Subgroups — C₆₁×#9318 #29512751

Order 15616.

580 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3038	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#1982	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1806	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1545	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1303	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1292	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×AGL(1,ℤ/8)×C₆₁	—	2	1	no	—
9	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
10	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
11	C₆₁×#460	—	2	1	no	—
12	C₆₁×#460	C₄	1	2	yes	complemented
13	C₆₁×#459	—	2	1	no	—
14	C₆₁×#459	C₄	1	2	yes	complemented
15	C₈×Q₈×C₆₁	—	2	1	no	—
16	C₈×D₄×C₆₁	—	2	2	no	—
17	C₈×D₄×C₆₁	—	2	1	no	—
18	C₆₁×#431	—	2	1	no	—
19	C₆₁×#431	C₂²	1	1	yes	characteristic
20	C₆₁×#423	C₂²	1	1	yes	characteristic
21	C₆₁×#423	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₆₁	—	2	1	no	—
23	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#104×C₆₁	—	2	1	no	—
25	C₆₁×#418	—	2	1	no	—
26	C₂×#102×C₆₁	—	2	2	no	—
27	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#339	—	2	1	no	—
29	C₆₁×#331	—	2	1	no	—
30	C₆₁×#331	—	2	1	no	—
31	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₆₁	—	2	1	no	—
33	C₂²×D₄×C₆₁	—	2	1	no	—
34	C₂²×D₄×C₆₁	—	2	1	no	—
35	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
36	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
37	C₂×SD₁₆×C₆₁	—	2	2	no	—
38	C₂×D₈×C₆₁	—	2	2	no	—
39	C₂×M₁₆×C₆₁	—	2	1	no	—
40	C₂×M₁₆×C₆₁	—	2	1	no	—
41	C₂²×C₈×C₆₁	—	2	2	no	—
42	C₂²×C₈×C₆₁	D₄	1	2	yes	—
43	#127×C₆₁	—	2	1	no	—
44	#127×C₆₁	—	2	1	no	—
45	#127×C₆₁	—	2	1	no	—
46	#127×C₆₁	C₂×C₄	1	2	yes	—
47	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
48	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
49	C₄×D₄×C₆₁	—	2	1	no	—
50	C₄×D₄×C₆₁	—	2	1	no	—
51	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
52	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
53	#117×C₆₁	—	2	1	no	—
54	#117×C₆₁	D₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
56	C₂×C₄²×C₆₁	—	2	1	no	—
57	C₂×C₄²×C₆₁	—	2	1	no	—
58	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₆₁	—	2	2	no	—
60	C₄⋊C₈×C₆₁	—	2	1	no	—
61	C₄⋊C₈×C₆₁	—	2	1	no	—
62	C₄⋊C₈×C₆₁	—	2	1	no	—
63	C₄⋊C₈×C₆₁	—	2	1	no	—
64	C₄⋊C₈×C₆₁	—	2	1	no	—
65	C₄⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
66	C₄⋊C₈×C₆₁	D₄	1	1	yes	characteristic
67	C₄⋊C₈×C₆₁	D₄	1	1	yes	characteristic
68	#104×C₆₁	—	4	2	no	—
69	#102×C₆₁	—	2	2	no	—
70	#102×C₆₁	—	2	2	no	—
