Subgroups — C₆₁×#17613 #29521046

Order 15616.

1350 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3496	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2972	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2349	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1519	C₂	1	4	yes	maximal, complemented
5	C₆₁×#1517	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1502	C₂	1	2	yes	maximal, complemented
7	C₂×C₆₁×#327	C₂	1	4	yes	maximal, complemented
8	C₂×H(5,𝔽₂)×C₆₁	—	2	1	no	—
9	C₆₁×#547	C₄	1	4	yes	complemented
10	C₆₁×#546	—	2	4	no	—
11	D₄²×C₆₁	C₄	1	4	yes	complemented
12	C₆₁×#537	—	2	1	no	—
13	C₆₁×#534	—	2	2	no	—
14	C₆₁×#532	C₂²	1	2	yes	—
15	C₂×#121×C₆₁	C₂²	1	4	yes	—
16	C₂×C₄×D₄×C₆₁	—	2	1	no	—
17	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
18	C₈×D₄×C₆₁	—	2	4	no	—
19	C₆₁×#431	C₂²	1	2	yes	complemented
20	C₂×C₂²⋊C₈×C₆₁	C₂²	1	4	yes	complemented
21	C₆₁×#389	—	2	1	no	—
22	C₆₁×#385	—	2	2	no	—
23	C₆₁×#382	C₂²	1	1	yes	characteristic, complemented
24	C₆₁×#380	C₂²	1	2	yes	complemented
25	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
26	C₂×#95×C₆₁	C₂²	1	2	yes	complemented
27	C₆₁×#327	C₂²	1	4	yes	complemented
28	C₆₁×#327	C₂²	1	8	yes	complemented
29	C₆₁×#327	C₂²	1	4	yes	complemented
30	H(5,𝔽₂)×C₆₁	—	4	4	no	—
31	H(5,𝔽₂)×C₆₁	—	4	4	no	—
32	C₂×#41×C₆₁	—	2	4	no	—
33	C₂×#41×C₆₁	—	2	2	no	—
34	C₂²×D₄×C₆₁	—	2	4	no	—
35	C₂²×D₄×C₆₁	—	2	4	no	—
36	C₂²×D₄×C₆₁	C₂×C₄	1	4	yes	complemented
37	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₆₁	—	2	2	no	—
39	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₆₁	—	2	4	no	—
41	C₄⋊Q₈×C₆₁	C₂×C₄	1	2	yes	complemented
42	#127×C₆₁	C₂×C₄	1	2	yes	complemented
43	#124×C₆₁	—	2	2	no	—
44	#123×C₆₁	—	2	8	no	—
45	C₂²⋊Q₈×C₆₁	—	2	4	no	—
46	#121×C₆₁	—	2	2	no	—
47	#121×C₆₁	—	2	4	no	—
48	#121×C₆₁	—	2	4	no	—
49	#121×C₆₁	—	2	4	no	—
50	#121×C₆₁	C₂×C₄	1	8	yes	complemented
51	#121×C₆₁	C₂³	1	4	yes	—
52	#120×C₆₁	—	2	8	no	—
53	C₄×D₄×C₆₁	—	2	2	no	—
54	C₄×D₄×C₆₁	—	4	4	no	—
55	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	—
56	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	complemented
57	C₄×D₄×C₆₁	D₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	complemented
62	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
66	C₂×C₄²×C₆₁	—	2	1	no	—
67	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₆₁	—	2	2	no	—
69	C₂²⋊C₈×C₆₁	—	2	4	no	—
70	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
71	C₄×C₈×C₆₁	—	2	2	no	—
72	#95×C₆₁	—	2	2	no	—
73	#95×C₆₁	—	2	1	no	—
74	#95×C₆₁	C₂³	1	1	yes	characteristic
75	#95×C₆₁	C₂³	1	2	yes	—
76	#95×C₆₁	C₂³	1	1	yes	characteristic
77	C₂⁴×C₆₁	—	2	4	no	—
