Subgroups — C₂×C₅×#11762246 #24925339

Order 10830.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#11762246	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₁₉²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×#11762246	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	#11762246	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₉²	C₃×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₁₉⋊C₃	—	19	2	no	maximal
8	C₁₉²	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Sylow
9	C₅×C₁₉⋊C₃	—	19	2	no	—
10	C₂×C₅×C₁₉	—	3	6	no	—
11	C₂×C₅×C₁₉	C₁₉⋊C₃	1	2	yes	complemented
12	C₂×C₁₉⋊C₃	—	19	2	no	—
13	C₅×C₁₉	—	3	6	no	—
14	C₅×C₁₉	C₂×C₁₉⋊C₃	1	2	yes	complemented
15	C₁₉⋊C₃	—	19	2	no	—
16	C₂×C₁₉	—	3	6	no	—
17	C₂×C₁₉	C₅×C₁₉⋊C₃	1	2	yes	complemented
18	C₂×C₃×C₅	—	361	1	no	Hall
19	C₁₉	—	3	6	no	—
20	C₁₉	C₂×C₅×C₁₉⋊C₃	1	2	yes	complemented
21	C₃×C₅	—	361	1	no	Hall
22	C₂×C₅	#11762246	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃	—	361	1	no	Hall
24	C₅	C₂×#11762246	1	1	yes	characteristic, direct product factor, Sylow
25	C₃	—	361	1	no	Sylow
26	C₂	C₅×#11762246	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅	#11762246
commutator, cosocle, hypocenter	C₁₉²	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉²	C₃
LCS	G ▷ C₁₉²
UCS	C₁ ◁ C₂×C₅

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.