Subgroups — C₅₃×#61275 #27268787

Order 13568.

1764 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3493	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3356	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3351	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3349	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3349	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3348	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3346	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3340	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3336	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3056	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
27	C₅₃×#556	—	2	1	no	—
28	C₅₃×#556	C₂²	1	2	yes	—
29	C₅₃×#556	C₂²	1	2	yes	—
30	C₅₃×#555	—	2	1	no	—
31	C₅₃×#555	C₂²	1	2	yes	—
32	C₅₃×#554	C₂²	1	2	yes	—
33	C₅₃×#553	—	2	1	no	—
34	C₅₃×#553	C₂²	1	2	yes	—
35	C₅₃×#552	—	2	2	no	—
36	C₅₃×#552	—	2	1	no	—
37	C₅₃×#552	C₂²	1	2	yes	—
38	C₅₃×#552	C₂²	1	2	yes	—
39	C₅₃×#552	C₂²	1	2	yes	—
40	C₅₃×#551	—	2	2	no	—
41	C₅₃×#544	C₂²	1	1	yes	characteristic
42	C₅₃×#544	C₂²	1	1	yes	characteristic
43	C₅₃×#542	—	2	1	no	—
44	C₅₃×#541	—	2	1	no	—
45	C₅₃×#538	—	2	2	no	—
46	C₅₃×#537	C₂²	1	1	yes	characteristic
47	C₅₃×#536	C₂²	1	1	yes	characteristic
48	C₅₃×#533	—	2	1	no	—
49	C₅₃×#529	—	2	2	no	—
50	C₅₃×#529	—	2	1	no	—
51	C₅₃×#525	C₂²	1	1	yes	characteristic
52	C₅₃×#525	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
54	C₅₃×#520	C₂²	1	1	yes	characteristic
55	C₅₃×#520	C₂²	1	1	yes	characteristic
56	C₅₃×#520	C₂²	1	1	yes	characteristic
57	C₅₃×#519	C₂²	1	1	yes	characteristic
58	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
59	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
60	C₅₃×#501	C₂²	1	2	yes	complemented
61	C₅₃×#501	C₂²	1	2	yes	complemented
62	C₅₃×#499	C₂²	1	2	yes	complemented
63	C₅₃×#498	C₂²	1	2	yes	complemented
64	C₅₃×#485	C₂²	1	1	yes	characteristic
65	C₅₃×#485	C₂²	1	2	yes	—
66	C₅₃×#485	C₂²	1	2	yes	—
67	C₅₃×#485	C₂²	1	2	yes	—
68	C₅₃×#485	C₂²	1	2	yes	—
69	C₅₃×#485	C₂²	1	1	yes	characteristic
70	C₅₃×#485	C₂²	1	2	yes	complemented
71	C₅₃×#485	C₂²	1	2	yes	complemented
72	C₅₃×#485	C₂²	1	2	yes	complemented
73	C₅₃×#484	C₂²	1	1	yes	characteristic
74	C₅₃×#484	C₂²	1	2	yes	complemented
75	C₅₃×#483	C₂²	1	1	yes	characteristic
76	C₅₃×#483	C₂²	1	2	yes	complemented
77	C₅₃×#483	C₂²	1	2	yes	complemented
78	C₅₃×#482	C₂²	1	1	yes	characteristic
79	C₅₃×#482	C₂²	1	1	yes	characteristic
80	C₅₃×#482	C₂²	1	2	yes	complemented
81	C₅₃×#481	C₂²	1	1	yes	characteristic
82	C₅₃×#481	C₂²	1	2	yes	complemented
83	C₅₃×#480	C₂²	1	1	yes	characteristic
84	C₅₃×#479	C₂²	1	2	yes	complemented
85	C₅₃×#479	C₂²	1	2	yes	complemented
86	C₅₃×#479	C₂²	1	2	yes	complemented
87	C₅₃×#478	C₂²	1	2	yes	complemented
88	C₅₃×#477	C₂²	1	2	yes	complemented
89	C₅₃×#477	C₂²	1	2	yes	complemented
90	C₅₃×#475	C₂²	1	2	yes	complemented
91	C₅₃×#474	C₂²	1	2	yes	complemented
92	C₅₃×#470	C₂²	1	2	yes	—
93	C₅₃×#470	C₂²	1	2	yes	complemented
94	C₅₃×#468	C₂²	1	2	yes	—
95	C₅₃×#468	C₂²	1	2	yes	complemented
96	C₅₃×#467	C₂²	1	2	yes	—
97	C₅₃×#467	C₂²	1	2	yes	complemented
98	C₅₃×#465	C₂²	1	2	yes	—
99	C₅₃×#465	C₂²	1	2	yes	complemented
100	C₅₃×#441	C₂²	1	2	yes	complemented
101	C₅₃×#440	C₂²	1	2	yes	complemented
102	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
104	C₅₃×#436	C₂²	1	2	yes	—
105	C₅₃×#435	C₂²	1	2	yes	—
106	C₅₃×#435	C₂²	1	2	yes	—
107	C₈×D₄×C₅₃	C₂²	1	2	yes	—
108	C₅₃×#428	C₂²	1	1	yes	characteristic
109	C₅₃×#428	C₂²	1	1	yes	characteristic
110	C₅₃×#428	C₂²	1	1	yes	characteristic
111	C₅₃×#428	C₂²	1	1	yes	characteristic
112	C₅₃×#428	C₂²	1	1	yes	characteristic
113	C₅₃×#428	C₂²	1	2	yes	—
114	C₅₃×#428	C₂²	1	2	yes	—
115	C₅₃×#428	C₂²	1	2	yes	complemented
116	C₅₃×#428	C₂²	1	2	yes	complemented
117	C₅₃×#427	C₂²	1	2	yes	—
118	C₅₃×#427	C₂²	1	1	yes	characteristic
119	C₅₃×#427	C₂²	1	2	yes	—
120	C₅₃×#427	C₂²	1	1	yes	characteristic
121	C₅₃×#427	C₂²	1	2	yes	complemented
122	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
123	C₂×#107×C₅₃	C₂²	1	2	yes	complemented
124	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
