Subgroups — C₃⁵×C₄×C₂₅ #72201575

Order 24300.

23976 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⁵×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃⁴×C₄×C₂₅	C₃	1	121	yes	maximal, direct product factor
3	C₃⁵×C₂₅	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₃⁵×C₄×C₅	C₅	1	1	yes	maximal, characteristic
5	C₂×C₃⁴×C₂₅	C₂×C₃	1	121	yes	—
6	C₃³×C₄×C₂₅	C₃²	1	1210	yes	direct product factor
7	C₂×C₃⁵×C₅	C₂×C₅	1	1	yes	characteristic
8	C₃⁴×C₂₅	C₃×C₄	1	121	yes	direct product factor
9	C₃⁴×C₄×C₅	C₃×C₅	1	121	yes	—
10	C₂×C₃³×C₂₅	C₂×C₃²	1	1210	yes	—
11	C₃⁵×C₅	C₄×C₅	1	1	yes	characteristic
12	C₃⁵×C₄	C₂₅	1	1	yes	characteristic, direct product factor, Hall
13	C₃²×C₄×C₂₅	C₃³	1	1210	yes	direct product factor
14	C₂×C₃⁴×C₅	C₂×C₃×C₅	1	121	yes	—
15	C₃³×C₂₅	C₃²×C₄	1	1210	yes	direct product factor
16	C₃³×C₄×C₅	C₃²×C₅	1	1210	yes	—
17	C₂×C₃⁵	C₂×C₂₅	1	1	yes	characteristic
18	C₂×C₃²×C₂₅	C₂×C₃³	1	1210	yes	—
19	C₃⁴×C₅	C₃×C₄×C₅	1	121	yes	—
20	C₃⁴×C₄	C₃×C₂₅	1	121	yes	direct product factor
21	C₃×C₄×C₂₅	C₃⁴	1	121	yes	direct product factor
22	C₂×C₃³×C₅	C₂×C₃²×C₅	1	1210	yes	—
23	C₃⁵	C₄×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
24	C₃²×C₂₅	C₃³×C₄	1	1210	yes	direct product factor
25	C₃²×C₄×C₅	C₃³×C₅	1	1210	yes	—
26	C₂×C₃⁴	C₂×C₃×C₂₅	1	121	yes	—
27	C₂×C₃×C₂₅	C₂×C₃⁴	1	121	yes	—
28	C₃³×C₅	C₃²×C₄×C₅	1	1210	yes	—
29	C₃³×C₄	C₃²×C₂₅	1	1210	yes	direct product factor
30	C₄×C₂₅	C₃⁵	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃²×C₅	C₂×C₃³×C₅	1	1210	yes	—
32	C₃⁴	C₃×C₄×C₂₅	1	121	yes	direct product factor
33	C₃×C₂₅	C₃⁴×C₄	1	121	yes	direct product factor
34	C₃×C₄×C₅	C₃⁴×C₅	1	121	yes	—
35	C₂×C₃³	C₂×C₃²×C₂₅	1	1210	yes	—
36	C₂×C₂₅	C₂×C₃⁵	1	1	yes	characteristic
37	C₃²×C₅	C₃³×C₄×C₅	1	1210	yes	—
38	C₃²×C₄	C₃³×C₂₅	1	1210	yes	direct product factor
39	C₂×C₃×C₅	C₂×C₃⁴×C₅	1	121	yes	—
40	C₃³	C₃²×C₄×C₂₅	1	1210	yes	direct product factor
41	C₂₅	C₃⁵×C₄	1	1	yes	characteristic, direct product factor, Sylow
42	C₄×C₅	C₃⁵×C₅	1	1	yes	characteristic
43	C₂×C₃²	C₂×C₃³×C₂₅	1	1210	yes	—
44	C₃×C₅	C₃⁴×C₄×C₅	1	121	yes	—
45	C₃×C₄	C₃⁴×C₂₅	1	121	yes	direct product factor
46	C₂×C₅	C₂×C₃⁵×C₅	1	1	yes	characteristic
47	C₃²	C₃³×C₄×C₂₅	1	1210	yes	direct product factor
48	C₂×C₃	C₂×C₃⁴×C₂₅	1	121	yes	—
49	C₅	C₃⁵×C₄×C₅	1	1	yes	characteristic
50	C₄	C₃⁵×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	C₃⁴×C₄×C₂₅	1	121	yes	direct product factor
52	C₂	C₂×C₃⁵×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂×C₃⁵×C₅
socle, prime radical	C₂×C₃⁵×C₅	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃⁴×C₄×C₂₅	C₃	direct (N × H)
3. C₃⁵×C₂₅	C₄	direct (N × H)
6. C₃³×C₄×C₂₅	C₃²	direct (N × H)
8. C₃⁴×C₂₅	C₃×C₄	direct (N × H)
12. C₃⁵×C₄	C₂₅	direct (N × H)
13. C₃²×C₄×C₂₅	C₃³	direct (N × H)
15. C₃³×C₂₅	C₃²×C₄	direct (N × H)
20. C₃⁴×C₄	C₃×C₂₅	direct (N × H)
21. C₃×C₄×C₂₅	C₃⁴	direct (N × H)
23. C₃⁵	C₄×C₂₅	direct (N × H)
24. C₃²×C₂₅	C₃³×C₄	direct (N × H)
29. C₃³×C₄	C₃²×C₂₅	direct (N × H)
30. C₄×C₂₅	C₃⁵	direct (N × H)
32. C₃⁴	C₃×C₄×C₂₅	direct (N × H)
33. C₃×C₂₅	C₃⁴×C₄	direct (N × H)
38. C₃²×C₄	C₃³×C₂₅	direct (N × H)
40. C₃³	C₃²×C₄×C₂₅	direct (N × H)
41. C₂₅	C₃⁵×C₄	direct (N × H)
45. C₃×C₄	C₃⁴×C₂₅	direct (N × H)
47. C₃²	C₃³×C₄×C₂₅	direct (N × H)
50. C₄	C₃⁵×C₂₅	direct (N × H)
51. C₃	C₃⁴×C₄×C₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃⁵×C₂₅	2
C₃⁴×C₄×C₂₅	3
C₃⁵×C₄×C₅	5

Subgroups — C35×C4×C25 #72201575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⁵×C₄×C₂₅ #72201575