Subgroups — C₆₁×#60800 #29564233

Order 15616.

2134 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3218	C₂	1	8	yes	maximal, complemented
4	C₆₁×#3209	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3206	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3152	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3139	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3039	C₂	1	4	yes	maximal, complemented
9	C₆₁×#3004	C₂	1	4	yes	maximal, complemented
10	C₆₁×#2920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₆₁	C₂²	1	2	yes	—
12	C₂×#137×C₆₁	C₂²	1	8	yes	—
13	C₆₁×#533	C₂²	1	2	yes	—
14	C₆₁×#533	C₂²	1	1	yes	characteristic
15	C₆₁×#532	C₂²	1	1	yes	characteristic
16	C₆₁×#532	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₆₁	—	2	2	no	—
18	C₂×C₄⋊Q₈×C₆₁	—	2	2	no	—
19	C₂×C₄⋊Q₈×C₆₁	—	2	2	no	—
20	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
21	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
22	C₂×C₄⋊Q₈×C₆₁	C₂²	1	4	yes	—
23	C₂×C₄⋊Q₈×C₆₁	C₂²	1	4	yes	—
24	C₆₁×#529	—	2	2	no	—
25	C₆₁×#529	—	2	2	no	—
26	C₆₁×#529	C₂²	1	4	yes	—
27	C₆₁×#525	—	2	2	no	—
28	C₆₁×#525	C₂²	1	2	yes	—
29	C₄×#41×C₆₁	—	2	2	no	—
30	C₄×#41×C₆₁	C₂²	1	2	yes	—
31	C₂²×C₄⋊C₄×C₆₁	—	2	2	no	—
32	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
33	C₆₁×#497	C₂²	1	8	yes	complemented
34	C₆₁×#494	C₂²	1	4	yes	complemented
35	C₆₁×#492	C₂²	1	4	yes	complemented
36	C₆₁×#491	C₂²	1	8	yes	complemented
37	C₆₁×#487	C₂²	1	8	yes	complemented
38	C₆₁×#462	C₂²	1	16	yes	complemented
39	C₆₁×#461	C₂²	1	16	yes	complemented
40	C₆₁×#451	C₂²	1	16	yes	—
41	C₆₁×#448	C₂²	1	16	yes	—
42	C₆₁×#432	C₂²	1	4	yes	—
43	C₆₁×#431	C₂²	1	4	yes	—
44	C₆₁×#423	C₂²	1	2	yes	—
45	C₆₁×#419	C₂²	1	8	yes	—
46	C₆₁×#407	C₂²	1	2	yes	—
47	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
48	C₂×#41×C₆₁	—	2	2	no	—
49	C₂×#41×C₆₁	C₂³	1	2	yes	—
50	C₂²×Q₈×C₆₁	—	2	4	no	—
51	C₂²×Q₈×C₆₁	—	2	2	no	—
52	C₂²×Q₈×C₆₁	—	4	8	no	—
53	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
54	C₂²×Q₈×C₆₁	C₂³	1	8	yes	—
55	C₂³×C₄×C₆₁	—	2	2	no	—
56	C₂³×C₄×C₆₁	D₄	1	2	yes	—
57	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
58	#137×C₆₁	—	4	16	no	—
59	C₂×Q₁₆×C₆₁	C₂³	1	16	yes	—
60	C₂×SD₁₆×C₆₁	C₂³	1	16	yes	—
61	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
62	C₄⋊Q₈×C₆₁	—	2	2	no	—
63	C₄⋊Q₈×C₆₁	—	2	2	no	—
64	C₄⋊Q₈×C₆₁	—	2	4	no	—
65	C₄⋊Q₈×C₆₁	—	2	4	no	—
66	C₄⋊Q₈×C₆₁	—	2	4	no	—
67	C₄⋊Q₈×C₆₁	—	2	4	no	—
68	C₄⋊Q₈×C₆₁	—	2	4	no	—
69	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
70	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
71	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
