Subgroups — C₁₃×#25911 #15712250

Order 3328.

1206 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#490	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2856	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2023	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1992	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1875	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#533	—	2	8	no	—
9	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
10	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#125	C₂²	1	2	yes	—
12	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
13	C₂×C₁₃×#121	—	2	2	no	—
14	C₂×C₁₃×#121	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₃	—	2	2	no	—
16	C₂×C₁₃×#117	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#490	—	2	8	no	—
19	C₂×C₁₃×#102	C₂²	1	8	yes	—
20	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×#97	C₂²	1	2	yes	—
22	C₁₃×#390	—	2	2	no	—
23	C₁₃×#390	C₂²	1	2	yes	—
24	C₁₃×#384	C₂²	1	1	yes	characteristic
25	C₁₃×#340	C₂²	1	8	yes	—
26	C₁₃×#336	C₂²	1	2	yes	—
27	C₂²×Q₈×C₁₃	—	2	2	no	—
28	C₂²×D₄×C₁₃	—	2	2	no	—
29	C₂²×D₄×C₁₃	—	2	2	no	—
30	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
31	C₂³×C₄×C₁₃	D₄	1	2	yes	—
32	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
33	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
34	C₁₃×C₄⋊Q₈	—	2	8	no	—
35	C₁₃×#127	—	2	4	no	—
36	C₁₃×#125	—	2	4	no	—
37	C₁₃×#125	D₄	1	8	yes	complemented
38	C₁₃×C₂²⋊Q₈	—	2	16	no	—
39	C₁₃×#121	—	2	8	no	—
40	C₁₃×#121	—	4	8	no	—
41	C₄×Q₈×C₁₃	—	2	16	no	—
42	C₁₃×#117	—	2	8	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
46	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
47	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
48	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
49	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
50	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
51	C₂×C₄²×C₁₃	—	2	2	no	—
52	C₂×C₄²×C₁₃	—	2	4	no	—
53	C₂×C₄²×C₁₃	D₄	1	2	yes	—
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×#102	—	2	16	no	—
57	C₁₃×C₂²⋊C₈	—	2	4	no	—
58	C₁₃×#97	—	2	4	no	—
59	#25911	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂⁴×C₁₃	—	2	2	no	—
61	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
62	C₂×Q₈×C₁₃	—	2	8	no	—
63	C₂×Q₈×C₁₃	—	4	4	no	—
64	C₂×Q₈×C₁₃	—	4	4	no	—
65	C₂×D₄×C₁₃	—	2	4	no	—
66	C₂×D₄×C₁₃	—	2	4	no	—
67	C₂×D₄×C₁₃	—	2	4	no	—
68	C₂×D₄×C₁₃	—	4	4	no	—
69	C₂×D₄×C₁₃	—	4	4	no	—
70	C₂×D₄×C₁₃	—	4	8	no	—
71	C₂×D₄×C₁₃	—	4	4	no	—
72	C₂×D₄×C₁₃	—	4	4	no	—
73	C₂²×C₄×C₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₃	—	2	4	no	—
76	C₂²×C₄×C₁₃	—	2	4	no	—
77	C₂²×C₄×C₁₃	—	2	4	no	—
78	C₂²×C₄×C₁₃	—	2	2	no	—
