Subgroups — C₅₃×#60832 #27268344

Order 13568.

2208 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3224	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3220	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3217	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3214	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3212	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3205	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3155	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3012	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3008	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
20	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
21	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
22	C₂²×D₈×C₅₃	C₂²	1	2	yes	complemented
23	C₅₃×#550	—	2	1	no	—
24	C₅₃×#550	—	2	1	no	—
25	D₄²×C₅₃	—	2	1	no	—
26	D₄²×C₅₃	—	2	1	no	—
27	D₄²×C₅₃	—	2	2	no	—
28	D₄²×C₅₃	—	2	2	no	—
29	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#542	—	2	1	no	—
31	C₅₃×#542	C₂²	1	2	yes	complemented
32	C₅₃×#540	—	2	1	no	—
33	C₅₃×#540	C₂²	1	2	yes	complemented
34	C₅₃×#538	—	2	2	no	—
35	C₅₃×#537	C₂²	1	1	yes	characteristic
36	C₅₃×#535	C₂²	1	2	yes	—
37	C₅₃×#535	C₂²	1	1	yes	characteristic
38	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#535	C₂²	1	4	yes	complemented
40	C₅₃×#532	—	2	1	no	—
41	C₅₃×#532	C₂²	1	1	yes	characteristic
42	C₅₃×#532	C₂²	1	2	yes	complemented
43	C₅₃×#532	C₂²	1	2	yes	complemented
44	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×#127×C₅₃	C₂²	1	2	yes	complemented
46	C₅₃×#529	—	2	1	no	—
47	C₅₃×#529	C₂²	1	2	yes	complemented
48	C₅₃×#525	—	2	2	no	—
49	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
50	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#496	C₂²	1	4	yes	complemented
53	C₅₃×#496	C₂²	1	4	yes	complemented
54	C₅₃×#495	C₂²	1	4	yes	complemented
55	C₅₃×#493	C₂²	1	4	yes	complemented
56	C₅₃×#490	C₂²	1	4	yes	complemented
57	C₅₃×#489	C₂²	1	4	yes	complemented
58	C₅₃×#488	C₂²	1	4	yes	complemented
59	C₅₃×#486	C₂²	1	4	yes	complemented
60	C₅₃×#464	C₂²	1	2	yes	complemented
61	C₅₃×#463	C₂²	1	2	yes	complemented
62	C₅₃×#463	C₂²	1	4	yes	complemented
63	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#461	C₂²	1	2	yes	complemented
65	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#460	C₂²	1	2	yes	complemented
67	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#460	C₂²	1	2	yes	complemented
69	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#459	C₂²	1	2	yes	complemented
71	C₅₃×#459	C₂²	1	2	yes	complemented
72	C₅₃×#459	C₂²	1	2	yes	complemented
73	C₅₃×#459	C₂²	1	2	yes	complemented
74	C₅₃×#459	C₂²	1	2	yes	complemented
75	C₅₃×#459	C₂²	1	4	yes	complemented
76	C₅₃×#452	C₂²	1	4	yes	complemented
77	C₅₃×#450	C₂²	1	4	yes	complemented
78	C₅₃×#449	C₂²	1	4	yes	complemented
79	C₅₃×#449	C₂²	1	4	yes	complemented
80	C₅₃×#449	C₂²	1	4	yes	complemented
81	C₅₃×#447	C₂²	1	4	yes	complemented
82	C₅₃×#447	C₂²	1	4	yes	complemented
83	C₅₃×#447	C₂²	1	4	yes	complemented
84	C₅₃×#433	C₂²	1	4	yes	complemented
85	C₅₃×#432	C₂²	1	2	yes	complemented
86	C₅₃×#431	C₂²	1	2	yes	complemented
87	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#418	C₂²	1	2	yes	complemented
90	C₅₃×#417	C₂²	1	2	yes	complemented
91	C₅₃×#416	C₂²	1	2	yes	complemented
92	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
93	C₅₃×#408	C₂²	1	2	yes	—
94	C₅₃×#405	C₂²	1	2	yes	complemented
95	H(5,𝔽₂)×C₅₃	—	4	4	no	—
96	H(5,𝔽₂)×C₅₃	—	4	4	no	—
97	C₂×#41×C₅₃	—	2	2	no	—
98	C₂×#41×C₅₃	—	2	2	no	—
99	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
100	C₂×#41×C₅₃	C₂³	1	2	yes	—
101	C₂×#41×C₅₃	C₂³	1	4	yes	—
102	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₅₃	—	2	4	no	—
104	C₂²×D₄×C₅₃	—	2	2	no	—
105	C₂²×D₄×C₅₃	—	2	1	no	—
106	C₂²×D₄×C₅₃	—	2	1	no	—
107	C₂²×D₄×C₅₃	—	2	2	no	—
108	C₂²×D₄×C₅₃	—	2	2	no	—
