Subgroups — C₂×#4150 #66282

Order 320.

794 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	#4150	C₂	1	16	yes	maximal, direct product factor
3	C₂×Q₈×D₅	C₂	1	2	yes	maximal, complemented
4	C₂×#711	C₂	1	6	yes	maximal, complemented
5	C₂×#709	C₂	1	3	yes	maximal, complemented
6	C₂²×Dic₁₀	C₂	1	3	yes	maximal, complemented
7	C₅×#41	C₂²	1	8	yes	complemented
8	C₂×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₅×D₄	C₂²	1	3	yes	—
10	C₂²×C₄×C₅	C₂²	1	3	yes	—
11	C₂×C₂²⋊D₅	C₂²	1	6	yes	—
12	C₂²×Dic₅	C₂²	1	6	yes	—
13	Q₈×D₅	C₂²	1	16	yes	complemented
14	#711	C₂²	1	48	yes	complemented
15	#709	C₂²	1	24	yes	complemented
16	C₂×D₂₀	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₅	C₂²	1	6	yes	—
18	C₂×Dic₁₀	C₂²	1	3	yes	—
19	C₂×Dic₁₀	C₂²	1	6	yes	—
20	C₂×Dic₁₀	C₂²	1	24	yes	complemented
21	C₂×2₋¹⁺⁴	—	5	1	no	maximal, Sylow
22	C₂³×C₅	C₂³	1	3	yes	—
23	C₂²×D₅	C₂³	1	2	yes	—
24	C₅×Q₈	C₂³	1	4	yes	—
25	C₅×D₄	C₂³	1	12	yes	—
26	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
27	C₂×C₄×C₅	C₂³	1	3	yes	—
28	C₂×C₄×C₅	C₂³	1	12	yes	—
29	C₂²⋊D₅	C₂³	1	24	yes	—
30	C₂×Dic₅	C₂³	1	6	yes	—
31	C₂×Dic₅	C₂³	1	24	yes	—
32	D₂₀	C₂³	1	4	yes	—
33	C₄×D₅	C₂³	1	24	yes	—
34	Dic₁₀	C₂³	1	12	yes	—
35	Dic₁₀	C₂³	1	24	yes	—
36	2₋¹⁺⁴	—	5	16	no	—
37	C₂×#41	—	5	6	no	—
38	C₂×#41	—	5	3	no	—
39	C₂×#41	D₅	1	1	yes	characteristic, complemented
40	C₂²×Q₈	—	5	2	no	—
41	C₂²×Q₈	—	5	3	no	—
42	C₂²×C₅	—	2	6	no	—
43	C₂²×C₅	C₂⁴	1	6	yes	—
44	C₂²×C₅	C₂⁴	1	1	yes	characteristic
45	C₂×D₅	—	2	4	no	—
46	C₂×D₅	C₂⁴	1	4	yes	—
47	C₄×C₅	C₂⁴	1	2	yes	—
48	C₄×C₅	C₂⁴	1	6	yes	—
49	Dic₅	C₂⁴	1	12	yes	—
50	#41	—	5	48	no	—
51	#41	—	5	24	no	—
52	#41	C₂×D₅	1	8	yes	complemented
53	C₂×Q₈	—	5	16	no	—
54	C₂×Q₈	—	5	6	no	—
55	C₂×Q₈	—	5	3	no	—
56	C₂×Q₈	—	5	24	no	—
57	C₂×Q₈	C₂×D₅	1	1	yes	characteristic
58	C₂×D₄	—	5	6	no	—
59	C₂×D₄	—	5	1	no	—
60	C₂×D₄	C₂×D₅	1	3	yes	—
61	C₂²×C₄	—	5	6	no	—
62	C₂²×C₄	—	5	6	no	—
63	C₂²×C₄	C₂×D₅	1	3	yes	—
64	C₂×C₅	—	2	6	no	—
65	C₂×C₅	2₋¹⁺⁴	1	2	yes	complemented
66	C₂×C₅	C₂⁵	1	1	yes	characteristic
67	D₅	—	2	4	no	—
68	C₂³	—	5	2	no	—
69	C₂³	C₂²×D₅	1	3	yes	—
70	Q₈	—	5	24	no	—
71	Q₈	—	5	12	no	—
72	Q₈	C₂²×D₅	1	4	yes	—
73	D₄	—	5	24	no	—
74	D₄	—	5	4	no	—
75	D₄	C₂²×D₅	1	12	yes	—
76	C₂×C₄	—	5	24	no	—
77	C₂×C₄	—	5	6	no	—
78	C₂×C₄	—	5	24	no	—
79	C₂×C₄	C₂²×D₅	1	12	yes	—
80	C₂×C₄	C₂²×D₅	1	3	yes	—
81	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
82	C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
83	C₂²	—	2	6	no	—
84	C₂²	—	5	4	no	—
85	C₂²	—	10	4	no	—
86	C₂²	C₂³×D₅	1	6	yes	—
87	C₂²	C₂³×D₅	1	1	yes	characteristic
88	C₄	—	5	12	no	—
89	C₄	C₂³×D₅	1	6	yes	—
90	C₄	C₂³×D₅	1	2	yes	—
91	C₂	—	2	6	no	—
92	C₂	—	10	4	no	—
93	C₂	#4150	1	2	yes	direct product factor
94	C₂	C₂⁴×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₅
commutator, cosocle	C₂×C₅	C₂⁵
Frattini	C₂	C₂⁴×D₅
Fitting	C₂×C₅×#41	C₂
socle	C₂²×C₅	C₂⁴
hypercenter	C₂×#41	D₅
hypocenter	C₅	C₂×2₋¹⁺⁴
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#41	C₂	semidirect
2. #4150	C₂	direct (N × H)
3. C₂×Q₈×D₅	C₂	semidirect
4. C₂×#711	C₂	semidirect
5. C₂×#709	C₂	semidirect
6. C₂²×Dic₁₀	C₂	semidirect
7. C₅×#41	C₂²	semidirect
13. Q₈×D₅	C₂²	semidirect
14. #711	C₂²	semidirect
15. #709	C₂²	semidirect
20. C₂×Dic₁₀	C₂²	semidirect
39. C₂×#41	D₅	semidirect
52. #41	C₂×D₅	semidirect
65. C₂×C₅	2₋¹⁺⁴	semidirect
82. C₅	C₂×2₋¹⁺⁴	semidirect
93. C₂	#4150	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×C₅×#41	2
#4150	2
C₂×Q₈×D₅	2
C₂×#711	2
C₂×#709	2
C₂²×Dic₁₀	2
C₂×2₋¹⁺⁴	5

Subgroups — C2×#4150 #66282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4150 #66282