Subgroups — #16792751

Order 3328.

798 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131647	C₂	1	1	yes	maximal, characteristic
2	#13131647	C₂	1	1	yes	maximal, characteristic
3	#13130060	C₂	1	1	yes	maximal, characteristic, complemented
4	#13130059	C₂	1	1	yes	maximal, characteristic, complemented
5	#13130056	C₂	1	1	yes	maximal, characteristic, complemented
6	#13130055	C₂	1	1	yes	maximal, characteristic, complemented
7	#13130050	C₂	1	1	yes	maximal, characteristic, complemented
8	#13130046	C₂	1	1	yes	maximal, characteristic, complemented
9	#13130045	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#6118	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#6122	C₂	1	1	yes	maximal, characteristic, complemented
12	#13130034	C₂	1	1	yes	maximal, characteristic, complemented
13	#13130034	C₂	1	1	yes	maximal, characteristic, complemented
14	#13130032	C₂	1	1	yes	maximal, characteristic, complemented
15	#13123258	C₂	1	1	yes	maximal, characteristic
16	C₂×#88161	C₄	1	1	yes	characteristic
17	C₂×#88155	C₄	1	1	yes	characteristic
18	#11719227	C₂²	1	1	yes	characteristic
19	#11719125	C₂²	1	1	yes	characteristic
20	#11719125	C₂²	1	1	yes	characteristic
21	C₄×#6122	C₂²	1	1	yes	characteristic
22	C₄×#6122	C₂²	1	1	yes	characteristic
23	#11719078	C₄	1	2	yes	—
24	#11719078	C₄	1	2	yes	—
25	#11719075	C₄	1	2	yes	—
26	#11719075	C₄	1	2	yes	—
27	#11719066	C₄	1	2	yes	—
28	#11719066	C₄	1	2	yes	—
29	#11719065	C₄	1	2	yes	—
30	#11719065	C₄	1	2	yes	—
31	#11719051	C₂²	1	1	yes	characteristic
32	#11719051	C₂²	1	1	yes	characteristic
33	#11719049	C₂²	1	1	yes	characteristic
34	#11719049	C₂²	1	1	yes	characteristic
35	C₄×#6118	C₂²	1	1	yes	characteristic
36	C₄×#6118	C₂²	1	1	yes	characteristic
37	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₃×#405	C₄	1	1	yes	characteristic
40	M₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
42	#11718658	C₄	1	1	yes	characteristic
43	#11718369	C₄	1	1	yes	characteristic
44	#11718369	C₄	1	1	yes	characteristic
45	#11718368	C₂²	1	1	yes	characteristic
46	#11718368	C₂²	1	1	yes	characteristic
47	#11718350	C₄	1	1	yes	characteristic
48	#11718350	C₄	1	1	yes	characteristic
49	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
50	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
51	#1057⋊C₈	C₂²	1	1	yes	characteristic
52	#1057⋊C₈	C₂²	1	1	yes	characteristic
53	#1057⋊C₈	C₂²	1	1	yes	characteristic
54	#1057⋊C₈	C₂²	1	1	yes	characteristic
55	#1057⋊C₈	C₂²	1	1	yes	characteristic
56	#1057⋊C₈	C₂²	1	1	yes	characteristic
57	#1057⋊C₈	C₂²	1	1	yes	characteristic
58	#1057⋊C₈	C₂²	1	1	yes	characteristic
59	#11718251	C₂²	1	1	yes	characteristic
