Subgroups — C₅₃×#61989 #27269501

Order 13568.

2138 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3308	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3306	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3298	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×D₈×C₅₃	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×#3251	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3247	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3213	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3114	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#463	C₂	1	2	yes	maximal, complemented
23	C₅₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₅₃	—	2	1	no	—
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
27	C₂²×D₈×C₅₃	C₂²	1	2	yes	—
28	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#555	—	2	1	no	—
31	C₅₃×#551	—	2	2	no	—
32	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
33	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
34	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₅₃×#548	—	2	1	no	—
36	C₅₃×#548	C₂²	1	2	yes	complemented
37	C₅₃×#547	C₂²	1	1	yes	characteristic
38	C₅₃×#547	C₂²	1	2	yes	complemented
39	C₅₃×#546	—	2	1	no	—
40	C₅₃×#546	—	2	1	no	—
41	C₅₃×#546	—	2	2	no	—
42	C₅₃×#546	C₂²	1	2	yes	complemented
43	D₄²×C₅₃	C₂²	1	1	yes	characteristic
44	D₄²×C₅₃	C₂²	1	2	yes	complemented
45	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#542	—	2	1	no	—
47	C₅₃×#538	—	2	2	no	—
48	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#532	C₂²	1	2	yes	complemented
51	C₅₃×#529	C₂²	1	2	yes	complemented
52	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
53	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
54	C₅₃×#525	—	2	2	no	—
55	C₅₃×#525	—	2	1	no	—
56	C₅₃×#518	—	2	1	no	—
57	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
59	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#496	C₂²	1	2	yes	complemented
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×#489	C₂²	1	2	yes	complemented
66	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#483	C₂²	1	2	yes	complemented
70	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#480	C₂²	1	2	yes	complemented
72	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#478	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#477	C₂²	1	2	yes	complemented
76	C₅₃×#476	C₂²	1	2	yes	complemented
77	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#469	C₂²	1	2	yes	complemented
80	C₅₃×#468	C₂²	1	2	yes	complemented
81	C₅₃×#466	C₂²	1	2	yes	complemented
82	C₅₃×#466	C₂²	1	2	yes	complemented
83	C₅₃×#465	C₂²	1	2	yes	complemented
84	C₅₃×#465	C₂²	1	2	yes	complemented
85	C₅₃×#463	C₂²	1	2	yes	—
86	C₅₃×#463	C₂²	1	1	yes	characteristic
87	C₅₃×#463	C₂²	1	2	yes	complemented
88	C₅₃×#463	C₂²	1	2	yes	complemented
89	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#463	C₂²	1	2	yes	complemented
91	C₅₃×#463	C₂²	1	2	yes	complemented
92	C₅₃×#463	C₂²	1	2	yes	complemented
93	C₅₃×#463	C₂²	1	2	yes	complemented
94	C₅₃×#463	C₂²	1	2	yes	complemented
95	C₅₃×#463	C₂²	1	2	yes	complemented
96	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#460	C₂²	1	2	yes	complemented
99	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#459	C₂²	1	1	yes	characteristic
101	C₅₃×#459	C₂²	1	2	yes	complemented
102	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#450	C₂²	1	2	yes	complemented
105	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#449	C₂²	1	2	yes	complemented
107	C₅₃×#449	C₂²	1	2	yes	complemented
108	C₅₃×#448	C₂²	1	2	yes	complemented
109	C₅₃×#448	C₂²	1	2	yes	complemented
110	C₅₃×#447	C₂²	1	1	yes	characteristic
111	C₅₃×#447	C₂²	1	2	yes	—
112	C₅₃×#447	C₂²	1	2	yes	complemented
113	C₅₃×#447	C₂²	1	2	yes	complemented
114	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#442	C₂²	1	2	yes	complemented
117	C₅₃×#442	C₂²	1	2	yes	complemented
118	C₅₃×#440	C₂²	1	2	yes	complemented
119	C₅₃×#440	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#435	C₂²	1	2	yes	complemented
125	C₅₃×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#432	C₂²	1	2	yes	complemented
129	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	complemented
132	C₅₃×#417	C₂²	1	2	yes	complemented
133	C₂×#103×C₅₃	C₂²	1	2	yes	complemented
134	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	1	no	—
137	C₂×#41×C₅₃	—	2	2	no	—
138	C₂×#41×C₅₃	—	2	2	no	—
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	4	8	no	—
141	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
142	C₂×#41×C₅₃	C₂³	1	2	yes	—
143	C₂²×Q₈×C₅₃	—	2	1	no	—
144	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
145	C₂²×D₄×C₅₃	—	2	1	no	—
146	C₂²×D₄×C₅₃	—	2	1	no	—
147	C₂²×D₄×C₅₃	—	2	2	no	—
148	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
149	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
150	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
151	C₂³×C₄×C₅₃	—	2	2	no	—
152	C₂³×C₄×C₅₃	—	2	1	no	—
153	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
154	C₂×SD₁₆×C₅₃	—	4	4	no	—
155	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
160	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
162	C₂×D₈×C₅₃	—	4	4	no	—
163	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
164	C₂×D₈×C₅₃	C₂³	1	2	yes	—
165	C₂×D₈×C₅₃	C₂³	1	2	yes	—
166	C₂×D₈×C₅₃	C₂³	1	2	yes	—
167	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
168	C₂×D₈×C₅₃	C₂³	1	2	yes	—
169	C₂×D₈×C₅₃	C₂³	1	2	yes	—
170	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
171	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