71	#102×C₆₁	—	4	4	no	—
72	C₂²⋊C₈×C₆₁	—	2	2	no	—
73	C₂²⋊C₈×C₆₁	—	2	1	no	—
74	C₄×C₈×C₆₁	—	2	2	no	—
75	C₄×C₈×C₆₁	—	2	1	no	—
76	#95×C₆₁	—	2	1	no	—
77	C₂⁴×C₆₁	—	4	1	no	—
78	#41×C₆₁	—	2	1	no	—
79	#41×C₆₁	—	2	1	no	—
80	#41×C₆₁	D₈	1	2	yes	—
81	#41×C₆₁	SD₁₆	1	2	yes	—
82	C₂×Q₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×D₄×C₆₁	—	2	1	no	—
84	C₂×D₄×C₆₁	—	2	2	no	—
85	C₂×D₄×C₆₁	—	2	2	no	—
86	C₂×D₄×C₆₁	—	2	2	no	—
87	C₂×D₄×C₆₁	—	4	2	no	—
88	C₂×D₄×C₆₁	—	4	2	no	—
89	C₂×D₄×C₆₁	—	4	1	no	—
90	C₂×D₄×C₆₁	—	4	1	no	—
91	C₂×D₄×C₆₁	—	4	1	no	—
92	C₂×D₄×C₆₁	—	4	1	no	—
93	C₂×D₄×C₆₁	—	4	1	no	—
94	C₂×D₄×C₆₁	—	4	1	no	—
95	C₂×D₄×C₆₁	—	4	1	no	—
96	C₂×D₄×C₆₁	—	8	2	no	—
97	C₂×D₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₁	—	2	1	no	—
99	C₂²×C₄×C₆₁	—	2	1	no	—
100	C₂²×C₄×C₆₁	—	2	1	no	—
101	C₂²×C₄×C₆₁	—	4	1	no	—
102	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
105	SD₁₆×C₆₁	—	4	4	no	—
106	D₈×C₆₁	—	4	4	no	—
107	M₁₆×C₆₁	—	4	1	no	—
108	M₁₆×C₆₁	—	4	1	no	—
109	M₁₆×C₆₁	—	4	1	no	—
110	M₁₆×C₆₁	—	4	1	no	—
111	C₂×C₈×C₆₁	—	2	2	no	—
112	C₂×C₈×C₆₁	—	2	1	no	—
113	C₂×C₈×C₆₁	—	2	2	no	—
114	C₂×C₈×C₆₁	—	2	1	no	—
115	C₂×C₈×C₆₁	—	4	2	no	—
116	C₂×C₈×C₆₁	—	4	1	no	—
117	C₂×C₈×C₆₁	—	8	2	no	—
118	C₄⋊C₄×C₆₁	—	2	1	no	—
119	C₄⋊C₄×C₆₁	—	2	1	no	—
120	C₄⋊C₄×C₆₁	—	2	2	no	—
121	C₄⋊C₄×C₆₁	—	4	1	no	—
122	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
123	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²⋊C₄×C₆₁	—	2	1	no	—
125	C₂²⋊C₄×C₆₁	—	2	1	no	—
126	C₂²⋊C₄×C₆₁	—	2	1	no	—
127	C₄²×C₆₁	—	2	1	no	—
128	C₄²×C₆₁	—	2	1	no	—
129	C₄²×C₆₁	—	2	1	no	—
130	C₄²×C₆₁	—	4	1	no	—
131	C₄²×C₆₁	—	4	1	no	—
132	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₆₁	#41	1	1	yes	characteristic
136	C₂³×C₆₁	—	2	1	no	—
137	C₂³×C₆₁	—	4	2	no	—
138	C₂³×C₆₁	—	8	2	no	—
139	C₂³×C₆₁	—	8	2	no	—
140	C₂³×C₆₁	—	8	1	no	—
141	C₂³×C₆₁	—	8	1	no	—
142	C₂³×C₆₁	#121	1	1	yes	characteristic
143	Q₈×C₆₁	—	2	1	no	—
144	Q₈×C₆₁	#102	1	2	yes	complemented
145	D₄×C₆₁	—	2	2	no	—
146	D₄×C₆₁	—	2	2	no	—
147	D₄×C₆₁	—	2	1	no	—
148	D₄×C₆₁	—	4	4	no	—
149	D₄×C₆₁	—	4	2	no	—
150	D₄×C₆₁	—	4	2	no	—
151	D₄×C₆₁	—	8	2	no	—
152	D₄×C₆₁	—	8	2	no	—
153	D₄×C₆₁	—	8	1	no	—
154	D₄×C₆₁	—	8	1	no	—
155	D₄×C₆₁	—	8	1	no	—
156	D₄×C₆₁	—	8	1	no	—
157	D₄×C₆₁	#102	1	2	yes	complemented
158	C₂×C₄×C₆₁	—	2	1	no	—
159	C₂×C₄×C₆₁	—	2	1	no	—
160	C₂×C₄×C₆₁	—	2	1	no	—
161	C₂×C₄×C₆₁	—	2	2	no	—
162	C₂×C₄×C₆₁	—	2	2	no	—
163	C₂×C₄×C₆₁	—	2	1	no	—
164	C₂×C₄×C₆₁	—	2	1	no	—
165	C₂×C₄×C₆₁	—	4	1	no	—
166	C₂×C₄×C₆₁	—	4	1	no	—
167	C₂×C₄×C₆₁	—	4	1	no	—
168	C₂×C₄×C₆₁	—	4	2	no	—
169	C₂×C₄×C₆₁	—	8	1	no	—
