Subgroups — C₆₁×#61942 #29565375

Order 15616.

1762 conjugacy classes of subgroups.

The subgroup lattice has 624 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×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3399	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3397	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3376	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3370	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3221	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3220	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3213	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3126	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3122	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3115	C₂	1	2	yes	maximal, complemented
13	C₆₁×#2987	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#562	—	2	2	no	—
15	C₆₁×#559	C₂²	1	4	yes	—
16	C₆₁×#556	C₂²	1	4	yes	—
17	C₆₁×#554	C₂²	1	4	yes	complemented
18	C₆₁×#551	—	2	4	no	—
19	C₆₁×#550	C₂²	1	4	yes	complemented
20	C₆₁×#547	—	2	2	no	—
21	C₆₁×#542	—	2	2	no	—
22	C₆₁×#540	C₂²	1	2	yes	—
23	C₆₁×#540	C₂²	1	2	yes	—
24	C₆₁×#537	—	2	4	no	—
25	C₆₁×#536	C₂²	1	1	yes	characteristic
26	C₆₁×#535	C₂²	1	1	yes	characteristic
27	C₆₁×#533	C₂²	1	1	yes	characteristic
28	C₆₁×#532	C₂²	1	2	yes	—
29	C₆₁×#529	—	2	2	no	—
30	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#519	C₂²	1	1	yes	characteristic
32	C₆₁×#518	C₂²	1	1	yes	characteristic
33	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#496	C₂²	1	2	yes	—
35	C₆₁×#496	C₂²	1	4	yes	—
36	C₆₁×#496	C₂²	1	2	yes	complemented
37	C₆₁×#493	C₂²	1	2	yes	—
38	C₆₁×#492	C₂²	1	2	yes	complemented
39	C₆₁×#491	C₂²	1	2	yes	complemented
40	C₆₁×#490	C₂²	1	2	yes	—
41	C₆₁×#489	C₂²	1	4	yes	—
42	C₆₁×#488	C₂²	1	2	yes	—
43	C₆₁×#488	C₂²	1	2	yes	complemented
44	C₆₁×#482	C₂²	1	4	yes	—
45	C₆₁×#479	C₂²	1	4	yes	complemented
46	C₆₁×#478	C₂²	1	4	yes	—
47	C₆₁×#475	C₂²	1	2	yes	complemented
48	C₆₁×#474	C₂²	1	2	yes	complemented
49	C₆₁×#463	C₂²	1	4	yes	—
50	C₆₁×#463	C₂²	1	4	yes	—
51	C₆₁×#463	C₂²	1	4	yes	—
52	C₆₁×#463	C₂²	1	4	yes	complemented
53	C₆₁×#461	C₂²	1	4	yes	complemented
54	C₆₁×#460	C₂²	1	2	yes	complemented
55	C₆₁×#460	C₂²	1	4	yes	complemented
56	C₆₁×#459	C₂²	1	4	yes	—
57	C₆₁×#459	C₂²	1	4	yes	—
58	C₆₁×#459	C₂²	1	2	yes	complemented
59	C₆₁×#449	C₂²	1	4	yes	—
60	C₆₁×#448	C₂²	1	4	yes	—
61	C₆₁×#447	C₂²	1	4	yes	—
62	C₆₁×#446	C₂²	1	4	yes	complemented
63	C₆₁×#446	C₂²	1	4	yes	complemented
64	C₆₁×#442	C₂²	1	4	yes	—
65	C₆₁×#442	C₂²	1	4	yes	complemented
66	C₆₁×#440	C₂²	1	4	yes	complemented
67	C₆₁×#440	C₂²	1	4	yes	complemented
68	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	complemented
