Subgroups — C₆₁×#60716 #29564149

Order 15616.

1942 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×#3511	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3185	C₂	1	2	yes	maximal, complemented
3	C₆₁×#3184	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3173	C₂	1	8	yes	maximal, complemented
5	C₆₁×#3167	C₂	1	4	yes	maximal, complemented
6	C₂×C₆₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3141	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3060	C₂	1	4	yes	maximal, complemented
10	C₆₁×#2952	C₂	1	4	yes	maximal, complemented
11	C₄×#131×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₆₁	C₂²	1	4	yes	—
13	C₂×#131×C₆₁	C₂²	1	2	yes	—
14	C₆₁×#556	—	2	2	no	—
15	C₆₁×#555	—	2	2	no	—
16	C₆₁×#554	—	2	2	no	—
17	C₆₁×#553	—	2	4	no	—
18	C₆₁×#548	—	2	4	no	—
19	C₆₁×#547	—	2	2	no	—
20	C₆₁×#542	C₂²	1	8	yes	—
21	C₆₁×#537	C₂²	1	4	yes	—
22	C₆₁×#533	C₂²	1	4	yes	—
23	C₆₁×#532	C₂²	1	2	yes	—
24	C₆₁×#532	C₂²	1	4	yes	—
25	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
26	C₆₁×#520	C₂²	1	4	yes	—
27	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#498	C₂²	1	2	yes	—
29	C₆₁×#498	C₂²	1	4	yes	—
30	C₆₁×#498	C₂²	1	2	yes	—
31	C₆₁×#495	C₂²	1	4	yes	—
32	C₆₁×#494	C₂²	1	1	yes	characteristic
33	C₆₁×#493	C₂²	1	1	yes	characteristic
34	C₆₁×#492	C₂²	1	2	yes	—
35	C₆₁×#489	C₂²	1	8	yes	—
36	C₆₁×#487	C₂²	1	4	yes	—
37	C₆₁×#486	C₂²	1	4	yes	—
38	C₆₁×#470	C₂²	1	8	yes	—
39	C₆₁×#469	C₂²	1	8	yes	—
40	C₆₁×#465	C₂²	1	16	yes	—
41	C₆₁×#442	C₂²	1	8	yes	—
42	C₆₁×#441	C₂²	1	8	yes	—
43	C₄×SD₁₆×C₆₁	C₂²	1	16	yes	—
44	C₂×#106×C₆₁	C₂²	1	4	yes	—
45	C₆₁×#417	C₂²	1	8	yes	—
46	C₆₁×#405	C₂²	1	4	yes	—
47	C₆₁×#405	C₂²	1	2	yes	—
48	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
49	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
50	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
52	C₂×#41×C₆₁	—	2	4	no	—
53	C₂×#41×C₆₁	C₂³	1	4	yes	—
54	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₆₁	—	2	2	no	—
56	#135×C₆₁	—	2	16	no	—
57	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
58	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
59	C₂×D₈×C₆₁	C₂³	1	4	yes	—
60	#131×C₆₁	—	2	8	no	—
61	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
62	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
63	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
64	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
65	C₄⋊Q₈×C₆₁	—	2	2	no	—
66	C₄⋊Q₈×C₆₁	—	2	2	no	—
67	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
69	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
70	#127×C₆₁	C₂³	1	2	yes	—
71	#126×C₆₁	—	2	8	no	—
72	#125×C₆₁	—	2	4	no	—
73	#124×C₆₁	—	2	8	no	—
74	#124×C₆₁	—	2	4	no	—
75	#124×C₆₁	C₂³	1	4	yes	—
76	#123×C₆₁	—	2	8	no	—
77	C₂²⋊Q₈×C₆₁	—	2	4	no	—
78	C₂²⋊Q₈×C₆₁	—	2	4	no	—
79	C₂²⋊Q₈×C₆₁	—	2	8	no	—
80	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
81	#121×C₆₁	—	2	4	no	—
82	#121×C₆₁	—	2	8	no	—
83	#121×C₆₁	—	2	2	no	—
84	#121×C₆₁	—	2	2	no	—
