Subgroups — C₁₃×#17917 #15704256

Order 3328.

692 conjugacy classes of subgroups.

The subgroup lattice has 480 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	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1583	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1581	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1580	C₂	1	2	yes	maximal, complemented
7	C₁₃×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1574	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1489	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1484	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#131	—	2	1	no	—
13	C₁₃×#532	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₁₃×#482	C₄	1	2	yes	—
16	C₁₃×#477	C₄	1	1	yes	characteristic
17	C₁₃×#476	C₄	1	1	yes	characteristic
18	C₁₃×#460	C₄	1	1	yes	characteristic
19	C₁₃×#459	C₄	1	1	yes	characteristic
20	C₁₃×#449	C₄	1	2	yes	—
21	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
24	C₄×C₁₃×D₈	C₂²	1	2	yes	—
25	C₁₃×#436	—	2	1	no	—
26	C₁₃×#436	C₂²	1	2	yes	—
27	C₈×D₄×C₁₃	—	2	1	no	—
28	C₈×D₄×C₁₃	—	2	1	no	—
29	C₈×D₄×C₁₃	—	2	1	no	—
30	C₈×D₄×C₁₃	C₂²	1	2	yes	—
31	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#431	—	2	1	no	—
34	C₁₃×#431	C₂²	1	1	yes	characteristic
35	C₁₃×#431	C₂²	1	1	yes	characteristic
36	C₁₃×#423	C₂²	1	1	yes	characteristic
37	C₁₃×#408	—	2	1	no	—
38	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₃	—	2	1	no	—
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#335	C₂²	1	2	yes	—
42	C₁₃×#334	C₂²	1	2	yes	—
43	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
45	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
46	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
47	C₁₃×#322	C₂²	1	2	yes	—
48	C₁₃×#322	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	—	2	1	no	—
50	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
53	C₁₃×#131	—	4	4	no	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	—	2	2	no	—
57	C₂²×C₈×C₁₃	—	2	1	no	—
58	C₂²×C₈×C₁₃	—	2	1	no	—
59	C₂²×C₈×C₁₃	—	2	2	no	—
60	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
63	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
64	C₁₃×#124	—	2	1	no	—
65	C₁₃×#121	—	2	1	no	—
66	C₁₃×#121	C₂×C₄	1	2	yes	—
67	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₁₃	—	2	1	no	—
70	C₄×D₄×C₁₃	—	2	1	no	—
71	C₄×D₄×C₁₃	—	2	1	no	—
72	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
73	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₄×D₄×C₁₃	C₂³	1	2	yes	—
75	C₁₃×#117	—	2	1	no	—
76	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#107	C₂×C₄	1	2	yes	—
80	C₁₃×#106	C₂×C₄	1	2	yes	—
81	C₁₃×C₄⋊C₈	—	2	1	no	—
82	C₁₃×C₄⋊C₈	—	2	1	no	—
83	C₁₃×C₄⋊C₈	—	2	1	no	—
84	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
89	C₁₃×#103	C₂×C₄	1	2	yes	—
90	C₁₃×#102	C₂×C₄	1	2	yes	—
91	C₁₃×#102	C₂×C₄	1	2	yes	—
92	C₁₃×#102	C₂×C₄	1	2	yes	—
93	C₁₃×C₂²⋊C₈	—	2	1	no	—
94	C₁₃×C₂²⋊C₈	—	2	2	no	—
95	C₁₃×C₂²⋊C₈	—	2	2	no	—
96	C₁₃×C₂²⋊C₈	—	2	1	no	—
97	C₁₃×C₂²⋊C₈	—	2	1	no	—
98	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
99	C₁₃×#97	—	2	1	no	—
100	C₄×C₈×C₁₃	—	2	1	no	—
101	C₄×C₈×C₁₃	—	2	1	no	—
102	C₄×C₈×C₁₃	—	2	1	no	—
103	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
104	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
105	C₄×C₈×C₁₃	C₂³	1	2	yes	—
106	C₄×C₈×C₁₃	C₂³	1	2	yes	—
107	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
109	#17917	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₁₃×#41	—	2	2	no	—
111	C₁₃×#41	—	2	2	no	—
112	C₁₃×#41	—	4	2	no	—
113	C₁₃×#41	—	4	2	no	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
121	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
129	C₁₃×SD₁₆	—	2	4	no	—
130	C₁₃×D₈	—	2	4	no	—
131	C₁₃×M₁₆	—	4	2	no	—
132	C₁₃×M₁₆	—	4	2	no	—
133	C₁₃×M₁₆	—	4	4	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	4	1	no	—
140	C₂×C₈×C₁₃	—	4	2	no	—
141	C₂×C₈×C₁₃	—	4	4	no	—
142	C₂×C₈×C₁₃	—	4	2	no	—
143	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
153	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
154	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
155	C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₁₃×C₂²⋊C₄	—	2	1	no	—
157	C₁₃×C₂²⋊C₄	—	2	2	no	—
158	C₁₃×C₂²⋊C₄	—	2	1	no	—
159	C₁₃×C₂²⋊C₄	—	2	2	no	—
160	C₄²×C₁₃	—	2	1	no	—
161	C₄²×C₁₃	—	2	1	no	—
162	C₄²×C₁₃	—	2	1	no	—
163	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₃	#41	1	1	yes	characteristic
166	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
