Subgroups — C₅₃×#61595 #27269107

Order 13568.

2116 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3330	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3315	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3302	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3283	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3276	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3269	C₂	1	4	yes	maximal, complemented
9	C₅₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3196	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3189	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3007	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3002	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₅₃	C₂²	1	2	yes	—
19	C₂×#137×C₅₃	C₂²	1	4	yes	complemented
20	C₂×#135×C₅₃	C₂²	1	4	yes	complemented
21	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
22	C₅₃×#554	—	2	1	no	—
23	C₅₃×#552	C₂²	1	2	yes	complemented
24	C₅₃×#551	—	2	2	no	—
25	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₅₃×#548	C₂²	1	2	yes	complemented
27	C₅₃×#547	—	2	1	no	—
28	C₅₃×#547	—	2	2	no	—
29	C₅₃×#547	—	2	1	no	—
30	C₅₃×#547	C₂²	1	4	yes	—
31	C₅₃×#547	C₂²	1	2	yes	—
32	C₅₃×#547	C₂²	1	2	yes	—
33	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
34	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
35	C₅₃×#546	—	2	1	no	—
36	C₅₃×#542	—	2	1	no	—
37	C₅₃×#539	—	2	2	no	—
38	C₅₃×#533	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
40	C₅₃×#529	C₂²	1	1	yes	characteristic
41	C₅₃×#525	C₂²	1	2	yes	—
42	C₂×#123×C₅₃	—	2	2	no	—
43	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
44	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
45	C₂×#121×C₅₃	—	2	1	no	—
46	C₅₃×#520	—	2	1	no	—
47	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₂²×C₄⋊C₄×C₅₃	—	2	1	no	—
50	C₅₃×#497	C₂²	1	2	yes	complemented
51	C₅₃×#494	C₂²	1	2	yes	complemented
52	C₅₃×#491	C₂²	1	2	yes	complemented
53	C₅₃×#487	C₂²	1	2	yes	complemented
54	C₅₃×#485	C₂²	1	4	yes	complemented
55	C₅₃×#484	C₂²	1	2	yes	—
56	C₅₃×#484	C₂²	1	1	yes	characteristic
57	C₅₃×#484	C₂²	1	4	yes	complemented
58	C₅₃×#481	C₂²	1	1	yes	characteristic
59	C₅₃×#478	C₂²	1	2	yes	complemented
60	C₅₃×#474	C₂²	1	2	yes	complemented
61	C₅₃×#470	C₂²	1	4	yes	complemented
62	C₅₃×#468	C₂²	1	4	yes	complemented
63	C₅₃×#467	C₂²	1	4	yes	complemented
64	C₅₃×#467	C₂²	1	4	yes	complemented
65	C₅₃×#463	C₂²	1	2	yes	complemented
66	C₅₃×#462	C₂²	1	4	yes	complemented
67	C₅₃×#462	C₂²	1	2	yes	complemented
68	C₅₃×#461	C₂²	1	2	yes	complemented
69	C₅₃×#461	C₂²	1	2	yes	complemented
70	C₅₃×#452	C₂²	1	4	yes	complemented
71	C₅₃×#452	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	—
75	C₅₃×#451	C₂²	1	2	yes	—
76	C₅₃×#451	C₂²	1	2	yes	—
77	C₅₃×#451	C₂²	1	4	yes	complemented
78	C₅₃×#450	C₂²	1	2	yes	—
79	C₅₃×#450	C₂²	1	1	yes	characteristic
80	C₅₃×#449	C₂²	1	4	yes	complemented
81	C₅₃×#448	C₂²	1	2	yes	—
82	C₅₃×#447	C₂²	1	1	yes	characteristic
83	C₅₃×#440	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
85	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
86	C₅₃×#436	C₂²	1	2	yes	complemented
87	C₅₃×#435	C₂²	1	4	yes	complemented
88	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
89	C₅₃×#432	C₂²	1	1	yes	characteristic
90	C₅₃×#431	C₂²	1	1	yes	characteristic
91	C₅₃×#417	C₂²	1	4	yes	complemented
92	C₅₃×#416	C₂²	1	4	yes	complemented
93	C₅₃×#407	C₂²	1	2	yes	—
94	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
95	C₂×#41×C₅₃	—	2	1	no	—
96	C₂×#41×C₅₃	—	2	2	no	—
97	C₂×#41×C₅₃	—	2	2	no	—
98	C₂×#41×C₅₃	—	4	8	no	—
99	C₂×#41×C₅₃	C₂³	1	4	yes	—
100	C₂×#41×C₅₃	C₂³	1	4	yes	—
101	C₂×#41×C₅₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
103	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
104	C₂²×D₄×C₅₃	—	2	2	no	—
105	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
106	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₅₃	—	2	1	no	—
108	C₂³×C₄×C₅₃	—	2	2	no	—
