Subgroups — C₆₁×#25804 #29529237

Order 15616.

1454 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#576	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3156	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#473	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#455	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3009	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2019	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2003	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1978	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1974	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	2	yes	—
13	C₆₁×#576	—	2	4	no	—
14	C₆₁×#576	—	2	4	no	—
15	C₂×#137×C₆₁	C₂²	1	2	yes	—
16	C₂×#137×C₆₁	C₂²	1	2	yes	complemented
17	C₂×AGL(1,ℤ/8)×C₆₁	—	2	2	no	—
18	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
19	C₂×#135×C₆₁	—	2	1	no	—
20	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
22	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
23	C₂²×D₈×C₆₁	—	2	1	no	—
24	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#536	C₂²	1	2	yes	complemented
27	C₂×#124×C₆₁	C₂²	1	2	yes	complemented
28	C₆₁×#497	—	2	2	no	—
29	C₆₁×#495	—	2	4	no	—
30	C₆₁×#495	—	2	1	no	—
31	C₆₁×#494	—	2	1	no	—
32	C₆₁×#473	—	2	4	no	—
33	C₆₁×#455	—	2	8	no	—
34	C₆₁×#452	—	2	4	no	—
35	C₆₁×#450	—	2	4	no	—
36	C₂×#108×C₆₁	C₂²	1	1	yes	characteristic, complemented
37	C₂×#104×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#104×C₆₁	C₂²	1	2	yes	complemented
39	C₆₁×#418	C₂²	1	2	yes	complemented
40	C₆₁×#416	C₂²	1	1	yes	characteristic
41	C₂×#101×C₆₁	C₂²	1	2	yes	complemented
42	C₂×#100×C₆₁	C₂²	1	2	yes	complemented
43	C₆₁×#408	C₂²	1	2	yes	complemented
44	C₆₁×#405	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
46	C₆₁×#341	C₂²	1	1	yes	characteristic, complemented
47	C₆₁×#339	C₂²	1	1	yes	characteristic, complemented
48	H(5,𝔽₂)×C₆₁	—	2	4	no	—
49	H(5,𝔽₂)×C₆₁	—	2	4	no	—
50	H(5,𝔽₂)×C₆₁	—	2	4	no	—
51	H(5,𝔽₂)×C₆₁	—	4	2	no	—
52	C₂×#41×C₆₁	—	2	2	no	—
53	C₂×#41×C₆₁	—	2	2	no	—
54	C₂×#41×C₆₁	C₂³	1	2	yes	—
55	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
56	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
57	C₂²×D₄×C₆₁	—	2	2	no	—
58	C₂²×D₄×C₆₁	—	2	2	no	—
59	C₂²×D₄×C₆₁	—	4	2	no	—
60	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
61	#137×C₆₁	—	2	4	no	—
62	#137×C₆₁	—	2	4	no	—
63	#137×C₆₁	—	2	4	no	—
64	#137×C₆₁	—	4	2	no	—
65	AGL(1,ℤ/8)×C₆₁	—	2	16	no	—
66	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
67	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