79	C₂²×C₄×C₁₃	—	4	2	no	—
80	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₁₃	#41	1	4	yes	—
84	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
85	C₂×C₈×C₁₃	—	2	4	no	—
86	C₂×C₈×C₁₃	—	2	4	no	—
87	C₂×C₈×C₁₃	—	2	4	no	—
88	C₁₃×C₄⋊C₄	—	2	8	no	—
89	C₁₃×C₄⋊C₄	—	2	16	no	—
90	C₁₃×C₄⋊C₄	—	2	4	no	—
91	C₁₃×C₄⋊C₄	—	2	4	no	—
92	C₁₃×C₄⋊C₄	—	4	4	no	—
93	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
94	C₁₃×C₂²⋊C₄	—	2	8	no	—
95	C₁₃×C₂²⋊C₄	—	4	4	no	—
96	C₁₃×C₂²⋊C₄	—	4	8	no	—
97	C₄²×C₁₃	—	2	8	no	—
98	C₄²×C₁₃	—	2	4	no	—
99	C₄²×C₁₃	—	2	2	no	—
100	C₄²×C₁₃	C₂×D₄	1	4	yes	—
101	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
102	C₂×#490	C₂×C₁₃	1	2	yes	complemented
103	#2856	C₂×C₁₃	1	1	yes	characteristic
104	#2023	C₂×C₁₃	1	4	yes	complemented
105	#1992	C₂×C₁₃	1	2	yes	complemented
106	#1875	C₂×C₁₃	1	4	yes	complemented
107	#1749	C₂×C₁₃	1	1	yes	characteristic, complemented
108	C₂³×C₁₃	—	2	1	no	—
109	C₂³×C₁₃	—	2	1	no	—
110	C₂³×C₁₃	—	2	2	no	—
111	C₂³×C₁₃	—	2	2	no	—
112	C₂³×C₁₃	—	4	2	no	—
113	C₂³×C₁₃	—	4	2	no	—
114	C₂³×C₁₃	—	4	2	no	—
115	C₂³×C₁₃	—	4	4	no	—
116	C₂³×C₁₃	—	4	4	no	—
117	C₂³×C₁₃	#124	1	2	yes	—
118	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
119	Q₈×C₁₃	—	4	16	no	—
120	D₄×C₁₃	—	4	8	no	—
121	D₄×C₁₃	—	8	8	no	—
122	D₄×C₁₃	—	8	8	no	—
123	C₂×C₄×C₁₃	—	2	1	no	—
124	C₂×C₄×C₁₃	—	2	2	no	—
125	C₂×C₄×C₁₃	—	2	1	no	—
126	C₂×C₄×C₁₃	—	2	2	no	—
127	C₂×C₄×C₁₃	—	2	2	no	—
128	C₂×C₄×C₁₃	—	2	2	no	—
129	C₂×C₄×C₁₃	—	2	8	no	—
130	C₂×C₄×C₁₃	—	2	8	no	—
131	C₂×C₄×C₁₃	—	4	8	no	—
132	C₂×C₄×C₁₃	—	4	4	no	—
133	C₂×C₄×C₁₃	—	4	4	no	—
134	C₂×C₄×C₁₃	—	4	2	no	—
135	C₂×C₄×C₁₃	—	4	4	no	—
136	C₂×C₄×C₁₃	#120	1	4	yes	—
137	C₂×C₄×C₁₃	#124	1	2	yes	—
138	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
139	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
140	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
141	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
142	C₈×C₁₃	—	4	4	no	—
143	#533	—	2	8	no	—
144	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
145	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
146	C₂×#125	C₂²×C₁₃	1	2	yes	—
147	C₂×C₂²⋊Q₈	—	2	2	no	—
148	C₂×#121	—	2	2	no	—
149	C₂×#121	C₂²×C₁₃	1	2	yes	—
150	C₂×C₄×Q₈	—	2	2	no	—
151	C₂×#117	C₂²×C₁₃	1	2	yes	—
152	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
153	#490	—	2	8	no	—
154	C₂×#102	C₂²×C₁₃	1	8	yes	—
155	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
156	C₂×#97	C₂²×C₁₃	1	2	yes	—
157	#390	—	2	2	no	—
158	#390	C₂²×C₁₃	1	2	yes	—
159	#384	C₂²×C₁₃	1	1	yes	characteristic
160	#340	C₂²×C₁₃	1	8	yes	—
161	#336	C₂²×C₁₃	1	2	yes	—
162	C₂²×C₁₃	—	2	2	no	—
163	C₂²×C₁₃	—	2	2	no	—
164	C₂²×C₁₃	—	2	2	no	—
165	C₂²×C₁₃	—	4	2	no	—
