Subgroups — D₅×D₃₂₃ #20264607

Order 6460.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃₂₃	—	5	1	no	maximal, Hall
6	C₂×C₁₇×C₁₉	—	5	1	no	—
7	D₃₂₃	—	5	1	no	—
8	D₃₂₃	D₅	1	1	yes	characteristic, direct product factor
9	D₅×D₁₉	—	17	1	no	maximal, Hall
10	D₅×D₁₇	—	19	1	no	maximal, Hall
11	C₁₇×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
12	D₉₅	—	17	1	no	—
13	C₅×D₁₉	—	17	1	no	—
14	D₅×C₁₉	D₁₇	1	1	yes	characteristic, complemented
15	D₈₅	—	19	1	no	—
16	C₅×D₁₇	—	19	1	no	—
17	D₅×C₁₇	D₁₉	1	1	yes	characteristic, complemented
18	C₅×C₁₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
19	C₅×C₁₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
20	C₂×D₁₉	—	85	1	no	Hall
21	C₂×D₁₇	—	95	1	no	Hall
22	C₂×C₁₉	—	5	1	no	—
23	D₁₉	—	17	1	no	—
24	D₁₉	—	85	1	no	—
25	C₂×C₁₇	—	5	1	no	—
26	D₁₇	—	19	1	no	—
27	D₁₇	—	95	1	no	—
28	C₂×D₅	—	323	1	no	Hall
29	C₁₉	D₅×D₁₇	1	1	yes	characteristic, complemented, Sylow
30	C₁₇	D₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	323	1	no	—
32	D₅	—	323	1	no	—
33	D₅	D₃₂₃	1	1	yes	characteristic, direct product factor
34	C₅	C₂×D₃₂₃	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	1615	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	323	1	no	—
38	C₂	—	1615	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₇×C₁₉	C₂²
LCS	G ▷ C₅×C₁₇×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₁₆₁₅	C₂	semidirect
2. D₅×C₁₇×C₁₉	C₂	semidirect
3. C₅×D₃₂₃	C₂	semidirect
4. C₅×C₁₇×C₁₉	C₂²	semidirect
8. D₃₂₃	D₅	direct (N × H)
11. C₁₇×C₁₉	C₂×D₅	semidirect
14. D₅×C₁₉	D₁₇	semidirect
17. D₅×C₁₇	D₁₉	semidirect
18. C₅×C₁₉	C₂×D₁₇	semidirect
19. C₅×C₁₇	C₂×D₁₉	semidirect
29. C₁₉	D₅×D₁₇	semidirect
30. C₁₇	D₅×D₁₉	semidirect
33. D₅	D₃₂₃	direct (N × H)
34. C₅	C₂×D₃₂₃	semidirect

Subgroups — D5×D323 #20264607

Conjugacy classes of subgroups

Complements

Subgroups — D₅×D₃₂₃ #20264607