Subgroups — C₂₅×#441 #13098590

Order 1600.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×C₂₅	C₂	1	2	yes	maximal
3	C₂₅×#106	C₂	1	1	yes	maximal, characteristic
4	C₂₅×#103	C₂	1	2	yes	maximal
5	C₂₅×#97	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₂₅	C₂²	1	2	yes	—
7	Q₁₆×C₂₅	C₄	1	4	yes	complemented
8	C₂×C₈×C₂₅	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₂₅	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₂₅	—	2	2	no	—
11	C₄⋊C₄×C₂₅	C₂²	1	2	yes	—
12	C₄²×C₂₅	—	2	2	no	—
13	C₄²×C₂₅	C₂²	1	1	yes	characteristic
14	C₅×#441	C₅	1	1	yes	maximal, characteristic
15	Q₈×C₂₅	—	2	2	no	—
16	Q₈×C₂₅	C₂×C₄	1	4	yes	—
17	C₂×C₄×C₂₅	—	2	2	no	—
18	C₂×C₄×C₂₅	—	2	2	no	—
19	C₂×C₄×C₂₅	D₄	1	2	yes	—
20	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
21	C₈×C₂₅	—	2	1	no	—
22	C₈×C₂₅	C₂×C₄	1	2	yes	—
23	C₂×C₅×Q₁₆	C₂×C₅	1	1	yes	characteristic
24	C₄×C₅×Q₈	C₂×C₅	1	2	yes	—
25	C₅×#106	C₂×C₅	1	1	yes	characteristic
26	C₅×#103	C₂×C₅	1	2	yes	—
27	C₅×#97	C₂×C₅	1	1	yes	characteristic
28	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
29	C₄×C₂₅	—	2	4	no	—
30	C₄×C₂₅	—	2	2	no	—
31	C₄×C₂₅	—	4	2	no	—
32	C₄×C₂₅	C₂²×C₄	1	1	yes	characteristic
33	C₄×C₂₅	#41	1	1	yes	characteristic
34	C₂×C₅×Q₈	C₂²×C₅	1	2	yes	—
35	C₅×Q₁₆	C₄×C₅	1	4	yes	—
36	C₂×C₅×C₈	C₂²×C₅	1	1	yes	characteristic
37	C₂×C₅×C₈	C₂²×C₅	1	1	yes	characteristic
38	C₅×C₄⋊C₄	—	2	2	no	—
39	C₅×C₄⋊C₄	C₂²×C₅	1	2	yes	—
40	C₄²×C₅	—	2	2	no	—
41	C₄²×C₅	C₂²×C₅	1	1	yes	characteristic
42	#441	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₂₅	C₄×D₄	1	1	yes	characteristic
44	C₂×C₂₅	#137	1	2	yes	—
45	C₅×Q₈	—	2	2	no	—
46	C₅×Q₈	C₂×C₄×C₅	1	4	yes	—
47	C₂×C₄×C₅	—	2	2	no	—
48	C₂×C₄×C₅	—	2	2	no	—
49	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
50	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
51	C₅×C₈	—	2	1	no	—
52	C₅×C₈	C₂×C₄×C₅	1	2	yes	—
53	C₂×Q₁₆	C₂×C₂₅	1	1	yes	characteristic
54	C₄×Q₈	C₂×C₂₅	1	2	yes	—
55	#106	C₂×C₂₅	1	1	yes	characteristic
56	#103	C₂×C₂₅	1	2	yes	—
57	#97	C₂×C₂₅	1	1	yes	characteristic
58	C₂₅	#441	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
60	C₄×C₅	—	2	4	no	—
61	C₄×C₅	—	2	2	no	—
62	C₄×C₅	—	4	2	no	—
63	C₄×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
64	C₄×C₅	C₅×#41	1	1	yes	characteristic
65	C₂×Q₈	C₂²×C₂₅	1	2	yes	—
66	Q₁₆	C₄×C₂₅	1	4	yes	complemented
67	C₂×C₈	C₂²×C₂₅	1	1	yes	characteristic
68	C₂×C₈	C₂²×C₂₅	1	1	yes	characteristic
69	C₄⋊C₄	—	2	2	no	—
70	C₄⋊C₄	C₂²×C₂₅	1	2	yes	—
71	C₄²	—	2	2	no	—
72	C₄²	C₂²×C₂₅	1	1	yes	characteristic
73	C₂×C₅	C₄×C₅×D₄	1	1	yes	characteristic
74	C₂×C₅	C₅×#137	1	2	yes	—
75	Q₈	—	2	2	no	—
76	Q₈	C₂×C₄×C₂₅	1	4	yes	—
77	C₂×C₄	—	2	2	no	—
78	C₂×C₄	—	2	2	no	—
79	C₂×C₄	D₄×C₂₅	1	2	yes	—
80	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	C₂×C₄×C₂₅	1	2	yes	—
83	C₅	C₅×#441	1	1	yes	characteristic
84	C₂²	C₂×D₄×C₂₅	1	1	yes	characteristic
85	C₄	—	2	4	no	—
86	C₄	—	2	2	no	—
87	C₄	—	4	2	no	—
88	C₄	C₂²×C₄×C₂₅	1	1	yes	characteristic
89	C₄	#41×C₂₅	1	1	yes	characteristic
90	C₂	C₄×D₄×C₂₅	1	1	yes	characteristic
91	C₂	C₂₅×#137	1	2	yes	—

	subgroup	G/H
center	C₂²×C₂₅	C₂×D₄
commutator	C₄	C₂²×C₄×C₂₅
Frattini, cosocle	C₂×C₄×C₅	C₂³×C₅
socle, prime radical	C₂²×C₅	C₂×C₅×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅ ◁ C₄²×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
7. Q₁₆×C₂₅	C₄	semidirect
42. #441	C₂₅	direct (N × H)
58. C₂₅	#441	direct (N × H)
66. Q₁₆	C₄×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×C₂₅	2
C₄×Q₈×C₂₅	2
C₂₅×#106	2
C₂₅×#103	2
C₂₅×#97	2
C₅×#441	5

Subgroups — C25×#441 #13098590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#441 #13098590