Subgroups — C₅₃×#61658 #27269170

Order 13568.

2110 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3323	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3296	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3283	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3282	C₂	1	2	yes	maximal, complemented
11	D₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3276	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3275	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3204	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3201	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3012	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3009	C₂	1	2	yes	maximal, complemented
23	C₅₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	2	yes	—
25	C₂×#137×C₅₃	C₂²	1	2	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
27	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
28	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
29	C₅₃×#562	—	2	2	no	—
30	C₅₃×#555	—	2	1	no	—
31	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
32	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
33	C₅₃×#553	—	2	1	no	—
34	C₅₃×#552	C₂²	1	2	yes	complemented
35	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#548	C₂²	1	2	yes	complemented
37	C₅₃×#547	—	2	1	no	—
38	C₅₃×#547	C₂²	1	1	yes	characteristic
39	C₅₃×#547	C₂²	1	1	yes	characteristic
40	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#546	—	2	2	no	—
42	C₅₃×#546	C₂²	1	2	yes	—
43	C₅₃×#546	C₂²	1	2	yes	—
44	D₄²×C₅₃	—	2	1	no	—
45	D₄²×C₅₃	C₂²	1	1	yes	characteristic
46	D₄²×C₅₃	C₂²	1	1	yes	characteristic
47	C₅₃×#544	—	2	1	no	—
48	C₅₃×#542	—	2	2	no	—
49	C₅₃×#540	—	2	1	no	—
50	C₅₃×#537	C₂²	1	2	yes	—
51	C₅₃×#537	C₂²	1	2	yes	complemented
52	C₅₃×#536	C₂²	1	2	yes	complemented
53	C₅₃×#534	—	2	2	no	—
54	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#532	C₂²	1	1	yes	characteristic
56	C₅₃×#532	C₂²	1	1	yes	characteristic
57	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
58	C₂×#121×C₅₃	—	2	1	no	—
59	C₂×#121×C₅₃	—	2	1	no	—
60	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
61	C₅₃×#495	C₂²	1	2	yes	complemented
62	C₅₃×#494	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#488	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×#485	C₂²	1	2	yes	complemented
68	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#483	C₂²	1	2	yes	complemented
70	C₅₃×#483	C₂²	1	2	yes	complemented
71	C₅₃×#482	C₂²	1	2	yes	complemented
72	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#481	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#470	C₂²	1	2	yes	complemented
79	C₅₃×#470	C₂²	1	2	yes	complemented
80	C₅₃×#469	C₂²	1	2	yes	complemented
81	C₅₃×#468	C₂²	1	2	yes	complemented
82	C₅₃×#467	C₂²	1	2	yes	complemented
83	C₅₃×#465	C₂²	1	2	yes	complemented
84	C₅₃×#465	C₂²	1	2	yes	complemented
85	C₅₃×#465	C₂²	1	2	yes	complemented
86	C₅₃×#464	C₂²	1	2	yes	complemented
87	C₅₃×#464	C₂²	1	2	yes	complemented
88	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#452	C₂²	1	2	yes	complemented
97	C₅₃×#452	C₂²	1	2	yes	complemented
98	C₅₃×#452	C₂²	1	2	yes	complemented
99	C₅₃×#452	C₂²	1	2	yes	complemented
100	C₅₃×#452	C₂²	1	2	yes	complemented
101	C₅₃×#452	C₂²	1	2	yes	complemented
102	C₅₃×#452	C₂²	1	2	yes	complemented
103	C₅₃×#451	C₂²	1	2	yes	complemented
104	C₅₃×#450	C₂²	1	1	yes	characteristic
105	C₅₃×#450	C₂²	1	2	yes	—
106	C₅₃×#450	C₂²	1	2	yes	complemented
107	C₅₃×#450	C₂²	1	2	yes	complemented
108	C₅₃×#450	C₂²	1	2	yes	complemented
109	C₅₃×#449	C₂²	1	2	yes	complemented
110	C₅₃×#449	C₂²	1	2	yes	complemented
111	C₅₃×#449	C₂²	1	2	yes	complemented
112	C₅₃×#448	C₂²	1	2	yes	complemented
113	C₅₃×#447	C₂²	1	1	yes	characteristic
114	C₅₃×#447	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
119	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
123	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
125	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
126	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#418	C₂²	1	2	yes	complemented
130	C₅₃×#417	C₂²	1	2	yes	complemented
131	C₅₃×#416	C₂²	1	2	yes	complemented
132	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
133	C₅₃×#408	C₂²	1	2	yes	complemented
134	C₅₃×#408	C₂²	1	2	yes	complemented
135	H(5,𝔽₂)×C₅₃	—	4	4	no	—
136	H(5,𝔽₂)×C₅₃	—	4	4	no	—
137	C₂×#41×C₅₃	—	2	2	no	—
138	C₂×#41×C₅₃	C₂³	1	2	yes	—
139	C₂×#41×C₅₃	C₂³	1	2	yes	—
140	C₂×#41×C₅₃	C₂³	1	2	yes	—
141	C₂×#41×C₅₃	C₂³	1	2	yes	—
142	C₂×#41×C₅₃	C₂³	1	2	yes	—
143	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
144	C₂²×D₄×C₅₃	—	2	2	no	—
145	C₂²×D₄×C₅₃	—	2	2	no	—
146	C₂²×D₄×C₅₃	—	2	2	no	—
147	C₂²×D₄×C₅₃	—	2	1	no	—
148	C₂²×D₄×C₅₃	—	2	1	no	—
149	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
150	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
151	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
152	C₂³×C₄×C₅₃	—	2	1	no	—
153	#137×C₅₃	—	4	4	no	—
154	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
155	#135×C₅₃	—	4	4	no	—
156	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
157	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
158	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₅₃	—	4	4	no	—
160	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
168	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
169	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
170	C₂×D₈×C₅₃	C₂³	1	2	yes	—
