Subgroups — D₅×#108 #65181

Order 320.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	#3954	C₂	1	2	yes	maximal, complemented
5	#3951	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₅	C₂²	1	1	yes	characteristic
7	C₅×M₁₆	C₂²	1	2	yes	—
8	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
9	#681	C₂²	1	2	yes	—
10	C₂×#168	C₂²	1	1	yes	characteristic
11	#676	—	2	2	no	—
12	C₈×D₅	—	2	2	no	—
13	C₈×D₅	C₄	1	2	yes	—
14	C₈×D₅	C₄	1	2	yes	—
15	C₂×#108	—	5	1	no	maximal, Sylow
16	C₂²×D₅	Q₈	1	1	yes	characteristic
17	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
18	C₂×Dic₅	Q₈	1	1	yes	characteristic
19	C₄×D₅	C₂×C₄	1	1	yes	characteristic
20	C₄×D₅	C₂×C₄	1	1	yes	characteristic
21	C₄×D₅	D₄	1	1	yes	characteristic
22	C₄×D₅	D₄	1	1	yes	characteristic
23	C₅×C₈	—	2	2	no	—
24	C₅×C₈	C₂×C₄	1	2	yes	—
25	#168	—	2	2	no	—
26	#168	C₂×C₄	1	2	yes	—
27	C₂×M₁₆	—	5	2	no	—
28	C₂²×C₈	—	5	1	no	—
29	#108	—	5	2	no	—
30	#108	—	5	1	no	—
31	#108	D₅	1	1	yes	characteristic, direct product factor
32	C₂²×C₅	C₂×Q₈	1	1	yes	characteristic
33	C₂×D₅	—	2	2	no	—
34	C₂×D₅	C₄⋊C₄	1	1	yes	characteristic
35	C₂×D₅	C₄⋊C₄	1	1	yes	characteristic
36	C₄×C₅	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₅	C₂×D₄	1	1	yes	characteristic
38	Dic₅	C₄⋊C₄	1	1	yes	characteristic
39	Dic₅	C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₄	—	5	1	no	—
41	M₁₆	—	5	2	no	—
42	M₁₆	—	10	2	no	—
43	M₁₆	C₂×D₅	1	2	yes	—
44	C₂×C₈	—	5	1	no	—
45	C₂×C₈	—	5	2	no	—
46	C₂×C₈	—	5	2	no	—
47	C₂×C₈	—	10	2	no	—
48	C₂×C₈	C₂×D₅	1	1	yes	characteristic
49	C₂×C₅	—	2	1	no	—
50	C₂×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
51	D₅	—	2	1	no	—
52	D₅	#108	1	2	yes	direct product factor
53	C₂³	—	5	1	no	—
54	C₂×C₄	—	5	1	no	—
55	C₂×C₄	—	5	1	no	—
56	C₂×C₄	—	5	1	no	—
57	C₂×C₄	—	5	1	no	—
58	C₂×C₄	—	5	1	no	—
59	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₈	—	5	2	no	—
62	C₈	—	10	2	no	—
63	C₈	C₄×D₅	1	2	yes	—
64	C₅	C₂×#108	1	1	yes	characteristic, complemented, Sylow
65	C₂²	—	5	1	no	—
66	C₂²	—	5	1	no	—
67	C₂²	—	10	2	no	—
68	C₂²	Q₈×D₅	1	1	yes	characteristic
69	C₄	—	5	1	no	—
70	C₄	—	5	1	no	—
71	C₄	C₂×C₄×D₅	1	1	yes	characteristic
72	C₄	D₄×D₅	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	—	5	2	no	—
75	C₂	—	10	1	no	—
76	C₂	D₅×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₅
commutator	C₄×C₅	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₅×#108	C₂
socle	C₂×C₅	C₂×C₄⋊C₄
prime radical	C₂²×D₅	Q₈
cosocle	C₂×C₄×C₅	C₂³
hypercenter	#108	D₅
hypocenter	C₅	C₂×#108
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
3. C₅×#108	C₂	semidirect
4. #3954	C₂	semidirect
5. #3951	C₂	semidirect
31. #108	D₅	direct (N × H)
52. D₅	#108	direct (N × H)
64. C₅	C₂×#108	semidirect

Maximal subgroups

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

subgroup	index
D₅×M₁₆	2
C₂×C₈×D₅	2
C₅×#108	2
#3954	2
#3951	2
C₂×#108	5

Subgroups — D5×#108 #65181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#108 #65181