Subgroups — C₅₃×#62145 #27269657

Order 13568.

1756 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3381	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3360	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3354	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3351	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3329	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3326	C₂	1	4	yes	maximal, complemented
9	C₅₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3251	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3233	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3103	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3078	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#557	C₂²	1	1	yes	characteristic
19	C₅₃×#556	—	2	1	no	—
20	C₅₃×#556	—	2	1	no	—
21	C₅₃×#556	C₂²	1	1	yes	characteristic
22	C₅₃×#555	C₂²	1	2	yes	—
23	C₅₃×#554	C₂²	1	2	yes	—
24	C₅₃×#553	C₂²	1	4	yes	—
25	C₅₃×#552	—	2	2	no	—
26	C₅₃×#552	C₂²	1	2	yes	—
27	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
28	C₅₃×#548	—	2	2	no	—
29	C₅₃×#548	C₂²	1	2	yes	—
30	C₅₃×#547	—	2	1	no	—
31	C₅₃×#547	—	2	1	no	—
32	C₅₃×#547	C₂²	1	1	yes	characteristic
33	C₅₃×#542	—	2	2	no	—
34	C₅₃×#537	—	2	1	no	—
35	C₅₃×#533	—	2	1	no	—
36	C₅₃×#533	C₂²	1	1	yes	characteristic
37	C₅₃×#533	C₂²	1	2	yes	—
38	C₅₃×#532	C₂²	1	2	yes	—
39	C₅₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#529	—	2	2	no	—
42	C₅₃×#529	C₂²	1	2	yes	—
43	C₅₃×#520	—	2	1	no	—
44	C₄×#41×C₅₃	—	2	1	no	—
45	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
46	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
48	C₅₃×#499	C₂²	1	4	yes	—
49	C₅₃×#498	C₂²	1	2	yes	—
50	C₅₃×#488	C₂²	1	4	yes	—
51	C₅₃×#487	C₂²	1	2	yes	—
52	C₅₃×#485	C₂²	1	4	yes	—
53	C₅₃×#483	C₂²	1	4	yes	—
54	C₅₃×#482	C₂²	1	4	yes	—
55	C₅₃×#482	C₂²	1	2	yes	—
56	C₅₃×#481	C₂²	1	4	yes	—
57	C₅₃×#479	C₂²	1	4	yes	—
58	C₅₃×#479	C₂²	1	4	yes	—
59	C₅₃×#478	C₂²	1	4	yes	—
60	C₅₃×#477	C₂²	1	2	yes	—
61	C₅₃×#477	C₂²	1	2	yes	—
62	C₅₃×#477	C₂²	1	1	yes	characteristic
63	C₅₃×#476	C₂²	1	1	yes	characteristic
64	C₅₃×#476	C₂²	1	2	yes	—
65	C₅₃×#475	C₂²	1	2	yes	—
66	C₅₃×#475	C₂²	1	2	yes	—
67	C₅₃×#475	C₂²	1	2	yes	—
68	C₅₃×#474	C₂²	1	2	yes	—
69	C₅₃×#474	C₂²	1	2	yes	—
70	C₅₃×#469	C₂²	1	4	yes	—
71	C₅₃×#468	C₂²	1	4	yes	—
72	C₅₃×#468	C₂²	1	4	yes	—
73	C₅₃×#463	C₂²	1	4	yes	—
74	C₅₃×#461	C₂²	1	2	yes	—
75	C₅₃×#460	C₂²	1	2	yes	—
76	C₅₃×#460	C₂²	1	1	yes	characteristic
77	C₅₃×#459	C₂²	1	1	yes	characteristic
78	C₅₃×#449	C₂²	1	2	yes	—
79	C₅₃×#448	C₂²	1	4	yes	—
80	C₈×Q₈×C₅₃	C₂²	1	2	yes	—
81	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	—
82	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
83	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	—
84	C₄×D₈×C₅₃	C₂²	1	2	yes	—
85	C₅₃×#436	C₂²	1	4	yes	—
86	C₅₃×#436	C₂²	1	2	yes	—
87	C₅₃×#431	C₂²	1	1	yes	characteristic
88	C₅₃×#431	C₂²	1	2	yes	—
89	C₅₃×#428	C₂²	1	4	yes	—
90	C₅₃×#428	C₂²	1	2	yes	—
91	C₅₃×#423	C₂²	1	2	yes	—
92	C₅₃×#423	C₂²	1	1	yes	characteristic
93	C₅₃×#419	C₂²	1	4	yes	—
94	C₅₃×#417	C₂²	1	2	yes	—
