Subgroups — C₆₁×#22468 #29525901

Order 15616.

1316 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#578	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#443	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2951	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2898	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1979	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1969	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1908	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1882	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1816	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1793	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	2	yes	—
13	C₆₁×#578	—	2	4	no	—
14	C₆₁×#578	C₄	1	8	yes	complemented
15	C₂×#137×C₆₁	—	2	2	no	—
16	C₂×#137×C₆₁	C₂²	1	2	yes	—
17	C₂×#135×C₆₁	—	2	1	no	—
18	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₆₁	—	2	1	no	—
20	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#131×C₆₁	C₂²	1	2	yes	—
22	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#520	C₂²	1	2	yes	—
24	C₆₁×#443	—	2	4	no	—
25	C₆₁×#440	—	2	2	no	—
26	C₄×Q₁₆×C₆₁	—	2	1	no	—
27	C₄×D₈×C₆₁	—	2	1	no	—
28	C₂×#108×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#104×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#104×C₆₁	C₂²	1	2	yes	—
32	C₆₁×#419	—	2	2	no	—
33	C₆₁×#419	C₂²	1	2	yes	—
34	C₆₁×#417	—	2	2	no	—
35	C₆₁×#417	C₂²	1	2	yes	—
36	C₆₁×#417	C₂²	1	2	yes	—
37	C₆₁×#416	—	2	2	no	—
38	C₆₁×#416	C₂²	1	1	yes	characteristic
39	C₂×#103×C₆₁	—	2	2	no	—
40	C₂×#103×C₆₁	C₂²	1	2	yes	—
41	C₂×#101×C₆₁	C₂²	1	2	yes	—
42	C₆₁×#405	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#391	C₂²	1	2	yes	—
45	C₆₁×#343	C₂²	1	2	yes	—
46	C₆₁×#341	C₂²	1	1	yes	characteristic
47	C₆₁×#339	C₂²	1	1	yes	characteristic
48	2₋¹⁺⁴×C₆₁	—	2	4	no	—
49	2₋¹⁺⁴×C₆₁	—	2	4	no	—
50	2₋¹⁺⁴×C₆₁	—	4	2	no	—
51	2₋¹⁺⁴×C₆₁	C₂×C₄	1	8	yes	complemented
52	C₂×#41×C₆₁	—	2	2	no	—
53	C₂×#41×C₆₁	—	2	2	no	—
54	C₂×#41×C₆₁	—	4	2	no	—
55	C₂×#41×C₆₁	C₂³	1	2	yes	—
56	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₆₁	—	2	2	no	—
58	C₂²×Q₈×C₆₁	—	2	2	no	—
59	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
60	#137×C₆₁	—	2	4	no	—
61	#137×C₆₁	—	2	16	no	—
62	#137×C₆₁	C₂×C₄	1	8	yes	complemented
63	#135×C₆₁	—	2	8	no	—
64	#135×C₆₁	C₂×C₄	1	4	yes	—
65	#135×C₆₁	D₄	1	4	yes	—
66	C₂×Q₁₆×C₆₁	—	2	2	no	—
67	C₂×Q₁₆×C₆₁	—	2	8	no	—
68	C₂×Q₁₆×C₆₁	—	2	1	no	—
69	C₂×Q₁₆×C₆₁	—	2	1	no	—
70	C₂×Q₁₆×C₆₁	—	2	2	no	—
71	C₂×Q₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
72	C₂×Q₁₆×C₆₁	D₄	1	1	yes	characteristic
73	C₂×SD₁₆×C₆₁	—	2	2	no	—
74	C₂×SD₁₆×C₆₁	D₄	1	2	yes	—
75	C₂×D₈×C₆₁	D₄	1	1	yes	characteristic
76	#131×C₆₁	—	2	2	no	—
77	#131×C₆₁	—	2	4	no	—
78	#131×C₆₁	—	4	2	no	—
79	#131×C₆₁	C₂×C₄	1	4	yes	complemented
80	C₂×M₁₆×C₆₁	—	2	1	no	—
81	C₂×M₁₆×C₆₁	—	2	2	no	—
82	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
