Subgroups — C₅₃×#62187 #27269699

Order 13568.

1812 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3355	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3347	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3341	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3325	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3318	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3259	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3253	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3241	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3122	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3081	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#562	—	2	2	no	—
25	C₅₃×#555	C₂²	1	1	yes	characteristic
26	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
27	C₅₃×#555	C₂²	1	2	yes	complemented
28	C₅₃×#554	C₂²	1	1	yes	characteristic
29	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#553	—	2	1	no	—
31	C₅₃×#553	C₂²	1	2	yes	—
32	C₅₃×#553	C₂²	1	2	yes	complemented
33	C₅₃×#552	—	2	1	no	—
34	C₅₃×#550	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#548	—	2	1	no	—
37	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#546	—	2	1	no	—
39	C₅₃×#546	—	2	2	no	—
40	D₄²×C₅₃	C₂²	1	1	yes	characteristic
41	D₄²×C₅₃	C₂²	1	2	yes	—
42	C₅₃×#544	C₂²	1	2	yes	complemented
43	C₅₃×#542	—	2	2	no	—
44	C₅₃×#540	C₂²	1	2	yes	—
45	C₅₃×#540	C₂²	1	2	yes	complemented
46	C₅₃×#538	—	2	2	no	—
47	C₅₃×#537	—	2	1	no	—
48	C₅₃×#536	—	2	1	no	—
49	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#532	C₂²	1	1	yes	characteristic
51	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#529	C₂²	1	1	yes	characteristic
53	C₅₃×#525	—	2	1	no	—
54	C₂×#121×C₅₃	—	2	1	no	—
55	C₅₃×#518	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#501	C₂²	1	2	yes	complemented
58	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#499	C₂²	1	2	yes	complemented
60	C₅₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#490	C₂²	1	2	yes	complemented
62	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#486	C₂²	1	2	yes	complemented
65	C₅₃×#482	C₂²	1	2	yes	complemented
66	C₅₃×#482	C₂²	1	2	yes	complemented
67	C₅₃×#482	C₂²	1	2	yes	complemented
68	C₅₃×#482	C₂²	1	2	yes	complemented
69	C₅₃×#482	C₂²	1	2	yes	complemented
70	C₅₃×#482	C₂²	1	2	yes	complemented
71	C₅₃×#481	C₂²	1	2	yes	complemented
72	C₅₃×#480	C₂²	1	2	yes	complemented
73	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
74	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#478	C₂²	1	2	yes	—
76	C₅₃×#478	C₂²	1	2	yes	—
77	C₅₃×#478	C₂²	1	2	yes	complemented
78	C₅₃×#478	C₂²	1	2	yes	complemented
79	C₅₃×#478	C₂²	1	2	yes	complemented
80	C₅₃×#478	C₂²	1	2	yes	complemented
81	C₅₃×#478	C₂²	1	2	yes	complemented
82	C₅₃×#478	C₂²	1	2	yes	complemented
83	C₅₃×#476	C₂²	1	1	yes	characteristic
84	C₅₃×#476	C₂²	1	2	yes	—
85	C₅₃×#476	C₂²	1	2	yes	complemented
86	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#474	C₂²	1	1	yes	characteristic
90	C₅₃×#474	C₂²	1	1	yes	characteristic
91	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#474	C₂²	1	2	yes	complemented
94	C₅₃×#469	C₂²	1	2	yes	complemented
95	C₅₃×#469	C₂²	1	2	yes	complemented
96	C₅₃×#469	C₂²	1	2	yes	complemented
97	C₅₃×#469	C₂²	1	2	yes	complemented
98	C₅₃×#466	C₂²	1	2	yes	complemented
99	C₅₃×#466	C₂²	1	2	yes	complemented
100	C₅₃×#459	C₂²	1	1	yes	characteristic
101	C₅₃×#459	C₂²	1	2	yes	complemented
102	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#459	C₂²	1	2	yes	complemented
106	C₅₃×#459	C₂²	1	2	yes	complemented
107	C₅₃×#447	C₂²	1	2	yes	—
108	C₅₃×#447	C₂²	1	1	yes	characteristic
109	C₅₃×#447	C₂²	1	2	yes	—
110	C₅₃×#447	C₂²	1	1	yes	characteristic
111	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#442	C₂²	1	2	yes	—
114	C₅₃×#442	C₂²	1	2	yes	complemented
115	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
116	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×D₈×C₅₃	C₂²	1	2	yes	—
118	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
121	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#436	C₂²	1	2	yes	complemented
123	C₅₃×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#433	C₂²	1	2	yes	complemented
126	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#428	C₂²	1	2	yes	complemented
128	C₅₃×#428	C₂²	1	2	yes	complemented
129	C₅₃×#427	C₂²	1	2	yes	complemented
130	C₅₃×#424	C₂²	1	2	yes	complemented
131	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#418	C₂²	1	2	yes	—
133	C₅₃×#418	C₂²	1	2	yes	—
134	C₂×#102×C₅₃	C₂²	1	2	yes	—
