Subgroups — C₆₁×#61803 #29565236

Order 15616.

1732 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3506	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3353	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3350	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3340	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3329	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3320	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3298	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3237	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3200	C₂	1	4	yes	maximal, complemented
12	C₆₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3097	C₂	1	4	yes	maximal, complemented
15	C₆₁×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#563	—	2	2	no	—
17	C₆₁×#559	—	2	1	no	—
18	C₆₁×#559	—	2	2	no	—
19	Q₈²×C₆₁	—	2	1	no	—
20	C₆₁×#556	—	2	1	no	—
21	C₆₁×#556	C₂²	1	2	yes	complemented
22	C₆₁×#556	C₂²	1	2	yes	complemented
23	C₆₁×#555	C₂²	1	2	yes	—
24	C₆₁×#553	C₂²	1	4	yes	—
25	C₆₁×#550	—	2	1	no	—
26	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
27	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
28	C₆₁×#547	C₂²	1	2	yes	—
29	C₆₁×#542	—	2	2	no	—
30	C₆₁×#542	—	2	2	no	—
31	C₆₁×#538	—	2	2	no	—
32	C₆₁×#536	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×#533	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×#491	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	—
49	C₆₁×#485	C₂²	1	4	yes	complemented
50	C₆₁×#485	C₂²	1	4	yes	complemented
51	C₆₁×#484	C₂²	1	2	yes	—
52	C₆₁×#484	C₂²	1	4	yes	complemented
53	C₆₁×#483	C₂²	1	2	yes	—
54	C₆₁×#483	C₂²	1	4	yes	complemented
55	C₆₁×#482	C₂²	1	4	yes	—
56	C₆₁×#482	C₂²	1	4	yes	—
57	C₆₁×#479	C₂²	1	4	yes	complemented
58	C₆₁×#477	C₂²	1	2	yes	complemented
59	C₆₁×#476	C₂²	1	2	yes	—
60	C₆₁×#475	C₂²	1	2	yes	complemented
61	C₆₁×#474	C₂²	1	2	yes	—
62	C₆₁×#468	C₂²	1	4	yes	—
63	C₆₁×#468	C₂²	1	4	yes	—
64	C₆₁×#465	C₂²	1	4	yes	—
65	C₆₁×#465	C₂²	1	4	yes	—
66	C₆₁×#461	C₂²	1	2	yes	—
67	C₆₁×#461	C₂²	1	2	yes	—
68	C₆₁×#450	C₂²	1	2	yes	—
69	C₆₁×#450	C₂²	1	2	yes	—
70	C₆₁×#448	C₂²	1	4	yes	—
71	C₆₁×#448	C₂²	1	4	yes	—
72	C₆₁×#440	C₂²	1	4	yes	—
73	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
74	C₄×SD₁₆×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	C₆₁×#427	C₂²	1	4	yes	complemented
82	C₆₁×#419	C₂²	1	4	yes	complemented
83	C₂×#103×C₆₁	C₂²	1	4	yes	complemented
84	C₆₁×#408	C₂²	1	4	yes	—
85	C₂×#41×C₆₁	—	2	2	no	—
86	C₂×#41×C₆₁	C₂³	1	2	yes	—
87	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
88	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₆₁	—	2	1	no	—
90	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
91	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
92	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
93	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
94	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
95	C₄⋊Q₈×C₆₁	—	2	4	no	—
96	C₄⋊Q₈×C₆₁	—	2	2	no	—
97	C₄⋊Q₈×C₆₁	—	2	2	no	—
98	C₄⋊Q₈×C₆₁	D₄	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	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