172	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
173	C₄⋊Q₈×C₅₃	—	2	1	no	—
174	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
175	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
176	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
177	#127×C₅₃	C₂³	1	1	yes	characteristic
178	#127×C₅₃	C₂³	1	1	yes	characteristic
179	#127×C₅₃	C₂³	1	2	yes	—
180	#126×C₅₃	—	2	2	no	—
181	#126×C₅₃	—	2	2	no	—
182	#126×C₅₃	—	2	1	no	—
183	#125×C₅₃	C₂³	1	1	yes	characteristic
184	#124×C₅₃	—	2	2	no	—
185	#124×C₅₃	—	2	2	no	—
186	#124×C₅₃	—	2	2	no	—
187	#124×C₅₃	—	2	1	no	—
188	#124×C₅₃	—	2	2	no	—
189	#124×C₅₃	—	2	1	no	—
190	#124×C₅₃	C₂³	1	2	yes	—
191	#124×C₅₃	C₂³	1	2	yes	—
192	#124×C₅₃	C₂³	1	1	yes	characteristic
193	#124×C₅₃	C₂³	1	2	yes	—
194	#123×C₅₃	—	2	2	no	—
195	#123×C₅₃	—	2	2	no	—
196	#123×C₅₃	—	2	2	no	—
197	#123×C₅₃	—	2	2	no	—
198	#123×C₅₃	—	2	2	no	—
199	#123×C₅₃	—	2	1	no	—
200	#123×C₅₃	—	2	2	no	—
201	C₂²⋊Q₈×C₅₃	—	2	1	no	—
202	C₂²⋊Q₈×C₅₃	—	2	2	no	—
203	C₂²⋊Q₈×C₅₃	—	2	1	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	1	no	—
208	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
210	#121×C₅₃	—	2	1	no	—
211	#121×C₅₃	—	2	2	no	—
212	#121×C₅₃	—	2	1	no	—
213	#121×C₅₃	—	2	2	no	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	—	2	2	no	—
216	#121×C₅₃	—	2	2	no	—
217	#121×C₅₃	—	2	1	no	—
218	#121×C₅₃	—	2	2	no	—
219	#121×C₅₃	—	2	1	no	—
220	#121×C₅₃	—	2	1	no	—
221	#121×C₅₃	C₂³	1	2	yes	—
222	#121×C₅₃	C₂³	1	1	yes	characteristic
223	#121×C₅₃	C₂³	1	2	yes	—
224	#121×C₅₃	C₂³	1	2	yes	—
225	#121×C₅₃	C₂³	1	2	yes	—
226	#120×C₅₃	—	2	2	no	—
227	#120×C₅₃	—	2	2	no	—
228	#120×C₅₃	—	2	2	no	—
229	#120×C₅₃	—	2	2	no	—
230	#120×C₅₃	—	2	2	no	—
231	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
232	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
234	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₅₃	—	2	1	no	—
236	C₄×D₄×C₅₃	—	2	2	no	—
237	C₄×D₄×C₅₃	—	2	2	no	—
238	C₄×D₄×C₅₃	—	2	1	no	—
239	C₄×D₄×C₅₃	—	2	1	no	—
240	C₄×D₄×C₅₃	—	2	2	no	—
241	C₄×D₄×C₅₃	—	2	1	no	—
242	C₄×D₄×C₅₃	—	2	2	no	—
243	C₄×D₄×C₅₃	—	2	1	no	—
244	C₄×D₄×C₅₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
249	C₄×D₄×C₅₃	D₄	1	2	yes	—
250	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₅₃	C₂³	1	2	yes	—
252	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₅₃	C₂³	1	2	yes	—
255	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₅₃	C₂³	1	2	yes	—
257	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₅₃	C₂³	1	2	yes	—
259	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₅₃	C₂³	1	2	yes	—
261	#117×C₅₃	—	2	1	no	—
262	#117×C₅₃	—	2	1	no	—
263	#117×C₅₃	—	2	2	no	—
264	#117×C₅₃	D₄	1	2	yes	—
265	#117×C₅₃	D₄	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
272	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
273	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
274	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
275	#107×C₅₃	C₂³	1	1	yes	characteristic
276	#107×C₅₃	C₂³	1	1	yes	characteristic
277	#107×C₅₃	C₂³	1	2	yes	—
278	#106×C₅₃	C₂³	1	1	yes	characteristic
279	#106×C₅₃	C₂³	1	1	yes	characteristic
280	#106×C₅₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
284	C₄⋊C₈×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	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	1	yes	characteristic
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	#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	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	2	yes	—
307	#102×C₅₃	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
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	#97×C₅₃	C₂³	1	2	yes	—
313	#97×C₅₃	C₂³	1	2	yes	—
314	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
315	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
316	C₂⁴×C₅₃	—	2	1	no	—
317	C₂⁴×C₅₃	—	2	2	no	—
318	C₂⁴×C₅₃	—	2	2	no	—
319	#41×C₅₃	—	2	4	no	—
320	#41×C₅₃	—	4	8	no	—
321	#41×C₅₃	—	4	4	no	—
322	#41×C₅₃	—	4	2	no	—
323	#41×C₅₃	—	4	2	no	—
324	#41×C₅₃	—	4	8	no	—
325	#41×C₅₃	—	4	4	no	—
326	#41×C₅₃	—	4	4	no	—
327	C₂×Q₈×C₅₃	—	2	2	no	—
328	C₂×Q₈×C₅₃	—	2	1	no	—
329	C₂×Q₈×C₅₃	—	2	2	no	—
330	C₂×Q₈×C₅₃	—	4	2	no	—
331	C₂×Q₈×C₅₃	—	4	2	no	—
332	C₂×Q₈×C₅₃	—	4	4	no	—
333	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
334	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
335	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
336	C₂×D₄×C₅₃	—	2	4	no	—
337	C₂×D₄×C₅₃	—	2	2	no	—
338	C₂×D₄×C₅₃	—	2	2	no	—
339	C₂×D₄×C₅₃	—	2	2	no	—
340	C₂×D₄×C₅₃	—	2	2	no	—
341	C₂×D₄×C₅₃	—	2	2	no	—
342	C₂×D₄×C₅₃	—	2	1	no	—
343	C₂×D₄×C₅₃	—	2	2	no	—
344	C₂×D₄×C₅₃	—	2	1	no	—
345	C₂×D₄×C₅₃	—	2	2	no	—
346	C₂×D₄×C₅₃	—	2	1	no	—
347	C₂×D₄×C₅₃	—	2	2	no	—
348	C₂×D₄×C₅₃	—	2	1	no	—
349	C₂×D₄×C₅₃	—	2	2	no	—
350	C₂×D₄×C₅₃	—	2	1	no	—
351	C₂×D₄×C₅₃	—	2	1	no	—
352	C₂×D₄×C₅₃	—	2	2	no	—
353	C₂×D₄×C₅₃	—	4	2	no	—
354	C₂×D₄×C₅₃	—	4	1	no	—
355	C₂×D₄×C₅₃	—	4	2	no	—
356	C₂×D₄×C₅₃	—	4	2	no	—
357	C₂×D₄×C₅₃	—	4	8	no	—
358	C₂×D₄×C₅₃	—	4	4	no	—
359	C₂×D₄×C₅₃	—	4	4	no	—
360	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
361	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
362	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
364	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
366	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₅₃	—	2	1	no	—
368	C₂²×C₄×C₅₃	—	2	2	no	—
369	C₂²×C₄×C₅₃	—	2	2	no	—
370	C₂²×C₄×C₅₃	—	2	1	no	—
371	C₂²×C₄×C₅₃	—	2	1	no	—
372	C₂²×C₄×C₅₃	—	2	2	no	—
373	C₂²×C₄×C₅₃	—	2	1	no	—
374	C₂²×C₄×C₅₃	—	2	2	no	—
375	C₂²×C₄×C₅₃	—	2	1	no	—
