Subgroups — C₅₃×#61598 #27269110

Order 13568.

2392 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3308	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3306	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3298	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3265	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3264	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3194	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3188	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3006	C₂	1	2	yes	maximal, complemented
22	C₂×C₅₃×#449	C₂	1	2	yes	maximal, complemented
23	C₅₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₅₃	—	2	1	no	—
25	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
27	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
28	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
29	C₂²×D₈×C₅₃	C₂²	1	2	yes	complemented
30	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
31	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
32	C₅₃×#548	C₂²	1	2	yes	complemented
33	C₅₃×#547	—	2	1	no	—
34	C₅₃×#547	C₂²	1	1	yes	characteristic
35	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#547	C₂²	1	2	yes	complemented
37	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#546	—	2	1	no	—
39	C₅₃×#546	—	2	2	no	—
40	C₅₃×#546	—	2	1	no	—
41	C₅₃×#546	—	2	2	no	—
42	C₅₃×#546	C₂²	1	2	yes	complemented
43	D₄²×C₅₃	—	2	1	no	—
44	D₄²×C₅₃	C₂²	1	1	yes	characteristic
45	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
46	D₄²×C₅₃	C₂²	1	2	yes	complemented
47	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#537	—	2	1	no	—
49	C₅₃×#534	—	2	2	no	—
50	C₅₃×#532	—	2	1	no	—
51	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#525	—	2	2	no	—
55	C₅₃×#525	C₂²	1	2	yes	complemented
56	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
57	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
58	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×D₄×C₅₃	—	2	1	no	—
60	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
61	C₅₃×#496	C₂²	1	2	yes	complemented
62	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#489	C₂²	1	2	yes	complemented
65	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#484	C₂²	1	2	yes	complemented
68	C₅₃×#483	C₂²	1	2	yes	complemented
69	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#482	C₂²	1	2	yes	complemented
71	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#481	C₂²	1	2	yes	complemented
73	C₅₃×#480	C₂²	1	2	yes	complemented
74	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#469	C₂²	1	2	yes	complemented
79	C₅₃×#469	C₂²	1	2	yes	complemented
80	C₅₃×#468	C₂²	1	2	yes	complemented
81	C₅₃×#468	C₂²	1	2	yes	complemented
82	C₅₃×#466	C₂²	1	2	yes	complemented
83	C₅₃×#466	C₂²	1	2	yes	complemented
84	C₅₃×#465	C₂²	1	2	yes	complemented
85	C₅₃×#465	C₂²	1	2	yes	complemented
86	C₅₃×#463	C₂²	1	2	yes	complemented
87	C₅₃×#463	C₂²	1	2	yes	complemented
88	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#450	C₂²	1	2	yes	complemented
97	C₅₃×#450	C₂²	1	2	yes	complemented
98	C₅₃×#449	C₂²	1	2	yes	complemented
99	C₅₃×#449	C₂²	1	2	yes	complemented
100	C₅₃×#449	C₂²	1	2	yes	complemented
101	C₅₃×#449	C₂²	1	2	yes	complemented
102	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#449	C₂²	1	2	yes	complemented
104	C₅₃×#449	C₂²	1	2	yes	complemented
105	C₅₃×#449	C₂²	1	2	yes	complemented
106	C₅₃×#449	C₂²	1	2	yes	complemented
107	C₅₃×#449	C₂²	1	2	yes	complemented
108	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#448	C₂²	1	2	yes	complemented
110	C₅₃×#448	C₂²	1	2	yes	complemented
111	C₅₃×#447	C₂²	1	2	yes	complemented
112	C₅₃×#447	C₂²	1	2	yes	complemented
113	C₅₃×#447	C₂²	1	2	yes	complemented
114	C₅₃×#447	C₂²	1	2	yes	complemented
115	C₅₃×#442	C₂²	1	2	yes	complemented
116	C₅₃×#440	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#435	C₂²	1	2	yes	complemented
124	C₅₃×#435	C₂²	1	2	yes	complemented
125	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
126	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#417	C₂²	1	2	yes	complemented
130	C₅₃×#417	C₂²	1	2	yes	complemented
131	C₂×#103×C₅₃	C₂²	1	2	yes	complemented
132	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
133	C₅₃×#407	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	complemented
135	H(5,𝔽₂)×C₅₃	—	4	8	no	—
136	C₂×#41×C₅₃	—	2	1	no	—
137	C₂×#41×C₅₃	—	2	2	no	—
138	C₂×#41×C₅₃	—	2	1	no	—
139	C₂×#41×C₅₃	—	2	2	no	—
140	C₂×#41×C₅₃	—	2	1	no	—
141	C₂×#41×C₅₃	—	2	1	no	—
142	C₂×#41×C₅₃	—	2	2	no	—
143	C₂×#41×C₅₃	—	4	4	no	—
144	C₂×#41×C₅₃	—	4	4	no	—
145	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
146	C₂×#41×C₅₃	C₂³	1	2	yes	—
147	C₂×#41×C₅₃	C₂³	1	2	yes	—
148	C₂×#41×C₅₃	C₂³	1	2	yes	—
149	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
150	C₂²×D₄×C₅₃	—	2	2	no	—
151	C₂²×D₄×C₅₃	—	2	2	no	—
152	C₂²×D₄×C₅₃	—	2	2	no	—
153	C₂²×D₄×C₅₃	—	2	1	no	—
154	C₂²×D₄×C₅₃	—	2	1	no	—
155	C₂²×D₄×C₅₃	—	2	2	no	—
156	C₂²×D₄×C₅₃	—	2	1	no	—
157	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
158	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
159	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
160	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
161	C₂³×C₄×C₅₃	—	2	2	no	—
162	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
163	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
164	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
165	C₂×SD₁₆×C₅₃	—	4	4	no	—
166	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
167	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
168	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
169	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
170	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
171	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
172	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
173	C₂×D₈×C₅₃	—	4	4	no	—
174	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
175	C₂×D₈×C₅₃	C₂³	1	2	yes	—
176	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
177	C₂×D₈×C₅₃	C₂³	1	2	yes	—
178	C₂×D₈×C₅₃	C₂³	1	2	yes	—
