Subgroups — #16792640

Order 3328.

874 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131515	C₂	1	1	yes	maximal, characteristic
2	#13131514	C₂	1	1	yes	maximal, characteristic
3	#13130050	C₂	1	2	yes	maximal, complemented
4	#13130046	C₂	1	2	yes	maximal, complemented
5	#13130045	C₂	1	2	yes	maximal, complemented
6	#13130040	C₂	1	2	yes	maximal, complemented
7	C₈×#6118	C₂	1	2	yes	maximal, complemented
8	C₈×#6122	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
12	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
13	#11719129	C₄	1	2	yes	—
14	#11719128	C₄	1	2	yes	—
15	#11719127	C₄	1	2	yes	—
16	#11719126	C₄	1	2	yes	—
17	#11719125	C₂²	1	2	yes	—
18	C₄×#6122	C₂²	1	2	yes	—
19	#11719055	C₄	1	2	yes	—
20	#11719055	C₄	1	2	yes	—
21	#11719054	C₄	1	2	yes	—
22	#11719053	C₄	1	2	yes	—
23	#11719051	C₂²	1	2	yes	—
24	#11719049	C₂²	1	2	yes	—
25	#11719049	C₂²	1	2	yes	—
26	C₄×#6118	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
28	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×#1055	C₄	1	1	yes	characteristic
31	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
32	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
33	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
34	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
35	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
36	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
37	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
38	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
39	#1057⋊C₈	C₂²	1	4	yes	complemented
40	#1057⋊C₈	C₂²	1	4	yes	complemented
41	#11718251	C₂²	1	4	yes	complemented
42	C₈×#1057	C₂²	1	4	yes	complemented
43	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×#6122	C₂×C₄	1	4	yes	—
47	C₂×#6118	C₂×C₄	1	4	yes	—
48	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
54	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
55	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₃	—	2	4	no	—
57	C₂×C₈×D₁₃	—	2	4	no	—
58	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
66	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₁₃	C₂×C₄	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	C₂³	1	1	yes	characteristic
73	C₄²×D₁₃	C₂³	1	1	yes	characteristic
74	C₂²⋊#1057	C₂×C₄	1	4	yes	—
75	#88112	C₂×C₄	1	4	yes	—
76	#88112	C₂×C₄	1	4	yes	—
77	#88112	C₂×C₄	1	4	yes	—
78	#88111	C₂×C₄	1	4	yes	—
79	#88111	C₂×C₄	1	4	yes	—
80	#88111	C₂×C₄	1	4	yes	—
81	#88110	C₂×C₄	1	4	yes	—
82	#88110	C₂×C₄	1	4	yes	—
83	C₄⋊#1057	C₂×C₄	1	4	yes	—
84	C₄×#1057	C₂³	1	4	yes	—
85	C₄×#1057	C₂³	1	4	yes	—
86	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
89	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
90	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
91	C₈×Dic₁₃	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	C₂³	1	1	yes	characteristic
95	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
96	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
97	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
98	C₄×#1055	C₂×C₄	1	1	yes	characteristic
99	C₄×#1055	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	#17323	—	13	1	no	maximal, Sylow
103	C₂³×D₁₃	C₄²	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
108	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	—	2	4	no	—
111	C₂×C₄×D₁₃	—	2	2	no	—
112	C₂×C₄×D₁₃	—	2	2	no	—
