Subgroups — C₆₁×#21424 #29524857

Order 15616.

1380 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#532	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1997	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1965	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1900	C₂	1	4	yes	maximal, complemented
7	C₄×#100×C₆₁	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₆₁	C₄	1	2	yes	—
9	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
10	C₆₁×#532	—	2	1	no	—
11	C₆₁×#532	—	2	1	no	—
12	C₆₁×#532	—	2	1	no	—
13	C₆₁×#532	—	2	1	no	—
14	C₆₁×#532	—	2	1	no	—
15	C₆₁×#532	—	2	1	no	—
16	C₆₁×#532	—	2	1	no	—
17	C₆₁×#532	—	2	1	no	—
18	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#124×C₆₁	C₄	1	2	yes	—
21	C₂×#121×C₆₁	C₄	1	2	yes	—
22	C₂×#121×C₆₁	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₆₁	C₄	1	2	yes	—
24	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
25	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#432	—	2	1	no	—
27	C₆₁×#432	—	2	1	no	—
28	C₆₁×#431	—	2	1	no	—
29	C₆₁×#431	—	2	1	no	—
30	C₆₁×#423	C₂²	1	2	yes	—
31	C₂×#100×C₆₁	C₂²	1	8	yes	—
32	C₆₁×#407	C₂²	1	2	yes	—
33	C₄×M₁₆×C₆₁	—	2	1	no	—
34	C₄×M₁₆×C₆₁	—	2	1	no	—
35	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
36	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
37	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
38	C₂×#97×C₆₁	—	2	1	no	—
39	C₂×C₄×C₈×C₆₁	—	2	1	no	—
40	C₆₁×#343	C₂²	1	8	yes	—
41	C₂×#41×C₆₁	—	2	2	no	—
42	C₂×#41×C₆₁	—	2	2	no	—
43	C₂×#41×C₆₁	—	2	2	no	—
44	C₂×#41×C₆₁	—	2	2	no	—
45	C₂×#41×C₆₁	—	4	8	no	—
46	C₂²×Q₈×C₆₁	C₂×C₄	1	2	yes	—
47	C₂²×D₄×C₆₁	C₂×C₄	1	2	yes	—
48	C₂²×D₄×C₆₁	C₂×C₄	1	2	yes	—
49	C₂²×D₄×C₆₁	C₂×C₄	1	4	yes	—
50	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
51	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₆₁	C₂×C₄	1	4	yes	—
53	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₆₁	—	2	2	no	—
56	C₂×M₁₆×C₆₁	—	2	8	no	—
57	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
58	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
59	C₂²×C₈×C₆₁	—	2	2	no	—
60	C₄⋊Q₈×C₆₁	—	2	1	no	—
61	C₄⋊Q₈×C₆₁	—	2	1	no	—
62	C₄⋊Q₈×C₆₁	—	2	1	no	—
63	C₄⋊Q₈×C₆₁	—	2	1	no	—
64	#127×C₆₁	—	2	1	no	—
65	#127×C₆₁	—	2	1	no	—
66	#127×C₆₁	—	2	1	no	—
67	#127×C₆₁	—	2	1	no	—
68	#124×C₆₁	—	2	2	no	—
69	#124×C₆₁	—	2	2	no	—
70	#124×C₆₁	—	2	2	no	—
71	#124×C₆₁	—	2	2	no	—
72	#121×C₆₁	—	2	2	no	—
73	#121×C₆₁	—	2	2	no	—
74	#121×C₆₁	—	2	2	no	—
75	#121×C₆₁	—	2	2	no	—
76	#121×C₆₁	—	2	2	no	—
77	#121×C₆₁	—	2	2	no	—
78	#121×C₆₁	—	2	2	no	—
79	#121×C₆₁	—	2	2	no	—
80	C₄×D₄×C₆₁	—	2	2	no	—
81	C₄×D₄×C₆₁	—	2	2	no	—
82	C₄×D₄×C₆₁	—	2	2	no	—
83	C₄×D₄×C₆₁	—	2	2	no	—
84	C₄×D₄×C₆₁	—	2	2	no	—
85	C₄×D₄×C₆₁	—	2	2	no	—
86	C₄×D₄×C₆₁	—	2	2	no	—
87	C₄×D₄×C₆₁	—	2	2	no	—
88	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
89	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
90	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
91	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
92	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
104	C₄⋊C₈×C₆₁	—	2	2	no	—
105	C₄⋊C₈×C₆₁	—	2	2	no	—
106	#100×C₆₁	—	2	16	no	—
107	C₂²⋊C₈×C₆₁	—	2	2	no	—
108	C₂²⋊C₈×C₆₁	—	2	2	no	—
109	#97×C₆₁	—	2	2	no	—
