Subgroups — D₂₃×D₂₁₅ #34089919

Order 19780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₉₄₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×D₂₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₄₃×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₂₃×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₃×D₄₃	—	5	1	no	maximal, Hall
6	D₉₈₉	—	5	1	no	—
7	C₂₃×D₄₃	—	5	1	no	—
8	C₄₃×D₂₃	D₅	1	1	yes	characteristic, complemented
9	C₂₃×C₄₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
10	C₂×D₂₁₅	—	23	1	no	maximal, Hall
11	D₅×D₂₃	—	43	1	no	maximal, Hall
12	C₂×C₅×C₄₃	—	23	1	no	—
13	D₂₁₅	—	23	1	no	—
14	D₂₁₅	D₂₃	1	1	yes	characteristic, direct product factor
15	D₁₁₅	—	43	1	no	—
16	C₅×D₂₃	D₄₃	1	1	yes	characteristic, complemented
17	D₅×C₂₃	—	43	1	no	—
18	C₅×C₄₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
19	C₂×D₄₃	—	115	1	no	Hall
20	C₅×C₂₃	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
21	C₂×D₂₃	—	215	1	no	Hall
22	C₂×C₄₃	—	23	1	no	—
23	D₄₃	—	5	1	no	—
24	D₄₃	—	115	1	no	—
25	C₂×C₂₃	—	215	1	no	—
26	D₂₃	—	215	1	no	—
27	D₂₃	D₂₁₅	1	1	yes	characteristic, direct product factor
28	C₄₃	D₅×D₂₃	1	1	yes	characteristic, complemented, Sylow
29	C₂₃	C₂×D₂₁₅	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₅	—	989	1	no	Hall
31	C₂×C₅	—	23	1	no	—
32	D₅	—	43	1	no	—
33	D₅	—	989	1	no	—
34	C₅	D₂₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	4945	1	no	Sylow
36	C₂	—	23	1	no	—
37	C₂	—	4945	1	no	—
38	C₂	—	215	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₄₉₄₅	C₂	semidirect
2. C₂₃×D₂₁₅	C₂	semidirect
3. C₅×C₄₃×D₂₃	C₂	semidirect
4. C₅×C₂₃×C₄₃	C₂²	semidirect
8. C₄₃×D₂₃	D₅	semidirect
9. C₂₃×C₄₃	C₂×D₅	semidirect
14. D₂₁₅	D₂₃	direct (N × H)
16. C₅×D₂₃	D₄₃	semidirect
18. C₅×C₄₃	C₂×D₂₃	semidirect
20. C₅×C₂₃	C₂×D₄₃	semidirect
27. D₂₃	D₂₁₅	direct (N × H)
28. C₄₃	D₅×D₂₃	semidirect
29. C₂₃	C₂×D₂₁₅	semidirect
34. C₅	D₂₃×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
D₄₉₄₅	2
C₂₃×D₂₁₅	2
C₅×C₄₃×D₂₃	2
D₂₃×D₄₃	5
C₂×D₂₁₅	23
D₅×D₂₃	43

Subgroups — D23×D215 #34089919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×D₂₁₅ #34089919