Subgroups — C₅₃×#61629 #27269141

Order 13568.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3314	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3306	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3295	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3294	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3282	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3280	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3265	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3264	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3224	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3198	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3190	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3188	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3118	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3012	C₂	1	2	yes	maximal, complemented
17	C₂×C₅₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2977	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
23	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
24	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
25	C₂²×D₈×C₅₃	C₂²	1	2	yes	complemented
26	C₅₃×#562	—	2	2	no	—
27	C₅₃×#554	C₂²	1	2	yes	complemented
28	C₅₃×#548	C₂²	1	2	yes	complemented
29	C₅₃×#547	C₂²	1	2	yes	complemented
30	C₅₃×#546	—	2	1	no	—
31	C₅₃×#546	—	2	1	no	—
32	C₅₃×#546	—	2	2	no	—
33	C₅₃×#546	C₂²	1	2	yes	—
34	C₅₃×#546	C₂²	1	2	yes	complemented
35	C₅₃×#546	C₂²	1	2	yes	complemented
36	D₄²×C₅₃	—	2	1	no	—
37	D₄²×C₅₃	—	2	1	no	—
38	D₄²×C₅₃	C₂²	1	2	yes	—
39	D₄²×C₅₃	C₂²	1	2	yes	complemented
40	C₅₃×#543	—	2	1	no	—
41	C₅₃×#542	C₂²	1	2	yes	complemented
42	C₅₃×#539	—	2	1	no	—
43	C₅₃×#538	—	2	1	no	—
44	C₅₃×#537	—	2	1	no	—
45	C₅₃×#537	C₂²	1	2	yes	complemented
46	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#534	—	2	2	no	—
49	C₅₃×#525	C₂²	1	1	yes	characteristic
50	C₅₃×#525	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
52	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×#120×C₅₃	—	2	2	no	—
54	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#496	C₂²	1	2	yes	complemented
56	C₅₃×#495	C₂²	1	2	yes	complemented
57	C₅₃×#489	C₂²	1	2	yes	complemented
58	C₅₃×#486	C₂²	1	2	yes	complemented
59	C₅₃×#485	C₂²	1	2	yes	complemented
60	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#482	C₂²	1	2	yes	complemented
63	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#481	C₂²	1	2	yes	complemented
65	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#480	C₂²	1	2	yes	complemented
67	C₅₃×#476	C₂²	1	2	yes	complemented
68	C₅₃×#474	C₂²	1	2	yes	complemented
69	C₅₃×#469	C₂²	1	2	yes	complemented
70	C₅₃×#468	C₂²	1	2	yes	complemented
71	C₅₃×#467	C₂²	1	2	yes	complemented
72	C₅₃×#466	C₂²	1	2	yes	complemented
73	C₅₃×#466	C₂²	1	2	yes	complemented
74	C₅₃×#465	C₂²	1	2	yes	complemented
75	C₅₃×#465	C₂²	1	2	yes	complemented
76	C₅₃×#465	C₂²	1	2	yes	complemented
77	C₅₃×#464	C₂²	1	2	yes	complemented
78	C₅₃×#463	C₂²	1	2	yes	complemented
79	C₅₃×#463	C₂²	1	2	yes	complemented
80	C₅₃×#463	C₂²	1	2	yes	complemented
81	C₅₃×#460	C₂²	1	2	yes	complemented
82	C₅₃×#459	C₂²	1	2	yes	complemented
83	C₅₃×#452	C₂²	1	2	yes	complemented
84	C₅₃×#452	C₂²	1	2	yes	complemented
85	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#450	C₂²	1	2	yes	complemented
87	C₅₃×#450	C₂²	1	2	yes	complemented
88	C₅₃×#450	C₂²	1	2	yes	complemented
89	C₅₃×#450	C₂²	1	2	yes	complemented
90	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#450	C₂²	1	2	yes	complemented
92	C₅₃×#449	C₂²	1	2	yes	complemented
93	C₅₃×#449	C₂²	1	2	yes	complemented
94	C₅₃×#449	C₂²	1	2	yes	complemented
95	C₅₃×#449	C₂²	1	2	yes	complemented
96	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#447	C₂²	1	2	yes	—
98	C₅₃×#447	C₂²	1	2	yes	complemented
99	C₅₃×#447	C₂²	1	2	yes	complemented
100	C₅₃×#447	C₂²	1	2	yes	complemented
101	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#447	C₂²	1	2	yes	complemented
103	C₅₃×#442	C₂²	1	2	yes	complemented
104	C₅₃×#440	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
106	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
107	C₅₃×#435	C₂²	1	2	yes	complemented
108	C₅₃×#435	C₂²	1	2	yes	complemented
109	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
110	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
111	C₅₃×#433	C₂²	1	2	yes	complemented
112	C₅₃×#417	C₂²	1	2	yes	complemented
113	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
114	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
115	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
116	C₅₃×#408	C₂²	1	2	yes	complemented
117	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₂⁵×C₅₃	—	2	1	no	—
120	H(5,𝔽₂)×C₅₃	—	4	4	no	—
121	C₂×#41×C₅₃	—	2	1	no	—
122	C₂×#41×C₅₃	—	2	2	no	—
123	C₂×#41×C₅₃	C₂³	1	2	yes	—
124	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
125	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
126	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
127	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₅₃	—	2	1	no	—
129	C₂²×D₄×C₅₃	—	2	2	no	—
130	C₂²×D₄×C₅₃	—	2	1	no	—
131	C₂²×D₄×C₅₃	—	2	2	no	—
132	C₂²×D₄×C₅₃	—	2	2	no	—
133	C₂²×D₄×C₅₃	—	2	1	no	—
134	C₂²×D₄×C₅₃	—	2	1	no	—
135	C₂²×D₄×C₅₃	—	2	1	no	—
136	C₂²×D₄×C₅₃	—	4	4	no	—