110	#97×C₆₁	—	2	2	no	—
111	#97×C₆₁	—	2	2	no	—
112	C₄×C₈×C₆₁	—	2	2	no	—
113	C₄×C₈×C₆₁	—	2	2	no	—
114	C₄×C₈×C₆₁	—	2	2	no	—
115	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
116	C₂⁴×C₆₁	C₂²×C₄	1	4	yes	—
117	#41×C₆₁	—	4	8	no	—
118	#41×C₆₁	—	4	8	no	—
119	#41×C₆₁	—	4	8	no	—
120	#41×C₆₁	—	4	8	no	—
121	C₂×Q₈×C₆₁	—	2	2	no	—
122	C₂×Q₈×C₆₁	—	2	2	no	—
123	C₂×Q₈×C₆₁	—	4	4	no	—
124	C₂×D₄×C₆₁	—	2	4	no	—
125	C₂×D₄×C₆₁	—	2	4	no	—
126	C₂×D₄×C₆₁	—	2	2	no	—
127	C₂×D₄×C₆₁	—	2	2	no	—
128	C₂×D₄×C₆₁	—	2	2	no	—
129	C₂×D₄×C₆₁	—	2	2	no	—
130	C₂×D₄×C₆₁	—	2	2	no	—
131	C₂×D₄×C₆₁	—	2	2	no	—
132	C₂×D₄×C₆₁	—	2	8	no	—
133	C₂×D₄×C₆₁	—	4	4	no	—
134	C₂×D₄×C₆₁	—	4	4	no	—
135	C₂×D₄×C₆₁	—	4	8	no	—
136	C₂²×C₄×C₆₁	—	2	4	no	—
137	C₂²×C₄×C₆₁	—	2	4	no	—
138	C₂²×C₄×C₆₁	—	2	4	no	—
139	C₂²×C₄×C₆₁	—	2	4	no	—
140	C₂²×C₄×C₆₁	—	4	2	no	—
141	C₂²×C₄×C₆₁	—	4	8	no	—
142	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
155	C₂²×C₄×C₆₁	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
161	M₁₆×C₆₁	—	2	8	no	—
162	M₁₆×C₆₁	—	2	4	no	—
163	M₁₆×C₆₁	—	2	8	no	—
164	M₁₆×C₆₁	#41	1	8	yes	complemented
165	C₂×C₈×C₆₁	—	2	8	no	—
166	C₂×C₈×C₆₁	—	2	4	no	—
167	C₂×C₈×C₆₁	—	2	4	no	—
168	C₄⋊C₄×C₆₁	—	2	2	no	—
169	C₄⋊C₄×C₆₁	—	2	2	no	—
170	C₄⋊C₄×C₆₁	—	2	2	no	—
171	C₄⋊C₄×C₆₁	—	2	2	no	—
172	C₂²⋊C₄×C₆₁	—	2	4	no	—
173	C₂²⋊C₄×C₆₁	—	2	4	no	—
174	C₂²⋊C₄×C₆₁	—	2	4	no	—
175	C₂²⋊C₄×C₆₁	—	2	4	no	—
176	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
177	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
178	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
179	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
180	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
181	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
182	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
183	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
184	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
192	C₂³×C₆₁	—	2	2	no	—
193	C₂³×C₆₁	—	2	2	no	—
194	C₂³×C₆₁	—	2	4	no	—
195	C₂³×C₆₁	—	2	8	no	—
196	C₂³×C₆₁	—	4	1	no	—
197	C₂³×C₆₁	—	4	4	no	—
198	C₂³×C₆₁	—	4	4	no	—
199	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
202	Q₈×C₆₁	—	4	4	no	—
203	Q₈×C₆₁	—	4	4	no	—
204	D₄×C₆₁	—	4	4	no	—
205	D₄×C₆₁	—	4	4	no	—
206	D₄×C₆₁	—	4	8	no	—
207	D₄×C₆₁	—	4	8	no	—
208	D₄×C₆₁	—	4	4	no	—
209	D₄×C₆₁	—	4	4	no	—
210	D₄×C₆₁	—	4	4	no	—
211	D₄×C₆₁	—	4	4	no	—
212	C₂×C₄×C₆₁	—	2	2	no	—
213	C₂×C₄×C₆₁	—	2	2	no	—
214	C₂×C₄×C₆₁	—	2	2	no	—
215	C₂×C₄×C₆₁	—	2	2	no	—
216	C₂×C₄×C₆₁	—	2	2	no	—
217	C₂×C₄×C₆₁	—	2	2	no	—
218	C₂×C₄×C₆₁	—	2	2	no	—
219	C₂×C₄×C₆₁	—	2	2	no	—
220	C₂×C₄×C₆₁	—	2	2	no	—
221	C₂×C₄×C₆₁	—	2	2	no	—
222	C₂×C₄×C₆₁	—	2	2	no	—
223	C₂×C₄×C₆₁	—	2	2	no	—
224	C₂×C₄×C₆₁	—	2	2	no	—
225	C₂×C₄×C₆₁	—	2	4	no	—
226	C₂×C₄×C₆₁	—	4	1	no	—
227	C₂×C₄×C₆₁	—	4	1	no	—
228	C₂×C₄×C₆₁	—	4	1	no	—
229	C₂×C₄×C₆₁	—	4	8	no	—
230	C₂×C₄×C₆₁	—	4	8	no	—
231	C₂×C₄×C₆₁	—	4	4	no	—
232	C₂×C₄×C₆₁	#100	1	4	yes	complemented
233	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
246	C₈×C₆₁	—	2	8	no	—
247	C₈×C₆₁	—	4	4	no	—
248	#21424	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
249	C₂²×C₆₁	—	2	1	no	—
250	C₂²×C₆₁	—	2	1	no	—
251	C₂²×C₆₁	—	2	1	no	—
252	C₂²×C₆₁	—	2	1	no	—
253	C₂²×C₆₁	—	2	1	no	—
