Subgroups — C₅₃×#61988 #27269500

Order 13568.

1960 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3399	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3375	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3319	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3305	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3287	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3268	C₂	1	4	yes	maximal, complemented
9	C₅₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3245	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3214	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3115	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3035	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
19	C₂×#135×C₅₃	C₂²	1	4	yes	complemented
20	C₅₃×#559	—	2	1	no	—
21	C₅₃×#559	C₂²	1	2	yes	—
22	Q₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₅₃×#555	—	2	2	no	—
24	C₅₃×#555	—	2	1	no	—
25	C₅₃×#555	C₂²	1	2	yes	—
26	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
27	C₅₃×#550	—	2	1	no	—
28	C₅₃×#550	—	2	1	no	—
29	C₅₃×#550	C₂²	1	2	yes	—
30	C₅₃×#550	C₂²	1	2	yes	—
31	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
32	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
33	C₅₃×#546	—	2	2	no	—
34	C₅₃×#546	C₂²	1	4	yes	—
35	C₅₃×#540	—	2	2	no	—
36	C₅₃×#535	—	2	1	no	—
37	C₅₃×#533	C₂²	1	1	yes	characteristic
38	C₅₃×#532	—	2	1	no	—
39	C₅₃×#532	—	2	2	no	—
40	C₅₃×#532	C₂²	1	2	yes	—
41	C₅₃×#532	C₂²	1	1	yes	characteristic
42	C₅₃×#532	C₂²	1	2	yes	—
43	C₅₃×#532	C₂²	1	2	yes	complemented
44	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#518	—	2	1	no	—
46	C₄×#41×C₅₃	—	2	1	no	—
47	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
48	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
49	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
50	C₅₃×#496	C₂²	1	4	yes	complemented
51	C₅₃×#493	C₂²	1	2	yes	—
52	C₅₃×#489	C₂²	1	4	yes	complemented
53	C₅₃×#486	C₂²	1	2	yes	—
54	C₅₃×#485	C₂²	1	2	yes	—
55	C₅₃×#482	C₂²	1	4	yes	complemented
56	C₅₃×#477	C₂²	1	2	yes	complemented
57	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#474	C₂²	1	2	yes	complemented
60	C₅₃×#474	C₂²	1	4	yes	complemented
61	C₅₃×#468	C₂²	1	4	yes	—
62	C₅₃×#466	C₂²	1	4	yes	complemented
63	C₅₃×#466	C₂²	1	4	yes	complemented
64	C₅₃×#464	C₂²	1	4	yes	complemented
65	C₅₃×#463	C₂²	1	4	yes	complemented
66	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#461	C₂²	1	2	yes	complemented
69	C₅₃×#460	C₂²	1	2	yes	—
70	C₅₃×#460	C₂²	1	2	yes	—
71	C₅₃×#460	C₂²	1	2	yes	complemented
72	C₅₃×#459	C₂²	1	2	yes	—
73	C₅₃×#459	C₂²	1	2	yes	—
74	C₅₃×#459	C₂²	1	2	yes	—
75	C₅₃×#459	C₂²	1	2	yes	—
76	C₅₃×#459	C₂²	1	4	yes	complemented
77	C₅₃×#452	C₂²	1	2	yes	—
78	C₅₃×#449	C₂²	1	4	yes	complemented
79	C₅₃×#449	C₂²	1	4	yes	complemented
80	C₅₃×#449	C₂²	1	4	yes	complemented
81	C₅₃×#447	C₂²	1	4	yes	—
82	C₅₃×#446	C₂²	1	2	yes	complemented
83	C₅₃×#442	C₂²	1	4	yes	complemented
84	C₅₃×#440	C₂²	1	4	yes	complemented
85	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
86	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
87	C₅₃×#435	C₂²	1	4	yes	—
88	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
89	C₅₃×#432	C₂²	1	2	yes	complemented
90	C₅₃×#431	C₂²	1	1	yes	characteristic
91	C₅₃×#423	C₂²	1	1	yes	characteristic
92	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	complemented
93	C₅₃×#418	C₂²	1	2	yes	—
94	C₅₃×#416	C₂²	1	4	yes	complemented
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	—	2	2	no	—
99	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
100	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
101	C₂×#41×C₅₃	C₂³	1	2	yes	—
102	C₂×#41×C₅₃	C₂³	1	4	yes	—
103	C₂²×D₄×C₅₃	—	2	1	no	—
104	C₂²×D₄×C₅₃	—	2	1	no	—
105	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