104	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
105	#127×C₆₁	—	2	2	no	—
106	#127×C₆₁	D₄	1	1	yes	characteristic
107	#126×C₆₁	—	2	4	no	—
108	#126×C₆₁	—	2	4	no	—
109	#126×C₆₁	—	2	4	no	—
110	#125×C₆₁	—	2	1	no	—
111	#125×C₆₁	—	2	1	no	—
112	#125×C₆₁	C₂³	1	2	yes	—
113	#124×C₆₁	—	2	2	no	—
114	#124×C₆₁	—	2	4	no	—
115	#124×C₆₁	—	2	2	no	—
116	#124×C₆₁	—	2	2	no	—
117	#124×C₆₁	—	2	4	no	—
118	#124×C₆₁	D₄	1	2	yes	—
119	#123×C₆₁	—	2	4	no	—
120	#123×C₆₁	—	2	4	no	—
121	#123×C₆₁	—	2	4	no	—
122	#123×C₆₁	—	2	4	no	—
123	C₂²⋊Q₈×C₆₁	—	2	1	no	—
124	C₂²⋊Q₈×C₆₁	—	2	1	no	—
125	C₂²⋊Q₈×C₆₁	—	2	1	no	—
126	C₂²⋊Q₈×C₆₁	—	2	1	no	—
127	C₂²⋊Q₈×C₆₁	—	2	2	no	—
128	C₂²⋊Q₈×C₆₁	—	2	4	no	—
129	C₂²⋊Q₈×C₆₁	—	2	4	no	—
130	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
131	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
132	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
133	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
134	#121×C₆₁	—	2	4	no	—
135	#121×C₆₁	—	2	2	no	—
136	#121×C₆₁	D₄	1	2	yes	—
137	#121×C₆₁	D₄	1	2	yes	—
138	#121×C₆₁	C₂³	1	4	yes	—
139	#121×C₆₁	C₂³	1	4	yes	—
140	#120×C₆₁	—	2	4	no	—
141	C₄×Q₈×C₆₁	—	2	2	no	—
142	C₄×Q₈×C₆₁	—	2	2	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	—	2	1	no	—
148	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
149	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
150	C₄×D₄×C₆₁	—	2	4	no	—
151	C₄×D₄×C₆₁	—	2	2	no	—
152	C₄×D₄×C₆₁	—	2	2	no	—
153	C₄×D₄×C₆₁	—	2	2	no	—
154	C₄×D₄×C₆₁	—	2	4	no	—
155	C₄×D₄×C₆₁	—	2	1	no	—
156	C₄×D₄×C₆₁	—	2	1	no	—
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	1	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	4	yes	—
172	#107×C₆₁	C₂³	1	4	yes	—
173	#107×C₆₁	C₂³	1	4	yes	—
174	#106×C₆₁	C₂³	1	2	yes	—
175	#106×C₆₁	C₂³	1	4	yes	—
176	#106×C₆₁	C₂³	1	2	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	2	yes	—
181	#103×C₆₁	C₂³	1	4	yes	—
182	#103×C₆₁	C₂³	1	4	yes	—
183	#103×C₆₁	C₂³	1	4	yes	—
184	#103×C₆₁	C₂³	1	2	yes	—
185	#103×C₆₁	C₂³	1	4	yes	—
186	#103×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	—	8	4	no	—
200	C₂×Q₈×C₆₁	—	2	1	no	—
201	C₂×Q₈×C₆₁	—	2	1	no	—
202	C₂×Q₈×C₆₁	—	2	1	no	—
203	C₂×Q₈×C₆₁	—	2	1	no	—
204	C₂×Q₈×C₆₁	—	2	4	no	—
205	C₂×Q₈×C₆₁	—	4	4	no	—
206	C₂×Q₈×C₆₁	—	4	4	no	—
207	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₆₁	C₂⁴	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	1	no	—
213	C₂×D₄×C₆₁	—	4	2	no	—
214	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
216	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
217	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
218	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₆₁	—	2	1	no	—
220	C₂²×C₄×C₆₁	—	2	4	no	—
221	C₂²×C₄×C₆₁	—	2	4	no	—
222	C₂²×C₄×C₆₁	—	2	2	no	—
223	C₂²×C₄×C₆₁	—	2	2	no	—
224	C₂²×C₄×C₆₁	—	8	2	no	—
225	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
229	SD₁₆×C₆₁	—	4	2	no	—
230	SD₁₆×C₆₁	—	4	4	no	—
231	SD₁₆×C₆₁	—	4	2	no	—
232	M₁₆×C₆₁	—	4	4	no	—
233	C₂×C₈×C₆₁	—	4	4	no	—
234	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
235	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
236	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
