Subgroups — D₅₃×#3508 #28292443

Order 13568.

8622 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288592	C₂	1	1	yes	maximal, characteristic, complemented
2	#20288591	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288590	C₂	1	2	yes	maximal, complemented
4	#20288589	C₂	1	1	yes	maximal, characteristic, complemented
5	#20288588	C₂	1	4	yes	maximal, complemented
6	#20288587	C₂	1	4	yes	maximal, complemented
7	#20288586	C₂	1	2	yes	maximal, complemented
8	#20288585	C₂	1	4	yes	maximal, complemented
9	#20288584	C₂	1	4	yes	maximal, complemented
10	#20288583	C₂	1	8	yes	maximal, complemented
11	#559×D₅₃	C₂	1	4	yes	maximal, complemented
12	#550×D₅₃	C₂	1	4	yes	maximal, complemented
13	#546×D₅₃	C₂	1	8	yes	maximal, complemented
14	#540×D₅₃	C₂	1	4	yes	maximal, complemented
15	#535×D₅₃	C₂	1	2	yes	maximal, complemented
16	#533×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#532×D₅₃	C₂	1	4	yes	maximal, complemented
18	C₂×#127×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#518×D₅₃	C₂	1	2	yes	maximal, complemented
20	C₄×#41×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
23	C₂×#41×D₅₃	C₂²	1	8	yes	complemented
24	C₂²×D₄×D₅₃	C₂²	1	2	yes	—
25	C₂²×D₄×D₅₃	C₂²	1	4	yes	—
26	#16811359	C₂²	1	4	yes	complemented
27	#16811358	C₂²	1	4	yes	complemented
28	#16811358	C₂²	1	4	yes	complemented
29	#16811357	C₂²	1	16	yes	complemented
30	#16811356	C₂²	1	8	yes	complemented
31	#16811356	C₂²	1	8	yes	complemented
32	#16811355	C₂²	1	8	yes	complemented
33	#16811355	C₂²	1	8	yes	complemented
34	#16811295	C₂²	1	4	yes	complemented
35	#16811294	C₂²	1	8	yes	complemented
36	#16811294	C₂²	1	4	yes	complemented
37	#16811293	C₂²	1	4	yes	complemented
38	#16811293	C₂²	1	8	yes	complemented
39	#16811292	C₂²	1	8	yes	complemented
40	#16811291	C₂²	1	8	yes	complemented
41	#16811291	C₂²	1	16	yes	complemented
42	#16811270	C₂²	1	8	yes	complemented
43	#16811269	C₂²	1	8	yes	complemented
44	#16811268	C₂²	1	8	yes	complemented
45	#16811267	C₂²	1	8	yes	complemented
46	#16811266	C₂²	1	8	yes	complemented
47	#16811265	C₂²	1	16	yes	complemented
48	#16811264	C₂²	1	8	yes	complemented
49	#16811263	C₂²	1	16	yes	complemented
50	#16811262	C₂²	1	16	yes	complemented
51	#16811261	C₂²	1	8	yes	complemented
52	#16811260	C₂²	1	16	yes	complemented
53	#16811229	C₂²	1	4	yes	complemented
54	#16811228	C₂²	1	4	yes	complemented
55	#16811227	C₂²	1	4	yes	complemented
56	#16811226	C₂²	1	8	yes	complemented
57	#16811225	C₂²	1	16	yes	complemented
58	#16811224	C₂²	1	8	yes	complemented
59	#16811223	C₂²	1	16	yes	complemented
60	#16811192	C₂²	1	2	yes	complemented
61	#16811191	C₂²	1	4	yes	complemented
62	#16811190	C₂²	1	2	yes	complemented
63	#16811189	C₂²	1	8	yes	complemented
64	#16811188	C₂²	1	8	yes	complemented
65	#16811187	C₂²	1	2	yes	complemented
66	#16811186	C₂²	1	4	yes	complemented
67	#16811180	C₂²	1	1	yes	characteristic, complemented
68	#16811179	C₂²	1	2	yes	complemented
69	#16811178	C₂²	1	2	yes	complemented
70	#16811177	C₂²	1	4	yes	complemented
71	#16811176	C₂²	1	2	yes	complemented
72	#16811175	C₂²	1	4	yes	complemented
73	#16811174	C₂²	1	4	yes	complemented
74	#16811173	C₂²	1	4	yes	complemented
75	#16811172	C₂²	1	8	yes	complemented
76	#16811171	C₂²	1	4	yes	complemented
77	#16811170	C₂²	1	8	yes	complemented
78	#16811170	C₂²	1	8	yes	complemented
79	#16811169	C₂²	1	8	yes	complemented
80	#16811168	C₂²	1	8	yes	complemented
81	#16811168	C₂²	1	8	yes	complemented
82	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	complemented
83	C₂×#13133214	C₂²	1	1	yes	characteristic, complemented
84	C₂×#13133213	C₂²	1	4	yes	complemented
85	C₂×#13133213	C₂²	1	2	yes	complemented
86	#127×D₅₃	C₂²	1	4	yes	—
87	#127×D₅₃	C₂²	1	2	yes	—
88	#127×D₅₃	C₂²	1	2	yes	—
89	#127×D₅₃	C₂²	1	2	yes	complemented
90	#127×D₅₃	C₂²	1	4	yes	complemented
91	#127×D₅₃	C₂²	1	2	yes	complemented
92	#127×D₅₃	C₂²	1	4	yes	complemented
93	#125×D₅₃	C₂²	1	2	yes	complemented
94	#124×D₅₃	C₂²	1	4	yes	complemented
95	#124×D₅₃	C₂²	1	8	yes	complemented
96	#123×D₅₃	C₂²	1	16	yes	complemented
97	C₂²⋊Q₈×D₅₃	C₂²	1	4	yes	—
98	#121×D₅₃	C₂²	1	8	yes	complemented
99	#121×D₅₃	C₂²	1	16	yes	complemented
100	#121×D₅₃	C₂²	1	8	yes	complemented
101	#120×D₅₃	C₂²	1	8	yes	—
102	#16811098	C₂²	1	2	yes	complemented
103	#16811097	C₂²	1	2	yes	complemented
104	#16811097	C₂²	1	2	yes	complemented
105	#16811096	C₂²	1	8	yes	complemented
106	#16811095	C₂²	1	8	yes	complemented
107	#16811095	C₂²	1	8	yes	complemented
108	#41×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
109	C₄×#11719949	C₂²	1	2	yes	complemented
110	C₄×#11719945	C₂²	1	1	yes	characteristic, complemented
111	C₄×#11719945	C₂²	1	2	yes	complemented
112	#16811091	C₂²	1	1	yes	characteristic, complemented
113	#16811091	C₂²	1	2	yes	complemented
114	C₄×#11719947	C₂²	1	4	yes	complemented
115	C₄×#11719947	C₂²	1	2	yes	complemented
116	C₄×Q₈×D₅₃	C₂²	1	4	yes	complemented
117	C₄×Q₈×D₅₃	C₂²	1	2	yes	complemented
118	C₄×D₄×D₅₃	C₂²	1	4	yes	—
119	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
120	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
121	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
122	C₄×D₄×D₅₃	C₂²	1	2	yes	complemented
123	#117×D₅₃	C₂²	1	2	yes	—
124	#117×D₅₃	C₂²	1	1	yes	characteristic
125	#117×D₅₃	C₂²	1	2	yes	complemented
126	C₂×C₂²⋊C₄×D₅₃	C₂²	1	8	yes	—
127	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
128	C₂×C₄²×D₅₃	C₂²	1	2	yes	complemented
129	C₅₃×#559	C₂²	1	4	yes	complemented
130	C₅₃×#550	C₂²	1	4	yes	complemented
131	C₅₃×#546	C₂²	1	8	yes	complemented
132	C₅₃×#540	C₂²	1	4	yes	complemented
133	C₅₃×#535	C₂²	1	2	yes	complemented
134	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#532	C₂²	1	4	yes	complemented
136	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#518	C₂²	1	2	yes	complemented
138	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
139	C₂⁴×D₅₃	C₂³	1	4	yes	—
140	C₂×#11719949	C₂³	1	1	yes	characteristic
141	C₂×#11719949	C₂³	1	8	yes	complemented
142	C₂×#11719945	C₂³	1	2	yes	—
143	C₂×#11719945	C₂³	1	1	yes	characteristic
144	C₂×#11719945	C₂³	1	16	yes	complemented
145	C₂×#11719945	C₂³	1	8	yes	complemented
146	C₂×#11719947	C₂³	1	1	yes	characteristic
147	C₂×#11719947	C₂³	1	2	yes	—
148	C₂×#11719947	C₂³	1	8	yes	complemented
149	C₂×#11719947	C₂³	1	16	yes	complemented
150	#41×D₅₃	—	2	8	no	—
151	#41×D₅₃	—	4	32	no	—
