Subgroups — D₅₃×#3449 #28290923

Order 13568.

11662 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#41×D₅₃	C₂	1	2	yes	maximal, complemented
2	#20288048	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288047	C₂	1	4	yes	maximal, complemented
4	#20288046	C₂	1	4	yes	maximal, complemented
5	#20288045	C₂	1	8	yes	maximal, complemented
6	#20288044	C₂	1	2	yes	maximal, complemented
7	#20288043	C₂	1	4	yes	maximal, complemented
8	#20288042	C₂	1	4	yes	maximal, complemented
9	#20288041	C₂	1	4	yes	maximal, complemented
10	#537×D₅₃	C₂	1	4	yes	maximal, complemented
11	#536×D₅₃	C₂	1	4	yes	maximal, complemented
12	#535×D₅₃	C₂	1	4	yes	maximal, complemented
13	#534×D₅₃	C₂	1	4	yes	maximal, complemented
14	#532×D₅₃	C₂	1	4	yes	maximal, complemented
15	#525×D₅₃	C₂	1	8	yes	maximal, complemented
16	C₂×#117×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#11719949	C₂²	1	2	yes	complemented
19	C₂²×#11719945	C₂²	1	2	yes	complemented
20	C₂²×#11719945	C₂²	1	4	yes	complemented
21	C₂²×#11719947	C₂²	1	4	yes	complemented
22	C₂²×#11719947	C₂²	1	2	yes	complemented
23	C₂×#41×D₅₃	—	2	32	no	—
24	C₂×#41×D₅₃	C₂²	1	4	yes	—
25	C₂×#41×D₅₃	C₂²	1	4	yes	—
26	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
27	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
28	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
29	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
30	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
31	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
32	C₂²×Q₈×D₅₃	C₂²	1	2	yes	complemented
33	C₂²×D₄×D₅₃	C₂²	1	4	yes	—
34	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
35	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
36	C₂³×C₄×D₅₃	C₂²	1	4	yes	complemented
37	#16811204	C₂²	1	4	yes	complemented
38	#16811203	C₂²	1	16	yes	complemented
39	#16811202	C₂²	1	16	yes	complemented
40	#16811201	C₂²	1	8	yes	complemented
41	#16811200	C₂²	1	16	yes	complemented
42	#16811199	C₂²	1	4	yes	complemented
43	#16811198	C₂²	1	8	yes	complemented
44	#16811197	C₂²	1	4	yes	complemented
45	#16811196	C₂²	1	16	yes	complemented
46	#16811195	C₂²	1	16	yes	complemented
47	#16811194	C₂²	1	4	yes	complemented
48	#16811193	C₂²	1	8	yes	complemented
49	#16811192	C₂²	1	4	yes	complemented
50	#16811191	C₂²	1	8	yes	complemented
51	#16811190	C₂²	1	4	yes	complemented
52	#16811189	C₂²	1	16	yes	complemented
53	#16811188	C₂²	1	16	yes	complemented
54	#16811187	C₂²	1	4	yes	complemented
55	#16811186	C₂²	1	8	yes	complemented
56	#16811185	C₂²	1	4	yes	complemented
57	#16811184	C₂²	1	16	yes	complemented
58	#16811183	C₂²	1	16	yes	complemented
59	#16811182	C₂²	1	8	yes	complemented
60	#16811181	C₂²	1	16	yes	complemented
61	#16811174	C₂²	1	4	yes	complemented
62	#16811173	C₂²	1	4	yes	complemented
63	#16811172	C₂²	1	8	yes	complemented
64	#16811171	C₂²	1	4	yes	complemented
65	#16811170	C₂²	1	16	yes	complemented
66	#16811169	C₂²	1	8	yes	complemented
67	#16811168	C₂²	1	16	yes	complemented
68	C₄⋊Q₈×D₅₃	C₂²	1	4	yes	complemented
69	#127×D₅₃	C₂²	1	4	yes	complemented
70	#124×D₅₃	C₂²	1	8	yes	complemented
71	#16811136	C₂²	1	16	yes	complemented
72	#16811135	C₂²	1	8	yes	complemented
73	#16811134	C₂²	1	8	yes	complemented
74	#16811133	C₂²	1	16	yes	complemented
75	#16811132	C₂²	1	32	yes	complemented
76	#16811131	C₂²	1	16	yes	complemented
77	#16811130	C₂²	1	8	yes	complemented
78	#16811129	C₂²	1	16	yes	complemented
79	#123×D₅₃	C₂²	1	16	yes	complemented
80	C₂²⋊Q₈×D₅₃	C₂²	1	16	yes	complemented
81	#121×D₅₃	C₂²	1	16	yes	complemented
82	#121×D₅₃	C₂²	1	16	yes	complemented
83	#120×D₅₃	C₂²	1	16	yes	complemented
84	C₄×D₄×D₅₃	C₂²	1	16	yes	complemented
85	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
86	C₂×#13133175	C₂²	1	2	yes	complemented
87	C₂×#13133174	C₂²	1	2	yes	complemented
88	C₂×#13133173	C₂²	1	2	yes	complemented
89	#117×D₅₃	C₂²	1	4	yes	complemented
90	#117×D₅₃	C₂²	1	4	yes	complemented
91	#117×D₅₃	C₂²	1	4	yes	complemented
92	#117×D₅₃	C₂²	1	4	yes	complemented
93	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
94	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
95	C₂×C₄²×D₅₃	C₂²	1	2	yes	complemented
96	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
97	C₅₃×#537	C₂²	1	4	yes	complemented
98	C₅₃×#536	C₂²	1	4	yes	complemented
99	C₅₃×#535	C₂²	1	4	yes	complemented
100	C₅₃×#534	C₂²	1	4	yes	complemented
101	C₅₃×#532	C₂²	1	4	yes	complemented
102	C₅₃×#525	C₂²	1	8	yes	complemented
103	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
104	C₂⁴×D₅₃	C₂³	1	4	yes	—
105	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
106	C₂×#11719949	—	2	16	no	—
107	C₂×#11719949	C₂³	1	4	yes	—
108	C₂×#11719949	C₂³	1	4	yes	—
109	C₂×#11719949	C₂³	1	4	yes	complemented
110	C₂×#11719949	C₂³	1	4	yes	complemented
111	C₂×#11719945	—	2	16	no	—
112	C₂×#11719945	—	2	32	no	—
113	C₂×#11719945	C₂³	1	8	yes	—
114	C₂×#11719945	C₂³	1	4	yes	—
115	C₂×#11719945	C₂³	1	8	yes	—
116	C₂×#11719945	C₂³	1	4	yes	—
117	C₂×#11719945	C₂³	1	4	yes	complemented
118	C₂×#11719945	C₂³	1	8	yes	complemented
119	C₂×#11719945	C₂³	1	4	yes	complemented
120	C₂×#11719945	C₂³	1	8	yes	complemented
121	C₂×#11719947	—	2	32	no	—
122	C₂×#11719947	—	2	16	no	—
123	C₂×#11719947	C₂³	1	8	yes	—
124	C₂×#11719947	C₂³	1	4	yes	—
125	C₂×#11719947	C₂³	1	4	yes	—
126	C₂×#11719947	C₂³	1	8	yes	—
127	C₂×#11719947	C₂³	1	8	yes	complemented
128	C₂×#11719947	C₂³	1	4	yes	complemented
129	C₂×#11719947	C₂³	1	8	yes	complemented
130	C₂×#11719947	C₂³	1	4	yes	complemented
131	#41×D₅₃	—	2	32	no	—
