Subgroups — C₆₁×#24989 #29528422

Order 15616.

620 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#473	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2082	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2049	C₂	1	2	yes	maximal
5	C₆₁×#1979	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1953	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1905	C₂	1	2	yes	maximal
8	C₆₁×#1833	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1830	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1814	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#1757	C₂	1	1	yes	maximal, characteristic
12	C₂×#137×C₆₁	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
15	C₆₁×#519	C₂²	1	2	yes	—
16	C₆₁×#473	—	2	2	no	—
17	C₆₁×#473	—	2	2	no	—
18	C₆₁×#441	—	2	2	no	—
19	C₄×Q₁₆×C₆₁	—	2	2	no	—
20	C₆₁×#430	C₂²	1	2	yes	—
21	C₂×#108×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×#108×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#427	C₂²	1	1	yes	characteristic
24	C₆₁×#421	C₂²	1	2	yes	—
25	C₆₁×#419	C₂²	1	2	yes	—
26	C₆₁×#419	C₂²	1	2	yes	—
27	C₆₁×#413	C₂²	1	1	yes	characteristic
28	C₂×#101×C₆₁	C₂²	1	2	yes	—
29	C₂×#101×C₆₁	C₂²	1	2	yes	—
30	C₆₁×#410	C₂²	1	1	yes	characteristic
31	C₆₁×#405	C₂²	1	1	yes	characteristic
32	C₆₁×#405	C₂²	1	1	yes	characteristic
33	C₆₁×#344	C₂²	1	1	yes	characteristic
34	C₆₁×#344	C₂²	1	1	yes	characteristic
35	C₆₁×#344	C₂²	1	2	yes	—
36	C₆₁×#344	C₂²	1	2	yes	—
37	C₆₁×#344	C₂²	1	2	yes	—
38	C₆₁×H(3,ℤ/4)	C₂²	1	2	yes	—
39	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
41	#137×C₆₁	—	2	4	no	—
42	#137×C₆₁	—	4	2	no	—
43	C₂×Q₁₆×C₆₁	—	2	2	no	—
44	C₂×Q₁₆×C₆₁	—	2	1	no	—
45	C₂×Q₁₆×C₆₁	—	2	1	no	—
46	C₂×Q₁₆×C₆₁	—	2	1	no	—
47	C₂×Q₁₆×C₆₁	—	2	1	no	—
48	C₂×Q₁₆×C₆₁	D₄	1	2	yes	—
49	C₂×Q₁₆×C₆₁	D₄	1	2	yes	—
50	C₂×SD₁₆×C₆₁	—	2	2	no	—
51	#131×C₆₁	—	2	1	no	—
52	#131×C₆₁	—	2	1	no	—
53	#131×C₆₁	—	2	1	no	—
54	#131×C₆₁	—	2	1	no	—
55	C₂×M₁₆×C₆₁	—	2	1	no	—
56	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
58	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
60	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₆₁	—	2	1	no	—
62	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₆₁	—	2	4	no	—
64	C₄×Q₈×C₆₁	—	4	2	no	—
65	#117×C₆₁	—	2	4	no	—
66	#117×C₆₁	C₂³	1	1	yes	characteristic
67	#117×C₆₁	C₂³	1	2	yes	—
68	#117×C₆₁	C₂³	1	1	yes	characteristic
69	#108×C₆₁	—	2	1	no	—
70	#108×C₆₁	—	2	1	no	—
71	#108×C₆₁	—	2	1	no	—
72	#108×C₆₁	—	2	1	no	—
73	#108×C₆₁	—	4	2	no	—
74	#107×C₆₁	—	2	1	no	—
75	#106×C₆₁	—	2	1	no	—
76	#104×C₆₁	—	4	2	no	—
77	#103×C₆₁	—	2	4	no	—
78	#103×C₆₁	—	4	2	no	—
79	#101×C₆₁	—	2	4	no	—
80	#101×C₆₁	—	2	1	no	—
81	#101×C₆₁	—	4	2	no	—
82	#100×C₆₁	—	2	1	no	—
83	#99×C₆₁	—	2	2	no	—
84	#97×C₆₁	—	2	1	no	—
85	#97×C₆₁	—	2	1	no	—
86	C₄×C₈×C₆₁	—	2	1	no	—
87	C₄×C₈×C₆₁	—	2	1	no	—
88	#41×C₆₁	—	2	1	no	—
89	#41×C₆₁	—	2	1	no	—
90	#41×C₆₁	—	2	1	no	—
91	#41×C₆₁	—	2	1	no	—
92	C₂×Q₈×C₆₁	—	2	2	no	—
93	C₂×Q₈×C₆₁	—	2	2	no	—
94	C₂×Q₈×C₆₁	—	2	2	no	—
95	C₂×Q₈×C₆₁	—	2	2	no	—
96	C₂×Q₈×C₆₁	—	2	2	no	—
