Subgroups — #16792753

Order 3328.

798 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131646	C₂	1	1	yes	maximal, characteristic
2	C₄×#88238	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	#13130054	C₂	1	1	yes	maximal, characteristic, complemented
6	#13130053	C₂	1	1	yes	maximal, characteristic, complemented
7	#13130051	C₂	1	1	yes	maximal, characteristic, complemented
8	#13130048	C₂	1	1	yes	maximal, characteristic, complemented
9	#13130047	C₂	1	1	yes	maximal, characteristic, complemented
10	#13130037	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	M₁₆×#1057	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#11718251	C₂	1	1	yes	maximal, characteristic, complemented
15	#13123796	C₂	1	1	yes	maximal, characteristic
16	C₂×#88238	C₄	1	2	yes	—
17	C₄×#6129	C₂²	1	1	yes	characteristic
18	#11719144	C₄	1	2	yes	—
19	#11719125	C₂²	1	1	yes	characteristic
20	C₄×#6122	C₂²	1	1	yes	characteristic
21	C₄×#6122	C₂²	1	1	yes	characteristic
22	C₄×#6122	C₂²	1	1	yes	characteristic
23	#11719119	C₂²	1	1	yes	characteristic
24	C₂×C₄×#1057	C₂²	1	1	yes	characteristic
25	C₂×C₄×#1057	C₂²	1	1	yes	characteristic
26	C₂×C₄×#1057	C₂²	1	1	yes	characteristic
27	#11719078	C₄	1	2	yes	—
28	#11719072	C₄	1	2	yes	—
29	#11719066	C₄	1	2	yes	—
30	#11719064	C₄	1	2	yes	—
31	#11719062	C₄	1	2	yes	—
32	#11719062	C₄	1	2	yes	—
33	#11719049	C₂²	1	1	yes	characteristic
34	C₄×#6118	C₂²	1	1	yes	characteristic
35	C₄×#6118	C₂²	1	1	yes	characteristic
36	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₃×#435	C₄	1	1	yes	characteristic
38	#11718789	C₄	1	1	yes	characteristic
39	M₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
40	#11718772	C₄	1	1	yes	characteristic
41	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
42	#11718672	C₄	1	1	yes	characteristic
43	#11718494	C₂²	1	1	yes	characteristic
44	#11718489	C₄	1	1	yes	characteristic
45	#11718391	C₄	1	1	yes	characteristic
46	#11718390	C₄	1	1	yes	characteristic
47	#11718379	C₂²	1	1	yes	characteristic
48	#11718379	C₂²	1	1	yes	characteristic
49	#11718368	C₂²	1	1	yes	characteristic
50	#11718362	C₄	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	#11718251	C₂²	1	1	yes	characteristic
58	#11718251	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×#6129	C₂×C₄	1	1	yes	characteristic
68	C₂×#6122	C₂×C₄	1	2	yes	—
69	C₂×#6122	C₂×C₄	1	2	yes	—
70	C₂×#6122	C₂×C₄	1	2	yes	—
71	C₂²×#1057	C₂×C₄	1	2	yes	—
72	C₂²×#1057	C₂×C₄	1	2	yes	—
73	C₂²×#1057	C₂×C₄	1	2	yes	—
74	#88238	—	2	8	no	—
75	C₂×#6118	C₂×C₄	1	2	yes	—
76	C₂×#6118	C₂×C₄	1	2	yes	—
77	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
78	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
80	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
81	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
82	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
83	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
86	C₂×#6099	C₂×C₄	1	1	yes	characteristic
87	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
88	C₂×#6094	C₂×C₄	1	1	yes	characteristic
89	C₂×#6094	C₂×C₄	1	1	yes	characteristic
90	#88146	C₂×C₄	1	1	yes	characteristic
91	#88141	C₂×C₄	1	1	yes	characteristic
92	#88135	C₂×C₄	1	1	yes	characteristic