109	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
110	#137×C₅₃	—	4	8	no	—
111	#135×C₅₃	—	4	8	no	—
112	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
113	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
114	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
115	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
118	C₂×D₈×C₅₃	C₂³	1	2	yes	—
119	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
120	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
121	C₄⋊Q₈×C₅₃	—	2	1	no	—
122	C₄⋊Q₈×C₅₃	—	2	1	no	—
123	C₄⋊Q₈×C₅₃	—	2	1	no	—
124	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
125	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
126	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
127	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
128	#126×C₅₃	—	2	2	no	—
129	#126×C₅₃	—	2	2	no	—
130	#126×C₅₃	—	2	1	no	—
131	#125×C₅₃	—	2	2	no	—
132	#125×C₅₃	—	2	1	no	—
133	#125×C₅₃	C₂³	1	1	yes	characteristic
134	#124×C₅₃	—	2	2	no	—
135	#124×C₅₃	—	2	1	no	—
136	#124×C₅₃	C₂³	1	1	yes	characteristic
137	#123×C₅₃	—	2	4	no	—
138	#123×C₅₃	—	2	4	no	—
139	#123×C₅₃	—	2	4	no	—
140	#123×C₅₃	—	2	4	no	—
141	#123×C₅₃	—	2	2	no	—
142	#123×C₅₃	—	2	2	no	—
143	#123×C₅₃	—	2	2	no	—
144	#123×C₅₃	—	2	2	no	—
145	#123×C₅₃	—	2	1	no	—
146	C₂²⋊Q₈×C₅₃	—	2	2	no	—
147	C₂²⋊Q₈×C₅₃	—	2	1	no	—
148	C₂²⋊Q₈×C₅₃	—	2	2	no	—
149	C₂²⋊Q₈×C₅₃	—	2	2	no	—
150	C₂²⋊Q₈×C₅₃	—	2	2	no	—
151	C₂²⋊Q₈×C₅₃	—	2	2	no	—
152	C₂²⋊Q₈×C₅₃	—	2	2	no	—
153	C₂²⋊Q₈×C₅₃	—	2	1	no	—
154	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
155	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
156	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
157	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
158	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
159	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
160	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
161	#121×C₅₃	—	2	2	no	—
162	#121×C₅₃	—	2	2	no	—
163	#121×C₅₃	—	2	4	no	—
164	#121×C₅₃	—	2	2	no	—
165	#121×C₅₃	—	2	1	no	—
166	#121×C₅₃	C₂³	1	1	yes	characteristic
167	#121×C₅₃	C₂³	1	2	yes	—
168	#120×C₅₃	—	2	2	no	—
169	C₄×Q₈×C₅₃	—	2	1	no	—
170	C₄×Q₈×C₅₃	—	2	1	no	—
171	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
173	C₄×D₄×C₅₃	—	2	2	no	—
174	C₄×D₄×C₅₃	—	2	1	no	—
175	C₄×D₄×C₅₃	—	2	1	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	1	no	—
180	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
181	C₄×D₄×C₅₃	D₄	1	2	yes	—
182	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
183	C₄×D₄×C₅₃	C₂³	1	2	yes	—
184	C₄×D₄×C₅₃	C₂³	1	2	yes	—
185	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₅₃	C₂³	1	2	yes	—
189	#117×C₅₃	—	2	2	no	—
190	#117×C₅₃	—	2	1	no	—
191	#117×C₅₃	—	2	1	no	—
192	#117×C₅₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
194	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
195	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
196	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
197	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
198	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
199	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
200	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
201	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
207	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
208	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
209	#107×C₅₃	C₂³	1	4	yes	—
210	#107×C₅₃	C₂³	1	2	yes	—
211	#106×C₅₃	C₂³	1	2	yes	—
212	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
213	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
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	#103×C₅₃	C₂³	1	4	yes	—
220	#102×C₅₃	C₂³	1	2	yes	—
221	#102×C₅₃	C₂³	1	4	yes	—
222	#102×C₅₃	C₂³	1	2	yes	—
223	#102×C₅₃	C₂³	1	2	yes	—
224	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
225	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
228	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
