Subgroups — C₆₁×#21785 #29525218

Order 15616.

1262 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3500	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2889	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2884	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1912	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1910	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1888	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1884	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1827	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1795	C₂	1	2	yes	maximal, complemented
10	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	1	yes	characteristic
12	C₆₁×#568	C₂²	1	2	yes	complemented
13	C₆₁×#548	—	2	2	no	—
14	C₆₁×#546	—	2	2	no	—
15	C₆₁×#546	—	2	4	no	—
16	C₆₁×#536	C₄	1	2	yes	complemented
17	C₆₁×#536	C₂²	1	1	yes	characteristic
18	C₆₁×#535	C₄	1	2	yes	complemented
19	C₆₁×#535	C₂²	1	1	yes	characteristic
20	C₆₁×#532	C₄	1	2	yes	complemented
21	C₆₁×#532	C₂²	1	1	yes	characteristic
22	C₂×#124×C₆₁	C₄	1	2	yes	complemented
23	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#519	C₂²	1	2	yes	complemented
25	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#421	C₂²	1	4	yes	—
27	C₆₁×#418	C₂²	1	4	yes	—
28	C₆₁×#413	—	2	2	no	—
29	C₆₁×#413	C₂²	1	2	yes	—
30	C₂×#101×C₆₁	—	2	2	no	—
31	C₂×#101×C₆₁	C₂²	1	2	yes	complemented
32	C₆₁×#410	—	2	4	no	—
33	C₆₁×#410	C₂²	1	2	yes	—
34	C₆₁×#410	C₂²	1	2	yes	complemented
35	C₆₁×#339	C₂²	1	4	yes	complemented
36	C₆₁×H(3,ℤ/4)	C₂²	1	4	yes	complemented
37	2₋¹⁺⁴×C₆₁	—	4	4	no	—
38	H(5,𝔽₂)×C₆₁	—	4	4	no	—
39	C₂×#41×C₆₁	—	2	1	no	—
40	C₂×#41×C₆₁	C₂×C₄	1	2	yes	—
41	C₂×#41×C₆₁	C₂×C₄	1	2	yes	—
42	C₂×#41×C₆₁	D₄	1	2	yes	—
43	C₂×#41×C₆₁	D₄	1	4	yes	—
44	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
45	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
46	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₆₁	C₂×C₄	1	2	yes	—
48	C₂²×Q₈×C₆₁	D₄	1	2	yes	—
49	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₆₁	—	2	2	no	—
51	C₂²×D₄×C₆₁	—	2	1	no	—
52	C₂²×D₄×C₆₁	C₂×C₄	1	2	yes	—
53	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
54	#131×C₆₁	—	4	4	no	—
55	C₂×M₁₆×C₆₁	—	2	4	no	—
56	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
57	C₄⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
58	C₄⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
59	#127×C₆₁	C₂×C₄	1	2	yes	—
60	#127×C₆₁	C₂×C₄	1	1	yes	characteristic
61	#124×C₆₁	—	2	4	no	—
62	#124×C₆₁	—	2	2	no	—
63	#124×C₆₁	C₂×C₄	1	1	yes	characteristic
64	#124×C₆₁	C₂×C₄	1	2	yes	—
65	#124×C₆₁	C₂×C₄	1	1	yes	characteristic
66	#124×C₆₁	C₂×C₄	1	2	yes	—
