Subgroups — #15860399

Order 3328.

1054 conjugacy classes of subgroups.

The subgroup lattice has 160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6099	C₂	1	2	yes	maximal
2	#13114588	C₂	1	8	yes	maximal, complemented
3	#13114530	C₂	1	4	yes	maximal
4	C₂×C₁₃×#376	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#6099	C₂²	1	4	yes	—
8	C₁₃×#376	C₄	1	4	yes	—
9	C₁₃×#376	C₂²	1	4	yes	—
10	C₂×C₁₃×#95	C₄	1	4	yes	—
11	C₄×#6099	C₄	1	16	yes	complemented
12	C₂×#88043	C₂²	1	4	yes	—
13	C₂×C₄×#1055	C₂²	1	4	yes	—
14	#11718116	C₂²	1	16	yes	—
15	C₂³×C₄×C₁₃	C₂×C₄	1	4	yes	—
16	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
17	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	—	2	8	no	—
19	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	—
20	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
23	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
24	C₂×#6099	—	2	16	no	—
25	C₂×#6099	C₂×C₄	1	16	yes	—
26	C₂²×#1055	C₂³	1	8	yes	—
27	C₁₃×#95	C₂×C₄	1	16	yes	—
28	#88043	C₂×C₄	1	16	yes	complemented
29	C₄×#1055	C₂×C₄	1	16	yes	complemented
30	#20365	—	13	1	no	maximal, Sylow
31	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₃	—	2	8	no	—
33	C₂²×C₄×C₁₃	—	4	4	no	—
34	C₂²×C₄×C₁₃	—	4	8	no	—
35	C₂²×C₄×C₁₃	C₄²	1	8	yes	—
36	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
37	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
38	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
39	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	#41	1	8	yes	—
41	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
42	C₄²×C₁₃	—	2	8	no	—
43	C₄²×C₁₃	—	2	8	no	—
44	C₄²×C₁₃	C₄²	1	8	yes	—
45	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
46	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
47	#6099	—	2	32	no	—
48	C₂×#1055	—	2	16	no	—
49	C₂×#1055	C₂²×C₄	1	16	yes	—
50	C₂×C₄×M₁₆	—	13	2	no	—
51	C₂×#376	D₁₃	1	1	yes	characteristic
52	#1746	—	13	8	no	—
53	#1728	—	13	4	no	—
54	C₂³×C₁₃	—	2	4	no	—
55	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
56	C₂³×C₁₃	#117	1	4	yes	—
57	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₃	—	2	8	no	—
59	C₂×C₄×C₁₃	—	2	8	no	—
60	C₂×C₄×C₁₃	—	2	16	no	—
61	C₂×C₄×C₁₃	—	4	8	no	—
62	C₂×C₄×C₁₃	—	4	16	no	—
63	C₂×C₄×C₁₃	C₂×C₄²	1	8	yes	—
64	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
65	C₂×C₄×C₁₃	#117	1	16	yes	—
66	C₂×C₄×C₁₃	#117	1	4	yes	—
67	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
68	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
69	#1055	—	2	16	no	—
70	C₂²×M₁₆	—	13	4	no	—
71	C₂²×C₄²	C₂×D₁₃	1	2	yes	—
72	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
73	C₄×M₁₆	—	13	16	no	—
74	C₂×#97	—	13	4	no	—
75	C₂×C₄×C₈	—	13	4	no	—
76	#376	Dic₁₃	1	4	yes	—
77	#376	C₂×D₁₃	1	4	yes	—
78	C₂×#95	Dic₁₃	1	4	yes	—
79	#336	—	13	16	no	—
80	C₂²×C₁₃	—	2	4	no	—
81	C₂²×C₁₃	—	2	8	no	—
82	C₂²×C₁₃	#376	1	4	yes	—
83	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
84	C₂²×C₁₃	C₂×#117	1	2	yes	—