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	1	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	—	2	1	no	—
139	C₂²×Q₈×C₅₃	—	2	1	no	—
140	C₂²×D₄×C₅₃	—	2	1	no	—
141	C₂²×D₄×C₅₃	—	2	2	no	—
142	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
144	C₂³×C₄×C₅₃	—	2	1	no	—
145	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
149	C₂×D₈×C₅₃	C₂³	1	2	yes	—
150	C₂×D₈×C₅₃	C₂³	1	2	yes	—
151	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
152	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₅₃	—	2	2	no	—
155	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
160	#127×C₅₃	C₂³	1	1	yes	characteristic
161	#127×C₅₃	C₂³	1	2	yes	—
162	#127×C₅₃	C₂³	1	1	yes	characteristic
163	#126×C₅₃	—	2	2	no	—
164	#126×C₅₃	—	2	2	no	—
165	#126×C₅₃	D₄	1	2	yes	—
166	#125×C₅₃	—	2	2	no	—
167	#125×C₅₃	D₄	1	1	yes	characteristic
168	#125×C₅₃	C₂³	1	2	yes	—
169	#125×C₅₃	C₂³	1	2	yes	—
170	#125×C₅₃	C₂³	1	2	yes	—
171	#124×C₅₃	—	2	2	no	—
172	#124×C₅₃	—	2	2	no	—
173	#124×C₅₃	—	2	2	no	—
174	#124×C₅₃	—	2	2	no	—
175	#124×C₅₃	—	2	1	no	—
176	#124×C₅₃	—	2	1	no	—
177	#124×C₅₃	D₄	1	1	yes	characteristic
178	#123×C₅₃	—	2	2	no	—
179	#123×C₅₃	—	2	2	no	—
180	#123×C₅₃	—	2	2	no	—
181	#123×C₅₃	—	2	2	no	—
182	#123×C₅₃	—	2	2	no	—
183	#123×C₅₃	—	2	2	no	—
184	#123×C₅₃	—	2	2	no	—
185	#123×C₅₃	D₄	1	2	yes	—
186	C₂²⋊Q₈×C₅₃	—	2	1	no	—
187	C₂²⋊Q₈×C₅₃	—	2	1	no	—
188	C₂²⋊Q₈×C₅₃	—	2	2	no	—
189	C₂²⋊Q₈×C₅₃	—	2	2	no	—
190	C₂²⋊Q₈×C₅₃	—	2	2	no	—
191	C₂²⋊Q₈×C₅₃	—	2	2	no	—
192	C₂²⋊Q₈×C₅₃	—	2	2	no	—
193	C₂²⋊Q₈×C₅₃	—	2	1	no	—
194	C₂²⋊Q₈×C₅₃	—	2	1	no	—
195	C₂²⋊Q₈×C₅₃	—	2	1	no	—
196	C₂²⋊Q₈×C₅₃	—	2	1	no	—
197	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
198	#121×C₅₃	—	2	1	no	—
199	#121×C₅₃	—	2	1	no	—
200	#121×C₅₃	—	2	2	no	—
201	#121×C₅₃	—	2	2	no	—
202	#121×C₅₃	—	2	2	no	—
203	#121×C₅₃	—	2	2	no	—
204	#121×C₅₃	—	2	2	no	—
205	#121×C₅₃	—	2	2	no	—
206	#121×C₅₃	—	2	2	no	—
207	#121×C₅₃	—	2	1	no	—
208	#121×C₅₃	—	2	1	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	—	2	2	no	—
211	#121×C₅₃	—	2	1	no	—
212	#121×C₅₃	—	2	1	no	—
213	#121×C₅₃	D₄	1	1	yes	characteristic
214	#121×C₅₃	C₂³	1	2	yes	—
215	#121×C₅₃	C₂³	1	1	yes	characteristic
216	#121×C₅₃	C₂³	1	1	yes	characteristic
217	#121×C₅₃	C₂³	1	2	yes	—
218	#121×C₅₃	C₂³	1	2	yes	—
219	#121×C₅₃	C₂³	1	2	yes	—
220	#121×C₅₃	C₂³	1	2	yes	—
221	#120×C₅₃	—	2	2	no	—
222	#120×C₅₃	—	2	2	no	—
223	#120×C₅₃	—	2	2	no	—
224	C₄×Q₈×C₅₃	—	2	1	no	—
225	C₄×Q₈×C₅₃	—	2	1	no	—
226	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	—	2	2	no	—
229	C₄×D₄×C₅₃	—	2	2	no	—
230	C₄×D₄×C₅₃	—	2	2	no	—
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	1	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	—	2	1	no	—
235	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₅₃	C₂³	1	2	yes	—
240	C₄×D₄×C₅₃	C₂³	1	2	yes	—
241	C₄×D₄×C₅₃	C₂³	1	2	yes	—
242	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₅₃	C₂³	1	2	yes	—
245	C₄×D₄×C₅₃	C₂³	1	2	yes	—
246	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₅₃	C₂³	1	2	yes	—
248	#117×C₅₃	—	2	1	no	—
249	#117×C₅₃	—	2	1	no	—
250	#117×C₅₃	—	2	2	no	—
251	#117×C₅₃	C₂³	1	2	yes	—
252	#117×C₅₃	C₂³	1	2	yes	—
253	#117×C₅₃	C₂³	1	2	yes	—
254	#117×C₅₃	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
256	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
259	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
261	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
262	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
263	#107×C₅₃	C₂³	1	1	yes	characteristic
264	#107×C₅₃	C₂³	1	2	yes	—
265	#107×C₅₃	C₂³	1	2	yes	—
266	#107×C₅₃	C₂³	1	1	yes	characteristic
267	#107×C₅₃	C₂³	1	2	yes	—
268	#107×C₅₃	C₂³	1	1	yes	characteristic
269	#107×C₅₃	C₂³	1	1	yes	characteristic
270	#107×C₅₃	C₂³	1	2	yes	—
271	#106×C₅₃	C₂³	1	2	yes	—
272	#106×C₅₃	C₂³	1	2	yes	—
273	#106×C₅₃	C₂³	1	2	yes	—
274	#106×C₅₃	C₂³	1	2	yes	—
275	#106×C₅₃	C₂³	1	2	yes	—
276	#106×C₅₃	C₂³	1	2	yes	—
277	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
278	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
282	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	#102×C₅₃	C₂³	1	1	yes	characteristic
285	#102×C₅₃	C₂³	1	2	yes	—
286	#102×C₅₃	C₂³	1	2	yes	—
287	#102×C₅₃	C₂³	1	2	yes	—
288	#102×C₅₃	C₂³	1	2	yes	—
289	#102×C₅₃	C₂³	1	2	yes	—
290	#102×C₅₃	C₂³	1	2	yes	—
291	#102×C₅₃	C₂³	1	1	yes	characteristic
292	#102×C₅₃	C₂³	1	2	yes	—
293	#102×C₅₃	C₂³	1	2	yes	—
294	#102×C₅₃	C₂³	1	1	yes	characteristic
295	#102×C₅₃	C₂³	1	2	yes	—
296	#102×C₅₃	C₂³	1	1	yes	characteristic
297	#102×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	1	yes	characteristic
299	#102×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	1	yes	characteristic
