Subgroups — C₁₃×#17918 #15704257

Order 3328.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3105	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2993	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1586	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1585	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1582	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1580	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1574	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1486	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1482	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1454	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#529	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#484	C₄	1	1	yes	characteristic
19	C₁₃×#481	C₄	1	1	yes	characteristic
20	C₁₃×#478	C₄	1	1	yes	characteristic
21	C₁₃×#478	C₄	1	1	yes	characteristic
22	C₁₃×#463	C₄	1	1	yes	characteristic
23	C₁₃×#463	C₄	1	1	yes	characteristic
24	C₁₃×#450	C₄	1	1	yes	characteristic
25	C₁₃×#447	C₄	1	1	yes	characteristic
26	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
27	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
31	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
32	C₁₃×#436	—	2	1	no	—
33	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#435	—	2	1	no	—
35	C₈×D₄×C₁₃	—	2	1	no	—
36	C₈×D₄×C₁₃	—	2	1	no	—
37	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#433	—	2	1	no	—
43	C₁₃×#431	C₂²	1	1	yes	characteristic
44	C₁₃×#431	C₂²	1	1	yes	characteristic
45	C₁₃×#431	C₂²	1	1	yes	characteristic
46	C₁₃×#431	C₂²	1	1	yes	characteristic
47	C₁₃×#424	—	2	1	no	—
48	C₁₃×#423	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
50	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
51	C₁₃×#335	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#335	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#334	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#334	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
58	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
59	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
66	C₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
67	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	—	2	1	no	—
69	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₃×M₁₆	—	2	1	no	—
74	C₂×C₁₃×M₁₆	—	2	1	no	—
75	C₂²×C₈×C₁₃	—	2	1	no	—
76	C₂²×C₈×C₁₃	—	2	1	no	—
77	C₂²×C₈×C₁₃	—	2	1	no	—
78	C₂²×C₈×C₁₃	—	2	1	no	—
79	C₂²×C₈×C₁₃	—	2	1	no	—
80	C₁₃×#126	—	2	1	no	—
81	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
82	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
83	C₁₃×#123	—	2	1	no	—
84	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
85	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₄×D₄×C₁₃	—	2	1	no	—
88	C₄×D₄×C₁₃	—	2	1	no	—
89	C₄×D₄×C₁₃	—	2	1	no	—
90	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
92	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×#117	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
100	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
101	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
102	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
103	C₁₃×C₄⋊C₈	—	2	1	no	—
104	C₁₃×C₄⋊C₈	—	2	1	no	—
105	C₁₃×C₄⋊C₈	—	2	1	no	—
106	C₁₃×C₄⋊C₈	—	2	1	no	—
107	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
108	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
109	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
110	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
111	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
116	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
117	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
118	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
119	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
120	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
121	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
122	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
123	C₁₃×C₂²⋊C₈	—	2	1	no	—
124	C₁₃×C₂²⋊C₈	—	2	1	no	—
125	C₁₃×C₂²⋊C₈	—	2	1	no	—
126	C₁₃×C₂²⋊C₈	—	2	1	no	—
127	C₁₃×C₂²⋊C₈	—	2	1	no	—
128	C₁₃×C₂²⋊C₈	—	2	1	no	—
129	C₁₃×C₂²⋊C₈	—	2	1	no	—
130	C₁₃×C₂²⋊C₈	—	2	1	no	—
131	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
132	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
133	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
134	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
135	C₁₃×#97	—	2	1	no	—
136	C₄×C₈×C₁₃	—	2	1	no	—
137	C₄×C₈×C₁₃	—	2	1	no	—
138	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	#17918	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	2	2	no	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	8	1	no	—
