Subgroups — C₅₃×#61646 #27269158

Order 13568.

2030 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3329	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3328	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3321	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3313	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3277	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3275	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3270	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3266	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3225	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3202	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3200	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3197	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3121	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3011	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3010	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3004	C₂	1	2	yes	maximal, complemented
19	C₅₃×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic
21	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×#137×C₅₃	C₂²	1	2	yes	—
23	C₂×#137×C₅₃	C₂²	1	2	yes	—
24	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₅₃×H(3,𝔽₄)	—	2	1	no	—
29	C₅₃×#560	—	2	1	no	—
30	C₅₃×#559	—	2	1	no	—
31	C₅₃×#556	C₂²	1	2	yes	—
32	C₅₃×#555	C₂²	1	2	yes	—
33	C₅₃×#551	—	2	1	no	—
34	D₄×Q₈×C₅₃	—	2	2	no	—
35	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
36	D₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
37	C₅₃×#548	—	2	2	no	—
38	C₅₃×#548	C₂²	1	2	yes	—
39	C₅₃×#548	C₂²	1	2	yes	—
40	C₅₃×#548	C₂²	1	2	yes	complemented
41	C₅₃×#546	C₂²	1	2	yes	—
42	C₅₃×#542	—	2	2	no	—
43	C₅₃×#542	C₂²	1	2	yes	—
44	C₅₃×#538	—	2	2	no	—
45	C₅₃×#536	—	2	1	no	—
46	C₅₃×#536	—	2	1	no	—
47	C₅₃×#536	C₂²	1	1	yes	characteristic
48	C₅₃×#536	C₂²	1	1	yes	characteristic
49	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#535	C₂²	1	1	yes	characteristic
51	C₅₃×#525	—	2	1	no	—
52	C₅₃×#525	—	2	1	no	—
53	C₅₃×#525	C₂²	1	2	yes	—
54	C₅₃×#525	C₂²	1	1	yes	characteristic
55	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#519	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#497	C₂²	1	2	yes	complemented
58	C₅₃×#495	C₂²	1	2	yes	complemented
59	C₅₃×#489	C₂²	1	2	yes	complemented
60	C₅₃×#487	C₂²	1	2	yes	complemented
61	C₅₃×#485	C₂²	1	2	yes	complemented
62	C₅₃×#485	C₂²	1	2	yes	complemented
63	C₅₃×#485	C₂²	1	2	yes	complemented
64	C₅₃×#485	C₂²	1	2	yes	complemented
65	C₅₃×#482	C₂²	1	2	yes	—
66	C₅₃×#482	C₂²	1	2	yes	complemented
67	C₅₃×#477	C₂²	1	2	yes	complemented
68	C₅₃×#475	C₂²	1	2	yes	complemented
69	C₅₃×#470	C₂²	1	2	yes	complemented
70	C₅₃×#470	C₂²	1	2	yes	complemented
71	C₅₃×#469	C₂²	1	2	yes	—
72	C₅₃×#468	C₂²	1	2	yes	—
73	C₅₃×#468	C₂²	1	2	yes	complemented
74	C₅₃×#468	C₂²	1	2	yes	complemented
75	C₅₃×#467	C₂²	1	2	yes	complemented
76	C₅₃×#465	C₂²	1	2	yes	complemented
77	C₅₃×#464	C₂²	1	2	yes	complemented
78	C₅₃×#464	C₂²	1	2	yes	complemented
79	C₅₃×#464	C₂²	1	2	yes	complemented
80	C₅₃×#463	C₂²	1	2	yes	complemented
81	C₅₃×#462	C₂²	1	2	yes	complemented
82	C₅₃×#461	C₂²	1	2	yes	complemented
83	C₅₃×#452	C₂²	1	2	yes	—
84	C₅₃×#452	C₂²	1	2	yes	complemented
85	C₅₃×#452	C₂²	1	2	yes	complemented
86	C₅₃×#451	C₂²	1	2	yes	complemented
87	C₅₃×#451	C₂²	1	2	yes	complemented
88	C₅₃×#451	C₂²	1	2	yes	complemented
89	C₅₃×#451	C₂²	1	2	yes	complemented
90	C₅₃×#451	C₂²	1	2	yes	complemented
91	C₅₃×#451	C₂²	1	2	yes	complemented
92	C₅₃×#450	C₂²	1	2	yes	complemented
93	C₅₃×#449	C₂²	1	2	yes	—
94	C₅₃×#449	C₂²	1	2	yes	—
95	C₅₃×#449	C₂²	1	2	yes	complemented
96	C₅₃×#448	C₂²	1	2	yes	—
97	C₅₃×#448	C₂²	1	2	yes	—
98	C₅₃×#448	C₂²	1	2	yes	—
99	C₅₃×#448	C₂²	1	2	yes	—
100	C₅₃×#448	C₂²	1	2	yes	complemented
101	C₅₃×#441	C₂²	1	2	yes	complemented
102	C₅₃×#440	C₂²	1	2	yes	complemented
103	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
105	C₅₃×#436	C₂²	1	2	yes	—
106	C₅₃×#436	C₂²	1	2	yes	complemented
107	C₅₃×#435	C₂²	1	2	yes	—
108	C₅₃×#435	C₂²	1	2	yes	complemented
109	C₅₃×#433	C₂²	1	2	yes	complemented
110	C₅₃×#419	C₂²	1	2	yes	complemented
111	C₅₃×#419	C₂²	1	2	yes	complemented
112	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#408	C₂²	1	1	yes	characteristic
117	C₅₃×#408	C₂²	1	1	yes	characteristic
118	C₅₃×#407	C₂²	1	2	yes	complemented
119	2₋¹⁺⁴×C₅₃	—	4	2	no	—
120	2₋¹⁺⁴×C₅₃	—	4	2	no	—
121	C₂×#41×C₅₃	—	2	1	no	—
122	C₂×#41×C₅₃	—	2	1	no	—
123	C₂×#41×C₅₃	—	2	1	no	—
