Subgroups — C₆₁×#25928 #29529361

Order 15616.

1034 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3038	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2641	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2027	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1998	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1995	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1883	C₂	1	4	yes	maximal, complemented
9	C₆₁×#1759	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
11	C₆₁×#557	—	2	2	no	—
12	C₆₁×#554	—	2	2	no	—
13	C₆₁×#554	—	2	4	no	—
14	C₆₁×#544	—	2	2	no	—
15	C₆₁×#544	C₂²	1	2	yes	—
16	C₆₁×#533	—	2	1	no	—
17	C₆₁×#533	C₂²	1	1	yes	characteristic
18	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×#125×C₆₁	—	2	1	no	—
20	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
21	C₆₁×#520	C₂²	1	2	yes	—
22	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#490	—	2	1	no	—
24	C₆₁×#490	—	2	1	no	—
25	C₆₁×#486	—	2	2	no	—
26	C₆₁×#460	—	2	2	no	—
27	C₆₁×#459	—	2	2	no	—
28	C₆₁×#423	C₂²	1	1	yes	characteristic
29	C₂×#104×C₆₁	C₂²	1	2	yes	—
30	C₆₁×#418	C₂²	1	2	yes	—
31	C₆₁×#418	C₂²	1	4	yes	—
32	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
33	C₆₁×#394	—	2	4	no	—
34	C₆₁×#390	C₂²	1	4	yes	—
35	C₆₁×#376	C₂²	1	1	yes	characteristic
36	C₆₁×#343	C₂²	1	4	yes	—
37	C₆₁×#339	C₂²	1	2	yes	—
38	C₆₁×#339	C₂²	1	4	yes	—
39	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₆₁	—	2	2	no	—
41	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
42	AGL(1,ℤ/8)×C₆₁	—	2	8	no	—
43	C₂×SD₁₆×C₆₁	—	2	2	no	—
44	C₂×D₈×C₆₁	—	2	2	no	—
45	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
46	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
47	C₄⋊Q₈×C₆₁	—	2	4	no	—
48	C₄⋊Q₈×C₆₁	—	2	2	no	—
49	C₄⋊Q₈×C₆₁	—	2	2	no	—
50	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
51	#127×C₆₁	—	2	2	no	—
52	#127×C₆₁	—	2	1	no	—
53	#127×C₆₁	—	2	1	no	—
54	#125×C₆₁	—	2	4	no	—
55	#125×C₆₁	—	2	4	no	—
56	#125×C₆₁	—	2	2	no	—
57	#125×C₆₁	—	2	2	no	—
58	#125×C₆₁	—	2	1	no	—
59	#125×C₆₁	—	2	1	no	—
60	#125×C₆₁	—	2	2	no	—
61	#125×C₆₁	D₄	1	1	yes	characteristic
62	#125×C₆₁	D₄	1	1	yes	characteristic
63	C₂²⋊Q₈×C₆₁	—	2	4	no	—
64	C₂²⋊Q₈×C₆₁	—	2	4	no	—
65	C₂²⋊Q₈×C₆₁	—	2	4	no	—
66	C₂²⋊Q₈×C₆₁	—	2	2	no	—
67	C₂²⋊Q₈×C₆₁	—	2	4	no	—
68	C₄×Q₈×C₆₁	—	2	4	no	—
69	C₄×Q₈×C₆₁	—	2	2	no	—
70	C₄×Q₈×C₆₁	—	2	2	no	—
71	C₄×Q₈×C₆₁	D₄	1	2	yes	—
72	C₄×D₄×C₆₁	—	2	2	no	—
73	C₄×D₄×C₆₁	—	2	2	no	—
74	C₄×D₄×C₆₁	—	2	4	no	—
75	C₄×D₄×C₆₁	D₄	1	2	yes	—
76	#117×C₆₁	—	2	2	no	—
77	#117×C₆₁	—	2	1	no	—
78	#117×C₆₁	C₂³	1	2	yes	—
79	#117×C₆₁	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
81	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
82	C₂×C₄⋊C₄×C₆₁	D₄	1	4	yes	—
83	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
85	C₂×C₄²×C₆₁	—	2	1	no	—
86	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
87	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₆₁	—	2	2	no	—
89	#104×C₆₁	—	2	4	no	—
90	#102×C₆₁	—	2	4	no	—
91	#102×C₆₁	—	2	4	no	—
92	#102×C₆₁	—	2	4	no	—
93	#97×C₆₁	—	2	1	no	—
94	C₄×C₈×C₆₁	—	2	1	no	—
