Subgroups — C₅×#19104885 #39908084

Order 26100.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₄₃₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	#19104885	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×#11760329	—	5	1	no	maximal
5	C₅×D₄₃₅	—	6	2	no	—
6	C₅×#10596814	—	9	1	no	maximal, Hall
7	C₃⋊D₄₃₅	C₂×C₅	1	1	yes	characteristic
8	C₅×C₃⋊D₈₇	—	5	1	no	—
9	C₃×C₅²×C₂₉	—	2	2	no	—
10	C₅×D₁₄₅	—	9	1	no	—
11	C₃²×C₅×C₂₉	—	4	1	no	—
12	C₃²×C₅×C₂₉	C₄×C₅	1	1	yes	characteristic, complemented
13	C₃²×C₅×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
14	#11760329	—	5	1	no	Hall
15	C₅×#4380	—	29	1	no	maximal, Hall
16	D₄₃₅	—	6	2	no	—
17	C₅×D₈₇	—	30	2	no	—
18	C₅²×C₂₉	#157	1	1	yes	characteristic, complemented, Hall
19	#10596814	—	9	1	no	—
20	C₅×#1181	—	45	1	no	—
21	C₃⋊D₈₇	—	5	1	no	—
22	C₅×C₃⋊D₁₅	—	29	1	no	—
23	C₃×C₅×C₂₉	—	2	2	no	—
24	C₃×C₅×C₂₉	—	2	2	no	—
25	C₃×C₅×C₂₉	—	4	4	no	—
26	D₁₄₅	—	9	1	no	—
27	C₅×D₂₉	—	45	1	no	—
28	C₃²×C₂₉	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
29	C₃²×C₅²	#1181	1	1	yes	characteristic, complemented, Hall
30	#4380	—	29	1	no	—
31	C₅×#157	—	145	1	no	—
32	D₈₇	—	30	2	no	—
33	C₅×D₁₅	—	174	2	no	—
34	C₅×C₂₉	—	4	1	no	—
35	C₅×C₂₉	C₅×#157	1	1	yes	characteristic, complemented
36	C₅×C₂₉	#4380	1	1	yes	characteristic, complemented
37	#1181	—	45	1	no	Hall
38	C₅×AGL(1,𝔽₅)	—	261	1	no	Hall
39	C₃⋊D₁₅	—	29	1	no	—
40	C₅×C₃⋊D₃	—	145	1	no	—
41	C₃×C₂₉	—	2	2	no	—
42	C₃×C₅²	—	2	2	no	—
43	D₂₉	—	45	1	no	—
44	C₅×D₅	—	261	1	no	—
45	C₃²×C₅	—	4	1	no	—
46	C₃²×C₅	C₅×#1181	1	1	yes	characteristic, complemented
47	C₃²×C₅	#10596814	1	1	yes	characteristic, complemented
48	#157	—	145	1	no	Hall
49	D₁₅	—	174	2	no	—
50	C₅×D₃	—	870	2	no	—
51	C₂₉	C₅×#4380	1	1	yes	characteristic, complemented, Sylow
52	C₅²	#11760329	1	1	yes	characteristic, complemented, Sylow
53	AGL(1,𝔽₅)	—	261	1	no	—
54	C₄×C₅	—	1305	1	no	—
55	C₃⋊D₃	—	145	1	no	—
56	C₃×C₅	—	2	2	no	—
57	C₃×C₅	—	2	2	no	—
58	C₃×C₅	—	4	4	no	—
59	C₂×C₅	—	1305	1	no	—
60	D₅	—	261	1	no	—
61	C₃²	C₅×#10596814	1	1	yes	characteristic, complemented, Sylow
62	D₃	—	870	2	no	—
63	C₅	—	4	1	no	—
64	C₅	C₅×#11760329	1	1	yes	characteristic, complemented
65	C₅	#19104885	1	1	yes	characteristic, direct product factor
66	C₄	—	1305	1	no	Sylow
67	C₃	—	2	2	no	—
68	C₂	—	1305	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#19104885
commutator, hypocenter	C₃²×C₅×C₂₉	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₂₉	C₄
prime radical	C₅×C₃⋊D₄₃₅	C₂
cosocle	C₃⋊D₄₃₅	C₂×C₅
LCS	G ▷ C₃²×C₅×C₂₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅²×C₂₉	C₄	semidirect
3. #19104885	C₅	direct (N × H)
12. C₃²×C₅×C₂₉	C₄×C₅	semidirect
13. C₃²×C₅×C₂₉	AGL(1,𝔽₅)	semidirect
18. C₅²×C₂₉	#157	semidirect
28. C₃²×C₂₉	C₅×AGL(1,𝔽₅)	semidirect
29. C₃²×C₅²	#1181	semidirect
35. C₅×C₂₉	C₅×#157	semidirect
36. C₅×C₂₉	#4380	semidirect
46. C₃²×C₅	C₅×#1181	semidirect
47. C₃²×C₅	#10596814	semidirect
51. C₂₉	C₅×#4380	semidirect
52. C₅²	#11760329	semidirect
61. C₃²	C₅×#10596814	semidirect
64. C₅	C₅×#11760329	semidirect
65. C₅	#19104885	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×C₃⋊D₄₃₅	2
#19104885	5
C₅×#11760329	5
C₅×#10596814	9
C₅×#4380	29

Subgroups — C5×#19104885 #39908084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19104885 #39908084