Subgroups — C₆₁×#61807 #29565240

Order 15616.

1788 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3354	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3346	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3334	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3330	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3309	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3303	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3198	C₂	1	4	yes	maximal, complemented
12	C₆₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3098	C₂	1	4	yes	maximal, complemented
15	C₆₁×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#562	—	2	2	no	—
17	C₆₁×#559	—	2	2	no	—
18	C₆₁×#556	—	2	1	no	—
19	C₆₁×#555	C₂²	1	2	yes	—
20	C₆₁×#554	—	2	1	no	—
21	C₆₁×#554	C₂²	1	2	yes	complemented
22	C₆₁×#553	C₂²	1	4	yes	—
23	C₆₁×#550	—	2	1	no	—
24	C₆₁×#550	—	2	1	no	—
25	C₆₁×#550	C₂²	1	2	yes	complemented
26	C₆₁×#547	C₂²	1	2	yes	—
27	C₆₁×#547	C₂²	1	2	yes	complemented
28	C₆₁×#547	C₂²	1	2	yes	complemented
29	C₆₁×#540	—	2	2	no	—
30	C₆₁×#538	—	2	2	no	—
31	C₆₁×#537	—	2	2	no	—
32	C₆₁×#537	C₂²	1	4	yes	—
33	C₆₁×#535	C₂²	1	2	yes	—
34	C₆₁×#533	C₂²	1	1	yes	characteristic
35	C₆₁×#533	C₂²	1	1	yes	characteristic
36	C₆₁×#532	C₂²	1	1	yes	characteristic
37	C₆₁×#532	C₂²	1	1	yes	characteristic
38	C₆₁×#525	—	2	2	no	—
39	C₆₁×#520	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#501	C₂²	1	2	yes	complemented
42	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
43	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
44	C₆₁×#490	C₂²	1	2	yes	complemented
45	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
46	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
47	C₆₁×#485	C₂²	1	4	yes	—
48	C₆₁×#485	C₂²	1	4	yes	complemented
49	C₆₁×#484	C₂²	1	2	yes	—
50	C₆₁×#484	C₂²	1	4	yes	complemented
51	C₆₁×#482	C₂²	1	4	yes	—
52	C₆₁×#482	C₂²	1	4	yes	complemented
53	C₆₁×#481	C₂²	1	4	yes	—
54	C₆₁×#480	C₂²	1	4	yes	—
55	C₆₁×#480	C₂²	1	2	yes	—
56	C₆₁×#480	C₂²	1	4	yes	complemented
57	C₆₁×#479	C₂²	1	4	yes	complemented
58	C₆₁×#476	C₂²	1	2	yes	complemented
59	C₆₁×#474	C₂²	1	2	yes	—
60	C₆₁×#474	C₂²	1	2	yes	—
61	C₆₁×#474	C₂²	1	2	yes	complemented
62	C₆₁×#469	C₂²	1	4	yes	—
63	C₆₁×#468	C₂²	1	4	yes	—
64	C₆₁×#466	C₂²	1	4	yes	—
65	C₆₁×#465	C₂²	1	4	yes	—
66	C₆₁×#461	C₂²	1	2	yes	—
67	C₆₁×#459	C₂²	1	2	yes	—
68	C₆₁×#450	C₂²	1	2	yes	—
69	C₆₁×#449	C₂²	1	4	yes	—
70	C₆₁×#449	C₂²	1	4	yes	—
71	C₆₁×#447	C₂²	1	2	yes	—
72	C₆₁×#440	C₂²	1	4	yes	—
73	C₄×D₈×C₆₁	C₂²	1	2	yes	—
74	C₄×D₈×C₆₁	C₂²	1	2	yes	—
75	C₆₁×#436	C₂²	1	2	yes	complemented
76	C₆₁×#435	C₂²	1	4	yes	complemented
77	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
78	C₆₁×#432	C₂²	1	1	yes	characteristic
79	C₆₁×#431	C₂²	1	1	yes	characteristic
80	C₆₁×#428	C₂²	1	4	yes	complemented
81	C₂×#107×C₆₁	C₂²	1	4	yes	complemented
82	C₆₁×#417	C₂²	1	4	yes	complemented
83	C₆₁×#416	C₂²	1	4	yes	complemented
