Subgroups — Dic₁₃×#430 #15861028

Order 3328.

1034 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	C₂×#11718786	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×Dic₁₃	C₂	1	2	yes	maximal
3	C₂×M₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	#13114744	C₂	1	4	yes	maximal, complemented
5	#108×Dic₁₃	C₂	1	4	yes	maximal, complemented
6	#13114562	C₂	1	2	yes	maximal
7	C₂×C₁₃×#430	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
11	C₂²×#6099	C₂²	1	2	yes	—
12	C₂²×#6099	C₂²	1	1	yes	characteristic
13	C₁₃×#430	C₄	1	8	yes	complemented
14	C₂×C₁₃×#108	C₂²	1	4	yes	—
15	#11718786	C₄	1	8	yes	complemented
16	M₁₆×Dic₁₃	—	2	2	no	—
17	M₁₆×Dic₁₃	—	2	2	no	—
18	M₁₆×Dic₁₃	C₄	1	8	yes	—
19	M₁₆×Dic₁₃	C₂²	1	4	yes	—
20	M₁₆×Dic₁₃	C₂²	1	4	yes	—
21	C₂×#88059	C₂²	1	4	yes	—
22	C₂×#88055	—	2	2	no	—
23	C₂×#88055	C₂²	1	2	yes	—
24	C₂×C₈×Dic₁₃	—	2	2	no	—
25	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
26	#11718150	C₂²	1	8	yes	—
27	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
28	C₂³×Dic₁₃	Q₈	1	2	yes	—
29	C₂×C₁₃×M₁₆	—	2	2	no	—
30	C₂×C₁₃×M₁₆	—	2	4	no	—
31	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
32	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
33	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
34	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
35	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
36	C₂²×C₈×C₁₃	—	2	2	no	—
37	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
38	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	—
39	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
40	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
41	C₂×C₄×Dic₁₃	Q₈	1	2	yes	—
42	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
43	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
44	C₂×#6099	—	2	2	no	—
45	C₂×#6099	—	2	2	no	—
46	C₂×#6099	—	2	4	no	—
47	C₂×#6099	—	2	2	no	—
48	C₂×#6099	C₂×C₄	1	8	yes	—
49	C₂×#6099	C₂×C₄	1	4	yes	—
50	C₂×#6099	C₂³	1	4	yes	—
51	C₂²×#1055	—	2	2	no	—
52	C₂²×#1055	C₂³	1	2	yes	—
53	C₁₃×#108	C₂×C₄	1	16	yes	complemented
54	#88059	C₂×C₄	1	16	yes	complemented
55	#88055	—	2	4	no	—
56	#88055	—	2	4	no	—
57	#88055	C₂×C₄	1	8	yes	—
58	C₈×Dic₁₃	—	2	4	no	—
59	C₈×Dic₁₃	—	2	4	no	—
60	C₈×Dic₁₃	C₂×C₄	1	8	yes	—
61	C₄×#430	—	13	1	no	maximal, Sylow
62	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
63	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
64	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
65	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
66	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
67	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	#41	1	2	yes	—
69	C₂²×C₄×C₁₃	#41	1	2	yes	—
70	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
71	C₂²×Dic₁₃	—	4	4	no	—
72	C₂²×Dic₁₃	C₄⋊C₄	1	4	yes	—
73	C₂²×Dic₁₃	C₄⋊C₄	1	4	yes	—
74	C₂²×Dic₁₃	C₂×Q₈	1	2	yes	—
75	C₂²×Dic₁₃	C₂×Q₈	1	2	yes	—
76	C₁₃×M₁₆	—	2	8	no	—
77	C₁₃×M₁₆	—	2	4	no	—
78	C₁₃×M₁₆	C₄²	1	16	yes	—
79	C₁₃×M₁₆	C₂²×C₄	1	8	yes	—
80	C₂×C₈×C₁₃	—	2	8	no	—
81	C₂×C₈×C₁₃	—	2	4	no	—
82	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
83	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
84	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
85	C₄×Dic₁₃	C₄⋊C₄	1	4	yes	—
86	C₄×Dic₁₃	C₄⋊C₄	1	4	yes	—
87	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
88	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
89	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
90	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
91	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
92	#6099	—	2	8	no	—
93	#6099	—	2	8	no	—
94	#6099	—	2	4	no	—
95	#6099	C₂²×C₄	1	8	yes	—
96	C₂×#1055	—	2	8	no	—
97	C₂×#1055	—	2	4	no	—
98	C₂×#1055	—	2	2	no	—
99	C₂×#1055	—	2	2	no	—
100	C₂×#1055	C₂²×C₄	1	4	yes	—
