Subgroups — #16797293

Order 3328.

990 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#432	C₂	1	1	yes	maximal, characteristic
2	#13131283	C₂	1	1	yes	maximal, characteristic
3	#13130630	C₂	1	2	yes	maximal, complemented
4	C₈×C₄⋊#261	C₂	1	2	yes	maximal, complemented
5	#13130572	C₂	1	2	yes	maximal
6	C₈×C₂²⋊#261	C₂	1	2	yes	maximal
7	#13130554	C₂	1	2	yes	maximal, complemented
8	#13130492	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
13	#11719136	C₄	1	2	yes	—
14	#11719135	C₄	1	2	yes	—
15	C₄×C₂²⋊#261	C₂²	1	2	yes	—
16	#11719130	C₄	1	2	yes	complemented
17	#11719128	C₄	1	2	yes	complemented
18	D₁₃⋊(C₂²⋊C₈)	C₂²	1	2	yes	—
19	C₂×#88100	C₂²	1	4	yes	—
20	C₂×C₈×#261	C₂²	1	4	yes	—
21	#11719061	C₄	1	2	yes	—
22	#11719060	C₄	1	2	yes	—
23	C₄×C₄⋊#261	C₂²	1	2	yes	—
24	#11719057	C₂²	1	2	yes	—
25	#11719055	C₄	1	2	yes	complemented
26	#11719054	C₄	1	2	yes	complemented
27	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
28	#11719047	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
30	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
31	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
32	C₂×C₄×#1055	C₄	1	1	yes	characteristic, complemented
33	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic, complemented
34	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic, complemented
35	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic, complemented
36	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic, complemented
37	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
38	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
39	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
41	(C₂×#261)⋊C₈	C₂²	1	4	yes	—
42	(C₂×#261)⋊C₈	C₂²	1	4	yes	—
43	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
46	C₂×C₂²⋊#261	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
48	C₂×C₄×#261	C₂³	1	4	yes	—
49	C₂×D₁₃⋊C₈	C₂³	1	4	yes	—
50	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
57	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₁₃	—	2	4	no	—
59	C₂×C₈×D₁₃	—	2	4	no	—
60	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
68	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₁₃	C₂³	1	1	yes	characteristic
75	C₄²×D₁₃	C₂³	1	1	yes	characteristic
76	C₂²⋊#1057	C₂×C₄	1	4	yes	—
77	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
78	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
79	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
80	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
81	#88112	C₂×C₄	1	4	yes	—
82	#88111	C₂×C₄	1	4	yes	—
83	#88110	C₂×C₄	1	4	yes	—
84	#88110	C₂×C₄	1	4	yes	—
85	C₄⋊#1057	C₂×C₄	1	4	yes	—
86	#88100	—	2	8	no	—
87	C₈×#261	—	2	8	no	—
88	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
89	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
100	C₄×#1055	C₂×C₄	1	1	yes	characteristic