237	C₄⋊C₄×C₆₁	—	2	1	no	—
238	C₄⋊C₄×C₆₁	—	2	4	no	—
239	C₄⋊C₄×C₆₁	—	2	1	no	—
240	C₄⋊C₄×C₆₁	—	2	1	no	—
241	C₄⋊C₄×C₆₁	—	2	1	no	—
242	C₄⋊C₄×C₆₁	—	2	1	no	—
243	C₄⋊C₄×C₆₁	—	2	1	no	—
244	C₄⋊C₄×C₆₁	—	2	2	no	—
245	C₄⋊C₄×C₆₁	—	2	1	no	—
246	C₄⋊C₄×C₆₁	—	2	1	no	—
247	C₄⋊C₄×C₆₁	—	2	2	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	2	no	—
252	C₄⋊C₄×C₆₁	—	2	2	no	—
253	C₄⋊C₄×C₆₁	—	2	2	no	—
254	C₄⋊C₄×C₆₁	—	2	2	no	—
255	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
262	C₂²⋊C₄×C₆₁	—	2	2	no	—
263	C₂²⋊C₄×C₆₁	—	2	2	no	—
264	C₂²⋊C₄×C₆₁	—	2	2	no	—
265	C₂²⋊C₄×C₆₁	—	2	4	no	—
266	C₂²⋊C₄×C₆₁	—	2	4	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	C₂×D₄	1	4	yes	—
274	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
275	C₄²×C₆₁	—	2	4	no	—
276	C₄²×C₆₁	—	2	2	no	—
277	C₄²×C₆₁	—	2	2	no	—
278	C₄²×C₆₁	—	2	2	no	—
279	C₄²×C₆₁	—	2	4	no	—
280	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
283	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
284	C₂³×C₆₁	—	2	2	no	—
285	C₂³×C₆₁	—	4	2	no	—
286	C₂³×C₆₁	—	8	1	no	—
287	C₂³×C₆₁	—	8	1	no	—
288	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
289	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
290	Q₈×C₆₁	—	2	2	no	—
291	Q₈×C₆₁	—	2	4	no	—
292	Q₈×C₆₁	—	2	2	no	—
293	Q₈×C₆₁	—	4	2	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	4	no	—
299	D₄×C₆₁	—	2	4	no	—
300	D₄×C₆₁	—	2	2	no	—
301	D₄×C₆₁	—	2	2	no	—
302	D₄×C₆₁	—	4	2	no	—
303	D₄×C₆₁	—	4	2	no	—
304	D₄×C₆₁	—	4	4	no	—
305	D₄×C₆₁	—	4	2	no	—
306	D₄×C₆₁	—	8	4	no	—
307	D₄×C₆₁	—	8	4	no	—
308	C₂×C₄×C₆₁	—	2	2	no	—
309	C₂×C₄×C₆₁	—	2	4	no	—
310	C₂×C₄×C₆₁	—	2	4	no	—
311	C₂×C₄×C₆₁	—	2	2	no	—
312	C₂×C₄×C₆₁	—	2	2	no	—
313	C₂×C₄×C₆₁	—	2	2	no	—
314	C₂×C₄×C₆₁	—	2	2	no	—
315	C₂×C₄×C₆₁	—	2	2	no	—
316	C₂×C₄×C₆₁	—	2	2	no	—
317	C₂×C₄×C₆₁	—	2	2	no	—
318	C₂×C₄×C₆₁	—	2	2	no	—
319	C₂×C₄×C₆₁	—	4	1	no	—
320	C₂×C₄×C₆₁	—	4	4	no	—
321	C₂×C₄×C₆₁	—	8	2	no	—
322	C₂×C₄×C₆₁	—	8	1	no	—
323	C₂×C₄×C₆₁	—	8	4	no	—
324	C₂×C₄×C₆₁	—	8	4	no	—
325	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
328	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
332	C₈×C₆₁	—	2	2	no	—
333	C₈×C₆₁	—	2	4	no	—
334	C₈×C₆₁	—	2	2	no	—
335	#61803	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂²×C₆₁	—	2	1	no	—
337	C₂²×C₆₁	—	2	4	no	—
338	C₂²×C₆₁	—	2	4	no	—
339	C₂²×C₆₁	—	2	1	no	—
340	C₂²×C₆₁	—	2	1	no	—
341	C₂²×C₆₁	—	2	4	no	—
342	C₂²×C₆₁	—	4	2	no	—
343	C₂²×C₆₁	—	4	2	no	—
344	C₂²×C₆₁	—	4	2	no	—
345	C₂²×C₆₁	—	8	4	no	—
346	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
347	C₄×C₆₁	—	2	1	no	—
348	C₄×C₆₁	—	2	1	no	—
349	C₄×C₆₁	—	2	1	no	—
350	C₄×C₆₁	—	2	4	no	—
351	C₄×C₆₁	—	2	1	no	—
352	C₄×C₆₁	—	4	2	no	—
353	C₄×C₆₁	—	4	2	no	—
354	C₄×C₆₁	—	4	2	no	—
355	C₄×C₆₁	—	4	2	no	—
356	C₄×C₆₁	—	4	2	no	—
357	C₄×C₆₁	—	4	2	no	—
358	C₄×C₆₁	—	4	2	no	—
359	C₄×C₆₁	#577	1	2	yes	—
360	C₄×C₆₁	#585	1	2	yes	—
361	#3550	C₂×C₆₁	1	1	yes	characteristic, complemented
362	#3506	C₂×C₆₁	1	1	yes	characteristic
363	#3353	C₂×C₆₁	1	2	yes	complemented
364	#3350	C₂×C₆₁	1	4	yes	complemented
365	#3340	C₂×C₆₁	1	2	yes	complemented
366	#3329	C₂×C₆₁	1	2	yes	complemented