97	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
98	C₂×Q₈×C₆₁	#41	1	1	yes	characteristic
99	C₂×D₄×C₆₁	—	2	1	no	—
100	C₂×D₄×C₆₁	#41	1	1	yes	characteristic
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	—	2	1	no	—
103	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
104	Q₁₆×C₆₁	—	2	2	no	—
105	Q₁₆×C₆₁	—	2	2	no	—
106	Q₁₆×C₆₁	—	2	2	no	—
107	Q₁₆×C₆₁	—	2	2	no	—
108	Q₁₆×C₆₁	—	4	4	no	—
109	SD₁₆×C₆₁	—	4	4	no	—
110	M₁₆×C₆₁	—	2	1	no	—
111	M₁₆×C₆₁	—	2	2	no	—
112	M₁₆×C₆₁	—	2	1	no	—
113	M₁₆×C₆₁	—	2	1	no	—
114	M₁₆×C₆₁	—	2	2	no	—
115	M₁₆×C₆₁	—	2	1	no	—
116	M₁₆×C₆₁	—	2	1	no	—
117	M₁₆×C₆₁	—	2	2	no	—
118	M₁₆×C₆₁	—	2	1	no	—
119	M₁₆×C₆₁	—	2	2	no	—
120	M₁₆×C₆₁	—	4	1	no	—
121	M₁₆×C₆₁	—	4	1	no	—
122	C₂×C₈×C₆₁	—	2	1	no	—
123	C₂×C₈×C₆₁	—	2	1	no	—
124	C₂×C₈×C₆₁	—	2	1	no	—
125	C₂×C₈×C₆₁	—	2	2	no	—
126	C₂×C₈×C₆₁	—	2	2	no	—
127	C₂×C₈×C₆₁	—	4	1	no	—
128	C₂×C₈×C₆₁	—	4	1	no	—
129	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
132	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
133	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
134	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
135	C₄⋊C₄×C₆₁	—	2	1	no	—
136	C₄⋊C₄×C₆₁	—	2	2	no	—
137	C₄⋊C₄×C₆₁	—	2	1	no	—
138	C₄⋊C₄×C₆₁	—	4	4	no	—
139	C₂²⋊C₄×C₆₁	—	2	1	no	—
140	C₂²⋊C₄×C₆₁	—	2	2	no	—
141	C₂²⋊C₄×C₆₁	#41	1	2	yes	—
142	C₄²×C₆₁	—	2	1	no	—
143	C₄²×C₆₁	—	2	1	no	—
144	C₄²×C₆₁	—	2	2	no	—
145	C₄²×C₆₁	—	4	4	no	—
146	C₂³×C₆₁	—	2	1	no	—
147	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
148	Q₈×C₆₁	—	2	4	no	—
149	Q₈×C₆₁	—	2	4	no	—
150	Q₈×C₆₁	—	2	1	no	—
151	Q₈×C₆₁	—	2	1	no	—
152	Q₈×C₆₁	—	4	2	no	—
153	Q₈×C₆₁	—	4	2	no	—
154	D₄×C₆₁	—	2	1	no	—
155	D₄×C₆₁	—	2	1	no	—
156	D₄×C₆₁	—	4	1	no	—
157	D₄×C₆₁	—	4	1	no	—
158	C₂×C₄×C₆₁	—	2	1	no	—
159	C₂×C₄×C₆₁	—	2	2	no	—
160	C₂×C₄×C₆₁	—	2	4	no	—
161	C₂×C₄×C₆₁	—	4	2	no	—
162	C₂×C₄×C₆₁	—	4	2	no	—
163	C₂×C₄×C₆₁	—	4	1	no	—
164	C₂×C₄×C₆₁	—	4	1	no	—
165	C₂×C₄×C₆₁	—	4	2	no	—
166	C₂×C₄×C₆₁	—	4	1	no	—
167	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
173	C₈×C₆₁	—	4	1	no	—
174	C₈×C₆₁	—	4	2	no	—
175	C₈×C₆₁	—	4	1	no	—
176	C₈×C₆₁	—	4	2	no	—
177	C₈×C₆₁	—	4	1	no	—
178	C₈×C₆₁	#123	1	1	yes	characteristic
179	C₈×C₆₁	#123	1	1	yes	characteristic
180	C₈×C₆₁	#123	1	1	yes	characteristic
181	C₈×C₆₁	#123	1	1	yes	characteristic
182	#24989	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂²×C₆₁	—	4	1	no	—
184	C₂²×C₆₁	—	4	1	no	—
185	C₂²×C₆₁	—	8	1	no	—
186	C₂²×C₆₁	#529	1	1	yes	characteristic
187	C₂²×C₆₁	#546	1	1	yes	characteristic
188	C₂²×C₆₁	#555	1	1	yes	characteristic
189	C₄×C₆₁	—	4	2	no	—
190	C₄×C₆₁	—	4	1	no	—
191	C₄×C₆₁	—	4	4	no	—
192	C₄×C₆₁	—	8	2	no	—
193	C₄×C₆₁	—	8	1	no	—
194	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
195	C₄×C₆₁	#540	1	1	yes	characteristic
196	C₄×C₆₁	#546	1	1	yes	characteristic
197	C₄×C₆₁	#553	1	1	yes	characteristic
198	C₂×#473	C₂×C₆₁	1	1	yes	characteristic
199	#2950	C₂×C₆₁	1	1	yes	characteristic, complemented
200	#2082	C₂×C₆₁	1	2	yes	complemented
201	#2049	C₂×C₆₁	1	2	yes	—
202	#1979	C₂×C₆₁	1	1	yes	characteristic, complemented
