Subgroups — C₆₁×#25603 #29529036

Order 15616.

1172 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2850	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2001	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2000	C₂	1	2	yes	maximal
7	C₆₁×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1960	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1880	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1878	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1749	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
14	C₆₁×#533	—	2	4	no	—
15	C₆₁×#533	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×#125×C₆₁	—	2	1	no	—
19	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
25	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
26	C₂×#117×C₆₁	—	2	1	no	—
27	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#497	—	2	4	no	—
29	C₆₁×#489	—	2	4	no	—
30	C₂×#103×C₆₁	C₂²	1	2	yes	—
31	C₂×#103×C₆₁	C₂²	1	2	yes	—
32	C₂×#103×C₆₁	C₂²	1	2	yes	—
33	C₂×#102×C₆₁	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
35	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#391	C₂²	1	1	yes	characteristic
38	C₆₁×#390	C₂²	1	1	yes	characteristic
39	C₆₁×#388	—	2	1	no	—
40	C₆₁×#388	—	2	1	no	—
41	C₆₁×#386	—	2	1	no	—
42	C₆₁×#386	—	2	1	no	—
43	C₆₁×#382	C₂²	1	1	yes	characteristic
44	C₆₁×#340	C₂²	1	2	yes	—
45	C₆₁×#340	C₂²	1	2	yes	—
46	C₆₁×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₆₁	—	2	1	no	—
48	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
50	C₂²×D₄×C₆₁	—	2	1	no	—
51	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
55	C₂×Q₁₆×C₆₁	—	2	4	no	—
56	C₂×Q₁₆×C₆₁	—	2	4	no	—
57	C₂×Q₁₆×C₆₁	—	4	2	no	—
58	C₂×SD₁₆×C₆₁	—	2	4	no	—
59	C₂×SD₁₆×C₆₁	—	2	4	no	—
60	C₂×SD₁₆×C₆₁	—	4	2	no	—
61	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
62	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
63	C₄⋊Q₈×C₆₁	—	2	2	no	—
64	C₄⋊Q₈×C₆₁	—	2	2	no	—
65	C₄⋊Q₈×C₆₁	D₄	1	4	yes	complemented
66	C₄⋊Q₈×C₆₁	D₄	1	4	yes	complemented
67	#125×C₆₁	—	2	8	no	—
68	#124×C₆₁	—	2	2	no	—
69	#124×C₆₁	—	2	2	no	—
70	C₂²⋊Q₈×C₆₁	—	2	8	no	—
71	C₂²⋊Q₈×C₆₁	—	2	4	no	—
72	C₂²⋊Q₈×C₆₁	—	2	4	no	—
73	C₂²⋊Q₈×C₆₁	—	4	2	no	—
74	#121×C₆₁	—	4	2	no	—
75	C₄×Q₈×C₆₁	—	2	8	no	—
76	C₄×Q₈×C₆₁	—	2	4	no	—
77	C₄×Q₈×C₆₁	—	2	4	no	—
78	#117×C₆₁	—	2	8	no	—
79	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
81	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
82	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
83	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
84	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
85	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
88	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
95	C₂×C₄²×C₆₁	—	2	2	no	—
96	C₂×C₄²×C₆₁	—	2	2	no	—
97	C₂×C₄²×C₆₁	—	2	2	no	—
98	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
102	#103×C₆₁	—	2	4	no	—
103	#103×C₆₁	—	4	2	no	—
104	#103×C₆₁	—	4	2	no	—
105	#102×C₆₁	—	2	4	no	—
106	C₂²⋊C₈×C₆₁	—	2	4	no	—
107	#97×C₆₁	—	2	2	no	—