166	C₂²×C₁₃	—	4	2	no	—
167	C₂²×C₁₃	—	8	2	no	—
168	C₂²×C₁₃	—	8	2	no	—
169	C₂²×C₁₃	—	8	2	no	—
170	C₂²×C₁₃	—	8	4	no	—
171	C₂²×C₁₃	—	8	4	no	—
172	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
173	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
174	C₂²×C₁₃	#536	1	1	yes	characteristic
175	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
176	C₂²×C₁₃	#575	1	2	yes	—
177	C₄×C₁₃	—	2	2	no	—
178	C₄×C₁₃	—	2	4	no	—
179	C₄×C₁₃	—	2	4	no	—
180	C₄×C₁₃	—	4	8	no	—
181	C₄×C₁₃	—	8	2	no	—
182	C₄×C₁₃	#548	1	4	yes	—
183	C₂²×Q₈	—	2	2	no	—
184	C₂²×D₄	—	2	2	no	—
185	C₂²×D₄	—	2	2	no	—
186	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
187	C₂³×C₄	D₄×C₁₃	1	2	yes	—
188	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
189	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
190	C₄⋊Q₈	—	2	8	no	—
191	#127	—	2	4	no	—
192	#125	—	2	4	no	—
193	#125	D₄×C₁₃	1	8	yes	complemented
194	C₂²⋊Q₈	—	2	16	no	—
195	#121	—	2	8	no	—
196	#121	—	4	8	no	—
197	C₄×Q₈	—	2	16	no	—
198	#117	—	2	8	no	—
199	C₂×C₄⋊C₄	—	2	4	no	—
200	C₂×C₄⋊C₄	—	2	2	no	—
201	C₂×C₄⋊C₄	—	2	2	no	—
202	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
203	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
204	C₂×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₂²⋊C₄	—	2	4	no	—
206	C₂×C₂²⋊C₄	—	2	2	no	—
207	C₂×C₄²	—	2	2	no	—
208	C₂×C₄²	—	2	4	no	—
209	C₂×C₄²	D₄×C₁₃	1	2	yes	—
210	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
211	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
212	#102	—	2	16	no	—
213	C₂²⋊C₈	—	2	4	no	—
214	#97	—	2	4	no	—
215	C₂×C₁₃	—	4	2	no	—
216	C₂×C₁₃	—	16	2	no	—
217	C₂×C₁₃	#2436	1	1	yes	characteristic
218	C₂×C₁₃	#3006	1	2	yes	—
219	C₂×C₁₃	#3135	1	1	yes	characteristic
220	C₂×C₁₃	#3138	1	1	yes	characteristic
221	C₂×C₁₃	#3235	1	2	yes	—
222	C₂⁴	—	2	2	no	—
223	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
224	C₂×Q₈	—	2	8	no	—
225	C₂×Q₈	—	4	4	no	—
226	C₂×Q₈	—	4	4	no	—
227	C₂×D₄	—	2	4	no	—
228	C₂×D₄	—	2	4	no	—
229	C₂×D₄	—	2	4	no	—
230	C₂×D₄	—	4	4	no	—
231	C₂×D₄	—	4	4	no	—
232	C₂×D₄	—	4	8	no	—
233	C₂×D₄	—	4	4	no	—
234	C₂×D₄	—	4	4	no	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	4	2	no	—
242	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
243	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
244	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
245	C₂²×C₄	C₁₃×#41	1	4	yes	—
246	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
247	C₂×C₈	—	2	4	no	—
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	—	2	4	no	—
250	C₄⋊C₄	—	2	8	no	—
251	C₄⋊C₄	—	2	16	no	—
252	C₄⋊C₄	—	2	4	no	—
253	C₄⋊C₄	—	2	4	no	—
254	C₄⋊C₄	—	4	4	no	—
255	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
