Subgroups — C₆₁×#29848 #29533281

Order 15616.

740 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#433	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2628	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2621	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2068	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2066	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2036	C₂	1	2	yes	maximal
8	C₆₁×#2035	C₂	1	2	yes	maximal
9	C₆₁×#1993	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1960	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1846	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
15	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
16	C₆₁×#487	—	2	4	no	—
17	C₆₁×#433	—	2	4	no	—
18	C₂×#107×C₆₁	C₂²	1	2	yes	—
19	C₂×#106×C₆₁	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×#103×C₆₁	C₂²	1	2	yes	—
23	C₂×#103×C₆₁	C₂²	1	2	yes	—
24	C₂×#103×C₆₁	C₂²	1	2	yes	—
25	C₂×#103×C₆₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#400	—	2	1	no	—
31	C₆₁×#399	—	2	1	no	—
32	C₆₁×#398	—	2	1	no	—
33	C₆₁×#398	—	2	1	no	—
34	C₆₁×#397	—	2	1	no	—
35	C₆₁×#397	—	2	1	no	—
36	C₆₁×#395	—	2	1	no	—
37	C₆₁×#393	—	2	1	no	—
38	C₆₁×#391	C₂²	1	2	yes	—
39	C₆₁×#389	C₂²	1	2	yes	—
40	C₆₁×#382	C₂²	1	1	yes	characteristic
41	C₆₁×#382	C₂²	1	1	yes	characteristic
42	C₆₁×#380	C₂²	1	2	yes	—
43	C₆₁×#340	C₂²	1	2	yes	—
44	C₆₁×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₆₁	—	2	1	no	—
46	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
47	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
52	C₄⋊Q₈×C₆₁	—	2	2	no	—
53	C₄⋊Q₈×C₆₁	—	2	2	no	—
54	C₄⋊Q₈×C₆₁	—	2	2	no	—
55	C₄⋊Q₈×C₆₁	—	2	2	no	—
56	C₂²⋊Q₈×C₆₁	—	4	2	no	—
57	C₂²⋊Q₈×C₆₁	—	4	2	no	—
58	#117×C₆₁	—	2	2	no	—
59	#117×C₆₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
76	#107×C₆₁	—	4	2	no	—
77	#106×C₆₁	—	4	2	no	—
78	C₄⋊C₈×C₆₁	—	2	2	no	—
79	C₄⋊C₈×C₆₁	—	2	2	no	—
80	#103×C₆₁	—	2	4	no	—
81	#103×C₆₁	—	2	4	no	—
82	#103×C₆₁	—	4	2	no	—
83	#103×C₆₁	—	4	2	no	—
84	C₂²⋊C₈×C₆₁	—	2	2	no	—
85	C₂²⋊C₈×C₆₁	—	2	2	no	—
86	#97×C₆₁	—	2	2	no	—
87	C₄×C₈×C₆₁	D₄	1	4	yes	—
88	#95×C₆₁	—	2	2	no	—
89	#95×C₆₁	—	2	1	no	—
90	#95×C₆₁	—	2	1	no	—
91	#95×C₆₁	—	2	1	no	—
92	#95×C₆₁	—	2	1	no	—
93	#95×C₆₁	—	2	2	no	—
94	#95×C₆₁	—	2	2	no	—
95	#95×C₆₁	—	2	2	no	—
96	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₆₁	—	2	2	no	—
98	C₂×Q₈×C₆₁	—	2	2	no	—
99	C₂×Q₈×C₆₁	—	2	2	no	—
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	—	4	2	no	—
104	C₂×Q₈×C₆₁	—	8	2	no	—
105	C₂²×C₄×C₆₁	—	2	1	no	—
106	C₂²×C₄×C₆₁	—	2	1	no	—
107	C₂²×C₄×C₆₁	—	2	1	no	—
108	C₂²×C₄×C₆₁	—	2	1	no	—
109	C₂²×C₄×C₆₁	—	2	1	no	—
110	C₂²×C₄×C₆₁	—	2	1	no	—
111	C₂²×C₄×C₆₁	—	2	2	no	—
112	C₂²×C₄×C₆₁	—	2	2	no	—
113	C₂²×C₄×C₆₁	—	2	2	no	—
114	C₂²×C₄×C₆₁	—	2	2	no	—
