Subgroups — C₆₁×#61802 #29565235

Order 15616.

1860 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3549	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×#3347	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3341	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3325	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3318	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3294	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3199	C₂	1	4	yes	maximal, complemented
12	C₆₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3096	C₂	1	4	yes	maximal, complemented
15	C₆₁×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×H(3,𝔽₄)	—	2	2	no	—
17	C₆₁×#559	—	2	2	no	—
18	C₆₁×#556	—	2	1	no	—
19	C₆₁×#555	—	2	1	no	—
20	C₆₁×#555	C₂²	1	2	yes	complemented
21	C₆₁×#555	C₂²	1	2	yes	complemented
22	C₆₁×#555	C₂²	1	2	yes	complemented
23	C₆₁×#553	C₂²	1	4	yes	complemented
24	C₆₁×#550	—	2	1	no	—
25	C₆₁×#547	C₂²	1	2	yes	complemented
26	D₄²×C₆₁	—	2	1	no	—
27	D₄²×C₆₁	C₂²	1	2	yes	complemented
28	D₄²×C₆₁	C₂²	1	2	yes	complemented
29	C₆₁×#538	—	2	2	no	—
30	C₆₁×#535	—	2	2	no	—
31	C₆₁×#535	—	2	2	no	—
32	C₆₁×#535	C₂²	1	4	yes	—
33	C₆₁×#535	C₂²	1	2	yes	complemented
34	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
35	C₆₁×#532	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	complemented
40	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
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×#486	C₂²	1	1	yes	characteristic, complemented
46	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
47	C₆₁×#482	C₂²	1	4	yes	complemented
48	C₆₁×#482	C₂²	1	4	yes	complemented
49	C₆₁×#482	C₂²	1	4	yes	complemented
50	C₆₁×#482	C₂²	1	4	yes	complemented
51	C₆₁×#482	C₂²	1	4	yes	complemented
52	C₆₁×#482	C₂²	1	4	yes	complemented
53	C₆₁×#481	C₂²	1	4	yes	complemented
54	C₆₁×#481	C₂²	1	2	yes	complemented
55	C₆₁×#480	C₂²	1	4	yes	complemented
56	C₆₁×#480	C₂²	1	2	yes	complemented
57	C₆₁×#478	C₂²	1	4	yes	complemented
58	C₆₁×#476	C₂²	1	2	yes	complemented
59	C₆₁×#476	C₂²	1	2	yes	complemented
60	C₆₁×#474	C₂²	1	2	yes	complemented
61	C₆₁×#474	C₂²	1	2	yes	complemented
62	C₆₁×#469	C₂²	1	4	yes	complemented
63	C₆₁×#469	C₂²	1	4	yes	complemented
64	C₆₁×#466	C₂²	1	4	yes	complemented
65	C₆₁×#466	C₂²	1	4	yes	complemented
66	C₆₁×#459	C₂²	1	2	yes	—
67	C₆₁×#459	C₂²	1	2	yes	—
68	C₆₁×#447	C₂²	1	4	yes	complemented
69	C₆₁×#447	C₂²	1	4	yes	complemented
70	C₆₁×#447	C₂²	1	2	yes	complemented
71	C₆₁×#447	C₂²	1	2	yes	complemented
72	C₆₁×#442	C₂²	1	4	yes	complemented
73	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
74	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
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, complemented
79	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
80	C₆₁×#428	C₂²	1	4	yes	complemented
81	C₆₁×#427	C₂²	1	4	yes	complemented
82	C₆₁×#418	C₂²	1	4	yes	complemented
83	C₂×#102×C₆₁	C₂²	1	4	yes	complemented
84	C₆₁×#408	C₂²	1	4	yes	complemented
85	C₂×#41×C₆₁	—	2	2	no	—
86	C₂×#41×C₆₁	—	2	1	no	—
87	C₂×#41×C₆₁	—	2	1	no	—
88	C₂×#41×C₆₁	C₂³	1	2	yes	—
89	C₂²×D₄×C₆₁	—	2	2	no	—
90	C₂²×D₄×C₆₁	—	2	2	no	—
91	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