124	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
125	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
126	C₂×#41×C₅₃	C₂³	1	2	yes	—
127	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
128	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₅₃	—	2	1	no	—
130	C₂²×Q₈×C₅₃	—	2	1	no	—
131	C₂²×Q₈×C₅₃	—	2	2	no	—
132	C₂²×Q₈×C₅₃	—	4	2	no	—
133	C₂²×Q₈×C₅₃	—	4	2	no	—
134	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
135	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
136	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
137	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₅₃	—	2	1	no	—
143	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
144	#137×C₅₃	—	4	4	no	—
145	#137×C₅₃	—	4	4	no	—
146	#137×C₅₃	—	4	2	no	—
147	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
148	C₂×Q₁₆×C₅₃	—	4	2	no	—
149	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₅₃	—	4	2	no	—
155	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
161	C₂×D₈×C₅₃	C₂³	1	2	yes	—
162	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
163	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
164	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
165	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₅₃	—	2	2	no	—
169	C₄⋊Q₈×C₅₃	—	2	2	no	—
170	C₄⋊Q₈×C₅₃	—	2	1	no	—
171	C₄⋊Q₈×C₅₃	—	2	1	no	—
172	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
173	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
174	#127×C₅₃	—	2	1	no	—
175	#126×C₅₃	—	2	2	no	—
176	#126×C₅₃	—	2	2	no	—
177	#126×C₅₃	—	2	2	no	—
178	#124×C₅₃	—	2	2	no	—
179	#124×C₅₃	—	2	2	no	—
180	#124×C₅₃	—	2	2	no	—
181	#124×C₅₃	—	2	2	no	—
182	#124×C₅₃	—	2	2	no	—
183	#124×C₅₃	—	2	2	no	—
184	#124×C₅₃	—	2	1	no	—
185	#124×C₅₃	—	2	1	no	—
186	#124×C₅₃	—	2	1	no	—
187	#124×C₅₃	—	2	2	no	—
188	#124×C₅₃	C₂³	1	2	yes	—
189	#124×C₅₃	C₂³	1	2	yes	—
190	#123×C₅₃	—	2	2	no	—
191	#123×C₅₃	—	2	1	no	—
192	#123×C₅₃	—	2	1	no	—
193	#123×C₅₃	—	2	2	no	—
194	#123×C₅₃	—	2	1	no	—
195	#123×C₅₃	—	2	1	no	—
196	#123×C₅₃	—	2	1	no	—
197	#123×C₅₃	—	2	1	no	—
198	#123×C₅₃	—	2	2	no	—
199	#123×C₅₃	—	2	1	no	—
200	#123×C₅₃	D₄	1	1	yes	characteristic
201	#123×C₅₃	D₄	1	1	yes	characteristic
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	—	2	2	no	—
207	C₂²⋊Q₈×C₅₃	—	2	2	no	—
208	C₂²⋊Q₈×C₅₃	—	2	2	no	—
209	C₂²⋊Q₈×C₅₃	—	2	2	no	—
210	C₂²⋊Q₈×C₅₃	—	2	2	no	—
211	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
212	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
215	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
216	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
218	#121×C₅₃	—	2	2	no	—
219	#121×C₅₃	—	2	2	no	—
220	#121×C₅₃	—	2	2	no	—
221	#121×C₅₃	—	2	2	no	—
222	#121×C₅₃	—	2	2	no	—
223	#121×C₅₃	D₄	1	2	yes	—
224	#121×C₅₃	C₂³	1	2	yes	—
225	#121×C₅₃	C₂³	1	2	yes	—
226	#121×C₅₃	C₂³	1	2	yes	—
227	#121×C₅₃	C₂³	1	2	yes	—
228	#120×C₅₃	—	2	1	no	—
229	#120×C₅₃	—	2	2	no	—
230	#120×C₅₃	—	2	1	no	—
231	#120×C₅₃	—	2	1	no	—
232	#120×C₅₃	—	2	2	no	—
233	#120×C₅₃	D₄	1	1	yes	characteristic
234	#120×C₅₃	D₄	1	1	yes	characteristic
235	C₄×Q₈×C₅₃	—	2	2	no	—
236	C₄×Q₈×C₅₃	—	2	2	no	—
237	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
238	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
239	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
240	C₄×D₄×C₅₃	—	2	2	no	—
241	C₄×D₄×C₅₃	—	2	2	no	—
242	C₄×D₄×C₅₃	—	2	2	no	—
243	C₄×D₄×C₅₃	—	2	2	no	—
244	C₄×D₄×C₅₃	—	2	2	no	—
245	C₄×D₄×C₅₃	—	2	2	no	—
246	C₄×D₄×C₅₃	—	2	2	no	—
247	C₄×D₄×C₅₃	—	2	2	no	—
248	C₄×D₄×C₅₃	C₂³	1	2	yes	—
249	C₄×D₄×C₅₃	C₂³	1	2	yes	—
250	C₄×D₄×C₅₃	C₂³	1	2	yes	—
251	#117×C₅₃	—	2	2	no	—
252	#117×C₅₃	—	2	1	no	—
253	#117×C₅₃	—	2	1	no	—
254	#117×C₅₃	C₂³	1	1	yes	characteristic
255	#117×C₅₃	C₂³	1	1	yes	characteristic
256	#117×C₅₃	C₂³	1	1	yes	characteristic
257	#117×C₅₃	C₂³	1	2	yes	—
258	#117×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
260	#107×C₅₃	C₂³	1	2	yes	—
261	#107×C₅₃	C₂³	1	2	yes	—
262	#106×C₅₃	C₂³	1	2	yes	—
263	#106×C₅₃	C₂³	1	2	yes	—
264	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
265	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
266	#103×C₅₃	C₂³	1	2	yes	—
267	#103×C₅₃	C₂³	1	2	yes	—
268	#103×C₅₃	C₂³	1	2	yes	—
269	#103×C₅₃	C₂³	1	2	yes	—
270	#103×C₅₃	C₂³	1	2	yes	—
271	#103×C₅₃	C₂³	1	2	yes	—
272	#103×C₅₃	C₂³	1	2	yes	—
273	#103×C₅₃	C₂³	1	2	yes	—
274	#103×C₅₃	C₂³	1	2	yes	—
275	#103×C₅₃	C₂³	1	2	yes	—
276	#103×C₅₃	C₂³	1	2	yes	—
277	#103×C₅₃	C₂³	1	2	yes	—