83	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₆₁	—	2	1	no	—
86	C₂²×C₈×C₆₁	—	2	2	no	—
87	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
89	C₄×Q₈×C₆₁	—	2	2	no	—
90	C₄×D₄×C₆₁	—	2	2	no	—
91	C₄×D₄×C₆₁	—	4	2	no	—
92	#117×C₆₁	—	2	2	no	—
93	#117×C₆₁	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
95	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
96	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
97	#108×C₆₁	—	2	2	no	—
98	#107×C₆₁	—	2	1	no	—
99	#107×C₆₁	—	2	1	no	—
100	#104×C₆₁	—	2	4	no	—
101	#104×C₆₁	—	2	2	no	—
102	#103×C₆₁	—	2	2	no	—
103	#103×C₆₁	—	2	2	no	—
104	#103×C₆₁	—	2	2	no	—
105	#103×C₆₁	—	2	2	no	—
106	#103×C₆₁	—	2	2	no	—
107	#103×C₆₁	—	2	2	no	—
108	#103×C₆₁	D₄	1	1	yes	characteristic
109	#103×C₆₁	D₄	1	1	yes	characteristic
110	#102×C₆₁	—	2	2	no	—
111	#102×C₆₁	—	2	2	no	—
112	#102×C₆₁	D₄	1	1	yes	characteristic
113	#102×C₆₁	D₄	1	1	yes	characteristic
114	#101×C₆₁	—	4	2	no	—
115	#97×C₆₁	—	2	1	no	—
116	C₄×C₈×C₆₁	—	2	2	no	—
117	C₄×C₈×C₆₁	—	2	1	no	—
118	#95×C₆₁	—	4	2	no	—
119	#41×C₆₁	—	2	1	no	—
120	#41×C₆₁	—	2	2	no	—
121	#41×C₆₁	—	2	2	no	—
122	#41×C₆₁	—	2	1	no	—
123	#41×C₆₁	—	2	8	no	—
124	#41×C₆₁	—	2	8	no	—
125	#41×C₆₁	—	4	8	no	—
126	#41×C₆₁	—	4	4	no	—
127	#41×C₆₁	—	4	4	no	—
128	#41×C₆₁	—	4	8	no	—
129	#41×C₆₁	C₂²×C₄	1	4	yes	—
130	#41×C₆₁	C₂²×C₄	1	2	yes	—
131	#41×C₆₁	C₂×D₄	1	4	yes	—
132	#41×C₆₁	#41	1	2	yes	—
133	C₂×Q₈×C₆₁	—	2	2	no	—
134	C₂×Q₈×C₆₁	—	2	8	no	—
135	C₂×Q₈×C₆₁	—	2	8	no	—
136	C₂×Q₈×C₆₁	—	2	2	no	—
137	C₂×Q₈×C₆₁	—	2	2	no	—
138	C₂×Q₈×C₆₁	—	2	2	no	—
139	C₂×Q₈×C₆₁	—	2	2	no	—
140	C₂×Q₈×C₆₁	—	4	2	no	—
141	C₂×Q₈×C₆₁	—	4	4	no	—
142	C₂×Q₈×C₆₁	—	4	4	no	—
143	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
144	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
145	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
146	C₂×D₄×C₆₁	—	2	2	no	—
147	C₂×D₄×C₆₁	—	2	1	no	—
148	C₂×D₄×C₆₁	—	4	2	no	—
149	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
150	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₁	—	2	2	no	—
152	C₂²×C₄×C₆₁	—	2	1	no	—
153	C₂²×C₄×C₆₁	—	2	1	no	—
154	C₂²×C₄×C₆₁	—	2	2	no	—
155	C₂²×C₄×C₆₁	—	2	2	no	—
156	C₂²×C₄×C₆₁	—	4	2	no	—
157	C₂²×C₄×C₆₁	—	4	2	no	—
158	C₂²×C₄×C₆₁	—	4	2	no	—
159	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
160	Q₁₆×C₆₁	—	2	8	no	—
161	Q₁₆×C₆₁	—	2	4	no	—
162	Q₁₆×C₆₁	—	2	4	no	—
163	Q₁₆×C₆₁	C₂²⋊C₄	1	4	yes	—
164	SD₁₆×C₆₁	—	2	8	no	—
165	SD₁₆×C₆₁	C₂²⋊C₄	1	8	yes	—
166	D₈×C₆₁	C₂²⋊C₄	1	4	yes	—
167	M₁₆×C₆₁	—	2	1	no	—
168	M₁₆×C₆₁	—	2	4	no	—
169	M₁₆×C₆₁	—	2	2	no	—
170	M₁₆×C₆₁	—	2	1	no	—
171	M₁₆×C₆₁	—	2	1	no	—
172	M₁₆×C₆₁	—	2	2	no	—
173	M₁₆×C₆₁	—	4	4	no	—
174	M₁₆×C₆₁	C₂²×C₄	1	2	yes	—
175	C₂×C₈×C₆₁	—	2	1	no	—
176	C₂×C₈×C₆₁	—	2	1	no	—
177	C₂×C₈×C₆₁	—	2	1	no	—
178	C₂×C₈×C₆₁	—	2	4	no	—
179	C₂×C₈×C₆₁	—	2	1	no	—
180	C₂×C₈×C₆₁	—	2	2	no	—
181	C₂×C₈×C₆₁	—	4	4	no	—
182	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