93	#88135	C₂×C₄	1	1	yes	characteristic
94	#88131	C₂×C₄	1	1	yes	characteristic
95	#88131	C₂×C₄	1	1	yes	characteristic
96	C₄²×D₁₃	C₂³	1	1	yes	characteristic
97	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊#1057	C₂×C₄	1	2	yes	—
99	C₂²⋊#1057	C₂×C₄	1	2	yes	—
100	#88112	C₂×C₄	1	2	yes	—
101	#88112	C₂×C₄	1	2	yes	—
102	#88111	C₂×C₄	1	2	yes	—
103	#88110	C₂×C₄	1	2	yes	—
104	#88110	C₂×C₄	1	2	yes	—
105	#88110	C₂×C₄	1	2	yes	—
106	#88110	C₂×C₄	1	2	yes	—
107	#88110	C₂×C₄	1	2	yes	—
108	C₄⋊#1057	C₂×C₄	1	2	yes	—
109	C₄×#1057	C₂×C₄	1	2	yes	—
110	C₄×#1057	C₂×C₄	1	2	yes	—
111	C₄×#1057	C₂×C₄	1	2	yes	—
112	C₄×#1057	C₂×C₄	1	2	yes	—
113	C₄×#1057	C₂³	1	1	yes	characteristic
114	C₄×#1057	C₂³	1	1	yes	characteristic
115	C₄×#1057	C₂³	1	1	yes	characteristic
116	C₄×#1057	C₂³	1	1	yes	characteristic
117	C₄×#1057	C₂³	1	1	yes	characteristic
118	C₄×#1057	C₂³	1	1	yes	characteristic
119	C₄×#1057	C₂³	1	1	yes	characteristic
120	C₄×#1057	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
122	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
123	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
124	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
125	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
126	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
127	#88060	C₂×C₄	1	1	yes	characteristic
128	#88060	C₂×C₄	1	1	yes	characteristic
129	#88055	C₂×C₄	1	1	yes	characteristic
130	#88055	C₂×C₄	1	1	yes	characteristic
131	#88054	C₂×C₄	1	1	yes	characteristic
132	#88054	C₂×C₄	1	1	yes	characteristic
133	#88054	C₂×C₄	1	1	yes	characteristic
134	#88054	C₂×C₄	1	1	yes	characteristic
135	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
136	C₈×Dic₁₃	C₂×C₄	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	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
141	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
142	#88043	C₂×C₄	1	1	yes	characteristic
143	#17337	—	13	1	no	maximal, Sylow
144	C₂×D₄×C₁₃	C₄²	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₂²⋊D₁₃	C₄²	1	1	yes	characteristic
148	C₂×C₂²⋊D₁₃	C₄²	1	1	yes	characteristic
149	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
153	#6129	—	2	4	no	—
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×Dic₂₆	C₄²	1	1	yes	characteristic
158	#6122	—	2	4	no	—
159	#6122	—	4	2	no	—
160	#6122	M₁₆	1	8	yes	complemented
161	C₂×#1057	—	2	4	no	—
162	C₂×#1057	—	2	4	no	—
163	C₂×#1057	—	4	2	no	—
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	C₂×#1057	C₂²×C₄	1	2	yes	—
171	C₂×#1057	C₂²×C₄	1	2	yes	—
172	#6118	—	2	4	no	—
173	#6118	—	4	2	no	—
174	D₁₃⋊C₈	—	2	4	no	—
175	C₁₃×M₁₆	—	2	2	no	—
176	C₂×C₈×C₁₃	—	2	2	no	—
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	C₂×C₈×C₁₃	C₂²×C₄	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	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
186	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
187	#6103	C₄²	1	1	yes	characteristic
188	#6103	C₄²	1	1	yes	characteristic
189	C₄⋊Dic₁₃	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	C₂²×C₄	1	1	yes	characteristic
202	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
203	#6099	—	2	2	no	—
204	C₂×#1055	—	2	2	no	—
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	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