254	C₂²×C₆₁	—	2	1	no	—
255	C₂²×C₆₁	—	2	1	no	—
256	C₂²×C₆₁	—	4	4	no	—
257	C₂²×C₆₁	—	4	4	no	—
258	C₂²×C₆₁	—	4	4	no	—
259	C₂²×C₆₁	—	4	4	no	—
260	C₂²×C₆₁	—	8	8	no	—
261	C₂²×C₆₁	C₂×#100	1	2	yes	—
262	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
263	C₂²×C₆₁	C₄×#41	1	2	yes	—
264	C₄×C₆₁	—	2	1	no	—
265	C₄×C₆₁	—	2	1	no	—
266	C₄×C₆₁	—	2	1	no	—
267	C₄×C₆₁	—	2	1	no	—
268	C₄×C₆₁	—	2	1	no	—
269	C₄×C₆₁	—	2	1	no	—
270	C₄×C₆₁	—	2	1	no	—
271	C₄×C₆₁	—	4	4	no	—
272	C₄×C₆₁	C₂×#100	1	2	yes	—
273	C₄×C₆₁	C₂×#100	1	2	yes	—
274	C₄×C₆₁	#413	1	2	yes	—
275	C₄×C₆₁	#525	1	2	yes	—
276	C₄×C₆₁	#532	1	2	yes	—
277	C₂×#532	C₂×C₆₁	1	1	yes	characteristic
278	#2920	C₂×C₆₁	1	1	yes	characteristic, complemented
279	C₂×C₄×M₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
280	#1997	C₂×C₆₁	1	2	yes	complemented
281	#1965	C₂×C₆₁	1	2	yes	complemented
282	#1900	C₂×C₆₁	1	4	yes	complemented
283	C₄×#100	C₂×C₆₁	1	4	yes	complemented
284	C₂×C₆₁	—	2	2	no	—
285	C₂×C₆₁	—	2	2	no	—
286	C₂×C₆₁	—	4	1	no	—
287	C₂×C₆₁	—	8	4	no	—
288	C₂×C₆₁	#2297	1	1	yes	characteristic
289	C₂×C₆₁	C₂²×#100	1	1	yes	characteristic
290	C₂×C₆₁	C₂×#413	1	1	yes	characteristic
291	C₂²×#41	C₄×C₆₁	1	2	yes	—
292	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
293	#532	—	2	1	no	—
294	#532	—	2	1	no	—
295	#532	—	2	1	no	—
296	#532	—	2	1	no	—
297	#532	—	2	1	no	—
298	#532	—	2	1	no	—
299	#532	—	2	1	no	—
300	#532	—	2	1	no	—
301	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
302	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
303	C₂×#124	C₄×C₆₁	1	2	yes	—
304	C₂×#121	C₄×C₆₁	1	2	yes	—
305	C₂×#121	C₂²×C₆₁	1	2	yes	—
306	C₂×C₄×D₄	C₄×C₆₁	1	2	yes	—
307	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
308	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
309	#432	—	2	1	no	—
310	#432	—	2	1	no	—
311	#431	—	2	1	no	—
312	#431	—	2	1	no	—
313	#423	C₂²×C₆₁	1	2	yes	—
314	C₂×#100	C₂²×C₆₁	1	8	yes	—
315	#407	C₂²×C₆₁	1	2	yes	—
316	C₄×M₁₆	—	2	1	no	—
317	C₄×M₁₆	—	2	1	no	—
318	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
319	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
320	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
321	C₂×#97	—	2	1	no	—
322	C₂×C₄×C₈	—	2	1	no	—
323	#343	C₂²×C₆₁	1	8	yes	—
324	C₆₁	#21424	1	1	yes	characteristic, direct product factor, Sylow
325	C₂×#41	—	2	2	no	—
326	C₂×#41	—	2	2	no	—
327	C₂×#41	—	2	2	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	4	8	no	—
330	C₂²×Q₈	C₂×C₄×C₆₁	1	2	yes	—
331	C₂²×D₄	C₂×C₄×C₆₁	1	2	yes	—
332	C₂²×D₄	C₂×C₄×C₆₁	1	4	yes	—
333	C₂²×D₄	C₂×C₄×C₆₁	1	2	yes	—
334	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
335	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
336	C₂³×C₄	C₂×C₄×C₆₁	1	4	yes	—
337	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
338	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	—	2	8	no	—
341	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
342	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
343	C₂²×C₈	—	2	2	no	—
344	C₄⋊Q₈	—	2	1	no	—
345	C₄⋊Q₈	—	2	1	no	—
346	C₄⋊Q₈	—	2	1	no	—
347	C₄⋊Q₈	—	2	1	no	—
348	#127	—	2	1	no	—
349	#127	—	2	1	no	—
350	#127	—	2	1	no	—
351	#127	—	2	1	no	—
352	#124	—	2	2	no	—
353	#124	—	2	2	no	—
