Subgroups — #15794125

Order 3328.

2286 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718596	C₂	1	14	yes	maximal
2	C₂×C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄²×C₁₃	C₂²	1	7	yes	—
4	C₂²×C₄⋊Dic₁₃	C₂²	1	28	yes	—
5	C₄³×C₁₃	C₄	1	8	yes	complemented
6	#11718596	—	2	56	no	—
7	C₂³×C₄×C₁₃	C₂³	1	7	yes	—
8	C₂³×Dic₁₃	C₂³	1	8	yes	—
9	C₂×C₄²×C₁₃	C₂×C₄	1	28	yes	—
10	C₂×C₄²×C₁₃	D₄	1	28	yes	—
11	C₂×C₄²×C₁₃	Q₈	1	28	yes	—
12	C₂×C₄⋊Dic₁₃	—	2	168	no	—
13	#14692	—	13	1	no	maximal, Sylow
14	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
15	C₂²×C₄×C₁₃	C₂²×C₄	1	14	yes	—
16	C₂²×C₄×C₁₃	C₂×D₄	1	42	yes	—
17	C₂²×C₄×C₁₃	C₂×Q₈	1	42	yes	—
18	C₂²×Dic₁₃	—	2	56	no	—
19	C₄²×C₁₃	C₄⋊C₄	1	112	yes	complemented
20	C₄⋊Dic₁₃	—	4	112	no	—
21	C₂×#384	—	13	14	no	—
22	C₂×C₄³	D₁₃	1	1	yes	characteristic
23	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
24	C₂³×C₁₃	C₂²×D₄	1	7	yes	—
25	C₂³×C₁₃	C₂²×Q₈	1	7	yes	—
26	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	84	yes	—
27	C₂×C₄×C₁₃	#127	1	28	yes	—
28	C₂×C₄×C₁₃	C₄⋊Q₈	1	84	yes	—
29	C₂×Dic₁₃	—	4	56	no	—
30	C₂²×C₄⋊C₄	—	13	28	no	—
31	C₂²×C₄²	C₂×D₁₃	1	7	yes	—
32	#384	—	26	56	no	—
33	C₄³	Dic₁₃	1	8	yes	complemented
34	C₂²×C₁₃	C₂²×C₄⋊C₄	1	7	yes	—
35	C₂²×C₁₃	C₂×#127	1	7	yes	—
36	C₂²×C₁₃	C₂×C₄⋊Q₈	1	21	yes	—
37	C₄×C₁₃	#384	1	56	yes	complemented
38	Dic₁₃	—	8	8	no	—
39	C₂³×C₄	—	13	8	no	—
40	C₂³×C₄	C₂²×D₁₃	1	7	yes	—
41	C₂×C₄⋊C₄	—	26	168	no	—
42	C₂×C₄²	Dic₂₆	1	28	yes	—
43	C₂×C₄²	D₅₂	1	28	yes	—
44	C₂×C₄²	C₂×Dic₁₃	1	28	yes	—
45	C₂×C₁₃	C₂×#384	1	7	yes	—
46	C₂×C₁₃	#2867	1	1	yes	characteristic
47	C₂×C₁₃	#2868	1	7	yes	—
48	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
49	C₂²×C₄	—	26	56	no	—
50	C₂²×C₄	C₂×Dic₂₆	1	42	yes	—
51	C₂²×C₄	C₂×D₅₂	1	42	yes	—
52	C₂²×C₄	C₂²×Dic₁₃	1	14	yes	—
53	C₄⋊C₄	—	52	112	no	—
54	C₄²	C₄⋊Dic₁₃	1	112	yes	complemented
55	C₁₃	#14692	1	1	yes	characteristic, complemented, Sylow
56	C₂³	C₂²×Dic₂₆	1	7	yes	—
57	C₂³	C₂²×D₅₂	1	7	yes	—
58	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
59	C₂×C₄	—	52	56	no	—
60	C₂×C₄	#88123	1	84	yes	—
61	C₂×C₄	#88128	1	28	yes	—
62	C₂×C₄	C₂×C₄⋊Dic₁₃	1	84	yes	—
63	C₂²	C₂×#88123	1	21	yes	—
64	C₂²	C₂×#88128	1	7	yes	—
65	C₂²	C₂²×C₄⋊Dic₁₃	1	7	yes	—
66	C₄	—	104	8	no	—
67	C₄	#11718596	1	56	yes	complemented
68	C₂	C₂×#11718596	1	7	yes	—
69	C₂	#13123231	1	1	yes	characteristic
70	C₂	#13123234	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₁₃
commutator	C₂³×C₁₃	C₂³×C₄
Fitting	C₂×C₄³×C₁₃	C₂
socle, prime radical, cosocle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂×C₄³	D₁₃
hypocenter	C₁₃	#14692
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
5. C₄³×C₁₃	C₄	semidirect
19. C₄²×C₁₃	C₄⋊C₄	semidirect
33. C₄³	Dic₁₃	semidirect
37. C₄×C₁₃	#384	semidirect
54. C₄²	C₄⋊Dic₁₃	semidirect
55. C₁₃	#14692	semidirect
67. C₄	#11718596	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718596	2
C₂×C₄³×C₁₃	2
#14692	13