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
308	#97×C₅₃	C₂³	1	2	yes	—
309	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₅₃	C₂³	1	2	yes	—
311	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
312	C₂⁴×C₅₃	—	2	1	no	—
313	C₂⁴×C₅₃	—	2	2	no	—
314	#41×C₅₃	—	8	2	no	—
315	#41×C₅₃	—	8	2	no	—
316	#41×C₅₃	—	8	2	no	—
317	#41×C₅₃	—	8	2	no	—
318	C₂×Q₈×C₅₃	—	2	1	no	—
319	C₂×Q₈×C₅₃	—	2	1	no	—
320	C₂×Q₈×C₅₃	—	2	1	no	—
321	C₂×Q₈×C₅₃	—	2	2	no	—
322	C₂×Q₈×C₅₃	—	2	1	no	—
323	C₂×Q₈×C₅₃	—	8	2	no	—
324	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
325	C₂×D₄×C₅₃	—	2	2	no	—
326	C₂×D₄×C₅₃	—	2	4	no	—
327	C₂×D₄×C₅₃	—	2	2	no	—
328	C₂×D₄×C₅₃	—	2	2	no	—
329	C₂×D₄×C₅₃	—	2	2	no	—
330	C₂×D₄×C₅₃	—	2	2	no	—
331	C₂×D₄×C₅₃	—	2	1	no	—
332	C₂×D₄×C₅₃	—	2	2	no	—
333	C₂×D₄×C₅₃	—	2	1	no	—
334	C₂×D₄×C₅₃	—	2	1	no	—
335	C₂×D₄×C₅₃	—	2	2	no	—
336	C₂×D₄×C₅₃	—	2	1	no	—
337	C₂×D₄×C₅₃	—	2	1	no	—
338	C₂×D₄×C₅₃	—	2	2	no	—
339	C₂×D₄×C₅₃	—	2	1	no	—
340	C₂×D₄×C₅₃	—	2	2	no	—
341	C₂×D₄×C₅₃	—	2	1	no	—
342	C₂×D₄×C₅₃	—	4	2	no	—
343	C₂×D₄×C₅₃	—	4	1	no	—
344	C₂×D₄×C₅₃	—	8	2	no	—
345	C₂×D₄×C₅₃	—	8	4	no	—
346	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
350	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₅₃	—	2	1	no	—
354	C₂²×C₄×C₅₃	—	2	2	no	—
355	C₂²×C₄×C₅₃	—	2	1	no	—
356	C₂²×C₄×C₅₃	—	2	1	no	—
357	C₂²×C₄×C₅₃	—	2	1	no	—
358	C₂²×C₄×C₅₃	—	2	1	no	—
359	C₂²×C₄×C₅₃	—	2	1	no	—
360	C₂²×C₄×C₅₃	—	2	2	no	—
361	C₂²×C₄×C₅₃	—	2	2	no	—
362	C₂²×C₄×C₅₃	—	2	2	no	—
363	C₂²×C₄×C₅₃	—	2	2	no	—
364	C₂²×C₄×C₅₃	—	2	1	no	—
365	C₂²×C₄×C₅₃	—	2	2	no	—
366	C₂²×C₄×C₅₃	—	8	2	no	—
367	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
371	D₈×C₅₃	—	2	2	no	—
372	D₈×C₅₃	—	2	2	no	—
373	D₈×C₅₃	—	4	1	no	—
374	D₈×C₅₃	—	4	2	no	—
375	D₈×C₅₃	—	4	1	no	—
376	D₈×C₅₃	—	4	2	no	—
377	M₁₆×C₅₃	—	4	2	no	—
378	M₁₆×C₅₃	—	4	2	no	—
379	C₂×C₈×C₅₃	—	4	2	no	—
380	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
384	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
386	C₄⋊C₄×C₅₃	—	2	1	no	—
387	C₄⋊C₄×C₅₃	—	2	1	no	—
388	C₄⋊C₄×C₅₃	—	2	2	no	—
389	C₄⋊C₄×C₅₃	—	2	2	no	—
390	C₄⋊C₄×C₅₃	—	2	1	no	—
391	C₄⋊C₄×C₅₃	—	2	2	no	—
392	C₄⋊C₄×C₅₃	—	2	2	no	—
393	C₄⋊C₄×C₅₃	—	2	2	no	—
394	C₄⋊C₄×C₅₃	—	2	1	no	—
395	C₄⋊C₄×C₅₃	—	2	2	no	—
396	C₄⋊C₄×C₅₃	—	2	2	no	—
397	C₄⋊C₄×C₅₃	—	2	2	no	—
398	C₄⋊C₄×C₅₃	—	2	1	no	—
399	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₅₃	—	2	2	no	—
413	C₂²⋊C₄×C₅₃	—	2	2	no	—
414	C₂²⋊C₄×C₅₃	—	2	2	no	—
415	C₂²⋊C₄×C₅₃	—	2	1	no	—
416	C₂²⋊C₄×C₅₃	—	2	1	no	—
417	C₂²⋊C₄×C₅₃	—	2	2	no	—
418	C₂²⋊C₄×C₅₃	—	2	2	no	—
419	C₂²⋊C₄×C₅₃	—	2	1	no	—
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	1	no	—
422	C₂²⋊C₄×C₅₃	—	2	1	no	—
423	C₂²⋊C₄×C₅₃	—	2	2	no	—
424	C₂²⋊C₄×C₅₃	—	2	2	no	—
425	C₂²⋊C₄×C₅₃	—	2	2	no	—
426	C₂²⋊C₄×C₅₃	—	2	1	no	—
427	C₂²⋊C₄×C₅₃	—	2	2	no	—
428	C₂²⋊C₄×C₅₃	—	2	2	no	—
429	C₂²⋊C₄×C₅₃	—	2	2	no	—
430	C₂²⋊C₄×C₅₃	—	2	1	no	—
431	C₂²⋊C₄×C₅₃	—	2	2	no	—
432	C₂²⋊C₄×C₅₃	—	2	1	no	—
433	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
438	C₄²×C₅₃	—	2	2	no	—
439	C₄²×C₅₃	—	2	2	no	—
440	C₄²×C₅₃	—	2	2	no	—
441	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₄²×C₅₃	C₂⁴	1	2	yes	—
445	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
446	C₂³×C₅₃	—	2	1	no	—
447	C₂³×C₅₃	—	2	1	no	—
448	C₂³×C₅₃	—	2	1	no	—
449	C₂³×C₅₃	—	2	2	no	—
450	C₂³×C₅₃	—	2	1	no	—
451	C₂³×C₅₃	—	4	2	no	—
452	C₂³×C₅₃	—	4	4	no	—
453	C₂³×C₅₃	—	4	2	no	—
454	C₂³×C₅₃	—	8	1	no	—
455	C₂³×C₅₃	—	8	2	no	—
456	C₂³×C₅₃	—	8	2	no	—
457	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
458	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
459	Q₈×C₅₃	—	2	2	no	—
460	Q₈×C₅₃	—	4	2	no	—
461	Q₈×C₅₃	—	8	1	no	—
462	Q₈×C₅₃	—	8	2	no	—
463	Q₈×C₅₃	—	8	1	no	—
464	Q₈×C₅₃	—	8	1	no	—
465	D₄×C₅₃	—	2	2	no	—
466	D₄×C₅₃	—	2	1	no	—
467	D₄×C₅₃	—	2	2	no	—
468	D₄×C₅₃	—	2	1	no	—
469	D₄×C₅₃	—	2	1	no	—
470	D₄×C₅₃	—	2	1	no	—
471	D₄×C₅₃	—	2	1	no	—
472	D₄×C₅₃	—	2	2	no	—
473	D₄×C₅₃	—	2	1	no	—
474	D₄×C₅₃	—	2	1	no	—
475	D₄×C₅₃	—	4	2	no	—
476	D₄×C₅₃	—	4	4	no	—
477	D₄×C₅₃	—	4	2	no	—
478	D₄×C₅₃	—	4	4	no	—
479	D₄×C₅₃	—	4	2	no	—
480	D₄×C₅₃	—	8	1	no	—
481	D₄×C₅₃	—	8	2	no	—
482	D₄×C₅₃	—	8	1	no	—
483	D₄×C₅₃	—	8	1	no	—
484	D₄×C₅₃	—	8	2	no	—
485	D₄×C₅₃	—	8	2	no	—
486	D₄×C₅₃	—	8	2	no	—
487	D₄×C₅₃	—	8	2	no	—
488	D₄×C₅₃	—	8	1	no	—
489	D₄×C₅₃	—	8	1	no	—
490	D₄×C₅₃	—	8	2	no	—
491	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
492	C₂×C₄×C₅₃	—	2	2	no	—
493	C₂×C₄×C₅₃	—	2	1	no	—
494	C₂×C₄×C₅₃	—	2	2	no	—
495	C₂×C₄×C₅₃	—	2	2	no	—
496	C₂×C₄×C₅₃	—	2	1	no	—
497	C₂×C₄×C₅₃	—	2	1	no	—
498	C₂×C₄×C₅₃	—	2	1	no	—
