Subgroups — C₆₁×#24749 #29528182

Order 15616.

1044 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#463	C₂	1	2	yes	maximal, complemented
2	C₂×C₆₁×#459	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2349	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2067	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2042	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1879	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₆₁	C₂²	1	2	yes	—
14	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#124×C₆₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#463	—	2	8	no	—
20	C₆₁×#459	—	2	4	no	—
21	C₆₁×#440	—	2	4	no	—
22	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#103×C₆₁	C₂²	1	2	yes	—
26	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#102×C₆₁	C₂²	1	2	yes	—
28	C₂×#102×C₆₁	C₂²	1	2	yes	—
29	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#102×C₆₁	C₂²	1	2	yes	—
31	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
32	C₆₁×#394	—	2	1	no	—
33	C₆₁×#394	—	2	1	no	—
34	C₆₁×#390	—	2	2	no	—
35	C₆₁×#390	C₂²	1	2	yes	—
36	C₆₁×#389	C₂²	1	2	yes	—
37	C₆₁×#385	—	2	2	no	—
38	C₆₁×#382	C₂²	1	1	yes	characteristic
39	C₆₁×#380	—	2	1	no	—
40	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×#95×C₆₁	—	2	1	no	—
42	C₆₁×#340	C₂²	1	2	yes	—
43	C₆₁×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₆₁	—	2	1	no	—
46	C₂²×D₄×C₆₁	—	2	1	no	—
47	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
48	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₆₁	—	2	1	no	—
50	C₂³×C₄×C₆₁	—	2	2	no	—
51	C₂×SD₁₆×C₆₁	—	2	2	no	—
52	C₂×SD₁₆×C₆₁	—	2	2	no	—
53	C₂×SD₁₆×C₆₁	D₄	1	4	yes	complemented
54	C₂×D₈×C₆₁	—	2	4	no	—
55	C₂×D₈×C₆₁	—	2	4	no	—
56	C₂×D₈×C₆₁	—	2	4	no	—
57	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
60	#127×C₆₁	—	2	2	no	—
61	#127×C₆₁	—	2	2	no	—
62	#124×C₆₁	—	2	4	no	—
63	#124×C₆₁	—	4	2	no	—
64	C₄×Q₈×C₆₁	—	2	2	no	—
65	C₄×Q₈×C₆₁	—	2	2	no	—
66	C₄×D₄×C₆₁	—	2	4	no	—
67	C₄×D₄×C₆₁	—	2	2	no	—
68	C₄×D₄×C₆₁	—	4	2	no	—
69	C₄×D₄×C₆₁	D₄	1	4	yes	—
70	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
82	C₂×C₄²×C₆₁	—	2	1	no	—
83	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
84	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
85	#107×C₆₁	—	2	2	no	—
86	C₄⋊C₈×C₆₁	—	2	4	no	—
87	C₄⋊C₈×C₆₁	—	2	2	no	—
88	#103×C₆₁	—	2	4	no	—
89	#103×C₆₁	—	2	2	no	—
90	#102×C₆₁	—	2	2	no	—
91	#102×C₆₁	—	2	4	no	—
92	#102×C₆₁	—	2	4	no	—
93	#102×C₆₁	—	4	2	no	—
94	#97×C₆₁	—	2	2	no	—
95	#95×C₆₁	—	2	1	no	—
96	#95×C₆₁	—	2	2	no	—
97	#95×C₆₁	—	2	1	no	—
98	#95×C₆₁	D₄	1	1	yes	characteristic
99	#95×C₆₁	D₄	1	1	yes	characteristic
100	C₂⁴×C₆₁	—	2	1	no	—
101	C₂⁴×C₆₁	—	2	2	no	—
102	C₂×Q₈×C₆₁	—	2	1	no	—
103	C₂×Q₈×C₆₁	—	2	1	no	—
