Subgroups — C₂×#11716792 #13104246

Order 1600.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#87770	C₂	1	2	yes	maximal, complemented
2	C₂×#87765	C₂	1	1	yes	maximal, characteristic, complemented
3	#11716792	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₅×D₂₀	—	2	2	no	—
5	C₂×#6029	C₂²	1	1	yes	characteristic
6	#87770	—	2	2	no	—
7	#87770	C₂²	1	4	yes	complemented
8	#87765	C₂²	1	2	yes	complemented
9	C₂²×C₅×D₅	—	4	2	no	—
10	C₂×C₄×C₅²	D₄	1	1	yes	characteristic
11	C₅×D₂₀	—	2	4	no	—
12	C₅×D₂₀	—	4	2	no	—
13	#6029	D₄	1	1	yes	characteristic
14	#6029	C₂³	1	1	yes	characteristic
15	C₂×#686	—	10	2	no	—
16	C₂×#674	—	10	1	no	—
17	C₂²×C₅²	D₈	1	1	yes	characteristic
18	C₂×C₅×D₅	—	4	4	no	—
19	C₂×C₅×D₅	—	8	4	no	—
20	C₄×C₅²	D₈	1	1	yes	characteristic
21	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
22	C₂×C₅×D₄	—	10	2	no	—
23	C₂×D₂₀	—	2	2	no	—
24	#686	—	10	4	no	—
25	#686	—	10	4	no	—
26	C₂×#168	—	10	1	no	—
27	C₂×#168	—	10	2	no	—
28	#674	—	10	2	no	—
29	C₂×D₁₆	—	25	1	no	maximal, Sylow
30	C₂×C₅²	D₁₆	1	2	yes	complemented
31	C₂×C₅²	C₂×D₈	1	1	yes	characteristic
32	C₅×D₅	—	8	4	no	—
33	C₂³×C₅	—	20	2	no	—
34	C₂²×D₅	—	4	2	no	—
35	C₅×D₄	—	10	4	no	—
36	C₅×D₄	—	20	2	no	—
37	C₂×C₄×C₅	—	2	1	no	—
38	C₂×C₄×C₅	—	2	2	no	—
39	D₂₀	—	2	4	no	—
40	D₂₀	—	4	2	no	—
41	#168	—	10	1	no	—
42	#168	—	10	2	no	—
43	#168	—	10	1	no	—
44	#168	—	10	2	no	—
45	C₂×D₈	—	25	2	no	—
46	D₁₆	—	25	4	no	—
47	C₂×C₁₆	—	25	1	no	—
48	C₅²	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₅	—	2	1	no	—
50	C₂²×C₅	—	2	2	no	—
51	C₂²×C₅	—	20	4	no	—
52	C₂²×C₅	—	40	4	no	—
53	C₂×D₅	—	4	4	no	—
54	C₂×D₅	—	8	4	no	—
55	C₄×C₅	—	2	2	no	—
56	C₄×C₅	—	2	1	no	—
57	C₄×C₅	—	2	2	no	—
58	C₄×C₅	—	2	1	no	—
59	C₂×D₄	—	10	2	no	—
60	D₈	—	25	4	no	—
61	D₈	—	50	2	no	—
62	C₂×C₈	—	25	1	no	—
63	C₁₆	—	25	2	no	—
64	C₂×C₅	—	2	2	no	—
65	C₂×C₅	—	2	1	no	—
66	C₂×C₅	—	2	4	no	—
67	C₂×C₅	—	2	2	no	—
68	C₂×C₅	—	40	4	no	—
69	D₅	—	8	4	no	—
70	C₂³	—	20	2	no	—
71	D₄	—	10	4	no	—
72	D₄	—	20	2	no	—
73	C₂×C₄	D₅²⋊C₂	1	1	yes	characteristic
74	C₈	—	25	1	no	—
75	C₈	—	25	1	no	—
76	C₅	—	2	2	no	—
77	C₅	—	2	1	no	—
78	C₂²	—	20	4	no	—
79	C₂²	—	40	4	no	—
80	C₂²	#87837	1	1	yes	characteristic
81	C₄	#87837	1	1	yes	characteristic
82	C₄	C₂×D₅²⋊C₂	1	1	yes	characteristic
83	C₂	—	40	4	no	—
84	C₂	#11716792	1	2	yes	direct product factor
85	C₂	C₂×#87837	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#87837
commutator, cosocle	#6029	C₂³
Frattini	C₄	C₂×D₅²⋊C₂
Fitting	C₂×C₄×C₅²	D₄
socle	C₂²×C₅²	D₈
hypercenter	C₂×C₄	D₅²⋊C₂
hypocenter	C₅²	C₂×D₁₆
LCS	G ▷ #6029 ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#87770	C₂	semidirect
2. C₂×#87765	C₂	semidirect
3. #11716792	C₂	direct (N × H)
7. #87770	C₂²	semidirect
8. #87765	C₂²	semidirect
30. C₂×C₅²	D₁₆	semidirect
48. C₅²	C₂×D₁₆	semidirect
84. C₂	#11716792	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×#87770	2
C₂×#87765	2
#11716792	2
C₂×D₁₆	25

Subgroups — C2×#11716792 #13104246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11716792 #13104246