Subgroups — C₅₃×#61155 #27268667

Order 13568.

2572 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3325	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3324	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3318	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3310	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3295	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3294	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3094	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3055	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3003	C₂	1	2	yes	maximal, complemented
15	C₄×AGL(1,ℤ/8)×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×M₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅₃×#418	C₂	1	2	yes	maximal, complemented
18	C₂³×D₄×C₅₃	—	2	1	no	—
19	C₂³×D₄×C₅₃	C₂²	1	2	yes	—
20	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
22	C₂²×M₁₆×C₅₃	C₂²	1	2	yes	complemented
23	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
24	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
25	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
26	C₅₃×#553	C₂²	1	2	yes	complemented
27	C₅₃×#552	—	2	1	no	—
28	C₅₃×#552	C₂²	1	2	yes	complemented
29	C₅₃×#551	—	2	2	no	—
30	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#546	—	2	1	no	—
32	D₄²×C₅₃	—	2	1	no	—
33	D₄²×C₅₃	—	2	1	no	—
34	D₄²×C₅₃	—	2	2	no	—
35	D₄²×C₅₃	C₂²	1	2	yes	—
36	D₄²×C₅₃	C₂²	1	4	yes	—
37	D₄²×C₅₃	C₂²	1	2	yes	—
38	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
39	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
40	C₅₃×#529	—	2	1	no	—
41	C₅₃×#529	—	2	2	no	—
42	C₅₃×#525	C₂²	1	2	yes	complemented
43	C₂×#121×C₅₃	—	2	1	no	—
44	C₂×#121×C₅₃	C₂²	1	2	yes	—
45	C₂×#120×C₅₃	—	2	2	no	—
46	C₄×#41×C₅₃	—	2	1	no	—
47	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
51	C₅₃×#490	C₂²	1	4	yes	complemented
52	C₅₃×#486	C₂²	1	2	yes	complemented
53	C₅₃×#486	C₂²	1	2	yes	complemented
54	C₅₃×#482	C₂²	1	4	yes	complemented
55	C₅₃×#482	C₂²	1	4	yes	complemented
56	C₅₃×#481	C₂²	1	4	yes	complemented
57	C₅₃×#480	C₂²	1	4	yes	complemented
58	C₅₃×#478	C₂²	1	4	yes	complemented
59	C₅₃×#476	C₂²	1	2	yes	complemented
60	C₅₃×#474	C₂²	1	2	yes	complemented
61	C₅₃×#469	C₂²	1	4	yes	complemented
62	C₅₃×#468	C₂²	1	4	yes	complemented
63	C₅₃×#466	C₂²	1	4	yes	complemented
64	C₅₃×#465	C₂²	1	4	yes	complemented
65	C₅₃×#460	C₂²	1	2	yes	complemented
66	C₅₃×#460	C₂²	1	2	yes	complemented
67	C₅₃×#459	C₂²	1	2	yes	complemented
68	C₅₃×#459	C₂²	1	2	yes	complemented
69	C₅₃×#450	C₂²	1	4	yes	complemented
70	C₅₃×#450	C₂²	1	4	yes	complemented
71	C₅₃×#447	C₂²	1	4	yes	complemented
72	C₅₃×#447	C₂²	1	4	yes	complemented
73	C₅₃×#442	C₂²	1	2	yes	complemented
74	C₅₃×#440	C₂²	1	2	yes	complemented
75	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
76	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
77	C₅₃×#436	C₂²	1	2	yes	complemented
78	C₅₃×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
80	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#428	C₂²	1	2	yes	complemented
82	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#418	C₂²	1	1	yes	characteristic
84	C₅₃×#418	C₂²	1	2	yes	—
85	C₅₃×#418	C₂²	1	4	yes	complemented
86	C₅₃×#418	C₂²	1	4	yes	complemented
87	C₅₃×#418	C₂²	1	2	yes	complemented
88	C₅₃×#418	C₂²	1	2	yes	complemented
89	C₅₃×#418	C₂²	1	2	yes	complemented
90	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
91	C₂×#102×C₅₃	C₂²	1	4	yes	complemented
92	C₂×#102×C₅₃	C₂²	1	4	yes	complemented
93	C₅₃×#407	C₂²	1	2	yes	complemented
94	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
95	C₂⁵×C₅₃	—	2	2	no	—
96	C₂×#41×C₅₃	—	2	1	no	—
97	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₅₃	—	2	8	no	—
99	C₂²×D₄×C₅₃	—	2	2	no	—
100	C₂²×D₄×C₅₃	—	2	4	no	—
101	C₂²×D₄×C₅₃	—	2	2	no	—
102	C₂²×D₄×C₅₃	—	2	2	no	—
103	C₂²×D₄×C₅₃	—	2	2	no	—
104	C₂²×D₄×C₅₃	—	2	1	no	—
105	C₂²×D₄×C₅₃	—	2	2	no	—
106	C₂²×D₄×C₅₃	—	2	2	no	—
107	C₂²×D₄×C₅₃	—	2	1	no	—
108	C₂²×D₄×C₅₃	—	4	4	no	—
109	C₂²×D₄×C₅₃	—	4	8	no	—
110	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
111	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
113	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
114	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₅₃	—	2	1	no	—
116	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
117	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
118	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
119	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
120	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	complemented
121	C₂×D₈×C₅₃	C₂³	1	2	yes	—
122	C₂×D₈×C₅₃	C₂³	1	4	yes	complemented
123	C₂×M₁₆×C₅₃	—	4	4	no	—
124	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
125	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
126	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