106	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
107	#135×C₅₃	—	4	8	no	—
108	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
111	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
112	C₂×D₈×C₅₃	C₂³	1	4	yes	—
113	C₂×D₈×C₅₃	C₂³	1	4	yes	—
114	C₂×D₈×C₅₃	C₂³	1	4	yes	—
115	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
116	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
117	C₄⋊Q₈×C₅₃	—	2	1	no	—
118	C₄⋊Q₈×C₅₃	—	2	2	no	—
119	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
121	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
122	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
123	#127×C₅₃	—	2	1	no	—
124	#127×C₅₃	—	2	1	no	—
125	#127×C₅₃	—	2	2	no	—
126	#127×C₅₃	—	2	1	no	—
127	#127×C₅₃	—	2	2	no	—
128	#127×C₅₃	C₂³	1	2	yes	—
129	#127×C₅₃	C₂³	1	1	yes	characteristic
130	#127×C₅₃	C₂³	1	2	yes	—
131	#127×C₅₃	C₂³	1	2	yes	—
132	#125×C₅₃	—	2	1	no	—
133	#124×C₅₃	—	2	2	no	—
134	#124×C₅₃	—	2	2	no	—
135	#124×C₅₃	—	2	2	no	—
136	#124×C₅₃	—	2	2	no	—
137	#124×C₅₃	—	2	1	no	—
138	#124×C₅₃	—	2	2	no	—
139	#124×C₅₃	—	2	2	no	—
140	#124×C₅₃	C₂³	1	4	yes	—
141	#123×C₅₃	—	2	4	no	—
142	#123×C₅₃	—	2	4	no	—
143	C₂²⋊Q₈×C₅₃	—	2	1	no	—
144	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
145	#121×C₅₃	—	2	1	no	—
146	#121×C₅₃	—	2	2	no	—
147	#121×C₅₃	—	2	2	no	—
148	#121×C₅₃	—	2	2	no	—
149	#121×C₅₃	—	2	2	no	—
150	#121×C₅₃	—	2	4	no	—
151	#121×C₅₃	—	2	4	no	—
152	#121×C₅₃	—	2	2	no	—
153	#121×C₅₃	—	2	1	no	—
154	#121×C₅₃	—	2	2	no	—
155	#121×C₅₃	—	2	2	no	—
156	#121×C₅₃	—	2	2	no	—
157	#121×C₅₃	—	2	1	no	—
158	#121×C₅₃	—	2	2	no	—
159	#121×C₅₃	C₂³	1	4	yes	—
160	#121×C₅₃	C₂³	1	2	yes	—
161	#121×C₅₃	C₂³	1	2	yes	—
162	#121×C₅₃	C₂³	1	2	yes	—
163	#120×C₅₃	—	2	4	no	—
164	C₄×Q₈×C₅₃	—	2	1	no	—
165	C₄×Q₈×C₅₃	—	2	1	no	—
166	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
171	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
172	C₄×D₄×C₅₃	—	2	2	no	—
173	C₄×D₄×C₅₃	—	2	1	no	—
174	C₄×D₄×C₅₃	—	2	2	no	—
175	C₄×D₄×C₅₃	—	2	2	no	—
176	C₄×D₄×C₅₃	—	2	1	no	—
177	C₄×D₄×C₅₃	—	2	2	no	—
178	C₄×D₄×C₅₃	—	2	2	no	—
179	C₄×D₄×C₅₃	—	2	2	no	—
180	C₄×D₄×C₅₃	—	2	2	no	—
181	C₄×D₄×C₅₃	—	2	1	no	—
182	C₄×D₄×C₅₃	—	2	1	no	—
183	C₄×D₄×C₅₃	—	2	2	no	—
184	C₄×D₄×C₅₃	—	2	2	no	—
185	C₄×D₄×C₅₃	D₄	1	2	yes	—
186	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
187	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₅₃	C₂³	1	2	yes	—
190	C₄×D₄×C₅₃	C₂³	1	2	yes	—
191	C₄×D₄×C₅₃	C₂³	1	4	yes	—
192	C₄×D₄×C₅₃	C₂³	1	2	yes	—
193	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
194	#117×C₅₃	—	2	2	no	—
195	#117×C₅₃	—	2	1	no	—
196	#117×C₅₃	—	2	1	no	—
197	#117×C₅₃	—	2	2	no	—
198	#117×C₅₃	—	2	1	no	—
199	#117×C₅₃	D₄	1	1	yes	characteristic
200	#117×C₅₃	D₄	1	2	yes	—
201	#117×C₅₃	C₂³	1	1	yes	characteristic
202	#117×C₅₃	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
204	C₂×C₄²×C₅₃	—	2	1	no	—
205	C₂×C₄²×C₅₃	—	2	2	no	—
206	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
208	#107×C₅₃	C₂³	1	2	yes	—
209	#107×C₅₃	C₂³	1	4	yes	—
210	#106×C₅₃	C₂³	1	2	yes	—
211	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
212	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
213	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
214	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
215	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
216	#103×C₅₃	C₂³	1	2	yes	—
217	#103×C₅₃	C₂³	1	2	yes	—
218	#103×C₅₃	C₂³	1	4	yes	—
219	#103×C₅₃	C₂³	1	2	yes	—
220	#102×C₅₃	C₂³	1	4	yes	—
221	#102×C₅₃	C₂³	1	4	yes	—
222	#102×C₅₃	C₂³	1	4	yes	—
223	#102×C₅₃	C₂³	1	4	yes	—
224	#102×C₅₃	C₂³	1	2	yes	—
225	#102×C₅₃	C₂³	1	4	yes	—
226	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
228	#97×C₅₃	C₂³	1	4	yes	—
229	C₄×C₈×C₅₃	C₂³	1	2	yes	—
230	C₂⁴×C₅₃	—	2	2	no	—
231	#41×C₅₃	—	2	4	no	—
232	#41×C₅₃	—	2	2	no	—
