Subgroups — C₁₃×#18006 #15704345

Order 3328.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 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×#2969	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1594	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1590	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1588	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1586	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1582	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×SD₁₆⋊C₈	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×#1495	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1478	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1453	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×M₁₆	—	2	1	no	—
17	C₁₃×#529	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#484	C₄	1	1	yes	characteristic
20	C₁₃×#481	C₄	1	1	yes	characteristic
21	C₁₃×#478	C₄	1	1	yes	characteristic
22	C₁₃×#478	C₄	1	1	yes	characteristic
23	C₁₃×#463	C₄	1	1	yes	characteristic
24	C₁₃×#463	C₄	1	1	yes	characteristic
25	C₁₃×#450	C₄	1	1	yes	characteristic
26	C₁₃×#447	C₄	1	1	yes	characteristic
27	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
28	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
31	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
33	C₁₃×#436	—	2	1	no	—
34	C₁₃×#436	C₂²	1	1	yes	characteristic
35	C₁₃×#436	C₂²	1	1	yes	characteristic
36	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#435	—	2	1	no	—
38	C₁₃×#435	—	2	1	no	—
39	C₁₃×#435	—	2	1	no	—
40	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#433	—	2	1	no	—
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×#423	C₂²	1	1	yes	characteristic
48	C₁₃×#407	—	2	1	no	—
49	C₁₃×#405	—	2	1	no	—
50	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
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	C₂×C₁₃×M₁₆	—	2	1	no	—
76	C₂×C₁₃×M₁₆	—	2	1	no	—
77	C₂×C₁₃×M₁₆	—	4	4	no	—
78	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
79	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	—	2	1	no	—
81	C₂²×C₈×C₁₃	—	2	1	no	—
82	C₂²×C₈×C₁₃	—	2	1	no	—
83	C₁₃×#126	—	2	1	no	—
84	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
85	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
86	C₁₃×#123	—	2	1	no	—
87	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
88	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
89	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₄×D₄×C₁₃	—	2	1	no	—
91	C₄×D₄×C₁₃	—	2	1	no	—
92	C₄×D₄×C₁₃	—	2	1	no	—
93	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
94	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
95	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×#117	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
103	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
104	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
105	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
106	C₁₃×C₄⋊C₈	—	2	1	no	—
107	C₁₃×C₄⋊C₈	—	2	1	no	—
108	C₁₃×C₄⋊C₈	—	2	1	no	—
109	C₁₃×C₄⋊C₈	—	2	1	no	—
110	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
111	C₁₃×C₄⋊C₈	C₂×C₄	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
117	C₁₃×#103	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×#102	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
132	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
133	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
134	C₁₃×#97	—	2	1	no	—
135	C₁₃×#97	D₄	1	1	yes	characteristic
136	C₁₃×#97	D₄	1	1	yes	characteristic
137	C₄×C₈×C₁₃	—	2	1	no	—
138	C₄×C₈×C₁₃	—	2	1	no	—
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	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
145	#18006	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂⁴×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
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	—	4	1	no	—
152	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	4	2	no	—
162	C₂²×C₄×C₁₃	—	4	2	no	—
163	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
166	C₁₃×SD₁₆	—	2	2	no	—
167	C₁₃×SD₁₆	—	4	1	no	—
168	C₁₃×D₈	—	2	2	no	—
169	C₁₃×D₈	—	4	1	no	—
170	C₁₃×M₁₆	—	2	2	no	—
171	C₁₃×M₁₆	—	4	1	no	—
172	C₁₃×M₁₆	—	4	2	no	—
173	C₁₃×M₁₆	—	4	2	no	—
174	C₁₃×M₁₆	—	4	2	no	—
175	C₁₃×M₁₆	—	4	2	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	4	2	no	—
183	C₂×C₈×C₁₃	—	4	2	no	—
184	C₂×C₈×C₁₃	—	4	2	no	—
185	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
199	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
200	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
201	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	C₁₃×C₂²⋊C₄	—	2	1	no	—
209	C₁₃×C₂²⋊C₄	—	2	1	no	—
210	C₁₃×C₂²⋊C₄	—	2	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
213	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₃	#41	1	1	yes	characteristic
215	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
216	#3105	C₂×C₁₃	1	1	yes	characteristic
217	#2969	C₂×C₁₃	1	1	yes	characteristic, complemented
218	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1594	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1590	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1588	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1586	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1582	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1581	C₂×C₁₃	1	1	yes	characteristic, complemented
225	SD₁₆⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₈×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1574	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1495	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1478	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1453	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	—	2	1	no	—