92	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₆₁	—	2	1	no	—
94	C₂×D₈×C₆₁	C₂³	1	2	yes	—
95	C₂×D₈×C₆₁	C₂³	1	2	yes	—
96	C₂×D₈×C₆₁	C₂³	1	4	yes	—
97	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
98	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
99	C₄⋊Q₈×C₆₁	D₄	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	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
104	#127×C₆₁	—	2	4	no	—
105	#127×C₆₁	—	2	2	no	—
106	#127×C₆₁	D₄	1	1	yes	characteristic
107	#127×C₆₁	C₂³	1	1	yes	characteristic
108	#127×C₆₁	C₂³	1	1	yes	characteristic
109	#126×C₆₁	—	2	4	no	—
110	#125×C₆₁	C₂³	1	2	yes	—
111	#124×C₆₁	—	2	4	no	—
112	#124×C₆₁	—	2	2	no	—
113	#124×C₆₁	—	2	4	no	—
114	#124×C₆₁	—	2	4	no	—
115	#124×C₆₁	—	2	4	no	—
116	#124×C₆₁	—	2	1	no	—
117	#124×C₆₁	—	2	1	no	—
118	#124×C₆₁	D₄	1	2	yes	—
119	#123×C₆₁	—	2	4	no	—
120	#123×C₆₁	—	2	4	no	—
121	C₂²⋊Q₈×C₆₁	—	2	1	no	—
122	C₂²⋊Q₈×C₆₁	—	2	1	no	—
123	C₂²⋊Q₈×C₆₁	—	2	2	no	—
124	#121×C₆₁	—	2	2	no	—
125	#121×C₆₁	—	2	2	no	—
126	#121×C₆₁	—	2	4	no	—
127	#121×C₆₁	—	2	2	no	—
128	#121×C₆₁	—	2	1	no	—
129	#121×C₆₁	—	2	1	no	—
130	#121×C₆₁	—	2	2	no	—
131	#121×C₆₁	—	2	2	no	—
132	#121×C₆₁	D₄	1	2	yes	—
133	#121×C₆₁	D₄	1	2	yes	—
134	#121×C₆₁	C₂³	1	2	yes	—
135	#121×C₆₁	C₂³	1	2	yes	—
136	#121×C₆₁	C₂³	1	4	yes	—
137	#121×C₆₁	C₂³	1	4	yes	—
138	#121×C₆₁	C₂³	1	4	yes	—
139	#121×C₆₁	C₂³	1	4	yes	—
140	#120×C₆₁	—	2	4	no	—
141	#120×C₆₁	—	2	4	no	—
142	#120×C₆₁	—	2	4	no	—
143	#120×C₆₁	—	2	4	no	—
144	#120×C₆₁	—	2	4	no	—
145	C₄×Q₈×C₆₁	—	2	2	no	—
146	C₄×Q₈×C₆₁	—	2	1	no	—
147	C₄×Q₈×C₆₁	—	2	1	no	—
148	C₄×D₄×C₆₁	—	2	4	no	—
149	C₄×D₄×C₆₁	—	2	2	no	—
150	C₄×D₄×C₆₁	—	2	4	no	—
151	C₄×D₄×C₆₁	—	2	1	no	—
152	C₄×D₄×C₆₁	—	2	1	no	—
153	C₄×D₄×C₆₁	—	2	1	no	—
154	C₄×D₄×C₆₁	—	2	1	no	—
155	C₄×D₄×C₆₁	C₂³	1	2	yes	—
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	2	no	—
162	#117×C₆₁	—	2	2	no	—
163	#117×C₆₁	—	2	2	no	—
164	#117×C₆₁	C₂³	1	2	yes	—
165	#117×C₆₁	C₂³	1	4	yes	—
166	#117×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	2	yes	—
174	#107×C₆₁	C₂³	1	4	yes	—
175	#106×C₆₁	C₂³	1	4	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	#102×C₆₁	C₂³	1	2	yes	—
181	#102×C₆₁	C₂³	1	4	yes	—
182	#102×C₆₁	C₂³	1	4	yes	—
183	#102×C₆₁	C₂³	1	4	yes	—
184	#102×C₆₁	C₂³	1	2	yes	—
185	#102×C₆₁	C₂³	1	4	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	C₂⁴×C₆₁	—	2	4	no	—
199	#41×C₆₁	—	4	4	no	—
200	#41×C₆₁	—	8	2	no	—
201	#41×C₆₁	—	8	2	no	—
202	#41×C₆₁	—	8	4	no	—
203	C₂×Q₈×C₆₁	—	2	1	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	C₂×D₄	1	2	yes	—
208	C₂×D₄×C₆₁	—	2	4	no	—
209	C₂×D₄×C₆₁	—	2	4	no	—
210	C₂×D₄×C₆₁	—	2	4	no	—
211	C₂×D₄×C₆₁	—	2	2	no	—
212	C₂×D₄×C₆₁	—	2	2	no	—
213	C₂×D₄×C₆₁	—	2	4	no	—
214	C₂×D₄×C₆₁	—	2	1	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	—	2	1	no	—
219	C₂×D₄×C₆₁	—	2	4	no	—
220	C₂×D₄×C₆₁	—	4	2	no	—
221	C₂×D₄×C₆₁	—	4	4	no	—
222	C₂×D₄×C₆₁	—	4	4	no	—
223	C₂×D₄×C₆₁	—	8	4	no	—
224	C₂×D₄×C₆₁	—	8	4	no	—
225	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
226	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
227	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