127	C₂×M₁₆×C₅₃	C₂³	1	4	yes	complemented
128	C₂²×C₈×C₅₃	C₂³	1	4	yes	complemented
129	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
130	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
131	#127×C₅₃	—	2	1	no	—
132	#127×C₅₃	—	2	1	no	—
133	#127×C₅₃	C₂³	1	2	yes	—
134	#127×C₅₃	C₂³	1	2	yes	—
135	#126×C₅₃	—	2	2	no	—
136	#126×C₅₃	—	2	2	no	—
137	#126×C₅₃	—	2	2	no	—
138	#125×C₅₃	—	2	2	no	—
139	#125×C₅₃	—	2	1	no	—
140	#125×C₅₃	C₂³	1	2	yes	complemented
141	#124×C₅₃	—	2	2	no	—
142	#124×C₅₃	—	2	1	no	—
143	#123×C₅₃	—	2	2	no	—
144	#123×C₅₃	—	2	2	no	—
145	#123×C₅₃	—	2	2	no	—
146	#123×C₅₃	—	2	2	no	—
147	C₂²⋊Q₈×C₅₃	—	2	1	no	—
148	C₂²⋊Q₈×C₅₃	—	2	2	no	—
149	C₂²⋊Q₈×C₅₃	—	2	1	no	—
150	C₂²⋊Q₈×C₅₃	—	2	1	no	—
151	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
152	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
153	#121×C₅₃	—	2	2	no	—
154	#121×C₅₃	—	2	2	no	—
155	#121×C₅₃	—	2	4	no	—
156	#121×C₅₃	—	2	2	no	—
157	#121×C₅₃	—	2	1	no	—
158	#121×C₅₃	—	2	2	no	—
159	#121×C₅₃	—	2	2	no	—
160	#121×C₅₃	C₂³	1	4	yes	—
161	#121×C₅₃	C₂³	1	4	yes	—
162	#121×C₅₃	C₂³	1	2	yes	complemented
163	#121×C₅₃	C₂³	1	2	yes	complemented
164	#120×C₅₃	—	2	4	no	—
165	#120×C₅₃	—	2	4	no	—
166	#120×C₅₃	—	2	4	no	—
167	#120×C₅₃	—	2	4	no	—
168	#120×C₅₃	—	2	2	no	—
169	C₄×Q₈×C₅₃	—	2	1	no	—
170	C₄×Q₈×C₅₃	—	2	1	no	—
171	C₄×Q₈×C₅₃	—	2	1	no	—
172	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
173	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
174	C₄×D₄×C₅₃	—	2	2	no	—
175	C₄×D₄×C₅₃	—	2	1	no	—
176	C₄×D₄×C₅₃	—	2	1	no	—
177	C₄×D₄×C₅₃	—	2	1	no	—
178	C₄×D₄×C₅₃	—	2	2	no	—
179	C₄×D₄×C₅₃	—	2	1	no	—
180	C₄×D₄×C₅₃	—	2	1	no	—
181	C₄×D₄×C₅₃	—	2	2	no	—
182	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
183	C₄×D₄×C₅₃	D₄	1	2	yes	—
184	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
185	C₄×D₄×C₅₃	C₂³	1	2	yes	—
186	C₄×D₄×C₅₃	C₂³	1	2	yes	—
187	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₅₃	C₂³	1	2	yes	—
189	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
191	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
192	#117×C₅₃	—	2	1	no	—
193	#117×C₅₃	—	2	2	no	—
194	#117×C₅₃	—	2	1	no	—
195	#117×C₅₃	—	2	2	no	—
196	#117×C₅₃	—	2	2	no	—
197	#117×C₅₃	C₂³	1	1	yes	characteristic
198	#117×C₅₃	C₂³	1	2	yes	—
199	#117×C₅₃	C₂³	1	2	yes	complemented
200	#117×C₅₃	C₂³	1	2	yes	complemented
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	complemented
204	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
205	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
207	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
208	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
209	C₂×C₄²×C₅₃	—	2	1	no	—
210	C₂×C₄²×C₅₃	—	2	2	no	—
211	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
212	#107×C₅₃	C₂³	1	2	yes	complemented
213	#107×C₅₃	C₂³	1	4	yes	complemented
214	#106×C₅₃	C₂³	1	2	yes	complemented
215	#106×C₅₃	C₂³	1	4	yes	complemented
216	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
217	C₄⋊C₈×C₅₃	C₂³	1	2	yes	complemented
218	#103×C₅₃	C₂³	1	2	yes	complemented
219	#102×C₅₃	C₂³	1	2	yes	—
220	#102×C₅₃	C₂³	1	2	yes	—
221	#102×C₅₃	C₂³	1	4	yes	—
222	#102×C₅₃	C₂³	1	4	yes	—
223	#102×C₅₃	C₂³	1	4	yes	complemented
224	#102×C₅₃	C₂³	1	4	yes	complemented
225	#102×C₅₃	C₂³	1	4	yes	complemented
226	#102×C₅₃	C₂³	1	4	yes	complemented
227	#102×C₅₃	C₂³	1	4	yes	complemented
228	#102×C₅₃	C₂³	1	4	yes	complemented
229	#102×C₅₃	C₂³	1	2	yes	complemented
230	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	complemented
231	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	complemented
232	#97×C₅₃	C₂³	1	2	yes	complemented
233	C₄×C₈×C₅₃	C₂³	1	2	yes	complemented
234	C₂⁴×C₅₃	—	2	1	no	—
235	C₂⁴×C₅₃	—	2	2	no	—
236	C₂⁴×C₅₃	—	2	4	no	—
237	C₂⁴×C₅₃	—	2	4	no	—
238	C₂⁴×C₅₃	—	4	8	no	—
239	C₂⁴×C₅₃	—	4	8	no	—
240	C₂⁴×C₅₃	—	8	4	no	—
241	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
242	#41×C₅₃	—	2	2	no	—
243	#41×C₅₃	—	2	2	no	—
244	#41×C₅₃	—	4	4	no	—
245	C₂×Q₈×C₅₃	—	2	1	no	—
246	C₂×Q₈×C₅₃	—	2	1	no	—
247	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₅₃	—	2	4	no	—
249	C₂×D₄×C₅₃	—	2	8	no	—
250	C₂×D₄×C₅₃	—	2	8	no	—
251	C₂×D₄×C₅₃	—	2	1	no	—
252	C₂×D₄×C₅₃	—	2	2	no	—
253	C₂×D₄×C₅₃	—	2	4	no	—
254	C₂×D₄×C₅₃	—	2	4	no	—
255	C₂×D₄×C₅₃	—	2	2	no	—
256	C₂×D₄×C₅₃	—	2	1	no	—
257	C₂×D₄×C₅₃	—	2	4	no	—
258	C₂×D₄×C₅₃	—	2	4	no	—
259	C₂×D₄×C₅₃	—	2	2	no	—
260	C₂×D₄×C₅₃	—	2	2	no	—
261	C₂×D₄×C₅₃	—	2	2	no	—
262	C₂×D₄×C₅₃	—	2	2	no	—
263	C₂×D₄×C₅₃	—	2	2	no	—
264	C₂×D₄×C₅₃	—	2	4	no	—
265	C₂×D₄×C₅₃	—	2	2	no	—
266	C₂×D₄×C₅₃	—	2	4	no	—
267	C₂×D₄×C₅₃	—	4	4	no	—
268	C₂×D₄×C₅₃	—	4	4	no	—
269	C₂×D₄×C₅₃	—	4	8	no	—
270	C₂×D₄×C₅₃	—	4	8	no	—
271	C₂×D₄×C₅₃	—	4	8	no	—
272	C₂×D₄×C₅₃	—	4	4	no	—
273	C₂×D₄×C₅₃	—	4	16	no	—
274	C₂×D₄×C₅₃	—	4	8	no	—
275	C₂×D₄×C₅₃	—	4	8	no	—
276	C₂×D₄×C₅₃	—	4	8	no	—
277	C₂×D₄×C₅₃	—	8	2	no	—
