Subgroups — C₅₃×#60758 #27268270

Order 13568.

2186 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3488	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3201	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3200	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3196	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3193	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3190	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3187	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3097	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3063	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3057	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3009	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
19	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
20	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×#137×C₅₃	C₂²	1	2	yes	complemented
22	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
23	C₂×#131×C₅₃	C₂²	1	2	yes	complemented
24	C₅₃×#550	—	2	1	no	—
25	C₅₃×#548	—	2	1	no	—
26	C₅₃×#546	—	2	2	no	—
27	C₅₃×#546	—	2	1	no	—
28	D₄²×C₅₃	—	2	2	no	—
29	D₄²×C₅₃	—	2	1	no	—
30	C₅₃×#537	C₂²	1	2	yes	—
31	C₅₃×#537	C₂²	1	1	yes	characteristic
32	C₅₃×#536	—	2	2	no	—
33	C₅₃×#536	—	2	1	no	—
34	C₅₃×#536	—	2	1	no	—
35	C₅₃×#536	C₂²	1	2	yes	—
36	C₅₃×#536	C₂²	1	4	yes	complemented
37	C₅₃×#536	C₂²	1	2	yes	complemented
38	C₅₃×#535	C₂²	1	2	yes	—
39	C₅₃×#535	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₅₃	—	2	1	no	—
41	C₂×#124×C₅₃	—	2	1	no	—
42	C₅₃×#525	C₂²	1	2	yes	—
43	C₅₃×#525	C₂²	1	1	yes	characteristic
44	C₂×#123×C₅₃	—	2	2	no	—
45	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
46	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
47	C₂×#121×C₅₃	C₂²	1	2	yes	—
48	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
49	C₅₃×#520	C₂²	1	1	yes	characteristic
50	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#485	C₂²	1	4	yes	complemented
52	C₅₃×#485	C₂²	1	4	yes	complemented
53	C₅₃×#485	C₂²	1	2	yes	complemented
54	C₅₃×#484	C₂²	1	4	yes	complemented
55	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#483	C₂²	1	4	yes	complemented
57	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#482	C₂²	1	2	yes	complemented
59	C₅₃×#482	C₂²	1	4	yes	complemented
60	C₅₃×#481	C₂²	1	2	yes	complemented
61	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#480	C₂²	1	2	yes	complemented
64	C₅₃×#470	C₂²	1	4	yes	complemented
65	C₅₃×#468	C₂²	1	4	yes	complemented
66	C₅₃×#468	C₂²	1	4	yes	complemented
67	C₅₃×#468	C₂²	1	4	yes	complemented
68	C₅₃×#467	C₂²	1	4	yes	complemented
69	C₅₃×#465	C₂²	1	4	yes	complemented
70	C₅₃×#465	C₂²	1	4	yes	complemented
71	C₅₃×#465	C₂²	1	4	yes	complemented
72	C₅₃×#452	C₂²	1	4	yes	complemented
73	C₅₃×#452	C₂²	1	4	yes	complemented
74	C₅₃×#451	C₂²	1	2	yes	complemented
75	C₅₃×#451	C₂²	1	2	yes	complemented
76	C₅₃×#450	C₂²	1	4	yes	complemented
77	C₅₃×#450	C₂²	1	4	yes	complemented
78	C₅₃×#448	C₂²	1	2	yes	complemented
79	C₅₃×#448	C₂²	1	2	yes	complemented
80	C₅₃×#448	C₂²	1	2	yes	complemented
81	C₅₃×#448	C₂²	1	4	yes	complemented
82	C₅₃×#448	C₂²	1	2	yes	complemented
83	C₅₃×#428	C₂²	1	2	yes	complemented
84	C₅₃×#427	C₂²	1	2	yes	complemented
85	C₅₃×#419	C₂²	1	2	yes	complemented
86	C₅₃×#418	C₂²	1	2	yes	complemented
87	C₅₃×#416	C₂²	1	2	yes	complemented
88	C₂×#103×C₅₃	C₂²	1	2	yes	complemented
89	C₅₃×#408	C₂²	1	2	yes	—
90	C₅₃×#408	C₂²	1	4	yes	complemented
91	C₅₃×#407	C₂²	1	2	yes	complemented
92	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
93	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	complemented
95	H(5,𝔽₂)×C₅₃	—	4	4	no	—
96	C₂×#41×C₅₃	—	2	1	no	—
97	C₂×#41×C₅₃	—	4	4	no	—
98	C₂×#41×C₅₃	D₄	1	2	yes	—
99	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
100	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
101	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
102	C₂×#41×C₅₃	C₂³	1	2	yes	—
103	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
104	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
105	C₂×#41×C₅₃	C₂³	1	2	yes	—
106	C₂²×Q₈×C₅₃	—	2	1	no	—
107	C₂²×Q₈×C₅₃	—	2	1	no	—
108	C₂²×Q₈×C₅₃	—	2	1	no	—
109	C₂²×Q₈×C₅₃	—	4	4	no	—
110	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
111	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
112	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
113	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₅₃	—	2	1	no	—
115	C₂²×D₄×C₅₃	—	2	2	no	—
116	C₂²×D₄×C₅₃	—	2	2	no	—