171	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
172	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
173	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
174	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
175	C₄⋊Q₈×C₅₃	—	2	1	no	—
176	C₄⋊Q₈×C₅₃	—	2	2	no	—
177	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
178	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
180	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
181	#127×C₅₃	D₄	1	1	yes	characteristic
182	#127×C₅₃	C₂³	1	1	yes	characteristic
183	#126×C₅₃	—	2	2	no	—
184	#126×C₅₃	—	2	1	no	—
185	#125×C₅₃	—	2	2	no	—
186	#125×C₅₃	—	2	1	no	—
187	#125×C₅₃	—	2	1	no	—
188	#125×C₅₃	C₂³	1	1	yes	characteristic
189	#124×C₅₃	—	2	2	no	—
190	#124×C₅₃	—	2	2	no	—
191	#124×C₅₃	—	2	2	no	—
192	#124×C₅₃	D₄	1	2	yes	—
193	#124×C₅₃	C₂³	1	2	yes	—
194	#124×C₅₃	C₂³	1	1	yes	characteristic
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	2	no	—
200	#123×C₅₃	—	2	2	no	—
201	#123×C₅₃	—	2	2	no	—
202	#123×C₅₃	—	2	2	no	—
203	#123×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	2	no	—
208	C₂²⋊Q₈×C₅₃	—	2	2	no	—
209	C₂²⋊Q₈×C₅₃	—	2	1	no	—
210	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
215	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
216	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
217	#121×C₅₃	—	2	1	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	2	no	—
226	#121×C₅₃	—	2	2	no	—
227	#121×C₅₃	—	2	2	no	—
228	#121×C₅₃	—	2	2	no	—
229	#121×C₅₃	—	2	1	no	—
230	#121×C₅₃	—	2	2	no	—
231	#121×C₅₃	—	2	1	no	—
232	#121×C₅₃	—	2	1	no	—
233	#121×C₅₃	—	2	1	no	—
234	#121×C₅₃	D₄	1	1	yes	characteristic
235	#121×C₅₃	D₄	1	1	yes	characteristic
236	#121×C₅₃	D₄	1	2	yes	—
237	#121×C₅₃	C₂³	1	1	yes	characteristic
238	#121×C₅₃	C₂³	1	2	yes	—
239	#121×C₅₃	C₂³	1	2	yes	—
240	#121×C₅₃	C₂³	1	2	yes	—
241	#120×C₅₃	—	2	2	no	—
242	#120×C₅₃	—	2	2	no	—
243	#120×C₅₃	—	2	2	no	—
244	#120×C₅₃	—	2	2	no	—
245	C₄×Q₈×C₅₃	—	2	1	no	—
246	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
248	C₄×D₄×C₅₃	—	2	2	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	1	no	—
253	C₄×D₄×C₅₃	—	2	1	no	—
254	C₄×D₄×C₅₃	—	2	1	no	—
255	C₄×D₄×C₅₃	—	2	1	no	—
256	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₅₃	C₂³	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	#117×C₅₃	—	2	1	no	—
265	#117×C₅₃	—	2	2	no	—
266	#117×C₅₃	—	2	1	no	—
267	#117×C₅₃	—	2	1	no	—
268	#117×C₅₃	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
270	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
271	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
272	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
274	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
276	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
277	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
278	#107×C₅₃	C₂³	1	1	yes	characteristic
279	#107×C₅₃	C₂³	1	1	yes	characteristic
280	#106×C₅₃	C₂³	1	2	yes	—
281	#106×C₅₃	C₂³	1	1	yes	characteristic
282	#106×C₅₃	C₂³	1	2	yes	—
283	#106×C₅₃	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#103×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
305	#102×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	1	yes	characteristic
307	#102×C₅₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×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	1	yes	characteristic
312	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
315	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₅₃	C₂³	1	2	yes	—
318	C₂⁴×C₅₃	—	2	1	no	—
319	C₂⁴×C₅₃	—	2	2	no	—
320	C₂⁴×C₅₃	—	2	2	no	—
321	#41×C₅₃	—	2	4	no	—
322	#41×C₅₃	—	2	4	no	—
323	#41×C₅₃	—	4	2	no	—
324	#41×C₅₃	—	4	2	no	—
325	#41×C₅₃	—	4	2	no	—
326	#41×C₅₃	—	4	2	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	C₂×Q₈×C₅₃	—	2	1	no	—
333	C₂×Q₈×C₅₃	—	2	2	no	—
334	C₂×Q₈×C₅₃	—	4	2	no	—
335	C₂×Q₈×C₅₃	—	4	2	no	—
336	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
337	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
338	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
340	C₂×D₄×C₅₃	—	2	2	no	—
341	C₂×D₄×C₅₃	—	2	2	no	—
342	C₂×D₄×C₅₃	—	2	4	no	—
343	C₂×D₄×C₅₃	—	2	4	no	—
344	C₂×D₄×C₅₃	—	2	2	no	—
345	C₂×D₄×C₅₃	—	2	2	no	—
346	C₂×D₄×C₅₃	—	2	2	no	—
347	C₂×D₄×C₅₃	—	2	1	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	1	no	—
353	C₂×D₄×C₅₃	—	2	1	no	—
354	C₂×D₄×C₅₃	—	2	2	no	—
355	C₂×D₄×C₅₃	—	2	2	no	—
356	C₂×D₄×C₅₃	—	2	1	no	—
357	C₂×D₄×C₅₃	—	4	2	no	—
358	C₂×D₄×C₅₃	—	4	2	no	—
359	C₂×D₄×C₅₃	—	4	8	no	—
360	C₂×D₄×C₅₃	—	4	8	no	—
361	C₂×D₄×C₅₃	—	4	8	no	—
362	C₂×D₄×C₅₃	—	8	2	no	—
363	C₂×D₄×C₅₃	—	8	2	no	—
364	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
365	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
367	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
371	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₅₃	—	2	1	no	—
375	C₂²×C₄×C₅₃	—	2	2	no	—
376	C₂²×C₄×C₅₃	—	2	2	no	—
377	C₂²×C₄×C₅₃	—	2	2	no	—
378	C₂²×C₄×C₅₃	—	2	2	no	—
379	C₂²×C₄×C₅₃	—	2	1	no	—
380	C₂²×C₄×C₅₃	—	2	1	no	—
381	C₂²×C₄×C₅₃	—	2	1	no	—
382	C₂²×C₄×C₅₃	—	2	2	no	—
383	C₂²×C₄×C₅₃	—	2	1	no	—
384	C₂²×C₄×C₅₃	—	2	1	no	—
385	C₂²×C₄×C₅₃	—	2	2	no	—
386	C₂²×C₄×C₅₃	—	8	2	no	—
387	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
392	Q₁₆×C₅₃	—	4	2	no	—
393	Q₁₆×C₅₃	—	4	2	no	—
394	Q₁₆×C₅₃	—	4	2	no	—
395	SD₁₆×C₅₃	—	2	2	no	—
396	SD₁₆×C₅₃	—	2	4	no	—
397	SD₁₆×C₅₃	—	2	4	no	—
398	SD₁₆×C₅₃	—	2	2	no	—
399	SD₁₆×C₅₃	—	4	2	no	—