278	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
279	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
280	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
281	C₂×D₄×C₅₃	#41	1	4	yes	complemented
282	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
283	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
284	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₅₃	—	2	4	no	—
286	C₂²×C₄×C₅₃	—	2	4	no	—
287	C₂²×C₄×C₅₃	—	2	2	no	—
288	C₂²×C₄×C₅₃	—	2	1	no	—
289	C₂²×C₄×C₅₃	—	2	2	no	—
290	C₂²×C₄×C₅₃	—	2	1	no	—
291	C₂²×C₄×C₅₃	—	2	1	no	—
292	C₂²×C₄×C₅₃	—	2	2	no	—
293	C₂²×C₄×C₅₃	—	2	2	no	—
294	C₂²×C₄×C₅₃	—	2	1	no	—
295	C₂²×C₄×C₅₃	—	4	4	no	—
296	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
297	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
299	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
300	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
304	SD₁₆×C₅₃	—	2	4	no	—
305	SD₁₆×C₅₃	—	4	4	no	—
306	D₈×C₅₃	—	2	4	no	—
307	D₈×C₅₃	—	4	4	no	—
308	M₁₆×C₅₃	—	2	2	no	—
309	M₁₆×C₅₃	—	2	2	no	—
310	M₁₆×C₅₃	—	2	4	no	—
311	M₁₆×C₅₃	—	4	4	no	—
312	C₂×C₈×C₅₃	—	4	4	no	—
313	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
314	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
315	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
316	C₄⋊C₄×C₅₃	—	2	1	no	—
317	C₄⋊C₄×C₅₃	—	2	2	no	—
318	C₄⋊C₄×C₅₃	—	2	2	no	—
319	C₄⋊C₄×C₅₃	—	2	1	no	—
320	C₄⋊C₄×C₅₃	—	2	2	no	—
321	C₄⋊C₄×C₅₃	—	2	2	no	—
322	C₄⋊C₄×C₅₃	—	2	1	no	—
323	C₄⋊C₄×C₅₃	—	2	1	no	—
324	C₄⋊C₄×C₅₃	—	2	2	no	—
325	C₄⋊C₄×C₅₃	—	2	2	no	—
326	C₄⋊C₄×C₅₃	—	2	1	no	—
327	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
328	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
329	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
330	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
332	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
333	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
334	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
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	—	2	2	no	—
342	C₂²⋊C₄×C₅₃	—	2	2	no	—
343	C₂²⋊C₄×C₅₃	—	2	4	no	—
344	C₂²⋊C₄×C₅₃	—	2	4	no	—
345	C₂²⋊C₄×C₅₃	—	2	2	no	—
346	C₂²⋊C₄×C₅₃	—	2	1	no	—
347	C₂²⋊C₄×C₅₃	—	2	1	no	—
348	C₂²⋊C₄×C₅₃	—	2	2	no	—
349	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
350	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
351	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
352	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
353	C₄²×C₅₃	—	2	1	no	—
354	C₄²×C₅₃	—	2	2	no	—
355	C₄²×C₅₃	—	2	1	no	—
356	C₄²×C₅₃	—	2	2	no	—
357	C₄²×C₅₃	—	2	2	no	—
358	C₄²×C₅₃	—	2	1	no	—
359	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
360	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
361	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂³×C₅₃	—	2	4	no	—
364	C₂³×C₅₃	—	2	4	no	—
365	C₂³×C₅₃	—	2	4	no	—
366	C₂³×C₅₃	—	2	2	no	—
367	C₂³×C₅₃	—	2	1	no	—
368	C₂³×C₅₃	—	2	4	no	—
369	C₂³×C₅₃	—	4	2	no	—
370	C₂³×C₅₃	—	4	8	no	—
371	C₂³×C₅₃	—	4	8	no	—
372	C₂³×C₅₃	—	4	2	no	—
373	C₂³×C₅₃	—	4	2	no	—
374	C₂³×C₅₃	—	4	4	no	—
375	C₂³×C₅₃	—	4	8	no	—
376	C₂³×C₅₃	—	4	4	no	—
377	C₂³×C₅₃	—	4	4	no	—
378	C₂³×C₅₃	—	4	8	no	—
379	C₂³×C₅₃	—	8	4	no	—
380	C₂³×C₅₃	—	8	4	no	—
381	C₂³×C₅₃	—	8	32	no	—
382	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
383	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
384	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
385	Q₈×C₅₃	—	2	1	no	—
386	Q₈×C₅₃	—	2	1	no	—
387	Q₈×C₅₃	—	4	2	no	—
388	Q₈×C₅₃	—	8	1	no	—
389	D₄×C₅₃	—	2	4	no	—
390	D₄×C₅₃	—	2	4	no	—
391	D₄×C₅₃	—	2	2	no	—
392	D₄×C₅₃	—	2	4	no	—
393	D₄×C₅₃	—	2	1	no	—
394	D₄×C₅₃	—	2	2	no	—
395	D₄×C₅₃	—	2	4	no	—
396	D₄×C₅₃	—	2	1	no	—
397	D₄×C₅₃	—	4	8	no	—
398	D₄×C₅₃	—	4	8	no	—
399	D₄×C₅₃	—	4	4	no	—
400	D₄×C₅₃	—	4	8	no	—
401	D₄×C₅₃	—	4	2	no	—
402	D₄×C₅₃	—	4	8	no	—
403	D₄×C₅₃	—	4	4	no	—
404	D₄×C₅₃	—	4	4	no	—
405	D₄×C₅₃	—	4	4	no	—
406	D₄×C₅₃	—	8	2	no	—
407	D₄×C₅₃	—	8	2	no	—
408	D₄×C₅₃	—	8	2	no	—
409	D₄×C₅₃	AGL(1,ℤ/8)	1	4	yes	complemented
410	D₄×C₅₃	C₂×#41	1	4	yes	—
411	C₂×C₄×C₅₃	—	2	4	no	—
412	C₂×C₄×C₅₃	—	2	4	no	—
413	C₂×C₄×C₅₃	—	2	4	no	—
414	C₂×C₄×C₅₃	—	2	2	no	—
415	C₂×C₄×C₅₃	—	2	2	no	—
416	C₂×C₄×C₅₃	—	2	2	no	—
417	C₂×C₄×C₅₃	—	2	2	no	—
418	C₂×C₄×C₅₃	—	2	2	no	—
419	C₂×C₄×C₅₃	—	2	2	no	—
420	C₂×C₄×C₅₃	—	2	1	no	—
421	C₂×C₄×C₅₃	—	2	1	no	—
422	C₂×C₄×C₅₃	—	2	2	no	—
423	C₂×C₄×C₅₃	—	2	2	no	—
424	C₂×C₄×C₅₃	—	2	1	no	—
425	C₂×C₄×C₅₃	—	4	1	no	—
426	C₂×C₄×C₅₃	—	4	4	no	—
427	C₂×C₄×C₅₃	—	4	2	no	—
428	C₂×C₄×C₅₃	—	4	4	no	—
429	C₂×C₄×C₅₃	—	4	2	no	—
430	C₂×C₄×C₅₃	—	4	4	no	—
431	C₂×C₄×C₅₃	—	4	2	no	—
432	C₂×C₄×C₅₃	—	8	1	no	—
433	C₂×C₄×C₅₃	—	8	2	no	—
434	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
437	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
442	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
443	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
