Subgroups — C₅×Q₈×C₃⋊Dic₃ #13088125

Order 1440.

420 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	C₅×C₄⋊(C₃⋊Dic₃)	C₂	1	3	yes	maximal
3	C₄×C₅×C₃⋊Dic₃	C₂	1	3	yes	maximal
4	C₅×Q₈×Dic₃	—	3	4	no	maximal
5	C₃²×C₅×Q₈	C₄	1	4	yes	complemented
6	C₂×C₃²×C₄×C₅	C₂²	1	3	yes	—
7	C₂×C₅×C₃⋊Dic₃	C₂²	1	3	yes	—
8	C₂×C₅×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
9	Q₈×C₃⋊Dic₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×Q₈	D₃	1	4	yes	—
11	C₅×C₄⋊Dic₃	—	3	12	no	—
12	C₄×C₅×Dic₃	—	3	12	no	—
13	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
14	C₃²×C₄×C₅	C₂×C₄	1	6	yes	—
15	C₅×C₃⋊Dic₃	—	2	3	no	—
16	C₅×C₃⋊Dic₃	Q₈	1	2	yes	direct product factor
17	C₄×C₅×Q₈	—	9	1	no	Hall
18	C₂×C₃²×Q₈	C₂×C₅	1	1	yes	characteristic
19	C₄⋊(C₃⋊Dic₃)	C₂×C₅	1	3	yes	—
20	C₄×C₃⋊Dic₃	C₂×C₅	1	3	yes	—
21	C₃×C₅×Q₈	Dic₃	1	16	yes	complemented
22	C₂×C₃×C₄×C₅	C₂×D₃	1	12	yes	—
23	C₂×C₅×Dic₃	—	3	4	no	—
24	C₂×C₅×Dic₃	—	3	12	no	—
25	Q₈×Dic₃	—	3	4	no	—
26	C₂×C₃²×C₅	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₃²×C₅	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₃²×C₅	#41	1	1	yes	characteristic
29	C₂×C₅×Q₈	C₃⋊D₃	1	1	yes	characteristic
30	C₅×C₄⋊C₄	—	9	3	no	—
31	C₄²×C₅	—	9	3	no	—
32	C₃²×Q₈	C₄×C₅	1	4	yes	complemented
33	C₂×C₃²×C₄	C₂²×C₅	1	3	yes	—
34	C₂×C₃⋊Dic₃	C₂²×C₅	1	3	yes	—
35	C₂×C₃⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
36	C₂²×C₃×C₅	C₂²×D₃	1	4	yes	—
37	C₃×C₄×C₅	C₂×Dic₃	1	24	yes	—
38	C₅×Dic₃	—	3	8	no	—
39	C₅×Dic₃	—	6	12	no	—
40	C₂×C₃×Q₈	C₅×D₃	1	4	yes	—
41	C₄⋊Dic₃	—	3	12	no	—
42	C₄×Dic₃	—	3	12	no	—
43	C₃²×C₅	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
44	C₅×Q₈	C₃⋊Dic₃	1	4	yes	direct product factor
45	C₂×C₄×C₅	—	9	1	no	—
46	C₂×C₄×C₅	—	9	3	no	—
47	C₂×C₄×C₅	C₂×C₃⋊D₃	1	3	yes	—
48	C₂²×C₃²	C₂³×C₅	1	1	yes	characteristic
49	C₃²×C₄	C₂×C₄×C₅	1	6	yes	—
50	C₃⋊Dic₃	—	2	3	no	—
51	C₃⋊Dic₃	C₅×Q₈	1	2	yes	direct product factor
52	C₄×Q₈	—	9	1	no	Sylow
53	C₂×C₃×C₅	D₃×Q₈	1	4	yes	—
54	C₂×C₃×C₅	#239	1	4	yes	—
55	C₂×C₃×C₅	C₂²×Dic₃	1	4	yes	—
56	C₃×Q₈	C₅×Dic₃	1	16	yes	complemented
57	C₂×C₃×C₄	C₂×C₅×D₃	1	12	yes	—
58	C₂×Dic₃	—	3	4	no	—
59	C₂×Dic₃	—	3	12	no	—
60	C₂²×C₅	C₂²×C₃⋊D₃	1	1	yes	characteristic
61	C₄×C₅	—	9	2	no	—
62	C₄×C₅	—	18	3	no	—
63	C₄×C₅	C₂×C₃⋊Dic₃	1	6	yes	—
64	C₂×C₃²	C₂²×C₄×C₅	1	1	yes	characteristic
65	C₂×C₃²	C₂×C₅×Q₈	1	1	yes	characteristic
66	C₂×C₃²	C₅×#41	1	1	yes	characteristic
67	C₂×Q₈	C₅×C₃⋊D₃	1	1	yes	characteristic
68	C₄⋊C₄	—	9	3	no	—
69	C₄²	—	9	3	no	—
70	C₃×C₅	Q₈×Dic₃	1	4	yes	complemented
71	C₂²×C₃	C₂²×C₅×D₃	1	4	yes	—
72	C₃×C₄	C₂×C₅×Dic₃	1	24	yes	—
73	Dic₃	—	3	8	no	—
74	Dic₃	—	6	12	no	—
75	C₂×C₅	Q₈×C₃⋊D₃	1	1	yes	characteristic
76	C₂×C₅	#3832	1	1	yes	characteristic
77	C₂×C₅	C₂²×C₃⋊Dic₃	1	1	yes	characteristic
78	C₃²	C₄×C₅×Q₈	1	1	yes	characteristic, complemented, Sylow
79	Q₈	C₅×C₃⋊Dic₃	1	4	yes	direct product factor
80	C₂×C₄	—	9	1	no	—
81	C₂×C₄	—	9	3	no	—
82	C₂×C₄	C₂×C₅×C₃⋊D₃	1	3	yes	—
83	C₂×C₃	C₅×D₃×Q₈	1	4	yes	—
84	C₂×C₃	C₅×#239	1	4	yes	—
85	C₂×C₃	C₂²×C₅×Dic₃	1	4	yes	—
86	C₅	Q₈×C₃⋊Dic₃	1	1	yes	characteristic, direct product factor, Sylow
87	C₂²	C₂²×C₅×C₃⋊D₃	1	1	yes	characteristic
88	C₄	—	9	2	no	—
89	C₄	—	18	3	no	—
90	C₄	C₂×C₅×C₃⋊Dic₃	1	6	yes	—
91	C₃	C₅×Q₈×Dic₃	1	4	yes	complemented
92	C₂	C₅×Q₈×C₃⋊D₃	1	1	yes	characteristic
93	C₂	C₅×#3832	1	1	yes	characteristic
94	C₂	C₂²×C₅×C₃⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×C₃⋊D₃
commutator	C₂×C₃²	C₂²×C₄×C₅
Frattini	C₂²	C₂²×C₅×C₃⋊D₃
Fitting	C₂×C₃²×C₅×Q₈	C₂
socle, prime radical	C₂²×C₃²×C₅	C₂³
cosocle	C₂²×C₃²	C₂³×C₅
hypercenter	C₂×C₅×Q₈	C₃⋊D₃
hypocenter	C₃²	C₄×C₅×Q₈
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×Q₈

