Subgroups — C₆₁×#60808 #29564241

Order 15616.

2162 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3221	C₂	1	8	yes	maximal, complemented
4	C₆₁×#3220	C₂	1	8	yes	maximal, complemented
5	C₆₁×#3151	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3142	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3036	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3006	C₂	1	4	yes	maximal, complemented
9	C₆₁×#2921	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₆₁	C₂²	1	2	yes	—
11	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	8	yes	complemented
12	C₆₁×#540	—	2	4	no	—
13	C₆₁×#540	C₂²	1	8	yes	complemented
14	C₆₁×#537	—	2	2	no	—
15	C₆₁×#536	C₂²	1	4	yes	complemented
16	C₆₁×#535	C₂²	1	4	yes	complemented
17	C₆₁×#534	—	2	2	no	—
18	C₆₁×#532	C₂²	1	2	yes	—
19	C₆₁×#532	C₂²	1	2	yes	—
20	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic, complemented
21	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic, complemented
22	C₆₁×#525	—	2	4	no	—
23	C₂×#123×C₆₁	—	2	2	no	—
24	C₂×#121×C₆₁	—	2	2	no	—
25	C₂×#121×C₆₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
27	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#496	C₂²	1	8	yes	complemented
29	C₆₁×#493	C₂²	1	4	yes	complemented
30	C₆₁×#492	C₂²	1	4	yes	complemented
31	C₆₁×#491	C₂²	1	4	yes	complemented
32	C₆₁×#490	C₂²	1	4	yes	complemented
33	C₆₁×#488	C₂²	1	8	yes	complemented
34	C₆₁×#463	C₂²	1	16	yes	complemented
35	C₆₁×#461	C₂²	1	8	yes	complemented
36	C₆₁×#459	C₂²	1	8	yes	complemented
37	C₆₁×#449	C₂²	1	16	yes	complemented
38	C₆₁×#448	C₂²	1	8	yes	complemented
39	C₆₁×#447	C₂²	1	8	yes	complemented
40	C₆₁×#433	C₂²	1	8	yes	complemented
41	C₆₁×#423	C₂²	1	2	yes	complemented
42	C₆₁×#417	C₂²	1	8	yes	complemented
43	C₆₁×#407	C₂²	1	2	yes	—
44	C₄×M₁₆×C₆₁	C₂²	1	2	yes	complemented
45	C₂×#41×C₆₁	—	2	2	no	—
46	C₂×#41×C₆₁	—	2	2	no	—
47	C₂×#41×C₆₁	—	4	8	no	—
48	C₂×#41×C₆₁	C₂³	1	4	yes	—
49	C₂×#41×C₆₁	C₂³	1	4	yes	—
50	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
51	C₂²×D₄×C₆₁	—	2	2	no	—
52	C₂²×D₄×C₆₁	—	2	2	no	—
53	C₂²×D₄×C₆₁	—	2	2	no	—
54	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
55	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₆₁	—	2	2	no	—
57	C₂³×C₄×C₆₁	—	2	2	no	—
58	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
59	AGL(1,ℤ/8)×C₆₁	—	4	16	no	—
60	C₂×SD₁₆×C₆₁	C₂³	1	16	yes	—
61	C₂×D₈×C₆₁	C₂³	1	16	yes	—
62	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
63	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
64	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
65	#127×C₆₁	—	2	2	no	—
66	#127×C₆₁	C₂³	1	4	yes	—
67	#127×C₆₁	C₂³	1	2	yes	—
68	#127×C₆₁	C₂³	1	2	yes	—
69	#125×C₆₁	—	2	2	no	—
70	#125×C₆₁	C₂³	1	4	yes	—
71	#124×C₆₁	C₂³	1	4	yes	—
72	#124×C₆₁	C₂³	1	4	yes	—
73	#123×C₆₁	—	2	16	no	—
74	#123×C₆₁	—	2	8	no	—
75	C₂²⋊Q₈×C₆₁	—	2	8	no	—
76	#121×C₆₁	—	2	4	no	—
77	#121×C₆₁	—	2	4	no	—
78	#121×C₆₁	—	2	4	no	—
79	#121×C₆₁	—	2	8	no	—
80	#121×C₆₁	—	2	16	no	—
81	#121×C₆₁	C₂³	1	8	yes	—
82	#120×C₆₁	—	2	8	no	—
83	C₄×D₄×C₆₁	—	2	4	no	—
84	C₄×D₄×C₆₁	—	2	4	no	—
85	C₄×D₄×C₆₁	—	2	4	no	—