117	C₂²×D₄×C₅₃	—	2	1	no	—
118	C₂²×D₄×C₅₃	D₄	1	2	yes	—
119	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
120	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
122	C₂³×C₄×C₅₃	—	2	1	no	—
123	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
125	#137×C₅₃	—	4	4	no	—
126	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
127	C₂×SD₁₆×C₅₃	—	4	4	no	—
128	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
129	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
130	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
131	#131×C₅₃	—	4	4	no	—
132	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
133	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
134	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
135	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
136	C₄⋊Q₈×C₅₃	—	2	2	no	—
137	C₄⋊Q₈×C₅₃	—	2	2	no	—
138	C₄⋊Q₈×C₅₃	—	2	4	no	—
139	#127×C₅₃	—	2	1	no	—
140	#127×C₅₃	—	2	2	no	—
141	#124×C₅₃	—	2	1	no	—
142	#124×C₅₃	—	2	2	no	—
143	#124×C₅₃	—	2	2	no	—
144	#124×C₅₃	—	2	2	no	—
145	#124×C₅₃	—	2	4	no	—
146	#123×C₅₃	—	2	4	no	—
147	#123×C₅₃	—	2	4	no	—
148	#123×C₅₃	—	2	4	no	—
149	#123×C₅₃	—	2	4	no	—
150	#123×C₅₃	—	2	1	no	—
151	#123×C₅₃	—	2	2	no	—
152	C₂²⋊Q₈×C₅₃	—	2	1	no	—
153	C₂²⋊Q₈×C₅₃	—	2	2	no	—
154	C₂²⋊Q₈×C₅₃	—	2	2	no	—
155	C₂²⋊Q₈×C₅₃	—	2	2	no	—
156	C₂²⋊Q₈×C₅₃	—	2	2	no	—
157	C₂²⋊Q₈×C₅₃	—	2	2	no	—
158	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
160	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
161	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
162	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
163	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
164	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
165	#121×C₅₃	—	2	2	no	—
166	#121×C₅₃	—	2	2	no	—
167	#121×C₅₃	—	2	2	no	—
168	#121×C₅₃	—	2	1	no	—
169	#121×C₅₃	—	2	2	no	—
170	#121×C₅₃	—	2	1	no	—
171	#121×C₅₃	—	2	2	no	—
172	#121×C₅₃	—	2	1	no	—
173	#121×C₅₃	—	2	2	no	—
174	#121×C₅₃	C₂³	1	1	yes	characteristic
175	#121×C₅₃	C₂³	1	2	yes	—
176	#121×C₅₃	C₂³	1	2	yes	—
177	#121×C₅₃	C₂³	1	2	yes	—
178	#121×C₅₃	C₂³	1	2	yes	—
179	#121×C₅₃	C₂³	1	1	yes	characteristic
180	#121×C₅₃	C₂³	1	2	yes	—
181	#120×C₅₃	—	2	1	no	—
182	#120×C₅₃	—	2	2	no	—
183	#120×C₅₃	—	2	2	no	—
184	#120×C₅₃	—	2	2	no	—
185	#120×C₅₃	—	2	2	no	—
186	C₄×Q₈×C₅₃	—	2	1	no	—
187	C₄×D₄×C₅₃	—	2	2	no	—
188	C₄×D₄×C₅₃	—	2	1	no	—
189	C₄×D₄×C₅₃	—	2	1	no	—
190	C₄×D₄×C₅₃	—	2	2	no	—
191	C₄×D₄×C₅₃	—	2	1	no	—
192	C₄×D₄×C₅₃	—	2	2	no	—
193	#117×C₅₃	—	2	1	no	—
194	#117×C₅₃	—	2	1	no	—
195	#117×C₅₃	C₂³	1	2	yes	—
196	#117×C₅₃	C₂³	1	2	yes	—
197	#117×C₅₃	C₂³	1	2	yes	—
198	#117×C₅₃	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
200	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
201	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
206	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
207	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
208	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
209	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
210	C₂×C₄²×C₅₃	—	2	1	no	—
211	#107×C₅₃	C₂³	1	2	yes	—
212	#107×C₅₃	C₂³	1	2	yes	—
213	#107×C₅₃	C₂³	1	4	yes	—
214	#106×C₅₃	C₂³	1	2	yes	—
215	#106×C₅₃	C₂³	1	2	yes	—
216	#106×C₅₃	C₂³	1	4	yes	—
217	#103×C₅₃	C₂³	1	4	yes	—
218	#103×C₅₃	C₂³	1	4	yes	—
219	#103×C₅₃	C₂³	1	4	yes	—
220	#103×C₅₃	C₂³	1	2	yes	—
221	#103×C₅₃	C₂³	1	2	yes	—
222	#103×C₅₃	C₂³	1	4	yes	—
223	#102×C₅₃	C₂³	1	2	yes	—
224	#102×C₅₃	C₂³	1	2	yes	—
225	#102×C₅₃	C₂³	1	4	yes	—
226	#102×C₅₃	C₂³	1	4	yes	—
227	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
228	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
229	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
230	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
231	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
232	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
233	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
234	C₂⁴×C₅₃	—	2	2	no	—
235	C₂⁴×C₅₃	—	2	1	no	—
236	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
237	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
238	#41×C₅₃	—	2	4	no	—
239	#41×C₅₃	—	2	4	no	—
240	#41×C₅₃	—	2	4	no	—
241	#41×C₅₃	—	4	4	no	—
242	#41×C₅₃	—	4	4	no	—
243	#41×C₅₃	—	4	2	no	—
244	#41×C₅₃	—	4	2	no	—
245	#41×C₅₃	—	4	4	no	—
246	#41×C₅₃	—	4	4	no	—
247	C₂×Q₈×C₅₃	—	2	2	no	—
248	C₂×Q₈×C₅₃	—	2	2	no	—
249	C₂×Q₈×C₅₃	—	2	2	no	—
250	C₂×Q₈×C₅₃	—	2	4	no	—
251	C₂×Q₈×C₅₃	—	2	4	no	—
252	C₂×Q₈×C₅₃	—	4	4	no	—
