Subgroups — C₂×(C₅⋊D₅)⋊(C₁₃⋊C₃) #16839128

Order 3900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃⋊(C₅²⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₅⋊D₅)⋊(C₁₃⋊C₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₃×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₃⋊(C₅²⋊C₃)	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₁₃×C₅⋊D₅	C₂×C₃	1	2	yes	complemented
7	C₅²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×(C₅⋊D₅)⋊C₃	—	13	1	no	maximal, Hall
9	C₂×D₅×C₁₃	—	15	2	no	—
10	C₂²×C₁₃⋊C₃	—	25	1	no	maximal, Hall
11	C₂×C₅²⋊C₃	—	13	1	no	—
12	(C₅⋊D₅)⋊C₃	—	13	2	no	—
13	C₂×C₅×C₁₃	—	3	2	no	—
14	D₅×C₁₃	—	15	4	no	—
15	C₂×C₅⋊D₅	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃⋊C₃	—	25	2	no	—
17	C₂×C₁₃⋊C₃	—	25	1	no	—
18	C₅²⋊C₃	—	13	1	no	Hall
19	C₅×C₁₃	—	3	2	no	—
20	C₂²×C₁₃	—	25	1	no	Hall
21	C₂×C₅²	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
22	C₅⋊D₅	C₂×C₁₃⋊C₃	1	2	yes	complemented
23	C₁₃⋊C₃	—	25	1	no	Hall
24	C₂×C₁₃	—	25	2	no	—
25	C₂×C₁₃	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
26	C₅²	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×D₅	—	15	2	no	—
28	C₁₃	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Sylow
29	C₂²×C₃	—	325	1	no	Hall
30	C₂×C₅	—	3	2	no	—
31	D₅	—	15	4	no	—
32	C₂×C₃	—	325	2	no	—
33	C₂×C₃	—	325	1	no	—
34	C₅	—	3	2	no	—
35	C₂²	—	25	1	no	Sylow
36	C₃	—	325	1	no	Sylow
37	C₂	—	25	2	no	—
38	C₂	(C₅⋊D₅)⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₅⋊D₅)⋊(C₁₃⋊C₃)
commutator, cosocle, hypocenter	C₅²×C₁₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₃	C₂×C₃
LCS	G ▷ C₅²×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃⋊(C₅²⋊C₃)	C₂	semidirect
2. (C₅⋊D₅)⋊(C₁₃⋊C₃)	C₂	direct (N × H)
3. C₂×C₁₃×C₅⋊D₅	C₃	semidirect
4. C₁₃⋊(C₅²⋊C₃)	C₂²	semidirect
5. C₂×C₅²×C₁₃	C₂×C₃	semidirect
6. C₁₃×C₅⋊D₅	C₂×C₃	semidirect
7. C₅²×C₁₃	C₂²×C₃	semidirect
15. C₂×C₅⋊D₅	C₁₃⋊C₃	semidirect
21. C₂×C₅²	C₂×C₁₃⋊C₃	semidirect
22. C₅⋊D₅	C₂×C₁₃⋊C₃	semidirect
25. C₂×C₁₃	(C₅⋊D₅)⋊C₃	semidirect
26. C₅²	C₂²×C₁₃⋊C₃	semidirect
28. C₁₃	C₂×(C₅⋊D₅)⋊C₃	semidirect
38. C₂	(C₅⋊D₅)⋊(C₁₃⋊C₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃⋊(C₅²⋊C₃)	2
(C₅⋊D₅)⋊(C₁₃⋊C₃)	2
C₂×C₁₃×C₅⋊D₅	3
C₂×(C₅⋊D₅)⋊C₃	13
C₂²×C₁₃⋊C₃	25

Subgroups — C2×(C5⋊D5)⋊(C13⋊C3) #16839128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×(C₅⋊D₅)⋊(C₁₃⋊C₃) #16839128