Subgroups — #27353616

Order 13568.

688 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283678	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈×#11719947	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13133236	C₂	1	1	yes	maximal, characteristic
4	#20273567	C₂	1	1	yes	maximal, characteristic, complemented
5	#20273564	C₂	1	1	yes	maximal, characteristic, complemented
6	#20273561	C₂	1	1	yes	maximal, characteristic, complemented
7	#20273556	C₂	1	1	yes	maximal, characteristic, complemented
8	#20273551	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273548	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273545	C₂	1	1	yes	maximal, characteristic, complemented
11	#20273462	C₂	1	1	yes	maximal, characteristic, complemented
12	#20273094	C₂	1	1	yes	maximal, characteristic, complemented
13	#20273094	C₂	1	1	yes	maximal, characteristic, complemented
14	#322×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13133236	C₄	1	1	yes	characteristic
17	C₄×#11719947	C₂²	1	1	yes	characteristic
18	C₄×#11719947	C₂²	1	1	yes	characteristic
19	#16810753	C₂²	1	1	yes	characteristic
20	#16810750	C₂²	1	1	yes	characteristic
21	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
22	#16810747	C₂²	1	1	yes	characteristic
23	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic
24	#16810717	C₄	1	1	yes	characteristic
25	#16810714	C₄	1	1	yes	characteristic
26	#16810714	C₄	1	1	yes	characteristic
27	C₄×#11719923	C₂²	1	1	yes	characteristic
28	C₄×#11719923	C₂²	1	1	yes	characteristic
29	D₈×Dic₅₃	C₄	1	1	yes	characteristic
30	#16810701	C₂²	1	1	yes	characteristic
31	#16810697	—	2	1	no	—
32	#16810692	—	2	1	no	—
33	D₄×#88322	C₂²	1	1	yes	characteristic
34	C₈×C₂²⋊D₅₃	—	2	1	no	—
35	#16810686	—	2	1	no	—
36	#16810675	C₂²	1	1	yes	characteristic
37	#16810675	C₂²	1	1	yes	characteristic
38	#16810673	—	2	1	no	—
39	#16810673	—	2	1	no	—
40	#16810660	C₄	1	1	yes	characteristic
41	#16810616	C₄	1	1	yes	characteristic
42	#16810616	C₄	1	1	yes	characteristic
43	M₁₆×Dic₅₃	—	2	1	no	—
44	C₂×C₈×Dic₅₃	—	2	1	no	—
45	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
48	#16810376	C₂²	1	1	yes	characteristic
49	#16810373	C₂²	1	1	yes	characteristic
50	#16810373	C₂²	1	1	yes	characteristic
51	#16810355	C₂²	1	1	yes	characteristic
52	#16810355	C₂²	1	1	yes	characteristic
53	#16810353	C₂²	1	1	yes	characteristic
54	#16810353	C₂²	1	1	yes	characteristic
55	D₄⋊#88322	C₂²	1	1	yes	characteristic
56	D₄⋊#88322	C₂²	1	1	yes	characteristic
57	#16810345	C₂²	1	1	yes	characteristic
58	#16810345	C₂²	1	1	yes	characteristic
59	#16810344	C₂²	1	1	yes	characteristic
60	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
61	C₅₃×#436	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
