Subgroups — C₂×C₅×#4326 #13183072

Order 1760.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₂₂	C₂	1	1	yes	maximal, characteristic
3	C₅×#4326	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₅×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₅×Q₈×C₁₁	—	2	1	no	—
6	C₅×Q₈×C₁₁	C₂²	1	2	yes	—
7	C₂×C₄×C₅×C₁₁	—	2	1	no	—
8	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₅×Dic₁₁	—	2	1	no	—
10	C₅×Dic₂₂	—	2	1	no	—
11	C₅×Dic₂₂	C₂²	1	2	yes	—
12	C₅×C₁₁⋊C₈	C₂²	1	2	yes	—
13	C₂×#4326	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂²×C₅×C₁₁	D₄	1	1	yes	characteristic
15	C₄×C₅×C₁₁	—	2	2	no	—
16	C₄×C₅×C₁₁	D₄	1	1	yes	characteristic
17	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
18	C₅×Dic₁₁	—	2	2	no	—
19	C₂×Q₈×C₁₁	C₂×C₅	1	1	yes	characteristic
20	C₂×Dic₂₂	C₂×C₅	1	1	yes	characteristic
21	#4326	C₂×C₅	1	4	yes	direct product factor
22	C₂×C₁₁⋊C₈	C₂×C₅	1	1	yes	characteristic
23	C₂×C₅×Q₁₆	—	11	1	no	maximal, Hall
24	C₂×C₅×C₁₁	Q₁₆	1	2	yes	complemented
25	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
26	Q₈×C₁₁	—	2	1	no	—
27	Q₈×C₁₁	C₂²×C₅	1	2	yes	—
28	C₂×C₄×C₁₁	—	2	1	no	—
29	C₂×C₄×C₁₁	C₂²×C₅	1	1	yes	characteristic
30	C₂×Dic₁₁	—	2	1	no	—
31	Dic₂₂	—	2	1	no	—
32	Dic₂₂	C₂²×C₅	1	2	yes	—
33	C₁₁⋊C₈	C₂²×C₅	1	2	yes	—
34	C₂×C₅×Q₈	—	11	1	no	—
35	C₂×C₅×Q₈	D₁₁	1	1	yes	characteristic
36	C₅×Q₁₆	—	11	4	no	—
37	C₂×C₅×C₈	—	11	1	no	—
38	C₅×C₁₁	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₁₁	C₅×D₄	1	1	yes	characteristic
40	C₄×C₁₁	—	2	2	no	—
41	C₄×C₁₁	C₅×D₄	1	1	yes	characteristic
42	C₄×C₁₁	C₂³×C₅	1	1	yes	characteristic
43	Dic₁₁	—	2	2	no	—
44	C₅×Q₈	—	2	1	no	—
45	C₅×Q₈	—	11	2	no	—
46	C₅×Q₈	—	22	1	no	—
47	C₅×Q₈	C₂×D₁₁	1	2	yes	—
48	C₂×C₄×C₅	—	2	1	no	—
49	C₂×C₄×C₅	—	22	1	no	—
50	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
51	C₅×C₈	—	11	2	no	—
52	C₂×Q₁₆	—	11	1	no	Sylow
53	C₂×C₁₁	C₅×Q₁₆	1	2	yes	complemented
54	C₂×C₁₁	C₂×C₅×D₄	1	1	yes	characteristic
55	C₂²×C₅	C₂²⋊D₁₁	1	1	yes	characteristic
56	C₄×C₅	—	2	2	no	—
57	C₄×C₅	—	22	2	no	—
58	C₄×C₅	C₂²⋊D₁₁	1	1	yes	characteristic
59	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
60	C₂×Q₈	—	11	1	no	—
61	C₂×Q₈	C₅×D₁₁	1	1	yes	characteristic
62	Q₁₆	—	11	4	no	—
63	C₂×C₈	—	11	1	no	—
64	C₁₁	C₂×C₅×Q₁₆	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₅	#4326	1	2	yes	direct product factor
66	C₂×C₅	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
67	Q₈	—	2	1	no	—
68	Q₈	—	11	2	no	—
69	Q₈	—	22	1	no	—
70	Q₈	C₂×C₅×D₁₁	1	2	yes	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	22	1	no	—
73	C₂×C₄	C₂×C₅×D₁₁	1	1	yes	characteristic
74	C₈	—	11	2	no	—
75	C₅	C₂×#4326	1	1	yes	characteristic, direct product factor, Sylow
76	C₂²	C₅×C₂²⋊D₁₁	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	22	2	no	—
79	C₄	C₅×C₂²⋊D₁₁	1	1	yes	characteristic
80	C₄	C₂²×C₅×D₁₁	1	1	yes	characteristic
81	C₂	C₅×#4326	1	2	yes	direct product factor
82	C₂	C₂×C₅×C₂²⋊D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²⋊D₁₁
commutator, cosocle	C₄×C₁₁	C₂³×C₅
Frattini	C₄	C₂²×C₅×D₁₁
Fitting	C₂×C₅×Q₈×C₁₁	C₂
socle, prime radical	C₂²×C₅×C₁₁	D₄
hypercenter	C₂×C₅×Q₈	D₁₁
hypocenter	C₁₁	C₂×C₅×Q₁₆
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×Q₈

Complements

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

N	H ≅ G/N	type
3. C₅×#4326	C₂	direct (N × H)
13. C₂×#4326	C₅	direct (N × H)
21. #4326	C₂×C₅	direct (N × H)
24. C₂×C₅×C₁₁	Q₁₆	semidirect
38. C₅×C₁₁	C₂×Q₁₆	semidirect
53. C₂×C₁₁	C₅×Q₁₆	semidirect
64. C₁₁	C₂×C₅×Q₁₆	semidirect
65. C₂×C₅	#4326	direct (N × H)
75. C₅	C₂×#4326	direct (N × H)
81. C₂	C₅×#4326	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×Q₈×C₁₁	2
C₂×C₅×Dic₂₂	2
C₅×#4326	2
C₂×C₅×C₁₁⋊C₈	2
C₂×#4326	5
C₂×C₅×Q₁₆	11

Subgroups — C2×C5×#4326 #13183072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4326 #13183072