137	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
140	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
144	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
145	#135×C₅₃	—	4	4	no	—
146	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	complemented
147	C₂×SD₁₆×C₅₃	—	4	4	no	—
148	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	complemented
153	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	complemented
154	C₂×D₈×C₅₃	—	4	4	no	—
155	C₂×D₈×C₅₃	C₂³	1	2	yes	—
156	C₂×D₈×C₅₃	C₂³	1	2	yes	—
157	C₂×D₈×C₅₃	C₂³	1	2	yes	—
158	C₂×D₈×C₅₃	C₂³	1	2	yes	—
159	C₂×D₈×C₅₃	C₂³	1	2	yes	complemented
160	C₂×M₁₆×C₅₃	C₂³	1	2	yes	complemented
161	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
162	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
163	C₂²×C₈×C₅₃	C₂³	1	2	yes	complemented
164	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
165	#127×C₅₃	—	2	1	no	—
166	#127×C₅₃	C₂³	1	2	yes	—
167	#126×C₅₃	—	2	2	no	—
168	#125×C₅₃	—	2	2	no	—
169	#124×C₅₃	—	2	2	no	—
170	#124×C₅₃	—	2	2	no	—
171	#124×C₅₃	—	2	1	no	—
172	#124×C₅₃	C₂³	1	2	yes	—
173	#124×C₅₃	C₂³	1	2	yes	complemented
174	#123×C₅₃	—	2	2	no	—
175	#123×C₅₃	—	2	2	no	—
176	#123×C₅₃	—	2	2	no	—
177	#123×C₅₃	—	2	2	no	—
178	#123×C₅₃	—	2	2	no	—
179	#123×C₅₃	—	2	2	no	—
180	#123×C₅₃	—	2	1	no	—
181	#123×C₅₃	D₄	1	2	yes	—
182	C₂²⋊Q₈×C₅₃	—	2	2	no	—
183	C₂²⋊Q₈×C₅₃	—	2	2	no	—
184	C₂²⋊Q₈×C₅₃	—	2	2	no	—
185	C₂²⋊Q₈×C₅₃	—	2	2	no	—
186	C₂²⋊Q₈×C₅₃	—	2	2	no	—
187	C₂²⋊Q₈×C₅₃	—	2	2	no	—
188	C₂²⋊Q₈×C₅₃	—	2	1	no	—
189	C₂²⋊Q₈×C₅₃	—	2	1	no	—
190	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
191	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
192	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
193	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
195	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
196	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
197	#121×C₅₃	—	2	2	no	—
198	#121×C₅₃	—	2	2	no	—
199	#121×C₅₃	—	2	1	no	—
200	#121×C₅₃	—	2	1	no	—
201	#121×C₅₃	—	2	2	no	—
202	#121×C₅₃	—	2	2	no	—
203	#121×C₅₃	—	2	2	no	—
204	#121×C₅₃	—	2	2	no	—
205	#121×C₅₃	—	2	2	no	—
206	#121×C₅₃	—	2	2	no	—
207	#121×C₅₃	—	2	2	no	—
208	#121×C₅₃	—	2	1	no	—
209	#121×C₅₃	—	2	1	no	—
210	#121×C₅₃	D₄	1	1	yes	characteristic
211	#121×C₅₃	D₄	1	1	yes	characteristic
212	#121×C₅₃	C₂³	1	2	yes	—
213	#121×C₅₃	C₂³	1	2	yes	—
214	#121×C₅₃	C₂³	1	1	yes	characteristic
215	#121×C₅₃	C₂³	1	1	yes	characteristic
216	#121×C₅₃	C₂³	1	2	yes	—
217	#121×C₅₃	C₂³	1	2	yes	—
218	#121×C₅₃	C₂³	1	2	yes	complemented
219	#120×C₅₃	—	2	2	no	—
220	#120×C₅₃	—	2	2	no	—
221	#120×C₅₃	—	2	2	no	—
222	#120×C₅₃	—	2	2	no	—
223	#120×C₅₃	—	2	2	no	—
224	#120×C₅₃	—	2	1	no	—
225	#120×C₅₃	—	2	2	no	—
226	#120×C₅₃	—	2	2	no	—
227	#120×C₅₃	—	2	2	no	—
228	#120×C₅₃	—	2	2	no	—
229	#120×C₅₃	D₄	1	2	yes	—
230	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	1	no	—
233	C₄×D₄×C₅₃	—	2	2	no	—
234	C₄×D₄×C₅₃	—	2	2	no	—
235	C₄×D₄×C₅₃	—	2	1	no	—
236	C₄×D₄×C₅₃	—	2	1	no	—
237	C₄×D₄×C₅₃	C₂³	1	2	yes	—
238	C₄×D₄×C₅₃	C₂³	1	2	yes	—
239	C₄×D₄×C₅₃	C₂³	1	2	yes	—
240	C₄×D₄×C₅₃	C₂³	1	2	yes	—
241	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
242	#117×C₅₃	C₂³	1	1	yes	characteristic
243	#117×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
245	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
248	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
249	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
250	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
251	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
252	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
253	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
254	#107×C₅₃	C₂³	1	2	yes	complemented
255	#107×C₅₃	C₂³	1	2	yes	complemented
256	#106×C₅₃	C₂³	1	2	yes	complemented
257	#106×C₅₃	C₂³	1	2	yes	complemented
258	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
259	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
260	#103×C₅₃	C₂³	1	2	yes	complemented
261	#103×C₅₃	C₂³	1	2	yes	complemented
262	#103×C₅₃	C₂³	1	2	yes	complemented
263	#103×C₅₃	C₂³	1	2	yes	complemented
264	#102×C₅₃	C₂³	1	2	yes	—
265	#102×C₅₃	C₂³	1	2	yes	—
266	#102×C₅₃	C₂³	1	2	yes	—
267	#102×C₅₃	C₂³	1	2	yes	—
268	#102×C₅₃	C₂³	1	2	yes	—
269	#102×C₅₃	C₂³	1	2	yes	—
270	#102×C₅₃	C₂³	1	2	yes	—
271	#102×C₅₃	C₂³	1	2	yes	—
272	#102×C₅₃	C₂³	1	2	yes	complemented
273	#102×C₅₃	C₂³	1	2	yes	complemented
274	#102×C₅₃	C₂³	1	2	yes	complemented
275	#102×C₅₃	C₂³	1	2	yes	complemented
276	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
279	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
280	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	complemented
283	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	complemented
284	#97×C₅₃	C₂³	1	2	yes	complemented
285	C₄×C₈×C₅₃	C₂³	1	2	yes	complemented
286	C₂⁴×C₅₃	—	2	1	no	—
287	C₂⁴×C₅₃	—	2	2	no	—
288	C₂⁴×C₅₃	—	2	2	no	—
289	C₂⁴×C₅₃	—	2	1	no	—
290	C₂⁴×C₅₃	—	2	1	no	—
291	C₂⁴×C₅₃	—	2	2	no	—
292	C₂⁴×C₅₃	—	4	4	no	—
293	C₂⁴×C₅₃	—	8	2	no	—
294	C₂⁴×C₅₃	—	8	2	no	—
295	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
296	#41×C₅₃	—	2	4	no	—
297	#41×C₅₃	—	4	2	no	—
298	#41×C₅₃	—	4	2	no	—
299	#41×C₅₃	—	4	2	no	—
300	#41×C₅₃	—	4	2	no	—
301	#41×C₅₃	—	4	2	no	—
302	#41×C₅₃	—	4	4	no	—
303	#41×C₅₃	—	8	4	no	—
304	C₂×Q₈×C₅₃	—	2	1	no	—
305	C₂×Q₈×C₅₃	—	2	2	no	—
