Subgroups — C₆₁×#25619 #29529052

Order 15616.

1052 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3512	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3152	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2642	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2007	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1998	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1963	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1882	C₂	1	4	yes	maximal, complemented
9	C₆₁×#1759	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#137×C₆₁	C₂²	1	4	yes	—
11	C₂×#137×C₆₁	C₂²	1	2	yes	—
12	C₆₁×#553	—	2	2	no	—
13	C₆₁×#553	—	2	4	no	—
14	C₆₁×#552	—	2	2	no	—
15	C₆₁×#541	—	2	1	no	—
16	C₆₁×#540	—	2	1	no	—
17	C₆₁×#537	C₂²	1	2	yes	—
18	C₆₁×#532	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#529	—	2	2	no	—
21	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
22	C₆₁×#520	C₂²	1	2	yes	—
23	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#497	—	2	2	no	—
25	C₆₁×#494	—	2	1	no	—
26	C₆₁×#492	—	2	1	no	—
27	C₆₁×#462	—	2	2	no	—
28	C₆₁×#461	—	2	2	no	—
29	C₆₁×#423	C₂²	1	1	yes	characteristic
30	C₂×#104×C₆₁	C₂²	1	2	yes	—
31	C₂×#104×C₆₁	C₂²	1	4	yes	—
32	C₆₁×#419	C₂²	1	2	yes	—
33	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#400	—	2	4	no	—
35	C₆₁×#391	C₂²	1	4	yes	—
36	C₆₁×#376	C₂²	1	1	yes	characteristic
37	C₆₁×#343	C₂²	1	4	yes	—
38	C₆₁×#339	C₂²	1	2	yes	—
39	C₂×#41×C₆₁	C₂³	1	2	yes	—
40	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
41	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
42	#137×C₆₁	—	2	8	no	—
43	#137×C₆₁	—	4	4	no	—
44	#137×C₆₁	—	4	4	no	—
45	C₂×Q₁₆×C₆₁	—	2	2	no	—
46	C₂×Q₁₆×C₆₁	—	2	4	no	—
47	C₂×SD₁₆×C₆₁	—	2	2	no	—
48	C₂×SD₁₆×C₆₁	—	2	4	no	—
49	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
50	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₆₁	—	2	2	no	—
52	C₄⋊Q₈×C₆₁	—	2	1	no	—
53	C₄⋊Q₈×C₆₁	—	2	1	no	—
54	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
55	#127×C₆₁	D₄	1	1	yes	characteristic
56	#126×C₆₁	—	2	4	no	—
57	#126×C₆₁	—	2	4	no	—
58	#125×C₆₁	—	2	4	no	—
59	#125×C₆₁	—	2	1	no	—
60	#125×C₆₁	—	2	2	no	—
61	#125×C₆₁	—	2	1	no	—
62	#124×C₆₁	D₄	1	2	yes	—
63	#123×C₆₁	—	2	4	no	—
64	#123×C₆₁	—	2	4	no	—
65	C₂²⋊Q₈×C₆₁	—	2	2	no	—
66	C₂²⋊Q₈×C₆₁	—	2	2	no	—
67	#121×C₆₁	—	2	4	no	—
68	#121×C₆₁	—	2	2	no	—
69	#121×C₆₁	—	2	2	no	—
70	#121×C₆₁	—	2	2	no	—
71	#121×C₆₁	—	2	4	no	—
72	C₄×Q₈×C₆₁	—	2	2	no	—
73	C₄×Q₈×C₆₁	D₄	1	2	yes	—
74	C₄×D₄×C₆₁	—	2	4	no	—
75	C₄×D₄×C₆₁	—	2	2	no	—
76	C₄×D₄×C₆₁	—	2	2	no	—
77	C₄×D₄×C₆₁	—	2	4	no	—
78	C₄×D₄×C₆₁	—	2	2	no	—
79	C₄×D₄×C₆₁	D₄	1	2	yes	—
80	#117×C₆₁	—	2	4	no	—
81	#117×C₆₁	—	2	2	no	—
82	#117×C₆₁	—	2	1	no	—
83	#117×C₆₁	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
85	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
86	C₂×C₄⋊C₄×C₆₁	D₄	1	4	yes	—
87	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
88	C₂×C₄²×C₆₁	—	2	1	no	—
89	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
90	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₆₁	—	2	2	no	—
92	#104×C₆₁	—	2	4	no	—
