Subgroups — C₁₃×#29113 #15715452

Order 3328.

910 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2072	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2071	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2024	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1936	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1935	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1825	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1788	C₂	1	2	yes	maximal
11	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#103	C₂²	1	2	yes	—
18	C₂×C₁₃×#103	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₃×#97	C₂²	1	2	yes	—
23	C₁₃×#391	—	2	1	no	—
24	C₁₃×#391	C₂²	1	1	yes	characteristic
25	C₁₃×#391	C₂²	1	1	yes	characteristic
26	C₁₃×#390	C₂²	1	1	yes	characteristic
27	C₁₃×#390	C₂²	1	1	yes	characteristic
28	C₁₃×#389	—	2	1	no	—
29	C₁₃×#389	C₂²	1	2	yes	—
30	C₁₃×#386	—	2	1	no	—
31	C₁₃×#386	—	2	1	no	—
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#380	—	2	1	no	—
34	C₁₃×#380	C₂²	1	2	yes	—
35	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
36	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	1	yes	characteristic
42	C₁₃×#336	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#41	—	2	2	no	—
44	C₂×C₁₃×#41	—	2	2	no	—
45	C₂×C₁₃×#41	—	2	4	no	—
46	C₂×C₁₃×#41	—	4	2	no	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₁₃×C₄⋊Q₈	—	4	2	no	—
58	C₁₃×C₂²⋊Q₈	—	4	4	no	—
59	C₁₃×#117	—	2	4	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	—	4	2	no	—
76	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#103	—	2	4	no	—
81	C₁₃×#103	—	4	2	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#102	—	4	2	no	—
84	C₁₃×C₂²⋊C₈	—	2	4	no	—
85	C₁₃×#97	—	4	2	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	1	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	#29113	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	1	no	—
94	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₁₃×#41	—	4	8	no	—
96	C₁₃×#41	—	4	8	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₃	—	4	2	no	—
101	C₂×Q₈×C₁₃	—	4	2	no	—
102	C₂×Q₈×C₁₃	—	4	2	no	—
103	C₂×Q₈×C₁₃	#41	1	2	yes	—
104	C₂×D₄×C₁₃	—	2	4	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	4	2	no	—
109	C₂×D₄×C₁₃	—	4	2	no	—
110	C₂×D₄×C₁₃	#41	1	2	yes	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	4	1	no	—
123	C₂²×C₄×C₁₃	—	4	1	no	—
124	C₂²×C₄×C₁₃	—	4	1	no	—
125	C₂²×C₄×C₁₃	—	4	1	no	—
126	C₂²×C₄×C₁₃	—	4	2	no	—
127	C₂²×C₄×C₁₃	—	4	2	no	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	#41	1	4	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	4	2	no	—
148	C₁₃×C₄⋊C₄	—	4	4	no	—
149	C₁₃×C₄⋊C₄	—	4	2	no	—
150	C₁₃×C₄⋊C₄	—	4	2	no	—
151	C₁₃×C₂²⋊C₄	—	4	2	no	—
152	C₁₃×C₂²⋊C₄	—	4	2	no	—
153	C₁₃×C₂²⋊C₄	—	4	4	no	—
154	C₁₃×C₂²⋊C₄	—	4	2	no	—
155	C₁₃×C₂²⋊C₄	—	4	2	no	—
156	C₁₃×C₂²⋊C₄	—	4	2	no	—
157	C₄²×C₁₃	—	2	2	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₄²×C₁₃	—	4	1	no	—
160	C₄²×C₁₃	—	4	1	no	—
161	C₄²×C₁₃	—	4	2	no	—
162	#2857	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#2297	C₂×C₁₃	1	1	yes	characteristic
164	#2072	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#2071	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#2024	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#2023	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1936	C₂×C₁₃	1	2	yes	complemented
169	#1935	C₂×C₁₃	1	2	yes	complemented
170	#1825	C₂×C₁₃	1	2	yes	complemented
171	#1788	C₂×C₁₃	1	2	yes	—
172	#1749	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂³×C₁₃	—	2	1	no	—
174	C₂³×C₁₃	—	2	1	no	—
175	C₂³×C₁₃	—	2	1	no	—
