Subgroups — C₁₃×#24209 #15710548

Order 3328.

1514 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#461	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#448	C₂	1	2	yes	maximal
4	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2043	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2013	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1981	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1787	C₂	1	2	yes	maximal, complemented
10	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
11	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	—
12	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
13	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃	—	2	1	no	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
21	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#461	—	2	8	no	—
24	C₁₃×#448	—	2	8	no	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×#103	C₂²	1	4	yes	—
27	C₂×C₁₃×#103	C₂²	1	4	yes	—
28	C₂×C₁₃×#103	C₂²	1	4	yes	—
29	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₁₃×#390	C₂²	1	1	yes	characteristic
31	C₁₃×#389	C₂²	1	1	yes	characteristic
32	C₁₃×#388	—	2	1	no	—
33	C₁₃×#386	—	2	1	no	—
34	C₁₃×#380	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
37	C₁₃×#336	C₂²	1	2	yes	—
38	C₂²×Q₈×C₁₃	—	2	8	no	—
39	C₂²×Q₈×C₁₃	—	2	2	no	—
40	C₂²×Q₈×C₁₃	—	2	4	no	—
41	C₂²×Q₈×C₁₃	—	2	4	no	—
42	C₂²×Q₈×C₁₃	—	4	4	no	—
43	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	2	no	—
47	C₂³×C₄×C₁₃	—	2	1	no	—
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×SD₁₆	—	2	8	no	—
52	C₂×C₁₃×SD₁₆	—	2	8	no	—
53	C₂×C₁₃×SD₁₆	—	4	4	no	—
54	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
55	C₁₃×C₄⋊Q₈	—	2	8	no	—
56	C₁₃×C₄⋊Q₈	—	2	8	no	—
57	C₁₃×C₄⋊Q₈	—	2	8	no	—
58	C₁₃×C₄⋊Q₈	—	2	4	no	—
59	C₁₃×C₄⋊Q₈	D₄	1	8	yes	complemented
60	C₁₃×#121	—	2	2	no	—
61	C₁₃×#121	D₄	1	4	yes	—
62	C₄×D₄×C₁₃	—	2	4	no	—
63	C₄×D₄×C₁₃	—	4	4	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	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	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₄²×C₁₃	—	2	4	no	—
80	C₂×C₄²×C₁₃	—	2	1	no	—
81	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊C₈	—	2	4	no	—
86	C₁₃×#103	—	2	8	no	—
87	C₁₃×#103	—	2	8	no	—
88	C₁₃×#103	—	4	4	no	—
89	C₁₃×C₂²⋊C₈	—	2	4	no	—
90	C₁₃×#95	—	2	1	no	—
91	C₁₃×#95	—	2	1	no	—
92	C₁₃×#95	—	2	1	no	—
93	#24209	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₃	—	2	1	no	—
95	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₁₃	—	2	8	no	—
97	C₂×Q₈×C₁₃	—	2	4	no	—
98	C₂×Q₈×C₁₃	—	2	4	no	—
99	C₂×Q₈×C₁₃	—	2	4	no	—
100	C₂×Q₈×C₁₃	—	2	4	no	—
101	C₂×Q₈×C₁₃	—	2	4	no	—
102	C₂×Q₈×C₁₃	—	4	16	no	—
103	C₂×Q₈×C₁₃	—	4	16	no	—
104	C₂×Q₈×C₁₃	—	4	4	no	—
105	C₂×Q₈×C₁₃	—	4	4	no	—
106	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
107	C₂×D₄×C₁₃	—	2	4	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	4	2	no	—
112	C₂×D₄×C₁₃	—	4	2	no	—
113	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	8	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	4	4	no	—
127	C₂²×C₄×C₁₃	—	4	4	no	—
128	C₂²×C₄×C₁₃	—	4	2	no	—
129	C₂²×C₄×C₁₃	—	4	2	no	—
130	C₂²×C₄×C₁₃	—	4	2	no	—
131	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	complemented
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
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	#41	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₁₃×SD₁₆	—	4	16	no	—