152	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
153	C₂×Q₈×D₅₃	C₂³	1	4	yes	—
154	C₂²×D₂₁₂	C₂³	1	2	yes	—
155	C₂²×D₂₁₂	C₂³	1	4	yes	—
156	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
157	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
158	C₂×D₄×D₅₃	—	2	16	no	—
159	C₂×D₄×D₅₃	—	4	16	no	—
160	C₂×D₄×D₅₃	C₂³	1	2	yes	—
161	C₂×D₄×D₅₃	C₂³	1	4	yes	—
162	C₂×D₄×D₅₃	C₂³	1	4	yes	—
163	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
164	C₂×D₄×D₅₃	C₂³	1	8	yes	—
165	C₂×D₄×D₅₃	C₂³	1	4	yes	—
166	C₂×D₄×D₅₃	C₂³	1	4	yes	—
167	C₂×D₄×D₅₃	C₂³	1	8	yes	—
168	C₂×D₄×D₅₃	C₂³	1	8	yes	—
169	C₂×D₄×D₅₃	C₂³	1	16	yes	—
170	C₂×D₄×D₅₃	C₂³	1	8	yes	—
171	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
172	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
173	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
174	C₂²×C₄×D₅₃	C₂³	1	16	yes	—
175	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
176	#13133217	C₂³	1	2	yes	complemented
177	#13133216	C₂³	1	4	yes	complemented
178	#13133216	C₂³	1	4	yes	complemented
179	#13133215	C₂³	1	4	yes	complemented
180	#13133214	C₂³	1	4	yes	—
181	#13133214	C₂³	1	2	yes	—
182	#13133214	C₂³	1	2	yes	—
183	#13133214	C₂³	1	4	yes	complemented
184	#13133213	C₂³	1	8	yes	—
185	#13133213	C₂³	1	8	yes	—
186	#13133213	C₂³	1	8	yes	—
187	#13133213	C₂³	1	4	yes	—
188	#13133213	C₂³	1	8	yes	—
189	#13133213	C₂³	1	8	yes	—
190	#13133213	C₂³	1	4	yes	—
191	#13133213	C₂³	1	16	yes	complemented
192	#13133213	C₂³	1	4	yes	complemented
193	#13133213	C₂³	1	4	yes	complemented
194	#13133209	C₂³	1	2	yes	complemented
195	#13133208	C₂³	1	4	yes	complemented
196	#13133207	C₂³	1	8	yes	complemented
197	#13133206	C₂³	1	8	yes	complemented
198	#13133206	C₂³	1	4	yes	complemented
199	#13133205	C₂³	1	8	yes	complemented
200	#13133205	C₂³	1	4	yes	complemented
201	#13133204	C₂³	1	8	yes	complemented
202	#13133204	C₂³	1	4	yes	complemented
203	#13133203	C₂³	1	16	yes	complemented
204	#13133203	C₂³	1	16	yes	complemented
205	#13133203	C₂³	1	16	yes	complemented
206	#13133202	C₂³	1	16	yes	complemented
207	#13133202	C₂³	1	16	yes	complemented
208	#13133201	C₂³	1	16	yes	complemented
209	#13133200	C₂³	1	16	yes	complemented
210	#13133199	C₂³	1	16	yes	complemented
211	#13133199	C₂³	1	16	yes	complemented
212	#13133198	C₂³	1	16	yes	complemented
213	#13133197	C₂³	1	4	yes	—
214	#13133196	C₂³	1	4	yes	—
215	#13133195	C₂³	1	8	yes	—
216	#13133194	C₂³	1	8	yes	—
217	#13133193	C₂³	1	4	yes	—
218	#13133192	C₂³	1	16	yes	complemented
219	#13133192	C₂³	1	8	yes	complemented
220	#13133192	C₂³	1	8	yes	complemented
221	#13133191	C₂³	1	16	yes	complemented
222	#13133191	C₂³	1	8	yes	complemented
223	#13133191	C₂³	1	8	yes	complemented
224	#13133190	C₂³	1	16	yes	complemented
225	#13133190	C₂³	1	16	yes	complemented
226	#13133190	C₂³	1	16	yes	complemented
227	#13133190	C₂³	1	16	yes	complemented
228	#13133189	C₂³	1	16	yes	complemented
229	#13133189	C₂³	1	16	yes	complemented
230	#13133189	C₂³	1	16	yes	complemented
231	#13133189	C₂³	1	16	yes	complemented
232	#13133188	C₂³	1	8	yes	complemented
233	#13133188	C₂³	1	16	yes	complemented
234	#13133188	C₂³	1	8	yes	complemented
235	#13133187	C₂³	1	8	yes	—
236	#13133187	C₂³	1	16	yes	—
237	#13133186	C₂³	1	8	yes	—
238	#13133185	C₂³	1	8	yes	—
239	#13133185	C₂³	1	16	yes	—
240	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
241	Q₈×Dic₅₃	C₂³	1	2	yes	complemented
242	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
243	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
244	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
245	C₄×Dic₁₀₆	C₂³	1	2	yes	complemented
246	#13133182	C₂³	1	4	yes	complemented
247	#13133182	C₂³	1	8	yes	complemented
248	#13133182	C₂³	1	2	yes	complemented
249	#13133182	C₂³	1	4	yes	complemented
250	C₄×D₂₁₂	C₂³	1	4	yes	—
251	C₄×D₂₁₂	C₂³	1	8	yes	complemented
252	C₄×D₂₁₂	C₂³	1	2	yes	complemented
253	C₄×D₂₁₂	C₂³	1	8	yes	complemented
254	C₄×D₂₁₂	C₂³	1	8	yes	complemented
255	D₄×Dic₅₃	C₂³	1	4	yes	—
256	D₄×Dic₅₃	C₂³	1	8	yes	complemented
257	D₄×Dic₅₃	C₂³	1	2	yes	complemented
258	D₄×Dic₅₃	C₂³	1	8	yes	complemented
259	D₄×Dic₅₃	C₂³	1	8	yes	complemented
260	#13133179	C₂³	1	4	yes	—
261	#13133179	C₂³	1	8	yes	complemented
262	#13133179	C₂³	1	2	yes	complemented
263	#13133179	C₂³	1	8	yes	complemented
264	#13133179	C₂³	1	8	yes	complemented
265	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
266	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
267	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
268	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
269	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
270	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
271	#13133177	C₂³	1	4	yes	—
272	#13133177	C₂³	1	4	yes	—
273	#13133177	C₂³	1	16	yes	complemented
274	#13133177	C₂³	1	4	yes	complemented
275	#13133177	C₂³	1	16	yes	complemented
276	#13133177	C₂³	1	16	yes	complemented
277	#13133176	C₂³	1	1	yes	characteristic
278	#13133176	C₂³	1	2	yes	—
279	#13133176	C₂³	1	2	yes	complemented
280	#13133175	C₂³	1	2	yes	—
281	#13133175	C₂³	1	4	yes	—
282	#13133175	C₂³	1	4	yes	complemented
283	#13133174	C₂³	1	2	yes	—
284	#13133174	C₂³	1	4	yes	—
285	#13133174	C₂³	1	2	yes	complemented
286	#13133174	C₂³	1	2	yes	complemented
287	#13133173	C₂³	1	2	yes	—
288	#13133173	C₂³	1	4	yes	—
289	#13133173	C₂³	1	4	yes	complemented
290	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
291	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
292	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
293	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
294	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
295	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	—
296	C₂×#11719921	C₂³	1	16	yes	—
297	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
298	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
299	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
300	C₂²⋊C₄×D₅₃	C₂³	1	2	yes	—
301	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
302	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
303	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
304	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
305	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
306	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
307	C₂×C₄×Dic₅₃	C₂³	1	4	yes	complemented
