Subgroups — C₂×C₅×#1132 #11765060

Order 1120.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₂₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₁₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1132	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅×D₇	—	2	1	no	—
6	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
7	C₂×C₅×Dic₇	—	2	1	no	—
8	C₅×D₂₈	—	2	1	no	—
9	C₅×D₂₈	C₂²	1	2	yes	—
10	C₅×Dic₁₄	—	2	1	no	—
11	C₅×Dic₁₄	C₂²	1	2	yes	complemented
12	C₅×C₇×C₈	C₂²	1	2	yes	complemented
13	C₂×#1132	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₅×SD₁₆	—	7	1	no	maximal, Hall
15	C₂²×C₅×C₇	D₄	1	1	yes	characteristic
16	C₂×C₅×D₇	—	2	2	no	—
17	C₂×C₅×D₇	—	4	2	no	—
18	C₄×C₅×C₇	D₄	1	1	yes	characteristic
19	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
20	C₅×Dic₇	—	2	2	no	—
21	C₂×D₂₈	C₂×C₅	1	1	yes	characteristic
22	C₂×Dic₁₄	C₂×C₅	1	1	yes	characteristic, complemented
23	C₂×C₇×C₈	C₂×C₅	1	1	yes	characteristic, complemented
24	#1132	C₂×C₅	1	4	yes	direct product factor
25	C₂×C₅×Q₈	—	7	1	no	—
26	C₂×C₅×D₄	—	7	1	no	—
27	C₅×SD₁₆	—	7	4	no	—
28	C₂×C₅×C₈	D₇	1	1	yes	characteristic, complemented
29	C₂×C₅×C₇	SD₁₆	1	2	yes	complemented
30	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
31	C₅×D₇	—	4	2	no	—
32	C₂²×D₇	—	2	1	no	—
33	C₂×C₄×C₇	C₂²×C₅	1	1	yes	characteristic
34	C₂×Dic₇	—	2	1	no	—
35	D₂₈	—	2	1	no	—
36	D₂₈	C₂²×C₅	1	2	yes	—
37	Dic₁₄	—	2	1	no	—
38	Dic₁₄	C₂²×C₅	1	2	yes	complemented
39	C₇×C₈	C₂²×C₅	1	2	yes	complemented
40	C₂³×C₅	—	14	1	no	—
41	C₅×Q₈	—	7	2	no	—
42	C₅×Q₈	—	14	1	no	—
43	C₅×D₄	—	7	2	no	—
44	C₅×D₄	—	14	1	no	—
45	C₂×C₄×C₅	—	14	1	no	—
46	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
47	C₅×C₈	C₂×D₇	1	2	yes	complemented
48	C₅×C₇	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
49	C₂×SD₁₆	—	7	1	no	Sylow
50	C₂²×C₇	C₅×D₄	1	1	yes	characteristic
51	C₂×D₇	—	2	2	no	—
52	C₂×D₇	—	4	2	no	—
53	C₄×C₇	C₅×D₄	1	1	yes	characteristic
54	C₄×C₇	C₂³×C₅	1	1	yes	characteristic
55	Dic₇	—	2	2	no	—
56	C₂²×C₅	—	14	2	no	—
57	C₂²×C₅	—	28	2	no	—
58	C₂²×C₅	D₂₈	1	1	yes	characteristic
59	C₄×C₅	—	14	2	no	—
60	C₄×C₅	D₂₈	1	1	yes	characteristic
61	C₄×C₅	C₂²×D₇	1	1	yes	characteristic
62	C₂×Q₈	—	7	1	no	—
63	C₂×D₄	—	7	1	no	—
64	SD₁₆	—	7	4	no	—
65	C₂×C₈	C₅×D₇	1	1	yes	characteristic, complemented
66	C₂×C₇	C₅×SD₁₆	1	2	yes	complemented
67	C₂×C₇	C₂×C₅×D₄	1	1	yes	characteristic
68	D₇	—	4	2	no	—
69	C₂×C₅	—	28	2	no	—
70	C₂×C₅	#1132	1	2	yes	direct product factor
71	C₂×C₅	C₂×D₂₈	1	1	yes	characteristic
72	C₂³	—	14	1	no	—
73	Q₈	—	7	2	no	—
74	Q₈	—	14	1	no	—
75	D₄	—	7	2	no	—
76	D₄	—	14	1	no	—
77	C₂×C₄	—	14	1	no	—
78	C₂×C₄	C₂×C₅×D₇	1	1	yes	characteristic
79	C₈	C₂×C₅×D₇	1	2	yes	complemented
80	C₇	C₂×C₅×SD₁₆	1	1	yes	characteristic, complemented, Sylow
81	C₅	C₂×#1132	1	1	yes	characteristic, direct product factor, Sylow
82	C₂²	—	14	2	no	—
83	C₂²	—	28	2	no	—
84	C₂²	C₅×D₂₈	1	1	yes	characteristic
85	C₄	—	14	2	no	—
86	C₄	C₅×D₂₈	1	1	yes	characteristic
87	C₄	C₂²×C₅×D₇	1	1	yes	characteristic
88	C₂	—	28	2	no	—
89	C₂	C₅×#1132	1	2	yes	direct product factor
90	C₂	C₂×C₅×D₂₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₂₈
commutator, cosocle	C₄×C₇	C₂³×C₅
Frattini	C₄	C₂²×C₅×D₇
Fitting	C₂×C₅×C₇×C₈	C₂
socle	C₂²×C₅×C₇	D₄
prime radical	C₂×C₅×D₂₈	C₂
hypercenter	C₂×C₅×C₈	D₇
hypocenter	C₇	C₂×C₅×SD₁₆
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Dic₁₄	C₂	semidirect
3. C₂×C₅×C₇×C₈	C₂	semidirect
4. C₅×#1132	C₂	direct (N × H)
11. C₅×Dic₁₄	C₂²	semidirect
12. C₅×C₇×C₈	C₂²	semidirect
13. C₂×#1132	C₅	direct (N × H)
22. C₂×Dic₁₄	C₂×C₅	semidirect
23. C₂×C₇×C₈	C₂×C₅	semidirect
24. #1132	C₂×C₅	direct (N × H)
28. C₂×C₅×C₈	D₇	semidirect
29. C₂×C₅×C₇	SD₁₆	semidirect
38. Dic₁₄	C₂²×C₅	semidirect
39. C₇×C₈	C₂²×C₅	semidirect
47. C₅×C₈	C₂×D₇	semidirect
48. C₅×C₇	C₂×SD₁₆	semidirect
65. C₂×C₈	C₅×D₇	semidirect
66. C₂×C₇	C₅×SD₁₆	semidirect
70. C₂×C₅	#1132	direct (N × H)
79. C₈	C₂×C₅×D₇	semidirect
80. C₇	C₂×C₅×SD₁₆	semidirect
81. C₅	C₂×#1132	direct (N × H)
89. C₂	C₅×#1132	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×D₂₈	2
C₂×C₅×Dic₁₄	2
C₂×C₅×C₇×C₈	2
C₅×#1132	2
C₂×#1132	5
C₂×C₅×SD₁₆	7

Subgroups — C2×C5×#1132 #11765060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1132 #11765060