161	C₂²×C₄×C₁₃	—	8	1	no	—
162	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
165	C₁₃×SD₁₆	—	2	2	no	—
166	C₁₃×SD₁₆	—	2	2	no	—
167	C₁₃×D₈	—	2	2	no	—
168	C₁₃×D₈	—	2	2	no	—
169	C₁₃×M₁₆	—	8	1	no	—
170	C₁₃×M₁₆	—	8	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	8	1	no	—
178	C₂×C₈×C₁₃	—	8	1	no	—
179	C₂×C₈×C₁₃	—	8	1	no	—
180	C₂×C₈×C₁₃	—	8	1	no	—
181	C₂×C₈×C₁₃	—	8	1	no	—
182	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
198	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
199	C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₁₃×C₂²⋊C₄	—	2	1	no	—
201	C₁₃×C₂²⋊C₄	—	2	1	no	—
202	C₁₃×C₂²⋊C₄	—	2	1	no	—
203	C₁₃×C₂²⋊C₄	—	2	1	no	—
204	C₁₃×C₂²⋊C₄	—	2	1	no	—
205	C₁₃×C₂²⋊C₄	—	2	1	no	—
206	C₁₃×C₂²⋊C₄	—	2	1	no	—
207	C₁₃×C₂²⋊C₄	—	2	1	no	—
208	C₄²×C₁₃	—	2	1	no	—
209	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
210	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₃	#41	1	1	yes	characteristic
212	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
213	#3105	C₂×C₁₃	1	1	yes	characteristic
214	#2993	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1586	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1585	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1582	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1581	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1580	C₂×C₁₃	1	1	yes	characteristic, complemented
221	SD₁₆⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₈×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₈×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1574	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1486	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1482	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1454	C₂×C₁₃	1	1	yes	characteristic, complemented
228	C₂³×C₁₃	—	2	4	no	—
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	—	2	1	no	—
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	—	8	1	no	—
233	C₂³×C₁₃	—	8	1	no	—
234	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
235	Q₈×C₁₃	—	2	1	no	—
236	Q₈×C₁₃	—	2	1	no	—
237	D₄×C₁₃	—	2	4	no	—
238	D₄×C₁₃	—	2	1	no	—
239	D₄×C₁₃	—	2	1	no	—
240	D₄×C₁₃	—	2	1	no	—
241	D₄×C₁₃	—	2	1	no	—
242	D₄×C₁₃	—	8	1	no	—
243	D₄×C₁₃	#131	1	2	yes	—
244	D₄×C₁₃	#131	1	2	yes	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	8	1	no	—
262	C₂×C₄×C₁₃	—	8	1	no	—
263	C₂×C₄×C₁₃	—	8	1	no	—
264	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
270	C₈×C₁₃	—	2	1	no	—
271	C₈×C₁₃	—	2	1	no	—
272	C₈×C₁₃	—	2	1	no	—
273	C₈×C₁₃	—	2	1	no	—
274	C₈×C₁₃	—	2	1	no	—
275	C₈×C₁₃	—	2	1	no	—
276	C₈×C₁₃	—	2	1	no	—
277	C₈×C₁₃	—	2	1	no	—
278	C₈×C₁₃	—	4	1	no	—
279	C₈×C₁₃	—	4	1	no	—
280	C₈×C₁₃	—	4	1	no	—
281	C₈×C₁₃	—	4	1	no	—
282	C₈×C₁₃	—	4	1	no	—
283	C₈×C₁₃	—	4	1	no	—
284	#529	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
286	#484	C₄×C₁₃	1	1	yes	characteristic
287	#481	C₄×C₁₃	1	1	yes	characteristic
288	#478	C₄×C₁₃	1	1	yes	characteristic
289	#478	C₄×C₁₃	1	1	yes	characteristic
290	#463	C₄×C₁₃	1	1	yes	characteristic
291	#463	C₄×C₁₃	1	1	yes	characteristic
292	#450	C₄×C₁₃	1	1	yes	characteristic
293	#447	C₄×C₁₃	1	1	yes	characteristic
294	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
295	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
296	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
297	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
298	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
299	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
300	#436	—	2	1	no	—
301	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
302	#435	—	2	1	no	—
303	C₈×D₄	—	2	1	no	—
304	C₈×D₄	—	2	1	no	—
305	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
306	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
307	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
308	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
309	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
310	#433	—	2	1	no	—
311	#431	C₂²×C₁₃	1	1	yes	characteristic
312	#431	C₂²×C₁₃	1	1	yes	characteristic
313	#431	C₂²×C₁₃	1	1	yes	characteristic
314	#431	C₂²×C₁₃	1	1	yes	characteristic
315	#424	—	2	1	no	—
316	#423	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₂²⋊C₈	—	2	1	no	—
318	C₂×C₂²⋊C₈	—	2	1	no	—
319	#335	C₂²×C₁₃	1	1	yes	characteristic, complemented
320	#335	C₂²×C₁₃	1	1	yes	characteristic, complemented
321	#334	C₂²×C₁₃	1	1	yes	characteristic, complemented
322	#334	C₂²×C₁₃	1	1	yes	characteristic, complemented
323	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
324	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