132	#41×D₅₃	—	2	32	no	—
133	#41×D₅₃	—	2	32	no	—
134	#41×D₅₃	—	2	32	no	—
135	#41×D₅₃	—	2	32	no	—
136	#41×D₅₃	—	2	32	no	—
137	#41×D₅₃	—	2	32	no	—
138	#41×D₅₃	—	2	32	no	—
139	C₂²×Dic₁₀₆	C₂³	1	2	yes	complemented
140	C₂²×Dic₁₀₆	C₂³	1	4	yes	complemented
141	C₂×Q₈×D₅₃	—	2	16	no	—
142	C₂×Q₈×D₅₃	C₂³	1	4	yes	—
143	C₂×Q₈×D₅₃	C₂³	1	4	yes	—
144	C₂×Q₈×D₅₃	C₂³	1	4	yes	complemented
145	C₂×Q₈×D₅₃	C₂³	1	4	yes	complemented
146	C₂²×D₂₁₂	C₂³	1	4	yes	—
147	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
148	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
149	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
150	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
151	C₂×D₄×D₅₃	—	2	32	no	—
152	C₂×D₄×D₅₃	—	2	16	no	—
153	C₂×D₄×D₅₃	C₂³	1	8	yes	—
154	C₂×D₄×D₅₃	C₂³	1	8	yes	—
155	C₂×D₄×D₅₃	C₂³	1	4	yes	—
156	C₂×D₄×D₅₃	C₂³	1	4	yes	—
157	C₂×D₄×D₅₃	C₂³	1	8	yes	—
158	C₂×D₄×D₅₃	C₂³	1	8	yes	—
159	C₂×D₄×D₅₃	C₂³	1	16	yes	—
160	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
161	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
162	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
163	C₂³×Dic₅₃	C₂³	1	4	yes	complemented
164	C₂²×C₄×D₅₃	—	2	32	no	—
165	C₂²×C₄×D₅₃	D₄	1	16	yes	complemented
166	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
167	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
168	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
169	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
170	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
171	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
172	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
173	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
174	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
175	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
176	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
177	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
178	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
179	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
180	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
181	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
182	#13133217	C₂³	1	4	yes	complemented
183	#13133216	C₂³	1	16	yes	complemented
184	#13133215	C₂³	1	8	yes	complemented
185	#13133214	C₂³	1	4	yes	complemented
186	#13133213	C₂³	1	16	yes	complemented
187	#13133213	C₂³	1	8	yes	complemented
188	#13133206	C₂³	1	8	yes	complemented
189	#13133205	C₂³	1	8	yes	complemented
190	#13133204	C₂³	1	8	yes	complemented
191	#13133203	C₂³	1	32	yes	complemented
192	#13133202	C₂³	1	32	yes	complemented
193	#13133201	C₂³	1	16	yes	complemented
194	#13133200	C₂³	1	16	yes	complemented
195	#13133199	C₂³	1	32	yes	complemented
196	#13133198	C₂³	1	16	yes	complemented
197	#13133197	C₂³	1	16	yes	complemented
198	#13133196	C₂³	1	16	yes	complemented
199	#13133195	C₂³	1	32	yes	complemented
200	#13133194	C₂³	1	32	yes	complemented
201	#13133193	C₂³	1	16	yes	complemented
202	#13133192	C₂³	1	16	yes	complemented
203	#13133192	C₂³	1	16	yes	complemented
204	#13133191	C₂³	1	16	yes	complemented
205	#13133191	C₂³	1	16	yes	complemented
206	#13133190	C₂³	1	32	yes	complemented
207	#13133190	C₂³	1	32	yes	complemented
208	#13133189	C₂³	1	32	yes	complemented
209	#13133189	C₂³	1	32	yes	complemented
210	#13133188	C₂³	1	16	yes	complemented
211	#13133188	C₂³	1	16	yes	complemented
212	#13133187	C₂³	1	16	yes	complemented
213	#13133187	C₂³	1	32	yes	complemented
214	#13133186	C₂³	1	16	yes	complemented
215	#13133185	C₂³	1	16	yes	complemented
216	#13133185	C₂³	1	32	yes	complemented
217	C₄×D₂₁₂	C₂³	1	16	yes	complemented
218	D₄×Dic₅₃	C₂³	1	16	yes	complemented
219	#13133179	C₂³	1	16	yes	complemented
220	C₄×C₂²⋊D₅₃	C₂³	1	32	yes	complemented
221	#13133177	C₂³	1	32	yes	complemented
222	#13133176	C₂³	1	4	yes	complemented
223	#13133176	C₂³	1	4	yes	complemented
224	#13133175	C₂³	1	8	yes	complemented
225	#13133175	C₂³	1	8	yes	complemented
226	#13133174	C₂³	1	8	yes	complemented
227	#13133174	C₂³	1	8	yes	complemented
228	#13133173	C₂³	1	8	yes	complemented
229	#13133173	C₂³	1	8	yes	complemented
230	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
231	C₂×#11719919	C₂³	1	4	yes	complemented
232	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
233	C₄⋊C₄×D₅₃	C₂³	1	16	yes	—
234	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
235	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
236	C₂×#11719921	C₂³	1	4	yes	—
237	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
238	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
239	C₂²⋊C₄×D₅₃	C₂³	1	32	yes	—
240	C₂×C₄×Dic₅₃	C₂³	1	4	yes	complemented
241	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
242	C₄²×D₅₃	C₂³	1	4	yes	—
243	C₄²×D₅₃	C₂³	1	4	yes	—
244	C₄²×D₅₃	C₂³	1	4	yes	complemented
245	C₄²×D₅₃	C₂³	1	4	yes	complemented
246	C₂×#41×C₅₃	—	2	16	no	—
247	C₂×#41×C₅₃	C₂³	1	4	yes	—
248	C₂×#41×C₅₃	C₂³	1	4	yes	—
249	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
250	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
251	C₂²×Q₈×C₅₃	C₂³	1	2	yes	complemented
252	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
253	C₂²×D₄×C₅₃	C₂³	1	2	yes	complemented
254	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂³×C₄×C₅₃	C₂³	1	4	yes	complemented
256	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
257	#127×C₅₃	C₂³	1	4	yes	complemented
258	#124×C₅₃	C₂³	1	8	yes	complemented
259	#123×C₅₃	C₂³	1	16	yes	complemented
