Subgroups — C₅²×#63271 #20291981

Order 6825.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×#63271	C₅	1	6	yes	maximal, direct product factor
3	C₅²×C₁₃⋊C₃	—	7	1	no	maximal, Hall
4	C₅²×ΓL(1,𝔽₈)	—	13	1	no	maximal, Hall
5	C₅×C₇×C₁₃	C₃×C₅	1	6	yes	complemented
6	C₅²×C₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
7	#63271	C₅²	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₁₃⋊C₃	—	7	6	no	—
9	C₅²×C₇	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
10	C₅×ΓL(1,𝔽₈)	—	13	6	no	—
11	C₇×C₁₃	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅²	—	91	1	no	Hall
13	C₅×C₁₃	C₅×ΓL(1,𝔽₈)	1	6	yes	complemented
14	C₁₃⋊C₃	—	7	1	no	Hall
15	C₅×C₇	C₅×C₁₃⋊C₃	1	6	yes	complemented
16	C₅²	#63271	1	1	yes	characteristic, direct product factor, Sylow
17	ΓL(1,𝔽₈)	—	13	1	no	Hall
18	C₃×C₅	—	91	6	no	—
19	C₁₃	C₅²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
20	C₇	C₅²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₅	C₅×#63271	1	6	yes	direct product factor
22	C₃	—	91	1	no	Sylow

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