Subgroups — C₆₁×#25634 #29529067

Order 15616.

1082 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#557	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#494	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#462	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2568	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2016	C₂	1	4	yes	maximal
6	C₆₁×#1984	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#1981	C₂	1	1	yes	maximal, characteristic
8	C₆₁×#1878	C₂	1	4	yes	maximal
9	C₄×#103×C₆₁	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₆₁	C₂²	1	4	yes	—
11	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
12	C₆₁×#557	—	2	4	no	—
13	C₆₁×#557	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#125×C₆₁	—	2	1	no	—
18	C₂×#125×C₆₁	—	2	2	no	—
19	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
20	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#494	—	2	4	no	—
24	C₆₁×#462	—	2	4	no	—
25	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₆₁	C₂²	1	2	yes	—
27	C₂×#103×C₆₁	C₂²	1	2	yes	—
28	C₂×#103×C₆₁	C₂²	1	4	yes	—
29	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#400	—	2	2	no	—
31	C₆₁×#391	—	2	1	no	—
32	C₆₁×#391	C₂²	1	4	yes	—
33	C₆₁×#382	—	2	1	no	—
34	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
35	C₆₁×#340	C₂²	1	2	yes	—
36	C₆₁×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
38	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
39	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
41	C₂×Q₁₆×C₆₁	—	2	4	no	—
42	C₂×Q₁₆×C₆₁	—	2	8	no	—
43	C₂×Q₁₆×C₆₁	—	2	8	no	—
44	C₂×Q₁₆×C₆₁	—	4	4	no	—
45	C₂×Q₁₆×C₆₁	—	4	4	no	—
46	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
48	C₄⋊Q₈×C₆₁	—	2	4	no	—
49	C₄⋊Q₈×C₆₁	—	2	4	no	—
50	C₄⋊Q₈×C₆₁	—	2	2	no	—
51	C₄⋊Q₈×C₆₁	—	2	2	no	—
52	C₄⋊Q₈×C₆₁	—	2	2	no	—
53	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
54	#125×C₆₁	—	2	16	no	—
55	#125×C₆₁	—	2	8	no	—
56	C₄×Q₈×C₆₁	—	2	8	no	—
57	C₄×Q₈×C₆₁	—	2	4	no	—
58	C₄×Q₈×C₆₁	—	2	4	no	—
59	C₄×Q₈×C₆₁	—	2	2	no	—
60	C₄×Q₈×C₆₁	—	2	2	no	—
61	C₄×Q₈×C₆₁	—	2	2	no	—
62	C₄×Q₈×C₆₁	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₆₁	—	2	2	no	—
76	C₂×C₄²×C₆₁	—	2	1	no	—
77	C₂×C₄²×C₆₁	—	2	1	no	—
78	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
79	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₆₁	—	2	2	no	—
81	#103×C₆₁	—	2	4	no	—
82	#103×C₆₁	—	2	4	no	—
83	#103×C₆₁	—	4	4	no	—
84	C₄×C₈×C₆₁	—	2	2	no	—
85	#95×C₆₁	—	2	1	no	—
86	#95×C₆₁	—	2	4	no	—
87	#95×C₆₁	—	2	4	no	—
88	C₂×Q₈×C₆₁	—	2	2	no	—
89	C₂×Q₈×C₆₁	—	2	2	no	—
90	C₂×Q₈×C₆₁	—	2	2	no	—
91	C₂×Q₈×C₆₁	—	2	1	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	—	2	4	no	—
96	C₂×Q₈×C₆₁	—	2	4	no	—
97	C₂×Q₈×C₆₁	—	2	4	no	—
98	C₂×Q₈×C₆₁	—	2	2	no	—
99	C₂×Q₈×C₆₁	—	2	4	no	—
100	C₂×Q₈×C₆₁	Q₁₆	1	4	yes	complemented
101	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
102	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₆₁	—	2	1	no	—
104	C₂²×C₄×C₆₁	—	2	2	no	—
105	C₂²×C₄×C₆₁	—	2	1	no	—
106	C₂²×C₄×C₆₁	—	2	2	no	—
107	C₂²×C₄×C₆₁	—	2	2	no	—
108	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
113	Q₁₆×C₆₁	—	4	16	no	—
114	Q₁₆×C₆₁	—	4	8	no	—
115	C₂×C₈×C₆₁	—	2	2	no	—
116	C₂×C₈×C₆₁	—	2	2	no	—
117	C₂×C₈×C₆₁	—	2	2	no	—
118	C₂×C₈×C₆₁	—	2	4	no	—
119	C₂×C₈×C₆₁	#41	1	4	yes	—
120	C₄⋊C₄×C₆₁	—	2	8	no	—
121	C₄⋊C₄×C₆₁	—	2	8	no	—
122	C₄⋊C₄×C₆₁	—	2	8	no	—
123	C₄⋊C₄×C₆₁	—	2	4	no	—
124	C₄⋊C₄×C₆₁	—	2	4	no	—
125	C₄⋊C₄×C₆₁	—	2	4	no	—
126	C₄⋊C₄×C₆₁	—	2	4	no	—
127	C₄⋊C₄×C₆₁	—	2	2	no	—
128	C₄⋊C₄×C₆₁	—	2	1	no	—
