Subgroups — D₅₃×#3081 #28251643

Order 13568.

2234 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#544×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#518×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#20284549	C₂	1	1	yes	maximal, characteristic, complemented
4	#20284548	C₂	1	1	yes	maximal, characteristic, complemented
5	#20284547	C₂	1	1	yes	maximal, characteristic, complemented
6	#20284546	C₂	1	1	yes	maximal, characteristic, complemented
7	#20284545	C₂	1	2	yes	maximal, complemented
8	#20284544	C₂	1	1	yes	maximal, characteristic, complemented
9	#20284543	C₂	1	2	yes	maximal, complemented
10	#20284542	C₂	1	1	yes	maximal, characteristic, complemented
11	#20284541	C₂	1	2	yes	maximal, complemented
12	#20284540	C₂	1	1	yes	maximal, characteristic, complemented
13	#20284539	C₂	1	2	yes	maximal, complemented
14	#478×D₅₃	C₂	1	2	yes	maximal, complemented
15	#478×D₅₃	C₂	1	2	yes	maximal, complemented
16	#476×D₅₃	C₂	1	2	yes	maximal, complemented
17	#474×D₅₃	C₂	1	2	yes	maximal, complemented
18	#428×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#427×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#424×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#418×D₅₃	C₂	1	1	yes	maximal, characteristic
22	C₂×#102×D₅₃	C₂	1	1	yes	maximal, characteristic
23	C₅₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
25	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
26	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
27	#16811254	C₂²	1	1	yes	characteristic, complemented
28	#16811253	—	2	1	no	—
29	#16811253	C₂²	1	2	yes	complemented
30	#16811252	—	2	2	no	—
31	#16811251	C₂²	1	1	yes	characteristic, complemented
32	#16811251	C₂²	1	1	yes	characteristic, complemented
33	#16811250	—	2	1	no	—
34	#16811250	C₂²	1	2	yes	complemented
35	C₄⋊Q₈×D₅₃	—	2	1	no	—
36	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	complemented
37	#125×D₅₃	—	2	1	no	—
38	#125×D₅₃	C₂²	1	2	yes	complemented
39	C₂²⋊Q₈×D₅₃	—	2	2	no	—
40	#16811098	C₂²	1	1	yes	characteristic
41	#16811097	C₂²	1	1	yes	characteristic
42	#16811097	C₂²	1	1	yes	characteristic
43	#16811096	—	2	2	no	—
44	#16811095	—	2	1	no	—
45	#16811095	—	2	1	no	—
46	#16811095	C₂²	1	2	yes	—
47	#16811095	C₂²	1	2	yes	—
48	C₄×D₄×D₅₃	—	2	1	no	—
49	C₄×D₄×D₅₃	—	2	1	no	—
50	C₄×D₄×D₅₃	C₂²	1	2	yes	—
51	C₄×D₄×D₅₃	C₂²	1	2	yes	—
52	#117×D₅₃	C₂²	1	1	yes	characteristic
53	#117×D₅₃	C₂²	1	1	yes	characteristic
54	#117×D₅₃	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×D₅₃	—	2	2	no	—
57	#16810926	C₂²	1	2	yes	complemented
58	#16810926	C₂²	1	2	yes	complemented
59	#16810925	C₂²	1	2	yes	complemented
60	#16810925	C₂²	1	2	yes	complemented
61	#16810924	C₂²	1	2	yes	complemented
62	#16810924	C₂²	1	2	yes	complemented
63	#16810923	C₂²	1	2	yes	complemented
64	#16810923	C₂²	1	2	yes	complemented
65	#16810922	C₂²	1	2	yes	complemented
66	#16810922	C₂²	1	2	yes	complemented
67	#16810921	C₂²	1	2	yes	complemented
68	#16810921	C₂²	1	2	yes	complemented
69	#16810920	C₂²	1	2	yes	complemented
70	#16810920	C₂²	1	2	yes	complemented
71	#16810914	C₂²	1	2	yes	complemented
72	#16810913	C₂²	1	2	yes	complemented
73	#16810912	C₂²	1	2	yes	complemented
74	#16810912	C₂²	1	2	yes	complemented
75	#16810911	C₂²	1	2	yes	complemented
76	#16810911	C₂²	1	2	yes	complemented
77	#16810910	C₂²	1	2	yes	complemented
78	#16810904	C₂²	1	2	yes	complemented
79	#16810903	C₂²	1	2	yes	complemented
80	#16810902	C₂²	1	2	yes	complemented
81	#16810902	C₂²	1	2	yes	complemented
82	#16810901	C₂²	1	2	yes	complemented
83	#16810901	C₂²	1	2	yes	complemented
84	#16810900	C₂²	1	2	yes	complemented
85	#16810666	C₂²	1	1	yes	characteristic, complemented
86	#16810665	C₂²	1	1	yes	characteristic, complemented
87	#16810664	C₂²	1	2	yes	complemented
88	#16810663	C₂²	1	1	yes	characteristic, complemented
89	#16810662	C₂²	1	2	yes	complemented
90	#16810661	C₂²	1	1	yes	characteristic, complemented
91	#16810660	C₂²	1	1	yes	characteristic, complemented
92	#16810660	C₂²	1	1	yes	characteristic, complemented
93	#16810659	C₂²	1	1	yes	characteristic, complemented
94	#16810659	C₂²	1	1	yes	characteristic, complemented
95	#16810658	C₂²	1	1	yes	characteristic, complemented
96	#16810658	C₂²	1	1	yes	characteristic, complemented
97	#107×D₅₃	C₂²	1	1	yes	characteristic, complemented
98	#107×D₅₃	C₂²	1	2	yes	complemented
99	#107×D₅₃	C₂²	1	1	yes	characteristic, complemented
100	#106×D₅₃	C₂²	1	1	yes	characteristic, complemented
101	#106×D₅₃	C₂²	1	2	yes	complemented
102	#106×D₅₃	C₂²	1	1	yes	characteristic, complemented
103	#16810651	C₂²	1	1	yes	characteristic, complemented
104	#16810650	C₂²	1	1	yes	characteristic, complemented
105	#16810649	C₂²	1	1	yes	characteristic, complemented
106	#16810648	C₂²	1	2	yes	complemented
107	#16810648	C₂²	1	2	yes	complemented
108	C₄⋊C₈×D₅₃	C₂²	1	2	yes	complemented
109	C₄⋊C₈×D₅₃	C₂²	1	2	yes	complemented
110	#16810629	C₂²	1	1	yes	characteristic
111	#16810628	C₂²	1	1	yes	characteristic
112	#16810627	C₂²	1	1	yes	characteristic
113	#16810626	C₂²	1	2	yes	—
114	#16810626	C₂²	1	2	yes	—
