Subgroups — C₆₁×#60472 #29563905

Order 15616.

2578 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3586	C₂	1	2	yes	maximal, complemented
2	C₂×C₆₁×#578	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3573	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3069	C₂	1	12	yes	maximal, complemented
5	C₆₁×#3067	C₂	1	6	yes	maximal, complemented
6	C₂×C₆₁×#473	C₂	1	6	yes	maximal, complemented
7	C₆₁×#2916	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2889	C₂	1	2	yes	maximal, complemented
9	C₆₁×#585	C₂²	1	1	yes	characteristic
10	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	2	yes	—
11	C₆₁×#578	—	2	8	no	—
12	C₆₁×#578	—	2	4	no	—
13	C₆₁×#578	—	2	4	no	—
14	C₆₁×#577	—	2	8	no	—
15	C₆₁×#575	C₂²	1	12	yes	—
16	C₂×#137×C₆₁	C₂²	1	12	yes	—
17	C₂×#137×C₆₁	C₂²	1	6	yes	complemented
18	C₂×#135×C₆₁	C₂²	1	3	yes	complemented
19	C₂²×Q₁₆×C₆₁	C₂²	1	3	yes	complemented
20	C₆₁×#568	—	2	4	no	—
21	C₆₁×#568	C₂²	1	6	yes	—
22	C₆₁×#568	C₂²	1	1	yes	characteristic
23	C₆₁×#568	C₂²	1	2	yes	—
24	C₂×#131×C₆₁	—	2	4	no	—
25	C₂×#131×C₆₁	C₂²	1	6	yes	—
26	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#473	C₂²	1	12	yes	complemented
28	C₆₁×#473	C₂²	1	24	yes	complemented
29	C₆₁×#472	C₂²	1	4	yes	complemented
30	C₆₁×#471	C₂²	1	24	yes	complemented
31	C₆₁×#430	C₂²	1	6	yes	complemented
32	C₂×#108×C₆₁	C₂²	1	6	yes	complemented
33	C₆₁×#413	C₂²	1	12	yes	complemented
34	C₂×#101×C₆₁	C₂²	1	12	yes	complemented
35	2₋¹⁺⁴×C₆₁	—	2	1	no	—
36	2₋¹⁺⁴×C₆₁	—	2	8	no	—
37	2₋¹⁺⁴×C₆₁	—	2	8	no	—
38	2₋¹⁺⁴×C₆₁	D₄	1	4	yes	—
39	H(5,𝔽₂)×C₆₁	—	2	3	no	—
40	H(5,𝔽₂)×C₆₁	D₄	1	4	yes	—
41	C₂×#41×C₆₁	—	2	4	no	—
42	C₂×#41×C₆₁	—	2	6	no	—
43	C₂×#41×C₆₁	C₂³	1	6	yes	—
44	C₂×#41×C₆₁	C₂³	1	6	yes	—
45	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₆₁	—	2	2	no	—
47	C₂²×Q₈×C₆₁	C₂³	1	6	yes	—
48	#137×C₆₁	—	2	24	no	—
49	#137×C₆₁	—	2	12	no	—
50	#137×C₆₁	—	2	24	no	—
51	#137×C₆₁	C₂³	1	24	yes	—
52	AGL(1,ℤ/8)×C₆₁	—	2	12	no	—
53	AGL(1,ℤ/8)×C₆₁	C₂³	1	8	yes	—
54	#135×C₆₁	—	2	24	no	—
55	#135×C₆₁	—	2	6	no	—
56	#135×C₆₁	—	2	6	no	—
57	C₂×Q₁₆×C₆₁	—	2	12	no	—
58	C₂×Q₁₆×C₆₁	—	2	6	no	—
59	C₂×Q₁₆×C₆₁	—	2	6	no	—
60	C₂×Q₁₆×C₆₁	C₂³	1	3	yes	—