278	#102×C₅₃	C₂³	1	2	yes	—
279	#102×C₅₃	C₂³	1	2	yes	—
280	#102×C₅₃	C₂³	1	2	yes	—
281	#102×C₅₃	C₂³	1	2	yes	—
282	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
284	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
285	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
286	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
287	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
288	#97×C₅₃	C₂³	1	2	yes	—
289	C₄×C₈×C₅₃	C₂³	1	2	yes	—
290	C₂⁴×C₅₃	—	2	1	no	—
291	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
292	#41×C₅₃	—	2	2	no	—
293	#41×C₅₃	—	2	2	no	—
294	#41×C₅₃	—	4	1	no	—
295	#41×C₅₃	—	4	1	no	—
296	#41×C₅₃	—	4	1	no	—
297	#41×C₅₃	—	4	1	no	—
298	#41×C₅₃	—	4	1	no	—
299	#41×C₅₃	—	4	1	no	—
300	#41×C₅₃	—	4	4	no	—
301	#41×C₅₃	—	4	4	no	—
302	#41×C₅₃	—	4	2	no	—
303	#41×C₅₃	—	4	2	no	—
304	#41×C₅₃	—	4	4	no	—
305	C₂×Q₈×C₅₃	—	2	2	no	—
306	C₂×Q₈×C₅₃	—	2	2	no	—
307	C₂×Q₈×C₅₃	—	2	1	no	—
308	C₂×Q₈×C₅₃	—	2	2	no	—
309	C₂×Q₈×C₅₃	—	2	2	no	—
310	C₂×Q₈×C₅₃	—	2	1	no	—
311	C₂×Q₈×C₅₃	—	2	1	no	—
312	C₂×Q₈×C₅₃	—	2	1	no	—
313	C₂×Q₈×C₅₃	—	2	2	no	—
314	C₂×Q₈×C₅₃	—	2	1	no	—
315	C₂×Q₈×C₅₃	—	2	2	no	—
316	C₂×Q₈×C₅₃	—	2	2	no	—
317	C₂×Q₈×C₅₃	—	2	4	no	—
318	C₂×Q₈×C₅₃	—	2	4	no	—
319	C₂×Q₈×C₅₃	—	4	1	no	—
320	C₂×Q₈×C₅₃	—	4	1	no	—
321	C₂×Q₈×C₅₃	—	4	2	no	—
322	C₂×Q₈×C₅₃	—	4	2	no	—
323	C₂×Q₈×C₅₃	—	4	1	no	—
324	C₂×Q₈×C₅₃	—	4	1	no	—
325	C₂×Q₈×C₅₃	—	4	4	no	—
326	C₂×Q₈×C₅₃	—	4	1	no	—
327	C₂×Q₈×C₅₃	—	4	1	no	—
328	C₂×Q₈×C₅₃	—	4	8	no	—
329	C₂×Q₈×C₅₃	—	4	4	no	—
330	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
335	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₅₃	—	2	2	no	—
337	C₂×D₄×C₅₃	—	2	1	no	—
338	C₂×D₄×C₅₃	—	2	1	no	—
339	C₂×D₄×C₅₃	—	2	1	no	—
340	C₂×D₄×C₅₃	—	2	2	no	—
341	C₂×D₄×C₅₃	—	2	2	no	—
342	C₂×D₄×C₅₃	—	2	2	no	—
343	C₂×D₄×C₅₃	—	2	2	no	—
344	C₂×D₄×C₅₃	—	2	1	no	—
345	C₂×D₄×C₅₃	—	4	1	no	—
346	C₂×D₄×C₅₃	—	4	1	no	—
347	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
352	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₅₃	—	2	1	no	—
355	C₂²×C₄×C₅₃	—	2	2	no	—
356	C₂²×C₄×C₅₃	—	2	2	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	1	no	—
361	C₂²×C₄×C₅₃	—	2	1	no	—
362	C₂²×C₄×C₅₃	—	2	1	no	—
363	C₂²×C₄×C₅₃	—	2	1	no	—
364	C₂²×C₄×C₅₃	—	2	2	no	—
365	C₂²×C₄×C₅₃	—	2	2	no	—
366	C₂²×C₄×C₅₃	—	4	1	no	—
367	C₂²×C₄×C₅₃	—	4	1	no	—
368	C₂²×C₄×C₅₃	—	4	4	no	—
369	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
370	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
375	Q₁₆×C₅₃	—	2	4	no	—
376	Q₁₆×C₅₃	—	2	4	no	—
377	Q₁₆×C₅₃	—	4	2	no	—
378	Q₁₆×C₅₃	—	4	2	no	—
379	Q₁₆×C₅₃	—	4	2	no	—
380	SD₁₆×C₅₃	—	2	4	no	—
381	SD₁₆×C₅₃	—	2	4	no	—
382	SD₁₆×C₅₃	—	4	2	no	—
383	SD₁₆×C₅₃	—	4	2	no	—
384	SD₁₆×C₅₃	—	4	2	no	—
385	SD₁₆×C₅₃	—	4	2	no	—
386	D₈×C₅₃	—	4	2	no	—
387	M₁₆×C₅₃	—	4	1	no	—
388	M₁₆×C₅₃	—	4	2	no	—
389	M₁₆×C₅₃	—	4	2	no	—
390	M₁₆×C₅₃	—	4	1	no	—
391	C₂×C₈×C₅₃	—	4	1	no	—
392	C₂×C₈×C₅₃	—	4	1	no	—
393	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
394	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
395	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
396	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
397	C₄⋊C₄×C₅₃	—	2	2	no	—
398	C₄⋊C₄×C₅₃	—	2	2	no	—
399	C₄⋊C₄×C₅₃	—	2	2	no	—
400	C₄⋊C₄×C₅₃	—	2	2	no	—
401	C₄⋊C₄×C₅₃	—	2	2	no	—
402	C₄⋊C₄×C₅₃	—	2	2	no	—
403	C₄⋊C₄×C₅₃	—	2	2	no	—
404	C₄⋊C₄×C₅₃	—	2	2	no	—
405	C₄⋊C₄×C₅₃	—	2	2	no	—
406	C₄⋊C₄×C₅₃	—	2	2	no	—
407	C₄⋊C₄×C₅₃	—	2	2	no	—
408	C₄⋊C₄×C₅₃	—	2	2	no	—
409	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
415	C₂²⋊C₄×C₅₃	—	2	2	no	—
416	C₂²⋊C₄×C₅₃	—	2	1	no	—
417	C₂²⋊C₄×C₅₃	—	2	1	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	2	no	—
422	C₂²⋊C₄×C₅₃	—	2	2	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	2	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	2	no	—
431	C₂²⋊C₄×C₅₃	—	2	2	no	—
432	C₂²⋊C₄×C₅₃	—	2	2	no	—
433	C₂²⋊C₄×C₅₃	—	2	2	no	—
434	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
436	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
437	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
440	C₄²×C₅₃	—	2	1	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	—	2	1	no	—
446	C₄²×C₅₃	—	2	2	no	—
447	C₄²×C₅₃	C₂⁴	1	2	yes	—
448	C₂³×C₅₃	—	2	1	no	—
449	C₂³×C₅₃	—	2	2	no	—
450	C₂³×C₅₃	—	4	1	no	—
451	C₂³×C₅₃	—	4	2	no	—
452	C₂³×C₅₃	—	8	1	no	—
453	C₂³×C₅₃	—	8	2	no	—
454	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
455	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
456	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