95	#95×C₆₁	—	2	2	no	—
96	C₂⁴×C₆₁	—	2	2	no	—
97	#41×C₆₁	—	2	2	no	—
98	#41×C₆₁	#41	1	4	yes	—
99	C₂×Q₈×C₆₁	—	2	4	no	—
100	C₂×Q₈×C₆₁	—	2	2	no	—
101	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₆₁	—	2	1	no	—
103	C₂×D₄×C₆₁	—	2	2	no	—
104	C₂×D₄×C₆₁	—	2	2	no	—
105	C₂×D₄×C₆₁	—	2	4	no	—
106	C₂×D₄×C₆₁	—	2	4	no	—
107	C₂×D₄×C₆₁	—	4	2	no	—
108	C₂×D₄×C₆₁	—	4	2	no	—
109	C₂×D₄×C₆₁	—	8	4	no	—
110	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	—	2	1	no	—
112	C₂²×C₄×C₆₁	—	2	4	no	—
113	C₂²×C₄×C₆₁	—	2	2	no	—
114	C₂²×C₄×C₆₁	—	2	2	no	—
115	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
118	SD₁₆×C₆₁	—	4	4	no	—
119	D₈×C₆₁	—	4	4	no	—
120	M₁₆×C₆₁	—	2	2	no	—
121	M₁₆×C₆₁	—	2	4	no	—
122	M₁₆×C₆₁	—	2	2	no	—
123	C₂×C₈×C₆₁	—	2	2	no	—
124	C₂×C₈×C₆₁	—	2	2	no	—
125	C₄⋊C₄×C₆₁	—	2	4	no	—
126	C₄⋊C₄×C₆₁	—	2	4	no	—
127	C₄⋊C₄×C₆₁	—	2	4	no	—
128	C₄⋊C₄×C₆₁	—	2	4	no	—
129	C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₄⋊C₄×C₆₁	—	2	4	no	—
131	C₄⋊C₄×C₆₁	—	2	4	no	—
132	C₄⋊C₄×C₆₁	—	2	2	no	—
133	C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	2	2	no	—
135	C₄⋊C₄×C₆₁	—	2	2	no	—
136	C₄⋊C₄×C₆₁	—	2	2	no	—
137	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₆₁	—	2	4	no	—
141	C₂²⋊C₄×C₆₁	—	2	2	no	—
142	C₂²⋊C₄×C₆₁	—	2	1	no	—
143	C₂²⋊C₄×C₆₁	—	2	2	no	—
144	C₂²⋊C₄×C₆₁	—	8	8	no	—
145	C₄²×C₆₁	—	2	4	no	—
146	C₄²×C₆₁	—	2	2	no	—
147	C₄²×C₆₁	—	2	1	no	—
148	C₄²×C₆₁	—	2	2	no	—
149	C₄²×C₆₁	—	2	2	no	—
150	C₄²×C₆₁	—	2	2	no	—
151	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₆₁	C₂×D₄	1	2	yes	—
154	C₂³×C₆₁	—	2	1	no	—
155	C₂³×C₆₁	—	4	8	no	—
156	C₂³×C₆₁	—	4	2	no	—
157	C₂³×C₆₁	—	4	4	no	—
158	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₆₁	—	2	1	no	—
160	Q₈×C₆₁	—	8	2	no	—
161	Q₈×C₆₁	—	8	4	no	—
162	Q₈×C₆₁	#124	1	2	yes	—
163	D₄×C₆₁	—	2	4	no	—
164	D₄×C₆₁	—	2	1	no	—
165	D₄×C₆₁	—	4	2	no	—
166	D₄×C₆₁	—	4	2	no	—
167	D₄×C₆₁	—	4	4	no	—
168	D₄×C₆₁	—	8	4	no	—
169	D₄×C₆₁	—	8	4	no	—
170	D₄×C₆₁	#124	1	2	yes	—
171	C₂×C₄×C₆₁	—	2	1	no	—
172	C₂×C₄×C₆₁	—	2	4	no	—
173	C₂×C₄×C₆₁	—	2	2	no	—
174	C₂×C₄×C₆₁	—	2	2	no	—
175	C₂×C₄×C₆₁	—	2	4	no	—
176	C₂×C₄×C₆₁	—	2	2	no	—
177	C₂×C₄×C₆₁	—	4	2	no	—
178	C₂×C₄×C₆₁	—	4	4	no	—
179	C₂×C₄×C₆₁	—	4	4	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	8	2	no	—
182	C₂×C₄×C₆₁	—	8	4	no	—
183	C₂×C₄×C₆₁	#120	1	2	yes	—
184	C₂×C₄×C₆₁	#120	1	2	yes	—
185	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
188	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
189	C₈×C₆₁	—	4	2	no	—
190	C₈×C₆₁	—	4	2	no	—
191	#25928	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₆₁	—	2	2	no	—
193	C₂²×C₆₁	—	2	2	no	—
194	C₂²×C₆₁	—	4	2	no	—
195	C₂²×C₆₁	—	8	8	no	—
196	C₂²×C₆₁	—	8	2	no	—
197	C₂²×C₆₁	—	8	4	no	—
198	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
199	C₂²×C₆₁	#548	1	2	yes	—
200	C₄×C₆₁	—	2	2	no	—
201	C₄×C₆₁	—	2	2	no	—
202	C₄×C₆₁	—	2	2	no	—
203	C₄×C₆₁	—	4	4	no	—
204	C₄×C₆₁	—	4	2	no	—
205	C₄×C₆₁	—	4	2	no	—
206	C₄×C₆₁	—	4	2	no	—
207	C₄×C₆₁	—	8	2	no	—
208	C₄×C₆₁	C₂×#124	1	1	yes	characteristic
209	C₄×C₆₁	#536	1	1	yes	characteristic
210	C₄×C₆₁	#548	1	2	yes	—
