Subgroups — C₅²×C₇×H(3,𝔽₅) #36346261

Order 21875.

4752 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⁴×C₇	C₅	1	6	yes	maximal, complemented
2	C₅×C₇×H(3,𝔽₅)	C₅	1	150	yes	maximal, direct product factor
3	C₅²×H(3,𝔽₅)	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₅³×C₇	—	5	150	no	—
5	C₅³×C₇	C₅²	1	1	yes	characteristic
6	C₅³×C₇	C₅²	1	180	yes	complemented
7	C₇×H(3,𝔽₅)	C₅²	1	625	yes	direct product factor
8	C₅⁴	C₅×C₇	1	6	yes	complemented
9	C₅×H(3,𝔽₅)	C₅×C₇	1	150	yes	direct product factor
10	C₅²×C₇	—	5	900	no	—
11	C₅²×C₇	H(3,𝔽₅)	1	25	yes	direct product factor
12	C₅²×C₇	C₅³	1	6	yes	—
13	C₅²×C₇	C₅³	1	150	yes	complemented
14	C₅³	—	5	150	no	—
15	C₅³	C₅²×C₇	1	1	yes	characteristic
16	C₅³	C₅²×C₇	1	180	yes	complemented
17	H(3,𝔽₅)	C₅²×C₇	1	625	yes	direct product factor
18	C₅×C₇	—	5	150	no	—
19	C₅×C₇	C₅×H(3,𝔽₅)	1	30	yes	direct product factor
20	C₅×C₇	C₅⁴	1	1	yes	characteristic
21	C₅²	—	5	900	no	—
22	C₅²	C₇×H(3,𝔽₅)	1	25	yes	direct product factor
23	C₅²	C₅³×C₇	1	6	yes	—
24	C₅²	C₅³×C₇	1	150	yes	complemented
25	C₇	C₅²×H(3,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
26	C₅	—	5	150	no	—
27	C₅	C₅×C₇×H(3,𝔽₅)	1	30	yes	direct product factor
28	C₅	C₅⁴×C₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₅³×C₇	C₅²
commutator, Frattini, cosocle	C₅	C₅⁴×C₇
LCS	G ▷ C₅ ▷ C₁
UCS	C₁ ◁ C₅³×C₇ ◁ G

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.