Subgroups — C₂⁵×C₅×C₁₆₉ #72204108

Order 27040.

2244 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×C₁₆₉	C₂	1	31	yes	maximal, direct product factor
2	C₂³×C₅×C₁₆₉	C₂²	1	155	yes	direct product factor
3	C₂⁵×C₁₆₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂⁴×C₁₆₉	C₂×C₅	1	31	yes	direct product factor
5	C₂⁵×C₅×C₁₃	C₁₃	1	1	yes	maximal, characteristic
6	C₂²×C₅×C₁₆₉	C₂³	1	155	yes	direct product factor
7	C₂×C₅×C₁₆₉	C₂⁴	1	31	yes	direct product factor
8	C₂³×C₁₆₉	C₂²×C₅	1	155	yes	direct product factor
9	C₂⁴×C₅×C₁₃	C₂×C₁₃	1	31	yes	—
10	C₅×C₁₆₉	C₂⁵	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₁₆₉	C₂³×C₅	1	155	yes	direct product factor
12	C₂³×C₅×C₁₃	C₂²×C₁₃	1	155	yes	—
13	C₂⁵×C₁₃	C₅×C₁₃	1	1	yes	characteristic
14	C₂×C₁₆₉	C₂⁴×C₅	1	31	yes	direct product factor
15	C₂²×C₅×C₁₃	C₂³×C₁₃	1	155	yes	—
16	C₂⁴×C₁₃	C₂×C₅×C₁₃	1	31	yes	—
17	C₁₆₉	C₂⁵×C₅	1	1	yes	characteristic, direct product factor, Sylow
18	C₂⁵×C₅	C₁₆₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅×C₁₃	C₂⁴×C₁₃	1	31	yes	—
20	C₂³×C₁₃	C₂²×C₅×C₁₃	1	155	yes	—
21	C₂⁴×C₅	C₂×C₁₆₉	1	31	yes	direct product factor
22	C₅×C₁₃	C₂⁵×C₁₃	1	1	yes	characteristic
23	C₂²×C₁₃	C₂³×C₅×C₁₃	1	155	yes	—
24	C₂³×C₅	C₂²×C₁₆₉	1	155	yes	direct product factor
25	C₂⁵	C₅×C₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₁₃	C₂⁴×C₅×C₁₃	1	31	yes	—
27	C₂²×C₅	C₂³×C₁₆₉	1	155	yes	direct product factor
28	C₂⁴	C₂×C₅×C₁₆₉	1	31	yes	direct product factor
29	C₁₃	C₂⁵×C₅×C₁₃	1	1	yes	characteristic
30	C₂×C₅	C₂⁴×C₁₆₉	1	31	yes	direct product factor
31	C₂³	C₂²×C₅×C₁₆₉	1	155	yes	direct product factor
32	C₅	C₂⁵×C₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₂²	C₂³×C₅×C₁₆₉	1	155	yes	direct product factor
34	C₂	C₂⁴×C₅×C₁₆₉	1	31	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₃	C₂⁵×C₅×C₁₃
socle, prime radical	C₂⁵×C₅×C₁₃	C₁₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₅×C₁₆₉	C₂	direct (N × H)
2. C₂³×C₅×C₁₆₉	C₂²	direct (N × H)
3. C₂⁵×C₁₆₉	C₅	direct (N × H)
4. C₂⁴×C₁₆₉	C₂×C₅	direct (N × H)
6. C₂²×C₅×C₁₆₉	C₂³	direct (N × H)
7. C₂×C₅×C₁₆₉	C₂⁴	direct (N × H)
8. C₂³×C₁₆₉	C₂²×C₅	direct (N × H)
10. C₅×C₁₆₉	C₂⁵	direct (N × H)
11. C₂²×C₁₆₉	C₂³×C₅	direct (N × H)
14. C₂×C₁₆₉	C₂⁴×C₅	direct (N × H)
17. C₁₆₉	C₂⁵×C₅	direct (N × H)
18. C₂⁵×C₅	C₁₆₉	direct (N × H)
21. C₂⁴×C₅	C₂×C₁₆₉	direct (N × H)
24. C₂³×C₅	C₂²×C₁₆₉	direct (N × H)
25. C₂⁵	C₅×C₁₆₉	direct (N × H)
27. C₂²×C₅	C₂³×C₁₆₉	direct (N × H)
28. C₂⁴	C₂×C₅×C₁₆₉	direct (N × H)
30. C₂×C₅	C₂⁴×C₁₆₉	direct (N × H)
31. C₂³	C₂²×C₅×C₁₆₉	direct (N × H)
32. C₅	C₂⁵×C₁₆₉	direct (N × H)
33. C₂²	C₂³×C₅×C₁₆₉	direct (N × H)
34. C₂	C₂⁴×C₅×C₁₆₉	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×C₅×C₁₆₉	2
C₂⁵×C₁₆₉	5
C₂⁵×C₅×C₁₃	13

Subgroups — C25×C5×C169 #72204108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₅×C₁₆₉ #72204108