Subgroups — C₅₃×#62180 #27269692

Order 13568.

1748 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3357	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3347	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3342	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3322	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3314	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3262	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3243	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3118	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3081	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#563	—	2	2	no	—
25	C₅₃×#559	C₂²	1	1	yes	characteristic
26	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
27	C₅₃×#556	C₂²	1	1	yes	characteristic
28	C₅₃×#556	C₂²	1	1	yes	characteristic
29	C₅₃×#555	C₂²	1	2	yes	—
30	C₅₃×#554	C₂²	1	2	yes	complemented
31	C₅₃×#553	C₂²	1	2	yes	complemented
32	C₅₃×#551	—	2	2	no	—
33	D₄×Q₈×C₅₃	—	2	1	no	—
34	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#548	—	2	1	no	—
37	C₅₃×#548	—	2	1	no	—
38	C₅₃×#547	C₂²	1	1	yes	characteristic
39	C₅₃×#546	—	2	1	no	—
40	C₅₃×#546	C₂²	1	2	yes	—
41	D₄²×C₅₃	C₂²	1	1	yes	characteristic
42	C₅₃×#544	C₂²	1	2	yes	complemented
43	C₅₃×#542	C₂²	1	2	yes	—
44	C₅₃×#542	C₂²	1	2	yes	complemented
45	C₅₃×#541	—	2	1	no	—
46	C₅₃×#539	—	2	2	no	—
47	C₅₃×#538	—	2	2	no	—
48	C₅₃×#536	—	2	1	no	—
49	C₅₃×#532	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#529	—	2	1	no	—
52	C₅₃×#529	C₂²	1	1	yes	characteristic
53	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
54	C₂×#124×C₅₃	—	2	1	no	—
55	C₅₃×#518	C₂²	1	2	yes	—
56	C₄×#41×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×#500	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#500	C₂²	1	2	yes	complemented
61	C₅₃×#489	C₂²	1	2	yes	complemented
62	C₅₃×#488	C₂²	1	2	yes	complemented
63	C₅₃×#486	C₂²	1	1	yes	characteristic
64	C₅₃×#486	C₂²	1	1	yes	characteristic
65	C₅₃×#485	C₂²	1	2	yes	complemented
66	C₅₃×#485	C₂²	1	2	yes	complemented
67	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#484	C₂²	1	2	yes	complemented
69	C₅₃×#482	C₂²	1	2	yes	—
70	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#482	C₂²	1	2	yes	complemented
72	C₅₃×#480	C₂²	1	2	yes	—
73	C₅₃×#480	C₂²	1	2	yes	complemented
74	C₅₃×#480	C₂²	1	2	yes	complemented
75	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#478	C₂²	1	2	yes	—
77	C₅₃×#478	C₂²	1	1	yes	characteristic
78	C₅₃×#478	C₂²	1	2	yes	complemented
79	C₅₃×#478	C₂²	1	2	yes	complemented
80	C₅₃×#477	C₂²	1	2	yes	complemented
81	C₅₃×#477	C₂²	1	2	yes	complemented
82	C₅₃×#476	C₂²	1	2	yes	—
83	C₅₃×#476	C₂²	1	2	yes	complemented
84	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#474	C₂²	1	1	yes	characteristic
88	C₅₃×#474	C₂²	1	2	yes	—
89	C₅₃×#474	C₂²	1	1	yes	characteristic
90	C₅₃×#474	C₂²	1	2	yes	complemented
91	C₅₃×#474	C₂²	1	2	yes	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×#468	C₂²	1	2	yes	—
96	C₅₃×#468	C₂²	1	2	yes	complemented
97	C₅₃×#468	C₂²	1	2	yes	complemented
98	C₅₃×#467	C₂²	1	2	yes	complemented
99	C₅₃×#466	C₂²	1	2	yes	—
100	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#464	C₂²	1	2	yes	complemented
102	C₅₃×#463	C₂²	1	1	yes	characteristic
103	C₅₃×#463	C₂²	1	2	yes	complemented
104	C₅₃×#463	C₂²	1	2	yes	complemented
105	C₅₃×#460	C₂²	1	1	yes	characteristic
106	C₅₃×#459	C₂²	1	1	yes	characteristic
107	C₅₃×#452	C₂²	1	1	yes	characteristic
108	C₅₃×#450	C₂²	1	2	yes	—
109	C₅₃×#449	C₂²	1	1	yes	characteristic
110	C₅₃×#447	C₂²	1	2	yes	—
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	complemented
114	C₅₃×#440	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
119	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₅₃	C₂²	1	2	yes	—
121	C₅₃×#436	C₂²	1	1	yes	characteristic
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
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×#417	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	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₅₃	—	2	1	no	—
139	C₂²×Q₈×C₅₃	—	2	1	no	—
