Subgroups — C₆₁×#25799 #29529232

Order 15616.

1458 conjugacy classes of subgroups.

The subgroup lattice has 474 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, complemented
2	C₆₁×#3155	C₂	1	2	yes	maximal, complemented
3	C₆₁×#3058	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3027	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3021	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2008	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×AGL(1,ℤ/8)×C₆₁	C₂²	1	4	yes	complemented
16	C₂×#135×C₆₁	—	2	2	no	—
17	C₂×#135×C₆₁	C₂²	1	2	yes	—
18	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
19	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#535	C₂²	1	2	yes	—
21	C₆₁×#535	C₂²	1	4	yes	complemented
22	C₆₁×#496	—	2	4	no	—
23	C₆₁×#495	—	2	2	no	—
24	C₆₁×#493	—	2	2	no	—
25	C₆₁×#469	—	2	2	no	—
26	C₆₁×#466	—	2	2	no	—
27	C₆₁×B(4,𝔽₂)	—	2	8	no	—
28	C₆₁×#454	—	2	4	no	—
29	C₆₁×#453	—	2	4	no	—
30	C₆₁×#427	C₂²	1	1	yes	characteristic, complemented
31	C₆₁×#421	C₂²	1	4	yes	complemented
32	C₆₁×#418	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×D₄×C₆₁	C₂³	1	2	yes	—
48	#137×C₆₁	—	2	8	no	—
49	#137×C₆₁	—	2	4	no	—
50	AGL(1,ℤ/8)×C₆₁	—	2	8	no	—
51	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
52	AGL(1,ℤ/8)×C₆₁	—	2	8	no	—
53	AGL(1,ℤ/8)×C₆₁	—	4	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	D₄	1	2	yes	complemented
63	C₂×SD₁₆×C₆₁	—	2	4	no	—
64	C₂×SD₁₆×C₆₁	—	2	4	no	—
65	C₂×SD₁₆×C₆₁	D₄	1	4	yes	complemented
66	C₂×D₈×C₆₁	—	2	2	no	—
67	C₂×D₈×C₆₁	—	2	4	no	—
68	C₂×D₈×C₆₁	—	2	1	no	—
69	C₂×D₈×C₆₁	—	2	1	no	—
70	C₂×D₈×C₆₁	—	2	2	no	—
71	C₂×D₈×C₆₁	—	2	2	no	—
72	C₂×D₈×C₆₁	D₄	1	2	yes	complemented
73	#131×C₆₁	—	2	2	no	—
74	#131×C₆₁	—	2	2	no	—
75	C₂×M₁₆×C₆₁	D₄	1	2	yes	complemented
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	complemented
79	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
80	#127×C₆₁	—	2	2	no	—
81	#127×C₆₁	—	2	4	no	—
82	#124×C₆₁	—	2	2	no	—
83	#124×C₆₁	—	2	4	no	—
84	#121×C₆₁	—	2	4	no	—
85	#121×C₆₁	—	4	4	no	—
86	#120×C₆₁	—	2	4	no	—
87	#120×C₆₁	—	2	8	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	#102×C₆₁	—	2	4	no	—
94	#101×C₆₁	D₄	1	2	yes	complemented
95	#100×C₆₁	D₄	1	2	yes	complemented
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	C₂⁴×C₆₁	—	2	2	no	—
101	#41×C₆₁	—	2	2	no	—
102	#41×C₆₁	—	2	2	no	—
103	#41×C₆₁	—	2	8	no	—
104	#41×C₆₁	—	2	4	no	—
105	#41×C₆₁	—	2	4	no	—
106	#41×C₆₁	—	2	4	no	—
107	#41×C₆₁	—	2	4	no	—
108	#41×C₆₁	—	4	8	no	—
109	#41×C₆₁	—	4	4	no	—
110	#41×C₆₁	—	4	4	no	—
111	#41×C₆₁	—	4	4	no	—
112	#41×C₆₁	—	4	4	no	—
113	C₂×Q₈×C₆₁	—	2	4	no	—
114	C₂×Q₈×C₆₁	—	4	4	no	—
115	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
116	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
117	C₂×D₄×C₆₁	—	2	4	no	—