376	C₂²×C₄×C₅₃	—	2	2	no	—
377	C₂²×C₄×C₅₃	—	2	1	no	—
378	C₂²×C₄×C₅₃	—	2	2	no	—
379	C₂²×C₄×C₅₃	—	2	2	no	—
380	C₂²×C₄×C₅₃	—	4	8	no	—
381	C₂²×C₄×C₅₃	—	4	4	no	—
382	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
383	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
385	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
387	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	SD₁₆×C₅₃	—	2	2	no	—
389	SD₁₆×C₅₃	—	2	4	no	—
390	SD₁₆×C₅₃	—	4	2	no	—
391	SD₁₆×C₅₃	—	4	2	no	—
392	SD₁₆×C₅₃	—	4	1	no	—
393	SD₁₆×C₅₃	—	4	2	no	—
394	SD₁₆×C₅₃	—	4	2	no	—
395	D₈×C₅₃	—	2	2	no	—
396	D₈×C₅₃	—	2	4	no	—
397	D₈×C₅₃	—	4	2	no	—
398	D₈×C₅₃	—	4	2	no	—
399	D₈×C₅₃	—	4	2	no	—
400	D₈×C₅₃	—	4	1	no	—
401	D₈×C₅₃	—	4	2	no	—
402	M₁₆×C₅₃	—	4	2	no	—
403	C₂×C₈×C₅₃	—	4	2	no	—
404	C₂×C₈×C₅₃	—	4	2	no	—
405	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
410	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₅₃	—	2	1	no	—
412	C₄⋊C₄×C₅₃	—	2	2	no	—
413	C₄⋊C₄×C₅₃	—	2	1	no	—
414	C₄⋊C₄×C₅₃	—	2	1	no	—
415	C₄⋊C₄×C₅₃	—	2	1	no	—
416	C₄⋊C₄×C₅₃	—	2	1	no	—
417	C₄⋊C₄×C₅₃	—	2	2	no	—
418	C₄⋊C₄×C₅₃	—	2	2	no	—
419	C₄⋊C₄×C₅₃	—	2	1	no	—
420	C₄⋊C₄×C₅₃	—	2	1	no	—
421	C₄⋊C₄×C₅₃	—	2	2	no	—
422	C₄⋊C₄×C₅₃	—	2	1	no	—
423	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
424	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
425	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
426	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
427	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
429	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
430	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
431	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₂²⋊C₄×C₅₃	—	2	2	no	—
433	C₂²⋊C₄×C₅₃	—	2	1	no	—
434	C₂²⋊C₄×C₅₃	—	2	1	no	—
435	C₂²⋊C₄×C₅₃	—	2	2	no	—
436	C₂²⋊C₄×C₅₃	—	2	1	no	—
437	C₂²⋊C₄×C₅₃	—	2	1	no	—
438	C₂²⋊C₄×C₅₃	—	2	1	no	—
439	C₂²⋊C₄×C₅₃	—	2	2	no	—
440	C₂²⋊C₄×C₅₃	—	2	2	no	—
441	C₂²⋊C₄×C₅₃	—	2	2	no	—
442	C₂²⋊C₄×C₅₃	—	2	2	no	—
443	C₂²⋊C₄×C₅₃	—	2	1	no	—
444	C₂²⋊C₄×C₅₃	—	2	2	no	—
445	C₂²⋊C₄×C₅₃	—	2	1	no	—
446	C₂²⋊C₄×C₅₃	—	2	2	no	—
447	C₂²⋊C₄×C₅₃	—	2	1	no	—
448	C₂²⋊C₄×C₅₃	—	2	2	no	—
449	C₂²⋊C₄×C₅₃	—	2	2	no	—
450	C₂²⋊C₄×C₅₃	—	2	2	no	—
451	C₂²⋊C₄×C₅₃	—	2	2	no	—
452	C₂²⋊C₄×C₅₃	—	2	2	no	—
453	C₂²⋊C₄×C₅₃	—	2	2	no	—
454	C₂²⋊C₄×C₅₃	—	2	1	no	—
455	C₂²⋊C₄×C₅₃	—	2	2	no	—
456	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
457	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
458	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
459	C₄²×C₅₃	—	2	2	no	—
460	C₄²×C₅₃	—	2	1	no	—
461	C₄²×C₅₃	C₂×D₄	1	2	yes	—
462	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
463	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
464	C₄²×C₅₃	C₂×D₄	1	2	yes	—
465	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
466	C₄²×C₅₃	C₂⁴	1	2	yes	—
467	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
468	C₂³×C₅₃	—	2	1	no	—
469	C₂³×C₅₃	—	2	2	no	—
470	C₂³×C₅₃	—	2	1	no	—
471	C₂³×C₅₃	—	2	2	no	—
472	C₂³×C₅₃	—	2	1	no	—
473	C₂³×C₅₃	—	4	4	no	—
474	C₂³×C₅₃	—	4	2	no	—
475	C₂³×C₅₃	—	4	2	no	—
476	C₂³×C₅₃	—	4	4	no	—
477	C₂³×C₅₃	—	4	4	no	—
478	C₂³×C₅₃	—	8	2	no	—
479	C₂³×C₅₃	—	8	1	no	—
480	C₂³×C₅₃	—	8	2	no	—
481	C₂³×C₅₃	—	8	2	no	—
482	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
483	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
484	Q₈×C₅₃	—	2	2	no	—
485	Q₈×C₅₃	—	2	1	no	—
486	Q₈×C₅₃	—	2	2	no	—
487	Q₈×C₅₃	—	2	1	no	—
488	Q₈×C₅₃	—	2	2	no	—
489	Q₈×C₅₃	—	4	4	no	—
490	Q₈×C₅₃	—	4	2	no	—
491	Q₈×C₅₃	—	8	2	no	—
492	D₄×C₅₃	—	2	4	no	—
493	D₄×C₅₃	—	2	2	no	—
494	D₄×C₅₃	—	2	1	no	—
495	D₄×C₅₃	—	2	1	no	—
496	D₄×C₅₃	—	2	2	no	—
497	D₄×C₅₃	—	2	1	no	—
498	D₄×C₅₃	—	2	1	no	—
499	D₄×C₅₃	—	2	2	no	—
500	D₄×C₅₃	—	2	2	no	—
501	D₄×C₅₃	—	2	1	no	—
502	D₄×C₅₃	—	4	2	no	—
503	D₄×C₅₃	—	4	4	no	—
504	D₄×C₅₃	—	4	4	no	—
505	D₄×C₅₃	—	4	4	no	—
506	D₄×C₅₃	—	4	4	no	—
507	D₄×C₅₃	—	4	4	no	—
508	D₄×C₅₃	—	4	4	no	—
509	D₄×C₅₃	—	4	2	no	—
510	D₄×C₅₃	—	4	2	no	—
511	D₄×C₅₃	—	8	2	no	—
512	D₄×C₅₃	—	8	1	no	—
513	D₄×C₅₃	—	8	1	no	—
514	D₄×C₅₃	—	8	2	no	—
515	D₄×C₅₃	—	8	1	no	—
516	D₄×C₅₃	—	8	2	no	—
517	D₄×C₅₃	AGL(1,ℤ/8)	1	4	yes	complemented
518	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
519	C₂×C₄×C₅₃	—	2	4	no	—
520	C₂×C₄×C₅₃	—	2	2	no	—
521	C₂×C₄×C₅₃	—	2	2	no	—
522	C₂×C₄×C₅₃	—	2	1	no	—
523	C₂×C₄×C₅₃	—	2	2	no	—
524	C₂×C₄×C₅₃	—	2	1	no	—
525	C₂×C₄×C₅₃	—	2	1	no	—
526	C₂×C₄×C₅₃	—	2	2	no	—
527	C₂×C₄×C₅₃	—	2	1	no	—
528	C₂×C₄×C₅₃	—	2	2	no	—
529	C₂×C₄×C₅₃	—	2	1	no	—
530	C₂×C₄×C₅₃	—	2	1	no	—
531	C₂×C₄×C₅₃	—	2	1	no	—
532	C₂×C₄×C₅₃	—	4	2	no	—
533	C₂×C₄×C₅₃	—	4	1	no	—
534	C₂×C₄×C₅₃	—	4	2	no	—
535	C₂×C₄×C₅₃	—	4	4	no	—
536	C₂×C₄×C₅₃	—	4	4	no	—
537	C₂×C₄×C₅₃	—	4	2	no	—
538	C₂×C₄×C₅₃	—	4	4	no	—
539	C₂×C₄×C₅₃	—	4	2	no	—
540	C₂×C₄×C₅₃	—	4	4	no	—
541	C₂×C₄×C₅₃	—	4	2	no	—
542	C₂×C₄×C₅₃	—	4	2	no	—
543	C₂×C₄×C₅₃	—	4	2	no	—
544	C₂×C₄×C₅₃	—	8	2	no	—
545	C₂×C₄×C₅₃	—	8	2	no	—
546	C₂×C₄×C₅₃	—	8	2	no	—
547	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
551	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
554	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
556	C₈×C₅₃	—	2	1	no	—
557	C₈×C₅₃	—	2	1	no	—
558	C₈×C₅₃	—	2	2	no	—
559	C₈×C₅₃	—	2	2	no	—
560	C₈×C₅₃	—	2	1	no	—
561	C₈×C₅₃	—	2	1	no	—
562	#61989	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
563	C₂²×C₅₃	—	2	2	no	—
564	C₂²×C₅₃	—	2	2	no	—
565	C₂²×C₅₃	—	2	1	no	—
566	C₂²×C₅₃	—	2	1	no	—
567	C₂²×C₅₃	—	2	2	no	—
568	C₂²×C₅₃	—	2	1	no	—
569	C₂²×C₅₃	—	4	1	no	—
570	C₂²×C₅₃	—	4	1	no	—
571	C₂²×C₅₃	—	4	2	no	—
572	C₂²×C₅₃	—	4	2	no	—
573	C₂²×C₅₃	—	4	1	no	—
