Subgroups — C₂×#87838 #11717396

Order 800.

125 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#6039	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#6037	C₂	1	1	yes	maximal, characteristic
3	C₂×#6034	C₂	1	1	yes	maximal, characteristic, complemented
4	#87838	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅×D₅	—	2	1	no	—
6	C₂×#1039	C₂²	1	1	yes	characteristic
7	C₂×C₅×Dic₅	—	2	1	no	—
8	#6039	—	2	1	no	—
9	#6039	C₂²	1	2	yes	complemented
10	#6037	—	2	1	no	—
11	#6037	C₂²	1	2	yes	—
12	#6034	C₂²	1	2	yes	complemented
13	C₂²×C₅²	D₄	1	1	yes	characteristic
14	C₂×C₅×D₅	—	2	2	no	—
15	C₂×C₅×D₅	—	4	2	no	—
16	#1039	D₄	1	1	yes	characteristic
17	#1039	C₂³	1	1	yes	characteristic
18	C₅×Dic₅	—	2	2	no	—
19	C₂×C₂²⋊D₅	—	10	1	no	—
20	C₂×Dic₁₀	—	10	1	no	—
21	C₂×#170	—	10	1	no	—
22	C₂×C₅²	SD₁₆	1	2	yes	complemented
23	C₂×C₅²	C₂×D₄	1	1	yes	characteristic
24	C₅×D₅	—	4	2	no	—
25	C₂³×C₅	—	10	1	no	—
26	C₂²×D₅	—	2	1	no	—
27	C₂×C₄×C₅	—	10	1	no	—
28	C₂²⋊D₅	—	10	2	no	—
29	C₂²⋊D₅	—	10	2	no	—
30	C₂×Dic₅	—	2	1	no	—
31	C₂×Dic₅	—	10	1	no	—
32	C₂×Dic₅	—	10	1	no	—
33	C₂×Dic₅	—	10	1	no	—
34	Dic₁₀	—	10	2	no	—
35	Dic₁₀	—	10	2	no	—
36	#170	—	10	2	no	—
37	C₂×SD₁₆	—	25	1	no	maximal, Sylow
38	C₅²	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₅	—	2	1	no	—
40	C₂²×C₅	—	2	1	no	—
41	C₂²×C₅	—	2	1	no	—
42	C₂²×C₅	—	10	2	no	—
43	C₂²×C₅	—	20	2	no	—
44	C₂×D₅	—	2	2	no	—
45	C₂×D₅	—	4	2	no	—
46	C₄×C₅	—	10	2	no	—
47	Dic₅	—	2	2	no	—
48	Dic₅	—	10	1	no	—
49	Dic₅	—	10	1	no	—
50	Dic₅	—	10	1	no	—
51	Dic₅	—	10	1	no	—
52	Dic₅	—	10	1	no	—
53	Dic₅	—	10	1	no	—
54	C₂×Q₈	—	25	1	no	—
55	C₂×D₄	—	25	1	no	—
56	SD₁₆	—	25	4	no	—
57	C₂×C₈	—	25	1	no	—
58	C₂×C₅	—	2	2	no	—
59	C₂×C₅	—	2	2	no	—
60	C₂×C₅	—	2	2	no	—
61	C₂×C₅	—	2	1	no	—
62	C₂×C₅	—	2	1	no	—
63	C₂×C₅	—	2	1	no	—
64	C₂×C₅	—	20	2	no	—
65	D₅	—	4	2	no	—
66	C₂³	—	10	1	no	—
67	Q₈	—	25	2	no	—
68	Q₈	—	50	1	no	—
69	D₄	—	25	2	no	—
70	D₄	—	50	1	no	—
71	C₂×C₄	—	10	1	no	—
72	C₂×C₄	—	25	1	no	—
73	C₈	—	25	2	no	—
74	C₅	—	2	1	no	—
75	C₅	—	2	1	no	—
76	C₅	—	2	1	no	—
77	C₂²	—	10	2	no	—
78	C₂²	—	20	2	no	—
79	C₂²	D₅²⋊C₂	1	1	yes	characteristic
80	C₄	—	10	2	no	—
81	C₄	—	25	1	no	—
82	C₄	—	25	1	no	—
83	C₂	—	20	2	no	—
84	C₂	#87838	1	2	yes	direct product factor
85	C₂	C₂×D₅²⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₅²⋊C₂
commutator, cosocle	#1039	C₂³
Frattini	C₂	C₂×D₅²⋊C₂
Fitting, socle	C₂²×C₅²	D₄
prime radical	C₂×#6037	C₂
hypocenter	C₅²	C₂×SD₁₆
LCS	G ▷ #1039 ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×#6039	C₂	semidirect
3. C₂×#6034	C₂	semidirect
4. #87838	C₂	direct (N × H)
9. #6039	C₂²	semidirect
12. #6034	C₂²	semidirect
22. C₂×C₅²	SD₁₆	semidirect
38. C₅²	C₂×SD₁₆	semidirect
84. C₂	#87838	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×#6039	2
C₂×#6037	2
C₂×#6034	2
#87838	2
C₂×SD₁₆	25

Subgroups — C2×#87838 #11717396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#87838 #11717396