Subgroups — C₁₃×#24752 #15711091

Order 3328.

992 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#467	C₂	1	2	yes	maximal
2	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic
5	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2068	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2056	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1892	C₂	1	2	yes	maximal
11	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
13	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#467	—	2	8	no	—
20	C₁₃×#462	—	2	4	no	—
21	C₂×C₁₃×#107	C₂²	1	2	yes	—
22	C₂×C₁₃×C₄⋊C₈	—	2	4	no	—
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#103	C₂²	1	2	yes	—
28	C₂×C₁₃×#103	C₂²	1	2	yes	—
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₁₃×#391	C₂²	1	1	yes	characteristic
31	C₁₃×#391	C₂²	1	2	yes	—
32	C₁₃×#389	—	2	1	no	—
33	C₁₃×#389	—	2	1	no	—
34	C₁₃×#389	C₂²	1	1	yes	characteristic
35	C₁₃×#387	—	2	1	no	—
36	C₁₃×#385	—	2	1	no	—
37	C₁₃×#384	C₂²	1	1	yes	characteristic
38	C₁₃×#380	—	2	1	no	—
39	C₁₃×#380	—	2	1	no	—
40	C₁₃×#380	C₂²	1	1	yes	characteristic
41	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
42	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₁₃×#340	C₂²	1	2	yes	—
46	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₁₃×Q₁₆	—	2	4	no	—
52	C₂×C₁₃×Q₁₆	—	2	4	no	—
53	C₂×C₁₃×Q₁₆	—	4	2	no	—
54	C₂²×C₈×C₁₃	—	2	4	no	—
55	C₂²×C₈×C₁₃	—	2	4	no	—
56	C₂²×C₈×C₁₃	—	4	2	no	—
57	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
59	C₁₃×C₄⋊Q₈	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	—	2	2	no	—
61	C₁₃×C₂²⋊Q₈	—	2	2	no	—
62	C₁₃×C₂²⋊Q₈	—	2	4	no	—
63	C₁₃×C₂²⋊Q₈	—	2	4	no	—
64	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
65	C₄×Q₈×C₁₃	—	2	2	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	—	2	2	no	—
84	C₂×C₄²×C₁₃	—	2	1	no	—
85	C₂×C₄²×C₁₃	—	2	1	no	—
86	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	C₁₃×#107	—	2	4	no	—
91	C₁₃×C₄⋊C₈	—	2	4	no	—
92	C₁₃×C₄⋊C₈	—	2	2	no	—
93	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
94	C₁₃×#103	—	2	4	no	—
95	C₁₃×#103	—	2	4	no	—
96	C₁₃×#103	—	2	4	no	—
97	C₁₃×#103	—	4	2	no	—
98	C₁₃×#95	—	2	1	no	—
99	C₁₃×#95	—	2	1	no	—
100	C₁₃×#95	—	2	1	no	—
101	C₁₃×#95	—	2	1	no	—
102	C₁₃×#95	—	2	1	no	—
103	C₁₃×#95	—	2	2	no	—
104	C₁₃×#95	—	2	2	no	—
105	#24752	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂×Q₈×C₁₃	—	2	1	no	—
108	C₂×Q₈×C₁₃	—	2	1	no	—
109	C₂×Q₈×C₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₃	—	2	2	no	—
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	2	no	—
118	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
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	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	4	1	no	—
134	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	complemented
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	#41	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₁₃×Q₁₆	—	4	8	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	—	4	8	no	—
150	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
151	C₁₃×C₄⋊C₄	—	2	4	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	4	2	no	—
160	C₁₃×C₄⋊C₄	—	4	2	no	—
161	C₁₃×C₄⋊C₄	—	4	2	no	—
162	C₁₃×C₄⋊C₄	—	4	4	no	—
163	C₁₃×C₄⋊C₄	—	4	2	no	—
164	C₁₃×C₄⋊C₄	—	4	2	no	—
165	C₁₃×C₄⋊C₄	—	4	2	no	—
166	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
167	C₁₃×C₂²⋊C₄	—	2	4	no	—
168	C₁₃×C₂²⋊C₄	—	4	4	no	—
169	C₁₃×C₂²⋊C₄	—	4	2	no	—
170	C₄²×C₁₃	—	2	2	no	—
171	C₄²×C₁₃	—	2	2	no	—
172	C₄²×C₁₃	—	2	1	no	—
173	C₄²×C₁₃	—	2	1	no	—
174	C₄²×C₁₃	—	4	2	no	—
175	C₄²×C₁₃	—	4	2	no	—
176	C₄²×C₁₃	C₂×D₄	1	2	yes	—
177	C₄²×C₁₃	#41	1	2	yes	—
178	C₂×#467	C₂×C₁₃	1	2	yes	—
179	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
180	C₂²×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
181	#2857	C₂×C₁₃	1	1	yes	characteristic
182	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
183	#2068	C₂×C₁₃	1	2	yes	complemented
184	#2056	C₂×C₁₃	1	2	yes	complemented
185	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#1892	C₂×C₁₃	1	2	yes	—
188	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂³×C₁₃	—	2	1	no	—
190	C₂³×C₁₃	—	2	1	no	—
191	C₂³×C₁₃	—	2	1	no	—