574	C₂²×C₅₃	—	4	1	no	—
575	C₂²×C₅₃	—	4	2	no	—
576	C₂²×C₅₃	—	4	2	no	—
577	C₂²×C₅₃	—	4	1	no	—
578	C₂²×C₅₃	—	4	1	no	—
579	C₂²×C₅₃	—	4	2	no	—
580	C₂²×C₅₃	—	4	1	no	—
581	C₂²×C₅₃	—	4	1	no	—
582	C₂²×C₅₃	—	4	2	no	—
583	C₂²×C₅₃	—	8	8	no	—
584	C₂²×C₅₃	—	8	4	no	—
585	C₂²×C₅₃	—	16	4	no	—
586	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
587	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
588	C₄×C₅₃	—	2	1	no	—
589	C₄×C₅₃	—	2	2	no	—
590	C₄×C₅₃	—	2	1	no	—
591	C₄×C₅₃	—	2	1	no	—
592	C₄×C₅₃	—	2	2	no	—
593	C₄×C₅₃	—	2	1	no	—
594	C₄×C₅₃	—	2	2	no	—
595	C₄×C₅₃	—	4	1	no	—
596	C₄×C₅₃	—	4	2	no	—
597	C₄×C₅₃	—	4	1	no	—
598	C₄×C₅₃	—	4	1	no	—
599	C₄×C₅₃	—	4	2	no	—
600	C₄×C₅₃	—	4	1	no	—
601	C₄×C₅₃	—	4	1	no	—
602	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
603	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
604	C₄×C₅₃	#585	1	1	yes	characteristic
605	#3514	C₂×C₅₃	1	1	yes	characteristic, complemented
606	D₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
607	#3399	C₂×C₅₃	1	1	yes	characteristic, complemented
608	#3397	C₂×C₅₃	1	1	yes	characteristic, complemented
609	#3373	C₂×C₅₃	1	1	yes	characteristic, complemented
610	#3367	C₂×C₅₃	1	1	yes	characteristic, complemented
611	#3308	C₂×C₅₃	1	2	yes	complemented
612	#3306	C₂×C₅₃	1	2	yes	complemented
613	#3298	C₂×C₅₃	1	1	yes	characteristic, complemented
614	#3294	C₂×C₅₃	1	1	yes	characteristic, complemented
615	D₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
616	D₄×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
617	#3265	C₂×C₅₃	1	2	yes	complemented
618	#3264	C₂×C₅₃	1	2	yes	complemented
619	#3251	C₂×C₅₃	1	1	yes	characteristic, complemented
620	#3247	C₂×C₅₃	1	2	yes	complemented
621	#3213	C₂×C₅₃	1	2	yes	complemented
622	#3207	C₂×C₅₃	1	1	yes	characteristic, complemented
623	#3114	C₂×C₅₃	1	2	yes	complemented
624	#3105	C₂×C₅₃	1	1	yes	characteristic, complemented
625	#3036	C₂×C₅₃	1	1	yes	characteristic, complemented
626	C₂×#463	C₂×C₅₃	1	2	yes	complemented
627	#2990	C₂×C₅₃	1	1	yes	characteristic, complemented
628	C₂×C₅₃	—	2	4	no	—
629	C₂×C₅₃	—	4	1	no	—
630	C₂×C₅₃	—	4	2	no	—
631	C₂×C₅₃	—	8	2	no	—
632	C₂×C₅₃	—	8	1	no	—
633	C₂×C₅₃	—	8	2	no	—
634	C₂×C₅₃	—	8	1	no	—
635	C₂×C₅₃	#3488	1	1	yes	characteristic
636	C₂×C₅₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
637	C₂×C₅₃	#3584	1	1	yes	characteristic
638	C₂²×#41	—	2	1	no	—
639	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
640	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
641	C₂²×D₈	C₂²×C₅₃	1	2	yes	—
642	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
643	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
644	#555	—	2	1	no	—
645	#551	—	2	2	no	—
646	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
647	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
648	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
649	#548	—	2	1	no	—
650	#548	C₂²×C₅₃	1	2	yes	complemented
651	#547	C₂²×C₅₃	1	1	yes	characteristic
652	#547	C₂²×C₅₃	1	2	yes	complemented
653	#546	—	2	1	no	—
654	#546	—	2	1	no	—
655	#546	—	2	2	no	—
656	#546	C₂²×C₅₃	1	2	yes	complemented
657	D₄²	C₂²×C₅₃	1	1	yes	characteristic
658	D₄²	C₂²×C₅₃	1	2	yes	complemented
659	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
660	#542	—	2	1	no	—
661	#538	—	2	2	no	—
662	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
664	#532	C₂²×C₅₃	1	2	yes	complemented
665	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
666	#529	C₂²×C₅₃	1	2	yes	complemented
667	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
668	#525	—	2	2	no	—
669	#525	—	2	1	no	—
670	#518	—	2	1	no	—
671	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
672	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
673	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
674	#496	C₂²×C₅₃	1	2	yes	complemented
675	#496	C₂²×C₅₃	1	2	yes	complemented
676	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
677	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
678	#489	C₂²×C₅₃	1	2	yes	complemented
679	#489	C₂²×C₅₃	1	2	yes	complemented
680	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
681	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
682	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
683	#483	C₂²×C₅₃	1	2	yes	complemented
684	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
685	#480	C₂²×C₅₃	1	2	yes	complemented
686	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
688	#478	C₂²×C₅₃	1	2	yes	complemented
689	#477	C₂²×C₅₃	1	2	yes	complemented
690	#476	C₂²×C₅₃	1	2	yes	complemented
691	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
692	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	#469	C₂²×C₅₃	1	2	yes	complemented
694	#468	C₂²×C₅₃	1	2	yes	complemented
695	#466	C₂²×C₅₃	1	2	yes	complemented
696	#466	C₂²×C₅₃	1	2	yes	complemented
697	#465	C₂²×C₅₃	1	2	yes	complemented
698	#465	C₂²×C₅₃	1	2	yes	complemented
699	#463	C₂²×C₅₃	1	1	yes	characteristic
700	#463	C₂²×C₅₃	1	2	yes	—
701	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
702	#463	C₂²×C₅₃	1	2	yes	complemented
703	#463	C₂²×C₅₃	1	2	yes	complemented
704	#463	C₂²×C₅₃	1	2	yes	complemented
705	#463	C₂²×C₅₃	1	2	yes	complemented
706	#463	C₂²×C₅₃	1	2	yes	complemented
707	#463	C₂²×C₅₃	1	2	yes	complemented
708	#463	C₂²×C₅₃	1	2	yes	complemented
709	#463	C₂²×C₅₃	1	2	yes	complemented
710	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
711	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	#460	C₂²×C₅₃	1	2	yes	complemented
713	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
