Subgroups — Q₈×#6014 #13098295

Order 1600.

153 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#6014	C₂	1	3	yes	maximal
3	C₄×#6014	C₂	1	3	yes	maximal
4	C₂×Q₈×C₂₅	C₄	1	1	yes	characteristic
5	C₄⋊C₄×C₂₅	C₄	1	3	yes	—
6	C₄²×C₂₅	C₂²	1	3	yes	—
7	C₂×#6014	C₂²	1	3	yes	—
8	C₂×#6014	C₂²	1	1	yes	characteristic
9	Q₈×#168	—	5	1	no	maximal
10	Q₈×C₂₅	C₈	1	4	yes	complemented
11	C₂×C₄×C₂₅	C₂×C₄	1	3	yes	—
12	C₂×C₄×C₂₅	C₂×C₄	1	3	yes	—
13	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
14	#6014	—	2	3	no	—
15	#6014	Q₈	1	2	yes	direct product factor
16	C₄×C₅×Q₈	D₅	1	1	yes	characteristic
17	C₄⋊#168	—	5	3	no	—
18	C₄×#168	—	5	3	no	—
19	C₂²×C₂₅	C₂²×C₄	1	1	yes	characteristic
20	C₄×C₂₅	—	2	3	no	—
21	C₄×C₂₅	C₂×C₈	1	6	yes	—
22	C₄×C₂₅	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₂₅	#41	1	1	yes	characteristic
24	C₂×C₅×Q₈	Dic₅	1	1	yes	characteristic
25	C₅×C₄⋊C₄	Dic₅	1	3	yes	—
26	C₄²×C₅	C₂×D₅	1	3	yes	—
27	C₂×#168	—	5	1	no	—
28	C₂×#168	—	5	3	no	—
29	C₈×Q₈	—	25	1	no	Sylow
30	C₂×C₂₅	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₂₅	C₂²×C₈	1	1	yes	characteristic
32	C₂×C₂₅	#131	1	1	yes	characteristic
33	C₅×Q₈	#168	1	4	yes	—
34	C₂×C₄×C₅	C₂×Dic₅	1	3	yes	—
35	C₂×C₄×C₅	C₂×Dic₅	1	3	yes	—
36	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
37	#168	—	5	2	no	—
38	#168	—	10	3	no	—
39	C₄×Q₈	D₂₅	1	1	yes	characteristic
40	C₄⋊C₈	—	25	3	no	—
41	C₄×C₈	—	25	3	no	—
42	C₂₅	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₅	C₂²×Dic₅	1	1	yes	characteristic
44	C₄×C₅	—	2	3	no	—
45	C₄×C₅	C₂×#168	1	6	yes	—
46	C₄×C₅	Q₈×D₅	1	1	yes	characteristic
47	C₄×C₅	#713	1	1	yes	characteristic
48	C₂×Q₈	Dic₂₅	1	1	yes	characteristic
49	C₂×C₈	—	25	1	no	—
50	C₂×C₈	—	25	3	no	—
51	C₄⋊C₄	Dic₂₅	1	3	yes	—
52	C₄²	C₂×D₂₅	1	3	yes	—
53	C₂×C₅	C₂²×#168	1	1	yes	characteristic
54	C₂×C₅	Q₈×Dic₅	1	1	yes	characteristic
55	C₂×C₅	#4094	1	1	yes	characteristic
56	Q₈	#6014	1	4	yes	direct product factor
57	C₂×C₄	C₂×Dic₂₅	1	3	yes	—
58	C₂×C₄	C₂×Dic₂₅	1	3	yes	—
59	C₂×C₄	C₂²×D₂₅	1	1	yes	characteristic
60	C₈	—	25	2	no	—
61	C₈	—	50	3	no	—
62	C₅	Q₈×#168	1	1	yes	characteristic
63	C₂²	C₂²×Dic₂₅	1	1	yes	characteristic
64	C₄	—	2	3	no	—
65	C₄	C₂×#6014	1	6	yes	—
66	C₄	Q₈×D₂₅	1	1	yes	characteristic
67	C₄	#87748	1	1	yes	characteristic
68	C₂	C₂²×#6014	1	1	yes	characteristic
69	C₂	Q₈×Dic₂₅	1	1	yes	characteristic
70	C₂	#11716510	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₅
commutator	C₂×C₂₅	C₂²×C₈
Frattini	C₂×C₄×C₅	C₂²×D₅
Fitting	C₄×Q₈×C₂₅	C₂
socle, prime radical	C₂²×C₅	C₂²×Dic₅
cosocle	C₂×C₄×C₂₅	C₂³
hypercenter	C₄×Q₈	D₂₅
hypocenter	C₂₅	C₈×Q₈
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
10. Q₈×C₂₅	C₈	semidirect
15. #6014	Q₈	direct (N × H)
42. C₂₅	C₈×Q₈	semidirect
56. Q₈	#6014	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×Q₈×C₂₅	2
C₄⋊#6014	2
C₄×#6014	2
Q₈×#168	5

Subgroups — Q8×#6014 #13098295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#6014 #13098295