Subgroups — C₁₃×#10442 #15696781

Order 3328.

460 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1801	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1571	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1545	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1545	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1301	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×SD₁₆	—	2	1	no	—
9	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#460	—	2	2	no	—
12	C₁₃×#460	—	2	2	no	—
13	C₁₃×#431	C₂²	1	1	yes	characteristic
14	C₁₃×#431	C₂²	1	1	yes	characteristic
15	C₁₃×#423	C₂²	1	1	yes	characteristic
16	C₁₃×#423	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#102	—	2	1	no	—
19	C₂×C₁₃×#101	—	2	1	no	—
20	C₁₃×#343	—	2	1	no	—
21	C₁₃×#335	—	2	2	no	—
22	C₁₃×#331	—	2	2	no	—
23	C₁₃×#331	—	2	2	no	—
24	C₁₃×Q₈⋊C₈	—	2	2	no	—
25	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
26	C₂²×D₄×C₁₃	—	2	1	no	—
27	C₂²×D₄×C₁₃	—	2	1	no	—
28	C₂²×D₄×C₁₃	—	2	1	no	—
29	C₂×C₁₃×SD₁₆	—	2	4	no	—
30	C₂×C₁₃×SD₁₆	—	4	2	no	—
31	C₂×C₁₃×SD₁₆	—	4	2	no	—
32	C₂×C₁₃×M₁₆	—	2	1	no	—
33	C₂×C₁₃×M₁₆	—	2	1	no	—
34	C₂²×C₈×C₁₃	—	2	1	no	—
35	C₁₃×#127	—	2	1	no	—
36	C₁₃×#127	—	2	1	no	—
37	C₁₃×#127	—	2	1	no	—
38	C₁₃×#127	D₄	1	2	yes	—
39	C₄×Q₈×C₁₃	—	2	1	no	—
40	C₄×Q₈×C₁₃	—	2	1	no	—
41	C₄×Q₈×C₁₃	—	2	1	no	—
42	C₄×Q₈×C₁₃	—	2	1	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
44	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	—	2	1	no	—
46	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
47	C₁₃×C₄⋊C₈	—	2	1	no	—
48	C₁₃×C₄⋊C₈	—	2	1	no	—
49	C₁₃×C₄⋊C₈	—	2	1	no	—
50	C₁₃×C₄⋊C₈	—	2	1	no	—
51	C₁₃×C₄⋊C₈	—	2	1	no	—
52	C₁₃×C₄⋊C₈	—	2	1	no	—
53	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
54	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
55	C₁₃×#102	—	2	4	no	—
56	C₁₃×#101	—	4	2	no	—
57	C₁₃×C₂²⋊C₈	—	2	1	no	—
58	C₁₃×C₂²⋊C₈	—	2	1	no	—
59	C₄×C₈×C₁₃	—	2	1	no	—
60	C₄×C₈×C₁₃	—	2	1	no	—
61	#10442	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂⁴×C₁₃	—	4	1	no	—
63	C₂×Q₈×C₁₃	—	2	1	no	—
64	C₂×Q₈×C₁₃	—	2	1	no	—
65	C₂×Q₈×C₁₃	—	2	1	no	—
66	C₂×Q₈×C₁₃	—	2	1	no	—
67	C₂×Q₈×C₁₃	—	2	1	no	—
68	C₂×Q₈×C₁₃	D₈	1	2	yes	—
69	C₂×D₄×C₁₃	—	2	2	no	—
70	C₂×D₄×C₁₃	—	2	2	no	—
71	C₂×D₄×C₁₃	—	2	2	no	—
72	C₂×D₄×C₁₃	—	4	1	no	—
73	C₂×D₄×C₁₃	—	4	1	no	—
74	C₂×D₄×C₁₃	—	4	1	no	—
75	C₂×D₄×C₁₃	—	4	1	no	—
76	C₂×D₄×C₁₃	—	4	1	no	—
77	C₂×D₄×C₁₃	—	4	1	no	—
78	C₂×D₄×C₁₃	—	4	1	no	—
79	C₂×D₄×C₁₃	—	8	2	no	—
80	C₂×D₄×C₁₃	—	8	2	no	—
81	C₂²×C₄×C₁₃	—	2	1	no	—
82	C₂²×C₄×C₁₃	—	2	1	no	—
83	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
86	C₁₃×SD₁₆	—	4	8	no	—
87	C₁₃×M₁₆	—	4	1	no	—
88	C₁₃×M₁₆	—	4	1	no	—