260	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
261	#121×C₅₃	C₂³	1	16	yes	complemented
262	#121×C₅₃	C₂³	1	16	yes	complemented
263	#120×C₅₃	C₂³	1	16	yes	complemented
264	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
265	#117×C₅₃	C₂³	1	4	yes	complemented
266	#117×C₅₃	C₂³	1	4	yes	complemented
267	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
268	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
269	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
270	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
271	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
272	C₂³×D₅₃	—	2	16	no	—
273	C₂³×D₅₃	—	4	4	no	—
274	C₂³×D₅₃	—	4	16	no	—
275	C₂³×D₅₃	C₂×D₄	1	8	yes	—
276	C₂³×D₅₃	C₂⁴	1	8	yes	—
277	C₂³×D₅₃	C₂⁴	1	2	yes	—
278	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
279	C₂³×D₅₃	C₂⁴	1	8	yes	—
280	C₂³×D₅₃	C₂⁴	1	4	yes	—
281	C₂³×D₅₃	C₂⁴	1	2	yes	—
282	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
283	#41×C₅₃	—	2	16	no	—
284	#41×C₅₃	—	2	16	no	—
285	#41×C₅₃	—	2	16	no	—
286	#41×C₅₃	—	2	16	no	—
287	C₂×Q₈×C₅₃	—	2	8	no	—
288	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
289	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
290	C₂×D₄×C₅₃	—	2	16	no	—
291	C₂×D₄×C₅₃	—	2	8	no	—
292	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
293	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
294	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
295	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
296	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
297	C₂²×C₄×C₅₃	—	2	16	no	—
298	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	complemented
299	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
300	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
301	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
302	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
307	C₂×C₂²⋊D₅₃	—	2	16	no	—
308	C₂×C₂²⋊D₅₃	—	2	16	no	—
309	C₂×C₂²⋊D₅₃	—	2	16	no	—
310	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
311	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
312	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
313	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
314	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
315	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
316	C₂×C₂²⋊D₅₃	C₂⁴	1	32	yes	—
317	C₂²×Dic₅₃	—	2	16	no	—
318	C₂²×Dic₅₃	C₂×D₄	1	8	yes	complemented
319	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
320	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
321	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
322	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
323	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
324	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
325	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
326	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
327	#11719949	—	2	16	no	—
328	#11719949	—	2	16	no	—
329	#11719949	—	2	16	no	—
330	#11719949	—	2	16	no	—
331	Q₈×D₅₃	—	2	16	no	—
332	Q₈×D₅₃	—	2	16	no	—
333	Q₈×D₅₃	—	2	16	no	—
334	Q₈×D₅₃	—	2	16	no	—
335	#11719947	—	2	32	no	—
336	#11719947	—	2	32	no	—
337	#11719947	—	2	32	no	—
338	#11719947	—	2	32	no	—
339	#11719947	—	2	16	no	—
340	#11719947	—	2	16	no	—
341	#11719947	—	2	16	no	—
342	#11719947	—	2	16	no	—
343	D₄×D₅₃	—	2	32	no	—
344	D₄×D₅₃	—	2	32	no	—
345	D₄×D₅₃	—	2	32	no	—
346	D₄×D₅₃	—	2	32	no	—
347	D₄×D₅₃	—	2	16	no	—
348	D₄×D₅₃	—	2	16	no	—
349	D₄×D₅₃	—	2	16	no	—
350	D₄×D₅₃	—	2	16	no	—
351	D₄×D₅₃	—	4	32	no	—
352	#11719945	—	2	16	no	—
353	#11719945	—	2	16	no	—
354	#11719945	—	2	16	no	—
355	#11719945	—	2	16	no	—
356	#11719945	—	2	32	no	—
357	#11719945	—	2	32	no	—
358	#11719945	—	2	32	no	—
359	#11719945	—	2	32	no	—
360	C₂×D₂₁₂	—	2	16	no	—
361	C₂×D₂₁₂	—	2	8	no	—
362	C₂×D₂₁₂	C₂⁴	1	8	yes	—
363	C₂×D₂₁₂	C₂⁴	1	8	yes	—
364	C₂×D₂₁₂	C₂⁴	1	4	yes	—
365	C₂×D₂₁₂	C₂⁴	1	4	yes	—
366	C₂×D₂₁₂	C₂⁴	1	16	yes	—
367	C₂×C₄×D₅₃	—	2	16	no	—
368	C₂×C₄×D₅₃	—	2	16	no	—
369	C₂×C₄×D₅₃	—	2	16	no	—
370	C₂×C₄×D₅₃	—	2	32	no	—
371	C₂×C₄×D₅₃	—	2	32	no	—
372	C₂×C₄×D₅₃	—	2	32	no	—
373	C₂×C₄×D₅₃	—	2	32	no	—
374	C₂×C₄×D₅₃	—	4	8	no	—
375	C₂×C₄×D₅₃	C₂×D₄	1	16	yes	—
376	C₂×C₄×D₅₃	C₂×D₄	1	16	yes	—
377	C₂×C₄×D₅₃	C₂×D₄	1	8	yes	—
378	C₂×C₄×D₅₃	C₂×D₄	1	8	yes	—
379	C₂×C₄×D₅₃	C₂×D₄	1	8	yes	complemented
380	C₂×C₄×D₅₃	C₂×D₄	1	8	yes	complemented
381	C₂×C₄×D₅₃	C₂×D₄	1	16	yes	complemented
382	C₂×C₄×D₅₃	C₂×D₄	1	16	yes	complemented
383	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
384	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
385	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
386	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
387	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
388	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
389	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
390	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
391	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
394	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
396	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
397	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
398	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
399	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
400	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
401	C₂×Dic₁₀₆	—	2	8	no	—
402	C₂×Dic₁₀₆	—	2	16	no	—
403	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
