Subgroups — #10602105

Order 640.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#494	C₂	1	1	yes	maximal, characteristic
2	C₂×#3961	C₂	1	4	yes	maximal
3	#64988	C₂	1	1	yes	maximal, characteristic
4	C₄×#672	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×Q₁₆	—	2	1	no	—
6	C₂×C₅×Q₁₆	C₂²	1	2	yes	—
7	C₅×C₄⋊Q₈	—	2	1	no	—
8	C₂×Dic₂₀	—	2	1	no	—
9	C₂×Dic₂₀	C₂²	1	2	yes	—
10	#4015	—	2	1	no	—
11	C₄×C₅×C₈	C₂²	1	1	yes	characteristic
12	#3961	—	2	8	no	—
13	C₂×#672	C₂²	1	2	yes	—
14	#2247	—	5	1	no	maximal, Sylow
15	C₂×C₅×Q₈	—	2	2	no	—
16	C₂×Dic₁₀	—	2	2	no	—
17	C₅×Q₁₆	—	2	4	no	—
18	C₅×Q₁₆	—	4	2	no	—
19	C₂×C₅×C₈	D₄	1	1	yes	characteristic
20	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
21	C₅×C₄⋊C₄	—	4	2	no	—
22	C₄²×C₅	D₄	1	1	yes	characteristic
23	C₄⋊Dic₅	—	4	2	no	—
24	Dic₂₀	—	2	4	no	—
25	Dic₂₀	—	4	2	no	—
26	#672	D₄	1	4	yes	—
27	C₂×Q₃₂	—	5	4	no	—
28	#494	—	5	1	no	—
29	#494	D₅	1	1	yes	characteristic
30	C₄×C₁₆	—	5	1	no	—
31	C₅×Q₈	—	4	2	no	—
32	C₅×Q₈	—	4	2	no	—
33	C₂×C₄×C₅	—	4	2	no	—
34	C₂×C₄×C₅	D₈	1	2	yes	—
35	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₅	—	4	2	no	—
37	Dic₁₀	—	4	2	no	—
38	Dic₁₀	—	4	2	no	—
39	C₅×C₈	D₈	1	2	yes	—
40	C₅×C₈	C₂×D₄	1	2	yes	—
41	C₂×Q₁₆	—	2	1	no	—
42	C₂×Q₁₆	—	5	2	no	—
43	C₂×Q₁₆	—	10	1	no	—
44	C₂×Q₁₆	C₂×D₅	1	2	yes	—
45	C₄⋊Q₈	—	2	1	no	—
46	C₄⋊Q₈	—	10	1	no	—
47	Q₃₂	—	10	8	no	—
48	C₂×C₁₆	—	5	2	no	—
49	C₄×C₈	C₂×D₅	1	1	yes	characteristic
50	C₂²×C₅	C₂×D₈	1	1	yes	characteristic
51	C₄×C₅	—	8	2	no	—
52	C₄×C₅	Q₃₂	1	4	yes	complemented
53	C₄×C₅	#127	1	1	yes	characteristic
54	C₄×C₅	C₂×D₈	1	1	yes	characteristic
55	Dic₅	—	8	2	no	—
56	C₂×Q₈	—	2	2	no	—
57	C₂×Q₈	—	10	2	no	—
58	Q₁₆	—	2	4	no	—
59	Q₁₆	—	4	2	no	—
60	Q₁₆	—	10	4	no	—
61	Q₁₆	—	20	2	no	—
62	C₂×C₈	C₂²⋊D₅	1	1	yes	characteristic
63	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
64	C₄⋊C₄	—	4	2	no	—
65	C₄⋊C₄	—	20	2	no	—
66	C₄²	C₂²⋊D₅	1	1	yes	characteristic
67	C₁₆	—	5	4	no	—
68	C₂×C₅	#493	1	1	yes	characteristic
69	C₂×C₅	C₂×Q₃₂	1	2	yes	—
70	Q₈	—	4	2	no	—
71	Q₈	—	4	2	no	—
72	Q₈	—	20	2	no	—
73	Q₈	—	20	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	20	2	no	—
76	C₂×C₄	#686	1	2	yes	—
77	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
78	C₈	#686	1	2	yes	—
79	C₈	D₄×D₅	1	2	yes	—
80	C₅	#2247	1	1	yes	characteristic, complemented, Sylow
81	C₂²	C₂×#686	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	40	2	no	—
84	C₄	#3961	1	4	yes	complemented
85	C₄	C₂×#686	1	1	yes	characteristic
86	C₄	#4086	1	1	yes	characteristic
87	C₂	#65362	1	1	yes	characteristic
88	C₂	C₂×#3961	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#686
commutator, cosocle	C₂×C₅×C₈	C₂³
Frattini	C₂×C₈	C₂²×D₅
Fitting	C₅×#494	C₂
socle, prime radical	C₂²×C₅	C₂×D₈
hypercenter	#494	D₅
hypocenter	C₅	#2247
LCS	G ▷ C₂×C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
52. C₄×C₅	Q₃₂	semidirect
80. C₅	#2247	semidirect
84. C₄	#3961	semidirect

Maximal subgroups

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

subgroup	index
C₅×#494	2
C₂×#3961	2
#64988	2
C₄×#672	2
#2247	5