61	C₂×Q₁₆×C₆₁	C₂³	1	6	yes	—
62	C₂×SD₁₆×C₆₁	—	2	12	no	—
63	C₂×SD₁₆×C₆₁	C₂³	1	6	yes	—
64	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
65	#131×C₆₁	—	2	4	no	—
66	#131×C₆₁	—	2	8	no	—
67	#131×C₆₁	—	2	12	no	—
68	#131×C₆₁	—	2	6	no	—
69	#131×C₆₁	—	2	6	no	—
70	#131×C₆₁	D₄	1	4	yes	—
71	#131×C₆₁	D₄	1	4	yes	—
72	#131×C₆₁	C₂³	1	4	yes	—
73	#131×C₆₁	C₂³	1	12	yes	—
74	C₂×M₁₆×C₆₁	—	2	12	no	—
75	C₂×M₁₆×C₆₁	—	2	6	no	—
76	C₂×M₁₆×C₆₁	C₂³	1	6	yes	—
77	C₂×M₁₆×C₆₁	C₂³	1	12	yes	—
78	C₂×M₁₆×C₆₁	C₂³	1	3	yes	—
79	C₂²×C₈×C₆₁	—	2	6	no	—
80	C₂²×C₈×C₆₁	C₂³	1	3	yes	—
81	#108×C₆₁	C₂³	1	4	yes	—
82	#108×C₆₁	C₂³	1	12	yes	—
83	#101×C₆₁	C₂³	1	24	yes	—
84	#100×C₆₁	C₂³	1	8	yes	—
85	#41×C₆₁	—	2	4	no	—
86	#41×C₆₁	—	2	12	no	—
87	#41×C₆₁	—	2	6	no	—
88	#41×C₆₁	—	2	6	no	—
89	#41×C₆₁	—	2	12	no	—
90	#41×C₆₁	—	2	12	no	—
91	#41×C₆₁	—	4	24	no	—
92	#41×C₆₁	C₂×D₄	1	12	yes	—
93	#41×C₆₁	C₂×D₄	1	4	yes	—
94	#41×C₆₁	C₂×D₄	1	4	yes	—
95	#41×C₆₁	C₂⁴	1	4	yes	—
96	C₂×Q₈×C₆₁	—	2	4	no	—
97	C₂×Q₈×C₆₁	—	2	6	no	—
98	C₂×Q₈×C₆₁	—	2	12	no	—
99	C₂×Q₈×C₆₁	—	2	12	no	—
100	C₂×Q₈×C₆₁	—	4	8	no	—
101	C₂×Q₈×C₆₁	C₂×D₄	1	6	yes	—
102	C₂×Q₈×C₆₁	#41	1	1	yes	characteristic
103	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
104	C₂×D₄×C₆₁	—	2	6	no	—
105	C₂×D₄×C₆₁	—	2	12	no	—
106	C₂×D₄×C₆₁	—	2	6	no	—
107	C₂×D₄×C₆₁	C₂×D₄	1	6	yes	—
108	C₂×D₄×C₆₁	#41	1	3	yes	—
109	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
110	C₂²×C₄×C₆₁	—	2	6	no	—
111	C₂²×C₄×C₆₁	—	2	6	no	—
112	C₂²×C₄×C₆₁	—	2	6	no	—
113	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
114	Q₁₆×C₆₁	—	2	24	no	—
115	Q₁₆×C₆₁	—	2	3	no	—
116	Q₁₆×C₆₁	—	2	3	no	—
117	Q₁₆×C₆₁	—	2	12	no	—
118	SD₁₆×C₆₁	—	2	8	no	—
119	SD₁₆×C₆₁	—	2	24	no	—
120	SD₁₆×C₆₁	—	2	12	no	—
121	D₈×C₆₁	—	2	8	no	—
122	D₈×C₆₁	—	2	1	no	—
123	D₈×C₆₁	—	2	1	no	—
124	M₁₆×C₆₁	—	2	6	no	—
125	M₁₆×C₆₁	—	2	12	no	—
126	M₁₆×C₆₁	—	2	12	no	—
127	M₁₆×C₆₁	—	2	4	no	—
128	M₁₆×C₆₁	C₂×D₄	1	12	yes	—
129	M₁₆×C₆₁	C₂⁴	1	4	yes	—
130	M₁₆×C₆₁	C₂⁴	1	8	yes	—
131	C₂×C₈×C₆₁	—	2	6	no	—
132	C₂×C₈×C₆₁	—	2	12	no	—
133	C₂×C₈×C₆₁	—	2	4	no	—
134	C₂×C₈×C₆₁	—	2	12	no	—
135	C₂×C₈×C₆₁	C₂×D₄	1	6	yes	—
136	C₂×C₈×C₆₁	C₂×D₄	1	6	yes	—
137	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
