Subgroups — C₃×#585 #5977

Order 192.

810 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×2₋¹⁺⁴	C₂	1	6	yes	maximal, complemented
2	C₃×H(5,𝔽₂)	C₂	1	10	yes	maximal, complemented
3	C₂×C₃×#41	C₂	1	15	yes	maximal, complemented
4	#585	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×#41	C₂²	1	20	yes	complemented
6	C₃×#41	C₂²	1	60	yes	complemented
7	C₂×C₃×Q₈	C₂²	1	15	yes	complemented
8	C₂×C₃×D₄	C₂²	1	45	yes	complemented
9	C₂²×C₃×C₄	C₂²	1	15	yes	complemented
10	2₋¹⁺⁴	C₂×C₃	1	6	yes	complemented
11	H(5,𝔽₂)	C₂×C₃	1	10	yes	complemented
12	C₂×#41	C₂×C₃	1	15	yes	complemented
13	C₂³×C₃	C₂³	1	15	yes	—
14	C₃×Q₈	C₂³	1	20	yes	—
15	C₃×D₄	C₂³	1	60	yes	—
16	C₂×C₃×C₄	C₂³	1	45	yes	—
17	C₂×C₃×C₄	C₂³	1	15	yes	—
18	#41	C₂²×C₃	1	20	yes	complemented
19	#41	C₂²×C₃	1	60	yes	complemented
20	C₂×Q₈	C₂²×C₃	1	15	yes	complemented
21	C₂×D₄	C₂²×C₃	1	45	yes	complemented
22	C₂²×C₄	C₂²×C₃	1	15	yes	complemented
23	C₂²×C₃	—	4	15	no	—
24	C₂²×C₃	C₂⁴	1	15	yes	—
25	C₃×C₄	C₂⁴	1	15	yes	—
26	C₃×C₄	C₂⁴	1	1	yes	characteristic
27	C₂³	C₂³×C₃	1	15	yes	—
28	Q₈	C₂³×C₃	1	20	yes	—
29	D₄	C₂³×C₃	1	60	yes	—
30	C₂×C₄	C₂³×C₃	1	15	yes	—
31	C₂×C₄	C₂³×C₃	1	45	yes	—
32	C₂×C₃	—	2	15	no	—
33	C₂×C₃	C₂⁵	1	1	yes	characteristic
34	C₂²	—	4	15	no	—
35	C₂²	C₂⁴×C₃	1	15	yes	—
36	C₄	C₂⁴×C₃	1	1	yes	characteristic
37	C₄	C₂⁴×C₃	1	15	yes	—
38	C₃	#585	1	1	yes	characteristic, direct product factor, Sylow
39	C₂	—	2	15	no	—
40	C₂	C₂⁵×C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂⁴
commutator, Frattini, cosocle	C₂	C₂⁵×C₃
socle	C₂×C₃	C₂⁵
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄ ◁ 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.