Subgroups — C₅₃×#61643 #27269155

Order 13568.

2230 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3323	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3322	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3318	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3310	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3274	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3272	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3268	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3267	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3222	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3220	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3198	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3197	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3123	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3122	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3012	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3003	C₂	1	2	yes	maximal, complemented
19	C₅₃×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
23	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
25	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
26	C₅₃×#560	—	2	2	no	—
27	C₅₃×#553	—	2	2	no	—
28	C₅₃×#553	C₂²	1	2	yes	complemented
29	C₅₃×#552	C₂²	1	2	yes	complemented
30	C₅₃×#550	C₂²	1	2	yes	complemented
31	C₅₃×#547	C₂²	1	2	yes	complemented
32	C₅₃×#546	—	2	2	no	—
33	C₅₃×#546	C₂²	1	2	yes	—
34	C₅₃×#546	C₂²	1	2	yes	—
35	D₄²×C₅₃	—	2	2	no	—
36	D₄²×C₅₃	C₂²	1	2	yes	—
37	D₄²×C₅₃	C₂²	1	2	yes	—
38	C₅₃×#541	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#540	—	2	2	no	—
40	C₅₃×#540	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#539	—	2	2	no	—
42	C₅₃×#537	C₂²	1	2	yes	complemented
43	C₅₃×#535	C₂²	1	1	yes	characteristic
44	C₅₃×#535	C₂²	1	1	yes	characteristic
45	C₅₃×#534	—	2	2	no	—
46	C₅₃×#525	C₂²	1	1	yes	characteristic
47	C₅₃×#525	C₂²	1	1	yes	characteristic
48	C₅₃×#525	C₂²	1	2	yes	complemented
49	C₂×#120×C₅₃	—	2	2	no	—
50	C₅₃×#518	C₂²	1	1	yes	characteristic
51	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#496	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#488	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#488	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#485	C₂²	1	2	yes	complemented
60	C₅₃×#485	C₂²	1	2	yes	complemented
61	C₅₃×#482	C₂²	1	2	yes	complemented
62	C₅₃×#482	C₂²	1	2	yes	complemented
63	C₅₃×#481	C₂²	1	2	yes	complemented
64	C₅₃×#480	C₂²	1	2	yes	complemented
65	C₅₃×#478	C₂²	1	2	yes	complemented
66	C₅₃×#478	C₂²	1	2	yes	complemented
67	C₅₃×#470	C₂²	1	2	yes	complemented
68	C₅₃×#469	C₂²	1	2	yes	complemented
69	C₅₃×#469	C₂²	1	2	yes	complemented
70	C₅₃×#468	C₂²	1	2	yes	complemented
71	C₅₃×#468	C₂²	1	2	yes	complemented
72	C₅₃×#468	C₂²	1	2	yes	complemented
73	C₅₃×#466	C₂²	1	2	yes	complemented
74	C₅₃×#465	C₂²	1	2	yes	complemented
75	C₅₃×#464	C₂²	1	2	yes	complemented
76	C₅₃×#463	C₂²	1	2	yes	complemented
77	C₅₃×#461	C₂²	1	2	yes	complemented
78	C₅₃×#460	C₂²	1	2	yes	complemented
79	C₅₃×#459	C₂²	1	2	yes	complemented
80	C₅₃×#459	C₂²	1	2	yes	complemented
81	C₅₃×#452	C₂²	1	2	yes	complemented
82	C₅₃×#452	C₂²	1	2	yes	complemented
83	C₅₃×#452	C₂²	1	2	yes	complemented
84	C₅₃×#450	C₂²	1	2	yes	—
85	C₅₃×#450	C₂²	1	2	yes	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×#449	C₂²	1	2	yes	complemented
90	C₅₃×#449	C₂²	1	2	yes	complemented
91	C₅₃×#449	C₂²	1	2	yes	complemented
92	C₅₃×#449	C₂²	1	2	yes	complemented
93	C₅₃×#449	C₂²	1	2	yes	complemented
94	C₅₃×#447	C₂²	1	2	yes	—
95	C₅₃×#447	C₂²	1	2	yes	complemented
96	C₅₃×#447	C₂²	1	2	yes	complemented
97	C₅₃×#447	C₂²	1	2	yes	complemented
98	C₅₃×#447	C₂²	1	2	yes	complemented
99	C₅₃×#442	C₂²	1	2	yes	complemented
100	C₅₃×#440	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
102	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
103	C₅₃×#436	C₂²	1	2	yes	complemented
104	C₅₃×#436	C₂²	1	2	yes	complemented
105	C₅₃×#435	C₂²	1	2	yes	complemented
106	C₅₃×#435	C₂²	1	2	yes	complemented
107	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#418	C₂²	1	2	yes	complemented
110	C₅₃×#418	C₂²	1	2	yes	complemented
111	C₅₃×#417	C₂²	1	2	yes	complemented
112	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
113	C₅₃×#408	C₂²	1	2	yes	complemented
114	C₅₃×#407	C₂²	1	2	yes	complemented
115	C₂⁵×C₅₃	—	2	1	no	—
116	H(5,𝔽₂)×C₅₃	—	4	4	no	—
117	C₂×#41×C₅₃	—	2	1	no	—
118	C₂×#41×C₅₃	C₂³	1	2	yes	—
119	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
120	C₂×#41×C₅₃	C₂³	1	2	yes	—
121	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
122	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
123	C₂²×D₄×C₅₃	—	2	2	no	—
124	C₂²×D₄×C₅₃	—	2	1	no	—
125	C₂²×D₄×C₅₃	—	2	2	no	—
126	C₂²×D₄×C₅₃	—	2	2	no	—
127	C₂²×D₄×C₅₃	—	2	1	no	—
128	C₂²×D₄×C₅₃	—	2	2	no	—
129	C₂²×D₄×C₅₃	—	4	4	no	—
130	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
132	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
133	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
134	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
136	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
137	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
138	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
