Subgroups — C₂₅×(C₂×D₃)⋊C₄ #11924849

Order 1200.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₃×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊C₄×C₂₅	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₂₅	C₂²	1	1	yes	characteristic
6	C₂×D₃×C₂₅	—	2	1	no	—
7	C₂×D₃×C₂₅	—	2	1	no	—
8	C₂×D₃×C₂₅	C₄	1	2	yes	complemented
9	C₃×C₄×C₂₅	—	2	1	no	—
10	Dic₃×C₂₅	—	2	1	no	—
11	C₅×(C₂×D₃)⋊C₄	C₅	1	1	yes	maximal, characteristic
12	C₂³×C₂₅	—	3	1	no	—
13	C₂×C₄×C₂₅	—	3	1	no	—
14	C₂×C₄×C₂₅	D₃	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	D₃×C₂₅	—	2	2	no	—
19	C₂²×C₅×D₃	C₂×C₅	1	1	yes	characteristic
20	C₂×C₃×C₄×C₅	C₂×C₅	1	1	yes	characteristic
21	C₂×C₅×Dic₃	C₂×C₅	1	1	yes	characteristic
22	C₂²×C₂₅	—	3	2	no	—
23	C₂²×C₂₅	—	6	1	no	—
24	C₂²×C₂₅	—	6	1	no	—
25	C₂²×C₂₅	C₂×D₃	1	1	yes	characteristic
26	C₄×C₂₅	—	2	1	no	—
27	C₄×C₂₅	—	6	1	no	—
28	C₅×C₂²⋊C₄	—	3	1	no	—
29	C₃×C₂₅	C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃×C₅	C₂²×C₅	1	1	yes	characteristic
31	C₂×C₅×D₃	—	2	1	no	—
32	C₂×C₅×D₃	—	2	1	no	—
33	C₂×C₅×D₃	C₄×C₅	1	2	yes	—
34	C₃×C₄×C₅	—	2	1	no	—
35	C₅×Dic₃	—	2	1	no	—
36	C₂×C₂₅	—	6	2	no	—
37	C₂×C₂₅	C₄×D₃	1	1	yes	characteristic
38	C₂×C₂₅	D₁₂	1	1	yes	characteristic
39	C₂×C₂₅	#67	1	1	yes	characteristic
40	(C₂×D₃)⋊C₄	C₂₅	1	1	yes	characteristic, direct product factor, Hall
41	C₂³×C₅	—	3	1	no	—
42	C₂×C₄×C₅	—	3	1	no	—
43	C₂×C₄×C₅	C₅×D₃	1	1	yes	characteristic
44	C₂×C₃×C₅	C₂×C₄×C₅	1	1	yes	characteristic
45	C₂×C₃×C₅	C₅×D₄	1	1	yes	characteristic
46	C₂×C₃×C₅	C₅×D₄	1	1	yes	characteristic
47	C₅×D₃	—	2	2	no	—
48	C₂₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²×D₃	C₂×C₂₅	1	1	yes	characteristic
50	C₂×C₃×C₄	C₂×C₂₅	1	1	yes	characteristic, complemented
51	C₂×Dic₃	C₂×C₂₅	1	1	yes	characteristic, complemented
52	C₂²×C₅	—	3	2	no	—
53	C₂²×C₅	—	6	1	no	—
54	C₂²×C₅	—	6	1	no	—
55	C₂²×C₅	C₂×C₅×D₃	1	1	yes	characteristic
56	C₄×C₅	—	2	1	no	—
57	C₄×C₅	—	6	1	no	—
58	C₂²⋊C₄	—	3	1	no	Sylow
59	C₃×C₅	C₅×C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₃	C₂²×C₂₅	1	1	yes	characteristic
61	C₂×D₃	—	2	1	no	—
62	C₂×D₃	—	2	1	no	—
63	C₂×D₃	C₄×C₂₅	1	2	yes	complemented
64	C₃×C₄	—	2	1	no	—
65	Dic₃	—	2	1	no	—
66	C₂×C₅	—	6	2	no	—
67	C₂×C₅	C₄×C₅×D₃	1	1	yes	characteristic
68	C₂×C₅	C₅×D₁₂	1	1	yes	characteristic
69	C₂×C₅	C₅×#67	1	1	yes	characteristic
70	C₂³	—	3	1	no	—
71	C₂×C₄	—	3	1	no	—
72	C₂×C₄	D₃×C₂₅	1	1	yes	characteristic, complemented
73	C₂×C₃	C₂×C₄×C₂₅	1	1	yes	characteristic
74	C₂×C₃	D₄×C₂₅	1	1	yes	characteristic
75	C₂×C₃	D₄×C₂₅	1	1	yes	characteristic
76	D₃	—	2	2	no	—
77	C₅	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
78	C₂²	—	3	2	no	—
79	C₂²	—	6	1	no	—
80	C₂²	—	6	1	no	—
81	C₂²	C₂×D₃×C₂₅	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	6	1	no	—
84	C₃	C₂²⋊C₄×C₂₅	1	1	yes	characteristic, complemented, Sylow
85	C₂	—	6	2	no	—
86	C₂	C₄×D₃×C₂₅	1	1	yes	characteristic
87	C₂	D₁₂×C₂₅	1	1	yes	characteristic
88	C₂	#67×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₂₅	C₂×D₃
commutator	C₂×C₃	C₂×C₄×C₂₅
Frattini	C₂²×C₅	C₂×C₅×D₃
Fitting	C₂×C₃×C₄×C₂₅	C₂
socle, cosocle	C₂²×C₃×C₅	C₂²×C₅
prime radical	C₂²×C₅×D₃	C₂×C₅
hypercenter	C₂×C₄×C₂₅	D₃
hypocenter	C₃	C₂²⋊C₄×C₂₅
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₂₅ ◁ C₂×C₄×C₂₅

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×Dic₃×C₂₅	C₂	semidirect
8. C₂×D₃×C₂₅	C₄	semidirect
14. C₂×C₄×C₂₅	D₃	semidirect
29. C₃×C₂₅	C₂²⋊C₄	semidirect
40. (C₂×D₃)⋊C₄	C₂₅	direct (N × H)
48. C₂₅	(C₂×D₃)⋊C₄	direct (N × H)
50. C₂×C₃×C₄	C₂×C₂₅	semidirect
51. C₂×Dic₃	C₂×C₂₅	semidirect
63. C₂×D₃	C₄×C₂₅	semidirect
72. C₂×C₄	D₃×C₂₅	semidirect
84. C₃	C₂²⋊C₄×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₃×C₂₅	2
C₂×C₃×C₄×C₂₅	2
C₂×Dic₃×C₂₅	2
C₂²⋊C₄×C₂₅	3
C₅×(C₂×D₃)⋊C₄	5

Subgroups — C25×(C2×D3)⋊C4 #11924849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×(C₂×D₃)⋊C₄ #11924849