118	C₂×D₄×C₆₁	—	2	4	no	—
119	C₂×D₄×C₆₁	—	2	2	no	—
120	C₂×D₄×C₆₁	—	2	4	no	—
121	C₂×D₄×C₆₁	—	2	2	no	—
122	C₂×D₄×C₆₁	—	2	4	no	—
123	C₂×D₄×C₆₁	—	4	8	no	—
124	C₂×D₄×C₆₁	—	4	4	no	—
125	C₂×D₄×C₆₁	—	4	8	no	—
126	C₂×D₄×C₆₁	—	4	4	no	—
127	C₂×D₄×C₆₁	—	4	4	no	—
128	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
129	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
130	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₆₁	—	2	4	no	—
132	C₂²×C₄×C₆₁	—	4	4	no	—
133	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
135	Q₁₆×C₆₁	—	2	4	no	—
136	Q₁₆×C₆₁	—	2	2	no	—
137	Q₁₆×C₆₁	—	2	2	no	—
138	SD₁₆×C₆₁	—	2	8	no	—
139	SD₁₆×C₆₁	—	2	4	no	—
140	SD₁₆×C₆₁	—	2	4	no	—
141	SD₁₆×C₆₁	—	4	8	no	—
142	D₈×C₆₁	—	2	4	no	—
143	D₈×C₆₁	—	2	2	no	—
144	D₈×C₆₁	—	2	2	no	—
145	D₈×C₆₁	—	4	8	no	—
146	D₈×C₆₁	—	4	1	no	—
147	D₈×C₆₁	—	4	1	no	—
148	D₈×C₆₁	—	4	2	no	—
149	M₁₆×C₆₁	—	2	2	no	—
150	M₁₆×C₆₁	—	2	2	no	—
151	M₁₆×C₆₁	—	2	4	no	—
152	M₁₆×C₆₁	C₂×D₄	1	4	yes	—
153	C₂×C₈×C₆₁	—	2	2	no	—
154	C₂×C₈×C₆₁	—	2	2	no	—
155	C₂×C₈×C₆₁	—	2	2	no	—
156	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
158	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
161	C₄⋊C₄×C₆₁	—	2	2	no	—
162	C₄⋊C₄×C₆₁	—	2	2	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	—	4	2	no	—
172	C₂³×C₆₁	—	4	4	no	—
173	C₂³×C₆₁	—	16	2	no	—
174	C₂³×C₆₁	#127	1	2	yes	—
175	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₆₁	—	2	2	no	—
177	Q₈×C₆₁	—	2	4	no	—
178	Q₈×C₆₁	—	2	4	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	D₄×C₆₁	—	4	2	no	—
189	D₄×C₆₁	—	4	2	no	—
190	D₄×C₆₁	—	4	4	no	—
191	D₄×C₆₁	—	16	8	no	—
192	D₄×C₆₁	—	16	4	no	—
193	C₂×C₄×C₆₁	—	2	2	no	—
194	C₂×C₄×C₆₁	—	2	2	no	—
195	C₂×C₄×C₆₁	—	2	4	no	—
196	C₂×C₄×C₆₁	—	2	4	no	—
197	C₂×C₄×C₆₁	—	4	8	no	—
198	C₂×C₄×C₆₁	—	4	4	no	—
199	C₂×C₄×C₆₁	—	4	4	no	—
200	C₂×C₄×C₆₁	—	4	4	no	—
201	C₂×C₄×C₆₁	—	4	2	no	—
202	C₂×C₄×C₆₁	#127	1	2	yes	—
203	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
205	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
207	C₈×C₆₁	—	2	2	no	—
208	C₈×C₆₁	—	2	4	no	—
209	C₈×C₆₁	#120	1	1	yes	characteristic
210	C₈×C₆₁	#120	1	1	yes	characteristic
211	C₈×C₆₁	#120	1	2	yes	—
212	#25799	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂²×C₆₁	—	2	2	no	—
214	C₂²×C₆₁	—	4	1	no	—
215	C₂²×C₆₁	—	4	2	no	—
216	C₂²×C₆₁	—	4	4	no	—
217	C₂²×C₆₁	—	8	4	no	—
218	C₂²×C₆₁	—	8	8	no	—
219	C₂²×C₆₁	—	8	4	no	—
220	C₂²×C₆₁	—	8	2	no	—
221	C₂²×C₆₁	—	16	4	no	—
222	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
223	C₂²×C₆₁	D₄²	1	2	yes	—
224	C₄×C₆₁	—	2	2	no	—
225	C₄×C₆₁	—	4	4	no	—
226	C₄×C₆₁	—	4	4	no	—
227	C₄×C₆₁	—	8	2	no	—
228	C₄×C₆₁	C₂×#120	1	1	yes	characteristic
229	C₄×C₆₁	#535	1	1	yes	characteristic
230	C₄×C₆₁	D₄²	1	2	yes	—
231	#3584	C₂×C₆₁	1	1	yes	characteristic, complemented