203	#1953	C₂×C₆₁	1	1	yes	characteristic, complemented
204	#1905	C₂×C₆₁	1	2	yes	—
205	#1833	C₂×C₆₁	1	1	yes	characteristic, complemented
206	#1830	C₂×C₆₁	1	2	yes	complemented
207	#1814	C₂×C₆₁	1	1	yes	characteristic
208	#1757	C₂×C₆₁	1	1	yes	characteristic
209	C₂×C₆₁	—	2	1	no	—
210	C₂×C₆₁	—	2	1	no	—
211	C₂×C₆₁	—	2	1	no	—
212	C₂×C₆₁	—	8	1	no	—
213	C₂×C₆₁	#2420	1	1	yes	characteristic
214	C₂×#137	C₂²×C₆₁	1	2	yes	—
215	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
216	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
217	#519	C₂²×C₆₁	1	2	yes	—
218	#473	—	2	2	no	—
219	#473	—	2	2	no	—
220	#441	—	2	2	no	—
221	C₄×Q₁₆	—	2	2	no	—
222	#430	C₂²×C₆₁	1	2	yes	—
223	C₂×#108	C₂²×C₆₁	1	1	yes	characteristic
224	C₂×#108	C₂²×C₆₁	1	1	yes	characteristic
225	#427	C₂²×C₆₁	1	1	yes	characteristic
226	#421	C₂²×C₆₁	1	2	yes	—
227	#419	C₂²×C₆₁	1	2	yes	—
228	#419	C₂²×C₆₁	1	2	yes	—
229	#413	C₂²×C₆₁	1	1	yes	characteristic
230	C₂×#101	C₂²×C₆₁	1	2	yes	—
231	C₂×#101	C₂²×C₆₁	1	2	yes	—
232	#410	C₂²×C₆₁	1	1	yes	characteristic
233	#405	C₂²×C₆₁	1	1	yes	characteristic
234	#405	C₂²×C₆₁	1	1	yes	characteristic
235	#344	C₂²×C₆₁	1	2	yes	—
236	#344	C₂²×C₆₁	1	2	yes	—
237	#344	C₂²×C₆₁	1	1	yes	characteristic
238	#344	C₂²×C₆₁	1	1	yes	characteristic
239	#344	C₂²×C₆₁	1	2	yes	—
240	H(3,ℤ/4)	C₂²×C₆₁	1	2	yes	—
241	C₆₁	#24989	1	1	yes	characteristic, direct product factor, Sylow
242	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
243	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
244	#137	—	2	4	no	—
245	#137	—	4	2	no	—
246	C₂×Q₁₆	—	2	2	no	—
247	C₂×Q₁₆	—	2	1	no	—
248	C₂×Q₁₆	—	2	1	no	—
249	C₂×Q₁₆	—	2	1	no	—
250	C₂×Q₁₆	—	2	1	no	—
251	C₂×Q₁₆	D₄×C₆₁	1	2	yes	—
252	C₂×Q₁₆	D₄×C₆₁	1	2	yes	—
253	C₂×SD₁₆	—	2	2	no	—
254	#131	—	2	1	no	—
255	#131	—	2	1	no	—
256	#131	—	2	1	no	—
257	#131	—	2	1	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
260	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
261	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
262	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
263	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
266	C₄×Q₈	—	2	4	no	—
267	C₄×Q₈	—	4	2	no	—
268	#117	—	2	4	no	—
269	#117	C₂³×C₆₁	1	2	yes	—
270	#117	C₂³×C₆₁	1	1	yes	characteristic
271	#117	C₂³×C₆₁	1	1	yes	characteristic
272	#108	—	2	1	no	—
273	#108	—	2	1	no	—
274	#108	—	2	1	no	—
275	#108	—	2	1	no	—
276	#108	—	4	2	no	—
277	#107	—	2	1	no	—
278	#106	—	2	1	no	—
279	#104	—	4	2	no	—
280	#103	—	2	4	no	—
281	#103	—	4	2	no	—
282	#101	—	2	4	no	—
283	#101	—	2	1	no	—
284	#101	—	4	2	no	—
285	#100	—	2	1	no	—
286	#99	—	2	2	no	—
287	#97	—	2	1	no	—
288	#97	—	2	1	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	—	2	1	no	—
291	#41	—	2	1	no	—
292	#41	—	2	1	no	—
293	#41	—	2	1	no	—
294	#41	—	2	1	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
301	C₂×Q₈	#41×C₆₁	1	1	yes	characteristic
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	#41×C₆₁	1	1	yes	characteristic
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