138	C₂×C₈×C₆₁	C₂⁴	1	3	yes	—
139	C₂³×C₆₁	—	2	6	no	—
140	C₂³×C₆₁	—	2	2	no	—
141	C₂³×C₆₁	C₂×#41	1	3	yes	—
142	Q₈×C₆₁	—	2	6	no	—
143	Q₈×C₆₁	—	2	6	no	—
144	Q₈×C₆₁	—	2	6	no	—
145	Q₈×C₆₁	—	4	12	no	—
146	Q₈×C₆₁	#121	1	4	yes	—
147	Q₈×C₆₁	C₂²×D₄	1	4	yes	—
148	D₄×C₆₁	—	2	12	no	—
149	D₄×C₆₁	—	2	4	no	—
150	D₄×C₆₁	—	2	6	no	—
151	D₄×C₆₁	—	2	2	no	—
152	D₄×C₆₁	—	2	2	no	—
153	D₄×C₆₁	—	4	12	no	—
154	D₄×C₆₁	#121	1	12	yes	—
155	D₄×C₆₁	C₂²×D₄	1	4	yes	—
156	C₂×C₄×C₆₁	—	2	6	no	—
157	C₂×C₄×C₆₁	—	2	12	no	—
158	C₂×C₄×C₆₁	—	2	4	no	—
159	C₂×C₄×C₆₁	—	2	6	no	—
160	C₂×C₄×C₆₁	—	4	12	no	—
161	C₂×C₄×C₆₁	—	4	12	no	—
162	C₂×C₄×C₆₁	C₂²×D₄	1	6	yes	—
163	C₂×C₄×C₆₁	C₂²×D₄	1	6	yes	—
164	C₂×C₄×C₆₁	C₂×#41	1	3	yes	—
165	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
166	C₈×C₆₁	—	2	4	no	—
167	C₈×C₆₁	—	2	8	no	—
168	C₈×C₆₁	C₂²×D₄	1	1	yes	characteristic
169	C₈×C₆₁	C₂²×D₄	1	6	yes	—
170	C₈×C₆₁	C₂²×D₄	1	1	yes	characteristic
171	#60472	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₆₁	—	2	4	no	—
173	C₂²×C₆₁	—	4	3	no	—
174	C₂²×C₆₁	—	4	2	no	—
175	C₂²×C₆₁	—	8	6	no	—
176	C₂²×C₆₁	—	8	2	no	—
177	C₂²×C₆₁	C₂×#121	1	6	yes	—
178	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
179	C₄×C₆₁	—	2	4	no	—
180	C₄×C₆₁	—	4	6	no	—
181	C₄×C₆₁	C₂×#121	1	6	yes	—
182	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
183	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
184	#3586	C₂×C₆₁	1	2	yes	complemented
185	C₂×#578	C₂×C₆₁	1	1	yes	characteristic, complemented
186	#3573	C₂×C₆₁	1	1	yes	characteristic, complemented
187	#3069	C₂×C₆₁	1	12	yes	complemented
188	#3067	C₂×C₆₁	1	6	yes	complemented
189	C₂×#473	C₂×C₆₁	1	6	yes	complemented
190	#2916	C₂×C₆₁	1	1	yes	characteristic, complemented
191	#2889	C₂×C₆₁	1	2	yes	complemented
192	C₂×C₆₁	—	2	1	no	—
193	C₂×C₆₁	—	2	6	no	—
194	C₂×C₆₁	—	4	4	no	—
195	C₂×C₆₁	—	8	2	no	—
196	C₂×C₆₁	C₂²×#121	1	1	yes	characteristic
197	#585	C₂²×C₆₁	1	1	yes	characteristic
198	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	2	yes	—
199	#578	—	2	8	no	—
200	#578	—	2	4	no	—
201	#578	—	2	4	no	—
202	#577	—	2	8	no	—
203	#575	C₂²×C₆₁	1	12	yes	—
204	C₂×#137	C₂²×C₆₁	1	12	yes	—
