Subgroups — C₄×C₁₁×C₁₉×C₃₇ #44525809

Order 30932.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₉×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₉×C₃₇	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₉×C₃₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₄×C₁₁×C₃₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₉×C₃₇	C₂×C₁₁	1	1	yes	characteristic
6	C₄×C₁₁×C₁₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₁×C₃₇	C₂×C₁₉	1	1	yes	characteristic
8	C₁₉×C₃₇	C₄×C₁₁	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₁₁×C₁₉	C₂×C₃₇	1	1	yes	characteristic
10	C₁₁×C₃₇	C₄×C₁₉	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁×C₁₉	C₄×C₃₇	1	1	yes	characteristic, direct product factor, Hall
12	C₄×C₃₇	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₁₉	C₁₁×C₃₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃₇	C₂×C₁₁×C₁₉	1	1	yes	characteristic
15	C₄×C₁₁	C₁₉×C₃₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₉	C₂×C₁₁×C₃₇	1	1	yes	characteristic
17	C₃₇	C₄×C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₁₁	C₂×C₁₉×C₃₇	1	1	yes	characteristic
19	C₁₉	C₄×C₁₁×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₁	C₄×C₁₉×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	C₁₁×C₁₉×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₁₁×C₁₉×C₃₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₁₁×C₁₉×C₃₇
socle, prime radical	C₂×C₁₁×C₁₉×C₃₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₁₉×C₃₇	C₄	direct (N × H)
3. C₄×C₁₉×C₃₇	C₁₁	direct (N × H)
4. C₄×C₁₁×C₃₇	C₁₉	direct (N × H)
6. C₄×C₁₁×C₁₉	C₃₇	direct (N × H)
8. C₁₉×C₃₇	C₄×C₁₁	direct (N × H)
10. C₁₁×C₃₇	C₄×C₁₉	direct (N × H)
11. C₁₁×C₁₉	C₄×C₃₇	direct (N × H)
12. C₄×C₃₇	C₁₁×C₁₉	direct (N × H)
13. C₄×C₁₉	C₁₁×C₃₇	direct (N × H)
15. C₄×C₁₁	C₁₉×C₃₇	direct (N × H)
17. C₃₇	C₄×C₁₁×C₁₉	direct (N × H)
19. C₁₉	C₄×C₁₁×C₃₇	direct (N × H)
20. C₁₁	C₄×C₁₉×C₃₇	direct (N × H)
21. C₄	C₁₁×C₁₉×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
C₂×C₁₁×C₁₉×C₃₇	2
C₄×C₁₉×C₃₇	11
C₄×C₁₁×C₃₇	19
C₄×C₁₁×C₁₉	37

Subgroups — C4×C11×C19×C37 #44525809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₁×C₁₉×C₃₇ #44525809