Subgroups — D₅₃×#2994 #28249186

Order 13568.

1982 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#529×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#20283878	C₂	1	1	yes	maximal, characteristic, complemented
3	#20283877	C₂	1	1	yes	maximal, characteristic, complemented
4	#20283876	C₂	1	1	yes	maximal, characteristic, complemented
5	#20283875	C₂	1	1	yes	maximal, characteristic, complemented
6	#20283874	C₂	1	1	yes	maximal, characteristic, complemented
7	#20283873	C₂	1	2	yes	maximal, complemented
8	#20283872	C₂	1	2	yes	maximal, complemented
9	#20283871	C₂	1	1	yes	maximal, characteristic, complemented
10	#20283870	C₂	1	1	yes	maximal, characteristic, complemented
11	#20283869	C₂	1	2	yes	maximal, complemented
12	#20283868	C₂	1	2	yes	maximal, complemented
13	#446×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#436×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#435×D₅₃	C₂	1	2	yes	maximal, complemented
17	C₈×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
19	#433×D₅₃	C₂	1	2	yes	maximal, complemented
20	#431×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#424×D₅₃	C₂	1	2	yes	maximal, complemented
22	C₂×C₄⋊C₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×M₁₆×D₅₃	C₂²	1	2	yes	—
25	C₂²×C₈×D₅₃	C₂²	1	2	yes	—
26	C₂²×C₈×D₅₃	C₂²	1	2	yes	—
27	#16811160	C₂²	1	1	yes	characteristic
28	#16811159	C₄	1	1	yes	characteristic
29	#16811158	C₄	1	1	yes	characteristic
30	#16811157	C₂²	1	1	yes	characteristic
31	#16811156	C₄	1	2	yes	—
32	#16811155	C₂²	1	1	yes	characteristic
33	#16811154	C₄	1	1	yes	characteristic
34	#16811153	C₂²	1	2	yes	—
35	#16811152	C₄	1	1	yes	characteristic
36	#16811151	C₂²	1	2	yes	—
37	#16811150	C₄	1	2	yes	—
38	#126×D₅₃	C₄	1	2	yes	—
39	#125×D₅₃	C₄	1	1	yes	characteristic
40	#124×D₅₃	C₄	1	1	yes	characteristic
41	#123×D₅₃	C₄	1	2	yes	—
42	C₂²⋊Q₈×D₅₃	C₄	1	1	yes	characteristic
43	#121×D₅₃	C₄	1	1	yes	characteristic
44	C₄×Q₈×D₅₃	C₂²	1	1	yes	characteristic
45	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic
46	C₄×D₄×D₅₃	C₂²	1	2	yes	—
47	#117×D₅₃	C₂²	1	2	yes	—
48	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
49	#16810754	C₂²	1	1	yes	characteristic, complemented
50	#16810753	C₂²	1	1	yes	characteristic, complemented
51	#16810752	C₂²	1	2	yes	complemented
52	#16810751	C₂²	1	2	yes	complemented
53	#16810750	C₂²	1	1	yes	characteristic, complemented
54	Q₈×#88322	C₂²	1	1	yes	characteristic, complemented
55	C₈×Dic₁₀₆	C₂²	1	2	yes	complemented
56	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
57	#16810747	C₂²	1	2	yes	complemented
58	#16810747	C₂²	1	1	yes	characteristic, complemented
59	#16810702	C₂²	1	1	yes	characteristic, complemented
60	#16810701	C₂²	1	1	yes	characteristic, complemented
61	#16810700	C₂²	1	1	yes	characteristic, complemented
62	#16810699	C₂²	1	2	yes	complemented
63	#16810698	C₂²	1	2	yes	complemented
64	#16810697	C₂²	1	2	yes	complemented
65	#16810696	C₂²	1	2	yes	complemented
66	#16810695	C₂²	1	2	yes	complemented
67	#16810694	C₂²	1	2	yes	complemented
68	#16810693	C₂²	1	2	yes	complemented
69	#16810692	C₂²	1	2	yes	complemented
70	#16810691	C₂²	1	2	yes	complemented
71	C₈×D₂₁₂	C₂²	1	2	yes	complemented
72	C₈×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
73	D₄×#88322	C₂²	1	2	yes	complemented
74	D₄×#88322	C₂²	1	1	yes	characteristic, complemented
75	#16810688	C₂²	1	1	yes	characteristic, complemented
76	#16810688	C₂²	1	2	yes	complemented
77	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
78	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
79	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
80	#16810686	C₂²	1	2	yes	complemented
81	#16810686	C₂²	1	2	yes	complemented
82	#16810686	C₂²	1	2	yes	complemented
83	#16810685	C₂²	1	2	yes	complemented
84	#16810684	C₂²	1	2	yes	complemented
85	#16810683	C₂²	1	2	yes	complemented
86	#16810683	C₂²	1	2	yes	complemented
87	#16810682	C₂²	1	2	yes	complemented
88	#16810681	C₂²	1	2	yes	complemented
89	#16810681	C₂²	1	2	yes	complemented
90	#16810676	C₂²	1	1	yes	characteristic, complemented
91	#16810675	C₂²	1	1	yes	characteristic, complemented
92	#16810675	C₂²	1	1	yes	characteristic, complemented
93	#16810674	C₂²	1	1	yes	characteristic, complemented
94	#16810674	C₂²	1	1	yes	characteristic, complemented
95	#16810673	C₂²	1	1	yes	characteristic, complemented
96	#16810673	C₂²	1	1	yes	characteristic, complemented
97	#16810651	C₂²	1	2	yes	complemented
98	#16810650	C₂²	1	2	yes	complemented
99	#16810649	C₂²	1	2	yes	complemented
100	#16810648	C₂²	1	2	yes	complemented
101	#16810648	C₂²	1	2	yes	complemented
102	#16810648	C₂²	1	2	yes	complemented
103	#16810648	C₂²	1	2	yes	complemented
104	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic, complemented
105	C₂×#13133146	C₂²	1	2	yes	complemented
106	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
107	C₄⋊C₈×D₅₃	C₂²	1	2	yes	—
108	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
109	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
110	C₄⋊C₈×D₅₃	C₂²	1	2	yes	—
111	C₄⋊C₈×D₅₃	C₂²	1	2	yes	—
112	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
113	C₄⋊C₈×D₅₃	C₂²	1	2	yes	complemented
114	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₂²⋊C₈×D₅₃	C₂²	1	2	yes	—
117	C₂²⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
118	C₂²⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