457	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
458	Q₈×C₅₃	—	2	4	no	—
459	Q₈×C₅₃	—	2	1	no	—
460	Q₈×C₅₃	—	2	1	no	—
461	Q₈×C₅₃	—	2	2	no	—
462	Q₈×C₅₃	—	2	2	no	—
463	Q₈×C₅₃	—	2	1	no	—
464	Q₈×C₅₃	—	2	1	no	—
465	Q₈×C₅₃	—	2	2	no	—
466	Q₈×C₅₃	—	2	2	no	—
467	Q₈×C₅₃	—	4	1	no	—
468	Q₈×C₅₃	—	4	4	no	—
469	Q₈×C₅₃	—	4	4	no	—
470	Q₈×C₅₃	—	4	2	no	—
471	Q₈×C₅₃	—	4	2	no	—
472	Q₈×C₅₃	—	4	2	no	—
473	Q₈×C₅₃	—	8	2	no	—
474	Q₈×C₅₃	—	8	1	no	—
475	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
476	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
477	D₄×C₅₃	—	2	2	no	—
478	D₄×C₅₃	—	2	2	no	—
479	D₄×C₅₃	—	2	1	no	—
480	D₄×C₅₃	—	2	1	no	—
481	D₄×C₅₃	—	4	2	no	—
482	D₄×C₅₃	—	4	2	no	—
483	D₄×C₅₃	—	4	1	no	—
484	D₄×C₅₃	—	4	1	no	—
485	D₄×C₅₃	—	4	1	no	—
486	D₄×C₅₃	—	4	2	no	—
487	D₄×C₅₃	—	4	2	no	—
488	D₄×C₅₃	—	4	4	no	—
489	D₄×C₅₃	—	4	2	no	—
490	D₄×C₅₃	—	8	1	no	—
491	D₄×C₅₃	—	8	2	no	—
492	D₄×C₅₃	—	8	2	no	—
493	D₄×C₅₃	—	8	2	no	—
494	D₄×C₅₃	—	8	2	no	—
495	C₂×C₄×C₅₃	—	2	4	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	1	no	—
504	C₂×C₄×C₅₃	—	2	1	no	—
505	C₂×C₄×C₅₃	—	2	1	no	—
506	C₂×C₄×C₅₃	—	2	1	no	—
507	C₂×C₄×C₅₃	—	2	2	no	—
508	C₂×C₄×C₅₃	—	2	2	no	—
509	C₂×C₄×C₅₃	—	2	2	no	—
510	C₂×C₄×C₅₃	—	2	2	no	—
511	C₂×C₄×C₅₃	—	2	2	no	—
512	C₂×C₄×C₅₃	—	4	2	no	—
513	C₂×C₄×C₅₃	—	4	1	no	—
514	C₂×C₄×C₅₃	—	4	2	no	—
515	C₂×C₄×C₅₃	—	4	2	no	—
516	C₂×C₄×C₅₃	—	4	4	no	—
517	C₂×C₄×C₅₃	—	4	4	no	—
518	C₂×C₄×C₅₃	—	4	2	no	—
519	C₂×C₄×C₅₃	—	4	2	no	—
520	C₂×C₄×C₅₃	—	4	2	no	—
521	C₂×C₄×C₅₃	—	4	2	no	—
522	C₂×C₄×C₅₃	—	8	2	no	—
523	C₂×C₄×C₅₃	—	8	2	no	—
524	C₂×C₄×C₅₃	—	8	1	no	—
525	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
532	C₈×C₅₃	—	2	2	no	—
533	C₈×C₅₃	—	2	2	no	—
534	C₈×C₅₃	—	2	2	no	—
535	C₈×C₅₃	—	2	2	no	—
536	#61646	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
537	C₂²×C₅₃	—	2	2	no	—
538	C₂²×C₅₃	—	2	2	no	—
539	C₂²×C₅₃	—	2	2	no	—
540	C₂²×C₅₃	—	2	2	no	—
541	C₂²×C₅₃	—	2	2	no	—
542	C₂²×C₅₃	—	2	1	no	—
543	C₂²×C₅₃	—	2	2	no	—
544	C₂²×C₅₃	—	2	1	no	—
545	C₂²×C₅₃	—	2	1	no	—
546	C₂²×C₅₃	—	4	4	no	—
547	C₂²×C₅₃	—	4	2	no	—
548	C₂²×C₅₃	—	4	2	no	—
549	C₂²×C₅₃	—	4	2	no	—
550	C₂²×C₅₃	—	4	1	no	—
551	C₂²×C₅₃	—	4	2	no	—
552	C₂²×C₅₃	—	16	2	no	—
553	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
554	C₄×C₅₃	—	2	2	no	—
555	C₄×C₅₃	—	2	2	no	—
556	C₄×C₅₃	—	2	2	no	—
557	C₄×C₅₃	—	2	2	no	—
558	C₄×C₅₃	—	2	1	no	—
559	C₄×C₅₃	—	2	2	no	—
560	C₄×C₅₃	—	2	1	no	—
561	C₄×C₅₃	—	2	1	no	—
562	C₄×C₅₃	—	4	2	no	—
563	C₄×C₅₃	—	4	2	no	—
564	C₄×C₅₃	—	4	2	no	—
565	C₄×C₅₃	—	4	1	no	—
566	C₄×C₅₃	—	4	2	no	—
567	C₄×C₅₃	—	4	2	no	—
568	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
569	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
570	#3540	C₂×C₅₃	1	1	yes	characteristic, complemented
571	#3486	C₂×C₅₃	1	1	yes	characteristic, complemented
572	#3329	C₂×C₅₃	1	2	yes	complemented
573	#3328	C₂×C₅₃	1	2	yes	complemented
574	#3321	C₂×C₅₃	1	2	yes	complemented
575	#3313	C₂×C₅₃	1	2	yes	complemented
576	#3277	C₂×C₅₃	1	2	yes	complemented
577	#3275	C₂×C₅₃	1	2	yes	complemented
578	#3270	C₂×C₅₃	1	2	yes	complemented
579	#3266	C₂×C₅₃	1	2	yes	complemented
580	#3225	C₂×C₅₃	1	2	yes	complemented
581	#3202	C₂×C₅₃	1	1	yes	characteristic, complemented
582	#3200	C₂×C₅₃	1	1	yes	characteristic, complemented
583	#3197	C₂×C₅₃	1	2	yes	complemented
584	#3121	C₂×C₅₃	1	2	yes	complemented
585	#3011	C₂×C₅₃	1	1	yes	characteristic, complemented
586	#3010	C₂×C₅₃	1	1	yes	characteristic, complemented
587	#3004	C₂×C₅₃	1	2	yes	complemented
588	#2978	C₂×C₅₃	1	1	yes	characteristic, complemented
589	C₂×C₅₃	—	4	1	no	—
590	C₂×C₅₃	—	4	2	no	—
591	C₂×C₅₃	—	4	1	no	—
592	C₂×C₅₃	—	4	1	no	—
593	C₂×C₅₃	—	8	1	no	—
594	C₂×C₅₃	—	8	2	no	—
595	C₂×C₅₃	#3484	1	1	yes	characteristic
596	C₂×C₅₃	#3586	1	2	yes	—
597	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic
598	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
599	C₂×#137	C₂²×C₅₃	1	2	yes	—
600	C₂×#137	C₂²×C₅₃	1	2	yes	—
601	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
602	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
603	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
604	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
605	H(3,𝔽₄)	—	2	1	no	—
606	#560	—	2	1	no	—
607	#559	—	2	1	no	—
608	#556	C₂²×C₅₃	1	2	yes	—
609	#555	C₂²×C₅₃	1	2	yes	—
610	#551	—	2	1	no	—
611	D₄×Q₈	—	2	2	no	—
612	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
613	D₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