205	C₂×#137	C₂²×C₆₁	1	6	yes	complemented
206	C₂×#135	C₂²×C₆₁	1	3	yes	complemented
207	C₂²×Q₁₆	C₂²×C₆₁	1	3	yes	complemented
208	#568	—	2	4	no	—
209	#568	C₂²×C₆₁	1	6	yes	—
210	#568	C₂²×C₆₁	1	2	yes	—
211	#568	C₂²×C₆₁	1	1	yes	characteristic
212	C₂×#131	—	2	4	no	—
213	C₂×#131	C₂²×C₆₁	1	6	yes	—
214	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
215	#473	C₂²×C₆₁	1	12	yes	complemented
216	#473	C₂²×C₆₁	1	24	yes	complemented
217	#472	C₂²×C₆₁	1	4	yes	complemented
218	#471	C₂²×C₆₁	1	24	yes	complemented
219	#430	C₂²×C₆₁	1	6	yes	complemented
220	C₂×#108	C₂²×C₆₁	1	6	yes	complemented
221	#413	C₂²×C₆₁	1	12	yes	complemented
222	C₂×#101	C₂²×C₆₁	1	12	yes	complemented
223	C₆₁	#60472	1	1	yes	characteristic, direct product factor, Sylow
224	2₋¹⁺⁴	—	2	1	no	—
225	2₋¹⁺⁴	—	2	8	no	—
226	2₋¹⁺⁴	—	2	8	no	—
227	2₋¹⁺⁴	D₄×C₆₁	1	4	yes	—
228	H(5,𝔽₂)	—	2	3	no	—
229	H(5,𝔽₂)	D₄×C₆₁	1	4	yes	—
230	C₂×#41	—	2	4	no	—
231	C₂×#41	—	2	6	no	—
232	C₂×#41	C₂³×C₆₁	1	6	yes	—
233	C₂×#41	C₂³×C₆₁	1	6	yes	—
234	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
235	C₂²×Q₈	—	2	2	no	—
236	C₂²×Q₈	C₂³×C₆₁	1	6	yes	—
237	#137	—	2	24	no	—
238	#137	—	2	12	no	—
239	#137	—	2	24	no	—
240	#137	C₂³×C₆₁	1	24	yes	—
241	AGL(1,ℤ/8)	—	2	12	no	—
242	AGL(1,ℤ/8)	C₂³×C₆₁	1	8	yes	—
243	#135	—	2	24	no	—
244	#135	—	2	6	no	—
245	#135	—	2	6	no	—
246	C₂×Q₁₆	—	2	12	no	—
247	C₂×Q₁₆	—	2	6	no	—
248	C₂×Q₁₆	—	2	6	no	—
249	C₂×Q₁₆	C₂³×C₆₁	1	3	yes	—
250	C₂×Q₁₆	C₂³×C₆₁	1	6	yes	—
251	C₂×SD₁₆	—	2	12	no	—
252	C₂×SD₁₆	C₂³×C₆₁	1	6	yes	—
253	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
254	#131	—	2	4	no	—
255	#131	—	2	8	no	—
256	#131	—	2	12	no	—
257	#131	—	2	6	no	—
258	#131	—	2	6	no	—
259	#131	D₄×C₆₁	1	4	yes	—
260	#131	D₄×C₆₁	1	4	yes	—
261	#131	C₂³×C₆₁	1	4	yes	—
262	#131	C₂³×C₆₁	1	12	yes	—
263	C₂×M₁₆	—	2	12	no	—
264	C₂×M₁₆	—	2	6	no	—
265	C₂×M₁₆	C₂³×C₆₁	1	6	yes	—
266	C₂×M₁₆	C₂³×C₆₁	1	12	yes	—
267	C₂×M₁₆	C₂³×C₆₁	1	3	yes	—
268	C₂²×C₈	—	2	6	no	—
269	C₂²×C₈	C₂³×C₆₁	1	3	yes	—
270	#108	C₂³×C₆₁	1	4	yes	—
271	#108	C₂³×C₆₁	1	12	yes	—
272	#101	C₂³×C₆₁	1	24	yes	—
273	#100	C₂³×C₆₁	1	8	yes	—
274	#41	—	2	4	no	—
275	#41	—	2	12	no	—
276	#41	—	2	6	no	—
277	#41	—	2	6	no	—