69	C₄×D₈×C₆₁	C₂²	1	4	yes	—
70	C₆₁×#433	C₂²	1	2	yes	—
71	C₆₁×#433	C₂²	1	2	yes	—
72	C₆₁×#432	C₂²	1	2	yes	—
73	C₂×#41×C₆₁	—	2	4	no	—
74	C₂×#41×C₆₁	—	2	2	no	—
75	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
78	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
79	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
80	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
81	C₂×D₈×C₆₁	C₂³	1	4	yes	—
82	C₂×D₈×C₆₁	C₂³	1	4	yes	—
83	C₂×D₈×C₆₁	C₂³	1	4	yes	—
84	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
85	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
86	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
87	#127×C₆₁	C₂³	1	2	yes	—
88	#127×C₆₁	C₂³	1	2	yes	—
89	#127×C₆₁	C₂³	1	2	yes	—
90	#127×C₆₁	C₂³	1	2	yes	—
91	#126×C₆₁	—	2	4	no	—
92	#126×C₆₁	—	2	4	no	—
93	#125×C₆₁	D₄	1	2	yes	—
94	#125×C₆₁	C₂³	1	2	yes	—
95	#125×C₆₁	C₂³	1	2	yes	—
96	#124×C₆₁	—	2	4	no	—
97	#124×C₆₁	—	2	2	no	—
98	#124×C₆₁	—	2	1	no	—
99	#124×C₆₁	—	2	1	no	—
100	#124×C₆₁	C₂³	1	2	yes	—
101	#124×C₆₁	C₂³	1	2	yes	—
102	#124×C₆₁	C₂³	1	4	yes	—
103	#123×C₆₁	—	2	4	no	—
104	#123×C₆₁	—	2	4	no	—
105	#123×C₆₁	—	2	4	no	—
106	#123×C₆₁	—	2	4	no	—
107	#123×C₆₁	—	2	2	no	—
108	C₂²⋊Q₈×C₆₁	—	2	4	no	—
109	C₂²⋊Q₈×C₆₁	—	2	4	no	—
110	C₂²⋊Q₈×C₆₁	—	2	2	no	—
111	C₂²⋊Q₈×C₆₁	—	2	4	no	—
112	C₂²⋊Q₈×C₆₁	—	2	4	no	—
113	C₂²⋊Q₈×C₆₁	D₄	1	4	yes	—
114	#121×C₆₁	—	2	2	no	—
115	#121×C₆₁	—	2	2	no	—
116	#121×C₆₁	—	2	4	no	—
117	#121×C₆₁	—	2	4	no	—
118	#121×C₆₁	—	2	4	no	—
119	#121×C₆₁	—	2	4	no	—
120	#121×C₆₁	—	2	4	no	—
121	#121×C₆₁	C₂³	1	4	yes	—
122	#120×C₆₁	—	2	2	no	—
123	C₄×Q₈×C₆₁	—	2	2	no	—
124	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
125	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
126	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
127	C₄×D₄×C₆₁	—	2	2	no	—
128	C₄×D₄×C₆₁	—	2	2	no	—
129	C₄×D₄×C₆₁	—	2	4	no	—
130	C₄×D₄×C₆₁	—	2	2	no	—
131	C₄×D₄×C₆₁	C₂³	1	4	yes	—
132	C₄×D₄×C₆₁	C₂³	1	4	yes	—
133	C₄×D₄×C₆₁	C₂³	1	4	yes	—
134	C₄×D₄×C₆₁	C₂³	1	4	yes	—
135	C₄×D₄×C₆₁	C₂³	1	2	yes	—
136	#117×C₆₁	—	2	4	no	—
137	#117×C₆₁	—	2	2	no	—
138	#117×C₆₁	—	2	1	no	—
139	#117×C₆₁	C₂³	1	1	yes	characteristic
140	#117×C₆₁	C₂³	1	1	yes	characteristic
141	#117×C₆₁	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
143	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
144	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
145	C₂×C₄²×C₆₁	—	2	1	no	—
146	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
147	#107×C₆₁	C₂³	1	4	yes	—
148	#106×C₆₁	C₂³	1	4	yes	—
149	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
150	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
151	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