306	C₂×Q₈×C₅₃	—	4	2	no	—
307	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
308	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
309	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
310	C₂×D₄×C₅₃	—	2	4	no	—
311	C₂×D₄×C₅₃	—	2	4	no	—
312	C₂×D₄×C₅₃	—	2	4	no	—
313	C₂×D₄×C₅₃	—	2	4	no	—
314	C₂×D₄×C₅₃	—	2	1	no	—
315	C₂×D₄×C₅₃	—	2	1	no	—
316	C₂×D₄×C₅₃	—	2	2	no	—
317	C₂×D₄×C₅₃	—	2	1	no	—
318	C₂×D₄×C₅₃	—	2	2	no	—
319	C₂×D₄×C₅₃	—	2	2	no	—
320	C₂×D₄×C₅₃	—	2	2	no	—
321	C₂×D₄×C₅₃	—	2	2	no	—
322	C₂×D₄×C₅₃	—	2	2	no	—
323	C₂×D₄×C₅₃	—	2	2	no	—
324	C₂×D₄×C₅₃	—	2	1	no	—
325	C₂×D₄×C₅₃	—	2	2	no	—
326	C₂×D₄×C₅₃	—	2	2	no	—
327	C₂×D₄×C₅₃	—	2	2	no	—
328	C₂×D₄×C₅₃	—	2	1	no	—
329	C₂×D₄×C₅₃	—	2	2	no	—
330	C₂×D₄×C₅₃	—	2	2	no	—
331	C₂×D₄×C₅₃	—	2	1	no	—
332	C₂×D₄×C₅₃	—	4	2	no	—
333	C₂×D₄×C₅₃	—	4	2	no	—
334	C₂×D₄×C₅₃	—	4	2	no	—
335	C₂×D₄×C₅₃	—	4	2	no	—
336	C₂×D₄×C₅₃	—	4	2	no	—
337	C₂×D₄×C₅₃	—	4	4	no	—
338	C₂×D₄×C₅₃	—	4	4	no	—
339	C₂×D₄×C₅₃	—	4	4	no	—
340	C₂×D₄×C₅₃	—	4	4	no	—
341	C₂×D₄×C₅₃	—	4	8	no	—
342	C₂×D₄×C₅₃	—	8	4	no	—
343	C₂×D₄×C₅₃	—	8	4	no	—
344	C₂×D₄×C₅₃	—	8	2	no	—
345	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
349	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
350	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
352	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₅₃	—	2	1	no	—
354	C₂²×C₄×C₅₃	—	2	1	no	—
355	C₂²×C₄×C₅₃	—	2	1	no	—
356	C₂²×C₄×C₅₃	—	2	2	no	—
357	C₂²×C₄×C₅₃	—	2	2	no	—
358	C₂²×C₄×C₅₃	—	2	1	no	—
359	C₂²×C₄×C₅₃	—	2	2	no	—
360	C₂²×C₄×C₅₃	—	2	2	no	—
361	C₂²×C₄×C₅₃	—	2	2	no	—
362	C₂²×C₄×C₅₃	—	2	2	no	—
363	C₂²×C₄×C₅₃	—	4	2	no	—
364	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
371	Q₁₆×C₅₃	—	4	2	no	—
372	SD₁₆×C₅₃	—	2	4	no	—
373	SD₁₆×C₅₃	—	2	4	no	—
374	SD₁₆×C₅₃	—	4	2	no	—
375	SD₁₆×C₅₃	—	4	2	no	—
376	SD₁₆×C₅₃	—	4	2	no	—
377	SD₁₆×C₅₃	—	4	2	no	—
378	D₈×C₅₃	—	2	4	no	—
379	D₈×C₅₃	—	2	4	no	—
380	D₈×C₅₃	—	4	2	no	—
381	D₈×C₅₃	—	4	2	no	—
382	D₈×C₅₃	—	4	2	no	—
383	M₁₆×C₅₃	—	4	2	no	—
384	C₂×C₈×C₅₃	—	4	2	no	—
385	C₂×C₈×C₅₃	—	4	2	no	—
386	C₂×C₈×C₅₃	—	4	2	no	—
387	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
388	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
389	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
390	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
391	C₄⋊C₄×C₅₃	—	2	2	no	—
392	C₄⋊C₄×C₅₃	—	2	2	no	—
393	C₄⋊C₄×C₅₃	—	2	1	no	—
394	C₄⋊C₄×C₅₃	—	2	1	no	—
395	C₄⋊C₄×C₅₃	—	2	2	no	—
396	C₄⋊C₄×C₅₃	—	2	1	no	—
397	C₄⋊C₄×C₅₃	—	2	1	no	—
398	C₄⋊C₄×C₅₃	—	2	2	no	—
399	C₄⋊C₄×C₅₃	—	2	2	no	—
400	C₄⋊C₄×C₅₃	—	2	2	no	—
401	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²⋊C₄×C₅₃	—	2	1	no	—
410	C₂²⋊C₄×C₅₃	—	2	1	no	—
411	C₂²⋊C₄×C₅₃	—	2	1	no	—
412	C₂²⋊C₄×C₅₃	—	2	2	no	—
413	C₂²⋊C₄×C₅₃	—	2	2	no	—
414	C₂²⋊C₄×C₅₃	—	2	2	no	—
415	C₂²⋊C₄×C₅₃	—	2	2	no	—
416	C₂²⋊C₄×C₅₃	—	2	2	no	—
417	C₂²⋊C₄×C₅₃	—	2	2	no	—
418	C₂²⋊C₄×C₅₃	—	2	2	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	no	—
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	2	no	—
422	C₂²⋊C₄×C₅₃	—	2	2	no	—
423	C₂²⋊C₄×C₅₃	—	2	2	no	—
424	C₂²⋊C₄×C₅₃	—	2	2	no	—
425	C₂²⋊C₄×C₅₃	—	2	1	no	—
426	C₂²⋊C₄×C₅₃	—	2	1	no	—
427	C₂²⋊C₄×C₅₃	—	2	2	no	—
428	C₂²⋊C₄×C₅₃	—	2	2	no	—
429	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
434	C₄²×C₅₃	—	2	1	no	—
435	C₄²×C₅₃	—	2	2	no	—
436	C₄²×C₅₃	C₂⁴	1	2	yes	—
437	C₂³×C₅₃	—	2	4	no	—
438	C₂³×C₅₃	—	2	2	no	—
439	C₂³×C₅₃	—	2	2	no	—
440	C₂³×C₅₃	—	2	2	no	—
441	C₂³×C₅₃	—	2	2	no	—
442	C₂³×C₅₃	—	2	1	no	—
443	C₂³×C₅₃	—	2	2	no	—
444	C₂³×C₅₃	—	4	1	no	—
445	C₂³×C₅₃	—	4	4	no	—
446	C₂³×C₅₃	—	4	4	no	—
447	C₂³×C₅₃	—	4	4	no	—
448	C₂³×C₅₃	—	4	2	no	—
449	C₂³×C₅₃	—	4	4	no	—
450	C₂³×C₅₃	—	4	4	no	—
451	C₂³×C₅₃	—	4	2	no	—
452	C₂³×C₅₃	—	8	2	no	—
453	C₂³×C₅₃	—	8	2	no	—
454	C₂³×C₅₃	—	8	1	no	—
455	C₂³×C₅₃	—	8	1	no	—
456	C₂³×C₅₃	—	8	1	no	—
457	C₂³×C₅₃	—	8	1	no	—
458	C₂³×C₅₃	—	8	1	no	—
459	C₂³×C₅₃	—	8	1	no	—
460	C₂³×C₅₃	—	8	2	no	—
461	C₂³×C₅₃	—	8	2	no	—
462	C₂³×C₅₃	—	8	16	no	—
463	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
464	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
465	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
466	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
467	Q₈×C₅₃	—	2	2	no	—
468	Q₈×C₅₃	—	2	2	no	—
469	Q₈×C₅₃	—	2	2	no	—
470	Q₈×C₅₃	—	4	1	no	—
471	Q₈×C₅₃	—	8	1	no	—
472	Q₈×C₅₃	—	8	2	no	—
473	D₄×C₅₃	—	2	4	no	—
474	D₄×C₅₃	—	2	4	no	—
475	D₄×C₅₃	—	2	4	no	—
476	D₄×C₅₃	—	2	2	no	—
477	D₄×C₅₃	—	2	2	no	—
478	D₄×C₅₃	—	2	2	no	—
479	D₄×C₅₃	—	2	2	no	—
480	D₄×C₅₃	—	2	2	no	—
481	D₄×C₅₃	—	2	2	no	—
482	D₄×C₅₃	—	4	1	no	—
483	D₄×C₅₃	—	4	2	no	—
484	D₄×C₅₃	—	4	4	no	—
485	D₄×C₅₃	—	4	4	no	—
486	D₄×C₅₃	—	4	4	no	—
487	D₄×C₅₃	—	4	2	no	—
488	D₄×C₅₃	—	4	4	no	—
489	D₄×C₅₃	—	4	2	no	—
490	D₄×C₅₃	—	4	2	no	—
491	D₄×C₅₃	—	4	4	no	—
492	D₄×C₅₃	—	4	2	no	—
493	D₄×C₅₃	—	8	1	no	—
494	D₄×C₅₃	—	8	2	no	—
495	D₄×C₅₃	—	8	2	no	—
496	D₄×C₅₃	—	8	2	no	—
497	D₄×C₅₃	—	8	2	no	—
498	D₄×C₅₃	—	8	2	no	—
499	D₄×C₅₃	—	8	2	no	—
500	D₄×C₅₃	—	8	2	no	—
501	D₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
502	C₂×C₄×C₅₃	—	2	2	no	—
503	C₂×C₄×C₅₃	—	2	2	no	—
504	C₂×C₄×C₅₃	—	2	2	no	—
505	C₂×C₄×C₅₃	—	2	2	no	—
506	C₂×C₄×C₅₃	—	2	2	no	—
507	C₂×C₄×C₅₃	—	2	1	no	—
508	C₂×C₄×C₅₃	—	2	2	no	—
509	C₂×C₄×C₅₃	—	2	1	no	—
510	C₂×C₄×C₅₃	—	2	1	no	—
511	C₂×C₄×C₅₃	—	2	2	no	—
512	C₂×C₄×C₅₃	—	2	2	no	—
