Subgroups — C₇×C₂₅×5₋¹⁺² #36346233

Order 21875.

340 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×5₋¹⁺²	C₅	1	1	yes	maximal, characteristic
2	C₅²×C₇×C₂₅	C₅	1	1	yes	maximal, characteristic
3	C₇×C₂₅⋊C₂₅	C₅	1	20	yes	maximal, complemented
4	C₇×C₅²⋊C₂₅	C₅	1	4	yes	maximal
5	C₇×C₂₅²	C₅	1	5	yes	maximal, complemented
6	C₂₅×5₋¹⁺²	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₅³×C₇	C₅²	1	1	yes	characteristic
8	C₇×5₋¹⁺²	C₂₅	1	25	yes	direct product factor
9	C₅×C₇×C₂₅	—	5	5	no	—
10	C₅×C₇×C₂₅	C₅²	1	20	yes	—
11	C₅×C₇×C₂₅	C₅²	1	4	yes	—
12	C₅×C₇×C₂₅	C₅²	1	5	yes	—
13	C₅×C₇×C₂₅	C₅²	1	1	yes	characteristic
14	C₅×5₋¹⁺²	C₅×C₇	1	1	yes	characteristic
15	C₅²×C₂₅	C₅×C₇	1	1	yes	characteristic
16	C₂₅⋊C₂₅	C₅×C₇	1	20	yes	complemented
17	C₅²⋊C₂₅	C₅×C₇	1	4	yes	—
18	C₂₅²	C₅×C₇	1	5	yes	complemented
19	C₅²×C₇	—	5	1	no	—
20	C₅²×C₇	—	5	4	no	—
21	C₅²×C₇	C₅×C₂₅	1	5	yes	—
22	C₅²×C₇	C₅³	1	1	yes	characteristic
23	C₇×C₂₅	—	5	4	no	—
24	C₇×C₂₅	—	5	20	no	—
25	C₇×C₂₅	C₅×C₂₅	1	25	yes	complemented
26	C₇×C₂₅	5₋¹⁺²	1	5	yes	direct product factor
27	C₅³	C₅²×C₇	1	1	yes	characteristic
28	5₋¹⁺²	C₇×C₂₅	1	25	yes	direct product factor
29	C₅×C₂₅	—	5	5	no	—
30	C₅×C₂₅	C₅²×C₇	1	20	yes	—
31	C₅×C₂₅	C₅²×C₇	1	4	yes	—
32	C₅×C₂₅	C₅²×C₇	1	5	yes	—
33	C₅×C₂₅	C₅²×C₇	1	1	yes	characteristic
34	C₅×C₇	—	5	5	no	—
35	C₅×C₇	C₅²×C₂₅	1	1	yes	characteristic
36	C₅×C₇	C₅×5₋¹⁺²	1	1	yes	characteristic
37	C₅×C₇	#10597837	1	4	yes	—
38	C₅²	—	5	1	no	—
39	C₅²	—	5	4	no	—
40	C₅²	C₅×C₇×C₂₅	1	5	yes	—
41	C₅²	C₅³×C₇	1	1	yes	characteristic
42	C₂₅	—	5	4	no	—
43	C₂₅	—	5	20	no	—
44	C₂₅	C₅×C₇×C₂₅	1	25	yes	complemented
45	C₂₅	C₇×5₋¹⁺²	1	5	yes	direct product factor
46	C₇	C₂₅×5₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
47	C₅	—	5	5	no	—
48	C₅	C₅²×C₇×C₂₅	1	1	yes	characteristic
49	C₅	C₅×C₇×5₋¹⁺²	1	1	yes	characteristic
50	C₅	C₇×#10597837	1	4	yes	—

	subgroup	G/H
center	C₅×C₇×C₂₅	C₅²
commutator	C₅	C₅²×C₇×C₂₅
Frattini, cosocle	C₅²	C₅³×C₇
socle	C₅²×C₇	C₅³
prime radical	C₅³×C₇	C₅²
LCS	G ▷ C₅ ▷ C₁
UCS	C₁ ◁ C₅×C₇×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×C₂₅⋊C₂₅	C₅	semidirect
5. C₇×C₂₅²	C₅	semidirect
6. C₂₅×5₋¹⁺²	C₇	direct (N × H)
8. C₇×5₋¹⁺²	C₂₅	direct (N × H)
16. C₂₅⋊C₂₅	C₅×C₇	semidirect
18. C₂₅²	C₅×C₇	semidirect
25. C₇×C₂₅	C₅×C₂₅	semidirect
26. C₇×C₂₅	5₋¹⁺²	direct (N × H)
28. 5₋¹⁺²	C₇×C₂₅	direct (N × H)
44. C₂₅	C₅×C₇×C₂₅	semidirect
45. C₂₅	C₇×5₋¹⁺²	direct (N × H)
46. C₇	C₂₅×5₋¹⁺²	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×5₋¹⁺²	5
C₅²×C₇×C₂₅	5
C₇×C₂₅⋊C₂₅	5
C₇×C₅²⋊C₂₅	5
C₇×C₂₅²	5
C₂₅×5₋¹⁺²	7

Subgroups — C7×C25×5−1+2 #36346233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₂₅×5₋¹⁺² #36346233