Subgroups — C₁₃×#26088 #15712427

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2552	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2096	C₂	1	2	yes	maximal
4	C₁₃×#2066	C₂	1	2	yes	maximal
5	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1948	C₂	1	2	yes	maximal
7	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1919	C₂	1	2	yes	maximal
9	C₁₃×#1844	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#125	—	2	1	no	—
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#106	C₂²	1	2	yes	—
15	C₂×C₁₃×#106	C₂²	1	2	yes	—
16	C₂×C₁₃×#106	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#103	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#398	—	2	2	no	—
24	C₁₃×#391	C₂²	1	2	yes	—
25	C₁₃×#389	—	2	1	no	—
26	C₁₃×#389	C₂²	1	2	yes	—
27	C₁₃×#387	—	2	2	no	—
28	C₁₃×#384	C₂²	1	1	yes	characteristic
29	C₁₃×#384	C₂²	1	2	yes	—
30	C₁₃×#384	C₂²	1	1	yes	characteristic
31	C₁₃×#382	—	2	1	no	—
32	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₁₃×#125	—	4	4	no	—
46	C₄×Q₈×C₁₃	—	2	2	no	—
47	C₄×Q₈×C₁₃	Q₈	1	4	yes	—
48	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
57	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	—	2	1	no	—
64	C₂×C₄²×C₁₃	—	2	1	no	—
65	C₂×C₄²×C₁₃	—	2	2	no	—
66	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×#106	—	2	4	no	—
69	C₁₃×#106	—	4	2	no	—
70	C₁₃×#106	—	4	2	no	—
71	C₁₃×C₄⋊C₈	—	2	4	no	—
72	C₁₃×C₄⋊C₈	—	2	2	no	—
73	C₁₃×#103	—	2	2	no	—
74	C₁₃×#103	—	2	2	no	—
75	C₁₃×#103	—	4	2	no	—
76	C₄×C₈×C₁₃	—	2	2	no	—
77	C₁₃×#95	—	2	2	no	—
78	C₁₃×#95	—	2	2	no	—
79	C₁₃×#95	—	2	1	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	D₄	1	2	yes	—
83	#26088	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂×Q₈×C₁₃	—	2	1	no	—
85	C₂×Q₈×C₁₃	—	2	1	no	—
86	C₂×Q₈×C₁₃	—	2	1	no	—
87	C₂×Q₈×C₁₃	—	2	1	no	—
88	C₂×Q₈×C₁₃	—	2	1	no	—
89	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₁₃	—	2	1	no	—
102	C₂×C₈×C₁₃	—	2	1	no	—
103	C₂×C₈×C₁₃	—	2	1	no	—
104	C₂×C₈×C₁₃	—	2	1	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	#41	1	2	yes	—
109	C₂×C₈×C₁₃	#41	1	2	yes	—
110	C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	4	4	no	—
122	C₁₃×C₄⋊C₄	—	4	4	no	—
123	C₁₃×C₄⋊C₄	—	4	2	no	—
124	C₁₃×C₄⋊C₄	—	4	2	no	—
125	C₁₃×C₄⋊C₄	—	8	1	no	—
126	C₁₃×C₄⋊C₄	—	8	1	no	—
127	C₁₃×C₄⋊C₄	—	8	2	no	—
128	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	—
129	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
130	C₄²×C₁₃	—	2	4	no	—
131	C₄²×C₁₃	—	2	2	no	—
132	C₄²×C₁₃	—	2	2	no	—
133	C₄²×C₁₃	—	4	2	no	—
134	C₄²×C₁₃	—	8	2	no	—
135	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
136	C₄²×C₁₃	#41	1	2	yes	—
137	#2552	C₂×C₁₃	1	1	yes	characteristic
138	#2355	C₂×C₁₃	1	1	yes	characteristic
139	#2096	C₂×C₁₃	1	2	yes	—
140	#2066	C₂×C₁₃	1	2	yes	—
141	#1948	C₂×C₁₃	1	2	yes	—
142	#1948	C₂×C₁₃	1	1	yes	characteristic
143	#1939	C₂×C₁₃	1	1	yes	characteristic
144	#1919	C₂×C₁₃	1	2	yes	—
145	#1844	C₂×C₁₃	1	1	yes	characteristic
146	#1803	C₂×C₁₃	1	1	yes	characteristic
147	C₄×#103	C₂×C₁₃	1	1	yes	characteristic
148	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₁₃	—	2	2	no	—
150	Q₈×C₁₃	—	2	2	no	—
151	Q₈×C₁₃	—	4	1	no	—
152	Q₈×C₁₃	—	4	1	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	2	1	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
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	—	4	1	no	—
163	C₂×C₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
180	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
181	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
182	C₂×C₄×C₁₃	#137	1	2	yes	—
183	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
189	C₈×C₁₃	—	2	2	no	—
190	C₈×C₁₃	—	2	2	no	—
191	C₈×C₁₃	—	4	2	no	—
192	C₂×#125	—	2	1	no	—
193	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×#106	C₂²×C₁₃	1	2	yes	—
195	C₂×#106	C₂²×C₁₃	1	2	yes	—
196	C₂×#106	C₂²×C₁₃	1	2	yes	—
197	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
199	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×#103	C₂²×C₁₃	1	2	yes	—
202	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
203	#398	—	2	2	no	—
204	#391	C₂²×C₁₃	1	2	yes	—
205	#389	—	2	1	no	—
206	#389	C₂²×C₁₃	1	2	yes	—
207	#387	—	2	2	no	—
208	#384	C₂²×C₁₃	1	1	yes	characteristic
209	#384	C₂²×C₁₃	1	2	yes	—
210	#384	C₂²×C₁₃	1	1	yes	characteristic
211	#382	—	2	1	no	—
212	C₄×C₄⋊C₄	—	2	1	no	—
213	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
214	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
215	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
216	#340	C₂²×C₁₃	1	2	yes	—
217	#340	C₂²×C₁₃	1	2	yes	—
218	#340	C₂²×C₁₃	1	1	yes	characteristic
