Subgroups — C₆₁×#10054 #29513487

Order 15616.

838 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2541	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1987	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₆₁×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₆₁	—	2	2	no	—
9	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₂×#127×C₆₁	—	2	1	no	—
11	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
12	C₂×#121×C₆₁	—	2	2	no	—
13	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#492	—	2	2	no	—
15	C₆₁×#492	—	2	2	no	—
16	C₆₁×#476	—	2	2	no	—
17	C₆₁×#476	—	2	2	no	—
18	C₂×#106×C₆₁	—	2	1	no	—
19	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#102×C₆₁	—	2	1	no	—
22	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#392	—	2	2	no	—
24	C₆₁×#390	—	2	1	no	—
25	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#340	—	2	2	no	—
27	C₆₁×#331	—	2	2	no	—
28	C₆₁×D₄⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₆₁	—	2	1	no	—
30	C₂²×D₄×C₆₁	—	2	4	no	—
31	C₂²×D₄×C₆₁	—	2	1	no	—
32	C₂²×D₄×C₆₁	—	2	1	no	—
33	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
34	C₂²×D₄×C₆₁	D₄	1	2	yes	—
35	C₂³×C₄×C₆₁	—	2	1	no	—
36	C₂×SD₁₆×C₆₁	—	2	8	no	—
37	C₂×SD₁₆×C₆₁	—	4	8	no	—
38	C₂²×C₈×C₆₁	—	2	1	no	—
39	C₂²×C₈×C₆₁	—	2	1	no	—
40	C₂²×C₈×C₆₁	—	2	1	no	—
41	C₄⋊Q₈×C₆₁	—	2	1	no	—
42	C₄⋊Q₈×C₆₁	—	2	1	no	—
43	C₄⋊Q₈×C₆₁	—	2	1	no	—
44	C₄⋊Q₈×C₆₁	D₄	1	2	yes	complemented
45	#127×C₆₁	—	2	1	no	—
46	#127×C₆₁	—	2	1	no	—
47	#127×C₆₁	—	2	1	no	—
48	#127×C₆₁	—	2	1	no	—
49	#127×C₆₁	—	4	2	no	—
50	#127×C₆₁	—	4	2	no	—
51	#121×C₆₁	—	4	4	no	—
52	#121×C₆₁	—	4	4	no	—
53	C₄×D₄×C₆₁	—	2	1	no	—
54	C₄×D₄×C₆₁	—	2	1	no	—
55	C₄×D₄×C₆₁	—	2	1	no	—
56	C₄×D₄×C₆₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
63	C₂×C₄²×C₆₁	—	2	1	no	—
64	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
65	#106×C₆₁	—	2	4	no	—
66	C₄⋊C₈×C₆₁	—	2	1	no	—
67	C₄⋊C₈×C₆₁	—	2	1	no	—
68	C₄⋊C₈×C₆₁	—	2	1	no	—
69	C₄⋊C₈×C₆₁	D₄	1	2	yes	complemented
70	#102×C₆₁	—	2	4	no	—
71	C₄×C₈×C₆₁	—	2	1	no	—
72	C₄×C₈×C₆₁	D₄	1	2	yes	complemented
73	#95×C₆₁	—	2	1	no	—
74	C₂⁴×C₆₁	—	2	1	no	—
75	C₂⁴×C₆₁	—	2	2	no	—
76	C₂×Q₈×C₆₁	—	2	2	no	—
77	C₂×Q₈×C₆₁	—	4	4	no	—
78	C₂×Q₈×C₆₁	—	4	1	no	—
79	C₂×D₄×C₆₁	—	2	1	no	—
80	C₂×D₄×C₆₁	—	2	2	no	—
81	C₂×D₄×C₆₁	—	2	1	no	—
82	C₂×D₄×C₆₁	—	2	2	no	—
83	C₂×D₄×C₆₁	—	2	1	no	—
84	C₂×D₄×C₆₁	—	2	1	no	—
85	C₂×D₄×C₆₁	—	2	1	no	—
86	C₂×D₄×C₆₁	—	4	4	no	—
87	C₂×D₄×C₆₁	—	4	8	no	—
88	C₂×D₄×C₆₁	—	4	8	no	—
89	C₂×D₄×C₆₁	—	4	1	no	—
90	C₂×D₄×C₆₁	—	4	1	no	—
91	C₂×D₄×C₆₁	—	4	1	no	—
92	C₂×D₄×C₆₁	—	4	1	no	—
93	C₂×D₄×C₆₁	—	4	2	no	—
94	C₂×D₄×C₆₁	—	4	1	no	—
95	C₂×D₄×C₆₁	—	4	1	no	—
96	C₂×D₄×C₆₁	—	4	2	no	—
97	C₂×D₄×C₆₁	—	4	1	no	—
98	C₂×D₄×C₆₁	—	4	1	no	—
99	C₂×D₄×C₆₁	—	8	4	no	—
100	C₂×D₄×C₆₁	SD₁₆	1	2	yes	complemented
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	—	2	1	no	—
103	C₂²×C₄×C₆₁	—	4	1	no	—
104	C₂²×C₄×C₆₁	—	4	1	no	—
105	C₂²×C₄×C₆₁	—	4	1	no	—
106	C₂²×C₄×C₆₁	—	4	2	no	—
107	C₂²×C₄×C₆₁	—	4	2	no	—
108	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
111	SD₁₆×C₆₁	—	4	16	no	—
112	C₂×C₈×C₆₁	—	2	4	no	—
113	C₂×C₈×C₆₁	—	2	2	no	—
114	C₂×C₈×C₆₁	—	2	2	no	—
