Subgroups — #16792577

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#431	C₂	1	2	yes	maximal
2	#13130040	C₂	1	4	yes	maximal, complemented
3	#13130039	C₂	1	4	yes	maximal, complemented
4	#13130030	C₂	1	2	yes	maximal, complemented
5	C₈×D₁₃⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₈×D₁₃	C₄	1	2	yes	—
8	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
9	#11719125	C₄	1	4	yes	—
10	D₁₃⋊(C₂²⋊C₈)	C₄	1	4	yes	—
11	#11719119	C₂²	1	4	yes	—
12	#11719051	C₄	1	4	yes	—
13	D₁₃⋊(C₄⋊C₈)	C₄	1	4	yes	—
14	#11719049	C₂²	1	4	yes	—
15	C₄×D₁₃⋊C₈	C₂²	1	4	yes	—
16	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
17	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
18	C₂×C₄×#1055	C₄	1	1	yes	characteristic
19	C₄×C₈×D₁₃	C₄	1	2	yes	—
20	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
21	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
22	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
23	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
24	C₄×C₈×D₁₃	C₂²	1	2	yes	—
25	#11718251	C₂²	1	8	yes	complemented
26	C₈×#1057	C₂²	1	8	yes	complemented
27	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	—
28	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂×D₁₃⋊C₈	C₂×C₄	1	8	yes	—
30	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
33	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
34	C₂²×#1055	C₂×C₄	1	2	yes	—
35	C₂×C₈×D₁₃	C₈	1	16	yes	complemented
36	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
37	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
38	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
39	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
40	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
41	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
42	C₄²×D₁₃	C₂×C₄	1	2	yes	—
43	C₄²×D₁₃	C₂×C₄	1	2	yes	—
44	C₄²×D₁₃	C₂³	1	1	yes	characteristic
45	C₄²×D₁₃	C₂³	1	1	yes	characteristic
46	C₂²⋊#1057	C₂×C₄	1	8	yes	—
47	#88112	C₂×C₄	1	8	yes	—
48	#88111	C₂×C₄	1	8	yes	—
49	C₄⋊#1057	C₂×C₄	1	8	yes	—
50	C₄×#1057	C₂×C₄	1	8	yes	—
51	C₄×#1057	C₂³	1	8	yes	—
52	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
54	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
56	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
57	C₈×Dic₁₃	C₂³	1	2	yes	—
58	C₈×Dic₁₃	C₂³	1	2	yes	—
59	C₄×#1055	C₂×C₄	1	1	yes	characteristic
60	C₄×#1055	C₂×C₄	1	1	yes	characteristic
61	C₄×#1055	C₂×C₄	1	2	yes	—
62	C₂×#1450	—	13	1	no	maximal, Sylow
63	C₂³×D₁₃	C₄²	1	1	yes	characteristic
64	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