125	C₅₃×#424	C₂²	1	1	yes	characteristic
126	C₅₃×#419	C₂²	1	1	yes	characteristic
127	C₅₃×#417	C₂²	1	1	yes	characteristic
128	C₅₃×#416	C₂²	1	1	yes	characteristic
129	C₅₃×#416	C₂²	1	1	yes	characteristic
130	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
131	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
132	C₅₃×#408	C₂²	1	1	yes	characteristic
133	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
134	C₅₃×#405	C₂²	1	1	yes	characteristic
135	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
136	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
139	#137×C₅₃	—	2	4	no	—
140	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
142	#131×C₅₃	—	2	4	no	—
143	C₂×M₁₆×C₅₃	—	2	4	no	—
144	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
146	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
149	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₅₃	—	2	1	no	—
153	C₄⋊Q₈×C₅₃	—	2	1	no	—
154	C₄⋊Q₈×C₅₃	—	2	1	no	—
155	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
157	#126×C₅₃	—	2	2	no	—
158	#126×C₅₃	—	2	2	no	—
159	#126×C₅₃	—	2	2	no	—
160	#126×C₅₃	—	2	2	no	—
161	#126×C₅₃	—	2	2	no	—
162	#126×C₅₃	—	2	2	no	—
163	#126×C₅₃	—	2	2	no	—
164	#126×C₅₃	—	2	2	no	—
165	#125×C₅₃	—	2	1	no	—
166	#125×C₅₃	—	2	2	no	—
167	#125×C₅₃	—	2	2	no	—
168	#125×C₅₃	—	2	2	no	—
169	#125×C₅₃	—	2	2	no	—
170	#125×C₅₃	—	2	1	no	—
171	#125×C₅₃	C₂³	1	2	yes	—
172	#125×C₅₃	C₂³	1	2	yes	—
173	#124×C₅₃	—	2	2	no	—
174	#124×C₅₃	—	2	2	no	—
175	#124×C₅₃	—	2	1	no	—
176	#124×C₅₃	—	2	2	no	—
177	#124×C₅₃	—	2	2	no	—
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	1	no	—
184	#123×C₅₃	D₄	1	2	yes	—
185	C₂²⋊Q₈×C₅₃	—	2	2	no	—
186	C₂²⋊Q₈×C₅₃	—	2	2	no	—
187	C₂²⋊Q₈×C₅₃	—	2	2	no	—
188	C₂²⋊Q₈×C₅₃	—	2	2	no	—
189	C₂²⋊Q₈×C₅₃	—	2	1	no	—
190	C₂²⋊Q₈×C₅₃	—	2	1	no	—
191	C₂²⋊Q₈×C₅₃	—	2	1	no	—
192	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
193	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
194	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
197	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
201	#121×C₅₃	—	2	2	no	—
202	#121×C₅₃	—	2	1	no	—
203	#121×C₅₃	—	2	2	no	—
204	#121×C₅₃	—	2	2	no	—
205	#121×C₅₃	D₄	1	1	yes	characteristic
206	#121×C₅₃	D₄	1	1	yes	characteristic
207	#121×C₅₃	C₂³	1	1	yes	characteristic
208	#121×C₅₃	C₂³	1	1	yes	characteristic
209	#121×C₅₃	C₂³	1	2	yes	—
210	#120×C₅₃	—	2	1	no	—
211	#120×C₅₃	D₄	1	2	yes	—
212	C₄×Q₈×C₅₃	—	2	1	no	—
213	C₄×Q₈×C₅₃	—	2	1	no	—
214	C₄×Q₈×C₅₃	—	2	2	no	—
215	C₄×Q₈×C₅₃	—	2	2	no	—
216	C₄×Q₈×C₅₃	—	2	1	no	—
217	C₄×Q₈×C₅₃	—	2	1	no	—
218	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
219	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
221	C₄×D₄×C₅₃	—	2	2	no	—
222	C₄×D₄×C₅₃	—	2	2	no	—
223	C₄×D₄×C₅₃	—	2	2	no	—
224	C₄×D₄×C₅₃	—	2	1	no	—
225	C₄×D₄×C₅₃	—	2	2	no	—
226	C₄×D₄×C₅₃	—	2	1	no	—
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	—	2	1	no	—
229	C₄×D₄×C₅₃	—	2	1	no	—
230	C₄×D₄×C₅₃	C₂³	1	2	yes	—
231	C₄×D₄×C₅₃	C₂³	1	2	yes	—
232	C₄×D₄×C₅₃	C₂³	1	2	yes	—
233	#117×C₅₃	—	2	1	no	—
234	#117×C₅₃	—	2	2	no	—
235	#117×C₅₃	—	2	2	no	—
236	#117×C₅₃	—	2	2	no	—
237	#117×C₅₃	—	2	2	no	—
238	#117×C₅₃	—	2	2	no	—
239	#117×C₅₃	—	2	1	no	—
240	#117×C₅₃	—	2	1	no	—
241	#117×C₅₃	—	2	1	no	—
242	#117×C₅₃	—	2	1	no	—
243	#117×C₅₃	C₂³	1	2	yes	—
244	#117×C₅₃	C₂³	1	2	yes	—
245	#117×C₅₃	C₂³	1	1	yes	characteristic
246	#117×C₅₃	C₂³	1	1	yes	characteristic
247	#117×C₅₃	C₂³	1	2	yes	—
248	#117×C₅₃	C₂³	1	2	yes	—
249	#117×C₅₃	C₂³	1	1	yes	characteristic
250	#117×C₅₃	C₂³	1	1	yes	characteristic
251	#117×C₅₃	C₂³	1	1	yes	characteristic
252	#117×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
254	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
255	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
262	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
263	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
265	C₂×C₄²×C₅₃	—	2	1	no	—
266	C₂×C₄²×C₅₃	—	2	1	no	—
267	#107×C₅₃	C₂³	1	2	yes	—
268	#107×C₅₃	C₂³	1	2	yes	—
269	#107×C₅₃	C₂³	1	1	yes	characteristic
270	#107×C₅₃	C₂³	1	1	yes	characteristic
271	#107×C₅₃	C₂³	1	1	yes	characteristic
272	#107×C₅₃	C₂³	1	2	yes	—
