Subgroups — C₆₁×#23028 #29526461

Order 15616.

970 conjugacy classes of subgroups.

The subgroup lattice has 438 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
2	C₂×C₆₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#106×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2360	C₂	1	2	yes	maximal
5	C₆₁×#1971	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1927	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1872	C₂	1	2	yes	maximal
9	C₆₁×#1865	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1776	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1752	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
17	C₆₁×#467	C₄	1	8	yes	complemented
18	C₆₁×#441	—	2	4	no	—
19	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#106×C₆₁	—	2	4	no	—
21	C₂×#106×C₆₁	C₂²	1	2	yes	—
22	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#103×C₆₁	C₂²	1	2	yes	—
25	C₂×#103×C₆₁	C₂²	1	2	yes	—
26	C₂×#103×C₆₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#391	C₂²	1	2	yes	—
31	C₆₁×#389	—	2	2	no	—
32	C₆₁×#389	C₂²	1	2	yes	—
33	C₆₁×#387	—	2	2	no	—
34	C₆₁×#385	—	2	2	no	—
35	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₆₁	—	2	2	no	—
37	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×#340	C₂²	1	2	yes	—
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#336	C₂²	1	1	yes	characteristic
41	C₆₁×#336	C₂²	1	1	yes	characteristic
42	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₆₁	—	2	2	no	—
44	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
45	C₂×Q₁₆×C₆₁	—	2	2	no	—
46	C₂×Q₁₆×C₆₁	—	2	2	no	—
47	C₂×Q₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
48	C₂²×C₈×C₆₁	—	2	2	no	—
49	C₂²×C₈×C₆₁	—	2	2	no	—
50	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	—
51	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
55	C₂²⋊Q₈×C₆₁	—	2	4	no	—
56	C₂²⋊Q₈×C₆₁	C₂×C₄	1	8	yes	—
57	C₄×Q₈×C₆₁	—	2	4	no	—
58	C₄×Q₈×C₆₁	—	4	2	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₆₁	—	4	2	no	—
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
70	C₂×C₄²×C₆₁	—	2	2	no	—
71	C₂×C₄²×C₆₁	—	2	2	no	—
72	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
74	#107×C₆₁	C₂×C₄	1	4	yes	complemented
75	#106×C₆₁	—	2	2	no	—
76	#106×C₆₁	—	2	4	no	—
77	#106×C₆₁	D₄	1	4	yes	—
78	#103×C₆₁	—	2	4	no	—
79	#103×C₆₁	—	4	2	no	—
80	#103×C₆₁	C₂×C₄	1	8	yes	complemented
81	C₂²⋊C₈×C₆₁	—	2	2	no	—
82	#97×C₆₁	—	2	2	no	—
83	#97×C₆₁	—	2	2	no	—
84	#95×C₆₁	—	2	2	no	—
85	#95×C₆₁	—	2	2	no	—
86	#95×C₆₁	—	2	2	no	—
87	#95×C₆₁	—	2	2	no	—
88	#95×C₆₁	D₄	1	2	yes	—
89	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
90	C₂×Q₈×C₆₁	—	2	2	no	—
91	C₂×Q₈×C₆₁	—	2	2	no	—
92	C₂×Q₈×C₆₁	—	2	2	no	—
93	C₂×Q₈×C₆₁	—	2	2	no	—
94	C₂×Q₈×C₆₁	—	2	2	no	—
95	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₆₁	—	2	1	no	—
97	C₂²×C₄×C₆₁	—	2	1	no	—
98	C₂²×C₄×C₆₁	—	2	1	no	—
99	C₂²×C₄×C₆₁	—	2	1	no	—
100	C₂²×C₄×C₆₁	—	2	2	no	—
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	—	2	2	no	—
103	C₂²×C₄×C₆₁	—	2	2	no	—
104	C₂²×C₄×C₆₁	—	4	4	no	—
105	C₂²×C₄×C₆₁	—	4	4	no	—
106	C₂²×C₄×C₆₁	—	8	2	no	—