78	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
79	#41×C₆₁	—	4	16	no	—
80	#41×C₆₁	—	4	4	no	—
81	#41×C₆₁	—	4	4	no	—
82	C₂×Q₈×C₆₁	—	2	2	no	—
83	C₂×D₄×C₆₁	—	2	8	no	—
84	C₂×D₄×C₆₁	—	2	4	no	—
85	C₂×D₄×C₆₁	—	2	2	no	—
86	C₂×D₄×C₆₁	—	2	2	no	—
87	C₂×D₄×C₆₁	—	2	4	no	—
88	C₂×D₄×C₆₁	—	4	8	no	—
89	C₂×D₄×C₆₁	—	4	8	no	—
90	C₂×D₄×C₆₁	—	4	16	no	—
91	C₂×D₄×C₆₁	—	8	4	no	—
92	C₂×D₄×C₆₁	C₂²⋊C₄	1	4	yes	—
93	C₂×D₄×C₆₁	D₈	1	4	yes	—
94	C₂×D₄×C₆₁	SD₁₆	1	4	yes	—
95	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₆₁	—	2	4	no	—
97	C₂²×C₄×C₆₁	—	2	1	no	—
98	C₂²×C₄×C₆₁	—	2	4	no	—
99	C₂²×C₄×C₆₁	—	2	2	no	—
100	C₂²×C₄×C₆₁	—	2	1	no	—
101	C₂²×C₄×C₆₁	—	4	4	no	—
102	C₂²×C₄×C₆₁	—	4	4	no	—
103	C₂²×C₄×C₆₁	—	8	2	no	—
104	C₂²×C₄×C₆₁	—	8	2	no	—
105	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
111	C₂×C₈×C₆₁	—	2	4	no	—
112	C₂×C₈×C₆₁	—	8	4	no	—
113	C₄⋊C₄×C₆₁	—	2	4	no	—
114	C₄⋊C₄×C₆₁	—	2	2	no	—
115	C₄⋊C₄×C₆₁	—	4	2	no	—
116	C₄⋊C₄×C₆₁	—	4	2	no	—
117	C₄⋊C₄×C₆₁	—	8	2	no	—
118	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
119	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
120	C₂²⋊C₄×C₆₁	—	2	8	no	—
121	C₂²⋊C₄×C₆₁	—	2	4	no	—
122	C₂²⋊C₄×C₆₁	—	2	4	no	—
123	C₂²⋊C₄×C₆₁	—	4	4	no	—
124	C₂²⋊C₄×C₆₁	C₂²⋊C₄	1	8	yes	—
125	C₄²×C₆₁	—	4	2	no	—
126	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
127	C₄²×C₆₁	C₂×D₄	1	2	yes	—
128	C₂³×C₆₁	—	2	4	no	—
129	C₂³×C₆₁	—	4	2	no	—
130	C₂³×C₆₁	—	4	2	no	—
131	C₂³×C₆₁	—	4	8	no	—
132	C₂³×C₆₁	—	8	4	no	—
133	C₂³×C₆₁	—	8	4	no	—
134	C₂³×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
135	C₂³×C₆₁	C₂×D₈	1	4	yes	—
136	C₂³×C₆₁	C₂×SD₁₆	1	4	yes	—
137	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
138	Q₈×C₆₁	—	4	4	no	—
139	D₄×C₆₁	—	4	4	no	—
140	D₄×C₆₁	—	4	4	no	—
141	D₄×C₆₁	—	4	4	no	—
142	D₄×C₆₁	—	4	16	no	—
143	D₄×C₆₁	—	4	4	no	—
144	D₄×C₆₁	—	8	2	no	—
145	D₄×C₆₁	—	8	4	no	—
146	D₄×C₆₁	#102	1	16	yes	—
147	C₂×C₄×C₆₁	—	2	2	no	—
148	C₂×C₄×C₆₁	—	2	4	no	—
149	C₂×C₄×C₆₁	—	4	1	no	—
150	C₂×C₄×C₆₁	—	4	2	no	—
151	C₂×C₄×C₆₁	—	4	4	no	—
152	C₂×C₄×C₆₁	—	4	1	no	—
153	C₂×C₄×C₆₁	—	4	4	no	—
154	C₂×C₄×C₆₁	—	4	1	no	—
155	C₂×C₄×C₆₁	—	4	1	no	—
156	C₂×C₄×C₆₁	—	4	8	no	—
157	C₂×C₄×C₆₁	—	4	8	no	—
158	C₂×C₄×C₆₁	—	4	1	no	—
159	C₂×C₄×C₆₁	—	4	1	no	—
160	C₂×C₄×C₆₁	—	4	2	no	—
161	C₂×C₄×C₆₁	—	4	2	no	—
162	C₂×C₄×C₆₁	—	4	1	no	—
163	C₂×C₄×C₆₁	—	4	2	no	—
164	C₂×C₄×C₆₁	—	8	8	no	—
165	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
167	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₆₁	C₂×D₈	1	2	yes	—
169	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
170	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
172	C₈×C₆₁	—	4	4	no	—
