Subgroups — C₆₁×#26318 #29529751

Order 15616.

802 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2548	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2094	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2071	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1982	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#1957	C₂	1	1	yes	maximal, characteristic
8	C₆₁×#1948	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1926	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1926	C₂	1	2	yes	maximal, complemented
11	C₄×#106×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₆₁	—	2	1	no	—
14	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
15	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×#106×C₆₁	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#102×C₆₁	C₂²	1	2	yes	—
21	C₂×#102×C₆₁	C₂²	1	2	yes	—
22	C₂×#102×C₆₁	C₂²	1	2	yes	—
23	C₂×#102×C₆₁	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₆₁×#394	—	2	2	no	—
26	C₆₁×#390	—	2	1	no	—
27	C₆₁×#390	C₂²	1	2	yes	—
28	C₆₁×#390	C₂²	1	2	yes	—
29	C₆₁×#389	—	2	1	no	—
30	C₆₁×#389	—	2	2	no	—
31	C₆₁×#384	C₂²	1	2	yes	—
32	C₆₁×#384	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
36	C₆₁×#340	C₂²	1	1	yes	characteristic
37	C₆₁×#340	C₂²	1	1	yes	characteristic
38	C₆₁×#340	C₂²	1	2	yes	—
39	C₆₁×#336	C₂²	1	2	yes	—
40	C₆₁×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₆₁	—	2	1	no	—
43	C₂²×D₄×C₆₁	—	2	1	no	—
44	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
48	#127×C₆₁	—	2	2	no	—
49	#127×C₆₁	—	2	2	no	—
50	#124×C₆₁	—	4	4	no	—
51	C₄×Q₈×C₆₁	—	2	2	no	—
52	C₄×Q₈×C₆₁	—	2	2	no	—
53	C₄×Q₈×C₆₁	—	4	4	no	—
54	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₄²×C₆₁	—	2	2	no	—
70	C₂×C₄²×C₆₁	—	2	1	no	—
71	C₂×C₄²×C₆₁	—	2	1	no	—
72	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
73	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
74	#106×C₆₁	—	2	2	no	—
75	#106×C₆₁	—	2	2	no	—
76	#106×C₆₁	—	4	2	no	—
77	C₄⋊C₈×C₆₁	—	2	2	no	—
78	#102×C₆₁	—	2	4	no	—
79	#102×C₆₁	—	2	4	no	—
80	#102×C₆₁	—	4	2	no	—
81	#102×C₆₁	—	4	2	no	—
82	C₄×C₈×C₆₁	—	2	2	no	—
83	#95×C₆₁	—	2	2	no	—
84	#95×C₆₁	—	2	1	no	—
85	#95×C₆₁	—	2	1	no	—
86	C₂⁴×C₆₁	—	2	2	no	—
87	C₂×Q₈×C₆₁	—	2	2	no	—
88	C₂×Q₈×C₆₁	—	2	2	no	—
89	C₂×Q₈×C₆₁	SD₁₆	1	4	yes	—
90	C₂×D₄×C₆₁	—	2	2	no	—
91	C₂×D₄×C₆₁	—	2	2	no	—
92	C₂×D₄×C₆₁	—	2	2	no	—
93	C₂×D₄×C₆₁	—	2	2	no	—
94	C₂×D₄×C₆₁	—	2	2	no	—
95	C₂×D₄×C₆₁	—	2	2	no	—
96	C₂×D₄×C₆₁	—	4	2	no	—
97	C₂×D₄×C₆₁	—	4	2	no	—
98	C₂×D₄×C₆₁	—	4	2	no	—
99	C₂×D₄×C₆₁	—	4	2	no	—
100	C₂×D₄×C₆₁	—	8	1	no	—
101	C₂×D₄×C₆₁	—	8	1	no	—
102	C₂²×C₄×C₆₁	—	2	1	no	—
103	C₂²×C₄×C₆₁	—	2	1	no	—
104	C₂²×C₄×C₆₁	—	2	1	no	—
105	C₂²×C₄×C₆₁	—	2	2	no	—
106	C₂²×C₄×C₆₁	—	2	1	no	—
107	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₆₁	—	2	1	no	—
113	C₂×C₈×C₆₁	—	2	1	no	—
114	C₂×C₈×C₆₁	—	2	1	no	—
115	C₂×C₈×C₆₁	—	2	2	no	—
116	C₂×C₈×C₆₁	—	2	2	no	—
117	C₂×C₈×C₆₁	—	2	1	no	—
118	C₂×C₈×C₆₁	—	2	2	no	—
119	C₂×C₈×C₆₁	—	2	1	no	—
120	C₂×C₈×C₆₁	#41	1	2	yes	—
121	C₄⋊C₄×C₆₁	—	2	4	no	—
122	C₄⋊C₄×C₆₁	—	2	2	no	—
