Subgroups — C₁₃×#24548 #15710887

Order 3328.

1024 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×#452	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2502	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2339	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2072	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2056	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1877	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1823	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1802	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₁₃×#452	—	2	4	no	—
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₁₃×#417	—	2	4	no	—
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₃×#398	—	2	1	no	—
29	C₁₃×#398	—	2	1	no	—
30	C₁₃×#391	C₂²	1	2	yes	—
31	C₁₃×#391	C₂²	1	2	yes	—
32	C₁₃×#386	—	2	2	no	—
33	C₁₃×#385	—	2	2	no	—
34	C₁₃×#384	C₂²	1	2	yes	—
35	C₁₃×#381	—	2	1	no	—
36	C₁₃×#380	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#95	—	2	1	no	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂×C₁₃×#41	—	2	2	no	—
44	C₂×C₁₃×#41	—	2	4	no	—
45	C₂×C₁₃×#41	—	4	2	no	—
46	C₂×C₁₃×#41	D₄	1	4	yes	—
47	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
53	C₂³×C₄×C₁₃	—	2	2	no	—
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×Q₁₆	—	2	2	no	—
56	C₂×C₁₃×Q₁₆	—	4	2	no	—
57	C₂×C₁₃×SD₁₆	—	2	2	no	—
58	C₂×C₁₃×SD₁₆	—	2	4	no	—
59	C₂×C₁₃×M₁₆	—	2	2	no	—
60	C₂×C₁₃×M₁₆	—	4	2	no	—
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
64	C₁₃×C₂²⋊Q₈	—	2	2	no	—
65	C₁₃×C₂²⋊Q₈	—	2	2	no	—
66	C₄×D₄×C₁₃	—	2	4	no	—
67	C₄×D₄×C₁₃	—	4	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
81	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
82	C₁₃×C₄⋊C₈	—	4	2	no	—
83	C₁₃×#103	—	2	4	no	—
84	C₁₃×#103	—	2	2	no	—
85	C₁₃×#103	—	4	2	no	—
86	C₁₃×#102	—	2	4	no	—
87	C₁₃×#102	—	2	2	no	—
88	C₁₃×C₂²⋊C₈	—	2	2	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	C₁₃×#95	—	2	2	no	—
93	C₁₃×#95	—	2	2	no	—
94	C₁₃×#95	D₄	1	1	yes	characteristic
95	C₁₃×#95	D₄	1	1	yes	characteristic
96	#24548	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₃	—	2	1	no	—
98	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₁₃×#41	—	2	8	no	—
100	C₁₃×#41	—	4	4	no	—
101	C₁₃×#41	—	4	8	no	—
102	C₂×Q₈×C₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₁₃	—	2	4	no	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	4	4	no	—
114	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂×D₄×C₁₃	#41	1	4	yes	—
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	4	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	4	4	no	—
125	C₂²×C₄×C₁₃	—	4	4	no	—
126	C₂²×C₄×C₁₃	—	4	2	no	—
127	C₂²×C₄×C₁₃	—	4	4	no	—
128	C₂²×C₄×C₁₃	—	8	2	no	—
129	C₂²×C₄×C₁₃	—	8	1	no	—
130	C₂²×C₄×C₁₃	—	8	1	no	—
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	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₃	#41	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₁₃×Q₁₆	—	4	4	no	—
138	C₁₃×SD₁₆	—	4	4	no	—
139	C₁₃×M₁₆	—	4	4	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	4	2	no	—
154	C₁₃×C₄⋊C₄	—	4	2	no	—
155	C₁₃×C₄⋊C₄	—	8	2	no	—
156	C₁₃×C₄⋊C₄	—	8	2	no	—
157	C₁₃×C₂²⋊C₄	—	2	4	no	—
158	C₁₃×C₂²⋊C₄	—	4	4	no	—
159	C₁₃×C₂²⋊C₄	—	4	2	no	—
160	C₁₃×C₂²⋊C₄	—	8	1	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	—	2	2	no	—
163	C₂×#452	C₂×C₁₃	1	1	yes	characteristic
164	C₂×#417	C₂×C₁₃	1	1	yes	characteristic
165	#2502	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#2339	C₂×C₁₃	1	1	yes	characteristic
167	#2072	C₂×C₁₃	1	2	yes	complemented
168	#2056	C₂×C₁₃	1	2	yes	complemented
169	#1894	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1877	C₂×C₁₃	1	2	yes	complemented
