Subgroups — C₁₃×#10881 #15697220

Order 3328.

926 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#340	C₂	1	2	yes	maximal
4	C₂×C₁₃×#340	C₂	1	2	yes	maximal
5	C₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
7	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
8	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
9	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#97	—	2	4	no	—
13	C₂×C₁₃×#97	—	2	2	no	—
14	C₁₃×#389	—	2	2	no	—
15	C₁₃×#389	C₄	1	4	yes	complemented
16	C₂×C₁₃×#95	—	2	1	no	—
17	C₂×C₁₃×#95	—	2	1	no	—
18	C₂×C₁₃×#95	—	2	1	no	—
19	C₁₃×#340	—	2	4	no	—
20	C₁₃×#340	C₄	1	8	yes	complemented
21	C₂³×C₄×C₁₃	—	2	1	no	—
22	C₂³×C₄×C₁₃	—	2	1	no	—
23	C₂³×C₄×C₁₃	—	2	2	no	—
24	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	—	2	2	no	—
28	C₂²×C₈×C₁₃	—	2	2	no	—
29	C₂²×C₈×C₁₃	—	2	2	no	—
30	C₂²×C₈×C₁₃	—	2	2	no	—
31	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
32	C₂²×C₈×C₁₃	D₄	1	4	yes	—
33	C₂²×C₈×C₁₃	Q₈	1	4	yes	—
34	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
35	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
36	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
37	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
38	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
39	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
40	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
41	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
42	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
45	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
46	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
50	C₂×C₄²×C₁₃	—	2	2	no	—
51	C₂×C₄²×C₁₃	—	2	2	no	—
52	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₁₃	D₄	1	2	yes	—
54	C₁₃×#97	—	2	8	no	—
55	C₁₃×#95	—	2	4	no	—
56	C₁₃×#95	—	4	2	no	—
57	C₁₃×#95	—	4	2	no	—
58	#10881	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
59	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	—	2	2	no	—
61	C₂²×C₄×C₁₃	—	2	4	no	—
62	C₂²×C₄×C₁₃	—	2	2	no	—
63	C₂²×C₄×C₁₃	—	2	2	no	—
64	C₂²×C₄×C₁₃	—	2	1	no	—
65	C₂²×C₄×C₁₃	—	2	1	no	—
66	C₂²×C₄×C₁₃	—	2	2	no	—
67	C₂²×C₄×C₁₃	—	2	1	no	—
68	C₂²×C₄×C₁₃	—	2	1	no	—
69	C₂²×C₄×C₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₃	—	2	2	no	—
71	C₂²×C₄×C₁₃	—	2	4	no	—
72	C₂²×C₄×C₁₃	—	4	2	no	—
73	C₂²×C₄×C₁₃	—	4	1	no	—
74	C₂²×C₄×C₁₃	—	4	1	no	—
75	C₂²×C₄×C₁₃	—	4	2	no	—
76	C₂²×C₄×C₁₃	—	4	2	no	—
77	C₂²×C₄×C₁₃	—	4	2	no	—
78	C₂²×C₄×C₁₃	—	4	2	no	—
79	C₂²×C₄×C₁₃	—	4	2	no	—
80	C₂²×C₄×C₁₃	—	4	2	no	—
81	C₂²×C₄×C₁₃	—	4	1	no	—
82	C₂²×C₄×C₁₃	—	4	2	no	—
83	C₂²×C₄×C₁₃	—	4	1	no	—
84	C₂²×C₄×C₁₃	—	4	2	no	—
85	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₁₃	#41	1	2	yes	—
93	C₂²×C₄×C₁₃	#41	1	2	yes	—
94	C₂²×C₄×C₁₃	#41	1	2	yes	—
95	C₂×C₈×C₁₃	—	2	4	no	—
96	C₂×C₈×C₁₃	—	2	4	no	—
97	C₂×C₈×C₁₃	—	2	4	no	—
98	C₂×C₈×C₁₃	—	2	4	no	—
99	C₂×C₈×C₁₃	—	2	4	no	—
100	C₂×C₈×C₁₃	—	2	4	no	—
101	C₂×C₈×C₁₃	C₄⋊C₄	1	8	yes	complemented
102	C₁₃×C₄⋊C₄	—	2	2	no	—
103	C₁₃×C₄⋊C₄	—	2	4	no	—
104	C₁₃×C₄⋊C₄	—	2	4	no	—