229	#97×C₅₃	C₂³	1	2	yes	—
230	C₄×C₈×C₅₃	C₂³	1	2	yes	—
231	C₂⁴×C₅₃	—	2	1	no	—
232	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
233	#41×C₅₃	—	2	8	no	—
234	#41×C₅₃	—	2	8	no	—
235	#41×C₅₃	—	4	4	no	—
236	#41×C₅₃	—	4	4	no	—
237	#41×C₅₃	—	4	4	no	—
238	#41×C₅₃	—	4	4	no	—
239	#41×C₅₃	—	4	8	no	—
240	#41×C₅₃	—	4	8	no	—
241	C₂×Q₈×C₅₃	—	2	1	no	—
242	C₂×Q₈×C₅₃	—	2	2	no	—
243	C₂×Q₈×C₅₃	—	2	2	no	—
244	C₂×Q₈×C₅₃	—	4	4	no	—
245	C₂×Q₈×C₅₃	—	4	4	no	—
246	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
248	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
249	C₂×D₄×C₅₃	—	2	4	no	—
250	C₂×D₄×C₅₃	—	2	1	no	—
251	C₂×D₄×C₅₃	—	2	2	no	—
252	C₂×D₄×C₅₃	—	2	4	no	—
253	C₂×D₄×C₅₃	—	2	4	no	—
254	C₂×D₄×C₅₃	—	2	2	no	—
255	C₂×D₄×C₅₃	—	2	1	no	—
256	C₂×D₄×C₅₃	—	4	2	no	—
257	C₂×D₄×C₅₃	—	4	8	no	—
258	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
259	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
260	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
262	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₅₃	—	2	1	no	—
264	C₂²×C₄×C₅₃	—	2	2	no	—
265	C₂²×C₄×C₅₃	—	2	2	no	—
266	C₂²×C₄×C₅₃	—	2	2	no	—
267	C₂²×C₄×C₅₃	—	2	2	no	—
268	C₂²×C₄×C₅₃	—	2	2	no	—
269	C₂²×C₄×C₅₃	—	2	4	no	—
270	C₂²×C₄×C₅₃	—	2	4	no	—
271	C₂²×C₄×C₅₃	—	2	1	no	—
272	C₂²×C₄×C₅₃	—	2	2	no	—
273	C₂²×C₄×C₅₃	—	4	4	no	—
274	C₂²×C₄×C₅₃	—	4	4	no	—
275	C₂²×C₄×C₅₃	—	4	8	no	—
276	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
279	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
280	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
284	Q₁₆×C₅₃	—	4	4	no	—
285	Q₁₆×C₅₃	—	4	4	no	—
286	Q₁₆×C₅₃	—	4	4	no	—
287	SD₁₆×C₅₃	—	2	8	no	—
288	SD₁₆×C₅₃	—	2	4	no	—
289	SD₁₆×C₅₃	—	4	4	no	—
290	D₈×C₅₃	—	2	4	no	—
291	M₁₆×C₅₃	—	4	4	no	—
292	C₂×C₈×C₅₃	—	4	4	no	—
293	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
294	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
295	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
296	C₄⋊C₄×C₅₃	—	2	2	no	—
297	C₄⋊C₄×C₅₃	—	2	2	no	—
298	C₄⋊C₄×C₅₃	—	2	4	no	—
299	C₄⋊C₄×C₅₃	—	2	4	no	—
300	C₄⋊C₄×C₅₃	—	2	1	no	—
301	C₄⋊C₄×C₅₃	—	2	2	no	—
302	C₄⋊C₄×C₅₃	—	2	1	no	—
303	C₄⋊C₄×C₅₃	—	2	2	no	—
304	C₄⋊C₄×C₅₃	—	2	2	no	—
305	C₄⋊C₄×C₅₃	—	2	2	no	—
306	C₄⋊C₄×C₅₃	—	2	2	no	—
307	C₄⋊C₄×C₅₃	—	2	1	no	—
308	C₄⋊C₄×C₅₃	—	2	2	no	—
309	C₄⋊C₄×C₅₃	—	2	1	no	—
310	C₄⋊C₄×C₅₃	—	2	1	no	—
311	C₄⋊C₄×C₅₃	—	2	1	no	—
312	C₄⋊C₄×C₅₃	—	2	2	no	—
313	C₄⋊C₄×C₅₃	—	2	1	no	—
314	C₄⋊C₄×C₅₃	—	2	2	no	—
315	C₄⋊C₄×C₅₃	—	2	1	no	—
316	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
317	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
318	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
319	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
320	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
321	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
322	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
323	C₂²⋊C₄×C₅₃	—	2	1	no	—
324	C₂²⋊C₄×C₅₃	—	2	2	no	—
325	C₂²⋊C₄×C₅₃	—	2	4	no	—
326	C₂²⋊C₄×C₅₃	—	2	4	no	—
327	C₂²⋊C₄×C₅₃	—	2	2	no	—
328	C₂²⋊C₄×C₅₃	—	2	2	no	—
329	C₂²⋊C₄×C₅₃	—	2	2	no	—
330	C₂²⋊C₄×C₅₃	—	2	2	no	—
331	C₂²⋊C₄×C₅₃	—	2	2	no	—
332	C₂²⋊C₄×C₅₃	—	2	2	no	—
333	C₂²⋊C₄×C₅₃	—	2	1	no	—
334	C₂²⋊C₄×C₅₃	—	2	1	no	—
335	C₂²⋊C₄×C₅₃	—	2	1	no	—
336	C₂²⋊C₄×C₅₃	—	2	2	no	—
337	C₂²⋊C₄×C₅₃	—	2	1	no	—
338	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
339	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
340	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
341	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
342	C₄²×C₅₃	—	2	2	no	—
343	C₄²×C₅₃	—	2	2	no	—
344	C₄²×C₅₃	—	2	1	no	—
345	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
346	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
348	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂³×C₅₃	—	2	4	no	—
350	C₂³×C₅₃	—	2	2	no	—
351	C₂³×C₅₃	—	2	4	no	—
352	C₂³×C₅₃	—	2	1	no	—
353	C₂³×C₅₃	—	4	2	no	—
354	C₂³×C₅₃	—	4	2	no	—
355	C₂³×C₅₃	—	4	2	no	—
356	C₂³×C₅₃	—	4	2	no	—