278	#41	—	2	12	no	—
279	#41	—	2	12	no	—
280	#41	—	4	24	no	—
281	#41	C₂×D₄×C₆₁	1	12	yes	—
282	#41	C₂×D₄×C₆₁	1	4	yes	—
283	#41	C₂×D₄×C₆₁	1	4	yes	—
284	#41	C₂⁴×C₆₁	1	4	yes	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	6	no	—
287	C₂×Q₈	—	2	12	no	—
288	C₂×Q₈	—	2	12	no	—
289	C₂×Q₈	—	4	8	no	—
290	C₂×Q₈	C₂×D₄×C₆₁	1	6	yes	—
291	C₂×Q₈	#41×C₆₁	1	1	yes	characteristic
292	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
293	C₂×D₄	—	2	6	no	—
294	C₂×D₄	—	2	12	no	—
295	C₂×D₄	—	2	6	no	—
296	C₂×D₄	C₂×D₄×C₆₁	1	6	yes	—
297	C₂×D₄	#41×C₆₁	1	3	yes	—
298	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
299	C₂²×C₄	—	2	6	no	—
300	C₂²×C₄	—	2	6	no	—
301	C₂²×C₄	—	2	6	no	—
302	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
303	Q₁₆	—	2	24	no	—
304	Q₁₆	—	2	3	no	—
305	Q₁₆	—	2	3	no	—
306	Q₁₆	—	2	12	no	—
307	SD₁₆	—	2	8	no	—
308	SD₁₆	—	2	24	no	—
309	SD₁₆	—	2	12	no	—
310	D₈	—	2	8	no	—
311	D₈	—	2	1	no	—
312	D₈	—	2	1	no	—
313	M₁₆	—	2	6	no	—
314	M₁₆	—	2	12	no	—
315	M₁₆	—	2	12	no	—
316	M₁₆	—	2	4	no	—
317	M₁₆	C₂×D₄×C₆₁	1	12	yes	—
318	M₁₆	C₂⁴×C₆₁	1	4	yes	—
319	M₁₆	C₂⁴×C₆₁	1	8	yes	—
320	C₂×C₈	—	2	6	no	—
321	C₂×C₈	—	2	12	no	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	12	no	—
324	C₂×C₈	C₂×D₄×C₆₁	1	6	yes	—
325	C₂×C₈	C₂×D₄×C₆₁	1	6	yes	—
326	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
327	C₂×C₈	C₂⁴×C₆₁	1	3	yes	—
328	C₂³	—	2	6	no	—
329	C₂³	—	2	2	no	—
330	C₂³	C₂×#41×C₆₁	1	3	yes	—
331	Q₈	—	2	6	no	—
332	Q₈	—	2	6	no	—
333	Q₈	—	2	6	no	—
334	Q₈	—	4	12	no	—
335	Q₈	#121×C₆₁	1	4	yes	—
336	Q₈	C₂²×D₄×C₆₁	1	4	yes	—
337	D₄	—	2	4	no	—
338	D₄	—	2	12	no	—
339	D₄	—	2	2	no	—
340	D₄	—	2	2	no	—
341	D₄	—	2	6	no	—
342	D₄	—	4	12	no	—
343	D₄	#121×C₆₁	1	12	yes	—
344	D₄	C₂²×D₄×C₆₁	1	4	yes	—
345	C₂×C₄	—	2	6	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	12	no	—
348	C₂×C₄	—	2	6	no	—
349	C₂×C₄	—	4	12	no	—
350	C₂×C₄	—	4	12	no	—
351	C₂×C₄	C₂²×D₄×C₆₁	1	6	yes	—
352	C₂×C₄	C₂²×D₄×C₆₁	1	6	yes	—
353	C₂×C₄	C₂×#41×C₆₁	1	3	yes	—
354	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
355	C₈	—	2	4	no	—
356	C₈	—	2	8	no	—
357	C₈	C₂²×D₄×C₆₁	1	1	yes	characteristic
358	C₈	C₂²×D₄×C₆₁	1	6	yes	—