63	C₅₃×#335	C₂²	1	1	yes	characteristic
64	C₅₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₅₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₅₃×#322	C₂²	1	1	yes	characteristic
67	C₂×#11719947	C₂×C₄	1	1	yes	characteristic
68	C₂×#11719947	C₂×C₄	1	1	yes	characteristic
69	#13133236	—	2	4	no	—
70	C₂×Dic₂₁₂	C₂×C₄	1	1	yes	characteristic
71	C₂×#11719923	C₂×C₄	1	1	yes	characteristic
72	C₂×#11719923	C₂×C₄	1	1	yes	characteristic
73	C₂×#11719917	—	2	1	no	—
74	C₂²×#88322	—	2	1	no	—
75	C₂×C₈×D₅₃	—	2	1	no	—
76	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
79	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
80	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
81	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
82	#13133182	C₂×C₄	1	1	yes	characteristic
83	#13133182	C₂×C₄	1	1	yes	characteristic
84	D₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
85	D₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
86	C₄×C₂²⋊D₅₃	—	2	1	no	—
87	C₄×C₂²⋊D₅₃	—	2	1	no	—
88	#13133177	—	2	1	no	—
89	#13133177	—	2	1	no	—
90	#13133175	C₂×C₄	1	1	yes	characteristic
91	#13133175	C₂×C₄	1	1	yes	characteristic
92	#13133173	—	2	1	no	—
93	#13133173	—	2	1	no	—
94	C₂×C₄×Dic₅₃	—	2	1	no	—
95	C₂×C₄×Dic₅₃	—	2	1	no	—
96	C₄²×D₅₃	C₂³	1	1	yes	characteristic
97	#13133151	C₂×C₄	1	1	yes	characteristic
98	#13133148	C₂×C₄	1	1	yes	characteristic
99	#13133148	C₂×C₄	1	1	yes	characteristic
100	C₄⋊#88322	C₂³	1	1	yes	characteristic
101	C₄⋊#88322	C₂³	1	1	yes	characteristic
102	#13133146	—	2	1	no	—
103	#13133146	—	2	1	no	—
104	#13133146	—	2	1	no	—
105	#13133146	—	2	1	no	—
106	#13133142	C₂×C₄	1	1	yes	characteristic
107	#13133142	C₂×C₄	1	1	yes	characteristic
108	#13133140	C₂×C₄	1	1	yes	characteristic
109	#13133140	C₂×C₄	1	1	yes	characteristic
110	#13133138	C₂×C₄	1	1	yes	characteristic
111	#13133138	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊#88322	—	2	1	no	—
113	C₂²⋊#88322	—	2	1	no	—
114	#13133129	—	2	1	no	—
115	#13133129	—	2	1	no	—
116	#13133127	—	2	1	no	—
117	#13133127	—	2	1	no	—
118	C₄×#88322	C₂³	1	1	yes	characteristic
119	C₄×#88322	C₂³	1	1	yes	characteristic
120	C₄×#88322	C₂³	1	1	yes	characteristic
121	C₈×Dic₅₃	—	2	1	no	—
122	C₈×Dic₅₃	—	2	1	no	—
123	C₈×Dic₅₃	—	2	1	no	—
124	C₈×Dic₅₃	—	2	1	no	—
125	C₈×Dic₅₃	—	2	1	no	—
126	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
127	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
128	C₈×Dic₅₃	D₄	1	1	yes	characteristic
129	C₈×Dic₅₃	D₄	1	1	yes	characteristic
130	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic
131	C₂×M₁₆×C₅₃	—	2	1	no	—
132	C₂²×C₈×C₅₃	—	2	1	no	—
133	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
134	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
