Subgroups — C₅×C₂²⋊#13131975 #46776597

Order 33540.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₁₃×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×#13131975	—	4	1	no	maximal, Hall
3	C₂²⋊#13131975	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₅×C₁₃×C₄₃	—	3	1	no	—
5	C₅×C₁₃×C₄₃	A₄	1	1	yes	characteristic, complemented, Hall
6	C₅×C₂²⋊(C₄₃⋊C₃)	—	13	1	no	maximal, Hall
7	C₂²×C₁₃×C₄₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	#13131975	—	4	1	no	Hall
9	C₂×C₁₃×C₄₃	—	3	1	no	—
10	C₂²×C₅×C₄₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
11	C₅×C₂²⋊(C₁₃⋊C₃)	—	43	1	no	maximal, Hall
12	C₅×C₄₃⋊C₃	—	52	1	no	Hall
13	C₁₃×C₄₃	C₅×A₄	1	1	yes	characteristic, complemented, Hall
14	C₂²⋊(C₄₃⋊C₃)	—	13	1	no	Hall
15	C₂×C₅×C₄₃	—	3	1	no	—
16	C₂²×C₅×C₁₃	C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₅×C₄₃	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented, Hall
18	C₅×C₁₃⋊C₃	—	172	1	no	Hall
19	C₂²×C₄₃	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₂²⋊(C₁₃⋊C₃)	—	43	1	no	Hall
21	C₂×C₅×C₁₃	—	3	1	no	—
22	C₄₃⋊C₃	—	52	1	no	Hall
23	C₂×C₄₃	—	3	1	no	—
24	C₅×C₁₃	C₂²⋊(C₄₃⋊C₃)	1	1	yes	characteristic, complemented, Hall
25	C₅×A₄	—	559	1	no	Hall
26	C₂²×C₁₃	C₅×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
27	C₄₃	C₅×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
28	C₁₃⋊C₃	—	172	1	no	Hall
29	C₂×C₁₃	—	3	1	no	—
30	C₂²×C₅	#13131975	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅	—	2236	1	no	Hall
32	C₁₃	C₅×C₂²⋊(C₄₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
33	A₄	—	559	1	no	Hall
34	C₂×C₅	—	3	1	no	—
35	C₅	C₂²⋊#13131975	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²	C₅×#13131975	1	1	yes	characteristic, complemented, Sylow
37	C₃	—	2236	1	no	Sylow
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₂²⋊#13131975
commutator, cosocle, hypocenter	C₂²×C₁₃×C₄₃	C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₃×C₄₃	C₃
LCS	G ▷ C₂²×C₁₃×C₄₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₁₃×C₄₃	C₃	semidirect
3. C₂²⋊#13131975	C₅	direct (N × H)
5. C₅×C₁₃×C₄₃	A₄	semidirect
7. C₂²×C₁₃×C₄₃	C₃×C₅	semidirect
10. C₂²×C₅×C₄₃	C₁₃⋊C₃	semidirect
13. C₁₃×C₄₃	C₅×A₄	semidirect
16. C₂²×C₅×C₁₃	C₄₃⋊C₃	semidirect
17. C₅×C₄₃	C₂²⋊(C₁₃⋊C₃)	semidirect
19. C₂²×C₄₃	C₅×C₁₃⋊C₃	semidirect
24. C₅×C₁₃	C₂²⋊(C₄₃⋊C₃)	semidirect
26. C₂²×C₁₃	C₅×C₄₃⋊C₃	semidirect
27. C₄₃	C₅×C₂²⋊(C₁₃⋊C₃)	semidirect
30. C₂²×C₅	#13131975	semidirect
32. C₁₃	C₅×C₂²⋊(C₄₃⋊C₃)	semidirect
35. C₅	C₂²⋊#13131975	direct (N × H)
36. C₂²	C₅×#13131975	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₁₃×C₄₃	3
C₅×#13131975	4
C₂²⋊#13131975	5
C₅×C₂²⋊(C₄₃⋊C₃)	13
C₅×C₂²⋊(C₁₃⋊C₃)	43

Subgroups — C5×C22⋊#13131975 #46776597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂²⋊#13131975 #46776597