354	#124	—	2	2	no	—
355	#124	—	2	2	no	—
356	#121	—	2	2	no	—
357	#121	—	2	2	no	—
358	#121	—	2	2	no	—
359	#121	—	2	2	no	—
360	#121	—	2	2	no	—
361	#121	—	2	2	no	—
362	#121	—	2	2	no	—
363	#121	—	2	2	no	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	2	no	—
372	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
374	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	4	yes	—
375	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	4	yes	—
376	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
377	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
378	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
379	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
380	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
381	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
382	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
383	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
384	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
385	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
388	C₄⋊C₈	—	2	2	no	—
389	C₄⋊C₈	—	2	2	no	—
390	#100	—	2	16	no	—
391	C₂²⋊C₈	—	2	2	no	—
392	C₂²⋊C₈	—	2	2	no	—
393	#97	—	2	2	no	—
394	#97	—	2	2	no	—
395	#97	—	2	2	no	—
396	C₄×C₈	—	2	2	no	—
397	C₄×C₈	—	2	2	no	—
398	C₄×C₈	—	2	2	no	—
399	C₂⁴	C₂²×C₄×C₆₁	1	1	yes	characteristic
400	C₂⁴	C₂²×C₄×C₆₁	1	4	yes	—
401	#41	—	4	8	no	—
402	#41	—	4	8	no	—
403	#41	—	4	8	no	—
404	#41	—	4	8	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	4	8	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	—	4	8	no	—
426	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
427	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
428	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
429	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
430	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
431	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
432	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
433	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
434	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
435	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
436	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
437	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
438	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
439	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
445	M₁₆	—	2	8	no	—
446	M₁₆	—	2	4	no	—
447	M₁₆	—	2	8	no	—
448	M₁₆	#41×C₆₁	1	8	yes	complemented
449	C₂×C₈	—	2	8	no	—
450	C₂×C₈	—	2	4	no	—
451	C₂×C₈	—	2	4	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	4	no	—
458	C₂²⋊C₄	—	2	4	no	—
459	C₂²⋊C₄	—	2	4	no	—
460	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
461	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
462	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
463	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
464	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
465	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
466	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
467	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
468	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