72	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
73	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
74	#127×C₆₁	C₂³	1	1	yes	characteristic
75	#126×C₆₁	—	2	4	no	—
76	#125×C₆₁	—	2	2	no	—
77	#125×C₆₁	C₂³	1	2	yes	—
78	#124×C₆₁	—	2	2	no	—
79	#124×C₆₁	C₂³	1	2	yes	—
80	#123×C₆₁	—	2	4	no	—
81	#123×C₆₁	—	2	2	no	—
82	C₂²⋊Q₈×C₆₁	—	2	2	no	—
83	C₂²⋊Q₈×C₆₁	—	2	2	no	—
84	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
85	#121×C₆₁	—	2	2	no	—
86	#121×C₆₁	—	2	2	no	—
87	#121×C₆₁	C₂³	1	4	yes	—
88	#120×C₆₁	—	2	2	no	—
89	C₄×Q₈×C₆₁	—	2	2	no	—
90	C₄×Q₈×C₆₁	—	2	2	no	—
91	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
92	C₄×D₄×C₆₁	—	2	4	no	—
93	C₄×D₄×C₆₁	—	2	4	no	—
94	C₄×D₄×C₆₁	—	2	4	no	—
95	C₄×D₄×C₆₁	—	2	2	no	—
96	C₄×D₄×C₆₁	—	2	2	no	—
97	C₄×D₄×C₆₁	C₂³	1	4	yes	—
98	#117×C₆₁	—	2	2	no	—
99	#117×C₆₁	—	2	4	no	—
100	#117×C₆₁	—	2	2	no	—
101	#117×C₆₁	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
103	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
104	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
105	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
106	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
107	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
108	C₂×C₄²×C₆₁	—	2	2	no	—
109	C₂×C₄²×C₆₁	D₄	1	2	yes	—
110	C₂×C₄²×C₆₁	D₄	1	2	yes	—
111	C₂×C₄²×C₆₁	D₄	1	2	yes	—
112	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
114	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
116	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
117	#103×C₆₁	C₂³	1	32	yes	—
118	C₂²⋊C₈×C₆₁	C₂³	1	8	yes	—
119	#97×C₆₁	C₂³	1	4	yes	—
120	C₄×C₈×C₆₁	C₂³	1	4	yes	—
121	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
122	#41×C₆₁	—	2	8	no	—
123	#41×C₆₁	—	4	8	no	—
124	C₂×Q₈×C₆₁	—	2	2	no	—
125	C₂×Q₈×C₆₁	—	2	8	no	—
126	C₂×Q₈×C₆₁	—	2	4	no	—
127	C₂×Q₈×C₆₁	—	2	16	no	—
128	C₂×Q₈×C₆₁	—	4	16	no	—
129	C₂×Q₈×C₆₁	—	4	8	no	—
130	C₂×Q₈×C₆₁	—	4	16	no	—
131	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
132	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
133	C₂×D₄×C₆₁	—	2	2	no	—
134	C₂×D₄×C₆₁	—	2	4	no	—
135	C₂×D₄×C₆₁	—	2	2	no	—
136	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₆₁	—	2	8	no	—
138	C₂²×C₄×C₆₁	—	2	4	no	—
139	C₂²×C₄×C₆₁	—	2	8	no	—
140	C₂²×C₄×C₆₁	—	2	4	no	—
141	C₂²×C₄×C₆₁	—	2	2	no	—
142	C₂²×C₄×C₆₁	—	2	4	no	—
143	C₂²×C₄×C₆₁	—	4	8	no	—
144	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
154	Q₁₆×C₆₁	—	4	16	no	—
155	SD₁₆×C₆₁	—	4	16	no	—
156	M₁₆×C₆₁	—	2	8	no	—
157	C₂×C₈×C₆₁	C₂⁴	1	8	yes	—
158	C₄⋊C₄×C₆₁	—	2	8	no	—
159	C₄⋊C₄×C₆₁	—	2	8	no	—
160	C₄⋊C₄×C₆₁	—	2	8	no	—
161	C₄⋊C₄×C₆₁	—	2	8	no	—
162	C₄⋊C₄×C₆₁	—	2	2	no	—