152	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
153	#103×C₆₁	C₂³	1	4	yes	—
154	#103×C₆₁	C₂³	1	4	yes	—
155	#103×C₆₁	C₂³	1	4	yes	—
156	#102×C₆₁	C₂³	1	4	yes	—
157	#102×C₆₁	C₂³	1	4	yes	—
158	#102×C₆₁	C₂³	1	4	yes	—
159	#102×C₆₁	C₂³	1	4	yes	—
160	#102×C₆₁	C₂³	1	4	yes	—
161	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
162	#97×C₆₁	C₂³	1	4	yes	—
163	#97×C₆₁	C₂³	1	2	yes	—
164	#97×C₆₁	C₂³	1	2	yes	—
165	C₄×C₈×C₆₁	C₂³	1	2	yes	—
166	C₄×C₈×C₆₁	C₂³	1	2	yes	—
167	C₂⁴×C₆₁	—	2	1	no	—
168	#41×C₆₁	—	4	2	no	—
169	#41×C₆₁	—	8	4	no	—
170	#41×C₆₁	—	8	8	no	—
171	C₂×Q₈×C₆₁	—	2	1	no	—
172	C₂×Q₈×C₆₁	—	2	2	no	—
173	C₂×Q₈×C₆₁	—	4	2	no	—
174	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
175	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
176	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
177	C₂×D₄×C₆₁	—	2	1	no	—
178	C₂×D₄×C₆₁	—	2	4	no	—
179	C₂×D₄×C₆₁	—	2	1	no	—
180	C₂×D₄×C₆₁	—	2	2	no	—
181	C₂×D₄×C₆₁	—	2	4	no	—
182	C₂×D₄×C₆₁	—	2	4	no	—
183	C₂×D₄×C₆₁	—	2	4	no	—
184	C₂×D₄×C₆₁	—	2	2	no	—
185	C₂×D₄×C₆₁	—	4	2	no	—
186	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
187	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
188	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₆₁	—	2	1	no	—
190	C₂²×C₄×C₆₁	—	2	1	no	—
191	C₂²×C₄×C₆₁	—	2	4	no	—
192	C₂²×C₄×C₆₁	—	2	2	no	—
193	C₂²×C₄×C₆₁	—	2	4	no	—
194	C₂²×C₄×C₆₁	—	2	4	no	—
195	C₂²×C₄×C₆₁	—	2	4	no	—
196	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
198	SD₁₆×C₆₁	—	4	4	no	—
199	SD₁₆×C₆₁	—	4	4	no	—
200	SD₁₆×C₆₁	—	4	4	no	—
201	D₈×C₆₁	—	4	4	no	—
202	D₈×C₆₁	—	4	4	no	—
203	D₈×C₆₁	—	4	4	no	—
204	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
205	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
206	C₄⋊C₄×C₆₁	—	2	2	no	—
207	C₄⋊C₄×C₆₁	—	2	4	no	—
208	C₄⋊C₄×C₆₁	—	2	4	no	—
209	C₄⋊C₄×C₆₁	—	2	2	no	—
210	C₄⋊C₄×C₆₁	—	2	4	no	—
211	C₄⋊C₄×C₆₁	—	2	4	no	—
212	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
213	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
214	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
215	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
216	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
217	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
218	C₄⋊C₄×C₆₁	C₂⁴	1	4	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	4	no	—
223	C₂²⋊C₄×C₆₁	—	2	2	no	—
224	C₂²⋊C₄×C₆₁	—	2	4	no	—
225	C₂²⋊C₄×C₆₁	—	2	4	no	—
226	C₂²⋊C₄×C₆₁	—	2	4	no	—
227	C₂²⋊C₄×C₆₁	—	2	4	no	—
228	C₂²⋊C₄×C₆₁	—	2	4	no	—
229	C₂²⋊C₄×C₆₁	—	2	4	no	—
230	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
231	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
