Subgroups — C₂×C₅²⋊#10625202 #49150310

Order 37050.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊#10625202	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅²×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉⋊(C₅²⋊C₃)	—	13	1	no	maximal, Hall
5	C₂×C₅×C₁₃×C₁₉	—	3	2	no	—
6	C₂×C₁₃⋊(C₅²⋊C₃)	—	19	1	no	maximal, Hall
7	C₂×#10625202	—	25	1	no	maximal, Hall
8	C₁₉⋊(C₅²⋊C₃)	—	13	1	no	Hall
9	C₅×C₁₃×C₁₉	—	3	2	no	—
10	C₁₃⋊(C₅²⋊C₃)	—	19	1	no	Hall
11	C₂×C₅²×C₁₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
12	#10625202	—	25	1	no	Hall
13	C₂×C₅²×C₁₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₃×C₁₉	C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₅²×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₅²×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₁₃×C₁₉	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₁₉	—	3	2	no	—
19	C₂×C₅²⋊C₃	—	247	1	no	Hall
20	C₂×C₅×C₁₃	—	3	2	no	—
21	C₂×C₁₉⋊C₃	—	325	1	no	Hall
22	C₅×C₁₉	—	3	2	no	—
23	C₂×C₁₃⋊C₃	—	475	1	no	Hall
24	C₅²⋊C₃	—	247	1	no	Hall
25	C₅×C₁₃	—	3	2	no	—
26	C₁₉⋊C₃	—	325	1	no	Hall
27	C₂×C₅²	#10625202	1	1	yes	characteristic, complemented, Hall
28	C₁₃⋊C₃	—	475	1	no	Hall
29	C₂×C₁₉	C₁₃⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented, Hall
30	C₂×C₁₃	C₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented, Hall
31	C₅²	C₂×#10625202	1	1	yes	characteristic, complemented, Sylow
32	C₁₉	C₂×C₁₃⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented, Sylow
33	C₁₃	C₂×C₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₅	—	3	2	no	—
35	C₂×C₃	—	6175	1	no	Hall
36	C₅	—	3	2	no	—
37	C₃	—	6175	1	no	Sylow
38	C₂	C₅²⋊#10625202	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	C₅²⋊#10625202
commutator, cosocle, hypocenter	C₅²×C₁₃×C₁₉	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₃×C₁₉	C₃
LCS	G ▷ C₅²×C₁₃×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₅²⋊#10625202	C₂	direct (N × H)
2. C₂×C₅²×C₁₃×C₁₉	C₃	semidirect
3. C₅²×C₁₃×C₁₉	C₂×C₃	semidirect
11. C₂×C₅²×C₁₉	C₁₃⋊C₃	semidirect
13. C₂×C₅²×C₁₃	C₁₉⋊C₃	semidirect
14. C₂×C₁₃×C₁₉	C₅²⋊C₃	semidirect
15. C₅²×C₁₉	C₂×C₁₃⋊C₃	semidirect
16. C₅²×C₁₃	C₂×C₁₉⋊C₃	semidirect
17. C₁₃×C₁₉	C₂×C₅²⋊C₃	semidirect
27. C₂×C₅²	#10625202	semidirect
29. C₂×C₁₉	C₁₃⋊(C₅²⋊C₃)	semidirect
30. C₂×C₁₃	C₁₉⋊(C₅²⋊C₃)	semidirect
31. C₅²	C₂×#10625202	semidirect
32. C₁₉	C₂×C₁₃⋊(C₅²⋊C₃)	semidirect
33. C₁₃	C₂×C₁₉⋊(C₅²⋊C₃)	semidirect
38. C₂	C₅²⋊#10625202	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²⋊#10625202	2
C₂×C₅²×C₁₃×C₁₉	3
C₂×C₁₉⋊(C₅²⋊C₃)	13
C₂×C₁₃⋊(C₅²⋊C₃)	19
C₂×#10625202	25

Subgroups — C2×C52⋊#10625202 #49150310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅²⋊#10625202 #49150310