119	C₂²⋊C₈×D₅₃	C₂²	1	2	yes	—
120	#97×D₅₃	C₂²	1	2	yes	—
121	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
122	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
123	C₄×C₈×D₅₃	C₂²	1	2	yes	—
124	C₅₃×#529	C₂²	1	1	yes	characteristic
125	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
126	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#435	C₂²	1	2	yes	complemented
129	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
130	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
131	C₅₃×#433	C₂²	1	2	yes	complemented
132	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#424	C₂²	1	2	yes	complemented
134	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×Q₈×D₅₃	C₂×C₄	1	1	yes	characteristic
136	C₂×D₄×D₅₃	C₂×C₄	1	2	yes	—
137	C₂×D₄×D₅₃	C₂×C₄	1	1	yes	characteristic
138	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
139	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
140	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
141	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
142	C₂×#11719917	C₂³	1	2	yes	—
143	C₂×#11719912	C₂³	1	2	yes	—
144	C₂×#11719912	C₂³	1	2	yes	—
145	M₁₆×D₅₃	—	4	4	no	—
146	C₂²×#88322	C₂³	1	2	yes	—
147	C₂²×#88322	C₂³	1	2	yes	—
148	C₂×C₈×D₅₃	—	4	4	no	—
149	C₂×C₈×D₅₃	—	4	4	no	—
150	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
151	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
152	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₅₃	C₂³	1	2	yes	—
154	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₅₃	C₂³	1	2	yes	—
156	C₂×C₈×D₅₃	C₂³	1	2	yes	—
157	C₂×C₈×D₅₃	C₂³	1	2	yes	—
158	C₂×C₈×D₅₃	C₂³	1	2	yes	—
159	C₂×C₈×D₅₃	C₂³	1	2	yes	—
160	#13133212	C₂×C₄	1	2	yes	—
161	#13133212	C₂×C₄	1	2	yes	—
162	#13133212	C₂×C₄	1	2	yes	—
163	#13133211	C₂×C₄	1	2	yes	—
164	#13133210	C₂×C₄	1	2	yes	—
165	#13133210	C₂×C₄	1	2	yes	—
166	#13133210	C₂×C₄	1	2	yes	—
167	#13133209	C₂×C₄	1	1	yes	characteristic
168	#13133208	C₂×C₄	1	1	yes	characteristic
169	#13133208	C₂×C₄	1	1	yes	characteristic
170	#13133207	C₂×C₄	1	2	yes	—
171	#13133207	C₂×C₄	1	2	yes	—
172	#13133206	C₂×C₄	1	1	yes	characteristic
173	#13133205	C₂×C₄	1	1	yes	characteristic
174	#13133204	C₂×C₄	1	1	yes	characteristic
175	#13133203	C₂×C₄	1	2	yes	—
176	#13133203	C₂×C₄	1	2	yes	—
177	#13133202	C₂×C₄	1	2	yes	—
178	#13133202	C₂×C₄	1	2	yes	—
179	#13133201	C₂×C₄	1	2	yes	—
180	#13133200	C₂×C₄	1	2	yes	—
181	#13133199	C₂×C₄	1	2	yes	—
182	#13133199	C₂×C₄	1	2	yes	—
183	#13133198	C₂×C₄	1	2	yes	—
184	#13133197	C₂×C₄	1	1	yes	characteristic
185	#13133196	C₂×C₄	1	1	yes	characteristic
186	#13133195	C₂×C₄	1	2	yes	—
187	#13133194	C₂×C₄	1	2	yes	—
188	#13133193	C₂×C₄	1	1	yes	characteristic
189	#13133192	C₂×C₄	1	1	yes	characteristic
190	#13133191	C₂×C₄	1	1	yes	characteristic
191	#13133190	C₂×C₄	1	2	yes	—
192	#13133189	C₂×C₄	1	2	yes	—
193	#13133188	C₂×C₄	1	1	yes	characteristic
194	Q₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
195	C₄×Dic₁₀₆	C₂³	1	2	yes	—
196	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
197	#13133182	C₂×C₄	1	2	yes	—
198	#13133182	C₂×C₄	1	1	yes	characteristic
199	C₄×D₂₁₂	C₂³	1	2	yes	—
200	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
201	D₄×Dic₅₃	C₂×C₄	1	2	yes	—
202	D₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
203	#13133179	C₂×C₄	1	2	yes	—
204	#13133179	C₂×C₄	1	1	yes	characteristic
205	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
206	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
207	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
208	#13133177	C₂×C₄	1	2	yes	—
209	#13133177	C₂×C₄	1	2	yes	—
210	#13133177	C₂×C₄	1	2	yes	—
211	#13133176	C₂³	1	2	yes	—
212	#13133175	C₂×C₄	1	2	yes	—
213	#13133175	C₂×C₄	1	2	yes	—
214	#13133174	C₂³	1	2	yes	—
215	#13133174	C₂³	1	2	yes	—
216	#13133173	C₂×C₄	1	2	yes	—
217	#13133173	C₂×C₄	1	2	yes	—
218	C₄⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
219	C₄⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
220	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
221	C₄⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
222	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
223	C₄⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
224	C₂²⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
225	C₂²⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
226	C₂²⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
227	C₂²⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
228	C₂²⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
229	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
230	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
231	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
232	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
233	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
234	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
235	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
236	C₄²×D₅₃	C₂³	1	1	yes	characteristic
237	C₄²×D₅₃	C₂³	1	1	yes	characteristic
238	C₄²×D₅₃	C₂³	1	1	yes	characteristic
239	C₄²×D₅₃	C₂³	1	1	yes	characteristic
240	C₄²×D₅₃	C₂³	1	2	yes	—
241	C₄⋊#88322	C₂³	1	1	yes	characteristic
242	C₄⋊#88322	C₂³	1	2	yes	—
243	C₄⋊#88322	C₂³	1	2	yes	—
244	C₄⋊#88322	C₂³	1	1	yes	characteristic
245	C₄⋊#88322	C₂³	1	1	yes	characteristic
246	C₄⋊#88322	C₂³	1	2	yes	—
