Subgroups — C₆₁×#24779 #29528212

Order 15616.

966 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₆₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2415	C₂	1	2	yes	maximal
6	C₆₁×#2066	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2035	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1969	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1873	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1808	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×#117×C₆₁	C₂²	1	2	yes	—
19	C₆₁×#467	—	2	4	no	—
20	C₆₁×#467	—	2	4	no	—
21	C₈×D₄×C₆₁	—	2	4	no	—
22	C₆₁×#427	—	2	4	no	—
23	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#106×C₆₁	C₂²	1	2	yes	—
27	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
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×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#397	—	2	2	no	—
35	C₆₁×#394	—	2	2	no	—
36	C₆₁×#391	C₂²	1	2	yes	—
37	C₆₁×#389	—	2	2	no	—
38	C₆₁×#389	C₂²	1	2	yes	—
39	C₆₁×#388	—	2	2	no	—
40	C₆₁×#380	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₆₁×#340	C₂²	1	2	yes	—
43	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
44	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₆₁	—	2	2	no	—
48	C₂×Q₁₆×C₆₁	—	2	2	no	—
49	C₂×Q₁₆×C₆₁	—	2	2	no	—
50	C₂²×C₈×C₆₁	—	2	2	no	—
51	C₂²×C₈×C₆₁	—	2	2	no	—
52	C₂²×C₈×C₆₁	—	2	2	no	—
53	C₂²×C₈×C₆₁	—	2	2	no	—
54	C₂²×C₈×C₆₁	—	2	2	no	—
55	C₂²×C₈×C₆₁	D₄	1	4	yes	—
56	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
60	C₂²⋊Q₈×C₆₁	—	2	4	no	—
61	C₂²⋊Q₈×C₆₁	—	2	4	no	—
62	C₂²⋊Q₈×C₆₁	—	2	4	no	—
63	C₂²⋊Q₈×C₆₁	—	4	2	no	—
64	C₄×D₄×C₆₁	—	2	2	no	—
65	C₄×D₄×C₆₁	—	2	2	no	—
66	#117×C₆₁	—	2	4	no	—
67	#117×C₆₁	—	4	2	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₆₁	—	2	2	no	—
82	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
83	#107×C₆₁	—	2	2	no	—
84	#107×C₆₁	—	2	2	no	—
85	#107×C₆₁	D₄	1	4	yes	complemented
86	#106×C₆₁	—	2	4	no	—
87	C₄⋊C₈×C₆₁	—	2	2	no	—
88	#103×C₆₁	—	2	4	no	—
89	#103×C₆₁	—	2	4	no	—
90	#103×C₆₁	—	4	2	no	—
91	C₂²⋊C₈×C₆₁	—	2	2	no	—
92	C₂²⋊C₈×C₆₁	—	2	2	no	—
93	C₄×C₈×C₆₁	—	2	2	no	—
94	#95×C₆₁	—	2	2	no	—
95	#95×C₆₁	—	2	2	no	—
96	#95×C₆₁	—	2	2	no	—
97	#95×C₆₁	—	2	2	no	—
98	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
99	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₆₁	—	2	2	no	—
101	C₂×Q₈×C₆₁	—	2	2	no	—
102	C₂×Q₈×C₆₁	—	2	2	no	—
103	C₂×Q₈×C₆₁	—	2	2	no	—
104	C₂×Q₈×C₆₁	—	2	2	no	—
105	C₂×Q₈×C₆₁	—	2	2	no	—
106	C₂×D₄×C₆₁	—	2	2	no	—
107	C₂×D₄×C₆₁	—	2	2	no	—
108	C₂×D₄×C₆₁	—	2	2	no	—
109	C₂²×C₄×C₆₁	—	2	1	no	—
110	C₂²×C₄×C₆₁	—	2	1	no	—
111	C₂²×C₄×C₆₁	—	2	1	no	—
112	C₂²×C₄×C₆₁	—	2	1	no	—
113	C₂²×C₄×C₆₁	—	2	2	no	—
114	C₂²×C₄×C₆₁	—	2	1	no	—
