Subgroups — C₆₁×#60433 #29563866

Order 15616.

2678 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#577	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×2₋¹⁺⁴×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3046	C₂	1	3	yes	maximal, complemented
6	C₆₁×#3045	C₂	1	3	yes	maximal, complemented
7	C₆₁×#3044	C₂	1	3	yes	maximal, complemented
8	C₆₁×#3043	C₂	1	3	yes	maximal, complemented
9	C₆₁×#3040	C₂	1	3	yes	maximal, complemented
10	C₆₁×#3037	C₂	1	3	yes	maximal, complemented
11	C₆₁×#3035	C₂	1	3	yes	maximal, complemented
12	C₂×C₆₁×#464	C₂	1	3	yes	maximal, complemented
13	C₆₁×#2906	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#2898	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2897	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#578	—	2	8	no	—
20	C₆₁×#577	—	2	8	no	—
21	C₂×#137×C₆₁	C₂²	1	3	yes	—
22	C₂×#137×C₆₁	C₂²	1	3	yes	complemented
23	C₂×#137×C₆₁	C₂²	1	3	yes	complemented
24	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	3	yes	—
25	C₂×#135×C₆₁	C₂²	1	3	yes	—
26	C₂×#135×C₆₁	C₂²	1	3	yes	complemented
27	C₂²×Q₁₆×C₆₁	C₂²	1	3	yes	complemented
28	C₂²×SD₁₆×C₆₁	C₂²	1	3	yes	—
29	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#548	—	2	1	no	—
32	C₆₁×#548	—	2	1	no	—
33	C₆₁×#546	—	2	3	no	—
34	C₆₁×#546	—	2	3	no	—
35	C₆₁×#536	C₂²	1	3	yes	—
36	C₆₁×#535	C₂²	1	3	yes	—
37	C₆₁×#532	C₂²	1	3	yes	—
38	C₂×#124×C₆₁	C₂²	1	3	yes	—
39	C₆₁×#520	—	2	3	no	—
40	C₆₁×#520	C₂²	1	1	yes	characteristic
41	C₆₁×#520	C₂²	1	3	yes	complemented
42	C₆₁×#519	—	2	1	no	—
43	C₆₁×#519	C₂²	1	3	yes	complemented
44	C₄×#41×C₆₁	—	2	3	no	—
45	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
46	C₄×#41×C₆₁	C₂²	1	3	yes	complemented
47	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
48	C₂×C₄×Q₈×C₆₁	C₂²	1	3	yes	complemented
49	C₆₁×#464	C₂²	1	3	yes	complemented
50	C₆₁×#464	C₂²	1	6	yes	complemented
51	C₆₁×#464	C₂²	1	6	yes	complemented
52	C₆₁×#464	C₂²	1	6	yes	complemented
53	C₆₁×#464	C₂²	1	3	yes	complemented
54	C₆₁×#464	C₂²	1	6	yes	complemented
55	C₆₁×#463	C₂²	1	1	yes	characteristic, complemented
56	C₆₁×#463	C₂²	1	3	yes	complemented
57	C₆₁×#463	C₂²	1	6	yes	complemented
58	C₆₁×#462	C₂²	1	3	yes	complemented
59	C₆₁×#462	C₂²	1	6	yes	complemented
60	C₆₁×#461	C₂²	1	3	yes	complemented
61	C₆₁×#460	C₂²	1	3	yes	complemented
62	C₆₁×#460	C₂²	1	6	yes	complemented
63	C₆₁×#459	C₂²	1	3	yes	complemented
64	C₆₁×#424	C₂²	1	3	yes	complemented
65	C₆₁×#424	C₂²	1	3	yes	complemented
66	C₆₁×#423	C₂²	1	3	yes	complemented
67	C₂×C₄⋊C₈×C₆₁	C₂²	1	3	yes	complemented
68	C₆₁×#419	C₂²	1	3	yes	complemented
69	C₆₁×#418	C₂²	1	3	yes	—
70	C₆₁×#417	C₂²	1	3	yes	—
71	C₆₁×#417	C₂²	1	3	yes	complemented
72	C₆₁×#416	C₂²	1	3	yes	—
73	C₆₁×#416	C₂²	1	3	yes	complemented
74	C₂×#103×C₆₁	C₂²	1	3	yes	complemented
75	C₂×#102×C₆₁	C₂²	1	3	yes	—
76	2₋¹⁺⁴×C₆₁	—	2	4	no	—
77	2₋¹⁺⁴×C₆₁	—	2	4	no	—
78	2₋¹⁺⁴×C₆₁	—	2	4	no	—
79	2₋¹⁺⁴×C₆₁	D₄	1	8	yes	complemented
80	H(5,𝔽₂)×C₆₁	—	2	4	no	—
81	H(5,𝔽₂)×C₆₁	—	2	4	no	—
82	C₂×#41×C₆₁	—	2	1	no	—
83	C₂×#41×C₆₁	—	2	3	no	—
84	C₂×#41×C₆₁	—	2	3	no	—
85	C₂×#41×C₆₁	C₂³	1	3	yes	—
86	C₂×#41×C₆₁	C₂³	1	3	yes	—
87	C₂×#41×C₆₁	C₂³	1	3	yes	—
88	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₆₁	—	2	1	no	—
90	C₂²×Q₈×C₆₁	—	2	1	no	—
91	C₂²×Q₈×C₆₁	C₂³	1	3	yes	—
