Subgroups — C₁₃×#32929 #15719268

Order 3328.

1708 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	C₂⁴×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#465	C₂	1	3	yes	maximal, complemented
3	C₁₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2847	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1893	C₂	1	3	yes	maximal, complemented
6	C₁₃×#1892	C₂	1	3	yes	maximal, complemented
7	C₁₃×#1807	C₂	1	3	yes	maximal, complemented
8	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
10	C₂³×C₈×C₁₃	—	2	12	no	—
11	C₂³×C₈×C₁₃	C₂²	1	3	yes	—
12	C₂³×C₈×C₁₃	C₂²	1	3	yes	—
13	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	3	yes	—
14	C₂×C₁₃×#121	C₂²	1	3	yes	—
15	C₂×C₁₃×#120	—	2	1	no	—
16	C₁₃×#465	—	2	12	no	—
17	C₂×C₁₃×#106	C₂²	1	3	yes	complemented
18	C₂×C₁₃×#103	C₂²	1	3	yes	complemented
19	C₂×C₁₃×#102	C₂²	1	3	yes	complemented
20	C₁₃×#386	—	2	3	no	—
21	C₁₃×#385	—	2	3	no	—
22	C₁₃×#380	C₂²	1	3	yes	—
23	C₁₃×#380	C₂²	1	3	yes	—
24	C₁₃×#379	—	2	1	no	—
25	C₁₃×#340	C₂²	1	6	yes	complemented
26	C₂⁵×C₁₃	D₄	1	1	yes	characteristic
27	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
28	C₂²×D₄×C₁₃	—	2	3	no	—
29	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
30	C₂³×C₄×C₁₃	—	2	6	no	—
31	C₂³×C₄×C₁₃	—	2	6	no	—
32	C₂³×C₄×C₁₃	D₄	1	3	yes	—
33	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
34	C₂×C₁₃×SD₁₆	—	2	6	no	—
35	C₂²×C₈×C₁₃	—	2	32	no	—
36	C₂²×C₈×C₁₃	—	2	6	no	—
37	C₂²×C₈×C₁₃	—	2	12	no	—
38	C₂²×C₈×C₁₃	—	2	12	no	—
39	C₂²×C₈×C₁₃	D₄	1	12	yes	complemented
40	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
41	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₁₃×C₂²⋊Q₈	—	2	6	no	—
43	C₁₃×C₂²⋊Q₈	—	2	6	no	—
44	C₁₃×#121	—	2	6	no	—
45	C₁₃×#121	—	2	6	no	—
46	C₁₃×#120	—	4	4	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
48	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
49	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
50	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
51	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
52	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
53	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
54	C₁₃×#106	—	2	6	no	—
55	C₁₃×#103	—	2	6	no	—
56	C₁₃×#102	—	2	6	no	—
57	C₁₃×#95	—	2	3	no	—
58	C₁₃×#95	—	2	3	no	—
59	#32929	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂⁴×C₁₃	—	2	6	no	—
61	C₂⁴×C₁₃	—	2	6	no	—
62	C₂⁴×C₁₃	—	2	1	no	—
63	C₂⁴×C₁₃	SD₁₆	1	4	yes	complemented
64	C₂⁴×C₁₃	C₂×D₄	1	3	yes	—
65	C₂×Q₈×C₁₃	—	2	3	no	—
66	C₂×Q₈×C₁₃	—	2	3	no	—
67	C₂×D₄×C₁₃	—	2	3	no	—
68	C₂×D₄×C₁₃	—	2	3	no	—
69	C₂×D₄×C₁₃	—	4	6	no	—
70	C₂×D₄×C₁₃	—	4	6	no	—
71	C₂×D₄×C₁₃	—	4	6	no	—
72	C₂²×C₄×C₁₃	—	2	8	no	—
73	C₂²×C₄×C₁₃	—	2	24	no	—
74	C₂²×C₄×C₁₃	—	2	6	no	—
75	C₂²×C₄×C₁₃	—	2	12	no	—