84	C₆₁×#408	C₂²	1	4	yes	—
85	C₂×#41×C₆₁	—	2	2	no	—
86	C₂×#41×C₆₁	—	2	2	no	—
87	C₂×#41×C₆₁	—	2	1	no	—
88	C₂×#41×C₆₁	C₂³	1	4	yes	—
89	C₂×#41×C₆₁	C₂³	1	2	yes	—
90	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₆₁	—	2	1	no	—
92	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
93	C₂×D₈×C₆₁	C₂³	1	2	yes	—
94	C₂×D₈×C₆₁	C₂³	1	2	yes	—
95	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
96	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
97	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
98	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
99	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
102	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
103	#127×C₆₁	—	2	2	no	—
104	#127×C₆₁	—	2	2	no	—
105	#127×C₆₁	D₄	1	1	yes	characteristic
106	#127×C₆₁	C₂³	1	1	yes	characteristic
107	#126×C₆₁	—	2	4	no	—
108	#125×C₆₁	—	2	2	no	—
109	#125×C₆₁	—	2	1	no	—
110	#125×C₆₁	C₂³	1	2	yes	—
111	#124×C₆₁	—	2	2	no	—
112	#124×C₆₁	—	2	4	no	—
113	#124×C₆₁	—	2	1	no	—
114	#124×C₆₁	D₄	1	2	yes	—
115	#123×C₆₁	—	2	4	no	—
116	#123×C₆₁	—	2	4	no	—
117	#123×C₆₁	—	2	4	no	—
118	#123×C₆₁	—	2	4	no	—
119	C₂²⋊Q₈×C₆₁	—	2	4	no	—
120	C₂²⋊Q₈×C₆₁	—	2	1	no	—
121	C₂²⋊Q₈×C₆₁	—	2	1	no	—
122	C₂²⋊Q₈×C₆₁	—	2	1	no	—
123	C₂²⋊Q₈×C₆₁	—	2	2	no	—
124	C₂²⋊Q₈×C₆₁	—	2	2	no	—
125	C₂²⋊Q₈×C₆₁	—	2	4	no	—
126	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
127	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
128	#121×C₆₁	—	2	4	no	—
129	#121×C₆₁	—	2	4	no	—
130	#121×C₆₁	—	2	2	no	—
131	#121×C₆₁	—	2	4	no	—
132	#121×C₆₁	—	2	4	no	—
133	#121×C₆₁	—	2	2	no	—
134	#121×C₆₁	—	2	1	no	—
135	#121×C₆₁	—	2	4	no	—
136	#121×C₆₁	D₄	1	2	yes	—
137	#121×C₆₁	D₄	1	2	yes	—
138	#121×C₆₁	C₂³	1	2	yes	—
139	#121×C₆₁	C₂³	1	4	yes	—
140	#121×C₆₁	C₂³	1	4	yes	—
141	#121×C₆₁	C₂³	1	4	yes	—
142	#120×C₆₁	—	2	4	no	—
143	C₄×Q₈×C₆₁	—	2	2	no	—
144	C₄×Q₈×C₆₁	—	2	1	no	—
145	C₄×Q₈×C₆₁	—	2	1	no	—
146	C₄×Q₈×C₆₁	—	2	1	no	—
147	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
148	C₄×D₄×C₆₁	—	2	4	no	—
149	C₄×D₄×C₆₁	—	2	2	no	—
150	C₄×D₄×C₆₁	—	2	2	no	—
151	C₄×D₄×C₆₁	—	2	2	no	—
152	C₄×D₄×C₆₁	—	2	4	no	—
153	C₄×D₄×C₆₁	—	2	1	no	—
154	C₄×D₄×C₆₁	—	2	1	no	—
155	C₄×D₄×C₆₁	—	2	1	no	—
156	C₄×D₄×C₆₁	C₂³	1	2	yes	—
157	C₄×D₄×C₆₁	C₂³	1	2	yes	—
158	C₄×D₄×C₆₁	C₂³	1	2	yes	—
159	C₄×D₄×C₆₁	C₂³	1	2	yes	—
160	C₄×D₄×C₆₁	C₂³	1	2	yes	—
161	#117×C₆₁	—	2	1	no	—
162	#117×C₆₁	—	2	2	no	—
163	#117×C₆₁	C₂³	1	2	yes	—
164	#117×C₆₁	C₂³	1	4	yes	—
165	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
166	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
167	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
168	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
170	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
171	#107×C₆₁	C₂³	1	2	yes	—
172	#107×C₆₁	C₂³	1	4	yes	—
173	#107×C₆₁	C₂³	1	4	yes	—
174	#107×C₆₁	C₂³	1	4	yes	—
175	#107×C₆₁	C₂³	1	2	yes	—
176	#106×C₆₁	C₂³	1	4	yes	—
177	#106×C₆₁	C₂³	1	4	yes	—