367	#3320	C₂×C₆₁	1	4	yes	complemented
368	#3298	C₂×C₆₁	1	2	yes	complemented
369	#3237	C₂×C₆₁	1	1	yes	characteristic, complemented
370	#3231	C₂×C₆₁	1	1	yes	characteristic, complemented
371	#3200	C₂×C₆₁	1	4	yes	complemented
372	#3110	C₂×C₆₁	1	1	yes	characteristic, complemented
373	#3101	C₂×C₆₁	1	1	yes	characteristic, complemented
374	#3097	C₂×C₆₁	1	4	yes	complemented
375	#2981	C₂×C₆₁	1	1	yes	characteristic, complemented
376	C₂×C₆₁	—	4	4	no	—
377	C₂×C₆₁	—	4	1	no	—
378	C₂×C₆₁	—	8	2	no	—
379	C₂×C₆₁	#3485	1	1	yes	characteristic
380	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
381	C₂×C₆₁	#3586	1	1	yes	characteristic
382	#563	—	2	2	no	—
383	#559	—	2	1	no	—
384	#559	—	2	2	no	—
385	Q₈²	—	2	1	no	—
386	#556	—	2	1	no	—
387	#556	C₂²×C₆₁	1	2	yes	complemented
388	#556	C₂²×C₆₁	1	2	yes	complemented
389	#555	C₂²×C₆₁	1	2	yes	—
390	#553	C₂²×C₆₁	1	4	yes	—
391	#550	—	2	1	no	—
392	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
393	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
394	#547	C₂²×C₆₁	1	2	yes	—
395	#542	—	2	2	no	—
396	#542	—	2	2	no	—
397	#538	—	2	2	no	—
398	#536	C₂²×C₆₁	1	4	yes	—
399	#535	C₂²×C₆₁	1	2	yes	—
400	#533	C₂²×C₆₁	1	1	yes	characteristic
401	#533	C₂²×C₆₁	1	1	yes	characteristic
402	#533	C₂²×C₆₁	1	1	yes	characteristic
403	#532	C₂²×C₆₁	1	1	yes	characteristic
404	#525	—	2	2	no	—
405	#520	C₂²×C₆₁	1	2	yes	—
406	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
407	#501	C₂²×C₆₁	1	2	yes	complemented
408	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
409	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
410	#491	C₂²×C₆₁	1	2	yes	complemented
411	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
412	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
413	#485	C₂²×C₆₁	1	4	yes	—
414	#485	C₂²×C₆₁	1	4	yes	—
415	#485	C₂²×C₆₁	1	4	yes	complemented
416	#485	C₂²×C₆₁	1	4	yes	complemented
417	#484	C₂²×C₆₁	1	2	yes	—
418	#484	C₂²×C₆₁	1	4	yes	complemented
419	#483	C₂²×C₆₁	1	2	yes	—
420	#483	C₂²×C₆₁	1	4	yes	complemented
421	#482	C₂²×C₆₁	1	4	yes	—
422	#482	C₂²×C₆₁	1	4	yes	—
423	#479	C₂²×C₆₁	1	4	yes	complemented
424	#477	C₂²×C₆₁	1	2	yes	complemented
425	#476	C₂²×C₆₁	1	2	yes	—
426	#475	C₂²×C₆₁	1	2	yes	complemented
427	#474	C₂²×C₆₁	1	2	yes	—
428	#468	C₂²×C₆₁	1	4	yes	—
429	#468	C₂²×C₆₁	1	4	yes	—
430	#465	C₂²×C₆₁	1	4	yes	—
431	#465	C₂²×C₆₁	1	4	yes	—
432	#461	C₂²×C₆₁	1	2	yes	—
433	#461	C₂²×C₆₁	1	2	yes	—
434	#450	C₂²×C₆₁	1	2	yes	—
435	#450	C₂²×C₆₁	1	2	yes	—
436	#448	C₂²×C₆₁	1	4	yes	—
437	#448	C₂²×C₆₁	1	4	yes	—
438	#440	C₂²×C₆₁	1	4	yes	—
439	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
440	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
441	#436	C₂²×C₆₁	1	2	yes	complemented
442	#435	C₂²×C₆₁	1	4	yes	complemented
443	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
444	#432	C₂²×C₆₁	1	1	yes	characteristic
445	#431	C₂²×C₆₁	1	1	yes	characteristic
446	#428	C₂²×C₆₁	1	4	yes	complemented
447	#427	C₂²×C₆₁	1	4	yes	complemented
448	#419	C₂²×C₆₁	1	4	yes	complemented
449	C₂×#103	C₂²×C₆₁	1	4	yes	complemented
450	#408	C₂²×C₆₁	1	4	yes	—
451	C₆₁	#61803	1	1	yes	characteristic, direct product factor, Sylow