308	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
309	C₄²×D₅₃	C₂³	1	1	yes	characteristic
310	C₄²×D₅₃	C₂³	1	1	yes	characteristic
311	C₄²×D₅₃	C₂³	1	2	yes	—
312	C₄²×D₅₃	C₂³	1	2	yes	—
313	C₄²×D₅₃	C₂³	1	1	yes	characteristic
314	C₄²×D₅₃	C₂³	1	1	yes	characteristic
315	C₄²×D₅₃	C₂³	1	2	yes	—
316	C₄²×D₅₃	C₂³	1	4	yes	—
317	C₄²×D₅₃	C₂³	1	4	yes	—
318	C₄²×D₅₃	C₂³	1	4	yes	complemented
319	C₄²×D₅₃	C₂³	1	2	yes	complemented
320	C₄²×D₅₃	C₂³	1	2	yes	complemented
321	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
322	C₂×#41×C₅₃	C₂³	1	8	yes	complemented
323	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
324	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
325	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
326	#127×C₅₃	C₂³	1	4	yes	—
327	#127×C₅₃	C₂³	1	2	yes	—
328	#127×C₅₃	C₂³	1	2	yes	—
329	#127×C₅₃	C₂³	1	4	yes	complemented
330	#125×C₅₃	C₂³	1	2	yes	complemented
331	#124×C₅₃	C₂³	1	8	yes	complemented
332	#124×C₅₃	C₂³	1	4	yes	complemented
333	#123×C₅₃	C₂³	1	16	yes	complemented
334	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
335	#121×C₅₃	C₂³	1	8	yes	complemented
336	#121×C₅₃	C₂³	1	16	yes	complemented
337	#121×C₅₃	C₂³	1	8	yes	complemented
338	#120×C₅₃	C₂³	1	8	yes	—
339	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
340	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
341	C₄×D₄×C₅₃	C₂³	1	4	yes	—
342	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
343	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
344	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
345	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
346	#117×C₅₃	C₂³	1	1	yes	characteristic
347	#117×C₅₃	C₂³	1	2	yes	—
348	#117×C₅₃	C₂³	1	2	yes	complemented
349	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
350	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
352	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
353	C₂³×D₅₃	—	2	16	no	—
354	C₂³×D₅₃	—	4	16	no	—
355	C₂³×D₅₃	C₂⁴	1	8	yes	—
356	C₂³×D₅₃	C₂⁴	1	2	yes	—
357	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
358	C₂³×D₅₃	C₂⁴	1	4	yes	—
359	C₂³×D₅₃	C₂⁴	1	8	yes	—
360	#41×C₅₃	—	2	4	no	—
361	#41×C₅₃	—	4	16	no	—
362	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
364	C₂×D₄×C₅₃	—	2	8	no	—
365	C₂×D₄×C₅₃	—	4	8	no	—
366	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
367	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
368	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
369	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
371	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
372	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
373	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
376	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
377	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂×C₂²⋊D₅₃	—	2	16	no	—
379	C₂×C₂²⋊D₅₃	—	4	16	no	—
380	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
381	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
382	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
383	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
384	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
385	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
386	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
387	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
388	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
389	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
390	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
391	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
392	C₂²×Dic₅₃	C₂⁴	1	16	yes	—
393	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
394	#11719949	—	2	4	no	—
395	#11719949	—	4	16	no	—
396	Q₈×D₅₃	—	2	4	no	—
397	Q₈×D₅₃	—	2	16	no	—
398	#11719947	—	2	8	no	—
399	#11719947	—	2	4	no	—
400	#11719947	—	4	16	no	—
401	#11719947	—	4	32	no	—
402	D₄×D₅₃	—	2	8	no	—
403	D₄×D₅₃	—	2	16	no	—
404	D₄×D₅₃	—	2	16	no	—
405	D₄×D₅₃	—	2	4	no	—
406	D₄×D₅₃	—	2	16	no	—
407	D₄×D₅₃	—	2	16	no	—
408	D₄×D₅₃	—	2	32	no	—
409	D₄×D₅₃	—	4	16	no	—
410	D₄×D₅₃	—	4	16	no	—
411	D₄×D₅₃	—	4	16	no	—
412	D₄×D₅₃	—	4	32	no	—
413	#11719945	—	2	4	no	—
414	#11719945	—	2	8	no	—
415	#11719945	—	4	32	no	—
416	#11719945	—	4	16	no	—
417	C₂×D₂₁₂	—	2	8	no	—
418	C₂×D₂₁₂	—	4	8	no	—
419	C₂×D₂₁₂	C₂⁴	1	2	yes	—
420	C₂×D₂₁₂	C₂⁴	1	4	yes	—
421	C₂×D₂₁₂	C₂⁴	1	4	yes	—
422	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
423	C₂×D₂₁₂	C₂⁴	1	8	yes	—
424	C₂×D₂₁₂	C₂⁴	1	16	yes	—
425	C₂×D₂₁₂	C₂⁴	1	8	yes	—
426	C₂×C₄×D₅₃	—	2	8	no	—
427	C₂×C₄×D₅₃	—	2	8	no	—
428	C₂×C₄×D₅₃	—	2	16	no	—
429	C₂×C₄×D₅₃	—	4	32	no	—
430	C₂×C₄×D₅₃	#41	1	8	yes	complemented
431	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
432	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
433	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
434	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
435	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
436	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
437	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
438	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
439	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
440	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
441	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
442	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
443	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
444	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
445	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
446	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
447	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
448	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
449	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
450	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
451	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
452	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
453	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
454	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
455	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
456	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
457	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
458	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
459	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
