Subgroups — C₅₃×#61262 #27268774

Order 13568.

1884 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3494	C₂	1	2	yes	maximal, complemented
2	C₅₃×#3347	C₂	1	4	yes	maximal, complemented
3	C₅₃×#3345	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3341	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3339	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3339	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3334	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3096	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3094	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3081	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
21	C₅₃×#555	C₂²	1	4	yes	complemented
22	C₅₃×#553	C₂²	1	4	yes	complemented
23	C₅₃×#553	C₂²	1	4	yes	complemented
24	C₅₃×#551	—	2	4	no	—
25	C₅₃×#547	C₂²	1	4	yes	complemented
26	C₅₃×#546	—	2	4	no	—
27	C₅₃×#544	C₂²	1	2	yes	—
28	C₅₃×#542	—	2	2	no	—
29	C₅₃×#540	—	2	2	no	—
30	C₅₃×#535	C₂²	1	2	yes	—
31	C₅₃×#532	—	2	2	no	—
32	C₅₃×#529	—	2	2	no	—
33	C₅₃×#525	C₂²	1	1	yes	characteristic
34	C₂×#121×C₅₃	C₂²	1	2	yes	—
35	C₅₃×#520	C₂²	1	2	yes	—
36	C₅₃×#518	C₂²	1	2	yes	—
37	C₂×#117×C₅₃	C₂²	1	2	yes	—
38	C₅₃×#501	C₂²	1	4	yes	complemented
39	C₅₃×#500	C₂²	1	2	yes	complemented
40	C₅₃×#499	C₂²	1	2	yes	complemented
41	C₅₃×#482	C₂²	1	4	yes	complemented
42	C₅₃×#482	C₂²	1	4	yes	complemented
43	C₅₃×#482	C₂²	1	4	yes	complemented
44	C₅₃×#482	C₂²	1	4	yes	complemented
45	C₅₃×#481	C₂²	1	4	yes	complemented
46	C₅₃×#481	C₂²	1	4	yes	complemented
47	C₅₃×#480	C₂²	1	4	yes	complemented
48	C₅₃×#480	C₂²	1	4	yes	complemented
49	C₅₃×#478	C₂²	1	4	yes	complemented
50	C₅₃×#478	C₂²	1	4	yes	complemented
51	C₅₃×#476	C₂²	1	4	yes	complemented
52	C₅₃×#474	C₂²	1	4	yes	complemented
53	C₅₃×#469	C₂²	1	4	yes	complemented
54	C₅₃×#466	C₂²	1	2	yes	—
55	C₅₃×#466	C₂²	1	2	yes	—
56	C₅₃×#466	C₂²	1	2	yes	—
57	C₅₃×#466	C₂²	1	2	yes	—
58	C₅₃×#466	C₂²	1	2	yes	complemented
59	C₅₃×#466	C₂²	1	2	yes	complemented
60	C₅₃×#442	C₂²	1	4	yes	complemented
61	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
62	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
63	C₅₃×#435	C₂²	1	2	yes	complemented
64	C₅₃×#435	C₂²	1	2	yes	complemented
65	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
66	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
67	C₅₃×#428	C₂²	1	2	yes	—
68	C₅₃×#428	C₂²	1	2	yes	—
69	C₅₃×#428	C₂²	1	4	yes	complemented
70	C₅₃×#427	C₂²	1	1	yes	characteristic
71	C₅₃×#427	C₂²	1	1	yes	characteristic
72	C₅₃×#427	C₂²	1	2	yes	—
73	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
74	C₅₃×#427	C₂²	1	2	yes	complemented
75	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#427	C₂²	1	2	yes	complemented
77	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic
78	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
79	C₂×#107×C₅₃	C₂²	1	2	yes	complemented
80	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×#106×C₅₃	C₂²	1	2	yes	complemented
82	C₅₃×#424	C₂²	1	1	yes	characteristic
83	C₅₃×#418	C₂²	1	2	yes	—
84	C₅₃×#418	C₂²	1	2	yes	—
85	C₂×#102×C₅₃	C₂²	1	2	yes	—
86	C₅₃×#408	C₂²	1	1	yes	characteristic
87	C₅₃×#407	C₂²	1	1	yes	characteristic
88	C₅₃×#405	C₂²	1	1	yes	characteristic
89	C₂×#41×C₅₃	—	2	4	no	—