178	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
179	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
180	#103×C₆₁	C₂³	1	4	yes	—
181	#103×C₆₁	C₂³	1	4	yes	—
182	#103×C₆₁	C₂³	1	4	yes	—
183	#102×C₆₁	C₂³	1	2	yes	—
184	#102×C₆₁	C₂³	1	4	yes	—
185	#102×C₆₁	C₂³	1	2	yes	—
186	#102×C₆₁	C₂³	1	4	yes	—
187	#102×C₆₁	C₂³	1	2	yes	—
188	#102×C₆₁	C₂³	1	2	yes	—
189	#102×C₆₁	C₂³	1	4	yes	—
190	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
192	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
194	#97×C₆₁	C₂³	1	2	yes	—
195	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
197	C₂⁴×C₆₁	—	2	1	no	—
198	#41×C₆₁	—	4	4	no	—
199	#41×C₆₁	—	4	4	no	—
200	#41×C₆₁	—	4	4	no	—
201	#41×C₆₁	—	8	2	no	—
202	#41×C₆₁	—	8	4	no	—
203	#41×C₆₁	—	8	4	no	—
204	C₂×Q₈×C₆₁	—	2	1	no	—
205	C₂×Q₈×C₆₁	—	2	1	no	—
206	C₂×Q₈×C₆₁	—	2	1	no	—
207	C₂×Q₈×C₆₁	—	2	1	no	—
208	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
210	C₂×D₄×C₆₁	—	2	4	no	—
211	C₂×D₄×C₆₁	—	2	4	no	—
212	C₂×D₄×C₆₁	—	2	2	no	—
213	C₂×D₄×C₆₁	—	2	4	no	—
214	C₂×D₄×C₆₁	—	2	4	no	—
215	C₂×D₄×C₆₁	—	2	1	no	—
216	C₂×D₄×C₆₁	—	2	1	no	—
217	C₂×D₄×C₆₁	—	2	1	no	—
218	C₂×D₄×C₆₁	—	4	2	no	—
219	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
222	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
223	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
224	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₆₁	—	2	1	no	—
226	C₂²×C₄×C₆₁	—	2	4	no	—
227	C₂²×C₄×C₆₁	—	2	4	no	—
228	C₂²×C₄×C₆₁	—	2	2	no	—
229	C₂²×C₄×C₆₁	—	2	2	no	—
230	C₂²×C₄×C₆₁	—	2	4	no	—
231	C₂²×C₄×C₆₁	—	2	2	no	—
232	C₂²×C₄×C₆₁	—	8	2	no	—
233	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
237	SD₁₆×C₆₁	—	4	4	no	—
238	D₈×C₆₁	—	4	2	no	—
239	D₈×C₆₁	—	4	2	no	—
240	M₁₆×C₆₁	—	4	4	no	—
241	C₂×C₈×C₆₁	—	4	4	no	—
242	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
243	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
244	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
245	C₄⋊C₄×C₆₁	—	2	1	no	—
246	C₄⋊C₄×C₆₁	—	2	4	no	—
247	C₄⋊C₄×C₆₁	—	2	1	no	—
248	C₄⋊C₄×C₆₁	—	2	4	no	—
249	C₄⋊C₄×C₆₁	—	2	4	no	—
250	C₄⋊C₄×C₆₁	—	2	1	no	—
251	C₄⋊C₄×C₆₁	—	2	1	no	—
252	C₄⋊C₄×C₆₁	—	2	1	no	—
253	C₄⋊C₄×C₆₁	—	2	1	no	—
254	C₄⋊C₄×C₆₁	—	2	2	no	—
255	C₄⋊C₄×C₆₁	—	2	2	no	—
256	C₄⋊C₄×C₆₁	—	2	2	no	—
257	C₄⋊C₄×C₆₁	—	2	1	no	—
258	C₄⋊C₄×C₆₁	—	2	2	no	—
259	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
266	C₂²⋊C₄×C₆₁	—	2	2	no	—
267	C₂²⋊C₄×C₆₁	—	2	2	no	—
268	C₂²⋊C₄×C₆₁	—	2	4	no	—
269	C₂²⋊C₄×C₆₁	—	2	4	no	—
270	C₂²⋊C₄×C₆₁	—	2	2	no	—
271	C₂²⋊C₄×C₆₁	—	2	2	no	—
272	C₂²⋊C₄×C₆₁	—	2	4	no	—
273	C₂²⋊C₄×C₆₁	—	2	4	no	—
274	C₂²⋊C₄×C₆₁	—	2	4	no	—
275	C₂²⋊C₄×C₆₁	—	2	2	no	—
276	C₂²⋊C₄×C₆₁	—	2	2	no	—
277	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
278	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
279	C₄²×C₆₁	—	2	4	no	—
280	C₄²×C₆₁	—	2	2	no	—
281	C₄²×C₆₁	—	2	2	no	—
282	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