179	C₂×D₈×C₅₃	C₂³	1	2	yes	—
180	C₂×D₈×C₅₃	C₂³	1	2	yes	—
181	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
182	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
183	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
184	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
185	C₄⋊Q₈×C₅₃	—	2	1	no	—
186	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
187	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
188	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
189	#127×C₅₃	—	2	1	no	—
190	#127×C₅₃	C₂³	1	1	yes	characteristic
191	#127×C₅₃	C₂³	1	1	yes	characteristic
192	#127×C₅₃	C₂³	1	1	yes	characteristic
193	#124×C₅₃	—	2	2	no	—
194	#124×C₅₃	—	2	1	no	—
195	#124×C₅₃	—	2	1	no	—
196	#124×C₅₃	C₂³	1	2	yes	—
197	#123×C₅₃	—	2	2	no	—
198	#123×C₅₃	—	2	2	no	—
199	#123×C₅₃	—	2	2	no	—
200	#123×C₅₃	—	2	2	no	—
201	#123×C₅₃	—	2	2	no	—
202	#123×C₅₃	—	2	2	no	—
203	#123×C₅₃	—	2	2	no	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	—	2	1	no	—
206	C₂²⋊Q₈×C₅₃	—	2	1	no	—
207	C₂²⋊Q₈×C₅₃	—	2	2	no	—
208	C₂²⋊Q₈×C₅₃	—	2	2	no	—
209	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
211	#121×C₅₃	—	2	1	no	—
212	#121×C₅₃	—	2	1	no	—
213	#121×C₅₃	—	2	1	no	—
214	#121×C₅₃	—	2	2	no	—
215	#121×C₅₃	—	2	2	no	—
216	#121×C₅₃	—	2	2	no	—
217	#121×C₅₃	—	2	2	no	—
218	#121×C₅₃	—	2	1	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	—	2	1	no	—
224	#121×C₅₃	—	2	1	no	—
225	#121×C₅₃	—	2	1	no	—
226	#121×C₅₃	—	2	1	no	—
227	#121×C₅₃	C₂³	1	1	yes	characteristic
228	#121×C₅₃	C₂³	1	2	yes	—
229	#121×C₅₃	C₂³	1	1	yes	characteristic
230	#121×C₅₃	C₂³	1	2	yes	—
231	#121×C₅₃	C₂³	1	2	yes	—
232	#121×C₅₃	C₂³	1	2	yes	—
233	#121×C₅₃	C₂³	1	2	yes	—
234	#121×C₅₃	C₂³	1	2	yes	—
235	#121×C₅₃	C₂³	1	2	yes	—
236	#120×C₅₃	—	2	2	no	—
237	#120×C₅₃	—	2	2	no	—
238	#120×C₅₃	—	2	2	no	—
239	#120×C₅₃	—	2	2	no	—
240	#120×C₅₃	—	2	2	no	—
241	#120×C₅₃	—	2	2	no	—
242	#120×C₅₃	—	2	2	no	—
243	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₅₃	—	2	1	no	—
246	C₄×D₄×C₅₃	—	2	2	no	—
247	C₄×D₄×C₅₃	—	2	1	no	—
248	C₄×D₄×C₅₃	—	2	1	no	—
249	C₄×D₄×C₅₃	—	2	1	no	—
250	C₄×D₄×C₅₃	—	2	1	no	—
251	C₄×D₄×C₅₃	—	2	1	no	—
252	C₄×D₄×C₅₃	—	2	2	no	—
253	C₄×D₄×C₅₃	—	2	1	no	—
254	C₄×D₄×C₅₃	—	2	1	no	—
255	C₄×D₄×C₅₃	—	2	2	no	—
256	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
257	C₄×D₄×C₅₃	D₄	1	2	yes	—
258	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
259	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₅₃	C₂³	1	2	yes	—
264	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₅₃	C₂³	1	2	yes	—
266	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
267	#117×C₅₃	—	2	1	no	—
268	#117×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
270	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
272	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
273	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
274	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
276	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
277	C₂×C₄²×C₅₃	—	2	1	no	—
278	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
279	#107×C₅₃	C₂³	1	1	yes	characteristic
280	#107×C₅₃	C₂³	1	1	yes	characteristic
281	#107×C₅₃	C₂³	1	2	yes	—
282	#106×C₅₃	C₂³	1	1	yes	characteristic
283	#106×C₅₃	C₂³	1	1	yes	characteristic
284	#106×C₅₃	C₂³	1	2	yes	—
285	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	2	yes	—
293	#103×C₅₃	C₂³	1	1	yes	characteristic
294	#103×C₅₃	C₂³	1	2	yes	—
295	#103×C₅₃	C₂³	1	1	yes	characteristic
296	#102×C₅₃	C₂³	1	2	yes	—
297	#102×C₅₃	C₂³	1	2	yes	—
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	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	1	yes	characteristic
307	#102×C₅₃	C₂³	1	2	yes	—
308	#102×C₅₃	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
315	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
316	#97×C₅₃	C₂³	1	2	yes	—
317	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
318	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
319	C₂⁴×C₅₃	—	2	2	no	—
320	C₂⁴×C₅₃	—	2	2	no	—
321	C₂⁴×C₅₃	—	2	2	no	—
322	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
323	#41×C₅₃	—	2	2	no	—
324	#41×C₅₃	—	2	2	no	—
325	#41×C₅₃	—	2	4	no	—
326	#41×C₅₃	—	2	4	no	—
327	#41×C₅₃	—	4	2	no	—
328	#41×C₅₃	—	4	2	no	—
329	#41×C₅₃	—	4	2	no	—
330	#41×C₅₃	—	4	2	no	—
331	#41×C₅₃	—	4	8	no	—
332	#41×C₅₃	—	4	4	no	—
333	#41×C₅₃	—	4	4	no	—
334	#41×C₅₃	—	4	8	no	—
335	#41×C₅₃	—	4	8	no	—
336	#41×C₅₃	—	4	4	no	—
337	#41×C₅₃	—	4	4	no	—
338	C₂×Q₈×C₅₃	—	2	2	no	—
339	C₂×Q₈×C₅₃	—	2	1	no	—
340	C₂×Q₈×C₅₃	—	2	1	no	—
341	C₂×Q₈×C₅₃	—	2	4	no	—
342	C₂×Q₈×C₅₃	—	4	2	no	—
343	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
344	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₅₃	—	2	1	no	—
346	C₂×D₄×C₅₃	—	2	4	no	—
347	C₂×D₄×C₅₃	—	2	4	no	—
348	C₂×D₄×C₅₃	—	2	2	no	—
349	C₂×D₄×C₅₃	—	2	2	no	—
350	C₂×D₄×C₅₃	—	2	2	no	—
351	C₂×D₄×C₅₃	—	2	2	no	—
352	C₂×D₄×C₅₃	—	2	2	no	—
353	C₂×D₄×C₅₃	—	2	2	no	—
354	C₂×D₄×C₅₃	—	2	2	no	—
355	C₂×D₄×C₅₃	—	2	1	no	—
356	C₂×D₄×C₅₃	—	2	2	no	—
357	C₂×D₄×C₅₃	—	2	1	no	—
358	C₂×D₄×C₅₃	—	2	2	no	—
359	C₂×D₄×C₅₃	—	2	2	no	—
360	C₂×D₄×C₅₃	—	2	1	no	—
361	C₂×D₄×C₅₃	—	2	2	no	—
362	C₂×D₄×C₅₃	—	2	1	no	—
363	C₂×D₄×C₅₃	—	2	1	no	—
364	C₂×D₄×C₅₃	—	2	1	no	—
365	C₂×D₄×C₅₃	—	2	1	no	—
366	C₂×D₄×C₅₃	—	2	1	no	—
367	C₂×D₄×C₅₃	—	2	2	no	—
368	C₂×D₄×C₅₃	—	2	2	no	—
369	C₂×D₄×C₅₃	—	4	2	no	—
370	C₂×D₄×C₅₃	—	4	2	no	—
371	C₂×D₄×C₅₃	—	4	2	no	—
372	C₂×D₄×C₅₃	—	4	2	no	—
373	C₂×D₄×C₅₃	—	4	2	no	—
374	C₂×D₄×C₅₃	—	4	8	no	—
375	C₂×D₄×C₅₃	—	4	8	no	—
376	C₂×D₄×C₅₃	—	4	4	no	—
377	C₂×D₄×C₅₃	—	4	8	no	—
378	C₂×D₄×C₅₃	—	4	8	no	—
379	C₂×D₄×C₅₃	—	4	4	no	—
380	C₂×D₄×C₅₃	—	4	4	no	—
381	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
382	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
384	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
385	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
387	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₅₃	—	2	1	no	—
390	C₂²×C₄×C₅₃	—	2	2	no	—
391	C₂²×C₄×C₅₃	—	2	2	no	—
392	C₂²×C₄×C₅₃	—	2	2	no	—
393	C₂²×C₄×C₅₃	—	2	1	no	—
394	C₂²×C₄×C₅₃	—	2	2	no	—
395	C₂²×C₄×C₅₃	—	2	2	no	—