499	C₂×C₄×C₅₃	—	2	1	no	—
500	C₂×C₄×C₅₃	—	2	2	no	—
501	C₂×C₄×C₅₃	—	2	2	no	—
502	C₂×C₄×C₅₃	—	2	1	no	—
503	C₂×C₄×C₅₃	—	2	2	no	—
504	C₂×C₄×C₅₃	—	4	1	no	—
505	C₂×C₄×C₅₃	—	4	2	no	—
506	C₂×C₄×C₅₃	—	4	2	no	—
507	C₂×C₄×C₅₃	—	4	2	no	—
508	C₂×C₄×C₅₃	—	4	2	no	—
509	C₂×C₄×C₅₃	—	8	2	no	—
510	C₂×C₄×C₅₃	—	8	1	no	—
511	C₂×C₄×C₅₃	—	8	1	no	—
512	C₂×C₄×C₅₃	—	8	2	no	—
513	C₂×C₄×C₅₃	—	8	2	no	—
514	C₂×C₄×C₅₃	—	8	2	no	—
515	C₂×C₄×C₅₃	—	8	2	no	—
516	C₂×C₄×C₅₃	—	8	1	no	—
517	C₂×C₄×C₅₃	—	8	2	no	—
518	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
527	C₈×C₅₃	—	2	1	no	—
528	C₈×C₅₃	—	2	1	no	—
529	C₈×C₅₃	—	2	1	no	—
530	C₈×C₅₃	—	2	2	no	—
531	C₈×C₅₃	—	2	1	no	—
532	C₈×C₅₃	—	2	2	no	—
533	#62187	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
534	C₂²×C₅₃	—	2	1	no	—
535	C₂²×C₅₃	—	2	2	no	—
536	C₂²×C₅₃	—	2	1	no	—
537	C₂²×C₅₃	—	2	2	no	—
538	C₂²×C₅₃	—	2	2	no	—
539	C₂²×C₅₃	—	2	1	no	—
540	C₂²×C₅₃	—	2	2	no	—
541	C₂²×C₅₃	—	4	1	no	—
542	C₂²×C₅₃	—	4	1	no	—
543	C₂²×C₅₃	—	4	1	no	—
544	C₂²×C₅₃	—	4	2	no	—
545	C₂²×C₅₃	—	4	1	no	—
546	C₂²×C₅₃	—	4	1	no	—
547	C₂²×C₅₃	—	4	1	no	—
548	C₂²×C₅₃	—	4	2	no	—
549	C₂²×C₅₃	—	4	1	no	—
550	C₂²×C₅₃	—	4	1	no	—
551	C₂²×C₅₃	—	4	1	no	—
552	C₂²×C₅₃	—	4	1	no	—
553	C₂²×C₅₃	—	4	1	no	—
554	C₂²×C₅₃	—	4	2	no	—
555	C₂²×C₅₃	—	8	4	no	—
556	C₂²×C₅₃	—	16	4	no	—
557	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
558	C₄×C₅₃	—	2	1	no	—
559	C₄×C₅₃	—	2	1	no	—
560	C₄×C₅₃	—	2	2	no	—
561	C₄×C₅₃	—	2	2	no	—
562	C₄×C₅₃	—	2	1	no	—
563	C₄×C₅₃	—	2	1	no	—
564	C₄×C₅₃	—	2	2	no	—
565	C₄×C₅₃	—	4	2	no	—
566	C₄×C₅₃	—	4	2	no	—
567	C₄×C₅₃	—	4	1	no	—
568	C₄×C₅₃	—	4	1	no	—
569	C₄×C₅₃	—	4	1	no	—
570	C₄×C₅₃	—	4	1	no	—
571	C₄×C₅₃	—	4	2	no	—
572	C₄×C₅₃	#576	1	2	yes	—
573	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
574	C₄×C₅₃	#585	1	1	yes	characteristic
575	#3547	C₂×C₅₃	1	1	yes	characteristic, complemented
576	#3519	C₂×C₅₃	1	1	yes	characteristic, complemented
577	#3384	C₂×C₅₃	1	1	yes	characteristic, complemented
578	#3380	C₂×C₅₃	1	1	yes	characteristic, complemented
579	#3366	C₂×C₅₃	1	1	yes	characteristic, complemented
580	#3358	C₂×C₅₃	1	1	yes	characteristic, complemented
581	#3355	C₂×C₅₃	1	2	yes	complemented
582	#3354	C₂×C₅₃	1	1	yes	characteristic, complemented
583	#3347	C₂×C₅₃	1	2	yes	complemented
584	#3341	C₂×C₅₃	1	1	yes	characteristic, complemented
585	#3325	C₂×C₅₃	1	1	yes	characteristic, complemented
586	#3325	C₂×C₅₃	1	2	yes	complemented
587	#3318	C₂×C₅₃	1	2	yes	complemented
588	#3294	C₂×C₅₃	1	1	yes	characteristic, complemented
589	#3259	C₂×C₅₃	1	2	yes	complemented
590	#3253	C₂×C₅₃	1	1	yes	characteristic, complemented
591	#3241	C₂×C₅₃	1	2	yes	complemented
592	#3228	C₂×C₅₃	1	1	yes	characteristic, complemented
593	#3122	C₂×C₅₃	1	2	yes	complemented
594	#3100	C₂×C₅₃	1	1	yes	characteristic, complemented
595	#3081	C₂×C₅₃	1	2	yes	complemented
596	#3077	C₂×C₅₃	1	1	yes	characteristic, complemented
597	#2993	C₂×C₅₃	1	1	yes	characteristic, complemented
598	C₂×C₅₃	—	4	1	no	—
599	C₂×C₅₃	—	4	2	no	—
600	C₂×C₅₃	—	4	2	no	—
601	C₂×C₅₃	—	8	1	no	—
602	C₂×C₅₃	—	8	1	no	—
603	C₂×C₅₃	—	8	1	no	—
604	C₂×C₅₃	—	8	2	no	—
605	C₂×C₅₃	#3489	1	1	yes	characteristic
606	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
607	C₂×C₅₃	#3585	1	1	yes	characteristic
608	#562	—	2	2	no	—
609	#555	C₂²×C₅₃	1	1	yes	characteristic
610	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
611	#555	C₂²×C₅₃	1	2	yes	complemented
612	#554	C₂²×C₅₃	1	1	yes	characteristic
613	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
614	#553	—	2	1	no	—
615	#553	C₂²×C₅₃	1	2	yes	—
616	#553	C₂²×C₅₃	1	2	yes	complemented
617	#552	—	2	1	no	—
618	#550	C₂²×C₅₃	1	1	yes	characteristic
619	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
620	#548	—	2	1	no	—
621	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
622	#546	—	2	1	no	—
623	#546	—	2	2	no	—
624	D₄²	C₂²×C₅₃	1	1	yes	characteristic
625	D₄²	C₂²×C₅₃	1	2	yes	—
626	#544	C₂²×C₅₃	1	2	yes	complemented
627	#542	—	2	2	no	—
628	#540	C₂²×C₅₃	1	2	yes	—
629	#540	C₂²×C₅₃	1	2	yes	complemented
630	#538	—	2	2	no	—
631	#537	—	2	1	no	—
632	#536	—	2	1	no	—
633	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
634	#532	C₂²×C₅₃	1	1	yes	characteristic
635	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
636	#529	C₂²×C₅₃	1	1	yes	characteristic
637	#525	—	2	1	no	—
638	C₂×#121	—	2	1	no	—
639	#518	C₂²×C₅₃	1	2	yes	—
640	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
641	#501	C₂²×C₅₃	1	2	yes	complemented
642	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
643	#499	C₂²×C₅₃	1	2	yes	complemented