68	#135×C₆₁	—	2	8	no	—
69	#135×C₆₁	—	2	2	no	—
70	#135×C₆₁	—	2	2	no	—
71	C₂×Q₁₆×C₆₁	—	2	2	no	—
72	C₂×Q₁₆×C₆₁	—	2	2	no	—
73	C₂×Q₁₆×C₆₁	—	2	2	no	—
74	C₂×Q₁₆×C₆₁	—	2	1	no	—
75	C₂×Q₁₆×C₆₁	—	2	2	no	—
76	C₂×Q₁₆×C₆₁	—	2	1	no	—
77	C₂×Q₁₆×C₆₁	D₄	1	1	yes	characteristic
78	C₂×SD₁₆×C₆₁	—	2	2	no	—
79	C₂×SD₁₆×C₆₁	—	2	4	no	—
80	C₂×SD₁₆×C₆₁	—	2	2	no	—
81	C₂×SD₁₆×C₆₁	—	2	2	no	—
82	C₂×SD₁₆×C₆₁	—	2	4	no	—
83	C₂×SD₁₆×C₆₁	—	4	2	no	—
84	C₂×SD₁₆×C₆₁	D₄	1	2	yes	—
85	C₂×D₈×C₆₁	—	2	8	no	—
86	C₂×D₈×C₆₁	—	2	2	no	—
87	C₂×D₈×C₆₁	—	2	1	no	—
88	C₂×D₈×C₆₁	—	2	1	no	—
89	C₂×D₈×C₆₁	—	2	2	no	—
90	C₂×D₈×C₆₁	D₄	1	1	yes	characteristic
91	C₂×D₈×C₆₁	D₄	1	4	yes	—
92	#131×C₆₁	—	2	2	no	—
93	#131×C₆₁	D₄	1	4	yes	—
94	C₂×M₁₆×C₆₁	—	2	1	no	—
95	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
96	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
97	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₆₁	—	2	1	no	—
99	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₆₁	—	2	2	no	—
102	#124×C₆₁	—	2	2	no	—
103	#124×C₆₁	—	2	4	no	—
104	#124×C₆₁	—	2	4	no	—
105	#123×C₆₁	—	4	2	no	—
106	C₂²⋊Q₈×C₆₁	—	2	4	no	—
107	#117×C₆₁	C₂³	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₆₁	—	4	2	no	—
109	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
110	#108×C₆₁	—	2	2	no	—
111	#104×C₆₁	—	2	4	no	—
112	#104×C₆₁	D₄	1	4	yes	—
113	#103×C₆₁	D₄	1	2	yes	—
114	#102×C₆₁	—	2	4	no	—
115	#102×C₆₁	D₄	1	2	yes	—
116	#101×C₆₁	—	2	4	no	—
117	#100×C₆₁	—	2	4	no	—
118	C₂²⋊C₈×C₆₁	—	2	4	no	—
119	#97×C₆₁	—	2	1	no	—
120	C₄×C₈×C₆₁	—	2	2	no	—
121	C₄×C₈×C₆₁	—	2	1	no	—
122	C₂⁴×C₆₁	—	2	2	no	—
123	C₂⁴×C₆₁	—	4	2	no	—
124	#41×C₆₁	—	2	1	no	—
125	#41×C₆₁	—	2	1	no	—
126	#41×C₆₁	—	2	8	no	—
127	#41×C₆₁	—	2	2	no	—
128	#41×C₆₁	—	2	2	no	—
129	#41×C₆₁	—	2	2	no	—
130	#41×C₆₁	—	2	2	no	—
131	#41×C₆₁	—	4	4	no	—
132	#41×C₆₁	—	4	4	no	—
133	#41×C₆₁	—	4	4	no	—
134	#41×C₆₁	C₂×D₄	1	2	yes	—
135	#41×C₆₁	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
141	C₂×Q₈×C₆₁	—	2	2	no	—
142	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
143	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
144	C₂×D₄×C₆₁	—	2	1	no	—
145	C₂×D₄×C₆₁	—	2	8	no	—
146	C₂×D₄×C₆₁	—	2	2	no	—
147	C₂×D₄×C₆₁	—	2	2	no	—
148	C₂×D₄×C₆₁	—	2	2	no	—
149	C₂×D₄×C₆₁	—	2	2	no	—
150	C₂×D₄×C₆₁	—	2	2	no	—
151	C₂×D₄×C₆₁	—	2	2	no	—
152	C₂×D₄×C₆₁	—	4	4	no	—
153	C₂×D₄×C₆₁	—	4	2	no	—
154	C₂×D₄×C₆₁	—	4	2	no	—
155	C₂×D₄×C₆₁	—	4	4	no	—
156	C₂×D₄×C₆₁	—	4	8	no	—
157	C₂×D₄×C₆₁	—	4	8	no	—
158	C₂×D₄×C₆₁	—	4	4	no	—
159	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
161	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₆₁	—	2	1	no	—