253	C₂×Q₈×C₅₃	—	4	4	no	—
254	C₂×Q₈×C₅₃	—	4	2	no	—
255	C₂×Q₈×C₅₃	—	4	4	no	—
256	C₂×Q₈×C₅₃	—	4	4	no	—
257	C₂×Q₈×C₅₃	—	4	4	no	—
258	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
259	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
260	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
261	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
262	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₅₃	—	2	1	no	—
264	C₂×D₄×C₅₃	—	2	2	no	—
265	C₂×D₄×C₅₃	—	2	2	no	—
266	C₂×D₄×C₅₃	—	2	1	no	—
267	C₂×D₄×C₅₃	—	2	1	no	—
268	C₂×D₄×C₅₃	—	2	2	no	—
269	C₂×D₄×C₅₃	—	2	2	no	—
270	C₂×D₄×C₅₃	—	2	2	no	—
271	C₂×D₄×C₅₃	—	2	2	no	—
272	C₂×D₄×C₅₃	—	2	2	no	—
273	C₂×D₄×C₅₃	—	2	1	no	—
274	C₂×D₄×C₅₃	—	2	4	no	—
275	C₂×D₄×C₅₃	—	4	2	no	—
276	C₂×D₄×C₅₃	—	4	4	no	—
277	C₂×D₄×C₅₃	—	4	4	no	—
278	C₂×D₄×C₅₃	—	4	8	no	—
279	C₂×D₄×C₅₃	—	4	4	no	—
280	C₂×D₄×C₅₃	—	8	2	no	—
281	C₂×D₄×C₅₃	—	8	4	no	—
282	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
283	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
284	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
285	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
286	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
287	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
288	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
289	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
290	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅₃	—	2	4	no	—
292	C₂²×C₄×C₅₃	—	2	1	no	—
293	C₂²×C₄×C₅₃	—	2	1	no	—
294	C₂²×C₄×C₅₃	—	2	2	no	—
295	C₂²×C₄×C₅₃	—	2	2	no	—
296	C₂²×C₄×C₅₃	—	2	2	no	—
297	C₂²×C₄×C₅₃	—	2	2	no	—
298	C₂²×C₄×C₅₃	—	2	1	no	—
299	C₂²×C₄×C₅₃	—	2	2	no	—
300	C₂²×C₄×C₅₃	—	2	1	no	—
301	C₂²×C₄×C₅₃	—	4	4	no	—
302	C₂²×C₄×C₅₃	—	4	4	no	—
303	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
307	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
308	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
309	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
314	Q₁₆×C₅₃	—	4	4	no	—
315	SD₁₆×C₅₃	—	4	4	no	—
316	SD₁₆×C₅₃	—	4	4	no	—
317	SD₁₆×C₅₃	—	4	4	no	—
318	M₁₆×C₅₃	—	2	4	no	—
319	M₁₆×C₅₃	—	4	4	no	—
320	C₂×C₈×C₅₃	—	2	4	no	—
321	C₂×C₈×C₅₃	—	4	4	no	—
322	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
323	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
324	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
325	C₄⋊C₄×C₅₃	—	2	4	no	—
326	C₄⋊C₄×C₅₃	—	2	4	no	—
327	C₄⋊C₄×C₅₃	—	2	4	no	—
328	C₄⋊C₄×C₅₃	—	2	4	no	—
329	C₄⋊C₄×C₅₃	—	2	1	no	—
330	C₄⋊C₄×C₅₃	—	2	1	no	—
331	C₄⋊C₄×C₅₃	—	2	2	no	—
332	C₄⋊C₄×C₅₃	—	2	1	no	—
333	C₄⋊C₄×C₅₃	—	2	1	no	—
334	C₄⋊C₄×C₅₃	—	2	1	no	—
335	C₄⋊C₄×C₅₃	—	2	2	no	—
336	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
337	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
339	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
341	C₂²⋊C₄×C₅₃	—	2	2	no	—
342	C₂²⋊C₄×C₅₃	—	2	2	no	—
343	C₂²⋊C₄×C₅₃	—	2	4	no	—
344	C₂²⋊C₄×C₅₃	—	2	4	no	—
345	C₂²⋊C₄×C₅₃	—	2	4	no	—
346	C₂²⋊C₄×C₅₃	—	2	4	no	—
347	C₂²⋊C₄×C₅₃	—	2	2	no	—
348	C₂²⋊C₄×C₅₃	—	2	1	no	—
349	C₂²⋊C₄×C₅₃	—	2	1	no	—
350	C₂²⋊C₄×C₅₃	—	2	1	no	—
351	C₂²⋊C₄×C₅₃	—	2	2	no	—
352	C₂²⋊C₄×C₅₃	—	2	2	no	—
353	C₂²⋊C₄×C₅₃	—	2	1	no	—
354	C₂²⋊C₄×C₅₃	—	2	2	no	—
355	C₂²⋊C₄×C₅₃	—	2	2	no	—
356	C₂²⋊C₄×C₅₃	—	2	2	no	—
357	C₂²⋊C₄×C₅₃	—	2	1	no	—
358	C₂²⋊C₄×C₅₃	—	2	2	no	—
359	C₄²×C₅₃	—	2	2	no	—
360	C₄²×C₅₃	—	2	2	no	—
361	C₄²×C₅₃	—	2	2	no	—
362	C₄²×C₅₃	—	2	1	no	—
363	C₂³×C₅₃	—	2	2	no	—
364	C₂³×C₅₃	—	2	2	no	—
365	C₂³×C₅₃	—	2	4	no	—
366	C₂³×C₅₃	—	2	2	no	—
367	C₂³×C₅₃	—	2	1	no	—
368	C₂³×C₅₃	—	4	1	no	—
369	C₂³×C₅₃	—	4	2	no	—
370	C₂³×C₅₃	—	4	2	no	—
371	C₂³×C₅₃	—	4	4	no	—
372	C₂³×C₅₃	—	4	2	no	—
373	C₂³×C₅₃	—	8	1	no	—
374	C₂³×C₅₃	—	8	2	no	—
375	C₂³×C₅₃	—	8	1	no	—
376	C₂³×C₅₃	—	8	2	no	—
377	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
378	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
379	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
380	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
381	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
382	Q₈×C₅₃	—	2	2	no	—
383	Q₈×C₅₃	—	2	2	no	—
384	Q₈×C₅₃	—	2	4	no	—
385	Q₈×C₅₃	—	2	4	no	—
386	Q₈×C₅₃	—	2	2	no	—
387	Q₈×C₅₃	—	4	2	no	—
388	Q₈×C₅₃	—	4	4	no	—
389	Q₈×C₅₃	—	4	4	no	—
390	Q₈×C₅₃	—	4	4	no	—
391	D₄×C₅₃	—	2	4	no	—
392	D₄×C₅₃	—	2	4	no	—
393	D₄×C₅₃	—	2	2	no	—
394	D₄×C₅₃	—	2	2	no	—
395	D₄×C₅₃	—	2	4	no	—
396	D₄×C₅₃	—	2	2	no	—
397	D₄×C₅₃	—	4	2	no	—
398	D₄×C₅₃	—	4	2	no	—
399	D₄×C₅₃	—	4	2	no	—
400	D₄×C₅₃	—	4	4	no	—
401	D₄×C₅₃	—	4	4	no	—