115	C₂×#13133139	C₂²	1	1	yes	characteristic
116	C₂×#13133138	C₂²	1	1	yes	characteristic
117	C₂×#13133137	C₂²	1	1	yes	characteristic
118	#102×D₅₃	C₂²	1	2	yes	—
119	#102×D₅₃	C₂²	1	2	yes	—
120	#102×D₅₃	C₂²	1	2	yes	—
121	#102×D₅₃	C₂²	1	2	yes	—
122	#102×D₅₃	C₂²	1	2	yes	—
123	#102×D₅₃	C₂²	1	2	yes	—
124	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#518	C₂²	1	1	yes	characteristic
126	C₅₃×#478	C₂²	1	2	yes	complemented
127	C₅₃×#478	C₂²	1	2	yes	complemented
128	C₅₃×#476	C₂²	1	2	yes	complemented
129	C₅₃×#474	C₂²	1	2	yes	complemented
130	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#418	C₂²	1	1	yes	characteristic
134	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
135	C₂⁴×D₅₃	—	2	1	no	—
136	C₂×Q₈×D₅₃	—	2	2	no	—
137	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
138	C₂²×C₂²⋊D₅₃	—	2	1	no	—
139	C₂×D₄×D₅₃	—	2	1	no	—
140	C₂×D₄×D₅₃	—	2	1	no	—
141	C₂×D₄×D₅₃	—	2	4	no	—
142	C₂×D₄×D₅₃	Q₈	1	8	yes	complemented
143	C₂×D₄×D₅₃	C₂³	1	2	yes	—
144	C₂×D₄×D₅₃	C₂³	1	2	yes	—
145	C₂²×C₄×D₅₃	—	2	1	no	—
146	C₂²×C₄×D₅₃	—	2	2	no	—
147	C₂²×C₄×D₅₃	—	2	2	no	—
148	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
149	C₂×#11719917	C₂³	1	1	yes	characteristic
150	C₂×#11719912	C₂³	1	2	yes	—
151	M₁₆×D₅₃	—	2	4	no	—
152	C₂²×#88322	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₅₃	—	2	4	no	—
154	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
156	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
157	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
158	C₂×C₈×D₅₃	C₂³	1	2	yes	—
159	#13133217	—	2	1	no	—
160	#13133217	C₂³	1	2	yes	complemented
161	#13133216	—	2	1	no	—
162	#13133216	—	2	1	no	—
163	#13133216	—	2	2	no	—
164	#13133216	—	2	2	no	—
165	#13133216	C₂³	1	2	yes	complemented
166	#13133216	C₂³	1	2	yes	complemented
167	#13133215	—	2	2	no	—
168	#13133215	—	2	2	no	—
169	#13133209	—	2	1	no	—
170	#13133209	C₂³	1	2	yes	complemented
171	#13133208	—	2	1	no	—
172	#13133208	—	2	1	no	—
173	#13133208	C₂³	1	2	yes	complemented
174	#13133208	C₂³	1	2	yes	complemented
175	#13133207	—	2	2	no	—
176	#13133207	—	2	2	no	—
177	#13133207	—	2	2	no	—
178	#13133207	—	2	2	no	—
179	#13133197	—	2	2	no	—
180	#13133196	—	2	2	no	—
181	#13133195	—	2	2	no	—
182	#13133195	—	2	2	no	—
183	#13133194	—	2	2	no	—
184	#13133194	—	2	2	no	—
185	#13133193	—	2	2	no	—
186	C₄×D₂₁₂	—	2	1	no	—
187	C₄×D₂₁₂	—	2	1	no	—
188	C₄×D₂₁₂	C₂³	1	2	yes	—
189	C₄×D₂₁₂	C₂³	1	2	yes	—
190	D₄×Dic₅₃	—	2	1	no	—
191	D₄×Dic₅₃	—	2	1	no	—
192	D₄×Dic₅₃	C₂³	1	2	yes	—
193	D₄×Dic₅₃	C₂³	1	2	yes	—
194	#13133179	—	2	1	no	—
195	#13133179	—	2	1	no	—
196	#13133179	C₂³	1	2	yes	—
197	#13133179	C₂³	1	2	yes	—
198	C₄×C₂²⋊D₅₃	—	2	2	no	—
199	C₄×C₂²⋊D₅₃	—	2	2	no	—
200	C₄×C₂²⋊D₅₃	—	2	2	no	—
201	C₄×C₂²⋊D₅₃	—	2	2	no	—
202	#13133177	—	2	2	no	—
203	#13133177	—	2	2	no	—
204	#13133177	—	2	2	no	—
205	#13133177	—	2	2	no	—
206	#13133176	C₂³	1	1	yes	characteristic
207	#13133176	C₂³	1	1	yes	characteristic
208	#13133176	C₂³	1	1	yes	characteristic
209	#13133175	D₄	1	1	yes	characteristic
210	#13133175	D₄	1	1	yes	characteristic
211	#13133175	C₂³	1	1	yes	characteristic
212	#13133175	C₂³	1	1	yes	characteristic
213	#13133175	C₂³	1	1	yes	characteristic
214	#13133175	C₂³	1	1	yes	characteristic
215	#13133174	—	2	1	no	—
216	#13133174	—	2	1	no	—
217	#13133174	C₂³	1	2	yes	—
218	#13133173	—	2	1	no	—
219	#13133173	—	2	1	no	—
220	#13133173	D₄	1	2	yes	—
221	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
222	C₂×#11719919	—	2	1	no	—
223	C₄⋊C₄×D₅₃	—	2	1	no	—
224	C₄⋊C₄×D₅₃	—	2	1	no	—
225	C₄⋊C₄×D₅₃	—	2	2	no	—
226	C₄⋊C₄×D₅₃	—	2	2	no	—
227	C₄⋊C₄×D₅₃	—	2	2	no	—
228	C₄⋊C₄×D₅₃	D₄	1	1	yes	characteristic
229	C₄⋊C₄×D₅₃	D₄	1	1	yes	characteristic
230	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
231	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
232	C₄⋊C₄×D₅₃	C₂³	1	1	yes	characteristic
233	C₄⋊C₄×D₅₃	C₂³	1	1	yes	characteristic
234	C₄⋊C₄×D₅₃	C₂³	1	1	yes	characteristic
235	C₄⋊C₄×D₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊Dic₅₃	—	2	2	no	—
237	C₂×#11719921	—	2	2	no	—
238	C₂×#11719921	—	2	2	no	—
239	C₂²⋊C₄×D₅₃	—	2	2	no	—
240	C₂²⋊C₄×D₅₃	—	2	2	no	—
241	C₂²⋊C₄×D₅₃	—	2	2	no	—
242	C₂²⋊C₄×D₅₃	—	2	2	no	—
243	C₂²⋊C₄×D₅₃	—	2	1	no	—
244	C₂²⋊C₄×D₅₃	—	2	1	no	—
245	C₂²⋊C₄×D₅₃	—	2	2	no	—
246	C₂²⋊C₄×D₅₃	—	2	2	no	—
247	C₂²⋊C₄×D₅₃	D₄	1	2	yes	—
248	C₄²×D₅₃	—	2	1	no	—
249	C₄²×D₅₃	—	2	1	no	—
250	C₄²×D₅₃	C₂³	1	2	yes	—
251	#13133151	C₂³	1	1	yes	characteristic, complemented
252	#13133151	C₂³	1	2	yes	complemented
253	#13133151	C₂³	1	1	yes	characteristic, complemented
254	#13133150	C₂³	1	1	yes	characteristic, complemented
255	#13133150	C₂³	1	2	yes	complemented
256	#13133150	C₂³	1	1	yes	characteristic, complemented
257	#13133150	C₂³	1	2	yes	complemented
258	#13133150	C₂³	1	1	yes	characteristic, complemented
259	#13133150	C₂³	1	1	yes	characteristic, complemented
260	#13133149	C₂³	1	1	yes	characteristic, complemented
261	#13133149	C₂³	1	2	yes	complemented
262	#13133149	C₂³	1	1	yes	characteristic, complemented
263	#13133148	C₂³	1	1	yes	characteristic, complemented
