Subgroups — C₂⁵×#92420 #30626735

Order 15616.

15454 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×#92420	C₂	1	62	yes	maximal, direct product factor
2	C₂⁵×Dic₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂³×#92420	C₂²	1	620	yes	direct product factor
4	C₂⁴×Dic₆₁	C₄	1	31	yes	—
5	C₂⁴×Dic₆₁	C₂²	1	31	yes	—
6	C₂⁶×C₆₁	C₄	1	1	yes	characteristic
7	C₂²×#92420	C₂³	1	1240	yes	direct product factor
8	C₂³×Dic₆₁	C₂×C₄	1	465	yes	—
9	C₂³×Dic₆₁	C₂³	1	155	yes	—
10	C₂⁵×C₆₁	C₈	1	32	yes	complemented
11	C₂⁵×C₆₁	C₂×C₄	1	31	yes	—
12	C₂⁴×C₆₁	C₂×C₈	1	496	yes	complemented
13	C₂⁴×C₆₁	C₂²×C₄	1	155	yes	—
14	C₂²×Dic₆₁	C₂²×C₄	1	1085	yes	—
15	C₂²×Dic₆₁	C₂⁴	1	155	yes	—
16	C₂×#92420	C₂⁴	1	496	yes	direct product factor
17	C₂³×C₆₁	C₂²×C₈	1	1240	yes	complemented
18	C₂³×C₆₁	C₂³×C₄	1	155	yes	—
19	C₂×Dic₆₁	C₂³×C₄	1	465	yes	—
20	C₂×Dic₆₁	C₂⁵	1	31	yes	—
21	#92420	C₂⁵	1	32	yes	direct product factor
22	C₂⁵×C₈	—	61	1	no	maximal, Sylow
23	C₂²×C₆₁	C₂³×C₈	1	620	yes	complemented
24	C₂²×C₆₁	C₂⁴×C₄	1	31	yes	—
25	Dic₆₁	C₂⁴×C₄	1	31	yes	—
26	Dic₆₁	C₂⁶	1	1	yes	characteristic
27	C₂⁵×C₄	—	61	1	no	—
28	C₂⁴×C₈	—	61	62	no	—
29	C₂×C₆₁	C₂⁴×C₈	1	62	yes	complemented
30	C₂×C₆₁	C₂⁵×C₄	1	1	yes	characteristic
31	C₂⁶	#6923	1	1	yes	characteristic
32	C₂⁴×C₄	—	61	31	no	—
33	C₂⁴×C₄	—	61	31	no	—
34	C₂³×C₈	—	61	620	no	—
35	C₆₁	C₂⁵×C₈	1	1	yes	characteristic, complemented, Sylow
36	C₂⁵	#92420	1	32	yes	direct product factor
37	C₂⁵	C₂×#6923	1	31	yes	—
38	C₂³×C₄	—	61	465	no	—
39	C₂³×C₄	—	61	155	no	—
40	C₂²×C₈	—	61	1240	no	—
41	C₂⁴	C₂×#92420	1	496	yes	direct product factor
42	C₂⁴	C₂²×#6923	1	155	yes	—
43	C₂²×C₄	—	61	155	no	—
44	C₂²×C₄	—	61	1085	no	—
45	C₂×C₈	—	61	496	no	—
46	C₂³	C₂²×#92420	1	1240	yes	direct product factor
47	C₂³	C₂³×#6923	1	155	yes	—
48	C₂×C₄	—	61	465	no	—
49	C₂×C₄	—	61	31	no	—
50	C₈	—	61	32	no	—
51	C₂²	C₂³×#92420	1	620	yes	direct product factor
52	C₂²	C₂⁴×#6923	1	31	yes	—
53	C₄	—	61	31	no	—
54	C₄	—	61	1	no	—
55	C₂	C₂⁴×#92420	1	62	yes	direct product factor
56	C₂	C₂⁵×#6923	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁶	#6923
commutator, hypocenter	C₆₁	C₂⁵×C₈
Frattini	C₂	C₂⁵×#6923
Fitting, socle, prime radical	C₂⁶×C₆₁	C₄
cosocle	Dic₆₁	C₂⁶
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂⁴×#92420	C₂	direct (N × H)
3. C₂³×#92420	C₂²	direct (N × H)
7. C₂²×#92420	C₂³	direct (N × H)
10. C₂⁵×C₆₁	C₈	semidirect
12. C₂⁴×C₆₁	C₂×C₈	semidirect
16. C₂×#92420	C₂⁴	direct (N × H)
17. C₂³×C₆₁	C₂²×C₈	semidirect
21. #92420	C₂⁵	direct (N × H)
23. C₂²×C₆₁	C₂³×C₈	semidirect
29. C₂×C₆₁	C₂⁴×C₈	semidirect
35. C₆₁	C₂⁵×C₈	semidirect
36. C₂⁵	#92420	direct (N × H)
41. C₂⁴	C₂×#92420	direct (N × H)
46. C₂³	C₂²×#92420	direct (N × H)
51. C₂²	C₂³×#92420	direct (N × H)
55. C₂	C₂⁴×#92420	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×#92420	2
C₂⁵×Dic₆₁	2
C₂⁵×C₈	61

Subgroups — C25×#92420 #30626735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×#92420 #30626735