Subgroups — D₁₃×#1455 #15828623

Order 3328.

994 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×M₁₆×D₁₃	C₂	1	3	yes	maximal
2	#13113140	C₂	1	3	yes	maximal, complemented
3	#13113139	C₂	1	3	yes	maximal, complemented
4	#13113138	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₃×#322	C₂	1	3	yes	maximal, complemented
6	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1455	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₁₃	C₄	1	6	yes	—
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	C₄×C₁₃×M₁₆	C₂²	1	3	yes	—
11	M₁₆×Dic₁₃	C₄	1	6	yes	—
12	C₄×#6099	C₂²	1	3	yes	—
13	#11718368	C₄	1	6	yes	—
14	D₁₃×#97	C₄	1	6	yes	—
15	C₄×#6094	C₂²	1	3	yes	—
16	C₄×#6094	C₂²	1	3	yes	—
17	C₄×C₈×D₁₃	C₂²	1	3	yes	—
18	C₄×C₈×D₁₃	C₂²	1	3	yes	—
19	C₁₃×#322	C₂²	1	3	yes	complemented
20	C₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	#11718047	C₂²	1	3	yes	complemented
22	#11718046	C₂²	1	6	yes	complemented
23	C₈×#1055	C₂²	1	3	yes	complemented
24	C₂²×C₄×D₁₃	C₂×C₄	1	3	yes	—
25	C₂×C₁₃×M₁₆	C₂×C₄	1	6	yes	—
26	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
27	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	—
28	C₂×#6099	C₂×C₄	1	6	yes	—
29	M₁₆×D₁₃	—	2	24	no	—
30	C₂×#6094	C₂×C₄	1	6	yes	—
31	C₂×#6094	C₂×C₄	1	6	yes	—
32	C₂×C₈×D₁₃	C₂×C₄	1	6	yes	—
33	C₂×C₈×D₁₃	C₂×C₄	1	6	yes	—
34	C₄²×D₁₃	C₂×C₄	1	3	yes	—
35	C₄²×D₁₃	C₂×C₄	1	3	yes	—
36	C₄²×D₁₃	C₂³	1	1	yes	characteristic
37	C₄²×D₁₃	C₂³	1	1	yes	characteristic
38	C₁₃×#97	C₂×C₄	1	6	yes	—
39	C₄×C₈×C₁₃	C₂³	1	3	yes	—
40	C₄×C₈×C₁₃	C₂³	1	3	yes	—
41	#88055	C₂×C₄	1	6	yes	—
42	#88055	C₂×C₄	1	6	yes	—
43	C₈×Dic₁₃	C₂×C₄	1	6	yes	—
44	C₈×Dic₁₃	C₂×C₄	1	6	yes	—
45	#88043	C₂×C₄	1	6	yes	—
46	C₄×#1055	C₂³	1	3	yes	—
47	C₄×#1055	C₂³	1	3	yes	—
48	C₂×#1455	—	13	1	no	maximal, Sylow
49	C₂³×D₁₃	C₄²	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
51	C₂²×Dic₁₃	C₄²	1	3	yes	—
52	C₂×C₄×D₁₃	—	2	12	no	—
53	C₂×C₄×D₁₃	C₄²	1	3	yes	—
54	C₂×C₄×D₁₃	C₄²	1	3	yes	—
55	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
56	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
57	C₁₃×M₁₆	—	2	12	no	—
58	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
59	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
60	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
61	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
62	C₄×Dic₁₃	C₄²	1	6	yes	—
63	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
64	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
65	#6099	—	2	12	no	—
66	C₂×#1055	C₂²×C₄	1	6	yes	—
67	C₂×#1055	C₂²×C₄	1	6	yes	—
68	#6094	—	2	12	no	—
69	#6094	—	2	12	no	—
70	C₈×D₁₃	—	2	12	no	—
71	C₈×D₁₃	M₁₆	1	24	yes	complemented
72	C₂×C₄×M₁₆	—	13	3	no	—
73	#1455	—	13	3	no	—
74	#1455	—	13	3	no	—
75	#1455	—	13	1	no	—
76	#1455	D₁₃	1	1	yes	characteristic, direct product factor
77	C₂×#322	—	13	3	no	—
78	C₂×C₈²	—	13	1	no	—
79	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
80	C₂²×D₁₃	—	2	6	no	—
81	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
82	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
83	C₂×C₄×C₁₃	—	2	6	no	—
84	C₂×C₄×C₁₃	C₂×C₄²	1	3	yes	—
85	C₂×C₄×C₁₃	C₂³×C₄	1	3	yes	—
86	C₂×Dic₁₃	—	2	6	no	—
87	C₂×Dic₁₃	C₂×C₄²	1	3	yes	—
88	C₂×Dic₁₃	C₂×C₄²	1	3	yes	—