211	#3504	C₂×C₆₁	1	1	yes	characteristic, complemented
212	#3138	C₂×C₆₁	1	1	yes	characteristic, complemented
213	#3038	C₂×C₆₁	1	1	yes	characteristic
214	#2641	C₂×C₆₁	1	1	yes	characteristic, complemented
215	#2027	C₂×C₆₁	1	4	yes	complemented
216	#1998	C₂×C₆₁	1	1	yes	characteristic, complemented
217	#1995	C₂×C₆₁	1	1	yes	characteristic, complemented
218	#1883	C₂×C₆₁	1	4	yes	complemented
219	#1759	C₂×C₆₁	1	1	yes	characteristic, complemented
220	C₂×C₆₁	—	2	2	no	—
221	C₂×C₆₁	—	4	2	no	—
222	C₂×C₆₁	—	16	2	no	—
223	C₂×C₆₁	#2436	1	1	yes	characteristic
224	C₂×C₆₁	#3021	1	2	yes	—
225	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
226	#557	—	2	2	no	—
227	#554	—	2	2	no	—
228	#554	—	2	4	no	—
229	#544	—	2	2	no	—
230	#544	C₂²×C₆₁	1	2	yes	—
231	#533	—	2	1	no	—
232	#533	C₂²×C₆₁	1	1	yes	characteristic
233	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
234	C₂×#125	—	2	1	no	—
235	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
236	#520	C₂²×C₆₁	1	2	yes	—
237	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
238	#490	—	2	1	no	—
239	#490	—	2	1	no	—
240	#486	—	2	2	no	—
241	#460	—	2	2	no	—
242	#459	—	2	2	no	—
243	#423	C₂²×C₆₁	1	1	yes	characteristic
244	C₂×#104	C₂²×C₆₁	1	2	yes	—
245	#418	C₂²×C₆₁	1	4	yes	—
246	#418	C₂²×C₆₁	1	2	yes	—
247	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
248	#394	—	2	4	no	—
249	#390	C₂²×C₆₁	1	4	yes	—
250	#376	C₂²×C₆₁	1	1	yes	characteristic
251	#343	C₂²×C₆₁	1	4	yes	—
252	#339	C₂²×C₆₁	1	4	yes	—
253	#339	C₂²×C₆₁	1	2	yes	—
254	C₆₁	#25928	1	1	yes	characteristic, direct product factor, Sylow
255	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
256	C₂²×D₄	—	2	2	no	—
257	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
258	AGL(1,ℤ/8)	—	2	8	no	—
259	C₂×SD₁₆	—	2	2	no	—
260	C₂×D₈	—	2	2	no	—
261	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
262	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
263	C₄⋊Q₈	—	2	4	no	—
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
267	#127	—	2	2	no	—
268	#127	—	2	1	no	—
269	#127	—	2	1	no	—
270	#125	—	2	4	no	—
271	#125	—	2	4	no	—
272	#125	—	2	2	no	—
273	#125	—	2	2	no	—
274	#125	—	2	1	no	—
275	#125	—	2	1	no	—
276	#125	—	2	2	no	—
277	#125	D₄×C₆₁	1	1	yes	characteristic
278	#125	D₄×C₆₁	1	1	yes	characteristic
279	C₂²⋊Q₈	—	2	4	no	—
280	C₂²⋊Q₈	—	2	4	no	—
281	C₂²⋊Q₈	—	2	4	no	—
282	C₂²⋊Q₈	—	2	2	no	—
283	C₂²⋊Q₈	—	2	4	no	—
284	C₄×Q₈	—	2	4	no	—
285	C₄×Q₈	—	2	2	no	—
286	C₄×Q₈	—	2	2	no	—
287	C₄×Q₈	D₄×C₆₁	1	2	yes	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	4	no	—
291	C₄×D₄	D₄×C₆₁	1	2	yes	—
292	#117	—	2	2	no	—
293	#117	—	2	1	no	—
294	#117	C₂³×C₆₁	1	1	yes	characteristic
295	#117	C₂³×C₆₁	1	2	yes	—
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	D₄×C₆₁	1	4	yes	—
299	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
300	C₂×C₂²⋊C₄	—	2	8	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
303	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
304	C₄⋊C₈	—	2	2	no	—
305	#104	—	2	4	no	—
306	#102	—	2	4	no	—
307	#102	—	2	4	no	—
308	#102	—	2	4	no	—
309	#97	—	2	1	no	—
