Subgroups — C₂₅×#494 #13098643

Order 1600.

183 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₅	C₂	1	4	yes	maximal
2	C₂₅×C₄⋊Q₈	C₂	1	2	yes	maximal
3	C₄×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₂₅	C₂²	1	4	yes	—
5	Q₁₆×C₂₅	—	2	8	no	—
6	C₂×C₈×C₂₅	C₂²	1	2	yes	—
7	C₄⋊C₄×C₂₅	—	2	4	no	—
8	C₄²×C₂₅	C₂²	1	1	yes	characteristic
9	C₅×#494	C₅	1	1	yes	maximal, characteristic
10	Q₈×C₂₅	—	2	8	no	—
11	C₂×C₄×C₂₅	—	2	4	no	—
12	C₂×C₄×C₂₅	D₄	1	2	yes	—
13	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
14	C₈×C₂₅	D₄	1	4	yes	—
15	C₂×C₅×Q₁₆	C₂×C₅	1	4	yes	—
16	C₅×C₄⋊Q₈	C₂×C₅	1	2	yes	—
17	C₄×C₅×C₈	C₂×C₅	1	1	yes	characteristic
18	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
19	C₄×C₂₅	—	4	4	no	—
20	C₄×C₂₅	Q₁₆	1	4	yes	complemented
21	C₄×C₂₅	C₂×D₄	1	2	yes	—
22	C₂×C₅×Q₈	C₂²×C₅	1	4	yes	—
23	C₅×Q₁₆	—	2	8	no	—
24	C₂×C₅×C₈	C₂²×C₅	1	2	yes	—
25	C₅×C₄⋊C₄	—	2	4	no	—
26	C₄²×C₅	C₂²×C₅	1	1	yes	characteristic
27	#494	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₂₅	#127	1	1	yes	characteristic
29	C₂×C₂₅	C₂×Q₁₆	1	2	yes	—
30	C₅×Q₈	—	2	8	no	—
31	C₂×C₄×C₅	—	2	4	no	—
32	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
33	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
34	C₅×C₈	C₅×D₄	1	4	yes	—
35	C₂×Q₁₆	C₂×C₂₅	1	4	yes	—
36	C₄⋊Q₈	C₂×C₂₅	1	2	yes	—
37	C₄×C₈	C₂×C₂₅	1	1	yes	characteristic
38	C₂₅	#494	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
40	C₄×C₅	—	4	4	no	—
41	C₄×C₅	C₅×Q₁₆	1	4	yes	—
42	C₄×C₅	C₂×C₅×D₄	1	2	yes	—
43	C₂×Q₈	C₂²×C₂₅	1	4	yes	—
44	Q₁₆	—	2	8	no	—
45	C₂×C₈	C₂²×C₂₅	1	2	yes	—
46	C₄⋊C₄	—	2	4	no	—
47	C₄²	C₂²×C₂₅	1	1	yes	characteristic
48	C₂×C₅	C₅×#127	1	1	yes	characteristic
49	C₂×C₅	C₂×C₅×Q₁₆	1	2	yes	—
50	Q₈	—	2	8	no	—
51	C₂×C₄	—	2	4	no	—
52	C₂×C₄	D₄×C₂₅	1	2	yes	—
53	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
54	C₈	D₄×C₂₅	1	4	yes	—
55	C₅	C₅×#494	1	1	yes	characteristic
56	C₂²	C₂×D₄×C₂₅	1	1	yes	characteristic
57	C₄	—	4	4	no	—
58	C₄	Q₁₆×C₂₅	1	4	yes	complemented
59	C₄	C₂×D₄×C₂₅	1	2	yes	—
60	C₂	C₂₅×#127	1	1	yes	characteristic
61	C₂	C₂×Q₁₆×C₂₅	1	2	yes	—

	subgroup	G/H
center	C₂²×C₂₅	C₂×D₄
commutator	C₂×C₄	C₂³×C₂₅
Frattini, cosocle	C₂×C₄×C₅	C₂³×C₅
socle, prime radical	C₂²×C₅	C₂×C₅×D₄
LCS	G ▷ C₂×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
20. C₄×C₂₅	Q₁₆	semidirect
27. #494	C₂₅	direct (N × H)
38. C₂₅	#494	direct (N × H)
58. C₄	Q₁₆×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
C₂₅×C₄⋊Q₈	2
C₄×C₈×C₂₅	2
C₅×#494	5

Subgroups — C25×#494 #13098643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#494 #13098643