714	#459	C₂²×C₅₃	1	1	yes	characteristic
715	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
716	#459	C₂²×C₅₃	1	2	yes	complemented
717	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
718	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
719	#450	C₂²×C₅₃	1	2	yes	complemented
720	#449	C₂²×C₅₃	1	2	yes	complemented
721	#449	C₂²×C₅₃	1	2	yes	complemented
722	#448	C₂²×C₅₃	1	2	yes	complemented
723	#448	C₂²×C₅₃	1	2	yes	complemented
724	#447	C₂²×C₅₃	1	1	yes	characteristic
725	#447	C₂²×C₅₃	1	2	yes	—
726	#447	C₂²×C₅₃	1	2	yes	complemented
727	#447	C₂²×C₅₃	1	2	yes	complemented
728	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
729	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
730	#442	C₂²×C₅₃	1	2	yes	complemented
731	#442	C₂²×C₅₃	1	2	yes	complemented
732	#440	C₂²×C₅₃	1	2	yes	complemented
733	#440	C₂²×C₅₃	1	2	yes	complemented
734	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
735	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
736	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
737	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
738	#435	C₂²×C₅₃	1	2	yes	complemented
739	#435	C₂²×C₅₃	1	2	yes	complemented
740	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
741	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
742	#432	C₂²×C₅₃	1	2	yes	complemented
743	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
744	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
745	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	complemented
746	#417	C₂²×C₅₃	1	2	yes	complemented
747	C₂×#103	C₂²×C₅₃	1	2	yes	complemented
748	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
749	C₅₃	#61989	1	1	yes	characteristic, direct product factor, Sylow
750	C₂×#41	—	2	1	no	—
751	C₂×#41	—	2	1	no	—
752	C₂×#41	—	2	2	no	—
753	C₂×#41	—	2	2	no	—
754	C₂×#41	—	2	1	no	—
755	C₂×#41	—	4	8	no	—
756	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
757	C₂×#41	C₂³×C₅₃	1	2	yes	—
758	C₂²×Q₈	—	2	1	no	—
759	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
760	C₂²×D₄	—	2	1	no	—
761	C₂²×D₄	—	2	1	no	—
762	C₂²×D₄	—	2	2	no	—
763	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
764	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
765	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
766	C₂³×C₄	—	2	2	no	—
767	C₂³×C₄	—	2	1	no	—
768	AGL(1,ℤ/8)	—	4	4	no	—
769	C₂×SD₁₆	—	4	4	no	—
770	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
771	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
772	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
773	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
776	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
777	C₂×D₈	—	4	4	no	—
778	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
779	C₂×D₈	C₂³×C₅₃	1	2	yes	—
780	C₂×D₈	C₂³×C₅₃	1	2	yes	—
781	C₂×D₈	C₂³×C₅₃	1	2	yes	—
782	C₂×D₈	C₂³×C₅₃	1	2	yes	—
783	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
784	C₂×D₈	C₂³×C₅₃	1	2	yes	—
785	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
786	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
787	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
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	2	yes	—
792	#127	C₂³×C₅₃	1	1	yes	characteristic
793	#127	C₂³×C₅₃	1	2	yes	—
794	#127	C₂³×C₅₃	1	1	yes	characteristic
795	#126	—	2	2	no	—
796	#126	—	2	2	no	—
797	#126	—	2	1	no	—
798	#125	C₂³×C₅₃	1	1	yes	characteristic
799	#124	—	2	1	no	—
800	#124	—	2	2	no	—
801	#124	—	2	2	no	—
802	#124	—	2	2	no	—
803	#124	—	2	1	no	—
804	#124	—	2	2	no	—
805	#124	C₂³×C₅₃	1	1	yes	characteristic
806	#124	C₂³×C₅₃	1	2	yes	—
807	#124	C₂³×C₅₃	1	2	yes	—
808	#124	C₂³×C₅₃	1	2	yes	—
809	#123	—	2	1	no	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	C₂²⋊Q₈	—	2	1	no	—
817	C₂²⋊Q₈	—	2	1	no	—
818	C₂²⋊Q₈	—	2	2	no	—
819	C₂²⋊Q₈	—	2	1	no	—
820	C₂²⋊Q₈	—	2	2	no	—
821	C₂²⋊Q₈	—	2	2	no	—
822	C₂²⋊Q₈	—	2	2	no	—
823	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
824	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
825	#121	—	2	2	no	—
826	#121	—	2	1	no	—
827	#121	—	2	2	no	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	2	no	—
832	#121	—	2	1	no	—
833	#121	—	2	2	no	—
834	#121	—	2	1	no	—
835	#121	—	2	2	no	—
836	#121	C₂³×C₅₃	1	2	yes	—
837	#121	C₂³×C₅₃	1	1	yes	characteristic
838	#121	C₂³×C₅₃	1	2	yes	—
839	#121	C₂³×C₅₃	1	2	yes	—
840	#121	C₂³×C₅₃	1	2	yes	—
841	#120	—	2	2	no	—
842	#120	—	2	2	no	—
843	#120	—	2	2	no	—
844	#120	—	2	2	no	—
845	#120	—	2	2	no	—
846	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
847	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
848	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
849	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	2	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	2	no	—
855	C₄×D₄	—	2	2	no	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	2	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	2	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	1	no	—
863	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
864	C₄×D₄	D₄×C₅₃	1	2	yes	—
865	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
866	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
867	C₄×D₄	C₂³×C₅₃	1	2	yes	—
868	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
869	C₄×D₄	C₂³×C₅₃	1	2	yes	—
870	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
871	C₄×D₄	C₂³×C₅₃	1	2	yes	—
872	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
873	C₄×D₄	C₂³×C₅₃	1	2	yes	—