108	#97×C₆₁	—	2	2	no	—
109	#95×C₆₁	—	2	1	no	—
110	#95×C₆₁	—	2	1	no	—
111	#95×C₆₁	—	2	1	no	—
112	#95×C₆₁	—	2	1	no	—
113	C₂⁴×C₆₁	—	2	1	no	—
114	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
115	C₂×Q₈×C₆₁	—	2	4	no	—
116	C₂×Q₈×C₆₁	—	2	2	no	—
117	C₂×Q₈×C₆₁	—	2	1	no	—
118	C₂×Q₈×C₆₁	—	2	1	no	—
119	C₂×Q₈×C₆₁	—	2	2	no	—
120	C₂×Q₈×C₆₁	—	2	2	no	—
121	C₂×Q₈×C₆₁	—	2	2	no	—
122	C₂×Q₈×C₆₁	—	2	2	no	—
123	C₂×Q₈×C₆₁	—	2	2	no	—
124	C₂×Q₈×C₆₁	—	2	2	no	—
125	C₂×Q₈×C₆₁	—	4	2	no	—
126	C₂×Q₈×C₆₁	—	4	2	no	—
127	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
128	C₂×D₄×C₆₁	—	2	1	no	—
129	C₂×D₄×C₆₁	—	2	1	no	—
130	C₂×D₄×C₆₁	—	2	2	no	—
131	C₂×D₄×C₆₁	—	2	2	no	—
132	C₂×D₄×C₆₁	—	4	2	no	—
133	C₂×D₄×C₆₁	—	4	2	no	—
134	C₂×D₄×C₆₁	—	4	2	no	—
135	C₂²×C₄×C₆₁	—	2	2	no	—
136	C₂²×C₄×C₆₁	—	2	2	no	—
137	C₂²×C₄×C₆₁	—	2	2	no	—
138	C₂²×C₄×C₆₁	—	2	2	no	—
139	C₂²×C₄×C₆₁	—	2	2	no	—
140	C₂²×C₄×C₆₁	—	2	2	no	—
141	C₂²×C₄×C₆₁	—	2	1	no	—
142	C₂²×C₄×C₆₁	—	2	1	no	—
143	C₂²×C₄×C₆₁	—	2	2	no	—
144	C₂²×C₄×C₆₁	—	2	2	no	—
145	C₂²×C₄×C₆₁	—	2	1	no	—
146	C₂²×C₄×C₆₁	—	2	1	no	—
147	C₂²×C₄×C₆₁	—	2	1	no	—
148	C₂²×C₄×C₆₁	—	4	1	no	—
149	C₂²×C₄×C₆₁	—	4	1	no	—
150	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
156	Q₁₆×C₆₁	—	4	8	no	—
157	SD₁₆×C₆₁	—	4	8	no	—
158	C₂×C₈×C₆₁	—	2	2	no	—
159	C₂×C₈×C₆₁	—	2	2	no	—
160	C₂×C₈×C₆₁	—	2	2	no	—
161	C₂×C₈×C₆₁	—	2	2	no	—
162	C₂×C₈×C₆₁	—	2	2	no	—
163	C₂×C₈×C₆₁	#41	1	4	yes	—
164	C₄⋊C₄×C₆₁	—	2	8	no	—
165	C₄⋊C₄×C₆₁	—	2	8	no	—
166	C₄⋊C₄×C₆₁	—	2	4	no	—
167	C₄⋊C₄×C₆₁	—	2	4	no	—
168	C₄⋊C₄×C₆₁	—	2	4	no	—
169	C₄⋊C₄×C₆₁	—	2	2	no	—
170	C₄⋊C₄×C₆₁	—	2	2	no	—
171	C₄⋊C₄×C₆₁	—	2	2	no	—
172	C₄⋊C₄×C₆₁	—	4	2	no	—
173	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
174	C₂²⋊C₄×C₆₁	—	2	8	no	—
175	C₂²⋊C₄×C₆₁	—	4	2	no	—
176	C₂²⋊C₄×C₆₁	—	4	2	no	—
177	C₂²⋊C₄×C₆₁	—	4	2	no	—
178	C₂²⋊C₄×C₆₁	—	4	2	no	—
179	C₂²⋊C₄×C₆₁	—	4	2	no	—
180	C₂²⋊C₄×C₆₁	—	4	2	no	—
181	C₄²×C₆₁	—	2	8	no	—
182	C₄²×C₆₁	—	2	2	no	—
183	C₄²×C₆₁	—	2	2	no	—
184	C₄²×C₆₁	—	2	1	no	—
185	C₄²×C₆₁	—	2	1	no	—
186	C₄²×C₆₁	C₂×D₄	1	2	yes	—
187	C₄²×C₆₁	C₂×D₄	1	2	yes	—
188	C₂³×C₆₁	—	2	1	no	—
189	C₂³×C₆₁	—	2	1	no	—
190	C₂³×C₆₁	—	2	1	no	—
191	C₂³×C₆₁	—	2	1	no	—
192	C₂³×C₆₁	—	2	1	no	—
193	C₂³×C₆₁	—	2	1	no	—
194	C₂³×C₆₁	—	4	1	no	—
195	C₂³×C₆₁	—	4	1	no	—
196	C₂³×C₆₁	—	4	1	no	—
197	C₂³×C₆₁	—	4	1	no	—
198	C₂³×C₆₁	—	4	1	no	—
199	C₂³×C₆₁	—	4	1	no	—
200	C₂³×C₆₁	—	4	1	no	—
201	C₂³×C₆₁	#137	1	2	yes	—
202	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
203	Q₈×C₆₁	—	2	4	no	—
204	Q₈×C₆₁	—	2	4	no	—
205	Q₈×C₆₁	—	4	8	no	—
206	Q₈×C₆₁	—	4	2	no	—
207	Q₈×C₆₁	—	4	2	no	—
208	Q₈×C₆₁	—	4	2	no	—
209	Q₈×C₆₁	—	4	2	no	—
210	D₄×C₆₁	—	4	2	no	—
211	D₄×C₆₁	—	4	2	no	—
212	D₄×C₆₁	—	8	4	no	—
213	C₂×C₄×C₆₁	—	2	8	no	—
214	C₂×C₄×C₆₁	—	2	1	no	—
215	C₂×C₄×C₆₁	—	2	1	no	—
216	C₂×C₄×C₆₁	—	2	1	no	—
217	C₂×C₄×C₆₁	—	2	1	no	—
218	C₂×C₄×C₆₁	—	2	1	no	—
219	C₂×C₄×C₆₁	—	2	1	no	—
220	C₂×C₄×C₆₁	—	2	1	no	—
221	C₂×C₄×C₆₁	—	2	1	no	—
222	C₂×C₄×C₆₁	—	2	4	no	—
223	C₂×C₄×C₆₁	—	2	4	no	—
224	C₂×C₄×C₆₁	—	2	1	no	—
225	C₂×C₄×C₆₁	—	2	1	no	—
