Subgroups — C₂₅×#137 #11716539

Order 800.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₁₆×C₂₅	C₂	1	2	yes	maximal, complemented
4	SD₁₆×C₂₅	C₂	1	2	yes	maximal, complemented
5	M₁₆×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×C₂₅	—	2	1	no	—
7	Q₈×C₂₅	C₂²	1	2	yes	—
8	Q₈×C₂₅	C₂²	1	1	yes	characteristic
9	D₄×C₂₅	—	2	1	no	—
10	D₄×C₂₅	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₂₅	—	2	1	no	—
12	C₂×C₄×C₂₅	—	2	1	no	—
13	C₂×C₄×C₂₅	C₂²	1	1	yes	characteristic
14	C₈×C₂₅	C₂²	1	2	yes	—
15	C₅×#137	C₅	1	1	yes	maximal, characteristic
16	C₂²×C₂₅	—	2	1	no	—
17	C₂²×C₂₅	D₄	1	1	yes	characteristic
18	C₄×C₂₅	—	2	1	no	—
19	C₄×C₂₅	—	2	2	no	—
20	C₄×C₂₅	D₄	1	1	yes	characteristic
21	C₄×C₂₅	C₂³	1	1	yes	characteristic
22	C₅×#41	C₂×C₅	1	1	yes	characteristic
23	C₂×C₅×Q₈	C₂×C₅	1	1	yes	characteristic
24	C₅×Q₁₆	C₂×C₅	1	2	yes	—
25	C₅×SD₁₆	C₂×C₅	1	2	yes	—
26	C₅×M₁₆	C₂×C₅	1	1	yes	characteristic
27	C₂×C₂₅	—	2	1	no	—
28	C₂×C₂₅	—	4	1	no	—
29	C₂×C₂₅	C₂×D₄	1	1	yes	characteristic
30	C₅×Q₈	—	2	1	no	—
31	C₅×Q₈	C₂²×C₅	1	2	yes	—
32	C₅×Q₈	C₂²×C₅	1	1	yes	characteristic
33	C₅×D₄	—	2	1	no	—
34	C₅×D₄	C₂²×C₅	1	1	yes	characteristic
35	C₂×C₄×C₅	—	2	1	no	—
36	C₂×C₄×C₅	—	2	1	no	—
37	C₂×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
38	C₅×C₈	C₂²×C₅	1	2	yes	—
39	#137	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₂₅	#137	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²×C₅	—	2	1	no	—
42	C₂²×C₅	C₅×D₄	1	1	yes	characteristic
43	C₄×C₅	—	2	1	no	—
44	C₄×C₅	—	2	2	no	—
45	C₄×C₅	C₅×D₄	1	1	yes	characteristic
46	C₄×C₅	C₂³×C₅	1	1	yes	characteristic
47	#41	C₂×C₂₅	1	1	yes	characteristic
48	C₂×Q₈	C₂×C₂₅	1	1	yes	characteristic, complemented
49	Q₁₆	C₂×C₂₅	1	2	yes	complemented
50	SD₁₆	C₂×C₂₅	1	2	yes	complemented
51	M₁₆	C₂×C₂₅	1	1	yes	characteristic, complemented
52	C₂×C₅	—	2	1	no	—
53	C₂×C₅	—	4	1	no	—
54	C₂×C₅	C₂×C₅×D₄	1	1	yes	characteristic
55	Q₈	—	2	1	no	—
56	Q₈	C₂²×C₂₅	1	2	yes	—
57	Q₈	C₂²×C₂₅	1	1	yes	characteristic
58	D₄	—	2	1	no	—
59	D₄	C₂²×C₂₅	1	1	yes	characteristic
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	C₂²×C₂₅	1	1	yes	characteristic
63	C₈	C₂²×C₂₅	1	2	yes	—
64	C₅	C₅×#137	1	1	yes	characteristic
65	C₂²	—	2	1	no	—
66	C₂²	D₄×C₂₅	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	2	2	no	—
69	C₄	D₄×C₂₅	1	1	yes	characteristic
70	C₄	C₂³×C₂₅	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	—	4	1	no	—
73	C₂	C₂×D₄×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₂₅	C₂×D₄
commutator	C₄	C₂³×C₂₅
Frattini, cosocle	C₄×C₅	C₂³×C₅
socle	C₂×C₅	C₂×C₅×D₄
prime radical	C₅×#41	C₂×C₅
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₅ ◁ C₂×C₄×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈×C₂₅	C₂	semidirect
3. Q₁₆×C₂₅	C₂	semidirect
4. SD₁₆×C₂₅	C₂	semidirect
5. M₁₆×C₂₅	C₂	semidirect
39. #137	C₂₅	direct (N × H)
40. C₂₅	#137	direct (N × H)
48. C₂×Q₈	C₂×C₂₅	semidirect
49. Q₁₆	C₂×C₂₅	semidirect
50. SD₁₆	C₂×C₂₅	semidirect
51. M₁₆	C₂×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
#41×C₂₅	2
C₂×Q₈×C₂₅	2
Q₁₆×C₂₅	2
SD₁₆×C₂₅	2
M₁₆×C₂₅	2
C₅×#137	5

Subgroups — C25×#137 #11716539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#137 #11716539