115	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₆₁	—	2	1	no	—
122	C₂×C₈×C₆₁	—	2	1	no	—
123	C₂×C₈×C₆₁	—	2	1	no	—
124	C₂×C₈×C₆₁	—	2	1	no	—
125	C₂×C₈×C₆₁	—	2	1	no	—
126	C₂×C₈×C₆₁	—	2	1	no	—
127	C₂×C₈×C₆₁	—	2	1	no	—
128	C₂×C₈×C₆₁	—	2	1	no	—
129	C₂×C₈×C₆₁	—	2	1	no	—
130	C₂×C₈×C₆₁	—	2	1	no	—
131	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
133	C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	2	2	no	—
135	C₄⋊C₄×C₆₁	—	2	2	no	—
136	C₄⋊C₄×C₆₁	—	2	2	no	—
137	C₄⋊C₄×C₆₁	—	2	2	no	—
138	C₄⋊C₄×C₆₁	—	2	2	no	—
139	C₄⋊C₄×C₆₁	—	2	2	no	—
140	C₄⋊C₄×C₆₁	—	2	2	no	—
141	C₄⋊C₄×C₆₁	—	4	4	no	—
142	C₄⋊C₄×C₆₁	—	4	2	no	—
143	C₄⋊C₄×C₆₁	—	4	2	no	—
144	C₄⋊C₄×C₆₁	—	4	2	no	—
145	C₄⋊C₄×C₆₁	—	8	2	no	—
146	C₂²⋊C₄×C₆₁	—	2	2	no	—
147	C₂²⋊C₄×C₆₁	—	2	2	no	—
148	C₂²⋊C₄×C₆₁	—	4	4	no	—
149	C₂²⋊C₄×C₆₁	—	8	2	no	—
150	C₄²×C₆₁	—	2	1	no	—
151	C₄²×C₆₁	—	2	1	no	—
152	C₄²×C₆₁	C₂×D₄	1	2	yes	—
153	C₄²×C₆₁	#41	1	2	yes	—
154	C₂³×C₆₁	—	2	1	no	—
155	C₂³×C₆₁	—	2	1	no	—
156	C₂³×C₆₁	—	2	1	no	—
157	C₂³×C₆₁	—	2	2	no	—
158	C₂³×C₆₁	—	2	2	no	—
159	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₆₁	—	4	2	no	—
161	Q₈×C₆₁	—	4	2	no	—
162	Q₈×C₆₁	—	4	2	no	—
163	Q₈×C₆₁	—	4	2	no	—
164	Q₈×C₆₁	—	8	4	no	—
165	C₂×C₄×C₆₁	—	2	2	no	—
166	C₂×C₄×C₆₁	—	2	2	no	—
167	C₂×C₄×C₆₁	—	2	1	no	—
168	C₂×C₄×C₆₁	—	2	1	no	—
169	C₂×C₄×C₆₁	—	2	1	no	—
170	C₂×C₄×C₆₁	—	2	1	no	—
171	C₂×C₄×C₆₁	—	2	1	no	—
172	C₂×C₄×C₆₁	—	2	2	no	—
173	C₂×C₄×C₆₁	—	2	2	no	—
174	C₂×C₄×C₆₁	—	4	1	no	—
175	C₂×C₄×C₆₁	—	4	1	no	—
176	C₂×C₄×C₆₁	—	4	1	no	—
177	C₂×C₄×C₆₁	—	4	1	no	—
178	C₂×C₄×C₆₁	—	4	2	no	—
179	C₂×C₄×C₆₁	—	4	2	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	4	2	no	—
182	C₂×C₄×C₆₁	—	4	2	no	—
183	C₂×C₄×C₆₁	—	4	2	no	—
184	C₂×C₄×C₆₁	—	4	2	no	—
185	C₂×C₄×C₆₁	—	4	2	no	—
186	C₂×C₄×C₆₁	—	4	2	no	—
187	C₂×C₄×C₆₁	—	4	2	no	—
188	C₂×C₄×C₆₁	—	4	2	no	—
189	C₂×C₄×C₆₁	—	4	2	no	—
190	C₂×C₄×C₆₁	#121	1	2	yes	—
191	C₂×C₄×C₆₁	#121	1	2	yes	—
192	C₂×C₄×C₆₁	C₂²×D₄	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	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
197	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
198	C₈×C₆₁	—	2	2	no	—
199	C₈×C₆₁	—	2	2	no	—
200	C₈×C₆₁	—	4	1	no	—
201	C₈×C₆₁	—	4	1	no	—
202	#29848	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂²×C₆₁	—	4	1	no	—
204	C₂²×C₆₁	—	4	2	no	—
205	C₂²×C₆₁	—	4	2	no	—
206	C₂²×C₆₁	—	4	1	no	—
207	C₂²×C₆₁	—	4	1	no	—
208	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
209	C₂²×C₆₁	#535	1	1	yes	characteristic
210	C₂²×C₆₁	#536	1	1	yes	characteristic
211	C₂²×C₆₁	#577	1	2	yes	—
212	C₂²×C₆₁	#578	1	2	yes	—
213	C₄×C₆₁	—	2	2	no	—
214	C₄×C₆₁	—	2	2	no	—
215	C₄×C₆₁	—	4	1	no	—
216	C₄×C₆₁	—	4	1	no	—
217	C₄×C₆₁	—	4	1	no	—
218	C₄×C₆₁	—	8	2	no	—
219	C₄×C₆₁	—	8	2	no	—
220	C₄×C₆₁	—	8	2	no	—