140	C₂²×Q₈×C₅₃	—	2	1	no	—
141	C₂²×D₄×C₅₃	—	2	1	no	—
142	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₅₃	C₂³	1	2	yes	—
149	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
150	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₅₃	—	2	2	no	—
153	C₄⋊Q₈×C₅₃	—	2	1	no	—
154	C₄⋊Q₈×C₅₃	—	2	1	no	—
155	C₄⋊Q₈×C₅₃	—	2	1	no	—
156	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
161	C₄⋊Q₈×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	—	2	2	no	—
166	#126×C₅₃	—	2	2	no	—
167	#126×C₅₃	—	2	2	no	—
168	#126×C₅₃	—	2	1	no	—
169	#126×C₅₃	D₄	1	2	yes	—
170	#125×C₅₃	—	2	2	no	—
171	#125×C₅₃	—	2	2	no	—
172	#125×C₅₃	—	2	2	no	—
173	#125×C₅₃	D₄	1	1	yes	characteristic
174	#125×C₅₃	C₂³	1	2	yes	—
175	#125×C₅₃	C₂³	1	1	yes	characteristic
176	#124×C₅₃	—	2	2	no	—
177	#124×C₅₃	—	2	2	no	—
178	#124×C₅₃	—	2	2	no	—
179	#124×C₅₃	—	2	2	no	—
180	#124×C₅₃	—	2	1	no	—
181	#124×C₅₃	—	2	1	no	—
182	#124×C₅₃	—	2	1	no	—
183	#124×C₅₃	—	2	1	no	—
184	#124×C₅₃	D₄	1	1	yes	characteristic
185	#124×C₅₃	C₂³	1	2	yes	—
186	#124×C₅₃	C₂³	1	1	yes	characteristic
187	#123×C₅₃	—	2	2	no	—
188	#123×C₅₃	—	2	2	no	—
189	#123×C₅₃	—	2	2	no	—
190	#123×C₅₃	—	2	2	no	—
191	#123×C₅₃	—	2	2	no	—
192	#123×C₅₃	—	2	2	no	—
193	#123×C₅₃	—	2	1	no	—
194	#123×C₅₃	D₄	1	2	yes	—
195	C₂²⋊Q₈×C₅₃	—	2	1	no	—
196	C₂²⋊Q₈×C₅₃	—	2	2	no	—
197	C₂²⋊Q₈×C₅₃	—	2	2	no	—
198	C₂²⋊Q₈×C₅₃	—	2	1	no	—
199	C₂²⋊Q₈×C₅₃	—	2	1	no	—
200	C₂²⋊Q₈×C₅₃	—	2	2	no	—
201	C₂²⋊Q₈×C₅₃	—	2	2	no	—
202	C₂²⋊Q₈×C₅₃	—	2	2	no	—
203	C₂²⋊Q₈×C₅₃	—	2	2	no	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	—	2	2	no	—
206	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
207	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
208	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
210	#121×C₅₃	—	2	1	no	—
211	#121×C₅₃	—	2	2	no	—
212	#121×C₅₃	—	2	2	no	—
213	#121×C₅₃	—	2	2	no	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	D₄	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	#120×C₅₃	—	2	2	no	—
221	#120×C₅₃	—	2	2	no	—
222	C₄×Q₈×C₅₃	—	2	1	no	—
223	C₄×Q₈×C₅₃	—	2	1	no	—
224	C₄×Q₈×C₅₃	—	2	1	no	—
225	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
230	C₄×D₄×C₅₃	—	2	2	no	—
231	C₄×D₄×C₅₃	—	2	2	no	—
232	C₄×D₄×C₅₃	—	2	1	no	—
233	C₄×D₄×C₅₃	—	2	2	no	—
234	C₄×D₄×C₅₃	—	2	1	no	—
235	C₄×D₄×C₅₃	—	2	2	no	—
236	C₄×D₄×C₅₃	—	2	1	no	—
237	C₄×D₄×C₅₃	—	2	1	no	—
238	C₄×D₄×C₅₃	—	2	1	no	—
239	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₅₃	C₂³	1	2	yes	—
242	C₄×D₄×C₅₃	C₂³	1	2	yes	—
243	C₄×D₄×C₅₃	C₂³	1	2	yes	—
244	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
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	2	no	—
249	#117×C₅₃	—	2	1	no	—
250	#117×C₅₃	—	2	1	no	—
251	#117×C₅₃	C₂³	1	1	yes	characteristic
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	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
261	C₂×C₄²×C₅₃	—	2	1	no	—
262	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
263	#107×C₅₃	C₂³	1	2	yes	—
264	#107×C₅₃	C₂³	1	1	yes	characteristic
265	#107×C₅₃	C₂³	1	2	yes	—
266	#107×C₅₃	C₂³	1	2	yes	—
267	#107×C₅₃	C₂³	1	2	yes	—
268	#107×C₅₃	C₂³	1	2	yes	—
269	#107×C₅₃	C₂³	1	2	yes	—
270	#107×C₅₃	C₂³	1	2	yes	—
271	#107×C₅₃	C₂³	1	1	yes	characteristic
272	#106×C₅₃	C₂³	1	2	yes	—
273	#106×C₅₃	C₂³	1	2	yes	—
274	#106×C₅₃	C₂³	1	1	yes	characteristic
275	#106×C₅₃	C₂³	1	1	yes	characteristic
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	#103×C₅₃	C₂³	1	1	yes	characteristic
285	#103×C₅₃	C₂³	1	1	yes	characteristic
286	#103×C₅₃	C₂³	1	2	yes	—
287	#103×C₅₃	C₂³	1	1	yes	characteristic
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	1	yes	characteristic
291	#102×C₅₃	C₂³	1	2	yes	—
292	#102×C₅₃	C₂³	1	2	yes	—
293	#102×C₅₃	C₂³	1	2	yes	—
294	#102×C₅₃	C₂³	1	2	yes	—
295	#102×C₅₃	C₂³	1	2	yes	—
296	#102×C₅₃	C₂³	1	2	yes	—
297	#102×C₅₃	C₂³	1	1	yes	characteristic
298	#102×C₅₃	C₂³	1	2	yes	—
299	#102×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
308	#97×C₅₃	C₂³	1	2	yes	—
309	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₅₃	C₂³	1	2	yes	—
312	C₂⁴×C₅₃	—	2	2	no	—
313	#41×C₅₃	—	2	2	no	—