139	#135×C₅₃	—	4	4	no	—
140	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	complemented
141	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	complemented
146	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	complemented
147	C₂×D₈×C₅₃	C₂³	1	2	yes	—
148	C₂×D₈×C₅₃	C₂³	1	2	yes	—
149	C₂×D₈×C₅₃	C₂³	1	2	yes	—
150	C₂×D₈×C₅₃	C₂³	1	2	yes	—
151	C₂×D₈×C₅₃	C₂³	1	2	yes	complemented
152	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×M₁₆×C₅₃	C₂³	1	2	yes	complemented
155	C₂²×C₈×C₅₃	C₂³	1	2	yes	complemented
156	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
157	#127×C₅₃	—	2	1	no	—
158	#127×C₅₃	—	2	2	no	—
159	#127×C₅₃	C₂³	1	1	yes	characteristic
160	#127×C₅₃	C₂³	1	1	yes	characteristic
161	#127×C₅₃	C₂³	1	1	yes	characteristic, complemented
162	#126×C₅₃	—	2	2	no	—
163	#126×C₅₃	—	2	2	no	—
164	#126×C₅₃	—	2	2	no	—
165	#125×C₅₃	—	2	2	no	—
166	#125×C₅₃	—	2	2	no	—
167	#125×C₅₃	C₂³	1	1	yes	characteristic, complemented
168	#125×C₅₃	C₂³	1	1	yes	characteristic, complemented
169	#124×C₅₃	—	2	1	no	—
170	#124×C₅₃	C₂³	1	1	yes	characteristic
171	#124×C₅₃	C₂³	1	1	yes	characteristic
172	#123×C₅₃	—	2	2	no	—
173	#123×C₅₃	—	2	2	no	—
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	1	no	—
180	#123×C₅₃	—	2	2	no	—
181	#123×C₅₃	D₄	1	2	yes	—
182	C₂²⋊Q₈×C₅₃	—	2	2	no	—
183	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
184	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
185	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
186	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
187	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
188	#121×C₅₃	—	2	2	no	—
189	#121×C₅₃	—	2	2	no	—
190	#121×C₅₃	—	2	2	no	—
191	#121×C₅₃	—	2	2	no	—
192	#121×C₅₃	—	2	2	no	—
193	#121×C₅₃	—	2	2	no	—
194	#121×C₅₃	—	2	2	no	—
195	#121×C₅₃	—	2	2	no	—
196	#121×C₅₃	—	2	2	no	—
197	#121×C₅₃	—	2	2	no	—
198	#121×C₅₃	—	2	2	no	—
199	#121×C₅₃	—	2	2	no	—
200	#121×C₅₃	—	2	2	no	—
201	#121×C₅₃	D₄	1	2	yes	—
202	#121×C₅₃	C₂³	1	2	yes	—
203	#121×C₅₃	C₂³	1	2	yes	—
204	#121×C₅₃	C₂³	1	2	yes	—
205	#121×C₅₃	C₂³	1	2	yes	—
206	#121×C₅₃	C₂³	1	2	yes	—
207	#121×C₅₃	C₂³	1	2	yes	complemented
208	#120×C₅₃	—	2	2	no	—
209	#120×C₅₃	—	2	2	no	—
210	#120×C₅₃	—	2	2	no	—
211	#120×C₅₃	—	2	2	no	—
212	#120×C₅₃	—	2	2	no	—
213	#120×C₅₃	—	2	1	no	—
214	#120×C₅₃	—	2	2	no	—
215	#120×C₅₃	—	2	2	no	—
216	#120×C₅₃	—	2	2	no	—
217	#120×C₅₃	—	2	2	no	—
218	#120×C₅₃	D₄	1	2	yes	—
219	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
220	C₄×D₄×C₅₃	—	2	2	no	—
221	C₄×D₄×C₅₃	—	2	2	no	—
222	C₄×D₄×C₅₃	—	2	2	no	—
223	C₄×D₄×C₅₃	—	2	2	no	—
224	C₄×D₄×C₅₃	—	2	2	no	—
225	C₄×D₄×C₅₃	—	2	2	no	—
226	C₄×D₄×C₅₃	C₂³	1	2	yes	—
227	C₄×D₄×C₅₃	C₂³	1	2	yes	—
228	C₄×D₄×C₅₃	C₂³	1	2	yes	—
229	C₄×D₄×C₅₃	C₂³	1	2	yes	—
230	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
231	#117×C₅₃	—	2	2	no	—
232	#117×C₅₃	C₂³	1	1	yes	characteristic
233	#117×C₅₃	C₂³	1	2	yes	—
234	#117×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
236	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
237	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
238	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
239	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
240	#107×C₅₃	C₂³	1	2	yes	complemented
241	#107×C₅₃	C₂³	1	2	yes	complemented
242	#106×C₅₃	C₂³	1	2	yes	complemented
243	#106×C₅₃	C₂³	1	2	yes	complemented
244	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
245	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
246	#103×C₅₃	C₂³	1	2	yes	complemented
247	#103×C₅₃	C₂³	1	2	yes	complemented
248	#103×C₅₃	C₂³	1	2	yes	complemented
249	#103×C₅₃	C₂³	1	2	yes	complemented
250	#102×C₅₃	C₂³	1	2	yes	—
251	#102×C₅₃	C₂³	1	2	yes	—
252	#102×C₅₃	C₂³	1	2	yes	—
253	#102×C₅₃	C₂³	1	2	yes	—
254	#102×C₅₃	C₂³	1	2	yes	—
255	#102×C₅₃	C₂³	1	2	yes	—
256	#102×C₅₃	C₂³	1	2	yes	—
257	#102×C₅₃	C₂³	1	2	yes	—
258	#102×C₅₃	C₂³	1	2	yes	complemented
259	#102×C₅₃	C₂³	1	2	yes	complemented
260	#102×C₅₃	C₂³	1	2	yes	complemented
261	#102×C₅₃	C₂³	1	2	yes	complemented
262	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
263	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
264	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
265	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
266	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	complemented
267	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	complemented
268	#97×C₅₃	C₂³	1	1	yes	characteristic, complemented
269	#97×C₅₃	C₂³	1	1	yes	characteristic, complemented
270	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
271	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
272	C₂⁴×C₅₃	—	2	1	no	—
273	C₂⁴×C₅₃	—	2	2	no	—
274	C₂⁴×C₅₃	—	2	2	no	—
275	C₂⁴×C₅₃	—	2	1	no	—
276	C₂⁴×C₅₃	—	2	2	no	—
277	C₂⁴×C₅₃	—	4	4	no	—
278	C₂⁴×C₅₃	—	8	4	no	—
279	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
280	#41×C₅₃	—	2	4	no	—
281	#41×C₅₃	—	4	2	no	—
282	#41×C₅₃	—	4	2	no	—
283	#41×C₅₃	—	4	2	no	—
284	#41×C₅₃	—	4	2	no	—
285	#41×C₅₃	—	4	2	no	—
286	#41×C₅₃	—	4	2	no	—
287	#41×C₅₃	—	4	2	no	—
288	#41×C₅₃	—	4	4	no	—
289	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
290	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
291	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
292	C₂×D₄×C₅₃	—	2	4	no	—