115	C₂×C₈×C₆₁	—	4	1	no	—
116	C₂×C₈×C₆₁	—	4	1	no	—
117	C₂×C₈×C₆₁	—	4	1	no	—
118	C₂×C₈×C₆₁	—	4	2	no	—
119	C₄⋊C₄×C₆₁	—	2	2	no	—
120	C₄⋊C₄×C₆₁	—	2	2	no	—
121	C₄⋊C₄×C₆₁	—	2	1	no	—
122	C₄⋊C₄×C₆₁	—	2	2	no	—
123	C₄⋊C₄×C₆₁	—	2	1	no	—
124	C₄⋊C₄×C₆₁	—	4	1	no	—
125	C₄⋊C₄×C₆₁	—	4	1	no	—
126	C₄⋊C₄×C₆₁	SD₁₆	1	4	yes	complemented
127	C₂²⋊C₄×C₆₁	—	4	8	no	—
128	C₂²⋊C₄×C₆₁	—	4	1	no	—
129	C₂²⋊C₄×C₆₁	—	4	1	no	—
130	C₄²×C₆₁	—	4	1	no	—
131	C₄²×C₆₁	—	4	1	no	—
132	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₆₁	#41	1	1	yes	characteristic
136	C₂³×C₆₁	—	2	2	no	—
137	C₂³×C₆₁	—	4	1	no	—
138	C₂³×C₆₁	—	4	2	no	—
139	C₂³×C₆₁	—	4	1	no	—
140	C₂³×C₆₁	—	4	2	no	—
141	C₂³×C₆₁	—	4	2	no	—
142	C₂³×C₆₁	—	4	4	no	—
143	C₂³×C₆₁	—	4	2	no	—
144	C₂³×C₆₁	—	4	2	no	—
145	C₂³×C₆₁	—	4	4	no	—
146	C₂³×C₆₁	#120	1	1	yes	characteristic
147	Q₈×C₆₁	—	4	4	no	—
148	Q₈×C₆₁	—	8	2	no	—
149	D₄×C₆₁	—	2	2	no	—
150	D₄×C₆₁	—	2	2	no	—
151	D₄×C₆₁	—	4	4	no	—
152	D₄×C₆₁	—	4	1	no	—
153	D₄×C₆₁	—	4	1	no	—
154	D₄×C₆₁	—	8	2	no	—
155	D₄×C₆₁	—	8	16	no	—
156	D₄×C₆₁	—	8	1	no	—
157	D₄×C₆₁	—	8	1	no	—
158	D₄×C₆₁	—	8	2	no	—
159	D₄×C₆₁	—	8	1	no	—
160	D₄×C₆₁	—	8	1	no	—
161	D₄×C₆₁	—	8	1	no	—
162	D₄×C₆₁	—	8	1	no	—
163	C₂×C₄×C₆₁	—	2	2	no	—
164	C₂×C₄×C₆₁	—	2	4	no	—
165	C₂×C₄×C₆₁	—	4	2	no	—
166	C₂×C₄×C₆₁	—	4	2	no	—
167	C₂×C₄×C₆₁	—	4	1	no	—
168	C₂×C₄×C₆₁	—	4	2	no	—
169	C₂×C₄×C₆₁	—	4	2	no	—
170	C₂×C₄×C₆₁	—	8	2	no	—
171	C₂×C₄×C₆₁	—	8	2	no	—
172	C₂×C₄×C₆₁	—	8	1	no	—
173	C₂×C₄×C₆₁	—	8	1	no	—
174	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
175	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
176	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
177	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
178	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
179	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
180	C₂×C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
181	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
182	C₂×C₄×C₆₁	#135	1	1	yes	characteristic
183	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
185	C₂×C₄×C₆₁	#137	1	1	yes	characteristic
186	C₈×C₆₁	—	2	4	no	—
187	C₈×C₆₁	—	4	2	no	—
188	C₈×C₆₁	—	8	1	no	—
189	#10054	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂²×C₆₁	—	4	4	no	—
191	C₂²×C₆₁	—	4	2	no	—
192	C₂²×C₆₁	—	8	2	no	—
193	C₂²×C₆₁	—	8	1	no	—
194	C₂²×C₆₁	—	8	1	no	—
195	C₂²×C₆₁	—	8	4	no	—
196	C₂²×C₆₁	—	8	4	no	—
197	C₂²×C₆₁	—	8	2	no	—
198	C₂²×C₆₁	—	8	2	no	—
199	C₂²×C₆₁	—	8	2	no	—
200	C₂²×C₆₁	#392	1	1	yes	characteristic
201	C₂²×C₆₁	#450	1	1	yes	characteristic
202	C₂²×C₆₁	#450	1	2	yes	—
203	C₂²×C₆₁	#452	1	1	yes	characteristic
204	C₂²×C₆₁	#453	1	2	yes	—
205	C₄×C₆₁	—	2	1	no	—
206	C₄×C₆₁	—	2	1	no	—
207	C₄×C₆₁	—	4	4	no	—
208	C₄×C₆₁	—	8	2	no	—
209	C₄×C₆₁	—	8	1	no	—
210	C₄×C₆₁	#448	1	1	yes	characteristic
211	C₄×C₆₁	#449	1	1	yes	characteristic
212	C₄×C₆₁	#460	1	2	yes	—
213	C₄×C₆₁	#465	1	1	yes	characteristic
214	C₄×C₆₁	#468	1	1	yes	characteristic
215	C₄×C₆₁	#492	1	1	yes	characteristic
216	C₄×C₆₁	#496	1	1	yes	characteristic
217	C₂×#492	C₂×C₆₁	1	1	yes	characteristic, complemented