247	C₄⋊#88322	C₂³	1	1	yes	characteristic
248	#13133146	C₂³	1	2	yes	—
249	#13133146	C₂³	1	2	yes	—
250	#13133146	C₂³	1	2	yes	—
251	#13133146	C₂³	1	2	yes	—
252	#13133146	C₂³	1	2	yes	—
253	#13133146	C₂³	1	1	yes	characteristic
254	#13133146	C₂³	1	1	yes	characteristic
255	#13133146	C₂³	1	2	yes	—
256	#13133146	C₂³	1	2	yes	—
257	#13133146	C₂³	1	2	yes	—
258	#13133146	C₂³	1	1	yes	characteristic
259	#13133146	C₂³	1	1	yes	characteristic
260	C₂²⋊#88322	C₂³	1	1	yes	characteristic
261	C₂²⋊#88322	C₂³	1	1	yes	characteristic
262	C₂²⋊#88322	C₂³	1	2	yes	—
263	C₂²⋊#88322	C₂³	1	2	yes	—
264	#13133129	C₂³	1	1	yes	characteristic
265	#13133129	C₂³	1	1	yes	characteristic
266	#13133129	C₂³	1	1	yes	characteristic
267	#13133129	C₂³	1	1	yes	characteristic
268	#13133129	C₂³	1	2	yes	—
269	#13133129	C₂³	1	2	yes	—
270	#13133129	C₂³	1	2	yes	—
271	#13133129	C₂³	1	2	yes	—
272	#13133128	C₂³	1	2	yes	—
273	#13133127	C₂³	1	2	yes	—
274	#13133127	C₂³	1	2	yes	—
275	C₄×#88322	C₂³	1	1	yes	characteristic
276	C₄×#88322	C₂³	1	1	yes	characteristic
277	C₄×#88322	C₂³	1	2	yes	—
278	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
279	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
280	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
281	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
282	C₈×Dic₅₃	C₂³	1	2	yes	—
283	C₈×Dic₅₃	C₂³	1	2	yes	—
284	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
285	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
286	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
287	#126×C₅₃	C₂×C₄	1	2	yes	—
288	#125×C₅₃	C₂×C₄	1	1	yes	characteristic
289	#124×C₅₃	C₂×C₄	1	1	yes	characteristic
290	#123×C₅₃	C₂×C₄	1	2	yes	—
291	C₂²⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
292	#121×C₅₃	C₂×C₄	1	1	yes	characteristic
293	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
294	C₄×D₄×C₅₃	C₂³	1	2	yes	—
295	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
296	#117×C₅₃	C₂³	1	2	yes	—
297	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
298	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
299	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
300	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
303	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
304	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
309	#97×C₅₃	C₂³	1	2	yes	—
310	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₅₃	C₂³	1	2	yes	—
313	C₂³×D₅₃	C₂²×C₄	1	2	yes	—
314	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
315	C₂×Q₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
316	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
317	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
318	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
319	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
320	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
322	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
323	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
324	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
325	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
326	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
327	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
328	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
329	Q₈×D₅₃	—	2	4	no	—
330	D₄×D₅₃	—	2	8	no	—
331	D₄×D₅₃	—	2	4	no	—
332	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
333	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
334	C₂×C₄×D₅₃	—	2	4	no	—
335	C₂×C₄×D₅₃	—	2	4	no	—
336	C₂×C₄×D₅₃	—	2	2	no	—
337	C₂×C₄×D₅₃	—	2	4	no	—
338	C₂×C₄×D₅₃	—	2	2	no	—
339	C₂×C₄×D₅₃	—	2	4	no	—
340	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
341	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
342	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
343	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
344	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
345	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
346	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
347	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
348	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
349	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
350	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
351	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
352	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
353	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
354	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
355	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
356	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
357	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
358	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
359	M₁₆×C₅₃	—	4	2	no	—
360	C₂×C₈×C₅₃	—	4	2	no	—
361	C₂×C₈×C₅₃	—	4	2	no	—
362	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
366	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
369	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
370	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
371	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
372	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
373	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
374	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
