Subgroups — C₁₃×#29133 #15715472

Order 3328.

754 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2647	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2328	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2101	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2041	C₂	1	2	yes	maximal
5	C₁₃×#1936	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1934	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1804	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1802	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
12	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₁₃×#102	C₂²	1	2	yes	—
14	C₂×C₁₃×#102	C₂²	1	2	yes	—
15	C₂×C₁₃×#102	C₂²	1	2	yes	—
16	C₂×C₁₃×#102	C₂²	1	2	yes	—
17	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#400	—	2	2	no	—
20	C₁₃×#398	—	2	2	no	—
21	C₁₃×#390	C₂²	1	2	yes	—
22	C₁₃×#389	C₂²	1	2	yes	—
23	C₁₃×#389	C₂²	1	2	yes	—
24	C₁₃×#386	—	2	2	no	—
25	C₁₃×#386	—	2	2	no	—
26	C₁₃×#384	C₂²	1	1	yes	characteristic
27	C₁₃×#382	C₂²	1	1	yes	characteristic
28	C₁₃×#382	C₂²	1	1	yes	characteristic
29	C₁₃×#376	C₂²	1	1	yes	characteristic
30	C₁₃×#340	C₂²	1	2	yes	—
31	C₁₃×#340	C₂²	1	2	yes	—
32	C₁₃×#340	C₂²	1	2	yes	—
33	C₁₃×#340	C₂²	1	2	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂²×D₄×C₁₃	—	2	1	no	—
36	C₂²×D₄×C₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃	—	2	2	no	—
39	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
41	C₁₃×#127	—	2	4	no	—
42	C₄×D₄×C₁₃	—	2	4	no	—
43	C₄×D₄×C₁₃	—	2	4	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
47	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
48	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
49	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
50	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
51	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
53	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×C₄⋊C₈	—	2	4	no	—
57	C₁₃×#102	—	2	4	no	—
58	C₁₃×#102	—	2	4	no	—
59	C₁₃×#102	—	4	2	no	—
60	C₁₃×#102	—	4	2	no	—
61	C₁₃×#97	—	4	1	no	—
62	C₄×C₈×C₁₃	—	4	1	no	—
63	C₁₃×#95	—	2	1	no	—
64	C₁₃×#95	—	2	1	no	—
65	C₁₃×#95	—	2	2	no	—
66	C₁₃×#95	—	2	2	no	—
67	C₁₃×#95	—	2	2	no	—
68	C₁₃×#95	D₄	1	2	yes	—
69	C₁₃×#95	D₄	1	2	yes	—
70	#29133	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂⁴×C₁₃	—	2	2	no	—
72	C₂×D₄×C₁₃	—	2	4	no	—
73	C₂×D₄×C₁₃	—	2	4	no	—
74	C₂×D₄×C₁₃	—	2	2	no	—
75	C₂×D₄×C₁₃	—	2	2	no	—
76	C₂×D₄×C₁₃	—	2	2	no	—
77	C₂×D₄×C₁₃	—	2	2	no	—
78	C₂×D₄×C₁₃	—	2	2	no	—
79	C₂×D₄×C₁₃	—	8	2	no	—
80	C₂×D₄×C₁₃	—	8	2	no	—
81	C₂×D₄×C₁₃	#41	1	4	yes	—
82	C₂²×C₄×C₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	—	4	4	no	—
86	C₂²×C₄×C₁₃	—	8	2	no	—
87	C₂²×C₄×C₁₃	—	8	2	no	—
88	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
93	C₂×C₈×C₁₃	—	2	2	no	—
94	C₂×C₈×C₁₃	—	2	2	no	—
95	C₂×C₈×C₁₃	—	2	2	no	—
96	C₂×C₈×C₁₃	—	2	2	no	—
97	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	—	2	2	no	—
99	C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₁₃×C₄⋊C₄	—	2	2	no	—
101	C₁₃×C₄⋊C₄	—	2	2	no	—
102	C₁₃×C₄⋊C₄	—	2	2	no	—
103	C₁₃×C₄⋊C₄	—	2	2	no	—
104	C₁₃×C₄⋊C₄	—	2	2	no	—
105	C₁₃×C₄⋊C₄	—	8	2	no	—
106	C₁₃×C₄⋊C₄	—	8	2	no	—
107	C₁₃×C₄⋊C₄	—	8	2	no	—
108	C₁₃×C₂²⋊C₄	—	4	4	no	—
109	C₁₃×C₂²⋊C₄	—	8	2	no	—
110	C₁₃×C₂²⋊C₄	—	8	2	no	—
111	C₄²×C₁₃	—	2	2	no	—
112	C₄²×C₁₃	—	2	1	no	—
113	C₄²×C₁₃	—	2	1	no	—
114	C₄²×C₁₃	#41	1	4	yes	—
115	#2647	C₂×C₁₃	1	1	yes	characteristic, complemented
