Subgroups — #15752294

Order 3328.

582 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#88055	C₂	1	3	yes	maximal
2	C₂×#11718047	C₂	1	3	yes	maximal
3	C₂×C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
5	C₂×#88055	C₄	1	12	yes	—
6	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×#1055	C₂²	1	3	yes	—
8	C₈²×C₁₃	C₄	1	4	yes	complemented
9	#11718047	C₄	1	12	yes	complemented
10	C₂²×C₈×C₁₃	C₂×C₄	1	6	yes	—
11	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
12	C₂×C₄×Dic₁₃	C₂×C₄	1	6	yes	—
13	C₂²×#1055	C₂×C₄	1	6	yes	—
14	C₄×C₈×C₁₃	C₂×C₄	1	6	yes	—
15	C₄×C₈×C₁₃	C₂×C₄	1	6	yes	—
16	#88055	—	2	24	no	—
17	C₄×#1055	C₂×C₄	1	12	yes	—
18	#7846	—	13	1	no	maximal, Sylow
19	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
20	C₂²×Dic₁₃	C₄²	1	4	yes	—
21	C₂×C₈×C₁₃	C₄²	1	12	yes	—
22	C₂×C₈×C₁₃	M₁₆	1	24	yes	—
23	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
24	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
25	C₄×Dic₁₃	—	2	12	no	—
26	C₂×#1055	—	2	12	no	—
27	C₂×#1055	C₄²	1	12	yes	—
28	C₄×#97	—	13	3	no	—
29	C₂×#322	—	13	3	no	—
30	C₂×C₈²	D₁₃	1	1	yes	characteristic
31	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
32	C₂×C₄×C₁₃	C₂×C₄²	1	3	yes	—
33	C₂×C₄×C₁₃	C₂×C₄²	1	3	yes	—
34	C₂×C₄×C₁₃	C₂×M₁₆	1	12	yes	—
35	C₂×Dic₁₃	—	2	12	no	—
36	C₈×C₁₃	#97	1	24	yes	complemented
37	#1055	—	2	12	no	—
38	C₂×#97	—	13	12	no	—
39	C₂×C₄×C₈	—	13	3	no	—
40	C₂×C₄×C₈	C₂×D₁₃	1	3	yes	—
41	C₄³	—	13	1	no	—
42	#322	—	13	12	no	—
43	C₈²	Dic₁₃	1	4	yes	complemented
44	C₂²×C₁₃	C₄³	1	1	yes	characteristic
45	C₂²×C₁₃	C₄×M₁₆	1	6	yes	—
46	C₄×C₁₃	C₂×#97	1	6	yes	—
47	C₄×C₁₃	C₄×M₁₆	1	6	yes	—
48	Dic₁₃	—	4	4	no	—
49	C₂²×C₈	—	13	6	no	—
50	C₂²×C₈	C₄×D₁₃	1	6	yes	—
51	C₂×C₄²	—	13	6	no	—
52	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
53	#97	—	26	24	no	—
54	C₄×C₈	—	13	12	no	—
55	C₄×C₈	C₄×D₁₃	1	6	yes	—
56	C₄×C₈	C₂×Dic₁₃	1	6	yes	—
57	C₂×C₁₃	#1455	1	4	yes	—
58	C₂×C₁₃	C₄×#97	1	3	yes	—
59	C₂²×C₄	—	13	4	no	—
60	C₂²×C₄	C₂×C₄×D₁₃	1	3	yes	—
61	C₂×C₈	—	13	12	no	—
62	C₂×C₈	—	26	12	no	—
63	C₂×C₈	#6094	1	24	yes	—
64	C₂×C₈	C₄×Dic₁₃	1	12	yes	—
65	C₄²	—	26	12	no	—
66	C₄²	C₂×C₄×D₁₃	1	3	yes	—
67	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
68	C₁₃	#7846	1	1	yes	characteristic, complemented, Sylow
69	C₂³	C₄²×D₁₃	1	1	yes	characteristic
70	C₂×C₄	—	26	12	no	—
71	C₂×C₄	C₄²×D₁₃	1	3	yes	—
72	C₂×C₄	C₂×#6094	1	12	yes	—
73	C₂×C₄	C₂×C₄×Dic₁₃	1	3	yes	—
74	C₈	—	26	12	no	—
75	C₈	#88055	1	24	yes	complemented
76	C₂²	C₄×#6094	1	6	yes	—
77	C₂²	C₄²×Dic₁₃	1	1	yes	characteristic
78	C₄	—	52	4	no	—
79	C₄	C₄×#6094	1	6	yes	—
80	C₄	C₂×#88055	1	6	yes	—
81	C₂	#13113138	1	4	yes	—
82	C₂	C₄×#88055	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₃
commutator	C₂²×C₁₃	C₄³
Fitting	C₂×C₈²×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₄²
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×C₈²	D₁₃
hypocenter	C₁₃	#7846
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
8. C₈²×C₁₃	C₄	semidirect
9. #11718047	C₄	semidirect
36. C₈×C₁₃	#97	semidirect
43. C₈²	Dic₁₃	semidirect
68. C₁₃	#7846	semidirect
75. C₈	#88055	semidirect

Maximal subgroups

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

subgroup	index
C₄×#88055	2
C₂×#11718047	2
C₂×C₈²×C₁₃	2
#7846	13