90	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₅₃	—	2	2	no	—
92	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
94	C₂×D₈×C₅₃	—	2	4	no	—
95	C₂×D₈×C₅₃	C₂³	1	2	yes	—
96	C₂×D₈×C₅₃	C₂³	1	2	yes	—
97	#131×C₅₃	—	2	4	no	—
98	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
99	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
100	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₅₃	—	2	4	no	—
102	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
109	C₄⋊Q₈×C₅₃	—	2	2	no	—
110	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
111	#127×C₅₃	—	2	2	no	—
112	#126×C₅₃	—	2	4	no	—
113	#126×C₅₃	—	2	4	no	—
114	#125×C₅₃	—	2	2	no	—
115	#125×C₅₃	C₂³	1	4	yes	—
116	#124×C₅₃	—	2	4	no	—
117	#124×C₅₃	—	2	4	no	—
118	#124×C₅₃	—	2	2	no	—
119	#123×C₅₃	—	2	4	no	—
120	#123×C₅₃	—	2	4	no	—
121	#123×C₅₃	—	2	4	no	—
122	#123×C₅₃	—	2	4	no	—
123	#123×C₅₃	D₄	1	2	yes	—
124	C₂²⋊Q₈×C₅₃	—	2	4	no	—
125	C₂²⋊Q₈×C₅₃	—	2	4	no	—
126	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
127	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
128	#121×C₅₃	—	2	4	no	—
129	#121×C₅₃	—	2	4	no	—
130	#121×C₅₃	—	2	4	no	—
131	#121×C₅₃	—	2	2	no	—
132	#121×C₅₃	—	2	2	no	—
133	#121×C₅₃	D₄	1	1	yes	characteristic
134	#121×C₅₃	D₄	1	1	yes	characteristic
135	#121×C₅₃	C₂³	1	4	yes	—
136	#121×C₅₃	C₂³	1	4	yes	—
137	#121×C₅₃	C₂³	1	4	yes	—
138	#121×C₅₃	C₂³	1	4	yes	—
139	#120×C₅₃	—	2	4	no	—
140	#120×C₅₃	D₄	1	2	yes	—
141	C₄×Q₈×C₅₃	—	2	2	no	—
142	C₄×D₄×C₅₃	—	2	2	no	—
143	C₄×D₄×C₅₃	—	2	2	no	—
144	C₄×D₄×C₅₃	—	2	4	no	—
145	C₄×D₄×C₅₃	—	2	4	no	—
146	C₄×D₄×C₅₃	—	2	2	no	—
147	C₄×D₄×C₅₃	—	2	4	no	—
148	C₄×D₄×C₅₃	C₂³	1	4	yes	—
149	C₄×D₄×C₅₃	C₂³	1	4	yes	—
150	C₄×D₄×C₅₃	C₂³	1	2	yes	—
151	C₄×D₄×C₅₃	C₂³	1	2	yes	—
152	#117×C₅₃	—	2	4	no	—
153	#117×C₅₃	—	2	2	no	—
154	#117×C₅₃	—	2	2	no	—
155	#117×C₅₃	C₂³	1	2	yes	—
156	#117×C₅₃	C₂³	1	2	yes	—
157	#117×C₅₃	C₂³	1	2	yes	—
158	#117×C₅₃	C₂³	1	2	yes	—
159	#117×C₅₃	C₂³	1	4	yes	—
160	#117×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
165	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
166	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
167	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
168	C₂×C₄²×C₅₃	—	2	2	no	—
169	#107×C₅₃	C₂³	1	1	yes	characteristic
170	#107×C₅₃	C₂³	1	2	yes	—
171	#107×C₅₃	C₂³	1	1	yes	characteristic
172	#107×C₅₃	C₂³	1	4	yes	—
173	#107×C₅₃	C₂³	1	2	yes	—
174	#107×C₅₃	C₂³	1	1	yes	characteristic
175	#107×C₅₃	C₂³	1	1	yes	characteristic
176	#107×C₅₃	C₂³	1	2	yes	—
177	#107×C₅₃	C₂³	1	2	yes	—
178	#107×C₅₃	C₂³	1	4	yes	—
179	#106×C₅₃	C₂³	1	4	yes	—
180	#106×C₅₃	C₂³	1	2	yes	—
181	#106×C₅₃	C₂³	1	2	yes	—
182	#106×C₅₃	C₂³	1	2	yes	—
183	#106×C₅₃	C₂³	1	2	yes	—
184	#106×C₅₃	C₂³	1	4	yes	—
185	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
186	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
187	#102×C₅₃	C₂³	1	4	yes	—
188	#102×C₅₃	C₂³	1	4	yes	—
189	#102×C₅₃	C₂³	1	4	yes	—
190	#102×C₅₃	C₂³	1	4	yes	—
191	#102×C₅₃	C₂³	1	4	yes	—
192	#102×C₅₃	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
194	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
195	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
196	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
197	#97×C₅₃	C₂³	1	2	yes	—