357	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
358	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
359	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
360	Q₈×C₅₃	—	2	2	no	—
361	Q₈×C₅₃	—	2	4	no	—
362	Q₈×C₅₃	—	2	4	no	—
363	Q₈×C₅₃	—	2	4	no	—
364	Q₈×C₅₃	—	4	4	no	—
365	Q₈×C₅₃	—	4	2	no	—
366	Q₈×C₅₃	—	8	2	no	—
367	D₄×C₅₃	—	2	4	no	—
368	D₄×C₅₃	—	2	2	no	—
369	D₄×C₅₃	—	2	2	no	—
370	D₄×C₅₃	—	2	2	no	—
371	D₄×C₅₃	—	2	2	no	—
372	D₄×C₅₃	—	4	2	no	—
373	D₄×C₅₃	—	4	8	no	—
374	D₄×C₅₃	—	4	8	no	—
375	D₄×C₅₃	—	4	4	no	—
376	D₄×C₅₃	—	4	2	no	—
377	D₄×C₅₃	—	8	2	no	—
378	D₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
379	C₂×C₄×C₅₃	—	2	2	no	—
380	C₂×C₄×C₅₃	—	2	2	no	—
381	C₂×C₄×C₅₃	—	2	2	no	—
382	C₂×C₄×C₅₃	—	2	4	no	—
383	C₂×C₄×C₅₃	—	2	4	no	—
384	C₂×C₄×C₅₃	—	2	4	no	—
385	C₂×C₄×C₅₃	—	2	2	no	—
386	C₂×C₄×C₅₃	—	2	1	no	—
387	C₂×C₄×C₅₃	—	2	2	no	—
388	C₂×C₄×C₅₃	—	2	1	no	—
389	C₂×C₄×C₅₃	—	2	2	no	—
390	C₂×C₄×C₅₃	—	2	1	no	—
391	C₂×C₄×C₅₃	—	4	2	no	—
392	C₂×C₄×C₅₃	—	4	2	no	—
393	C₂×C₄×C₅₃	—	4	2	no	—
394	C₂×C₄×C₅₃	—	4	8	no	—
395	C₂×C₄×C₅₃	—	4	8	no	—
396	C₂×C₄×C₅₃	—	4	4	no	—
397	C₂×C₄×C₅₃	—	4	2	no	—
398	C₂×C₄×C₅₃	—	4	4	no	—
399	C₂×C₄×C₅₃	—	4	4	no	—
400	C₂×C₄×C₅₃	—	4	4	no	—
401	C₂×C₄×C₅₃	—	4	2	no	—
402	C₂×C₄×C₅₃	—	8	2	no	—
403	C₂×C₄×C₅₃	—	8	2	no	—
404	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
412	C₈×C₅₃	—	2	2	no	—
413	C₈×C₅₃	—	2	4	no	—
414	C₈×C₅₃	—	2	2	no	—
415	#61595	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
416	C₂²×C₅₃	—	2	1	no	—
417	C₂²×C₅₃	—	2	1	no	—
418	C₂²×C₅₃	—	2	2	no	—
419	C₂²×C₅₃	—	2	2	no	—
420	C₂²×C₅₃	—	2	4	no	—
421	C₂²×C₅₃	—	2	2	no	—
422	C₂²×C₅₃	—	2	2	no	—
423	C₂²×C₅₃	—	2	2	no	—
424	C₂²×C₅₃	—	2	2	no	—
425	C₂²×C₅₃	—	4	8	no	—
426	C₂²×C₅₃	—	4	2	no	—
427	C₂²×C₅₃	—	4	2	no	—
428	C₂²×C₅₃	—	4	1	no	—
429	C₂²×C₅₃	—	4	1	no	—
430	C₂²×C₅₃	—	4	1	no	—
431	C₂²×C₅₃	—	8	4	no	—
432	C₂²×C₅₃	#578	1	2	yes	—
433	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
434	C₄×C₅₃	—	2	2	no	—
435	C₄×C₅₃	—	2	2	no	—
436	C₄×C₅₃	—	2	1	no	—
437	C₄×C₅₃	—	2	1	no	—
438	C₄×C₅₃	—	2	1	no	—
439	C₄×C₅₃	—	2	1	no	—
440	C₄×C₅₃	—	4	4	no	—
441	C₄×C₅₃	—	4	2	no	—
442	C₄×C₅₃	—	4	1	no	—
443	C₄×C₅₃	—	4	2	no	—
444	C₄×C₅₃	—	4	1	no	—
445	C₄×C₅₃	—	4	2	no	—
446	C₄×C₅₃	—	4	1	no	—
447	C₄×C₅₃	#575	1	2	yes	—
448	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
449	#3520	C₂×C₅₃	1	1	yes	characteristic, complemented
450	C₂×#547	C₂×C₅₃	1	1	yes	characteristic, complemented
451	#3330	C₂×C₅₃	1	2	yes	complemented
452	#3315	C₂×C₅₃	1	4	yes	complemented
453	#3302	C₂×C₅₃	1	2	yes	complemented
454	#3283	C₂×C₅₃	1	2	yes	complemented
455	#3276	C₂×C₅₃	1	2	yes	complemented
456	#3269	C₂×C₅₃	1	4	yes	complemented
457	#3218	C₂×C₅₃	1	1	yes	characteristic, complemented
458	#3209	C₂×C₅₃	1	1	yes	characteristic, complemented
459	#3196	C₂×C₅₃	1	2	yes	complemented
460	#3189	C₂×C₅₃	1	2	yes	complemented
461	#3110	C₂×C₅₃	1	1	yes	characteristic, complemented
462	#3105	C₂×C₅₃	1	1	yes	characteristic, complemented
463	#3007	C₂×C₅₃	1	2	yes	complemented
464	#3002	C₂×C₅₃	1	2	yes	complemented
465	#2974	C₂×C₅₃	1	1	yes	characteristic, complemented
466	C₂×C₅₃	—	2	2	no	—
467	C₂×C₅₃	—	4	2	no	—
468	C₂×C₅₃	—	4	2	no	—
469	C₂×C₅₃	—	4	4	no	—
470	C₂×C₅₃	—	8	1	no	—
471	C₂×C₅₃	#3484	1	1	yes	characteristic
472	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
473	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
474	C₂²×#41	C₂²×C₅₃	1	2	yes	—
475	C₂×#137	C₂²×C₅₃	1	4	yes	complemented
476	C₂×#135	C₂²×C₅₃	1	4	yes	complemented
477	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
478	#554	—	2	1	no	—
479	#552	C₂²×C₅₃	1	2	yes	complemented
480	#551	—	2	2	no	—
481	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
482	#548	C₂²×C₅₃	1	2	yes	complemented
483	#547	—	2	1	no	—
484	#547	—	2	2	no	—
485	#547	—	2	1	no	—
486	#547	C₂²×C₅₃	1	2	yes	—
487	#547	C₂²×C₅₃	1	4	yes	—
488	#547	C₂²×C₅₃	1	2	yes	—
489	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