86	C₄×D₄×C₆₁	C₂³	1	8	yes	—
87	#117×C₆₁	D₄	1	4	yes	—
88	#117×C₆₁	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
90	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
92	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
95	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
98	#103×C₆₁	C₂³	1	16	yes	—
99	#102×C₆₁	C₂³	1	16	yes	—
100	C₂²⋊C₈×C₆₁	C₂³	1	8	yes	—
101	#97×C₆₁	C₂³	1	4	yes	—
102	C₄×C₈×C₆₁	C₂³	1	4	yes	—
103	C₂⁴×C₆₁	—	2	2	no	—
104	C₂⁴×C₆₁	—	2	2	no	—
105	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
106	#41×C₆₁	—	2	16	no	—
107	#41×C₆₁	—	4	8	no	—
108	#41×C₆₁	—	4	8	no	—
109	#41×C₆₁	—	4	8	no	—
110	C₂×Q₈×C₆₁	—	2	2	no	—
111	C₂×Q₈×C₆₁	—	4	4	no	—
112	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
113	C₂×D₄×C₆₁	—	2	4	no	—
114	C₂×D₄×C₆₁	—	2	4	no	—
115	C₂×D₄×C₆₁	—	2	8	no	—
116	C₂×D₄×C₆₁	—	2	2	no	—
117	C₂×D₄×C₆₁	—	2	2	no	—
118	C₂×D₄×C₆₁	—	2	4	no	—
119	C₂×D₄×C₆₁	—	2	4	no	—
120	C₂×D₄×C₆₁	—	2	8	no	—
121	C₂×D₄×C₆₁	—	2	8	no	—
122	C₂×D₄×C₆₁	—	4	4	no	—
123	C₂×D₄×C₆₁	—	4	8	no	—
124	C₂×D₄×C₆₁	—	8	4	no	—
125	C₂×D₄×C₆₁	—	8	4	no	—
126	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
127	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₆₁	—	2	4	no	—
129	C₂²×C₄×C₆₁	—	2	2	no	—
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	2	4	no	—
132	C₂²×C₄×C₆₁	—	2	4	no	—
133	C₂²×C₄×C₆₁	—	2	8	no	—
134	C₂²×C₄×C₆₁	—	4	8	no	—
135	C₂²×C₄×C₆₁	—	8	4	no	—
136	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
142	SD₁₆×C₆₁	—	4	16	no	—
143	D₈×C₆₁	—	4	16	no	—
144	M₁₆×C₆₁	—	2	8	no	—
145	C₂×C₈×C₆₁	C₂⁴	1	8	yes	—
146	C₄⋊C₄×C₆₁	—	2	8	no	—
147	C₄⋊C₄×C₆₁	—	2	2	no	—
148	C₄⋊C₄×C₆₁	—	2	4	no	—
149	C₄⋊C₄×C₆₁	—	2	4	no	—
150	C₄⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
151	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
152	C₂²⋊C₄×C₆₁	—	2	8	no	—
153	C₂²⋊C₄×C₆₁	—	2	8	no	—
154	C₂²⋊C₄×C₆₁	—	2	8	no	—
155	C₂²⋊C₄×C₆₁	—	2	8	no	—
156	C₂²⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
157	C₄²×C₆₁	C₂×D₄	1	2	yes	—
158	C₄²×C₆₁	C₂×D₄	1	2	yes	—
159	C₄²×C₆₁	C₂⁴	1	2	yes	—
160	C₄²×C₆₁	C₂⁴	1	2	yes	—
161	C₂³×C₆₁	—	2	2	no	—
162	C₂³×C₆₁	—	2	4	no	—
163	C₂³×C₆₁	—	2	4	no	—
164	C₂³×C₆₁	—	4	2	no	—
165	C₂³×C₆₁	—	4	4	no	—
166	C₂³×C₆₁	—	4	4	no	—
167	C₂³×C₆₁	—	4	4	no	—
168	C₂³×C₆₁	—	4	4	no	—
169	C₂³×C₆₁	—	8	4	no	—
170	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
171	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₆₁	—	2	8	no	—
173	Q₈×C₆₁	—	4	4	no	—
174	D₄×C₆₁	—	2	8	no	—
175	D₄×C₆₁	—	2	8	no	—
176	D₄×C₆₁	—	4	4	no	—
177	D₄×C₆₁	—	4	8	no	—
178	D₄×C₆₁	—	4	8	no	—
179	D₄×C₆₁	—	4	4	no	—
180	D₄×C₆₁	—	8	4	no	—
181	D₄×C₆₁	—	8	4	no	—
182	D₄×C₆₁	—	8	8	no	—
183	D₄×C₆₁	—	8	8	no	—
184	C₂×C₄×C₆₁	—	2	2	no	—
185	C₂×C₄×C₆₁	—	2	4	no	—
186	C₂×C₄×C₆₁	—	2	4	no	—
187	C₂×C₄×C₆₁	—	2	4	no	—
188	C₂×C₄×C₆₁	—	2	4	no	—
189	C₂×C₄×C₆₁	—	4	2	no	—
190	C₂×C₄×C₆₁	—	4	2	no	—
191	C₂×C₄×C₆₁	—	4	8	no	—
192	C₂×C₄×C₆₁	—	4	4	no	—
193	C₂×C₄×C₆₁	—	4	4	no	—
194	C₂×C₄×C₆₁	—	4	8	no	—
195	C₂×C₄×C₆₁	—	8	8	no	—
196	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
197	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
