Subgroups — C₂₅×#430 #13098579

Order 1600.

153 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₂₅	C₂	1	2	yes	maximal
2	C₂×M₁₆×C₂₅	C₂	1	1	yes	maximal, characteristic
3	C₂₅×#108	C₂	1	4	yes	maximal, complemented
4	C₂²×C₄×C₂₅	C₂²	1	1	yes	characteristic
5	M₁₆×C₂₅	—	2	2	no	—
6	M₁₆×C₂₅	C₄	1	4	yes	—
7	M₁₆×C₂₅	C₂²	1	4	yes	—
8	C₂×C₈×C₂₅	—	2	2	no	—
9	C₂×C₈×C₂₅	C₂²	1	2	yes	—
10	C₅×#430	C₅	1	1	yes	maximal, characteristic
11	C₂³×C₂₅	Q₈	1	1	yes	characteristic
12	C₂×C₄×C₂₅	C₂×C₄	1	2	yes	—
13	C₂×C₄×C₂₅	D₄	1	2	yes	—
14	C₂×C₄×C₂₅	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
16	C₈×C₂₅	—	2	4	no	—
17	C₈×C₂₅	C₂×C₄	1	4	yes	—
18	C₂×C₅×M₁₆	C₂×C₅	1	2	yes	—
19	C₂×C₅×M₁₆	C₂×C₅	1	1	yes	characteristic
20	C₅×#108	C₂×C₅	1	4	yes	—
21	C₂²×C₂₅	—	4	1	no	—
22	C₂²×C₂₅	C₄⋊C₄	1	2	yes	—
23	C₂²×C₂₅	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₂₅	C₄⋊C₄	1	2	yes	—
25	C₄×C₂₅	C₂²×C₄	1	1	yes	characteristic
26	C₄×C₂₅	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
28	C₅×M₁₆	—	2	2	no	—
29	C₅×M₁₆	C₄×C₅	1	4	yes	—
30	C₅×M₁₆	C₂²×C₅	1	4	yes	—
31	C₂×C₅×C₈	—	2	2	no	—
32	C₂×C₅×C₈	C₂²×C₅	1	2	yes	—
33	#430	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₂₅	—	2	2	no	—
35	C₂×C₂₅	—	2	1	no	—
36	C₂×C₂₅	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₂³×C₅	C₅×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₅	C₂×C₄×C₅	1	2	yes	—
39	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
40	C₂×C₄×C₅	C₅×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
42	C₅×C₈	—	2	4	no	—
43	C₅×C₈	C₂×C₄×C₅	1	4	yes	—
44	C₂×M₁₆	C₂×C₂₅	1	2	yes	—
45	C₂×M₁₆	C₂×C₂₅	1	1	yes	characteristic
46	#108	C₂×C₂₅	1	4	yes	complemented
47	C₂₅	#430	1	1	yes	characteristic, direct product factor, Sylow
48	C₂²×C₅	—	4	1	no	—
49	C₂²×C₅	C₅×C₄⋊C₄	1	2	yes	—
50	C₂²×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
51	C₄×C₅	C₅×C₄⋊C₄	1	2	yes	—
52	C₄×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
53	C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
54	C₂²×C₄	C₂²×C₂₅	1	1	yes	characteristic
55	M₁₆	—	2	2	no	—
56	M₁₆	C₄×C₂₅	1	4	yes	—
57	M₁₆	C₂²×C₂₅	1	4	yes	—
58	C₂×C₈	—	2	2	no	—
59	C₂×C₈	C₂²×C₂₅	1	2	yes	—
60	C₂×C₅	—	2	2	no	—
61	C₂×C₅	—	2	1	no	—
62	C₂×C₅	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
63	C₂³	Q₈×C₂₅	1	1	yes	characteristic
64	C₂×C₄	C₂×C₄×C₂₅	1	2	yes	—
65	C₂×C₄	D₄×C₂₅	1	2	yes	—
66	C₂×C₄	Q₈×C₂₅	1	1	yes	characteristic
67	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
68	C₈	—	2	4	no	—
69	C₈	C₂×C₄×C₂₅	1	4	yes	—
70	C₅	C₅×#430	1	1	yes	characteristic
71	C₂²	—	4	1	no	—
72	C₂²	C₄⋊C₄×C₂₅	1	2	yes	—
73	C₂²	C₂×Q₈×C₂₅	1	1	yes	characteristic
74	C₄	C₄⋊C₄×C₂₅	1	2	yes	—
75	C₄	C₂²×C₄×C₂₅	1	1	yes	characteristic
76	C₄	C₂×D₄×C₂₅	1	1	yes	characteristic
77	C₂	—	2	2	no	—
78	C₂	—	2	1	no	—
79	C₂	C₂×C₄⋊C₄×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₂₅	C₂×D₄
commutator	C₄	C₂²×C₄×C₂₅
Frattini, cosocle	C₂×C₄×C₅	C₂³×C₅
socle	C₂×C₅	C₂×C₅×C₄⋊C₄
prime radical	C₂³×C₅	C₅×Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₅ ◁ C₂²×C₄×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₅×#108	C₂	semidirect
33. #430	C₂₅	direct (N × H)
46. #108	C₂×C₂₅	semidirect
47. C₂₅	#430	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×M₁₆×C₂₅	2
C₂₅×#108	2
C₅×#430	5

Subgroups — C25×#430 #13098579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#430 #13098579