Subgroups — C₆₁×#25800 #29529233

Order 15616.

1402 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3584	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3156	C₂	1	2	yes	maximal, complemented
3	C₆₁×#3059	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3028	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3022	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2009	C₂	1	4	yes	maximal, complemented
7	C₆₁×#1976	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1757	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#585	C₂²	1	2	yes	—
10	C₆₁×#578	—	2	2	no	—
11	C₆₁×#577	—	2	4	no	—
12	C₆₁×#576	—	2	2	no	—
13	C₆₁×#575	—	2	2	no	—
14	C₆₁×#575	C₂²	1	2	yes	—
15	C₂×#137×C₆₁	C₂²	1	4	yes	complemented
16	C₂×#135×C₆₁	—	2	2	no	—
17	C₂×#135×C₆₁	C₂²	1	2	yes	—
18	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
19	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#536	C₂²	1	2	yes	—
21	C₆₁×#536	C₂²	1	4	yes	complemented
22	C₆₁×#497	—	2	4	no	—
23	C₆₁×#495	—	2	2	no	—
24	C₆₁×#494	—	2	2	no	—
25	C₆₁×#470	—	2	2	no	—
26	C₆₁×#467	—	2	2	no	—
27	C₆₁×#458	—	2	8	no	—
28	C₆₁×#456	—	2	4	no	—
29	C₆₁×#455	—	2	4	no	—
30	C₆₁×#427	C₂²	1	1	yes	characteristic, complemented
31	C₆₁×#421	C₂²	1	4	yes	complemented
32	C₆₁×#419	C₂²	1	2	yes	complemented
33	C₆₁×#413	C₂²	1	1	yes	characteristic
34	C₆₁×#410	C₂²	1	1	yes	characteristic
35	C₆₁×#410	C₂²	1	4	yes	complemented
36	C₆₁×#405	C₂²	1	2	yes	complemented
37	C₆₁×#344	C₂²	1	2	yes	complemented
38	2₋¹⁺⁴×C₆₁	—	2	4	no	—
39	2₋¹⁺⁴×C₆₁	—	2	2	no	—
40	H(5,𝔽₂)×C₆₁	—	2	4	no	—
41	H(5,𝔽₂)×C₆₁	—	2	4	no	—
42	H(5,𝔽₂)×C₆₁	—	2	2	no	—
43	C₂×#41×C₆₁	—	2	4	no	—
44	C₂×#41×C₆₁	—	4	4	no	—
45	C₂×#41×C₆₁	C₂³	1	4	yes	—
46	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
48	#137×C₆₁	—	2	8	no	—
49	#137×C₆₁	—	2	4	no	—
50	#137×C₆₁	—	2	8	no	—
51	#137×C₆₁	—	4	4	no	—
52	AGL(1,ℤ/8)×C₆₁	—	2	8	no	—
53	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
54	#135×C₆₁	—	2	4	no	—
55	#135×C₆₁	—	2	4	no	—
56	#135×C₆₁	—	2	2	no	—
57	#135×C₆₁	—	2	4	no	—
58	#135×C₆₁	—	2	2	no	—
59	#135×C₆₁	—	2	2	no	—
60	#135×C₆₁	—	2	2	no	—
61	C₂×Q₁₆×C₆₁	—	2	2	no	—
62	C₂×Q₁₆×C₆₁	—	2	4	no	—
63	C₂×Q₁₆×C₆₁	—	2	1	no	—
64	C₂×Q₁₆×C₆₁	—	2	1	no	—
65	C₂×Q₁₆×C₆₁	—	2	2	no	—
66	C₂×Q₁₆×C₆₁	—	2	2	no	—
67	C₂×Q₁₆×C₆₁	D₄	1	2	yes	—
68	C₂×SD₁₆×C₆₁	—	2	4	no	—
69	C₂×SD₁₆×C₆₁	—	2	4	no	—
70	C₂×SD₁₆×C₆₁	D₄	1	4	yes	—
71	C₂×D₈×C₆₁	—	2	2	no	—
72	C₂×D₈×C₆₁	D₄	1	2	yes	—
73	#131×C₆₁	—	2	2	no	—
74	#131×C₆₁	—	2	2	no	—
75	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
76	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
77	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₆₁	D₄	1	2	yes	—
79	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
80	C₄⋊Q₈×C₆₁	—	2	2	no	—
81	C₄⋊Q₈×C₆₁	—	2	4	no	—
82	#124×C₆₁	—	2	2	no	—