107	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	#41	1	2	yes	—
112	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
113	Q₁₆×C₆₁	—	2	8	no	—
114	C₂×C₈×C₆₁	—	2	1	no	—
115	C₂×C₈×C₆₁	—	2	1	no	—
116	C₂×C₈×C₆₁	—	2	8	no	—
117	C₂×C₈×C₆₁	—	2	1	no	—
118	C₂×C₈×C₆₁	—	2	1	no	—
119	C₂×C₈×C₆₁	—	2	1	no	—
120	C₂×C₈×C₆₁	—	2	1	no	—
121	C₂×C₈×C₆₁	—	2	1	no	—
122	C₂×C₈×C₆₁	—	2	1	no	—
123	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₆₁	#41	1	2	yes	—
127	C₄⋊C₄×C₆₁	—	2	8	no	—
128	C₄⋊C₄×C₆₁	—	2	2	no	—
129	C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₄⋊C₄×C₆₁	—	2	2	no	—
131	C₄⋊C₄×C₆₁	—	2	2	no	—
132	C₄⋊C₄×C₆₁	—	4	4	no	—
133	C₄⋊C₄×C₆₁	—	4	4	no	—
134	C₄⋊C₄×C₆₁	—	8	2	no	—
135	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
136	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
137	C₂²⋊C₄×C₆₁	—	2	8	no	—
138	C₂²⋊C₄×C₆₁	—	2	4	no	—
139	C₄²×C₆₁	—	2	1	no	—
140	C₄²×C₆₁	—	2	1	no	—
141	C₄²×C₆₁	—	2	1	no	—
142	C₄²×C₆₁	—	2	1	no	—
143	C₄²×C₆₁	—	4	4	no	—
144	C₄²×C₆₁	—	8	2	no	—
145	C₂³×C₆₁	—	2	1	no	—
146	C₂³×C₆₁	—	2	1	no	—
147	C₂³×C₆₁	—	2	2	no	—
148	C₂³×C₆₁	C₄×D₄	1	2	yes	—
149	C₂³×C₆₁	#137	1	4	yes	—
150	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₆₁	—	2	4	no	—
152	Q₈×C₆₁	—	2	4	no	—
153	Q₈×C₆₁	—	4	2	no	—
154	Q₈×C₆₁	—	4	2	no	—
155	C₂×C₄×C₆₁	—	2	1	no	—
156	C₂×C₄×C₆₁	—	2	1	no	—
157	C₂×C₄×C₆₁	—	2	2	no	—
158	C₂×C₄×C₆₁	—	2	2	no	—
159	C₂×C₄×C₆₁	—	2	2	no	—
160	C₂×C₄×C₆₁	—	2	2	no	—
161	C₂×C₄×C₆₁	—	2	4	no	—
162	C₂×C₄×C₆₁	—	2	4	no	—
163	C₂×C₄×C₆₁	—	2	2	no	—
164	C₂×C₄×C₆₁	—	2	4	no	—
165	C₂×C₄×C₆₁	—	2	2	no	—
166	C₂×C₄×C₆₁	—	2	2	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	—	4	2	no	—
171	C₂×C₄×C₆₁	—	4	2	no	—
172	C₂×C₄×C₆₁	—	4	2	no	—
173	C₂×C₄×C₆₁	—	4	2	no	—
174	C₂×C₄×C₆₁	—	4	2	no	—
175	C₂×C₄×C₆₁	—	4	2	no	—
176	C₂×C₄×C₆₁	—	4	2	no	—
177	C₂×C₄×C₆₁	—	4	2	no	—
178	C₂×C₄×C₆₁	—	4	2	no	—
179	C₂×C₄×C₆₁	—	8	8	no	—
180	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
187	C₈×C₆₁	—	2	2	no	—
188	C₈×C₆₁	—	4	1	no	—
189	C₈×C₆₁	—	4	1	no	—
190	C₈×C₆₁	C₄×D₄	1	4	yes	—
191	#23028	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₆₁	—	2	4	no	—
193	C₂²×C₆₁	—	2	2	no	—
194	C₂²×C₆₁	—	2	2	no	—
195	C₂²×C₆₁	—	2	4	no	—
196	C₂²×C₆₁	#441	1	4	yes	complemented
197	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₆₁	D₄²	1	1	yes	characteristic
199	C₂²×C₆₁	#547	1	1	yes	characteristic
200	C₂²×C₆₁	C₂×#137	1	2	yes	—
201	C₂²×C₆₁	#577	1	2	yes	—
202	C₄×C₆₁	—	2	2	no	—
203	C₄×C₆₁	—	4	2	no	—
204	C₄×C₆₁	—	4	4	no	—
205	C₄×C₆₁	—	4	4	no	—
206	C₄×C₆₁	—	4	2	no	—
207	C₄×C₆₁	—	4	4	no	—
208	C₄×C₆₁	—	8	2	no	—
209	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
210	C₄×C₆₁	#520	1	1	yes	characteristic
211	C₄×C₆₁	#548	1	1	yes	characteristic
212	C₄×C₆₁	#553	1	1	yes	characteristic
213	C₂×#467	C₂×C₆₁	1	1	yes	characteristic
214	C₂×#441	C₂×C₆₁	1	1	yes	characteristic, complemented
215	C₂²×#106	C₂×C₆₁	1	1	yes	characteristic
216	#2360	C₂×C₆₁	1	2	yes	—
217	#1971	C₂×C₆₁	1	1	yes	characteristic, complemented
218	#1943	C₂×C₆₁	1	1	yes	characteristic, complemented
219	#1927	C₂×C₆₁	1	2	yes	complemented
220	#1872	C₂×C₆₁	1	2	yes	—