232	C₄²×C₆₁	—	2	2	no	—
233	C₄²×C₆₁	—	2	1	no	—
234	C₄²×C₆₁	—	2	4	no	—
235	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
237	C₄²×C₆₁	C₂⁴	1	2	yes	—
238	C₄²×C₆₁	C₂⁴	1	2	yes	—
239	C₄²×C₆₁	C₂⁴	1	2	yes	—
240	C₂³×C₆₁	—	2	2	no	—
241	C₂³×C₆₁	—	2	1	no	—
242	C₂³×C₆₁	—	2	4	no	—
243	C₂³×C₆₁	—	4	2	no	—
244	C₂³×C₆₁	—	8	2	no	—
245	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
246	Q₈×C₆₁	—	2	4	no	—
247	Q₈×C₆₁	—	2	2	no	—
248	Q₈×C₆₁	—	4	4	no	—
249	Q₈×C₆₁	—	4	2	no	—
250	Q₈×C₆₁	—	8	2	no	—
251	D₄×C₆₁	—	2	4	no	—
252	D₄×C₆₁	—	2	4	no	—
253	D₄×C₆₁	—	2	2	no	—
254	D₄×C₆₁	—	2	4	no	—
255	D₄×C₆₁	—	4	2	no	—
256	D₄×C₆₁	—	4	4	no	—
257	D₄×C₆₁	—	4	2	no	—
258	D₄×C₆₁	—	8	4	no	—
259	D₄×C₆₁	—	8	2	no	—
260	D₄×C₆₁	—	8	4	no	—
261	D₄×C₆₁	—	8	4	no	—
262	D₄×C₆₁	—	8	4	no	—
263	C₂×C₄×C₆₁	—	2	2	no	—
264	C₂×C₄×C₆₁	—	2	2	no	—
265	C₂×C₄×C₆₁	—	2	2	no	—
266	C₂×C₄×C₆₁	—	2	1	no	—
267	C₂×C₄×C₆₁	—	2	4	no	—
268	C₂×C₄×C₆₁	—	4	2	no	—
269	C₂×C₄×C₆₁	—	4	2	no	—
270	C₂×C₄×C₆₁	—	4	8	no	—
271	C₂×C₄×C₆₁	—	4	2	no	—
272	C₂×C₄×C₆₁	—	8	2	no	—
273	C₂×C₄×C₆₁	—	8	4	no	—
274	C₂×C₄×C₆₁	—	8	4	no	—
275	C₂×C₄×C₆₁	—	8	4	no	—
276	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
279	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
281	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
282	C₈×C₆₁	—	2	4	no	—
283	C₈×C₆₁	—	2	4	no	—
284	#61942	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₂²×C₆₁	—	2	2	no	—
286	C₂²×C₆₁	—	2	1	no	—
287	C₂²×C₆₁	—	4	4	no	—
288	C₂²×C₆₁	—	4	4	no	—
289	C₂²×C₆₁	—	4	2	no	—
290	C₂²×C₆₁	—	4	4	no	—
291	C₂²×C₆₁	—	4	1	no	—
292	C₂²×C₆₁	—	4	2	no	—
293	C₂²×C₆₁	—	4	4	no	—
294	C₂²×C₆₁	—	16	2	no	—
295	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
296	C₄×C₆₁	—	2	2	no	—
297	C₄×C₆₁	—	2	2	no	—
298	C₄×C₆₁	—	2	4	no	—
299	C₄×C₆₁	—	2	4	no	—
300	C₄×C₆₁	—	2	1	no	—
301	C₄×C₆₁	—	4	4	no	—
302	C₄×C₆₁	—	4	2	no	—
303	C₄×C₆₁	—	4	1	no	—
304	C₄×C₆₁	—	4	2	no	—
305	C₄×C₆₁	#585	1	2	yes	—
306	#3548	C₂×C₆₁	1	1	yes	characteristic, complemented
307	#3510	C₂×C₆₁	1	1	yes	characteristic, complemented
308	#3399	C₂×C₆₁	1	4	yes	complemented
309	#3397	C₂×C₆₁	1	4	yes	complemented
310	#3376	C₂×C₆₁	1	4	yes	complemented
311	#3370	C₂×C₆₁	1	4	yes	complemented
312	#3221	C₂×C₆₁	1	2	yes	complemented
313	#3220	C₂×C₆₁	1	2	yes	complemented
314	#3213	C₂×C₆₁	1	2	yes	complemented
315	#3126	C₂×C₆₁	1	2	yes	complemented
316	#3122	C₂×C₆₁	1	2	yes	complemented
317	#3115	C₂×C₆₁	1	2	yes	complemented
318	#2987	C₂×C₆₁	1	1	yes	characteristic, complemented
319	C₂×C₆₁	—	4	1	no	—
320	C₂×C₆₁	—	8	4	no	—
321	C₂×C₆₁	—	8	1	no	—
322	C₂×C₆₁	—	8	2	no	—
323	C₂×C₆₁	#3487	1	1	yes	characteristic
324	C₂×C₆₁	#3585	1	2	yes	—
325	#562	—	2	2	no	—
326	#559	C₂²×C₆₁	1	4	yes	—