163	C₂²×C₄×C₆₁	—	2	1	no	—
164	C₂²×C₄×C₆₁	—	2	2	no	—
165	C₂²×C₄×C₆₁	—	2	2	no	—
166	C₂²×C₄×C₆₁	—	4	2	no	—
167	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
168	Q₁₆×C₆₁	—	2	2	no	—
169	Q₁₆×C₆₁	—	4	4	no	—
170	Q₁₆×C₆₁	—	4	4	no	—
171	Q₁₆×C₆₁	—	4	2	no	—
172	Q₁₆×C₆₁	—	4	2	no	—
173	SD₁₆×C₆₁	—	2	8	no	—
174	SD₁₆×C₆₁	—	2	4	no	—
175	SD₁₆×C₆₁	—	4	8	no	—
176	SD₁₆×C₆₁	—	4	4	no	—
177	SD₁₆×C₆₁	—	4	4	no	—
178	D₈×C₆₁	—	2	8	no	—
179	D₈×C₆₁	—	2	2	no	—
180	D₈×C₆₁	—	2	4	no	—
181	D₈×C₆₁	—	2	4	no	—
182	M₁₆×C₆₁	—	2	1	no	—
183	M₁₆×C₆₁	—	2	1	no	—
184	M₁₆×C₆₁	—	2	4	no	—
185	M₁₆×C₆₁	—	2	2	no	—
186	M₁₆×C₆₁	—	2	2	no	—
187	M₁₆×C₆₁	C₂×D₄	1	2	yes	—
188	M₁₆×C₆₁	C₂×D₄	1	2	yes	—
189	C₂×C₈×C₆₁	—	2	1	no	—
190	C₂×C₈×C₆₁	—	2	1	no	—
191	C₂×C₈×C₆₁	—	2	1	no	—
192	C₂×C₈×C₆₁	—	2	1	no	—
193	C₂×C₈×C₆₁	—	2	4	no	—
194	C₂×C₈×C₆₁	—	2	2	no	—
195	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
196	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
198	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
200	C₄⋊C₄×C₆₁	—	4	4	no	—
201	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
202	C₂²⋊C₄×C₆₁	—	2	1	no	—
203	C₂²⋊C₄×C₆₁	—	4	8	no	—
204	C₂²⋊C₄×C₆₁	—	4	4	no	—
205	C₄²×C₆₁	—	2	1	no	—
206	C₄²×C₆₁	—	2	1	no	—
207	C₄²×C₆₁	C₂×D₄	1	2	yes	—
208	C₂³×C₆₁	—	2	1	no	—
209	C₂³×C₆₁	—	2	2	no	—
210	C₂³×C₆₁	—	2	4	no	—
211	C₂³×C₆₁	—	4	8	no	—
212	C₂³×C₆₁	—	4	2	no	—
213	C₂³×C₆₁	—	4	2	no	—
214	C₂³×C₆₁	—	8	4	no	—
215	C₂³×C₆₁	—	16	4	no	—
216	C₂³×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
217	Q₈×C₆₁	—	2	1	no	—
218	Q₈×C₆₁	—	2	2	no	—
219	Q₈×C₆₁	—	2	2	no	—
220	Q₈×C₆₁	—	4	2	no	—
221	Q₈×C₆₁	—	4	2	no	—
222	Q₈×C₆₁	—	4	2	no	—
223	Q₈×C₆₁	—	4	2	no	—
224	Q₈×C₆₁	#127	1	2	yes	—
225	D₄×C₆₁	—	2	2	no	—
226	D₄×C₆₁	—	2	2	no	—
227	D₄×C₆₁	—	2	2	no	—
228	D₄×C₆₁	—	2	4	no	—
229	D₄×C₆₁	—	2	1	no	—
230	D₄×C₆₁	—	2	4	no	—
231	D₄×C₆₁	—	2	2	no	—
232	D₄×C₆₁	—	4	8	no	—
233	D₄×C₆₁	—	4	8	no	—
234	D₄×C₆₁	—	4	2	no	—
235	D₄×C₆₁	—	4	2	no	—
236	D₄×C₆₁	—	4	2	no	—
237	D₄×C₆₁	—	4	2	no	—
238	D₄×C₆₁	#127	1	2	yes	—
239	C₂×C₄×C₆₁	—	2	1	no	—
240	C₂×C₄×C₆₁	—	2	2	no	—
241	C₂×C₄×C₆₁	—	2	2	no	—
242	C₂×C₄×C₆₁	—	2	2	no	—
243	C₂×C₄×C₆₁	—	2	2	no	—
244	C₂×C₄×C₆₁	—	2	2	no	—
245	C₂×C₄×C₆₁	—	4	8	no	—
246	C₂×C₄×C₆₁	—	4	2	no	—
247	C₂×C₄×C₆₁	—	4	2	no	—
248	C₂×C₄×C₆₁	—	4	2	no	—
249	C₂×C₄×C₆₁	—	4	2	no	—
250	C₂×C₄×C₆₁	—	4	2	no	—
251	C₂×C₄×C₆₁	—	4	2	no	—
252	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
258	C₈×C₆₁	—	2	2	no	—
259	C₈×C₆₁	—	2	2	no	—
260	C₈×C₆₁	—	2	2	no	—
261	C₈×C₆₁	—	4	2	no	—
262	C₈×C₆₁	#120	1	2	yes	—
263	C₈×C₆₁	#120	1	2	yes	—
