Subgroups — C₂×#11716376 #13098453

Order 1600.

135 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, complemented
2	C₂×D₂₀₀	C₂	1	1	yes	maximal, characteristic
3	#11716376	C₂	1	4	yes	maximal, direct product factor
4	C₂×#87707	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₂₅	—	2	1	no	—
6	C₂×D₁₀₀	—	2	1	no	—
7	Q₁₆×C₂₅	—	2	1	no	—
8	Q₁₆×C₂₅	C₂²	1	2	yes	complemented
9	C₂×C₈×C₂₅	C₂²	1	1	yes	characteristic
10	D₂₀₀	—	2	1	no	—
11	D₂₀₀	C₂²	1	2	yes	—
12	#87707	C₂²	1	2	yes	complemented
13	C₂×#3960	—	5	1	no	maximal
14	C₂²×D₂₅	—	4	1	no	—
15	Q₈×C₂₅	—	2	2	no	—
16	Q₈×C₂₅	—	4	1	no	—
17	C₂×C₄×C₂₅	—	4	1	no	—
18	C₂×C₄×C₂₅	D₄	1	1	yes	characteristic
19	D₁₀₀	—	2	2	no	—
20	D₁₀₀	—	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×D₄₀	—	5	1	no	—
25	#3960	—	5	4	no	—
26	C₂×#672	—	5	1	no	—
27	C₂²×C₂₅	D₈	1	1	yes	characteristic
28	C₂×D₂₅	—	4	2	no	—
29	C₂×D₂₅	—	8	2	no	—
30	C₄×C₂₅	—	4	2	no	—
31	C₄×C₂₅	D₈	1	1	yes	characteristic
32	C₄×C₂₅	C₂×D₄	1	1	yes	characteristic
33	C₂×C₅×Q₈	—	2	1	no	—
34	C₂×D₂₀	—	10	1	no	—
35	C₅×Q₁₆	—	2	1	no	—
36	C₅×Q₁₆	C₂×D₅	1	2	yes	—
37	C₂×C₅×C₈	C₂×D₅	1	1	yes	characteristic
38	D₄₀	—	5	2	no	—
39	D₄₀	—	10	1	no	—
40	#672	—	5	2	no	—
41	C₂×SD₃₂	—	25	1	no	Sylow
42	C₂×C₂₅	SD₃₂	1	2	yes	complemented
43	C₂×C₂₅	C₂×D₈	1	1	yes	characteristic
44	D₂₅	—	8	2	no	—
45	C₂²×D₅	—	20	1	no	—
46	C₅×Q₈	—	2	2	no	—
47	C₅×Q₈	—	4	1	no	—
48	C₂×C₄×C₅	—	4	1	no	—
49	C₂×C₄×C₅	C₂²⋊D₅	1	1	yes	characteristic
50	D₂₀	—	10	2	no	—
51	D₂₀	—	20	1	no	—
52	C₅×C₈	C₂²⋊D₅	1	1	yes	characteristic
53	C₅×C₈	C₂²×D₅	1	1	yes	characteristic
54	C₂×Q₁₆	D₂₅	1	1	yes	characteristic, complemented
55	C₂×D₈	—	25	1	no	—
56	SD₃₂	—	25	4	no	—
57	C₂×C₁₆	—	25	1	no	—
58	C₂₅	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₅	#686	1	1	yes	characteristic
60	C₂×D₅	—	20	2	no	—
61	C₂×D₅	—	40	2	no	—
62	C₄×C₅	—	4	2	no	—
63	C₄×C₅	#686	1	1	yes	characteristic
64	C₄×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
65	C₂×Q₈	—	2	1	no	—
66	C₂×D₄	—	50	1	no	—
67	Q₁₆	—	2	1	no	—
68	Q₁₆	C₂×D₂₅	1	2	yes	complemented
69	D₈	—	25	2	no	—
70	D₈	—	50	1	no	—
71	C₂×C₈	C₂×D₂₅	1	1	yes	characteristic
72	C₁₆	—	25	2	no	—
73	C₂×C₅	#3960	1	2	yes	—
74	C₂×C₅	C₂×#686	1	1	yes	characteristic
75	D₅	—	40	2	no	—
76	C₂³	—	100	1	no	—
77	Q₈	—	2	2	no	—
78	Q₈	—	4	1	no	—
79	D₄	—	50	2	no	—
80	D₄	—	100	1	no	—
81	C₂×C₄	—	4	1	no	—
82	C₂×C₄	C₂²⋊D₂₅	1	1	yes	characteristic
83	C₈	C₂²⋊D₂₅	1	1	yes	characteristic
84	C₈	C₂²×D₂₅	1	1	yes	characteristic
85	C₅	C₂×#3960	1	1	yes	characteristic
86	C₂²	—	100	2	no	—
87	C₂²	—	200	2	no	—
88	C₂²	#87722	1	1	yes	characteristic
89	C₄	—	4	2	no	—
90	C₄	#87722	1	1	yes	characteristic
91	C₄	C₂×C₂²⋊D₂₅	1	1	yes	characteristic
92	C₂	—	200	2	no	—
93	C₂	#11716376	1	2	yes	direct product factor
94	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	C₂²×C₅	#686
prime radical	C₂×D₂₀₀	C₂
hypercenter	C₂×Q₁₆	D₂₅
hypocenter	C₂₅	C₂×SD₃₂
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
1. C₂×Q₁₆×C₂₅	C₂	semidirect
3. #11716376	C₂	direct (N × H)
4. C₂×#87707	C₂	semidirect
8. Q₁₆×C₂₅	C₂²	semidirect
12. #87707	C₂²	semidirect
42. C₂×C₂₅	SD₃₂	semidirect
54. C₂×Q₁₆	D₂₅	semidirect
58. C₂₅	C₂×SD₃₂	semidirect
68. Q₁₆	C₂×D₂₅	semidirect
93. C₂	#11716376	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×D₂₀₀	2
#11716376	2
C₂×#87707	2
C₂×#3960	5

Subgroups — C2×#11716376 #13098453

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11716376 #13098453