101	C₄×#1055	C₂×C₄	1	1	yes	characteristic
102	C₄×#1055	C₂×C₄	1	1	yes	characteristic
103	C₄×#1055	C₂×C₄	1	1	yes	characteristic
104	#20476	—	13	1	no	maximal, Sylow
105	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×#261	C₂²×C₄	1	8	yes	—
107	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
111	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
112	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₁₃	—	2	4	no	—
114	C₂×C₄×D₁₃	—	2	4	no	—
115	C₂×C₄×D₁₃	—	2	2	no	—
116	C₂×C₄×D₁₃	—	2	2	no	—
117	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
119	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
120	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
121	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
129	C₂²⋊#261	—	2	8	no	—
130	C₂×#1057	C₂²×C₄	1	8	yes	—
131	C₄⋊#261	—	2	8	no	—
132	C₄×#261	—	2	4	no	—
133	C₄×#261	—	2	4	no	—
134	D₁₃⋊C₈	—	2	4	no	—
135	D₁₃⋊C₈	—	2	4	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₁₃	C₄²	1	1	yes	characteristic
143	C₄²×C₁₃	C₄²	1	1	yes	characteristic
144	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
147	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
148	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
149	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
150	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
151	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
152	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×#1055	—	2	2	no	—
159	C₂×#1055	—	2	2	no	—
160	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
161	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
162	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
163	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
164	C₈×D₁₃	—	2	2	no	—
165	C₈×D₁₃	—	2	2	no	—
166	C₈×D₁₃	—	2	2	no	—
167	C₈×D₁₃	—	2	2	no	—
168	C₈×D₁₃	—	2	2	no	—
169	C₈×D₁₃	—	2	2	no	—
170	C₈×D₁₃	#41	1	4	yes	—
171	C₈×D₁₃	#41	1	4	yes	—
172	C₂×#432	—	13	1	no	—
173	C₂²×C₄×C₈	—	13	1	no	—
174	#2283	—	13	1	no	—
175	#1770	—	13	2	no	—
176	C₈×C₄⋊C₄	—	13	2	no	—
177	#1752	—	13	2	no	—
178	C₈×C₂²⋊C₄	—	13	2	no	—
179	#1746	—	13	2	no	—
180	#1726	—	13	2	no	—
181	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
182	C₂²×D₁₃	—	2	2	no	—
183	C₂²×D₁₃	—	2	2	no	—
184	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
185	C₂²×D₁₃	#131	1	4	yes	—
186	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×#261	—	2	8	no	—
188	C₂×#261	—	2	8	no	—
189	C₂×#261	—	2	8	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
200	C₂×Dic₁₃	—	2	2	no	—
201	C₂×Dic₁₃	—	2	2	no	—
202	C₂×Dic₁₃	—	2	2	no	—
203	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
204	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
205	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
206	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
