Subgroups — C₂×C₃²×C₂₅×C₅₃ #37558680

Order 23850.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₅×C₅₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₂₅×C₅₃	C₃	1	4	yes	maximal, direct product factor
3	C₂×C₃²×C₅×C₅₃	C₅	1	1	yes	maximal, characteristic
4	C₃×C₂₅×C₅₃	C₂×C₃	1	4	yes	direct product factor
5	C₂×C₂₅×C₅₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₅×C₅₃	C₂×C₅	1	1	yes	characteristic
7	C₂×C₃×C₅×C₅₃	C₃×C₅	1	4	yes	—
8	C₂₅×C₅₃	C₂×C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃²×C₅₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅×C₅₃	C₂×C₃×C₅	1	4	yes	—
11	C₂×C₅×C₅₃	C₃²×C₅	1	1	yes	characteristic
12	C₃²×C₅₃	C₂×C₂₅	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃²×C₂₅	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₅₃	C₃×C₂₅	1	4	yes	direct product factor
15	C₅×C₅₃	C₂×C₃²×C₅	1	1	yes	characteristic
16	C₃²×C₂₅	C₂×C₅₃	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₅₃	C₂×C₃×C₂₅	1	4	yes	direct product factor
18	C₂×C₃×C₂₅	C₃×C₅₃	1	4	yes	direct product factor
19	C₂×C₅₃	C₃²×C₂₅	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃²×C₅	C₅×C₅₃	1	1	yes	characteristic
21	C₃×C₂₅	C₂×C₃×C₅₃	1	4	yes	direct product factor
22	C₅₃	C₂×C₃²×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₂₅	C₃²×C₅₃	1	1	yes	characteristic, direct product factor, Hall
24	C₃²×C₅	C₂×C₅×C₅₃	1	1	yes	characteristic
25	C₂×C₃×C₅	C₃×C₅×C₅₃	1	4	yes	—
26	C₂₅	C₂×C₃²×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃²	C₂₅×C₅₃	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₅	C₂×C₃×C₅×C₅₃	1	4	yes	—
29	C₂×C₅	C₃²×C₅×C₅₃	1	1	yes	characteristic
30	C₃²	C₂×C₂₅×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₃×C₂₅×C₅₃	1	4	yes	direct product factor
32	C₅	C₂×C₃²×C₅×C₅₃	1	1	yes	characteristic
33	C₃	C₂×C₃×C₂₅×C₅₃	1	4	yes	direct product factor
34	C₂	C₃²×C₂₅×C₅₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂×C₃²×C₅×C₅₃
socle, prime radical	C₂×C₃²×C₅×C₅₃	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₅×C₅₃	C₂	direct (N × H)
2. C₂×C₃×C₂₅×C₅₃	C₃	direct (N × H)
4. C₃×C₂₅×C₅₃	C₂×C₃	direct (N × H)
5. C₂×C₂₅×C₅₃	C₃²	direct (N × H)
8. C₂₅×C₅₃	C₂×C₃²	direct (N × H)
9. C₂×C₃²×C₅₃	C₂₅	direct (N × H)
12. C₃²×C₅₃	C₂×C₂₅	direct (N × H)
13. C₂×C₃²×C₂₅	C₅₃	direct (N × H)
14. C₂×C₃×C₅₃	C₃×C₂₅	direct (N × H)
16. C₃²×C₂₅	C₂×C₅₃	direct (N × H)
17. C₃×C₅₃	C₂×C₃×C₂₅	direct (N × H)
18. C₂×C₃×C₂₅	C₃×C₅₃	direct (N × H)
19. C₂×C₅₃	C₃²×C₂₅	direct (N × H)
21. C₃×C₂₅	C₂×C₃×C₅₃	direct (N × H)
22. C₅₃	C₂×C₃²×C₂₅	direct (N × H)
23. C₂×C₂₅	C₃²×C₅₃	direct (N × H)
26. C₂₅	C₂×C₃²×C₅₃	direct (N × H)
27. C₂×C₃²	C₂₅×C₅₃	direct (N × H)
30. C₃²	C₂×C₂₅×C₅₃	direct (N × H)
31. C₂×C₃	C₃×C₂₅×C₅₃	direct (N × H)
33. C₃	C₂×C₃×C₂₅×C₅₃	direct (N × H)
34. C₂	C₃²×C₂₅×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
C₃²×C₂₅×C₅₃	2
C₂×C₃×C₂₅×C₅₃	3
C₂×C₃²×C₅×C₅₃	5
C₂×C₃²×C₂₅	53

Subgroups — C2×C32×C25×C53 #37558680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₂₅×C₅₃ #37558680