Subgroups — C₅×Q₈×C₃⋊C₈ #11750522

Order 960.

204 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×C₄⋊(C₃⋊C₈)	C₂	1	3	yes	maximal
3	C₄×C₅×C₃⋊C₈	C₂	1	3	yes	maximal
4	C₅×C₈×Q₈	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅×Q₈	C₄	1	1	yes	characteristic
6	C₃×C₅×C₄⋊C₄	C₄	1	3	yes	—
7	C₃×C₄²×C₅	C₂²	1	3	yes	—
8	C₂×C₅×C₃⋊C₈	C₂²	1	3	yes	—
9	C₂×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
10	Q₈×C₃⋊C₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₄×C₅×Q₈	D₃	1	1	yes	characteristic
12	C₅×C₄⋊C₈	—	3	3	no	—
13	C₄×C₅×C₈	—	3	3	no	—
14	C₃×C₅×Q₈	C₈	1	4	yes	complemented
15	C₂×C₃×C₄×C₅	C₂×C₄	1	3	yes	—
16	C₂×C₃×C₄×C₅	C₂×C₄	1	3	yes	—
17	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
18	C₅×C₃⋊C₈	—	2	3	no	—
19	C₅×C₃⋊C₈	Q₈	1	2	yes	direct product factor
20	C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
21	C₄⋊(C₃⋊C₈)	C₂×C₅	1	3	yes	—
22	C₄×C₃⋊C₈	C₂×C₅	1	3	yes	—
23	C₂×C₅×Q₈	Dic₃	1	1	yes	characteristic
24	C₂×C₅×C₈	—	3	1	no	—
25	C₂×C₅×C₈	—	3	3	no	—
26	C₅×C₄⋊C₄	Dic₃	1	3	yes	—
27	C₄²×C₅	C₂×D₃	1	3	yes	—
28	C₈×Q₈	—	3	1	no	Sylow
29	C₂²×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
30	C₃×C₄×C₅	—	2	3	no	—
31	C₃×C₄×C₅	C₂×C₈	1	6	yes	—
32	C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
33	C₃×C₄×C₅	#41	1	1	yes	characteristic
34	C₂×C₃×Q₈	C₄×C₅	1	1	yes	characteristic
35	C₃×C₄⋊C₄	C₄×C₅	1	3	yes	—
36	C₃×C₄²	C₂²×C₅	1	3	yes	—
37	C₂×C₃⋊C₈	C₂²×C₅	1	3	yes	—
38	C₂×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
39	C₅×Q₈	C₃⋊C₈	1	4	yes	direct product factor
40	C₂×C₄×C₅	C₂×Dic₃	1	3	yes	—
41	C₂×C₄×C₅	C₂×Dic₃	1	3	yes	—
42	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
43	C₅×C₈	—	3	2	no	—
44	C₅×C₈	—	6	3	no	—
45	C₄×Q₈	C₅×D₃	1	1	yes	characteristic
46	C₄⋊C₈	—	3	3	no	—
47	C₄×C₈	—	3	3	no	—
48	C₂×C₃×C₅	C₄×Q₈	1	1	yes	characteristic
49	C₂×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
50	C₂×C₃×C₅	#131	1	1	yes	characteristic
51	C₃×Q₈	C₅×C₈	1	4	yes	complemented
52	C₂×C₃×C₄	C₂×C₄×C₅	1	3	yes	—
53	C₂×C₃×C₄	C₂×C₄×C₅	1	3	yes	—
54	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
55	C₃⋊C₈	—	2	3	no	—
56	C₃⋊C₈	C₅×Q₈	1	2	yes	direct product factor
57	C₂²×C₅	C₂²×Dic₃	1	1	yes	characteristic
58	C₄×C₅	—	2	3	no	—
59	C₄×C₅	C₂×C₃⋊C₈	1	6	yes	—
60	C₄×C₅	D₃×Q₈	1	1	yes	characteristic
61	C₄×C₅	#239	1	1	yes	characteristic
62	C₂×Q₈	C₅×Dic₃	1	1	yes	characteristic
63	C₂×C₈	—	3	1	no	—
64	C₂×C₈	—	3	3	no	—
65	C₄⋊C₄	C₅×Dic₃	1	3	yes	—
66	C₄²	C₂×C₅×D₃	1	3	yes	—
67	C₃×C₅	C₈×Q₈	1	1	yes	characteristic, complemented, Hall
68	C₂²×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
69	C₃×C₄	—	2	3	no	—
70	C₃×C₄	C₂×C₅×C₈	1	6	yes	—
71	C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
72	C₃×C₄	C₅×#41	1	1	yes	characteristic
73	C₂×C₅	C₂²×C₃⋊C₈	1	1	yes	characteristic
74	C₂×C₅	Q₈×Dic₃	1	1	yes	characteristic
75	C₂×C₅	#948	1	1	yes	characteristic
76	Q₈	C₅×C₃⋊C₈	1	4	yes	direct product factor
77	C₂×C₄	C₂×C₅×Dic₃	1	3	yes	—
78	C₂×C₄	C₂×C₅×Dic₃	1	3	yes	—
79	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
80	C₈	—	3	2	no	—
81	C₈	—	6	3	no	—
82	C₂×C₃	C₄×C₅×Q₈	1	1	yes	characteristic
83	C₂×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
84	C₂×C₃	C₅×#131	1	1	yes	characteristic
85	C₅	Q₈×C₃⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
86	C₂²	C₂²×C₅×Dic₃	1	1	yes	characteristic
87	C₄	—	2	3	no	—
88	C₄	C₂×C₅×C₃⋊C₈	1	6	yes	—
89	C₄	C₅×D₃×Q₈	1	1	yes	characteristic
90	C₄	C₅×#239	1	1	yes	characteristic
91	C₃	C₅×C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
92	C₂	C₂²×C₅×C₃⋊C₈	1	1	yes	characteristic
93	C₂	C₅×Q₈×Dic₃	1	1	yes	characteristic
94	C₂	C₅×#948	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₃
commutator	C₂×C₃	C₂²×C₅×C₈
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×Q₈	C₂
socle, prime radical	C₂²×C₃×C₅	C₂²×C₄
cosocle	C₂×C₃×C₄	C₂³×C₅
hypercenter	C₄×C₅×Q₈	D₃
hypocenter	C₃	C₅×C₈×Q₈
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×Q₈

Complements

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

N	H ≅ G/N	type
10. Q₈×C₃⋊C₈	C₅	direct (N × H)
14. C₃×C₅×Q₈	C₈	semidirect
19. C₅×C₃⋊C₈	Q₈	direct (N × H)
39. C₅×Q₈	C₃⋊C₈	direct (N × H)
51. C₃×Q₈	C₅×C₈	semidirect
56. C₃⋊C₈	C₅×Q₈	direct (N × H)
67. C₃×C₅	C₈×Q₈	semidirect
76. Q₈	C₅×C₃⋊C₈	direct (N × H)
85. C₅	Q₈×C₃⋊C₈	direct (N × H)
91. C₃	C₅×C₈×Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₅×Q₈	2
C₅×C₄⋊(C₃⋊C₈)	2
C₄×C₅×C₃⋊C₈	2
C₅×C₈×Q₈	3
Q₈×C₃⋊C₈	5

Subgroups — C5×Q8×C3⋊C8 #11750522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Q₈×C₃⋊C₈ #11750522