Subgroups — C₆₁×#60718 #29564151

Order 15616.

1942 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3511	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3182	C₂	1	4	yes	maximal, complemented
3	C₆₁×#3175	C₂	1	8	yes	maximal, complemented
4	C₆₁×#3170	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3169	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3141	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3061	C₂	1	4	yes	maximal, complemented
10	C₆₁×#2951	C₂	1	4	yes	maximal, complemented
11	C₄×#131×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₆₁	C₂²	1	4	yes	—
13	C₂×#131×C₆₁	C₂²	1	2	yes	—
14	C₆₁×#556	—	2	2	no	—
15	C₆₁×#555	—	2	2	no	—
16	C₆₁×#554	—	2	2	no	—
17	C₆₁×#553	—	2	4	no	—
18	C₆₁×#548	—	2	4	no	—
19	C₆₁×#547	—	2	2	no	—
20	C₆₁×#542	C₂²	1	8	yes	—
21	C₆₁×#537	C₂²	1	4	yes	—
22	C₆₁×#533	C₂²	1	4	yes	—
23	C₆₁×#532	C₂²	1	2	yes	—
24	C₆₁×#532	C₂²	1	4	yes	—
25	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
26	C₆₁×#520	C₂²	1	4	yes	—
27	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#500	C₂²	1	2	yes	—
29	C₆₁×#500	C₂²	1	4	yes	—
30	C₆₁×#500	C₂²	1	2	yes	—
31	C₆₁×#495	C₂²	1	4	yes	—
32	C₆₁×#494	C₂²	1	1	yes	characteristic
33	C₆₁×#493	C₂²	1	1	yes	characteristic
34	C₆₁×#492	C₂²	1	2	yes	—
35	C₆₁×#489	C₂²	1	8	yes	—
36	C₆₁×#487	C₂²	1	4	yes	—
37	C₆₁×#486	C₂²	1	4	yes	—
38	C₆₁×#468	C₂²	1	16	yes	—
39	C₆₁×#467	C₂²	1	8	yes	—
40	C₆₁×#466	C₂²	1	8	yes	—
41	C₆₁×#440	C₂²	1	16	yes	—
42	C₄×Q₁₆×C₆₁	C₂²	1	8	yes	—
43	C₄×D₈×C₆₁	C₂²	1	8	yes	—
44	C₂×#107×C₆₁	C₂²	1	4	yes	—
45	C₆₁×#417	C₂²	1	8	yes	—
46	C₆₁×#405	C₂²	1	4	yes	—
47	C₆₁×#405	C₂²	1	2	yes	—
48	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
49	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
50	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
52	C₂×#41×C₆₁	—	2	4	no	—
53	C₂×#41×C₆₁	C₂³	1	4	yes	—
54	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₆₁	—	2	2	no	—
56	#135×C₆₁	—	2	16	no	—
57	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
58	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
59	C₂×D₈×C₆₁	C₂³	1	4	yes	—
60	#131×C₆₁	—	2	8	no	—
61	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
62	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
63	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
64	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
65	C₄⋊Q₈×C₆₁	—	2	2	no	—
66	C₄⋊Q₈×C₆₁	—	2	2	no	—
67	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
69	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
70	#127×C₆₁	C₂³	1	2	yes	—
71	#126×C₆₁	—	2	8	no	—
72	#125×C₆₁	—	2	4	no	—
73	#124×C₆₁	—	2	8	no	—
74	#124×C₆₁	—	2	4	no	—
75	#124×C₆₁	C₂³	1	4	yes	—
76	#123×C₆₁	—	2	8	no	—
77	C₂²⋊Q₈×C₆₁	—	2	4	no	—
78	C₂²⋊Q₈×C₆₁	—	2	4	no	—
79	C₂²⋊Q₈×C₆₁	—	2	8	no	—
80	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
81	#121×C₆₁	—	2	4	no	—
82	#121×C₆₁	—	2	8	no	—
83	#121×C₆₁	—	2	2	no	—
84	#121×C₆₁	—	2	2	no	—
85	#121×C₆₁	—	2	4	no	—
86	#121×C₆₁	C₂³	1	8	yes	—
87	C₄×Q₈×C₆₁	—	2	4	no	—
88	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
89	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
91	C₄×D₄×C₆₁	—	2	8	no	—
92	C₄×D₄×C₆₁	—	2	2	no	—
93	C₄×D₄×C₆₁	—	2	4	no	—
94	C₄×D₄×C₆₁	—	2	2	no	—
95	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