256	C₂²⋊C₄	—	2	8	no	—
257	C₂²⋊C₄	—	4	4	no	—
258	C₂²⋊C₄	—	4	8	no	—
259	C₄²	—	2	8	no	—
260	C₄²	—	2	4	no	—
261	C₄²	—	2	2	no	—
262	C₄²	C₂×D₄×C₁₃	1	4	yes	—
263	C₁₃	#25911	1	1	yes	characteristic, direct product factor, Sylow
264	C₂³	—	2	1	no	—
265	C₂³	—	2	1	no	—
266	C₂³	—	2	2	no	—
267	C₂³	—	2	2	no	—
268	C₂³	—	4	2	no	—
269	C₂³	—	4	2	no	—
270	C₂³	—	4	2	no	—
271	C₂³	—	4	4	no	—
272	C₂³	—	4	4	no	—
273	C₂³	C₁₃×#124	1	2	yes	—
274	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
275	Q₈	—	4	16	no	—
276	D₄	—	4	8	no	—
277	D₄	—	8	8	no	—
278	D₄	—	8	8	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	8	no	—
286	C₂×C₄	—	2	8	no	—
287	C₂×C₄	—	4	8	no	—
288	C₂×C₄	—	4	4	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	—	4	2	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	C₁₃×#120	1	4	yes	—
293	C₂×C₄	C₁₃×#124	1	2	yes	—
294	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
295	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
296	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
297	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
298	C₈	—	4	4	no	—
299	C₂²	—	2	2	no	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	2	no	—
302	C₂²	—	4	2	no	—
303	C₂²	—	4	2	no	—
304	C₂²	—	8	4	no	—
305	C₂²	—	8	2	no	—
306	C₂²	—	8	2	no	—
307	C₂²	—	8	2	no	—
308	C₂²	—	8	4	no	—
309	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
310	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
311	C₂²	C₁₃×#536	1	1	yes	characteristic
312	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
313	C₂²	C₁₃×#575	1	2	yes	—
314	C₄	—	2	4	no	—
315	C₄	—	2	4	no	—
316	C₄	—	2	2	no	—
317	C₄	—	4	8	no	—
318	C₄	—	8	2	no	—
319	C₄	C₁₃×#548	1	4	yes	—
320	C₂	—	4	2	no	—
321	C₂	—	16	2	no	—
322	C₂	C₁₃×#2436	1	1	yes	characteristic
323	C₂	C₁₃×#3006	1	2	yes	—
324	C₂	C₁₃×#3135	1	1	yes	characteristic
325	C₂	C₁₃×#3138	1	1	yes	characteristic
326	C₂	C₁₃×#3235	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2856	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#533	C₂	semidirect
2. C₂×C₁₃×#490	C₂	semidirect
4. C₁₃×#2023	C₂	semidirect
5. C₁₃×#1992	C₂	semidirect
6. C₁₃×#1875	C₂	semidirect
7. C₁₃×#1749	C₂	semidirect
37. C₁₃×#125	D₄	semidirect
59. #25911	C₁₃	direct (N × H)
101. C₂×#533	C₂×C₁₃	semidirect
102. C₂×#490	C₂×C₁₃	semidirect
104. #2023	C₂×C₁₃	semidirect
105. #1992	C₂×C₁₃	semidirect
106. #1875	C₂×C₁₃	semidirect
107. #1749	C₂×C₁₃	semidirect
193. #125	D₄×C₁₃	semidirect
263. C₁₃	#25911	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×#533	2
C₂×C₁₃×#490	2
C₁₃×#2856	2
C₁₃×#2023	2
C₁₃×#1992	2
C₁₃×#1875	2
C₁₃×#1749	2
#25911	13

Subgroups — C13×#25911 #15712250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25911 #15712250