490	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
491	#546	—	2	1	no	—
492	#542	—	2	1	no	—
493	#539	—	2	2	no	—
494	#533	C₂²×C₅₃	1	1	yes	characteristic
495	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
496	#529	C₂²×C₅₃	1	1	yes	characteristic
497	#525	C₂²×C₅₃	1	2	yes	—
498	C₂×#123	—	2	2	no	—
499	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
500	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
501	C₂×#121	—	2	1	no	—
502	#520	—	2	1	no	—
503	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
504	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
505	C₂²×C₄⋊C₄	—	2	1	no	—
506	#497	C₂²×C₅₃	1	2	yes	complemented
507	#494	C₂²×C₅₃	1	2	yes	complemented
508	#491	C₂²×C₅₃	1	2	yes	complemented
509	#487	C₂²×C₅₃	1	2	yes	complemented
510	#485	C₂²×C₅₃	1	4	yes	complemented
511	#484	C₂²×C₅₃	1	1	yes	characteristic
512	#484	C₂²×C₅₃	1	2	yes	—
513	#484	C₂²×C₅₃	1	4	yes	complemented
514	#481	C₂²×C₅₃	1	1	yes	characteristic
515	#478	C₂²×C₅₃	1	2	yes	complemented
516	#474	C₂²×C₅₃	1	2	yes	complemented
517	#470	C₂²×C₅₃	1	4	yes	complemented
518	#468	C₂²×C₅₃	1	4	yes	complemented
519	#467	C₂²×C₅₃	1	4	yes	complemented
520	#467	C₂²×C₅₃	1	4	yes	complemented
521	#463	C₂²×C₅₃	1	2	yes	complemented
522	#462	C₂²×C₅₃	1	4	yes	complemented
523	#462	C₂²×C₅₃	1	2	yes	complemented
524	#461	C₂²×C₅₃	1	2	yes	complemented
525	#461	C₂²×C₅₃	1	2	yes	complemented
526	#452	C₂²×C₅₃	1	4	yes	complemented
527	#452	C₂²×C₅₃	1	4	yes	complemented
528	#452	C₂²×C₅₃	1	4	yes	complemented
529	#452	C₂²×C₅₃	1	4	yes	complemented
530	#451	C₂²×C₅₃	1	2	yes	—
531	#451	C₂²×C₅₃	1	2	yes	—
532	#451	C₂²×C₅₃	1	2	yes	—
533	#451	C₂²×C₅₃	1	4	yes	complemented
534	#450	C₂²×C₅₃	1	1	yes	characteristic
535	#450	C₂²×C₅₃	1	2	yes	—
536	#449	C₂²×C₅₃	1	4	yes	complemented
537	#448	C₂²×C₅₃	1	2	yes	—
538	#447	C₂²×C₅₃	1	1	yes	characteristic
539	#440	C₂²×C₅₃	1	4	yes	complemented
540	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
541	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
542	#436	C₂²×C₅₃	1	2	yes	complemented
543	#435	C₂²×C₅₃	1	4	yes	complemented
544	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
545	#432	C₂²×C₅₃	1	1	yes	characteristic
546	#431	C₂²×C₅₃	1	1	yes	characteristic
547	#417	C₂²×C₅₃	1	4	yes	complemented
548	#416	C₂²×C₅₃	1	4	yes	complemented
549	#407	C₂²×C₅₃	1	2	yes	—
550	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
551	C₅₃	#61595	1	1	yes	characteristic, direct product factor, Sylow
552	C₂×#41	—	2	1	no	—
553	C₂×#41	—	2	2	no	—
554	C₂×#41	—	2	2	no	—
555	C₂×#41	—	4	8	no	—
556	C₂×#41	C₂³×C₅₃	1	4	yes	—
557	C₂×#41	C₂³×C₅₃	1	4	yes	—
558	C₂×#41	C₂³×C₅₃	1	2	yes	—
559	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
560	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
561	C₂²×D₄	—	2	2	no	—
562	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
563	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
564	C₂³×C₄	—	2	1	no	—
565	C₂³×C₄	—	2	2	no	—
566	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
567	#137	—	4	8	no	—
568	#135	—	4	8	no	—
569	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
570	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
571	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
572	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
573	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
574	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
575	C₂×D₈	C₂³×C₅₃	1	2	yes	—
576	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
577	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
578	C₄⋊Q₈	—	2	1	no	—
579	C₄⋊Q₈	—	2	1	no	—
580	C₄⋊Q₈	—	2	1	no	—
581	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
582	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
583	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
584	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
585	#126	—	2	2	no	—
586	#126	—	2	2	no	—
587	#126	—	2	1	no	—
588	#125	—	2	2	no	—
589	#125	—	2	1	no	—
590	#125	C₂³×C₅₃	1	1	yes	characteristic
