Subgroups — C₄×#22555291 #46801913

Order 34100.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22555291	C₂	1	1	yes	maximal, characteristic
2	#22555291	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₅×C₁₁×C₃₁	C₅	1	1	yes	maximal, characteristic
4	C₂×C₅×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic
5	C₄×C₃₁⋊C₂₅	—	11	1	no	maximal, Hall
6	C₅×C₁₁×C₃₁	C₄×C₅	1	1	yes	characteristic
7	C₂×C₃₁⋊C₂₅	—	11	1	no	—
8	C₄×C₁₁×C₃₁	C₂₅	1	1	yes	characteristic, complemented, Hall
9	C₄×C₁₁⋊C₂₅	—	31	1	no	maximal, Hall
10	C₃₁⋊C₂₅	—	11	1	no	Hall
11	C₂×C₁₁×C₃₁	C₂×C₂₅	1	1	yes	characteristic
12	C₄×C₅×C₃₁	C₁₁⋊C₅	1	1	yes	characteristic
13	C₂×C₁₁⋊C₂₅	—	31	1	no	—
14	C₁₁×C₃₁	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₃₁	C₂×C₁₁⋊C₅	1	1	yes	characteristic
16	C₁₁⋊C₂₅	—	31	1	no	Hall
17	C₄×C₅×C₁₁	ΓL(1,𝔽₃₂)	1	1	yes	characteristic
18	C₅×C₃₁	C₄×C₁₁⋊C₅	1	1	yes	characteristic
19	C₄×C₃₁	C₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₁₁	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
21	C₄×C₂₅	—	341	1	no	Hall
22	C₂×C₃₁	C₂×C₁₁⋊C₂₅	1	1	yes	characteristic
23	C₅×C₁₁	C₄×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
24	C₂×C₂₅	—	341	1	no	—
25	C₄×C₁₁	C₃₁⋊C₂₅	1	1	yes	characteristic, complemented, Hall
26	C₃₁	C₄×C₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
27	C₂₅	—	341	1	no	Sylow
28	C₂×C₁₁	C₂×C₃₁⋊C₂₅	1	1	yes	characteristic
29	C₄×C₅	#13133721	1	1	yes	characteristic
30	C₁₁	C₄×C₃₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	C₂×#13133721	1	1	yes	characteristic
32	C₅	C₄×#13133721	1	1	yes	characteristic
33	C₄	#22555291	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×#22555291	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₅	#13133721
commutator, hypocenter	C₁₁×C₃₁	C₄×C₂₅
Frattini	C₂×C₅	C₂×#13133721
Fitting	C₄×C₅×C₁₁×C₃₁	C₅
socle, prime radical, cosocle	C₂×C₅×C₁₁×C₃₁	C₂×C₅
LCS	G ▷ C₁₁×C₃₁
UCS	C₁ ◁ C₄×C₅

Complements

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

N	H ≅ G/N	type
2. #22555291	C₄	direct (N × H)
8. C₄×C₁₁×C₃₁	C₂₅	semidirect
14. C₁₁×C₃₁	C₄×C₂₅	semidirect
19. C₄×C₃₁	C₁₁⋊C₂₅	semidirect
25. C₄×C₁₁	C₃₁⋊C₂₅	semidirect
26. C₃₁	C₄×C₁₁⋊C₂₅	semidirect
30. C₁₁	C₄×C₃₁⋊C₂₅	semidirect
33. C₄	#22555291	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×#22555291	2
C₄×C₅×C₁₁×C₃₁	5
C₄×C₃₁⋊C₂₅	11
C₄×C₁₁⋊C₂₅	31

Subgroups — C4×#22555291 #46801913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#22555291 #46801913