67	#124×C₆₁	C₂×C₄	1	2	yes	—
68	#124×C₆₁	C₂×C₄	1	2	yes	—
69	#123×C₆₁	—	2	4	no	—
70	#123×C₆₁	—	2	2	no	—
71	C₂²⋊Q₈×C₆₁	—	2	4	no	—
72	C₂²⋊Q₈×C₆₁	—	2	2	no	—
73	#121×C₆₁	—	2	4	no	—
74	#121×C₆₁	—	2	2	no	—
75	#121×C₆₁	—	2	4	no	—
76	#121×C₆₁	—	2	2	no	—
77	#120×C₆₁	—	2	4	no	—
78	#120×C₆₁	—	2	2	no	—
79	C₄×Q₈×C₆₁	—	2	1	no	—
80	C₄×Q₈×C₆₁	—	4	4	no	—
81	C₄×D₄×C₆₁	—	2	2	no	—
82	C₄×D₄×C₆₁	—	2	1	no	—
83	C₄×D₄×C₆₁	—	2	4	no	—
84	C₄×D₄×C₆₁	—	2	2	no	—
85	#117×C₆₁	—	2	4	no	—
86	#117×C₆₁	C₂×C₄	1	2	yes	—
87	#117×C₆₁	C₂³	1	4	yes	—
88	#117×C₆₁	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
91	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
92	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
93	#104×C₆₁	—	4	4	no	—
94	#102×C₆₁	—	4	4	no	—
95	#101×C₆₁	—	2	2	no	—
96	#101×C₆₁	—	2	4	no	—
97	#100×C₆₁	—	2	2	no	—
98	#99×C₆₁	—	2	4	no	—
99	#99×C₆₁	—	2	4	no	—
100	C₂⁴×C₆₁	—	2	2	no	—
101	C₂⁴×C₆₁	—	2	1	no	—
102	#41×C₆₁	—	2	4	no	—
103	#41×C₆₁	—	2	4	no	—
104	#41×C₆₁	—	2	4	no	—
105	#41×C₆₁	—	4	8	no	—
106	#41×C₆₁	—	4	4	no	—
107	#41×C₆₁	—	4	4	no	—
108	#41×C₆₁	—	4	4	no	—
109	#41×C₆₁	—	4	4	no	—
110	C₂×Q₈×C₆₁	—	2	4	no	—
111	C₂×Q₈×C₆₁	—	4	4	no	—
112	C₂×Q₈×C₆₁	—	4	4	no	—
113	C₂×Q₈×C₆₁	C₂²⋊C₄	1	4	yes	—
114	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
116	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
117	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
118	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₆₁	—	2	2	no	—
120	C₂×D₄×C₆₁	—	2	1	no	—
121	C₂×D₄×C₆₁	—	2	4	no	—
122	C₂×D₄×C₆₁	—	2	2	no	—
123	C₂×D₄×C₆₁	—	2	2	no	—
124	C₂×D₄×C₆₁	—	2	1	no	—
125	C₂×D₄×C₆₁	—	2	4	no	—
126	C₂×D₄×C₆₁	—	4	4	no	—
127	C₂×D₄×C₆₁	—	4	8	no	—
128	C₂×D₄×C₆₁	—	4	4	no	—
129	C₂×D₄×C₆₁	C₂²⋊C₄	1	4	yes	—
130	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
132	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
133	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
134	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₁	—	2	2	no	—
137	C₂²×C₄×C₆₁	—	2	1	no	—
138	C₂²×C₄×C₆₁	—	2	2	no	—
139	C₂²×C₄×C₆₁	—	2	1	no	—
140	C₂²×C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
141	C₂²×C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
142	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
146	M₁₆×C₆₁	—	2	4	no	—
147	M₁₆×C₆₁	—	2	4	no	—
148	M₁₆×C₆₁	—	4	4	no	—
149	C₂×C₈×C₆₁	—	2	4	no	—
150	C₂×C₈×C₆₁	—	4	4	no	—
151	C₄⋊C₄×C₆₁	—	2	2	no	—
152	C₄⋊C₄×C₆₁	—	2	4	no	—
153	C₄⋊C₄×C₆₁	—	2	2	no	—
154	C₄⋊C₄×C₆₁	—	2	1	no	—
155	C₄⋊C₄×C₆₁	—	2	4	no	—
156	C₄⋊C₄×C₆₁	—	4	4	no	—
157	C₂²⋊C₄×C₆₁	—	2	2	no	—
158	C₂²⋊C₄×C₆₁	—	2	2	no	—
159	C₂²⋊C₄×C₆₁	—	2	1	no	—
160	C₂²⋊C₄×C₆₁	—	2	4	no	—