115	C₂²×C₄×C₆₁	—	2	1	no	—
116	C₂²×C₄×C₆₁	—	2	1	no	—
117	C₂²×C₄×C₆₁	—	2	1	no	—
118	C₂²×C₄×C₆₁	—	2	1	no	—
119	C₂²×C₄×C₆₁	—	2	1	no	—
120	C₂²×C₄×C₆₁	—	2	2	no	—
121	C₂²×C₄×C₆₁	—	2	2	no	—
122	C₂²×C₄×C₆₁	—	2	2	no	—
123	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	#41	1	2	yes	—
129	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
130	Q₁₆×C₆₁	—	4	4	no	—
131	C₂×C₈×C₆₁	—	2	1	no	—
132	C₂×C₈×C₆₁	—	2	1	no	—
133	C₂×C₈×C₆₁	—	2	8	no	—
134	C₂×C₈×C₆₁	—	2	1	no	—
135	C₂×C₈×C₆₁	—	2	1	no	—
136	C₂×C₈×C₆₁	—	2	1	no	—
137	C₂×C₈×C₆₁	—	2	1	no	—
138	C₂×C₈×C₆₁	—	2	1	no	—
139	C₂×C₈×C₆₁	—	2	1	no	—
140	C₂×C₈×C₆₁	—	4	4	no	—
141	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₆₁	#41	1	2	yes	—
145	C₄⋊C₄×C₆₁	—	2	2	no	—
146	C₄⋊C₄×C₆₁	—	2	2	no	—
147	C₄⋊C₄×C₆₁	—	2	2	no	—
148	C₄⋊C₄×C₆₁	—	2	2	no	—
149	C₄⋊C₄×C₆₁	—	2	2	no	—
150	C₄⋊C₄×C₆₁	—	2	2	no	—
151	C₄⋊C₄×C₆₁	—	4	4	no	—
152	C₄⋊C₄×C₆₁	—	4	4	no	—
153	C₄⋊C₄×C₆₁	—	4	4	no	—
154	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
155	C₂²⋊C₄×C₆₁	—	2	2	no	—
156	C₂²⋊C₄×C₆₁	—	2	2	no	—
157	C₂²⋊C₄×C₆₁	—	4	4	no	—
158	C₂²⋊C₄×C₆₁	—	4	4	no	—
159	C₂²⋊C₄×C₆₁	—	4	4	no	—
160	C₂²⋊C₄×C₆₁	—	4	4	no	—
161	C₄²×C₆₁	—	2	1	no	—
162	C₄²×C₆₁	—	2	1	no	—
163	C₄²×C₆₁	—	4	4	no	—
164	C₂³×C₆₁	—	2	1	no	—
165	C₂³×C₆₁	—	2	1	no	—
166	C₂³×C₆₁	—	2	1	no	—
167	C₂³×C₆₁	—	2	1	no	—
168	C₂³×C₆₁	—	2	1	no	—
169	C₂³×C₆₁	—	2	1	no	—
170	C₂³×C₆₁	—	2	1	no	—
171	C₂³×C₆₁	—	2	1	no	—
172	C₂³×C₆₁	—	2	1	no	—
173	C₂³×C₆₁	—	2	1	no	—
174	C₂³×C₆₁	—	2	1	no	—
175	C₂³×C₆₁	—	2	1	no	—
176	C₂³×C₆₁	#121	1	2	yes	—
177	C₂³×C₆₁	#135	1	2	yes	—
178	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₆₁	—	4	2	no	—
180	Q₈×C₆₁	—	4	2	no	—
181	Q₈×C₆₁	—	4	2	no	—
182	Q₈×C₆₁	—	4	2	no	—
183	D₄×C₆₁	—	2	8	no	—
184	C₂×C₄×C₆₁	—	2	1	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	—	2	2	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	2	1	no	—
193	C₂×C₄×C₆₁	—	2	1	no	—
194	C₂×C₄×C₆₁	—	2	4	no	—
195	C₂×C₄×C₆₁	—	2	1	no	—
196	C₂×C₄×C₆₁	—	2	1	no	—
197	C₂×C₄×C₆₁	—	2	1	no	—
198	C₂×C₄×C₆₁	—	2	1	no	—
199	C₂×C₄×C₆₁	—	4	2	no	—
200	C₂×C₄×C₆₁	—	4	2	no	—
201	C₂×C₄×C₆₁	—	4	1	no	—
202	C₂×C₄×C₆₁	—	4	1	no	—
203	C₂×C₄×C₆₁	—	4	1	no	—
204	C₂×C₄×C₆₁	—	4	1	no	—
205	C₂×C₄×C₆₁	—	4	2	no	—
206	C₂×C₄×C₆₁	—	4	2	no	—
207	C₂×C₄×C₆₁	—	4	2	no	—
208	C₂×C₄×C₆₁	—	4	2	no	—
209	C₂×C₄×C₆₁	—	4	2	no	—
210	C₂×C₄×C₆₁	—	4	2	no	—
211	C₂×C₄×C₆₁	—	4	2	no	—
212	C₂×C₄×C₆₁	—	4	2	no	—
213	C₂×C₄×C₆₁	—	4	2	no	—
214	C₂×C₄×C₆₁	#121	1	2	yes	—
215	C₂×C₄×C₆₁	#135	1	2	yes	—
216	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
221	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
222	C₈×C₆₁	—	2	2	no	—
223	C₈×C₆₁	—	4	1	no	—
224	C₈×C₆₁	—	4	1	no	—
225	C₈×C₆₁	#121	1	4	yes	—
