Subgroups — C₅²×C₃⋊(C₃⋊#1181) #39908184

Order 26100.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₃⋊#1181	—	3	4	no	maximal
3	C₃²×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×C₃⋊(C₃⋊#1181)	C₅	1	6	yes	maximal, direct product factor
5	C₃×C₅²×D₂₉	D₃	1	4	yes	—
6	C₅²×#1181	—	9	1	no	Hall
7	C₃²×C₅×D₂₉	C₂×C₅	1	6	yes	—
8	C₃×C₅²×C₂₉	Dic₃	1	4	yes	complemented
9	C₅×C₃⋊#1181	—	3	24	no	—
10	C₅²×D₂₉	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₅×C₂₉	C₄×C₅	1	6	yes	complemented
12	C₃⋊(C₃⋊#1181)	C₅²	1	1	yes	characteristic, direct product factor, Hall
13	C₅²×C₃⋊Dic₃	—	29	1	no	maximal, Hall
14	C₃×C₅×D₂₉	C₅×D₃	1	24	yes	—
15	C₅²×C₂₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
16	C₅×#1181	—	9	6	no	—
17	C₃²×D₂₉	C₂×C₅²	1	1	yes	characteristic
18	C₂×C₃²×C₅²	—	29	1	no	—
19	C₃×C₅×C₂₉	C₅×Dic₃	1	24	yes	complemented
20	C₃⋊#1181	—	3	4	no	—
21	C₅²×Dic₃	—	87	4	no	—
22	C₅×D₂₉	C₅×C₃⋊D₃	1	6	yes	—
23	C₃²×C₂₉	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
24	C₃²×C₅²	#1181	1	1	yes	characteristic, complemented, Hall
25	C₅×C₃⋊Dic₃	—	29	6	no	—
26	C₃×D₂₉	C₅²×D₃	1	4	yes	—
27	C₂×C₃×C₅²	—	29	4	no	—
28	C₅×C₂₉	C₅×C₃⋊Dic₃	1	6	yes	complemented
29	#1181	—	9	1	no	Hall
30	C₄×C₅²	—	261	1	no	Hall
31	C₂×C₃²×C₅	—	29	6	no	—
32	C₃×C₂₉	C₅²×Dic₃	1	4	yes	complemented
33	C₃×C₅²	C₃⋊#1181	1	4	yes	complemented
34	C₅×Dic₃	—	87	24	no	—
35	D₂₉	C₅²×C₃⋊D₃	1	1	yes	characteristic
36	C₂×C₅²	—	29	1	no	—
37	C₃²×C₅	C₅×#1181	1	6	yes	complemented
38	C₃⋊Dic₃	—	29	1	no	Hall
39	C₂×C₃×C₅	—	29	24	no	—
40	C₂₉	C₅²×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
41	C₅²	C₃⋊(C₃⋊#1181)	1	1	yes	characteristic, direct product factor, Sylow
42	C₄×C₅	—	261	6	no	—
43	C₂×C₃²	—	29	1	no	—
44	C₃×C₅	C₅×C₃⋊#1181	1	24	yes	complemented
45	Dic₃	—	87	4	no	—
46	C₂×C₅	—	29	6	no	—
47	C₃²	C₅²×#1181	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	29	4	no	—
49	C₅	C₅×C₃⋊(C₃⋊#1181)	1	6	yes	direct product factor
50	C₄	—	261	1	no	Sylow
51	C₃	C₅²×C₃⋊#1181	1	4	yes	complemented
52	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₅²	C₃⋊(C₃⋊#1181)
commutator, hypocenter	C₃²×C₂₉	C₄×C₅²
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₂₉	C₄
prime radical	C₃²×C₅²×D₂₉	C₂
cosocle	C₃²×D₂₉	C₂×C₅²
LCS	G ▷ C₃²×C₂₉
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₂₉	C₄	semidirect
4. C₅×C₃⋊(C₃⋊#1181)	C₅	direct (N × H)
8. C₃×C₅²×C₂₉	Dic₃	semidirect
11. C₃²×C₅×C₂₉	C₄×C₅	semidirect
12. C₃⋊(C₃⋊#1181)	C₅²	direct (N × H)
15. C₅²×C₂₉	C₃⋊Dic₃	semidirect
19. C₃×C₅×C₂₉	C₅×Dic₃	semidirect
23. C₃²×C₂₉	C₄×C₅²	semidirect
24. C₃²×C₅²	#1181	semidirect
28. C₅×C₂₉	C₅×C₃⋊Dic₃	semidirect
32. C₃×C₂₉	C₅²×Dic₃	semidirect
33. C₃×C₅²	C₃⋊#1181	semidirect
37. C₃²×C₅	C₅×#1181	semidirect
40. C₂₉	C₅²×C₃⋊Dic₃	semidirect
41. C₅²	C₃⋊(C₃⋊#1181)	direct (N × H)
44. C₃×C₅	C₅×C₃⋊#1181	semidirect
47. C₃²	C₅²×#1181	semidirect
49. C₅	C₅×C₃⋊(C₃⋊#1181)	direct (N × H)
51. C₃	C₅²×C₃⋊#1181	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅²×D₂₉	2
C₅²×C₃⋊#1181	3
C₅×C₃⋊(C₃⋊#1181)	5
C₅²×C₃⋊Dic₃	29

Subgroups — C52×C3⋊(C3⋊#1181) #39908184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₃⋊(C₃⋊#1181) #39908184