327	#556	C₂²×C₆₁	1	4	yes	—
328	#554	C₂²×C₆₁	1	4	yes	complemented
329	#551	—	2	4	no	—
330	#550	C₂²×C₆₁	1	4	yes	complemented
331	#547	—	2	2	no	—
332	#542	—	2	2	no	—
333	#540	C₂²×C₆₁	1	2	yes	—
334	#540	C₂²×C₆₁	1	2	yes	—
335	#537	—	2	4	no	—
336	#536	C₂²×C₆₁	1	1	yes	characteristic
337	#535	C₂²×C₆₁	1	1	yes	characteristic
338	#533	C₂²×C₆₁	1	1	yes	characteristic
339	#532	C₂²×C₆₁	1	2	yes	—
340	#529	—	2	2	no	—
341	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
342	#519	C₂²×C₆₁	1	1	yes	characteristic
343	#518	C₂²×C₆₁	1	1	yes	characteristic
344	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
345	#496	C₂²×C₆₁	1	2	yes	—
346	#496	C₂²×C₆₁	1	4	yes	—
347	#496	C₂²×C₆₁	1	2	yes	complemented
348	#493	C₂²×C₆₁	1	2	yes	—
349	#492	C₂²×C₆₁	1	2	yes	complemented
350	#491	C₂²×C₆₁	1	2	yes	complemented
351	#490	C₂²×C₆₁	1	2	yes	—
352	#489	C₂²×C₆₁	1	4	yes	—
353	#488	C₂²×C₆₁	1	2	yes	—
354	#488	C₂²×C₆₁	1	2	yes	complemented
355	#482	C₂²×C₆₁	1	4	yes	—
356	#479	C₂²×C₆₁	1	4	yes	complemented
357	#478	C₂²×C₆₁	1	4	yes	—
358	#475	C₂²×C₆₁	1	2	yes	complemented
359	#474	C₂²×C₆₁	1	2	yes	complemented
360	#463	C₂²×C₆₁	1	4	yes	—
361	#463	C₂²×C₆₁	1	4	yes	—
362	#463	C₂²×C₆₁	1	4	yes	—
363	#463	C₂²×C₆₁	1	4	yes	complemented
364	#461	C₂²×C₆₁	1	4	yes	complemented
365	#460	C₂²×C₆₁	1	2	yes	complemented
366	#460	C₂²×C₆₁	1	4	yes	complemented
367	#459	C₂²×C₆₁	1	4	yes	—
368	#459	C₂²×C₆₁	1	4	yes	—
369	#459	C₂²×C₆₁	1	2	yes	complemented
370	#449	C₂²×C₆₁	1	4	yes	—
371	#448	C₂²×C₆₁	1	4	yes	—
372	#447	C₂²×C₆₁	1	4	yes	—
373	#446	C₂²×C₆₁	1	4	yes	complemented
374	#446	C₂²×C₆₁	1	4	yes	complemented
375	#442	C₂²×C₆₁	1	4	yes	—
376	#442	C₂²×C₆₁	1	4	yes	complemented
377	#440	C₂²×C₆₁	1	4	yes	complemented
378	#440	C₂²×C₆₁	1	4	yes	complemented
379	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	complemented
380	C₄×D₈	C₂²×C₆₁	1	4	yes	—
381	#433	C₂²×C₆₁	1	2	yes	—
382	#433	C₂²×C₆₁	1	2	yes	—
383	#432	C₂²×C₆₁	1	2	yes	—
384	C₆₁	#61942	1	1	yes	characteristic, direct product factor, Sylow
385	C₂×#41	—	2	4	no	—
386	C₂×#41	—	2	2	no	—
387	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
388	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
389	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
390	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
391	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
392	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
393	C₂×D₈	C₂³×C₆₁	1	4	yes	—
394	C₂×D₈	C₂³×C₆₁	1	4	yes	—
395	C₂×D₈	C₂³×C₆₁	1	4	yes	—
396	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
397	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
398	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