226	#24779	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂²×C₆₁	—	2	2	no	—
228	C₂²×C₆₁	—	2	2	no	—
229	C₂²×C₆₁	—	2	2	no	—
230	C₂²×C₆₁	—	2	2	no	—
231	C₂²×C₆₁	—	2	2	no	—
232	C₂²×C₆₁	—	2	2	no	—
233	C₂²×C₆₁	—	4	1	no	—
234	C₂²×C₆₁	—	4	1	no	—
235	C₂²×C₆₁	—	4	1	no	—
236	C₂²×C₆₁	—	4	1	no	—
237	C₂²×C₆₁	—	4	1	no	—
238	C₂²×C₆₁	—	4	1	no	—
239	C₂²×C₆₁	—	4	1	no	—
240	C₂²×C₆₁	—	4	1	no	—
241	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
242	C₂²×C₆₁	D₄²	1	1	yes	characteristic
243	C₂²×C₆₁	#547	1	1	yes	characteristic
244	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
245	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
246	C₂²×C₆₁	#578	1	1	yes	characteristic
247	C₂²×C₆₁	#578	1	1	yes	characteristic
248	C₄×C₆₁	—	2	2	no	—
249	C₄×C₆₁	—	2	2	no	—
250	C₄×C₆₁	—	4	1	no	—
251	C₄×C₆₁	—	4	4	no	—
252	C₄×C₆₁	—	4	1	no	—
253	C₄×C₆₁	—	8	2	no	—
254	C₄×C₆₁	—	8	2	no	—
255	C₄×C₆₁	—	8	2	no	—
256	C₄×C₆₁	C₂×#121	1	1	yes	characteristic
257	C₄×C₆₁	#537	1	1	yes	characteristic
258	C₄×C₆₁	#548	1	1	yes	characteristic
259	C₄×C₆₁	#553	1	1	yes	characteristic
260	C₂×#467	C₂×C₆₁	1	1	yes	characteristic, complemented
261	C₂×#467	C₂×C₆₁	1	1	yes	characteristic, complemented
262	C₂×C₈×D₄	C₂×C₆₁	1	1	yes	characteristic
263	C₂×#427	C₂×C₆₁	1	1	yes	characteristic, complemented
264	#2415	C₂×C₆₁	1	2	yes	—
265	#2066	C₂×C₆₁	1	2	yes	complemented
266	#2035	C₂×C₆₁	1	2	yes	complemented
267	#1969	C₂×C₆₁	1	1	yes	characteristic, complemented
268	#1942	C₂×C₆₁	1	1	yes	characteristic, complemented
269	#1873	C₂×C₆₁	1	2	yes	complemented
270	#1808	C₂×C₆₁	1	1	yes	characteristic, complemented
271	C₂×C₆₁	—	4	2	no	—
272	C₂×C₆₁	—	4	2	no	—
273	C₂×C₆₁	#2416	1	1	yes	characteristic
274	C₂×C₆₁	#3050	1	1	yes	characteristic
275	C₂×C₆₁	#3059	1	1	yes	characteristic
276	C₂×C₆₁	#3283	1	1	yes	characteristic
277	C₂×C₆₁	#3285	1	1	yes	characteristic
278	C₂×C₆₁	#3336	1	1	yes	characteristic
279	C₂×C₆₁	#3342	1	1	yes	characteristic
280	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
281	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
282	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
283	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
284	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
285	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
286	C₂×#117	C₂²×C₆₁	1	2	yes	—
287	#467	—	2	4	no	—
288	#467	—	2	4	no	—
289	C₈×D₄	—	2	4	no	—
290	#427	—	2	4	no	—
291	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
292	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
293	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
294	C₂×#106	C₂²×C₆₁	1	2	yes	—
295	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