325	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
326	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
327	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
328	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
329	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
330	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
331	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
332	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
333	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
334	C₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
335	C₂²×C₁₃	—	2	1	no	—
336	C₂²×C₁₃	—	2	2	no	—
337	C₂²×C₁₃	—	2	2	no	—
338	C₂²×C₁₃	—	2	1	no	—
339	C₂²×C₁₃	—	2	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	—	4	1	no	—
343	C₂²×C₁₃	—	4	1	no	—
344	C₂²×C₁₃	—	4	1	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	—	4	1	no	—
347	C₂²×C₁₃	—	8	4	no	—
348	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
349	C₄×C₁₃	—	2	1	no	—
350	C₄×C₁₃	—	2	1	no	—
351	C₄×C₁₃	—	2	1	no	—
352	C₄×C₁₃	—	2	1	no	—
353	C₄×C₁₃	—	4	1	no	—
354	C₄×C₁₃	—	4	1	no	—
355	C₄×C₁₃	—	4	1	no	—
356	C₄×C₁₃	—	4	1	no	—
357	C₄×C₁₃	—	4	1	no	—
358	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
359	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
360	C₄×C₁₃	#576	1	1	yes	characteristic
361	C₄×C₁₃	#577	1	1	yes	characteristic
362	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
363	C₂³×C₄	—	2	1	no	—
364	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
365	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
366	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
367	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	#126	—	2	1	no	—
376	#125	C₂×C₄×C₁₃	1	1	yes	characteristic
377	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
378	#123	—	2	1	no	—
379	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
380	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
381	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
386	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
387	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
388	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
389	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
390	#117	—	2	1	no	—
391	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
394	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
395	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
396	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
397	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
398	C₄⋊C₈	—	2	1	no	—
399	C₄⋊C₈	—	2	1	no	—
400	C₄⋊C₈	—	2	1	no	—
401	C₄⋊C₈	—	2	1	no	—
402	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
403	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
404	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
405	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
406	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
407	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
408	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
409	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
410	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
411	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
412	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
413	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
414	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
415	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
416	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
417	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
418	C₂²⋊C₈	—	2	1	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	C₂²⋊C₈	—	2	1	no	—
423	C₂²⋊C₈	—	2	1	no	—
424	C₂²⋊C₈	—	2	1	no	—
425	C₂²⋊C₈	—	2	1	no	—
426	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
427	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
428	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
429	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
430	#97	—	2	1	no	—
431	C₄×C₈	—	2	1	no	—
432	C₄×C₈	—	2	1	no	—
433	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
434	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
435	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
436	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
437	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
438	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
439	C₂×C₁₃	—	4	1	no	—
440	C₂×C₁₃	—	4	2	no	—
441	C₂×C₁₃	—	4	2	no	—
442	C₂×C₁₃	—	8	1	no	—
443	C₂×C₁₃	#2929	1	1	yes	characteristic
444	C₂×C₁₃	#2946	1	1	yes	characteristic
445	C₂×C₁₃	#2957	1	1	yes	characteristic
446	C₂⁴	—	2	1	no	—