93	#104×C₆₁	—	4	4	no	—
94	#103×C₆₁	—	2	4	no	—
95	#97×C₆₁	—	2	1	no	—
96	C₄×C₈×C₆₁	—	2	1	no	—
97	#95×C₆₁	—	2	2	no	—
98	#95×C₆₁	—	2	8	no	—
99	#41×C₆₁	—	2	2	no	—
100	#41×C₆₁	—	2	4	no	—
101	#41×C₆₁	—	2	4	no	—
102	#41×C₆₁	—	2	2	no	—
103	C₂×Q₈×C₆₁	—	2	2	no	—
104	C₂×Q₈×C₆₁	—	2	2	no	—
105	C₂×Q₈×C₆₁	—	2	4	no	—
106	C₂×Q₈×C₆₁	—	2	4	no	—
107	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
108	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₂×D₄×C₆₁	—	2	1	no	—
110	C₂×D₄×C₆₁	—	2	2	no	—
111	C₂×D₄×C₆₁	—	2	4	no	—
112	C₂×D₄×C₆₁	—	2	2	no	—
113	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
114	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₁	—	2	4	no	—
116	C₂²×C₄×C₆₁	—	2	1	no	—
117	C₂²×C₄×C₆₁	—	2	2	no	—
118	C₂²×C₄×C₆₁	—	2	2	no	—
119	C₂²×C₄×C₆₁	—	2	2	no	—
120	C₂²×C₄×C₆₁	—	2	2	no	—
121	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
124	Q₁₆×C₆₁	—	4	8	no	—
125	Q₁₆×C₆₁	—	4	4	no	—
126	SD₁₆×C₆₁	—	4	8	no	—
127	SD₁₆×C₆₁	—	4	4	no	—
128	M₁₆×C₆₁	—	2	2	no	—
129	M₁₆×C₆₁	—	2	4	no	—
130	M₁₆×C₆₁	#41	1	4	yes	—
131	C₂×C₈×C₆₁	—	2	2	no	—
132	C₂×C₈×C₆₁	—	2	2	no	—
133	C₄⋊C₄×C₆₁	—	2	4	no	—
134	C₄⋊C₄×C₆₁	—	2	4	no	—
135	C₄⋊C₄×C₆₁	—	2	4	no	—
136	C₄⋊C₄×C₆₁	—	2	4	no	—
137	C₄⋊C₄×C₆₁	—	2	2	no	—
138	C₄⋊C₄×C₆₁	—	2	2	no	—
139	C₄⋊C₄×C₆₁	—	2	2	no	—
140	C₄⋊C₄×C₆₁	—	2	2	no	—
141	C₄⋊C₄×C₆₁	—	4	2	no	—
142	C₄⋊C₄×C₆₁	—	4	2	no	—
143	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
144	C₂²⋊C₄×C₆₁	—	2	4	no	—
145	C₂²⋊C₄×C₆₁	—	2	4	no	—
146	C₂²⋊C₄×C₆₁	—	2	4	no	—
147	C₂²⋊C₄×C₆₁	—	2	1	no	—
148	C₂²⋊C₄×C₆₁	—	2	2	no	—
149	C₂²⋊C₄×C₆₁	—	2	2	no	—
150	C₂²⋊C₄×C₆₁	—	2	2	no	—
151	C₄²×C₆₁	—	2	4	no	—
152	C₄²×C₆₁	—	2	2	no	—
153	C₄²×C₆₁	—	2	1	no	—
154	C₄²×C₆₁	—	2	2	no	—
155	C₄²×C₆₁	—	2	2	no	—
156	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₆₁	C₂×D₄	1	2	yes	—
159	C₂³×C₆₁	—	2	2	no	—
160	C₂³×C₆₁	—	2	1	no	—
161	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₆₁	—	2	1	no	—
163	Q₈×C₆₁	—	2	1	no	—
164	Q₈×C₆₁	—	2	4	no	—
165	Q₈×C₆₁	—	4	2	no	—
166	Q₈×C₆₁	—	4	2	no	—
167	Q₈×C₆₁	—	4	4	no	—
168	D₄×C₆₁	—	2	1	no	—
169	D₄×C₆₁	—	2	1	no	—
170	D₄×C₆₁	—	2	4	no	—
171	D₄×C₆₁	—	4	2	no	—
172	D₄×C₆₁	—	4	4	no	—
173	D₄×C₆₁	—	8	2	no	—
174	D₄×C₆₁	—	8	4	no	—
175	C₂×C₄×C₆₁	—	2	2	no	—
176	C₂×C₄×C₆₁	—	2	2	no	—
177	C₂×C₄×C₆₁	—	2	1	no	—
178	C₂×C₄×C₆₁	—	2	4	no	—
179	C₂×C₄×C₆₁	—	4	2	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	4	2	no	—
182	C₂×C₄×C₆₁	—	4	2	no	—
183	C₂×C₄×C₆₁	—	4	4	no	—
184	C₂×C₄×C₆₁	—	4	4	no	—
185	C₂×C₄×C₆₁	—	4	2	no	—
186	C₂×C₄×C₆₁	—	4	2	no	—
187	C₂×C₄×C₆₁	—	4	4	no	—
188	C₂×C₄×C₆₁	—	8	2	no	—
189	C₂×C₄×C₆₁	—	8	4	no	—
190	C₂×C₄×C₆₁	#120	1	2	yes	—
191	C₂×C₄×C₆₁	#120	1	2	yes	—
192	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
195	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
196	C₈×C₆₁	—	2	4	no	—
197	C₈×C₆₁	—	4	2	no	—
198	#25619	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₆₁	—	2	2	no	—
200	C₂²×C₆₁	—	4	2	no	—
201	C₂²×C₆₁	—	4	1	no	—
202	C₂²×C₆₁	—	4	2	no	—
203	C₂²×C₆₁	—	4	2	no	—
204	C₂²×C₆₁	—	4	2	no	—
205	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
206	C₂²×C₆₁	#550	1	2	yes	—
