Subgroups — C₃²×#4022 #13087801

Order 1440.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#685	C₂	1	3	yes	maximal
3	C₃²×#683	C₂	1	3	yes	maximal, complemented
4	C₃×#4022	C₃	1	4	yes	maximal, direct product factor
5	C₂²×C₃²×D₅	C₂²	1	1	yes	characteristic
6	C₂×C₃²×C₄×C₅	C₂²	1	3	yes	—
7	C₂×C₃²×Dic₅	C₂²	1	3	yes	—
8	C₃²×#126	—	5	1	no	maximal, Hall
9	C₃×C₄²×C₅	C₂×C₃	1	4	yes	complemented
10	C₃×#685	C₂×C₃	1	12	yes	—
11	C₃×#683	C₂×C₃	1	12	yes	complemented
12	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
13	C₂×C₃²×D₅	—	2	3	no	—
14	C₃²×C₄×C₅	—	2	3	no	—
15	C₃²×Dic₅	—	2	3	no	—
16	#4022	C₃²	1	1	yes	characteristic, direct product factor, Hall
17	C₃²×C₄⋊C₄	—	5	3	no	—
18	C₃²×C₂²⋊C₄	—	5	3	no	—
19	C₃²×C₄²	D₅	1	1	yes	characteristic, complemented
20	C₂²×C₃×D₅	C₂²×C₃	1	4	yes	—
21	C₂×C₃×C₄×C₅	C₂²×C₃	1	12	yes	—
22	C₂×C₃×Dic₅	C₂²×C₃	1	12	yes	—
23	C₃×#126	—	5	4	no	—
24	C₂×C₃²×C₅	#41	1	3	yes	—
25	C₃²×D₅	—	4	1	no	—
26	C₄²×C₅	C₂×C₃²	1	1	yes	characteristic, complemented
27	#685	C₂×C₃²	1	3	yes	—
28	#683	C₂×C₃²	1	3	yes	complemented
29	C₂³×C₃²	—	5	1	no	—
30	C₂×C₃²×C₄	—	5	3	no	—
31	C₂×C₃²×C₄	C₂×D₅	1	3	yes	—
32	C₂²×C₃×C₅	C₂³×C₃	1	4	yes	—
33	C₂×C₃×D₅	—	2	12	no	—
34	C₃×C₄×C₅	—	2	12	no	—
35	C₃×Dic₅	—	2	12	no	—
36	C₃×C₄⋊C₄	—	5	12	no	—
37	C₃×C₂²⋊C₄	—	5	12	no	—
38	C₃×C₄²	C₃×D₅	1	4	yes	complemented
39	C₃²×C₅	#126	1	1	yes	characteristic, complemented, Hall
40	C₂²×D₅	C₂²×C₃²	1	1	yes	characteristic
41	C₂×C₄×C₅	C₂²×C₃²	1	3	yes	—
42	C₂×Dic₅	C₂²×C₃²	1	3	yes	—
43	C₂²×C₃²	—	10	3	no	—
44	C₂²×C₃²	C₂²×D₅	1	1	yes	characteristic
45	C₃²×C₄	—	2	3	no	—
46	C₃²×C₄	—	10	3	no	—
47	#126	—	5	1	no	Sylow
48	C₂×C₃×C₅	C₃×#41	1	12	yes	—
49	C₃×D₅	—	4	4	no	—
50	C₂³×C₃	—	5	4	no	—
51	C₂×C₃×C₄	—	5	12	no	—
52	C₂×C₃×C₄	C₂×C₃×D₅	1	12	yes	—
53	C₂²×C₅	C₂³×C₃²	1	1	yes	characteristic
54	C₂×D₅	—	2	3	no	—
55	C₄×C₅	—	2	3	no	—
56	Dic₅	—	2	3	no	—
57	C₂×C₃²	—	20	1	no	—
58	C₂×C₃²	#709	1	3	yes	—
59	C₄⋊C₄	—	5	3	no	—
60	C₂²⋊C₄	—	5	3	no	—
61	C₄²	C₃²×D₅	1	1	yes	characteristic, complemented
62	C₃×C₅	C₃×#126	1	4	yes	complemented
63	C₂²×C₃	—	10	12	no	—
64	C₂²×C₃	C₂²×C₃×D₅	1	4	yes	—
65	C₃×C₄	—	2	12	no	—
66	C₃×C₄	—	10	12	no	—
67	C₂×C₅	C₃²×#41	1	3	yes	—
68	D₅	—	4	1	no	—
69	C₃²	#4022	1	1	yes	characteristic, direct product factor, Sylow
70	C₂³	—	5	1	no	—
71	C₂×C₄	—	5	3	no	—
72	C₂×C₄	C₂×C₃²×D₅	1	3	yes	—
73	C₂×C₃	—	20	4	no	—
74	C₂×C₃	C₃×#709	1	12	yes	—
75	C₅	C₃²×#126	1	1	yes	characteristic, complemented, Sylow
76	C₂²	—	10	3	no	—
77	C₂²	C₂²×C₃²×D₅	1	1	yes	characteristic
78	C₄	—	2	3	no	—
79	C₄	—	10	3	no	—
80	C₃	C₃×#4022	1	4	yes	direct product factor
81	C₂	—	20	1	no	—
82	C₂	C₃²×#709	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃²	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂³×C₃²
Frattini	C₂²	C₂²×C₃²×D₅
Fitting	C₃²×C₄²×C₅	C₂
socle	C₂²×C₃²×C₅	C₂³
prime radical	C₂²×C₃²×D₅	C₂²
hypercenter	C₃²×C₄²	D₅
hypocenter	C₅	C₃²×#126
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₄²×C₅	C₂	semidirect
3. C₃²×#683	C₂	semidirect
4. C₃×#4022	C₃	direct (N × H)
9. C₃×C₄²×C₅	C₂×C₃	semidirect
11. C₃×#683	C₂×C₃	semidirect
16. #4022	C₃²	direct (N × H)
19. C₃²×C₄²	D₅	semidirect
26. C₄²×C₅	C₂×C₃²	semidirect
28. #683	C₂×C₃²	semidirect
38. C₃×C₄²	C₃×D₅	semidirect
39. C₃²×C₅	#126	semidirect
61. C₄²	C₃²×D₅	semidirect
62. C₃×C₅	C₃×#126	semidirect
69. C₃²	#4022	direct (N × H)
75. C₅	C₃²×#126	semidirect
80. C₃	C₃×#4022	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×C₄²×C₅	2
C₃²×#685	2
C₃²×#683	2
C₃×#4022	3
C₃²×#126	5

Subgroups — C32×#4022 #13087801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#4022 #13087801