198	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₆₁	H(5,𝔽₂)	1	4	yes	—
201	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
202	C₈×C₆₁	—	2	8	no	—
203	#60808	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂²×C₆₁	—	2	2	no	—
205	C₂²×C₆₁	—	2	4	no	—
206	C₂²×C₆₁	—	2	2	no	—
207	C₂²×C₆₁	—	4	4	no	—
208	C₂²×C₆₁	—	4	4	no	—
209	C₂²×C₆₁	—	4	8	no	—
210	C₂²×C₆₁	—	4	4	no	—
211	C₂²×C₆₁	—	4	4	no	—
212	C₂²×C₆₁	—	8	2	no	—
213	C₂²×C₆₁	—	8	8	no	—
214	C₂²×C₆₁	—	8	8	no	—
215	C₂²×C₆₁	#535	1	2	yes	—
216	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
217	C₄×C₆₁	—	2	4	no	—
218	C₄×C₆₁	—	2	4	no	—
219	C₄×C₆₁	—	2	2	no	—
220	C₄×C₆₁	—	4	4	no	—
221	C₄×C₆₁	—	4	4	no	—
222	C₄×C₆₁	#535	1	2	yes	—
223	C₄×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
224	C₂×#540	C₂×C₆₁	1	1	yes	characteristic, complemented
225	#3449	C₂×C₆₁	1	1	yes	characteristic, complemented
226	#3221	C₂×C₆₁	1	8	yes	complemented
227	#3220	C₂×C₆₁	1	8	yes	complemented
228	#3151	C₂×C₆₁	1	2	yes	complemented
229	#3142	C₂×C₆₁	1	2	yes	complemented
230	#3036	C₂×C₆₁	1	4	yes	complemented
231	#3006	C₂×C₆₁	1	4	yes	complemented
232	#2921	C₂×C₆₁	1	1	yes	characteristic, complemented
233	C₂×C₆₁	—	2	2	no	—
234	C₂×C₆₁	—	4	2	no	—
235	C₂×C₆₁	—	8	4	no	—
236	C₂×C₆₁	—	8	4	no	—
237	C₂×C₆₁	C₂×#535	1	1	yes	characteristic
238	C₂×C₆₁	#3585	1	2	yes	—
239	C₂²×#41	C₂²×C₆₁	1	2	yes	—
240	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	8	yes	complemented
241	#540	—	2	4	no	—
242	#540	C₂²×C₆₁	1	8	yes	complemented
243	#537	—	2	2	no	—
244	#536	C₂²×C₆₁	1	4	yes	complemented
245	#535	C₂²×C₆₁	1	4	yes	complemented
246	#534	—	2	2	no	—
247	#532	C₂²×C₆₁	1	2	yes	—
248	#532	C₂²×C₆₁	1	2	yes	—
249	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic, complemented
250	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic, complemented
251	#525	—	2	4	no	—
252	C₂×#123	—	2	2	no	—
253	C₂×#121	—	2	2	no	—
254	C₂×#121	C₂²×C₆₁	1	2	yes	—
255	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	complemented
256	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
257	#496	C₂²×C₆₁	1	8	yes	complemented
258	#493	C₂²×C₆₁	1	4	yes	complemented
259	#492	C₂²×C₆₁	1	4	yes	complemented
260	#491	C₂²×C₆₁	1	4	yes	complemented
261	#490	C₂²×C₆₁	1	4	yes	complemented
262	#488	C₂²×C₆₁	1	8	yes	complemented
263	#463	C₂²×C₆₁	1	16	yes	complemented
264	#461	C₂²×C₆₁	1	8	yes	complemented
265	#459	C₂²×C₆₁	1	8	yes	complemented
266	#449	C₂²×C₆₁	1	16	yes	complemented
267	#448	C₂²×C₆₁	1	8	yes	complemented
268	#447	C₂²×C₆₁	1	8	yes	complemented
269	#433	C₂²×C₆₁	1	8	yes	complemented
270	#423	C₂²×C₆₁	1	2	yes	complemented
271	#417	C₂²×C₆₁	1	8	yes	complemented
272	#407	C₂²×C₆₁	1	2	yes	—
273	C₄×M₁₆	C₂²×C₆₁	1	2	yes	complemented
274	C₆₁	#60808	1	1	yes	characteristic, direct product factor, Sylow
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	4	8	no	—
278	C₂×#41	C₂³×C₆₁	1	4	yes	—
279	C₂×#41	C₂³×C₆₁	1	4	yes	—
280	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	—	2	2	no	—
284	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
285	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