293	C₂×D₄×C₅₃	—	2	4	no	—
294	C₂×D₄×C₅₃	—	2	4	no	—
295	C₂×D₄×C₅₃	—	2	4	no	—
296	C₂×D₄×C₅₃	—	2	2	no	—
297	C₂×D₄×C₅₃	—	2	1	no	—
298	C₂×D₄×C₅₃	—	2	2	no	—
299	C₂×D₄×C₅₃	—	2	2	no	—
300	C₂×D₄×C₅₃	—	2	2	no	—
301	C₂×D₄×C₅₃	—	2	2	no	—
302	C₂×D₄×C₅₃	—	2	2	no	—
303	C₂×D₄×C₅₃	—	2	2	no	—
304	C₂×D₄×C₅₃	—	2	2	no	—
305	C₂×D₄×C₅₃	—	2	2	no	—
306	C₂×D₄×C₅₃	—	2	1	no	—
307	C₂×D₄×C₅₃	—	2	2	no	—
308	C₂×D₄×C₅₃	—	2	2	no	—
309	C₂×D₄×C₅₃	—	2	2	no	—
310	C₂×D₄×C₅₃	—	2	1	no	—
311	C₂×D₄×C₅₃	—	2	2	no	—
312	C₂×D₄×C₅₃	—	2	2	no	—
313	C₂×D₄×C₅₃	—	2	2	no	—
314	C₂×D₄×C₅₃	—	4	2	no	—
315	C₂×D₄×C₅₃	—	4	2	no	—
316	C₂×D₄×C₅₃	—	4	2	no	—
317	C₂×D₄×C₅₃	—	4	2	no	—
318	C₂×D₄×C₅₃	—	4	8	no	—
319	C₂×D₄×C₅₃	—	4	4	no	—
320	C₂×D₄×C₅₃	—	4	4	no	—
321	C₂×D₄×C₅₃	—	4	8	no	—
322	C₂×D₄×C₅₃	—	8	4	no	—
323	C₂×D₄×C₅₃	—	8	4	no	—
324	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
325	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
326	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
327	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
328	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
332	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₅₃	—	2	2	no	—
334	C₂²×C₄×C₅₃	—	2	2	no	—
335	C₂²×C₄×C₅₃	—	2	1	no	—
336	C₂²×C₄×C₅₃	—	2	2	no	—
337	C₂²×C₄×C₅₃	—	2	2	no	—
338	C₂²×C₄×C₅₃	—	2	2	no	—
339	C₂²×C₄×C₅₃	—	2	2	no	—
340	C₂²×C₄×C₅₃	—	2	2	no	—
341	C₂²×C₄×C₅₃	—	4	2	no	—
342	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
343	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
347	Q₁₆×C₅₃	—	4	2	no	—
348	SD₁₆×C₅₃	—	2	4	no	—
349	SD₁₆×C₅₃	—	2	4	no	—
350	SD₁₆×C₅₃	—	4	2	no	—
351	SD₁₆×C₅₃	—	4	2	no	—
352	SD₁₆×C₅₃	—	4	2	no	—
353	SD₁₆×C₅₃	—	4	2	no	—
354	D₈×C₅₃	—	2	4	no	—
355	D₈×C₅₃	—	2	4	no	—
356	D₈×C₅₃	—	4	2	no	—
357	D₈×C₅₃	—	4	2	no	—
358	D₈×C₅₃	—	4	2	no	—
359	M₁₆×C₅₃	—	4	2	no	—
360	M₁₆×C₅₃	—	4	2	no	—
361	M₁₆×C₅₃	—	4	2	no	—
362	C₂×C₈×C₅₃	—	4	2	no	—
363	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
364	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
365	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
366	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₅₃	—	2	2	no	—
368	C₄⋊C₄×C₅₃	—	2	2	no	—
369	C₄⋊C₄×C₅₃	—	2	2	no	—
370	C₄⋊C₄×C₅₃	—	2	2	no	—
371	C₄⋊C₄×C₅₃	—	2	2	no	—
372	C₄⋊C₄×C₅₃	—	2	2	no	—
373	C₄⋊C₄×C₅₃	—	2	2	no	—
374	C₄⋊C₄×C₅₃	—	2	2	no	—
375	C₄⋊C₄×C₅₃	—	2	2	no	—
376	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
379	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
380	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
381	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
382	C₂²⋊C₄×C₅₃	—	2	1	no	—
383	C₂²⋊C₄×C₅₃	—	2	2	no	—
384	C₂²⋊C₄×C₅₃	—	2	2	no	—
385	C₂²⋊C₄×C₅₃	—	2	2	no	—
386	C₂²⋊C₄×C₅₃	—	2	2	no	—
387	C₂²⋊C₄×C₅₃	—	2	2	no	—
388	C₂²⋊C₄×C₅₃	—	2	2	no	—
389	C₂²⋊C₄×C₅₃	—	2	2	no	—
390	C₂²⋊C₄×C₅₃	—	2	2	no	—
391	C₂²⋊C₄×C₅₃	—	2	2	no	—
392	C₂²⋊C₄×C₅₃	—	2	2	no	—
393	C₂²⋊C₄×C₅₃	—	2	2	no	—
394	C₂²⋊C₄×C₅₃	—	2	2	no	—
395	C₂²⋊C₄×C₅₃	—	2	2	no	—
396	C₂²⋊C₄×C₅₃	—	2	2	no	—
397	C₂²⋊C₄×C₅₃	—	2	2	no	—
398	C₂²⋊C₄×C₅₃	—	2	2	no	—
399	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
400	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
401	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
402	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
403	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
404	C₄²×C₅₃	—	2	2	no	—
405	C₄²×C₅₃	—	2	2	no	—
406	C₄²×C₅₃	—	2	1	no	—
407	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂³×C₅₃	—	2	4	no	—
410	C₂³×C₅₃	—	2	2	no	—
411	C₂³×C₅₃	—	2	2	no	—
412	C₂³×C₅₃	—	2	1	no	—
413	C₂³×C₅₃	—	2	1	no	—
414	C₂³×C₅₃	—	2	1	no	—
415	C₂³×C₅₃	—	4	1	no	—
416	C₂³×C₅₃	—	4	2	no	—
417	C₂³×C₅₃	—	4	4	no	—
418	C₂³×C₅₃	—	4	4	no	—
419	C₂³×C₅₃	—	4	4	no	—
420	C₂³×C₅₃	—	4	2	no	—
421	C₂³×C₅₃	—	4	4	no	—
422	C₂³×C₅₃	—	4	4	no	—
423	C₂³×C₅₃	—	8	2	no	—
424	C₂³×C₅₃	—	8	2	no	—
425	C₂³×C₅₃	—	8	2	no	—
426	C₂³×C₅₃	—	8	2	no	—
427	C₂³×C₅₃	—	8	2	no	—
428	C₂³×C₅₃	—	8	2	no	—
429	C₂³×C₅₃	—	8	16	no	—
430	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
431	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
432	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
433	Q₈×C₅₃	—	2	2	no	—
434	Q₈×C₅₃	—	2	2	no	—
435	Q₈×C₅₃	—	2	2	no	—
436	Q₈×C₅₃	—	4	1	no	—
437	D₄×C₅₃	—	2	4	no	—
438	D₄×C₅₃	—	2	2	no	—
439	D₄×C₅₃	—	2	2	no	—
440	D₄×C₅₃	—	2	2	no	—
441	D₄×C₅₃	—	2	2	no	—
442	D₄×C₅₃	—	2	2	no	—
443	D₄×C₅₃	—	2	2	no	—
444	D₄×C₅₃	—	4	1	no	—
445	D₄×C₅₃	—	4	2	no	—
446	D₄×C₅₃	—	4	2	no	—
447	D₄×C₅₃	—	4	2	no	—
448	D₄×C₅₃	—	4	4	no	—
449	D₄×C₅₃	—	4	4	no	—
450	D₄×C₅₃	—	4	4	no	—
451	D₄×C₅₃	—	4	2	no	—
452	D₄×C₅₃	—	4	4	no	—
453	D₄×C₅₃	—	4	2	no	—
454	D₄×C₅₃	—	4	4	no	—
455	D₄×C₅₃	—	8	2	no	—
456	D₄×C₅₃	—	8	2	no	—
457	D₄×C₅₃	—	8	2	no	—
458	D₄×C₅₃	—	8	2	no	—
459	D₄×C₅₃	—	8	2	no	—
460	D₄×C₅₃	—	8	2	no	—
461	D₄×C₅₃	—	8	2	no	—
462	D₄×C₅₃	—	8	2	no	—
463	D₄×C₅₃	—	8	2	no	—
464	D₄×C₅₃	—	8	2	no	—
465	D₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
466	C₂×C₄×C₅₃	—	2	2	no	—
467	C₂×C₄×C₅₃	—	2	2	no	—
468	C₂×C₄×C₅₃	—	2	2	no	—
469	C₂×C₄×C₅₃	—	2	2	no	—
470	C₂×C₄×C₅₃	—	2	2	no	—
471	C₂×C₄×C₅₃	—	2	1	no	—
472	C₂×C₄×C₅₃	—	2	2	no	—
473	C₂×C₄×C₅₃	—	2	2	no	—
474	C₂×C₄×C₅₃	—	2	2	no	—
475	C₂×C₄×C₅₃	—	2	2	no	—
476	C₂×C₄×C₅₃	—	4	2	no	—
477	C₂×C₄×C₅₃	—	4	1	no	—
478	C₂×C₄×C₅₃	—	4	4	no	—
