Subgroups — C₂₅×#382 #13098531

Order 1600.

231 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₂₅	C₂	1	2	yes	maximal
2	C₂×C₄²×C₂₅	C₂	1	1	yes	maximal, characteristic
3	C₂₅×#95	C₂	1	4	yes	maximal
4	C₂²×C₄×C₂₅	C₂²	1	4	yes	—
5	C₂²×C₄×C₂₅	C₂²	1	2	yes	—
6	C₂²×C₄×C₂₅	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₂₅	—	2	4	no	—
8	C₄²×C₂₅	C₄	1	4	yes	complemented
9	C₅×#382	C₅	1	1	yes	maximal, characteristic
10	C₂³×C₂₅	C₂³	1	1	yes	characteristic
11	C₂×C₄×C₂₅	—	2	4	no	—
12	C₂×C₄×C₂₅	—	2	4	no	—
13	C₂×C₄×C₂₅	—	2	8	no	—
14	C₂×C₄×C₂₅	C₂×C₄	1	4	yes	—
15	C₂×C₄×C₂₅	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₂₅	D₄	1	2	yes	—
17	C₂×C₄×C₂₅	Q₈	1	2	yes	—
18	C₂×C₅×C₄⋊C₄	C₂×C₅	1	2	yes	—
19	C₂×C₄²×C₅	C₂×C₅	1	1	yes	characteristic
20	C₅×#95	C₂×C₅	1	4	yes	—
21	C₂²×C₂₅	C₂²×C₄	1	1	yes	characteristic
22	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
23	C₂²×C₂₅	C₂×Q₈	1	1	yes	characteristic
24	C₂²×C₂₅	#41	1	4	yes	—
25	C₄×C₂₅	—	2	4	no	—
26	C₄×C₂₅	—	4	4	no	—
27	C₄×C₂₅	C₄⋊C₄	1	4	yes	—
28	C₂²×C₄×C₅	C₂²×C₅	1	4	yes	—
29	C₂²×C₄×C₅	C₂²×C₅	1	2	yes	—
30	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
31	C₅×C₄⋊C₄	—	2	4	no	—
32	C₄²×C₅	C₄×C₅	1	4	yes	—
33	#382	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₂₅	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₂₅	#117	1	2	yes	—
36	C₂×C₂₅	#124	1	2	yes	—
37	C₂×C₂₅	#125	1	2	yes	—
38	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
39	C₂×C₄×C₅	—	2	4	no	—
40	C₂×C₄×C₅	—	2	4	no	—
41	C₂×C₄×C₅	—	2	8	no	—
42	C₂×C₄×C₅	C₂×C₄×C₅	1	4	yes	—
43	C₂×C₄×C₅	C₂×C₄×C₅	1	2	yes	—
44	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
45	C₂×C₄×C₅	C₅×Q₈	1	2	yes	—
46	C₂×C₄⋊C₄	C₂×C₂₅	1	2	yes	—
47	C₂×C₄²	C₂×C₂₅	1	1	yes	characteristic
48	#95	C₂×C₂₅	1	4	yes	—
49	C₂₅	#382	1	1	yes	characteristic, direct product factor, Sylow
50	C₂²×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
51	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
52	C₂²×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
53	C₂²×C₅	C₅×#41	1	4	yes	—
54	C₄×C₅	—	2	4	no	—
55	C₄×C₅	—	4	4	no	—
56	C₄×C₅	C₅×C₄⋊C₄	1	4	yes	—
57	C₂²×C₄	C₂²×C₂₅	1	4	yes	—
58	C₂²×C₄	C₂²×C₂₅	1	2	yes	—
59	C₂²×C₄	C₂²×C₂₅	1	1	yes	characteristic
60	C₄⋊C₄	—	2	4	no	—
61	C₄²	C₄×C₂₅	1	4	yes	complemented
62	C₂×C₅	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₅	C₅×#117	1	2	yes	—
64	C₂×C₅	C₅×#124	1	2	yes	—
65	C₂×C₅	C₅×#125	1	2	yes	—
66	C₂³	C₂³×C₂₅	1	1	yes	characteristic
67	C₂×C₄	—	2	4	no	—
68	C₂×C₄	—	2	4	no	—
69	C₂×C₄	—	2	8	no	—
70	C₂×C₄	C₂×C₄×C₂₅	1	4	yes	—
71	C₂×C₄	C₂×C₄×C₂₅	1	2	yes	—
72	C₂×C₄	D₄×C₂₅	1	2	yes	—
73	C₂×C₄	Q₈×C₂₅	1	2	yes	—
74	C₅	C₅×#382	1	1	yes	characteristic
75	C₂²	C₂²×C₄×C₂₅	1	1	yes	characteristic
76	C₂²	C₂×D₄×C₂₅	1	1	yes	characteristic
77	C₂²	C₂×Q₈×C₂₅	1	1	yes	characteristic
78	C₂²	#41×C₂₅	1	4	yes	—
79	C₄	—	2	4	no	—
80	C₄	—	4	4	no	—
81	C₄	C₄⋊C₄×C₂₅	1	4	yes	—
82	C₂	C₂×C₄⋊C₄×C₂₅	1	1	yes	characteristic
83	C₂	C₂₅×#117	1	2	yes	—
84	C₂	C₂₅×#124	1	2	yes	—
85	C₂	C₂₅×#125	1	2	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
8. C₄²×C₂₅	C₄	semidirect
33. #382	C₂₅	direct (N × H)
49. C₂₅	#382	direct (N × H)
61. 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×C₄⋊C₄×C₂₅	2
C₂×C₄²×C₂₅	2
C₂₅×#95	2
C₅×#382	5

Subgroups — C25×#382 #13098531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#382 #13098531