314	#41×C₅₃	—	4	1	no	—
315	#41×C₅₃	—	8	2	no	—
316	#41×C₅₃	—	8	2	no	—
317	C₂×Q₈×C₅₃	—	2	1	no	—
318	C₂×Q₈×C₅₃	—	2	1	no	—
319	C₂×Q₈×C₅₃	—	2	1	no	—
320	C₂×Q₈×C₅₃	—	2	2	no	—
321	C₂×Q₈×C₅₃	—	2	2	no	—
322	C₂×Q₈×C₅₃	—	2	2	no	—
323	C₂×Q₈×C₅₃	—	8	2	no	—
324	C₂×Q₈×C₅₃	—	8	2	no	—
325	C₂×Q₈×C₅₃	—	8	2	no	—
326	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₅₃	—	2	4	no	—
330	C₂×D₄×C₅₃	—	2	1	no	—
331	C₂×D₄×C₅₃	—	2	1	no	—
332	C₂×D₄×C₅₃	—	2	2	no	—
333	C₂×D₄×C₅₃	—	2	2	no	—
334	C₂×D₄×C₅₃	—	2	2	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	—	4	2	no	—
339	C₂×D₄×C₅₃	—	8	2	no	—
340	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
343	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
349	C₂²×C₄×C₅₃	—	2	1	no	—
350	C₂²×C₄×C₅₃	—	2	1	no	—
351	C₂²×C₄×C₅₃	—	2	2	no	—
352	C₂²×C₄×C₅₃	—	2	2	no	—
353	C₂²×C₄×C₅₃	—	2	2	no	—
354	C₂²×C₄×C₅₃	—	2	2	no	—
355	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
359	Q₁₆×C₅₃	—	4	1	no	—
360	SD₁₆×C₅₃	—	2	2	no	—
361	SD₁₆×C₅₃	—	4	2	no	—
362	SD₁₆×C₅₃	—	4	1	no	—
363	D₈×C₅₃	—	2	2	no	—
364	D₈×C₅₃	—	4	2	no	—
365	M₁₆×C₅₃	—	4	2	no	—
366	M₁₆×C₅₃	—	4	2	no	—
367	C₂×C₈×C₅₃	—	4	2	no	—
368	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
373	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
374	C₄⋊C₄×C₅₃	—	2	1	no	—
375	C₄⋊C₄×C₅₃	—	2	2	no	—
376	C₄⋊C₄×C₅₃	—	2	1	no	—
377	C₄⋊C₄×C₅₃	—	2	2	no	—
378	C₄⋊C₄×C₅₃	—	2	2	no	—
379	C₄⋊C₄×C₅₃	—	2	1	no	—
380	C₄⋊C₄×C₅₃	—	2	1	no	—
381	C₄⋊C₄×C₅₃	—	2	2	no	—
382	C₄⋊C₄×C₅₃	—	2	1	no	—
383	C₄⋊C₄×C₅₃	—	2	1	no	—
384	C₄⋊C₄×C₅₃	—	2	1	no	—
385	C₄⋊C₄×C₅₃	—	2	2	no	—
386	C₄⋊C₄×C₅₃	—	2	1	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	2	no	—
391	C₄⋊C₄×C₅₃	—	2	2	no	—
392	C₄⋊C₄×C₅₃	—	2	1	no	—
393	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
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	C₂²⋊C₄×C₅₃	—	2	2	no	—
407	C₂²⋊C₄×C₅₃	—	2	2	no	—
408	C₂²⋊C₄×C₅₃	—	2	1	no	—
409	C₂²⋊C₄×C₅₃	—	2	2	no	—
410	C₂²⋊C₄×C₅₃	—	2	1	no	—
411	C₂²⋊C₄×C₅₃	—	2	2	no	—
412	C₂²⋊C₄×C₅₃	—	2	1	no	—
413	C₂²⋊C₄×C₅₃	—	2	2	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	1	no	—
421	C₂²⋊C₄×C₅₃	—	2	1	no	—
422	C₂²⋊C₄×C₅₃	—	2	2	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	1	no	—
427	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	C₄²×C₅₃	—	2	1	no	—
433	C₄²×C₅₃	—	2	1	no	—
434	C₄²×C₅₃	—	2	1	no	—
435	C₄²×C₅₃	—	2	2	no	—
436	C₄²×C₅₃	—	2	1	no	—
437	C₄²×C₅₃	—	2	2	no	—
438	C₄²×C₅₃	—	2	2	no	—
439	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
442	C₄²×C₅₃	C₂⁴	1	2	yes	—
443	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₂³×C₅₃	—	2	1	no	—
445	C₂³×C₅₃	—	2	1	no	—
446	C₂³×C₅₃	—	2	2	no	—
447	C₂³×C₅₃	—	4	4	no	—
448	C₂³×C₅₃	—	8	2	no	—
449	C₂³×C₅₃	—	8	2	no	—
450	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
451	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
452	Q₈×C₅₃	—	2	2	no	—
453	Q₈×C₅₃	—	2	1	no	—
454	Q₈×C₅₃	—	2	1	no	—
455	Q₈×C₅₃	—	2	1	no	—
456	Q₈×C₅₃	—	2	1	no	—
457	Q₈×C₅₃	—	4	2	no	—
458	Q₈×C₅₃	—	4	2	no	—
459	Q₈×C₅₃	—	4	2	no	—
460	Q₈×C₅₃	—	8	2	no	—
461	Q₈×C₅₃	—	8	2	no	—
462	Q₈×C₅₃	—	8	2	no	—
463	D₄×C₅₃	—	2	2	no	—
464	D₄×C₅₃	—	2	2	no	—
465	D₄×C₅₃	—	2	1	no	—
466	D₄×C₅₃	—	2	1	no	—
467	D₄×C₅₃	—	2	2	no	—
468	D₄×C₅₃	—	2	1	no	—
469	D₄×C₅₃	—	4	2	no	—
470	D₄×C₅₃	—	4	4	no	—
471	D₄×C₅₃	—	4	2	no	—
472	D₄×C₅₃	—	4	2	no	—
473	D₄×C₅₃	—	4	2	no	—
474	D₄×C₅₃	—	8	1	no	—
475	D₄×C₅₃	—	8	2	no	—
476	D₄×C₅₃	—	8	2	no	—
477	D₄×C₅₃	—	8	2	no	—
478	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
479	C₂×C₄×C₅₃	—	2	2	no	—
480	C₂×C₄×C₅₃	—	2	2	no	—
481	C₂×C₄×C₅₃	—	2	1	no	—
482	C₂×C₄×C₅₃	—	2	2	no	—
483	C₂×C₄×C₅₃	—	2	1	no	—
484	C₂×C₄×C₅₃	—	2	1	no	—
485	C₂×C₄×C₅₃	—	2	1	no	—
486	C₂×C₄×C₅₃	—	2	2	no	—
487	C₂×C₄×C₅₃	—	2	2	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	—	2	1	no	—
493	C₂×C₄×C₅₃	—	4	1	no	—
494	C₂×C₄×C₅₃	—	4	2	no	—
495	C₂×C₄×C₅₃	—	4	2	no	—
496	C₂×C₄×C₅₃	—	4	2	no	—
497	C₂×C₄×C₅₃	—	8	1	no	—
498	C₂×C₄×C₅₃	—	8	2	no	—
499	C₂×C₄×C₅₃	—	8	2	no	—
500	C₂×C₄×C₅₃	—	8	2	no	—
501	C₂×C₄×C₅₃	—	8	2	no	—
502	C₂×C₄×C₅₃	—	8	2	no	—
503	C₂×C₄×C₅₃	—	8	2	no	—