163	C₄⋊C₄×C₆₁	—	2	2	no	—
164	C₄⋊C₄×C₆₁	—	2	4	no	—
165	C₄⋊C₄×C₆₁	—	2	4	no	—
166	C₄⋊C₄×C₆₁	—	2	4	no	—
167	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
168	C₂²⋊C₄×C₆₁	—	2	4	no	—
169	C₂²⋊C₄×C₆₁	—	2	2	no	—
170	C₂²⋊C₄×C₆₁	—	2	4	no	—
171	C₂²⋊C₄×C₆₁	—	2	4	no	—
172	C₂²⋊C₄×C₆₁	—	2	4	no	—
173	C₄²×C₆₁	—	2	4	no	—
174	C₄²×C₆₁	—	2	2	no	—
175	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₆₁	C₂×D₄	1	2	yes	—
177	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₆₁	C₂×D₄	1	2	yes	—
179	C₄²×C₆₁	C₂×D₄	1	2	yes	—
180	C₄²×C₆₁	C₂×D₄	1	2	yes	—
181	C₄²×C₆₁	C₂×D₄	1	2	yes	—
182	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
183	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
184	C₄²×C₆₁	C₂⁴	1	2	yes	—
185	C₂³×C₆₁	—	2	2	no	—
186	C₂³×C₆₁	—	2	4	no	—
187	C₂³×C₆₁	—	2	2	no	—
188	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
189	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
190	Q₈×C₆₁	—	2	16	no	—
191	Q₈×C₆₁	—	2	4	no	—
192	Q₈×C₆₁	—	4	16	no	—
193	Q₈×C₆₁	—	4	8	no	—
194	Q₈×C₆₁	—	4	4	no	—
195	D₄×C₆₁	—	2	4	no	—
196	D₄×C₆₁	—	4	4	no	—
197	D₄×C₆₁	—	4	8	no	—
198	D₄×C₆₁	—	4	4	no	—
199	C₂×C₄×C₆₁	—	2	2	no	—
200	C₂×C₄×C₆₁	—	2	4	no	—
201	C₂×C₄×C₆₁	—	2	4	no	—
202	C₂×C₄×C₆₁	—	2	4	no	—
203	C₂×C₄×C₆₁	—	2	4	no	—
204	C₂×C₄×C₆₁	—	2	4	no	—
205	C₂×C₄×C₆₁	—	2	4	no	—
206	C₂×C₄×C₆₁	—	2	4	no	—
207	C₂×C₄×C₆₁	—	2	2	no	—
208	C₂×C₄×C₆₁	—	2	4	no	—
209	C₂×C₄×C₆₁	—	2	8	no	—
210	C₂×C₄×C₆₁	—	4	16	no	—
211	C₂×C₄×C₆₁	—	4	8	no	—
212	C₂×C₄×C₆₁	—	4	4	no	—
213	C₂×C₄×C₆₁	—	4	8	no	—
214	C₂×C₄×C₆₁	#137	1	8	yes	complemented
215	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₆₁	H(5,𝔽₂)	1	4	yes	—
222	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
223	C₈×C₆₁	—	2	8	no	—
224	#60800	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂²×C₆₁	—	2	8	no	—
226	C₂²×C₆₁	—	2	2	no	—
227	C₂²×C₆₁	—	2	2	no	—
228	C₂²×C₆₁	—	2	2	no	—
229	C₂²×C₆₁	—	4	2	no	—
230	C₂²×C₆₁	—	4	4	no	—
231	C₂²×C₆₁	#535	1	2	yes	—
232	C₂²×C₆₁	C₂×#137	1	4	yes	—
233	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
234	C₄×C₆₁	—	2	2	no	—
235	C₄×C₆₁	—	2	2	no	—
236	C₄×C₆₁	—	2	2	no	—
237	C₄×C₆₁	—	4	8	no	—
238	C₄×C₆₁	—	4	2	no	—
239	C₄×C₆₁	—	4	4	no	—
240	C₄×C₆₁	#535	1	2	yes	—
241	C₄×C₆₁	C₂×#137	1	4	yes	—
242	C₄×C₆₁	C₂×#137	1	4	yes	—
243	C₄×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
244	#3444	C₂×C₆₁	1	1	yes	characteristic
245	C₂²×C₄⋊Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
246	#3218	C₂×C₆₁	1	8	yes	complemented
247	#3209	C₂×C₆₁	1	4	yes	complemented
248	#3206	C₂×C₆₁	1	4	yes	complemented
249	#3152	C₂×C₆₁	1	2	yes	complemented
250	#3139	C₂×C₆₁	1	2	yes	complemented
