Subgroups — C₁₃×#17923 #15704262

Order 3328.

626 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2982	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2981	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1588	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1583	C₂	1	2	yes	maximal, complemented
6	C₁₃×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1572	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1491	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1484	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1453	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#532	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#481	C₄	1	2	yes	—
15	C₁₃×#475	C₄	1	2	yes	—
16	C₁₃×#460	C₄	1	2	yes	—
17	C₁₃×#448	C₄	1	2	yes	—
18	C₈×Q₈×C₁₃	—	2	2	no	—
19	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
20	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
21	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
22	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
23	C₁₃×#436	C₂²	1	2	yes	—
24	C₁₃×#435	—	2	2	no	—
25	C₈×D₄×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#432	C₂²	1	1	yes	characteristic
27	C₁₃×#431	—	2	2	no	—
28	C₁₃×#431	C₂²	1	1	yes	characteristic
29	C₁₃×#431	C₂²	1	1	yes	characteristic
30	C₁₃×#431	C₂²	1	1	yes	characteristic
31	C₁₃×#408	—	2	2	no	—
32	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
33	C₁₃×#335	C₂²	1	2	yes	—
34	C₁₃×#334	C₂²	1	2	yes	—
35	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
36	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
37	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
38	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
39	C₁₃×#322	C₂²	1	1	yes	characteristic
40	C₁₃×#322	C₂²	1	1	yes	characteristic
41	C₁₃×#322	C₂²	1	1	yes	characteristic
42	C₈²×C₁₃	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
46	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
47	C₂×C₁₃×M₁₆	—	2	1	no	—
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
51	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
52	C₁₃×#124	—	2	1	no	—
53	C₁₃×#121	—	2	1	no	—
54	C₁₃×#121	C₂×C₄	1	2	yes	—
55	C₄×Q₈×C₁₃	—	2	1	no	—
56	C₄×Q₈×C₁₃	—	2	1	no	—
57	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
58	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
59	C₄×D₄×C₁₃	—	2	1	no	—
60	C₄×D₄×C₁₃	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	—	2	1	no	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#106	C₂×C₄	1	2	yes	—
66	C₁₃×#106	C₂×C₄	1	2	yes	—
67	C₁₃×C₄⋊C₈	—	2	2	no	—
68	C₁₃×C₄⋊C₈	—	2	2	no	—
69	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
70	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
71	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
72	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₃×#103	C₂×C₄	1	2	yes	—
74	C₁₃×#103	C₂×C₄	1	2	yes	—
75	C₁₃×#102	C₂×C₄	1	2	yes	—
76	C₁₃×#102	C₂×C₄	1	2	yes	—
77	C₁₃×C₂²⋊C₈	—	2	1	no	—
78	C₁₃×C₂²⋊C₈	—	2	1	no	—
79	C₁₃×C₂²⋊C₈	—	2	2	no	—
80	C₁₃×C₂²⋊C₈	—	2	2	no	—
81	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
82	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
83	C₁₃×#97	—	2	1	no	—
84	C₁₃×#97	—	2	1	no	—
85	C₄×C₈×C₁₃	—	2	2	no	—
86	C₄×C₈×C₁₃	—	2	2	no	—
87	C₄×C₈×C₁₃	—	2	1	no	—
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	#17923	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₁₃×#41	—	8	2	no	—
96	C₂×Q₈×C₁₃	—	2	4	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	2	1	no	—
103	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
110	C₁₃×SD₁₆	—	2	4	no	—
111	C₁₃×SD₁₆	—	2	4	no	—
112	C₁₃×M₁₆	—	4	2	no	—
113	C₁₃×M₁₆	—	8	2	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	8	2	no	—