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	#121	1	2	yes	—
194	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
195	C₂³×C₁₃	#137	1	2	yes	—
196	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	2	no	—
198	Q₈×C₁₃	—	2	2	no	—
199	Q₈×C₁₃	—	4	1	no	—
200	Q₈×C₁₃	—	4	1	no	—
201	Q₈×C₁₃	—	4	2	no	—
202	Q₈×C₁₃	—	4	2	no	—
203	Q₈×C₁₃	—	4	2	no	—
204	Q₈×C₁₃	—	4	2	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	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	8	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	4	4	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	1	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	#121	1	2	yes	—
239	C₂×C₄×C₁₃	#121	1	2	yes	—
240	C₂×C₄×C₁₃	#121	1	2	yes	—
241	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
242	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
243	C₂×C₄×C₁₃	#135	1	2	yes	—
244	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
249	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
250	C₈×C₁₃	—	2	4	no	—
251	C₈×C₁₃	—	4	2	no	—
252	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
253	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
254	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
256	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
258	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
259	#467	—	2	8	no	—
260	#462	—	2	4	no	—
261	C₂×#107	C₂²×C₁₃	1	2	yes	—
262	C₂×C₄⋊C₈	—	2	4	no	—
263	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
264	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#103	C₂²×C₁₃	1	2	yes	—
267	C₂×#103	C₂²×C₁₃	1	2	yes	—
268	C₂×#103	C₂²×C₁₃	1	2	yes	—
269	C₂×#103	C₂²×C₁₃	1	2	yes	—
270	#391	C₂²×C₁₃	1	1	yes	characteristic
271	#391	C₂²×C₁₃	1	2	yes	—
272	#389	—	2	1	no	—
273	#389	—	2	1	no	—
274	#389	C₂²×C₁₃	1	1	yes	characteristic
275	#387	—	2	1	no	—
276	#385	—	2	1	no	—
277	#384	C₂²×C₁₃	1	1	yes	characteristic
278	#380	—	2	1	no	—
279	#380	—	2	1	no	—
280	#380	C₂²×C₁₃	1	1	yes	characteristic
281	C₄×C₄⋊C₄	—	2	1	no	—
282	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
283	C₄×C₂²⋊C₄	—	2	1	no	—
284	#340	C₂²×C₁₃	1	2	yes	—
285	#340	C₂²×C₁₃	1	2	yes	—
286	C₂²×C₁₃	—	2	2	no	—
287	C₂²×C₁₃	—	2	2	no	—
288	C₂²×C₁₃	—	2	2	no	—
289	C₂²×C₁₃	—	2	2	no	—
290	C₂²×C₁₃	—	2	2	no	—
291	C₂²×C₁₃	—	2	2	no	—
292	C₂²×C₁₃	#462	1	4	yes	complemented
293	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
294	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
295	C₂²×C₁₃	#537	1	1	yes	characteristic
296	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
297	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
298	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
299	C₂²×C₁₃	#575	1	1	yes	characteristic
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	2	2	no	—
302	C₄×C₁₃	—	2	2	no	—
303	C₄×C₁₃	—	4	2	no	—
304	C₄×C₁₃	—	4	2	no	—
305	C₄×C₁₃	—	4	1	no	—
306	C₄×C₁₃	—	8	2	no	—
307	C₄×C₁₃	—	8	1	no	—
308	C₄×C₁₃	—	8	2	no	—
309	C₄×C₁₃	—	8	1	no	—
310	C₄×C₁₃	#467	1	4	yes	complemented
311	C₄×C₁₃	D₄²	1	1	yes	characteristic
312	C₄×C₁₃	#547	1	1	yes	characteristic
313	C₄×C₁₃	#548	1	1	yes	characteristic
314	C₄×C₁₃	#553	1	1	yes	characteristic
315	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
316	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
317	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
318	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
320	C₂×Q₁₆	—	2	4	no	—
321	C₂×Q₁₆	—	2	4	no	—
322	C₂×Q₁₆	—	4	2	no	—
323	C₂²×C₈	—	2	4	no	—
324	C₂²×C₈	—	2	4	no	—
325	C₂²×C₈	—	4	2	no	—
326	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
327	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
328	C₄⋊Q₈	—	2	2	no	—
329	C₄⋊Q₈	—	2	2	no	—
330	C₂²⋊Q₈	—	2	2	no	—
331	C₂²⋊Q₈	—	2	4	no	—
332	C₂²⋊Q₈	—	2	4	no	—
333	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₄²	—	2	2	no	—
352	C₂×C₄²	—	2	2	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	—	2	1	no	—
355	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
356	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
359	#107	—	2	4	no	—
360	C₄⋊C₈	—	2	4	no	—
361	C₄⋊C₈	—	2	2	no	—
362	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
363	#103	—	2	4	no	—
364	#103	—	2	4	no	—
365	#103	—	2	4	no	—