129	C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₄⋊C₄×C₆₁	—	2	2	no	—
131	C₄⋊C₄×C₆₁	—	4	2	no	—
132	C₄⋊C₄×C₆₁	—	4	2	no	—
133	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
134	C₄²×C₆₁	—	2	8	no	—
135	C₄²×C₆₁	—	2	4	no	—
136	C₄²×C₆₁	—	2	2	no	—
137	C₄²×C₆₁	—	2	2	no	—
138	C₄²×C₆₁	—	4	2	no	—
139	C₄²×C₆₁	C₂×D₄	1	2	yes	—
140	C₄²×C₆₁	C₂×D₄	1	2	yes	—
141	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
142	Q₈×C₆₁	—	2	8	no	—
143	Q₈×C₆₁	—	2	2	no	—
144	Q₈×C₆₁	—	2	2	no	—
145	Q₈×C₆₁	—	2	8	no	—
146	Q₈×C₆₁	—	4	2	no	—
147	Q₈×C₆₁	—	4	2	no	—
148	Q₈×C₆₁	—	4	2	no	—
149	Q₈×C₆₁	—	4	2	no	—
150	Q₈×C₆₁	—	4	2	no	—
151	Q₈×C₆₁	—	4	4	no	—
152	C₂×C₄×C₆₁	—	2	2	no	—
153	C₂×C₄×C₆₁	—	2	2	no	—
154	C₂×C₄×C₆₁	—	2	2	no	—
155	C₂×C₄×C₆₁	—	2	2	no	—
156	C₂×C₄×C₆₁	—	2	2	no	—
157	C₂×C₄×C₆₁	—	2	4	no	—
158	C₂×C₄×C₆₁	—	2	2	no	—
159	C₂×C₄×C₆₁	—	2	4	no	—
160	C₂×C₄×C₆₁	—	4	2	no	—
161	C₂×C₄×C₆₁	—	4	4	no	—
162	C₂×C₄×C₆₁	—	4	2	no	—
163	C₂×C₄×C₆₁	—	4	2	no	—
164	C₂×C₄×C₆₁	—	4	2	no	—
165	C₂×C₄×C₆₁	—	4	4	no	—
166	C₂×C₄×C₆₁	—	4	2	no	—
167	C₂×C₄×C₆₁	—	4	2	no	—
168	C₂×C₄×C₆₁	#120	1	2	yes	—
169	C₂×C₄×C₆₁	#120	1	2	yes	—
170	C₂×C₄×C₆₁	C₂×Q₁₆	1	4	yes	—
171	C₂×C₄×C₆₁	C₂×Q₁₆	1	2	yes	—
172	C₂×C₄×C₆₁	#137	1	2	yes	—
173	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
176	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
177	C₈×C₆₁	—	2	4	no	—
178	C₈×C₆₁	—	4	2	no	—
179	#25634	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
181	C₂²×C₆₁	#550	1	2	yes	—
182	C₂²×C₆₁	C₂²×Q₁₆	1	1	yes	characteristic
183	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
184	C₂²×C₆₁	#578	1	2	yes	—
185	C₄×C₆₁	—	2	4	no	—
186	C₄×C₆₁	—	2	2	no	—
187	C₄×C₆₁	—	4	2	no	—
188	C₄×C₆₁	—	4	4	no	—
189	C₄×C₆₁	—	4	2	no	—
190	C₄×C₆₁	—	4	2	no	—
191	C₄×C₆₁	—	8	2	no	—
192	C₄×C₆₁	—	8	2	no	—
193	C₄×C₆₁	#451	1	4	yes	—
194	C₄×C₆₁	#532	1	1	yes	characteristic
195	C₄×C₆₁	#535	1	1	yes	characteristic
196	C₄×C₆₁	#546	1	2	yes	—
197	C₂×#557	C₂×C₆₁	1	1	yes	characteristic
198	C₂×#494	C₂×C₆₁	1	1	yes	characteristic
199	C₂×#462	C₂×C₆₁	1	1	yes	characteristic
200	#2568	C₂×C₆₁	1	1	yes	characteristic
201	#2016	C₂×C₆₁	1	4	yes	—
202	#1984	C₂×C₆₁	1	1	yes	characteristic
203	#1981	C₂×C₆₁	1	1	yes	characteristic
204	#1878	C₂×C₆₁	1	4	yes	—
205	C₄×#103	C₂×C₆₁	1	1	yes	characteristic
206	C₂×C₆₁	#2431	1	1	yes	characteristic
207	C₂×C₆₁	C₂×#451	1	1	yes	characteristic
208	C₂×C₆₁	#3011	1	1	yes	characteristic
209	C₂×C₆₁	#3395	1	2	yes	—
210	C₂×C₆₁	#3398	1	2	yes	—
211	C₂²×Q₁₆	C₂²×C₆₁	1	4	yes	—
212	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
213	#557	—	2	4	no	—
214	#557	—	2	4	no	—
215	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
217	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
218	C₂×#125	—	2	1	no	—
219	C₂×#125	—	2	2	no	—
220	C₂×C₄×Q₈	—	2	1	no	—
221	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
222	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
224	#494	—	2	4	no	—
225	#462	—	2	4	no	—
226	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
227	C₂×#103	C₂²×C₆₁	1	2	yes	—
228	C₂×#103	C₂²×C₆₁	1	2	yes	—
229	C₂×#103	C₂²×C₆₁	1	4	yes	—
230	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
231	#400	—	2	2	no	—
232	#391	—	2	1	no	—
233	#391	C₂²×C₆₁	1	4	yes	—
234	#382	—	2	1	no	—
235	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
236	#340	C₂²×C₆₁	1	2	yes	—
237	#336	C₂²×C₆₁	1	4	yes	—
238	C₆₁	#25634	1	1	yes	characteristic, direct product factor, Sylow
239	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
240	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