273	#107×C₅₃	C₂³	1	2	yes	—
274	#107×C₅₃	C₂³	1	2	yes	—
275	#107×C₅₃	C₂³	1	2	yes	—
276	#107×C₅₃	C₂³	1	2	yes	—
277	#107×C₅₃	C₂³	1	1	yes	characteristic
278	#106×C₅₃	C₂³	1	2	yes	—
279	#106×C₅₃	C₂³	1	2	yes	—
280	#106×C₅₃	C₂³	1	1	yes	characteristic
281	#106×C₅₃	C₂³	1	1	yes	characteristic
282	#106×C₅₃	C₂³	1	1	yes	characteristic
283	#106×C₅₃	C₂³	1	2	yes	—
284	#106×C₅₃	C₂³	1	2	yes	—
285	#106×C₅₃	C₂³	1	2	yes	—
286	#106×C₅₃	C₂³	1	2	yes	—
287	#106×C₅₃	C₂³	1	2	yes	—
288	#106×C₅₃	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
290	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	2	yes	—
293	#103×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	2	yes	—
295	#103×C₅₃	C₂³	1	1	yes	characteristic
296	#103×C₅₃	C₂³	1	1	yes	characteristic
297	#103×C₅₃	C₂³	1	1	yes	characteristic
298	#103×C₅₃	C₂³	1	1	yes	characteristic
299	#103×C₅₃	C₂³	1	2	yes	—
300	#103×C₅₃	C₂³	1	2	yes	—
301	#103×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
313	#97×C₅₃	C₂³	1	2	yes	—
314	C₄×C₈×C₅₃	C₂³	1	2	yes	—
315	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
316	#41×C₅₃	—	2	2	no	—
317	#41×C₅₃	—	2	2	no	—
318	#41×C₅₃	—	2	2	no	—
319	#41×C₅₃	—	2	2	no	—
320	C₂×Q₈×C₅₃	—	2	1	no	—
321	C₂×Q₈×C₅₃	—	2	2	no	—
322	C₂×Q₈×C₅₃	—	2	2	no	—
323	C₂×Q₈×C₅₃	—	2	2	no	—
324	C₂×Q₈×C₅₃	—	2	2	no	—
325	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₅₃	—	2	1	no	—
329	C₂×D₄×C₅₃	—	2	1	no	—
330	C₂×D₄×C₅₃	—	2	1	no	—
331	C₂×D₄×C₅₃	—	2	2	no	—
332	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
333	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
334	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₅₃	—	2	2	no	—
338	C₂²×C₄×C₅₃	—	2	2	no	—
339	C₂²×C₄×C₅₃	—	2	1	no	—
340	C₂²×C₄×C₅₃	—	2	1	no	—
341	C₂²×C₄×C₅₃	—	2	1	no	—
342	C₂²×C₄×C₅₃	—	2	1	no	—
343	C₂²×C₄×C₅₃	—	2	1	no	—
344	C₂²×C₄×C₅₃	—	2	1	no	—
345	C₂²×C₄×C₅₃	—	2	2	no	—
346	C₂²×C₄×C₅₃	—	2	2	no	—
347	C₂²×C₄×C₅₃	—	2	1	no	—
348	C₂²×C₄×C₅₃	—	2	2	no	—
349	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
356	Q₁₆×C₅₃	—	2	4	no	—
357	SD₁₆×C₅₃	—	2	4	no	—
358	M₁₆×C₅₃	—	2	2	no	—
359	M₁₆×C₅₃	—	2	4	no	—
360	M₁₆×C₅₃	—	2	4	no	—
361	M₁₆×C₅₃	#41	1	4	yes	—
362	C₂×C₈×C₅₃	—	2	2	no	—
363	C₂×C₈×C₅₃	—	2	2	no	—
364	C₂×C₈×C₅₃	—	2	4	no	—
365	C₂×C₈×C₅₃	—	2	4	no	—
366	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
370	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
372	C₄⋊C₄×C₅₃	—	2	1	no	—
373	C₄⋊C₄×C₅₃	—	2	2	no	—
374	C₄⋊C₄×C₅₃	—	2	2	no	—
375	C₄⋊C₄×C₅₃	—	2	2	no	—
376	C₄⋊C₄×C₅₃	—	2	1	no	—
377	C₄⋊C₄×C₅₃	—	2	1	no	—
378	C₄⋊C₄×C₅₃	—	2	1	no	—
379	C₄⋊C₄×C₅₃	—	2	1	no	—
380	C₄⋊C₄×C₅₃	—	2	2	no	—
381	C₄⋊C₄×C₅₃	—	2	2	no	—
382	C₄⋊C₄×C₅₃	—	2	1	no	—
383	C₄⋊C₄×C₅₃	—	2	2	no	—
384	C₄⋊C₄×C₅₃	—	2	2	no	—
385	C₄⋊C₄×C₅₃	—	2	2	no	—
386	C₄⋊C₄×C₅₃	—	2	2	no	—
387	C₄⋊C₄×C₅₃	—	2	2	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	2	no	—
395	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₅₃	C₂⁴	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	1	yes	characteristic
408	C₂²⋊C₄×C₅₃	—	2	1	no	—
409	C₂²⋊C₄×C₅₃	—	2	2	no	—
410	C₂²⋊C₄×C₅₃	—	2	2	no	—
411	C₂²⋊C₄×C₅₃	—	2	1	no	—
412	C₂²⋊C₄×C₅₃	—	2	1	no	—
413	C₂²⋊C₄×C₅₃	—	2	1	no	—
414	C₂²⋊C₄×C₅₃	—	2	2	no	—
415	C₂²⋊C₄×C₅₃	—	2	2	no	—
416	C₂²⋊C₄×C₅₃	—	2	2	no	—
417	C₂²⋊C₄×C₅₃	—	2	2	no	—
418	C₂²⋊C₄×C₅₃	—	2	1	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	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	1	no	—
425	C₂²⋊C₄×C₅₃	—	2	2	no	—
426	C₂²⋊C₄×C₅₃	—	2	2	no	—
427	C₂²⋊C₄×C₅₃	—	2	1	no	—
428	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
433	C₄²×C₅₃	—	2	2	no	—
434	C₄²×C₅₃	—	2	1	no	—
435	C₄²×C₅₃	—	2	1	no	—
436	C₄²×C₅₃	—	2	2	no	—
437	C₄²×C₅₃	—	2	1	no	—
438	C₄²×C₅₃	—	2	1	no	—
439	C₄²×C₅₃	—	2	2	no	—
440	C₄²×C₅₃	—	2	2	no	—
441	C₄²×C₅₃	—	2	2	no	—
442	C₄²×C₅₃	—	2	2	no	—
443	C₄²×C₅₃	—	2	2	no	—
444	C₄²×C₅₃	—	2	1	no	—
445	C₄²×C₅₃	C₂⁴	1	2	yes	—
446	C₂³×C₅₃	—	2	2	no	—
447	C₂³×C₅₃	—	2	1	no	—
448	C₂³×C₅₃	—	4	1	no	—
449	C₂³×C₅₃	—	4	1	no	—
450	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
451	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
452	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
453	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