513	C₂×C₄×C₅₃	—	4	1	no	—
514	C₂×C₄×C₅₃	—	4	1	no	—
515	C₂×C₄×C₅₃	—	4	1	no	—
516	C₂×C₄×C₅₃	—	4	4	no	—
517	C₂×C₄×C₅₃	—	4	2	no	—
518	C₂×C₄×C₅₃	—	4	2	no	—
519	C₂×C₄×C₅₃	—	8	2	no	—
520	C₂×C₄×C₅₃	—	8	2	no	—
521	C₂×C₄×C₅₃	—	8	2	no	—
522	C₂×C₄×C₅₃	—	8	2	no	—
523	C₂×C₄×C₅₃	—	8	1	no	—
524	C₂×C₄×C₅₃	—	8	1	no	—
525	C₂×C₄×C₅₃	—	8	2	no	—
526	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
533	C₈×C₅₃	—	2	2	no	—
534	C₈×C₅₃	—	2	2	no	—
535	C₈×C₅₃	—	2	2	no	—
536	C₈×C₅₃	—	2	2	no	—
537	#61629	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
538	C₂²×C₅₃	—	2	1	no	—
539	C₂²×C₅₃	—	2	1	no	—
540	C₂²×C₅₃	—	2	1	no	—
541	C₂²×C₅₃	—	2	1	no	—
542	C₂²×C₅₃	—	2	1	no	—
543	C₂²×C₅₃	—	2	2	no	—
544	C₂²×C₅₃	—	2	4	no	—
545	C₂²×C₅₃	—	2	2	no	—
546	C₂²×C₅₃	—	2	1	no	—
547	C₂²×C₅₃	—	2	2	no	—
548	C₂²×C₅₃	—	2	1	no	—
549	C₂²×C₅₃	—	4	4	no	—
550	C₂²×C₅₃	—	4	2	no	—
551	C₂²×C₅₃	—	4	2	no	—
552	C₂²×C₅₃	—	4	1	no	—
553	C₂²×C₅₃	—	4	2	no	—
554	C₂²×C₅₃	—	4	2	no	—
555	C₂²×C₅₃	—	4	2	no	—
556	C₂²×C₅₃	—	4	1	no	—
557	C₂²×C₅₃	—	4	2	no	—
558	C₂²×C₅₃	—	4	1	no	—
559	C₂²×C₅₃	—	4	2	no	—
560	C₂²×C₅₃	—	4	2	no	—
561	C₂²×C₅₃	—	8	8	no	—
562	C₂²×C₅₃	—	8	8	no	—
563	C₂²×C₅₃	—	8	4	no	—
564	C₂²×C₅₃	—	8	4	no	—
565	C₂²×C₅₃	—	16	2	no	—
566	C₂²×C₅₃	—	16	4	no	—
567	C₂²×C₅₃	#576	1	2	yes	—
568	C₂²×C₅₃	#577	1	2	yes	—
569	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
570	C₄×C₅₃	—	2	1	no	—
571	C₄×C₅₃	—	2	2	no	—
572	C₄×C₅₃	—	2	1	no	—
573	C₄×C₅₃	—	2	1	no	—
574	C₄×C₅₃	—	2	2	no	—
575	C₄×C₅₃	—	2	2	no	—
576	C₄×C₅₃	—	4	1	no	—
577	C₄×C₅₃	—	4	2	no	—
578	C₄×C₅₃	—	4	2	no	—
579	C₄×C₅₃	—	4	1	no	—
580	C₄×C₅₃	—	4	2	no	—
581	C₄×C₅₃	—	4	1	no	—
582	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
583	#3536	C₂×C₅₃	1	1	yes	characteristic, complemented
584	#3484	C₂×C₅₃	1	1	yes	characteristic, complemented
585	#3314	C₂×C₅₃	1	2	yes	complemented
586	#3306	C₂×C₅₃	1	2	yes	complemented
587	#3295	C₂×C₅₃	1	2	yes	complemented
588	#3294	C₂×C₅₃	1	2	yes	complemented
589	#3282	C₂×C₅₃	1	2	yes	complemented
590	#3280	C₂×C₅₃	1	2	yes	complemented
591	#3265	C₂×C₅₃	1	2	yes	complemented
592	#3264	C₂×C₅₃	1	2	yes	complemented
593	#3224	C₂×C₅₃	1	2	yes	complemented
594	#3198	C₂×C₅₃	1	2	yes	complemented
595	#3190	C₂×C₅₃	1	1	yes	characteristic, complemented
596	#3188	C₂×C₅₃	1	1	yes	characteristic, complemented
597	#3118	C₂×C₅₃	1	2	yes	complemented
598	#3012	C₂×C₅₃	1	2	yes	complemented
599	C₂×#450	C₂×C₅₃	1	1	yes	characteristic, complemented
600	C₂×#447	C₂×C₅₃	1	1	yes	characteristic, complemented
601	#2977	C₂×C₅₃	1	1	yes	characteristic, complemented
602	C₂×C₅₃	—	2	2	no	—
603	C₂×C₅₃	—	2	2	no	—
604	C₂×C₅₃	—	4	1	no	—
605	C₂×C₅₃	—	4	2	no	—
606	C₂×C₅₃	—	4	4	no	—
607	C₂×C₅₃	—	8	2	no	—
608	C₂×C₅₃	—	8	2	no	—
609	C₂×C₅₃	—	8	1	no	—
610	C₂×C₅₃	#3484	1	1	yes	characteristic
611	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
612	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
613	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic, complemented
614	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
615	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
616	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
617	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
618	C₂²×D₈	C₂²×C₅₃	1	2	yes	complemented
619	#562	—	2	2	no	—
620	#554	C₂²×C₅₃	1	2	yes	complemented
621	#548	C₂²×C₅₃	1	2	yes	complemented
622	#547	C₂²×C₅₃	1	2	yes	complemented
623	#546	—	2	1	no	—
624	#546	—	2	1	no	—
625	#546	—	2	2	no	—
626	#546	C₂²×C₅₃	1	2	yes	—
627	#546	C₂²×C₅₃	1	2	yes	complemented
628	#546	C₂²×C₅₃	1	2	yes	complemented
629	D₄²	—	2	1	no	—
630	D₄²	—	2	1	no	—
631	D₄²	C₂²×C₅₃	1	2	yes	—
632	D₄²	C₂²×C₅₃	1	2	yes	complemented
633	#543	—	2	1	no	—
634	#542	C₂²×C₅₃	1	2	yes	complemented
635	#539	—	2	1	no	—
636	#538	—	2	1	no	—
637	#537	—	2	1	no	—
638	#537	C₂²×C₅₃	1	2	yes	complemented
639	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
640	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
641	#534	—	2	2	no	—
642	#525	C₂²×C₅₃	1	1	yes	characteristic
643	#525	C₂²×C₅₃	1	1	yes	characteristic
644	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
645	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
646	C₂×#120	—	2	2	no	—
647	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
648	#496	C₂²×C₅₃	1	2	yes	complemented
649	#495	C₂²×C₅₃	1	2	yes	complemented
650	#489	C₂²×C₅₃	1	2	yes	complemented
651	#486	C₂²×C₅₃	1	2	yes	complemented
652	#485	C₂²×C₅₃	1	2	yes	complemented
653	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
654	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
655	#482	C₂²×C₅₃	1	2	yes	complemented
656	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
657	#481	C₂²×C₅₃	1	2	yes	complemented
658	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
659	#480	C₂²×C₅₃	1	2	yes	complemented
660	#476	C₂²×C₅₃	1	2	yes	complemented
661	#474	C₂²×C₅₃	1	2	yes	complemented
662	#469	C₂²×C₅₃	1	2	yes	complemented
663	#468	C₂²×C₅₃	1	2	yes	complemented
664	#467	C₂²×C₅₃	1	2	yes	complemented
665	#466	C₂²×C₅₃	1	2	yes	complemented
666	#466	C₂²×C₅₃	1	2	yes	complemented
667	#465	C₂²×C₅₃	1	2	yes	complemented
668	#465	C₂²×C₅₃	1	2	yes	complemented
669	#465	C₂²×C₅₃	1	2	yes	complemented
670	#464	C₂²×C₅₃	1	2	yes	complemented
671	#463	C₂²×C₅₃	1	2	yes	complemented
672	#463	C₂²×C₅₃	1	2	yes	complemented
