Subgroups — C₆₁×#10934 #29514367

Order 15616.

982 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#104×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#416	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#408	C₂	1	1	yes	maximal, characteristic
4	C₂×C₆₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₆₁×#339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₆₁×#336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#104×C₆₁	—	2	2	no	—
16	C₂×#104×C₆₁	—	2	2	no	—
17	C₂×#104×C₆₁	C₄	1	4	yes	complemented
18	C₆₁×#416	—	2	2	no	—
19	C₆₁×#416	—	2	2	no	—
20	C₂×#103×C₆₁	C₄	1	2	yes	complemented
21	C₂×#102×C₆₁	C₄	1	2	yes	complemented
22	C₆₁×#408	—	2	2	no	—
23	C₆₁×#408	C₄	1	4	yes	complemented
24	C₂×C₂²⋊C₈×C₆₁	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₆₁	—	2	1	no	—
26	C₆₁×#405	—	2	2	no	—
27	C₆₁×#405	—	2	2	no	—
28	C₂×#97×C₆₁	—	2	1	no	—
29	C₂×C₄×C₈×C₆₁	—	2	1	no	—
30	C₆₁×#341	—	2	2	no	—
31	C₆₁×#339	—	2	2	no	—
32	C₆₁×#336	—	2	2	no	—
33	C₂×#41×C₆₁	—	2	1	no	—
34	C₂×#41×C₆₁	—	2	1	no	—
35	C₂×#41×C₆₁	—	2	1	no	—
36	C₂×#41×C₆₁	—	2	1	no	—
37	C₂×#41×C₆₁	—	2	1	no	—
38	C₂×#41×C₆₁	—	2	1	no	—
39	C₂×#41×C₆₁	—	2	1	no	—
40	C₂×#41×C₆₁	—	2	1	no	—
41	C₂×#41×C₆₁	—	2	1	no	—
42	C₂×#41×C₆₁	—	2	1	no	—
43	C₂×#41×C₆₁	C₂×C₄	1	2	yes	—
44	C₂×#41×C₆₁	C₂×C₄	1	2	yes	—
45	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₄×C₆₁	—	2	1	no	—
47	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₆₁	—	2	1	no	—
49	C₂³×C₄×C₆₁	—	2	1	no	—
50	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₆₁	—	2	1	no	—
52	C₂×M₁₆×C₆₁	—	2	1	no	—
53	C₂×M₁₆×C₆₁	—	2	1	no	—
54	C₂×M₁₆×C₆₁	—	2	1	no	—
55	C₂×M₁₆×C₆₁	—	2	1	no	—
56	C₂×M₁₆×C₆₁	—	2	1	no	—
57	C₂×M₁₆×C₆₁	—	2	1	no	—
58	C₂×M₁₆×C₆₁	—	2	1	no	—
59	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
60	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
61	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
62	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
63	C₂²×C₈×C₆₁	—	2	1	no	—
64	C₂²×C₈×C₆₁	—	2	1	no	—
65	C₂²×C₈×C₆₁	—	2	1	no	—
66	C₂²×C₈×C₆₁	—	2	1	no	—
67	C₂²×C₈×C₆₁	—	2	1	no	—
68	C₂²×C₈×C₆₁	—	2	1	no	—
69	C₂²×C₈×C₆₁	—	2	1	no	—
70	C₂²×C₈×C₆₁	—	2	1	no	—
71	C₂²×C₈×C₆₁	—	2	1	no	—
72	C₂²×C₈×C₆₁	—	2	1	no	—
73	C₂²×C₈×C₆₁	—	2	1	no	—
74	C₂²×C₈×C₆₁	—	2	1	no	—
75	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
76	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
77	C₂²×C₈×C₆₁	D₄	1	2	yes	—
78	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
80	#117×C₆₁	—	2	1	no	—
81	#117×C₆₁	—	2	1	no	—
82	#117×C₆₁	D₄	1	2	yes	—
83	#117×C₆₁	D₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
86	C₂×C₄²×C₆₁	—	2	1	no	—
87	C₂×C₄²×C₆₁	—	2	1	no	—
88	C₂×C₄²×C₆₁	—	2	1	no	—
89	C₂×C₄²×C₆₁	—	2	1	no	—
90	C₂×C₄²×C₆₁	—	2	1	no	—
91	C₂×C₄²×C₆₁	—	2	1	no	—
92	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
93	#104×C₆₁	—	2	8	no	—
94	#103×C₆₁	—	2	4	no	—
95	#102×C₆₁	—	2	4	no	—
96	C₂²⋊C₈×C₆₁	—	2	4	no	—
97	C₂²⋊C₈×C₆₁	—	2	4	no	—
98	#97×C₆₁	—	2	4	no	—
99	C₄×C₈×C₆₁	—	2	4	no	—
100	C₂⁴×C₆₁	—	2	1	no	—
