Subgroups — C₅₃×#60916 #27268428

Order 13568.

2168 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3254	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3253	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3251	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3247	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3246	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3245	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3079	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3077	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3055	C₂	1	4	yes	maximal, complemented
12	C₅₃×#3038	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3036	C₂	1	2	yes	maximal, complemented
14	C₂×C₅₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₅₃	—	2	1	no	—
16	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	4	yes	—
17	C₂²×M₁₆×C₅₃	C₂²	1	2	yes	—
18	C₅₃×#533	C₂²	1	1	yes	characteristic
19	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
20	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
21	C₅₃×#532	—	2	1	no	—
22	C₅₃×#532	—	2	1	no	—
23	C₅₃×#532	—	2	1	no	—
24	C₅₃×#532	—	2	1	no	—
25	C₅₃×#532	C₂²	1	1	yes	characteristic
26	C₅₃×#532	C₂²	1	2	yes	—
27	C₅₃×#532	C₂²	1	2	yes	—
28	C₅₃×#532	C₂²	1	2	yes	—
29	C₅₃×#532	C₂²	1	2	yes	—
30	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
34	C₅₃×#529	—	2	1	no	—
35	C₅₃×#529	—	2	1	no	—
36	C₅₃×#529	—	2	1	no	—
37	C₅₃×#529	—	2	1	no	—
38	C₅₃×#529	C₂²	1	2	yes	complemented
39	C₅₃×#529	C₂²	1	2	yes	complemented
40	C₂×#124×C₅₃	—	2	1	no	—
41	C₅₃×#525	—	2	1	no	—
42	C₅₃×#525	—	2	1	no	—
43	C₅₃×#525	C₂²	1	2	yes	—
44	C₂×#121×C₅₃	—	2	1	no	—
45	C₂×#121×C₅₃	C₂²	1	2	yes	—
46	C₄×#41×C₅₃	—	2	1	no	—
47	C₄×#41×C₅₃	—	2	1	no	—
48	C₄×#41×C₅₃	C₂²	1	2	yes	—
49	C₂×C₄×D₄×C₅₃	—	2	1	no	—
50	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
51	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
52	C₅₃×#478	C₂²	1	8	yes	complemented
53	C₅₃×#477	C₂²	1	4	yes	complemented
54	C₅₃×#476	C₂²	1	4	yes	complemented
55	C₅₃×#476	C₂²	1	4	yes	complemented
56	C₅₃×#475	C₂²	1	4	yes	complemented
57	C₅₃×#474	C₂²	1	4	yes	complemented
58	C₅₃×#474	C₂²	1	4	yes	complemented
59	C₅₃×#469	C₂²	1	8	yes	complemented
60	C₅₃×#468	C₂²	1	8	yes	complemented
61	C₅₃×#466	C₂²	1	8	yes	complemented
62	C₅₃×#465	C₂²	1	8	yes	complemented
63	C₅₃×#463	C₂²	1	8	yes	complemented
64	C₅₃×#461	C₂²	1	4	yes	complemented
65	C₅₃×#460	C₂²	1	4	yes	complemented
66	C₅₃×#460	C₂²	1	4	yes	complemented
67	C₅₃×#459	C₂²	1	4	yes	complemented
68	C₅₃×#459	C₂²	1	4	yes	complemented
69	C₅₃×#459	C₂²	1	4	yes	complemented
70	C₅₃×#428	C₂²	1	4	yes	—
71	C₅₃×#423	C₂²	1	2	yes	—
72	C₅₃×#423	C₂²	1	2	yes	—
73	C₅₃×#423	C₂²	1	2	yes	complemented
74	C₅₃×#423	C₂²	1	2	yes	complemented
75	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	complemented
76	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	complemented
77	C₅₃×#418	C₂²	1	4	yes	—
78	C₅₃×#417	C₂²	1	4	yes	—
79	C₂×#41×C₅₃	—	2	1	no	—
80	C₂×#41×C₅₃	—	2	1	no	—
81	C₂×#41×C₅₃	—	2	2	no	—
82	C₂×#41×C₅₃	—	2	2	no	—
83	C₂×#41×C₅₃	—	2	2	no	—
84	C₂×#41×C₅₃	—	2	2	no	—
85	C₂×#41×C₅₃	—	4	8	no	—
86	C₂×#41×C₅₃	C₂³	1	2	yes	—
87	C₂²×Q₈×C₅₃	—	2	1	no	—
88	C₂²×D₄×C₅₃	—	2	2	no	—
89	C₂²×D₄×C₅₃	—	2	1	no	—
90	C₂²×D₄×C₅₃	—	2	1	no	—
