Subgroups — C₂×Q₈×#1039 #13107336

Order 1600.

1192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×Q₈	C₂	1	1	yes	maximal, characteristic
2	Q₈×#1039	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊#1039	C₂	1	3	yes	maximal
4	C₂×C₄×#1039	C₂	1	3	yes	maximal
5	C₂×C₅²×Q₈	C₄	1	8	yes	complemented
6	C₂×C₅²×Q₈	C₂²	1	4	yes	—
7	C₂²×C₄×C₅²	C₂²	1	3	yes	—
8	C₂²×#1039	C₂²	1	3	yes	—
9	C₂²×#1039	C₂²	1	1	yes	characteristic
10	C₄⋊#1039	C₂²	1	12	yes	—
11	C₄×#1039	C₂²	1	12	yes	—
12	C₂×Q₈×Dic₅	—	5	6	no	maximal
13	C₂³×C₅²	C₂³	1	1	yes	characteristic
14	C₅²×Q₈	C₂×C₄	1	16	yes	complemented
15	C₂×C₄×C₅²	C₂×C₄	1	12	yes	—
16	C₂×C₄×C₅²	C₂³	1	6	yes	—
17	C₂×#1039	—	2	6	no	—
18	C₂×#1039	Q₈	1	4	yes	direct product factor
19	C₂×#1039	C₂³	1	6	yes	—
20	C₂×#1039	C₂³	1	2	yes	—
21	C₂²×C₅×Q₈	D₅	1	6	yes	—
22	Q₈×Dic₅	—	5	48	no	—
23	C₂×C₄⋊Dic₅	—	5	18	no	—
24	C₂×C₄×Dic₅	—	5	18	no	—
25	C₂²×C₅²	C₂²×C₄	1	2	yes	—
26	C₂²×C₅²	C₂×Q₈	1	2	yes	—
27	C₂²×C₅²	#41	1	2	yes	—
28	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
29	C₄×C₅²	C₂²×C₄	1	12	yes	—
30	#1039	—	2	6	no	—
31	#1039	C₂×Q₈	1	4	yes	direct product factor
32	C₂×C₅×Q₈	Dic₅	1	48	yes	complemented
33	C₂×C₅×Q₈	C₂×D₅	1	24	yes	—
34	C₂²×C₄×C₅	C₂×D₅	1	18	yes	—
35	C₂²×Dic₅	—	5	6	no	—
36	C₂²×Dic₅	—	5	18	no	—
37	C₄⋊Dic₅	—	5	72	no	—
38	C₄×Dic₅	—	5	72	no	—
39	C₂×C₄×Q₈	—	25	1	no	Sylow
40	C₂×C₅²	C₄×Q₈	1	4	yes	complemented
41	C₂×C₅²	C₂³×C₄	1	1	yes	characteristic
42	C₂×C₅²	C₂²×Q₈	1	1	yes	characteristic
43	C₂×C₅²	C₂×#41	1	1	yes	characteristic
44	C₂³×C₅	C₂²×D₅	1	6	yes	—
45	C₅×Q₈	C₂×Dic₅	1	96	yes	complemented
46	C₂×C₄×C₅	C₂×Dic₅	1	72	yes	—
47	C₂×C₄×C₅	C₂²×D₅	1	36	yes	—
48	C₂×Dic₅	—	5	24	no	—
49	C₂×Dic₅	—	5	12	no	—
50	C₂×Dic₅	—	5	36	no	—
51	C₂×Dic₅	—	10	36	no	—
52	C₂²×Q₈	C₅⋊D₅	1	1	yes	characteristic
53	C₄×Q₈	—	25	8	no	—
54	C₂×C₄⋊C₄	—	25	3	no	—
55	C₂×C₄²	—	25	3	no	—
56	C₅²	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₅	Q₈×D₅	1	12	yes	—
58	C₂²×C₅	#713	1	12	yes	—