460	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
461	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
462	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
463	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
464	C₄²×C₅₃	C₂⁴	1	2	yes	—
465	C₄²×C₅₃	C₂⁴	1	2	yes	—
466	C₄²×C₅₃	C₂⁴	1	4	yes	—
467	C₄²×C₅₃	C₂⁴	1	4	yes	—
468	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
469	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
470	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
471	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
472	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
473	#11719921	C₂⁴	1	4	yes	—
474	#11719921	C₂⁴	1	8	yes	—
475	#11719921	C₂⁴	1	16	yes	—
476	#11719921	C₂⁴	1	16	yes	—
477	#11719921	C₂⁴	1	4	yes	—
478	#11719921	C₂⁴	1	4	yes	—
479	#11719921	C₂⁴	1	16	yes	—
480	#11719921	C₂⁴	1	16	yes	—
481	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
482	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
483	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
484	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
485	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
486	#11719919	C₂⁴	1	4	yes	—
487	#11719919	C₂⁴	1	8	yes	—
488	#11719919	C₂⁴	1	4	yes	—
489	#11719919	C₂⁴	1	4	yes	—
490	#11719919	C₂⁴	1	8	yes	—
491	#11719919	C₂⁴	1	8	yes	—
492	#11719919	C₂⁴	1	8	yes	—
493	C₄×Dic₅₃	C₂⁴	1	2	yes	—
494	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
495	C₄×Dic₅₃	C₂⁴	1	2	yes	—
496	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
497	C₄×Dic₅₃	C₂⁴	1	2	yes	—
498	C₄×Dic₅₃	C₂⁴	1	2	yes	—
499	C₄×Dic₅₃	C₂⁴	1	2	yes	—
500	C₄×Dic₅₃	C₂⁴	1	4	yes	—
501	C₄×Dic₅₃	C₂⁴	1	2	yes	—
502	C₄×Dic₅₃	C₂⁴	1	4	yes	—
503	C₄×Dic₅₃	C₂⁴	1	4	yes	—
504	C₄×Dic₅₃	C₂⁴	1	4	yes	—
505	C₄×Dic₅₃	C₂⁴	1	8	yes	—
506	C₄×Dic₅₃	C₂⁴	1	4	yes	—
507	C₂³×C₅₃	—	2	8	no	—
508	C₂³×C₅₃	—	4	8	no	—
509	C₂³×C₅₃	C₂⁵	1	2	yes	—
510	C₂³×C₅₃	C₂⁵	1	8	yes	—
511	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
512	C₂²×D₅₃	—	2	4	no	—
513	C₂²×D₅₃	—	2	8	no	—
514	C₂²×D₅₃	—	2	4	no	—
515	C₂²×D₅₃	—	2	16	no	—
516	C₂²×D₅₃	—	2	8	no	—
517	C₂²×D₅₃	—	2	32	no	—
518	C₂²×D₅₃	—	2	16	no	—
519	C₂²×D₅₃	—	4	8	no	—
520	C₂²×D₅₃	—	4	16	no	—
521	C₂²×D₅₃	—	8	32	no	—
522	C₂²×D₅₃	C₂×#41	1	4	yes	—
523	C₂²×D₅₃	C₂⁵	1	2	yes	—
524	C₂²×D₅₃	C₂⁵	1	8	yes	—
525	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
526	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
527	Q₈×C₅₃	—	2	2	no	—
528	Q₈×C₅₃	—	2	8	no	—
529	D₄×C₅₃	—	2	4	no	—
530	D₄×C₅₃	—	2	8	no	—
531	D₄×C₅₃	—	2	8	no	—
532	D₄×C₅₃	—	2	2	no	—
533	D₄×C₅₃	—	2	16	no	—
534	D₄×C₅₃	—	4	8	no	—
535	D₄×C₅₃	—	4	16	no	—
536	C₂×C₄×C₅₃	—	2	4	no	—
537	C₂×C₄×C₅₃	—	2	4	no	—
538	C₂×C₄×C₅₃	—	2	8	no	—
539	C₂×C₄×C₅₃	—	4	16	no	—
540	C₂×C₄×C₅₃	C₂×#41	1	4	yes	complemented
541	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
542	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
543	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
544	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
545	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
546	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
547	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
548	C₂²⋊D₅₃	—	2	4	no	—
549	C₂²⋊D₅₃	—	2	4	no	—
550	C₂²⋊D₅₃	—	2	4	no	—
551	C₂²⋊D₅₃	—	2	16	no	—
552	C₂²⋊D₅₃	—	2	16	no	—
553	C₂²⋊D₅₃	—	2	32	no	—
554	C₂²⋊D₅₃	—	4	16	no	—
555	C₂²⋊D₅₃	—	4	16	no	—
556	C₂²⋊D₅₃	—	4	16	no	—
557	C₂×Dic₅₃	—	2	4	no	—
558	C₂×Dic₅₃	—	2	8	no	—
559	C₂×Dic₅₃	—	2	4	no	—
560	C₂×Dic₅₃	—	4	16	no	—
561	C₂×Dic₅₃	C₂×#41	1	4	yes	complemented
562	C₂×Dic₅₃	C₂⁵	1	8	yes	—
563	C₂×Dic₅₃	C₂⁵	1	2	yes	—
564	C₂×Dic₅₃	C₂⁵	1	4	yes	—
565	C₂×Dic₅₃	C₂⁵	1	2	yes	—
566	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
567	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
568	C₂×Dic₅₃	C₂⁵	1	2	yes	—
569	D₂₁₂	—	2	4	no	—
570	D₂₁₂	—	2	8	no	—
571	D₂₁₂	—	2	8	no	—
572	D₂₁₂	—	2	2	no	—
573	D₂₁₂	—	2	16	no	—
574	D₂₁₂	—	4	8	no	—
575	D₂₁₂	—	4	16	no	—
576	C₄×D₅₃	—	2	4	no	—
577	C₄×D₅₃	—	2	8	no	—
578	C₄×D₅₃	—	2	4	no	—
579	C₄×D₅₃	—	2	16	no	—
580	C₄×D₅₃	—	2	4	no	—
581	C₄×D₅₃	—	2	4	no	—
582	C₄×D₅₃	—	2	8	no	—
583	C₄×D₅₃	—	2	4	no	—
584	C₄×D₅₃	—	2	8	no	—
585	C₄×D₅₃	—	2	4	no	—
586	C₄×D₅₃	—	4	16	no	—
587	C₄×D₅₃	—	4	16	no	—
588	C₄×D₅₃	C₂×#41	1	4	yes	—
589	C₄×D₅₃	C₂×#41	1	4	yes	—
590	C₄×D₅₃	C₂×#41	1	4	yes	complemented
591	C₄×D₅₃	C₂×#41	1	4	yes	complemented
592	C₄×D₅₃	H(5,𝔽₂)	1	8	yes	—
593	Dic₁₀₆	—	2	2	no	—
594	Dic₁₀₆	—	2	8	no	—
595	Dic₁₀₆	—	2	4	no	—
596	Dic₁₀₆	—	2	16	no	—
597	C₂×#3508	—	53	1	no	maximal, Sylow
598	C₂²×C₅₃	—	2	2	no	—
599	C₂²×C₅₃	—	2	2	no	—
600	C₂²×C₅₃	—	2	8	no	—
601	C₂²×C₅₃	—	2	4	no	—
602	C₂²×C₅₃	—	2	16	no	—
603	C₂²×C₅₃	—	8	8	no	—
604	C₂²×C₅₃	C₂²×#41	1	2	yes	—
605	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
606	C₂×D₅₃	—	2	2	no	—
607	C₂×D₅₃	—	2	8	no	—
608	C₂×D₅₃	—	2	2	no	—
609	C₂×D₅₃	—	2	8	no	—
610	C₂×D₅₃	—	2	4	no	—
611	C₂×D₅₃	—	2	16	no	—
612	C₂×D₅₃	—	4	8	no	—
613	C₂×D₅₃	—	4	32	no	—
614	C₂×D₅₃	—	8	16	no	—
615	C₂×D₅₃	—	8	8	no	—
616	C₂×D₅₃	C₂²×#41	1	2	yes	—
617	C₂×D₅₃	C₂²×#41	1	2	yes	—
618	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
619	C₄×C₅₃	—	2	2	no	—
620	C₄×C₅₃	—	2	8	no	—
621	C₄×C₅₃	—	2	4	no	—
622	C₄×C₅₃	—	2	2	no	—
623	C₄×C₅₃	C₂²×#41	1	2	yes	—
624	C₄×C₅₃	C₂²×#41	1	2	yes	—
625	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
626	Dic₅₃	—	2	2	no	—
627	Dic₅₃	—	2	8	no	—
628	Dic₅₃	—	2	4	no	—
629	Dic₅₃	—	2	2	no	—
630	Dic₅₃	C₂²×#41	1	2	yes	—
631	Dic₅₃	C₂²×#41	1	2	yes	—
632	Dic₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
633	#3508	—	53	4	no	—
634	#3508	—	53	4	no	—
635	#3508	—	53	8	no	—
636	#3508	—	53	4	no	—
637	#3508	—	53	2	no	—
638	#3508	—	53	1	no	—
639	#3508	—	53	4	no	—
640	#3508	—	53	1	no	—
641	#3508	—	53	2	no	—
642	#3508	—	53	1	no	—
643	#3508	D₅₃	1	1	yes	characteristic, direct product factor
644	C₂×#559	—	53	4	no	—
645	C₂×#550	—	53	4	no	—
646	C₂×#546	—	53	8	no	—
647	C₂×#540	—	53	4	no	—
648	C₂×#535	—	53	2	no	—
649	C₂×#533	—	53	1	no	—
650	C₂×#532	—	53	4	no	—
651	C₂²×#127	—	53	1	no	—
652	C₂×#518	—	53	2	no	—
653	C₂×C₄×#41	—	53	1	no	—
654	C₂×C₅₃	—	2	2	no	—
655	C₂×C₅₃	—	4	8	no	—
656	C₂×C₅₃	—	4	2	no	—
657	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
658	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	2	yes	—
659	D₅₃	—	2	2	no	—
660	D₅₃	—	4	2	no	—
661	D₅₃	—	4	8	no	—
662	D₅₃	#3508	1	4	yes	direct product factor