226	C₂×C₄×C₆₁	—	2	1	no	—
227	C₂×C₄×C₆₁	—	2	1	no	—
228	C₂×C₄×C₆₁	—	4	4	no	—
229	C₂×C₄×C₆₁	—	4	2	no	—
230	C₂×C₄×C₆₁	—	4	2	no	—
231	C₂×C₄×C₆₁	—	4	2	no	—
232	C₂×C₄×C₆₁	—	4	2	no	—
233	C₂×C₄×C₆₁	—	4	2	no	—
234	C₂×C₄×C₆₁	—	4	2	no	—
235	C₂×C₄×C₆₁	—	4	1	no	—
236	C₂×C₄×C₆₁	—	4	1	no	—
237	C₂×C₄×C₆₁	—	4	1	no	—
238	C₂×C₄×C₆₁	—	4	1	no	—
239	C₂×C₄×C₆₁	—	4	1	no	—
240	C₂×C₄×C₆₁	—	4	1	no	—
241	C₂×C₄×C₆₁	—	4	1	no	—
242	C₂×C₄×C₆₁	—	4	1	no	—
243	C₂×C₄×C₆₁	—	4	1	no	—
244	C₂×C₄×C₆₁	#120	1	2	yes	—
245	C₂×C₄×C₆₁	#120	1	2	yes	—
246	C₂×C₄×C₆₁	#137	1	2	yes	—
247	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
250	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
251	C₈×C₆₁	—	2	4	no	—
252	C₈×C₆₁	—	4	2	no	—
253	#25603	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂²×C₆₁	—	2	2	no	—
255	C₂²×C₆₁	—	2	2	no	—
256	C₂²×C₆₁	—	2	2	no	—
257	C₂²×C₆₁	—	4	1	no	—
258	C₂²×C₆₁	—	4	1	no	—
259	C₂²×C₆₁	—	4	1	no	—
260	C₂²×C₆₁	—	4	1	no	—
261	C₂²×C₆₁	—	8	1	no	—
262	C₂²×C₆₁	—	8	1	no	—
263	C₂²×C₆₁	—	8	1	no	—
264	C₂²×C₆₁	—	8	1	no	—
265	C₂²×C₆₁	—	8	1	no	—
266	C₂²×C₆₁	—	8	1	no	—
267	C₂²×C₆₁	—	8	1	no	—
268	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
269	C₂²×C₆₁	#532	1	1	yes	characteristic
270	C₂²×C₆₁	#535	1	1	yes	characteristic
271	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
272	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
273	C₂²×C₆₁	#575	1	1	yes	characteristic
274	C₂²×C₆₁	#575	1	1	yes	characteristic
275	C₄×C₆₁	—	2	2	no	—
276	C₄×C₆₁	—	2	2	no	—
277	C₄×C₆₁	—	2	2	no	—
278	C₄×C₆₁	—	4	1	no	—
279	C₄×C₆₁	—	4	4	no	—
280	C₄×C₆₁	—	4	1	no	—
281	C₄×C₆₁	—	4	4	no	—
282	C₄×C₆₁	—	8	1	no	—
283	C₄×C₆₁	—	8	1	no	—
284	C₄×C₆₁	—	8	1	no	—
285	C₄×C₆₁	#546	1	2	yes	—
286	C₄×C₆₁	#550	1	2	yes	—
287	C₂×#533	C₂×C₆₁	1	1	yes	characteristic, complemented
288	C₂×#497	C₂×C₆₁	1	1	yes	characteristic, complemented
289	C₂×#489	C₂×C₆₁	1	1	yes	characteristic, complemented
290	#2850	C₂×C₆₁	1	1	yes	characteristic
291	#2001	C₂×C₆₁	1	2	yes	complemented
292	#2000	C₂×C₆₁	1	2	yes	—
293	#1993	C₂×C₆₁	1	1	yes	characteristic, complemented
294	#1960	C₂×C₆₁	1	1	yes	characteristic, complemented
295	#1880	C₂×C₆₁	1	2	yes	complemented
296	#1878	C₂×C₆₁	1	2	yes	complemented
297	#1749	C₂×C₆₁	1	1	yes	characteristic, complemented
298	C₂×C₆₁	—	4	2	no	—
299	C₂×C₆₁	—	16	1	no	—
300	C₂×C₆₁	#2431	1	1	yes	characteristic
301	C₂×C₆₁	#3004	1	1	yes	characteristic
302	C₂×C₆₁	#3005	1	1	yes	characteristic
303	C₂×C₆₁	#3172	1	1	yes	characteristic
304	C₂×C₆₁	#3181	1	1	yes	characteristic
305	C₂×C₆₁	#3215	1	1	yes	characteristic
306	C₂×C₆₁	#3216	1	1	yes	characteristic
307	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
308	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
309	#533	—	2	4	no	—
310	#533	—	2	4	no	—
311	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
312	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
313	C₂×#125	—	2	1	no	—
314	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
315	C₂×C₂²⋊Q₈	—	2	1	no	—