264	#25804	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂²×C₆₁	—	2	2	no	—
266	C₂²×C₆₁	—	2	2	no	—
267	C₂²×C₆₁	—	4	2	no	—
268	C₂²×C₆₁	—	4	2	no	—
269	C₂²×C₆₁	—	4	4	no	—
270	C₂²×C₆₁	—	4	4	no	—
271	C₂²×C₆₁	—	8	4	no	—
272	C₂²×C₆₁	—	8	4	no	—
273	C₂²×C₆₁	—	16	2	no	—
274	C₂²×C₆₁	—	16	8	no	—
275	C₂²×C₆₁	#535	1	1	yes	characteristic
276	C₂²×C₆₁	D₄²	1	1	yes	characteristic
277	C₂²×C₆₁	D₄²	1	1	yes	characteristic
278	C₄×C₆₁	—	2	2	no	—
279	C₄×C₆₁	—	4	2	no	—
280	C₄×C₆₁	—	4	2	no	—
281	C₄×C₆₁	—	4	2	no	—
282	C₄×C₆₁	—	8	2	no	—
283	C₄×C₆₁	C₂×#120	1	1	yes	characteristic
284	C₄×C₆₁	C₂×#127	1	1	yes	characteristic
285	C₄×C₆₁	D₄²	1	1	yes	characteristic
286	C₄×C₆₁	D₄²	1	1	yes	characteristic
287	C₂×#576	C₂×C₆₁	1	1	yes	characteristic
288	#3156	C₂×C₆₁	1	1	yes	characteristic, complemented
289	C₂×#495	C₂×C₆₁	1	1	yes	characteristic, complemented
290	C₂×#473	C₂×C₆₁	1	1	yes	characteristic, complemented
291	C₂×#455	C₂×C₆₁	1	2	yes	complemented
292	#3009	C₂×C₆₁	1	2	yes	complemented
293	#2019	C₂×C₆₁	1	2	yes	complemented
294	#2003	C₂×C₆₁	1	2	yes	complemented
295	#1978	C₂×C₆₁	1	1	yes	characteristic, complemented
296	#1974	C₂×C₆₁	1	1	yes	characteristic, complemented
297	#1764	C₂×C₆₁	1	1	yes	characteristic, complemented
298	C₂×C₆₁	—	2	1	no	—
299	C₂×C₆₁	—	2	1	no	—
300	C₂×C₆₁	—	4	2	no	—
301	C₂×C₆₁	—	8	2	no	—
302	C₂×C₆₁	—	8	4	no	—
303	C₂×C₆₁	#2433	1	1	yes	characteristic
304	C₂×C₆₁	#3290	1	2	yes	—
305	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	2	yes	—
306	#576	—	2	4	no	—
307	#576	—	2	4	no	—
308	C₂×#137	C₂²×C₆₁	1	2	yes	—
309	C₂×#137	C₂²×C₆₁	1	2	yes	complemented
310	C₂×AGL(1,ℤ/8)	—	2	2	no	—
311	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
312	C₂×#135	—	2	1	no	—
313	C₂×#135	C₂²×C₆₁	1	1	yes	characteristic
314	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
315	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
316	C₂²×D₈	—	2	1	no	—
317	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
318	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
319	#536	C₂²×C₆₁	1	2	yes	complemented
320	C₂×#124	C₂²×C₆₁	1	2	yes	complemented
321	#497	—	2	2	no	—
322	#495	—	2	4	no	—
323	#495	—	2	1	no	—
324	#494	—	2	1	no	—
325	#473	—	2	4	no	—
326	#455	—	2	8	no	—
327	#452	—	2	4	no	—
328	#450	—	2	4	no	—
329	C₂×#108	C₂²×C₆₁	1	1	yes	characteristic, complemented
330	C₂×#104	C₂²×C₆₁	1	1	yes	characteristic
331	C₂×#104	C₂²×C₆₁	1	2	yes	complemented
332	#418	C₂²×C₆₁	1	2	yes	complemented
333	#416	C₂²×C₆₁	1	1	yes	characteristic
334	C₂×#101	C₂²×C₆₁	1	2	yes	complemented
335	C₂×#100	C₂²×C₆₁	1	2	yes	complemented