95	C₂×#41×C₅₃	—	2	1	no	—
96	C₂×#41×C₅₃	—	2	1	no	—
97	C₂×#41×C₅₃	—	2	2	no	—
98	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
99	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₅₃	—	2	1	no	—
101	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
104	C₂×D₈×C₅₃	C₂³	1	2	yes	—
105	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
106	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
107	C₄⋊Q₈×C₅₃	—	2	1	no	—
108	C₄⋊Q₈×C₅₃	—	2	1	no	—
109	C₄⋊Q₈×C₅₃	—	2	1	no	—
110	C₄⋊Q₈×C₅₃	—	2	1	no	—
111	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
116	#127×C₅₃	C₂³	1	1	yes	characteristic
117	#126×C₅₃	—	2	2	no	—
118	#126×C₅₃	—	2	4	no	—
119	#126×C₅₃	—	2	2	no	—
120	#126×C₅₃	—	2	2	no	—
121	#125×C₅₃	—	2	2	no	—
122	#125×C₅₃	—	2	2	no	—
123	#125×C₅₃	—	2	1	no	—
124	#125×C₅₃	C₂³	1	4	yes	—
125	#125×C₅₃	C₂³	1	2	yes	—
126	#124×C₅₃	—	2	2	no	—
127	#124×C₅₃	—	2	4	no	—
128	#124×C₅₃	—	2	1	no	—
129	#124×C₅₃	—	2	2	no	—
130	#124×C₅₃	C₂³	1	2	yes	—
131	#123×C₅₃	—	2	2	no	—
132	#123×C₅₃	—	2	4	no	—
133	#123×C₅₃	—	2	2	no	—
134	#123×C₅₃	—	2	2	no	—
135	C₂²⋊Q₈×C₅₃	—	2	1	no	—
136	C₂²⋊Q₈×C₅₃	—	2	2	no	—
137	C₂²⋊Q₈×C₅₃	—	2	4	no	—
138	C₂²⋊Q₈×C₅₃	—	2	2	no	—
139	C₂²⋊Q₈×C₅₃	—	2	1	no	—
140	C₂²⋊Q₈×C₅₃	—	2	2	no	—
141	C₂²⋊Q₈×C₅₃	—	2	2	no	—
142	C₂²⋊Q₈×C₅₃	—	2	2	no	—
143	C₂²⋊Q₈×C₅₃	—	2	1	no	—
144	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
145	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
146	#121×C₅₃	—	2	2	no	—
147	#121×C₅₃	—	2	2	no	—
148	#121×C₅₃	—	2	4	no	—
149	#121×C₅₃	—	2	2	no	—
150	#121×C₅₃	—	2	1	no	—
151	#121×C₅₃	C₂³	1	2	yes	—
152	#121×C₅₃	C₂³	1	2	yes	—
153	#121×C₅₃	C₂³	1	4	yes	—
154	C₄×Q₈×C₅₃	—	2	1	no	—
155	C₄×Q₈×C₅₃	—	2	2	no	—
156	C₄×Q₈×C₅₃	—	2	2	no	—
157	C₄×Q₈×C₅₃	—	2	1	no	—
158	C₄×Q₈×C₅₃	—	2	2	no	—
159	C₄×Q₈×C₅₃	—	2	2	no	—
160	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
165	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₅₃	—	2	2	no	—
168	C₄×D₄×C₅₃	—	2	4	no	—
169	C₄×D₄×C₅₃	—	2	2	no	—
170	C₄×D₄×C₅₃	—	2	1	no	—
171	C₄×D₄×C₅₃	—	2	1	no	—
172	C₄×D₄×C₅₃	—	2	2	no	—
173	C₄×D₄×C₅₃	—	2	1	no	—
174	C₄×D₄×C₅₃	—	2	1	no	—
175	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
176	C₄×D₄×C₅₃	D₄	1	2	yes	—
177	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₅₃	C₂³	1	4	yes	—
180	C₄×D₄×C₅₃	C₂³	1	2	yes	—
181	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₅₃	C₂³	1	2	yes	—
183	#117×C₅₃	—	2	1	no	—
184	#117×C₅₃	—	2	2	no	—
185	#117×C₅₃	—	2	2	no	—
186	#117×C₅₃	—	2	1	no	—
187	#117×C₅₃	—	2	2	no	—
188	#117×C₅₃	—	2	1	no	—
189	#117×C₅₃	D₄	1	1	yes	characteristic
190	#117×C₅₃	D₄	1	2	yes	—
191	#117×C₅₃	C₂³	1	4	yes	—
192	#117×C₅₃	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
194	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
195	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
196	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₅₃	—	2	1	no	—
199	C₂×C₄²×C₅₃	—	2	2	no	—
200	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
202	#107×C₅₃	C₂³	1	4	yes	—
203	#107×C₅₃	C₂³	1	4	yes	—
204	#107×C₅₃	C₂³	1	2	yes	—