359	C₈	C₂²×D₄×C₆₁	1	1	yes	characteristic
360	C₂²	—	2	4	no	—
361	C₂²	—	4	3	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	8	6	no	—
364	C₂²	—	8	2	no	—
365	C₂²	C₂×#121×C₆₁	1	6	yes	—
366	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
367	C₄	—	2	4	no	—
368	C₄	—	4	6	no	—
369	C₄	C₂×#121×C₆₁	1	6	yes	—
370	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
371	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
372	C₂	—	2	1	no	—
373	C₂	—	2	6	no	—
374	C₂	—	4	4	no	—
375	C₂	—	8	2	no	—
376	C₂	C₂²×#121×C₆₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₆₁	C₂²×#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₁ ◁ C₂×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3586	C₂	semidirect
2. C₂×C₆₁×#578	C₂	semidirect
3. C₆₁×#3573	C₂	semidirect
4. C₆₁×#3069	C₂	semidirect
5. C₆₁×#3067	C₂	semidirect
6. C₂×C₆₁×#473	C₂	semidirect
7. C₆₁×#2916	C₂	semidirect
8. C₆₁×#2889	C₂	semidirect
17. C₂×#137×C₆₁	C₂²	semidirect
18. C₂×#135×C₆₁	C₂²	semidirect
19. C₂²×Q₁₆×C₆₁	C₂²	semidirect
27. C₆₁×#473	C₂²	semidirect
28. C₆₁×#473	C₂²	semidirect
29. C₆₁×#472	C₂²	semidirect
30. C₆₁×#471	C₂²	semidirect
31. C₆₁×#430	C₂²	semidirect
32. C₂×#108×C₆₁	C₂²	semidirect
33. C₆₁×#413	C₂²	semidirect
34. C₂×#101×C₆₁	C₂²	semidirect
171. #60472	C₆₁	direct (N × H)
184. #3586	C₂×C₆₁	semidirect
185. C₂×#578	C₂×C₆₁	semidirect
186. #3573	C₂×C₆₁	semidirect
187. #3069	C₂×C₆₁	semidirect
188. #3067	C₂×C₆₁	semidirect
189. C₂×#473	C₂×C₆₁	semidirect
190. #2916	C₂×C₆₁	semidirect
191. #2889	C₂×C₆₁	semidirect
205. C₂×#137	C₂²×C₆₁	semidirect
206. C₂×#135	C₂²×C₆₁	semidirect
207. C₂²×Q₁₆	C₂²×C₆₁	semidirect
215. #473	C₂²×C₆₁	semidirect
216. #473	C₂²×C₆₁	semidirect
217. #472	C₂²×C₆₁	semidirect
218. #471	C₂²×C₆₁	semidirect
219. #430	C₂²×C₆₁	semidirect
220. C₂×#108	C₂²×C₆₁	semidirect
221. #413	C₂²×C₆₁	semidirect
222. C₂×#101	C₂²×C₆₁	semidirect
223. C₆₁	#60472	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×#3586	2
C₂×C₆₁×#578	2
C₆₁×#3573	2
C₆₁×#3069	2
C₆₁×#3067	2
C₂×C₆₁×#473	2
C₆₁×#2916	2
C₆₁×#2889	2
#60472	61

Subgroups — C61×#60472 #29563905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60472 #29563905