454	Q₈×C₅₃	—	2	2	no	—
455	Q₈×C₅₃	—	2	2	no	—
456	Q₈×C₅₃	—	2	1	no	—
457	Q₈×C₅₃	—	2	2	no	—
458	Q₈×C₅₃	—	2	1	no	—
459	Q₈×C₅₃	—	4	2	no	—
460	Q₈×C₅₃	—	8	2	no	—
461	Q₈×C₅₃	—	8	2	no	—
462	D₄×C₅₃	—	2	4	no	—
463	D₄×C₅₃	—	2	2	no	—
464	D₄×C₅₃	—	2	1	no	—
465	D₄×C₅₃	—	2	1	no	—
466	D₄×C₅₃	—	4	2	no	—
467	D₄×C₅₃	—	4	2	no	—
468	D₄×C₅₃	—	4	2	no	—
469	D₄×C₅₃	—	8	1	no	—
470	D₄×C₅₃	—	8	2	no	—
471	D₄×C₅₃	—	8	1	no	—
472	C₂×C₄×C₅₃	—	2	2	no	—
473	C₂×C₄×C₅₃	—	2	2	no	—
474	C₂×C₄×C₅₃	—	2	2	no	—
475	C₂×C₄×C₅₃	—	2	1	no	—
476	C₂×C₄×C₅₃	—	2	1	no	—
477	C₂×C₄×C₅₃	—	2	2	no	—
478	C₂×C₄×C₅₃	—	2	1	no	—
479	C₂×C₄×C₅₃	—	2	1	no	—
480	C₂×C₄×C₅₃	—	2	2	no	—
481	C₂×C₄×C₅₃	—	2	2	no	—
482	C₂×C₄×C₅₃	—	2	1	no	—
483	C₂×C₄×C₅₃	—	2	1	no	—
484	C₂×C₄×C₅₃	—	2	2	no	—
485	C₂×C₄×C₅₃	—	2	2	no	—
486	C₂×C₄×C₅₃	—	2	1	no	—
487	C₂×C₄×C₅₃	—	2	1	no	—
488	C₂×C₄×C₅₃	—	2	2	no	—
489	C₂×C₄×C₅₃	—	2	1	no	—
490	C₂×C₄×C₅₃	—	2	1	no	—
491	C₂×C₄×C₅₃	—	2	1	no	—
492	C₂×C₄×C₅₃	—	4	2	no	—
493	C₂×C₄×C₅₃	—	4	2	no	—
494	C₂×C₄×C₅₃	—	4	2	no	—
495	C₂×C₄×C₅₃	—	8	2	no	—
496	C₂×C₄×C₅₃	—	8	1	no	—
497	C₂×C₄×C₅₃	—	8	2	no	—
498	C₂×C₄×C₅₃	—	8	2	no	—
499	C₂×C₄×C₅₃	—	8	1	no	—
500	C₂×C₄×C₅₃	—	8	1	no	—
501	C₂×C₄×C₅₃	—	8	1	no	—
502	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
509	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
510	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
511	C₈×C₅₃	—	2	1	no	—
512	C₈×C₅₃	—	2	1	no	—
513	C₈×C₅₃	—	2	2	no	—
514	C₈×C₅₃	—	2	1	no	—
515	C₈×C₅₃	—	2	1	no	—
516	C₈×C₅₃	C₂×#41	1	4	yes	—
517	#61275	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
518	C₂²×C₅₃	—	2	1	no	—
519	C₂²×C₅₃	—	2	1	no	—
520	C₂²×C₅₃	—	2	2	no	—
521	C₂²×C₅₃	—	2	1	no	—
522	C₂²×C₅₃	—	2	1	no	—
523	C₂²×C₅₃	—	2	1	no	—
524	C₂²×C₅₃	—	2	2	no	—
525	C₂²×C₅₃	—	2	1	no	—
526	C₂²×C₅₃	—	2	1	no	—
527	C₂²×C₅₃	—	2	1	no	—
528	C₂²×C₅₃	—	2	2	no	—
529	C₂²×C₅₃	—	4	1	no	—
530	C₂²×C₅₃	—	4	1	no	—
531	C₂²×C₅₃	—	4	1	no	—
532	C₂²×C₅₃	—	8	2	no	—
533	C₂²×C₅₃	#547	1	2	yes	—
534	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
535	C₄×C₅₃	—	2	2	no	—
536	C₄×C₅₃	—	2	2	no	—
537	C₄×C₅₃	—	2	1	no	—
538	C₄×C₅₃	—	2	1	no	—
539	C₄×C₅₃	—	2	2	no	—
540	C₄×C₅₃	—	4	2	no	—
541	C₄×C₅₃	—	4	1	no	—
542	C₄×C₅₃	—	4	1	no	—
543	C₄×C₅₃	—	4	2	no	—
544	C₄×C₅₃	—	4	1	no	—
545	C₄×C₅₃	—	4	1	no	—
546	C₄×C₅₃	—	4	1	no	—
547	C₄×C₅₃	—	4	2	no	—
548	C₄×C₅₃	—	4	1	no	—
549	C₄×C₅₃	—	4	1	no	—
550	C₄×C₅₃	—	4	2	no	—
551	C₄×C₅₃	#547	1	2	yes	—
552	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
553	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
554	#3495	C₂×C₅₃	1	1	yes	characteristic, complemented
555	#3493	C₂×C₅₃	1	1	yes	characteristic
556	#3356	C₂×C₅₃	1	2	yes	complemented
557	#3351	C₂×C₅₃	1	2	yes	complemented
558	#3349	C₂×C₅₃	1	2	yes	complemented
559	#3349	C₂×C₅₃	1	2	yes	complemented
560	#3348	C₂×C₅₃	1	2	yes	complemented
561	#3346	C₂×C₅₃	1	2	yes	complemented
562	#3340	C₂×C₅₃	1	2	yes	complemented
563	#3336	C₂×C₅₃	1	2	yes	complemented
564	#3163	C₂×C₅₃	1	1	yes	characteristic, complemented
565	#3099	C₂×C₅₃	1	1	yes	characteristic, complemented
566	#3097	C₂×C₅₃	1	1	yes	characteristic, complemented
567	#3091	C₂×C₅₃	1	1	yes	characteristic, complemented
568	C₂×#485	C₂×C₅₃	1	1	yes	characteristic, complemented
569	#3083	C₂×C₅₃	1	1	yes	characteristic, complemented
570	#3082	C₂×C₅₃	1	1	yes	characteristic, complemented
571	#3063	C₂×C₅₃	1	1	yes	characteristic, complemented
572	#3056	C₂×C₅₃	1	1	yes	characteristic, complemented
573	#2947	C₂×C₅₃	1	1	yes	characteristic, complemented
574	#2933	C₂×C₅₃	1	1	yes	characteristic, complemented
575	#2913	C₂×C₅₃	1	1	yes	characteristic, complemented
576	#2911	C₂×C₅₃	1	1	yes	characteristic, complemented
577	C₂×C₅₃	—	2	2	no	—
578	C₂×C₅₃	—	4	2	no	—
579	C₂×C₅₃	—	4	1	no	—
580	C₂×C₅₃	—	4	1	no	—
581	C₂×C₅₃	—	8	1	no	—
582	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
583	C₂×C₅₃	#3584	1	1	yes	characteristic
584	C₂×C₅₃	#3586	1	1	yes	characteristic
585	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
586	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
587	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
588	#556	—	2	1	no	—
589	#556	C₂²×C₅₃	1	2	yes	—
