Subgroups — C₆₁×#25612 #29529045

Order 15616.

1094 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2620	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2001	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2000	C₂	1	2	yes	maximal
7	C₆₁×#1992	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1880	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1878	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1750	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
14	C₆₁×#541	—	2	4	no	—
15	C₆₁×#541	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#126×C₆₁	—	2	2	no	—
18	C₂×#125×C₆₁	—	2	2	no	—
19	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
25	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#497	—	2	4	no	—
27	C₆₁×#488	—	2	4	no	—
28	C₂×#103×C₆₁	C₂²	1	2	yes	—
29	C₂×#103×C₆₁	C₂²	1	2	yes	—
30	C₂×#103×C₆₁	C₂²	1	2	yes	—
31	C₂×#102×C₆₁	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
33	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
35	C₆₁×#396	—	2	2	no	—
36	C₆₁×#394	—	2	2	no	—
37	C₆₁×#391	C₂²	1	1	yes	characteristic
38	C₆₁×#390	C₂²	1	1	yes	characteristic
39	C₆₁×#384	C₂²	1	1	yes	characteristic
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₆₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
45	C₂²×D₄×C₆₁	—	2	1	no	—
46	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
48	C₂×Q₁₆×C₆₁	—	2	4	no	—
49	C₂×Q₁₆×C₆₁	—	2	4	no	—
50	C₂×Q₁₆×C₆₁	—	4	2	no	—
51	C₂×SD₁₆×C₆₁	—	2	4	no	—
52	C₂×SD₁₆×C₆₁	—	2	4	no	—
53	C₂×SD₁₆×C₆₁	—	4	2	no	—
54	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₆₁	—	2	2	no	—
57	C₄⋊Q₈×C₆₁	D₄	1	4	yes	complemented
58	#126×C₆₁	—	2	16	no	—
59	#125×C₆₁	—	2	16	no	—
60	#125×C₆₁	—	2	2	no	—
61	#125×C₆₁	D₄	1	4	yes	complemented
62	#124×C₆₁	—	2	2	no	—
63	#124×C₆₁	—	2	2	no	—
64	C₂²⋊Q₈×C₆₁	—	2	4	no	—
65	C₂²⋊Q₈×C₆₁	—	2	4	no	—
66	C₂²⋊Q₈×C₆₁	—	4	2	no	—
67	#121×C₆₁	—	4	2	no	—
68	C₄×Q₈×C₆₁	—	2	4	no	—
69	C₄×Q₈×C₆₁	—	2	4	no	—
70	#117×C₆₁	—	2	2	no	—
71	#117×C₆₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
75	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
78	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
82	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
88	C₂×C₄²×C₆₁	—	2	2	no	—
89	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
91	#103×C₆₁	—	2	4	no	—
92	#103×C₆₁	—	4	2	no	—
93	#103×C₆₁	—	4	2	no	—
94	#102×C₆₁	—	2	4	no	—
95	C₂²⋊C₈×C₆₁	—	2	4	no	—
96	#97×C₆₁	—	2	2	no	—
97	C₄×C₈×C₆₁	—	2	2	no	—
98	#95×C₆₁	—	2	2	no	—
99	C₂⁴×C₆₁	—	2	1	no	—
100	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
101	C₂×Q₈×C₆₁	—	2	2	no	—
102	C₂×Q₈×C₆₁	—	2	1	no	—
103	C₂×Q₈×C₆₁	—	2	1	no	—
104	C₂×Q₈×C₆₁	—	2	2	no	—
105	C₂×Q₈×C₆₁	—	2	2	no	—
106	C₂×Q₈×C₆₁	—	2	2	no	—
107	C₂×Q₈×C₆₁	—	2	2	no	—
108	C₂×Q₈×C₆₁	—	2	2	no	—
109	C₂×Q₈×C₆₁	—	2	2	no	—
110	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
111	C₂×D₄×C₆₁	—	2	1	no	—
112	C₂×D₄×C₆₁	—	2	1	no	—
113	C₂×D₄×C₆₁	—	2	2	no	—
114	C₂×D₄×C₆₁	—	2	2	no	—
115	C₂×D₄×C₆₁	—	4	2	no	—
116	C₂×D₄×C₆₁	—	8	2	no	—