92	C₂²×Q₈×C₆₁	C₂³	1	3	yes	—
93	C₂²×D₄×C₆₁	—	2	3	no	—
94	C₂²×D₄×C₆₁	C₂³	1	3	yes	—
95	#137×C₆₁	—	2	12	no	—
96	#137×C₆₁	—	2	12	no	—
97	#137×C₆₁	—	2	12	no	—
98	AGL(1,ℤ/8)×C₆₁	—	2	12	no	—
99	#135×C₆₁	—	2	12	no	—
100	#135×C₆₁	—	2	12	no	—
101	C₂×Q₁₆×C₆₁	—	2	12	no	—
102	C₂×Q₁₆×C₆₁	C₂³	1	3	yes	—
103	C₂×Q₁₆×C₆₁	C₂³	1	6	yes	—
104	C₂×Q₁₆×C₆₁	C₂³	1	3	yes	—
105	C₂×SD₁₆×C₆₁	—	2	12	no	—
106	C₂×SD₁₆×C₆₁	C₂³	1	3	yes	—
107	C₂×SD₁₆×C₆₁	C₂³	1	6	yes	—
108	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
109	C₂×SD₁₆×C₆₁	C₂³	1	3	yes	—
110	C₂×SD₁₆×C₆₁	C₂³	1	3	yes	—
111	C₂×D₈×C₆₁	C₂³	1	3	yes	—
112	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
113	#131×C₆₁	—	2	4	no	—
114	#131×C₆₁	—	2	4	no	—
115	C₂×M₁₆×C₆₁	C₂³	1	3	yes	—
116	C₂×M₁₆×C₆₁	C₂³	1	3	yes	—
117	C₂²×C₈×C₆₁	C₂³	1	3	yes	—
118	C₂²×C₈×C₆₁	C₂³	1	3	yes	—
119	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
120	#127×C₆₁	C₂³	1	3	yes	—
121	#124×C₆₁	—	2	3	no	—
122	#124×C₆₁	—	2	3	no	—
123	#124×C₆₁	C₂³	1	1	yes	characteristic
124	#124×C₆₁	C₂³	1	3	yes	—
125	#124×C₆₁	C₂³	1	6	yes	—
126	#123×C₆₁	—	2	6	no	—
127	C₂²⋊Q₈×C₆₁	—	2	3	no	—
128	C₂²⋊Q₈×C₆₁	—	2	3	no	—
129	#121×C₆₁	—	2	3	no	—
130	#121×C₆₁	—	2	3	no	—
131	#121×C₆₁	—	2	3	no	—
132	#121×C₆₁	—	2	3	no	—
133	#120×C₆₁	—	2	6	no	—
134	C₄×Q₈×C₆₁	—	2	1	no	—
135	C₄×Q₈×C₆₁	—	2	3	no	—
136	C₄×Q₈×C₆₁	—	2	3	no	—
137	C₄×Q₈×C₆₁	—	2	3	no	—
138	C₄×Q₈×C₆₁	—	2	3	no	—
139	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
140	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
141	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
142	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
143	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
144	C₄×D₄×C₆₁	—	2	3	no	—
145	C₄×D₄×C₆₁	—	2	3	no	—
146	C₄×D₄×C₆₁	—	2	3	no	—
147	C₄×D₄×C₆₁	—	2	6	no	—
148	C₄×D₄×C₆₁	—	2	3	no	—
149	C₄×D₄×C₆₁	—	2	3	no	—
150	C₄×D₄×C₆₁	D₄	1	3	yes	—
151	C₄×D₄×C₆₁	D₄	1	3	yes	—
152	C₄×D₄×C₆₁	C₂³	1	3	yes	—
153	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
154	#117×C₆₁	—	2	3	no	—
155	#117×C₆₁	—	2	6	no	—
156	#117×C₆₁	—	2	3	no	—
157	#117×C₆₁	C₂³	1	3	yes	—
158	#117×C₆₁	C₂³	1	3	yes	—
159	C₂×C₄⋊C₄×C₆₁	—	2	3	no	—
160	C₂×C₄⋊C₄×C₆₁	—	2	3	no	—
161	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
162	C₂×C₂²⋊C₄×C₆₁	—	2	3	no	—
163	C₂×C₂²⋊C₄×C₆₁	—	2	3	no	—
164	C₂×C₄²×C₆₁	—	2	3	no	—
165	C₂×C₄²×C₆₁	—	2	3	no	—
166	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
167	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
168	C₄⋊C₈×C₆₁	C₂³	1	3	yes	—
169	C₄⋊C₈×C₆₁	C₂³	1	3	yes	—
170	C₄⋊C₈×C₆₁	C₂³	1	3	yes	—
171	C₄⋊C₈×C₆₁	C₂³	1	6	yes	—
172	#103×C₆₁	C₂³	1	3	yes	—
173	#103×C₆₁	C₂³	1	6	yes	—
174	#103×C₆₁	C₂³	1	1	yes	characteristic
175	#103×C₆₁	C₂³	1	3	yes	—
176	#103×C₆₁	C₂³	1	3	yes	—
177	#102×C₆₁	C₂³	1	3	yes	—
178	#102×C₆₁	C₂³	1	6	yes	—
179	#102×C₆₁	C₂³	1	3	yes	—
180	#102×C₆₁	C₂³	1	1	yes	characteristic
181	#102×C₆₁	C₂³	1	3	yes	—
182	C₂⁴×C₆₁	—	2	3	no	—
183	#41×C₆₁	—	2	24	no	—
184	#41×C₆₁	—	2	6	no	—
185	#41×C₆₁	—	2	6	no	—
186	#41×C₆₁	—	2	6	no	—
187	#41×C₆₁	—	2	6	no	—
188	#41×C₆₁	—	2	6	no	—
189	#41×C₆₁	—	4	4	no	—
190	#41×C₆₁	—	4	12	no	—
191	#41×C₆₁	C₂×D₄	1	12	yes	—
192	#41×C₆₁	C₂×D₄	1	4	yes	—
193	#41×C₆₁	#41	1	4	yes	—
194	C₂×Q₈×C₆₁	—	2	8	no	—
195	C₂×Q₈×C₆₁	—	2	3	no	—