591	#124	—	2	1	no	—
592	#124	—	2	2	no	—
593	#124	C₂³×C₅₃	1	1	yes	characteristic
594	#123	—	2	2	no	—
595	#123	—	2	2	no	—
596	#123	—	2	1	no	—
597	#123	—	2	4	no	—
598	#123	—	2	4	no	—
599	#123	—	2	4	no	—
600	#123	—	2	4	no	—
601	#123	—	2	2	no	—
602	#123	—	2	2	no	—
603	C₂²⋊Q₈	—	2	2	no	—
604	C₂²⋊Q₈	—	2	2	no	—
605	C₂²⋊Q₈	—	2	2	no	—
606	C₂²⋊Q₈	—	2	2	no	—
607	C₂²⋊Q₈	—	2	1	no	—
608	C₂²⋊Q₈	—	2	2	no	—
609	C₂²⋊Q₈	—	2	1	no	—
610	C₂²⋊Q₈	—	2	2	no	—
611	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
612	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
613	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
614	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
615	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
616	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
617	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
618	#121	—	2	2	no	—
619	#121	—	2	2	no	—
620	#121	—	2	4	no	—
621	#121	—	2	2	no	—
622	#121	—	2	1	no	—
623	#121	C₂³×C₅₃	1	1	yes	characteristic
624	#121	C₂³×C₅₃	1	2	yes	—
625	#120	—	2	2	no	—
626	C₄×Q₈	—	2	1	no	—
627	C₄×Q₈	—	2	1	no	—
628	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
629	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	1	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
638	C₄×D₄	D₄×C₅₃	1	2	yes	—
639	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
640	C₄×D₄	C₂³×C₅₃	1	2	yes	—
641	C₄×D₄	C₂³×C₅₃	1	2	yes	—
642	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
643	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
644	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
645	C₄×D₄	C₂³×C₅₃	1	2	yes	—
646	#117	—	2	1	no	—
647	#117	—	2	2	no	—
648	#117	—	2	1	no	—
649	#117	C₂³×C₅₃	1	2	yes	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	—	2	2	no	—
652	C₂×C₄⋊C₄	—	2	2	no	—
653	C₂×C₄⋊C₄	—	2	1	no	—
654	C₂×C₄⋊C₄	—	2	2	no	—
655	C₂×C₄⋊C₄	—	2	4	no	—
656	C₂×C₄⋊C₄	—	2	2	no	—
657	C₂×C₄⋊C₄	—	2	1	no	—
658	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
661	C₂×C₂²⋊C₄	—	2	2	no	—
662	C₂×C₂²⋊C₄	—	2	2	no	—
663	C₂×C₂²⋊C₄	—	2	1	no	—
664	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
665	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
666	#107	C₂³×C₅₃	1	2	yes	—
667	#107	C₂³×C₅₃	1	4	yes	—
668	#106	C₂³×C₅₃	1	2	yes	—
669	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
670	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
671	#103	C₂³×C₅₃	1	4	yes	—
672	#103	C₂³×C₅₃	1	4	yes	—
673	#103	C₂³×C₅₃	1	4	yes	—
674	#103	C₂³×C₅₃	1	4	yes	—
675	#103	C₂³×C₅₃	1	2	yes	—
676	#103	C₂³×C₅₃	1	4	yes	—
677	#102	C₂³×C₅₃	1	2	yes	—
678	#102	C₂³×C₅₃	1	4	yes	—
679	#102	C₂³×C₅₃	1	2	yes	—
680	#102	C₂³×C₅₃	1	2	yes	—
681	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
682	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
683	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
684	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
685	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
686	#97	C₂³×C₅₃	1	2	yes	—
687	C₄×C₈	C₂³×C₅₃	1	2	yes	—
688	C₂⁴	—	2	1	no	—
689	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
690	#41	—	2	8	no	—
691	#41	—	2	8	no	—
692	#41	—	4	4	no	—
693	#41	—	4	4	no	—
694	#41	—	4	4	no	—
695	#41	—	4	4	no	—
696	#41	—	4	8	no	—
697	#41	—	4	8	no	—
698	C₂×Q₈	—	2	1	no	—
699	C₂×Q₈	—	2	2	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	4	4	no	—
702	C₂×Q₈	—	4	4	no	—
703	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
704	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
705	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
706	C₂×D₄	—	2	4	no	—
707	C₂×D₄	—	2	1	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	4	no	—
710	C₂×D₄	—	2	4	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	4	2	no	—
714	C₂×D₄	—	4	8	no	—
715	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
716	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
717	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