296	C₂×#103	C₂²×C₆₁	1	2	yes	—
297	C₂×#103	C₂²×C₆₁	1	2	yes	—
298	C₂×#103	C₂²×C₆₁	1	2	yes	—
299	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
300	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
301	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
302	#397	—	2	2	no	—
303	#394	—	2	2	no	—
304	#391	C₂²×C₆₁	1	2	yes	—
305	#389	—	2	2	no	—
306	#389	C₂²×C₆₁	1	2	yes	—
307	#388	—	2	2	no	—
308	#380	C₂²×C₆₁	1	2	yes	—
309	#340	C₂²×C₆₁	1	2	yes	—
310	#340	C₂²×C₆₁	1	2	yes	—
311	C₆₁	#24779	1	1	yes	characteristic, direct product factor, Sylow
312	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
313	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
314	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
316	C₂×Q₁₆	—	2	2	no	—
317	C₂×Q₁₆	—	2	2	no	—
318	C₂×Q₁₆	—	2	2	no	—
319	C₂²×C₈	—	2	2	no	—
320	C₂²×C₈	—	2	2	no	—
321	C₂²×C₈	—	2	2	no	—
322	C₂²×C₈	—	2	2	no	—
323	C₂²×C₈	—	2	2	no	—
324	C₂²×C₈	D₄×C₆₁	1	4	yes	—
325	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
329	C₂²⋊Q₈	—	2	4	no	—
330	C₂²⋊Q₈	—	2	4	no	—
331	C₂²⋊Q₈	—	2	4	no	—
332	C₂²⋊Q₈	—	4	2	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	2	no	—
335	#117	—	2	4	no	—
336	#117	—	4	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
349	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
350	C₂×C₄²	—	2	2	no	—
351	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
352	#107	—	2	2	no	—
353	#107	—	2	2	no	—
354	#107	D₄×C₆₁	1	4	yes	complemented
355	#106	—	2	4	no	—
356	C₄⋊C₈	—	2	2	no	—
357	#103	—	2	4	no	—
358	#103	—	2	4	no	—
359	#103	—	4	2	no	—
360	C₂²⋊C₈	—	2	2	no	—
361	C₂²⋊C₈	—	2	2	no	—
362	C₄×C₈	—	2	2	no	—
363	#95	—	2	2	no	—
364	#95	—	2	2	no	—
365	#95	—	2	2	no	—
366	#95	—	2	2	no	—
367	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
368	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
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	1	yes	characteristic
397	C₂²×C₄	#41×C₆₁	1	2	yes	—
398	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
399	Q₁₆	—	4	4	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	8	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	4	4	no	—
410	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
411	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
412	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
413	C₂×C₈	#41×C₆₁	1	2	yes	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	4	4	no	—
421	C₄⋊C₄	—	4	4	no	—
422	C₄⋊C₄	—	4	4	no	—
423	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	4	4	no	—
427	C₂²⋊C₄	—	4	4	no	—
428	C₂²⋊C₄	—	4	4	no	—
429	C₂²⋊C₄	—	4	4	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	4	4	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	1	no	—