105	C₁₃×C₄⋊C₄	—	2	4	no	—
106	C₁₃×C₄⋊C₄	—	2	4	no	—
107	C₁₃×C₄⋊C₄	—	4	8	no	—
108	C₁₃×C₄⋊C₄	—	4	1	no	—
109	C₁₃×C₄⋊C₄	—	4	1	no	—
110	C₁₃×C₄⋊C₄	—	4	2	no	—
111	C₁₃×C₄⋊C₄	—	4	2	no	—
112	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
113	C₄²×C₁₃	—	2	4	no	—
114	C₄²×C₁₃	—	2	2	no	—
115	C₄²×C₁₃	—	2	2	no	—
116	C₂²×#97	C₂×C₁₃	1	1	yes	characteristic
117	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
118	C₂×#340	C₂×C₁₃	1	2	yes	—
119	C₂×#340	C₂×C₁₃	1	2	yes	—
120	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic
121	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂³×C₁₃	C₄×D₄	1	2	yes	—
123	C₂³×C₁₃	#121	1	2	yes	—
124	C₂³×C₁₃	#124	1	1	yes	characteristic
125	C₂³×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
126	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
127	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
128	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
129	C₂³×C₁₃	#137	1	1	yes	characteristic
130	C₂³×C₁₃	#137	1	1	yes	characteristic
131	C₂³×C₁₃	#137	1	2	yes	—
132	C₂×C₄×C₁₃	—	2	4	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	2	2	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	2	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	4	2	no	—
140	C₂×C₄×C₁₃	—	4	2	no	—
141	C₂×C₄×C₁₃	—	4	4	no	—
142	C₂×C₄×C₁₃	—	4	4	no	—
143	C₂×C₄×C₁₃	—	4	2	no	—
144	C₂×C₄×C₁₃	—	4	2	no	—
145	C₂×C₄×C₁₃	—	4	2	no	—
146	C₂×C₄×C₁₃	—	4	2	no	—
147	C₂×C₄×C₁₃	—	4	2	no	—
148	C₂×C₄×C₁₃	—	4	4	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	4	4	no	—
152	C₂×C₄×C₁₃	—	4	4	no	—
153	C₂×C₄×C₁₃	—	8	2	no	—
154	C₂×C₄×C₁₃	—	8	2	no	—
155	C₂×C₄×C₁₃	—	8	2	no	—
156	C₂×C₄×C₁₃	—	8	2	no	—
157	C₂×C₄×C₁₃	—	8	2	no	—
158	C₂×C₄×C₁₃	—	8	2	no	—
159	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₃	#117	1	2	yes	—
162	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
167	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
168	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
170	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
171	C₂×C₄×C₁₃	#123	1	2	yes	—
172	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
173	C₂×C₄×C₁₃	#125	1	2	yes	—
174	C₂×C₄×C₁₃	#126	1	2	yes	—
175	C₈×C₁₃	—	2	8	no	—
176	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
177	C₂²×C₄⋊C₄	—	2	1	no	—
178	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
179	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
180	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
181	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
182	C₂×#97	—	2	4	no	—
183	C₂×#97	—	2	2	no	—
184	#389	—	2	2	no	—
185	#389	C₄×C₁₃	1	4	yes	complemented
186	C₂×#95	—	2	1	no	—
187	C₂×#95	—	2	1	no	—
188	C₂×#95	—	2	1	no	—
189	#340	—	2	4	no	—
190	#340	C₄×C₁₃	1	8	yes	complemented
191	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₁₃	#386	1	1	yes	characteristic
193	C₂²×C₁₃	#388	1	2	yes	—
194	C₂²×C₁₃	#389	1	2	yes	—
195	C₂²×C₁₃	#391	1	1	yes	characteristic
196	C₂²×C₁₃	#417	1	1	yes	characteristic
197	C₂²×C₁₃	#417	1	1	yes	characteristic