718	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
719	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	4	4	no	—
731	C₂²×C₄	—	4	4	no	—
732	C₂²×C₄	—	4	8	no	—
733	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
735	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
736	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
737	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
741	Q₁₆	—	4	4	no	—
742	Q₁₆	—	4	4	no	—
743	Q₁₆	—	4	4	no	—
744	SD₁₆	—	2	8	no	—
745	SD₁₆	—	2	4	no	—
746	SD₁₆	—	4	4	no	—
747	D₈	—	2	4	no	—
748	M₁₆	—	4	4	no	—
749	C₂×C₈	—	4	4	no	—
750	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
751	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
752	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	1	no	—
773	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
774	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
775	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
776	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
777	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
778	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
779	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
780	C₂²⋊C₄	—	2	1	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	2	2	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	2	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
796	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
797	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
798	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	1	no	—
802	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
803	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
804	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
805	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
806	C₂³	—	2	4	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	4	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	4	2	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	2	no	—
813	C₂³	—	4	2	no	—
814	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
815	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
816	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
817	Q₈	—	2	2	no	—
818	Q₈	—	2	4	no	—
819	Q₈	—	2	4	no	—
820	Q₈	—	2	4	no	—
821	Q₈	—	4	4	no	—
822	Q₈	—	4	2	no	—
823	Q₈	—	8	2	no	—
824	D₄	—	2	4	no	—
825	D₄	—	2	2	no	—
826	D₄	—	2	2	no	—
827	D₄	—	2	2	no	—
828	D₄	—	2	2	no	—
829	D₄	—	4	2	no	—
830	D₄	—	4	8	no	—
831	D₄	—	4	8	no	—
832	D₄	—	4	4	no	—
833	D₄	—	4	2	no	—
834	D₄	—	8	2	no	—
835	D₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	4	no	—
839	C₂×C₄	—	2	4	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	4	2	no	—
849	C₂×C₄	—	4	2	no	—
850	C₂×C₄	—	4	2	no	—
851	C₂×C₄	—	4	8	no	—
852	C₂×C₄	—	4	8	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	2	no	—
855	C₂×C₄	—	4	4	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	4	no	—
858	C₂×C₄	—	4	2	no	—
859	C₂×C₄	—	8	2	no	—
860	C₂×C₄	—	8	2	no	—
861	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
863	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
864	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
865	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
866	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
867	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
868	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
869	C₈	—	2	2	no	—
870	C₈	—	2	4	no	—
871	C₈	—	2	2	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	4	8	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	8	4	no	—
888	C₂²	C₅₃×#578	1	2	yes	—
889	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	4	4	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	1	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	1	no	—
903	C₄	C₅₃×#575	1	2	yes	—
904	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
905	C₂	—	2	2	no	—
906	C₂	—	4	2	no	—
907	C₂	—	4	2	no	—
908	C₂	—	4	4	no	—
909	C₂	—	8	1	no	—