209	#6094	—	2	2	no	—
210	#6094	—	2	2	no	—
211	#2965	—	13	1	no	—
212	#2965	—	13	1	no	—
213	C₄×#131	—	13	1	no	—
214	#1455	—	13	1	no	—
215	#1455	—	13	1	no	—
216	#1453	—	13	1	no	—
217	#1453	—	13	1	no	—
218	#1452	—	13	1	no	—
219	#1451	—	13	1	no	—
220	#1451	—	13	1	no	—
221	C₈×M₁₆	—	13	1	no	—
222	C₈×M₁₆	—	13	1	no	—
223	C₈×M₁₆	—	13	1	no	—
224	C₈×M₁₆	—	13	1	no	—
225	C₂×#322	—	13	1	no	—
226	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
227	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
228	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
229	D₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
239	C₂²⋊D₁₃	—	2	2	no	—
240	C₂²⋊D₁₃	—	2	2	no	—
241	C₂×Dic₁₃	—	2	2	no	—
242	C₂×Dic₁₃	—	2	2	no	—
243	C₂×Dic₁₃	—	2	2	no	—
244	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
245	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
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×M₁₆	1	4	yes	—
250	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
251	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
252	C₄×D₁₃	—	2	1	no	—
253	C₄×D₁₃	—	2	1	no	—
254	C₄×D₁₃	—	2	2	no	—
255	C₄×D₁₃	—	2	2	no	—
256	Dic₂₆	—	2	2	no	—
257	#1057	—	2	2	no	—
258	#1057	—	2	2	no	—
259	#1057	—	2	2	no	—
260	#1057	—	2	2	no	—
261	#1057	—	2	2	no	—
262	#1057	—	2	2	no	—
263	#1057	C₂×M₁₆	1	4	yes	—
264	#1057	C₂×M₁₆	1	4	yes	—
265	C₈×C₁₃	—	2	1	no	—
266	C₈×C₁₃	—	2	1	no	—
267	C₈×C₁₃	—	2	1	no	—
268	C₈×C₁₃	#131	1	2	yes	complemented
269	#1055	—	2	1	no	—
270	#1055	—	2	1	no	—
271	#1055	—	2	1	no	—
272	#1055	#131	1	2	yes	complemented
273	C₂×#131	—	13	2	no	—
274	C₄×#41	—	13	1	no	—
275	#446	—	13	2	no	—
276	#446	—	13	1	no	—
277	#446	—	13	1	no	—
278	#436	—	13	2	no	—
279	#436	—	13	1	no	—
280	#436	—	13	1	no	—
281	#435	—	13	2	no	—
282	#435	—	13	2	no	—
283	#435	—	13	1	no	—
284	#435	—	13	1	no	—
285	#435	—	13	1	no	—
286	#435	#261	1	1	yes	characteristic
287	#431	—	13	1	no	—
288	#431	—	13	1	no	—
289	#431	—	13	1	no	—
290	#431	—	13	1	no	—
291	#431	—	13	1	no	—
292	#431	—	13	1	no	—
293	#405	—	13	2	no	—
294	#405	—	13	2	no	—
295	#405	—	13	2	no	—
296	C₄×M₁₆	—	13	1	no	—
297	C₄×M₁₆	—	13	1	no	—
298	C₄×M₁₆	—	13	1	no	—
299	C₄×M₁₆	—	13	1	no	—
300	C₄×M₁₆	—	13	1	no	—
301	C₄×M₁₆	—	13	1	no	—
302	C₄×M₁₆	—	13	1	no	—
303	C₂×C₄×C₈	—	13	1	no	—
304	C₂×C₄×C₈	—	13	1	no	—
305	C₂×C₄×C₈	—	13	1	no	—
306	C₂×C₄×C₈	—	13	1	no	—
307	C₂×C₄×C₈	—	13	1	no	—
308	#322	—	13	1	no	—
309	#322	—	13	1	no	—
310	#322	—	13	1	no	—
311	#322	—	13	1	no	—
312	#322	—	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	C₈²	—	13	1	no	—
321	C₈²	—	13	1	no	—
322	C₈²	—	13	1	no	—
323	C₈²	—	13	1	no	—
324	C₂²×C₁₃	—	2	1	no	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	1	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
330	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
331	C₂×D₁₃	—	2	1	no	—
332	C₂×D₁₃	—	2	1	no	—
333	C₂×D₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
339	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
340	Dic₁₃	—	2	1	no	—
341	Dic₁₃	—	2	1	no	—
342	Dic₁₃	—	2	1	no	—
343	Dic₁₃	—	2	1	no	—
344	Dic₁₃	C₄×M₁₆	1	2	yes	—
345	Dic₁₃	C₂²×M₁₆	1	2	yes	—
346	Dic₁₃	#568	1	2	yes	—
347	C₂×#41	—	13	1	no	—
348	#131	—	26	8	no	—