219	#340	C₂²×C₁₃	1	1	yes	characteristic
220	#336	C₂²×C₁₃	1	2	yes	—
221	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
222	C₂²×C₁₃	#547	1	1	yes	characteristic
223	C₂²×C₁₃	#550	1	1	yes	characteristic
224	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
225	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
226	C₂²×C₁₃	#577	1	1	yes	characteristic
227	C₂²×C₁₃	#577	1	1	yes	characteristic
228	C₄×C₁₃	—	2	4	no	—
229	C₄×C₁₃	—	2	2	no	—
230	C₄×C₁₃	—	4	2	no	—
231	C₄×C₁₃	—	4	2	no	—
232	C₄×C₁₃	—	4	2	no	—
233	C₄×C₁₃	—	8	1	no	—
234	C₄×C₁₃	—	8	1	no	—
235	C₄×C₁₃	—	8	2	no	—
236	C₄×C₁₃	—	8	2	no	—
237	C₄×C₁₃	#475	1	4	yes	—
238	C₄×C₁₃	#533	1	1	yes	characteristic
239	C₄×C₁₃	#544	1	1	yes	characteristic
240	C₄×C₁₃	#552	1	1	yes	characteristic
241	C₄×C₁₃	#553	1	1	yes	characteristic
242	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
244	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
246	#125	—	4	4	no	—
247	C₄×Q₈	—	2	2	no	—
248	C₄×Q₈	Q₈×C₁₃	1	4	yes	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
268	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
269	#106	—	2	4	no	—
270	#106	—	4	2	no	—
271	#106	—	4	2	no	—
272	C₄⋊C₈	—	2	4	no	—
273	C₄⋊C₈	—	2	2	no	—
274	#103	—	2	2	no	—
275	#103	—	2	2	no	—
276	#103	—	4	2	no	—
277	C₄×C₈	—	2	2	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	1	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	D₄×C₁₃	1	2	yes	—
284	C₂×C₁₃	#2441	1	1	yes	characteristic
285	C₂×C₁₃	C₂×#475	1	1	yes	characteristic
286	C₂×C₁₃	#3084	1	1	yes	characteristic
287	C₂×C₁₃	#3335	1	1	yes	characteristic
288	C₂×C₁₃	#3356	1	1	yes	characteristic
289	C₂×C₁₃	#3392	1	1	yes	characteristic
290	C₂×C₁₃	#3400	1	1	yes	characteristic
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	C₁₃×#41	1	2	yes	—
316	C₂×C₈	C₁₃×#41	1	2	yes	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	4	4	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	8	1	no	—
333	C₄⋊C₄	—	8	1	no	—
334	C₄⋊C₄	—	8	2	no	—
335	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	—
336	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
337	C₄²	—	2	4	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	4	2	no	—
341	C₄²	—	8	2	no	—
342	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
343	C₄²	C₁₃×#41	1	2	yes	—
344	C₁₃	#26088	1	1	yes	characteristic, direct product factor, Sylow
345	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
346	Q₈	—	2	2	no	—
347	Q₈	—	2	2	no	—
348	Q₈	—	4	1	no	—
349	Q₈	—	4	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
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	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
376	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
377	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
378	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
379	C₂×C₄	C₁₃×#137	1	2	yes	—
380	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
382	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
383	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
384	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
385	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
386	C₈	—	2	2	no	—
387	C₈	—	2	2	no	—
388	C₈	—	4	2	no	—
389	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
390	C₂²	C₁₃×#547	1	1	yes	characteristic
391	C₂²	C₁₃×#550	1	1	yes	characteristic
392	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
393	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
394	C₂²	C₁₃×#577	1	1	yes	characteristic
395	C₂²	C₁₃×#577	1	1	yes	characteristic
396	C₄	—	2	4	no	—
397	C₄	—	2	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	2	no	—
405	C₄	C₁₃×#475	1	4	yes	—
406	C₄	C₁₃×#533	1	1	yes	characteristic
407	C₄	C₁₃×#544	1	1	yes	characteristic
408	C₄	C₁₃×#552	1	1	yes	characteristic
409	C₄	C₁₃×#553	1	1	yes	characteristic
410	C₂	C₁₃×#2441	1	1	yes	characteristic
411	C₂	C₂×C₁₃×#475	1	1	yes	characteristic
412	C₂	C₁₃×#3084	1	1	yes	characteristic
413	C₂	C₁₃×#3335	1	1	yes	characteristic
414	C₂	C₁₃×#3356	1	1	yes	characteristic
415	C₂	C₁₃×#3392	1	1	yes	characteristic
416	C₂	C₁₃×#3400	1	1	yes	characteristic

	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 ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
83. #26088	C₁₃	direct (N × H)
344. C₁₃	#26088	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×#2552	2
C₁₃×#2355	2
C₁₃×#2096	2
C₁₃×#2066	2
C₁₃×#1948	2
C₁₃×#1939	2
C₁₃×#1919	2
C₁₃×#1844	2
C₁₃×#1803	2
C₄×C₁₃×#103	2
#26088	13

Subgroups — C13×#26088 #15712427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26088 #15712427