447	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
453	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
454	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	8	1	no	—
462	C₂²×C₄	—	8	1	no	—
463	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
466	SD₁₆	—	2	2	no	—
467	SD₁₆	—	2	2	no	—
468	D₈	—	2	2	no	—
469	D₈	—	2	2	no	—
470	M₁₆	—	8	1	no	—
471	M₁₆	—	8	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	8	1	no	—
479	C₂×C₈	—	8	1	no	—
480	C₂×C₈	—	8	1	no	—
481	C₂×C₈	—	8	1	no	—
482	C₂×C₈	—	8	1	no	—
483	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
484	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
485	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
486	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
487	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
489	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
511	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
512	C₄²	C₁₃×#41	1	1	yes	characteristic
513	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
514	C₁₃	#17918	1	1	yes	characteristic, direct product factor, Sylow
515	C₂³	—	2	4	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	8	1	no	—
520	C₂³	—	8	1	no	—
521	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
522	Q₈	—	2	1	no	—
523	Q₈	—	2	1	no	—
524	D₄	—	2	4	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	8	1	no	—
530	D₄	C₁₃×#131	1	2	yes	—
531	D₄	C₁₃×#131	1	2	yes	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	8	1	no	—
549	C₂×C₄	—	8	1	no	—
550	C₂×C₄	—	8	1	no	—
551	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
552	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
553	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
554	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
555	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
556	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	—	2	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	1	no	—
569	C₈	—	4	1	no	—
570	C₈	—	4	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	8	4	no	—
584	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
595	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
596	C₄	C₁₃×#576	1	1	yes	characteristic
597	C₄	C₁₃×#577	1	1	yes	characteristic
598	C₂	—	4	1	no	—
599	C₂	—	4	2	no	—
600	C₂	—	4	2	no	—
601	C₂	—	8	1	no	—
602	C₂	C₁₃×#2929	1	1	yes	characteristic
603	C₂	C₁₃×#2946	1	1	yes	characteristic
604	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×#447	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2993	C₂	semidirect
3. C₁₃×#2972	C₂	semidirect
4. C₁₃×#1586	C₂	semidirect
5. C₁₃×#1585	C₂	semidirect
6. C₁₃×#1582	C₂	semidirect
7. C₁₃×#1581	C₂	semidirect
8. C₁₃×#1580	C₂	semidirect
9. C₁₃×SD₁₆⋊C₈	C₂	semidirect
10. C₈×C₁₃×SD₁₆	C₂	semidirect
11. C₈×C₁₃×D₈	C₂	semidirect
12. C₁₃×#1574	C₂	semidirect
13. C₁₃×#1486	C₂	semidirect
14. C₁₃×#1482	C₂	semidirect
15. C₁₃×#1454	C₂	semidirect
26. C₁₃×#446	C₂²	semidirect
27. C₈×Q₈×C₁₃	C₂²	semidirect
33. C₁₃×#436	C₂²	semidirect
41. C₈×D₄×C₁₃	C₂²	semidirect
51. C₁₃×#335	C₂²	semidirect
52. C₁₃×#335	C₂²	semidirect
53. C₁₃×#334	C₂²	semidirect
54. C₁₃×#334	C₂²	semidirect
55. C₁₃×Q₈⋊C₈	C₂²	semidirect
56. C₁₃×Q₈⋊C₈	C₂²	semidirect
61. C₁₃×D₄⋊C₈	C₂²	semidirect
62. C₁₃×D₄⋊C₈	C₂²	semidirect
63. C₁₃×#322	C₂²	semidirect
64. C₁₃×#322	C₂²	semidirect
65. C₁₃×#322	C₂²	semidirect
66. C₈²×C₁₃	C₂²	semidirect
144. #17918	C₁₃	direct (N × H)
214. #2993	C₂×C₁₃	semidirect
215. #2972	C₂×C₁₃	semidirect
216. #1586	C₂×C₁₃	semidirect
217. #1585	C₂×C₁₃	semidirect
218. #1582	C₂×C₁₃	semidirect
219. #1581	C₂×C₁₃	semidirect
220. #1580	C₂×C₁₃	semidirect
221. SD₁₆⋊C₈	C₂×C₁₃	semidirect
222. C₈×SD₁₆	C₂×C₁₃	semidirect
223. C₈×D₈	C₂×C₁₃	semidirect
224. #1574	C₂×C₁₃	semidirect
225. #1486	C₂×C₁₃	semidirect
226. #1482	C₂×C₁₃	semidirect
227. #1454	C₂×C₁₃	semidirect
294. #446	C₂²×C₁₃	semidirect
295. C₈×Q₈	C₂²×C₁₃	semidirect
301. #436	C₂²×C₁₃	semidirect
309. C₈×D₄	C₂²×C₁₃	semidirect
319. #335	C₂²×C₁₃	semidirect
320. #335	C₂²×C₁₃	semidirect
321. #334	C₂²×C₁₃	semidirect
322. #334	C₂²×C₁₃	semidirect
323. Q₈⋊C₈	C₂²×C₁₃	semidirect
324. Q₈⋊C₈	C₂²×C₁₃	semidirect
329. D₄⋊C₈	C₂²×C₁₃	semidirect
330. D₄⋊C₈	C₂²×C₁₃	semidirect
331. #322	C₂²×C₁₃	semidirect
332. #322	C₂²×C₁₃	semidirect
333. #322	C₂²×C₁₃	semidirect
334. C₈²	C₂²×C₁₃	semidirect
514. C₁₃	#17918	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×#3105	2
C₁₃×#2993	2
C₁₃×#2972	2
C₁₃×#1586	2
C₁₃×#1585	2
C₁₃×#1582	2
C₁₃×#1581	2
C₁₃×#1580	2
C₁₃×SD₁₆⋊C₈	2
C₈×C₁₃×SD₁₆	2
C₈×C₁₃×D₈	2
C₁₃×#1574	2
C₁₃×#1486	2
C₁₃×#1482	2
C₁₃×#1454	2
#17918	13

Subgroups — C13×#17918 #15704257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17918 #15704257