Subgroups — C₂×#10597128 #11925661

Order 1200.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₁₅	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×#1039	C₂	1	1	yes	maximal, characteristic, complemented
3	#10597128	C₂	1	4	yes	maximal, direct product factor
4	C₂×#6037	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₅²	C₂²	1	1	yes	characteristic
6	C₂×C₅×D₁₅	—	2	4	no	—
7	C₂×C₅×D₁₅	C₂²	1	4	yes	complemented
8	C₃×#1039	C₂²	1	2	yes	complemented
9	C₂×#1203	—	5	2	no	maximal
10	C₂²×C₅×D₅	—	3	2	no	—
11	C₂×#1039	D₃	1	1	yes	characteristic, complemented
12	#6037	—	3	4	no	—
13	C₂×C₃×C₅²	D₄	1	2	yes	complemented
14	C₂×C₃×C₅²	C₂³	1	1	yes	characteristic
15	C₅×D₁₅	—	2	4	no	—
16	C₂²×D₁₅	D₅	1	2	yes	complemented
17	C₂²×C₅×D₃	—	5	2	no	—
18	C₂×C₃×Dic₅	—	5	2	no	—
19	C₂×C₃×Dic₅	—	10	2	no	—
20	#1203	—	5	8	no	—
21	C₂²×C₅²	C₂×D₃	1	1	yes	characteristic
22	C₂×C₅×D₅	—	3	4	no	—
23	C₂×C₅×D₅	—	6	4	no	—
24	#1039	C₂×D₃	1	2	yes	complemented
25	C₂×C₂²⋊D₅	—	15	2	no	—
26	C₃×C₅²	C₂×D₄	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₃×C₅	—	2	2	no	—
28	C₂²×C₃×C₅	C₂×D₅	1	2	yes	—
29	C₂×D₁₅	—	2	4	no	—
30	C₂×D₁₅	C₂×D₅	1	4	yes	complemented
31	C₂×C₅×D₃	—	5	4	no	—
32	C₂×C₅×D₃	—	10	4	no	—
33	C₃×Dic₅	—	5	4	no	—
34	C₃×Dic₅	—	10	4	no	—
35	C₂×C₅²	D₁₂	1	2	yes	complemented
36	C₂×C₅²	C₂²×D₃	1	1	yes	characteristic
37	C₅×D₅	—	6	4	no	—
38	C₂×D₁₂	—	25	1	no	Hall
39	C₂³×C₅	—	15	2	no	—
40	C₂²×D₅	—	3	2	no	—
41	C₂²⋊D₅	—	15	8	no	—
42	C₂×Dic₅	—	5	2	no	—
43	C₂×Dic₅	—	10	2	no	—
44	C₂×C₃×C₅	—	2	4	no	—
45	C₂×C₃×C₅	—	2	2	no	—
46	C₂×C₃×C₅	C₂²⋊D₅	1	4	yes	complemented
47	C₂×C₃×C₅	C₂²×D₅	1	2	yes	—
48	D₁₅	—	2	4	no	—
49	C₅×D₃	—	10	4	no	—
50	C₅²	C₂×D₁₂	1	1	yes	characteristic, complemented, Sylow
51	C₂²×D₃	—	5	2	no	—
52	C₂×C₃×C₄	—	25	1	no	—
53	D₁₂	—	25	4	no	—
54	C₂²×C₅	—	2	2	no	—
55	C₂²×C₅	—	15	4	no	—
56	C₂²×C₅	—	30	4	no	—
57	C₂²×C₅	D₃×D₅	1	2	yes	—
58	C₂×D₅	—	3	4	no	—
59	C₂×D₅	—	6	4	no	—
60	Dic₅	—	5	4	no	—
61	Dic₅	—	10	4	no	—
62	C₂×D₄	—	75	1	no	Sylow
63	C₃×C₅	—	2	2	no	—
64	C₃×C₅	C₂×C₂²⋊D₅	1	2	yes	complemented
65	C₂²×C₃	D₅²	1	1	yes	characteristic
66	C₂×D₃	—	5	4	no	—
67	C₂×D₃	—	10	4	no	—
68	C₃×C₄	—	25	2	no	—
69	C₂×C₅	—	2	4	no	—
70	C₂×C₅	—	2	2	no	—
71	C₂×C₅	—	30	4	no	—
72	C₂×C₅	#1203	1	4	yes	complemented
73	C₂×C₅	C₂×D₃×D₅	1	2	yes	—
74	D₅	—	6	4	no	—
75	C₂³	—	15	2	no	—
76	D₄	—	75	4	no	—
77	C₂×C₄	—	25	1	no	—
78	C₂×C₃	#6037	1	2	yes	complemented
79	C₂×C₃	C₂×D₅²	1	1	yes	characteristic
80	D₃	—	10	4	no	—
81	C₅	—	2	2	no	—
82	C₅	C₂×#1203	1	2	yes	complemented
83	C₂²	—	15	4	no	—
84	C₂²	—	30	4	no	—
85	C₂²	D₁₅⋊D₅	1	1	yes	characteristic
86	C₄	—	25	2	no	—
87	C₃	C₂×#6037	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	30	4	no	—
89	C₂	#10597128	1	2	yes	direct product factor
90	C₂	C₂×D₁₅⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₁₅⋊D₅
commutator, cosocle	C₂×C₃×C₅²	C₂³
Frattini	C₂	C₂×D₁₅⋊D₅
Fitting, socle	C₂²×C₃×C₅²	C₂²
hypocenter	C₃×C₅²	C₂×D₄
LCS	G ▷ C₂×C₃×C₅² ▷ C₃×C₅²
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₁₅	C₂	semidirect
2. C₂×C₃×#1039	C₂	semidirect
3. #10597128	C₂	direct (N × H)
7. C₂×C₅×D₁₅	C₂²	semidirect
8. C₃×#1039	C₂²	semidirect
11. C₂×#1039	D₃	semidirect
13. C₂×C₃×C₅²	D₄	semidirect
16. C₂²×D₁₅	D₅	semidirect
24. #1039	C₂×D₃	semidirect
26. C₃×C₅²	C₂×D₄	semidirect
30. C₂×D₁₅	C₂×D₅	semidirect
35. C₂×C₅²	D₁₂	semidirect
46. C₂×C₃×C₅	C₂²⋊D₅	semidirect
50. C₅²	C₂×D₁₂	semidirect
64. C₃×C₅	C₂×C₂²⋊D₅	semidirect
72. C₂×C₅	#1203	semidirect
78. C₂×C₃	#6037	semidirect
82. C₅	C₂×#1203	semidirect
87. C₃	C₂×#6037	semidirect
89. C₂	#10597128	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×D₁₅	2
C₂×C₃×#1039	2
#10597128	2
C₂×#6037	3
C₂×#1203	5

Subgroups — C2×#10597128 #11925661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10597128 #11925661