221	#1865	C₂×C₆₁	1	2	yes	complemented
222	#1776	C₂×C₆₁	1	1	yes	characteristic, complemented
223	#1752	C₂×C₆₁	1	1	yes	characteristic
224	C₂×C₆₁	—	2	4	no	—
225	C₂×C₆₁	#2361	1	1	yes	characteristic
226	C₂×C₆₁	C₂×#441	1	1	yes	characteristic
227	C₂×C₆₁	#2952	1	1	yes	characteristic
228	C₂×C₆₁	#3266	1	2	yes	—
229	C₂×C₆₁	#3344	1	2	yes	—
230	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
231	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
232	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
233	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
234	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
235	#467	C₄×C₆₁	1	8	yes	complemented
236	#441	—	2	4	no	—
237	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
238	C₂×#106	—	2	4	no	—
239	C₂×#106	C₂²×C₆₁	1	2	yes	—
240	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
241	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
242	C₂×#103	C₂²×C₆₁	1	2	yes	—
243	C₂×#103	C₂²×C₆₁	1	2	yes	—
244	C₂×#103	C₂²×C₆₁	1	2	yes	—
245	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
246	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
247	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
248	#391	C₂²×C₆₁	1	2	yes	—
249	#389	—	2	2	no	—
250	#389	C₂²×C₆₁	1	2	yes	—
251	#387	—	2	2	no	—
252	#385	—	2	2	no	—
253	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
254	C₄×C₂²⋊C₄	—	2	2	no	—
255	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
256	#340	C₂²×C₆₁	1	2	yes	—
257	#340	C₂²×C₆₁	1	2	yes	—
258	#336	C₂²×C₆₁	1	1	yes	characteristic
259	#336	C₂²×C₆₁	1	1	yes	characteristic
260	C₆₁	#23028	1	1	yes	characteristic, direct product factor, Sylow
261	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
262	C₂³×C₄	—	2	2	no	—
263	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
264	C₂×Q₁₆	—	2	2	no	—
265	C₂×Q₁₆	—	2	2	no	—
266	C₂×Q₁₆	C₂×C₄×C₆₁	1	4	yes	complemented
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	C₂×C₄×C₆₁	1	4	yes	—
270	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
274	C₂²⋊Q₈	—	2	4	no	—
275	C₂²⋊Q₈	C₂×C₄×C₆₁	1	8	yes	—
276	C₄×Q₈	—	2	4	no	—
277	C₄×Q₈	—	4	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	4	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	4	2	no	—
284	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	—	2	2	no	—
291	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
293	#107	C₂×C₄×C₆₁	1	4	yes	complemented
294	#106	—	2	2	no	—
295	#106	—	2	4	no	—
296	#106	D₄×C₆₁	1	4	yes	—
297	#103	—	2	4	no	—
298	#103	—	4	2	no	—
299	#103	C₂×C₄×C₆₁	1	8	yes	complemented
300	C₂²⋊C₈	—	2	2	no	—
301	#97	—	2	2	no	—
302	#97	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	D₄×C₆₁	1	2	yes	—
308	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	4	4	no	—
324	C₂²×C₄	—	4	4	no	—
325	C₂²×C₄	—	8	2	no	—
326	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
330	C₂²×C₄	#41×C₆₁	1	2	yes	—
331	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
332	Q₁₆	—	2	8	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	8	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
