Subgroups — C₂²×C₅×#11925881 #37563997

Order 24180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#11925881	C₂	direct (N × H)
2. C₂²×C₅×C₁₃×C₃₁	C₃	semidirect
3. C₅×#11925881	C₂²	direct (N × H)
4. C₂²×#11925881	C₅	direct (N × H)
5. C₂×C₅×C₁₃×C₃₁	C₂×C₃	semidirect
6. C₂×#11925881	C₂×C₅	direct (N × H)
7. C₅×C₁₃×C₃₁	C₂²×C₃	semidirect
9. C₂²×C₁₃×C₃₁	C₃×C₅	semidirect
10. #11925881	C₂²×C₅	direct (N × H)
12. C₂×C₁₃×C₃₁	C₂×C₃×C₅	semidirect
14. C₂²×C₅×C₃₁	C₁₃⋊C₃	semidirect
16. C₁₃×C₃₁	C₂²×C₃×C₅	semidirect
19. C₂×C₅×C₃₁	C₂×C₁₃⋊C₃	semidirect
20. C₂²×C₅×C₁₃	C₃₁⋊C₃	semidirect
24. C₅×C₃₁	C₂²×C₁₃⋊C₃	semidirect
25. C₂×C₅×C₁₃	C₂×C₃₁⋊C₃	semidirect
26. C₂²×C₃₁	C₅×C₁₃⋊C₃	semidirect
29. C₅×C₁₃	C₂²×C₃₁⋊C₃	semidirect
30. C₂×C₃₁	C₂×C₅×C₁₃⋊C₃	semidirect
32. C₂²×C₁₃	C₅×C₃₁⋊C₃	semidirect
34. C₃₁	C₂²×C₅×C₁₃⋊C₃	semidirect
36. C₂×C₁₃	C₂×C₅×C₃₁⋊C₃	semidirect
37. C₂²×C₅	#11925881	direct (N × H)
39. C₁₃	C₂²×C₅×C₃₁⋊C₃	semidirect
41. C₂×C₅	C₂×#11925881	direct (N × H)
43. C₅	C₂²×#11925881	direct (N × H)
44. C₂²	C₅×#11925881	direct (N × H)
46. C₂	C₂×C₅×#11925881	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×#11925881	2
C₂²×C₅×C₁₃×C₃₁	3
C₂²×#11925881	5
C₂²×C₅×C₃₁⋊C₃	13
C₂²×C₅×C₁₃⋊C₃	31

Subgroups — C22×C5×#11925881 #37563997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×#11925881 #37563997