59	C₂²×C₅	C₂²×Dic₅	1	12	yes	—
60	C₂²×C₅	C₂³×D₅	1	6	yes	—
61	C₄×C₅	C₂²×Dic₅	1	72	yes	—
62	Dic₅	—	5	24	no	—
63	Dic₅	—	10	36	no	—
64	C₂×Q₈	#1039	1	8	yes	direct product factor
65	C₂×Q₈	C₂×C₅⋊D₅	1	4	yes	—
66	C₂²×C₄	—	25	1	no	—
67	C₂²×C₄	—	25	3	no	—
68	C₂²×C₄	C₂×C₅⋊D₅	1	3	yes	—
69	C₄⋊C₄	—	25	12	no	—
70	C₄²	—	25	12	no	—
71	C₂×C₅	Q₈×Dic₅	1	24	yes	complemented
72	C₂×C₅	C₂×Q₈×D₅	1	6	yes	—
73	C₂×C₅	C₂×#713	1	6	yes	—
74	C₂×C₅	C₂³×Dic₅	1	6	yes	—
75	C₂³	C₂²×C₅⋊D₅	1	1	yes	characteristic
76	Q₈	C₂×#1039	1	16	yes	direct product factor
77	C₂×C₄	—	25	4	no	—
78	C₂×C₄	—	25	2	no	—
79	C₂×C₄	—	25	6	no	—
80	C₂×C₄	—	50	6	no	—
81	C₂×C₄	C₂×#1039	1	12	yes	—
82	C₂×C₄	C₂²×C₅⋊D₅	1	6	yes	—
83	C₅	C₂×Q₈×Dic₅	1	6	yes	complemented
84	C₂²	Q₈×C₅⋊D₅	1	2	yes	—
85	C₂²	#87904	1	2	yes	—
86	C₂²	C₂²×#1039	1	2	yes	—
87	C₂²	C₂³×C₅⋊D₅	1	1	yes	characteristic
88	C₄	—	25	4	no	—
89	C₄	—	50	6	no	—
90	C₄	C₂²×#1039	1	12	yes	—
91	C₂	Q₈×#1039	1	4	yes	direct product factor
92	C₂	C₂×Q₈×C₅⋊D₅	1	1	yes	characteristic
93	C₂	C₂×#87904	1	1	yes	characteristic
94	C₂	C₂³×#1039	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₅⋊D₅
commutator	C₂×C₅²	C₂³×C₄
Frattini	C₂²	C₂³×C₅⋊D₅
Fitting	C₂²×C₅²×Q₈	C₂
socle, prime radical	C₂³×C₅²	C₂³
cosocle	C₂²×C₅²	C₂⁴
hypercenter	C₂²×Q₈	C₅⋊D₅
hypocenter	C₅²	C₂×C₄×Q₈
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. Q₈×#1039	C₂	direct (N × H)
5. C₂×C₅²×Q₈	C₄	semidirect
14. C₅²×Q₈	C₂×C₄	semidirect
18. C₂×#1039	Q₈	direct (N × H)
31. #1039	C₂×Q₈	direct (N × H)
32. C₂×C₅×Q₈	Dic₅	semidirect
40. C₂×C₅²	C₄×Q₈	semidirect
45. C₅×Q₈	C₂×Dic₅	semidirect
56. C₅²	C₂×C₄×Q₈	semidirect
64. C₂×Q₈	#1039	direct (N × H)
71. C₂×C₅	Q₈×Dic₅	semidirect
76. Q₈	C₂×#1039	direct (N × H)
83. C₅	C₂×Q₈×Dic₅	semidirect
91. C₂	Q₈×#1039	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅²×Q₈	2
Q₈×#1039	2
C₂×C₄⋊#1039	2
C₂×C₄×#1039	2
C₂×Q₈×Dic₅	5

Subgroups — C2×Q8×#1039 #13107336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×#1039 #13107336