336	#408	C₂²×C₆₁	1	2	yes	complemented
337	#405	C₂²×C₆₁	1	1	yes	characteristic, complemented
338	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
339	#341	C₂²×C₆₁	1	1	yes	characteristic, complemented
340	#339	C₂²×C₆₁	1	1	yes	characteristic, complemented
341	C₆₁	#25804	1	1	yes	characteristic, direct product factor, Sylow
342	H(5,𝔽₂)	—	2	4	no	—
343	H(5,𝔽₂)	—	2	4	no	—
344	H(5,𝔽₂)	—	2	4	no	—
345	H(5,𝔽₂)	—	4	2	no	—
346	C₂×#41	—	2	2	no	—
347	C₂×#41	—	2	2	no	—
348	C₂×#41	C₂³×C₆₁	1	2	yes	—
349	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
350	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
351	C₂²×D₄	—	2	2	no	—
352	C₂²×D₄	—	2	2	no	—
353	C₂²×D₄	—	4	2	no	—
354	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
355	#137	—	2	4	no	—
356	#137	—	2	4	no	—
357	#137	—	2	4	no	—
358	#137	—	4	2	no	—
359	AGL(1,ℤ/8)	—	2	16	no	—
360	AGL(1,ℤ/8)	—	2	4	no	—
361	AGL(1,ℤ/8)	—	2	4	no	—
362	#135	—	2	8	no	—
363	#135	—	2	2	no	—
364	#135	—	2	2	no	—
365	C₂×Q₁₆	—	2	2	no	—
366	C₂×Q₁₆	—	2	2	no	—
367	C₂×Q₁₆	—	2	2	no	—
368	C₂×Q₁₆	—	2	1	no	—
369	C₂×Q₁₆	—	2	2	no	—
370	C₂×Q₁₆	—	2	1	no	—
371	C₂×Q₁₆	D₄×C₆₁	1	1	yes	characteristic
372	C₂×SD₁₆	—	2	2	no	—
373	C₂×SD₁₆	—	2	4	no	—
374	C₂×SD₁₆	—	2	2	no	—
375	C₂×SD₁₆	—	2	2	no	—
376	C₂×SD₁₆	—	2	4	no	—
377	C₂×SD₁₆	—	4	2	no	—
378	C₂×SD₁₆	D₄×C₆₁	1	2	yes	—
379	C₂×D₈	—	2	8	no	—
380	C₂×D₈	—	2	2	no	—
381	C₂×D₈	—	2	1	no	—
382	C₂×D₈	—	2	1	no	—
383	C₂×D₈	—	2	2	no	—
384	C₂×D₈	D₄×C₆₁	1	1	yes	characteristic
385	C₂×D₈	D₄×C₆₁	1	4	yes	—
386	#131	—	2	2	no	—
387	#131	D₄×C₆₁	1	4	yes	—
388	C₂×M₁₆	—	2	1	no	—
389	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
390	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
391	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
395	C₄⋊Q₈	—	2	2	no	—
396	#124	—	2	4	no	—
397	#124	—	2	2	no	—
398	#124	—	2	4	no	—
399	#123	—	4	2	no	—
400	C₂²⋊Q₈	—	2	4	no	—
401	#117	C₂³×C₆₁	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	—	4	2	no	—
403	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
404	#108	—	2	2	no	—
405	#104	—	2	4	no	—
406	#104	D₄×C₆₁	1	4	yes	—
407	#103	D₄×C₆₁	1	2	yes	—
408	#102	—	2	4	no	—
409	#102	D₄×C₆₁	1	2	yes	—
410	#101	—	2	4	no	—
411	#100	—	2	4	no	—
412	C₂²⋊C₈	—	2	4	no	—
413	#97	—	2	1	no	—
414	C₄×C₈	—	2	2	no	—
415	C₄×C₈	—	2	1	no	—
416	C₂⁴	—	2	2	no	—
417	C₂⁴	—	4	2	no	—
418	#41	—	2	1	no	—
419	#41	—	2	1	no	—
420	#41	—	2	8	no	—
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	4	4	no	—
426	#41	—	4	4	no	—
427	#41	—	4	4	no	—
428	#41	C₂×D₄×C₆₁	1	2	yes	—
429	#41	C₂×D₄×C₆₁	1	2	yes	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
