Subgroups — C₆₁×#25035 #29528468

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2423	C₂	1	2	yes	maximal
4	C₆₁×#2072	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2036	C₂	1	2	yes	maximal
6	C₆₁×#1969	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1863	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1808	C₂	1	1	yes	maximal, characteristic
11	C₈×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
16	C₆₁×#467	—	2	4	no	—
17	C₄×Q₁₆×C₆₁	—	2	4	no	—
18	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#107×C₆₁	C₂²	1	2	yes	—
22	C₂×#103×C₆₁	C₂²	1	2	yes	—
23	C₂×#103×C₆₁	C₂²	1	2	yes	—
24	C₂×#103×C₆₁	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#399	—	2	2	no	—
29	C₆₁×#398	—	2	2	no	—
30	C₆₁×#391	C₂²	1	2	yes	—
31	C₆₁×#389	C₂²	1	2	yes	—
32	C₆₁×#388	—	2	2	no	—
33	C₆₁×#387	—	2	2	no	—
34	C₆₁×#384	C₂²	1	2	yes	—
35	C₆₁×#380	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#340	C₂²	1	2	yes	—
38	C₆₁×#340	C₂²	1	2	yes	—
39	C₆₁×#336	C₂²	1	1	yes	characteristic
40	C₆₁×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
43	C₂×Q₁₆×C₆₁	—	2	2	no	—
44	C₂×Q₁₆×C₆₁	—	2	2	no	—
45	C₂×Q₁₆×C₆₁	D₄	1	4	yes	—
46	C₂²×C₈×C₆₁	—	2	2	no	—
47	C₂²×C₈×C₆₁	—	2	2	no	—
48	C₂²×C₈×C₆₁	—	2	2	no	—
49	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
53	C₂²⋊Q₈×C₆₁	—	2	4	no	—
54	C₂²⋊Q₈×C₆₁	—	4	2	no	—
55	C₄×Q₈×C₆₁	—	2	4	no	—
56	C₄×Q₈×C₆₁	—	4	2	no	—
57	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
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	2	no	—
66	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₆₁	—	2	2	no	—
70	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
72	#107×C₆₁	—	2	2	no	—
73	#107×C₆₁	—	2	2	no	—
74	#107×C₆₁	—	2	2	no	—
75	#107×C₆₁	—	4	2	no	—
76	#103×C₆₁	—	2	4	no	—
77	#103×C₆₁	—	2	4	no	—
78	#103×C₆₁	—	2	4	no	—
79	C₂²⋊C₈×C₆₁	—	2	2	no	—
80	C₄×C₈×C₆₁	—	2	2	no	—
81	C₄×C₈×C₆₁	—	2	2	no	—
82	#95×C₆₁	—	2	2	no	—
83	#95×C₆₁	—	2	2	no	—
84	#95×C₆₁	—	2	2	no	—
85	#95×C₆₁	—	2	2	no	—
86	#95×C₆₁	D₄	1	1	yes	characteristic
87	#95×C₆₁	D₄	1	1	yes	characteristic
88	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
89	C₂×Q₈×C₆₁	—	2	2	no	—
90	C₂×Q₈×C₆₁	—	2	2	no	—
91	C₂×Q₈×C₆₁	—	2	2	no	—
92	C₂×Q₈×C₆₁	—	2	2	no	—
93	C₂×Q₈×C₆₁	—	2	2	no	—
94	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₆₁	—	2	2	no	—
96	C₂²×C₄×C₆₁	—	2	1	no	—
97	C₂²×C₄×C₆₁	—	2	1	no	—
98	C₂²×C₄×C₆₁	—	2	1	no	—
99	C₂²×C₄×C₆₁	—	2	1	no	—
100	C₂²×C₄×C₆₁	—	2	1	no	—
101	C₂²×C₄×C₆₁	—	2	1	no	—
102	C₂²×C₄×C₆₁	—	2	2	no	—
103	C₂²×C₄×C₆₁	—	2	2	no	—
104	C₂²×C₄×C₆₁	—	2	2	no	—
105	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
111	Q₁₆×C₆₁	—	2	8	no	—
112	C₂×C₈×C₆₁	—	2	1	no	—
113	C₂×C₈×C₆₁	—	2	1	no	—
114	C₂×C₈×C₆₁	—	2	1	no	—
115	C₂×C₈×C₆₁	—	2	1	no	—
116	C₂×C₈×C₆₁	—	2	1	no	—
117	C₂×C₈×C₆₁	—	2	1	no	—
118	C₂×C₈×C₆₁	—	2	1	no	—
119	C₂×C₈×C₆₁	—	2	1	no	—
120	C₂×C₈×C₆₁	—	4	4	no	—