183	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
187	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
188	C₄⋊C₄×C₆₁	—	2	2	no	—
189	C₄⋊C₄×C₆₁	—	2	2	no	—
190	C₄⋊C₄×C₆₁	—	4	2	no	—
191	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₆₁	—	2	1	no	—
194	C₂²⋊C₄×C₆₁	—	4	2	no	—
195	C₄²×C₆₁	—	2	1	no	—
196	C₄²×C₆₁	—	2	1	no	—
197	C₄²×C₆₁	—	2	1	no	—
198	C₄²×C₆₁	—	4	2	no	—
199	C₂³×C₆₁	—	2	2	no	—
200	C₂³×C₆₁	—	2	1	no	—
201	C₂³×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
202	Q₈×C₆₁	—	2	1	no	—
203	Q₈×C₆₁	—	2	2	no	—
204	Q₈×C₆₁	—	2	4	no	—
205	Q₈×C₆₁	—	2	4	no	—
206	Q₈×C₆₁	—	4	8	no	—
207	Q₈×C₆₁	—	4	2	no	—
208	Q₈×C₆₁	—	4	2	no	—
209	Q₈×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
210	Q₈×C₆₁	C₄×D₄	1	2	yes	—
211	D₄×C₆₁	—	2	2	no	—
212	D₄×C₆₁	—	2	4	no	—
213	D₄×C₆₁	—	2	2	no	—
214	D₄×C₆₁	—	2	4	no	—
215	D₄×C₆₁	—	2	1	no	—
216	D₄×C₆₁	—	2	2	no	—
217	D₄×C₆₁	—	4	8	no	—
218	D₄×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
219	D₄×C₆₁	C₄×D₄	1	2	yes	—
220	C₂×C₄×C₆₁	—	2	2	no	—
221	C₂×C₄×C₆₁	—	2	1	no	—
222	C₂×C₄×C₆₁	—	2	2	no	—
223	C₂×C₄×C₆₁	—	2	4	no	—
224	C₂×C₄×C₆₁	—	2	4	no	—
225	C₂×C₄×C₆₁	—	2	2	no	—
226	C₂×C₄×C₆₁	—	2	2	no	—
227	C₂×C₄×C₆₁	—	2	4	no	—
228	C₂×C₄×C₆₁	—	2	1	no	—
229	C₂×C₄×C₆₁	—	2	1	no	—
230	C₂×C₄×C₆₁	—	4	8	no	—
231	C₂×C₄×C₆₁	—	4	8	no	—
232	C₂×C₄×C₆₁	—	4	1	no	—
233	C₂×C₄×C₆₁	—	4	2	no	—
234	C₂×C₄×C₆₁	—	4	1	no	—
235	C₂×C₄×C₆₁	—	4	2	no	—
236	C₂×C₄×C₆₁	—	4	2	no	—
237	C₂×C₄×C₆₁	—	8	2	no	—
238	C₂×C₄×C₆₁	—	16	2	no	—
239	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
240	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
245	C₈×C₆₁	—	2	2	no	—
246	C₈×C₆₁	—	2	1	no	—
247	C₈×C₆₁	—	2	1	no	—
248	C₈×C₆₁	—	4	2	no	—
249	C₈×C₆₁	—	4	1	no	—
250	C₈×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
251	C₈×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
252	#22468	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂²×C₆₁	—	2	1	no	—
254	C₂²×C₆₁	—	2	1	no	—
255	C₂²×C₆₁	—	2	2	no	—
256	C₂²×C₆₁	—	2	4	no	—
257	C₂²×C₆₁	—	4	2	no	—
258	C₂²×C₆₁	—	4	1	no	—
259	C₂²×C₆₁	—	4	2	no	—
260	C₂²×C₆₁	—	4	1	no	—
261	C₂²×C₆₁	#518	1	1	yes	characteristic
262	C₂²×C₆₁	D₄²	1	1	yes	characteristic
263	C₂²×C₆₁	#546	1	1	yes	characteristic
264	C₄×C₆₁	—	2	2	no	—
265	C₄×C₆₁	—	2	4	no	—
266	C₄×C₆₁	—	4	2	no	—
267	C₄×C₆₁	—	4	4	no	—
268	C₄×C₆₁	—	4	1	no	—
269	C₄×C₆₁	—	4	1	no	—
270	C₄×C₆₁	—	8	2	no	—
271	C₄×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
272	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
273	C₄×C₆₁	D₄²	1	1	yes	characteristic
274	C₄×C₆₁	#546	1	1	yes	characteristic
275	C₂×#578	C₂×C₆₁	1	1	yes	characteristic
276	C₂×#443	C₂×C₆₁	1	1	yes	characteristic, complemented
277	#2951	C₂×C₆₁	1	1	yes	characteristic, complemented
278	#2898	C₂×C₆₁	1	2	yes	complemented
279	#1979	C₂×C₆₁	1	1	yes	characteristic, complemented
280	#1969	C₂×C₆₁	1	1	yes	characteristic, complemented