286	C₂³×C₄	—	2	2	no	—
287	C₂³×C₄	—	2	2	no	—
288	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
289	AGL(1,ℤ/8)	—	4	16	no	—
290	C₂×SD₁₆	C₂³×C₆₁	1	16	yes	—
291	C₂×D₈	C₂³×C₆₁	1	16	yes	—
292	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
293	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
294	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
295	#127	—	2	2	no	—
296	#127	C₂³×C₆₁	1	4	yes	—
297	#127	C₂³×C₆₁	1	2	yes	—
298	#127	C₂³×C₆₁	1	2	yes	—
299	#125	—	2	2	no	—
300	#125	C₂³×C₆₁	1	4	yes	—
301	#124	C₂³×C₆₁	1	4	yes	—
302	#124	C₂³×C₆₁	1	4	yes	—
303	#123	—	2	16	no	—
304	#123	—	2	8	no	—
305	C₂²⋊Q₈	—	2	8	no	—
306	#121	—	2	4	no	—
307	#121	—	2	4	no	—
308	#121	—	2	4	no	—
309	#121	—	2	8	no	—
310	#121	—	2	16	no	—
311	#121	C₂³×C₆₁	1	8	yes	—
312	#120	—	2	8	no	—
313	C₄×D₄	—	2	4	no	—
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	—	2	4	no	—
316	C₄×D₄	C₂³×C₆₁	1	8	yes	—
317	#117	D₄×C₆₁	1	4	yes	—
318	#117	C₂³×C₆₁	1	4	yes	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
325	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
327	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
328	#103	C₂³×C₆₁	1	16	yes	—
329	#102	C₂³×C₆₁	1	16	yes	—
330	C₂²⋊C₈	C₂³×C₆₁	1	8	yes	—
331	#97	C₂³×C₆₁	1	4	yes	—
332	C₄×C₈	C₂³×C₆₁	1	4	yes	—
333	C₂⁴	—	2	2	no	—
334	C₂⁴	—	2	2	no	—
335	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
336	#41	—	2	16	no	—
337	#41	—	4	8	no	—
338	#41	—	4	8	no	—
339	#41	—	4	8	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	4	no	—
342	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	8	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	8	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	4	4	no	—
353	C₂×D₄	—	4	8	no	—
354	C₂×D₄	—	8	4	no	—
355	C₂×D₄	—	8	4	no	—
356	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
357	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	8	no	—
364	C₂²×C₄	—	4	8	no	—
365	C₂²×C₄	—	8	4	no	—
366	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
370	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
371	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
372	SD₁₆	—	4	16	no	—
373	D₈	—	4	16	no	—
374	M₁₆	—	2	8	no	—
375	C₂×C₈	C₂⁴×C₆₁	1	8	yes	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
381	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
387	C₄²	C₂×D₄×C₆₁	1	2	yes	—
388	C₄²	C₂×D₄×C₆₁	1	2	yes	—
389	C₄²	C₂⁴×C₆₁	1	2	yes	—
390	C₄²	C₂⁴×C₆₁	1	2	yes	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	4	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	4	4	no	—
398	C₂³	—	4	4	no	—
399	C₂³	—	8	4	no	—
400	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
401	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
402	Q₈	—	2	8	no	—
403	Q₈	—	4	4	no	—
404	D₄	—	2	8	no	—
405	D₄	—	2	8	no	—
406	D₄	—	4	4	no	—
407	D₄	—	4	8	no	—
408	D₄	—	4	8	no	—
409	D₄	—	4	4	no	—
410	D₄	—	8	4	no	—
411	D₄	—	8	4	no	—
412	D₄	—	8	8	no	—
413	D₄	—	8	8	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	—	8	8	no	—
426	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
427	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