89	C₁₃×M₁₆	—	4	1	no	—
90	C₁₃×M₁₆	—	4	1	no	—
91	C₂×C₈×C₁₃	—	2	2	no	—
92	C₂×C₈×C₁₃	—	2	2	no	—
93	C₂×C₈×C₁₃	—	4	1	no	—
94	C₂×C₈×C₁₃	—	4	1	no	—
95	C₂×C₈×C₁₃	—	4	1	no	—
96	C₂×C₈×C₁₃	—	4	1	no	—
97	C₂×C₈×C₁₃	—	4	1	no	—
98	C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₁₃×C₄⋊C₄	—	4	1	no	—
101	C₁₃×C₄⋊C₄	—	4	1	no	—
102	C₄²×C₁₃	—	4	1	no	—
103	C₄²×C₁₃	—	4	1	no	—
104	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₁₃	#41	1	1	yes	characteristic
108	C₂×#460	C₂×C₁₃	1	1	yes	characteristic
109	#1801	C₂×C₁₃	1	1	yes	characteristic, complemented
110	#1571	C₂×C₁₃	1	1	yes	characteristic, complemented
111	#1545	C₂×C₁₃	1	1	yes	characteristic
112	#1545	C₂×C₁₃	1	1	yes	characteristic
113	#1479	C₂×C₁₃	1	1	yes	characteristic, complemented
114	#1301	C₂×C₁₃	1	1	yes	characteristic, complemented
115	C₂³×C₁₃	—	4	2	no	—
116	C₂³×C₁₃	—	8	2	no	—
117	C₂³×C₁₃	—	8	2	no	—
118	C₂³×C₁₃	—	8	1	no	—
119	C₂³×C₁₃	—	8	1	no	—
120	C₂³×C₁₃	#123	1	1	yes	characteristic
121	Q₈×C₁₃	—	2	2	no	—
122	Q₈×C₁₃	—	2	2	no	—
123	Q₈×C₁₃	—	4	1	no	—
124	Q₈×C₁₃	—	4	1	no	—
125	D₄×C₁₃	—	4	2	no	—
126	D₄×C₁₃	—	4	2	no	—
127	D₄×C₁₃	—	8	2	no	—
128	D₄×C₁₃	—	8	2	no	—
129	D₄×C₁₃	—	8	2	no	—
130	D₄×C₁₃	—	8	1	no	—
131	D₄×C₁₃	—	8	1	no	—
132	D₄×C₁₃	—	8	2	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	4	1	no	—
136	C₂×C₄×C₁₃	—	4	1	no	—
137	C₂×C₄×C₁₃	—	4	1	no	—
138	C₂×C₄×C₁₃	—	4	1	no	—
139	C₂×C₄×C₁₃	—	8	1	no	—
140	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
141	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
142	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
143	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
144	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
145	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
148	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
150	C₈×C₁₃	—	4	2	no	—
151	C₈×C₁₃	—	4	2	no	—
152	C₈×C₁₃	—	8	1	no	—
153	C₈×C₁₃	—	8	1	no	—
154	C₈×C₁₃	—	8	1	no	—
155	C₂²×SD₁₆	—	2	1	no	—
156	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
157	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
158	#460	—	2	2	no	—
159	#460	—	2	2	no	—
160	#431	C₂²×C₁₃	1	1	yes	characteristic
161	#431	C₂²×C₁₃	1	1	yes	characteristic
162	#423	C₂²×C₁₃	1	1	yes	characteristic
163	#423	C₂²×C₁₃	1	1	yes	characteristic
164	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
165	C₂×#102	—	2	1	no	—
166	C₂×#101	—	2	1	no	—
167	#343	—	2	1	no	—
168	#335	—	2	2	no	—
169	#331	—	2	2	no	—
170	#331	—	2	2	no	—
171	Q₈⋊C₈	—	2	2	no	—
172	C₂²×C₁₃	—	2	1	no	—
173	C₂²×C₁₃	—	2	1	no	—
174	C₂²×C₁₃	—	8	2	no	—
175	C₂²×C₁₃	—	8	2	no	—
176	C₂²×C₁₃	—	8	2	no	—
177	C₂²×C₁₃	—	16	2	no	—
178	C₂²×C₁₃	—	16	2	no	—
