Subgroups — C₁₃×#17924 #15704263

Order 3328.

638 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1585	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1582	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×#1490	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1485	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1453	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#483	C₄	1	2	yes	—
15	C₁₃×#476	C₄	1	2	yes	—
16	C₁₃×#461	C₄	1	2	yes	—
17	C₁₃×#450	C₄	1	2	yes	—
18	C₁₃×#446	—	2	2	no	—
19	C₁₃×#446	C₂²	1	2	yes	complemented
20	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
21	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
22	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
23	C₈×D₄×C₁₃	—	2	2	no	—
24	C₈×D₄×C₁₃	C₂²	1	2	yes	—
25	C₈×D₄×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#433	—	2	2	no	—
27	C₁₃×#432	C₂²	1	1	yes	characteristic
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	C₂×C₁₃×C₂²⋊C₈	—	2	2	no	—
32	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
33	C₁₃×#335	C₂²	1	2	yes	complemented
34	C₁₃×#334	C₂²	1	2	yes	complemented
35	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
36	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
37	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
38	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
39	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
42	C₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	—	2	1	no	—
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	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
51	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₁₃×#125	—	2	1	no	—
53	C₁₃×C₂²⋊Q₈	—	2	1	no	—
54	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
55	C₄×Q₈×C₁₃	—	2	1	no	—
56	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
57	C₄×D₄×C₁₃	—	2	1	no	—
58	C₄×D₄×C₁₃	—	2	1	no	—
59	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
60	C₄×D₄×C₁₃	C₂³	1	2	yes	—
61	C₁₃×#117	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₁₃×C₂²⋊C₄	—	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	2	no	—
84	C₁₃×#97	—	2	1	no	—
85	C₁₃×#97	—	2	1	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	#17924	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂×D₄×C₁₃	—	2	4	no	—
99	C₂×D₄×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	8	2	no	—
105	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
108	C₁₃×SD₁₆	—	2	4	no	—
109	C₁₃×SD₁₆	—	2	4	no	—
110	C₁₃×M₁₆	—	4	2	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	8	2	no	—
116	C₂×C₈×C₁₃	—	8	2	no	—
117	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
121	C₁₃×C₄⋊C₄	—	2	1	no	—
122	C₁₃×C₄⋊C₄	—	2	1	no	—
123	C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	2	2	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	C₁₃×C₂²⋊C₄	—	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	#3101	C₂×C₁₃	1	1	yes	characteristic
138	#2985	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#2972	C₂×C₁₃	1	1	yes	characteristic
140	#1585	C₂×C₁₃	1	2	yes	complemented
141	#1582	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	#1490	C₂×C₁₃	1	1	yes	characteristic
146	#1485	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#1453	C₂×C₁₃	1	1	yes	characteristic, complemented
148	C₂³×C₁₃	—	2	4	no	—
149	C₂³×C₁₃	—	2	2	no	—
150	C₂³×C₁₃	—	8	1	no	—
151	C₂³×C₁₃	—	8	1	no	—
152	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
153	Q₈×C₁₃	—	2	2	no	—
154	Q₈×C₁₃	—	2	2	no	—
155	Q₈×C₁₃	—	8	1	no	—
156	D₄×C₁₃	—	2	4	no	—
157	D₄×C₁₃	—	2	2	no	—
158	D₄×C₁₃	#131	1	4	yes	—
159	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	8	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	#533	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
185	#483	C₄×C₁₃	1	2	yes	—
186	#476	C₄×C₁₃	1	2	yes	—
187	#461	C₄×C₁₃	1	2	yes	—
188	#450	C₄×C₁₃	1	2	yes	—
189	#446	—	2	2	no	—
190	#446	C₂²×C₁₃	1	2	yes	complemented
191	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
192	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
193	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
194	C₈×D₄	—	2	2	no	—
195	C₈×D₄	C₂²×C₁₃	1	2	yes	—
196	C₈×D₄	C₂²×C₁₃	1	2	yes	—
197	#433	—	2	2	no	—
198	#432	C₂²×C₁₃	1	1	yes	characteristic
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	C₂×C₂²⋊C₈	—	2	2	no	—
203	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
204	#335	C₂²×C₁₃	1	2	yes	complemented
205	#334	C₂²×C₁₃	1	2	yes	complemented
206	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	complemented
207	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	complemented
208	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
209	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
210	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
211	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
212	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
213	C₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
214	C₂²×C₁₃	—	2	1	no	—
215	C₂²×C₁₃	—	2	4	no	—
216	C₂²×C₁₃	—	2	1	no	—
217	C₂²×C₁₃	—	2	1	no	—
218	C₂²×C₁₃	—	4	2	no	—
219	C₂²×C₁₃	—	4	2	no	—
220	C₂²×C₁₃	—	8	4	no	—