444	C₈×C₅₃	—	2	2	no	—
445	C₈×C₅₃	—	2	2	no	—
446	C₈×C₅₃	—	2	4	no	—
447	#61155	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
448	C₂²×C₅₃	—	2	1	no	—
449	C₂²×C₅₃	—	2	2	no	—
450	C₂²×C₅₃	—	2	2	no	—
451	C₂²×C₅₃	—	2	1	no	—
452	C₂²×C₅₃	—	2	2	no	—
453	C₂²×C₅₃	—	2	2	no	—
454	C₂²×C₅₃	—	2	4	no	—
455	C₂²×C₅₃	—	2	2	no	—
456	C₂²×C₅₃	—	4	8	no	—
457	C₂²×C₅₃	—	4	8	no	—
458	C₂²×C₅₃	—	4	2	no	—
459	C₂²×C₅₃	—	4	2	no	—
460	C₂²×C₅₃	—	4	1	no	—
461	C₂²×C₅₃	—	4	4	no	—
462	C₂²×C₅₃	—	4	1	no	—
463	C₂²×C₅₃	—	4	4	no	—
464	C₂²×C₅₃	—	4	1	no	—
465	C₂²×C₅₃	—	4	4	no	—
466	C₂²×C₅₃	—	8	16	no	—
467	C₂²×C₅₃	—	8	8	no	—
468	C₂²×C₅₃	—	8	16	no	—
469	C₂²×C₅₃	#546	1	2	yes	—
470	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
471	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
472	C₄×C₅₃	—	2	1	no	—
473	C₄×C₅₃	—	2	1	no	—
474	C₄×C₅₃	—	2	2	no	—
475	C₄×C₅₃	—	2	2	no	—
476	C₄×C₅₃	—	2	1	no	—
477	C₄×C₅₃	—	4	1	no	—
478	C₄×C₅₃	—	4	2	no	—
479	C₄×C₅₃	—	4	1	no	—
480	C₄×C₅₃	—	4	1	no	—
481	C₄×C₅₃	—	4	2	no	—
482	C₄×C₅₃	—	4	2	no	—
483	C₄×C₅₃	#546	1	2	yes	—
484	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
485	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
486	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
487	#3475	C₂×C₅₃	1	1	yes	characteristic, complemented
488	C₂×D₄²	C₂×C₅₃	1	1	yes	characteristic, complemented
489	#3325	C₂×C₅₃	1	2	yes	complemented
490	#3324	C₂×C₅₃	1	2	yes	complemented
491	#3318	C₂×C₅₃	1	4	yes	complemented
492	#3310	C₂×C₅₃	1	4	yes	complemented
493	#3295	C₂×C₅₃	1	2	yes	complemented
494	#3294	C₂×C₅₃	1	2	yes	complemented
495	#3138	C₂×C₅₃	1	1	yes	characteristic, complemented
496	#3094	C₂×C₅₃	1	2	yes	complemented
497	#3077	C₂×C₅₃	1	1	yes	characteristic, complemented
498	#3055	C₂×C₅₃	1	2	yes	complemented
499	#3038	C₂×C₅₃	1	1	yes	characteristic, complemented
500	#3003	C₂×C₅₃	1	2	yes	complemented
501	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	1	yes	characteristic, complemented
502	D₄×M₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
503	C₂×#418	C₂×C₅₃	1	2	yes	complemented
504	C₂×C₅₃	—	2	2	no	—
505	C₂×C₅₃	—	2	4	no	—
506	C₂×C₅₃	—	4	2	no	—
507	C₂×C₅₃	—	4	4	no	—
508	C₂×C₅₃	—	8	1	no	—
509	C₂×C₅₃	—	8	4	no	—
510	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
511	C₂×C₅₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
512	C₂×C₅₃	#3585	1	1	yes	characteristic
513	C₂³×D₄	—	2	1	no	—
514	C₂³×D₄	C₂²×C₅₃	1	2	yes	—
515	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
516	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
517	C₂²×M₁₆	C₂²×C₅₃	1	2	yes	complemented
518	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
519	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
520	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
521	#553	C₂²×C₅₃	1	2	yes	complemented
522	#552	—	2	1	no	—
523	#552	C₂²×C₅₃	1	2	yes	complemented
524	#551	—	2	2	no	—
525	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
526	#546	—	2	1	no	—
527	D₄²	—	2	1	no	—
528	D₄²	—	2	1	no	—
529	D₄²	—	2	2	no	—
530	D₄²	C₂²×C₅₃	1	2	yes	—
531	D₄²	C₂²×C₅₃	1	4	yes	—
532	D₄²	C₂²×C₅₃	1	2	yes	—
533	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
534	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
535	#529	—	2	2	no	—
536	#529	—	2	1	no	—
537	#525	C₂²×C₅₃	1	2	yes	complemented
538	C₂×#121	—	2	1	no	—
539	C₂×#121	C₂²×C₅₃	1	2	yes	—
540	C₂×#120	—	2	2	no	—
541	C₄×#41	—	2	1	no	—
542	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
543	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
544	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
545	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
546	#490	C₂²×C₅₃	1	4	yes	complemented
547	#486	C₂²×C₅₃	1	2	yes	complemented
548	#486	C₂²×C₅₃	1	2	yes	complemented
549	#482	C₂²×C₅₃	1	4	yes	complemented
550	#482	C₂²×C₅₃	1	4	yes	complemented
551	#481	C₂²×C₅₃	1	4	yes	complemented
552	#480	C₂²×C₅₃	1	4	yes	complemented
553	#478	C₂²×C₅₃	1	4	yes	complemented
554	#476	C₂²×C₅₃	1	2	yes	complemented
555	#474	C₂²×C₅₃	1	2	yes	complemented
556	#469	C₂²×C₅₃	1	4	yes	complemented
557	#468	C₂²×C₅₃	1	4	yes	complemented
558	#466	C₂²×C₅₃	1	4	yes	complemented
559	#465	C₂²×C₅₃	1	4	yes	complemented
560	#460	C₂²×C₅₃	1	2	yes	complemented
561	#460	C₂²×C₅₃	1	2	yes	complemented
562	#459	C₂²×C₅₃	1	2	yes	complemented
563	#459	C₂²×C₅₃	1	2	yes	complemented
564	#450	C₂²×C₅₃	1	4	yes	complemented
565	#450	C₂²×C₅₃	1	4	yes	complemented
566	#447	C₂²×C₅₃	1	4	yes	complemented
567	#447	C₂²×C₅₃	1	4	yes	complemented
568	#442	C₂²×C₅₃	1	2	yes	complemented
569	#440	C₂²×C₅₃	1	2	yes	complemented
570	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
571	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
572	#436	C₂²×C₅₃	1	2	yes	complemented
573	#435	C₂²×C₅₃	1	4	yes	complemented
574	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