179	C₂²×C₁₃	#394	1	1	yes	characteristic
180	C₂²×C₁₃	#480	1	1	yes	characteristic
181	C₂²×C₁₃	#482	1	1	yes	characteristic
182	C₄×C₁₃	—	2	1	no	—
183	C₄×C₁₃	—	2	1	no	—
184	C₄×C₁₃	—	2	1	no	—
185	C₄×C₁₃	—	4	2	no	—
186	C₄×C₁₃	—	8	1	no	—
187	C₄×C₁₃	#447	1	1	yes	characteristic
188	C₄×C₁₃	#452	1	1	yes	characteristic
189	C₄×C₁₃	#466	1	1	yes	characteristic
190	C₄×C₁₃	#468	1	1	yes	characteristic
191	C₄×C₁₃	#471	1	2	yes	—
192	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
193	C₂²×D₄	—	2	1	no	—
194	C₂²×D₄	—	2	1	no	—
195	C₂²×D₄	—	2	1	no	—
196	C₂×SD₁₆	—	2	4	no	—
197	C₂×SD₁₆	—	4	2	no	—
198	C₂×SD₁₆	—	4	2	no	—
199	C₂×M₁₆	—	2	1	no	—
200	C₂×M₁₆	—	2	1	no	—
201	C₂²×C₈	—	2	1	no	—
202	#127	—	2	1	no	—
203	#127	—	2	1	no	—
204	#127	—	2	1	no	—
205	#127	D₄×C₁₃	1	2	yes	—
206	C₄×Q₈	—	2	1	no	—
207	C₄×Q₈	—	2	1	no	—
208	C₄×Q₈	—	2	1	no	—
209	C₄×Q₈	—	2	1	no	—
210	C₂×C₄⋊C₄	—	2	1	no	—
211	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
212	C₂×C₄²	—	2	1	no	—
213	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
214	C₄⋊C₈	—	2	1	no	—
215	C₄⋊C₈	—	2	1	no	—
216	C₄⋊C₈	—	2	1	no	—
217	C₄⋊C₈	—	2	1	no	—
218	C₄⋊C₈	—	2	1	no	—
219	C₄⋊C₈	—	2	1	no	—
220	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
221	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
222	#102	—	2	4	no	—
223	#101	—	4	2	no	—
224	C₂²⋊C₈	—	2	1	no	—
225	C₂²⋊C₈	—	2	1	no	—
226	C₄×C₈	—	2	1	no	—
227	C₄×C₈	—	2	1	no	—
228	C₂×C₁₃	—	2	1	no	—
229	C₂×C₁₃	—	2	1	no	—
230	C₂×C₁₃	—	16	2	no	—
231	C₂×C₁₃	#2033	1	1	yes	characteristic
232	C₂×C₁₃	#2046	1	1	yes	characteristic
233	C₂×C₁₃	#2048	1	1	yes	characteristic
234	C₂⁴	—	4	1	no	—
235	C₂×Q₈	—	2	1	no	—
236	C₂×Q₈	—	2	1	no	—
237	C₂×Q₈	—	2	1	no	—
238	C₂×Q₈	—	2	1	no	—
239	C₂×Q₈	—	2	1	no	—
240	C₂×Q₈	C₁₃×D₈	1	2	yes	—
241	C₂×D₄	—	2	2	no	—
242	C₂×D₄	—	2	2	no	—
243	C₂×D₄	—	2	2	no	—
244	C₂×D₄	—	4	1	no	—
245	C₂×D₄	—	4	1	no	—
246	C₂×D₄	—	4	1	no	—
247	C₂×D₄	—	4	1	no	—
248	C₂×D₄	—	4	1	no	—
249	C₂×D₄	—	4	1	no	—
250	C₂×D₄	—	4	1	no	—
251	C₂×D₄	—	8	2	no	—
252	C₂×D₄	—	8	2	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
256	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
257	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
258	SD₁₆	—	4	8	no	—
259	M₁₆	—	4	1	no	—
260	M₁₆	—	4	1	no	—
261	M₁₆	—	4	1	no	—
262	M₁₆	—	4	1	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	4	1	no	—
266	C₂×C₈	—	4	1	no	—
267	C₂×C₈	—	4	1	no	—
268	C₂×C₈	—	4	1	no	—
269	C₂×C₈	—	4	1	no	—
270	C₄⋊C₄	—	2	1	no	—
271	C₄⋊C₄	—	2	1	no	—
272	C₄⋊C₄	—	4	1	no	—
273	C₄⋊C₄	—	4	1	no	—
274	C₄²	—	4	1	no	—
275	C₄²	—	4	1	no	—
276	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
