Subgroups — #10600153

Order 640.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3930	C₂	1	1	yes	maximal, characteristic
2	D₅×#108	C₂	1	2	yes	maximal
3	C₅×#368	C₂	1	1	yes	maximal, characteristic, complemented
4	#64726	C₂	1	1	yes	maximal, characteristic, complemented
5	#64713	C₂	1	2	yes	maximal, complemented
6	D₅×M₁₆	—	2	2	no	—
7	C₂×C₈×D₅	C₂²	1	1	yes	characteristic
8	C₂×C₅×C₁₆	C₂²	1	1	yes	characteristic
9	C₅×#108	C₂²	1	2	yes	—
10	#3954	—	2	2	no	—
11	#3951	C₂²	1	2	yes	—
12	C₂×#672	C₂²	1	1	yes	characteristic
13	#3930	C₄	1	4	yes	—
14	#2161	—	5	1	no	maximal, Sylow
15	C₂×C₄×D₅	D₄	1	1	yes	characteristic
16	C₅×M₁₆	—	2	2	no	—
17	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
18	#681	—	2	2	no	—
19	C₂×#168	D₄	1	1	yes	characteristic
20	#676	—	4	2	no	—
21	C₈×D₅	—	4	2	no	—
22	C₈×D₅	C₂×C₄	1	2	yes	—
23	C₈×D₅	Q₈	1	2	yes	—
24	C₅×C₁₆	C₂×C₄	1	2	yes	—
25	#672	C₂×C₄	1	2	yes	—
26	C₂×M₃₂	—	5	1	no	—
27	C₂×#108	—	5	2	no	—
28	#368	—	5	1	no	—
29	#368	—	5	2	no	—
30	#368	D₅	1	1	yes	characteristic, complemented
31	C₂²×D₅	Q₁₆	1	1	yes	characteristic
32	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₅	Q₁₆	1	1	yes	characteristic
34	C₄×D₅	C₄⋊C₄	1	2	yes	—
35	C₄×D₅	D₈	1	2	yes	—
36	C₅×C₈	—	4	2	no	—
37	C₅×C₈	C₂²×C₄	1	1	yes	characteristic
38	C₅×C₈	C₂×Q₈	1	1	yes	characteristic
39	#168	—	4	2	no	—
40	#168	C₄⋊C₄	1	2	yes	—
41	C₂×M₁₆	—	10	2	no	—
42	C₂²×C₈	—	5	1	no	—
43	M₃₂	—	5	4	no	—
44	C₂×C₁₆	—	5	1	no	—
45	C₂×C₁₆	C₂×D₅	1	1	yes	characteristic
46	#108	—	5	2	no	—
47	#108	—	10	2	no	—
48	#108	C₂×D₅	1	2	yes	—
49	C₂²×C₅	C₂×Q₁₆	1	1	yes	characteristic
50	C₂×D₅	—	4	1	no	—
51	C₂×D₅	#107	1	2	yes	—
52	C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₅	C₂×D₈	1	1	yes	characteristic
54	Dic₅	#107	1	2	yes	—
55	C₂²×C₄	—	5	1	no	—
56	M₁₆	—	2	2	no	—
57	M₁₆	—	10	2	no	—
58	M₁₆	—	20	2	no	—
59	C₂×C₈	—	5	1	no	—
60	C₂×C₈	—	5	2	no	—
61	C₂×C₈	—	5	2	no	—
62	C₂×C₈	—	20	2	no	—
63	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
64	C₁₆	—	5	2	no	—
65	C₁₆	C₄×D₅	1	2	yes	—
66	C₂×C₅	—	2	1	no	—
67	C₂×C₅	C₂×#107	1	1	yes	characteristic
68	D₅	—	2	2	no	—
69	C₂³	—	5	1	no	—
70	C₂×C₄	—	5	1	no	—
71	C₂×C₄	—	5	2	no	—
72	C₂×C₄	—	5	2	no	—
73	C₂×C₄	D₄×D₅	1	1	yes	characteristic
74	C₈	—	4	2	no	—
75	C₈	—	5	2	no	—
76	C₈	—	20	2	no	—
77	C₈	C₂×C₄×D₅	1	1	yes	characteristic
78	C₈	Q₈×D₅	1	1	yes	characteristic
79	C₅	#2161	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	5	2	no	—
81	C₂²	—	20	1	no	—
82	C₂²	D₅×Q₁₆	1	1	yes	characteristic
83	C₄	—	5	2	no	—
84	C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
85	C₄	D₅×D₈	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	10	2	no	—
88	C₂	D₅×#107	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₅×D₈
commutator	C₅×C₈	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₅
Fitting	C₅×#368	C₂
socle	C₂×C₅	C₂×#107
prime radical	C₂²×D₅	Q₁₆
cosocle	C₂×C₅×C₈	C₂³
hypercenter	#368	D₅
hypocenter	C₅	#2161
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

Complements

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

N	H ≅ G/N	type
3. C₅×#368	C₂	semidirect
4. #64726	C₂	semidirect
5. #64713	C₂	semidirect
30. #368	D₅	semidirect
79. C₅	#2161	semidirect

Maximal subgroups

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

subgroup	index
C₂×#3930	2
D₅×#108	2
C₅×#368	2
#64726	2
#64713	2
#2161	5