Subgroups — C₅₃×#60833 #27268345

Order 13568.

2144 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3224	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3222	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3217	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3216	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3212	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3208	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3154	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3012	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3009	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	2	yes	—
19	C₂×#137×C₅₃	C₂²	1	2	yes	complemented
20	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
21	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
22	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
23	C₅₃×#550	—	2	1	no	—
24	C₅₃×#550	—	2	1	no	—
25	D₄²×C₅₃	—	2	1	no	—
26	D₄²×C₅₃	—	2	2	no	—
27	D₄²×C₅₃	—	2	2	no	—
28	D₄²×C₅₃	—	2	1	no	—
29	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#542	—	2	1	no	—
31	C₅₃×#542	C₂²	1	2	yes	complemented
32	C₅₃×#541	—	2	1	no	—
33	C₅₃×#541	C₂²	1	2	yes	complemented
34	C₅₃×#539	—	2	2	no	—
35	C₅₃×#537	C₂²	1	1	yes	characteristic
36	C₅₃×#536	C₂²	1	1	yes	characteristic
37	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#535	C₂²	1	4	yes	—
39	C₅₃×#535	C₂²	1	2	yes	—
40	C₅₃×#533	—	2	1	no	—
41	C₅₃×#533	C₂²	1	2	yes	complemented
42	C₅₃×#532	C₂²	1	2	yes	—
43	C₅₃×#532	C₂²	1	1	yes	characteristic
44	C₂×#127×C₅₃	C₂²	1	2	yes	—
45	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
46	C₅₃×#529	—	2	1	no	—
47	C₅₃×#529	—	2	2	no	—
48	C₅₃×#529	C₂²	1	2	yes	complemented
49	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
50	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#497	C₂²	1	4	yes	complemented
53	C₅₃×#496	C₂²	1	4	yes	complemented
54	C₅₃×#495	C₂²	1	4	yes	complemented
55	C₅₃×#492	C₂²	1	4	yes	complemented
56	C₅₃×#490	C₂²	1	4	yes	complemented
57	C₅₃×#489	C₂²	1	4	yes	complemented
58	C₅₃×#488	C₂²	1	4	yes	complemented
59	C₅₃×#486	C₂²	1	4	yes	complemented
60	C₅₃×#464	C₂²	1	2	yes	complemented
61	C₅₃×#464	C₂²	1	4	yes	complemented
62	C₅₃×#463	C₂²	1	2	yes	complemented
63	C₅₃×#462	C₂²	1	2	yes	complemented
64	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#460	C₂²	1	2	yes	complemented
68	C₅₃×#460	C₂²	1	2	yes	complemented
69	C₅₃×#460	C₂²	1	2	yes	complemented
70	C₅₃×#460	C₂²	1	2	yes	complemented
71	C₅₃×#460	C₂²	1	2	yes	complemented
72	C₅₃×#460	C₂²	1	4	yes	complemented
73	C₅₃×#459	C₂²	1	2	yes	complemented
74	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#459	C₂²	1	2	yes	complemented
76	C₅₃×#452	C₂²	1	4	yes	complemented
77	C₅₃×#452	C₂²	1	4	yes	complemented
78	C₅₃×#452	C₂²	1	4	yes	complemented
79	C₅₃×#450	C₂²	1	4	yes	complemented
80	C₅₃×#450	C₂²	1	4	yes	complemented
81	C₅₃×#450	C₂²	1	4	yes	complemented
82	C₅₃×#449	C₂²	1	4	yes	complemented
83	C₅₃×#447	C₂²	1	4	yes	complemented
84	C₅₃×#433	C₂²	1	4	yes	complemented
85	C₅₃×#432	C₂²	1	2	yes	complemented
86	C₅₃×#431	C₂²	1	2	yes	complemented
87	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#418	C₂²	1	2	yes	complemented
90	C₅₃×#417	C₂²	1	2	yes	complemented
91	C₅₃×#416	C₂²	1	2	yes	complemented
92	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
93	C₅₃×#408	C₂²	1	2	yes	—
94	C₅₃×#405	C₂²	1	2	yes	complemented
95	H(5,𝔽₂)×C₅₃	—	4	4	no	—
96	H(5,𝔽₂)×C₅₃	—	4	4	no	—
97	C₂×#41×C₅₃	—	2	2	no	—
98	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
99	C₂×#41×C₅₃	C₂³	1	2	yes	—
100	C₂×#41×C₅₃	C₂³	1	4	yes	—
101	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₅₃	—	2	4	no	—
104	C₂²×D₄×C₅₃	—	2	2	no	—
105	C₂²×D₄×C₅₃	—	2	1	no	—
106	C₂²×D₄×C₅₃	—	2	2	no	—
107	C₂²×D₄×C₅₃	—	2	1	no	—
108	C₂²×D₄×C₅₃	—	2	2	no	—
109	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
111	#137×C₅₃	—	4	4	no	—
112	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
113	#135×C₅₃	—	4	4	no	—
114	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
115	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₅₃	—	4	4	no	—
117	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
118	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
120	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
121	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