113	C₂×C₄×D₁₃	—	2	4	no	—
114	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
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	C₂²×C₄	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	#6122	—	2	8	no	—
127	C₂×#1057	C₂²×C₄	1	8	yes	—
128	C₂×#1057	C₂²×C₄	1	8	yes	—
129	#6118	—	2	8	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₁₃	C₄²	1	1	yes	characteristic
137	C₄²×C₁₃	C₄²	1	1	yes	characteristic
138	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
141	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
142	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
143	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
144	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
152	C₂×#1055	—	2	2	no	—
153	C₂×#1055	—	2	2	no	—
154	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
155	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
156	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
157	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
158	C₈×D₁₃	—	2	2	no	—
159	C₈×D₁₃	—	2	2	no	—
160	C₈×D₁₃	—	2	2	no	—
161	C₈×D₁₃	—	2	2	no	—
162	C₈×D₁₃	—	2	2	no	—
163	C₈×D₁₃	—	2	2	no	—
164	C₈×D₁₃	M₁₆	1	4	yes	complemented
165	C₈×D₁₃	M₁₆	1	4	yes	complemented
166	#2920	—	13	1	no	—
167	#2920	—	13	1	no	—
168	C₂²×C₄×C₈	—	13	1	no	—
169	#1452	—	13	2	no	—
170	#1451	—	13	2	no	—
171	#1451	—	13	2	no	—
172	#1450	—	13	2	no	—
173	C₈×M₁₆	—	13	2	no	—
174	C₈×M₁₆	—	13	2	no	—
175	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
176	C₂²×D₁₃	—	2	2	no	—
177	C₂²×D₁₃	—	2	2	no	—
178	C₂²×D₁₃	—	2	2	no	—
179	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
180	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
191	C₂×Dic₁₃	—	2	2	no	—
192	C₂×Dic₁₃	—	2	2	no	—
193	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
194	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
195	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
196	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
197	C₂×Dic₁₃	#131	1	4	yes	—
198	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
199	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
200	C₄×D₁₃	—	2	2	no	—
201	C₄×D₁₃	—	2	2	no	—
202	C₄×D₁₃	—	2	1	no	—
203	C₄×D₁₃	—	2	1	no	—
204	C₄×D₁₃	—	2	2	no	—
205	C₄×D₁₃	—	2	2	no	—
206	C₄×D₁₃	—	2	2	no	—
207	C₄×D₁₃	—	2	2	no	—
208	C₄×D₁₃	—	2	2	no	—
209	C₄×D₁₃	—	2	2	no	—
210	C₄×D₁₃	—	2	2	no	—
211	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
212	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
213	C₄×D₁₃	#131	1	4	yes	—
214	#1057	—	2	8	no	—
215	#1057	—	2	8	no	—
216	C₈×C₁₃	—	2	1	no	—
217	C₈×C₁₃	—	2	1	no	—
218	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
219	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
220	#1055	—	2	1	no	—
221	#1055	—	2	1	no	—
222	#1055	C₂×M₁₆	1	2	yes	—
223	#1055	C₂×M₁₆	1	2	yes	—
224	C₂³×C₈	—	13	1	no	—
225	C₂³×C₈	—	13	1	no	—
226	C₂²×C₄²	—	13	1	no	—
227	#432	—	13	2	no	—
228	#432	—	13	2	no	—
229	#432	—	13	2	no	—
230	#432	—	13	2	no	—
231	#431	—	13	2	no	—
232	#431	—	13	2	no	—
233	#431	—	13	2	no	—
234	#431	—	13	2	no	—
235	#423	—	13	2	no	—
236	#423	—	13	2	no	—
237	#407	—	13	2	no	—
238	#407	—	13	2	no	—
239	C₄×M₁₆	—	13	2	no	—
240	C₄×M₁₆	—	13	2	no	—
241	C₂×C₄×C₈	—	13	1	no	—
242	C₂×C₄×C₈	—	13	1	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	#261	1	1	yes	characteristic
253	#322	—	13	4	no	—
254	#322	—	13	4	no	—
