Subgroups — C₁₃×#18067 #15704406

Order 3328.

654 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	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2935	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1590	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1583	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1582	C₂	1	2	yes	maximal, complemented
7	C₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1481	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1480	C₂	1	1	yes	maximal, characteristic
11	C₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#131	—	2	1	no	—
13	C₁₃×#533	C₂²	1	1	yes	characteristic
14	C₁₃×#532	C₂²	1	1	yes	characteristic
15	C₁₃×#498	C₄	1	1	yes	characteristic
16	C₁₃×#492	C₄	1	1	yes	characteristic
17	C₁₃×#487	C₄	1	1	yes	characteristic
18	C₁₃×#486	C₄	1	1	yes	characteristic
19	C₁₃×#465	C₄	1	2	yes	—
20	C₁₃×#465	C₄	1	2	yes	—
21	C₁₃×#446	—	2	2	no	—
22	C₁₃×#446	C₂²	1	2	yes	—
23	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
24	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
25	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
26	C₁₃×#436	C₂²	1	2	yes	—
27	C₁₃×#435	—	2	2	no	—
28	C₈×D₄×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#431	C₂²	1	1	yes	characteristic
30	C₁₃×#424	—	2	1	no	—
31	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₃×#408	—	2	1	no	—
34	C₁₃×#405	—	2	1	no	—
35	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#334	C₂²	1	1	yes	characteristic
38	C₁₃×#334	C₂²	1	1	yes	characteristic
39	C₁₃×#334	C₂²	1	1	yes	characteristic
40	C₁₃×#334	C₂²	1	1	yes	characteristic
41	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
42	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
44	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
45	C₁₃×#322	C₂²	1	2	yes	—
46	C₈²×C₁₃	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	—	2	1	no	—
48	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
49	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
50	C₁₃×#131	—	4	4	no	—
51	C₂×C₁₃×M₁₆	—	2	2	no	—
52	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
53	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	—	2	1	no	—
55	C₂²×C₈×C₁₃	—	2	1	no	—
56	C₂²×C₈×C₁₃	—	2	2	no	—
57	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
60	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
61	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
62	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
63	C₁₃×#125	—	2	1	no	—
64	C₁₃×#124	—	2	1	no	—
65	C₁₃×C₂²⋊Q₈	—	2	1	no	—
66	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
67	C₁₃×#121	—	2	1	no	—
68	C₁₃×#121	C₂×C₄	1	2	yes	—
69	C₄×Q₈×C₁₃	—	2	1	no	—
70	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
71	C₄×D₄×C₁₃	—	2	1	no	—
72	C₄×D₄×C₁₃	C₂³	1	2	yes	—
73	C₁₃×#117	—	2	1	no	—
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#106	C₂×C₄	1	2	yes	—
76	C₁₃×#106	C₂×C₄	1	2	yes	—
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×C₄⋊C₈	—	2	1	no	—
80	C₁₃×C₄⋊C₈	—	2	1	no	—
81	C₁₃×C₄⋊C₈	—	2	1	no	—
82	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₁₃×#103	C₂×C₄	1	2	yes	—
87	C₁₃×#103	C₂×C₄	1	2	yes	—
88	C₁₃×#102	C₂×C₄	1	2	yes	—
89	C₁₃×#102	C₂×C₄	1	2	yes	—
90	C₁₃×C₂²⋊C₈	—	2	1	no	—
91	C₁₃×C₂²⋊C₈	—	2	2	no	—
92	C₁₃×C₂²⋊C₈	—	2	2	no	—
93	C₁₃×#97	—	2	2	no	—
94	C₁₃×#97	D₄	1	2	yes	—
95	C₄×C₈×C₁₃	—	2	2	no	—
96	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
97	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
98	C₄×C₈×C₁₃	C₂³	1	2	yes	—
99	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₁₃	C₂³	1	2	yes	—
102	#18067	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₁₃×#41	—	4	2	no	—
104	C₁₃×#41	—	4	2	no	—
105	C₂×Q₈×C₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
116	C₁₃×SD₁₆	—	2	4	no	—
117	C₁₃×SD₁₆	—	4	2	no	—
118	C₁₃×M₁₆	—	2	2	no	—
119	C₁₃×M₁₆	—	4	4	no	—
120	C₁₃×M₁₆	SD₁₆	1	4	yes	complemented
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	4	1	no	—
128	C₂×C₈×C₁₃	—	4	2	no	—
129	C₂×C₈×C₁₃	—	4	2	no	—
130	C₂×C₈×C₁₃	—	4	4	no	—
131	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