161	C₂²⋊C₄×C₆₁	—	2	2	no	—
162	C₂²⋊C₄×C₆₁	—	2	4	no	—
163	C₂²⋊C₄×C₆₁	—	2	4	no	—
164	C₂²⋊C₄×C₆₁	—	2	4	no	—
165	C₂²⋊C₄×C₆₁	—	2	4	no	—
166	C₄²×C₆₁	—	2	2	no	—
167	C₄²×C₆₁	—	2	1	no	—
168	C₄²×C₆₁	—	2	4	no	—
169	C₄²×C₆₁	—	4	4	no	—
170	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
172	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
173	C₂³×C₆₁	—	2	2	no	—
174	C₂³×C₆₁	—	2	1	no	—
175	C₂³×C₆₁	—	4	4	no	—
176	C₂³×C₆₁	—	4	2	no	—
177	C₂³×C₆₁	—	8	2	no	—
178	C₂³×C₆₁	—	8	4	no	—
179	C₂³×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂³×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₆₁	—	2	4	no	—
183	Q₈×C₆₁	—	2	2	no	—
184	Q₈×C₆₁	—	2	4	no	—
185	Q₈×C₆₁	—	2	2	no	—
186	Q₈×C₆₁	—	2	2	no	—
187	Q₈×C₆₁	—	4	4	no	—
188	D₄×C₆₁	—	2	4	no	—
189	D₄×C₆₁	—	2	4	no	—
190	D₄×C₆₁	—	2	2	no	—
191	D₄×C₆₁	—	2	4	no	—
192	D₄×C₆₁	—	2	2	no	—
193	D₄×C₆₁	—	2	2	no	—
194	D₄×C₆₁	—	4	4	no	—
195	D₄×C₆₁	—	4	4	no	—
196	D₄×C₆₁	—	4	4	no	—
197	D₄×C₆₁	—	4	2	no	—
198	D₄×C₆₁	—	4	2	no	—
199	D₄×C₆₁	—	8	4	no	—
200	D₄×C₆₁	—	8	2	no	—
201	C₂×C₄×C₆₁	—	2	4	no	—
202	C₂×C₄×C₆₁	—	2	4	no	—
203	C₂×C₄×C₆₁	—	2	4	no	—
204	C₂×C₄×C₆₁	—	2	1	no	—
205	C₂×C₄×C₆₁	—	2	2	no	—
206	C₂×C₄×C₆₁	—	2	1	no	—
207	C₂×C₄×C₆₁	—	2	1	no	—
208	C₂×C₄×C₆₁	—	4	4	no	—
209	C₂×C₄×C₆₁	—	4	4	no	—
210	C₂×C₄×C₆₁	—	4	4	no	—
211	C₂×C₄×C₆₁	—	4	2	no	—
212	C₂×C₄×C₆₁	—	4	4	no	—
213	C₂×C₄×C₆₁	—	8	1	no	—
214	C₂×C₄×C₆₁	—	8	2	no	—
215	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
216	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
217	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₆₁	H(5,𝔽₂)	1	4	yes	—
221	C₈×C₆₁	—	4	4	no	—
222	#21785	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂²×C₆₁	—	2	2	no	—
224	C₂²×C₆₁	—	2	2	no	—
225	C₂²×C₆₁	—	4	1	no	—
226	C₂²×C₆₁	—	4	2	no	—
227	C₂²×C₆₁	—	4	2	no	—
228	C₂²×C₆₁	—	4	4	no	—
229	C₂²×C₆₁	—	4	2	no	—
230	C₂²×C₆₁	—	4	2	no	—
231	C₂²×C₆₁	—	4	1	no	—
232	C₂²×C₆₁	—	16	2	no	—
233	C₂²×C₆₁	—	16	4	no	—
234	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
235	C₂²×C₆₁	#534	1	2	yes	—
236	C₄×C₆₁	—	2	2	no	—
237	C₄×C₆₁	—	2	2	no	—
238	C₄×C₆₁	—	2	4	no	—
239	C₄×C₆₁	—	4	1	no	—
240	C₄×C₆₁	—	4	2	no	—
241	C₄×C₆₁	—	4	1	no	—
242	C₄×C₆₁	—	4	1	no	—
243	C₄×C₆₁	—	8	4	no	—
244	C₄×C₆₁	#518	1	2	yes	—
245	C₄×C₆₁	#534	1	2	yes	—
246	#3500	C₂×C₆₁	1	1	yes	characteristic
247	#2889	C₂×C₆₁	1	1	yes	characteristic, complemented
248	#2884	C₂×C₆₁	1	1	yes	characteristic, complemented
249	#1912	C₂×C₆₁	1	2	yes	complemented
250	#1910	C₂×C₆₁	1	2	yes	complemented
251	#1888	C₂×C₆₁	1	2	yes	complemented
252	#1884	C₂×C₆₁	1	2	yes	complemented
253	#1827	C₂×C₆₁	1	2	yes	complemented
254	#1795	C₂×C₆₁	1	2	yes	complemented
255	C₂×C₆₁	—	2	1	no	—
