Subgroups — C₁₃×#25839 #15712178

Order 3328.

1062 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2059	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1862	C₂	1	4	yes	maximal
9	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#554	—	2	4	no	—
11	C₁₃×#554	—	2	4	no	—
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#125	C₂²	1	2	yes	—
15	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
16	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
17	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
21	C₁₃×#500	—	2	4	no	—
22	C₁₃×#476	—	2	4	no	—
23	C₂×C₁₃×#107	C₂²	1	4	yes	—
24	C₂×C₁₃×#106	C₂²	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#395	—	2	2	no	—
30	C₁₃×#391	—	2	1	no	—
31	C₁₃×#389	C₂²	1	4	yes	—
32	C₁₃×#384	—	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	1	no	—
38	C₂²×Q₈×C₁₃	—	2	1	no	—
39	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
40	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	—	2	1	no	—
42	C₂³×C₄×C₁₃	—	2	2	no	—
43	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₁₃×C₄⋊Q₈	—	2	2	no	—
46	C₁₃×C₄⋊Q₈	—	2	2	no	—
47	C₁₃×C₄⋊Q₈	—	2	2	no	—
48	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
49	C₁₃×#125	—	2	4	no	—
50	C₁₃×#125	—	2	4	no	—
51	C₁₃×C₂²⋊Q₈	—	2	8	no	—
52	C₁₃×C₂²⋊Q₈	—	2	16	no	—
53	C₄×Q₈×C₁₃	—	2	2	no	—
54	C₄×Q₈×C₁₃	—	2	2	no	—
55	C₄×D₄×C₁₃	—	2	4	no	—
56	C₄×D₄×C₁₃	—	2	4	no	—
57	C₄×D₄×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	D₄	1	4	yes	—
59	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
65	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	2	1	no	—
74	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#107	—	2	8	no	—
77	C₁₃×#106	—	2	4	no	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×#102	—	2	4	no	—
80	C₁₃×#102	Q₈	1	8	yes	complemented
81	C₄×C₈×C₁₃	—	2	2	no	—
82	C₁₃×#95	—	2	1	no	—
83	C₁₃×#95	—	2	4	no	—
84	#25839	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂⁴×C₁₃	—	2	1	no	—
86	C₂×Q₈×C₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₃	—	2	4	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	4	2	no	—
91	C₂×Q₈×C₁₃	—	8	2	no	—
92	C₂×Q₈×C₁₃	—	8	2	no	—
93	C₂×D₄×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
96	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	8	no	—
101	C₂²×C₄×C₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	4	2	no	—
104	C₂²×C₄×C₁₃	—	4	2	no	—
105	C₂²×C₄×C₁₃	—	8	4	no	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	4	no	—
115	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
116	C₁₃×C₄⋊C₄	—	2	8	no	—
117	C₁₃×C₄⋊C₄	—	2	8	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	4	no	—
120	C₁₃×C₄⋊C₄	—	2	4	no	—
121	C₁₃×C₄⋊C₄	—	2	1	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	4	2	no	—
127	C₁₃×C₄⋊C₄	—	8	4	no	—
128	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
129	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
130	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
131	C₁₃×C₂²⋊C₄	—	2	8	no	—
132	C₁₃×C₂²⋊C₄	—	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×#554	C₂×C₁₃	1	1	yes	characteristic
139	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂×#476	C₂×C₁₃	1	1	yes	characteristic
141	#2567	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#2059	C₂×C₁₃	1	4	yes	complemented
143	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#1862	C₂×C₁₃	1	4	yes	—
146	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
