Subgroups — C₄×#3951 #10600583

Order 640.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#3951	C₂	1	2	yes	maximal
3	C₄×#681	C₂	1	2	yes	maximal
4	#64772	C₂	1	2	yes	maximal
5	C₂²×C₅×C₈	C₂²	1	1	yes	characteristic
6	C₂²×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₂×#681	C₂²	1	4	yes	—
9	C₄×C₅×C₈	C₄	1	4	yes	—
10	#3951	C₄	1	8	yes	direct product factor
11	#3935	—	2	2	no	—
12	C₄×#168	—	2	2	no	—
13	C₄×#108	—	5	1	no	maximal, Sylow
14	C₂²×C₄×C₅	Q₈	1	2	yes	—
15	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
16	C₂×C₅×C₈	—	2	2	no	—
17	C₂×C₅×C₈	C₂×C₄	1	4	yes	—
18	C₂×C₅×C₈	C₂×C₄	1	2	yes	—
19	C₂×C₅×C₈	C₂×C₄	1	2	yes	—
20	C₄²×C₅	C₂×C₄	1	2	yes	—
21	C₄²×C₅	D₄	1	1	yes	characteristic
22	C₄²×C₅	D₄	1	1	yes	characteristic
23	#681	—	2	4	no	—
24	#681	C₂×C₄	1	8	yes	—
25	C₂×#168	—	2	4	no	—
26	C₂×#108	—	5	2	no	—
27	C₄×M₁₆	—	5	2	no	—
28	C₂×C₄×C₈	D₅	1	1	yes	characteristic
29	#341	—	5	2	no	—
30	C₂³×C₅	C₂×Q₈	1	1	yes	characteristic
31	C₂×C₄×C₅	—	2	4	no	—
32	C₂×C₄×C₅	C₄⋊C₄	1	2	yes	—
33	C₂×C₄×C₅	C₄⋊C₄	1	2	yes	—
34	C₂×C₄×C₅	C₂²×C₄	1	2	yes	—
35	C₂×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₅	#41	1	2	yes	—
38	C₅×C₈	—	2	2	no	—
39	C₅×C₈	C₄²	1	4	yes	—
40	#168	—	2	8	no	—
41	C₂×M₁₆	—	5	4	no	—
42	C₂²×C₈	C₂×D₅	1	1	yes	characteristic
43	C₂²×C₈	C₂×D₅	1	1	yes	characteristic
44	C₂×C₄²	C₂×D₅	1	1	yes	characteristic
45	#108	—	5	8	no	—
46	#97	—	10	2	no	—
47	C₄×C₈	—	10	2	no	—
48	C₄×C₈	Dic₅	1	4	yes	—
49	C₂²×C₅	—	2	2	no	—
50	C₂²×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₅	C₄×Q₈	1	2	yes	—
52	C₄×C₅	—	2	2	no	—
53	C₄×C₅	#108	1	4	yes	complemented
54	C₄×C₅	C₂×C₄²	1	1	yes	characteristic
55	C₄×C₅	#117	1	1	yes	characteristic
56	C₄×C₅	C₄×D₄	1	2	yes	—
57	C₂²×C₄	Dic₁₀	1	2	yes	—
58	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
59	M₁₆	—	5	8	no	—
60	M₁₆	—	10	4	no	—
61	C₂×C₈	—	2	2	no	—
62	C₂×C₈	—	10	4	no	—
63	C₂×C₈	C₄×D₅	1	4	yes	—
64	C₂×C₈	C₂×Dic₅	1	2	yes	—
65	C₂×C₈	C₂×Dic₅	1	2	yes	—
66	C₄²	D₂₀	1	1	yes	characteristic
67	C₄²	D₂₀	1	1	yes	characteristic
68	C₄²	C₂×Dic₅	1	2	yes	—
69	C₂×C₅	—	2	2	no	—
70	C₂×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₅	C₂×#108	1	2	yes	—
72	C₂³	C₂×Dic₁₀	1	1	yes	characteristic
73	C₂×C₄	—	2	4	no	—
74	C₂×C₄	C₄⋊Dic₅	1	2	yes	—
75	C₂×C₄	C₄⋊Dic₅	1	2	yes	—
76	C₂×C₄	C₂×C₄×D₅	1	2	yes	—
77	C₂×C₄	C₂×D₂₀	1	1	yes	characteristic
78	C₂×C₄	#709	1	2	yes	—
79	C₂×C₄	C₂²×Dic₅	1	1	yes	characteristic
80	C₈	—	2	2	no	—
81	C₈	—	10	8	no	—
82	C₈	C₄×Dic₅	1	4	yes	—
83	C₅	C₄×#108	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	2	2	no	—
85	C₂²	C₄×Dic₁₀	1	2	yes	—
86	C₂²	C₂×C₄⋊Dic₅	1	1	yes	characteristic
87	C₄	—	2	2	no	—
88	C₄	#3951	1	4	yes	direct product factor
89	C₄	C₄×D₂₀	1	2	yes	—
90	C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
91	C₄	#4072	1	1	yes	characteristic
92	C₂	—	2	2	no	—
93	C₂	C₄×C₄⋊Dic₅	1	1	yes	characteristic
94	C₂	C₂×#3951	1	2	yes	—

	subgroup	G/H
center	C₄²	D₂₀
commutator	C₄×C₅	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₅
Fitting	C₂×C₄×C₅×C₈	C₂
socle	C₂²×C₅	C₂×C₄⋊C₄
prime radical	C₂³×C₅	C₂×Q₈
cosocle	C₂²×C₄×C₅	C₂³
hypercenter	C₂×C₄×C₈	D₅
hypocenter	C₅	C₄×#108
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
10. #3951	C₄	direct (N × H)
53. C₄×C₅	#108	semidirect
83. C₅	C₄×#108	semidirect
88. C₄	#3951	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×C₄×C₅×C₈	2
C₂×#3951	2
C₄×#681	2
#64772	2
C₄×#108	5

Subgroups — C4×#3951 #10600583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#3951 #10600583