663	C₂²×#41	—	53	1	no	—
664	C₂²×#41	—	53	8	no	—
665	C₂³×D₄	—	53	2	no	—
666	C₂³×D₄	—	53	4	no	—
667	#559	—	53	4	no	—
668	#559	—	53	8	no	—
669	#559	—	53	8	no	—
670	#559	—	53	16	no	—
671	#559	—	53	4	no	—
672	#559	—	53	4	no	—
673	#559	—	53	8	no	—
674	#559	—	53	8	no	—
675	#559	C₂×D₅₃	1	4	yes	complemented
676	#550	—	53	8	no	—
677	#550	—	53	4	no	—
678	#550	—	53	8	no	—
679	#550	—	53	8	no	—
680	#550	—	53	16	no	—
681	#550	—	53	4	no	—
682	#550	—	53	8	no	—
683	#550	—	53	4	no	—
684	#550	C₂×D₅₃	1	4	yes	complemented
685	#546	—	53	8	no	—
686	#546	—	53	8	no	—
687	#546	—	53	8	no	—
688	#546	—	53	16	no	—
689	#546	—	53	8	no	—
690	#546	—	53	8	no	—
691	#546	—	53	16	no	—
692	#546	—	53	16	no	—
693	#546	—	53	8	no	—
694	#546	—	53	8	no	—
695	#546	—	53	16	no	—
696	#546	C₂×D₅₃	1	8	yes	complemented
697	#540	—	53	4	no	—
698	#540	—	53	4	no	—
699	#540	—	53	16	no	—
700	#540	—	53	16	no	—
701	#540	—	53	8	no	—
702	#540	—	53	8	no	—
703	#540	—	53	4	no	—
704	#540	C₂×D₅₃	1	4	yes	complemented
705	#535	—	53	2	no	—
706	#535	—	53	2	no	—
707	#535	—	53	4	no	—
708	#535	—	53	4	no	—
709	#535	—	53	8	no	—
710	#535	—	53	8	no	—
711	#535	—	53	2	no	—
712	#535	C₂×D₅₃	1	2	yes	complemented
713	#533	—	53	2	no	—
714	#533	—	53	2	no	—
715	#533	—	53	4	no	—
716	#533	—	53	4	no	—
717	#533	—	53	2	no	—
718	#533	—	53	1	no	—
719	#533	C₂×D₅₃	1	1	yes	characteristic, complemented
720	#532	—	53	8	no	—
721	#532	—	53	4	no	—
722	#532	—	53	4	no	—
723	#532	—	53	8	no	—
724	#532	—	53	8	no	—
725	#532	—	53	8	no	—
726	#532	—	53	8	no	—
727	#532	—	53	8	no	—
728	#532	—	53	4	no	—
729	#532	C₂×D₅₃	1	4	yes	complemented
730	C₂×C₄⋊Q₈	—	53	2	no	—
731	C₂×#127	—	53	4	no	—
732	C₂×#127	—	53	2	no	—
733	C₂×#127	—	53	2	no	—
734	C₂×#127	—	53	2	no	—
735	C₂×#127	—	53	4	no	—
736	C₂×#127	—	53	4	no	—
737	C₂×#127	—	53	2	no	—
738	C₂×#127	—	53	2	no	—
739	C₂×#127	—	53	4	no	—
740	C₂×#127	—	53	1	no	—
741	C₂×#127	C₂×D₅₃	1	1	yes	characteristic, complemented
742	C₂×#125	—	53	2	no	—
743	C₂×#124	—	53	8	no	—
744	C₂×#124	—	53	4	no	—
745	C₂×#123	—	53	16	no	—
746	C₂×C₂²⋊Q₈	—	53	4	no	—
747	C₂×#121	—	53	8	no	—
748	C₂×#121	—	53	8	no	—
749	C₂×#121	—	53	16	no	—
750	C₂×#120	—	53	8	no	—
751	#518	—	53	2	no	—
752	#518	—	53	8	no	—
753	#518	—	53	8	no	—
754	#518	—	53	2	no	—
755	#518	—	53	2	no	—
756	#518	—	53	8	no	—
757	#518	C₂×D₅₃	1	2	yes	complemented
758	C₄×#41	—	53	1	no	—
759	C₄×#41	—	53	2	no	—
760	C₄×#41	—	53	4	no	—
761	C₄×#41	—	53	2	no	—
762	C₄×#41	—	53	1	no	—
763	C₄×#41	—	53	2	no	—
764	C₄×#41	—	53	1	no	—
765	C₄×#41	—	53	2	no	—
766	C₄×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
767	C₂×C₄×Q₈	—	53	2	no	—
768	C₂×C₄×Q₈	—	53	4	no	—
769	C₂×C₄×D₄	—	53	4	no	—
770	C₂×C₄×D₄	—	53	2	no	—
771	C₂×C₄×D₄	—	53	8	no	—
772	C₂×C₄×D₄	—	53	8	no	—
773	C₂×C₄×D₄	—	53	8	no	—
774	C₂×#117	—	53	1	no	—
775	C₂×#117	—	53	2	no	—
776	C₂×#117	—	53	2	no	—
777	C₂²×C₂²⋊C₄	—	53	8	no	—
778	C₂²×C₄²	—	53	1	no	—
779	C₂²×C₄²	—	53	2	no	—
780	C₅₃	C₂×#3508	1	1	yes	characteristic, complemented, Sylow
781	C₂⁵	—	53	4	no	—
782	C₂×#41	—	53	1	no	—
783	C₂×#41	—	53	8	no	—
784	C₂×#41	—	53	2	no	—
785	C₂×#41	—	53	1	no	—
786	C₂×#41	—	53	16	no	—
787	C₂×#41	—	53	8	no	—
788	C₂×#41	—	53	2	no	—
789	C₂×#41	—	53	1	no	—
790	C₂×#41	—	53	16	no	—
791	C₂×#41	—	53	8	no	—
792	C₂×#41	—	106	8	no	—
793	C₂×#41	—	212	32	no	—
794	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
795	C₂×#41	C₂²×D₅₃	1	8	yes	complemented
796	C₂²×Q₈	—	53	1	no	—
797	C₂²×Q₈	—	53	4	no	—
798	C₂²×D₄	—	53	4	no	—
799	C₂²×D₄	—	53	8	no	—
800	C₂²×D₄	—	53	2	no	—
801	C₂²×D₄	—	53	4	no	—
802	C₂²×D₄	—	53	4	no	—
803	C₂²×D₄	—	53	1	no	—
804	C₂²×D₄	—	53	8	no	—
805	C₂²×D₄	—	53	4	no	—
806	C₂²×D₄	—	53	4	no	—
807	C₂²×D₄	—	53	16	no	—
808	C₂²×D₄	—	53	8	no	—
809	C₂²×D₄	—	53	8	no	—
810	C₂²×D₄	—	53	8	no	—
811	C₂²×D₄	—	53	2	no	—
812	C₂²×D₄	—	53	4	no	—
813	C₂²×D₄	—	106	16	no	—
814	C₂²×D₄	—	212	16	no	—
815	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
816	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
817	C₂³×C₄	—	53	1	no	—
818	C₂³×C₄	—	53	2	no	—
819	C₂³×C₄	—	53	4	no	—
820	C₂³×C₄	—	53	2	no	—
821	C₂³×C₄	—	53	16	no	—
822	C₄⋊Q₈	—	53	4	no	—
823	C₄⋊Q₈	—	53	4	no	—
824	C₄⋊Q₈	—	53	4	no	—
825	C₄⋊Q₈	—	53	2	no	—
826	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
827	#127	—	53	8	no	—
828	#127	—	53	4	no	—
829	#127	—	53	8	no	—
830	#127	—	53	4	no	—
831	#127	—	53	8	no	—
832	#127	—	53	8	no	—
833	#127	—	53	8	no	—
834	#127	—	53	16	no	—
835	#127	—	53	4	no	—
836	#127	—	53	4	no	—
837	#127	—	53	2	no	—
838	#127	—	53	2	no	—
839	#127	—	53	4	no	—
840	#127	—	53	4	no	—
841	#127	C₂²×D₅₃	1	2	yes	—
842	#127	C₂²×D₅₃	1	2	yes	—
843	#127	C₂²×D₅₃	1	4	yes	—
844	#127	C₂²×D₅₃	1	4	yes	complemented
845	#125	—	53	8	no	—
846	#125	—	53	4	no	—
847	#125	—	53	2	no	—
848	#125	C₂²×D₅₃	1	2	yes	complemented
849	#124	—	53	8	no	—
850	#124	—	53	4	no	—
851	#124	—	53	8	no	—
852	#124	—	53	4	no	—
853	#124	—	53	16	no	—
854	#124	—	53	16	no	—
855	#124	—	53	16	no	—
856	#124	—	53	8	no	—
857	#124	—	53	4	no	—
858	#124	C₂²×D₅₃	1	8	yes	complemented
859	#124	C₂²×D₅₃	1	4	yes	complemented
860	#123	—	53	16	no	—
861	#123	—	53	16	no	—
862	#123	—	53	16	no	—
863	#123	—	53	16	no	—
864	#123	—	53	16	no	—
865	#123	—	53	16	no	—
866	#123	—	53	16	no	—
867	#123	C₂²×D₅₃	1	16	yes	complemented
868	C₂²⋊Q₈	—	53	4	no	—
869	C₂²⋊Q₈	—	53	4	no	—
870	C₂²⋊Q₈	—	53	8	no	—
871	C₂²⋊Q₈	—	53	4	no	—
872	C₂²⋊Q₈	—	53	8	no	—
873	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
874	#121	—	53	8	no	—
875	#121	—	53	16	no	—
876	#121	—	53	8	no	—
877	#121	—	53	16	no	—
878	#121	—	53	16	no	—
879	#121	—	53	16	no	—
880	#121	—	53	16	no	—
881	#121	—	53	8	no	—
882	#121	—	53	8	no	—
883	#121	—	53	16	no	—
884	#121	—	53	8	no	—
885	#121	—	53	8	no	—
886	#121	—	53	16	no	—
887	#121	—	53	16	no	—
888	#121	—	53	16	no	—
889	#121	—	53	16	no	—
890	#121	—	53	16	no	—
891	#121	C₂²×D₅₃	1	8	yes	complemented
892	#121	C₂²×D₅₃	1	8	yes	complemented
893	#121	C₂²×D₅₃	1	16	yes	complemented
894	#120	—	53	8	no	—
895	#120	—	53	8	no	—
896	#120	—	53	16	no	—
897	#120	—	53	16	no	—
898	#120	—	53	8	no	—
899	#120	C₂²×D₅₃	1	8	yes	—
900	C₄×Q₈	—	53	2	no	—
901	C₄×Q₈	—	53	4	no	—
902	C₄×Q₈	—	53	4	no	—
903	C₄×Q₈	—	53	2	no	—
904	C₄×Q₈	—	53	8	no	—
905	C₄×Q₈	—	53	4	no	—
906	C₄×Q₈	—	53	2	no	—
907	C₄×Q₈	—	53	4	no	—
908	C₄×Q₈	—	53	8	no	—
909	C₄×Q₈	—	53	4	no	—
910	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
