Subgroups — C₅×#19104890 #39908082

Order 26100.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₃⋊D₃×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	#19104890	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×#11760330	—	5	1	no	maximal
5	C₅²×D₃×C₂₉	—	6	2	no	—
6	C₅×Dic₁₄₅	—	9	1	no	maximal, Hall
7	C₅×C₃⋊D₃×C₂₉	—	2	2	no	—
8	C₅×C₃⋊D₃×C₂₉	D₅	1	1	yes	characteristic
9	C₅×C₃⋊D₃×C₂₉	C₂×C₅	1	1	yes	characteristic
10	C₃×C₅²×C₂₉	—	2	2	no	—
11	C₂×C₅²×C₂₉	—	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	#11760330	—	5	1	no	Hall
16	C₅×#4379	—	29	1	no	maximal, Hall
17	C₅×D₃×C₂₉	—	6	2	no	—
18	C₅×D₃×C₂₉	—	6	2	no	—
19	C₅×D₃×C₂₉	—	6	8	no	—
20	C₅²×C₂₉	#157	1	1	yes	characteristic, complemented, Hall
21	Dic₁₄₅	—	9	1	no	—
22	C₅×Dic₂₉	—	45	1	no	—
23	C₃⋊D₃×C₂₉	C₅×D₅	1	1	yes	characteristic
24	C₅²×C₃⋊D₃	D₂₉	1	1	yes	characteristic
25	C₃×C₅×C₂₉	—	2	8	no	—
26	C₃×C₅×C₂₉	—	2	2	no	—
27	C₃×C₅×C₂₉	—	2	2	no	—
28	C₂×C₅×C₂₉	—	9	1	no	—
29	C₂×C₅×C₂₉	—	9	1	no	—
30	C₂×C₅×C₂₉	—	18	2	no	—
31	C₃²×C₂₉	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
32	C₃²×C₅²	Dic₂₉	1	1	yes	characteristic, complemented, Hall
33	#4379	—	29	1	no	—
34	C₅×#157	—	145	1	no	—
35	D₃×C₂₉	—	6	2	no	—
36	C₅²×D₃	—	6	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	Dic₂₉	—	45	1	no	Hall
41	C₅×Dic₅	—	261	1	no	Hall
42	C₅×C₃⋊D₃	—	2	2	no	—
43	C₅×C₃⋊D₃	C₅×D₂₉	1	1	yes	characteristic
44	C₅×C₃⋊D₃	D₁₄₅	1	1	yes	characteristic
45	C₃×C₂₉	—	2	2	no	—
46	C₃×C₅²	—	2	2	no	—
47	C₂×C₂₉	—	9	1	no	—
48	C₂×C₅²	—	9	1	no	—
49	C₃²×C₅	—	2	2	no	—
50	C₃²×C₅	C₅×Dic₂₉	1	1	yes	characteristic, complemented
51	C₃²×C₅	Dic₁₄₅	1	1	yes	characteristic, complemented
52	#157	—	145	1	no	Hall
53	C₅×D₃	—	6	2	no	—
54	C₅×D₃	—	6	2	no	—
55	C₅×D₃	—	6	8	no	—
56	C₂₉	C₅×#4379	1	1	yes	characteristic, complemented, Sylow
57	C₅²	#11760330	1	1	yes	characteristic, complemented, Sylow
58	C₄×C₅	—	1305	1	no	—
59	Dic₅	—	261	1	no	—
60	C₃⋊D₃	C₅×D₁₄₅	1	1	yes	characteristic
61	C₃×C₅	—	2	8	no	—
62	C₃×C₅	—	2	2	no	—
63	C₃×C₅	—	2	2	no	—
64	C₂×C₅	—	9	1	no	—
65	C₂×C₅	—	9	1	no	—
66	C₂×C₅	—	18	2	no	—
67	C₃²	C₅×Dic₁₄₅	1	1	yes	characteristic, complemented, Sylow
68	D₃	—	6	2	no	—
69	C₅	—	2	2	no	—
70	C₅	C₅×#11760330	1	1	yes	characteristic, complemented
71	C₅	#19104890	1	1	yes	characteristic, direct product factor
72	C₄	—	1305	1	no	Sylow
73	C₃	—	2	2	no	—
74	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#19104890
commutator, hypocenter	C₃²×C₅×C₂₉	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₂₉	C₄
prime radical	C₅²×C₃⋊D₃×C₂₉	C₂
cosocle	C₅×C₃⋊D₃×C₂₉	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. #19104890	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	Dic₂₉	semidirect
38. C₅×C₂₉	C₅×#157	semidirect
39. C₅×C₂₉	#4379	semidirect
50. C₃²×C₅	C₅×Dic₂₉	semidirect
51. C₃²×C₅	Dic₁₄₅	semidirect
56. C₂₉	C₅×#4379	semidirect
57. C₅²	#11760330	semidirect
67. C₃²	C₅×Dic₁₄₅	semidirect
70. C₅	C₅×#11760330	semidirect
71. C₅	#19104890	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⋊D₃×C₂₉	2
#19104890	5
C₅×#11760330	5
C₅×Dic₁₄₅	9
C₅×#4379	29

Subgroups — C5×#19104890 #39908082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19104890 #39908082