60	#11718251	C₂²	1	1	yes	characteristic
61	#11718251	C₂²	1	1	yes	characteristic
62	#11718251	C₂²	1	1	yes	characteristic
63	C₈×#1057	C₂²	1	1	yes	characteristic
64	C₈×#1057	C₂²	1	1	yes	characteristic
65	C₈×#1057	C₂²	1	1	yes	characteristic
66	C₈×#1057	C₂²	1	1	yes	characteristic
67	C₂×#6127	C₂×C₄	1	1	yes	characteristic
68	C₂×#6122	C₂×C₄	1	2	yes	—
69	C₂×#6122	C₂×C₄	1	2	yes	—
70	C₂×#6118	C₂×C₄	1	2	yes	—
71	C₂×#6118	C₂×C₄	1	2	yes	—
72	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
73	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
74	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
78	C₂×#6099	C₂×C₄	1	1	yes	characteristic
79	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
80	#88161	—	2	4	no	—
81	#88155	—	2	4	no	—
82	C₂×#6094	C₂×C₄	1	1	yes	characteristic
83	C₂×#6094	C₂×C₄	1	1	yes	characteristic
84	C₂×#6094	C₂×C₄	1	1	yes	characteristic
85	C₂×#6094	C₂×C₄	1	1	yes	characteristic
86	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
90	#88147	C₂×C₄	1	1	yes	characteristic
91	#88147	C₂×C₄	1	1	yes	characteristic
92	#88141	C₂×C₄	1	1	yes	characteristic
93	#88141	C₂×C₄	1	1	yes	characteristic
94	#88135	C₂×C₄	1	1	yes	characteristic
95	#88135	C₂×C₄	1	1	yes	characteristic
96	#88135	C₂×C₄	1	1	yes	characteristic
97	#88135	C₂×C₄	1	1	yes	characteristic
98	#88126	C₂×C₄	1	1	yes	characteristic
99	#88126	C₂×C₄	1	1	yes	characteristic
100	C₄²×D₁₃	C₂³	1	1	yes	characteristic
101	C₄²×D₁₃	C₂³	1	1	yes	characteristic
102	C₂²⋊#1057	C₂×C₄	1	2	yes	—
103	C₂²⋊#1057	C₂×C₄	1	2	yes	—
104	#88112	C₂×C₄	1	2	yes	—
105	#88112	C₂×C₄	1	2	yes	—
106	#88112	C₂×C₄	1	2	yes	—
107	#88112	C₂×C₄	1	2	yes	—
108	#88111	C₂×C₄	1	2	yes	—
109	#88111	C₂×C₄	1	2	yes	—
110	#88111	C₂×C₄	1	2	yes	—
111	#88111	C₂×C₄	1	2	yes	—
112	#88110	C₂×C₄	1	2	yes	—
113	#88110	C₂×C₄	1	2	yes	—
114	#88110	C₂×C₄	1	2	yes	—
115	#88110	C₂×C₄	1	2	yes	—
116	C₄⋊#1057	C₂×C₄	1	2	yes	—
117	C₄⋊#1057	C₂×C₄	1	2	yes	—
118	C₄×#1057	C₂×C₄	1	2	yes	—
119	C₄×#1057	C₂×C₄	1	2	yes	—
120	C₄×#1057	C₂³	1	1	yes	characteristic
121	C₄×#1057	C₂³	1	1	yes	characteristic
122	C₄×#1057	C₂³	1	1	yes	characteristic
123	C₄×#1057	C₂³	1	1	yes	characteristic
124	C₄×#1057	C₂³	1	1	yes	characteristic
125	C₄×#1057	C₂³	1	1	yes	characteristic
126	C₄×#1057	C₂³	1	1	yes	characteristic
127	C₄×#1057	C₂³	1	1	yes	characteristic
128	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
129	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
130	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
131	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
132	#88055	C₂×C₄	1	1	yes	characteristic
133	#88055	C₂×C₄	1	1	yes	characteristic
134	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
