Subgroups — C₆₁×#25050 #29528483

Order 15616.

720 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3098	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3060	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2952	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2078	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2040	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1974	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1951	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1860	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1815	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#537	C₂²	1	2	yes	—
15	C₆₁×#520	C₂²	1	2	yes	—
16	C₆₁×#485	—	2	2	no	—
17	C₆₁×#484	—	2	2	no	—
18	C₆₁×#482	—	2	2	no	—
19	C₆₁×#480	—	2	2	no	—
20	C₆₁×#470	—	2	1	no	—
21	C₆₁×#469	—	2	1	no	—
22	C₆₁×#465	—	2	2	no	—
23	C₆₁×#442	—	2	1	no	—
24	C₆₁×#441	—	2	1	no	—
25	C₄×SD₁₆×C₆₁	—	2	2	no	—
26	C₂×#108×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#428	C₂²	1	2	yes	—
28	C₂×#107×C₆₁	C₂²	1	2	yes	—
29	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#104×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#104×C₆₁	C₂²	1	2	yes	—
33	C₆₁×#417	C₂²	1	2	yes	—
34	C₆₁×#417	C₂²	1	2	yes	—
35	C₆₁×#417	C₂²	1	2	yes	—
36	C₆₁×#416	C₂²	1	1	yes	characteristic
37	C₆₁×#408	C₂²	1	2	yes	—
38	C₆₁×#405	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#382	C₂²	1	2	yes	—
41	C₆₁×#343	C₂²	1	2	yes	—
42	C₆₁×#343	C₂²	1	2	yes	—
43	C₆₁×#341	C₂²	1	1	yes	characteristic
44	C₆₁×#339	C₂²	1	1	yes	characteristic
45	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
46	C₂×#41×C₆₁	C₂³	1	2	yes	—
47	#135×C₆₁	—	2	2	no	—
48	#135×C₆₁	—	2	2	no	—
49	C₂×Q₁₆×C₆₁	D₄	1	1	yes	characteristic
50	C₂×SD₁₆×C₆₁	D₄	1	2	yes	—
51	C₂×D₈×C₆₁	D₄	1	1	yes	characteristic
52	#131×C₆₁	—	2	2	no	—
53	#131×C₆₁	—	2	2	no	—
54	C₂×M₁₆×C₆₁	—	2	1	no	—
55	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₆₁	—	2	1	no	—
59	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
61	C₂²⋊Q₈×C₆₁	—	2	2	no	—
62	C₂²⋊Q₈×C₆₁	—	2	2	no	—
63	#121×C₆₁	—	2	2	no	—
64	#121×C₆₁	—	2	2	no	—
65	#121×C₆₁	—	4	2	no	—
66	C₄×Q₈×C₆₁	—	2	2	no	—
67	C₄×D₄×C₆₁	—	2	2	no	—
68	C₄×D₄×C₆₁	—	4	2	no	—
69	#117×C₆₁	—	2	2	no	—
70	#117×C₆₁	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
74	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
75	#108×C₆₁	—	2	2	no	—
76	#107×C₆₁	—	2	2	no	—
77	#107×C₆₁	—	2	2	no	—
78	#107×C₆₁	—	2	2	no	—
79	#106×C₆₁	—	2	1	no	—
80	#106×C₆₁	—	2	1	no	—
81	#106×C₆₁	—	2	1	no	—
82	#106×C₆₁	—	2	1	no	—
83	#106×C₆₁	—	2	2	no	—
84	#104×C₆₁	—	2	2	no	—
85	#104×C₆₁	—	2	4	no	—
86	#103×C₆₁	—	2	2	no	—
87	#103×C₆₁	—	2	2	no	—
88	#103×C₆₁	—	2	2	no	—
89	#103×C₆₁	D₄	1	2	yes	—
90	#102×C₆₁	—	2	2	no	—
91	#102×C₆₁	—	2	2	no	—
92	#102×C₆₁	—	2	2	no	—
93	#102×C₆₁	D₄	1	2	yes	—
94	C₂²⋊C₈×C₆₁	—	2	2	no	—
95	C₂²⋊C₈×C₆₁	—	2	2	no	—
96	#97×C₆₁	—	2	1	no	—
97	C₄×C₈×C₆₁	—	2	1	no	—
98	C₄×C₈×C₆₁	—	2	2	no	—
99	#95×C₆₁	—	4	2	no	—
100	#41×C₆₁	—	2	2	no	—
101	#41×C₆₁	—	2	1	no	—
102	#41×C₆₁	—	2	1	no	—
103	#41×C₆₁	—	2	1	no	—
104	#41×C₆₁	—	2	2	no	—
105	#41×C₆₁	—	2	2	no	—
106	#41×C₆₁	—	2	1	no	—
107	#41×C₆₁	—	2	2	no	—
108	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₆₁	—	2	2	no	—
