Subgroups — D₃×D₂₅₇₃ #44525261

Order 30876.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₇₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₃₁×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₅₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₅₇₃	—	3	1	no	maximal, Hall
5	C₃×C₃₁×C₈₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃₁×C₈₃	—	3	1	no	—
7	D₂₅₇₃	—	3	1	no	—
8	D₂₅₇₃	D₃	1	1	yes	characteristic, direct product factor
9	C₃₁×C₈₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₈₃	—	31	1	no	maximal, Hall
11	D₂₄₉	—	31	1	no	—
12	C₃×D₈₃	—	31	1	no	—
13	D₃×C₈₃	D₃₁	1	1	yes	characteristic, complemented
14	D₃×D₃₁	—	83	1	no	maximal, Hall
15	C₂×D₈₃	—	93	1	no	Hall
16	C₃×C₈₃	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
17	D₉₃	—	83	1	no	—
18	C₃×D₃₁	—	83	1	no	—
19	D₃×C₃₁	D₈₃	1	1	yes	characteristic, complemented
20	C₂×C₈₃	—	3	1	no	—
21	D₈₃	—	31	1	no	—
22	D₈₃	—	93	1	no	—
23	C₂×D₃₁	—	249	1	no	Hall
24	C₃×C₃₁	C₂×D₈₃	1	1	yes	characteristic, complemented, Hall
25	C₈₃	D₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃₁	—	3	1	no	—
27	D₃₁	—	83	1	no	—
28	D₃₁	—	249	1	no	—
29	C₃₁	D₃×D₈₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	2573	1	no	Hall
31	C₂×C₃	—	2573	1	no	—
32	D₃	—	2573	1	no	—
33	D₃	D₂₅₇₃	1	1	yes	characteristic, direct product factor
34	C₂²	—	7719	1	no	Sylow
35	C₃	C₂×D₂₅₇₃	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	2573	1	no	—
38	C₂	—	7719	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₃₁×C₈₃	C₂²
LCS	G ▷ C₃×C₃₁×C₈₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₇₇₁₉	C₂	semidirect
2. D₃×C₃₁×C₈₃	C₂	semidirect
3. C₃×D₂₅₇₃	C₂	semidirect
5. C₃×C₃₁×C₈₃	C₂²	semidirect
8. D₂₅₇₃	D₃	direct (N × H)
9. C₃₁×C₈₃	C₂×D₃	semidirect
13. D₃×C₈₃	D₃₁	semidirect
16. C₃×C₈₃	C₂×D₃₁	semidirect
19. D₃×C₃₁	D₈₃	semidirect
24. C₃×C₃₁	C₂×D₈₃	semidirect
25. C₈₃	D₃×D₃₁	semidirect
29. C₃₁	D₃×D₈₃	semidirect
33. D₃	D₂₅₇₃	direct (N × H)
35. C₃	C₂×D₂₅₇₃	semidirect

Maximal subgroups

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

subgroup	index
D₇₇₁₉	2
D₃×C₃₁×C₈₃	2
C₃×D₂₅₇₃	2
C₂×D₂₅₇₃	3
D₃×D₈₃	31
D₃×D₃₁	83

Subgroups — D3×D2573 #44525261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₂₅₇₃ #44525261