96	C₄×D₄×C₆₁	D₄	1	2	yes	—
97	C₄×D₄×C₆₁	D₄	1	2	yes	—
98	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
99	C₄×D₄×C₆₁	C₂³	1	8	yes	—
100	#117×C₆₁	—	2	4	no	—
101	#117×C₆₁	—	2	4	no	—
102	#117×C₆₁	C₂³	1	2	yes	—
103	#117×C₆₁	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
105	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
106	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
107	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
109	#107×C₆₁	C₂³	1	8	yes	—
110	#107×C₆₁	C₂³	1	8	yes	—
111	#103×C₆₁	C₂³	1	16	yes	—
112	#102×C₆₁	C₂³	1	16	yes	—
113	#97×C₆₁	C₂³	1	4	yes	—
114	#97×C₆₁	C₂³	1	2	yes	—
115	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
116	C₄×C₈×C₆₁	C₂³	1	2	yes	—
117	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
118	C₄×C₈×C₆₁	C₂³	1	4	yes	—
119	C₄×C₈×C₆₁	C₂³	1	2	yes	—
120	#41×C₆₁	—	2	4	no	—
121	#41×C₆₁	—	2	16	no	—
122	#41×C₆₁	—	8	8	no	—
123	C₂×Q₈×C₆₁	—	2	4	no	—
124	C₂×Q₈×C₆₁	—	2	4	no	—
125	C₂×Q₈×C₆₁	—	8	4	no	—
126	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
127	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
128	C₂×D₄×C₆₁	—	2	4	no	—
129	C₂×D₄×C₆₁	—	2	8	no	—
130	C₂×D₄×C₆₁	—	2	2	no	—
131	C₂×D₄×C₆₁	—	2	2	no	—
132	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
133	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
134	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₆₁	—	2	4	no	—
136	C₂²×C₄×C₆₁	—	2	4	no	—
137	C₂²×C₄×C₆₁	—	2	8	no	—
138	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
144	Q₁₆×C₆₁	—	2	8	no	—
145	SD₁₆×C₆₁	—	2	16	no	—
146	D₈×C₆₁	—	2	8	no	—
147	M₁₆×C₆₁	—	2	4	no	—
148	M₁₆×C₆₁	—	2	8	no	—
149	C₂×C₈×C₆₁	—	2	8	no	—
150	C₂×C₈×C₆₁	#41	1	8	yes	complemented
151	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
152	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
153	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
154	C₄⋊C₄×C₆₁	—	2	4	no	—
155	C₄⋊C₄×C₆₁	—	2	4	no	—
156	C₄⋊C₄×C₆₁	—	2	8	no	—
157	C₄⋊C₄×C₆₁	—	2	4	no	—
158	C₄⋊C₄×C₆₁	—	2	2	no	—
159	C₄⋊C₄×C₆₁	—	2	2	no	—
160	C₄⋊C₄×C₆₁	—	2	8	no	—
161	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
162	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
163	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
165	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
166	C₂²⋊C₄×C₆₁	—	2	8	no	—
167	C₂²⋊C₄×C₆₁	—	2	8	no	—
168	C₂²⋊C₄×C₆₁	—	2	8	no	—
169	C₂²⋊C₄×C₆₁	—	2	4	no	—
170	C₂²⋊C₄×C₆₁	—	2	4	no	—
171	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
172	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
173	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
174	C₄²×C₆₁	—	2	8	no	—
175	C₄²×C₆₁	C₂×D₄	1	2	yes	—
176	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₆₁	C₂×D₄	1	2	yes	—
179	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
180	C₄²×C₆₁	C₂⁴	1	2	yes	—
181	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
182	C₂³×C₆₁	—	2	4	no	—
183	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
184	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
185	Q₈×C₆₁	—	2	2	no	—
186	Q₈×C₆₁	—	2	8	no	—
187	Q₈×C₆₁	—	4	8	no	—
188	Q₈×C₆₁	—	8	4	no	—
189	D₄×C₆₁	—	2	4	no	—
190	D₄×C₆₁	—	2	2	no	—
191	D₄×C₆₁	—	2	8	no	—
192	D₄×C₆₁	—	4	8	no	—
193	D₄×C₆₁	—	4	4	no	—