101	C₂⁴×C₆₁	#41	1	1	yes	characteristic
102	#41×C₆₁	—	2	2	no	—
103	#41×C₆₁	—	2	2	no	—
104	#41×C₆₁	—	2	2	no	—
105	#41×C₆₁	—	2	2	no	—
106	#41×C₆₁	—	2	2	no	—
107	#41×C₆₁	—	2	2	no	—
108	#41×C₆₁	—	2	2	no	—
109	#41×C₆₁	—	2	2	no	—
110	#41×C₆₁	—	4	1	no	—
111	#41×C₆₁	—	4	1	no	—
112	#41×C₆₁	—	4	1	no	—
113	#41×C₆₁	—	4	1	no	—
114	#41×C₆₁	—	4	1	no	—
115	#41×C₆₁	—	4	1	no	—
116	#41×C₆₁	—	4	1	no	—
117	#41×C₆₁	—	4	1	no	—
118	C₂×Q₈×C₆₁	—	2	1	no	—
119	C₂×Q₈×C₆₁	—	2	1	no	—
120	C₂×Q₈×C₆₁	—	2	1	no	—
121	C₂×Q₈×C₆₁	—	2	1	no	—
122	C₂×Q₈×C₆₁	—	2	1	no	—
123	C₂×Q₈×C₆₁	C₄²	1	2	yes	—
124	C₂×D₄×C₆₁	—	2	2	no	—
125	C₂×D₄×C₆₁	—	2	2	no	—
126	C₂×D₄×C₆₁	—	2	1	no	—
127	C₂×D₄×C₆₁	—	2	1	no	—
128	C₂×D₄×C₆₁	—	2	1	no	—
129	C₂×D₄×C₆₁	—	2	1	no	—
130	C₂×D₄×C₆₁	—	2	1	no	—
131	C₂×D₄×C₆₁	—	4	1	no	—
132	C₂×D₄×C₆₁	—	4	1	no	—
133	C₂×D₄×C₆₁	—	4	1	no	—
134	C₂×D₄×C₆₁	—	4	1	no	—
135	C₂×D₄×C₆₁	C₄²	1	2	yes	—
136	C₂²×C₄×C₆₁	—	2	4	no	—
137	C₂²×C₄×C₆₁	—	2	2	no	—
138	C₂²×C₄×C₆₁	—	2	2	no	—
139	C₂²×C₄×C₆₁	—	2	1	no	—
140	C₂²×C₄×C₆₁	—	2	2	no	—
141	C₂²×C₄×C₆₁	—	2	2	no	—
142	C₂²×C₄×C₆₁	—	4	2	no	—
143	C₂²×C₄×C₆₁	—	4	1	no	—
144	C₂²×C₄×C₆₁	—	4	1	no	—
145	C₂²×C₄×C₆₁	—	4	1	no	—
146	C₂²×C₄×C₆₁	—	4	1	no	—
147	C₂²×C₄×C₆₁	—	4	1	no	—
148	C₂²×C₄×C₆₁	—	4	1	no	—
149	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₁	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
159	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
160	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
161	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
162	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
163	M₁₆×C₆₁	—	2	2	no	—
164	M₁₆×C₆₁	—	2	2	no	—
165	M₁₆×C₆₁	—	2	2	no	—
166	M₁₆×C₆₁	—	2	2	no	—
167	M₁₆×C₆₁	—	2	2	no	—
168	M₁₆×C₆₁	—	4	1	no	—
169	M₁₆×C₆₁	—	4	1	no	—
170	M₁₆×C₆₁	C₂²⋊C₄	1	4	yes	—
171	C₂×C₈×C₆₁	—	2	2	no	—
172	C₂×C₈×C₆₁	—	2	2	no	—
173	C₂×C₈×C₆₁	—	2	2	no	—
174	C₂×C₈×C₆₁	—	2	1	no	—
175	C₂×C₈×C₆₁	—	2	2	no	—
176	C₂×C₈×C₆₁	—	2	1	no	—
177	C₂×C₈×C₆₁	—	2	2	no	—
178	C₂×C₈×C₆₁	—	2	2	no	—
179	C₂×C₈×C₆₁	—	2	2	no	—
180	C₂×C₈×C₆₁	—	2	1	no	—
181	C₂×C₈×C₆₁	—	2	1	no	—
182	C₂×C₈×C₆₁	—	2	2	no	—
183	C₂×C₈×C₆₁	—	2	2	no	—
184	C₂×C₈×C₆₁	—	2	2	no	—
185	C₂×C₈×C₆₁	—	2	2	no	—
186	C₂×C₈×C₆₁	—	4	1	no	—
187	C₂×C₈×C₆₁	—	4	1	no	—
188	C₂×C₈×C₆₁	—	4	1	no	—
189	C₂×C₈×C₆₁	—	4	1	no	—
190	C₂×C₈×C₆₁	—	4	1	no	—
191	C₂×C₈×C₆₁	—	4	1	no	—
192	C₂×C₈×C₆₁	C₂²⋊C₄	1	2	yes	—
193	C₂×C₈×C₆₁	C₂²⋊C₄	1	2	yes	—
194	C₄⋊C₄×C₆₁	—	2	2	no	—
195	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
196	C₂²⋊C₄×C₆₁	—	2	2	no	—
197	C₂²⋊C₄×C₆₁	—	2	2	no	—
198	C₄²×C₆₁	—	2	2	no	—
199	C₄²×C₆₁	—	2	2	no	—
200	C₄²×C₆₁	—	2	2	no	—
201	C₄²×C₆₁	—	2	2	no	—
202	C₄²×C₆₁	—	4	1	no	—
203	C₄²×C₆₁	—	4	1	no	—
204	C₂³×C₆₁	—	2	2	no	—
205	C₂³×C₆₁	—	2	2	no	—
206	C₂³×C₆₁	—	2	2	no	—
207	C₂³×C₆₁	—	4	1	no	—
208	C₂³×C₆₁	—	4	1	no	—
209	C₂³×C₆₁	—	4	2	no	—
210	C₂³×C₆₁	—	4	2	no	—
211	C₂³×C₆₁	#117	1	1	yes	characteristic
212	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
213	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
214	C₂³×C₆₁	#121	1	1	yes	characteristic