144	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
145	C₁₃×C₂²⋊C₄	—	2	2	no	—
146	C₁₃×C₂²⋊C₄	—	2	2	no	—
147	C₁₃×C₂²⋊C₄	—	2	2	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₃	#41	1	1	yes	characteristic
152	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
153	#3167	C₂×C₁₃	1	1	yes	characteristic
154	#2962	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#2935	C₂×C₁₃	1	1	yes	characteristic
156	#1590	C₂×C₁₃	1	2	yes	complemented
157	#1583	C₂×C₁₃	1	2	yes	complemented
158	#1582	C₂×C₁₃	1	2	yes	complemented
159	C₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
160	C₂×#334	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#1481	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#1480	C₂×C₁₃	1	1	yes	characteristic
163	C₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
166	Q₈×C₁₃	—	2	2	no	—
167	Q₈×C₁₃	—	2	2	no	—
168	Q₈×C₁₃	—	4	2	no	—
169	Q₈×C₁₃	—	8	1	no	—
170	D₄×C₁₃	—	2	2	no	—
171	D₄×C₁₃	—	2	2	no	—
172	D₄×C₁₃	—	4	4	no	—
173	D₄×C₁₃	—	4	2	no	—
174	D₄×C₁₃	—	8	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
187	C₂×C₄×C₁₃	#135	1	2	yes	—
188	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
191	C₈×C₁₃	—	2	1	no	—
192	C₈×C₁₃	—	2	1	no	—
193	C₈×C₁₃	—	2	1	no	—
194	C₈×C₁₃	—	2	2	no	—
195	C₈×C₁₃	—	4	2	no	—
196	C₈×C₁₃	—	4	1	no	—
197	C₈×C₁₃	—	4	1	no	—
198	C₈×C₁₃	—	4	1	no	—
199	C₈×C₁₃	—	4	1	no	—
200	C₈×C₁₃	#131	1	2	yes	complemented
201	C₈×C₁₃	C₂×SD₁₆	1	4	yes	—
202	C₂×#131	—	2	1	no	—
203	#533	C₂²×C₁₃	1	1	yes	characteristic
204	#532	C₂²×C₁₃	1	1	yes	characteristic
205	#498	C₄×C₁₃	1	1	yes	characteristic
206	#492	C₄×C₁₃	1	1	yes	characteristic
207	#487	C₄×C₁₃	1	1	yes	characteristic
208	#486	C₄×C₁₃	1	1	yes	characteristic
209	#465	C₄×C₁₃	1	2	yes	—
210	#465	C₄×C₁₃	1	2	yes	—
211	#446	—	2	2	no	—
212	#446	C₂²×C₁₃	1	2	yes	—
213	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
214	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
215	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
216	#436	C₂²×C₁₃	1	2	yes	—
217	#435	—	2	2	no	—
218	C₈×D₄	C₂²×C₁₃	1	2	yes	—
219	#431	C₂²×C₁₃	1	1	yes	characteristic
220	#424	—	2	1	no	—
221	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
223	#408	—	2	1	no	—
224	#405	—	2	1	no	—
225	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
227	#334	C₂²×C₁₃	1	1	yes	characteristic
228	#334	C₂²×C₁₃	1	1	yes	characteristic
229	#334	C₂²×C₁₃	1	1	yes	characteristic
230	#334	C₂²×C₁₃	1	1	yes	characteristic
231	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
232	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
233	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
234	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
235	#322	C₂²×C₁₃	1	2	yes	—
236	C₈²	C₂²×C₁₃	1	2	yes	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	4	2	no	—
242	C₂²×C₁₃	C₄×SD₁₆	1	2	yes	—
243	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	4	2	no	—
250	C₄×C₁₃	C₄×SD₁₆	1	2	yes	—
251	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
252	C₄×C₁₃	#568	1	1	yes	characteristic
253	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
254	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
255	C₂×#41	—	2	1	no	—
256	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
257	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
258	#131	—	4	4	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
261	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	2	no	—
265	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
266	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
267	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
268	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
269	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
270	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
271	#125	—	2	1	no	—
272	#124	—	2	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
275	#121	—	2	1	no	—
276	#121	C₂×C₄×C₁₃	1	2	yes	—
277	C₄×Q₈	—	2	1	no	—
278	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	C₂³×C₁₃	1	2	yes	—
281	#117	—	2	1	no	—
282	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
