Subgroups — C₁₃×#25936 #15712275

Order 3328.

1034 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2568	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2024	C₂	1	4	yes	maximal
6	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1878	C₂	1	4	yes	maximal
9	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
11	Q₈²×C₁₃	—	2	4	no	—
12	Q₈²×C₁₃	—	2	4	no	—
13	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#487	—	2	4	no	—
23	C₁₃×#462	—	2	4	no	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#103	C₂²	1	4	yes	—
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#400	—	2	2	no	—
30	C₁₃×#391	—	2	1	no	—
31	C₁₃×#391	C₂²	1	4	yes	—
32	C₁₃×#382	—	2	1	no	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	4	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₃	—	2	2	no	—
38	C₂²×Q₈×C₁₃	—	2	1	no	—
39	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
40	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
41	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₂×C₁₃×Q₁₆	—	2	4	no	—
43	C₂×C₁₃×Q₁₆	—	2	8	no	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₁₃×C₄⋊Q₈	—	2	16	no	—
47	C₁₃×C₄⋊Q₈	—	2	8	no	—
48	C₁₃×C₄⋊Q₈	—	2	4	no	—
49	C₁₃×C₄⋊Q₈	—	2	4	no	—
50	C₁₃×C₄⋊Q₈	—	2	2	no	—
51	C₁₃×C₄⋊Q₈	—	2	2	no	—
52	C₁₃×C₄⋊Q₈	—	2	2	no	—
53	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
54	C₄×Q₈×C₁₃	—	2	8	no	—
55	C₄×Q₈×C₁₃	—	2	4	no	—
56	C₄×Q₈×C₁₃	—	2	4	no	—
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×Q₈×C₁₃	—	2	2	no	—
59	C₄×Q₈×C₁₃	—	2	2	no	—
60	C₄×Q₈×C₁₃	D₄	1	4	yes	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	—	2	2	no	—
73	C₂×C₄²×C₁₃	—	2	1	no	—
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×#103	—	2	4	no	—
79	C₁₃×#103	—	2	4	no	—
80	C₁₃×#103	—	2	8	no	—
81	C₄×C₈×C₁₃	—	2	2	no	—
82	C₁₃×#95	—	2	1	no	—
83	C₁₃×#95	—	2	4	no	—
84	C₁₃×#95	—	2	4	no	—
85	#25936	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂×Q₈×C₁₃	—	2	8	no	—
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	4	no	—
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	2	1	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	4	no	—
95	C₂×Q₈×C₁₃	—	2	4	no	—
96	C₂×Q₈×C₁₃	—	8	2	no	—
97	C₂×Q₈×C₁₃	—	8	4	no	—
98	C₂×Q₈×C₁₃	Q₁₆	1	4	yes	complemented
99	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
100	C₂×Q₈×C₁₃	#41	1	4	yes	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
111	C₁₃×Q₁₆	—	4	8	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	4	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	8	no	—
118	C₁₃×C₄⋊C₄	—	2	8	no	—
119	C₁₃×C₄⋊C₄	—	2	4	no	—
120	C₁₃×C₄⋊C₄	—	2	4	no	—
121	C₁₃×C₄⋊C₄	—	2	4	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	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	—	4	2	no	—
128	C₁₃×C₄⋊C₄	—	4	2	no	—
129	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
130	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
131	C₄²×C₁₃	—	2	8	no	—
132	C₄²×C₁₃	—	2	4	no	—
133	C₄²×C₁₃	—	2	2	no	—
134	C₄²×C₁₃	—	2	2	no	—
135	C₄²×C₁₃	—	4	2	no	—
136	C₄²×C₁₃	C₂×D₄	1	2	yes	—
137	C₄²×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×Q₈²	C₂×C₁₃	1	1	yes	characteristic
139	C₂×#487	C₂×C₁₃	1	1	yes	characteristic
140	C₂×#462	C₂×C₁₃	1	1	yes	characteristic
141	#2568	C₂×C₁₃	1	1	yes	characteristic
142	#2024	C₂×C₁₃	1	4	yes	—
143	#1987	C₂×C₁₃	1	1	yes	characteristic
144	#1984	C₂×C₁₃	1	1	yes	characteristic
145	#1878	C₂×C₁₃	1	4	yes	—
146	C₄×#103	C₂×C₁₃	1	1	yes	characteristic
147	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₁₃	—	2	2	no	—
149	Q₈×C₁₃	—	2	4	no	—
150	Q₈×C₁₃	—	2	8	no	—
151	Q₈×C₁₃	—	4	2	no	—
152	Q₈×C₁₃	—	4	2	no	—
153	Q₈×C₁₃	—	4	4	no	—
154	Q₈×C₁₃	—	8	4	no	—
155	Q₈×C₁₃	—	8	8	no	—
156	Q₈×C₁₃	#124	1	4	yes	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	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	4	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	4	no	—
166	C₂×C₄×C₁₃	—	4	4	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	4	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	#120	1	2	yes	—
174	C₂×C₄×C₁₃	#120	1	2	yes	—
175	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
176	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
177	C₂×C₄×C₁₃	#137	1	2	yes	—
178	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
181	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
182	C₈×C₁₃	—	4	2	no	—
183	C₈×C₁₃	—	4	2	no	—
184	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
185	Q₈²	—	2	4	no	—
186	Q₈²	—	2	4	no	—
187	C₂×C₄⋊Q₈	—	2	1	no	—
188	C₂×C₄⋊Q₈	—	2	2	no	—
189	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
190	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
191	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×C₄×Q₈	—	2	1	no	—
193	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
194	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
196	#487	—	2	4	no	—
197	#462	—	2	4	no	—