255	#322	—	13	4	no	—
256	C₈²	—	13	4	no	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	—	2	1	no	—
259	C₂²×C₁₃	#405	1	2	yes	—
260	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
261	C₂×D₁₃	—	2	8	no	—
262	C₂×D₁₃	—	2	1	no	—
263	C₂×D₁₃	—	2	1	no	—
264	C₂×D₁₃	—	2	1	no	—
265	C₂×D₁₃	—	2	1	no	—
266	C₂×D₁₃	C₄×M₁₆	1	2	yes	—
267	C₂×D₁₃	#405	1	2	yes	—
268	C₄×C₁₃	—	2	1	no	—
269	C₄×C₁₃	—	2	1	no	—
270	C₄×C₁₃	—	2	1	no	—
271	C₄×C₁₃	—	2	1	no	—
272	C₄×C₁₃	#405	1	2	yes	—
273	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
274	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
275	Dic₁₃	—	2	1	no	—
276	Dic₁₃	—	2	1	no	—
277	Dic₁₃	C₄×M₁₆	1	2	yes	—
278	Dic₁₃	#405	1	2	yes	—
279	Dic₁₃	C₂×#131	1	2	yes	—
280	Dic₁₃	C₂×#131	1	2	yes	—
281	C₂³×C₄	—	13	1	no	—
282	C₂³×C₄	—	13	1	no	—
283	C₂³×C₄	—	13	1	no	—
284	C₂×M₁₆	—	13	4	no	—
285	C₂×M₁₆	—	13	4	no	—
286	C₂²×C₈	—	13	1	no	—
287	C₂²×C₈	—	13	1	no	—
288	C₂²×C₈	—	13	1	no	—
289	C₂²×C₈	—	13	1	no	—
290	C₂²×C₈	—	13	1	no	—
291	C₂²×C₈	—	13	1	no	—
292	C₂²×C₈	—	13	1	no	—
293	C₂²×C₈	—	13	1	no	—
294	C₂²×C₈	—	13	1	no	—
295	C₂²×C₈	—	13	1	no	—
296	C₂²×C₈	—	26	4	no	—
297	C₂²×C₈	—	26	4	no	—
298	C₂²×C₈	C₂×#261	1	1	yes	characteristic
299	C₂²×C₈	C₂×#261	1	1	yes	characteristic
300	C₂×C₄²	—	13	1	no	—
301	C₂×C₄²	—	13	1	no	—
302	C₂×C₄²	—	13	1	no	—
303	C₂×C₄²	—	13	1	no	—
304	C₂×C₄²	—	13	1	no	—
305	C₂×C₄²	—	13	1	no	—
306	C₂×C₄²	—	13	1	no	—
307	C₂×C₄²	—	13	1	no	—
308	C₂×C₄²	—	13	1	no	—
309	C₂×C₄²	—	13	1	no	—
310	C₂×C₄²	—	13	1	no	—
311	C₂×C₄²	C₂×#261	1	1	yes	characteristic
312	C₄⋊C₈	—	13	4	no	—
313	C₄⋊C₈	—	13	4	no	—
314	C₄⋊C₈	—	13	4	no	—
315	C₄⋊C₈	—	13	4	no	—
316	C₂²⋊C₈	—	13	4	no	—
317	C₂²⋊C₈	—	13	4	no	—
318	C₂²⋊C₈	—	13	4	no	—
319	C₂²⋊C₈	—	13	4	no	—
320	#97	—	13	4	no	—
321	#97	—	13	4	no	—
322	C₄×C₈	—	13	4	no	—
323	C₄×C₈	—	13	4	no	—
324	C₄×C₈	—	13	1	no	—
325	C₄×C₈	—	13	1	no	—
326	C₄×C₈	—	13	1	no	—
327	C₄×C₈	—	13	1	no	—
328	C₄×C₈	—	13	1	no	—
329	C₄×C₈	—	13	1	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	C₂×#261	1	1	yes	characteristic
337	C₄×C₈	C₂×#261	1	1	yes	characteristic
338	C₄×C₈	C₂×#261	1	1	yes	characteristic
339	C₄×C₈	C₂×#261	1	1	yes	characteristic
340	C₂×C₁₃	—	2	2	no	—
341	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
342	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
343	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
344	D₁₃	—	2	2	no	—
345	D₁₃	—	2	2	no	—
346	C₂⁴	—	13	1	no	—
347	C₂²×C₄	—	13	1	no	—
348	C₂²×C₄	—	13	1	no	—
349	C₂²×C₄	—	13	1	no	—
350	C₂²×C₄	—	13	1	no	—
351	C₂²×C₄	—	13	1	no	—
352	C₂²×C₄	—	13	1	no	—
353	C₂²×C₄	—	13	1	no	—
354	C₂²×C₄	—	13	1	no	—
355	C₂²×C₄	—	13	1	no	—
356	C₂²×C₄	—	13	1	no	—
357	C₂²×C₄	—	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	—	26	2	no	—
363	C₂²×C₄	—	26	2	no	—
364	C₂²×C₄	—	26	4	no	—
365	C₂²×C₄	—	26	4	no	—
366	C₂²×C₄	C₄×#261	1	1	yes	characteristic
367	C₂²×C₄	C₄×#261	1	1	yes	characteristic
368	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
369	M₁₆	—	26	8	no	—
370	M₁₆	—	26	8	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	13	1	no	—
374	C₂×C₈	—	13	1	no	—
375	C₂×C₈	—	13	4	no	—
376	C₂×C₈	—	13	4	no	—
377	C₂×C₈	—	13	8	no	—
378	C₂×C₈	—	13	8	no	—
379	C₂×C₈	—	13	1	no	—
380	C₂×C₈	—	13	1	no	—
381	C₂×C₈	—	26	2	no	—
382	C₂×C₈	—	26	2	no	—
383	C₂×C₈	—	26	2	no	—
384	C₂×C₈	—	26	2	no	—
385	C₂×C₈	—	26	2	no	—
386	C₂×C₈	—	26	2	no	—