232	#3155	C₂×C₆₁	1	2	yes	complemented
233	#3058	C₂×C₆₁	1	1	yes	characteristic, complemented
234	#3027	C₂×C₆₁	1	2	yes	complemented
235	#3021	C₂×C₆₁	1	2	yes	complemented
236	#2008	C₂×C₆₁	1	4	yes	complemented
237	#1976	C₂×C₆₁	1	2	yes	complemented
238	#1757	C₂×C₆₁	1	1	yes	characteristic, complemented
239	C₂×C₆₁	—	2	2	no	—
240	C₂×C₆₁	—	2	1	no	—
241	C₂×C₆₁	—	4	2	no	—
242	C₂×C₆₁	—	8	4	no	—
243	C₂×C₆₁	—	16	2	no	—
244	C₂×C₆₁	#2433	1	1	yes	characteristic
245	#585	C₂²×C₆₁	1	2	yes	—
246	#578	—	2	2	no	—
247	#577	—	2	4	no	—
248	#576	—	2	2	no	—
249	#575	—	2	2	no	—
250	#575	C₂²×C₆₁	1	2	yes	—
251	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	4	yes	complemented
252	C₂×#135	—	2	2	no	—
253	C₂×#135	C₂²×C₆₁	1	2	yes	—
254	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
255	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
256	#535	C₂²×C₆₁	1	2	yes	—
257	#535	C₂²×C₆₁	1	4	yes	complemented
258	#496	—	2	4	no	—
259	#495	—	2	2	no	—
260	#493	—	2	2	no	—
261	#469	—	2	2	no	—
262	#466	—	2	2	no	—
263	B(4,𝔽₂)	—	2	8	no	—
264	#454	—	2	4	no	—
265	#453	—	2	4	no	—
266	#427	C₂²×C₆₁	1	1	yes	characteristic, complemented
267	#421	C₂²×C₆₁	1	4	yes	complemented
268	#418	C₂²×C₆₁	1	2	yes	complemented
269	#413	C₂²×C₆₁	1	1	yes	characteristic
270	#410	C₂²×C₆₁	1	1	yes	characteristic
271	#410	C₂²×C₆₁	1	4	yes	complemented
272	#405	C₂²×C₆₁	1	2	yes	complemented
273	#344	C₂²×C₆₁	1	2	yes	complemented
274	C₆₁	#25799	1	1	yes	characteristic, direct product factor, Sylow
275	2₋¹⁺⁴	—	2	4	no	—
276	2₋¹⁺⁴	—	2	2	no	—
277	H(5,𝔽₂)	—	2	4	no	—
278	H(5,𝔽₂)	—	2	4	no	—
279	H(5,𝔽₂)	—	2	2	no	—
280	C₂×#41	—	2	4	no	—
281	C₂×#41	—	4	4	no	—
282	C₂×#41	C₂³×C₆₁	1	4	yes	—
283	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
284	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
285	#137	—	2	8	no	—
286	#137	—	2	4	no	—
287	AGL(1,ℤ/8)	—	2	8	no	—
288	AGL(1,ℤ/8)	—	2	4	no	—
289	AGL(1,ℤ/8)	—	2	8	no	—
290	AGL(1,ℤ/8)	—	4	4	no	—
291	#135	—	2	4	no	—
292	#135	—	2	4	no	—
293	#135	—	2	2	no	—
294	#135	—	2	4	no	—
295	#135	—	2	2	no	—
296	#135	—	2	2	no	—
297	#135	—	2	2	no	—
298	C₂×Q₁₆	—	2	2	no	—
299	C₂×Q₁₆	D₄×C₆₁	1	2	yes	complemented
300	C₂×SD₁₆	—	2	4	no	—
301	C₂×SD₁₆	—	2	4	no	—
302	C₂×SD₁₆	D₄×C₆₁	1	4	yes	complemented
303	C₂×D₈	—	2	2	no	—
304	C₂×D₈	—	2	4	no	—
305	C₂×D₈	—	2	1	no	—
306	C₂×D₈	—	2	1	no	—
307	C₂×D₈	—	2	2	no	—
308	C₂×D₈	—	2	2	no	—
309	C₂×D₈	D₄×C₆₁	1	2	yes	complemented
310	#131	—	2	2	no	—
311	#131	—	2	2	no	—
312	C₂×M₁₆	D₄×C₆₁	1	2	yes	complemented
313	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
314	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
315	C₂²×C₈	D₄×C₆₁	1	2	yes	complemented
316	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
317	#127	—	2	2	no	—
318	#127	—	2	4	no	—