479	C₂×C₄×C₅₃	—	4	2	no	—
480	C₂×C₄×C₅₃	—	8	2	no	—
481	C₂×C₄×C₅₃	—	8	2	no	—
482	C₂×C₄×C₅₃	—	8	2	no	—
483	C₂×C₄×C₅₃	—	8	2	no	—
484	C₂×C₄×C₅₃	—	8	2	no	—
485	C₂×C₄×C₅₃	—	8	2	no	—
486	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
492	C₈×C₅₃	—	2	2	no	—
493	C₈×C₅₃	—	2	2	no	—
494	C₈×C₅₃	—	2	2	no	—
495	C₈×C₅₃	—	2	2	no	—
496	#61643	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
497	C₂²×C₅₃	—	2	2	no	—
498	C₂²×C₅₃	—	2	2	no	—
499	C₂²×C₅₃	—	2	2	no	—
500	C₂²×C₅₃	—	2	2	no	—
501	C₂²×C₅₃	—	2	2	no	—
502	C₂²×C₅₃	—	2	1	no	—
503	C₂²×C₅₃	—	2	2	no	—
504	C₂²×C₅₃	—	2	2	no	—
505	C₂²×C₅₃	—	2	4	no	—
506	C₂²×C₅₃	—	4	4	no	—
507	C₂²×C₅₃	—	4	2	no	—
508	C₂²×C₅₃	—	4	2	no	—
509	C₂²×C₅₃	—	4	2	no	—
510	C₂²×C₅₃	—	4	2	no	—
511	C₂²×C₅₃	—	4	2	no	—
512	C₂²×C₅₃	—	4	2	no	—
513	C₂²×C₅₃	—	4	2	no	—
514	C₂²×C₅₃	—	4	1	no	—
515	C₂²×C₅₃	—	4	2	no	—
516	C₂²×C₅₃	—	4	1	no	—
517	C₂²×C₅₃	—	4	1	no	—
518	C₂²×C₅₃	—	8	4	no	—
519	C₂²×C₅₃	—	8	8	no	—
520	C₂²×C₅₃	—	8	8	no	—
521	C₂²×C₅₃	—	8	4	no	—
522	C₂²×C₅₃	—	16	4	no	—
523	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
524	C₄×C₅₃	—	2	2	no	—
525	C₄×C₅₃	—	2	2	no	—
526	C₄×C₅₃	—	2	1	no	—
527	C₄×C₅₃	—	2	2	no	—
528	C₄×C₅₃	—	2	2	no	—
529	C₄×C₅₃	—	4	2	no	—
530	C₄×C₅₃	—	4	2	no	—
531	C₄×C₅₃	—	4	2	no	—
532	C₄×C₅₃	—	4	1	no	—
533	C₄×C₅₃	—	4	2	no	—
534	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
535	#3539	C₂×C₅₃	1	1	yes	characteristic, complemented
536	#3484	C₂×C₅₃	1	1	yes	characteristic, complemented
537	#3323	C₂×C₅₃	1	2	yes	complemented
538	#3322	C₂×C₅₃	1	2	yes	complemented
539	#3318	C₂×C₅₃	1	2	yes	complemented
540	#3310	C₂×C₅₃	1	2	yes	complemented
541	#3274	C₂×C₅₃	1	2	yes	complemented
542	#3272	C₂×C₅₃	1	2	yes	complemented
543	#3268	C₂×C₅₃	1	2	yes	complemented
544	#3267	C₂×C₅₃	1	2	yes	complemented
545	#3222	C₂×C₅₃	1	1	yes	characteristic, complemented
546	#3220	C₂×C₅₃	1	1	yes	characteristic, complemented
547	#3198	C₂×C₅₃	1	2	yes	complemented
548	#3197	C₂×C₅₃	1	2	yes	complemented
549	#3123	C₂×C₅₃	1	1	yes	characteristic, complemented
550	#3122	C₂×C₅₃	1	1	yes	characteristic, complemented
551	#3012	C₂×C₅₃	1	2	yes	complemented
552	#3003	C₂×C₅₃	1	2	yes	complemented
553	#2978	C₂×C₅₃	1	1	yes	characteristic, complemented
554	C₂×C₅₃	—	4	2	no	—
555	C₂×C₅₃	—	4	1	no	—
556	C₂×C₅₃	—	4	2	no	—
557	C₂×C₅₃	—	4	4	no	—
558	C₂×C₅₃	—	8	2	no	—
559	C₂×C₅₃	—	8	1	no	—
560	C₂×C₅₃	—	8	1	no	—
561	C₂×C₅₃	—	8	1	no	—
562	C₂×C₅₃	#3484	1	1	yes	characteristic
563	C₂×C₅₃	#3585	1	2	yes	—
564	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
565	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
566	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
567	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
568	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
569	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
570	#560	—	2	2	no	—
571	#553	—	2	2	no	—
572	#553	C₂²×C₅₃	1	2	yes	complemented
573	#552	C₂²×C₅₃	1	2	yes	complemented
574	#550	C₂²×C₅₃	1	2	yes	complemented
575	#547	C₂²×C₅₃	1	2	yes	complemented
576	#546	—	2	2	no	—
577	#546	C₂²×C₅₃	1	2	yes	—
578	#546	C₂²×C₅₃	1	2	yes	—
579	D₄²	—	2	2	no	—
580	D₄²	C₂²×C₅₃	1	2	yes	—
581	D₄²	C₂²×C₅₃	1	2	yes	—
582	#541	C₂²×C₅₃	1	1	yes	characteristic, complemented
583	#540	—	2	2	no	—
584	#540	C₂²×C₅₃	1	1	yes	characteristic, complemented
585	#539	—	2	2	no	—
586	#537	C₂²×C₅₃	1	2	yes	complemented
587	#535	C₂²×C₅₃	1	1	yes	characteristic
588	#535	C₂²×C₅₃	1	1	yes	characteristic
589	#534	—	2	2	no	—
590	#525	C₂²×C₅₃	1	1	yes	characteristic
591	#525	C₂²×C₅₃	1	1	yes	characteristic
592	#525	C₂²×C₅₃	1	2	yes	complemented
593	C₂×#120	—	2	2	no	—
594	#518	C₂²×C₅₃	1	1	yes	characteristic
595	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
596	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
597	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
598	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
599	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
600	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
601	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
602	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
603	#485	C₂²×C₅₃	1	2	yes	complemented
604	#485	C₂²×C₅₃	1	2	yes	complemented
605	#482	C₂²×C₅₃	1	2	yes	complemented
606	#482	C₂²×C₅₃	1	2	yes	complemented
607	#481	C₂²×C₅₃	1	2	yes	complemented
608	#480	C₂²×C₅₃	1	2	yes	complemented
609	#478	C₂²×C₅₃	1	2	yes	complemented
610	#478	C₂²×C₅₃	1	2	yes	complemented
611	#470	C₂²×C₅₃	1	2	yes	complemented
612	#469	C₂²×C₅₃	1	2	yes	complemented
613	#469	C₂²×C₅₃	1	2	yes	complemented
614	#468	C₂²×C₅₃	1	2	yes	complemented
615	#468	C₂²×C₅₃	1	2	yes	complemented
616	#468	C₂²×C₅₃	1	2	yes	complemented
617	#466	C₂²×C₅₃	1	2	yes	complemented
618	#465	C₂²×C₅₃	1	2	yes	complemented
619	#464	C₂²×C₅₃	1	2	yes	complemented
620	#463	C₂²×C₅₃	1	2	yes	complemented
621	#461	C₂²×C₅₃	1	2	yes	complemented
622	#460	C₂²×C₅₃	1	2	yes	complemented
623	#459	C₂²×C₅₃	1	2	yes	complemented
624	#459	C₂²×C₅₃	1	2	yes	complemented
625	#452	C₂²×C₅₃	1	2	yes	complemented
626	#452	C₂²×C₅₃	1	2	yes	complemented
627	#452	C₂²×C₅₃	1	2	yes	complemented
628	#450	C₂²×C₅₃	1	2	yes	—
629	#450	C₂²×C₅₃	1	2	yes	complemented
630	#450	C₂²×C₅₃	1	2	yes	complemented
631	#450	C₂²×C₅₃	1	2	yes	complemented
