Subgroups — C₅×#19104889 #39908081

Order 26100.

128 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	#19104889	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×#11760329	—	5	1	no	maximal
5	C₅²×D₈₇	—	6	2	no	—
6	C₅×#10596817	—	9	1	no	maximal, Hall
7	C₅×C₃⋊D₈₇	—	2	2	no	—
8	C₅×C₃⋊D₈₇	D₅	1	1	yes	characteristic
9	C₅×C₃⋊D₈₇	C₂×C₅	1	1	yes	characteristic
10	C₃×C₅²×C₂₉	—	2	2	no	—
11	C₅²×D₂₉	—	9	1	no	—
12	C₃²×C₅×C₂₉	—	2	2	no	—
13	C₃²×C₅×C₂₉	Dic₅	1	1	yes	characteristic, complemented
14	C₃²×C₅×C₂₉	C₄×C₅	1	1	yes	characteristic, complemented
15	#11760329	—	5	1	no	Hall
16	C₅×#4379	—	29	1	no	maximal, Hall
17	C₅×D₈₇	—	6	2	no	—
18	C₅×D₈₇	—	6	2	no	—
19	C₅×D₈₇	—	6	8	no	—
20	C₅²×C₂₉	#157	1	1	yes	characteristic, complemented, Hall
21	#10596817	—	9	1	no	—
22	C₅×#1181	—	45	1	no	—
23	C₃⋊D₈₇	C₅×D₅	1	1	yes	characteristic
24	C₅²×C₃⋊D₃	—	29	1	no	—
25	C₃×C₅×C₂₉	—	2	8	no	—
26	C₃×C₅×C₂₉	—	2	2	no	—
27	C₃×C₅×C₂₉	—	2	2	no	—
28	C₅×D₂₉	—	9	1	no	—
29	C₅×D₂₉	—	9	1	no	—
30	C₅×D₂₉	—	18	2	no	—
31	C₃²×C₂₉	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
32	C₃²×C₅²	#1181	1	1	yes	characteristic, complemented, Hall
33	#4379	—	29	1	no	—
34	C₅×#157	—	145	1	no	—
35	D₈₇	—	6	2	no	—
36	C₅²×D₃	—	174	2	no	—
37	C₅×C₂₉	—	2	2	no	—
38	C₅×C₂₉	C₅×#157	1	1	yes	characteristic, complemented
39	C₅×C₂₉	#4379	1	1	yes	characteristic, complemented
40	#1181	—	45	1	no	Hall
41	C₅×Dic₅	—	261	1	no	Hall
42	C₅×C₃⋊D₃	—	29	1	no	—
43	C₅×C₃⋊D₃	—	29	1	no	—
44	C₅×C₃⋊D₃	—	58	2	no	—
45	C₃×C₂₉	—	2	2	no	—
46	C₃×C₅²	—	2	2	no	—
47	D₂₉	—	9	1	no	—
48	C₂×C₅²	—	261	1	no	—
49	C₃²×C₅	—	2	2	no	—
50	C₃²×C₅	C₅×#1181	1	1	yes	characteristic, complemented
51	C₃²×C₅	#10596817	1	1	yes	characteristic, complemented
52	#157	—	145	1	no	Hall
53	C₅×D₃	—	174	2	no	—
54	C₅×D₃	—	174	2	no	—
55	C₅×D₃	—	174	8	no	—
56	C₂₉	C₅×#4379	1	1	yes	characteristic, complemented, Sylow
57	C₅²	#11760329	1	1	yes	characteristic, complemented, Sylow
58	C₄×C₅	—	1305	1	no	—
59	Dic₅	—	261	1	no	—
60	C₃⋊D₃	—	29	1	no	—
61	C₃×C₅	—	2	8	no	—
62	C₃×C₅	—	2	2	no	—
63	C₃×C₅	—	2	2	no	—
64	C₂×C₅	—	261	1	no	—
65	C₂×C₅	—	261	1	no	—
66	C₂×C₅	—	522	2	no	—
67	C₃²	C₅×#10596817	1	1	yes	characteristic, complemented, Sylow
68	D₃	—	174	2	no	—
69	C₅	—	2	2	no	—
70	C₅	C₅×#11760329	1	1	yes	characteristic, complemented
71	C₅	#19104889	1	1	yes	characteristic, direct product factor
72	C₄	—	1305	1	no	Sylow
73	C₃	—	2	2	no	—
74	C₂	—	261	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#19104889
commutator, hypocenter	C₃²×C₅×C₂₉	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₂₉	C₄
prime radical	C₅²×C₃⋊D₈₇	C₂
cosocle	C₅×C₃⋊D₈₇	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. #19104889	C₅	direct (N × H)
13. C₃²×C₅×C₂₉	Dic₅	semidirect
14. C₃²×C₅×C₂₉	C₄×C₅	semidirect
20. C₅²×C₂₉	#157	semidirect
31. C₃²×C₂₉	C₅×Dic₅	semidirect
32. C₃²×C₅²	#1181	semidirect
38. C₅×C₂₉	C₅×#157	semidirect
39. C₅×C₂₉	#4379	semidirect
50. C₃²×C₅	C₅×#1181	semidirect
51. C₃²×C₅	#10596817	semidirect
56. C₂₉	C₅×#4379	semidirect
57. C₅²	#11760329	semidirect
67. C₃²	C₅×#10596817	semidirect
70. C₅	C₅×#11760329	semidirect
71. C₅	#19104889	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
#19104889	5
C₅×#11760329	5
C₅×#10596817	9
C₅×#4379	29

Subgroups — C5×#19104889 #39908081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19104889 #39908081