91	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₅₃	—	2	2	no	—
93	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
94	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
95	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
96	AGL(1,ℤ/8)×C₅₃	—	4	8	no	—
97	C₂×SD₁₆×C₅₃	C₂³	1	8	yes	—
98	C₂×D₈×C₅₃	C₂³	1	8	yes	—
99	C₂×M₁₆×C₅₃	—	4	4	no	—
100	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
101	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
102	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
103	C₄⋊Q₈×C₅₃	—	2	1	no	—
104	C₄⋊Q₈×C₅₃	—	2	1	no	—
105	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
106	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
107	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
108	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
109	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
110	#127×C₅₃	—	2	1	no	—
111	#127×C₅₃	—	2	1	no	—
112	#127×C₅₃	C₂³	1	2	yes	—
113	#127×C₅₃	C₂³	1	2	yes	—
114	#127×C₅₃	C₂³	1	1	yes	characteristic
115	#126×C₅₃	—	2	2	no	—
116	#126×C₅₃	—	2	2	no	—
117	#125×C₅₃	—	2	1	no	—
118	#125×C₅₃	—	2	1	no	—
119	#125×C₅₃	C₂³	1	2	yes	—
120	#124×C₅₃	—	2	2	no	—
121	#124×C₅₃	—	2	2	no	—
122	#124×C₅₃	—	2	2	no	—
123	#124×C₅₃	—	2	2	no	—
124	#124×C₅₃	—	2	1	no	—
125	#124×C₅₃	—	2	1	no	—
126	#124×C₅₃	C₂³	1	2	yes	—
127	#123×C₅₃	—	2	2	no	—
128	#123×C₅₃	—	2	2	no	—
129	#123×C₅₃	—	2	2	no	—
130	C₂²⋊Q₈×C₅₃	—	2	1	no	—
131	C₂²⋊Q₈×C₅₃	—	2	1	no	—
132	C₂²⋊Q₈×C₅₃	—	2	1	no	—
133	C₂²⋊Q₈×C₅₃	—	2	1	no	—
134	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
135	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
136	#121×C₅₃	—	2	2	no	—
137	#121×C₅₃	—	2	2	no	—
138	#121×C₅₃	—	2	2	no	—
139	#121×C₅₃	—	2	2	no	—
140	#121×C₅₃	—	2	2	no	—
141	#121×C₅₃	—	2	2	no	—
142	#121×C₅₃	—	2	1	no	—
143	#121×C₅₃	—	2	1	no	—
144	#121×C₅₃	—	2	1	no	—
145	#121×C₅₃	—	2	1	no	—
146	#121×C₅₃	C₂³	1	4	yes	—
147	#121×C₅₃	C₂³	1	4	yes	—
148	#121×C₅₃	C₂³	1	2	yes	—
149	#121×C₅₃	C₂³	1	2	yes	—
150	#120×C₅₃	—	2	2	no	—
151	C₄×Q₈×C₅₃	—	2	1	no	—
152	C₄×Q₈×C₅₃	—	2	1	no	—
153	C₄×Q₈×C₅₃	—	2	1	no	—
154	C₄×Q₈×C₅₃	—	2	1	no	—
155	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
156	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
157	C₄×D₄×C₅₃	—	2	2	no	—
158	C₄×D₄×C₅₃	—	2	2	no	—
159	C₄×D₄×C₅₃	—	2	2	no	—
160	C₄×D₄×C₅₃	—	2	2	no	—
161	C₄×D₄×C₅₃	—	2	2	no	—
162	C₄×D₄×C₅₃	—	2	2	no	—
163	C₄×D₄×C₅₃	—	2	1	no	—
164	C₄×D₄×C₅₃	—	2	1	no	—
165	C₄×D₄×C₅₃	—	2	1	no	—
166	C₄×D₄×C₅₃	—	2	1	no	—
167	C₄×D₄×C₅₃	—	2	2	no	—
168	C₄×D₄×C₅₃	—	2	2	no	—
169	C₄×D₄×C₅₃	—	2	2	no	—
170	C₄×D₄×C₅₃	—	2	2	no	—
171	C₄×D₄×C₅₃	—	2	2	no	—
172	C₄×D₄×C₅₃	—	2	2	no	—
173	C₄×D₄×C₅₃	C₂³	1	4	yes	—
174	C₄×D₄×C₅₃	C₂³	1	4	yes	—
175	C₄×D₄×C₅₃	C₂³	1	2	yes	—
176	C₄×D₄×C₅₃	C₂³	1	2	yes	—
177	#117×C₅₃	—	2	2	no	—
178	#117×C₅₃	—	2	2	no	—
179	#117×C₅₃	—	2	2	no	—
180	#117×C₅₃	—	2	1	no	—
181	#117×C₅₃	—	2	1	no	—
182	#117×C₅₃	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
184	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
186	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
187	C₂×C₄²×C₅₃	—	2	2	no	—
188	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
194	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
200	#107×C₅₃	C₂³	1	8	yes	—
201	#106×C₅₃	C₂³	1	8	yes	—
