Subgroups — C₂×#65429 #10615510

Order 640.

368 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#131	C₂	1	1	yes	maximal, characteristic
2	#65429	C₂	1	8	yes	maximal, direct product factor
3	C₂×#3944	C₂	1	3	yes	maximal, complemented
4	C₂²×#672	C₂	1	3	yes	maximal, complemented
5	C₂×C₅×#41	C₄	1	1	yes	characteristic
6	C₅×#131	C₄	1	4	yes	—
7	C₅×#131	C₂²	1	4	yes	—
8	C₂×C₅×M₁₆	C₄	1	3	yes	—
9	C₂²×C₅×C₈	C₂²	1	3	yes	—
10	#3944	C₂²	1	12	yes	complemented
11	C₂×#672	C₂²	1	1	yes	characteristic
12	C₂×#672	C₂²	1	3	yes	—
13	C₂×#672	C₂²	1	12	yes	complemented
14	C₂×#504	—	5	1	no	maximal, Sylow
15	C₅×#41	C₈	1	4	yes	—
16	C₅×#41	C₂×C₄	1	4	yes	—
17	C₂×C₅×Q₈	C₈	1	1	yes	characteristic
18	C₂×C₅×D₄	C₈	1	3	yes	—
19	C₂²×C₄×C₅	C₂×C₄	1	3	yes	—
20	C₅×M₁₆	C₂×C₄	1	12	yes	—
21	C₂×C₅×C₈	C₂×C₄	1	3	yes	—
22	C₂×C₅×C₈	C₂×C₄	1	6	yes	—
23	C₂×C₅×C₈	C₂³	1	6	yes	—
24	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
25	#672	C₂³	1	2	yes	—
26	#672	C₂³	1	6	yes	—
27	C₂×#131	D₅	1	1	yes	characteristic
28	#504	—	5	8	no	—
29	C₂×M₃₂	—	5	3	no	—
30	C₂²×C₁₆	—	5	3	no	—
31	C₂³×C₅	C₂×C₈	1	3	yes	—
32	C₅×Q₈	C₂×C₈	1	4	yes	—
33	C₅×D₄	C₂×C₈	1	12	yes	—
34	C₂×C₄×C₅	C₂×C₈	1	3	yes	—
35	C₂×C₄×C₅	C₂×C₈	1	6	yes	—
36	C₂×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₅	C₂²×C₄	1	6	yes	—
38	C₅×C₈	C₂²×C₄	1	1	yes	characteristic
39	C₅×C₈	C₂²×C₄	1	6	yes	—
40	C₅×C₈	C₂⁴	1	1	yes	characteristic
41	C₂×#41	Dic₅	1	1	yes	characteristic
42	#131	Dic₅	1	4	yes	—
43	#131	C₂×D₅	1	4	yes	—
44	C₂×M₁₆	Dic₅	1	3	yes	—
45	C₂²×C₈	C₂×D₅	1	3	yes	—
46	M₃₂	—	5	12	no	—
47	C₂×C₁₆	—	5	12	no	—
48	C₂×C₁₆	—	5	1	no	—
49	C₂×C₁₆	—	5	3	no	—
50	C₂²×C₅	—	2	6	no	—
51	C₂²×C₅	C₂²×C₈	1	6	yes	—
52	C₂²×C₅	C₂²×C₈	1	1	yes	characteristic
53	C₄×C₅	C₂²×C₈	1	1	yes	characteristic
54	C₄×C₅	C₂²×C₈	1	6	yes	—
55	C₄×C₅	C₂³×C₄	1	1	yes	characteristic
56	#41	#168	1	4	yes	—
57	#41	C₂×Dic₅	1	4	yes	—
58	C₂×Q₈	#168	1	1	yes	characteristic
59	C₂×D₄	#168	1	3	yes	—
60	C₂²×C₄	C₂×Dic₅	1	3	yes	—
61	M₁₆	C₂×Dic₅	1	12	yes	—
62	C₂×C₈	C₂×Dic₅	1	3	yes	—
63	C₂×C₈	C₂×Dic₅	1	6	yes	—
64	C₂×C₈	C₂²×D₅	1	6	yes	—
65	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
66	C₁₆	—	5	2	no	—
67	C₁₆	—	5	6	no	—
68	C₂×C₅	—	2	6	no	—
69	C₂×C₅	#504	1	2	yes	complemented
70	C₂×C₅	C₂³×C₈	1	1	yes	characteristic
71	C₂³	C₂×#168	1	3	yes	—
72	Q₈	C₂×#168	1	4	yes	—
73	D₄	C₂×#168	1	12	yes	—
74	C₂×C₄	C₂×#168	1	3	yes	—
75	C₂×C₄	C₂×#168	1	6	yes	—
76	C₂×C₄	C₂²×Dic₅	1	1	yes	characteristic
77	C₂×C₄	C₂²×Dic₅	1	6	yes	—
78	C₈	C₂²×Dic₅	1	1	yes	characteristic
79	C₈	C₂²×Dic₅	1	6	yes	—
80	C₈	C₂³×D₅	1	1	yes	characteristic
81	C₅	C₂×#504	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	2	6	no	—
83	C₂²	C₂²×#168	1	6	yes	—
84	C₂²	C₂²×#168	1	1	yes	characteristic
85	C₄	C₂²×#168	1	1	yes	characteristic
86	C₄	C₂²×#168	1	6	yes	—
87	C₄	C₂³×Dic₅	1	1	yes	characteristic
88	C₂	—	2	6	no	—
89	C₂	#65429	1	2	yes	direct product factor
90	C₂	C₂³×#168	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₅
commutator	C₂×C₅	C₂³×C₈
Frattini	C₈	C₂³×D₅
Fitting	C₂×C₅×#131	C₂
socle	C₂²×C₅	C₂²×C₈
prime radical	C₂×C₅×#41	C₄
cosocle	C₅×C₈	C₂⁴
hypercenter	C₂×#131	D₅
hypocenter	C₅	C₂×#504
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#131

Complements

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

N	H ≅ G/N	type
2. #65429	C₂	direct (N × H)
3. C₂×#3944	C₂	semidirect
4. C₂²×#672	C₂	semidirect
10. #3944	C₂²	semidirect
13. C₂×#672	C₂²	semidirect
69. C₂×C₅	#504	semidirect
81. C₅	C₂×#504	semidirect
89. C₂	#65429	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×#131	2
#65429	2
C₂×#3944	2
C₂²×#672	2
C₂×#504	5

Subgroups — C2×#65429 #10615510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#65429 #10615510