65	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
67	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
68	C₂×C₄×D₁₃	—	2	8	no	—
69	C₂×C₄×D₁₃	C₄²	1	2	yes	—
70	C₂×C₄×D₁₃	C₄²	1	2	yes	—
71	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
72	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
73	C₂×C₄×D₁₃	C₂×C₈	1	8	yes	—
74	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
75	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
78	C₂×#1057	C₂²×C₄	1	16	yes	—
79	D₁₃⋊C₈	—	2	16	no	—
80	C₂×C₈×C₁₃	C₂×C₈	1	8	yes	complemented
81	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
82	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
83	C₄²×C₁₃	C₄²	1	2	yes	—
84	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₄×Dic₁₃	C₄²	1	2	yes	—
87	C₄×Dic₁₃	C₄²	1	2	yes	—
88	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
90	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
91	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
92	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
93	C₂×#1055	C₂×C₈	1	8	yes	complemented
94	C₂×#1055	C₂²×C₄	1	2	yes	—
95	C₂×#1055	C₂²×C₄	1	2	yes	—
96	C₈×D₁₃	C₂×C₈	1	8	yes	—
97	C₈×D₁₃	C₂×C₈	1	8	yes	—
98	C₈×D₁₃	C₂×C₈	1	8	yes	complemented
99	C₈×D₁₃	C₂×C₈	1	8	yes	complemented
100	C₂×#431	—	13	2	no	—
101	C₂²×C₄×C₈	—	13	1	no	—
102	#1450	—	13	4	no	—
103	#1450	—	13	4	no	—
104	C₂×#322	—	13	2	no	—
105	C₂×C₈²	—	13	2	no	—
106	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
107	C₂²×D₁₃	—	2	4	no	—
108	C₂²×D₁₃	C₄×C₈	1	4	yes	—
109	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
110	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
111	C₂×C₄×C₁₃	—	2	4	no	—
112	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
113	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
114	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
115	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
116	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
117	C₂×Dic₁₃	—	2	4	no	—
118	C₂×Dic₁₃	C₄×C₈	1	4	yes	—
119	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
120	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
121	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
122	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
123	C₄×D₁₃	—	2	4	no	—
124	C₄×D₁₃	—	2	4	no	—
125	C₄×D₁₃	—	2	4	no	—
126	C₄×D₁₃	C₄×C₈	1	4	yes	—
127	C₄×D₁₃	C₄×C₈	1	4	yes	—
128	C₄×D₁₃	C₂²×C₈	1	4	yes	—
129	C₄×D₁₃	C₂²×C₈	1	4	yes	—
130	C₄×D₁₃	#131	1	8	yes	—
131	#1057	—	2	16	no	—
132	C₈×C₁₃	C₂²×C₈	1	4	yes	—
133	C₈×C₁₃	C₂²×C₈	1	4	yes	—
134	#1055	C₂²×C₈	1	4	yes	—
135	#1055	C₂²×C₈	1	4	yes	—
