Subgroups — D₁₃⋊M₃₂ #11719086

Order 832.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
2	#88106	C₂	1	2	yes	maximal, complemented
3	#88098	C₂	1	2	yes	maximal, complemented
4	D₁₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×D₁₃	C₄	1	1	yes	characteristic
6	C₂×C₈×C₁₃	C₄	1	1	yes	characteristic
7	C₂×#1055	C₂²	1	1	yes	characteristic
8	C₈×D₁₃	C₄	1	1	yes	characteristic
9	C₈×D₁₃	C₄	1	1	yes	characteristic
10	C₈×D₁₃	C₂²	1	1	yes	characteristic
11	C₈×D₁₃	C₂²	1	1	yes	characteristic
12	#6092	C₂²	1	4	yes	complemented
13	C₂²×D₁₃	C₈	1	1	yes	characteristic
14	C₂×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₁₃	C₈	1	1	yes	characteristic
16	C₄×D₁₃	C₈	1	1	yes	characteristic
17	C₄×D₁₃	C₈	1	1	yes	characteristic
18	C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
19	C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
20	C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	#1055	C₂×C₄	1	1	yes	characteristic
23	#1055	C₂³	1	1	yes	characteristic
24	C₂×M₃₂	—	13	1	no	maximal, Sylow
25	C₂²×C₁₃	C₂×C₈	1	1	yes	characteristic
26	C₂×D₁₃	—	2	2	no	—
27	C₂×D₁₃	C₂×C₈	1	1	yes	characteristic
28	C₂×D₁₃	C₂×C₈	1	1	yes	characteristic
29	C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
30	C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
31	Dic₁₃	C₂×C₈	1	1	yes	characteristic
32	Dic₁₃	C₂×C₈	1	1	yes	characteristic
33	C₂²×C₈	—	13	1	no	—
34	M₃₂	—	13	2	no	—
35	M₃₂	—	13	2	no	—
36	C₂×C₁₆	—	13	2	no	—
37	C₂×C₁₃	—	2	1	no	—
38	C₂×C₁₃	C₂²×C₈	1	1	yes	characteristic
39	D₁₃	—	2	1	no	—
40	D₁₃	M₃₂	1	2	yes	complemented
41	C₂²×C₄	—	13	1	no	—
42	C₂×C₈	—	13	1	no	—
43	C₂×C₈	—	13	1	no	—
44	C₂×C₈	—	13	1	no	—
45	C₂×C₈	—	13	1	no	—
46	C₂×C₈	—	13	1	no	—
47	C₂×C₈	#261	1	1	yes	characteristic
48	C₁₆	—	13	4	no	—
49	C₁₃	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
50	C₂³	—	13	1	no	—
51	C₂×C₄	—	13	1	no	—
52	C₂×C₄	—	13	1	no	—
53	C₂×C₄	—	13	1	no	—
54	C₂×C₄	—	13	1	no	—
55	C₂×C₄	—	13	1	no	—
56	C₂×C₄	C₂×#261	1	1	yes	characteristic
57	C₈	—	13	1	no	—
58	C₈	—	13	1	no	—
59	C₈	C₂×#261	1	1	yes	characteristic
60	C₈	C₂×#261	1	1	yes	characteristic
61	C₂²	—	13	1	no	—
62	C₂²	—	13	1	no	—
63	C₂²	—	26	2	no	—
64	C₂²	D₁₃⋊C₈	1	1	yes	characteristic
65	C₄	—	13	1	no	—
66	C₄	—	13	1	no	—
67	C₄	D₁₃⋊C₈	1	1	yes	characteristic
68	C₄	C₂²×#261	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	—	13	2	no	—
71	C₂	—	26	1	no	—
72	C₂	C₂×D₁₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×#261
commutator, socle	C₂×C₁₃	C₂²×C₈
Frattini	C₄	C₂²×#261
Fitting	C₂×C₈×C₁₃	C₄
prime radical	C₂²×D₁₃	C₈
cosocle	#1055	C₂³
hypercenter	C₂×C₈	#261
hypocenter	C₁₃	C₂×M₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #88106	C₂	semidirect
3. #88098	C₂	semidirect
4. D₁₃⋊C₁₆	C₂	semidirect
12. #6092	C₂²	semidirect
40. D₁₃	M₃₂	semidirect
49. C₁₃	C₂×M₃₂	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₈×D₁₃	2
#88106	2
#88098	2
D₁₃⋊C₁₆	2
C₂×M₃₂	13

Subgroups — D13⋊M32 #11719086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊M₃₂ #11719086