122	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
123	C₂×D₈×C₅₃	C₂³	1	4	yes	—
124	C₂×D₈×C₅₃	C₂³	1	2	yes	—
125	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
126	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
127	C₄⋊Q₈×C₅₃	—	2	1	no	—
128	C₄⋊Q₈×C₅₃	—	2	1	no	—
129	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
131	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
132	#127×C₅₃	—	2	1	no	—
133	#127×C₅₃	—	2	2	no	—
134	#127×C₅₃	—	2	1	no	—
135	#127×C₅₃	—	2	2	no	—
136	#127×C₅₃	C₂³	1	4	yes	—
137	#127×C₅₃	C₂³	1	1	yes	characteristic
138	#127×C₅₃	C₂³	1	2	yes	—
139	#127×C₅₃	C₂³	1	2	yes	—
140	#126×C₅₃	—	2	2	no	—
141	#126×C₅₃	—	2	2	no	—
142	#126×C₅₃	—	2	2	no	—
143	#126×C₅₃	—	2	2	no	—
144	#125×C₅₃	—	2	2	no	—
145	#125×C₅₃	—	2	1	no	—
146	#125×C₅₃	—	2	2	no	—
147	#125×C₅₃	—	2	2	no	—
148	#125×C₅₃	C₂³	1	2	yes	—
149	#124×C₅₃	—	2	2	no	—
150	#124×C₅₃	—	2	1	no	—
151	#124×C₅₃	C₂³	1	4	yes	—
152	#124×C₅₃	C₂³	1	2	yes	—
153	#124×C₅₃	C₂³	1	2	yes	—
154	#123×C₅₃	—	2	2	no	—
155	#123×C₅₃	—	2	2	no	—
156	#123×C₅₃	—	2	2	no	—
157	#123×C₅₃	—	2	2	no	—
158	C₂²⋊Q₈×C₅₃	—	2	1	no	—
159	C₂²⋊Q₈×C₅₃	—	2	1	no	—
160	C₂²⋊Q₈×C₅₃	—	2	2	no	—
161	C₂²⋊Q₈×C₅₃	—	2	2	no	—
162	C₂²⋊Q₈×C₅₃	—	2	1	no	—
163	C₂²⋊Q₈×C₅₃	—	2	2	no	—
164	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
165	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
166	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
167	#121×C₅₃	—	2	4	no	—
168	#121×C₅₃	—	2	2	no	—
169	#121×C₅₃	—	2	2	no	—
170	#121×C₅₃	—	2	4	no	—
171	#121×C₅₃	—	2	2	no	—
172	#121×C₅₃	—	2	1	no	—
173	#121×C₅₃	—	2	1	no	—
174	#121×C₅₃	—	2	2	no	—
175	#121×C₅₃	—	2	1	no	—
176	#121×C₅₃	—	2	2	no	—
177	#121×C₅₃	C₂³	1	2	yes	—
178	#120×C₅₃	—	2	4	no	—
179	#120×C₅₃	—	2	4	no	—
180	#120×C₅₃	—	2	4	no	—
181	C₄×Q₈×C₅₃	—	2	1	no	—
182	C₄×Q₈×C₅₃	—	2	1	no	—
183	C₄×Q₈×C₅₃	—	2	2	no	—
184	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
185	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
186	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
187	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
188	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
189	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₅₃	—	2	1	no	—
191	C₄×D₄×C₅₃	—	2	2	no	—
192	C₄×D₄×C₅₃	—	2	1	no	—
193	C₄×D₄×C₅₃	—	2	2	no	—
194	C₄×D₄×C₅₃	—	2	1	no	—
195	C₄×D₄×C₅₃	—	2	1	no	—
196	C₄×D₄×C₅₃	—	2	2	no	—
197	C₄×D₄×C₅₃	D₄	1	2	yes	—
198	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
199	C₄×D₄×C₅₃	D₄	1	2	yes	—
200	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
201	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
203	#117×C₅₃	—	2	1	no	—
204	#117×C₅₃	—	2	2	no	—
205	#117×C₅₃	—	2	2	no	—
206	#117×C₅₃	C₂³	1	1	yes	characteristic
207	#117×C₅₃	C₂³	1	1	yes	characteristic
208	#117×C₅₃	C₂³	1	2	yes	—
209	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
210	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₅₃	—	2	1	no	—
212	C₂×C₄²×C₅₃	—	2	1	no	—
213	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
215	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
216	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
217	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
218	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
219	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
220	#103×C₅₃	C₂³	1	2	yes	—
221	#103×C₅₃	C₂³	1	4	yes	—
222	#103×C₅₃	C₂³	1	2	yes	—
223	#102×C₅₃	C₂³	1	2	yes	—
224	#102×C₅₃	C₂³	1	4	yes	—
225	#102×C₅₃	C₂³	1	4	yes	—
226	#102×C₅₃	C₂³	1	4	yes	—
227	#102×C₅₃	C₂³	1	4	yes	—
228	#102×C₅₃	C₂³	1	4	yes	—
229	#102×C₅₃	C₂³	1	2	yes	—
230	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
231	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
232	#97×C₅₃	C₂³	1	4	yes	—
233	C₄×C₈×C₅₃	C₂³	1	4	yes	—
234	C₂⁴×C₅₃	—	2	4	no	—
235	C₂⁴×C₅₃	—	2	2	no	—
236	#41×C₅₃	—	2	2	no	—
237	#41×C₅₃	—	2	2	no	—
238	#41×C₅₃	—	2	2	no	—
239	#41×C₅₃	—	2	4	no	—
240	#41×C₅₃	—	2	2	no	—
241	#41×C₅₃	—	2	4	no	—
242	#41×C₅₃	—	4	4	no	—
243	#41×C₅₃	—	4	4	no	—
244	#41×C₅₃	—	4	8	no	—
245	C₂×Q₈×C₅₃	—	2	1	no	—
246	C₂×Q₈×C₅₃	—	2	2	no	—
247	C₂×Q₈×C₅₃	—	2	2	no	—
248	C₂×Q₈×C₅₃	—	2	2	no	—
249	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
250	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