281	#1908	C₂×C₆₁	1	2	yes	complemented
282	#1882	C₂×C₆₁	1	2	yes	complemented
283	#1816	C₂×C₆₁	1	1	yes	characteristic, complemented
284	#1793	C₂×C₆₁	1	2	yes	complemented
285	#1764	C₂×C₆₁	1	1	yes	characteristic, complemented
286	C₂×C₆₁	—	2	1	no	—
287	C₂×C₆₁	—	2	1	no	—
288	C₂×C₆₁	—	4	2	no	—
289	C₂×C₆₁	—	4	4	no	—
290	C₂×C₆₁	D₄×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×C₆₁	#3290	1	1	yes	characteristic
292	C₂×C₆₁	#3293	1	1	yes	characteristic
293	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	2	yes	—
294	#578	—	2	4	no	—
295	#578	C₄×C₆₁	1	8	yes	complemented
296	C₂×#137	—	2	2	no	—
297	C₂×#137	C₂²×C₆₁	1	2	yes	—
298	C₂×#135	—	2	1	no	—
299	C₂×#135	C₂²×C₆₁	1	1	yes	characteristic
300	C₂²×Q₁₆	—	2	1	no	—
301	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
302	C₂×#131	C₂²×C₆₁	1	2	yes	—
303	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
304	#520	C₂²×C₆₁	1	2	yes	—
305	#443	—	2	4	no	—
306	#440	—	2	2	no	—
307	C₄×Q₁₆	—	2	1	no	—
308	C₄×D₈	—	2	1	no	—
309	C₂×#108	C₂²×C₆₁	1	1	yes	characteristic
310	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
311	C₂×#104	C₂²×C₆₁	1	1	yes	characteristic
312	C₂×#104	C₂²×C₆₁	1	2	yes	—
313	#419	—	2	2	no	—
314	#419	C₂²×C₆₁	1	2	yes	—
315	#417	—	2	2	no	—
316	#417	C₂²×C₆₁	1	2	yes	—
317	#417	C₂²×C₆₁	1	2	yes	—
318	#416	—	2	2	no	—
319	#416	C₂²×C₆₁	1	1	yes	characteristic
320	C₂×#103	—	2	2	no	—
321	C₂×#103	C₂²×C₆₁	1	2	yes	—
322	C₂×#101	C₂²×C₆₁	1	2	yes	—
323	#405	C₂²×C₆₁	1	1	yes	characteristic
324	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
325	#391	C₂²×C₆₁	1	2	yes	—
326	#343	C₂²×C₆₁	1	2	yes	—
327	#341	C₂²×C₆₁	1	1	yes	characteristic
328	#339	C₂²×C₆₁	1	1	yes	characteristic
329	C₆₁	#22468	1	1	yes	characteristic, direct product factor, Sylow
330	2₋¹⁺⁴	—	2	4	no	—
331	2₋¹⁺⁴	—	2	4	no	—
332	2₋¹⁺⁴	—	4	2	no	—
333	2₋¹⁺⁴	C₂×C₄×C₆₁	1	8	yes	complemented
334	C₂×#41	—	2	2	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	4	2	no	—
337	C₂×#41	C₂³×C₆₁	1	2	yes	—
338	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
339	C₂²×Q₈	—	2	2	no	—
340	C₂²×Q₈	—	2	2	no	—
341	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
342	#137	—	2	4	no	—
343	#137	—	2	16	no	—
344	#137	C₂×C₄×C₆₁	1	8	yes	complemented
345	#135	—	2	8	no	—
346	#135	C₂×C₄×C₆₁	1	4	yes	—
347	#135	D₄×C₆₁	1	4	yes	—
348	C₂×Q₁₆	—	2	2	no	—
349	C₂×Q₁₆	—	2	8	no	—
350	C₂×Q₁₆	—	2	1	no	—
351	C₂×Q₁₆	—	2	1	no	—
352	C₂×Q₁₆	—	2	2	no	—
353	C₂×Q₁₆	C₂×C₄×C₆₁	1	4	yes	complemented
354	C₂×Q₁₆	D₄×C₆₁	1	1	yes	characteristic
355	C₂×SD₁₆	—	2	2	no	—
356	C₂×SD₁₆	D₄×C₆₁	1	2	yes	—
357	C₂×D₈	D₄×C₆₁	1	1	yes	characteristic
358	#131	—	2	2	no	—
359	#131	—	2	4	no	—
360	#131	—	4	2	no	—
361	#131	C₂×C₄×C₆₁	1	4	yes	complemented
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	2	no	—
364	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
365	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
