Subgroups — D₃×#261 #64630

Order 312.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#261	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#261	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#261	—	3	1	no	maximal, Hall
5	D₃₉	C₄	1	1	yes	characteristic, complemented
6	C₃×D₁₃	C₂²	1	1	yes	characteristic
7	D₃×C₁₃	C₄	1	1	yes	characteristic, complemented
8	C₂×D₁₃	—	3	1	no	—
9	#261	—	3	1	no	—
10	#261	D₃	1	1	yes	characteristic, direct product factor
11	C₃×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₃	—	3	1	no	—
13	D₁₃	—	3	1	no	—
14	D₁₃	C₂×D₃	1	1	yes	characteristic
15	C₄×D₃	—	13	1	no	maximal, Hall
16	C₁₃	C₄×D₃	1	1	yes	characteristic, complemented, Sylow
17	C₂×D₃	—	13	1	no	—
18	C₃×C₄	—	13	1	no	—
19	Dic₃	—	13	1	no	—
20	C₂×C₄	—	39	1	no	Sylow
21	C₂×C₃	—	13	1	no	—
22	D₃	—	13	1	no	—
23	D₃	#261	1	1	yes	characteristic, direct product factor
24	C₂²	—	39	1	no	—
25	C₄	—	13	1	no	—
26	C₄	—	39	1	no	—
27	C₃	C₂×#261	1	1	yes	characteristic, complemented, Sylow
28	C₂	—	3	1	no	—
29	C₂	—	13	1	no	—
30	C₂	—	39	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₃	C₂×C₄
prime radical	D₃×D₁₃	C₂
cosocle	C₃×D₁₃	C₂²
LCS	G ▷ C₃×C₁₃
UCS	C₁

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.