Subgroups — C₂×C₃×D₂₅₆₁ #44502248

Order 30732.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₅₆₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃×C₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₅₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₃×C₁₉₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₁₉₇	C₂×C₃	1	1	yes	characteristic, complemented
6	D₂₅₆₁	C₂×C₃	1	2	yes	direct product factor
7	C₁₃×C₁₉₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×D₁₉₇	—	13	1	no	maximal, Hall
9	C₂×C₃×C₁₉₇	D₁₃	1	1	yes	characteristic, complemented
10	C₃×D₁₉₇	—	13	2	no	—
11	C₂×D₁₉₇	—	13	1	no	Hall
12	C₃×C₁₉₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₉₇	C₃×D₁₃	1	1	yes	characteristic, complemented
14	D₁₉₇	—	13	2	no	—
15	C₁₉₇	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×D₁₃	—	197	1	no	maximal, Hall
17	C₂×C₃×C₁₃	D₁₉₇	1	1	yes	characteristic, complemented
18	C₃×D₁₃	—	197	2	no	—
19	C₂×D₁₃	—	197	1	no	Hall
20	C₃×C₁₃	C₂×D₁₉₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₃	C₃×D₁₉₇	1	1	yes	characteristic, complemented
22	D₁₃	—	197	2	no	—
23	C₁₃	C₂×C₃×D₁₉₇	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	2561	1	no	Hall
25	C₂×C₃	—	2561	2	no	—
26	C₂×C₃	D₂₅₆₁	1	1	yes	characteristic, direct product factor
27	C₂²	—	2561	1	no	Sylow
28	C₃	C₂×D₂₅₆₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	2561	2	no	—
30	C₂	C₃×D₂₅₆₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₅₆₁
commutator, cosocle, hypocenter	C₁₃×C₁₉₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₁₉₇	C₂
LCS	G ▷ C₁₃×C₁₉₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₅₆₁	C₂	direct (N × H)
2. C₂×C₃×C₁₃×C₁₉₇	C₂	semidirect
3. C₂×D₂₅₆₁	C₃	direct (N × H)
4. C₃×C₁₃×C₁₉₇	C₂²	semidirect
5. C₂×C₁₃×C₁₉₇	C₂×C₃	semidirect
6. D₂₅₆₁	C₂×C₃	direct (N × H)
7. C₁₃×C₁₉₇	C₂²×C₃	semidirect
9. C₂×C₃×C₁₉₇	D₁₃	semidirect
12. C₃×C₁₉₇	C₂×D₁₃	semidirect
13. C₂×C₁₉₇	C₃×D₁₃	semidirect
15. C₁₉₇	C₂×C₃×D₁₃	semidirect
17. C₂×C₃×C₁₃	D₁₉₇	semidirect
20. C₃×C₁₃	C₂×D₁₉₇	semidirect
21. C₂×C₁₃	C₃×D₁₉₇	semidirect
23. C₁₃	C₂×C₃×D₁₉₇	semidirect
26. C₂×C₃	D₂₅₆₁	direct (N × H)
28. C₃	C₂×D₂₅₆₁	direct (N × H)
30. C₂	C₃×D₂₅₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₂₅₆₁	2
C₂×C₃×C₁₃×C₁₉₇	2
C₂×D₂₅₆₁	3
C₂×C₃×D₁₉₇	13
C₂×C₃×D₁₃	197

Subgroups — C2×C3×D2561 #44502248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₂₅₆₁ #44502248