194	D₄×C₆₁	—	4	4	no	—
195	D₄×C₆₁	—	8	8	no	—
196	C₂×C₄×C₆₁	—	2	2	no	—
197	C₂×C₄×C₆₁	—	2	4	no	—
198	C₂×C₄×C₆₁	—	2	2	no	—
199	C₂×C₄×C₆₁	—	2	4	no	—
200	C₂×C₄×C₆₁	—	2	4	no	—
201	C₂×C₄×C₆₁	—	2	4	no	—
202	C₂×C₄×C₆₁	—	2	8	no	—
203	C₂×C₄×C₆₁	—	4	8	no	—
204	C₂×C₄×C₆₁	—	8	8	no	—
205	C₂×C₄×C₆₁	—	8	4	no	—
206	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
208	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
215	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
216	C₈×C₆₁	—	2	4	no	—
217	C₈×C₆₁	C₂×#41	1	4	yes	—
218	C₈×C₆₁	C₂×#41	1	4	yes	—
219	#60718	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂²×C₆₁	—	2	1	no	—
221	C₂²×C₆₁	—	2	1	no	—
222	C₂²×C₆₁	—	2	2	no	—
223	C₂²×C₆₁	—	2	2	no	—
224	C₂²×C₆₁	—	2	2	no	—
225	C₂²×C₆₁	—	4	4	no	—
226	C₂²×C₆₁	—	4	4	no	—
227	C₂²×C₆₁	—	4	4	no	—
228	C₂²×C₆₁	#532	1	2	yes	—
229	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
230	C₄×C₆₁	—	2	2	no	—
231	C₄×C₆₁	—	2	2	no	—
232	C₄×C₆₁	—	2	1	no	—
233	C₄×C₆₁	—	2	2	no	—
234	C₄×C₆₁	—	2	1	no	—
235	C₄×C₆₁	—	4	4	no	—
236	C₄×C₆₁	—	4	8	no	—
237	C₄×C₆₁	#532	1	2	yes	—
238	C₄×C₆₁	#576	1	2	yes	—
239	C₄×C₆₁	#578	1	2	yes	—
240	C₄×C₆₁	C₂²×#41	1	2	yes	—
241	#3511	C₂×C₆₁	1	2	yes	complemented
242	#3182	C₂×C₆₁	1	4	yes	complemented
243	#3175	C₂×C₆₁	1	8	yes	complemented
244	#3170	C₂×C₆₁	1	2	yes	complemented
245	#3169	C₂×C₆₁	1	2	yes	complemented
246	C₂×#500	C₂×C₆₁	1	1	yes	characteristic, complemented
247	#3147	C₂×C₆₁	1	1	yes	characteristic, complemented
248	#3141	C₂×C₆₁	1	2	yes	complemented
249	#3061	C₂×C₆₁	1	4	yes	complemented
250	#2951	C₂×C₆₁	1	4	yes	complemented
251	C₄×#131	C₂×C₆₁	1	1	yes	characteristic, complemented
252	C₂×C₆₁	—	2	2	no	—
253	C₂×C₆₁	—	4	2	no	—
254	C₂×C₆₁	—	8	4	no	—
255	C₂×C₆₁	C₂×#532	1	1	yes	characteristic
256	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
257	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
258	C₂×#135	C₂²×C₆₁	1	4	yes	—
259	C₂×#131	C₂²×C₆₁	1	2	yes	—
260	#556	—	2	2	no	—
261	#555	—	2	2	no	—
262	#554	—	2	2	no	—
263	#553	—	2	4	no	—
264	#548	—	2	4	no	—
265	#547	—	2	2	no	—
266	#542	C₂²×C₆₁	1	8	yes	—
267	#537	C₂²×C₆₁	1	4	yes	—
268	#533	C₂²×C₆₁	1	4	yes	—
269	#532	C₂²×C₆₁	1	2	yes	—
270	#532	C₂²×C₆₁	1	4	yes	—
271	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
272	#520	C₂²×C₆₁	1	4	yes	—
273	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
274	#500	C₂²×C₆₁	1	2	yes	—
275	#500	C₂²×C₆₁	1	4	yes	—
276	#500	C₂²×C₆₁	1	2	yes	—
277	#495	C₂²×C₆₁	1	4	yes	—
278	#494	C₂²×C₆₁	1	1	yes	characteristic
279	#493	C₂²×C₆₁	1	1	yes	characteristic
280	#492	C₂²×C₆₁	1	2	yes	—
281	#489	C₂²×C₆₁	1	8	yes	—
282	#487	C₂²×C₆₁	1	4	yes	—
283	#486	C₂²×C₆₁	1	4	yes	—
284	#468	C₂²×C₆₁	1	16	yes	—
285	#467	C₂²×C₆₁	1	8	yes	—
286	#466	C₂²×C₆₁	1	8	yes	—
287	#440	C₂²×C₆₁	1	16	yes	—
288	C₄×Q₁₆	C₂²×C₆₁	1	8	yes	—
289	C₄×D₈	C₂²×C₆₁	1	8	yes	—
290	C₂×#107	C₂²×C₆₁	1	4	yes	—
291	#417	C₂²×C₆₁	1	8	yes	—
292	#405	C₂²×C₆₁	1	4	yes	—
293	#405	C₂²×C₆₁	1	2	yes	—
294	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
295	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
296	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
297	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
298	C₆₁	#60718	1	1	yes	characteristic, direct product factor, Sylow
299	C₂×#41	—	2	4	no	—
