Subgroups — #16778215

Order 3328.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129997	C₂	1	2	yes	maximal
2	D₁₃×C₆₄	C₂	1	1	yes	maximal, characteristic
3	#11718221	—	2	2	no	—
4	D₁₃×C₃₂	C₂²	1	1	yes	characteristic
5	C₁₃×C₆₄	C₄	1	1	yes	characteristic, complemented
6	#11718035	C₄	1	1	yes	characteristic, complemented
7	#88102	—	4	2	no	—
8	C₁₆×D₁₃	D₄	1	1	yes	characteristic
9	C₁₃×C₃₂	C₂×C₄	1	1	yes	characteristic
10	#88034	Q₈	1	1	yes	characteristic
11	#7545	—	13	1	no	maximal, Sylow
12	C₄⋊#261	—	8	2	no	—
13	C₈×D₁₃	D₈	1	1	yes	characteristic
14	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
15	#6090	Q₁₆	1	1	yes	characteristic
16	C₂×C₆₄	—	13	1	no	—
17	#1423	—	13	2	no	—
18	C₂×#261	—	16	2	no	—
19	C₄×D₁₃	D₁₆	1	1	yes	characteristic
20	C₈×C₁₃	#107	1	1	yes	characteristic
21	#1055	Q₃₂	1	1	yes	characteristic
22	C₂×C₃₂	—	13	1	no	—
23	#366	—	26	2	no	—
24	C₆₄	—	13	1	no	—
25	C₆₄	#261	1	1	yes	characteristic, complemented
26	C₂×D₁₃	D₃₂	1	1	yes	characteristic
27	#261	—	32	2	no	—
28	C₄×C₁₃	#366	1	1	yes	characteristic
29	Dic₁₃	Q₆₄	1	1	yes	characteristic
30	C₂×C₁₆	—	13	1	no	—
31	#107	—	52	2	no	—
32	C₃₂	—	13	1	no	—
33	C₃₂	C₂×#261	1	1	yes	characteristic
34	C₂×C₁₃	#1423	1	1	yes	characteristic
35	D₁₃	D₆₄	1	1	yes	characteristic
36	D₁₃	Q₁₂₈	1	1	yes	characteristic
37	C₂×C₈	—	13	1	no	—
38	C₄⋊C₄	—	104	2	no	—
39	C₁₆	—	13	1	no	—
40	C₁₆	C₄⋊#261	1	1	yes	characteristic
41	C₁₃	#7545	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₄	—	13	1	no	—
43	C₂×C₄	—	208	2	no	—
44	C₈	—	13	1	no	—
45	C₈	#88102	1	1	yes	characteristic
46	C₂²	—	13	1	no	—
47	C₄	—	13	1	no	—
48	C₄	—	416	2	no	—
49	C₄	#11718221	1	1	yes	characteristic
50	C₂	—	13	1	no	—
51	C₂	—	13	1	no	—
52	C₂	#13129997	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13129997
commutator	C₁₃×C₃₂	C₂×C₄
Frattini	C₃₂	C₂×#261
Fitting	C₁₃×C₆₄	C₄
socle	C₂×C₁₃	#1423
prime radical	C₂×D₁₃	D₃₂
cosocle	D₁₃×C₃₂	C₂²
hypercenter	C₆₄	#261
hypocenter	C₁₃	#7545
LCS	G ▷ C₁₃×C₃₂ ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ C₆₄

Complements

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

N	H ≅ G/N	type
5. C₁₃×C₆₄	C₄	semidirect
6. #11718035	C₄	semidirect
25. C₆₄	#261	semidirect
41. C₁₃	#7545	semidirect

Maximal subgroups

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

subgroup	index
#13129997	2
D₁₃×C₆₄	2
#7545	13