76	C₂²×C₄×C₁₃	—	2	6	no	—
77	C₂²×C₄×C₁₃	—	2	6	no	—
78	C₂²×C₄×C₁₃	—	2	3	no	—
79	C₂²×C₄×C₁₃	—	2	3	no	—
80	C₂²×C₄×C₁₃	—	2	1	no	—
81	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
82	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
83	C₂²×C₄×C₁₃	#41	1	6	yes	—
84	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
85	C₁₃×SD₁₆	—	4	4	no	—
86	C₂×C₈×C₁₃	—	2	24	no	—
87	C₂×C₈×C₁₃	—	2	6	no	—
88	C₂×C₈×C₁₃	—	2	24	no	—
89	C₂×C₈×C₁₃	C₂×D₄	1	6	yes	—
90	C₂×C₈×C₁₃	C₂×D₄	1	6	yes	—
91	C₁₃×C₄⋊C₄	—	2	3	no	—
92	C₁₃×C₄⋊C₄	—	2	3	no	—
93	C₁₃×C₄⋊C₄	—	2	3	no	—
94	C₁₃×C₄⋊C₄	—	2	3	no	—
95	C₁₃×C₄⋊C₄	—	4	6	no	—
96	C₁₃×C₂²⋊C₄	—	4	6	no	—
97	C₁₃×C₂²⋊C₄	—	4	6	no	—
98	C₁₃×C₂²⋊C₄	—	4	6	no	—
99	C₁₃×C₂²⋊C₄	—	4	6	no	—
100	C₂⁴×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
101	C₂×#465	C₂×C₁₃	1	3	yes	complemented
102	#2848	C₂×C₁₃	1	1	yes	characteristic, complemented
103	#2847	C₂×C₁₃	1	1	yes	characteristic
104	#1893	C₂×C₁₃	1	3	yes	complemented
105	#1892	C₂×C₁₃	1	3	yes	complemented
106	#1807	C₂×C₁₃	1	3	yes	complemented
107	C₂³×C₁₃	—	2	8	no	—
108	C₂³×C₁₃	—	2	24	no	—
109	C₂³×C₁₃	—	2	6	no	—
110	C₂³×C₁₃	—	2	6	no	—
111	C₂³×C₁₃	—	2	24	no	—
112	C₂³×C₁₃	—	4	3	no	—
113	C₂³×C₁₃	—	4	1	no	—
114	C₂³×C₁₃	—	4	3	no	—
115	C₂³×C₁₃	#121	1	6	yes	—
116	C₂³×C₁₃	C₂×SD₁₆	1	6	yes	—
117	C₂³×C₁₃	#135	1	6	yes	—
118	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
119	Q₈×C₁₃	—	4	1	no	—
120	Q₈×C₁₃	—	4	3	no	—
121	D₄×C₁₃	—	4	1	no	—
122	D₄×C₁₃	—	4	3	no	—
123	D₄×C₁₃	—	8	12	no	—
124	C₂×C₄×C₁₃	—	2	24	no	—
125	C₂×C₄×C₁₃	—	2	6	no	—
126	C₂×C₄×C₁₃	—	2	6	no	—
127	C₂×C₄×C₁₃	—	2	6	no	—
128	C₂×C₄×C₁₃	—	2	12	no	—
129	C₂×C₄×C₁₃	—	4	3	no	—
130	C₂×C₄×C₁₃	—	4	3	no	—
131	C₂×C₄×C₁₃	—	4	3	no	—
132	C₂×C₄×C₁₃	—	4	3	no	—
133	C₂×C₄×C₁₃	—	4	6	no	—
134	C₂×C₄×C₁₃	—	4	3	no	—
135	C₂×C₄×C₁₃	#121	1	6	yes	—
136	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
137	C₂×C₄×C₁₃	C₂×#41	1	3	yes	—
138	C₈×C₁₃	—	2	6	no	—
139	C₈×C₁₃	#120	1	4	yes	complemented
140	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
141	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
142	C₂³×C₈	—	2	12	no	—
143	C₂³×C₈	C₂²×C₁₃	1	3	yes	—
144	C₂³×C₈	C₂²×C₁₃	1	3	yes	—
145	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	3	yes	—
146	C₂×#121	C₂²×C₁₃	1	3	yes	—
147	C₂×#120	—	2	1	no	—
148	#465	—	2	12	no	—
149	C₂×#106	C₂²×C₁₃	1	3	yes	complemented
150	C₂×#103	C₂²×C₁₃	1	3	yes	complemented
151	C₂×#102	C₂²×C₁₃	1	3	yes	complemented
152	#386	—	2	3	no	—
153	#385	—	2	3	no	—
154	#380	C₂²×C₁₃	1	3	yes	—
155	#380	C₂²×C₁₃	1	3	yes	—
156	#379	—	2	1	no	—
157	#340	C₂²×C₁₃	1	6	yes	complemented
158	C₂²×C₁₃	—	2	32	no	—
159	C₂²×C₁₃	—	2	6	no	—
160	C₂²×C₁₃	—	2	12	no	—
161	C₂²×C₁₃	—	2	6	no	—
162	C₂²×C₁₃	—	2	12	no	—
163	C₂²×C₁₃	—	8	1	no	—