251	#3039	C₂×C₆₁	1	4	yes	complemented
252	#3004	C₂×C₆₁	1	4	yes	complemented
253	#2920	C₂×C₆₁	1	1	yes	characteristic, complemented
254	C₂×C₆₁	—	2	2	no	—
255	C₂×C₆₁	—	2	4	no	—
256	C₂×C₆₁	—	8	2	no	—
257	C₂×C₆₁	C₂×#535	1	1	yes	characteristic
258	C₂×C₆₁	C₂²×#137	1	2	yes	—
259	C₂³×Q₈	C₂²×C₆₁	1	2	yes	—
260	C₂×#137	C₂²×C₆₁	1	8	yes	—
261	#533	C₂²×C₆₁	1	2	yes	—
262	#533	C₂²×C₆₁	1	1	yes	characteristic
263	#532	C₂²×C₆₁	1	1	yes	characteristic
264	#532	C₂²×C₆₁	1	2	yes	—
265	C₂×C₄⋊Q₈	—	2	2	no	—
266	C₂×C₄⋊Q₈	—	2	2	no	—
267	C₂×C₄⋊Q₈	—	2	2	no	—
268	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
269	C₂×C₄⋊Q₈	C₂²×C₆₁	1	4	yes	—
270	C₂×C₄⋊Q₈	C₂²×C₆₁	1	4	yes	—
271	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
272	#529	—	2	2	no	—
273	#529	—	2	2	no	—
274	#529	C₂²×C₆₁	1	4	yes	—
275	#525	—	2	2	no	—
276	#525	C₂²×C₆₁	1	2	yes	—
277	C₄×#41	—	2	2	no	—
278	C₄×#41	C₂²×C₆₁	1	2	yes	—
279	C₂²×C₄⋊C₄	—	2	2	no	—
280	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
281	#497	C₂²×C₆₁	1	8	yes	complemented
282	#494	C₂²×C₆₁	1	4	yes	complemented
283	#492	C₂²×C₆₁	1	4	yes	complemented
284	#491	C₂²×C₆₁	1	8	yes	complemented
285	#487	C₂²×C₆₁	1	8	yes	complemented
286	#462	C₂²×C₆₁	1	16	yes	complemented
287	#461	C₂²×C₆₁	1	16	yes	complemented
288	#451	C₂²×C₆₁	1	16	yes	—
289	#448	C₂²×C₆₁	1	16	yes	—
290	#432	C₂²×C₆₁	1	4	yes	—
291	#431	C₂²×C₆₁	1	4	yes	—
292	#423	C₂²×C₆₁	1	2	yes	—
293	#419	C₂²×C₆₁	1	8	yes	—
294	#407	C₂²×C₆₁	1	2	yes	—
295	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
296	C₆₁	#60800	1	1	yes	characteristic, direct product factor, Sylow
297	C₂×#41	—	2	2	no	—
298	C₂×#41	C₂³×C₆₁	1	2	yes	—
299	C₂²×Q₈	—	2	4	no	—
300	C₂²×Q₈	—	2	2	no	—
301	C₂²×Q₈	—	4	8	no	—
302	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
303	C₂²×Q₈	C₂³×C₆₁	1	8	yes	—
304	C₂³×C₄	—	2	2	no	—
305	C₂³×C₄	D₄×C₆₁	1	2	yes	—
306	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
307	#137	—	4	16	no	—
308	C₂×Q₁₆	C₂³×C₆₁	1	16	yes	—
309	C₂×SD₁₆	C₂³×C₆₁	1	16	yes	—
310	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	—	2	4	no	—
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	—	2	4	no	—
315	C₄⋊Q₈	—	2	4	no	—
316	C₄⋊Q₈	—	2	4	no	—
317	C₄⋊Q₈	—	2	4	no	—
318	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
319	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
320	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
321	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
322	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
323	#127	C₂³×C₆₁	1	1	yes	characteristic
324	#126	—	2	4	no	—
325	#125	—	2	2	no	—
326	#125	C₂³×C₆₁	1	2	yes	—
327	#124	—	2	2	no	—