575	#428	C₂²×C₅₃	1	2	yes	complemented
576	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
577	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
578	#418	C₂²×C₅₃	1	2	yes	—
579	#418	C₂²×C₅₃	1	1	yes	characteristic
580	#418	C₂²×C₅₃	1	4	yes	complemented
581	#418	C₂²×C₅₃	1	4	yes	complemented
582	#418	C₂²×C₅₃	1	2	yes	complemented
583	#418	C₂²×C₅₃	1	2	yes	complemented
584	#418	C₂²×C₅₃	1	2	yes	complemented
585	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
586	C₂×#102	C₂²×C₅₃	1	4	yes	complemented
587	C₂×#102	C₂²×C₅₃	1	4	yes	complemented
588	#407	C₂²×C₅₃	1	2	yes	complemented
589	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
590	C₅₃	#61155	1	1	yes	characteristic, direct product factor, Sylow
591	C₂⁵	—	2	2	no	—
592	C₂×#41	—	2	1	no	—
593	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
594	C₂²×D₄	—	2	8	no	—
595	C₂²×D₄	—	2	2	no	—
596	C₂²×D₄	—	2	4	no	—
597	C₂²×D₄	—	2	2	no	—
598	C₂²×D₄	—	2	2	no	—
599	C₂²×D₄	—	2	2	no	—
600	C₂²×D₄	—	2	1	no	—
601	C₂²×D₄	—	2	2	no	—
602	C₂²×D₄	—	2	2	no	—
603	C₂²×D₄	—	2	1	no	—
604	C₂²×D₄	—	4	4	no	—
605	C₂²×D₄	—	4	8	no	—
606	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
607	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
608	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
609	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
610	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
611	C₂³×C₄	—	2	1	no	—
612	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
613	AGL(1,ℤ/8)	—	2	4	no	—
614	AGL(1,ℤ/8)	—	4	4	no	—
615	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
616	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	complemented
617	C₂×D₈	C₂³×C₅₃	1	2	yes	—
618	C₂×D₈	C₂³×C₅₃	1	4	yes	complemented
619	C₂×M₁₆	—	4	4	no	—
620	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
621	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
622	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
623	C₂×M₁₆	C₂³×C₅₃	1	4	yes	complemented
624	C₂²×C₈	C₂³×C₅₃	1	4	yes	complemented
625	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
626	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
627	#127	—	2	1	no	—
628	#127	—	2	1	no	—
629	#127	C₂³×C₅₃	1	2	yes	—
630	#127	C₂³×C₅₃	1	2	yes	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#125	—	2	2	no	—
635	#125	—	2	1	no	—
636	#125	C₂³×C₅₃	1	2	yes	complemented
637	#124	—	2	1	no	—
638	#124	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	#123	—	2	2	no	—
643	C₂²⋊Q₈	—	2	1	no	—
644	C₂²⋊Q₈	—	2	1	no	—
645	C₂²⋊Q₈	—	2	1	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
648	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
649	#121	—	2	2	no	—
650	#121	—	2	1	no	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	—	2	4	no	—
656	#121	C₂³×C₅₃	1	4	yes	—
657	#121	C₂³×C₅₃	1	4	yes	—
658	#121	C₂³×C₅₃	1	2	yes	complemented
659	#121	C₂³×C₅₃	1	2	yes	complemented
660	#120	—	2	2	no	—
661	#120	—	2	4	no	—
662	#120	—	2	4	no	—
663	#120	—	2	4	no	—
664	#120	—	2	4	no	—
665	C₄×Q₈	—	2	1	no	—
666	C₄×Q₈	—	2	1	no	—
667	C₄×Q₈	—	2	1	no	—
668	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
669	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
670	C₄×D₄	—	2	1	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	1	no	—
673	C₄×D₄	—	2	1	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	1	no	—
677	C₄×D₄	—	2	1	no	—
678	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
679	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
680	C₄×D₄	D₄×C₅₃	1	2	yes	—
681	C₄×D₄	C₂³×C₅₃	1	2	yes	—
682	C₄×D₄	C₂³×C₅₃	1	2	yes	—
683	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
684	C₄×D₄	C₂³×C₅₃	1	2	yes	—
685	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
686	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic, complemented
687	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic, complemented
688	#117	—	2	2	no	—
689	#117	—	2	2	no	—
690	#117	—	2	1	no	—
691	#117	—	2	2	no	—
692	#117	—	2	1	no	—
693	#117	C₂³×C₅₃	1	1	yes	characteristic
694	#117	C₂³×C₅₃	1	2	yes	—
695	#117	C₂³×C₅₃	1	2	yes	complemented
696	#117	C₂³×C₅₃	1	2	yes	complemented
697	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
699	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
700	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	complemented
701	C₂×C₂²⋊C₄	—	2	2	no	—
702	C₂×C₂²⋊C₄	—	2	1	no	—
703	C₂×C₂²⋊C₄	—	2	2	no	—
704	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
705	C₂×C₄²	—	2	2	no	—
706	C₂×C₄²	—	2	1	no	—
707	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
708	#107	C₂³×C₅₃	1	2	yes	complemented
709	#107	C₂³×C₅₃	1	4	yes	complemented
710	#106	C₂³×C₅₃	1	2	yes	complemented
711	#106	C₂³×C₅₃	1	4	yes	complemented
712	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
713	C₄⋊C₈	C₂³×C₅₃	1	2	yes	complemented
714	#103	C₂³×C₅₃	1	2	yes	complemented
715	#102	C₂³×C₅₃	1	2	yes	—