614	#548	—	2	2	no	—
615	#548	C₂²×C₅₃	1	2	yes	—
616	#548	C₂²×C₅₃	1	2	yes	—
617	#548	C₂²×C₅₃	1	2	yes	complemented
618	#546	C₂²×C₅₃	1	2	yes	—
619	#542	—	2	2	no	—
620	#542	C₂²×C₅₃	1	2	yes	—
621	#538	—	2	2	no	—
622	#536	—	2	1	no	—
623	#536	—	2	1	no	—
624	#536	C₂²×C₅₃	1	1	yes	characteristic
625	#536	C₂²×C₅₃	1	1	yes	characteristic
626	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
627	#535	C₂²×C₅₃	1	1	yes	characteristic
628	#525	—	2	1	no	—
629	#525	—	2	1	no	—
630	#525	C₂²×C₅₃	1	2	yes	—
631	#525	C₂²×C₅₃	1	1	yes	characteristic
632	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
633	#519	C₂²×C₅₃	1	1	yes	characteristic, complemented
634	#497	C₂²×C₅₃	1	2	yes	complemented
635	#495	C₂²×C₅₃	1	2	yes	complemented
636	#489	C₂²×C₅₃	1	2	yes	complemented
637	#487	C₂²×C₅₃	1	2	yes	complemented
638	#485	C₂²×C₅₃	1	2	yes	complemented
639	#485	C₂²×C₅₃	1	2	yes	complemented
640	#485	C₂²×C₅₃	1	2	yes	complemented
641	#485	C₂²×C₅₃	1	2	yes	complemented
642	#482	C₂²×C₅₃	1	2	yes	—
643	#482	C₂²×C₅₃	1	2	yes	complemented
644	#477	C₂²×C₅₃	1	2	yes	complemented
645	#475	C₂²×C₅₃	1	2	yes	complemented
646	#470	C₂²×C₅₃	1	2	yes	complemented
647	#470	C₂²×C₅₃	1	2	yes	complemented
648	#469	C₂²×C₅₃	1	2	yes	—
649	#468	C₂²×C₅₃	1	2	yes	—
650	#468	C₂²×C₅₃	1	2	yes	complemented
651	#468	C₂²×C₅₃	1	2	yes	complemented
652	#467	C₂²×C₅₃	1	2	yes	complemented
653	#465	C₂²×C₅₃	1	2	yes	complemented
654	#464	C₂²×C₅₃	1	2	yes	complemented
655	#464	C₂²×C₅₃	1	2	yes	complemented
656	#464	C₂²×C₅₃	1	2	yes	complemented
657	#463	C₂²×C₅₃	1	2	yes	complemented
658	#462	C₂²×C₅₃	1	2	yes	complemented
659	#461	C₂²×C₅₃	1	2	yes	complemented
660	#452	C₂²×C₅₃	1	2	yes	—
661	#452	C₂²×C₅₃	1	2	yes	complemented
662	#452	C₂²×C₅₃	1	2	yes	complemented
663	#451	C₂²×C₅₃	1	2	yes	complemented
664	#451	C₂²×C₅₃	1	2	yes	complemented
665	#451	C₂²×C₅₃	1	2	yes	complemented
666	#451	C₂²×C₅₃	1	2	yes	complemented
667	#451	C₂²×C₅₃	1	2	yes	complemented
668	#451	C₂²×C₅₃	1	2	yes	complemented
669	#450	C₂²×C₅₃	1	2	yes	complemented
670	#449	C₂²×C₅₃	1	2	yes	—
671	#449	C₂²×C₅₃	1	2	yes	—
672	#449	C₂²×C₅₃	1	2	yes	complemented
673	#448	C₂²×C₅₃	1	2	yes	—
674	#448	C₂²×C₅₃	1	2	yes	—
675	#448	C₂²×C₅₃	1	2	yes	—
676	#448	C₂²×C₅₃	1	2	yes	—
677	#448	C₂²×C₅₃	1	2	yes	complemented
678	#441	C₂²×C₅₃	1	2	yes	complemented
679	#440	C₂²×C₅₃	1	2	yes	complemented
680	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
681	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
682	#436	C₂²×C₅₃	1	2	yes	—
683	#436	C₂²×C₅₃	1	2	yes	complemented
684	#435	C₂²×C₅₃	1	2	yes	—
685	#435	C₂²×C₅₃	1	2	yes	complemented
686	#433	C₂²×C₅₃	1	2	yes	complemented
687	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
688	#419	C₂²×C₅₃	1	2	yes	complemented
689	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
690	#419	C₂²×C₅₃	1	2	yes	complemented
691	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
692	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	#408	C₂²×C₅₃	1	1	yes	characteristic
694	#408	C₂²×C₅₃	1	1	yes	characteristic
695	#407	C₂²×C₅₃	1	2	yes	complemented
696	C₅₃	#61646	1	1	yes	characteristic, direct product factor, Sylow
697	2₋¹⁺⁴	—	4	2	no	—
698	2₋¹⁺⁴	—	4	2	no	—
699	C₂×#41	—	2	1	no	—
700	C₂×#41	—	2	1	no	—
701	C₂×#41	—	2	1	no	—
702	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
703	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
704	C₂×#41	C₂³×C₅₃	1	2	yes	—
705	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
706	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
707	C₂²×Q₈	—	2	1	no	—
708	C₂²×Q₈	—	2	1	no	—
709	C₂²×Q₈	—	2	2	no	—
710	C₂²×Q₈	—	4	2	no	—
711	C₂²×Q₈	—	4	2	no	—
712	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
713	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
714	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
715	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
716	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
717	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
718	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
719	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
720	C₂³×C₄	—	2	1	no	—
721	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
722	#137	—	4	4	no	—
723	#137	—	4	4	no	—
724	#137	—	4	2	no	—
725	AGL(1,ℤ/8)	—	4	2	no	—
726	C₂×Q₁₆	—	4	2	no	—
727	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
728	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
730	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