123	C₄⋊C₄×C₆₁	—	2	1	no	—
124	C₄⋊C₄×C₆₁	—	2	2	no	—
125	C₄⋊C₄×C₆₁	—	2	1	no	—
126	C₄⋊C₄×C₆₁	—	2	1	no	—
127	C₄⋊C₄×C₆₁	—	2	1	no	—
128	C₄⋊C₄×C₆₁	—	2	1	no	—
129	C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₄⋊C₄×C₆₁	—	2	1	no	—
131	C₄⋊C₄×C₆₁	—	2	1	no	—
132	C₄⋊C₄×C₆₁	—	4	4	no	—
133	C₄⋊C₄×C₆₁	—	4	2	no	—
134	C₄⋊C₄×C₆₁	—	8	1	no	—
135	C₄⋊C₄×C₆₁	—	8	2	no	—
136	C₄⋊C₄×C₆₁	#41	1	2	yes	—
137	C₂²⋊C₄×C₆₁	—	4	4	no	—
138	C₂²⋊C₄×C₆₁	—	4	4	no	—
139	C₂²⋊C₄×C₆₁	—	8	2	no	—
140	C₂²⋊C₄×C₆₁	—	8	2	no	—
141	C₄²×C₆₁	—	2	2	no	—
142	C₄²×C₆₁	—	2	2	no	—
143	C₄²×C₆₁	—	4	4	no	—
144	C₄²×C₆₁	—	4	2	no	—
145	C₄²×C₆₁	—	4	2	no	—
146	C₄²×C₆₁	#41	1	2	yes	—
147	C₄²×C₆₁	#41	1	2	yes	—
148	C₂³×C₆₁	—	4	2	no	—
149	C₂³×C₆₁	—	4	2	no	—
150	C₂³×C₆₁	—	4	2	no	—
151	C₂³×C₆₁	—	4	2	no	—
152	C₂³×C₆₁	—	4	2	no	—
153	C₂³×C₆₁	—	4	2	no	—
154	C₂³×C₆₁	—	4	2	no	—
155	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₆₁	—	2	8	no	—
157	D₄×C₆₁	—	4	2	no	—
158	D₄×C₆₁	—	4	2	no	—
159	D₄×C₆₁	—	4	2	no	—
160	D₄×C₆₁	—	4	2	no	—
161	D₄×C₆₁	—	8	4	no	—
162	D₄×C₆₁	—	8	4	no	—
163	C₂×C₄×C₆₁	—	2	2	no	—
164	C₂×C₄×C₆₁	—	2	2	no	—
165	C₂×C₄×C₆₁	—	2	1	no	—
166	C₂×C₄×C₆₁	—	2	1	no	—
167	C₂×C₄×C₆₁	—	2	2	no	—
168	C₂×C₄×C₆₁	—	2	2	no	—
169	C₂×C₄×C₆₁	—	2	2	no	—
170	C₂×C₄×C₆₁	—	2	2	no	—
171	C₂×C₄×C₆₁	—	4	1	no	—
172	C₂×C₄×C₆₁	—	4	1	no	—
173	C₂×C₄×C₆₁	—	4	1	no	—
174	C₂×C₄×C₆₁	—	4	1	no	—
175	C₂×C₄×C₆₁	—	4	2	no	—
176	C₂×C₄×C₆₁	—	4	1	no	—
177	C₂×C₄×C₆₁	—	4	1	no	—
178	C₂×C₄×C₆₁	—	4	1	no	—
179	C₂×C₄×C₆₁	—	4	2	no	—
180	C₂×C₄×C₆₁	—	4	1	no	—
181	C₂×C₄×C₆₁	—	4	1	no	—
182	C₂×C₄×C₆₁	—	4	2	no	—
183	C₂×C₄×C₆₁	—	4	1	no	—
184	C₂×C₄×C₆₁	—	4	1	no	—
185	C₂×C₄×C₆₁	#123	1	2	yes	—
186	C₂×C₄×C₆₁	#123	1	2	yes	—
187	C₂×C₄×C₆₁	C₂×SD₁₆	1	4	yes	—
188	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
189	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
190	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
196	C₈×C₆₁	—	2	2	no	—
197	C₈×C₆₁	—	4	1	no	—
198	C₈×C₆₁	—	4	2	no	—
199	#26318	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₆₁	—	8	2	no	—
201	C₂²×C₆₁	—	8	2	no	—
202	C₂²×C₆₁	—	8	2	no	—
203	C₂²×C₆₁	—	8	2	no	—
204	C₂²×C₆₁	—	8	2	no	—
205	C₂²×C₆₁	—	8	2	no	—
206	C₂²×C₆₁	—	8	2	no	—
207	C₂²×C₆₁	C₂×#123	1	1	yes	characteristic
208	C₂²×C₆₁	#548	1	1	yes	characteristic
209	C₂²×C₆₁	#550	1	1	yes	characteristic
210	C₂²×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
211	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₂²×C₆₁	#576	1	1	yes	characteristic
213	C₂²×C₆₁	#577	1	1	yes	characteristic
214	C₄×C₆₁	—	2	4	no	—
215	C₄×C₆₁	—	2	2	no	—
216	C₄×C₆₁	—	4	2	no	—
217	C₄×C₆₁	—	4	2	no	—
218	C₄×C₆₁	—	8	1	no	—
219	C₄×C₆₁	—	8	1	no	—
220	C₄×C₆₁	—	8	2	no	—
221	C₄×C₆₁	—	8	1	no	—
222	C₄×C₆₁	#481	1	4	yes	—
223	C₄×C₆₁	#529	1	1	yes	characteristic
224	C₄×C₆₁	#542	1	1	yes	characteristic
225	C₄×C₆₁	#556	1	1	yes	characteristic
226	C₄×C₆₁	#559	1	1	yes	characteristic
227	#2548	C₂×C₆₁	1	1	yes	characteristic
228	Q₈×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
229	#2094	C₂×C₆₁	1	2	yes	complemented
230	#2071	C₂×C₆₁	1	2	yes	complemented
