Subgroups — C₃×C₅⋊(#127⋊C₃) #13086221

Order 1440.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₄²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#4020	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅⋊(#127⋊C₃)	C₃	1	3	yes	maximal, direct product factor
4	C₃×D₅×A₄	—	4	1	no	maximal
5	C₃×#127⋊C₃	—	5	1	no	maximal, Hall
6	C₂×C₃×D₂₀	—	3	1	no	—
7	C₂×C₃×D₂₀	—	3	1	no	—
8	C₃×C₄²×C₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₄²⋊C₃	C₂×C₃	1	3	yes	complemented
10	C₃×C₅×A₄	—	4	1	no	—
11	#4020	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₄²⋊C₃	D₅	1	1	yes	characteristic, complemented
13	C₂²×C₃×D₅	—	3	1	no	—
14	C₂²×C₃×D₅	A₄	1	1	yes	characteristic
15	D₅×A₄	—	4	3	no	—
16	C₂×C₃×C₄×C₅	—	3	1	no	—
17	C₃×D₂₀	—	6	2	no	—
18	C₃×D₂₀	—	6	2	no	—
19	C₃×#127	—	5	1	no	—
20	#127⋊C₃	—	5	3	no	—
21	C₃²×D₅	—	16	1	no	—
22	C₂×D₂₀	—	3	1	no	—
23	C₂×D₂₀	—	3	1	no	—
24	C₄²×C₅	C₂×C₃²	1	1	yes	characteristic, complemented
25	C₂×C₃×A₄	—	20	1	no	—
26	C₂²×C₃×C₅	C₂×A₄	1	1	yes	characteristic
27	C₂×C₃×D₅	—	6	1	no	—
28	C₂×C₃×D₅	—	6	1	no	—
29	C₂×C₃×D₅	—	6	2	no	—
30	C₅×A₄	—	4	3	no	—
31	C₃×C₄×C₅	—	3	2	no	—
32	C₂×C₃×D₄	—	15	1	no	—
33	C₂×C₃×D₄	—	15	1	no	—
34	C₃×C₄²	C₃×D₅	1	1	yes	characteristic, complemented
35	C₄²⋊C₃	C₃×D₅	1	3	yes	complemented
36	C₃²×C₅	—	16	1	no	Hall
37	C₂²×D₅	—	3	1	no	—
38	C₂²×D₅	C₃×A₄	1	1	yes	characteristic
39	C₂×C₄×C₅	—	3	1	no	—
40	D₂₀	—	6	2	no	—
41	D₂₀	—	6	2	no	—
42	C₃×A₄	—	4	1	no	—
43	#127	—	5	1	no	Sylow
44	C₂×C₃×C₅	—	3	1	no	—
45	C₃×D₅	—	4	1	no	—
46	C₃×D₅	—	12	1	no	—
47	C₃×D₅	—	16	3	no	—
48	C₂³×C₃	—	5	1	no	—
49	C₂³×C₃	—	15	1	no	—
50	C₂×A₄	—	20	3	no	—
51	C₃×D₄	—	30	2	no	—
52	C₃×D₄	—	30	2	no	—
53	C₂×C₃×C₄	—	3	1	no	—
54	C₂²×C₅	C₂×C₃×A₄	1	1	yes	characteristic
55	C₂×D₅	—	6	1	no	—
56	C₂×D₅	—	6	1	no	—
57	C₂×D₅	—	6	2	no	—
58	C₄×C₅	—	3	2	no	—
59	C₂×C₃²	—	80	1	no	—
60	C₂×D₄	—	15	1	no	—
61	C₂×D₄	—	15	1	no	—
62	C₄²	C₃²×D₅	1	1	yes	characteristic, complemented
63	C₃×C₅	—	16	3	no	—
64	C₃×C₅	#127⋊C₃	1	1	yes	characteristic, complemented
65	C₂²×C₃	—	30	1	no	—
66	C₂²×C₃	—	30	1	no	—
67	C₂²×C₃	—	30	2	no	—
68	C₂²×C₃	D₅×A₄	1	1	yes	characteristic
69	A₄	—	4	3	no	—
70	C₃×C₄	—	3	2	no	—
71	C₂×C₅	—	3	1	no	—
72	D₅	—	4	1	no	—
73	D₅	—	12	1	no	—
74	C₃²	—	16	1	no	Sylow
75	C₂³	—	5	1	no	—
76	C₂³	—	15	1	no	—
77	D₄	—	30	2	no	—
78	D₄	—	30	2	no	—
79	C₂×C₄	—	3	1	no	—
80	C₂×C₃	—	3	1	no	—
81	C₂×C₃	—	20	1	no	—
82	C₂×C₃	—	60	1	no	—
83	C₂×C₃	—	80	3	no	—
84	C₅	C₃×#127⋊C₃	1	1	yes	characteristic, complemented, Sylow
85	C₂²	—	30	1	no	—
86	C₂²	—	30	1	no	—
87	C₂²	—	30	2	no	—
88	C₂²	C₃×D₅×A₄	1	1	yes	characteristic
89	C₄	—	3	2	no	—
90	C₃	—	16	3	no	—
91	C₃	C₅⋊(#127⋊C₃)	1	1	yes	characteristic, direct product factor
92	C₂	—	3	1	no	—
93	C₂	—	20	1	no	—
94	C₂	—	60	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₅⋊(#127⋊C₃)
commutator, cosocle, hypocenter	C₄²×C₅	C₂×C₃²
Frattini	C₂²	C₃×D₅×A₄
Fitting	C₃×C₄²×C₅	C₂×C₃
socle	C₂²×C₃×C₅	C₂×A₄
LCS	G ▷ C₄²×C₅
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₄²⋊C₃	C₂	semidirect
2. C₃×#4020	C₃	semidirect
3. C₅⋊(#127⋊C₃)	C₃	direct (N × H)
8. C₃×C₄²×C₅	C₂×C₃	semidirect
9. C₅×C₄²⋊C₃	C₂×C₃	semidirect
11. #4020	C₃²	semidirect
12. C₃×C₄²⋊C₃	D₅	semidirect
24. C₄²×C₅	C₂×C₃²	semidirect
34. C₃×C₄²	C₃×D₅	semidirect
35. C₄²⋊C₃	C₃×D₅	semidirect
62. C₄²	C₃²×D₅	semidirect
64. C₃×C₅	#127⋊C₃	semidirect
84. C₅	C₃×#127⋊C₃	semidirect
91. C₃	C₅⋊(#127⋊C₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₄²⋊C₃	2
C₃×#4020	3
C₅⋊(#127⋊C₃)	3
C₃×D₅×A₄	4
C₃×#127⋊C₃	5

Subgroups — C3×C5⋊(#127⋊C3) #13086221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅⋊(#127⋊C₃) #13086221