251	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
252	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
253	C₂×D₄×C₅₃	—	2	1	no	—
254	C₂×D₄×C₅₃	—	2	4	no	—
255	C₂×D₄×C₅₃	—	2	2	no	—
256	C₂×D₄×C₅₃	—	2	2	no	—
257	C₂×D₄×C₅₃	—	2	1	no	—
258	C₂×D₄×C₅₃	—	2	2	no	—
259	C₂×D₄×C₅₃	—	2	1	no	—
260	C₂×D₄×C₅₃	—	2	2	no	—
261	C₂×D₄×C₅₃	—	2	4	no	—
262	C₂×D₄×C₅₃	—	2	2	no	—
263	C₂×D₄×C₅₃	—	2	2	no	—
264	C₂×D₄×C₅₃	—	2	4	no	—
265	C₂×D₄×C₅₃	—	2	2	no	—
266	C₂×D₄×C₅₃	—	2	4	no	—
267	C₂×D₄×C₅₃	—	2	4	no	—
268	C₂×D₄×C₅₃	—	2	4	no	—
269	C₂×D₄×C₅₃	—	4	4	no	—
270	C₂×D₄×C₅₃	—	4	4	no	—
271	C₂×D₄×C₅₃	—	4	16	no	—
272	C₂×D₄×C₅₃	—	4	8	no	—
273	C₂×D₄×C₅₃	—	8	2	no	—
274	C₂×D₄×C₅₃	—	8	4	no	—
275	C₂×D₄×C₅₃	—	8	2	no	—
276	C₂×D₄×C₅₃	—	8	4	no	—
277	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
278	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
279	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
280	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
281	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₅₃	—	2	1	no	—
283	C₂²×C₄×C₅₃	—	2	1	no	—
284	C₂²×C₄×C₅₃	—	2	1	no	—
285	C₂²×C₄×C₅₃	—	2	1	no	—
286	C₂²×C₄×C₅₃	—	2	4	no	—
287	C₂²×C₄×C₅₃	—	2	2	no	—
288	C₂²×C₄×C₅₃	—	2	1	no	—
289	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
291	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
293	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
295	Q₁₆×C₅₃	—	4	2	no	—
296	Q₁₆×C₅₃	—	4	4	no	—
297	SD₁₆×C₅₃	—	4	4	no	—
298	SD₁₆×C₅₃	—	4	4	no	—
299	SD₁₆×C₅₃	—	4	2	no	—
300	SD₁₆×C₅₃	—	4	2	no	—
301	SD₁₆×C₅₃	—	4	4	no	—
302	SD₁₆×C₅₃	—	4	4	no	—
303	D₈×C₅₃	—	4	2	no	—
304	D₈×C₅₃	—	4	4	no	—
305	M₁₆×C₅₃	—	2	4	no	—
306	C₂×C₈×C₅₃	—	2	4	no	—
307	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
308	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
309	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₅₃	—	2	2	no	—
311	C₄⋊C₄×C₅₃	—	2	2	no	—
312	C₄⋊C₄×C₅₃	—	2	1	no	—
313	C₄⋊C₄×C₅₃	—	2	1	no	—
314	C₄⋊C₄×C₅₃	—	2	1	no	—
315	C₄⋊C₄×C₅₃	—	2	2	no	—
316	C₄⋊C₄×C₅₃	—	2	2	no	—
317	C₄⋊C₄×C₅₃	—	2	2	no	—
318	C₄⋊C₄×C₅₃	—	2	2	no	—
319	C₄⋊C₄×C₅₃	—	2	1	no	—
320	C₄⋊C₄×C₅₃	—	2	1	no	—
321	C₄⋊C₄×C₅₃	—	2	2	no	—
322	C₄⋊C₄×C₅₃	—	2	2	no	—
323	C₄⋊C₄×C₅₃	—	2	2	no	—
324	C₄⋊C₄×C₅₃	—	2	2	no	—
325	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
326	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
327	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
328	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
329	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
330	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
332	C₂²⋊C₄×C₅₃	—	2	2	no	—
333	C₂²⋊C₄×C₅₃	—	2	2	no	—
334	C₂²⋊C₄×C₅₃	—	2	1	no	—
335	C₂²⋊C₄×C₅₃	—	2	2	no	—
336	C₂²⋊C₄×C₅₃	—	2	1	no	—
337	C₂²⋊C₄×C₅₃	—	2	1	no	—
338	C₂²⋊C₄×C₅₃	—	2	2	no	—
339	C₂²⋊C₄×C₅₃	—	2	2	no	—
340	C₂²⋊C₄×C₅₃	—	2	2	no	—
341	C₂²⋊C₄×C₅₃	—	2	4	no	—
342	C₂²⋊C₄×C₅₃	—	2	2	no	—
343	C₂²⋊C₄×C₅₃	—	2	4	no	—
344	C₂²⋊C₄×C₅₃	—	2	2	no	—
345	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
346	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
347	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
348	C₄²×C₅₃	—	2	2	no	—
349	C₄²×C₅₃	—	2	1	no	—
350	C₄²×C₅₃	—	2	1	no	—
351	C₄²×C₅₃	—	2	1	no	—
352	C₄²×C₅₃	—	2	2	no	—
353	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
354	C₄²×C₅₃	C₂×D₄	1	2	yes	—
355	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
356	C₄²×C₅₃	C₂×D₄	1	2	yes	—
357	C₄²×C₅₃	C₂⁴	1	2	yes	—
358	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂³×C₅₃	—	2	1	no	—
361	C₂³×C₅₃	—	2	4	no	—
362	C₂³×C₅₃	—	2	2	no	—
363	C₂³×C₅₃	—	4	8	no	—
364	C₂³×C₅₃	—	4	4	no	—
365	C₂³×C₅₃	—	8	2	no	—
366	C₂³×C₅₃	—	8	2	no	—
367	C₂³×C₅₃	—	8	4	no	—
368	C₂³×C₅₃	—	8	4	no	—
369	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
370	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
371	Q₈×C₅₃	—	2	2	no	—
372	Q₈×C₅₃	—	2	2	no	—
373	Q₈×C₅₃	—	2	2	no	—
374	Q₈×C₅₃	—	2	2	no	—
375	Q₈×C₅₃	—	2	2	no	—
376	Q₈×C₅₃	—	2	1	no	—
377	Q₈×C₅₃	—	2	1	no	—
378	Q₈×C₅₃	—	4	2	no	—
379	Q₈×C₅₃	—	8	2	no	—
380	D₄×C₅₃	—	2	4	no	—
381	D₄×C₅₃	—	2	2	no	—
382	D₄×C₅₃	—	2	4	no	—
383	D₄×C₅₃	—	2	4	no	—
384	D₄×C₅₃	—	2	2	no	—
385	D₄×C₅₃	—	2	2	no	—
386	D₄×C₅₃	—	2	1	no	—
387	D₄×C₅₃	—	2	1	no	—
388	D₄×C₅₃	—	4	8	no	—
389	D₄×C₅₃	—	4	4	no	—
390	D₄×C₅₃	—	4	2	no	—
391	D₄×C₅₃	—	4	8	no	—