207	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
208	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
209	C₄×D₁₃	—	2	2	no	—
210	C₄×D₁₃	—	2	2	no	—
211	C₄×D₁₃	—	2	2	no	—
212	C₄×D₁₃	—	2	2	no	—
213	C₄×D₁₃	—	2	2	no	—
214	C₄×D₁₃	—	2	2	no	—
215	C₄×D₁₃	—	2	1	no	—
216	C₄×D₁₃	—	2	1	no	—
217	C₄×D₁₃	—	2	2	no	—
218	C₄×D₁₃	—	2	2	no	—
219	C₄×D₁₃	—	2	2	no	—
220	C₄×D₁₃	#131	1	4	yes	—
221	C₄×D₁₃	C₂×#41	1	2	yes	—
222	C₄×D₁₃	C₂×#41	1	2	yes	—
223	#1057	—	2	8	no	—
224	C₈×C₁₃	—	2	1	no	—
225	C₈×C₁₃	—	2	1	no	—
226	C₈×C₁₃	#117	1	2	yes	—
227	C₈×C₁₃	#117	1	2	yes	—
228	#1055	—	2	1	no	—
229	#1055	—	2	1	no	—
230	#1055	#117	1	2	yes	—
231	#1055	#117	1	2	yes	—
232	C₂³×C₈	—	13	1	no	—
233	C₂³×C₈	—	13	1	no	—
234	C₂²×C₄²	—	13	1	no	—
235	#432	—	13	2	no	—
236	#432	—	13	2	no	—
237	#432	—	13	2	no	—
238	#432	—	13	2	no	—
239	C₂×C₄⋊C₈	—	13	2	no	—
240	C₂×C₂²⋊C₈	—	13	2	no	—
241	C₂×#97	—	13	2	no	—
242	C₂×#97	—	13	4	no	—
243	C₂×C₄×C₈	—	13	1	no	—
244	C₂×C₄×C₈	—	13	1	no	—
245	C₂×C₄×C₈	—	13	1	no	—
246	C₂×C₄×C₈	—	13	1	no	—
247	C₂×C₄×C₈	—	13	1	no	—
248	C₂×C₄×C₈	—	13	1	no	—
249	C₂×C₄×C₈	—	13	1	no	—
250	C₂×C₄×C₈	—	13	1	no	—
251	C₂×C₄×C₈	—	13	1	no	—
252	C₂×C₄×C₈	—	13	1	no	—
253	C₂×C₄×C₈	—	13	1	no	—
254	C₂×C₄×C₈	—	13	4	no	—
255	C₂×C₄×C₈	#261	1	1	yes	characteristic, complemented
256	#383	—	13	2	no	—
257	#382	—	13	2	no	—
258	#381	—	13	2	no	—
259	#380	—	13	2	no	—
260	C₄×C₄⋊C₄	—	13	2	no	—
261	C₄×C₂²⋊C₄	—	13	2	no	—
262	#376	—	13	2	no	—
263	#336	—	13	4	no	—
264	#336	—	13	4	no	—
265	C₂²×C₁₃	—	2	1	no	—
266	C₂²×C₁₃	—	2	1	no	—
267	C₂²×C₁₃	#405	1	2	yes	—
268	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
269	C₂×D₁₃	—	2	1	no	—
270	C₂×D₁₃	—	2	1	no	—
271	C₂×D₁₃	—	2	8	no	—
272	C₂×D₁₃	#405	1	2	yes	—
273	C₂×D₁₃	C₄×#41	1	2	yes	—
274	C₂×D₁₃	C₂×#131	1	2	yes	—
275	C₂×D₁₃	C₂×#131	1	2	yes	—
276	#261	—	4	8	no	—
277	C₄×C₁₃	—	2	1	no	—
278	C₄×C₁₃	—	2	1	no	—
279	C₄×C₁₃	—	2	1	no	—
280	C₄×C₁₃	—	2	1	no	—
281	C₄×C₁₃	#405	1	2	yes	—
282	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
283	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
284	Dic₁₃	—	2	1	no	—
285	Dic₁₃	—	2	1	no	—
286	Dic₁₃	—	2	1	no	—
287	Dic₁₃	—	2	1	no	—
288	Dic₁₃	#405	1	2	yes	—
289	Dic₁₃	C₄×#41	1	2	yes	—
290	C₂³×C₄	—	13	1	no	—
291	C₂³×C₄	—	13	1	no	—
292	C₂³×C₄	—	13	1	no	—
293	C₂²×C₈	—	13	1	no	—
294	C₂²×C₈	—	13	1	no	—
295	C₂²×C₈	—	13	4	no	—
296	C₂²×C₈	—	13	1	no	—
297	C₂²×C₈	—	13	1	no	—
298	C₂²×C₈	—	13	1	no	—
299	C₂²×C₈	—	13	1	no	—
300	C₂²×C₈	—	13	1	no	—
301	C₂²×C₈	—	13	1	no	—
302	C₂²×C₈	—	13	1	no	—
303	C₂²×C₈	—	13	1	no	—
304	C₂²×C₈	—	26	4	no	—
305	C₂²×C₈	—	26	4	no	—
306	C₂²×C₈	C₂×#261	1	1	yes	characteristic
307	C₂²×C₈	C₂×#261	1	1	yes	characteristic
308	C₂×C₄⋊C₄	—	13	4	no	—
309	C₂×C₂²⋊C₄	—	13	4	no	—
310	C₂×C₄²	—	13	1	no	—
311	C₂×C₄²	—	13	1	no	—
312	C₂×C₄²	—	13	1	no	—
313	C₂×C₄²	—	13	1	no	—
314	C₂×C₄²	—	13	1	no	—