349	C₂×M₁₆	—	13	2	no	—
350	C₂×M₁₆	—	13	2	no	—
351	C₂×M₁₆	—	13	2	no	—
352	C₂×M₁₆	—	13	1	no	—
353	C₂×M₁₆	—	13	2	no	—
354	C₂×M₁₆	—	13	2	no	—
355	C₂×M₁₆	—	13	1	no	—
356	C₂×M₁₆	—	13	1	no	—
357	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
358	C₂²×C₈	—	13	2	no	—
359	C₂²×C₈	—	13	2	no	—
360	C₂²×C₈	—	13	2	no	—
361	C₂²×C₈	—	13	1	no	—
362	C₂²×C₈	—	13	2	no	—
363	C₂²×C₈	C₂×#261	1	1	yes	characteristic
364	C₄×Q₈	—	13	1	no	—
365	C₄×Q₈	—	13	1	no	—
366	C₄×D₄	—	13	1	no	—
367	C₄×D₄	—	13	1	no	—
368	C₄×D₄	—	13	1	no	—
369	C₄×D₄	—	13	1	no	—
370	C₄×D₄	—	13	1	no	—
371	C₄×D₄	C₂×#261	1	1	yes	characteristic
372	#117	—	13	1	no	—
373	#117	—	13	1	no	—
374	#117	—	13	1	no	—
375	C₂×C₄²	—	13	1	no	—
376	C₂×C₄²	—	13	1	no	—
377	C₂×C₄²	—	13	1	no	—
378	C₄⋊C₈	—	13	2	no	—
379	C₄⋊C₈	—	13	2	no	—
380	C₄⋊C₈	—	13	2	no	—
381	C₄⋊C₈	—	13	1	no	—
382	C₄⋊C₈	—	13	1	no	—
383	C₄⋊C₈	—	13	1	no	—
384	C₄⋊C₈	—	13	1	no	—
385	C₄⋊C₈	—	13	1	no	—
386	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
387	C₂²⋊C₈	—	13	2	no	—
388	C₂²⋊C₈	—	13	2	no	—
389	C₂²⋊C₈	—	13	2	no	—
390	C₂²⋊C₈	—	13	1	no	—
391	C₂²⋊C₈	—	13	1	no	—
392	C₂²⋊C₈	—	13	1	no	—
393	C₂²⋊C₈	—	13	1	no	—
394	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
395	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
396	#97	—	13	2	no	—
397	#97	—	13	2	no	—
398	#97	—	13	2	no	—
399	#97	—	13	2	no	—
400	#97	—	13	2	no	—
401	#97	—	13	1	no	—
402	#97	—	13	1	no	—
403	#97	—	13	1	no	—
404	#97	C₂×#261	1	1	yes	characteristic
405	C₄×C₈	—	13	2	no	—
406	C₄×C₈	—	13	2	no	—
407	C₄×C₈	—	13	2	no	—
408	C₄×C₈	—	13	2	no	—
409	C₄×C₈	—	13	1	no	—
410	C₄×C₈	—	13	1	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	C₂×C₁₃	—	2	2	no	—
424	C₂×C₁₃	—	4	1	no	—
425	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
426	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
427	C₂×C₁₃	#2875	1	1	yes	characteristic
428	D₁₃	—	4	1	no	—
429	#41	—	26	4	no	—
430	C₂×Q₈	—	13	1	no	—
431	C₂×D₄	—	13	1	no	—
432	C₂×D₄	—	13	1	no	—
433	C₂×D₄	C₄×#261	1	1	yes	characteristic
434	C₂²×C₄	—	13	1	no	—
435	C₂²×C₄	—	13	1	no	—
436	C₂²×C₄	—	13	1	no	—
437	C₂²×C₄	—	13	1	no	—
438	C₂²×C₄	—	13	1	no	—
439	C₂²×C₄	—	13	1	no	—
440	C₂²×C₄	—	13	1	no	—
441	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
442	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
443	M₁₆	—	2	2	no	—
444	M₁₆	—	13	8	no	—
445	M₁₆	—	26	2	no	—
446	M₁₆	—	26	2	no	—
447	M₁₆	—	26	4	no	—
448	M₁₆	—	26	4	no	—
449	M₁₆	—	26	2	no	—
450	M₁₆	—	52	2	no	—
451	M₁₆	—	52	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	13	2	no	—
454	C₂×C₈	—	13	2	no	—
455	C₂×C₈	—	13	1	no	—
456	C₂×C₈	—	13	2	no	—
457	C₂×C₈	—	13	2	no	—
458	C₂×C₈	—	13	2	no	—
459	C₂×C₈	—	13	2	no	—
460	C₂×C₈	—	13	2	no	—
461	C₂×C₈	—	13	2	no	—
462	C₂×C₈	—	13	1	no	—
463	C₂×C₈	—	13	1	no	—
464	C₂×C₈	—	13	1	no	—
465	C₂×C₈	—	26	2	no	—
466	C₂×C₈	—	26	4	no	—
467	C₂×C₈	—	26	4	no	—
468	C₂×C₈	—	26	4	no	—
469	C₂×C₈	—	52	2	no	—
470	C₂×C₈	C₂²×#261	1	1	yes	characteristic
471	C₂×C₈	C₂²×#261	1	1	yes	characteristic
472	C₂×C₈	C₂²×#261	1	1	yes	characteristic
473	C₂×C₈	C₂²×#261	1	1	yes	characteristic
474	C₄⋊C₄	—	13	1	no	—
475	C₄⋊C₄	—	13	1	no	—
476	C₄⋊C₄	—	13	1	no	—
477	C₄⋊C₄	—	13	1	no	—
478	C₄⋊C₄	—	13	1	no	—
479	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