277	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
278	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
279	C₄²	C₁₃×#41	1	1	yes	characteristic
280	C₁₃	#10442	1	1	yes	characteristic, direct product factor, Sylow
281	C₂³	—	4	2	no	—
282	C₂³	—	8	2	no	—
283	C₂³	—	8	2	no	—
284	C₂³	—	8	1	no	—
285	C₂³	—	8	1	no	—
286	C₂³	C₁₃×#123	1	1	yes	characteristic
287	Q₈	—	2	2	no	—
288	Q₈	—	2	2	no	—
289	Q₈	—	4	1	no	—
290	Q₈	—	4	1	no	—
291	D₄	—	4	2	no	—
292	D₄	—	4	2	no	—
293	D₄	—	8	2	no	—
294	D₄	—	8	2	no	—
295	D₄	—	8	2	no	—
296	D₄	—	8	1	no	—
297	D₄	—	8	1	no	—
298	D₄	—	8	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	4	1	no	—
302	C₂×C₄	—	4	1	no	—
303	C₂×C₄	—	4	1	no	—
304	C₂×C₄	—	4	1	no	—
305	C₂×C₄	—	8	1	no	—
306	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
307	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
308	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
309	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
310	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
311	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
312	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
313	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
314	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
315	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
316	C₈	—	4	2	no	—
317	C₈	—	4	2	no	—
318	C₈	—	8	1	no	—
319	C₈	—	8	1	no	—
320	C₈	—	8	1	no	—
321	C₂²	—	2	1	no	—
322	C₂²	—	2	1	no	—
323	C₂²	—	8	2	no	—
324	C₂²	—	8	2	no	—
325	C₂²	—	8	2	no	—
326	C₂²	—	16	2	no	—
327	C₂²	—	16	2	no	—
328	C₂²	C₁₃×#394	1	1	yes	characteristic
329	C₂²	C₁₃×#480	1	1	yes	characteristic
330	C₂²	C₁₃×#482	1	1	yes	characteristic
331	C₄	—	2	1	no	—
332	C₄	—	2	1	no	—
333	C₄	—	2	1	no	—
334	C₄	—	4	2	no	—
335	C₄	—	8	1	no	—
336	C₄	C₁₃×#447	1	1	yes	characteristic
337	C₄	C₁₃×#452	1	1	yes	characteristic
338	C₄	C₁₃×#466	1	1	yes	characteristic
339	C₄	C₁₃×#468	1	1	yes	characteristic
340	C₄	C₁₃×#471	1	2	yes	—
341	C₂	—	2	1	no	—
342	C₂	—	2	1	no	—
343	C₂	—	16	2	no	—
344	C₂	C₁₃×#2033	1	1	yes	characteristic
345	C₂	C₁₃×#2046	1	1	yes	characteristic
346	C₂	C₁₃×#2048	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#1801	C₂	semidirect
3. C₁₃×#1571	C₂	semidirect
6. C₁₃×#1479	C₂	semidirect
7. C₁₃×#1301	C₂	semidirect
61. #10442	C₁₃	direct (N × H)
109. #1801	C₂×C₁₃	semidirect
110. #1571	C₂×C₁₃	semidirect
113. #1479	C₂×C₁₃	semidirect
114. #1301	C₂×C₁₃	semidirect
280. C₁₃	#10442	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#460	2
C₁₃×#1801	2
C₁₃×#1571	2
C₁₃×#1545	2
C₁₃×#1479	2
C₁₃×#1301	2
#10442	13

Subgroups — C13×#10442 #15696781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10442 #15696781