Subgroups — C₂×#10597129 #11925662

Order 1200.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Dic₁₅	C₂	1	2	yes	maximal
2	C₂×C₃×#1039	C₂	1	1	yes	maximal, characteristic
3	#10597129	C₂	1	4	yes	maximal, direct product factor
4	C₂×#6039	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₅²	C₂²	1	1	yes	characteristic
6	C₅×Dic₁₅	C₂²	1	4	yes	—
7	C₃×#1039	C₂²	1	2	yes	—
8	C₂×#1204	—	5	2	no	maximal
9	C₂×#1039	D₃	1	1	yes	characteristic
10	C₂×C₅×Dic₅	—	3	2	no	—
11	#6039	—	3	4	no	—
12	C₂×C₃×C₅²	Q₈	1	2	yes	complemented
13	C₂×C₃×C₅²	C₂³	1	1	yes	characteristic
14	C₂×Dic₁₅	D₅	1	2	yes	—
15	C₂×C₅×Dic₃	—	5	2	no	—
16	C₂×C₃×Dic₅	—	5	2	no	—
17	C₂×C₃×Dic₅	—	10	2	no	—
18	#1204	—	5	8	no	—
19	C₂²×C₅²	C₂×D₃	1	1	yes	characteristic
20	#1039	C₂×D₃	1	2	yes	—
21	C₅×Dic₅	—	3	4	no	—
22	C₂×Dic₁₀	—	15	2	no	—
23	C₃×C₅²	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₃×C₅	—	2	2	no	—
25	C₂²×C₃×C₅	C₂×D₅	1	2	yes	—
26	Dic₁₅	C₂×D₅	1	4	yes	—
27	C₃×Dic₅	—	5	4	no	—
28	C₃×Dic₅	—	10	4	no	—
29	C₅×Dic₃	—	5	4	no	—
30	C₂×C₅²	Dic₆	1	2	yes	complemented
31	C₂×C₅²	C₂²×D₃	1	1	yes	characteristic
32	C₂×Dic₆	—	25	1	no	Hall
33	C₂×C₄×C₅	—	15	2	no	—
34	C₂×Dic₅	—	3	2	no	—
35	C₂×Dic₅	—	5	2	no	—
36	C₂×Dic₅	—	10	2	no	—
37	Dic₁₀	—	15	8	no	—
38	C₂×C₃×C₅	—	2	4	no	—
39	C₂×C₃×C₅	—	2	2	no	—
40	C₂×C₃×C₅	Dic₁₀	1	4	yes	complemented
41	C₂×C₃×C₅	C₂²×D₅	1	2	yes	—
42	C₅²	C₂×Dic₆	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃×C₄	—	25	1	no	—
44	C₂×Dic₃	—	5	2	no	—
45	Dic₆	—	25	4	no	—
46	C₂²×C₅	—	2	2	no	—
47	C₂²×C₅	D₃×D₅	1	2	yes	—
48	C₄×C₅	—	15	4	no	—
49	Dic₅	—	3	4	no	—
50	Dic₅	—	5	4	no	—
51	Dic₅	—	10	4	no	—
52	C₂×Q₈	—	75	1	no	Sylow
53	C₃×C₅	—	2	2	no	—
54	C₃×C₅	C₂×Dic₁₀	1	2	yes	complemented
55	C₂²×C₃	D₅²	1	1	yes	characteristic
56	C₃×C₄	—	25	2	no	—
57	Dic₃	—	5	4	no	—
58	C₂×C₅	—	2	4	no	—
59	C₂×C₅	—	2	2	no	—
60	C₂×C₅	#1204	1	4	yes	complemented
61	C₂×C₅	C₂×D₃×D₅	1	2	yes	—
62	Q₈	—	75	4	no	—
63	C₂×C₄	—	15	2	no	—
64	C₂×C₄	—	25	1	no	—
65	C₂×C₃	#6039	1	2	yes	complemented
66	C₂×C₃	C₂×D₅²	1	1	yes	characteristic
67	C₅	—	2	2	no	—
68	C₅	C₂×#1204	1	2	yes	complemented
69	C₂²	D₁₅⋊D₅	1	1	yes	characteristic
70	C₄	—	15	4	no	—
71	C₄	—	25	2	no	—
72	C₃	C₂×#6039	1	1	yes	characteristic, complemented, Sylow
73	C₂	#10597129	1	2	yes	direct product factor
74	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, prime radical	C₂²×C₃×C₅²	C₂²
hypocenter	C₃×C₅²	C₂×Q₈
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
3. #10597129	C₂	direct (N × H)
12. C₂×C₃×C₅²	Q₈	semidirect
23. C₃×C₅²	C₂×Q₈	semidirect
30. C₂×C₅²	Dic₆	semidirect
40. C₂×C₃×C₅	Dic₁₀	semidirect
42. C₅²	C₂×Dic₆	semidirect
54. C₃×C₅	C₂×Dic₁₀	semidirect
60. C₂×C₅	#1204	semidirect
65. C₂×C₃	#6039	semidirect
68. C₅	C₂×#1204	semidirect
72. C₃	C₂×#6039	semidirect
73. C₂	#10597129	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×Dic₁₅	2
C₂×C₃×#1039	2
#10597129	2
C₂×#6039	3
C₂×#1204	5

Subgroups — C2×#10597129 #11925662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10597129 #11925662