400	SD₁₆×C₅₃	—	4	2	no	—
401	SD₁₆×C₅₃	—	4	2	no	—
402	SD₁₆×C₅₃	—	4	2	no	—
403	D₈×C₅₃	—	2	2	no	—
404	D₈×C₅₃	—	2	2	no	—
405	D₈×C₅₃	—	4	2	no	—
406	M₁₆×C₅₃	—	4	2	no	—
407	M₁₆×C₅₃	—	4	2	no	—
408	C₂×C₈×C₅₃	—	4	2	no	—
409	C₂×C₈×C₅₃	—	4	2	no	—
410	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
411	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
414	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
415	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₅₃	—	2	1	no	—
417	C₄⋊C₄×C₅₃	—	2	1	no	—
418	C₄⋊C₄×C₅₃	—	2	2	no	—
419	C₄⋊C₄×C₅₃	—	2	2	no	—
420	C₄⋊C₄×C₅₃	—	2	2	no	—
421	C₄⋊C₄×C₅₃	—	2	1	no	—
422	C₄⋊C₄×C₅₃	—	2	2	no	—
423	C₄⋊C₄×C₅₃	—	2	1	no	—
424	C₄⋊C₄×C₅₃	—	2	1	no	—
425	C₄⋊C₄×C₅₃	—	2	2	no	—
426	C₄⋊C₄×C₅₃	—	2	1	no	—
427	C₄⋊C₄×C₅₃	—	2	1	no	—
428	C₄⋊C₄×C₅₃	—	2	1	no	—
429	C₄⋊C₄×C₅₃	—	2	2	no	—
430	C₄⋊C₄×C₅₃	—	2	2	no	—
431	C₄⋊C₄×C₅₃	—	2	1	no	—
432	C₄⋊C₄×C₅₃	—	2	2	no	—
433	C₄⋊C₄×C₅₃	—	2	1	no	—
434	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
437	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
439	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
442	C₂²⋊C₄×C₅₃	—	2	2	no	—
443	C₂²⋊C₄×C₅₃	—	2	2	no	—
444	C₂²⋊C₄×C₅₃	—	2	2	no	—
445	C₂²⋊C₄×C₅₃	—	2	2	no	—
446	C₂²⋊C₄×C₅₃	—	2	2	no	—
447	C₂²⋊C₄×C₅₃	—	2	2	no	—
448	C₂²⋊C₄×C₅₃	—	2	2	no	—
449	C₂²⋊C₄×C₅₃	—	2	1	no	—
450	C₂²⋊C₄×C₅₃	—	2	2	no	—
451	C₂²⋊C₄×C₅₃	—	2	1	no	—
452	C₂²⋊C₄×C₅₃	—	2	1	no	—
453	C₂²⋊C₄×C₅₃	—	2	1	no	—
454	C₂²⋊C₄×C₅₃	—	2	1	no	—
455	C₂²⋊C₄×C₅₃	—	2	2	no	—
456	C₂²⋊C₄×C₅₃	—	2	2	no	—
457	C₂²⋊C₄×C₅₃	—	2	1	no	—
458	C₂²⋊C₄×C₅₃	—	2	1	no	—
459	C₂²⋊C₄×C₅₃	—	2	2	no	—
460	C₂²⋊C₄×C₅₃	—	2	1	no	—
461	C₂²⋊C₄×C₅₃	—	2	2	no	—
462	C₂²⋊C₄×C₅₃	—	2	1	no	—
463	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
465	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
466	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
467	C₄²×C₅₃	—	2	2	no	—
468	C₄²×C₅₃	—	2	2	no	—
469	C₄²×C₅₃	—	2	1	no	—
470	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
473	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
474	C₂³×C₅₃	—	2	4	no	—
475	C₂³×C₅₃	—	2	1	no	—
476	C₂³×C₅₃	—	2	1	no	—
477	C₂³×C₅₃	—	2	1	no	—
478	C₂³×C₅₃	—	2	2	no	—
479	C₂³×C₅₃	—	4	4	no	—
480	C₂³×C₅₃	—	4	4	no	—
481	C₂³×C₅₃	—	8	1	no	—
482	C₂³×C₅₃	—	8	1	no	—
483	C₂³×C₅₃	—	8	2	no	—
484	C₂³×C₅₃	—	8	2	no	—
485	C₂³×C₅₃	—	8	2	no	—
486	C₂³×C₅₃	—	8	2	no	—
487	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
488	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
489	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
490	Q₈×C₅₃	—	2	1	no	—
491	Q₈×C₅₃	—	2	1	no	—
492	Q₈×C₅₃	—	2	2	no	—
493	Q₈×C₅₃	—	2	2	no	—
494	Q₈×C₅₃	—	2	2	no	—
495	Q₈×C₅₃	—	2	2	no	—
496	Q₈×C₅₃	—	4	2	no	—
497	Q₈×C₅₃	—	8	1	no	—
498	Q₈×C₅₃	—	8	2	no	—
499	D₄×C₅₃	—	2	4	no	—
500	D₄×C₅₃	—	2	2	no	—
501	D₄×C₅₃	—	2	2	no	—
502	D₄×C₅₃	—	2	1	no	—
503	D₄×C₅₃	—	2	1	no	—
504	D₄×C₅₃	—	2	2	no	—
505	D₄×C₅₃	—	2	2	no	—
506	D₄×C₅₃	—	2	1	no	—
507	D₄×C₅₃	—	2	1	no	—
508	D₄×C₅₃	—	4	2	no	—
509	D₄×C₅₃	—	4	2	no	—
510	D₄×C₅₃	—	4	2	no	—
511	D₄×C₅₃	—	4	2	no	—
512	D₄×C₅₃	—	4	4	no	—
513	D₄×C₅₃	—	4	4	no	—
514	D₄×C₅₃	—	4	4	no	—
515	D₄×C₅₃	—	4	4	no	—
516	D₄×C₅₃	—	4	4	no	—
517	D₄×C₅₃	—	4	2	no	—
518	D₄×C₅₃	—	8	1	no	—
519	D₄×C₅₃	—	8	1	no	—
520	D₄×C₅₃	—	8	2	no	—
521	D₄×C₅₃	—	8	2	no	—
522	D₄×C₅₃	—	8	2	no	—
523	D₄×C₅₃	—	8	2	no	—
524	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
525	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
526	C₂×C₄×C₅₃	—	2	2	no	—
527	C₂×C₄×C₅₃	—	2	2	no	—
528	C₂×C₄×C₅₃	—	2	1	no	—
529	C₂×C₄×C₅₃	—	2	1	no	—
530	C₂×C₄×C₅₃	—	2	2	no	—
531	C₂×C₄×C₅₃	—	2	2	no	—
532	C₂×C₄×C₅₃	—	2	2	no	—
533	C₂×C₄×C₅₃	—	2	2	no	—
534	C₂×C₄×C₅₃	—	2	1	no	—
535	C₂×C₄×C₅₃	—	2	1	no	—
536	C₂×C₄×C₅₃	—	2	2	no	—
537	C₂×C₄×C₅₃	—	2	1	no	—
538	C₂×C₄×C₅₃	—	2	1	no	—
539	C₂×C₄×C₅₃	—	2	2	no	—
540	C₂×C₄×C₅₃	—	2	1	no	—
541	C₂×C₄×C₅₃	—	4	1	no	—
542	C₂×C₄×C₅₃	—	4	4	no	—
543	C₂×C₄×C₅₃	—	4	4	no	—
544	C₂×C₄×C₅₃	—	4	4	no	—
545	C₂×C₄×C₅₃	—	4	2	no	—
546	C₂×C₄×C₅₃	—	4	2	no	—
547	C₂×C₄×C₅₃	—	4	2	no	—
548	C₂×C₄×C₅₃	—	8	1	no	—
549	C₂×C₄×C₅₃	—	8	1	no	—
550	C₂×C₄×C₅₃	—	8	2	no	—
551	C₂×C₄×C₅₃	—	8	2	no	—
552	C₂×C₄×C₅₃	—	8	1	no	—
553	C₂×C₄×C₅₃	—	8	2	no	—
554	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
557	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
558	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
562	C₈×C₅₃	—	2	1	no	—
563	C₈×C₅₃	—	2	1	no	—
564	C₈×C₅₃	—	2	2	no	—
565	C₈×C₅₃	—	2	1	no	—
566	C₈×C₅₃	—	2	2	no	—
567	C₈×C₅₃	—	2	1	no	—
568	#61658	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
569	C₂²×C₅₃	—	2	1	no	—
570	C₂²×C₅₃	—	2	2	no	—
571	C₂²×C₅₃	—	2	2	no	—
572	C₂²×C₅₃	—	2	2	no	—
573	C₂²×C₅₃	—	2	1	no	—
574	C₂²×C₅₃	—	2	2	no	—
575	C₂²×C₅₃	—	2	2	no	—
576	C₂²×C₅₃	—	2	2	no	—
577	C₂²×C₅₃	—	2	1	no	—
578	C₂²×C₅₃	—	2	2	no	—
579	C₂²×C₅₃	—	2	2	no	—
580	C₂²×C₅₃	—	4	1	no	—
581	C₂²×C₅₃	—	4	1	no	—
582	C₂²×C₅₃	—	4	1	no	—
583	C₂²×C₅₃	—	4	1	no	—
584	C₂²×C₅₃	—	4	1	no	—
585	C₂²×C₅₃	—	4	2	no	—
586	C₂²×C₅₃	—	4	2	no	—
587	C₂²×C₅₃	—	4	1	no	—
588	C₂²×C₅₃	—	4	1	no	—
589	C₂²×C₅₃	—	4	2	no	—
590	C₂²×C₅₃	—	8	4	no	—
591	C₂²×C₅₃	—	16	4	no	—
592	C₂²×C₅₃	—	16	4	no	—
593	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
594	C₄×C₅₃	—	2	1	no	—
595	C₄×C₅₃	—	2	1	no	—
596	C₄×C₅₃	—	2	1	no	—
597	C₄×C₅₃	—	2	2	no	—
598	C₄×C₅₃	—	2	2	no	—
599	C₄×C₅₃	—	2	1	no	—
600	C₄×C₅₃	—	4	1	no	—
601	C₄×C₅₃	—	4	2	no	—
602	C₄×C₅₃	—	4	2	no	—
603	C₄×C₅₃	—	4	2	no	—
604	C₄×C₅₃	—	4	1	no	—
605	C₄×C₅₃	—	4	1	no	—