428	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
430	C₂×C₄	H(5,𝔽₂)×C₆₁	1	4	yes	—
431	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
432	C₈	—	2	8	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	8	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	8	no	—
443	C₂²	—	8	8	no	—
444	C₂²	C₆₁×#535	1	2	yes	—
445	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
446	C₄	—	2	4	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	4	no	—
451	C₄	C₆₁×#535	1	2	yes	—
452	C₄	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
453	C₂	—	2	2	no	—
454	C₂	—	4	2	no	—
455	C₂	—	8	4	no	—
456	C₂	—	8	4	no	—
457	C₂	C₂×C₆₁×#535	1	1	yes	characteristic
458	C₂	C₆₁×#3585	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 ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#540	C₂	semidirect
2. C₆₁×#3449	C₂	semidirect
3. C₆₁×#3221	C₂	semidirect
4. C₆₁×#3220	C₂	semidirect
5. C₆₁×#3151	C₂	semidirect
6. C₆₁×#3142	C₂	semidirect
7. C₆₁×#3036	C₂	semidirect
8. C₆₁×#3006	C₂	semidirect
9. C₆₁×#2921	C₂	semidirect
11. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
13. C₆₁×#540	C₂²	semidirect
15. C₆₁×#536	C₂²	semidirect
16. C₆₁×#535	C₂²	semidirect
20. C₂×#127×C₆₁	C₂²	semidirect
21. C₂×#125×C₆₁	C₂²	semidirect
26. C₂×C₄×D₄×C₆₁	C₂²	semidirect
28. C₆₁×#496	C₂²	semidirect
29. C₆₁×#493	C₂²	semidirect
30. C₆₁×#492	C₂²	semidirect
31. C₆₁×#491	C₂²	semidirect
32. C₆₁×#490	C₂²	semidirect
33. C₆₁×#488	C₂²	semidirect
34. C₆₁×#463	C₂²	semidirect
35. C₆₁×#461	C₂²	semidirect
36. C₆₁×#459	C₂²	semidirect
37. C₆₁×#449	C₂²	semidirect
38. C₆₁×#448	C₂²	semidirect
39. C₆₁×#447	C₂²	semidirect
40. C₆₁×#433	C₂²	semidirect
41. C₆₁×#423	C₂²	semidirect
42. C₆₁×#417	C₂²	semidirect
44. C₄×M₁₆×C₆₁	C₂²	semidirect
203. #60808	C₆₁	direct (N × H)
224. C₂×#540	C₂×C₆₁	semidirect
225. #3449	C₂×C₆₁	semidirect
226. #3221	C₂×C₆₁	semidirect
227. #3220	C₂×C₆₁	semidirect
228. #3151	C₂×C₆₁	semidirect
229. #3142	C₂×C₆₁	semidirect
230. #3036	C₂×C₆₁	semidirect
231. #3006	C₂×C₆₁	semidirect
232. #2921	C₂×C₆₁	semidirect
240. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
242. #540	C₂²×C₆₁	semidirect
244. #536	C₂²×C₆₁	semidirect
245. #535	C₂²×C₆₁	semidirect
249. C₂×#127	C₂²×C₆₁	semidirect
250. C₂×#125	C₂²×C₆₁	semidirect
255. C₂×C₄×D₄	C₂²×C₆₁	semidirect
257. #496	C₂²×C₆₁	semidirect
258. #493	C₂²×C₆₁	semidirect
259. #492	C₂²×C₆₁	semidirect
260. #491	C₂²×C₆₁	semidirect
261. #490	C₂²×C₆₁	semidirect
262. #488	C₂²×C₆₁	semidirect
263. #463	C₂²×C₆₁	semidirect
264. #461	C₂²×C₆₁	semidirect
265. #459	C₂²×C₆₁	semidirect
266. #449	C₂²×C₆₁	semidirect
267. #448	C₂²×C₆₁	semidirect
268. #447	C₂²×C₆₁	semidirect
269. #433	C₂²×C₆₁	semidirect
270. #423	C₂²×C₆₁	semidirect
271. #417	C₂²×C₆₁	semidirect
273. C₄×M₁₆	C₂²×C₆₁	semidirect
274. C₆₁	#60808	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×#540	2
C₆₁×#3449	2
C₆₁×#3221	2
C₆₁×#3220	2
C₆₁×#3151	2
C₆₁×#3142	2
C₆₁×#3036	2
C₆₁×#3006	2
C₆₁×#2921	2
#60808	61

Subgroups — C61×#60808 #29564241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60808 #29564241