221	C₄×C₆₁	—	8	2	no	—
222	C₄×C₆₁	#537	1	1	yes	characteristic
223	C₄×C₆₁	#537	1	1	yes	characteristic
224	C₄×C₆₁	#542	1	1	yes	characteristic
225	C₄×C₆₁	#542	1	1	yes	characteristic
226	C₂×#487	C₂×C₆₁	1	1	yes	characteristic, complemented
227	C₂×#433	C₂×C₆₁	1	1	yes	characteristic
228	#2628	C₂×C₆₁	1	1	yes	characteristic
229	#2621	C₂×C₆₁	1	1	yes	characteristic
230	#2068	C₂×C₆₁	1	2	yes	complemented
231	#2066	C₂×C₆₁	1	2	yes	complemented
232	#2036	C₂×C₆₁	1	2	yes	—
233	#2035	C₂×C₆₁	1	2	yes	—
234	#1993	C₂×C₆₁	1	1	yes	characteristic, complemented
235	#1960	C₂×C₆₁	1	1	yes	characteristic, complemented
236	#1846	C₂×C₆₁	1	1	yes	characteristic, complemented
237	C₂×C₆₁	—	8	1	no	—
238	C₂×C₆₁	#2620	1	1	yes	characteristic
239	C₂×C₆₁	#3057	1	1	yes	characteristic
240	C₂×C₆₁	#3059	1	1	yes	characteristic
241	C₂×C₆₁	#3225	1	2	yes	—
242	C₂×C₆₁	#3242	1	2	yes	—
243	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
244	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
245	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
246	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
247	#487	—	2	4	no	—
248	#433	—	2	4	no	—
249	C₂×#107	C₂²×C₆₁	1	2	yes	—
250	C₂×#106	C₂²×C₆₁	1	2	yes	—
251	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
253	C₂×#103	C₂²×C₆₁	1	2	yes	—
254	C₂×#103	C₂²×C₆₁	1	2	yes	—
255	C₂×#103	C₂²×C₆₁	1	2	yes	—
256	C₂×#103	C₂²×C₆₁	1	2	yes	—
257	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
258	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
259	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
260	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
261	#400	—	2	1	no	—
262	#399	—	2	1	no	—
263	#398	—	2	1	no	—
264	#398	—	2	1	no	—
265	#397	—	2	1	no	—
266	#397	—	2	1	no	—
267	#395	—	2	1	no	—
268	#393	—	2	1	no	—
269	#391	C₂²×C₆₁	1	2	yes	—
270	#389	C₂²×C₆₁	1	2	yes	—
271	#382	C₂²×C₆₁	1	1	yes	characteristic
272	#382	C₂²×C₆₁	1	1	yes	characteristic
273	#380	C₂²×C₆₁	1	2	yes	—
274	#340	C₂²×C₆₁	1	2	yes	—
275	#340	C₂²×C₆₁	1	2	yes	—
276	C₆₁	#29848	1	1	yes	characteristic, direct product factor, Sylow
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
279	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
284	C₄⋊Q₈	—	2	2	no	—
285	C₄⋊Q₈	—	2	2	no	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	—	2	2	no	—
288	C₂²⋊Q₈	—	4	2	no	—
289	C₂²⋊Q₈	—	4	2	no	—
290	#117	—	2	2	no	—
291	#117	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
298	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
308	#107	—	4	2	no	—
309	#106	—	4	2	no	—
310	C₄⋊C₈	—	2	2	no	—
311	C₄⋊C₈	—	2	2	no	—
312	#103	—	2	4	no	—
313	#103	—	2	4	no	—
314	#103	—	4	2	no	—
315	#103	—	4	2	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	#97	—	2	2	no	—
319	C₄×C₈	D₄×C₆₁	1	4	yes	—
320	#95	—	2	2	no	—
