Subgroups — D₁₃⋊#2151 #16806996

Order 3328.

734 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×D₁₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#13131173	C₂	1	2	yes	maximal, complemented
4	#13131172	C₂	1	4	yes	maximal, complemented
5	#13131171	C₂	1	2	yes	maximal, complemented
6	D₁₃⋊(C₄⋊C₁₆)	C₂	1	4	yes	maximal, complemented
7	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
8	C₂×M₁₆×D₁₃	C₄	1	1	yes	characteristic
9	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	D₁₃×#117	C₄	1	1	yes	characteristic
11	C₂×#88106	C₂²	1	2	yes	—
12	C₂²×#6092	C₂²	1	2	yes	—
13	D₁₃⋊M₃₂	—	2	4	no	—
14	C₂×#88098	C₂²	1	2	yes	—
15	C₂×D₁₃⋊C₁₆	—	2	4	no	—
16	C₂×D₁₃⋊C₁₆	C₂²	1	2	yes	—
17	C₂×D₁₃⋊C₁₆	C₂²	1	2	yes	—
18	C₂×D₁₃⋊C₁₆	C₂²	1	2	yes	—
19	C₁₃×#405	C₄	1	1	yes	characteristic
20	#11718783	C₂²	1	1	yes	characteristic
21	#11718762	C₄	1	1	yes	characteristic
22	#11718658	C₂²	1	1	yes	characteristic
23	#11718369	C₂²	1	2	yes	—
24	D₁₃×#97	C₄	1	2	yes	—
25	#11718350	C₄	1	2	yes	—
26	C₄×C₈×D₁₃	C₂²	1	2	yes	—
27	#11718260	C₂²	1	8	yes	complemented
28	C₄⋊#6092	C₂²	1	8	yes	complemented
29	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
33	#88180	C₂×C₄	1	1	yes	characteristic
34	C₂×#6099	C₂×C₄	1	1	yes	characteristic
35	C₂²×#1055	C₂³	1	1	yes	characteristic
36	M₁₆×D₁₃	—	2	4	no	—
37	C₂×#6094	C₂×C₄	1	2	yes	—
38	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
39	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₈×D₁₃	D₄	1	4	yes	—
42	C₂×C₈×D₁₃	Q₈	1	4	yes	—
43	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
44	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
45	#88146	C₈	1	2	yes	—
46	C₄⋊C₄×D₁₃	C₈	1	2	yes	—
47	C₂²⋊C₄×D₁₃	C₈	1	2	yes	—
48	#88131	C₈	1	2	yes	—
49	#88126	C₂×C₄	1	2	yes	—
50	C₄²×D₁₃	C₂×C₄	1	2	yes	—
51	#88106	—	2	4	no	—
52	C₂×#6092	—	2	4	no	—
53	C₂×#6092	C₂³	1	4	yes	—
54	C₂×#6092	C₂³	1	4	yes	—
55	#88098	—	2	4	no	—
56	D₁₃⋊C₁₆	—	2	4	no	—
57	D₁₃⋊C₁₆	—	2	4	no	—
58	D₁₃⋊C₁₆	—	2	4	no	—
59	C₁₃×#97	C₂×C₄	1	2	yes	—
60	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
61	#88055	C₂×C₄	1	2	yes	—
62	#88055	C₂×C₄	1	2	yes	—
63	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
64	C₈×Dic₁₃	C₂³	1	2	yes	—
65	#88043	C₂×C₄	1	2	yes	—
66	C₄×#1055	C₂³	1	2	yes	—
67	C₂×#2151	—	13	1	no	maximal, Sylow
68	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
71	C₂×C₄×D₁₃	C₄⋊C₄	1	4	yes	—
72	C₂×C₄×D₁₃	C₂×C₈	1	4	yes	—
73	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
74	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
75	C₂×C₄×D₁₃	M₁₆	1	4	yes	—
76	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₁₃×M₁₆	—	2	2	no	—