173	#17613	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₆₁	—	2	1	no	—
175	C₂²×C₆₁	—	2	4	no	—
176	C₂²×C₆₁	—	2	1	no	—
177	C₂²×C₆₁	—	2	4	no	—
178	C₂²×C₆₁	—	4	4	no	—
179	C₂²×C₆₁	—	4	4	no	—
180	C₂²×C₆₁	—	4	4	no	—
181	C₂²×C₆₁	—	4	4	no	—
182	C₂²×C₆₁	—	4	4	no	—
183	C₂²×C₆₁	—	16	8	no	—
184	C₂²×C₆₁	C₂×#102	1	8	yes	—
185	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×C₆₁	C₂²×D₈	1	1	yes	characteristic
187	C₂²×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
188	C₄×C₆₁	—	2	1	no	—
189	C₄×C₆₁	—	2	1	no	—
190	C₄×C₆₁	—	2	4	no	—
191	C₄×C₆₁	—	2	2	no	—
192	C₄×C₆₁	—	4	2	no	—
193	C₄×C₆₁	—	4	4	no	—
194	C₄×C₆₁	—	8	1	no	—
195	C₄×C₆₁	—	8	2	no	—
196	C₄×C₆₁	C₂×#102	1	4	yes	—
197	#3496	C₂×C₆₁	1	1	yes	characteristic
198	#2972	C₂×C₆₁	1	1	yes	characteristic, complemented
199	#2349	C₂×C₆₁	1	1	yes	characteristic, complemented
200	#1519	C₂×C₆₁	1	4	yes	complemented
201	#1517	C₂×C₆₁	1	2	yes	complemented
202	#1502	C₂×C₆₁	1	2	yes	complemented
203	C₂×#327	C₂×C₆₁	1	4	yes	complemented
204	C₂×C₆₁	—	2	1	no	—
205	C₂×C₆₁	—	2	1	no	—
206	C₂×C₆₁	—	2	8	no	—
207	C₂×C₆₁	—	8	4	no	—
208	C₂×C₆₁	#2883	1	1	yes	characteristic
209	C₂×C₆₁	C₂²×#102	1	1	yes	characteristic
210	C₂×C₆₁	#2901	1	1	yes	characteristic
211	C₂×H(5,𝔽₂)	—	2	1	no	—
212	#547	C₄×C₆₁	1	4	yes	complemented
213	#546	—	2	4	no	—
214	D₄²	C₄×C₆₁	1	4	yes	complemented
215	#537	—	2	1	no	—
216	#534	—	2	2	no	—
217	#532	C₂²×C₆₁	1	2	yes	—
218	C₂×#121	C₂²×C₆₁	1	4	yes	—
219	C₂×C₄×D₄	—	2	1	no	—
220	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
221	C₈×D₄	—	2	4	no	—
222	#431	C₂²×C₆₁	1	2	yes	complemented
223	C₂×C₂²⋊C₈	C₂²×C₆₁	1	4	yes	complemented
224	#389	—	2	1	no	—
225	#385	—	2	2	no	—
226	#382	C₂²×C₆₁	1	1	yes	characteristic, complemented
227	#380	C₂²×C₆₁	1	2	yes	complemented
228	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
229	C₂×#95	C₂²×C₆₁	1	2	yes	complemented
230	#327	C₂²×C₆₁	1	4	yes	complemented
231	#327	C₂²×C₆₁	1	8	yes	complemented
232	#327	C₂²×C₆₁	1	4	yes	complemented
233	C₆₁	#17613	1	1	yes	characteristic, direct product factor, Sylow
234	H(5,𝔽₂)	—	4	4	no	—
235	H(5,𝔽₂)	—	4	4	no	—
236	C₂×#41	—	2	4	no	—
237	C₂×#41	—	2	2	no	—
238	C₂²×D₄	—	2	4	no	—
239	C₂²×D₄	—	2	4	no	—
240	C₂²×D₄	C₂×C₄×C₆₁	1	4	yes	complemented
241	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
242	C₂³×C₄	—	2	2	no	—
243	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
244	C₂²×C₈	—	2	4	no	—
245	C₄⋊Q₈	C₂×C₄×C₆₁	1	2	yes	complemented
246	#127	C₂×C₄×C₆₁	1	2	yes	complemented
247	#124	—	2	2	no	—
248	#123	—	2	8	no	—
249	C₂²⋊Q₈	—	2	4	no	—
250	#121	—	2	4	no	—
251	#121	—	2	4	no	—
252	#121	—	2	2	no	—
253	#121	—	2	4	no	—