135	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
136	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
137	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
138	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
139	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
140	#88043	C₂×C₄	1	1	yes	characteristic
141	#88043	C₂×C₄	1	1	yes	characteristic
142	C₄×#1055	C₂×C₄	1	1	yes	characteristic
143	C₄×#1055	C₂×C₄	1	1	yes	characteristic
144	#17337	—	13	1	no	maximal, Sylow
145	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₂²⋊D₁₃	C₄²	1	1	yes	characteristic
147	C₂×C₂²⋊D₁₃	C₄²	1	1	yes	characteristic
148	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
150	#6127	—	2	2	no	—
151	#6127	—	2	2	no	—
152	C₂×D₅₂	C₄²	1	1	yes	characteristic
153	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×Dic₂₆	C₄²	1	1	yes	characteristic
160	#6122	—	2	4	no	—
161	#6122	—	4	2	no	—
162	C₂×#1057	C₂²×C₄	1	2	yes	—
163	C₂×#1057	C₂²×C₄	1	2	yes	—
164	C₂×#1057	C₂²×C₄	1	2	yes	—
165	C₂×#1057	C₂²×C₄	1	2	yes	—
166	C₂×#1057	C₂²×C₄	1	2	yes	—
167	C₂×#1057	C₂²×C₄	1	2	yes	—
168	C₂×#1057	C₂²×C₄	1	2	yes	—
169	C₂×#1057	C₂²×C₄	1	2	yes	—
170	#6118	—	2	4	no	—
171	#6118	—	4	2	no	—
172	D₁₃⋊C₈	—	2	4	no	—
173	D₁₃⋊C₈	—	4	2	no	—
174	C₁₃×M₁₆	—	2	2	no	—
175	C₂×C₈×C₁₃	—	2	2	no	—
176	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
180	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
181	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
182	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
183	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
184	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
185	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
186	#6103	C₄²	1	1	yes	characteristic
187	#6103	C₄²	1	1	yes	characteristic
188	#6103	C₄²	1	1	yes	characteristic
189	#6103	C₄²	1	1	yes	characteristic
190	#6101	C₄²	1	1	yes	characteristic
191	#6101	C₄²	1	1	yes	characteristic
192	#6101	C₄²	1	1	yes	characteristic
193	#6101	C₄²	1	1	yes	characteristic
194	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
195	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
196	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
197	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
198	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
199	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
200	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
201	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
202	#6099	—	2	2	no	—
203	C₂×#1055	—	2	2	no	—
204	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
205	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