85	#121×C₆₁	—	2	4	no	—
86	#121×C₆₁	C₂³	1	8	yes	—
87	C₄×Q₈×C₆₁	—	2	4	no	—
88	C₄×Q₈×C₆₁	D₄	1	2	yes	—
89	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
90	C₄×D₄×C₆₁	—	2	8	no	—
91	C₄×D₄×C₆₁	—	2	2	no	—
92	C₄×D₄×C₆₁	—	2	4	no	—
93	C₄×D₄×C₆₁	—	2	2	no	—
94	C₄×D₄×C₆₁	D₄	1	2	yes	—
95	C₄×D₄×C₆₁	D₄	1	4	yes	—
96	C₄×D₄×C₆₁	C₂³	1	8	yes	—
97	#117×C₆₁	—	2	4	no	—
98	#117×C₆₁	—	2	4	no	—
99	#117×C₆₁	C₂³	1	2	yes	—
100	#117×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
102	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
103	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
104	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
106	#106×C₆₁	C₂³	1	8	yes	—
107	#106×C₆₁	C₂³	1	8	yes	—
108	#103×C₆₁	C₂³	1	16	yes	—
109	#102×C₆₁	C₂³	1	16	yes	—
110	#97×C₆₁	C₂³	1	4	yes	—
111	#97×C₆₁	C₂³	1	2	yes	—
112	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
113	C₄×C₈×C₆₁	C₂³	1	2	yes	—
114	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
115	C₄×C₈×C₆₁	C₂³	1	4	yes	—
116	C₄×C₈×C₆₁	C₂³	1	2	yes	—
117	#41×C₆₁	—	2	4	no	—
118	#41×C₆₁	—	2	16	no	—
119	#41×C₆₁	—	8	8	no	—
120	C₂×Q₈×C₆₁	—	2	4	no	—
121	C₂×Q₈×C₆₁	—	2	4	no	—
122	C₂×Q₈×C₆₁	—	8	4	no	—
123	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
125	C₂×D₄×C₆₁	—	2	4	no	—
126	C₂×D₄×C₆₁	—	2	8	no	—
127	C₂×D₄×C₆₁	—	2	2	no	—
128	C₂×D₄×C₆₁	—	2	2	no	—
129	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
130	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
131	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₆₁	—	2	4	no	—
133	C₂²×C₄×C₆₁	—	2	4	no	—
134	C₂²×C₄×C₆₁	—	2	8	no	—
135	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
139	Q₁₆×C₆₁	—	2	8	no	—
140	SD₁₆×C₆₁	—	2	16	no	—
141	D₈×C₆₁	—	2	8	no	—
142	M₁₆×C₆₁	—	2	4	no	—
143	M₁₆×C₆₁	—	2	8	no	—
144	C₂×C₈×C₆₁	—	2	8	no	—
145	C₂×C₈×C₆₁	#41	1	8	yes	complemented
146	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
147	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
148	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
149	C₄⋊C₄×C₆₁	—	2	4	no	—
150	C₄⋊C₄×C₆₁	—	2	4	no	—
151	C₄⋊C₄×C₆₁	—	2	8	no	—
152	C₄⋊C₄×C₆₁	—	2	4	no	—
153	C₄⋊C₄×C₆₁	—	2	2	no	—
154	C₄⋊C₄×C₆₁	—	2	2	no	—
155	C₄⋊C₄×C₆₁	—	2	8	no	—
156	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
158	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
159	C₂²⋊C₄×C₆₁	—	2	8	no	—
160	C₂²⋊C₄×C₆₁	—	2	8	no	—
161	C₂²⋊C₄×C₆₁	—	2	8	no	—
162	C₂²⋊C₄×C₆₁	—	2	4	no	—
163	C₂²⋊C₄×C₆₁	—	2	4	no	—
164	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
165	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
166	C₄²×C₆₁	—	2	8	no	—
167	C₄²×C₆₁	C₂×D₄	1	2	yes	—
168	C₄²×C₆₁	C₂×D₄	1	4	yes	—
169	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
170	C₄²×C₆₁	C₂⁴	1	2	yes	—
171	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
172	C₂³×C₆₁	—	2	4	no	—
173	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
174	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₆₁	—	2	2	no	—