366	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	—	2	2	no	—
369	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
371	C₄×Q₈	—	2	2	no	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	—	4	2	no	—
374	#117	—	2	2	no	—
375	#117	C₂³×C₆₁	1	1	yes	characteristic
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
378	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
379	#108	—	2	2	no	—
380	#107	—	2	1	no	—
381	#107	—	2	1	no	—
382	#104	—	2	4	no	—
383	#104	—	2	2	no	—
384	#103	—	2	2	no	—
385	#103	—	2	2	no	—
386	#103	—	2	2	no	—
387	#103	—	2	2	no	—
388	#103	—	2	2	no	—
389	#103	—	2	2	no	—
390	#103	D₄×C₆₁	1	1	yes	characteristic
391	#103	D₄×C₆₁	1	1	yes	characteristic
392	#102	—	2	2	no	—
393	#102	—	2	2	no	—
394	#102	D₄×C₆₁	1	1	yes	characteristic
395	#102	D₄×C₆₁	1	1	yes	characteristic
396	#101	—	4	2	no	—
397	#97	—	2	1	no	—
398	C₄×C₈	—	2	2	no	—
399	C₄×C₈	—	2	1	no	—
400	#95	—	4	2	no	—
401	#41	—	2	1	no	—
402	#41	—	2	2	no	—
403	#41	—	2	2	no	—
404	#41	—	2	1	no	—
405	#41	—	2	8	no	—
406	#41	—	2	8	no	—
407	#41	—	4	8	no	—
408	#41	—	4	4	no	—
409	#41	—	4	4	no	—
410	#41	—	4	8	no	—
411	#41	C₂²×C₄×C₆₁	1	4	yes	—
412	#41	C₂²×C₄×C₆₁	1	2	yes	—
413	#41	C₂×D₄×C₆₁	1	4	yes	—
414	#41	#41×C₆₁	1	2	yes	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	8	no	—
417	C₂×Q₈	—	2	8	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	4	2	no	—
423	C₂×Q₈	—	4	4	no	—
424	C₂×Q₈	—	4	4	no	—
425	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
426	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
427	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
432	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
442	Q₁₆	—	2	8	no	—
443	Q₁₆	—	2	4	no	—
444	Q₁₆	—	2	4	no	—
445	Q₁₆	C₂²⋊C₄×C₆₁	1	4	yes	—
446	SD₁₆	—	2	8	no	—
447	SD₁₆	C₂²⋊C₄×C₆₁	1	8	yes	—
448	D₈	C₂²⋊C₄×C₆₁	1	4	yes	—
449	M₁₆	—	2	1	no	—
450	M₁₆	—	2	4	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	1	no	—
453	M₁₆	—	2	1	no	—
454	M₁₆	—	2	2	no	—
455	M₁₆	—	4	4	no	—
456	M₁₆	C₂²×C₄×C₆₁	1	2	yes	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	4	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	4	4	no	—
464	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
465	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
466	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
467	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
468	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
469	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
474	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	4	2	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	4	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	1	no	—
483	C₂³	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
484	Q₈	—	2	1	no	—
485	Q₈	—	2	2	no	—
486	Q₈	—	2	4	no	—
487	Q₈	—	2	4	no	—
488	Q₈	—	4	8	no	—
489	Q₈	—	4	2	no	—
490	Q₈	—	4	2	no	—
491	Q₈	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