206	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
207	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
208	#6094	—	2	2	no	—
209	#6094	—	2	2	no	—
210	#6094	M₁₆	1	4	yes	complemented
211	#6094	M₁₆	1	4	yes	complemented
212	C₈×D₁₃	—	2	2	no	—
213	C₈×D₁₃	—	2	2	no	—
214	C₈×D₁₃	—	2	2	no	—
215	C₈×D₁₃	—	2	2	no	—
216	#2965	—	13	1	no	—
217	#2965	—	13	1	no	—
218	C₄×#131	—	13	1	no	—
219	#1455	—	13	1	no	—
220	#1455	—	13	1	no	—
221	#1453	—	13	1	no	—
222	#1453	—	13	1	no	—
223	#1452	—	13	1	no	—
224	#1451	—	13	1	no	—
225	#1451	—	13	1	no	—
226	C₈×M₁₆	—	13	1	no	—
227	C₈×M₁₆	—	13	1	no	—
228	C₈×M₁₆	—	13	1	no	—
229	C₈×M₁₆	—	13	1	no	—
230	C₂×#322	—	13	1	no	—
231	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
232	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
233	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
242	C₂²⋊D₁₃	—	2	2	no	—
243	C₂²⋊D₁₃	—	2	2	no	—
244	C₂×Dic₁₃	—	2	2	no	—
245	C₂×Dic₁₃	—	2	2	no	—
246	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
247	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
248	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
249	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
250	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
251	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
252	D₅₂	—	2	2	no	—
253	C₄×D₁₃	—	2	1	no	—
254	C₄×D₁₃	—	2	1	no	—
255	C₄×D₁₃	—	2	2	no	—
256	C₄×D₁₃	—	2	2	no	—
257	C₄×D₁₃	—	2	2	no	—
258	C₄×D₁₃	—	2	2	no	—
259	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
260	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
261	Dic₂₆	—	2	2	no	—
262	#1057	—	2	2	no	—
263	#1057	—	2	2	no	—
264	#1057	—	2	2	no	—
265	#1057	—	2	2	no	—
266	#1057	—	2	2	no	—
267	#1057	—	2	2	no	—
268	#1057	—	2	2	no	—
269	#1057	#131	1	4	yes	complemented
270	C₈×C₁₃	—	2	1	no	—
271	C₈×C₁₃	—	2	1	no	—
272	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
273	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
274	#1055	—	2	1	no	—
275	#1055	—	2	1	no	—
276	#1055	C₂×M₁₆	1	2	yes	—
277	#1055	C₂×M₁₆	1	2	yes	—
278	C₂×#131	—	13	1	no	—
279	C₂×#131	—	13	1	no	—
280	C₄×#41	—	13	1	no	—
281	#446	—	13	2	no	—
282	#446	—	13	2	no	—
283	#436	—	13	2	no	—
284	#436	—	13	2	no	—
285	#435	—	13	2	no	—
286	#435	—	13	2	no	—
287	#435	—	13	2	no	—
288	#435	—	13	2	no	—
289	#431	—	13	1	no	—
290	#431	—	13	1	no	—
291	#431	—	13	1	no	—
292	#431	—	13	1	no	—
293	#431	—	13	1	no	—
294	#431	—	13	1	no	—
295	#405	—	13	1	no	—
296	#405	—	13	1	no	—
297	#405	—	13	1	no	—
298	#405	—	13	1	no	—
299	#405	—	13	1	no	—
300	#405	#261	1	1	yes	characteristic
301	C₄×M₁₆	—	13	1	no	—
302	C₄×M₁₆	—	13	1	no	—
303	C₄×M₁₆	—	13	1	no	—