135	#107×C₅₃	C₂×C₄	1	1	yes	characteristic
136	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
138	#102×C₅₃	C₂×C₄	1	1	yes	characteristic
139	#102×C₅₃	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₅₃	—	2	1	no	—
141	C₂²⋊C₈×C₅₃	—	2	1	no	—
142	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅₃	—	2	1	no	—
148	C₂²×C₄×C₅₃	—	2	1	no	—
149	C₂×C₂²⋊D₅₃	—	2	1	no	—
150	C₂×C₂²⋊D₅₃	—	2	1	no	—
151	C₂²×Dic₅₃	—	2	1	no	—
152	C₂²×Dic₅₃	—	2	1	no	—
153	C₂²×Dic₅₃	—	2	1	no	—
154	C₂²×Dic₅₃	—	2	1	no	—
155	#11719947	—	2	2	no	—
156	#11719947	—	2	2	no	—
157	#11719947	—	2	2	no	—
158	#11719947	M₁₆	1	4	yes	complemented
159	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
162	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
163	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
164	D₈×C₅₃	—	2	2	no	—
165	M₁₆×C₅₃	—	4	2	no	—
166	C₂×C₈×C₅₃	—	2	1	no	—
167	C₂×C₈×C₅₃	—	2	1	no	—
168	C₂×C₈×C₅₃	—	2	1	no	—
169	C₂×C₈×C₅₃	—	4	2	no	—
170	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
174	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
175	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
176	C₂²⋊C₄×C₅₃	—	2	1	no	—
177	C₂²⋊C₄×C₅₃	—	2	1	no	—
178	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
179	C₂²⋊Dic₅₃	—	2	1	no	—
180	C₂²⋊Dic₅₃	—	2	1	no	—
181	#11719923	—	2	2	no	—
182	#11719923	—	2	2	no	—
183	#11719921	—	2	1	no	—
184	#11719921	—	2	1	no	—
185	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
186	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
187	#11719919	—	2	1	no	—
188	#11719919	—	2	1	no	—
189	#11719919	—	2	1	no	—
190	#11719919	—	2	1	no	—
191	C₄×Dic₅₃	—	2	1	no	—
192	C₄×Dic₅₃	—	2	1	no	—
193	C₄×Dic₅₃	—	2	1	no	—
194	C₄×Dic₅₃	—	2	1	no	—
195	C₄×Dic₅₃	—	2	1	no	—
196	C₄×Dic₅₃	—	2	1	no	—
197	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
198	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
199	C₄×Dic₅₃	#41	1	1	yes	characteristic
200	#11719917	—	4	2	no	—
201	C₂×#88322	—	2	1	no	—
202	C₂×#88322	—	2	1	no	—
203	C₂×#88322	—	2	1	no	—
204	C₂×#88322	—	4	2	no	—
205	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
206	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
207	C₂×#88322	C₂×D₄	1	1	yes	characteristic
208	C₂×#88322	C₂×D₄	1	1	yes	characteristic
209	Dic₂₁₂	—	2	2	no	—
210	C₈×D₅₃	—	2	2	no	—
211	C₈×D₅₃	—	2	2	no	—
212	C₈×D₅₃	—	2	2	no	—
213	C₈×D₅₃	—	2	2	no	—
214	C₈×D₅₃	—	4	2	no	—
215	C₂³×C₅₃	—	2	1	no	—
216	C₂³×C₅₃	—	2	1	no	—
217	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
218	D₄×C₅₃	—	2	1	no	—
219	D₄×C₅₃	—	2	1	no	—
220	D₄×C₅₃	—	2	1	no	—
221	D₄×C₅₃	C₂×M₁₆	1	2	yes	—
222	C₂×C₄×C₅₃	—	2	1	no	—
223	C₂×C₄×C₅₃	—	2	1	no	—
224	C₂×C₄×C₅₃	—	4	1	no	—
225	C₂×C₄×C₅₃	—	4	1	no	—
