Subgroups — C₆₁×#32897 #29536330

Order 15616.

3512 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×2₋¹⁺⁶	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3028	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3022	C₂	1	3	yes	maximal, complemented
4	C₆₁×#3011	C₂	1	3	yes	maximal, complemented
5	C₆₁×#1796	C₂	1	3	yes	maximal, complemented
6	C₆₁×#1794	C₂	1	3	yes	maximal, complemented
7	C₆₁×#1791	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#585	—	2	6	no	—
9	C₆₁×#585	—	2	4	no	—
10	C₆₁×#585	—	2	6	no	—
11	C₆₁×#585	C₂²	1	3	yes	—
12	C₆₁×#585	C₂²	1	1	yes	characteristic
13	C₂×2₋¹⁺⁴×C₆₁	—	2	6	no	—
14	C₂×2₋¹⁺⁴×C₆₁	—	2	6	no	—
15	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	3	yes	—
16	C₂×#137×C₆₁	C₂²	1	3	yes	complemented
17	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
18	C₆₁×#536	C₂²	1	3	yes	complemented
19	C₆₁×#458	—	2	4	no	—
20	C₆₁×#456	—	2	6	no	—
21	C₆₁×#455	—	2	6	no	—
22	C₆₁×#452	—	2	6	no	—
23	C₆₁×#451	—	2	6	no	—
24	C₆₁×#421	C₂²	1	6	yes	complemented
25	C₆₁×#419	C₂²	1	3	yes	complemented
26	C₆₁×#416	C₂²	1	3	yes	complemented
27	C₆₁×#413	C₂²	1	3	yes	complemented
28	C₆₁×#410	C₂²	1	3	yes	complemented
29	C₆₁×#408	C₂²	1	3	yes	complemented
30	2₋¹⁺⁴×C₆₁	—	2	12	no	—
31	2₋¹⁺⁴×C₆₁	—	2	24	no	—
32	2₋¹⁺⁴×C₆₁	—	2	24	no	—
33	2₋¹⁺⁴×C₆₁	—	2	12	no	—
34	2₋¹⁺⁴×C₆₁	—	2	12	no	—
35	2₋¹⁺⁴×C₆₁	—	2	3	no	—
36	2₋¹⁺⁴×C₆₁	—	2	6	no	—
37	2₋¹⁺⁴×C₆₁	—	2	12	no	—
38	2₋¹⁺⁴×C₆₁	D₄	1	6	yes	—
39	H(5,𝔽₂)×C₆₁	—	2	4	no	—
40	H(5,𝔽₂)×C₆₁	—	2	12	no	—
41	H(5,𝔽₂)×C₆₁	—	2	24	no	—
42	H(5,𝔽₂)×C₆₁	—	2	6	no	—
43	H(5,𝔽₂)×C₆₁	—	2	3	no	—
44	H(5,𝔽₂)×C₆₁	—	2	6	no	—
45	H(5,𝔽₂)×C₆₁	D₄	1	6	yes	—
46	H(5,𝔽₂)×C₆₁	D₄	1	4	yes	—
47	C₂×#41×C₆₁	—	2	12	no	—
48	C₂×#41×C₆₁	—	2	12	no	—
49	C₂×#41×C₆₁	—	2	24	no	—
50	C₂×#41×C₆₁	—	2	24	no	—
51	C₂×#41×C₆₁	—	2	24	no	—
52	C₂×#41×C₆₁	—	2	12	no	—
53	C₂×#41×C₆₁	—	2	3	no	—
54	C₂×#41×C₆₁	—	2	6	no	—
55	C₂×#41×C₆₁	—	2	6	no	—
56	C₂×#41×C₆₁	—	2	6	no	—
57	C₂×#41×C₆₁	D₄	1	6	yes	—
58	C₂×#41×C₆₁	C₂³	1	3	yes	—
59	C₂×#41×C₆₁	C₂³	1	3	yes	—
60	C₂²×Q₈×C₆₁	—	2	12	no	—
61	C₂²×Q₈×C₆₁	—	2	4	no	—
62	C₂²×Q₈×C₆₁	—	2	3	no	—
63	C₂²×Q₈×C₆₁	D₄	1	6	yes	—
64	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
66	#137×C₆₁	—	2	12	no	—
