Subgroups — D₅₁×D₈₉ #31827770

Order 18156.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₅₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×D₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₇×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₇×D₈₉	—	3	1	no	maximal, Hall
5	C₃×C₁₇×C₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₅₁₃	—	3	1	no	—
7	C₁₇×D₈₉	D₃	1	1	yes	characteristic, complemented
8	D₁₇×C₈₉	—	3	1	no	—
9	C₁₇×C₈₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₈₉	—	17	1	no	maximal, Hall
11	D₂₆₇	—	17	1	no	—
12	C₃×D₈₉	D₁₇	1	1	yes	characteristic, complemented
13	D₃×C₈₉	—	17	1	no	—
14	C₂×D₈₉	—	51	1	no	Hall
15	C₃×C₈₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
16	C₂×D₅₁	—	89	1	no	maximal, Hall
17	C₂×C₈₉	—	51	1	no	—
18	D₈₉	—	51	1	no	—
19	D₈₉	D₅₁	1	1	yes	characteristic, direct product factor
20	C₂×C₃×C₁₇	—	89	1	no	—
21	D₅₁	—	89	1	no	—
22	D₅₁	D₈₉	1	1	yes	characteristic, direct product factor
23	C₈₉	C₂×D₅₁	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₁₇	—	267	1	no	Hall
25	C₃×C₁₇	C₂×D₈₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₇	—	89	1	no	—
27	D₁₇	—	3	1	no	—
28	D₁₇	—	267	1	no	—
29	C₁₇	D₃×D₈₉	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	1513	1	no	Hall
31	C₂×C₃	—	89	1	no	—
32	D₃	—	17	1	no	—
33	D₃	—	1513	1	no	—
34	C₂²	—	4539	1	no	Sylow
35	C₃	D₁₇×D₈₉	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	51	1	no	—
37	C₂	—	89	1	no	—
38	C₂	—	4539	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₇×C₈₉	C₂²
LCS	G ▷ C₃×C₁₇×C₈₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₄₅₃₉	C₂	semidirect
2. C₈₉×D₅₁	C₂	semidirect
3. C₃×C₁₇×D₈₉	C₂	semidirect
5. C₃×C₁₇×C₈₉	C₂²	semidirect
7. C₁₇×D₈₉	D₃	semidirect
9. C₁₇×C₈₉	C₂×D₃	semidirect
12. C₃×D₈₉	D₁₇	semidirect
15. C₃×C₈₉	C₂×D₁₇	semidirect
19. D₈₉	D₅₁	direct (N × H)
22. D₅₁	D₈₉	direct (N × H)
23. C₈₉	C₂×D₅₁	semidirect
25. C₃×C₁₇	C₂×D₈₉	semidirect
29. C₁₇	D₃×D₈₉	semidirect
35. C₃	D₁₇×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
D₄₅₃₉	2
C₈₉×D₅₁	2
C₃×C₁₇×D₈₉	2
D₁₇×D₈₉	3
D₃×D₈₉	17
C₂×D₅₁	89

Subgroups — D51×D89 #31827770

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₁×D₈₉ #31827770