176	C₂³×C₁₃	—	2	1	no	—
177	C₂³×C₁₃	—	2	1	no	—
178	C₂³×C₁₃	—	2	1	no	—
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	—	4	1	no	—
183	C₂³×C₁₃	—	4	1	no	—
184	C₂³×C₁₃	—	4	1	no	—
185	C₂³×C₁₃	—	4	1	no	—
186	C₂³×C₁₃	#124	1	2	yes	—
187	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₁₃	—	2	4	no	—
189	Q₈×C₁₃	—	4	2	no	—
190	Q₈×C₁₃	—	8	4	no	—
191	D₄×C₁₃	—	2	4	no	—
192	D₄×C₁₃	—	4	8	no	—
193	D₄×C₁₃	—	4	2	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	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	4	4	no	—
210	C₂×C₄×C₁₃	—	4	4	no	—
211	C₂×C₄×C₁₃	—	4	8	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	#124	1	2	yes	—
227	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
228	C₂×C₄×C₁₃	#137	1	2	yes	—
229	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
232	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
233	C₈×C₁₃	—	4	2	no	—
234	C₈×C₁₃	—	4	2	no	—
235	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×C₂²⋊Q₈	—	2	1	no	—
238	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
239	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#103	C₂²×C₁₃	1	2	yes	—
241	C₂×#103	C₂²×C₁₃	1	2	yes	—
242	C₂×#102	C₂²×C₁₃	1	2	yes	—
243	C₂×#102	C₂²×C₁₃	1	2	yes	—
244	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
245	C₂×#97	C₂²×C₁₃	1	2	yes	—
246	#391	—	2	1	no	—
247	#391	C₂²×C₁₃	1	1	yes	characteristic
248	#391	C₂²×C₁₃	1	1	yes	characteristic
249	#390	C₂²×C₁₃	1	1	yes	characteristic
250	#390	C₂²×C₁₃	1	1	yes	characteristic
251	#389	—	2	1	no	—
252	#389	C₂²×C₁₃	1	2	yes	—
253	#386	—	2	1	no	—
254	#386	—	2	1	no	—
255	#384	C₂²×C₁₃	1	1	yes	characteristic
256	#380	—	2	1	no	—
257	#380	C₂²×C₁₃	1	2	yes	—
258	C₄×C₂²⋊C₄	—	2	1	no	—
259	C₄×C₂²⋊C₄	—	2	1	no	—
260	#340	C₂²×C₁₃	1	2	yes	—
261	#340	C₂²×C₁₃	1	2	yes	—
262	#340	C₂²×C₁₃	1	2	yes	—
263	#340	C₂²×C₁₃	1	2	yes	—
264	#336	C₂²×C₁₃	1	1	yes	characteristic
265	#336	C₂²×C₁₃	1	1	yes	characteristic
266	C₂²×C₁₃	—	2	2	no	—
267	C₂²×C₁₃	—	2	2	no	—
268	C₂²×C₁₃	—	2	2	no	—
269	C₂²×C₁₃	—	4	1	no	—
270	C₂²×C₁₃	—	4	1	no	—
271	C₂²×C₁₃	—	4	1	no	—
272	C₂²×C₁₃	—	4	1	no	—
273	C₂²×C₁₃	—	4	2	no	—
274	C₂²×C₁₃	—	4	2	no	—
275	C₂²×C₁₃	—	4	2	no	—
276	C₂²×C₁₃	—	8	1	no	—
277	C₂²×C₁₃	—	8	1	no	—
278	C₂²×C₁₃	—	8	1	no	—
279	C₂²×C₁₃	—	8	1	no	—
280	C₂²×C₁₃	#525	1	1	yes	characteristic
281	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
282	C₂²×C₁₃	#534	1	1	yes	characteristic
283	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
284	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
285	C₂²×C₁₃	#575	1	1	yes	characteristic
286	C₂²×C₁₃	#575	1	1	yes	characteristic
287	C₄×C₁₃	—	2	2	no	—
288	C₄×C₁₃	—	2	2	no	—
289	C₄×C₁₃	—	2	2	no	—
290	C₄×C₁₃	—	4	2	no	—
291	C₄×C₁₃	—	4	1	no	—
292	C₄×C₁₃	—	4	1	no	—
293	C₄×C₁₃	—	8	2	no	—
294	C₄×C₁₃	—	8	1	no	—
295	C₄×C₁₃	—	8	1	no	—
296	C₄×C₁₃	—	8	2	no	—
297	C₄×C₁₃	#551	1	2	yes	—
298	C₄×C₁₃	#551	1	2	yes	—
299	C₂×#41	—	2	2	no	—
300	C₂×#41	—	2	2	no	—
301	C₂×#41	—	2	4	no	—
302	C₂×#41	—	4	2	no	—
303	C₂²×Q₈	—	2	1	no	—
304	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂³×C₄	—	2	1	no	—
308	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
309	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
312	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
313	C₄⋊Q₈	—	4	2	no	—
314	C₂²⋊Q₈	—	4	4	no	—
315	#117	—	2	4	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	—	4	2	no	—
332	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
336	#103	—	2	4	no	—
337	#103	—	4	2	no	—
338	#102	—	2	4	no	—
339	#102	—	4	2	no	—
340	C₂²⋊C₈	—	2	4	no	—
341	#97	—	4	2	no	—
342	#95	—	2	1	no	—
343	#95	—	2	1	no	—
344	#95	—	2	1	no	—
