Subgroups — C₂×#14584115 #19150331

Order 5586.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14584115	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×#87704	—	7	8	no	maximal
5	#87704	—	7	8	no	—
6	C₂×#3861	—	19	1	no	maximal, Hall
7	C₂×C₇×C₁₉	ΓL(1,𝔽₈)	1	8	yes	complemented
8	#3861	—	19	1	no	Hall
9	C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
10	C₂×C₁₉⋊C₃	—	49	1	no	Hall
11	C₂×C₇²	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₁₉⋊C₃	—	49	1	no	Hall
13	C₇²	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
14	C₂×ΓL(1,𝔽₈)	—	133	8	no	—
15	C₂×C₁₉	#3861	1	1	yes	characteristic, complemented, Hall
16	ΓL(1,𝔽₈)	—	133	8	no	—
17	C₁₉	C₂×#3861	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₇	#87704	1	8	yes	complemented
19	C₇	C₂×#87704	1	8	yes	complemented
20	C₂×C₃	—	931	1	no	Hall
21	C₃	—	931	1	no	Sylow
22	C₂	#14584115	1	1	yes	characteristic, direct product factor, Sylow

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