Subgroups — #10602289

Order 640.

148 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	Q₁₆×Dic₅	C₂	1	2	yes	maximal
3	#64784	C₂	1	2	yes	maximal
4	#64725	C₂	1	1	yes	maximal, characteristic
5	#64722	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×Q₁₆	C₂²	1	2	yes	—
7	Q₈×Dic₅	—	2	2	no	—
8	C₅×Q₃₂	C₄	1	4	yes	complemented
9	C₂×C₅×C₁₆	C₂²	1	1	yes	characteristic
10	#3967	—	2	2	no	—
11	#3950	C₂²	1	2	yes	—
12	C₈×Dic₅	C₂²	1	1	yes	characteristic
13	C₂×#672	C₂²	1	1	yes	characteristic
14	#2176	—	5	1	no	maximal, Sylow
15	C₂×C₅×Q₈	—	2	2	no	—
16	C₅×Q₁₆	—	2	2	no	—
17	C₅×Q₁₆	C₂×C₄	1	4	yes	—
18	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
19	C₄⋊Dic₅	—	2	2	no	—
20	C₄⋊Dic₅	—	4	2	no	—
21	C₄×Dic₅	—	4	2	no	—
22	C₄×Dic₅	D₄	1	1	yes	characteristic
23	C₂×#168	D₄	1	1	yes	characteristic
24	C₅×C₁₆	C₂×C₄	1	2	yes	—
25	#672	—	2	1	no	—
26	C₂×Q₃₂	D₅	1	1	yes	characteristic
27	C₄×Q₁₆	—	5	2	no	—
28	#367	—	5	1	no	—
29	#358	—	5	2	no	—
30	#346	—	5	1	no	—
31	C₅×Q₈	—	2	4	no	—
32	C₅×Q₈	—	4	2	no	—
33	C₂×C₄×C₅	—	4	2	no	—
34	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₅	—	4	2	no	—
36	C₂×Dic₅	D₈	1	2	yes	—
37	C₅×C₈	C₂²×C₄	1	1	yes	characteristic
38	C₅×C₈	#41	1	1	yes	characteristic
39	#168	—	2	1	no	—
40	C₂×Q₁₆	C₂×D₅	1	2	yes	—
41	C₄×Q₈	—	10	2	no	—
42	Q₃₂	Dic₅	1	4	yes	complemented
43	C₂×C₁₆	—	5	1	no	—
44	C₂×C₁₆	C₂×D₅	1	1	yes	characteristic
45	#107	—	5	2	no	—
46	#103	—	10	2	no	—
47	C₄×C₈	—	5	1	no	—
48	C₂²×C₅	C₂×D₈	1	1	yes	characteristic
49	C₄×C₅	—	4	4	no	—
50	C₄×C₅	C₄×D₄	1	1	yes	characteristic
51	C₄×C₅	#135	1	1	yes	characteristic
52	Dic₅	—	2	2	no	—
53	Dic₅	—	8	2	no	—
54	C₂×Q₈	—	2	2	no	—
55	Q₁₆	—	2	2	no	—
56	Q₁₆	C₂×Dic₅	1	4	yes	—
57	C₂×C₈	—	5	1	no	—
58	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
59	C₄⋊C₄	—	10	2	no	—
60	C₄⋊C₄	—	20	2	no	—
61	C₄²	—	5	1	no	—
62	C₄²	—	20	2	no	—
63	C₁₆	—	10	1	no	—
64	C₁₆	C₂×Dic₅	1	2	yes	—
65	C₂×C₅	C₄×D₈	1	1	yes	characteristic
66	C₂×C₅	#510	1	2	yes	—
67	Q₈	—	2	4	no	—
68	Q₈	—	4	2	no	—
69	C₂×C₄	—	4	2	no	—
70	C₂×C₄	—	5	2	no	—
71	C₂×C₄	—	20	2	no	—
72	C₂×C₄	D₄×D₅	1	1	yes	characteristic
73	C₈	—	10	1	no	—
74	C₈	#711	1	1	yes	characteristic
75	C₈	C₂²×Dic₅	1	1	yes	characteristic
76	C₅	#2176	1	1	yes	characteristic, complemented, Sylow
77	C₂²	D₅×D₈	1	1	yes	characteristic
78	C₄	—	4	4	no	—
79	C₄	—	10	2	no	—
80	C₄	—	40	2	no	—
81	C₄	#4058	1	1	yes	characteristic
82	C₄	D₄×Dic₅	1	1	yes	characteristic
83	C₂	#65207	1	2	yes	—
84	C₂	D₈×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₅×D₈
commutator	C₅×C₈	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₅
Fitting	C₂×C₅×Q₃₂	C₂
socle, prime radical	C₂²×C₅	C₂×D₈
cosocle	C₂×C₅×C₈	C₂³
hypercenter	C₂×Q₃₂	D₅
hypocenter	C₅	#2176
LCS	G ▷ 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
8. C₅×Q₃₂	C₄	semidirect
42. Q₃₂	Dic₅	semidirect
76. C₅	#2176	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
Q₁₆×Dic₅	2
#64784	2
#64725	2
#64722	2
#2176	5