Subgroups — D₅₅×D₈₃ #32912432

Order 18260.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₅₆₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₃×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₁×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₁×C₈₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×D₈₃	—	5	1	no	maximal, Hall
6	D₉₁₃	—	5	1	no	—
7	C₁₁×D₈₃	D₅	1	1	yes	characteristic, complemented
8	D₁₁×C₈₃	—	5	1	no	—
9	D₅×D₈₃	—	11	1	no	maximal, Hall
10	C₁₁×C₈₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	D₄₁₅	—	11	1	no	—
12	C₅×D₈₃	D₁₁	1	1	yes	characteristic, complemented
13	D₅×C₈₃	—	11	1	no	—
14	C₅×C₈₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×D₈₃	—	55	1	no	Hall
16	C₂×D₅₅	—	83	1	no	maximal, Hall
17	C₂×C₈₃	—	55	1	no	—
18	D₈₃	—	55	1	no	—
19	D₈₃	D₅₅	1	1	yes	characteristic, direct product factor
20	C₂×C₅×C₁₁	—	83	1	no	—
21	D₅₅	—	83	1	no	—
22	D₅₅	D₈₃	1	1	yes	characteristic, direct product factor
23	C₈₃	C₂×D₅₅	1	1	yes	characteristic, complemented, Sylow
24	C₅×C₁₁	C₂×D₈₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₁₁	—	415	1	no	Hall
26	C₂×C₁₁	—	83	1	no	—
27	D₁₁	—	5	1	no	—
28	D₁₁	—	415	1	no	—
29	C₂×D₅	—	913	1	no	Hall
30	C₁₁	D₅×D₈₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	83	1	no	—
32	D₅	—	11	1	no	—
33	D₅	—	913	1	no	—
34	C₅	D₁₁×D₈₃	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	4565	1	no	Sylow
36	C₂	—	55	1	no	—
37	C₂	—	83	1	no	—
38	C₂	—	4565	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₁×C₈₃	C₂²
LCS	G ▷ C₅×C₁₁×C₈₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₄₅₆₅	C₂	semidirect
2. C₈₃×D₅₅	C₂	semidirect
3. C₅×C₁₁×D₈₃	C₂	semidirect
4. C₅×C₁₁×C₈₃	C₂²	semidirect
7. C₁₁×D₈₃	D₅	semidirect
10. C₁₁×C₈₃	C₂×D₅	semidirect
12. C₅×D₈₃	D₁₁	semidirect
14. C₅×C₈₃	C₂×D₁₁	semidirect
19. D₈₃	D₅₅	direct (N × H)
22. D₅₅	D₈₃	direct (N × H)
23. C₈₃	C₂×D₅₅	semidirect
24. C₅×C₁₁	C₂×D₈₃	semidirect
30. C₁₁	D₅×D₈₃	semidirect
34. C₅	D₁₁×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
D₄₅₆₅	2
C₈₃×D₅₅	2
C₅×C₁₁×D₈₃	2
D₁₁×D₈₃	5
D₅×D₈₃	11
C₂×D₅₅	83

Subgroups — D55×D83 #32912432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₅×D₈₃ #32912432