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	1	yes	characteristic
507	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
513	C₈×C₅₃	—	2	1	no	—
514	C₈×C₅₃	—	2	1	no	—
515	C₈×C₅₃	—	2	1	no	—
516	C₈×C₅₃	—	2	2	no	—
517	C₈×C₅₃	—	2	1	no	—
518	C₈×C₅₃	—	2	2	no	—
519	#62180	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
520	C₂²×C₅₃	—	2	1	no	—
521	C₂²×C₅₃	—	2	2	no	—
522	C₂²×C₅₃	—	2	1	no	—
523	C₂²×C₅₃	—	2	2	no	—
524	C₂²×C₅₃	—	2	2	no	—
525	C₂²×C₅₃	—	2	1	no	—
526	C₂²×C₅₃	—	2	2	no	—
527	C₂²×C₅₃	—	4	1	no	—
528	C₂²×C₅₃	—	4	1	no	—
529	C₂²×C₅₃	—	4	2	no	—
530	C₂²×C₅₃	—	4	1	no	—
531	C₂²×C₅₃	—	4	2	no	—
532	C₂²×C₅₃	—	4	1	no	—
533	C₂²×C₅₃	—	4	1	no	—
534	C₂²×C₅₃	—	4	2	no	—
535	C₂²×C₅₃	—	16	4	no	—
536	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
537	C₄×C₅₃	—	2	1	no	—
538	C₄×C₅₃	—	2	1	no	—
539	C₄×C₅₃	—	2	2	no	—
540	C₄×C₅₃	—	2	1	no	—
541	C₄×C₅₃	—	2	2	no	—
542	C₄×C₅₃	—	2	1	no	—
543	C₄×C₅₃	—	2	2	no	—
544	C₄×C₅₃	—	4	1	no	—
545	C₄×C₅₃	—	4	1	no	—
546	C₄×C₅₃	—	4	1	no	—
547	C₄×C₅₃	—	4	1	no	—
548	C₄×C₅₃	—	4	1	no	—
549	C₄×C₅₃	—	4	1	no	—
550	C₄×C₅₃	—	4	2	no	—
551	C₄×C₅₃	—	4	2	no	—
552	C₄×C₅₃	—	4	2	no	—
553	C₄×C₅₃	#576	1	2	yes	—
554	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
555	C₄×C₅₃	#585	1	1	yes	characteristic
556	#3552	C₂×C₅₃	1	1	yes	characteristic, complemented
557	#3514	C₂×C₅₃	1	1	yes	characteristic, complemented
558	#3386	C₂×C₅₃	1	1	yes	characteristic, complemented
559	Q₈×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
560	#3373	C₂×C₅₃	1	1	yes	characteristic, complemented
561	#3365	C₂×C₅₃	1	1	yes	characteristic, complemented
562	#3357	C₂×C₅₃	1	2	yes	complemented
563	#3353	C₂×C₅₃	1	1	yes	characteristic, complemented
564	#3347	C₂×C₅₃	1	2	yes	complemented
565	#3342	C₂×C₅₃	1	1	yes	characteristic, complemented
566	#3324	C₂×C₅₃	1	1	yes	characteristic, complemented
567	#3322	C₂×C₅₃	1	2	yes	complemented
568	#3314	C₂×C₅₃	1	2	yes	complemented
569	#3294	C₂×C₅₃	1	1	yes	characteristic, complemented
570	#3262	C₂×C₅₃	1	2	yes	complemented
571	#3251	C₂×C₅₃	1	1	yes	characteristic, complemented
572	#3243	C₂×C₅₃	1	2	yes	complemented
573	#3226	C₂×C₅₃	1	1	yes	characteristic, complemented
574	#3118	C₂×C₅₃	1	2	yes	complemented
575	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
576	#3081	C₂×C₅₃	1	2	yes	complemented
577	#3079	C₂×C₅₃	1	1	yes	characteristic, complemented
578	#2993	C₂×C₅₃	1	1	yes	characteristic, complemented
579	C₂×C₅₃	—	4	1	no	—
580	C₂×C₅₃	—	4	2	no	—
581	C₂×C₅₃	—	4	2	no	—
582	C₂×C₅₃	—	8	1	no	—
583	C₂×C₅₃	—	8	2	no	—
584	C₂×C₅₃	#3489	1	1	yes	characteristic
585	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
586	C₂×C₅₃	#3586	1	1	yes	characteristic
587	#563	—	2	2	no	—
588	#559	C₂²×C₅₃	1	1	yes	characteristic
589	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
590	#556	C₂²×C₅₃	1	1	yes	characteristic
591	#556	C₂²×C₅₃	1	1	yes	characteristic
592	#555	C₂²×C₅₃	1	2	yes	—
593	#554	C₂²×C₅₃	1	2	yes	complemented
594	#553	C₂²×C₅₃	1	2	yes	complemented
595	#551	—	2	2	no	—
596	D₄×Q₈	—	2	1	no	—
597	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
598	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
599	#548	—	2	1	no	—
600	#548	—	2	1	no	—
601	#547	C₂²×C₅₃	1	1	yes	characteristic
602	#546	—	2	1	no	—
603	#546	C₂²×C₅₃	1	2	yes	—
604	D₄²	C₂²×C₅₃	1	1	yes	characteristic
605	#544	C₂²×C₅₃	1	2	yes	complemented
606	#542	C₂²×C₅₃	1	2	yes	—
607	#542	C₂²×C₅₃	1	2	yes	complemented
608	#541	—	2	1	no	—
609	#539	—	2	2	no	—
610	#538	—	2	2	no	—
611	#536	—	2	1	no	—
612	#532	C₂²×C₅₃	1	1	yes	characteristic
613	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
614	#529	—	2	1	no	—
615	#529	C₂²×C₅₃	1	1	yes	characteristic
616	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
617	C₂×#124	—	2	1	no	—
618	#518	C₂²×C₅₃	1	2	yes	—
619	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
620	#501	C₂²×C₅₃	1	2	yes	complemented
621	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
622	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
623	#500	C₂²×C₅₃	1	2	yes	complemented
624	#489	C₂²×C₅₃	1	2	yes	complemented
625	#488	C₂²×C₅₃	1	2	yes	complemented