198	C₂²×C₁₃	#418	1	1	yes	characteristic
199	C₂²×C₁₃	#419	1	1	yes	characteristic
200	C₂²×C₁₃	#440	1	2	yes	—
201	C₂²×C₁₃	#440	1	2	yes	—
202	C₂²×C₁₃	#441	1	2	yes	—
203	C₂²×C₁₃	#442	1	2	yes	—
204	C₂²×C₁₃	#468	1	2	yes	—
205	C₂²×C₁₃	#468	1	2	yes	—
206	C₂²×C₁₃	#469	1	2	yes	—
207	C₂²×C₁₃	#470	1	2	yes	—
208	C₂²×C₁₃	#489	1	2	yes	—
209	C₂²×C₁₃	#490	1	1	yes	characteristic
210	C₂²×C₁₃	#491	1	1	yes	characteristic
211	C₂²×C₁₃	#501	1	1	yes	characteristic
212	C₂²×C₁₃	#501	1	2	yes	—
213	C₂²×C₁₃	#501	1	1	yes	characteristic
214	C₄×C₁₃	—	4	2	no	—
215	C₄×C₁₃	—	4	2	no	—
216	C₄×C₁₃	—	4	4	no	—
217	C₄×C₁₃	—	8	2	no	—
218	C₄×C₁₃	—	8	4	no	—
219	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
220	C₄×C₁₃	#385	1	2	yes	—
221	C₄×C₁₃	#387	1	2	yes	—
222	C₄×C₁₃	#387	1	2	yes	—
223	C₂³×C₄	—	2	1	no	—
224	C₂³×C₄	—	2	1	no	—
225	C₂³×C₄	—	2	2	no	—
226	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
227	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
228	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
229	C₂²×C₈	—	2	2	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
234	C₂²×C₈	D₄×C₁₃	1	4	yes	—
235	C₂²×C₈	Q₈×C₁₃	1	4	yes	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	4	4	no	—
248	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
249	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
250	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
251	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
255	C₂×C₄²	D₄×C₁₃	1	2	yes	—
256	#97	—	2	8	no	—
257	#95	—	2	4	no	—
258	#95	—	4	2	no	—
259	#95	—	4	2	no	—
260	C₂×C₁₃	#1436	1	1	yes	characteristic
261	C₂×C₁₃	#1762	1	1	yes	characteristic
262	C₂×C₁₃	#1763	1	1	yes	characteristic
263	C₂×C₁₃	#1894	1	1	yes	characteristic
264	C₂×C₁₃	#1895	1	1	yes	characteristic
265	C₂×C₁₃	#1935	1	2	yes	—
266	C₂×C₁₃	#1936	1	2	yes	—
267	C₂×C₁₃	#1943	1	2	yes	—
268	C₂×C₁₃	#1944	1	2	yes	—
269	C₂×C₁₃	#1992	1	1	yes	characteristic
270	C₂×C₁₃	#1993	1	1	yes	characteristic
271	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
298	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
304	C₂²×C₄	C₁₃×#41	1	2	yes	—
305	C₂²×C₄	C₁₃×#41	1	2	yes	—
306	C₂²×C₄	C₁₃×#41	1	2	yes	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	2	4	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	C₁₃×C₄⋊C₄	1	8	yes	complemented
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	4	8	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
325	C₄²	—	2	4	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₁₃	#10881	1	1	yes	characteristic, direct product factor, Sylow
329	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
330	C₂³	C₄×D₄×C₁₃	1	2	yes	—
331	C₂³	C₁₃×#121	1	2	yes	—
332	C₂³	C₁₃×#124	1	1	yes	characteristic
333	C₂³	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
334	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
335	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
336	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
337	C₂³	C₁₃×#137	1	1	yes	characteristic