218	C₂×#476	C₂×C₆₁	1	1	yes	characteristic, complemented
219	#2541	C₂×C₆₁	1	1	yes	characteristic
220	#1987	C₂×C₆₁	1	1	yes	characteristic, complemented
221	C₂×#331	C₂×C₆₁	1	1	yes	characteristic, complemented
222	C₂×D₄⋊C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
223	#1279	C₂×C₆₁	1	1	yes	characteristic, complemented
224	C₂×C₆₁	—	8	2	no	—
225	C₂×C₆₁	—	16	2	no	—
226	C₂×C₆₁	#1629	1	2	yes	—
227	C₂×C₆₁	#1631	1	2	yes	—
228	C₂×C₆₁	#2000	1	1	yes	characteristic
229	C₂×C₆₁	#2002	1	1	yes	characteristic
230	C₂×C₆₁	#2014	1	1	yes	characteristic
231	C₂²×SD₁₆	—	2	2	no	—
232	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
233	C₂×#127	—	2	1	no	—
234	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
235	C₂×#121	—	2	2	no	—
236	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
237	#492	—	2	2	no	—
238	#492	—	2	2	no	—
239	#476	—	2	2	no	—
240	#476	—	2	2	no	—
241	C₂×#106	—	2	1	no	—
242	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
244	C₂×#102	—	2	1	no	—
245	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
246	#392	—	2	2	no	—
247	#390	—	2	1	no	—
248	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
249	#340	—	2	2	no	—
250	#331	—	2	2	no	—
251	D₄⋊C₈	—	2	2	no	—
252	C₆₁	#10054	1	1	yes	characteristic, direct product factor, Sylow
253	C₂²×Q₈	—	2	1	no	—
254	C₂²×D₄	—	2	4	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
258	C₂²×D₄	D₄×C₆₁	1	2	yes	—
259	C₂³×C₄	—	2	1	no	—
260	C₂×SD₁₆	—	2	8	no	—
261	C₂×SD₁₆	—	4	8	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	D₄×C₆₁	1	2	yes	complemented
269	#127	—	2	1	no	—
270	#127	—	2	1	no	—
271	#127	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	—	4	2	no	—
274	#127	—	4	2	no	—
275	#121	—	4	4	no	—
276	#121	—	4	4	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
284	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	4	no	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
289	#106	—	2	4	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	D₄×C₆₁	1	2	yes	complemented
294	#102	—	2	4	no	—
295	C₄×C₈	—	2	1	no	—
296	C₄×C₈	D₄×C₆₁	1	2	yes	complemented
297	#95	—	2	1	no	—
298	C₂⁴	—	2	1	no	—
299	C₂⁴	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	4	4	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	4	4	no	—
311	C₂×D₄	—	4	8	no	—
312	C₂×D₄	—	4	8	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	8	4	no	—
324	C₂×D₄	SD₁₆×C₆₁	1	2	yes	complemented
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
335	SD₁₆	—	4	16	no	—
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	SD₁₆×C₆₁	1	4	yes	complemented
351	C₂²⋊C₄	—	4	8	no	—
352	C₂²⋊C₄	—	4	1	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₄²	—	4	1	no	—
355	C₄²	—	4	1	no	—
356	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
357	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
358	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
359	C₄²	#41×C₆₁	1	1	yes	characteristic
360	C₂³	—	2	2	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	4	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	4	no	—
370	C₂³	#120×C₆₁	1	1	yes	characteristic
371	Q₈	—	4	4	no	—
