288	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
289	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
290	C₂³×C₄	—	2	2	no	—
291	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
292	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
293	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
294	C₂×Q₁₆	—	2	8	no	—
295	C₂×Q₁₆	—	2	8	no	—
296	C₂×Q₁₆	—	4	4	no	—
297	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
298	C₄⋊Q₈	—	2	8	no	—
299	C₄⋊Q₈	—	2	8	no	—
300	C₄⋊Q₈	—	2	8	no	—
301	C₄⋊Q₈	—	2	4	no	—
302	C₄⋊Q₈	D₄×C₆₁	1	8	yes	—
303	C₂²⋊Q₈	—	2	2	no	—
304	C₂²⋊Q₈	D₄×C₆₁	1	4	yes	—
305	C₄×Q₈	—	2	4	no	—
306	C₂×C₄⋊C₄	—	2	8	no	—
307	C₂×C₄⋊C₄	—	2	8	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₄²	—	2	4	no	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
324	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
327	C₄⋊C₈	—	2	4	no	—
328	#103	—	2	8	no	—
329	#103	—	2	8	no	—
330	#103	—	4	4	no	—
331	C₂²⋊C₈	—	2	4	no	—
332	#95	—	2	1	no	—
333	#95	—	2	1	no	—
334	#95	—	2	1	no	—
335	#95	—	2	1	no	—
336	#95	—	2	1	no	—
337	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
338	C₂×Q₈	—	2	8	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	4	no	—
347	C₂×Q₈	—	4	16	no	—
348	C₂×Q₈	—	4	16	no	—
349	C₂×Q₈	—	4	4	no	—
350	C₂×Q₈	—	4	4	no	—
351	C₂×Q₈	C₂×D₄×C₆₁	1	8	yes	—
352	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	4	4	no	—
368	C₂²×C₄	Q₁₆×C₆₁	1	4	yes	complemented
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	2	yes	—
372	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
375	C₂²×C₄	#41×C₆₁	1	2	yes	—
376	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
377	Q₁₆	—	4	16	no	—
378	C₂×C₈	—	2	4	no	—
379	C₂×C₈	—	2	4	no	—
380	C₂×C₈	—	2	4	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	4	2	no	—
398	C₄²	—	4	2	no	—
399	C₄²	C₂×D₄×C₆₁	1	4	yes	—
400	C₂³	—	2	1	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	#121×C₆₁	1	2	yes	—
405	C₂³	C₂×Q₁₆×C₆₁	1	2	yes	—
406	C₂³	#137×C₆₁	1	2	yes	—
407	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
408	Q₈	—	2	4	no	—
409	Q₈	—	2	8	no	—
410	Q₈	—	2	8	no	—
411	Q₈	—	4	16	no	—
412	Q₈	—	4	4	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	4	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	16	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	#120×C₆₁	1	2	yes	—
444	C₂×C₄	#120×C₆₁	1	2	yes	—
445	C₂×C₄	#121×C₆₁	1	2	yes	—
446	C₂×C₄	C₂×Q₁₆×C₆₁	1	2	yes	—
447	C₂×C₄	C₂×Q₁₆×C₆₁	1	2	yes	—
448	C₂×C₄	#137×C₆₁	1	2	yes	—
449	C₂×C₄	#137×C₆₁	1	2	yes	—
450	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
452	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
453	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
454	C₈	—	4	4	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	C₆₁×#462	1	4	yes	complemented
462	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
463	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
464	C₂²	C₆₁×#535	1	1	yes	characteristic
465	C₂²	C₂²×Q₁₆×C₆₁	1	1	yes	characteristic
466	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
467	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
468	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	8	no	—
475	C₄	—	4	2	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	1	no	—
478	C₄	C₆₁×#451	1	4	yes	complemented
479	C₄	D₄²×C₆₁	1	2	yes	—
480	C₄	C₆₁×#546	1	2	yes	—
481	C₂	—	2	4	no	—
482	C₂	C₆₁×#2408	1	1	yes	characteristic
483	C₂	C₂×C₆₁×#451	1	1	yes	characteristic
484	C₂	C₆₁×#3004	1	1	yes	characteristic
485	C₂	C₂×C₆₁×#462	1	1	yes	characteristic
486	C₂	C₆₁×#3039	1	1	yes	characteristic
487	C₂	C₆₁×#3209	1	1	yes	characteristic
488	C₂	C₆₁×#3218	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂⁴×C₆₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#462	C₂	semidirect
5. C₆₁×#2043	C₂	semidirect
6. C₆₁×#2016	C₂	semidirect
7. C₆₁×#1981	C₂	semidirect
123. C₂²×C₄×C₆₁	Q₁₆	semidirect
210. #24212	C₆₁	direct (N × H)
217. C₂²×C₆₁	#462	semidirect
234. C₄×C₆₁	#451	semidirect
238. C₂×#462	C₂×C₆₁	semidirect
241. #2043	C₂×C₆₁	semidirect
242. #2016	C₂×C₆₁	semidirect
243. #1981	C₂×C₆₁	semidirect
282. C₆₁	#24212	direct (N × H)
368. C₂²×C₄	Q₁₆×C₆₁	semidirect
461. C₂²	C₆₁×#462	semidirect
478. C₄	C₆₁×#451	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₆₁	2
C₂×C₆₁×#462	2
C₂×C₆₁×#451	2
C₄×C₂²⋊Q₈×C₆₁	2
C₆₁×#2043	2
C₆₁×#2016	2
C₆₁×#1981	2
C₆₁×#1797	2
C₆₁×#1787	2
#24212	61

Subgroups — C61×#24212 #29527645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24212 #29527645