Subgroups — C₄×C₁₆×C₂₃₉ #29504249

Order 15296.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×C₂₃₉	C₂	1	2	yes	maximal
2	C₄×C₈×C₂₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₂₃₉	C₄	1	1	yes	characteristic
4	C₂×C₈×C₂₃₉	C₂²	1	1	yes	characteristic
5	C₄²×C₂₃₉	C₄	1	1	yes	characteristic
6	C₁₆×C₂₃₉	C₄	1	4	yes	direct product factor
7	C₂×C₄×C₂₃₉	C₈	1	2	yes	—
8	C₂×C₄×C₂₃₉	C₂×C₄	1	1	yes	characteristic
9	C₈×C₂₃₉	C₈	1	2	yes	—
10	C₈×C₂₃₉	C₂×C₄	1	2	yes	—
11	C₂²×C₂₃₉	C₂×C₈	1	1	yes	characteristic
12	C₄×C₂₃₉	C₁₆	1	4	yes	direct product factor
13	C₄×C₂₃₉	C₄²	1	1	yes	characteristic
14	C₄×C₂₃₉	C₂×C₈	1	1	yes	characteristic
15	C₂×C₂₃₉	C₄×C₈	1	1	yes	characteristic
16	C₂×C₂₃₉	C₂×C₁₆	1	2	yes	—
17	C₂₃₉	C₄×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
18	C₄×C₁₆	C₂₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₁₆	C₂×C₂₃₉	1	2	yes	—
20	C₄×C₈	C₂×C₂₃₉	1	1	yes	characteristic
21	C₂×C₈	C₄×C₂₃₉	1	1	yes	characteristic
22	C₂×C₈	C₂²×C₂₃₉	1	1	yes	characteristic
23	C₄²	C₄×C₂₃₉	1	1	yes	characteristic
24	C₁₆	C₄×C₂₃₉	1	4	yes	direct product factor
25	C₂×C₄	C₈×C₂₃₉	1	2	yes	—
26	C₂×C₄	C₂×C₄×C₂₃₉	1	1	yes	characteristic
27	C₈	C₈×C₂₃₉	1	2	yes	—
28	C₈	C₂×C₄×C₂₃₉	1	2	yes	—
29	C₂²	C₂×C₈×C₂₃₉	1	1	yes	characteristic
30	C₄	C₁₆×C₂₃₉	1	4	yes	direct product factor
31	C₄	C₄²×C₂₃₉	1	1	yes	characteristic
32	C₄	C₂×C₈×C₂₃₉	1	1	yes	characteristic
33	C₂	C₄×C₈×C₂₃₉	1	1	yes	characteristic
34	C₂	C₂×C₁₆×C₂₃₉	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈	C₂²×C₂₃₉
socle, prime radical	C₂²×C₂₃₉	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₁₆×C₂₃₉	C₄	direct (N × H)
12. C₄×C₂₃₉	C₁₆	direct (N × H)
17. C₂₃₉	C₄×C₁₆	direct (N × H)
18. C₄×C₁₆	C₂₃₉	direct (N × H)
24. C₁₆	C₄×C₂₃₉	direct (N × H)
30. C₄	C₁₆×C₂₃₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₆×C₂₃₉	2
C₄×C₈×C₂₃₉	2
C₄×C₁₆	239

Subgroups — C4×C16×C239 #29504249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₆×C₂₃₉ #29504249