606	C₄×C₅₃	—	4	1	no	—
607	C₄×C₅₃	—	4	1	no	—
608	C₄×C₅₃	#577	1	2	yes	—
609	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
610	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
611	#3547	C₂×C₅₃	1	1	yes	characteristic, complemented
612	#3496	C₂×C₅₃	1	1	yes	characteristic, complemented
613	#3331	C₂×C₅₃	1	1	yes	characteristic, complemented
614	#3325	C₂×C₅₃	1	1	yes	characteristic, complemented
615	#3323	C₂×C₅₃	1	2	yes	complemented
616	#3303	C₂×C₅₃	1	1	yes	characteristic, complemented
617	#3296	C₂×C₅₃	1	2	yes	complemented
618	#3295	C₂×C₅₃	1	1	yes	characteristic, complemented
619	#3283	C₂×C₅₃	1	1	yes	characteristic, complemented
620	#3282	C₂×C₅₃	1	2	yes	complemented
621	D₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
622	#3276	C₂×C₅₃	1	1	yes	characteristic, complemented
623	#3275	C₂×C₅₃	1	2	yes	complemented
624	#3272	C₂×C₅₃	1	1	yes	characteristic, complemented
625	#3212	C₂×C₅₃	1	1	yes	characteristic, complemented
626	#3210	C₂×C₅₃	1	1	yes	characteristic, complemented
627	#3204	C₂×C₅₃	1	2	yes	complemented
628	#3201	C₂×C₅₃	1	2	yes	complemented
629	#3105	C₂×C₅₃	1	1	yes	characteristic, complemented
630	#3101	C₂×C₅₃	1	1	yes	characteristic, complemented
631	#3012	C₂×C₅₃	1	2	yes	complemented
632	#3009	C₂×C₅₃	1	2	yes	complemented
633	#2979	C₂×C₅₃	1	1	yes	characteristic, complemented
634	C₂×C₅₃	—	4	1	no	—
635	C₂×C₅₃	—	4	2	no	—
636	C₂×C₅₃	—	4	2	no	—
637	C₂×C₅₃	—	4	2	no	—
638	C₂×C₅₃	—	4	2	no	—
639	C₂×C₅₃	—	8	1	no	—
640	C₂×C₅₃	—	8	2	no	—
641	C₂×C₅₃	#3484	1	1	yes	characteristic
642	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
643	C₂×C₅₃	#3584	1	1	yes	characteristic
644	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	2	yes	—
645	C₂×#137	C₂²×C₅₃	1	2	yes	complemented
646	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
647	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
648	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
649	#562	—	2	2	no	—
650	#555	—	2	1	no	—
651	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
652	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
653	#553	—	2	1	no	—
654	#552	C₂²×C₅₃	1	2	yes	complemented
655	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
656	#548	C₂²×C₅₃	1	2	yes	complemented
657	#547	—	2	1	no	—
658	#547	C₂²×C₅₃	1	1	yes	characteristic
659	#547	C₂²×C₅₃	1	1	yes	characteristic
660	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
661	#546	—	2	2	no	—
662	#546	C₂²×C₅₃	1	2	yes	—
663	#546	C₂²×C₅₃	1	2	yes	—
664	D₄²	—	2	1	no	—
665	D₄²	C₂²×C₅₃	1	1	yes	characteristic
666	D₄²	C₂²×C₅₃	1	1	yes	characteristic
667	#544	—	2	1	no	—
668	#542	—	2	2	no	—
669	#540	—	2	1	no	—
670	#537	C₂²×C₅₃	1	2	yes	—
671	#537	C₂²×C₅₃	1	2	yes	complemented
672	#536	C₂²×C₅₃	1	2	yes	complemented
673	#534	—	2	2	no	—
674	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
675	#532	C₂²×C₅₃	1	1	yes	characteristic
676	#532	C₂²×C₅₃	1	1	yes	characteristic
677	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
678	C₂×#121	—	2	1	no	—
679	C₂×#121	—	2	1	no	—
680	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
681	#495	C₂²×C₅₃	1	2	yes	complemented
682	#494	C₂²×C₅₃	1	1	yes	characteristic, complemented
683	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
684	#488	C₂²×C₅₃	1	2	yes	complemented
685	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
686	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	#485	C₂²×C₅₃	1	2	yes	complemented
688	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
689	#483	C₂²×C₅₃	1	2	yes	complemented
690	#483	C₂²×C₅₃	1	2	yes	complemented
691	#482	C₂²×C₅₃	1	2	yes	complemented
692	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	#481	C₂²×C₅₃	1	2	yes	complemented
694	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
695	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
696	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
697	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
698	#470	C₂²×C₅₃	1	2	yes	complemented
699	#470	C₂²×C₅₃	1	2	yes	complemented
700	#469	C₂²×C₅₃	1	2	yes	complemented
701	#468	C₂²×C₅₃	1	2	yes	complemented
702	#467	C₂²×C₅₃	1	2	yes	complemented
703	#465	C₂²×C₅₃	1	2	yes	complemented
704	#465	C₂²×C₅₃	1	2	yes	complemented
705	#465	C₂²×C₅₃	1	2	yes	complemented
706	#464	C₂²×C₅₃	1	2	yes	complemented
707	#464	C₂²×C₅₃	1	2	yes	complemented
708	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
710	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
711	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
714	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
715	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
716	#452	C₂²×C₅₃	1	2	yes	complemented
717	#452	C₂²×C₅₃	1	2	yes	complemented
718	#452	C₂²×C₅₃	1	2	yes	complemented
719	#452	C₂²×C₅₃	1	2	yes	complemented
720	#452	C₂²×C₅₃	1	2	yes	complemented
721	#452	C₂²×C₅₃	1	2	yes	complemented
722	#452	C₂²×C₅₃	1	2	yes	complemented
723	#451	C₂²×C₅₃	1	2	yes	complemented
724	#450	C₂²×C₅₃	1	2	yes	—
725	#450	C₂²×C₅₃	1	1	yes	characteristic
726	#450	C₂²×C₅₃	1	2	yes	complemented
727	#450	C₂²×C₅₃	1	2	yes	complemented
728	#450	C₂²×C₅₃	1	2	yes	complemented
729	#449	C₂²×C₅₃	1	2	yes	complemented
730	#449	C₂²×C₅₃	1	2	yes	complemented
731	#449	C₂²×C₅₃	1	2	yes	complemented
732	#448	C₂²×C₅₃	1	2	yes	complemented
733	#447	C₂²×C₅₃	1	1	yes	characteristic
734	#447	C₂²×C₅₃	1	2	yes	complemented
735	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