116	#2328	C₂×C₁₃	1	1	yes	characteristic
117	#2101	C₂×C₁₃	1	2	yes	complemented
118	#2041	C₂×C₁₃	1	2	yes	—
119	#1936	C₂×C₁₃	1	2	yes	complemented
120	#1934	C₂×C₁₃	1	2	yes	complemented
121	#1804	C₂×C₁₃	1	2	yes	complemented
122	#1802	C₂×C₁₃	1	2	yes	complemented
123	#1768	C₂×C₁₃	1	1	yes	characteristic, complemented
124	C₂³×C₁₃	—	2	4	no	—
125	C₂³×C₁₃	—	4	2	no	—
126	C₂³×C₁₃	—	4	2	no	—
127	C₂³×C₁₃	—	4	2	no	—
128	C₂³×C₁₃	—	4	2	no	—
129	C₂³×C₁₃	—	4	2	no	—
130	C₂³×C₁₃	—	4	2	no	—
131	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
132	D₄×C₁₃	—	2	4	no	—
133	D₄×C₁₃	—	2	4	no	—
134	D₄×C₁₃	—	4	2	no	—
135	D₄×C₁₃	—	4	2	no	—
136	D₄×C₁₃	—	8	4	no	—
137	D₄×C₁₃	—	8	4	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	2	1	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	4	2	no	—
148	C₂×C₄×C₁₃	—	4	2	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	4	2	no	—
152	C₂×C₄×C₁₃	—	4	2	no	—
153	C₂×C₄×C₁₃	—	4	2	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	8	8	no	—
157	C₂×C₄×C₁₃	#124	1	4	yes	—
158	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
159	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
160	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
162	C₈×C₁₃	—	4	2	no	—
163	C₈×C₁₃	—	4	2	no	—
164	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
165	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
166	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
167	C₂×#102	C₂²×C₁₃	1	2	yes	—
168	C₂×#102	C₂²×C₁₃	1	2	yes	—
169	C₂×#102	C₂²×C₁₃	1	2	yes	—
170	C₂×#102	C₂²×C₁₃	1	2	yes	—
171	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
172	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
173	#400	—	2	2	no	—
174	#398	—	2	2	no	—
175	#390	C₂²×C₁₃	1	2	yes	—
176	#389	C₂²×C₁₃	1	2	yes	—
177	#389	C₂²×C₁₃	1	2	yes	—
178	#386	—	2	2	no	—
179	#386	—	2	2	no	—
180	#384	C₂²×C₁₃	1	1	yes	characteristic
181	#382	C₂²×C₁₃	1	1	yes	characteristic
182	#382	C₂²×C₁₃	1	1	yes	characteristic
183	#376	C₂²×C₁₃	1	1	yes	characteristic
184	#340	C₂²×C₁₃	1	2	yes	—
185	#340	C₂²×C₁₃	1	2	yes	—
186	#340	C₂²×C₁₃	1	2	yes	—
187	#340	C₂²×C₁₃	1	2	yes	—
188	#336	C₂²×C₁₃	1	2	yes	—
189	C₂²×C₁₃	—	4	4	no	—
190	C₂²×C₁₃	—	4	4	no	—
191	C₂²×C₁₃	—	4	4	no	—
192	C₂²×C₁₃	—	8	2	no	—
193	C₂²×C₁₃	—	8	2	no	—
194	C₂²×C₁₃	—	8	2	no	—
195	C₂²×C₁₃	—	8	2	no	—
196	C₂²×C₁₃	#525	1	1	yes	characteristic
197	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
198	C₂²×C₁₃	#537	1	1	yes	characteristic
199	C₂²×C₁₃	#576	1	2	yes	—
200	C₂²×C₁₃	#577	1	2	yes	—
201	C₄×C₁₃	—	2	4	no	—
202	C₄×C₁₃	—	4	1	no	—
203	C₄×C₁₃	—	4	1	no	—
204	C₄×C₁₃	—	4	2	no	—
205	C₄×C₁₃	—	8	2	no	—
206	C₄×C₁₃	—	8	2	no	—
207	C₄×C₁₃	—	8	2	no	—
208	C₄×C₁₃	#552	1	2	yes	—
209	C₄×C₁₃	#553	1	2	yes	—
210	C₂²×D₄	—	2	1	no	—
211	C₂²×D₄	—	2	1	no	—
212	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
213	C₂³×C₄	—	2	2	no	—
214	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
215	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
216	#127	—	2	4	no	—
217	C₄×D₄	—	2	4	no	—
218	C₄×D₄	—	2	4	no	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
223	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
224	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
225	C₂×C₂²⋊C₄	—	2	2	no	—
226	C₂×C₂²⋊C₄	—	2	2	no	—
227	C₂×C₂²⋊C₄	—	2	2	no	—
228	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
231	C₄⋊C₈	—	2	4	no	—
232	#102	—	2	4	no	—
233	#102	—	2	4	no	—