256	C₂×C₆₁	—	2	2	no	—
257	C₂×C₆₁	—	4	2	no	—
258	C₂×C₆₁	—	4	2	no	—
259	C₂×C₆₁	—	8	2	no	—
260	C₂×C₆₁	—	8	1	no	—
261	C₂×C₆₁	#2308	1	1	yes	characteristic
262	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	1	yes	characteristic
263	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	1	yes	characteristic
264	#568	C₂²×C₆₁	1	2	yes	complemented
265	#548	—	2	2	no	—
266	#546	—	2	2	no	—
267	#546	—	2	4	no	—
268	#536	C₄×C₆₁	1	2	yes	complemented
269	#536	C₂²×C₆₁	1	1	yes	characteristic
270	#535	C₄×C₆₁	1	2	yes	complemented
271	#535	C₂²×C₆₁	1	1	yes	characteristic
272	#532	C₄×C₆₁	1	2	yes	complemented
273	#532	C₂²×C₆₁	1	1	yes	characteristic
274	C₂×#124	C₄×C₆₁	1	2	yes	complemented
275	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
276	#519	C₂²×C₆₁	1	2	yes	complemented
277	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
278	#421	C₂²×C₆₁	1	4	yes	—
279	#418	C₂²×C₆₁	1	4	yes	—
280	#413	—	2	2	no	—
281	#413	C₂²×C₆₁	1	2	yes	—
282	C₂×#101	—	2	2	no	—
283	C₂×#101	C₂²×C₆₁	1	2	yes	complemented
284	#410	—	2	4	no	—
285	#410	C₂²×C₆₁	1	2	yes	—
286	#410	C₂²×C₆₁	1	2	yes	complemented
287	#339	C₂²×C₆₁	1	4	yes	complemented
288	H(3,ℤ/4)	C₂²×C₆₁	1	4	yes	complemented
289	C₆₁	#21785	1	1	yes	characteristic, direct product factor, Sylow
290	2₋¹⁺⁴	—	4	4	no	—
291	H(5,𝔽₂)	—	4	4	no	—
292	C₂×#41	—	2	1	no	—
293	C₂×#41	C₂×C₄×C₆₁	1	2	yes	—
294	C₂×#41	C₂×C₄×C₆₁	1	2	yes	—
295	C₂×#41	D₄×C₆₁	1	2	yes	—
296	C₂×#41	D₄×C₆₁	1	4	yes	—
297	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
298	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
299	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
300	C₂²×Q₈	C₂×C₄×C₆₁	1	2	yes	—
301	C₂²×Q₈	D₄×C₆₁	1	2	yes	—
302	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	—	2	1	no	—
305	C₂²×D₄	C₂×C₄×C₆₁	1	2	yes	—
306	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
307	#131	—	4	4	no	—
308	C₂×M₁₆	—	2	4	no	—
309	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
310	C₄⋊Q₈	C₂×C₄×C₆₁	1	2	yes	—
311	C₄⋊Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
312	#127	C₂×C₄×C₆₁	1	2	yes	—
313	#127	C₂×C₄×C₆₁	1	1	yes	characteristic
314	#124	—	2	4	no	—
315	#124	—	2	2	no	—
316	#124	C₂×C₄×C₆₁	1	1	yes	characteristic
317	#124	C₂×C₄×C₆₁	1	2	yes	—
318	#124	C₂×C₄×C₆₁	1	2	yes	—
319	#124	C₂×C₄×C₆₁	1	2	yes	—
320	#124	C₂×C₄×C₆₁	1	2	yes	—
321	#124	C₂×C₄×C₆₁	1	1	yes	characteristic
322	#123	—	2	4	no	—
323	#123	—	2	2	no	—
324	C₂²⋊Q₈	—	2	4	no	—
325	C₂²⋊Q₈	—	2	2	no	—
326	#121	—	2	4	no	—
327	#121	—	2	2	no	—
328	#121	—	2	4	no	—
329	#121	—	2	2	no	—
330	#120	—	2	4	no	—
331	#120	—	2	2	no	—
332	C₄×Q₈	—	2	1	no	—
333	C₄×Q₈	—	4	4	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	4	no	—
