Subgroups — #13085510

Order 1440.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#4379	C₂	1	1	yes	maximal, characteristic
2	C₅×C₄⋊#157	C₂	1	1	yes	maximal, characteristic
3	C₃⋊D₃×#168	C₂	1	1	yes	maximal, characteristic
4	C₂×#4379	—	2	1	no	—
5	C₂×C₅×#157	—	2	1	no	—
6	C₄×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic
7	C₃⋊(C₃⋊#168)	C₄	1	1	yes	characteristic, complemented
8	C₃²×#168	C₄	1	1	yes	characteristic, complemented
9	#63768	—	5	1	no	maximal, Hall
10	D₃×#168	—	6	2	no	—
11	C₂×C₅×C₃⋊D₃	D₄	1	1	yes	characteristic
12	#4379	—	4	1	no	—
13	C₅×#157	—	4	1	no	—
14	C₃²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
15	C₅×C₃⋊Dic₃	Q₈	1	1	yes	characteristic
16	#3940	—	9	1	no	maximal, Hall
17	C₄⋊#157	—	5	1	no	—
18	C₄⋊#157	D₅	1	1	yes	characteristic
19	C₈×C₃⋊D₃	—	5	1	no	—
20	C₄×C₅×D₃	—	6	2	no	—
21	C₃⋊#168	—	6	2	no	—
22	C₃×#168	—	2	2	no	—
23	C₂×C₃²×C₅	C₄⋊C₄	1	1	yes	characteristic
24	C₅×C₃⋊D₃	SD₁₆	1	1	yes	characteristic
25	C₅×C₃⋊D₃	SD₁₆	1	1	yes	characteristic
26	C₅×C₄⋊C₄	—	9	1	no	—
27	C₄⋊Dic₅	—	9	1	no	—
28	C₂×#168	—	9	1	no	—
29	C₂×#157	—	2	1	no	—
30	C₂×#157	—	10	1	no	—
31	C₄×C₃⋊D₃	C₂×D₅	1	1	yes	characteristic
32	C₃²×C₈	—	5	1	no	—
33	C₃⋊(C₃⋊C₈)	—	5	1	no	—
34	C₂×C₅×D₃	—	6	2	no	—
35	C₃×C₄×C₅	—	2	2	no	—
36	C₅×Dic₃	—	6	2	no	—
37	D₃×C₈	—	30	2	no	—
38	C₃²×C₅	#106	1	1	yes	characteristic, complemented, Hall
39	C₂×C₄×C₅	—	9	1	no	—
40	C₂×C₄×C₅	—	18	1	no	—
41	C₂×Dic₅	—	18	1	no	—
42	#168	—	9	1	no	—
43	#168	#157	1	1	yes	characteristic, complemented
44	C₂×C₃⋊D₃	C₂²⋊D₅	1	1	yes	characteristic
45	#157	—	4	1	no	—
46	#157	—	20	1	no	—
47	C₃²×C₄	C₄×D₅	1	1	yes	characteristic
48	C₃⋊Dic₃	Dic₁₀	1	1	yes	characteristic
49	#106	—	45	1	no	Sylow
50	C₂×C₃×C₅	—	2	2	no	—
51	C₅×D₃	—	6	2	no	—
52	C₅×D₃	—	6	2	no	—
53	C₄×D₃	—	6	2	no	—
54	C₃×C₈	—	10	2	no	—
55	C₃⋊C₈	—	30	2	no	—
56	C₂²×C₅	—	9	1	no	—
57	C₄×C₅	—	9	1	no	—
58	C₄×C₅	—	36	1	no	—
59	C₄×C₅	C₂×#157	1	1	yes	characteristic
60	Dic₅	—	36	1	no	—
61	C₂×C₃²	#683	1	1	yes	characteristic
62	C₃⋊D₃	#687	1	1	yes	characteristic
63	C₃⋊D₃	#688	1	1	yes	characteristic
64	C₂×C₈	—	45	1	no	—
65	C₄⋊C₄	—	9	1	no	—
66	C₄⋊C₄	—	45	1	no	—
67	C₃×C₅	—	2	2	no	—
68	C₂×D₃	—	6	2	no	—
69	C₃×C₄	—	2	2	no	—
70	Dic₃	—	6	2	no	—
71	C₂×C₅	—	9	1	no	—
72	C₂×C₅	—	9	1	no	—
73	C₂×C₅	C₄⋊#157	1	1	yes	characteristic
74	C₃²	#3940	1	1	yes	characteristic, complemented, Sylow
75	C₂×C₄	—	9	1	no	—
76	C₂×C₄	—	18	1	no	—
77	C₂×C₄	—	90	1	no	—
78	C₈	—	5	1	no	—
79	C₈	—	45	1	no	—
80	C₂×C₃	—	2	2	no	—
81	D₃	—	6	2	no	—
82	D₃	—	6	2	no	—
83	C₅	#63768	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	9	1	no	—
85	C₄	—	9	1	no	—
86	C₄	—	36	1	no	—
87	C₄	—	180	1	no	—
88	C₄	D₅×#157	1	1	yes	characteristic
89	C₃	—	2	2	no	—
90	C₂	—	9	1	no	—
91	C₂	—	9	1	no	—
92	C₂	#10623986	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10623986
commutator, Fitting	C₃²×C₄×C₅	C₂×C₄
Frattini, hypercenter	C₄	D₅×#157
socle	C₂×C₃²×C₅	C₄⋊C₄
prime radical	C₂×C₅×C₃⋊D₃	D₄
cosocle	C₄×C₅×C₃⋊D₃	C₂²
hypocenter	C₃²×C₅	#106
LCS	G ▷ C₃²×C₄×C₅ ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
7. C₃⋊(C₃⋊#168)	C₄	semidirect
8. C₃²×#168	C₄	semidirect
38. C₃²×C₅	#106	semidirect
43. #168	#157	semidirect
74. C₃²	#3940	semidirect
83. C₅	#63768	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#4379	2
C₅×C₄⋊#157	2
C₃⋊D₃×#168	2
#63768	5
#3940	9