264	#13133148	C₂³	1	2	yes	complemented
265	#13133148	C₂³	1	1	yes	characteristic, complemented
266	#13133148	C₂³	1	2	yes	complemented
267	#13133148	C₂³	1	1	yes	characteristic, complemented
268	#13133148	C₂³	1	1	yes	characteristic, complemented
269	C₄⋊#88322	C₂³	1	2	yes	complemented
270	C₄⋊#88322	C₂³	1	2	yes	complemented
271	#13133146	C₂³	1	2	yes	complemented
272	#13133146	C₂³	1	2	yes	complemented
273	#13133146	C₂³	1	2	yes	complemented
274	#13133146	C₂³	1	2	yes	complemented
275	#13133139	C₂³	1	2	yes	—
276	#13133139	C₂³	1	2	yes	—
277	#13133139	C₂³	1	2	yes	—
278	#13133139	C₂³	1	2	yes	—
279	#13133138	C₂³	1	2	yes	—
280	#13133138	C₂³	1	2	yes	—
281	#13133138	C₂³	1	2	yes	—
282	#13133138	C₂³	1	2	yes	—
283	#13133137	C₂³	1	2	yes	—
284	#13133137	C₂³	1	2	yes	—
285	#13133137	C₂³	1	2	yes	—
286	#13133137	C₂³	1	2	yes	—
287	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
288	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
289	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
290	C₄⋊Q₈×C₅₃	—	2	1	no	—
291	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
292	#125×C₅₃	—	2	1	no	—
293	#125×C₅₃	C₂³	1	2	yes	complemented
294	C₂²⋊Q₈×C₅₃	—	2	2	no	—
295	C₄×D₄×C₅₃	—	2	1	no	—
296	C₄×D₄×C₅₃	—	2	1	no	—
297	C₄×D₄×C₅₃	C₂³	1	2	yes	—
298	C₄×D₄×C₅₃	C₂³	1	2	yes	—
299	#117×C₅₃	C₂³	1	1	yes	characteristic
300	#117×C₅₃	C₂³	1	1	yes	characteristic
301	#117×C₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
304	#107×C₅₃	C₂³	1	1	yes	characteristic, complemented
305	#107×C₅₃	C₂³	1	2	yes	complemented
306	#107×C₅₃	C₂³	1	1	yes	characteristic, complemented
307	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
308	#106×C₅₃	C₂³	1	2	yes	complemented
309	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
310	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
311	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
312	#102×C₅₃	C₂³	1	2	yes	—
313	#102×C₅₃	C₂³	1	2	yes	—
314	#102×C₅₃	C₂³	1	2	yes	—
315	#102×C₅₃	C₂³	1	2	yes	—
316	C₂⁴×C₅₃	—	2	1	no	—
317	C₂³×D₅₃	—	2	1	no	—
318	C₂³×D₅₃	—	2	2	no	—
319	C₂³×D₅₃	—	2	8	no	—
320	C₂³×D₅₃	—	2	2	no	—
321	C₂³×D₅₃	—	8	2	no	—
322	C₂³×D₅₃	—	8	2	no	—
323	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₅₃	—	2	2	no	—
325	C₂×D₄×C₅₃	—	2	1	no	—
326	C₂×D₄×C₅₃	—	2	2	no	—
327	C₂×D₄×C₅₃	C₂×Q₈	1	4	yes	complemented
328	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₅₃	—	2	1	no	—
330	C₂²×C₄×C₅₃	—	2	2	no	—
331	C₂²×C₄×C₅₃	—	2	2	no	—
332	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
333	C₂×C₂²⋊D₅₃	—	2	8	no	—
334	C₂×C₂²⋊D₅₃	—	2	2	no	—
335	C₂×C₂²⋊D₅₃	—	2	2	no	—
336	C₂²×Dic₅₃	—	2	1	no	—
337	C₂²×Dic₅₃	—	2	2	no	—
338	C₂²×Dic₅₃	—	2	2	no	—
339	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
340	Q₈×D₅₃	—	8	4	no	—
341	D₄×D₅₃	—	2	8	no	—
342	D₄×D₅₃	—	2	8	no	—
343	D₄×D₅₃	—	2	4	no	—
344	D₄×D₅₃	—	2	4	no	—
345	D₄×D₅₃	C₂×Q₈	1	8	yes	—
346	D₄×D₅₃	C₂×Q₈	1	8	yes	complemented
347	C₂×D₂₁₂	—	2	1	no	—
348	C₂×D₂₁₂	—	2	2	no	—
349	C₂×D₂₁₂	C₂×Q₈	1	4	yes	complemented
350	C₂×D₂₁₂	C₂⁴	1	2	yes	—
351	C₂×C₄×D₅₃	—	2	1	no	—
352	C₂×C₄×D₅₃	—	2	1	no	—
353	C₂×C₄×D₅₃	—	2	1	no	—
354	C₂×C₄×D₅₃	—	2	1	no	—
355	C₂×C₄×D₅₃	—	2	2	no	—
356	C₂×C₄×D₅₃	—	2	2	no	—
357	C₂×C₄×D₅₃	—	2	2	no	—
358	C₂×C₄×D₅₃	—	2	2	no	—
359	C₂×C₄×D₅₃	—	2	2	no	—
360	C₂×C₄×D₅₃	—	2	2	no	—
361	C₂×C₄×D₅₃	—	8	4	no	—
362	C₂×C₄×D₅₃	—	8	4	no	—
363	C₂×C₄×D₅₃	—	8	2	no	—
364	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
365	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
366	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
367	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
368	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	—
369	C₂×C₄×D₅₃	#41	1	4	yes	—
370	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
372	C₂×Dic₁₀₆	—	2	2	no	—
373	C₂×Dic₁₀₆	—	2	2	no	—
374	C₂×Dic₁₀₆	—	2	2	no	—
375	M₁₆×C₅₃	—	2	2	no	—
376	C₂×C₈×C₅₃	—	2	2	no	—
377	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
379	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₄⋊C₄×C₅₃	—	2	1	no	—
381	C₄⋊C₄×C₅₃	—	2	2	no	—
382	C₄⋊C₄×C₅₃	—	2	2	no	—
383	C₄⋊C₄×C₅₃	—	2	2	no	—
384	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
385	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
386	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
387	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²⋊C₄×C₅₃	—	2	1	no	—
392	C₂²⋊C₄×C₅₃	—	2	1	no	—
393	C₂²⋊C₄×C₅₃	—	2	2	no	—
394	C₂²⋊C₄×C₅₃	—	2	2	no	—
395	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
396	C₄²×C₅₃	—	2	1	no	—
397	C₄²×C₅₃	—	2	1	no	—
398	C₄²×C₅₃	C₂⁴	1	2	yes	—
399	C₂²⋊Dic₅₃	—	2	1	no	—
400	C₂²⋊Dic₅₃	—	2	1	no	—
401	C₂²⋊Dic₅₃	—	2	2	no	—
402	C₂²⋊Dic₅₃	—	2	2	no	—
403	C₂²⋊Dic₅₃	C₂×D₄	1	2	yes	—
404	#11719921	—	2	1	no	—
405	#11719921	—	2	1	no	—
406	#11719921	—	2	1	no	—
407	#11719921	—	2	1	no	—
408	#11719921	—	2	2	no	—
409	#11719921	—	2	2	no	—
410	#11719921	—	2	2	no	—
411	#11719921	—	2	2	no	—
412	#11719921	C₂×D₄	1	2	yes	—
413	#11719921	C₂×D₄	1	2	yes	—
414	C₄⋊Dic₅₃	—	2	1	no	—
415	C₄⋊Dic₅₃	—	2	2	no	—
416	C₄⋊Dic₅₃	—	2	2	no	—
417	C₄⋊Dic₅₃	—	2	2	no	—