315	C₂×C₄²	—	13	1	no	—
316	C₂×C₄²	—	13	1	no	—
317	C₂×C₄²	—	13	1	no	—
318	C₂×C₄²	—	13	1	no	—
319	C₂×C₄²	—	13	1	no	—
320	C₂×C₄²	—	13	1	no	—
321	C₂×C₄²	—	13	4	no	—
322	C₂×C₄²	C₂×#261	1	1	yes	characteristic
323	C₄⋊C₈	—	13	4	no	—
324	C₄⋊C₈	—	13	4	no	—
325	C₂²⋊C₈	—	13	4	no	—
326	C₂²⋊C₈	—	13	4	no	—
327	#97	—	13	4	no	—
328	#97	—	13	4	no	—
329	#97	—	26	8	no	—
330	C₄×C₈	—	13	1	no	—
331	C₄×C₈	—	13	1	no	—
332	C₄×C₈	—	13	1	no	—
333	C₄×C₈	—	13	1	no	—
334	C₄×C₈	—	13	1	no	—
335	C₄×C₈	—	13	1	no	—
336	C₄×C₈	—	13	1	no	—
337	C₄×C₈	—	13	1	no	—
338	C₄×C₈	—	13	1	no	—
339	C₄×C₈	—	13	1	no	—
340	C₄×C₈	—	13	1	no	—
341	C₄×C₈	—	13	1	no	—
342	C₄×C₈	—	26	8	no	—
343	C₄×C₈	C₂×#261	1	1	yes	characteristic
344	C₄×C₈	C₂×#261	1	1	yes	characteristic
345	C₄×C₈	C₂×#261	1	1	yes	characteristic
346	C₄×C₈	C₂×#261	1	1	yes	characteristic
347	#95	—	13	4	no	—
348	#95	—	13	4	no	—
349	#95	—	13	4	no	—
350	#95	—	13	4	no	—
351	C₂×C₁₃	—	2	2	no	—
352	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
353	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
354	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
355	D₁₃	—	2	2	no	—
356	D₁₃	#2966	1	4	yes	—
357	C₂⁴	—	13	1	no	—
358	C₂²×C₄	—	13	1	no	—
359	C₂²×C₄	—	13	1	no	—
360	C₂²×C₄	—	13	1	no	—
361	C₂²×C₄	—	13	1	no	—
362	C₂²×C₄	—	13	1	no	—
363	C₂²×C₄	—	13	1	no	—
364	C₂²×C₄	—	13	1	no	—
365	C₂²×C₄	—	13	1	no	—
366	C₂²×C₄	—	13	1	no	—
367	C₂²×C₄	—	13	1	no	—
368	C₂²×C₄	—	13	1	no	—
369	C₂²×C₄	—	13	1	no	—
370	C₂²×C₄	—	13	1	no	—
371	C₂²×C₄	—	13	1	no	—
372	C₂²×C₄	—	13	1	no	—
373	C₂²×C₄	—	13	8	no	—
374	C₂²×C₄	—	26	2	no	—
375	C₂²×C₄	—	26	2	no	—
376	C₂²×C₄	—	26	4	no	—
377	C₂²×C₄	—	26	4	no	—
378	C₂²×C₄	C₄×#261	1	1	yes	characteristic
379	C₂²×C₄	C₄×#261	1	1	yes	characteristic
380	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	13	1	no	—
384	C₂×C₈	—	13	1	no	—
385	C₂×C₈	—	13	4	no	—
386	C₂×C₈	—	13	4	no	—
387	C₂×C₈	—	13	8	no	—
388	C₂×C₈	—	13	1	no	—
389	C₂×C₈	—	13	1	no	—
390	C₂×C₈	—	26	2	no	—
391	C₂×C₈	—	26	2	no	—
392	C₂×C₈	—	26	2	no	—
393	C₂×C₈	—	26	2	no	—
394	C₂×C₈	—	26	2	no	—
395	C₂×C₈	—	26	2	no	—
396	C₂×C₈	—	26	4	no	—
397	C₂×C₈	—	26	4	no	—
398	C₂×C₈	—	26	2	no	—
399	C₂×C₈	—	26	2	no	—
400	C₂×C₈	C₂²×#261	1	1	yes	characteristic
401	C₂×C₈	C₂²×#261	1	1	yes	characteristic
402	C₂×C₈	C₂²×#261	1	1	yes	characteristic
403	C₂×C₈	C₂²×#261	1	1	yes	characteristic
404	C₄⋊C₄	—	26	8	no	—
405	C₂²⋊C₄	—	26	8	no	—
406	C₄²	—	13	1	no	—
407	C₄²	—	13	1	no	—
408	C₄²	—	13	1	no	—
409	C₄²	—	13	1	no	—
410	C₄²	—	13	1	no	—
411	C₄²	—	13	1	no	—
412	C₄²	—	13	1	no	—
413	C₄²	—	13	1	no	—
414	C₄²	—	13	1	no	—
415	C₄²	—	13	1	no	—
416	C₄²	—	13	1	no	—
417	C₄²	—	13	1	no	—
418	C₄²	—	26	4	no	—
419	C₄²	—	26	4	no	—
420	C₄²	C₄×#261	1	1	yes	characteristic
421	C₄²	C₄×#261	1	1	yes	characteristic
422	C₄²	C₂²×#261	1	1	yes	characteristic
423	C₄²	C₂²×#261	1	1	yes	characteristic