590	#556	C₂²×C₅₃	1	2	yes	—
591	#555	—	2	1	no	—
592	#555	C₂²×C₅₃	1	2	yes	—
593	#554	C₂²×C₅₃	1	2	yes	—
594	#553	—	2	1	no	—
595	#553	C₂²×C₅₃	1	2	yes	—
596	#552	—	2	2	no	—
597	#552	—	2	1	no	—
598	#552	C₂²×C₅₃	1	2	yes	—
599	#552	C₂²×C₅₃	1	2	yes	—
600	#552	C₂²×C₅₃	1	2	yes	—
601	#551	—	2	2	no	—
602	#544	C₂²×C₅₃	1	1	yes	characteristic
603	#544	C₂²×C₅₃	1	1	yes	characteristic
604	#542	—	2	1	no	—
605	#541	—	2	1	no	—
606	#538	—	2	2	no	—
607	#537	C₂²×C₅₃	1	1	yes	characteristic
608	#536	C₂²×C₅₃	1	1	yes	characteristic
609	#533	—	2	1	no	—
610	#529	—	2	2	no	—
611	#529	—	2	1	no	—
612	#525	C₂²×C₅₃	1	1	yes	characteristic
613	#525	C₂²×C₅₃	1	1	yes	characteristic
614	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
615	#520	C₂²×C₅₃	1	1	yes	characteristic
616	#520	C₂²×C₅₃	1	1	yes	characteristic
617	#520	C₂²×C₅₃	1	1	yes	characteristic
618	#519	C₂²×C₅₃	1	1	yes	characteristic
619	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
620	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
621	#501	C₂²×C₅₃	1	2	yes	complemented
622	#501	C₂²×C₅₃	1	2	yes	complemented
623	#499	C₂²×C₅₃	1	2	yes	complemented
624	#498	C₂²×C₅₃	1	2	yes	complemented
625	#485	C₂²×C₅₃	1	1	yes	characteristic
626	#485	C₂²×C₅₃	1	2	yes	—
627	#485	C₂²×C₅₃	1	2	yes	—
628	#485	C₂²×C₅₃	1	2	yes	—
629	#485	C₂²×C₅₃	1	2	yes	—
630	#485	C₂²×C₅₃	1	1	yes	characteristic
631	#485	C₂²×C₅₃	1	2	yes	complemented
632	#485	C₂²×C₅₃	1	2	yes	complemented
633	#485	C₂²×C₅₃	1	2	yes	complemented
634	#484	C₂²×C₅₃	1	1	yes	characteristic
635	#484	C₂²×C₅₃	1	2	yes	complemented
636	#483	C₂²×C₅₃	1	1	yes	characteristic
637	#483	C₂²×C₅₃	1	2	yes	complemented
638	#483	C₂²×C₅₃	1	2	yes	complemented
639	#482	C₂²×C₅₃	1	1	yes	characteristic
640	#482	C₂²×C₅₃	1	1	yes	characteristic
641	#482	C₂²×C₅₃	1	2	yes	complemented
642	#481	C₂²×C₅₃	1	1	yes	characteristic
643	#481	C₂²×C₅₃	1	2	yes	complemented
644	#480	C₂²×C₅₃	1	1	yes	characteristic
645	#479	C₂²×C₅₃	1	2	yes	complemented
646	#479	C₂²×C₅₃	1	2	yes	complemented
647	#479	C₂²×C₅₃	1	2	yes	complemented
648	#478	C₂²×C₅₃	1	2	yes	complemented
649	#477	C₂²×C₅₃	1	2	yes	complemented
650	#477	C₂²×C₅₃	1	2	yes	complemented
651	#475	C₂²×C₅₃	1	2	yes	complemented
652	#474	C₂²×C₅₃	1	2	yes	complemented
653	#470	C₂²×C₅₃	1	2	yes	—
654	#470	C₂²×C₅₃	1	2	yes	complemented
655	#468	C₂²×C₅₃	1	2	yes	—
656	#468	C₂²×C₅₃	1	2	yes	complemented
657	#467	C₂²×C₅₃	1	2	yes	—
658	#467	C₂²×C₅₃	1	2	yes	complemented
659	#465	C₂²×C₅₃	1	2	yes	—
660	#465	C₂²×C₅₃	1	2	yes	complemented
661	#441	C₂²×C₅₃	1	2	yes	complemented
662	#440	C₂²×C₅₃	1	2	yes	complemented
663	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
664	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
665	#436	C₂²×C₅₃	1	2	yes	—
666	#435	C₂²×C₅₃	1	2	yes	—
667	#435	C₂²×C₅₃	1	2	yes	—
668	C₈×D₄	C₂²×C₅₃	1	2	yes	—
669	#428	C₂²×C₅₃	1	1	yes	characteristic
670	#428	C₂²×C₅₃	1	1	yes	characteristic
671	#428	C₂²×C₅₃	1	2	yes	—
672	#428	C₂²×C₅₃	1	2	yes	—
673	#428	C₂²×C₅₃	1	1	yes	characteristic
674	#428	C₂²×C₅₃	1	1	yes	characteristic
675	#428	C₂²×C₅₃	1	1	yes	characteristic
676	#428	C₂²×C₅₃	1	2	yes	complemented
677	#428	C₂²×C₅₃	1	2	yes	complemented
678	#427	C₂²×C₅₃	1	2	yes	—
679	#427	C₂²×C₅₃	1	1	yes	characteristic
680	#427	C₂²×C₅₃	1	2	yes	—
681	#427	C₂²×C₅₃	1	1	yes	characteristic
682	#427	C₂²×C₅₃	1	2	yes	complemented
683	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
684	C₂×#107	C₂²×C₅₃	1	2	yes	complemented
685	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic
686	#424	C₂²×C₅₃	1	1	yes	characteristic
687	#419	C₂²×C₅₃	1	1	yes	characteristic
688	#417	C₂²×C₅₃	1	1	yes	characteristic
689	#416	C₂²×C₅₃	1	1	yes	characteristic
690	#416	C₂²×C₅₃	1	1	yes	characteristic
691	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
692	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
693	#408	C₂²×C₅₃	1	1	yes	characteristic
694	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
695	#405	C₂²×C₅₃	1	1	yes	characteristic
696	C₅₃	#61275	1	1	yes	characteristic, direct product factor, Sylow
697	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
698	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
