Subgroups — C₂×C₃×C₂₅×C₁₇₉ #41001608

Order 26850.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₅×C₁₇₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₂₅×C₁₇₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₅×C₁₇₉	C₅	1	1	yes	maximal, characteristic
4	C₂₅×C₁₇₉	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₅×C₁₇₉	C₂×C₅	1	1	yes	characteristic
6	C₂×C₅×C₁₇₉	C₃×C₅	1	1	yes	characteristic
7	C₂×C₃×C₁₇₉	C₂₅	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₁₇₉	C₂×C₃×C₅	1	1	yes	characteristic
9	C₃×C₁₇₉	C₂×C₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₇₉	C₃×C₂₅	1	1	yes	characteristic, direct product factor, Hall
11	C₁₇₉	C₂×C₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃×C₂₅	C₁₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₂₅	C₂×C₁₇₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₂₅	C₃×C₁₇₉	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃×C₅	C₅×C₁₇₉	1	1	yes	characteristic
16	C₂₅	C₂×C₃×C₁₇₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₅	C₂×C₅×C₁₇₉	1	1	yes	characteristic
18	C₂×C₅	C₃×C₅×C₁₇₉	1	1	yes	characteristic
19	C₂×C₃	C₂₅×C₁₇₉	1	1	yes	characteristic, direct product factor, Hall
20	C₅	C₂×C₃×C₅×C₁₇₉	1	1	yes	characteristic
21	C₃	C₂×C₂₅×C₁₇₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×C₂₅×C₁₇₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂×C₃×C₅×C₁₇₉
socle, prime radical	C₂×C₃×C₅×C₁₇₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₅×C₁₇₉	C₂	direct (N × H)
2. C₂×C₂₅×C₁₇₉	C₃	direct (N × H)
4. C₂₅×C₁₇₉	C₂×C₃	direct (N × H)
7. C₂×C₃×C₁₇₉	C₂₅	direct (N × H)
9. C₃×C₁₇₉	C₂×C₂₅	direct (N × H)
10. C₂×C₁₇₉	C₃×C₂₅	direct (N × H)
11. C₁₇₉	C₂×C₃×C₂₅	direct (N × H)
12. C₂×C₃×C₂₅	C₁₇₉	direct (N × H)
13. C₃×C₂₅	C₂×C₁₇₉	direct (N × H)
14. C₂×C₂₅	C₃×C₁₇₉	direct (N × H)
16. C₂₅	C₂×C₃×C₁₇₉	direct (N × H)
19. C₂×C₃	C₂₅×C₁₇₉	direct (N × H)
21. C₃	C₂×C₂₅×C₁₇₉	direct (N × H)
22. C₂	C₃×C₂₅×C₁₇₉	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×C₂₅×C₁₇₉	2
C₂×C₂₅×C₁₇₉	3
C₂×C₃×C₅×C₁₇₉	5
C₂×C₃×C₂₅	179

Subgroups — C2×C3×C25×C179 #41001608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₂₅×C₁₇₉ #41001608