307	Q₁₆	—	2	2	no	—
308	Q₁₆	—	2	2	no	—
309	Q₁₆	—	2	2	no	—
310	Q₁₆	—	2	2	no	—
311	Q₁₆	—	4	4	no	—
312	SD₁₆	—	4	4	no	—
313	M₁₆	—	2	1	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	1	no	—
316	M₁₆	—	2	1	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	1	no	—
319	M₁₆	—	2	1	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	2	1	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	4	1	no	—
324	M₁₆	—	4	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
333	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
334	C₂×C₈	#41×C₆₁	1	1	yes	characteristic
335	C₂×C₈	#41×C₆₁	1	1	yes	characteristic
336	C₂×C₈	#41×C₆₁	1	1	yes	characteristic
337	C₂×C₈	#41×C₆₁	1	1	yes	characteristic
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	—	2	1	no	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	#41×C₆₁	1	2	yes	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	4	4	no	—
349	C₂³	—	2	1	no	—
350	C₂³	C₂×#41×C₆₁	1	1	yes	characteristic
351	Q₈	—	2	4	no	—
352	Q₈	—	2	1	no	—
353	Q₈	—	2	1	no	—
354	Q₈	—	2	4	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	4	2	no	—
357	D₄	—	2	1	no	—
358	D₄	—	2	1	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
374	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
375	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
376	C₈	—	4	2	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	1	no	—
380	C₈	—	4	1	no	—
381	C₈	#123×C₆₁	1	1	yes	characteristic
382	C₈	#123×C₆₁	1	1	yes	characteristic
383	C₈	#123×C₆₁	1	1	yes	characteristic
384	C₈	#123×C₆₁	1	1	yes	characteristic
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	8	1	no	—
388	C₂²	C₆₁×#529	1	1	yes	characteristic
389	C₂²	C₆₁×#546	1	1	yes	characteristic
390	C₂²	C₆₁×#555	1	1	yes	characteristic
391	C₄	—	4	2	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	4	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	1	no	—
396	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
397	C₄	C₆₁×#540	1	1	yes	characteristic
398	C₄	C₆₁×#546	1	1	yes	characteristic
399	C₄	C₆₁×#553	1	1	yes	characteristic
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	8	1	no	—
404	C₂	C₆₁×#2420	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₆₁	#2420
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#41×C₆₁	C₂³
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×#2950	C₂	semidirect
3. C₆₁×#2082	C₂	semidirect
5. C₆₁×#1979	C₂	semidirect
6. C₆₁×#1953	C₂	semidirect
8. C₆₁×#1833	C₂	semidirect
9. C₆₁×#1830	C₂	semidirect
182. #24989	C₆₁	direct (N × H)
199. #2950	C₂×C₆₁	semidirect
200. #2082	C₂×C₆₁	semidirect
202. #1979	C₂×C₆₁	semidirect
203. #1953	C₂×C₆₁	semidirect
205. #1833	C₂×C₆₁	semidirect
206. #1830	C₂×C₆₁	semidirect
241. C₆₁	#24989	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#473	2
C₆₁×#2950	2
C₆₁×#2082	2
C₆₁×#2049	2
C₆₁×#1979	2
C₆₁×#1953	2
C₆₁×#1905	2
C₆₁×#1833	2
C₆₁×#1830	2
C₆₁×#1814	2
C₆₁×#1757	2
#24989	61

Subgroups — C61×#24989 #29528422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24989 #29528422