202	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
203	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
204	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
205	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
206	#103×C₅₃	C₂³	1	8	yes	—
207	#102×C₅₃	C₂³	1	8	yes	—
208	#102×C₅₃	C₂³	1	8	yes	—
209	#102×C₅₃	C₂³	1	8	yes	—
210	C₂⁴×C₅₃	—	2	2	no	—
211	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
212	#41×C₅₃	—	2	4	no	—
213	#41×C₅₃	—	2	4	no	—
214	#41×C₅₃	—	4	4	no	—
215	#41×C₅₃	—	4	8	no	—
216	#41×C₅₃	—	4	8	no	—
217	#41×C₅₃	—	4	8	no	—
218	#41×C₅₃	—	4	4	no	—
219	#41×C₅₃	—	4	8	no	—
220	C₂×Q₈×C₅₃	—	2	1	no	—
221	C₂×Q₈×C₅₃	—	2	1	no	—
222	C₂×Q₈×C₅₃	—	2	2	no	—
223	C₂×Q₈×C₅₃	—	2	2	no	—
224	C₂×Q₈×C₅₃	—	4	4	no	—
225	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
226	C₂×D₄×C₅₃	—	2	2	no	—
227	C₂×D₄×C₅₃	—	2	2	no	—
228	C₂×D₄×C₅₃	—	2	2	no	—
229	C₂×D₄×C₅₃	—	2	4	no	—
230	C₂×D₄×C₅₃	—	2	4	no	—
231	C₂×D₄×C₅₃	—	2	1	no	—
232	C₂×D₄×C₅₃	—	2	1	no	—
233	C₂×D₄×C₅₃	—	2	2	no	—
234	C₂×D₄×C₅₃	—	2	2	no	—
235	C₂×D₄×C₅₃	—	2	2	no	—
236	C₂×D₄×C₅₃	—	2	2	no	—
237	C₂×D₄×C₅₃	—	2	2	no	—
238	C₂×D₄×C₅₃	—	2	4	no	—
239	C₂×D₄×C₅₃	—	2	4	no	—
240	C₂×D₄×C₅₃	—	4	4	no	—
241	C₂×D₄×C₅₃	—	4	4	no	—
242	C₂×D₄×C₅₃	—	4	8	no	—
243	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
244	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
245	C₂²×C₄×C₅₃	—	2	4	no	—
246	C₂²×C₄×C₅₃	—	2	2	no	—
247	C₂²×C₄×C₅₃	—	2	2	no	—
248	C₂²×C₄×C₅₃	—	2	2	no	—
249	C₂²×C₄×C₅₃	—	2	2	no	—
250	C₂²×C₄×C₅₃	—	2	2	no	—
251	C₂²×C₄×C₅₃	—	2	2	no	—
252	C₂²×C₄×C₅₃	—	2	4	no	—
253	C₂²×C₄×C₅₃	—	2	4	no	—
254	C₂²×C₄×C₅₃	—	4	2	no	—
255	C₂²×C₄×C₅₃	—	4	8	no	—
256	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
274	SD₁₆×C₅₃	—	4	8	no	—
275	D₈×C₅₃	—	4	8	no	—
276	M₁₆×C₅₃	—	2	8	no	—
277	M₁₆×C₅₃	—	4	4	no	—
278	C₂×C₈×C₅₃	—	4	4	no	—
279	C₂×C₈×C₅₃	C₂⁴	1	8	yes	—
280	C₄⋊C₄×C₅₃	—	2	2	no	—
281	C₄⋊C₄×C₅₃	—	2	2	no	—
282	C₄⋊C₄×C₅₃	—	2	2	no	—
283	C₄⋊C₄×C₅₃	—	2	1	no	—
284	C₄⋊C₄×C₅₃	—	2	1	no	—
285	C₄⋊C₄×C₅₃	—	2	1	no	—
286	C₄⋊C₄×C₅₃	—	2	1	no	—
287	C₄⋊C₄×C₅₃	—	2	2	no	—
288	C₄⋊C₄×C₅₃	—	2	2	no	—
289	C₄⋊C₄×C₅₃	—	2	2	no	—
290	C₄⋊C₄×C₅₃	—	2	2	no	—
291	C₄⋊C₄×C₅₃	—	2	2	no	—
292	C₄⋊C₄×C₅₃	—	2	2	no	—
293	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
294	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
295	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
296	C₂²⋊C₄×C₅₃	—	2	2	no	—
297	C₂²⋊C₄×C₅₃	—	2	2	no	—
298	C₂²⋊C₄×C₅₃	—	2	2	no	—
299	C₂²⋊C₄×C₅₃	—	2	4	no	—
300	C₂²⋊C₄×C₅₃	—	2	4	no	—
301	C₂²⋊C₄×C₅₃	—	2	4	no	—
302	C₂²⋊C₄×C₅₃	—	2	4	no	—
303	C₂²⋊C₄×C₅₃	—	2	2	no	—
304	C₂²⋊C₄×C₅₃	—	2	2	no	—
305	C₂²⋊C₄×C₅₃	—	2	2	no	—
306	C₂²⋊C₄×C₅₃	—	2	2	no	—
307	C₂²⋊C₄×C₅₃	—	2	2	no	—
308	C₂²⋊C₄×C₅₃	—	2	2	no	—
309	C₄²×C₅₃	—	2	2	no	—
310	C₄²×C₅₃	—	2	2	no	—
311	C₄²×C₅₃	—	2	2	no	—
312	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
325	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
326	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
327	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
328	C₂³×C₅₃	—	2	2	no	—
329	C₂³×C₅₃	—	2	2	no	—
330	C₂³×C₅₃	—	2	2	no	—
331	C₂³×C₅₃	—	2	4	no	—
332	C₂³×C₅₃	—	4	1	no	—
333	C₂³×C₅₃	—	4	4	no	—
334	C₂³×C₅₃	—	4	4	no	—
335	C₂³×C₅₃	—	4	4	no	—
336	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