404	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
405	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
406	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
407	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
408	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
409	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
410	C₂²⋊C₄×C₅₃	C₂⁴	1	32	yes	—
411	C₄²×C₅₃	C₂⁴	1	4	yes	—
412	C₄²×C₅₃	C₂⁴	1	4	yes	—
413	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
414	C₂²⋊Dic₅₃	C₂⁴	1	32	yes	—
415	#11719921	C₂⁴	1	16	yes	—
416	#11719921	C₂⁴	1	32	yes	—
417	#11719921	C₂⁴	1	32	yes	—
418	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
419	C₄⋊Dic₅₃	C₂⁴	1	16	yes	—
420	#11719919	C₂⁴	1	16	yes	—
421	#11719919	C₂⁴	1	32	yes	—
422	C₄×Dic₅₃	C₂⁴	1	8	yes	—
423	C₄×Dic₅₃	C₂⁴	1	8	yes	—
424	C₄×Dic₅₃	C₂⁴	1	4	yes	—
425	C₄×Dic₅₃	C₂⁴	1	4	yes	—
426	C₂³×C₅₃	—	2	8	no	—
427	C₂³×C₅₃	—	4	2	no	—
428	C₂³×C₅₃	—	4	8	no	—
429	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
430	C₂³×C₅₃	C₂⁵	1	8	yes	—
431	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
432	C₂³×C₅₃	C₂⁵	1	2	yes	—
433	C₂²×D₅₃	—	2	4	no	—
434	C₂²×D₅₃	—	2	8	no	—
435	C₂²×D₅₃	—	2	8	no	—
436	C₂²×D₅₃	—	2	16	no	—
437	C₂²×D₅₃	—	2	16	no	—
438	C₂²×D₅₃	—	2	32	no	—
439	C₂²×D₅₃	—	4	16	no	—
440	C₂²×D₅₃	—	4	4	no	—
441	C₂²×D₅₃	—	4	2	no	—
442	C₂²×D₅₃	—	4	16	no	—
443	C₂²×D₅₃	—	4	8	no	—
444	C₂²×D₅₃	—	4	64	no	—
445	C₂²×D₅₃	C₂²×D₄	1	8	yes	—
446	C₂²×D₅₃	C₂²×D₄	1	4	yes	—
447	C₂²×D₅₃	C₂²×D₄	1	8	yes	—
448	C₂²×D₅₃	C₂²×D₄	1	4	yes	—
449	C₂²×D₅₃	C₂⁵	1	8	yes	—
450	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
451	C₂²×D₅₃	C₂⁵	1	2	yes	—
452	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
453	Q₈×C₅₃	—	2	8	no	—
454	Q₈×C₅₃	—	2	8	no	—
455	D₄×C₅₃	—	2	16	no	—
456	D₄×C₅₃	—	2	16	no	—
457	D₄×C₅₃	—	2	8	no	—
458	D₄×C₅₃	—	2	8	no	—
459	D₄×C₅₃	—	4	16	no	—
460	C₂×C₄×C₅₃	—	2	8	no	—
461	C₂×C₄×C₅₃	—	2	16	no	—
462	C₂×C₄×C₅₃	—	2	16	no	—
463	C₂×C₄×C₅₃	—	4	4	no	—
464	C₂×C₄×C₅₃	C₂²×D₄	1	8	yes	—
465	C₂×C₄×C₅₃	C₂²×D₄	1	8	yes	—
466	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
467	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
468	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
469	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
470	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
471	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
472	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
473	C₂²⋊D₅₃	—	2	16	no	—
474	C₂²⋊D₅₃	—	2	16	no	—
475	C₂²⋊D₅₃	—	2	16	no	—
476	C₂²⋊D₅₃	—	2	16	no	—
477	C₂²⋊D₅₃	—	2	16	no	—
478	C₂²⋊D₅₃	—	2	16	no	—
479	C₂²⋊D₅₃	—	4	32	no	—
480	C₂×Dic₅₃	—	2	8	no	—
481	C₂×Dic₅₃	—	2	16	no	—
482	C₂×Dic₅₃	—	2	16	no	—
483	C₂×Dic₅₃	—	4	4	no	—
484	C₂×Dic₅₃	C₂²×D₄	1	8	yes	—
485	C₂×Dic₅₃	C₂²×D₄	1	8	yes	—
486	C₂×Dic₅₃	C₂²×D₄	1	4	yes	—
487	C₂×Dic₅₃	C₂²×D₄	1	4	yes	—
488	C₂×Dic₅₃	C₂⁵	1	8	yes	—
489	C₂×Dic₅₃	C₂⁵	1	8	yes	—
490	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
491	C₂×Dic₅₃	C₂⁵	1	2	yes	—
492	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
493	D₂₁₂	—	2	16	no	—
494	D₂₁₂	—	2	16	no	—
495	D₂₁₂	—	2	8	no	—
496	D₂₁₂	—	2	8	no	—
497	D₂₁₂	—	4	16	no	—
498	C₄×D₅₃	—	2	16	no	—
499	C₄×D₅₃	—	2	16	no	—
500	C₄×D₅₃	—	2	16	no	—
501	C₄×D₅₃	—	2	16	no	—
502	C₄×D₅₃	—	2	16	no	—
503	C₄×D₅₃	—	2	16	no	—
504	C₄×D₅₃	—	2	16	no	—
505	C₄×D₅₃	—	4	8	no	—
506	C₄×D₅₃	C₂²×D₄	1	4	yes	—
507	C₄×D₅₃	C₂²×D₄	1	8	yes	—
508	C₄×D₅₃	C₂²×D₄	1	8	yes	—
509	C₄×D₅₃	C₂²×D₄	1	8	yes	—
510	C₄×D₅₃	C₂²×D₄	1	4	yes	—
511	C₄×D₅₃	C₂²×D₄	1	4	yes	—
512	C₄×D₅₃	C₂²×D₄	1	8	yes	—
513	C₄×D₅₃	C₂²×D₄	1	8	yes	—
514	C₄×D₅₃	C₂²×D₄	1	8	yes	—
515	C₄×D₅₃	C₂²×D₄	1	4	yes	—
516	Dic₁₀₆	—	2	8	no	—
517	Dic₁₀₆	—	2	8	no	—
518	Dic₁₀₆	—	2	16	no	—
519	Dic₁₀₆	—	2	16	no	—
520	C₂×#3449	—	53	1	no	maximal, Sylow
521	C₂²×C₅₃	—	2	2	no	—
522	C₂²×C₅₃	—	2	4	no	—
523	C₂²×C₅₃	—	2	8	no	—
524	C₂²×C₅₃	—	2	16	no	—
525	C₂²×C₅₃	—	4	4	no	—
526	C₂²×C₅₃	—	4	16	no	—
527	C₂²×C₅₃	C₂³×D₄	1	4	yes	—
528	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
529	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
530	C₂×D₅₃	—	2	2	no	—
531	C₂×D₅₃	—	2	4	no	—
532	C₂×D₅₃	—	2	16	no	—
533	C₂×D₅₃	—	2	8	no	—
534	C₂×D₅₃	—	2	8	no	—
535	C₂×D₅₃	—	2	16	no	—
536	C₂×D₅₃	—	4	4	no	—
537	C₂×D₅₃	—	4	8	no	—
538	C₂×D₅₃	—	4	32	no	—
539	C₂×D₅₃	—	4	16	no	—
540	C₂×D₅₃	—	4	32	no	—
541	C₂×D₅₃	C₂³×D₄	1	4	yes	—
542	C₂×D₅₃	C₂³×D₄	1	2	yes	—
543	C₂×D₅₃	C₂³×D₄	1	2	yes	—
544	C₂×D₅₃	#585	1	4	yes	—
545	C₄×C₅₃	—	2	8	no	—
546	C₄×C₅₃	—	2	8	no	—
547	C₄×C₅₃	C₂³×D₄	1	2	yes	—
548	C₄×C₅₃	C₂³×D₄	1	4	yes	—
549	C₄×C₅₃	C₂³×D₄	1	2	yes	—
550	Dic₅₃	—	2	8	no	—
551	Dic₅₃	—	2	8	no	—
552	Dic₅₃	C₂³×D₄	1	2	yes	—
553	Dic₅₃	C₂³×D₄	1	4	yes	—
554	Dic₅₃	C₂³×D₄	1	2	yes	—
555	C₂³×#41	—	53	2	no	—
556	#3449	—	53	2	no	—
557	#3449	—	53	4	no	—
558	#3449	—	53	4	no	—
559	#3449	—	53	4	no	—
560	#3449	—	53	4	no	—
561	#3449	—	53	4	no	—
562	#3449	—	53	8	no	—
563	#3449	—	53	1	no	—
564	#3449	D₅₃	1	1	yes	characteristic, direct product factor
565	C₂×#537	—	53	4	no	—
566	C₂×#536	—	53	4	no	—
567	C₂×#535	—	53	4	no	—
568	C₂×#534	—	53	4	no	—
569	C₂×#532	—	53	4	no	—
570	C₂×#525	—	53	8	no	—
571	C₂²×#117	—	53	1	no	—
572	C₂×C₅₃	—	2	4	no	—
573	C₂×C₅₃	—	2	2	no	—
574	C₂×C₅₃	—	4	8	no	—
575	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
576	C₂×C₅₃	C₂×#585	1	2	yes	—
577	D₅₃	—	2	4	no	—
578	D₅₃	—	2	2	no	—
579	D₅₃	—	4	8	no	—
580	D₅₃	#3449	1	4	yes	direct product factor
581	C₂²×#41	—	53	4	no	—
582	C₂²×#41	—	53	4	no	—
583	C₂²×#41	—	53	4	no	—
584	C₂²×#41	—	53	4	no	—
585	C₂²×#41	—	53	4	no	—