911	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
912	C₄×D₄	—	53	4	no	—
913	C₄×D₄	—	53	2	no	—
914	C₄×D₄	—	53	8	no	—
915	C₄×D₄	—	53	8	no	—
916	C₄×D₄	—	53	8	no	—
917	C₄×D₄	—	53	4	no	—
918	C₄×D₄	—	53	4	no	—
919	C₄×D₄	—	53	4	no	—
920	C₄×D₄	—	53	16	no	—
921	C₄×D₄	—	53	16	no	—
922	C₄×D₄	—	53	16	no	—
923	C₄×D₄	—	53	4	no	—
924	C₄×D₄	—	53	2	no	—
925	C₄×D₄	—	53	8	no	—
926	C₄×D₄	—	53	8	no	—
927	C₄×D₄	—	53	8	no	—
928	C₄×D₄	—	53	4	no	—
929	C₄×D₄	—	53	4	no	—
930	C₄×D₄	—	53	4	no	—
931	C₄×D₄	—	53	16	no	—
932	C₄×D₄	—	53	16	no	—
933	C₄×D₄	—	53	16	no	—
934	C₄×D₄	—	53	4	no	—
935	C₄×D₄	—	53	2	no	—
936	C₄×D₄	—	53	8	no	—
937	C₄×D₄	—	53	8	no	—
938	C₄×D₄	—	53	8	no	—
939	C₄×D₄	C₂²×D₅₃	1	4	yes	—
940	C₄×D₄	C₂²×D₅₃	1	2	yes	complemented
941	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
942	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
943	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
944	#117	—	53	1	no	—
945	#117	—	53	2	no	—
946	#117	—	53	2	no	—
947	#117	—	53	2	no	—
948	#117	—	53	4	no	—
949	#117	—	53	4	no	—
950	#117	—	53	2	no	—
951	#117	—	53	4	no	—
952	#117	—	53	4	no	—
953	#117	—	53	2	no	—
954	#117	—	53	2	no	—
955	#117	—	53	2	no	—
956	#117	—	53	4	no	—
957	#117	C₂²×D₅₃	1	1	yes	characteristic
958	#117	C₂²×D₅₃	1	2	yes	—
959	#117	C₂²×D₅₃	1	2	yes	complemented
960	C₂×C₄⋊C₄	—	53	2	no	—
961	C₂×C₄⋊C₄	—	53	4	no	—
962	C₂×C₄⋊C₄	—	53	4	no	—
963	C₂×C₄⋊C₄	—	53	4	no	—
964	C₂×C₄⋊C₄	—	53	8	no	—
965	C₂×C₂²⋊C₄	—	53	8	no	—
966	C₂×C₂²⋊C₄	—	53	16	no	—
967	C₂×C₂²⋊C₄	—	53	2	no	—
968	C₂×C₂²⋊C₄	—	53	4	no	—
969	C₂×C₂²⋊C₄	—	53	16	no	—
970	C₂×C₂²⋊C₄	—	53	8	no	—
971	C₂×C₂²⋊C₄	—	53	8	no	—
972	C₂×C₂²⋊C₄	—	53	16	no	—
973	C₂×C₂²⋊C₄	—	53	4	no	—
974	C₂×C₂²⋊C₄	—	53	16	no	—
975	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	—
976	C₂×C₄²	—	53	2	no	—
977	C₂×C₄²	—	53	1	no	—
978	C₂×C₄²	—	53	4	no	—
979	C₂×C₄²	—	53	2	no	—
980	C₂×C₄²	—	53	2	no	—
981	C₂×C₄²	—	53	1	no	—
982	C₂×C₄²	—	53	4	no	—
983	C₂×C₄²	—	53	4	no	—
984	C₂×C₄²	—	53	2	no	—
985	C₂×C₄²	—	53	2	no	—
986	C₂×C₄²	—	53	1	no	—
987	C₂×C₄²	—	53	1	no	—
988	C₂×C₄²	—	53	4	no	—
989	C₂×C₄²	—	53	2	no	—
990	C₂×C₄²	—	53	2	no	—
991	C₂×C₄²	—	53	1	no	—
992	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
993	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
994	C₂⁴	—	53	1	no	—
995	C₂⁴	—	53	8	no	—
996	C₂⁴	—	53	2	no	—
997	C₂⁴	—	53	8	no	—
998	C₂⁴	—	53	4	no	—
999	C₂⁴	—	106	16	no	—
1000	C₂⁴	—	212	16	no	—
1001	C₂⁴	C₂³×D₅₃	1	4	yes	—
1002	#41	—	2	4	no	—
1003	#41	—	4	16	no	—
1004	#41	—	106	8	no	—
1005	#41	—	106	8	no	—
1006	#41	—	106	4	no	—
1007	#41	—	106	4	no	—
1008	#41	—	106	4	no	—
1009	#41	—	212	16	no	—
1010	#41	—	212	32	no	—
1011	#41	—	212	16	no	—
1012	#41	—	212	32	no	—
1013	#41	—	212	16	no	—
1014	C₂×Q₈	—	53	2	no	—
1015	C₂×Q₈	—	53	1	no	—
1016	C₂×Q₈	—	53	8	no	—
1017	C₂×Q₈	—	53	4	no	—
1018	C₂×Q₈	—	106	4	no	—
1019	C₂×Q₈	—	106	16	no	—
1020	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1021	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1022	C₂×D₄	—	2	8	no	—
1023	C₂×D₄	—	4	8	no	—
1024	C₂×D₄	—	53	2	no	—
1025	C₂×D₄	—	53	2	no	—
1026	C₂×D₄	—	53	8	no	—
1027	C₂×D₄	—	53	8	no	—
1028	C₂×D₄	—	53	2	no	—
1029	C₂×D₄	—	53	16	no	—
1030	C₂×D₄	—	53	16	no	—
1031	C₂×D₄	—	53	16	no	—
1032	C₂×D₄	—	53	16	no	—
1033	C₂×D₄	—	53	2	no	—
1034	C₂×D₄	—	53	4	no	—
1035	C₂×D₄	—	53	4	no	—
1036	C₂×D₄	—	53	1	no	—
1037	C₂×D₄	—	53	8	no	—
1038	C₂×D₄	—	53	16	no	—
1039	C₂×D₄	—	53	8	no	—
1040	C₂×D₄	—	106	16	no	—
1041	C₂×D₄	—	106	16	no	—
1042	C₂×D₄	—	106	16	no	—
1043	C₂×D₄	—	106	16	no	—
1044	C₂×D₄	—	106	32	no	—
1045	C₂×D₄	—	106	4	no	—
1046	C₂×D₄	—	106	16	no	—
1047	C₂×D₄	—	106	8	no	—
1048	C₂×D₄	—	106	8	no	—
1049	C₂×D₄	—	212	8	no	—
1050	C₂×D₄	—	212	16	no	—
1051	C₂×D₄	—	212	16	no	—
1052	C₂×D₄	—	212	16	no	—
1053	C₂×D₄	—	212	32	no	—
1054	C₂×D₄	—	212	16	no	—
1055	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1056	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1057	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1058	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1059	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1060	C₂×D₄	C₂³×D₅₃	1	16	yes	—
1061	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1062	C₂²×C₄	—	53	1	no	—
1063	C₂²×C₄	—	53	8	no	—
1064	C₂²×C₄	—	53	1	no	—
1065	C₂²×C₄	—	53	1	no	—
1066	C₂²×C₄	—	53	2	no	—
1067	C₂²×C₄	—	53	1	no	—
1068	C₂²×C₄	—	53	1	no	—
1069	C₂²×C₄	—	53	2	no	—
1070	C₂²×C₄	—	53	4	no	—
1071	C₂²×C₄	—	53	2	no	—
1072	C₂²×C₄	—	53	16	no	—
1073	C₂²×C₄	—	53	2	no	—
1074	C₂²×C₄	—	53	4	no	—
1075	C₂²×C₄	—	53	2	no	—
1076	C₂²×C₄	—	53	2	no	—
1077	C₂²×C₄	—	53	2	no	—
1078	C₂²×C₄	—	53	4	no	—
1079	C₂²×C₄	—	53	4	no	—
1080	C₂²×C₄	—	53	2	no	—
1081	C₂²×C₄	—	53	2	no	—
1082	C₂²×C₄	—	53	8	no	—
1083	C₂²×C₄	—	53	16	no	—
1084	C₂²×C₄	—	53	16	no	—
1085	C₂²×C₄	—	106	8	no	—
1086	C₂²×C₄	—	106	8	no	—
1087	C₂²×C₄	—	106	16	no	—
1088	C₂²×C₄	—	212	32	no	—
1089	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1090	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1091	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1092	C₂²×C₄	C₂³×D₅₃	1	16	yes	—
1093	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1094	C₄⋊C₄	—	53	4	no	—
1095	C₄⋊C₄	—	53	2	no	—
1096	C₄⋊C₄	—	53	8	no	—
1097	C₄⋊C₄	—	53	4	no	—
1098	C₄⋊C₄	—	53	4	no	—
1099	C₄⋊C₄	—	53	4	no	—
1100	C₄⋊C₄	—	53	4	no	—
1101	C₄⋊C₄	—	53	8	no	—
1102	C₄⋊C₄	—	53	4	no	—
1103	C₄⋊C₄	—	53	8	no	—
1104	C₄⋊C₄	—	53	8	no	—
1105	C₄⋊C₄	—	53	8	no	—
1106	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1107	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1108	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1109	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1110	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1111	C₂²⋊C₄	—	53	2	no	—
1112	C₂²⋊C₄	—	53	4	no	—
1113	C₂²⋊C₄	—	53	16	no	—
1114	C₂²⋊C₄	—	53	4	no	—
1115	C₂²⋊C₄	—	53	16	no	—
1116	C₂²⋊C₄	—	53	4	no	—
1117	C₂²⋊C₄	—	53	8	no	—
1118	C₂²⋊C₄	—	53	16	no	—
1119	C₂²⋊C₄	—	53	16	no	—
1120	C₂²⋊C₄	—	53	4	no	—
1121	C₂²⋊C₄	—	53	4	no	—
1122	C₂²⋊C₄	—	53	16	no	—
1123	C₂²⋊C₄	—	53	16	no	—
1124	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1125	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1126	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
1127	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1128	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
1129	C₄²	—	53	2	no	—
1130	C₄²	—	53	1	no	—