673	#463	C₂²×C₅₃	1	2	yes	complemented
674	#460	C₂²×C₅₃	1	2	yes	complemented
675	#459	C₂²×C₅₃	1	2	yes	complemented
676	#452	C₂²×C₅₃	1	2	yes	complemented
677	#452	C₂²×C₅₃	1	2	yes	complemented
678	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
679	#450	C₂²×C₅₃	1	2	yes	complemented
680	#450	C₂²×C₅₃	1	2	yes	complemented
681	#450	C₂²×C₅₃	1	2	yes	complemented
682	#450	C₂²×C₅₃	1	2	yes	complemented
683	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
684	#450	C₂²×C₅₃	1	2	yes	complemented
685	#449	C₂²×C₅₃	1	2	yes	complemented
686	#449	C₂²×C₅₃	1	2	yes	complemented
687	#449	C₂²×C₅₃	1	2	yes	complemented
688	#449	C₂²×C₅₃	1	2	yes	complemented
689	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
690	#447	C₂²×C₅₃	1	2	yes	—
691	#447	C₂²×C₅₃	1	2	yes	complemented
692	#447	C₂²×C₅₃	1	2	yes	complemented
693	#447	C₂²×C₅₃	1	2	yes	complemented
694	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
695	#447	C₂²×C₅₃	1	2	yes	complemented
696	#442	C₂²×C₅₃	1	2	yes	complemented
697	#440	C₂²×C₅₃	1	2	yes	complemented
698	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
699	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
700	#435	C₂²×C₅₃	1	2	yes	complemented
701	#435	C₂²×C₅₃	1	2	yes	complemented
702	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
703	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
704	#433	C₂²×C₅₃	1	2	yes	complemented
705	#417	C₂²×C₅₃	1	2	yes	complemented
706	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
707	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
708	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
709	#408	C₂²×C₅₃	1	2	yes	complemented
710	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
711	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	C₅₃	#61629	1	1	yes	characteristic, direct product factor, Sylow
713	C₂⁵	—	2	1	no	—
714	H(5,𝔽₂)	—	4	4	no	—
715	C₂×#41	—	2	1	no	—
716	C₂×#41	—	2	2	no	—
717	C₂×#41	C₂³×C₅₃	1	2	yes	—
718	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
719	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
720	C₂×#41	C₂³×C₅₃	1	2	yes	complemented
721	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
722	C₂²×D₄	—	2	1	no	—
723	C₂²×D₄	—	2	2	no	—
724	C₂²×D₄	—	2	1	no	—
725	C₂²×D₄	—	2	2	no	—
726	C₂²×D₄	—	2	2	no	—
727	C₂²×D₄	—	2	1	no	—
728	C₂²×D₄	—	2	1	no	—
729	C₂²×D₄	—	2	1	no	—
730	C₂²×D₄	—	4	4	no	—
731	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
732	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
733	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
734	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
735	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
736	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
737	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
738	AGL(1,ℤ/8)	—	4	4	no	—
739	#135	—	4	4	no	—
740	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	complemented
741	C₂×SD₁₆	—	4	4	no	—
742	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	complemented
747	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	complemented
748	C₂×D₈	—	4	4	no	—
749	C₂×D₈	C₂³×C₅₃	1	2	yes	—
750	C₂×D₈	C₂³×C₅₃	1	2	yes	—
751	C₂×D₈	C₂³×C₅₃	1	2	yes	—
752	C₂×D₈	C₂³×C₅₃	1	2	yes	—
753	C₂×D₈	C₂³×C₅₃	1	2	yes	complemented
754	C₂×M₁₆	C₂³×C₅₃	1	2	yes	complemented
755	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
756	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
757	C₂²×C₈	C₂³×C₅₃	1	2	yes	complemented
758	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
759	#127	—	2	1	no	—
760	#127	C₂³×C₅₃	1	2	yes	—
761	#126	—	2	2	no	—
762	#125	—	2	2	no	—
763	#124	—	2	1	no	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	C₂³×C₅₃	1	2	yes	—
767	#124	C₂³×C₅₃	1	2	yes	complemented
768	#123	—	2	1	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	D₄×C₅₃	1	2	yes	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
785	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
786	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
788	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
789	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
790	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
791	#121	—	2	2	no	—
792	#121	—	2	2	no	—
793	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	—	2	1	no	—
796	#121	—	2	1	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	—	2	1	no	—
800	#121	—	2	1	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	D₄×C₅₃	1	1	yes	characteristic
805	#121	D₄×C₅₃	1	1	yes	characteristic
806	#121	C₂³×C₅₃	1	2	yes	—
807	#121	C₂³×C₅₃	1	2	yes	—
808	#121	C₂³×C₅₃	1	1	yes	characteristic
809	#121	C₂³×C₅₃	1	1	yes	characteristic
810	#121	C₂³×C₅₃	1	2	yes	—
811	#121	C₂³×C₅₃	1	2	yes	—
812	#121	C₂³×C₅₃	1	2	yes	complemented
813	#120	—	2	1	no	—
814	#120	—	2	2	no	—
815	#120	—	2	2	no	—
816	#120	—	2	2	no	—
817	#120	—	2	2	no	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	#120	D₄×C₅₃	1	2	yes	—
824	C₄×Q₈	C₂³×C₅₃	1	2	yes	complemented
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	C₂³×C₅₃	1	2	yes	—
832	C₄×D₄	C₂³×C₅₃	1	2	yes	—
833	C₄×D₄	C₂³×C₅₃	1	2	yes	—
834	C₄×D₄	C₂³×C₅₃	1	2	yes	—
835	C₄×D₄	C₂³×C₅₃	1	2	yes	complemented
836	#117	C₂³×C₅₃	1	1	yes	characteristic
837	#117	C₂³×C₅₃	1	1	yes	characteristic
838	C₂×C₄⋊C₄	—	2	1	no	—
839	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