234	C₂³×C₁₃	—	4	2	no	—
235	C₂³×C₁₃	—	4	2	no	—
236	C₂³×C₁₃	—	8	1	no	—
237	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
238	Q₈×C₁₃	—	2	1	no	—
239	Q₈×C₁₃	—	2	1	no	—
240	D₄×C₁₃	—	2	1	no	—
241	D₄×C₁₃	—	2	1	no	—
242	D₄×C₁₃	—	2	1	no	—
243	D₄×C₁₃	—	2	1	no	—
244	D₄×C₁₃	—	2	1	no	—
245	D₄×C₁₃	—	4	2	no	—
246	D₄×C₁₃	—	8	1	no	—
247	D₄×C₁₃	#131	1	2	yes	—
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	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	4	2	no	—
260	C₂×C₄×C₁₃	—	4	2	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
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	—	2	1	no	—
279	C₈×C₁₃	—	2	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	C₈×C₁₃	—	4	1	no	—
285	C₈×C₁₃	—	4	1	no	—
286	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
287	C₂²×M₁₆	—	2	1	no	—
288	#529	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
290	#484	C₄×C₁₃	1	1	yes	characteristic
291	#481	C₄×C₁₃	1	1	yes	characteristic
292	#478	C₄×C₁₃	1	1	yes	characteristic
293	#478	C₄×C₁₃	1	1	yes	characteristic
294	#463	C₄×C₁₃	1	1	yes	characteristic
295	#463	C₄×C₁₃	1	1	yes	characteristic
296	#450	C₄×C₁₃	1	1	yes	characteristic
297	#447	C₄×C₁₃	1	1	yes	characteristic
298	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
299	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
300	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
301	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
302	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
303	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
304	#436	—	2	1	no	—
305	#436	C₂²×C₁₃	1	1	yes	characteristic
306	#436	C₂²×C₁₃	1	1	yes	characteristic
307	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
308	#435	—	2	1	no	—
309	#435	—	2	1	no	—
310	#435	—	2	1	no	—
311	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
312	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
313	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
314	#433	—	2	1	no	—
315	#431	C₂²×C₁₃	1	1	yes	characteristic
316	#431	C₂²×C₁₃	1	1	yes	characteristic
317	#431	C₂²×C₁₃	1	1	yes	characteristic
318	#423	C₂²×C₁₃	1	1	yes	characteristic
319	#407	—	2	1	no	—
320	#405	—	2	1	no	—
321	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
322	#335	C₂²×C₁₃	1	1	yes	characteristic, complemented
323	#335	C₂²×C₁₃	1	1	yes	characteristic, complemented
324	#334	C₂²×C₁₃	1	1	yes	characteristic, complemented
325	#334	C₂²×C₁₃	1	1	yes	characteristic, complemented
326	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
327	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
328	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
329	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
330	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
331	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
332	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
333	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
334	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
335	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
336	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
337	C₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
338	C₂²×C₁₃	—	2	1	no	—
339	C₂²×C₁₃	—	2	2	no	—
340	C₂²×C₁₃	—	2	1	no	—
341	C₂²×C₁₃	—	2	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	—	4	1	no	—
348	C₂²×C₁₃	—	4	1	no	—
349	C₂²×C₁₃	—	4	1	no	—
350	C₂²×C₁₃	—	8	4	no	—
351	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
352	C₄×C₁₃	—	2	1	no	—
353	C₄×C₁₃	—	2	1	no	—
354	C₄×C₁₃	—	2	1	no	—
355	C₄×C₁₃	—	2	1	no	—
356	C₄×C₁₃	—	4	1	no	—
357	C₄×C₁₃	—	4	1	no	—
358	C₄×C₁₃	—	4	1	no	—
359	C₄×C₁₃	—	4	1	no	—
360	C₄×C₁₃	—	4	1	no	—
361	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
362	C₄×C₁₃	#568	1	1	yes	characteristic
363	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
364	C₄×C₁₃	#575	1	1	yes	characteristic
365	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
366	C₂³×C₄	—	2	1	no	—
367	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
368	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
369	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
370	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	4	4	no	—
376	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
377	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	#126	—	2	1	no	—
382	#125	C₂×C₄×C₁₃	1	1	yes	characteristic
383	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
384	#123	—	2	1	no	—
385	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
386	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
387	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
392	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
393	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
394	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
395	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
396	#117	—	2	1	no	—
397	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
400	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
401	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
402	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
403	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	—	2	1	no	—
408	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
409	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
410	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
411	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
412	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
413	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
414	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
