Subgroups — C₂⁵×C₉×C₁₀₇ #72207613

Order 30816.

2244 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₉×C₁₀₇	C₂	1	31	yes	maximal, direct product factor
2	C₂⁵×C₃×C₁₀₇	C₃	1	1	yes	maximal, characteristic
3	C₂³×C₉×C₁₀₇	C₂²	1	155	yes	direct product factor
4	C₂⁴×C₃×C₁₀₇	C₂×C₃	1	31	yes	—
5	C₂³×C₃×C₁₀₇	C₂²×C₃	1	155	yes	—
6	C₂²×C₉×C₁₀₇	C₂³	1	155	yes	direct product factor
7	C₂⁵×C₁₀₇	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₉×C₁₀₇	C₂⁴	1	31	yes	direct product factor
9	C₂⁴×C₁₀₇	C₂×C₉	1	31	yes	direct product factor
10	C₂²×C₃×C₁₀₇	C₂³×C₃	1	155	yes	—
11	C₉×C₁₀₇	C₂⁵	1	1	yes	characteristic, direct product factor, Hall
12	C₂³×C₁₀₇	C₂²×C₉	1	155	yes	direct product factor
13	C₂×C₃×C₁₀₇	C₂⁴×C₃	1	31	yes	—
14	C₂²×C₁₀₇	C₂³×C₉	1	155	yes	direct product factor
15	C₃×C₁₀₇	C₂⁵×C₃	1	1	yes	characteristic
16	C₂⁵×C₉	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₁₀₇	C₂⁴×C₉	1	31	yes	direct product factor
18	C₂⁴×C₉	C₂×C₁₀₇	1	31	yes	direct product factor
19	C₁₀₇	C₂⁵×C₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₂⁵×C₃	C₃×C₁₀₇	1	1	yes	characteristic
21	C₂³×C₉	C₂²×C₁₀₇	1	155	yes	direct product factor
22	C₂⁴×C₃	C₂×C₃×C₁₀₇	1	31	yes	—
23	C₂²×C₉	C₂³×C₁₀₇	1	155	yes	direct product factor
24	C₂⁵	C₉×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₂³×C₃	C₂²×C₃×C₁₀₇	1	155	yes	—
26	C₂×C₉	C₂⁴×C₁₀₇	1	31	yes	direct product factor
27	C₂⁴	C₂×C₉×C₁₀₇	1	31	yes	direct product factor
28	C₂²×C₃	C₂³×C₃×C₁₀₇	1	155	yes	—
29	C₉	C₂⁵×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂³	C₂²×C₉×C₁₀₇	1	155	yes	direct product factor
31	C₂×C₃	C₂⁴×C₃×C₁₀₇	1	31	yes	—
32	C₂²	C₂³×C₉×C₁₀₇	1	155	yes	direct product factor
33	C₃	C₂⁵×C₃×C₁₀₇	1	1	yes	characteristic
34	C₂	C₂⁴×C₉×C₁₀₇	1	31	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂⁵×C₃×C₁₀₇
socle, prime radical	C₂⁵×C₃×C₁₀₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₉×C₁₀₇	C₂	direct (N × H)
3. C₂³×C₉×C₁₀₇	C₂²	direct (N × H)
6. C₂²×C₉×C₁₀₇	C₂³	direct (N × H)
7. C₂⁵×C₁₀₇	C₉	direct (N × H)
8. C₂×C₉×C₁₀₇	C₂⁴	direct (N × H)
9. C₂⁴×C₁₀₇	C₂×C₉	direct (N × H)
11. C₉×C₁₀₇	C₂⁵	direct (N × H)
12. C₂³×C₁₀₇	C₂²×C₉	direct (N × H)
14. C₂²×C₁₀₇	C₂³×C₉	direct (N × H)
16. C₂⁵×C₉	C₁₀₇	direct (N × H)
17. C₂×C₁₀₇	C₂⁴×C₉	direct (N × H)
18. C₂⁴×C₉	C₂×C₁₀₇	direct (N × H)
19. C₁₀₇	C₂⁵×C₉	direct (N × H)
21. C₂³×C₉	C₂²×C₁₀₇	direct (N × H)
23. C₂²×C₉	C₂³×C₁₀₇	direct (N × H)
24. C₂⁵	C₉×C₁₀₇	direct (N × H)
26. C₂×C₉	C₂⁴×C₁₀₇	direct (N × H)
27. C₂⁴	C₂×C₉×C₁₀₇	direct (N × H)
29. C₉	C₂⁵×C₁₀₇	direct (N × H)
30. C₂³	C₂²×C₉×C₁₀₇	direct (N × H)
32. C₂²	C₂³×C₉×C₁₀₇	direct (N × H)
34. C₂	C₂⁴×C₉×C₁₀₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₉×C₁₀₇	2
C₂⁵×C₃×C₁₀₇	3
C₂⁵×C₉	107

Subgroups — C25×C9×C107 #72207613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₉×C₁₀₇ #72207613