842	C₂×C₂²⋊C₄	—	2	1	no	—
843	C₂×C₂²⋊C₄	—	2	1	no	—
844	C₂×C₂²⋊C₄	—	2	2	no	—
845	C₂×C₂²⋊C₄	—	2	2	no	—
846	C₂×C₂²⋊C₄	—	2	2	no	—
847	C₂×C₂²⋊C₄	—	2	2	no	—
848	#107	C₂³×C₅₃	1	2	yes	complemented
849	#107	C₂³×C₅₃	1	2	yes	complemented
850	#106	C₂³×C₅₃	1	2	yes	complemented
851	#106	C₂³×C₅₃	1	2	yes	complemented
852	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
853	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
854	#103	C₂³×C₅₃	1	2	yes	complemented
855	#103	C₂³×C₅₃	1	2	yes	complemented
856	#103	C₂³×C₅₃	1	2	yes	complemented
857	#103	C₂³×C₅₃	1	2	yes	complemented
858	#102	C₂³×C₅₃	1	2	yes	—
859	#102	C₂³×C₅₃	1	2	yes	—
860	#102	C₂³×C₅₃	1	2	yes	—
861	#102	C₂³×C₅₃	1	2	yes	—
862	#102	C₂³×C₅₃	1	2	yes	—
863	#102	C₂³×C₅₃	1	2	yes	—
864	#102	C₂³×C₅₃	1	2	yes	—
865	#102	C₂³×C₅₃	1	2	yes	—
866	#102	C₂³×C₅₃	1	2	yes	complemented
867	#102	C₂³×C₅₃	1	2	yes	complemented
868	#102	C₂³×C₅₃	1	2	yes	complemented
869	#102	C₂³×C₅₃	1	2	yes	complemented
870	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
874	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
875	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
876	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	complemented
877	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	complemented
878	#97	C₂³×C₅₃	1	2	yes	complemented
879	C₄×C₈	C₂³×C₅₃	1	2	yes	complemented
880	C₂⁴	—	2	1	no	—
881	C₂⁴	—	2	2	no	—
882	C₂⁴	—	2	2	no	—
883	C₂⁴	—	2	1	no	—
884	C₂⁴	—	2	1	no	—
885	C₂⁴	—	2	2	no	—
886	C₂⁴	—	4	4	no	—
887	C₂⁴	—	8	2	no	—
888	C₂⁴	—	8	2	no	—
889	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
890	#41	—	2	4	no	—
891	#41	—	4	2	no	—
892	#41	—	4	2	no	—
893	#41	—	4	2	no	—
894	#41	—	4	2	no	—
895	#41	—	4	2	no	—
896	#41	—	4	4	no	—
897	#41	—	8	4	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	4	2	no	—
901	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
902	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
903	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
904	C₂×D₄	—	2	4	no	—
905	C₂×D₄	—	2	4	no	—
906	C₂×D₄	—	2	4	no	—
907	C₂×D₄	—	2	4	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	4	2	no	—
927	C₂×D₄	—	4	2	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	4	2	no	—
930	C₂×D₄	—	4	2	no	—
931	C₂×D₄	—	4	4	no	—
932	C₂×D₄	—	4	4	no	—
933	C₂×D₄	—	4	4	no	—
934	C₂×D₄	—	4	4	no	—
935	C₂×D₄	—	4	8	no	—
936	C₂×D₄	—	8	4	no	—
937	C₂×D₄	—	8	4	no	—
938	C₂×D₄	—	8	2	no	—
939	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
940	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
941	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
942	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
943	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
944	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
946	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	4	2	no	—
958	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
959	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
960	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
961	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
962	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
963	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
965	Q₁₆	—	4	2	no	—
966	SD₁₆	—	2	4	no	—
967	SD₁₆	—	2	4	no	—
968	SD₁₆	—	4	2	no	—
969	SD₁₆	—	4	2	no	—
970	SD₁₆	—	4	2	no	—
971	SD₁₆	—	4	2	no	—
972	D₈	—	2	4	no	—
973	D₈	—	2	4	no	—
974	D₈	—	4	2	no	—
975	D₈	—	4	2	no	—
976	D₈	—	4	2	no	—
977	M₁₆	—	4	2	no	—
978	C₂×C₈	—	4	2	no	—
979	C₂×C₈	—	4	2	no	—
980	C₂×C₈	—	4	2	no	—
981	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
982	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
983	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
984	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
996	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
997	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
998	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1000	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	C₂⁴×C₅₃	1	2	yes	—
1031	C₂³	—	2	4	no	—
1032	C₂³	—	2	2	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	4	1	no	—
1039	C₂³	—	4	4	no	—
1040	C₂³	—	4	4	no	—
1041	C₂³	—	4	4	no	—
1042	C₂³	—	4	2	no	—
1043	C₂³	—	4	4	no	—
1044	C₂³	—	4	4	no	—
1045	C₂³	—	4	2	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	—	8	2	no	—
1048	C₂³	—	8	1	no	—
1049	C₂³	—	8	1	no	—
1050	C₂³	—	8	1	no	—
1051	C₂³	—	8	1	no	—
1052	C₂³	—	8	1	no	—
1053	C₂³	—	8	1	no	—
1054	C₂³	—	8	2	no	—
1055	C₂³	—	8	2	no	—
1056	C₂³	—	8	16	no	—
1057	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1058	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1059	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1060	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1061	Q₈	—	2	2	no	—
1062	Q₈	—	2	2	no	—
1063	Q₈	—	2	2	no	—
1064	Q₈	—	4	1	no	—
1065	Q₈	—	8	1	no	—
1066	Q₈	—	8	2	no	—
1067	D₄	—	2	4	no	—
1068	D₄	—	2	4	no	—
1069	D₄	—	2	4	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	2	2	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	2	no	—
1074	D₄	—	2	2	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	4	1	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	4	4	no	—
1079	D₄	—	4	4	no	—
1080	D₄	—	4	4	no	—
1081	D₄	—	4	2	no	—
1082	D₄	—	4	4	no	—