198	C₄×C₈×C₅₃	C₂³	1	2	yes	—
199	C₂⁴×C₅₃	—	2	2	no	—
200	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
201	#41×C₅₃	—	2	2	no	—
202	#41×C₅₃	—	2	2	no	—
203	#41×C₅₃	—	8	8	no	—
204	C₂×Q₈×C₅₃	—	2	4	no	—
205	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
206	C₂×D₄×C₅₃	—	2	4	no	—
207	C₂×D₄×C₅₃	—	2	4	no	—
208	C₂×D₄×C₅₃	—	2	4	no	—
209	C₂×D₄×C₅₃	—	2	4	no	—
210	C₂×D₄×C₅₃	—	2	2	no	—
211	C₂×D₄×C₅₃	—	2	4	no	—
212	C₂×D₄×C₅₃	—	2	4	no	—
213	C₂×D₄×C₅₃	—	8	4	no	—
214	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
217	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
218	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₅₃	—	2	2	no	—
220	C₂²×C₄×C₅₃	—	2	2	no	—
221	C₂²×C₄×C₅₃	—	2	2	no	—
222	C₂²×C₄×C₅₃	—	2	2	no	—
223	C₂²×C₄×C₅₃	—	2	2	no	—
224	C₂²×C₄×C₅₃	—	2	4	no	—
225	C₂²×C₄×C₅₃	—	2	4	no	—
226	C₂²×C₄×C₅₃	—	2	4	no	—
227	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
234	D₈×C₅₃	—	2	4	no	—
235	D₈×C₅₃	—	2	4	no	—
236	M₁₆×C₅₃	—	2	2	no	—
237	M₁₆×C₅₃	—	2	2	no	—
238	M₁₆×C₅₃	—	2	4	no	—
239	C₂×C₈×C₅₃	—	2	2	no	—
240	C₂×C₈×C₅₃	—	2	2	no	—
241	C₂×C₈×C₅₃	—	2	2	no	—
242	C₂×C₈×C₅₃	—	2	2	no	—
243	C₂×C₈×C₅₃	—	2	2	no	—
244	C₂×C₈×C₅₃	—	2	4	no	—
245	C₂×C₈×C₅₃	#41	1	4	yes	complemented
246	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
247	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
249	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
252	C₄⋊C₄×C₅₃	—	2	2	no	—
253	C₄⋊C₄×C₅₃	—	2	2	no	—
254	C₄⋊C₄×C₅₃	—	2	2	no	—
255	C₄⋊C₄×C₅₃	—	2	4	no	—
256	C₄⋊C₄×C₅₃	—	2	4	no	—
257	C₄⋊C₄×C₅₃	—	2	4	no	—
258	C₄⋊C₄×C₅₃	—	2	4	no	—
259	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
261	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
262	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
267	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
268	C₂²⋊C₄×C₅₃	—	2	2	no	—
269	C₂²⋊C₄×C₅₃	—	2	2	no	—
270	C₂²⋊C₄×C₅₃	—	2	2	no	—
271	C₂²⋊C₄×C₅₃	—	2	2	no	—
272	C₂²⋊C₄×C₅₃	—	2	4	no	—
273	C₂²⋊C₄×C₅₃	—	2	4	no	—
274	C₂²⋊C₄×C₅₃	—	2	4	no	—
275	C₂²⋊C₄×C₅₃	—	2	4	no	—
276	C₂²⋊C₄×C₅₃	—	2	4	no	—
277	C₂²⋊C₄×C₅₃	—	2	4	no	—
278	C₂²⋊C₄×C₅₃	—	2	4	no	—
279	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
280	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
281	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
282	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
284	C₄²×C₅₃	—	2	2	no	—
285	C₄²×C₅₃	—	2	2	no	—
286	C₄²×C₅₃	—	2	2	no	—
287	C₄²×C₅₃	—	2	2	no	—
288	C₄²×C₅₃	—	2	4	no	—
289	C₄²×C₅₃	C₂⁴	1	2	yes	—
290	C₂³×C₅₃	—	2	2	no	—
291	C₂³×C₅₃	—	2	2	no	—
292	C₂³×C₅₃	—	2	4	no	—
293	C₂³×C₅₃	—	4	1	no	—
294	C₂³×C₅₃	—	4	4	no	—
295	C₂³×C₅₃	—	8	2	no	—
296	C₂³×C₅₃	—	8	2	no	—
297	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
298	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
299	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
300	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
301	Q₈×C₅₃	—	2	2	no	—
302	Q₈×C₅₃	—	8	4	no	—
303	D₄×C₅₃	—	2	4	no	—
304	D₄×C₅₃	—	2	4	no	—
305	D₄×C₅₃	—	2	2	no	—
306	D₄×C₅₃	—	2	4	no	—
307	D₄×C₅₃	—	2	4	no	—
308	D₄×C₅₃	—	4	2	no	—
309	D₄×C₅₃	—	4	8	no	—
310	D₄×C₅₃	—	4	4	no	—
311	D₄×C₅₃	—	8	4	no	—
312	D₄×C₅₃	—	8	4	no	—
313	D₄×C₅₃	—	8	4	no	—
314	C₂×C₄×C₅₃	—	2	2	no	—
315	C₂×C₄×C₅₃	—	2	2	no	—
