Subgroups — C₂²×#87735 #13099662

Order 1600.

447 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6016	C₂	1	2	yes	maximal, complemented
3	C₂×#87735	C₂	1	12	yes	maximal, direct product factor
4	C₂³×D₂₅	C₄	1	1	yes	characteristic
5	C₂²×C₄×C₂₅	C₄	1	1	yes	characteristic
6	C₂²×Dic₂₅	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₂₅	C₄	1	6	yes	—
8	C₂×C₄×D₂₅	C₂²	1	6	yes	—
9	C₂×#6016	C₂²	1	12	yes	complemented
10	#87735	C₂²	1	16	yes	direct product factor
11	C₂²×#700	—	5	1	no	maximal
12	C₂³×C₂₅	C₂×C₄	1	1	yes	characteristic
13	C₂²×D₂₅	—	2	4	no	—
14	C₂²×D₂₅	C₂×C₄	1	6	yes	—
15	C₂×C₄×C₂₅	C₂×C₄	1	6	yes	—
16	C₂×Dic₂₅	C₂×C₄	1	3	yes	—
17	C₂×Dic₂₅	C₂³	1	3	yes	—
18	C₄×D₂₅	C₂×C₄	1	12	yes	—
19	C₄×D₂₅	C₂³	1	4	yes	—
20	#6016	C₂³	1	8	yes	complemented
21	C₂²×C₄×D₅	—	5	1	no	—
22	C₂²×#170	—	5	2	no	—
23	C₂×#700	—	5	12	no	—
24	C₂²×C₂₅	M₁₆	1	4	yes	complemented
25	C₂²×C₂₅	C₂²×C₄	1	3	yes	—
26	C₂×D₂₅	—	2	12	no	—
27	C₂×D₂₅	C₂²×C₄	1	4	yes	—
28	C₄×C₂₅	C₂²×C₄	1	4	yes	—
29	Dic₂₅	C₂²×C₄	1	3	yes	—
30	Dic₂₅	C₂⁴	1	1	yes	characteristic
31	C₂³×D₅	—	5	1	no	—
32	C₂²×C₄×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic
33	C₂²×Dic₅	—	5	1	no	—
34	C₂×C₄×D₅	—	5	6	no	—
35	C₂×C₄×D₅	—	5	6	no	—
36	C₂×#170	—	5	12	no	—
37	#700	—	5	16	no	—
38	C₂²×M₁₆	—	25	1	no	Sylow
39	C₂×C₂₅	C₂×M₁₆	1	6	yes	complemented
40	C₂×C₂₅	C₂³×C₄	1	1	yes	characteristic
41	D₂₅	—	2	4	no	—
42	C₂³×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
43	C₂²×D₅	—	5	6	no	—
44	C₂²×D₅	—	10	4	no	—
45	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	6	yes	—
46	C₂×Dic₅	—	5	3	no	—
47	C₂×Dic₅	—	5	3	no	—
48	C₄×D₅	—	5	12	no	—
49	C₄×D₅	—	5	4	no	—
50	#170	—	5	8	no	—
51	C₂³×C₄	—	25	1	no	—
52	C₂×M₁₆	—	25	12	no	—
53	C₂²×C₈	—	25	2	no	—
54	C₂₅	C₂²×M₁₆	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₅	#700	1	4	yes	—
56	C₂²×C₅	C₂²×AGL(1,𝔽₅)	1	3	yes	—
57	C₂×D₅	—	5	4	no	—
58	C₂×D₅	—	10	12	no	—
59	C₄×C₅	C₂²×AGL(1,𝔽₅)	1	4	yes	—
60	Dic₅	—	5	3	no	—
61	Dic₅	—	5	1	no	—
62	C₂⁴	—	25	1	no	—
63	C₂²×C₄	—	25	1	no	—
64	C₂²×C₄	—	25	6	no	—
65	C₂²×C₄	—	25	6	no	—
66	C₂²×C₄	#1035	1	1	yes	characteristic
67	M₁₆	—	25	16	no	—
68	C₂×C₈	—	25	12	no	—
69	C₂×C₅	C₂×#700	1	6	yes	—
70	C₂×C₅	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
71	D₅	—	10	4	no	—
72	C₂³	—	25	6	no	—
73	C₂³	—	50	4	no	—
74	C₂³	C₂×#1035	1	1	yes	characteristic
75	C₂×C₄	—	25	3	no	—
76	C₂×C₄	—	25	3	no	—
77	C₂×C₄	—	25	4	no	—
78	C₂×C₄	—	25	12	no	—
79	C₂×C₄	C₂×#1035	1	6	yes	—
80	C₈	—	25	8	no	—
81	C₅	C₂²×#700	1	1	yes	characteristic
82	C₂²	—	25	4	no	—
83	C₂²	—	50	12	no	—
84	C₂²	#87735	1	4	yes	direct product factor
85	C₂²	C₂²×#1035	1	3	yes	—
86	C₄	—	25	1	no	—
87	C₄	—	25	3	no	—
88	C₄	C₂²×#1035	1	4	yes	—
89	C₂	—	50	4	no	—
90	C₂	C₂×#87735	1	6	yes	direct product factor
91	C₂	C₂³×#1035	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#1035
commutator	C₂×C₂₅	C₂³×C₄
Frattini	C₂×C₅	C₂³×AGL(1,𝔽₅)
Fitting	C₂²×C₄×C₂₅	C₄
socle	C₂³×C₅	C₂×AGL(1,𝔽₅)
prime radical	C₂³×D₂₅	C₄
cosocle	Dic₂₅	C₂⁴
hypercenter	C₂²×C₄	#1035
hypocenter	C₂₅	C₂²×M₁₆
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×#6016	C₂	semidirect
3. C₂×#87735	C₂	direct (N × H)
9. C₂×#6016	C₂²	semidirect
10. #87735	C₂²	direct (N × H)
20. #6016	C₂³	semidirect
24. C₂²×C₂₅	M₁₆	semidirect
39. C₂×C₂₅	C₂×M₁₆	semidirect
54. C₂₅	C₂²×M₁₆	semidirect
84. C₂²	#87735	direct (N × H)
90. C₂	C₂×#87735	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₂₅	2
C₂²×#6016	2
C₂×#87735	2
C₂²×#700	5

Subgroups — C22×#87735 #13099662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#87735 #13099662