Subgroups — #15753383

Order 3328.

726 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₄×#88060	C₂	1	2	yes	maximal
3	C₂×C₈×#1055	C₂	1	2	yes	maximal, complemented
4	#13112663	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1273	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₁₃	C₄	1	2	yes	—
7	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×#88060	C₄	1	4	yes	—
11	C₂×C₈×Dic₁₃	C₄	1	2	yes	—
12	C₂×C₄×#1055	C₂²	1	2	yes	—
13	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
14	C₄×C₈×D₁₃	—	2	4	no	—
15	#11718142	C₄	1	4	yes	—
16	C₈×#1055	—	2	4	no	—
17	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	—
19	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
20	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
24	C₂²×#1055	C₂×C₄	1	4	yes	—
25	C₂²×#1055	C₂×C₄	1	2	yes	—
26	C₂×C₈×D₁₃	—	2	4	no	—
27	C₂×C₈×D₁₃	—	2	4	no	—
28	C₂×C₈×D₁₃	C₈	1	8	yes	complemented
29	C₄²×D₁₃	—	2	2	no	—
30	C₄²×D₁₃	—	2	1	no	—
31	C₄²×D₁₃	—	2	1	no	—
32	C₄×C₈×C₁₃	—	2	2	no	—
33	C₄×C₈×C₁₃	—	2	2	no	—
34	C₄×C₈×C₁₃	—	2	2	no	—
35	#88060	C₈	1	16	yes	complemented
36	C₈×Dic₁₃	—	2	4	no	—
37	C₄×#1055	—	2	2	no	—
38	C₄×#1055	—	2	2	no	—
39	C₄×#1055	D₄	1	4	yes	—
40	C₈×C₂²⋊C₈	—	13	1	no	maximal, Sylow
41	C₂³×D₁₃	C₄²	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
44	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
45	C₂²×Dic₁₃	C₄²	1	2	yes	—
46	C₂×C₄×D₁₃	—	2	1	no	—
47	C₂×C₄×D₁₃	—	2	1	no	—
48	C₂×C₄×D₁₃	—	2	2	no	—
49	C₂×C₄×D₁₃	—	2	2	no	—
50	C₂×C₄×D₁₃	—	2	2	no	—
51	C₂×C₄×D₁₃	—	2	4	no	—
52	C₂×C₄×D₁₃	C₂×C₈	1	4	yes	—
53	C₂×C₄×D₁₃	C₂×C₈	1	8	yes	—
54	C₂×C₈×C₁₃	—	2	2	no	—
55	C₂×C₈×C₁₃	—	2	4	no	—
56	C₂×C₈×C₁₃	—	2	2	no	—
57	C₂×C₈×C₁₃	—	2	4	no	—
58	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
59	C₂×C₈×C₁₃	C₂×C₈	1	8	yes	complemented
60	C₄²×C₁₃	C₂×D₄	1	2	yes	—
61	C₄²×C₁₃	#41	1	1	yes	characteristic
62	C₄²×C₁₃	#41	1	1	yes	characteristic
63	C₄×Dic₁₃	—	2	1	no	—
64	C₄×Dic₁₃	—	2	1	no	—
65	C₄×Dic₁₃	—	2	2	no	—
66	C₄×Dic₁₃	—	2	2	no	—
67	C₂×#1055	—	2	4	no	—
68	C₂×#1055	—	2	4	no	—
69	C₂×#1055	C₂²⋊C₄	1	4	yes	—
70	C₂×#1055	C₂×C₈	1	4	yes	—
71	C₂×#1055	C₂×C₈	1	8	yes	complemented
72	C₂×#1055	M₁₆	1	4	yes	—
73	C₈×D₁₃	—	2	16	no	—
74	C₂²×C₄×C₈	—	13	1	no	—
75	C₄×C₂²⋊C₈	—	13	2	no	—
76	C₂×C₈²	—	13	2	no	—
77	#1273	—	13	1	no	—
78	#1273	D₁₃	1	1	yes	characteristic, complemented
79	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
80	C₂²×D₁₃	—	2	1	no	—
81	C₂²×D₁₃	—	2	1	no	—
82	C₂²×D₁₃	—	2	2	no	—
83	C₂²×D₁₃	C₄×C₈	1	4	yes	—
84	C₂²×D₁₃	C₄×C₈	1	2	yes	—
85	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
88	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
89	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