121	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₆₁	#41	1	2	yes	—
123	C₂×C₈×C₆₁	#41	1	2	yes	—
124	C₂×C₈×C₆₁	#41	1	2	yes	—
125	C₄⋊C₄×C₆₁	—	2	2	no	—
126	C₄⋊C₄×C₆₁	—	2	2	no	—
127	C₄⋊C₄×C₆₁	—	2	2	no	—
128	C₄⋊C₄×C₆₁	—	2	2	no	—
129	C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₄⋊C₄×C₆₁	—	2	2	no	—
131	C₄⋊C₄×C₆₁	—	4	4	no	—
132	C₄⋊C₄×C₆₁	—	4	4	no	—
133	C₄⋊C₄×C₆₁	—	4	4	no	—
134	C₄⋊C₄×C₆₁	—	8	2	no	—
135	C₄⋊C₄×C₆₁	—	8	2	no	—
136	C₂²⋊C₄×C₆₁	—	2	2	no	—
137	C₂²⋊C₄×C₆₁	—	4	4	no	—
138	C₂²⋊C₄×C₆₁	—	8	2	no	—
139	C₂²⋊C₄×C₆₁	Q₁₆	1	4	yes	complemented
140	C₄²×C₆₁	—	2	1	no	—
141	C₄²×C₆₁	—	2	1	no	—
142	C₄²×C₆₁	—	2	1	no	—
143	C₄²×C₆₁	—	2	1	no	—
144	C₄²×C₆₁	—	4	4	no	—
145	C₂³×C₆₁	—	2	1	no	—
146	C₂³×C₆₁	—	2	1	no	—
147	C₂³×C₆₁	—	2	1	no	—
148	C₂³×C₆₁	—	2	1	no	—
149	C₂³×C₆₁	—	2	1	no	—
150	C₂³×C₆₁	—	2	1	no	—
151	C₂³×C₆₁	C₂×Q₁₆	1	2	yes	—
152	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₆₁	—	2	4	no	—
154	Q₈×C₆₁	—	2	4	no	—
155	Q₈×C₆₁	—	4	2	no	—
156	Q₈×C₆₁	—	4	2	no	—
157	C₂×C₄×C₆₁	—	2	1	no	—
158	C₂×C₄×C₆₁	—	2	1	no	—
159	C₂×C₄×C₆₁	—	2	1	no	—
160	C₂×C₄×C₆₁	—	2	1	no	—
161	C₂×C₄×C₆₁	—	2	1	no	—
162	C₂×C₄×C₆₁	—	2	1	no	—
163	C₂×C₄×C₆₁	—	2	1	no	—
164	C₂×C₄×C₆₁	—	2	1	no	—
165	C₂×C₄×C₆₁	—	2	4	no	—
166	C₂×C₄×C₆₁	—	2	1	no	—
167	C₂×C₄×C₆₁	—	2	1	no	—
168	C₂×C₄×C₆₁	—	2	1	no	—
169	C₂×C₄×C₆₁	—	2	1	no	—
170	C₂×C₄×C₆₁	—	4	2	no	—
171	C₂×C₄×C₆₁	—	4	2	no	—
172	C₂×C₄×C₆₁	—	4	1	no	—
173	C₂×C₄×C₆₁	—	4	1	no	—
174	C₂×C₄×C₆₁	—	4	1	no	—
175	C₂×C₄×C₆₁	—	4	1	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	—	4	2	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	4	2	no	—
182	C₂×C₄×C₆₁	—	4	2	no	—
183	C₂×C₄×C₆₁	—	4	2	no	—
184	C₂×C₄×C₆₁	—	4	2	no	—
185	C₂×C₄×C₆₁	C₂×Q₁₆	1	2	yes	—
186	C₂×C₄×C₆₁	C₂×Q₁₆	1	2	yes	—
187	C₂×C₄×C₆₁	#135	1	2	yes	—
188	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
194	C₈×C₆₁	—	2	2	no	—
195	C₈×C₆₁	—	4	1	no	—
196	C₈×C₆₁	—	4	1	no	—
197	C₈×C₆₁	#123	1	4	yes	—
198	#25035	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₆₁	—	2	2	no	—
200	C₂²×C₆₁	—	2	2	no	—
201	C₂²×C₆₁	—	2	2	no	—
202	C₂²×C₆₁	—	4	1	no	—
203	C₂²×C₆₁	—	4	1	no	—
204	C₂²×C₆₁	—	4	1	no	—
205	C₂²×C₆₁	—	4	1	no	—
206	C₂²×C₆₁	#532	1	1	yes	characteristic
207	C₂²×C₆₁	D₄²	1	1	yes	characteristic
208	C₂²×C₆₁	#547	1	1	yes	characteristic
209	C₂²×C₆₁	C₂²×Q₁₆	1	1	yes	characteristic
210	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
211	C₂²×C₆₁	#576	1	1	yes	characteristic
212	C₂²×C₆₁	#578	1	1	yes	characteristic
213	C₄×C₆₁	—	2	2	no	—
214	C₄×C₆₁	—	2	2	no	—
215	C₄×C₆₁	—	2	2	no	—
216	C₄×C₆₁	—	4	1	no	—
217	C₄×C₆₁	—	4	4	no	—
218	C₄×C₆₁	—	4	1	no	—
219	C₄×C₆₁	—	8	2	no	—
220	C₄×C₆₁	—	8	2	no	—
221	C₄×C₆₁	—	8	2	no	—
222	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
223	C₄×C₆₁	#542	1	1	yes	characteristic
224	C₄×C₆₁	#547	1	1	yes	characteristic
225	C₄×C₆₁	#553	1	1	yes	characteristic
226	C₂×#467	C₂×C₆₁	1	1	yes	characteristic
227	C₂×C₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