207	C₄×C₆₁	—	2	2	no	—
208	C₄×C₆₁	—	2	2	no	—
209	C₄×C₆₁	—	4	2	no	—
210	C₄×C₆₁	—	4	1	no	—
211	C₄×C₆₁	—	4	4	no	—
212	C₄×C₆₁	—	4	2	no	—
213	C₄×C₆₁	—	8	2	no	—
214	C₄×C₆₁	—	8	2	no	—
215	C₄×C₆₁	#532	1	1	yes	characteristic
216	C₄×C₆₁	#535	1	1	yes	characteristic
217	C₄×C₆₁	#546	1	2	yes	—
218	#3512	C₂×C₆₁	1	1	yes	characteristic
219	#3152	C₂×C₆₁	1	1	yes	characteristic, complemented
220	#3039	C₂×C₆₁	1	1	yes	characteristic, complemented
221	#2642	C₂×C₆₁	1	1	yes	characteristic, complemented
222	#2007	C₂×C₆₁	1	4	yes	complemented
223	#1998	C₂×C₆₁	1	1	yes	characteristic, complemented
224	#1963	C₂×C₆₁	1	1	yes	characteristic, complemented
225	#1882	C₂×C₆₁	1	4	yes	complemented
226	#1759	C₂×C₆₁	1	1	yes	characteristic, complemented
227	C₂×C₆₁	—	2	2	no	—
228	C₂×C₆₁	—	8	2	no	—
229	C₂×C₆₁	—	8	1	no	—
230	C₂×C₆₁	#2431	1	1	yes	characteristic
231	C₂×C₆₁	#3022	1	2	yes	—
232	C₂×#137	C₂²×C₆₁	1	4	yes	—
233	C₂×#137	C₂²×C₆₁	1	2	yes	—
234	#553	—	2	2	no	—
235	#553	—	2	4	no	—
236	#552	—	2	2	no	—
237	#541	—	2	1	no	—
238	#540	—	2	1	no	—
239	#537	C₂²×C₆₁	1	2	yes	—
240	#532	C₂²×C₆₁	1	1	yes	characteristic
241	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
242	#529	—	2	2	no	—
243	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
244	#520	C₂²×C₆₁	1	2	yes	—
245	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
246	#497	—	2	2	no	—
247	#494	—	2	1	no	—
248	#492	—	2	1	no	—
249	#462	—	2	2	no	—
250	#461	—	2	2	no	—
251	#423	C₂²×C₆₁	1	1	yes	characteristic
252	C₂×#104	C₂²×C₆₁	1	2	yes	—
253	C₂×#104	C₂²×C₆₁	1	4	yes	—
254	#419	C₂²×C₆₁	1	2	yes	—
255	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
256	#400	—	2	4	no	—
257	#391	C₂²×C₆₁	1	4	yes	—
258	#376	C₂²×C₆₁	1	1	yes	characteristic
259	#343	C₂²×C₆₁	1	4	yes	—
260	#339	C₂²×C₆₁	1	2	yes	—
261	C₆₁	#25619	1	1	yes	characteristic, direct product factor, Sylow
262	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
263	C₂×#41	C₂³×C₆₁	1	2	yes	—
264	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
265	#137	—	2	8	no	—
266	#137	—	4	4	no	—
267	#137	—	4	4	no	—
268	C₂×Q₁₆	—	2	2	no	—
269	C₂×Q₁₆	—	2	4	no	—
270	C₂×SD₁₆	—	2	2	no	—
271	C₂×SD₁₆	—	2	4	no	—
272	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
273	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
274	C₄⋊Q₈	—	2	2	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
278	#127	D₄×C₆₁	1	1	yes	characteristic
279	#126	—	2	4	no	—
280	#126	—	2	4	no	—
281	#125	—	2	4	no	—
282	#125	—	2	1	no	—
283	#125	—	2	1	no	—
284	#125	—	2	2	no	—
285	#124	D₄×C₆₁	1	2	yes	—
286	#123	—	2	4	no	—
287	#123	—	2	4	no	—
288	C₂²⋊Q₈	—	2	2	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	#121	—	2	4	no	—
291	#121	—	2	2	no	—
292	#121	—	2	2	no	—
293	#121	—	2	2	no	—
294	#121	—	2	4	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	D₄×C₆₁	1	2	yes	—
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	D₄×C₆₁	1	2	yes	—
303	#117	—	2	4	no	—
304	#117	—	2	2	no	—
305	#117	—	2	1	no	—
306	#117	C₂³×C₆₁	1	1	yes	characteristic
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	D₄×C₆₁	1	4	yes	—
