Subgroups — C₃²×C₄×C₁₉×C₅₃ #49136242

Order 36252.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₉×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₁₉×C₅₃	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₉×C₅₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₉×C₅₃	C₂×C₃	1	4	yes	—
5	C₄×C₁₉×C₅₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₉×C₅₃	C₃×C₄	1	4	yes	direct product factor
7	C₂×C₁₉×C₅₃	C₂×C₃²	1	1	yes	characteristic
8	C₃²×C₄×C₅₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₉×C₅₃	C₃²×C₄	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃²×C₅₃	C₂×C₁₉	1	1	yes	characteristic
11	C₃²×C₄×C₁₉	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃×C₄×C₅₃	C₃×C₁₉	1	4	yes	direct product factor
13	C₃²×C₅₃	C₄×C₁₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃²×C₁₉	C₂×C₅₃	1	1	yes	characteristic
15	C₂×C₃×C₅₃	C₂×C₃×C₁₉	1	4	yes	—
16	C₃×C₄×C₁₉	C₃×C₅₃	1	4	yes	direct product factor
17	C₄×C₅₃	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
18	C₃²×C₁₉	C₄×C₅₃	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₅₃	C₃×C₄×C₁₉	1	4	yes	direct product factor
20	C₂×C₃×C₁₉	C₂×C₃×C₅₃	1	4	yes	—
21	C₂×C₅₃	C₂×C₃²×C₁₉	1	1	yes	characteristic
22	C₄×C₁₉	C₃²×C₅₃	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₁₉	C₃×C₄×C₅₃	1	4	yes	direct product factor
24	C₅₃	C₃²×C₄×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₁₉	C₂×C₃²×C₅₃	1	1	yes	characteristic
26	C₃²×C₄	C₁₉×C₅₃	1	1	yes	characteristic, direct product factor, Hall
27	C₁₉	C₃²×C₄×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃²	C₂×C₁₉×C₅₃	1	1	yes	characteristic
29	C₃×C₄	C₃×C₁₉×C₅₃	1	4	yes	direct product factor
30	C₃²	C₄×C₁₉×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₂×C₃×C₁₉×C₅₃	1	4	yes	—
32	C₄	C₃²×C₁₉×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₃×C₄×C₁₉×C₅₃	1	4	yes	direct product factor
34	C₂	C₂×C₃²×C₁₉×C₅₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃²×C₁₉×C₅₃
socle, prime radical	C₂×C₃²×C₁₉×C₅₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₁₉×C₅₃	C₃	direct (N × H)
3. C₃²×C₁₉×C₅₃	C₄	direct (N × H)
5. C₄×C₁₉×C₅₃	C₃²	direct (N × H)
6. C₃×C₁₉×C₅₃	C₃×C₄	direct (N × H)
8. C₃²×C₄×C₅₃	C₁₉	direct (N × H)
9. C₁₉×C₅₃	C₃²×C₄	direct (N × H)
11. C₃²×C₄×C₁₉	C₅₃	direct (N × H)
12. C₃×C₄×C₅₃	C₃×C₁₉	direct (N × H)
13. C₃²×C₅₃	C₄×C₁₉	direct (N × H)
16. C₃×C₄×C₁₉	C₃×C₅₃	direct (N × H)
17. C₄×C₅₃	C₃²×C₁₉	direct (N × H)
18. C₃²×C₁₉	C₄×C₅₃	direct (N × H)
19. C₃×C₅₃	C₃×C₄×C₁₉	direct (N × H)
22. C₄×C₁₉	C₃²×C₅₃	direct (N × H)
23. C₃×C₁₉	C₃×C₄×C₅₃	direct (N × H)
24. C₅₃	C₃²×C₄×C₁₉	direct (N × H)
26. C₃²×C₄	C₁₉×C₅₃	direct (N × H)
27. C₁₉	C₃²×C₄×C₅₃	direct (N × H)
29. C₃×C₄	C₃×C₁₉×C₅₃	direct (N × H)
30. C₃²	C₄×C₁₉×C₅₃	direct (N × H)
32. C₄	C₃²×C₁₉×C₅₃	direct (N × H)
33. C₃	C₃×C₄×C₁₉×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
C₂×C₃²×C₁₉×C₅₃	2
C₃×C₄×C₁₉×C₅₃	3
C₃²×C₄×C₅₃	19
C₃²×C₄×C₁₉	53

Subgroups — C32×C4×C19×C53 #49136242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₄×C₁₉×C₅₃ #49136242