136	C₂³×C₈	—	13	2	no	—
137	C₂²×C₄²	—	13	1	no	—
138	#431	—	13	4	no	—
139	#431	—	13	4	no	—
140	#431	—	13	4	no	—
141	#431	—	13	4	no	—
142	C₂×C₄⋊C₈	—	13	4	no	—
143	C₂×C₂²⋊C₈	—	13	4	no	—
144	C₂×C₄×C₈	—	13	4	no	—
145	C₂×C₄×C₈	—	13	2	no	—
146	C₂×C₄×C₈	—	13	1	no	—
147	C₂×C₄×C₈	—	13	1	no	—
148	C₂×C₄×C₈	—	13	2	no	—
149	C₂×C₄×C₈	—	13	1	no	—
150	C₂×C₄×C₈	—	13	2	no	—
151	C₂×C₄×C₈	—	13	1	no	—
152	C₂×C₄×C₈	—	13	1	no	—
153	C₂×C₄×C₈	#261	1	1	yes	characteristic
154	#322	—	13	8	no	—
155	C₈²	—	13	8	no	—
156	C₂²×C₁₃	—	2	2	no	—
157	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
158	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
159	C₂×D₁₃	—	2	2	no	—
160	C₂×D₁₃	—	2	8	no	—
161	C₂×D₁₃	C₂×C₄×C₈	1	2	yes	—
162	C₂×D₁₃	C₂×C₄×C₈	1	2	yes	—
163	C₂×D₁₃	#405	1	4	yes	—
164	C₄×C₁₃	—	2	2	no	—
165	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
166	C₄×C₁₃	#405	1	4	yes	—
167	C₄×C₁₃	C₂³×C₈	1	2	yes	—
168	Dic₁₃	—	2	2	no	—
169	Dic₁₃	C₂×C₄×C₈	1	2	yes	—
170	Dic₁₃	C₂×C₄×C₈	1	2	yes	—
171	Dic₁₃	C₂×#131	1	4	yes	—
172	C₂³×C₄	—	13	1	no	—
173	C₂³×C₄	—	13	2	no	—
174	C₂²×C₈	—	13	2	no	—
175	C₂²×C₈	—	13	16	no	—
176	C₂²×C₈	—	13	2	no	—
177	C₂²×C₈	—	13	2	no	—
178	C₂²×C₈	—	13	2	no	—
179	C₂²×C₈	—	13	2	no	—
180	C₂²×C₈	—	13	8	no	—
181	C₂²×C₈	C₂×#261	1	2	yes	—
182	C₂×C₄²	—	13	2	no	—
183	C₂×C₄²	—	13	1	no	—
184	C₂×C₄²	—	13	2	no	—
185	C₂×C₄²	—	13	2	no	—
186	C₂×C₄²	—	13	1	no	—
187	C₂×C₄²	—	13	1	no	—
188	C₂×C₄²	—	13	1	no	—
189	C₂×C₄²	—	13	1	no	—
190	C₂×C₄²	C₂×#261	1	1	yes	characteristic
191	C₄⋊C₈	—	13	8	no	—
192	C₄⋊C₈	—	13	8	no	—
193	C₂²⋊C₈	—	13	8	no	—
194	C₂²⋊C₈	—	13	8	no	—
195	C₄×C₈	—	13	8	no	—
196	C₄×C₈	—	13	8	no	—
197	C₄×C₈	—	13	2	no	—
198	C₄×C₈	—	13	2	no	—
199	C₄×C₈	—	13	2	no	—
200	C₄×C₈	—	13	2	no	—
201	C₄×C₈	—	13	2	no	—
202	C₄×C₈	—	13	1	no	—
203	C₄×C₈	—	13	1	no	—
204	C₄×C₈	C₂×#261	1	2	yes	—
205	C₄×C₈	C₂×#261	1	1	yes	characteristic
206	C₄×C₈	C₂×#261	1	1	yes	characteristic
207	C₂×C₁₃	—	2	2	no	—
208	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
209	C₂×C₁₃	C₂×#405	1	2	yes	—
210	D₁₃	—	2	2	no	—
211	D₁₃	#1450	1	4	yes	complemented
212	C₂⁴	—	13	1	no	—
213	C₂²×C₄	—	13	1	no	—
214	C₂²×C₄	—	13	8	no	—
215	C₂²×C₄	—	13	2	no	—
216	C₂²×C₄	—	13	1	no	—
217	C₂²×C₄	—	13	1	no	—
218	C₂²×C₄	—	13	1	no	—
219	C₂²×C₄	—	13	1	no	—
220	C₂²×C₄	—	13	2	no	—
221	C₂²×C₄	—	13	2	no	—
222	C₂²×C₄	—	13	2	no	—
223	C₂²×C₄	—	13	2	no	—
224	C₂²×C₄	—	26	8	no	—
225	C₂²×C₄	C₄×#261	1	2	yes	—
226	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
227	C₂×C₈	—	13	8	no	—
228	C₂×C₈	—	13	2	no	—
229	C₂×C₈	—	13	2	no	—
230	C₂×C₈	—	13	8	no	—
231	C₂×C₈	—	13	8	no	—