337	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
338	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
339	Q₈×C₅₃	—	2	2	no	—
340	Q₈×C₅₃	—	2	2	no	—
341	Q₈×C₅₃	—	4	4	no	—
342	Q₈×C₅₃	—	4	2	no	—
343	Q₈×C₅₃	—	4	4	no	—
344	Q₈×C₅₃	—	4	2	no	—
345	D₄×C₅₃	—	2	4	no	—
346	D₄×C₅₃	—	2	2	no	—
347	D₄×C₅₃	—	2	4	no	—
348	D₄×C₅₃	—	2	2	no	—
349	D₄×C₅₃	—	4	4	no	—
350	D₄×C₅₃	—	4	4	no	—
351	D₄×C₅₃	—	4	2	no	—
352	D₄×C₅₃	—	4	8	no	—
353	D₄×C₅₃	—	4	4	no	—
354	D₄×C₅₃	—	4	4	no	—
355	D₄×C₅₃	—	4	8	no	—
356	D₄×C₅₃	—	4	4	no	—
357	D₄×C₅₃	—	4	4	no	—
358	D₄×C₅₃	—	4	4	no	—
359	D₄×C₅₃	—	4	2	no	—
360	D₄×C₅₃	—	4	4	no	—
361	C₂×C₄×C₅₃	—	2	2	no	—
362	C₂×C₄×C₅₃	—	2	2	no	—
363	C₂×C₄×C₅₃	—	2	2	no	—
364	C₂×C₄×C₅₃	—	2	2	no	—
365	C₂×C₄×C₅₃	—	2	2	no	—
366	C₂×C₄×C₅₃	—	2	2	no	—
367	C₂×C₄×C₅₃	—	2	2	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	2	2	no	—
371	C₂×C₄×C₅₃	—	2	2	no	—
372	C₂×C₄×C₅₃	—	2	1	no	—
373	C₂×C₄×C₅₃	—	2	1	no	—
374	C₂×C₄×C₅₃	—	2	1	no	—
375	C₂×C₄×C₅₃	—	2	1	no	—
376	C₂×C₄×C₅₃	—	2	4	no	—
377	C₂×C₄×C₅₃	—	2	2	no	—
378	C₂×C₄×C₅₃	—	2	2	no	—
379	C₂×C₄×C₅₃	—	2	2	no	—
380	C₂×C₄×C₅₃	—	4	1	no	—
381	C₂×C₄×C₅₃	—	4	1	no	—
382	C₂×C₄×C₅₃	—	4	1	no	—
383	C₂×C₄×C₅₃	—	4	8	no	—
384	C₂×C₄×C₅₃	—	4	4	no	—
385	C₂×C₄×C₅₃	—	4	4	no	—
386	C₂×C₄×C₅₃	—	4	8	no	—
387	C₂×C₄×C₅₃	—	4	4	no	—
388	C₂×C₄×C₅₃	—	4	4	no	—
389	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	4	yes	complemented
390	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
402	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
403	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
404	C₈×C₅₃	—	2	8	no	—
405	#60916	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
406	C₂²×C₅₃	—	2	1	no	—
407	C₂²×C₅₃	—	2	1	no	—
408	C₂²×C₅₃	—	2	1	no	—
409	C₂²×C₅₃	—	2	1	no	—
410	C₂²×C₅₃	—	2	1	no	—
411	C₂²×C₅₃	—	2	1	no	—
412	C₂²×C₅₃	—	2	1	no	—
413	C₂²×C₅₃	—	4	4	no	—
414	C₂²×C₅₃	—	4	2	no	—
415	C₂²×C₅₃	—	4	4	no	—
416	C₂²×C₅₃	—	4	4	no	—
417	C₂²×C₅₃	—	4	2	no	—
418	C₂²×C₅₃	—	4	2	no	—
419	C₂²×C₅₃	—	4	4	no	—
420	C₂²×C₅₃	—	8	8	no	—
421	C₂²×C₅₃	#537	1	2	yes	—
422	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
423	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
424	C₄×C₅₃	—	2	1	no	—
425	C₄×C₅₃	—	2	1	no	—
426	C₄×C₅₃	—	2	1	no	—
427	C₄×C₅₃	—	2	1	no	—
428	C₄×C₅₃	—	2	1	no	—
429	C₄×C₅₃	—	2	1	no	—
430	C₄×C₅₃	—	2	1	no	—
431	C₄×C₅₃	—	4	2	no	—
432	C₄×C₅₃	—	4	4	no	—
433	C₄×C₅₃	—	4	2	no	—
434	C₄×C₅₃	—	4	2	no	—
435	C₄×C₅₃	#537	1	2	yes	—
436	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
437	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
438	C₄×C₅₃	#575	1	2	yes	—
439	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
440	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
441	#3444	C₂×C₅₃	1	1	yes	characteristic, complemented
442	C₂×#532	C₂×C₅₃	1	1	yes	characteristic, complemented
443	#3254	C₂×C₅₃	1	2	yes	complemented
444	#3253	C₂×C₅₃	1	2	yes	complemented
445	#3251	C₂×C₅₃	1	4	yes	complemented
446	#3247	C₂×C₅₃	1	4	yes	complemented
447	#3246	C₂×C₅₃	1	2	yes	complemented
448	#3245	C₂×C₅₃	1	2	yes	complemented
449	#3079	C₂×C₅₃	1	2	yes	complemented
450	#3077	C₂×C₅₃	1	2	yes	complemented
451	#3055	C₂×C₅₃	1	4	yes	complemented
452	#3038	C₂×C₅₃	1	2	yes	complemented
453	#3036	C₂×C₅₃	1	2	yes	complemented