480	C₂²⋊C₄	—	13	1	no	—
481	C₂²⋊C₄	—	13	1	no	—
482	C₂²⋊C₄	—	13	1	no	—
483	C₂²⋊C₄	—	13	1	no	—
484	C₂²⋊C₄	C₄×#261	1	1	yes	characteristic
485	C₂²⋊C₄	C₄×#261	1	1	yes	characteristic
486	C₄²	—	13	1	no	—
487	C₄²	—	13	1	no	—
488	C₄²	—	13	1	no	—
489	C₄²	—	13	1	no	—
490	C₄²	—	13	1	no	—
491	C₄²	—	13	1	no	—
492	C₄²	—	13	1	no	—
493	C₄²	—	13	1	no	—
494	C₄²	—	13	1	no	—
495	C₄²	C₂²×#261	1	1	yes	characteristic
496	C₁₃	#17337	1	1	yes	characteristic, complemented, Sylow
497	C₂³	—	13	1	no	—
498	C₂³	C₂×C₄×#261	1	1	yes	characteristic
499	C₂³	C₂×C₄×#261	1	1	yes	characteristic
500	Q₈	—	26	2	no	—
501	D₄	—	2	2	no	—
502	D₄	—	26	2	no	—
503	D₄	—	26	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	13	4	no	—
509	C₂×C₄	—	13	1	no	—
510	C₂×C₄	—	13	1	no	—
511	C₂×C₄	—	13	1	no	—
512	C₂×C₄	—	13	1	no	—
513	C₂×C₄	—	13	1	no	—
514	C₂×C₄	—	13	1	no	—
515	C₂×C₄	—	13	1	no	—
516	C₂×C₄	—	26	2	no	—
517	C₂×C₄	—	26	2	no	—
518	C₂×C₄	—	26	2	no	—
519	C₂×C₄	—	26	2	no	—
520	C₂×C₄	—	26	2	no	—
521	C₂×C₄	—	26	1	no	—
522	C₂×C₄	—	26	1	no	—
523	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
524	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
525	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
526	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
527	C₂×C₄	C₂³×#261	1	1	yes	characteristic
528	C₈	—	2	1	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	13	4	no	—
532	C₈	—	13	4	no	—
533	C₈	—	13	2	no	—
534	C₈	—	26	2	no	—
535	C₈	—	26	2	no	—
536	C₈	—	26	2	no	—
537	C₈	—	26	2	no	—
538	C₈	—	26	2	no	—
539	C₈	—	26	2	no	—
540	C₈	—	26	1	no	—
541	C₈	—	26	1	no	—
542	C₈	—	26	1	no	—
543	C₈	#88238	1	2	yes	complemented
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	26	1	no	—
550	C₂²	—	26	1	no	—
551	C₂²	—	26	1	no	—
552	C₂²	M₁₆×#261	1	2	yes	—
553	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	13	2	no	—
559	C₄	—	13	2	no	—
560	C₄	—	13	2	no	—
561	C₄	—	26	1	no	—
562	C₄	—	26	1	no	—
563	C₄	—	26	1	no	—
564	C₄	—	26	1	no	—
565	C₄	C₂×#88238	1	1	yes	characteristic
566	C₄	D₁₃⋊#131	1	1	yes	characteristic
567	C₂	—	2	2	no	—
568	C₂	—	4	1	no	—
569	C₂	—	52	1	no	—
570	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
571	C₂	C₄×#88238	1	1	yes	characteristic
572	C₂	#13131406	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#435	C₄
prime radical	C₂×#6129	C₂×C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	#435	#261
hypocenter	C₁₃	#17337
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

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. #13130054	C₂	semidirect
6. #13130053	C₂	semidirect
7. #13130051	C₂	semidirect
8. #13130048	C₂	semidirect
9. #13130047	C₂	semidirect
10. #13130037	C₂	semidirect
11. C₈×#6122	C₂	semidirect
12. #13130034	C₂	semidirect
13. M₁₆×#1057	C₂	semidirect
14. C₂×#11718251	C₂	semidirect
160. #6122	M₁₆	semidirect
268. C₈×C₁₃	#131	semidirect
272. #1055	#131	semidirect
496. C₁₃	#17337	semidirect
543. C₈	#88238	semidirect

Maximal subgroups

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

subgroup	index
#13131646	2
C₄×#88238	2
#13130060	2
#13130059	2
#13130054	2
#13130053	2
#13130051	2
#13130048	2
#13130047	2
#13130037	2
C₈×#6122	2
#13130034	2
M₁₆×#1057	2
C₂×#11718251	2
#13123796	2
#17337	13