83	#124×C₆₁	—	2	4	no	—
84	#123×C₆₁	—	2	4	no	—
85	#123×C₆₁	—	2	8	no	—
86	C₂²⋊Q₈×C₆₁	—	2	4	no	—
87	C₂²⋊Q₈×C₆₁	—	4	4	no	—
88	#117×C₆₁	C₂³	1	2	yes	—
89	#117×C₆₁	C₂³	1	2	yes	—
90	#107×C₆₁	—	2	1	no	—
91	#106×C₆₁	—	2	1	no	—
92	#104×C₆₁	—	2	8	no	—
93	#103×C₆₁	—	2	4	no	—
94	#101×C₆₁	D₄	1	2	yes	—
95	#100×C₆₁	D₄	1	2	yes	—
96	#99×C₆₁	—	2	8	no	—
97	#99×C₆₁	D₄	1	4	yes	—
98	#97×C₆₁	—	2	2	no	—
99	C₄×C₈×C₆₁	—	2	2	no	—
100	#41×C₆₁	—	2	2	no	—
101	#41×C₆₁	—	2	2	no	—
102	#41×C₆₁	—	2	8	no	—
103	#41×C₆₁	—	2	4	no	—
104	#41×C₆₁	—	2	4	no	—
105	#41×C₆₁	—	2	4	no	—
106	#41×C₆₁	—	2	4	no	—
107	#41×C₆₁	—	4	8	no	—
108	#41×C₆₁	—	4	4	no	—
109	#41×C₆₁	—	4	4	no	—
110	#41×C₆₁	—	4	4	no	—
111	#41×C₆₁	—	4	4	no	—
112	C₂×Q₈×C₆₁	—	2	4	no	—
113	C₂×Q₈×C₆₁	—	2	2	no	—
114	C₂×Q₈×C₆₁	—	2	4	no	—
115	C₂×Q₈×C₆₁	—	2	2	no	—
116	C₂×Q₈×C₆₁	—	2	4	no	—
117	C₂×Q₈×C₆₁	—	4	4	no	—
118	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
119	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
120	C₂×D₄×C₆₁	—	2	4	no	—
121	C₂×D₄×C₆₁	—	2	4	no	—
122	C₂×D₄×C₆₁	—	4	4	no	—
123	C₂×D₄×C₆₁	—	4	8	no	—
124	C₂×D₄×C₆₁	—	4	4	no	—
125	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
126	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
127	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	—	2	4	no	—
129	C₂²×C₄×C₆₁	—	2	2	no	—
130	C₂²×C₄×C₆₁	—	4	4	no	—
131	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
133	Q₁₆×C₆₁	—	2	4	no	—
134	Q₁₆×C₆₁	—	2	2	no	—
135	Q₁₆×C₆₁	—	2	2	no	—
136	Q₁₆×C₆₁	—	4	8	no	—
137	Q₁₆×C₆₁	—	4	1	no	—
138	Q₁₆×C₆₁	—	4	1	no	—
139	Q₁₆×C₆₁	—	4	2	no	—
140	SD₁₆×C₆₁	—	2	8	no	—
141	SD₁₆×C₆₁	—	2	4	no	—
142	SD₁₆×C₆₁	—	2	4	no	—
143	SD₁₆×C₆₁	—	4	8	no	—
144	D₈×C₆₁	—	2	4	no	—
145	D₈×C₆₁	—	2	2	no	—
146	D₈×C₆₁	—	2	2	no	—
147	M₁₆×C₆₁	—	2	2	no	—
148	M₁₆×C₆₁	—	2	2	no	—
149	M₁₆×C₆₁	—	2	4	no	—
150	M₁₆×C₆₁	C₂×D₄	1	4	yes	—
151	C₂×C₈×C₆₁	—	2	2	no	—
152	C₂×C₈×C₆₁	—	2	2	no	—
153	C₂×C₈×C₆₁	—	2	2	no	—
154	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
159	C₄⋊C₄×C₆₁	—	2	2	no	—
160	C₄⋊C₄×C₆₁	—	2	2	no	—
161	C₄⋊C₄×C₆₁	—	4	8	no	—
162	C₄⋊C₄×C₆₁	—	4	4	no	—
163	C₂²⋊C₄×C₆₁	—	2	2	no	—
164	C₂²⋊C₄×C₆₁	—	4	8	no	—
165	C₂²⋊C₄×C₆₁	—	4	4	no	—
166	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
167	C₄²×C₆₁	—	2	2	no	—
168	C₄²×C₆₁	—	2	2	no	—
169	C₂³×C₆₁	—	2	4	no	—
170	C₂³×C₆₁	—	4	4	no	—
171	C₂³×C₆₁	#127	1	2	yes	—
172	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₆₁	—	2	2	no	—
174	Q₈×C₆₁	—	2	4	no	—
175	Q₈×C₆₁	—	2	4	no	—
176	Q₈×C₆₁	—	4	4	no	—
177	Q₈×C₆₁	—	4	2	no	—
178	Q₈×C₆₁	—	4	2	no	—
179	Q₈×C₆₁	—	4	4	no	—
180	D₄×C₆₁	—	2	4	no	—
181	D₄×C₆₁	—	2	4	no	—
182	D₄×C₆₁	—	2	2	no	—
183	D₄×C₆₁	—	2	4	no	—
184	D₄×C₆₁	—	4	4	no	—
185	D₄×C₆₁	—	4	8	no	—
186	D₄×C₆₁	—	4	4	no	—
187	D₄×C₆₁	—	4	4	no	—
188	C₂×C₄×C₆₁	—	2	2	no	—
189	C₂×C₄×C₆₁	—	2	2	no	—
190	C₂×C₄×C₆₁	—	2	4	no	—