454	C₂×#423	C₂×C₅₃	1	1	yes	characteristic, complemented
455	C₂×C₅₃	—	2	2	no	—
456	C₂×C₅₃	—	2	2	no	—
457	C₂×C₅₃	—	4	1	no	—
458	C₂×C₅₃	—	8	2	no	—
459	C₂×C₅₃	—	8	4	no	—
460	C₂×C₅₃	C₂×#537	1	1	yes	characteristic
461	C₂×C₅₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
462	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
463	C₂²×#41	—	2	1	no	—
464	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	4	yes	—
465	C₂²×M₁₆	C₂²×C₅₃	1	2	yes	—
466	#533	C₂²×C₅₃	1	1	yes	characteristic
467	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
468	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
469	#532	—	2	1	no	—
470	#532	—	2	1	no	—
471	#532	—	2	1	no	—
472	#532	—	2	1	no	—
473	#532	C₂²×C₅₃	1	1	yes	characteristic
474	#532	C₂²×C₅₃	1	2	yes	—
475	#532	C₂²×C₅₃	1	2	yes	—
476	#532	C₂²×C₅₃	1	2	yes	—
477	#532	C₂²×C₅₃	1	2	yes	—
478	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
479	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
480	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
481	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
482	#529	—	2	1	no	—
483	#529	—	2	1	no	—
484	#529	—	2	1	no	—
485	#529	—	2	1	no	—
486	#529	C₂²×C₅₃	1	2	yes	complemented
487	#529	C₂²×C₅₃	1	2	yes	complemented
488	C₂×#124	—	2	1	no	—
489	#525	—	2	1	no	—
490	#525	—	2	1	no	—
491	#525	C₂²×C₅₃	1	2	yes	—
492	C₂×#121	—	2	1	no	—
493	C₂×#121	C₂²×C₅₃	1	2	yes	—
494	C₄×#41	—	2	1	no	—
495	C₄×#41	—	2	1	no	—
496	C₄×#41	C₂²×C₅₃	1	2	yes	—
497	C₂×C₄×D₄	—	2	1	no	—
498	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
499	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
500	#478	C₂²×C₅₃	1	8	yes	complemented
501	#477	C₂²×C₅₃	1	4	yes	complemented
502	#476	C₂²×C₅₃	1	4	yes	complemented
503	#476	C₂²×C₅₃	1	4	yes	complemented
504	#475	C₂²×C₅₃	1	4	yes	complemented
505	#474	C₂²×C₅₃	1	4	yes	complemented
506	#474	C₂²×C₅₃	1	4	yes	complemented
507	#469	C₂²×C₅₃	1	8	yes	complemented
508	#468	C₂²×C₅₃	1	8	yes	complemented
509	#466	C₂²×C₅₃	1	8	yes	complemented
510	#465	C₂²×C₅₃	1	8	yes	complemented
511	#463	C₂²×C₅₃	1	8	yes	complemented
512	#461	C₂²×C₅₃	1	4	yes	complemented
513	#460	C₂²×C₅₃	1	4	yes	complemented
514	#460	C₂²×C₅₃	1	4	yes	complemented
515	#459	C₂²×C₅₃	1	4	yes	complemented
516	#459	C₂²×C₅₃	1	4	yes	complemented
517	#459	C₂²×C₅₃	1	4	yes	complemented
518	#428	C₂²×C₅₃	1	4	yes	—
519	#423	C₂²×C₅₃	1	2	yes	—
520	#423	C₂²×C₅₃	1	2	yes	—
521	#423	C₂²×C₅₃	1	2	yes	complemented
522	#423	C₂²×C₅₃	1	2	yes	complemented
523	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	complemented
524	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	complemented
525	#418	C₂²×C₅₃	1	4	yes	—
526	#417	C₂²×C₅₃	1	4	yes	—
527	C₅₃	#60916	1	1	yes	characteristic, direct product factor, Sylow
528	C₂×#41	—	2	1	no	—
529	C₂×#41	—	2	1	no	—
530	C₂×#41	—	2	2	no	—
531	C₂×#41	—	2	2	no	—
532	C₂×#41	—	2	2	no	—
533	C₂×#41	—	2	2	no	—
534	C₂×#41	—	4	8	no	—
535	C₂×#41	C₂³×C₅₃	1	2	yes	—
536	C₂²×Q₈	—	2	1	no	—
537	C₂²×D₄	—	2	2	no	—
538	C₂²×D₄	—	2	1	no	—
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
541	C₂³×C₄	—	2	2	no	—
542	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
543	C₂³×C₄	D₄×C₅₃	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
545	AGL(1,ℤ/8)	—	4	8	no	—