402	D₄×C₅₃	—	4	2	no	—
403	D₄×C₅₃	—	4	4	no	—
404	D₄×C₅₃	—	4	2	no	—
405	D₄×C₅₃	—	4	2	no	—
406	D₄×C₅₃	—	8	1	no	—
407	D₄×C₅₃	—	8	2	no	—
408	D₄×C₅₃	—	8	2	no	—
409	D₄×C₅₃	—	8	2	no	—
410	D₄×C₅₃	—	8	2	no	—
411	C₂×C₄×C₅₃	—	2	2	no	—
412	C₂×C₄×C₅₃	—	2	2	no	—
413	C₂×C₄×C₅₃	—	2	2	no	—
414	C₂×C₄×C₅₃	—	2	2	no	—
415	C₂×C₄×C₅₃	—	2	2	no	—
416	C₂×C₄×C₅₃	—	2	4	no	—
417	C₂×C₄×C₅₃	—	2	4	no	—
418	C₂×C₄×C₅₃	—	2	1	no	—
419	C₂×C₄×C₅₃	—	2	4	no	—
420	C₂×C₄×C₅₃	—	2	1	no	—
421	C₂×C₄×C₅₃	—	2	2	no	—
422	C₂×C₄×C₅₃	—	2	2	no	—
423	C₂×C₄×C₅₃	—	2	2	no	—
424	C₂×C₄×C₅₃	—	2	1	no	—
425	C₂×C₄×C₅₃	—	4	2	no	—
426	C₂×C₄×C₅₃	—	4	2	no	—
427	C₂×C₄×C₅₃	—	4	2	no	—
428	C₂×C₄×C₅₃	—	4	4	no	—
429	C₂×C₄×C₅₃	—	4	2	no	—
430	C₂×C₄×C₅₃	—	4	4	no	—
431	C₂×C₄×C₅₃	—	4	4	no	—
432	C₂×C₄×C₅₃	—	4	4	no	—
433	C₂×C₄×C₅₃	—	4	2	no	—
434	C₂×C₄×C₅₃	—	4	2	no	—
435	C₂×C₄×C₅₃	—	8	1	no	—
436	C₂×C₄×C₅₃	—	8	2	no	—
437	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
443	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
444	C₈×C₅₃	—	2	2	no	—
445	C₈×C₅₃	—	2	2	no	—
446	C₈×C₅₃	—	2	4	no	—
447	#60758	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
448	C₂²×C₅₃	—	2	1	no	—
449	C₂²×C₅₃	—	2	1	no	—
450	C₂²×C₅₃	—	2	1	no	—
451	C₂²×C₅₃	—	2	1	no	—
452	C₂²×C₅₃	—	2	1	no	—
453	C₂²×C₅₃	—	2	2	no	—
454	C₂²×C₅₃	—	2	2	no	—
455	C₂²×C₅₃	—	2	1	no	—
456	C₂²×C₅₃	—	2	2	no	—
457	C₂²×C₅₃	—	2	2	no	—
458	C₂²×C₅₃	—	2	2	no	—
459	C₂²×C₅₃	—	2	1	no	—
460	C₂²×C₅₃	—	2	2	no	—
461	C₂²×C₅₃	—	4	4	no	—
462	C₂²×C₅₃	—	4	2	no	—
463	C₂²×C₅₃	—	4	1	no	—
464	C₂²×C₅₃	—	4	2	no	—
465	C₂²×C₅₃	—	4	1	no	—
466	C₂²×C₅₃	—	4	2	no	—
467	C₂²×C₅₃	—	4	1	no	—
468	C₂²×C₅₃	—	8	4	no	—
469	C₂²×C₅₃	—	16	2	no	—
470	C₂²×C₅₃	—	16	4	no	—
471	C₂²×C₅₃	#534	1	2	yes	—
472	C₂²×C₅₃	#577	1	2	yes	—
473	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
474	C₄×C₅₃	—	2	1	no	—
475	C₄×C₅₃	—	2	1	no	—
476	C₄×C₅₃	—	2	2	no	—
477	C₄×C₅₃	—	2	2	no	—
478	C₄×C₅₃	—	4	2	no	—
479	C₄×C₅₃	—	4	1	no	—
480	C₄×C₅₃	—	4	1	no	—
481	C₄×C₅₃	—	4	4	no	—
482	C₄×C₅₃	—	4	2	no	—
483	C₄×C₅₃	—	4	2	no	—
484	C₄×C₅₃	—	4	1	no	—
485	C₄×C₅₃	#534	1	2	yes	—
486	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
487	#3488	C₂×C₅₃	1	1	yes	characteristic
488	C₂×#536	C₂×C₅₃	1	1	yes	characteristic, complemented
489	#3201	C₂×C₅₃	1	4	yes	complemented
490	#3200	C₂×C₅₃	1	4	yes	complemented
491	#3196	C₂×C₅₃	1	2	yes	complemented
492	#3193	C₂×C₅₃	1	2	yes	complemented
493	#3190	C₂×C₅₃	1	2	yes	complemented
494	#3187	C₂×C₅₃	1	2	yes	complemented
495	#3097	C₂×C₅₃	1	2	yes	complemented
496	#3094	C₂×C₅₃	1	1	yes	characteristic, complemented
497	#3091	C₂×C₅₃	1	1	yes	characteristic, complemented
498	#3063	C₂×C₅₃	1	2	yes	complemented
499	#3057	C₂×C₅₃	1	2	yes	complemented
500	#3009	C₂×C₅₃	1	2	yes	complemented
501	#3004	C₂×C₅₃	1	1	yes	characteristic, complemented
502	C₂×#448	C₂×C₅₃	1	1	yes	characteristic, complemented
503	#2880	C₂×C₅₃	1	1	yes	characteristic, complemented
504	C₂×C₅₃	—	2	2	no	—
505	C₂×C₅₃	—	2	2	no	—
506	C₂×C₅₃	—	4	1	no	—
507	C₂×C₅₃	—	4	2	no	—
508	C₂×C₅₃	—	4	2	no	—
509	C₂×C₅₃	—	8	2	no	—
510	C₂×C₅₃	—	8	1	no	—
511	C₂×C₅₃	C₂×#534	1	1	yes	characteristic
512	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
513	C₂×C₅₃	#3586	1	1	yes	characteristic
514	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
515	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
516	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
517	C₂×#137	C₂²×C₅₃	1	2	yes	complemented
518	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
519	C₂×#131	C₂²×C₅₃	1	2	yes	complemented
520	#550	—	2	1	no	—
521	#548	—	2	1	no	—
522	#546	—	2	2	no	—
523	#546	—	2	1	no	—
524	D₄²	—	2	2	no	—
525	D₄²	—	2	1	no	—
526	#537	C₂²×C₅₃	1	2	yes	—
527	#537	C₂²×C₅₃	1	1	yes	characteristic
528	#536	—	2	2	no	—
529	#536	—	2	1	no	—
530	#536	—	2	1	no	—
531	#536	C₂²×C₅₃	1	2	yes	—
532	#536	C₂²×C₅₃	1	4	yes	complemented
533	#536	C₂²×C₅₃	1	2	yes	complemented
534	#535	C₂²×C₅₃	1	2	yes	—
535	#535	C₂²×C₅₃	1	1	yes	characteristic
536	C₂×C₄⋊Q₈	—	2	1	no	—
537	C₂×#124	—	2	1	no	—
538	#525	C₂²×C₅₃	1	1	yes	characteristic
539	#525	C₂²×C₅₃	1	2	yes	—
540	C₂×#123	—	2	2	no	—
541	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
542	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
543	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
544	C₂×#121	C₂²×C₅₃	1	2	yes	—
545	#520	C₂²×C₅₃	1	1	yes	characteristic
546	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
547	#485	C₂²×C₅₃	1	2	yes	complemented
548	#485	C₂²×C₅₃	1	4	yes	complemented
