Subgroups — C₂₅×#383 #13098532

Order 1600.

207 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂₅×#95	C₂	1	6	yes	maximal
3	C₂²×C₄×C₂₅	C₂²	1	4	yes	—
4	C₂²×C₄×C₂₅	C₂²	1	3	yes	—
5	C₄²×C₂₅	C₄	1	4	yes	complemented
6	C₅×#383	C₅	1	1	yes	maximal, characteristic
7	C₂³×C₂₅	C₂³	1	1	yes	characteristic
8	C₂×C₄×C₂₅	—	2	6	no	—
9	C₂×C₄×C₂₅	—	2	12	no	—
10	C₂×C₄×C₂₅	C₂×C₄	1	6	yes	—
11	C₂×C₄²×C₅	C₂×C₅	1	1	yes	characteristic
12	C₅×#95	C₂×C₅	1	6	yes	—
13	C₂²×C₂₅	C₂²×C₄	1	1	yes	characteristic
14	C₂²×C₂₅	#41	1	6	yes	—
15	C₄×C₂₅	—	2	6	no	—
16	C₄×C₂₅	—	4	4	no	—
17	C₂²×C₄×C₅	C₂²×C₅	1	4	yes	—
18	C₂²×C₄×C₅	C₂²×C₅	1	3	yes	—
19	C₄²×C₅	C₄×C₅	1	4	yes	—
20	#383	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₂₅	#117	1	3	yes	—
22	C₂×C₂₅	#126	1	4	yes	—
23	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
24	C₂×C₄×C₅	—	2	6	no	—
25	C₂×C₄×C₅	—	2	12	no	—
26	C₂×C₄×C₅	C₂×C₄×C₅	1	6	yes	—
27	C₂×C₄²	C₂×C₂₅	1	1	yes	characteristic
28	#95	C₂×C₂₅	1	6	yes	—
29	C₂₅	#383	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
31	C₂²×C₅	C₅×#41	1	6	yes	—
32	C₄×C₅	—	2	6	no	—
33	C₄×C₅	—	4	4	no	—
34	C₂²×C₄	C₂²×C₂₅	1	4	yes	—
35	C₂²×C₄	C₂²×C₂₅	1	3	yes	—
36	C₄²	C₄×C₂₅	1	4	yes	complemented
37	C₂×C₅	C₅×#117	1	3	yes	—
38	C₂×C₅	C₅×#126	1	4	yes	—
39	C₂³	C₂³×C₂₅	1	1	yes	characteristic
40	C₂×C₄	—	2	6	no	—
41	C₂×C₄	—	2	12	no	—
42	C₂×C₄	C₂×C₄×C₂₅	1	6	yes	—
43	C₅	C₅×#383	1	1	yes	characteristic
44	C₂²	C₂²×C₄×C₂₅	1	1	yes	characteristic
45	C₂²	#41×C₂₅	1	6	yes	—
46	C₄	—	2	6	no	—
47	C₄	—	4	4	no	—
48	C₂	C₂₅×#117	1	3	yes	—
49	C₂	C₂₅×#126	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
5. C₄²×C₂₅	C₄	semidirect
20. #383	C₂₅	direct (N × H)
29. C₂₅	#383	direct (N × H)
36. C₄²	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×C₄²×C₂₅	2
C₂₅×#95	2
C₅×#383	5

Subgroups — C25×#383 #13098532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#383 #13098532