Subgroups — Dic₁₂₉₉₀ #72288511

Order 51960.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₄₃₃₀	—	3	1	no	maximal, Hall
2	Dic₂₅₉₈	—	5	1	no	maximal, Hall
3	Dic₆₄₉₅	C₂	1	2	yes	maximal
4	C₃×C₄×C₅×C₄₃₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×C₅×C₄₃₃	C₂²	1	1	yes	characteristic
6	Dic₂₁₆₅	—	3	2	no	—
7	C₄×C₅×C₄₃₃	D₃	1	1	yes	characteristic
8	C₃×C₅×C₄₃₃	Q₈	1	1	yes	characteristic, complemented, Hall
9	Dic₁₂₉₉	—	5	2	no	—
10	C₃×C₄×C₄₃₃	D₅	1	1	yes	characteristic
11	C₂×C₅×C₄₃₃	C₂×D₃	1	1	yes	characteristic
12	Dic₈₆₆	—	15	1	no	Hall
13	C₂×C₃×C₄₃₃	C₂×D₅	1	1	yes	characteristic
14	C₅×C₄₃₃	Dic₆	1	1	yes	characteristic, complemented, Hall
15	C₄×C₄₃₃	D₁₅	1	1	yes	characteristic
16	Dic₄₃₃	—	15	2	no	—
17	C₃×C₄₃₃	Dic₁₀	1	1	yes	characteristic, complemented, Hall
18	C₂×C₄₃₃	C₂×D₁₅	1	1	yes	characteristic
19	C₄₃₃	Dic₃₀	1	1	yes	characteristic, complemented, Sylow
20	Dic₃₀	—	433	1	no	maximal, Hall
21	C₃×C₄×C₅	D₄₃₃	1	1	yes	characteristic
22	Dic₁₅	—	433	2	no	—
23	Dic₁₀	—	1299	1	no	Hall
24	C₂×C₃×C₅	C₂×D₄₃₃	1	1	yes	characteristic
25	Dic₆	—	2165	1	no	Hall
26	C₄×C₅	D₁₂₉₉	1	1	yes	characteristic
27	Dic₅	—	1299	2	no	—
28	C₃×C₅	Dic₈₆₆	1	1	yes	characteristic, complemented, Hall
29	C₃×C₄	D₂₁₆₅	1	1	yes	characteristic
30	Dic₃	—	2165	2	no	—
31	C₂×C₅	C₂×D₁₂₉₉	1	1	yes	characteristic
32	Q₈	—	6495	1	no	Sylow
33	C₂×C₃	C₂×D₂₁₆₅	1	1	yes	characteristic
34	C₅	Dic₂₅₉₈	1	1	yes	characteristic, complemented, Sylow
35	C₄	—	6495	2	no	—
36	C₄	D₆₄₉₅	1	1	yes	characteristic
37	C₃	Dic₄₃₃₀	1	1	yes	characteristic, complemented, Sylow
38	C₂	C₂×D₆₄₉₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₆₄₉₅
commutator, socle, prime radical, cosocle	C₂×C₃×C₅×C₄₃₃	C₂²
Fitting	C₃×C₄×C₅×C₄₃₃	C₂
hypercenter	C₄	D₆₄₉₅
hypocenter	C₃×C₅×C₄₃₃	Q₈
LCS	G ▷ C₂×C₃×C₅×C₄₃₃ ▷ C₃×C₅×C₄₃₃
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
8. C₃×C₅×C₄₃₃	Q₈	semidirect
14. C₅×C₄₃₃	Dic₆	semidirect
17. C₃×C₄₃₃	Dic₁₀	semidirect
19. C₄₃₃	Dic₃₀	semidirect
28. C₃×C₅	Dic₈₆₆	semidirect
34. C₅	Dic₂₅₉₈	semidirect
37. C₃	Dic₄₃₃₀	semidirect

Maximal subgroups

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

subgroup	index
Dic₄₃₃₀	3
Dic₂₅₉₈	5
Dic₆₄₉₅	2
C₃×C₄×C₅×C₄₃₃	2
Dic₃₀	433

Subgroups — Dic12990 #72288511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₂₉₉₀ #72288511