285	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
286	C₂³×C₆₁	—	2	2	no	—
287	C₂³×C₆₁	—	2	2	no	—
288	C₂³×C₆₁	—	4	2	no	—
289	C₂³×C₆₁	—	8	1	no	—
290	C₂³×C₆₁	—	8	1	no	—
291	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
292	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
293	Q₈×C₆₁	—	2	4	no	—
294	Q₈×C₆₁	—	4	2	no	—
295	Q₈×C₆₁	—	4	2	no	—
296	Q₈×C₆₁	—	4	2	no	—
297	Q₈×C₆₁	—	8	1	no	—
298	Q₈×C₆₁	—	8	1	no	—
299	D₄×C₆₁	—	2	4	no	—
300	D₄×C₆₁	—	2	2	no	—
301	D₄×C₆₁	—	2	2	no	—
302	D₄×C₆₁	—	2	2	no	—
303	D₄×C₆₁	—	2	2	no	—
304	D₄×C₆₁	—	4	2	no	—
305	D₄×C₆₁	—	4	4	no	—
306	D₄×C₆₁	—	4	2	no	—
307	D₄×C₆₁	—	4	2	no	—
308	D₄×C₆₁	—	4	2	no	—
309	D₄×C₆₁	—	8	1	no	—
310	D₄×C₆₁	—	8	4	no	—
311	D₄×C₆₁	—	8	4	no	—
312	D₄×C₆₁	—	8	2	no	—
313	D₄×C₆₁	—	8	4	no	—
314	D₄×C₆₁	—	8	4	no	—
315	C₂×C₄×C₆₁	—	2	2	no	—
316	C₂×C₄×C₆₁	—	2	4	no	—
317	C₂×C₄×C₆₁	—	2	4	no	—
318	C₂×C₄×C₆₁	—	2	2	no	—
319	C₂×C₄×C₆₁	—	2	2	no	—
320	C₂×C₄×C₆₁	—	2	2	no	—
321	C₂×C₄×C₆₁	—	2	2	no	—
322	C₂×C₄×C₆₁	—	2	2	no	—
323	C₂×C₄×C₆₁	—	2	2	no	—
324	C₂×C₄×C₆₁	—	2	2	no	—
325	C₂×C₄×C₆₁	—	4	1	no	—
326	C₂×C₄×C₆₁	—	4	4	no	—
327	C₂×C₄×C₆₁	—	4	4	no	—
328	C₂×C₄×C₆₁	—	8	2	no	—
329	C₂×C₄×C₆₁	—	8	4	no	—
330	C₂×C₄×C₆₁	—	8	1	no	—
331	C₂×C₄×C₆₁	—	8	4	no	—
332	C₂×C₄×C₆₁	—	8	4	no	—
333	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
336	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
340	C₈×C₆₁	—	2	2	no	—
341	C₈×C₆₁	—	2	4	no	—
342	C₈×C₆₁	—	2	2	no	—
343	#61807	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂²×C₆₁	—	2	1	no	—
345	C₂²×C₆₁	—	2	4	no	—
346	C₂²×C₆₁	—	2	1	no	—
347	C₂²×C₆₁	—	2	4	no	—
348	C₂²×C₆₁	—	2	1	no	—
349	C₂²×C₆₁	—	2	4	no	—
350	C₂²×C₆₁	—	4	2	no	—
351	C₂²×C₆₁	—	4	2	no	—
352	C₂²×C₆₁	—	4	2	no	—
353	C₂²×C₆₁	—	4	2	no	—
354	C₂²×C₆₁	—	4	2	no	—
355	C₂²×C₆₁	—	4	2	no	—
356	C₂²×C₆₁	—	8	4	no	—
357	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
358	C₄×C₆₁	—	2	1	no	—
359	C₄×C₆₁	—	2	1	no	—
360	C₄×C₆₁	—	2	4	no	—
361	C₄×C₆₁	—	2	1	no	—
362	C₄×C₆₁	—	2	1	no	—
363	C₄×C₆₁	—	4	2	no	—
364	C₄×C₆₁	—	4	2	no	—
365	C₄×C₆₁	—	4	2	no	—
366	C₄×C₆₁	—	4	2	no	—
367	C₄×C₆₁	—	4	2	no	—
368	C₄×C₆₁	—	4	2	no	—
369	C₄×C₆₁	#576	1	2	yes	—
370	C₄×C₆₁	#585	1	2	yes	—
371	#3548	C₂×C₆₁	1	1	yes	characteristic, complemented
372	#3506	C₂×C₆₁	1	1	yes	characteristic, complemented
373	#3354	C₂×C₆₁	1	2	yes	complemented
374	#3346	C₂×C₆₁	1	4	yes	complemented
375	#3334	C₂×C₆₁	1	2	yes	complemented
376	#3330	C₂×C₆₁	1	2	yes	complemented
377	#3309	C₂×C₆₁	1	4	yes	complemented
378	#3303	C₂×C₆₁	1	2	yes	complemented
379	#3235	C₂×C₆₁	1	1	yes	characteristic, complemented
380	#3231	C₂×C₆₁	1	1	yes	characteristic, complemented
381	#3198	C₂×C₆₁	1	4	yes	complemented
382	#3110	C₂×C₆₁	1	1	yes	characteristic, complemented
383	#3100	C₂×C₆₁	1	1	yes	characteristic, complemented
384	#3098	C₂×C₆₁	1	4	yes	complemented
385	#2981	C₂×C₆₁	1	1	yes	characteristic, complemented
386	C₂×C₆₁	—	4	4	no	—