254	#121	C₂×C₄×C₆₁	1	8	yes	complemented
255	#121	C₂³×C₆₁	1	4	yes	—
256	#120	—	2	8	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	4	4	no	—
259	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	—
260	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	complemented
261	C₄×D₄	D₄×C₆₁	1	4	yes	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	4	yes	complemented
266	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	—	2	4	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
272	C₄⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	—	2	4	no	—
274	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
275	C₄×C₈	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	1	no	—
278	#95	C₂³×C₆₁	1	1	yes	characteristic
279	#95	C₂³×C₆₁	1	2	yes	—
280	#95	C₂³×C₆₁	1	1	yes	characteristic
281	C₂⁴	—	2	4	no	—
282	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
283	#41	—	4	16	no	—
284	#41	—	4	4	no	—
285	#41	—	4	4	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×D₄	—	2	8	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	4	8	no	—
293	C₂×D₄	—	4	8	no	—
294	C₂×D₄	—	4	16	no	—
295	C₂×D₄	—	8	4	no	—
296	C₂×D₄	C₂²⋊C₄×C₆₁	1	4	yes	—
297	C₂×D₄	D₈×C₆₁	1	4	yes	—
298	C₂×D₄	SD₁₆×C₆₁	1	4	yes	—
299	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	8	2	no	—
308	C₂²×C₄	—	8	2	no	—
309	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
310	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
313	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	8	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	8	2	no	—
322	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
323	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
324	C₂²⋊C₄	—	2	8	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₂²⋊C₄	C₂²⋊C₄×C₆₁	1	8	yes	—
329	C₄²	—	4	2	no	—
330	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
331	C₄²	C₂×D₄×C₆₁	1	2	yes	—
332	C₂³	—	2	4	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	8	no	—
336	C₂³	—	8	4	no	—
337	C₂³	—	8	4	no	—
338	C₂³	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
339	C₂³	C₂×D₈×C₆₁	1	4	yes	—
340	C₂³	C₂×SD₁₆×C₆₁	1	4	yes	—
341	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
342	Q₈	—	4	4	no	—
343	D₄	—	4	4	no	—
344	D₄	—	4	4	no	—
345	D₄	—	4	4	no	—
346	D₄	—	4	16	no	—
347	D₄	—	4	4	no	—
348	D₄	—	8	2	no	—
349	D₄	—	8	4	no	—
350	D₄	#102×C₆₁	1	16	yes	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	4	8	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	8	no	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
370	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
371	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