546	C₂×SD₁₆	C₂³×C₅₃	1	8	yes	—
547	C₂×D₈	C₂³×C₅₃	1	8	yes	—
548	C₂×M₁₆	—	4	4	no	—
549	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
550	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
551	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
552	C₄⋊Q₈	—	2	1	no	—
553	C₄⋊Q₈	—	2	1	no	—
554	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
555	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
556	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
557	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
558	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
559	#127	—	2	1	no	—
560	#127	—	2	1	no	—
561	#127	C₂³×C₅₃	1	2	yes	—
562	#127	C₂³×C₅₃	1	2	yes	—
563	#127	C₂³×C₅₃	1	1	yes	characteristic
564	#126	—	2	2	no	—
565	#126	—	2	2	no	—
566	#125	—	2	1	no	—
567	#125	—	2	1	no	—
568	#125	C₂³×C₅₃	1	2	yes	—
569	#124	—	2	2	no	—
570	#124	—	2	2	no	—
571	#124	—	2	2	no	—
572	#124	—	2	2	no	—
573	#124	—	2	1	no	—
574	#124	—	2	1	no	—
575	#124	C₂³×C₅₃	1	2	yes	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	—	2	1	no	—
581	C₂²⋊Q₈	—	2	1	no	—
582	C₂²⋊Q₈	—	2	1	no	—
583	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
584	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	2	no	—
589	#121	—	2	2	no	—
590	#121	—	2	2	no	—
591	#121	—	2	1	no	—
592	#121	—	2	1	no	—
593	#121	—	2	1	no	—
594	#121	—	2	1	no	—
595	#121	C₂³×C₅₃	1	4	yes	—
596	#121	C₂³×C₅₃	1	4	yes	—
597	#121	C₂³×C₅₃	1	2	yes	—
598	#121	C₂³×C₅₃	1	2	yes	—
599	#120	—	2	2	no	—
600	C₄×Q₈	—	2	1	no	—
601	C₄×Q₈	—	2	1	no	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
605	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	C₂³×C₅₃	1	4	yes	—
623	C₄×D₄	C₂³×C₅₃	1	4	yes	—
624	C₄×D₄	C₂³×C₅₃	1	2	yes	—
625	C₄×D₄	C₂³×C₅₃	1	2	yes	—
626	#117	—	2	1	no	—
627	#117	—	2	1	no	—
628	#117	—	2	2	no	—
629	#117	—	2	2	no	—
630	#117	—	2	2	no	—
631	#117	C₂³×C₅₃	1	2	yes	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
634	C₂×C₂²⋊C₄	—	2	2	no	—
635	C₂×C₂²⋊C₄	—	2	2	no	—
636	C₂×C₄²	—	2	2	no	—
637	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
638	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
639	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
640	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
641	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
642	C₂×C₄²	D₄×C₅₃	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
649	#107	C₂³×C₅₃	1	8	yes	—
650	#106	C₂³×C₅₃	1	8	yes	—
651	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
652	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
653	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
654	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
655	#103	C₂³×C₅₃	1	8	yes	—
656	#102	C₂³×C₅₃	1	8	yes	—
657	#102	C₂³×C₅₃	1	8	yes	—
658	#102	C₂³×C₅₃	1	8	yes	—
659	C₂⁴	—	2	2	no	—
660	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
661	#41	—	2	4	no	—
662	#41	—	2	4	no	—
663	#41	—	4	4	no	—
664	#41	—	4	8	no	—
665	#41	—	4	8	no	—
666	#41	—	4	8	no	—
667	#41	—	4	4	no	—
668	#41	—	4	8	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	4	4	no	—
674	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	4	4	no	—
690	C₂×D₄	—	4	4	no	—
691	C₂×D₄	—	4	8	no	—
692	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