736	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
737	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
738	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
739	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
740	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
741	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
742	#436	C₂²×C₅₃	1	2	yes	complemented
743	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
744	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
745	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
746	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
747	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
748	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
749	#418	C₂²×C₅₃	1	2	yes	complemented
750	#417	C₂²×C₅₃	1	2	yes	complemented
751	#416	C₂²×C₅₃	1	2	yes	complemented
752	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
753	#408	C₂²×C₅₃	1	2	yes	complemented
754	#408	C₂²×C₅₃	1	2	yes	complemented
755	C₅₃	#61658	1	1	yes	characteristic, direct product factor, Sylow
756	H(5,𝔽₂)	—	4	4	no	—
757	H(5,𝔽₂)	—	4	4	no	—
758	C₂×#41	—	2	2	no	—
759	C₂×#41	C₂³×C₅₃	1	2	yes	—
760	C₂×#41	C₂³×C₅₃	1	2	yes	—
761	C₂×#41	C₂³×C₅₃	1	2	yes	—
762	C₂×#41	C₂³×C₅₃	1	2	yes	—
763	C₂×#41	C₂³×C₅₃	1	2	yes	—
764	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
765	C₂²×D₄	—	2	2	no	—
766	C₂²×D₄	—	2	2	no	—
767	C₂²×D₄	—	2	2	no	—
768	C₂²×D₄	—	2	1	no	—
769	C₂²×D₄	—	2	1	no	—
770	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
771	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
772	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
773	C₂³×C₄	—	2	1	no	—
774	#137	—	4	4	no	—
775	AGL(1,ℤ/8)	—	4	4	no	—
776	#135	—	4	4	no	—
777	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
778	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
779	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
780	C₂×SD₁₆	—	4	4	no	—
781	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
782	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
783	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
785	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
786	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
787	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
788	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
789	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
790	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
791	C₂×D₈	C₂³×C₅₃	1	2	yes	—
792	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
793	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
794	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
795	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
796	C₄⋊Q₈	—	2	2	no	—
797	C₄⋊Q₈	—	2	1	no	—
798	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
799	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
800	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
801	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
802	#127	D₄×C₅₃	1	1	yes	characteristic
803	#127	C₂³×C₅₃	1	1	yes	characteristic
804	#126	—	2	2	no	—
805	#126	—	2	1	no	—
806	#125	—	2	2	no	—
807	#125	—	2	1	no	—
808	#125	—	2	1	no	—
809	#125	C₂³×C₅₃	1	1	yes	characteristic
810	#124	—	2	2	no	—
811	#124	—	2	2	no	—
812	#124	—	2	2	no	—
813	#124	D₄×C₅₃	1	2	yes	—
814	#124	C₂³×C₅₃	1	1	yes	characteristic
815	#124	C₂³×C₅₃	1	2	yes	—
816	#123	—	2	2	no	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	1	no	—
820	#123	—	2	2	no	—
821	#123	—	2	2	no	—
822	#123	—	2	2	no	—
823	#123	—	2	2	no	—
824	#123	—	2	2	no	—
825	C₂²⋊Q₈	—	2	2	no	—
826	C₂²⋊Q₈	—	2	2	no	—
827	C₂²⋊Q₈	—	2	1	no	—
828	C₂²⋊Q₈	—	2	2	no	—
829	C₂²⋊Q₈	—	2	2	no	—
830	C₂²⋊Q₈	—	2	2	no	—
831	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
832	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
833	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
834	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
835	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
836	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
837	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	1	no	—
841	#121	—	2	1	no	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#121	—	2	2	no	—
845	#121	—	2	2	no	—
846	#121	—	2	1	no	—
847	#121	—	2	2	no	—
848	#121	—	2	1	no	—
849	#121	—	2	1	no	—
850	#121	—	2	1	no	—
851	#121	—	2	1	no	—
852	#121	—	2	1	no	—
853	#121	—	2	2	no	—
854	#121	—	2	2	no	—
855	#121	D₄×C₅₃	1	1	yes	characteristic
856	#121	D₄×C₅₃	1	1	yes	characteristic
857	#121	D₄×C₅₃	1	2	yes	—
858	#121	C₂³×C₅₃	1	1	yes	characteristic
859	#121	C₂³×C₅₃	1	2	yes	—
860	#121	C₂³×C₅₃	1	2	yes	—
861	#121	C₂³×C₅₃	1	2	yes	—
862	#120	—	2	2	no	—
863	#120	—	2	2	no	—
864	#120	—	2	2	no	—
865	#120	—	2	2	no	—
866	C₄×Q₈	—	2	1	no	—
867	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
868	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
869	C₄×D₄	—	2	1	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	—	2	2	no	—
873	C₄×D₄	—	2	1	no	—
874	C₄×D₄	—	2	1	no	—
875	C₄×D₄	—	2	1	no	—
876	C₄×D₄	—	2	1	no	—
877	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
878	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
879	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
880	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
881	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
882	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