234	#102	—	4	2	no	—
235	#102	—	4	2	no	—
236	#97	—	4	1	no	—
237	C₄×C₈	—	4	1	no	—
238	#95	—	2	1	no	—
239	#95	—	2	1	no	—
240	#95	—	2	2	no	—
241	#95	—	2	2	no	—
242	#95	—	2	2	no	—
243	#95	D₄×C₁₃	1	2	yes	—
244	#95	D₄×C₁₃	1	2	yes	—
245	C₂×C₁₃	—	8	4	no	—
246	C₂×C₁₃	#2562	1	1	yes	characteristic
247	C₂×C₁₃	#3122	1	1	yes	characteristic
248	C₂×C₁₃	#3123	1	1	yes	characteristic
249	C₂×C₁₃	#3136	1	2	yes	—
250	C₂×C₁₃	#3257	1	2	yes	—
251	C₂⁴	—	2	2	no	—
252	C₂×D₄	—	2	4	no	—
253	C₂×D₄	—	2	4	no	—
254	C₂×D₄	—	2	2	no	—
255	C₂×D₄	—	2	2	no	—
256	C₂×D₄	—	2	2	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	—	8	2	no	—
260	C₂×D₄	—	8	2	no	—
261	C₂×D₄	C₁₃×#41	1	4	yes	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	4	4	no	—
266	C₂²×C₄	—	8	2	no	—
267	C₂²×C₄	—	8	2	no	—
268	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
270	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
272	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	8	2	no	—
286	C₄⋊C₄	—	8	2	no	—
287	C₄⋊C₄	—	8	2	no	—
288	C₂²⋊C₄	—	4	4	no	—
289	C₂²⋊C₄	—	8	2	no	—
290	C₂²⋊C₄	—	8	2	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	1	no	—
293	C₄²	—	2	1	no	—
294	C₄²	C₁₃×#41	1	4	yes	—
295	C₁₃	#29133	1	1	yes	characteristic, direct product factor, Sylow
296	C₂³	—	2	4	no	—
297	C₂³	—	4	2	no	—
298	C₂³	—	4	2	no	—
299	C₂³	—	4	2	no	—
300	C₂³	—	4	2	no	—
301	C₂³	—	4	2	no	—
302	C₂³	—	4	2	no	—
303	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
304	D₄	—	2	4	no	—
305	D₄	—	2	4	no	—
306	D₄	—	4	2	no	—
307	D₄	—	4	2	no	—
308	D₄	—	8	4	no	—
309	D₄	—	8	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	8	8	no	—
329	C₂×C₄	C₁₃×#124	1	4	yes	—
330	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
331	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
332	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
333	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
334	C₈	—	4	2	no	—
335	C₈	—	4	2	no	—
336	C₂²	—	4	4	no	—
337	C₂²	—	4	4	no	—
338	C₂²	—	4	4	no	—
339	C₂²	—	8	2	no	—
340	C₂²	—	8	2	no	—
341	C₂²	—	8	2	no	—
342	C₂²	—	8	2	no	—
343	C₂²	C₁₃×#525	1	1	yes	characteristic
344	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
345	C₂²	C₁₃×#537	1	1	yes	characteristic
346	C₂²	C₁₃×#576	1	2	yes	—
347	C₂²	C₁₃×#577	1	2	yes	—
348	C₄	—	2	4	no	—
349	C₄	—	4	1	no	—
350	C₄	—	4	1	no	—
351	C₄	—	4	2	no	—
352	C₄	—	8	2	no	—
353	C₄	—	8	2	no	—
354	C₄	—	8	2	no	—
355	C₄	C₁₃×#552	1	2	yes	—
356	C₄	C₁₃×#553	1	2	yes	—
357	C₂	—	8	4	no	—
358	C₂	C₁₃×#2562	1	1	yes	characteristic
359	C₂	C₁₃×#3122	1	1	yes	characteristic
360	C₂	C₁₃×#3123	1	1	yes	characteristic
361	C₂	C₁₃×#3136	1	2	yes	—
362	C₂	C₁₃×#3257	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2647	C₂	semidirect
3. C₁₃×#2101	C₂	semidirect
5. C₁₃×#1936	C₂	semidirect
6. C₁₃×#1934	C₂	semidirect
7. C₁₃×#1804	C₂	semidirect
8. C₁₃×#1802	C₂	semidirect
9. C₁₃×#1768	C₂	semidirect
70. #29133	C₁₃	direct (N × H)
115. #2647	C₂×C₁₃	semidirect
117. #2101	C₂×C₁₃	semidirect
119. #1936	C₂×C₁₃	semidirect
120. #1934	C₂×C₁₃	semidirect
121. #1804	C₂×C₁₃	semidirect
122. #1802	C₂×C₁₃	semidirect
123. #1768	C₂×C₁₃	semidirect
295. C₁₃	#29133	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2647	2
C₁₃×#2328	2
C₁₃×#2101	2
C₁₃×#2041	2
C₁₃×#1936	2
C₁₃×#1934	2
C₁₃×#1804	2
C₁₃×#1802	2
C₁₃×#1768	2
#29133	13

Subgroups — C13×#29133 #15715472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29133 #15715472