387	C₂×C₆₁	—	4	1	no	—
388	C₂×C₆₁	—	8	2	no	—
389	C₂×C₆₁	—	8	2	no	—
390	C₂×C₆₁	#3485	1	1	yes	characteristic
391	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
392	C₂×C₆₁	#3586	1	1	yes	characteristic
393	#562	—	2	2	no	—
394	#559	—	2	2	no	—
395	#556	—	2	1	no	—
396	#555	C₂²×C₆₁	1	2	yes	—
397	#554	—	2	1	no	—
398	#554	C₂²×C₆₁	1	2	yes	complemented
399	#553	C₂²×C₆₁	1	4	yes	—
400	#550	—	2	1	no	—
401	#550	—	2	1	no	—
402	#550	C₂²×C₆₁	1	2	yes	complemented
403	#547	C₂²×C₆₁	1	2	yes	—
404	#547	C₂²×C₆₁	1	2	yes	complemented
405	#547	C₂²×C₆₁	1	2	yes	complemented
406	#540	—	2	2	no	—
407	#538	—	2	2	no	—
408	#537	—	2	2	no	—
409	#537	C₂²×C₆₁	1	4	yes	—
410	#535	C₂²×C₆₁	1	2	yes	—
411	#533	C₂²×C₆₁	1	1	yes	characteristic
412	#533	C₂²×C₆₁	1	1	yes	characteristic
413	#532	C₂²×C₆₁	1	1	yes	characteristic
414	#532	C₂²×C₆₁	1	1	yes	characteristic
415	#525	—	2	2	no	—
416	#520	C₂²×C₆₁	1	2	yes	—
417	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
418	#501	C₂²×C₆₁	1	2	yes	complemented
419	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
420	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
421	#490	C₂²×C₆₁	1	2	yes	complemented
422	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
423	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
424	#485	C₂²×C₆₁	1	4	yes	—
425	#485	C₂²×C₆₁	1	4	yes	complemented
426	#484	C₂²×C₆₁	1	2	yes	—
427	#484	C₂²×C₆₁	1	4	yes	complemented
428	#482	C₂²×C₆₁	1	4	yes	—
429	#482	C₂²×C₆₁	1	4	yes	complemented
430	#481	C₂²×C₆₁	1	4	yes	—
431	#480	C₂²×C₆₁	1	4	yes	—
432	#480	C₂²×C₆₁	1	2	yes	—
433	#480	C₂²×C₆₁	1	4	yes	complemented
434	#479	C₂²×C₆₁	1	4	yes	complemented
435	#476	C₂²×C₆₁	1	2	yes	complemented
436	#474	C₂²×C₆₁	1	2	yes	—
437	#474	C₂²×C₆₁	1	2	yes	—
438	#474	C₂²×C₆₁	1	2	yes	complemented
439	#469	C₂²×C₆₁	1	4	yes	—
440	#468	C₂²×C₆₁	1	4	yes	—
441	#466	C₂²×C₆₁	1	4	yes	—
442	#465	C₂²×C₆₁	1	4	yes	—
443	#461	C₂²×C₆₁	1	2	yes	—
444	#459	C₂²×C₆₁	1	2	yes	—
445	#450	C₂²×C₆₁	1	2	yes	—
446	#449	C₂²×C₆₁	1	4	yes	—
447	#449	C₂²×C₆₁	1	4	yes	—
448	#447	C₂²×C₆₁	1	2	yes	—
449	#440	C₂²×C₆₁	1	4	yes	—
450	C₄×D₈	C₂²×C₆₁	1	2	yes	—
451	C₄×D₈	C₂²×C₆₁	1	2	yes	—
452	#436	C₂²×C₆₁	1	2	yes	complemented
453	#435	C₂²×C₆₁	1	4	yes	complemented
454	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
455	#432	C₂²×C₆₁	1	1	yes	characteristic
456	#431	C₂²×C₆₁	1	1	yes	characteristic
457	#428	C₂²×C₆₁	1	4	yes	complemented
458	C₂×#107	C₂²×C₆₁	1	4	yes	complemented
459	#417	C₂²×C₆₁	1	4	yes	complemented
460	#416	C₂²×C₆₁	1	4	yes	complemented
461	#408	C₂²×C₆₁	1	4	yes	—
462	C₆₁	#61807	1	1	yes	characteristic, direct product factor, Sylow
463	C₂×#41	—	2	2	no	—
464	C₂×#41	—	2	2	no	—
465	C₂×#41	—	2	1	no	—
466	C₂×#41	C₂³×C₆₁	1	4	yes	—
467	C₂×#41	C₂³×C₆₁	1	2	yes	—
468	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
469	C₂³×C₄	—	2	1	no	—
470	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
471	C₂×D₈	C₂³×C₆₁	1	2	yes	—
472	C₂×D₈	C₂³×C₆₁	1	2	yes	—