141	C₂×C₈×C₁₃	—	2	4	no	—
142	C₂×C₈×C₁₃	—	2	4	no	—
143	C₂×C₈×C₁₃	—	2	4	no	—
144	C₁₃×C₄⋊C₄	—	2	8	no	—
145	C₁₃×C₄⋊C₄	—	2	8	no	—
146	C₁₃×C₄⋊C₄	—	2	8	no	—
147	C₁₃×C₄⋊C₄	—	2	8	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	—	4	2	no	—
152	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₁₃×C₂²⋊C₄	—	2	4	no	—
154	C₁₃×C₂²⋊C₄	—	4	2	no	—
155	C₁₃×C₂²⋊C₄	—	4	2	no	—
156	C₁₃×C₂²⋊C₄	—	4	2	no	—
157	C₁₃×C₂²⋊C₄	—	4	2	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₄²×C₁₃	—	2	2	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	4	2	no	—
162	C₄²×C₁₃	C₂×D₄	1	4	yes	—
163	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂×#461	C₂×C₁₃	1	2	yes	complemented
165	C₂×#448	C₂×C₁₃	1	2	yes	—
166	C₄×#121	C₂×C₁₃	1	1	yes	characteristic
167	#2043	C₂×C₁₃	1	2	yes	complemented
168	#2013	C₂×C₁₃	1	2	yes	complemented
169	#1981	C₂×C₁₃	1	2	yes	complemented
170	#1797	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#1787	C₂×C₁₃	1	2	yes	complemented
172	C₂³×C₁₃	—	2	1	no	—
173	C₂³×C₁₃	—	2	1	no	—
174	C₂³×C₁₃	—	2	1	no	—
175	C₂³×C₁₃	—	2	1	no	—
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	—	4	1	no	—
178	C₂³×C₁₃	—	4	1	no	—
179	C₂³×C₁₃	—	4	1	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	—	4	1	no	—
183	C₂³×C₁₃	#121	1	2	yes	—
184	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
185	C₂³×C₁₃	#137	1	2	yes	—
186	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₁₃	—	2	8	no	—
188	Q₈×C₁₃	—	2	8	no	—
189	Q₈×C₁₃	—	4	16	no	—
190	Q₈×C₁₃	—	4	4	no	—
191	Q₈×C₁₃	—	4	4	no	—
192	D₄×C₁₃	—	2	4	no	—
193	D₄×C₁₃	—	4	8	no	—
194	D₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	2	8	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	1	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	8	no	—
207	C₂×C₄×C₁₃	—	2	8	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	4	16	no	—
210	C₂×C₄×C₁₃	—	4	4	no	—
211	C₂×C₄×C₁₃	—	4	4	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	8	4	no	—
221	C₂×C₄×C₁₃	#120	1	2	yes	—
222	C₂×C₄×C₁₃	#120	1	2	yes	—
223	C₂×C₄×C₁₃	#121	1	2	yes	—
224	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
225	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
226	C₂×C₄×C₁₃	#137	1	2	yes	—
227	C₂×C₄×C₁₃	#137	1	2	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
232	C₈×C₁₃	—	4	4	no	—
233	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
234	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	—
235	C₂×C₄⋊Q₈	—	2	8	no	—
236	C₂×C₄⋊Q₈	—	2	1	no	—
237	C₂×C₄⋊Q₈	—	2	1	no	—
238	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
239	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
240	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×C₄×D₄	—	2	1	no	—
242	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
243	C₂²×C₄⋊C₄	—	2	1	no	—
244	C₂²×C₄⋊C₄	—	2	1	no	—
245	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
246	#461	—	2	8	no	—
247	#448	—	2	8	no	—
248	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
249	C₂×#103	C₂²×C₁₃	1	4	yes	—
250	C₂×#103	C₂²×C₁₃	1	4	yes	—
251	C₂×#103	C₂²×C₁₃	1	4	yes	—
252	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
253	#390	C₂²×C₁₃	1	1	yes	characteristic
254	#389	C₂²×C₁₃	1	1	yes	characteristic
255	#388	—	2	1	no	—
256	#386	—	2	1	no	—
257	#380	C₂²×C₁₃	1	1	yes	characteristic
258	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