626	#486	C₂²×C₅₃	1	1	yes	characteristic
627	#486	C₂²×C₅₃	1	1	yes	characteristic
628	#485	C₂²×C₅₃	1	2	yes	complemented
629	#485	C₂²×C₅₃	1	2	yes	complemented
630	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
631	#484	C₂²×C₅₃	1	2	yes	complemented
632	#482	C₂²×C₅₃	1	2	yes	—
633	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
634	#482	C₂²×C₅₃	1	2	yes	complemented
635	#480	C₂²×C₅₃	1	2	yes	—
636	#480	C₂²×C₅₃	1	2	yes	complemented
637	#480	C₂²×C₅₃	1	2	yes	complemented
638	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
639	#478	C₂²×C₅₃	1	1	yes	characteristic
640	#478	C₂²×C₅₃	1	2	yes	—
641	#478	C₂²×C₅₃	1	2	yes	complemented
642	#478	C₂²×C₅₃	1	2	yes	complemented
643	#477	C₂²×C₅₃	1	2	yes	complemented
644	#477	C₂²×C₅₃	1	2	yes	complemented
645	#476	C₂²×C₅₃	1	2	yes	—
646	#476	C₂²×C₅₃	1	2	yes	complemented
647	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
648	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
649	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
650	#474	C₂²×C₅₃	1	1	yes	characteristic
651	#474	C₂²×C₅₃	1	1	yes	characteristic
652	#474	C₂²×C₅₃	1	2	yes	—
653	#474	C₂²×C₅₃	1	2	yes	complemented
654	#474	C₂²×C₅₃	1	2	yes	complemented
655	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
656	#474	C₂²×C₅₃	1	2	yes	complemented
657	#469	C₂²×C₅₃	1	2	yes	complemented
658	#468	C₂²×C₅₃	1	2	yes	—
659	#468	C₂²×C₅₃	1	2	yes	complemented
660	#468	C₂²×C₅₃	1	2	yes	complemented
661	#467	C₂²×C₅₃	1	2	yes	complemented
662	#466	C₂²×C₅₃	1	2	yes	—
663	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
664	#464	C₂²×C₅₃	1	2	yes	complemented
665	#463	C₂²×C₅₃	1	1	yes	characteristic
666	#463	C₂²×C₅₃	1	2	yes	complemented
667	#463	C₂²×C₅₃	1	2	yes	complemented
668	#460	C₂²×C₅₃	1	1	yes	characteristic
669	#459	C₂²×C₅₃	1	1	yes	characteristic
670	#452	C₂²×C₅₃	1	1	yes	characteristic
671	#450	C₂²×C₅₃	1	2	yes	—
672	#449	C₂²×C₅₃	1	1	yes	characteristic
673	#447	C₂²×C₅₃	1	2	yes	—
674	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
675	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
676	#442	C₂²×C₅₃	1	2	yes	complemented
677	#440	C₂²×C₅₃	1	2	yes	—
678	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
679	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
680	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
681	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
682	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
683	C₄×D₈	C₂²×C₅₃	1	2	yes	—
684	#436	C₂²×C₅₃	1	1	yes	characteristic
685	#436	C₂²×C₅₃	1	2	yes	complemented
686	#435	C₂²×C₅₃	1	2	yes	complemented
687	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
688	#433	C₂²×C₅₃	1	2	yes	complemented
689	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
690	#428	C₂²×C₅₃	1	2	yes	complemented
691	#428	C₂²×C₅₃	1	2	yes	complemented
692	#427	C₂²×C₅₃	1	2	yes	complemented
693	#424	C₂²×C₅₃	1	2	yes	complemented
694	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
695	#418	C₂²×C₅₃	1	2	yes	—
696	#417	C₂²×C₅₃	1	2	yes	—
697	C₂×#102	C₂²×C₅₃	1	2	yes	—
698	C₅₃	#62180	1	1	yes	characteristic, direct product factor, Sylow
699	C₂×#41	—	2	1	no	—
700	C₂×#41	—	2	1	no	—
701	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
702	C₂²×Q₈	—	2	1	no	—
703	C₂²×Q₈	—	2	1	no	—
704	C₂²×Q₈	—	2	1	no	—
705	C₂²×D₄	—	2	1	no	—
706	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
707	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
709	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
710	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
711	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
712	C₂×D₈	C₂³×C₅₃	1	2	yes	—
713	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
714	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
715	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	—	2	2	no	—
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	—	2	1	no	—
720	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
721	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
725	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
