Subgroups — #13114967

Order 1664.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	#11718597	C₂	1	2	yes	maximal
3	#11718143	C₂	1	4	yes	maximal
4	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
5	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₄⋊Dic₁₃	C₂²	1	4	yes	—
7	C₄×C₈×C₁₃	C₄	1	4	yes	complemented
8	#88071	—	2	4	no	—
9	C₂²×C₄×C₁₃	D₄	1	2	yes	—
10	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
11	C₂²×Dic₁₃	—	2	4	no	—
12	C₂×C₈×C₁₃	—	2	4	no	—
13	C₂×C₈×C₁₃	C₂×C₄	1	4	yes	—
14	C₄²×C₁₃	C₂×C₄	1	2	yes	—
15	C₄²×C₁₃	Q₈	1	2	yes	—
16	C₄⋊Dic₁₃	—	2	8	no	—
17	#1835	—	13	1	no	maximal, Sylow
18	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₃	—	2	4	no	—
20	C₂×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
21	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
22	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
23	C₂×C₄×C₁₃	#41	1	4	yes	—
24	C₂×Dic₁₃	—	4	4	no	—
25	C₂×Dic₁₃	—	4	8	no	—
26	C₈×C₁₃	—	2	4	no	—
27	C₂×C₄×C₈	D₁₃	1	1	yes	characteristic
28	#382	—	13	2	no	—
29	#340	—	13	4	no	—
30	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₁₃	#124	1	2	yes	—
32	C₂²×C₁₃	#135	1	4	yes	—
33	C₄×C₁₃	—	2	4	no	—
34	C₄×C₁₃	#117	1	2	yes	—
35	C₄×C₁₃	#125	1	2	yes	—
36	Dic₁₃	—	8	4	no	—
37	C₂²×C₈	C₂×D₁₃	1	2	yes	—
38	C₂×C₄⋊C₄	—	13	4	no	—
39	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
40	C₄×C₈	Dic₁₃	1	4	yes	complemented
41	#95	—	26	4	no	—
42	C₂×C₁₃	#382	1	1	yes	characteristic
43	C₂×C₁₃	#427	1	2	yes	—
44	C₂×C₁₃	#488	1	4	yes	—
45	C₂²×C₄	—	26	4	no	—
46	C₂²×C₄	D₅₂	1	2	yes	—
47	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
48	C₂×C₈	—	2	4	no	—
49	C₂×C₈	C₂×Dic₁₃	1	4	yes	—
50	C₄⋊C₄	—	26	8	no	—
51	C₄²	Dic₂₆	1	2	yes	—
52	C₄²	C₂×Dic₁₃	1	2	yes	—
53	C₁₃	#1835	1	1	yes	characteristic, complemented, Sylow
54	C₂³	C₂×D₅₂	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	52	4	no	—
57	C₂×C₄	—	52	8	no	—
58	C₂×C₄	C₄⋊Dic₁₃	1	4	yes	—
59	C₂×C₄	C₂×Dic₂₆	1	1	yes	characteristic
60	C₂×C₄	#6127	1	4	yes	—
61	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
62	C₈	—	2	4	no	—
63	C₂²	#88129	1	2	yes	—
64	C₂²	#88158	1	4	yes	—
65	C₂²	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
66	C₄	—	2	4	no	—
67	C₄	—	104	4	no	—
68	C₄	#88124	1	2	yes	—
69	C₄	#88180	1	2	yes	—
70	C₂	#11718358	1	4	yes	—
71	C₂	#11718597	1	1	yes	characteristic
72	C₂	#11718767	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₂×C₄×C₈×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₄
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	C₂×C₄×C₈	D₁₃
hypocenter	C₁₃	#1835
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
7. C₄×C₈×C₁₃	C₄	semidirect
40. C₄×C₈	Dic₁₃	semidirect
53. C₁₃	#1835	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₈×C₁₃	2
#11718597	2
#11718143	2
#1835	13