164	C₂²×C₁₃	—	8	3	no	—
165	C₂²×C₁₃	—	8	3	no	—
166	C₂²×C₁₃	#465	1	12	yes	complemented
167	C₂²×C₁₃	C₂×#121	1	3	yes	—
168	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
169	C₂²×C₁₃	C₂×#135	1	3	yes	—
170	C₄×C₁₃	—	2	6	no	—
171	C₄×C₁₃	—	8	1	no	—
172	C₄×C₁₃	—	8	3	no	—
173	C₄×C₁₃	—	8	3	no	—
174	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
175	C₄×C₁₃	#525	1	3	yes	—
176	C₂⁵	D₄×C₁₃	1	1	yes	characteristic
177	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
178	C₂²×D₄	—	2	3	no	—
179	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
180	C₂³×C₄	—	2	6	no	—
181	C₂³×C₄	—	2	6	no	—
182	C₂³×C₄	D₄×C₁₃	1	3	yes	—
183	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
184	C₂×SD₁₆	—	2	6	no	—
185	C₂²×C₈	—	2	32	no	—
186	C₂²×C₈	—	2	6	no	—
187	C₂²×C₈	—	2	12	no	—
188	C₂²×C₈	—	2	12	no	—
189	C₂²×C₈	D₄×C₁₃	1	12	yes	complemented
190	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
191	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
192	C₂²⋊Q₈	—	2	6	no	—
193	C₂²⋊Q₈	—	2	6	no	—
194	#121	—	2	6	no	—
195	#121	—	2	6	no	—
196	#120	—	4	4	no	—
197	C₂×C₄⋊C₄	—	2	3	no	—
198	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
199	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
200	C₂×C₂²⋊C₄	—	2	3	no	—
201	C₂×C₂²⋊C₄	—	2	3	no	—
202	C₂×C₂²⋊C₄	—	2	3	no	—
203	C₂×C₂²⋊C₄	—	2	3	no	—
204	#106	—	2	6	no	—
205	#103	—	2	6	no	—
206	#102	—	2	6	no	—
207	#95	—	2	3	no	—
208	#95	—	2	3	no	—
209	C₂×C₁₃	—	2	12	no	—
210	C₂×C₁₃	—	16	1	no	—
211	C₂×C₁₃	#2847	1	1	yes	characteristic
212	C₂×C₁₃	C₂×#465	1	3	yes	—
213	C₂×C₁₃	#3050	1	3	yes	—
214	C₂⁴	—	2	6	no	—
215	C₂⁴	—	2	6	no	—
216	C₂⁴	—	2	1	no	—
217	C₂⁴	C₁₃×SD₁₆	1	4	yes	complemented
218	C₂⁴	C₂×D₄×C₁₃	1	3	yes	—
219	C₂×Q₈	—	2	3	no	—
220	C₂×Q₈	—	2	3	no	—
221	C₂×D₄	—	2	3	no	—
222	C₂×D₄	—	2	3	no	—
223	C₂×D₄	—	4	6	no	—
224	C₂×D₄	—	4	6	no	—
225	C₂×D₄	—	4	6	no	—
226	C₂²×C₄	—	2	8	no	—
227	C₂²×C₄	—	2	24	no	—
228	C₂²×C₄	—	2	6	no	—
229	C₂²×C₄	—	2	12	no	—
230	C₂²×C₄	—	2	6	no	—
231	C₂²×C₄	—	2	6	no	—
232	C₂²×C₄	—	2	3	no	—
233	C₂²×C₄	—	2	3	no	—
234	C₂²×C₄	—	2	1	no	—
235	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
236	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
237	C₂²×C₄	C₁₃×#41	1	6	yes	—
238	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
239	SD₁₆	—	4	4	no	—
240	C₂×C₈	—	2	24	no	—
241	C₂×C₈	—	2	6	no	—
242	C₂×C₈	—	2	24	no	—
243	C₂×C₈	C₂×D₄×C₁₃	1	6	yes	—
244	C₂×C₈	C₂×D₄×C₁₃	1	6	yes	—
245	C₄⋊C₄	—	2	3	no	—
246	C₄⋊C₄	—	2	3	no	—
247	C₄⋊C₄	—	2	3	no	—
248	C₄⋊C₄	—	2	3	no	—
249	C₄⋊C₄	—	4	6	no	—
250	C₂²⋊C₄	—	4	6	no	—
251	C₂²⋊C₄	—	4	6	no	—
252	C₂²⋊C₄	—	4	6	no	—
253	C₂²⋊C₄	—	4	6	no	—
254	C₁₃	#32929	1	1	yes	characteristic, direct product factor, Sylow
255	C₂³	—	2	8	no	—
256	C₂³	—	2	24	no	—
257	C₂³	—	2	24	no	—