191	C₂×C₄×C₆₁	—	2	4	no	—
192	C₂×C₄×C₆₁	—	4	8	no	—
193	C₂×C₄×C₆₁	—	4	4	no	—
194	C₂×C₄×C₆₁	—	4	4	no	—
195	C₂×C₄×C₆₁	—	4	4	no	—
196	C₂×C₄×C₆₁	—	4	2	no	—
197	C₂×C₄×C₆₁	—	4	2	no	—
198	C₂×C₄×C₆₁	—	4	4	no	—
199	C₂×C₄×C₆₁	#127	1	2	yes	—
200	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
204	C₈×C₆₁	—	2	2	no	—
205	C₈×C₆₁	—	2	4	no	—
206	C₈×C₆₁	#120	1	1	yes	characteristic
207	C₈×C₆₁	#120	1	1	yes	characteristic
208	C₈×C₆₁	#120	1	2	yes	—
209	#25800	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂²×C₆₁	—	2	2	no	—
211	C₂²×C₆₁	—	4	1	no	—
212	C₂²×C₆₁	—	4	2	no	—
213	C₂²×C₆₁	—	4	4	no	—
214	C₂²×C₆₁	—	8	4	no	—
215	C₂²×C₆₁	—	16	4	no	—
216	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
217	C₂²×C₆₁	D₄²	1	2	yes	—
218	C₄×C₆₁	—	2	2	no	—
219	C₄×C₆₁	—	4	4	no	—
220	C₄×C₆₁	—	4	4	no	—
221	C₄×C₆₁	—	8	2	no	—
222	C₄×C₆₁	—	8	2	no	—
223	C₄×C₆₁	C₂×#120	1	1	yes	characteristic
224	C₄×C₆₁	#535	1	1	yes	characteristic
225	C₄×C₆₁	D₄²	1	2	yes	—
226	#3584	C₂×C₆₁	1	1	yes	characteristic
227	#3156	C₂×C₆₁	1	2	yes	complemented
228	#3059	C₂×C₆₁	1	1	yes	characteristic, complemented
229	#3028	C₂×C₆₁	1	2	yes	complemented
230	#3022	C₂×C₆₁	1	2	yes	complemented
231	#2009	C₂×C₆₁	1	4	yes	complemented
232	#1976	C₂×C₆₁	1	2	yes	complemented
233	#1757	C₂×C₆₁	1	1	yes	characteristic, complemented
234	C₂×C₆₁	—	2	2	no	—
235	C₂×C₆₁	—	2	1	no	—
236	C₂×C₆₁	—	4	2	no	—
237	C₂×C₆₁	—	8	4	no	—
238	C₂×C₆₁	#2433	1	1	yes	characteristic
239	#585	C₂²×C₆₁	1	2	yes	—
240	#578	—	2	2	no	—
241	#577	—	2	4	no	—
242	#576	—	2	2	no	—
243	#575	—	2	2	no	—
244	#575	C₂²×C₆₁	1	2	yes	—
245	C₂×#137	C₂²×C₆₁	1	4	yes	complemented
246	C₂×#135	—	2	2	no	—
247	C₂×#135	C₂²×C₆₁	1	2	yes	—
248	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
249	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
250	#536	C₂²×C₆₁	1	2	yes	—
251	#536	C₂²×C₆₁	1	4	yes	complemented
252	#497	—	2	4	no	—
253	#495	—	2	2	no	—
254	#494	—	2	2	no	—
255	#470	—	2	2	no	—
256	#467	—	2	2	no	—
257	#458	—	2	8	no	—
258	#456	—	2	4	no	—
259	#455	—	2	4	no	—
260	#427	C₂²×C₆₁	1	1	yes	characteristic, complemented
261	#421	C₂²×C₆₁	1	4	yes	complemented
262	#419	C₂²×C₆₁	1	2	yes	complemented
263	#413	C₂²×C₆₁	1	1	yes	characteristic
264	#410	C₂²×C₆₁	1	1	yes	characteristic
265	#410	C₂²×C₆₁	1	4	yes	complemented
266	#405	C₂²×C₆₁	1	2	yes	complemented
267	#344	C₂²×C₆₁	1	2	yes	complemented
268	C₆₁	#25800	1	1	yes	characteristic, direct product factor, Sylow
269	2₋¹⁺⁴	—	2	4	no	—
270	2₋¹⁺⁴	—	2	2	no	—
271	H(5,𝔽₂)	—	2	4	no	—
272	H(5,𝔽₂)	—	2	4	no	—
273	H(5,𝔽₂)	—	2	2	no	—
274	C₂×#41	—	2	4	no	—
275	C₂×#41	—	4	4	no	—
276	C₂×#41	C₂³×C₆₁	1	4	yes	—
277	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
278	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
279	#137	—	2	8	no	—
280	#137	—	2	4	no	—
281	#137	—	2	8	no	—