387	C₂×C₈	—	26	2	no	—
388	C₂×C₈	—	26	2	no	—
389	C₂×C₈	C₂²×#261	1	1	yes	characteristic
390	C₂×C₈	C₂²×#261	1	1	yes	characteristic
391	C₂×C₈	C₂²×#261	1	1	yes	characteristic
392	C₂×C₈	C₂²×#261	1	1	yes	characteristic
393	C₄²	—	13	1	no	—
394	C₄²	—	13	1	no	—
395	C₄²	—	13	1	no	—
396	C₄²	—	13	1	no	—
397	C₄²	—	13	1	no	—
398	C₄²	—	13	1	no	—
399	C₄²	—	13	1	no	—
400	C₄²	—	13	1	no	—
401	C₄²	—	13	1	no	—
402	C₄²	—	13	1	no	—
403	C₄²	—	13	1	no	—
404	C₄²	—	13	1	no	—
405	C₄²	C₄×#261	1	1	yes	characteristic
406	C₄²	C₄×#261	1	1	yes	characteristic
407	C₄²	C₂²×#261	1	1	yes	characteristic
408	C₄²	C₂²×#261	1	1	yes	characteristic
409	C₁₃	#17323	1	1	yes	characteristic, complemented, Sylow
410	C₂³	—	13	1	no	—
411	C₂³	—	13	1	no	—
412	C₂³	—	26	2	no	—
413	C₂³	—	26	2	no	—
414	C₂³	—	26	2	no	—
415	C₂³	C₂×C₄×#261	1	1	yes	characteristic
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	13	4	no	—
421	C₂×C₄	—	13	1	no	—
422	C₂×C₄	—	13	1	no	—
423	C₂×C₄	—	13	1	no	—
424	C₂×C₄	—	13	1	no	—
425	C₂×C₄	—	13	4	no	—
426	C₂×C₄	—	13	2	no	—
427	C₂×C₄	—	13	2	no	—
428	C₂×C₄	—	13	1	no	—
429	C₂×C₄	—	13	1	no	—
430	C₂×C₄	—	26	2	no	—
431	C₂×C₄	—	26	2	no	—
432	C₂×C₄	—	26	2	no	—
433	C₂×C₄	—	26	2	no	—
434	C₂×C₄	—	26	2	no	—
435	C₂×C₄	—	26	2	no	—
436	C₂×C₄	—	26	2	no	—
437	C₂×C₄	—	26	2	no	—
438	C₂×C₄	—	26	2	no	—
439	C₂×C₄	—	26	2	no	—
440	C₂×C₄	—	26	2	no	—
441	C₂×C₄	—	26	1	no	—
442	C₂×C₄	—	26	1	no	—
443	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
444	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
445	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
446	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
447	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
448	C₂×C₄	C₂³×#261	1	1	yes	characteristic
449	C₈	—	2	1	no	—
450	C₈	—	2	1	no	—
451	C₈	—	13	2	no	—
452	C₈	—	13	2	no	—
453	C₈	—	26	8	no	—
454	C₈	—	26	8	no	—
455	C₈	—	26	1	no	—
456	C₈	—	26	1	no	—
457	C₈	D₁₃⋊M₁₆	1	2	yes	—
458	C₈	D₁₃⋊M₁₆	1	2	yes	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	13	2	no	—
462	C₂²	—	13	2	no	—
463	C₂²	—	26	8	no	—
464	C₂²	—	26	1	no	—
465	C₂²	—	26	1	no	—
466	C₂²	—	26	1	no	—
467	C₂²	—	26	1	no	—
468	C₂²	#11719089	1	2	yes	—
469	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	13	2	no	—
475	C₄	—	13	2	no	—
476	C₄	—	13	2	no	—
477	C₄	—	13	2	no	—
478	C₄	—	26	1	no	—
479	C₄	—	26	1	no	—
480	C₄	#11719089	1	2	yes	—
481	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
482	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
483	C₂	—	2	2	no	—
484	C₂	—	26	2	no	—
485	C₂	—	26	2	no	—
486	C₂	C₄×D₁₃⋊M₁₆	1	1	yes	characteristic
487	C₂	C₂×#11719089	1	1	yes	characteristic
488	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	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	#17323
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. #13130050	C₂	semidirect
4. #13130046	C₂	semidirect
5. #13130045	C₂	semidirect
6. #13130040	C₂	semidirect
7. C₈×#6118	C₂	semidirect
8. C₈×#6122	C₂	semidirect
39. #1057⋊C₈	C₂²	semidirect
40. #1057⋊C₈	C₂²	semidirect
41. #11718251	C₂²	semidirect
42. C₈×#1057	C₂²	semidirect
164. C₈×D₁₃	M₁₆	semidirect
165. C₈×D₁₃	M₁₆	semidirect
409. C₁₃	#17323	semidirect

Maximal subgroups

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

subgroup	index
#13131515	2
#13131514	2
#13130050	2
#13130046	2
#13130045	2
#13130040	2
C₈×#6118	2
C₈×#6122	2
C₂×C₄×C₈×D₁₃	2
#17323	13