198	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×#103	C₂²×C₁₃	1	4	yes	—
200	C₂×#103	C₂²×C₁₃	1	2	yes	—
201	C₂×#103	C₂²×C₁₃	1	2	yes	—
202	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
203	#400	—	2	2	no	—
204	#391	—	2	1	no	—
205	#391	C₂²×C₁₃	1	4	yes	—
206	#382	—	2	1	no	—
207	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
208	#340	C₂²×C₁₃	1	4	yes	—
209	#340	C₂²×C₁₃	1	2	yes	—
210	#336	C₂²×C₁₃	1	4	yes	—
211	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
212	C₂²×C₁₃	#548	1	2	yes	—
213	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
214	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
215	C₂²×C₁₃	#577	1	2	yes	—
216	C₄×C₁₃	—	2	4	no	—
217	C₄×C₁₃	—	2	4	no	—
218	C₄×C₁₃	—	2	2	no	—
219	C₄×C₁₃	—	4	2	no	—
220	C₄×C₁₃	—	4	4	no	—
221	C₄×C₁₃	—	4	2	no	—
222	C₄×C₁₃	—	8	2	no	—
223	C₄×C₁₃	—	8	2	no	—
224	C₄×C₁₃	#451	1	4	yes	—
225	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
226	C₄×C₁₃	#536	1	1	yes	characteristic
227	C₄×C₁₃	#548	1	2	yes	—
228	C₂²×Q₈	—	2	2	no	—
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
231	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
232	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
233	C₂×Q₁₆	—	2	4	no	—
234	C₂×Q₁₆	—	2	8	no	—
235	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
236	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
237	C₄⋊Q₈	—	2	16	no	—
238	C₄⋊Q₈	—	2	8	no	—
239	C₄⋊Q₈	—	2	4	no	—
240	C₄⋊Q₈	—	2	4	no	—
241	C₄⋊Q₈	—	2	2	no	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
245	C₄×Q₈	—	2	8	no	—
246	C₄×Q₈	—	2	4	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	D₄×C₁₃	1	4	yes	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
259	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
261	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
267	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
268	C₄⋊C₈	—	2	2	no	—
269	#103	—	2	4	no	—
270	#103	—	2	4	no	—
271	#103	—	2	8	no	—
272	C₄×C₈	—	2	2	no	—
273	#95	—	2	1	no	—
274	#95	—	2	4	no	—
275	#95	—	2	4	no	—
276	C₂×C₁₃	#2436	1	1	yes	characteristic
277	C₂×C₁₃	C₂×#451	1	1	yes	characteristic
278	C₂×C₁₃	#3009	1	1	yes	characteristic
279	C₂×C₁₃	#3363	1	2	yes	—
280	C₂×C₁₃	#3369	1	2	yes	—
281	C₂×Q₈	—	2	8	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	8	2	no	—
292	C₂×Q₈	—	8	4	no	—
293	C₂×Q₈	C₁₃×Q₁₆	1	4	yes	complemented
294	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
295	C₂×Q₈	C₁₃×#41	1	4	yes	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
306	Q₁₆	—	4	8	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	2	2	no	—
312	C₄⋊C₄	—	2	8	no	—
313	C₄⋊C₄	—	2	8	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
325	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
326	C₄²	—	2	8	no	—
327	C₄²	—	2	4	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	4	2	no	—
331	C₄²	C₂×D₄×C₁₃	1	2	yes	—
332	C₄²	C₂×D₄×C₁₃	1	2	yes	—
333	C₁₃	#25936	1	1	yes	characteristic, direct product factor, Sylow
334	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
335	Q₈	—	2	8	no	—
336	Q₈	—	2	2	no	—
337	Q₈	—	2	4	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	4	4	no	—
341	Q₈	—	8	4	no	—
342	Q₈	—	8	8	no	—
343	Q₈	C₁₃×#124	1	4	yes	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	C₁₃×#120	1	2	yes	—
361	C₂×C₄	C₁₃×#120	1	2	yes	—
362	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
363	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
364	C₂×C₄	C₁₃×#137	1	2	yes	—
365	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
367	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
368	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
369	C₈	—	4	2	no	—
370	C₈	—	4	2	no	—
371	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
372	C₂²	C₁₃×#548	1	2	yes	—
373	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
374	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
375	C₂²	C₁₃×#577	1	2	yes	—
376	C₄	—	2	2	no	—
377	C₄	—	2	4	no	—
378	C₄	—	2	4	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	4	no	—
381	C₄	—	4	2	no	—
382	C₄	—	8	2	no	—
383	C₄	—	8	2	no	—
384	C₄	C₁₃×#451	1	4	yes	—
385	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
386	C₄	C₁₃×#536	1	1	yes	characteristic
387	C₄	C₁₃×#548	1	2	yes	—
388	C₂	C₁₃×#2436	1	1	yes	characteristic
389	C₂	C₂×C₁₃×#451	1	1	yes	characteristic
390	C₂	C₁₃×#3009	1	1	yes	characteristic
391	C₂	C₁₃×#3363	1	2	yes	—
392	C₂	C₁₃×#3369	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
85. #25936	C₁₃	direct (N × H)
98. C₂×Q₈×C₁₃	Q₁₆	semidirect
293. C₂×Q₈	C₁₃×Q₁₆	semidirect
333. C₁₃	#25936	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×Q₈²×C₁₃	2
C₂×C₁₃×#487	2
C₂×C₁₃×#462	2
C₁₃×#2568	2
C₁₃×#2024	2
C₁₃×#1987	2
C₁₃×#1984	2
C₁₃×#1878	2
C₄×C₁₃×#103	2
#25936	13

Subgroups — C13×#25936 #15712275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25936 #15712275