Subgroups — C₁₃×#11716327 #23780596

Order 10374.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#87704	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₁₃₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₁₉⋊C₃	—	7	1	no	maximal, Hall
5	#11716327	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₁₉⋊C₃	—	7	1	no	Hall
7	C₁₃×AGL(1,𝔽₇)	—	19	1	no	maximal, Hall
8	C₁₃×D₁₉	—	7	1	no	Hall
9	#87704	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₁₃×ΓL(1,𝔽₈)	—	19	1	no	Hall
11	D₁₃₃	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
13	C₁₃×D₇	—	19	1	no	Hall
14	C₇×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
15	D₁₉⋊C₃	—	7	1	no	Hall
16	C₇×C₁₃	D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₃	—	133	1	no	Hall
18	C₁₉⋊C₃	—	7	1	no	Hall
19	AGL(1,𝔽₇)	—	19	1	no	Hall
20	C₃×C₁₃	—	133	1	no	Hall
21	D₁₉	—	7	1	no	Hall
22	C₂×C₁₃	—	133	1	no	Hall
23	ΓL(1,𝔽₈)	—	19	1	no	Hall
24	C₁₉	C₁₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
25	D₇	—	19	1	no	Hall
26	C₁₃	#11716327	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₁₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	133	1	no	Hall
29	C₃	—	133	1	no	Sylow
30	C₂	—	133	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	#11716327
commutator, cosocle, hypocenter	C₇×C₁₉	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₁₃

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