Subgroups — C₃×#87720 #11924833

Order 1200.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×Dic₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	#87720	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₂₅	C₂²	1	1	yes	characteristic
6	C₂×C₃×D₂₅	—	2	1	no	—
7	C₂×C₃×D₂₅	—	2	1	no	—
8	C₂×C₃×D₂₅	C₄	1	2	yes	complemented
9	C₃×C₄×C₂₅	—	2	1	no	—
10	C₃×Dic₂₅	—	2	1	no	—
11	C₃×#685	—	5	1	no	maximal
12	C₂²×D₂₅	C₂×C₃	1	1	yes	characteristic
13	C₂×C₄×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×Dic₂₅	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×C₃×C₂₅	C₂×C₄	1	1	yes	characteristic
16	C₂×C₃×C₂₅	D₄	1	1	yes	characteristic
17	C₂×C₃×C₂₅	D₄	1	1	yes	characteristic
18	C₃×D₂₅	—	2	2	no	—
19	C₂²×C₃×D₅	—	5	1	no	—
20	C₂×C₃×C₄×C₅	D₅	1	1	yes	characteristic
21	C₂×C₃×Dic₅	—	5	1	no	—
22	C₂²×C₂₅	C₂²×C₃	1	1	yes	characteristic
23	C₂×D₂₅	—	2	1	no	—
24	C₂×D₂₅	—	2	1	no	—
25	C₂×D₂₅	C₃×C₄	1	2	yes	complemented
26	C₄×C₂₅	—	2	1	no	—
27	Dic₂₅	—	2	1	no	—
28	#685	—	5	1	no	—
29	C₃×C₂₅	C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃×C₅	C₂×D₅	1	1	yes	characteristic
31	C₂×C₃×D₅	—	5	2	no	—
32	C₂×C₃×D₅	—	10	1	no	—
33	C₂×C₃×D₅	—	10	1	no	—
34	C₃×C₄×C₅	—	2	1	no	—
35	C₃×Dic₅	—	10	1	no	—
36	C₂×C₂₅	C₂×C₃×C₄	1	1	yes	characteristic
37	C₂×C₂₅	C₃×D₄	1	1	yes	characteristic
38	C₂×C₂₅	C₃×D₄	1	1	yes	characteristic
39	D₂₅	—	2	2	no	—
40	C₃×C₂²⋊C₄	—	25	1	no	Hall
41	C₂²×D₅	—	5	1	no	—
42	C₂×C₄×C₅	C₃×D₅	1	1	yes	characteristic
43	C₂×Dic₅	—	5	1	no	—
44	C₂×C₃×C₅	C₄×D₅	1	1	yes	characteristic
45	C₂×C₃×C₅	D₂₀	1	1	yes	characteristic
46	C₂×C₃×C₅	C₂²⋊D₅	1	1	yes	characteristic
47	C₃×D₅	—	10	2	no	—
48	C₂₅	C₃×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
49	C₂³×C₃	—	25	1	no	—
50	C₂×C₃×C₄	—	25	1	no	—
51	C₂×C₃×C₄	D₂₅	1	1	yes	characteristic, complemented
52	C₂²×C₅	C₂×C₃×D₅	1	1	yes	characteristic
53	C₂×D₅	—	5	2	no	—
54	C₂×D₅	—	10	1	no	—
55	C₂×D₅	—	10	1	no	—
56	C₄×C₅	—	2	1	no	—
57	Dic₅	—	10	1	no	—
58	C₂²⋊C₄	—	25	1	no	Sylow
59	C₃×C₅	#685	1	1	yes	characteristic
60	C₂²×C₃	—	25	2	no	—
61	C₂²×C₃	—	50	1	no	—
62	C₂²×C₃	—	50	1	no	—
63	C₂²×C₃	C₂×D₂₅	1	1	yes	characteristic
64	C₃×C₄	—	2	1	no	—
65	C₃×C₄	—	50	1	no	—
66	C₂×C₅	C₃×C₄×D₅	1	1	yes	characteristic
67	C₂×C₅	C₃×D₂₀	1	1	yes	characteristic
68	C₂×C₅	C₃×C₂²⋊D₅	1	1	yes	characteristic
69	D₅	—	10	2	no	—
70	C₂³	—	25	1	no	—
71	C₂×C₄	—	25	1	no	—
72	C₂×C₄	C₃×D₂₅	1	1	yes	characteristic, complemented
73	C₂×C₃	—	50	2	no	—
74	C₂×C₃	C₄×D₂₅	1	1	yes	characteristic
75	C₂×C₃	D₁₀₀	1	1	yes	characteristic
76	C₂×C₃	C₂²⋊D₂₅	1	1	yes	characteristic
77	C₅	C₃×#685	1	1	yes	characteristic
78	C₂²	—	25	2	no	—
79	C₂²	—	50	1	no	—
80	C₂²	—	50	1	no	—
81	C₂²	C₂×C₃×D₂₅	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	50	1	no	—
84	C₃	#87720	1	1	yes	characteristic, direct product factor, Sylow
85	C₂	—	50	2	no	—
86	C₂	C₃×C₄×D₂₅	1	1	yes	characteristic
87	C₂	C₃×D₁₀₀	1	1	yes	characteristic
88	C₂	C₃×C₂²⋊D₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₂₅
commutator	C₂×C₂₅	C₂×C₃×C₄
Frattini	C₂²×C₅	C₂×C₃×D₅
Fitting	C₂×C₃×C₄×C₂₅	C₂
socle	C₂²×C₃×C₅	C₂×D₅
prime radical	C₂²×C₃×D₂₅	C₂
cosocle	C₂²×C₂₅	C₂²×C₃
hypercenter	C₂×C₃×C₄	D₂₅
hypocenter	C₂₅	C₃×C₂²⋊C₄
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₂₅	C₂	semidirect
3. C₂×C₃×Dic₂₅	C₂	semidirect
4. #87720	C₃	direct (N × H)
8. C₂×C₃×D₂₅	C₄	semidirect
13. C₂×C₄×C₂₅	C₂×C₃	semidirect
14. C₂×Dic₂₅	C₂×C₃	semidirect
25. C₂×D₂₅	C₃×C₄	semidirect
29. C₃×C₂₅	C₂²⋊C₄	semidirect
48. C₂₅	C₃×C₂²⋊C₄	semidirect
51. C₂×C₃×C₄	D₂₅	semidirect
72. C₂×C₄	C₃×D₂₅	semidirect
84. C₃	#87720	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×C₃×D₂₅	2
C₂×C₃×C₄×C₂₅	2
C₂×C₃×Dic₂₅	2
#87720	3
C₃×#685	5

Subgroups — C3×#87720 #11924833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#87720 #11924833