233	#41×C₅₃	—	4	2	no	—
234	#41×C₅₃	—	4	1	no	—
235	#41×C₅₃	—	4	2	no	—
236	#41×C₅₃	—	4	4	no	—
237	#41×C₅₃	—	4	4	no	—
238	#41×C₅₃	—	4	4	no	—
239	#41×C₅₃	—	8	2	no	—
240	#41×C₅₃	—	8	4	no	—
241	#41×C₅₃	—	8	4	no	—
242	C₂×Q₈×C₅₃	—	2	1	no	—
243	C₂×Q₈×C₅₃	—	2	2	no	—
244	C₂×Q₈×C₅₃	—	2	1	no	—
245	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₅₃	—	2	2	no	—
249	C₂×D₄×C₅₃	—	2	1	no	—
250	C₂×D₄×C₅₃	—	2	4	no	—
251	C₂×D₄×C₅₃	—	2	4	no	—
252	C₂×D₄×C₅₃	—	2	2	no	—
253	C₂×D₄×C₅₃	—	2	2	no	—
254	C₂×D₄×C₅₃	—	2	2	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	2	no	—
260	C₂×D₄×C₅₃	—	2	2	no	—
261	C₂×D₄×C₅₃	—	2	1	no	—
262	C₂×D₄×C₅₃	—	2	2	no	—
263	C₂×D₄×C₅₃	—	2	2	no	—
264	C₂×D₄×C₅₃	—	4	2	no	—
265	C₂×D₄×C₅₃	—	4	2	no	—
266	C₂×D₄×C₅₃	—	4	4	no	—
267	C₂×D₄×C₅₃	—	8	2	no	—
268	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
269	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
270	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
271	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
272	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₅₃	—	2	2	no	—
274	C₂²×C₄×C₅₃	—	2	1	no	—
275	C₂²×C₄×C₅₃	—	2	2	no	—
276	C₂²×C₄×C₅₃	—	2	1	no	—
277	C₂²×C₄×C₅₃	—	2	1	no	—
278	C₂²×C₄×C₅₃	—	2	2	no	—
279	C₂²×C₄×C₅₃	—	2	4	no	—
280	C₂²×C₄×C₅₃	—	2	4	no	—
281	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
287	Q₁₆×C₅₃	—	2	4	no	—
288	SD₁₆×C₅₃	—	2	8	no	—
289	SD₁₆×C₅₃	—	4	2	no	—
290	SD₁₆×C₅₃	—	4	4	no	—
291	D₈×C₅₃	—	4	4	no	—
292	D₈×C₅₃	—	4	4	no	—
293	D₈×C₅₃	—	4	4	no	—
294	M₁₆×C₅₃	—	4	2	no	—
295	C₂×C₈×C₅₃	—	4	4	no	—
296	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
297	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
298	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
299	C₄⋊C₄×C₅₃	—	2	1	no	—
300	C₄⋊C₄×C₅₃	—	2	1	no	—
301	C₄⋊C₄×C₅₃	—	2	1	no	—
302	C₄⋊C₄×C₅₃	—	2	2	no	—
303	C₄⋊C₄×C₅₃	—	2	1	no	—
304	C₄⋊C₄×C₅₃	—	2	2	no	—
305	C₄⋊C₄×C₅₃	—	2	1	no	—
306	C₄⋊C₄×C₅₃	—	2	1	no	—
307	C₄⋊C₄×C₅₃	—	2	2	no	—
308	C₄⋊C₄×C₅₃	—	2	2	no	—
309	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
312	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
315	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
316	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
317	C₂²⋊C₄×C₅₃	—	2	2	no	—
318	C₂²⋊C₄×C₅₃	—	2	2	no	—
319	C₂²⋊C₄×C₅₃	—	2	1	no	—
320	C₂²⋊C₄×C₅₃	—	2	4	no	—
321	C₂²⋊C₄×C₅₃	—	2	4	no	—
322	C₂²⋊C₄×C₅₃	—	2	2	no	—
323	C₂²⋊C₄×C₅₃	—	2	2	no	—
324	C₂²⋊C₄×C₅₃	—	2	2	no	—
325	C₂²⋊C₄×C₅₃	—	2	2	no	—
326	C₂²⋊C₄×C₅₃	—	2	1	no	—
327	C₂²⋊C₄×C₅₃	—	2	1	no	—
328	C₂²⋊C₄×C₅₃	—	2	2	no	—
329	C₂²⋊C₄×C₅₃	—	2	4	no	—
330	C₂²⋊C₄×C₅₃	—	2	4	no	—
331	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
333	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
334	C₄²×C₅₃	—	2	1	no	—
335	C₄²×C₅₃	—	2	2	no	—
336	C₄²×C₅₃	—	2	1	no	—
337	C₄²×C₅₃	—	2	2	no	—
338	C₄²×C₅₃	—	2	1	no	—
339	C₄²×C₅₃	—	2	2	no	—
340	C₄²×C₅₃	C₂×D₄	1	2	yes	—
341	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₅₃	C₂×D₄	1	2	yes	—
343	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
344	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
345	C₄²×C₅₃	C₂⁴	1	2	yes	—
346	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
347	C₂³×C₅₃	—	2	1	no	—
348	C₂³×C₅₃	—	2	2	no	—
349	C₂³×C₅₃	—	2	4	no	—
350	C₂³×C₅₃	—	4	4	no	—
351	C₂³×C₅₃	—	8	2	no	—
352	C₂³×C₅₃	—	8	2	no	—
353	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
354	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
355	Q₈×C₅₃	—	2	2	no	—
356	Q₈×C₅₃	—	2	1	no	—
357	Q₈×C₅₃	—	2	2	no	—
358	Q₈×C₅₃	—	2	2	no	—
359	Q₈×C₅₃	—	4	2	no	—
360	Q₈×C₅₃	—	8	2	no	—
361	Q₈×C₅₃	—	8	1	no	—
362	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
363	D₄×C₅₃	—	2	2	no	—
364	D₄×C₅₃	—	2	4	no	—
365	D₄×C₅₃	—	2	1	no	—
366	D₄×C₅₃	—	2	2	no	—
367	D₄×C₅₃	—	2	4	no	—
368	D₄×C₅₃	—	2	2	no	—