90	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
91	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
92	C₂×C₄×C₁₃	#131	1	4	yes	—
93	C₂×Dic₁₃	—	2	1	no	—
94	C₂×Dic₁₃	—	2	2	no	—
95	C₂×Dic₁₃	—	2	1	no	—
96	C₂×Dic₁₃	—	2	2	no	—
97	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
98	C₂×Dic₁₃	C₄×C₈	1	4	yes	—
99	C₄×D₁₃	—	2	4	no	—
100	C₄×D₁₃	—	2	4	no	—
101	C₄×D₁₃	—	2	8	no	—
102	C₄×D₁₃	—	2	8	no	—
103	C₈×C₁₃	—	2	4	no	—
104	C₈×C₁₃	—	2	8	no	—
105	#1055	—	2	8	no	—
106	#1055	C₂²⋊C₈	1	8	yes	complemented
107	C₂³×C₈	—	13	2	no	—
108	C₂²×C₄²	—	13	1	no	—
109	C₂×C₂²⋊C₈	—	13	4	no	—
110	C₂×C₄×C₈	—	13	1	no	—
111	C₂×C₄×C₈	—	13	2	no	—
112	C₂×C₄×C₈	—	13	2	no	—
113	C₂×C₄×C₈	—	26	4	no	—
114	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
115	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
116	#336	—	13	4	no	—
117	C₈²	—	26	4	no	—
118	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
120	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
121	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
122	C₂²×C₁₃	#405	1	2	yes	—
123	C₂×D₁₃	—	2	4	no	—
124	C₂×D₁₃	—	2	2	no	—
125	C₂×D₁₃	—	2	2	no	—
126	C₂×D₁₃	—	2	4	no	—
127	C₂×D₁₃	C₈²	1	4	yes	complemented
128	C₄×C₁₃	C₂×C₂²⋊C₈	1	2	yes	—
129	C₄×C₁₃	#431	1	2	yes	—
130	C₄×C₁₃	C₈×D₄	1	4	yes	—
131	C₄×C₁₃	C₈×D₄	1	4	yes	—
132	Dic₁₃	—	2	2	no	—
133	Dic₁₃	—	2	4	no	—
134	C₂³×C₄	—	13	1	no	—
135	C₂³×C₄	—	13	2	no	—
136	C₂²×C₈	—	13	2	no	—
137	C₂²×C₈	—	13	4	no	—
138	C₂²×C₈	—	13	8	no	—
139	C₂²×C₈	—	26	4	no	—
140	C₂²×C₈	—	26	4	no	—
141	C₂²×C₈	C₄×D₁₃	1	2	yes	—
142	C₂²×C₈	C₄×D₁₃	1	4	yes	—
143	C₂×C₄²	—	13	2	no	—
144	C₂×C₄²	—	13	1	no	—
145	C₂×C₄²	—	26	2	no	—
146	C₂×C₄²	—	26	1	no	—
147	C₂×C₄²	—	26	1	no	—
148	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
149	C₂²⋊C₈	—	13	16	no	—
150	C₄×C₈	—	2	2	no	—
151	C₄×C₈	—	2	2	no	—
152	C₄×C₈	—	2	2	no	—
153	C₄×C₈	—	13	4	no	—
154	C₄×C₈	—	26	4	no	—
155	C₄×C₈	—	26	2	no	—
156	C₄×C₈	—	26	2	no	—
157	C₂×C₁₃	C₂×C₈²	1	1	yes	characteristic
158	C₂×C₁₃	C₈×M₁₆	1	2	yes	—
159	C₂×C₁₃	#1450	1	1	yes	characteristic
160	C₂×C₁₃	C₄×C₂²⋊C₈	1	1	yes	characteristic
161	C₂×C₁₃	C₈×C₂²⋊C₄	1	2	yes	—
162	D₁₃	—	2	4	no	—
163	C₂⁴	—	13	1	no	—
164	C₂²×C₄	—	13	1	no	—
165	C₂²×C₄	—	13	2	no	—
166	C₂²×C₄	—	13	8	no	—
167	C₂²×C₄	—	13	4	no	—
168	C₂²×C₄	—	26	1	no	—
169	C₂²×C₄	—	26	2	no	—
170	C₂²×C₄	—	26	1	no	—
171	C₂²×C₄	—	26	2	no	—
172	C₂²×C₄	—	26	2	no	—
173	C₂²×C₄	—	26	4	no	—
174	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
175	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
176	C₂×C₈	—	2	2	no	—
177	C₂×C₈	—	2	4	no	—
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	13	4	no	—
181	C₂×C₈	—	13	4	no	—
182	C₂×C₈	—	13	4	no	—