316	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
317	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
318	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
319	C₂×C₄×Q₈	—	2	1	no	—
320	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
321	C₂×#117	—	2	1	no	—
322	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
323	#497	—	2	4	no	—
324	#489	—	2	4	no	—
325	C₂×#103	C₂²×C₆₁	1	2	yes	—
326	C₂×#103	C₂²×C₆₁	1	2	yes	—
327	C₂×#103	C₂²×C₆₁	1	2	yes	—
328	C₂×#102	C₂²×C₆₁	1	2	yes	—
329	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
330	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
331	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
332	#391	C₂²×C₆₁	1	1	yes	characteristic
333	#390	C₂²×C₆₁	1	1	yes	characteristic
334	#388	—	2	1	no	—
335	#388	—	2	1	no	—
336	#386	—	2	1	no	—
337	#386	—	2	1	no	—
338	#382	C₂²×C₆₁	1	1	yes	characteristic
339	#340	C₂²×C₆₁	1	2	yes	—
340	#340	C₂²×C₆₁	1	2	yes	—
341	#336	C₂²×C₆₁	1	2	yes	—
342	C₆₁	#25603	1	1	yes	characteristic, direct product factor, Sylow
343	C₂²×Q₈	—	2	1	no	—
344	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
345	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
348	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
349	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
351	C₂×Q₁₆	—	2	4	no	—
352	C₂×Q₁₆	—	2	4	no	—
353	C₂×Q₁₆	—	4	2	no	—
354	C₂×SD₁₆	—	2	4	no	—
355	C₂×SD₁₆	—	2	4	no	—
356	C₂×SD₁₆	—	4	2	no	—
357	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
358	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
359	C₄⋊Q₈	—	2	2	no	—
360	C₄⋊Q₈	—	2	2	no	—
361	C₄⋊Q₈	D₄×C₆₁	1	4	yes	complemented
362	C₄⋊Q₈	D₄×C₆₁	1	4	yes	complemented
363	#125	—	2	8	no	—
364	#124	—	2	2	no	—
365	#124	—	2	2	no	—
366	C₂²⋊Q₈	—	2	8	no	—
367	C₂²⋊Q₈	—	2	4	no	—
368	C₂²⋊Q₈	—	2	4	no	—
369	C₂²⋊Q₈	—	4	2	no	—
370	#121	—	4	2	no	—
371	C₄×Q₈	—	2	8	no	—
372	C₄×Q₈	—	2	4	no	—
373	C₄×Q₈	—	2	4	no	—
374	#117	—	2	8	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
384	C₂×C₂²⋊C₄	—	2	2	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₄²	—	2	2	no	—
392	C₂×C₄²	—	2	2	no	—
393	C₂×C₄²	—	2	2	no	—
394	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
395	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
397	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
398	#103	—	2	4	no	—
399	#103	—	4	2	no	—
400	#103	—	4	2	no	—
401	#102	—	2	4	no	—
402	C₂²⋊C₈	—	2	4	no	—
403	#97	—	2	2	no	—
404	#97	—	2	2	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	C₂⁴	—	2	1	no	—
410	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
411	C₂×Q₈	—	2	4	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	4	2	no	—
422	C₂×Q₈	—	4	2	no	—
423	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	4	2	no	—
429	C₂×D₄	—	4	2	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
451	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
452	Q₁₆	—	4	8	no	—
453	SD₁₆	—	4	8	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	#41×C₆₁	1	4	yes	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	4	2	no	—
