Subgroups — C₂×C₂₃×D₃₆₅ #46777178

Order 33580.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₃₆₅	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	—	5	1	no	maximal, Hall
5	C₂×C₂₃×C₇₃	D₅	1	1	yes	characteristic, complemented
6	C₂₃×D₇₃	—	5	2	no	—
7	C₂₃×C₇₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
8	C₂×D₃₆₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₅×C₇₃	C₂×C₂₃	1	1	yes	characteristic, complemented
10	D₃₆₅	C₂×C₂₃	1	2	yes	direct product factor
11	C₂×D₅×C₂₃	—	73	1	no	maximal, Hall
12	C₅×C₇₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
13	C₂×D₇₃	—	5	1	no	Hall
14	C₂×C₅×C₂₃	D₇₃	1	1	yes	characteristic, complemented
15	D₅×C₂₃	—	73	2	no	—
16	C₂×C₇₃	D₅×C₂₃	1	1	yes	characteristic, complemented
17	D₇₃	—	5	2	no	—
18	C₅×C₂₃	C₂×D₇₃	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₂₃	—	365	1	no	Hall
20	C₇₃	C₂×D₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₂₃	—	365	2	no	—
22	C₂×C₂₃	D₃₆₅	1	1	yes	characteristic, direct product factor
23	C₂₃	C₂×D₃₆₅	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₅	—	73	1	no	Hall
25	C₂×C₅	C₂₃×D₇₃	1	1	yes	characteristic, complemented
26	D₅	—	73	2	no	—
27	C₅	C₂×C₂₃×D₇₃	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	365	1	no	Sylow
29	C₂	—	365	2	no	—
30	C₂	C₂₃×D₃₆₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₃	D₃₆₅
commutator, cosocle, hypocenter	C₅×C₇₃	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₂₃×C₇₃	C₂
LCS	G ▷ C₅×C₇₃
UCS	C₁ ◁ C₂×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×D₃₆₅	C₂	direct (N × H)
2. C₂×C₅×C₂₃×C₇₃	C₂	semidirect
3. C₅×C₂₃×C₇₃	C₂²	semidirect
5. C₂×C₂₃×C₇₃	D₅	semidirect
7. C₂₃×C₇₃	C₂×D₅	semidirect
8. C₂×D₃₆₅	C₂₃	direct (N × H)
9. C₂×C₅×C₇₃	C₂×C₂₃	semidirect
10. D₃₆₅	C₂×C₂₃	direct (N × H)
12. C₅×C₇₃	C₂²×C₂₃	semidirect
14. C₂×C₅×C₂₃	D₇₃	semidirect
16. C₂×C₇₃	D₅×C₂₃	semidirect
18. C₅×C₂₃	C₂×D₇₃	semidirect
20. C₇₃	C₂×D₅×C₂₃	semidirect
22. C₂×C₂₃	D₃₆₅	direct (N × H)
23. C₂₃	C₂×D₃₆₅	direct (N × H)
25. C₂×C₅	C₂₃×D₇₃	semidirect
27. C₅	C₂×C₂₃×D₇₃	semidirect
30. C₂	C₂₃×D₃₆₅	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×D₃₆₅	2
C₂×C₅×C₂₃×C₇₃	2
C₂×C₂₃×D₇₃	5
C₂×D₃₆₅	23
C₂×D₅×C₂₃	73

Subgroups — C2×C23×D365 #46777178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×D₃₆₅ #46777178