Subgroups — C₂×C₂₃×D₂₁₅ #34089924

Order 19780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₂₁₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₂₃×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂₃×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₂₃×D₄₃	—	5	1	no	maximal, Hall
5	C₂×C₂₃×C₄₃	D₅	1	1	yes	characteristic, complemented
6	C₂₃×D₄₃	—	5	2	no	—
7	C₂₃×C₄₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
8	C₂×D₂₁₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×D₅×C₂₃	—	43	1	no	maximal, Hall
10	C₂×C₅×C₄₃	C₂×C₂₃	1	1	yes	characteristic, complemented
11	D₂₁₅	C₂×C₂₃	1	2	yes	direct product factor
12	C₂×C₅×C₂₃	D₄₃	1	1	yes	characteristic, complemented
13	D₅×C₂₃	—	43	2	no	—
14	C₅×C₄₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₄₃	—	5	1	no	Hall
16	C₅×C₂₃	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₂₃	—	215	1	no	Hall
18	C₂×C₄₃	D₅×C₂₃	1	1	yes	characteristic, complemented
19	D₄₃	—	5	2	no	—
20	C₂×C₂₃	—	215	2	no	—
21	C₂×C₂₃	D₂₁₅	1	1	yes	characteristic, direct product factor
22	C₄₃	C₂×D₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
23	C₂₃	C₂×D₂₁₅	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₅	—	43	1	no	Hall
25	C₂×C₅	C₂₃×D₄₃	1	1	yes	characteristic, complemented
26	D₅	—	43	2	no	—
27	C₅	C₂×C₂₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	215	1	no	Sylow
29	C₂	—	215	2	no	—
30	C₂	C₂₃×D₂₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₃	D₂₁₅
commutator, cosocle, hypocenter	C₅×C₄₃	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₂₃×C₄₃	C₂
LCS	G ▷ C₅×C₄₃
UCS	C₁ ◁ C₂×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×D₂₁₅	C₂	direct (N × H)
2. C₂×C₅×C₂₃×C₄₃	C₂	semidirect
3. C₅×C₂₃×C₄₃	C₂²	semidirect
5. C₂×C₂₃×C₄₃	D₅	semidirect
7. C₂₃×C₄₃	C₂×D₅	semidirect
8. C₂×D₂₁₅	C₂₃	direct (N × H)
10. C₂×C₅×C₄₃	C₂×C₂₃	semidirect
11. D₂₁₅	C₂×C₂₃	direct (N × H)
12. C₂×C₅×C₂₃	D₄₃	semidirect
14. C₅×C₄₃	C₂²×C₂₃	semidirect
16. C₅×C₂₃	C₂×D₄₃	semidirect
18. C₂×C₄₃	D₅×C₂₃	semidirect
21. C₂×C₂₃	D₂₁₅	direct (N × H)
22. C₄₃	C₂×D₅×C₂₃	semidirect
23. C₂₃	C₂×D₂₁₅	direct (N × H)
25. C₂×C₅	C₂₃×D₄₃	semidirect
27. C₅	C₂×C₂₃×D₄₃	semidirect
30. C₂	C₂₃×D₂₁₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×D₂₁₅	2
C₂×C₅×C₂₃×C₄₃	2
C₂×C₂₃×D₄₃	5
C₂×D₂₁₅	23
C₂×D₅×C₂₃	43

Subgroups — C2×C23×D215 #34089924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×D₂₁₅ #34089924