731	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
732	C₂×SD₁₆	—	4	2	no	—
733	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
739	C₂×D₈	C₂³×C₅₃	1	2	yes	—
740	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
741	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
742	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
743	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
744	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
745	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
746	C₄⋊Q₈	—	2	1	no	—
747	C₄⋊Q₈	—	2	1	no	—
748	C₄⋊Q₈	—	2	2	no	—
749	C₄⋊Q₈	—	2	2	no	—
750	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
751	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
752	#127	—	2	1	no	—
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#124	—	2	1	no	—
757	#124	—	2	1	no	—
758	#124	—	2	1	no	—
759	#124	—	2	2	no	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	—	2	2	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	C₂³×C₅₃	1	2	yes	—
767	#124	C₂³×C₅₃	1	2	yes	—
768	#123	—	2	1	no	—
769	#123	—	2	1	no	—
770	#123	—	2	1	no	—
771	#123	—	2	1	no	—
772	#123	—	2	2	no	—
773	#123	—	2	1	no	—
774	#123	—	2	2	no	—
775	#123	—	2	1	no	—
776	#123	—	2	1	no	—
777	#123	—	2	2	no	—
778	#123	D₄×C₅₃	1	1	yes	characteristic
779	#123	D₄×C₅₃	1	1	yes	characteristic
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
790	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
791	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
792	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
795	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	D₄×C₅₃	1	2	yes	—
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	1	no	—
807	#120	—	2	2	no	—
808	#120	—	2	1	no	—
809	#120	—	2	1	no	—
810	#120	—	2	2	no	—
811	#120	D₄×C₅₃	1	1	yes	characteristic
812	#120	D₄×C₅₃	1	1	yes	characteristic
813	C₄×Q₈	—	2	2	no	—
814	C₄×Q₈	—	2	2	no	—
815	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
816	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
817	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	C₂³×C₅₃	1	2	yes	—
827	C₄×D₄	C₂³×C₅₃	1	2	yes	—
828	C₄×D₄	C₂³×C₅₃	1	2	yes	—
829	#117	—	2	2	no	—
830	#117	—	2	1	no	—
831	#117	—	2	1	no	—
832	#117	C₂³×C₅₃	1	1	yes	characteristic
833	#117	C₂³×C₅₃	1	2	yes	—
834	#117	C₂³×C₅₃	1	1	yes	characteristic
835	#117	C₂³×C₅₃	1	1	yes	characteristic
836	#117	C₂³×C₅₃	1	1	yes	characteristic
837	C₂×C₂²⋊C₄	—	2	2	no	—
838	#107	C₂³×C₅₃	1	2	yes	—
839	#107	C₂³×C₅₃	1	2	yes	—
840	#106	C₂³×C₅₃	1	2	yes	—
841	#106	C₂³×C₅₃	1	2	yes	—
842	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
843	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
844	#103	C₂³×C₅₃	1	2	yes	—
845	#103	C₂³×C₅₃	1	2	yes	—
846	#103	C₂³×C₅₃	1	2	yes	—
847	#103	C₂³×C₅₃	1	2	yes	—
848	#103	C₂³×C₅₃	1	2	yes	—
849	#103	C₂³×C₅₃	1	2	yes	—
850	#103	C₂³×C₅₃	1	2	yes	—
851	#103	C₂³×C₅₃	1	2	yes	—
852	#103	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	#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	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
861	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
862	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
863	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
864	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
866	#97	C₂³×C₅₃	1	2	yes	—
867	C₄×C₈	C₂³×C₅₃	1	2	yes	—
868	C₂⁴	—	2	1	no	—
869	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
870	#41	—	2	2	no	—
871	#41	—	2	2	no	—
872	#41	—	4	1	no	—
873	#41	—	4	1	no	—
874	#41	—	4	1	no	—
875	#41	—	4	1	no	—
876	#41	—	4	1	no	—
877	#41	—	4	1	no	—
878	#41	—	4	4	no	—
879	#41	—	4	4	no	—
880	#41	—	4	2	no	—
881	#41	—	4	2	no	—
882	#41	—	4	4	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	—	2	2	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	1	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	2	no	—
892	C₂×Q₈	—	2	1	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	2	no	—
895	C₂×Q₈	—	2	4	no	—
896	C₂×Q₈	—	2	4	no	—
897	C₂×Q₈	—	4	2	no	—
898	C₂×Q₈	—	4	2	no	—
899	C₂×Q₈	—	4	1	no	—
900	C₂×Q₈	—	4	1	no	—
901	C₂×Q₈	—	4	1	no	—
902	C₂×Q₈	—	4	1	no	—
903	C₂×Q₈	—	4	4	no	—
904	C₂×Q₈	—	4	1	no	—
905	C₂×Q₈	—	4	1	no	—
906	C₂×Q₈	—	4	8	no	—
907	C₂×Q₈	—	4	4	no	—
908	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
909	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
910	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
