Subgroups — C₅×#11924777 #20238708

Order 5985.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₉	C₃	1	1	yes	maximal, characteristic
2	#11924777	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×#4294	—	7	1	no	maximal, Hall
4	C₅×C₇×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×C₁₉	C₃×C₅	1	1	yes	characteristic
6	C₅×C₇⋊C₉	—	19	1	no	maximal, Hall
7	C₃×C₅×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
8	#4294	—	7	1	no	Hall
9	C₇×C₁₉	C₅×C₉	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×C₇	C₁₉⋊C₃	1	1	yes	characteristic
11	C₅×C₁₉	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
12	C₇⋊C₉	—	19	1	no	Hall
13	C₃×C₁₉	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
14	C₅×C₉	—	133	1	no	Hall
15	C₅×C₇	#4294	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇	C₅×C₁₉⋊C₃	1	1	yes	characteristic
17	C₁₉	C₅×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₅	#87705	1	1	yes	characteristic
19	C₉	—	133	1	no	Sylow
20	C₇	C₅×#4294	1	1	yes	characteristic, complemented, Sylow
21	C₅	#11924777	1	1	yes	characteristic, direct product factor, Sylow
22	C₃	C₅×#87705	1	1	yes	characteristic

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