699	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
700	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
701	#137	—	2	4	no	—
702	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
703	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
704	#131	—	2	4	no	—
705	C₂×M₁₆	—	2	4	no	—
706	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
707	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
708	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
709	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
710	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
711	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
712	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
713	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
714	C₄⋊Q₈	—	2	1	no	—
715	C₄⋊Q₈	—	2	1	no	—
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
718	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#125	—	2	1	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	2	2	no	—
731	#125	—	2	2	no	—
732	#125	—	2	1	no	—
733	#125	C₂³×C₅₃	1	2	yes	—
734	#125	C₂³×C₅₃	1	2	yes	—
735	#124	—	2	1	no	—
736	#124	—	2	2	no	—
737	#124	—	2	2	no	—
738	#124	—	2	2	no	—
739	#124	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	1	no	—
745	#123	—	2	2	no	—
746	#123	D₄×C₅₃	1	2	yes	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
755	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
756	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
757	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
758	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
760	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
763	#121	—	2	2	no	—
764	#121	—	2	1	no	—
765	#121	—	2	2	no	—
766	#121	—	2	2	no	—
767	#121	D₄×C₅₃	1	1	yes	characteristic
768	#121	D₄×C₅₃	1	1	yes	characteristic
769	#121	C₂³×C₅₃	1	1	yes	characteristic
770	#121	C₂³×C₅₃	1	1	yes	characteristic
771	#121	C₂³×C₅₃	1	2	yes	—
772	#120	—	2	1	no	—
773	#120	D₄×C₅₃	1	2	yes	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	2	no	—
779	C₄×Q₈	—	2	2	no	—
780	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
781	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
782	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
783	C₄×D₄	—	2	2	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	2	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	C₂³×C₅₃	1	2	yes	—
793	C₄×D₄	C₂³×C₅₃	1	2	yes	—
794	C₄×D₄	C₂³×C₅₃	1	2	yes	—
795	#117	—	2	1	no	—
796	#117	—	2	1	no	—
797	#117	—	2	1	no	—
798	#117	—	2	1	no	—
799	#117	—	2	1	no	—
800	#117	—	2	2	no	—
801	#117	—	2	2	no	—
802	#117	—	2	2	no	—
803	#117	—	2	2	no	—
804	#117	—	2	2	no	—
805	#117	C₂³×C₅₃	1	1	yes	characteristic
806	#117	C₂³×C₅₃	1	1	yes	characteristic
807	#117	C₂³×C₅₃	1	1	yes	characteristic
808	#117	C₂³×C₅₃	1	2	yes	—
809	#117	C₂³×C₅₃	1	2	yes	—
810	#117	C₂³×C₅₃	1	1	yes	characteristic
811	#117	C₂³×C₅₃	1	1	yes	characteristic
812	#117	C₂³×C₅₃	1	2	yes	—
813	#117	C₂³×C₅₃	1	2	yes	—
814	#117	C₂³×C₅₃	1	1	yes	characteristic
815	C₂×C₄⋊C₄	—	2	1	no	—
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
818	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
819	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
820	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
821	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
822	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
823	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
824	C₂×C₂²⋊C₄	—	2	1	no	—
825	C₂×C₂²⋊C₄	—	2	1	no	—
826	C₂×C₂²⋊C₄	—	2	1	no	—
827	C₂×C₄²	—	2	1	no	—
828	C₂×C₄²	—	2	1	no	—
829	#107	C₂³×C₅₃	1	2	yes	—
830	#107	C₂³×C₅₃	1	2	yes	—
831	#107	C₂³×C₅₃	1	1	yes	characteristic
832	#107	C₂³×C₅₃	1	2	yes	—
833	#107	C₂³×C₅₃	1	2	yes	—
834	#107	C₂³×C₅₃	1	1	yes	characteristic
835	#107	C₂³×C₅₃	1	2	yes	—
836	#107	C₂³×C₅₃	1	2	yes	—
837	#107	C₂³×C₅₃	1	2	yes	—
838	#107	C₂³×C₅₃	1	1	yes	characteristic
839	#107	C₂³×C₅₃	1	1	yes	characteristic
840	#106	C₂³×C₅₃	1	2	yes	—
841	#106	C₂³×C₅₃	1	2	yes	—
842	#106	C₂³×C₅₃	1	2	yes	—
843	#106	C₂³×C₅₃	1	2	yes	—
844	#106	C₂³×C₅₃	1	2	yes	—
845	#106	C₂³×C₅₃	1	2	yes	—
846	#106	C₂³×C₅₃	1	1	yes	characteristic
