Subgroups — D₅×#15692436 #44570556

Order 32490.

56 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	D₅×#11762246	C₃	1	1	yes	maximal, characteristic
3	C₂×#15692436	—	5	1	no	maximal, Hall
4	C₅×#11762246	C₂×C₃	1	1	yes	characteristic
5	D₅×C₁₉²	C₉	1	1	yes	characteristic, complemented, Hall
6	#15692436	D₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×#11762246	—	5	1	no	—
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	D₅×#4296	—	19	2	no	maximal
10	#11762246	C₃×D₅	1	1	yes	characteristic
11	C₅×#4296	—	19	2	no	—
12	C₂×C₁₉²	—	5	1	no	Hall
13	D₅×C₁₉⋊C₃	—	19	2	no	—
14	C₁₉²	C₉×D₅	1	1	yes	characteristic, complemented, Sylow
15	C₂×#4296	—	95	2	no	—
16	C₅×C₁₉⋊C₃	—	19	2	no	—
17	D₅×C₁₉	—	9	2	no	—
18	D₅×C₁₉	#4296	1	2	yes	complemented
19	#4296	—	19	2	no	—
20	C₂×C₁₉⋊C₃	—	95	2	no	—
21	C₅×C₁₉	—	9	2	no	—
22	C₅×C₁₉	C₂×#4296	1	2	yes	complemented
23	C₉×D₅	—	361	1	no	Hall
24	C₁₉⋊C₃	—	19	2	no	—
25	C₅×C₉	—	361	1	no	Hall
26	C₂×C₁₉	—	5	2	no	—
27	C₂×C₁₉	—	45	2	no	—
28	C₃×D₅	—	361	1	no	—
29	C₁₉	—	9	2	no	—
30	C₁₉	D₅×#4296	1	2	yes	complemented
31	C₂×C₉	—	1805	1	no	Hall
32	C₃×C₅	—	361	1	no	—
33	D₅	#15692436	1	1	yes	characteristic, direct product factor, Hall
34	C₉	—	361	1	no	Sylow
35	C₂×C₃	—	1805	1	no	—
36	C₅	C₂×#15692436	1	1	yes	characteristic, complemented, Sylow
37	C₃	—	361	1	no	—
38	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₉²	C₂×C₉
prime radical	D₅×#11762246	C₃
cosocle	C₅×#11762246	C₂×C₃
LCS	G ▷ C₅×C₁₉²
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.