632	#450	C₂²×C₅₃	1	2	yes	complemented
633	#449	C₂²×C₅₃	1	2	yes	complemented
634	#449	C₂²×C₅₃	1	2	yes	complemented
635	#449	C₂²×C₅₃	1	2	yes	complemented
636	#449	C₂²×C₅₃	1	2	yes	complemented
637	#449	C₂²×C₅₃	1	2	yes	complemented
638	#447	C₂²×C₅₃	1	2	yes	—
639	#447	C₂²×C₅₃	1	2	yes	complemented
640	#447	C₂²×C₅₃	1	2	yes	complemented
641	#447	C₂²×C₅₃	1	2	yes	complemented
642	#447	C₂²×C₅₃	1	2	yes	complemented
643	#442	C₂²×C₅₃	1	2	yes	complemented
644	#440	C₂²×C₅₃	1	2	yes	complemented
645	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
646	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
647	#436	C₂²×C₅₃	1	2	yes	complemented
648	#436	C₂²×C₅₃	1	2	yes	complemented
649	#435	C₂²×C₅₃	1	2	yes	complemented
650	#435	C₂²×C₅₃	1	2	yes	complemented
651	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
652	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
653	#418	C₂²×C₅₃	1	2	yes	complemented
654	#418	C₂²×C₅₃	1	2	yes	complemented
655	#417	C₂²×C₅₃	1	2	yes	complemented
656	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
657	#408	C₂²×C₅₃	1	2	yes	complemented
658	#407	C₂²×C₅₃	1	2	yes	complemented
659	C₅₃	#61643	1	1	yes	characteristic, direct product factor, Sylow
660	C₂⁵	—	2	1	no	—
661	H(5,𝔽₂)	—	4	4	no	—
662	C₂×#41	—	2	1	no	—
663	C₂×#41	C₂³×C₅₃	1	2	yes	—
664	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
665	C₂×#41	C₂³×C₅₃	1	2	yes	—
666	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
667	C₂×#41	C₂³×C₅₃	1	2	yes	complemented
668	C₂²×D₄	—	2	2	no	—
669	C₂²×D₄	—	2	1	no	—
670	C₂²×D₄	—	2	2	no	—
671	C₂²×D₄	—	2	2	no	—
672	C₂²×D₄	—	2	1	no	—
673	C₂²×D₄	—	2	2	no	—
674	C₂²×D₄	—	4	4	no	—
675	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
676	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
677	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
678	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
679	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
680	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
681	AGL(1,ℤ/8)	—	4	4	no	—
682	AGL(1,ℤ/8)	—	4	4	no	—
683	AGL(1,ℤ/8)	—	4	4	no	—
684	#135	—	4	4	no	—
685	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	complemented
686	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
689	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
690	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	complemented
691	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	complemented
692	C₂×D₈	C₂³×C₅₃	1	2	yes	—
693	C₂×D₈	C₂³×C₅₃	1	2	yes	—
694	C₂×D₈	C₂³×C₅₃	1	2	yes	—
695	C₂×D₈	C₂³×C₅₃	1	2	yes	—
696	C₂×D₈	C₂³×C₅₃	1	2	yes	complemented
697	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
698	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
699	C₂×M₁₆	C₂³×C₅₃	1	2	yes	complemented
700	C₂²×C₈	C₂³×C₅₃	1	2	yes	complemented
701	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
702	#127	—	2	1	no	—
703	#127	—	2	2	no	—
704	#127	C₂³×C₅₃	1	1	yes	characteristic
705	#127	C₂³×C₅₃	1	1	yes	characteristic
706	#127	C₂³×C₅₃	1	1	yes	characteristic, complemented
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#125	—	2	2	no	—
711	#125	—	2	2	no	—
712	#125	C₂³×C₅₃	1	1	yes	characteristic, complemented
713	#125	C₂³×C₅₃	1	1	yes	characteristic, complemented
714	#124	—	2	1	no	—
715	#124	C₂³×C₅₃	1	1	yes	characteristic
716	#124	C₂³×C₅₃	1	1	yes	characteristic
717	#123	—	2	2	no	—
718	#123	—	2	1	no	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	#123	—	2	2	no	—
722	#123	—	2	2	no	—
723	#123	—	2	2	no	—
724	#123	—	2	2	no	—
725	#123	—	2	2	no	—
726	#123	D₄×C₅₃	1	2	yes	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
729	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
730	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
731	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
732	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
733	#121	—	2	2	no	—
734	#121	—	2	2	no	—
735	#121	—	2	2	no	—
736	#121	—	2	2	no	—
737	#121	—	2	2	no	—
738	#121	—	2	2	no	—
739	#121	—	2	2	no	—
740	#121	—	2	2	no	—
741	#121	—	2	2	no	—
742	#121	—	2	2	no	—
743	#121	—	2	2	no	—
744	#121	—	2	2	no	—
745	#121	—	2	2	no	—
746	#121	D₄×C₅₃	1	2	yes	—
747	#121	C₂³×C₅₃	1	2	yes	—
748	#121	C₂³×C₅₃	1	2	yes	—
749	#121	C₂³×C₅₃	1	2	yes	—
750	#121	C₂³×C₅₃	1	2	yes	—
751	#121	C₂³×C₅₃	1	2	yes	—
752	#121	C₂³×C₅₃	1	2	yes	complemented
753	#120	—	2	1	no	—
754	#120	—	2	2	no	—
755	#120	—	2	2	no	—
756	#120	—	2	2	no	—
757	#120	—	2	2	no	—
758	#120	—	2	2	no	—
759	#120	—	2	2	no	—
760	#120	—	2	2	no	—
761	#120	—	2	2	no	—
762	#120	—	2	2	no	—
763	#120	D₄×C₅₃	1	2	yes	—
764	C₄×Q₈	C₂³×C₅₃	1	2	yes	complemented
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	—	2	2	no	—
771	C₄×D₄	C₂³×C₅₃	1	2	yes	—
772	C₄×D₄	C₂³×C₅₃	1	2	yes	—
773	C₄×D₄	C₂³×C₅₃	1	2	yes	—
774	C₄×D₄	C₂³×C₅₃	1	2	yes	—
775	C₄×D₄	C₂³×C₅₃	1	2	yes	complemented
776	#117	—	2	2	no	—
777	#117	C₂³×C₅₃	1	1	yes	characteristic
778	#117	C₂³×C₅₃	1	2	yes	—
779	#117	C₂³×C₅₃	1	1	yes	characteristic
780	C₂×C₄⋊C₄	—	2	2	no	—
781	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
782	C₂×C₂²⋊C₄	—	2	2	no	—
783	C₂×C₂²⋊C₄	—	2	2	no	—
784	C₂×C₂²⋊C₄	—	2	2	no	—
785	#107	C₂³×C₅₃	1	2	yes	complemented
786	#107	C₂³×C₅₃	1	2	yes	complemented
787	#106	C₂³×C₅₃	1	2	yes	complemented
788	#106	C₂³×C₅₃	1	2	yes	complemented