343	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
344	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
345	C₂×C₈	#41×C₆₁	1	2	yes	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	4	no	—
352	C₄⋊C₄	—	4	4	no	—
353	C₄⋊C₄	—	8	2	no	—
354	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
355	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
356	C₂²⋊C₄	—	2	8	no	—
357	C₂²⋊C₄	—	2	4	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	4	4	no	—
363	C₄²	—	8	2	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	2	no	—
367	C₂³	C₄×D₄×C₆₁	1	2	yes	—
368	C₂³	#137×C₆₁	1	4	yes	—
369	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
370	Q₈	—	2	4	no	—
371	Q₈	—	2	4	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	4	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	8	8	no	—
399	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
400	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
402	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
403	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
404	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
405	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	4	1	no	—
408	C₈	—	4	1	no	—
409	C₈	C₄×D₄×C₆₁	1	4	yes	—
410	C₂²	—	2	4	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	4	no	—
414	C₂²	C₆₁×#441	1	4	yes	complemented
415	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
416	C₂²	D₄²×C₆₁	1	1	yes	characteristic
417	C₂²	C₆₁×#547	1	1	yes	characteristic
418	C₂²	C₂×#137×C₆₁	1	2	yes	—
419	C₂²	C₆₁×#577	1	2	yes	—
420	C₄	—	2	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	4	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	8	2	no	—
427	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
428	C₄	C₆₁×#520	1	1	yes	characteristic
429	C₄	C₆₁×#548	1	1	yes	characteristic
430	C₄	C₆₁×#553	1	1	yes	characteristic
431	C₂	—	2	4	no	—
432	C₂	C₆₁×#2361	1	1	yes	characteristic
433	C₂	C₂×C₆₁×#441	1	1	yes	characteristic
434	C₂	C₆₁×#2952	1	1	yes	characteristic
435	C₂	C₆₁×#3266	1	2	yes	—
436	C₂	C₆₁×#3344	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#441	C₂	semidirect
5. C₆₁×#1971	C₂	semidirect
6. C₆₁×#1943	C₂	semidirect
7. C₆₁×#1927	C₂	semidirect
9. C₆₁×#1865	C₂	semidirect
10. C₆₁×#1776	C₂	semidirect
17. C₆₁×#467	C₄	semidirect
47. C₂×Q₁₆×C₆₁	C₂×C₄	semidirect
74. #107×C₆₁	C₂×C₄	semidirect
80. #103×C₆₁	C₂×C₄	semidirect
191. #23028	C₆₁	direct (N × H)
196. C₂²×C₆₁	#441	semidirect
214. C₂×#441	C₂×C₆₁	semidirect
217. #1971	C₂×C₆₁	semidirect
218. #1943	C₂×C₆₁	semidirect
219. #1927	C₂×C₆₁	semidirect
221. #1865	C₂×C₆₁	semidirect
222. #1776	C₂×C₆₁	semidirect
235. #467	C₄×C₆₁	semidirect
260. C₆₁	#23028	direct (N × H)
266. C₂×Q₁₆	C₂×C₄×C₆₁	semidirect
293. #107	C₂×C₄×C₆₁	semidirect
299. #103	C₂×C₄×C₆₁	semidirect
414. C₂²	C₆₁×#441	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×C₆₁×#441	2
C₂²×#106×C₆₁	2
C₆₁×#2360	2
C₆₁×#1971	2
C₆₁×#1943	2
C₆₁×#1927	2
C₆₁×#1872	2
C₆₁×#1865	2
C₆₁×#1776	2
C₆₁×#1752	2
#23028	61

Subgroups — C61×#23028 #29526461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#23028 #29526461