328	#124	C₂³×C₆₁	1	2	yes	—
329	#123	—	2	4	no	—
330	#123	—	2	2	no	—
331	C₂²⋊Q₈	—	2	2	no	—
332	C₂²⋊Q₈	—	2	2	no	—
333	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
334	#121	—	2	2	no	—
335	#121	—	2	2	no	—
336	#121	C₂³×C₆₁	1	4	yes	—
337	#120	—	2	2	no	—
338	C₄×Q₈	—	2	2	no	—
339	C₄×Q₈	—	2	2	no	—
340	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
341	C₄×D₄	—	2	4	no	—
342	C₄×D₄	—	2	4	no	—
343	C₄×D₄	—	2	4	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	2	2	no	—
346	C₄×D₄	C₂³×C₆₁	1	4	yes	—
347	#117	—	2	2	no	—
348	#117	—	2	4	no	—
349	#117	—	2	2	no	—
350	#117	C₂³×C₆₁	1	2	yes	—
351	C₂×C₄⋊C₄	—	2	4	no	—
352	C₂×C₄⋊C₄	—	2	4	no	—
353	C₂×C₄⋊C₄	—	2	4	no	—
354	C₂×C₄⋊C₄	—	2	4	no	—
355	C₂×C₄⋊C₄	—	2	4	no	—
356	C₂×C₄⋊C₄	—	2	4	no	—
357	C₂×C₄²	—	2	2	no	—
358	C₂×C₄²	D₄×C₆₁	1	2	yes	—
359	C₂×C₄²	D₄×C₆₁	1	2	yes	—
360	C₂×C₄²	D₄×C₆₁	1	2	yes	—
361	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
363	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
365	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
366	#103	C₂³×C₆₁	1	32	yes	—
367	C₂²⋊C₈	C₂³×C₆₁	1	8	yes	—
368	#97	C₂³×C₆₁	1	4	yes	—
369	C₄×C₈	C₂³×C₆₁	1	4	yes	—
370	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
371	#41	—	2	8	no	—
372	#41	—	4	8	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	8	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	16	no	—
377	C₂×Q₈	—	4	16	no	—
378	C₂×Q₈	—	4	8	no	—
379	C₂×Q₈	—	4	16	no	—
380	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
381	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
386	C₂²×C₄	—	2	8	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	4	8	no	—
393	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
394	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
400	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
401	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
403	Q₁₆	—	4	16	no	—
404	SD₁₆	—	4	16	no	—
405	M₁₆	—	2	8	no	—
406	C₂×C₈	C₂⁴×C₆₁	1	8	yes	—
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	—	2	8	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₄²	—	2	4	no	—
423	C₄²	—	2	2	no	—
424	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
425	C₄²	C₂×D₄×C₆₁	1	2	yes	—
426	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₆₁	1	2	yes	—
428	C₄²	C₂×D₄×C₆₁	1	2	yes	—
429	C₄²	C₂×D₄×C₆₁	1	2	yes	—
430	C₄²	C₂×D₄×C₆₁	1	2	yes	—
431	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
432	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
433	C₄²	C₂⁴×C₆₁	1	2	yes	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	2	no	—
437	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