205	#106×C₅₃	C₂³	1	2	yes	—
206	#106×C₅₃	C₂³	1	4	yes	—
207	#106×C₅₃	C₂³	1	4	yes	—
208	#106×C₅₃	C₂³	1	4	yes	—
209	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
210	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
211	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
212	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
213	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
214	#103×C₅₃	C₂³	1	4	yes	—
215	#103×C₅₃	C₂³	1	4	yes	—
216	#103×C₅₃	C₂³	1	4	yes	—
217	#103×C₅₃	C₂³	1	4	yes	—
218	#103×C₅₃	C₂³	1	2	yes	—
219	#102×C₅₃	C₂³	1	2	yes	—
220	#102×C₅₃	C₂³	1	4	yes	—
221	#102×C₅₃	C₂³	1	2	yes	—
222	#102×C₅₃	C₂³	1	2	yes	—
223	#102×C₅₃	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
225	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
226	C₄×C₈×C₅₃	C₂³	1	2	yes	—
227	C₄×C₈×C₅₃	C₂³	1	4	yes	—
228	#41×C₅₃	—	2	2	no	—
229	#41×C₅₃	—	4	2	no	—
230	#41×C₅₃	—	4	1	no	—
231	#41×C₅₃	—	4	4	no	—
232	#41×C₅₃	—	4	4	no	—
233	#41×C₅₃	—	8	4	no	—
234	C₂×Q₈×C₅₃	—	2	2	no	—
235	C₂×Q₈×C₅₃	—	2	1	no	—
236	C₂×Q₈×C₅₃	—	2	1	no	—
237	C₂×Q₈×C₅₃	—	2	2	no	—
238	C₂×Q₈×C₅₃	—	2	2	no	—
239	C₂×Q₈×C₅₃	—	2	4	no	—
240	C₂×Q₈×C₅₃	—	4	2	no	—
241	C₂×Q₈×C₅₃	—	8	2	no	—
242	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
244	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₅₃	—	2	2	no	—
246	C₂×D₄×C₅₃	—	2	1	no	—
247	C₂×D₄×C₅₃	—	2	2	no	—
248	C₂×D₄×C₅₃	—	2	4	no	—
249	C₂×D₄×C₅₃	—	2	1	no	—
250	C₂×D₄×C₅₃	—	2	1	no	—
251	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
252	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
254	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₅₃	—	2	2	no	—
256	C₂²×C₄×C₅₃	—	2	2	no	—
257	C₂²×C₄×C₅₃	—	2	2	no	—
258	C₂²×C₄×C₅₃	—	2	1	no	—
259	C₂²×C₄×C₅₃	—	2	1	no	—
260	C₂²×C₄×C₅₃	—	2	1	no	—
261	C₂²×C₄×C₅₃	—	2	2	no	—
262	C₂²×C₄×C₅₃	—	2	4	no	—
263	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
269	SD₁₆×C₅₃	—	2	4	no	—
270	SD₁₆×C₅₃	—	4	4	no	—
271	D₈×C₅₃	—	4	2	no	—
272	M₁₆×C₅₃	—	4	4	no	—
273	M₁₆×C₅₃	—	4	2	no	—
274	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
276	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₅₃	—	2	1	no	—
278	C₄⋊C₄×C₅₃	—	2	2	no	—
279	C₄⋊C₄×C₅₃	—	2	2	no	—
280	C₄⋊C₄×C₅₃	—	2	4	no	—
281	C₄⋊C₄×C₅₃	—	2	2	no	—
282	C₄⋊C₄×C₅₃	—	2	2	no	—
283	C₄⋊C₄×C₅₃	—	2	2	no	—
284	C₄⋊C₄×C₅₃	—	2	2	no	—
285	C₄⋊C₄×C₅₃	—	2	2	no	—
286	C₄⋊C₄×C₅₃	—	2	1	no	—
287	C₄⋊C₄×C₅₃	—	2	2	no	—
288	C₄⋊C₄×C₅₃	—	2	2	no	—
289	C₄⋊C₄×C₅₃	—	2	1	no	—
290	C₄⋊C₄×C₅₃	—	2	1	no	—
291	C₄⋊C₄×C₅₃	—	2	2	no	—
292	C₄⋊C₄×C₅₃	—	2	1	no	—
293	C₄⋊C₄×C₅₃	—	2	2	no	—
294	C₄⋊C₄×C₅₃	—	2	1	no	—
295	C₄⋊C₄×C₅₃	—	2	4	no	—
296	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
305	C₂²⋊C₄×C₅₃	—	2	2	no	—
306	C₂²⋊C₄×C₅₃	—	2	2	no	—
307	C₂²⋊C₄×C₅₃	—	2	1	no	—
308	C₂²⋊C₄×C₅₃	—	2	4	no	—
309	C₂²⋊C₄×C₅₃	—	2	4	no	—
310	C₂²⋊C₄×C₅₃	—	2	2	no	—
311	C₂²⋊C₄×C₅₃	—	2	1	no	—
312	C₂²⋊C₄×C₅₃	—	2	1	no	—
313	C₂²⋊C₄×C₅₃	—	2	2	no	—
314	C₂²⋊C₄×C₅₃	—	2	2	no	—
315	C₂²⋊C₄×C₅₃	—	2	2	no	—
316	C₂²⋊C₄×C₅₃	—	2	4	no	—
317	C₂²⋊C₄×C₅₃	—	2	2	no	—
318	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