304	C₄×M₁₆	—	13	1	no	—
305	C₄×M₁₆	—	13	1	no	—
306	C₄×M₁₆	—	13	1	no	—
307	C₄×M₁₆	—	13	1	no	—
308	C₂×C₄×C₈	—	13	1	no	—
309	C₂×C₄×C₈	—	13	1	no	—
310	C₂×C₄×C₈	—	13	1	no	—
311	C₂×C₄×C₈	—	13	1	no	—
312	C₂×C₄×C₈	—	13	1	no	—
313	#322	—	13	1	no	—
314	#322	—	13	1	no	—
315	#322	—	13	1	no	—
316	#322	—	13	1	no	—
317	#322	—	13	1	no	—
318	#322	—	13	1	no	—
319	#322	—	13	1	no	—
320	#322	—	13	1	no	—
321	#322	—	13	1	no	—
322	#322	—	13	1	no	—
323	#322	—	13	1	no	—
324	#322	—	13	1	no	—
325	C₈²	—	13	1	no	—
326	C₈²	—	13	1	no	—
327	C₈²	—	13	1	no	—
328	C₈²	—	13	1	no	—
329	C₂²×C₁₃	—	2	1	no	—
330	C₂²×C₁₃	—	2	1	no	—
331	C₂²×C₁₃	—	2	1	no	—
332	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
333	C₂×D₁₃	—	2	1	no	—
334	C₂×D₁₃	—	2	1	no	—
335	C₂×D₁₃	—	2	1	no	—
336	C₂×D₁₃	—	2	1	no	—
337	C₂×D₁₃	—	2	1	no	—
338	C₂×D₁₃	C₄×M₁₆	1	2	yes	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	—	2	1	no	—
344	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
345	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
346	Dic₁₃	—	2	1	no	—
347	Dic₁₃	—	2	1	no	—
348	Dic₁₃	—	2	1	no	—
349	Dic₁₃	C₄×M₁₆	1	2	yes	—
350	Dic₁₃	C₂×#131	1	2	yes	—
351	Dic₁₃	#568	1	2	yes	—
352	C₂×#41	—	13	1	no	—
353	#131	—	26	4	no	—
354	#131	—	26	4	no	—
355	C₂×M₁₆	—	13	2	no	—
356	C₂×M₁₆	—	13	2	no	—
357	C₂×M₁₆	—	13	1	no	—
358	C₂×M₁₆	—	13	2	no	—
359	C₂×M₁₆	—	13	2	no	—
360	C₂×M₁₆	—	13	1	no	—
361	C₂×M₁₆	—	13	1	no	—
362	C₂×M₁₆	—	13	1	no	—
363	C₂×M₁₆	—	13	1	no	—
364	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
365	C₂²×C₈	—	13	2	no	—
366	C₂²×C₈	—	13	1	no	—
367	C₂²×C₈	—	13	2	no	—
368	C₂²×C₈	—	13	1	no	—
369	C₂²×C₈	—	13	1	no	—
370	C₂²×C₈	—	13	1	no	—
371	C₂²×C₈	—	13	1	no	—
372	C₂²×C₈	C₂×#261	1	1	yes	characteristic
373	C₄×Q₈	—	13	1	no	—
374	C₄×Q₈	—	13	1	no	—
375	C₄×D₄	—	13	1	no	—
376	C₄×D₄	—	13	1	no	—
377	C₄×D₄	—	13	1	no	—
378	C₄×D₄	—	13	1	no	—
379	C₄×D₄	—	13	1	no	—
380	C₄×D₄	—	13	1	no	—
381	#117	—	13	1	no	—
382	#117	—	13	1	no	—
383	#117	C₂×#261	1	1	yes	characteristic
384	C₂×C₄²	—	13	1	no	—
385	C₂×C₄²	—	13	1	no	—
386	C₂×C₄²	—	13	1	no	—
387	C₄⋊C₈	—	13	2	no	—
388	C₄⋊C₈	—	13	2	no	—
389	C₄⋊C₈	—	13	2	no	—
390	C₄⋊C₈	—	13	2	no	—
391	C₄⋊C₈	—	13	2	no	—
392	C₄⋊C₈	—	13	2	no	—
393	C₂²⋊C₈	—	13	2	no	—
394	C₂²⋊C₈	—	13	2	no	—
395	C₂²⋊C₈	—	13	2	no	—
396	C₂²⋊C₈	—	13	2	no	—
397	C₂²⋊C₈	—	13	2	no	—
398	C₂²⋊C₈	—	13	2	no	—
399	#97	—	13	2	no	—
400	#97	—	13	2	no	—
401	#97	—	13	2	no	—
402	#97	—	13	2	no	—
403	#97	—	13	1	no	—
404	#97	—	13	1	no	—
405	#97	—	13	1	no	—
406	#97	—	13	1	no	—
407	#97	C₂×#261	1	1	yes	characteristic
408	#97	C₂×#261	1	1	yes	characteristic
409	C₄×C₈	—	13	2	no	—
410	C₄×C₈	—	13	2	no	—
411	C₄×C₈	—	13	1	no	—
412	C₄×C₈	—	13	1	no	—
