Subgroups — C₅²×#11760329 #39908078

Order 26100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₃⋊D₈₇	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×#11760329	C₅	1	6	yes	maximal, direct product factor
4	C₅²×D₈₇	—	6	2	no	—
5	C₅²×#1181	—	9	1	no	maximal, Hall
6	C₅×C₃⋊D₈₇	C₂×C₅	1	6	yes	—
7	C₃×C₅²×C₂₉	—	2	2	no	—
8	C₅²×D₂₉	—	9	1	no	—
9	C₃²×C₅×C₂₉	C₄×C₅	1	6	yes	complemented
10	#11760329	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₅²×#157	—	29	1	no	maximal, Hall
12	C₅×D₈₇	—	6	12	no	—
13	C₅²×C₂₉	#157	1	1	yes	characteristic, complemented, Hall
14	C₅×#1181	—	9	6	no	—
15	C₃⋊D₈₇	C₂×C₅²	1	1	yes	characteristic
16	C₅²×C₃⋊D₃	—	29	1	no	—
17	C₃×C₅×C₂₉	—	2	12	no	—
18	C₅×D₂₉	—	9	6	no	—
19	C₃²×C₂₉	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₅²	#1181	1	1	yes	characteristic, complemented, Hall
21	C₅×#157	—	29	6	no	—
22	D₈₇	—	6	2	no	—
23	C₅²×D₃	—	174	2	no	—
24	C₅×C₂₉	C₅×#157	1	6	yes	complemented
25	#1181	—	9	1	no	Hall
26	C₄×C₅²	—	261	1	no	Hall
27	C₅×C₃⋊D₃	—	29	6	no	—
28	C₃×C₂₉	—	2	2	no	—
29	C₃×C₅²	—	2	2	no	—
30	D₂₉	—	9	1	no	—
31	C₂×C₅²	—	261	1	no	—
32	C₃²×C₅	C₅×#1181	1	6	yes	complemented
33	#157	—	29	1	no	Hall
34	C₅×D₃	—	174	12	no	—
35	C₂₉	C₅²×#157	1	1	yes	characteristic, complemented, Sylow
36	C₅²	#11760329	1	1	yes	characteristic, direct product factor, Sylow
37	C₄×C₅	—	261	6	no	—
38	C₃⋊D₃	—	29	1	no	—
39	C₃×C₅	—	2	12	no	—
40	C₂×C₅	—	261	6	no	—
41	C₃²	C₅²×#1181	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	174	2	no	—
43	C₅	C₅×#11760329	1	6	yes	direct product factor
44	C₄	—	261	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	261	1	no	—

	subgroup	G/H
center, hypercenter	C₅²	#11760329
commutator, hypocenter	C₃²×C₂₉	C₄×C₅²
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₂₉	C₄
prime radical	C₅²×C₃⋊D₈₇	C₂
cosocle	C₃⋊D₈₇	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
2. C₃²×C₅²×C₂₉	C₄	semidirect
3. C₅×#11760329	C₅	direct (N × H)
9. C₃²×C₅×C₂₉	C₄×C₅	semidirect
10. #11760329	C₅²	direct (N × H)
13. C₅²×C₂₉	#157	semidirect
19. C₃²×C₂₉	C₄×C₅²	semidirect
20. C₃²×C₅²	#1181	semidirect
24. C₅×C₂₉	C₅×#157	semidirect
32. C₃²×C₅	C₅×#1181	semidirect
35. C₂₉	C₅²×#157	semidirect
36. C₅²	#11760329	direct (N × H)
41. C₃²	C₅²×#1181	semidirect
43. C₅	C₅×#11760329	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×C₃⋊D₈₇	2
C₅×#11760329	5
C₅²×#1181	9
C₅²×#157	29

Subgroups — C52×#11760329 #39908078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×#11760329 #39908078