912	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	4	1	no	—
924	C₂×D₄	—	4	1	no	—
925	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
926	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
927	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
928	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
929	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
930	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
931	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	4	1	no	—
945	C₂²×C₄	—	4	1	no	—
946	C₂²×C₄	—	4	4	no	—
947	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
948	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
952	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
953	Q₁₆	—	2	4	no	—
954	Q₁₆	—	2	4	no	—
955	Q₁₆	—	4	2	no	—
956	Q₁₆	—	4	2	no	—
957	Q₁₆	—	4	2	no	—
958	SD₁₆	—	2	4	no	—
959	SD₁₆	—	2	4	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	—	4	2	no	—
962	SD₁₆	—	4	2	no	—
963	SD₁₆	—	4	2	no	—
964	D₈	—	4	2	no	—
965	M₁₆	—	4	1	no	—
966	M₁₆	—	4	2	no	—
967	M₁₆	—	4	2	no	—
968	M₁₆	—	4	1	no	—
969	C₂×C₈	—	4	1	no	—
970	C₂×C₈	—	4	1	no	—
971	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
972	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
973	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
974	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
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	2	yes	—
991	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
992	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1014	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1015	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	C₂⁴×C₅₃	1	2	yes	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	2	no	—
1028	C₂³	—	4	1	no	—
1029	C₂³	—	4	2	no	—
1030	C₂³	—	8	1	no	—
1031	C₂³	—	8	2	no	—
1032	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1033	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1034	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1035	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1036	Q₈	—	2	4	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	2	2	no	—
1041	Q₈	—	2	2	no	—
1042	Q₈	—	2	2	no	—
1043	Q₈	—	2	2	no	—
1044	Q₈	—	2	1	no	—
1045	Q₈	—	4	1	no	—
1046	Q₈	—	4	4	no	—
1047	Q₈	—	4	4	no	—
1048	Q₈	—	4	2	no	—
1049	Q₈	—	4	2	no	—
1050	Q₈	—	4	2	no	—
1051	Q₈	—	8	2	no	—
1052	Q₈	—	8	1	no	—
1053	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1054	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1055	D₄	—	2	1	no	—
1056	D₄	—	2	2	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	4	2	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	4	1	no	—
1062	D₄	—	4	1	no	—
1063	D₄	—	4	1	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	8	1	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	2	no	—
1073	C₂×C₄	—	2	4	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	4	no	—
1095	C₂×C₄	—	4	4	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	1	no	—
1103	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1104	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
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	1	yes	characteristic
1109	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1110	C₈	—	2	2	no	—
1111	C₈	—	2	2	no	—
1112	C₈	—	2	2	no	—
1113	C₈	—	2	2	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	4	4	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	16	2	no	—
1130	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1131	C₄	—	2	2	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	2	no	—
1145	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1146	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1147	C₂	—	4	1	no	—
1148	C₂	—	4	2	no	—
1149	C₂	—	4	1	no	—
1150	C₂	—	4	1	no	—
1151	C₂	—	8	2	no	—
1152	C₂	—	8	1	no	—
1153	C₂	C₅₃×#3484	1	1	yes	characteristic
1154	C₂	C₅₃×#3586	1	2	yes	—

	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3540	C₂	semidirect
2. C₅₃×#3486	C₂	semidirect
3. C₅₃×#3329	C₂	semidirect
4. C₅₃×#3328	C₂	semidirect
5. C₅₃×#3321	C₂	semidirect
6. C₅₃×#3313	C₂	semidirect
7. C₅₃×#3277	C₂	semidirect
8. C₅₃×#3275	C₂	semidirect
9. C₅₃×#3270	C₂	semidirect
10. C₅₃×#3266	C₂	semidirect
11. C₅₃×#3225	C₂	semidirect
12. C₅₃×#3202	C₂	semidirect
13. C₅₃×#3200	C₂	semidirect
14. C₅₃×#3197	C₂	semidirect
15. C₅₃×#3121	C₂	semidirect
16. C₅₃×#3011	C₂	semidirect
17. C₅₃×#3010	C₂	semidirect
18. C₅₃×#3004	C₂	semidirect
19. C₅₃×#2978	C₂	semidirect
21. C₂³×Q₈×C₅₃	C₂²	semidirect