111	C₂×D₄×C₆₁	—	2	1	no	—
112	C₂×D₄×C₆₁	—	4	2	no	—
113	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
114	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₆₁	—	2	1	no	—
116	C₂²×C₄×C₆₁	—	2	2	no	—
117	C₂²×C₄×C₆₁	—	2	1	no	—
118	C₂²×C₄×C₆₁	—	2	2	no	—
119	C₂²×C₄×C₆₁	—	2	2	no	—
120	C₂²×C₄×C₆₁	—	4	2	no	—
121	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
122	Q₁₆×C₆₁	—	2	2	no	—
123	SD₁₆×C₆₁	—	2	4	no	—
124	D₈×C₆₁	—	2	2	no	—
125	M₁₆×C₆₁	—	2	2	no	—
126	M₁₆×C₆₁	—	2	1	no	—
127	M₁₆×C₆₁	—	2	2	no	—
128	M₁₆×C₆₁	—	2	1	no	—
129	M₁₆×C₆₁	—	2	1	no	—
130	M₁₆×C₆₁	—	2	1	no	—
131	M₁₆×C₆₁	—	4	2	no	—
132	C₂×C₈×C₆₁	—	2	1	no	—
133	C₂×C₈×C₆₁	—	2	1	no	—
134	C₂×C₈×C₆₁	—	2	1	no	—
135	C₂×C₈×C₆₁	—	2	2	no	—
136	C₂×C₈×C₆₁	—	2	1	no	—
137	C₂×C₈×C₆₁	—	4	2	no	—
138	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₆₁	#41	1	2	yes	—
142	C₂×C₈×C₆₁	#41	1	2	yes	—
143	C₄⋊C₄×C₆₁	—	2	2	no	—
144	C₄⋊C₄×C₆₁	—	2	2	no	—
145	C₄⋊C₄×C₆₁	—	2	2	no	—
146	C₄⋊C₄×C₆₁	—	2	2	no	—
147	C₄⋊C₄×C₆₁	—	4	2	no	—
148	C₄⋊C₄×C₆₁	—	4	2	no	—
149	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
150	C₂²⋊C₄×C₆₁	—	2	1	no	—
151	C₂²⋊C₄×C₆₁	—	4	2	no	—
152	C₂²⋊C₄×C₆₁	—	4	2	no	—
153	C₂²⋊C₄×C₆₁	—	4	2	no	—
154	C₄²×C₆₁	—	2	1	no	—
155	C₄²×C₆₁	—	2	1	no	—
156	C₄²×C₆₁	—	4	2	no	—
157	C₄²×C₆₁	#41	1	2	yes	—
158	C₂³×C₆₁	—	2	2	no	—
159	C₂³×C₆₁	—	2	1	no	—
160	C₂³×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
161	Q₈×C₆₁	—	2	2	no	—
162	Q₈×C₆₁	—	2	1	no	—
163	Q₈×C₆₁	—	2	1	no	—
164	Q₈×C₆₁	—	2	2	no	—
165	D₄×C₆₁	—	2	2	no	—
166	D₄×C₆₁	—	2	1	no	—
167	D₄×C₆₁	—	2	1	no	—
168	D₄×C₆₁	—	2	2	no	—
169	D₄×C₆₁	—	4	2	no	—
170	D₄×C₆₁	—	4	1	no	—
171	D₄×C₆₁	—	4	2	no	—
172	D₄×C₆₁	—	4	1	no	—
173	D₄×C₆₁	—	16	2	no	—
174	C₂×C₄×C₆₁	—	2	2	no	—
175	C₂×C₄×C₆₁	—	2	2	no	—
176	C₂×C₄×C₆₁	—	2	1	no	—
177	C₂×C₄×C₆₁	—	2	2	no	—
178	C₂×C₄×C₆₁	—	4	2	no	—
179	C₂×C₄×C₆₁	—	4	1	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	4	2	no	—
182	C₂×C₄×C₆₁	—	4	1	no	—
183	C₂×C₄×C₆₁	—	4	2	no	—
184	C₂×C₄×C₆₁	—	4	2	no	—
185	C₂×C₄×C₆₁	—	8	2	no	—
186	C₂×C₄×C₆₁	—	8	2	no	—
187	C₂×C₄×C₆₁	—	16	2	no	—
188	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
194	C₈×C₆₁	—	2	2	no	—
195	C₈×C₆₁	—	4	1	no	—
196	C₈×C₆₁	—	4	2	no	—
197	C₈×C₆₁	—	4	1	no	—
198	C₈×C₆₁	#123	1	2	yes	—
199	C₈×C₆₁	#123	1	2	yes	—
200	#25050	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂²×C₆₁	—	2	2	no	—
202	C₂²×C₆₁	—	4	1	no	—
203	C₂²×C₆₁	—	4	2	no	—
204	C₂²×C₆₁	—	4	2	no	—
205	C₂²×C₆₁	—	4	2	no	—
206	C₂²×C₆₁	—	4	2	no	—
207	C₂²×C₆₁	#542	1	1	yes	characteristic
208	C₂²×C₆₁	D₄²	1	1	yes	characteristic
209	C₂²×C₆₁	#553	1	1	yes	characteristic
210	C₄×C₆₁	—	4	2	no	—
211	C₄×C₆₁	—	4	2	no	—
212	C₄×C₆₁	—	4	1	no	—
213	C₄×C₆₁	—	4	2	no	—
214	C₄×C₆₁	—	8	2	no	—
215	C₄×C₆₁	—	8	2	no	—
216	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
217	C₄×C₆₁	#532	1	1	yes	characteristic
218	C₄×C₆₁	#547	1	1	yes	characteristic
219	C₄×C₆₁	#547	1	1	yes	characteristic
220	#3098	C₂×C₆₁	1	2	yes	complemented
221	#3060	C₂×C₆₁	1	1	yes	characteristic
222	#2952	C₂×C₆₁	1	1	yes	characteristic, complemented
223	#2078	C₂×C₆₁	1	2	yes	complemented
224	#2040	C₂×C₆₁	1	2	yes	complemented
225	#1974	C₂×C₆₁	1	1	yes	characteristic, complemented
