Subgroups — D₅⋊#101 #65789

Order 320.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₅	C₂	1	1	yes	maximal, characteristic
2	D₅⋊M₁₆	C₂	1	2	yes	maximal
3	#4005	C₂	1	4	yes	maximal, complemented
4	C₂×C₅×Q₈	C₄	1	1	yes	characteristic
5	Q₈×D₅	—	2	2	no	—
6	Q₈×D₅	—	2	2	no	—
7	C₂×C₄×D₅	C₄	1	2	yes	—
8	C₂×C₄×D₅	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₀	C₄	1	1	yes	characteristic
10	C₂×Dic₁₀	C₂²	1	2	yes	—
11	#704	C₂²	1	4	yes	—
12	#700	—	2	2	no	—
13	D₅⋊C₈	—	2	2	no	—
14	C₂×#101	—	5	1	no	maximal, Sylow
15	C₂²×D₅	C₂×C₄	1	1	yes	characteristic
16	C₅×Q₈	—	2	2	no	—
17	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₅	C₂×C₄	1	2	yes	—
20	C₂×Dic₅	C₂³	1	1	yes	characteristic
21	C₄×D₅	—	2	2	no	—
22	C₄×D₅	—	2	2	no	—
23	C₄×D₅	D₄	1	2	yes	—
24	C₄×D₅	D₄	1	2	yes	—
25	Dic₁₀	—	2	2	no	—
26	Dic₁₀	—	2	4	no	—
27	#170	—	2	4	no	—
28	C₂²×Q₈	—	5	1	no	—
29	C₂×M₁₆	—	5	2	no	—
30	#101	—	5	4	no	—
31	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
32	C₂×D₅	—	2	2	no	—
33	C₂×D₅	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×D₅	C₂²⋊C₄	1	1	yes	characteristic
35	C₄×C₅	—	2	2	no	—
36	C₄×C₅	C₂²⋊C₄	1	2	yes	—
37	Dic₅	—	2	2	no	—
38	Dic₅	C₂×D₄	1	2	yes	—
39	C₂×Q₈	—	5	2	no	—
40	C₂×Q₈	—	5	1	no	—
41	C₂×Q₈	—	10	2	no	—
42	C₂×Q₈	—	10	2	no	—
43	C₂×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic
44	C₂²×C₄	—	5	1	no	—
45	C₂²×C₄	—	5	2	no	—
46	M₁₆	—	5	4	no	—
47	M₁₆	—	10	2	no	—
48	C₂×C₈	—	10	2	no	—
49	C₂×C₅	—	2	1	no	—
50	C₂×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
51	D₅	—	2	1	no	—
52	D₅	#101	1	2	yes	complemented
53	C₂³	—	5	1	no	—
54	Q₈	—	2	2	no	—
55	Q₈	—	10	4	no	—
56	Q₈	—	10	2	no	—
57	C₂×C₄	—	5	1	no	—
58	C₂×C₄	—	5	2	no	—
59	C₂×C₄	—	5	2	no	—
60	C₂×C₄	—	5	2	no	—
61	C₂×C₄	—	10	2	no	—
62	C₂×C₄	—	10	2	no	—
63	C₂×C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
64	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
65	C₈	—	10	4	no	—
66	C₅	C₂×#101	1	1	yes	characteristic, complemented, Sylow
67	C₂²	—	5	1	no	—
68	C₂²	—	5	1	no	—
69	C₂²	—	10	2	no	—
70	C₂²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	5	2	no	—
73	C₄	—	10	2	no	—
74	C₄	C₂²⋊AGL(1,𝔽₅)	1	2	yes	—
75	C₂	—	2	1	no	—
76	C₂	—	5	2	no	—
77	C₂	—	10	1	no	—
78	C₂	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂²×C₄
Frattini	C₂²	C₂²×AGL(1,𝔽₅)
Fitting	C₂×C₅×Q₈	C₄
socle	C₂×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×D₅	C₂×C₄
cosocle	C₂×Dic₅	C₂³
hypercenter	C₂×Q₈	AGL(1,𝔽₅)
hypocenter	C₅	C₂×#101
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
3. #4005	C₂	semidirect
52. D₅	#101	semidirect
66. C₅	C₂×#101	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×D₅	2
D₅⋊M₁₆	2
#4005	2
C₂×#101	5

Subgroups — D5⋊#101 #65789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅⋊#101 #65789