418	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
419	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
420	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
421	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
422	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
423	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
424	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
425	#11719919	—	2	2	no	—
426	#11719919	—	2	2	no	—
427	#11719919	—	2	2	no	—
428	#11719919	—	2	2	no	—
429	#11719919	—	2	2	no	—
430	#11719919	—	2	2	no	—
431	#11719919	—	2	2	no	—
432	#11719919	—	2	2	no	—
433	#11719919	—	2	1	no	—
434	#11719919	—	2	1	no	—
435	#11719919	—	2	1	no	—
436	#11719919	—	2	1	no	—
437	#11719919	C₂×D₄	1	2	yes	—
438	#11719919	C₂×D₄	1	2	yes	—
439	C₄×Dic₅₃	—	2	1	no	—
440	C₄×Dic₅₃	—	2	1	no	—
441	C₄×Dic₅₃	—	2	1	no	—
442	C₄×Dic₅₃	—	2	1	no	—
443	C₄×Dic₅₃	—	2	1	no	—
444	C₄×Dic₅₃	—	2	1	no	—
445	C₄×Dic₅₃	C₂×D₄	1	2	yes	—
446	C₄×Dic₅₃	C₂×D₄	1	2	yes	—
447	C₄×Dic₅₃	C₂⁴	1	2	yes	—
448	#11719917	—	2	2	no	—
449	C₂×#88322	—	2	2	no	—
450	C₂×#88322	C₂⁴	1	1	yes	characteristic
451	C₂×#88322	C₂⁴	1	2	yes	—
452	C₂×#88322	C₂⁴	1	1	yes	characteristic
453	#11719912	—	2	4	no	—
454	C₈×D₅₃	—	2	2	no	—
455	C₈×D₅₃	—	2	2	no	—
456	C₈×D₅₃	—	2	2	no	—
457	C₈×D₅₃	—	2	2	no	—
458	C₈×D₅₃	—	2	4	no	—
459	C₂³×C₅₃	—	2	2	no	—
460	C₂³×C₅₃	—	2	4	no	—
461	C₂³×C₅₃	—	8	1	no	—
462	C₂³×C₅₃	—	8	1	no	—
463	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
464	C₂²×D₅₃	—	2	2	no	—
465	C₂²×D₅₃	—	2	2	no	—
466	C₂²×D₅₃	—	2	2	no	—
467	C₂²×D₅₃	—	2	4	no	—
468	C₂²×D₅₃	—	2	8	no	—
469	C₂²×D₅₃	—	2	8	no	—
470	C₂²×D₅₃	—	4	4	no	—
471	C₂²×D₅₃	—	4	4	no	—
472	C₂²×D₅₃	—	8	16	no	—
473	C₂²×D₅₃	—	8	2	no	—
474	C₂²×D₅₃	—	8	2	no	—
475	C₂²×D₅₃	—	8	1	no	—
476	C₂²×D₅₃	—	8	1	no	—
477	C₂²×D₅₃	C₂²⋊Q₈	1	4	yes	—
478	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
479	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
480	Q₈×C₅₃	—	8	2	no	—
481	D₄×C₅₃	—	2	4	no	—
482	D₄×C₅₃	—	2	2	no	—
483	D₄×C₅₃	C₂²×Q₈	1	4	yes	—
484	C₂×C₄×C₅₃	—	2	1	no	—
485	C₂×C₄×C₅₃	—	2	2	no	—
486	C₂×C₄×C₅₃	—	2	1	no	—
487	C₂×C₄×C₅₃	—	2	1	no	—
488	C₂×C₄×C₅₃	—	2	1	no	—
489	C₂×C₄×C₅₃	—	8	2	no	—
490	C₂×C₄×C₅₃	—	8	2	no	—
491	C₂×C₄×C₅₃	—	8	1	no	—
492	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
496	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
497	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
498	C₂²⋊D₅₃	—	2	8	no	—
499	C₂²⋊D₅₃	—	2	8	no	—
500	C₂×Dic₅₃	—	2	1	no	—
501	C₂×Dic₅₃	—	2	2	no	—
502	C₂×Dic₅₃	—	2	1	no	—
503	C₂×Dic₅₃	—	2	1	no	—
504	C₂×Dic₅₃	—	2	1	no	—
505	C₂×Dic₅₃	—	8	2	no	—
506	C₂×Dic₅₃	—	8	2	no	—
507	C₂×Dic₅₃	—	8	1	no	—
508	C₂×Dic₅₃	C₂²⋊Q₈	1	4	yes	—
509	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
510	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
511	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
513	D₂₁₂	—	2	4	no	—
514	D₂₁₂	—	2	2	no	—
515	D₂₁₂	C₂²×Q₈	1	4	yes	—
516	C₄×D₅₃	—	2	4	no	—
517	C₄×D₅₃	—	2	4	no	—
518	C₄×D₅₃	—	4	2	no	—
519	C₄×D₅₃	—	4	4	no	—
520	C₄×D₅₃	—	4	2	no	—
521	C₄×D₅₃	—	4	2	no	—
522	C₄×D₅₃	—	4	2	no	—
523	C₄×D₅₃	—	8	2	no	—
524	C₄×D₅₃	—	8	2	no	—
525	C₄×D₅₃	—	8	2	no	—
526	C₄×D₅₃	—	8	2	no	—
527	C₄×D₅₃	—	8	2	no	—
528	C₄×D₅₃	C₂²⋊Q₈	1	4	yes	—
529	C₄×D₅₃	C₂²⋊Q₈	1	4	yes	—
530	C₄×D₅₃	C₂²×Q₈	1	2	yes	—
531	C₄×D₅₃	C₂²×Q₈	1	2	yes	—
532	C₄×D₅₃	C₂×#41	1	2	yes	—
533	C₄×D₅₃	C₂×#41	1	2	yes	—
534	Dic₁₀₆	—	8	2	no	—
535	Dic₁₀₆	—	8	2	no	—
536	Dic₁₀₆	—	8	2	no	—
537	C₈×C₅₃	—	2	1	no	—
538	C₈×C₅₃	—	2	1	no	—
539	C₈×C₅₃	—	2	2	no	—
540	#88322	—	2	1	no	—
541	#88322	—	2	1	no	—
542	#88322	—	2	2	no	—
543	C₂×#3081	—	53	1	no	maximal, Sylow
544	C₂²×C₅₃	—	2	1	no	—
545	C₂²×C₅₃	—	2	1	no	—
546	C₂²×C₅₃	—	2	4	no	—
547	C₂²×C₅₃	—	4	2	no	—
548	C₂²×C₅₃	—	4	2	no	—
549	C₂²×C₅₃	—	8	4	no	—
550	C₂²×C₅₃	C₂×C₂²⋊Q₈	1	2	yes	—
551	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
552	C₂×D₅₃	—	2	1	no	—
553	C₂×D₅₃	—	2	1	no	—
554	C₂×D₅₃	—	2	8	no	—
555	C₂×D₅₃	—	2	4	no	—
556	C₂×D₅₃	—	4	2	no	—
557	C₂×D₅₃	—	4	2	no	—
558	C₂×D₅₃	—	4	16	no	—
559	C₂×D₅₃	—	8	8	no	—
560	C₂×D₅₃	—	8	4	no	—
561	C₂×D₅₃	C₂×C₂²⋊Q₈	1	2	yes	—
562	C₂×D₅₃	C₂×C₂²⋊Q₈	1	2	yes	—
563	C₂×D₅₃	#576	1	2	yes	—
564	C₂×D₅₃	#577	1	2	yes	—
565	C₄×C₅₃	—	2	2	no	—
566	C₄×C₅₃	—	2	2	no	—
567	C₄×C₅₃	—	4	1	no	—
568	C₄×C₅₃	—	4	2	no	—
569	C₄×C₅₃	—	4	1	no	—
570	C₄×C₅₃	—	4	1	no	—
571	C₄×C₅₃	—	4	1	no	—
572	C₄×C₅₃	C₂×C₂²⋊Q₈	1	2	yes	—
573	C₄×C₅₃	C₂³×Q₈	1	1	yes	characteristic
574	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
575	Dic₅₃	—	2	2	no	—
576	Dic₅₃	—	2	2	no	—
577	Dic₅₃	—	4	1	no	—
578	Dic₅₃	—	4	2	no	—
579	Dic₅₃	—	4	1	no	—
580	Dic₅₃	—	4	1	no	—
581	Dic₅₃	—	4	1	no	—
582	Dic₅₃	C₂×C₂²⋊Q₈	1	2	yes	—
583	Dic₅₃	C₂×C₂²⋊Q₈	1	2	yes	—
584	C₂×#544	—	53	1	no	—
585	C₂×#518	—	53	1	no	—
586	#3081	—	53	2	no	—
587	#3081	—	53	2	no	—
588	#3081	—	53	2	no	—
589	#3081	—	53	2	no	—
590	#3081	—	53	1	no	—
591	#3081	—	53	1	no	—
592	#3081	—	53	1	no	—
593	#3081	—	53	1	no	—
594	#3081	—	53	1	no	—
595	#3081	—	53	1	no	—
596	#3081	—	53	1	no	—
597	#3081	D₅₃	1	1	yes	characteristic, direct product factor