170	C₂×C₄×C₆₁	—	8	1	no	—
171	C₂×C₄×C₆₁	—	8	1	no	—
172	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
176	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
177	C₂×C₄×C₆₁	#123	1	1	yes	characteristic
178	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
180	C₂×C₄×C₆₁	#135	1	1	yes	characteristic
181	C₂×C₄×C₆₁	#135	1	1	yes	characteristic
182	C₈×C₆₁	—	4	2	no	—
183	C₈×C₆₁	—	4	2	no	—
184	C₈×C₆₁	—	4	1	no	—
185	C₈×C₆₁	—	4	1	no	—
186	C₈×C₆₁	—	8	1	no	—
187	#9318	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂²×C₆₁	—	2	1	no	—
189	C₂²×C₆₁	—	2	1	no	—
190	C₂²×C₆₁	—	2	2	no	—
191	C₂²×C₆₁	—	4	1	no	—
192	C₂²×C₆₁	—	4	1	no	—
193	C₂²×C₆₁	—	8	2	no	—
194	C₂²×C₆₁	—	8	2	no	—
195	C₂²×C₆₁	—	8	2	no	—
196	C₂²×C₆₁	—	16	2	no	—
197	C₂²×C₆₁	—	16	2	no	—
198	C₂²×C₆₁	#386	1	1	yes	characteristic
199	C₂²×C₆₁	#465	1	1	yes	characteristic
200	C₂²×C₆₁	#466	1	1	yes	characteristic
201	C₄×C₆₁	—	2	1	no	—
202	C₄×C₆₁	—	2	2	no	—
203	C₄×C₆₁	—	2	1	no	—
204	C₄×C₆₁	—	2	1	no	—
205	C₄×C₆₁	—	4	1	no	—
206	C₄×C₆₁	—	4	1	no	—
207	C₄×C₆₁	—	8	2	no	—
208	C₄×C₆₁	C₂×#102	1	1	yes	characteristic
209	C₄×C₆₁	#416	1	1	yes	characteristic
210	C₄×C₆₁	#453	1	1	yes	characteristic
211	C₄×C₆₁	#454	1	1	yes	characteristic
212	C₄×C₆₁	#465	1	1	yes	characteristic
213	C₄×C₆₁	#466	1	1	yes	characteristic
214	#3038	C₂×C₆₁	1	1	yes	characteristic
215	#2988	C₂×C₆₁	1	1	yes	characteristic, complemented
216	#1982	C₂×C₆₁	1	1	yes	characteristic, complemented
217	#1806	C₂×C₆₁	1	1	yes	characteristic, complemented
218	#1545	C₂×C₆₁	1	1	yes	characteristic, complemented
219	#1303	C₂×C₆₁	1	1	yes	characteristic, complemented
220	#1292	C₂×C₆₁	1	1	yes	characteristic, complemented
221	C₂×C₆₁	—	2	1	no	—
222	C₂×C₆₁	—	2	1	no	—
223	C₂×C₆₁	—	4	2	no	—
224	C₂×C₆₁	—	16	2	no	—
225	C₂×C₆₁	#1883	1	1	yes	characteristic
226	C₂×C₆₁	#1893	1	1	yes	characteristic
227	C₂×C₆₁	#1903	1	1	yes	characteristic
228	C₂×AGL(1,ℤ/8)	—	2	1	no	—
229	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
230	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
231	#460	—	2	1	no	—
232	#460	C₄×C₆₁	1	2	yes	complemented
233	#459	—	2	1	no	—
234	#459	C₄×C₆₁	1	2	yes	complemented
235	C₈×Q₈	—	2	1	no	—
236	C₈×D₄	—	2	2	no	—
237	C₈×D₄	—	2	1	no	—
238	#431	—	2	1	no	—
239	#431	C₂²×C₆₁	1	1	yes	characteristic
240	#423	C₂²×C₆₁	1	1	yes	characteristic
241	#423	C₂²×C₆₁	1	1	yes	characteristic
242	C₂×C₄⋊C₈	—	2	1	no	—
243	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
244	C₂×#104	—	2	1	no	—
245	#418	—	2	1	no	—
246	C₂×#102	—	2	2	no	—
247	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
