Subgroups — #13123225

Order 1664.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#11718601	C₂	1	7	yes	maximal
3	#11718594	C₂	1	7	yes	maximal, complemented
4	C₂×C₄²×C₁₃	C₂²	1	7	yes	—
5	C₂×#6103	C₂²	1	7	yes	—
6	C₂×#6101	C₂²	1	7	yes	—
7	#88071	C₂²	1	14	yes	—
8	C₂³×D₁₃	C₂³	1	1	yes	characteristic
9	C₂²×C₄×C₁₃	C₂³	1	7	yes	—
10	C₂²×Dic₁₃	C₂³	1	7	yes	—
11	C₄²×C₁₃	—	2	14	no	—
12	#6103	—	2	14	no	—
13	#6101	—	2	14	no	—
14	#2865	—	13	1	no	maximal, Sylow
15	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
16	C₂²×D₁₃	—	2	7	no	—
17	C₂×C₄×C₁₃	—	2	14	no	—
18	C₂×C₄×C₁₃	#41	1	14	yes	—
19	C₂×Dic₁₃	—	2	14	no	—
20	C₂×Dic₁₃	—	2	7	no	—
21	#388	—	13	7	no	—
22	#387	—	13	7	no	—
23	C₄³	D₁₃	1	1	yes	characteristic, complemented
24	C₂²×C₁₃	C₂×#41	1	7	yes	—
25	C₂×D₁₃	—	4	7	no	—
26	C₄×C₁₃	—	2	14	no	—
27	Dic₁₃	—	4	7	no	—
28	C₂×C₄⋊C₄	—	13	7	no	—
29	C₂×C₂²⋊C₄	—	13	7	no	—
30	C₂×C₄²	C₂×D₁₃	1	7	yes	—
31	#95	—	13	14	no	—
32	C₂×C₁₃	#529	1	7	yes	—
33	D₁₃	—	8	1	no	—
34	C₂⁴	—	13	1	no	—
35	C₂²×C₄	—	13	7	no	—
36	C₂²×C₄	C₂²×D₁₃	1	7	yes	—
37	C₄⋊C₄	—	26	14	no	—
38	C₂²⋊C₄	—	26	14	no	—
39	C₄²	—	2	14	no	—
40	C₁₃	#2865	1	1	yes	characteristic, complemented, Sylow
41	C₂³	—	26	7	no	—
42	C₂³	C₂³×D₁₃	1	1	yes	characteristic
43	C₂×C₄	—	2	14	no	—
44	C₂×C₄	—	26	7	no	—
45	C₂×C₄	—	26	14	no	—
46	C₂×C₄	#6127	1	14	yes	—
47	C₂²	—	52	7	no	—
48	C₂²	C₂×#6127	1	7	yes	—
49	C₄	—	2	14	no	—
50	C₄	—	52	7	no	—
51	C₂	—	104	1	no	—
52	C₂	#11719184	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₄³×C₁₃	C₂
prime radical	C₂³×D₁₃	C₂³
hypercenter	C₄³	D₁₃
hypocenter	C₁₃	#2865
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
1. C₄³×C₁₃	C₂	semidirect
3. #11718594	C₂	semidirect
23. C₄³	D₁₃	semidirect
40. C₁₃	#2865	semidirect

Maximal subgroups

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

subgroup	index
C₄³×C₁₃	2
#11718601	2
#11718594	2
#2865	13