910	C₂	C₅₃×#3484	1	1	yes	characteristic
911	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
912	C₂	C₂×C₅₃×#578	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 ◁ C₂×C₄×D₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3520	C₂	semidirect
2. C₂×C₅₃×#547	C₂	semidirect
3. C₅₃×#3330	C₂	semidirect
4. C₅₃×#3315	C₂	semidirect
5. C₅₃×#3302	C₂	semidirect
6. C₅₃×#3283	C₂	semidirect
7. C₅₃×#3276	C₂	semidirect
8. C₅₃×#3269	C₂	semidirect
9. C₅₃×#3218	C₂	semidirect
10. C₅₃×#3209	C₂	semidirect
11. C₅₃×#3196	C₂	semidirect
12. C₅₃×#3189	C₂	semidirect
13. C₅₃×#3110	C₂	semidirect
14. C₅₃×#3105	C₂	semidirect
15. C₅₃×#3007	C₂	semidirect
16. C₅₃×#3002	C₂	semidirect
17. C₅₃×#2974	C₂	semidirect
19. C₂×#137×C₅₃	C₂²	semidirect
20. C₂×#135×C₅₃	C₂²	semidirect
21. C₅₃×#556	C₂²	semidirect
23. C₅₃×#552	C₂²	semidirect
25. D₄×Q₈×C₅₃	C₂²	semidirect
26. C₅₃×#548	C₂²	semidirect
33. C₅₃×#547	C₂²	semidirect
34. C₅₃×#547	C₂²	semidirect
50. C₅₃×#497	C₂²	semidirect
51. C₅₃×#494	C₂²	semidirect
52. C₅₃×#491	C₂²	semidirect
53. C₅₃×#487	C₂²	semidirect
54. C₅₃×#485	C₂²	semidirect
57. C₅₃×#484	C₂²	semidirect
59. C₅₃×#478	C₂²	semidirect
60. C₅₃×#474	C₂²	semidirect
61. C₅₃×#470	C₂²	semidirect
62. C₅₃×#468	C₂²	semidirect
63. C₅₃×#467	C₂²	semidirect
64. C₅₃×#467	C₂²	semidirect
65. C₅₃×#463	C₂²	semidirect
66. C₅₃×#462	C₂²	semidirect
67. C₅₃×#462	C₂²	semidirect
68. C₅₃×#461	C₂²	semidirect
69. C₅₃×#461	C₂²	semidirect
70. C₅₃×#452	C₂²	semidirect
71. C₅₃×#452	C₂²	semidirect
72. C₅₃×#452	C₂²	semidirect
73. C₅₃×#452	C₂²	semidirect
77. C₅₃×#451	C₂²	semidirect
80. C₅₃×#449	C₂²	semidirect
83. C₅₃×#440	C₂²	semidirect
84. C₄×SD₁₆×C₅₃	C₂²	semidirect
85. C₄×D₈×C₅₃	C₂²	semidirect
86. C₅₃×#436	C₂²	semidirect
87. C₅₃×#435	C₂²	semidirect
88. C₈×D₄×C₅₃	C₂²	semidirect
91. C₅₃×#417	C₂²	semidirect
92. C₅₃×#416	C₂²	semidirect
415. #61595	C₅₃	direct (N × H)
449. #3520	C₂×C₅₃	semidirect
450. C₂×#547	C₂×C₅₃	semidirect
451. #3330	C₂×C₅₃	semidirect
452. #3315	C₂×C₅₃	semidirect
453. #3302	C₂×C₅₃	semidirect
454. #3283	C₂×C₅₃	semidirect
455. #3276	C₂×C₅₃	semidirect
456. #3269	C₂×C₅₃	semidirect
457. #3218	C₂×C₅₃	semidirect
458. #3209	C₂×C₅₃	semidirect
459. #3196	C₂×C₅₃	semidirect
460. #3189	C₂×C₅₃	semidirect
461. #3110	C₂×C₅₃	semidirect
462. #3105	C₂×C₅₃	semidirect
463. #3007	C₂×C₅₃	semidirect
464. #3002	C₂×C₅₃	semidirect
465. #2974	C₂×C₅₃	semidirect
475. C₂×#137	C₂²×C₅₃	semidirect
476. C₂×#135	C₂²×C₅₃	semidirect
477. #556	C₂²×C₅₃	semidirect
479. #552	C₂²×C₅₃	semidirect
481. D₄×Q₈	C₂²×C₅₃	semidirect
482. #548	C₂²×C₅₃	semidirect
489. #547	C₂²×C₅₃	semidirect
490. #547	C₂²×C₅₃	semidirect
506. #497	C₂²×C₅₃	semidirect
507. #494	C₂²×C₅₃	semidirect
508. #491	C₂²×C₅₃	semidirect
509. #487	C₂²×C₅₃	semidirect
510. #485	C₂²×C₅₃	semidirect
513. #484	C₂²×C₅₃	semidirect
515. #478	C₂²×C₅₃	semidirect
516. #474	C₂²×C₅₃	semidirect
517. #470	C₂²×C₅₃	semidirect
518. #468	C₂²×C₅₃	semidirect
519. #467	C₂²×C₅₃	semidirect
520. #467	C₂²×C₅₃	semidirect
521. #463	C₂²×C₅₃	semidirect
522. #462	C₂²×C₅₃	semidirect
523. #462	C₂²×C₅₃	semidirect
524. #461	C₂²×C₅₃	semidirect
525. #461	C₂²×C₅₃	semidirect
526. #452	C₂²×C₅₃	semidirect
527. #452	C₂²×C₅₃	semidirect
528. #452	C₂²×C₅₃	semidirect
529. #452	C₂²×C₅₃	semidirect
533. #451	C₂²×C₅₃	semidirect
536. #449	C₂²×C₅₃	semidirect
539. #440	C₂²×C₅₃	semidirect
540. C₄×SD₁₆	C₂²×C₅₃	semidirect
541. C₄×D₈	C₂²×C₅₃	semidirect
542. #436	C₂²×C₅₃	semidirect
543. #435	C₂²×C₅₃	semidirect
544. C₈×D₄	C₂²×C₅₃	semidirect
547. #417	C₂²×C₅₃	semidirect
548. #416	C₂²×C₅₃	semidirect
551. C₅₃	#61595	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×#3520	2
C₂×C₅₃×#547	2
C₅₃×#3330	2
C₅₃×#3315	2
C₅₃×#3302	2
C₅₃×#3283	2
C₅₃×#3276	2
C₅₃×#3269	2
C₅₃×#3218	2
C₅₃×#3209	2
C₅₃×#3196	2
C₅₃×#3189	2
C₅₃×#3110	2
C₅₃×#3105	2
C₅₃×#3007	2
C₅₃×#3002	2
C₅₃×#2974	2
#61595	53

Subgroups — C53×#61595 #27269107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61595 #27269107