369	D₄×C₅₃	—	2	1	no	—
370	D₄×C₅₃	—	4	2	no	—
371	D₄×C₅₃	—	4	4	no	—
372	D₄×C₅₃	—	4	2	no	—
373	D₄×C₅₃	—	4	4	no	—
374	D₄×C₅₃	—	4	4	no	—
375	D₄×C₅₃	—	4	4	no	—
376	D₄×C₅₃	—	4	2	no	—
377	D₄×C₅₃	—	4	4	no	—
378	D₄×C₅₃	—	8	2	no	—
379	D₄×C₅₃	—	8	2	no	—
380	D₄×C₅₃	—	8	2	no	—
381	D₄×C₅₃	—	8	1	no	—
382	D₄×C₅₃	—	8	4	no	—
383	D₄×C₅₃	—	8	2	no	—
384	D₄×C₅₃	—	8	2	no	—
385	D₄×C₅₃	—	8	2	no	—
386	D₄×C₅₃	—	8	4	no	—
387	C₂×C₄×C₅₃	—	2	1	no	—
388	C₂×C₄×C₅₃	—	2	2	no	—
389	C₂×C₄×C₅₃	—	2	2	no	—
390	C₂×C₄×C₅₃	—	2	4	no	—
391	C₂×C₄×C₅₃	—	2	1	no	—
392	C₂×C₄×C₅₃	—	2	2	no	—
393	C₂×C₄×C₅₃	—	2	1	no	—
394	C₂×C₄×C₅₃	—	2	2	no	—
395	C₂×C₄×C₅₃	—	2	1	no	—
396	C₂×C₄×C₅₃	—	2	2	no	—
397	C₂×C₄×C₅₃	—	2	2	no	—
398	C₂×C₄×C₅₃	—	2	1	no	—
399	C₂×C₄×C₅₃	—	2	2	no	—
400	C₂×C₄×C₅₃	—	4	2	no	—
401	C₂×C₄×C₅₃	—	4	4	no	—
402	C₂×C₄×C₅₃	—	4	2	no	—
403	C₂×C₄×C₅₃	—	4	4	no	—
404	C₂×C₄×C₅₃	—	4	2	no	—
405	C₂×C₄×C₅₃	—	4	2	no	—
406	C₂×C₄×C₅₃	—	4	4	no	—
407	C₂×C₄×C₅₃	—	8	4	no	—
408	C₂×C₄×C₅₃	—	8	4	no	—
409	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
418	C₈×C₅₃	—	2	2	no	—
419	C₈×C₅₃	—	2	4	no	—
420	C₈×C₅₃	—	2	2	no	—
421	#61988	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
422	C₂²×C₅₃	—	2	2	no	—
423	C₂²×C₅₃	—	2	1	no	—
424	C₂²×C₅₃	—	2	1	no	—
425	C₂²×C₅₃	—	2	2	no	—
426	C₂²×C₅₃	—	2	2	no	—
427	C₂²×C₅₃	—	2	1	no	—
428	C₂²×C₅₃	—	4	1	no	—
429	C₂²×C₅₃	—	4	2	no	—
430	C₂²×C₅₃	—	4	4	no	—
431	C₂²×C₅₃	—	4	2	no	—
432	C₂²×C₅₃	—	4	1	no	—
433	C₂²×C₅₃	—	4	4	no	—
434	C₂²×C₅₃	—	4	1	no	—
435	C₂²×C₅₃	—	4	2	no	—
436	C₂²×C₅₃	—	4	4	no	—
437	C₂²×C₅₃	—	16	4	no	—
438	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
439	C₄×C₅₃	—	2	2	no	—
440	C₄×C₅₃	—	2	1	no	—
441	C₄×C₅₃	—	2	2	no	—
442	C₄×C₅₃	—	2	1	no	—
443	C₄×C₅₃	—	2	2	no	—
444	C₄×C₅₃	—	2	2	no	—
445	C₄×C₅₃	—	2	1	no	—
446	C₄×C₅₃	—	4	2	no	—
447	C₄×C₅₃	—	4	1	no	—
448	C₄×C₅₃	—	4	1	no	—
449	C₄×C₅₃	—	4	2	no	—
450	C₄×C₅₃	—	4	2	no	—
451	C₄×C₅₃	#575	1	2	yes	—
452	C₄×C₅₃	#576	1	2	yes	—
453	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
454	C₄×C₅₃	#585	1	1	yes	characteristic
455	#3508	C₂×C₅₃	1	1	yes	characteristic, complemented
456	#3483	C₂×C₅₃	1	1	yes	characteristic, complemented
457	#3399	C₂×C₅₃	1	2	yes	complemented
458	#3375	C₂×C₅₃	1	2	yes	complemented
459	#3319	C₂×C₅₃	1	4	yes	complemented
460	#3305	C₂×C₅₃	1	2	yes	complemented
461	#3287	C₂×C₅₃	1	2	yes	complemented
462	#3268	C₂×C₅₃	1	4	yes	complemented
463	#3254	C₂×C₅₃	1	1	yes	characteristic, complemented
464	#3245	C₂×C₅₃	1	2	yes	complemented
465	#3214	C₂×C₅₃	1	2	yes	complemented
466	#3205	C₂×C₅₃	1	1	yes	characteristic, complemented
467	#3115	C₂×C₅₃	1	2	yes	complemented
468	#3107	C₂×C₅₃	1	1	yes	characteristic, complemented
469	#3038	C₂×C₅₃	1	1	yes	characteristic, complemented
470	#3035	C₂×C₅₃	1	2	yes	complemented
471	#2990	C₂×C₅₃	1	1	yes	characteristic, complemented
472	C₂×C₅₃	—	4	2	no	—
473	C₂×C₅₃	—	4	1	no	—
474	C₂×C₅₃	—	8	1	no	—
475	C₂×C₅₃	—	8	2	no	—
476	C₂×C₅₃	—	8	4	no	—
477	C₂×C₅₃	#3488	1	1	yes	characteristic
478	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
479	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
480	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
481	C₂×#135	C₂²×C₅₃	1	4	yes	complemented
482	#559	—	2	1	no	—
483	#559	C₂²×C₅₃	1	2	yes	—
484	Q₈²	C₂²×C₅₃	1	1	yes	characteristic, complemented
485	#555	—	2	2	no	—
486	#555	—	2	1	no	—
487	#555	C₂²×C₅₃	1	2	yes	—
488	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
489	#550	—	2	1	no	—
490	#550	—	2	1	no	—
491	#550	C₂²×C₅₃	1	2	yes	—
492	#550	C₂²×C₅₃	1	2	yes	—
493	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
494	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
495	#546	—	2	2	no	—
496	#546	C₂²×C₅₃	1	4	yes	—
497	#540	—	2	2	no	—
498	#535	—	2	1	no	—
499	#533	C₂²×C₅₃	1	1	yes	characteristic
500	#532	—	2	1	no	—
501	#532	—	2	2	no	—