847	#106	C₂³×C₅₃	1	1	yes	characteristic
848	#106	C₂³×C₅₃	1	1	yes	characteristic
849	#106	C₂³×C₅₃	1	1	yes	characteristic
850	#106	C₂³×C₅₃	1	2	yes	—
851	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
852	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
853	#103	C₂³×C₅₃	1	2	yes	—
854	#103	C₂³×C₅₃	1	2	yes	—
855	#103	C₂³×C₅₃	1	2	yes	—
856	#103	C₂³×C₅₃	1	2	yes	—
857	#103	C₂³×C₅₃	1	1	yes	characteristic
858	#103	C₂³×C₅₃	1	1	yes	characteristic
859	#103	C₂³×C₅₃	1	1	yes	characteristic
860	#103	C₂³×C₅₃	1	1	yes	characteristic
861	#103	C₂³×C₅₃	1	2	yes	—
862	#103	C₂³×C₅₃	1	2	yes	—
863	#103	C₂³×C₅₃	1	2	yes	—
864	#102	C₂³×C₅₃	1	1	yes	characteristic
865	#102	C₂³×C₅₃	1	1	yes	characteristic
866	#102	C₂³×C₅₃	1	1	yes	characteristic
867	#102	C₂³×C₅₃	1	1	yes	characteristic
868	#102	C₂³×C₅₃	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
870	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
871	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
872	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
875	#97	C₂³×C₅₃	1	2	yes	—
876	C₄×C₈	C₂³×C₅₃	1	2	yes	—
877	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
878	#41	—	2	2	no	—
879	#41	—	2	2	no	—
880	#41	—	2	2	no	—
881	#41	—	2	2	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
889	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
895	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
896	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
897	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
898	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
912	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
913	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
914	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
915	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
918	Q₁₆	—	2	4	no	—
919	SD₁₆	—	2	4	no	—
920	M₁₆	—	2	2	no	—
921	M₁₆	—	2	4	no	—
922	M₁₆	—	2	4	no	—
923	M₁₆	#41×C₅₃	1	4	yes	—
924	C₂×C₈	—	2	2	no	—
925	C₂×C₈	—	2	2	no	—
926	C₂×C₈	—	2	4	no	—
927	C₂×C₈	—	2	4	no	—
928	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
932	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
958	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
959	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
960	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
963	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
964	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
991	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
992	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
993	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
994	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	C₂⁴×C₅₃	1	2	yes	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	4	1	no	—
1011	C₂³	—	4	1	no	—
1012	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1013	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1014	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1015	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1016	Q₈	—	2	2	no	—
1017	Q₈	—	2	2	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	8	2	no	—
1023	Q₈	—	8	2	no	—
1024	D₄	—	2	4	no	—
1025	D₄	—	2	2	no	—
1026	D₄	—	2	1	no	—
1027	D₄	—	2	1	no	—
1028	D₄	—	4	2	no	—
1029	D₄	—	4	2	no	—
1030	D₄	—	4	2	no	—
1031	D₄	—	8	1	no	—
1032	D₄	—	8	2	no	—
1033	D₄	—	8	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	8	2	no	—
1058	C₂×C₄	—	8	1	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	—	8	2	no	—
1061	C₂×C₄	—	8	1	no	—
1062	C₂×C₄	—	8	1	no	—
1063	C₂×C₄	—	8	1	no	—
1064	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1065	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1070	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1071	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1072	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1073	C₈	—	2	1	no	—
1074	C₈	—	2	1	no	—
1075	C₈	—	2	2	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	1	no	—
1078	C₈	C₂×#41×C₅₃	1	4	yes	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	8	2	no	—
1094	C₂²	C₅₃×#547	1	2	yes	—