79	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
80	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
81	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
84	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
85	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂²⋊Dic₁₃	C₂×C₈	1	2	yes	—
87	#6103	C₂×C₈	1	4	yes	—
88	C₄⋊Dic₁₃	C₂×C₈	1	2	yes	—
89	#6101	C₂×C₈	1	4	yes	—
90	C₄×Dic₁₃	C₂×C₈	1	4	yes	—
91	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
92	#6099	—	2	2	no	—
93	C₂×#1055	C₂²×C₄	1	2	yes	—
94	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
95	C₂×#1055	C₂×D₄	1	2	yes	—
96	C₂×#1055	C₂×Q₈	1	2	yes	—
97	C₂×#1055	C₂⁴	1	1	yes	characteristic
98	#6094	—	2	4	no	—
99	C₈×D₁₃	—	2	4	no	—
100	C₈×D₁₃	C₄⋊C₄	1	4	yes	—
101	C₈×D₁₃	C₄⋊C₄	1	4	yes	—
102	C₈×D₁₃	C₂×D₄	1	2	yes	—
103	C₈×D₁₃	C₂×D₄	1	2	yes	—
104	C₈×D₁₃	C₂×Q₈	1	2	yes	—
105	C₈×D₁₃	C₂×Q₈	1	2	yes	—
106	#6092	—	2	4	no	—
107	#6092	—	2	4	no	—
108	C₂²×M₃₂	—	13	1	no	—
109	C₂³×C₁₆	—	13	1	no	—
110	C₂×#405	—	13	1	no	—
111	#2151	—	13	2	no	—
112	#2151	—	13	4	no	—
113	#2151	—	13	2	no	—
114	C₂×C₄⋊C₁₆	—	13	4	no	—
115	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
116	C₂²×D₁₃	—	2	4	no	—
117	C₂²×D₁₃	C₄⋊C₈	1	4	yes	—
118	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
119	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
120	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
121	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
122	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
123	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
124	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
125	C₂×Dic₁₃	C₄⋊C₈	1	4	yes	—
126	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
127	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
128	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
129	C₄×D₁₃	—	2	8	no	—
130	C₄×D₁₃	C₄⋊C₈	1	4	yes	—
131	C₄×D₁₃	C₄⋊C₈	1	4	yes	—
132	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
133	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
134	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
135	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
136	C₈×C₁₃	—	2	2	no	—
137	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
138	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
139	#1055	—	2	2	no	—
140	#1055	C₂×C₄⋊C₄	1	2	yes	—
141	#1055	C₂²×D₄	1	1	yes	characteristic
142	#1055	C₂²×Q₈	1	1	yes	characteristic
143	C₂²×M₁₆	—	13	1	no	—
144	C₂³×C₈	—	13	1	no	—
145	C₂×#117	—	13	1	no	—
146	C₂×M₃₂	—	13	2	no	—
147	C₂×M₃₂	—	13	2	no	—