282	#137	—	4	4	no	—
283	AGL(1,ℤ/8)	—	2	8	no	—
284	AGL(1,ℤ/8)	—	2	4	no	—
285	#135	—	2	4	no	—
286	#135	—	2	4	no	—
287	#135	—	2	2	no	—
288	#135	—	2	4	no	—
289	#135	—	2	2	no	—
290	#135	—	2	2	no	—
291	#135	—	2	2	no	—
292	C₂×Q₁₆	—	2	2	no	—
293	C₂×Q₁₆	—	2	4	no	—
294	C₂×Q₁₆	—	2	1	no	—
295	C₂×Q₁₆	—	2	1	no	—
296	C₂×Q₁₆	—	2	2	no	—
297	C₂×Q₁₆	—	2	2	no	—
298	C₂×Q₁₆	D₄×C₆₁	1	2	yes	—
299	C₂×SD₁₆	—	2	4	no	—
300	C₂×SD₁₆	—	2	4	no	—
301	C₂×SD₁₆	D₄×C₆₁	1	4	yes	—
302	C₂×D₈	—	2	2	no	—
303	C₂×D₈	D₄×C₆₁	1	2	yes	—
304	#131	—	2	2	no	—
305	#131	—	2	2	no	—
306	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
307	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
308	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
309	C₂²×C₈	D₄×C₆₁	1	2	yes	—
310	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	—	2	4	no	—
313	#124	—	2	2	no	—
314	#124	—	2	4	no	—
315	#123	—	2	4	no	—
316	#123	—	2	8	no	—
317	C₂²⋊Q₈	—	2	4	no	—
318	C₂²⋊Q₈	—	4	4	no	—
319	#117	C₂³×C₆₁	1	2	yes	—
320	#117	C₂³×C₆₁	1	2	yes	—
321	#107	—	2	1	no	—
322	#106	—	2	1	no	—
323	#104	—	2	8	no	—
324	#103	—	2	4	no	—
325	#101	D₄×C₆₁	1	2	yes	—
326	#100	D₄×C₆₁	1	2	yes	—
327	#99	—	2	8	no	—
328	#99	D₄×C₆₁	1	4	yes	—
329	#97	—	2	2	no	—
330	C₄×C₈	—	2	2	no	—
331	#41	—	2	2	no	—
332	#41	—	2	2	no	—
333	#41	—	2	8	no	—
334	#41	—	2	4	no	—
335	#41	—	2	4	no	—
336	#41	—	2	4	no	—
337	#41	—	2	4	no	—
338	#41	—	4	8	no	—
339	#41	—	4	4	no	—
340	#41	—	4	4	no	—
341	#41	—	4	4	no	—
342	#41	—	4	4	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	4	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	4	no	—
348	C₂×Q₈	—	4	4	no	—
349	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
350	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	4	4	no	—
354	C₂×D₄	—	4	8	no	—
355	C₂×D₄	—	4	4	no	—
356	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
357	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
358	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	4	4	no	—
362	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
363	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
364	Q₁₆	—	2	4	no	—
365	Q₁₆	—	2	2	no	—
366	Q₁₆	—	2	2	no	—
367	Q₁₆	—	4	8	no	—
368	Q₁₆	—	4	1	no	—
369	Q₁₆	—	4	1	no	—
370	Q₁₆	—	4	2	no	—
371	SD₁₆	—	2	8	no	—
372	SD₁₆	—	2	4	no	—
373	SD₁₆	—	2	4	no	—
374	SD₁₆	—	4	8	no	—
375	D₈	—	2	4	no	—
376	D₈	—	2	2	no	—
377	D₈	—	2	2	no	—
378	M₁₆	—	2	2	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	4	no	—
381	M₁₆	C₂×D₄×C₆₁	1	4	yes	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
386	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
387	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
388	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
389	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	4	8	no	—