167	#3106	C₂×C₁₃	1	1	yes	characteristic
168	C₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1583	C₂×C₁₃	1	2	yes	complemented
171	#1581	C₂×C₁₃	1	2	yes	complemented
172	#1580	C₂×C₁₃	1	2	yes	complemented
173	SD₁₆⋊C₈	C₂×C₁₃	1	2	yes	complemented
174	#1574	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#1489	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#1484	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#1451	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂³×C₁₃	—	2	1	no	—
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
181	Q₈×C₁₃	—	2	1	no	—
182	Q₈×C₁₃	—	4	2	no	—
183	Q₈×C₁₃	#131	1	2	yes	complemented
184	D₄×C₁₃	—	2	4	no	—
185	D₄×C₁₃	—	2	1	no	—
186	D₄×C₁₃	—	2	2	no	—
187	D₄×C₁₃	—	2	2	no	—
188	D₄×C₁₃	—	4	2	no	—
189	D₄×C₁₃	—	4	4	no	—
190	D₄×C₁₃	—	4	2	no	—
191	D₄×C₁₃	#131	1	2	yes	complemented
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
213	C₈×C₁₃	—	2	2	no	—
214	C₈×C₁₃	—	2	2	no	—
215	C₈×C₁₃	—	2	1	no	—
216	C₈×C₁₃	—	2	1	no	—
217	C₈×C₁₃	—	2	1	no	—
218	C₈×C₁₃	—	4	2	no	—
219	C₈×C₁₃	—	4	1	no	—
220	C₈×C₁₃	—	4	2	no	—
221	C₈×C₁₃	—	4	1	no	—
222	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
223	C₂×#131	—	2	1	no	—
224	#532	C₂²×C₁₃	1	1	yes	characteristic
225	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
226	#482	C₄×C₁₃	1	2	yes	—
227	#477	C₄×C₁₃	1	1	yes	characteristic
228	#476	C₄×C₁₃	1	1	yes	characteristic
229	#460	C₄×C₁₃	1	1	yes	characteristic
230	#459	C₄×C₁₃	1	1	yes	characteristic
231	#449	C₄×C₁₃	1	2	yes	—
232	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
234	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
235	C₄×D₈	C₂²×C₁₃	1	2	yes	—
236	#436	—	2	1	no	—
237	#436	C₂²×C₁₃	1	2	yes	—
238	C₈×D₄	—	2	1	no	—
239	C₈×D₄	—	2	1	no	—
240	C₈×D₄	—	2	1	no	—
241	C₈×D₄	C₂²×C₁₃	1	2	yes	—
242	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
243	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
244	#431	—	2	1	no	—
245	#431	C₂²×C₁₃	1	1	yes	characteristic
246	#431	C₂²×C₁₃	1	1	yes	characteristic
247	#423	C₂²×C₁₃	1	1	yes	characteristic
248	#408	—	2	1	no	—
249	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×C₄×C₈	—	2	1	no	—
251	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
252	#335	C₂²×C₁₃	1	2	yes	—
253	#334	C₂²×C₁₃	1	2	yes	—
254	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
255	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
256	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
257	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
258	#322	C₂²×C₁₃	1	2	yes	—
259	#322	C₂²×C₁₃	1	2	yes	—
260	C₂²×C₁₃	—	2	1	no	—
261	C₂²×C₁₃	—	2	2	no	—
262	C₂²×C₁₃	—	2	1	no	—
263	C₂²×C₁₃	—	2	1	no	—
264	C₂²×C₁₃	—	4	1	no	—
265	C₂²×C₁₃	—	4	1	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₁₃	—	2	1	no	—
271	C₄×C₁₃	—	2	2	no	—
272	C₄×C₁₃	—	2	1	no	—
273	C₄×C₁₃	—	2	1	no	—
274	C₄×C₁₃	—	4	1	no	—
275	C₄×C₁₃	—	4	2	no	—
276	C₄×C₁₃	—	4	1	no	—
277	C₄×C₁₃	#444	1	2	yes	—
278	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
279	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
280	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
281	C₄×C₁₃	#575	1	1	yes	characteristic
282	C₂×#41	—	2	1	no	—
283	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
284	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
285	C₂×D₈	C₂×C₄×C₁₃	1	2	yes	—
286	#131	—	4	4	no	—
287	C₂×M₁₆	—	2	1	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
294	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
295	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
296	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
297	#124	—	2	1	no	—
298	#121	—	2	1	no	—
299	#121	C₂×C₄×C₁₃	1	2	yes	—
300	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
301	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
306	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₄×D₄	C₂³×C₁₃	1	2	yes	—
308	#117	—	2	1	no	—
309	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
312	#107	C₂×C₄×C₁₃	1	2	yes	—
313	#106	C₂×C₄×C₁₃	1	2	yes	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	2	1	no	—
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
318	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
319	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
320	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
321	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
322	#103	C₂×C₄×C₁₃	1	2	yes	—
323	#102	C₂×C₄×C₁₃	1	2	yes	—
324	#102	C₂×C₄×C₁₃	1	2	yes	—