104	C₂×Q₈×C₆₁	—	2	1	no	—
105	C₂×Q₈×C₆₁	—	2	1	no	—
106	C₂×Q₈×C₆₁	—	2	1	no	—
107	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
108	C₂×D₄×C₆₁	—	2	2	no	—
109	C₂×D₄×C₆₁	—	2	2	no	—
110	C₂×D₄×C₆₁	—	2	1	no	—
111	C₂×D₄×C₆₁	—	2	2	no	—
112	C₂×D₄×C₆₁	—	2	2	no	—
113	C₂×D₄×C₆₁	—	2	1	no	—
114	C₂×D₄×C₆₁	—	2	2	no	—
115	C₂×D₄×C₆₁	—	2	1	no	—
116	C₂×D₄×C₆₁	—	2	2	no	—
117	C₂×D₄×C₆₁	—	4	4	no	—
118	C₂×D₄×C₆₁	—	4	2	no	—
119	C₂×D₄×C₆₁	—	4	2	no	—
120	C₂×D₄×C₆₁	—	8	2	no	—
121	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
122	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₆₁	#41	1	2	yes	—
124	C₂²×C₄×C₆₁	—	2	1	no	—
125	C₂²×C₄×C₆₁	—	2	1	no	—
126	C₂²×C₄×C₆₁	—	2	4	no	—
127	C₂²×C₄×C₆₁	—	2	2	no	—
128	C₂²×C₄×C₆₁	—	2	1	no	—
129	C₂²×C₄×C₆₁	—	4	4	no	—
130	C₂²×C₄×C₆₁	—	4	4	no	—
131	C₂²×C₄×C₆₁	—	8	2	no	—
132	C₂²×C₄×C₆₁	—	8	2	no	—
133	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
138	SD₁₆×C₆₁	—	2	8	no	—
139	D₈×C₆₁	—	4	8	no	—
140	C₂×C₈×C₆₁	—	2	1	no	—
141	C₂×C₈×C₆₁	—	2	1	no	—
142	C₂×C₈×C₆₁	—	2	1	no	—
143	C₂×C₈×C₆₁	—	2	2	no	—
144	C₂×C₈×C₆₁	—	2	2	no	—
145	C₂×C₈×C₆₁	—	2	2	no	—
146	C₂×C₈×C₆₁	—	2	1	no	—
147	C₂×C₈×C₆₁	—	2	1	no	—
148	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
149	C₄⋊C₄×C₆₁	—	2	1	no	—
150	C₄⋊C₄×C₆₁	—	2	2	no	—
151	C₄⋊C₄×C₆₁	—	2	1	no	—
152	C₄⋊C₄×C₆₁	—	2	1	no	—
153	C₄⋊C₄×C₆₁	—	2	2	no	—
154	C₄⋊C₄×C₆₁	—	4	2	no	—
155	C₄⋊C₄×C₆₁	—	4	2	no	—
156	C₄⋊C₄×C₆₁	—	8	2	no	—
157	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
158	C₂²⋊C₄×C₆₁	—	2	4	no	—
159	C₂²⋊C₄×C₆₁	—	4	4	no	—
160	C₂²⋊C₄×C₆₁	—	4	4	no	—
161	C₂²⋊C₄×C₆₁	—	4	4	no	—
162	C₂²⋊C₄×C₆₁	—	8	2	no	—
163	C₂²⋊C₄×C₆₁	—	8	2	no	—
164	C₄²×C₆₁	—	2	2	no	—
165	C₄²×C₆₁	—	2	2	no	—
166	C₄²×C₆₁	—	4	2	no	—
167	C₄²×C₆₁	C₂×D₄	1	2	yes	—
168	C₄²×C₆₁	#41	1	2	yes	—
169	C₂³×C₆₁	—	2	2	no	—
170	C₂³×C₆₁	—	2	2	no	—
171	C₂³×C₆₁	—	2	2	no	—
172	C₂³×C₆₁	—	4	2	no	—
173	C₂³×C₆₁	—	4	2	no	—
174	C₂³×C₆₁	—	4	2	no	—
175	C₂³×C₆₁	—	4	2	no	—
176	C₂³×C₆₁	—	4	2	no	—
177	C₂³×C₆₁	—	4	2	no	—
178	C₂³×C₆₁	—	4	2	no	—
179	C₂³×C₆₁	—	4	2	no	—
180	C₂³×C₆₁	—	4	2	no	—
181	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₆₁	—	2	2	no	—
183	Q₈×C₆₁	—	2	2	no	—
184	Q₈×C₆₁	—	4	1	no	—
185	Q₈×C₆₁	—	4	1	no	—
186	D₄×C₆₁	—	2	2	no	—
187	D₄×C₆₁	—	2	2	no	—
188	D₄×C₆₁	—	2	2	no	—
189	D₄×C₆₁	—	4	2	no	—
190	D₄×C₆₁	—	4	2	no	—
191	D₄×C₆₁	—	4	2	no	—
192	D₄×C₆₁	—	4	2	no	—
193	D₄×C₆₁	—	8	4	no	—
194	D₄×C₆₁	—	8	4	no	—
195	D₄×C₆₁	#121	1	4	yes	—
196	C₂×C₄×C₆₁	—	2	2	no	—
197	C₂×C₄×C₆₁	—	2	2	no	—
198	C₂×C₄×C₆₁	—	2	2	no	—
199	C₂×C₄×C₆₁	—	2	2	no	—
200	C₂×C₄×C₆₁	—	2	2	no	—
201	C₂×C₄×C₆₁	—	2	2	no	—
202	C₂×C₄×C₆₁	—	2	2	no	—
203	C₂×C₄×C₆₁	—	2	2	no	—
204	C₂×C₄×C₆₁	—	2	2	no	—
205	C₂×C₄×C₆₁	—	2	2	no	—
206	C₂×C₄×C₆₁	—	4	1	no	—
207	C₂×C₄×C₆₁	—	4	1	no	—