228	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
229	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
230	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
231	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₆₁	—	2	1	no	—
233	C₂²×C₄×C₆₁	—	2	4	no	—
234	C₂²×C₄×C₆₁	—	2	2	no	—
235	C₂²×C₄×C₆₁	—	2	2	no	—
236	C₂²×C₄×C₆₁	—	2	2	no	—
237	C₂²×C₄×C₆₁	—	2	2	no	—
238	C₂²×C₄×C₆₁	—	8	2	no	—
239	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
243	D₈×C₆₁	—	4	2	no	—
244	D₈×C₆₁	—	4	4	no	—
245	D₈×C₆₁	—	4	2	no	—
246	M₁₆×C₆₁	—	4	4	no	—
247	C₂×C₈×C₆₁	—	4	4	no	—
248	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
249	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
250	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
251	C₄⋊C₄×C₆₁	—	2	1	no	—
252	C₄⋊C₄×C₆₁	—	2	4	no	—
253	C₄⋊C₄×C₆₁	—	2	1	no	—
254	C₄⋊C₄×C₆₁	—	2	1	no	—
255	C₄⋊C₄×C₆₁	—	2	1	no	—
256	C₄⋊C₄×C₆₁	—	2	2	no	—
257	C₄⋊C₄×C₆₁	—	2	2	no	—
258	C₄⋊C₄×C₆₁	—	2	1	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	4	no	—
268	C₂²⋊C₄×C₆₁	—	2	4	no	—
269	C₂²⋊C₄×C₆₁	—	2	2	no	—
270	C₂²⋊C₄×C₆₁	—	2	2	no	—
271	C₂²⋊C₄×C₆₁	—	2	4	no	—
272	C₂²⋊C₄×C₆₁	—	2	4	no	—
273	C₂²⋊C₄×C₆₁	—	2	4	no	—
274	C₂²⋊C₄×C₆₁	—	2	2	no	—
275	C₂²⋊C₄×C₆₁	—	2	2	no	—
276	C₂²⋊C₄×C₆₁	—	2	4	no	—
277	C₂²⋊C₄×C₆₁	—	2	2	no	—
278	C₂²⋊C₄×C₆₁	—	2	2	no	—
279	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
280	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
281	C₄²×C₆₁	—	2	4	no	—
282	C₄²×C₆₁	—	2	4	no	—
283	C₄²×C₆₁	—	2	2	no	—
284	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
287	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
288	C₂³×C₆₁	—	2	2	no	—
289	C₂³×C₆₁	—	2	2	no	—
290	C₂³×C₆₁	—	2	2	no	—
291	C₂³×C₆₁	—	4	2	no	—
292	C₂³×C₆₁	—	8	1	no	—
293	C₂³×C₆₁	—	8	1	no	—
294	C₂³×C₆₁	—	8	4	no	—
295	C₂³×C₆₁	—	8	4	no	—
296	C₂³×C₆₁	—	8	4	no	—
297	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
298	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
299	Q₈×C₆₁	—	4	2	no	—
300	Q₈×C₆₁	—	4	2	no	—
301	Q₈×C₆₁	—	8	1	no	—
302	Q₈×C₆₁	—	8	1	no	—
303	Q₈×C₆₁	—	8	1	no	—
304	D₄×C₆₁	—	2	4	no	—
305	D₄×C₆₁	—	2	2	no	—
306	D₄×C₆₁	—	2	2	no	—
307	D₄×C₆₁	—	2	2	no	—
308	D₄×C₆₁	—	2	4	no	—
309	D₄×C₆₁	—	2	2	no	—
310	D₄×C₆₁	—	4	2	no	—
311	D₄×C₆₁	—	4	2	no	—
312	D₄×C₆₁	—	4	4	no	—
313	D₄×C₆₁	—	4	2	no	—
314	D₄×C₆₁	—	4	2	no	—
315	D₄×C₆₁	—	4	2	no	—
316	D₄×C₆₁	—	8	4	no	—
317	D₄×C₆₁	—	8	1	no	—
318	D₄×C₆₁	—	8	1	no	—
319	D₄×C₆₁	—	8	4	no	—
320	D₄×C₆₁	—	8	4	no	—
321	D₄×C₆₁	—	8	4	no	—
322	D₄×C₆₁	—	8	2	no	—
323	D₄×C₆₁	—	8	2	no	—
324	D₄×C₆₁	—	8	4	no	—
325	C₂×C₄×C₆₁	—	2	2	no	—
326	C₂×C₄×C₆₁	—	2	4	no	—
327	C₂×C₄×C₆₁	—	2	4	no	—
328	C₂×C₄×C₆₁	—	2	2	no	—
329	C₂×C₄×C₆₁	—	2	2	no	—
330	C₂×C₄×C₆₁	—	2	2	no	—
331	C₂×C₄×C₆₁	—	2	2	no	—
332	C₂×C₄×C₆₁	—	2	2	no	—
333	C₂×C₄×C₆₁	—	2	2	no	—
334	C₂×C₄×C₆₁	—	4	1	no	—
335	C₂×C₄×C₆₁	—	4	4	no	—
336	C₂×C₄×C₆₁	—	4	4	no	—
337	C₂×C₄×C₆₁	—	4	4	no	—
338	C₂×C₄×C₆₁	—	8	2	no	—
339	C₂×C₄×C₆₁	—	8	1	no	—
340	C₂×C₄×C₆₁	—	8	4	no	—
341	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
343	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
348	C₈×C₆₁	—	2	2	no	—
349	C₈×C₆₁	—	2	4	no	—
350	C₈×C₆₁	—	2	2	no	—