338	C₂³	C₁₃×#137	1	1	yes	characteristic
339	C₂³	C₁₃×#137	1	2	yes	—
340	C₂×C₄	—	2	4	no	—
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	—	2	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	8	2	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	8	2	no	—
366	C₂×C₄	—	8	2	no	—
367	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
368	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
369	C₂×C₄	C₁₃×#117	1	2	yes	—
370	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
371	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
372	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
373	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
374	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
375	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
376	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
377	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
378	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
379	C₂×C₄	C₁₃×#123	1	2	yes	—
380	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
381	C₂×C₄	C₁₃×#125	1	2	yes	—
382	C₂×C₄	C₁₃×#126	1	2	yes	—
383	C₈	—	2	8	no	—
384	C₂²	C₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
385	C₂²	C₁₃×#386	1	1	yes	characteristic
386	C₂²	C₁₃×#388	1	2	yes	—
387	C₂²	C₁₃×#389	1	2	yes	—
388	C₂²	C₁₃×#391	1	1	yes	characteristic
389	C₂²	C₁₃×#417	1	1	yes	characteristic
390	C₂²	C₁₃×#417	1	1	yes	characteristic
391	C₂²	C₁₃×#418	1	1	yes	characteristic
392	C₂²	C₁₃×#419	1	1	yes	characteristic
393	C₂²	C₁₃×#440	1	2	yes	—
394	C₂²	C₁₃×#440	1	2	yes	—
395	C₂²	C₁₃×#441	1	2	yes	—
396	C₂²	C₁₃×#442	1	2	yes	—
397	C₂²	C₁₃×#468	1	2	yes	—
398	C₂²	C₁₃×#468	1	2	yes	—
399	C₂²	C₁₃×#469	1	2	yes	—
400	C₂²	C₁₃×#470	1	2	yes	—
401	C₂²	C₁₃×#489	1	2	yes	—
402	C₂²	C₁₃×#490	1	1	yes	characteristic
403	C₂²	C₁₃×#491	1	1	yes	characteristic
404	C₂²	C₁₃×#501	1	1	yes	characteristic
405	C₂²	C₁₃×#501	1	1	yes	characteristic
406	C₂²	C₁₃×#501	1	2	yes	—
407	C₄	—	4	4	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	4	no	—
412	C₄	C₄×C₁₃×C₄⋊C₄	1	2	yes	—
413	C₄	C₁₃×#385	1	2	yes	—
414	C₄	C₁₃×#387	1	2	yes	—
415	C₄	C₁₃×#387	1	2	yes	—
416	C₂	C₁₃×#1436	1	1	yes	characteristic
417	C₂	C₁₃×#1762	1	1	yes	characteristic
418	C₂	C₁₃×#1763	1	1	yes	characteristic
419	C₂	C₁₃×#1894	1	1	yes	characteristic
420	C₂	C₁₃×#1895	1	1	yes	characteristic
421	C₂	C₁₃×#1935	1	2	yes	—
422	C₂	C₁₃×#1936	1	2	yes	—
423	C₂	C₁₃×#1943	1	2	yes	—
424	C₂	C₁₃×#1944	1	2	yes	—
425	C₂	C₁₃×#1992	1	1	yes	characteristic
426	C₂	C₁₃×#1993	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₁₃×#389	C₄	semidirect
20. C₁₃×#340	C₄	semidirect
58. #10881	C₁₃	direct (N × H)
101. C₂×C₈×C₁₃	C₄⋊C₄	semidirect
185. #389	C₄×C₁₃	semidirect
190. #340	C₄×C₁₃	semidirect
313. C₂×C₈	C₁₃×C₄⋊C₄	semidirect
328. C₁₃	#10881	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₃×#97	2
C₂×C₁₃×#389	2
C₂×C₁₃×#340	2
C₁₃×C₄⋊#95	2
#10881	13

Subgroups — C13×#10881 #15697220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10881 #15697220