437	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	8	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂×D₄	—	4	2	no	—
448	C₂×D₄	—	4	2	no	—
449	C₂×D₄	—	4	4	no	—
450	C₂×D₄	—	4	8	no	—
451	C₂×D₄	—	4	8	no	—
452	C₂×D₄	—	4	4	no	—
453	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
454	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
455	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	4	2	no	—
461	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
462	Q₁₆	—	2	2	no	—
463	Q₁₆	—	4	4	no	—
464	Q₁₆	—	4	4	no	—
465	Q₁₆	—	4	2	no	—
466	Q₁₆	—	4	2	no	—
467	SD₁₆	—	2	8	no	—
468	SD₁₆	—	2	4	no	—
469	SD₁₆	—	4	8	no	—
470	SD₁₆	—	4	4	no	—
471	SD₁₆	—	4	4	no	—
472	D₈	—	2	8	no	—
473	D₈	—	2	2	no	—
474	D₈	—	2	4	no	—
475	D₈	—	2	4	no	—
476	M₁₆	—	2	1	no	—
477	M₁₆	—	2	1	no	—
478	M₁₆	—	2	4	no	—
479	M₁₆	—	2	2	no	—
480	M₁₆	—	2	2	no	—
481	M₁₆	C₂×D₄×C₆₁	1	2	yes	—
482	M₁₆	C₂×D₄×C₆₁	1	2	yes	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	4	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
490	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
491	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
492	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
493	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
494	C₄⋊C₄	—	4	4	no	—
495	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	4	8	no	—
498	C₂²⋊C₄	—	4	4	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	C₂×D₄×C₆₁	1	2	yes	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	4	8	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	8	4	no	—
509	C₂³	—	16	4	no	—
510	C₂³	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
511	Q₈	—	2	1	no	—
512	Q₈	—	2	2	no	—
513	Q₈	—	2	2	no	—
514	Q₈	—	4	2	no	—
515	Q₈	—	4	2	no	—
516	Q₈	—	4	2	no	—
517	Q₈	—	4	2	no	—
518	Q₈	#127×C₆₁	1	2	yes	—
519	D₄	—	2	2	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	4	no	—
523	D₄	—	2	2	no	—
524	D₄	—	2	2	no	—
525	D₄	—	2	4	no	—
526	D₄	—	4	8	no	—
527	D₄	—	4	8	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	#127×C₆₁	1	2	yes	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	4	8	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
548	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
549	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
551	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
552	C₈	—	2	2	no	—
553	C₈	—	2	2	no	—
554	C₈	—	2	2	no	—
555	C₈	—	4	2	no	—
556	C₈	#120×C₆₁	1	2	yes	—
557	C₈	#120×C₆₁	1	2	yes	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	8	4	no	—
565	C₂²	—	8	4	no	—
566	C₂²	—	16	2	no	—
