Subgroups — #11986281

Order 1280.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1452	C₂	1	1	yes	maximal, characteristic
2	#10600537	C₂	1	2	yes	maximal
3	C₅×#431	C₄	1	2	yes	—
4	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
5	C₅×#322	—	2	2	no	—
6	C₂²⋊#672	C₄	1	4	yes	—
7	C₄⋊#672	—	2	2	no	—
8	C₄×#672	—	2	2	no	—
9	#7198	—	5	1	no	maximal, Sylow
10	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
11	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
12	C₅×C₄⋊C₈	C₈	1	4	yes	—
13	C₅×C₂²⋊C₈	—	2	2	no	—
14	C₄×C₅×C₈	—	2	2	no	—
15	C₄×C₅×C₈	D₄	1	1	yes	characteristic
16	C₄×C₅×C₈	D₄	1	2	yes	—
17	C₄×C₅×C₈	Q₈	1	1	yes	characteristic
18	C₂×#672	—	2	4	no	—
19	#2162	—	5	2	no	—
20	#1452	D₅	1	1	yes	characteristic
21	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
22	C₂²×C₄×C₅	M₁₆	1	2	yes	—
23	C₂×C₅×C₈	—	2	4	no	—
24	C₂×C₅×C₈	—	4	2	no	—
25	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
26	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
27	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
28	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
29	C₄²×C₅	C₂×C₈	1	2	yes	—
30	#672	—	4	4	no	—
31	#431	Dic₅	1	2	yes	—
32	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
33	C₄⋊C₁₆	—	10	2	no	—
34	C₂²⋊C₁₆	—	5	4	no	—
35	C₄×C₁₆	—	10	2	no	—
36	#322	—	2	2	no	—
37	C₂³×C₅	#97	1	1	yes	characteristic
38	C₂×C₄×C₅	—	2	2	no	—
39	C₂×C₄×C₅	—	2	4	no	—
40	C₂×C₄×C₅	#95	1	1	yes	characteristic
41	C₂×C₄×C₅	C₄×C₈	1	1	yes	characteristic
42	C₂×C₄×C₅	C₂²⋊C₈	1	2	yes	—
43	C₂×C₄×C₅	C₄⋊C₈	1	2	yes	—
44	C₅×C₈	—	2	2	no	—
45	C₅×C₈	—	2	2	no	—
46	C₅×C₈	—	4	4	no	—
47	C₂²×C₈	C₄×D₅	1	2	yes	—
48	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
49	C₂×C₁₆	—	10	4	no	—
50	C₄⋊C₈	#168	1	4	yes	—
51	C₂²⋊C₈	—	2	2	no	—
52	C₄×C₈	—	2	2	no	—
53	C₄×C₈	Dic₁₀	1	1	yes	characteristic
54	C₄×C₈	D₂₀	1	1	yes	characteristic
55	C₄×C₈	C₂²⋊D₅	1	2	yes	—
56	C₂²×C₅	—	2	1	no	—
57	C₂²×C₅	—	2	2	no	—
58	C₂²×C₅	#336	1	1	yes	characteristic
59	C₄×C₅	—	2	1	no	—
60	C₄×C₅	—	2	2	no	—
61	C₄×C₅	#344	1	2	yes	—
62	C₄×C₅	#350	1	4	yes	—
63	C₂²×C₄	#681	1	2	yes	—
64	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
65	C₂×C₈	—	2	4	no	—
66	C₂×C₈	—	4	2	no	—
67	C₂×C₈	#683	1	2	yes	—
68	C₂×C₈	#685	1	2	yes	—
69	C₄²	C₂×#168	1	2	yes	—
70	C₄²	C₄⋊Dic₅	1	1	yes	characteristic
71	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
72	C₁₆	—	20	4	no	—
73	C₂×C₅	—	4	1	no	—
74	C₂×C₅	#1281	1	1	yes	characteristic
75	C₂×C₅	#1379	1	2	yes	—
76	C₂³	#3935	1	1	yes	characteristic
77	C₂×C₄	—	2	2	no	—
78	C₂×C₄	—	2	4	no	—
79	C₂×C₄	C₄×#168	1	1	yes	characteristic
80	C₂×C₄	C₄⋊#168	1	2	yes	—
81	C₂×C₄	C₂²⋊#168	1	2	yes	—
82	C₂×C₄	#3963	1	1	yes	characteristic
83	C₈	—	2	2	no	—
84	C₈	—	2	2	no	—
85	C₈	—	4	4	no	—
86	C₅	#7198	1	1	yes	characteristic, complemented, Sylow
87	C₂²	—	2	1	no	—
88	C₂²	—	2	2	no	—
89	C₂²	#64744	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	2	2	no	—
92	C₄	#64776	1	2	yes	—
93	C₄	#64781	1	4	yes	—
94	C₂	—	4	1	no	—
95	C₂	#10598152	1	1	yes	characteristic
96	C₂	#10598162	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂²⋊Dic₅
commutator	C₂×C₄×C₅	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₅
Fitting	C₅×#1452	C₂
socle	C₂²×C₅	#336
prime radical	C₂³×C₅	#97
cosocle	C₂×C₄×C₅×C₈	C₂²
hypercenter	#1452	D₅
hypocenter	C₅	#7198
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ #1452

Complements

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

N	H ≅ G/N	type
86. C₅	#7198	semidirect

Maximal subgroups

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

subgroup	index
C₅×#1452	2
#10600537	2
#7198	5