598	C₂×#478	—	53	2	no	—
599	C₂×#478	—	53	2	no	—
600	C₂×#476	—	53	2	no	—
601	C₂×#474	—	53	2	no	—
602	C₂×#428	—	53	1	no	—
603	C₂×#427	—	53	1	no	—
604	C₂×#424	—	53	1	no	—
605	C₂×#418	—	53	1	no	—
606	C₂²×#102	—	53	1	no	—
607	C₂×C₅₃	—	2	2	no	—
608	C₂×C₅₃	—	4	4	no	—
609	C₂×C₅₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
610	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
611	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
612	D₅₃	—	2	2	no	—
613	D₅₃	—	4	4	no	—
614	D₅₃	#3081	1	4	yes	direct product factor
615	C₂³×D₄	—	53	1	no	—
616	C₂²×M₁₆	—	53	1	no	—
617	C₂³×C₈	—	53	1	no	—
618	#544	—	53	2	no	—
619	#544	—	53	2	no	—
620	#544	—	53	1	no	—
621	#544	—	53	1	no	—
622	#544	—	53	1	no	—
623	#544	—	106	2	no	—
624	#544	—	106	1	no	—
625	#544	—	106	1	no	—
626	#544	C₂×D₅₃	1	1	yes	characteristic, complemented
627	C₂×C₄⋊Q₈	—	53	2	no	—
628	C₂×C₄⋊Q₈	—	106	1	no	—
629	C₂×#125	—	53	2	no	—
630	C₂×#125	—	106	1	no	—
631	C₂×C₂²⋊Q₈	—	106	2	no	—
632	#518	—	53	1	no	—
633	#518	—	53	2	no	—
634	#518	—	53	2	no	—
635	#518	—	53	1	no	—
636	#518	—	53	1	no	—
637	#518	—	106	2	no	—
638	#518	—	106	1	no	—
639	#518	—	106	1	no	—
640	#518	C₂×D₅₃	1	1	yes	characteristic
641	C₂×C₄×D₄	—	53	2	no	—
642	C₂×C₄×D₄	—	53	2	no	—
643	C₂×C₄×D₄	—	106	1	no	—
644	C₂×C₄×D₄	—	106	1	no	—
645	C₂×#117	—	53	1	no	—
646	C₂×#117	—	53	1	no	—
647	C₂×#117	—	53	1	no	—
648	C₂²×C₄⋊C₄	—	53	1	no	—
649	C₂²×C₂²⋊C₄	—	106	2	no	—
650	#478	—	53	2	no	—
651	#478	—	53	2	no	—
652	#478	—	53	2	no	—
653	#478	—	53	2	no	—
654	#478	—	53	2	no	—
655	#478	—	53	2	no	—
656	#478	—	53	2	no	—
657	#478	—	53	2	no	—
658	#478	—	53	2	no	—
659	#478	—	53	2	no	—
660	#478	—	53	2	no	—
661	#478	—	53	2	no	—
662	#478	—	53	2	no	—
663	#478	—	53	2	no	—
664	#478	C₂×D₅₃	1	2	yes	complemented
665	#478	C₂×D₅₃	1	2	yes	complemented
666	#476	—	53	2	no	—
667	#476	—	53	2	no	—
668	#476	—	53	2	no	—
669	#476	—	53	2	no	—
670	#476	—	53	2	no	—
671	#476	—	53	2	no	—
672	#476	—	53	2	no	—
673	#476	C₂×D₅₃	1	2	yes	complemented
674	#474	—	53	2	no	—
675	#474	—	53	2	no	—
676	#474	—	53	2	no	—
677	#474	—	53	2	no	—
678	#474	—	53	2	no	—
679	#474	—	53	2	no	—
680	#474	—	53	2	no	—
681	#474	C₂×D₅₃	1	2	yes	complemented
682	#428	—	53	1	no	—
683	#428	—	53	1	no	—
684	#428	—	53	1	no	—
685	#428	—	53	2	no	—
686	#428	—	53	2	no	—
687	#428	C₂×D₅₃	1	1	yes	characteristic, complemented
688	#427	—	53	1	no	—
689	#427	—	53	1	no	—
690	#427	—	53	1	no	—
691	#427	—	53	1	no	—
692	#427	—	53	1	no	—
693	#427	—	53	1	no	—
694	#427	—	53	1	no	—
695	#427	C₂×D₅₃	1	1	yes	characteristic, complemented
696	C₂×#107	—	53	1	no	—
697	C₂×#107	—	53	2	no	—
698	C₂×#107	—	53	1	no	—
699	C₂×#106	—	53	1	no	—
700	C₂×#106	—	53	2	no	—
701	C₂×#106	—	53	1	no	—
702	#424	—	53	1	no	—
703	#424	—	53	1	no	—
704	#424	—	53	1	no	—
705	#424	—	53	2	no	—
706	#424	—	53	2	no	—
707	#424	C₂×D₅₃	1	1	yes	characteristic, complemented
708	C₂×C₄⋊C₈	—	53	2	no	—
709	C₂×C₄⋊C₈	—	53	2	no	—
710	#418	—	53	1	no	—
711	#418	—	53	1	no	—
712	#418	—	53	1	no	—
713	#418	—	53	2	no	—
714	#418	—	53	2	no	—
715	#418	C₂×D₅₃	1	1	yes	characteristic
716	C₂×#102	—	53	1	no	—
717	C₂×#102	—	53	1	no	—
718	C₂×#102	—	53	1	no	—
719	C₂×#102	—	53	2	no	—
720	C₂×#102	—	53	2	no	—
721	C₂×#102	—	53	2	no	—
722	C₂×#102	—	53	2	no	—
723	C₂×#102	—	53	2	no	—
724	C₂×#102	—	53	2	no	—
725	C₂×#102	C₂×D₅₃	1	1	yes	characteristic
726	C₅₃	C₂×#3081	1	1	yes	characteristic, complemented, Sylow
727	C₂⁵	—	106	1	no	—
728	C₂²×Q₈	—	106	2	no	—
729	C₂²×D₄	—	53	8	no	—
730	C₂²×D₄	—	53	2	no	—
731	C₂²×D₄	—	53	2	no	—
732	C₂²×D₄	—	53	1	no	—
733	C₂²×D₄	—	106	1	no	—
734	C₂²×D₄	—	106	1	no	—
735	C₂²×D₄	—	106	4	no	—
736	C₂²×D₄	—	106	1	no	—
737	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
738	C₂³×C₄	—	53	1	no	—
739	C₂³×C₄	—	106	2	no	—
740	C₂³×C₄	—	106	2	no	—
741	C₂³×C₄	—	106	1	no	—
742	C₂×M₁₆	—	53	1	no	—
743	C₂×M₁₆	—	53	2	no	—
744	C₂×M₁₆	—	106	4	no	—
745	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
746	C₂²×C₈	—	53	1	no	—
747	C₂²×C₈	—	53	1	no	—
748	C₂²×C₈	—	53	1	no	—
749	C₂²×C₈	—	53	1	no	—
750	C₂²×C₈	—	53	1	no	—
751	C₂²×C₈	—	53	2	no	—
752	C₂²×C₈	—	106	4	no	—
753	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
754	C₄⋊Q₈	—	2	1	no	—
755	C₄⋊Q₈	—	53	2	no	—
756	C₄⋊Q₈	—	53	2	no	—
757	C₄⋊Q₈	—	53	2	no	—
758	C₄⋊Q₈	—	106	1	no	—
759	C₄⋊Q₈	—	106	2	no	—
760	C₄⋊Q₈	—	106	2	no	—
761	C₄⋊Q₈	—	106	2	no	—
762	C₄⋊Q₈	—	106	1	no	—
763	C₄⋊Q₈	—	106	2	no	—
764	C₄⋊Q₈	—	106	1	no	—
765	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
766	#125	—	2	1	no	—
767	#125	—	53	2	no	—
768	#125	—	53	2	no	—
769	#125	—	53	2	no	—
770	#125	—	106	1	no	—
771	#125	—	106	2	no	—
772	#125	—	106	2	no	—
773	#125	—	106	2	no	—
774	#125	—	106	2	no	—
775	#125	—	106	1	no	—
776	#125	—	106	1	no	—
777	#125	C₂²×D₅₃	1	2	yes	complemented
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	106	2	no	—
780	C₂²⋊Q₈	—	106	2	no	—
781	C₂²⋊Q₈	—	106	2	no	—
782	C₂²⋊Q₈	—	106	2	no	—
783	C₂²⋊Q₈	—	106	2	no	—
784	C₂²⋊Q₈	—	106	2	no	—
785	C₂²⋊Q₈	—	106	2	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	53	2	no	—
789	C₄×D₄	—	53	2	no	—
790	C₄×D₄	—	53	2	no	—