196	C₂×Q₈×C₆₁	—	2	3	no	—
197	C₂×Q₈×C₆₁	—	2	6	no	—
198	C₂×Q₈×C₆₁	—	2	6	no	—
199	C₂×Q₈×C₆₁	—	2	6	no	—
200	C₂×Q₈×C₆₁	—	4	4	no	—
201	C₂×Q₈×C₆₁	C₂×D₄	1	12	yes	—
202	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
203	C₂×Q₈×C₆₁	C₂⁴	1	3	yes	—
204	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
205	C₂×Q₈×C₆₁	C₂⁴	1	3	yes	—
206	C₂×D₄×C₆₁	—	2	3	no	—
207	C₂×D₄×C₆₁	—	2	3	no	—
208	C₂×D₄×C₆₁	—	2	3	no	—
209	C₂×D₄×C₆₁	—	2	6	no	—
210	C₂×D₄×C₆₁	—	2	3	no	—
211	C₂×D₄×C₆₁	—	2	3	no	—
212	C₂×D₄×C₆₁	—	2	3	no	—
213	C₂×D₄×C₆₁	—	2	6	no	—
214	C₂×D₄×C₆₁	—	4	12	no	—
215	C₂×D₄×C₆₁	C₂×D₄	1	3	yes	—
216	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
217	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
218	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₆₁	—	2	3	no	—
220	C₂²×C₄×C₆₁	—	2	3	no	—
221	C₂²×C₄×C₆₁	—	2	3	no	—
222	C₂²×C₄×C₆₁	—	2	3	no	—
223	C₂²×C₄×C₆₁	—	2	1	no	—
224	C₂²×C₄×C₆₁	—	2	3	no	—
225	C₂²×C₄×C₆₁	—	2	3	no	—
226	C₂²×C₄×C₆₁	—	2	3	no	—
227	C₂²×C₄×C₆₁	C₂×D₄	1	3	yes	—
228	C₂²×C₄×C₆₁	C₂×D₄	1	3	yes	—
229	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
230	Q₁₆×C₆₁	—	2	6	no	—
231	Q₁₆×C₆₁	—	2	12	no	—
232	Q₁₆×C₆₁	—	2	6	no	—
233	SD₁₆×C₆₁	—	2	6	no	—
234	SD₁₆×C₆₁	—	2	12	no	—
235	SD₁₆×C₆₁	—	2	6	no	—
236	SD₁₆×C₆₁	—	2	2	no	—
237	SD₁₆×C₆₁	—	2	6	no	—
238	D₈×C₆₁	—	2	2	no	—
239	D₈×C₆₁	—	2	6	no	—
240	M₁₆×C₆₁	—	2	6	no	—
241	M₁₆×C₆₁	—	2	6	no	—
242	C₂×C₈×C₆₁	—	2	6	no	—
243	C₂×C₈×C₆₁	—	2	6	no	—
244	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₆₁	C₂⁴	1	3	yes	—
246	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₆₁	C₂⁴	1	3	yes	—
248	C₄⋊C₄×C₆₁	—	2	6	no	—
249	C₄⋊C₄×C₆₁	—	2	3	no	—
250	C₄⋊C₄×C₆₁	—	2	3	no	—
251	C₄⋊C₄×C₆₁	—	2	3	no	—
252	C₄⋊C₄×C₆₁	—	2	3	no	—
253	C₄⋊C₄×C₆₁	—	2	3	no	—
254	C₄⋊C₄×C₆₁	C₂×D₄	1	3	yes	—
255	C₄⋊C₄×C₆₁	C₂×D₄	1	3	yes	—
256	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
257	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
258	C₂²⋊C₄×C₆₁	—	2	3	no	—
259	C₂²⋊C₄×C₆₁	—	2	3	no	—
260	C₂²⋊C₄×C₆₁	—	2	3	no	—
261	C₂²⋊C₄×C₆₁	—	2	6	no	—
262	C₂²⋊C₄×C₆₁	—	2	6	no	—
263	C₂²⋊C₄×C₆₁	—	2	1	no	—
264	C₂²⋊C₄×C₆₁	—	2	3	no	—
265	C₂²⋊C₄×C₆₁	—	2	1	no	—
266	C₂²⋊C₄×C₆₁	—	2	1	no	—
267	C₂²⋊C₄×C₆₁	C₂×D₄	1	6	yes	—
268	C₄²×C₆₁	—	2	3	no	—
269	C₄²×C₆₁	—	2	3	no	—
270	C₄²×C₆₁	—	2	6	no	—
271	C₄²×C₆₁	—	2	3	no	—
272	C₄²×C₆₁	C₂×D₄	1	3	yes	—
273	C₄²×C₆₁	C₂×D₄	1	3	yes	—
274	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
275	C₄²×C₆₁	C₂⁴	1	3	yes	—
276	C₂³×C₆₁	—	2	1	no	—
277	C₂³×C₆₁	—	2	3	no	—
278	C₂³×C₆₁	—	2	1	no	—
279	C₂³×C₆₁	—	4	6	no	—
280	C₂³×C₆₁	—	8	3	no	—
281	C₂³×C₆₁	—	8	3	no	—
282	C₂³×C₆₁	C₂²×D₄	1	3	yes	—
283	Q₈×C₆₁	—	2	12	no	—
284	Q₈×C₆₁	—	2	3	no	—
285	Q₈×C₆₁	—	2	3	no	—
286	Q₈×C₆₁	—	2	1	no	—
287	Q₈×C₆₁	—	2	3	no	—
288	Q₈×C₆₁	—	2	1	no	—
289	Q₈×C₆₁	—	4	6	no	—
290	Q₈×C₆₁	#121	1	4	yes	—
291	Q₈×C₆₁	C₂²×D₄	1	6	yes	—
292	D₄×C₆₁	—	2	12	no	—
293	D₄×C₆₁	—	2	3	no	—
294	D₄×C₆₁	—	2	1	no	—
295	D₄×C₆₁	—	2	1	no	—
296	D₄×C₆₁	—	2	3	no	—
297	D₄×C₆₁	—	2	1	no	—
298	D₄×C₆₁	—	4	6	no	—
299	D₄×C₆₁	—	4	6	no	—
300	D₄×C₆₁	—	4	6	no	—
301	D₄×C₆₁	—	8	3	no	—
302	D₄×C₆₁	—	8	3	no	—
303	D₄×C₆₁	#121	1	12	yes	—
304	D₄×C₆₁	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₆₁	—	2	12	no	—
306	C₂×C₄×C₆₁	—	2	3	no	—
307	C₂×C₄×C₆₁	—	2	12	no	—