258	C₂³	—	2	6	no	—
259	C₂³	—	2	6	no	—
260	C₂³	—	4	3	no	—
261	C₂³	—	4	1	no	—
262	C₂³	—	4	3	no	—
263	C₂³	C₁₃×#121	1	6	yes	—
264	C₂³	C₂×C₁₃×SD₁₆	1	6	yes	—
265	C₂³	C₁₃×#135	1	6	yes	—
266	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
267	Q₈	—	4	1	no	—
268	Q₈	—	4	3	no	—
269	D₄	—	4	1	no	—
270	D₄	—	4	3	no	—
271	D₄	—	8	12	no	—
272	C₂×C₄	—	2	24	no	—
273	C₂×C₄	—	2	6	no	—
274	C₂×C₄	—	2	6	no	—
275	C₂×C₄	—	2	6	no	—
276	C₂×C₄	—	2	12	no	—
277	C₂×C₄	—	4	3	no	—
278	C₂×C₄	—	4	3	no	—
279	C₂×C₄	—	4	3	no	—
280	C₂×C₄	—	4	3	no	—
281	C₂×C₄	—	4	6	no	—
282	C₂×C₄	—	4	3	no	—
283	C₂×C₄	C₁₃×#121	1	6	yes	—
284	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
285	C₂×C₄	C₂×C₁₃×#41	1	3	yes	—
286	C₈	—	2	6	no	—
287	C₈	C₁₃×#120	1	4	yes	complemented
288	C₂²	—	2	32	no	—
289	C₂²	—	2	12	no	—
290	C₂²	—	2	6	no	—
291	C₂²	—	2	12	no	—
292	C₂²	—	2	6	no	—
293	C₂²	—	8	3	no	—
294	C₂²	—	8	3	no	—
295	C₂²	—	8	1	no	—
296	C₂²	C₁₃×#465	1	12	yes	complemented
297	C₂²	C₂×C₁₃×#121	1	3	yes	—
298	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
299	C₂²	C₂×C₁₃×#135	1	3	yes	—
300	C₄	—	2	6	no	—
301	C₄	—	8	3	no	—
302	C₄	—	8	3	no	—
303	C₄	—	8	1	no	—
304	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
305	C₄	C₁₃×#525	1	3	yes	—
306	C₂	—	2	12	no	—
307	C₂	—	16	1	no	—
308	C₂	C₁₃×#2847	1	1	yes	characteristic
309	C₂	C₂×C₁₃×#465	1	3	yes	—
310	C₂	C₁₃×#3050	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2847	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂⁴×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₈×C₁₃	C₂	semidirect
2. C₂×C₁₃×#465	C₂	semidirect
3. C₁₃×#2848	C₂	semidirect
5. C₁₃×#1893	C₂	semidirect
6. C₁₃×#1892	C₂	semidirect
7. C₁₃×#1807	C₂	semidirect
9. C₂²×C₁₃×SD₁₆	C₂²	semidirect
17. C₂×C₁₃×#106	C₂²	semidirect
18. C₂×C₁₃×#103	C₂²	semidirect
19. C₂×C₁₃×#102	C₂²	semidirect
25. C₁₃×#340	C₂²	semidirect
39. C₂²×C₈×C₁₃	D₄	semidirect
59. #32929	C₁₃	direct (N × H)
63. C₂⁴×C₁₃	SD₁₆	semidirect
100. C₂⁴×C₈	C₂×C₁₃	semidirect
101. C₂×#465	C₂×C₁₃	semidirect
102. #2848	C₂×C₁₃	semidirect
104. #1893	C₂×C₁₃	semidirect
105. #1892	C₂×C₁₃	semidirect
106. #1807	C₂×C₁₃	semidirect
139. C₈×C₁₃	#120	semidirect
141. C₂²×SD₁₆	C₂²×C₁₃	semidirect
149. C₂×#106	C₂²×C₁₃	semidirect
150. C₂×#103	C₂²×C₁₃	semidirect
151. C₂×#102	C₂²×C₁₃	semidirect
157. #340	C₂²×C₁₃	semidirect
166. C₂²×C₁₃	#465	semidirect
189. C₂²×C₈	D₄×C₁₃	semidirect
217. C₂⁴	C₁₃×SD₁₆	semidirect
254. C₁₃	#32929	direct (N × H)
287. C₈	C₁₃×#120	semidirect
296. C₂²	C₁₃×#465	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×C₈×C₁₃	2
C₂×C₁₃×#465	2
C₁₃×#2848	2
C₁₃×#2847	2
C₁₃×#1893	2
C₁₃×#1892	2
C₁₃×#1807	2
#32929	13

Subgroups — C13×#32929 #15719268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32929 #15719268