791	C₄×D₄	—	53	2	no	—
792	C₄×D₄	—	53	2	no	—
793	C₄×D₄	—	53	2	no	—
794	C₄×D₄	—	106	1	no	—
795	C₄×D₄	—	106	1	no	—
796	C₄×D₄	—	106	2	no	—
797	C₄×D₄	—	106	2	no	—
798	C₄×D₄	—	106	2	no	—
799	C₄×D₄	—	106	2	no	—
800	C₄×D₄	—	106	2	no	—
801	C₄×D₄	—	106	2	no	—
802	C₄×D₄	—	106	2	no	—
803	C₄×D₄	—	106	2	no	—
804	C₄×D₄	—	106	1	no	—
805	C₄×D₄	—	106	1	no	—
806	C₄×D₄	—	106	1	no	—
807	C₄×D₄	—	106	1	no	—
808	C₄×D₄	C₂²×D₅₃	1	2	yes	—
809	C₄×D₄	C₂²×D₅₃	1	2	yes	—
810	#117	—	53	1	no	—
811	#117	—	53	1	no	—
812	#117	—	53	1	no	—
813	#117	—	53	2	no	—
814	#117	—	53	2	no	—
815	#117	—	53	1	no	—
816	#117	—	53	1	no	—
817	#117	—	53	1	no	—
818	#117	—	53	1	no	—
819	#117	—	53	1	no	—
820	#117	—	53	1	no	—
821	#117	—	106	1	no	—
822	#117	—	106	1	no	—
823	#117	—	106	1	no	—
824	#117	—	106	1	no	—
825	#117	C₂²×D₅₃	1	1	yes	characteristic
826	#117	C₂²×D₅₃	1	1	yes	characteristic
827	#117	C₂²×D₅₃	1	1	yes	characteristic
828	C₂×C₄⋊C₄	—	53	1	no	—
829	C₂×C₄⋊C₄	—	53	1	no	—
830	C₂×C₄⋊C₄	—	53	1	no	—
831	C₂×C₄⋊C₄	—	53	2	no	—
832	C₂×C₄⋊C₄	—	53	2	no	—
833	C₂×C₄⋊C₄	—	53	1	no	—
834	C₂×C₄⋊C₄	—	53	1	no	—
835	C₂×C₄⋊C₄	—	53	1	no	—
836	C₂×C₄⋊C₄	—	53	1	no	—
837	C₂×C₄⋊C₄	—	106	1	no	—
838	C₂×C₄⋊C₄	—	106	1	no	—
839	C₂×C₄⋊C₄	—	106	2	no	—
840	C₂×C₄⋊C₄	—	106	2	no	—
841	C₂×C₄⋊C₄	—	106	2	no	—
842	C₂×C₄⋊C₄	—	106	1	no	—
843	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
844	C₂×C₂²⋊C₄	—	2	2	no	—
845	C₂×C₂²⋊C₄	—	53	2	no	—
846	C₂×C₂²⋊C₄	—	106	2	no	—
847	C₂×C₂²⋊C₄	—	106	2	no	—
848	C₂×C₂²⋊C₄	—	106	2	no	—
849	C₂×C₂²⋊C₄	—	106	2	no	—
850	C₂×C₂²⋊C₄	—	106	2	no	—
851	C₂×C₂²⋊C₄	—	106	1	no	—
852	C₂×C₂²⋊C₄	—	106	1	no	—
853	C₂×C₂²⋊C₄	—	106	2	no	—
854	C₂×C₂²⋊C₄	—	106	2	no	—
855	C₂×C₂²⋊C₄	—	106	2	no	—
856	C₂×C₂²⋊C₄	—	106	2	no	—
857	C₂×C₄²	—	53	2	no	—
858	C₂×C₄²	—	106	1	no	—
859	C₂×C₄²	—	106	1	no	—
860	#107	—	53	1	no	—
861	#107	—	53	1	no	—
862	#107	—	53	2	no	—
863	#107	—	53	1	no	—
864	#107	—	53	1	no	—
865	#107	—	53	1	no	—
866	#107	—	53	1	no	—
867	#107	—	53	2	no	—
868	#107	—	53	2	no	—
869	#107	C₂²×D₅₃	1	1	yes	characteristic, complemented
870	#107	C₂²×D₅₃	1	1	yes	characteristic, complemented
871	#107	C₂²×D₅₃	1	2	yes	complemented
872	#106	—	53	1	no	—
873	#106	—	53	1	no	—
874	#106	—	53	2	no	—
875	#106	—	53	1	no	—
876	#106	—	53	1	no	—
877	#106	—	53	1	no	—
878	#106	—	53	1	no	—
879	#106	—	53	2	no	—
880	#106	—	53	2	no	—
881	#106	C₂²×D₅₃	1	1	yes	characteristic, complemented
882	#106	C₂²×D₅₃	1	1	yes	characteristic, complemented
883	#106	C₂²×D₅₃	1	2	yes	complemented
884	C₄⋊C₈	—	53	2	no	—
885	C₄⋊C₈	—	53	2	no	—
886	C₄⋊C₈	—	53	2	no	—
887	C₄⋊C₈	—	53	2	no	—
888	C₄⋊C₈	—	53	2	no	—
889	C₄⋊C₈	—	53	2	no	—
890	C₄⋊C₈	C₂²×D₅₃	1	2	yes	complemented
891	C₄⋊C₈	C₂²×D₅₃	1	2	yes	complemented
892	#102	—	53	2	no	—
893	#102	—	53	2	no	—
894	#102	—	53	2	no	—
895	#102	—	53	2	no	—
896	#102	—	53	2	no	—
897	#102	—	53	2	no	—
898	#102	—	53	2	no	—
899	#102	—	53	2	no	—
900	#102	—	53	2	no	—
901	#102	—	53	2	no	—
902	#102	—	53	2	no	—
903	#102	—	53	2	no	—
904	#102	C₂²×D₅₃	1	2	yes	—
905	#102	C₂²×D₅₃	1	2	yes	—
906	#102	C₂²×D₅₃	1	2	yes	—
907	#102	C₂²×D₅₃	1	2	yes	—
908	C₂⁴	—	2	1	no	—
909	C₂⁴	—	53	1	no	—
910	C₂⁴	—	106	2	no	—
911	C₂⁴	—	106	8	no	—
912	C₂⁴	—	106	2	no	—
913	C₂⁴	—	106	1	no	—
914	C₂⁴	—	424	2	no	—
915	C₂⁴	—	424	2	no	—
916	C₂×Q₈	—	2	2	no	—
917	C₂×Q₈	—	106	2	no	—
918	C₂×Q₈	—	106	2	no	—
919	C₂×Q₈	—	106	2	no	—
920	C₂×Q₈	—	424	4	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	53	8	no	—
924	C₂×D₄	—	53	8	no	—
925	C₂×D₄	—	53	4	no	—
926	C₂×D₄	—	53	2	no	—
927	C₂×D₄	—	106	8	no	—
928	C₂×D₄	—	106	8	no	—
929	C₂×D₄	—	106	4	no	—
930	C₂×D₄	—	106	4	no	—
931	C₂×D₄	—	106	2	no	—
932	C₂×D₄	—	106	2	no	—
933	C₂×D₄	—	106	8	no	—
934	C₂×D₄	—	106	1	no	—
935	C₂×D₄	—	106	2	no	—
936	C₂×D₄	Q₈×D₅₃	1	4	yes	complemented
937	C₂×D₄	C₂³×D₅₃	1	2	yes	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	53	1	no	—
942	C₂²×C₄	—	53	1	no	—
943	C₂²×C₄	—	53	1	no	—
944	C₂²×C₄	—	53	4	no	—
945	C₂²×C₄	—	53	4	no	—
946	C₂²×C₄	—	53	1	no	—
947	C₂²×C₄	—	53	1	no	—
948	C₂²×C₄	—	53	2	no	—
949	C₂²×C₄	—	53	2	no	—
950	C₂²×C₄	—	106	2	no	—
951	C₂²×C₄	—	106	2	no	—
952	C₂²×C₄	—	106	2	no	—
953	C₂²×C₄	—	106	1	no	—
954	C₂²×C₄	—	106	1	no	—
955	C₂²×C₄	—	106	1	no	—
956	C₂²×C₄	—	106	1	no	—
957	C₂²×C₄	—	106	2	no	—
958	C₂²×C₄	—	106	2	no	—
959	C₂²×C₄	—	106	2	no	—
960	C₂²×C₄	—	106	1	no	—
961	C₂²×C₄	—	106	2	no	—
962	C₂²×C₄	—	106	2	no	—
963	C₂²×C₄	—	424	4	no	—
964	C₂²×C₄	—	424	4	no	—
965	C₂²×C₄	—	424	2	no	—
966	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
967	M₁₆	—	2	2	no	—
968	M₁₆	—	106	4	no	—
969	M₁₆	—	106	2	no	—
970	C₂×C₈	—	2	2	no	—
971	C₂×C₈	—	53	1	no	—
972	C₂×C₈	—	53	2	no	—
973	C₂×C₈	—	53	1	no	—
974	C₂×C₈	—	106	2	no	—
975	C₂×C₈	—	106	2	no	—
976	C₂×C₈	—	106	2	no	—
977	C₂×C₈	—	106	2	no	—
978	C₂×C₈	—	106	4	no	—
979	C₂×C₈	—	106	2	no	—
980	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
981	C₂×C₈	C₂³×D₅₃	1	2	yes	—
982	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	53	2	no	—
988	C₄⋊C₄	—	53	1	no	—
989	C₄⋊C₄	—	53	2	no	—
990	C₄⋊C₄	—	53	1	no	—
991	C₄⋊C₄	—	53	2	no	—
992	C₄⋊C₄	—	53	1	no	—
993	C₄⋊C₄	—	53	1	no	—