171	#1851	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1823	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#1802	C₂×C₁₃	1	2	yes	complemented
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	4	no	—
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	—	2	2	no	—
178	C₂³×C₁₃	—	2	1	no	—
179	C₂³×C₁₃	—	2	1	no	—
180	C₂³×C₁₃	—	4	2	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	—	4	1	no	—
183	C₂³×C₁₃	#121	1	2	yes	—
184	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	Q₈×C₁₃	—	2	2	no	—
186	Q₈×C₁₃	—	2	2	no	—
187	Q₈×C₁₃	—	4	2	no	—
188	Q₈×C₁₃	—	4	1	no	—
189	Q₈×C₁₃	—	4	1	no	—
190	Q₈×C₁₃	—	4	2	no	—
191	D₄×C₁₃	—	2	2	no	—
192	D₄×C₁₃	—	2	4	no	—
193	D₄×C₁₃	—	4	8	no	—
194	D₄×C₁₃	#123	1	4	yes	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	4	8	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	8	8	no	—
219	C₂×C₄×C₁₃	—	8	4	no	—
220	C₂×C₄×C₁₃	#121	1	2	yes	—
221	C₂×C₄×C₁₃	#137	1	4	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	2	no	—
228	C₈×C₁₃	—	4	1	no	—
229	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
230	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
231	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
232	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
235	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
236	#452	—	2	4	no	—
237	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
238	#417	—	2	4	no	—
239	C₂×#103	C₂²×C₁₃	1	2	yes	—
240	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×#103	C₂²×C₁₃	1	2	yes	—
242	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#102	C₂²×C₁₃	1	2	yes	—
244	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
245	#398	—	2	1	no	—
246	#398	—	2	1	no	—
247	#391	C₂²×C₁₃	1	2	yes	—
248	#391	C₂²×C₁₃	1	2	yes	—
249	#386	—	2	2	no	—
250	#385	—	2	2	no	—
251	#384	C₂²×C₁₃	1	2	yes	—
252	#381	—	2	1	no	—
253	#380	C₂²×C₁₃	1	1	yes	characteristic
254	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×#95	—	2	1	no	—
256	#340	C₂²×C₁₃	1	2	yes	—
257	#340	C₂²×C₁₃	1	2	yes	—
258	#340	C₂²×C₁₃	1	2	yes	—
259	#336	C₂²×C₁₃	1	2	yes	—
260	C₂²×C₁₃	—	2	2	no	—
261	C₂²×C₁₃	—	2	4	no	—
262	C₂²×C₁₃	—	2	2	no	—
263	C₂²×C₁₃	—	2	2	no	—
264	C₂²×C₁₃	—	4	2	no	—
265	C₂²×C₁₃	—	4	4	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	4	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
271	C₂²×C₁₃	#546	1	2	yes	—
272	C₂²×C₁₃	C₂×#137	1	2	yes	—
273	C₂²×C₁₃	#576	1	1	yes	characteristic
274	C₂²×C₁₃	#577	1	1	yes	characteristic
275	C₄×C₁₃	—	2	2	no	—
276	C₄×C₁₃	—	2	4	no	—
277	C₄×C₁₃	—	4	2	no	—
278	C₄×C₁₃	—	4	2	no	—
279	C₄×C₁₃	—	8	1	no	—
280	C₄×C₁₃	—	8	1	no	—
281	C₄×C₁₃	—	8	2	no	—
282	C₄×C₁₃	—	8	2	no	—
283	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
284	C₄×C₁₃	#534	1	1	yes	characteristic
285	C₄×C₁₃	#551	1	2	yes	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	4	no	—
288	C₂×#41	—	4	2	no	—
289	C₂×#41	D₄×C₁₃	1	4	yes	—
290	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
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	—	2	2	no	—
297	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂×Q₁₆	—	2	2	no	—
299	C₂×Q₁₆	—	4	2	no	—
300	C₂×SD₁₆	—	2	2	no	—
301	C₂×SD₁₆	—	2	4	no	—
302	C₂×M₁₆	—	2	2	no	—
303	C₂×M₁₆	—	4	2	no	—
304	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
305	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
307	C₂²⋊Q₈	—	2	2	no	—
308	C₂²⋊Q₈	—	2	2	no	—
309	C₄×D₄	—	2	4	no	—
310	C₄×D₄	—	4	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
324	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
325	C₄⋊C₈	—	4	2	no	—
326	#103	—	2	4	no	—
327	#103	—	2	2	no	—
328	#103	—	4	2	no	—
329	#102	—	2	4	no	—
330	#102	—	2	2	no	—