549	#485	C₂²×C₅₃	1	4	yes	complemented
550	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
551	#484	C₂²×C₅₃	1	4	yes	complemented
552	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
553	#483	C₂²×C₅₃	1	4	yes	complemented
554	#482	C₂²×C₅₃	1	2	yes	complemented
555	#482	C₂²×C₅₃	1	4	yes	complemented
556	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
557	#481	C₂²×C₅₃	1	2	yes	complemented
558	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
559	#480	C₂²×C₅₃	1	2	yes	complemented
560	#470	C₂²×C₅₃	1	4	yes	complemented
561	#468	C₂²×C₅₃	1	4	yes	complemented
562	#468	C₂²×C₅₃	1	4	yes	complemented
563	#468	C₂²×C₅₃	1	4	yes	complemented
564	#467	C₂²×C₅₃	1	4	yes	complemented
565	#465	C₂²×C₅₃	1	4	yes	complemented
566	#465	C₂²×C₅₃	1	4	yes	complemented
567	#465	C₂²×C₅₃	1	4	yes	complemented
568	#452	C₂²×C₅₃	1	4	yes	complemented
569	#452	C₂²×C₅₃	1	4	yes	complemented
570	#451	C₂²×C₅₃	1	2	yes	complemented
571	#451	C₂²×C₅₃	1	2	yes	complemented
572	#450	C₂²×C₅₃	1	4	yes	complemented
573	#450	C₂²×C₅₃	1	4	yes	complemented
574	#448	C₂²×C₅₃	1	2	yes	complemented
575	#448	C₂²×C₅₃	1	2	yes	complemented
576	#448	C₂²×C₅₃	1	2	yes	complemented
577	#448	C₂²×C₅₃	1	2	yes	complemented
578	#448	C₂²×C₅₃	1	4	yes	complemented
579	#428	C₂²×C₅₃	1	2	yes	complemented
580	#427	C₂²×C₅₃	1	2	yes	complemented
581	#419	C₂²×C₅₃	1	2	yes	complemented
582	#418	C₂²×C₅₃	1	2	yes	complemented
583	#416	C₂²×C₅₃	1	2	yes	complemented
584	C₂×#103	C₂²×C₅₃	1	2	yes	complemented
585	#408	C₂²×C₅₃	1	2	yes	—
586	#408	C₂²×C₅₃	1	4	yes	complemented
587	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
588	#407	C₂²×C₅₃	1	2	yes	complemented
589	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
590	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	complemented
591	C₅₃	#60758	1	1	yes	characteristic, direct product factor, Sylow
592	H(5,𝔽₂)	—	4	4	no	—
593	C₂×#41	—	2	1	no	—
594	C₂×#41	—	4	4	no	—
595	C₂×#41	D₄×C₅₃	1	2	yes	—
596	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
597	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
598	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
599	C₂×#41	C₂³×C₅₃	1	2	yes	—
600	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
601	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
602	C₂×#41	C₂³×C₅₃	1	2	yes	—
603	C₂²×Q₈	—	2	1	no	—
604	C₂²×Q₈	—	2	1	no	—
605	C₂²×Q₈	—	2	1	no	—
606	C₂²×Q₈	—	4	4	no	—
607	C₂²×Q₈	D₄×C₅₃	1	1	yes	characteristic
608	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
609	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
610	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
611	C₂²×D₄	—	2	1	no	—
612	C₂²×D₄	—	2	2	no	—
613	C₂²×D₄	—	2	2	no	—
614	C₂²×D₄	—	2	1	no	—
615	C₂²×D₄	D₄×C₅₃	1	2	yes	—
616	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
617	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
618	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
619	C₂³×C₄	—	2	1	no	—
620	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
621	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
622	#137	—	4	4	no	—
623	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
624	C₂×SD₁₆	—	4	4	no	—
625	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
626	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
627	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
628	#131	—	4	4	no	—
629	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
630	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
631	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
632	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
633	C₄⋊Q₈	—	2	2	no	—
634	C₄⋊Q₈	—	2	2	no	—
635	C₄⋊Q₈	—	2	4	no	—
636	#127	—	2	1	no	—
637	#127	—	2	2	no	—
638	#124	—	2	1	no	—
639	#124	—	2	2	no	—
640	#124	—	2	2	no	—
641	#124	—	2	2	no	—
642	#124	—	2	4	no	—
643	#123	—	2	4	no	—
644	#123	—	2	4	no	—
645	#123	—	2	4	no	—
646	#123	—	2	4	no	—
647	#123	—	2	1	no	—
648	#123	—	2	2	no	—
649	C₂²⋊Q₈	—	2	1	no	—
650	C₂²⋊Q₈	—	2	2	no	—
651	C₂²⋊Q₈	—	2	2	no	—
652	C₂²⋊Q₈	—	2	2	no	—
653	C₂²⋊Q₈	—	2	2	no	—
654	C₂²⋊Q₈	—	2	2	no	—
655	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
656	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
657	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
658	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
659	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
660	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
661	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