319	#124	—	2	2	no	—
320	#124	—	2	4	no	—
321	#121	—	2	4	no	—
322	#121	—	4	4	no	—
323	#120	—	2	4	no	—
324	#120	—	2	8	no	—
325	#117	C₂³×C₆₁	1	2	yes	—
326	#117	C₂³×C₆₁	1	2	yes	—
327	#107	—	2	1	no	—
328	#106	—	2	1	no	—
329	#104	—	2	8	no	—
330	#102	—	2	4	no	—
331	#101	D₄×C₆₁	1	2	yes	complemented
332	#100	D₄×C₆₁	1	2	yes	complemented
333	#99	—	2	8	no	—
334	#99	D₄×C₆₁	1	4	yes	—
335	#97	—	2	2	no	—
336	C₄×C₈	—	2	2	no	—
337	C₂⁴	—	2	2	no	—
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	#41	—	2	8	no	—
341	#41	—	2	4	no	—
342	#41	—	2	4	no	—
343	#41	—	2	4	no	—
344	#41	—	2	4	no	—
345	#41	—	4	8	no	—
346	#41	—	4	4	no	—
347	#41	—	4	4	no	—
348	#41	—	4	4	no	—
349	#41	—	4	4	no	—
350	C₂×Q₈	—	2	4	no	—
351	C₂×Q₈	—	4	4	no	—
352	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
353	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	4	8	no	—
361	C₂×D₄	—	4	4	no	—
362	C₂×D₄	—	4	8	no	—
363	C₂×D₄	—	4	4	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
366	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
367	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	4	4	no	—
370	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
371	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
372	Q₁₆	—	2	4	no	—
373	Q₁₆	—	2	2	no	—
374	Q₁₆	—	2	2	no	—
375	SD₁₆	—	2	8	no	—
376	SD₁₆	—	2	4	no	—
377	SD₁₆	—	2	4	no	—
378	SD₁₆	—	4	8	no	—
379	D₈	—	2	4	no	—
380	D₈	—	2	2	no	—
381	D₈	—	2	2	no	—
382	D₈	—	4	8	no	—
383	D₈	—	4	1	no	—
384	D₈	—	4	1	no	—
385	D₈	—	4	2	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	2	no	—
388	M₁₆	—	2	4	no	—
389	M₁₆	C₂×D₄×C₆₁	1	4	yes	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
394	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
395	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
396	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
397	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	4	8	no	—
402	C₂²⋊C₄	—	4	4	no	—
403	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₂³	—	2	4	no	—
407	C₂³	—	4	4	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	4	no	—
410	C₂³	—	16	2	no	—
411	C₂³	#127×C₆₁	1	2	yes	—
412	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
413	Q₈	—	2	2	no	—
414	Q₈	—	2	4	no	—
415	Q₈	—	2	4	no	—
416	Q₈	—	4	4	no	—
417	D₄	—	2	4	no	—
418	D₄	—	2	2	no	—
419	D₄	—	2	4	no	—
420	D₄	—	2	4	no	—
421	D₄	—	4	4	no	—
422	D₄	—	4	8	no	—
423	D₄	—	4	4	no	—
424	D₄	—	4	4	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	4	no	—
427	D₄	—	4	2	no	—
428	D₄	—	16	8	no	—
429	D₄	—	16	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	4	8	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	#127×C₆₁	1	2	yes	—
440	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
441	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
