Subgroups — #64603

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, complemented
2	C₂×C₃×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅₂	—	3	1	no	maximal, Hall
5	C₂×C₃×C₁₃	C₂²	1	1	yes	characteristic
6	D₃₉	—	2	1	no	—
7	C₃×D₁₃	—	2	1	no	—
8	C₂×D₁₃	—	3	1	no	—
9	C₂×D₁₃	D₃	1	1	yes	characteristic, complemented
10	C₄×C₁₃	—	3	1	no	—
11	C₃×C₁₃	D₄	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₃	C₂×D₃	1	1	yes	characteristic
13	D₁₃	—	2	1	no	—
14	D₁₃	—	6	1	no	—
15	#67	—	13	1	no	maximal, Hall
16	C₁₃	#67	1	1	yes	characteristic, complemented, Sylow
17	C₂²×C₃	—	13	1	no	—
18	C₂×D₃	—	13	1	no	—
19	Dic₃	D₁₃	1	1	yes	characteristic, complemented
20	D₄	—	39	1	no	Sylow
21	C₂×C₃	—	26	1	no	—
22	C₂×C₃	C₂×D₁₃	1	1	yes	characteristic
23	D₃	—	26	1	no	—
24	C₂²	—	13	1	no	—
25	C₂²	—	39	1	no	—
26	C₄	—	3	1	no	—
27	C₃	D₅₂	1	1	yes	characteristic, complemented, Sylow
28	C₂	—	26	1	no	—
29	C₂	—	78	1	no	—
30	C₂	D₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₁₃
commutator, Fitting, socle, cosocle	C₂×C₃×C₁₃	C₂²
hypocenter	C₃×C₁₃	D₄
LCS	G ▷ C₂×C₃×C₁₃ ▷ 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.