Subgroups — C₁₃×#18007 #15704346

Order 3328.

662 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1592	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1590	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1586	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1585	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×#1580	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1573	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1496	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1477	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1453	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#131	—	2	1	no	—
17	C₁₃×#532	C₂²	1	1	yes	characteristic
18	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₁₃×#482	C₄	1	1	yes	characteristic
20	C₁₃×#482	C₄	1	1	yes	characteristic
21	C₁₃×#477	C₄	1	1	yes	characteristic
22	C₁₃×#476	C₄	1	1	yes	characteristic
23	C₁₃×#460	C₄	1	1	yes	characteristic
24	C₁₃×#459	C₄	1	1	yes	characteristic
25	C₁₃×#449	C₄	1	1	yes	characteristic
26	C₁₃×#449	C₄	1	1	yes	characteristic
27	C₁₃×#446	C₂²	1	1	yes	characteristic
28	C₁₃×#446	C₂²	1	1	yes	characteristic
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	C₂²	1	1	yes	characteristic
34	C₁₃×#436	C₂²	1	1	yes	characteristic
35	C₁₃×#435	—	2	1	no	—
36	C₁₃×#435	—	2	1	no	—
37	C₁₃×#435	—	2	1	no	—
38	C₁₃×#435	—	2	1	no	—
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
42	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₁₃×#432	—	2	1	no	—
44	C₁₃×#432	C₂²	1	1	yes	characteristic
45	C₁₃×#431	C₂²	1	1	yes	characteristic
46	C₁₃×#431	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₁₃×#408	—	2	1	no	—
49	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#97	—	2	1	no	—
51	C₁₃×#335	C₂²	1	1	yes	characteristic
52	C₁₃×#335	C₂²	1	1	yes	characteristic
53	C₁₃×#334	C₂²	1	1	yes	characteristic
54	C₁₃×#334	C₂²	1	1	yes	characteristic
55	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
56	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
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
62	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₃×#322	C₂²	1	1	yes	characteristic
64	C₁₃×#322	C₂²	1	1	yes	characteristic
65	C₁₃×#322	C₂²	1	1	yes	characteristic
66	C₈²×C₁₃	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	—	2	1	no	—
68	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
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	C₁₃×#131	—	4	4	no	—
74	C₂×C₁₃×M₁₆	—	2	1	no	—
75	C₂×C₁₃×M₁₆	—	2	1	no	—
76	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
77	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	—	2	1	no	—
79	C₂²×C₈×C₁₃	—	2	1	no	—
80	C₂²×C₈×C₁₃	—	2	1	no	—
81	C₂²×C₈×C₁₃	—	2	1	no	—
82	C₂²×C₈×C₁₃	—	2	1	no	—
83	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
84	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
85	C₁₃×#124	—	2	1	no	—
86	C₁₃×#121	—	2	1	no	—
87	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
88	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
89	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
90	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₄×D₄×C₁₃	—	2	1	no	—
92	C₄×D₄×C₁₃	—	2	1	no	—
93	C₄×D₄×C₁₃	—	2	1	no	—
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	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	—	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	—	2	1	no	—
136	C₁₃×#97	—	2	1	no	—
137	C₁₃×#97	D₄	1	1	yes	characteristic
138	C₁₃×#97	D₄	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	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
145	#18007	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₁₃×#41	—	2	2	no	—
147	C₁₃×#41	—	4	1	no	—
148	C₁₃×#41	—	4	2	no	—
149	C₁₃×#41	—	4	2	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
168	C₁₃×SD₁₆	—	4	1	no	—
169	C₁₃×SD₁₆	—	4	1	no	—
170	C₁₃×D₈	—	2	2	no	—
171	C₁₃×D₈	—	2	2	no	—
172	C₁₃×M₁₆	—	2	2	no	—
173	C₁₃×M₁₆	—	4	1	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	—	4	2	no	—
186	C₂×C₈×C₁₃	—	4	2	no	—
187	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₈×C₁₃	C₂²×C₄	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	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	—	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	#3106	C₂×C₁₃	1	1	yes	characteristic