424	C₁₃	#20476	1	1	yes	characteristic, complemented, Sylow
425	C₂³	—	13	1	no	—
426	C₂³	—	13	4	no	—
427	C₂³	—	13	1	no	—
428	C₂³	—	26	2	no	—
429	C₂³	—	26	2	no	—
430	C₂³	C₂×C₄×#261	1	1	yes	characteristic
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	13	1	no	—
436	C₂×C₄	—	13	1	no	—
437	C₂×C₄	—	13	4	no	—
438	C₂×C₄	—	13	2	no	—
439	C₂×C₄	—	13	2	no	—
440	C₂×C₄	—	13	1	no	—
441	C₂×C₄	—	13	1	no	—
442	C₂×C₄	—	13	1	no	—
443	C₂×C₄	—	13	1	no	—
444	C₂×C₄	—	26	2	no	—
445	C₂×C₄	—	26	2	no	—
446	C₂×C₄	—	26	2	no	—
447	C₂×C₄	—	26	2	no	—
448	C₂×C₄	—	26	2	no	—
449	C₂×C₄	—	26	2	no	—
450	C₂×C₄	—	26	2	no	—
451	C₂×C₄	—	26	2	no	—
452	C₂×C₄	—	26	2	no	—
453	C₂×C₄	—	26	2	no	—
454	C₂×C₄	—	26	2	no	—
455	C₂×C₄	—	26	2	no	—
456	C₂×C₄	—	26	1	no	—
457	C₂×C₄	—	26	1	no	—
458	C₂×C₄	—	26	8	no	—
459	C₂×C₄	—	26	8	no	—
460	C₂×C₄	—	26	8	no	—
461	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
462	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
463	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
464	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
465	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
466	C₂×C₄	C₂³×#261	1	1	yes	characteristic
467	C₈	—	2	1	no	—
468	C₈	—	2	1	no	—
469	C₈	—	13	2	no	—
470	C₈	—	13	2	no	—
471	C₈	—	26	8	no	—
472	C₈	—	26	1	no	—
473	C₈	—	26	1	no	—
474	C₈	#88237	1	2	yes	—
475	C₈	#88237	1	2	yes	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	13	2	no	—
479	C₂²	—	13	2	no	—
480	C₂²	—	13	2	no	—
481	C₂²	—	13	2	no	—
482	C₂²	—	26	8	no	—
483	C₂²	—	26	1	no	—
484	C₂²	—	26	1	no	—
485	C₂²	#11719089	1	2	yes	—
486	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	13	2	no	—
492	C₄	—	13	2	no	—
493	C₄	—	26	1	no	—
494	C₄	—	26	1	no	—
495	C₄	—	26	1	no	—
496	C₄	—	26	1	no	—
497	C₄	—	52	8	no	—
498	C₄	#11719089	1	2	yes	—
499	C₄	C₂×#88237	1	1	yes	characteristic
500	C₄	C₂×#88237	1	1	yes	characteristic
501	C₂	—	2	2	no	—
502	C₂	—	13	4	no	—
503	C₂	—	26	2	no	—
504	C₂	C₄×#88237	1	1	yes	characteristic
505	C₂	C₂×#11719089	1	1	yes	characteristic
506	C₂	C₂×#11719089	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	#20476
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #13130630	C₂	semidirect
4. C₈×C₄⋊#261	C₂	semidirect
7. #13130554	C₂	semidirect
8. #13130492	C₂	semidirect
16. #11719130	C₄	semidirect
17. #11719128	C₄	semidirect
25. #11719055	C₄	semidirect
26. #11719054	C₄	semidirect
29. C₂×C₄×C₈×C₁₃	C₄	semidirect
30. C₂×C₈×Dic₁₃	C₄	semidirect
31. C₂×C₈×Dic₁₃	C₄	semidirect
32. C₂×C₄×#1055	C₄	semidirect
33. C₄×C₈×D₁₃	C₄	semidirect
34. C₄×C₈×D₁₃	C₄	semidirect
35. C₄×C₈×D₁₃	C₄	semidirect
36. C₄×C₈×D₁₃	C₄	semidirect
255. C₂×C₄×C₈	#261	semidirect
424. C₁₃	#20476	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#432	2
#13131283	2
#13130630	2
C₈×C₄⋊#261	2
#13130572	2
C₈×C₂²⋊#261	2
#13130554	2
#13130492	2
C₂×C₄×C₈×D₁₃	2
#20476	13