Subgroups — #64601

Order 312.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₁₃	—	3	1	no	maximal, Hall
5	C₂×C₃×C₁₃	C₂²	1	1	yes	characteristic
6	D₃₉	C₄	1	2	yes	complemented
7	C₂×D₁₃	—	3	1	no	—
8	C₄×C₁₃	—	3	1	no	—
9	Dic₁₃	D₃	1	1	yes	characteristic, complemented
10	C₃×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₃	C₂×D₃	1	1	yes	characteristic
12	D₁₃	—	3	2	no	—
13	C₄×D₃	—	13	1	no	maximal, Hall
14	C₁₃	C₄×D₃	1	1	yes	characteristic, complemented, Sylow
15	C₂×D₃	—	13	1	no	—
16	C₃×C₄	—	13	1	no	—
17	Dic₃	D₁₃	1	1	yes	characteristic, complemented
18	C₂×C₄	—	39	1	no	Sylow
19	C₂×C₃	C₂×D₁₃	1	1	yes	characteristic
20	D₃	—	13	2	no	—
21	C₂²	—	39	1	no	—
22	C₄	—	3	1	no	—
23	C₄	—	13	1	no	—
24	C₃	C₄×D₁₃	1	1	yes	characteristic, complemented, Sylow
25	C₂	—	39	2	no	—
26	C₂	D₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₁₃
commutator, hypocenter	C₃×C₁₃	C₂×C₄
Fitting, socle, cosocle	C₂×C₃×C₁₃	C₂²
prime radical	C₂×D₃₉	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂

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.