586	C₂²×#41	—	53	4	no	—
587	C₂²×#41	—	53	4	no	—
588	C₂²×#41	—	53	4	no	—
589	C₂²×#41	—	53	2	no	—
590	C₂²×#41	—	53	4	no	—
591	C₂²×#41	—	53	2	no	—
592	C₂²×#41	—	53	2	no	—
593	C₂²×#41	—	53	4	no	—
594	C₂²×#41	—	106	32	no	—
595	C₂²×#41	C₂×D₅₃	1	2	yes	complemented
596	C₂³×Q₈	—	53	2	no	—
597	C₂³×D₄	—	53	4	no	—
598	C₂³×D₄	—	53	2	no	—
599	C₂⁴×C₄	—	53	1	no	—
600	C₂⁴×C₄	—	53	4	no	—
601	#537	—	53	8	no	—
602	#537	—	53	16	no	—
603	#537	—	53	16	no	—
604	#537	—	53	16	no	—
605	#537	—	53	4	no	—
606	#537	C₂×D₅₃	1	4	yes	complemented
607	#536	—	53	4	no	—
608	#536	—	53	4	no	—
609	#536	—	53	8	no	—
610	#536	—	53	8	no	—
611	#536	—	53	16	no	—
612	#536	—	53	16	no	—
613	#536	—	53	4	no	—
614	#536	C₂×D₅₃	1	4	yes	complemented
615	#535	—	53	4	no	—
616	#535	—	53	4	no	—
617	#535	—	53	8	no	—
618	#535	—	53	8	no	—
619	#535	—	53	16	no	—
620	#535	—	53	16	no	—
621	#535	—	53	4	no	—
622	#535	C₂×D₅₃	1	4	yes	complemented
623	#534	—	53	8	no	—
624	#534	—	53	16	no	—
625	#534	—	53	16	no	—
626	#534	—	53	16	no	—
627	#534	—	53	4	no	—
628	#534	C₂×D₅₃	1	4	yes	complemented
629	#532	—	53	8	no	—
630	#532	—	53	4	no	—
631	#532	—	53	4	no	—
632	#532	—	53	8	no	—
633	#532	—	53	16	no	—
634	#532	—	53	16	no	—
635	#532	—	53	4	no	—
636	#532	C₂×D₅₃	1	4	yes	complemented
637	C₂×C₄⋊Q₈	—	53	4	no	—
638	C₂×#127	—	53	4	no	—
639	C₂×#124	—	53	8	no	—
640	#525	—	53	8	no	—
641	#525	—	53	8	no	—
642	#525	—	53	16	no	—
643	#525	—	53	16	no	—
644	#525	—	53	16	no	—
645	#525	—	53	16	no	—
646	#525	—	53	32	no	—
647	#525	—	53	8	no	—
648	#525	C₂×D₅₃	1	8	yes	complemented
649	C₂×#123	—	53	16	no	—
650	C₂×C₂²⋊Q₈	—	53	16	no	—
651	C₂×#121	—	53	16	no	—
652	C₂×#121	—	53	16	no	—
653	C₂×#120	—	53	16	no	—
654	C₂×C₄×D₄	—	53	16	no	—
655	C₂×#117	—	53	1	no	—
656	C₂×#117	—	53	4	no	—
657	C₂×#117	—	53	4	no	—
658	C₂×#117	—	53	4	no	—
659	C₂×#117	—	53	4	no	—
660	C₂×#117	—	53	2	no	—
661	C₂×#117	—	53	2	no	—
662	C₂×#117	—	53	2	no	—
663	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
664	C₂²×C₄⋊C₄	—	53	2	no	—
665	C₂²×C₂²⋊C₄	—	53	2	no	—
666	C₂²×C₄²	—	53	2	no	—
667	C₅₃	C₂×#3449	1	1	yes	characteristic, complemented, Sylow
668	C₂⁵	—	53	1	no	—
669	C₂⁵	—	53	4	no	—
670	C₂×#41	—	2	16	no	—
671	C₂×#41	—	53	4	no	—
672	C₂×#41	—	53	4	no	—
673	C₂×#41	—	53	4	no	—
674	C₂×#41	—	53	4	no	—
675	C₂×#41	—	53	8	no	—
676	C₂×#41	—	53	4	no	—
677	C₂×#41	—	53	8	no	—
678	C₂×#41	—	53	4	no	—
679	C₂×#41	—	53	8	no	—
680	C₂×#41	—	53	4	no	—
681	C₂×#41	—	53	8	no	—
682	C₂×#41	—	53	4	no	—
683	C₂×#41	—	53	8	no	—
684	C₂×#41	—	53	4	no	—
685	C₂×#41	—	53	8	no	—
686	C₂×#41	—	53	4	no	—
687	C₂×#41	—	53	8	no	—
688	C₂×#41	—	53	4	no	—
689	C₂×#41	—	53	8	no	—
690	C₂×#41	—	53	4	no	—
691	C₂×#41	—	106	32	no	—
692	C₂×#41	—	106	32	no	—
693	C₂×#41	—	106	16	no	—
694	C₂×#41	—	106	16	no	—
695	C₂×#41	—	106	32	no	—
696	C₂×#41	—	106	32	no	—
697	C₂×#41	—	106	32	no	—
698	C₂×#41	—	106	32	no	—
699	C₂×#41	—	106	32	no	—
700	C₂×#41	—	106	32	no	—
701	C₂×#41	—	106	32	no	—
702	C₂×#41	—	106	32	no	—
703	C₂×#41	—	106	16	no	—
704	C₂×#41	C₂²×D₅₃	1	4	yes	—
705	C₂×#41	C₂²×D₅₃	1	4	yes	—
706	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
707	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
708	C₂²×Q₈	—	53	4	no	—
709	C₂²×Q₈	—	53	4	no	—
710	C₂²×Q₈	—	53	4	no	—
711	C₂²×Q₈	—	53	4	no	—
712	C₂²×Q₈	—	53	4	no	—
713	C₂²×Q₈	—	53	2	no	—
714	C₂²×Q₈	—	106	16	no	—
715	C₂²×Q₈	C₂²×D₅₃	1	2	yes	complemented
716	C₂²×D₄	—	53	4	no	—
717	C₂²×D₄	—	53	4	no	—
718	C₂²×D₄	—	53	4	no	—
719	C₂²×D₄	—	53	8	no	—
720	C₂²×D₄	—	53	4	no	—
721	C₂²×D₄	—	53	8	no	—
722	C₂²×D₄	—	53	4	no	—
723	C₂²×D₄	—	53	8	no	—
724	C₂²×D₄	—	53	8	no	—
725	C₂²×D₄	—	53	4	no	—
726	C₂²×D₄	—	53	4	no	—
727	C₂²×D₄	—	53	16	no	—
728	C₂²×D₄	—	53	4	no	—
729	C₂²×D₄	—	53	2	no	—
730	C₂²×D₄	—	106	16	no	—
731	C₂²×D₄	—	106	32	no	—
732	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
733	C₂²×D₄	C₂²×D₅₃	1	2	yes	complemented
734	C₂³×C₄	—	53	1	no	—
735	C₂³×C₄	—	53	16	no	—
736	C₂³×C₄	—	53	1	no	—
737	C₂³×C₄	—	53	2	no	—
738	C₂³×C₄	—	53	2	no	—
739	C₂³×C₄	—	53	1	no	—
740	C₂³×C₄	—	53	1	no	—
741	C₂³×C₄	—	53	2	no	—
742	C₂³×C₄	—	53	2	no	—
743	C₂³×C₄	—	53	1	no	—
744	C₂³×C₄	—	53	4	no	—
745	C₂³×C₄	—	53	8	no	—
746	C₂³×C₄	—	53	8	no	—
747	C₂³×C₄	—	53	4	no	—
748	C₂³×C₄	—	53	4	no	—
749	C₂³×C₄	—	53	8	no	—
750	C₂³×C₄	—	53	8	no	—
751	C₂³×C₄	—	53	4	no	—
752	C₂³×C₄	—	53	4	no	—
753	C₂³×C₄	—	106	32	no	—
754	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
755	C₂³×C₄	C₂²×D₅₃	1	4	yes	complemented
756	C₄⋊Q₈	—	53	8	no	—
757	C₄⋊Q₈	—	53	16	no	—
758	C₄⋊Q₈	—	53	4	no	—
759	C₄⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
760	#127	—	53	16	no	—
761	#127	—	53	8	no	—
762	#127	—	53	4	no	—
763	#127	C₂²×D₅₃	1	4	yes	complemented
764	#124	—	53	8	no	—
765	#124	—	53	8	no	—
766	#124	—	53	32	no	—
767	#124	—	53	8	no	—
768	#124	C₂²×D₅₃	1	8	yes	complemented
769	#123	—	53	16	no	—
770	#123	—	53	16	no	—
771	#123	—	53	32	no	—
772	#123	—	53	32	no	—
773	#123	—	53	16	no	—
774	#123	C₂²×D₅₃	1	16	yes	complemented
775	C₂²⋊Q₈	—	53	16	no	—
776	C₂²⋊Q₈	—	53	16	no	—
777	C₂²⋊Q₈	—	53	32	no	—
778	C₂²⋊Q₈	—	53	16	no	—
779	C₂²⋊Q₈	—	53	32	no	—
780	C₂²⋊Q₈	C₂²×D₅₃	1	16	yes	complemented
781	#121	—	53	16	no	—
782	#121	—	53	32	no	—
783	#121	—	53	16	no	—
784	#121	—	53	32	no	—
785	#121	—	53	16	no	—
786	#121	—	53	16	no	—
787	#121	—	53	16	no	—
788	#121	—	53	16	no	—
789	#121	—	53	32	no	—
790	#121	—	53	32	no	—
791	#121	C₂²×D₅₃	1	16	yes	complemented
792	#121	C₂²×D₅₃	1	16	yes	complemented
793	#120	—	53	16	no	—
794	#120	—	53	16	no	—
795	#120	—	53	32	no	—
796	#120	—	53	32	no	—
