Subgroups — C₃²×C₅₃×Dic₁₉ #49136264

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×C₅₃×Dic₁₉	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₉×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₉×C₅₃	C₂×C₃	1	4	yes	—
5	C₅₃×Dic₁₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₉×C₅₃	C₃×C₄	1	4	yes	complemented
7	C₂×C₁₉×C₅₃	C₂×C₃²	1	1	yes	characteristic
8	C₃²×C₄×C₅₃	—	19	1	no	maximal, Hall
9	C₁₉×C₅₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃²×C₅₃	D₁₉	1	1	yes	characteristic
11	C₃²×Dic₁₉	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃×C₄×C₅₃	—	19	4	no	—
13	C₃²×C₅₃	Dic₁₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃²×C₁₉	C₂×C₅₃	1	1	yes	characteristic
15	C₂×C₃×C₅₃	C₃×D₁₉	1	4	yes	—
16	C₃×Dic₁₉	C₃×C₅₃	1	4	yes	direct product factor
17	C₄×C₅₃	—	19	1	no	Hall
18	C₃²×C₁₉	C₄×C₅₃	1	1	yes	characteristic, complemented, Hall
19	C₃×C₅₃	C₃×Dic₁₉	1	4	yes	direct product factor
20	C₂×C₃×C₁₉	C₂×C₃×C₅₃	1	4	yes	—
21	C₂×C₅₃	C₃²×D₁₉	1	1	yes	characteristic
22	Dic₁₉	C₃²×C₅₃	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₁₉	C₃×C₄×C₅₃	1	4	yes	complemented
24	C₅₃	C₃²×Dic₁₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₁₉	C₂×C₃²×C₅₃	1	1	yes	characteristic
26	C₃²×C₄	—	19	1	no	Hall
27	C₁₉	C₃²×C₄×C₅₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃²	D₁₉×C₅₃	1	1	yes	characteristic
29	C₃×C₄	—	19	4	no	—
30	C₃²	C₅₃×Dic₁₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₃×D₁₉×C₅₃	1	4	yes	—
32	C₄	—	19	1	no	Sylow
33	C₃	C₃×C₅₃×Dic₁₉	1	4	yes	direct product factor
34	C₂	C₃²×D₁₉×C₅₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅₃	D₁₉
commutator, hypocenter	C₁₉	C₃²×C₄×C₅₃
Frattini	C₂	C₃²×D₁₉×C₅₃
Fitting, socle, prime radical	C₂×C₃²×C₁₉×C₅₃	C₂
cosocle	C₂×C₁₉	C₂×C₃²×C₅₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₃²×C₅₃

Complements

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

N	H ≅ G/N	type
2. C₃×C₅₃×Dic₁₉	C₃	direct (N × H)
3. C₃²×C₁₉×C₅₃	C₄	semidirect
5. C₅₃×Dic₁₉	C₃²	direct (N × H)
6. C₃×C₁₉×C₅₃	C₃×C₄	semidirect
9. C₁₉×C₅₃	C₃²×C₄	semidirect
11. C₃²×Dic₁₉	C₅₃	direct (N × H)
13. C₃²×C₅₃	Dic₁₉	direct (N × H)
16. C₃×Dic₁₉	C₃×C₅₃	direct (N × H)
18. C₃²×C₁₉	C₄×C₅₃	semidirect
19. C₃×C₅₃	C₃×Dic₁₉	direct (N × H)
22. Dic₁₉	C₃²×C₅₃	direct (N × H)
23. C₃×C₁₉	C₃×C₄×C₅₃	semidirect
24. C₅₃	C₃²×Dic₁₉	direct (N × H)
27. C₁₉	C₃²×C₄×C₅₃	semidirect
30. C₃²	C₅₃×Dic₁₉	direct (N × H)
33. C₃	C₃×C₅₃×Dic₁₉	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×C₅₃×Dic₁₉	3
C₃²×C₄×C₅₃	19
C₃²×Dic₁₉	53

Subgroups — C32×C53×Dic19 #49136264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅₃×Dic₁₉ #49136264