Subgroups — C₂×#11724923 #13183199

Order 1760.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₅₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#11724923	C₂	1	4	yes	maximal, direct product factor
5	C₂²×D₅₅	C₄	1	1	yes	characteristic
6	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×Dic₅₅	C₄	1	1	yes	characteristic
8	C₄×D₅₅	C₄	1	2	yes	—
9	C₄×D₅₅	C₂²	1	2	yes	—
10	C₅×C₈×C₁₁	C₂²	1	2	yes	complemented
11	C₁₁⋊#168	C₂²	1	2	yes	complemented
12	C₂×#4313	—	5	1	no	maximal, Hall
13	C₂²×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic
14	C₂×D₅₅	—	2	2	no	—
15	C₂×D₅₅	C₂×C₄	1	2	yes	—
16	C₄×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
18	Dic₅₅	C₂×C₄	1	2	yes	—
19	C₂×C₄×D₁₁	—	5	1	no	—
20	C₂×C₈×C₁₁	D₅	1	1	yes	characteristic, complemented
21	C₂×C₁₁⋊C₈	—	5	1	no	—
22	#4313	—	5	4	no	—
23	C₂×#676	—	11	1	no	maximal, Hall
24	C₂×C₅×C₁₁	M₁₆	1	2	yes	complemented
25	C₂×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
26	D₅₅	—	2	2	no	—
27	C₂²×D₁₁	—	5	1	no	—
28	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
29	C₂×Dic₁₁	—	5	1	no	—
30	C₄×D₁₁	—	5	2	no	—
31	C₄×D₁₁	—	5	2	no	—
32	C₈×C₁₁	C₂×D₅	1	2	yes	complemented
33	C₁₁⋊C₈	—	5	2	no	—
34	C₂×C₄×D₅	—	11	1	no	—
35	C₂×C₅×C₈	D₁₁	1	1	yes	characteristic, complemented
36	C₂×#168	—	11	1	no	—
37	#676	—	11	4	no	—
38	C₅×C₁₁	C₂×M₁₆	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₁₁	C₄×D₅	1	1	yes	characteristic
40	C₂×D₁₁	—	5	2	no	—
41	C₂×D₁₁	—	10	2	no	—
42	C₄×C₁₁	C₄×D₅	1	1	yes	characteristic
43	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
44	Dic₁₁	—	5	2	no	—
45	C₂²×D₅	—	11	1	no	—
46	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
47	C₂×Dic₅	—	11	1	no	—
48	C₄×D₅	—	11	2	no	—
49	C₄×D₅	—	11	2	no	—
50	C₅×C₈	C₂×D₁₁	1	2	yes	complemented
51	#168	—	11	2	no	—
52	C₂×M₁₆	—	55	1	no	Sylow
53	C₂×C₁₁	#676	1	2	yes	complemented
54	C₂×C₁₁	C₂×C₄×D₅	1	1	yes	characteristic
55	D₁₁	—	10	2	no	—
56	C₂²×C₅	C₄×D₁₁	1	1	yes	characteristic
57	C₂×D₅	—	11	2	no	—
58	C₂×D₅	—	22	2	no	—
59	C₄×C₅	C₄×D₁₁	1	1	yes	characteristic
60	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
61	Dic₅	—	11	2	no	—
62	C₂²×C₄	—	55	1	no	—
63	M₁₆	—	55	4	no	—
64	C₂×C₈	—	55	1	no	—
65	C₂×C₈	D₅₅	1	1	yes	characteristic, complemented
66	C₁₁	C₂×#676	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₅	#4313	1	2	yes	complemented
68	C₂×C₅	C₂×C₄×D₁₁	1	1	yes	characteristic
69	D₅	—	22	2	no	—
70	C₂³	—	55	1	no	—
71	C₂×C₄	—	55	1	no	—
72	C₂×C₄	—	55	2	no	—
73	C₂×C₄	—	55	2	no	—
74	C₂×C₄	C₂×D₅₅	1	1	yes	characteristic
75	C₈	—	55	2	no	—
76	C₈	C₂×D₅₅	1	2	yes	complemented
77	C₅	C₂×#4313	1	1	yes	characteristic, complemented, Sylow
78	C₂²	—	55	2	no	—
79	C₂²	—	110	2	no	—
80	C₂²	C₄×D₅₅	1	1	yes	characteristic
81	C₄	—	55	2	no	—
82	C₄	C₄×D₅₅	1	1	yes	characteristic
83	C₄	C₂²×D₅₅	1	1	yes	characteristic
84	C₂	—	110	2	no	—
85	C₂	#11724923	1	2	yes	direct product factor
86	C₂	C₂×C₄×D₅₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₅₅
commutator	C₂×C₅×C₁₁	C₂²×C₄
Frattini	C₄	C₂²×D₅₅
Fitting	C₂×C₅×C₈×C₁₁	C₂
socle	C₂²×C₅×C₁₁	C₂×C₄
prime radical	C₂²×D₅₅	C₄
cosocle	C₄×C₅×C₁₁	C₂³
hypercenter	C₂×C₈	D₅₅
hypocenter	C₅×C₁₁	C₂×M₁₆
LCS	G ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×C₈×C₁₁	C₂	semidirect
3. C₂×C₁₁⋊#168	C₂	semidirect
4. #11724923	C₂	direct (N × H)
10. C₅×C₈×C₁₁	C₂²	semidirect
11. C₁₁⋊#168	C₂²	semidirect
20. C₂×C₈×C₁₁	D₅	semidirect
24. C₂×C₅×C₁₁	M₁₆	semidirect
32. C₈×C₁₁	C₂×D₅	semidirect
35. C₂×C₅×C₈	D₁₁	semidirect
38. C₅×C₁₁	C₂×M₁₆	semidirect
50. C₅×C₈	C₂×D₁₁	semidirect
53. C₂×C₁₁	#676	semidirect
65. C₂×C₈	D₅₅	semidirect
66. C₁₁	C₂×#676	semidirect
67. C₂×C₅	#4313	semidirect
76. C₈	C₂×D₅₅	semidirect
77. C₅	C₂×#4313	semidirect
85. C₂	#11724923	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×C₄×D₅₅	2
C₂×C₅×C₈×C₁₁	2
C₂×C₁₁⋊#168	2
#11724923	2
C₂×#4313	5
C₂×#676	11

Subgroups — C2×#11724923 #13183199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11724923 #13183199