Subgroups — C₅²×#376 #13103113

Order 1600.

712 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₅²	C₂	1	3	yes	maximal
2	C₅²×#95	C₂	1	4	yes	maximal
3	C₂²×C₄×C₅²	C₂²	1	6	yes	—
4	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic
5	C₄²×C₅²	C₄	1	12	yes	complemented
6	C₅×#376	C₅	1	6	yes	maximal, direct product factor
7	C₂³×C₅²	C₂³	1	1	yes	characteristic
8	C₂×C₄×C₅²	—	2	12	no	—
9	C₂×C₄×C₅²	C₂×C₄	1	12	yes	—
10	C₂×C₄×C₅²	C₂×C₄	1	6	yes	—
11	C₂×C₄²×C₅	C₂×C₅	1	18	yes	—
12	C₅×#95	C₂×C₅	1	24	yes	—
13	C₂²×C₅²	C₂²×C₄	1	3	yes	—
14	C₂²×C₅²	#41	1	4	yes	—
15	C₄×C₅²	—	2	12	no	—
16	C₄×C₅²	C₄²	1	4	yes	—
17	C₂²×C₄×C₅	C₂²×C₅	1	36	yes	—
18	C₂²×C₄×C₅	C₂²×C₅	1	6	yes	—
19	C₄²×C₅	C₄×C₅	1	72	yes	complemented
20	#376	C₅²	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₅²	C₂×C₄²	1	1	yes	characteristic
22	C₂×C₅²	#117	1	6	yes	—
23	C₂³×C₅	C₂³×C₅	1	6	yes	—
24	C₂×C₄×C₅	—	2	72	no	—
25	C₂×C₄×C₅	C₂×C₄×C₅	1	72	yes	—
26	C₂×C₄×C₅	C₂×C₄×C₅	1	36	yes	—
27	C₂×C₄²	C₂×C₅²	1	3	yes	—
28	#95	C₂×C₅²	1	4	yes	—
29	C₅²	#376	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²×C₅	C₂²×C₄×C₅	1	18	yes	—
31	C₂²×C₅	C₅×#41	1	24	yes	—
32	C₄×C₅	—	2	72	no	—
33	C₄×C₅	C₄²×C₅	1	24	yes	—
34	C₂²×C₄	C₂²×C₅²	1	6	yes	—
35	C₂²×C₄	C₂²×C₅²	1	1	yes	characteristic
36	C₄²	C₄×C₅²	1	12	yes	complemented
37	C₂×C₅	C₂×C₄²×C₅	1	6	yes	—
38	C₂×C₅	C₅×#117	1	36	yes	—
39	C₂³	C₂³×C₅²	1	1	yes	characteristic
40	C₂×C₄	—	2	12	no	—
41	C₂×C₄	C₂×C₄×C₅²	1	12	yes	—
42	C₂×C₄	C₂×C₄×C₅²	1	6	yes	—
43	C₅	C₅×#376	1	6	yes	direct product factor
44	C₂²	C₂²×C₄×C₅²	1	3	yes	—
45	C₂²	C₅²×#41	1	4	yes	—
46	C₄	—	2	12	no	—
47	C₄	C₄²×C₅²	1	4	yes	—
48	C₂	C₂×C₄²×C₅²	1	1	yes	characteristic
49	C₂	C₅²×#117	1	6	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅²	C₂²
commutator	C₂	C₂×C₄²×C₅²
Frattini, cosocle	C₂³	C₂³×C₅²
socle, prime radical	C₂³×C₅²	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅² ◁ G

Complements

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

N	H ≅ G/N	type
5. C₄²×C₅²	C₄	semidirect
6. C₅×#376	C₅	direct (N × H)
19. C₄²×C₅	C₄×C₅	semidirect
20. #376	C₅²	direct (N × H)
29. C₅²	#376	direct (N × H)
36. C₄²	C₄×C₅²	semidirect
43. C₅	C₅×#376	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₅²	2
C₅²×#95	2
C₅×#376	5

Subgroups — C52×#376 #13103113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×#376 #13103113