Subgroups — C₅⋊#20266620 #44570528

Order 32490.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15692436	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊#14524212	—	3	1	no	maximal
3	#20266620	—	5	1	no	maximal, Hall
4	C₅×#11762246	D₃	1	1	yes	characteristic
5	C₁₉×D₉₅	—	9	1	no	Hall
6	#15692436	D₅	1	1	yes	characteristic, complemented, Hall
7	#14524212	—	15	1	no	—
8	C₅×C₁₉²	D₉	1	1	yes	characteristic, complemented, Hall
9	#11762246	D₁₅	1	1	yes	characteristic
10	C₅×#4296	—	38	1	no	—
11	C₁₉×D₁₉	—	45	1	no	Hall
12	C₁₉²	D₄₅	1	1	yes	characteristic, complemented, Sylow
13	C₅×C₁₉⋊C₃	—	38	1	no	—
14	D₉₅	—	9	1	no	—
15	D₅×C₁₉	—	171	1	no	—
16	#4296	—	38	1	no	—
17	C₅×C₁₉	—	2	1	no	—
18	C₅×C₁₉	—	9	1	no	—
19	C₅×C₁₉	—	9	1	no	—
20	D₄₅	—	361	1	no	maximal, Hall
21	C₁₉⋊C₃	—	38	1	no	—
22	C₅×C₉	—	361	1	no	Hall
23	C₂×C₁₉	—	855	1	no	—
24	D₁₉	—	45	1	no	—
25	D₁₅	—	1083	1	no	—
26	C₁₉	—	2	1	no	—
27	C₁₉	—	9	1	no	—
28	C₁₉	—	9	1	no	—
29	D₉	—	1805	1	no	Hall
30	C₃×C₅	—	361	1	no	—
31	D₅	—	171	1	no	Hall
32	C₉	—	361	1	no	Sylow
33	D₃	—	5415	1	no	—
34	C₅	#20266620	1	1	yes	characteristic, complemented, Sylow
35	C₃	—	361	1	no	—
36	C₂	—	855	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₅×#15692436	C₂
Fitting, socle	C₅×C₁₉²	D₉
LCS	G ▷ C₅×#15692436
UCS	C₁

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

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