994	C₄⋊C₄	—	53	1	no	—
995	C₄⋊C₄	—	53	1	no	—
996	C₄⋊C₄	—	106	2	no	—
997	C₄⋊C₄	—	106	2	no	—
998	C₄⋊C₄	—	106	1	no	—
999	C₄⋊C₄	—	106	1	no	—
1000	C₄⋊C₄	—	106	1	no	—
1001	C₄⋊C₄	—	106	1	no	—
1002	C₄⋊C₄	—	106	2	no	—
1003	C₄⋊C₄	—	106	2	no	—
1004	C₄⋊C₄	—	106	2	no	—
1005	C₄⋊C₄	—	106	2	no	—
1006	C₄⋊C₄	—	106	2	no	—
1007	C₄⋊C₄	—	106	2	no	—
1008	C₄⋊C₄	—	106	1	no	—
1009	C₄⋊C₄	—	106	2	no	—
1010	C₄⋊C₄	—	106	2	no	—
1011	C₄⋊C₄	—	106	2	no	—
1012	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1013	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1014	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1015	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1016	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1017	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1018	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	53	2	no	—
1024	C₂²⋊C₄	—	53	2	no	—
1025	C₂²⋊C₄	—	53	2	no	—
1026	C₂²⋊C₄	—	106	2	no	—
1027	C₂²⋊C₄	—	106	2	no	—
1028	C₂²⋊C₄	—	106	1	no	—
1029	C₂²⋊C₄	—	106	1	no	—
1030	C₂²⋊C₄	—	106	1	no	—
1031	C₂²⋊C₄	—	106	1	no	—
1032	C₂²⋊C₄	—	106	2	no	—
1033	C₂²⋊C₄	—	106	2	no	—
1034	C₂²⋊C₄	—	106	1	no	—
1035	C₂²⋊C₄	—	106	1	no	—
1036	C₂²⋊C₄	—	106	2	no	—
1037	C₂²⋊C₄	—	106	2	no	—
1038	C₂²⋊C₄	D₄×D₅₃	1	2	yes	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	53	2	no	—
1042	C₄²	—	53	2	no	—
1043	C₄²	—	53	2	no	—
1044	C₄²	—	106	1	no	—
1045	C₄²	—	106	1	no	—
1046	C₄²	—	106	1	no	—
1047	C₄²	—	106	1	no	—
1048	C₄²	—	106	1	no	—
1049	C₄²	—	106	1	no	—
1050	C₄²	C₂³×D₅₃	1	2	yes	—
1051	C₂³	—	2	2	no	—
1052	C₂³	—	2	4	no	—
1053	C₂³	—	8	1	no	—
1054	C₂³	—	8	1	no	—
1055	C₂³	—	53	1	no	—
1056	C₂³	—	53	4	no	—
1057	C₂³	—	53	1	no	—
1058	C₂³	—	106	2	no	—
1059	C₂³	—	106	2	no	—
1060	C₂³	—	106	8	no	—
1061	C₂³	—	106	8	no	—
1062	C₂³	—	106	4	no	—
1063	C₂³	—	106	2	no	—
1064	C₂³	—	424	1	no	—
1065	C₂³	—	424	1	no	—
1066	C₂³	—	424	2	no	—
1067	C₂³	—	424	2	no	—
1068	C₂³	—	424	16	no	—
1069	C₂³	—	212	4	no	—
1070	C₂³	—	212	4	no	—
1071	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
1072	Q₈	—	8	2	no	—
1073	Q₈	—	424	2	no	—
1074	Q₈	—	424	2	no	—
1075	Q₈	—	424	2	no	—
1076	D₄	—	2	4	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	53	4	no	—
1079	D₄	—	106	8	no	—
1080	D₄	—	106	8	no	—
1081	D₄	—	106	4	no	—
1082	D₄	—	106	2	no	—
1083	D₄	C₂×Q₈×D₅₃	1	4	yes	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	8	2	no	—
1091	C₂×C₄	—	8	1	no	—
1092	C₂×C₄	—	53	4	no	—
1093	C₂×C₄	—	53	1	no	—
1094	C₂×C₄	—	53	1	no	—
1095	C₂×C₄	—	53	4	no	—
1096	C₂×C₄	—	53	4	no	—
1097	C₂×C₄	—	53	2	no	—
1098	C₂×C₄	—	53	2	no	—
1099	C₂×C₄	—	53	2	no	—
1100	C₂×C₄	—	53	2	no	—
1101	C₂×C₄	—	53	2	no	—
1102	C₂×C₄	—	53	2	no	—
1103	C₂×C₄	—	106	4	no	—
1104	C₂×C₄	—	106	4	no	—
1105	C₂×C₄	—	106	1	no	—
1106	C₂×C₄	—	106	1	no	—
1107	C₂×C₄	—	106	1	no	—
1108	C₂×C₄	—	106	1	no	—
1109	C₂×C₄	—	106	2	no	—
1110	C₂×C₄	—	424	2	no	—
1111	C₂×C₄	—	424	2	no	—
1112	C₂×C₄	—	424	2	no	—
1113	C₂×C₄	—	424	2	no	—
1114	C₂×C₄	—	424	2	no	—
1115	C₂×C₄	—	424	2	no	—
1116	C₂×C₄	—	424	2	no	—
1117	C₂×C₄	—	424	1	no	—
1118	C₂×C₄	—	212	2	no	—
1119	C₂×C₄	—	212	2	no	—
1120	C₂×C₄	—	212	2	no	—
1121	C₂×C₄	—	212	4	no	—
1122	C₂×C₄	—	212	2	no	—
1123	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1124	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1125	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1126	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1127	C₂×C₄	#41×D₅₃	1	2	yes	—
1128	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1129	C₈	—	2	1	no	—
1130	C₈	—	2	1	no	—
1131	C₈	—	2	2	no	—
1132	C₈	—	106	1	no	—
1133	C₈	—	106	1	no	—
1134	C₈	—	106	2	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	1	no	—
1137	C₂²	—	2	4	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	8	4	no	—
1141	C₂²	—	53	2	no	—
1142	C₂²	—	53	2	no	—
1143	C₂²	—	53	2	no	—
1144	C₂²	—	53	2	no	—
1145	C₂²	—	106	8	no	—
1146	C₂²	—	106	1	no	—
1147	C₂²	—	106	1	no	—
1148	C₂²	—	106	4	no	—
1149	C₂²	—	424	4	no	—
1150	C₂²	—	424	8	no	—
1151	C₂²	—	212	16	no	—
1152	C₂²	—	212	2	no	—
1153	C₂²	—	212	2	no	—
1154	C₂²	C₂²⋊Q₈×D₅₃	1	2	yes	—
1155	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1156	C₄	—	2	2	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	53	2	no	—
1164	C₄	—	53	2	no	—
1165	C₄	—	106	2	no	—
1166	C₄	—	106	2	no	—
1167	C₄	—	212	1	no	—
1168	C₄	—	212	2	no	—
1169	C₄	—	212	1	no	—
1170	C₄	—	212	1	no	—
1171	C₄	—	212	1	no	—
1172	C₄	C₂²⋊Q₈×D₅₃	1	2	yes	—
1173	C₄	C₂²×Q₈×D₅₃	1	1	yes	characteristic
1174	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1175	C₂	—	2	2	no	—
1176	C₂	—	4	4	no	—
1177	C₂	—	53	4	no	—
1178	C₂	—	106	2	no	—
1179	C₂	—	212	4	no	—
1180	C₂	C₂×C₂²⋊Q₈×D₅₃	1	1	yes	characteristic
1181	C₂	#576×D₅₃	1	1	yes	characteristic
1182	C₂	#577×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₅₃
commutator, cosocle	C₂×C₄×C₅₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₅₃×#3081	C₂
socle	C₂²×C₅₃	C₂³×D₄
prime radical	C₂²×D₄×D₅₃	C₂²
hypercenter	#3081	D₅₃
hypocenter	C₅₃	C₂×#3081
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3081

Complements