492	Q₈	C₄×D₄×C₆₁	1	2	yes	—
493	D₄	—	2	2	no	—
494	D₄	—	2	4	no	—
495	D₄	—	2	2	no	—
496	D₄	—	2	4	no	—
497	D₄	—	2	1	no	—
498	D₄	—	2	2	no	—
499	D₄	—	4	8	no	—
500	D₄	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
501	D₄	C₄×D₄×C₆₁	1	2	yes	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	4	8	no	—
513	C₂×C₄	—	4	8	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	8	2	no	—
520	C₂×C₄	—	16	2	no	—
521	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
525	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
526	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	2	2	no	—
530	C₈	—	4	2	no	—
531	C₈	—	4	1	no	—
532	C₈	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
533	C₈	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	1	no	—
542	C₂²	C₆₁×#518	1	1	yes	characteristic
543	C₂²	D₄²×C₆₁	1	1	yes	characteristic
544	C₂²	C₆₁×#546	1	1	yes	characteristic
545	C₄	—	2	2	no	—
546	C₄	—	2	4	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	4	no	—
551	C₄	—	8	2	no	—
552	C₄	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
553	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
554	C₄	D₄²×C₆₁	1	1	yes	characteristic
555	C₄	C₆₁×#546	1	1	yes	characteristic
556	C₂	—	2	1	no	—
557	C₂	—	2	1	no	—
558	C₂	—	4	2	no	—
559	C₂	—	4	4	no	—
560	C₂	D₄×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
561	C₂	C₆₁×#3290	1	1	yes	characteristic
562	C₂	C₆₁×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	D₄²
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×C₆₁×#578	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂²×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#443	C₂	semidirect
3. C₆₁×#2951	C₂	semidirect
4. C₆₁×#2898	C₂	semidirect
5. C₆₁×#1979	C₂	semidirect
6. C₆₁×#1969	C₂	semidirect
7. C₆₁×#1908	C₂	semidirect
8. C₆₁×#1882	C₂	semidirect
9. C₆₁×#1816	C₂	semidirect
10. C₆₁×#1793	C₂	semidirect
11. C₆₁×#1764	C₂	semidirect
14. C₆₁×#578	C₄	semidirect
51. 2₋¹⁺⁴×C₆₁	C₂×C₄	semidirect
62. #137×C₆₁	C₂×C₄	semidirect
71. C₂×Q₁₆×C₆₁	C₂×C₄	semidirect
79. #131×C₆₁	C₂×C₄	semidirect
252. #22468	C₆₁	direct (N × H)
276. C₂×#443	C₂×C₆₁	semidirect
277. #2951	C₂×C₆₁	semidirect
278. #2898	C₂×C₆₁	semidirect
279. #1979	C₂×C₆₁	semidirect
280. #1969	C₂×C₆₁	semidirect
281. #1908	C₂×C₆₁	semidirect
282. #1882	C₂×C₆₁	semidirect
283. #1816	C₂×C₆₁	semidirect
284. #1793	C₂×C₆₁	semidirect
285. #1764	C₂×C₆₁	semidirect
295. #578	C₄×C₆₁	semidirect
329. C₆₁	#22468	direct (N × H)
333. 2₋¹⁺⁴	C₂×C₄×C₆₁	semidirect
344. #137	C₂×C₄×C₆₁	semidirect
353. C₂×Q₁₆	C₂×C₄×C₆₁	semidirect
361. #131	C₂×C₄×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×#578	2
C₂×C₆₁×#443	2
C₆₁×#2951	2
C₆₁×#2898	2
C₆₁×#1979	2
C₆₁×#1969	2
C₆₁×#1908	2
C₆₁×#1882	2
C₆₁×#1816	2
C₆₁×#1793	2
C₆₁×#1764	2
#22468	61

Subgroups — C61×#22468 #29525901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#22468 #29525901