Subgroups — C₂₅×#360 #13097813

Order 1600.

87 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×#135	C₂	1	1	yes	maximal, characteristic
2	C₂₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	#41×C₂₅	—	2	1	no	—
5	Q₁₆×C₂₅	C₄	1	1	yes	characteristic, complemented
6	SD₁₆×C₂₅	—	2	1	no	—
7	D₈×C₂₅	C₄	1	1	yes	characteristic, complemented
8	C₂×C₈×C₂₅	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₂₅	—	2	1	no	—
10	C₁₆×C₂₅	—	2	1	no	—
11	C₅×#360	C₅	1	1	yes	maximal, characteristic
12	Q₈×C₂₅	—	2	1	no	—
13	D₄×C₂₅	—	2	1	no	—
14	D₄×C₂₅	—	4	1	no	—
15	C₂×C₄×C₂₅	—	4	1	no	—
16	C₂×C₄×C₂₅	—	4	1	no	—
17	C₂×C₄×C₂₅	D₄	1	1	yes	characteristic
18	C₈×C₂₅	C₂×C₄	1	1	yes	characteristic
19	C₈×C₂₅	D₄	1	1	yes	characteristic
20	C₅×#135	C₂×C₅	1	1	yes	characteristic
21	C₅×M₃₂	C₂×C₅	1	1	yes	characteristic
22	C₅×#106	C₂×C₅	1	1	yes	characteristic
23	C₂²×C₂₅	—	4	1	no	—
24	C₂²×C₂₅	D₈	1	1	yes	characteristic
25	C₄×C₂₅	—	4	1	no	—
26	C₄×C₂₅	—	8	1	no	—
27	C₄×C₂₅	C₂²⋊C₄	1	1	yes	characteristic
28	C₄×C₂₅	SD₁₆	1	1	yes	characteristic
29	C₅×#41	—	2	1	no	—
30	C₅×Q₁₆	C₄×C₅	1	1	yes	characteristic
31	C₅×SD₁₆	—	2	1	no	—
32	C₅×D₈	C₄×C₅	1	1	yes	characteristic
33	C₂×C₅×C₈	C₂²×C₅	1	1	yes	characteristic
34	C₅×C₄⋊C₄	—	2	1	no	—
35	C₅×C₁₆	—	2	1	no	—
36	#360	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₂₅	—	2	1	no	—
38	C₂×C₂₅	—	8	1	no	—
39	C₂×C₂₅	#102	1	1	yes	characteristic
40	C₅×Q₈	—	2	1	no	—
41	C₅×D₄	—	2	1	no	—
42	C₅×D₄	—	4	1	no	—
43	C₂×C₄×C₅	—	4	1	no	—
44	C₂×C₄×C₅	—	4	1	no	—
45	C₂×C₄×C₅	C₅×D₄	1	1	yes	characteristic
46	C₅×C₈	C₂×C₄×C₅	1	1	yes	characteristic
47	C₅×C₈	C₅×D₄	1	1	yes	characteristic
48	#135	C₂×C₂₅	1	1	yes	characteristic
49	M₃₂	C₂×C₂₅	1	1	yes	characteristic, complemented
50	#106	C₂×C₂₅	1	1	yes	characteristic, complemented
51	C₂₅	#360	1	1	yes	characteristic, direct product factor, Sylow
52	C₂²×C₅	—	4	1	no	—
53	C₂²×C₅	C₅×D₈	1	1	yes	characteristic
54	C₄×C₅	—	4	1	no	—
55	C₄×C₅	—	8	1	no	—
56	C₄×C₅	C₅×C₂²⋊C₄	1	1	yes	characteristic
57	C₄×C₅	C₅×SD₁₆	1	1	yes	characteristic
58	#41	—	2	1	no	—
59	Q₁₆	C₄×C₂₅	1	1	yes	characteristic, complemented
60	SD₁₆	—	2	1	no	—
61	D₈	C₄×C₂₅	1	1	yes	characteristic, complemented
62	C₂×C₈	C₂²×C₂₅	1	1	yes	characteristic
63	C₄⋊C₄	—	2	1	no	—
64	C₁₆	—	2	1	no	—
65	C₂×C₅	—	2	1	no	—
66	C₂×C₅	—	8	1	no	—
67	C₂×C₅	C₅×#102	1	1	yes	characteristic
68	Q₈	—	2	1	no	—
69	D₄	—	2	1	no	—
70	D₄	—	4	1	no	—
71	C₂×C₄	—	4	1	no	—
72	C₂×C₄	—	4	1	no	—
73	C₂×C₄	D₄×C₂₅	1	1	yes	characteristic
74	C₈	C₂×C₄×C₂₅	1	1	yes	characteristic
75	C₈	D₄×C₂₅	1	1	yes	characteristic
76	C₅	C₅×#360	1	1	yes	characteristic
77	C₂²	—	4	1	no	—
78	C₂²	D₈×C₂₅	1	1	yes	characteristic
79	C₄	—	4	1	no	—
80	C₄	—	8	1	no	—
81	C₄	C₂²⋊C₄×C₂₅	1	1	yes	characteristic
82	C₄	SD₁₆×C₂₅	1	1	yes	characteristic
83	C₂	—	2	1	no	—
84	C₂	—	8	1	no	—
85	C₂	C₂₅×#102	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₂₅	#102
commutator	C₈	C₂×C₄×C₂₅
Frattini, cosocle	C₂×C₅×C₈	C₂²×C₅
socle	C₂×C₅	C₅×#102
prime radical	C₅×#135	C₂×C₅
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₅ ◁ C₂×C₄×C₂₅ ◁ C₂×C₈×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₅×M₃₂	C₂	semidirect
3. C₂₅×#106	C₂	semidirect
5. Q₁₆×C₂₅	C₄	semidirect
7. D₈×C₂₅	C₄	semidirect
36. #360	C₂₅	direct (N × H)
49. M₃₂	C₂×C₂₅	semidirect
50. #106	C₂×C₂₅	semidirect
51. C₂₅	#360	direct (N × H)
59. Q₁₆	C₄×C₂₅	semidirect
61. D₈	C₄×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂₅×#135	2
C₂₅×M₃₂	2
C₂₅×#106	2
C₅×#360	5

Subgroups — C25×#360 #13097813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#360 #13097813