226	C₂×C₄×C₅₃	—	4	1	no	—
227	C₂×C₄×C₅₃	—	4	1	no	—
228	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
231	C₂²⋊D₅₃	—	2	4	no	—
232	C₂²⋊D₅₃	—	4	2	no	—
233	C₂×Dic₅₃	—	2	1	no	—
234	C₂×Dic₅₃	—	2	4	no	—
235	C₂×Dic₅₃	—	2	1	no	—
236	C₂×Dic₅₃	—	2	1	no	—
237	C₂×Dic₅₃	—	2	1	no	—
238	C₂×Dic₅₃	—	4	2	no	—
239	C₂×Dic₅₃	—	4	2	no	—
240	C₂×Dic₅₃	—	4	2	no	—
241	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
242	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
243	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
244	C₄×D₅₃	—	2	1	no	—
245	C₄×D₅₃	—	2	1	no	—
246	C₄×D₅₃	—	2	2	no	—
247	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
248	C₄×D₅₃	#131	1	2	yes	—
249	Dic₁₀₆	—	2	1	no	—
250	Dic₁₀₆	—	2	1	no	—
251	Dic₁₀₆	—	2	1	no	—
252	Dic₁₀₆	C₂×M₁₆	1	2	yes	—
253	C₈×C₅₃	—	2	1	no	—
254	C₈×C₅₃	—	2	1	no	—
255	C₈×C₅₃	—	2	1	no	—
256	C₈×C₅₃	—	4	1	no	—
257	C₈×C₅₃	—	4	1	no	—
258	C₈×C₅₃	—	4	1	no	—
259	C₈×C₅₃	#135	1	2	yes	complemented
260	#88322	—	2	1	no	—
261	#88322	—	2	1	no	—
262	#88322	—	2	1	no	—
263	#88322	—	4	1	no	—
264	#88322	—	4	1	no	—
265	#88322	—	4	1	no	—
266	#88322	#135	1	2	yes	complemented
267	#17863	—	53	1	no	maximal, Sylow
268	C₂²×C₅₃	—	2	2	no	—
269	C₂²×C₅₃	—	4	1	no	—
270	C₂²×C₅₃	—	4	1	no	—
271	C₂²×C₅₃	—	4	1	no	—
272	C₂²×C₅₃	—	4	1	no	—
273	C₂²×C₅₃	—	4	1	no	—
274	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
275	C₂×D₅₃	—	2	1	no	—
276	C₂×D₅₃	—	2	1	no	—
277	C₂×D₅₃	#435	1	2	yes	—
278	C₄×C₅₃	—	2	1	no	—
279	C₄×C₅₃	—	4	1	no	—
280	C₄×C₅₃	—	4	1	no	—
281	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
282	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
283	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
284	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
285	Dic₅₃	—	2	2	no	—
286	Dic₅₃	—	2	1	no	—
287	Dic₅₃	—	4	1	no	—
288	Dic₅₃	—	4	1	no	—
289	Dic₅₃	—	4	1	no	—
290	Dic₅₃	#435	1	2	yes	—
291	Dic₅₃	#444	1	2	yes	—
292	#2965	—	53	1	no	—
293	C₈×#41	—	53	1	no	—
294	C₄×#135	—	53	1	no	—
295	#1584	—	53	1	no	—
296	#1584	—	53	1	no	—
297	#1583	—	53	1	no	—
298	#1583	—	53	1	no	—
299	#1582	—	53	1	no	—
300	#1582	—	53	1	no	—
301	#1581	—	53	1	no	—
302	#1581	D₅₃	1	1	yes	characteristic, complemented
303	#1564	—	53	1	no	—
304	#1476	—	53	1	no	—
305	#1476	—	53	1	no	—
306	C₂×#322	—	53	1	no	—
307	C₂×C₅₃	—	4	2	no	—
308	C₂×C₅₃	—	8	1	no	—
309	C₂×C₅₃	C₂×#435	1	1	yes	characteristic
310	C₂×C₅₃	C₄×#135	1	1	yes	characteristic
311	C₂×C₅₃	C₂×#444	1	1	yes	characteristic
312	D₅₃	—	2	2	no	—
313	C₂×#135	—	53	1	no	—
314	C₄×#41	—	53	1	no	—
315	C₄×#41	—	53	1	no	—
316	#446	—	53	1	no	—
317	#446	—	53	1	no	—
318	C₈×Q₈	—	53	1	no	—
319	C₈×Q₈	—	53	1	no	—
320	C₄×Q₁₆	—	53	1	no	—
321	C₄×Q₁₆	—	53	1	no	—
322	C₄×SD₁₆	—	53	1	no	—
