Subgroups — C₁₃×#24580 #15710919

Order 3328.

842 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#483	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×#106	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2502	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2344	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2084	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2066	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1948	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1927	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1892	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1850	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1824	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	—	2	1	no	—
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₁₃×#483	—	2	4	no	—
18	C₂×C₁₃×#106	—	2	4	no	—
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	2	yes	—
22	C₂×C₁₃×#106	C₂²	1	2	yes	—
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₃×#398	—	2	2	no	—
29	C₁₃×#391	C₂²	1	2	yes	—
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#387	—	2	2	no	—
32	C₁₃×#385	—	2	1	no	—
33	C₁₃×#385	—	2	1	no	—
34	C₁₃×#384	C₂²	1	2	yes	—
35	C₁₃×#381	—	2	1	no	—
36	C₁₃×#380	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
38	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	—	2	1	no	—
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	—	2	2	no	—
48	C₂²×C₈×C₁₃	—	2	4	no	—
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₁₃×C₂²⋊Q₈	—	2	2	no	—
53	C₁₃×C₂²⋊Q₈	—	2	2	no	—
54	C₁₃×#117	—	4	4	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
73	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	—	2	2	no	—
75	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
76	C₁₃×#106	—	2	4	no	—
77	C₁₃×#106	—	2	4	no	—
78	C₁₃×#106	—	2	2	no	—
79	C₁₃×#106	—	2	2	no	—
80	C₁₃×C₄⋊C₈	—	2	4	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#103	—	2	2	no	—
83	C₁₃×#103	—	2	2	no	—
84	C₁₃×C₂²⋊C₈	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	D₄	1	2	yes	—
91	#24580	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	4	2	no	—
107	C₂²×C₄×C₁₃	—	4	2	no	—
108	C₂²×C₄×C₁₃	—	4	2	no	—
109	C₂²×C₄×C₁₃	—	8	2	no	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	#41	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₁₃	—	2	8	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	#41	1	4	yes	—
124	C₁₃×C₄⋊C₄	—	2	4	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	4	2	no	—
134	C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₁₃×C₄⋊C₄	—	4	4	no	—
136	C₁₃×C₄⋊C₄	—	8	2	no	—
137	C₁₃×C₄⋊C₄	—	8	2	no	—
138	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
139	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
140	C₁₃×C₂²⋊C₄	—	2	2	no	—
141	C₁₃×C₂²⋊C₄	—	4	2	no	—
142	C₁₃×C₂²⋊C₄	—	4	2	no	—
143	C₁₃×C₂²⋊C₄	SD₁₆	1	4	yes	—
144	C₄²×C₁₃	—	2	2	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	—	4	4	no	—
147	C₂×#483	C₂×C₁₃	1	1	yes	characteristic
148	C₂²×#106	C₂×C₁₃	1	1	yes	characteristic
149	#2502	C₂×C₁₃	1	1	yes	characteristic
150	#2344	C₂×C₁₃	1	1	yes	characteristic
151	#2084	C₂×C₁₃	1	2	yes	complemented
152	#2066	C₂×C₁₃	1	2	yes	complemented
153	#1948	C₂×C₁₃	1	2	yes	complemented
154	#1927	C₂×C₁₃	1	2	yes	complemented
155	#1892	C₂×C₁₃	1	1	yes	characteristic
156	#1850	C₂×C₁₃	1	1	yes	characteristic
157	#1824	C₂×C₁₃	1	1	yes	characteristic
158	C₂³×C₁₃	—	2	2	no	—
159	C₂³×C₁₃	—	2	2	no	—
160	C₂³×C₁₃	#121	1	2	yes	—
161	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
162	C₂³×C₁₃	#137	1	2	yes	—
163	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₁₃	—	4	1	no	—
165	Q₈×C₁₃	—	4	1	no	—
166	Q₈×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	8	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	8	4	no	—
194	C₂×C₄×C₁₃	#121	1	2	yes	—
195	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
198	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
200	C₈×C₁₃	—	2	4	no	—
201	C₈×C₁₃	—	4	1	no	—
202	C₈×C₁₃	—	4	1	no	—
203	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×#117	—	2	1	no	—
206	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
207	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
208	#483	—	2	4	no	—
209	C₂×#106	—	2	4	no	—
210	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#106	C₂²×C₁₃	1	2	yes	—
213	C₂×#106	C₂²×C₁₃	1	2	yes	—
214	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
215	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#103	C₂²×C₁₃	1	2	yes	—
218	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
219	#398	—	2	2	no	—
220	#391	C₂²×C₁₃	1	2	yes	—
221	#389	C₂²×C₁₃	1	2	yes	—
222	#387	—	2	2	no	—
223	#385	—	2	1	no	—
224	#385	—	2	1	no	—
225	#384	C₂²×C₁₃	1	2	yes	—
226	#381	—	2	1	no	—