413	C₄×C₈	—	13	1	no	—
414	C₄×C₈	—	13	1	no	—
415	C₄×C₈	—	13	1	no	—
416	C₄×C₈	—	13	1	no	—
417	C₄×C₈	—	13	1	no	—
418	C₄×C₈	—	13	1	no	—
419	C₄×C₈	—	13	1	no	—
420	C₄×C₈	—	13	1	no	—
421	C₄×C₈	—	13	1	no	—
422	C₄×C₈	—	13	1	no	—
423	C₄×C₈	—	13	1	no	—
424	C₄×C₈	—	13	1	no	—
425	C₄×C₈	—	13	1	no	—
426	C₄×C₈	—	13	1	no	—
427	C₄×C₈	C₂×#261	1	1	yes	characteristic
428	C₄×C₈	C₂×#261	1	1	yes	characteristic
429	C₂×C₁₃	—	4	1	no	—
430	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
431	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
432	C₂×C₁₃	#2875	1	1	yes	characteristic
433	D₁₃	—	2	2	no	—
434	D₁₃	—	4	1	no	—
435	#41	—	26	2	no	—
436	#41	—	26	2	no	—
437	C₂×Q₈	—	13	1	no	—
438	C₂×D₄	—	13	1	no	—
439	C₂×D₄	—	13	1	no	—
440	C₂×D₄	—	13	1	no	—
441	C₂²×C₄	—	13	1	no	—
442	C₂²×C₄	—	13	1	no	—
443	C₂²×C₄	—	13	1	no	—
444	C₂²×C₄	—	13	1	no	—
445	C₂²×C₄	—	13	1	no	—
446	C₂²×C₄	—	13	1	no	—
447	C₂²×C₄	—	13	1	no	—
448	C₂²×C₄	—	13	1	no	—
449	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
450	M₁₆	—	2	2	no	—
451	M₁₆	—	13	4	no	—
452	M₁₆	—	13	4	no	—
453	M₁₆	—	26	2	no	—
454	M₁₆	—	26	2	no	—
455	M₁₆	—	26	4	no	—
456	M₁₆	—	26	4	no	—
457	M₁₆	—	26	2	no	—
458	M₁₆	—	52	2	no	—
459	M₁₆	—	52	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	13	2	no	—
462	C₂×C₈	—	13	1	no	—
463	C₂×C₈	—	13	1	no	—
464	C₂×C₈	—	13	2	no	—
465	C₂×C₈	—	13	2	no	—
466	C₂×C₈	—	13	2	no	—
467	C₂×C₈	—	13	2	no	—
468	C₂×C₈	—	13	2	no	—
469	C₂×C₈	—	13	2	no	—
470	C₂×C₈	—	13	2	no	—
471	C₂×C₈	—	13	1	no	—
472	C₂×C₈	—	13	1	no	—
473	C₂×C₈	—	26	2	no	—
474	C₂×C₈	—	26	2	no	—
475	C₂×C₈	—	26	2	no	—
476	C₂×C₈	—	26	2	no	—
477	C₂×C₈	—	26	4	no	—
478	C₂×C₈	—	26	2	no	—
479	C₂×C₈	—	52	2	no	—
480	C₂×C₈	C₂²×#261	1	1	yes	characteristic
481	C₂×C₈	C₂²×#261	1	1	yes	characteristic
482	C₂×C₈	C₂²×#261	1	1	yes	characteristic
483	C₂×C₈	C₂²×#261	1	1	yes	characteristic
484	C₄⋊C₄	—	13	1	no	—
485	C₄⋊C₄	—	13	1	no	—
486	C₄⋊C₄	—	13	1	no	—
487	C₄⋊C₄	—	13	1	no	—
488	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
489	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
490	C₂²⋊C₄	—	13	1	no	—
491	C₂²⋊C₄	—	13	1	no	—
492	C₂²⋊C₄	—	13	1	no	—
493	C₂²⋊C₄	—	13	1	no	—
494	C₂²⋊C₄	C₄×#261	1	1	yes	characteristic
495	C₂²⋊C₄	C₄×#261	1	1	yes	characteristic
496	C₄²	—	13	1	no	—
497	C₄²	—	13	1	no	—
498	C₄²	—	13	1	no	—
499	C₄²	—	13	1	no	—
500	C₄²	—	13	1	no	—
501	C₄²	—	13	1	no	—
502	C₄²	—	13	1	no	—
503	C₄²	—	13	1	no	—
504	C₄²	C₂²×#261	1	1	yes	characteristic
505	C₄²	C₂²×#261	1	1	yes	characteristic
506	C₁₃	#17337	1	1	yes	characteristic, complemented, Sylow
507	C₂³	—	13	1	no	—
508	C₂³	—	13	1	no	—
509	C₂³	C₂×C₄×#261	1	1	yes	characteristic
510	Q₈	—	26	2	no	—
511	D₄	—	26	2	no	—