874	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
875	C₄×D₄	C₂³×C₅₃	1	2	yes	—
876	#117	—	2	1	no	—
877	#117	—	2	1	no	—
878	#117	—	2	2	no	—
879	#117	D₄×C₅₃	1	2	yes	—
880	#117	D₄×C₅₃	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
882	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
883	C₂×C₂²⋊C₄	—	2	2	no	—
884	C₂×C₂²⋊C₄	—	2	1	no	—
885	C₂×C₂²⋊C₄	—	2	2	no	—
886	C₂×C₂²⋊C₄	—	2	2	no	—
887	C₂×C₂²⋊C₄	—	2	2	no	—
888	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
889	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
890	#107	C₂³×C₅₃	1	1	yes	characteristic
891	#107	C₂³×C₅₃	1	1	yes	characteristic
892	#107	C₂³×C₅₃	1	2	yes	—
893	#106	C₂³×C₅₃	1	1	yes	characteristic
894	#106	C₂³×C₅₃	1	1	yes	characteristic
895	#106	C₂³×C₅₃	1	2	yes	—
896	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
897	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
898	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
899	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
900	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
901	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
902	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
903	#103	C₂³×C₅₃	1	1	yes	characteristic
904	#103	C₂³×C₅₃	1	2	yes	—
905	#103	C₂³×C₅₃	1	2	yes	—
906	#103	C₂³×C₅₃	1	2	yes	—
907	#103	C₂³×C₅₃	1	2	yes	—
908	#103	C₂³×C₅₃	1	1	yes	characteristic
909	#103	C₂³×C₅₃	1	2	yes	—
910	#102	C₂³×C₅₃	1	1	yes	characteristic
911	#102	C₂³×C₅₃	1	2	yes	—
912	#102	C₂³×C₅₃	1	2	yes	—
913	#102	C₂³×C₅₃	1	2	yes	—
914	#102	C₂³×C₅₃	1	2	yes	—
915	#102	C₂³×C₅₃	1	1	yes	characteristic
916	#102	C₂³×C₅₃	1	1	yes	characteristic
917	#102	C₂³×C₅₃	1	1	yes	characteristic
918	#102	C₂³×C₅₃	1	1	yes	characteristic
919	#102	C₂³×C₅₃	1	1	yes	characteristic
920	#102	C₂³×C₅₃	1	2	yes	—
921	#102	C₂³×C₅₃	1	2	yes	—
922	#102	C₂³×C₅₃	1	2	yes	—
923	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
924	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
925	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
926	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
927	#97	C₂³×C₅₃	1	2	yes	—
928	#97	C₂³×C₅₃	1	2	yes	—
929	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
930	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
931	C₂⁴	—	2	1	no	—
932	C₂⁴	—	2	2	no	—
933	C₂⁴	—	2	2	no	—
934	#41	—	2	4	no	—
935	#41	—	4	8	no	—
936	#41	—	4	4	no	—
937	#41	—	4	2	no	—
938	#41	—	4	2	no	—
939	#41	—	4	8	no	—
940	#41	—	4	4	no	—
941	#41	—	4	4	no	—
942	C₂×Q₈	—	2	2	no	—
943	C₂×Q₈	—	2	1	no	—
944	C₂×Q₈	—	2	2	no	—
945	C₂×Q₈	—	4	2	no	—
946	C₂×Q₈	—	4	2	no	—
947	C₂×Q₈	—	4	4	no	—
948	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
949	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
950	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
951	C₂×D₄	—	2	4	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	1	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	4	2	no	—
969	C₂×D₄	—	4	1	no	—
970	C₂×D₄	—	4	2	no	—
971	C₂×D₄	—	4	2	no	—
972	C₂×D₄	—	4	8	no	—
973	C₂×D₄	—	4	4	no	—
974	C₂×D₄	—	4	4	no	—
975	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
976	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
977	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
978	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
979	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
980	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
981	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
982	C₂²×C₄	—	2	1	no	—
983	C₂²×C₄	—	2	2	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	1	no	—
986	C₂²×C₄	—	2	1	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	—	2	2	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	4	8	no	—
996	C₂²×C₄	—	4	4	no	—
997	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
998	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
999	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1000	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1001	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1002	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1003	SD₁₆	—	2	2	no	—
1004	SD₁₆	—	2	4	no	—
1005	SD₁₆	—	4	2	no	—
1006	SD₁₆	—	4	2	no	—
1007	SD₁₆	—	4	2	no	—
1008	SD₁₆	—	4	1	no	—
1009	SD₁₆	—	4	2	no	—
1010	D₈	—	2	2	no	—
1011	D₈	—	2	4	no	—
1012	D₈	—	4	2	no	—
1013	D₈	—	4	2	no	—
1014	D₈	—	4	2	no	—
1015	D₈	—	4	2	no	—
1016	D₈	—	4	1	no	—
1017	M₁₆	—	4	2	no	—
1018	C₂×C₈	—	4	2	no	—
1019	C₂×C₈	—	4	2	no	—
1020	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1021	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1022	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1023	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1024	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1025	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1039	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1040	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1041	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1042	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1043	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1044	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1045	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1046	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	1	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	1	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1072	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1073	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1074	C₄²	—	2	2	no	—
1075	C₄²	—	2	1	no	—