321	C₄²×C₅₃	—	2	1	no	—
322	C₄²×C₅₃	—	2	1	no	—
323	C₄²×C₅₃	—	2	2	no	—
324	C₄²×C₅₃	—	2	2	no	—
325	C₄²×C₅₃	—	2	1	no	—
326	C₄²×C₅₃	—	2	2	no	—
327	C₄²×C₅₃	—	2	4	no	—
328	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₅₃	C₂×D₄	1	2	yes	—
331	C₄²×C₅₃	C₂×D₄	1	2	yes	—
332	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₅₃	C₂⁴	1	2	yes	—
334	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
335	C₂³×C₅₃	—	2	2	no	—
336	C₂³×C₅₃	—	2	1	no	—
337	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
338	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
339	Q₈×C₅₃	—	2	2	no	—
340	Q₈×C₅₃	—	2	1	no	—
341	Q₈×C₅₃	—	2	2	no	—
342	Q₈×C₅₃	—	2	2	no	—
343	Q₈×C₅₃	—	4	4	no	—
344	Q₈×C₅₃	—	4	2	no	—
345	Q₈×C₅₃	—	4	2	no	—
346	Q₈×C₅₃	—	4	4	no	—
347	Q₈×C₅₃	—	8	2	no	—
348	Q₈×C₅₃	2₋¹⁺⁴	1	2	yes	—
349	D₄×C₅₃	—	2	2	no	—
350	D₄×C₅₃	—	2	1	no	—
351	D₄×C₅₃	—	2	2	no	—
352	D₄×C₅₃	—	2	1	no	—
353	D₄×C₅₃	—	2	2	no	—
354	D₄×C₅₃	—	4	2	no	—
355	D₄×C₅₃	—	4	2	no	—
356	D₄×C₅₃	—	4	2	no	—
357	D₄×C₅₃	—	4	4	no	—
358	D₄×C₅₃	—	4	4	no	—
359	D₄×C₅₃	—	4	2	no	—
360	D₄×C₅₃	—	8	4	no	—
361	C₂×C₄×C₅₃	—	2	1	no	—
362	C₂×C₄×C₅₃	—	2	2	no	—
363	C₂×C₄×C₅₃	—	2	2	no	—
364	C₂×C₄×C₅₃	—	2	4	no	—
365	C₂×C₄×C₅₃	—	2	2	no	—
366	C₂×C₄×C₅₃	—	2	1	no	—
367	C₂×C₄×C₅₃	—	2	2	no	—
368	C₂×C₄×C₅₃	—	2	1	no	—
369	C₂×C₄×C₅₃	—	2	1	no	—
370	C₂×C₄×C₅₃	—	2	4	no	—
371	C₂×C₄×C₅₃	—	2	2	no	—
372	C₂×C₄×C₅₃	—	2	2	no	—
373	C₂×C₄×C₅₃	—	2	2	no	—
374	C₂×C₄×C₅₃	—	2	1	no	—
375	C₂×C₄×C₅₃	—	4	2	no	—
376	C₂×C₄×C₅₃	—	4	2	no	—
377	C₂×C₄×C₅₃	—	4	4	no	—
378	C₂×C₄×C₅₃	—	4	4	no	—
379	C₂×C₄×C₅₃	—	4	2	no	—
380	C₂×C₄×C₅₃	—	4	4	no	—
381	C₂×C₄×C₅₃	—	4	2	no	—
382	C₂×C₄×C₅₃	—	8	4	no	—
383	C₂×C₄×C₅₃	—	8	2	no	—
384	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
393	C₈×C₅₃	—	2	2	no	—
394	C₈×C₅₃	—	2	2	no	—
395	C₈×C₅₃	—	2	4	no	—
396	#62145	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
397	C₂²×C₅₃	—	2	2	no	—
398	C₂²×C₅₃	—	2	1	no	—
399	C₂²×C₅₃	—	2	1	no	—
400	C₂²×C₅₃	—	2	2	no	—
401	C₂²×C₅₃	—	2	1	no	—
402	C₂²×C₅₃	—	2	2	no	—
403	C₂²×C₅₃	—	4	1	no	—
404	C₂²×C₅₃	—	4	2	no	—
405	C₂²×C₅₃	—	4	2	no	—
406	C₂²×C₅₃	—	4	1	no	—
407	C₂²×C₅₃	—	4	1	no	—
408	C₂²×C₅₃	—	4	2	no	—
409	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
410	C₄×C₅₃	—	2	1	no	—
411	C₄×C₅₃	—	2	2	no	—
412	C₄×C₅₃	—	2	2	no	—
413	C₄×C₅₃	—	2	1	no	—
414	C₄×C₅₃	—	2	2	no	—
415	C₄×C₅₃	—	2	2	no	—
416	C₄×C₅₃	—	2	1	no	—
417	C₄×C₅₃	—	4	2	no	—
418	C₄×C₅₃	—	4	1	no	—
419	C₄×C₅₃	—	4	2	no	—
420	C₄×C₅₃	—	4	2	no	—
421	C₄×C₅₃	—	4	1	no	—
422	C₄×C₅₃	—	4	4	no	—
423	C₄×C₅₃	#575	1	2	yes	—
424	C₄×C₅₃	#577	1	2	yes	—
425	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
426	C₄×C₅₃	#585	1	1	yes	characteristic
427	#3511	C₂×C₅₃	1	1	yes	characteristic, complemented
428	#3482	C₂×C₅₃	1	1	yes	characteristic, complemented
429	#3381	C₂×C₅₃	1	2	yes	complemented
430	#3360	C₂×C₅₃	1	2	yes	complemented
431	#3354	C₂×C₅₃	1	2	yes	complemented
432	#3351	C₂×C₅₃	1	4	yes	complemented
433	#3329	C₂×C₅₃	1	2	yes	complemented
434	#3326	C₂×C₅₃	1	4	yes	complemented
435	#3254	C₂×C₅₃	1	1	yes	characteristic, complemented