396	C₂²×C₄×C₅₃	—	2	2	no	—
397	C₂²×C₄×C₅₃	—	2	2	no	—
398	C₂²×C₄×C₅₃	—	2	1	no	—
399	C₂²×C₄×C₅₃	—	2	1	no	—
400	C₂²×C₄×C₅₃	—	2	1	no	—
401	C₂²×C₄×C₅₃	—	4	2	no	—
402	C₂²×C₄×C₅₃	—	4	2	no	—
403	C₂²×C₄×C₅₃	—	4	8	no	—
404	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
405	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
406	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
407	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
408	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
409	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
411	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
412	SD₁₆×C₅₃	—	2	2	no	—
413	SD₁₆×C₅₃	—	2	4	no	—
414	SD₁₆×C₅₃	—	2	2	no	—
415	SD₁₆×C₅₃	—	4	2	no	—
416	SD₁₆×C₅₃	—	4	2	no	—
417	SD₁₆×C₅₃	—	4	2	no	—
418	SD₁₆×C₅₃	—	4	2	no	—
419	D₈×C₅₃	—	2	2	no	—
420	D₈×C₅₃	—	2	4	no	—
421	D₈×C₅₃	—	2	2	no	—
422	D₈×C₅₃	—	4	2	no	—
423	D₈×C₅₃	—	4	2	no	—
424	D₈×C₅₃	—	4	2	no	—
425	D₈×C₅₃	—	4	2	no	—
426	M₁₆×C₅₃	—	4	2	no	—
427	M₁₆×C₅₃	—	4	2	no	—
428	C₂×C₈×C₅₃	—	4	2	no	—
429	C₂×C₈×C₅₃	—	4	2	no	—
430	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
431	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
433	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
434	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
435	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
436	C₄⋊C₄×C₅₃	—	2	1	no	—
437	C₄⋊C₄×C₅₃	—	2	2	no	—
438	C₄⋊C₄×C₅₃	—	2	2	no	—
439	C₄⋊C₄×C₅₃	—	2	2	no	—
440	C₄⋊C₄×C₅₃	—	2	1	no	—
441	C₄⋊C₄×C₅₃	—	2	1	no	—
442	C₄⋊C₄×C₅₃	—	2	1	no	—
443	C₄⋊C₄×C₅₃	—	2	2	no	—
444	C₄⋊C₄×C₅₃	—	2	1	no	—
445	C₄⋊C₄×C₅₃	—	2	1	no	—
446	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
449	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
452	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
454	C₂²⋊C₄×C₅₃	—	2	2	no	—
455	C₂²⋊C₄×C₅₃	—	2	1	no	—
456	C₂²⋊C₄×C₅₃	—	2	2	no	—
457	C₂²⋊C₄×C₅₃	—	2	1	no	—
458	C₂²⋊C₄×C₅₃	—	2	2	no	—
459	C₂²⋊C₄×C₅₃	—	2	1	no	—
460	C₂²⋊C₄×C₅₃	—	2	2	no	—
461	C₂²⋊C₄×C₅₃	—	2	2	no	—
462	C₂²⋊C₄×C₅₃	—	2	2	no	—
463	C₂²⋊C₄×C₅₃	—	2	2	no	—
464	C₂²⋊C₄×C₅₃	—	2	2	no	—
465	C₂²⋊C₄×C₅₃	—	2	2	no	—
466	C₂²⋊C₄×C₅₃	—	2	1	no	—
467	C₂²⋊C₄×C₅₃	—	2	1	no	—
468	C₂²⋊C₄×C₅₃	—	2	2	no	—
469	C₂²⋊C₄×C₅₃	—	2	2	no	—
470	C₂²⋊C₄×C₅₃	—	2	2	no	—
471	C₂²⋊C₄×C₅₃	—	2	1	no	—
472	C₂²⋊C₄×C₅₃	—	2	1	no	—
473	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
474	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
475	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
476	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
477	C₄²×C₅₃	—	2	1	no	—
478	C₄²×C₅₃	—	2	1	no	—
479	C₄²×C₅₃	—	2	1	no	—
480	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
481	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
482	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
483	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
484	C₂³×C₅₃	—	2	1	no	—
485	C₂³×C₅₃	—	2	4	no	—
486	C₂³×C₅₃	—	2	2	no	—
487	C₂³×C₅₃	—	2	1	no	—
488	C₂³×C₅₃	—	2	2	no	—
489	C₂³×C₅₃	—	2	1	no	—
490	C₂³×C₅₃	—	4	2	no	—
491	C₂³×C₅₃	—	4	2	no	—
492	C₂³×C₅₃	—	4	4	no	—
493	C₂³×C₅₃	—	4	4	no	—
494	C₂³×C₅₃	—	4	4	no	—
495	C₂³×C₅₃	—	4	4	no	—
496	C₂³×C₅₃	—	8	2	no	—
497	C₂³×C₅₃	—	8	2	no	—
498	C₂³×C₅₃	—	8	2	no	—
499	C₂³×C₅₃	—	8	2	no	—
500	C₂³×C₅₃	—	8	2	no	—
501	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
502	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
503	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
504	Q₈×C₅₃	—	2	1	no	—
505	Q₈×C₅₃	—	2	2	no	—
506	Q₈×C₅₃	—	2	2	no	—
507	Q₈×C₅₃	—	4	4	no	—
508	Q₈×C₅₃	—	4	2	no	—
509	Q₈×C₅₃	—	4	2	no	—
510	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	complemented
511	D₄×C₅₃	—	2	4	no	—
512	D₄×C₅₃	—	2	4	no	—
513	D₄×C₅₃	—	2	2	no	—
514	D₄×C₅₃	—	2	1	no	—
515	D₄×C₅₃	—	2	2	no	—
516	D₄×C₅₃	—	2	1	no	—
517	D₄×C₅₃	—	2	2	no	—
518	D₄×C₅₃	—	2	1	no	—
519	D₄×C₅₃	—	2	1	no	—
520	D₄×C₅₃	—	2	2	no	—
521	D₄×C₅₃	—	2	1	no	—
522	D₄×C₅₃	—	2	2	no	—
523	D₄×C₅₃	—	4	4	no	—
524	D₄×C₅₃	—	4	4	no	—
525	D₄×C₅₃	—	4	2	no	—
526	D₄×C₅₃	—	4	4	no	—
527	D₄×C₅₃	—	4	4	no	—
528	D₄×C₅₃	—	4	2	no	—
529	D₄×C₅₃	—	4	2	no	—
530	D₄×C₅₃	—	4	4	no	—
531	D₄×C₅₃	—	4	4	no	—
532	D₄×C₅₃	—	4	4	no	—
533	D₄×C₅₃	—	4	4	no	—
534	D₄×C₅₃	—	4	4	no	—
535	D₄×C₅₃	—	4	4	no	—
536	D₄×C₅₃	—	4	2	no	—
537	D₄×C₅₃	—	4	2	no	—
538	D₄×C₅₃	—	8	1	no	—
539	D₄×C₅₃	—	8	1	no	—
540	D₄×C₅₃	—	8	1	no	—
541	D₄×C₅₃	—	8	2	no	—
542	D₄×C₅₃	—	8	2	no	—
543	D₄×C₅₃	—	8	2	no	—
544	D₄×C₅₃	AGL(1,ℤ/8)	1	4	yes	complemented
545	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	complemented
546	C₂×C₄×C₅₃	—	2	4	no	—
547	C₂×C₄×C₅₃	—	2	1	no	—
548	C₂×C₄×C₅₃	—	2	2	no	—
549	C₂×C₄×C₅₃	—	2	1	no	—
550	C₂×C₄×C₅₃	—	2	1	no	—
551	C₂×C₄×C₅₃	—	2	2	no	—
552	C₂×C₄×C₅₃	—	2	2	no	—
553	C₂×C₄×C₅₃	—	2	2	no	—
554	C₂×C₄×C₅₃	—	2	2	no	—
555	C₂×C₄×C₅₃	—	2	2	no	—
556	C₂×C₄×C₅₃	—	2	1	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	2	no	—
559	C₂×C₄×C₅₃	—	2	1	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	4	2	no	—
562	C₂×C₄×C₅₃	—	4	2	no	—
563	C₂×C₄×C₅₃	—	4	2	no	—
564	C₂×C₄×C₅₃	—	4	1	no	—
565	C₂×C₄×C₅₃	—	4	4	no	—
566	C₂×C₄×C₅₃	—	4	4	no	—
567	C₂×C₄×C₅₃	—	4	4	no	—
568	C₂×C₄×C₅₃	—	4	4	no	—
569	C₂×C₄×C₅₃	—	4	4	no	—
570	C₂×C₄×C₅₃	—	4	4	no	—
571	C₂×C₄×C₅₃	—	4	4	no	—
572	C₂×C₄×C₅₃	—	4	2	no	—
573	C₂×C₄×C₅₃	—	4	2	no	—
574	C₂×C₄×C₅₃	—	4	2	no	—
575	C₂×C₄×C₅₃	—	8	1	no	—
576	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
578	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
581	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
584	C₈×C₅₃	—	2	1	no	—
585	C₈×C₅₃	—	2	1	no	—
586	C₈×C₅₃	—	2	2	no	—
587	C₈×C₅₃	—	2	2	no	—
588	C₈×C₅₃	—	2	1	no	—
589	C₈×C₅₃	—	2	1	no	—
590	#61598	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
591	C₂²×C₅₃	—	2	2	no	—
592	C₂²×C₅₃	—	2	2	no	—
593	C₂²×C₅₃	—	2	1	no	—
594	C₂²×C₅₃	—	2	2	no	—
595	C₂²×C₅₃	—	2	1	no	—
596	C₂²×C₅₃	—	2	2	no	—
597	C₂²×C₅₃	—	2	2	no	—
598	C₂²×C₅₃	—	2	1	no	—
599	C₂²×C₅₃	—	2	2	no	—
600	C₂²×C₅₃	—	4	1	no	—
601	C₂²×C₅₃	—	4	1	no	—
602	C₂²×C₅₃	—	4	2	no	—
603	C₂²×C₅₃	—	4	1	no	—
604	C₂²×C₅₃	—	4	2	no	—
605	C₂²×C₅₃	—	4	1	no	—
606	C₂²×C₅₃	—	4	2	no	—
607	C₂²×C₅₃	—	4	1	no	—
608	C₂²×C₅₃	—	4	2	no	—
