Subgroups — C₂×C₅×C₂₃×D₇₃ #46777174

Order 33580.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₃×D₇₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₂₃×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂₃×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₂₃×D₇₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₂₃×C₇₃	C₂×C₅	1	1	yes	characteristic, complemented
6	C₂₃×D₇₃	C₂×C₅	1	2	yes	direct product factor
7	C₂₃×C₇₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅×D₇₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₅×C₇₃	C₂×C₂₃	1	1	yes	characteristic, complemented
10	C₅×D₇₃	C₂×C₂₃	1	2	yes	direct product factor
11	C₂²×C₅×C₂₃	—	73	1	no	maximal, Hall
12	C₅×C₇₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
13	C₂×D₇₃	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₂₃	—	73	2	no	—
15	C₂×C₅×C₂₃	D₇₃	1	1	yes	characteristic, direct product factor
16	C₂×C₇₃	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented
17	D₇₃	C₂×C₅×C₂₃	1	2	yes	direct product factor
18	C₅×C₂₃	C₂×D₇₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₂₃	—	73	1	no	Hall
20	C₇₃	C₂²×C₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₂₃	—	73	2	no	—
22	C₂×C₂₃	C₅×D₇₃	1	1	yes	characteristic, direct product factor
23	C₂₃	C₂×C₅×D₇₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₅	—	73	1	no	Hall
25	C₂×C₅	—	73	2	no	—
26	C₂×C₅	C₂₃×D₇₃	1	1	yes	characteristic, direct product factor
27	C₅	C₂×C₂₃×D₇₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	73	1	no	Sylow
29	C₂	—	73	2	no	—
30	C₂	C₅×C₂₃×D₇₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₂₃	D₇₃
commutator, cosocle, hypocenter	C₇₃	C₂²×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₂₃×C₇₃	C₂
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂×C₅×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₃×D₇₃	C₂	direct (N × H)
2. C₂×C₅×C₂₃×C₇₃	C₂	semidirect
3. C₅×C₂₃×C₇₃	C₂²	semidirect
4. C₂×C₂₃×D₇₃	C₅	direct (N × H)
5. C₂×C₂₃×C₇₃	C₂×C₅	semidirect
6. C₂₃×D₇₃	C₂×C₅	direct (N × H)
7. C₂₃×C₇₃	C₂²×C₅	semidirect
8. C₂×C₅×D₇₃	C₂₃	direct (N × H)
9. C₂×C₅×C₇₃	C₂×C₂₃	semidirect
10. C₅×D₇₃	C₂×C₂₃	direct (N × H)
12. C₅×C₇₃	C₂²×C₂₃	semidirect
13. C₂×D₇₃	C₅×C₂₃	direct (N × H)
15. C₂×C₅×C₂₃	D₇₃	direct (N × H)
16. C₂×C₇₃	C₂×C₅×C₂₃	semidirect
17. D₇₃	C₂×C₅×C₂₃	direct (N × H)
18. C₅×C₂₃	C₂×D₇₃	direct (N × H)
20. C₇₃	C₂²×C₅×C₂₃	semidirect
22. C₂×C₂₃	C₅×D₇₃	direct (N × H)
23. C₂₃	C₂×C₅×D₇₃	direct (N × H)
26. C₂×C₅	C₂₃×D₇₃	direct (N × H)
27. C₅	C₂×C₂₃×D₇₃	direct (N × H)
30. C₂	C₅×C₂₃×D₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₂₃×D₇₃	2
C₂×C₅×C₂₃×C₇₃	2
C₂×C₂₃×D₇₃	5
C₂×C₅×D₇₃	23
C₂²×C₅×C₂₃	73

Subgroups — C2×C5×C23×D73 #46777174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₂₃×D₇₃ #46777174