Subgroups — C₂⁵×C₃×C₄ #87577

Order 384.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₃	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₃×C₄	C₂	1	62	yes	maximal, direct product factor
3	C₂⁵×C₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂⁵×C₃	C₄	1	32	yes	direct product factor
5	C₂⁵×C₃	C₂²	1	31	yes	—
6	C₂³×C₃×C₄	C₂²	1	620	yes	direct product factor
7	C₂⁶	C₂×C₃	1	1	yes	characteristic
8	C₂⁴×C₄	C₂×C₃	1	62	yes	direct product factor
9	C₂⁴×C₃	C₂×C₄	1	496	yes	direct product factor
10	C₂⁴×C₃	C₂³	1	155	yes	—
11	C₂²×C₃×C₄	C₂³	1	1240	yes	direct product factor
12	C₂⁵	C₃×C₄	1	32	yes	direct product factor
13	C₂⁵	C₂²×C₃	1	31	yes	—
14	C₂³×C₄	C₂²×C₃	1	620	yes	direct product factor
15	C₂³×C₃	C₂²×C₄	1	1240	yes	direct product factor
16	C₂³×C₃	C₂⁴	1	155	yes	—
17	C₂×C₃×C₄	C₂⁴	1	496	yes	direct product factor
18	C₂⁴	C₂×C₃×C₄	1	496	yes	direct product factor
19	C₂⁴	C₂³×C₃	1	155	yes	—
20	C₂²×C₄	C₂³×C₃	1	1240	yes	direct product factor
21	C₂²×C₃	C₂³×C₄	1	620	yes	direct product factor
22	C₂²×C₃	C₂⁵	1	31	yes	—
23	C₃×C₄	C₂⁵	1	32	yes	direct product factor
24	C₂³	C₂²×C₃×C₄	1	1240	yes	direct product factor
25	C₂³	C₂⁴×C₃	1	155	yes	—
26	C₂×C₄	C₂⁴×C₃	1	496	yes	direct product factor
27	C₂×C₃	C₂⁴×C₄	1	62	yes	direct product factor
28	C₂×C₃	C₂⁶	1	1	yes	characteristic
29	C₂²	C₂³×C₃×C₄	1	620	yes	direct product factor
30	C₂²	C₂⁵×C₃	1	31	yes	—
31	C₄	C₂⁵×C₃	1	32	yes	direct product factor
32	C₃	C₂⁵×C₄	1	1	yes	characteristic, direct product factor, Sylow
33	C₂	C₂⁴×C₃×C₄	1	62	yes	direct product factor
34	C₂	C₂⁶×C₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁶×C₃
socle, prime radical	C₂⁶×C₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₃×C₄	C₂	direct (N × H)
3. C₂⁵×C₄	C₃	direct (N × H)
4. C₂⁵×C₃	C₄	direct (N × H)
6. C₂³×C₃×C₄	C₂²	direct (N × H)
8. C₂⁴×C₄	C₂×C₃	direct (N × H)
9. C₂⁴×C₃	C₂×C₄	direct (N × H)
11. C₂²×C₃×C₄	C₂³	direct (N × H)
12. C₂⁵	C₃×C₄	direct (N × H)
14. C₂³×C₄	C₂²×C₃	direct (N × H)
15. C₂³×C₃	C₂²×C₄	direct (N × H)
17. C₂×C₃×C₄	C₂⁴	direct (N × H)
18. C₂⁴	C₂×C₃×C₄	direct (N × H)
20. C₂²×C₄	C₂³×C₃	direct (N × H)
21. C₂²×C₃	C₂³×C₄	direct (N × H)
23. C₃×C₄	C₂⁵	direct (N × H)
24. C₂³	C₂²×C₃×C₄	direct (N × H)
26. C₂×C₄	C₂⁴×C₃	direct (N × H)
27. C₂×C₃	C₂⁴×C₄	direct (N × H)
29. C₂²	C₂³×C₃×C₄	direct (N × H)
31. C₄	C₂⁵×C₃	direct (N × H)
32. C₃	C₂⁵×C₄	direct (N × H)
33. C₂	C₂⁴×C₃×C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁶×C₃	2
C₂⁴×C₃×C₄	2
C₂⁵×C₄	3

Subgroups — C25×C3×C4 #87577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₃×C₄ #87577