Subgroups — C₇×#15691099 #36346231

Order 21875.

322 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×C₂₅	C₅	1	1	yes	maximal, characteristic
2	C₇×C₂₅⋊C₂₅	C₅	1	20	yes	maximal, complemented
3	C₇×C₅²⋊C₂₅	C₅	1	5	yes	maximal
4	C₇×C₂₅²	C₅	1	5	yes	maximal, complemented
5	#15691099	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₅³×C₇	C₅²	1	1	yes	characteristic
7	C₅×C₇×C₂₅	C₂₅	1	25	yes	complemented
8	C₅×C₇×C₂₅	C₅²	1	25	yes	—
9	C₅×C₇×C₂₅	C₅²	1	4	yes	—
10	C₅×C₇×C₂₅	C₅²	1	1	yes	characteristic
11	C₅²×C₂₅	C₅×C₇	1	1	yes	characteristic
12	C₂₅⋊C₂₅	C₅×C₇	1	20	yes	complemented
13	C₅²⋊C₂₅	C₅×C₇	1	5	yes	—
14	C₂₅²	C₅×C₇	1	5	yes	complemented
15	C₅²×C₇	—	5	5	no	—
16	C₅²×C₇	C₅×C₂₅	1	5	yes	—
17	C₅²×C₇	C₅³	1	1	yes	characteristic
18	C₇×C₂₅	—	5	25	no	—
19	C₇×C₂₅	C₅×C₂₅	1	20	yes	—
20	C₇×C₂₅	C₅×C₂₅	1	5	yes	—
21	C₅³	C₅²×C₇	1	1	yes	characteristic
22	C₅×C₂₅	C₇×C₂₅	1	25	yes	complemented
23	C₅×C₂₅	C₅²×C₇	1	25	yes	—
24	C₅×C₂₅	C₅²×C₇	1	4	yes	—
25	C₅×C₂₅	C₅²×C₇	1	1	yes	characteristic
26	C₅×C₇	—	5	5	no	—
27	C₅×C₇	C₅²×C₂₅	1	1	yes	characteristic
28	C₅×C₇	#10597837	1	5	yes	—
29	C₅²	—	5	5	no	—
30	C₅²	C₅×C₇×C₂₅	1	5	yes	—
31	C₅²	C₅³×C₇	1	1	yes	characteristic
32	C₂₅	—	5	25	no	—
33	C₂₅	C₅×C₇×C₂₅	1	20	yes	—
34	C₂₅	C₅×C₇×C₂₅	1	5	yes	—
35	C₇	#15691099	1	1	yes	characteristic, direct product factor, Sylow
36	C₅	—	5	5	no	—
37	C₅	C₅²×C₇×C₂₅	1	1	yes	characteristic
38	C₅	C₇×#10597837	1	5	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
2. C₇×C₂₅⋊C₂₅	C₅	semidirect
4. C₇×C₂₅²	C₅	semidirect
5. #15691099	C₇	direct (N × H)
7. C₅×C₇×C₂₅	C₂₅	semidirect
12. C₂₅⋊C₂₅	C₅×C₇	semidirect
14. C₂₅²	C₅×C₇	semidirect
22. C₅×C₂₅	C₇×C₂₅	semidirect
35. C₇	#15691099	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₇×C₂₅	5
C₇×C₂₅⋊C₂₅	5
C₇×C₅²⋊C₂₅	5
C₇×C₂₅²	5
#15691099	7

Subgroups — C7×#15691099 #36346231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#15691099 #36346231