Subgroups — C₃×H(5,𝔽₂) #1017

Order 96.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41	C₂	1	6	yes	maximal, complemented
2	C₂×C₃×D₄	C₂	1	9	yes	maximal, complemented
3	H(5,𝔽₂)	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂³×C₃	C₂²	1	6	yes	complemented
5	C₃×Q₈	C₂²	1	2	yes	complemented
6	C₃×D₄	C₂²	1	18	yes	complemented
7	C₂×C₃×C₄	C₂²	1	9	yes	complemented
8	#41	C₂×C₃	1	6	yes	complemented
9	C₂×D₄	C₂×C₃	1	9	yes	complemented
10	C₂²×C₃	—	4	6	no	—
11	C₂²×C₃	C₂³	1	9	yes	—
12	C₃×C₄	C₂³	1	6	yes	—
13	C₂³	C₂²×C₃	1	6	yes	complemented
14	Q₈	C₂²×C₃	1	2	yes	complemented
15	D₄	C₂²×C₃	1	18	yes	complemented
16	C₂×C₄	C₂²×C₃	1	9	yes	complemented
17	C₂×C₃	—	2	9	no	—
18	C₂×C₃	C₂⁴	1	1	yes	characteristic
19	C₂²	—	4	6	no	—
20	C₂²	C₂³×C₃	1	9	yes	—
21	C₄	C₂³×C₃	1	6	yes	—
22	C₃	H(5,𝔽₂)	1	1	yes	characteristic, direct product factor, Sylow
23	C₂	—	2	9	no	—
24	C₂	C₂⁴×C₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	C₂⁴
commutator, Frattini, cosocle	C₂	C₂⁴×C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ 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.