726	#127	C₂³×C₅₃	1	1	yes	characteristic
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	1	no	—
733	#126	D₄×C₅₃	1	2	yes	—
734	#125	—	2	2	no	—
735	#125	—	2	2	no	—
736	#125	—	2	2	no	—
737	#125	D₄×C₅₃	1	1	yes	characteristic
738	#125	C₂³×C₅₃	1	1	yes	characteristic
739	#125	C₂³×C₅₃	1	2	yes	—
740	#124	—	2	1	no	—
741	#124	—	2	1	no	—
742	#124	—	2	1	no	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	—	2	2	no	—
747	#124	—	2	1	no	—
748	#124	D₄×C₅₃	1	1	yes	characteristic
749	#124	C₂³×C₅₃	1	1	yes	characteristic
750	#124	C₂³×C₅₃	1	2	yes	—
751	#123	—	2	1	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	D₄×C₅₃	1	2	yes	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
771	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
772	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
773	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	—	2	1	no	—
777	#121	—	2	1	no	—
778	#121	—	2	2	no	—
779	#121	D₄×C₅₃	1	1	yes	characteristic
780	#121	C₂³×C₅₃	1	1	yes	characteristic
781	#121	C₂³×C₅₃	1	2	yes	—
782	#121	C₂³×C₅₃	1	2	yes	—
783	#121	C₂³×C₅₃	1	2	yes	—
784	#120	—	2	2	no	—
785	#120	—	2	2	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	—	2	1	no	—
789	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
793	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₅₃	1	2	yes	—
806	C₄×D₄	C₂³×C₅₃	1	2	yes	—
807	C₄×D₄	C₂³×C₅₃	1	2	yes	—
808	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₅₃	1	2	yes	—
810	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
811	C₄×D₄	C₂³×C₅₃	1	2	yes	—
812	#117	—	2	2	no	—
813	#117	—	2	1	no	—
814	#117	—	2	1	no	—
815	#117	C₂³×C₅₃	1	1	yes	characteristic
816	#117	C₂³×C₅₃	1	2	yes	—
817	#117	C₂³×C₅₃	1	2	yes	—
818	#117	C₂³×C₅₃	1	2	yes	—
819	C₂×C₄⋊C₄	—	2	1	no	—
820	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
821	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
822	C₂×C₂²⋊C₄	—	2	2	no	—
823	C₂×C₂²⋊C₄	—	2	2	no	—
824	C₂×C₂²⋊C₄	—	2	2	no	—
825	C₂×C₄²	—	2	1	no	—
826	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
827	#107	C₂³×C₅₃	1	1	yes	characteristic
828	#107	C₂³×C₅₃	1	2	yes	—
829	#107	C₂³×C₅₃	1	2	yes	—
830	#107	C₂³×C₅₃	1	2	yes	—
831	#107	C₂³×C₅₃	1	2	yes	—
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	#106	C₂³×C₅₃	1	2	yes	—
837	#106	C₂³×C₅₃	1	2	yes	—
838	#106	C₂³×C₅₃	1	2	yes	—
839	#106	C₂³×C₅₃	1	1	yes	characteristic
840	#106	C₂³×C₅₃	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
842	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
846	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
847	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
848	#103	C₂³×C₅₃	1	2	yes	—
849	#103	C₂³×C₅₃	1	2	yes	—
850	#103	C₂³×C₅₃	1	1	yes	characteristic
851	#103	C₂³×C₅₃	1	1	yes	characteristic
852	#103	C₂³×C₅₃	1	1	yes	characteristic
853	#103	C₂³×C₅₃	1	1	yes	characteristic
854	#103	C₂³×C₅₃	1	2	yes	—
855	#102	C₂³×C₅₃	1	1	yes	characteristic
856	#102	C₂³×C₅₃	1	2	yes	—
857	#102	C₂³×C₅₃	1	2	yes	—
858	#102	C₂³×C₅₃	1	2	yes	—
859	#102	C₂³×C₅₃	1	2	yes	—
860	#102	C₂³×C₅₃	1	1	yes	characteristic
861	#102	C₂³×C₅₃	1	2	yes	—
862	#102	C₂³×C₅₃	1	2	yes	—
863	#102	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	2	yes	—
867	#102	C₂³×C₅₃	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
869	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
870	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
872	#97	C₂³×C₅₃	1	2	yes	—
873	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
875	C₄×C₈	C₂³×C₅₃	1	2	yes	—
876	C₂⁴	—	2	2	no	—
877	#41	—	2	2	no	—
878	#41	—	4	1	no	—
879	#41	—	8	2	no	—
880	#41	—	8	2	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	—	8	2	no	—
888	C₂×Q₈	—	8	2	no	—
889	C₂×Q₈	—	8	2	no	—
890	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
891	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
892	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
893	C₂×D₄	—	2	4	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	4	2	no	—
903	C₂×D₄	—	8	2	no	—
904	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