208	C₂×C₄×C₆₁	—	4	2	no	—
209	C₂×C₄×C₆₁	—	4	1	no	—
210	C₂×C₄×C₆₁	—	4	2	no	—
211	C₂×C₄×C₆₁	—	4	2	no	—
212	C₂×C₄×C₆₁	—	4	2	no	—
213	C₂×C₄×C₆₁	—	4	2	no	—
214	C₂×C₄×C₆₁	—	8	4	no	—
215	C₂×C₄×C₆₁	—	8	8	no	—
216	C₂×C₄×C₆₁	#121	1	2	yes	—
217	C₂×C₄×C₆₁	#121	1	2	yes	—
218	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
224	C₈×C₆₁	—	2	2	no	—
225	C₈×C₆₁	—	4	2	no	—
226	C₈×C₆₁	—	4	1	no	—
227	#24749	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂²×C₆₁	—	2	4	no	—
229	C₂²×C₆₁	—	4	4	no	—
230	C₂²×C₆₁	—	4	4	no	—
231	C₂²×C₆₁	—	4	2	no	—
232	C₂²×C₆₁	—	4	2	no	—
233	C₂²×C₆₁	—	8	2	no	—
234	C₂²×C₆₁	—	8	2	no	—
235	C₂²×C₆₁	—	8	2	no	—
236	C₂²×C₆₁	—	8	2	no	—
237	C₂²×C₆₁	—	8	2	no	—
238	C₂²×C₆₁	—	8	2	no	—
239	C₂²×C₆₁	—	8	2	no	—
240	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
241	C₂²×C₆₁	D₄²	1	1	yes	characteristic
242	C₂²×C₆₁	#548	1	1	yes	characteristic
243	C₂²×C₆₁	#575	1	2	yes	—
244	C₂²×C₆₁	#576	1	2	yes	—
245	C₄×C₆₁	—	2	2	no	—
246	C₄×C₆₁	—	2	2	no	—
247	C₄×C₆₁	—	4	2	no	—
248	C₄×C₆₁	—	4	2	no	—
249	C₄×C₆₁	—	4	2	no	—
250	C₄×C₆₁	—	4	2	no	—
251	C₄×C₆₁	—	8	2	no	—
252	C₄×C₆₁	—	8	1	no	—
253	C₄×C₆₁	C₂×#121	1	1	yes	characteristic
254	C₄×C₆₁	#537	1	1	yes	characteristic
255	C₄×C₆₁	#547	1	1	yes	characteristic
256	C₄×C₆₁	#553	1	1	yes	characteristic
257	C₂×#463	C₂×C₆₁	1	2	yes	complemented
258	C₂×#459	C₂×C₆₁	1	1	yes	characteristic
259	C₂×#440	C₂×C₆₁	1	1	yes	characteristic, complemented
260	#2548	C₂×C₆₁	1	1	yes	characteristic, complemented
261	#2349	C₂×C₆₁	1	1	yes	characteristic, complemented
262	#2067	C₂×C₆₁	1	2	yes	complemented
263	#2042	C₂×C₆₁	1	2	yes	complemented
264	#1961	C₂×C₆₁	1	1	yes	characteristic, complemented
265	#1940	C₂×C₆₁	1	1	yes	characteristic, complemented
266	#1879	C₂×C₆₁	1	2	yes	complemented
267	#1805	C₂×C₆₁	1	1	yes	characteristic, complemented
268	C₂×C₆₁	—	4	4	no	—
269	C₂×C₆₁	—	16	2	no	—
270	C₂×C₆₁	#2416	1	1	yes	characteristic
271	C₂×C₆₁	#3040	1	1	yes	characteristic
272	C₂×C₆₁	#3041	1	1	yes	characteristic
273	C₂×C₆₁	#3268	1	2	yes	—
274	C₂×C₆₁	#3370	1	2	yes	—
275	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
276	C₂²×D₈	C₂²×C₆₁	1	2	yes	—
277	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
278	C₂×#124	C₂²×C₆₁	1	2	yes	—
279	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
280	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
281	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
282	#463	—	2	8	no	—
283	#459	—	2	4	no	—
284	#440	—	2	4	no	—
285	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
286	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
287	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
288	C₂×#103	C₂²×C₆₁	1	2	yes	—
289	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