372	Q₈	—	8	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	4	4	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	1	no	—
378	D₄	—	8	2	no	—
379	D₄	—	8	16	no	—
380	D₄	—	8	1	no	—
381	D₄	—	8	1	no	—
382	D₄	—	8	2	no	—
383	D₄	—	8	1	no	—
384	D₄	—	8	1	no	—
385	D₄	—	8	1	no	—
386	D₄	—	8	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	—	8	2	no	—
396	C₂×C₄	—	8	1	no	—
397	C₂×C₄	—	8	1	no	—
398	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
399	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
400	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
401	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
402	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
403	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
404	C₂×C₄	C₂×SD₁₆×C₆₁	1	1	yes	characteristic
405	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
406	C₂×C₄	#135×C₆₁	1	1	yes	characteristic
407	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
408	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
409	C₂×C₄	#137×C₆₁	1	1	yes	characteristic
410	C₈	—	2	4	no	—
411	C₈	—	4	2	no	—
412	C₈	—	8	1	no	—
413	C₂²	—	4	4	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	4	no	—
420	C₂²	—	8	4	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	C₆₁×#392	1	1	yes	characteristic
424	C₂²	C₆₁×#450	1	2	yes	—
425	C₂²	C₆₁×#450	1	1	yes	characteristic
426	C₂²	C₆₁×#452	1	1	yes	characteristic
427	C₂²	C₆₁×#453	1	2	yes	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	4	4	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	2	no	—
433	C₄	C₆₁×#448	1	1	yes	characteristic
434	C₄	C₆₁×#449	1	1	yes	characteristic
435	C₄	C₆₁×#460	1	2	yes	—
436	C₄	C₆₁×#465	1	1	yes	characteristic
437	C₄	C₆₁×#468	1	1	yes	characteristic
438	C₄	C₆₁×#492	1	1	yes	characteristic
439	C₄	C₆₁×#496	1	1	yes	characteristic
440	C₂	—	8	2	no	—
441	C₂	—	16	2	no	—
442	C₂	C₆₁×#1629	1	2	yes	—
443	C₂	C₆₁×#1631	1	2	yes	—
444	C₂	C₆₁×#2000	1	1	yes	characteristic
445	C₂	C₆₁×#2002	1	1	yes	characteristic
446	C₂	C₆₁×#2014	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₆₁
prime radical	C₆₁×#2541	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#492	C₂	semidirect
2. C₂×C₆₁×#476	C₂	semidirect
4. C₆₁×#1987	C₂	semidirect
5. C₂×C₆₁×#331	C₂	semidirect
6. C₂×C₆₁×D₄⋊C₈	C₂	semidirect
7. C₆₁×#1279	C₂	semidirect
44. C₄⋊Q₈×C₆₁	D₄	semidirect
69. C₄⋊C₈×C₆₁	D₄	semidirect
72. C₄×C₈×C₆₁	D₄	semidirect
100. C₂×D₄×C₆₁	SD₁₆	semidirect
126. C₄⋊C₄×C₆₁	SD₁₆	semidirect
189. #10054	C₆₁	direct (N × H)
217. C₂×#492	C₂×C₆₁	semidirect
218. C₂×#476	C₂×C₆₁	semidirect
220. #1987	C₂×C₆₁	semidirect
221. C₂×#331	C₂×C₆₁	semidirect
222. C₂×D₄⋊C₈	C₂×C₆₁	semidirect
223. #1279	C₂×C₆₁	semidirect
252. C₆₁	#10054	direct (N × H)
268. C₄⋊Q₈	D₄×C₆₁	semidirect
293. C₄⋊C₈	D₄×C₆₁	semidirect
296. C₄×C₈	D₄×C₆₁	semidirect
324. C₂×D₄	SD₁₆×C₆₁	semidirect
350. C₄⋊C₄	SD₁₆×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#492	2
C₂×C₆₁×#476	2
C₆₁×#2541	2
C₆₁×#1987	2
C₂×C₆₁×#331	2
C₂×C₆₁×D₄⋊C₈	2
C₆₁×#1279	2
#10054	61

Subgroups — C61×#10054 #29513487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#10054 #29513487