693	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	8	no	—
705	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
723	SD₁₆	—	4	8	no	—
724	D₈	—	4	8	no	—
725	M₁₆	—	2	8	no	—
726	M₁₆	—	4	4	no	—
727	C₂×C₈	—	4	4	no	—
728	C₂×C₈	C₂⁴×C₅₃	1	8	yes	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
743	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	2	no	—
761	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
762	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
763	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
764	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
765	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
766	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
769	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
772	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
773	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
774	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
775	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
776	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
777	C₂³	—	2	2	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	4	no	—
781	C₂³	—	4	1	no	—
782	C₂³	—	4	4	no	—
783	C₂³	—	4	4	no	—
784	C₂³	—	4	4	no	—
785	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
786	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
787	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
788	Q₈	—	2	2	no	—
789	Q₈	—	2	2	no	—
790	Q₈	—	4	4	no	—
791	Q₈	—	4	2	no	—
792	Q₈	—	4	4	no	—
793	Q₈	—	4	2	no	—
794	D₄	—	2	2	no	—
795	D₄	—	2	4	no	—
796	D₄	—	2	4	no	—
797	D₄	—	2	2	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	2	no	—
801	D₄	—	4	8	no	—
802	D₄	—	4	4	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	8	no	—
805	D₄	—	4	4	no	—
806	D₄	—	4	4	no	—
807	D₄	—	4	4	no	—
808	D₄	—	4	2	no	—
809	D₄	—	4	4	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	4	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	8	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	8	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	4	yes	complemented
839	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
847	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
850	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
851	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
852	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
853	C₈	—	2	8	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	4	4	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	4	no	—
864	C₂²	—	4	4	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	4	no	—
868	C₂²	—	8	8	no	—
869	C₂²	C₅₃×#537	1	2	yes	—
870	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
871	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	1	no	—
878	C₄	—	2	1	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	4	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	C₅₃×#537	1	2	yes	—
884	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
885	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	2	yes	—
886	C₄	C₅₃×#575	1	2	yes	—
887	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
888	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
889	C₂	—	2	2	no	—
890	C₂	—	2	2	no	—
891	C₂	—	4	1	no	—
892	C₂	—	8	4	no	—
893	C₂	—	8	2	no	—
