Subgroups — Q₈×C₃⋊Dic₁₅ #13088211

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	C₄⋊(C₃⋊Dic₁₅)	C₂	1	3	yes	maximal
3	C₄×C₃⋊Dic₁₅	C₂	1	3	yes	maximal
4	Q₈×Dic₁₅	—	3	4	no	maximal
5	C₃²×C₅×Q₈	C₄	1	4	yes	complemented
6	C₂×C₃²×C₄×C₅	C₂²	1	3	yes	—
7	C₂×C₃⋊Dic₁₅	C₂²	1	3	yes	—
8	C₂×C₃⋊Dic₁₅	C₂²	1	1	yes	characteristic
9	Q₈×C₃⋊Dic₃	—	5	1	no	maximal, Hall
10	C₂×C₃×C₅×Q₈	D₃	1	4	yes	—
11	C₄⋊Dic₁₅	—	3	12	no	—
12	C₄×Dic₁₅	—	3	12	no	—
13	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
14	C₃²×C₄×C₅	C₂×C₄	1	6	yes	—
15	C₃⋊Dic₁₅	—	2	3	no	—
16	C₃⋊Dic₁₅	Q₈	1	2	yes	direct product factor
17	Q₈×Dic₅	—	9	1	no	Hall
18	C₂×C₃²×Q₈	D₅	1	1	yes	characteristic
19	C₄⋊(C₃⋊Dic₃)	—	5	3	no	—
20	C₄×C₃⋊Dic₃	—	5	3	no	—
21	C₃×C₅×Q₈	Dic₃	1	16	yes	complemented
22	C₂×C₃×C₄×C₅	C₂×D₃	1	12	yes	—
23	C₂×Dic₁₅	—	3	4	no	—
24	C₂×Dic₁₅	—	3	12	no	—
25	Q₈×Dic₃	—	15	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	C₄⋊Dic₅	—	9	3	no	—
31	C₄×Dic₅	—	9	3	no	—
32	C₃²×Q₈	Dic₅	1	4	yes	complemented
33	C₂×C₃²×C₄	C₂×D₅	1	3	yes	—
34	C₂×C₃⋊Dic₃	—	5	1	no	—
35	C₂×C₃⋊Dic₃	—	5	3	no	—
36	C₂²×C₃×C₅	C₂²×D₃	1	4	yes	—
37	C₃×C₄×C₅	C₂×Dic₃	1	24	yes	—
38	Dic₁₅	—	3	8	no	—
39	Dic₁₅	—	6	12	no	—
40	C₂×C₃×Q₈	D₁₅	1	4	yes	—
41	C₄⋊Dic₃	—	15	12	no	—
42	C₄×Dic₃	—	15	12	no	—
43	C₃²×C₅	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
44	C₅×Q₈	C₃⋊Dic₃	1	4	yes	complemented
45	C₂×C₄×C₅	C₂×C₃⋊D₃	1	3	yes	—
46	C₂×Dic₅	—	9	1	no	—
47	C₂×Dic₅	—	9	3	no	—
48	C₂²×C₃²	C₂²×D₅	1	1	yes	characteristic
49	C₃²×C₄	C₂×Dic₅	1	6	yes	—
50	C₃⋊Dic₃	—	5	2	no	—
51	C₃⋊Dic₃	—	10	3	no	—
52	C₄×Q₈	—	45	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	Dic₁₅	1	16	yes	complemented
57	C₂×C₃×C₄	C₂×D₁₅	1	12	yes	—
58	C₂×Dic₃	—	15	4	no	—
59	C₂×Dic₃	—	15	12	no	—
60	C₂²×C₅	C₂²×C₃⋊D₃	1	1	yes	characteristic
61	C₄×C₅	C₂×C₃⋊Dic₃	1	6	yes	—
62	Dic₅	—	9	2	no	—
63	Dic₅	—	18	3	no	—
64	C₂×C₃²	Q₈×D₅	1	1	yes	characteristic
65	C₂×C₃²	#713	1	1	yes	characteristic
66	C₂×C₃²	C₂²×Dic₅	1	1	yes	characteristic
67	C₂×Q₈	C₃⋊D₁₅	1	1	yes	characteristic
68	C₄⋊C₄	—	45	3	no	—
69	C₄²	—	45	3	no	—
70	C₃×C₅	Q₈×Dic₃	1	4	yes	complemented
71	C₂²×C₃	C₂²×D₁₅	1	4	yes	—
72	C₃×C₄	C₂×Dic₁₅	1	24	yes	—
73	Dic₃	—	15	8	no	—
74	Dic₃	—	30	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	Q₈×Dic₅	1	1	yes	characteristic, complemented, Sylow
79	Q₈	C₃⋊Dic₁₅	1	4	yes	direct product factor
80	C₂×C₄	—	45	1	no	—
81	C₂×C₄	—	45	3	no	—
82	C₂×C₄	C₂×C₃⋊D₁₅	1	3	yes	—
83	C₂×C₃	Q₈×D₁₅	1	4	yes	—
84	C₂×C₃	#6821	1	4	yes	—
85	C₂×C₃	C₂²×Dic₁₅	1	4	yes	—
86	C₅	Q₈×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
87	C₂²	C₂²×C₃⋊D₁₅	1	1	yes	characteristic
88	C₄	—	45	2	no	—
89	C₄	—	90	3	no	—
90	C₄	C₂×C₃⋊Dic₁₅	1	6	yes	—
91	C₃	Q₈×Dic₁₅	1	4	yes	complemented
92	C₂	Q₈×C₃⋊D₁₅	1	1	yes	characteristic
93	C₂	#10624287	1	1	yes	characteristic
94	C₂	C₂²×C₃⋊Dic₁₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×C₃⋊D₁₅
commutator	C₂×C₃²×C₅	C₂²×C₄
Fitting	C₂×C₃²×C₅×Q₈	C₂
socle, prime radical, cosocle	C₂²×C₃²×C₅	C₂³
hypercenter	C₂×Q₈	C₃⋊D₁₅
hypocenter	C₃²×C₅	C₄×Q₈
LCS	G ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
5. C₃²×C₅×Q₈	C₄	semidirect
16. C₃⋊Dic₁₅	Q₈	direct (N × H)
21. C₃×C₅×Q₈	Dic₃	semidirect
32. C₃²×Q₈	Dic₅	semidirect
43. C₃²×C₅	C₄×Q₈	semidirect
44. C₅×Q₈	C₃⋊Dic₃	semidirect
56. C₃×Q₈	Dic₁₅	semidirect
70. C₃×C₅	Q₈×Dic₃	semidirect
78. C₃²	Q₈×Dic₅	semidirect
79. Q₈	C₃⋊Dic₁₅	direct (N × H)
86. C₅	Q₈×C₃⋊Dic₃	semidirect
91. C₃	Q₈×Dic₁₅	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
C₄⋊(C₃⋊Dic₁₅)	2
C₄×C₃⋊Dic₁₅	2
Q₈×Dic₁₅	3
Q₈×C₃⋊Dic₃	5

Subgroups — Q8×C3⋊Dic15 #13088211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₃⋊Dic₁₅ #13088211