67	C₂×Q₁₆×C₆₁	—	2	6	no	—
68	C₂×Q₁₆×C₆₁	—	2	3	no	—
69	C₂×SD₁₆×C₆₁	—	2	3	no	—
70	C₂×M₁₆×C₆₁	C₂³	1	3	yes	—
71	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₄⋊Q₈×C₆₁	—	2	3	no	—
73	#124×C₆₁	—	2	3	no	—
74	#123×C₆₁	—	2	6	no	—
75	C₂²⋊Q₈×C₆₁	—	2	6	no	—
76	#117×C₆₁	C₂³	1	3	yes	—
77	#104×C₆₁	—	2	12	no	—
78	#103×C₆₁	—	2	3	no	—
79	#103×C₆₁	—	2	6	no	—
80	#102×C₆₁	—	2	3	no	—
81	#101×C₆₁	—	2	3	no	—
82	#100×C₆₁	—	2	3	no	—
83	#99×C₆₁	—	2	6	no	—
84	C₂²⋊C₈×C₆₁	—	2	6	no	—
85	#41×C₆₁	—	2	48	no	—
86	#41×C₆₁	—	2	24	no	—
87	#41×C₆₁	—	2	48	no	—
88	#41×C₆₁	—	2	8	no	—
89	#41×C₆₁	—	2	24	no	—
90	#41×C₆₁	—	2	48	no	—
91	#41×C₆₁	—	2	24	no	—
92	#41×C₆₁	—	2	12	no	—
93	#41×C₆₁	—	2	12	no	—
94	#41×C₆₁	—	2	12	no	—
95	#41×C₆₁	—	2	4	no	—
96	#41×C₆₁	—	2	12	no	—
97	#41×C₆₁	—	2	12	no	—
98	#41×C₆₁	—	2	12	no	—
99	#41×C₆₁	—	2	12	no	—
100	#41×C₆₁	—	2	12	no	—
101	#41×C₆₁	—	2	12	no	—
102	#41×C₆₁	—	2	6	no	—
103	#41×C₆₁	—	2	6	no	—
104	#41×C₆₁	—	2	6	no	—
105	#41×C₆₁	C₂×D₄	1	12	yes	—
106	C₂×Q₈×C₆₁	—	2	24	no	—
107	C₂×Q₈×C₆₁	—	2	24	no	—
108	C₂×Q₈×C₆₁	—	2	24	no	—
109	C₂×Q₈×C₆₁	—	2	6	no	—
110	C₂×Q₈×C₆₁	—	2	6	no	—
111	C₂×Q₈×C₆₁	—	2	12	no	—
112	C₂×Q₈×C₆₁	—	2	12	no	—
113	C₂×Q₈×C₆₁	—	2	12	no	—
114	C₂×Q₈×C₆₁	—	2	6	no	—
115	C₂×Q₈×C₆₁	—	2	3	no	—
116	C₂×Q₈×C₆₁	—	2	3	no	—
117	C₂×Q₈×C₆₁	—	2	3	no	—
118	C₂×Q₈×C₆₁	C₂×D₄	1	3	yes	—
119	C₂×Q₈×C₆₁	C₂×D₄	1	6	yes	—
120	C₂×Q₈×C₆₁	C₂×D₄	1	3	yes	—
121	C₂×D₄×C₆₁	—	2	24	no	—
122	C₂×D₄×C₆₁	—	2	24	no	—
123	C₂×D₄×C₆₁	—	2	24	no	—
124	C₂×D₄×C₆₁	—	2	6	no	—
125	C₂×D₄×C₆₁	—	2	6	no	—
126	C₂×D₄×C₆₁	—	2	12	no	—
127	C₂×D₄×C₆₁	—	2	12	no	—
128	C₂×D₄×C₆₁	—	2	6	no	—
129	C₂×D₄×C₆₁	—	2	3	no	—
130	C₂×D₄×C₆₁	—	2	12	no	—
131	C₂×D₄×C₆₁	C₂×D₄	1	6	yes	—
132	C₂×D₄×C₆₁	C₂×D₄	1	3	yes	—
133	C₂×D₄×C₆₁	C₂×D₄	1	3	yes	—
134	C₂²×C₄×C₆₁	—	2	8	no	—
135	C₂²×C₄×C₆₁	—	2	24	no	—
136	C₂²×C₄×C₆₁	—	2	12	no	—
137	C₂²×C₄×C₆₁	—	2	4	no	—
138	C₂²×C₄×C₆₁	—	2	6	no	—
139	C₂²×C₄×C₆₁	—	2	1	no	—
140	C₂²×C₄×C₆₁	—	2	6	no	—
141	C₂²×C₄×C₆₁	—	2	3	no	—
142	C₂²×C₄×C₆₁	—	2	1	no	—
143	C₂²×C₄×C₆₁	C₂×D₄	1	6	yes	—
144	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
145	Q₁₆×C₆₁	—	4	4	no	—
146	Q₁₆×C₆₁	—	4	6	no	—
147	SD₁₆×C₆₁	—	4	6	no	—
148	M₁₆×C₆₁	—	2	6	no	—
149	C₂×C₈×C₆₁	—	2	3	no	—
150	C₂×C₈×C₆₁	—	2	3	no	—
