Subgroups — C₂×C₅×D₃×C₃₉₇ #37558437

Order 23820.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×C₃₉₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₃₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×C₃₉₇	—	3	1	no	maximal, Hall
4	C₃×C₅×C₃₉₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₃₉₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₃₉₇	—	3	2	no	—
7	C₂×C₅×C₃₉₇	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₃×C₃₉₇	C₂×C₅	1	1	yes	characteristic, complemented
9	D₃×C₃₉₇	C₂×C₅	1	2	yes	direct product factor
10	C₅×C₃₉₇	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₃₉₇	—	3	1	no	Hall
12	C₃×C₃₉₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃₉₇	—	3	2	no	—
14	C₂×C₃₉₇	C₅×D₃	1	1	yes	characteristic, direct product factor
15	C₃₉₇	C₂×C₅×D₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₅×D₃	C₃₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅	C₂×C₃₉₇	1	1	yes	characteristic, complemented
18	C₅×D₃	C₂×C₃₉₇	1	2	yes	direct product factor
19	C₂²×C₅	—	3	1	no	Hall
20	C₃×C₅	C₂²×C₃₉₇	1	1	yes	characteristic, complemented, Hall
21	C₂×D₃	C₅×C₃₉₇	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₅	—	3	2	no	—
23	C₂×C₅	D₃×C₃₉₇	1	1	yes	characteristic, direct product factor
24	C₂×C₃	C₂×C₅×C₃₉₇	1	1	yes	characteristic, complemented
25	D₃	C₂×C₅×C₃₉₇	1	2	yes	direct product factor
26	C₅	C₂×D₃×C₃₉₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₂²	—	3	1	no	Sylow
28	C₃	C₂²×C₅×C₃₉₇	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	3	2	no	—
30	C₂	C₅×D₃×C₃₉₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₃₉₇	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₅×C₃₉₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₃₉₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₃₉₇

Complements

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

N	H ≅ G/N	type
1. C₅×D₃×C₃₉₇	C₂	direct (N × H)
2. C₂×C₃×C₅×C₃₉₇	C₂	semidirect
4. C₃×C₅×C₃₉₇	C₂²	semidirect
5. C₂×D₃×C₃₉₇	C₅	direct (N × H)
7. C₂×C₅×C₃₉₇	D₃	direct (N × H)
8. C₂×C₃×C₃₉₇	C₂×C₅	semidirect
9. D₃×C₃₉₇	C₂×C₅	direct (N × H)
10. C₅×C₃₉₇	C₂×D₃	direct (N × H)
12. C₃×C₃₉₇	C₂²×C₅	semidirect
14. C₂×C₃₉₇	C₅×D₃	direct (N × H)
15. C₃₉₇	C₂×C₅×D₃	direct (N × H)
16. C₂×C₅×D₃	C₃₉₇	direct (N × H)
17. C₂×C₃×C₅	C₂×C₃₉₇	semidirect
18. C₅×D₃	C₂×C₃₉₇	direct (N × H)
20. C₃×C₅	C₂²×C₃₉₇	semidirect
21. C₂×D₃	C₅×C₃₉₇	direct (N × H)
23. C₂×C₅	D₃×C₃₉₇	direct (N × H)
24. C₂×C₃	C₂×C₅×C₃₉₇	semidirect
25. D₃	C₂×C₅×C₃₉₇	direct (N × H)
26. C₅	C₂×D₃×C₃₉₇	direct (N × H)
28. C₃	C₂²×C₅×C₃₉₇	semidirect
30. C₂	C₅×D₃×C₃₉₇	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×D₃×C₃₉₇	2
C₂×C₃×C₅×C₃₉₇	2
C₂²×C₅×C₃₉₇	3
C₂×D₃×C₃₉₇	5
C₂×C₅×D₃	397

Subgroups — C2×C5×D3×C397 #37558437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₃×C₃₉₇ #37558437