215	C₂³×C₆₁	#123	1	1	yes	characteristic
216	C₂³×C₆₁	#124	1	1	yes	characteristic
217	C₂³×C₆₁	#126	1	1	yes	characteristic
218	Q₈×C₆₁	—	2	2	no	—
219	Q₈×C₆₁	—	2	2	no	—
220	Q₈×C₆₁	—	4	1	no	—
221	Q₈×C₆₁	—	4	1	no	—
222	D₄×C₆₁	—	2	2	no	—
223	D₄×C₆₁	—	2	2	no	—
224	D₄×C₆₁	—	4	2	no	—
225	D₄×C₆₁	—	4	2	no	—
226	D₄×C₆₁	—	4	2	no	—
227	D₄×C₆₁	—	4	2	no	—
228	D₄×C₆₁	—	4	1	no	—
229	D₄×C₆₁	—	4	1	no	—
230	C₂×C₄×C₆₁	—	2	4	no	—
231	C₂×C₄×C₆₁	—	2	2	no	—
232	C₂×C₄×C₆₁	—	2	4	no	—
233	C₂×C₄×C₆₁	—	4	4	no	—
234	C₂×C₄×C₆₁	—	4	4	no	—
235	C₂×C₄×C₆₁	—	4	2	no	—
236	C₂×C₄×C₆₁	—	4	1	no	—
237	C₂×C₄×C₆₁	—	4	1	no	—
238	C₂×C₄×C₆₁	—	4	2	no	—
239	C₂×C₄×C₆₁	—	4	2	no	—
240	C₂×C₄×C₆₁	—	4	2	no	—
241	C₂×C₄×C₆₁	—	4	2	no	—
242	C₂×C₄×C₆₁	—	4	2	no	—
243	C₂×C₄×C₆₁	—	4	2	no	—
244	C₂×C₄×C₆₁	—	4	2	no	—
245	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
246	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₆₁	#117	1	1	yes	characteristic
250	C₂×C₄×C₆₁	#117	1	1	yes	characteristic
251	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
260	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
261	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
262	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
263	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
264	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
265	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
266	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
267	C₂×C₄×C₆₁	#123	1	1	yes	characteristic
268	C₂×C₄×C₆₁	#123	1	1	yes	characteristic
269	C₂×C₄×C₆₁	#124	1	1	yes	characteristic
270	C₂×C₄×C₆₁	#124	1	1	yes	characteristic
271	C₂×C₄×C₆₁	#126	1	1	yes	characteristic
272	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
273	C₈×C₆₁	—	2	2	no	—
274	C₈×C₆₁	—	2	2	no	—
275	C₈×C₆₁	—	2	4	no	—
276	C₈×C₆₁	—	4	2	no	—
277	C₈×C₆₁	—	4	2	no	—
278	#10934	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
279	C₂²×C₆₁	—	2	2	no	—
280	C₂²×C₆₁	—	2	2	no	—
281	C₂²×C₆₁	—	2	2	no	—
282	C₂²×C₆₁	—	2	2	no	—
283	C₂²×C₆₁	—	2	1	no	—
284	C₂²×C₆₁	—	2	1	no	—
285	C₂²×C₆₁	—	2	1	no	—
286	C₂²×C₆₁	—	2	1	no	—
287	C₂²×C₆₁	—	4	2	no	—
288	C₂²×C₆₁	—	4	2	no	—
289	C₂²×C₆₁	—	4	2	no	—
290	C₂²×C₆₁	—	8	2	no	—
291	C₂²×C₆₁	—	8	2	no	—
292	C₂²×C₆₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
293	C₂²×C₆₁	#386	1	1	yes	characteristic
294	C₂²×C₆₁	#388	1	1	yes	characteristic
295	C₂²×C₆₁	#388	1	1	yes	characteristic
296	C₂²×C₆₁	#388	1	1	yes	characteristic
297	C₂²×C₆₁	#388	1	1	yes	characteristic
298	C₂²×C₆₁	#390	1	1	yes	characteristic
299	C₂²×C₆₁	#443	1	2	yes	—
300	C₂²×C₆₁	#444	1	2	yes	—
301	C₄×C₆₁	—	4	4	no	—
302	C₄×C₆₁	—	4	4	no	—
303	C₄×C₆₁	—	4	2	no	—
304	C₄×C₆₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
305	C₄×C₆₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
306	C₄×C₆₁	#386	1	1	yes	characteristic
307	C₄×C₆₁	#386	1	1	yes	characteristic
308	C₄×C₆₁	#388	1	1	yes	characteristic
309	C₄×C₆₁	#388	1	1	yes	characteristic
310	C₄×C₆₁	#390	1	1	yes	characteristic
311	C₄×C₆₁	#390	1	1	yes	characteristic