226	#1951	C₂×C₆₁	1	1	yes	characteristic, complemented
227	#1860	C₂×C₆₁	1	2	yes	complemented
228	#1846	C₂×C₆₁	1	1	yes	characteristic, complemented
229	#1815	C₂×C₆₁	1	1	yes	characteristic, complemented
230	#1764	C₂×C₆₁	1	1	yes	characteristic, complemented
231	C₂×C₆₁	—	2	1	no	—
232	C₂×C₆₁	—	2	1	no	—
233	C₂×C₆₁	—	8	2	no	—
234	C₂×C₆₁	—	8	1	no	—
235	C₂×C₆₁	#2422	1	1	yes	characteristic
236	C₂×C₆₁	#3290	1	2	yes	—
237	C₂×#135	C₂²×C₆₁	1	1	yes	characteristic
238	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
239	#537	C₂²×C₆₁	1	2	yes	—
240	#520	C₂²×C₆₁	1	2	yes	—
241	#485	—	2	2	no	—
242	#484	—	2	2	no	—
243	#482	—	2	2	no	—
244	#480	—	2	2	no	—
245	#470	—	2	1	no	—
246	#469	—	2	1	no	—
247	#465	—	2	2	no	—
248	#442	—	2	1	no	—
249	#441	—	2	1	no	—
250	C₄×SD₁₆	—	2	2	no	—
251	C₂×#108	C₂²×C₆₁	1	1	yes	characteristic
252	#428	C₂²×C₆₁	1	2	yes	—
253	C₂×#107	C₂²×C₆₁	1	2	yes	—
254	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
255	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
256	C₂×#104	C₂²×C₆₁	1	2	yes	—
257	C₂×#104	C₂²×C₆₁	1	1	yes	characteristic
258	#417	C₂²×C₆₁	1	2	yes	—
259	#417	C₂²×C₆₁	1	2	yes	—
260	#417	C₂²×C₆₁	1	2	yes	—
261	#416	C₂²×C₆₁	1	1	yes	characteristic
262	#408	C₂²×C₆₁	1	2	yes	—
263	#405	C₂²×C₆₁	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
265	#382	C₂²×C₆₁	1	2	yes	—
266	#343	C₂²×C₆₁	1	2	yes	—
267	#343	C₂²×C₆₁	1	2	yes	—
268	#341	C₂²×C₆₁	1	1	yes	characteristic
269	#339	C₂²×C₆₁	1	1	yes	characteristic
270	C₆₁	#25050	1	1	yes	characteristic, direct product factor, Sylow
271	C₂×#41	C₂³×C₆₁	1	2	yes	—
272	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
273	#135	—	2	2	no	—
274	#135	—	2	2	no	—
275	C₂×Q₁₆	D₄×C₆₁	1	1	yes	characteristic
276	C₂×SD₁₆	D₄×C₆₁	1	2	yes	—
277	C₂×D₈	D₄×C₆₁	1	1	yes	characteristic
278	#131	—	2	2	no	—
279	#131	—	2	2	no	—
280	C₂×M₁₆	—	2	1	no	—
281	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
282	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
283	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
287	C₂²⋊Q₈	—	2	2	no	—
288	C₂²⋊Q₈	—	2	2	no	—
289	#121	—	2	2	no	—
290	#121	—	2	2	no	—
291	#121	—	4	2	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	—	4	2	no	—
295	#117	—	2	2	no	—
296	#117	C₂³×C₆₁	1	1	yes	characteristic
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
300	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
301	#108	—	2	2	no	—
302	#107	—	2	2	no	—
303	#107	—	2	2	no	—
304	#107	—	2	2	no	—
305	#106	—	2	1	no	—
306	#106	—	2	1	no	—
307	#106	—	2	1	no	—
308	#106	—	2	1	no	—
309	#106	—	2	2	no	—
310	#104	—	2	4	no	—
311	#104	—	2	2	no	—
312	#103	—	2	2	no	—
313	#103	—	2	2	no	—
314	#103	—	2	2	no	—
315	#103	D₄×C₆₁	1	2	yes	—
316	#102	—	2	2	no	—
317	#102	—	2	2	no	—
318	#102	—	2	2	no	—
319	#102	D₄×C₆₁	1	2	yes	—
320	C₂²⋊C₈	—	2	2	no	—
321	C₂²⋊C₈	—	2	2	no	—
322	#97	—	2	1	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	—	2	2	no	—
325	#95	—	4	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	1	no	—
328	#41	—	2	1	no	—
329	#41	—	2	1	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	#41	—	2	2	no	—
333	#41	—	2	1	no	—
334	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