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

N	H ≅ G/N	type
1. #544×D₅₃	C₂	semidirect
3. #20284549	C₂	semidirect
4. #20284548	C₂	semidirect
5. #20284547	C₂	semidirect
6. #20284546	C₂	semidirect
7. #20284545	C₂	semidirect
8. #20284544	C₂	semidirect
9. #20284543	C₂	semidirect
10. #20284542	C₂	semidirect
11. #20284541	C₂	semidirect
12. #20284540	C₂	semidirect
13. #20284539	C₂	semidirect
14. #478×D₅₃	C₂	semidirect
15. #478×D₅₃	C₂	semidirect
16. #476×D₅₃	C₂	semidirect
17. #474×D₅₃	C₂	semidirect
18. #428×D₅₃	C₂	semidirect
19. #427×D₅₃	C₂	semidirect
20. #424×D₅₃	C₂	semidirect
23. C₅₃×#3081	C₂	semidirect
27. #16811254	C₂²	semidirect
29. #16811253	C₂²	semidirect
31. #16811251	C₂²	semidirect
32. #16811251	C₂²	semidirect
34. #16811250	C₂²	semidirect
36. C₄⋊Q₈×D₅₃	C₂²	semidirect
38. #125×D₅₃	C₂²	semidirect
57. #16810926	C₂²	semidirect
58. #16810926	C₂²	semidirect
59. #16810925	C₂²	semidirect
60. #16810925	C₂²	semidirect
61. #16810924	C₂²	semidirect
62. #16810924	C₂²	semidirect
63. #16810923	C₂²	semidirect
64. #16810923	C₂²	semidirect
65. #16810922	C₂²	semidirect
66. #16810922	C₂²	semidirect
67. #16810921	C₂²	semidirect
68. #16810921	C₂²	semidirect
69. #16810920	C₂²	semidirect
70. #16810920	C₂²	semidirect
71. #16810914	C₂²	semidirect
72. #16810913	C₂²	semidirect
73. #16810912	C₂²	semidirect
74. #16810912	C₂²	semidirect
75. #16810911	C₂²	semidirect
76. #16810911	C₂²	semidirect
77. #16810910	C₂²	semidirect
78. #16810904	C₂²	semidirect
79. #16810903	C₂²	semidirect
80. #16810902	C₂²	semidirect
81. #16810902	C₂²	semidirect
82. #16810901	C₂²	semidirect
83. #16810901	C₂²	semidirect
84. #16810900	C₂²	semidirect
85. #16810666	C₂²	semidirect
86. #16810665	C₂²	semidirect
87. #16810664	C₂²	semidirect
88. #16810663	C₂²	semidirect
89. #16810662	C₂²	semidirect
90. #16810661	C₂²	semidirect
91. #16810660	C₂²	semidirect
92. #16810660	C₂²	semidirect
93. #16810659	C₂²	semidirect
94. #16810659	C₂²	semidirect
95. #16810658	C₂²	semidirect
96. #16810658	C₂²	semidirect
97. #107×D₅₃	C₂²	semidirect
98. #107×D₅₃	C₂²	semidirect
99. #107×D₅₃	C₂²	semidirect
100. #106×D₅₃	C₂²	semidirect
101. #106×D₅₃	C₂²	semidirect
102. #106×D₅₃	C₂²	semidirect
103. #16810651	C₂²	semidirect
104. #16810650	C₂²	semidirect
105. #16810649	C₂²	semidirect
106. #16810648	C₂²	semidirect
107. #16810648	C₂²	semidirect
108. C₄⋊C₈×D₅₃	C₂²	semidirect
109. C₄⋊C₈×D₅₃	C₂²	semidirect
124. C₅₃×#544	C₂²	semidirect
126. C₅₃×#478	C₂²	semidirect
127. C₅₃×#478	C₂²	semidirect
128. C₅₃×#476	C₂²	semidirect
129. C₅₃×#474	C₂²	semidirect
130. C₅₃×#428	C₂²	semidirect
131. C₅₃×#427	C₂²	semidirect
132. C₅₃×#424	C₂²	semidirect
142. C₂×D₄×D₅₃	Q₈	semidirect
160. #13133217	C₂³	semidirect
165. #13133216	C₂³	semidirect
166. #13133216	C₂³	semidirect
170. #13133209	C₂³	semidirect
173. #13133208	C₂³	semidirect
174. #13133208	C₂³	semidirect
251. #13133151	C₂³	semidirect
252. #13133151	C₂³	semidirect
253. #13133151	C₂³	semidirect
254. #13133150	C₂³	semidirect
255. #13133150	C₂³	semidirect
256. #13133150	C₂³	semidirect
257. #13133150	C₂³	semidirect
258. #13133150	C₂³	semidirect
259. #13133150	C₂³	semidirect
260. #13133149	C₂³	semidirect
261. #13133149	C₂³	semidirect
262. #13133149	C₂³	semidirect
263. #13133148	C₂³	semidirect
264. #13133148	C₂³	semidirect
265. #13133148	C₂³	semidirect
266. #13133148	C₂³	semidirect
267. #13133148	C₂³	semidirect
268. #13133148	C₂³	semidirect
269. C₄⋊#88322	C₂³	semidirect
270. C₄⋊#88322	C₂³	semidirect
271. #13133146	C₂³	semidirect
272. #13133146	C₂³	semidirect
273. #13133146	C₂³	semidirect
274. #13133146	C₂³	semidirect
291. C₄⋊Q₈×C₅₃	C₂³	semidirect
293. #125×C₅₃	C₂³	semidirect
304. #107×C₅₃	C₂³	semidirect
305. #107×C₅₃	C₂³	semidirect
306. #107×C₅₃	C₂³	semidirect
307. #106×C₅₃	C₂³	semidirect
308. #106×C₅₃	C₂³	semidirect
309. #106×C₅₃	C₂³	semidirect
310. C₄⋊C₈×C₅₃	C₂³	semidirect
311. C₄⋊C₈×C₅₃	C₂³	semidirect
327. C₂×D₄×C₅₃	C₂×Q₈	semidirect
346. D₄×D₅₃	C₂×Q₈	semidirect
349. C₂×D₂₁₂	C₂×Q₈	semidirect
597. #3081	D₅₃	direct (N × H)
614. D₅₃	#3081	direct (N × H)
626. #544	C₂×D₅₃	semidirect
664. #478	C₂×D₅₃	semidirect
665. #478	C₂×D₅₃	semidirect
673. #476	C₂×D₅₃	semidirect
681. #474	C₂×D₅₃	semidirect
687. #428	C₂×D₅₃	semidirect
695. #427	C₂×D₅₃	semidirect
707. #424	C₂×D₅₃	semidirect
726. C₅₃	C₂×#3081	semidirect
765. C₄⋊Q₈	C₂²×D₅₃	semidirect
777. #125	C₂²×D₅₃	semidirect
869. #107	C₂²×D₅₃	semidirect
870. #107	C₂²×D₅₃	semidirect
871. #107	C₂²×D₅₃	semidirect
881. #106	C₂²×D₅₃	semidirect
882. #106	C₂²×D₅₃	semidirect
883. #106	C₂²×D₅₃	semidirect
890. C₄⋊C₈	C₂²×D₅₃	semidirect
891. C₄⋊C₈	C₂²×D₅₃	semidirect
936. C₂×D₄	Q₈×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#544×D₅₃	2
#518×D₅₃	2
#20284549	2
#20284548	2
#20284547	2
#20284546	2
#20284545	2
#20284544	2
#20284543	2
#20284542	2
#20284541	2
#20284540	2
#20284539	2
#478×D₅₃	2
#476×D₅₃	2
#474×D₅₃	2
#428×D₅₃	2
#427×D₅₃	2
#424×D₅₃	2
#418×D₅₃	2
C₂×#102×D₅₃	2
C₅₃×#3081	2
C₂×#3081	53

Subgroups — D53×#3081 #28251643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3081 #28251643