Subgroups — D₅×C₄⋊Q₈ #66057

Order 320.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₅	C₂	1	2	yes	maximal
2	C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#4090	C₂	1	2	yes	maximal, complemented
4	D₅×C₄⋊C₄	C₂	1	4	yes	maximal
5	#4034	C₂	1	4	yes	maximal, complemented
6	C₄²×D₅	C₂	1	1	yes	maximal, characteristic
7	#4015	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×Q₈	C₂²	1	2	yes	—
9	Q₈×D₅	—	2	8	no	—
10	C₂×C₄×D₅	C₂²	1	4	yes	—
11	C₂×C₄×D₅	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₅	C₂²	1	2	yes	—
13	C₂×Dic₁₀	C₂²	1	2	yes	—
14	C₂×Dic₁₀	C₂²	1	4	yes	—
15	C₅×C₄⋊C₄	C₂²	1	4	yes	—
16	C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₄⋊Dic₅	C₂²	1	4	yes	—
18	#683	C₂²	1	8	yes	—
19	C₄×Dic₅	C₂²	1	2	yes	—
20	C₄×Dic₅	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈	—	5	1	no	maximal, Sylow
22	C₂²×D₅	C₂³	1	1	yes	characteristic
23	C₅×Q₈	—	2	4	no	—
24	C₂×C₄×C₅	C₂³	1	4	yes	—
25	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
26	C₂×C₄×C₅	C₂³	1	2	yes	—
27	C₂×Dic₅	C₂³	1	4	yes	—
28	C₂×Dic₅	C₂³	1	1	yes	characteristic
29	C₂×Dic₅	C₂³	1	2	yes	—
30	C₄×D₅	—	2	8	no	—
31	C₄×D₅	D₄	1	4	yes	—
32	C₄×D₅	Q₈	1	8	yes	complemented
33	Dic₁₀	—	2	4	no	—
34	Dic₁₀	—	2	8	no	—
35	C₂²×Q₈	—	5	2	no	—
36	C₄⋊Q₈	—	5	2	no	—
37	C₄⋊Q₈	—	5	4	no	—
38	C₄⋊Q₈	—	5	1	no	—
39	C₄⋊Q₈	D₅	1	1	yes	characteristic, direct product factor
40	C₂×C₄⋊C₄	—	5	4	no	—
41	C₂×C₄²	—	5	1	no	—
42	C₂²×C₅	C₂⁴	1	1	yes	characteristic
43	C₂×D₅	C₂×D₄	1	2	yes	—
44	C₂×D₅	C₂×Q₈	1	4	yes	—
45	C₄×C₅	—	2	4	no	—
46	C₄×C₅	C₂×D₄	1	2	yes	—
47	C₄×C₅	C₂×Q₈	1	4	yes	complemented
48	Dic₅	—	2	4	no	—
49	Dic₅	C₂×D₄	1	2	yes	—
50	Dic₅	C₂×Q₈	1	4	yes	complemented
51	C₂×Q₈	—	5	4	no	—
52	C₂×Q₈	—	5	2	no	—
53	C₂×Q₈	—	10	8	no	—
54	C₂×Q₈	C₂×D₅	1	2	yes	—
55	C₂²×C₄	—	5	2	no	—
56	C₂²×C₄	—	5	1	no	—
57	C₂²×C₄	—	5	4	no	—
58	C₄⋊C₄	—	5	8	no	—
59	C₄⋊C₄	—	5	4	no	—
60	C₄⋊C₄	C₂×D₅	1	4	yes	—
61	C₄²	—	5	1	no	—
62	C₄²	—	5	2	no	—
63	C₄²	C₂×D₅	1	1	yes	characteristic
64	C₂×C₅	C₂²×D₄	1	1	yes	characteristic
65	C₂×C₅	C₂²×Q₈	1	2	yes	—
66	D₅	C₄⋊Q₈	1	4	yes	direct product factor
67	C₂³	—	5	1	no	—
68	Q₈	—	2	4	no	—
69	Q₈	—	10	8	no	—
70	Q₈	—	10	4	no	—
71	C₂×C₄	—	5	2	no	—
72	C₂×C₄	—	5	1	no	—
73	C₂×C₄	—	5	4	no	—
74	C₂×C₄	—	5	8	no	—
75	C₂×C₄	—	5	4	no	—
76	C₂×C₄	—	10	8	no	—
77	C₂×C₄	C₂²×D₅	1	4	yes	—
78	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
79	C₂×C₄	C₂²×D₅	1	2	yes	—
80	C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
81	C₂²	—	5	2	no	—
82	C₂²	—	5	4	no	—
83	C₂²	C₂³×D₅	1	1	yes	characteristic
84	C₄	—	2	4	no	—
85	C₄	—	5	2	no	—
86	C₄	—	5	4	no	—
87	C₄	—	10	4	no	—
88	C₄	D₄×D₅	1	2	yes	—
89	C₄	Q₈×D₅	1	4	yes	complemented
90	C₂	—	5	4	no	—
91	C₂	C₂×D₄×D₅	1	1	yes	characteristic
92	C₂	C₂×Q₈×D₅	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁴
Fitting	C₅×C₄⋊Q₈	C₂
prime radical	C₂²×D₅	C₂³
hypercenter	C₄⋊Q₈	D₅
hypocenter	C₅	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₅×C₄⋊Q₈	C₂	semidirect
3. #4090	C₂	semidirect
5. #4034	C₂	semidirect
7. #4015	C₂	semidirect
32. C₄×D₅	Q₈	semidirect
39. C₄⋊Q₈	D₅	direct (N × H)
47. C₄×C₅	C₂×Q₈	semidirect
50. Dic₅	C₂×Q₈	semidirect
66. D₅	C₄⋊Q₈	direct (N × H)
80. C₅	C₂×C₄⋊Q₈	semidirect
89. C₄	Q₈×D₅	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
C₅×C₄⋊Q₈	2
#4090	2
D₅×C₄⋊C₄	2
#4034	2
C₄²×D₅	2
#4015	2
C₂×C₄⋊Q₈	5

Subgroups — D5×C4⋊Q8 #66057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₄⋊Q₈ #66057