1131	C₄²	—	53	4	no	—
1132	C₄²	—	53	2	no	—
1133	C₄²	—	53	2	no	—
1134	C₄²	—	53	1	no	—
1135	C₄²	—	53	4	no	—
1136	C₄²	—	53	4	no	—
1137	C₄²	—	53	4	no	—
1138	C₄²	—	53	2	no	—
1139	C₄²	—	53	2	no	—
1140	C₄²	—	53	2	no	—
1141	C₄²	—	53	8	no	—
1142	C₄²	—	53	4	no	—
1143	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1144	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1145	C₄²	C₂³×D₅₃	1	2	yes	—
1146	C₄²	C₂³×D₅₃	1	2	yes	—
1147	C₄²	C₂³×D₅₃	1	4	yes	—
1148	C₄²	C₂³×D₅₃	1	4	yes	—
1149	C₂³	—	2	8	no	—
1150	C₂³	—	4	8	no	—
1151	C₂³	—	53	1	no	—
1152	C₂³	—	53	4	no	—
1153	C₂³	—	53	1	no	—
1154	C₂³	—	53	8	no	—
1155	C₂³	—	53	2	no	—
1156	C₂³	—	106	4	no	—
1157	C₂³	—	106	16	no	—
1158	C₂³	—	106	4	no	—
1159	C₂³	—	106	8	no	—
1160	C₂³	—	106	32	no	—
1161	C₂³	—	106	16	no	—
1162	C₂³	—	106	8	no	—
1163	C₂³	—	424	32	no	—
1164	C₂³	—	212	8	no	—
1165	C₂³	—	212	16	no	—
1166	C₂³	C₂⁴×D₅₃	1	8	yes	—
1167	C₂³	C₂⁴×D₅₃	1	2	yes	—
1168	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1169	Q₈	—	2	2	no	—
1170	Q₈	—	2	8	no	—
1171	Q₈	—	106	4	no	—
1172	Q₈	—	106	16	no	—
1173	Q₈	—	106	2	no	—
1174	Q₈	—	106	8	no	—
1175	D₄	—	2	4	no	—
1176	D₄	—	2	8	no	—
1177	D₄	—	2	8	no	—
1178	D₄	—	2	2	no	—
1179	D₄	—	2	16	no	—
1180	D₄	—	4	8	no	—
1181	D₄	—	4	16	no	—
1182	D₄	—	106	4	no	—
1183	D₄	—	106	16	no	—
1184	D₄	—	106	16	no	—
1185	D₄	—	106	32	no	—
1186	D₄	—	106	4	no	—
1187	D₄	—	106	4	no	—
1188	D₄	—	106	4	no	—
1189	D₄	—	106	8	no	—
1190	D₄	—	106	8	no	—
1191	D₄	—	106	2	no	—
1192	D₄	—	106	16	no	—
1193	D₄	—	212	8	no	—
1194	D₄	—	212	16	no	—
1195	D₄	—	212	16	no	—
1196	D₄	—	212	16	no	—
1197	D₄	—	212	16	no	—
1198	C₂×C₄	—	2	4	no	—
1199	C₂×C₄	—	2	4	no	—
1200	C₂×C₄	—	2	8	no	—
1201	C₂×C₄	—	4	16	no	—
1202	C₂×C₄	—	53	4	no	—
1203	C₂×C₄	—	53	1	no	—
1204	C₂×C₄	—	53	1	no	—
1205	C₂×C₄	—	53	2	no	—
1206	C₂×C₄	—	53	4	no	—
1207	C₂×C₄	—	53	4	no	—
1208	C₂×C₄	—	53	4	no	—
1209	C₂×C₄	—	53	4	no	—
1210	C₂×C₄	—	53	8	no	—
1211	C₂×C₄	—	53	2	no	—
1212	C₂×C₄	—	53	4	no	—
1213	C₂×C₄	—	53	2	no	—
1214	C₂×C₄	—	53	8	no	—
1215	C₂×C₄	—	106	4	no	—
1216	C₂×C₄	—	106	4	no	—
1217	C₂×C₄	—	106	8	no	—
1218	C₂×C₄	—	106	8	no	—
1219	C₂×C₄	—	106	4	no	—
1220	C₂×C₄	—	106	4	no	—
1221	C₂×C₄	—	106	16	no	—
1222	C₂×C₄	—	106	4	no	—
1223	C₂×C₄	—	106	4	no	—
1224	C₂×C₄	—	106	8	no	—
1225	C₂×C₄	—	106	4	no	—
1226	C₂×C₄	—	106	4	no	—
1227	C₂×C₄	—	106	8	no	—
1228	C₂×C₄	—	212	16	no	—
1229	C₂×C₄	—	212	16	no	—
1230	C₂×C₄	—	212	16	no	—
1231	C₂×C₄	#41×D₅₃	1	4	yes	complemented
1232	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1233	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1234	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1235	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1236	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1237	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1238	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1239	C₂²	—	2	2	no	—
1240	C₂²	—	2	2	no	—
1241	C₂²	—	2	8	no	—
1242	C₂²	—	2	4	no	—
1243	C₂²	—	2	16	no	—
1244	C₂²	—	8	8	no	—
1245	C₂²	—	53	2	no	—
1246	C₂²	—	53	4	no	—
1247	C₂²	—	53	2	no	—
1248	C₂²	—	106	8	no	—
1249	C₂²	—	106	2	no	—
1250	C₂²	—	106	2	no	—
1251	C₂²	—	106	8	no	—
1252	C₂²	—	106	4	no	—
1253	C₂²	—	106	16	no	—
1254	C₂²	—	424	8	no	—
1255	C₂²	—	424	16	no	—
1256	C₂²	—	212	32	no	—
1257	C₂²	—	212	8	no	—
1258	C₂²	C₂×#41×D₅₃	1	2	yes	—
1259	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1260	C₄	—	2	2	no	—
1261	C₄	—	2	4	no	—
1262	C₄	—	2	2	no	—
1263	C₄	—	2	8	no	—
1264	C₄	—	53	2	no	—
1265	C₄	—	53	2	no	—
1266	C₄	—	53	4	no	—
1267	C₄	—	106	2	no	—
1268	C₄	—	106	4	no	—
1269	C₄	—	106	2	no	—
1270	C₄	—	106	8	no	—
1271	C₄	C₂×#41×D₅₃	1	2	yes	—
1272	C₄	C₂×#41×D₅₃	1	2	yes	—
1273	C₄	H(5,𝔽₂)×D₅₃	1	4	yes	—
1274	C₂	—	2	2	no	—
1275	C₂	—	4	8	no	—
1276	C₂	—	4	2	no	—
1277	C₂	—	53	4	no	—
1278	C₂	—	106	2	no	—
1279	C₂	—	212	8	no	—
1280	C₂	—	212	2	no	—
1281	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1282	C₂	C₂×H(5,𝔽₂)×D₅₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3508	C₂
hypercenter	#3508	D₅₃
hypocenter	C₅₃	C₂×#3508
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3508

Complements

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

N	H ≅ G/N	type
1. #20288592	C₂	semidirect
2. #20288591	C₂	semidirect
3. #20288590	C₂	semidirect
4. #20288589	C₂	semidirect
5. #20288588	C₂	semidirect
6. #20288587	C₂	semidirect
7. #20288586	C₂	semidirect
8. #20288585	C₂	semidirect
9. #20288584	C₂	semidirect
10. #20288583	C₂	semidirect
11. #559×D₅₃	C₂	semidirect
12. #550×D₅₃	C₂	semidirect
13. #546×D₅₃	C₂	semidirect
14. #540×D₅₃	C₂	semidirect
15. #535×D₅₃	C₂	semidirect
16. #533×D₅₃	C₂	semidirect
17. #532×D₅₃	C₂	semidirect
18. C₂×#127×D₅₃	C₂	semidirect
19. #518×D₅₃	C₂	semidirect
20. C₄×#41×D₅₃	C₂	semidirect
21. C₅₃×#3508	C₂	semidirect
23. C₂×#41×D₅₃	C₂²	semidirect
26. #16811359	C₂²	semidirect
27. #16811358	C₂²	semidirect
28. #16811358	C₂²	semidirect
29. #16811357	C₂²	semidirect
30. #16811356	C₂²	semidirect
31. #16811356	C₂²	semidirect
32. #16811355	C₂²	semidirect
33. #16811355	C₂²	semidirect
34. #16811295	C₂²	semidirect
35. #16811294	C₂²	semidirect
36. #16811294	C₂²	semidirect
37. #16811293	C₂²	semidirect
38. #16811293	C₂²	semidirect
39. #16811292	C₂²	semidirect
40. #16811291	C₂²	semidirect
41. #16811291	C₂²	semidirect
42. #16811270	C₂²	semidirect
43. #16811269	C₂²	semidirect
44. #16811268	C₂²	semidirect
45. #16811267	C₂²	semidirect
46. #16811266	C₂²	semidirect
47. #16811265	C₂²	semidirect
48. #16811264	C₂²	semidirect
49. #16811263	C₂²	semidirect
50. #16811262	C₂²	semidirect
51. #16811261	C₂²	semidirect
52. #16811260	C₂²	semidirect
53. #16811229	C₂²	semidirect
54. #16811228	C₂²	semidirect
55. #16811227	C₂²	semidirect
56. #16811226	C₂²	semidirect
57. #16811225	C₂²	semidirect
58. #16811224	C₂²	semidirect
59. #16811223	C₂²	semidirect
60. #16811192	C₂²	semidirect
61. #16811191	C₂²	semidirect
62. #16811190	C₂²	semidirect
63. #16811189	C₂²	semidirect
64. #16811188	C₂²	semidirect
65. #16811187	C₂²	semidirect
66. #16811186	C₂²	semidirect
67. #16811180	C₂²	semidirect
68. #16811179	C₂²	semidirect
69. #16811178	C₂²	semidirect
70. #16811177	C₂²	semidirect
71. #16811176	C₂²	semidirect
72. #16811175	C₂²	semidirect
73. #16811174	C₂²	semidirect
74. #16811173	C₂²	semidirect
75. #16811172	C₂²	semidirect
76. #16811171	C₂²	semidirect
77. #16811170	C₂²	semidirect
78. #16811170	C₂²	semidirect