883	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
884	C₄×D₄	C₂³×C₅₃	1	2	yes	—
885	#117	—	2	1	no	—
886	#117	—	2	1	no	—
887	#117	—	2	2	no	—
888	#117	—	2	1	no	—
889	#117	C₂³×C₅₃	1	2	yes	—
890	C₂×C₄⋊C₄	—	2	1	no	—
891	C₂×C₄⋊C₄	—	2	1	no	—
892	C₂×C₄⋊C₄	—	2	1	no	—
893	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
894	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
895	C₂×C₂²⋊C₄	—	2	1	no	—
896	C₂×C₂²⋊C₄	—	2	2	no	—
897	C₂×C₂²⋊C₄	—	2	2	no	—
898	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
899	#107	C₂³×C₅₃	1	1	yes	characteristic
900	#107	C₂³×C₅₃	1	1	yes	characteristic
901	#106	C₂³×C₅₃	1	2	yes	—
902	#106	C₂³×C₅₃	1	1	yes	characteristic
903	#106	C₂³×C₅₃	1	2	yes	—
904	#106	C₂³×C₅₃	1	1	yes	characteristic
905	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
906	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
907	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
908	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
909	#103	C₂³×C₅₃	1	2	yes	—
910	#103	C₂³×C₅₃	1	2	yes	—
911	#103	C₂³×C₅₃	1	2	yes	—
912	#103	C₂³×C₅₃	1	2	yes	—
913	#103	C₂³×C₅₃	1	1	yes	characteristic
914	#103	C₂³×C₅₃	1	2	yes	—
915	#103	C₂³×C₅₃	1	2	yes	—
916	#103	C₂³×C₅₃	1	1	yes	characteristic
917	#102	C₂³×C₅₃	1	1	yes	characteristic
918	#102	C₂³×C₅₃	1	2	yes	—
919	#102	C₂³×C₅₃	1	2	yes	—
920	#102	C₂³×C₅₃	1	2	yes	—
921	#102	C₂³×C₅₃	1	1	yes	characteristic
922	#102	C₂³×C₅₃	1	1	yes	characteristic
923	#102	C₂³×C₅₃	1	2	yes	—
924	#102	C₂³×C₅₃	1	1	yes	characteristic
925	#102	C₂³×C₅₃	1	2	yes	—
926	#102	C₂³×C₅₃	1	2	yes	—
927	#102	C₂³×C₅₃	1	1	yes	characteristic
928	#102	C₂³×C₅₃	1	1	yes	characteristic
929	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
930	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
931	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
932	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
933	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
934	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
935	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
936	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
937	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
938	C₄×C₈	C₂³×C₅₃	1	2	yes	—
939	C₂⁴	—	2	1	no	—
940	C₂⁴	—	2	2	no	—
941	C₂⁴	—	2	2	no	—
942	#41	—	2	4	no	—
943	#41	—	2	4	no	—
944	#41	—	4	2	no	—
945	#41	—	4	2	no	—
946	#41	—	4	2	no	—
947	#41	—	4	2	no	—
948	#41	—	4	2	no	—
949	#41	—	4	2	no	—
950	#41	—	4	2	no	—
951	#41	—	4	2	no	—
952	#41	—	4	8	no	—
953	C₂×Q₈	—	2	1	no	—
954	C₂×Q₈	—	2	2	no	—
955	C₂×Q₈	—	4	2	no	—
956	C₂×Q₈	—	4	2	no	—
957	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
958	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
959	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
960	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	4	no	—
964	C₂×D₄	—	2	4	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	2	1	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	1	no	—
974	C₂×D₄	—	2	1	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	1	no	—
978	C₂×D₄	—	4	2	no	—
979	C₂×D₄	—	4	2	no	—
980	C₂×D₄	—	4	8	no	—
981	C₂×D₄	—	4	8	no	—
982	C₂×D₄	—	4	8	no	—
983	C₂×D₄	—	8	2	no	—
984	C₂×D₄	—	8	2	no	—
985	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
986	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
987	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
988	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
989	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
990	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
991	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
992	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
993	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
994	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
995	C₂²×C₄	—	2	1	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	2	no	—
1007	C₂²×C₄	—	8	2	no	—
1008	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1009	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1010	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1011	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1012	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1013	Q₁₆	—	4	2	no	—
1014	Q₁₆	—	4	2	no	—
1015	Q₁₆	—	4	2	no	—
1016	SD₁₆	—	2	2	no	—
1017	SD₁₆	—	2	4	no	—
1018	SD₁₆	—	2	4	no	—
1019	SD₁₆	—	2	2	no	—
1020	SD₁₆	—	4	2	no	—
1021	SD₁₆	—	4	2	no	—
1022	SD₁₆	—	4	2	no	—
1023	SD₁₆	—	4	2	no	—
1024	D₈	—	2	2	no	—
1025	D₈	—	2	2	no	—
1026	D₈	—	4	2	no	—
1027	M₁₆	—	4	2	no	—
1028	M₁₆	—	4	2	no	—
1029	C₂×C₈	—	4	2	no	—
1030	C₂×C₈	—	4	2	no	—
1031	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1032	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1033	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1034	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1035	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1036	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1056	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1057	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1058	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1059	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1060	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1061	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1062	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	2	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1085	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1086	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1087	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1088	C₄²	—	2	2	no	—