221	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
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	—	4	2	no	—
229	C₄×C₁₃	C₂×#131	1	2	yes	—
230	C₄×C₁₃	#577	1	2	yes	—
231	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
232	C₂³×C₄	—	2	1	no	—
233	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
234	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
235	C₂×M₁₆	—	2	1	no	—
236	C₂²×C₈	—	2	2	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
239	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
240	#125	—	2	1	no	—
241	C₂²⋊Q₈	—	2	1	no	—
242	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
243	C₄×Q₈	—	2	1	no	—
244	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
248	C₄×D₄	C₂³×C₁₃	1	2	yes	—
249	#117	—	2	1	no	—
250	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
253	#106	C₂×C₄×C₁₃	1	2	yes	—
254	#106	C₂×C₄×C₁₃	1	2	yes	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
258	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
259	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
260	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
261	#103	C₂×C₄×C₁₃	1	2	yes	—
262	#103	C₂×C₄×C₁₃	1	2	yes	—
263	#102	C₂×C₄×C₁₃	1	2	yes	—
264	#102	C₂×C₄×C₁₃	1	2	yes	—
265	C₂²⋊C₈	—	2	1	no	—
266	C₂²⋊C₈	—	2	1	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	—	2	2	no	—
269	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
270	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
271	#97	—	2	2	no	—
272	#97	—	2	1	no	—
273	#97	—	2	1	no	—
274	C₄×C₈	—	2	2	no	—
275	C₄×C₈	—	2	1	no	—
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	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
282	C₂×C₁₃	—	4	1	no	—
283	C₂×C₁₃	—	4	4	no	—
284	C₂×C₁₃	#2929	1	1	yes	characteristic
285	C₂×C₁₃	#2949	1	1	yes	characteristic
286	C₂×C₁₃	#2956	1	1	yes	characteristic
287	C₂⁴	—	2	1	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	8	2	no	—
297	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
300	SD₁₆	—	2	4	no	—
301	SD₁₆	—	2	4	no	—
302	M₁₆	—	4	2	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	8	2	no	—
308	C₂×C₈	—	8	2	no	—
309	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
310	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
311	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
312	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
320	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
326	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
327	C₄²	C₁₃×#41	1	1	yes	characteristic
328	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
329	C₁₃	#17924	1	1	yes	characteristic, direct product factor, Sylow
330	C₂³	—	2	4	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	8	1	no	—
333	C₂³	—	8	1	no	—
334	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
335	Q₈	—	2	2	no	—
336	Q₈	—	2	2	no	—
337	Q₈	—	8	1	no	—
338	D₄	—	2	4	no	—
339	D₄	—	2	2	no	—
340	D₄	C₁₃×#131	1	4	yes	—
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	2	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
354	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
356	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
357	C₈	—	2	2	no	—
358	C₈	—	2	2	no	—
359	C₈	—	2	2	no	—
360	C₈	—	2	2	no	—
361	C₈	—	2	2	no	—
362	C₈	—	4	1	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	2	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	8	4	no	—
372	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	C₂×C₁₃×#131	1	2	yes	—
381	C₄	C₁₃×#577	1	2	yes	—
382	C₂	—	4	1	no	—
383	C₂	—	4	4	no	—
384	C₂	C₁₃×#2929	1	1	yes	characteristic
385	C₂	C₁₃×#2949	1	1	yes	characteristic
386	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	C₂²×D₄×C₁₃	C₂×C₄
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×#2985	C₂	semidirect
4. C₁₃×#1585	C₂	semidirect
5. C₁₃×#1582	C₂	semidirect
6. C₁₃×SD₁₆⋊C₈	C₂	semidirect
7. C₈×C₁₃×SD₁₆	C₂	semidirect
8. C₁₃×#1572	C₂	semidirect
10. C₁₃×#1485	C₂	semidirect
11. C₁₃×#1453	C₂	semidirect
19. C₁₃×#446	C₂²	semidirect
20. C₈×Q₈×C₁₃	C₂²	semidirect
33. C₁₃×#335	C₂²	semidirect
34. C₁₃×#334	C₂²	semidirect
35. C₁₃×Q₈⋊C₈	C₂²	semidirect
36. C₁₃×Q₈⋊C₈	C₂²	semidirect
39. C₁₃×#322	C₂²	semidirect
40. C₁₃×#322	C₂²	semidirect
41. C₁₃×#322	C₂²	semidirect
42. C₈²×C₁₃	C₂²	semidirect
94. #17924	C₁₃	direct (N × H)
138. #2985	C₂×C₁₃	semidirect
140. #1585	C₂×C₁₃	semidirect
141. #1582	C₂×C₁₃	semidirect
142. SD₁₆⋊C₈	C₂×C₁₃	semidirect
143. C₈×SD₁₆	C₂×C₁₃	semidirect
144. #1572	C₂×C₁₃	semidirect
146. #1485	C₂×C₁₃	semidirect
147. #1453	C₂×C₁₃	semidirect
190. #446	C₂²×C₁₃	semidirect
191. C₈×Q₈	C₂²×C₁₃	semidirect
204. #335	C₂²×C₁₃	semidirect
205. #334	C₂²×C₁₃	semidirect
206. Q₈⋊C₈	C₂²×C₁₃	semidirect
207. Q₈⋊C₈	C₂²×C₁₃	semidirect
210. #322	C₂²×C₁₃	semidirect
211. #322	C₂²×C₁₃	semidirect
212. #322	C₂²×C₁₃	semidirect
213. C₈²	C₂²×C₁₃	semidirect
329. C₁₃	#17924	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×#3101	2
C₁₃×#2985	2
C₁₃×#2972	2
C₁₃×#1585	2
C₁₃×#1582	2
C₁₃×SD₁₆⋊C₈	2
C₈×C₁₃×SD₁₆	2
C₁₃×#1572	2
C₁₃×#1490	2
C₁₃×#1485	2
C₁₃×#1453	2
#17924	13

Subgroups — C13×#17924 #15704263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17924 #15704263