469	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
470	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
471	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
472	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
473	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
474	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
475	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	2	8	no	—
480	C₂³	—	4	1	no	—
481	C₂³	—	4	4	no	—
482	C₂³	—	4	4	no	—
483	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
484	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
485	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
486	Q₈	—	4	4	no	—
487	Q₈	—	4	4	no	—
488	D₄	—	4	4	no	—
489	D₄	—	4	4	no	—
490	D₄	—	4	8	no	—
491	D₄	—	4	8	no	—
492	D₄	—	4	4	no	—
493	D₄	—	4	4	no	—
494	D₄	—	4	4	no	—
495	D₄	—	4	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	8	no	—
514	C₂×C₄	—	4	8	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	#100×C₆₁	1	4	yes	complemented
517	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
518	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
519	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
520	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
521	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
522	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
523	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
524	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
525	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
526	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
529	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
530	C₈	—	2	8	no	—
531	C₈	—	4	4	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	8	8	no	—
544	C₂²	C₂×#100×C₆₁	1	2	yes	—
545	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
546	C₂²	C₄×#41×C₆₁	1	2	yes	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	4	4	no	—
555	C₄	C₂×#100×C₆₁	1	2	yes	—
556	C₄	C₂×#100×C₆₁	1	2	yes	—
557	C₄	C₆₁×#413	1	2	yes	—
558	C₄	C₆₁×#525	1	2	yes	—
559	C₄	C₆₁×#532	1	2	yes	—
560	C₂	—	2	2	no	—
561	C₂	—	2	2	no	—
562	C₂	—	4	1	no	—
563	C₂	—	8	4	no	—
564	C₂	C₆₁×#2297	1	1	yes	characteristic
565	C₂	C₂²×#100×C₆₁	1	1	yes	characteristic
566	C₂	C₂×C₆₁×#413	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
socle	C₂²×C₆₁	C₂²×C₂²⋊C₄
prime radical	C₂×C₆₁×#532	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2920	C₂	semidirect
3. C₂×C₄×M₁₆×C₆₁	C₂	semidirect
4. C₆₁×#1997	C₂	semidirect
5. C₆₁×#1965	C₂	semidirect
6. C₆₁×#1900	C₂	semidirect
7. C₄×#100×C₆₁	C₂	semidirect
164. M₁₆×C₆₁	#41	semidirect
232. C₂×C₄×C₆₁	#100	semidirect
248. #21424	C₆₁	direct (N × H)
278. #2920	C₂×C₆₁	semidirect
279. C₂×C₄×M₁₆	C₂×C₆₁	semidirect
280. #1997	C₂×C₆₁	semidirect
281. #1965	C₂×C₆₁	semidirect
282. #1900	C₂×C₆₁	semidirect
283. C₄×#100	C₂×C₆₁	semidirect
324. C₆₁	#21424	direct (N × H)
448. M₁₆	#41×C₆₁	semidirect
516. C₂×C₄	#100×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×#532	2
C₆₁×#2920	2
C₂×C₄×M₁₆×C₆₁	2
C₆₁×#1997	2
C₆₁×#1965	2
C₆₁×#1900	2
C₄×#100×C₆₁	2
#21424	61

Subgroups — C61×#21424 #29524857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21424 #29524857