Subgroups — C₂×#11716685 #13102967

Order 1600.

520 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#1039	C₂	1	2	yes	maximal
3	#11716685	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic
5	C₂²×#1039	—	2	2	no	—
6	C₂×C₅²×C₈	C₄	1	4	yes	complemented
7	C₂×C₅²×C₈	C₂²	1	2	yes	—
8	C₄⋊#1039	—	2	2	no	—
9	C₄⋊#1039	C₂²	1	4	yes	—
10	C₂×#3950	—	5	6	no	maximal
11	C₂³×C₅²	D₄	1	1	yes	characteristic
12	C₂×C₄×C₅²	C₂×C₄	1	2	yes	—
13	C₂×C₄×C₅²	D₄	1	1	yes	characteristic
14	C₂×C₄×C₅²	Q₈	1	2	yes	—
15	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
16	C₂×#1039	—	2	4	no	—
17	C₂×#1039	—	4	4	no	—
18	C₅²×C₈	C₂×C₄	1	4	yes	complemented
19	C₂²×C₅×C₈	D₅	1	6	yes	—
20	C₂×C₄⋊Dic₅	—	5	12	no	—
21	#3950	—	5	24	no	—
22	C₂²×C₅²	C₄⋊C₄	1	2	yes	—
23	C₂²×C₅²	D₈	1	2	yes	—
24	C₂²×C₅²	Q₁₆	1	2	yes	—
25	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
26	C₄×C₅²	C₄⋊C₄	1	2	yes	—
27	C₄×C₅²	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₅²	C₂×Q₈	1	1	yes	characteristic
29	#1039	—	4	4	no	—
30	C₂²×C₄×C₅	C₂×D₅	1	6	yes	—
31	C₂²×Dic₅	—	10	12	no	—
32	C₂×C₅×C₈	Dic₅	1	24	yes	complemented
33	C₂×C₅×C₈	C₂×D₅	1	12	yes	—
34	C₄⋊Dic₅	—	5	24	no	—
35	C₄⋊Dic₅	—	10	12	no	—
36	C₂×#107	—	25	1	no	Sylow
37	C₂×C₅²	#107	1	4	yes	complemented
38	C₂×C₅²	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₅²	C₂×D₈	1	1	yes	characteristic
40	C₂×C₅²	C₂×Q₁₆	1	1	yes	characteristic
41	C₂³×C₅	D₂₀	1	6	yes	—
42	C₂×C₄×C₅	Dic₁₀	1	12	yes	—
43	C₂×C₄×C₅	D₂₀	1	6	yes	—
44	C₂×C₄×C₅	C₂×Dic₅	1	12	yes	—
45	C₂×C₄×C₅	C₂²×D₅	1	6	yes	—
46	C₂×Dic₅	—	10	24	no	—
47	C₂×Dic₅	—	20	24	no	—
48	C₅×C₈	C₂×Dic₅	1	24	yes	complemented
49	C₂²×C₈	C₅⋊D₅	1	1	yes	characteristic
50	C₂×C₄⋊C₄	—	25	2	no	—
51	#107	—	25	4	no	—
52	C₅²	C₂×#107	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₅	D₄₀	1	12	yes	—
54	C₂²×C₅	Dic₂₀	1	12	yes	—
55	C₂²×C₅	C₄⋊Dic₅	1	12	yes	—
56	C₂²×C₅	C₂×D₂₀	1	6	yes	—
57	C₄×C₅	C₄⋊Dic₅	1	12	yes	—
58	C₄×C₅	C₂×Dic₁₀	1	6	yes	—
59	C₄×C₅	C₂²×Dic₅	1	6	yes	—
60	Dic₅	—	20	24	no	—
61	C₂²×C₄	—	50	2	no	—
62	C₂²×C₄	C₂×C₅⋊D₅	1	1	yes	characteristic
63	C₂×C₈	#1039	1	4	yes	complemented
64	C₂×C₈	C₂×C₅⋊D₅	1	2	yes	—
65	C₄⋊C₄	—	25	4	no	—
66	C₄⋊C₄	—	50	2	no	—
67	C₂×C₅	#3950	1	24	yes	complemented
68	C₂×C₅	C₂×D₄₀	1	6	yes	—
69	C₂×C₅	C₂×Dic₂₀	1	6	yes	—
70	C₂×C₅	C₂×C₄⋊Dic₅	1	6	yes	—
71	C₂³	C₄⋊(C₅⋊D₅)	1	1	yes	characteristic
72	C₂×C₄	—	50	4	no	—
73	C₂×C₄	—	100	4	no	—
74	C₂×C₄	#6045	1	2	yes	—
75	C₂×C₄	C₄⋊(C₅⋊D₅)	1	1	yes	characteristic
76	C₂×C₄	C₂×#1039	1	2	yes	—
77	C₂×C₄	C₂²×C₅⋊D₅	1	1	yes	characteristic
78	C₈	C₂×#1039	1	4	yes	complemented
79	C₅	C₂×#3950	1	6	yes	complemented
80	C₂²	#87801	1	2	yes	—
81	C₂²	#87802	1	2	yes	—
82	C₂²	C₄⋊#1039	1	2	yes	—
83	C₂²	C₂×C₄⋊(C₅⋊D₅)	1	1	yes	characteristic
84	C₄	—	100	4	no	—
85	C₄	C₄⋊#1039	1	2	yes	—
86	C₄	C₂×#6045	1	1	yes	characteristic
87	C₄	C₂²×#1039	1	1	yes	characteristic
88	C₂	#11716685	1	4	yes	direct product factor
89	C₂	C₂×#87801	1	1	yes	characteristic
90	C₂	C₂×#87802	1	1	yes	characteristic
91	C₂	C₂×C₄⋊#1039	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₄⋊(C₅⋊D₅)
commutator	C₄×C₅²	C₂²×C₄
Frattini	C₂×C₄	C₂²×C₅⋊D₅
Fitting	C₂²×C₅²×C₈	C₂
socle, prime radical	C₂³×C₅²	D₄
cosocle	C₂×C₄×C₅²	C₂³
hypercenter	C₂²×C₈	C₅⋊D₅
hypocenter	C₅²	C₂×#107
LCS	G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #11716685	C₂	direct (N × H)
6. C₂×C₅²×C₈	C₄	semidirect
18. C₅²×C₈	C₂×C₄	semidirect
32. C₂×C₅×C₈	Dic₅	semidirect
37. C₂×C₅²	#107	semidirect
48. C₅×C₈	C₂×Dic₅	semidirect
52. C₅²	C₂×#107	semidirect
63. C₂×C₈	#1039	semidirect
67. C₂×C₅	#3950	semidirect
78. C₈	C₂×#1039	semidirect
79. C₅	C₂×#3950	semidirect
88. C₂	#11716685	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×C₈	2
C₂×C₄⋊#1039	2
#11716685	2
C₂×#3950	5

Subgroups — C2×#11716685 #13102967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11716685 #13102967