351	#61802	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
352	C₂²×C₆₁	—	2	1	no	—
353	C₂²×C₆₁	—	2	4	no	—
354	C₂²×C₆₁	—	2	1	no	—
355	C₂²×C₆₁	—	2	4	no	—
356	C₂²×C₆₁	—	2	1	no	—
357	C₂²×C₆₁	—	2	4	no	—
358	C₂²×C₆₁	—	4	2	no	—
359	C₂²×C₆₁	—	4	2	no	—
360	C₂²×C₆₁	—	4	2	no	—
361	C₂²×C₆₁	—	4	2	no	—
362	C₂²×C₆₁	—	4	2	no	—
363	C₂²×C₆₁	—	4	2	no	—
364	C₂²×C₆₁	—	4	2	no	—
365	C₂²×C₆₁	—	4	2	no	—
366	C₂²×C₆₁	—	4	2	no	—
367	C₂²×C₆₁	—	8	4	no	—
368	C₂²×C₆₁	—	16	8	no	—
369	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
370	C₄×C₆₁	—	2	1	no	—
371	C₄×C₆₁	—	2	1	no	—
372	C₄×C₆₁	—	2	1	no	—
373	C₄×C₆₁	—	2	4	no	—
374	C₄×C₆₁	—	2	1	no	—
375	C₄×C₆₁	—	4	2	no	—
376	C₄×C₆₁	—	4	2	no	—
377	C₄×C₆₁	—	4	2	no	—
378	C₄×C₆₁	—	4	2	no	—
379	C₄×C₆₁	—	4	2	no	—
380	C₄×C₆₁	#576	1	2	yes	—
381	C₄×C₆₁	#585	1	2	yes	—
382	#3549	C₂×C₆₁	1	1	yes	characteristic, complemented
383	#3506	C₂×C₆₁	1	1	yes	characteristic, complemented
384	#3354	C₂×C₆₁	1	2	yes	complemented
385	#3347	C₂×C₆₁	1	4	yes	complemented
386	#3341	C₂×C₆₁	1	2	yes	complemented
387	#3325	C₂×C₆₁	1	2	yes	complemented
388	#3318	C₂×C₆₁	1	4	yes	complemented
389	#3294	C₂×C₆₁	1	2	yes	complemented
390	#3235	C₂×C₆₁	1	1	yes	characteristic, complemented
391	#3228	C₂×C₆₁	1	1	yes	characteristic, complemented
392	#3199	C₂×C₆₁	1	4	yes	complemented
393	#3109	C₂×C₆₁	1	1	yes	characteristic, complemented
394	#3100	C₂×C₆₁	1	1	yes	characteristic, complemented
395	#3096	C₂×C₆₁	1	4	yes	complemented
396	#2981	C₂×C₆₁	1	1	yes	characteristic, complemented
397	C₂×C₆₁	—	4	1	no	—
398	C₂×C₆₁	—	4	4	no	—
399	C₂×C₆₁	—	8	2	no	—
400	C₂×C₆₁	—	8	2	no	—
401	C₂×C₆₁	—	8	2	no	—
402	C₂×C₆₁	#3485	1	1	yes	characteristic
403	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
404	C₂×C₆₁	#3585	1	1	yes	characteristic
405	H(3,𝔽₄)	—	2	2	no	—
406	#559	—	2	2	no	—
407	#556	—	2	1	no	—
408	#555	—	2	1	no	—
409	#555	C₂²×C₆₁	1	2	yes	complemented
410	#555	C₂²×C₆₁	1	2	yes	complemented
411	#555	C₂²×C₆₁	1	2	yes	complemented
412	#553	C₂²×C₆₁	1	4	yes	complemented
413	#550	—	2	1	no	—
414	#547	C₂²×C₆₁	1	2	yes	complemented
415	D₄²	—	2	1	no	—
416	D₄²	C₂²×C₆₁	1	2	yes	complemented
417	D₄²	C₂²×C₆₁	1	2	yes	complemented
418	#538	—	2	2	no	—
419	#535	—	2	2	no	—
420	#535	—	2	2	no	—
421	#535	C₂²×C₆₁	1	4	yes	—
422	#535	C₂²×C₆₁	1	2	yes	complemented
423	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
424	#532	C₂²×C₆₁	1	1	yes	characteristic
425	#532	C₂²×C₆₁	1	1	yes	characteristic
426	#532	C₂²×C₆₁	1	1	yes	characteristic
427	#525	—	2	2	no	—
428	#520	C₂²×C₆₁	1	2	yes	complemented
429	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
430	#501	C₂²×C₆₁	1	2	yes	complemented
431	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
432	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
433	#490	C₂²×C₆₁	1	2	yes	complemented
434	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
435	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
436	#482	C₂²×C₆₁	1	4	yes	complemented
437	#482	C₂²×C₆₁	1	4	yes	complemented
438	#482	C₂²×C₆₁	1	4	yes	complemented
439	#482	C₂²×C₆₁	1	4	yes	complemented
440	#482	C₂²×C₆₁	1	4	yes	complemented
441	#482	C₂²×C₆₁	1	4	yes	complemented
442	#481	C₂²×C₆₁	1	2	yes	complemented