331	C₂²⋊C₈	—	2	2	no	—
332	#95	—	2	1	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	#95	—	2	2	no	—
337	#95	D₄×C₁₃	1	1	yes	characteristic
338	#95	D₄×C₁₃	1	1	yes	characteristic
339	C₂×C₁₃	—	4	2	no	—
340	C₂×C₁₃	—	4	4	no	—
341	C₂×C₁₃	#2412	1	1	yes	characteristic
342	C₂×C₁₃	#3039	1	1	yes	characteristic
343	C₂×C₁₃	#3045	1	1	yes	characteristic
344	C₂×C₁₃	#3314	1	2	yes	—
345	C₂×C₁₃	#3331	1	2	yes	—
346	C₂⁴	—	2	1	no	—
347	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
348	#41	—	2	8	no	—
349	#41	—	4	4	no	—
350	#41	—	4	8	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	4	4	no	—
363	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
364	C₂×D₄	C₁₃×#41	1	4	yes	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	—	4	4	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	8	2	no	—
378	C₂²×C₄	—	8	1	no	—
379	C₂²×C₄	—	8	1	no	—
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	C₂×D₄×C₁₃	1	2	yes	—
384	C₂²×C₄	C₁₃×#41	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
386	Q₁₆	—	4	4	no	—
387	SD₁₆	—	4	4	no	—
388	M₁₆	—	4	4	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	4	2	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	8	2	no	—
405	C₄⋊C₄	—	8	2	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₂²⋊C₄	—	8	1	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₁₃	#24548	1	1	yes	characteristic, direct product factor, Sylow
413	C₂³	—	2	2	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	C₁₃×#121	1	2	yes	—
423	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
424	Q₈	—	2	2	no	—
425	Q₈	—	2	2	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	1	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	4	2	no	—
430	D₄	—	2	2	no	—
431	D₄	—	2	4	no	—
432	D₄	—	4	8	no	—
433	D₄	C₁₃×#123	1	4	yes	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	8	8	no	—
458	C₂×C₄	—	8	4	no	—
459	C₂×C₄	C₁₃×#121	1	2	yes	—
460	C₂×C₄	C₁₃×#137	1	4	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	2	no	—
467	C₈	—	4	1	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	4	no	—
478	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
479	C₂²	C₁₃×#546	1	2	yes	—
480	C₂²	C₂×C₁₃×#137	1	2	yes	—
481	C₂²	C₁₃×#576	1	1	yes	characteristic
482	C₂²	C₁₃×#577	1	1	yes	characteristic
483	C₄	—	2	4	no	—
484	C₄	—	2	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	8	1	no	—
488	C₄	—	8	2	no	—
489	C₄	—	8	2	no	—
490	C₄	—	8	1	no	—
491	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
492	C₄	C₁₃×#534	1	1	yes	characteristic
493	C₄	C₁₃×#551	1	2	yes	—
494	C₂	—	4	2	no	—
495	C₂	—	4	4	no	—
496	C₂	C₁₃×#2412	1	1	yes	characteristic
497	C₂	C₁₃×#3039	1	1	yes	characteristic
498	C₂	C₁₃×#3045	1	1	yes	characteristic
499	C₂	C₁₃×#3314	1	2	yes	—
500	C₂	C₁₃×#3331	1	2	yes	—

	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 ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2502	C₂	semidirect
5. C₁₃×#2072	C₂	semidirect
6. C₁₃×#2056	C₂	semidirect
7. C₁₃×#1894	C₂	semidirect
8. C₁₃×#1877	C₂	semidirect
9. C₁₃×#1851	C₂	semidirect
10. C₁₃×#1823	C₂	semidirect
11. C₁₃×#1802	C₂	semidirect
96. #24548	C₁₃	direct (N × H)
165. #2502	C₂×C₁₃	semidirect
167. #2072	C₂×C₁₃	semidirect
168. #2056	C₂×C₁₃	semidirect
169. #1894	C₂×C₁₃	semidirect
170. #1877	C₂×C₁₃	semidirect
171. #1851	C₂×C₁₃	semidirect
172. #1823	C₂×C₁₃	semidirect
173. #1802	C₂×C₁₃	semidirect
412. C₁₃	#24548	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×#452	2
C₂×C₁₃×#417	2
C₁₃×#2502	2
C₁₃×#2339	2
C₁₃×#2072	2
C₁₃×#2056	2
C₁₃×#1894	2
C₁₃×#1877	2
C₁₃×#1851	2
C₁₃×#1823	2
C₁₃×#1802	2
#24548	13

Subgroups — C13×#24548 #15710887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24548 #15710887