392	D₄×C₅₃	—	4	4	no	—
393	D₄×C₅₃	—	4	2	no	—
394	D₄×C₅₃	—	4	4	no	—
395	D₄×C₅₃	—	4	4	no	—
396	D₄×C₅₃	—	4	2	no	—
397	D₄×C₅₃	—	8	2	no	—
398	D₄×C₅₃	—	8	4	no	—
399	D₄×C₅₃	—	8	2	no	—
400	D₄×C₅₃	—	8	4	no	—
401	D₄×C₅₃	—	8	2	no	—
402	C₂×C₄×C₅₃	—	2	2	no	—
403	C₂×C₄×C₅₃	—	2	4	no	—
404	C₂×C₄×C₅₃	—	2	2	no	—
405	C₂×C₄×C₅₃	—	2	2	no	—
406	C₂×C₄×C₅₃	—	2	2	no	—
407	C₂×C₄×C₅₃	—	2	2	no	—
408	C₂×C₄×C₅₃	—	2	1	no	—
409	C₂×C₄×C₅₃	—	2	1	no	—
410	C₂×C₄×C₅₃	—	2	2	no	—
411	C₂×C₄×C₅₃	—	2	1	no	—
412	C₂×C₄×C₅₃	—	4	1	no	—
413	C₂×C₄×C₅₃	—	4	2	no	—
414	C₂×C₄×C₅₃	—	4	8	no	—
415	C₂×C₄×C₅₃	—	4	2	no	—
416	C₂×C₄×C₅₃	—	4	4	no	—
417	C₂×C₄×C₅₃	—	4	2	no	—
418	C₂×C₄×C₅₃	—	4	2	no	—
419	C₂×C₄×C₅₃	—	8	1	no	—
420	C₂×C₄×C₅₃	—	8	1	no	—
421	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
430	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
431	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
432	C₈×C₅₃	—	2	2	no	—
433	C₈×C₅₃	—	2	2	no	—
434	C₈×C₅₃	—	2	4	no	—
435	#60833	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
436	C₂²×C₅₃	—	2	1	no	—
437	C₂²×C₅₃	—	2	1	no	—
438	C₂²×C₅₃	—	2	2	no	—
439	C₂²×C₅₃	—	2	2	no	—
440	C₂²×C₅₃	—	2	2	no	—
441	C₂²×C₅₃	—	4	1	no	—
442	C₂²×C₅₃	—	4	4	no	—
443	C₂²×C₅₃	—	4	2	no	—
444	C₂²×C₅₃	—	4	4	no	—
445	C₂²×C₅₃	—	4	2	no	—
446	C₂²×C₅₃	—	4	1	no	—
447	C₂²×C₅₃	—	4	1	no	—
448	C₂²×C₅₃	—	4	4	no	—
449	C₂²×C₅₃	—	4	2	no	—
450	C₂²×C₅₃	—	16	4	no	—
451	C₂²×C₅₃	—	16	8	no	—
452	C₂²×C₅₃	#535	1	2	yes	—
453	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
454	C₄×C₅₃	—	2	1	no	—
455	C₄×C₅₃	—	2	1	no	—
456	C₄×C₅₃	—	2	2	no	—
457	C₄×C₅₃	—	2	2	no	—
458	C₄×C₅₃	—	2	1	no	—
459	C₄×C₅₃	—	2	2	no	—
460	C₄×C₅₃	—	4	2	no	—
461	C₄×C₅₃	—	4	1	no	—
462	C₄×C₅₃	—	4	2	no	—
463	C₄×C₅₃	—	4	1	no	—
464	C₄×C₅₃	—	4	2	no	—
465	C₄×C₅₃	—	4	1	no	—
466	C₄×C₅₃	#535	1	2	yes	—
467	C₄×C₅₃	#577	1	2	yes	—
468	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
469	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
470	#3498	C₂×C₅₃	1	1	yes	characteristic, complemented
471	#3461	C₂×C₅₃	1	1	yes	characteristic, complemented
472	#3224	C₂×C₅₃	1	4	yes	complemented
473	#3222	C₂×C₅₃	1	4	yes	complemented
474	#3217	C₂×C₅₃	1	2	yes	complemented
475	#3216	C₂×C₅₃	1	2	yes	complemented
476	#3212	C₂×C₅₃	1	2	yes	complemented
477	#3208	C₂×C₅₃	1	2	yes	complemented
478	#3154	C₂×C₅₃	1	2	yes	complemented
479	#3136	C₂×C₅₃	1	2	yes	complemented
480	#3038	C₂×C₅₃	1	1	yes	characteristic, complemented
481	#3037	C₂×C₅₃	1	1	yes	characteristic, complemented
482	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
483	C₂×#460	C₂×C₅₃	1	1	yes	characteristic, complemented
484	#3012	C₂×C₅₃	1	2	yes	complemented
485	#3009	C₂×C₅₃	1	2	yes	complemented
486	#2925	C₂×C₅₃	1	1	yes	characteristic, complemented
487	C₂×C₅₃	—	2	2	no	—
488	C₂×C₅₃	—	4	2	no	—
489	C₂×C₅₃	—	8	1	no	—
490	C₂×C₅₃	—	8	4	no	—
491	C₂×C₅₃	—	8	2	no	—
492	C₂×C₅₃	C₂×#535	1	1	yes	characteristic
493	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
494	C₂×C₅₃	#3585	1	1	yes	characteristic
495	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	2	yes	—
496	C₂×#137	C₂²×C₅₃	1	2	yes	complemented
497	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
498	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
499	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
500	#550	—	2	1	no	—
501	#550	—	2	1	no	—
502	D₄²	—	2	1	no	—
503	D₄²	—	2	2	no	—
504	D₄²	—	2	2	no	—
505	D₄²	—	2	1	no	—
506	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
507	#542	—	2	1	no	—
508	#542	C₂²×C₅₃	1	2	yes	complemented
509	#541	—	2	1	no	—
510	#541	C₂²×C₅₃	1	2	yes	complemented
511	#539	—	2	2	no	—
512	#537	C₂²×C₅₃	1	1	yes	characteristic
513	#536	C₂²×C₅₃	1	1	yes	characteristic
514	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
515	#535	C₂²×C₅₃	1	2	yes	—
516	#535	C₂²×C₅₃	1	4	yes	—
517	#533	—	2	1	no	—
518	#533	C₂²×C₅₃	1	2	yes	complemented
519	#532	C₂²×C₅₃	1	2	yes	—
520	#532	C₂²×C₅₃	1	1	yes	characteristic
521	C₂×#127	C₂²×C₅₃	1	2	yes	—
522	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
523	#529	—	2	2	no	—
524	#529	—	2	1	no	—
525	#529	C₂²×C₅₃	1	2	yes	complemented
526	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
527	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
528	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
529	#497	C₂²×C₅₃	1	4	yes	complemented