473	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
474	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
475	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
476	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
477	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
478	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
479	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
480	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
481	#127	—	2	2	no	—
482	#127	—	2	2	no	—
483	#127	D₄×C₆₁	1	1	yes	characteristic
484	#127	C₂³×C₆₁	1	1	yes	characteristic
485	#126	—	2	4	no	—
486	#125	—	2	2	no	—
487	#125	—	2	1	no	—
488	#125	C₂³×C₆₁	1	2	yes	—
489	#124	—	2	2	no	—
490	#124	—	2	4	no	—
491	#124	—	2	1	no	—
492	#124	D₄×C₆₁	1	2	yes	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	#123	—	2	4	no	—
496	#123	—	2	4	no	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	—	2	1	no	—
499	C₂²⋊Q₈	—	2	1	no	—
500	C₂²⋊Q₈	—	2	1	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	4	no	—
504	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
505	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
506	#121	—	2	2	no	—
507	#121	—	2	4	no	—
508	#121	—	2	4	no	—
509	#121	—	2	2	no	—
510	#121	—	2	4	no	—
511	#121	—	2	4	no	—
512	#121	—	2	1	no	—
513	#121	—	2	4	no	—
514	#121	D₄×C₆₁	1	2	yes	—
515	#121	D₄×C₆₁	1	2	yes	—
516	#121	C₂³×C₆₁	1	2	yes	—
517	#121	C₂³×C₆₁	1	4	yes	—
518	#121	C₂³×C₆₁	1	4	yes	—
519	#121	C₂³×C₆₁	1	4	yes	—
520	#120	—	2	4	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	—	2	1	no	—
523	C₄×Q₈	—	2	1	no	—
524	C₄×Q₈	—	2	1	no	—
525	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
526	C₄×D₄	—	2	4	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	4	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	C₂³×C₆₁	1	2	yes	—
535	C₄×D₄	C₂³×C₆₁	1	2	yes	—
536	C₄×D₄	C₂³×C₆₁	1	2	yes	—
537	C₄×D₄	C₂³×C₆₁	1	2	yes	—
538	C₄×D₄	C₂³×C₆₁	1	2	yes	—
539	#117	—	2	1	no	—
540	#117	—	2	2	no	—
541	#117	C₂³×C₆₁	1	2	yes	—
542	#117	C₂³×C₆₁	1	4	yes	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
546	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
549	#107	C₂³×C₆₁	1	2	yes	—
550	#107	C₂³×C₆₁	1	4	yes	—
551	#107	C₂³×C₆₁	1	4	yes	—
552	#107	C₂³×C₆₁	1	4	yes	—
553	#107	C₂³×C₆₁	1	2	yes	—
554	#106	C₂³×C₆₁	1	4	yes	—
555	#106	C₂³×C₆₁	1	4	yes	—
556	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
557	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
558	#103	C₂³×C₆₁	1	4	yes	—
559	#103	C₂³×C₆₁	1	4	yes	—
560	#103	C₂³×C₆₁	1	4	yes	—
561	#102	C₂³×C₆₁	1	2	yes	—
562	#102	C₂³×C₆₁	1	4	yes	—
563	#102	C₂³×C₆₁	1	2	yes	—
564	#102	C₂³×C₆₁	1	4	yes	—
565	#102	C₂³×C₆₁	1	2	yes	—
566	#102	C₂³×C₆₁	1	2	yes	—
567	#102	C₂³×C₆₁	1	4	yes	—
568	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
569	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
570	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