372	C₂×C₄	C₂×D₈×C₆₁	1	2	yes	—
373	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
374	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
376	C₈	—	4	4	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	16	8	no	—
387	C₂²	C₂×#102×C₆₁	1	8	yes	—
388	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
389	C₂²	C₂²×D₈×C₆₁	1	1	yes	characteristic
390	C₂²	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	4	no	—
394	C₄	—	2	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	4	no	—
397	C₄	—	8	1	no	—
398	C₄	—	8	2	no	—
399	C₄	C₂×#102×C₆₁	1	4	yes	—
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	8	no	—
403	C₂	—	8	4	no	—
404	C₂	C₆₁×#2883	1	1	yes	characteristic
405	C₂	C₂²×#102×C₆₁	1	1	yes	characteristic
406	C₂	C₆₁×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄×D₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2972	C₂	semidirect
3. C₆₁×#2349	C₂	semidirect
4. C₆₁×#1519	C₂	semidirect
5. C₆₁×#1517	C₂	semidirect
6. C₆₁×#1502	C₂	semidirect
7. C₂×C₆₁×#327	C₂	semidirect
9. C₆₁×#547	C₄	semidirect
11. D₄²×C₆₁	C₄	semidirect
19. C₆₁×#431	C₂²	semidirect
20. C₂×C₂²⋊C₈×C₆₁	C₂²	semidirect
23. C₆₁×#382	C₂²	semidirect
24. C₆₁×#380	C₂²	semidirect
25. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
26. C₂×#95×C₆₁	C₂²	semidirect
27. C₆₁×#327	C₂²	semidirect
28. C₆₁×#327	C₂²	semidirect
29. C₆₁×#327	C₂²	semidirect
36. C₂²×D₄×C₆₁	C₂×C₄	semidirect
41. C₄⋊Q₈×C₆₁	C₂×C₄	semidirect
42. #127×C₆₁	C₂×C₄	semidirect
50. #121×C₆₁	C₂×C₄	semidirect
56. C₄×D₄×C₆₁	C₂×C₄	semidirect
61. C₂×C₄⋊C₄×C₆₁	C₂×C₄	semidirect
173. #17613	C₆₁	direct (N × H)
198. #2972	C₂×C₆₁	semidirect
199. #2349	C₂×C₆₁	semidirect
200. #1519	C₂×C₆₁	semidirect
201. #1517	C₂×C₆₁	semidirect
202. #1502	C₂×C₆₁	semidirect
203. C₂×#327	C₂×C₆₁	semidirect
212. #547	C₄×C₆₁	semidirect
214. D₄²	C₄×C₆₁	semidirect
222. #431	C₂²×C₆₁	semidirect
223. C₂×C₂²⋊C₈	C₂²×C₆₁	semidirect
226. #382	C₂²×C₆₁	semidirect
227. #380	C₂²×C₆₁	semidirect
228. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
229. C₂×#95	C₂²×C₆₁	semidirect
230. #327	C₂²×C₆₁	semidirect
231. #327	C₂²×C₆₁	semidirect
232. #327	C₂²×C₆₁	semidirect
233. C₆₁	#17613	direct (N × H)
240. C₂²×D₄	C₂×C₄×C₆₁	semidirect
245. C₄⋊Q₈	C₂×C₄×C₆₁	semidirect
246. #127	C₂×C₄×C₆₁	semidirect
254. #121	C₂×C₄×C₆₁	semidirect
260. C₄×D₄	C₂×C₄×C₆₁	semidirect
265. C₂×C₄⋊C₄	C₂×C₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3496	2
C₆₁×#2972	2
C₆₁×#2349	2
C₆₁×#1519	2
C₆₁×#1517	2
C₆₁×#1502	2
C₂×C₆₁×#327	2
#17613	61

Subgroups — C61×#17613 #29521046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#17613 #29521046