310	C₄×C₈	—	2	1	no	—
311	#95	—	2	2	no	—
312	C₂⁴	—	2	2	no	—
313	#41	—	2	2	no	—
314	#41	#41×C₆₁	1	4	yes	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	8	4	no	—
326	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
332	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
333	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
334	SD₁₆	—	4	4	no	—
335	D₈	—	4	4	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	4	no	—
338	M₁₆	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
354	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
355	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	1	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	8	8	no	—
361	C₄²	—	2	4	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
368	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
369	C₄²	C₂×D₄×C₆₁	1	2	yes	—
370	C₂³	—	2	1	no	—
371	C₂³	—	4	8	no	—
372	C₂³	—	4	4	no	—
373	C₂³	—	4	2	no	—
374	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
375	Q₈	—	2	1	no	—
376	Q₈	—	8	2	no	—
377	Q₈	—	8	4	no	—
378	Q₈	#124×C₆₁	1	2	yes	—
379	D₄	—	2	4	no	—
380	D₄	—	2	1	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	4	no	—
383	D₄	—	4	2	no	—
384	D₄	—	8	4	no	—
385	D₄	—	8	4	no	—
386	D₄	#124×C₆₁	1	2	yes	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	—	8	4	no	—
399	C₂×C₄	#120×C₆₁	1	2	yes	—
400	C₂×C₄	#120×C₆₁	1	2	yes	—
401	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
402	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
403	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
404	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
405	C₈	—	4	2	no	—
406	C₈	—	4	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	8	8	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	4	no	—
413	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
414	C₂²	C₆₁×#548	1	2	yes	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	4	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	8	2	no	—
423	C₄	C₂×#124×C₆₁	1	1	yes	characteristic
424	C₄	C₆₁×#536	1	1	yes	characteristic
425	C₄	C₆₁×#548	1	2	yes	—
426	C₂	—	2	2	no	—
427	C₂	—	4	2	no	—
428	C₂	—	16	2	no	—
429	C₂	C₆₁×#2436	1	1	yes	characteristic
430	C₂	C₆₁×#3021	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#3038	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3504	C₂	semidirect
2. C₆₁×#3138	C₂	semidirect
4. C₆₁×#2641	C₂	semidirect
5. C₆₁×#2027	C₂	semidirect
6. C₆₁×#1998	C₂	semidirect
7. C₆₁×#1995	C₂	semidirect
8. C₆₁×#1883	C₂	semidirect
9. C₆₁×#1759	C₂	semidirect
191. #25928	C₆₁	direct (N × H)
211. #3504	C₂×C₆₁	semidirect
212. #3138	C₂×C₆₁	semidirect
214. #2641	C₂×C₆₁	semidirect
215. #2027	C₂×C₆₁	semidirect
216. #1998	C₂×C₆₁	semidirect
217. #1995	C₂×C₆₁	semidirect
218. #1883	C₂×C₆₁	semidirect
219. #1759	C₂×C₆₁	semidirect
254. C₆₁	#25928	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×#3504	2
C₆₁×#3138	2
C₆₁×#3038	2
C₆₁×#2641	2
C₆₁×#2027	2
C₆₁×#1998	2
C₆₁×#1995	2
C₆₁×#1883	2
C₆₁×#1759	2
#25928	61

Subgroups — C61×#25928 #29529361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25928 #29529361