443	#481	C₂²×C₆₁	1	4	yes	complemented
444	#480	C₂²×C₆₁	1	4	yes	complemented
445	#480	C₂²×C₆₁	1	2	yes	complemented
446	#478	C₂²×C₆₁	1	4	yes	complemented
447	#476	C₂²×C₆₁	1	2	yes	complemented
448	#476	C₂²×C₆₁	1	2	yes	complemented
449	#474	C₂²×C₆₁	1	2	yes	complemented
450	#474	C₂²×C₆₁	1	2	yes	complemented
451	#469	C₂²×C₆₁	1	4	yes	complemented
452	#469	C₂²×C₆₁	1	4	yes	complemented
453	#466	C₂²×C₆₁	1	4	yes	complemented
454	#466	C₂²×C₆₁	1	4	yes	complemented
455	#459	C₂²×C₆₁	1	2	yes	—
456	#459	C₂²×C₆₁	1	2	yes	—
457	#447	C₂²×C₆₁	1	2	yes	complemented
458	#447	C₂²×C₆₁	1	2	yes	complemented
459	#447	C₂²×C₆₁	1	4	yes	complemented
460	#447	C₂²×C₆₁	1	4	yes	complemented
461	#442	C₂²×C₆₁	1	4	yes	complemented
462	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
463	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
464	#436	C₂²×C₆₁	1	2	yes	complemented
465	#435	C₂²×C₆₁	1	4	yes	complemented
466	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
467	#432	C₂²×C₆₁	1	1	yes	characteristic, complemented
468	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
469	#428	C₂²×C₆₁	1	4	yes	complemented
470	#427	C₂²×C₆₁	1	4	yes	complemented
471	#418	C₂²×C₆₁	1	4	yes	complemented
472	C₂×#102	C₂²×C₆₁	1	4	yes	complemented
473	#408	C₂²×C₆₁	1	4	yes	complemented
474	C₆₁	#61802	1	1	yes	characteristic, direct product factor, Sylow
475	C₂×#41	—	2	2	no	—
476	C₂×#41	—	2	1	no	—
477	C₂×#41	—	2	1	no	—
478	C₂×#41	C₂³×C₆₁	1	2	yes	—
479	C₂²×D₄	—	2	2	no	—
480	C₂²×D₄	—	2	2	no	—
481	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
482	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
483	C₂³×C₄	—	2	1	no	—
484	C₂×D₈	C₂³×C₆₁	1	2	yes	—
485	C₂×D₈	C₂³×C₆₁	1	2	yes	—
486	C₂×D₈	C₂³×C₆₁	1	4	yes	—
487	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
488	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
489	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
490	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
491	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
492	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
493	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
494	#127	—	2	4	no	—
495	#127	—	2	2	no	—
496	#127	D₄×C₆₁	1	1	yes	characteristic
497	#127	C₂³×C₆₁	1	1	yes	characteristic
498	#127	C₂³×C₆₁	1	1	yes	characteristic
499	#126	—	2	4	no	—
500	#125	C₂³×C₆₁	1	2	yes	—
501	#124	—	2	4	no	—
502	#124	—	2	2	no	—
503	#124	—	2	4	no	—
504	#124	—	2	4	no	—
505	#124	—	2	4	no	—
506	#124	—	2	1	no	—
507	#124	—	2	1	no	—
508	#124	D₄×C₆₁	1	2	yes	—
509	#123	—	2	4	no	—
510	#123	—	2	4	no	—
511	C₂²⋊Q₈	—	2	1	no	—
512	C₂²⋊Q₈	—	2	1	no	—
513	C₂²⋊Q₈	—	2	2	no	—
514	#121	—	2	2	no	—
515	#121	—	2	2	no	—
516	#121	—	2	2	no	—
517	#121	—	2	4	no	—
518	#121	—	2	1	no	—
519	#121	—	2	1	no	—
520	#121	—	2	2	no	—
521	#121	—	2	2	no	—
522	#121	D₄×C₆₁	1	2	yes	—
523	#121	D₄×C₆₁	1	2	yes	—
524	#121	C₂³×C₆₁	1	2	yes	—
525	#121	C₂³×C₆₁	1	2	yes	—
526	#121	C₂³×C₆₁	1	4	yes	—
527	#121	C₂³×C₆₁	1	4	yes	—
528	#121	C₂³×C₆₁	1	4	yes	—
529	#121	C₂³×C₆₁	1	4	yes	—
530	#120	—	2	4	no	—
531	#120	—	2	4	no	—
532	#120	—	2	4	no	—
533	#120	—	2	4	no	—
534	#120	—	2	4	no	—
535	C₄×Q₈	—	2	2	no	—
536	C₄×Q₈	—	2	1	no	—