716	#102	C₂³×C₅₃	1	2	yes	—
717	#102	C₂³×C₅₃	1	4	yes	—
718	#102	C₂³×C₅₃	1	4	yes	—
719	#102	C₂³×C₅₃	1	4	yes	complemented
720	#102	C₂³×C₅₃	1	4	yes	complemented
721	#102	C₂³×C₅₃	1	4	yes	complemented
722	#102	C₂³×C₅₃	1	4	yes	complemented
723	#102	C₂³×C₅₃	1	2	yes	complemented
724	#102	C₂³×C₅₃	1	4	yes	complemented
725	#102	C₂³×C₅₃	1	4	yes	complemented
726	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
727	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	complemented
728	#97	C₂³×C₅₃	1	2	yes	complemented
729	C₄×C₈	C₂³×C₅₃	1	2	yes	complemented
730	C₂⁴	—	2	1	no	—
731	C₂⁴	—	2	2	no	—
732	C₂⁴	—	2	4	no	—
733	C₂⁴	—	2	4	no	—
734	C₂⁴	—	4	8	no	—
735	C₂⁴	—	4	8	no	—
736	C₂⁴	—	8	4	no	—
737	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
738	#41	—	2	2	no	—
739	#41	—	2	2	no	—
740	#41	—	4	4	no	—
741	C₂×Q₈	—	2	1	no	—
742	C₂×Q₈	—	2	1	no	—
743	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	8	no	—
746	C₂×D₄	—	2	8	no	—
747	C₂×D₄	—	2	1	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	4	no	—
750	C₂×D₄	—	2	4	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	4	no	—
754	C₂×D₄	—	2	4	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	4	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	4	no	—
763	C₂×D₄	—	4	4	no	—
764	C₂×D₄	—	4	4	no	—
765	C₂×D₄	—	4	8	no	—
766	C₂×D₄	—	4	8	no	—
767	C₂×D₄	—	4	8	no	—
768	C₂×D₄	—	4	4	no	—
769	C₂×D₄	—	4	16	no	—
770	C₂×D₄	—	4	8	no	—
771	C₂×D₄	—	4	8	no	—
772	C₂×D₄	—	4	8	no	—
773	C₂×D₄	—	8	2	no	—
774	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
775	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
776	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
777	C₂×D₄	#41×C₅₃	1	4	yes	complemented
778	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
779	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
780	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
781	C₂²×C₄	—	2	4	no	—
782	C₂²×C₄	—	2	4	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	1	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	1	no	—
787	C₂²×C₄	—	2	1	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	4	4	no	—
792	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
793	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
794	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
795	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
796	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
799	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
800	SD₁₆	—	2	4	no	—
801	SD₁₆	—	4	4	no	—
802	D₈	—	2	4	no	—
803	D₈	—	4	4	no	—
804	M₁₆	—	2	2	no	—
805	M₁₆	—	2	2	no	—
806	M₁₆	—	2	4	no	—
807	M₁₆	—	4	4	no	—
808	C₂×C₈	—	4	4	no	—
809	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
810	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
811	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	1	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
824	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
825	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
827	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
828	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
829	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
830	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
831	C₂²⋊C₄	—	2	1	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	4	no	—
840	C₂²⋊C₄	—	2	4	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	1	no	—
843	C₂²⋊C₄	—	2	1	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
846	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
847	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
848	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
849	C₄²	—	2	1	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	1	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	1	no	—
855	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
856	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
857	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
858	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
859	C₂³	—	2	4	no	—
860	C₂³	—	2	4	no	—
861	C₂³	—	2	4	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	4	no	—
865	C₂³	—	4	2	no	—
866	C₂³	—	4	8	no	—
867	C₂³	—	4	8	no	—
868	C₂³	—	4	2	no	—
869	C₂³	—	4	2	no	—
870	C₂³	—	4	4	no	—
871	C₂³	—	4	8	no	—
872	C₂³	—	4	4	no	—
873	C₂³	—	4	4	no	—
874	C₂³	—	4	8	no	—
875	C₂³	—	8	4	no	—
876	C₂³	—	8	4	no	—
877	C₂³	—	8	32	no	—
878	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
879	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
880	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
881	Q₈	—	2	1	no	—
882	Q₈	—	2	1	no	—
883	Q₈	—	4	2	no	—
884	Q₈	—	8	1	no	—
885	D₄	—	2	4	no	—
886	D₄	—	2	4	no	—
887	D₄	—	2	2	no	—
888	D₄	—	2	1	no	—
889	D₄	—	2	4	no	—
890	D₄	—	2	2	no	—
891	D₄	—	2	1	no	—
892	D₄	—	2	4	no	—
893	D₄	—	4	8	no	—
894	D₄	—	4	8	no	—
