Subgroups — C₂×C₃×C₃₇×C₄₉ #24925909

Order 10878.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×C₄₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃₇×C₄₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₇×C₄₉	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇×C₃₇	C₇	1	1	yes	maximal, characteristic
5	C₃×C₇×C₃₇	C₂×C₇	1	1	yes	characteristic
6	C₂×C₇×C₃₇	C₃×C₇	1	1	yes	characteristic
7	C₂×C₃×C₄₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₃₇	C₂×C₃×C₇	1	1	yes	characteristic
9	C₂×C₃×C₃₇	C₄₉	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₄₉	C₂×C₃₇	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₃₇	C₂×C₄₉	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₄₉	C₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃₇	C₃×C₄₉	1	1	yes	characteristic, direct product factor, Hall
14	C₄₉	C₂×C₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₂×C₃×C₇	C₇×C₃₇	1	1	yes	characteristic
16	C₃₇	C₂×C₃×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₇	C₂×C₇×C₃₇	1	1	yes	characteristic
18	C₂×C₇	C₃×C₇×C₃₇	1	1	yes	characteristic
19	C₇	C₂×C₃×C₇×C₃₇	1	1	yes	characteristic
20	C₂×C₃	C₃₇×C₄₉	1	1	yes	characteristic, direct product factor, Hall
21	C₃	C₂×C₃₇×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×C₃₇×C₄₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₂×C₃×C₇×C₃₇
socle, prime radical	C₂×C₃×C₇×C₃₇	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₇×C₄₉	C₂	direct (N × H)
2. C₂×C₃₇×C₄₉	C₃	direct (N × H)
3. C₃₇×C₄₉	C₂×C₃	direct (N × H)
7. C₂×C₃×C₄₉	C₃₇	direct (N × H)
9. C₂×C₃×C₃₇	C₄₉	direct (N × H)
10. C₃×C₄₉	C₂×C₃₇	direct (N × H)
11. C₃×C₃₇	C₂×C₄₉	direct (N × H)
12. C₂×C₄₉	C₃×C₃₇	direct (N × H)
13. C₂×C₃₇	C₃×C₄₉	direct (N × H)
14. C₄₉	C₂×C₃×C₃₇	direct (N × H)
16. C₃₇	C₂×C₃×C₄₉	direct (N × H)
20. C₂×C₃	C₃₇×C₄₉	direct (N × H)
21. C₃	C₂×C₃₇×C₄₉	direct (N × H)
22. C₂	C₃×C₃₇×C₄₉	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×C₃₇×C₄₉	2
C₂×C₃₇×C₄₉	3
C₂×C₃×C₇×C₃₇	7
C₂×C₃×C₄₉	37

Subgroups — C2×C3×C37×C49 #24925909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₃₇×C₄₉ #24925909