366	#103	—	4	2	no	—
367	#95	—	2	1	no	—
368	#95	—	2	1	no	—
369	#95	—	2	1	no	—
370	#95	—	2	1	no	—
371	#95	—	2	1	no	—
372	#95	—	2	2	no	—
373	#95	—	2	2	no	—
374	C₂×C₁₃	—	2	4	no	—
375	C₂×C₁₃	#2416	1	1	yes	characteristic
376	C₂×C₁₃	C₂×#462	1	1	yes	characteristic
377	C₂×C₁₃	#3035	1	1	yes	characteristic
378	C₂×C₁₃	C₂×#467	1	1	yes	characteristic
379	C₂×C₁₃	#3056	1	1	yes	characteristic
380	C₂×C₁₃	#3248	1	1	yes	characteristic
381	C₂×C₁₃	#3249	1	1	yes	characteristic
382	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	4	1	no	—
410	C₂²×C₄	C₁₃×Q₁₆	1	4	yes	complemented
411	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
417	C₂²×C₄	C₁₃×#41	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
419	Q₁₆	—	4	8	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	4	8	no	—
426	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	4	2	no	—
436	C₄⋊C₄	—	4	2	no	—
437	C₄⋊C₄	—	4	2	no	—
438	C₄⋊C₄	—	4	4	no	—
439	C₄⋊C₄	—	4	2	no	—
440	C₄⋊C₄	—	4	2	no	—
441	C₄⋊C₄	—	4	2	no	—
442	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	4	4	no	—
445	C₂²⋊C₄	—	4	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	4	2	no	—
451	C₄²	—	4	2	no	—
452	C₄²	C₂×D₄×C₁₃	1	2	yes	—
453	C₄²	C₁₃×#41	1	2	yes	—
454	C₁₃	#24752	1	1	yes	characteristic, direct product factor, Sylow
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	C₁₃×#121	1	2	yes	—
460	C₂³	C₂×C₁₃×Q₁₆	1	2	yes	—
461	C₂³	C₁₃×#137	1	2	yes	—
462	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	2	2	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	C₁₃×#121	1	2	yes	—
505	C₂×C₄	C₁₃×#121	1	2	yes	—
506	C₂×C₄	C₁₃×#121	1	2	yes	—
507	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
508	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
509	C₂×C₄	C₁₃×#135	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
512	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
513	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
514	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
516	C₈	—	2	4	no	—
517	C₈	—	4	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	C₁₃×#462	1	4	yes	complemented
525	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
526	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
527	C₂²	C₁₃×#537	1	1	yes	characteristic
528	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
529	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
530	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
531	C₂²	C₁₃×#575	1	1	yes	characteristic
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	2	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	2	no	—
538	C₄	—	8	2	no	—
539	C₄	—	8	1	no	—
540	C₄	—	8	2	no	—
541	C₄	—	8	1	no	—
542	C₄	C₁₃×#467	1	4	yes	complemented
543	C₄	D₄²×C₁₃	1	1	yes	characteristic
544	C₄	C₁₃×#547	1	1	yes	characteristic
545	C₄	C₁₃×#548	1	1	yes	characteristic
546	C₄	C₁₃×#553	1	1	yes	characteristic
547	C₂	—	2	4	no	—
548	C₂	C₁₃×#2416	1	1	yes	characteristic
549	C₂	C₂×C₁₃×#462	1	1	yes	characteristic
550	C₂	C₁₃×#3035	1	1	yes	characteristic
551	C₂	C₂×C₁₃×#467	1	1	yes	characteristic
552	C₂	C₁₃×#3056	1	1	yes	characteristic
553	C₂	C₁₃×#3248	1	1	yes	characteristic
554	C₂	C₁₃×#3249	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
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
2. C₂×C₁₃×#462	C₂	semidirect
6. C₁₃×#2068	C₂	semidirect
7. C₁₃×#2056	C₂	semidirect
8. C₁₃×#1981	C₂	semidirect
9. C₁₃×#1947	C₂	semidirect
11. C₁₃×#1803	C₂	semidirect
105. #24752	C₁₃	direct (N × H)
134. C₂²×C₄×C₁₃	Q₁₆	semidirect
179. C₂×#462	C₂×C₁₃	semidirect
183. #2068	C₂×C₁₃	semidirect
184. #2056	C₂×C₁₃	semidirect
185. #1981	C₂×C₁₃	semidirect
186. #1947	C₂×C₁₃	semidirect
188. #1803	C₂×C₁₃	semidirect
292. C₂²×C₁₃	#462	semidirect
310. C₄×C₁₃	#467	semidirect
410. C₂²×C₄	C₁₃×Q₁₆	semidirect
454. C₁₃	#24752	direct (N × H)
524. C₂²	C₁₃×#462	semidirect
542. C₄	C₁₃×#467	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#467	2
C₂×C₁₃×#462	2
C₂²×C₁₃×C₄⋊C₈	2
C₁₃×#2857	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2068	2
C₁₃×#2056	2
C₁₃×#1981	2
C₁₃×#1947	2
C₁₃×#1892	2
C₁₃×#1803	2
#24752	13

Subgroups — C13×#24752 #15711091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24752 #15711091