Subgroups — C₁₃×#24481 #15710820

Order 3328.

1012 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#480	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2436	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2344	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2068	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2042	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1983	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1928	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1893	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#124	C₂²	1	2	yes	—
15	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	—	2	1	no	—
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₁₃×#480	—	2	4	no	—
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₃×#103	—	2	4	no	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₁₃×#393	—	2	2	no	—
32	C₁₃×#391	C₂²	1	2	yes	—
33	C₁₃×#389	C₂²	1	2	yes	—
34	C₁₃×#387	—	2	2	no	—
35	C₁₃×#386	—	2	1	no	—
36	C₁₃×#386	—	2	1	no	—
37	C₁₃×#381	—	2	1	no	—
38	C₁₃×#380	C₂²	1	1	yes	characteristic
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
40	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₃	—	2	4	no	—
45	C₂²×Q₈×C₁₃	—	2	2	no	—
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	—	4	2	no	—
48	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
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	—	2	1	no	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	—	2	2	no	—
55	C₂²×C₈×C₁₃	—	4	2	no	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
59	C₁₃×#124	—	2	4	no	—
60	C₁₃×#124	—	4	2	no	—
61	C₁₃×#121	—	2	2	no	—
62	C₁₃×#121	—	2	2	no	—
63	C₁₃×#117	—	4	4	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
77	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	—	2	2	no	—
79	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
80	C₁₃×#107	—	2	2	no	—
81	C₁₃×#107	—	2	2	no	—
82	C₁₃×C₄⋊C₈	—	4	2	no	—
83	C₁₃×#103	—	2	4	no	—
84	C₁₃×#103	—	2	4	no	—
85	C₁₃×#103	—	2	4	no	—
86	C₁₃×#103	—	4	2	no	—
87	C₁₃×#102	—	2	2	no	—
88	C₁₃×#102	—	2	2	no	—
89	C₁₃×#102	—	4	2	no	—
90	C₁₃×C₂²⋊C₈	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	C₁₃×#95	—	2	1	no	—
93	C₁₃×#95	—	2	2	no	—
94	C₁₃×#95	—	2	2	no	—
95	C₁₃×#95	—	2	2	no	—
96	C₁₃×#95	D₄	1	2	yes	—
97	#24481	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂⁴×C₁₃	—	2	1	no	—
99	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	8	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	4	4	no	—
107	C₂×Q₈×C₁₃	—	4	8	no	—
108	C₂×Q₈×C₁₃	—	4	4	no	—
109	C₂×Q₈×C₁₃	—	4	2	no	—
110	C₂×Q₈×C₁₃	#41	1	4	yes	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	—	2	1	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	2	no	—
115	C₂×D₄×C₁₃	—	4	2	no	—
116	C₂×D₄×C₁₃	—	4	2	no	—
117	C₂×D₄×C₁₃	—	4	2	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	2	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	—	4	4	no	—
127	C₂²×C₄×C₁₃	—	4	2	no	—
128	C₂²×C₄×C₁₃	—	4	2	no	—
129	C₂²×C₄×C₁₃	—	4	2	no	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	#41	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	4	4	no	—
144	C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	4	4	no	—
152	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
154	C₁₃×C₂²⋊C₄	—	2	2	no	—
155	C₁₃×C₂²⋊C₄	—	2	2	no	—
156	C₁₃×C₂²⋊C₄	—	4	4	no	—
157	C₁₃×C₂²⋊C₄	—	4	4	no	—
158	C₁₃×C₂²⋊C₄	—	4	2	no	—
159	C₁₃×C₂²⋊C₄	—	4	2	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	—	4	4	no	—
163	C₂×#480	C₂×C₁₃	1	1	yes	characteristic
164	C₂²×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#2436	C₂×C₁₃	1	1	yes	characteristic
166	#2344	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#2068	C₂×C₁₃	1	2	yes	complemented