1089	C₄²	—	2	2	no	—
1090	C₄²	—	2	1	no	—
1091	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1092	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1093	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1094	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1095	C₂³	—	2	4	no	—
1096	C₂³	—	2	1	no	—
1097	C₂³	—	2	1	no	—
1098	C₂³	—	2	1	no	—
1099	C₂³	—	2	2	no	—
1100	C₂³	—	4	4	no	—
1101	C₂³	—	4	4	no	—
1102	C₂³	—	8	1	no	—
1103	C₂³	—	8	1	no	—
1104	C₂³	—	8	2	no	—
1105	C₂³	—	8	2	no	—
1106	C₂³	—	8	2	no	—
1107	C₂³	—	8	2	no	—
1108	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1109	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1110	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1111	Q₈	—	2	1	no	—
1112	Q₈	—	2	2	no	—
1113	Q₈	—	2	2	no	—
1114	Q₈	—	2	1	no	—
1115	Q₈	—	2	2	no	—
1116	Q₈	—	2	2	no	—
1117	Q₈	—	4	2	no	—
1118	Q₈	—	8	1	no	—
1119	Q₈	—	8	2	no	—
1120	D₄	—	2	4	no	—
1121	D₄	—	2	2	no	—
1122	D₄	—	2	2	no	—
1123	D₄	—	2	1	no	—
1124	D₄	—	2	1	no	—
1125	D₄	—	2	1	no	—
1126	D₄	—	2	1	no	—
1127	D₄	—	2	2	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	4	2	no	—
1130	D₄	—	4	2	no	—
1131	D₄	—	4	2	no	—
1132	D₄	—	4	2	no	—
1133	D₄	—	4	4	no	—
1134	D₄	—	4	4	no	—
1135	D₄	—	4	4	no	—
1136	D₄	—	4	4	no	—
1137	D₄	—	4	4	no	—
1138	D₄	—	4	2	no	—
1139	D₄	—	8	1	no	—
1140	D₄	—	8	1	no	—
1141	D₄	—	8	2	no	—
1142	D₄	—	8	2	no	—
1143	D₄	—	8	2	no	—
1144	D₄	—	8	2	no	—
1145	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1146	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1147	C₂×C₄	—	2	2	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	2	no	—
1162	C₂×C₄	—	4	1	no	—
1163	C₂×C₄	—	4	4	no	—
1164	C₂×C₄	—	4	4	no	—
1165	C₂×C₄	—	4	4	no	—
1166	C₂×C₄	—	4	2	no	—
1167	C₂×C₄	—	4	2	no	—
1168	C₂×C₄	—	4	2	no	—
1169	C₂×C₄	—	8	1	no	—
1170	C₂×C₄	—	8	1	no	—
1171	C₂×C₄	—	8	2	no	—
1172	C₂×C₄	—	8	2	no	—
1173	C₂×C₄	—	8	1	no	—
1174	C₂×C₄	—	8	2	no	—
1175	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1176	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1177	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1178	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1179	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1180	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1181	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1182	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1183	C₈	—	2	1	no	—
1184	C₈	—	2	1	no	—
1185	C₈	—	2	2	no	—
1186	C₈	—	2	1	no	—
1187	C₈	—	2	2	no	—
1188	C₈	—	2	1	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	2	1	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	2	no	—
1193	C₂²	—	2	2	no	—
1194	C₂²	—	2	1	no	—
1195	C₂²	—	2	2	no	—
1196	C₂²	—	2	2	no	—
1197	C₂²	—	2	1	no	—
1198	C₂²	—	2	2	no	—
1199	C₂²	—	2	2	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	1	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	2	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	2	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	2	no	—
1210	C₂²	—	8	4	no	—
1211	C₂²	—	16	4	no	—
1212	C₂²	—	16	4	no	—
1213	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1214	C₄	—	2	1	no	—
1215	C₄	—	2	2	no	—
1216	C₄	—	2	2	no	—
1217	C₄	—	2	1	no	—
1218	C₄	—	2	1	no	—
1219	C₄	—	2	1	no	—
1220	C₄	—	4	2	no	—
1221	C₄	—	4	2	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	1	no	—
1227	C₄	—	4	2	no	—
1228	C₄	C₅₃×#577	1	2	yes	—
1229	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1230	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1231	C₂	—	4	1	no	—
1232	C₂	—	4	2	no	—
1233	C₂	—	4	2	no	—
1234	C₂	—	4	2	no	—
1235	C₂	—	4	2	no	—
1236	C₂	—	8	2	no	—
1237	C₂	—	8	1	no	—
1238	C₂	C₅₃×#3484	1	1	yes	characteristic
1239	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1240	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 ◁ C₅₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3547	C₂	semidirect
2. C₅₃×#3496	C₂	semidirect
3. C₅₃×#3331	C₂	semidirect
4. C₅₃×#3325	C₂	semidirect
5. C₅₃×#3323	C₂	semidirect
6. C₅₃×#3303	C₂	semidirect
7. C₅₃×#3296	C₂	semidirect
8. C₅₃×#3295	C₂	semidirect
9. C₅₃×#3283	C₂	semidirect
10. C₅₃×#3282	C₂	semidirect
11. D₄×SD₁₆×C₅₃	C₂	semidirect
12. C₅₃×#3276	C₂	semidirect
13. C₅₃×#3275	C₂	semidirect
14. C₅₃×#3272	C₂	semidirect
15. C₅₃×#3212	C₂	semidirect
16. C₅₃×#3210	C₂	semidirect
17. C₅₃×#3204	C₂	semidirect
18. C₅₃×#3201	C₂	semidirect
19. C₅₃×#3105	C₂	semidirect
20. C₅₃×#3101	C₂	semidirect
21. C₅₃×#3012	C₂	semidirect
22. C₅₃×#3009	C₂	semidirect
23. C₅₃×#2979	C₂	semidirect
25. C₂×#137×C₅₃	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
27. C₂×#135×C₅₃	C₂²	semidirect
28. C₂²×SD₁₆×C₅₃	C₂²	semidirect
31. C₅₃×#555	C₂²	semidirect
32. C₅₃×#554	C₂²	semidirect
34. C₅₃×#552	C₂²	semidirect
35. D₄×Q₈×C₅₃	C₂²	semidirect
36. C₅₃×#548	C₂²	semidirect
40. C₅₃×#547	C₂²	semidirect
51. C₅₃×#537	C₂²	semidirect
52. C₅₃×#536	C₂²	semidirect
54. C₅₃×#533	C₂²	semidirect
57. C₅₃×#529	C₂²	semidirect
61. C₅₃×#495	C₂²	semidirect
62. C₅₃×#494	C₂²	semidirect
63. C₅₃×#492	C₂²	semidirect
64. C₅₃×#488	C₂²	semidirect
65. C₅₃×#487	C₂²	semidirect
66. C₅₃×#486	C₂²	semidirect
67. C₅₃×#485	C₂²	semidirect
68. C₅₃×#484	C₂²	semidirect
69. C₅₃×#483	C₂²	semidirect
70. C₅₃×#483	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#481	C₂²	semidirect