316	C₂×C₄×C₅₃	—	2	2	no	—
317	C₂×C₄×C₅₃	—	2	1	no	—
318	C₂×C₄×C₅₃	—	2	1	no	—
319	C₂×C₄×C₅₃	—	2	2	no	—
320	C₂×C₄×C₅₃	—	2	1	no	—
321	C₂×C₄×C₅₃	—	2	1	no	—
322	C₂×C₄×C₅₃	—	2	2	no	—
323	C₂×C₄×C₅₃	—	2	2	no	—
324	C₂×C₄×C₅₃	—	2	2	no	—
325	C₂×C₄×C₅₃	—	2	4	no	—
326	C₂×C₄×C₅₃	—	2	2	no	—
327	C₂×C₄×C₅₃	—	2	2	no	—
328	C₂×C₄×C₅₃	—	4	4	no	—
329	C₂×C₄×C₅₃	—	8	4	no	—
330	C₂×C₄×C₅₃	—	8	4	no	—
331	C₂×C₄×C₅₃	—	8	2	no	—
332	C₂×C₄×C₅₃	—	8	2	no	—
333	C₂×C₄×C₅₃	—	8	4	no	—
334	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
341	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
342	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
343	C₈×C₅₃	—	2	1	no	—
344	C₈×C₅₃	—	2	1	no	—
345	C₈×C₅₃	—	2	2	no	—
346	C₈×C₅₃	—	2	2	no	—
347	C₈×C₅₃	C₂×#41	1	2	yes	—
348	C₈×C₅₃	C₂×#41	1	2	yes	—
349	#61262	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
350	C₂²×C₅₃	—	2	1	no	—
351	C₂²×C₅₃	—	2	1	no	—
352	C₂²×C₅₃	—	2	1	no	—
353	C₂²×C₅₃	—	2	1	no	—
354	C₂²×C₅₃	—	2	1	no	—
355	C₂²×C₅₃	—	2	2	no	—
356	C₂²×C₅₃	—	2	1	no	—
357	C₂²×C₅₃	—	2	2	no	—
358	C₂²×C₅₃	—	2	2	no	—
359	C₂²×C₅₃	—	2	1	no	—
360	C₂²×C₅₃	—	4	4	no	—
361	C₂²×C₅₃	—	4	4	no	—
362	C₂²×C₅₃	—	4	4	no	—
363	C₂²×C₅₃	—	4	4	no	—
364	C₂²×C₅₃	—	16	4	no	—
365	C₂²×C₅₃	#547	1	2	yes	—
366	C₂²×C₅₃	#576	1	2	yes	—
367	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
368	C₄×C₅₃	—	2	2	no	—
369	C₄×C₅₃	—	2	1	no	—
370	C₄×C₅₃	—	2	1	no	—
371	C₄×C₅₃	—	2	2	no	—
372	C₄×C₅₃	—	2	2	no	—
373	C₄×C₅₃	—	4	2	no	—
374	C₄×C₅₃	—	4	2	no	—
375	C₄×C₅₃	—	4	2	no	—
376	C₄×C₅₃	—	4	2	no	—
377	C₄×C₅₃	—	4	4	no	—
378	C₄×C₅₃	#547	1	2	yes	—
379	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
380	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
381	#3494	C₂×C₅₃	1	2	yes	complemented
382	#3347	C₂×C₅₃	1	4	yes	complemented
383	#3345	C₂×C₅₃	1	4	yes	complemented
384	#3341	C₂×C₅₃	1	2	yes	complemented
385	#3339	C₂×C₅₃	1	2	yes	complemented
386	#3339	C₂×C₅₃	1	2	yes	complemented
387	#3334	C₂×C₅₃	1	2	yes	complemented
388	#3164	C₂×C₅₃	1	1	yes	characteristic, complemented
389	#3096	C₂×C₅₃	1	2	yes	complemented
390	#3094	C₂×C₅₃	1	2	yes	complemented
391	#3081	C₂×C₅₃	1	2	yes	complemented
392	#3058	C₂×C₅₃	1	1	yes	characteristic, complemented
393	C₂×#466	C₂×C₅₃	1	1	yes	characteristic, complemented
394	#2948	C₂×C₅₃	1	1	yes	characteristic, complemented
395	#2929	C₂×C₅₃	1	1	yes	characteristic, complemented
396	#2913	C₂×C₅₃	1	1	yes	characteristic, complemented
397	C₂×#427	C₂×C₅₃	1	1	yes	characteristic, complemented
398	C₂×C₅₃	—	2	2	no	—
399	C₂×C₅₃	—	2	2	no	—
400	C₂×C₅₃	—	4	2	no	—
401	C₂×C₅₃	—	4	1	no	—
402	C₂×C₅₃	—	8	4	no	—
403	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
404	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
405	C₂×C₅₃	#3584	1	1	yes	characteristic
406	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
407	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
408	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
409	#555	C₂²×C₅₃	1	4	yes	complemented
410	#553	C₂²×C₅₃	1	4	yes	complemented
411	#553	C₂²×C₅₃	1	4	yes	complemented
412	#551	—	2	4	no	—
413	#547	C₂²×C₅₃	1	4	yes	complemented
414	#546	—	2	4	no	—
415	#544	C₂²×C₅₃	1	2	yes	—
416	#542	—	2	2	no	—
417	#540	—	2	2	no	—
418	#535	C₂²×C₅₃	1	2	yes	—