168	#2042	C₂×C₁₃	1	2	yes	complemented
169	#1983	C₂×C₁₃	1	2	yes	complemented
170	#1928	C₂×C₁₃	1	2	yes	complemented
171	#1893	C₂×C₁₃	1	1	yes	characteristic
172	#1850	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#1787	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	4	1	no	—
177	C₂³×C₁₃	—	4	2	no	—
178	C₂³×C₁₃	—	4	1	no	—
179	C₂³×C₁₃	—	4	1	no	—
180	C₂³×C₁₃	—	4	2	no	—
181	C₂³×C₁₃	#121	1	2	yes	—
182	C₂³×C₁₃	#135	1	2	yes	—
183	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
184	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	Q₈×C₁₃	—	2	4	no	—
186	Q₈×C₁₃	—	2	4	no	—
187	Q₈×C₁₃	—	4	8	no	—
188	Q₈×C₁₃	—	4	2	no	—
189	Q₈×C₁₃	—	4	2	no	—
190	D₄×C₁₃	—	4	1	no	—
191	D₄×C₁₃	—	4	1	no	—
192	D₄×C₁₃	—	4	2	no	—
193	D₄×C₁₃	—	8	4	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	4	8	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	8	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	#121	1	2	yes	—
222	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
224	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
226	C₈×C₁₃	—	4	1	no	—
227	C₈×C₁₃	—	4	1	no	—
228	C₈×C₁₃	—	4	2	no	—
229	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
230	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×#124	C₂²×C₁₃	1	2	yes	—
232	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#117	—	2	1	no	—
234	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
235	#480	—	2	4	no	—
236	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
239	C₂×#103	—	2	4	no	—
240	C₂×#103	C₂²×C₁₃	1	2	yes	—
241	C₂×#103	C₂²×C₁₃	1	2	yes	—
242	C₂×#103	C₂²×C₁₃	1	2	yes	—
243	C₂×#103	C₂²×C₁₃	1	2	yes	—
244	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#102	C₂²×C₁₃	1	2	yes	—
247	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
248	#393	—	2	2	no	—
249	#391	C₂²×C₁₃	1	2	yes	—
250	#389	C₂²×C₁₃	1	2	yes	—
251	#387	—	2	2	no	—
252	#386	—	2	1	no	—
253	#386	—	2	1	no	—
254	#381	—	2	1	no	—
255	#380	C₂²×C₁₃	1	1	yes	characteristic
256	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
257	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
258	#340	C₂²×C₁₃	1	2	yes	—
259	#336	C₂²×C₁₃	1	2	yes	—
260	C₂²×C₁₃	—	2	2	no	—
261	C₂²×C₁₃	—	2	2	no	—
262	C₂²×C₁₃	—	2	4	no	—
263	C₂²×C₁₃	—	2	4	no	—
264	C₂²×C₁₃	—	8	1	no	—
265	C₂²×C₁₃	—	8	1	no	—
266	C₂²×C₁₃	—	8	1	no	—
267	C₂²×C₁₃	—	8	2	no	—
268	C₂²×C₁₃	—	8	2	no	—
269	C₂²×C₁₃	#463	1	4	yes	—
270	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
271	C₂²×C₁₃	#546	1	2	yes	—
272	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
273	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
274	C₂²×C₁₃	#578	1	2	yes	—
275	C₄×C₁₃	—	2	2	no	—
276	C₄×C₁₃	—	4	4	no	—
277	C₄×C₁₃	—	4	2	no	—
278	C₄×C₁₃	—	4	2	no	—
279	C₄×C₁₃	—	4	2	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	8	1	no	—
282	C₄×C₁₃	—	8	2	no	—
283	C₄×C₁₃	#525	1	1	yes	characteristic
284	C₄×C₁₃	#535	1	1	yes	characteristic
285	C₄×C₁₃	#551	1	2	yes	—
286	C₂²×Q₈	—	2	1	no	—
287	C₂²×Q₈	—	2	4	no	—
288	C₂²×Q₈	—	2	2	no	—
289	C₂²×Q₈	—	2	2	no	—
290	C₂²×Q₈	—	4	2	no	—
291	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂³×C₄	—	2	1	no	—
295	C₂³×C₄	—	2	1	no	—
296	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	4	2	no	—
299	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
300	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
302	#124	—	2	4	no	—
303	#124	—	4	2	no	—
304	#121	—	2	2	no	—
305	#121	—	2	2	no	—
306	#117	—	4	4	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
323	#107	—	2	2	no	—
324	#107	—	2	2	no	—
325	C₄⋊C₈	—	4	2	no	—
326	#103	—	2	4	no	—
327	#103	—	2	4	no	—
328	#103	—	2	4	no	—
329	#103	—	4	2	no	—
330	#102	—	2	2	no	—
331	#102	—	2	2	no	—
332	#102	—	4	2	no	—