436	#3251	C₂×C₅₃	1	2	yes	complemented
437	#3233	C₂×C₅₃	1	2	yes	complemented
438	#3229	C₂×C₅₃	1	1	yes	characteristic, complemented
439	#3106	C₂×C₅₃	1	1	yes	characteristic, complemented
440	#3103	C₂×C₅₃	1	2	yes	complemented
441	#3079	C₂×C₅₃	1	1	yes	characteristic, complemented
442	#3078	C₂×C₅₃	1	2	yes	complemented
443	#2991	C₂×C₅₃	1	1	yes	characteristic, complemented
444	C₂×C₅₃	—	4	2	no	—
445	C₂×C₅₃	—	4	1	no	—
446	C₂×C₅₃	—	8	1	no	—
447	C₂×C₅₃	—	8	2	no	—
448	C₂×C₅₃	#3489	1	1	yes	characteristic
449	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
450	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
451	#557	C₂²×C₅₃	1	1	yes	characteristic
452	#556	—	2	1	no	—
453	#556	—	2	1	no	—
454	#556	C₂²×C₅₃	1	1	yes	characteristic
455	#555	C₂²×C₅₃	1	2	yes	—
456	#554	C₂²×C₅₃	1	2	yes	—
457	#553	C₂²×C₅₃	1	4	yes	—
458	#552	—	2	2	no	—
459	#552	C₂²×C₅₃	1	2	yes	—
460	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
461	#548	—	2	2	no	—
462	#548	C₂²×C₅₃	1	2	yes	—
463	#547	—	2	1	no	—
464	#547	—	2	1	no	—
465	#547	C₂²×C₅₃	1	1	yes	characteristic
466	#542	—	2	2	no	—
467	#537	—	2	1	no	—
468	#533	—	2	1	no	—
469	#533	C₂²×C₅₃	1	1	yes	characteristic
470	#533	C₂²×C₅₃	1	2	yes	—
471	#532	C₂²×C₅₃	1	2	yes	—
472	#532	C₂²×C₅₃	1	1	yes	characteristic
473	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
474	#529	—	2	2	no	—
475	#529	C₂²×C₅₃	1	2	yes	—
476	#520	—	2	1	no	—
477	C₄×#41	—	2	1	no	—
478	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
479	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
480	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
481	#499	C₂²×C₅₃	1	4	yes	—
482	#498	C₂²×C₅₃	1	2	yes	—
483	#488	C₂²×C₅₃	1	4	yes	—
484	#487	C₂²×C₅₃	1	2	yes	—
485	#485	C₂²×C₅₃	1	4	yes	—
486	#483	C₂²×C₅₃	1	4	yes	—
487	#482	C₂²×C₅₃	1	2	yes	—
488	#482	C₂²×C₅₃	1	4	yes	—
489	#481	C₂²×C₅₃	1	4	yes	—
490	#479	C₂²×C₅₃	1	4	yes	—
491	#479	C₂²×C₅₃	1	4	yes	—
492	#478	C₂²×C₅₃	1	4	yes	—
493	#477	C₂²×C₅₃	1	2	yes	—
494	#477	C₂²×C₅₃	1	1	yes	characteristic
495	#477	C₂²×C₅₃	1	2	yes	—
496	#476	C₂²×C₅₃	1	2	yes	—
497	#476	C₂²×C₅₃	1	1	yes	characteristic
498	#475	C₂²×C₅₃	1	2	yes	—
499	#475	C₂²×C₅₃	1	2	yes	—
500	#475	C₂²×C₅₃	1	2	yes	—
501	#474	C₂²×C₅₃	1	2	yes	—
502	#474	C₂²×C₅₃	1	2	yes	—
503	#469	C₂²×C₅₃	1	4	yes	—
504	#468	C₂²×C₅₃	1	4	yes	—
505	#468	C₂²×C₅₃	1	4	yes	—
506	#463	C₂²×C₅₃	1	4	yes	—
507	#461	C₂²×C₅₃	1	2	yes	—
508	#460	C₂²×C₅₃	1	1	yes	characteristic
509	#460	C₂²×C₅₃	1	2	yes	—
510	#459	C₂²×C₅₃	1	1	yes	characteristic
511	#449	C₂²×C₅₃	1	2	yes	—
512	#448	C₂²×C₅₃	1	4	yes	—
513	C₈×Q₈	C₂²×C₅₃	1	2	yes	—
514	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
515	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	—
516	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	—
517	C₄×D₈	C₂²×C₅₃	1	2	yes	—
518	#436	C₂²×C₅₃	1	2	yes	—
519	#436	C₂²×C₅₃	1	4	yes	—
520	#431	C₂²×C₅₃	1	2	yes	—
521	#431	C₂²×C₅₃	1	1	yes	characteristic
522	#428	C₂²×C₅₃	1	4	yes	—
523	#428	C₂²×C₅₃	1	2	yes	—
524	#423	C₂²×C₅₃	1	2	yes	—
525	#423	C₂²×C₅₃	1	1	yes	characteristic