644	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
645	#490	C₂²×C₅₃	1	2	yes	complemented
646	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
647	#486	C₂²×C₅₃	1	2	yes	complemented
648	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
649	#482	C₂²×C₅₃	1	2	yes	complemented
650	#482	C₂²×C₅₃	1	2	yes	complemented
651	#482	C₂²×C₅₃	1	2	yes	complemented
652	#482	C₂²×C₅₃	1	2	yes	complemented
653	#482	C₂²×C₅₃	1	2	yes	complemented
654	#482	C₂²×C₅₃	1	2	yes	complemented
655	#481	C₂²×C₅₃	1	2	yes	complemented
656	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
657	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
658	#480	C₂²×C₅₃	1	2	yes	complemented
659	#478	C₂²×C₅₃	1	2	yes	—
660	#478	C₂²×C₅₃	1	2	yes	—
661	#478	C₂²×C₅₃	1	2	yes	complemented
662	#478	C₂²×C₅₃	1	2	yes	complemented
663	#478	C₂²×C₅₃	1	2	yes	complemented
664	#478	C₂²×C₅₃	1	2	yes	complemented
665	#478	C₂²×C₅₃	1	2	yes	complemented
666	#478	C₂²×C₅₃	1	2	yes	complemented
667	#476	C₂²×C₅₃	1	1	yes	characteristic
668	#476	C₂²×C₅₃	1	2	yes	—
669	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
670	#476	C₂²×C₅₃	1	2	yes	complemented
671	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
672	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
673	#474	C₂²×C₅₃	1	1	yes	characteristic
674	#474	C₂²×C₅₃	1	1	yes	characteristic
675	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
676	#474	C₂²×C₅₃	1	2	yes	complemented
677	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
678	#469	C₂²×C₅₃	1	2	yes	complemented
679	#469	C₂²×C₅₃	1	2	yes	complemented
680	#469	C₂²×C₅₃	1	2	yes	complemented
681	#469	C₂²×C₅₃	1	2	yes	complemented
682	#466	C₂²×C₅₃	1	2	yes	complemented
683	#466	C₂²×C₅₃	1	2	yes	complemented
684	#459	C₂²×C₅₃	1	1	yes	characteristic
685	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
686	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	#459	C₂²×C₅₃	1	2	yes	complemented
688	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
689	#459	C₂²×C₅₃	1	2	yes	complemented
690	#459	C₂²×C₅₃	1	2	yes	complemented
691	#447	C₂²×C₅₃	1	1	yes	characteristic
692	#447	C₂²×C₅₃	1	1	yes	characteristic
693	#447	C₂²×C₅₃	1	2	yes	—
694	#447	C₂²×C₅₃	1	2	yes	—
695	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
696	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
697	#442	C₂²×C₅₃	1	2	yes	—
698	#442	C₂²×C₅₃	1	2	yes	complemented
699	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
700	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
701	C₄×D₈	C₂²×C₅₃	1	2	yes	—
702	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
703	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
704	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
705	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
706	#436	C₂²×C₅₃	1	2	yes	complemented
707	#435	C₂²×C₅₃	1	2	yes	complemented
708	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#433	C₂²×C₅₃	1	2	yes	complemented
710	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
711	#428	C₂²×C₅₃	1	2	yes	complemented
712	#428	C₂²×C₅₃	1	2	yes	complemented
713	#427	C₂²×C₅₃	1	2	yes	complemented
714	#424	C₂²×C₅₃	1	2	yes	complemented
715	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
716	#418	C₂²×C₅₃	1	2	yes	—
717	#418	C₂²×C₅₃	1	2	yes	—
718	C₂×#102	C₂²×C₅₃	1	2	yes	—
719	C₅₃	#62187	1	1	yes	characteristic, direct product factor, Sylow
720	C₂×#41	—	2	1	no	—
721	C₂×#41	—	2	1	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	—	2	1	no	—
724	C₂²×Q₈	—	2	1	no	—
725	C₂²×D₄	—	2	1	no	—
726	C₂²×D₄	—	2	2	no	—
727	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
728	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
729	C₂³×C₄	—	2	1	no	—
730	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
731	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
732	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
733	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
734	C₂×D₈	C₂³×C₅₃	1	2	yes	—
735	C₂×D₈	C₂³×C₅₃	1	2	yes	—
736	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
737	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
738	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
739	C₄⋊Q₈	—	2	2	no	—
740	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
742	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
743	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
744	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
745	#127	C₂³×C₅₃	1	1	yes	characteristic
746	#127	C₂³×C₅₃	1	1	yes	characteristic
747	#127	C₂³×C₅₃	1	2	yes	—
748	#126	—	2	2	no	—
749	#126	—	2	2	no	—
750	#126	D₄×C₅₃	1	2	yes	—