905	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
906	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
907	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
908	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
920	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
921	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
922	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
923	Q₁₆	—	4	1	no	—
924	SD₁₆	—	2	2	no	—
925	SD₁₆	—	4	1	no	—
926	SD₁₆	—	4	2	no	—
927	D₈	—	2	2	no	—
928	D₈	—	4	2	no	—
929	M₁₆	—	4	2	no	—
930	M₁₆	—	4	2	no	—
931	C₂×C₈	—	4	2	no	—
932	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
937	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
958	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
959	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
960	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
961	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
962	C₄⋊C₄	C₂×D₄×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	2	yes	—
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	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1004	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1006	C₄²	C₂⁴×C₅₃	1	2	yes	—
1007	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1008	C₂³	—	2	1	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	4	4	no	—
1012	C₂³	—	8	2	no	—
1013	C₂³	—	8	2	no	—
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	1	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	2	1	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	4	2	no	—
1023	Q₈	—	4	2	no	—
1024	Q₈	—	8	2	no	—
1025	Q₈	—	8	2	no	—
1026	Q₈	—	8	2	no	—
1027	D₄	—	2	2	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	2	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	2	2	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	4	4	no	—
1035	D₄	—	4	2	no	—
1036	D₄	—	4	2	no	—
1037	D₄	—	4	2	no	—
1038	D₄	—	8	1	no	—
1039	D₄	—	8	2	no	—
1040	D₄	—	8	2	no	—
1041	D₄	—	8	2	no	—
1042	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	4	1	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	8	1	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1075	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1076	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1077	C₈	—	2	1	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₈	—	2	2	no	—
1081	C₈	—	2	1	no	—
1082	C₈	—	2	2	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	16	4	no	—
1099	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1100	C₄	—	2	1	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	C₅₃×#576	1	2	yes	—
1117	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1118	C₄	C₅₃×#585	1	1	yes	characteristic
1119	C₂	—	4	2	no	—
1120	C₂	—	4	1	no	—
1121	C₂	—	4	2	no	—
1122	C₂	—	8	2	no	—
1123	C₂	—	8	1	no	—
1124	C₂	C₅₃×#3489	1	1	yes	characteristic
1125	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1126	C₂	C₅₃×#3586	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×#3552	C₂	semidirect
2. C₅₃×#3514	C₂	semidirect
3. C₅₃×#3386	C₂	semidirect
4. Q₈×D₈×C₅₃	C₂	semidirect
5. C₅₃×#3373	C₂	semidirect
6. C₅₃×#3365	C₂	semidirect
7. C₅₃×#3357	C₂	semidirect
8. C₅₃×#3353	C₂	semidirect
9. C₅₃×#3347	C₂	semidirect
10. C₅₃×#3342	C₂	semidirect
11. C₅₃×#3324	C₂	semidirect
12. C₅₃×#3322	C₂	semidirect
13. C₅₃×#3314	C₂	semidirect
14. C₅₃×#3294	C₂	semidirect
15. C₅₃×#3262	C₂	semidirect
16. C₅₃×#3251	C₂	semidirect
17. C₅₃×#3243	C₂	semidirect
18. C₅₃×#3226	C₂	semidirect
19. C₅₃×#3118	C₂	semidirect
20. C₅₃×#3102	C₂	semidirect
21. C₅₃×#3081	C₂	semidirect
22. C₅₃×#3079	C₂	semidirect
23. C₅₃×#2993	C₂	semidirect
26. C₅₃×#557	C₂²	semidirect
30. C₅₃×#554	C₂²	semidirect
31. C₅₃×#553	C₂²	semidirect
35. D₄×Q₈×C₅₃	C₂²	semidirect
42. C₅₃×#544	C₂²	semidirect
44. C₅₃×#542	C₂²	semidirect
50. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
53. C₅₃×#529	C₂²	semidirect
57. C₅₃×#501	C₂²	semidirect
58. C₅₃×#500	C₂²	semidirect
59. C₅₃×#500	C₂²	semidirect
60. C₅₃×#500	C₂²	semidirect
61. C₅₃×#489	C₂²	semidirect
62. C₅₃×#488	C₂²	semidirect