217	#2970	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2935	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1592	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1590	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1586	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1585	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	#1580	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₈×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1573	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1496	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1477	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	C₄×D₄	1	1	yes	characteristic
235	Q₈×C₁₃	—	2	1	no	—
236	Q₈×C₁₃	—	2	1	no	—
237	Q₈×C₁₃	—	4	2	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	—	2	1	no	—
243	D₄×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	4	2	no	—
245	D₄×C₁₃	—	4	2	no	—
246	D₄×C₁₃	—	4	2	no	—
247	D₄×C₁₃	—	8	1	no	—
248	D₄×C₁₃	#131	1	2	yes	complemented
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	—	2	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	2	no	—
260	C₂×C₄×C₁₃	—	4	1	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	—	8	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	C₂×#131	—	2	1	no	—
288	#532	C₂²×C₁₃	1	1	yes	characteristic
289	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
290	#482	C₄×C₁₃	1	1	yes	characteristic
291	#482	C₄×C₁₃	1	1	yes	characteristic
292	#477	C₄×C₁₃	1	1	yes	characteristic
293	#476	C₄×C₁₃	1	1	yes	characteristic
294	#460	C₄×C₁₃	1	1	yes	characteristic
295	#459	C₄×C₁₃	1	1	yes	characteristic
296	#449	C₄×C₁₃	1	1	yes	characteristic
297	#449	C₄×C₁₃	1	1	yes	characteristic
298	#446	C₂²×C₁₃	1	1	yes	characteristic
299	#446	C₂²×C₁₃	1	1	yes	characteristic
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	C₂²×C₁₃	1	1	yes	characteristic
305	#436	C₂²×C₁₃	1	1	yes	characteristic
306	#435	—	2	1	no	—
307	#435	—	2	1	no	—
308	#435	—	2	1	no	—
309	#435	—	2	1	no	—
310	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
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
314	#432	—	2	1	no	—
315	#432	C₂²×C₁₃	1	1	yes	characteristic
316	#431	C₂²×C₁₃	1	1	yes	characteristic
317	#431	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
319	#408	—	2	1	no	—
320	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#97	—	2	1	no	—
322	#335	C₂²×C₁₃	1	1	yes	characteristic
323	#335	C₂²×C₁₃	1	1	yes	characteristic
324	#334	C₂²×C₁₃	1	1	yes	characteristic
325	#334	C₂²×C₁₃	1	1	yes	characteristic
326	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
327	Q₈⋊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
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
333	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
334	#322	C₂²×C₁₃	1	1	yes	characteristic
335	#322	C₂²×C₁₃	1	1	yes	characteristic
336	#322	C₂²×C₁₃	1	1	yes	characteristic
337	C₈²	C₂²×C₁₃	1	1	yes	characteristic
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	C₂×C₄×D₄	1	1	yes	characteristic
351	C₄×C₁₃	—	2	1	no	—
352	C₄×C₁₃	—	2	1	no	—
353	C₄×C₁₃	—	2	1	no	—
354	C₄×C₁₃	—	2	1	no	—
355	C₄×C₁₃	—	4	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	C₂×#131	1	1	yes	characteristic
361	C₄×C₁₃	#568	1	1	yes	characteristic
362	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
363	C₄×C₁₃	#575	1	1	yes	characteristic
364	C₂×#41	—	2	1	no	—
365	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
366	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
367	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
368	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
369	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
370	#131	—	4	4	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
374	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
381	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
382	#124	—	2	1	no	—
383	#121	—	2	1	no	—
384	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
385	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
386	C₄×Q₈	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	C₂³×C₁₃	1	1	yes	characteristic
393	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
394	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
395	#117	—	2	1	no	—
396	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
399	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
400	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
401	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
402	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
403	C₄⋊C₈	—	2	1	no	—
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
408	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
409	C₄⋊C₈	C₂³×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	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
414	#103	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	#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	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	—	2	1	no	—