526	#419	C₂²×C₅₃	1	4	yes	—
527	#417	C₂²×C₅₃	1	2	yes	—
528	C₅₃	#62145	1	1	yes	characteristic, direct product factor, Sylow
529	C₂×#41	—	2	1	no	—
530	C₂×#41	—	2	1	no	—
531	C₂×#41	—	2	2	no	—
532	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
533	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
534	C₂²×Q₈	—	2	1	no	—
535	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
536	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
537	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
538	C₂×D₈	C₂³×C₅₃	1	2	yes	—
539	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
540	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
541	C₄⋊Q₈	—	2	1	no	—
542	C₄⋊Q₈	—	2	1	no	—
543	C₄⋊Q₈	—	2	1	no	—
544	C₄⋊Q₈	—	2	1	no	—
545	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
546	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
547	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
548	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
550	#127	C₂³×C₅₃	1	1	yes	characteristic
551	#126	—	2	2	no	—
552	#126	—	2	4	no	—
553	#126	—	2	2	no	—
554	#126	—	2	2	no	—
555	#125	—	2	2	no	—
556	#125	—	2	2	no	—
557	#125	—	2	1	no	—
558	#125	C₂³×C₅₃	1	2	yes	—
559	#125	C₂³×C₅₃	1	4	yes	—
560	#124	—	2	2	no	—
561	#124	—	2	4	no	—
562	#124	—	2	1	no	—
563	#124	—	2	2	no	—
564	#124	C₂³×C₅₃	1	2	yes	—
565	#123	—	2	2	no	—
566	#123	—	2	2	no	—
567	#123	—	2	2	no	—
568	#123	—	2	4	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	4	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
579	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
580	#121	—	2	2	no	—
581	#121	—	2	2	no	—
582	#121	—	2	4	no	—
583	#121	—	2	2	no	—
584	#121	—	2	1	no	—
585	#121	C₂³×C₅₃	1	2	yes	—
586	#121	C₂³×C₅₃	1	2	yes	—
587	#121	C₂³×C₅₃	1	4	yes	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	—	2	2	no	—
590	C₄×Q₈	—	2	2	no	—
591	C₄×Q₈	—	2	1	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
595	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
596	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
597	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
598	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
599	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	4	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
610	C₄×D₄	D₄×C₅₃	1	2	yes	—
611	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
612	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
613	C₄×D₄	C₂³×C₅₃	1	4	yes	—
614	C₄×D₄	C₂³×C₅₃	1	2	yes	—
615	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₅₃	1	2	yes	—
617	#117	—	2	1	no	—
618	#117	—	2	1	no	—
619	#117	—	2	2	no	—
620	#117	—	2	2	no	—
621	#117	—	2	1	no	—
622	#117	—	2	2	no	—
623	#117	D₄×C₅₃	1	1	yes	characteristic
624	#117	D₄×C₅₃	1	2	yes	—
625	#117	C₂³×C₅₃	1	1	yes	characteristic
626	#117	C₂³×C₅₃	1	4	yes	—
627	C₂×C₄⋊C₄	—	2	2	no	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	—	2	2	no	—
630	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
632	C₂×C₄²	—	2	2	no	—
633	C₂×C₄²	—	2	1	no	—
634	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