419	#532	—	2	2	no	—
420	#529	—	2	2	no	—
421	#525	C₂²×C₅₃	1	1	yes	characteristic
422	C₂×#121	C₂²×C₅₃	1	2	yes	—
423	#520	C₂²×C₅₃	1	2	yes	—
424	#518	C₂²×C₅₃	1	2	yes	—
425	C₂×#117	C₂²×C₅₃	1	2	yes	—
426	#501	C₂²×C₅₃	1	4	yes	complemented
427	#500	C₂²×C₅₃	1	2	yes	complemented
428	#499	C₂²×C₅₃	1	2	yes	complemented
429	#482	C₂²×C₅₃	1	4	yes	complemented
430	#482	C₂²×C₅₃	1	4	yes	complemented
431	#482	C₂²×C₅₃	1	4	yes	complemented
432	#482	C₂²×C₅₃	1	4	yes	complemented
433	#481	C₂²×C₅₃	1	4	yes	complemented
434	#481	C₂²×C₅₃	1	4	yes	complemented
435	#480	C₂²×C₅₃	1	4	yes	complemented
436	#480	C₂²×C₅₃	1	4	yes	complemented
437	#478	C₂²×C₅₃	1	4	yes	complemented
438	#478	C₂²×C₅₃	1	4	yes	complemented
439	#476	C₂²×C₅₃	1	4	yes	complemented
440	#474	C₂²×C₅₃	1	4	yes	complemented
441	#469	C₂²×C₅₃	1	4	yes	complemented
442	#466	C₂²×C₅₃	1	2	yes	—
443	#466	C₂²×C₅₃	1	2	yes	—
444	#466	C₂²×C₅₃	1	2	yes	—
445	#466	C₂²×C₅₃	1	2	yes	—
446	#466	C₂²×C₅₃	1	2	yes	complemented
447	#466	C₂²×C₅₃	1	2	yes	complemented
448	#442	C₂²×C₅₃	1	4	yes	complemented
449	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
450	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
451	#435	C₂²×C₅₃	1	2	yes	complemented
452	#435	C₂²×C₅₃	1	2	yes	complemented
453	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
454	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
455	#428	C₂²×C₅₃	1	2	yes	—
456	#428	C₂²×C₅₃	1	2	yes	—
457	#428	C₂²×C₅₃	1	4	yes	complemented
458	#427	C₂²×C₅₃	1	2	yes	—
459	#427	C₂²×C₅₃	1	1	yes	characteristic
460	#427	C₂²×C₅₃	1	1	yes	characteristic
461	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
462	#427	C₂²×C₅₃	1	2	yes	complemented
463	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
464	#427	C₂²×C₅₃	1	2	yes	complemented
465	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic
466	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
467	C₂×#107	C₂²×C₅₃	1	2	yes	complemented
468	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
469	C₂×#106	C₂²×C₅₃	1	2	yes	complemented
470	#424	C₂²×C₅₃	1	1	yes	characteristic
471	#418	C₂²×C₅₃	1	2	yes	—
472	#418	C₂²×C₅₃	1	2	yes	—
473	C₂×#102	C₂²×C₅₃	1	2	yes	—
474	#408	C₂²×C₅₃	1	1	yes	characteristic
475	#407	C₂²×C₅₃	1	1	yes	characteristic
476	#405	C₂²×C₅₃	1	1	yes	characteristic
477	C₅₃	#61262	1	1	yes	characteristic, direct product factor, Sylow
478	C₂×#41	—	2	4	no	—
479	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
480	C₂²×D₄	—	2	2	no	—
481	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
482	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
483	C₂×D₈	—	2	4	no	—
484	C₂×D₈	C₂³×C₅₃	1	2	yes	—
485	C₂×D₈	C₂³×C₅₃	1	2	yes	—
486	#131	—	2	4	no	—
487	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
488	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
489	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
490	C₂²×C₈	—	2	4	no	—
491	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
497	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
498	C₄⋊Q₈	—	2	2	no	—
499	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
500	#127	—	2	2	no	—
501	#126	—	2	4	no	—
502	#126	—	2	4	no	—
503	#125	—	2	2	no	—
504	#125	C₂³×C₅₃	1	4	yes	—
505	#124	—	2	2	no	—
506	#124	—	2	4	no	—