248	#339	—	2	1	no	—
249	#331	—	2	1	no	—
250	#331	—	2	1	no	—
251	C₆₁	#9318	1	1	yes	characteristic, direct product factor, Sylow
252	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	AGL(1,ℤ/8)	—	4	2	no	—
257	AGL(1,ℤ/8)	—	4	2	no	—
258	C₂×SD₁₆	—	2	2	no	—
259	C₂×D₈	—	2	2	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	D₄×C₆₁	1	2	yes	—
264	#127	—	2	1	no	—
265	#127	—	2	1	no	—
266	#127	—	2	1	no	—
267	#127	C₂×C₄×C₆₁	1	2	yes	—
268	C₄×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
269	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
273	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
274	#117	—	2	1	no	—
275	#117	D₄×C₆₁	1	1	yes	characteristic
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
280	C₄⋊C₈	—	2	2	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	C₂×C₄×C₆₁	1	2	yes	—
287	C₄⋊C₈	D₄×C₆₁	1	1	yes	characteristic
288	C₄⋊C₈	D₄×C₆₁	1	1	yes	characteristic
289	#104	—	4	2	no	—
290	#102	—	2	2	no	—
291	#102	—	2	2	no	—
292	#102	—	4	4	no	—
293	C₂²⋊C₈	—	2	2	no	—
294	C₂²⋊C₈	—	2	1	no	—
295	C₄×C₈	—	2	2	no	—
296	C₄×C₈	—	2	1	no	—
297	#95	—	2	1	no	—
298	C₂⁴	—	4	1	no	—
299	#41	—	2	1	no	—
300	#41	—	2	1	no	—
301	#41	D₈×C₆₁	1	2	yes	—
302	#41	SD₁₆×C₆₁	1	2	yes	—
303	C₂×Q₈	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	8	2	no	—
318	C₂×D₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
325	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
326	SD₁₆	—	4	4	no	—
327	D₈	—	4	4	no	—
328	M₁₆	—	4	1	no	—
329	M₁₆	—	4	1	no	—
330	M₁₆	—	4	1	no	—
331	M₁₆	—	4	1	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	8	2	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
344	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
345	C₂²⋊C₄	—	2	1	no	—
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	2	1	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	4	1	no	—
352	C₄²	—	4	1	no	—
353	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
354	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
355	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
356	C₄²	#41×C₆₁	1	1	yes	characteristic
357	C₂³	—	2	1	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	8	2	no	—
360	C₂³	—	8	2	no	—
361	C₂³	—	8	1	no	—
362	C₂³	—	8	1	no	—
363	C₂³	#121×C₆₁	1	1	yes	characteristic
364	Q₈	—	2	1	no	—
365	Q₈	#102×C₆₁	1	2	yes	complemented
366	D₄	—	2	2	no	—
367	D₄	—	2	2	no	—
368	D₄	—	2	1	no	—
369	D₄	—	4	4	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	8	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	8	1	no	—
375	D₄	—	8	1	no	—
376	D₄	—	8	1	no	—
