Subgroups — D₁₃×#2253 #16018397

Order 3328.

494 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#499	C₂	1	2	yes	maximal
2	#13117115	C₂	1	1	yes	maximal, characteristic, complemented
3	#13117114	C₂	1	2	yes	maximal, complemented
4	#13117113	C₂	1	2	yes	maximal, complemented
5	#13117112	C₂	1	2	yes	maximal, complemented
6	D₁₃×#367	C₂	1	2	yes	maximal
7	D₁₃×#366	C₂	1	2	yes	maximal
8	C₄×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2253	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₃×#125	—	2	2	no	—
11	C₁₃×#499	C₂²	1	2	yes	—
12	#11718725	—	2	2	no	—
13	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
15	D₁₃×#107	C₂²	1	4	yes	—
16	#11718539	C₂²	1	4	yes	—
17	D₁₃×#106	—	2	2	no	—
18	#11718519	—	2	2	no	—
19	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
20	#11718344	C₂²	1	2	yes	—
21	C₁₃×#367	C₂²	1	2	yes	—
22	C₁₃×#366	C₂²	1	2	yes	—
23	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
24	#11718097	C₂²	1	2	yes	—
25	#11718096	C₂²	1	2	yes	—
26	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
27	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
28	#11718082	C₂²	1	4	yes	—
29	#11718081	C₂²	1	4	yes	—
30	C₄×#6090	C₂²	1	1	yes	characteristic
31	C₁₃×#125	—	2	2	no	—
32	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
33	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
34	C₄⋊C₄×D₁₃	—	2	4	no	—
35	C₄⋊C₄×D₁₃	—	4	4	no	—
36	#88144	—	2	4	no	—
37	#88143	—	4	4	no	—
38	C₄²×D₁₃	D₄	1	1	yes	characteristic
39	#88124	—	2	2	no	—
40	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
41	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
42	C₁₃×#107	C₂³	1	4	yes	—
43	C₁₃×#106	—	2	2	no	—
44	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	#88058	C₂³	1	4	yes	—
46	#88057	—	2	2	no	—
47	C₈×Dic₁₃	D₄	1	1	yes	characteristic
48	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
49	C₂×#6090	C₂³	1	1	yes	characteristic
50	C₂×#6090	C₂³	1	1	yes	characteristic
51	#88048	—	2	4	no	—
52	#88047	—	2	4	no	—
53	C₄×#1055	D₄	1	1	yes	characteristic
54	C₁₆×D₁₃	Q₈	1	4	yes	—
55	C₁₆×D₁₃	Q₈	1	4	yes	—
56	C₂×#2253	—	13	1	no	maximal, Sylow
57	C₂×C₄×D₁₃	—	4	4	no	—
58	C₂×C₄×D₁₃	D₈	1	2	yes	—
59	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
61	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
62	C₁₃×C₄⋊C₄	—	2	4	no	—
63	C₁₃×C₄⋊C₄	—	4	4	no	—
64	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
65	C₄⋊Dic₁₃	—	2	4	no	—
66	C₄⋊Dic₁₃	—	4	4	no	—
67	#6101	—	4	4	no	—
68	#6101	—	4	4	no	—
69	#6101	—	4	4	no	—
70	C₄×Dic₁₃	D₈	1	2	yes	—
71	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
72	C₂×#1055	C₂×D₄	1	1	yes	characteristic
73	C₂×#1055	C₂×D₄	1	1	yes	characteristic
74	C₈×D₁₃	Q₁₆	1	4	yes	—
75	C₈×D₁₃	C₂×Q₈	1	2	yes	—
76	C₈×D₁₃	C₂×Q₈	1	2	yes	—
77	C₁₃×C₁₆	C₂×Q₈	1	2	yes	—
78	C₁₃×C₁₆	C₂×Q₈	1	2	yes	—
79	#6090	C₂×Q₈	1	2	yes	—
80	#6090	C₂×Q₈	1	2	yes	—
81	C₂×#499	—	13	2	no	—
82	#2253	—	13	2	no	—
83	#2253	—	13	2	no	—
84	#2253	—	13	2	no	—
85	#2253	—	13	1	no	—
86	#2253	D₁₃	1	1	yes	characteristic, direct product factor
87	C₂×#367	—	13	2	no	—
88	C₂×#366	—	13	2	no	—
89	C₂×C₄×C₁₆	—	13	1	no	—
90	C₂²×D₁₃	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₁₃	—	4	4	no	—
92	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
93	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
94	C₂×Dic₁₃	—	4	4	no	—
95	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
96	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
97	C₄×D₁₃	—	2	4	no	—
98	C₄×D₁₃	—	8	8	no	—
99	C₄×D₁₃	C₄⋊Q₈	1	2	yes	—
100	C₄×D₁₃	C₂×Q₁₆	1	2	yes	—
101	C₈×C₁₃	C₂×Q₁₆	1	2	yes	—
102	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
103	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
104	#1055	C₄⋊Q₈	1	2	yes	—
105	#1055	C₂×Q₁₆	1	2	yes	—
106	C₂×#125	—	26	2	no	—
107	C₂²×C₁₆	—	13	1	no	—
108	C₂²×C₁₆	—	13	1	no	—
109	#499	—	13	4	no	—
110	#499	—	13	2	no	—
111	#499	—	26	2	no	—
112	#499	—	26	2	no	—