231	#1984	C₂×C₆₁	1	1	yes	characteristic, complemented
232	#1982	C₂×C₆₁	1	1	yes	characteristic
233	#1957	C₂×C₆₁	1	1	yes	characteristic
234	#1948	C₂×C₆₁	1	1	yes	characteristic, complemented
235	#1926	C₂×C₆₁	1	2	yes	complemented
236	#1926	C₂×C₆₁	1	2	yes	complemented
237	C₄×#106	C₂×C₆₁	1	1	yes	characteristic, complemented
238	C₂×C₆₁	—	16	2	no	—
239	C₂×C₆₁	#2448	1	1	yes	characteristic
240	C₂×C₆₁	C₂×#481	1	1	yes	characteristic
241	C₂×C₆₁	#3096	1	1	yes	characteristic
242	C₂×C₆₁	#3362	1	1	yes	characteristic
243	C₂×C₆₁	#3373	1	1	yes	characteristic
244	C₂×C₆₁	#3392	1	1	yes	characteristic
245	C₂×C₆₁	#3399	1	1	yes	characteristic
246	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
247	C₂×#124	—	2	1	no	—
248	C₂×C₄×Q₈	—	2	1	no	—
249	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
250	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
251	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
252	C₂×#106	C₂²×C₆₁	1	2	yes	—
253	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
254	C₂×#102	C₂²×C₆₁	1	2	yes	—
255	C₂×#102	C₂²×C₆₁	1	2	yes	—
256	C₂×#102	C₂²×C₆₁	1	2	yes	—
257	C₂×#102	C₂²×C₆₁	1	2	yes	—
258	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
259	#394	—	2	2	no	—
260	#390	—	2	1	no	—
261	#390	C₂²×C₆₁	1	2	yes	—
262	#390	C₂²×C₆₁	1	2	yes	—
263	#389	—	2	1	no	—
264	#389	—	2	2	no	—
265	#384	C₂²×C₆₁	1	2	yes	—
266	#384	C₂²×C₆₁	1	1	yes	characteristic
267	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
268	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
269	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
270	#340	C₂²×C₆₁	1	1	yes	characteristic
271	#340	C₂²×C₆₁	1	2	yes	—
272	#340	C₂²×C₆₁	1	1	yes	characteristic
273	#336	C₂²×C₆₁	1	2	yes	—
274	#336	C₂²×C₆₁	1	2	yes	—
275	C₆₁	#26318	1	1	yes	characteristic, direct product factor, Sylow
276	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
277	C₂²×D₄	—	2	1	no	—
278	C₂²×D₄	—	2	1	no	—
279	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
280	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
282	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
283	#127	—	2	2	no	—
284	#127	—	2	2	no	—
285	#124	—	4	4	no	—
286	C₄×Q₈	—	2	2	no	—
287	C₄×Q₈	—	2	2	no	—
288	C₄×Q₈	—	4	4	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
294	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
308	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
309	#106	—	2	2	no	—
310	#106	—	2	2	no	—
311	#106	—	4	2	no	—
312	C₄⋊C₈	—	2	2	no	—
313	#102	—	2	4	no	—
314	#102	—	2	4	no	—
315	#102	—	4	2	no	—
316	#102	—	4	2	no	—
317	C₄×C₈	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	—	2	1	no	—
320	#95	—	2	1	no	—
321	C₂⁴	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	SD₁₆×C₆₁	1	4	yes	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	8	1	no	—
336	C₂×D₄	—	8	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
346	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	#41×C₆₁	1	2	yes	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	4	4	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	8	1	no	—