232	C₂×C₈	—	13	8	no	—
233	C₂×C₈	—	13	8	no	—
234	C₂×C₈	—	13	16	no	—
235	C₂×C₈	—	26	16	no	—
236	C₂×C₈	D₁₃⋊C₈	1	8	yes	complemented
237	C₂×C₈	C₂²×#261	1	2	yes	—
238	C₂×C₈	C₂²×#261	1	2	yes	—
239	C₄²	—	13	2	no	—
240	C₄²	—	13	2	no	—
241	C₄²	—	13	2	no	—
242	C₄²	—	13	2	no	—
243	C₄²	—	13	2	no	—
244	C₄²	—	13	1	no	—
245	C₄²	—	13	1	no	—
246	C₄²	C₄×#261	1	2	yes	—
247	C₄²	C₂²×#261	1	1	yes	characteristic
248	C₄²	C₂²×#261	1	1	yes	characteristic
249	C₁₃	C₂×#1450	1	1	yes	characteristic, complemented, Sylow
250	C₂³	—	13	1	no	—
251	C₂³	—	13	4	no	—
252	C₂³	—	13	1	no	—
253	C₂³	—	26	4	no	—
254	C₂³	C₂×C₄×#261	1	1	yes	characteristic
255	C₂×C₄	—	2	4	no	—
256	C₂×C₄	—	13	4	no	—
257	C₂×C₄	—	13	2	no	—
258	C₂×C₄	—	13	1	no	—
259	C₂×C₄	—	13	1	no	—
260	C₂×C₄	—	13	4	no	—
261	C₂×C₄	—	13	4	no	—
262	C₂×C₄	—	13	8	no	—
263	C₂×C₄	—	13	4	no	—
264	C₂×C₄	—	13	4	no	—
265	C₂×C₄	—	13	2	no	—
266	C₂×C₄	—	26	4	no	—
267	C₂×C₄	—	26	4	no	—
268	C₂×C₄	—	26	4	no	—
269	C₂×C₄	—	26	4	no	—
270	C₂×C₄	C₂×D₁₃⋊C₈	1	4	yes	—
271	C₂×C₄	C₂×C₄×#261	1	2	yes	—
272	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
273	C₂×C₄	C₂×C₄×#261	1	2	yes	—
274	C₂×C₄	C₂³×#261	1	1	yes	characteristic
275	C₈	—	13	4	no	—
276	C₈	—	13	4	no	—
277	C₈	—	26	16	no	—
278	C₈	C₂×D₁₃⋊C₈	1	4	yes	—
279	C₈	C₂×D₁₃⋊C₈	1	4	yes	—
280	C₂²	—	2	2	no	—
281	C₂²	—	13	2	no	—
282	C₂²	—	13	4	no	—
283	C₂²	—	13	2	no	—
284	C₂²	—	26	8	no	—
285	C₂²	—	26	2	no	—
286	C₂²	C₄×D₁₃⋊C₈	1	2	yes	—
287	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
288	C₄	—	2	2	no	—
289	C₄	—	13	2	no	—
290	C₄	—	13	2	no	—
291	C₄	—	13	4	no	—
292	C₄	—	26	2	no	—
293	C₄	C₄×D₁₃⋊C₈	1	2	yes	—
294	C₄	#11719089	1	4	yes	—
295	C₄	C₂²×D₁₃⋊C₈	1	2	yes	—
296	C₂	—	2	2	no	—
297	C₂	—	13	4	no	—
298	C₂	—	26	2	no	—
299	C₂	C₂×C₄×D₁₃⋊C₈	1	1	yes	characteristic
300	C₂	C₂×#11719089	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×#261
commutator	C₂×C₁₃	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂²×C₄²
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂×#1450
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13130040	C₂	semidirect
3. #13130039	C₂	semidirect
4. #13130030	C₂	semidirect
5. C₈×D₁₃⋊C₈	C₂	semidirect
25. #11718251	C₂²	semidirect
26. C₈×#1057	C₂²	semidirect
35. C₂×C₈×D₁₃	C₈	semidirect
80. C₂×C₈×C₁₃	C₂×C₈	semidirect
93. C₂×#1055	C₂×C₈	semidirect
98. C₈×D₁₃	C₂×C₈	semidirect
99. C₈×D₁₃	C₂×C₈	semidirect
211. D₁₃	#1450	semidirect
236. C₂×C₈	D₁₃⋊C₈	semidirect
249. C₁₃	C₂×#1450	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#431	2
#13130040	2
#13130039	2
#13130030	2
C₈×D₁₃⋊C₈	2
C₂×C₄×C₈×D₁₃	2
C₂×#1450	13