183	C₂×C₈	—	13	8	no	—
184	C₂×C₈	—	26	16	no	—
185	C₂×C₈	—	26	4	no	—
186	C₂×C₈	—	26	4	no	—
187	C₂×C₈	C₈×D₁₃	1	4	yes	—
188	C₂×C₈	C₈×D₁₃	1	8	yes	complemented
189	C₄²	—	26	1	no	—
190	C₄²	—	26	2	no	—
191	C₄²	—	26	1	no	—
192	C₄²	—	26	2	no	—
193	C₄²	D₄×D₁₃	1	2	yes	—
194	C₄²	#6129	1	1	yes	characteristic
195	C₄²	#6131	1	1	yes	characteristic
196	C₁₃	C₈×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
197	C₂³	—	13	4	no	—
198	C₂³	—	13	2	no	—
199	C₂³	—	26	1	no	—
200	C₂³	—	26	1	no	—
201	C₂³	—	26	2	no	—
202	C₂³	C₄²×D₁₃	1	1	yes	characteristic
203	C₂×C₄	—	13	2	no	—
204	C₂×C₄	—	13	4	no	—
205	C₂×C₄	—	26	1	no	—
206	C₂×C₄	—	26	2	no	—
207	C₂×C₄	—	26	1	no	—
208	C₂×C₄	—	26	2	no	—
209	C₂×C₄	—	26	4	no	—
210	C₂×C₄	—	26	8	no	—
211	C₂×C₄	—	26	4	no	—
212	C₂×C₄	—	26	8	no	—
213	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
214	C₂×C₄	#88135	1	2	yes	—
215	C₂×C₄	#88146	1	1	yes	characteristic
216	C₂×C₄	#88147	1	2	yes	—
217	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
218	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
219	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
220	C₂×C₄	#88161	1	4	yes	—
221	C₈	—	2	4	no	—
222	C₈	—	2	8	no	—
223	C₈	—	13	8	no	—
224	C₈	—	26	8	no	—
225	C₂²	—	13	4	no	—
226	C₂²	—	26	4	no	—
227	C₂²	—	26	2	no	—
228	C₂²	—	26	2	no	—
229	C₂²	—	26	4	no	—
230	C₂²	#11718327	1	1	yes	characteristic
231	C₂²	C₄×C₈×D₁₃	1	2	yes	—
232	C₂²	C₄×C₈×D₁₃	1	1	yes	characteristic
233	C₂²	#11718368	1	1	yes	characteristic
234	C₂²	#11718369	1	2	yes	—
235	C₄	—	26	2	no	—
236	C₄	—	26	4	no	—
237	C₄	D₁₃×C₂²⋊C₈	1	2	yes	—
238	C₄	#11718386	1	4	yes	—
239	C₄	#11718494	1	2	yes	—
240	C₄	#11718495	1	4	yes	—
241	C₂	—	26	4	no	—
242	C₂	C₈²×D₁₃	1	1	yes	characteristic
243	C₂	#13113115	1	2	yes	—
244	C₂	#13113121	1	1	yes	characteristic
245	C₂	#13114593	1	1	yes	characteristic
246	C₂	#13114606	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₃
commutator	C₂×C₁₃	C₂×C₈²
Fitting	C₁₃×#1273	C₂
socle	C₂³×C₁₃	C₂×C₄²
prime radical	C₂³×D₁₃	C₄²
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1273	D₁₃
hypocenter	C₁₃	C₈×C₂²⋊C₈
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ #1273

Complements

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

N	H ≅ G/N	type
3. C₂×C₈×#1055	C₂	semidirect
4. #13112663	C₂	semidirect
5. C₁₃×#1273	C₂	semidirect
28. C₂×C₈×D₁₃	C₈	semidirect
35. #88060	C₈	semidirect
59. C₂×C₈×C₁₃	C₂×C₈	semidirect
71. C₂×#1055	C₂×C₈	semidirect
78. #1273	D₁₃	semidirect
106. #1055	C₂²⋊C₈	semidirect
127. C₂×D₁₃	C₈²	semidirect
188. C₂×C₈	C₈×D₁₃	semidirect
196. C₁₃	C₈×C₂²⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₈×D₁₃	2
C₄×#88060	2
C₂×C₈×#1055	2
#13112663	2
C₁₃×#1273	2
C₈×C₂²⋊C₈	13