Subgroups — C₅×C₂²⋊#11925881 #37563993

Order 24180.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₁₃×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×#11925881	—	4	1	no	maximal, Hall
3	C₂²⋊#11925881	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₅×C₁₃×C₃₁	—	3	1	no	—
5	C₅×C₁₃×C₃₁	A₄	1	1	yes	characteristic, complemented, Hall
6	C₅×C₂²⋊(C₃₁⋊C₃)	—	13	1	no	maximal, Hall
7	C₂²×C₁₃×C₃₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	#11925881	—	4	1	no	Hall
9	C₂×C₁₃×C₃₁	—	3	1	no	—
10	C₅×C₂²⋊(C₁₃⋊C₃)	—	31	1	no	maximal, Hall
11	C₂²×C₅×C₃₁	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₅×C₃₁⋊C₃	—	52	1	no	Hall
13	C₁₃×C₃₁	C₅×A₄	1	1	yes	characteristic, complemented, Hall
14	C₂²⋊(C₃₁⋊C₃)	—	13	1	no	Hall
15	C₂×C₅×C₃₁	—	3	1	no	—
16	C₂²×C₅×C₁₃	C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₅×C₁₃⋊C₃	—	124	1	no	Hall
18	C₂²⋊(C₁₃⋊C₃)	—	31	1	no	Hall
19	C₅×C₃₁	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₁₃	—	3	1	no	—
21	C₂²×C₃₁	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
22	C₃₁⋊C₃	—	52	1	no	Hall
23	C₅×C₁₃	C₂²⋊(C₃₁⋊C₃)	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃₁	—	3	1	no	—
25	C₅×A₄	—	403	1	no	Hall
26	C₂²×C₁₃	C₅×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
27	C₁₃⋊C₃	—	124	1	no	Hall
28	C₃₁	C₅×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₃	—	3	1	no	—
30	C₂²×C₅	#11925881	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅	—	1612	1	no	Hall
32	C₁₃	C₅×C₂²⋊(C₃₁⋊C₃)	1	1	yes	characteristic, complemented, Sylow
33	A₄	—	403	1	no	Hall
34	C₂×C₅	—	3	1	no	—
35	C₅	C₂²⋊#11925881	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²	C₅×#11925881	1	1	yes	characteristic, complemented, Sylow
37	C₃	—	1612	1	no	Sylow
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₂²⋊#11925881
commutator, cosocle, hypocenter	C₂²×C₁₃×C₃₁	C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₃×C₃₁	C₃
LCS	G ▷ C₂²×C₁₃×C₃₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₁₃×C₃₁	C₃	semidirect
3. C₂²⋊#11925881	C₅	direct (N × H)
5. C₅×C₁₃×C₃₁	A₄	semidirect
7. C₂²×C₁₃×C₃₁	C₃×C₅	semidirect
11. C₂²×C₅×C₃₁	C₁₃⋊C₃	semidirect
13. C₁₃×C₃₁	C₅×A₄	semidirect
16. C₂²×C₅×C₁₃	C₃₁⋊C₃	semidirect
19. C₅×C₃₁	C₂²⋊(C₁₃⋊C₃)	semidirect
21. C₂²×C₃₁	C₅×C₁₃⋊C₃	semidirect
23. C₅×C₁₃	C₂²⋊(C₃₁⋊C₃)	semidirect
26. C₂²×C₁₃	C₅×C₃₁⋊C₃	semidirect
28. C₃₁	C₅×C₂²⋊(C₁₃⋊C₃)	semidirect
30. C₂²×C₅	#11925881	semidirect
32. C₁₃	C₅×C₂²⋊(C₃₁⋊C₃)	semidirect
35. C₅	C₂²⋊#11925881	direct (N × H)
36. C₂²	C₅×#11925881	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₁₃×C₃₁	3
C₅×#11925881	4
C₂²⋊#11925881	5
C₅×C₂²⋊(C₃₁⋊C₃)	13
C₅×C₂²⋊(C₁₃⋊C₃)	31

Subgroups — C5×C22⋊#11925881 #37563993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂²⋊#11925881 #37563993