502	#532	C₂²×C₅₃	1	2	yes	—
503	#532	C₂²×C₅₃	1	2	yes	—
504	#532	C₂²×C₅₃	1	1	yes	characteristic
505	#532	C₂²×C₅₃	1	2	yes	complemented
506	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
507	#518	—	2	1	no	—
508	C₄×#41	—	2	1	no	—
509	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
510	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
511	C₄×#41	C₂²×C₅₃	1	2	yes	complemented
512	#496	C₂²×C₅₃	1	4	yes	complemented
513	#493	C₂²×C₅₃	1	2	yes	—
514	#489	C₂²×C₅₃	1	4	yes	complemented
515	#486	C₂²×C₅₃	1	2	yes	—
516	#485	C₂²×C₅₃	1	2	yes	—
517	#482	C₂²×C₅₃	1	4	yes	complemented
518	#477	C₂²×C₅₃	1	2	yes	complemented
519	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
520	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
521	#474	C₂²×C₅₃	1	2	yes	complemented
522	#474	C₂²×C₅₃	1	4	yes	complemented
523	#468	C₂²×C₅₃	1	4	yes	—
524	#466	C₂²×C₅₃	1	4	yes	complemented
525	#466	C₂²×C₅₃	1	4	yes	complemented
526	#464	C₂²×C₅₃	1	4	yes	complemented
527	#463	C₂²×C₅₃	1	4	yes	complemented
528	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
529	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
530	#461	C₂²×C₅₃	1	2	yes	complemented
531	#460	C₂²×C₅₃	1	2	yes	—
532	#460	C₂²×C₅₃	1	2	yes	—
533	#460	C₂²×C₅₃	1	2	yes	complemented
534	#459	C₂²×C₅₃	1	2	yes	—
535	#459	C₂²×C₅₃	1	2	yes	—
536	#459	C₂²×C₅₃	1	2	yes	—
537	#459	C₂²×C₅₃	1	2	yes	—
538	#459	C₂²×C₅₃	1	4	yes	complemented
539	#452	C₂²×C₅₃	1	2	yes	—
540	#449	C₂²×C₅₃	1	4	yes	complemented
541	#449	C₂²×C₅₃	1	4	yes	complemented
542	#449	C₂²×C₅₃	1	4	yes	complemented
543	#447	C₂²×C₅₃	1	4	yes	—
544	#446	C₂²×C₅₃	1	2	yes	complemented
545	#442	C₂²×C₅₃	1	4	yes	complemented
546	#440	C₂²×C₅₃	1	4	yes	complemented
547	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
548	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
549	#435	C₂²×C₅₃	1	4	yes	—
550	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
551	#432	C₂²×C₅₃	1	2	yes	complemented
552	#431	C₂²×C₅₃	1	1	yes	characteristic
553	#423	C₂²×C₅₃	1	1	yes	characteristic
554	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	complemented
555	#418	C₂²×C₅₃	1	2	yes	—
556	#416	C₂²×C₅₃	1	4	yes	complemented
557	C₅₃	#61988	1	1	yes	characteristic, direct product factor, Sylow
558	C₂×#41	—	2	1	no	—
559	C₂×#41	—	2	1	no	—
560	C₂×#41	—	2	2	no	—
561	C₂×#41	—	2	2	no	—
562	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
563	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
564	C₂×#41	C₂³×C₅₃	1	2	yes	—
565	C₂×#41	C₂³×C₅₃	1	4	yes	—
566	C₂²×D₄	—	2	1	no	—
567	C₂²×D₄	—	2	1	no	—
568	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
569	AGL(1,ℤ/8)	—	4	4	no	—
570	#135	—	4	8	no	—
571	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
572	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
573	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
574	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
575	C₂×D₈	C₂³×C₅₃	1	4	yes	—
576	C₂×D₈	C₂³×C₅₃	1	4	yes	—
577	C₂×D₈	C₂³×C₅₃	1	4	yes	—
578	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
579	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
580	C₄⋊Q₈	—	2	1	no	—
581	C₄⋊Q₈	—	2	2	no	—
582	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
583	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
584	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
585	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
586	#127	—	2	2	no	—
587	#127	—	2	1	no	—
588	#127	—	2	2	no	—
589	#127	—	2	1	no	—
590	#127	—	2	1	no	—
591	#127	C₂³×C₅₃	1	2	yes	—
592	#127	C₂³×C₅₃	1	2	yes	—
593	#127	C₂³×C₅₃	1	1	yes	characteristic
594	#127	C₂³×C₅₃	1	2	yes	—
595	#125	—	2	1	no	—
596	#124	—	2	2	no	—
597	#124	—	2	2	no	—
598	#124	—	2	2	no	—
599	#124	—	2	2	no	—
600	#124	—	2	2	no	—
601	#124	—	2	1	no	—
602	#124	—	2	2	no	—
