Subgroups — #10602292

Order 640.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	#65470	C₂	1	2	yes	maximal
3	C₂×#3961	C₂	1	2	yes	maximal
4	C₂×Dic₄₀	C₂	1	1	yes	maximal, characteristic
5	C₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×Q₁₆	C₂²	1	2	yes	—
7	#4090	—	2	2	no	—
8	C₂×#689	—	2	2	no	—
9	C₂×Dic₂₀	C₂²	1	2	yes	—
10	C₅×Q₃₂	—	2	2	no	—
11	C₂×C₅×C₁₆	C₂²	1	1	yes	characteristic
12	#3961	—	2	4	no	—
13	C₈×Dic₅	C₂²	1	1	yes	characteristic
14	C₂×#672	C₂²	1	1	yes	characteristic
15	Dic₄₀	—	2	2	no	—
16	#2247	—	5	1	no	maximal, Sylow
17	C₂×C₅×Q₈	—	2	2	no	—
18	C₂×Dic₁₀	—	2	2	no	—
19	C₅×Q₁₆	—	2	2	no	—
20	C₅×Q₁₆	—	2	2	no	—
21	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
22	#689	—	4	4	no	—
23	#683	—	4	4	no	—
24	C₄×Dic₅	D₄	1	1	yes	characteristic
25	C₂×#168	D₄	1	1	yes	characteristic
26	Dic₂₀	—	2	2	no	—
27	Dic₂₀	—	2	2	no	—
28	C₅×C₁₆	D₄	1	2	yes	—
29	#672	D₄	1	2	yes	—
30	C₂×Q₃₂	—	5	2	no	—
31	C₂×Q₃₂	—	5	1	no	—
32	C₂×Q₃₂	D₅	1	1	yes	characteristic
33	#494	—	5	2	no	—
34	C₄×C₁₆	—	5	1	no	—
35	C₅×Q₈	—	4	2	no	—
36	C₅×Q₈	—	4	2	no	—
37	C₂×C₄×C₅	—	4	2	no	—
38	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
39	C₂×Dic₅	—	4	2	no	—
40	C₂×Dic₅	D₈	1	2	yes	—
41	Dic₁₀	—	4	2	no	—
42	Dic₁₀	—	4	2	no	—
43	C₅×C₈	C₂×D₄	1	1	yes	characteristic
44	C₅×C₈	C₂×D₄	1	1	yes	characteristic
45	#168	D₈	1	2	yes	—
46	C₂×Q₁₆	—	5	2	no	—
47	C₂×Q₁₆	—	10	2	no	—
48	C₂×Q₁₆	C₂×D₅	1	2	yes	—
49	C₄⋊Q₈	—	10	2	no	—
50	Q₃₂	—	2	2	no	—
51	Q₃₂	—	10	4	no	—
52	Q₃₂	—	10	2	no	—
53	C₂×C₁₆	—	5	1	no	—
54	C₂×C₁₆	C₂×D₅	1	1	yes	characteristic
55	C₄×C₈	—	5	1	no	—
56	C₂²×C₅	C₂×D₈	1	1	yes	characteristic
57	C₄×C₅	—	8	2	no	—
58	C₄×C₅	#127	1	1	yes	characteristic
59	C₄×C₅	C₂×D₈	1	1	yes	characteristic
60	Dic₅	—	8	2	no	—
61	Dic₅	Q₃₂	1	4	yes	complemented
62	C₂×Q₈	—	2	2	no	—
63	C₂×Q₈	—	10	2	no	—
64	Q₁₆	—	2	2	no	—
65	Q₁₆	—	2	2	no	—
66	Q₁₆	—	10	2	no	—
67	Q₁₆	—	10	2	no	—
68	Q₁₆	—	20	4	no	—
69	C₂×C₈	—	5	1	no	—
70	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
71	C₄⋊C₄	—	20	4	no	—
72	C₄²	—	5	1	no	—
73	C₁₆	—	5	2	no	—
74	C₁₆	C₂²⋊D₅	1	2	yes	—
75	C₂×C₅	#493	1	1	yes	characteristic
76	C₂×C₅	C₂×Q₃₂	1	2	yes	—
77	Q₈	—	4	2	no	—
78	Q₈	—	4	2	no	—
79	Q₈	—	20	2	no	—
80	Q₈	—	20	2	no	—
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	5	2	no	—
83	C₂×C₄	—	20	2	no	—
84	C₂×C₄	D₄×D₅	1	1	yes	characteristic
85	C₈	—	5	2	no	—
86	C₈	D₄×D₅	1	1	yes	characteristic
87	C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
88	C₅	#2247	1	1	yes	characteristic, complemented, Sylow
89	C₂²	D₅×D₈	1	1	yes	characteristic
90	C₄	—	5	4	no	—
91	C₄	—	8	2	no	—
92	C₄	—	40	2	no	—
93	C₄	D₅×D₈	1	1	yes	characteristic
94	C₄	#4086	1	1	yes	characteristic
95	C₂	D₅×Q₃₂	1	2	yes	—
96	C₂	#65440	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₅×D₈
commutator, cosocle	C₂×C₅×C₈	C₂³
Frattini	C₂×C₈	C₂²×D₅
Fitting	C₂×C₅×Q₃₂	C₂
socle, prime radical	C₂²×C₅	C₂×D₈
hypercenter	C₂×Q₃₂	D₅
hypocenter	C₅	#2247
LCS	G ▷ C₂×C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
61. Dic₅	Q₃₂	semidirect
88. C₅	#2247	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×Q₃₂	2
#65470	2
C₂×#3961	2
C₂×Dic₄₀	2
C₁₆×Dic₅	2
#2247	5