1076	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1077	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1078	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1079	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1080	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1081	C₄²	C₂⁴×C₅₃	1	2	yes	—
1082	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1083	C₂³	—	2	1	no	—
1084	C₂³	—	2	1	no	—
1085	C₂³	—	2	2	no	—
1086	C₂³	—	2	2	no	—
1087	C₂³	—	2	1	no	—
1088	C₂³	—	4	4	no	—
1089	C₂³	—	4	2	no	—
1090	C₂³	—	4	2	no	—
1091	C₂³	—	4	4	no	—
1092	C₂³	—	4	4	no	—
1093	C₂³	—	8	2	no	—
1094	C₂³	—	8	1	no	—
1095	C₂³	—	8	2	no	—
1096	C₂³	—	8	2	no	—
1097	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1098	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	2	1	no	—
1101	Q₈	—	2	2	no	—
1102	Q₈	—	2	1	no	—
1103	Q₈	—	2	2	no	—
1104	Q₈	—	4	4	no	—
1105	Q₈	—	4	2	no	—
1106	Q₈	—	8	2	no	—
1107	D₄	—	2	4	no	—
1108	D₄	—	2	1	no	—
1109	D₄	—	2	2	no	—
1110	D₄	—	2	2	no	—
1111	D₄	—	2	1	no	—
1112	D₄	—	2	1	no	—
1113	D₄	—	2	2	no	—
1114	D₄	—	2	1	no	—
1115	D₄	—	2	1	no	—
1116	D₄	—	2	2	no	—
1117	D₄	—	4	2	no	—
1118	D₄	—	4	4	no	—
1119	D₄	—	4	4	no	—
1120	D₄	—	4	4	no	—
1121	D₄	—	4	4	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	8	2	no	—
1127	D₄	—	8	1	no	—
1128	D₄	—	8	1	no	—
1129	D₄	—	8	2	no	—
1130	D₄	—	8	1	no	—
1131	D₄	—	8	2	no	—
1132	D₄	AGL(1,ℤ/8)×C₅₃	1	4	yes	complemented
1133	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1134	C₂×C₄	—	2	4	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	4	2	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	2	no	—
1150	C₂×C₄	—	4	4	no	—
1151	C₂×C₄	—	4	4	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	4	4	no	—
1154	C₂×C₄	—	4	2	no	—
1155	C₂×C₄	—	4	4	no	—
1156	C₂×C₄	—	4	2	no	—
1157	C₂×C₄	—	4	2	no	—
1158	C₂×C₄	—	4	2	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	—	8	2	no	—
1161	C₂×C₄	—	8	2	no	—
1162	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1163	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1165	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1166	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1167	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1168	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1169	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1170	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1171	C₈	—	2	1	no	—
1172	C₈	—	2	1	no	—
1173	C₈	—	2	2	no	—
1174	C₈	—	2	2	no	—
1175	C₈	—	2	1	no	—
1176	C₈	—	2	1	no	—
1177	C₂²	—	2	2	no	—
1178	C₂²	—	2	2	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	4	2	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	2	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	2	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	8	8	no	—
1198	C₂²	—	8	4	no	—
1199	C₂²	—	16	4	no	—
1200	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	4	yes	—
1201	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1202	C₄	—	2	1	no	—
1203	C₄	—	2	2	no	—
1204	C₄	—	2	1	no	—
1205	C₄	—	2	2	no	—
1206	C₄	—	2	1	no	—
1207	C₄	—	2	2	no	—
1208	C₄	—	2	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	2	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	1	no	—
1216	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
1217	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1218	C₄	C₅₃×#585	1	1	yes	characteristic
1219	C₂	—	2	4	no	—
1220	C₂	—	4	1	no	—
1221	C₂	—	4	2	no	—
1222	C₂	—	8	2	no	—
1223	C₂	—	8	1	no	—
1224	C₂	—	8	1	no	—
1225	C₂	—	8	2	no	—
1226	C₂	C₅₃×#3488	1	1	yes	characteristic
1227	C₂	C₂²×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
1228	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 ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3514	C₂	semidirect
2. D₄×#41×C₅₃	C₂	semidirect
3. C₅₃×#3399	C₂	semidirect
4. C₅₃×#3397	C₂	semidirect
5. C₅₃×#3373	C₂	semidirect
6. C₅₃×#3367	C₂	semidirect
7. C₅₃×#3308	C₂	semidirect
8. C₅₃×#3306	C₂	semidirect
9. C₅₃×#3298	C₂	semidirect
10. C₅₃×#3294	C₂	semidirect
11. D₄×SD₁₆×C₅₃	C₂	semidirect
12. D₄×D₈×C₅₃	C₂	semidirect
13. C₅₃×#3265	C₂	semidirect
14. C₅₃×#3264	C₂	semidirect
15. C₅₃×#3251	C₂	semidirect
16. C₅₃×#3247	C₂	semidirect
17. C₅₃×#3213	C₂	semidirect
18. C₅₃×#3207	C₂	semidirect
19. C₅₃×#3114	C₂	semidirect
20. C₅₃×#3105	C₂	semidirect
21. C₅₃×#3036	C₂	semidirect
22. C₂×C₅₃×#463	C₂	semidirect
23. C₅₃×#2990	C₂	semidirect
25. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
26. C₂²×SD₁₆×C₅₃	C₂²	semidirect
28. C₅₃×#559	C₂²	semidirect
29. C₅₃×#556	C₂²	semidirect
32. C₅₃×#550	C₂²	semidirect
33. D₄×Q₈×C₅₃	C₂²	semidirect
34. D₄×Q₈×C₅₃	C₂²	semidirect
36. C₅₃×#548	C₂²	semidirect
38. C₅₃×#547	C₂²	semidirect
42. C₅₃×#546	C₂²	semidirect
44. D₄²×C₅₃	C₂²	semidirect
45. D₄²×C₅₃	C₂²	semidirect
48. C₅₃×#532	C₂²	semidirect
49. C₅₃×#532	C₂²	semidirect
50. C₅₃×#532	C₂²	semidirect
51. C₅₃×#529	C₂²	semidirect
52. C₅₃×#529	C₂²	semidirect
53. C₂×#124×C₅₃	C₂²	semidirect
58. C₂×C₄×D₄×C₅₃	C₂²	semidirect
59. C₂×C₄×D₄×C₅₃	C₂²	semidirect
60. C₅₃×#496	C₂²	semidirect
61. C₅₃×#496	C₂²	semidirect
62. C₅₃×#493	C₂²	semidirect
63. C₅₃×#492	C₂²	semidirect
64. C₅₃×#489	C₂²	semidirect
65. C₅₃×#489	C₂²	semidirect
66. C₅₃×#487	C₂²	semidirect
67. C₅₃×#486	C₂²	semidirect
68. C₅₃×#484	C₂²	semidirect
69. C₅₃×#483	C₂²	semidirect
70. C₅₃×#481	C₂²	semidirect
71. C₅₃×#480	C₂²	semidirect
72. C₅₃×#478	C₂²	semidirect
73. C₅₃×#478	C₂²	semidirect
74. C₅₃×#478	C₂²	semidirect
75. C₅₃×#477	C₂²	semidirect
76. C₅₃×#476	C₂²	semidirect
77. C₅₃×#475	C₂²	semidirect