89	C₄×D₁₃	—	2	6	no	—
90	C₄×D₁₃	—	2	6	no	—
91	C₄×D₁₃	—	2	6	no	—
92	C₄×D₁₃	C₂×M₁₆	1	12	yes	—
93	C₈×C₁₃	—	2	6	no	—
94	C₈×C₁₃	C₂×M₁₆	1	12	yes	complemented
95	#1055	—	2	6	no	—
96	#1055	C₂×M₁₆	1	12	yes	complemented
97	C₂²×M₁₆	—	13	6	no	—
98	C₂²×C₄²	—	13	1	no	—
99	C₄×M₁₆	—	13	6	no	—
100	C₄×M₁₆	—	13	3	no	—
101	C₄×M₁₆	—	13	6	no	—
102	C₄×M₁₆	—	13	3	no	—
103	C₄×M₁₆	—	13	3	no	—
104	C₄×M₁₆	C₂×D₁₃	1	3	yes	—
105	C₂×#97	—	13	6	no	—
106	C₂×C₄×C₈	—	13	3	no	—
107	C₂×C₄×C₈	—	13	3	no	—
108	#322	—	13	6	no	—
109	#322	—	13	3	no	—
110	#322	C₂×D₁₃	1	3	yes	complemented
111	C₈²	—	13	3	no	—
112	C₈²	C₂×D₁₃	1	1	yes	characteristic, complemented
113	C₂²×C₁₃	—	2	3	no	—
114	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
115	C₂×D₁₃	—	2	3	no	—
116	C₂×D₁₃	—	4	4	no	—
117	C₂×D₁₃	C₄×M₁₆	1	6	yes	—
118	C₄×C₁₃	—	2	3	no	—
119	C₄×C₁₃	C₂²×M₁₆	1	6	yes	—
120	Dic₁₃	—	2	3	no	—
121	Dic₁₃	C₄×M₁₆	1	6	yes	—
122	C₂³×C₄	—	13	3	no	—
123	C₂×M₁₆	—	13	6	no	—
124	C₂×M₁₆	—	13	6	no	—
125	C₂×M₁₆	—	13	6	no	—
126	C₂×M₁₆	—	26	24	no	—
127	C₂×M₁₆	C₄×D₁₃	1	6	yes	—
128	C₂²×C₈	—	13	6	no	—
129	C₂²×C₈	—	13	6	no	—
130	C₂×C₄²	—	13	3	no	—
131	C₂×C₄²	—	13	3	no	—
132	C₂×C₄²	—	13	3	no	—
133	C₂×C₄²	—	13	1	no	—
134	C₂×C₄²	—	13	1	no	—
135	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
136	#97	—	13	6	no	—
137	#97	—	13	6	no	—
138	#97	—	13	6	no	—
139	#97	C₄×D₁₃	1	6	yes	—
140	C₄×C₈	—	13	6	no	—
141	C₄×C₈	—	13	6	no	—
142	C₄×C₈	—	13	3	no	—
143	C₄×C₈	—	13	3	no	—
144	C₄×C₈	C₂²×D₁₃	1	3	yes	—
145	C₄×C₈	C₂²×D₁₃	1	3	yes	—
146	C₂×C₁₃	—	4	1	no	—
147	C₂×C₁₃	C₂×C₄×M₁₆	1	3	yes	—
148	D₁₃	—	4	1	no	—
149	D₁₃	#1455	1	4	yes	direct product factor
150	C₂⁴	—	13	1	no	—
151	C₂²×C₄	—	13	3	no	—
152	C₂²×C₄	—	13	3	no	—
153	C₂²×C₄	—	13	3	no	—
154	C₂²×C₄	—	13	3	no	—
155	C₂²×C₄	—	13	3	no	—
156	C₂²×C₄	—	26	12	no	—
157	C₂²×C₄	C₂×C₄×D₁₃	1	3	yes	—
158	M₁₆	—	2	12	no	—
159	M₁₆	—	26	12	no	—
160	M₁₆	—	26	12	no	—
161	M₁₆	—	26	12	no	—
162	C₂×C₈	—	13	6	no	—
163	C₂×C₈	—	13	24	no	—
164	C₂×C₈	—	13	6	no	—
165	C₂×C₈	—	26	12	no	—
166	C₂×C₈	C₂×C₄×D₁₃	1	6	yes	—
167	C₂×C₈	C₂×C₄×D₁₃	1	6	yes	—
168	C₄²	—	13	6	no	—
169	C₄²	—	13	3	no	—
170	C₄²	—	13	3	no	—
171	C₄²	C₂×C₄×D₁₃	1	3	yes	—
172	C₄²	C₂³×D₁₃	1	1	yes	characteristic
173	C₁₃	C₂×#1455	1	1	yes	characteristic, complemented, Sylow
174	C₂³	—	13	1	no	—
175	C₂³	—	13	1	no	—
176	C₂³	—	26	6	no	—
177	C₂³	C₄²×D₁₃	1	1	yes	characteristic
178	C₂×C₄	—	2	6	no	—
179	C₂×C₄	—	13	3	no	—
180	C₂×C₄	—	13	12	no	—
181	C₂×C₄	—	13	3	no	—
182	C₂×C₄	—	26	6	no	—
183	C₂×C₄	—	26	6	no	—
184	C₂×C₄	—	26	6	no	—
185	C₂×C₄	—	26	6	no	—
186	C₂×C₄	C₄²×D₁₃	1	3	yes	—
187	C₂×C₄	C₂²×C₄×D₁₃	1	3	yes	—
188	C₈	—	2	6	no	—
189	C₈	—	13	12	no	—
190	C₈	—	26	6	no	—
191	C₈	M₁₆×D₁₃	1	12	yes	complemented
192	C₂²	—	2	3	no	—
193	C₂²	—	13	6	no	—
194	C₂²	—	26	3	no	—
195	C₂²	—	52	4	no	—
196	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
197	C₄	—	2	3	no	—
198	C₄	—	13	6	no	—
199	C₄	—	26	3	no	—
200	C₄	C₂×M₁₆×D₁₃	1	6	yes	—
201	C₂	—	4	1	no	—
202	C₂	—	13	4	no	—
203	C₂	—	52	1	no	—
204	C₂	C₄×M₁₆×D₁₃	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#1455	C₂
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1455	D₁₃
hypocenter	C₁₃	C₂×#1455
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #1455

