Subgroups — C₂×C₂₅×#107 #13098575

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×#107	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×#107	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×#107	C₂×C₅	1	4	yes	—
22	C₂²×C₂₅	C₄⋊C₄	1	2	yes	—
23	C₂²×C₂₅	D₈	1	2	yes	—
24	C₂²×C₂₅	Q₁₆	1	2	yes	—
25	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
26	C₄×C₂₅	—	4	4	no	—
27	C₄×C₂₅	C₄⋊C₄	1	2	yes	—
28	C₄×C₂₅	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₂₅	C₂×Q₈	1	1	yes	characteristic
30	C₂²×C₄×C₅	—	2	2	no	—
31	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
32	C₂×C₅×C₈	C₄×C₅	1	4	yes	—
33	C₂×C₅×C₈	C₂²×C₅	1	2	yes	—
34	C₅×C₄⋊C₄	—	2	2	no	—
35	C₅×C₄⋊C₄	C₂²×C₅	1	4	yes	—
36	C₂×#107	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₂₅	#107	1	4	yes	direct product factor
38	C₂×C₂₅	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₂₅	C₂×D₈	1	1	yes	characteristic
40	C₂×C₂₅	C₂×Q₁₆	1	1	yes	characteristic
41	C₂³×C₅	C₅×D₄	1	1	yes	characteristic
42	C₂×C₄×C₅	—	2	4	no	—
43	C₂×C₄×C₅	—	4	4	no	—
44	C₂×C₄×C₅	C₂×C₄×C₅	1	2	yes	—
45	C₂×C₄×C₅	C₅×D₄	1	1	yes	characteristic
46	C₂×C₄×C₅	C₅×Q₈	1	2	yes	—
47	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
48	C₅×C₈	C₂×C₄×C₅	1	4	yes	—
49	C₂²×C₈	C₂×C₂₅	1	1	yes	characteristic
50	C₂×C₄⋊C₄	C₂×C₂₅	1	2	yes	—
51	#107	C₂×C₂₅	1	4	yes	direct product factor
52	C₂₅	C₂×#107	1	1	yes	characteristic, direct product factor, Sylow
53	C₂²×C₅	C₅×C₄⋊C₄	1	2	yes	—
54	C₂²×C₅	C₅×D₈	1	2	yes	—
55	C₂²×C₅	C₅×Q₁₆	1	2	yes	—
56	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
57	C₄×C₅	—	4	4	no	—
58	C₄×C₅	C₅×C₄⋊C₄	1	2	yes	—
59	C₄×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
60	C₄×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
61	C₂²×C₄	—	2	2	no	—
62	C₂²×C₄	C₂²×C₂₅	1	1	yes	characteristic
63	C₂×C₈	C₄×C₂₅	1	4	yes	complemented
64	C₂×C₈	C₂²×C₂₅	1	2	yes	—
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	C₂²×C₂₅	1	4	yes	—
67	C₂×C₅	C₅×#107	1	4	yes	—
68	C₂×C₅	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₅	C₂×C₅×D₈	1	1	yes	characteristic
70	C₂×C₅	C₂×C₅×Q₁₆	1	1	yes	characteristic
71	C₂³	D₄×C₂₅	1	1	yes	characteristic
72	C₂×C₄	—	2	4	no	—
73	C₂×C₄	—	4	4	no	—
74	C₂×C₄	C₂×C₄×C₂₅	1	2	yes	—
75	C₂×C₄	D₄×C₂₅	1	1	yes	characteristic
76	C₂×C₄	Q₈×C₂₅	1	2	yes	—
77	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
78	C₈	C₂×C₄×C₂₅	1	4	yes	complemented
79	C₅	C₂×C₅×#107	1	1	yes	characteristic
80	C₂²	C₄⋊C₄×C₂₅	1	2	yes	—
81	C₂²	D₈×C₂₅	1	2	yes	—
82	C₂²	Q₁₆×C₂₅	1	2	yes	—
83	C₂²	C₂×D₄×C₂₅	1	1	yes	characteristic
84	C₄	—	4	4	no	—
85	C₄	C₄⋊C₄×C₂₅	1	2	yes	—
86	C₄	C₂²×C₄×C₂₅	1	1	yes	characteristic
87	C₄	C₂×Q₈×C₂₅	1	1	yes	characteristic
88	C₂	C₂₅×#107	1	4	yes	direct product factor
89	C₂	C₂×C₄⋊C₄×C₂₅	1	1	yes	characteristic
90	C₂	C₂×D₈×C₂₅	1	1	yes	characteristic
91	C₂	C₂×Q₁₆×C₂₅	1	1	yes	characteristic

	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×#107	C₂	direct (N × H)
6. C₂×C₈×C₂₅	C₄	semidirect
18. C₈×C₂₅	C₂×C₄	semidirect
36. C₂×#107	C₂₅	direct (N × H)
37. C₂×C₂₅	#107	direct (N × H)
51. #107	C₂×C₂₅	direct (N × H)
52. C₂₅	C₂×#107	direct (N × H)
63. C₂×C₈	C₄×C₂₅	semidirect
78. C₈	C₂×C₄×C₂₅	semidirect
88. C₂	C₂₅×#107	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×#107	2
C₂×C₅×#107	5

Subgroups — C2×C25×#107 #13098575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₅×#107 #13098575