507	#124	—	2	4	no	—
508	#123	—	2	4	no	—
509	#123	—	2	4	no	—
510	#123	—	2	4	no	—
511	#123	—	2	4	no	—
512	#123	D₄×C₅₃	1	2	yes	—
513	C₂²⋊Q₈	—	2	4	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
516	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
517	#121	—	2	4	no	—
518	#121	—	2	4	no	—
519	#121	—	2	4	no	—
520	#121	—	2	2	no	—
521	#121	—	2	2	no	—
522	#121	D₄×C₅₃	1	1	yes	characteristic
523	#121	D₄×C₅₃	1	1	yes	characteristic
524	#121	C₂³×C₅₃	1	4	yes	—
525	#121	C₂³×C₅₃	1	4	yes	—
526	#121	C₂³×C₅₃	1	4	yes	—
527	#121	C₂³×C₅₃	1	4	yes	—
528	#120	—	2	4	no	—
529	#120	D₄×C₅₃	1	2	yes	—
530	C₄×Q₈	—	2	2	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	4	no	—
533	C₄×D₄	—	2	2	no	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	—	2	4	no	—
537	C₄×D₄	C₂³×C₅₃	1	4	yes	—
538	C₄×D₄	C₂³×C₅₃	1	4	yes	—
539	C₄×D₄	C₂³×C₅₃	1	2	yes	—
540	C₄×D₄	C₂³×C₅₃	1	2	yes	—
541	#117	—	2	2	no	—
542	#117	—	2	2	no	—
543	#117	—	2	4	no	—
544	#117	C₂³×C₅₃	1	2	yes	—
545	#117	C₂³×C₅₃	1	2	yes	—
546	#117	C₂³×C₅₃	1	2	yes	—
547	#117	C₂³×C₅₃	1	2	yes	—
548	#117	C₂³×C₅₃	1	4	yes	—
549	#117	C₂³×C₅₃	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
554	C₂×C₂²⋊C₄	—	2	2	no	—
555	C₂×C₂²⋊C₄	—	2	2	no	—
556	C₂×C₂²⋊C₄	—	2	4	no	—
557	C₂×C₄²	—	2	2	no	—
558	#107	C₂³×C₅₃	1	2	yes	—
559	#107	C₂³×C₅₃	1	2	yes	—
560	#107	C₂³×C₅₃	1	1	yes	characteristic
561	#107	C₂³×C₅₃	1	1	yes	characteristic
562	#107	C₂³×C₅₃	1	1	yes	characteristic
563	#107	C₂³×C₅₃	1	1	yes	characteristic
564	#107	C₂³×C₅₃	1	2	yes	—
565	#107	C₂³×C₅₃	1	2	yes	—
566	#107	C₂³×C₅₃	1	4	yes	—
567	#107	C₂³×C₅₃	1	4	yes	—
568	#106	C₂³×C₅₃	1	2	yes	—
569	#106	C₂³×C₅₃	1	2	yes	—
570	#106	C₂³×C₅₃	1	2	yes	—
571	#106	C₂³×C₅₃	1	2	yes	—
572	#106	C₂³×C₅₃	1	4	yes	—
573	#106	C₂³×C₅₃	1	4	yes	—
574	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
575	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
576	#102	C₂³×C₅₃	1	4	yes	—
577	#102	C₂³×C₅₃	1	4	yes	—
578	#102	C₂³×C₅₃	1	4	yes	—
579	#102	C₂³×C₅₃	1	4	yes	—
580	#102	C₂³×C₅₃	1	4	yes	—
581	#102	C₂³×C₅₃	1	4	yes	—
582	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
583	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
584	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
585	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
586	#97	C₂³×C₅₃	1	2	yes	—
587	C₄×C₈	C₂³×C₅₃	1	2	yes	—
588	C₂⁴	—	2	2	no	—
589	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
590	#41	—	2	2	no	—
591	#41	—	2	2	no	—
592	#41	—	8	8	no	—
593	C₂×Q₈	—	2	4	no	—
594	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	8	4	no	—
603	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
604	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
605	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
606	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
607	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
623	D₈	—	2	4	no	—
624	D₈	—	2	4	no	—
625	M₁₆	—	2	2	no	—
626	M₁₆	—	2	2	no	—
627	M₁₆	—	2	4	no	—
628	C₂×C₈	—	2	2	no	—
629	C₂×C₈	—	2	2	no	—
630	C₂×C₈	—	2	2	no	—
631	C₂×C₈	—	2	2	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	4	no	—
634	C₂×C₈	#41×C₅₃	1	4	yes	complemented
635	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
636	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