147	C₂³×C₁₃	—	2	2	no	—
148	C₂³×C₁₃	—	2	4	no	—
149	C₂³×C₁₃	—	4	1	no	—
150	C₂³×C₁₃	—	4	1	no	—
151	C₂³×C₁₃	—	4	2	no	—
152	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₁₃	—	4	4	no	—
154	Q₈×C₁₃	—	8	4	no	—
155	Q₈×C₁₃	—	8	4	no	—
156	D₄×C₁₃	—	2	2	no	—
157	D₄×C₁₃	—	2	4	no	—
158	D₄×C₁₃	C₄⋊Q₈	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	4	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	4	no	—
173	C₂×C₄×C₁₃	—	4	8	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	4	no	—
176	C₂×C₄×C₁₃	—	8	8	no	—
177	C₂×C₄×C₁₃	#120	1	2	yes	—
178	C₂×C₄×C₁₃	#120	1	2	yes	—
179	C₂×C₄×C₁₃	#135	1	2	yes	—
180	C₂×C₄×C₁₃	#137	1	2	yes	—
181	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
184	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
185	C₈×C₁₃	—	2	4	no	—
186	C₈×C₁₃	—	4	2	no	—
187	#554	—	2	4	no	—
188	#554	—	2	4	no	—
189	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
190	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×#125	C₂²×C₁₃	1	2	yes	—
192	C₂×C₂²⋊Q₈	—	2	1	no	—
193	C₂×C₂²⋊Q₈	—	2	2	no	—
194	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
196	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
197	C₂²×C₄⋊C₄	—	2	1	no	—
198	#500	—	2	4	no	—
199	#476	—	2	4	no	—
200	C₂×#107	C₂²×C₁₃	1	4	yes	—
201	C₂×#106	C₂²×C₁₃	1	2	yes	—
202	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×#102	C₂²×C₁₃	1	2	yes	—
204	C₂×#102	C₂²×C₁₃	1	2	yes	—
205	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
206	#395	—	2	2	no	—
207	#391	—	2	1	no	—
208	#389	C₂²×C₁₃	1	4	yes	—
209	#384	—	2	1	no	—
210	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
211	#340	C₂²×C₁₃	1	2	yes	—
212	#340	C₂²×C₁₃	1	4	yes	—
213	#336	C₂²×C₁₃	1	4	yes	—
214	C₂²×C₁₃	—	2	4	no	—
215	C₂²×C₁₃	—	4	4	no	—
216	C₂²×C₁₃	—	4	4	no	—
217	C₂²×C₁₃	—	4	2	no	—
218	C₂²×C₁₃	—	4	2	no	—
219	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
220	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
221	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
222	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
223	C₂²×C₁₃	#576	1	2	yes	—
224	C₄×C₁₃	—	2	2	no	—
225	C₄×C₁₃	—	4	4	no	—
226	C₄×C₁₃	—	4	2	no	—
227	C₄×C₁₃	—	4	2	no	—
228	C₄×C₁₃	—	4	2	no	—
229	C₄×C₁₃	—	4	4	no	—
230	C₄×C₁₃	—	8	2	no	—
231	C₄×C₁₃	#452	1	4	yes	—
232	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
233	C₄×C₁₃	#536	1	1	yes	characteristic
234	C₄×C₁₃	D₄×Q₈	1	2	yes	—
235	C₂²×Q₈	—	2	1	no	—
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
238	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
239	C₂³×C₄	—	2	1	no	—
240	C₂³×C₄	—	2	2	no	—
241	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
242	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	—	2	2	no	—
245	C₄⋊Q₈	—	2	2	no	—
246	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
247	#125	—	2	4	no	—
248	#125	—	2	4	no	—
249	C₂²⋊Q₈	—	2	8	no	—
250	C₂²⋊Q₈	—	2	16	no	—
251	C₄×Q₈	—	2	2	no	—
252	C₄×Q₈	—	2	2	no	—
253	C₄×D₄	—	2	4	no	—
254	C₄×D₄	—	2	4	no	—
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	D₄×C₁₃	1	4	yes	—
257	C₂×C₄⋊C₄	—	2	8	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	4	no	—
263	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
264	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
273	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
274	#107	—	2	8	no	—
275	#106	—	2	4	no	—
276	C₄⋊C₈	—	2	2	no	—
277	#102	—	2	4	no	—