290	C₂×#102	C₂²×C₆₁	1	2	yes	—
291	C₂×#102	C₂²×C₆₁	1	2	yes	—
292	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
293	C₂×#102	C₂²×C₆₁	1	2	yes	—
294	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
295	#394	—	2	1	no	—
296	#394	—	2	1	no	—
297	#390	—	2	2	no	—
298	#390	C₂²×C₆₁	1	2	yes	—
299	#389	C₂²×C₆₁	1	2	yes	—
300	#385	—	2	2	no	—
301	#382	C₂²×C₆₁	1	1	yes	characteristic
302	#380	—	2	1	no	—
303	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
304	C₂×#95	—	2	1	no	—
305	#340	C₂²×C₆₁	1	2	yes	—
306	#336	C₂²×C₆₁	1	2	yes	—
307	C₆₁	#24749	1	1	yes	characteristic, direct product factor, Sylow
308	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
309	C₂²×D₄	—	2	1	no	—
310	C₂²×D₄	—	2	1	no	—
311	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
312	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	—	2	2	no	—
315	C₂×SD₁₆	—	2	2	no	—
316	C₂×SD₁₆	—	2	2	no	—
317	C₂×SD₁₆	D₄×C₆₁	1	4	yes	complemented
318	C₂×D₈	—	2	4	no	—
319	C₂×D₈	—	2	4	no	—
320	C₂×D₈	—	2	4	no	—
321	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
322	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
324	#127	—	2	2	no	—
325	#127	—	2	2	no	—
326	#124	—	2	4	no	—
327	#124	—	4	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×D₄	—	2	4	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	—	4	2	no	—
333	C₄×D₄	D₄×C₆₁	1	4	yes	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
348	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
349	#107	—	2	2	no	—
350	C₄⋊C₈	—	2	4	no	—
351	C₄⋊C₈	—	2	2	no	—
352	#103	—	2	4	no	—
353	#103	—	2	2	no	—
354	#102	—	2	2	no	—
355	#102	—	2	4	no	—
356	#102	—	2	4	no	—
357	#102	—	4	2	no	—
358	#97	—	2	2	no	—
359	#95	—	2	1	no	—
360	#95	—	2	2	no	—
361	#95	—	2	1	no	—
362	#95	D₄×C₆₁	1	1	yes	characteristic
363	#95	D₄×C₆₁	1	1	yes	characteristic
364	C₂⁴	—	2	1	no	—
365	C₂⁴	—	2	2	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	4	4	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	8	2	no	—
385	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
386	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
387	C₂×D₄	#41×C₆₁	1	2	yes	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	4	4	no	—
394	C₂²×C₄	—	4	4	no	—
395	C₂²×C₄	—	8	2	no	—
396	C₂²×C₄	—	8	2	no	—
397	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
401	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
402	SD₁₆	—	2	8	no	—
403	D₈	—	4	8	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	—	4	2	no	—
420	C₄⋊C₄	—	8	2	no	—
421	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₂²⋊C₄	—	4	4	no	—
424	C₂²⋊C₄	—	4	4	no	—
425	C₂²⋊C₄	—	4	4	no	—
426	C₂²⋊C₄	—	8	2	no	—
427	C₂²⋊C₄	—	8	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	4	2	no	—
