Subgroups — C₂²×C₂₅×C₂₄₃ #72201577

Order 24300.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₅×C₂₄₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₂₅×C₈₁	C₃	1	1	yes	maximal, characteristic
3	C₂₅×C₂₄₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₅×C₂₄₃	C₅	1	1	yes	maximal, characteristic
5	C₂×C₂₅×C₈₁	C₂×C₃	1	3	yes	—
6	C₂²×C₂₅×C₂₇	C₉	1	1	yes	characteristic
7	C₂×C₅×C₂₄₃	C₂×C₅	1	3	yes	—
8	C₂₅×C₈₁	C₂²×C₃	1	1	yes	characteristic
9	C₂²×C₅×C₈₁	C₃×C₅	1	1	yes	characteristic
10	C₂×C₂₅×C₂₇	C₂×C₉	1	3	yes	—
11	C₅×C₂₄₃	C₂²×C₅	1	1	yes	characteristic
12	C₂²×C₂₄₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
13	C₂²×C₉×C₂₅	C₂₇	1	1	yes	characteristic
14	C₂×C₅×C₈₁	C₂×C₃×C₅	1	3	yes	—
15	C₂₅×C₂₇	C₂²×C₉	1	1	yes	characteristic
16	C₂²×C₅×C₂₇	C₅×C₉	1	1	yes	characteristic
17	C₂×C₂₄₃	C₂×C₂₅	1	3	yes	direct product factor
18	C₂×C₉×C₂₅	C₂×C₂₇	1	3	yes	—
19	C₅×C₈₁	C₂²×C₃×C₅	1	1	yes	characteristic
20	C₂²×C₈₁	C₃×C₂₅	1	1	yes	characteristic
21	C₂²×C₃×C₂₅	C₈₁	1	1	yes	characteristic
22	C₂×C₅×C₂₇	C₂×C₅×C₉	1	3	yes	—
23	C₂₄₃	C₂²×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
24	C₉×C₂₅	C₂²×C₂₇	1	1	yes	characteristic
25	C₂²×C₅×C₉	C₅×C₂₇	1	1	yes	characteristic
26	C₂×C₈₁	C₂×C₃×C₂₅	1	3	yes	—
27	C₂×C₃×C₂₅	C₂×C₈₁	1	3	yes	—
28	C₅×C₂₇	C₂²×C₅×C₉	1	1	yes	characteristic
29	C₂²×C₂₇	C₉×C₂₅	1	1	yes	characteristic
30	C₂²×C₂₅	C₂₄₃	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₅×C₉	C₂×C₅×C₂₇	1	3	yes	—
32	C₈₁	C₂²×C₃×C₂₅	1	1	yes	characteristic
33	C₃×C₂₅	C₂²×C₈₁	1	1	yes	characteristic
34	C₂²×C₃×C₅	C₅×C₈₁	1	1	yes	characteristic
35	C₂×C₂₇	C₂×C₉×C₂₅	1	3	yes	—
36	C₂×C₂₅	C₂×C₂₄₃	1	3	yes	direct product factor
37	C₅×C₉	C₂²×C₅×C₂₇	1	1	yes	characteristic
38	C₂²×C₉	C₂₅×C₂₇	1	1	yes	characteristic
39	C₂×C₃×C₅	C₂×C₅×C₈₁	1	3	yes	—
40	C₂₇	C₂²×C₉×C₂₅	1	1	yes	characteristic
41	C₂₅	C₂²×C₂₄₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²×C₅	C₅×C₂₄₃	1	1	yes	characteristic
43	C₂×C₉	C₂×C₂₅×C₂₇	1	3	yes	—
44	C₃×C₅	C₂²×C₅×C₈₁	1	1	yes	characteristic
45	C₂²×C₃	C₂₅×C₈₁	1	1	yes	characteristic
46	C₂×C₅	C₂×C₅×C₂₄₃	1	3	yes	—
47	C₉	C₂²×C₂₅×C₂₇	1	1	yes	characteristic
48	C₂×C₃	C₂×C₂₅×C₈₁	1	3	yes	—
49	C₅	C₂²×C₅×C₂₄₃	1	1	yes	characteristic
50	C₂²	C₂₅×C₂₄₃	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	C₂²×C₂₅×C₈₁	1	1	yes	characteristic
52	C₂	C₂×C₂₅×C₂₄₃	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅×C₈₁	C₂²×C₃×C₅
socle, prime radical	C₂²×C₃×C₅	C₅×C₈₁
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₅×C₂₄₃	C₂	direct (N × H)
3. C₂₅×C₂₄₃	C₂²	direct (N × H)
12. C₂²×C₂₄₃	C₂₅	direct (N × H)
17. C₂×C₂₄₃	C₂×C₂₅	direct (N × H)
23. C₂₄₃	C₂²×C₂₅	direct (N × H)
30. C₂²×C₂₅	C₂₄₃	direct (N × H)
36. C₂×C₂₅	C₂×C₂₄₃	direct (N × H)
41. C₂₅	C₂²×C₂₄₃	direct (N × H)
50. C₂²	C₂₅×C₂₄₃	direct (N × H)
52. C₂	C₂×C₂₅×C₂₄₃	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×C₂₅×C₂₄₃	2
C₂²×C₂₅×C₈₁	3
C₂²×C₅×C₂₄₃	5

Subgroups — C22×C25×C243 #72201577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂₅×C₂₄₃ #72201577