151	C₄⋊C₄×C₆₁	—	2	3	no	—
152	C₄⋊C₄×C₆₁	—	4	6	no	—
153	C₂²⋊C₄×C₆₁	—	2	3	no	—
154	C₂²⋊C₄×C₆₁	—	4	6	no	—
155	C₄²×C₆₁	—	2	3	no	—
156	C₂³×C₆₁	—	2	4	no	—
157	C₂³×C₆₁	—	2	12	no	—
158	C₂³×C₆₁	—	2	3	no	—
159	C₂³×C₆₁	#120	1	6	yes	—
160	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₆₁	—	2	12	no	—
162	Q₈×C₆₁	—	2	24	no	—
163	Q₈×C₆₁	—	2	4	no	—
164	Q₈×C₆₁	—	2	3	no	—
165	Q₈×C₆₁	—	2	6	no	—
166	Q₈×C₆₁	—	2	6	no	—
167	Q₈×C₆₁	—	4	3	no	—
168	Q₈×C₆₁	—	4	1	no	—
169	Q₈×C₆₁	#120	1	6	yes	—
170	Q₈×C₆₁	#120	1	4	yes	—
171	D₄×C₆₁	—	2	24	no	—
172	D₄×C₆₁	—	2	24	no	—
173	D₄×C₆₁	—	2	12	no	—
174	D₄×C₆₁	—	2	12	no	—
175	D₄×C₆₁	—	2	12	no	—
176	D₄×C₆₁	—	2	12	no	—
177	D₄×C₆₁	—	2	3	no	—
178	D₄×C₆₁	—	2	6	no	—
179	D₄×C₆₁	#120	1	6	yes	—
180	C₂×C₄×C₆₁	—	2	12	no	—
181	C₂×C₄×C₆₁	—	2	24	no	—
182	C₂×C₄×C₆₁	—	2	24	no	—
183	C₂×C₄×C₆₁	—	2	24	no	—
184	C₂×C₄×C₆₁	—	2	12	no	—
185	C₂×C₄×C₆₁	—	2	3	no	—
186	C₂×C₄×C₆₁	—	2	6	no	—
187	C₂×C₄×C₆₁	—	2	12	no	—
188	C₂×C₄×C₆₁	—	2	6	no	—
189	C₂×C₄×C₆₁	—	2	6	no	—
190	C₂×C₄×C₆₁	—	4	3	no	—
191	C₂×C₄×C₆₁	—	4	3	no	—
192	C₂×C₄×C₆₁	#120	1	6	yes	—
193	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
194	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
195	C₈×C₆₁	—	4	1	no	—
196	C₈×C₆₁	—	4	3	no	—
197	#32897	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂²×C₆₁	—	2	6	no	—
199	C₂²×C₆₁	—	2	6	no	—
200	C₂²×C₆₁	—	4	1	no	—
201	C₂²×C₆₁	—	4	6	no	—
202	C₂²×C₆₁	—	8	3	no	—
203	C₂²×C₆₁	—	8	4	no	—
204	C₂²×C₆₁	—	8	12	no	—
205	C₂²×C₆₁	C₂×#120	1	3	yes	—
206	C₄×C₆₁	—	2	4	no	—
207	C₄×C₆₁	—	2	6	no	—
208	C₄×C₆₁	—	2	6	no	—
209	C₄×C₆₁	—	8	3	no	—
210	C₄×C₆₁	—	8	1	no	—
211	C₄×C₆₁	C₂×#120	1	1	yes	characteristic
212	C₄×C₆₁	C₂×#120	1	3	yes	—
213	2₋¹⁺⁶	C₂×C₆₁	1	1	yes	characteristic
214	#3028	C₂×C₆₁	1	1	yes	characteristic, complemented
215	#3022	C₂×C₆₁	1	3	yes	complemented
216	#3011	C₂×C₆₁	1	3	yes	complemented
217	#1796	C₂×C₆₁	1	3	yes	complemented
218	#1794	C₂×C₆₁	1	3	yes	complemented
219	#1791	C₂×C₆₁	1	1	yes	characteristic, complemented
220	C₂×C₆₁	—	2	3	no	—
221	C₂×C₆₁	—	4	6	no	—
222	C₂×C₆₁	—	4	6	no	—
223	C₂×C₆₁	#2846	1	1	yes	characteristic
224	#585	—	2	6	no	—
225	#585	—	2	4	no	—
226	#585	—	2	6	no	—
227	#585	C₂²×C₆₁	1	3	yes	—