637	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
638	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
639	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
640	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
649	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
650	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
651	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
655	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
656	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
669	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
670	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
671	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
672	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
673	C₄²	—	2	2	no	—
674	C₄²	—	2	2	no	—
675	C₄²	—	2	2	no	—
676	C₄²	—	2	2	no	—
677	C₄²	—	2	4	no	—
678	C₄²	C₂⁴×C₅₃	1	2	yes	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	4	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	4	no	—
684	C₂³	—	8	2	no	—
685	C₂³	—	8	2	no	—
686	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
687	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
688	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
689	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
690	Q₈	—	2	2	no	—
691	Q₈	—	8	4	no	—
692	D₄	—	2	4	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	4	no	—
696	D₄	—	2	4	no	—
697	D₄	—	4	2	no	—
698	D₄	—	4	8	no	—
699	D₄	—	4	4	no	—
700	D₄	—	8	4	no	—
701	D₄	—	8	4	no	—
702	D₄	—	8	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	8	4	no	—
719	C₂×C₄	—	8	4	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	—	8	4	no	—
723	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
724	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
729	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
730	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
731	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
732	C₈	—	2	1	no	—
733	C₈	—	2	1	no	—
734	C₈	—	2	2	no	—
735	C₈	—	2	2	no	—
736	C₈	C₂×#41×C₅₃	1	2	yes	—
737	C₈	C₂×#41×C₅₃	1	2	yes	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	16	4	no	—
753	C₂²	C₅₃×#547	1	2	yes	—
754	C₂²	C₅₃×#576	1	2	yes	—
755	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	4	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	C₅₃×#547	1	2	yes	—
767	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
768	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
769	C₂	—	2	2	no	—
770	C₂	—	2	2	no	—
771	C₂	—	4	1	no	—
772	C₂	—	4	2	no	—
773	C₂	—	8	4	no	—
774	C₂	C₂×C₅₃×#547	1	1	yes	characteristic
775	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
776	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3494	C₂	semidirect
2. C₅₃×#3347	C₂	semidirect
3. C₅₃×#3345	C₂	semidirect
4. C₅₃×#3341	C₂	semidirect
5. C₅₃×#3339	C₂	semidirect
6. C₅₃×#3339	C₂	semidirect
7. C₅₃×#3334	C₂	semidirect
8. C₅₃×#3164	C₂	semidirect
9. C₅₃×#3096	C₂	semidirect
10. C₅₃×#3094	C₂	semidirect
11. C₅₃×#3081	C₂	semidirect
12. C₅₃×#3058	C₂	semidirect
13. C₂×C₅₃×#466	C₂	semidirect
14. C₅₃×#2948	C₂	semidirect
15. C₅₃×#2929	C₂	semidirect
16. C₅₃×#2913	C₂	semidirect
17. C₂×C₅₃×#427	C₂	semidirect