308	C₂×C₄×C₆₁	—	2	1	no	—
309	C₂×C₄×C₆₁	—	2	3	no	—
310	C₂×C₄×C₆₁	—	2	3	no	—
311	C₂×C₄×C₆₁	—	2	1	no	—
312	C₂×C₄×C₆₁	—	4	3	no	—
313	C₂×C₄×C₆₁	—	4	3	no	—
314	C₂×C₄×C₆₁	—	4	2	no	—
315	C₂×C₄×C₆₁	—	4	6	no	—
316	C₂×C₄×C₆₁	—	4	6	no	—
317	C₂×C₄×C₆₁	—	4	6	no	—
318	C₂×C₄×C₆₁	—	8	3	no	—
319	C₂×C₄×C₆₁	—	8	3	no	—
320	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
322	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
323	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
325	C₂×C₄×C₆₁	C₂²×D₄	1	6	yes	—
326	C₂×C₄×C₆₁	C₂×#41	1	6	yes	—
327	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
328	C₈×C₆₁	—	2	1	no	—
329	C₈×C₆₁	—	2	1	no	—
330	C₈×C₆₁	—	2	3	no	—
331	C₈×C₆₁	—	2	3	no	—
332	#60433	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
333	C₂²×C₆₁	—	2	3	no	—
334	C₂²×C₆₁	—	2	3	no	—
335	C₂²×C₆₁	—	2	2	no	—
336	C₂²×C₆₁	—	4	1	no	—
337	C₂²×C₆₁	—	4	1	no	—
338	C₂²×C₆₁	—	4	1	no	—
339	C₂²×C₆₁	—	4	3	no	—
340	C₂²×C₆₁	—	4	1	no	—
341	C₂²×C₆₁	—	4	3	no	—
342	C₂²×C₆₁	—	4	1	no	—
343	C₂²×C₆₁	—	4	3	no	—
344	C₂²×C₆₁	—	16	6	no	—
345	C₂²×C₆₁	C₂×#121	1	6	yes	—
346	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
347	C₄×C₆₁	—	2	1	no	—
348	C₄×C₆₁	—	2	3	no	—
349	C₄×C₆₁	—	2	1	no	—
350	C₄×C₆₁	—	2	3	no	—
351	C₄×C₆₁	—	2	6	no	—
352	C₄×C₆₁	—	4	3	no	—
353	C₄×C₆₁	—	4	1	no	—
354	C₄×C₆₁	—	4	1	no	—
355	C₄×C₆₁	—	4	3	no	—
356	C₄×C₆₁	C₂×#121	1	6	yes	—
357	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
358	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
359	C₂×#578	C₂×C₆₁	1	1	yes	characteristic, complemented
360	C₂×#577	C₂×C₆₁	1	1	yes	characteristic, complemented
361	#3500	C₂×C₆₁	1	1	yes	characteristic, complemented
362	C₄×2₋¹⁺⁴	C₂×C₆₁	1	1	yes	characteristic, complemented
363	#3046	C₂×C₆₁	1	3	yes	complemented
364	#3045	C₂×C₆₁	1	3	yes	complemented
365	#3044	C₂×C₆₁	1	3	yes	complemented
366	#3043	C₂×C₆₁	1	3	yes	complemented
367	#3040	C₂×C₆₁	1	3	yes	complemented
368	#3037	C₂×C₆₁	1	3	yes	complemented
369	#3035	C₂×C₆₁	1	3	yes	complemented
370	C₂×#464	C₂×C₆₁	1	3	yes	complemented
371	#2906	C₂×C₆₁	1	1	yes	characteristic, complemented
372	#2898	C₂×C₆₁	1	1	yes	characteristic, complemented
373	#2897	C₂×C₆₁	1	1	yes	characteristic, complemented
374	C₂×C₆₁	—	2	6	no	—
375	C₂×C₆₁	—	4	2	no	—
376	C₂×C₆₁	—	8	1	no	—
377	C₂×C₆₁	—	8	3	no	—
378	C₂×C₆₁	C₂²×#121	1	1	yes	characteristic
379	C₂×C₆₁	#3584	1	1	yes	characteristic
380	C₂×C₆₁	#3586	1	1	yes	characteristic
381	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	1	yes	characteristic
382	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	1	yes	characteristic
383	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	1	yes	characteristic
384	#578	—	2	8	no	—
385	#577	—	2	8	no	—
386	C₂×#137	C₂²×C₆₁	1	3	yes	—
387	C₂×#137	C₂²×C₆₁	1	3	yes	complemented
388	C₂×#137	C₂²×C₆₁	1	3	yes	complemented
389	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	3	yes	—
390	C₂×#135	C₂²×C₆₁	1	3	yes	—
391	C₂×#135	C₂²×C₆₁	1	3	yes	complemented
392	C₂²×Q₁₆	C₂²×C₆₁	1	3	yes	complemented
393	C₂²×SD₁₆	C₂²×C₆₁	1	3	yes	—
394	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
395	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
396	#548	—	2	1	no	—
397	#548	—	2	1	no	—
398	#546	—	2	3	no	—
399	#546	—	2	3	no	—
400	#536	C₂²×C₆₁	1	3	yes	—