751	#125	—	2	2	no	—
752	#125	D₄×C₅₃	1	1	yes	characteristic
753	#125	C₂³×C₅₃	1	2	yes	—
754	#125	C₂³×C₅₃	1	2	yes	—
755	#125	C₂³×C₅₃	1	2	yes	—
756	#124	—	2	2	no	—
757	#124	—	2	2	no	—
758	#124	—	2	2	no	—
759	#124	—	2	2	no	—
760	#124	—	2	1	no	—
761	#124	—	2	1	no	—
762	#124	D₄×C₅₃	1	1	yes	characteristic
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	D₄×C₅₃	1	2	yes	—
771	C₂²⋊Q₈	—	2	1	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	1	no	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
783	#121	—	2	2	no	—
784	#121	—	2	1	no	—
785	#121	—	2	1	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	1	no	—
789	#121	—	2	1	no	—
790	#121	—	2	1	no	—
791	#121	—	2	1	no	—
792	#121	—	2	2	no	—
793	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	D₄×C₅₃	1	1	yes	characteristic
799	#121	C₂³×C₅₃	1	2	yes	—
800	#121	C₂³×C₅₃	1	1	yes	characteristic
801	#121	C₂³×C₅₃	1	1	yes	characteristic
802	#121	C₂³×C₅₃	1	2	yes	—
803	#121	C₂³×C₅₃	1	2	yes	—
804	#121	C₂³×C₅₃	1	2	yes	—
805	#121	C₂³×C₅₃	1	2	yes	—
806	#120	—	2	2	no	—
807	#120	—	2	2	no	—
808	#120	—	2	2	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	—	2	1	no	—
811	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₅₃	1	2	yes	—
825	C₄×D₄	C₂³×C₅₃	1	2	yes	—
826	C₄×D₄	C₂³×C₅₃	1	2	yes	—
827	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₅₃	1	2	yes	—
830	C₄×D₄	C₂³×C₅₃	1	2	yes	—
831	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₅₃	1	2	yes	—
833	#117	—	2	1	no	—
834	#117	—	2	1	no	—
835	#117	—	2	2	no	—
836	#117	C₂³×C₅₃	1	2	yes	—
837	#117	C₂³×C₅₃	1	2	yes	—
838	#117	C₂³×C₅₃	1	2	yes	—
839	#117	C₂³×C₅₃	1	2	yes	—
840	C₂×C₄⋊C₄	—	2	1	no	—
841	C₂×C₄⋊C₄	—	2	1	no	—
842	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
843	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
844	C₂×C₂²⋊C₄	—	2	1	no	—
845	C₂×C₂²⋊C₄	—	2	2	no	—
846	C₂×C₂²⋊C₄	—	2	2	no	—
847	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
848	#107	C₂³×C₅₃	1	1	yes	characteristic
849	#107	C₂³×C₅₃	1	2	yes	—
850	#107	C₂³×C₅₃	1	1	yes	characteristic
851	#107	C₂³×C₅₃	1	2	yes	—
852	#107	C₂³×C₅₃	1	2	yes	—
853	#107	C₂³×C₅₃	1	1	yes	characteristic
854	#107	C₂³×C₅₃	1	1	yes	characteristic
855	#107	C₂³×C₅₃	1	2	yes	—
856	#106	C₂³×C₅₃	1	2	yes	—
857	#106	C₂³×C₅₃	1	2	yes	—
858	#106	C₂³×C₅₃	1	2	yes	—
859	#106	C₂³×C₅₃	1	2	yes	—
860	#106	C₂³×C₅₃	1	2	yes	—
861	#106	C₂³×C₅₃	1	2	yes	—
862	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
863	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
864	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
865	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
866	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
867	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
868	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
869	#102	C₂³×C₅₃	1	1	yes	characteristic
870	#102	C₂³×C₅₃	1	2	yes	—
871	#102	C₂³×C₅₃	1	2	yes	—
872	#102	C₂³×C₅₃	1	2	yes	—
873	#102	C₂³×C₅₃	1	1	yes	characteristic
874	#102	C₂³×C₅₃	1	2	yes	—
875	#102	C₂³×C₅₃	1	2	yes	—
876	#102	C₂³×C₅₃	1	2	yes	—
877	#102	C₂³×C₅₃	1	2	yes	—
878	#102	C₂³×C₅₃	1	2	yes	—
879	#102	C₂³×C₅₃	1	1	yes	characteristic
880	#102	C₂³×C₅₃	1	2	yes	—
881	#102	C₂³×C₅₃	1	1	yes	characteristic
882	#102	C₂³×C₅₃	1	1	yes	characteristic
883	#102	C₂³×C₅₃	1	1	yes	characteristic
884	#102	C₂³×C₅₃	1	1	yes	characteristic
885	#102	C₂³×C₅₃	1	1	yes	characteristic
886	#102	C₂³×C₅₃	1	2	yes	—
887	#102	C₂³×C₅₃	1	2	yes	—
888	#102	C₂³×C₅₃	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
890	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
891	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
893	#97	C₂³×C₅₃	1	2	yes	—
894	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₅₃	1	2	yes	—
897	C₂⁴	—	2	1	no	—
898	C₂⁴	—	2	2	no	—
899	#41	—	8	2	no	—
900	#41	—	8	2	no	—
901	#41	—	8	2	no	—
902	#41	—	8	2	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	—	2	1	no	—
908	C₂×Q₈	—	8	2	no	—
909	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	4	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	4	2	no	—
928	C₂×D₄	—	4	1	no	—
929	C₂×D₄	—	8	2	no	—
930	C₂×D₄	—	8	4	no	—
931	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
932	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
933	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
934	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
935	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
936	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
937	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	8	2	no	—
952	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
