Subgroups — C₃²×#3994 #13086246

Order 1440.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal
2	C₃²×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	C₃×#3994	C₃	1	4	yes	maximal, direct product factor
4	C₂×C₃²×AGL(1,𝔽₅)	—	2	2	no	—
5	C₃²×C₄×D₅	C₂²	1	1	yes	characteristic
6	C₃²×C₅×C₈	C₄	1	1	yes	characteristic, complemented
7	C₃²×#168	C₄	1	1	yes	characteristic, complemented
8	C₃²×#107	—	5	1	no	maximal, Hall
9	C₃×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	8	yes	—
10	C₃×C₈×D₅	C₂×C₃	1	4	yes	—
11	C₂×C₃²×D₅	D₄	1	1	yes	characteristic
12	C₃²×AGL(1,𝔽₅)	—	4	2	no	—
13	C₃²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
14	C₃²×Dic₅	Q₈	1	1	yes	characteristic
15	#3994	C₃²	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃²×C₈	—	5	1	no	—
17	C₃²×C₄⋊C₄	—	5	2	no	—
18	C₂×C₃×AGL(1,𝔽₅)	—	2	8	no	—
19	C₃×C₄×D₅	C₂²×C₃	1	4	yes	—
20	C₃×C₅×C₈	C₃×C₄	1	4	yes	complemented
21	C₃×#168	C₃×C₄	1	4	yes	complemented
22	C₃×#107	—	5	4	no	—
23	C₂×C₃²×C₅	C₄⋊C₄	1	1	yes	characteristic
24	C₃²×D₅	D₈	1	1	yes	characteristic
25	C₃²×D₅	Q₁₆	1	1	yes	characteristic
26	C₄⋊AGL(1,𝔽₅)	C₂×C₃²	1	2	yes	—
27	C₈×D₅	C₂×C₃²	1	1	yes	characteristic
28	C₂×C₃²×C₄	—	5	1	no	—
29	C₂×C₃²×C₄	—	10	2	no	—
30	C₃²×C₈	—	5	1	no	—
31	C₃²×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
32	C₂×C₃×D₅	C₃×D₄	1	4	yes	—
33	C₃×AGL(1,𝔽₅)	—	4	8	no	—
34	C₃×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
35	C₃×Dic₅	C₃×Q₈	1	4	yes	—
36	C₂×C₃×C₈	—	5	4	no	—
37	C₃×C₄⋊C₄	—	5	8	no	—
38	C₃²×C₅	#107	1	1	yes	characteristic, complemented, Hall
39	C₂×AGL(1,𝔽₅)	—	2	2	no	—
40	C₄×D₅	C₂²×C₃²	1	1	yes	characteristic
41	C₅×C₈	C₃²×C₄	1	1	yes	characteristic, complemented
42	#168	C₃²×C₄	1	1	yes	characteristic, complemented
43	C₂²×C₃²	—	5	1	no	—
44	C₃²×C₄	—	5	1	no	—
45	C₃²×C₄	—	20	2	no	—
46	C₃²×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
47	#107	—	5	1	no	Sylow
48	C₂×C₃×C₅	C₃×C₄⋊C₄	1	4	yes	—
49	C₃×D₅	C₃×D₈	1	4	yes	—
50	C₃×D₅	C₃×Q₁₆	1	4	yes	—
51	C₂×C₃×C₄	—	5	4	no	—
52	C₂×C₃×C₄	—	10	8	no	—
53	C₃×C₈	—	5	4	no	—
54	C₃×C₈	C₃×AGL(1,𝔽₅)	1	4	yes	complemented
55	C₂×D₅	C₃²×D₄	1	1	yes	characteristic
56	AGL(1,𝔽₅)	—	4	2	no	—
57	C₄×C₅	C₂×C₃²×C₄	1	1	yes	characteristic
58	Dic₅	C₃²×Q₈	1	1	yes	characteristic
59	C₂×C₃²	—	5	1	no	—
60	C₂×C₃²	—	5	1	no	—
61	C₂×C₃²	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
62	C₂×C₈	—	5	1	no	—
63	C₄⋊C₄	—	5	2	no	—
64	C₃×C₅	C₃×#107	1	4	yes	complemented
65	C₂²×C₃	—	5	4	no	—
66	C₃×C₄	—	5	4	no	—
67	C₃×C₄	—	20	8	no	—
68	C₃×C₄	C₂×C₃×AGL(1,𝔽₅)	1	4	yes	—
69	C₂×C₅	C₃²×C₄⋊C₄	1	1	yes	characteristic
70	D₅	C₃²×D₈	1	1	yes	characteristic
71	D₅	C₃²×Q₁₆	1	1	yes	characteristic
72	C₃²	#3994	1	1	yes	characteristic, direct product factor, Sylow
73	C₂×C₄	—	5	1	no	—
74	C₂×C₄	—	10	2	no	—
75	C₈	—	5	1	no	—
76	C₈	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
77	C₂×C₃	—	5	4	no	—
78	C₂×C₃	—	5	4	no	—
79	C₂×C₃	C₃×C₄⋊AGL(1,𝔽₅)	1	4	yes	—
80	C₅	C₃²×#107	1	1	yes	characteristic, complemented, Sylow
81	C₂²	—	5	1	no	—
82	C₄	—	5	1	no	—
83	C₄	—	20	2	no	—
84	C₄	C₂×C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic
85	C₃	C₃×#3994	1	4	yes	direct product factor
86	C₂	—	5	1	no	—
87	C₂	—	5	1	no	—
88	C₂	C₃²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²	C₄⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂×C₃²×C₄
Frattini	C₄	C₂×C₃²×AGL(1,𝔽₅)
Fitting	C₃²×C₅×C₈	C₄
socle	C₂×C₃²×C₅	C₄⋊C₄
prime radical	C₂×C₃²×D₅	D₄
cosocle	C₄×D₅	C₂²×C₃²
hypercenter	C₃²×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃²×#107
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃² ◁ C₃²×C₄ ◁ C₃²×C₈

Complements

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

N	H ≅ G/N	type
3. C₃×#3994	C₃	direct (N × H)
6. C₃²×C₅×C₈	C₄	semidirect
7. C₃²×#168	C₄	semidirect
15. #3994	C₃²	direct (N × H)
20. C₃×C₅×C₈	C₃×C₄	semidirect
21. C₃×#168	C₃×C₄	semidirect
31. C₃²×C₈	AGL(1,𝔽₅)	semidirect
38. C₃²×C₅	#107	semidirect
41. C₅×C₈	C₃²×C₄	semidirect
42. #168	C₃²×C₄	semidirect
54. C₃×C₈	C₃×AGL(1,𝔽₅)	semidirect
64. C₃×C₅	C₃×#107	semidirect
72. C₃²	#3994	direct (N × H)
76. C₈	C₃²×AGL(1,𝔽₅)	semidirect
80. C₅	C₃²×#107	semidirect
85. C₃	C₃×#3994	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₄⋊AGL(1,𝔽₅)	2
C₃²×C₈×D₅	2
C₃×#3994	3
C₃²×#107	5

Subgroups — C32×#3994 #13086246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3994 #13086246