337	C₄×D₄	—	2	2	no	—
338	#117	—	2	4	no	—
339	#117	C₂×C₄×C₆₁	1	2	yes	—
340	#117	C₂³×C₆₁	1	4	yes	—
341	#117	C₂³×C₆₁	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	4	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₄²	C₂×C₄×C₆₁	1	2	yes	—
345	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
346	#104	—	4	4	no	—
347	#102	—	4	4	no	—
348	#101	—	2	2	no	—
349	#101	—	2	4	no	—
350	#100	—	2	2	no	—
351	#99	—	2	4	no	—
352	#99	—	2	4	no	—
353	C₂⁴	—	2	2	no	—
354	C₂⁴	—	2	1	no	—
355	#41	—	2	4	no	—
356	#41	—	2	4	no	—
357	#41	—	2	4	no	—
358	#41	—	4	8	no	—
359	#41	—	4	4	no	—
360	#41	—	4	4	no	—
361	#41	—	4	4	no	—
362	#41	—	4	4	no	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	4	4	no	—
365	C₂×Q₈	—	4	4	no	—
366	C₂×Q₈	C₂²⋊C₄×C₆₁	1	4	yes	—
367	C₂×Q₈	C₂²×C₄×C₆₁	1	1	yes	characteristic
368	C₂×Q₈	C₂²×C₄×C₆₁	1	1	yes	characteristic
369	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
370	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
371	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	—	4	8	no	—
381	C₂×D₄	—	4	4	no	—
382	C₂×D₄	C₂²⋊C₄×C₆₁	1	4	yes	—
383	C₂×D₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
384	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
385	C₂×D₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
386	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
387	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
388	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
394	C₂²×C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
395	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
398	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
399	M₁₆	—	2	4	no	—
400	M₁₆	—	2	4	no	—
401	M₁₆	—	4	4	no	—
402	C₂×C₈	—	2	4	no	—
403	C₂×C₈	—	4	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	4	4	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	4	no	—
422	C₄²	—	4	4	no	—
423	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
424	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
425	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
426	C₂³	—	2	2	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	8	2	no	—
431	C₂³	—	8	4	no	—
432	C₂³	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
433	C₂³	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
434	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
435	Q₈	—	2	4	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	2	4	no	—
438	Q₈	—	2	2	no	—
439	Q₈	—	2	2	no	—
440	Q₈	—	4	4	no	—
441	D₄	—	2	4	no	—
442	D₄	—	2	4	no	—
443	D₄	—	2	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	4	no	—
446	D₄	—	2	2	no	—
447	D₄	—	4	4	no	—