79. #16811169	C₂²	semidirect
80. #16811168	C₂²	semidirect
81. #16811168	C₂²	semidirect
82. C₄⋊Q₈×D₅₃	C₂²	semidirect
83. C₂×#13133214	C₂²	semidirect
84. C₂×#13133213	C₂²	semidirect
85. C₂×#13133213	C₂²	semidirect
89. #127×D₅₃	C₂²	semidirect
90. #127×D₅₃	C₂²	semidirect
91. #127×D₅₃	C₂²	semidirect
92. #127×D₅₃	C₂²	semidirect
93. #125×D₅₃	C₂²	semidirect
94. #124×D₅₃	C₂²	semidirect
95. #124×D₅₃	C₂²	semidirect
96. #123×D₅₃	C₂²	semidirect
98. #121×D₅₃	C₂²	semidirect
99. #121×D₅₃	C₂²	semidirect
100. #121×D₅₃	C₂²	semidirect
102. #16811098	C₂²	semidirect
103. #16811097	C₂²	semidirect
104. #16811097	C₂²	semidirect
105. #16811096	C₂²	semidirect
106. #16811095	C₂²	semidirect
107. #16811095	C₂²	semidirect
108. #41×Dic₅₃	C₂²	semidirect
109. C₄×#11719949	C₂²	semidirect
110. C₄×#11719945	C₂²	semidirect
111. C₄×#11719945	C₂²	semidirect
112. #16811091	C₂²	semidirect
113. #16811091	C₂²	semidirect
114. C₄×#11719947	C₂²	semidirect
115. C₄×#11719947	C₂²	semidirect
116. C₄×Q₈×D₅₃	C₂²	semidirect
117. C₄×Q₈×D₅₃	C₂²	semidirect
119. C₄×D₄×D₅₃	C₂²	semidirect
120. C₄×D₄×D₅₃	C₂²	semidirect
121. C₄×D₄×D₅₃	C₂²	semidirect
122. C₄×D₄×D₅₃	C₂²	semidirect
125. #117×D₅₃	C₂²	semidirect
128. C₂×C₄²×D₅₃	C₂²	semidirect
129. C₅₃×#559	C₂²	semidirect
130. C₅₃×#550	C₂²	semidirect
131. C₅₃×#546	C₂²	semidirect
132. C₅₃×#540	C₂²	semidirect
133. C₅₃×#535	C₂²	semidirect
134. C₅₃×#533	C₂²	semidirect
135. C₅₃×#532	C₂²	semidirect
136. C₂×#127×C₅₃	C₂²	semidirect
137. C₅₃×#518	C₂²	semidirect
138. C₄×#41×C₅₃	C₂²	semidirect
141. C₂×#11719949	C₂³	semidirect
144. C₂×#11719945	C₂³	semidirect
145. C₂×#11719945	C₂³	semidirect
148. C₂×#11719947	C₂³	semidirect
149. C₂×#11719947	C₂³	semidirect
176. #13133217	C₂³	semidirect
177. #13133216	C₂³	semidirect
178. #13133216	C₂³	semidirect
179. #13133215	C₂³	semidirect
183. #13133214	C₂³	semidirect
191. #13133213	C₂³	semidirect
192. #13133213	C₂³	semidirect
193. #13133213	C₂³	semidirect
194. #13133209	C₂³	semidirect
195. #13133208	C₂³	semidirect
196. #13133207	C₂³	semidirect
197. #13133206	C₂³	semidirect
198. #13133206	C₂³	semidirect
199. #13133205	C₂³	semidirect
200. #13133205	C₂³	semidirect
201. #13133204	C₂³	semidirect
202. #13133204	C₂³	semidirect
203. #13133203	C₂³	semidirect
204. #13133203	C₂³	semidirect
205. #13133203	C₂³	semidirect
206. #13133202	C₂³	semidirect
207. #13133202	C₂³	semidirect
208. #13133201	C₂³	semidirect
209. #13133200	C₂³	semidirect
210. #13133199	C₂³	semidirect
211. #13133199	C₂³	semidirect
212. #13133198	C₂³	semidirect
218. #13133192	C₂³	semidirect
219. #13133192	C₂³	semidirect
220. #13133192	C₂³	semidirect
221. #13133191	C₂³	semidirect
222. #13133191	C₂³	semidirect
223. #13133191	C₂³	semidirect
224. #13133190	C₂³	semidirect
225. #13133190	C₂³	semidirect
226. #13133190	C₂³	semidirect
227. #13133190	C₂³	semidirect
228. #13133189	C₂³	semidirect
229. #13133189	C₂³	semidirect
230. #13133189	C₂³	semidirect
231. #13133189	C₂³	semidirect
232. #13133188	C₂³	semidirect
233. #13133188	C₂³	semidirect
234. #13133188	C₂³	semidirect
240. Q₈×Dic₅₃	C₂³	semidirect
241. Q₈×Dic₅₃	C₂³	semidirect
242. C₄×Dic₁₀₆	C₂³	semidirect
243. C₄×Dic₁₀₆	C₂³	semidirect
244. C₄×Dic₁₀₆	C₂³	semidirect
245. C₄×Dic₁₀₆	C₂³	semidirect
246. #13133182	C₂³	semidirect
247. #13133182	C₂³	semidirect
248. #13133182	C₂³	semidirect
249. #13133182	C₂³	semidirect
251. C₄×D₂₁₂	C₂³	semidirect
252. C₄×D₂₁₂	C₂³	semidirect
253. C₄×D₂₁₂	C₂³	semidirect
254. C₄×D₂₁₂	C₂³	semidirect
256. D₄×Dic₅₃	C₂³	semidirect
257. D₄×Dic₅₃	C₂³	semidirect
258. D₄×Dic₅₃	C₂³	semidirect
259. D₄×Dic₅₃	C₂³	semidirect
261. #13133179	C₂³	semidirect
262. #13133179	C₂³	semidirect
263. #13133179	C₂³	semidirect
264. #13133179	C₂³	semidirect
267. C₄×C₂²⋊D₅₃	C₂³	semidirect
268. C₄×C₂²⋊D₅₃	C₂³	semidirect
269. C₄×C₂²⋊D₅₃	C₂³	semidirect
270. C₄×C₂²⋊D₅₃	C₂³	semidirect
273. #13133177	C₂³	semidirect
274. #13133177	C₂³	semidirect
275. #13133177	C₂³	semidirect
276. #13133177	C₂³	semidirect
279. #13133176	C₂³	semidirect
282. #13133175	C₂³	semidirect
285. #13133174	C₂³	semidirect
286. #13133174	C₂³	semidirect
289. #13133173	C₂³	semidirect
307. C₂×C₄×Dic₅₃	C₂³	semidirect
308. C₂×C₄×Dic₅₃	C₂³	semidirect
318. C₄²×D₅₃	C₂³	semidirect
319. C₄²×D₅₃	C₂³	semidirect
320. C₄²×D₅₃	C₂³	semidirect
322. C₂×#41×C₅₃	C₂³	semidirect
325. C₄⋊Q₈×C₅₃	C₂³	semidirect
329. #127×C₅₃	C₂³	semidirect
330. #125×C₅₃	C₂³	semidirect
331. #124×C₅₃	C₂³	semidirect
332. #124×C₅₃	C₂³	semidirect
333. #123×C₅₃	C₂³	semidirect
335. #121×C₅₃	C₂³	semidirect
336. #121×C₅₃	C₂³	semidirect
337. #121×C₅₃	C₂³	semidirect
339. C₄×Q₈×C₅₃	C₂³	semidirect
340. C₄×Q₈×C₅₃	C₂³	semidirect
342. C₄×D₄×C₅₃	C₂³	semidirect
343. C₄×D₄×C₅₃	C₂³	semidirect
344. C₄×D₄×C₅₃	C₂³	semidirect
345. C₄×D₄×C₅₃	C₂³	semidirect
348. #117×C₅₃	C₂³	semidirect
351. C₂×C₄²×C₅₃	C₂³	semidirect
430. C₂×C₄×D₅₃	#41	semidirect
540. C₂×C₄×C₅₃	C₂×#41	semidirect
561. C₂×Dic₅₃	C₂×#41	semidirect
590. C₄×D₅₃	C₂×#41	semidirect
591. C₄×D₅₃	C₂×#41	semidirect
643. #3508	D₅₃	direct (N × H)
662. D₅₃	#3508	direct (N × H)
675. #559	C₂×D₅₃	semidirect
684. #550	C₂×D₅₃	semidirect
696. #546	C₂×D₅₃	semidirect
704. #540	C₂×D₅₃	semidirect
712. #535	C₂×D₅₃	semidirect
719. #533	C₂×D₅₃	semidirect
729. #532	C₂×D₅₃	semidirect
741. C₂×#127	C₂×D₅₃	semidirect
757. #518	C₂×D₅₃	semidirect
766. C₄×#41	C₂×D₅₃	semidirect
780. C₅₃	C₂×#3508	semidirect
795. C₂×#41	C₂²×D₅₃	semidirect
826. C₄⋊Q₈	C₂²×D₅₃	semidirect
844. #127	C₂²×D₅₃	semidirect
848. #125	C₂²×D₅₃	semidirect
858. #124	C₂²×D₅₃	semidirect
859. #124	C₂²×D₅₃	semidirect
867. #123	C₂²×D₅₃	semidirect
891. #121	C₂²×D₅₃	semidirect
892. #121	C₂²×D₅₃	semidirect
893. #121	C₂²×D₅₃	semidirect
910. C₄×Q₈	C₂²×D₅₃	semidirect
911. C₄×Q₈	C₂²×D₅₃	semidirect
940. C₄×D₄	C₂²×D₅₃	semidirect
941. C₄×D₄	C₂²×D₅₃	semidirect
942. C₄×D₄	C₂²×D₅₃	semidirect
943. C₄×D₄	C₂²×D₅₃	semidirect
959. #117	C₂²×D₅₃	semidirect
993. C₂×C₄²	C₂²×D₅₃	semidirect
1231. C₂×C₄	#41×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20288592	2
#20288591	2
#20288590	2
#20288589	2
#20288588	2
#20288587	2
#20288586	2
#20288585	2
#20288584	2
#20288583	2
#559×D₅₃	2
#550×D₅₃	2
#546×D₅₃	2
#540×D₅₃	2
#535×D₅₃	2
#533×D₅₃	2
#532×D₅₃	2
C₂×#127×D₅₃	2
#518×D₅₃	2
C₄×#41×D₅₃	2
C₅₃×#3508	2
C₂×#3508	53

Subgroups — D53×#3508 #28292443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3508 #28292443