431	C₄²	C₂×D₄×C₆₁	1	2	yes	—
432	C₄²	#41×C₆₁	1	2	yes	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
446	Q₈	—	2	2	no	—
447	Q₈	—	2	2	no	—
448	Q₈	—	4	1	no	—
449	Q₈	—	4	1	no	—
450	D₄	—	2	2	no	—
451	D₄	—	2	2	no	—
452	D₄	—	2	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	8	4	no	—
458	D₄	—	8	4	no	—
459	D₄	#121×C₆₁	1	4	yes	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	8	4	no	—
479	C₂×C₄	—	8	8	no	—
480	C₂×C₄	#121×C₆₁	1	2	yes	—
481	C₂×C₄	#121×C₆₁	1	2	yes	—
482	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
484	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
485	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
486	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
487	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
488	C₈	—	2	2	no	—
489	C₈	—	4	1	no	—
490	C₈	—	4	2	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	8	2	no	—
499	C₂²	—	8	2	no	—
500	C₂²	—	8	2	no	—
501	C₂²	—	8	2	no	—
502	C₂²	—	8	2	no	—
503	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
504	C₂²	D₄²×C₆₁	1	1	yes	characteristic
505	C₂²	C₆₁×#548	1	1	yes	characteristic
506	C₂²	C₆₁×#575	1	2	yes	—
507	C₂²	C₆₁×#576	1	2	yes	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	2	no	—
516	C₄	C₂×#121×C₆₁	1	1	yes	characteristic
517	C₄	C₆₁×#537	1	1	yes	characteristic
518	C₄	C₆₁×#547	1	1	yes	characteristic
519	C₄	C₆₁×#553	1	1	yes	characteristic
520	C₂	—	4	4	no	—
521	C₂	—	16	2	no	—
522	C₂	C₆₁×#2416	1	1	yes	characteristic
523	C₂	C₆₁×#3040	1	1	yes	characteristic
524	C₂	C₆₁×#3041	1	1	yes	characteristic
525	C₂	C₆₁×#3268	1	2	yes	—
526	C₂	C₆₁×#3370	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×C₆₁×#459	C₂
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. C₂×C₆₁×#463	C₂	semidirect
3. C₂×C₆₁×#440	C₂	semidirect
4. C₆₁×#2548	C₂	semidirect
5. C₆₁×#2349	C₂	semidirect
6. C₆₁×#2067	C₂	semidirect
7. C₆₁×#2042	C₂	semidirect
8. C₆₁×#1961	C₂	semidirect
9. C₆₁×#1940	C₂	semidirect
10. C₆₁×#1879	C₂	semidirect
11. C₆₁×#1805	C₂	semidirect
53. C₂×SD₁₆×C₆₁	D₄	semidirect
227. #24749	C₆₁	direct (N × H)
257. C₂×#463	C₂×C₆₁	semidirect
259. C₂×#440	C₂×C₆₁	semidirect
260. #2548	C₂×C₆₁	semidirect
261. #2349	C₂×C₆₁	semidirect
262. #2067	C₂×C₆₁	semidirect
263. #2042	C₂×C₆₁	semidirect
264. #1961	C₂×C₆₁	semidirect
265. #1940	C₂×C₆₁	semidirect
266. #1879	C₂×C₆₁	semidirect
267. #1805	C₂×C₆₁	semidirect
307. C₆₁	#24749	direct (N × H)
317. C₂×SD₁₆	D₄×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×#463	2
C₂×C₆₁×#459	2
C₂×C₆₁×#440	2
C₆₁×#2548	2
C₆₁×#2349	2
C₆₁×#2067	2
C₆₁×#2042	2
C₆₁×#1961	2
C₆₁×#1940	2
C₆₁×#1879	2
C₆₁×#1805	2
#24749	61

Subgroups — C61×#24749 #29528182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24749 #29528182