24. C₂×#137×C₅₃	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
26. C₂²×Q₁₆×C₅₃	C₂²	semidirect
27. C₂²×SD₁₆×C₅₃	C₂²	semidirect
36. D₄×Q₈×C₅₃	C₂²	semidirect
40. C₅₃×#548	C₂²	semidirect
49. C₅₃×#536	C₂²	semidirect
55. C₅₃×#525	C₂²	semidirect
56. C₅₃×#519	C₂²	semidirect
57. C₅₃×#497	C₂²	semidirect
58. C₅₃×#495	C₂²	semidirect
59. C₅₃×#489	C₂²	semidirect
60. C₅₃×#487	C₂²	semidirect
61. C₅₃×#485	C₂²	semidirect
62. C₅₃×#485	C₂²	semidirect
63. C₅₃×#485	C₂²	semidirect
64. C₅₃×#485	C₂²	semidirect
66. C₅₃×#482	C₂²	semidirect
67. C₅₃×#477	C₂²	semidirect
68. C₅₃×#475	C₂²	semidirect
69. C₅₃×#470	C₂²	semidirect
70. C₅₃×#470	C₂²	semidirect
73. C₅₃×#468	C₂²	semidirect
74. C₅₃×#468	C₂²	semidirect
75. C₅₃×#467	C₂²	semidirect
76. C₅₃×#465	C₂²	semidirect
77. C₅₃×#464	C₂²	semidirect
78. C₅₃×#464	C₂²	semidirect
79. C₅₃×#464	C₂²	semidirect
80. C₅₃×#463	C₂²	semidirect
81. C₅₃×#462	C₂²	semidirect
82. C₅₃×#461	C₂²	semidirect
84. C₅₃×#452	C₂²	semidirect
85. C₅₃×#452	C₂²	semidirect
86. C₅₃×#451	C₂²	semidirect
87. C₅₃×#451	C₂²	semidirect
88. C₅₃×#451	C₂²	semidirect
89. C₅₃×#451	C₂²	semidirect
90. C₅₃×#451	C₂²	semidirect
91. C₅₃×#451	C₂²	semidirect
92. C₅₃×#450	C₂²	semidirect
95. C₅₃×#449	C₂²	semidirect
100. C₅₃×#448	C₂²	semidirect
101. C₅₃×#441	C₂²	semidirect
102. C₅₃×#440	C₂²	semidirect
103. C₄×Q₁₆×C₅₃	C₂²	semidirect
104. C₄×SD₁₆×C₅₃	C₂²	semidirect
106. C₅₃×#436	C₂²	semidirect
108. C₅₃×#435	C₂²	semidirect
109. C₅₃×#433	C₂²	semidirect
110. C₅₃×#419	C₂²	semidirect
111. C₅₃×#419	C₂²	semidirect
112. C₅₃×#419	C₂²	semidirect
113. C₅₃×#419	C₂²	semidirect
114. C₅₃×#416	C₂²	semidirect
115. C₅₃×#416	C₂²	semidirect
118. C₅₃×#407	C₂²	semidirect
536. #61646	C₅₃	direct (N × H)
570. #3540	C₂×C₅₃	semidirect
571. #3486	C₂×C₅₃	semidirect
572. #3329	C₂×C₅₃	semidirect
573. #3328	C₂×C₅₃	semidirect
574. #3321	C₂×C₅₃	semidirect
575. #3313	C₂×C₅₃	semidirect
576. #3277	C₂×C₅₃	semidirect
577. #3275	C₂×C₅₃	semidirect
578. #3270	C₂×C₅₃	semidirect
579. #3266	C₂×C₅₃	semidirect
580. #3225	C₂×C₅₃	semidirect
581. #3202	C₂×C₅₃	semidirect
582. #3200	C₂×C₅₃	semidirect
583. #3197	C₂×C₅₃	semidirect
584. #3121	C₂×C₅₃	semidirect
585. #3011	C₂×C₅₃	semidirect
586. #3010	C₂×C₅₃	semidirect
587. #3004	C₂×C₅₃	semidirect
588. #2978	C₂×C₅₃	semidirect
598. C₂³×Q₈	C₂²×C₅₃	semidirect
601. C₂×#137	C₂²×C₅₃	semidirect
602. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
603. C₂²×Q₁₆	C₂²×C₅₃	semidirect
604. C₂²×SD₁₆	C₂²×C₅₃	semidirect
613. D₄×Q₈	C₂²×C₅₃	semidirect
617. #548	C₂²×C₅₃	semidirect
626. #536	C₂²×C₅₃	semidirect
632. #525	C₂²×C₅₃	semidirect
633. #519	C₂²×C₅₃	semidirect
634. #497	C₂²×C₅₃	semidirect
635. #495	C₂²×C₅₃	semidirect
636. #489	C₂²×C₅₃	semidirect
637. #487	C₂²×C₅₃	semidirect
638. #485	C₂²×C₅₃	semidirect
639. #485	C₂²×C₅₃	semidirect
640. #485	C₂²×C₅₃	semidirect
641. #485	C₂²×C₅₃	semidirect
643. #482	C₂²×C₅₃	semidirect
644. #477	C₂²×C₅₃	semidirect
645. #475	C₂²×C₅₃	semidirect
646. #470	C₂²×C₅₃	semidirect
647. #470	C₂²×C₅₃	semidirect
650. #468	C₂²×C₅₃	semidirect
651. #468	C₂²×C₅₃	semidirect
652. #467	C₂²×C₅₃	semidirect
653. #465	C₂²×C₅₃	semidirect
654. #464	C₂²×C₅₃	semidirect
655. #464	C₂²×C₅₃	semidirect
656. #464	C₂²×C₅₃	semidirect
657. #463	C₂²×C₅₃	semidirect
658. #462	C₂²×C₅₃	semidirect
659. #461	C₂²×C₅₃	semidirect
661. #452	C₂²×C₅₃	semidirect
662. #452	C₂²×C₅₃	semidirect
663. #451	C₂²×C₅₃	semidirect
664. #451	C₂²×C₅₃	semidirect
665. #451	C₂²×C₅₃	semidirect
666. #451	C₂²×C₅₃	semidirect
667. #451	C₂²×C₅₃	semidirect
668. #451	C₂²×C₅₃	semidirect
669. #450	C₂²×C₅₃	semidirect
672. #449	C₂²×C₅₃	semidirect
677. #448	C₂²×C₅₃	semidirect
678. #441	C₂²×C₅₃	semidirect
679. #440	C₂²×C₅₃	semidirect
680. C₄×Q₁₆	C₂²×C₅₃	semidirect
681. C₄×SD₁₆	C₂²×C₅₃	semidirect
683. #436	C₂²×C₅₃	semidirect
685. #435	C₂²×C₅₃	semidirect
686. #433	C₂²×C₅₃	semidirect
687. #419	C₂²×C₅₃	semidirect
688. #419	C₂²×C₅₃	semidirect
689. #419	C₂²×C₅₃	semidirect
690. #419	C₂²×C₅₃	semidirect
691. #416	C₂²×C₅₃	semidirect
692. #416	C₂²×C₅₃	semidirect
695. #407	C₂²×C₅₃	semidirect
696. C₅₃	#61646	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×#3540	2
C₅₃×#3486	2
C₅₃×#3329	2
C₅₃×#3328	2
C₅₃×#3321	2
C₅₃×#3313	2
C₅₃×#3277	2
C₅₃×#3275	2
C₅₃×#3270	2
C₅₃×#3266	2
C₅₃×#3225	2
C₅₃×#3202	2
C₅₃×#3200	2
C₅₃×#3197	2
C₅₃×#3121	2
C₅₃×#3011	2
C₅₃×#3010	2
C₅₃×#3004	2
C₅₃×#2978	2
#61646	53

Subgroups — C53×#61646 #27269158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61646 #27269158