894	C₂	C₂×C₅₃×#537	1	1	yes	characteristic
895	C₂	C₂²×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
896	C₂	C₂×C₅₃×#575	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 ◁ C₂²×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3444	C₂	semidirect
2. C₂×C₅₃×#532	C₂	semidirect
3. C₅₃×#3254	C₂	semidirect
4. C₅₃×#3253	C₂	semidirect
5. C₅₃×#3251	C₂	semidirect
6. C₅₃×#3247	C₂	semidirect
7. C₅₃×#3246	C₂	semidirect
8. C₅₃×#3245	C₂	semidirect
9. C₅₃×#3079	C₂	semidirect
10. C₅₃×#3077	C₂	semidirect
11. C₅₃×#3055	C₂	semidirect
12. C₅₃×#3038	C₂	semidirect
13. C₅₃×#3036	C₂	semidirect
14. C₂×C₅₃×#423	C₂	semidirect
19. C₅₃×#533	C₂²	semidirect
20. C₅₃×#533	C₂²	semidirect
30. C₅₃×#532	C₂²	semidirect
31. C₅₃×#532	C₂²	semidirect
38. C₅₃×#529	C₂²	semidirect
39. C₅₃×#529	C₂²	semidirect
52. C₅₃×#478	C₂²	semidirect
53. C₅₃×#477	C₂²	semidirect
54. C₅₃×#476	C₂²	semidirect
55. C₅₃×#476	C₂²	semidirect
56. C₅₃×#475	C₂²	semidirect
57. C₅₃×#474	C₂²	semidirect
58. C₅₃×#474	C₂²	semidirect
59. C₅₃×#469	C₂²	semidirect
60. C₅₃×#468	C₂²	semidirect
61. C₅₃×#466	C₂²	semidirect
62. C₅₃×#465	C₂²	semidirect
63. C₅₃×#463	C₂²	semidirect
64. C₅₃×#461	C₂²	semidirect
65. C₅₃×#460	C₂²	semidirect
66. C₅₃×#460	C₂²	semidirect
67. C₅₃×#459	C₂²	semidirect
68. C₅₃×#459	C₂²	semidirect
69. C₅₃×#459	C₂²	semidirect
73. C₅₃×#423	C₂²	semidirect
74. C₅₃×#423	C₂²	semidirect
75. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
76. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
389. C₂×C₄×C₅₃	AGL(1,ℤ/8)	semidirect
405. #60916	C₅₃	direct (N × H)
441. #3444	C₂×C₅₃	semidirect
442. C₂×#532	C₂×C₅₃	semidirect
443. #3254	C₂×C₅₃	semidirect
444. #3253	C₂×C₅₃	semidirect
445. #3251	C₂×C₅₃	semidirect
446. #3247	C₂×C₅₃	semidirect
447. #3246	C₂×C₅₃	semidirect
448. #3245	C₂×C₅₃	semidirect
449. #3079	C₂×C₅₃	semidirect
450. #3077	C₂×C₅₃	semidirect
451. #3055	C₂×C₅₃	semidirect
452. #3038	C₂×C₅₃	semidirect
453. #3036	C₂×C₅₃	semidirect
454. C₂×#423	C₂×C₅₃	semidirect
467. #533	C₂²×C₅₃	semidirect
468. #533	C₂²×C₅₃	semidirect
478. #532	C₂²×C₅₃	semidirect
479. #532	C₂²×C₅₃	semidirect
486. #529	C₂²×C₅₃	semidirect
487. #529	C₂²×C₅₃	semidirect
500. #478	C₂²×C₅₃	semidirect
501. #477	C₂²×C₅₃	semidirect
502. #476	C₂²×C₅₃	semidirect
503. #476	C₂²×C₅₃	semidirect
504. #475	C₂²×C₅₃	semidirect
505. #474	C₂²×C₅₃	semidirect
506. #474	C₂²×C₅₃	semidirect
507. #469	C₂²×C₅₃	semidirect
508. #468	C₂²×C₅₃	semidirect
509. #466	C₂²×C₅₃	semidirect
510. #465	C₂²×C₅₃	semidirect
511. #463	C₂²×C₅₃	semidirect
512. #461	C₂²×C₅₃	semidirect
513. #460	C₂²×C₅₃	semidirect
514. #460	C₂²×C₅₃	semidirect
515. #459	C₂²×C₅₃	semidirect
516. #459	C₂²×C₅₃	semidirect
517. #459	C₂²×C₅₃	semidirect
521. #423	C₂²×C₅₃	semidirect
522. #423	C₂²×C₅₃	semidirect
523. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
524. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
527. C₅₃	#60916	direct (N × H)
838. C₂×C₄	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×#3444	2
C₂×C₅₃×#532	2
C₅₃×#3254	2
C₅₃×#3253	2
C₅₃×#3251	2
C₅₃×#3247	2
C₅₃×#3246	2
C₅₃×#3245	2
C₅₃×#3079	2
C₅₃×#3077	2
C₅₃×#3055	2
C₅₃×#3038	2
C₅₃×#3036	2
C₂×C₅₃×#423	2
#60916	53

Subgroups — C53×#60916 #27268428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60916 #27268428