953	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
956	D₈	—	2	2	no	—
957	D₈	—	2	2	no	—
958	D₈	—	4	1	no	—
959	D₈	—	4	2	no	—
960	D₈	—	4	1	no	—
961	D₈	—	4	2	no	—
962	M₁₆	—	4	2	no	—
963	M₁₆	—	4	2	no	—
964	C₂×C₈	—	4	2	no	—
965	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
966	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
969	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
986	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
987	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
988	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
989	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
991	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
992	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1019	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1020	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1021	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1027	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1028	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1029	C₄²	C₂⁴×C₅₃	1	2	yes	—
1030	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	4	2	no	—
1037	C₂³	—	4	4	no	—
1038	C₂³	—	4	2	no	—
1039	C₂³	—	8	1	no	—
1040	C₂³	—	8	2	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1043	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1044	Q₈	—	2	2	no	—
1045	Q₈	—	4	2	no	—
1046	Q₈	—	8	1	no	—
1047	Q₈	—	8	2	no	—
1048	Q₈	—	8	1	no	—
1049	Q₈	—	8	1	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	2	1	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	2	1	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	4	4	no	—
1062	D₄	—	4	2	no	—
1063	D₄	—	4	4	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	8	1	no	—
1066	D₄	—	8	2	no	—
1067	D₄	—	8	1	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	1	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	8	1	no	—
1074	D₄	—	8	1	no	—
1075	D₄	—	8	2	no	—
1076	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	1	no	—
1096	C₂×C₄	—	8	1	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	1	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1104	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1108	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1110	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1111	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1112	C₈	—	2	1	no	—
1113	C₈	—	2	1	no	—
1114	C₈	—	2	1	no	—
1115	C₈	—	2	2	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	2	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	8	4	no	—
1140	C₂²	—	16	4	no	—
1141	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1142	C₄	—	2	2	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	2	no	—
1154	C₄	—	4	2	no	—
1155	C₄	—	4	2	no	—
1156	C₄	C₅₃×#576	1	2	yes	—
1157	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1158	C₄	C₅₃×#585	1	1	yes	characteristic
1159	C₂	—	4	1	no	—
1160	C₂	—	4	2	no	—
1161	C₂	—	4	2	no	—
1162	C₂	—	8	1	no	—
1163	C₂	—	8	2	no	—
1164	C₂	—	8	1	no	—
1165	C₂	—	8	1	no	—
1166	C₂	C₅₃×#3489	1	1	yes	characteristic
1167	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1168	C₂	C₅₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3547	C₂	semidirect
2. C₅₃×#3519	C₂	semidirect
3. C₅₃×#3384	C₂	semidirect
4. C₅₃×#3380	C₂	semidirect
5. C₅₃×#3366	C₂	semidirect
6. C₅₃×#3358	C₂	semidirect
7. C₅₃×#3355	C₂	semidirect
8. C₅₃×#3354	C₂	semidirect
9. C₅₃×#3347	C₂	semidirect
10. C₅₃×#3341	C₂	semidirect
11. C₅₃×#3325	C₂	semidirect
12. C₅₃×#3325	C₂	semidirect
13. C₅₃×#3318	C₂	semidirect
14. C₅₃×#3294	C₂	semidirect
15. C₅₃×#3259	C₂	semidirect
16. C₅₃×#3253	C₂	semidirect
17. C₅₃×#3241	C₂	semidirect
18. C₅₃×#3228	C₂	semidirect
19. C₅₃×#3122	C₂	semidirect
20. C₅₃×#3100	C₂	semidirect
21. C₅₃×#3081	C₂	semidirect
22. C₅₃×#3077	C₂	semidirect
23. C₅₃×#2993	C₂	semidirect
26. C₅₃×#555	C₂²	semidirect
27. C₅₃×#555	C₂²	semidirect
29. C₅₃×#554	C₂²	semidirect
32. C₅₃×#553	C₂²	semidirect
35. D₄×Q₈×C₅₃	C₂²	semidirect
37. C₅₃×#547	C₂²	semidirect
42. C₅₃×#544	C₂²	semidirect
45. C₅₃×#540	C₂²	semidirect
49. C₅₃×#533	C₂²	semidirect
51. C₅₃×#532	C₂²	semidirect
57. C₅₃×#501	C₂²	semidirect
58. C₅₃×#500	C₂²	semidirect
59. C₅₃×#499	C₂²	semidirect
60. C₅₃×#498	C₂²	semidirect
61. C₅₃×#490	C₂²	semidirect
62. C₅₃×#486	C₂²	semidirect
63. C₅₃×#486	C₂²	semidirect
64. C₅₃×#486	C₂²	semidirect
65. C₅₃×#482	C₂²	semidirect
66. C₅₃×#482	C₂²	semidirect
67. C₅₃×#482	C₂²	semidirect
68. C₅₃×#482	C₂²	semidirect
69. C₅₃×#482	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#481	C₂²	semidirect