401	#535	C₂²×C₆₁	1	3	yes	—
402	#532	C₂²×C₆₁	1	3	yes	—
403	C₂×#124	C₂²×C₆₁	1	3	yes	—
404	#520	—	2	3	no	—
405	#520	C₂²×C₆₁	1	1	yes	characteristic
406	#520	C₂²×C₆₁	1	3	yes	complemented
407	#519	—	2	1	no	—
408	#519	C₂²×C₆₁	1	3	yes	complemented
409	C₄×#41	—	2	3	no	—
410	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
411	C₄×#41	C₂²×C₆₁	1	3	yes	complemented
412	C₂×C₄×Q₈	—	2	1	no	—
413	C₂×C₄×Q₈	C₂²×C₆₁	1	3	yes	complemented
414	#464	C₂²×C₆₁	1	3	yes	complemented
415	#464	C₂²×C₆₁	1	6	yes	complemented
416	#464	C₂²×C₆₁	1	6	yes	complemented
417	#464	C₂²×C₆₁	1	6	yes	complemented
418	#464	C₂²×C₆₁	1	3	yes	complemented
419	#464	C₂²×C₆₁	1	6	yes	complemented
420	#463	C₂²×C₆₁	1	1	yes	characteristic, complemented
421	#463	C₂²×C₆₁	1	3	yes	complemented
422	#463	C₂²×C₆₁	1	6	yes	complemented
423	#462	C₂²×C₆₁	1	3	yes	complemented
424	#462	C₂²×C₆₁	1	6	yes	complemented
425	#461	C₂²×C₆₁	1	3	yes	complemented
426	#460	C₂²×C₆₁	1	3	yes	complemented
427	#460	C₂²×C₆₁	1	6	yes	complemented
428	#459	C₂²×C₆₁	1	3	yes	complemented
429	#424	C₂²×C₆₁	1	3	yes	complemented
430	#424	C₂²×C₆₁	1	3	yes	complemented
431	#423	C₂²×C₆₁	1	3	yes	complemented
432	C₂×C₄⋊C₈	C₂²×C₆₁	1	3	yes	complemented
433	#419	C₂²×C₆₁	1	3	yes	complemented
434	#418	C₂²×C₆₁	1	3	yes	—
435	#417	C₂²×C₆₁	1	3	yes	—
436	#417	C₂²×C₆₁	1	3	yes	complemented
437	#416	C₂²×C₆₁	1	3	yes	—
438	#416	C₂²×C₆₁	1	3	yes	complemented
439	C₂×#103	C₂²×C₆₁	1	3	yes	complemented
440	C₂×#102	C₂²×C₆₁	1	3	yes	—
441	C₆₁	#60433	1	1	yes	characteristic, direct product factor, Sylow
442	2₋¹⁺⁴	—	2	4	no	—
443	2₋¹⁺⁴	—	2	4	no	—
444	2₋¹⁺⁴	—	2	4	no	—
445	2₋¹⁺⁴	D₄×C₆₁	1	8	yes	complemented
446	H(5,𝔽₂)	—	2	4	no	—
447	H(5,𝔽₂)	—	2	4	no	—
448	C₂×#41	—	2	1	no	—
449	C₂×#41	—	2	3	no	—
450	C₂×#41	—	2	3	no	—
451	C₂×#41	C₂³×C₆₁	1	3	yes	—
452	C₂×#41	C₂³×C₆₁	1	3	yes	—
453	C₂×#41	C₂³×C₆₁	1	3	yes	—
454	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
455	C₂²×Q₈	—	2	1	no	—
456	C₂²×Q₈	—	2	1	no	—
457	C₂²×Q₈	C₂³×C₆₁	1	3	yes	—
458	C₂²×Q₈	C₂³×C₆₁	1	3	yes	—
459	C₂²×D₄	—	2	3	no	—
460	C₂²×D₄	C₂³×C₆₁	1	3	yes	—
461	#137	—	2	12	no	—
462	#137	—	2	12	no	—
463	#137	—	2	12	no	—
464	AGL(1,ℤ/8)	—	2	12	no	—
465	#135	—	2	12	no	—
466	#135	—	2	12	no	—
467	C₂×Q₁₆	—	2	12	no	—
468	C₂×Q₁₆	C₂³×C₆₁	1	3	yes	—
469	C₂×Q₁₆	C₂³×C₆₁	1	6	yes	—
470	C₂×Q₁₆	C₂³×C₆₁	1	3	yes	—
471	C₂×SD₁₆	—	2	12	no	—
472	C₂×SD₁₆	C₂³×C₆₁	1	3	yes	—
473	C₂×SD₁₆	C₂³×C₆₁	1	6	yes	—
474	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
475	C₂×SD₁₆	C₂³×C₆₁	1	3	yes	—
476	C₂×SD₁₆	C₂³×C₆₁	1	3	yes	—
477	C₂×D₈	C₂³×C₆₁	1	3	yes	—
478	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
479	#131	—	2	4	no	—
480	#131	—	2	4	no	—
481	C₂×M₁₆	C₂³×C₆₁	1	3	yes	—
482	C₂×M₁₆	C₂³×C₆₁	1	3	yes	—
483	C₂²×C₈	C₂³×C₆₁	1	3	yes	—
484	C₂²×C₈	C₂³×C₆₁	1	3	yes	—
485	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
486	#127	C₂³×C₆₁	1	3	yes	—
487	#124	—	2	3	no	—
488	#124	—	2	3	no	—
489	#124	C₂³×C₆₁	1	3	yes	—
490	#124	C₂³×C₆₁	1	6	yes	—
491	#124	C₂³×C₆₁	1	1	yes	characteristic
492	#123	—	2	6	no	—
493	C₂²⋊Q₈	—	2	3	no	—
494	C₂²⋊Q₈	—	2	3	no	—
495	#121	—	2	3	no	—
496	#121	—	2	3	no	—
497	#121	—	2	3	no	—
498	#121	—	2	3	no	—
499	#120	—	2	6	no	—
500	C₄×Q₈	—	2	1	no	—
501	C₄×Q₈	—	2	3	no	—
502	C₄×Q₈	—	2	3	no	—