452	C₂×#41	—	2	2	no	—
453	C₂×#41	C₂³×C₆₁	1	2	yes	—
454	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
455	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
456	C₂³×C₄	—	2	1	no	—
457	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
458	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
459	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
460	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
461	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
462	C₄⋊Q₈	—	2	4	no	—
463	C₄⋊Q₈	—	2	2	no	—
464	C₄⋊Q₈	—	2	2	no	—
465	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
466	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
468	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
469	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
470	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
471	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
472	#127	—	2	2	no	—
473	#127	D₄×C₆₁	1	1	yes	characteristic
474	#126	—	2	4	no	—
475	#126	—	2	4	no	—
476	#126	—	2	4	no	—
477	#125	—	2	1	no	—
478	#125	—	2	1	no	—
479	#125	C₂³×C₆₁	1	2	yes	—
480	#124	—	2	2	no	—
481	#124	—	2	4	no	—
482	#124	—	2	2	no	—
483	#124	—	2	2	no	—
484	#124	—	2	4	no	—
485	#124	D₄×C₆₁	1	2	yes	—
486	#123	—	2	4	no	—
487	#123	—	2	4	no	—
488	#123	—	2	4	no	—
489	#123	—	2	4	no	—
490	C₂²⋊Q₈	—	2	1	no	—
491	C₂²⋊Q₈	—	2	1	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	1	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
498	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
499	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
500	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
501	#121	—	2	2	no	—
502	#121	—	2	4	no	—
503	#121	D₄×C₆₁	1	2	yes	—
504	#121	D₄×C₆₁	1	2	yes	—
505	#121	C₂³×C₆₁	1	4	yes	—
506	#121	C₂³×C₆₁	1	4	yes	—
507	#120	—	2	4	no	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	—	2	2	no	—
511	C₄×Q₈	—	2	1	no	—
512	C₄×Q₈	—	2	1	no	—
513	C₄×Q₈	—	2	1	no	—
514	C₄×Q₈	—	2	1	no	—
515	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
516	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
517	C₄×D₄	—	2	4	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	C₂³×C₆₁	1	2	yes	—
525	C₄×D₄	C₂³×C₆₁	1	2	yes	—
526	C₄×D₄	C₂³×C₆₁	1	2	yes	—
527	C₄×D₄	C₂³×C₆₁	1	2	yes	—
528	#117	—	2	1	no	—
529	#117	—	2	1	no	—
530	#117	—	2	2	no	—
531	#117	C₂³×C₆₁	1	2	yes	—
532	#117	C₂³×C₆₁	1	4	yes	—
533	#117	C₂³×C₆₁	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
538	#107	C₂³×C₆₁	1	4	yes	—
539	#107	C₂³×C₆₁	1	4	yes	—
540	#107	C₂³×C₆₁	1	4	yes	—
541	#106	C₂³×C₆₁	1	2	yes	—
542	#106	C₂³×C₆₁	1	4	yes	—
543	#106	C₂³×C₆₁	1	2	yes	—
544	#106	C₂³×C₆₁	1	4	yes	—
545	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
546	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
547	#103	C₂³×C₆₁	1	2	yes	—
548	#103	C₂³×C₆₁	1	4	yes	—
549	#103	C₂³×C₆₁	1	4	yes	—
550	#103	C₂³×C₆₁	1	4	yes	—
551	#103	C₂³×C₆₁	1	2	yes	—
552	#103	C₂³×C₆₁	1	4	yes	—
553	#103	C₂³×C₆₁	1	4	yes	—
554	#102	C₂³×C₆₁	1	2	yes	—
555	#102	C₂³×C₆₁	1	2	yes	—
556	#102	C₂³×C₆₁	1	4	yes	—
557	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
