Subgroups — C₂⁴×C₅×C₂₈₉ #72200486

Order 23120.

402 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×C₂₈₉	C₂	1	15	yes	maximal, direct product factor
2	C₂⁴×C₂₈₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂³×C₂₈₉	C₂×C₅	1	15	yes	direct product factor
4	C₂²×C₅×C₂₈₉	C₂²	1	35	yes	direct product factor
5	C₂×C₅×C₂₈₉	C₂³	1	15	yes	direct product factor
6	C₅×C₂₈₉	C₂⁴	1	1	yes	characteristic, direct product factor, Hall
7	C₂⁴×C₅×C₁₇	C₁₇	1	1	yes	maximal, characteristic
8	C₂²×C₂₈₉	C₂²×C₅	1	35	yes	direct product factor
9	C₂³×C₅×C₁₇	C₂×C₁₇	1	15	yes	—
10	C₂×C₂₈₉	C₂³×C₅	1	15	yes	direct product factor
11	C₂²×C₅×C₁₇	C₂²×C₁₇	1	35	yes	—
12	C₂₈₉	C₂⁴×C₅	1	1	yes	characteristic, direct product factor, Sylow
13	C₂⁴×C₁₇	C₅×C₁₇	1	1	yes	characteristic
14	C₂×C₅×C₁₇	C₂³×C₁₇	1	15	yes	—
15	C₂³×C₁₇	C₂×C₅×C₁₇	1	15	yes	—
16	C₅×C₁₇	C₂⁴×C₁₇	1	1	yes	characteristic
17	C₂⁴×C₅	C₂₈₉	1	1	yes	characteristic, direct product factor, Hall
18	C₂²×C₁₇	C₂²×C₅×C₁₇	1	35	yes	—
19	C₂³×C₅	C₂×C₂₈₉	1	15	yes	direct product factor
20	C₂×C₁₇	C₂³×C₅×C₁₇	1	15	yes	—
21	C₂²×C₅	C₂²×C₂₈₉	1	35	yes	direct product factor
22	C₁₇	C₂⁴×C₅×C₁₇	1	1	yes	characteristic
23	C₂⁴	C₅×C₂₈₉	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₅	C₂³×C₂₈₉	1	15	yes	direct product factor
25	C₂³	C₂×C₅×C₂₈₉	1	15	yes	direct product factor
26	C₅	C₂⁴×C₂₈₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₂²	C₂²×C₅×C₂₈₉	1	35	yes	direct product factor
28	C₂	C₂³×C₅×C₂₈₉	1	15	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₇	C₂⁴×C₅×C₁₇
socle, prime radical	C₂⁴×C₅×C₁₇	C₁₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅×C₂₈₉	C₂	direct (N × H)
2. C₂⁴×C₂₈₉	C₅	direct (N × H)
3. C₂³×C₂₈₉	C₂×C₅	direct (N × H)
4. C₂²×C₅×C₂₈₉	C₂²	direct (N × H)
5. C₂×C₅×C₂₈₉	C₂³	direct (N × H)
6. C₅×C₂₈₉	C₂⁴	direct (N × H)
8. C₂²×C₂₈₉	C₂²×C₅	direct (N × H)
10. C₂×C₂₈₉	C₂³×C₅	direct (N × H)
12. C₂₈₉	C₂⁴×C₅	direct (N × H)
17. C₂⁴×C₅	C₂₈₉	direct (N × H)
19. C₂³×C₅	C₂×C₂₈₉	direct (N × H)
21. C₂²×C₅	C₂²×C₂₈₉	direct (N × H)
23. C₂⁴	C₅×C₂₈₉	direct (N × H)
24. C₂×C₅	C₂³×C₂₈₉	direct (N × H)
25. C₂³	C₂×C₅×C₂₈₉	direct (N × H)
26. C₅	C₂⁴×C₂₈₉	direct (N × H)
27. C₂²	C₂²×C₅×C₂₈₉	direct (N × H)
28. C₂	C₂³×C₅×C₂₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅×C₂₈₉	2
C₂⁴×C₂₈₉	5
C₂⁴×C₅×C₁₇	17

Subgroups — C24×C5×C289 #72200486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₅×C₂₈₉ #72200486