Subgroups — C₂×C₃²×C₇²×C₂₅ #36347714

Order 22050.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×C₂₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₇²×C₂₅	C₃	1	4	yes	maximal, direct product factor
3	C₂×C₃²×C₅×C₇²	C₅	1	1	yes	maximal, characteristic
4	C₃×C₇²×C₂₅	C₂×C₃	1	4	yes	direct product factor
5	C₂×C₃²×C₇×C₂₅	C₇	1	8	yes	maximal, direct product factor
6	C₂×C₇²×C₂₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅×C₇²	C₂×C₅	1	1	yes	characteristic
8	C₃²×C₇×C₂₅	C₂×C₇	1	8	yes	direct product factor
9	C₂×C₃×C₅×C₇²	C₃×C₅	1	4	yes	—
10	C₇²×C₂₅	C₂×C₃²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₇×C₂₅	C₃×C₇	1	32	yes	direct product factor
12	C₂×C₃²×C₇²	C₂₅	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₇²	C₂×C₃×C₅	1	4	yes	—
14	C₂×C₃²×C₅×C₇	C₅×C₇	1	8	yes	—
15	C₃×C₇×C₂₅	C₂×C₃×C₇	1	32	yes	direct product factor
16	C₂×C₅×C₇²	C₃²×C₅	1	1	yes	characteristic
17	C₂×C₃²×C₂₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
18	C₃²×C₇²	C₂×C₂₅	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₇×C₂₅	C₃²×C₇	1	8	yes	direct product factor
20	C₃²×C₅×C₇	C₂×C₅×C₇	1	8	yes	—
21	C₂×C₃×C₇²	C₃×C₂₅	1	4	yes	direct product factor
22	C₅×C₇²	C₂×C₃²×C₅	1	1	yes	characteristic
23	C₃²×C₂₅	C₂×C₇²	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₃×C₅×C₇	C₃×C₅×C₇	1	32	yes	—
25	C₇×C₂₅	C₂×C₃²×C₇	1	8	yes	direct product factor
26	C₂×C₃×C₂₅	C₃×C₇²	1	4	yes	direct product factor
27	C₃×C₇²	C₂×C₃×C₂₅	1	4	yes	direct product factor
28	C₂×C₃²×C₇	C₇×C₂₅	1	8	yes	direct product factor
29	C₃×C₅×C₇	C₂×C₃×C₅×C₇	1	32	yes	—
30	C₂×C₇²	C₃²×C₂₅	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃²×C₅	C₅×C₇²	1	1	yes	characteristic
32	C₃×C₂₅	C₂×C₃×C₇²	1	4	yes	direct product factor
33	C₂×C₅×C₇	C₃²×C₅×C₇	1	8	yes	—
34	C₃²×C₇	C₂×C₇×C₂₅	1	8	yes	direct product factor
35	C₂×C₂₅	C₃²×C₇²	1	1	yes	characteristic, direct product factor, Hall
36	C₇²	C₂×C₃²×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
37	C₃²×C₅	C₂×C₅×C₇²	1	1	yes	characteristic
38	C₂×C₃×C₇	C₃×C₇×C₂₅	1	32	yes	direct product factor
39	C₅×C₇	C₂×C₃²×C₅×C₇	1	8	yes	—
40	C₂×C₃×C₅	C₃×C₅×C₇²	1	4	yes	—
41	C₂₅	C₂×C₃²×C₇²	1	1	yes	characteristic, direct product factor, Sylow
42	C₃×C₇	C₂×C₃×C₇×C₂₅	1	32	yes	direct product factor
43	C₂×C₃²	C₇²×C₂₅	1	1	yes	characteristic, direct product factor, Hall
44	C₃×C₅	C₂×C₃×C₅×C₇²	1	4	yes	—
45	C₂×C₇	C₃²×C₇×C₂₅	1	8	yes	direct product factor
46	C₂×C₅	C₃²×C₅×C₇²	1	1	yes	characteristic
47	C₃²	C₂×C₇²×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
48	C₇	C₂×C₃²×C₇×C₂₅	1	8	yes	direct product factor
49	C₂×C₃	C₃×C₇²×C₂₅	1	4	yes	direct product factor
50	C₅	C₂×C₃²×C₅×C₇²	1	1	yes	characteristic
51	C₃	C₂×C₃×C₇²×C₂₅	1	4	yes	direct product factor
52	C₂	C₃²×C₇²×C₂₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂×C₃²×C₅×C₇²
socle, prime radical	C₂×C₃²×C₅×C₇²	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×C₂₅	C₂	direct (N × H)
2. C₂×C₃×C₇²×C₂₅	C₃	direct (N × H)
4. C₃×C₇²×C₂₅	C₂×C₃	direct (N × H)
5. C₂×C₃²×C₇×C₂₅	C₇	direct (N × H)
6. C₂×C₇²×C₂₅	C₃²	direct (N × H)
8. C₃²×C₇×C₂₅	C₂×C₇	direct (N × H)
10. C₇²×C₂₅	C₂×C₃²	direct (N × H)
11. C₂×C₃×C₇×C₂₅	C₃×C₇	direct (N × H)
12. C₂×C₃²×C₇²	C₂₅	direct (N × H)
15. C₃×C₇×C₂₅	C₂×C₃×C₇	direct (N × H)
17. C₂×C₃²×C₂₅	C₇²	direct (N × H)
18. C₃²×C₇²	C₂×C₂₅	direct (N × H)
19. C₂×C₇×C₂₅	C₃²×C₇	direct (N × H)
21. C₂×C₃×C₇²	C₃×C₂₅	direct (N × H)
23. C₃²×C₂₅	C₂×C₇²	direct (N × H)
25. C₇×C₂₅	C₂×C₃²×C₇	direct (N × H)
26. C₂×C₃×C₂₅	C₃×C₇²	direct (N × H)
27. C₃×C₇²	C₂×C₃×C₂₅	direct (N × H)
28. C₂×C₃²×C₇	C₇×C₂₅	direct (N × H)
30. C₂×C₇²	C₃²×C₂₅	direct (N × H)
32. C₃×C₂₅	C₂×C₃×C₇²	direct (N × H)
34. C₃²×C₇	C₂×C₇×C₂₅	direct (N × H)
35. C₂×C₂₅	C₃²×C₇²	direct (N × H)
36. C₇²	C₂×C₃²×C₂₅	direct (N × H)
38. C₂×C₃×C₇	C₃×C₇×C₂₅	direct (N × H)
41. C₂₅	C₂×C₃²×C₇²	direct (N × H)
42. C₃×C₇	C₂×C₃×C₇×C₂₅	direct (N × H)
43. C₂×C₃²	C₇²×C₂₅	direct (N × H)
45. C₂×C₇	C₃²×C₇×C₂₅	direct (N × H)
47. C₃²	C₂×C₇²×C₂₅	direct (N × H)
48. C₇	C₂×C₃²×C₇×C₂₅	direct (N × H)
49. C₂×C₃	C₃×C₇²×C₂₅	direct (N × H)
51. C₃	C₂×C₃×C₇²×C₂₅	direct (N × H)
52. C₂	C₃²×C₇²×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
C₃²×C₇²×C₂₅	2
C₂×C₃×C₇²×C₂₅	3
C₂×C₃²×C₅×C₇²	5
C₂×C₃²×C₇×C₂₅	7

Subgroups — C2×C32×C72×C25 #36347714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₇²×C₂₅ #36347714