Complements

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

N	H ≅ G/N	type
2. #13113140	C₂	semidirect
3. #13113139	C₂	semidirect
4. #13113138	C₂	semidirect
5. D₁₃×#322	C₂	semidirect
6. C₈²×D₁₃	C₂	semidirect
7. C₁₃×#1455	C₂	semidirect
19. C₁₃×#322	C₂²	semidirect
20. C₈²×C₁₃	C₂²	semidirect
21. #11718047	C₂²	semidirect
22. #11718046	C₂²	semidirect
23. C₈×#1055	C₂²	semidirect
71. C₈×D₁₃	M₁₆	semidirect
76. #1455	D₁₃	direct (N × H)
94. C₈×C₁₃	C₂×M₁₆	semidirect
96. #1055	C₂×M₁₆	semidirect
110. #322	C₂×D₁₃	semidirect
112. C₈²	C₂×D₁₃	semidirect
149. D₁₃	#1455	direct (N × H)
173. C₁₃	C₂×#1455	semidirect
191. C₈	M₁₆×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×M₁₆×D₁₃	2
#13113140	2
#13113139	2
#13113138	2
D₁₃×#322	2
C₈²×D₁₃	2
C₁₃×#1455	2
C₂×#1455	13

Subgroups — D13×#1455 #15828623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#1455 #15828623