Subgroups — #16809622

Order 3328.

2038 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131803	C₂	1	15	yes	maximal, complemented
2	C₂×#11719162	C₂	1	15	yes	maximal, complemented
3	#13129548	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#585	C₄	1	1	yes	characteristic
5	#11719524	C₄	1	15	yes	—
6	C₂×#88202	C₂²	1	15	yes	—
7	#11719162	C₂²	1	20	yes	complemented
8	#11719162	C₂²	1	60	yes	complemented
9	C₂×#88106	C₂²	1	45	yes	complemented
10	C₂²×#6092	C₂²	1	15	yes	complemented
11	C₁₃×2₋¹⁺⁴	C₈	1	6	yes	—
12	C₁₃×H(5,𝔽₂)	C₈	1	10	yes	—
13	C₂×C₁₃×#41	C₂×C₄	1	15	yes	—
14	#88202	C₂×C₄	1	60	yes	—
15	#88202	C₂³	1	20	yes	—
16	C₂×#6099	C₂×C₄	1	45	yes	—
17	C₂²×#1055	C₂³	1	15	yes	—
18	#88106	C₂³	1	60	yes	—
19	C₂×#6092	C₂³	1	15	yes	—
20	C₂×#6092	C₂³	1	45	yes	—
21	#62624	—	13	1	no	maximal, Sylow
22	C₁₃×#41	C₂×C₈	1	60	yes	—
23	C₁₃×#41	C₂²×C₄	1	20	yes	—
24	C₂×Q₈×C₁₃	C₂×C₈	1	15	yes	—
25	C₂×D₄×C₁₃	C₂×C₈	1	45	yes	—
26	C₂²×C₄×C₁₃	C₂²×C₄	1	15	yes	—
27	#6099	C₂²×C₄	1	60	yes	—
28	C₂×#1055	C₂²×C₄	1	45	yes	—
29	C₂×#1055	C₂⁴	1	15	yes	—
30	#6092	C₂⁴	1	1	yes	characteristic
31	#6092	C₂⁴	1	15	yes	—
32	#3573	—	13	1	no	—
33	#3407	—	13	15	no	—
34	C₂×#504	—	13	15	no	—
35	C₂³×C₁₃	C₂²×C₈	1	15	yes	—
36	Q₈×C₁₃	C₂²×C₈	1	20	yes	—
37	D₄×C₁₃	C₂²×C₈	1	60	yes	—
38	C₂×C₄×C₁₃	C₂²×C₈	1	45	yes	—
39	C₂×C₄×C₁₃	C₂³×C₄	1	15	yes	—
40	#1055	C₂³×C₄	1	15	yes	—
41	#1055	C₂⁵	1	1	yes	characteristic
42	#585	#261	1	1	yes	characteristic
43	#568	—	13	15	no	—
44	C₂×#131	—	13	15	no	—
45	#504	—	13	20	no	—
46	#504	—	13	60	no	—
47	C₂×M₃₂	—	13	45	no	—
48	C₂²×C₁₆	—	13	15	no	—
49	C₂²×C₁₃	—	4	15	no	—
50	C₂²×C₁₃	C₂³×C₈	1	15	yes	—
51	C₄×C₁₃	C₂³×C₈	1	15	yes	—
52	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
53	2₋¹⁺⁴	#1057	1	6	yes	—
54	H(5,𝔽₂)	#1057	1	10	yes	—
55	C₂×#41	C₂×#261	1	15	yes	—
56	#131	—	13	20	no	—
57	#131	—	13	60	no	—
58	C₂×M₁₆	—	13	45	no	—
59	C₂²×C₈	—	13	15	no	—
60	M₃₂	—	13	60	no	—
61	C₂×C₁₆	—	13	15	no	—
62	C₂×C₁₆	—	13	45	no	—
63	C₂×C₁₃	—	2	15	no	—
64	C₂×C₁₃	C₂⁴×C₈	1	1	yes	characteristic
65	#41	C₂×#1057	1	60	yes	—
66	#41	C₂²×#261	1	20	yes	—
67	C₂×Q₈	C₂×#1057	1	15	yes	—
68	C₂×D₄	C₂×#1057	1	45	yes	—
69	C₂²×C₄	C₂²×#261	1	15	yes	—
70	M₁₆	—	13	60	no	—
71	C₂×C₈	—	13	15	no	—
72	C₂×C₈	—	13	45	no	—
73	C₁₆	—	13	1	no	—
74	C₁₆	—	13	15	no	—
75	C₁₃	#62624	1	1	yes	characteristic, complemented, Sylow
76	C₂³	C₂²×#1057	1	15	yes	—
77	Q₈	C₂²×#1057	1	20	yes	—
78	D₄	C₂²×#1057	1	60	yes	—
79	C₂×C₄	C₂²×#1057	1	45	yes	—
80	C₂×C₄	C₂³×#261	1	15	yes	—
81	C₈	—	13	1	no	—
82	C₈	—	13	15	no	—
83	C₂²	—	4	15	no	—
84	C₂²	C₂³×#1057	1	15	yes	—
85	C₄	C₂³×#1057	1	15	yes	—
86	C₄	C₂⁴×#261	1	1	yes	characteristic
87	C₂	—	2	15	no	—
88	C₂	C₂⁴×#1057	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂⁴×#261
commutator, socle	C₂×C₁₃	C₂⁴×C₈
Fitting, prime radical	C₁₃×#585	C₄
cosocle	#1055	C₂⁵
hypercenter	#585	#261
hypocenter	C₁₃	#62624
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ #585

Complements

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

N	H ≅ G/N	type
1. #13131803	C₂	semidirect
2. C₂×#11719162	C₂	semidirect
7. #11719162	C₂²	semidirect
8. #11719162	C₂²	semidirect
9. C₂×#88106	C₂²	semidirect
10. C₂²×#6092	C₂²	semidirect
75. C₁₃	#62624	semidirect

Maximal subgroups

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

subgroup	index
#13131803	2
C₂×#11719162	2
#13129548	2
#62624	13