228	#2423	C₂×C₆₁	1	2	yes	—
229	#2072	C₂×C₆₁	1	2	yes	complemented
230	#2036	C₂×C₆₁	1	2	yes	—
231	#1969	C₂×C₆₁	1	1	yes	characteristic, complemented
232	#1942	C₂×C₆₁	1	1	yes	characteristic, complemented
233	#1863	C₂×C₆₁	1	2	yes	complemented
234	#1845	C₂×C₆₁	1	1	yes	characteristic, complemented
235	#1808	C₂×C₆₁	1	1	yes	characteristic
236	C₈×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic
237	C₂×C₆₁	—	4	2	no	—
238	C₂×C₆₁	#2422	1	1	yes	characteristic
239	C₂×C₆₁	#3170	1	1	yes	characteristic
240	C₂×C₆₁	#3175	1	1	yes	characteristic
241	C₂×C₆₁	D₄×Q₁₆	1	1	yes	characteristic
242	C₂×C₆₁	#3287	1	1	yes	characteristic
243	C₂×C₆₁	#3336	1	1	yes	characteristic
244	C₂×C₆₁	#3338	1	1	yes	characteristic
245	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
246	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
247	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
248	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
249	#467	—	2	4	no	—
250	C₄×Q₁₆	—	2	4	no	—
251	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
252	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
253	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
254	C₂×#107	C₂²×C₆₁	1	2	yes	—
255	C₂×#103	C₂²×C₆₁	1	2	yes	—
256	C₂×#103	C₂²×C₆₁	1	2	yes	—
257	C₂×#103	C₂²×C₆₁	1	2	yes	—
258	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
260	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
261	#399	—	2	2	no	—
262	#398	—	2	2	no	—
263	#391	C₂²×C₆₁	1	2	yes	—
264	#389	C₂²×C₆₁	1	2	yes	—
265	#388	—	2	2	no	—
266	#387	—	2	2	no	—
267	#384	C₂²×C₆₁	1	2	yes	—
268	#380	C₂²×C₆₁	1	2	yes	—
269	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
270	#340	C₂²×C₆₁	1	2	yes	—
271	#340	C₂²×C₆₁	1	2	yes	—
272	#336	C₂²×C₆₁	1	1	yes	characteristic
273	#336	C₂²×C₆₁	1	1	yes	characteristic
274	C₆₁	#25035	1	1	yes	characteristic, direct product factor, Sylow
275	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
276	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
277	C₂×Q₁₆	—	2	2	no	—
278	C₂×Q₁₆	—	2	2	no	—
279	C₂×Q₁₆	D₄×C₆₁	1	4	yes	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
287	C₂²⋊Q₈	—	2	4	no	—
288	C₂²⋊Q₈	—	4	2	no	—
289	C₄×Q₈	—	2	4	no	—
290	C₄×Q₈	—	4	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
306	#107	—	2	2	no	—
307	#107	—	2	2	no	—
308	#107	—	2	2	no	—
309	#107	—	4	2	no	—
310	#103	—	2	4	no	—
311	#103	—	2	4	no	—
312	#103	—	2	4	no	—
313	C₂²⋊C₈	—	2	2	no	—
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	—	2	2	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	#95	D₄×C₆₁	1	1	yes	characteristic
321	#95	D₄×C₆₁	1	1	yes	characteristic
322	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
345	Q₁₆	—	2	8	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	4	4	no	—
355	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
356	C₂×C₈	#41×C₆₁	1	2	yes	—
357	C₂×C₈	#41×C₆₁	1	2	yes	—