1083	D₄	—	4	2	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	4	4	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	8	1	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	—	8	2	no	—
1095	D₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	1	no	—
1109	C₂×C₄	—	4	1	no	—
1110	C₂×C₄	—	4	4	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	8	2	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	—	8	1	no	—
1118	C₂×C₄	—	8	1	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1121	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1123	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1124	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1125	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1126	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1127	C₈	—	2	2	no	—
1128	C₈	—	2	2	no	—
1129	C₈	—	2	2	no	—
1130	C₈	—	2	2	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	4	no	—
1138	C₂²	—	2	2	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	4	4	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	8	8	no	—
1155	C₂²	—	8	8	no	—
1156	C₂²	—	8	4	no	—
1157	C₂²	—	8	4	no	—
1158	C₂²	—	16	2	no	—
1159	C₂²	—	16	4	no	—
1160	C₂²	C₅₃×#576	1	2	yes	—
1161	C₂²	C₅₃×#577	1	2	yes	—
1162	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1163	C₄	—	2	1	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	1	no	—
1166	C₄	—	2	1	no	—
1167	C₄	—	2	2	no	—
1168	C₄	—	2	2	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	2	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	4	2	no	—
1174	C₄	—	4	1	no	—
1175	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1176	C₂	—	2	2	no	—
1177	C₂	—	2	2	no	—
1178	C₂	—	4	1	no	—
1179	C₂	—	4	2	no	—
1180	C₂	—	4	4	no	—
1181	C₂	—	8	2	no	—
1182	C₂	—	8	1	no	—
1183	C₂	—	8	2	no	—
1184	C₂	C₅₃×#3484	1	1	yes	characteristic
1185	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1186	C₂	C₂×C₅₃×#577	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3536	C₂	semidirect
2. C₅₃×#3484	C₂	semidirect
3. C₅₃×#3314	C₂	semidirect
4. C₅₃×#3306	C₂	semidirect
5. C₅₃×#3295	C₂	semidirect
6. C₅₃×#3294	C₂	semidirect
7. C₅₃×#3282	C₂	semidirect
8. C₅₃×#3280	C₂	semidirect
9. C₅₃×#3265	C₂	semidirect
10. C₅₃×#3264	C₂	semidirect
11. C₅₃×#3224	C₂	semidirect
12. C₅₃×#3198	C₂	semidirect
13. C₅₃×#3190	C₂	semidirect
14. C₅₃×#3188	C₂	semidirect
15. C₅₃×#3118	C₂	semidirect
16. C₅₃×#3012	C₂	semidirect
17. C₂×C₅₃×#450	C₂	semidirect
18. C₂×C₅₃×#447	C₂	semidirect
19. C₅₃×#2977	C₂	semidirect
20. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
22. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
23. C₂×#135×C₅₃	C₂²	semidirect
24. C₂²×SD₁₆×C₅₃	C₂²	semidirect
25. C₂²×D₈×C₅₃	C₂²	semidirect
27. C₅₃×#554	C₂²	semidirect
28. C₅₃×#548	C₂²	semidirect
29. C₅₃×#547	C₂²	semidirect
34. C₅₃×#546	C₂²	semidirect
35. C₅₃×#546	C₂²	semidirect
39. D₄²×C₅₃	C₂²	semidirect
41. C₅₃×#542	C₂²	semidirect
45. C₅₃×#537	C₂²	semidirect
46. C₅₃×#535	C₂²	semidirect
47. C₅₃×#535	C₂²	semidirect
51. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
52. C₂×#121×C₅₃	C₂²	semidirect
54. C₅₃×#518	C₂²	semidirect
55. C₅₃×#496	C₂²	semidirect
56. C₅₃×#495	C₂²	semidirect
57. C₅₃×#489	C₂²	semidirect
58. C₅₃×#486	C₂²	semidirect
59. C₅₃×#485	C₂²	semidirect
60. C₅₃×#484	C₂²	semidirect
61. C₅₃×#483	C₂²	semidirect
62. C₅₃×#482	C₂²	semidirect
63. C₅₃×#481	C₂²	semidirect
64. C₅₃×#481	C₂²	semidirect
65. C₅₃×#480	C₂²	semidirect
66. C₅₃×#480	C₂²	semidirect
67. C₅₃×#476	C₂²	semidirect
68. C₅₃×#474	C₂²	semidirect
69. C₅₃×#469	C₂²	semidirect
70. C₅₃×#468	C₂²	semidirect
71. C₅₃×#467	C₂²	semidirect
72. C₅₃×#466	C₂²	semidirect
73. C₅₃×#466	C₂²	semidirect
74. C₅₃×#465	C₂²	semidirect
75. C₅₃×#465	C₂²	semidirect
76. C₅₃×#465	C₂²	semidirect
77. C₅₃×#464	C₂²	semidirect
78. C₅₃×#463	C₂²	semidirect
79. C₅₃×#463	C₂²	semidirect
80. C₅₃×#463	C₂²	semidirect
81. C₅₃×#460	C₂²	semidirect
82. C₅₃×#459	C₂²	semidirect
83. C₅₃×#452	C₂²	semidirect
84. C₅₃×#452	C₂²	semidirect
85. C₅₃×#451	C₂²	semidirect
86. C₅₃×#450	C₂²	semidirect
87. C₅₃×#450	C₂²	semidirect
88. C₅₃×#450	C₂²	semidirect
89. C₅₃×#450	C₂²	semidirect
90. C₅₃×#450	C₂²	semidirect
91. C₅₃×#450	C₂²	semidirect
92. C₅₃×#449	C₂²	semidirect
93. C₅₃×#449	C₂²	semidirect
94. C₅₃×#449	C₂²	semidirect
95. C₅₃×#449	C₂²	semidirect
96. C₅₃×#448	C₂²	semidirect
98. C₅₃×#447	C₂²	semidirect
99. C₅₃×#447	C₂²	semidirect
100. C₅₃×#447	C₂²	semidirect
101. C₅₃×#447	C₂²	semidirect
102. C₅₃×#447	C₂²	semidirect
103. C₅₃×#442	C₂²	semidirect
104. C₅₃×#440	C₂²	semidirect
105. C₄×SD₁₆×C₅₃	C₂²	semidirect
106. C₄×D₈×C₅₃	C₂²	semidirect
107. C₅₃×#435	C₂²	semidirect
108. C₅₃×#435	C₂²	semidirect
109. C₈×D₄×C₅₃	C₂²	semidirect
110. C₈×D₄×C₅₃	C₂²	semidirect
111. C₅₃×#433	C₂²	semidirect
112. C₅₃×#417	C₂²	semidirect
113. C₂×#102×C₅₃	C₂²	semidirect
114. C₂×#102×C₅₃	C₂²	semidirect
115. C₂×#102×C₅₃	C₂²	semidirect
116. C₅₃×#408	C₂²	semidirect
117. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
118. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
126. C₂×#41×C₅₃	C₂³	semidirect
146. C₂×Q₁₆×C₅₃	C₂³	semidirect
152. C₂×SD₁₆×C₅₃	C₂³	semidirect
153. C₂×SD₁₆×C₅₃	C₂³	semidirect
159. C₂×D₈×C₅₃	C₂³	semidirect
160. C₂×M₁₆×C₅₃	C₂³	semidirect
163. C₂²×C₈×C₅₃	C₂³	semidirect
164. C₄⋊Q₈×C₅₃	C₂³	semidirect
173. #124×C₅₃	C₂³	semidirect
196. C₂²⋊Q₈×C₅₃	C₂³	semidirect
