Subgroups — #13129982

Order 1664.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718729	C₂	1	1	yes	maximal, characteristic
2	#11718228	C₂	1	1	yes	maximal, characteristic
3	#11718226	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#125	C₄	1	1	yes	characteristic, complemented
5	#88129	C₂²	1	1	yes	characteristic
6	#88113	—	2	1	no	—
7	#88107	—	2	1	no	—
8	#88050	—	2	1	no	—
9	#88049	—	2	1	no	—
10	C₄×#1055	C₄	1	1	yes	characteristic, complemented
11	C₂×D₅₂	D₄	1	1	yes	characteristic
12	C₂×Dic₂₆	D₄	1	1	yes	characteristic
13	C₂²⋊#261	—	4	1	no	—
14	#6122	—	4	1	no	—
15	C₁₃×C₄⋊C₄	—	2	1	no	—
16	C₁₃×C₄⋊C₄	—	4	1	no	—
17	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	#6103	—	4	1	no	—
19	C₂×#1055	—	2	1	no	—
20	#1414	—	13	1	no	maximal, Sylow
21	C₂²×D₁₃	—	2	1	no	—
22	C₂×#261	—	8	1	no	—
23	C₂×C₄×C₁₃	—	2	1	no	—
24	C₂×C₄×C₁₃	—	4	1	no	—
25	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×Dic₁₃	—	2	1	no	—
27	D₅₂	—	4	1	no	—
28	Dic₂₆	—	4	1	no	—
29	#1057	—	8	1	no	—
30	#1055	—	4	1	no	—
31	#488	—	13	1	no	—
32	#355	—	13	1	no	—
33	#354	—	13	1	no	—
34	C₂²×C₁₃	#99	1	1	yes	characteristic
35	C₂×D₁₃	—	4	1	no	—
36	C₂×D₁₃	—	8	1	no	—
37	#261	—	16	1	no	—
38	C₄×C₁₃	—	2	1	no	—
39	C₄×C₁₃	—	4	1	no	—
40	C₄×C₁₃	—	8	1	no	—
41	Dic₁₃	—	4	1	no	—
42	#125	#261	1	1	yes	characteristic, complemented
43	#124	—	13	1	no	—
44	#103	—	26	1	no	—
45	#102	—	26	1	no	—
46	#101	—	26	1	no	—
47	#99	—	26	1	no	—
48	C₄×C₈	—	13	1	no	—
49	C₂×C₁₃	—	2	1	no	—
50	C₂×C₁₃	#354	1	1	yes	characteristic
51	D₁₃	—	8	1	no	—
52	C₂×Q₈	—	13	1	no	—
53	C₂×D₄	—	13	1	no	—
54	M₁₆	—	52	1	no	—
55	C₂×C₈	—	26	1	no	—
56	C₄⋊C₄	—	2	1	no	—
57	C₄⋊C₄	—	4	1	no	—
58	C₂²⋊C₄	—	52	1	no	—
59	C₂²⋊C₄	—	52	1	no	—
60	C₄²	C₂×#261	1	1	yes	characteristic
61	C₁₃	#1414	1	1	yes	characteristic, complemented, Sylow
62	C₂³	—	26	1	no	—
63	Q₈	—	52	1	no	—
64	D₄	—	52	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	4	1	no	—
67	C₂×C₄	—	26	1	no	—
68	C₂×C₄	—	104	1	no	—
69	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
70	C₈	—	52	1	no	—
71	C₈	—	104	1	no	—
72	C₂²	—	52	1	no	—
73	C₂²	—	104	1	no	—
74	C₂²	#88119	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	8	1	no	—
78	C₄	—	52	1	no	—
79	C₄	—	208	1	no	—
80	C₂	—	2	1	no	—
81	C₂	—	104	1	no	—
82	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	C₂×D₅₂	D₄
cosocle	#88129	C₂²
hypercenter	#125	#261
hypocenter	C₁₃	#1414
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
4. C₁₃×#125	C₄	semidirect
10. C₄×#1055	C₄	semidirect
42. #125	#261	semidirect
61. C₁₃	#1414	semidirect

Maximal subgroups

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

subgroup	index
#11718729	2
#11718228	2
#11718226	2
#1414	13