321	#95	—	2	1	no	—
322	#95	—	2	1	no	—
323	#95	—	2	1	no	—
324	#95	—	2	1	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	4	2	no	—
336	C₂×Q₈	—	8	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
352	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
364	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	8	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₂²⋊C₄	—	8	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	C₂×D₄×C₆₁	1	2	yes	—
385	C₄²	#41×C₆₁	1	2	yes	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	1	no	—
391	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	8	4	no	—
397	C₂×C₄	—	2	2	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	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	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	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	#121×C₆₁	1	2	yes	—
423	C₂×C₄	#121×C₆₁	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
426	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
427	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
428	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
429	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	2	2	no	—
432	C₈	—	4	1	no	—
433	C₈	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
440	C₂²	C₆₁×#535	1	1	yes	characteristic
441	C₂²	C₆₁×#536	1	1	yes	characteristic
442	C₂²	C₆₁×#577	1	2	yes	—
443	C₂²	C₆₁×#578	1	2	yes	—
444	C₄	—	2	2	no	—
445	C₄	—	2	2	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	1	no	—
448	C₄	—	4	1	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	2	no	—
453	C₄	C₆₁×#537	1	1	yes	characteristic
454	C₄	C₆₁×#537	1	1	yes	characteristic
455	C₄	C₆₁×#542	1	1	yes	characteristic
456	C₄	C₆₁×#542	1	1	yes	characteristic
457	C₂	—	8	1	no	—
458	C₂	C₆₁×#2620	1	1	yes	characteristic
459	C₂	C₆₁×#3057	1	1	yes	characteristic
460	C₂	C₆₁×#3059	1	1	yes	characteristic
461	C₂	C₆₁×#3225	1	2	yes	—
462	C₂	C₆₁×#3242	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂⁴×C₆₁	C₂×D₄
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×#487	C₂	semidirect
5. C₆₁×#2068	C₂	semidirect
6. C₆₁×#2066	C₂	semidirect
9. C₆₁×#1993	C₂	semidirect
10. C₆₁×#1960	C₂	semidirect
11. C₆₁×#1846	C₂	semidirect
202. #29848	C₆₁	direct (N × H)
226. C₂×#487	C₂×C₆₁	semidirect
230. #2068	C₂×C₆₁	semidirect
231. #2066	C₂×C₆₁	semidirect
234. #1993	C₂×C₆₁	semidirect
235. #1960	C₂×C₆₁	semidirect
236. #1846	C₂×C₆₁	semidirect
276. C₆₁	#29848	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×#487	2
C₂×C₆₁×#433	2
C₆₁×#2628	2
C₆₁×#2621	2
C₆₁×#2068	2
C₆₁×#2066	2
C₆₁×#2036	2
C₆₁×#2035	2
C₆₁×#1993	2
C₆₁×#1960	2
C₆₁×#1846	2
#29848	61

Subgroups — C61×#29848 #29533281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#29848 #29533281