Subgroups — C₂×#18011727 #23748950

Order 9516.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18011727	C₂	1	2	yes	maximal, direct product factor
2	C₂×#14558652	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₃×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#14558652	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented
6	D₁₃×C₆₁	C₂×C₃	1	2	yes	complemented
7	C₁₃×C₆₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₆₁⋊C₃	—	13	1	no	maximal, Hall
9	C₂×C₆₁⋊C₃	—	13	2	no	—
10	C₂×C₆₁⋊C₃	—	13	1	no	—
11	C₂²×C₆₁	—	13	1	no	Hall
12	C₆₁⋊C₃	—	13	1	no	Hall
13	C₂×D₁₃⋊C₃	—	61	1	no	maximal, Hall
14	C₂×C₆₁	—	13	2	no	—
15	C₂×C₆₁	D₁₃⋊C₃	1	1	yes	characteristic, complemented
16	C₂×C₁₃⋊C₃	—	61	1	no	—
17	D₁₃⋊C₃	—	61	2	no	—
18	C₆₁	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×D₁₃	C₆₁⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₁₃⋊C₃	—	61	1	no	Hall
21	C₂×C₁₃	C₂×C₆₁⋊C₃	1	1	yes	characteristic, complemented
22	D₁₃	C₂×C₆₁⋊C₃	1	2	yes	complemented
23	C₁₃	C₂²×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	793	1	no	Hall
25	C₂×C₃	—	793	2	no	—
26	C₂×C₃	—	793	1	no	—
27	C₂²	—	13	1	no	Sylow
28	C₃	—	793	1	no	Sylow
29	C₂	—	13	2	no	—
30	C₂	#18011727	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#18011727
commutator, cosocle, hypocenter	C₁₃×C₆₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₆₁	C₂×C₃
LCS	G ▷ C₁₃×C₆₁
UCS	C₁ ◁ C₂

Splittings G = N ⋊ H with N normal; H ≅ G/N.