444	C₂³	—	2	1	no	—
445	C₂³	#121×C₆₁	1	2	yes	—
446	C₂³	#135×C₆₁	1	2	yes	—
447	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
448	Q₈	—	4	2	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	4	2	no	—
452	D₄	—	2	8	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	#121×C₆₁	1	2	yes	—
484	C₂×C₄	#135×C₆₁	1	2	yes	—
485	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
487	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
488	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
489	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
490	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	4	1	no	—
493	C₈	—	4	1	no	—
494	C₈	#121×C₆₁	1	4	yes	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	1	no	—
509	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
510	C₂²	D₄²×C₆₁	1	1	yes	characteristic
511	C₂²	C₆₁×#547	1	1	yes	characteristic
512	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
513	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
514	C₂²	C₆₁×#578	1	1	yes	characteristic
515	C₂²	C₆₁×#578	1	1	yes	characteristic
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	4	no	—
521	C₄	—	8	2	no	—
522	C₄	—	8	2	no	—
523	C₄	—	8	2	no	—
524	C₄	C₂×#121×C₆₁	1	1	yes	characteristic
525	C₄	C₆₁×#537	1	1	yes	characteristic
526	C₄	C₆₁×#548	1	1	yes	characteristic
527	C₄	C₆₁×#553	1	1	yes	characteristic
528	C₂	—	4	2	no	—
529	C₂	—	4	2	no	—
530	C₂	C₆₁×#2416	1	1	yes	characteristic
531	C₂	C₆₁×#3050	1	1	yes	characteristic
532	C₂	C₆₁×#3059	1	1	yes	characteristic
533	C₂	C₆₁×#3283	1	1	yes	characteristic
534	C₂	C₆₁×#3285	1	1	yes	characteristic
535	C₂	C₆₁×#3336	1	1	yes	characteristic
536	C₂	C₆₁×#3342	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#467	C₂	semidirect
2. C₂×C₆₁×#467	C₂	semidirect
4. C₂×C₆₁×#427	C₂	semidirect
6. C₆₁×#2066	C₂	semidirect
7. C₆₁×#2035	C₂	semidirect
8. C₆₁×#1969	C₂	semidirect
9. C₆₁×#1942	C₂	semidirect
10. C₆₁×#1873	C₂	semidirect
11. C₆₁×#1808	C₂	semidirect
85. #107×C₆₁	D₄	semidirect
226. #24779	C₆₁	direct (N × H)
260. C₂×#467	C₂×C₆₁	semidirect
261. C₂×#467	C₂×C₆₁	semidirect
263. C₂×#427	C₂×C₆₁	semidirect
265. #2066	C₂×C₆₁	semidirect
266. #2035	C₂×C₆₁	semidirect
267. #1969	C₂×C₆₁	semidirect
268. #1942	C₂×C₆₁	semidirect
269. #1873	C₂×C₆₁	semidirect
270. #1808	C₂×C₆₁	semidirect
311. C₆₁	#24779	direct (N × H)
354. #107	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×#467	2
C₂×C₈×D₄×C₆₁	2
C₂×C₆₁×#427	2
C₆₁×#2415	2
C₆₁×#2066	2
C₆₁×#2035	2
C₆₁×#1969	2
C₆₁×#1942	2
C₆₁×#1873	2
C₆₁×#1808	2
#24779	61

Subgroups — C61×#24779 #29528212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24779 #29528212