65. C₅₃×#485	C₂²	semidirect
66. C₅₃×#485	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#484	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
73. C₅₃×#480	C₂²	semidirect
74. C₅₃×#480	C₂²	semidirect
75. C₅₃×#479	C₂²	semidirect
78. C₅₃×#478	C₂²	semidirect
79. C₅₃×#478	C₂²	semidirect
80. C₅₃×#477	C₂²	semidirect
81. C₅₃×#477	C₂²	semidirect
83. C₅₃×#476	C₂²	semidirect
84. C₅₃×#475	C₂²	semidirect
85. C₅₃×#475	C₂²	semidirect
86. C₅₃×#475	C₂²	semidirect
90. C₅₃×#474	C₂²	semidirect
91. C₅₃×#474	C₂²	semidirect
92. C₅₃×#474	C₂²	semidirect
93. C₅₃×#474	C₂²	semidirect
94. C₅₃×#469	C₂²	semidirect
96. C₅₃×#468	C₂²	semidirect
97. C₅₃×#468	C₂²	semidirect
98. C₅₃×#467	C₂²	semidirect
100. C₅₃×#464	C₂²	semidirect
101. C₅₃×#464	C₂²	semidirect
103. C₅₃×#463	C₂²	semidirect
104. C₅₃×#463	C₂²	semidirect
111. C₅₃×#446	C₂²	semidirect
112. C₈×Q₈×C₅₃	C₂²	semidirect
113. C₅₃×#442	C₂²	semidirect
115. C₄×Q₁₆×C₅₃	C₂²	semidirect
117. C₄×SD₁₆×C₅₃	C₂²	semidirect
118. C₄×SD₁₆×C₅₃	C₂²	semidirect
122. C₅₃×#436	C₂²	semidirect
123. C₅₃×#435	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
519. #62180	C₅₃	direct (N × H)
556. #3552	C₂×C₅₃	semidirect
557. #3514	C₂×C₅₃	semidirect
558. #3386	C₂×C₅₃	semidirect
559. Q₈×D₈	C₂×C₅₃	semidirect
560. #3373	C₂×C₅₃	semidirect
561. #3365	C₂×C₅₃	semidirect
562. #3357	C₂×C₅₃	semidirect
563. #3353	C₂×C₅₃	semidirect
564. #3347	C₂×C₅₃	semidirect
565. #3342	C₂×C₅₃	semidirect
566. #3324	C₂×C₅₃	semidirect
567. #3322	C₂×C₅₃	semidirect
568. #3314	C₂×C₅₃	semidirect
569. #3294	C₂×C₅₃	semidirect
570. #3262	C₂×C₅₃	semidirect
571. #3251	C₂×C₅₃	semidirect
572. #3243	C₂×C₅₃	semidirect
573. #3226	C₂×C₅₃	semidirect
574. #3118	C₂×C₅₃	semidirect
575. #3102	C₂×C₅₃	semidirect
576. #3081	C₂×C₅₃	semidirect
577. #3079	C₂×C₅₃	semidirect
578. #2993	C₂×C₅₃	semidirect
589. #557	C₂²×C₅₃	semidirect
593. #554	C₂²×C₅₃	semidirect
594. #553	C₂²×C₅₃	semidirect
598. D₄×Q₈	C₂²×C₅₃	semidirect
605. #544	C₂²×C₅₃	semidirect
607. #542	C₂²×C₅₃	semidirect
613. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
616. #529	C₂²×C₅₃	semidirect
620. #501	C₂²×C₅₃	semidirect
621. #500	C₂²×C₅₃	semidirect
622. #500	C₂²×C₅₃	semidirect
623. #500	C₂²×C₅₃	semidirect
624. #489	C₂²×C₅₃	semidirect
625. #488	C₂²×C₅₃	semidirect
628. #485	C₂²×C₅₃	semidirect
629. #485	C₂²×C₅₃	semidirect
630. #485	C₂²×C₅₃	semidirect
631. #484	C₂²×C₅₃	semidirect
633. #482	C₂²×C₅₃	semidirect
634. #482	C₂²×C₅₃	semidirect
636. #480	C₂²×C₅₃	semidirect
637. #480	C₂²×C₅₃	semidirect
638. #479	C₂²×C₅₃	semidirect
641. #478	C₂²×C₅₃	semidirect
642. #478	C₂²×C₅₃	semidirect
643. #477	C₂²×C₅₃	semidirect
644. #477	C₂²×C₅₃	semidirect
646. #476	C₂²×C₅₃	semidirect
647. #475	C₂²×C₅₃	semidirect
648. #475	C₂²×C₅₃	semidirect
649. #475	C₂²×C₅₃	semidirect
653. #474	C₂²×C₅₃	semidirect
654. #474	C₂²×C₅₃	semidirect
655. #474	C₂²×C₅₃	semidirect
656. #474	C₂²×C₅₃	semidirect
657. #469	C₂²×C₅₃	semidirect
659. #468	C₂²×C₅₃	semidirect
660. #468	C₂²×C₅₃	semidirect
661. #467	C₂²×C₅₃	semidirect
663. #464	C₂²×C₅₃	semidirect
664. #464	C₂²×C₅₃	semidirect
666. #463	C₂²×C₅₃	semidirect
667. #463	C₂²×C₅₃	semidirect
674. #446	C₂²×C₅₃	semidirect
675. C₈×Q₈	C₂²×C₅₃	semidirect
676. #442	C₂²×C₅₃	semidirect
678. C₄×Q₁₆	C₂²×C₅₃	semidirect
680. C₄×SD₁₆	C₂²×C₅₃	semidirect
681. C₄×SD₁₆	C₂²×C₅₃	semidirect
685. #436	C₂²×C₅₃	semidirect
686. #435	C₂²×C₅₃	semidirect
688. #433	C₂²×C₅₃	semidirect
689. #431	C₂²×C₅₃	semidirect
690. #428	C₂²×C₅₃	semidirect
691. #428	C₂²×C₅₃	semidirect
692. #427	C₂²×C₅₃	semidirect
693. #424	C₂²×C₅₃	semidirect
694. #423	C₂²×C₅₃	semidirect
698. C₅₃	#62180	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×#3552	2
C₅₃×#3514	2
C₅₃×#3386	2
Q₈×D₈×C₅₃	2
C₅₃×#3373	2
C₅₃×#3365	2
C₅₃×#3357	2
C₅₃×#3353	2
C₅₃×#3347	2
C₅₃×#3342	2
C₅₃×#3324	2
C₅₃×#3322	2
C₅₃×#3314	2
C₅₃×#3294	2
C₅₃×#3262	2
C₅₃×#3251	2
C₅₃×#3243	2
C₅₃×#3226	2
C₅₃×#3118	2
C₅₃×#3102	2
C₅₃×#3081	2
C₅₃×#3079	2
C₅₃×#2993	2
#62180	53

Subgroups — C53×#62180 #27269692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62180 #27269692