Subgroups — C₂×D₅×C₂₃²⋊C₃ #44540726

Order 31740.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₃²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₂₃²⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₅×C₂₃²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₂₃²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₂₃²⋊C₃	—	5	1	no	maximal, Hall
6	D₅×C₂₃²	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₂₃²	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₂₃²⋊C₃	—	5	2	no	—
9	C₂×C₂₃²⋊C₃	D₅	1	1	yes	characteristic, direct product factor
10	C₅×C₂₃²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₂₃²	—	5	1	no	Hall
12	C₂₃²⋊C₃	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₂₃²	—	5	2	no	—
14	C₂×C₂₃²	C₃×D₅	1	1	yes	characteristic, complemented
15	C₂₃²	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₅×C₂₃	—	3	8	no	—
17	C₂×C₅×C₂₃	—	3	8	no	—
18	D₅×C₂₃	—	3	16	no	—
19	C₅×C₂₃	—	3	8	no	—
20	C₂²×C₂₃	—	15	8	no	—
21	C₂×C₃×D₅	—	529	1	no	maximal, Hall
22	C₂×C₂₃	—	3	8	no	—
23	C₂×C₂₃	—	15	16	no	—
24	C₂×C₃×C₅	—	529	1	no	—
25	C₃×D₅	—	529	2	no	—
26	C₂₃	—	3	8	no	—
27	C₂×D₅	C₂₃²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₅	—	529	1	no	Hall
29	C₂²×C₃	—	2645	1	no	Hall
30	C₂×C₅	C₂×C₂₃²⋊C₃	1	1	yes	characteristic, complemented
31	D₅	C₂×C₂₃²⋊C₃	1	2	yes	direct product factor
32	C₂×C₃	—	529	1	no	—
33	C₂×C₃	—	2645	2	no	—
34	C₅	C₂²×C₂₃²⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	5	1	no	Sylow
36	C₃	—	529	1	no	Sylow
37	C₂	—	5	2	no	—
38	C₂	D₅×C₂₃²⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₅×C₂₃²⋊C₃
commutator, cosocle, hypocenter	C₅×C₂₃²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₂₃²	C₂×C₃
LCS	G ▷ C₅×C₂₃²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₂₃²⋊C₃	C₂	semidirect
2. D₅×C₂₃²⋊C₃	C₂	direct (N × H)
3. C₂×D₅×C₂₃²	C₃	semidirect
4. C₅×C₂₃²⋊C₃	C₂²	semidirect
6. D₅×C₂₃²	C₂×C₃	semidirect
7. C₂×C₅×C₂₃²	C₂×C₃	semidirect
9. C₂×C₂₃²⋊C₃	D₅	direct (N × H)
10. C₅×C₂₃²	C₂²×C₃	semidirect
12. C₂₃²⋊C₃	C₂×D₅	direct (N × H)
14. C₂×C₂₃²	C₃×D₅	semidirect
15. C₂₃²	C₂×C₃×D₅	semidirect
27. C₂×D₅	C₂₃²⋊C₃	direct (N × H)
30. C₂×C₅	C₂×C₂₃²⋊C₃	semidirect
31. D₅	C₂×C₂₃²⋊C₃	direct (N × H)
34. C₅	C₂²×C₂₃²⋊C₃	semidirect
38. C₂	D₅×C₂₃²⋊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×C₂₃²⋊C₃	2
D₅×C₂₃²⋊C₃	2
C₂×D₅×C₂₃²	3
C₂²×C₂₃²⋊C₃	5
C₂×C₃×D₅	529

Subgroups — C2×D5×C232⋊C3 #44540726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×C₂₃²⋊C₃ #44540726