278	#102	Q₈×C₁₃	1	8	yes	complemented
279	C₄×C₈	—	2	2	no	—
280	#95	—	2	1	no	—
281	#95	—	2	4	no	—
282	C₂×C₁₃	—	4	4	no	—
283	C₂×C₁₃	#2434	1	1	yes	characteristic
284	C₂×C₁₃	C₂×#452	1	1	yes	characteristic
285	C₂×C₁₃	#3008	1	1	yes	characteristic
286	C₂×C₁₃	#3380	1	2	yes	—
287	C₂×C₁₃	#3385	1	2	yes	—
288	C₂⁴	—	2	1	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	—	8	2	no	—
295	C₂×Q₈	—	8	2	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
299	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	8	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	8	4	no	—
309	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
313	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
319	C₄⋊C₄	—	2	8	no	—
320	C₄⋊C₄	—	2	8	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	—	8	4	no	—
331	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
332	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
333	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
334	C₂²⋊C₄	—	2	8	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	4	2	no	—
339	C₄²	C₂×D₄×C₁₃	1	2	yes	—
340	C₄²	C₂×D₄×C₁₃	1	2	yes	—
341	C₁₃	#25839	1	1	yes	characteristic, direct product factor, Sylow
342	C₂³	—	2	2	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
348	Q₈	—	4	4	no	—
349	Q₈	—	8	4	no	—
350	Q₈	—	8	4	no	—
351	D₄	—	2	2	no	—
352	D₄	—	2	4	no	—
353	D₄	C₁₃×C₄⋊Q₈	1	4	yes	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	8	8	no	—
372	C₂×C₄	C₁₃×#120	1	2	yes	—
373	C₂×C₄	C₁₃×#120	1	2	yes	—
374	C₂×C₄	C₁₃×#135	1	2	yes	—
375	C₂×C₄	C₁₃×#137	1	2	yes	—
376	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
378	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
379	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
380	C₈	—	2	4	no	—
381	C₈	—	4	2	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	4	2	no	—
387	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
388	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
389	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
390	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
391	C₂²	C₁₃×#576	1	2	yes	—
392	C₄	—	2	2	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	4	no	—
395	C₄	—	4	4	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	8	2	no	—
399	C₄	C₁₃×#452	1	4	yes	—
400	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
401	C₄	C₁₃×#536	1	1	yes	characteristic
402	C₄	D₄×Q₈×C₁₃	1	2	yes	—
403	C₂	—	4	4	no	—
404	C₂	C₁₃×#2434	1	1	yes	characteristic
405	C₂	C₂×C₁₃×#452	1	1	yes	characteristic
406	C₂	C₁₃×#3008	1	1	yes	characteristic
407	C₂	C₁₃×#3380	1	2	yes	—
408	C₂	C₁₃×#3385	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
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
2. C₂×C₁₃×#500	C₂	semidirect
4. C₁₃×#2567	C₂	semidirect
5. C₁₃×#2059	C₂	semidirect
6. C₁₃×#1987	C₂	semidirect
7. C₁₃×#1984	C₂	semidirect
80. C₁₃×#102	Q₈	semidirect
84. #25839	C₁₃	direct (N × H)
139. C₂×#500	C₂×C₁₃	semidirect
141. #2567	C₂×C₁₃	semidirect
142. #2059	C₂×C₁₃	semidirect
143. #1987	C₂×C₁₃	semidirect
144. #1984	C₂×C₁₃	semidirect
278. #102	Q₈×C₁₃	semidirect
341. C₁₃	#25839	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×#554	2
C₂×C₁₃×#500	2
C₂×C₁₃×#476	2
C₁₃×#2567	2
C₁₃×#2059	2
C₁₃×#1987	2
C₁₃×#1984	2
C₁₃×#1862	2
C₄×C₁₃×#102	2
#25839	13

Subgroups — C13×#25839 #15712178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25839 #15712178