312	C₂²×#104	C₂×C₆₁	1	1	yes	characteristic
313	C₂×#416	C₂×C₆₁	1	1	yes	characteristic
314	C₂×#408	C₂×C₆₁	1	1	yes	characteristic
315	C₂×#405	C₂×C₆₁	1	1	yes	characteristic, complemented
316	C₂×#341	C₂×C₆₁	1	1	yes	characteristic, complemented
317	C₂×#339	C₂×C₆₁	1	1	yes	characteristic, complemented
318	C₂×#336	C₂×C₆₁	1	1	yes	characteristic, complemented
319	C₂×C₆₁	—	2	1	no	—
320	C₂×C₆₁	—	2	1	no	—
321	C₂×C₆₁	—	2	1	no	—
322	C₂×C₆₁	—	2	1	no	—
323	C₂×C₆₁	—	8	2	no	—
324	C₂×C₆₁	#1437	1	1	yes	characteristic
325	C₂×C₆₁	#1764	1	1	yes	characteristic
326	C₂×C₆₁	#1765	1	1	yes	characteristic
327	C₂×C₆₁	#1876	1	2	yes	—
328	C₂×C₆₁	#1929	1	2	yes	—
329	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
330	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
331	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
332	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
333	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
334	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
335	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
336	C₂×#104	—	2	2	no	—
337	C₂×#104	—	2	2	no	—
338	C₂×#104	C₄×C₆₁	1	4	yes	complemented
339	#416	—	2	2	no	—
340	#416	—	2	2	no	—
341	C₂×#103	C₄×C₆₁	1	2	yes	complemented
342	C₂×#102	C₄×C₆₁	1	2	yes	complemented
343	#408	—	2	2	no	—
344	#408	C₄×C₆₁	1	4	yes	complemented
345	C₂×C₂²⋊C₈	—	2	1	no	—
346	C₂×C₂²⋊C₈	—	2	1	no	—
347	#405	—	2	2	no	—
348	#405	—	2	2	no	—
349	C₂×#97	—	2	1	no	—
350	C₂×C₄×C₈	—	2	1	no	—
351	#341	—	2	2	no	—
352	#339	—	2	2	no	—
353	#336	—	2	2	no	—
354	C₆₁	#10934	1	1	yes	characteristic, direct product factor, Sylow
355	C₂×#41	—	2	1	no	—
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	—	2	1	no	—
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	1	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	2	1	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	—	2	1	no	—
365	C₂×#41	C₂×C₄×C₆₁	1	2	yes	—
366	C₂×#41	C₂×C₄×C₆₁	1	2	yes	—
367	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
368	C₂²×D₄	—	2	1	no	—
369	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	C₂×C₄×C₆₁	1	2	yes	—
382	C₂×M₁₆	C₂×C₄×C₆₁	1	2	yes	—
383	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
384	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
385	C₂²×C₈	—	2	1	no	—
386	C₂²×C₈	—	2	1	no	—
387	C₂²×C₈	—	2	1	no	—
388	C₂²×C₈	—	2	1	no	—
389	C₂²×C₈	—	2	1	no	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	—	2	1	no	—
394	C₂²×C₈	—	2	1	no	—
395	C₂²×C₈	—	2	1	no	—
396	C₂²×C₈	—	2	1	no	—
397	C₂²×C₈	C₂×C₄×C₆₁	1	2	yes	—
398	C₂²×C₈	C₂×C₄×C₆₁	1	2	yes	—
399	C₂²×C₈	D₄×C₆₁	1	2	yes	—
400	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
401	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
402	#117	—	2	1	no	—
403	#117	—	2	1	no	—
404	#117	D₄×C₆₁	1	2	yes	—
405	#117	D₄×C₆₁	1	2	yes	—
406	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	C₂×C₄×C₆₁	1	2	yes	—
415	#104	—	2	8	no	—
416	#103	—	2	4	no	—
417	#102	—	2	4	no	—
418	C₂²⋊C₈	—	2	4	no	—
419	C₂²⋊C₈	—	2	4	no	—
420	#97	—	2	4	no	—