797	#120	—	53	16	no	—
798	#120	C₂²×D₅₃	1	16	yes	complemented
799	C₄×D₄	—	53	16	no	—
800	C₄×D₄	—	53	32	no	—
801	C₄×D₄	—	53	16	no	—
802	C₄×D₄	—	53	32	no	—
803	C₄×D₄	—	53	16	no	—
804	C₄×D₄	C₂²×D₅₃	1	16	yes	complemented
805	#117	—	53	4	no	—
806	#117	—	53	4	no	—
807	#117	—	53	8	no	—
808	#117	—	53	8	no	—
809	#117	—	53	8	no	—
810	#117	—	53	8	no	—
811	#117	—	53	8	no	—
812	#117	—	53	8	no	—
813	#117	C₂²×D₅₃	1	4	yes	complemented
814	#117	C₂²×D₅₃	1	4	yes	complemented
815	C₂×C₄⋊C₄	—	53	4	no	—
816	C₂×C₄⋊C₄	—	53	2	no	—
817	C₂×C₄⋊C₄	—	53	8	no	—
818	C₂×C₄⋊C₄	—	53	8	no	—
819	C₂×C₄⋊C₄	—	53	16	no	—
820	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
821	C₂×C₂²⋊C₄	—	53	2	no	—
822	C₂×C₂²⋊C₄	—	53	4	no	—
823	C₂×C₂²⋊C₄	—	53	8	no	—
824	C₂×C₂²⋊C₄	—	53	8	no	—
825	C₂×C₂²⋊C₄	—	53	32	no	—
826	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
827	C₂×C₄²	—	53	4	no	—
828	C₂×C₄²	—	53	2	no	—
829	C₂×C₄²	—	53	4	no	—
830	C₂×C₄²	—	53	4	no	—
831	C₂×C₄²	—	53	4	no	—
832	C₂×C₄²	—	53	4	no	—
833	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
834	C₂⁴	—	53	2	no	—
835	C₂⁴	—	53	1	no	—
836	C₂⁴	—	53	8	no	—
837	C₂⁴	—	53	1	no	—
838	C₂⁴	—	53	2	no	—
839	C₂⁴	—	53	8	no	—
840	C₂⁴	—	53	8	no	—
841	C₂⁴	—	53	4	no	—
842	C₂⁴	—	106	16	no	—
843	C₂⁴	—	212	4	no	—
844	C₂⁴	—	212	16	no	—
845	C₂⁴	C₂³×D₅₃	1	4	yes	—
846	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
847	#41	—	2	16	no	—
848	#41	—	2	16	no	—
849	#41	—	2	16	no	—
850	#41	—	2	16	no	—
851	#41	—	106	32	no	—
852	#41	—	106	32	no	—
853	#41	—	106	32	no	—
854	#41	—	106	32	no	—
855	#41	—	106	32	no	—
856	#41	—	106	32	no	—
857	#41	—	106	32	no	—
858	#41	—	106	32	no	—
859	#41	—	106	16	no	—
860	#41	—	106	16	no	—
861	#41	—	106	16	no	—
862	#41	—	106	16	no	—
863	#41	—	106	16	no	—
864	#41	—	106	16	no	—
865	#41	—	106	16	no	—
866	#41	—	106	16	no	—
867	#41	—	106	16	no	—
868	#41	—	106	16	no	—
869	#41	—	106	16	no	—
870	#41	—	106	16	no	—
871	C₂×Q₈	—	2	8	no	—
872	C₂×Q₈	—	53	8	no	—
873	C₂×Q₈	—	53	4	no	—
874	C₂×Q₈	—	53	8	no	—
875	C₂×Q₈	—	53	4	no	—
876	C₂×Q₈	—	106	16	no	—
877	C₂×Q₈	—	106	16	no	—
878	C₂×Q₈	—	106	16	no	—
879	C₂×Q₈	—	106	16	no	—
880	C₂×Q₈	—	106	16	no	—
881	C₂×Q₈	—	106	8	no	—
882	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
883	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
884	C₂×D₄	—	2	16	no	—
885	C₂×D₄	—	2	8	no	—
886	C₂×D₄	—	53	8	no	—
887	C₂×D₄	—	53	8	no	—
888	C₂×D₄	—	53	8	no	—
889	C₂×D₄	—	53	8	no	—
890	C₂×D₄	—	53	8	no	—
891	C₂×D₄	—	53	8	no	—
892	C₂×D₄	—	53	32	no	—
893	C₂×D₄	—	53	8	no	—
894	C₂×D₄	—	53	8	no	—
895	C₂×D₄	—	53	4	no	—
896	C₂×D₄	—	53	4	no	—
897	C₂×D₄	—	53	16	no	—
898	C₂×D₄	—	106	16	no	—
899	C₂×D₄	—	106	16	no	—
900	C₂×D₄	—	106	16	no	—
901	C₂×D₄	—	106	16	no	—
902	C₂×D₄	—	106	16	no	—
903	C₂×D₄	—	106	16	no	—
904	C₂×D₄	—	106	32	no	—
905	C₂×D₄	—	106	32	no	—
906	C₂×D₄	—	106	32	no	—
907	C₂×D₄	—	106	32	no	—
908	C₂×D₄	—	106	16	no	—
909	C₂×D₄	—	106	16	no	—
910	C₂×D₄	—	106	8	no	—
911	C₂×D₄	—	212	32	no	—
912	C₂×D₄	C₂³×D₅₃	1	8	yes	—
913	C₂×D₄	C₂³×D₅₃	1	8	yes	—
914	C₂×D₄	C₂³×D₅₃	1	4	yes	—
915	C₂×D₄	C₂³×D₅₃	1	4	yes	—
916	C₂×D₄	C₂³×D₅₃	1	16	yes	—
917	C₂²×C₄	—	2	16	no	—
918	C₂²×C₄	—	53	8	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	16	no	—
924	C₂²×C₄	—	53	16	no	—
925	C₂²×C₄	—	53	8	no	—
926	C₂²×C₄	—	53	8	no	—
927	C₂²×C₄	—	53	16	no	—
928	C₂²×C₄	—	53	16	no	—
929	C₂²×C₄	—	53	8	no	—
930	C₂²×C₄	—	53	8	no	—
931	C₂²×C₄	—	53	1	no	—
932	C₂²×C₄	—	53	1	no	—
933	C₂²×C₄	—	53	2	no	—
934	C₂²×C₄	—	53	2	no	—
935	C₂²×C₄	—	53	2	no	—
936	C₂²×C₄	—	53	2	no	—
937	C₂²×C₄	—	53	2	no	—
938	C₂²×C₄	—	53	1	no	—
939	C₂²×C₄	—	53	1	no	—
940	C₂²×C₄	—	53	2	no	—
941	C₂²×C₄	—	53	8	no	—
942	C₂²×C₄	—	53	8	no	—
943	C₂²×C₄	—	53	4	no	—
944	C₂²×C₄	—	53	4	no	—
945	C₂²×C₄	—	53	8	no	—
946	C₂²×C₄	—	53	8	no	—
947	C₂²×C₄	—	53	8	no	—
948	C₂²×C₄	—	53	8	no	—
949	C₂²×C₄	—	53	8	no	—
950	C₂²×C₄	—	53	8	no	—
951	C₂²×C₄	—	53	8	no	—
952	C₂²×C₄	—	53	8	no	—
953	C₂²×C₄	—	106	16	no	—
954	C₂²×C₄	—	106	32	no	—
955	C₂²×C₄	—	106	32	no	—
956	C₂²×C₄	—	106	32	no	—
957	C₂²×C₄	—	106	32	no	—
958	C₂²×C₄	—	106	16	no	—
959	C₂²×C₄	—	106	16	no	—
960	C₂²×C₄	—	106	16	no	—
961	C₂²×C₄	—	212	8	no	—
962	C₂²×C₄	D₄×D₅₃	1	8	yes	complemented
963	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
964	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
965	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
966	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
967	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
968	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
969	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
970	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
971	C₄⋊C₄	—	53	16	no	—
972	C₄⋊C₄	—	53	8	no	—
973	C₄⋊C₄	—	53	32	no	—
974	C₄⋊C₄	—	53	16	no	—
975	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
976	C₄⋊C₄	C₂³×D₅₃	1	16	yes	—
977	C₂²⋊C₄	—	53	8	no	—
978	C₂²⋊C₄	—	53	32	no	—
979	C₂²⋊C₄	—	53	16	no	—
980	C₂²⋊C₄	—	53	32	no	—
981	C₂²⋊C₄	—	53	32	no	—
982	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
983	C₂²⋊C₄	C₂³×D₅₃	1	32	yes	—
984	C₄²	—	53	8	no	—
985	C₄²	—	53	8	no	—
986	C₄²	—	53	4	no	—
987	C₄²	—	53	4	no	—
988	C₄²	C₂³×D₅₃	1	4	yes	—
989	C₄²	C₂³×D₅₃	1	4	yes	—
990	C₂³	—	2	8	no	—
991	C₂³	—	4	2	no	—
992	C₂³	—	4	8	no	—
993	C₂³	—	53	1	no	—
994	C₂³	—	53	8	no	—
995	C₂³	—	53	4	no	—
996	C₂³	—	53	2	no	—
997	C₂³	—	53	1	no	—
998	C₂³	—	53	4	no	—
999	C₂³	—	53	8	no	—
1000	C₂³	—	53	8	no	—
1001	C₂³	—	106	4	no	—
1002	C₂³	—	106	8	no	—
1003	C₂³	—	106	16	no	—
1004	C₂³	—	106	16	no	—