399	#127	C₂³×C₆₁	1	2	yes	—
400	#127	C₂³×C₆₁	1	2	yes	—
401	#127	C₂³×C₆₁	1	2	yes	—
402	#127	C₂³×C₆₁	1	2	yes	—
403	#126	—	2	4	no	—
404	#126	—	2	4	no	—
405	#125	D₄×C₆₁	1	2	yes	—
406	#125	C₂³×C₆₁	1	2	yes	—
407	#125	C₂³×C₆₁	1	2	yes	—
408	#124	—	2	4	no	—
409	#124	—	2	1	no	—
410	#124	—	2	1	no	—
411	#124	—	2	2	no	—
412	#124	C₂³×C₆₁	1	4	yes	—
413	#124	C₂³×C₆₁	1	2	yes	—
414	#124	C₂³×C₆₁	1	2	yes	—
415	#123	—	2	4	no	—
416	#123	—	2	4	no	—
417	#123	—	2	4	no	—
418	#123	—	2	4	no	—
419	#123	—	2	2	no	—
420	C₂²⋊Q₈	—	2	4	no	—
421	C₂²⋊Q₈	—	2	4	no	—
422	C₂²⋊Q₈	—	2	2	no	—
423	C₂²⋊Q₈	—	2	4	no	—
424	C₂²⋊Q₈	—	2	4	no	—
425	C₂²⋊Q₈	D₄×C₆₁	1	4	yes	—
426	#121	—	2	2	no	—
427	#121	—	2	2	no	—
428	#121	—	2	4	no	—
429	#121	—	2	4	no	—
430	#121	—	2	4	no	—
431	#121	—	2	4	no	—
432	#121	—	2	4	no	—
433	#121	C₂³×C₆₁	1	4	yes	—
434	#120	—	2	2	no	—
435	C₄×Q₈	—	2	2	no	—
436	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
437	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
438	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
439	C₄×D₄	—	2	2	no	—
440	C₄×D₄	—	2	2	no	—
441	C₄×D₄	—	2	4	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	C₂³×C₆₁	1	2	yes	—
444	C₄×D₄	C₂³×C₆₁	1	4	yes	—
445	C₄×D₄	C₂³×C₆₁	1	4	yes	—
446	C₄×D₄	C₂³×C₆₁	1	4	yes	—
447	C₄×D₄	C₂³×C₆₁	1	4	yes	—
448	#117	—	2	4	no	—
449	#117	—	2	2	no	—
450	#117	—	2	1	no	—
451	#117	C₂³×C₆₁	1	1	yes	characteristic
452	#117	C₂³×C₆₁	1	1	yes	characteristic
453	#117	C₂³×C₆₁	1	1	yes	characteristic
454	C₂×C₄⋊C₄	—	2	4	no	—
455	C₂×C₂²⋊C₄	—	2	2	no	—
456	C₂×C₂²⋊C₄	—	2	2	no	—
457	C₂×C₄²	—	2	1	no	—
458	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
459	#107	C₂³×C₆₁	1	4	yes	—
460	#106	C₂³×C₆₁	1	4	yes	—
461	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
462	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
463	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
464	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
465	#103	C₂³×C₆₁	1	4	yes	—
466	#103	C₂³×C₆₁	1	4	yes	—
467	#103	C₂³×C₆₁	1	4	yes	—
468	#102	C₂³×C₆₁	1	4	yes	—
469	#102	C₂³×C₆₁	1	4	yes	—
470	#102	C₂³×C₆₁	1	4	yes	—
471	#102	C₂³×C₆₁	1	4	yes	—
472	#102	C₂³×C₆₁	1	4	yes	—
473	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
474	#97	C₂³×C₆₁	1	4	yes	—
475	#97	C₂³×C₆₁	1	2	yes	—
476	#97	C₂³×C₆₁	1	2	yes	—
477	C₄×C₈	C₂³×C₆₁	1	2	yes	—
478	C₄×C₈	C₂³×C₆₁	1	2	yes	—
479	C₂⁴	—	2	1	no	—
480	#41	—	4	2	no	—
481	#41	—	8	4	no	—
482	#41	—	8	8	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	2	no	—
485	C₂×Q₈	—	4	2	no	—
486	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
487	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
488	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	4	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	4	no	—