448	D₄	—	4	4	no	—
449	D₄	—	4	4	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	2	no	—
452	D₄	—	8	4	no	—
453	D₄	—	8	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	8	1	no	—
467	C₂×C₄	—	8	2	no	—
468	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
469	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
470	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
471	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
472	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
473	C₂×C₄	H(5,𝔽₂)×C₆₁	1	4	yes	—
474	C₈	—	4	4	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	16	2	no	—
485	C₂²	—	16	4	no	—
486	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
487	C₂²	C₆₁×#534	1	2	yes	—
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	2	4	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	8	4	no	—
496	C₄	C₆₁×#518	1	2	yes	—
497	C₄	C₆₁×#534	1	2	yes	—
498	C₂	—	2	1	no	—
499	C₂	—	2	2	no	—
500	C₂	—	4	2	no	—
501	C₂	—	4	2	no	—
502	C₂	—	8	2	no	—
503	C₂	—	8	1	no	—
504	C₂	C₆₁×#2308	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₆₁	#2308
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#3500	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₁ ◁ C₂²×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2889	C₂	semidirect
3. C₆₁×#2884	C₂	semidirect
4. C₆₁×#1912	C₂	semidirect
5. C₆₁×#1910	C₂	semidirect
6. C₆₁×#1888	C₂	semidirect
7. C₆₁×#1884	C₂	semidirect
8. C₆₁×#1827	C₂	semidirect
9. C₆₁×#1795	C₂	semidirect
12. C₆₁×#568	C₂²	semidirect
16. C₆₁×#536	C₄	semidirect
18. C₆₁×#535	C₄	semidirect
20. C₆₁×#532	C₄	semidirect
22. C₂×#124×C₆₁	C₄	semidirect
24. C₆₁×#519	C₂²	semidirect
31. C₂×#101×C₆₁	C₂²	semidirect
34. C₆₁×#410	C₂²	semidirect
35. C₆₁×#339	C₂²	semidirect
36. C₆₁×H(3,ℤ/4)	C₂²	semidirect
222. #21785	C₆₁	direct (N × H)
247. #2889	C₂×C₆₁	semidirect
248. #2884	C₂×C₆₁	semidirect
249. #1912	C₂×C₆₁	semidirect
250. #1910	C₂×C₆₁	semidirect
251. #1888	C₂×C₆₁	semidirect
252. #1884	C₂×C₆₁	semidirect
253. #1827	C₂×C₆₁	semidirect
254. #1795	C₂×C₆₁	semidirect
264. #568	C₂²×C₆₁	semidirect
268. #536	C₄×C₆₁	semidirect
270. #535	C₄×C₆₁	semidirect
272. #532	C₄×C₆₁	semidirect
274. C₂×#124	C₄×C₆₁	semidirect
276. #519	C₂²×C₆₁	semidirect
283. C₂×#101	C₂²×C₆₁	semidirect
286. #410	C₂²×C₆₁	semidirect
287. #339	C₂²×C₆₁	semidirect
288. H(3,ℤ/4)	C₂²×C₆₁	semidirect
289. C₆₁	#21785	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#3500	2
C₆₁×#2889	2
C₆₁×#2884	2
C₆₁×#1912	2
C₆₁×#1910	2
C₆₁×#1888	2
C₆₁×#1884	2
C₆₁×#1827	2
C₆₁×#1795	2
#21785	61

Subgroups — C61×#21785 #29525218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21785 #29525218