377	D₄	—	8	1	no	—
378	D₄	#102×C₆₁	1	2	yes	complemented
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	—	8	1	no	—
392	C₂×C₄	—	8	1	no	—
393	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
394	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
395	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
396	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
397	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
398	C₂×C₄	#123×C₆₁	1	1	yes	characteristic
399	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
400	C₂×C₄	C₂×SD₁₆×C₆₁	1	1	yes	characteristic
401	C₂×C₄	#135×C₆₁	1	1	yes	characteristic
402	C₂×C₄	#135×C₆₁	1	1	yes	characteristic
403	C₈	—	4	2	no	—
404	C₈	—	4	2	no	—
405	C₈	—	4	1	no	—
406	C₈	—	4	1	no	—
407	C₈	—	8	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	16	2	no	—
417	C₂²	—	16	2	no	—
418	C₂²	C₆₁×#386	1	1	yes	characteristic
419	C₂²	C₆₁×#465	1	1	yes	characteristic
420	C₂²	C₆₁×#466	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	8	2	no	—
428	C₄	C₂×#102×C₆₁	1	1	yes	characteristic
429	C₄	C₆₁×#416	1	1	yes	characteristic
430	C₄	C₆₁×#453	1	1	yes	characteristic
431	C₄	C₆₁×#454	1	1	yes	characteristic
432	C₄	C₆₁×#465	1	1	yes	characteristic
433	C₄	C₆₁×#466	1	1	yes	characteristic
434	C₂	—	2	1	no	—
435	C₂	—	2	1	no	—
436	C₂	—	4	2	no	—
437	C₂	—	16	2	no	—
438	C₂	C₆₁×#1883	1	1	yes	characteristic
439	C₂	C₆₁×#1893	1	1	yes	characteristic
440	C₂	C₆₁×#1903	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	#386
commutator	C₄²	C₂²×C₄×C₆₁
Frattini, cosocle	C₂×C₄²	C₂³×C₆₁
prime radical	C₆₁×#3038	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ 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
2. C₆₁×#2988	C₂	semidirect
3. C₆₁×#1982	C₂	semidirect
4. C₆₁×#1806	C₂	semidirect
5. C₆₁×#1545	C₂	semidirect
6. C₆₁×#1303	C₂	semidirect
7. C₆₁×#1292	C₂	semidirect
12. C₆₁×#460	C₄	semidirect
14. C₆₁×#459	C₄	semidirect
144. Q₈×C₆₁	#102	semidirect
157. D₄×C₆₁	#102	semidirect
187. #9318	C₆₁	direct (N × H)
215. #2988	C₂×C₆₁	semidirect
216. #1982	C₂×C₆₁	semidirect
217. #1806	C₂×C₆₁	semidirect
218. #1545	C₂×C₆₁	semidirect
219. #1303	C₂×C₆₁	semidirect
220. #1292	C₂×C₆₁	semidirect
232. #460	C₄×C₆₁	semidirect
234. #459	C₄×C₆₁	semidirect
251. C₆₁	#9318	direct (N × H)
365. Q₈	#102×C₆₁	semidirect
378. D₄	#102×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3038	2
C₆₁×#2988	2
C₆₁×#1982	2
C₆₁×#1806	2
C₆₁×#1545	2
C₆₁×#1303	2
C₆₁×#1292	2
#9318	61

Subgroups — C61×#9318 #29512751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#9318 #29512751