415	#103	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	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
419	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
420	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
421	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
427	C₂²⋊C₈	—	2	1	no	—
428	C₂²⋊C₈	—	2	1	no	—
429	C₂²⋊C₈	—	2	1	no	—
430	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
431	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
432	#97	—	2	1	no	—
433	#97	D₄×C₁₃	1	1	yes	characteristic
434	#97	D₄×C₁₃	1	1	yes	characteristic
435	C₄×C₈	—	2	1	no	—
436	C₄×C₈	—	2	1	no	—
437	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
438	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
439	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
440	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
441	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
442	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×C₁₃	—	4	1	no	—
444	C₂×C₁₃	—	4	2	no	—
445	C₂×C₁₃	—	8	1	no	—
446	C₂×C₁₃	—	8	1	no	—
447	C₂×C₁₃	#2933	1	1	yes	characteristic
448	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
449	C₂×C₁₃	#2957	1	1	yes	characteristic
450	C₂⁴	—	2	1	no	—
451	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
457	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
458	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	4	2	no	—
466	C₂²×C₄	—	4	2	no	—
467	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
470	SD₁₆	—	2	2	no	—
471	SD₁₆	—	4	1	no	—
472	D₈	—	2	2	no	—
473	D₈	—	4	1	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	4	1	no	—
476	M₁₆	—	4	2	no	—
477	M₁₆	—	4	2	no	—
478	M₁₆	—	4	2	no	—
479	M₁₆	—	4	2	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	4	2	no	—
487	C₂×C₈	—	4	2	no	—
488	C₂×C₈	—	4	2	no	—
489	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
490	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
491	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
492	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
493	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
494	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
496	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
517	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
518	C₄²	C₁₃×#41	1	1	yes	characteristic
519	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
520	C₁₃	#18006	1	1	yes	characteristic, direct product factor, Sylow
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	—	2	1	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	8	1	no	—
527	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
528	Q₈	—	2	1	no	—
529	Q₈	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	2	1	no	—
532	D₄	—	2	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	2	1	no	—
535	D₄	—	4	2	no	—
536	D₄	—	8	1	no	—
537	D₄	C₁₃×#131	1	2	yes	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
558	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
559	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
560	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
561	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
562	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
563	C₈	—	2	1	no	—
564	C₈	—	2	1	no	—
565	C₈	—	2	1	no	—
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	—	2	1	no	—
569	C₈	—	2	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	8	4	no	—
590	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
601	C₄	C₁₃×#568	1	1	yes	characteristic
602	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
603	C₄	C₁₃×#575	1	1	yes	characteristic
604	C₂	—	4	1	no	—
605	C₂	—	4	2	no	—
606	C₂	—	8	1	no	—
607	C₂	—	8	1	no	—
608	C₂	C₁₃×#2933	1	1	yes	characteristic
609	C₂	C₄×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
610	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 ◁ C₄×C₁₃×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2969	C₂	semidirect
3. D₄×C₁₃×M₁₆	C₂	semidirect
4. C₁₃×#1594	C₂	semidirect
5. C₁₃×#1590	C₂	semidirect
6. C₁₃×#1588	C₂	semidirect
7. C₁₃×#1586	C₂	semidirect
8. C₁₃×#1582	C₂	semidirect
9. C₁₃×#1581	C₂	semidirect
10. C₁₃×SD₁₆⋊C₈	C₂	semidirect
11. C₈×C₁₃×D₈	C₂	semidirect
12. C₁₃×#1574	C₂	semidirect
13. C₁₃×#1495	C₂	semidirect
14. C₁₃×#1478	C₂	semidirect
15. C₁₃×#1453	C₂	semidirect
27. C₁₃×#446	C₂²	semidirect
28. C₈×Q₈×C₁₃	C₂²	semidirect
36. C₁₃×#436	C₂²	semidirect
42. 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
145. #18006	C₁₃	direct (N × H)
217. #2969	C₂×C₁₃	semidirect
218. D₄×M₁₆	C₂×C₁₃	semidirect
219. #1594	C₂×C₁₃	semidirect
220. #1590	C₂×C₁₃	semidirect
221. #1588	C₂×C₁₃	semidirect
222. #1586	C₂×C₁₃	semidirect
223. #1582	C₂×C₁₃	semidirect
224. #1581	C₂×C₁₃	semidirect
225. SD₁₆⋊C₈	C₂×C₁₃	semidirect
226. C₈×D₈	C₂×C₁₃	semidirect
227. #1574	C₂×C₁₃	semidirect
228. #1495	C₂×C₁₃	semidirect
229. #1478	C₂×C₁₃	semidirect
230. #1453	C₂×C₁₃	semidirect
298. #446	C₂²×C₁₃	semidirect
299. C₈×Q₈	C₂²×C₁₃	semidirect
307. #436	C₂²×C₁₃	semidirect
313. C₈×D₄	C₂²×C₁₃	semidirect
322. #335	C₂²×C₁₃	semidirect
323. #335	C₂²×C₁₃	semidirect
324. #334	C₂²×C₁₃	semidirect
325. #334	C₂²×C₁₃	semidirect
326. Q₈⋊C₈	C₂²×C₁₃	semidirect
327. Q₈⋊C₈	C₂²×C₁₃	semidirect
332. D₄⋊C₈	C₂²×C₁₃	semidirect
333. D₄⋊C₈	C₂²×C₁₃	semidirect
334. #322	C₂²×C₁₃	semidirect
335. #322	C₂²×C₁₃	semidirect
336. #322	C₂²×C₁₃	semidirect
337. C₈²	C₂²×C₁₃	semidirect
520. C₁₃	#18006	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×#2969	2
D₄×C₁₃×M₁₆	2
C₁₃×#1594	2
C₁₃×#1590	2
C₁₃×#1588	2
C₁₃×#1586	2
C₁₃×#1582	2
C₁₃×#1581	2
C₁₃×SD₁₆⋊C₈	2
C₈×C₁₃×D₈	2
C₁₃×#1574	2
C₁₃×#1495	2
C₁₃×#1478	2
C₁₃×#1453	2
#18006	13

Subgroups — C13×#18006 #15704345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18006 #15704345