300	C₂×#41	C₂³×C₆₁	1	4	yes	—
301	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
302	C₂²×Q₈	—	2	2	no	—
303	#135	—	2	16	no	—
304	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
305	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
306	C₂×D₈	C₂³×C₆₁	1	4	yes	—
307	#131	—	2	8	no	—
308	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
309	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
310	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
311	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
312	C₄⋊Q₈	—	2	2	no	—
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
315	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
316	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
317	#127	C₂³×C₆₁	1	2	yes	—
318	#126	—	2	8	no	—
319	#125	—	2	4	no	—
320	#124	—	2	8	no	—
321	#124	—	2	4	no	—
322	#124	C₂³×C₆₁	1	4	yes	—
323	#123	—	2	8	no	—
324	C₂²⋊Q₈	—	2	4	no	—
325	C₂²⋊Q₈	—	2	4	no	—
326	C₂²⋊Q₈	—	2	8	no	—
327	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
328	#121	—	2	4	no	—
329	#121	—	2	8	no	—
330	#121	—	2	2	no	—
331	#121	—	2	2	no	—
332	#121	—	2	4	no	—
333	#121	C₂³×C₆₁	1	8	yes	—
334	C₄×Q₈	—	2	4	no	—
335	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
336	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
337	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
338	C₄×D₄	—	2	8	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	—	2	4	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
343	C₄×D₄	D₄×C₆₁	1	2	yes	—
344	C₄×D₄	D₄×C₆₁	1	2	yes	—
345	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
346	C₄×D₄	C₂³×C₆₁	1	8	yes	—
347	#117	—	2	4	no	—
348	#117	—	2	4	no	—
349	#117	C₂³×C₆₁	1	1	yes	characteristic
350	#117	C₂³×C₆₁	1	2	yes	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	4	no	—
353	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
354	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
356	#107	C₂³×C₆₁	1	8	yes	—
357	#107	C₂³×C₆₁	1	8	yes	—
358	#103	C₂³×C₆₁	1	16	yes	—
359	#102	C₂³×C₆₁	1	16	yes	—
360	#97	C₂³×C₆₁	1	4	yes	—
361	#97	C₂³×C₆₁	1	2	yes	—
362	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
363	C₄×C₈	C₂³×C₆₁	1	2	yes	—
364	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
365	C₄×C₈	C₂³×C₆₁	1	4	yes	—
366	C₄×C₈	C₂³×C₆₁	1	2	yes	—
367	#41	—	2	4	no	—
368	#41	—	2	16	no	—
369	#41	—	8	8	no	—
370	C₂×Q₈	—	2	4	no	—
371	C₂×Q₈	—	2	4	no	—
372	C₂×Q₈	—	8	4	no	—
373	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
374	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	8	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
380	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
381	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
389	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
390	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
391	Q₁₆	—	2	8	no	—
392	SD₁₆	—	2	16	no	—
393	D₈	—	2	8	no	—
394	M₁₆	—	2	4	no	—
395	M₁₆	—	2	8	no	—
396	C₂×C₈	—	2	8	no	—
397	C₂×C₈	#41×C₆₁	1	8	yes	complemented
398	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
399	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
400	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	8	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