567	C₂²	—	16	8	no	—
568	C₂²	C₆₁×#535	1	1	yes	characteristic
569	C₂²	D₄²×C₆₁	1	1	yes	characteristic
570	C₂²	D₄²×C₆₁	1	1	yes	characteristic
571	C₄	—	2	2	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	2	no	—
575	C₄	—	8	2	no	—
576	C₄	C₂×#120×C₆₁	1	1	yes	characteristic
577	C₄	C₂×#127×C₆₁	1	1	yes	characteristic
578	C₄	D₄²×C₆₁	1	1	yes	characteristic
579	C₄	D₄²×C₆₁	1	1	yes	characteristic
580	C₂	—	2	1	no	—
581	C₂	—	2	1	no	—
582	C₂	—	4	2	no	—
583	C₂	—	8	2	no	—
584	C₂	—	8	4	no	—
585	C₂	C₆₁×#2433	1	1	yes	characteristic
586	C₂	C₆₁×#3290	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×C₆₁×#576	C₂
LCS	G ▷ C₂²×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. C₆₁×#3156	C₂	semidirect
3. C₂×C₆₁×#495	C₂	semidirect
4. C₂×C₆₁×#473	C₂	semidirect
5. C₂×C₆₁×#455	C₂	semidirect
6. C₆₁×#3009	C₂	semidirect
7. C₆₁×#2019	C₂	semidirect
8. C₆₁×#2003	C₂	semidirect
9. C₆₁×#1978	C₂	semidirect
10. C₆₁×#1974	C₂	semidirect
11. C₆₁×#1764	C₂	semidirect
16. C₂×#137×C₆₁	C₂²	semidirect
21. C₂²×Q₁₆×C₆₁	C₂²	semidirect
22. C₂²×SD₁₆×C₆₁	C₂²	semidirect
26. C₆₁×#536	C₂²	semidirect
27. C₂×#124×C₆₁	C₂²	semidirect
36. C₂×#108×C₆₁	C₂²	semidirect
38. C₂×#104×C₆₁	C₂²	semidirect
39. C₆₁×#418	C₂²	semidirect
41. C₂×#101×C₆₁	C₂²	semidirect
42. C₂×#100×C₆₁	C₂²	semidirect
43. C₆₁×#408	C₂²	semidirect
44. C₆₁×#405	C₂²	semidirect
45. C₂×C₄×C₈×C₆₁	C₂²	semidirect
46. C₆₁×#341	C₂²	semidirect
47. C₆₁×#339	C₂²	semidirect
264. #25804	C₆₁	direct (N × H)
288. #3156	C₂×C₆₁	semidirect
289. C₂×#495	C₂×C₆₁	semidirect
290. C₂×#473	C₂×C₆₁	semidirect
291. C₂×#455	C₂×C₆₁	semidirect
292. #3009	C₂×C₆₁	semidirect
293. #2019	C₂×C₆₁	semidirect
294. #2003	C₂×C₆₁	semidirect
295. #1978	C₂×C₆₁	semidirect
296. #1974	C₂×C₆₁	semidirect
297. #1764	C₂×C₆₁	semidirect
309. C₂×#137	C₂²×C₆₁	semidirect
314. C₂²×Q₁₆	C₂²×C₆₁	semidirect
315. C₂²×SD₁₆	C₂²×C₆₁	semidirect
319. #536	C₂²×C₆₁	semidirect
320. C₂×#124	C₂²×C₆₁	semidirect
329. C₂×#108	C₂²×C₆₁	semidirect
331. C₂×#104	C₂²×C₆₁	semidirect
332. #418	C₂²×C₆₁	semidirect
334. C₂×#101	C₂²×C₆₁	semidirect
335. C₂×#100	C₂²×C₆₁	semidirect
336. #408	C₂²×C₆₁	semidirect
337. #405	C₂²×C₆₁	semidirect
338. C₂×C₄×C₈	C₂²×C₆₁	semidirect
339. #341	C₂²×C₆₁	semidirect
340. #339	C₂²×C₆₁	semidirect
341. C₆₁	#25804	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#576	2
C₆₁×#3156	2
C₂×C₆₁×#495	2
C₂×C₆₁×#473	2
C₂×C₆₁×#455	2
C₆₁×#3009	2
C₆₁×#2019	2
C₆₁×#2003	2
C₆₁×#1978	2
C₆₁×#1974	2
C₆₁×#1764	2
#25804	61

Subgroups — C61×#25804 #29529237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25804 #29529237