635	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
636	#107	C₂³×C₅₃	1	2	yes	—
637	#107	C₂³×C₅₃	1	4	yes	—
638	#107	C₂³×C₅₃	1	4	yes	—
639	#106	C₂³×C₅₃	1	4	yes	—
640	#106	C₂³×C₅₃	1	4	yes	—
641	#106	C₂³×C₅₃	1	4	yes	—
642	#106	C₂³×C₅₃	1	2	yes	—
643	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
644	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
645	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
646	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
647	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
648	#103	C₂³×C₅₃	1	4	yes	—
649	#103	C₂³×C₅₃	1	2	yes	—
650	#103	C₂³×C₅₃	1	4	yes	—
651	#103	C₂³×C₅₃	1	4	yes	—
652	#103	C₂³×C₅₃	1	4	yes	—
653	#102	C₂³×C₅₃	1	4	yes	—
654	#102	C₂³×C₅₃	1	2	yes	—
655	#102	C₂³×C₅₃	1	2	yes	—
656	#102	C₂³×C₅₃	1	2	yes	—
657	#102	C₂³×C₅₃	1	4	yes	—
658	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
659	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
660	C₄×C₈	C₂³×C₅₃	1	2	yes	—
661	C₄×C₈	C₂³×C₅₃	1	4	yes	—
662	#41	—	2	2	no	—
663	#41	—	4	2	no	—
664	#41	—	4	1	no	—
665	#41	—	4	4	no	—
666	#41	—	4	4	no	—
667	#41	—	8	4	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	4	no	—
674	C₂×Q₈	—	4	2	no	—
675	C₂×Q₈	—	8	2	no	—
676	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
677	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
678	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
686	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
687	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
688	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
698	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
703	SD₁₆	—	2	4	no	—
704	SD₁₆	—	4	4	no	—
705	D₈	—	4	2	no	—
706	M₁₆	—	4	4	no	—
707	M₁₆	—	4	2	no	—
708	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
709	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
710	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
731	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
733	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
734	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
735	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
737	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
738	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
753	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
754	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
755	C₄²	—	2	1	no	—
756	C₄²	—	2	1	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	4	no	—
762	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
763	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
764	C₄²	C₂×D₄×C₅₃	1	2	yes	—
765	C₄²	C₂×D₄×C₅₃	1	2	yes	—
766	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
767	C₄²	C₂⁴×C₅₃	1	2	yes	—
768	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
769	C₂³	—	2	1	no	—
770	C₂³	—	2	2	no	—
771	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
772	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
773	Q₈	—	2	2	no	—
774	Q₈	—	2	1	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	2	no	—
