Subgroups — C₂×#10597114 #11925613

Order 1200.

432 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊#1039	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597114	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₂²⋊(C₅⋊D₅)	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₅²	C₂²	1	1	yes	characteristic
7	C₂×C₅²×D₃	—	2	2	no	—
8	C₂×C₅²×D₃	C₂²	1	2	yes	complemented
9	C₂×C₃×C₅⋊D₅	—	2	2	no	—
10	C₂×C₃×C₅⋊D₅	C₂²	1	2	yes	complemented
11	C₃⋊#1039	C₂²	1	2	yes	complemented
12	C₂×#1201	—	5	6	no	maximal
13	C₂³×C₅²	—	3	1	no	—
14	C₂²×C₅⋊D₅	D₃	1	1	yes	characteristic, complemented
15	C₂²⋊(C₅⋊D₅)	—	3	4	no	—
16	C₂×#1039	—	3	1	no	—
17	C₂×C₃×C₅²	D₄	1	2	yes	complemented
18	C₂×C₃×C₅²	C₂³	1	1	yes	characteristic
19	C₅²×D₃	—	2	2	no	—
20	C₃×C₅⋊D₅	—	2	2	no	—
21	C₂²×C₅×D₃	D₅	1	6	yes	complemented
22	C₂²×C₃×D₅	—	5	6	no	—
23	C₂×Dic₁₅	—	5	6	no	—
24	#1201	—	5	24	no	—
25	C₂²×C₅²	—	3	2	no	—
26	C₂²×C₅²	—	6	2	no	—
27	C₂²×C₅²	C₂×D₃	1	1	yes	characteristic
28	C₂×C₅⋊D₅	—	2	2	no	—
29	C₂×C₅⋊D₅	C₂×D₃	1	2	yes	complemented
30	#1039	—	3	2	no	—
31	C₂×C₂²⋊D₅	—	15	6	no	—
32	C₃×C₅²	C₂×D₄	1	1	yes	characteristic, complemented, Hall
33	C₂²×C₃×C₅	C₂×D₅	1	6	yes	—
34	C₂×C₅×D₃	—	2	12	no	—
35	C₂×C₅×D₃	C₂×D₅	1	12	yes	complemented
36	C₂×C₃×D₅	—	5	12	no	—
37	C₂×C₃×D₅	—	10	12	no	—
38	Dic₁₅	—	5	12	no	—
39	C₂×C₅²	—	6	2	no	—
40	C₂×C₅²	#67	1	2	yes	complemented
41	C₂×C₅²	C₂²×D₃	1	1	yes	characteristic
42	C₅⋊D₅	—	2	2	no	—
43	C₂×#67	—	25	1	no	Hall
44	C₂³×C₅	—	3	6	no	—
45	C₂²×D₅	—	5	6	no	—
46	C₂²⋊D₅	—	15	24	no	—
47	C₂×Dic₅	—	15	6	no	—
48	C₂×C₃×C₅	C₂²⋊D₅	1	12	yes	complemented
49	C₂×C₃×C₅	C₂²×D₅	1	6	yes	—
50	C₃×D₅	—	10	12	no	—
51	C₅×D₃	—	2	12	no	—
52	C₅²	C₂×#67	1	1	yes	characteristic, complemented, Sylow
53	C₂³×C₃	—	25	1	no	—
54	C₂²×D₃	C₅⋊D₅	1	1	yes	characteristic, complemented
55	#67	—	25	4	no	—
56	C₂×Dic₃	—	25	1	no	—
57	C₂²×C₅	—	3	12	no	—
58	C₂²×C₅	—	6	12	no	—
59	C₂²×C₅	D₃×D₅	1	6	yes	—
60	C₂×D₅	—	5	12	no	—
61	C₂×D₅	—	10	12	no	—
62	Dic₅	—	15	12	no	—
63	C₂×D₄	—	75	1	no	Sylow
64	C₃×C₅	C₂×C₂²⋊D₅	1	6	yes	complemented
65	C₂²×C₃	—	25	2	no	—
66	C₂²×C₃	—	50	2	no	—
67	C₂²×C₃	C₂×C₅⋊D₅	1	1	yes	characteristic
68	C₂×D₃	—	2	2	no	—
69	C₂×D₃	C₂×C₅⋊D₅	1	2	yes	complemented
70	Dic₃	—	25	2	no	—
71	C₂×C₅	—	6	12	no	—
72	C₂×C₅	#1201	1	12	yes	complemented
73	C₂×C₅	C₂×D₃×D₅	1	6	yes	—
74	D₅	—	10	12	no	—
75	C₂³	—	3	1	no	—
76	C₂³	—	25	1	no	—
77	D₄	—	75	4	no	—
78	C₂×C₄	—	75	1	no	—
79	C₂×C₃	—	50	2	no	—
80	C₂×C₃	C₂²⋊(C₅⋊D₅)	1	2	yes	complemented
81	C₂×C₃	C₂²×C₅⋊D₅	1	1	yes	characteristic
82	D₃	—	2	2	no	—
83	C₅	C₂×#1201	1	6	yes	complemented
84	C₂²	—	3	2	no	—
85	C₂²	—	6	2	no	—
86	C₂²	—	25	2	no	—
87	C₂²	—	50	2	no	—
88	C₂²	D₃×C₅⋊D₅	1	1	yes	characteristic
89	C₄	—	75	2	no	—
90	C₃	C₂×C₂²⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	6	2	no	—
92	C₂	—	50	2	no	—
93	C₂	#10597114	1	2	yes	direct product factor
94	C₂	C₂×D₃×C₅⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃×C₅⋊D₅
commutator, cosocle	C₂×C₃×C₅²	C₂³
Frattini	C₂	C₂×D₃×C₅⋊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×C₅²×D₃	C₂	semidirect
2. C₂²×C₃×C₅⋊D₅	C₂	semidirect
3. C₂×C₃⋊#1039	C₂	semidirect
4. #10597114	C₂	direct (N × H)
8. C₂×C₅²×D₃	C₂²	semidirect
10. C₂×C₃×C₅⋊D₅	C₂²	semidirect
11. C₃⋊#1039	C₂²	semidirect
14. C₂²×C₅⋊D₅	D₃	semidirect
17. C₂×C₃×C₅²	D₄	semidirect
21. C₂²×C₅×D₃	D₅	semidirect
29. C₂×C₅⋊D₅	C₂×D₃	semidirect
32. C₃×C₅²	C₂×D₄	semidirect
35. C₂×C₅×D₃	C₂×D₅	semidirect
40. C₂×C₅²	#67	semidirect
48. C₂×C₃×C₅	C₂²⋊D₅	semidirect
52. C₅²	C₂×#67	semidirect
54. C₂²×D₃	C₅⋊D₅	semidirect
64. C₃×C₅	C₂×C₂²⋊D₅	semidirect
69. C₂×D₃	C₂×C₅⋊D₅	semidirect
72. C₂×C₅	#1201	semidirect
80. C₂×C₃	C₂²⋊(C₅⋊D₅)	semidirect
83. C₅	C₂×#1201	semidirect
90. C₃	C₂×C₂²⋊(C₅⋊D₅)	semidirect
93. C₂	#10597114	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×C₅²×D₃	2
C₂²×C₃×C₅⋊D₅	2
C₂×C₃⋊#1039	2
#10597114	2
C₂×C₂²⋊(C₅⋊D₅)	3
C₂×#1201	5

Subgroups — C2×#10597114 #11925613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10597114 #11925613