358	C₂×C₈	#41×C₆₁	1	2	yes	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	4	no	—
366	C₄⋊C₄	—	4	4	no	—
367	C₄⋊C₄	—	4	4	no	—
368	C₄⋊C₄	—	8	2	no	—
369	C₄⋊C₄	—	8	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	4	4	no	—
372	C₂²⋊C₄	—	8	2	no	—
373	C₂²⋊C₄	Q₁₆×C₆₁	1	4	yes	complemented
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	4	4	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	C₂×Q₁₆×C₆₁	1	2	yes	—
386	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
387	Q₈	—	2	4	no	—
388	Q₈	—	2	4	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	4	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	C₂×Q₁₆×C₆₁	1	2	yes	—
420	C₂×C₄	C₂×Q₁₆×C₆₁	1	2	yes	—
421	C₂×C₄	#135×C₆₁	1	2	yes	—
422	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
423	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
424	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
426	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
427	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
428	C₈	—	2	2	no	—
429	C₈	—	4	1	no	—
430	C₈	—	4	1	no	—
431	C₈	#123×C₆₁	1	4	yes	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	C₆₁×#532	1	1	yes	characteristic
440	C₂²	D₄²×C₆₁	1	1	yes	characteristic
441	C₂²	C₆₁×#547	1	1	yes	characteristic
442	C₂²	C₂²×Q₁₆×C₆₁	1	1	yes	characteristic
443	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
444	C₂²	C₆₁×#576	1	1	yes	characteristic
445	C₂²	C₆₁×#578	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	4	no	—
452	C₄	—	8	2	no	—
453	C₄	—	8	2	no	—
454	C₄	—	8	2	no	—
455	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
456	C₄	C₆₁×#542	1	1	yes	characteristic
457	C₄	C₆₁×#547	1	1	yes	characteristic
458	C₄	C₆₁×#553	1	1	yes	characteristic
459	C₂	—	4	2	no	—
460	C₂	C₆₁×#2422	1	1	yes	characteristic
461	C₂	C₆₁×#3170	1	1	yes	characteristic
462	C₂	C₆₁×#3175	1	1	yes	characteristic
463	C₂	D₄×Q₁₆×C₆₁	1	1	yes	characteristic
464	C₂	C₆₁×#3287	1	1	yes	characteristic
465	C₂	C₆₁×#3336	1	1	yes	characteristic
466	C₂	C₆₁×#3338	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 ◁ C₄×C₂²⋊C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₆₁	C₂	semidirect
4. C₆₁×#2072	C₂	semidirect
6. C₆₁×#1969	C₂	semidirect
7. C₆₁×#1942	C₂	semidirect
8. C₆₁×#1863	C₂	semidirect
9. C₆₁×#1845	C₂	semidirect
139. C₂²⋊C₄×C₆₁	Q₁₆	semidirect
198. #25035	C₆₁	direct (N × H)
227. C₂×C₄×Q₁₆	C₂×C₆₁	semidirect
229. #2072	C₂×C₆₁	semidirect
231. #1969	C₂×C₆₁	semidirect
232. #1942	C₂×C₆₁	semidirect
233. #1863	C₂×C₆₁	semidirect
234. #1845	C₂×C₆₁	semidirect
274. C₆₁	#25035	direct (N × H)
373. C₂²⋊C₄	Q₁₆×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×#467	2
C₂×C₄×Q₁₆×C₆₁	2
C₆₁×#2423	2
C₆₁×#2072	2
C₆₁×#2036	2
C₆₁×#1969	2
C₆₁×#1942	2
C₆₁×#1863	2
C₆₁×#1845	2
C₆₁×#1808	2
C₈×C₂²⋊C₄×C₆₁	2
#25035	61

Subgroups — C61×#25035 #29528468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25035 #29528468