Subgroups — #13129976

Order 1664.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718728	C₂	1	1	yes	maximal, characteristic
2	#11718225	C₂	1	2	yes	maximal
3	C₁₃×#125	C₄	1	1	yes	characteristic, complemented
4	#88128	C₂²	1	1	yes	characteristic
5	#88107	—	2	2	no	—
6	#88049	—	2	2	no	—
7	#88043	C₄	1	1	yes	characteristic, complemented
8	C₂×D₅₂	—	4	1	no	—
9	C₂×D₅₂	D₄	1	2	yes	—
10	C₂²⋊#261	—	4	2	no	—
11	C₁₃×C₄⋊C₄	—	2	1	no	—
12	C₁₃×C₄⋊C₄	—	4	1	no	—
13	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×#1055	—	2	1	no	—
15	#1412	—	13	1	no	maximal, Sylow
16	C₂²×D₁₃	—	2	2	no	—
17	C₂×#261	—	8	2	no	—
18	C₂×C₄×C₁₃	—	2	1	no	—
19	C₂×C₄×C₁₃	—	4	1	no	—
20	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
21	D₅₂	—	4	2	no	—
22	D₅₂	—	8	2	no	—
23	#1055	—	4	1	no	—
24	#490	—	13	1	no	—
25	#353	—	13	2	no	—
26	C₂²×C₁₃	#99	1	1	yes	characteristic
27	C₂×D₁₃	—	4	2	no	—
28	C₂×D₁₃	—	8	2	no	—
29	#261	—	16	2	no	—
30	C₄×C₁₃	—	2	1	no	—
31	C₄×C₁₃	—	4	1	no	—
32	C₄×C₁₃	—	8	1	no	—
33	#127	—	13	1	no	—
34	#125	#261	1	1	yes	characteristic, complemented
35	#102	—	26	2	no	—
36	#99	—	26	2	no	—
37	#97	—	13	1	no	—
38	C₂×C₁₃	—	2	1	no	—
39	C₂×C₁₃	#354	1	1	yes	characteristic
40	D₁₃	—	8	2	no	—
41	C₂×D₄	—	13	2	no	—
42	C₂×D₄	—	52	1	no	—
43	C₂×C₈	—	26	1	no	—
44	C₄⋊C₄	—	2	1	no	—
45	C₄⋊C₄	—	4	1	no	—
46	C₂²⋊C₄	—	52	2	no	—
47	C₄²	C₂×#261	1	1	yes	characteristic
48	C₁₃	#1412	1	1	yes	characteristic, complemented, Sylow
49	C₂³	—	26	2	no	—
50	D₄	—	52	2	no	—
51	D₄	—	104	2	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	—	104	2	no	—
55	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
56	C₈	—	52	1	no	—
57	C₂²	—	52	2	no	—
58	C₂²	—	104	2	no	—
59	C₂²	#88119	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	—	4	1	no	—
62	C₄	—	8	1	no	—
63	C₄	—	208	2	no	—
64	C₂	—	2	1	no	—
65	C₂	—	104	2	no	—
66	C₂	#11718300	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718300
commutator	C₄²×C₁₃	C₂×C₄
Frattini	C₄²	C₂×#261
Fitting	C₁₃×#125	C₄
socle	C₂×C₁₃	#354
prime radical, cosocle	#88128	C₂²
hypercenter	#125	#261
hypocenter	C₁₃	#1412
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
3. C₁₃×#125	C₄	semidirect
7. #88043	C₄	semidirect
34. #125	#261	semidirect
48. C₁₃	#1412	semidirect

Maximal subgroups

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

subgroup	index
#11718728	2
#11718225	2
#1412	13