176	Q₈×C₆₁	—	2	8	no	—
177	Q₈×C₆₁	—	4	8	no	—
178	Q₈×C₆₁	—	8	4	no	—
179	D₄×C₆₁	—	2	4	no	—
180	D₄×C₆₁	—	2	2	no	—
181	D₄×C₆₁	—	2	8	no	—
182	D₄×C₆₁	—	4	8	no	—
183	D₄×C₆₁	—	4	4	no	—
184	D₄×C₆₁	—	4	4	no	—
185	D₄×C₆₁	—	8	8	no	—
186	C₂×C₄×C₆₁	—	2	4	no	—
187	C₂×C₄×C₆₁	—	2	8	no	—
188	C₂×C₄×C₆₁	—	2	4	no	—
189	C₂×C₄×C₆₁	—	2	4	no	—
190	C₂×C₄×C₆₁	—	2	8	no	—
191	C₂×C₄×C₆₁	—	4	8	no	—
192	C₂×C₄×C₆₁	—	8	8	no	—
193	C₂×C₄×C₆₁	—	8	4	no	—
194	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
195	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
200	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
201	C₈×C₆₁	—	2	4	no	—
202	C₈×C₆₁	C₂×#41	1	4	yes	—
203	C₈×C₆₁	C₂×#41	1	4	yes	—
204	#60716	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂²×C₆₁	—	2	2	no	—
206	C₂²×C₆₁	—	2	2	no	—
207	C₂²×C₆₁	—	2	4	no	—
208	C₂²×C₆₁	—	4	4	no	—
209	C₂²×C₆₁	—	4	4	no	—
210	C₂²×C₆₁	—	4	4	no	—
211	C₂²×C₆₁	#532	1	2	yes	—
212	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
213	C₄×C₆₁	—	2	2	no	—
214	C₄×C₆₁	—	2	4	no	—
215	C₄×C₆₁	—	2	2	no	—
216	C₄×C₆₁	—	4	4	no	—
217	C₄×C₆₁	—	4	8	no	—
218	C₄×C₆₁	#532	1	2	yes	—
219	C₄×C₆₁	#577	1	4	yes	—
220	C₄×C₆₁	C₂²×#41	1	2	yes	—
221	#3511	C₂×C₆₁	1	2	yes	complemented
222	#3185	C₂×C₆₁	1	2	yes	complemented
223	#3184	C₂×C₆₁	1	2	yes	complemented
224	#3173	C₂×C₆₁	1	8	yes	complemented
225	#3167	C₂×C₆₁	1	4	yes	complemented
226	C₂×#498	C₂×C₆₁	1	1	yes	characteristic, complemented
227	#3147	C₂×C₆₁	1	1	yes	characteristic, complemented
228	#3141	C₂×C₆₁	1	2	yes	complemented
229	#3060	C₂×C₆₁	1	4	yes	complemented
230	#2952	C₂×C₆₁	1	4	yes	complemented
231	C₄×#131	C₂×C₆₁	1	1	yes	characteristic, complemented
232	C₂×C₆₁	—	2	2	no	—
233	C₂×C₆₁	—	4	2	no	—
234	C₂×C₆₁	—	8	4	no	—
235	C₂×C₆₁	C₂×#532	1	1	yes	characteristic
236	C₂×C₆₁	C₂×#577	1	2	yes	—
237	C₂×#135	C₂²×C₆₁	1	4	yes	—
238	C₂×#131	C₂²×C₆₁	1	2	yes	—
239	#556	—	2	2	no	—
240	#555	—	2	2	no	—
241	#554	—	2	2	no	—
242	#553	—	2	4	no	—
243	#548	—	2	4	no	—
244	#547	—	2	2	no	—
245	#542	C₂²×C₆₁	1	8	yes	—
246	#537	C₂²×C₆₁	1	4	yes	—
247	#533	C₂²×C₆₁	1	4	yes	—
248	#532	C₂²×C₆₁	1	2	yes	—
249	#532	C₂²×C₆₁	1	4	yes	—
250	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
251	#520	C₂²×C₆₁	1	4	yes	—
252	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
253	#498	C₂²×C₆₁	1	2	yes	—
254	#498	C₂²×C₆₁	1	4	yes	—
255	#498	C₂²×C₆₁	1	2	yes	—
256	#495	C₂²×C₆₁	1	4	yes	—
257	#494	C₂²×C₆₁	1	1	yes	characteristic
258	#493	C₂²×C₆₁	1	1	yes	characteristic
259	#492	C₂²×C₆₁	1	2	yes	—
260	#489	C₂²×C₆₁	1	8	yes	—
261	#487	C₂²×C₆₁	1	4	yes	—
262	#486	C₂²×C₆₁	1	4	yes	—
263	#470	C₂²×C₆₁	1	8	yes	—
264	#469	C₂²×C₆₁	1	8	yes	—
265	#465	C₂²×C₆₁	1	16	yes	—
266	#442	C₂²×C₆₁	1	8	yes	—
267	#441	C₂²×C₆₁	1	8	yes	—
268	C₄×SD₁₆	C₂²×C₆₁	1	16	yes	—
269	C₂×#106	C₂²×C₆₁	1	4	yes	—
270	#417	C₂²×C₆₁	1	8	yes	—
271	#405	C₂²×C₆₁	1	4	yes	—
272	#405	C₂²×C₆₁	1	2	yes	—
273	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
274	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