375	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
376	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
377	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
378	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
379	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
380	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
381	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₄²×C₅₃	C₂⁴	1	2	yes	—
383	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
385	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
386	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
387	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
388	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
389	#11719921	C₂²×C₄	1	2	yes	—
390	#11719921	C₂²×C₄	1	2	yes	—
391	#11719921	C₂²×C₄	1	2	yes	—
392	#11719921	C₂²×C₄	1	2	yes	—
393	#11719921	C₂²×C₄	1	2	yes	—
394	#11719921	C₂²×C₄	1	2	yes	—
395	#11719921	C₂²×C₄	1	2	yes	—
396	#11719921	C₂²×C₄	1	2	yes	—
397	#11719921	C₂²×C₄	1	2	yes	—
398	#11719921	C₂²×C₄	1	2	yes	—
399	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
400	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
401	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
403	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
404	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
405	#11719919	C₂²×C₄	1	2	yes	—
406	#11719919	C₂²×C₄	1	2	yes	—
407	#11719919	C₂²×C₄	1	2	yes	—
408	#11719919	C₂²×C₄	1	2	yes	—
409	#11719919	C₂²×C₄	1	2	yes	—
410	#11719919	C₂²×C₄	1	2	yes	—
411	#11719919	C₂²×C₄	1	2	yes	—
412	#11719919	C₂²×C₄	1	2	yes	—
413	#11719919	C₂²×C₄	1	2	yes	—
414	#11719919	C₂²×C₄	1	2	yes	—
415	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
416	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
417	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
418	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
419	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
420	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
421	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
422	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
423	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
424	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
425	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
426	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
427	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
428	C₄×Dic₅₃	C₂⁴	1	2	yes	—
429	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
430	#11719917	—	4	2	no	—
431	C₂×#88322	—	4	2	no	—
432	C₂×#88322	—	4	2	no	—
433	C₂×#88322	C₂⁴	1	1	yes	characteristic
434	C₂×#88322	C₂⁴	1	1	yes	characteristic
435	C₂×#88322	C₂⁴	1	1	yes	characteristic
436	C₂×#88322	C₂⁴	1	2	yes	—
437	C₂×#88322	C₂⁴	1	1	yes	characteristic
438	C₂×#88322	C₂⁴	1	2	yes	—
439	#11719912	—	4	2	no	—
440	#11719912	—	4	2	no	—
441	C₈×D₅₃	—	2	4	no	—
442	C₈×D₅₃	—	2	2	no	—
443	C₈×D₅₃	—	2	4	no	—
444	C₈×D₅₃	—	2	2	no	—
445	C₈×D₅₃	—	2	2	no	—
446	C₈×D₅₃	—	2	2	no	—
447	C₈×D₅₃	—	4	2	no	—
448	C₈×D₅₃	—	4	2	no	—
449	C₈×D₅₃	—	4	2	no	—
450	C₈×D₅₃	—	4	2	no	—
451	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
452	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
453	C₂²×D₅₃	—	2	2	no	—
454	C₂²×D₅₃	—	2	2	no	—
455	C₂²×D₅₃	—	2	4	no	—
456	C₂²×D₅₃	—	2	4	no	—
457	C₂²×D₅₃	—	2	4	no	—
458	C₂²×D₅₃	#131	1	4	yes	—
459	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
460	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
461	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
462	Q₈×C₅₃	—	2	2	no	—
463	D₄×C₅₃	—	2	4	no	—
464	D₄×C₅₃	—	2	2	no	—
465	C₂×C₄×C₅₃	—	2	2	no	—
466	C₂×C₄×C₅₃	—	2	2	no	—
467	C₂×C₄×C₅₃	—	2	1	no	—
468	C₂×C₄×C₅₃	—	2	2	no	—
469	C₂×C₄×C₅₃	—	2	1	no	—
470	C₂×C₄×C₅₃	—	2	2	no	—
471	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
472	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
473	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
474	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
475	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
476	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
477	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
478	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
479	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
480	C₂²⋊D₅₃	—	2	4	no	—
481	C₂²⋊D₅₃	—	2	4	no	—
482	C₂²⋊D₅₃	—	2	4	no	—
483	C₂×Dic₅₃	—	2	2	no	—
484	C₂×Dic₅₃	—	2	2	no	—
485	C₂×Dic₅₃	—	2	4	no	—
486	C₂×Dic₅₃	—	2	2	no	—
487	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
488	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
489	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
490	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
491	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
492	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
493	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
494	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
495	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
496	D₂₁₂	—	2	4	no	—
497	D₂₁₂	—	2	2	no	—
498	C₄×D₅₃	—	2	2	no	—
499	C₄×D₅₃	—	2	4	no	—
500	C₄×D₅₃	—	2	2	no	—
501	C₄×D₅₃	—	2	2	no	—
502	C₄×D₅₃	—	2	2	no	—
503	C₄×D₅₃	—	2	2	no	—
504	C₄×D₅₃	—	2	2	no	—
505	C₄×D₅₃	—	2	4	no	—
506	C₄×D₅₃	—	2	4	no	—
507	C₄×D₅₃	—	2	2	no	—
508	C₄×D₅₃	—	2	1	no	—
509	C₄×D₅₃	—	2	2	no	—
510	C₄×D₅₃	—	2	1	no	—
