Subgroups — C₃²×#4005 #13086257

Order 1440.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×Dic₁₀	C₂	1	1	yes	maximal, characteristic
2	C₃²×#704	C₂	1	2	yes	maximal
3	C₃×#4005	C₃	1	4	yes	maximal, direct product factor
4	C₂×C₃²×C₄×C₅	C₄	1	1	yes	characteristic
5	C₂×C₃²×Dic₅	C₄	1	1	yes	characteristic
6	C₂×C₃²×Dic₅	C₂²	1	1	yes	characteristic
7	C₃²×Dic₁₀	—	2	2	no	—
8	C₃²×#170	—	2	2	no	—
9	C₃²×#101	—	5	1	no	maximal, Hall
10	C₂×C₃×Dic₁₀	C₂×C₃	1	4	yes	—
11	C₃×#704	C₂×C₃	1	8	yes	—
12	C₂²×C₃²×C₅	C₂×C₄	1	1	yes	characteristic
13	C₃²×C₄×C₅	—	2	1	no	—
14	C₃²×Dic₅	—	2	1	no	—
15	C₃²×Dic₅	D₄	1	2	yes	—
16	#4005	C₃²	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃²×Q₈	—	5	1	no	—
18	C₃²×M₁₆	—	5	2	no	—
19	C₂×C₃×C₄×C₅	C₃×C₄	1	4	yes	—
20	C₂×C₃×Dic₅	C₃×C₄	1	4	yes	—
21	C₂×C₃×Dic₅	C₂²×C₃	1	4	yes	—
22	C₃×Dic₁₀	—	2	8	no	—
23	C₃×#170	—	2	8	no	—
24	C₃×#101	—	5	4	no	—
25	C₂×C₃²×C₅	—	2	1	no	—
26	C₂×C₃²×C₅	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₁₀	C₂×C₃²	1	1	yes	characteristic
28	#704	C₂×C₃²	1	2	yes	—
29	C₃²×Q₈	—	10	2	no	—
30	C₂×C₃²×C₄	—	5	1	no	—
31	C₂×C₃²×C₄	—	5	1	no	—
32	C₂×C₃²×C₄	AGL(1,𝔽₅)	1	1	yes	characteristic
33	C₃²×C₈	—	10	2	no	—
34	C₂²×C₃×C₅	C₂×C₃×C₄	1	4	yes	—
35	C₃×C₄×C₅	—	2	4	no	—
36	C₃×Dic₅	—	2	4	no	—
37	C₃×Dic₅	C₃×D₄	1	8	yes	—
38	C₂×C₃×Q₈	—	5	4	no	—
39	C₃×M₁₆	—	5	8	no	—
40	C₃²×C₅	#101	1	1	yes	characteristic, complemented, Hall
41	C₂×C₄×C₅	C₃²×C₄	1	1	yes	characteristic
42	C₂×Dic₅	C₃²×C₄	1	1	yes	characteristic
43	C₂×Dic₅	C₂²×C₃²	1	1	yes	characteristic
44	Dic₁₀	—	2	2	no	—
45	#170	—	2	2	no	—
46	C₂²×C₃²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
47	C₃²×C₄	—	2	1	no	—
48	C₃²×C₄	—	5	2	no	—
49	C₃²×C₄	—	10	1	no	—
50	#101	—	5	1	no	Sylow
51	C₂×C₃×C₅	—	2	4	no	—
52	C₂×C₃×C₅	C₃×C₂²⋊C₄	1	4	yes	—
53	C₃×Q₈	—	10	8	no	—
54	C₂×C₃×C₄	—	5	4	no	—
55	C₂×C₃×C₄	—	5	4	no	—
56	C₂×C₃×C₄	C₃×AGL(1,𝔽₅)	1	4	yes	—
57	C₃×C₈	—	10	8	no	—
58	C₂²×C₅	C₂×C₃²×C₄	1	1	yes	characteristic
59	C₄×C₅	—	2	1	no	—
60	Dic₅	—	2	1	no	—
61	Dic₅	C₃²×D₄	1	2	yes	—
62	C₂×C₃²	—	2	1	no	—
63	C₂×C₃²	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
64	C₂×Q₈	—	5	1	no	—
65	M₁₆	—	5	2	no	—
66	C₃×C₅	C₃×#101	1	4	yes	complemented
67	C₂²×C₃	C₂×C₃×AGL(1,𝔽₅)	1	4	yes	—
68	C₃×C₄	—	2	4	no	—
69	C₃×C₄	—	5	8	no	—
70	C₃×C₄	—	10	4	no	—
71	C₂×C₅	—	2	1	no	—
72	C₂×C₅	C₃²×C₂²⋊C₄	1	1	yes	characteristic
73	C₃²	#4005	1	1	yes	characteristic, direct product factor, Sylow
74	Q₈	—	10	2	no	—
75	C₂×C₄	—	5	1	no	—
76	C₂×C₄	—	5	1	no	—
77	C₂×C₄	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic
78	C₈	—	10	2	no	—
79	C₂×C₃	—	2	4	no	—
80	C₂×C₃	C₃×C₂²⋊AGL(1,𝔽₅)	1	4	yes	—
81	C₅	C₃²×#101	1	1	yes	characteristic, complemented, Sylow
82	C₂²	C₂×C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	5	2	no	—
85	C₄	—	10	1	no	—
86	C₃	C₃×#4005	1	4	yes	direct product factor
87	C₂	—	2	1	no	—
88	C₂	C₃²×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²	C₂²⋊AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂×C₃²×C₄
Frattini	C₂²	C₂×C₃²×AGL(1,𝔽₅)
Fitting	C₂×C₃²×C₄×C₅	C₄
socle	C₂×C₃²×C₅	C₂²⋊C₄
prime radical	C₂²×C₃²×C₅	C₂×C₄
cosocle	C₂×Dic₅	C₂²×C₃²
hypercenter	C₂×C₃²×C₄	AGL(1,𝔽₅)
hypocenter	C₅	C₃²×#101
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃² ◁ C₂²×C₃² ◁ C₂×C₃²×C₄

Complements

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

N	H ≅ G/N	type
3. C₃×#4005	C₃	direct (N × H)
16. #4005	C₃²	direct (N × H)
40. C₃²×C₅	#101	semidirect
66. C₃×C₅	C₃×#101	semidirect
73. C₃²	#4005	direct (N × H)
81. C₅	C₃²×#101	semidirect
86. C₃	C₃×#4005	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×Dic₁₀	2
C₃²×#704	2
C₃×#4005	3
C₃²×#101	5

Subgroups — C32×#4005 #13086257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#4005 #13086257