609	C₂²×C₅₃	—	4	1	no	—
610	C₂²×C₅₃	—	4	2	no	—
611	C₂²×C₅₃	—	4	1	no	—
612	C₂²×C₅₃	—	4	1	no	—
613	C₂²×C₅₃	—	4	2	no	—
614	C₂²×C₅₃	—	8	4	no	—
615	C₂²×C₅₃	—	8	8	no	—
616	C₂²×C₅₃	—	16	4	no	—
617	C₂²×C₅₃	—	16	4	no	—
618	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
619	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
620	C₄×C₅₃	—	2	1	no	—
621	C₄×C₅₃	—	2	1	no	—
622	C₄×C₅₃	—	2	1	no	—
623	C₄×C₅₃	—	2	2	no	—
624	C₄×C₅₃	—	2	2	no	—
625	C₄×C₅₃	—	2	2	no	—
626	C₄×C₅₃	—	2	1	no	—
627	C₄×C₅₃	—	4	1	no	—
628	C₄×C₅₃	—	4	2	no	—
629	C₄×C₅₃	—	4	2	no	—
630	C₄×C₅₃	—	4	1	no	—
631	C₄×C₅₃	—	4	1	no	—
632	C₄×C₅₃	—	4	1	no	—
633	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
634	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
635	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
636	#3496	C₂×C₅₃	1	1	yes	characteristic, complemented
637	D₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
638	#3332	C₂×C₅₃	1	1	yes	characteristic, complemented
639	#3330	C₂×C₅₃	1	1	yes	characteristic, complemented
640	#3308	C₂×C₅₃	1	2	yes	complemented
641	#3306	C₂×C₅₃	1	2	yes	complemented
642	#3298	C₂×C₅₃	1	1	yes	characteristic, complemented
643	#3294	C₂×C₅₃	1	1	yes	characteristic, complemented
644	D₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
645	D₄×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
646	#3274	C₂×C₅₃	1	1	yes	characteristic, complemented
647	#3272	C₂×C₅₃	1	1	yes	characteristic, complemented
648	#3265	C₂×C₅₃	1	2	yes	complemented
649	#3264	C₂×C₅₃	1	2	yes	complemented
650	#3214	C₂×C₅₃	1	1	yes	characteristic, complemented
651	#3207	C₂×C₅₃	1	1	yes	characteristic, complemented
652	#3194	C₂×C₅₃	1	2	yes	complemented
653	#3188	C₂×C₅₃	1	2	yes	complemented
654	#3115	C₂×C₅₃	1	1	yes	characteristic, complemented
655	#3106	C₂×C₅₃	1	1	yes	characteristic, complemented
656	#3006	C₂×C₅₃	1	2	yes	complemented
657	C₂×#449	C₂×C₅₃	1	2	yes	complemented
658	#2974	C₂×C₅₃	1	1	yes	characteristic, complemented
659	C₂×C₅₃	—	2	4	no	—
660	C₂×C₅₃	—	4	1	no	—
661	C₂×C₅₃	—	4	2	no	—
662	C₂×C₅₃	—	4	2	no	—
663	C₂×C₅₃	—	8	2	no	—
664	C₂×C₅₃	—	8	1	no	—
665	C₂×C₅₃	—	8	2	no	—
666	C₂×C₅₃	—	8	1	no	—
667	C₂×C₅₃	#3484	1	1	yes	characteristic
668	C₂×C₅₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
669	C₂×C₅₃	#3584	1	1	yes	characteristic
670	C₂×H(5,𝔽₂)	—	2	1	no	—
671	C₂²×#41	C₂²×C₅₃	1	2	yes	complemented
672	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
673	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
674	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
675	C₂²×D₈	C₂²×C₅₃	1	2	yes	complemented
676	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
677	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
678	#548	C₂²×C₅₃	1	2	yes	complemented
679	#547	—	2	1	no	—
680	#547	C₂²×C₅₃	1	1	yes	characteristic
681	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
682	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
683	#547	C₂²×C₅₃	1	2	yes	complemented
684	#546	—	2	1	no	—
685	#546	—	2	2	no	—
686	#546	—	2	1	no	—
687	#546	—	2	2	no	—
688	#546	C₂²×C₅₃	1	2	yes	complemented
689	D₄²	—	2	1	no	—
690	D₄²	C₂²×C₅₃	1	1	yes	characteristic
691	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
692	D₄²	C₂²×C₅₃	1	2	yes	complemented
693	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
694	#537	—	2	1	no	—
695	#534	—	2	2	no	—
696	#532	—	2	1	no	—
697	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
698	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
699	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
700	#525	—	2	2	no	—
701	#525	C₂²×C₅₃	1	2	yes	complemented
702	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
703	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
704	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
705	C₂×C₄×D₄	—	2	1	no	—
706	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
707	#496	C₂²×C₅₃	1	2	yes	complemented
708	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
710	#489	C₂²×C₅₃	1	2	yes	complemented
711	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	#484	C₂²×C₅₃	1	2	yes	complemented
714	#483	C₂²×C₅₃	1	2	yes	complemented
715	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
716	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
717	#482	C₂²×C₅₃	1	2	yes	complemented
718	#481	C₂²×C₅₃	1	2	yes	complemented
719	#480	C₂²×C₅₃	1	2	yes	complemented
720	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
721	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
723	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
724	#469	C₂²×C₅₃	1	2	yes	complemented
725	#469	C₂²×C₅₃	1	2	yes	complemented
726	#468	C₂²×C₅₃	1	2	yes	complemented
727	#468	C₂²×C₅₃	1	2	yes	complemented
728	#466	C₂²×C₅₃	1	2	yes	complemented
729	#466	C₂²×C₅₃	1	2	yes	complemented
730	#465	C₂²×C₅₃	1	2	yes	complemented
731	#465	C₂²×C₅₃	1	2	yes	complemented
732	#463	C₂²×C₅₃	1	2	yes	complemented
733	#463	C₂²×C₅₃	1	2	yes	complemented
734	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
735	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
736	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
737	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
738	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
739	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
740	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
741	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
742	#450	C₂²×C₅₃	1	2	yes	complemented
743	#450	C₂²×C₅₃	1	2	yes	complemented
744	#449	C₂²×C₅₃	1	2	yes	complemented
745	#449	C₂²×C₅₃	1	2	yes	complemented
746	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
747	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
748	#449	C₂²×C₅₃	1	2	yes	complemented
749	#449	C₂²×C₅₃	1	2	yes	complemented
750	#449	C₂²×C₅₃	1	2	yes	complemented
751	#449	C₂²×C₅₃	1	2	yes	complemented
752	#449	C₂²×C₅₃	1	2	yes	complemented
753	#449	C₂²×C₅₃	1	2	yes	complemented
754	#449	C₂²×C₅₃	1	2	yes	complemented
755	#448	C₂²×C₅₃	1	2	yes	complemented
756	#448	C₂²×C₅₃	1	2	yes	complemented
757	#447	C₂²×C₅₃	1	2	yes	complemented