662	#121	—	2	2	no	—
663	#121	—	2	2	no	—
664	#121	—	2	2	no	—
665	#121	—	2	1	no	—
666	#121	—	2	2	no	—
667	#121	—	2	1	no	—
668	#121	—	2	2	no	—
669	#121	—	2	1	no	—
670	#121	—	2	2	no	—
671	#121	C₂³×C₅₃	1	2	yes	—
672	#121	C₂³×C₅₃	1	1	yes	characteristic
673	#121	C₂³×C₅₃	1	2	yes	—
674	#121	C₂³×C₅₃	1	2	yes	—
675	#121	C₂³×C₅₃	1	2	yes	—
676	#121	C₂³×C₅₃	1	1	yes	characteristic
677	#121	C₂³×C₅₃	1	2	yes	—
678	#120	—	2	1	no	—
679	#120	—	2	2	no	—
680	#120	—	2	2	no	—
681	#120	—	2	2	no	—
682	#120	—	2	2	no	—
683	C₄×Q₈	—	2	1	no	—
684	C₄×D₄	—	2	2	no	—
685	C₄×D₄	—	2	1	no	—
686	C₄×D₄	—	2	1	no	—
687	C₄×D₄	—	2	2	no	—
688	C₄×D₄	—	2	1	no	—
689	C₄×D₄	—	2	2	no	—
690	#117	—	2	1	no	—
691	#117	—	2	1	no	—
692	#117	C₂³×C₅₃	1	2	yes	—
693	#117	C₂³×C₅₃	1	2	yes	—
694	#117	C₂³×C₅₃	1	1	yes	characteristic
695	#117	C₂³×C₅₃	1	2	yes	—
696	C₂×C₄⋊C₄	—	2	2	no	—
697	C₂×C₄⋊C₄	—	2	2	no	—
698	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
699	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
702	C₂×C₂²⋊C₄	—	2	1	no	—
703	C₂×C₂²⋊C₄	—	2	2	no	—
704	C₂×C₂²⋊C₄	—	2	2	no	—
705	C₂×C₂²⋊C₄	—	2	1	no	—
706	C₂×C₂²⋊C₄	—	2	2	no	—
707	C₂×C₄²	—	2	1	no	—
708	#107	C₂³×C₅₃	1	2	yes	—
709	#107	C₂³×C₅₃	1	2	yes	—
710	#107	C₂³×C₅₃	1	4	yes	—
711	#106	C₂³×C₅₃	1	2	yes	—
712	#106	C₂³×C₅₃	1	2	yes	—
713	#106	C₂³×C₅₃	1	4	yes	—
714	#103	C₂³×C₅₃	1	4	yes	—
715	#103	C₂³×C₅₃	1	4	yes	—
716	#103	C₂³×C₅₃	1	2	yes	—
717	#103	C₂³×C₅₃	1	2	yes	—
718	#103	C₂³×C₅₃	1	4	yes	—
719	#103	C₂³×C₅₃	1	4	yes	—
720	#102	C₂³×C₅₃	1	2	yes	—
721	#102	C₂³×C₅₃	1	2	yes	—
722	#102	C₂³×C₅₃	1	4	yes	—
723	#102	C₂³×C₅₃	1	4	yes	—
724	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
725	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
726	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
727	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
728	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
729	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
730	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
731	C₂⁴	—	2	2	no	—
732	C₂⁴	—	2	1	no	—
733	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
734	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
735	#41	—	2	4	no	—
736	#41	—	2	4	no	—
737	#41	—	2	4	no	—
738	#41	—	4	4	no	—
739	#41	—	4	4	no	—
740	#41	—	4	2	no	—
741	#41	—	4	2	no	—
742	#41	—	4	4	no	—
743	#41	—	4	4	no	—
744	C₂×Q₈	—	2	2	no	—
745	C₂×Q₈	—	2	2	no	—
746	C₂×Q₈	—	2	2	no	—
747	C₂×Q₈	—	2	4	no	—
748	C₂×Q₈	—	2	4	no	—
749	C₂×Q₈	—	4	4	no	—
750	C₂×Q₈	—	4	4	no	—
751	C₂×Q₈	—	4	2	no	—
752	C₂×Q₈	—	4	4	no	—
753	C₂×Q₈	—	4	4	no	—
754	C₂×Q₈	—	4	4	no	—
755	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
756	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
757	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
758	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
759	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
760	C₂×D₄	—	2	1	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	1	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	1	no	—
771	C₂×D₄	—	2	4	no	—
772	C₂×D₄	—	4	2	no	—
773	C₂×D₄	—	4	4	no	—
774	C₂×D₄	—	4	4	no	—
775	C₂×D₄	—	4	8	no	—
776	C₂×D₄	—	4	4	no	—
777	C₂×D₄	—	8	2	no	—
778	C₂×D₄	—	8	4	no	—
779	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
780	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
781	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
782	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
783	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
784	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
785	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
786	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
787	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
788	C₂²×C₄	—	2	4	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	1	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	4	4	no	—
799	C₂²×C₄	—	4	4	no	—
800	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
801	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
802	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
803	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
804	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
805	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
808	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
810	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
811	Q₁₆	—	4	4	no	—
812	SD₁₆	—	4	4	no	—
813	SD₁₆	—	4	4	no	—
814	SD₁₆	—	4	4	no	—