558	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
559	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
560	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
561	#97	C₂³×C₆₁	1	2	yes	—
562	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
563	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
564	C₂⁴	—	2	1	no	—
565	#41	—	4	4	no	—
566	#41	—	8	4	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	—	4	4	no	—
573	C₂×Q₈	—	4	4	no	—
574	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
575	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
576	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	4	2	no	—
581	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
582	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
583	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
584	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
585	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	8	2	no	—
592	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
596	SD₁₆	—	4	2	no	—
597	SD₁₆	—	4	4	no	—
598	SD₁₆	—	4	2	no	—
599	M₁₆	—	4	4	no	—
600	C₂×C₈	—	4	4	no	—
601	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
602	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
603	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
623	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
624	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
625	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
641	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	2	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	2	no	—
646	C₄²	—	2	4	no	—
647	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
648	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
649	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
650	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
651	C₂³	—	2	2	no	—
652	C₂³	—	4	2	no	—
653	C₂³	—	8	1	no	—
654	C₂³	—	8	1	no	—
655	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
656	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
657	Q₈	—	2	2	no	—
658	Q₈	—	2	4	no	—
659	Q₈	—	2	2	no	—
660	Q₈	—	4	2	no	—
661	Q₈	—	4	2	no	—
662	Q₈	—	4	2	no	—
663	Q₈	—	4	2	no	—
664	Q₈	—	8	1	no	—
665	Q₈	—	8	4	no	—
666	D₄	—	2	4	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	2	no	—
669	D₄	—	4	2	no	—
670	D₄	—	4	2	no	—
671	D₄	—	4	4	no	—
672	D₄	—	4	2	no	—
673	D₄	—	8	4	no	—
674	D₄	—	8	4	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	8	2	no	—
689	C₂×C₄	—	8	1	no	—
690	C₂×C₄	—	8	4	no	—
691	C₂×C₄	—	8	4	no	—
692	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
693	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
695	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
696	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
697	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
698	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
699	C₈	—	2	2	no	—
700	C₈	—	2	4	no	—
701	C₈	—	2	2	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	4	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	4	no	—
706	C₂²	—	2	4	no	—