21. C₅₃×#555	C₂²	semidirect
22. C₅₃×#553	C₂²	semidirect
23. C₅₃×#553	C₂²	semidirect
25. C₅₃×#547	C₂²	semidirect
38. C₅₃×#501	C₂²	semidirect
39. C₅₃×#500	C₂²	semidirect
40. C₅₃×#499	C₂²	semidirect
41. C₅₃×#482	C₂²	semidirect
42. C₅₃×#482	C₂²	semidirect
43. C₅₃×#482	C₂²	semidirect
44. C₅₃×#482	C₂²	semidirect
45. C₅₃×#481	C₂²	semidirect
46. C₅₃×#481	C₂²	semidirect
47. C₅₃×#480	C₂²	semidirect
48. C₅₃×#480	C₂²	semidirect
49. C₅₃×#478	C₂²	semidirect
50. C₅₃×#478	C₂²	semidirect
51. C₅₃×#476	C₂²	semidirect
52. C₅₃×#474	C₂²	semidirect
53. C₅₃×#469	C₂²	semidirect
58. C₅₃×#466	C₂²	semidirect
59. C₅₃×#466	C₂²	semidirect
60. C₅₃×#442	C₂²	semidirect
61. C₄×D₈×C₅₃	C₂²	semidirect
62. C₄×D₈×C₅₃	C₂²	semidirect
63. C₅₃×#435	C₂²	semidirect
64. C₅₃×#435	C₂²	semidirect
65. C₈×D₄×C₅₃	C₂²	semidirect
66. C₈×D₄×C₅₃	C₂²	semidirect
69. C₅₃×#428	C₂²	semidirect
73. C₅₃×#427	C₂²	semidirect
74. C₅₃×#427	C₂²	semidirect
75. C₅₃×#427	C₂²	semidirect
76. C₅₃×#427	C₂²	semidirect
78. C₂×#107×C₅₃	C₂²	semidirect
79. C₂×#107×C₅₃	C₂²	semidirect
80. C₂×#107×C₅₃	C₂²	semidirect
81. C₂×#106×C₅₃	C₂²	semidirect
245. C₂×C₈×C₅₃	#41	semidirect
349. #61262	C₅₃	direct (N × H)
381. #3494	C₂×C₅₃	semidirect
382. #3347	C₂×C₅₃	semidirect
383. #3345	C₂×C₅₃	semidirect
384. #3341	C₂×C₅₃	semidirect
385. #3339	C₂×C₅₃	semidirect
386. #3339	C₂×C₅₃	semidirect
387. #3334	C₂×C₅₃	semidirect
388. #3164	C₂×C₅₃	semidirect
389. #3096	C₂×C₅₃	semidirect
390. #3094	C₂×C₅₃	semidirect
391. #3081	C₂×C₅₃	semidirect
392. #3058	C₂×C₅₃	semidirect
393. C₂×#466	C₂×C₅₃	semidirect
394. #2948	C₂×C₅₃	semidirect
395. #2929	C₂×C₅₃	semidirect
396. #2913	C₂×C₅₃	semidirect
397. C₂×#427	C₂×C₅₃	semidirect
409. #555	C₂²×C₅₃	semidirect
410. #553	C₂²×C₅₃	semidirect
411. #553	C₂²×C₅₃	semidirect
413. #547	C₂²×C₅₃	semidirect
426. #501	C₂²×C₅₃	semidirect
427. #500	C₂²×C₅₃	semidirect
428. #499	C₂²×C₅₃	semidirect
429. #482	C₂²×C₅₃	semidirect
430. #482	C₂²×C₅₃	semidirect
431. #482	C₂²×C₅₃	semidirect
432. #482	C₂²×C₅₃	semidirect
433. #481	C₂²×C₅₃	semidirect
434. #481	C₂²×C₅₃	semidirect
435. #480	C₂²×C₅₃	semidirect
436. #480	C₂²×C₅₃	semidirect
437. #478	C₂²×C₅₃	semidirect
438. #478	C₂²×C₅₃	semidirect
439. #476	C₂²×C₅₃	semidirect
440. #474	C₂²×C₅₃	semidirect
441. #469	C₂²×C₅₃	semidirect
446. #466	C₂²×C₅₃	semidirect
447. #466	C₂²×C₅₃	semidirect
448. #442	C₂²×C₅₃	semidirect
449. C₄×D₈	C₂²×C₅₃	semidirect
450. C₄×D₈	C₂²×C₅₃	semidirect
451. #435	C₂²×C₅₃	semidirect
452. #435	C₂²×C₅₃	semidirect
453. C₈×D₄	C₂²×C₅₃	semidirect
454. C₈×D₄	C₂²×C₅₃	semidirect
457. #428	C₂²×C₅₃	semidirect
461. #427	C₂²×C₅₃	semidirect
462. #427	C₂²×C₅₃	semidirect
463. #427	C₂²×C₅₃	semidirect
464. #427	C₂²×C₅₃	semidirect
466. C₂×#107	C₂²×C₅₃	semidirect
467. C₂×#107	C₂²×C₅₃	semidirect
468. C₂×#107	C₂²×C₅₃	semidirect
469. C₂×#106	C₂²×C₅₃	semidirect
477. C₅₃	#61262	direct (N × H)
634. C₂×C₈	#41×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3494	2
C₅₃×#3347	2
C₅₃×#3345	2
C₅₃×#3341	2
C₅₃×#3339	2
C₅₃×#3334	2
C₅₃×#3164	2
C₅₃×#3096	2
C₅₃×#3094	2
C₅₃×#3081	2
C₅₃×#3058	2
C₂×C₅₃×#466	2
C₅₃×#2948	2
C₅₃×#2929	2
C₅₃×#2913	2
C₂×C₅₃×#427	2
#61262	53

Subgroups — C53×#61262 #27268774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61262 #27268774