Subgroups — C₃²×C₄×C₅₃⋊C₁₃ #37613639

Order 24804.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅₃⋊C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅₃⋊C₁₃	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅₃⋊C₁₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₅₃⋊C₁₃	C₂×C₃	1	4	yes	—
5	C₄×C₅₃⋊C₁₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₅₃⋊C₁₃	C₃×C₄	1	4	yes	direct product factor
7	C₃²×C₄×C₅₃	C₁₃	1	1	yes	maximal, characteristic, complemented, Hall
8	C₂×C₅₃⋊C₁₃	C₂×C₃²	1	1	yes	characteristic
9	C₂×C₃²×C₅₃	C₂×C₁₃	1	1	yes	characteristic
10	C₅₃⋊C₁₃	C₃²×C₄	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₄×C₅₃	C₃×C₁₃	1	4	yes	complemented
12	C₃²×C₅₃	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₃²×C₄×C₁₃	—	53	1	no	maximal, Hall
14	C₂×C₃×C₅₃	C₂×C₃×C₁₃	1	4	yes	—
15	C₂×C₃²×C₁₃	—	53	1	no	—
16	C₄×C₅₃	C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅₃	C₃×C₄×C₁₃	1	4	yes	complemented
18	C₃×C₄×C₁₃	—	53	4	no	—
19	C₃²×C₁₃	—	53	1	no	Hall
20	C₂×C₅₃	C₂×C₃²×C₁₃	1	1	yes	characteristic
21	C₂×C₃×C₁₃	—	53	4	no	—
22	C₅₃	C₃²×C₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
23	C₄×C₁₃	—	53	1	no	Hall
24	C₃×C₁₃	—	53	4	no	—
25	C₃²×C₄	C₅₃⋊C₁₃	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₁₃	—	53	1	no	—
27	C₂×C₃²	C₂×C₅₃⋊C₁₃	1	1	yes	characteristic
28	C₁₃	—	53	1	no	Sylow
29	C₃×C₄	C₃×C₅₃⋊C₁₃	1	4	yes	direct product factor
30	C₃²	C₄×C₅₃⋊C₁₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₂×C₃×C₅₃⋊C₁₃	1	4	yes	—
32	C₄	C₃²×C₅₃⋊C₁₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₃×C₄×C₅₃⋊C₁₃	1	4	yes	direct product factor
34	C₂	C₂×C₃²×C₅₃⋊C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃²×C₄	C₅₃⋊C₁₃
commutator, hypocenter	C₅₃	C₃²×C₄×C₁₃
Frattini	C₂	C₂×C₃²×C₅₃⋊C₁₃
Fitting	C₃²×C₄×C₅₃	C₁₃
socle	C₂×C₃²×C₅₃	C₂×C₁₃
prime radical	C₂×C₃²×C₅₃⋊C₁₃	C₂
cosocle	C₂×C₅₃	C₂×C₃²×C₁₃
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₃²×C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅₃⋊C₁₃	C₃	direct (N × H)
3. C₃²×C₅₃⋊C₁₃	C₄	direct (N × H)
5. C₄×C₅₃⋊C₁₃	C₃²	direct (N × H)
6. C₃×C₅₃⋊C₁₃	C₃×C₄	direct (N × H)
7. C₃²×C₄×C₅₃	C₁₃	semidirect
10. C₅₃⋊C₁₃	C₃²×C₄	direct (N × H)
11. C₃×C₄×C₅₃	C₃×C₁₃	semidirect
12. C₃²×C₅₃	C₄×C₁₃	semidirect
16. C₄×C₅₃	C₃²×C₁₃	semidirect
17. C₃×C₅₃	C₃×C₄×C₁₃	semidirect
22. C₅₃	C₃²×C₄×C₁₃	semidirect
25. C₃²×C₄	C₅₃⋊C₁₃	direct (N × H)
29. C₃×C₄	C₃×C₅₃⋊C₁₃	direct (N × H)
30. C₃²	C₄×C₅₃⋊C₁₃	direct (N × H)
32. C₄	C₃²×C₅₃⋊C₁₃	direct (N × H)
33. C₃	C₃×C₄×C₅₃⋊C₁₃	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×C₃²×C₅₃⋊C₁₃	2
C₃×C₄×C₅₃⋊C₁₃	3
C₃²×C₄×C₅₃	13
C₃²×C₄×C₁₃	53

Subgroups — C32×C4×C53⋊C13 #37613639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₄×C₅₃⋊C₁₃ #37613639