530	#496	C₂²×C₅₃	1	4	yes	complemented
531	#495	C₂²×C₅₃	1	4	yes	complemented
532	#492	C₂²×C₅₃	1	4	yes	complemented
533	#490	C₂²×C₅₃	1	4	yes	complemented
534	#489	C₂²×C₅₃	1	4	yes	complemented
535	#488	C₂²×C₅₃	1	4	yes	complemented
536	#486	C₂²×C₅₃	1	4	yes	complemented
537	#464	C₂²×C₅₃	1	2	yes	complemented
538	#464	C₂²×C₅₃	1	4	yes	complemented
539	#463	C₂²×C₅₃	1	2	yes	complemented
540	#462	C₂²×C₅₃	1	2	yes	complemented
541	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
542	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
543	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
544	#460	C₂²×C₅₃	1	2	yes	complemented
545	#460	C₂²×C₅₃	1	2	yes	complemented
546	#460	C₂²×C₅₃	1	2	yes	complemented
547	#460	C₂²×C₅₃	1	2	yes	complemented
548	#460	C₂²×C₅₃	1	2	yes	complemented
549	#460	C₂²×C₅₃	1	4	yes	complemented
550	#459	C₂²×C₅₃	1	2	yes	complemented
551	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
552	#459	C₂²×C₅₃	1	2	yes	complemented
553	#452	C₂²×C₅₃	1	4	yes	complemented
554	#452	C₂²×C₅₃	1	4	yes	complemented
555	#452	C₂²×C₅₃	1	4	yes	complemented
556	#450	C₂²×C₅₃	1	4	yes	complemented
557	#450	C₂²×C₅₃	1	4	yes	complemented
558	#450	C₂²×C₅₃	1	4	yes	complemented
559	#449	C₂²×C₅₃	1	4	yes	complemented
560	#447	C₂²×C₅₃	1	4	yes	complemented
561	#433	C₂²×C₅₃	1	4	yes	complemented
562	#432	C₂²×C₅₃	1	2	yes	complemented
563	#431	C₂²×C₅₃	1	2	yes	complemented
564	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
565	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
566	#418	C₂²×C₅₃	1	2	yes	complemented
567	#417	C₂²×C₅₃	1	2	yes	complemented
568	#416	C₂²×C₅₃	1	2	yes	complemented
569	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
570	#408	C₂²×C₅₃	1	2	yes	—
571	#405	C₂²×C₅₃	1	2	yes	complemented
572	C₅₃	#60833	1	1	yes	characteristic, direct product factor, Sylow
573	H(5,𝔽₂)	—	4	4	no	—
574	H(5,𝔽₂)	—	4	4	no	—
575	C₂×#41	—	2	2	no	—
576	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
577	C₂×#41	C₂³×C₅₃	1	2	yes	—
578	C₂×#41	C₂³×C₅₃	1	4	yes	—
579	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
580	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
581	C₂²×D₄	—	2	4	no	—
582	C₂²×D₄	—	2	2	no	—
583	C₂²×D₄	—	2	1	no	—
584	C₂²×D₄	—	2	2	no	—
585	C₂²×D₄	—	2	1	no	—
586	C₂²×D₄	—	2	2	no	—
587	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
588	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
589	#137	—	4	4	no	—
590	AGL(1,ℤ/8)	—	4	4	no	—
591	#135	—	4	4	no	—
592	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
593	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
594	C₂×SD₁₆	—	4	4	no	—
595	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
596	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
597	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
598	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
599	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
600	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
601	C₂×D₈	C₂³×C₅₃	1	2	yes	—
602	C₂×D₈	C₂³×C₅₃	1	4	yes	—
603	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
604	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
605	C₄⋊Q₈	—	2	1	no	—
606	C₄⋊Q₈	—	2	1	no	—
607	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
608	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
609	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
610	#127	—	2	1	no	—
611	#127	—	2	2	no	—
612	#127	—	2	1	no	—
613	#127	—	2	2	no	—
614	#127	C₂³×C₅₃	1	1	yes	characteristic
615	#127	C₂³×C₅₃	1	2	yes	—
616	#127	C₂³×C₅₃	1	2	yes	—
617	#127	C₂³×C₅₃	1	4	yes	—
618	#126	—	2	2	no	—
619	#126	—	2	2	no	—
620	#126	—	2	2	no	—
621	#126	—	2	2	no	—
622	#125	—	2	2	no	—
623	#125	—	2	1	no	—
624	#125	—	2	2	no	—
625	#125	—	2	2	no	—
626	#125	C₂³×C₅₃	1	2	yes	—
627	#124	—	2	1	no	—
628	#124	—	2	2	no	—
629	#124	C₂³×C₅₃	1	2	yes	—
630	#124	C₂³×C₅₃	1	2	yes	—
631	#124	C₂³×C₅₃	1	4	yes	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	C₂²⋊Q₈	—	2	1	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	1	no	—
639	C₂²⋊Q₈	—	2	1	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
643	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
644	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
645	#121	—	2	2	no	—
646	#121	—	2	1	no	—
647	#121	—	2	1	no	—
