Subgroups — #13100566

Order 1600.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#4015	C₂	1	2	yes	maximal
2	C₂×#87775	C₂	1	4	yes	maximal
3	C₄×#6029	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×Dic₁₀	C₂²	1	4	yes	—
5	C₄²×C₅²	C₂²	1	1	yes	characteristic
6	C₂×#6029	C₂²	1	2	yes	—
7	C₅×C₄⋊Dic₅	—	2	4	no	—
8	#87775	—	2	8	no	—
9	#65381	—	5	2	no	maximal
10	C₂×C₄×C₅²	D₄	1	2	yes	—
11	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
12	C₂×C₅×Dic₅	—	2	4	no	—
13	C₅×Dic₁₀	—	2	8	no	—
14	#6029	D₄	1	4	yes	—
15	C₅×C₄⋊Q₈	—	5	2	no	—
16	C₂×#689	—	5	8	no	—
17	#4015	D₅	1	2	yes	—
18	C₄×#168	—	5	2	no	—
19	C₄×#168	—	10	2	no	—
20	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
21	C₄×C₅²	Q₁₆	1	4	yes	complemented
22	C₄×C₅²	C₂×D₄	1	2	yes	—
23	C₅×Dic₅	—	4	4	no	—
24	C₂×C₅×Q₈	—	5	4	no	—
25	C₂×Dic₁₀	C₂×D₅	1	4	yes	—
26	C₅×C₄⋊C₄	—	10	4	no	—
27	C₄²×C₅	—	2	2	no	—
28	C₄²×C₅	C₂×D₅	1	2	yes	—
29	#689	—	10	16	no	—
30	C₄⋊Dic₅	—	2	4	no	—
31	C₂×#168	—	5	4	no	—
32	C₂×#168	—	10	4	no	—
33	#494	—	25	1	no	Sylow
34	C₂×C₅²	#127	1	1	yes	characteristic
35	C₂×C₅²	C₂×Q₁₆	1	2	yes	—
36	C₅×Q₈	—	10	8	no	—
37	C₂×C₄×C₅	—	2	4	no	—
38	C₂×C₄×C₅	—	2	2	no	—
39	C₂×C₄×C₅	—	10	4	no	—
40	C₂×C₄×C₅	C₂²⋊D₅	1	4	yes	—
41	C₂×C₄×C₅	C₂²×D₅	1	2	yes	—
42	C₂×Dic₅	—	2	4	no	—
43	Dic₁₀	—	2	8	no	—
44	#168	—	5	8	no	—
45	#168	—	10	8	no	—
46	C₂×Q₁₆	—	25	4	no	—
47	C₄⋊Q₈	—	5	2	no	—
48	C₄×C₈	—	25	1	no	—
49	C₅²	#494	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₅	—	2	2	no	—
51	C₂²×C₅	C₂×C₂²⋊D₅	1	2	yes	—
52	C₄×C₅	—	2	4	no	—
53	C₄×C₅	—	2	8	no	—
54	C₄×C₅	—	20	4	no	—
55	C₄×C₅	#689	1	8	yes	complemented
56	C₄×C₅	D₄×D₅	1	4	yes	—
57	Dic₅	—	4	4	no	—
58	C₂×Q₈	—	5	4	no	—
59	Q₁₆	—	50	8	no	—
60	C₂×C₈	—	25	2	no	—
61	C₄⋊C₄	—	10	4	no	—
62	C₄²	D₅²	1	1	yes	characteristic
63	C₂×C₅	—	2	4	no	—
64	C₂×C₅	—	2	2	no	—
65	C₂×C₅	#4086	1	2	yes	—
66	C₂×C₅	C₂×#689	1	4	yes	—
67	Q₈	—	10	8	no	—
68	C₂×C₄	—	10	4	no	—
69	C₂×C₄	#6037	1	2	yes	—
70	C₂×C₄	C₂×D₅²	1	1	yes	characteristic
71	C₈	—	25	4	no	—
72	C₅	—	2	2	no	—
73	C₅	#65381	1	2	yes	complemented
74	C₂²	C₂×#6037	1	1	yes	characteristic
75	C₄	—	20	4	no	—
76	C₄	#87775	1	4	yes	complemented
77	C₄	#87877	1	2	yes	—
78	C₂	C₂×#87775	1	2	yes	—
79	C₂	#11717032	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#6037
commutator, cosocle	C₂×C₄×C₅²	C₂³
Frattini	C₂×C₄	C₂×D₅²
Fitting	C₄²×C₅²	C₂²
socle, prime radical	C₂²×C₅²	C₂×D₄
hypercenter	C₄²	D₅²
hypocenter	C₅²	#494
LCS	G ▷ C₂×C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
21. C₄×C₅²	Q₁₆	semidirect
49. C₅²	#494	semidirect
55. C₄×C₅	#689	semidirect
73. C₅	#65381	semidirect
76. C₄	#87775	semidirect

Maximal subgroups

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

subgroup	index
C₅×#4015	2
C₂×#87775	2
C₄×#6029	2
#65381	5