571	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
572	#97	C₂³×C₆₁	1	2	yes	—
573	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
574	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
575	C₂⁴	—	2	1	no	—
576	#41	—	4	4	no	—
577	#41	—	4	4	no	—
578	#41	—	4	4	no	—
579	#41	—	8	2	no	—
580	#41	—	8	4	no	—
581	#41	—	8	4	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
587	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
598	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
599	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
600	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
601	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
602	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	8	2	no	—
611	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
615	SD₁₆	—	4	4	no	—
616	D₈	—	4	2	no	—
617	D₈	—	4	2	no	—
618	M₁₆	—	4	4	no	—
619	C₂×C₈	—	4	4	no	—
620	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
621	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
622	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
638	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
642	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
656	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	2	no	—
660	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
661	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
662	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
663	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	4	2	no	—
667	C₂³	—	8	1	no	—
668	C₂³	—	8	1	no	—
669	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
670	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
671	Q₈	—	2	4	no	—
672	Q₈	—	4	2	no	—
673	Q₈	—	4	2	no	—
674	Q₈	—	4	2	no	—
675	Q₈	—	8	1	no	—
676	Q₈	—	8	1	no	—
677	D₄	—	2	4	no	—
678	D₄	—	2	2	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	2	no	—
681	D₄	—	2	2	no	—
682	D₄	—	4	2	no	—
683	D₄	—	4	4	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	2	no	—
686	D₄	—	4	2	no	—
687	D₄	—	8	1	no	—
688	D₄	—	8	4	no	—
689	D₄	—	8	4	no	—
690	D₄	—	8	2	no	—
691	D₄	—	8	4	no	—
692	D₄	—	8	4	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	—	8	2	no	—
707	C₂×C₄	—	8	4	no	—
708	C₂×C₄	—	8	1	no	—
709	C₂×C₄	—	8	4	no	—
710	C₂×C₄	—	8	4	no	—
711	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
714	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
715	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
716	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
717	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
718	C₈	—	2	2	no	—
719	C₈	—	2	4	no	—
720	C₈	—	2	2	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	8	4	no	—
734	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	4	no	—
739	C₄	—	2	1	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	C₆₁×#576	1	2	yes	—
747	C₄	C₆₁×#585	1	2	yes	—
748	C₂	—	4	1	no	—
749	C₂	—	4	4	no	—