1005	C₂³	—	106	32	no	—
1006	C₂³	—	106	8	no	—
1007	C₂³	—	212	2	no	—
1008	C₂³	—	212	4	no	—
1009	C₂³	—	212	8	no	—
1010	C₂³	—	212	16	no	—
1011	C₂³	—	212	16	no	—
1012	C₂³	—	212	64	no	—
1013	C₂³	C₂×D₄×D₅₃	1	4	yes	—
1014	C₂³	C₂⁴×D₅₃	1	8	yes	—
1015	C₂³	C₂⁴×D₅₃	1	2	yes	—
1016	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1017	Q₈	—	2	8	no	—
1018	Q₈	—	2	8	no	—
1019	Q₈	—	106	16	no	—
1020	Q₈	—	106	16	no	—
1021	Q₈	—	106	8	no	—
1022	Q₈	—	106	8	no	—
1023	D₄	—	2	16	no	—
1024	D₄	—	2	16	no	—
1025	D₄	—	2	8	no	—
1026	D₄	—	2	8	no	—
1027	D₄	—	4	16	no	—
1028	D₄	—	106	16	no	—
1029	D₄	—	106	16	no	—
1030	D₄	—	106	16	no	—
1031	D₄	—	106	16	no	—
1032	D₄	—	106	16	no	—
1033	D₄	—	106	16	no	—
1034	D₄	—	106	16	no	—
1035	D₄	—	106	16	no	—
1036	D₄	—	106	8	no	—
1037	D₄	—	106	8	no	—
1038	D₄	—	212	16	no	—
1039	D₄	—	212	32	no	—
1040	C₂×C₄	—	2	8	no	—
1041	C₂×C₄	—	2	16	no	—
1042	C₂×C₄	—	2	16	no	—
1043	C₂×C₄	—	4	4	no	—
1044	C₂×C₄	—	53	8	no	—
1045	C₂×C₄	—	53	8	no	—
1046	C₂×C₄	—	53	4	no	—
1047	C₂×C₄	—	53	4	no	—
1048	C₂×C₄	—	53	1	no	—
1049	C₂×C₄	—	53	1	no	—
1050	C₂×C₄	—	53	2	no	—
1051	C₂×C₄	—	53	4	no	—
1052	C₂×C₄	—	53	8	no	—
1053	C₂×C₄	—	53	8	no	—
1054	C₂×C₄	—	53	8	no	—
1055	C₂×C₄	—	53	4	no	—
1056	C₂×C₄	—	53	8	no	—
1057	C₂×C₄	—	53	8	no	—
1058	C₂×C₄	—	53	4	no	—
1059	C₂×C₄	—	53	8	no	—
1060	C₂×C₄	—	53	4	no	—
1061	C₂×C₄	—	53	8	no	—
1062	C₂×C₄	—	53	8	no	—
1063	C₂×C₄	—	106	16	no	—
1064	C₂×C₄	—	106	16	no	—
1065	C₂×C₄	—	106	16	no	—
1066	C₂×C₄	—	106	16	no	—
1067	C₂×C₄	—	106	16	no	—
1068	C₂×C₄	—	106	16	no	—
1069	C₂×C₄	—	106	16	no	—
1070	C₂×C₄	—	106	8	no	—
1071	C₂×C₄	—	106	16	no	—
1072	C₂×C₄	—	106	16	no	—
1073	C₂×C₄	—	212	8	no	—
1074	C₂×C₄	—	212	4	no	—
1075	C₂×C₄	C₂×D₄×D₅₃	1	8	yes	—
1076	C₂×C₄	C₂×D₄×D₅₃	1	8	yes	—
1077	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1078	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1079	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1080	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1081	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1082	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1083	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1084	C₂²	—	2	2	no	—
1085	C₂²	—	2	4	no	—
1086	C₂²	—	2	8	no	—
1087	C₂²	—	2	16	no	—
1088	C₂²	—	4	4	no	—
1089	C₂²	—	4	16	no	—
1090	C₂²	—	53	2	no	—
1091	C₂²	—	53	4	no	—
1092	C₂²	—	53	4	no	—
1093	C₂²	—	53	2	no	—
1094	C₂²	—	106	16	no	—
1095	C₂²	—	106	8	no	—
1096	C₂²	—	106	2	no	—
1097	C₂²	—	106	4	no	—
1098	C₂²	—	106	8	no	—
1099	C₂²	—	106	16	no	—
1100	C₂²	—	212	8	no	—
1101	C₂²	—	212	4	no	—
1102	C₂²	—	212	16	no	—
1103	C₂²	—	212	32	no	—
1104	C₂²	—	212	32	no	—
1105	C₂²	C₂²×D₄×D₅₃	1	4	yes	—
1106	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
1107	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1108	C₄	—	2	8	no	—
1109	C₄	—	2	8	no	—
1110	C₄	—	53	2	no	—
1111	C₄	—	53	4	no	—
1112	C₄	—	53	2	no	—
1113	C₄	—	106	8	no	—
1114	C₄	—	106	8	no	—
1115	C₄	C₂²×D₄×D₅₃	1	2	yes	—
1116	C₄	C₂²×D₄×D₅₃	1	4	yes	—
1117	C₄	C₂²×D₄×D₅₃	1	2	yes	—
1118	C₂	—	2	4	no	—
1119	C₂	—	2	2	no	—
1120	C₂	—	4	8	no	—
1121	C₂	—	53	4	no	—
1122	C₂	—	106	4	no	—
1123	C₂	—	106	2	no	—
1124	C₂	—	212	8	no	—
1125	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
1126	C₂	#585×D₅₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₅₃×#3449	C₂
hypercenter	#3449	D₅₃
hypocenter	C₅₃	C₂×#3449
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #3449

Complements

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

N	H ≅ G/N	type
1. C₂²×#41×D₅₃	C₂	semidirect
2. #20288048	C₂	semidirect
3. #20288047	C₂	semidirect
4. #20288046	C₂	semidirect
5. #20288045	C₂	semidirect
6. #20288044	C₂	semidirect
7. #20288043	C₂	semidirect
8. #20288042	C₂	semidirect
9. #20288041	C₂	semidirect
10. #537×D₅₃	C₂	semidirect
11. #536×D₅₃	C₂	semidirect
12. #535×D₅₃	C₂	semidirect
13. #534×D₅₃	C₂	semidirect
14. #532×D₅₃	C₂	semidirect
15. #525×D₅₃	C₂	semidirect
16. C₂×#117×D₅₃	C₂	semidirect
17. C₅₃×#3449	C₂	semidirect
18. C₂²×#11719949	C₂²	semidirect
19. C₂²×#11719945	C₂²	semidirect
20. C₂²×#11719945	C₂²	semidirect
21. C₂²×#11719947	C₂²	semidirect
22. C₂²×#11719947	C₂²	semidirect
26. C₂×#41×D₅₃	C₂²	semidirect
27. C₂×#41×D₅₃	C₂²	semidirect
28. C₂×#41×D₅₃	C₂²	semidirect
29. C₂×#41×D₅₃	C₂²	semidirect
30. C₂×#41×D₅₃	C₂²	semidirect
31. C₂×#41×D₅₃	C₂²	semidirect
32. C₂²×Q₈×D₅₃	C₂²	semidirect
34. C₂²×D₄×D₅₃	C₂²	semidirect
36. C₂³×C₄×D₅₃	C₂²	semidirect
37. #16811204	C₂²	semidirect
38. #16811203	C₂²	semidirect
39. #16811202	C₂²	semidirect
40. #16811201	C₂²	semidirect
41. #16811200	C₂²	semidirect
42. #16811199	C₂²	semidirect
43. #16811198	C₂²	semidirect
44. #16811197	C₂²	semidirect
45. #16811196	C₂²	semidirect
46. #16811195	C₂²	semidirect
47. #16811194	C₂²	semidirect
48. #16811193	C₂²	semidirect
49. #16811192	C₂²	semidirect
50. #16811191	C₂²	semidirect
51. #16811190	C₂²	semidirect
52. #16811189	C₂²	semidirect
53. #16811188	C₂²	semidirect
54. #16811187	C₂²	semidirect
55. #16811186	C₂²	semidirect
56. #16811185	C₂²	semidirect
57. #16811184	C₂²	semidirect
58. #16811183	C₂²	semidirect
59. #16811182	C₂²	semidirect
60. #16811181	C₂²	semidirect
61. #16811174	C₂²	semidirect
62. #16811173	C₂²	semidirect
63. #16811172	C₂²	semidirect
64. #16811171	C₂²	semidirect
65. #16811170	C₂²	semidirect
66. #16811169	C₂²	semidirect
67. #16811168	C₂²	semidirect
68. C₄⋊Q₈×D₅₃	C₂²	semidirect
69. #127×D₅₃	C₂²	semidirect
70. #124×D₅₃	C₂²	semidirect
71. #16811136	C₂²	semidirect
72. #16811135	C₂²	semidirect