537	C₄×Q₈	—	2	1	no	—
538	C₄×D₄	—	2	4	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	4	no	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	—	2	1	no	—
543	C₄×D₄	—	2	1	no	—
544	C₄×D₄	—	2	1	no	—
545	C₄×D₄	C₂³×C₆₁	1	2	yes	—
546	C₄×D₄	C₂³×C₆₁	1	2	yes	—
547	C₄×D₄	C₂³×C₆₁	1	2	yes	—
548	C₄×D₄	C₂³×C₆₁	1	2	yes	—
549	C₄×D₄	C₂³×C₆₁	1	2	yes	—
550	C₄×D₄	C₂³×C₆₁	1	2	yes	—
551	#117	—	2	2	no	—
552	#117	—	2	2	no	—
553	#117	—	2	2	no	—
554	#117	C₂³×C₆₁	1	2	yes	—
555	#117	C₂³×C₆₁	1	4	yes	—
556	#117	C₂³×C₆₁	1	4	yes	—
557	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
561	#107	C₂³×C₆₁	1	2	yes	—
562	#107	C₂³×C₆₁	1	4	yes	—
563	#107	C₂³×C₆₁	1	2	yes	—
564	#107	C₂³×C₆₁	1	4	yes	—
565	#106	C₂³×C₆₁	1	4	yes	—
566	#106	C₂³×C₆₁	1	4	yes	—
567	#106	C₂³×C₆₁	1	4	yes	—
568	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
569	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
570	#102	C₂³×C₆₁	1	2	yes	—
571	#102	C₂³×C₆₁	1	4	yes	—
572	#102	C₂³×C₆₁	1	4	yes	—
573	#102	C₂³×C₆₁	1	4	yes	—
574	#102	C₂³×C₆₁	1	2	yes	—
575	#102	C₂³×C₆₁	1	4	yes	—
576	#102	C₂³×C₆₁	1	4	yes	—
577	#102	C₂³×C₆₁	1	2	yes	—
578	#102	C₂³×C₆₁	1	2	yes	—
579	#102	C₂³×C₆₁	1	4	yes	—
580	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
581	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
582	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
583	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
584	#97	C₂³×C₆₁	1	2	yes	—
585	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
586	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
587	C₂⁴	—	2	1	no	—
588	C₂⁴	—	2	4	no	—
589	#41	—	4	4	no	—
590	#41	—	8	2	no	—
591	#41	—	8	2	no	—
592	#41	—	8	4	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	4	2	no	—
611	C₂×D₄	—	4	4	no	—
612	C₂×D₄	—	4	4	no	—
613	C₂×D₄	—	8	4	no	—
614	C₂×D₄	—	8	4	no	—
615	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
616	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
617	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
618	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
619	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
620	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
621	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	8	2	no	—
629	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
633	D₈	—	4	2	no	—
634	D₈	—	4	4	no	—
635	D₈	—	4	2	no	—
636	M₁₆	—	4	4	no	—
637	C₂×C₈	—	4	4	no	—
638	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
639	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
640	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
650	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
651	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
655	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	2	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
670	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
671	C₄²	—	2	4	no	—
672	C₄²	—	2	4	no	—
673	C₄²	—	2	2	no	—
674	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
675	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
676	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
677	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	8	1	no	—