323	C₄×SD₁₆	—	53	1	no	—
324	C₄×SD₁₆	—	53	1	no	—
325	C₄×SD₁₆	—	53	1	no	—
326	C₄×D₈	—	53	1	no	—
327	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic
328	#436	—	53	1	no	—
329	#436	C₂×D₅₃	1	1	yes	characteristic
330	#435	—	106	1	no	—
331	#435	—	106	1	no	—
332	C₈×D₄	—	53	1	no	—
333	C₈×D₄	—	106	1	no	—
334	C₈×D₄	—	106	1	no	—
335	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
336	#431	—	53	1	no	—
337	#431	—	53	1	no	—
338	#431	—	106	1	no	—
339	#431	—	106	1	no	—
340	#427	—	53	1	no	—
341	#416	—	53	1	no	—
342	#416	—	53	1	no	—
343	C₄×M₁₆	—	106	1	no	—
344	C₂×C₄×C₈	—	53	1	no	—
345	C₂×C₄×C₈	—	53	1	no	—
346	C₂×C₄×C₈	—	53	1	no	—
347	C₂×C₄×C₈	—	106	1	no	—
348	#335	—	53	1	no	—
349	#335	C₂×D₅₃	1	1	yes	characteristic
350	#334	—	53	1	no	—
351	#334	—	53	1	no	—
352	Q₈⋊C₈	—	53	1	no	—
353	Q₈⋊C₈	—	53	1	no	—
354	Q₈⋊C₈	—	53	1	no	—
355	Q₈⋊C₈	—	53	1	no	—
356	D₄⋊C₈	—	53	1	no	—
357	D₄⋊C₈	—	53	1	no	—
358	D₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
359	D₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
360	#322	—	53	1	no	—
361	#322	—	53	1	no	—
362	#322	—	53	1	no	—
363	#322	C₂×D₅₃	1	1	yes	characteristic
364	C₅₃	#17863	1	1	yes	characteristic, complemented, Sylow
365	C₂×#41	—	53	1	no	—
366	C₂×#41	—	53	1	no	—
367	#135	—	106	4	no	—
368	C₂×Q₁₆	—	53	1	no	—
369	C₂×SD₁₆	—	53	1	no	—
370	C₂×SD₁₆	—	53	1	no	—
371	C₂×D₈	C₄×D₅₃	1	1	yes	characteristic
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	106	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	53	1	no	—
376	C₂²×C₈	—	53	1	no	—
377	C₂²×C₈	—	53	1	no	—
378	C₂²×C₈	—	53	1	no	—
379	C₂²×C₈	—	106	1	no	—
380	C₂²×C₈	—	106	1	no	—
381	C₄×Q₈	—	53	1	no	—
382	C₄×Q₈	—	53	1	no	—
383	C₄×Q₈	—	53	1	no	—
384	C₄×Q₈	—	53	1	no	—
385	C₄×D₄	—	53	1	no	—
386	C₄×D₄	—	53	1	no	—
387	C₄×D₄	—	106	1	no	—
388	C₄×D₄	—	106	1	no	—
389	C₄×D₄	—	106	1	no	—
390	C₄×D₄	—	106	1	no	—
391	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
392	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
393	#117	—	53	1	no	—
394	#117	—	53	1	no	—
395	#117	—	106	1	no	—
396	#117	—	106	1	no	—
397	C₂×C₄²	—	53	1	no	—
398	C₂×C₄²	—	106	1	no	—
399	C₂×C₄²	—	106	1	no	—
400	#107	—	53	1	no	—
401	#107	C₄×D₅₃	1	1	yes	characteristic
402	#106	—	53	1	no	—
403	#106	—	53	1	no	—
404	C₄⋊C₈	—	53	1	no	—
405	C₄⋊C₈	—	53	1	no	—
406	C₄⋊C₈	—	106	1	no	—
407	C₄⋊C₈	—	106	1	no	—
408	C₄⋊C₈	—	106	1	no	—
409	C₄⋊C₈	—	106	1	no	—
410	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
411	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
412	#103	—	53	1	no	—
413	#103	—	53	1	no	—
414	#103	—	53	1	no	—
415	#103	—	53	1	no	—
416	#102	—	53	1	no	—
417	#102	—	53	1	no	—
418	#102	C₄×D₅₃	1	1	yes	characteristic
419	#102	C₄×D₅₃	1	1	yes	characteristic