789	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
790	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
791	#103	C₂³×C₅₃	1	2	yes	complemented
792	#103	C₂³×C₅₃	1	2	yes	complemented
793	#103	C₂³×C₅₃	1	2	yes	complemented
794	#103	C₂³×C₅₃	1	2	yes	complemented
795	#102	C₂³×C₅₃	1	2	yes	—
796	#102	C₂³×C₅₃	1	2	yes	—
797	#102	C₂³×C₅₃	1	2	yes	—
798	#102	C₂³×C₅₃	1	2	yes	—
799	#102	C₂³×C₅₃	1	2	yes	—
800	#102	C₂³×C₅₃	1	2	yes	—
801	#102	C₂³×C₅₃	1	2	yes	—
802	#102	C₂³×C₅₃	1	2	yes	—
803	#102	C₂³×C₅₃	1	2	yes	complemented
804	#102	C₂³×C₅₃	1	2	yes	complemented
805	#102	C₂³×C₅₃	1	2	yes	complemented
806	#102	C₂³×C₅₃	1	2	yes	complemented
807	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
808	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
809	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
810	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
811	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	complemented
812	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	complemented
813	#97	C₂³×C₅₃	1	1	yes	characteristic, complemented
814	#97	C₂³×C₅₃	1	1	yes	characteristic, complemented
815	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
816	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
817	C₂⁴	—	2	1	no	—
818	C₂⁴	—	2	2	no	—
819	C₂⁴	—	2	2	no	—
820	C₂⁴	—	2	1	no	—
821	C₂⁴	—	2	2	no	—
822	C₂⁴	—	4	4	no	—
823	C₂⁴	—	8	4	no	—
824	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
825	#41	—	2	4	no	—
826	#41	—	4	2	no	—
827	#41	—	4	2	no	—
828	#41	—	4	2	no	—
829	#41	—	4	2	no	—
830	#41	—	4	2	no	—
831	#41	—	4	2	no	—
832	#41	—	4	2	no	—
833	#41	—	4	4	no	—
834	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
835	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
836	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
837	C₂×D₄	—	2	4	no	—
838	C₂×D₄	—	2	4	no	—
839	C₂×D₄	—	2	4	no	—
840	C₂×D₄	—	2	4	no	—
841	C₂×D₄	—	2	2	no	—
842	C₂×D₄	—	2	1	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	2	2	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	1	no	—
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	1	no	—
856	C₂×D₄	—	2	2	no	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	2	2	no	—
859	C₂×D₄	—	4	2	no	—
860	C₂×D₄	—	4	2	no	—
861	C₂×D₄	—	4	2	no	—
862	C₂×D₄	—	4	2	no	—
863	C₂×D₄	—	4	8	no	—
864	C₂×D₄	—	4	4	no	—
865	C₂×D₄	—	4	4	no	—
866	C₂×D₄	—	4	8	no	—
867	C₂×D₄	—	8	4	no	—
868	C₂×D₄	—	8	4	no	—
869	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
870	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
871	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
872	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
873	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
874	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
875	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
876	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
877	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	4	2	no	—
887	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
888	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
891	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
892	Q₁₆	—	4	2	no	—
893	SD₁₆	—	2	4	no	—
894	SD₁₆	—	2	4	no	—
895	SD₁₆	—	4	2	no	—
896	SD₁₆	—	4	2	no	—
897	SD₁₆	—	4	2	no	—
898	SD₁₆	—	4	2	no	—
899	D₈	—	2	4	no	—
900	D₈	—	2	4	no	—
901	D₈	—	4	2	no	—
902	D₈	—	4	2	no	—
903	D₈	—	4	2	no	—
904	M₁₆	—	4	2	no	—
905	M₁₆	—	4	2	no	—
906	M₁₆	—	4	2	no	—
907	C₂×C₈	—	4	2	no	—
908	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
909	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
910	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
911	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
922	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
923	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
924	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
925	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
926	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
927	C₂²⋊C₄	—	2	1	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
945	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
946	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
947	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
948	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	1	no	—
952	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
953	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
954	C₂³	—	2	4	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	1	no	—
958	C₂³	—	2	1	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	4	1	no	—
961	C₂³	—	4	2	no	—
962	C₂³	—	4	4	no	—
963	C₂³	—	4	4	no	—
964	C₂³	—	4	4	no	—
965	C₂³	—	4	2	no	—
966	C₂³	—	4	4	no	—
967	C₂³	—	4	4	no	—
968	C₂³	—	8	2	no	—
969	C₂³	—	8	2	no	—
970	C₂³	—	8	2	no	—
971	C₂³	—	8	2	no	—
972	C₂³	—	8	2	no	—
973	C₂³	—	8	2	no	—
974	C₂³	—	8	16	no	—
975	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
976	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
977	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
978	Q₈	—	2	2	no	—
979	Q₈	—	2	2	no	—
980	Q₈	—	2	2	no	—
981	Q₈	—	4	1	no	—
982	D₄	—	2	4	no	—
983	D₄	—	2	2	no	—
984	D₄	—	2	2	no	—
985	D₄	—	2	2	no	—
986	D₄	—	2	2	no	—
987	D₄	—	2	2	no	—
