Subgroups — C₃²×#3995 #13086247

Order 1440.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#700	C₂	1	2	yes	maximal
2	C₃²×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	C₃×#3995	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₄×D₅	C₂²	1	1	yes	characteristic
5	C₃²×#170	—	2	2	no	—
6	C₃²×C₅×C₈	C₄	1	1	yes	characteristic
7	C₃²×#168	C₄	1	1	yes	characteristic
8	C₃²×#108	—	5	1	no	maximal, Hall
9	C₃×#700	C₂×C₃	1	8	yes	—
10	C₃×C₈×D₅	C₂×C₃	1	4	yes	—
11	C₂×C₃²×D₅	Q₈	1	1	yes	characteristic
12	C₃²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
13	C₃²×Dic₅	D₄	1	1	yes	characteristic
14	#3995	C₃²	1	1	yes	characteristic, direct product factor, Hall
15	C₃²×M₁₆	—	5	2	no	—
16	C₂×C₃²×C₈	—	5	1	no	—
17	C₃×C₄×D₅	C₂²×C₃	1	4	yes	—
18	C₃×#170	—	2	8	no	—
19	C₃×C₅×C₈	C₃×C₄	1	4	yes	—
20	C₃×#168	C₃×C₄	1	4	yes	—
21	C₃×#108	—	5	4	no	—
22	C₂×C₃²×C₅	C₄⋊C₄	1	1	yes	characteristic
23	C₃²×D₅	—	2	1	no	—
24	#700	C₂×C₃²	1	2	yes	—
25	C₈×D₅	C₂×C₃²	1	1	yes	characteristic
26	C₂×C₃²×C₄	—	5	1	no	—
27	C₃²×C₈	—	5	1	no	—
28	C₃²×C₈	—	10	2	no	—
29	C₃²×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
30	C₂×C₃×D₅	C₃×Q₈	1	4	yes	—
31	C₃×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
32	C₃×Dic₅	C₃×D₄	1	4	yes	—
33	C₃×M₁₆	—	5	8	no	—
34	C₂×C₃×C₈	—	5	4	no	—
35	C₃²×C₅	#108	1	1	yes	characteristic, complemented, Hall
36	C₄×D₅	C₂²×C₃²	1	1	yes	characteristic
37	#170	—	2	2	no	—
38	C₅×C₈	C₃²×C₄	1	1	yes	characteristic
39	#168	C₃²×C₄	1	1	yes	characteristic
40	C₂²×C₃²	—	5	1	no	—
41	C₃²×C₄	—	5	1	no	—
42	C₃²×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
43	#108	—	5	1	no	Sylow
44	C₂×C₃×C₅	C₃×C₄⋊C₄	1	4	yes	—
45	C₃×D₅	—	2	4	no	—
46	C₂×C₃×C₄	—	5	4	no	—
47	C₃×C₈	—	5	4	no	—
48	C₃×C₈	—	10	8	no	—
49	C₃×C₈	C₃×AGL(1,𝔽₅)	1	4	yes	—
50	C₂×D₅	C₃²×Q₈	1	1	yes	characteristic
51	C₄×C₅	C₂×C₃²×C₄	1	1	yes	characteristic
52	Dic₅	C₃²×D₄	1	1	yes	characteristic
53	C₂×C₃²	—	10	1	no	—
54	C₂×C₃²	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
55	M₁₆	—	5	2	no	—
56	C₂×C₈	—	5	1	no	—
57	C₃×C₅	C₃×#108	1	4	yes	complemented
58	C₂²×C₃	—	5	4	no	—
59	C₃×C₄	—	5	4	no	—
60	C₃×C₄	C₂×C₃×AGL(1,𝔽₅)	1	4	yes	—
61	C₂×C₅	C₃²×C₄⋊C₄	1	1	yes	characteristic
62	D₅	—	2	1	no	—
63	C₃²	#3995	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₄	—	5	1	no	—
65	C₈	—	5	1	no	—
66	C₈	—	10	2	no	—
67	C₈	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic
68	C₂×C₃	—	10	4	no	—
69	C₂×C₃	C₃×C₄⋊AGL(1,𝔽₅)	1	4	yes	—
70	C₅	C₃²×#108	1	1	yes	characteristic, complemented, Sylow
71	C₂²	—	5	1	no	—
72	C₄	—	5	1	no	—
73	C₄	C₂×C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic
74	C₃	C₃×#3995	1	4	yes	direct product factor
75	C₂	—	10	1	no	—
76	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	Q₈
cosocle	C₄×D₅	C₂²×C₃²
hypercenter	C₃²×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃²×#108
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×#3995	C₃	direct (N × H)
14. #3995	C₃²	direct (N × H)
35. C₃²×C₅	#108	semidirect
57. C₃×C₅	C₃×#108	semidirect
63. C₃²	#3995	direct (N × H)
70. C₅	C₃²×#108	semidirect
74. C₃	C₃×#3995	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×#700	2
C₃²×C₈×D₅	2
C₃×#3995	3
C₃²×#108	5

Subgroups — C32×#3995 #13086247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3995 #13086247