73. #16811134	C₂²	semidirect
74. #16811133	C₂²	semidirect
75. #16811132	C₂²	semidirect
76. #16811131	C₂²	semidirect
77. #16811130	C₂²	semidirect
78. #16811129	C₂²	semidirect
79. #123×D₅₃	C₂²	semidirect
80. C₂²⋊Q₈×D₅₃	C₂²	semidirect
81. #121×D₅₃	C₂²	semidirect
82. #121×D₅₃	C₂²	semidirect
83. #120×D₅₃	C₂²	semidirect
84. C₄×D₄×D₅₃	C₂²	semidirect
85. C₂×#13133176	C₂²	semidirect
86. C₂×#13133175	C₂²	semidirect
87. C₂×#13133174	C₂²	semidirect
88. C₂×#13133173	C₂²	semidirect
89. #117×D₅₃	C₂²	semidirect
90. #117×D₅₃	C₂²	semidirect
91. #117×D₅₃	C₂²	semidirect
92. #117×D₅₃	C₂²	semidirect
93. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
95. C₂×C₄²×D₅₃	C₂²	semidirect
96. C₂²×#41×C₅₃	C₂²	semidirect
97. C₅₃×#537	C₂²	semidirect
98. C₅₃×#536	C₂²	semidirect
99. C₅₃×#535	C₂²	semidirect
100. C₅₃×#534	C₂²	semidirect
101. C₅₃×#532	C₂²	semidirect
102. C₅₃×#525	C₂²	semidirect
103. C₂×#117×C₅₃	C₂²	semidirect
109. C₂×#11719949	C₂³	semidirect
110. C₂×#11719949	C₂³	semidirect
117. C₂×#11719945	C₂³	semidirect
118. C₂×#11719945	C₂³	semidirect
119. C₂×#11719945	C₂³	semidirect
120. C₂×#11719945	C₂³	semidirect
127. C₂×#11719947	C₂³	semidirect
128. C₂×#11719947	C₂³	semidirect
129. C₂×#11719947	C₂³	semidirect
130. C₂×#11719947	C₂³	semidirect
139. C₂²×Dic₁₀₆	C₂³	semidirect
140. C₂²×Dic₁₀₆	C₂³	semidirect
144. C₂×Q₈×D₅₃	C₂³	semidirect
145. C₂×Q₈×D₅₃	C₂³	semidirect
147. C₂²×D₂₁₂	C₂³	semidirect
150. C₂²×C₂²⋊D₅₃	C₂³	semidirect
160. C₂×D₄×D₅₃	C₂³	semidirect
161. C₂×D₄×D₅₃	C₂³	semidirect
163. C₂³×Dic₅₃	C₂³	semidirect
165. C₂²×C₄×D₅₃	D₄	semidirect
178. C₂²×C₄×D₅₃	C₂³	semidirect
179. C₂²×C₄×D₅₃	C₂³	semidirect
180. C₂²×C₄×D₅₃	C₂³	semidirect
181. C₂²×C₄×D₅₃	C₂³	semidirect
182. #13133217	C₂³	semidirect
183. #13133216	C₂³	semidirect
184. #13133215	C₂³	semidirect
185. #13133214	C₂³	semidirect
186. #13133213	C₂³	semidirect
187. #13133213	C₂³	semidirect
188. #13133206	C₂³	semidirect
189. #13133205	C₂³	semidirect
190. #13133204	C₂³	semidirect
191. #13133203	C₂³	semidirect
192. #13133202	C₂³	semidirect
193. #13133201	C₂³	semidirect
194. #13133200	C₂³	semidirect
195. #13133199	C₂³	semidirect
196. #13133198	C₂³	semidirect
197. #13133197	C₂³	semidirect
198. #13133196	C₂³	semidirect
199. #13133195	C₂³	semidirect
200. #13133194	C₂³	semidirect
201. #13133193	C₂³	semidirect
202. #13133192	C₂³	semidirect
203. #13133192	C₂³	semidirect
204. #13133191	C₂³	semidirect
205. #13133191	C₂³	semidirect
206. #13133190	C₂³	semidirect
207. #13133190	C₂³	semidirect
208. #13133189	C₂³	semidirect
209. #13133189	C₂³	semidirect
210. #13133188	C₂³	semidirect
211. #13133188	C₂³	semidirect
212. #13133187	C₂³	semidirect
213. #13133187	C₂³	semidirect
214. #13133186	C₂³	semidirect
215. #13133185	C₂³	semidirect
216. #13133185	C₂³	semidirect
217. C₄×D₂₁₂	C₂³	semidirect
218. D₄×Dic₅₃	C₂³	semidirect
219. #13133179	C₂³	semidirect
220. C₄×C₂²⋊D₅₃	C₂³	semidirect
221. #13133177	C₂³	semidirect
222. #13133176	C₂³	semidirect
223. #13133176	C₂³	semidirect
224. #13133175	C₂³	semidirect
225. #13133175	C₂³	semidirect
226. #13133174	C₂³	semidirect
227. #13133174	C₂³	semidirect
228. #13133173	C₂³	semidirect
229. #13133173	C₂³	semidirect
230. C₂×C₄⋊Dic₅₃	C₂³	semidirect
231. C₂×#11719919	C₂³	semidirect
234. C₄⋊C₄×D₅₃	C₂³	semidirect
240. C₂×C₄×Dic₅₃	C₂³	semidirect
241. C₂×C₄×Dic₅₃	C₂³	semidirect
244. C₄²×D₅₃	C₂³	semidirect
245. C₄²×D₅₃	C₂³	semidirect
249. C₂×#41×C₅₃	C₂³	semidirect
250. C₂×#41×C₅₃	C₂³	semidirect
251. C₂²×Q₈×C₅₃	C₂³	semidirect
253. C₂²×D₄×C₅₃	C₂³	semidirect
255. C₂³×C₄×C₅₃	C₂³	semidirect
256. C₄⋊Q₈×C₅₃	C₂³	semidirect
257. #127×C₅₃	C₂³	semidirect
258. #124×C₅₃	C₂³	semidirect
259. #123×C₅₃	C₂³	semidirect
260. C₂²⋊Q₈×C₅₃	C₂³	semidirect
261. #121×C₅₃	C₂³	semidirect
262. #121×C₅₃	C₂³	semidirect
263. #120×C₅₃	C₂³	semidirect
264. C₄×D₄×C₅₃	C₂³	semidirect
265. #117×C₅₃	C₂³	semidirect
266. #117×C₅₃	C₂³	semidirect
267. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
269. C₂×C₄²×C₅₃	C₂³	semidirect
298. C₂²×C₄×C₅₃	C₂×D₄	semidirect
318. C₂²×Dic₅₃	C₂×D₄	semidirect
379. C₂×C₄×D₅₃	C₂×D₄	semidirect
380. C₂×C₄×D₅₃	C₂×D₄	semidirect
381. C₂×C₄×D₅₃	C₂×D₄	semidirect
382. C₂×C₄×D₅₃	C₂×D₄	semidirect
564. #3449	D₅₃	direct (N × H)
580. D₅₃	#3449	direct (N × H)
595. C₂²×#41	C₂×D₅₃	semidirect
606. #537	C₂×D₅₃	semidirect
614. #536	C₂×D₅₃	semidirect
622. #535	C₂×D₅₃	semidirect
628. #534	C₂×D₅₃	semidirect
636. #532	C₂×D₅₃	semidirect
648. #525	C₂×D₅₃	semidirect
663. C₂×#117	C₂×D₅₃	semidirect
667. C₅₃	C₂×#3449	semidirect
706. C₂×#41	C₂²×D₅₃	semidirect
707. C₂×#41	C₂²×D₅₃	semidirect
715. C₂²×Q₈	C₂²×D₅₃	semidirect
733. C₂²×D₄	C₂²×D₅₃	semidirect
755. C₂³×C₄	C₂²×D₅₃	semidirect
759. C₄⋊Q₈	C₂²×D₅₃	semidirect
763. #127	C₂²×D₅₃	semidirect
768. #124	C₂²×D₅₃	semidirect
774. #123	C₂²×D₅₃	semidirect
780. C₂²⋊Q₈	C₂²×D₅₃	semidirect
791. #121	C₂²×D₅₃	semidirect
792. #121	C₂²×D₅₃	semidirect
798. #120	C₂²×D₅₃	semidirect
804. C₄×D₄	C₂²×D₅₃	semidirect
813. #117	C₂²×D₅₃	semidirect
814. #117	C₂²×D₅₃	semidirect
820. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
833. C₂×C₄²	C₂²×D₅₃	semidirect
962. C₂²×C₄	D₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#41×D₅₃	2
#20288048	2
#20288047	2
#20288046	2
#20288045	2
#20288044	2
#20288043	2
#20288042	2
#20288041	2
#537×D₅₃	2
#536×D₅₃	2
#535×D₅₃	2
#534×D₅₃	2
#532×D₅₃	2
#525×D₅₃	2
C₂×#117×D₅₃	2
C₅₃×#3449	2
C₂×#3449	53

Subgroups — D53×#3449 #28290923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3449 #28290923