117	C₂²×C₄×C₆₁	—	2	2	no	—
118	C₂²×C₄×C₆₁	—	2	2	no	—
119	C₂²×C₄×C₆₁	—	2	1	no	—
120	C₂²×C₄×C₆₁	—	2	1	no	—
121	C₂²×C₄×C₆₁	—	2	2	no	—
122	C₂²×C₄×C₆₁	—	2	2	no	—
123	C₂²×C₄×C₆₁	—	2	1	no	—
124	C₂²×C₄×C₆₁	—	2	1	no	—
125	C₂²×C₄×C₆₁	—	2	1	no	—
126	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
130	Q₁₆×C₆₁	—	4	8	no	—
131	SD₁₆×C₆₁	—	4	8	no	—
132	C₂×C₈×C₆₁	—	2	2	no	—
133	C₂×C₈×C₆₁	—	2	2	no	—
134	C₂×C₈×C₆₁	—	2	2	no	—
135	C₂×C₈×C₆₁	—	2	2	no	—
136	C₂×C₈×C₆₁	—	2	2	no	—
137	C₂×C₈×C₆₁	#41	1	4	yes	—
138	C₄⋊C₄×C₆₁	—	2	8	no	—
139	C₄⋊C₄×C₆₁	—	2	8	no	—
140	C₄⋊C₄×C₆₁	—	2	8	no	—
141	C₄⋊C₄×C₆₁	—	2	8	no	—
142	C₄⋊C₄×C₆₁	—	2	4	no	—
143	C₄⋊C₄×C₆₁	—	2	2	no	—
144	C₄⋊C₄×C₆₁	—	2	2	no	—
145	C₄⋊C₄×C₆₁	—	2	2	no	—
146	C₄⋊C₄×C₆₁	—	4	2	no	—
147	C₄⋊C₄×C₆₁	—	8	2	no	—
148	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
149	C₂²⋊C₄×C₆₁	—	2	8	no	—
150	C₂²⋊C₄×C₆₁	—	2	4	no	—
151	C₂²⋊C₄×C₆₁	—	4	2	no	—
152	C₂²⋊C₄×C₆₁	—	4	2	no	—
153	C₂²⋊C₄×C₆₁	—	4	4	no	—
154	C₂²⋊C₄×C₆₁	—	8	2	no	—
155	C₄²×C₆₁	—	2	8	no	—
156	C₄²×C₆₁	—	2	1	no	—
157	C₄²×C₆₁	—	2	1	no	—
158	C₄²×C₆₁	C₂×D₄	1	2	yes	—
159	C₄²×C₆₁	C₂×D₄	1	2	yes	—
160	C₂³×C₆₁	—	2	1	no	—
161	C₂³×C₆₁	—	2	1	no	—
162	C₂³×C₆₁	—	2	1	no	—
163	C₂³×C₆₁	—	2	2	no	—
164	C₂³×C₆₁	—	2	2	no	—
165	C₂³×C₆₁	—	4	1	no	—
166	C₂³×C₆₁	—	4	1	no	—
167	C₂³×C₆₁	—	4	1	no	—
168	C₂³×C₆₁	—	4	2	no	—
169	C₂³×C₆₁	—	4	2	no	—
170	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₆₁	—	2	4	no	—
172	Q₈×C₆₁	—	2	4	no	—
173	Q₈×C₆₁	—	4	2	no	—
174	Q₈×C₆₁	—	4	2	no	—
175	Q₈×C₆₁	—	4	2	no	—
176	Q₈×C₆₁	—	4	2	no	—
177	D₄×C₆₁	—	4	2	no	—
178	D₄×C₆₁	—	4	2	no	—
179	D₄×C₆₁	—	8	4	no	—
180	C₂×C₄×C₆₁	—	2	2	no	—
181	C₂×C₄×C₆₁	—	2	2	no	—
182	C₂×C₄×C₆₁	—	2	2	no	—
183	C₂×C₄×C₆₁	—	2	4	no	—
184	C₂×C₄×C₆₁	—	2	4	no	—
185	C₂×C₄×C₆₁	—	2	1	no	—
186	C₂×C₄×C₆₁	—	2	1	no	—
187	C₂×C₄×C₆₁	—	2	1	no	—
188	C₂×C₄×C₆₁	—	2	2	no	—
189	C₂×C₄×C₆₁	—	2	2	no	—
190	C₂×C₄×C₆₁	—	4	2	no	—
191	C₂×C₄×C₆₁	—	4	2	no	—
192	C₂×C₄×C₆₁	—	4	2	no	—
193	C₂×C₄×C₆₁	—	4	2	no	—
194	C₂×C₄×C₆₁	—	4	2	no	—
195	C₂×C₄×C₆₁	—	4	2	no	—
196	C₂×C₄×C₆₁	—	4	1	no	—
197	C₂×C₄×C₆₁	—	4	1	no	—
198	C₂×C₄×C₆₁	—	4	1	no	—
199	C₂×C₄×C₆₁	—	4	1	no	—
200	C₂×C₄×C₆₁	—	4	1	no	—
201	C₂×C₄×C₆₁	—	4	2	no	—
202	C₂×C₄×C₆₁	—	4	2	no	—
203	C₂×C₄×C₆₁	#120	1	4	yes	—
204	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
207	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
208	C₈×C₆₁	—	2	4	no	—
209	C₈×C₆₁	—	4	2	no	—
210	#25612	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂²×C₆₁	—	4	2	no	—
212	C₂²×C₆₁	—	4	1	no	—
213	C₂²×C₆₁	—	4	1	no	—
214	C₂²×C₆₁	—	4	1	no	—
215	C₂²×C₆₁	—	4	2	no	—
216	C₂²×C₆₁	—	8	2	no	—
217	C₂²×C₆₁	—	8	1	no	—
218	C₂²×C₆₁	—	8	1	no	—
219	C₂²×C₆₁	—	8	1	no	—
220	C₂²×C₆₁	—	8	2	no	—
221	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
222	C₂²×C₆₁	#532	1	1	yes	characteristic
223	C₂²×C₆₁	#535	1	1	yes	characteristic
224	C₂²×C₆₁	#577	1	2	yes	—
225	C₂²×C₆₁	#578	1	2	yes	—
226	C₄×C₆₁	—	2	4	no	—
227	C₄×C₆₁	—	4	1	no	—
228	C₄×C₆₁	—	4	4	no	—
229	C₄×C₆₁	—	4	2	no	—
230	C₄×C₆₁	—	4	4	no	—
231	C₄×C₆₁	—	8	1	no	—
232	C₄×C₆₁	—	8	1	no	—