148	C₂×M₃₂	—	26	4	no	—
149	C₂²×C₁₆	—	13	2	no	—
150	C₂²×C₁₆	—	13	2	no	—
151	C₂²×C₁₆	—	13	2	no	—
152	C₂²×C₁₆	—	13	2	no	—
153	C₂²×C₁₆	—	26	4	no	—
154	#405	—	13	1	no	—
155	#405	—	13	1	no	—
156	#405	—	13	1	no	—
157	#405	—	13	2	no	—
158	#405	—	13	2	no	—
159	#405	#261	1	1	yes	characteristic
160	C₂×#97	—	13	2	no	—
161	C₂×C₄×C₈	—	13	2	no	—
162	C₄⋊C₁₆	—	13	8	no	—
163	C₄⋊C₁₆	—	13	8	no	—
164	C₂²×C₁₃	—	2	2	no	—
165	C₂²×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
166	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
167	C₂×D₁₃	—	2	2	no	—
168	C₂×D₁₃	—	2	8	no	—
169	C₂×D₁₃	C₂×C₄⋊C₈	1	2	yes	—
170	C₂×D₁₃	C₂×C₄⋊C₈	1	2	yes	—
171	C₂×D₁₃	#504	1	4	yes	—
172	C₄×C₁₃	—	2	4	no	—
173	C₄×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
174	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
175	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
176	Dic₁₃	—	2	4	no	—
177	Dic₁₃	C₂×C₄⋊C₈	1	2	yes	—
178	Dic₁₃	C₂×C₄⋊C₈	1	2	yes	—
179	C₂³×C₄	—	13	1	no	—
180	C₂×M₁₆	—	13	1	no	—
181	C₂×M₁₆	—	13	2	no	—
182	C₂×M₁₆	—	26	4	no	—
183	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
184	C₂²×C₈	—	13	1	no	—
185	C₂²×C₈	—	13	4	no	—
186	C₂²×C₈	—	13	4	no	—
187	C₂²×C₈	—	13	1	no	—
188	C₂²×C₈	—	13	1	no	—
189	C₂²×C₈	—	13	1	no	—
190	C₂²×C₈	—	13	1	no	—
191	C₂²×C₈	—	13	2	no	—
192	C₂²×C₈	C₂×#261	1	1	yes	characteristic
193	#117	—	13	1	no	—
194	#117	—	13	2	no	—
195	#117	—	13	2	no	—
196	#117	—	13	2	no	—
197	#117	C₂×#261	1	1	yes	characteristic
198	C₂×C₄⋊C₄	—	13	2	no	—
199	C₂×C₂²⋊C₄	—	13	2	no	—
200	C₂×C₄²	—	13	2	no	—
201	M₃₂	—	26	4	no	—
202	M₃₂	—	26	4	no	—
203	C₂×C₁₆	—	13	4	no	—
204	C₂×C₁₆	—	13	4	no	—
205	C₂×C₁₆	—	26	4	no	—
206	C₂×C₁₆	—	26	4	no	—
207	C₂×C₁₆	—	26	4	no	—
208	C₂×C₁₆	—	26	4	no	—
209	#97	—	13	2	no	—
210	#97	—	13	2	no	—
211	#97	—	13	2	no	—
212	#97	C₂×#261	1	2	yes	—
213	C₄×C₈	—	13	2	no	—
214	C₄×C₈	—	13	2	no	—
215	C₄×C₈	—	13	2	no	—
216	C₄×C₈	C₂×#261	1	2	yes	—
217	C₂×C₁₃	—	2	2	no	—
218	C₂×C₁₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
219	C₂×C₁₃	C₂×#504	1	2	yes	—
220	D₁₃	—	2	2	no	—
221	D₁₃	#2151	1	4	yes	complemented
222	C₂⁴	—	13	1	no	—
223	C₂²×C₄	—	13	1	no	—
224	C₂²×C₄	—	13	1	no	—
225	C₂²×C₄	—	13	1	no	—
226	C₂²×C₄	—	13	4	no	—
227	C₂²×C₄	—	13	4	no	—
228	C₂²×C₄	—	13	1	no	—
229	C₂²×C₄	—	13	1	no	—
230	C₂²×C₄	—	13	4	no	—
231	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
232	M₁₆	—	2	2	no	—
233	M₁₆	—	26	4	no	—
234	M₁₆	—	26	2	no	—
235	C₂×C₈	—	13	2	no	—
236	C₂×C₈	—	13	2	no	—
237	C₂×C₈	—	13	1	no	—
238	C₂×C₈	—	13	1	no	—
239	C₂×C₈	—	13	2	no	—
240	C₂×C₈	—	13	2	no	—
241	C₂×C₈	—	13	4	no	—