73. C₅₃×#481	C₂²	semidirect
74. C₅₃×#478	C₂²	semidirect
75. C₅₃×#478	C₂²	semidirect
76. C₅₃×#476	C₂²	semidirect
77. C₅₃×#476	C₂²	semidirect
78. C₅₃×#470	C₂²	semidirect
79. C₅₃×#470	C₂²	semidirect
80. C₅₃×#469	C₂²	semidirect
81. C₅₃×#468	C₂²	semidirect
82. C₅₃×#467	C₂²	semidirect
83. C₅₃×#465	C₂²	semidirect
84. C₅₃×#465	C₂²	semidirect
85. C₅₃×#465	C₂²	semidirect
86. C₅₃×#464	C₂²	semidirect
87. C₅₃×#464	C₂²	semidirect
88. C₅₃×#463	C₂²	semidirect
89. C₅₃×#463	C₂²	semidirect
90. C₅₃×#462	C₂²	semidirect
91. C₅₃×#461	C₂²	semidirect
92. C₅₃×#461	C₂²	semidirect
93. C₅₃×#461	C₂²	semidirect
94. C₅₃×#460	C₂²	semidirect
95. C₅₃×#459	C₂²	semidirect
96. C₅₃×#452	C₂²	semidirect
97. C₅₃×#452	C₂²	semidirect
98. C₅₃×#452	C₂²	semidirect
99. C₅₃×#452	C₂²	semidirect
100. C₅₃×#452	C₂²	semidirect
101. C₅₃×#452	C₂²	semidirect
102. C₅₃×#452	C₂²	semidirect
103. C₅₃×#451	C₂²	semidirect
106. C₅₃×#450	C₂²	semidirect
107. C₅₃×#450	C₂²	semidirect
108. C₅₃×#450	C₂²	semidirect
109. C₅₃×#449	C₂²	semidirect
110. C₅₃×#449	C₂²	semidirect
111. C₅₃×#449	C₂²	semidirect
112. C₅₃×#448	C₂²	semidirect
114. C₅₃×#447	C₂²	semidirect
115. C₄×SD₁₆×C₅₃	C₂²	semidirect
116. C₄×SD₁₆×C₅₃	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×#436	C₂²	semidirect
124. C₈×D₄×C₅₃	C₂²	semidirect
125. C₈×D₄×C₅₃	C₂²	semidirect
126. C₈×D₄×C₅₃	C₂²	semidirect
127. C₅₃×#431	C₂²	semidirect
128. C₅₃×#431	C₂²	semidirect
129. C₅₃×#418	C₂²	semidirect
130. C₅₃×#417	C₂²	semidirect
131. C₅₃×#416	C₂²	semidirect
132. C₂×#102×C₅₃	C₂²	semidirect
133. C₅₃×#408	C₂²	semidirect
134. C₅₃×#408	C₂²	semidirect
568. #61658	C₅₃	direct (N × H)
611. #3547	C₂×C₅₃	semidirect
612. #3496	C₂×C₅₃	semidirect
613. #3331	C₂×C₅₃	semidirect
614. #3325	C₂×C₅₃	semidirect
615. #3323	C₂×C₅₃	semidirect
616. #3303	C₂×C₅₃	semidirect
617. #3296	C₂×C₅₃	semidirect
618. #3295	C₂×C₅₃	semidirect
619. #3283	C₂×C₅₃	semidirect
620. #3282	C₂×C₅₃	semidirect
621. D₄×SD₁₆	C₂×C₅₃	semidirect
622. #3276	C₂×C₅₃	semidirect
623. #3275	C₂×C₅₃	semidirect
624. #3272	C₂×C₅₃	semidirect
625. #3212	C₂×C₅₃	semidirect
626. #3210	C₂×C₅₃	semidirect
627. #3204	C₂×C₅₃	semidirect
628. #3201	C₂×C₅₃	semidirect
629. #3105	C₂×C₅₃	semidirect
630. #3101	C₂×C₅₃	semidirect
631. #3012	C₂×C₅₃	semidirect
632. #3009	C₂×C₅₃	semidirect
633. #2979	C₂×C₅₃	semidirect
645. C₂×#137	C₂²×C₅₃	semidirect
646. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
647. C₂×#135	C₂²×C₅₃	semidirect
648. C₂²×SD₁₆	C₂²×C₅₃	semidirect
651. #555	C₂²×C₅₃	semidirect
652. #554	C₂²×C₅₃	semidirect
654. #552	C₂²×C₅₃	semidirect
655. D₄×Q₈	C₂²×C₅₃	semidirect
656. #548	C₂²×C₅₃	semidirect
660. #547	C₂²×C₅₃	semidirect
671. #537	C₂²×C₅₃	semidirect
672. #536	C₂²×C₅₃	semidirect
674. #533	C₂²×C₅₃	semidirect
677. #529	C₂²×C₅₃	semidirect
681. #495	C₂²×C₅₃	semidirect
682. #494	C₂²×C₅₃	semidirect
683. #492	C₂²×C₅₃	semidirect
684. #488	C₂²×C₅₃	semidirect
685. #487	C₂²×C₅₃	semidirect
686. #486	C₂²×C₅₃	semidirect
687. #485	C₂²×C₅₃	semidirect
688. #484	C₂²×C₅₃	semidirect
689. #483	C₂²×C₅₃	semidirect
690. #483	C₂²×C₅₃	semidirect
691. #482	C₂²×C₅₃	semidirect
692. #481	C₂²×C₅₃	semidirect
693. #481	C₂²×C₅₃	semidirect
694. #478	C₂²×C₅₃	semidirect
695. #478	C₂²×C₅₃	semidirect
696. #476	C₂²×C₅₃	semidirect
697. #476	C₂²×C₅₃	semidirect
698. #470	C₂²×C₅₃	semidirect
699. #470	C₂²×C₅₃	semidirect
700. #469	C₂²×C₅₃	semidirect
701. #468	C₂²×C₅₃	semidirect
702. #467	C₂²×C₅₃	semidirect
703. #465	C₂²×C₅₃	semidirect
704. #465	C₂²×C₅₃	semidirect
705. #465	C₂²×C₅₃	semidirect
706. #464	C₂²×C₅₃	semidirect
707. #464	C₂²×C₅₃	semidirect
708. #463	C₂²×C₅₃	semidirect
709. #463	C₂²×C₅₃	semidirect
710. #462	C₂²×C₅₃	semidirect
711. #461	C₂²×C₅₃	semidirect
712. #461	C₂²×C₅₃	semidirect
713. #461	C₂²×C₅₃	semidirect
714. #460	C₂²×C₅₃	semidirect
715. #459	C₂²×C₅₃	semidirect
716. #452	C₂²×C₅₃	semidirect
717. #452	C₂²×C₅₃	semidirect
718. #452	C₂²×C₅₃	semidirect
719. #452	C₂²×C₅₃	semidirect
720. #452	C₂²×C₅₃	semidirect
721. #452	C₂²×C₅₃	semidirect
722. #452	C₂²×C₅₃	semidirect
723. #451	C₂²×C₅₃	semidirect
726. #450	C₂²×C₅₃	semidirect
727. #450	C₂²×C₅₃	semidirect
728. #450	C₂²×C₅₃	semidirect
729. #449	C₂²×C₅₃	semidirect
730. #449	C₂²×C₅₃	semidirect
731. #449	C₂²×C₅₃	semidirect
732. #448	C₂²×C₅₃	semidirect
734. #447	C₂²×C₅₃	semidirect
735. C₄×SD₁₆	C₂²×C₅₃	semidirect
736. C₄×SD₁₆	C₂²×C₅₃	semidirect
737. C₄×SD₁₆	C₂²×C₅₃	semidirect
738. C₄×SD₁₆	C₂²×C₅₃	semidirect
739. C₄×D₈	C₂²×C₅₃	semidirect
740. C₄×D₈	C₂²×C₅₃	semidirect
741. #436	C₂²×C₅₃	semidirect
742. #436	C₂²×C₅₃	semidirect
743. #436	C₂²×C₅₃	semidirect
744. C₈×D₄	C₂²×C₅₃	semidirect
745. C₈×D₄	C₂²×C₅₃	semidirect
746. C₈×D₄	C₂²×C₅₃	semidirect
747. #431	C₂²×C₅₃	semidirect
748. #431	C₂²×C₅₃	semidirect
749. #418	C₂²×C₅₃	semidirect
750. #417	C₂²×C₅₃	semidirect
751. #416	C₂²×C₅₃	semidirect
752. C₂×#102	C₂²×C₅₃	semidirect
753. #408	C₂²×C₅₃	semidirect
754. #408	C₂²×C₅₃	semidirect
755. C₅₃	#61658	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3547	2
C₅₃×#3496	2
C₅₃×#3331	2
C₅₃×#3325	2
C₅₃×#3323	2
C₅₃×#3303	2
C₅₃×#3296	2
C₅₃×#3295	2
C₅₃×#3283	2
C₅₃×#3282	2
D₄×SD₁₆×C₅₃	2
C₅₃×#3276	2
C₅₃×#3275	2
C₅₃×#3272	2
C₅₃×#3212	2
C₅₃×#3210	2
C₅₃×#3204	2
C₅₃×#3201	2
C₅₃×#3105	2
C₅₃×#3101	2
C₅₃×#3012	2
C₅₃×#3009	2
C₅₃×#2979	2
#61658	53

Subgroups — C53×#61658 #27269170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61658 #27269170