988	D₄	—	2	2	no	—
989	D₄	—	4	1	no	—
990	D₄	—	4	2	no	—
991	D₄	—	4	2	no	—
992	D₄	—	4	2	no	—
993	D₄	—	4	4	no	—
994	D₄	—	4	4	no	—
995	D₄	—	4	4	no	—
996	D₄	—	4	2	no	—
997	D₄	—	4	4	no	—
998	D₄	—	4	2	no	—
999	D₄	—	4	4	no	—
1000	D₄	—	8	2	no	—
1001	D₄	—	8	2	no	—
1002	D₄	—	8	2	no	—
1003	D₄	—	8	2	no	—
1004	D₄	—	8	2	no	—
1005	D₄	—	8	2	no	—
1006	D₄	—	8	2	no	—
1007	D₄	—	8	2	no	—
1008	D₄	—	8	2	no	—
1009	D₄	—	8	2	no	—
1010	D₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	4	2	no	—
1022	C₂×C₄	—	4	1	no	—
1023	C₂×C₄	—	4	4	no	—
1024	C₂×C₄	—	4	2	no	—
1025	C₂×C₄	—	8	2	no	—
1026	C₂×C₄	—	8	2	no	—
1027	C₂×C₄	—	8	2	no	—
1028	C₂×C₄	—	8	2	no	—
1029	C₂×C₄	—	8	2	no	—
1030	C₂×C₄	—	8	2	no	—
1031	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1032	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1033	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1034	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1035	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1036	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1037	C₈	—	2	2	no	—
1038	C₈	—	2	2	no	—
1039	C₈	—	2	2	no	—
1040	C₈	—	2	2	no	—
1041	C₂²	—	2	1	no	—
1042	C₂²	—	2	2	no	—
1043	C₂²	—	2	2	no	—
1044	C₂²	—	2	4	no	—
1045	C₂²	—	2	2	no	—
1046	C₂²	—	2	2	no	—
1047	C₂²	—	2	2	no	—
1048	C₂²	—	2	2	no	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	4	4	no	—
1051	C₂²	—	4	2	no	—
1052	C₂²	—	4	2	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	8	4	no	—
1063	C₂²	—	8	8	no	—
1064	C₂²	—	8	8	no	—
1065	C₂²	—	8	4	no	—
1066	C₂²	—	16	4	no	—
1067	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1068	C₄	—	2	1	no	—
1069	C₄	—	2	2	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	2	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	2	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	2	no	—
1077	C₄	—	4	2	no	—
1078	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1079	C₂	—	4	1	no	—
1080	C₂	—	4	2	no	—
1081	C₂	—	4	2	no	—
1082	C₂	—	4	4	no	—
1083	C₂	—	8	1	no	—
1084	C₂	—	8	1	no	—
1085	C₂	—	8	1	no	—
1086	C₂	—	8	2	no	—
1087	C₂	C₅₃×#3484	1	1	yes	characteristic
1088	C₂	C₅₃×#3585	1	2	yes	—

	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×#3539	C₂	semidirect
2. C₅₃×#3484	C₂	semidirect
3. C₅₃×#3323	C₂	semidirect
4. C₅₃×#3322	C₂	semidirect
5. C₅₃×#3318	C₂	semidirect
6. C₅₃×#3310	C₂	semidirect
7. C₅₃×#3274	C₂	semidirect
8. C₅₃×#3272	C₂	semidirect
9. C₅₃×#3268	C₂	semidirect
10. C₅₃×#3267	C₂	semidirect
11. C₅₃×#3222	C₂	semidirect
12. C₅₃×#3220	C₂	semidirect
13. C₅₃×#3198	C₂	semidirect
14. C₅₃×#3197	C₂	semidirect
15. C₅₃×#3123	C₂	semidirect
16. C₅₃×#3122	C₂	semidirect
17. C₅₃×#3012	C₂	semidirect
18. C₅₃×#3003	C₂	semidirect
19. C₅₃×#2978	C₂	semidirect
22. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
23. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
24. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
25. C₂×#135×C₅₃	C₂²	semidirect
28. C₅₃×#553	C₂²	semidirect
29. C₅₃×#552	C₂²	semidirect
30. C₅₃×#550	C₂²	semidirect
31. C₅₃×#547	C₂²	semidirect
38. C₅₃×#541	C₂²	semidirect
40. C₅₃×#540	C₂²	semidirect
42. C₅₃×#537	C₂²	semidirect
48. C₅₃×#525	C₂²	semidirect
51. C₅₃×#497	C₂²	semidirect
52. C₅₃×#496	C₂²	semidirect
53. C₅₃×#493	C₂²	semidirect
54. C₅₃×#492	C₂²	semidirect
55. C₅₃×#490	C₂²	semidirect
56. C₅₃×#490	C₂²	semidirect
57. C₅₃×#488	C₂²	semidirect
58. C₅₃×#488	C₂²	semidirect
59. C₅₃×#485	C₂²	semidirect
60. C₅₃×#485	C₂²	semidirect
61. C₅₃×#482	C₂²	semidirect
62. C₅₃×#482	C₂²	semidirect
63. C₅₃×#481	C₂²	semidirect
64. C₅₃×#480	C₂²	semidirect
65. C₅₃×#478	C₂²	semidirect
66. C₅₃×#478	C₂²	semidirect
67. C₅₃×#470	C₂²	semidirect
68. C₅₃×#469	C₂²	semidirect
69. C₅₃×#469	C₂²	semidirect
70. C₅₃×#468	C₂²	semidirect
71. C₅₃×#468	C₂²	semidirect
72. C₅₃×#468	C₂²	semidirect
73. C₅₃×#466	C₂²	semidirect
74. C₅₃×#465	C₂²	semidirect
75. C₅₃×#464	C₂²	semidirect
76. C₅₃×#463	C₂²	semidirect
77. C₅₃×#461	C₂²	semidirect
78. C₅₃×#460	C₂²	semidirect
79. C₅₃×#459	C₂²	semidirect
80. C₅₃×#459	C₂²	semidirect
81. C₅₃×#452	C₂²	semidirect
82. C₅₃×#452	C₂²	semidirect
83. C₅₃×#452	C₂²	semidirect
85. C₅₃×#450	C₂²	semidirect
86. C₅₃×#450	C₂²	semidirect
87. C₅₃×#450	C₂²	semidirect
88. C₅₃×#450	C₂²	semidirect
89. C₅₃×#449	C₂²	semidirect
90. C₅₃×#449	C₂²	semidirect
91. C₅₃×#449	C₂²	semidirect
92. C₅₃×#449	C₂²	semidirect
93. C₅₃×#449	C₂²	semidirect
95. C₅₃×#447	C₂²	semidirect
96. C₅₃×#447	C₂²	semidirect
97. C₅₃×#447	C₂²	semidirect
98. C₅₃×#447	C₂²	semidirect
99. C₅₃×#442	C₂²	semidirect
100. C₅₃×#440	C₂²	semidirect
101. C₄×SD₁₆×C₅₃	C₂²	semidirect
102. C₄×D₈×C₅₃	C₂²	semidirect
103. C₅₃×#436	C₂²	semidirect
104. C₅₃×#436	C₂²	semidirect
105. C₅₃×#435	C₂²	semidirect
106. C₅₃×#435	C₂²	semidirect
107. C₅₃×#433	C₂²	semidirect
108. C₅₃×#433	C₂²	semidirect
109. C₅₃×#418	C₂²	semidirect
110. C₅₃×#418	C₂²	semidirect
111. C₅₃×#417	C₂²	semidirect
112. C₂×#102×C₅₃	C₂²	semidirect
113. C₅₃×#408	C₂²	semidirect
114. C₅₃×#407	C₂²	semidirect
122. C₂×#41×C₅₃	C₂³	semidirect
140. C₂×Q₁₆×C₅₃	C₂³	semidirect
145. C₂×SD₁₆×C₅₃	C₂³	semidirect
146. C₂×SD₁₆×C₅₃	C₂³	semidirect
151. C₂×D₈×C₅₃	C₂³	semidirect
154. C₂×M₁₆×C₅₃	C₂³	semidirect
155. C₂²×C₈×C₅₃	C₂³	semidirect
156. C₄⋊Q₈×C₅₃	C₂³	semidirect
161. #127×C₅₃	C₂³	semidirect
167. #125×C₅₃	C₂³	semidirect