335	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
340	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
348	Q₁₆	—	2	2	no	—
349	SD₁₆	—	2	4	no	—
350	D₈	—	2	2	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	1	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	2	1	no	—
357	M₁₆	—	4	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	4	2	no	—
364	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
365	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
366	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
367	C₂×C₈	#41×C₆₁	1	2	yes	—
368	C₂×C₈	#41×C₆₁	1	2	yes	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
376	C₂²⋊C₄	—	2	1	no	—
377	C₂²⋊C₄	—	4	2	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	4	2	no	—
383	C₄²	#41×C₆₁	1	2	yes	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	1	no	—
386	C₂³	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
387	Q₈	—	2	1	no	—
388	Q₈	—	2	1	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	2	2	no	—
391	D₄	—	2	1	no	—
392	D₄	—	2	1	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	1	no	—
399	D₄	—	16	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	8	2	no	—
412	C₂×C₄	—	8	2	no	—
413	C₂×C₄	—	16	2	no	—
414	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
418	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
419	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	1	no	—
424	C₈	#123×C₆₁	1	2	yes	—
425	C₈	#123×C₆₁	1	2	yes	—
426	C₂²	—	2	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	1	no	—
432	C₂²	C₆₁×#542	1	1	yes	characteristic
433	C₂²	D₄²×C₆₁	1	1	yes	characteristic
434	C₂²	C₆₁×#553	1	1	yes	characteristic
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	1	no	—
439	C₄	—	8	2	no	—
440	C₄	—	8	2	no	—
441	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
442	C₄	C₆₁×#532	1	1	yes	characteristic
443	C₄	C₆₁×#547	1	1	yes	characteristic
444	C₄	C₆₁×#547	1	1	yes	characteristic
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	8	2	no	—
448	C₂	—	8	1	no	—
449	C₂	C₆₁×#2422	1	1	yes	characteristic
450	C₂	C₆₁×#3290	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#3060	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂²×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3098	C₂	semidirect
3. C₆₁×#2952	C₂	semidirect
4. C₆₁×#2078	C₂	semidirect
5. C₆₁×#2040	C₂	semidirect
6. C₆₁×#1974	C₂	semidirect
7. C₆₁×#1951	C₂	semidirect
8. C₆₁×#1860	C₂	semidirect
9. C₆₁×#1846	C₂	semidirect
10. C₆₁×#1815	C₂	semidirect
11. C₆₁×#1764	C₂	semidirect
200. #25050	C₆₁	direct (N × H)
220. #3098	C₂×C₆₁	semidirect
222. #2952	C₂×C₆₁	semidirect
223. #2078	C₂×C₆₁	semidirect
224. #2040	C₂×C₆₁	semidirect
225. #1974	C₂×C₆₁	semidirect
226. #1951	C₂×C₆₁	semidirect
227. #1860	C₂×C₆₁	semidirect
228. #1846	C₂×C₆₁	semidirect
229. #1815	C₂×C₆₁	semidirect
230. #1764	C₂×C₆₁	semidirect
270. C₆₁	#25050	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×#3098	2
C₆₁×#3060	2
C₆₁×#2952	2
C₆₁×#2078	2
C₆₁×#2040	2
C₆₁×#1974	2
C₆₁×#1951	2
C₆₁×#1860	2
C₆₁×#1846	2
C₆₁×#1815	2
C₆₁×#1764	2
#25050	61

Subgroups — C61×#25050 #29528483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25050 #29528483