Subgroups — C₃²×#3968 #13084955

Order 1440.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃²×#681	C₂	1	2	yes	maximal
3	C₃×#3968	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅×Q₈	—	2	2	no	—
5	C₂×C₃²×C₄×C₅	C₄	1	2	yes	—
6	C₂×C₃²×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₃²×#168	—	2	2	no	—
8	C₃²×#101	—	5	1	no	maximal, Hall
9	C₂×C₃×C₅×Q₈	C₂×C₃	1	4	yes	—
10	C₃×#681	C₂×C₃	1	8	yes	—
11	C₂²×C₃²×C₅	C₂×C₄	1	1	yes	characteristic
12	C₃²×C₄×C₅	—	2	2	no	—
13	C₃²×C₄×C₅	D₄	1	2	yes	—
14	#3968	C₃²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃²×Q₈	D₅	1	1	yes	characteristic
16	C₃²×M₁₆	—	5	2	no	—
17	C₃×C₅×Q₈	—	2	8	no	—
18	C₂×C₃×C₄×C₅	C₃×C₄	1	8	yes	—
19	C₂×C₃×C₄×C₅	C₂²×C₃	1	4	yes	—
20	C₃×#168	—	2	8	no	—
21	C₃×#101	—	5	4	no	—
22	C₂×C₃²×C₅	—	2	1	no	—
23	C₂×C₃²×C₅	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₅×Q₈	C₂×C₃²	1	1	yes	characteristic
25	#681	C₂×C₃²	1	2	yes	—
26	C₃²×Q₈	—	2	2	no	—
27	C₂×C₃²×C₄	Dic₅	1	2	yes	—
28	C₂×C₃²×C₄	C₂×D₅	1	1	yes	characteristic
29	C₃²×C₈	—	10	2	no	—
30	C₂²×C₃×C₅	C₂×C₃×C₄	1	4	yes	—
31	C₃×C₄×C₅	—	2	8	no	—
32	C₃×C₄×C₅	C₃×D₄	1	8	yes	—
33	C₂×C₃×Q₈	C₃×D₅	1	4	yes	—
34	C₃×M₁₆	—	5	8	no	—
35	C₃²×C₅	#101	1	1	yes	characteristic, complemented, Hall
36	C₅×Q₈	—	2	2	no	—
37	C₂×C₄×C₅	C₃²×C₄	1	2	yes	—
38	C₂×C₄×C₅	C₂²×C₃²	1	1	yes	characteristic
39	#168	—	2	2	no	—
40	C₂²×C₃²	C₂×Dic₅	1	1	yes	characteristic
41	C₃²×C₄	—	2	2	no	—
42	C₃²×C₄	C₂²⋊D₅	1	2	yes	—
43	#101	—	5	1	no	Sylow
44	C₂×C₃×C₅	—	2	4	no	—
45	C₂×C₃×C₅	C₃×C₂²⋊C₄	1	4	yes	—
46	C₃×Q₈	—	2	8	no	—
47	C₂×C₃×C₄	C₃×Dic₅	1	8	yes	—
48	C₂×C₃×C₄	C₂×C₃×D₅	1	4	yes	—
49	C₃×C₈	—	10	8	no	—
50	C₂²×C₅	C₂×C₃²×C₄	1	1	yes	characteristic
51	C₄×C₅	—	2	2	no	—
52	C₄×C₅	C₃²×D₄	1	2	yes	—
53	C₂×C₃²	—	2	1	no	—
54	C₂×C₃²	C₂²⋊Dic₅	1	1	yes	characteristic
55	C₂×Q₈	C₃²×D₅	1	1	yes	characteristic
56	M₁₆	—	5	2	no	—
57	C₃×C₅	C₃×#101	1	4	yes	complemented
58	C₂²×C₃	C₂×C₃×Dic₅	1	4	yes	—
59	C₃×C₄	—	2	8	no	—
60	C₃×C₄	C₃×C₂²⋊D₅	1	8	yes	—
61	C₂×C₅	—	2	1	no	—
62	C₂×C₅	C₃²×C₂²⋊C₄	1	1	yes	characteristic
63	C₃²	#3968	1	1	yes	characteristic, direct product factor, Sylow
64	Q₈	—	2	2	no	—
65	C₂×C₄	C₃²×Dic₅	1	2	yes	—
66	C₂×C₄	C₂×C₃²×D₅	1	1	yes	characteristic
67	C₈	—	10	2	no	—
68	C₂×C₃	—	2	4	no	—
69	C₂×C₃	C₃×C₂²⋊Dic₅	1	4	yes	—
70	C₅	C₃²×#101	1	1	yes	characteristic, complemented, Sylow
71	C₂²	C₂×C₃²×Dic₅	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	C₃²×C₂²⋊D₅	1	2	yes	—
74	C₃	C₃×#3968	1	4	yes	direct product factor
75	C₂	—	2	1	no	—
76	C₂	C₃²×C₂²⋊Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²	C₂²⋊Dic₅
commutator	C₂²×C₅	C₂×C₃²×C₄
Frattini	C₂×C₄	C₂×C₃²×D₅
Fitting	C₂×C₃²×C₅×Q₈	C₂
socle	C₂×C₃²×C₅	C₂²⋊C₄
prime radical	C₂²×C₃²×C₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂²×C₃²
hypercenter	C₂×C₃²×Q₈	D₅
hypocenter	C₅	C₃²×#101
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃² ◁ C₂×C₃²×C₄ ◁ C₂×C₃²×Q₈

Complements

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

N	H ≅ G/N	type
3. C₃×#3968	C₃	direct (N × H)
14. #3968	C₃²	direct (N × H)
35. C₃²×C₅	#101	semidirect
57. C₃×C₅	C₃×#101	semidirect
63. C₃²	#3968	direct (N × H)
70. C₅	C₃²×#101	semidirect
74. C₃	C₃×#3968	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×C₅×Q₈	2
C₃²×#681	2
C₃×#3968	3
C₃²×#101	5

Subgroups — C32×#3968 #13084955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3968 #13084955