78. C₅₃×#474	C₂²	semidirect
79. C₅₃×#469	C₂²	semidirect
80. C₅₃×#468	C₂²	semidirect
81. C₅₃×#466	C₂²	semidirect
82. C₅₃×#466	C₂²	semidirect
83. C₅₃×#465	C₂²	semidirect
84. C₅₃×#465	C₂²	semidirect
87. C₅₃×#463	C₂²	semidirect
88. C₅₃×#463	C₂²	semidirect
89. C₅₃×#463	C₂²	semidirect
90. C₅₃×#463	C₂²	semidirect
91. C₅₃×#463	C₂²	semidirect
92. C₅₃×#463	C₂²	semidirect
93. C₅₃×#463	C₂²	semidirect
94. C₅₃×#463	C₂²	semidirect
95. C₅₃×#463	C₂²	semidirect
96. C₅₃×#461	C₂²	semidirect
97. C₅₃×#461	C₂²	semidirect
98. C₅₃×#460	C₂²	semidirect
99. C₅₃×#460	C₂²	semidirect
101. C₅₃×#459	C₂²	semidirect
102. C₅₃×#459	C₂²	semidirect
103. C₅₃×#459	C₂²	semidirect
104. C₅₃×#450	C₂²	semidirect
105. C₅₃×#450	C₂²	semidirect
106. C₅₃×#449	C₂²	semidirect
107. C₅₃×#449	C₂²	semidirect
108. C₅₃×#448	C₂²	semidirect
109. C₅₃×#448	C₂²	semidirect
112. C₅₃×#447	C₂²	semidirect
113. C₅₃×#447	C₂²	semidirect
114. C₅₃×#446	C₂²	semidirect
115. C₅₃×#446	C₂²	semidirect
116. C₅₃×#442	C₂²	semidirect
117. C₅₃×#442	C₂²	semidirect
118. C₅₃×#440	C₂²	semidirect
119. C₅₃×#440	C₂²	semidirect
120. C₄×SD₁₆×C₅₃	C₂²	semidirect
121. C₄×SD₁₆×C₅₃	C₂²	semidirect
123. C₄×D₈×C₅₃	C₂²	semidirect
124. C₅₃×#435	C₂²	semidirect
125. C₅₃×#435	C₂²	semidirect
126. C₈×D₄×C₅₃	C₂²	semidirect
127. C₈×D₄×C₅₃	C₂²	semidirect
128. C₅₃×#432	C₂²	semidirect
129. C₅₃×#431	C₂²	semidirect
130. C₅₃×#423	C₂²	semidirect
131. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
132. C₅₃×#417	C₂²	semidirect
133. C₂×#103×C₅₃	C₂²	semidirect
134. C₂×#102×C₅₃	C₂²	semidirect
517. D₄×C₅₃	AGL(1,ℤ/8)	semidirect
562. #61989	C₅₃	direct (N × H)
605. #3514	C₂×C₅₃	semidirect
606. D₄×#41	C₂×C₅₃	semidirect
607. #3399	C₂×C₅₃	semidirect
608. #3397	C₂×C₅₃	semidirect
609. #3373	C₂×C₅₃	semidirect
610. #3367	C₂×C₅₃	semidirect
611. #3308	C₂×C₅₃	semidirect
612. #3306	C₂×C₅₃	semidirect
613. #3298	C₂×C₅₃	semidirect
614. #3294	C₂×C₅₃	semidirect
615. D₄×SD₁₆	C₂×C₅₃	semidirect
616. D₄×D₈	C₂×C₅₃	semidirect
617. #3265	C₂×C₅₃	semidirect
618. #3264	C₂×C₅₃	semidirect
619. #3251	C₂×C₅₃	semidirect
620. #3247	C₂×C₅₃	semidirect
621. #3213	C₂×C₅₃	semidirect
622. #3207	C₂×C₅₃	semidirect
623. #3114	C₂×C₅₃	semidirect
624. #3105	C₂×C₅₃	semidirect
625. #3036	C₂×C₅₃	semidirect
626. C₂×#463	C₂×C₅₃	semidirect
627. #2990	C₂×C₅₃	semidirect
639. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
640. C₂²×SD₁₆	C₂²×C₅₃	semidirect
642. #559	C₂²×C₅₃	semidirect
643. #556	C₂²×C₅₃	semidirect
646. #550	C₂²×C₅₃	semidirect
647. D₄×Q₈	C₂²×C₅₃	semidirect
648. D₄×Q₈	C₂²×C₅₃	semidirect
650. #548	C₂²×C₅₃	semidirect
652. #547	C₂²×C₅₃	semidirect
656. #546	C₂²×C₅₃	semidirect
658. D₄²	C₂²×C₅₃	semidirect
659. D₄²	C₂²×C₅₃	semidirect
662. #532	C₂²×C₅₃	semidirect
663. #532	C₂²×C₅₃	semidirect
664. #532	C₂²×C₅₃	semidirect
665. #529	C₂²×C₅₃	semidirect
666. #529	C₂²×C₅₃	semidirect
667. C₂×#124	C₂²×C₅₃	semidirect
672. C₂×C₄×D₄	C₂²×C₅₃	semidirect
673. C₂×C₄×D₄	C₂²×C₅₃	semidirect
674. #496	C₂²×C₅₃	semidirect
675. #496	C₂²×C₅₃	semidirect
676. #493	C₂²×C₅₃	semidirect
677. #492	C₂²×C₅₃	semidirect
678. #489	C₂²×C₅₃	semidirect
679. #489	C₂²×C₅₃	semidirect
680. #487	C₂²×C₅₃	semidirect
681. #486	C₂²×C₅₃	semidirect
682. #484	C₂²×C₅₃	semidirect
683. #483	C₂²×C₅₃	semidirect
684. #481	C₂²×C₅₃	semidirect
685. #480	C₂²×C₅₃	semidirect
686. #478	C₂²×C₅₃	semidirect
687. #478	C₂²×C₅₃	semidirect
688. #478	C₂²×C₅₃	semidirect
689. #477	C₂²×C₅₃	semidirect
690. #476	C₂²×C₅₃	semidirect
691. #475	C₂²×C₅₃	semidirect
692. #474	C₂²×C₅₃	semidirect
693. #469	C₂²×C₅₃	semidirect
694. #468	C₂²×C₅₃	semidirect
695. #466	C₂²×C₅₃	semidirect
696. #466	C₂²×C₅₃	semidirect
697. #465	C₂²×C₅₃	semidirect
698. #465	C₂²×C₅₃	semidirect
701. #463	C₂²×C₅₃	semidirect
702. #463	C₂²×C₅₃	semidirect
703. #463	C₂²×C₅₃	semidirect
704. #463	C₂²×C₅₃	semidirect
705. #463	C₂²×C₅₃	semidirect
706. #463	C₂²×C₅₃	semidirect
707. #463	C₂²×C₅₃	semidirect
708. #463	C₂²×C₅₃	semidirect
709. #463	C₂²×C₅₃	semidirect
710. #461	C₂²×C₅₃	semidirect
711. #461	C₂²×C₅₃	semidirect
712. #460	C₂²×C₅₃	semidirect
713. #460	C₂²×C₅₃	semidirect
715. #459	C₂²×C₅₃	semidirect
716. #459	C₂²×C₅₃	semidirect
717. #459	C₂²×C₅₃	semidirect
718. #450	C₂²×C₅₃	semidirect
719. #450	C₂²×C₅₃	semidirect
720. #449	C₂²×C₅₃	semidirect
721. #449	C₂²×C₅₃	semidirect
722. #448	C₂²×C₅₃	semidirect
723. #448	C₂²×C₅₃	semidirect
726. #447	C₂²×C₅₃	semidirect
727. #447	C₂²×C₅₃	semidirect
728. #446	C₂²×C₅₃	semidirect
729. #446	C₂²×C₅₃	semidirect
730. #442	C₂²×C₅₃	semidirect
731. #442	C₂²×C₅₃	semidirect
732. #440	C₂²×C₅₃	semidirect
733. #440	C₂²×C₅₃	semidirect
734. C₄×SD₁₆	C₂²×C₅₃	semidirect
735. C₄×SD₁₆	C₂²×C₅₃	semidirect
737. C₄×D₈	C₂²×C₅₃	semidirect
738. #435	C₂²×C₅₃	semidirect
739. #435	C₂²×C₅₃	semidirect
740. C₈×D₄	C₂²×C₅₃	semidirect
741. C₈×D₄	C₂²×C₅₃	semidirect
742. #432	C₂²×C₅₃	semidirect
743. #431	C₂²×C₅₃	semidirect
744. #423	C₂²×C₅₃	semidirect
745. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
746. #417	C₂²×C₅₃	semidirect
747. C₂×#103	C₂²×C₅₃	semidirect
748. C₂×#102	C₂²×C₅₃	semidirect
749. C₅₃	#61989	direct (N × H)
1132. D₄	AGL(1,ℤ/8)×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3514	2
D₄×#41×C₅₃	2
C₅₃×#3399	2
C₅₃×#3397	2
C₅₃×#3373	2
C₅₃×#3367	2
C₅₃×#3308	2
C₅₃×#3306	2
C₅₃×#3298	2
C₅₃×#3294	2
D₄×SD₁₆×C₅₃	2
D₄×D₈×C₅₃	2
C₅₃×#3265	2
C₅₃×#3264	2
C₅₃×#3251	2
C₅₃×#3247	2
C₅₃×#3213	2
C₅₃×#3207	2
C₅₃×#3114	2
C₅₃×#3105	2
C₅₃×#3036	2
C₂×C₅₃×#463	2
C₅₃×#2990	2
#61989	53

Subgroups — C53×#61989 #27269501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61989 #27269501