Subgroups — C₃×C₈×C₁₃×C₅₃ #72194559

Order 16536.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₃×C₅₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₄×C₁₃×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₁₃×C₅₃	C₄	1	1	yes	characteristic
4	C₄×C₁₃×C₅₃	C₂×C₃	1	1	yes	characteristic
5	C₃×C₁₃×C₅₃	C₈	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₃×C₅₃	C₃×C₄	1	1	yes	characteristic
7	C₃×C₈×C₅₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₃×C₅₃	C₃×C₈	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₄×C₅₃	C₂×C₁₃	1	1	yes	characteristic
10	C₈×C₅₃	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₅₃	C₄×C₁₃	1	1	yes	characteristic
12	C₃×C₈×C₁₃	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₄×C₅₃	C₂×C₃×C₁₃	1	1	yes	characteristic
14	C₃×C₅₃	C₈×C₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₄×C₁₃	C₂×C₅₃	1	1	yes	characteristic
16	C₂×C₅₃	C₃×C₄×C₁₃	1	1	yes	characteristic
17	C₈×C₁₃	C₃×C₅₃	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₁₃	C₄×C₅₃	1	1	yes	characteristic
19	C₅₃	C₃×C₈×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₄×C₁₃	C₂×C₃×C₅₃	1	1	yes	characteristic
21	C₃×C₁₃	C₈×C₅₃	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₃	C₃×C₄×C₅₃	1	1	yes	characteristic
23	C₃×C₈	C₁₃×C₅₃	1	1	yes	characteristic, direct product factor, Hall
24	C₁₃	C₃×C₈×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₄	C₂×C₁₃×C₅₃	1	1	yes	characteristic
26	C₈	C₃×C₁₃×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₄×C₁₃×C₅₃	1	1	yes	characteristic
28	C₄	C₂×C₃×C₁₃×C₅₃	1	1	yes	characteristic
29	C₃	C₈×C₁₃×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₃×C₄×C₁₃×C₅₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₁₃×C₅₃
socle, prime radical	C₂×C₃×C₁₃×C₅₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈×C₁₃×C₅₃	C₃	direct (N × H)
5. C₃×C₁₃×C₅₃	C₈	direct (N × H)
7. C₃×C₈×C₅₃	C₁₃	direct (N × H)
8. C₁₃×C₅₃	C₃×C₈	direct (N × H)
10. C₈×C₅₃	C₃×C₁₃	direct (N × H)
12. C₃×C₈×C₁₃	C₅₃	direct (N × H)
14. C₃×C₅₃	C₈×C₁₃	direct (N × H)
17. C₈×C₁₃	C₃×C₅₃	direct (N × H)
19. C₅₃	C₃×C₈×C₁₃	direct (N × H)
21. C₃×C₁₃	C₈×C₅₃	direct (N × H)
23. C₃×C₈	C₁₃×C₅₃	direct (N × H)
24. C₁₃	C₃×C₈×C₅₃	direct (N × H)
26. C₈	C₃×C₁₃×C₅₃	direct (N × H)
29. C₃	C₈×C₁₃×C₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×C₁₃×C₅₃	3
C₃×C₄×C₁₃×C₅₃	2
C₃×C₈×C₅₃	13
C₃×C₈×C₁₃	53

Subgroups — C3×C8×C13×C53 #72194559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×C₁₃×C₅₃ #72194559