815	M₁₆	—	2	4	no	—
816	M₁₆	—	4	4	no	—
817	C₂×C₈	—	2	4	no	—
818	C₂×C₈	—	4	4	no	—
819	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
820	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
821	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
822	C₄⋊C₄	—	2	4	no	—
823	C₄⋊C₄	—	2	4	no	—
824	C₄⋊C₄	—	2	4	no	—
825	C₄⋊C₄	—	2	4	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	1	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
834	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
835	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
836	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
837	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	4	no	—
841	C₂²⋊C₄	—	2	4	no	—
842	C₂²⋊C₄	—	2	4	no	—
843	C₂²⋊C₄	—	2	4	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	1	no	—
846	C₂²⋊C₄	—	2	1	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	1	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	1	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	1	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₄²	—	2	2	no	—
857	C₄²	—	2	2	no	—
858	C₄²	—	2	2	no	—
859	C₄²	—	2	1	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	4	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	4	1	no	—
866	C₂³	—	4	2	no	—
867	C₂³	—	4	2	no	—
868	C₂³	—	4	4	no	—
869	C₂³	—	4	2	no	—
870	C₂³	—	8	1	no	—
871	C₂³	—	8	2	no	—
872	C₂³	—	8	1	no	—
873	C₂³	—	8	2	no	—
874	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
875	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
876	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
877	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
878	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
879	Q₈	—	2	2	no	—
880	Q₈	—	2	2	no	—
881	Q₈	—	2	4	no	—
882	Q₈	—	2	4	no	—
883	Q₈	—	2	2	no	—
884	Q₈	—	4	2	no	—
885	Q₈	—	4	4	no	—
886	Q₈	—	4	4	no	—
887	Q₈	—	4	4	no	—
888	D₄	—	2	4	no	—
889	D₄	—	2	4	no	—
890	D₄	—	2	2	no	—
891	D₄	—	2	2	no	—
892	D₄	—	2	4	no	—
893	D₄	—	2	2	no	—
894	D₄	—	4	2	no	—
895	D₄	—	4	2	no	—
896	D₄	—	4	2	no	—
897	D₄	—	4	4	no	—
898	D₄	—	4	4	no	—
899	D₄	—	4	2	no	—
900	D₄	—	4	4	no	—
901	D₄	—	4	2	no	—
902	D₄	—	4	2	no	—
903	D₄	—	8	1	no	—
904	D₄	—	8	2	no	—
905	D₄	—	8	2	no	—
906	D₄	—	8	2	no	—
907	D₄	—	8	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	4	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	4	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	4	no	—
922	C₂×C₄	—	4	2	no	—
923	C₂×C₄	—	4	2	no	—
924	C₂×C₄	—	4	2	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	2	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	4	4	no	—
929	C₂×C₄	—	4	4	no	—
930	C₂×C₄	—	4	2	no	—
931	C₂×C₄	—	4	2	no	—
932	C₂×C₄	—	8	1	no	—
933	C₂×C₄	—	8	2	no	—
934	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
936	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
937	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
938	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
939	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
940	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
941	C₈	—	2	2	no	—
942	C₈	—	2	2	no	—
943	C₈	—	2	4	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	1	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	1	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	4	4	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	1	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	8	4	no	—
965	C₂²	—	16	2	no	—
966	C₂²	—	16	4	no	—
967	C₂²	C₅₃×#534	1	2	yes	—
968	C₂²	C₅₃×#577	1	2	yes	—
969	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
970	C₄	—	2	1	no	—
971	C₄	—	2	1	no	—
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	1	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	1	no	—
979	C₄	—	4	1	no	—
980	C₄	—	4	4	no	—
981	C₄	C₅₃×#534	1	2	yes	—
982	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
983	C₂	—	2	2	no	—
984	C₂	—	2	2	no	—
985	C₂	—	4	1	no	—
986	C₂	—	4	2	no	—
987	C₂	—	4	2	no	—
988	C₂	—	8	2	no	—
989	C₂	—	8	1	no	—
990	C₂	C₂×C₅₃×#534	1	1	yes	characteristic
991	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
992	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3488	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂²×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₃×#536	C₂	semidirect
3. C₅₃×#3201	C₂	semidirect
4. C₅₃×#3200	C₂	semidirect
5. C₅₃×#3196	C₂	semidirect
6. C₅₃×#3193	C₂	semidirect
7. C₅₃×#3190	C₂	semidirect
8. C₅₃×#3187	C₂	semidirect
9. C₅₃×#3097	C₂	semidirect