648	#121	—	2	2	no	—
649	#121	—	2	1	no	—
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	—	2	4	no	—
653	#121	—	2	2	no	—
654	#121	—	2	4	no	—
655	#121	C₂³×C₅₃	1	2	yes	—
656	#120	—	2	4	no	—
657	#120	—	2	4	no	—
658	#120	—	2	4	no	—
659	C₄×Q₈	—	2	1	no	—
660	C₄×Q₈	—	2	1	no	—
661	C₄×Q₈	—	2	2	no	—
662	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
663	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
664	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
665	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
666	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
667	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
668	C₄×D₄	—	2	1	no	—
669	C₄×D₄	—	2	1	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	1	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	1	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
676	C₄×D₄	D₄×C₅₃	1	2	yes	—
677	C₄×D₄	D₄×C₅₃	1	2	yes	—
678	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
679	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
680	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
681	#117	—	2	2	no	—
682	#117	—	2	1	no	—
683	#117	—	2	2	no	—
684	#117	C₂³×C₅₃	1	1	yes	characteristic
685	#117	C₂³×C₅₃	1	1	yes	characteristic
686	#117	C₂³×C₅₃	1	2	yes	—
687	C₂×C₄⋊C₄	—	2	1	no	—
688	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
689	C₂×C₄²	—	2	1	no	—
690	C₂×C₄²	—	2	1	no	—
691	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
693	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
694	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
695	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
696	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
697	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
698	#103	C₂³×C₅₃	1	2	yes	—
699	#103	C₂³×C₅₃	1	2	yes	—
700	#103	C₂³×C₅₃	1	4	yes	—
701	#102	C₂³×C₅₃	1	4	yes	—
702	#102	C₂³×C₅₃	1	4	yes	—
703	#102	C₂³×C₅₃	1	2	yes	—
704	#102	C₂³×C₅₃	1	2	yes	—
705	#102	C₂³×C₅₃	1	4	yes	—
706	#102	C₂³×C₅₃	1	4	yes	—
707	#102	C₂³×C₅₃	1	4	yes	—
708	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
709	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
710	#97	C₂³×C₅₃	1	4	yes	—
711	C₄×C₈	C₂³×C₅₃	1	4	yes	—
712	C₂⁴	—	2	4	no	—
713	C₂⁴	—	2	2	no	—
714	#41	—	2	2	no	—
715	#41	—	2	2	no	—
716	#41	—	2	2	no	—
717	#41	—	2	4	no	—
718	#41	—	2	2	no	—
719	#41	—	2	4	no	—
720	#41	—	4	4	no	—
721	#41	—	4	4	no	—
722	#41	—	4	8	no	—
723	C₂×Q₈	—	2	1	no	—
724	C₂×Q₈	—	2	2	no	—
725	C₂×Q₈	—	2	2	no	—
726	C₂×Q₈	—	2	2	no	—
727	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
728	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
729	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
730	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
731	C₂×D₄	—	2	1	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	1	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	1	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	4	no	—
747	C₂×D₄	—	4	4	no	—
748	C₂×D₄	—	4	4	no	—
749	C₂×D₄	—	4	16	no	—
750	C₂×D₄	—	4	8	no	—
751	C₂×D₄	—	8	2	no	—
752	C₂×D₄	—	8	4	no	—
753	C₂×D₄	—	8	2	no	—
754	C₂×D₄	—	8	4	no	—
755	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
756	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
757	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
758	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
759	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	1	no	—
762	C₂²×C₄	—	2	1	no	—
763	C₂²×C₄	—	2	1	no	—
764	C₂²×C₄	—	2	4	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	1	no	—
767	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
768	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
769	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
770	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
773	Q₁₆	—	4	2	no	—
774	Q₁₆	—	4	4	no	—
775	SD₁₆	—	4	4	no	—
776	SD₁₆	—	4	4	no	—
777	SD₁₆	—	4	2	no	—
778	SD₁₆	—	4	2	no	—
779	SD₁₆	—	4	4	no	—
780	SD₁₆	—	4	4	no	—
781	D₈	—	4	2	no	—
782	D₈	—	4	4	no	—
783	M₁₆	—	2	4	no	—
784	C₂×C₈	—	2	4	no	—
785	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
786	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
787	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	—	2	1	no	—