683	C₂³	—	8	1	no	—
684	C₂³	—	8	4	no	—
685	C₂³	—	8	4	no	—
686	C₂³	—	8	4	no	—
687	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
688	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
689	Q₈	—	4	2	no	—
690	Q₈	—	4	2	no	—
691	Q₈	—	8	1	no	—
692	Q₈	—	8	1	no	—
693	Q₈	—	8	1	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	4	no	—
699	D₄	—	2	2	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	2	no	—
702	D₄	—	4	4	no	—
703	D₄	—	4	2	no	—
704	D₄	—	4	2	no	—
705	D₄	—	4	2	no	—
706	D₄	—	8	4	no	—
707	D₄	—	8	1	no	—
708	D₄	—	8	1	no	—
709	D₄	—	8	4	no	—
710	D₄	—	8	4	no	—
711	D₄	—	8	4	no	—
712	D₄	—	8	2	no	—
713	D₄	—	8	4	no	—
714	D₄	—	8	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	4	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	8	2	no	—
729	C₂×C₄	—	8	1	no	—
730	C₂×C₄	—	8	4	no	—
731	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
733	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
735	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
736	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
737	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
738	C₈	—	2	2	no	—
739	C₈	—	2	4	no	—
740	C₈	—	2	2	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	4	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	4	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	4	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	8	4	no	—
757	C₂²	—	16	8	no	—
758	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
759	C₄	—	2	1	no	—
760	C₄	—	2	1	no	—
761	C₄	—	2	1	no	—
762	C₄	—	2	1	no	—
763	C₄	—	2	4	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	C₆₁×#576	1	2	yes	—
770	C₄	C₆₁×#585	1	2	yes	—
771	C₂	—	4	1	no	—
772	C₂	—	4	4	no	—
773	C₂	—	8	2	no	—
774	C₂	—	8	2	no	—
775	C₂	—	8	2	no	—
776	C₂	C₆₁×#3485	1	1	yes	characteristic
777	C₂	C₂×C₆₁×#576	1	1	yes	characteristic
778	C₂	C₆₁×#3585	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×#3549	C₂	semidirect
2. C₆₁×#3506	C₂	semidirect
3. C₆₁×#3354	C₂	semidirect
4. C₆₁×#3347	C₂	semidirect
5. C₆₁×#3341	C₂	semidirect
6. C₆₁×#3325	C₂	semidirect
7. C₆₁×#3318	C₂	semidirect
8. C₆₁×#3294	C₂	semidirect
9. C₆₁×#3235	C₂	semidirect
10. C₆₁×#3228	C₂	semidirect
11. C₆₁×#3199	C₂	semidirect
12. C₆₁×#3109	C₂	semidirect
13. C₆₁×#3100	C₂	semidirect
14. C₆₁×#3096	C₂	semidirect
15. C₆₁×#2981	C₂	semidirect
20. C₆₁×#555	C₂²	semidirect
21. C₆₁×#555	C₂²	semidirect
22. C₆₁×#555	C₂²	semidirect
23. C₆₁×#553	C₂²	semidirect
25. C₆₁×#547	C₂²	semidirect
27. D₄²×C₆₁	C₂²	semidirect
28. D₄²×C₆₁	C₂²	semidirect
33. C₆₁×#535	C₂²	semidirect
34. C₆₁×#533	C₂²	semidirect
39. C₆₁×#520	C₂²	semidirect
40. C₂×C₄×D₄×C₆₁	C₂²	semidirect
41. C₆₁×#501	C₂²	semidirect
42. C₆₁×#500	C₂²	semidirect
43. C₆₁×#498	C₂²	semidirect
44. C₆₁×#490	C₂²	semidirect
45. C₆₁×#486	C₂²	semidirect
46. C₆₁×#486	C₂²	semidirect
47. C₆₁×#482	C₂²	semidirect
48. C₆₁×#482	C₂²	semidirect
49. C₆₁×#482	C₂²	semidirect
50. C₆₁×#482	C₂²	semidirect
51. C₆₁×#482	C₂²	semidirect
52. C₆₁×#482	C₂²	semidirect
53. C₆₁×#481	C₂²	semidirect
54. C₆₁×#481	C₂²	semidirect
55. C₆₁×#480	C₂²	semidirect
56. C₆₁×#480	C₂²	semidirect
57. C₆₁×#478	C₂²	semidirect
