Subgroups — #10602106

Order 640.

196 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, complemented
2	C₂×#3960	C₂	1	4	yes	maximal, complemented
3	#64984	C₂	1	1	yes	maximal, characteristic
4	C₄×#672	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×Q₁₆	—	2	1	no	—
6	C₂×C₅×Q₁₆	C₂²	1	2	yes	—
7	C₅×C₄⋊Q₈	—	2	1	no	—
8	C₂×D₄₀	—	2	1	no	—
9	C₂×D₄₀	C₂²	1	2	yes	—
10	#4020	—	2	1	no	—
11	C₄×C₅×C₈	C₂²	1	1	yes	characteristic
12	#3960	—	2	8	no	—
13	C₂×#672	C₂²	1	2	yes	—
14	#2248	—	5	1	no	maximal, Sylow
15	C₂×C₅×Q₈	—	2	2	no	—
16	C₂×D₂₀	—	2	2	no	—
17	C₂×D₂₀	—	4	2	no	—
18	C₅×Q₁₆	—	2	4	no	—
19	C₅×Q₁₆	—	4	2	no	—
20	C₂×C₅×C₈	D₄	1	1	yes	characteristic
21	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
22	C₅×C₄⋊C₄	—	4	2	no	—
23	C₄²×C₅	D₄	1	1	yes	characteristic
24	D₄₀	—	2	4	no	—
25	D₄₀	—	4	2	no	—
26	#672	D₄	1	4	yes	complemented
27	C₂×SD₃₂	—	5	4	no	—
28	#494	D₅	1	1	yes	characteristic, complemented
29	#493	—	5	1	no	—
30	C₄×C₁₆	—	5	1	no	—
31	C₂²×D₅	—	4	2	no	—
32	C₅×Q₈	—	4	2	no	—
33	C₅×Q₈	—	4	2	no	—
34	C₂×C₄×C₅	—	4	2	no	—
35	C₂×C₄×C₅	D₈	1	2	yes	—
36	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
37	D₂₀	—	4	2	no	—
38	D₂₀	—	4	2	no	—
39	D₂₀	—	8	4	no	—
40	C₅×C₈	D₈	1	2	yes	—
41	C₅×C₈	C₂×D₄	1	2	yes	—
42	C₂×Q₁₆	—	2	1	no	—
43	C₂×Q₁₆	C₂×D₅	1	2	yes	—
44	C₂×D₈	—	5	2	no	—
45	C₂×D₈	—	10	1	no	—
46	C₄⋊Q₈	—	2	1	no	—
47	#127	—	10	1	no	—
48	SD₃₂	—	10	8	no	—
49	C₂×C₁₆	—	5	2	no	—
50	C₄×C₈	C₂×D₅	1	1	yes	characteristic
51	C₂²×C₅	C₂×D₈	1	1	yes	characteristic
52	C₂×D₅	—	8	2	no	—
53	C₂×D₅	—	8	4	no	—
54	C₄×C₅	—	8	2	no	—
55	C₄×C₅	SD₃₂	1	4	yes	complemented
56	C₄×C₅	#127	1	1	yes	characteristic
57	C₄×C₅	C₂×D₈	1	1	yes	characteristic
58	C₂×Q₈	—	2	2	no	—
59	C₂×D₄	—	10	2	no	—
60	C₂×D₄	—	20	2	no	—
61	Q₁₆	—	2	4	no	—
62	Q₁₆	—	4	2	no	—
63	D₈	—	10	4	no	—
64	D₈	—	20	2	no	—
65	C₂×C₈	C₂²⋊D₅	1	1	yes	characteristic
66	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
67	C₄⋊C₄	—	4	2	no	—
68	C₄²	C₂²⋊D₅	1	1	yes	characteristic
69	C₁₆	—	5	4	no	—
70	C₂×C₅	#493	1	1	yes	characteristic
71	C₂×C₅	C₂×SD₃₂	1	2	yes	—
72	D₅	—	16	2	no	—
73	C₂³	—	20	2	no	—
74	Q₈	—	4	2	no	—
75	Q₈	—	4	2	no	—
76	D₄	—	20	2	no	—
77	D₄	—	20	2	no	—
78	D₄	—	40	4	no	—
79	C₂×C₄	—	4	2	no	—
80	C₂×C₄	#686	1	2	yes	—
81	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
82	C₈	#686	1	2	yes	—
83	C₈	D₄×D₅	1	2	yes	—
84	C₅	#2248	1	1	yes	characteristic, complemented, Sylow
85	C₂²	—	40	2	no	—
86	C₂²	—	40	4	no	—
87	C₂²	C₂×#686	1	1	yes	characteristic
88	C₄	—	8	2	no	—
89	C₄	#3960	1	4	yes	complemented
90	C₄	C₂×#686	1	1	yes	characteristic
91	C₄	#4086	1	1	yes	characteristic
92	C₂	—	80	2	no	—
93	C₂	#65362	1	1	yes	characteristic
94	C₂	C₂×#3960	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	C₂²×C₅	C₂×D₈
prime radical	#64984	C₂
hypercenter	#494	D₅
hypocenter	C₅	#2248
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
1. C₅×#494	C₂	semidirect
2. C₂×#3960	C₂	semidirect
4. C₄×#672	C₂	semidirect
26. #672	D₄	semidirect
28. #494	D₅	semidirect
55. C₄×C₅	SD₃₂	semidirect
84. C₅	#2248	semidirect
89. C₄	#3960	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×#3960	2
#64984	2
C₄×#672	2
#2248	5