421	C₄×C₈	—	2	4	no	—
422	C₂⁴	—	2	1	no	—
423	C₂⁴	#41×C₆₁	1	1	yes	characteristic
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	#41	—	2	2	no	—
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	4	1	no	—
433	#41	—	4	1	no	—
434	#41	—	4	1	no	—
435	#41	—	4	1	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	4	1	no	—
439	#41	—	4	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	C₄²×C₆₁	1	2	yes	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	4	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	C₄²×C₆₁	1	2	yes	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	—	4	1	no	—
471	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
472	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
473	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
480	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
481	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
482	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
483	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
484	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	2	2	no	—
489	M₁₆	—	2	2	no	—
490	M₁₆	—	4	1	no	—
491	M₁₆	—	4	1	no	—
492	M₁₆	C₂²⋊C₄×C₆₁	1	4	yes	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	4	1	no	—
509	C₂×C₈	—	4	1	no	—
510	C₂×C₈	—	4	1	no	—
511	C₂×C₈	—	4	1	no	—
512	C₂×C₈	—	4	1	no	—
513	C₂×C₈	—	4	1	no	—
514	C₂×C₈	C₂²⋊C₄×C₆₁	1	2	yes	—
515	C₂×C₈	C₂²⋊C₄×C₆₁	1	2	yes	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	2	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	4	1	no	—
525	C₄²	—	4	1	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	4	2	no	—
532	C₂³	—	4	2	no	—
533	C₂³	#117×C₆₁	1	1	yes	characteristic
534	C₂³	C₄×D₄×C₆₁	1	1	yes	characteristic
535	C₂³	C₄×D₄×C₆₁	1	1	yes	characteristic
536	C₂³	#121×C₆₁	1	1	yes	characteristic
537	C₂³	#123×C₆₁	1	1	yes	characteristic
538	C₂³	#124×C₆₁	1	1	yes	characteristic
539	C₂³	#126×C₆₁	1	1	yes	characteristic
540	Q₈	—	2	2	no	—
541	Q₈	—	2	2	no	—
542	Q₈	—	4	1	no	—
543	Q₈	—	4	1	no	—
544	D₄	—	2	2	no	—
545	D₄	—	2	2	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	2	no	—
548	D₄	—	4	2	no	—
549	D₄	—	4	2	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	1	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	C₂×C₄²×C₆₁	1	1	yes	characteristic
568	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
569	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
570	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
571	C₂×C₄	#117×C₆₁	1	1	yes	characteristic
572	C₂×C₄	#117×C₆₁	1	1	yes	characteristic
573	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
574	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
575	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
576	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
577	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
578	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
579	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
580	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
