Subgroups — C₂×C₂₅×#108 #13098578

Order 1600.

159 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	C₂²×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic
3	C₂₅×#108	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₂₅	C₂²	1	1	yes	characteristic
5	M₁₆×C₂₅	—	2	2	no	—
6	M₁₆×C₂₅	C₂²	1	4	yes	—
7	C₂×C₈×C₂₅	—	2	2	no	—
8	C₂×C₈×C₂₅	C₄	1	2	yes	—
9	C₂×C₈×C₂₅	C₄	1	2	yes	—
10	C₂×C₈×C₂₅	C₂²	1	2	yes	—
11	C₂×C₅×#108	C₅	1	1	yes	maximal, characteristic
12	C₂³×C₂₅	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₂₅	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₂₅	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₂₅	D₄	1	1	yes	characteristic
16	C₂×C₄×C₂₅	D₄	1	1	yes	characteristic
17	C₂×C₄×C₂₅	Q₈	1	1	yes	characteristic
18	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
19	C₈×C₂₅	—	2	4	no	—
20	C₈×C₂₅	C₂×C₄	1	4	yes	—
21	C₂×C₅×M₁₆	C₂×C₅	1	2	yes	—
22	C₂²×C₅×C₈	C₂×C₅	1	1	yes	characteristic
23	C₅×#108	C₂×C₅	1	4	yes	—
24	C₂²×C₂₅	—	2	2	no	—
25	C₂²×C₂₅	C₄⋊C₄	1	1	yes	characteristic
26	C₂²×C₂₅	C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₂₅	C₂×Q₈	1	1	yes	characteristic
28	C₄×C₂₅	C₄⋊C₄	1	1	yes	characteristic
29	C₄×C₂₅	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₂₅	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₂₅	C₂×D₄	1	1	yes	characteristic
32	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
33	C₅×M₁₆	—	2	2	no	—
34	C₅×M₁₆	C₂²×C₅	1	4	yes	—
35	C₂×C₅×C₈	—	2	2	no	—
36	C₂×C₅×C₈	C₄×C₅	1	2	yes	—
37	C₂×C₅×C₈	C₄×C₅	1	2	yes	—
38	C₂×C₅×C₈	C₂²×C₅	1	2	yes	—
39	C₂×#108	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₂₅	—	2	1	no	—
41	C₂×C₂₅	—	2	1	no	—
42	C₂×C₂₅	#108	1	2	yes	direct product factor
43	C₂×C₂₅	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂³×C₅	C₅×Q₈	1	1	yes	characteristic
45	C₂×C₄×C₅	C₂×C₄×C₅	1	1	yes	characteristic
46	C₂×C₄×C₅	C₂×C₄×C₅	1	1	yes	characteristic
47	C₂×C₄×C₅	C₅×D₄	1	1	yes	characteristic
48	C₂×C₄×C₅	C₅×D₄	1	1	yes	characteristic
49	C₂×C₄×C₅	C₅×Q₈	1	1	yes	characteristic
50	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
51	C₅×C₈	—	2	4	no	—
52	C₅×C₈	C₂×C₄×C₅	1	4	yes	—
53	C₂×M₁₆	C₂×C₂₅	1	2	yes	—
54	C₂²×C₈	C₂×C₂₅	1	1	yes	characteristic
55	#108	C₂×C₂₅	1	4	yes	direct product factor
56	C₂₅	C₂×#108	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²×C₅	—	2	2	no	—
58	C₂²×C₅	C₅×C₄⋊C₄	1	1	yes	characteristic
59	C₂²×C₅	C₅×C₄⋊C₄	1	1	yes	characteristic
60	C₂²×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
61	C₄×C₅	C₅×C₄⋊C₄	1	1	yes	characteristic
62	C₄×C₅	C₅×C₄⋊C₄	1	1	yes	characteristic
63	C₄×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
64	C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
65	C₂²×C₄	C₂²×C₂₅	1	1	yes	characteristic
66	M₁₆	—	2	2	no	—
67	M₁₆	C₂²×C₂₅	1	4	yes	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	C₄×C₂₅	1	2	yes	—
70	C₂×C₈	C₄×C₂₅	1	2	yes	—
71	C₂×C₈	C₂²×C₂₅	1	2	yes	—
72	C₂×C₅	—	2	1	no	—
73	C₂×C₅	—	2	1	no	—
74	C₂×C₅	C₅×#108	1	2	yes	—
75	C₂×C₅	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
76	C₂³	Q₈×C₂₅	1	1	yes	characteristic
77	C₂×C₄	C₂×C₄×C₂₅	1	1	yes	characteristic
78	C₂×C₄	C₂×C₄×C₂₅	1	1	yes	characteristic
79	C₂×C₄	D₄×C₂₅	1	1	yes	characteristic
80	C₂×C₄	D₄×C₂₅	1	1	yes	characteristic
81	C₂×C₄	Q₈×C₂₅	1	1	yes	characteristic
82	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
83	C₈	—	2	4	no	—
84	C₈	C₂×C₄×C₂₅	1	4	yes	—
85	C₅	C₂×C₅×#108	1	1	yes	characteristic
86	C₂²	—	2	2	no	—
87	C₂²	C₄⋊C₄×C₂₅	1	1	yes	characteristic
88	C₂²	C₄⋊C₄×C₂₅	1	1	yes	characteristic
89	C₂²	C₂×Q₈×C₂₅	1	1	yes	characteristic
90	C₄	C₄⋊C₄×C₂₅	1	1	yes	characteristic
91	C₄	C₄⋊C₄×C₂₅	1	1	yes	characteristic
92	C₄	C₂²×C₄×C₂₅	1	1	yes	characteristic
93	C₄	C₂×D₄×C₂₅	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	2	1	no	—
96	C₂	C₂₅×#108	1	2	yes	direct product factor
97	C₂	C₂×C₄⋊C₄×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₅	D₄
commutator	C₄	C₂²×C₄×C₂₅
Frattini, cosocle	C₂×C₄×C₅	C₂³×C₅
socle	C₂²×C₅	C₅×C₄⋊C₄
prime radical	C₂³×C₅	C₅×Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×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	direct (N × H)
39. C₂×#108	C₂₅	direct (N × H)
42. C₂×C₂₅	#108	direct (N × H)
55. #108	C₂×C₂₅	direct (N × H)
56. C₂₅	C₂×#108	direct (N × H)
96. C₂	C₂₅×#108	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
C₂²×C₈×C₂₅	2
C₂₅×#108	2
C₂×C₅×#108	5

Subgroups — C2×C25×#108 #13098578

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₅×#108 #13098578