Subgroups — C₂₅×#13093287 #49146753

Order 36900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₃⋊D₁₂₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₂₅×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×#13093287	C₅	1	1	yes	maximal, characteristic
4	C₂₅×D₁₂₃	—	6	2	no	—
5	C₂₅×#4223	—	9	1	no	maximal, Hall
6	C₅×C₃⋊D₁₂₃	C₂×C₅	1	1	yes	characteristic
7	C₃×C₂₅×C₄₁	—	2	2	no	—
8	C₂₅×D₄₁	—	9	1	no	—
9	C₃²×C₅×C₄₁	C₄×C₅	1	1	yes	characteristic
10	#13093287	C₂₅	1	1	yes	characteristic, direct product factor, Hall
11	C₅×D₁₂₃	—	6	2	no	—
12	C₂₅×C₄₁	#157	1	1	yes	characteristic, complemented, Hall
13	C₂₅×#157	—	41	1	no	maximal, Hall
14	C₅×#4223	—	9	1	no	—
15	C₃⋊D₁₂₃	C₂×C₂₅	1	1	yes	characteristic
16	C₃×C₅×C₄₁	—	2	2	no	—
17	C₃⋊D₃×C₂₅	—	41	1	no	—
18	C₅×D₄₁	—	9	1	no	—
19	C₃²×C₄₁	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
20	D₁₂₃	—	6	2	no	—
21	C₃²×C₂₅	#4223	1	1	yes	characteristic, complemented, Hall
22	C₅×C₄₁	C₅×#157	1	1	yes	characteristic
23	C₅×#157	—	41	1	no	—
24	#4223	—	9	1	no	Hall
25	D₃×C₂₅	—	246	2	no	—
26	C₃×C₄₁	—	2	2	no	—
27	C₄×C₂₅	—	369	1	no	Hall
28	C₅×C₃⋊D₃	—	41	1	no	—
29	D₄₁	—	9	1	no	—
30	C₃×C₂₅	—	2	2	no	—
31	C₂×C₂₅	—	369	1	no	—
32	C₃²×C₅	C₅×#4223	1	1	yes	characteristic
33	C₄₁	C₂₅×#157	1	1	yes	characteristic, complemented, Sylow
34	#157	—	41	1	no	Hall
35	C₅×D₃	—	246	2	no	—
36	C₂₅	#13093287	1	1	yes	characteristic, direct product factor, Sylow
37	C₄×C₅	—	369	1	no	—
38	C₃⋊D₃	—	41	1	no	—
39	C₃×C₅	—	2	2	no	—
40	C₂×C₅	—	369	1	no	—
41	C₃²	C₂₅×#4223	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	246	2	no	—
43	C₅	C₅×#13093287	1	1	yes	characteristic
44	C₄	—	369	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	369	1	no	—

	subgroup	G/H
center, hypercenter	C₂₅	#13093287
commutator, hypocenter	C₃²×C₄₁	C₄×C₂₅
Frattini	C₅	C₅×#13093287
Fitting	C₃²×C₂₅×C₄₁	C₄
socle	C₃²×C₅×C₄₁	C₄×C₅
prime radical, cosocle	C₅×C₃⋊D₁₂₃	C₂×C₅
LCS	G ▷ C₃²×C₄₁
UCS	C₁ ◁ C₂₅

Complements

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

N	H ≅ G/N	type
2. C₃²×C₂₅×C₄₁	C₄	semidirect
10. #13093287	C₂₅	direct (N × H)
12. C₂₅×C₄₁	#157	semidirect
19. C₃²×C₄₁	C₄×C₂₅	semidirect
21. C₃²×C₂₅	#4223	semidirect
33. C₄₁	C₂₅×#157	semidirect
36. C₂₅	#13093287	direct (N × H)
41. C₃²	C₂₅×#4223	semidirect

Maximal subgroups

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

subgroup	index
C₂₅×C₃⋊D₁₂₃	2
C₅×#13093287	5
C₂₅×#4223	9
C₂₅×#157	41

Subgroups — C25×#13093287 #49146753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#13093287 #49146753