512	D₄	—	26	2	no	—
513	D₄	—	26	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	13	1	no	—
517	C₂×C₄	—	13	1	no	—
518	C₂×C₄	—	13	1	no	—
519	C₂×C₄	—	13	2	no	—
520	C₂×C₄	—	13	2	no	—
521	C₂×C₄	—	13	1	no	—
522	C₂×C₄	—	13	1	no	—
523	C₂×C₄	—	13	1	no	—
524	C₂×C₄	—	26	2	no	—
525	C₂×C₄	—	26	2	no	—
526	C₂×C₄	—	26	2	no	—
527	C₂×C₄	—	26	2	no	—
528	C₂×C₄	—	26	2	no	—
529	C₂×C₄	—	26	2	no	—
530	C₂×C₄	—	26	1	no	—
531	C₂×C₄	—	26	1	no	—
532	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
533	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
534	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
535	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
536	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
537	C₂×C₄	C₂³×#261	1	1	yes	characteristic
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	13	4	no	—
541	C₈	—	13	2	no	—
542	C₈	—	13	2	no	—
543	C₈	—	26	2	no	—
544	C₈	—	26	2	no	—
545	C₈	—	26	2	no	—
546	C₈	—	26	2	no	—
547	C₈	—	26	2	no	—
548	C₈	—	26	2	no	—
549	C₈	—	26	2	no	—
550	C₈	—	26	1	no	—
551	C₈	—	26	1	no	—
552	C₈	D₁₃⋊M₁₆	1	2	yes	—
553	C₈	D₁₃⋊M₁₆	1	2	yes	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	13	2	no	—
558	C₂²	—	26	1	no	—
559	C₂²	—	26	1	no	—
560	C₂²	—	26	1	no	—
561	C₂²	—	26	1	no	—
562	C₂²	—	26	1	no	—
563	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	13	2	no	—
570	C₄	—	13	2	no	—
571	C₄	—	13	2	no	—
572	C₄	—	26	1	no	—
573	C₄	—	26	1	no	—
574	C₄	—	26	1	no	—
575	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
576	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
577	C₂	—	4	1	no	—
578	C₂	—	26	2	no	—
579	C₂	—	52	1	no	—
580	C₂	C₄×D₁₃⋊M₁₆	1	1	yes	characteristic
581	C₂	#131×#261	1	1	yes	characteristic
582	C₂	#13131406	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#405	C₄
prime radical	C₂×#6127	C₂×C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	#405	#261
hypocenter	C₁₃	#17337
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #13130060	C₂	semidirect
4. #13130059	C₂	semidirect
5. #13130056	C₂	semidirect
6. #13130055	C₂	semidirect
7. #13130050	C₂	semidirect
8. #13130046	C₂	semidirect
9. #13130045	C₂	semidirect
10. C₈×#6118	C₂	semidirect
11. C₈×#6122	C₂	semidirect
12. #13130034	C₂	semidirect
13. #13130034	C₂	semidirect
14. #13130032	C₂	semidirect
210. #6094	M₁₆	semidirect
211. #6094	M₁₆	semidirect
269. #1057	#131	semidirect
506. C₁₃	#17337	semidirect

Maximal subgroups

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

subgroup	index
#13131647	2
#13130060	2
#13130059	2
#13130056	2
#13130055	2
#13130050	2
#13130046	2
#13130045	2
C₈×#6118	2
C₈×#6122	2
#13130034	2
#13130032	2
#13123258	2
#17337	13