511	C₄×D₅₃	—	2	2	no	—
512	C₄×D₅₃	—	2	2	no	—
513	C₄×D₅₃	—	2	4	no	—
514	C₄×D₅₃	—	2	2	no	—
515	C₄×D₅₃	#131	1	4	yes	—
516	C₄×D₅₃	H(5,𝔽₂)	1	2	yes	—
517	C₄×D₅₃	2₋¹⁺⁴	1	2	yes	—
518	Dic₁₀₆	—	2	2	no	—
519	Dic₁₀₆	—	2	4	no	—
520	C₈×C₅₃	—	2	1	no	—
521	C₈×C₅₃	—	2	2	no	—
522	C₈×C₅₃	—	2	2	no	—
523	C₈×C₅₃	—	2	1	no	—
524	C₈×C₅₃	—	2	1	no	—
525	C₈×C₅₃	—	2	1	no	—
526	#88322	—	2	1	no	—
527	#88322	—	2	2	no	—
528	#88322	—	2	2	no	—
529	#88322	—	2	1	no	—
530	#88322	—	2	1	no	—
531	#88322	—	2	1	no	—
532	C₂×#2994	—	53	1	no	maximal, Sylow
533	C₂²×C₅₃	—	2	1	no	—
534	C₂²×C₅₃	—	2	1	no	—
535	C₂²×C₅₃	—	2	2	no	—
536	C₂²×C₅₃	—	2	2	no	—
537	C₂²×C₅₃	—	2	2	no	—
538	C₂²×C₅₃	C₂×#131	1	2	yes	—
539	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
540	C₂×D₅₃	—	2	1	no	—
541	C₂×D₅₃	—	2	1	no	—
542	C₂×D₅₃	—	2	8	no	—
543	C₂×D₅₃	—	2	2	no	—
544	C₂×D₅₃	—	2	2	no	—
545	C₂×D₅₃	—	2	2	no	—
546	C₂×D₅₃	—	4	8	no	—
547	C₂×D₅₃	#520	1	2	yes	—
548	C₂×D₅₃	C₂×#131	1	2	yes	—
549	C₂×D₅₃	C₂×#131	1	2	yes	—
550	C₂×D₅₃	C₂×#131	1	2	yes	—
551	C₄×C₅₃	—	2	1	no	—
552	C₄×C₅₃	—	2	2	no	—
553	C₄×C₅₃	—	2	2	no	—
554	C₄×C₅₃	—	2	1	no	—
555	C₄×C₅₃	—	2	1	no	—
556	C₄×C₅₃	—	2	1	no	—
557	C₄×C₅₃	—	2	2	no	—
558	C₄×C₅₃	C₂×#131	1	2	yes	—
559	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
560	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
561	Dic₅₃	—	2	1	no	—
562	Dic₅₃	—	2	2	no	—
563	Dic₅₃	—	2	2	no	—
564	Dic₅₃	—	2	1	no	—
565	Dic₅₃	—	2	1	no	—
566	Dic₅₃	—	2	1	no	—
567	Dic₅₃	—	2	2	no	—
568	Dic₅₃	#520	1	2	yes	—
569	Dic₅₃	C₂×#131	1	2	yes	—
570	C₂×#529	—	53	1	no	—
571	#2994	—	53	1	no	—
572	#2994	—	53	1	no	—
573	#2994	—	53	1	no	—
574	#2994	—	53	2	no	—
575	#2994	—	53	1	no	—
576	#2994	—	53	2	no	—
577	#2994	—	53	2	no	—
578	#2994	—	53	1	no	—
579	#2994	—	53	2	no	—
580	#2994	—	53	1	no	—
581	#2994	—	53	1	no	—
582	#2994	D₅₃	1	1	yes	characteristic, direct product factor
583	C₂×#446	—	53	1	no	—
584	C₂×C₈×Q₈	—	53	1	no	—
585	C₂×#436	—	53	1	no	—
586	C₂×#435	—	53	2	no	—
587	C₂×C₈×D₄	—	53	2	no	—
588	C₂×C₈×D₄	—	53	1	no	—
589	C₂×#433	—	53	2	no	—
590	C₂×#431	—	53	1	no	—
591	C₂×#424	—	53	2	no	—
592	C₂²×C₄⋊C₈	—	53	1	no	—
593	C₂×C₅₃	—	2	2	no	—
594	C₂×C₅₃	—	4	2	no	—
595	C₂×C₅₃	C₂×#520	1	1	yes	characteristic
596	C₂×C₅₃	C₂²×#131	1	1	yes	characteristic
597	C₂×C₅₃	C₂²×#131	1	1	yes	characteristic
598	D₅₃	—	2	2	no	—
599	D₅₃	—	4	2	no	—
600	D₅₃	#2994	1	4	yes	direct product factor
601	C₂²×M₁₆	—	53	2	no	—
602	C₂³×C₈	—	53	2	no	—
603	C₂³×C₈	—	53	2	no	—
604	#529	—	53	2	no	—
605	#529	—	53	1	no	—
606	#529	—	53	1	no	—
607	#529	—	53	2	no	—
608	#529	—	53	1	no	—
609	#529	—	53	1	no	—
610	#529	—	53	1	no	—
611	#529	—	53	2	no	—
612	#529	—	53	1	no	—
613	#529	—	53	2	no	—
614	#529	—	53	1	no	—
615	#529	C₂×D₅₃	1	1	yes	characteristic
616	C₂×#126	—	53	2	no	—
617	C₂×#125	—	53	1	no	—
618	C₂×#124	—	53	1	no	—
619	C₂×#123	—	53	2	no	—
620	C₂×C₂²⋊Q₈	—	53	1	no	—
621	C₂×#121	—	53	1	no	—
622	C₂×C₄×Q₈	—	53	1	no	—
623	C₂×C₄×D₄	—	53	2	no	—
624	C₂×C₄×D₄	—	53	1	no	—
625	C₂×#117	—	53	2	no	—
626	C₂²×C₄²	—	53	1	no	—
627	#446	—	53	1	no	—
628	#446	—	53	2	no	—
629	#446	—	53	1	no	—
630	#446	—	53	2	no	—
631	#446	—	53	1	no	—
632	#446	C₂×D₅₃	1	1	yes	characteristic, complemented
633	C₈×Q₈	—	53	1	no	—
634	C₈×Q₈	—	53	2	no	—
635	C₈×Q₈	—	53	1	no	—
636	C₈×Q₈	—	53	2	no	—
637	C₈×Q₈	—	53	1	no	—
638	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
639	#436	—	53	2	no	—
640	#436	—	53	1	no	—
641	#436	—	53	1	no	—
642	#436	—	53	2	no	—
643	#436	—	53	1	no	—
644	#436	C₂×D₅₃	1	1	yes	characteristic, complemented
645	#435	—	53	2	no	—
646	#435	—	53	2	no	—
647	#435	—	53	2	no	—
648	#435	—	53	2	no	—
649	#435	—	53	2	no	—
650	#435	—	53	2	no	—
651	#435	—	53	2	no	—
652	#435	C₂×D₅₃	1	2	yes	complemented
653	C₈×D₄	—	53	2	no	—
654	C₈×D₄	—	53	2	no	—
655	C₈×D₄	—	53	2	no	—
656	C₈×D₄	—	53	1	no	—
657	C₈×D₄	—	53	2	no	—
658	C₈×D₄	—	53	1	no	—
659	C₈×D₄	—	53	2	no	—
660	C₈×D₄	—	53	2	no	—
661	C₈×D₄	—	53	2	no	—
662	C₈×D₄	—	53	2	no	—
663	C₈×D₄	—	53	1	no	—
664	C₈×D₄	—	53	2	no	—
665	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
666	C₈×D₄	C₂×D₅₃	1	2	yes	complemented
667	#433	—	53	2	no	—
668	#433	—	53	2	no	—
669	#433	—	53	2	no	—
670	#433	—	53	2	no	—
671	#433	—	53	2	no	—
672	#433	—	53	2	no	—
673	#433	—	53	2	no	—
674	#433	C₂×D₅₃	1	2	yes	complemented
675	#431	—	53	1	no	—
676	#431	—	53	1	no	—
677	#431	—	53	1	no	—
678	#431	—	53	1	no	—
679	#431	—	53	1	no	—
680	#431	—	53	1	no	—
681	#431	—	53	1	no	—
682	#431	C₂×D₅₃	1	1	yes	characteristic, complemented
683	#424	—	53	2	no	—
684	#424	—	53	2	no	—
685	#424	—	53	2	no	—
686	#424	—	53	2	no	—
687	#424	—	53	2	no	—
688	#424	—	53	2	no	—
689	#424	—	53	2	no	—
690	#424	C₂×D₅₃	1	2	yes	complemented
691	C₂×C₄⋊C₈	—	53	2	no	—
692	C₂×C₄⋊C₈	—	53	1	no	—
693	C₂×C₄⋊C₈	—	53	2	no	—
694	C₂×C₄⋊C₈	—	53	1	no	—
695	C₂×C₄⋊C₈	—	53	1	no	—
696	C₂×C₄⋊C₈	—	53	1	no	—
697	C₂×C₄⋊C₈	—	53	1	no	—
698	C₂×C₄⋊C₈	—	53	2	no	—
699	C₂×C₄⋊C₈	—	53	1	no	—
700	C₂×C₄⋊C₈	—	53	2	no	—
701	C₂×C₄⋊C₈	—	53	2	no	—
702	C₂×C₄⋊C₈	—	53	1	no	—
703	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
704	C₂×C₂²⋊C₈	—	53	1	no	—
705	C₂×C₂²⋊C₈	—	53	1	no	—
706	C₂×C₂²⋊C₈	—	53	2	no	—
707	C₂×C₂²⋊C₈	—	53	2	no	—
708	C₂×#97	—	53	2	no	—
709	C₂×C₄×C₈	—	53	1	no	—
710	C₂×C₄×C₈	—	53	1	no	—
711	C₂×C₄×C₈	—	53	2	no	—
712	C₅₃	C₂×#2994	1	1	yes	characteristic, complemented, Sylow
713	C₂²×Q₈	—	53	1	no	—
714	C₂²×D₄	—	53	2	no	—
715	C₂²×D₄	—	53	1	no	—