101	C₂×#430	—	13	1	no	—
102	C₂×#430	D₁₃	1	1	yes	characteristic
103	C₂×C₄×M₁₆	—	13	1	no	—
104	C₂×C₄×M₁₆	—	13	2	no	—
105	#1778	—	13	4	no	—
106	C₄×#108	—	13	4	no	—
107	#1738	—	13	2	no	—
108	C₂³×C₁₃	—	4	2	no	—
109	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
110	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
111	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
112	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
113	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
114	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
115	C₂×C₄×C₁₃	#117	1	4	yes	—
116	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
117	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
118	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
119	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
120	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
123	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
124	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
125	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
126	C₂×Dic₁₃	—	2	8	no	—
127	C₂×Dic₁₃	—	2	4	no	—
128	C₂×Dic₁₃	—	4	4	no	—
129	C₂×Dic₁₃	—	4	2	no	—
130	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
131	C₂×Dic₁₃	C₂×C₄⋊C₄	1	4	yes	—
132	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
133	C₈×C₁₃	—	2	8	no	—
134	C₈×C₁₃	C₂×C₄²	1	8	yes	—
135	#1055	—	2	4	no	—
136	#1055	—	2	8	no	—
137	C₂²×M₁₆	—	13	1	no	—
138	C₂²×M₁₆	—	13	2	no	—
139	C₂²×M₁₆	C₂×D₁₃	1	2	yes	—
140	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
141	C₂²×C₄²	—	13	1	no	—
142	#430	—	13	8	no	—
143	#430	Dic₁₃	1	8	yes	direct product factor
144	C₂×#108	—	13	4	no	—
145	C₂×#108	C₂×D₁₃	1	4	yes	—
146	C₄×M₁₆	—	13	8	no	—
147	C₄×M₁₆	—	13	4	no	—
148	C₄×M₁₆	—	13	4	no	—
149	C₄×M₁₆	—	26	2	no	—
150	C₄×M₁₆	—	26	2	no	—
151	C₂×#97	—	13	2	no	—
152	C₂×#97	—	26	2	no	—
153	C₂×C₄×C₈	—	13	2	no	—
154	C₂×C₄×C₈	—	26	2	no	—
155	#341	—	13	8	no	—
156	C₂²×C₁₃	—	2	4	no	—
157	C₂²×C₁₃	—	2	2	no	—
158	C₂²×C₁₃	—	4	2	no	—
159	C₂²×C₁₃	—	4	2	no	—
160	C₂²×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
161	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
162	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
163	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
164	C₄×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
165	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
166	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
167	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
168	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
169	Dic₁₃	—	2	4	no	—
170	Dic₁₃	—	2	2	no	—
171	Dic₁₃	#430	1	4	yes	direct product factor
172	C₂³×C₄	—	13	2	no	—
173	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
174	C₂×M₁₆	—	2	2	no	—
175	C₂×M₁₆	—	2	4	no	—
176	C₂×M₁₆	—	13	4	no	—
177	C₂×M₁₆	—	13	8	no	—
178	C₂×M₁₆	—	13	4	no	—
179	C₂×M₁₆	—	26	2	no	—
180	C₂×M₁₆	—	26	2	no	—
181	C₂×M₁₆	—	26	4	no	—
182	C₂×M₁₆	—	26	2	no	—
183	C₂×M₁₆	C₄×D₁₃	1	4	yes	—
184	C₂×M₁₆	C₄×D₁₃	1	4	yes	—
185	C₂×M₁₆	C₂×Dic₁₃	1	8	yes	—
186	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
187	C₂×M₁₆	C₂²×D₁₃	1	4	yes	—
188	C₂²×C₈	—	2	2	no	—
189	C₂²×C₈	—	13	2	no	—
190	C₂²×C₈	—	26	2	no	—
191	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
192	C₂×C₄²	—	13	4	no	—
193	C₂×C₄²	—	13	2	no	—
194	C₂×C₄²	—	13	2	no	—
195	C₂×C₄²	—	13	2	no	—
196	C₂×C₄²	—	13	1	no	—
197	C₂×C₄²	—	13	1	no	—
198	#108	—	13	16	no	—
199	#108	C₂×Dic₁₃	1	16	yes	complemented
200	#97	—	13	8	no	—
201	#97	—	26	4	no	—
202	#97	—	26	4	no	—
203	C₄×C₈	—	13	8	no	—
204	C₄×C₈	—	26	4	no	—
205	C₄×C₈	—	26	4	no	—
206	C₂×C₁₃	—	2	1	no	—
207	C₂×C₁₃	—	2	1	no	—
208	C₂×C₁₃	—	2	4	no	—
209	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₁₃	C₂×#430	1	2	yes	—