758	#447	C₂²×C₅₃	1	2	yes	complemented
759	#447	C₂²×C₅₃	1	2	yes	complemented
760	#447	C₂²×C₅₃	1	2	yes	complemented
761	#442	C₂²×C₅₃	1	2	yes	complemented
762	#440	C₂²×C₅₃	1	2	yes	complemented
763	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
764	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
765	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
766	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
767	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
768	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
769	#435	C₂²×C₅₃	1	2	yes	complemented
770	#435	C₂²×C₅₃	1	2	yes	complemented
771	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
772	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
773	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
774	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
775	#417	C₂²×C₅₃	1	2	yes	complemented
776	#417	C₂²×C₅₃	1	2	yes	complemented
777	C₂×#103	C₂²×C₅₃	1	2	yes	complemented
778	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
779	#407	C₂²×C₅₃	1	2	yes	complemented
780	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	complemented
781	C₅₃	#61598	1	1	yes	characteristic, direct product factor, Sylow
782	H(5,𝔽₂)	—	4	8	no	—
783	C₂×#41	—	2	1	no	—
784	C₂×#41	—	2	2	no	—
785	C₂×#41	—	2	1	no	—
786	C₂×#41	—	2	2	no	—
787	C₂×#41	—	2	1	no	—
788	C₂×#41	—	2	1	no	—
789	C₂×#41	—	2	2	no	—
790	C₂×#41	—	4	4	no	—
791	C₂×#41	—	4	4	no	—
792	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
793	C₂×#41	C₂³×C₅₃	1	2	yes	—
794	C₂×#41	C₂³×C₅₃	1	2	yes	—
795	C₂×#41	C₂³×C₅₃	1	2	yes	—
796	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
797	C₂²×D₄	—	2	2	no	—
798	C₂²×D₄	—	2	2	no	—
799	C₂²×D₄	—	2	2	no	—
800	C₂²×D₄	—	2	1	no	—
801	C₂²×D₄	—	2	1	no	—
802	C₂²×D₄	—	2	2	no	—
803	C₂²×D₄	—	2	1	no	—
804	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
805	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
806	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
807	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
808	C₂³×C₄	—	2	2	no	—
809	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
810	AGL(1,ℤ/8)	—	4	4	no	—
811	AGL(1,ℤ/8)	—	4	4	no	—
812	C₂×SD₁₆	—	4	4	no	—
813	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
814	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
815	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
816	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
817	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
818	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
819	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
820	C₂×D₈	—	4	4	no	—
821	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
822	C₂×D₈	C₂³×C₅₃	1	2	yes	—
823	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
824	C₂×D₈	C₂³×C₅₃	1	2	yes	—
825	C₂×D₈	C₂³×C₅₃	1	2	yes	—
826	C₂×D₈	C₂³×C₅₃	1	2	yes	—
827	C₂×D₈	C₂³×C₅₃	1	2	yes	—
828	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
829	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
830	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
831	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
832	C₄⋊Q₈	—	2	1	no	—
833	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
834	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
835	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
836	#127	—	2	1	no	—
837	#127	C₂³×C₅₃	1	1	yes	characteristic
838	#127	C₂³×C₅₃	1	1	yes	characteristic
839	#127	C₂³×C₅₃	1	1	yes	characteristic
840	#124	—	2	2	no	—
841	#124	—	2	1	no	—
842	#124	—	2	1	no	—
843	#124	C₂³×C₅₃	1	2	yes	—
844	#123	—	2	2	no	—
845	#123	—	2	2	no	—
846	#123	—	2	2	no	—
847	#123	—	2	2	no	—
848	#123	—	2	2	no	—
849	#123	—	2	2	no	—
850	#123	—	2	2	no	—
851	C₂²⋊Q₈	—	2	2	no	—
852	C₂²⋊Q₈	—	2	1	no	—
853	C₂²⋊Q₈	—	2	1	no	—
854	C₂²⋊Q₈	—	2	2	no	—
855	C₂²⋊Q₈	—	2	2	no	—
856	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
857	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
858	#121	—	2	2	no	—
859	#121	—	2	1	no	—
860	#121	—	2	2	no	—
861	#121	—	2	2	no	—
862	#121	—	2	2	no	—
863	#121	—	2	2	no	—
864	#121	—	2	1	no	—
865	#121	—	2	1	no	—
866	#121	—	2	1	no	—
867	#121	—	2	1	no	—
868	#121	—	2	1	no	—
869	#121	—	2	1	no	—
870	#121	—	2	1	no	—
871	#121	—	2	2	no	—
872	#121	—	2	2	no	—
873	#121	—	2	2	no	—
874	#121	C₂³×C₅₃	1	1	yes	characteristic
875	#121	C₂³×C₅₃	1	2	yes	—
876	#121	C₂³×C₅₃	1	1	yes	characteristic
877	#121	C₂³×C₅₃	1	2	yes	—
878	#121	C₂³×C₅₃	1	2	yes	—
879	#121	C₂³×C₅₃	1	2	yes	—
880	#121	C₂³×C₅₃	1	2	yes	—
881	#121	C₂³×C₅₃	1	2	yes	—
882	#121	C₂³×C₅₃	1	2	yes	—
883	#120	—	2	2	no	—
884	#120	—	2	2	no	—
885	#120	—	2	2	no	—
886	#120	—	2	2	no	—
887	#120	—	2	2	no	—
888	#120	—	2	2	no	—
889	#120	—	2	2	no	—
890	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
891	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	2	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	—	2	2	no	—
897	C₄×D₄	—	2	1	no	—
898	C₄×D₄	—	2	2	no	—
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	—	2	1	no	—
903	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
904	C₄×D₄	D₄×C₅₃	1	2	yes	—
905	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
906	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
907	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
908	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
909	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
910	C₄×D₄	C₂³×C₅₃	1	2	yes	—
911	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
912	C₄×D₄	C₂³×C₅₃	1	2	yes	—
913	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
914	#117	—	2	1	no	—
915	#117	C₂³×C₅₃	1	1	yes	characteristic
916	C₂×C₄⋊C₄	—	2	1	no	—
917	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
918	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
919	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
920	C₂×C₂²⋊C₄	—	2	2	no	—
921	C₂×C₂²⋊C₄	—	2	2	no	—
922	C₂×C₂²⋊C₄	—	2	2	no	—
923	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
924	C₂×C₄²	—	2	1	no	—
925	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