603	#124	C₂³×C₅₃	1	4	yes	—
604	#123	—	2	4	no	—
605	#123	—	2	4	no	—
606	C₂²⋊Q₈	—	2	1	no	—
607	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
608	#121	—	2	2	no	—
609	#121	—	2	1	no	—
610	#121	—	2	2	no	—
611	#121	—	2	2	no	—
612	#121	—	2	2	no	—
613	#121	—	2	1	no	—
614	#121	—	2	2	no	—
615	#121	—	2	1	no	—
616	#121	—	2	2	no	—
617	#121	—	2	2	no	—
618	#121	—	2	2	no	—
619	#121	—	2	2	no	—
620	#121	—	2	4	no	—
621	#121	—	2	4	no	—
622	#121	C₂³×C₅₃	1	4	yes	—
623	#121	C₂³×C₅₃	1	2	yes	—
624	#121	C₂³×C₅₃	1	2	yes	—
625	#121	C₂³×C₅₃	1	2	yes	—
626	#120	—	2	4	no	—
627	C₄×Q₈	—	2	1	no	—
628	C₄×Q₈	—	2	1	no	—
629	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
630	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
631	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
632	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
633	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
634	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	1	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	D₄×C₅₃	1	2	yes	—
649	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
650	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
651	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
652	C₄×D₄	C₂³×C₅₃	1	2	yes	—
653	C₄×D₄	C₂³×C₅₃	1	2	yes	—
654	C₄×D₄	C₂³×C₅₃	1	4	yes	—
655	C₄×D₄	C₂³×C₅₃	1	2	yes	—
656	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
657	#117	—	2	1	no	—
658	#117	—	2	2	no	—
659	#117	—	2	1	no	—
660	#117	—	2	1	no	—
661	#117	—	2	2	no	—
662	#117	D₄×C₅₃	1	1	yes	characteristic
663	#117	D₄×C₅₃	1	2	yes	—
664	#117	C₂³×C₅₃	1	1	yes	characteristic
665	#117	C₂³×C₅₃	1	2	yes	—
666	C₂×C₂²⋊C₄	—	2	4	no	—
667	C₂×C₄²	—	2	1	no	—
668	C₂×C₄²	—	2	2	no	—
669	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
671	#107	C₂³×C₅₃	1	2	yes	—
672	#107	C₂³×C₅₃	1	4	yes	—
673	#106	C₂³×C₅₃	1	2	yes	—
674	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
675	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
676	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
677	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
678	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
679	#103	C₂³×C₅₃	1	2	yes	—
680	#103	C₂³×C₅₃	1	4	yes	—
681	#103	C₂³×C₅₃	1	2	yes	—
682	#103	C₂³×C₅₃	1	2	yes	—
683	#102	C₂³×C₅₃	1	4	yes	—
684	#102	C₂³×C₅₃	1	4	yes	—
685	#102	C₂³×C₅₃	1	4	yes	—
686	#102	C₂³×C₅₃	1	2	yes	—
687	#102	C₂³×C₅₃	1	4	yes	—
688	#102	C₂³×C₅₃	1	4	yes	—
689	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
690	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
691	#97	C₂³×C₅₃	1	4	yes	—
692	C₄×C₈	C₂³×C₅₃	1	2	yes	—
693	C₂⁴	—	2	2	no	—
694	#41	—	2	4	no	—
695	#41	—	2	2	no	—
696	#41	—	4	2	no	—
697	#41	—	4	1	no	—
698	#41	—	4	2	no	—
699	#41	—	4	4	no	—
700	#41	—	4	4	no	—
701	#41	—	4	4	no	—
702	#41	—	8	2	no	—
703	#41	—	8	4	no	—
704	#41	—	8	4	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	2	no	—
707	C₂×Q₈	—	2	1	no	—
708	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
709	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
710	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	1	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	4	2	no	—
728	C₂×D₄	—	4	2	no	—
729	C₂×D₄	—	4	4	no	—
730	C₂×D₄	—	8	2	no	—
731	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
732	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
733	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
734	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
735	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	1	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
745	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
746	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
747	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
750	Q₁₆	—	2	4	no	—
751	SD₁₆	—	2	8	no	—