1095	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	C₅₃×#547	1	2	yes	—
1113	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1114	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1115	C₂	—	2	2	no	—
1116	C₂	—	4	1	no	—
1117	C₂	—	4	1	no	—
1118	C₂	—	4	2	no	—
1119	C₂	—	8	1	no	—
1120	C₂	C₂×C₅₃×#547	1	1	yes	characteristic
1121	C₂	C₅₃×#3584	1	1	yes	characteristic
1122	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3493	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3495	C₂	semidirect
3. C₅₃×#3356	C₂	semidirect
4. C₅₃×#3351	C₂	semidirect
5. C₅₃×#3349	C₂	semidirect
6. C₅₃×#3349	C₂	semidirect
7. C₅₃×#3348	C₂	semidirect
8. C₅₃×#3346	C₂	semidirect
9. C₅₃×#3340	C₂	semidirect
10. C₅₃×#3336	C₂	semidirect
11. C₅₃×#3163	C₂	semidirect
12. C₅₃×#3099	C₂	semidirect
13. C₅₃×#3097	C₂	semidirect
14. C₅₃×#3091	C₂	semidirect
15. C₂×C₅₃×#485	C₂	semidirect
16. C₅₃×#3083	C₂	semidirect
17. C₅₃×#3082	C₂	semidirect
18. C₅₃×#3063	C₂	semidirect
19. C₅₃×#3056	C₂	semidirect
20. C₅₃×#2947	C₂	semidirect
21. C₅₃×#2933	C₂	semidirect
22. C₅₃×#2913	C₂	semidirect
23. C₅₃×#2911	C₂	semidirect
60. C₅₃×#501	C₂²	semidirect
61. C₅₃×#501	C₂²	semidirect
62. C₅₃×#499	C₂²	semidirect
63. C₅₃×#498	C₂²	semidirect
70. C₅₃×#485	C₂²	semidirect
71. C₅₃×#485	C₂²	semidirect
72. C₅₃×#485	C₂²	semidirect
74. C₅₃×#484	C₂²	semidirect
76. C₅₃×#483	C₂²	semidirect
77. C₅₃×#483	C₂²	semidirect
80. C₅₃×#482	C₂²	semidirect
82. C₅₃×#481	C₂²	semidirect
84. C₅₃×#479	C₂²	semidirect
85. C₅₃×#479	C₂²	semidirect
86. C₅₃×#479	C₂²	semidirect
87. C₅₃×#478	C₂²	semidirect
88. C₅₃×#477	C₂²	semidirect
89. C₅₃×#477	C₂²	semidirect
90. C₅₃×#475	C₂²	semidirect
91. C₅₃×#474	C₂²	semidirect
93. C₅₃×#470	C₂²	semidirect
95. C₅₃×#468	C₂²	semidirect
97. C₅₃×#467	C₂²	semidirect
99. C₅₃×#465	C₂²	semidirect
100. C₅₃×#441	C₂²	semidirect
101. C₅₃×#440	C₂²	semidirect
102. C₄×Q₁₆×C₅₃	C₂²	semidirect
103. C₄×SD₁₆×C₅₃	C₂²	semidirect
115. C₅₃×#428	C₂²	semidirect
116. C₅₃×#428	C₂²	semidirect
121. C₅₃×#427	C₂²	semidirect
123. C₂×#107×C₅₃	C₂²	semidirect
517. #61275	C₅₃	direct (N × H)
554. #3495	C₂×C₅₃	semidirect
556. #3356	C₂×C₅₃	semidirect
557. #3351	C₂×C₅₃	semidirect
558. #3349	C₂×C₅₃	semidirect
559. #3349	C₂×C₅₃	semidirect
560. #3348	C₂×C₅₃	semidirect
561. #3346	C₂×C₅₃	semidirect
562. #3340	C₂×C₅₃	semidirect
563. #3336	C₂×C₅₃	semidirect
564. #3163	C₂×C₅₃	semidirect
565. #3099	C₂×C₅₃	semidirect
566. #3097	C₂×C₅₃	semidirect
567. #3091	C₂×C₅₃	semidirect
568. C₂×#485	C₂×C₅₃	semidirect
569. #3083	C₂×C₅₃	semidirect
570. #3082	C₂×C₅₃	semidirect
571. #3063	C₂×C₅₃	semidirect
572. #3056	C₂×C₅₃	semidirect
573. #2947	C₂×C₅₃	semidirect
574. #2933	C₂×C₅₃	semidirect
575. #2913	C₂×C₅₃	semidirect
576. #2911	C₂×C₅₃	semidirect
621. #501	C₂²×C₅₃	semidirect
622. #501	C₂²×C₅₃	semidirect
623. #499	C₂²×C₅₃	semidirect
624. #498	C₂²×C₅₃	semidirect
631. #485	C₂²×C₅₃	semidirect
632. #485	C₂²×C₅₃	semidirect
633. #485	C₂²×C₅₃	semidirect
635. #484	C₂²×C₅₃	semidirect
637. #483	C₂²×C₅₃	semidirect
638. #483	C₂²×C₅₃	semidirect
641. #482	C₂²×C₅₃	semidirect
643. #481	C₂²×C₅₃	semidirect
645. #479	C₂²×C₅₃	semidirect
646. #479	C₂²×C₅₃	semidirect
647. #479	C₂²×C₅₃	semidirect
648. #478	C₂²×C₅₃	semidirect
649. #477	C₂²×C₅₃	semidirect
650. #477	C₂²×C₅₃	semidirect
651. #475	C₂²×C₅₃	semidirect
652. #474	C₂²×C₅₃	semidirect
654. #470	C₂²×C₅₃	semidirect
656. #468	C₂²×C₅₃	semidirect
658. #467	C₂²×C₅₃	semidirect
660. #465	C₂²×C₅₃	semidirect
661. #441	C₂²×C₅₃	semidirect
662. #440	C₂²×C₅₃	semidirect
663. C₄×Q₁₆	C₂²×C₅₃	semidirect
664. C₄×SD₁₆	C₂²×C₅₃	semidirect
676. #428	C₂²×C₅₃	semidirect
677. #428	C₂²×C₅₃	semidirect
682. #427	C₂²×C₅₃	semidirect
684. C₂×#107	C₂²×C₅₃	semidirect
696. C₅₃	#61275	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×#3495	2
C₅₃×#3493	2
C₅₃×#3356	2
C₅₃×#3351	2
C₅₃×#3349	2
C₅₃×#3348	2
C₅₃×#3346	2
C₅₃×#3340	2
C₅₃×#3336	2
C₅₃×#3163	2
C₅₃×#3099	2
C₅₃×#3097	2
C₅₃×#3091	2
C₂×C₅₃×#485	2
C₅₃×#3083	2
C₅₃×#3082	2
C₅₃×#3063	2
C₅₃×#3056	2
C₅₃×#2947	2
C₅₃×#2933	2
C₅₃×#2913	2
C₅₃×#2911	2
#61275	53

Subgroups — C53×#61275 #27268787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61275 #27268787