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	C₂²⋊C₈	—	106	1	no	—
423	C₂²⋊C₈	—	106	1	no	—
424	C₂²⋊C₈	—	106	1	no	—
425	C₂²⋊C₈	—	106	1	no	—
426	#97	—	106	1	no	—
427	#97	—	106	1	no	—
428	C₄×C₈	—	53	1	no	—
429	C₄×C₈	—	53	1	no	—
430	C₄×C₈	—	53	1	no	—
431	C₄×C₈	—	53	1	no	—
432	C₄×C₈	—	53	1	no	—
433	C₄×C₈	—	53	1	no	—
434	C₄×C₈	—	53	1	no	—
435	C₄×C₈	—	106	1	no	—
436	C₄×C₈	—	106	1	no	—
437	C₄×C₈	—	106	1	no	—
438	C₄×C₈	—	106	1	no	—
439	C₄×C₈	—	106	1	no	—
440	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
441	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
442	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
443	#41	—	53	4	no	—
444	#41	—	106	2	no	—
445	#41	—	106	2	no	—
446	#41	—	106	2	no	—
447	C₂×Q₈	—	53	1	no	—
448	C₂×Q₈	—	53	1	no	—
449	C₂×D₄	—	106	1	no	—
450	C₂×D₄	—	106	1	no	—
451	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
452	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	53	1	no	—
456	C₂²×C₄	—	53	1	no	—
457	C₂²×C₄	—	53	1	no	—
458	C₂²×C₄	—	106	1	no	—
459	C₂²×C₄	—	106	1	no	—
460	C₂²×C₄	—	106	1	no	—
461	C₂²×C₄	—	106	1	no	—
462	Q₁₆	—	106	2	no	—
463	SD₁₆	—	106	2	no	—
464	SD₁₆	—	106	2	no	—
465	D₈	—	2	2	no	—
466	M₁₆	—	4	2	no	—
467	M₁₆	—	212	2	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	4	2	no	—
472	C₂×C₈	—	53	1	no	—
473	C₂×C₈	—	53	1	no	—
474	C₂×C₈	—	53	1	no	—
475	C₂×C₈	—	53	1	no	—
476	C₂×C₈	—	106	2	no	—
477	C₂×C₈	—	106	2	no	—
478	C₂×C₈	—	106	2	no	—
479	C₂×C₈	—	106	2	no	—
480	C₂×C₈	—	106	1	no	—
481	C₂×C₈	—	106	1	no	—
482	C₂×C₈	—	106	1	no	—
483	C₂×C₈	—	212	2	no	—
484	C₂×C₈	—	212	2	no	—
485	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
486	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
487	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
488	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
489	C₄⋊C₄	—	53	1	no	—
490	C₄⋊C₄	—	53	1	no	—
491	C₄⋊C₄	—	106	1	no	—
492	C₄⋊C₄	—	106	1	no	—
493	C₄⋊C₄	—	106	1	no	—
494	C₄⋊C₄	—	106	1	no	—
495	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
496	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	106	1	no	—
500	C₂²⋊C₄	—	106	1	no	—
501	C₂²⋊C₄	—	106	1	no	—
502	C₂²⋊C₄	—	106	1	no	—
503	C₄²	—	53	1	no	—
504	C₄²	—	53	1	no	—
505	C₄²	—	53	1	no	—
506	C₄²	—	106	1	no	—
507	C₄²	—	106	1	no	—
508	C₄²	—	106	1	no	—
509	C₄²	—	106	1	no	—
510	C₄²	—	106	1	no	—
511	C₄²	—	106	1	no	—
512	C₄²	C₂³×D₅₃	1	1	yes	characteristic
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	53	1	no	—
516	Q₈	—	53	2	no	—
517	Q₈	—	106	1	no	—
518	Q₈	—	106	1	no	—
519	Q₈	—	106	1	no	—
520	D₄	—	2	1	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	106	4	no	—
524	D₄	—	212	2	no	—
525	D₄	M₁₆×D₅₃	1	2	yes	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	53	1	no	—