895	D₄	—	4	4	no	—
896	D₄	—	4	8	no	—
897	D₄	—	4	2	no	—
898	D₄	—	4	8	no	—
899	D₄	—	4	4	no	—
900	D₄	—	4	4	no	—
901	D₄	—	4	4	no	—
902	D₄	—	8	2	no	—
903	D₄	—	8	2	no	—
904	D₄	—	8	2	no	—
905	D₄	AGL(1,ℤ/8)×C₅₃	1	4	yes	complemented
906	D₄	C₂×#41×C₅₃	1	4	yes	—
907	C₂×C₄	—	2	4	no	—
908	C₂×C₄	—	2	4	no	—
909	C₂×C₄	—	2	4	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	4	1	no	—
922	C₂×C₄	—	4	4	no	—
923	C₂×C₄	—	4	2	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	—	4	2	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	2	no	—
928	C₂×C₄	—	8	1	no	—
929	C₂×C₄	—	8	2	no	—
930	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
931	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
932	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
933	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
935	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
936	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
937	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
938	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
939	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
940	C₈	—	2	2	no	—
941	C₈	—	2	2	no	—
942	C₈	—	2	4	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	4	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	4	8	no	—
952	C₂²	—	4	8	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	4	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	4	no	—
959	C₂²	—	4	1	no	—
960	C₂²	—	4	4	no	—
961	C₂²	—	8	16	no	—
962	C₂²	—	8	8	no	—
963	C₂²	—	8	16	no	—
964	C₂²	C₅₃×#546	1	2	yes	—
965	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	4	yes	—
966	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
967	C₄	—	2	2	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	1	no	—
970	C₄	—	2	1	no	—
971	C₄	—	2	1	no	—
972	C₄	—	4	1	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	1	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	1	no	—
977	C₄	—	4	2	no	—
978	C₄	C₅₃×#546	1	2	yes	—
979	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
980	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
981	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
982	C₂	—	2	2	no	—
983	C₂	—	2	4	no	—
984	C₂	—	4	2	no	—
985	C₂	—	4	4	no	—
986	C₂	—	8	4	no	—
987	C₂	—	8	1	no	—
988	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
989	C₂	C₂²×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
990	C₂	C₅₃×#3585	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×#3475	C₂	semidirect
2. C₂×D₄²×C₅₃	C₂	semidirect
3. C₅₃×#3325	C₂	semidirect
4. C₅₃×#3324	C₂	semidirect
5. C₅₃×#3318	C₂	semidirect
6. C₅₃×#3310	C₂	semidirect
7. C₅₃×#3295	C₂	semidirect
8. C₅₃×#3294	C₂	semidirect
9. C₅₃×#3138	C₂	semidirect
10. C₅₃×#3094	C₂	semidirect
11. C₅₃×#3077	C₂	semidirect
12. C₅₃×#3055	C₂	semidirect
13. C₅₃×#3038	C₂	semidirect
14. C₅₃×#3003	C₂	semidirect
15. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
16. D₄×M₁₆×C₅₃	C₂	semidirect
17. C₂×C₅₃×#418	C₂	semidirect
21. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
22. C₂²×M₁₆×C₅₃	C₂²	semidirect
23. C₅₃×#556	C₂²	semidirect
24. C₅₃×#555	C₂²	semidirect
25. C₅₃×#554	C₂²	semidirect
26. C₅₃×#553	C₂²	semidirect
28. C₅₃×#552	C₂²	semidirect
30. C₅₃×#547	C₂²	semidirect
38. C₅₃×#533	C₂²	semidirect
42. C₅₃×#525	C₂²	semidirect
47. C₄×#41×C₅₃	C₂²	semidirect
50. C₂×#117×C₅₃	C₂²	semidirect
51. C₅₃×#490	C₂²	semidirect
52. C₅₃×#486	C₂²	semidirect
53. C₅₃×#486	C₂²	semidirect
54. C₅₃×#482	C₂²	semidirect
55. C₅₃×#482	C₂²	semidirect
56. C₅₃×#481	C₂²	semidirect
57. C₅₃×#480	C₂²	semidirect
58. C₅₃×#478	C₂²	semidirect
59. C₅₃×#476	C₂²	semidirect
60. C₅₃×#474	C₂²	semidirect
61. C₅₃×#469	C₂²	semidirect
62. C₅₃×#468	C₂²	semidirect
63. C₅₃×#466	C₂²	semidirect
64. C₅₃×#465	C₂²	semidirect
65. C₅₃×#460	C₂²	semidirect
66. C₅₃×#460	C₂²	semidirect
67. C₅₃×#459	C₂²	semidirect
68. C₅₃×#459	C₂²	semidirect
69. C₅₃×#450	C₂²	semidirect
70. C₅₃×#450	C₂²	semidirect
71. C₅₃×#447	C₂²	semidirect
72. C₅₃×#447	C₂²	semidirect
73. C₅₃×#442	C₂²	semidirect
74. C₅₃×#440	C₂²	semidirect
75. C₄×SD₁₆×C₅₃	C₂²	semidirect
76. C₄×D₈×C₅₃	C₂²	semidirect
77. C₅₃×#436	C₂²	semidirect
78. C₅₃×#435	C₂²	semidirect
79. C₈×D₄×C₅₃	C₂²	semidirect
80. C₅₃×#428	C₂²	semidirect
81. C₅₃×#428	C₂²	semidirect
82. C₅₃×#423	C₂²	semidirect
85. C₅₃×#418	C₂²	semidirect
86. C₅₃×#418	C₂²	semidirect
87. C₅₃×#418	C₂²	semidirect
88. C₅₃×#418	C₂²	semidirect
89. C₅₃×#418	C₂²	semidirect
90. C₅₃×#417	C₂²	semidirect
91. C₂×#102×C₅₃	C₂²	semidirect
92. C₂×#102×C₅₃	C₂²	semidirect
93. C₅₃×#407	C₂²	semidirect
94. C₄×M₁₆×C₅₃	C₂²	semidirect
120. C₂×SD₁₆×C₅₃	C₂³	semidirect
122. C₂×D₈×C₅₃	C₂³	semidirect
127. C₂×M₁₆×C₅₃	C₂³	semidirect
128. C₂²×C₈×C₅₃	C₂³	semidirect
129. C₄⋊Q₈×C₅₃	C₂³	semidirect
130. C₄⋊Q₈×C₅₃	C₂³	semidirect
140. #125×C₅₃	C₂³	semidirect
151. C₂²⋊Q₈×C₅₃	C₂³	semidirect
152. C₂²⋊Q₈×C₅₃	C₂³	semidirect