333	C₂²⋊C₈	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	1	no	—
336	#95	—	2	2	no	—
337	#95	—	2	2	no	—
338	#95	—	2	2	no	—
339	#95	D₄×C₁₃	1	2	yes	—
340	C₂×C₁₃	—	2	4	no	—
341	C₂×C₁₃	—	16	1	no	—
342	C₂×C₁₃	#2411	1	1	yes	characteristic
343	C₂×C₁₃	C₂×#463	1	1	yes	characteristic
344	C₂×C₁₃	#3044	1	1	yes	characteristic
345	C₂×C₁₃	#3300	1	2	yes	—
346	C₂×C₁₃	#3308	1	2	yes	—
347	C₂⁴	—	2	1	no	—
348	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	8	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	4	4	no	—
356	C₂×Q₈	—	4	8	no	—
357	C₂×Q₈	—	4	4	no	—
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	C₁₃×#41	1	4	yes	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	4	4	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
383	C₂²×C₄	C₁₃×#41	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	4	4	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	4	4	no	—
401	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
402	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	4	4	no	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	4	2	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	4	4	no	—
412	C₁₃	#24481	1	1	yes	characteristic, direct product factor, Sylow
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	2	no	—
420	C₂³	C₁₃×#121	1	2	yes	—
421	C₂³	C₁₃×#135	1	2	yes	—
422	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
423	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
424	Q₈	—	2	4	no	—
425	Q₈	—	2	4	no	—
426	Q₈	—	4	8	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	4	2	no	—
429	D₄	—	4	1	no	—
430	D₄	—	4	1	no	—
431	D₄	—	4	2	no	—
432	D₄	—	8	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	4	8	no	—
447	C₂×C₄	—	4	8	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	C₁₃×#121	1	2	yes	—
461	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
462	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
463	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
464	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
465	C₈	—	4	1	no	—
466	C₈	—	4	1	no	—
467	C₈	—	4	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	1	no	—
477	C₂²	C₁₃×#463	1	4	yes	—
478	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
479	C₂²	C₁₃×#546	1	2	yes	—
480	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
481	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
482	C₂²	C₁₃×#578	1	2	yes	—
483	C₄	—	2	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	4	no	—
489	C₄	—	8	1	no	—
490	C₄	—	8	2	no	—
491	C₄	C₁₃×#525	1	1	yes	characteristic
492	C₄	C₁₃×#535	1	1	yes	characteristic
493	C₄	C₁₃×#551	1	2	yes	—
494	C₂	—	2	4	no	—
495	C₂	—	16	1	no	—
496	C₂	C₁₃×#2411	1	1	yes	characteristic
497	C₂	C₂×C₁₃×#463	1	1	yes	characteristic
498	C₂	C₁₃×#3044	1	1	yes	characteristic
499	C₂	C₁₃×#3300	1	2	yes	—
500	C₂	C₁₃×#3308	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×#103	C₂	semidirect
4. C₁₃×#2344	C₂	semidirect
5. C₁₃×#2068	C₂	semidirect
6. C₁₃×#2042	C₂	semidirect
7. C₁₃×#1983	C₂	semidirect
8. C₁₃×#1928	C₂	semidirect
10. C₁₃×#1850	C₂	semidirect
11. C₁₃×#1787	C₂	semidirect
97. #24481	C₁₃	direct (N × H)
164. C₂²×#103	C₂×C₁₃	semidirect
166. #2344	C₂×C₁₃	semidirect
167. #2068	C₂×C₁₃	semidirect
168. #2042	C₂×C₁₃	semidirect
169. #1983	C₂×C₁₃	semidirect
170. #1928	C₂×C₁₃	semidirect
172. #1850	C₂×C₁₃	semidirect
173. #1787	C₂×C₁₃	semidirect
412. C₁₃	#24481	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#480	2
C₂²×C₁₃×#103	2
C₁₃×#2436	2
C₁₃×#2344	2
C₁₃×#2068	2
C₁₃×#2042	2
C₁₃×#1983	2
C₁₃×#1928	2
C₁₃×#1893	2
C₁₃×#1850	2
C₁₃×#1787	2
#24481	13

Subgroups — C13×#24481 #15710820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24481 #15710820