Subgroups — C₂×#11716361 #13098373

Order 1600.

159 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	C₂×#87716	C₂	1	2	yes	maximal
3	#11716361	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₂₅	C₂²	1	1	yes	characteristic
5	C₂×C₈×C₂₅	C₄	1	2	yes	—
6	C₂×C₈×C₂₅	C₄	1	2	yes	—
7	C₂×C₈×C₂₅	C₂²	1	2	yes	—
8	#87716	—	2	2	no	—
9	#87716	C₂²	1	4	yes	—
10	C₂×#6014	—	2	2	no	—
11	C₂×#3951	—	5	1	no	maximal
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	C₂×C₄	1	4	yes	—
20	#6014	—	2	4	no	—
21	C₂²×C₅×C₈	D₅	1	1	yes	characteristic
22	C₂×#681	—	5	2	no	—
23	#3951	—	5	4	no	—
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	C₂×D₅	1	1	yes	characteristic
33	C₂×C₅×C₈	Dic₅	1	2	yes	—
34	C₂×C₅×C₈	Dic₅	1	2	yes	—
35	C₂×C₅×C₈	C₂×D₅	1	2	yes	—
36	#681	—	5	4	no	—
37	#681	—	10	2	no	—
38	C₂×#168	—	10	2	no	—
39	C₂×#108	—	25	1	no	Sylow
40	C₂×C₂₅	—	2	1	no	—
41	C₂×C₂₅	—	2	1	no	—
42	C₂×C₂₅	#108	1	2	yes	complemented
43	C₂×C₂₅	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂³×C₅	Dic₁₀	1	1	yes	characteristic
45	C₂×C₄×C₅	Dic₁₀	1	1	yes	characteristic
46	C₂×C₄×C₅	D₂₀	1	1	yes	characteristic
47	C₂×C₄×C₅	D₂₀	1	1	yes	characteristic
48	C₂×C₄×C₅	C₂×Dic₅	1	1	yes	characteristic
49	C₂×C₄×C₅	C₂×Dic₅	1	1	yes	characteristic
50	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
51	C₅×C₈	C₂×Dic₅	1	4	yes	—
52	#168	—	10	4	no	—
53	C₂×M₁₆	—	25	2	no	—
54	C₂²×C₈	D₂₅	1	1	yes	characteristic
55	#108	—	25	4	no	—
56	C₂₅	C₂×#108	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₅	—	2	2	no	—
58	C₂²×C₅	C₄⋊Dic₅	1	1	yes	characteristic
59	C₂²×C₅	C₄⋊Dic₅	1	1	yes	characteristic
60	C₂²×C₅	C₂×Dic₁₀	1	1	yes	characteristic
61	C₄×C₅	C₄⋊Dic₅	1	1	yes	characteristic
62	C₄×C₅	C₄⋊Dic₅	1	1	yes	characteristic
63	C₄×C₅	C₂×D₂₀	1	1	yes	characteristic
64	C₄×C₅	C₂²×Dic₅	1	1	yes	characteristic
65	C₂²×C₄	C₂×D₂₅	1	1	yes	characteristic
66	M₁₆	—	25	4	no	—
67	M₁₆	—	50	2	no	—
68	C₂×C₈	—	50	2	no	—
69	C₂×C₈	Dic₂₅	1	2	yes	—
70	C₂×C₈	Dic₂₅	1	2	yes	—
71	C₂×C₈	C₂×D₂₅	1	2	yes	—
72	C₂×C₅	—	2	1	no	—
73	C₂×C₅	—	2	1	no	—
74	C₂×C₅	#3951	1	2	yes	—
75	C₂×C₅	C₂×C₄⋊Dic₅	1	1	yes	characteristic
76	C₂³	Dic₅₀	1	1	yes	characteristic
77	C₂×C₄	Dic₅₀	1	1	yes	characteristic
78	C₂×C₄	D₁₀₀	1	1	yes	characteristic
79	C₂×C₄	D₁₀₀	1	1	yes	characteristic
80	C₂×C₄	C₂×Dic₂₅	1	1	yes	characteristic
81	C₂×C₄	C₂×Dic₂₅	1	1	yes	characteristic
82	C₂×C₄	C₂²×D₂₅	1	1	yes	characteristic
83	C₈	—	50	4	no	—
84	C₈	C₂×Dic₂₅	1	4	yes	—
85	C₅	C₂×#3951	1	1	yes	characteristic
86	C₂²	—	2	2	no	—
87	C₂²	C₄⋊Dic₂₅	1	1	yes	characteristic
88	C₂²	C₄⋊Dic₂₅	1	1	yes	characteristic
89	C₂²	C₂×Dic₅₀	1	1	yes	characteristic
90	C₄	C₄⋊Dic₂₅	1	1	yes	characteristic
91	C₄	C₄⋊Dic₂₅	1	1	yes	characteristic
92	C₄	C₂×D₁₀₀	1	1	yes	characteristic
93	C₄	C₂²×Dic₂₅	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	2	1	no	—
96	C₂	#11716361	1	2	yes	direct product factor
97	C₂	C₂×C₄⋊Dic₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₀₀
commutator	C₄×C₂₅	C₂²×C₄
Frattini	C₂×C₄×C₅	C₂²×D₅
Fitting	C₂²×C₈×C₂₅	C₂
socle	C₂²×C₅	C₄⋊Dic₅
prime radical	C₂³×C₅	Dic₁₀
cosocle	C₂×C₄×C₂₅	C₂³
hypercenter	C₂²×C₈	D₂₅
hypocenter	C₂₅	C₂×#108
LCS	G ▷ C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #11716361	C₂	direct (N × H)
42. C₂×C₂₅	#108	semidirect
56. C₂₅	C₂×#108	semidirect
96. C₂	#11716361	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
C₂×#87716	2
#11716361	2
C₂×#3951	5

Subgroups — C2×#11716361 #13098373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11716361 #13098373