777	Q₈	—	4	4	no	—
778	Q₈	—	4	2	no	—
779	Q₈	—	4	2	no	—
780	Q₈	—	4	4	no	—
781	Q₈	—	8	2	no	—
782	Q₈	2₋¹⁺⁴×C₅₃	1	2	yes	—
783	D₄	—	2	2	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	1	no	—
786	D₄	—	2	1	no	—
787	D₄	—	2	2	no	—
788	D₄	—	4	2	no	—
789	D₄	—	4	2	no	—
790	D₄	—	4	2	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	2	no	—
794	D₄	—	8	4	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	4	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	4	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	4	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	8	4	no	—
817	C₂×C₄	—	8	2	no	—
818	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
823	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
826	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
827	C₈	—	2	2	no	—
828	C₈	—	2	2	no	—
829	C₈	—	2	4	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	2	1	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	2	no	—
842	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
843	C₄	—	2	1	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	1	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	1	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	4	no	—
856	C₄	C₅₃×#575	1	2	yes	—
857	C₄	C₅₃×#577	1	2	yes	—
858	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
859	C₄	C₅₃×#585	1	1	yes	characteristic
860	C₂	—	4	2	no	—
861	C₂	—	4	1	no	—
862	C₂	—	8	1	no	—
863	C₂	—	8	2	no	—
864	C₂	C₅₃×#3489	1	1	yes	characteristic
865	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
866	C₂	C₂×C₅₃×#577	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×#3511	C₂	semidirect
2. C₅₃×#3482	C₂	semidirect
3. C₅₃×#3381	C₂	semidirect
4. C₅₃×#3360	C₂	semidirect
5. C₅₃×#3354	C₂	semidirect
6. C₅₃×#3351	C₂	semidirect
7. C₅₃×#3329	C₂	semidirect
8. C₅₃×#3326	C₂	semidirect
9. C₅₃×#3254	C₂	semidirect
10. C₅₃×#3251	C₂	semidirect
11. C₅₃×#3233	C₂	semidirect
12. C₅₃×#3229	C₂	semidirect
13. C₅₃×#3106	C₂	semidirect
14. C₅₃×#3103	C₂	semidirect
15. C₅₃×#3079	C₂	semidirect
16. C₅₃×#3078	C₂	semidirect
17. C₅₃×#2991	C₂	semidirect
396. #62145	C₅₃	direct (N × H)
427. #3511	C₂×C₅₃	semidirect
428. #3482	C₂×C₅₃	semidirect
429. #3381	C₂×C₅₃	semidirect
430. #3360	C₂×C₅₃	semidirect
431. #3354	C₂×C₅₃	semidirect
432. #3351	C₂×C₅₃	semidirect
433. #3329	C₂×C₅₃	semidirect
434. #3326	C₂×C₅₃	semidirect
435. #3254	C₂×C₅₃	semidirect
436. #3251	C₂×C₅₃	semidirect
437. #3233	C₂×C₅₃	semidirect
438. #3229	C₂×C₅₃	semidirect
439. #3106	C₂×C₅₃	semidirect
440. #3103	C₂×C₅₃	semidirect
441. #3079	C₂×C₅₃	semidirect
442. #3078	C₂×C₅₃	semidirect
443. #2991	C₂×C₅₃	semidirect
528. C₅₃	#62145	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×#3511	2
C₅₃×#3482	2
C₅₃×#3381	2
C₅₃×#3360	2
C₅₃×#3354	2
C₅₃×#3351	2
C₅₃×#3329	2
C₅₃×#3326	2
C₅₃×#3254	2
C₅₃×#3251	2
C₅₃×#3233	2
C₅₃×#3229	2
C₅₃×#3106	2
C₅₃×#3103	2
C₅₃×#3079	2
C₅₃×#3078	2
C₅₃×#2991	2
#62145	53

Subgroups — C53×#62145 #27269657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62145 #27269657