503	C₄×Q₈	—	2	3	no	—
504	C₄×Q₈	—	2	3	no	—
505	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
506	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
507	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
508	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
509	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
510	C₄×D₄	—	2	3	no	—
511	C₄×D₄	—	2	3	no	—
512	C₄×D₄	—	2	3	no	—
513	C₄×D₄	—	2	6	no	—
514	C₄×D₄	—	2	3	no	—
515	C₄×D₄	—	2	3	no	—
516	C₄×D₄	D₄×C₆₁	1	3	yes	—
517	C₄×D₄	D₄×C₆₁	1	3	yes	—
518	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
519	C₄×D₄	C₂³×C₆₁	1	3	yes	—
520	#117	—	2	3	no	—
521	#117	—	2	6	no	—
522	#117	—	2	3	no	—
523	#117	C₂³×C₆₁	1	3	yes	—
524	#117	C₂³×C₆₁	1	3	yes	—
525	C₂×C₄⋊C₄	—	2	3	no	—
526	C₂×C₄⋊C₄	—	2	3	no	—
527	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
528	C₂×C₂²⋊C₄	—	2	3	no	—
529	C₂×C₂²⋊C₄	—	2	3	no	—
530	C₂×C₄²	—	2	3	no	—
531	C₂×C₄²	—	2	3	no	—
532	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
533	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
534	C₄⋊C₈	C₂³×C₆₁	1	3	yes	—
535	C₄⋊C₈	C₂³×C₆₁	1	3	yes	—
536	C₄⋊C₈	C₂³×C₆₁	1	3	yes	—
537	C₄⋊C₈	C₂³×C₆₁	1	6	yes	—
538	#103	C₂³×C₆₁	1	3	yes	—
539	#103	C₂³×C₆₁	1	6	yes	—
540	#103	C₂³×C₆₁	1	1	yes	characteristic
541	#103	C₂³×C₆₁	1	3	yes	—
542	#103	C₂³×C₆₁	1	3	yes	—
543	#102	C₂³×C₆₁	1	3	yes	—
544	#102	C₂³×C₆₁	1	6	yes	—
545	#102	C₂³×C₆₁	1	3	yes	—
546	#102	C₂³×C₆₁	1	1	yes	characteristic
547	#102	C₂³×C₆₁	1	3	yes	—
548	C₂⁴	—	2	3	no	—
549	#41	—	2	24	no	—
550	#41	—	2	6	no	—
551	#41	—	2	6	no	—
552	#41	—	2	6	no	—
553	#41	—	2	6	no	—
554	#41	—	2	6	no	—
555	#41	—	4	4	no	—
556	#41	—	4	12	no	—
557	#41	C₂×D₄×C₆₁	1	12	yes	—
558	#41	C₂×D₄×C₆₁	1	4	yes	—
559	#41	#41×C₆₁	1	4	yes	—
560	C₂×Q₈	—	2	8	no	—
561	C₂×Q₈	—	2	3	no	—
562	C₂×Q₈	—	2	3	no	—
563	C₂×Q₈	—	2	6	no	—
564	C₂×Q₈	—	2	6	no	—
565	C₂×Q₈	—	2	6	no	—
566	C₂×Q₈	—	4	4	no	—
567	C₂×Q₈	C₂×D₄×C₆₁	1	12	yes	—
568	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
569	C₂×Q₈	C₂⁴×C₆₁	1	3	yes	—
570	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
571	C₂×Q₈	C₂⁴×C₆₁	1	3	yes	—
572	C₂×D₄	—	2	3	no	—
573	C₂×D₄	—	2	3	no	—
574	C₂×D₄	—	2	3	no	—
575	C₂×D₄	—	2	6	no	—
576	C₂×D₄	—	2	3	no	—
577	C₂×D₄	—	2	3	no	—
578	C₂×D₄	—	2	3	no	—
579	C₂×D₄	—	2	6	no	—
580	C₂×D₄	—	4	12	no	—
581	C₂×D₄	C₂×D₄×C₆₁	1	3	yes	—
582	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
583	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
584	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
585	C₂²×C₄	—	2	3	no	—
586	C₂²×C₄	—	2	3	no	—
587	C₂²×C₄	—	2	3	no	—
588	C₂²×C₄	—	2	3	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	3	no	—
591	C₂²×C₄	—	2	3	no	—
592	C₂²×C₄	—	2	3	no	—
593	C₂²×C₄	C₂×D₄×C₆₁	1	3	yes	—
594	C₂²×C₄	C₂×D₄×C₆₁	1	3	yes	—
595	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
596	Q₁₆	—	2	6	no	—
597	Q₁₆	—	2	12	no	—
598	Q₁₆	—	2	6	no	—
599	SD₁₆	—	2	6	no	—
600	SD₁₆	—	2	12	no	—
601	SD₁₆	—	2	6	no	—
602	SD₁₆	—	2	2	no	—
603	SD₁₆	—	2	6	no	—
604	D₈	—	2	2	no	—
605	D₈	—	2	6	no	—
606	M₁₆	—	2	6	no	—
607	M₁₆	—	2	6	no	—
608	C₂×C₈	—	2	6	no	—
609	C₂×C₈	—	2	6	no	—
610	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
611	C₂×C₈	C₂⁴×C₆₁	1	3	yes	—
612	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