259	C₄×C₂²⋊C₄	—	2	1	no	—
260	#336	C₂²×C₁₃	1	2	yes	—
261	C₂²×C₁₃	—	2	2	no	—
262	C₂²×C₁₃	—	2	2	no	—
263	C₂²×C₁₃	—	2	2	no	—
264	C₂²×C₁₃	—	2	2	no	—
265	C₂²×C₁₃	—	2	2	no	—
266	C₂²×C₁₃	—	2	2	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	8	1	no	—
271	C₂²×C₁₃	—	8	1	no	—
272	C₂²×C₁₃	—	8	1	no	—
273	C₂²×C₁₃	—	8	1	no	—
274	C₂²×C₁₃	#461	1	4	yes	complemented
275	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
276	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
277	C₂²×C₁₃	#535	1	1	yes	characteristic
278	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
279	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
280	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
281	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
282	C₄×C₁₃	—	2	2	no	—
283	C₄×C₁₃	—	2	2	no	—
284	C₄×C₁₃	—	2	2	no	—
285	C₄×C₁₃	—	2	2	no	—
286	C₄×C₁₃	—	4	8	no	—
287	C₄×C₁₃	—	4	2	no	—
288	C₄×C₁₃	—	8	1	no	—
289	C₄×C₁₃	—	8	1	no	—
290	C₄×C₁₃	#448	1	4	yes	complemented
291	C₄×C₁₃	D₄²	1	2	yes	—
292	C₄×C₁₃	#546	1	2	yes	—
293	C₂²×Q₈	—	2	8	no	—
294	C₂²×Q₈	—	2	2	no	—
295	C₂²×Q₈	—	2	4	no	—
296	C₂²×Q₈	—	2	4	no	—
297	C₂²×Q₈	—	4	4	no	—
298	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
299	C₂²×D₄	—	2	1	no	—
300	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
301	C₂³×C₄	—	2	2	no	—
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
304	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
305	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
306	C₂×SD₁₆	—	2	8	no	—
307	C₂×SD₁₆	—	2	8	no	—
308	C₂×SD₁₆	—	4	4	no	—
309	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
310	C₄⋊Q₈	—	2	8	no	—
311	C₄⋊Q₈	—	2	8	no	—
312	C₄⋊Q₈	—	2	8	no	—
313	C₄⋊Q₈	—	2	4	no	—
314	C₄⋊Q₈	D₄×C₁₃	1	8	yes	complemented
315	#121	—	2	2	no	—
316	#121	D₄×C₁₃	1	4	yes	—
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	4	4	no	—
319	C₂×C₄⋊C₄	—	2	8	no	—
320	C₂×C₄⋊C₄	—	2	8	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₄²	—	2	4	no	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
337	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
340	C₄⋊C₈	—	2	4	no	—
341	#103	—	2	8	no	—
342	#103	—	2	8	no	—
343	#103	—	4	4	no	—
344	C₂²⋊C₈	—	2	4	no	—
345	#95	—	2	1	no	—
346	#95	—	2	1	no	—
347	#95	—	2	1	no	—
348	C₂×C₁₃	—	2	4	no	—
349	C₂×C₁₃	—	8	2	no	—
350	C₂×C₁₃	#2408	1	1	yes	characteristic
351	C₂×C₁₃	C₂×#448	1	1	yes	characteristic
352	C₂×C₁₃	#3004	1	1	yes	characteristic
353	C₂×C₁₃	C₂×#461	1	1	yes	characteristic
354	C₂×C₁₃	#3039	1	1	yes	characteristic
355	C₂×C₁₃	#3206	1	1	yes	characteristic
356	C₂×C₁₃	#3218	1	1	yes	characteristic
357	C₂⁴	—	2	1	no	—
358	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₂×Q₈	—	2	8	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×Q₈	—	4	16	no	—
366	C₂×Q₈	—	4	16	no	—
367	C₂×Q₈	—	4	4	no	—
368	C₂×Q₈	—	4	4	no	—
369	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	4	2	no	—
375	C₂×D₄	—	4	2	no	—
376	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	4	4	no	—
390	C₂²×C₄	—	4	4	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	complemented
395	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
401	C₂²×C₄	C₁₃×#41	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
403	SD₁₆	—	4	16	no	—
404	C₂×C₈	—	2	4	no	—
405	C₂×C₈	—	2	4	no	—
406	C₂×C₈	—	2	4	no	—