168. #125×C₅₃	C₂³	semidirect
187. C₂²⋊Q₈×C₅₃	C₂³	semidirect
207. #121×C₅₃	C₂³	semidirect
219. C₄×Q₈×C₅₃	C₂³	semidirect
230. C₄×D₄×C₅₃	C₂³	semidirect
236. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
240. #107×C₅₃	C₂³	semidirect
241. #107×C₅₃	C₂³	semidirect
242. #106×C₅₃	C₂³	semidirect
243. #106×C₅₃	C₂³	semidirect
244. C₄⋊C₈×C₅₃	C₂³	semidirect
245. C₄⋊C₈×C₅₃	C₂³	semidirect
246. #103×C₅₃	C₂³	semidirect
247. #103×C₅₃	C₂³	semidirect
248. #103×C₅₃	C₂³	semidirect
249. #103×C₅₃	C₂³	semidirect
258. #102×C₅₃	C₂³	semidirect
259. #102×C₅₃	C₂³	semidirect
260. #102×C₅₃	C₂³	semidirect
261. #102×C₅₃	C₂³	semidirect
266. C₂²⋊C₈×C₅₃	C₂³	semidirect
267. C₂²⋊C₈×C₅₃	C₂³	semidirect
268. #97×C₅₃	C₂³	semidirect
269. #97×C₅₃	C₂³	semidirect
270. C₄×C₈×C₅₃	C₂³	semidirect
271. C₄×C₈×C₅₃	C₂³	semidirect
496. #61643	C₅₃	direct (N × H)
535. #3539	C₂×C₅₃	semidirect
536. #3484	C₂×C₅₃	semidirect
537. #3323	C₂×C₅₃	semidirect
538. #3322	C₂×C₅₃	semidirect
539. #3318	C₂×C₅₃	semidirect
540. #3310	C₂×C₅₃	semidirect
541. #3274	C₂×C₅₃	semidirect
542. #3272	C₂×C₅₃	semidirect
543. #3268	C₂×C₅₃	semidirect
544. #3267	C₂×C₅₃	semidirect
545. #3222	C₂×C₅₃	semidirect
546. #3220	C₂×C₅₃	semidirect
547. #3198	C₂×C₅₃	semidirect
548. #3197	C₂×C₅₃	semidirect
549. #3123	C₂×C₅₃	semidirect
550. #3122	C₂×C₅₃	semidirect
551. #3012	C₂×C₅₃	semidirect
552. #3003	C₂×C₅₃	semidirect
553. #2978	C₂×C₅₃	semidirect
566. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
567. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
568. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
569. C₂×#135	C₂²×C₅₃	semidirect
572. #553	C₂²×C₅₃	semidirect
573. #552	C₂²×C₅₃	semidirect
574. #550	C₂²×C₅₃	semidirect
575. #547	C₂²×C₅₃	semidirect
582. #541	C₂²×C₅₃	semidirect
584. #540	C₂²×C₅₃	semidirect
586. #537	C₂²×C₅₃	semidirect
592. #525	C₂²×C₅₃	semidirect
595. #497	C₂²×C₅₃	semidirect
596. #496	C₂²×C₅₃	semidirect
597. #493	C₂²×C₅₃	semidirect
598. #492	C₂²×C₅₃	semidirect
599. #490	C₂²×C₅₃	semidirect
600. #490	C₂²×C₅₃	semidirect
601. #488	C₂²×C₅₃	semidirect
602. #488	C₂²×C₅₃	semidirect
603. #485	C₂²×C₅₃	semidirect
604. #485	C₂²×C₅₃	semidirect
605. #482	C₂²×C₅₃	semidirect
606. #482	C₂²×C₅₃	semidirect
607. #481	C₂²×C₅₃	semidirect
608. #480	C₂²×C₅₃	semidirect
609. #478	C₂²×C₅₃	semidirect
610. #478	C₂²×C₅₃	semidirect
611. #470	C₂²×C₅₃	semidirect
612. #469	C₂²×C₅₃	semidirect
613. #469	C₂²×C₅₃	semidirect
614. #468	C₂²×C₅₃	semidirect
615. #468	C₂²×C₅₃	semidirect
616. #468	C₂²×C₅₃	semidirect
617. #466	C₂²×C₅₃	semidirect
618. #465	C₂²×C₅₃	semidirect
619. #464	C₂²×C₅₃	semidirect
620. #463	C₂²×C₅₃	semidirect
621. #461	C₂²×C₅₃	semidirect
622. #460	C₂²×C₅₃	semidirect
623. #459	C₂²×C₅₃	semidirect
624. #459	C₂²×C₅₃	semidirect
625. #452	C₂²×C₅₃	semidirect
626. #452	C₂²×C₅₃	semidirect
627. #452	C₂²×C₅₃	semidirect
629. #450	C₂²×C₅₃	semidirect
630. #450	C₂²×C₅₃	semidirect
631. #450	C₂²×C₅₃	semidirect
632. #450	C₂²×C₅₃	semidirect
633. #449	C₂²×C₅₃	semidirect
634. #449	C₂²×C₅₃	semidirect
635. #449	C₂²×C₅₃	semidirect
636. #449	C₂²×C₅₃	semidirect
637. #449	C₂²×C₅₃	semidirect
639. #447	C₂²×C₅₃	semidirect
640. #447	C₂²×C₅₃	semidirect
641. #447	C₂²×C₅₃	semidirect
642. #447	C₂²×C₅₃	semidirect
643. #442	C₂²×C₅₃	semidirect
644. #440	C₂²×C₅₃	semidirect
645. C₄×SD₁₆	C₂²×C₅₃	semidirect
646. C₄×D₈	C₂²×C₅₃	semidirect
647. #436	C₂²×C₅₃	semidirect
648. #436	C₂²×C₅₃	semidirect
649. #435	C₂²×C₅₃	semidirect
650. #435	C₂²×C₅₃	semidirect
651. #433	C₂²×C₅₃	semidirect
652. #433	C₂²×C₅₃	semidirect
653. #418	C₂²×C₅₃	semidirect
654. #418	C₂²×C₅₃	semidirect
655. #417	C₂²×C₅₃	semidirect
656. C₂×#102	C₂²×C₅₃	semidirect
657. #408	C₂²×C₅₃	semidirect
658. #407	C₂²×C₅₃	semidirect
659. C₅₃	#61643	direct (N × H)
667. C₂×#41	C₂³×C₅₃	semidirect
685. C₂×Q₁₆	C₂³×C₅₃	semidirect
690. C₂×SD₁₆	C₂³×C₅₃	semidirect
691. C₂×SD₁₆	C₂³×C₅₃	semidirect
696. C₂×D₈	C₂³×C₅₃	semidirect
699. C₂×M₁₆	C₂³×C₅₃	semidirect
700. C₂²×C₈	C₂³×C₅₃	semidirect
701. C₄⋊Q₈	C₂³×C₅₃	semidirect
706. #127	C₂³×C₅₃	semidirect
712. #125	C₂³×C₅₃	semidirect
713. #125	C₂³×C₅₃	semidirect
732. C₂²⋊Q₈	C₂³×C₅₃	semidirect
752. #121	C₂³×C₅₃	semidirect
764. C₄×Q₈	C₂³×C₅₃	semidirect
775. C₄×D₄	C₂³×C₅₃	semidirect
781. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
785. #107	C₂³×C₅₃	semidirect
786. #107	C₂³×C₅₃	semidirect
787. #106	C₂³×C₅₃	semidirect
788. #106	C₂³×C₅₃	semidirect
789. C₄⋊C₈	C₂³×C₅₃	semidirect
790. C₄⋊C₈	C₂³×C₅₃	semidirect
791. #103	C₂³×C₅₃	semidirect
792. #103	C₂³×C₅₃	semidirect
793. #103	C₂³×C₅₃	semidirect
794. #103	C₂³×C₅₃	semidirect
803. #102	C₂³×C₅₃	semidirect
804. #102	C₂³×C₅₃	semidirect
805. #102	C₂³×C₅₃	semidirect
806. #102	C₂³×C₅₃	semidirect
811. C₂²⋊C₈	C₂³×C₅₃	semidirect
812. C₂²⋊C₈	C₂³×C₅₃	semidirect
813. #97	C₂³×C₅₃	semidirect
814. #97	C₂³×C₅₃	semidirect
815. C₄×C₈	C₂³×C₅₃	semidirect
816. 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×#3539	2
C₅₃×#3484	2
C₅₃×#3323	2
C₅₃×#3322	2
C₅₃×#3318	2
C₅₃×#3310	2
C₅₃×#3274	2
C₅₃×#3272	2
C₅₃×#3268	2
C₅₃×#3267	2
C₅₃×#3222	2
C₅₃×#3220	2
C₅₃×#3198	2
C₅₃×#3197	2
C₅₃×#3123	2
C₅₃×#3122	2
C₅₃×#3012	2
C₅₃×#3003	2
C₅₃×#2978	2
#61643	53

Subgroups — C53×#61643 #27269155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61643 #27269155