581	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
582	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
583	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
584	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
585	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
586	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
587	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
588	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
589	C₂×C₄	#123×C₆₁	1	1	yes	characteristic
590	C₂×C₄	#123×C₆₁	1	1	yes	characteristic
591	C₂×C₄	#124×C₆₁	1	1	yes	characteristic
592	C₂×C₄	#124×C₆₁	1	1	yes	characteristic
593	C₂×C₄	#126×C₆₁	1	1	yes	characteristic
594	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
595	C₈	—	2	2	no	—
596	C₈	—	2	2	no	—
597	C₈	—	2	4	no	—
598	C₈	—	4	2	no	—
599	C₈	—	4	2	no	—
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	8	2	no	—
612	C₂²	—	8	2	no	—
613	C₂²	C₄×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
614	C₂²	C₆₁×#386	1	1	yes	characteristic
615	C₂²	C₆₁×#388	1	1	yes	characteristic
616	C₂²	C₆₁×#388	1	1	yes	characteristic
617	C₂²	C₆₁×#388	1	1	yes	characteristic
618	C₂²	C₆₁×#388	1	1	yes	characteristic
619	C₂²	C₆₁×#390	1	1	yes	characteristic
620	C₂²	C₆₁×#443	1	2	yes	—
621	C₂²	C₆₁×#444	1	2	yes	—
622	C₄	—	4	4	no	—
623	C₄	—	4	4	no	—
624	C₄	—	4	2	no	—
625	C₄	C₄×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
626	C₄	C₄×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
627	C₄	C₆₁×#386	1	1	yes	characteristic
628	C₄	C₆₁×#386	1	1	yes	characteristic
629	C₄	C₆₁×#388	1	1	yes	characteristic
630	C₄	C₆₁×#388	1	1	yes	characteristic
631	C₄	C₆₁×#390	1	1	yes	characteristic
632	C₄	C₆₁×#390	1	1	yes	characteristic
633	C₂	—	2	1	no	—
634	C₂	—	2	1	no	—
635	C₂	—	2	1	no	—
636	C₂	—	2	1	no	—
637	C₂	—	8	2	no	—
638	C₂	C₆₁×#1437	1	1	yes	characteristic
639	C₂	C₆₁×#1764	1	1	yes	characteristic
640	C₂	C₆₁×#1765	1	1	yes	characteristic
641	C₂	C₆₁×#1876	1	2	yes	—
642	C₂	C₆₁×#1929	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₆₁
Frattini, cosocle	C₂³×C₄	C₂³×C₆₁
socle	C₂³×C₆₁	C₄×D₄
prime radical	C₂²×#41×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ C₂³×C₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₆₁×#405	C₂	semidirect
5. C₂×C₆₁×#341	C₂	semidirect
6. C₂×C₆₁×#339	C₂	semidirect
7. C₂×C₆₁×#336	C₂	semidirect
17. C₂×#104×C₆₁	C₄	semidirect
20. C₂×#103×C₆₁	C₄	semidirect
21. C₂×#102×C₆₁	C₄	semidirect
23. C₆₁×#408	C₄	semidirect
278. #10934	C₆₁	direct (N × H)
315. C₂×#405	C₂×C₆₁	semidirect
316. C₂×#341	C₂×C₆₁	semidirect
317. C₂×#339	C₂×C₆₁	semidirect
318. C₂×#336	C₂×C₆₁	semidirect
338. C₂×#104	C₄×C₆₁	semidirect
341. C₂×#103	C₄×C₆₁	semidirect
342. C₂×#102	C₄×C₆₁	semidirect
344. #408	C₄×C₆₁	semidirect
354. C₆₁	#10934	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#104×C₆₁	2
C₂×C₆₁×#416	2
C₂×C₆₁×#408	2
C₂×C₆₁×#405	2
C₂×C₆₁×#341	2
C₂×C₆₁×#339	2
C₂×C₆₁×#336	2
#10934	61

Subgroups — C61×#10934 #29514367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#10934 #29514367