613	C₂×C₈	C₂⁴×C₆₁	1	3	yes	—
614	C₄⋊C₄	—	2	6	no	—
615	C₄⋊C₄	—	2	3	no	—
616	C₄⋊C₄	—	2	3	no	—
617	C₄⋊C₄	—	2	3	no	—
618	C₄⋊C₄	—	2	3	no	—
619	C₄⋊C₄	—	2	3	no	—
620	C₄⋊C₄	C₂×D₄×C₆₁	1	3	yes	—
621	C₄⋊C₄	C₂×D₄×C₆₁	1	3	yes	—
622	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
623	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
624	C₂²⋊C₄	—	2	3	no	—
625	C₂²⋊C₄	—	2	3	no	—
626	C₂²⋊C₄	—	2	3	no	—
627	C₂²⋊C₄	—	2	6	no	—
628	C₂²⋊C₄	—	2	6	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	3	no	—
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	C₂×D₄×C₆₁	1	6	yes	—
634	C₄²	—	2	3	no	—
635	C₄²	—	2	3	no	—
636	C₄²	—	2	6	no	—
637	C₄²	—	2	3	no	—
638	C₄²	C₂×D₄×C₆₁	1	3	yes	—
639	C₄²	C₂×D₄×C₆₁	1	3	yes	—
640	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
641	C₄²	C₂⁴×C₆₁	1	3	yes	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	3	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	4	6	no	—
646	C₂³	—	8	3	no	—
647	C₂³	—	8	3	no	—
648	C₂³	C₂²×D₄×C₆₁	1	3	yes	—
649	Q₈	—	2	3	no	—
650	Q₈	—	2	12	no	—
651	Q₈	—	2	3	no	—
652	Q₈	—	2	1	no	—
653	Q₈	—	2	3	no	—
654	Q₈	—	2	1	no	—
655	Q₈	—	4	6	no	—
656	Q₈	#121×C₆₁	1	4	yes	—
657	Q₈	C₂²×D₄×C₆₁	1	6	yes	—
658	D₄	—	2	12	no	—
659	D₄	—	2	3	no	—
660	D₄	—	2	1	no	—
661	D₄	—	2	1	no	—
662	D₄	—	2	3	no	—
663	D₄	—	2	1	no	—
664	D₄	—	4	6	no	—
665	D₄	—	4	6	no	—
666	D₄	—	4	6	no	—
667	D₄	—	8	3	no	—
668	D₄	—	8	3	no	—
669	D₄	#121×C₆₁	1	12	yes	—
670	D₄	C₂²×D₄×C₆₁	1	2	yes	—
671	C₂×C₄	—	2	3	no	—
672	C₂×C₄	—	2	12	no	—
673	C₂×C₄	—	2	12	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	3	no	—
676	C₂×C₄	—	2	3	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	4	3	no	—
679	C₂×C₄	—	4	3	no	—
680	C₂×C₄	—	4	2	no	—
681	C₂×C₄	—	4	6	no	—
682	C₂×C₄	—	4	6	no	—
683	C₂×C₄	—	4	6	no	—
684	C₂×C₄	—	8	3	no	—
685	C₂×C₄	—	8	3	no	—
686	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
687	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
688	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
689	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
690	C₂×C₄	C₂²×D₄×C₆₁	1	6	yes	—
691	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
692	C₂×C₄	C₂×#41×C₆₁	1	6	yes	—
693	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
694	C₈	—	2	1	no	—
695	C₈	—	2	1	no	—
696	C₈	—	2	3	no	—
697	C₈	—	2	3	no	—
698	C₂²	—	2	3	no	—
699	C₂²	—	2	3	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	3	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	3	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	3	no	—
709	C₂²	—	16	6	no	—
710	C₂²	C₂×#121×C₆₁	1	6	yes	—
711	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
712	C₄	—	2	1	no	—
713	C₄	—	2	3	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	3	no	—
716	C₄	—	2	6	no	—
717	C₄	—	4	3	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	3	no	—
721	C₄	C₂×#121×C₆₁	1	6	yes	—
722	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
723	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
724	C₂	—	2	6	no	—
725	C₂	—	4	2	no	—
726	C₂	—	8	3	no	—
727	C₂	—	8	1	no	—
728	C₂	C₂²×#121×C₆₁	1	1	yes	characteristic
729	C₂	C₆₁×#3584	1	1	yes	characteristic
730	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#578	C₂	semidirect
2. C₂×C₆₁×#577	C₂	semidirect
3. C₆₁×#3500	C₂	semidirect