752	SD₁₆	—	4	4	no	—
753	SD₁₆	—	4	2	no	—
754	D₈	—	4	4	no	—
755	D₈	—	4	4	no	—
756	D₈	—	4	4	no	—
757	M₁₆	—	4	2	no	—
758	C₂×C₈	—	4	4	no	—
759	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
760	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
761	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	—	2	1	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
773	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
774	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
775	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
776	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
777	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
778	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
779	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	1	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
795	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
796	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
797	C₄²	—	2	1	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	1	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	1	no	—
802	C₄²	—	2	2	no	—
803	C₄²	C₂×D₄×C₅₃	1	2	yes	—
804	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
805	C₄²	C₂×D₄×C₅₃	1	2	yes	—
806	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
807	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
808	C₄²	C₂⁴×C₅₃	1	2	yes	—
809	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
810	C₂³	—	2	1	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	4	no	—
813	C₂³	—	4	4	no	—
814	C₂³	—	8	2	no	—
815	C₂³	—	8	2	no	—
816	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
817	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
818	Q₈	—	2	2	no	—
819	Q₈	—	2	1	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	2	2	no	—
822	Q₈	—	4	2	no	—
823	Q₈	—	8	2	no	—
824	Q₈	—	8	1	no	—
825	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
826	D₄	—	2	2	no	—
827	D₄	—	2	1	no	—
828	D₄	—	2	4	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	2	no	—
831	D₄	—	2	4	no	—
832	D₄	—	2	1	no	—
833	D₄	—	4	2	no	—
834	D₄	—	4	4	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	2	no	—
840	D₄	—	4	4	no	—
841	D₄	—	8	2	no	—
842	D₄	—	8	2	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	1	no	—
845	D₄	—	8	4	no	—
846	D₄	—	8	2	no	—
847	D₄	—	8	2	no	—
848	D₄	—	8	2	no	—
849	D₄	—	8	4	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	4	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	4	no	—
867	C₂×C₄	—	4	2	no	—
868	C₂×C₄	—	4	2	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	8	4	no	—
871	C₂×C₄	—	8	4	no	—
872	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
873	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
875	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
876	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
878	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
880	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
881	C₈	—	2	2	no	—
882	C₈	—	2	4	no	—
883	C₈	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	1	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	1	no	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	4	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	4	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	4	no	—
899	C₂²	—	16	4	no	—
900	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
901	C₄	—	2	2	no	—
902	C₄	—	2	1	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	1	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	1	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	C₅₃×#575	1	2	yes	—
914	C₄	C₅₃×#576	1	2	yes	—
915	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
916	C₄	C₅₃×#585	1	1	yes	characteristic
917	C₂	—	4	1	no	—
918	C₂	—	4	2	no	—
919	C₂	—	8	4	no	—