233	C₄×C₆₁	—	8	1	no	—
234	C₄×C₆₁	#546	1	2	yes	—
235	C₄×C₆₁	#550	1	2	yes	—
236	C₂×#541	C₂×C₆₁	1	1	yes	characteristic, complemented
237	C₂×#497	C₂×C₆₁	1	1	yes	characteristic, complemented
238	C₂×#488	C₂×C₆₁	1	1	yes	characteristic, complemented
239	#2620	C₂×C₆₁	1	1	yes	characteristic
240	#2001	C₂×C₆₁	1	2	yes	complemented
241	#2000	C₂×C₆₁	1	2	yes	—
242	#1992	C₂×C₆₁	1	1	yes	characteristic, complemented
243	#1956	C₂×C₆₁	1	1	yes	characteristic, complemented
244	#1880	C₂×C₆₁	1	2	yes	complemented
245	#1878	C₂×C₆₁	1	2	yes	complemented
246	#1750	C₂×C₆₁	1	1	yes	characteristic, complemented
247	C₂×C₆₁	—	8	1	no	—
248	C₂×C₆₁	—	16	1	no	—
249	C₂×C₆₁	#2431	1	1	yes	characteristic
250	C₂×C₆₁	#3013	1	2	yes	—
251	C₂×C₆₁	#3178	1	2	yes	—
252	C₂×C₆₁	#3222	1	1	yes	characteristic
253	C₂×C₆₁	#3223	1	1	yes	characteristic
254	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
255	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
256	#541	—	2	4	no	—
257	#541	—	2	4	no	—
258	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
259	C₂×#126	—	2	2	no	—
260	C₂×#125	—	2	2	no	—
261	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
262	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
263	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
264	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
265	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
266	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
267	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
268	#497	—	2	4	no	—
269	#488	—	2	4	no	—
270	C₂×#103	C₂²×C₆₁	1	2	yes	—
271	C₂×#103	C₂²×C₆₁	1	2	yes	—
272	C₂×#103	C₂²×C₆₁	1	2	yes	—
273	C₂×#102	C₂²×C₆₁	1	2	yes	—
274	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
275	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
277	#396	—	2	2	no	—
278	#394	—	2	2	no	—
279	#391	C₂²×C₆₁	1	1	yes	characteristic
280	#390	C₂²×C₆₁	1	1	yes	characteristic
281	#384	C₂²×C₆₁	1	1	yes	characteristic
282	#340	C₂²×C₆₁	1	2	yes	—
283	#340	C₂²×C₆₁	1	2	yes	—
284	#336	C₂²×C₆₁	1	2	yes	—
285	C₆₁	#25612	1	1	yes	characteristic, direct product factor, Sylow
286	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
287	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
291	C₂×Q₁₆	—	2	4	no	—
292	C₂×Q₁₆	—	2	4	no	—
293	C₂×Q₁₆	—	4	2	no	—
294	C₂×SD₁₆	—	2	4	no	—
295	C₂×SD₁₆	—	2	4	no	—
296	C₂×SD₁₆	—	4	2	no	—
297	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
298	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	D₄×C₆₁	1	4	yes	complemented
301	#126	—	2	16	no	—
302	#125	—	2	16	no	—
303	#125	—	2	2	no	—
304	#125	D₄×C₆₁	1	4	yes	complemented
305	#124	—	2	2	no	—
306	#124	—	2	2	no	—
307	C₂²⋊Q₈	—	2	4	no	—
308	C₂²⋊Q₈	—	2	4	no	—
309	C₂²⋊Q₈	—	4	2	no	—
310	#121	—	4	2	no	—
311	C₄×Q₈	—	2	4	no	—
312	C₄×Q₈	—	2	4	no	—
313	#117	—	2	2	no	—
314	#117	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
331	C₂×C₄²	—	2	2	no	—
332	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
334	#103	—	2	4	no	—
335	#103	—	4	2	no	—
336	#103	—	4	2	no	—