716	C₂³×C₄	—	53	1	no	—
717	C₂³×C₄	—	53	1	no	—
718	C₂³×C₄	—	53	2	no	—
719	C₂³×C₄	—	53	1	no	—
720	C₂×M₁₆	—	53	2	no	—
721	C₂×M₁₆	—	53	2	no	—
722	C₂×M₁₆	—	53	2	no	—
723	C₂×M₁₆	—	212	4	no	—
724	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
725	C₂²×C₈	—	53	2	no	—
726	C₂²×C₈	—	53	2	no	—
727	C₂²×C₈	—	53	2	no	—
728	C₂²×C₈	—	53	1	no	—
729	C₂²×C₈	—	53	2	no	—
730	C₂²×C₈	—	53	1	no	—
731	C₂²×C₈	—	53	1	no	—
732	C₂²×C₈	—	53	1	no	—
733	C₂²×C₈	—	53	2	no	—
734	C₂²×C₈	—	53	2	no	—
735	C₂²×C₈	—	53	2	no	—
736	C₂²×C₈	—	53	2	no	—
737	C₂²×C₈	—	212	4	no	—
738	C₂²×C₈	—	212	4	no	—
739	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
740	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
741	#126	—	53	2	no	—
742	#126	—	53	2	no	—
743	#126	—	53	2	no	—
744	#126	—	53	2	no	—
745	#126	—	53	2	no	—
746	#126	—	53	2	no	—
747	#126	—	53	2	no	—
748	#126	C₄×D₅₃	1	2	yes	—
749	#125	—	53	2	no	—
750	#125	—	53	2	no	—
751	#125	—	53	1	no	—
752	#125	—	53	1	no	—
753	#125	—	53	1	no	—
754	#125	C₄×D₅₃	1	1	yes	characteristic
755	#124	—	53	1	no	—
756	#124	—	53	1	no	—
757	#124	—	53	2	no	—
758	#124	—	53	2	no	—
759	#124	—	53	1	no	—
760	#124	C₄×D₅₃	1	1	yes	characteristic
761	#123	—	53	2	no	—
762	#123	—	53	2	no	—
763	#123	—	53	2	no	—
764	#123	—	53	2	no	—
765	#123	—	53	2	no	—
766	#123	—	53	2	no	—
767	#123	—	53	2	no	—
768	#123	C₄×D₅₃	1	2	yes	—
769	C₂²⋊Q₈	—	53	1	no	—
770	C₂²⋊Q₈	—	53	1	no	—
771	C₂²⋊Q₈	—	53	2	no	—
772	C₂²⋊Q₈	—	53	1	no	—
773	C₂²⋊Q₈	—	53	2	no	—
774	C₂²⋊Q₈	C₄×D₅₃	1	1	yes	characteristic
775	#121	—	53	1	no	—
776	#121	—	53	2	no	—
777	#121	—	53	1	no	—
778	#121	—	53	1	no	—
779	#121	—	53	2	no	—
780	#121	C₄×D₅₃	1	1	yes	characteristic
781	C₄×Q₈	—	53	1	no	—
782	C₄×Q₈	—	53	2	no	—
783	C₄×Q₈	—	53	1	no	—
784	C₄×Q₈	—	53	2	no	—
785	C₄×Q₈	—	53	1	no	—
786	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
787	C₄×D₄	—	53	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	1	no	—
793	C₄×D₄	—	53	2	no	—
794	C₄×D₄	—	53	2	no	—
795	C₄×D₄	—	53	2	no	—
796	C₄×D₄	—	53	2	no	—
797	C₄×D₄	—	53	2	no	—
798	C₄×D₄	—	53	1	no	—
799	C₄×D₄	C₂²×D₅₃	1	2	yes	—
800	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
801	#117	—	53	2	no	—
802	#117	—	53	2	no	—
803	#117	—	53	2	no	—
804	#117	—	53	2	no	—
805	#117	—	53	2	no	—
806	#117	—	53	2	no	—
807	#117	—	53	2	no	—
808	#117	C₂²×D₅₃	1	2	yes	—
809	C₂×C₄⋊C₄	—	53	2	no	—
810	C₂×C₄⋊C₄	—	53	2	no	—
811	C₂×C₄⋊C₄	—	53	1	no	—
812	C₂×C₄⋊C₄	—	53	2	no	—
813	C₂×C₄⋊C₄	—	53	1	no	—
814	C₂×C₄⋊C₄	—	53	2	no	—
815	C₂×C₂²⋊C₄	—	53	2	no	—
816	C₂×C₂²⋊C₄	—	53	2	no	—
817	C₂×C₂²⋊C₄	—	53	2	no	—
818	C₂×C₂²⋊C₄	—	53	2	no	—
819	C₂×C₂²⋊C₄	—	53	2	no	—
820	C₂×C₄²	—	53	1	no	—
821	C₂×C₄²	—	53	1	no	—
822	C₂×C₄²	—	53	1	no	—
823	C₂×C₄²	—	53	1	no	—
824	C₂×C₄²	—	53	1	no	—
825	C₂×C₄²	—	53	1	no	—
826	C₂×C₄²	—	53	1	no	—
827	C₂×C₄²	—	53	1	no	—
828	C₂×C₄²	—	53	2	no	—
829	C₂×C₄²	—	53	1	no	—
830	C₂×C₄²	—	53	1	no	—
831	C₂×C₄²	—	53	1	no	—
832	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
833	C₄⋊C₈	—	53	2	no	—
834	C₄⋊C₈	—	53	2	no	—
835	C₄⋊C₈	—	53	2	no	—
836	C₄⋊C₈	—	53	2	no	—
837	C₄⋊C₈	—	53	1	no	—
838	C₄⋊C₈	—	53	1	no	—
839	C₄⋊C₈	—	53	2	no	—
840	C₄⋊C₈	—	53	2	no	—
841	C₄⋊C₈	—	53	2	no	—
842	C₄⋊C₈	—	53	2	no	—
843	C₄⋊C₈	—	53	1	no	—
844	C₄⋊C₈	—	53	1	no	—
845	C₄⋊C₈	—	53	2	no	—
846	C₄⋊C₈	—	53	1	no	—
847	C₄⋊C₈	—	53	1	no	—
848	C₄⋊C₈	—	53	1	no	—
849	C₄⋊C₈	—	53	2	no	—
850	C₄⋊C₈	—	53	2	no	—
851	C₄⋊C₈	—	53	1	no	—
852	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
853	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
854	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
855	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
856	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
857	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
858	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
859	C₂²⋊C₈	—	53	1	no	—
860	C₂²⋊C₈	—	53	1	no	—
861	C₂²⋊C₈	—	53	2	no	—
862	C₂²⋊C₈	—	53	2	no	—
863	C₂²⋊C₈	—	53	1	no	—
864	C₂²⋊C₈	—	53	1	no	—
865	C₂²⋊C₈	—	53	1	no	—
866	C₂²⋊C₈	—	53	1	no	—
867	C₂²⋊C₈	—	53	2	no	—
868	C₂²⋊C₈	—	53	2	no	—
869	C₂²⋊C₈	—	53	2	no	—
870	C₂²⋊C₈	—	53	2	no	—
871	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
872	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
873	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
874	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
875	#97	—	53	2	no	—
876	#97	—	53	2	no	—
877	#97	—	53	2	no	—
878	#97	C₂²×D₅₃	1	2	yes	—
879	C₄×C₈	—	53	1	no	—
880	C₄×C₈	—	53	1	no	—
881	C₄×C₈	—	53	1	no	—
882	C₄×C₈	—	53	1	no	—
883	C₄×C₈	—	53	2	no	—
884	C₄×C₈	—	53	2	no	—
885	C₄×C₈	—	53	1	no	—
886	C₄×C₈	—	53	1	no	—
887	C₄×C₈	—	53	2	no	—
888	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
889	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
890	C₄×C₈	C₂²×D₅₃	1	2	yes	—
891	C₂⁴	—	53	1	no	—
892	C₂⁴	—	53	2	no	—
893	C₂×Q₈	—	53	2	no	—
894	C₂×Q₈	—	53	1	no	—
895	C₂×Q₈	—	106	4	no	—
896	C₂×Q₈	C₂×C₄×D₅₃	1	1	yes	characteristic
897	C₂×D₄	—	53	2	no	—
898	C₂×D₄	—	53	2	no	—
899	C₂×D₄	—	53	2	no	—
900	C₂×D₄	—	53	2	no	—
901	C₂×D₄	—	53	1	no	—
902	C₂×D₄	—	106	4	no	—
903	C₂×D₄	—	106	8	no	—
904	C₂×D₄	C₂×C₄×D₅₃	1	2	yes	—
905	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
906	C₂²×C₄	—	53	1	no	—
907	C₂²×C₄	—	53	1	no	—
908	C₂²×C₄	—	53	1	no	—
909	C₂²×C₄	—	53	1	no	—
910	C₂²×C₄	—	53	1	no	—
911	C₂²×C₄	—	53	2	no	—
912	C₂²×C₄	—	53	1	no	—
913	C₂²×C₄	—	53	1	no	—
