Subgroups — #4379×C₄₁⋊C₅ #49146948

Order 36900.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₃×C₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₄₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄₁×#4379	C₅	1	1	yes	maximal, characteristic, complemented
4	#157×C₄₁⋊C₅	—	5	1	no	maximal
5	C₅×D₃×C₄₁⋊C₅	—	6	2	no	—
6	Dic₅×C₄₁⋊C₅	—	9	1	no	maximal, Hall
7	C₅×C₃⋊D₃×C₄₁	C₂×C₅	1	1	yes	characteristic
8	C₃⋊D₃×C₄₁⋊C₅	—	2	2	no	—
9	C₃⋊D₃×C₄₁⋊C₅	D₅	1	1	yes	characteristic
10	C₃×C₅×C₄₁⋊C₅	—	2	2	no	—
11	C₂×C₅×C₄₁⋊C₅	—	9	1	no	—
12	C₃²×C₅×C₄₁	C₄×C₅	1	1	yes	characteristic, complemented
13	C₃²×C₄₁⋊C₅	—	2	2	no	—
14	C₃²×C₄₁⋊C₅	Dic₅	1	1	yes	characteristic, complemented
15	#157×C₄₁	—	5	1	no	Hall
16	C₅×D₃×C₄₁	—	6	2	no	—
17	D₃×C₄₁⋊C₅	—	6	2	no	—
18	D₃×C₄₁⋊C₅	—	6	8	no	—
19	C₅×C₄₁⋊C₅	#157	1	1	yes	characteristic, complemented, Hall
20	C₅×#4379	—	41	1	no	maximal, Hall
21	Dic₅×C₄₁	—	9	1	no	—
22	C₄×C₄₁⋊C₅	—	45	1	no	—
23	C₃⋊D₃×C₄₁	C₅×D₅	1	1	yes	characteristic
24	C₃×C₅×C₄₁	—	2	2	no	—
25	C₃×C₄₁⋊C₅	—	2	8	no	—
26	C₃×C₄₁⋊C₅	—	2	2	no	—
27	C₅²×C₃⋊D₃	—	41	1	no	—
28	C₂×C₅×C₄₁	—	9	1	no	—
29	C₂×C₄₁⋊C₅	—	9	1	no	—
30	C₂×C₄₁⋊C₅	—	18	2	no	—
31	C₃²×C₄₁	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
32	D₃×C₄₁	—	6	2	no	—
33	C₃²×C₅²	—	41	1	no	Hall
34	C₅×C₄₁	C₅×#157	1	1	yes	characteristic, complemented
35	C₄₁⋊C₅	—	2	2	no	—
36	C₄₁⋊C₅	#4379	1	1	yes	characteristic, direct product factor
37	#4379	C₄₁⋊C₅	1	1	yes	characteristic, direct product factor
38	C₅×#157	—	205	1	no	—
39	C₄×C₄₁	—	45	1	no	Hall
40	C₅²×D₃	—	246	2	no	—
41	C₃×C₄₁	—	2	2	no	—
42	C₅×Dic₅	—	369	1	no	Hall
43	C₅×C₃⋊D₃	—	41	1	no	—
44	C₅×C₃⋊D₃	—	82	2	no	—
45	C₅×C₃⋊D₃	C₂×C₄₁⋊C₅	1	1	yes	characteristic
46	C₂×C₄₁	—	9	1	no	—
47	C₃×C₅²	—	82	2	no	—
48	C₂×C₅²	—	369	1	no	—
49	C₃²×C₅	—	41	1	no	—
50	C₃²×C₅	—	82	2	no	—
51	C₃²×C₅	C₄×C₄₁⋊C₅	1	1	yes	characteristic, complemented
52	C₄₁	C₅×#4379	1	1	yes	characteristic, complemented, Sylow
53	#157	—	5	1	no	Hall
54	C₅×D₃	—	6	2	no	—
55	C₅×D₃	—	246	2	no	—
56	C₅×D₃	—	246	8	no	—
57	C₅²	—	41	1	no	Sylow
58	C₄×C₅	—	1845	1	no	—
59	Dic₅	—	9	1	no	—
60	C₃⋊D₃	D₅×C₄₁⋊C₅	1	1	yes	characteristic
61	C₃×C₅	—	2	2	no	—
62	C₃×C₅	—	82	2	no	—
63	C₃×C₅	—	82	8	no	—
64	C₂×C₅	—	9	1	no	—
65	C₂×C₅	—	369	1	no	—
66	C₂×C₅	—	738	2	no	—
67	C₃²	Dic₅×C₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
68	D₃	—	6	2	no	—
69	C₅	—	41	1	no	—
70	C₅	—	82	2	no	—
71	C₅	#157×C₄₁⋊C₅	1	1	yes	characteristic, complemented
72	C₄	—	45	1	no	Sylow
73	C₃	—	2	2	no	—
74	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₄₁	C₄×C₅
prime radical	C₅×C₃⋊D₃×C₄₁⋊C₅	C₂
cosocle	C₅×C₃⋊D₃×C₄₁	C₂×C₅
LCS	G ▷ C₃²×C₅×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₄₁⋊C₅	C₄	semidirect
3. C₄₁×#4379	C₅	semidirect
12. C₃²×C₅×C₄₁	C₄×C₅	semidirect
14. C₃²×C₄₁⋊C₅	Dic₅	semidirect
19. C₅×C₄₁⋊C₅	#157	semidirect
31. C₃²×C₄₁	C₅×Dic₅	semidirect
34. C₅×C₄₁	C₅×#157	semidirect
36. C₄₁⋊C₅	#4379	direct (N × H)
37. #4379	C₄₁⋊C₅	direct (N × H)
51. C₃²×C₅	C₄×C₄₁⋊C₅	semidirect
52. C₄₁	C₅×#4379	semidirect
67. C₃²	Dic₅×C₄₁⋊C₅	semidirect
71. C₅	#157×C₄₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₃⋊D₃×C₄₁⋊C₅	2
C₄₁×#4379	5
#157×C₄₁⋊C₅	5
Dic₅×C₄₁⋊C₅	9
C₅×#4379	41

Subgroups — #4379×C41⋊C5 #49146948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #4379×C₄₁⋊C₅ #49146948