72. C₅₃×#480	C₂²	semidirect
73. C₅₃×#480	C₂²	semidirect
74. C₅₃×#480	C₂²	semidirect
77. C₅₃×#478	C₂²	semidirect
78. C₅₃×#478	C₂²	semidirect
79. C₅₃×#478	C₂²	semidirect
80. C₅₃×#478	C₂²	semidirect
81. C₅₃×#478	C₂²	semidirect
82. C₅₃×#478	C₂²	semidirect
85. C₅₃×#476	C₂²	semidirect
86. C₅₃×#476	C₂²	semidirect
87. C₅₃×#476	C₂²	semidirect
88. C₅₃×#476	C₂²	semidirect
91. C₅₃×#474	C₂²	semidirect
92. C₅₃×#474	C₂²	semidirect
93. C₅₃×#474	C₂²	semidirect
94. C₅₃×#469	C₂²	semidirect
95. C₅₃×#469	C₂²	semidirect
96. C₅₃×#469	C₂²	semidirect
97. C₅₃×#469	C₂²	semidirect
98. C₅₃×#466	C₂²	semidirect
99. C₅₃×#466	C₂²	semidirect
101. C₅₃×#459	C₂²	semidirect
102. C₅₃×#459	C₂²	semidirect
103. C₅₃×#459	C₂²	semidirect
104. C₅₃×#459	C₂²	semidirect
105. C₅₃×#459	C₂²	semidirect
106. C₅₃×#459	C₂²	semidirect
111. C₅₃×#446	C₂²	semidirect
112. C₈×Q₈×C₅₃	C₂²	semidirect
114. C₅₃×#442	C₂²	semidirect
118. C₄×D₈×C₅₃	C₂²	semidirect
119. C₄×D₈×C₅₃	C₂²	semidirect
120. C₄×D₈×C₅₃	C₂²	semidirect
121. C₅₃×#436	C₂²	semidirect
122. C₅₃×#436	C₂²	semidirect
123. C₅₃×#435	C₂²	semidirect
124. C₈×D₄×C₅₃	C₂²	semidirect
125. C₅₃×#433	C₂²	semidirect
126. C₅₃×#431	C₂²	semidirect
127. C₅₃×#428	C₂²	semidirect
128. C₅₃×#428	C₂²	semidirect
129. C₅₃×#427	C₂²	semidirect
130. C₅₃×#424	C₂²	semidirect
131. C₅₃×#423	C₂²	semidirect
533. #62187	C₅₃	direct (N × H)
575. #3547	C₂×C₅₃	semidirect
576. #3519	C₂×C₅₃	semidirect
577. #3384	C₂×C₅₃	semidirect
578. #3380	C₂×C₅₃	semidirect
579. #3366	C₂×C₅₃	semidirect
580. #3358	C₂×C₅₃	semidirect
581. #3355	C₂×C₅₃	semidirect
582. #3354	C₂×C₅₃	semidirect
583. #3347	C₂×C₅₃	semidirect
584. #3341	C₂×C₅₃	semidirect
585. #3325	C₂×C₅₃	semidirect
586. #3325	C₂×C₅₃	semidirect
587. #3318	C₂×C₅₃	semidirect
588. #3294	C₂×C₅₃	semidirect
589. #3259	C₂×C₅₃	semidirect
590. #3253	C₂×C₅₃	semidirect
591. #3241	C₂×C₅₃	semidirect
592. #3228	C₂×C₅₃	semidirect
593. #3122	C₂×C₅₃	semidirect
594. #3100	C₂×C₅₃	semidirect
595. #3081	C₂×C₅₃	semidirect
596. #3077	C₂×C₅₃	semidirect
597. #2993	C₂×C₅₃	semidirect
610. #555	C₂²×C₅₃	semidirect
611. #555	C₂²×C₅₃	semidirect
613. #554	C₂²×C₅₃	semidirect
616. #553	C₂²×C₅₃	semidirect
619. D₄×Q₈	C₂²×C₅₃	semidirect
621. #547	C₂²×C₅₃	semidirect
626. #544	C₂²×C₅₃	semidirect
629. #540	C₂²×C₅₃	semidirect
633. #533	C₂²×C₅₃	semidirect
635. #532	C₂²×C₅₃	semidirect
641. #501	C₂²×C₅₃	semidirect
642. #500	C₂²×C₅₃	semidirect
643. #499	C₂²×C₅₃	semidirect
644. #498	C₂²×C₅₃	semidirect
645. #490	C₂²×C₅₃	semidirect
646. #486	C₂²×C₅₃	semidirect
647. #486	C₂²×C₅₃	semidirect
648. #486	C₂²×C₅₃	semidirect
649. #482	C₂²×C₅₃	semidirect
650. #482	C₂²×C₅₃	semidirect
651. #482	C₂²×C₅₃	semidirect
652. #482	C₂²×C₅₃	semidirect
653. #482	C₂²×C₅₃	semidirect
654. #482	C₂²×C₅₃	semidirect
655. #481	C₂²×C₅₃	semidirect
656. #480	C₂²×C₅₃	semidirect
657. #480	C₂²×C₅₃	semidirect
658. #480	C₂²×C₅₃	semidirect
661. #478	C₂²×C₅₃	semidirect
662. #478	C₂²×C₅₃	semidirect
663. #478	C₂²×C₅₃	semidirect
664. #478	C₂²×C₅₃	semidirect
665. #478	C₂²×C₅₃	semidirect
666. #478	C₂²×C₅₃	semidirect
669. #476	C₂²×C₅₃	semidirect
670. #476	C₂²×C₅₃	semidirect
671. #476	C₂²×C₅₃	semidirect
672. #476	C₂²×C₅₃	semidirect
675. #474	C₂²×C₅₃	semidirect
676. #474	C₂²×C₅₃	semidirect
677. #474	C₂²×C₅₃	semidirect
678. #469	C₂²×C₅₃	semidirect
679. #469	C₂²×C₅₃	semidirect
680. #469	C₂²×C₅₃	semidirect
681. #469	C₂²×C₅₃	semidirect
682. #466	C₂²×C₅₃	semidirect
683. #466	C₂²×C₅₃	semidirect
685. #459	C₂²×C₅₃	semidirect
686. #459	C₂²×C₅₃	semidirect
687. #459	C₂²×C₅₃	semidirect
688. #459	C₂²×C₅₃	semidirect
689. #459	C₂²×C₅₃	semidirect
690. #459	C₂²×C₅₃	semidirect
695. #446	C₂²×C₅₃	semidirect
696. C₈×Q₈	C₂²×C₅₃	semidirect
698. #442	C₂²×C₅₃	semidirect
702. C₄×D₈	C₂²×C₅₃	semidirect
703. C₄×D₈	C₂²×C₅₃	semidirect
704. C₄×D₈	C₂²×C₅₃	semidirect
705. #436	C₂²×C₅₃	semidirect
706. #436	C₂²×C₅₃	semidirect
707. #435	C₂²×C₅₃	semidirect
708. C₈×D₄	C₂²×C₅₃	semidirect
709. #433	C₂²×C₅₃	semidirect
710. #431	C₂²×C₅₃	semidirect
711. #428	C₂²×C₅₃	semidirect
712. #428	C₂²×C₅₃	semidirect
713. #427	C₂²×C₅₃	semidirect
714. #424	C₂²×C₅₃	semidirect
715. #423	C₂²×C₅₃	semidirect
719. C₅₃	#62187	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3547	2
C₅₃×#3519	2
C₅₃×#3384	2
C₅₃×#3380	2
C₅₃×#3366	2
C₅₃×#3358	2
C₅₃×#3355	2
C₅₃×#3354	2
C₅₃×#3347	2
C₅₃×#3341	2
C₅₃×#3325	2
C₅₃×#3318	2
C₅₃×#3294	2
C₅₃×#3259	2
C₅₃×#3253	2
C₅₃×#3241	2
C₅₃×#3228	2
C₅₃×#3122	2
C₅₃×#3100	2
C₅₃×#3081	2
C₅₃×#3077	2
C₅₃×#2993	2
#62187	53

Subgroups — C53×#62187 #27269699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62187 #27269699