920	C₂	—	8	1	no	—
921	C₂	—	8	2	no	—
922	C₂	C₅₃×#3488	1	1	yes	characteristic
923	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
924	C₂	C₂×C₅₃×#576	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×#3508	C₂	semidirect
2. C₅₃×#3483	C₂	semidirect
3. C₅₃×#3399	C₂	semidirect
4. C₅₃×#3375	C₂	semidirect
5. C₅₃×#3319	C₂	semidirect
6. C₅₃×#3305	C₂	semidirect
7. C₅₃×#3287	C₂	semidirect
8. C₅₃×#3268	C₂	semidirect
9. C₅₃×#3254	C₂	semidirect
10. C₅₃×#3245	C₂	semidirect
11. C₅₃×#3214	C₂	semidirect
12. C₅₃×#3205	C₂	semidirect
13. C₅₃×#3115	C₂	semidirect
14. C₅₃×#3107	C₂	semidirect
15. C₅₃×#3038	C₂	semidirect
16. C₅₃×#3035	C₂	semidirect
17. C₅₃×#2990	C₂	semidirect
19. C₂×#135×C₅₃	C₂²	semidirect
22. Q₈²×C₅₃	C₂²	semidirect
26. C₅₃×#555	C₂²	semidirect
31. C₅₃×#550	C₂²	semidirect
32. C₅₃×#550	C₂²	semidirect
43. C₅₃×#532	C₂²	semidirect
49. C₄×#41×C₅₃	C₂²	semidirect
50. C₅₃×#496	C₂²	semidirect
52. C₅₃×#489	C₂²	semidirect
55. C₅₃×#482	C₂²	semidirect
56. C₅₃×#477	C₂²	semidirect
57. C₅₃×#475	C₂²	semidirect
58. C₅₃×#474	C₂²	semidirect
59. C₅₃×#474	C₂²	semidirect
60. C₅₃×#474	C₂²	semidirect
62. C₅₃×#466	C₂²	semidirect
63. C₅₃×#466	C₂²	semidirect
64. C₅₃×#464	C₂²	semidirect
65. C₅₃×#463	C₂²	semidirect
66. C₅₃×#462	C₂²	semidirect
67. C₅₃×#461	C₂²	semidirect
68. C₅₃×#461	C₂²	semidirect
71. C₅₃×#460	C₂²	semidirect
76. C₅₃×#459	C₂²	semidirect
78. C₅₃×#449	C₂²	semidirect
79. C₅₃×#449	C₂²	semidirect
80. C₅₃×#449	C₂²	semidirect
82. C₅₃×#446	C₂²	semidirect
83. C₅₃×#442	C₂²	semidirect
84. C₅₃×#440	C₂²	semidirect
85. C₄×Q₁₆×C₅₃	C₂²	semidirect
86. C₄×SD₁₆×C₅₃	C₂²	semidirect
88. C₈×D₄×C₅₃	C₂²	semidirect
89. C₅₃×#432	C₂²	semidirect
92. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
94. C₅₃×#416	C₂²	semidirect
421. #61988	C₅₃	direct (N × H)
455. #3508	C₂×C₅₃	semidirect
456. #3483	C₂×C₅₃	semidirect
457. #3399	C₂×C₅₃	semidirect
458. #3375	C₂×C₅₃	semidirect
459. #3319	C₂×C₅₃	semidirect
460. #3305	C₂×C₅₃	semidirect
461. #3287	C₂×C₅₃	semidirect
462. #3268	C₂×C₅₃	semidirect
463. #3254	C₂×C₅₃	semidirect
464. #3245	C₂×C₅₃	semidirect
465. #3214	C₂×C₅₃	semidirect
466. #3205	C₂×C₅₃	semidirect
467. #3115	C₂×C₅₃	semidirect
468. #3107	C₂×C₅₃	semidirect
469. #3038	C₂×C₅₃	semidirect
470. #3035	C₂×C₅₃	semidirect
471. #2990	C₂×C₅₃	semidirect
481. C₂×#135	C₂²×C₅₃	semidirect
484. Q₈²	C₂²×C₅₃	semidirect
488. #555	C₂²×C₅₃	semidirect
493. #550	C₂²×C₅₃	semidirect
494. #550	C₂²×C₅₃	semidirect
505. #532	C₂²×C₅₃	semidirect
511. C₄×#41	C₂²×C₅₃	semidirect
512. #496	C₂²×C₅₃	semidirect
514. #489	C₂²×C₅₃	semidirect
517. #482	C₂²×C₅₃	semidirect
518. #477	C₂²×C₅₃	semidirect
519. #475	C₂²×C₅₃	semidirect
520. #474	C₂²×C₅₃	semidirect
521. #474	C₂²×C₅₃	semidirect
522. #474	C₂²×C₅₃	semidirect
524. #466	C₂²×C₅₃	semidirect
525. #466	C₂²×C₅₃	semidirect
526. #464	C₂²×C₅₃	semidirect
527. #463	C₂²×C₅₃	semidirect
528. #462	C₂²×C₅₃	semidirect
529. #461	C₂²×C₅₃	semidirect
530. #461	C₂²×C₅₃	semidirect
533. #460	C₂²×C₅₃	semidirect
538. #459	C₂²×C₅₃	semidirect
540. #449	C₂²×C₅₃	semidirect
541. #449	C₂²×C₅₃	semidirect
542. #449	C₂²×C₅₃	semidirect
544. #446	C₂²×C₅₃	semidirect
545. #442	C₂²×C₅₃	semidirect
546. #440	C₂²×C₅₃	semidirect
547. C₄×Q₁₆	C₂²×C₅₃	semidirect
548. C₄×SD₁₆	C₂²×C₅₃	semidirect
550. C₈×D₄	C₂²×C₅₃	semidirect
551. #432	C₂²×C₅₃	semidirect
554. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
556. #416	C₂²×C₅₃	semidirect
557. C₅₃	#61988	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×#3508	2
C₅₃×#3483	2
C₅₃×#3399	2
C₅₃×#3375	2
C₅₃×#3319	2
C₅₃×#3305	2
C₅₃×#3287	2
C₅₃×#3268	2
C₅₃×#3254	2
C₅₃×#3245	2
C₅₃×#3214	2
C₅₃×#3205	2
C₅₃×#3115	2
C₅₃×#3107	2
C₅₃×#3038	2
C₅₃×#3035	2
C₅₃×#2990	2
#61988	53

Subgroups — C53×#61988 #27269500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61988 #27269500