Subgroups — C₂×#11716586 #13100809

Order 1600.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄₀	C₂	1	2	yes	maximal, complemented
2	C₂×#87756	C₂	1	1	yes	maximal, characteristic, complemented
3	#11716586	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₅×D₂₀	—	2	2	no	—
5	C₂×C₅²×C₈	C₂²	1	1	yes	characteristic
6	C₅×D₄₀	—	2	2	no	—
7	C₅×D₄₀	C₂²	1	4	yes	complemented
8	#87756	C₂²	1	2	yes	complemented
9	C₂×#3958	—	5	2	no	maximal
10	C₂²×C₅×D₅	—	4	2	no	—
11	C₂×C₄×C₅²	D₄	1	1	yes	characteristic
12	C₅×D₂₀	—	2	4	no	—
13	C₅×D₂₀	—	4	2	no	—
14	C₅²×C₈	D₄	1	1	yes	characteristic
15	C₅²×C₈	C₂³	1	1	yes	characteristic
16	C₂×C₅×D₈	—	5	2	no	—
17	C₂×D₄₀	D₅	1	2	yes	complemented
18	#3958	—	5	8	no	—
19	C₂×#672	—	5	2	no	—
20	C₂×#672	—	10	2	no	—
21	C₂²×C₅²	D₈	1	1	yes	characteristic
22	C₂×C₅×D₅	—	4	4	no	—
23	C₂×C₅×D₅	—	8	4	no	—
24	C₄×C₅²	D₈	1	1	yes	characteristic
25	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
26	C₂×C₅×D₄	—	10	2	no	—
27	C₂×D₂₀	—	2	2	no	—
28	C₅×D₈	—	5	4	no	—
29	C₅×D₈	—	10	2	no	—
30	C₂×C₅×C₈	—	2	2	no	—
31	C₂×C₅×C₈	C₂×D₅	1	2	yes	—
32	D₄₀	—	2	2	no	—
33	D₄₀	C₂×D₅	1	4	yes	complemented
34	#672	—	5	4	no	—
35	#672	—	10	4	no	—
36	C₂×D₁₆	—	25	1	no	Sylow
37	C₂×C₅²	D₁₆	1	2	yes	complemented
38	C₂×C₅²	C₂×D₈	1	1	yes	characteristic
39	C₅×D₅	—	8	4	no	—
40	C₂³×C₅	—	20	2	no	—
41	C₂²×D₅	—	4	2	no	—
42	C₅×D₄	—	10	4	no	—
43	C₅×D₄	—	20	2	no	—
44	C₂×C₄×C₅	—	2	2	no	—
45	C₂×C₄×C₅	C₂²⋊D₅	1	2	yes	—
46	D₂₀	—	2	4	no	—
47	D₂₀	—	4	2	no	—
48	C₅×C₈	—	2	2	no	—
49	C₅×C₈	—	2	2	no	—
50	C₅×C₈	C₂²⋊D₅	1	2	yes	—
51	C₅×C₈	C₂²×D₅	1	2	yes	—
52	C₂×D₈	—	5	2	no	—
53	D₁₆	—	25	4	no	—
54	C₂×C₁₆	—	25	1	no	—
55	C₅²	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₅	—	2	2	no	—
57	C₂²×C₅	—	20	4	no	—
58	C₂²×C₅	—	40	4	no	—
59	C₂²×C₅	#686	1	2	yes	—
60	C₂×D₅	—	4	4	no	—
61	C₂×D₅	—	8	4	no	—
62	C₄×C₅	—	2	2	no	—
63	C₄×C₅	—	2	2	no	—
64	C₄×C₅	#686	1	2	yes	—
65	C₄×C₅	C₂×C₂²⋊D₅	1	2	yes	—
66	C₂×D₄	—	10	2	no	—
67	D₈	—	5	4	no	—
68	D₈	—	10	2	no	—
69	C₂×C₈	D₅²	1	1	yes	characteristic
70	C₁₆	—	25	2	no	—
71	C₂×C₅	—	2	2	no	—
72	C₂×C₅	—	2	4	no	—
73	C₂×C₅	—	40	4	no	—
74	C₂×C₅	#3958	1	4	yes	complemented
75	C₂×C₅	C₂×#686	1	2	yes	—
76	D₅	—	8	4	no	—
77	C₂³	—	20	2	no	—
78	D₄	—	10	4	no	—
79	D₄	—	20	2	no	—
80	C₂×C₄	#6037	1	1	yes	characteristic
81	C₈	#6037	1	1	yes	characteristic
82	C₈	C₂×D₅²	1	1	yes	characteristic
83	C₅	—	2	2	no	—
84	C₅	C₂×#3958	1	2	yes	complemented
85	C₂²	—	20	4	no	—
86	C₂²	—	40	4	no	—
87	C₂²	#87770	1	1	yes	characteristic
88	C₄	#87770	1	1	yes	characteristic
89	C₄	C₂×#6037	1	1	yes	characteristic
90	C₂	—	40	4	no	—
91	C₂	#11716586	1	2	yes	direct product factor
92	C₂	C₂×#87770	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#87770
commutator, cosocle	C₅²×C₈	C₂³
Frattini	C₈	C₂×D₅²
Fitting	C₂×C₅²×C₈	C₂²
socle	C₂²×C₅²	D₈
hypercenter	C₂×C₈	D₅²
hypocenter	C₅²	C₂×D₁₆
LCS	G ▷ C₅²×C₈ ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₄₀	C₂	semidirect
2. C₂×#87756	C₂	semidirect
3. #11716586	C₂	direct (N × H)
7. C₅×D₄₀	C₂²	semidirect
8. #87756	C₂²	semidirect
17. C₂×D₄₀	D₅	semidirect
33. D₄₀	C₂×D₅	semidirect
37. C₂×C₅²	D₁₆	semidirect
55. C₅²	C₂×D₁₆	semidirect
74. C₂×C₅	#3958	semidirect
84. C₅	C₂×#3958	semidirect
91. C₂	#11716586	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×D₄₀	2
C₂×#87756	2
#11716586	2
C₂×#3958	5

Subgroups — C2×#11716586 #13100809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11716586 #13100809