533	C₂×C₄	—	53	1	no	—
534	C₂×C₄	—	53	2	no	—
535	C₂×C₄	—	53	2	no	—
536	C₂×C₄	—	53	1	no	—
537	C₂×C₄	—	106	2	no	—
538	C₂×C₄	—	106	4	no	—
539	C₂×C₄	—	106	1	no	—
540	C₂×C₄	—	106	1	no	—
541	C₂×C₄	—	106	1	no	—
542	C₂×C₄	—	106	1	no	—
543	C₂×C₄	—	106	1	no	—
544	C₂×C₄	—	106	1	no	—
545	C₂×C₄	—	212	2	no	—
546	C₂×C₄	—	212	2	no	—
547	C₂×C₄	—	212	2	no	—
548	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
549	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
550	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
551	C₈	—	2	1	no	—
552	C₈	—	2	1	no	—
553	C₈	—	2	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	4	1	no	—
557	C₈	—	53	2	no	—
558	C₈	—	106	1	no	—
559	C₈	—	106	1	no	—
560	C₈	—	106	1	no	—
561	C₈	—	212	1	no	—
562	C₈	—	212	1	no	—
563	C₈	—	212	1	no	—
564	C₈	#13133236	1	2	yes	complemented
565	C₂²	—	2	2	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	53	2	no	—
572	C₂²	—	106	1	no	—
573	C₂²	—	106	1	no	—
574	C₂²	C₄×D₄×D₅₃	1	1	yes	characteristic
575	C₄	—	2	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	53	2	no	—
579	C₄	—	53	2	no	—
580	C₄	—	106	1	no	—
581	C₄	—	106	2	no	—
582	C₄	—	212	1	no	—
583	C₄	—	212	1	no	—
584	C₄	—	212	1	no	—
585	C₄	C₂×M₁₆×D₅₃	1	1	yes	characteristic
586	C₄	#131×D₅₃	1	1	yes	characteristic
587	C₄	#135×D₅₃	1	1	yes	characteristic
588	C₄	C₂×#13133236	1	1	yes	characteristic
589	C₂	—	4	2	no	—
590	C₂	—	8	1	no	—
591	C₂	—	106	2	no	—
592	C₂	#435×D₅₃	1	1	yes	characteristic
593	C₂	C₄×#13133236	1	1	yes	characteristic
594	C₂	#444×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1581	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂×#13133236	C₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	#1581	D₅₃
hypocenter	C₅₃	#17863
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1581

Complements

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

N	H ≅ G/N	type
1. #20283678	C₂	semidirect
2. C₈×#11719947	C₂	semidirect
4. #20273567	C₂	semidirect
5. #20273564	C₂	semidirect
6. #20273561	C₂	semidirect
7. #20273556	C₂	semidirect
8. #20273551	C₂	semidirect
9. #20273548	C₂	semidirect
10. #20273545	C₂	semidirect
11. #20273462	C₂	semidirect
12. #20273094	C₂	semidirect
13. #20273094	C₂	semidirect
14. #322×D₅₃	C₂	semidirect
15. C₅₃×#1581	C₂	semidirect
158. #11719947	M₁₆	semidirect
259. C₈×C₅₃	#135	semidirect
266. #88322	#135	semidirect
302. #1581	D₅₃	semidirect
364. C₅₃	#17863	semidirect
564. C₈	#13133236	semidirect

Maximal subgroups

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

subgroup	index
#20283678	2
C₈×#11719947	2
C₄×#13133236	2
#20273567	2
#20273564	2
#20273561	2
#20273556	2
#20273551	2
#20273548	2
#20273545	2
#20273462	2
#20273094	2
#322×D₅₃	2
C₅₃×#1581	2
#17863	53