427	C₂²⋊C₈	—	2	1	no	—
428	C₂²⋊C₈	—	2	1	no	—
429	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
430	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
431	#97	—	2	1	no	—
432	#97	—	2	1	no	—
433	#97	—	2	1	no	—
434	#97	D₄×C₁₃	1	1	yes	characteristic
435	#97	D₄×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	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	C₂×C₁₃	—	4	1	no	—
443	C₂×C₁₃	—	4	2	no	—
444	C₂×C₁₃	—	8	1	no	—
445	C₂×C₁₃	—	8	1	no	—
446	C₂×C₁₃	#2933	1	1	yes	characteristic
447	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
448	C₂×C₁₃	#2957	1	1	yes	characteristic
449	#41	—	2	2	no	—
450	#41	—	4	1	no	—
451	#41	—	4	2	no	—
452	#41	—	4	2	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
461	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
462	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
471	SD₁₆	—	4	1	no	—
472	SD₁₆	—	4	1	no	—
473	D₈	—	2	2	no	—
474	D₈	—	2	2	no	—
475	M₁₆	—	2	2	no	—
476	M₁₆	—	4	1	no	—
477	M₁₆	—	4	2	no	—
478	M₁₆	—	4	2	no	—
479	C₂×C₈	—	2	1	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	—	4	2	no	—
486	C₂×C₈	—	4	2	no	—
487	C₂×C₈	—	4	2	no	—
488	C₂×C₈	—	4	2	no	—
489	C₂×C₈	—	4	2	no	—
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	C₂²×C₄×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	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
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	C₂²⋊C₄	—	2	1	no	—
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	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
516	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
517	C₄²	C₁₃×#41	1	1	yes	characteristic
518	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
519	C₁₃	#18007	1	1	yes	characteristic, direct product factor, Sylow
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
524	Q₈	—	2	1	no	—
525	Q₈	—	2	1	no	—
526	Q₈	—	4	2	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	2	1	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	8	1	no	—
537	D₄	C₁₃×#131	1	2	yes	complemented
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	1	no	—
550	C₂×C₄	—	4	1	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	—	8	1	no	—
556	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
557	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
558	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
559	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
560	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
561	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
562	C₈	—	2	1	no	—
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	—	4	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	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	4	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	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
599	C₄	C₁₃×#568	1	1	yes	characteristic
600	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
601	C₄	C₁₃×#575	1	1	yes	characteristic
602	C₂	—	4	1	no	—
603	C₂	—	4	2	no	—
604	C₂	—	8	1	no	—
605	C₂	—	8	1	no	—
606	C₂	C₁₃×#2933	1	1	yes	characteristic
607	C₂	C₄×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
608	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×#3106	C₂
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×#2970	C₂	semidirect
3. C₁₃×#2935	C₂	semidirect
4. C₁₃×#1592	C₂	semidirect
5. C₁₃×#1590	C₂	semidirect
6. C₁₃×#1586	C₂	semidirect
7. C₁₃×#1585	C₂	semidirect
8. C₁₃×#1582	C₂	semidirect
9. C₁₃×#1581	C₂	semidirect
10. C₁₃×#1580	C₂	semidirect
11. C₈×C₁₃×D₈	C₂	semidirect
12. C₁₃×#1573	C₂	semidirect
13. C₁₃×#1496	C₂	semidirect
14. C₁₃×#1477	C₂	semidirect
15. C₁₃×#1453	C₂	semidirect
145. #18007	C₁₃	direct (N × H)
217. #2970	C₂×C₁₃	semidirect
218. #2935	C₂×C₁₃	semidirect
219. #1592	C₂×C₁₃	semidirect
220. #1590	C₂×C₁₃	semidirect
221. #1586	C₂×C₁₃	semidirect
222. #1585	C₂×C₁₃	semidirect
223. #1582	C₂×C₁₃	semidirect
224. #1581	C₂×C₁₃	semidirect
225. #1580	C₂×C₁₃	semidirect
226. C₈×D₈	C₂×C₁₃	semidirect
227. #1573	C₂×C₁₃	semidirect
228. #1496	C₂×C₁₃	semidirect
229. #1477	C₂×C₁₃	semidirect
230. #1453	C₂×C₁₃	semidirect
248. D₄×C₁₃	#131	semidirect
519. C₁₃	#18007	direct (N × H)
537. D₄	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×#3106	2
C₁₃×#2970	2
C₁₃×#2935	2
C₁₃×#1592	2
C₁₃×#1590	2
C₁₃×#1586	2
C₁₃×#1585	2
C₁₃×#1582	2
C₁₃×#1581	2
C₁₃×#1580	2
C₈×C₁₃×D₈	2
C₁₃×#1573	2
C₁₃×#1496	2
C₁₃×#1477	2
C₁₃×#1453	2
#18007	13

Subgroups — C13×#18007 #15704346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18007 #15704346