Subgroups — C₃×C₅×C₁₇×C₃₇⋊C₃ #43246700

Order 28305.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×C₃₇⋊C₃	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₅×C₁₇×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₇×C₃₇⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₇×C₃₇	C₃²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×C₃₇	C₃×C₅	1	1	yes	characteristic, complemented
6	C₁₇×C₃₇⋊C₃	C₃×C₅	1	3	yes	direct product factor
7	C₃×C₅×C₃₇⋊C₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃²×C₅×C₁₇	—	37	1	no	maximal, Hall
9	C₁₇×C₃₇	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×C₃₇	C₃×C₁₇	1	1	yes	characteristic, complemented
11	C₅×C₃₇⋊C₃	C₃×C₁₇	1	3	yes	direct product factor
12	C₃×C₃₇⋊C₃	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₁₇	—	37	3	no	—
14	C₃×C₅×C₁₇	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
15	C₅×C₃₇	C₃²×C₁₇	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₁₇	—	37	1	no	Hall
17	C₃×C₃₇	C₃×C₅×C₁₇	1	1	yes	characteristic, complemented
18	C₃₇⋊C₃	C₃×C₅×C₁₇	1	3	yes	direct product factor
19	C₅×C₁₇	C₃×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₁₇	—	37	3	no	—
21	C₃×C₁₇	C₅×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
22	C₃²×C₅	—	37	1	no	Hall
23	C₃₇	C₃²×C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
24	C₁₇	C₃×C₅×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	—	37	3	no	—
26	C₃×C₅	C₁₇×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
27	C₃²	—	37	1	no	Sylow
28	C₅	C₃×C₁₇×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	37	3	no	—
30	C₃	C₅×C₁₇×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₇	C₃₇⋊C₃
commutator, cosocle, hypocenter	C₃₇	C₃²×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₃₇	C₃
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₃×C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₇×C₃₇⋊C₃	C₃	direct (N × H)
2. C₃×C₅×C₁₇×C₃₇	C₃	semidirect
3. C₃×C₁₇×C₃₇⋊C₃	C₅	direct (N × H)
4. C₅×C₁₇×C₃₇	C₃²	semidirect
5. C₃×C₁₇×C₃₇	C₃×C₅	semidirect
6. C₁₇×C₃₇⋊C₃	C₃×C₅	direct (N × H)
7. C₃×C₅×C₃₇⋊C₃	C₁₇	direct (N × H)
9. C₁₇×C₃₇	C₃²×C₅	semidirect
10. C₃×C₅×C₃₇	C₃×C₁₇	semidirect
11. C₅×C₃₇⋊C₃	C₃×C₁₇	direct (N × H)
12. C₃×C₃₇⋊C₃	C₅×C₁₇	direct (N × H)
14. C₃×C₅×C₁₇	C₃₇⋊C₃	direct (N × H)
15. C₅×C₃₇	C₃²×C₁₇	semidirect
17. C₃×C₃₇	C₃×C₅×C₁₇	semidirect
18. C₃₇⋊C₃	C₃×C₅×C₁₇	direct (N × H)
19. C₅×C₁₇	C₃×C₃₇⋊C₃	direct (N × H)
21. C₃×C₁₇	C₅×C₃₇⋊C₃	direct (N × H)
23. C₃₇	C₃²×C₅×C₁₇	semidirect
24. C₁₇	C₃×C₅×C₃₇⋊C₃	direct (N × H)
26. C₃×C₅	C₁₇×C₃₇⋊C₃	direct (N × H)
28. C₅	C₃×C₁₇×C₃₇⋊C₃	direct (N × H)
30. C₃	C₅×C₁₇×C₃₇⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₇×C₃₇⋊C₃	3
C₃×C₅×C₁₇×C₃₇	3
C₃×C₁₇×C₃₇⋊C₃	5
C₃×C₅×C₃₇⋊C₃	17
C₃²×C₅×C₁₇	37

Subgroups — C3×C5×C17×C37⋊C3 #43246700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₇×C₃₇⋊C₃ #43246700