241	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
242	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
243	C₂×Q₁₆	—	2	4	no	—
244	C₂×Q₁₆	—	2	8	no	—
245	C₂×Q₁₆	—	2	8	no	—
246	C₂×Q₁₆	—	4	4	no	—
247	C₂×Q₁₆	—	4	4	no	—
248	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
249	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
250	C₄⋊Q₈	—	2	4	no	—
251	C₄⋊Q₈	—	2	4	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
256	#125	—	2	16	no	—
257	#125	—	2	8	no	—
258	C₄×Q₈	—	2	8	no	—
259	C₄×Q₈	—	2	4	no	—
260	C₄×Q₈	—	2	4	no	—
261	C₄×Q₈	—	2	2	no	—
262	C₄×Q₈	—	2	2	no	—
263	C₄×Q₈	—	2	2	no	—
264	C₄×Q₈	D₄×C₆₁	1	4	yes	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
274	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
281	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
282	C₄⋊C₈	—	2	2	no	—
283	#103	—	2	4	no	—
284	#103	—	2	4	no	—
285	#103	—	4	4	no	—
286	C₄×C₈	—	2	2	no	—
287	#95	—	2	1	no	—
288	#95	—	2	4	no	—
289	#95	—	2	4	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	Q₁₆×C₆₁	1	4	yes	complemented
303	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
304	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
315	Q₁₆	—	4	16	no	—
316	Q₁₆	—	4	8	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	#41×C₆₁	1	4	yes	—
322	C₄⋊C₄	—	2	8	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	—	2	8	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
336	C₄²	—	2	8	no	—
337	C₄²	—	2	4	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	4	2	no	—
341	C₄²	C₂×D₄×C₆₁	1	2	yes	—
342	C₄²	C₂×D₄×C₆₁	1	2	yes	—
343	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
344	Q₈	—	2	8	no	—
345	Q₈	—	2	2	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	2	8	no	—
348	Q₈	—	4	2	no	—
349	Q₈	—	4	2	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	4	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	#120×C₆₁	1	2	yes	—
371	C₂×C₄	#120×C₆₁	1	2	yes	—
372	C₂×C₄	C₂×Q₁₆×C₆₁	1	4	yes	—
373	C₂×C₄	C₂×Q₁₆×C₆₁	1	2	yes	—
374	C₂×C₄	#137×C₆₁	1	2	yes	—
375	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
376	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
377	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
378	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
379	C₈	—	2	4	no	—
380	C₈	—	4	2	no	—
381	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
382	C₂²	C₆₁×#550	1	2	yes	—
383	C₂²	C₂²×Q₁₆×C₆₁	1	1	yes	characteristic
384	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
385	C₂²	C₆₁×#578	1	2	yes	—
386	C₄	—	2	4	no	—
387	C₄	—	2	2	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	4	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	8	2	no	—
393	C₄	—	8	2	no	—
394	C₄	C₆₁×#451	1	4	yes	—
395	C₄	C₆₁×#532	1	1	yes	characteristic
396	C₄	C₆₁×#535	1	1	yes	characteristic
397	C₄	C₆₁×#546	1	2	yes	—
398	C₂	C₆₁×#2431	1	1	yes	characteristic
399	C₂	C₂×C₆₁×#451	1	1	yes	characteristic
400	C₂	C₆₁×#3011	1	1	yes	characteristic
401	C₂	C₆₁×#3395	1	2	yes	—
402	C₂	C₆₁×#3398	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
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
100. C₂×Q₈×C₆₁	Q₁₆	semidirect
179. #25634	C₆₁	direct (N × H)
238. C₆₁	#25634	direct (N × H)
302. C₂×Q₈	Q₁₆×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×#557	2
C₂×C₆₁×#494	2
C₂×C₆₁×#462	2
C₆₁×#2568	2
C₆₁×#2016	2
C₆₁×#1984	2
C₆₁×#1981	2
C₆₁×#1878	2
C₄×#103×C₆₁	2
#25634	61

Subgroups — C61×#25634 #29529067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25634 #29529067