228	#585	C₂²×C₆₁	1	1	yes	characteristic
229	C₂×2₋¹⁺⁴	—	2	6	no	—
230	C₂×2₋¹⁺⁴	—	2	6	no	—
231	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	3	yes	—
232	C₂×#137	C₂²×C₆₁	1	3	yes	complemented
233	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
234	#536	C₂²×C₆₁	1	3	yes	complemented
235	#458	—	2	4	no	—
236	#456	—	2	6	no	—
237	#455	—	2	6	no	—
238	#452	—	2	6	no	—
239	#451	—	2	6	no	—
240	#421	C₂²×C₆₁	1	6	yes	complemented
241	#419	C₂²×C₆₁	1	3	yes	complemented
242	#416	C₂²×C₆₁	1	3	yes	complemented
243	#413	C₂²×C₆₁	1	3	yes	complemented
244	#410	C₂²×C₆₁	1	3	yes	complemented
245	#408	C₂²×C₆₁	1	3	yes	complemented
246	C₆₁	#32897	1	1	yes	characteristic, direct product factor, Sylow
247	2₋¹⁺⁴	—	2	12	no	—
248	2₋¹⁺⁴	—	2	24	no	—
249	2₋¹⁺⁴	—	2	24	no	—
250	2₋¹⁺⁴	—	2	12	no	—
251	2₋¹⁺⁴	—	2	12	no	—
252	2₋¹⁺⁴	—	2	3	no	—
253	2₋¹⁺⁴	—	2	6	no	—
254	2₋¹⁺⁴	—	2	12	no	—
255	2₋¹⁺⁴	D₄×C₆₁	1	6	yes	—
256	H(5,𝔽₂)	—	2	4	no	—
257	H(5,𝔽₂)	—	2	12	no	—
258	H(5,𝔽₂)	—	2	24	no	—
259	H(5,𝔽₂)	—	2	6	no	—
260	H(5,𝔽₂)	—	2	3	no	—
261	H(5,𝔽₂)	—	2	6	no	—
262	H(5,𝔽₂)	D₄×C₆₁	1	6	yes	—
263	H(5,𝔽₂)	D₄×C₆₁	1	4	yes	—
264	C₂×#41	—	2	12	no	—
265	C₂×#41	—	2	12	no	—
266	C₂×#41	—	2	24	no	—
267	C₂×#41	—	2	24	no	—
268	C₂×#41	—	2	24	no	—
269	C₂×#41	—	2	12	no	—
270	C₂×#41	—	2	3	no	—
271	C₂×#41	—	2	6	no	—
272	C₂×#41	—	2	6	no	—
273	C₂×#41	—	2	6	no	—
274	C₂×#41	D₄×C₆₁	1	6	yes	—
275	C₂×#41	C₂³×C₆₁	1	3	yes	—
276	C₂×#41	C₂³×C₆₁	1	3	yes	—
277	C₂²×Q₈	—	2	12	no	—
278	C₂²×Q₈	—	2	4	no	—
279	C₂²×Q₈	—	2	3	no	—
280	C₂²×Q₈	D₄×C₆₁	1	6	yes	—
281	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
282	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
283	#137	—	2	12	no	—
284	C₂×Q₁₆	—	2	6	no	—
285	C₂×Q₁₆	—	2	3	no	—
286	C₂×SD₁₆	—	2	3	no	—
287	C₂×M₁₆	C₂³×C₆₁	1	3	yes	—
288	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
289	C₄⋊Q₈	—	2	3	no	—
290	#124	—	2	3	no	—
291	#123	—	2	6	no	—
292	C₂²⋊Q₈	—	2	6	no	—
293	#117	C₂³×C₆₁	1	3	yes	—
294	#104	—	2	12	no	—
295	#103	—	2	3	no	—
296	#103	—	2	6	no	—
297	#102	—	2	3	no	—
298	#101	—	2	3	no	—
299	#100	—	2	3	no	—
300	#99	—	2	6	no	—
301	C₂²⋊C₈	—	2	6	no	—
302	#41	—	2	48	no	—
303	#41	—	2	24	no	—
304	#41	—	2	48	no	—
305	#41	—	2	8	no	—
306	#41	—	2	24	no	—