310	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
313	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
314	C₄⋊C₈	—	2	2	no	—
315	#104	—	2	4	no	—
316	#104	—	4	4	no	—
317	#103	—	2	4	no	—
318	#97	—	2	1	no	—
319	C₄×C₈	—	2	1	no	—
320	#95	—	2	2	no	—
321	#95	—	2	8	no	—
322	#41	—	2	2	no	—
323	#41	—	2	4	no	—
324	#41	—	2	4	no	—
325	#41	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	4	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
331	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
337	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
345	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
346	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
347	Q₁₆	—	4	8	no	—
348	Q₁₆	—	4	4	no	—
349	SD₁₆	—	4	8	no	—
350	SD₁₆	—	4	4	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	4	no	—
353	M₁₆	#41×C₆₁	1	4	yes	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₄²	—	2	4	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
380	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
381	C₄²	C₂×D₄×C₆₁	1	2	yes	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	1	no	—
384	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
385	Q₈	—	2	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	—	2	4	no	—
388	Q₈	—	4	2	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	4	4	no	—
391	D₄	—	2	1	no	—
392	D₄	—	2	1	no	—
393	D₄	—	2	4	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	4	no	—
396	D₄	—	8	2	no	—
397	D₄	—	8	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	8	2	no	—
412	C₂×C₄	—	8	4	no	—
413	C₂×C₄	#120×C₆₁	1	2	yes	—
414	C₂×C₄	#120×C₆₁	1	2	yes	—
415	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
418	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
419	C₈	—	2	4	no	—
420	C₈	—	4	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
428	C₂²	C₆₁×#550	1	2	yes	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	4	no	—
434	C₄	—	4	2	no	—
435	C₄	—	8	2	no	—
436	C₄	—	8	2	no	—
437	C₄	C₆₁×#532	1	1	yes	characteristic
438	C₄	C₆₁×#535	1	1	yes	characteristic
439	C₄	C₆₁×#546	1	2	yes	—
440	C₂	—	2	2	no	—
441	C₂	—	8	2	no	—
442	C₂	—	8	1	no	—
443	C₂	C₆₁×#2431	1	1	yes	characteristic
444	C₂	C₆₁×#3022	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#3512	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#3152	C₂	semidirect
3. C₆₁×#3039	C₂	semidirect
4. C₆₁×#2642	C₂	semidirect
5. C₆₁×#2007	C₂	semidirect
6. C₆₁×#1998	C₂	semidirect
7. C₆₁×#1963	C₂	semidirect
8. C₆₁×#1882	C₂	semidirect
9. C₆₁×#1759	C₂	semidirect
198. #25619	C₆₁	direct (N × H)
219. #3152	C₂×C₆₁	semidirect
220. #3039	C₂×C₆₁	semidirect
221. #2642	C₂×C₆₁	semidirect
222. #2007	C₂×C₆₁	semidirect
223. #1998	C₂×C₆₁	semidirect
224. #1963	C₂×C₆₁	semidirect
225. #1882	C₂×C₆₁	semidirect
226. #1759	C₂×C₆₁	semidirect
261. C₆₁	#25619	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×#3512	2
C₆₁×#3152	2
C₆₁×#3039	2
C₆₁×#2642	2
C₆₁×#2007	2
C₆₁×#1998	2
C₆₁×#1963	2
C₆₁×#1882	2
C₆₁×#1759	2
#25619	61

Subgroups — C61×#25619 #29529052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25619 #29529052