337	#102	—	2	4	no	—
338	C₂²⋊C₈	—	2	4	no	—
339	#97	—	2	2	no	—
340	C₄×C₈	—	2	2	no	—
341	#95	—	2	2	no	—
342	C₂⁴	—	2	1	no	—
343	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	8	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
373	Q₁₆	—	4	8	no	—
374	SD₁₆	—	4	8	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	#41×C₆₁	1	4	yes	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	8	2	no	—
391	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
392	C₂²⋊C₄	—	2	8	no	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	4	no	—
397	C₂²⋊C₄	—	8	2	no	—
398	C₄²	—	2	8	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	C₂×D₄×C₆₁	1	2	yes	—
402	C₄²	C₂×D₄×C₆₁	1	2	yes	—
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	1	no	—
413	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
414	Q₈	—	2	4	no	—
415	Q₈	—	2	4	no	—
416	Q₈	—	4	2	no	—
417	Q₈	—	4	2	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	8	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	#120×C₆₁	1	4	yes	—
447	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
449	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
450	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
451	C₈	—	2	4	no	—
452	C₈	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	2	no	—
463	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
464	C₂²	C₆₁×#532	1	1	yes	characteristic
465	C₂²	C₆₁×#535	1	1	yes	characteristic
466	C₂²	C₆₁×#577	1	2	yes	—
467	C₂²	C₆₁×#578	1	2	yes	—
468	C₄	—	2	4	no	—
469	C₄	—	4	1	no	—
470	C₄	—	4	4	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	4	no	—
473	C₄	—	8	1	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	1	no	—
476	C₄	C₆₁×#546	1	2	yes	—
477	C₄	C₆₁×#550	1	2	yes	—
478	C₂	—	8	1	no	—
479	C₂	—	16	1	no	—
480	C₂	C₆₁×#2431	1	1	yes	characteristic
481	C₂	C₆₁×#3013	1	2	yes	—
482	C₂	C₆₁×#3178	1	2	yes	—
483	C₂	C₆₁×#3222	1	1	yes	characteristic
484	C₂	C₆₁×#3223	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#121×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#541	C₂	semidirect
2. C₂×C₆₁×#497	C₂	semidirect
3. C₂×C₆₁×#488	C₂	semidirect
5. C₆₁×#2001	C₂	semidirect
7. C₆₁×#1992	C₂	semidirect
8. C₆₁×#1956	C₂	semidirect
9. C₆₁×#1880	C₂	semidirect
10. C₆₁×#1878	C₂	semidirect
11. C₆₁×#1750	C₂	semidirect
57. C₄⋊Q₈×C₆₁	D₄	semidirect
61. #125×C₆₁	D₄	semidirect
210. #25612	C₆₁	direct (N × H)
236. C₂×#541	C₂×C₆₁	semidirect
237. C₂×#497	C₂×C₆₁	semidirect
238. C₂×#488	C₂×C₆₁	semidirect
240. #2001	C₂×C₆₁	semidirect
242. #1992	C₂×C₆₁	semidirect
243. #1956	C₂×C₆₁	semidirect
244. #1880	C₂×C₆₁	semidirect
245. #1878	C₂×C₆₁	semidirect
246. #1750	C₂×C₆₁	semidirect
285. C₆₁	#25612	direct (N × H)
300. C₄⋊Q₈	D₄×C₆₁	semidirect
304. #125	D₄×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×#541	2
C₂×C₆₁×#497	2
C₂×C₆₁×#488	2
C₆₁×#2620	2
C₆₁×#2001	2
C₆₁×#2000	2
C₆₁×#1992	2
C₆₁×#1956	2
C₆₁×#1880	2
C₆₁×#1878	2
C₆₁×#1750	2
#25612	61

Subgroups — C61×#25612 #29529045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25612 #29529045