58. C₆₁×#476	C₂²	semidirect
59. C₆₁×#476	C₂²	semidirect
60. C₆₁×#474	C₂²	semidirect
61. C₆₁×#474	C₂²	semidirect
62. C₆₁×#469	C₂²	semidirect
63. C₆₁×#469	C₂²	semidirect
64. C₆₁×#466	C₂²	semidirect
65. C₆₁×#466	C₂²	semidirect
68. C₆₁×#447	C₂²	semidirect
69. C₆₁×#447	C₂²	semidirect
70. C₆₁×#447	C₂²	semidirect
71. C₆₁×#447	C₂²	semidirect
72. C₆₁×#442	C₂²	semidirect
73. C₄×D₈×C₆₁	C₂²	semidirect
74. C₄×D₈×C₆₁	C₂²	semidirect
75. C₆₁×#436	C₂²	semidirect
76. C₆₁×#435	C₂²	semidirect
77. C₈×D₄×C₆₁	C₂²	semidirect
78. C₆₁×#432	C₂²	semidirect
79. C₆₁×#431	C₂²	semidirect
80. C₆₁×#428	C₂²	semidirect
81. C₆₁×#427	C₂²	semidirect
82. C₆₁×#418	C₂²	semidirect
83. C₂×#102×C₆₁	C₂²	semidirect
84. C₆₁×#408	C₂²	semidirect
351. #61802	C₆₁	direct (N × H)
382. #3549	C₂×C₆₁	semidirect
383. #3506	C₂×C₆₁	semidirect
384. #3354	C₂×C₆₁	semidirect
385. #3347	C₂×C₆₁	semidirect
386. #3341	C₂×C₆₁	semidirect
387. #3325	C₂×C₆₁	semidirect
388. #3318	C₂×C₆₁	semidirect
389. #3294	C₂×C₆₁	semidirect
390. #3235	C₂×C₆₁	semidirect
391. #3228	C₂×C₆₁	semidirect
392. #3199	C₂×C₆₁	semidirect
393. #3109	C₂×C₆₁	semidirect
394. #3100	C₂×C₆₁	semidirect
395. #3096	C₂×C₆₁	semidirect
396. #2981	C₂×C₆₁	semidirect
409. #555	C₂²×C₆₁	semidirect
410. #555	C₂²×C₆₁	semidirect
411. #555	C₂²×C₆₁	semidirect
412. #553	C₂²×C₆₁	semidirect
414. #547	C₂²×C₆₁	semidirect
416. D₄²	C₂²×C₆₁	semidirect
417. D₄²	C₂²×C₆₁	semidirect
422. #535	C₂²×C₆₁	semidirect
423. #533	C₂²×C₆₁	semidirect
428. #520	C₂²×C₆₁	semidirect
429. C₂×C₄×D₄	C₂²×C₆₁	semidirect
430. #501	C₂²×C₆₁	semidirect
431. #500	C₂²×C₆₁	semidirect
432. #498	C₂²×C₆₁	semidirect
433. #490	C₂²×C₆₁	semidirect
434. #486	C₂²×C₆₁	semidirect
435. #486	C₂²×C₆₁	semidirect
436. #482	C₂²×C₆₁	semidirect
437. #482	C₂²×C₆₁	semidirect
438. #482	C₂²×C₆₁	semidirect
439. #482	C₂²×C₆₁	semidirect
440. #482	C₂²×C₆₁	semidirect
441. #482	C₂²×C₆₁	semidirect
442. #481	C₂²×C₆₁	semidirect
443. #481	C₂²×C₆₁	semidirect
444. #480	C₂²×C₆₁	semidirect
445. #480	C₂²×C₆₁	semidirect
446. #478	C₂²×C₆₁	semidirect
447. #476	C₂²×C₆₁	semidirect
448. #476	C₂²×C₆₁	semidirect
449. #474	C₂²×C₆₁	semidirect
450. #474	C₂²×C₆₁	semidirect
451. #469	C₂²×C₆₁	semidirect
452. #469	C₂²×C₆₁	semidirect
453. #466	C₂²×C₆₁	semidirect
454. #466	C₂²×C₆₁	semidirect
457. #447	C₂²×C₆₁	semidirect
458. #447	C₂²×C₆₁	semidirect
459. #447	C₂²×C₆₁	semidirect
460. #447	C₂²×C₆₁	semidirect
461. #442	C₂²×C₆₁	semidirect
462. C₄×D₈	C₂²×C₆₁	semidirect
463. C₄×D₈	C₂²×C₆₁	semidirect
464. #436	C₂²×C₆₁	semidirect
465. #435	C₂²×C₆₁	semidirect
466. C₈×D₄	C₂²×C₆₁	semidirect
467. #432	C₂²×C₆₁	semidirect
468. #431	C₂²×C₆₁	semidirect
469. #428	C₂²×C₆₁	semidirect
470. #427	C₂²×C₆₁	semidirect
471. #418	C₂²×C₆₁	semidirect
472. C₂×#102	C₂²×C₆₁	semidirect
473. #408	C₂²×C₆₁	semidirect
474. C₆₁	#61802	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×#3549	2
C₆₁×#3506	2
C₆₁×#3354	2
C₆₁×#3347	2
C₆₁×#3341	2
C₆₁×#3325	2
C₆₁×#3318	2
C₆₁×#3294	2
C₆₁×#3235	2
C₆₁×#3228	2
C₆₁×#3199	2
C₆₁×#3109	2
C₆₁×#3100	2
C₆₁×#3096	2
C₆₁×#2981	2
#61802	61

Subgroups — C61×#61802 #29565235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61802 #29565235