275	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
277	C₆₁	#60716	1	1	yes	characteristic, direct product factor, Sylow
278	C₂×#41	—	2	4	no	—
279	C₂×#41	C₂³×C₆₁	1	4	yes	—
280	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
281	C₂²×Q₈	—	2	2	no	—
282	#135	—	2	16	no	—
283	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
284	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
285	C₂×D₈	C₂³×C₆₁	1	4	yes	—
286	#131	—	2	8	no	—
287	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
288	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
289	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
290	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
291	C₄⋊Q₈	—	2	2	no	—
292	C₄⋊Q₈	—	2	2	no	—
293	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
294	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
295	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
296	#127	C₂³×C₆₁	1	2	yes	—
297	#126	—	2	8	no	—
298	#125	—	2	4	no	—
299	#124	—	2	8	no	—
300	#124	—	2	4	no	—
301	#124	C₂³×C₆₁	1	4	yes	—
302	#123	—	2	8	no	—
303	C₂²⋊Q₈	—	2	4	no	—
304	C₂²⋊Q₈	—	2	4	no	—
305	C₂²⋊Q₈	—	2	8	no	—
306	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
307	#121	—	2	4	no	—
308	#121	—	2	8	no	—
309	#121	—	2	2	no	—
310	#121	—	2	2	no	—
311	#121	—	2	4	no	—
312	#121	C₂³×C₆₁	1	8	yes	—
313	C₄×Q₈	—	2	4	no	—
314	C₄×Q₈	D₄×C₆₁	1	2	yes	—
315	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
316	C₄×D₄	—	2	8	no	—
317	C₄×D₄	—	2	2	no	—
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	D₄×C₆₁	1	2	yes	—
321	C₄×D₄	D₄×C₆₁	1	4	yes	—
322	C₄×D₄	C₂³×C₆₁	1	8	yes	—
323	#117	—	2	4	no	—
324	#117	—	2	4	no	—
325	#117	C₂³×C₆₁	1	1	yes	characteristic
326	#117	C₂³×C₆₁	1	2	yes	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	4	no	—
329	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
330	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
332	#106	C₂³×C₆₁	1	8	yes	—
333	#106	C₂³×C₆₁	1	8	yes	—
334	#103	C₂³×C₆₁	1	16	yes	—
335	#102	C₂³×C₆₁	1	16	yes	—
336	#97	C₂³×C₆₁	1	4	yes	—
337	#97	C₂³×C₆₁	1	2	yes	—
338	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
339	C₄×C₈	C₂³×C₆₁	1	2	yes	—
340	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
341	C₄×C₈	C₂³×C₆₁	1	4	yes	—
342	C₄×C₈	C₂³×C₆₁	1	2	yes	—
343	#41	—	2	4	no	—
344	#41	—	2	16	no	—
345	#41	—	8	8	no	—
346	C₂×Q₈	—	2	4	no	—
347	C₂×Q₈	—	2	4	no	—
348	C₂×Q₈	—	8	4	no	—
349	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
350	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	8	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
356	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
357	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
363	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
365	Q₁₆	—	2	8	no	—
366	SD₁₆	—	2	16	no	—
367	D₈	—	2	8	no	—
368	M₁₆	—	2	4	no	—
369	M₁₆	—	2	8	no	—
370	C₂×C₈	—	2	8	no	—
371	C₂×C₈	#41×C₆₁	1	8	yes	complemented
372	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