926	#107	C₂³×C₅₃	1	1	yes	characteristic
927	#107	C₂³×C₅₃	1	1	yes	characteristic
928	#107	C₂³×C₅₃	1	2	yes	—
929	#106	C₂³×C₅₃	1	1	yes	characteristic
930	#106	C₂³×C₅₃	1	1	yes	characteristic
931	#106	C₂³×C₅₃	1	2	yes	—
932	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
933	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
934	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
935	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
936	#103	C₂³×C₅₃	1	1	yes	characteristic
937	#103	C₂³×C₅₃	1	2	yes	—
938	#103	C₂³×C₅₃	1	2	yes	—
939	#103	C₂³×C₅₃	1	2	yes	—
940	#103	C₂³×C₅₃	1	1	yes	characteristic
941	#103	C₂³×C₅₃	1	2	yes	—
942	#103	C₂³×C₅₃	1	2	yes	—
943	#102	C₂³×C₅₃	1	1	yes	characteristic
944	#102	C₂³×C₅₃	1	2	yes	—
945	#102	C₂³×C₅₃	1	2	yes	—
946	#102	C₂³×C₅₃	1	2	yes	—
947	#102	C₂³×C₅₃	1	1	yes	characteristic
948	#102	C₂³×C₅₃	1	2	yes	—
949	#102	C₂³×C₅₃	1	2	yes	—
950	#102	C₂³×C₅₃	1	1	yes	characteristic
951	#102	C₂³×C₅₃	1	1	yes	characteristic
952	#102	C₂³×C₅₃	1	1	yes	characteristic
953	#102	C₂³×C₅₃	1	1	yes	characteristic
954	#102	C₂³×C₅₃	1	2	yes	—
955	#102	C₂³×C₅₃	1	2	yes	—
956	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
957	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
958	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
959	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
960	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
961	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
962	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
963	#97	C₂³×C₅₃	1	2	yes	—
964	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
965	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
966	C₂⁴	—	2	2	no	—
967	C₂⁴	—	2	2	no	—
968	C₂⁴	—	2	2	no	—
969	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
970	#41	—	2	2	no	—
971	#41	—	2	2	no	—
972	#41	—	2	4	no	—
973	#41	—	2	4	no	—
974	#41	—	4	2	no	—
975	#41	—	4	2	no	—
976	#41	—	4	2	no	—
977	#41	—	4	2	no	—
978	#41	—	4	8	no	—
979	#41	—	4	4	no	—
980	#41	—	4	4	no	—
981	#41	—	4	8	no	—
982	#41	—	4	8	no	—
983	#41	—	4	4	no	—
984	#41	—	4	4	no	—
985	C₂×Q₈	—	2	2	no	—
986	C₂×Q₈	—	2	1	no	—
987	C₂×Q₈	—	2	1	no	—
988	C₂×Q₈	—	2	4	no	—
989	C₂×Q₈	—	4	2	no	—
990	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
991	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	4	no	—
994	C₂×D₄	—	2	4	no	—
995	C₂×D₄	—	2	2	no	—
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	2	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	2	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	2	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	1	no	—
1012	C₂×D₄	—	2	1	no	—
1013	C₂×D₄	—	2	1	no	—
1014	C₂×D₄	—	2	2	no	—
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	4	2	no	—
1017	C₂×D₄	—	4	2	no	—
1018	C₂×D₄	—	4	2	no	—
1019	C₂×D₄	—	4	2	no	—
1020	C₂×D₄	—	4	2	no	—
1021	C₂×D₄	—	4	8	no	—
1022	C₂×D₄	—	4	8	no	—
1023	C₂×D₄	—	4	4	no	—
1024	C₂×D₄	—	4	8	no	—
1025	C₂×D₄	—	4	8	no	—
1026	C₂×D₄	—	4	4	no	—
1027	C₂×D₄	—	4	4	no	—
1028	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1029	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1030	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1031	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1032	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1033	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1034	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1035	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1036	C₂²×C₄	—	2	1	no	—
1037	C₂²×C₄	—	2	2	no	—
1038	C₂²×C₄	—	2	2	no	—
1039	C₂²×C₄	—	2	2	no	—
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	2	no	—
1042	C₂²×C₄	—	2	2	no	—
1043	C₂²×C₄	—	2	2	no	—
1044	C₂²×C₄	—	2	2	no	—
1045	C₂²×C₄	—	2	1	no	—
1046	C₂²×C₄	—	2	1	no	—
1047	C₂²×C₄	—	2	1	no	—
1048	C₂²×C₄	—	4	2	no	—
1049	C₂²×C₄	—	4	2	no	—
1050	C₂²×C₄	—	4	8	no	—
1051	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1052	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1053	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1054	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1055	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1056	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1057	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1058	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1059	SD₁₆	—	2	2	no	—
1060	SD₁₆	—	2	4	no	—
1061	SD₁₆	—	2	2	no	—
1062	SD₁₆	—	4	2	no	—
1063	SD₁₆	—	4	2	no	—
1064	SD₁₆	—	4	2	no	—
1065	SD₁₆	—	4	2	no	—
1066	D₈	—	2	2	no	—
1067	D₈	—	2	4	no	—
1068	D₈	—	2	2	no	—
1069	D₈	—	4	2	no	—
1070	D₈	—	4	2	no	—
1071	D₈	—	4	2	no	—
1072	D₈	—	4	2	no	—
1073	M₁₆	—	4	2	no	—
1074	M₁₆	—	4	2	no	—
1075	C₂×C₈	—	4	2	no	—
1076	C₂×C₈	—	4	2	no	—
1077	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1078	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1079	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1080	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1081	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1082	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	1	no	—
1089	C₄⋊C₄	—	2	1	no	—
1090	C₄⋊C₄	—	2	2	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1094	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1095	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1096	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1097	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1098	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1099	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1100	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	2	no	—
1117	C₂²⋊C₄	—	2	2	no	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	—	2	1	no	—
1120	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1121	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1122	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1123	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	—	2	1	no	—
1127	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1128	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1129	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1130	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1131	C₂³	—	2	1	no	—
