Subgroups — C₃×C₅²×C₁₃×C₃₇ #49115239

Order 36075.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₃×C₃₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₅×C₁₃×C₃₇	C₅	1	6	yes	maximal, direct product factor
3	C₃×C₅²×C₃₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₃×C₃₇	C₃×C₅	1	6	yes	direct product factor
5	C₃×C₁₃×C₃₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₅²×C₁₃	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅²×C₃₇	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₅×C₃₇	C₅×C₁₃	1	6	yes	direct product factor
9	C₁₃×C₃₇	C₃×C₅²	1	1	yes	characteristic, direct product factor, Hall
10	C₅²×C₁₃	C₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₅×C₁₃	C₅×C₃₇	1	6	yes	direct product factor
12	C₅×C₃₇	C₃×C₅×C₁₃	1	6	yes	direct product factor
13	C₃×C₃₇	C₅²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₅²	C₁₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₁₃	C₃×C₅×C₃₇	1	6	yes	direct product factor
16	C₃×C₁₃	C₅²×C₃₇	1	1	yes	characteristic, direct product factor, Hall
17	C₃₇	C₃×C₅²×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₅²	C₃×C₁₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₅	C₅×C₁₃×C₃₇	1	6	yes	direct product factor
20	C₁₃	C₃×C₅²×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₃×C₅×C₁₃×C₃₇	1	6	yes	direct product factor
22	C₃	C₅²×C₁₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅²×C₁₃×C₃₇	C₃	direct (N × H)
2. C₃×C₅×C₁₃×C₃₇	C₅	direct (N × H)
3. C₃×C₅²×C₃₇	C₁₃	direct (N × H)
4. C₅×C₁₃×C₃₇	C₃×C₅	direct (N × H)
5. C₃×C₁₃×C₃₇	C₅²	direct (N × H)
6. C₃×C₅²×C₁₃	C₃₇	direct (N × H)
7. C₅²×C₃₇	C₃×C₁₃	direct (N × H)
8. C₃×C₅×C₃₇	C₅×C₁₃	direct (N × H)
9. C₁₃×C₃₇	C₃×C₅²	direct (N × H)
10. C₅²×C₁₃	C₃×C₃₇	direct (N × H)
11. C₃×C₅×C₁₃	C₅×C₃₇	direct (N × H)
12. C₅×C₃₇	C₃×C₅×C₁₃	direct (N × H)
13. C₃×C₃₇	C₅²×C₁₃	direct (N × H)
14. C₃×C₅²	C₁₃×C₃₇	direct (N × H)
15. C₅×C₁₃	C₃×C₅×C₃₇	direct (N × H)
16. C₃×C₁₃	C₅²×C₃₇	direct (N × H)
17. C₃₇	C₃×C₅²×C₁₃	direct (N × H)
18. C₅²	C₃×C₁₃×C₃₇	direct (N × H)
19. C₃×C₅	C₅×C₁₃×C₃₇	direct (N × H)
20. C₁₃	C₃×C₅²×C₃₇	direct (N × H)
21. C₅	C₃×C₅×C₁₃×C₃₇	direct (N × H)
22. C₃	C₅²×C₁₃×C₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₁₃×C₃₇	3
C₃×C₅×C₁₃×C₃₇	5
C₃×C₅²×C₃₇	13
C₃×C₅²×C₁₃	37

Subgroups — C3×C52×C13×C37 #49115239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅²×C₁₃×C₃₇ #49115239