469	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	—	4	2	no	—
472	C₂²⋊C₄	—	4	2	no	—
473	C₂²⋊C₄	—	4	2	no	—
474	C₂²⋊C₄	—	4	2	no	—
475	C₂²⋊C₄	—	4	2	no	—
476	C₂²⋊C₄	—	4	2	no	—
477	C₄²	—	2	8	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	C₂×D₄×C₆₁	1	2	yes	—
483	C₄²	C₂×D₄×C₆₁	1	2	yes	—
484	C₂³	—	2	1	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	#137×C₆₁	1	2	yes	—
498	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
499	Q₈	—	2	4	no	—
500	Q₈	—	2	4	no	—
501	Q₈	—	4	8	no	—
502	Q₈	—	4	2	no	—
503	Q₈	—	4	2	no	—
504	Q₈	—	4	2	no	—
505	Q₈	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	8	4	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	#120×C₆₁	1	2	yes	—
541	C₂×C₄	#120×C₆₁	1	2	yes	—
542	C₂×C₄	#137×C₆₁	1	2	yes	—
543	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
545	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
546	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
547	C₈	—	2	4	no	—
548	C₈	—	4	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	—	8	1	no	—
560	C₂²	—	8	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
564	C₂²	C₆₁×#532	1	1	yes	characteristic
565	C₂²	C₆₁×#535	1	1	yes	characteristic
566	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
567	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
568	C₂²	C₆₁×#575	1	1	yes	characteristic
569	C₂²	C₆₁×#575	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	4	no	—
577	C₄	—	8	1	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	1	no	—
580	C₄	C₆₁×#546	1	2	yes	—
581	C₄	C₆₁×#550	1	2	yes	—
582	C₂	—	4	2	no	—
583	C₂	—	16	1	no	—
584	C₂	C₆₁×#2431	1	1	yes	characteristic
585	C₂	C₆₁×#3004	1	1	yes	characteristic
586	C₂	C₆₁×#3005	1	1	yes	characteristic
587	C₂	C₆₁×#3172	1	1	yes	characteristic
588	C₂	C₆₁×#3181	1	1	yes	characteristic
589	C₂	C₆₁×#3215	1	1	yes	characteristic
590	C₂	C₆₁×#3216	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#121×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#533	C₂	semidirect
2. C₂×C₆₁×#497	C₂	semidirect
3. C₂×C₆₁×#489	C₂	semidirect
5. C₆₁×#2001	C₂	semidirect
7. C₆₁×#1993	C₂	semidirect
8. C₆₁×#1960	C₂	semidirect
9. C₆₁×#1880	C₂	semidirect
10. C₆₁×#1878	C₂	semidirect
11. C₆₁×#1749	C₂	semidirect
65. C₄⋊Q₈×C₆₁	D₄	semidirect
66. C₄⋊Q₈×C₆₁	D₄	semidirect
253. #25603	C₆₁	direct (N × H)
287. C₂×#533	C₂×C₆₁	semidirect
288. C₂×#497	C₂×C₆₁	semidirect
289. C₂×#489	C₂×C₆₁	semidirect
291. #2001	C₂×C₆₁	semidirect
293. #1993	C₂×C₆₁	semidirect
294. #1960	C₂×C₆₁	semidirect
295. #1880	C₂×C₆₁	semidirect
296. #1878	C₂×C₆₁	semidirect
297. #1749	C₂×C₆₁	semidirect
342. C₆₁	#25603	direct (N × H)
361. C₄⋊Q₈	D₄×C₆₁	semidirect
362. C₄⋊Q₈	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×#533	2
C₂×C₆₁×#497	2
C₂×C₆₁×#489	2
C₆₁×#2850	2
C₆₁×#2001	2
C₆₁×#2000	2
C₆₁×#1993	2
C₆₁×#1960	2
C₆₁×#1880	2
C₆₁×#1878	2
C₆₁×#1749	2
#25603	61

Subgroups — C61×#25603 #29529036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25603 #29529036