119	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
128	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
129	C₁₃×C₂²⋊C₄	—	2	2	no	—
130	C₁₃×C₂²⋊C₄	—	2	2	no	—
131	C₄²×C₁₃	—	2	2	no	—
132	C₄²×C₁₃	—	2	2	no	—
133	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₃	#41	1	1	yes	characteristic
136	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
137	#3103	C₂×C₁₃	1	1	yes	characteristic
138	#2982	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#2981	C₂×C₁₃	1	1	yes	characteristic
140	#1588	C₂×C₁₃	1	2	yes	complemented
141	#1583	C₂×C₁₃	1	2	yes	complemented
142	SD₁₆⋊C₈	C₂×C₁₃	1	2	yes	complemented
143	C₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
144	#1572	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#1491	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#1484	C₂×C₁₃	1	1	yes	characteristic
147	#1453	C₂×C₁₃	1	1	yes	characteristic, complemented
148	C₂³×C₁₃	—	2	2	no	—
149	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
150	Q₈×C₁₃	—	2	4	no	—
151	Q₈×C₁₃	—	2	2	no	—
152	Q₈×C₁₃	—	8	1	no	—
153	Q₈×C₁₃	#131	1	4	yes	—
154	D₄×C₁₃	—	2	2	no	—
155	D₄×C₁₃	—	2	2	no	—
156	D₄×C₁₃	—	8	1	no	—
157	D₄×C₁₃	—	8	1	no	—
158	D₄×C₁₃	—	8	2	no	—
159	C₂×C₄×C₁₃	—	2	4	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	8	1	no	—
169	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
175	C₈×C₁₃	—	2	2	no	—
176	C₈×C₁₃	—	2	2	no	—
177	C₈×C₁₃	—	2	2	no	—
178	C₈×C₁₃	—	2	2	no	—
179	C₈×C₁₃	—	2	2	no	—
180	C₈×C₁₃	—	4	1	no	—
181	C₈×C₁₃	—	4	2	no	—
182	C₈×C₁₃	—	4	2	no	—
183	#532	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
185	#481	C₄×C₁₃	1	2	yes	—
186	#475	C₄×C₁₃	1	2	yes	—
187	#460	C₄×C₁₃	1	2	yes	—
188	#448	C₄×C₁₃	1	2	yes	—
189	C₈×Q₈	—	2	2	no	—
190	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
191	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
192	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
193	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
194	#436	C₂²×C₁₃	1	2	yes	—
195	#435	—	2	2	no	—
196	C₈×D₄	C₂²×C₁₃	1	2	yes	—
197	#432	C₂²×C₁₃	1	1	yes	characteristic
198	#431	—	2	2	no	—
199	#431	C₂²×C₁₃	1	1	yes	characteristic
200	#431	C₂²×C₁₃	1	1	yes	characteristic
201	#431	C₂²×C₁₃	1	1	yes	characteristic
202	#408	—	2	2	no	—
203	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
204	#335	C₂²×C₁₃	1	2	yes	—
205	#334	C₂²×C₁₃	1	2	yes	—
206	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
207	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
208	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
209	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
210	#322	C₂²×C₁₃	1	1	yes	characteristic
211	#322	C₂²×C₁₃	1	1	yes	characteristic
212	#322	C₂²×C₁₃	1	1	yes	characteristic
213	C₈²	C₂²×C₁₃	1	1	yes	characteristic
214	C₂²×C₁₃	—	2	1	no	—
215	C₂²×C₁₃	—	2	1	no	—
216	C₂²×C₁₃	—	2	1	no	—
217	C₂²×C₁₃	—	4	2	no	—
218	C₂²×C₁₃	—	4	2	no	—
219	C₂²×C₁₃	—	4	2	no	—
220	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
221	C₄×C₁₃	—	2	4	no	—
222	C₄×C₁₃	—	2	1	no	—
223	C₄×C₁₃	—	2	1	no	—
224	C₄×C₁₃	—	2	1	no	—
225	C₄×C₁₃	—	2	1	no	—
226	C₄×C₁₃	—	4	2	no	—
227	C₄×C₁₃	—	4	2	no	—
228	C₄×C₁₃	C₂×#131	1	2	yes	—
229	C₄×C₁₃	#577	1	2	yes	—
230	C₂×#41	—	2	1	no	—
231	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
232	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
233	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
234	C₂×M₁₆	—	2	1	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂²×C₈	—	2	2	no	—
237	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
238	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
239	#124	—	2	1	no	—
240	#121	—	2	1	no	—
241	#121	C₂×C₄×C₁₃	1	2	yes	—
242	C₄×Q₈	—	2	1	no	—
243	C₄×Q₈	—	2	1	no	—