370	C₄⋊C₄	—	8	2	no	—
371	C₄⋊C₄	#41×C₆₁	1	2	yes	—
372	C₂²⋊C₄	—	4	4	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	8	2	no	—
375	C₂²⋊C₄	—	8	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	4	4	no	—
379	C₄²	—	4	2	no	—
380	C₄²	—	4	2	no	—
381	C₄²	#41×C₆₁	1	2	yes	—
382	C₄²	#41×C₆₁	1	2	yes	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
391	Q₈	—	2	8	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	8	4	no	—
397	D₄	—	8	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	#123×C₆₁	1	2	yes	—
421	C₂×C₄	#123×C₆₁	1	2	yes	—
422	C₂×C₄	C₂×SD₁₆×C₆₁	1	4	yes	—
423	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
424	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
425	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
427	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
428	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
429	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
430	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	4	1	no	—
433	C₈	—	4	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	2	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	2	no	—
441	C₂²	C₂×#123×C₆₁	1	1	yes	characteristic
442	C₂²	C₆₁×#548	1	1	yes	characteristic
443	C₂²	C₆₁×#550	1	1	yes	characteristic
444	C₂²	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
445	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
446	C₂²	C₆₁×#576	1	1	yes	characteristic
447	C₂²	C₆₁×#577	1	1	yes	characteristic
448	C₄	—	2	4	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	8	1	no	—
453	C₄	—	8	1	no	—
454	C₄	—	8	2	no	—
455	C₄	—	8	1	no	—
456	C₄	C₆₁×#481	1	4	yes	—
457	C₄	C₆₁×#529	1	1	yes	characteristic
458	C₄	C₆₁×#542	1	1	yes	characteristic
459	C₄	C₆₁×#556	1	1	yes	characteristic
460	C₄	C₆₁×#559	1	1	yes	characteristic
461	C₂	—	16	2	no	—
462	C₂	C₆₁×#2448	1	1	yes	characteristic
463	C₂	C₂×C₆₁×#481	1	1	yes	characteristic
464	C₂	C₆₁×#3096	1	1	yes	characteristic
465	C₂	C₆₁×#3362	1	1	yes	characteristic
466	C₂	C₆₁×#3373	1	1	yes	characteristic
467	C₂	C₆₁×#3392	1	1	yes	characteristic
468	C₂	C₆₁×#3399	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#127×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₄⋊C₄×C₆₁	C₂	semidirect
3. C₆₁×#2094	C₂	semidirect
4. C₆₁×#2071	C₂	semidirect
5. C₆₁×#1984	C₂	semidirect
8. C₆₁×#1948	C₂	semidirect
9. C₆₁×#1926	C₂	semidirect
10. C₆₁×#1926	C₂	semidirect
11. C₄×#106×C₆₁	C₂	semidirect
199. #26318	C₆₁	direct (N × H)
228. Q₈×C₄⋊C₄	C₂×C₆₁	semidirect
229. #2094	C₂×C₆₁	semidirect
230. #2071	C₂×C₆₁	semidirect
231. #1984	C₂×C₆₁	semidirect
234. #1948	C₂×C₆₁	semidirect
235. #1926	C₂×C₆₁	semidirect
236. #1926	C₂×C₆₁	semidirect
237. C₄×#106	C₂×C₆₁	semidirect
275. C₆₁	#26318	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×#2548	2
Q₈×C₄⋊C₄×C₆₁	2
C₆₁×#2094	2
C₆₁×#2071	2
C₆₁×#1984	2
C₆₁×#1982	2
C₆₁×#1957	2
C₆₁×#1948	2
C₆₁×#1926	2
C₄×#106×C₆₁	2
#26318	61

Subgroups — C61×#26318 #29529751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#26318 #29529751