409	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
410	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
411	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
412	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	2	8	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
419	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
420	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
421	C₄²	—	2	8	no	—
422	C₄²	C₂×D₄×C₆₁	1	2	yes	—
423	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
424	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
425	C₄²	C₂×D₄×C₆₁	1	2	yes	—
426	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
427	C₄²	C₂⁴×C₆₁	1	2	yes	—
428	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
429	C₂³	—	2	4	no	—
430	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
431	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
432	Q₈	—	2	2	no	—
433	Q₈	—	2	8	no	—
434	Q₈	—	4	8	no	—
435	Q₈	—	8	4	no	—
436	D₄	—	2	4	no	—
437	D₄	—	2	2	no	—
438	D₄	—	2	8	no	—
439	D₄	—	4	8	no	—
440	D₄	—	4	4	no	—
441	D₄	—	4	4	no	—
442	D₄	—	8	8	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	4	8	no	—
451	C₂×C₄	—	8	8	no	—
452	C₂×C₄	—	8	4	no	—
453	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
454	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
455	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
456	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
458	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
461	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
462	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
463	C₈	—	2	4	no	—
464	C₈	C₂×#41×C₆₁	1	4	yes	—
465	C₈	C₂×#41×C₆₁	1	4	yes	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	4	4	no	—
474	C₂²	C₆₁×#532	1	2	yes	—
475	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	2	no	—
481	C₄	—	4	8	no	—
482	C₄	—	4	4	no	—
483	C₄	C₆₁×#532	1	2	yes	—
484	C₄	C₆₁×#576	1	2	yes	—
485	C₄	C₆₁×#578	1	2	yes	—
486	C₄	C₂²×#41×C₆₁	1	2	yes	—
487	C₂	—	2	2	no	—
488	C₂	—	4	2	no	—
489	C₂	—	8	4	no	—
490	C₂	C₂×C₆₁×#532	1	1	yes	characteristic
491	C₂	C₂×C₆₁×#576	1	1	yes	characteristic
492	C₂	C₂×C₆₁×#578	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3511	C₂	semidirect
2. C₆₁×#3182	C₂	semidirect
3. C₆₁×#3175	C₂	semidirect
4. C₆₁×#3170	C₂	semidirect
5. C₆₁×#3169	C₂	semidirect
6. C₂×C₆₁×#500	C₂	semidirect
7. C₆₁×#3147	C₂	semidirect
8. C₆₁×#3141	C₂	semidirect
9. C₆₁×#3061	C₂	semidirect
10. C₆₁×#2951	C₂	semidirect
11. C₄×#131×C₆₁	C₂	semidirect
150. C₂×C₈×C₆₁	#41	semidirect
219. #60718	C₆₁	direct (N × H)
241. #3511	C₂×C₆₁	semidirect
242. #3182	C₂×C₆₁	semidirect
243. #3175	C₂×C₆₁	semidirect
244. #3170	C₂×C₆₁	semidirect
245. #3169	C₂×C₆₁	semidirect
246. C₂×#500	C₂×C₆₁	semidirect
247. #3147	C₂×C₆₁	semidirect
248. #3141	C₂×C₆₁	semidirect
249. #3061	C₂×C₆₁	semidirect
250. #2951	C₂×C₆₁	semidirect
251. C₄×#131	C₂×C₆₁	semidirect
298. C₆₁	#60718	direct (N × H)
397. C₂×C₈	#41×C₆₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₁×#3511	2
C₆₁×#3182	2
C₆₁×#3175	2
C₆₁×#3170	2
C₆₁×#3169	2
C₂×C₆₁×#500	2
C₆₁×#3147	2
C₆₁×#3141	2
C₆₁×#3061	2
C₆₁×#2951	2
C₄×#131×C₆₁	2
#60718	61

Subgroups — C61×#60718 #29564151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60718 #29564151