Complements

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

N	H ≅ G/N	type
5. C₃²×C₅×Q₈	C₄	semidirect
9. Q₈×C₃⋊Dic₃	C₅	direct (N × H)
16. C₅×C₃⋊Dic₃	Q₈	direct (N × H)
21. C₃×C₅×Q₈	Dic₃	semidirect
32. C₃²×Q₈	C₄×C₅	semidirect
43. C₃²×C₅	C₄×Q₈	semidirect
44. C₅×Q₈	C₃⋊Dic₃	direct (N × H)
51. C₃⋊Dic₃	C₅×Q₈	direct (N × H)
56. C₃×Q₈	C₅×Dic₃	semidirect
70. C₃×C₅	Q₈×Dic₃	semidirect
78. C₃²	C₄×C₅×Q₈	semidirect
79. Q₈	C₅×C₃⋊Dic₃	direct (N × H)
86. C₅	Q₈×C₃⋊Dic₃	direct (N × H)
91. C₃	C₅×Q₈×Dic₃	semidirect

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
C₅×C₄⋊(C₃⋊Dic₃)	2
C₄×C₅×C₃⋊Dic₃	2
C₅×Q₈×Dic₃	3
Q₈×C₃⋊Dic₃	5

Subgroups — C5×Q8×C3⋊Dic3 #13088125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Q₈×C₃⋊Dic₃ #13088125