211	C₂⁴	Q₈×D₁₃	1	1	yes	characteristic
212	C₂²×C₄	—	13	4	no	—
213	C₂²×C₄	—	13	2	no	—
214	C₂²×C₄	—	13	4	no	—
215	C₂²×C₄	—	13	2	no	—
216	C₂²×C₄	—	52	4	no	—
217	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
218	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
219	C₂²×C₄	D₄×D₁₃	1	2	yes	—
220	C₂²×C₄	#6129	1	2	yes	—
221	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
222	C₂²×C₄	#6131	1	2	yes	—
223	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
224	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
225	M₁₆	—	2	8	no	—
226	M₁₆	—	2	4	no	—
227	M₁₆	—	13	8	no	—
228	M₁₆	—	26	8	no	—
229	M₁₆	—	26	8	no	—
230	M₁₆	—	26	4	no	—
231	M₁₆	C₄×Dic₁₃	1	16	yes	—
232	M₁₆	C₂²×Dic₁₃	1	8	yes	—
233	C₂×C₈	—	2	8	no	—
234	C₂×C₈	—	2	4	no	—
235	C₂×C₈	—	13	4	no	—
236	C₂×C₈	—	26	8	no	—
237	C₂×C₈	—	26	4	no	—
238	C₂×C₈	—	26	2	no	—
239	C₂×C₈	—	26	2	no	—
240	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
241	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
242	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
243	C₄²	—	13	4	no	—
244	C₄²	—	13	4	no	—
245	C₄²	—	13	2	no	—
246	C₄²	—	13	2	no	—
247	C₄²	—	13	1	no	—
248	C₄²	—	13	2	no	—
249	C₄²	—	13	1	no	—
250	C₁₃	C₄×#430	1	1	yes	characteristic, complemented, Sylow
251	C₂³	—	4	2	no	—
252	C₂³	#88141	1	2	yes	—
253	C₂³	C₄⋊C₄×D₁₃	1	2	yes	—
254	C₂³	Q₈×Dic₁₃	1	2	yes	—
255	C₂³	C₂×Q₈×D₁₃	1	1	yes	characteristic
256	C₂×C₄	—	13	2	no	—
257	C₂×C₄	—	13	2	no	—
258	C₂×C₄	—	13	4	no	—
259	C₂×C₄	—	26	8	no	—
260	C₂×C₄	—	26	4	no	—
261	C₂×C₄	—	52	4	no	—
262	C₂×C₄	—	52	2	no	—
263	C₂×C₄	#88141	1	2	yes	—
264	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
265	C₂×C₄	#88146	1	4	yes	—
266	C₂×C₄	#88147	1	4	yes	—
267	C₂×C₄	C₂×C₄×Dic₁₃	1	4	yes	—
268	C₂×C₄	D₄×Dic₁₃	1	4	yes	—
269	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
270	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
271	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
272	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
273	C₂×C₄	C₂×#6129	1	1	yes	characteristic
274	C₂×C₄	C₂×#6131	1	1	yes	characteristic
275	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
276	C₈	—	2	8	no	—
277	C₈	—	26	4	no	—
278	C₈	—	26	8	no	—
279	C₈	C₂×C₄×Dic₁₃	1	8	yes	—
280	C₂²	—	2	4	no	—
281	C₂²	—	2	2	no	—
282	C₂²	—	4	2	no	—
283	C₂²	—	4	2	no	—
284	C₂²	C₄⋊C₄×Dic₁₃	1	4	yes	—
285	C₂²	C₂×#88141	1	1	yes	characteristic
286	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
287	C₂²	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
288	C₄	—	13	4	no	—
289	C₄	—	26	4	no	—
290	C₄	—	26	2	no	—
291	C₄	C₄⋊C₄×Dic₁₃	1	4	yes	—
292	C₄	C₂×#88146	1	1	yes	characteristic
293	C₄	C₂×#88147	1	1	yes	characteristic
294	C₄	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
295	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
296	C₂	—	2	1	no	—
297	C₂	—	2	1	no	—
298	C₂	—	2	4	no	—
299	C₂	C₂×C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
300	C₂	D₁₃×#430	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#430	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#430	D₁₃
hypocenter	C₁₃	C₄×#430
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#430

Complements

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

N	H ≅ G/N	type
4. #13114744	C₂	semidirect
5. #108×Dic₁₃	C₂	semidirect
13. C₁₃×#430	C₄	semidirect
15. #11718786	C₄	semidirect
53. C₁₃×#108	C₂×C₄	semidirect
54. #88059	C₂×C₄	semidirect
143. #430	Dic₁₃	direct (N × H)
171. Dic₁₃	#430	direct (N × H)
199. #108	C₂×Dic₁₃	semidirect
250. C₁₃	C₄×#430	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718786	2
C₂×M₁₆×Dic₁₃	2
#13114744	2
#108×Dic₁₃	2
#13114562	2
C₂×C₁₃×#430	2
C₄×#430	13

Subgroups — Dic13×#430 #15861028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₃×#430 #15861028