Subgroups — C₂₅×#330 #13097783

Order 1600.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×#125	C₂	1	1	yes	maximal, characteristic
2	C₂₅×#97	C₂	1	2	yes	maximal
3	C₂×C₈×C₂₅	—	2	2	no	—
4	C₄⋊C₄×C₂₅	—	2	2	no	—
5	C₄⋊C₄×C₂₅	C₄	1	2	yes	—
6	C₄²×C₂₅	C₂²	1	1	yes	characteristic
7	C₅×#330	C₅	1	1	yes	maximal, characteristic
8	C₂×C₄×C₂₅	—	2	2	no	—
9	C₂×C₄×C₂₅	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₂₅	D₄	1	2	yes	—
11	C₈×C₂₅	—	2	4	no	—
12	C₅×#125	C₂×C₅	1	1	yes	characteristic
13	C₅×#97	C₂×C₅	1	2	yes	—
14	C₂²×C₂₅	C₂²⋊C₄	1	1	yes	characteristic
15	C₄×C₂₅	—	2	1	no	—
16	C₄×C₂₅	—	2	2	no	—
17	C₄×C₂₅	—	4	2	no	—
18	C₂×C₅×C₈	—	2	2	no	—
19	C₅×C₄⋊C₄	—	2	2	no	—
20	C₅×C₄⋊C₄	C₄×C₅	1	2	yes	—
21	C₄²×C₅	C₂²×C₅	1	1	yes	characteristic
22	#330	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₂₅	#101	1	1	yes	characteristic
24	C₂×C₂₅	#104	1	2	yes	—
25	C₂×C₄×C₅	—	2	2	no	—
26	C₂×C₄×C₅	C₂×C₄×C₅	1	1	yes	characteristic
27	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
28	C₅×C₈	—	2	4	no	—
29	#125	C₂×C₂₅	1	1	yes	characteristic
30	#97	C₂×C₂₅	1	2	yes	—
31	C₂₅	#330	1	1	yes	characteristic, direct product factor, Sylow
32	C₂²×C₅	C₅×C₂²⋊C₄	1	1	yes	characteristic
33	C₄×C₅	—	2	1	no	—
34	C₄×C₅	—	2	2	no	—
35	C₄×C₅	—	4	2	no	—
36	C₂×C₈	—	2	2	no	—
37	C₄⋊C₄	—	2	2	no	—
38	C₄⋊C₄	C₄×C₂₅	1	2	yes	—
39	C₄²	C₂²×C₂₅	1	1	yes	characteristic
40	C₂×C₅	C₅×#101	1	1	yes	characteristic
41	C₂×C₅	C₅×#104	1	2	yes	—
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	C₂×C₄×C₂₅	1	1	yes	characteristic
44	C₂×C₄	D₄×C₂₅	1	2	yes	—
45	C₈	—	2	4	no	—
46	C₅	C₅×#330	1	1	yes	characteristic
47	C₂²	C₂²⋊C₄×C₂₅	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	—	2	2	no	—
50	C₄	—	4	2	no	—
51	C₂	C₂₅×#101	1	1	yes	characteristic
52	C₂	C₂₅×#104	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
22. #330	C₂₅	direct (N × H)
31. C₂₅	#330	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₅×#125	2
C₂₅×#97	2
C₅×#330	5

Subgroups — C25×#330 #13097783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#330 #13097783