393	C₄⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	4	8	no	—
396	C₂²⋊C₄	—	4	4	no	—
397	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	4	4	no	—
402	C₂³	#127×C₆₁	1	2	yes	—
403	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
404	Q₈	—	2	2	no	—
405	Q₈	—	2	4	no	—
406	Q₈	—	2	4	no	—
407	Q₈	—	4	4	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	4	no	—
410	Q₈	—	4	2	no	—
411	D₄	—	2	4	no	—
412	D₄	—	2	2	no	—
413	D₄	—	2	4	no	—
414	D₄	—	2	4	no	—
415	D₄	—	4	4	no	—
416	D₄	—	4	8	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	#127×C₆₁	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
433	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
434	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
435	C₈	—	2	4	no	—
436	C₈	—	2	2	no	—
437	C₈	#120×C₆₁	1	1	yes	characteristic
438	C₈	#120×C₆₁	1	1	yes	characteristic
439	C₈	#120×C₆₁	1	2	yes	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	8	4	no	—
445	C₂²	—	16	4	no	—
446	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
447	C₂²	D₄²×C₆₁	1	2	yes	—
448	C₄	—	2	2	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	4	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	2	no	—
453	C₄	C₂×#120×C₆₁	1	1	yes	characteristic
454	C₄	C₆₁×#535	1	1	yes	characteristic
455	C₄	D₄²×C₆₁	1	2	yes	—
456	C₂	—	2	2	no	—
457	C₂	—	2	1	no	—
458	C₂	—	4	2	no	—
459	C₂	—	8	4	no	—
460	C₂	C₆₁×#2433	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₆₁	#2433
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#3584	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×#3156	C₂	semidirect
3. C₆₁×#3059	C₂	semidirect
4. C₆₁×#3028	C₂	semidirect
5. C₆₁×#3022	C₂	semidirect
6. C₆₁×#2009	C₂	semidirect
7. C₆₁×#1976	C₂	semidirect
8. C₆₁×#1757	C₂	semidirect
15. C₂×#137×C₆₁	C₂²	semidirect
18. C₂²×Q₁₆×C₆₁	C₂²	semidirect
21. C₆₁×#536	C₂²	semidirect
30. C₆₁×#427	C₂²	semidirect
31. C₆₁×#421	C₂²	semidirect
32. C₆₁×#419	C₂²	semidirect
35. C₆₁×#410	C₂²	semidirect
36. C₆₁×#405	C₂²	semidirect
37. C₆₁×#344	C₂²	semidirect
209. #25800	C₆₁	direct (N × H)
227. #3156	C₂×C₆₁	semidirect
228. #3059	C₂×C₆₁	semidirect
229. #3028	C₂×C₆₁	semidirect
230. #3022	C₂×C₆₁	semidirect
231. #2009	C₂×C₆₁	semidirect
232. #1976	C₂×C₆₁	semidirect
233. #1757	C₂×C₆₁	semidirect
245. C₂×#137	C₂²×C₆₁	semidirect
248. C₂²×Q₁₆	C₂²×C₆₁	semidirect
251. #536	C₂²×C₆₁	semidirect
260. #427	C₂²×C₆₁	semidirect
261. #421	C₂²×C₆₁	semidirect
262. #419	C₂²×C₆₁	semidirect
265. #410	C₂²×C₆₁	semidirect
266. #405	C₂²×C₆₁	semidirect
267. #344	C₂²×C₆₁	semidirect
268. C₆₁	#25800	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×#3584	2
C₆₁×#3156	2
C₆₁×#3059	2
C₆₁×#3028	2
C₆₁×#3022	2
C₆₁×#2009	2
C₆₁×#1976	2
C₆₁×#1757	2
#25800	61

Subgroups — C61×#25800 #29529233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25800 #29529233