Subgroups — D₅×#15692433 #44570545

Order 32490.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15692433	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×#11762245	C₃	1	1	yes	maximal, characteristic
3	C₂×#15692433	—	5	1	no	maximal, Hall
4	C₅×#11762245	C₂×C₃	1	1	yes	characteristic
5	D₅×C₁₉²	C₉	1	1	yes	characteristic, complemented, Hall
6	#15692433	D₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×#11762245	—	5	1	no	—
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	D₅×#4296	—	19	20	no	maximal
10	#11762245	C₃×D₅	1	1	yes	characteristic
11	C₅×#4296	—	19	20	no	—
12	C₂×C₁₉²	—	5	1	no	Hall
13	D₅×C₁₉⋊C₃	—	19	20	no	—
14	C₁₉²	C₉×D₅	1	1	yes	characteristic, complemented, Sylow
15	C₂×#4296	—	95	20	no	—
16	C₅×C₁₉⋊C₃	—	19	20	no	—
17	D₅×C₁₉	#4296	1	20	yes	complemented
18	#4296	—	19	20	no	—
19	C₂×C₁₉⋊C₃	—	95	20	no	—
20	C₅×C₁₉	C₂×#4296	1	20	yes	complemented
21	C₉×D₅	—	361	1	no	Hall
22	C₁₉⋊C₃	—	19	20	no	—
23	C₅×C₉	—	361	1	no	Hall
24	C₂×C₁₉	—	5	20	no	—
25	C₃×D₅	—	361	1	no	—
26	C₁₉	D₅×#4296	1	20	yes	complemented
27	C₂×C₉	—	1805	1	no	Hall
28	C₃×C₅	—	361	1	no	—
29	D₅	#15692433	1	1	yes	characteristic, direct product factor, Hall
30	C₉	—	361	1	no	Sylow
31	C₂×C₃	—	1805	1	no	—
32	C₅	C₂×#15692433	1	1	yes	characteristic, complemented, Sylow
33	C₃	—	361	1	no	—
34	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₉²	C₂×C₉
prime radical	D₅×#11762245	C₃
cosocle	C₅×#11762245	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.