Subgroups — C₅₉×#10596816 #46803775

Order 34220.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₂₉×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₉×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅₉×Dic₂₉	—	5	1	no	maximal, Hall
4	C₂×C₂₉×C₅₉	—	5	1	no	—
5	C₂₉×C₅₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
6	AGL(1,𝔽₅)×C₅₉	—	29	1	no	maximal, Hall
7	D₅×C₅₉	D₂₉	1	1	yes	characteristic
8	#10596816	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₅₉	Dic₂₉	1	1	yes	characteristic, complemented, Hall
10	D₅×C₂₉	C₂×C₅₉	1	1	yes	characteristic
11	C₄×C₅₉	—	145	1	no	Hall
12	C₅×C₂₉	C₄×C₅₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅₉	—	5	1	no	—
14	Dic₂₉	—	5	1	no	Hall
15	C₅₉	#10596816	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₂₉	—	5	1	no	—
17	C₂₉	AGL(1,𝔽₅)×C₅₉	1	1	yes	characteristic, complemented, Sylow
18	AGL(1,𝔽₅)	—	29	1	no	Hall
19	D₅	D₂₉×C₅₉	1	1	yes	characteristic
20	C₅	C₅₉×Dic₂₉	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	145	1	no	Sylow
22	C₂	—	5	1	no	—

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.