Subgroups — C₂×C₁₃×D₆₂₉ #45658477

Order 32708.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₆₂₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₃×C₁₇×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₁₇×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₆₂₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₃×D₃₇	—	17	1	no	maximal, Hall
6	C₂×C₁₇×C₃₇	C₂×C₁₃	1	1	yes	characteristic, complemented
7	D₆₂₉	C₂×C₁₃	1	2	yes	direct product factor
8	C₂×C₁₃×C₃₇	D₁₇	1	1	yes	characteristic, complemented
9	C₁₃×D₃₇	—	17	2	no	—
10	C₂×C₁₃×D₁₇	—	37	1	no	maximal, Hall
11	C₁₇×C₃₇	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₃₇	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₃×C₁₇	D₃₇	1	1	yes	characteristic, complemented
14	C₁₃×D₁₇	—	37	2	no	—
15	C₁₃×C₁₇	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
16	C₂×D₃₇	—	17	1	no	Hall
17	C₂×C₃₇	C₁₃×D₁₇	1	1	yes	characteristic, complemented
18	D₃₇	—	17	2	no	—
19	C₂×D₁₇	—	37	1	no	Hall
20	C₂²×C₁₃	—	629	1	no	Hall
21	C₃₇	C₂×C₁₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₁₇	C₁₃×D₃₇	1	1	yes	characteristic, complemented
23	D₁₇	—	37	2	no	—
24	C₂×C₁₃	—	629	2	no	—
25	C₂×C₁₃	D₆₂₉	1	1	yes	characteristic, direct product factor
26	C₁₇	C₂×C₁₃×D₃₇	1	1	yes	characteristic, complemented, Sylow
27	C₁₃	C₂×D₆₂₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	629	1	no	Sylow
29	C₂	—	629	2	no	—
30	C₂	C₁₃×D₆₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₆₂₉
commutator, cosocle, hypocenter	C₁₇×C₃₇	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₁₇×C₃₇	C₂
LCS	G ▷ C₁₇×C₃₇
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₆₂₉	C₂	direct (N × H)
2. C₂×C₁₃×C₁₇×C₃₇	C₂	semidirect
3. C₁₃×C₁₇×C₃₇	C₂²	semidirect
4. C₂×D₆₂₉	C₁₃	direct (N × H)
6. C₂×C₁₇×C₃₇	C₂×C₁₃	semidirect
7. D₆₂₉	C₂×C₁₃	direct (N × H)
8. C₂×C₁₃×C₃₇	D₁₇	semidirect
11. C₁₇×C₃₇	C₂²×C₁₃	semidirect
12. C₁₃×C₃₇	C₂×D₁₇	semidirect
13. C₂×C₁₃×C₁₇	D₃₇	semidirect
15. C₁₃×C₁₇	C₂×D₃₇	semidirect
17. C₂×C₃₇	C₁₃×D₁₇	semidirect
21. C₃₇	C₂×C₁₃×D₁₇	semidirect
22. C₂×C₁₇	C₁₃×D₃₇	semidirect
25. C₂×C₁₃	D₆₂₉	direct (N × H)
26. C₁₇	C₂×C₁₃×D₃₇	semidirect
27. C₁₃	C₂×D₆₂₉	direct (N × H)
30. C₂	C₁₃×D₆₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×D₆₂₉	2
C₂×C₁₃×C₁₇×C₃₇	2
C₂×D₆₂₉	13
C₂×C₁₃×D₃₇	17
C₂×C₁₃×D₁₇	37

Subgroups — C2×C13×D629 #45658477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×D₆₂₉ #45658477