1132	C₂³	—	2	4	no	—
1133	C₂³	—	2	2	no	—
1134	C₂³	—	2	1	no	—
1135	C₂³	—	2	2	no	—
1136	C₂³	—	2	1	no	—
1137	C₂³	—	4	2	no	—
1138	C₂³	—	4	2	no	—
1139	C₂³	—	4	4	no	—
1140	C₂³	—	4	4	no	—
1141	C₂³	—	4	4	no	—
1142	C₂³	—	4	4	no	—
1143	C₂³	—	8	2	no	—
1144	C₂³	—	8	2	no	—
1145	C₂³	—	8	2	no	—
1146	C₂³	—	8	2	no	—
1147	C₂³	—	8	2	no	—
1148	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1149	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1150	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1151	Q₈	—	2	1	no	—
1152	Q₈	—	2	2	no	—
1153	Q₈	—	2	2	no	—
1154	Q₈	—	4	4	no	—
1155	Q₈	—	4	2	no	—
1156	Q₈	—	4	2	no	—
1157	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	complemented
1158	D₄	—	2	4	no	—
1159	D₄	—	2	4	no	—
1160	D₄	—	2	2	no	—
1161	D₄	—	2	1	no	—
1162	D₄	—	2	1	no	—
1163	D₄	—	2	2	no	—
1164	D₄	—	2	1	no	—
1165	D₄	—	2	1	no	—
1166	D₄	—	2	2	no	—
1167	D₄	—	2	2	no	—
1168	D₄	—	2	2	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	4	4	no	—
1171	D₄	—	4	4	no	—
1172	D₄	—	4	2	no	—
1173	D₄	—	4	4	no	—
1174	D₄	—	4	4	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	4	2	no	—
1177	D₄	—	4	4	no	—
1178	D₄	—	4	4	no	—
1179	D₄	—	4	4	no	—
1180	D₄	—	4	4	no	—
1181	D₄	—	4	4	no	—
1182	D₄	—	4	4	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	8	1	no	—
1186	D₄	—	8	1	no	—
1187	D₄	—	8	1	no	—
1188	D₄	—	8	2	no	—
1189	D₄	—	8	2	no	—
1190	D₄	—	8	2	no	—
1191	D₄	AGL(1,ℤ/8)×C₅₃	1	4	yes	complemented
1192	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	complemented
1193	C₂×C₄	—	2	4	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	2	no	—
1205	C₂×C₄	—	2	2	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	4	2	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	1	no	—
1212	C₂×C₄	—	4	4	no	—
1213	C₂×C₄	—	4	4	no	—
1214	C₂×C₄	—	4	4	no	—
1215	C₂×C₄	—	4	4	no	—
1216	C₂×C₄	—	4	4	no	—
1217	C₂×C₄	—	4	4	no	—
1218	C₂×C₄	—	4	4	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	—	4	2	no	—
1221	C₂×C₄	—	4	2	no	—
1222	C₂×C₄	—	8	1	no	—
1223	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1224	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1225	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1226	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1227	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1228	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1229	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1230	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1231	C₈	—	2	1	no	—
1232	C₈	—	2	1	no	—
1233	C₈	—	2	2	no	—
1234	C₈	—	2	2	no	—
1235	C₈	—	2	1	no	—
1236	C₈	—	2	1	no	—
1237	C₂²	—	2	2	no	—
1238	C₂²	—	2	2	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	2	no	—
1241	C₂²	—	2	2	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	2	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	2	no	—
1246	C₂²	—	4	1	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	2	no	—
1249	C₂²	—	4	1	no	—
1250	C₂²	—	4	2	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	1	no	—
1255	C₂²	—	4	2	no	—
1256	C₂²	—	4	2	no	—
1257	C₂²	—	4	1	no	—
1258	C₂²	—	4	2	no	—
1259	C₂²	—	4	1	no	—
1260	C₂²	—	8	4	no	—
1261	C₂²	—	8	8	no	—
1262	C₂²	—	16	4	no	—
1263	C₂²	—	16	4	no	—
1264	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	4	yes	—
1265	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1266	C₄	—	2	1	no	—
1267	C₄	—	2	2	no	—
1268	C₄	—	2	2	no	—
1269	C₄	—	2	2	no	—
1270	C₄	—	2	1	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	2	1	no	—
1273	C₄	—	4	2	no	—
1274	C₄	—	4	2	no	—
1275	C₄	—	4	1	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	1	no	—
1278	C₄	—	4	1	no	—
1279	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
1280	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1281	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1282	C₂	—	2	4	no	—
1283	C₂	—	4	1	no	—
1284	C₂	—	4	2	no	—
1285	C₂	—	4	2	no	—
1286	C₂	—	8	2	no	—
1287	C₂	—	8	1	no	—
1288	C₂	—	8	2	no	—
1289	C₂	—	8	1	no	—
1290	C₂	C₅₃×#3484	1	1	yes	characteristic
1291	C₂	C₂²×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
1292	C₂	C₅₃×#3584	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 ◁ C₂×C₄×D₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3496	C₂	semidirect
2. D₄×#41×C₅₃	C₂	semidirect
3. C₅₃×#3332	C₂	semidirect
4. C₅₃×#3330	C₂	semidirect
5. C₅₃×#3308	C₂	semidirect
6. C₅₃×#3306	C₂	semidirect
7. C₅₃×#3298	C₂	semidirect
8. C₅₃×#3294	C₂	semidirect
9. D₄×SD₁₆×C₅₃	C₂	semidirect
10. D₄×D₈×C₅₃	C₂	semidirect
11. C₅₃×#3274	C₂	semidirect
12. C₅₃×#3272	C₂	semidirect
13. C₅₃×#3265	C₂	semidirect
14. C₅₃×#3264	C₂	semidirect
15. C₅₃×#3214	C₂	semidirect
16. C₅₃×#3207	C₂	semidirect
17. C₅₃×#3194	C₂	semidirect
18. C₅₃×#3188	C₂	semidirect
19. C₅₃×#3115	C₂	semidirect
20. C₅₃×#3106	C₂	semidirect
21. C₅₃×#3006	C₂	semidirect
22. C₂×C₅₃×#449	C₂	semidirect
23. C₅₃×#2974	C₂	semidirect
25. C₂²×#41×C₅₃	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
27. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
28. C₂²×SD₁₆×C₅₃	C₂²	semidirect
29. C₂²×D₈×C₅₃	C₂²	semidirect
30. C₅₃×#550	C₂²	semidirect
31. D₄×Q₈×C₅₃	C₂²	semidirect
32. C₅₃×#548	C₂²	semidirect
35. C₅₃×#547	C₂²	semidirect
36. C₅₃×#547	C₂²	semidirect
37. C₅₃×#547	C₂²	semidirect
42. C₅₃×#546	C₂²	semidirect
45. D₄²×C₅₃	C₂²	semidirect
46. D₄²×C₅₃	C₂²	semidirect
47. D₄²×C₅₃	C₂²	semidirect
51. C₅₃×#532	C₂²	semidirect
52. C₅₃×#532	C₂²	semidirect
53. C₅₃×#532	C₂²	semidirect
55. C₅₃×#525	C₂²	semidirect
56. C₂×#121×C₅₃	C₂²	semidirect
57. C₂×#121×C₅₃	C₂²	semidirect
58. C₄×#41×C₅₃	C₂²	semidirect
61. C₅₃×#496	C₂²	semidirect
62. C₅₃×#493	C₂²	semidirect
63. C₅₃×#492	C₂²	semidirect
64. C₅₃×#489	C₂²	semidirect
65. C₅₃×#487	C₂²	semidirect
66. C₅₃×#486	C₂²	semidirect
67. C₅₃×#484	C₂²	semidirect
68. C₅₃×#483	C₂²	semidirect
69. C₅₃×#482	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#481	C₂²	semidirect
73. C₅₃×#480	C₂²	semidirect
74. C₅₃×#477	C₂²	semidirect
75. C₅₃×#476	C₂²	semidirect
76. C₅₃×#475	C₂²	semidirect
77. C₅₃×#474	C₂²	semidirect