750	C₂	—	8	2	no	—
751	C₂	—	8	2	no	—
752	C₂	C₆₁×#3485	1	1	yes	characteristic
753	C₂	C₂×C₆₁×#576	1	1	yes	characteristic
754	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 ◁ C₆₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3548	C₂	semidirect
2. C₆₁×#3506	C₂	semidirect
3. C₆₁×#3354	C₂	semidirect
4. C₆₁×#3346	C₂	semidirect
5. C₆₁×#3334	C₂	semidirect
6. C₆₁×#3330	C₂	semidirect
7. C₆₁×#3309	C₂	semidirect
8. C₆₁×#3303	C₂	semidirect
9. C₆₁×#3235	C₂	semidirect
10. C₆₁×#3231	C₂	semidirect
11. C₆₁×#3198	C₂	semidirect
12. C₆₁×#3110	C₂	semidirect
13. C₆₁×#3100	C₂	semidirect
14. C₆₁×#3098	C₂	semidirect
15. C₆₁×#2981	C₂	semidirect
21. C₆₁×#554	C₂²	semidirect
25. C₆₁×#550	C₂²	semidirect
27. C₆₁×#547	C₂²	semidirect
28. C₆₁×#547	C₂²	semidirect
41. C₆₁×#501	C₂²	semidirect
42. C₆₁×#500	C₂²	semidirect
43. C₆₁×#498	C₂²	semidirect
44. C₆₁×#490	C₂²	semidirect
45. C₆₁×#487	C₂²	semidirect
46. C₆₁×#487	C₂²	semidirect
48. C₆₁×#485	C₂²	semidirect
50. C₆₁×#484	C₂²	semidirect
52. C₆₁×#482	C₂²	semidirect
56. C₆₁×#480	C₂²	semidirect
57. C₆₁×#479	C₂²	semidirect
58. C₆₁×#476	C₂²	semidirect
61. C₆₁×#474	C₂²	semidirect
75. C₆₁×#436	C₂²	semidirect
76. C₆₁×#435	C₂²	semidirect
77. C₈×D₄×C₆₁	C₂²	semidirect
80. C₆₁×#428	C₂²	semidirect
81. C₂×#107×C₆₁	C₂²	semidirect
82. C₆₁×#417	C₂²	semidirect
83. C₆₁×#416	C₂²	semidirect
343. #61807	C₆₁	direct (N × H)
371. #3548	C₂×C₆₁	semidirect
372. #3506	C₂×C₆₁	semidirect
373. #3354	C₂×C₆₁	semidirect
374. #3346	C₂×C₆₁	semidirect
375. #3334	C₂×C₆₁	semidirect
376. #3330	C₂×C₆₁	semidirect
377. #3309	C₂×C₆₁	semidirect
378. #3303	C₂×C₆₁	semidirect
379. #3235	C₂×C₆₁	semidirect
380. #3231	C₂×C₆₁	semidirect
381. #3198	C₂×C₆₁	semidirect
382. #3110	C₂×C₆₁	semidirect
383. #3100	C₂×C₆₁	semidirect
384. #3098	C₂×C₆₁	semidirect
385. #2981	C₂×C₆₁	semidirect
398. #554	C₂²×C₆₁	semidirect
402. #550	C₂²×C₆₁	semidirect
404. #547	C₂²×C₆₁	semidirect
405. #547	C₂²×C₆₁	semidirect
418. #501	C₂²×C₆₁	semidirect
419. #500	C₂²×C₆₁	semidirect
420. #498	C₂²×C₆₁	semidirect
421. #490	C₂²×C₆₁	semidirect
422. #487	C₂²×C₆₁	semidirect
423. #487	C₂²×C₆₁	semidirect
425. #485	C₂²×C₆₁	semidirect
427. #484	C₂²×C₆₁	semidirect
429. #482	C₂²×C₆₁	semidirect
433. #480	C₂²×C₆₁	semidirect
434. #479	C₂²×C₆₁	semidirect
435. #476	C₂²×C₆₁	semidirect
438. #474	C₂²×C₆₁	semidirect
452. #436	C₂²×C₆₁	semidirect
453. #435	C₂²×C₆₁	semidirect
454. C₈×D₄	C₂²×C₆₁	semidirect
457. #428	C₂²×C₆₁	semidirect
458. C₂×#107	C₂²×C₆₁	semidirect
459. #417	C₂²×C₆₁	semidirect
460. #416	C₂²×C₆₁	semidirect
462. C₆₁	#61807	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×#3548	2
C₆₁×#3506	2
C₆₁×#3354	2
C₆₁×#3346	2
C₆₁×#3334	2
C₆₁×#3330	2
C₆₁×#3309	2
C₆₁×#3303	2
C₆₁×#3235	2
C₆₁×#3231	2
C₆₁×#3198	2
C₆₁×#3110	2
C₆₁×#3100	2
C₆₁×#3098	2
C₆₁×#2981	2
#61807	61

Subgroups — C61×#61807 #29565240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61807 #29565240