Finite Group Databasebeta

← C₂×C₄×C₆₇₃ #19129083

Subgroups — C₂×C₄×C₆₇₃ #19129083

Order 5384.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₆₇₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₆₇₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₆₇₃	C₄	1	2	yes	direct product factor
4	C₂×C₆₇₃	C₂²	1	1	yes	characteristic
5	C₆₇₃	C₂×C₄	1	1	yes	characteristic, direct product factor, Sylow
6	C₂×C₄	C₆₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²	C₂×C₆₇₃	1	1	yes	characteristic
8	C₄	C₂×C₆₇₃	1	2	yes	direct product factor
9	C₂	C₄×C₆₇₃	1	2	yes	direct product factor
10	C₂	C₂²×C₆₇₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂	C₂²×C₆₇₃
socle	C₂²×C₆₇₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₆₇₃	C₂	direct (N × H)
3. C₂×C₆₇₃	C₄	direct (N × H)
5. C₆₇₃	C₂×C₄	direct (N × H)
6. C₂×C₄	C₆₇₃	direct (N × H)
8. C₄	C₂×C₆₇₃	direct (N × H)
9. C₂	C₄×C₆₇₃	direct (N × H)