Subgroups — C₂×C₅×#4324 #13183065

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×C₅×Dic₂₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4324	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₅×C₁₁⋊C₈	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×C₅×Dic₁₁	—	2	1	no	—
10	C₅×Dic₂₂	—	2	1	no	—
11	C₅×Dic₂₂	C₂²	1	2	yes	complemented
12	C₅×C₁₁⋊C₈	C₂²	1	2	yes	complemented
13	C₂×#4324	C₅	1	1	yes	maximal, characteristic, direct product factor, 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	C₅×Dic₁₁	—	2	2	no	—
20	C₂×D₄×C₁₁	C₂×C₅	1	1	yes	characteristic
21	C₂×Dic₂₂	C₂×C₅	1	1	yes	characteristic, complemented
22	#4324	C₂×C₅	1	4	yes	direct product factor
23	C₂×C₁₁⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
24	C₂×C₅×SD₁₆	—	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	C₂²×C₅	1	2	yes	—
31	C₂×C₄×C₁₁	C₂²×C₅	1	1	yes	characteristic
32	C₂×Dic₁₁	—	2	1	no	—
33	Dic₂₂	—	2	1	no	—
34	Dic₂₂	C₂²×C₅	1	2	yes	complemented
35	C₁₁⋊C₈	C₂²×C₅	1	2	yes	complemented
36	C₂×C₅×Q₈	—	11	1	no	—
37	C₂×C₅×D₄	D₁₁	1	1	yes	characteristic
38	C₅×SD₁₆	—	11	4	no	—
39	C₂×C₅×C₈	—	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	C₅×D₄	1	1	yes	characteristic
44	C₄×C₁₁	C₅×D₄	1	1	yes	characteristic
45	C₄×C₁₁	C₂³×C₅	1	1	yes	characteristic
46	Dic₁₁	—	2	2	no	—
47	C₂³×C₅	—	2	1	no	—
48	C₅×Q₈	—	11	2	no	—
49	C₅×Q₈	—	22	1	no	—
50	C₅×D₄	—	2	1	no	—
51	C₅×D₄	C₂×D₁₁	1	2	yes	—
52	C₂×C₄×C₅	—	22	1	no	—
53	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
54	C₅×C₈	—	11	2	no	—
55	C₂×SD₁₆	—	11	1	no	Sylow
56	C₂×C₁₁	—	4	2	no	—
57	C₂×C₁₁	C₅×SD₁₆	1	2	yes	complemented
58	C₂×C₁₁	C₂×C₅×D₄	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	—	22	2	no	—
63	C₄×C₅	C₂²⋊D₁₁	1	1	yes	characteristic
64	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
65	C₂×Q₈	—	11	1	no	—
66	C₂×D₄	C₅×D₁₁	1	1	yes	characteristic
67	SD₁₆	—	11	4	no	—
68	C₂×C₈	—	11	1	no	—
69	C₁₁	C₂×C₅×SD₁₆	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₅	—	4	2	no	—
71	C₂×C₅	#4324	1	2	yes	direct product factor
72	C₂×C₅	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
73	C₂³	—	2	1	no	—
74	Q₈	—	11	2	no	—
75	Q₈	—	22	1	no	—
76	D₄	—	2	1	no	—
77	D₄	C₂×C₅×D₁₁	1	2	yes	—
78	C₂×C₄	—	22	1	no	—
79	C₂×C₄	C₂×C₅×D₁₁	1	1	yes	characteristic
80	C₈	—	11	2	no	—
81	C₅	C₂×#4324	1	1	yes	characteristic, direct product factor, Sylow
82	C₂²	—	2	2	no	—
83	C₂²	—	4	2	no	—
84	C₂²	C₅×C₂²⋊D₁₁	1	1	yes	characteristic
85	C₄	—	22	2	no	—
86	C₄	C₅×C₂²⋊D₁₁	1	1	yes	characteristic
87	C₄	C₂²×C₅×D₁₁	1	1	yes	characteristic
88	C₂	—	4	2	no	—
89	C₂	C₅×#4324	1	2	yes	direct product factor
90	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, prime radical	C₂×C₅×D₄×C₁₁	C₂
socle	C₂²×C₅×C₁₁	D₄
hypercenter	C₂×C₅×D₄	D₁₁
hypocenter	C₁₁	C₂×C₅×SD₁₆
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Dic₂₂	C₂	semidirect
3. C₅×#4324	C₂	direct (N × H)
4. C₂×C₅×C₁₁⋊C₈	C₂	semidirect
11. C₅×Dic₂₂	C₂²	semidirect
12. C₅×C₁₁⋊C₈	C₂²	semidirect
13. C₂×#4324	C₅	direct (N × H)
21. C₂×Dic₂₂	C₂×C₅	semidirect
22. #4324	C₂×C₅	direct (N × H)
23. C₂×C₁₁⋊C₈	C₂×C₅	semidirect
26. C₂×C₅×C₁₁	SD₁₆	semidirect
34. Dic₂₂	C₂²×C₅	semidirect
35. C₁₁⋊C₈	C₂²×C₅	semidirect
40. C₅×C₁₁	C₂×SD₁₆	semidirect
57. C₂×C₁₁	C₅×SD₁₆	semidirect
69. C₁₁	C₂×C₅×SD₁₆	semidirect
71. C₂×C₅	#4324	direct (N × H)
81. C₅	C₂×#4324	direct (N × H)
89. C₂	C₅×#4324	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×C₅×Dic₂₂	2
C₅×#4324	2
C₂×C₅×C₁₁⋊C₈	2
C₂×#4324	5
C₂×C₅×SD₁₆	11

Subgroups — C2×C5×#4324 #13183065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4324 #13183065