78. C₅₃×#469	C₂²	semidirect
79. C₅₃×#469	C₂²	semidirect
80. C₅₃×#468	C₂²	semidirect
81. C₅₃×#468	C₂²	semidirect
82. C₅₃×#466	C₂²	semidirect
83. C₅₃×#466	C₂²	semidirect
84. C₅₃×#465	C₂²	semidirect
85. C₅₃×#465	C₂²	semidirect
86. C₅₃×#463	C₂²	semidirect
87. C₅₃×#463	C₂²	semidirect
88. C₅₃×#461	C₂²	semidirect
89. C₅₃×#461	C₂²	semidirect
90. C₅₃×#460	C₂²	semidirect
91. C₅₃×#460	C₂²	semidirect
92. C₅₃×#459	C₂²	semidirect
93. C₅₃×#459	C₂²	semidirect
94. C₅₃×#459	C₂²	semidirect
95. C₅₃×#459	C₂²	semidirect
96. C₅₃×#450	C₂²	semidirect
97. C₅₃×#450	C₂²	semidirect
98. C₅₃×#449	C₂²	semidirect
99. C₅₃×#449	C₂²	semidirect
100. C₅₃×#449	C₂²	semidirect
101. C₅₃×#449	C₂²	semidirect
102. C₅₃×#449	C₂²	semidirect
103. C₅₃×#449	C₂²	semidirect
104. C₅₃×#449	C₂²	semidirect
105. C₅₃×#449	C₂²	semidirect
106. C₅₃×#449	C₂²	semidirect
107. C₅₃×#449	C₂²	semidirect
108. C₅₃×#449	C₂²	semidirect
109. C₅₃×#448	C₂²	semidirect
110. C₅₃×#448	C₂²	semidirect
111. C₅₃×#447	C₂²	semidirect
112. C₅₃×#447	C₂²	semidirect
113. C₅₃×#447	C₂²	semidirect
114. C₅₃×#447	C₂²	semidirect
115. C₅₃×#442	C₂²	semidirect
116. C₅₃×#440	C₂²	semidirect
117. C₄×SD₁₆×C₅₃	C₂²	semidirect
118. C₄×SD₁₆×C₅₃	C₂²	semidirect
119. C₄×D₈×C₅₃	C₂²	semidirect
120. C₄×D₈×C₅₃	C₂²	semidirect
121. C₅₃×#436	C₂²	semidirect
122. C₅₃×#436	C₂²	semidirect
123. C₅₃×#435	C₂²	semidirect
124. C₅₃×#435	C₂²	semidirect
125. C₈×D₄×C₅₃	C₂²	semidirect
126. C₈×D₄×C₅₃	C₂²	semidirect
127. C₅₃×#432	C₂²	semidirect
128. C₅₃×#431	C₂²	semidirect
129. C₅₃×#417	C₂²	semidirect
130. C₅₃×#417	C₂²	semidirect
131. C₂×#103×C₅₃	C₂²	semidirect
132. C₂×#102×C₅₃	C₂²	semidirect
133. C₅₃×#407	C₂²	semidirect
134. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
510. Q₈×C₅₃	H(5,𝔽₂)	semidirect
544. D₄×C₅₃	AGL(1,ℤ/8)	semidirect
545. D₄×C₅₃	H(5,𝔽₂)	semidirect
590. #61598	C₅₃	direct (N × H)
636. #3496	C₂×C₅₃	semidirect
637. D₄×#41	C₂×C₅₃	semidirect
638. #3332	C₂×C₅₃	semidirect
639. #3330	C₂×C₅₃	semidirect
640. #3308	C₂×C₅₃	semidirect
641. #3306	C₂×C₅₃	semidirect
642. #3298	C₂×C₅₃	semidirect
643. #3294	C₂×C₅₃	semidirect
644. D₄×SD₁₆	C₂×C₅₃	semidirect
645. D₄×D₈	C₂×C₅₃	semidirect
646. #3274	C₂×C₅₃	semidirect
647. #3272	C₂×C₅₃	semidirect
648. #3265	C₂×C₅₃	semidirect
649. #3264	C₂×C₅₃	semidirect
650. #3214	C₂×C₅₃	semidirect
651. #3207	C₂×C₅₃	semidirect
652. #3194	C₂×C₅₃	semidirect
653. #3188	C₂×C₅₃	semidirect
654. #3115	C₂×C₅₃	semidirect
655. #3106	C₂×C₅₃	semidirect
656. #3006	C₂×C₅₃	semidirect
657. C₂×#449	C₂×C₅₃	semidirect
658. #2974	C₂×C₅₃	semidirect
671. C₂²×#41	C₂²×C₅₃	semidirect
672. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
673. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
674. C₂²×SD₁₆	C₂²×C₅₃	semidirect
675. C₂²×D₈	C₂²×C₅₃	semidirect
676. #550	C₂²×C₅₃	semidirect
677. D₄×Q₈	C₂²×C₅₃	semidirect
678. #548	C₂²×C₅₃	semidirect
681. #547	C₂²×C₅₃	semidirect
682. #547	C₂²×C₅₃	semidirect
683. #547	C₂²×C₅₃	semidirect
688. #546	C₂²×C₅₃	semidirect
691. D₄²	C₂²×C₅₃	semidirect
692. D₄²	C₂²×C₅₃	semidirect
693. D₄²	C₂²×C₅₃	semidirect
697. #532	C₂²×C₅₃	semidirect
698. #532	C₂²×C₅₃	semidirect
699. #532	C₂²×C₅₃	semidirect
701. #525	C₂²×C₅₃	semidirect
702. C₂×#121	C₂²×C₅₃	semidirect
703. C₂×#121	C₂²×C₅₃	semidirect
704. C₄×#41	C₂²×C₅₃	semidirect
707. #496	C₂²×C₅₃	semidirect
708. #493	C₂²×C₅₃	semidirect
709. #492	C₂²×C₅₃	semidirect
710. #489	C₂²×C₅₃	semidirect
711. #487	C₂²×C₅₃	semidirect
712. #486	C₂²×C₅₃	semidirect
713. #484	C₂²×C₅₃	semidirect
714. #483	C₂²×C₅₃	semidirect
715. #482	C₂²×C₅₃	semidirect
716. #482	C₂²×C₅₃	semidirect
717. #482	C₂²×C₅₃	semidirect
718. #481	C₂²×C₅₃	semidirect
719. #480	C₂²×C₅₃	semidirect
720. #477	C₂²×C₅₃	semidirect
721. #476	C₂²×C₅₃	semidirect
722. #475	C₂²×C₅₃	semidirect
723. #474	C₂²×C₅₃	semidirect
724. #469	C₂²×C₅₃	semidirect
725. #469	C₂²×C₅₃	semidirect
726. #468	C₂²×C₅₃	semidirect
727. #468	C₂²×C₅₃	semidirect
728. #466	C₂²×C₅₃	semidirect
729. #466	C₂²×C₅₃	semidirect
730. #465	C₂²×C₅₃	semidirect
731. #465	C₂²×C₅₃	semidirect
732. #463	C₂²×C₅₃	semidirect
733. #463	C₂²×C₅₃	semidirect
734. #461	C₂²×C₅₃	semidirect
735. #461	C₂²×C₅₃	semidirect
736. #460	C₂²×C₅₃	semidirect
737. #460	C₂²×C₅₃	semidirect
738. #459	C₂²×C₅₃	semidirect
739. #459	C₂²×C₅₃	semidirect
740. #459	C₂²×C₅₃	semidirect
741. #459	C₂²×C₅₃	semidirect
742. #450	C₂²×C₅₃	semidirect
743. #450	C₂²×C₅₃	semidirect
744. #449	C₂²×C₅₃	semidirect
745. #449	C₂²×C₅₃	semidirect
746. #449	C₂²×C₅₃	semidirect
747. #449	C₂²×C₅₃	semidirect
748. #449	C₂²×C₅₃	semidirect
749. #449	C₂²×C₅₃	semidirect
750. #449	C₂²×C₅₃	semidirect
751. #449	C₂²×C₅₃	semidirect
752. #449	C₂²×C₅₃	semidirect
753. #449	C₂²×C₅₃	semidirect
754. #449	C₂²×C₅₃	semidirect
755. #448	C₂²×C₅₃	semidirect
756. #448	C₂²×C₅₃	semidirect
757. #447	C₂²×C₅₃	semidirect
758. #447	C₂²×C₅₃	semidirect
759. #447	C₂²×C₅₃	semidirect
760. #447	C₂²×C₅₃	semidirect
761. #442	C₂²×C₅₃	semidirect
762. #440	C₂²×C₅₃	semidirect
763. C₄×SD₁₆	C₂²×C₅₃	semidirect
764. C₄×SD₁₆	C₂²×C₅₃	semidirect
765. C₄×D₈	C₂²×C₅₃	semidirect
766. C₄×D₈	C₂²×C₅₃	semidirect
767. #436	C₂²×C₅₃	semidirect
768. #436	C₂²×C₅₃	semidirect
769. #435	C₂²×C₅₃	semidirect
770. #435	C₂²×C₅₃	semidirect
771. C₈×D₄	C₂²×C₅₃	semidirect
772. C₈×D₄	C₂²×C₅₃	semidirect
773. #432	C₂²×C₅₃	semidirect
774. #431	C₂²×C₅₃	semidirect
775. #417	C₂²×C₅₃	semidirect
776. #417	C₂²×C₅₃	semidirect
777. C₂×#103	C₂²×C₅₃	semidirect
778. C₂×#102	C₂²×C₅₃	semidirect
779. #407	C₂²×C₅₃	semidirect
780. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
781. C₅₃	#61598	direct (N × H)
1157. Q₈	H(5,𝔽₂)×C₅₃	semidirect
1191. D₄	AGL(1,ℤ/8)×C₅₃	semidirect
1192. D₄	H(5,𝔽₂)×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3496	2
D₄×#41×C₅₃	2
C₅₃×#3332	2
C₅₃×#3330	2
C₅₃×#3308	2
C₅₃×#3306	2
C₅₃×#3298	2
C₅₃×#3294	2
D₄×SD₁₆×C₅₃	2
D₄×D₈×C₅₃	2
C₅₃×#3274	2
C₅₃×#3272	2
C₅₃×#3265	2
C₅₃×#3264	2
C₅₃×#3214	2
C₅₃×#3207	2
C₅₃×#3194	2
C₅₃×#3188	2
C₅₃×#3115	2
C₅₃×#3106	2
C₅₃×#3006	2
C₂×C₅₃×#449	2
C₅₃×#2974	2
#61598	53

Subgroups — C53×#61598 #27269110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61598 #27269110