113	#499	C₂×D₁₃	1	2	yes	—
114	C₂×#107	—	13	4	no	—
115	C₂×#106	—	26	2	no	—
116	C₂×C₄×C₈	—	13	1	no	—
117	#367	—	13	2	no	—
118	#367	—	13	4	no	—
119	#367	C₂×D₁₃	1	2	yes	—
120	#366	—	13	2	no	—
121	#366	—	13	4	no	—
122	#366	C₂×D₁₃	1	2	yes	—
123	C₄×C₁₆	—	13	1	no	—
124	C₄×C₁₆	—	13	1	no	—
125	C₄×C₁₆	—	13	1	no	—
126	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
127	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
128	C₂×D₁₃	#500	1	2	yes	—
129	C₂×D₁₃	#508	1	4	yes	—
130	C₄×C₁₃	—	2	2	no	—
131	C₄×C₁₃	—	8	4	no	—
132	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
133	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
134	Dic₁₃	—	2	2	no	—
135	Dic₁₃	—	8	4	no	—
136	Dic₁₃	#500	1	2	yes	—
137	C₂²×C₈	—	13	1	no	—
138	C₂²×C₈	—	13	1	no	—
139	#125	—	2	2	no	—
140	#125	—	26	4	no	—
141	#125	—	26	2	no	—
142	#125	—	52	4	no	—
143	C₂×C₄⋊C₄	—	26	4	no	—
144	C₂×C₄⋊C₄	—	52	4	no	—
145	C₂×C₄²	—	13	1	no	—
146	C₂×C₁₆	—	13	1	no	—
147	C₂×C₁₆	—	13	1	no	—
148	C₂×C₁₆	—	13	4	no	—
149	C₂×C₁₆	—	13	4	no	—
150	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
151	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
152	#107	—	13	4	no	—
153	#107	—	26	4	no	—
154	#107	C₂²×D₁₃	1	4	yes	—
155	#106	—	2	2	no	—
156	#106	—	26	4	no	—
157	#106	—	26	2	no	—
158	C₄×C₈	—	13	1	no	—
159	C₄×C₈	—	13	1	no	—
160	C₄×C₈	—	13	1	no	—
161	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
162	C₂×C₁₃	C₂×#500	1	1	yes	characteristic
163	C₂×C₁₃	C₂×#508	1	2	yes	—
164	D₁₃	#2253	1	4	yes	direct product factor
165	C₂²×C₄	—	13	1	no	—
166	C₂²×C₄	—	13	2	no	—
167	C₂²×C₄	—	52	4	no	—
168	C₂×C₈	—	13	1	no	—
169	C₂×C₈	—	13	1	no	—
170	C₂×C₈	—	13	4	no	—
171	C₂×C₈	—	13	2	no	—
172	C₂×C₈	—	13	2	no	—
173	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
174	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
175	C₄⋊C₄	—	2	4	no	—
176	C₄⋊C₄	—	4	4	no	—
177	C₄⋊C₄	—	26	4	no	—
178	C₄⋊C₄	—	52	4	no	—
179	C₄⋊C₄	—	52	4	no	—
180	C₄⋊C₄	—	52	4	no	—
181	C₄⋊C₄	—	52	4	no	—
182	C₄²	—	13	2	no	—
183	C₄²	—	13	1	no	—
184	C₄²	D₄×D₁₃	1	1	yes	characteristic
185	C₁₆	—	13	2	no	—
186	C₁₆	—	13	2	no	—
187	C₁₆	Q₈×D₁₃	1	2	yes	—
188	C₁₆	Q₈×D₁₃	1	2	yes	—
189	C₁₃	C₂×#2253	1	1	yes	characteristic, complemented, Sylow
190	C₂³	—	13	1	no	—
191	C₂×C₄	—	4	4	no	—
192	C₂×C₄	—	13	1	no	—
193	C₂×C₄	—	13	2	no	—
194	C₂×C₄	—	13	2	no	—
195	C₂×C₄	—	13	2	no	—
196	C₂×C₄	—	26	4	no	—
197	C₂×C₄	—	52	4	no	—
198	C₂×C₄	—	104	8	no	—
199	C₂×C₄	D₈×D₁₃	1	2	yes	—
200	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
201	C₈	—	13	2	no	—
202	C₈	—	13	2	no	—
203	C₈	Q₁₆×D₁₃	1	2	yes	—
204	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
205	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
206	C₂²	—	13	4	no	—
207	C₂²	—	13	2	no	—
208	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
209	C₄	—	2	2	no	—
210	C₄	—	8	4	no	—
211	C₄	—	13	2	no	—
212	C₄	—	26	2	no	—
213	C₄	—	104	4	no	—
214	C₄	D₁₃×C₄⋊Q₈	1	1	yes	characteristic
215	C₄	C₂×Q₁₆×D₁₃	1	1	yes	characteristic
216	C₂	—	13	4	no	—
217	C₂	D₁₃×#500	1	1	yes	characteristic
218	C₂	D₁₃×#508	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₃
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#2253	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂²×D₁₃	C₂×D₈
hypercenter	#2253	D₁₃
hypocenter	C₁₃	C₂×#2253
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2253

Complements

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

N	H ≅ G/N	type
2. #13117115	C₂	semidirect
3. #13117114	C₂	semidirect
4. #13117113	C₂	semidirect
5. #13117112	C₂	semidirect
9. C₁₃×#2253	C₂	semidirect
86. #2253	D₁₃	direct (N × H)
164. D₁₃	#2253	direct (N × H)
189. C₁₃	C₂×#2253	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×#499	2
#13117115	2
#13117114	2
#13117113	2
#13117112	2
D₁₃×#367	2
D₁₃×#366	2
C₄×C₁₆×D₁₃	2
C₁₃×#2253	2
C₂×#2253	13

Subgroups — D13×#2253 #16018397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#2253 #16018397