Subgroups — C₂×#11716360 #13098372

Order 1600.

135 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic
2	#11716360	C₂	1	4	yes	maximal, direct product factor
3	C₂×#87707	C₂	1	2	yes	maximal, complemented
4	C₂²×C₄×C₂₅	C₄	1	1	yes	characteristic
5	C₂×C₈×C₂₅	C₄	1	2	yes	—
6	C₂×C₈×C₂₅	C₄	1	1	yes	characteristic
7	C₂×C₈×C₂₅	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₂₅	C₂²	1	2	yes	—
9	#87707	C₂²	1	4	yes	complemented
10	C₂×#3944	—	5	1	no	maximal
11	C₂³×C₂₅	C₈	1	1	yes	characteristic
12	C₂×C₄×C₂₅	C₈	1	2	yes	—
13	C₂×C₄×C₂₅	C₈	1	1	yes	characteristic
14	C₂×C₄×C₂₅	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₂₅	C₂×C₄	1	1	yes	characteristic
16	C₈×C₂₅	C₂×C₄	1	1	yes	characteristic
17	C₈×C₂₅	C₂×C₄	1	2	yes	—
18	C₈×C₂₅	C₂³	1	1	yes	characteristic
19	C₂²×C₅×C₈	D₅	1	1	yes	characteristic
20	#3944	—	5	4	no	—
21	C₂×#672	—	5	2	no	—
22	C₂²×C₂₅	—	2	2	no	—
23	C₂²×C₂₅	C₂×C₈	1	2	yes	—
24	C₂²×C₂₅	C₂×C₈	1	1	yes	characteristic
25	C₄×C₂₅	C₂×C₈	1	1	yes	characteristic
26	C₄×C₂₅	C₂×C₈	1	2	yes	—
27	C₄×C₂₅	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₅	Dic₅	1	1	yes	characteristic
29	C₂×C₅×C₈	Dic₅	1	1	yes	characteristic
30	C₂×C₅×C₈	Dic₅	1	2	yes	—
31	C₂×C₅×C₈	C₂×D₅	1	2	yes	—
32	C₂×C₅×C₈	C₂×D₅	1	1	yes	characteristic
33	#672	—	5	4	no	—
34	C₂×M₃₂	—	25	1	no	Sylow
35	C₂×C₂₅	—	2	2	no	—
36	C₂×C₂₅	M₃₂	1	2	yes	complemented
37	C₂×C₂₅	C₂²×C₈	1	1	yes	characteristic
38	C₂³×C₅	#168	1	1	yes	characteristic
39	C₂×C₄×C₅	#168	1	2	yes	—
40	C₂×C₄×C₅	#168	1	1	yes	characteristic
41	C₂×C₄×C₅	C₂×Dic₅	1	2	yes	—
42	C₂×C₄×C₅	C₂×Dic₅	1	1	yes	characteristic
43	C₅×C₈	C₂×Dic₅	1	2	yes	—
44	C₅×C₈	C₂×Dic₅	1	1	yes	characteristic
45	C₅×C₈	C₂²×D₅	1	1	yes	characteristic
46	C₂²×C₈	D₂₅	1	1	yes	characteristic
47	M₃₂	—	25	4	no	—
48	C₂×C₁₆	—	25	2	no	—
49	C₂₅	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₅	—	2	2	no	—
51	C₂²×C₅	C₂×#168	1	2	yes	—
52	C₂²×C₅	C₂×#168	1	1	yes	characteristic
53	C₄×C₅	C₂×#168	1	2	yes	—
54	C₄×C₅	C₂×#168	1	1	yes	characteristic
55	C₄×C₅	C₂²×Dic₅	1	1	yes	characteristic
56	C₂²×C₄	Dic₂₅	1	1	yes	characteristic
57	C₂×C₈	Dic₂₅	1	1	yes	characteristic
58	C₂×C₈	Dic₂₅	1	2	yes	—
59	C₂×C₈	C₂×D₂₅	1	2	yes	—
60	C₂×C₈	C₂×D₂₅	1	1	yes	characteristic
61	C₁₆	—	25	4	no	—
62	C₂×C₅	—	2	2	no	—
63	C₂×C₅	#3944	1	2	yes	—
64	C₂×C₅	C₂²×#168	1	1	yes	characteristic
65	C₂³	#6014	1	1	yes	characteristic
66	C₂×C₄	#6014	1	2	yes	—
67	C₂×C₄	#6014	1	1	yes	characteristic
68	C₂×C₄	C₂×Dic₂₅	1	2	yes	—
69	C₂×C₄	C₂×Dic₂₅	1	1	yes	characteristic
70	C₈	C₂×Dic₂₅	1	2	yes	—
71	C₈	C₂×Dic₂₅	1	1	yes	characteristic
72	C₈	C₂²×D₂₅	1	1	yes	characteristic
73	C₅	C₂×#3944	1	1	yes	characteristic
74	C₂²	—	2	2	no	—
75	C₂²	C₂×#6014	1	2	yes	—
76	C₂²	C₂×#6014	1	1	yes	characteristic
77	C₄	C₂×#6014	1	2	yes	—
78	C₄	C₂×#6014	1	1	yes	characteristic
79	C₄	C₂²×Dic₂₅	1	1	yes	characteristic
80	C₂	—	2	2	no	—
81	C₂	#11716360	1	2	yes	direct product factor
82	C₂	C₂²×#6014	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₂₅
commutator	C₂×C₂₅	C₂²×C₈
Frattini	C₅×C₈	C₂²×D₅
Fitting	C₂²×C₈×C₂₅	C₂
socle	C₂²×C₅	C₂×#168
prime radical	C₂³×C₅	#168
cosocle	C₈×C₂₅	C₂³
hypercenter	C₂²×C₈	D₂₅
hypocenter	C₂₅	C₂×M₃₂
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #11716360	C₂	direct (N × H)
3. C₂×#87707	C₂	semidirect
9. #87707	C₂²	semidirect
36. C₂×C₂₅	M₃₂	semidirect
49. C₂₅	C₂×M₃₂	semidirect
81. C₂	#11716360	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×C₈×C₂₅	2
#11716360	2
C₂×#87707	2
C₂×#3944	5

Subgroups — C2×#11716360 #13098372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11716360 #13098372