244	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
245	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	C₂³×C₁₃	1	2	yes	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
252	#106	C₂×C₄×C₁₃	1	2	yes	—
253	#106	C₂×C₄×C₁₃	1	2	yes	—
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
257	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
258	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
259	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
260	#103	C₂×C₄×C₁₃	1	2	yes	—
261	#103	C₂×C₄×C₁₃	1	2	yes	—
262	#102	C₂×C₄×C₁₃	1	2	yes	—
263	#102	C₂×C₄×C₁₃	1	2	yes	—
264	C₂²⋊C₈	—	2	1	no	—
265	C₂²⋊C₈	—	2	1	no	—
266	C₂²⋊C₈	—	2	2	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
269	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
270	#97	—	2	1	no	—
271	#97	—	2	1	no	—
272	C₄×C₈	—	2	2	no	—
273	C₄×C₈	—	2	2	no	—
274	C₄×C₈	—	2	1	no	—
275	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
276	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×C₁₃	—	4	1	no	—
282	C₂×C₁₃	—	8	2	no	—
283	C₂×C₁₃	#2929	1	1	yes	characteristic
284	C₂×C₁₃	#2949	1	1	yes	characteristic
285	C₂×C₁₃	#2956	1	1	yes	characteristic
286	#41	—	8	2	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
301	SD₁₆	—	2	4	no	—
302	SD₁₆	—	2	4	no	—
303	M₁₆	—	4	2	no	—
304	M₁₆	—	8	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	8	2	no	—
310	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
311	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
312	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
313	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
319	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
325	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
326	C₄²	C₁₃×#41	1	1	yes	characteristic
327	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
328	C₁₃	#17923	1	1	yes	characteristic, direct product factor, Sylow
329	C₂³	—	2	2	no	—
330	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
331	Q₈	—	2	4	no	—
332	Q₈	—	2	2	no	—
333	Q₈	—	8	1	no	—
334	Q₈	C₁₃×#131	1	4	yes	—
335	D₄	—	2	2	no	—
336	D₄	—	2	2	no	—
337	D₄	—	8	1	no	—
338	D₄	—	8	1	no	—
339	D₄	—	8	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	1	no	—
350	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
351	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
355	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
356	C₈	—	2	2	no	—
357	C₈	—	2	2	no	—
358	C₈	—	2	2	no	—
359	C₈	—	2	2	no	—
360	C₈	—	2	2	no	—
361	C₈	—	4	1	no	—
362	C₈	—	4	2	no	—
363	C₈	—	4	2	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
371	C₄	—	2	4	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	C₂×C₁₃×#131	1	2	yes	—
379	C₄	C₁₃×#577	1	2	yes	—
380	C₂	—	4	1	no	—
381	C₂	—	8	2	no	—
382	C₂	C₁₃×#2929	1	1	yes	characteristic
383	C₂	C₁₃×#2949	1	1	yes	characteristic
384	C₂	C₁₃×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2982	C₂	semidirect
4. C₁₃×#1588	C₂	semidirect
5. C₁₃×#1583	C₂	semidirect
6. C₁₃×SD₁₆⋊C₈	C₂	semidirect
7. C₈×C₁₃×SD₁₆	C₂	semidirect
8. C₁₃×#1572	C₂	semidirect
9. C₁₃×#1491	C₂	semidirect
11. C₁₃×#1453	C₂	semidirect
94. #17923	C₁₃	direct (N × H)
138. #2982	C₂×C₁₃	semidirect
140. #1588	C₂×C₁₃	semidirect
141. #1583	C₂×C₁₃	semidirect
142. SD₁₆⋊C₈	C₂×C₁₃	semidirect
143. C₈×SD₁₆	C₂×C₁₃	semidirect
144. #1572	C₂×C₁₃	semidirect
145. #1491	C₂×C₁₃	semidirect
147. #1453	C₂×C₁₃	semidirect
328. C₁₃	#17923	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×#3103	2
C₁₃×#2982	2
C₁₃×#2981	2
C₁₃×#1588	2
C₁₃×#1583	2
C₁₃×SD₁₆⋊C₈	2
C₈×C₁₃×SD₁₆	2
C₁₃×#1572	2
C₁₃×#1491	2
C₁₃×#1484	2
C₁₃×#1453	2
#17923	13

Subgroups — C13×#17923 #15704262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17923 #15704262