218. #121×C₅₃	C₂³	semidirect
230. C₄×Q₈×C₅₃	C₂³	semidirect
241. C₄×D₄×C₅₃	C₂³	semidirect
247. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
254. #107×C₅₃	C₂³	semidirect
255. #107×C₅₃	C₂³	semidirect
256. #106×C₅₃	C₂³	semidirect
257. #106×C₅₃	C₂³	semidirect
258. C₄⋊C₈×C₅₃	C₂³	semidirect
259. C₄⋊C₈×C₅₃	C₂³	semidirect
260. #103×C₅₃	C₂³	semidirect
261. #103×C₅₃	C₂³	semidirect
262. #103×C₅₃	C₂³	semidirect
263. #103×C₅₃	C₂³	semidirect
272. #102×C₅₃	C₂³	semidirect
273. #102×C₅₃	C₂³	semidirect
274. #102×C₅₃	C₂³	semidirect
275. #102×C₅₃	C₂³	semidirect
282. C₂²⋊C₈×C₅₃	C₂³	semidirect
283. C₂²⋊C₈×C₅₃	C₂³	semidirect
284. #97×C₅₃	C₂³	semidirect
285. C₄×C₈×C₅₃	C₂³	semidirect
537. #61629	C₅₃	direct (N × H)
583. #3536	C₂×C₅₃	semidirect
584. #3484	C₂×C₅₃	semidirect
585. #3314	C₂×C₅₃	semidirect
586. #3306	C₂×C₅₃	semidirect
587. #3295	C₂×C₅₃	semidirect
588. #3294	C₂×C₅₃	semidirect
589. #3282	C₂×C₅₃	semidirect
590. #3280	C₂×C₅₃	semidirect
591. #3265	C₂×C₅₃	semidirect
592. #3264	C₂×C₅₃	semidirect
593. #3224	C₂×C₅₃	semidirect
594. #3198	C₂×C₅₃	semidirect
595. #3190	C₂×C₅₃	semidirect
596. #3188	C₂×C₅₃	semidirect
597. #3118	C₂×C₅₃	semidirect
598. #3012	C₂×C₅₃	semidirect
599. C₂×#450	C₂×C₅₃	semidirect
600. C₂×#447	C₂×C₅₃	semidirect
601. #2977	C₂×C₅₃	semidirect
613. C₂×H(5,𝔽₂)	C₂²×C₅₃	semidirect
615. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
616. C₂×#135	C₂²×C₅₃	semidirect
617. C₂²×SD₁₆	C₂²×C₅₃	semidirect
618. C₂²×D₈	C₂²×C₅₃	semidirect
620. #554	C₂²×C₅₃	semidirect
621. #548	C₂²×C₅₃	semidirect
622. #547	C₂²×C₅₃	semidirect
627. #546	C₂²×C₅₃	semidirect
628. #546	C₂²×C₅₃	semidirect
632. D₄²	C₂²×C₅₃	semidirect
634. #542	C₂²×C₅₃	semidirect
638. #537	C₂²×C₅₃	semidirect
639. #535	C₂²×C₅₃	semidirect
640. #535	C₂²×C₅₃	semidirect
644. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
645. C₂×#121	C₂²×C₅₃	semidirect
647. #518	C₂²×C₅₃	semidirect
648. #496	C₂²×C₅₃	semidirect
649. #495	C₂²×C₅₃	semidirect
650. #489	C₂²×C₅₃	semidirect
651. #486	C₂²×C₅₃	semidirect
652. #485	C₂²×C₅₃	semidirect
653. #484	C₂²×C₅₃	semidirect
654. #483	C₂²×C₅₃	semidirect
655. #482	C₂²×C₅₃	semidirect
656. #481	C₂²×C₅₃	semidirect
657. #481	C₂²×C₅₃	semidirect
658. #480	C₂²×C₅₃	semidirect
659. #480	C₂²×C₅₃	semidirect
660. #476	C₂²×C₅₃	semidirect
661. #474	C₂²×C₅₃	semidirect
662. #469	C₂²×C₅₃	semidirect
663. #468	C₂²×C₅₃	semidirect
664. #467	C₂²×C₅₃	semidirect
665. #466	C₂²×C₅₃	semidirect
666. #466	C₂²×C₅₃	semidirect
667. #465	C₂²×C₅₃	semidirect
668. #465	C₂²×C₅₃	semidirect
669. #465	C₂²×C₅₃	semidirect
670. #464	C₂²×C₅₃	semidirect
671. #463	C₂²×C₅₃	semidirect
672. #463	C₂²×C₅₃	semidirect
673. #463	C₂²×C₅₃	semidirect
674. #460	C₂²×C₅₃	semidirect
675. #459	C₂²×C₅₃	semidirect
676. #452	C₂²×C₅₃	semidirect
677. #452	C₂²×C₅₃	semidirect
678. #451	C₂²×C₅₃	semidirect
679. #450	C₂²×C₅₃	semidirect
680. #450	C₂²×C₅₃	semidirect
681. #450	C₂²×C₅₃	semidirect
682. #450	C₂²×C₅₃	semidirect
683. #450	C₂²×C₅₃	semidirect
684. #450	C₂²×C₅₃	semidirect
685. #449	C₂²×C₅₃	semidirect
686. #449	C₂²×C₅₃	semidirect
687. #449	C₂²×C₅₃	semidirect
688. #449	C₂²×C₅₃	semidirect
689. #448	C₂²×C₅₃	semidirect
691. #447	C₂²×C₅₃	semidirect
692. #447	C₂²×C₅₃	semidirect
693. #447	C₂²×C₅₃	semidirect
694. #447	C₂²×C₅₃	semidirect
695. #447	C₂²×C₅₃	semidirect
696. #442	C₂²×C₅₃	semidirect
697. #440	C₂²×C₅₃	semidirect
698. C₄×SD₁₆	C₂²×C₅₃	semidirect
699. C₄×D₈	C₂²×C₅₃	semidirect
700. #435	C₂²×C₅₃	semidirect
701. #435	C₂²×C₅₃	semidirect
702. C₈×D₄	C₂²×C₅₃	semidirect
703. C₈×D₄	C₂²×C₅₃	semidirect
704. #433	C₂²×C₅₃	semidirect
705. #417	C₂²×C₅₃	semidirect
706. C₂×#102	C₂²×C₅₃	semidirect
707. C₂×#102	C₂²×C₅₃	semidirect
708. C₂×#102	C₂²×C₅₃	semidirect
709. #408	C₂²×C₅₃	semidirect
710. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
711. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
712. C₅₃	#61629	direct (N × H)
720. C₂×#41	C₂³×C₅₃	semidirect
740. C₂×Q₁₆	C₂³×C₅₃	semidirect
746. C₂×SD₁₆	C₂³×C₅₃	semidirect
747. C₂×SD₁₆	C₂³×C₅₃	semidirect
753. C₂×D₈	C₂³×C₅₃	semidirect
754. C₂×M₁₆	C₂³×C₅₃	semidirect
757. C₂²×C₈	C₂³×C₅₃	semidirect
758. C₄⋊Q₈	C₂³×C₅₃	semidirect
767. #124	C₂³×C₅₃	semidirect
790. C₂²⋊Q₈	C₂³×C₅₃	semidirect
812. #121	C₂³×C₅₃	semidirect
824. C₄×Q₈	C₂³×C₅₃	semidirect
835. C₄×D₄	C₂³×C₅₃	semidirect
841. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
848. #107	C₂³×C₅₃	semidirect
849. #107	C₂³×C₅₃	semidirect
850. #106	C₂³×C₅₃	semidirect
851. #106	C₂³×C₅₃	semidirect
852. C₄⋊C₈	C₂³×C₅₃	semidirect
853. C₄⋊C₈	C₂³×C₅₃	semidirect
854. #103	C₂³×C₅₃	semidirect
855. #103	C₂³×C₅₃	semidirect
856. #103	C₂³×C₅₃	semidirect
857. #103	C₂³×C₅₃	semidirect
866. #102	C₂³×C₅₃	semidirect
867. #102	C₂³×C₅₃	semidirect
868. #102	C₂³×C₅₃	semidirect
869. #102	C₂³×C₅₃	semidirect
876. C₂²⋊C₈	C₂³×C₅₃	semidirect
877. C₂²⋊C₈	C₂³×C₅₃	semidirect
878. #97	C₂³×C₅₃	semidirect
879. C₄×C₈	C₂³×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3536	2
C₅₃×#3484	2
C₅₃×#3314	2
C₅₃×#3306	2
C₅₃×#3295	2
C₅₃×#3294	2
C₅₃×#3282	2
C₅₃×#3280	2
C₅₃×#3265	2
C₅₃×#3264	2
C₅₃×#3224	2
C₅₃×#3198	2
C₅₃×#3190	2
C₅₃×#3188	2
C₅₃×#3118	2
C₅₃×#3012	2
C₂×C₅₃×#450	2
C₂×C₅₃×#447	2
C₅₃×#2977	2
#61629	53

Subgroups — C53×#61629 #27269141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61629 #27269141