914	C₂²×C₄	—	53	1	no	—
915	C₂²×C₄	—	53	1	no	—
916	C₂²×C₄	—	53	1	no	—
917	C₂²×C₄	—	53	1	no	—
918	C₂²×C₄	—	53	1	no	—
919	C₂²×C₄	—	53	1	no	—
920	C₂²×C₄	—	53	1	no	—
921	C₂²×C₄	—	53	2	no	—
922	C₂²×C₄	—	53	2	no	—
923	C₂²×C₄	—	53	2	no	—
924	C₂²×C₄	—	53	2	no	—
925	C₂²×C₄	—	53	1	no	—
926	C₂²×C₄	—	53	2	no	—
927	C₂²×C₄	—	106	2	no	—
928	C₂²×C₄	—	106	4	no	—
929	C₂²×C₄	—	106	4	no	—
930	C₂²×C₄	—	106	2	no	—
931	C₂²×C₄	—	106	4	no	—
932	C₂²×C₄	—	106	4	no	—
933	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
934	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
935	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
936	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
937	M₁₆	—	4	2	no	—
938	M₁₆	—	212	2	no	—
939	M₁₆	—	212	2	no	—
940	M₁₆	—	212	2	no	—
941	C₂×C₈	—	4	2	no	—
942	C₂×C₈	—	4	2	no	—
943	C₂×C₈	—	53	1	no	—
944	C₂×C₈	—	53	1	no	—
945	C₂×C₈	—	53	1	no	—
946	C₂×C₈	—	53	2	no	—
947	C₂×C₈	—	53	1	no	—
948	C₂×C₈	—	53	2	no	—
949	C₂×C₈	—	106	4	no	—
950	C₂×C₈	—	106	2	no	—
951	C₂×C₈	—	106	4	no	—
952	C₂×C₈	—	106	2	no	—
953	C₂×C₈	—	106	2	no	—
954	C₂×C₈	—	106	2	no	—
955	C₂×C₈	—	212	2	no	—
956	C₂×C₈	—	212	2	no	—
957	C₂×C₈	—	212	2	no	—
958	C₂×C₈	—	212	2	no	—
959	C₂×C₈	—	212	2	no	—
960	C₂×C₈	—	212	2	no	—
961	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
962	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
963	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
964	C₂×C₈	C₂³×D₅₃	1	2	yes	—
965	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
966	C₂×C₈	C₂³×D₅₃	1	2	yes	—
967	C₄⋊C₄	—	53	2	no	—
968	C₄⋊C₄	—	53	2	no	—
969	C₄⋊C₄	—	53	2	no	—
970	C₄⋊C₄	—	53	2	no	—
971	C₄⋊C₄	—	53	2	no	—
972	C₄⋊C₄	—	53	2	no	—
973	C₄⋊C₄	—	53	2	no	—
974	C₄⋊C₄	—	53	1	no	—
975	C₄⋊C₄	—	53	2	no	—
976	C₄⋊C₄	—	53	2	no	—
977	C₄⋊C₄	—	53	2	no	—
978	C₄⋊C₄	—	53	2	no	—
979	C₄⋊C₄	—	53	1	no	—
980	C₄⋊C₄	—	53	2	no	—
981	C₄⋊C₄	—	53	2	no	—
982	C₄⋊C₄	—	53	2	no	—
983	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
984	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
985	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
986	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
987	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
988	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
989	C₂²⋊C₄	—	53	2	no	—
990	C₂²⋊C₄	—	53	2	no	—
991	C₂²⋊C₄	—	53	2	no	—
992	C₂²⋊C₄	—	53	2	no	—
993	C₂²⋊C₄	—	53	2	no	—
994	C₂²⋊C₄	—	53	2	no	—
995	C₂²⋊C₄	—	53	2	no	—
996	C₂²⋊C₄	—	53	2	no	—
997	C₂²⋊C₄	—	53	2	no	—
998	C₂²⋊C₄	—	53	2	no	—
999	C₂²⋊C₄	—	53	2	no	—
1000	C₂²⋊C₄	—	53	2	no	—
1001	C₂²⋊C₄	—	53	2	no	—
1002	C₂²⋊C₄	—	53	2	no	—
1003	C₂²⋊C₄	—	53	2	no	—
1004	C₂²⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
1005	C₂²⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
1006	C₂²⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
1007	C₂²⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
1008	C₂²⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
1009	C₄²	—	53	1	no	—
1010	C₄²	—	53	1	no	—
1011	C₄²	—	53	1	no	—
1012	C₄²	—	53	1	no	—
1013	C₄²	—	53	1	no	—
1014	C₄²	—	53	1	no	—
1015	C₄²	—	53	1	no	—
1016	C₄²	—	53	1	no	—
1017	C₄²	—	53	1	no	—
1018	C₄²	—	53	1	no	—
1019	C₄²	—	53	2	no	—
1020	C₄²	—	53	2	no	—
1021	C₄²	—	53	1	no	—
1022	C₄²	—	53	2	no	—
1023	C₄²	—	53	1	no	—
1024	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1025	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1026	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1027	C₄²	C₂³×D₅₃	1	2	yes	—
1028	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1029	C₂³	—	53	1	no	—
1030	C₂³	—	53	4	no	—
1031	C₂³	—	53	1	no	—
1032	C₂³	—	53	2	no	—
1033	C₂³	—	106	2	no	—
1034	C₂³	—	106	2	no	—
1035	C₂³	—	106	4	no	—
1036	C₂³	—	106	4	no	—
1037	C₂³	—	106	4	no	—
1038	C₂³	C₂²×C₄×D₅₃	1	2	yes	—
1039	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1040	Q₈	—	2	2	no	—
1041	Q₈	—	106	4	no	—
1042	Q₈	—	106	2	no	—
1043	D₄	—	2	4	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	106	4	no	—
1046	D₄	—	106	4	no	—
1047	D₄	—	106	4	no	—
1048	D₄	—	106	4	no	—
1049	D₄	—	106	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	53	1	no	—
1057	C₂×C₄	—	53	1	no	—
1058	C₂×C₄	—	53	4	no	—
1059	C₂×C₄	—	53	2	no	—
1060	C₂×C₄	—	53	2	no	—
1061	C₂×C₄	—	53	1	no	—
1062	C₂×C₄	—	53	1	no	—
1063	C₂×C₄	—	53	1	no	—
1064	C₂×C₄	—	53	1	no	—
1065	C₂×C₄	—	53	2	no	—
1066	C₂×C₄	—	53	2	no	—
1067	C₂×C₄	—	53	2	no	—
1068	C₂×C₄	—	106	2	no	—
1069	C₂×C₄	—	106	2	no	—
1070	C₂×C₄	—	106	4	no	—
1071	C₂×C₄	—	106	2	no	—
1072	C₂×C₄	—	106	2	no	—
1073	C₂×C₄	—	106	2	no	—
1074	C₂×C₄	—	106	2	no	—
1075	C₂×C₄	—	106	2	no	—
1076	C₂×C₄	—	106	2	no	—
1077	C₂×C₄	—	106	4	no	—
1078	C₂×C₄	—	106	4	no	—
1079	C₂×C₄	—	106	4	no	—
1080	C₂×C₄	—	106	2	no	—
1081	C₂×C₄	—	106	2	no	—
1082	C₂×C₄	—	106	4	no	—
1083	C₂×C₄	—	106	2	no	—
1084	C₂×C₄	—	106	2	no	—
1085	C₂×C₄	—	106	1	no	—
1086	C₂×C₄	—	106	2	no	—
1087	C₂×C₄	—	106	1	no	—
1088	C₂×C₄	—	106	2	no	—
1089	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1090	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1091	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1092	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1093	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1094	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1095	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1096	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1097	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1098	C₈	—	2	1	no	—
