Subgroups — #15783974

Order 3328.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13117146	C₂	1	2	yes	maximal, complemented
2	#13113050	C₂	1	2	yes	maximal, complemented
3	D₈₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#11718580	—	2	2	no	—
7	C₁₃×Q₆₄	C₂²	1	2	yes	—
8	#11718113	—	2	2	no	—
9	D₄₁₆	C₂²	1	2	yes	—
10	D₁₃×C₃₂	C₂²	1	1	yes	characteristic
11	C₁₃×C₆₄	C₂²	1	1	yes	characteristic
12	#11718035	C₂²	1	1	yes	characteristic
13	#88173	—	4	2	no	—
14	C₁₃×Q₃₂	—	2	2	no	—
15	#88068	—	4	2	no	—
16	D₂₀₈	—	2	2	no	—
17	C₁₆×D₁₃	D₄	1	1	yes	characteristic
18	C₁₃×C₃₂	C₂³	1	1	yes	characteristic
19	#88034	D₄	1	1	yes	characteristic
20	#13741	—	13	1	no	maximal, Sylow
21	#6131	—	8	2	no	—
22	C₁₃×Q₁₆	—	4	2	no	—
23	#6106	—	8	2	no	—
24	D₁₀₄	—	4	2	no	—
25	C₈×D₁₃	D₈	1	1	yes	characteristic
26	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
27	#6090	D₈	1	1	yes	characteristic
28	#2262	—	13	2	no	—
29	Q₁₂₈	D₁₃	1	1	yes	characteristic, complemented
30	SD₁₂₈	—	13	2	no	—
31	D₆₄	—	13	1	no	—
32	C₂×C₆₄	—	13	1	no	—
33	Q₈×C₁₃	—	8	2	no	—
34	D₅₂	—	8	2	no	—
35	D₅₂	—	16	2	no	—
36	C₄×D₁₃	—	16	2	no	—
37	C₄×D₁₃	D₁₆	1	1	yes	characteristic
38	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
39	#1055	D₁₆	1	1	yes	characteristic
40	#508	—	26	2	no	—
41	Q₆₄	C₂×D₁₃	1	2	yes	—
42	SD₆₄	—	26	2	no	—
43	D₃₂	—	13	2	no	—
44	C₂×C₃₂	—	13	1	no	—
45	C₆₄	—	13	1	no	—
46	C₆₄	C₂×D₁₃	1	1	yes	characteristic
47	C₂×D₁₃	—	16	2	no	—
48	C₂×D₁₃	D₃₂	1	1	yes	characteristic
49	C₄×C₁₃	—	16	2	no	—
50	C₄×C₁₃	C₂×D₁₆	1	1	yes	characteristic
51	Dic₁₃	D₃₂	1	1	yes	characteristic
52	#135	—	52	2	no	—
53	Q₃₂	—	2	2	no	—
54	SD₃₂	—	52	2	no	—
55	D₁₆	—	26	2	no	—
56	C₂×C₁₆	—	13	1	no	—
57	C₃₂	—	13	1	no	—
58	C₃₂	C₂²×D₁₃	1	1	yes	characteristic
59	C₂×C₁₃	C₂×D₃₂	1	1	yes	characteristic
60	D₁₃	—	2	1	no	—
61	D₁₃	—	32	2	no	—
62	#41	—	104	2	no	—
63	Q₁₆	—	4	2	no	—
64	SD₁₆	—	104	2	no	—
65	D₈	—	52	2	no	—
66	C₂×C₈	—	13	1	no	—
67	C₁₆	—	13	1	no	—
68	C₁₆	D₄×D₁₃	1	1	yes	characteristic
69	C₁₃	#13741	1	1	yes	characteristic, complemented, Sylow
70	Q₈	—	8	2	no	—
71	D₄	—	104	2	no	—
72	D₄	—	208	2	no	—
73	C₂×C₄	—	13	1	no	—
74	C₂×C₄	—	208	2	no	—
75	C₈	—	13	1	no	—
76	C₈	D₈×D₁₃	1	1	yes	characteristic
77	C₂²	—	13	1	no	—
78	C₂²	—	208	2	no	—
79	C₄	—	13	1	no	—
80	C₄	—	16	2	no	—
81	C₄	D₁₃×D₁₆	1	1	yes	characteristic
82	C₂	—	26	1	no	—
83	C₂	—	416	2	no	—
84	C₂	D₁₃×D₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₃×D₃₂
commutator, cosocle	C₁₃×C₃₂	C₂³
Frattini	C₃₂	C₂²×D₁₃
Fitting	C₁₃×Q₁₂₈	C₂
socle	C₂×C₁₃	C₂×D₃₂
hypercenter	Q₁₂₈	D₁₃
hypocenter	C₁₃	#13741
LCS	G ▷ C₁₃×C₃₂ ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ Q₁₂₈

Complements

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

N	H ≅ G/N	type
1. #13117146	C₂	semidirect
2. #13113050	C₂	semidirect
3. D₈₃₂	C₂	semidirect
4. D₁₃×C₆₄	C₂	semidirect
5. C₁₃×Q₁₂₈	C₂	semidirect
29. Q₁₂₈	D₁₃	semidirect
69. C₁₃	#13741	semidirect

Maximal subgroups

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

subgroup	index
#13117146	2
#13113050	2
D₈₃₂	2
D₁₃×C₆₄	2
C₁₃×Q₁₂₈	2
#13741	13