442	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
443	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
444	C₈	—	2	4	no	—
445	C₈	—	2	2	no	—
446	C₈	#120×C₆₁	1	1	yes	characteristic
447	C₈	#120×C₆₁	1	1	yes	characteristic
448	C₈	#120×C₆₁	1	2	yes	—
449	C₂²	—	2	2	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	8	4	no	—
454	C₂²	—	8	8	no	—
455	C₂²	—	8	4	no	—
456	C₂²	—	8	2	no	—
457	C₂²	—	16	4	no	—
458	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
459	C₂²	D₄²×C₆₁	1	2	yes	—
460	C₄	—	2	2	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	4	no	—
463	C₄	—	8	2	no	—
464	C₄	C₂×#120×C₆₁	1	1	yes	characteristic
465	C₄	C₆₁×#535	1	1	yes	characteristic
466	C₄	D₄²×C₆₁	1	2	yes	—
467	C₂	—	2	2	no	—
468	C₂	—	2	1	no	—
469	C₂	—	4	2	no	—
470	C₂	—	8	4	no	—
471	C₂	—	16	2	no	—
472	C₂	C₆₁×#2433	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₆₁	#2433
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
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
1. C₆₁×#3584	C₂	semidirect
2. C₆₁×#3155	C₂	semidirect
3. C₆₁×#3058	C₂	semidirect
4. C₆₁×#3027	C₂	semidirect
5. C₆₁×#3021	C₂	semidirect
6. C₆₁×#2008	C₂	semidirect
7. C₆₁×#1976	C₂	semidirect
8. C₆₁×#1757	C₂	semidirect
15. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
18. C₂²×D₈×C₆₁	C₂²	semidirect
21. C₆₁×#535	C₂²	semidirect
30. C₆₁×#427	C₂²	semidirect
31. C₆₁×#421	C₂²	semidirect
32. C₆₁×#418	C₂²	semidirect
35. C₆₁×#410	C₂²	semidirect
36. C₆₁×#405	C₂²	semidirect
37. C₆₁×#344	C₂²	semidirect
62. C₂×Q₁₆×C₆₁	D₄	semidirect
65. C₂×SD₁₆×C₆₁	D₄	semidirect
72. C₂×D₈×C₆₁	D₄	semidirect
75. C₂×M₁₆×C₆₁	D₄	semidirect
78. C₂²×C₈×C₆₁	D₄	semidirect
94. #101×C₆₁	D₄	semidirect
95. #100×C₆₁	D₄	semidirect
212. #25799	C₆₁	direct (N × H)
231. #3584	C₂×C₆₁	semidirect
232. #3155	C₂×C₆₁	semidirect
233. #3058	C₂×C₆₁	semidirect
234. #3027	C₂×C₆₁	semidirect
235. #3021	C₂×C₆₁	semidirect
236. #2008	C₂×C₆₁	semidirect
237. #1976	C₂×C₆₁	semidirect
238. #1757	C₂×C₆₁	semidirect
251. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
254. C₂²×D₈	C₂²×C₆₁	semidirect
257. #535	C₂²×C₆₁	semidirect
266. #427	C₂²×C₆₁	semidirect
267. #421	C₂²×C₆₁	semidirect
268. #418	C₂²×C₆₁	semidirect
271. #410	C₂²×C₆₁	semidirect
272. #405	C₂²×C₆₁	semidirect
273. #344	C₂²×C₆₁	semidirect
274. C₆₁	#25799	direct (N × H)
299. C₂×Q₁₆	D₄×C₆₁	semidirect
302. C₂×SD₁₆	D₄×C₆₁	semidirect
309. C₂×D₈	D₄×C₆₁	semidirect
312. C₂×M₁₆	D₄×C₆₁	semidirect
315. C₂²×C₈	D₄×C₆₁	semidirect
331. #101	D₄×C₆₁	semidirect
332. #100	D₄×C₆₁	semidirect

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×#3155	2
C₆₁×#3058	2
C₆₁×#3027	2
C₆₁×#3021	2
C₆₁×#2008	2
C₆₁×#1976	2
C₆₁×#1757	2
#25799	61

Subgroups — C61×#25799 #29529232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25799 #29529232