Subgroups — C₂×C₂₅×#106 #13098574

Order 1600.

195 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×C₂₅	C₂	1	2	yes	maximal
3	C₂₅×#106	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₂₅	—	2	2	no	—
5	C₂²×C₄×C₂₅	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₂₅	C₄	1	4	yes	complemented
7	C₂×C₈×C₂₅	C₂²	1	2	yes	—
8	C₄⋊C₄×C₂₅	—	2	2	no	—
9	C₄⋊C₄×C₂₅	C₂²	1	4	yes	—
10	C₂×C₅×#106	C₅	1	1	yes	maximal, characteristic
11	C₂³×C₂₅	D₄	1	1	yes	characteristic
12	C₂×C₄×C₂₅	—	2	4	no	—
13	C₂×C₄×C₂₅	—	4	4	no	—
14	C₂×C₄×C₂₅	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₂₅	D₄	1	1	yes	characteristic
16	C₂×C₄×C₂₅	Q₈	1	2	yes	—
17	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
18	C₈×C₂₅	C₂×C₄	1	4	yes	complemented
19	C₂²×C₅×C₈	C₂×C₅	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₄	C₂×C₅	1	2	yes	—
21	C₅×#106	C₂×C₅	1	4	yes	—
22	C₂²×C₂₅	C₄⋊C₄	1	2	yes	—
23	C₂²×C₂₅	SD₁₆	1	4	yes	—
24	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
25	C₄×C₂₅	—	4	4	no	—
26	C₄×C₂₅	C₄⋊C₄	1	2	yes	—
27	C₄×C₂₅	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₂₅	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₄×C₅	—	2	2	no	—
30	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
31	C₂×C₅×C₈	C₄×C₅	1	4	yes	—
32	C₂×C₅×C₈	C₂²×C₅	1	2	yes	—
33	C₅×C₄⋊C₄	—	2	2	no	—
34	C₅×C₄⋊C₄	C₂²×C₅	1	4	yes	—
35	C₂×#106	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₂₅	#106	1	4	yes	direct product factor
37	C₂×C₂₅	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₂₅	C₂×SD₁₆	1	2	yes	—
39	C₂³×C₅	C₅×D₄	1	1	yes	characteristic
40	C₂×C₄×C₅	—	2	4	no	—
41	C₂×C₄×C₅	—	4	4	no	—
42	C₂×C₄×C₅	C₂×C₄×C₅	1	2	yes	—
43	C₂×C₄×C₅	C₅×D₄	1	1	yes	characteristic
44	C₂×C₄×C₅	C₅×Q₈	1	2	yes	—
45	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
46	C₅×C₈	C₂×C₄×C₅	1	4	yes	—
47	C₂²×C₈	C₂×C₂₅	1	1	yes	characteristic
48	C₂×C₄⋊C₄	C₂×C₂₅	1	2	yes	—
49	#106	C₂×C₂₅	1	4	yes	direct product factor
50	C₂₅	C₂×#106	1	1	yes	characteristic, direct product factor, Sylow
51	C₂²×C₅	C₅×C₄⋊C₄	1	2	yes	—
52	C₂²×C₅	C₅×SD₁₆	1	4	yes	—
53	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
54	C₄×C₅	—	4	4	no	—
55	C₄×C₅	C₅×C₄⋊C₄	1	2	yes	—
56	C₄×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
57	C₄×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
58	C₂²×C₄	—	2	2	no	—
59	C₂²×C₄	C₂²×C₂₅	1	1	yes	characteristic
60	C₂×C₈	C₄×C₂₅	1	4	yes	complemented
61	C₂×C₈	C₂²×C₂₅	1	2	yes	—
62	C₄⋊C₄	—	2	2	no	—
63	C₄⋊C₄	C₂²×C₂₅	1	4	yes	—
64	C₂×C₅	C₅×#106	1	4	yes	—
65	C₂×C₅	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
66	C₂×C₅	C₂×C₅×SD₁₆	1	2	yes	—
67	C₂³	D₄×C₂₅	1	1	yes	characteristic
68	C₂×C₄	—	2	4	no	—
69	C₂×C₄	—	4	4	no	—
70	C₂×C₄	C₂×C₄×C₂₅	1	2	yes	—
71	C₂×C₄	D₄×C₂₅	1	1	yes	characteristic
72	C₂×C₄	Q₈×C₂₅	1	2	yes	—
73	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
74	C₈	C₂×C₄×C₂₅	1	4	yes	complemented
75	C₅	C₂×C₅×#106	1	1	yes	characteristic
76	C₂²	C₄⋊C₄×C₂₅	1	2	yes	—
77	C₂²	SD₁₆×C₂₅	1	4	yes	—
78	C₂²	C₂×D₄×C₂₅	1	1	yes	characteristic
79	C₄	—	4	4	no	—
80	C₄	C₄⋊C₄×C₂₅	1	2	yes	—
81	C₄	C₂²×C₄×C₂₅	1	1	yes	characteristic
82	C₄	C₂×Q₈×C₂₅	1	1	yes	characteristic
83	C₂	C₂₅×#106	1	4	yes	direct product factor
84	C₂	C₂×C₄⋊C₄×C₂₅	1	1	yes	characteristic
85	C₂	C₂×SD₁₆×C₂₅	1	2	yes	—

	subgroup	G/H
center	C₂³×C₂₅	D₄
commutator	C₄	C₂²×C₄×C₂₅
Frattini, cosocle	C₂×C₄×C₅	C₂³×C₅
socle, prime radical	C₂³×C₅	C₅×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₅ ◁ C₂²×C₄×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₅×#106	C₂	direct (N × H)
6. C₂×C₈×C₂₅	C₄	semidirect
18. C₈×C₂₅	C₂×C₄	semidirect
35. C₂×#106	C₂₅	direct (N × H)
36. C₂×C₂₅	#106	direct (N × H)
49. #106	C₂×C₂₅	direct (N × H)
50. C₂₅	C₂×#106	direct (N × H)
60. C₂×C₈	C₄×C₂₅	semidirect
74. C₈	C₂×C₄×C₂₅	semidirect
83. C₂	C₂₅×#106	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×C₈×C₂₅	2
C₂×C₄⋊C₄×C₂₅	2
C₂₅×#106	2
C₂×C₅×#106	5

Subgroups — C2×C25×#106 #13098574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₅×#106 #13098574