Subgroups — #15893908

Order 3328.

604 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊#2104	C₂	1	7	yes	maximal
2	#13114567	C₂	1	7	yes	maximal
3	C₁₃×#2104	C₂	1	1	yes	maximal, characteristic
4	C₂×#88131	C₂²	1	7	yes	—
5	C₁₃×#342	C₂²	1	7	yes	—
6	#11718119	C₂²	1	14	yes	—
7	#11718118	C₂²	1	7	yes	—
8	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
9	C₂×C₁₃×C₂²⋊C₄	C₂³	1	7	yes	—
10	C₂×C₂²⋊Dic₁₃	C₂³	1	7	yes	—
11	C₂×#6101	—	2	7	no	—
12	C₂×C₄×Dic₁₃	—	2	7	no	—
13	#88131	—	2	14	no	—
14	#88131	—	2	14	no	—
15	#23847	—	13	1	no	maximal, Sylow
16	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
17	C₂²×C₄×C₁₃	—	2	7	no	—
18	C₂²×Dic₁₃	—	2	7	no	—
19	C₂²×Dic₁₃	#41	1	7	yes	—
20	C₂²×Dic₁₃	#41	1	7	yes	—
21	C₁₃×C₂²⋊C₄	—	2	14	no	—
22	C₂²⋊Dic₁₃	—	2	14	no	—
23	#6101	—	4	14	no	—
24	C₄×Dic₁₃	—	4	7	no	—
25	C₄×Dic₁₃	—	4	7	no	—
26	#2104	—	13	7	no	—
27	#2104	D₁₃	1	1	yes	characteristic
28	#1740	—	13	7	no	—
29	C₂³×C₁₃	—	8	1	no	—
30	C₂³×C₁₃	C₂×#41	1	7	yes	—
31	C₂×C₄×C₁₃	—	4	7	no	—
32	C₂×C₄×C₁₃	—	8	7	no	—
33	C₂×Dic₁₃	—	4	7	no	—
34	C₂×Dic₁₃	—	8	7	no	—
35	C₂×Dic₁₃	#126	1	7	yes	—
36	C₂×Dic₁₃	#126	1	7	yes	—
37	C₂×Dic₁₃	#126	1	14	yes	—
38	C₂×#117	—	13	7	no	—
39	#342	—	13	7	no	—
40	#342	—	13	14	no	—
41	#342	C₂×D₁₃	1	7	yes	—
42	C₂²×C₁₃	—	4	7	no	—
43	C₂²×C₁₃	C₂×#126	1	7	yes	—
44	C₄×C₁₃	—	8	7	no	—
45	Dic₁₃	—	8	7	no	—
46	Dic₁₃	#401	1	1	yes	characteristic
47	Dic₁₃	#401	1	7	yes	—
48	C₂³×C₄	—	13	1	no	—
49	#117	—	26	14	no	—
50	#117	—	26	14	no	—
51	C₂×C₄⋊C₄	—	26	7	no	—
52	C₂×C₂²⋊C₄	—	13	7	no	—
53	C₂×C₂²⋊C₄	C₂²×D₁₃	1	7	yes	—
54	C₂×C₄²	—	26	7	no	—
55	C₂×C₁₃	—	2	7	no	—
56	C₂×C₁₃	C₂×#401	1	1	yes	characteristic
57	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
58	C₂²×C₄	—	2	7	no	—
59	C₂²×C₄	—	13	7	no	—
60	C₂²×C₄	—	13	7	no	—
61	C₂²×C₄	—	26	7	no	—
62	C₄⋊C₄	—	52	14	no	—
63	C₂²⋊C₄	—	2	14	no	—
64	C₂²⋊C₄	—	26	14	no	—
65	C₄²	—	52	7	no	—
66	C₄²	—	52	7	no	—
67	C₁₃	#23847	1	1	yes	characteristic, complemented, Sylow
68	C₂³	—	8	1	no	—
69	C₂³	#41×D₁₃	1	7	yes	—
70	C₂×C₄	—	4	7	no	—
71	C₂×C₄	—	8	7	no	—
72	C₂×C₄	—	13	7	no	—
73	C₂×C₄	—	13	7	no	—
74	C₂×C₄	—	13	14	no	—
75	C₂×C₄	—	52	7	no	—
76	C₂×C₄	—	104	7	no	—
77	C₂²	—	4	7	no	—
78	C₂²	D₁₃×#126	1	7	yes	—
79	C₄	—	8	7	no	—
80	C₄	—	13	1	no	—
81	C₄	—	13	7	no	—
82	C₄	—	104	7	no	—
83	C₂	—	2	7	no	—
84	C₂	D₁₃×#401	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₃×#401
commutator, prime radical, cosocle	C₂⁴×C₁₃	C₂⁴
Frattini	C₂⁴	C₂³×D₁₃
Fitting	C₁₃×#2104	C₂
socle	C₂×C₁₃	C₂×#401
hypercenter	#2104	D₁₃
hypocenter	C₁₃	#23847
LCS	G ▷ C₂⁴×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ #2104

Complements

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

N	H ≅ G/N	type
67. C₁₃	#23847	semidirect

Maximal subgroups

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

subgroup	index
C₁₃⋊#2104	2
#13114567	2
C₁₃×#2104	2
#23847	13