162. #121×C₅₃	C₂³	semidirect
163. #121×C₅₃	C₂³	semidirect
172. C₄×Q₈×C₅₃	C₂³	semidirect
173. C₄×Q₈×C₅₃	C₂³	semidirect
190. C₄×D₄×C₅₃	C₂³	semidirect
191. C₄×D₄×C₅₃	C₂³	semidirect
199. #117×C₅₃	C₂³	semidirect
200. #117×C₅₃	C₂³	semidirect
203. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
204. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
212. #107×C₅₃	C₂³	semidirect
213. #107×C₅₃	C₂³	semidirect
214. #106×C₅₃	C₂³	semidirect
215. #106×C₅₃	C₂³	semidirect
216. C₄⋊C₈×C₅₃	C₂³	semidirect
217. C₄⋊C₈×C₅₃	C₂³	semidirect
218. #103×C₅₃	C₂³	semidirect
223. #102×C₅₃	C₂³	semidirect
224. #102×C₅₃	C₂³	semidirect
225. #102×C₅₃	C₂³	semidirect
226. #102×C₅₃	C₂³	semidirect
227. #102×C₅₃	C₂³	semidirect
228. #102×C₅₃	C₂³	semidirect
229. #102×C₅₃	C₂³	semidirect
230. C₂²⋊C₈×C₅₃	C₂³	semidirect
231. C₂²⋊C₈×C₅₃	C₂³	semidirect
232. #97×C₅₃	C₂³	semidirect
233. C₄×C₈×C₅₃	C₂³	semidirect
281. C₂×D₄×C₅₃	#41	semidirect
409. D₄×C₅₃	AGL(1,ℤ/8)	semidirect
447. #61155	C₅₃	direct (N × H)
487. #3475	C₂×C₅₃	semidirect
488. C₂×D₄²	C₂×C₅₃	semidirect
489. #3325	C₂×C₅₃	semidirect
490. #3324	C₂×C₅₃	semidirect
491. #3318	C₂×C₅₃	semidirect
492. #3310	C₂×C₅₃	semidirect
493. #3295	C₂×C₅₃	semidirect
494. #3294	C₂×C₅₃	semidirect
495. #3138	C₂×C₅₃	semidirect
496. #3094	C₂×C₅₃	semidirect
497. #3077	C₂×C₅₃	semidirect
498. #3055	C₂×C₅₃	semidirect
499. #3038	C₂×C₅₃	semidirect
500. #3003	C₂×C₅₃	semidirect
501. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
502. D₄×M₁₆	C₂×C₅₃	semidirect
503. C₂×#418	C₂×C₅₃	semidirect
516. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
517. C₂²×M₁₆	C₂²×C₅₃	semidirect
518. #556	C₂²×C₅₃	semidirect
519. #555	C₂²×C₅₃	semidirect
520. #554	C₂²×C₅₃	semidirect
521. #553	C₂²×C₅₃	semidirect
523. #552	C₂²×C₅₃	semidirect
525. #547	C₂²×C₅₃	semidirect
533. #533	C₂²×C₅₃	semidirect
537. #525	C₂²×C₅₃	semidirect
542. C₄×#41	C₂²×C₅₃	semidirect
545. C₂×#117	C₂²×C₅₃	semidirect
546. #490	C₂²×C₅₃	semidirect
547. #486	C₂²×C₅₃	semidirect
548. #486	C₂²×C₅₃	semidirect
549. #482	C₂²×C₅₃	semidirect
550. #482	C₂²×C₅₃	semidirect
551. #481	C₂²×C₅₃	semidirect
552. #480	C₂²×C₅₃	semidirect
553. #478	C₂²×C₅₃	semidirect
554. #476	C₂²×C₅₃	semidirect
555. #474	C₂²×C₅₃	semidirect
556. #469	C₂²×C₅₃	semidirect
557. #468	C₂²×C₅₃	semidirect
558. #466	C₂²×C₅₃	semidirect
559. #465	C₂²×C₅₃	semidirect
560. #460	C₂²×C₅₃	semidirect
561. #460	C₂²×C₅₃	semidirect
562. #459	C₂²×C₅₃	semidirect
563. #459	C₂²×C₅₃	semidirect
564. #450	C₂²×C₅₃	semidirect
565. #450	C₂²×C₅₃	semidirect
566. #447	C₂²×C₅₃	semidirect
567. #447	C₂²×C₅₃	semidirect
568. #442	C₂²×C₅₃	semidirect
569. #440	C₂²×C₅₃	semidirect
570. C₄×SD₁₆	C₂²×C₅₃	semidirect
571. C₄×D₈	C₂²×C₅₃	semidirect
572. #436	C₂²×C₅₃	semidirect
573. #435	C₂²×C₅₃	semidirect
574. C₈×D₄	C₂²×C₅₃	semidirect
575. #428	C₂²×C₅₃	semidirect
576. #428	C₂²×C₅₃	semidirect
577. #423	C₂²×C₅₃	semidirect
580. #418	C₂²×C₅₃	semidirect
581. #418	C₂²×C₅₃	semidirect
582. #418	C₂²×C₅₃	semidirect
583. #418	C₂²×C₅₃	semidirect
584. #418	C₂²×C₅₃	semidirect
585. #417	C₂²×C₅₃	semidirect
586. C₂×#102	C₂²×C₅₃	semidirect
587. C₂×#102	C₂²×C₅₃	semidirect
588. #407	C₂²×C₅₃	semidirect
589. C₄×M₁₆	C₂²×C₅₃	semidirect
590. C₅₃	#61155	direct (N × H)
616. C₂×SD₁₆	C₂³×C₅₃	semidirect
618. C₂×D₈	C₂³×C₅₃	semidirect
623. C₂×M₁₆	C₂³×C₅₃	semidirect
624. C₂²×C₈	C₂³×C₅₃	semidirect
625. C₄⋊Q₈	C₂³×C₅₃	semidirect
626. C₄⋊Q₈	C₂³×C₅₃	semidirect
636. #125	C₂³×C₅₃	semidirect
647. C₂²⋊Q₈	C₂³×C₅₃	semidirect
648. C₂²⋊Q₈	C₂³×C₅₃	semidirect
658. #121	C₂³×C₅₃	semidirect
659. #121	C₂³×C₅₃	semidirect
668. C₄×Q₈	C₂³×C₅₃	semidirect
669. C₄×Q₈	C₂³×C₅₃	semidirect
686. C₄×D₄	C₂³×C₅₃	semidirect
687. C₄×D₄	C₂³×C₅₃	semidirect
695. #117	C₂³×C₅₃	semidirect
696. #117	C₂³×C₅₃	semidirect
699. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
700. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
708. #107	C₂³×C₅₃	semidirect
709. #107	C₂³×C₅₃	semidirect
710. #106	C₂³×C₅₃	semidirect
711. #106	C₂³×C₅₃	semidirect
712. C₄⋊C₈	C₂³×C₅₃	semidirect
713. C₄⋊C₈	C₂³×C₅₃	semidirect
714. #103	C₂³×C₅₃	semidirect
719. #102	C₂³×C₅₃	semidirect
720. #102	C₂³×C₅₃	semidirect
721. #102	C₂³×C₅₃	semidirect
722. #102	C₂³×C₅₃	semidirect
723. #102	C₂³×C₅₃	semidirect
724. #102	C₂³×C₅₃	semidirect
725. #102	C₂³×C₅₃	semidirect
726. C₂²⋊C₈	C₂³×C₅₃	semidirect
727. C₂²⋊C₈	C₂³×C₅₃	semidirect
728. #97	C₂³×C₅₃	semidirect
729. C₄×C₈	C₂³×C₅₃	semidirect
777. C₂×D₄	#41×C₅₃	semidirect
905. D₄	AGL(1,ℤ/8)×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3475	2
C₂×D₄²×C₅₃	2
C₅₃×#3325	2
C₅₃×#3324	2
C₅₃×#3318	2
C₅₃×#3310	2
C₅₃×#3295	2
C₅₃×#3294	2
C₅₃×#3138	2
C₅₃×#3094	2
C₅₃×#3077	2
C₅₃×#3055	2
C₅₃×#3038	2
C₅₃×#3003	2
C₄×AGL(1,ℤ/8)×C₅₃	2
D₄×M₁₆×C₅₃	2
C₂×C₅₃×#418	2
#61155	53

Subgroups — C53×#61155 #27268667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61155 #27268667