792	C₄⋊C₄	—	2	1	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	1	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
804	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
805	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
806	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
807	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
808	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
809	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	1	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	1	no	—
815	C₂²⋊C₄	—	2	1	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
824	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
825	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
826	C₄²	—	2	2	no	—
827	C₄²	—	2	1	no	—
828	C₄²	—	2	1	no	—
829	C₄²	—	2	1	no	—
830	C₄²	—	2	2	no	—
831	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
832	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
833	C₄²	C₂×D₄×C₅₃	1	2	yes	—
834	C₄²	C₂×D₄×C₅₃	1	2	yes	—
835	C₄²	C₂⁴×C₅₃	1	2	yes	—
836	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
837	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
838	C₂³	—	2	1	no	—
839	C₂³	—	2	4	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	4	8	no	—
842	C₂³	—	4	4	no	—
843	C₂³	—	8	2	no	—
844	C₂³	—	8	2	no	—
845	C₂³	—	8	4	no	—
846	C₂³	—	8	4	no	—
847	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
848	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
849	Q₈	—	2	2	no	—
850	Q₈	—	2	2	no	—
851	Q₈	—	2	1	no	—
852	Q₈	—	2	2	no	—
853	Q₈	—	2	1	no	—
854	Q₈	—	2	2	no	—
855	Q₈	—	2	2	no	—
856	Q₈	—	4	2	no	—
857	Q₈	—	8	2	no	—
858	D₄	—	2	4	no	—
859	D₄	—	2	2	no	—
860	D₄	—	2	1	no	—
861	D₄	—	2	1	no	—
862	D₄	—	2	4	no	—
863	D₄	—	2	2	no	—
864	D₄	—	2	4	no	—
865	D₄	—	2	2	no	—
866	D₄	—	4	8	no	—
867	D₄	—	4	4	no	—
868	D₄	—	4	2	no	—
869	D₄	—	4	8	no	—
870	D₄	—	4	4	no	—
871	D₄	—	4	2	no	—
872	D₄	—	4	4	no	—
873	D₄	—	4	4	no	—
874	D₄	—	4	2	no	—
875	D₄	—	8	2	no	—
876	D₄	—	8	4	no	—
877	D₄	—	8	2	no	—
878	D₄	—	8	4	no	—
879	D₄	—	8	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	4	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	—	4	2	no	—
892	C₂×C₄	—	4	8	no	—
893	C₂×C₄	—	4	2	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	4	2	no	—
896	C₂×C₄	—	4	2	no	—
897	C₂×C₄	—	8	1	no	—
898	C₂×C₄	—	8	1	no	—
899	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
903	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
904	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
905	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
906	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
907	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
908	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
909	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
910	C₈	—	2	2	no	—
911	C₈	—	2	2	no	—
912	C₈	—	2	4	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	4	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	4	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	4	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	16	4	no	—
928	C₂²	—	16	8	no	—
929	C₂²	C₅₃×#535	1	2	yes	—
930	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
931	C₄	—	2	1	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	4	1	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	1	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	2	no	—
943	C₄	C₅₃×#535	1	2	yes	—
944	C₄	C₅₃×#577	1	2	yes	—
945	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
946	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
947	C₂	—	2	2	no	—
948	C₂	—	4	2	no	—
949	C₂	—	8	4	no	—
950	C₂	—	8	2	no	—
951	C₂	—	8	1	no	—
952	C₂	C₂×C₅₃×#535	1	1	yes	characteristic
953	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
954	C₂	C₅₃×#3585	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×#3498	C₂	semidirect
2. C₅₃×#3461	C₂	semidirect
3. C₅₃×#3224	C₂	semidirect
4. C₅₃×#3222	C₂	semidirect
5. C₅₃×#3217	C₂	semidirect
6. C₅₃×#3216	C₂	semidirect
7. C₅₃×#3212	C₂	semidirect
8. C₅₃×#3208	C₂	semidirect
9. C₅₃×#3154	C₂	semidirect
10. C₅₃×#3136	C₂	semidirect
11. C₅₃×#3038	C₂	semidirect
12. C₅₃×#3037	C₂	semidirect
13. C₅₃×#3035	C₂	semidirect
14. C₂×C₅₃×#460	C₂	semidirect
15. C₅₃×#3012	C₂	semidirect
16. C₅₃×#3009	C₂	semidirect
17. C₅₃×#2925	C₂	semidirect
19. C₂×#137×C₅₃	C₂²	semidirect
20. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
21. C₂×#135×C₅₃	C₂²	semidirect
22. C₂²×SD₁₆×C₅₃	C₂²	semidirect
29. C₅₃×#544	C₂²	semidirect
31. C₅₃×#542	C₂²	semidirect
33. C₅₃×#541	C₂²	semidirect
37. C₅₃×#536	C₂²	semidirect
41. C₅₃×#533	C₂²	semidirect
48. C₅₃×#529	C₂²	semidirect
50. C₄×#41×C₅₃	C₂²	semidirect
51. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
52. C₅₃×#497	C₂²	semidirect
53. C₅₃×#496	C₂²	semidirect
54. C₅₃×#495	C₂²	semidirect
55. C₅₃×#492	C₂²	semidirect
56. C₅₃×#490	C₂²	semidirect
57. C₅₃×#489	C₂²	semidirect
58. C₅₃×#488	C₂²	semidirect
59. C₅₃×#486	C₂²	semidirect
60. C₅₃×#464	C₂²	semidirect
61. C₅₃×#464	C₂²	semidirect
62. C₅₃×#463	C₂²	semidirect
63. C₅₃×#462	C₂²	semidirect
64. C₅₃×#462	C₂²	semidirect
65. C₅₃×#461	C₂²	semidirect
66. C₅₃×#460	C₂²	semidirect
67. C₅₃×#460	C₂²	semidirect
68. C₅₃×#460	C₂²	semidirect
69. C₅₃×#460	C₂²	semidirect
70. C₅₃×#460	C₂²	semidirect
71. C₅₃×#460	C₂²	semidirect
72. C₅₃×#460	C₂²	semidirect
73. C₅₃×#459	C₂²	semidirect
74. C₅₃×#459	C₂²	semidirect
75. C₅₃×#459	C₂²	semidirect
76. C₅₃×#452	C₂²	semidirect
77. C₅₃×#452	C₂²	semidirect
78. C₅₃×#452	C₂²	semidirect
79. C₅₃×#450	C₂²	semidirect
80. C₅₃×#450	C₂²	semidirect
81. C₅₃×#450	C₂²	semidirect
82. C₅₃×#449	C₂²	semidirect
83. C₅₃×#447	C₂²	semidirect
84. C₅₃×#433	C₂²	semidirect
85. C₅₃×#432	C₂²	semidirect
86. C₅₃×#431	C₂²	semidirect
87. C₅₃×#423	C₂²	semidirect
88. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
89. C₅₃×#418	C₂²	semidirect
90. C₅₃×#417	C₂²	semidirect
91. C₅₃×#416	C₂²	semidirect
92. C₂×#102×C₅₃	C₂²	semidirect
94. C₅₃×#405	C₂²	semidirect
435. #60833	C₅₃	direct (N × H)
470. #3498	C₂×C₅₃	semidirect
471. #3461	C₂×C₅₃	semidirect
472. #3224	C₂×C₅₃	semidirect
473. #3222	C₂×C₅₃	semidirect
474. #3217	C₂×C₅₃	semidirect
475. #3216	C₂×C₅₃	semidirect
476. #3212	C₂×C₅₃	semidirect
477. #3208	C₂×C₅₃	semidirect
478. #3154	C₂×C₅₃	semidirect
479. #3136	C₂×C₅₃	semidirect
480. #3038	C₂×C₅₃	semidirect
481. #3037	C₂×C₅₃	semidirect
482. #3035	C₂×C₅₃	semidirect
483. C₂×#460	C₂×C₅₃	semidirect
484. #3012	C₂×C₅₃	semidirect
485. #3009	C₂×C₅₃	semidirect
486. #2925	C₂×C₅₃	semidirect
496. C₂×#137	C₂²×C₅₃	semidirect
497. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
498. C₂×#135	C₂²×C₅₃	semidirect
499. C₂²×SD₁₆	C₂²×C₅₃	semidirect
506. #544	C₂²×C₅₃	semidirect
508. #542	C₂²×C₅₃	semidirect
510. #541	C₂²×C₅₃	semidirect
514. #536	C₂²×C₅₃	semidirect
518. #533	C₂²×C₅₃	semidirect
525. #529	C₂²×C₅₃	semidirect
527. C₄×#41	C₂²×C₅₃	semidirect
528. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
529. #497	C₂²×C₅₃	semidirect
530. #496	C₂²×C₅₃	semidirect
531. #495	C₂²×C₅₃	semidirect
532. #492	C₂²×C₅₃	semidirect
533. #490	C₂²×C₅₃	semidirect
534. #489	C₂²×C₅₃	semidirect
535. #488	C₂²×C₅₃	semidirect
536. #486	C₂²×C₅₃	semidirect
537. #464	C₂²×C₅₃	semidirect
538. #464	C₂²×C₅₃	semidirect
539. #463	C₂²×C₅₃	semidirect
540. #462	C₂²×C₅₃	semidirect
541. #462	C₂²×C₅₃	semidirect
542. #461	C₂²×C₅₃	semidirect
543. #460	C₂²×C₅₃	semidirect
544. #460	C₂²×C₅₃	semidirect
545. #460	C₂²×C₅₃	semidirect
546. #460	C₂²×C₅₃	semidirect
547. #460	C₂²×C₅₃	semidirect
548. #460	C₂²×C₅₃	semidirect
549. #460	C₂²×C₅₃	semidirect
550. #459	C₂²×C₅₃	semidirect
551. #459	C₂²×C₅₃	semidirect
552. #459	C₂²×C₅₃	semidirect
553. #452	C₂²×C₅₃	semidirect
554. #452	C₂²×C₅₃	semidirect
555. #452	C₂²×C₅₃	semidirect
556. #450	C₂²×C₅₃	semidirect
557. #450	C₂²×C₅₃	semidirect
558. #450	C₂²×C₅₃	semidirect
559. #449	C₂²×C₅₃	semidirect
560. #447	C₂²×C₅₃	semidirect
561. #433	C₂²×C₅₃	semidirect
562. #432	C₂²×C₅₃	semidirect
563. #431	C₂²×C₅₃	semidirect
564. #423	C₂²×C₅₃	semidirect
565. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
566. #418	C₂²×C₅₃	semidirect
567. #417	C₂²×C₅₃	semidirect
568. #416	C₂²×C₅₃	semidirect
569. C₂×#102	C₂²×C₅₃	semidirect
571. #405	C₂²×C₅₃	semidirect
572. C₅₃	#60833	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×#3498	2
C₅₃×#3461	2
C₅₃×#3224	2
C₅₃×#3222	2
C₅₃×#3217	2
C₅₃×#3216	2
C₅₃×#3212	2
C₅₃×#3208	2
C₅₃×#3154	2
C₅₃×#3136	2
C₅₃×#3038	2
C₅₃×#3037	2
C₅₃×#3035	2
C₂×C₅₃×#460	2
C₅₃×#3012	2
C₅₃×#3009	2
C₅₃×#2925	2
#60833	53

Subgroups — C53×#60833 #27268345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60833 #27268345