494	C₂×D₄	—	2	4	no	—
495	C₂×D₄	—	2	4	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	—	4	2	no	—
498	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
499	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
500	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	4	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
510	SD₁₆	—	4	4	no	—
511	SD₁₆	—	4	4	no	—
512	SD₁₆	—	4	4	no	—
513	D₈	—	4	4	no	—
514	D₈	—	4	4	no	—
515	D₈	—	4	4	no	—
516	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
517	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
525	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
526	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
527	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
528	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
529	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
530	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	4	no	—
537	C₂²⋊C₄	—	2	4	no	—
538	C₂²⋊C₄	—	2	4	no	—
539	C₂²⋊C₄	—	2	4	no	—
540	C₂²⋊C₄	—	2	4	no	—
541	C₂²⋊C₄	—	2	4	no	—
542	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
543	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
544	C₄²	—	2	2	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	4	no	—
547	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
548	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
549	C₄²	C₂⁴×C₆₁	1	2	yes	—
550	C₄²	C₂⁴×C₆₁	1	2	yes	—
551	C₄²	C₂⁴×C₆₁	1	2	yes	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	4	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	8	2	no	—
557	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
558	Q₈	—	2	4	no	—
559	Q₈	—	2	2	no	—
560	Q₈	—	4	4	no	—
561	Q₈	—	4	2	no	—
562	Q₈	—	8	2	no	—
563	D₄	—	2	4	no	—
564	D₄	—	2	4	no	—
565	D₄	—	2	2	no	—
566	D₄	—	2	4	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	4	no	—
569	D₄	—	4	2	no	—
570	D₄	—	8	4	no	—
571	D₄	—	8	2	no	—
572	D₄	—	8	4	no	—
573	D₄	—	8	4	no	—
574	D₄	—	8	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	8	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	8	2	no	—
585	C₂×C₄	—	8	4	no	—
586	C₂×C₄	—	8	4	no	—
587	C₂×C₄	—	8	4	no	—
588	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
589	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
590	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
591	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
592	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
593	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
594	C₈	—	2	4	no	—
595	C₈	—	2	4	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	16	2	no	—