10. C₅₃×#3094	C₂	semidirect
11. C₅₃×#3091	C₂	semidirect
12. C₅₃×#3063	C₂	semidirect
13. C₅₃×#3057	C₂	semidirect
14. C₅₃×#3009	C₂	semidirect
15. C₅₃×#3004	C₂	semidirect
16. C₂×C₅₃×#448	C₂	semidirect
17. C₅₃×#2880	C₂	semidirect
20. C₂³×Q₈×C₅₃	C₂²	semidirect
21. C₂×#137×C₅₃	C₂²	semidirect
22. C₂²×SD₁₆×C₅₃	C₂²	semidirect
23. C₂×#131×C₅₃	C₂²	semidirect
36. C₅₃×#536	C₂²	semidirect
37. C₅₃×#536	C₂²	semidirect
45. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
46. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
50. C₂×#117×C₅₃	C₂²	semidirect
51. C₅₃×#485	C₂²	semidirect
52. C₅₃×#485	C₂²	semidirect
53. C₅₃×#485	C₂²	semidirect
54. C₅₃×#484	C₂²	semidirect
55. C₅₃×#484	C₂²	semidirect
56. C₅₃×#483	C₂²	semidirect
57. C₅₃×#483	C₂²	semidirect
58. C₅₃×#482	C₂²	semidirect
59. C₅₃×#482	C₂²	semidirect
60. C₅₃×#481	C₂²	semidirect
61. C₅₃×#481	C₂²	semidirect
62. C₅₃×#480	C₂²	semidirect
63. C₅₃×#480	C₂²	semidirect
64. C₅₃×#470	C₂²	semidirect
65. C₅₃×#468	C₂²	semidirect
66. C₅₃×#468	C₂²	semidirect
67. C₅₃×#468	C₂²	semidirect
68. C₅₃×#467	C₂²	semidirect
69. C₅₃×#465	C₂²	semidirect
70. C₅₃×#465	C₂²	semidirect
71. C₅₃×#465	C₂²	semidirect
72. C₅₃×#452	C₂²	semidirect
73. C₅₃×#452	C₂²	semidirect
74. C₅₃×#451	C₂²	semidirect
75. C₅₃×#451	C₂²	semidirect
76. C₅₃×#450	C₂²	semidirect
77. C₅₃×#450	C₂²	semidirect
78. C₅₃×#448	C₂²	semidirect
79. C₅₃×#448	C₂²	semidirect
80. C₅₃×#448	C₂²	semidirect
81. C₅₃×#448	C₂²	semidirect
82. C₅₃×#448	C₂²	semidirect
83. C₅₃×#428	C₂²	semidirect
84. C₅₃×#427	C₂²	semidirect
85. C₅₃×#419	C₂²	semidirect
86. C₅₃×#418	C₂²	semidirect
87. C₅₃×#416	C₂²	semidirect
88. C₂×#103×C₅₃	C₂²	semidirect
90. C₅₃×#408	C₂²	semidirect
91. C₅₃×#407	C₂²	semidirect
92. C₅₃×#407	C₂²	semidirect
93. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
94. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
447. #60758	C₅₃	direct (N × H)
488. C₂×#536	C₂×C₅₃	semidirect
489. #3201	C₂×C₅₃	semidirect
490. #3200	C₂×C₅₃	semidirect
491. #3196	C₂×C₅₃	semidirect
492. #3193	C₂×C₅₃	semidirect
493. #3190	C₂×C₅₃	semidirect
494. #3187	C₂×C₅₃	semidirect
495. #3097	C₂×C₅₃	semidirect
496. #3094	C₂×C₅₃	semidirect
497. #3091	C₂×C₅₃	semidirect
498. #3063	C₂×C₅₃	semidirect
499. #3057	C₂×C₅₃	semidirect
500. #3009	C₂×C₅₃	semidirect
501. #3004	C₂×C₅₃	semidirect
502. C₂×#448	C₂×C₅₃	semidirect
503. #2880	C₂×C₅₃	semidirect
516. C₂³×Q₈	C₂²×C₅₃	semidirect
517. C₂×#137	C₂²×C₅₃	semidirect
518. C₂²×SD₁₆	C₂²×C₅₃	semidirect
519. C₂×#131	C₂²×C₅₃	semidirect
532. #536	C₂²×C₅₃	semidirect
533. #536	C₂²×C₅₃	semidirect
541. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
542. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
546. C₂×#117	C₂²×C₅₃	semidirect
547. #485	C₂²×C₅₃	semidirect
548. #485	C₂²×C₅₃	semidirect
549. #485	C₂²×C₅₃	semidirect
550. #484	C₂²×C₅₃	semidirect
551. #484	C₂²×C₅₃	semidirect
552. #483	C₂²×C₅₃	semidirect
553. #483	C₂²×C₅₃	semidirect
554. #482	C₂²×C₅₃	semidirect
555. #482	C₂²×C₅₃	semidirect
556. #481	C₂²×C₅₃	semidirect
557. #481	C₂²×C₅₃	semidirect
558. #480	C₂²×C₅₃	semidirect
559. #480	C₂²×C₅₃	semidirect
560. #470	C₂²×C₅₃	semidirect
561. #468	C₂²×C₅₃	semidirect
562. #468	C₂²×C₅₃	semidirect
563. #468	C₂²×C₅₃	semidirect
564. #467	C₂²×C₅₃	semidirect
565. #465	C₂²×C₅₃	semidirect
566. #465	C₂²×C₅₃	semidirect
567. #465	C₂²×C₅₃	semidirect
568. #452	C₂²×C₅₃	semidirect
569. #452	C₂²×C₅₃	semidirect
570. #451	C₂²×C₅₃	semidirect
571. #451	C₂²×C₅₃	semidirect
572. #450	C₂²×C₅₃	semidirect
573. #450	C₂²×C₅₃	semidirect
574. #448	C₂²×C₅₃	semidirect
575. #448	C₂²×C₅₃	semidirect
576. #448	C₂²×C₅₃	semidirect
577. #448	C₂²×C₅₃	semidirect
578. #448	C₂²×C₅₃	semidirect
579. #428	C₂²×C₅₃	semidirect
580. #427	C₂²×C₅₃	semidirect
581. #419	C₂²×C₅₃	semidirect
582. #418	C₂²×C₅₃	semidirect
583. #416	C₂²×C₅₃	semidirect
584. C₂×#103	C₂²×C₅₃	semidirect
586. #408	C₂²×C₅₃	semidirect
587. #407	C₂²×C₅₃	semidirect
588. #407	C₂²×C₅₃	semidirect
589. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
590. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
591. C₅₃	#60758	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×#3488	2
C₂×C₅₃×#536	2
C₅₃×#3201	2
C₅₃×#3200	2
C₅₃×#3196	2
C₅₃×#3193	2
C₅₃×#3190	2
C₅₃×#3187	2
C₅₃×#3097	2
C₅₃×#3094	2
C₅₃×#3091	2
C₅₃×#3063	2
C₅₃×#3057	2
C₅₃×#3009	2
C₅₃×#3004	2
C₂×C₅₃×#448	2
C₅₃×#2880	2
#60758	53

Subgroups — C53×#60758 #27268270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60758 #27268270