438	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
439	Q₈	—	2	16	no	—
440	Q₈	—	2	4	no	—
441	Q₈	—	4	16	no	—
442	Q₈	—	4	8	no	—
443	Q₈	—	4	4	no	—
444	D₄	—	2	4	no	—
445	D₄	—	4	4	no	—
446	D₄	—	4	8	no	—
447	D₄	—	4	4	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	4	16	no	—
460	C₂×C₄	—	4	8	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	#137×C₆₁	1	8	yes	complemented
464	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
466	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
467	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
469	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
470	C₂×C₄	H(5,𝔽₂)×C₆₁	1	4	yes	—
471	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
472	C₈	—	2	8	no	—
473	C₂²	—	2	8	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	2	no	—
479	C₂²	C₆₁×#535	1	2	yes	—
480	C₂²	C₂×#137×C₆₁	1	4	yes	—
481	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	4	4	no	—
486	C₄	—	4	8	no	—
487	C₄	—	4	2	no	—
488	C₄	C₆₁×#535	1	2	yes	—
489	C₄	C₂×#137×C₆₁	1	4	yes	—
490	C₄	C₂×#137×C₆₁	1	4	yes	—
491	C₄	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
492	C₂	—	2	2	no	—
493	C₂	—	2	4	no	—
494	C₂	—	8	2	no	—
495	C₂	C₂×C₆₁×#535	1	1	yes	characteristic
496	C₂	C₂²×#137×C₆₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊Q₈×C₆₁	C₂	semidirect
3. C₆₁×#3218	C₂	semidirect
4. C₆₁×#3209	C₂	semidirect
5. C₆₁×#3206	C₂	semidirect
6. C₆₁×#3152	C₂	semidirect
7. C₆₁×#3139	C₂	semidirect
8. C₆₁×#3039	C₂	semidirect
9. C₆₁×#3004	C₂	semidirect
10. C₆₁×#2920	C₂	semidirect
33. C₆₁×#497	C₂²	semidirect
34. C₆₁×#494	C₂²	semidirect
35. C₆₁×#492	C₂²	semidirect
36. C₆₁×#491	C₂²	semidirect
37. C₆₁×#487	C₂²	semidirect
38. C₆₁×#462	C₂²	semidirect
39. C₆₁×#461	C₂²	semidirect
214. C₂×C₄×C₆₁	#137	semidirect
224. #60800	C₆₁	direct (N × H)
245. C₂²×C₄⋊Q₈	C₂×C₆₁	semidirect
246. #3218	C₂×C₆₁	semidirect
247. #3209	C₂×C₆₁	semidirect
248. #3206	C₂×C₆₁	semidirect
249. #3152	C₂×C₆₁	semidirect
250. #3139	C₂×C₆₁	semidirect
251. #3039	C₂×C₆₁	semidirect
252. #3004	C₂×C₆₁	semidirect
253. #2920	C₂×C₆₁	semidirect
281. #497	C₂²×C₆₁	semidirect
282. #494	C₂²×C₆₁	semidirect
283. #492	C₂²×C₆₁	semidirect
284. #491	C₂²×C₆₁	semidirect
285. #487	C₂²×C₆₁	semidirect
286. #462	C₂²×C₆₁	semidirect
287. #461	C₂²×C₆₁	semidirect
296. C₆₁	#60800	direct (N × H)
463. C₂×C₄	#137×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3444	2
C₂²×C₄⋊Q₈×C₆₁	2
C₆₁×#3218	2
C₆₁×#3209	2
C₆₁×#3206	2
C₆₁×#3152	2
C₆₁×#3139	2
C₆₁×#3039	2
C₆₁×#3004	2
C₆₁×#2920	2
#60800	61

Subgroups — C61×#60800 #29564233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60800 #29564233