307	#41	—	2	48	no	—
308	#41	—	2	24	no	—
309	#41	—	2	12	no	—
310	#41	—	2	12	no	—
311	#41	—	2	12	no	—
312	#41	—	2	4	no	—
313	#41	—	2	12	no	—
314	#41	—	2	12	no	—
315	#41	—	2	12	no	—
316	#41	—	2	12	no	—
317	#41	—	2	12	no	—
318	#41	—	2	12	no	—
319	#41	—	2	6	no	—
320	#41	—	2	6	no	—
321	#41	—	2	6	no	—
322	#41	C₂×D₄×C₆₁	1	12	yes	—
323	C₂×Q₈	—	2	24	no	—
324	C₂×Q₈	—	2	24	no	—
325	C₂×Q₈	—	2	24	no	—
326	C₂×Q₈	—	2	6	no	—
327	C₂×Q₈	—	2	6	no	—
328	C₂×Q₈	—	2	12	no	—
329	C₂×Q₈	—	2	12	no	—
330	C₂×Q₈	—	2	12	no	—
331	C₂×Q₈	—	2	6	no	—
332	C₂×Q₈	—	2	3	no	—
333	C₂×Q₈	—	2	3	no	—
334	C₂×Q₈	—	2	3	no	—
335	C₂×Q₈	C₂×D₄×C₆₁	1	3	yes	—
336	C₂×Q₈	C₂×D₄×C₆₁	1	6	yes	—
337	C₂×Q₈	C₂×D₄×C₆₁	1	3	yes	—
338	C₂×D₄	—	2	24	no	—
339	C₂×D₄	—	2	24	no	—
340	C₂×D₄	—	2	24	no	—
341	C₂×D₄	—	2	6	no	—
342	C₂×D₄	—	2	6	no	—
343	C₂×D₄	—	2	12	no	—
344	C₂×D₄	—	2	12	no	—
345	C₂×D₄	—	2	6	no	—
346	C₂×D₄	—	2	3	no	—
347	C₂×D₄	—	2	12	no	—
348	C₂×D₄	C₂×D₄×C₆₁	1	6	yes	—
349	C₂×D₄	C₂×D₄×C₆₁	1	3	yes	—
350	C₂×D₄	C₂×D₄×C₆₁	1	3	yes	—
351	C₂²×C₄	—	2	8	no	—
352	C₂²×C₄	—	2	24	no	—
353	C₂²×C₄	—	2	12	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	6	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	6	no	—
358	C₂²×C₄	—	2	3	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	C₂×D₄×C₆₁	1	6	yes	—
361	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
362	Q₁₆	—	4	4	no	—
363	Q₁₆	—	4	6	no	—
364	SD₁₆	—	4	6	no	—
365	M₁₆	—	2	6	no	—
366	C₂×C₈	—	2	3	no	—
367	C₂×C₈	—	2	3	no	—
368	C₄⋊C₄	—	2	3	no	—
369	C₄⋊C₄	—	4	6	no	—
370	C₂²⋊C₄	—	2	3	no	—
371	C₂²⋊C₄	—	4	6	no	—
372	C₄²	—	2	3	no	—
373	C₂³	—	2	4	no	—
374	C₂³	—	2	12	no	—
375	C₂³	—	2	3	no	—
376	C₂³	#120×C₆₁	1	6	yes	—
377	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
378	Q₈	—	2	12	no	—
379	Q₈	—	2	24	no	—
380	Q₈	—	2	4	no	—
381	Q₈	—	2	3	no	—
382	Q₈	—	2	6	no	—
383	Q₈	—	2	6	no	—
384	Q₈	—	4	3	no	—
385	Q₈	—	4	1	no	—
386	Q₈	#120×C₆₁	1	6	yes	—
387	Q₈	#120×C₆₁	1	4	yes	—
388	D₄	—	2	24	no	—
389	D₄	—	2	24	no	—
390	D₄	—	2	12	no	—
391	D₄	—	2	12	no	—
392	D₄	—	2	12	no	—
393	D₄	—	2	12	no	—
394	D₄	—	2	3	no	—
395	D₄	—	2	6	no	—
396	D₄	#120×C₆₁	1	6	yes	—
397	C₂×C₄	—	2	12	no	—
398	C₂×C₄	—	2	24	no	—
399	C₂×C₄	—	2	24	no	—
400	C₂×C₄	—	2	24	no	—