242	C₂×C₈	—	13	4	no	—
243	C₂×C₈	—	13	2	no	—
244	C₂×C₈	—	13	2	no	—
245	C₂×C₈	—	13	2	no	—
246	C₂×C₈	—	26	4	no	—
247	C₂×C₈	C₄⋊#261	1	4	yes	—
248	C₂×C₈	C₂²×#261	1	2	yes	—
249	C₂×C₈	C₂²×#261	1	1	yes	characteristic
250	C₂×C₈	C₂²×#261	1	1	yes	characteristic
251	C₄⋊C₄	—	13	4	no	—
252	C₄⋊C₄	—	13	2	no	—
253	C₄⋊C₄	D₁₃⋊C₈	1	2	yes	—
254	C₂²⋊C₄	—	13	2	no	—
255	C₂²⋊C₄	—	13	4	no	—
256	C₂²⋊C₄	D₁₃⋊C₈	1	2	yes	—
257	C₄²	—	13	4	no	—
258	C₄²	—	13	2	no	—
259	C₄²	C₂²×#261	1	2	yes	—
260	C₁₆	—	26	4	no	—
261	C₁₆	—	26	4	no	—
262	C₁₃	C₂×#2151	1	1	yes	characteristic, complemented, Sylow
263	C₂³	—	13	1	no	—
264	C₂³	—	13	4	no	—
265	C₂³	—	13	1	no	—
266	C₂³	—	26	4	no	—
267	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
268	C₂×C₄	—	13	4	no	—
269	C₂×C₄	—	13	1	no	—
270	C₂×C₄	—	13	1	no	—
271	C₂×C₄	—	13	4	no	—
272	C₂×C₄	—	13	4	no	—
273	C₂×C₄	—	13	2	no	—
274	C₂×C₄	—	13	2	no	—
275	C₂×C₄	—	13	2	no	—
276	C₂×C₄	—	13	2	no	—
277	C₂×C₄	—	13	4	no	—
278	C₂×C₄	—	26	8	no	—
279	C₂×C₄	C₂×D₁₃⋊C₈	1	4	yes	—
280	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
281	C₂×C₄	D₁₃⋊M₁₆	1	2	yes	—
282	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
283	C₂×C₄	C₂³×#261	1	1	yes	characteristic
284	C₈	—	2	2	no	—
285	C₈	—	13	1	no	—
286	C₈	—	13	2	no	—
287	C₈	—	13	1	no	—
288	C₈	—	26	2	no	—
289	C₈	C₂×C₄⋊#261	1	2	yes	—
290	C₈	C₂×C₄⋊#261	1	2	yes	—
291	C₂²	—	2	2	no	—
292	C₂²	—	13	4	no	—
293	C₂²	—	13	2	no	—
294	C₂²	—	13	2	no	—
295	C₂²	—	26	8	no	—
296	C₂²	—	26	2	no	—
297	C₂²	D₁₃⋊(C₄⋊C₈)	1	2	yes	—
298	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
299	C₄	—	2	4	no	—
300	C₄	—	13	2	no	—
301	C₄	—	13	2	no	—
302	C₄	—	26	4	no	—
303	C₄	D₁₃⋊(C₄⋊C₈)	1	2	yes	—
304	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
305	C₄	C₂²×C₄⋊#261	1	1	yes	characteristic
306	C₂	—	2	2	no	—
307	C₂	—	13	4	no	—
308	C₂	—	26	2	no	—
309	C₂	C₂×D₁₃⋊(C₄⋊C₈)	1	1	yes	characteristic
310	C₂	D₁₃⋊#504	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#405	C₄
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂×#1055	C₂⁴
hypercenter	#405	#261
hypocenter	C₁₃	C₂×#2151
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #13131173	C₂	semidirect
4. #13131172	C₂	semidirect
5. #13131171	C₂	semidirect
6. D₁₃⋊(C₄⋊C₁₆)	C₂	semidirect
27. #11718260	C₂²	semidirect
28. C₄⋊#6092	C₂²	semidirect
221. D₁₃	#2151	semidirect
262. C₁₃	C₂×#2151	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃⋊M₃₂	2
C₂²×D₁₃⋊C₁₆	2
#13131173	2
#13131172	2
#13131171	2
D₁₃⋊(C₄⋊C₁₆)	2
D₁₃×#405	2
C₂×#2151	13

Subgroups — D13⋊#2151 #16806996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊#2151 #16806996