345	#95	—	2	1	no	—
346	#95	—	2	2	no	—
347	#95	—	2	2	no	—
348	C₂×C₁₃	—	4	2	no	—
349	C₂×C₁₃	—	8	2	no	—
350	C₂×C₁₃	#2561	1	1	yes	characteristic
351	C₂×C₁₃	#3115	1	1	yes	characteristic
352	C₂×C₁₃	#3116	1	1	yes	characteristic
353	C₂×C₁₃	#3135	1	1	yes	characteristic
354	C₂×C₁₃	#3141	1	1	yes	characteristic
355	C₂×C₁₃	#3194	1	1	yes	characteristic
356	C₂×C₁₃	#3196	1	1	yes	characteristic
357	C₂⁴	—	2	1	no	—
358	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
359	#41	—	4	8	no	—
360	#41	—	4	8	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	4	2	no	—
365	C₂×Q₈	—	4	2	no	—
366	C₂×Q₈	—	4	2	no	—
367	C₂×Q₈	C₁₃×#41	1	2	yes	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	C₁₃×#41	1	2	yes	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₁₃×#41	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	4	4	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₂²⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₂²⋊C₄	—	4	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	4	1	no	—
424	C₄²	—	4	1	no	—
425	C₄²	—	4	2	no	—
426	C₁₃	#29113	1	1	yes	characteristic, direct product factor, Sylow
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	4	1	no	—
440	C₂³	C₁₃×#124	1	2	yes	—
441	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
442	Q₈	—	2	4	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	8	4	no	—
445	D₄	—	2	4	no	—
446	D₄	—	4	8	no	—
447	D₄	—	4	2	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	C₁₃×#124	1	2	yes	—
481	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
482	C₂×C₄	C₁₃×#137	1	2	yes	—
483	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
484	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
485	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
486	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
487	C₈	—	4	2	no	—
488	C₈	—	4	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	C₁₃×#525	1	1	yes	characteristic
504	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
505	C₂²	C₁₃×#534	1	1	yes	characteristic
506	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
507	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
508	C₂²	C₁₃×#575	1	1	yes	characteristic
509	C₂²	C₁₃×#575	1	1	yes	characteristic
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	8	2	no	—
517	C₄	—	8	1	no	—
518	C₄	—	8	1	no	—
519	C₄	—	8	2	no	—
520	C₄	C₁₃×#551	1	2	yes	—
521	C₄	C₁₃×#551	1	2	yes	—
522	C₂	—	4	2	no	—
523	C₂	—	8	2	no	—
524	C₂	C₁₃×#2561	1	1	yes	characteristic
525	C₂	C₁₃×#3115	1	1	yes	characteristic
526	C₂	C₁₃×#3116	1	1	yes	characteristic
527	C₂	C₁₃×#3135	1	1	yes	characteristic
528	C₂	C₁₃×#3141	1	1	yes	characteristic
529	C₂	C₁₃×#3194	1	1	yes	characteristic
530	C₂	C₁₃×#3196	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2857	C₂	semidirect
3. C₁₃×#2072	C₂	semidirect
4. C₁₃×#2071	C₂	semidirect
5. C₁₃×#2024	C₂	semidirect
6. C₁₃×#2023	C₂	semidirect
7. C₁₃×#1936	C₂	semidirect
8. C₁₃×#1935	C₂	semidirect
9. C₁₃×#1825	C₂	semidirect
11. C₁₃×#1749	C₂	semidirect
92. #29113	C₁₃	direct (N × H)
162. #2857	C₂×C₁₃	semidirect
164. #2072	C₂×C₁₃	semidirect
165. #2071	C₂×C₁₃	semidirect
166. #2024	C₂×C₁₃	semidirect
167. #2023	C₂×C₁₃	semidirect
168. #1936	C₂×C₁₃	semidirect
169. #1935	C₂×C₁₃	semidirect
170. #1825	C₂×C₁₃	semidirect
172. #1749	C₂×C₁₃	semidirect
426. C₁₃	#29113	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×#2857	2
C₁₃×#2297	2
C₁₃×#2072	2
C₁₃×#2071	2
C₁₃×#2024	2
C₁₃×#2023	2
C₁₃×#1936	2
C₁₃×#1935	2
C₁₃×#1825	2
C₁₃×#1788	2
C₁₃×#1749	2
#29113	13

Subgroups — C13×#29113 #15715452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29113 #15715452