Subgroups — C₄×C₅×C₃₁×C₁₃⋊C₃ #37563705

Order 24180.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃₁×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₁₃×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₃₁×C₁₃⋊C₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₄×C₃₁×C₁₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₃×C₃₁	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃₁×C₁₃⋊C₃	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₃×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×C₄×C₅×C₃₁	—	13	1	no	maximal, Hall
9	C₄×C₁₃×C₃₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₃₁×C₁₃⋊C₃	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₅×C₃₁	—	13	1	no	—
12	C₂×C₁₃×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic
13	C₄×C₅×C₁₃⋊C₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₄×C₅×C₃₁	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅×C₃₁	—	13	1	no	Hall
16	C₁₃×C₃₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₁₃⋊C₃	C₂×C₃₁	1	1	yes	characteristic
18	C₃×C₄×C₃₁	—	13	1	no	Hall
19	C₂×C₅×C₃₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic
20	C₄×C₅×C₁₃	C₃×C₃₁	1	1	yes	characteristic, complemented, Hall
21	C₅×C₁₃⋊C₃	C₄×C₃₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₃₁	—	13	1	no	—
23	C₄×C₁₃⋊C₃	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
24	C₅×C₃₁	C₄×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₅×C₁₃	C₂×C₃×C₃₁	1	1	yes	characteristic
26	C₄×C₃₁	C₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
27	C₃×C₃₁	—	13	1	no	Hall
28	C₂×C₁₃⋊C₃	C₂×C₅×C₃₁	1	1	yes	characteristic
29	C₅×C₁₃	C₃×C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃₁	C₂×C₅×C₁₃⋊C₃	1	1	yes	characteristic
31	C₃×C₄×C₅	—	13	1	no	Hall
32	C₄×C₁₃	C₃×C₅×C₃₁	1	1	yes	characteristic, complemented, Hall
33	C₁₃⋊C₃	C₄×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
34	C₃₁	C₄×C₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₃×C₅	—	13	1	no	—
36	C₂×C₁₃	C₂×C₃×C₅×C₃₁	1	1	yes	characteristic
37	C₄×C₅	C₃₁×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
38	C₃×C₅	—	13	1	no	Hall
39	C₁₃	C₃×C₄×C₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	13	1	no	Hall
41	C₂×C₅	C₂×C₃₁×C₁₃⋊C₃	1	1	yes	characteristic
42	C₂×C₃	—	13	1	no	—
43	C₅	C₄×C₃₁×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	C₅×C₃₁×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	C₂×C₅×C₃₁×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₅×C₃₁	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₃×C₄×C₅×C₃₁
Frattini	C₂	C₂×C₅×C₃₁×C₁₃⋊C₃
Fitting	C₄×C₅×C₁₃×C₃₁	C₃
socle	C₂×C₅×C₁₃×C₃₁	C₂×C₃
prime radical	C₂×C₅×C₃₁×C₁₃⋊C₃	C₂
cosocle	C₂×C₁₃	C₂×C₃×C₅×C₃₁
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₄×C₅×C₃₁

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×C₁₃×C₃₁	C₃	semidirect
3. C₅×C₃₁×C₁₃⋊C₃	C₄	direct (N × H)
4. C₄×C₃₁×C₁₃⋊C₃	C₅	direct (N × H)
7. C₅×C₁₃×C₃₁	C₃×C₄	semidirect
9. C₄×C₁₃×C₃₁	C₃×C₅	semidirect
10. C₃₁×C₁₃⋊C₃	C₄×C₅	direct (N × H)
13. C₄×C₅×C₁₃⋊C₃	C₃₁	direct (N × H)
14. C₄×C₅×C₃₁	C₁₃⋊C₃	direct (N × H)
16. C₁₃×C₃₁	C₃×C₄×C₅	semidirect
20. C₄×C₅×C₁₃	C₃×C₃₁	semidirect
21. C₅×C₁₃⋊C₃	C₄×C₃₁	direct (N × H)
23. C₄×C₁₃⋊C₃	C₅×C₃₁	direct (N × H)
24. C₅×C₃₁	C₄×C₁₃⋊C₃	direct (N × H)
26. C₄×C₃₁	C₅×C₁₃⋊C₃	direct (N × H)
29. C₅×C₁₃	C₃×C₄×C₃₁	semidirect
32. C₄×C₁₃	C₃×C₅×C₃₁	semidirect
33. C₁₃⋊C₃	C₄×C₅×C₃₁	direct (N × H)
34. C₃₁	C₄×C₅×C₁₃⋊C₃	direct (N × H)
37. C₄×C₅	C₃₁×C₁₃⋊C₃	direct (N × H)
39. C₁₃	C₃×C₄×C₅×C₃₁	semidirect
43. C₅	C₄×C₃₁×C₁₃⋊C₃	direct (N × H)
44. C₄	C₅×C₃₁×C₁₃⋊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
C₂×C₅×C₃₁×C₁₃⋊C₃	2
C₄×C₅×C₁₃×C₃₁	3
C₄×C₃₁×C₁₃⋊C₃	5
C₃×C₄×C₅×C₃₁	13
C₄×C₅×C₁₃⋊C₃	31

Subgroups — C4×C5×C31×C13⋊C3 #37563705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₃₁×C₁₃⋊C₃ #37563705