606	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	4	no	—
610	C₄	—	2	4	no	—
611	C₄	—	2	1	no	—
612	C₄	—	4	4	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	2	no	—
616	C₄	C₆₁×#585	1	2	yes	—
617	C₂	—	4	1	no	—
618	C₂	—	8	2	no	—
619	C₂	—	8	4	no	—
620	C₂	—	8	1	no	—
621	C₂	C₆₁×#3487	1	1	yes	characteristic
622	C₂	C₆₁×#3585	1	2	yes	—

	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3548	C₂	semidirect
2. C₆₁×#3510	C₂	semidirect
3. C₆₁×#3399	C₂	semidirect
4. C₆₁×#3397	C₂	semidirect
5. C₆₁×#3376	C₂	semidirect
6. C₆₁×#3370	C₂	semidirect
7. C₆₁×#3221	C₂	semidirect
8. C₆₁×#3220	C₂	semidirect
9. C₆₁×#3213	C₂	semidirect
10. C₆₁×#3126	C₂	semidirect
11. C₆₁×#3122	C₂	semidirect
12. C₆₁×#3115	C₂	semidirect
13. C₆₁×#2987	C₂	semidirect
17. C₆₁×#554	C₂²	semidirect
19. C₆₁×#550	C₂²	semidirect
36. C₆₁×#496	C₂²	semidirect
38. C₆₁×#492	C₂²	semidirect
39. C₆₁×#491	C₂²	semidirect
43. C₆₁×#488	C₂²	semidirect
45. C₆₁×#479	C₂²	semidirect
47. C₆₁×#475	C₂²	semidirect
48. C₆₁×#474	C₂²	semidirect
52. C₆₁×#463	C₂²	semidirect
53. C₆₁×#461	C₂²	semidirect
54. C₆₁×#460	C₂²	semidirect
55. C₆₁×#460	C₂²	semidirect
58. C₆₁×#459	C₂²	semidirect
62. C₆₁×#446	C₂²	semidirect
63. C₆₁×#446	C₂²	semidirect
65. C₆₁×#442	C₂²	semidirect
66. C₆₁×#440	C₂²	semidirect
67. C₆₁×#440	C₂²	semidirect
68. C₄×SD₁₆×C₆₁	C₂²	semidirect
284. #61942	C₆₁	direct (N × H)
306. #3548	C₂×C₆₁	semidirect
307. #3510	C₂×C₆₁	semidirect
308. #3399	C₂×C₆₁	semidirect
309. #3397	C₂×C₆₁	semidirect
310. #3376	C₂×C₆₁	semidirect
311. #3370	C₂×C₆₁	semidirect
312. #3221	C₂×C₆₁	semidirect
313. #3220	C₂×C₆₁	semidirect
314. #3213	C₂×C₆₁	semidirect
315. #3126	C₂×C₆₁	semidirect
316. #3122	C₂×C₆₁	semidirect
317. #3115	C₂×C₆₁	semidirect
318. #2987	C₂×C₆₁	semidirect
328. #554	C₂²×C₆₁	semidirect
330. #550	C₂²×C₆₁	semidirect
347. #496	C₂²×C₆₁	semidirect
349. #492	C₂²×C₆₁	semidirect
350. #491	C₂²×C₆₁	semidirect
354. #488	C₂²×C₆₁	semidirect
356. #479	C₂²×C₆₁	semidirect
358. #475	C₂²×C₆₁	semidirect
359. #474	C₂²×C₆₁	semidirect
363. #463	C₂²×C₆₁	semidirect
364. #461	C₂²×C₆₁	semidirect
365. #460	C₂²×C₆₁	semidirect
366. #460	C₂²×C₆₁	semidirect
369. #459	C₂²×C₆₁	semidirect
373. #446	C₂²×C₆₁	semidirect
374. #446	C₂²×C₆₁	semidirect
376. #442	C₂²×C₆₁	semidirect
377. #440	C₂²×C₆₁	semidirect
378. #440	C₂²×C₆₁	semidirect
379. C₄×SD₁₆	C₂²×C₆₁	semidirect
384. C₆₁	#61942	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×#3510	2
C₆₁×#3399	2
C₆₁×#3397	2
C₆₁×#3376	2
C₆₁×#3370	2
C₆₁×#3221	2
C₆₁×#3220	2
C₆₁×#3213	2
C₆₁×#3126	2
C₆₁×#3122	2
C₆₁×#3115	2
C₆₁×#2987	2
#61942	61

Subgroups — C61×#61942 #29565375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61942 #29565375