373	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
374	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	8	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
383	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
384	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
391	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
392	C₄²	—	2	8	no	—
393	C₄²	C₂×D₄×C₆₁	1	2	yes	—
394	C₄²	C₂×D₄×C₆₁	1	4	yes	—
395	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
396	C₄²	C₂⁴×C₆₁	1	2	yes	—
397	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
398	C₂³	—	2	4	no	—
399	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
400	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
401	Q₈	—	2	2	no	—
402	Q₈	—	2	8	no	—
403	Q₈	—	4	8	no	—
404	Q₈	—	8	4	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	8	no	—
408	D₄	—	4	8	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	4	no	—
411	D₄	—	8	8	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	—	8	8	no	—
419	C₂×C₄	—	8	4	no	—
420	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
421	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
422	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
425	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
426	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
427	C₈	—	2	4	no	—
428	C₈	C₂×#41×C₆₁	1	4	yes	—
429	C₈	C₂×#41×C₆₁	1	4	yes	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	C₆₁×#532	1	2	yes	—
437	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
438	C₄	—	2	4	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	4	8	no	—
442	C₄	—	4	4	no	—
443	C₄	C₆₁×#532	1	2	yes	—
444	C₄	C₆₁×#577	1	4	yes	—
445	C₄	C₂²×#41×C₆₁	1	2	yes	—
446	C₂	—	2	2	no	—
447	C₂	—	4	2	no	—
448	C₂	—	8	4	no	—
449	C₂	C₂×C₆₁×#532	1	1	yes	characteristic
450	C₂	C₂×C₆₁×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3511	C₂	semidirect
2. C₆₁×#3185	C₂	semidirect
3. C₆₁×#3184	C₂	semidirect
4. C₆₁×#3173	C₂	semidirect
5. C₆₁×#3167	C₂	semidirect
6. C₂×C₆₁×#498	C₂	semidirect
7. C₆₁×#3147	C₂	semidirect
8. C₆₁×#3141	C₂	semidirect
9. C₆₁×#3060	C₂	semidirect
10. C₆₁×#2952	C₂	semidirect
11. C₄×#131×C₆₁	C₂	semidirect
145. C₂×C₈×C₆₁	#41	semidirect
204. #60716	C₆₁	direct (N × H)
221. #3511	C₂×C₆₁	semidirect
222. #3185	C₂×C₆₁	semidirect
223. #3184	C₂×C₆₁	semidirect
224. #3173	C₂×C₆₁	semidirect
225. #3167	C₂×C₆₁	semidirect
226. C₂×#498	C₂×C₆₁	semidirect
227. #3147	C₂×C₆₁	semidirect
228. #3141	C₂×C₆₁	semidirect
229. #3060	C₂×C₆₁	semidirect
230. #2952	C₂×C₆₁	semidirect
231. C₄×#131	C₂×C₆₁	semidirect
277. C₆₁	#60716	direct (N × H)
371. C₂×C₈	#41×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3511	2
C₆₁×#3185	2
C₆₁×#3184	2
C₆₁×#3173	2
C₆₁×#3167	2
C₂×C₆₁×#498	2
C₆₁×#3147	2
C₆₁×#3141	2
C₆₁×#3060	2
C₆₁×#2952	2
C₄×#131×C₆₁	2
#60716	61

Subgroups — C61×#60716 #29564149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60716 #29564149