85	C₂²×C₁₃	#568	1	4	yes	—
86	C₄×C₁₃	—	2	8	no	—
87	C₄×C₁₃	—	4	8	no	—
88	C₄×C₁₃	#376	1	4	yes	—
89	C₄×C₁₃	C₂×#117	1	4	yes	—
90	C₂³×C₄	C₂×Dic₁₃	1	4	yes	—
91	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
92	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
93	C₂×M₁₆	—	13	16	no	—
94	C₂×M₁₆	—	26	16	no	—
95	C₂²×C₈	—	13	8	no	—
96	C₂×C₄²	—	2	8	no	—
97	C₂×C₄²	C₄×D₁₃	1	8	yes	—
98	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
99	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
100	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
101	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
102	#97	—	13	16	no	—
103	C₄×C₈	—	13	16	no	—
104	#95	C₂×Dic₁₃	1	16	yes	—
105	C₂×C₁₃	—	2	4	no	—
106	C₂×C₁₃	C₂×#376	1	1	yes	characteristic
107	C₂×C₁₃	#2873	1	2	yes	—
108	C₂×C₁₃	#2921	1	4	yes	—
109	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
110	C₂²×C₄	—	2	8	no	—
111	C₂²×C₄	—	4	4	no	—
112	C₂²×C₄	—	4	8	no	—
113	C₂²×C₄	C₄×Dic₁₃	1	8	yes	—
114	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
115	C₂²×C₄	#6127	1	8	yes	—
116	C₂²×C₄	C₂²×Dic₁₃	1	8	yes	—
117	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
118	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
119	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
120	M₁₆	—	26	32	no	—
121	C₂×C₈	—	13	16	no	—
122	C₂×C₈	—	26	16	no	—
123	C₄²	—	2	8	no	—
124	C₄²	—	2	8	no	—
125	C₄²	C₄×Dic₁₃	1	8	yes	—
126	C₄²	C₂×C₄×D₁₃	1	4	yes	—
127	C₄²	C₂×C₄×D₁₃	1	4	yes	—
128	C₁₃	#20365	1	1	yes	characteristic, complemented, Sylow
129	C₂³	—	2	4	no	—
130	C₂³	C₂×C₄×Dic₁₃	1	2	yes	—
131	C₂³	#88180	1	4	yes	—
132	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
133	C₂×C₄	—	2	8	no	—
134	C₂×C₄	—	2	8	no	—
135	C₂×C₄	—	2	16	no	—
136	C₂×C₄	—	4	8	no	—
137	C₂×C₄	—	4	16	no	—
138	C₂×C₄	#88126	1	16	yes	—
139	C₂×C₄	C₂×C₄×Dic₁₃	1	8	yes	—
140	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
141	C₂×C₄	#88180	1	4	yes	—
142	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
143	C₂×C₄	C₂×#6127	1	4	yes	—
144	C₈	—	26	16	no	—
145	C₂²	—	2	8	no	—
146	C₂²	—	2	4	no	—
147	C₂²	#11718593	1	4	yes	—
148	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
149	C₂²	C₂×#88180	1	2	yes	—
150	C₂²	#11719524	1	4	yes	—
151	C₄	—	2	8	no	—
152	C₄	—	4	8	no	—
153	C₄	#11718593	1	4	yes	—
154	C₄	C₂×#88126	1	4	yes	—
155	C₂	—	2	4	no	—
156	C₂	C₂×#11718593	1	1	yes	characteristic
157	C₂	#13123255	1	2	yes	—
158	C₂	#13123474	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Fitting	C₂×C₁₃×#376	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#376	D₁₃
hypocenter	C₁₃	#20365
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#376

Complements

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

N	H ≅ G/N	type
2. #13114588	C₂	semidirect
11. C₄×#6099	C₄	semidirect
28. #88043	C₂×C₄	semidirect
29. C₄×#1055	C₂×C₄	semidirect
128. C₁₃	#20365	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#6099	2
#13114588	2
#13114530	2
C₂×C₁₃×#376	2
#20365	13