Subgroups — C₂×#11724934 #13183237

Order 1760.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	#11724934	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₅×C₁₁	—	2	1	no	—
6	C₅×D₄×C₁₁	—	2	1	no	—
7	C₅×D₄×C₁₁	C₂²	1	2	yes	—
8	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₅₅	—	2	1	no	—
10	Dic₁₁₀	—	2	1	no	—
11	Dic₁₁₀	C₂²	1	2	yes	complemented
12	C₁₁⋊#168	C₂²	1	2	yes	complemented
13	C₂×#4324	—	5	1	no	maximal, Hall
14	C₂²×C₅×C₁₁	—	2	2	no	—
15	C₂²×C₅×C₁₁	—	4	2	no	—
16	C₂²×C₅×C₁₁	D₄	1	1	yes	characteristic
17	C₄×C₅×C₁₁	D₄	1	1	yes	characteristic
18	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
19	Dic₅₅	—	2	2	no	—
20	C₂×D₄×C₁₁	D₅	1	1	yes	characteristic
21	C₂×Dic₂₂	—	5	1	no	—
22	#4324	—	5	4	no	—
23	C₂×C₁₁⋊C₈	—	5	1	no	—
24	C₂×#687	—	11	1	no	maximal, Hall
25	C₂×C₅×C₁₁	—	4	2	no	—
26	C₂×C₅×C₁₁	SD₁₆	1	2	yes	complemented
27	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
28	C₂³×C₁₁	—	2	1	no	—
29	D₄×C₁₁	—	2	1	no	—
30	D₄×C₁₁	C₂×D₅	1	2	yes	—
31	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
32	C₂×Dic₁₁	—	10	1	no	—
33	Dic₂₂	—	5	2	no	—
34	Dic₂₂	—	10	1	no	—
35	C₁₁⋊C₈	—	5	2	no	—
36	C₂×C₅×D₄	D₁₁	1	1	yes	characteristic
37	C₂×Dic₁₀	—	11	1	no	—
38	#687	—	11	4	no	—
39	C₂×#168	—	11	1	no	—
40	C₅×C₁₁	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₁₁	—	2	2	no	—
42	C₂²×C₁₁	—	4	2	no	—
43	C₂²×C₁₁	C₂²⋊D₅	1	1	yes	characteristic
44	C₄×C₁₁	C₂²⋊D₅	1	1	yes	characteristic
45	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
46	Dic₁₁	—	10	2	no	—
47	C₂³×C₅	—	2	1	no	—
48	C₅×D₄	—	2	1	no	—
49	C₅×D₄	C₂×D₁₁	1	2	yes	—
50	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
51	C₂×Dic₅	—	22	1	no	—
52	Dic₁₀	—	11	2	no	—
53	Dic₁₀	—	22	1	no	—
54	#168	—	11	2	no	—
55	C₂×SD₁₆	—	55	1	no	Sylow
56	C₂×C₁₁	—	4	2	no	—
57	C₂×C₁₁	#687	1	2	yes	complemented
58	C₂×C₁₁	C₂×C₂²⋊D₅	1	1	yes	characteristic
59	C₂²×C₅	—	2	2	no	—
60	C₂²×C₅	—	4	2	no	—
61	C₂²×C₅	C₂²⋊D₁₁	1	1	yes	characteristic
62	C₄×C₅	C₂²⋊D₁₁	1	1	yes	characteristic
63	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
64	Dic₅	—	22	2	no	—
65	C₂×Q₈	—	55	1	no	—
66	C₂×D₄	D₅₅	1	1	yes	characteristic
67	SD₁₆	—	55	4	no	—
68	C₂×C₈	—	55	1	no	—
69	C₁₁	C₂×#687	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₅	—	4	2	no	—
71	C₂×C₅	#4324	1	2	yes	complemented
72	C₂×C₅	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
73	C₂³	—	2	1	no	—
74	Q₈	—	55	2	no	—
75	Q₈	—	110	1	no	—
76	D₄	—	2	1	no	—
77	D₄	C₂×D₅₅	1	2	yes	—
78	C₂×C₄	—	110	1	no	—
79	C₂×C₄	C₂×D₅₅	1	1	yes	characteristic
80	C₈	—	55	2	no	—
81	C₅	C₂×#4324	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	2	2	no	—
83	C₂²	—	4	2	no	—
84	C₂²	C₂²⋊D₅₅	1	1	yes	characteristic
85	C₄	—	110	2	no	—
86	C₄	C₂²⋊D₅₅	1	1	yes	characteristic
87	C₄	C₂²×D₅₅	1	1	yes	characteristic
88	C₂	—	4	2	no	—
89	C₂	#11724934	1	2	yes	direct product factor
90	C₂	C₂×C₂²⋊D₅₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₅₅
commutator, cosocle	C₄×C₅×C₁₁	C₂³
Frattini	C₄	C₂²×D₅₅
Fitting, prime radical	C₂×C₅×D₄×C₁₁	C₂
socle	C₂²×C₅×C₁₁	D₄
hypercenter	C₂×D₄	D₅₅
hypocenter	C₅×C₁₁	C₂×SD₁₆
LCS	G ▷ C₄×C₅×C₁₁ ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₁₁₀	C₂	semidirect
3. #11724934	C₂	direct (N × H)
4. C₂×C₁₁⋊#168	C₂	semidirect
11. Dic₁₁₀	C₂²	semidirect
12. C₁₁⋊#168	C₂²	semidirect
26. C₂×C₅×C₁₁	SD₁₆	semidirect
40. C₅×C₁₁	C₂×SD₁₆	semidirect
57. C₂×C₁₁	#687	semidirect
69. C₁₁	C₂×#687	semidirect
71. C₂×C₅	#4324	semidirect
81. C₅	C₂×#4324	semidirect
89. C₂	#11724934	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×D₄×C₁₁	2
C₂×Dic₁₁₀	2
#11724934	2
C₂×C₁₁⋊#168	2
C₂×#4324	5
C₂×#687	11

Subgroups — C2×#11724934 #13183237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11724934 #13183237