Subgroups — D₃₁₃⋊M₁₆ #23756582

Order 10016.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097571	C₂	1	2	yes	maximal, complemented
2	#19097570	C₂	1	2	yes	maximal, complemented
3	#19097569	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₃₁₃	C₂	1	1	yes	maximal, characteristic
5	#14578816	C₂²	1	4	yes	complemented
6	C₂²×D₃₁₃	C₄	1	1	yes	characteristic
7	C₂×Dic₃₁₃	C₂²	1	1	yes	characteristic
8	C₄×D₃₁₃	C₄	1	1	yes	characteristic
9	C₄×D₃₁₃	C₄	1	1	yes	characteristic
10	C₄×D₃₁₃	C₂²	1	1	yes	characteristic
11	C₄×D₃₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₃₁₃	C₄	1	1	yes	characteristic
13	C₂²×C₃₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×D₃₁₃	—	2	2	no	—
15	C₂×D₃₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×D₃₁₃	C₂×C₄	1	1	yes	characteristic
17	C₄×C₃₁₃	C₂×C₄	1	1	yes	characteristic
18	C₄×C₃₁₃	C₂×C₄	1	1	yes	characteristic
19	Dic₃₁₃	C₂×C₄	1	1	yes	characteristic
20	Dic₃₁₃	C₂³	1	1	yes	characteristic
21	C₂×C₃₁₃	—	2	1	no	—
22	C₂×C₃₁₃	C₂²×C₄	1	1	yes	characteristic
23	D₃₁₃	—	2	1	no	—
24	D₃₁₃	M₁₆	1	2	yes	complemented
25	C₃₁₃	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	313	1	no	maximal, Sylow
27	C₂²×C₄	—	313	1	no	—
28	M₁₆	—	313	2	no	—
29	M₁₆	—	313	2	no	—
30	C₂×C₈	—	313	2	no	—
31	C₂³	—	313	1	no	—
32	C₂×C₄	—	313	1	no	—
33	C₂×C₄	—	313	1	no	—
34	C₂×C₄	—	313	1	no	—
35	C₂×C₄	—	313	1	no	—
36	C₂×C₄	—	313	1	no	—
37	C₂×C₄	#11929411	1	1	yes	characteristic
38	C₈	—	313	4	no	—
39	C₂²	—	313	1	no	—
40	C₂²	—	313	1	no	—
41	C₂²	—	626	2	no	—
42	C₂²	C₂×#11929411	1	1	yes	characteristic
43	C₄	—	313	1	no	—
44	C₄	—	313	1	no	—
45	C₄	C₂×#11929411	1	1	yes	characteristic
46	C₄	C₂×#11929411	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	313	2	no	—
49	C₂	—	626	1	no	—
50	C₂	C₂²×#11929411	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#11929411
commutator, socle	C₂×C₃₁₃	C₂²×C₄
Frattini	C₂	C₂²×#11929411
Fitting	C₂×C₄×C₃₁₃	C₄
prime radical	C₂²×D₃₁₃	C₄
cosocle	Dic₃₁₃	C₂³
hypercenter	C₂×C₄	#11929411
hypocenter	C₃₁₃	C₂×M₁₆
LCS	G ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #19097571	C₂	semidirect
2. #19097570	C₂	semidirect
3. #19097569	C₂	semidirect
5. #14578816	C₂²	semidirect
24. D₃₁₃	M₁₆	semidirect
25. C₃₁₃	C₂×M₁₆	semidirect

Subgroups — D313⋊M16 #23756582

Conjugacy classes of subgroups

Complements

Subgroups — D₃₁₃⋊M₁₆ #23756582