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	—	2	8	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	4	2	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	—	2	2	no	—
424	C₄²	—	4	2	no	—
425	C₄²	C₂×D₄×C₁₃	1	4	yes	—
426	C₁₃	#24209	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	2	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	C₁₃×#121	1	2	yes	—
439	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
440	C₂³	C₁₃×#137	1	2	yes	—
441	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
442	Q₈	—	2	8	no	—
443	Q₈	—	2	8	no	—
444	Q₈	—	4	16	no	—
445	Q₈	—	4	4	no	—
446	Q₈	—	4	4	no	—
447	D₄	—	2	4	no	—
448	D₄	—	4	8	no	—
449	D₄	—	4	2	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	8	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	16	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	8	4	no	—
476	C₂×C₄	C₁₃×#120	1	2	yes	—
477	C₂×C₄	C₁₃×#120	1	2	yes	—
478	C₂×C₄	C₁₃×#121	1	2	yes	—
479	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
480	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
481	C₂×C₄	C₁₃×#137	1	2	yes	—
482	C₂×C₄	C₁₃×#137	1	2	yes	—
483	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
485	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
486	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
487	C₈	—	4	4	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	8	1	no	—
498	C₂²	—	8	1	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	C₁₃×#461	1	4	yes	complemented
502	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
503	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
504	C₂²	C₁₃×#535	1	1	yes	characteristic
505	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
506	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
507	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
508	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
509	C₄	—	2	2	no	—
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	4	8	no	—
515	C₄	—	8	1	no	—
516	C₄	—	8	1	no	—
517	C₄	C₁₃×#448	1	4	yes	complemented
518	C₄	D₄²×C₁₃	1	2	yes	—
519	C₄	C₁₃×#546	1	2	yes	—
520	C₂	—	2	4	no	—
521	C₂	—	8	2	no	—
522	C₂	C₁₃×#2408	1	1	yes	characteristic
523	C₂	C₂×C₁₃×#448	1	1	yes	characteristic
524	C₂	C₁₃×#3004	1	1	yes	characteristic
525	C₂	C₂×C₁₃×#461	1	1	yes	characteristic
526	C₂	C₁₃×#3039	1	1	yes	characteristic
527	C₂	C₁₃×#3206	1	1	yes	characteristic
528	C₂	C₁₃×#3218	1	1	yes	characteristic

	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
2. C₂×C₁₃×#461	C₂	semidirect
5. C₁₃×#2043	C₂	semidirect
6. C₁₃×#2013	C₂	semidirect
7. C₁₃×#1981	C₂	semidirect
8. C₁₃×#1797	C₂	semidirect
9. C₁₃×#1787	C₂	semidirect
59. C₁₃×C₄⋊Q₈	D₄	semidirect
93. #24209	C₁₃	direct (N × H)
131. C₂²×C₄×C₁₃	SD₁₆	semidirect
163. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
164. C₂×#461	C₂×C₁₃	semidirect
167. #2043	C₂×C₁₃	semidirect
168. #2013	C₂×C₁₃	semidirect
169. #1981	C₂×C₁₃	semidirect
170. #1797	C₂×C₁₃	semidirect
171. #1787	C₂×C₁₃	semidirect
274. C₂²×C₁₃	#461	semidirect
290. C₄×C₁₃	#448	semidirect
314. C₄⋊Q₈	D₄×C₁₃	semidirect
394. C₂²×C₄	C₁₃×SD₁₆	semidirect
426. C₁₃	#24209	direct (N × H)
501. C₂²	C₁₃×#461	semidirect
517. C₄	C₁₃×#448	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₄⋊Q₈	2
C₂×C₁₃×#461	2
C₂×C₁₃×#448	2
C₄×C₁₃×#121	2
C₁₃×#2043	2
C₁₃×#2013	2
C₁₃×#1981	2
C₁₃×#1797	2
C₁₃×#1787	2
#24209	13

Subgroups — C13×#24209 #15710548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24209 #15710548