4. C₄×2₋¹⁺⁴×C₆₁	C₂	semidirect
5. C₆₁×#3046	C₂	semidirect
6. C₆₁×#3045	C₂	semidirect
7. C₆₁×#3044	C₂	semidirect
8. C₆₁×#3043	C₂	semidirect
9. C₆₁×#3040	C₂	semidirect
10. C₆₁×#3037	C₂	semidirect
11. C₆₁×#3035	C₂	semidirect
12. C₂×C₆₁×#464	C₂	semidirect
13. C₆₁×#2906	C₂	semidirect
14. C₆₁×#2898	C₂	semidirect
15. C₆₁×#2897	C₂	semidirect
22. C₂×#137×C₆₁	C₂²	semidirect
23. C₂×#137×C₆₁	C₂²	semidirect
26. C₂×#135×C₆₁	C₂²	semidirect
27. C₂²×Q₁₆×C₆₁	C₂²	semidirect
41. C₆₁×#520	C₂²	semidirect
43. C₆₁×#519	C₂²	semidirect
46. C₄×#41×C₆₁	C₂²	semidirect
48. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
49. C₆₁×#464	C₂²	semidirect
50. C₆₁×#464	C₂²	semidirect
51. C₆₁×#464	C₂²	semidirect
52. C₆₁×#464	C₂²	semidirect
53. C₆₁×#464	C₂²	semidirect
54. C₆₁×#464	C₂²	semidirect
55. C₆₁×#463	C₂²	semidirect
56. C₆₁×#463	C₂²	semidirect
57. C₆₁×#463	C₂²	semidirect
58. C₆₁×#462	C₂²	semidirect
59. C₆₁×#462	C₂²	semidirect
60. C₆₁×#461	C₂²	semidirect
61. C₆₁×#460	C₂²	semidirect
62. C₆₁×#460	C₂²	semidirect
63. C₆₁×#459	C₂²	semidirect
64. C₆₁×#424	C₂²	semidirect
65. C₆₁×#424	C₂²	semidirect
66. C₆₁×#423	C₂²	semidirect
67. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
68. C₆₁×#419	C₂²	semidirect
71. C₆₁×#417	C₂²	semidirect
73. C₆₁×#416	C₂²	semidirect
74. C₂×#103×C₆₁	C₂²	semidirect
79. 2₋¹⁺⁴×C₆₁	D₄	semidirect
332. #60433	C₆₁	direct (N × H)
359. C₂×#578	C₂×C₆₁	semidirect
360. C₂×#577	C₂×C₆₁	semidirect
361. #3500	C₂×C₆₁	semidirect
362. C₄×2₋¹⁺⁴	C₂×C₆₁	semidirect
363. #3046	C₂×C₆₁	semidirect
364. #3045	C₂×C₆₁	semidirect
365. #3044	C₂×C₆₁	semidirect
366. #3043	C₂×C₆₁	semidirect
367. #3040	C₂×C₆₁	semidirect
368. #3037	C₂×C₆₁	semidirect
369. #3035	C₂×C₆₁	semidirect
370. C₂×#464	C₂×C₆₁	semidirect
371. #2906	C₂×C₆₁	semidirect
372. #2898	C₂×C₆₁	semidirect
373. #2897	C₂×C₆₁	semidirect
387. C₂×#137	C₂²×C₆₁	semidirect
388. C₂×#137	C₂²×C₆₁	semidirect
391. C₂×#135	C₂²×C₆₁	semidirect
392. C₂²×Q₁₆	C₂²×C₆₁	semidirect
406. #520	C₂²×C₆₁	semidirect
408. #519	C₂²×C₆₁	semidirect
411. C₄×#41	C₂²×C₆₁	semidirect
413. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
414. #464	C₂²×C₆₁	semidirect
415. #464	C₂²×C₆₁	semidirect
416. #464	C₂²×C₆₁	semidirect
417. #464	C₂²×C₆₁	semidirect
418. #464	C₂²×C₆₁	semidirect
419. #464	C₂²×C₆₁	semidirect
420. #463	C₂²×C₆₁	semidirect
421. #463	C₂²×C₆₁	semidirect
422. #463	C₂²×C₆₁	semidirect
423. #462	C₂²×C₆₁	semidirect
424. #462	C₂²×C₆₁	semidirect
425. #461	C₂²×C₆₁	semidirect
426. #460	C₂²×C₆₁	semidirect
427. #460	C₂²×C₆₁	semidirect
428. #459	C₂²×C₆₁	semidirect
429. #424	C₂²×C₆₁	semidirect
430. #424	C₂²×C₆₁	semidirect
431. #423	C₂²×C₆₁	semidirect
432. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
433. #419	C₂²×C₆₁	semidirect
436. #417	C₂²×C₆₁	semidirect
438. #416	C₂²×C₆₁	semidirect
439. C₂×#103	C₂²×C₆₁	semidirect
441. C₆₁	#60433	direct (N × H)
445. 2₋¹⁺⁴	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×#578	2
C₂×C₆₁×#577	2
C₆₁×#3500	2
C₄×2₋¹⁺⁴×C₆₁	2
C₆₁×#3046	2
C₆₁×#3045	2
C₆₁×#3044	2
C₆₁×#3043	2
C₆₁×#3040	2
C₆₁×#3037	2
C₆₁×#3035	2
C₂×C₆₁×#464	2
C₆₁×#2906	2
C₆₁×#2898	2
C₆₁×#2897	2
#60433	61

Subgroups — C61×#60433 #29563866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60433 #29563866