325	#102	C₂×C₄×C₁₃	1	2	yes	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	2	2	no	—
328	C₂²⋊C₈	—	2	2	no	—
329	C₂²⋊C₈	—	2	1	no	—
330	C₂²⋊C₈	—	2	1	no	—
331	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
332	#97	—	2	1	no	—
333	C₄×C₈	—	2	1	no	—
334	C₄×C₈	—	2	1	no	—
335	C₄×C₈	—	2	1	no	—
336	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
337	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
338	C₄×C₈	C₂³×C₁₃	1	2	yes	—
339	C₄×C₈	C₂³×C₁₃	1	2	yes	—
340	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
341	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
342	C₂×C₁₃	—	4	1	no	—
343	C₂×C₁₃	—	4	2	no	—
344	C₂×C₁₃	—	8	2	no	—
345	C₂×C₁₃	#2929	1	1	yes	characteristic
346	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
347	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
348	#41	—	2	2	no	—
349	#41	—	2	2	no	—
350	#41	—	4	2	no	—
351	#41	—	4	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
359	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
367	SD₁₆	—	2	4	no	—
368	D₈	—	2	4	no	—
369	M₁₆	—	4	2	no	—
370	M₁₆	—	4	2	no	—
371	M₁₆	—	4	4	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	4	1	no	—
378	C₂×C₈	—	4	4	no	—
379	C₂×C₈	—	4	2	no	—
380	C₂×C₈	—	4	2	no	—
381	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
382	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
383	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
384	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
385	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
386	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
391	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
392	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₂²⋊C₄	—	2	1	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	2	1	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
402	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
403	C₄²	C₁₃×#41	1	1	yes	characteristic
404	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
405	C₁₃	#17917	1	1	yes	characteristic, direct product factor, Sylow
406	C₂³	—	2	1	no	—
407	C₂³	—	2	2	no	—
408	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
409	Q₈	—	2	1	no	—
410	Q₈	—	4	2	no	—
411	Q₈	C₁₃×#131	1	2	yes	complemented
412	D₄	—	2	4	no	—
413	D₄	—	2	1	no	—
414	D₄	—	2	2	no	—
415	D₄	—	2	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	2	no	—
419	D₄	C₁₃×#131	1	2	yes	complemented
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
436	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
437	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
438	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
440	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
441	C₈	—	2	2	no	—
442	C₈	—	2	2	no	—
443	C₈	—	2	1	no	—
444	C₈	—	2	1	no	—
445	C₈	—	2	1	no	—
446	C₈	—	4	2	no	—
447	C₈	—	4	1	no	—
448	C₈	—	4	2	no	—
449	C₈	—	4	1	no	—
450	C₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	1	no	—
468	C₄	C₁₃×#444	1	2	yes	—
469	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
470	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
471	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
472	C₄	C₁₃×#575	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	4	2	no	—
475	C₂	—	8	2	no	—
476	C₂	C₁₃×#2929	1	1	yes	characteristic
477	C₂	C₄×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
478	C₂	C₂×C₁₃×#444	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 ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈×C₁₃×#41	C₂	semidirect
3. C₁₃×#2931	C₂	semidirect
4. C₁₃×#1583	C₂	semidirect
5. C₁₃×#1581	C₂	semidirect
6. C₁₃×#1580	C₂	semidirect
7. C₁₃×SD₁₆⋊C₈	C₂	semidirect
8. C₁₃×#1574	C₂	semidirect
9. C₁₃×#1489	C₂	semidirect
10. C₁₃×#1484	C₂	semidirect
11. C₁₃×#1451	C₂	semidirect
109. #17917	C₁₃	direct (N × H)
168. C₈×#41	C₂×C₁₃	semidirect
169. #2931	C₂×C₁₃	semidirect
170. #1583	C₂×C₁₃	semidirect
171. #1581	C₂×C₁₃	semidirect
172. #1580	C₂×C₁₃	semidirect
173. SD₁₆⋊C₈	C₂×C₁₃	semidirect
174. #1574	C₂×C₁₃	semidirect
175. #1489	C₂×C₁₃	semidirect
176. #1484	C₂×C₁₃	semidirect
177. #1451	C₂×C₁₃	semidirect
183. Q₈×C₁₃	#131	semidirect
191. D₄×C₁₃	#131	semidirect
405. C₁₃	#17917	direct (N × H)
411. Q₈	C₁₃×#131	semidirect
419. 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
C₈×C₁₃×#41	2
C₁₃×#2931	2
C₁₃×#1583	2
C₁₃×#1581	2
C₁₃×#1580	2
C₁₃×SD₁₆⋊C₈	2
C₁₃×#1574	2
C₁₃×#1489	2
C₁₃×#1484	2
C₁₃×#1451	2
#17917	13

Subgroups — C13×#17917 #15704256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17917 #15704256