Subgroups — C₂₅×#423 #13098572

Order 1600.

189 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×C₄²×C₂₅	C₂	1	1	yes	maximal, characteristic
3	C₂₅×C₄⋊C₈	C₂	1	4	yes	maximal, complemented
4	C₂²×C₄×C₂₅	C₄	1	2	yes	—
5	C₂²×C₄×C₂₅	C₂²	1	1	yes	characteristic
6	M₁₆×C₂₅	—	2	4	no	—
7	C₂×C₈×C₂₅	C₂²	1	4	yes	—
8	C₄²×C₂₅	C₄	1	1	yes	characteristic
9	C₄²×C₂₅	C₄	1	1	yes	characteristic
10	C₄²×C₂₅	C₂²	1	2	yes	—
11	C₅×#423	C₅	1	1	yes	maximal, characteristic
12	C₂³×C₂₅	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₂₅	—	2	4	no	—
14	C₂×C₄×C₂₅	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₂₅	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₂₅	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₂₅	D₄	1	2	yes	—
18	C₂×C₄×C₂₅	Q₈	1	2	yes	—
19	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
20	C₈×C₂₅	—	2	4	no	—
21	C₂×C₅×M₁₆	C₂×C₅	1	2	yes	—
22	C₂×C₄²×C₅	C₂×C₅	1	1	yes	characteristic
23	C₅×C₄⋊C₈	C₂×C₅	1	4	yes	—
24	C₂²×C₂₅	—	2	2	no	—
25	C₂²×C₂₅	C₄⋊C₄	1	2	yes	—
26	C₂²×C₂₅	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₂₅	—	2	2	no	—
28	C₄×C₂₅	C₄⋊C₄	1	2	yes	—
29	C₄×C₂₅	M₁₆	1	4	yes	complemented
30	C₄×C₂₅	C₂×D₄	1	1	yes	characteristic
31	C₄×C₂₅	C₂×Q₈	1	1	yes	characteristic
32	C₂²×C₄×C₅	C₄×C₅	1	2	yes	—
33	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
34	C₅×M₁₆	—	2	4	no	—
35	C₂×C₅×C₈	C₂²×C₅	1	4	yes	—
36	C₄²×C₅	C₄×C₅	1	1	yes	characteristic
37	C₄²×C₅	C₄×C₅	1	1	yes	characteristic
38	C₄²×C₅	C₂²×C₅	1	2	yes	—
39	#423	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₂₅	—	2	2	no	—
41	C₂×C₂₅	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₂₅	C₂×M₁₆	1	2	yes	—
43	C₂³×C₅	C₂×C₄×C₅	1	1	yes	characteristic
44	C₂×C₄×C₅	—	2	4	no	—
45	C₂×C₄×C₅	C₂×C₄×C₅	1	2	yes	—
46	C₂×C₄×C₅	C₂×C₄×C₅	1	1	yes	characteristic
47	C₂×C₄×C₅	C₂×C₄×C₅	1	2	yes	—
48	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
49	C₂×C₄×C₅	C₅×Q₈	1	2	yes	—
50	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
51	C₅×C₈	—	2	4	no	—
52	C₂×M₁₆	C₂×C₂₅	1	2	yes	—
53	C₂×C₄²	C₂×C₂₅	1	1	yes	characteristic
54	C₄⋊C₈	C₂×C₂₅	1	4	yes	complemented
55	C₂₅	#423	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²×C₅	—	2	2	no	—
57	C₂²×C₅	C₅×C₄⋊C₄	1	2	yes	—
58	C₂²×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
59	C₄×C₅	—	2	2	no	—
60	C₄×C₅	C₅×C₄⋊C₄	1	2	yes	—
61	C₄×C₅	C₅×M₁₆	1	4	yes	—
62	C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
63	C₄×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
64	C₂²×C₄	C₄×C₂₅	1	2	yes	—
65	C₂²×C₄	C₂²×C₂₅	1	1	yes	characteristic
66	M₁₆	—	2	4	no	—
67	C₂×C₈	C₂²×C₂₅	1	4	yes	—
68	C₄²	C₄×C₂₅	1	1	yes	characteristic
69	C₄²	C₄×C₂₅	1	1	yes	characteristic
70	C₄²	C₂²×C₂₅	1	2	yes	—
71	C₂×C₅	—	2	2	no	—
72	C₂×C₅	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₅	C₂×C₅×M₁₆	1	2	yes	—
74	C₂³	C₂×C₄×C₂₅	1	1	yes	characteristic
75	C₂×C₄	—	2	4	no	—
76	C₂×C₄	C₂×C₄×C₂₅	1	2	yes	—
77	C₂×C₄	C₂×C₄×C₂₅	1	1	yes	characteristic
78	C₂×C₄	C₂×C₄×C₂₅	1	2	yes	—
79	C₂×C₄	D₄×C₂₅	1	2	yes	—
80	C₂×C₄	Q₈×C₂₅	1	2	yes	—
81	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
82	C₈	—	2	4	no	—
83	C₅	C₅×#423	1	1	yes	characteristic
84	C₂²	—	2	2	no	—
85	C₂²	C₄⋊C₄×C₂₅	1	2	yes	—
86	C₂²	C₂²×C₄×C₂₅	1	1	yes	characteristic
87	C₄	—	2	2	no	—
88	C₄	C₄⋊C₄×C₂₅	1	2	yes	—
89	C₄	M₁₆×C₂₅	1	4	yes	complemented
90	C₄	C₂×D₄×C₂₅	1	1	yes	characteristic
91	C₄	C₂×Q₈×C₂₅	1	1	yes	characteristic
92	C₂	—	2	2	no	—
93	C₂	C₂×C₄⋊C₄×C₂₅	1	1	yes	characteristic
94	C₂	C₂×M₁₆×C₂₅	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₂₅×C₄⋊C₈	C₂	semidirect
29. C₄×C₂₅	M₁₆	semidirect
39. #423	C₂₅	direct (N × H)
54. C₄⋊C₈	C₂×C₂₅	semidirect
55. C₂₅	#423	direct (N × H)
89. C₄	M₁₆×C₂₅	semidirect

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
C₂×C₄²×C₂₅	2
C₂₅×C₄⋊C₈	2
C₅×#423	5

Subgroups — C25×#423 #13098572

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#423 #13098572