283	#106	C₂×C₄×C₁₃	1	2	yes	—
284	#106	C₂×C₄×C₁₃	1	2	yes	—
285	C₄⋊C₈	—	2	2	no	—
286	C₄⋊C₈	—	2	2	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
293	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
294	#103	C₂×C₄×C₁₃	1	2	yes	—
295	#103	C₂×C₄×C₁₃	1	2	yes	—
296	#102	C₂×C₄×C₁₃	1	2	yes	—
297	#102	C₂×C₄×C₁₃	1	2	yes	—
298	C₂²⋊C₈	—	2	1	no	—
299	C₂²⋊C₈	—	2	2	no	—
300	C₂²⋊C₈	—	2	2	no	—
301	#97	—	2	2	no	—
302	#97	D₄×C₁₃	1	2	yes	—
303	C₄×C₈	—	2	2	no	—
304	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
305	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
306	C₄×C₈	C₂³×C₁₃	1	2	yes	—
307	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
308	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
309	C₄×C₈	C₂³×C₁₃	1	2	yes	—
310	C₂×C₁₃	—	2	2	no	—
311	C₂×C₁₃	—	8	2	no	—
312	C₂×C₁₃	#2935	1	1	yes	characteristic
313	C₂×C₁₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
314	C₂×C₁₃	#2957	1	1	yes	characteristic
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
327	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
328	SD₁₆	—	2	4	no	—
329	SD₁₆	—	4	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	4	4	no	—
332	M₁₆	C₁₃×SD₁₆	1	4	yes	complemented
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	2	no	—
341	C₂×C₈	—	4	2	no	—
342	C₂×C₈	—	4	4	no	—
343	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
344	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
345	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
346	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
347	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
348	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
356	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
362	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₄²	C₁₃×#41	1	1	yes	characteristic
364	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
365	C₁₃	#18067	1	1	yes	characteristic, direct product factor, Sylow
366	C₂³	—	2	2	no	—
367	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	8	1	no	—
372	D₄	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	2	no	—
376	D₄	—	8	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
386	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
387	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
388	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
389	C₂×C₄	C₁₃×#135	1	2	yes	—
390	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
392	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	4	1	no	—
401	C₈	—	4	1	no	—
402	C₈	C₁₃×#131	1	2	yes	complemented
403	C₈	C₂×C₁₃×SD₁₆	1	4	yes	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	C₄×C₁₃×SD₁₆	1	2	yes	—
410	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	C₄×C₁₃×SD₁₆	1	2	yes	—
418	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
419	C₄	C₁₃×#568	1	1	yes	characteristic
420	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
421	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	8	2	no	—
424	C₂	C₁₃×#2935	1	1	yes	characteristic
425	C₂	C₂×C₄×C₁₃×SD₁₆	1	1	yes	characteristic
426	C₂	C₁₃×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2962	C₂	semidirect
4. C₁₃×#1590	C₂	semidirect
5. C₁₃×#1583	C₂	semidirect
6. C₁₃×#1582	C₂	semidirect
7. C₈×C₁₃×SD₁₆	C₂	semidirect
8. C₂×C₁₃×#334	C₂	semidirect
9. C₁₃×#1481	C₂	semidirect
11. C₈×C₁₃×M₁₆	C₂	semidirect
102. #18067	C₁₃	direct (N × H)
120. C₁₃×M₁₆	SD₁₆	semidirect
154. #2962	C₂×C₁₃	semidirect
156. #1590	C₂×C₁₃	semidirect
157. #1583	C₂×C₁₃	semidirect
158. #1582	C₂×C₁₃	semidirect
159. C₈×SD₁₆	C₂×C₁₃	semidirect
160. C₂×#334	C₂×C₁₃	semidirect
161. #1481	C₂×C₁₃	semidirect
163. C₈×M₁₆	C₂×C₁₃	semidirect
200. C₈×C₁₃	#131	semidirect
332. M₁₆	C₁₃×SD₁₆	semidirect
365. C₁₃	#18067	direct (N × H)
402. C₈	C₁₃×#131	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3167	2
C₁₃×#2962	2
C₁₃×#2935	2
C₁₃×#1590	2
C₁₃×#1583	2
C₁₃×#1582	2
C₈×C₁₃×SD₁₆	2
C₂×C₁₃×#334	2
C₁₃×#1481	2
C₁₃×#1480	2
C₈×C₁₃×M₁₆	2
#18067	13

Subgroups — C13×#18067 #15704406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18067 #15704406