707	C₂²	—	2	1	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	8	4	no	—
712	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	4	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	2	no	—
725	C₄	C₆₁×#577	1	2	yes	—
726	C₄	C₆₁×#585	1	2	yes	—
727	C₂	—	4	1	no	—
728	C₂	—	4	4	no	—
729	C₂	—	8	2	no	—
730	C₂	C₆₁×#3485	1	1	yes	characteristic
731	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
732	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3506	C₂
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×#3550	C₂	semidirect
3. C₆₁×#3353	C₂	semidirect
4. C₆₁×#3350	C₂	semidirect
5. C₆₁×#3340	C₂	semidirect
6. C₆₁×#3329	C₂	semidirect
7. C₆₁×#3320	C₂	semidirect
8. C₆₁×#3298	C₂	semidirect
9. C₆₁×#3237	C₂	semidirect
10. C₆₁×#3231	C₂	semidirect
11. C₆₁×#3200	C₂	semidirect
12. C₆₁×#3110	C₂	semidirect
13. C₆₁×#3101	C₂	semidirect
14. C₆₁×#3097	C₂	semidirect
15. C₆₁×#2981	C₂	semidirect
21. C₆₁×#556	C₂²	semidirect
22. C₆₁×#556	C₂²	semidirect
26. D₄×Q₈×C₆₁	C₂²	semidirect
27. D₄×Q₈×C₆₁	C₂²	semidirect
41. C₆₁×#501	C₂²	semidirect
42. C₆₁×#500	C₂²	semidirect
43. C₆₁×#498	C₂²	semidirect
44. C₆₁×#491	C₂²	semidirect
45. C₆₁×#487	C₂²	semidirect
46. C₆₁×#487	C₂²	semidirect
49. C₆₁×#485	C₂²	semidirect
50. C₆₁×#485	C₂²	semidirect
52. C₆₁×#484	C₂²	semidirect
54. C₆₁×#483	C₂²	semidirect
57. C₆₁×#479	C₂²	semidirect
58. C₆₁×#477	C₂²	semidirect
60. C₆₁×#475	C₂²	semidirect
75. C₆₁×#436	C₂²	semidirect
76. C₆₁×#435	C₂²	semidirect
77. C₈×D₄×C₆₁	C₂²	semidirect
80. C₆₁×#428	C₂²	semidirect
81. C₆₁×#427	C₂²	semidirect
82. C₆₁×#419	C₂²	semidirect
83. C₂×#103×C₆₁	C₂²	semidirect
335. #61803	C₆₁	direct (N × H)
361. #3550	C₂×C₆₁	semidirect
363. #3353	C₂×C₆₁	semidirect
364. #3350	C₂×C₆₁	semidirect
365. #3340	C₂×C₆₁	semidirect
366. #3329	C₂×C₆₁	semidirect
367. #3320	C₂×C₆₁	semidirect
368. #3298	C₂×C₆₁	semidirect
369. #3237	C₂×C₆₁	semidirect
370. #3231	C₂×C₆₁	semidirect
371. #3200	C₂×C₆₁	semidirect
372. #3110	C₂×C₆₁	semidirect
373. #3101	C₂×C₆₁	semidirect
374. #3097	C₂×C₆₁	semidirect
375. #2981	C₂×C₆₁	semidirect
387. #556	C₂²×C₆₁	semidirect
388. #556	C₂²×C₆₁	semidirect
392. D₄×Q₈	C₂²×C₆₁	semidirect
393. D₄×Q₈	C₂²×C₆₁	semidirect
407. #501	C₂²×C₆₁	semidirect
408. #500	C₂²×C₆₁	semidirect
409. #498	C₂²×C₆₁	semidirect
410. #491	C₂²×C₆₁	semidirect
411. #487	C₂²×C₆₁	semidirect
412. #487	C₂²×C₆₁	semidirect
415. #485	C₂²×C₆₁	semidirect
416. #485	C₂²×C₆₁	semidirect
418. #484	C₂²×C₆₁	semidirect
420. #483	C₂²×C₆₁	semidirect
423. #479	C₂²×C₆₁	semidirect
424. #477	C₂²×C₆₁	semidirect
426. #475	C₂²×C₆₁	semidirect
441. #436	C₂²×C₆₁	semidirect
442. #435	C₂²×C₆₁	semidirect
443. C₈×D₄	C₂²×C₆₁	semidirect
446. #428	C₂²×C₆₁	semidirect
447. #427	C₂²×C₆₁	semidirect
448. #419	C₂²×C₆₁	semidirect
449. C₂×#103	C₂²×C₆₁	semidirect
451. C₆₁	#61803	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×#3550	2
C₆₁×#3506	2
C₆₁×#3353	2
C₆₁×#3350	2
C₆₁×#3340	2
C₆₁×#3329	2
C₆₁×#3320	2
C₆₁×#3298	2
C₆₁×#3237	2
C₆₁×#3231	2
C₆₁×#3200	2
C₆₁×#3110	2
C₆₁×#3101	2
C₆₁×#3097	2
C₆₁×#2981	2
#61803	61

Subgroups — C61×#61803 #29565236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61803 #29565236