Subgroups — C₂×#11716377 #13098455

Order 1600.

123 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₀₀	C₂	1	1	yes	maximal, characteristic
3	#11716377	C₂	1	4	yes	maximal, direct product factor
4	C₂×#87707	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₂₅	—	2	1	no	—
6	C₂×Dic₅₀	—	2	1	no	—
7	Q₁₆×C₂₅	—	2	1	no	—
8	Q₁₆×C₂₅	C₂²	1	2	yes	—
9	C₂×C₈×C₂₅	C₂²	1	1	yes	characteristic
10	Dic₁₀₀	—	2	1	no	—
11	Dic₁₀₀	C₂²	1	2	yes	—
12	#87707	C₂²	1	2	yes	—
13	C₂×#3961	—	5	1	no	maximal
14	Q₈×C₂₅	—	2	2	no	—
15	Q₈×C₂₅	—	4	1	no	—
16	C₂×C₄×C₂₅	—	4	1	no	—
17	C₂×C₄×C₂₅	D₄	1	1	yes	characteristic
18	C₂×Dic₂₅	—	4	1	no	—
19	Dic₅₀	—	2	2	no	—
20	Dic₅₀	—	4	1	no	—
21	C₈×C₂₅	D₄	1	1	yes	characteristic
22	C₈×C₂₅	C₂³	1	1	yes	characteristic
23	C₂×C₅×Q₁₆	D₅	1	1	yes	characteristic
24	C₂×Dic₂₀	—	5	1	no	—
25	#3961	—	5	4	no	—
26	C₂×#672	—	5	1	no	—
27	C₂²×C₂₅	D₈	1	1	yes	characteristic
28	C₄×C₂₅	—	4	2	no	—
29	C₄×C₂₅	D₈	1	1	yes	characteristic
30	C₄×C₂₅	C₂×D₄	1	1	yes	characteristic
31	Dic₂₅	—	4	2	no	—
32	C₂×C₅×Q₈	—	2	1	no	—
33	C₂×Dic₁₀	—	10	1	no	—
34	C₅×Q₁₆	—	2	1	no	—
35	C₅×Q₁₆	C₂×D₅	1	2	yes	—
36	C₂×C₅×C₈	C₂×D₅	1	1	yes	characteristic
37	Dic₂₀	—	5	2	no	—
38	Dic₂₀	—	10	1	no	—
39	#672	—	5	2	no	—
40	C₂×Q₃₂	—	25	1	no	Sylow
41	C₂×C₂₅	Q₃₂	1	2	yes	complemented
42	C₂×C₂₅	C₂×D₈	1	1	yes	characteristic
43	C₅×Q₈	—	2	2	no	—
44	C₅×Q₈	—	4	1	no	—
45	C₂×C₄×C₅	—	4	1	no	—
46	C₂×C₄×C₅	C₂²⋊D₅	1	1	yes	characteristic
47	C₂×Dic₅	—	20	1	no	—
48	Dic₁₀	—	10	2	no	—
49	Dic₁₀	—	20	1	no	—
50	C₅×C₈	C₂²⋊D₅	1	1	yes	characteristic
51	C₅×C₈	C₂²×D₅	1	1	yes	characteristic
52	C₂×Q₁₆	—	25	1	no	—
53	C₂×Q₁₆	D₂₅	1	1	yes	characteristic
54	Q₃₂	—	25	4	no	—
55	C₂×C₁₆	—	25	1	no	—
56	C₂₅	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₅	#686	1	1	yes	characteristic
58	C₄×C₅	—	4	2	no	—
59	C₄×C₅	#686	1	1	yes	characteristic
60	C₄×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
61	Dic₅	—	20	2	no	—
62	C₂×Q₈	—	2	1	no	—
63	C₂×Q₈	—	50	1	no	—
64	Q₁₆	—	2	1	no	—
65	Q₁₆	—	25	2	no	—
66	Q₁₆	—	50	1	no	—
67	Q₁₆	C₂×D₂₅	1	2	yes	—
68	C₂×C₈	C₂×D₂₅	1	1	yes	characteristic
69	C₁₆	—	25	2	no	—
70	C₂×C₅	#3961	1	2	yes	—
71	C₂×C₅	C₂×#686	1	1	yes	characteristic
72	Q₈	—	2	2	no	—
73	Q₈	—	4	1	no	—
74	Q₈	—	50	2	no	—
75	Q₈	—	100	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	—	100	1	no	—
78	C₂×C₄	C₂²⋊D₂₅	1	1	yes	characteristic
79	C₈	C₂²⋊D₂₅	1	1	yes	characteristic
80	C₈	C₂²×D₂₅	1	1	yes	characteristic
81	C₅	C₂×#3961	1	1	yes	characteristic
82	C₂²	#87722	1	1	yes	characteristic
83	C₄	—	4	2	no	—
84	C₄	—	100	2	no	—
85	C₄	#87722	1	1	yes	characteristic
86	C₄	C₂×C₂²⋊D₂₅	1	1	yes	characteristic
87	C₂	#11716377	1	2	yes	direct product factor
88	C₂	C₂×#87722	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#87722
commutator, cosocle	C₈×C₂₅	C₂³
Frattini	C₅×C₈	C₂²×D₅
Fitting	C₂×Q₁₆×C₂₅	C₂
socle, prime radical	C₂²×C₅	#686
hypercenter	C₂×Q₁₆	D₂₅
hypocenter	C₂₅	C₂×Q₃₂
LCS	G ▷ C₈×C₂₅ ▷ C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
3. #11716377	C₂	direct (N × H)
41. C₂×C₂₅	Q₃₂	semidirect
56. C₂₅	C₂×Q₃₂	semidirect
87. C₂	#11716377	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×Q₁₆×C₂₅	2
C₂×Dic₁₀₀	2
#11716377	2
C₂×#87707	2
C₂×#3961	5

Subgroups — C2×#11716377 #13098455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11716377 #13098455