Subgroups — C₅×#4093 #11717181

Order 800.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₂₀	C₂	1	1	yes	maximal, characteristic
3	C₅×#685	C₂	1	4	yes	maximal, complemented
4	C₄×C₅×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₅×D₅	C₂²	1	2	yes	—
6	C₅²×Q₈	—	2	2	no	—
7	C₂×C₄×C₅²	C₂²	1	2	yes	—
8	C₂×C₄×C₅²	C₂²	1	1	yes	characteristic
9	C₂×C₅×Dic₅	C₂²	1	2	yes	—
10	C₅×D₂₀	—	2	2	no	—
11	C₅×#124	—	5	1	no	maximal
12	#4093	C₅	1	1	yes	maximal, characteristic, direct product factor
13	C₂²×C₅²	C₂³	1	1	yes	characteristic
14	C₂×C₅×D₅	—	2	2	no	—
15	C₂×C₅×D₅	—	2	4	no	—
16	C₄×C₅²	—	2	2	no	—
17	C₄×C₅²	D₄	1	2	yes	—
18	C₅×Dic₅	—	2	2	no	—
19	C₂×C₅×Q₈	—	2	2	no	—
20	C₂×C₅×Q₈	D₅	1	1	yes	characteristic, complemented
21	C₂×C₅×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
22	C₂×C₅×D₄	—	5	1	no	—
23	C₂×D₂₀	C₂×C₅	1	1	yes	characteristic
24	C₅×C₂²⋊C₄	—	5	4	no	—
25	C₄²×C₅	—	5	1	no	—
26	#685	C₂×C₅	1	4	yes	complemented
27	C₄×Dic₅	C₂×C₅	1	1	yes	characteristic, complemented
28	C₂×C₅²	C₂×D₄	1	1	yes	characteristic
29	C₂×C₅²	#41	1	2	yes	—
30	C₅×D₅	—	4	2	no	—
31	C₂³×C₅	—	5	2	no	—
32	C₂²×D₅	C₂²×C₅	1	2	yes	—
33	C₅×Q₈	—	2	8	no	—
34	C₅×Q₈	—	2	2	no	—
35	C₅×Q₈	—	2	2	no	—
36	C₅×D₄	—	10	2	no	—
37	C₂×C₄×C₅	—	2	4	no	—
38	C₂×C₄×C₅	—	2	2	no	—
39	C₂×C₄×C₅	—	5	2	no	—
40	C₂×C₄×C₅	C₂×D₅	1	2	yes	—
41	C₂×C₄×C₅	C₂×D₅	1	1	yes	characteristic
42	C₂×C₄×C₅	C₂²×C₅	1	2	yes	—
43	C₂×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
44	C₂×Dic₅	C₂²×C₅	1	2	yes	—
45	D₂₀	—	2	2	no	—
46	#124	—	5	1	no	Sylow
47	C₅²	#124	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₅	—	2	2	no	—
49	C₂²×C₅	—	10	4	no	—
50	C₂²×C₅	—	10	2	no	—
51	C₂²×C₅	C₂²×D₅	1	1	yes	characteristic
52	C₂²×C₅	C₂³×C₅	1	1	yes	characteristic
53	C₂×D₅	—	2	2	no	—
54	C₂×D₅	—	2	4	no	—
55	C₄×C₅	—	2	8	no	—
56	C₄×C₅	—	2	2	no	—
57	C₄×C₅	—	2	2	no	—
58	C₄×C₅	—	2	4	no	—
59	C₄×C₅	—	10	2	no	—
60	C₄×C₅	C₂²⋊D₅	1	2	yes	—
61	C₄×C₅	C₅×D₄	1	2	yes	—
62	Dic₅	—	2	2	no	—
63	C₂×Q₈	C₅×D₅	1	1	yes	characteristic, complemented
64	C₂×D₄	—	5	1	no	—
65	C₂²⋊C₄	—	5	4	no	—
66	C₄²	—	5	1	no	—
67	C₂×C₅	—	2	4	no	—
68	C₂×C₅	—	2	2	no	—
69	C₂×C₅	—	20	2	no	—
70	C₂×C₅	#713	1	2	yes	—
71	C₂×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
72	C₂×C₅	C₂×C₅×D₄	1	1	yes	characteristic
73	C₂×C₅	C₅×#41	1	2	yes	—
74	D₅	—	4	2	no	—
75	C₂³	—	5	2	no	—
76	Q₈	—	2	2	no	—
77	D₄	—	10	2	no	—
78	C₂×C₄	—	5	2	no	—
79	C₂×C₄	C₂×C₅×D₅	1	2	yes	—
80	C₂×C₄	C₂×C₅×D₅	1	1	yes	characteristic
81	C₅	—	2	2	no	—
82	C₅	#4093	1	1	yes	characteristic, direct product factor
83	C₅	C₅×#124	1	1	yes	characteristic, complemented
84	C₂²	—	10	4	no	—
85	C₂²	—	10	2	no	—
86	C₂²	C₂²×C₅×D₅	1	1	yes	characteristic
87	C₄	—	2	2	no	—
88	C₄	—	10	2	no	—
89	C₄	C₅×C₂²⋊D₅	1	2	yes	—
90	C₂	—	20	2	no	—
91	C₂	C₅×#713	1	2	yes	—
92	C₂	C₂×C₅×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂³×C₅
Frattini	C₂²	C₂²×C₅×D₅
Fitting	C₂×C₅²×Q₈	C₂
socle	C₂²×C₅²	C₂³
prime radical	C₂×C₅×D₂₀	C₂
hypercenter	C₂×C₅×Q₈	D₅
hypocenter	C₅	C₅×#124
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²×Q₈	C₂	semidirect
3. C₅×#685	C₂	semidirect
4. C₄×C₅×Dic₅	C₂	semidirect
12. #4093	C₅	direct (N × H)
20. C₂×C₅×Q₈	D₅	semidirect
21. C₂×C₅×Q₈	C₂×C₅	semidirect
26. #685	C₂×C₅	semidirect
27. C₄×Dic₅	C₂×C₅	semidirect
47. C₅²	#124	semidirect
63. C₂×Q₈	C₅×D₅	semidirect
82. C₅	#4093	direct (N × H)
83. C₅	C₅×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅²×Q₈	2
C₂×C₅×D₂₀	2
C₅×#685	2
C₄×C₅×Dic₅	2
C₅×#124	5
#4093	5

Subgroups — C5×#4093 #11717181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#4093 #11717181