1099	C₈	—	2	2	no	—
1100	C₈	—	2	2	no	—
1101	C₈	—	2	1	no	—
1102	C₈	—	2	1	no	—
1103	C₈	—	2	1	no	—
1104	C₈	—	106	1	no	—
1105	C₈	—	106	2	no	—
1106	C₈	—	106	2	no	—
1107	C₈	—	106	1	no	—
1108	C₈	—	106	1	no	—
1109	C₈	—	106	1	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	2	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	53	2	no	—
1116	C₂²	—	53	2	no	—
1117	C₂²	—	53	2	no	—
1118	C₂²	—	53	2	no	—
1119	C₂²	—	106	8	no	—
1120	C₂²	—	106	1	no	—
1121	C₂²	—	106	1	no	—
1122	C₂²	—	106	2	no	—
1123	C₂²	—	106	2	no	—
1124	C₂²	—	106	2	no	—
1125	C₂²	—	212	8	no	—
1126	C₂²	#131×D₅₃	1	2	yes	—
1127	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1128	C₄	—	2	1	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	1	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	53	2	no	—
1136	C₄	—	53	2	no	—
1137	C₄	—	106	1	no	—
1138	C₄	—	106	1	no	—
1139	C₄	—	106	1	no	—
1140	C₄	—	106	2	no	—
1141	C₄	—	106	2	no	—
1142	C₄	—	106	1	no	—
1143	C₄	—	106	2	no	—
1144	C₄	#131×D₅₃	1	2	yes	—
1145	C₄	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1146	C₄	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1147	C₂	—	2	2	no	—
1148	C₂	—	4	2	no	—
1149	C₂	—	53	4	no	—
1150	C₂	—	106	2	no	—
1151	C₂	—	212	2	no	—
1152	C₂	#520×D₅₃	1	1	yes	characteristic
1153	C₂	C₂×#131×D₅₃	1	1	yes	characteristic
1154	C₂	C₂×#131×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₅₃×#2994	C₂
prime radical	#121×D₅₃	C₄
cosocle	C₂×C₄×C₅₃	C₂⁵
hypercenter	#2994	D₅₃
hypocenter	C₅₃	C₂×#2994
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #2994

Complements

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

N	H ≅ G/N	type
2. #20283878	C₂	semidirect
3. #20283877	C₂	semidirect
4. #20283876	C₂	semidirect
5. #20283875	C₂	semidirect
6. #20283874	C₂	semidirect
7. #20283873	C₂	semidirect
8. #20283872	C₂	semidirect
9. #20283871	C₂	semidirect
10. #20283870	C₂	semidirect
11. #20283869	C₂	semidirect
12. #20283868	C₂	semidirect
13. #446×D₅₃	C₂	semidirect
14. C₈×Q₈×D₅₃	C₂	semidirect
15. #436×D₅₃	C₂	semidirect
16. #435×D₅₃	C₂	semidirect
17. C₈×D₄×D₅₃	C₂	semidirect
18. C₈×D₄×D₅₃	C₂	semidirect
19. #433×D₅₃	C₂	semidirect
20. #431×D₅₃	C₂	semidirect
21. #424×D₅₃	C₂	semidirect
22. C₂×C₄⋊C₈×D₅₃	C₂	semidirect
23. C₅₃×#2994	C₂	semidirect
49. #16810754	C₂²	semidirect
50. #16810753	C₂²	semidirect
51. #16810752	C₂²	semidirect
52. #16810751	C₂²	semidirect
53. #16810750	C₂²	semidirect
54. Q₈×#88322	C₂²	semidirect
55. C₈×Dic₁₀₆	C₂²	semidirect
56. C₈×Dic₁₀₆	C₂²	semidirect
57. #16810747	C₂²	semidirect
58. #16810747	C₂²	semidirect
59. #16810702	C₂²	semidirect
60. #16810701	C₂²	semidirect
61. #16810700	C₂²	semidirect
62. #16810699	C₂²	semidirect
63. #16810698	C₂²	semidirect
64. #16810697	C₂²	semidirect
65. #16810696	C₂²	semidirect
66. #16810695	C₂²	semidirect
67. #16810694	C₂²	semidirect
68. #16810693	C₂²	semidirect
69. #16810692	C₂²	semidirect
70. #16810691	C₂²	semidirect
71. C₈×D₂₁₂	C₂²	semidirect
72. C₈×D₂₁₂	C₂²	semidirect
73. D₄×#88322	C₂²	semidirect
74. D₄×#88322	C₂²	semidirect
75. #16810688	C₂²	semidirect
76. #16810688	C₂²	semidirect
77. C₈×C₂²⋊D₅₃	C₂²	semidirect
78. C₈×C₂²⋊D₅₃	C₂²	semidirect
79. C₈×C₂²⋊D₅₃	C₂²	semidirect
80. #16810686	C₂²	semidirect
81. #16810686	C₂²	semidirect
82. #16810686	C₂²	semidirect
83. #16810685	C₂²	semidirect
84. #16810684	C₂²	semidirect
85. #16810683	C₂²	semidirect
86. #16810683	C₂²	semidirect
87. #16810682	C₂²	semidirect
88. #16810681	C₂²	semidirect
89. #16810681	C₂²	semidirect
90. #16810676	C₂²	semidirect
91. #16810675	C₂²	semidirect
92. #16810675	C₂²	semidirect
93. #16810674	C₂²	semidirect
94. #16810674	C₂²	semidirect
95. #16810673	C₂²	semidirect
96. #16810673	C₂²	semidirect
97. #16810651	C₂²	semidirect
98. #16810650	C₂²	semidirect
99. #16810649	C₂²	semidirect
100. #16810648	C₂²	semidirect
101. #16810648	C₂²	semidirect
102. #16810648	C₂²	semidirect
103. #16810648	C₂²	semidirect
104. C₂×C₄⋊#88322	C₂²	semidirect
105. C₂×#13133146	C₂²	semidirect
113. C₄⋊C₈×D₅₃	C₂²	semidirect
114. C₄⋊C₈×D₅₃	C₂²	semidirect
115. C₄⋊C₈×D₅₃	C₂²	semidirect
125. C₅₃×#446	C₂²	semidirect
126. C₈×Q₈×C₅₃	C₂²	semidirect
127. C₅₃×#436	C₂²	semidirect
128. C₅₃×#435	C₂²	semidirect
129. C₈×D₄×C₅₃	C₂²	semidirect
130. C₈×D₄×C₅₃	C₂²	semidirect
131. C₅₃×#433	C₂²	semidirect
132. C₅₃×#431	C₂²	semidirect
133. C₅₃×#424	C₂²	semidirect
134. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
582. #2994	D₅₃	direct (N × H)
600. D₅₃	#2994	direct (N × H)
632. #446	C₂×D₅₃	semidirect
638. C₈×Q₈	C₂×D₅₃	semidirect
644. #436	C₂×D₅₃	semidirect
652. #435	C₂×D₅₃	semidirect
665. C₈×D₄	C₂×D₅₃	semidirect
666. C₈×D₄	C₂×D₅₃	semidirect
674. #433	C₂×D₅₃	semidirect
682. #431	C₂×D₅₃	semidirect
690. #424	C₂×D₅₃	semidirect
703. C₂×C₄⋊C₈	C₂×D₅₃	semidirect
712. C₅₃	C₂×#2994	semidirect

Maximal subgroups

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

subgroup	index
#529×D₅₃	2
#20283878	2
#20283877	2
#20283876	2
#20283875	2
#20283874	2
#20283873	2
#20283872	2
#20283871	2
#20283870	2
#20283869	2
#20283868	2
#446×D₅₃	2
C₈×Q₈×D₅₃	2
#436×D₅₃	2
#435×D₅₃	2
C₈×D₄×D₅₃	2
#433×D₅₃	2
#431×D₅₃	2
#424×D₅₃	2
C₂×C₄⋊C₈×D₅₃	2
C₅₃×#2994	2
C₂×#2994	53

Subgroups — D53×#2994 #28249186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2994 #28249186