Subgroups — C₂×#11716438 #13098801

Order 1600.

369 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#87720	C₂	1	3	yes	maximal
3	C₂×#87718	C₂	1	3	yes	maximal, complemented
4	#11716438	C₂	1	8	yes	maximal, direct product factor
5	C₂³×D₂₅	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₂₅	C₂²	1	3	yes	—
7	C₂²×Dic₂₅	C₂²	1	3	yes	—
8	C₄²×C₂₅	C₂²	1	4	yes	complemented
9	#87720	C₂²	1	12	yes	—
10	#87718	C₂²	1	12	yes	complemented
11	C₂×#4022	—	5	1	no	maximal
12	C₂³×C₂₅	C₂³	1	1	yes	characteristic
13	C₂²×D₂₅	—	2	6	no	—
14	C₂²×D₂₅	C₂³	1	2	yes	—
15	C₂×C₄×C₂₅	—	2	6	no	—
16	C₂×C₄×C₂₅	C₂³	1	6	yes	—
17	C₂×Dic₂₅	—	2	6	no	—
18	C₂×Dic₂₅	C₂³	1	6	yes	—
19	C₂×C₄²×C₅	D₅	1	1	yes	characteristic
20	C₂×#685	—	5	3	no	—
21	C₂×#683	—	5	3	no	—
22	#4022	—	5	8	no	—
23	C₂²×C₂₅	#41	1	6	yes	—
24	C₂²×C₂₅	C₂⁴	1	1	yes	characteristic
25	C₂×D₂₅	—	2	6	no	—
26	C₂×D₂₅	—	4	4	no	—
27	C₄×C₂₅	—	2	6	no	—
28	Dic₂₅	—	2	6	no	—
29	C₂³×D₅	—	5	1	no	—
30	C₂²×C₄×C₅	C₂×D₅	1	3	yes	—
31	C₂²×Dic₅	—	5	3	no	—
32	C₄²×C₅	C₂×D₅	1	4	yes	—
33	#685	—	5	12	no	—
34	#683	—	5	12	no	—
35	C₂×#126	—	25	1	no	Sylow
36	C₂×C₂₅	#126	1	4	yes	complemented
37	C₂×C₂₅	C₂×#41	1	3	yes	—
38	D₂₅	—	4	2	no	—
39	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
40	C₂²×D₅	—	5	2	no	—
41	C₂²×D₅	—	10	6	no	—
42	C₂×C₄×C₅	—	2	6	no	—
43	C₂×C₄×C₅	C₂²×D₅	1	6	yes	—
44	C₂×Dic₅	—	5	6	no	—
45	C₂×Dic₅	—	10	6	no	—
46	#126	—	25	8	no	—
47	C₂×C₄⋊C₄	—	25	3	no	—
48	C₂×C₂²⋊C₄	—	25	3	no	—
49	C₂×C₄²	D₂₅	1	1	yes	characteristic, complemented
50	C₂₅	C₂×#126	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₅	#709	1	6	yes	—
52	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
53	C₂×D₅	—	10	6	no	—
54	C₂×D₅	—	20	4	no	—
55	C₄×C₅	—	2	6	no	—
56	Dic₅	—	10	6	no	—
57	C₂⁴	—	25	1	no	—
58	C₂²×C₄	—	25	3	no	—
59	C₂²×C₄	C₂×D₂₅	1	3	yes	—
60	C₄⋊C₄	—	25	12	no	—
61	C₂²⋊C₄	—	25	12	no	—
62	C₄²	C₂×D₂₅	1	4	yes	complemented
63	C₂×C₅	#4022	1	4	yes	—
64	C₂×C₅	C₂×#709	1	3	yes	—
65	D₅	—	20	2	no	—
66	C₂³	—	25	2	no	—
67	C₂³	—	50	6	no	—
68	C₂³	C₂²×D₂₅	1	1	yes	characteristic
69	C₂×C₄	—	2	6	no	—
70	C₂×C₄	—	25	6	no	—
71	C₂×C₄	—	50	6	no	—
72	C₂×C₄	C₂²×D₂₅	1	6	yes	—
73	C₅	C₂×#4022	1	1	yes	characteristic
74	C₂²	—	50	6	no	—
75	C₂²	—	100	4	no	—
76	C₂²	#87744	1	6	yes	—
77	C₂²	C₂³×D₂₅	1	1	yes	characteristic
78	C₄	—	2	6	no	—
79	C₄	—	50	6	no	—
80	C₂	—	100	2	no	—
81	C₂	#11716438	1	4	yes	direct product factor
82	C₂	C₂×#87744	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₂₅
commutator, cosocle	C₂²×C₂₅	C₂⁴
Frattini	C₂²×C₅	C₂³×D₅
Fitting	C₂×C₄²×C₂₅	C₂
socle	C₂³×C₅	C₂²×D₅
prime radical	C₂³×D₂₅	C₂²
hypercenter	C₂×C₄²	D₂₅
hypocenter	C₂₅	C₂×#126
LCS	G ▷ C₂²×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×C₄²×C₂₅	C₂	semidirect
3. C₂×#87718	C₂	semidirect
4. #11716438	C₂	direct (N × H)
8. C₄²×C₂₅	C₂²	semidirect
10. #87718	C₂²	semidirect
36. C₂×C₂₅	#126	semidirect
49. C₂×C₄²	D₂₅	semidirect
50. C₂₅	C₂×#126	semidirect
62. C₄²	C₂×D₂₅	semidirect
81. C₂	#11716438	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×C₄²×C₂₅	2
C₂×#87720	2
C₂×#87718	2
#11716438	2
C₂×#4022	5

Subgroups — C2×#11716438 #13098801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11716438 #13098801