227	#380	C₂²×C₁₃	1	1	yes	characteristic
228	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
229	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
230	#340	C₂²×C₁₃	1	2	yes	—
231	#340	C₂²×C₁₃	1	2	yes	—
232	#340	C₂²×C₁₃	1	2	yes	—
233	#336	C₂²×C₁₃	1	2	yes	—
234	C₂²×C₁₃	—	2	4	no	—
235	C₂²×C₁₃	—	2	4	no	—
236	C₂²×C₁₃	—	2	2	no	—
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	#461	1	4	yes	—
239	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
240	C₂²×C₁₃	#547	1	2	yes	—
241	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
242	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
243	C₂²×C₁₃	#577	1	2	yes	—
244	C₄×C₁₃	—	2	4	no	—
245	C₄×C₁₃	—	2	2	no	—
246	C₄×C₁₃	—	4	2	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	8	2	no	—
250	C₄×C₁₃	—	8	1	no	—
251	C₄×C₁₃	—	8	1	no	—
252	C₄×C₁₃	—	8	2	no	—
253	C₄×C₁₃	#525	1	1	yes	characteristic
254	C₄×C₁₃	#536	1	1	yes	characteristic
255	C₄×C₁₃	#552	1	2	yes	—
256	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
257	C₂³×C₄	—	2	1	no	—
258	C₂³×C₄	—	2	1	no	—
259	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	4	no	—
262	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
265	C₂²⋊Q₈	—	2	2	no	—
266	C₂²⋊Q₈	—	2	2	no	—
267	#117	—	4	4	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
279	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
289	#106	—	2	4	no	—
290	#106	—	2	4	no	—
291	#106	—	2	2	no	—
292	#106	—	2	2	no	—
293	C₄⋊C₈	—	2	4	no	—
294	#103	—	2	4	no	—
295	#103	—	2	2	no	—
296	#103	—	2	2	no	—
297	C₂²⋊C₈	—	2	2	no	—
298	#95	—	2	2	no	—
299	#95	—	2	1	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	D₄×C₁₃	1	2	yes	—
304	C₂×C₁₃	—	2	4	no	—
305	C₂×C₁₃	#2413	1	1	yes	characteristic
306	C₂×C₁₃	C₂×#461	1	1	yes	characteristic
307	C₂×C₁₃	#3043	1	1	yes	characteristic
308	C₂×C₁₃	#3335	1	2	yes	—
309	C₂×C₁₃	#3344	1	2	yes	—
310	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	8	2	no	—
328	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
332	C₂²×C₄	C₁₃×#41	1	2	yes	—
333	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
334	C₂×C₈	—	2	8	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	C₁₃×#41	1	4	yes	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	8	2	no	—
355	C₄⋊C₄	—	8	2	no	—
356	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
357	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	C₁₃×SD₁₆	1	4	yes	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	4	4	no	—
365	C₁₃	#24580	1	1	yes	characteristic, direct product factor, Sylow
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	C₁₃×#121	1	2	yes	—
369	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
370	C₂³	C₁₃×#137	1	2	yes	—
371	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
372	Q₈	—	4	1	no	—
373	Q₈	—	4	1	no	—
374	Q₈	—	4	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	8	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	8	4	no	—
402	C₂×C₄	C₁₃×#121	1	2	yes	—
403	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
404	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
405	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
406	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
407	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
408	C₈	—	2	4	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	1	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	2	no	—
415	C₂²	C₁₃×#461	1	4	yes	—
416	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
417	C₂²	C₁₃×#547	1	2	yes	—
418	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
419	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
420	C₂²	C₁₃×#577	1	2	yes	—
421	C₄	—	2	4	no	—
422	C₄	—	2	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	8	1	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	1	no	—
430	C₄	C₁₃×#525	1	1	yes	characteristic
431	C₄	C₁₃×#536	1	1	yes	characteristic
432	C₄	C₁₃×#552	1	2	yes	—
433	C₂	—	2	4	no	—
434	C₂	C₁₃×#2413	1	1	yes	characteristic
435	C₂	C₂×C₁₃×#461	1	1	yes	characteristic
436	C₂	C₁₃×#3043	1	1	yes	characteristic
437	C₂	C₁₃×#3335	1	2	yes	—
438	C₂	C₁₃×#3344	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
5. C₁₃×#2084	C₂	semidirect
6. C₁₃×#2066	C₂	semidirect
7. C₁₃×#1948	C₂	semidirect
8. C₁₃×#1927	C₂	semidirect
91. #24580	C₁₃	direct (N × H)
151. #2084	C₂×C₁₃	semidirect
152. #2066	C₂×C₁₃	semidirect
153. #1948	C₂×C₁₃	semidirect
154. #1927	C₂×C₁₃	semidirect
365. C₁₃	#24580	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×#483	2
C₂²×C₁₃×#106	2
C₁₃×#2502	2
C₁₃×#2344	2
C₁₃×#2084	2
C₁₃×#2066	2
C₁₃×#1948	2
C₁₃×#1927	2
C₁₃×#1892	2
C₁₃×#1850	2
C₁₃×#1824	2
#24580	13

Subgroups — C13×#24580 #15710919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24580 #15710919