401	C₂×C₄	—	2	12	no	—
402	C₂×C₄	—	2	3	no	—
403	C₂×C₄	—	2	6	no	—
404	C₂×C₄	—	2	12	no	—
405	C₂×C₄	—	2	6	no	—
406	C₂×C₄	—	2	6	no	—
407	C₂×C₄	—	4	3	no	—
408	C₂×C₄	—	4	3	no	—
409	C₂×C₄	#120×C₆₁	1	6	yes	—
410	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
411	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
412	C₈	—	4	1	no	—
413	C₈	—	4	3	no	—
414	C₂²	—	2	6	no	—
415	C₂²	—	2	6	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	6	no	—
418	C₂²	—	8	3	no	—
419	C₂²	—	8	4	no	—
420	C₂²	—	8	12	no	—
421	C₂²	C₂×#120×C₆₁	1	3	yes	—
422	C₄	—	2	4	no	—
423	C₄	—	2	6	no	—
424	C₄	—	2	6	no	—
425	C₄	—	8	3	no	—
426	C₄	—	8	1	no	—
427	C₄	C₂×#120×C₆₁	1	1	yes	characteristic
428	C₄	C₂×#120×C₆₁	1	3	yes	—
429	C₂	—	2	3	no	—
430	C₂	—	4	6	no	—
431	C₂	—	4	6	no	—
432	C₂	C₆₁×#2846	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₆₁	#2846
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×2₋¹⁺⁶	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₁ ◁ C₂²×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#3028	C₂	semidirect
3. C₆₁×#3022	C₂	semidirect
4. C₆₁×#3011	C₂	semidirect
5. C₆₁×#1796	C₂	semidirect
6. C₆₁×#1794	C₂	semidirect
7. C₆₁×#1791	C₂	semidirect
16. C₂×#137×C₆₁	C₂²	semidirect
17. C₂²×Q₁₆×C₆₁	C₂²	semidirect
18. C₆₁×#536	C₂²	semidirect
24. C₆₁×#421	C₂²	semidirect
25. C₆₁×#419	C₂²	semidirect
26. C₆₁×#416	C₂²	semidirect
27. C₆₁×#413	C₂²	semidirect
28. C₆₁×#410	C₂²	semidirect
29. C₆₁×#408	C₂²	semidirect
197. #32897	C₆₁	direct (N × H)
214. #3028	C₂×C₆₁	semidirect
215. #3022	C₂×C₆₁	semidirect
216. #3011	C₂×C₆₁	semidirect
217. #1796	C₂×C₆₁	semidirect
218. #1794	C₂×C₆₁	semidirect
219. #1791	C₂×C₆₁	semidirect
232. C₂×#137	C₂²×C₆₁	semidirect
233. C₂²×Q₁₆	C₂²×C₆₁	semidirect
234. #536	C₂²×C₆₁	semidirect
240. #421	C₂²×C₆₁	semidirect
241. #419	C₂²×C₆₁	semidirect
242. #416	C₂²×C₆₁	semidirect
243. #413	C₂²×C₆₁	semidirect
244. #410	C₂²×C₆₁	semidirect
245. #408	C₂²×C₆₁	semidirect
246. C₆₁	#32897	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×2₋¹⁺⁶	2
C₆₁×#3028	2
C₆₁×#3022	2
C₆₁×#3011	2
C₆₁×#1796	2
C₆₁×#1794	2
C₆₁×#1791	2
#32897	61

Subgroups — C61×#32897 #29536330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#32897 #29536330