109	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
112	C₂³×C₄×C₅₃	—	2	1	no	—
113	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
114	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
115	#135×C₅₃	—	4	4	no	—
116	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
120	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
121	C₂×D₈×C₅₃	—	4	4	no	—
122	C₂×D₈×C₅₃	C₂³	1	2	yes	—
123	C₂×D₈×C₅₃	C₂³	1	4	yes	—
124	C₂×D₈×C₅₃	C₂³	1	4	yes	—
125	C₂×D₈×C₅₃	C₂³	1	4	yes	—
126	C₂×D₈×C₅₃	C₂³	1	4	yes	—
127	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
128	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₅₃	—	2	1	no	—
130	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
131	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
132	#127×C₅₃	—	2	1	no	—
133	#127×C₅₃	—	2	1	no	—
134	#127×C₅₃	—	2	2	no	—
135	#127×C₅₃	—	2	2	no	—
136	#127×C₅₃	—	2	1	no	—
137	#127×C₅₃	C₂³	1	4	yes	—
138	#127×C₅₃	C₂³	1	2	yes	—
139	#127×C₅₃	C₂³	1	2	yes	—
140	#127×C₅₃	C₂³	1	2	yes	—
141	#127×C₅₃	C₂³	1	1	yes	characteristic
142	#126×C₅₃	—	2	2	no	—
143	#126×C₅₃	—	2	2	no	—
144	#125×C₅₃	—	2	1	no	—
145	#125×C₅₃	C₂³	1	2	yes	—
146	#124×C₅₃	—	2	2	no	—
147	#124×C₅₃	—	2	2	no	—
148	#124×C₅₃	—	2	1	no	—
149	#124×C₅₃	C₂³	1	4	yes	—
150	#124×C₅₃	C₂³	1	2	yes	—
151	#124×C₅₃	C₂³	1	2	yes	—
152	#123×C₅₃	—	2	2	no	—
153	#123×C₅₃	—	2	2	no	—
154	#123×C₅₃	—	2	2	no	—
155	#123×C₅₃	—	2	2	no	—
156	C₂²⋊Q₈×C₅₃	—	2	2	no	—
157	C₂²⋊Q₈×C₅₃	—	2	2	no	—
158	C₂²⋊Q₈×C₅₃	—	2	1	no	—
159	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
160	#121×C₅₃	—	2	1	no	—
161	#121×C₅₃	—	2	1	no	—
162	#121×C₅₃	—	2	2	no	—
163	#121×C₅₃	—	2	2	no	—
164	#121×C₅₃	—	2	4	no	—
165	#121×C₅₃	—	2	4	no	—
166	#121×C₅₃	—	2	2	no	—
167	#121×C₅₃	—	2	2	no	—
168	#121×C₅₃	—	2	2	no	—
169	#121×C₅₃	—	2	1	no	—
170	#121×C₅₃	—	2	1	no	—
171	#121×C₅₃	—	2	1	no	—
172	#121×C₅₃	—	2	2	no	—
173	#121×C₅₃	—	2	2	no	—
174	#121×C₅₃	—	2	2	no	—
175	#121×C₅₃	C₂³	1	2	yes	—
176	#121×C₅₃	C₂³	1	2	yes	—
177	#121×C₅₃	C₂³	1	2	yes	—
178	#120×C₅₃	—	2	2	no	—
179	#120×C₅₃	—	2	4	no	—
180	#120×C₅₃	—	2	4	no	—
181	#120×C₅₃	—	2	4	no	—
182	#120×C₅₃	—	2	2	no	—
183	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
184	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
185	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
186	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₅₃	—	2	1	no	—
188	C₄×D₄×C₅₃	—	2	1	no	—
189	C₄×D₄×C₅₃	—	2	2	no	—
190	C₄×D₄×C₅₃	—	2	1	no	—
191	C₄×D₄×C₅₃	—	2	1	no	—
192	C₄×D₄×C₅₃	—	2	2	no	—
193	C₄×D₄×C₅₃	—	2	2	no	—
194	C₄×D₄×C₅₃	—	2	1	no	—
195	C₄×D₄×C₅₃	—	2	1	no	—
196	C₄×D₄×C₅₃	—	2	2	no	—
197	C₄×D₄×C₅₃	D₄	1	2	yes	—
198	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
199	C₄×D₄×C₅₃	D₄	1	2	yes	—
200	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
201	C₄×D₄×C₅₃	C₂³	1	2	yes	—
202	C₄×D₄×C₅₃	C₂³	1	2	yes	—
203	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
205	#117×C₅₃	—	2	1	no	—
206	#117×C₅₃	—	2	2	no	—
207	#117×C₅₃	C₂³	1	1	yes	characteristic
208	#117×C₅₃	C₂³	1	1	yes	characteristic
209	#117×C₅₃	C₂³	1	2	yes	—
210	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
212	C₂×C₄²×C₅₃	—	2	1	no	—
213	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
215	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
216	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
217	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
218	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
219	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
220	#103×C₅₃	C₂³	1	2	yes	—
221	#103×C₅₃	C₂³	1	4	yes	—
222	#103×C₅₃	C₂³	1	2	yes	—
223	#102×C₅₃	C₂³	1	2	yes	—
224	#102×C₅₃	C₂³	1	4	yes	—
225	#102×C₅₃	C₂³	1	4	yes	—
226	#102×C₅₃	C₂³	1	4	yes	—
227	#102×C₅₃	C₂³	1	4	yes	—
228	#102×C₅₃	C₂³	1	4	yes	—
229	#102×C₅₃	C₂³	1	2	yes	—
230	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
231	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
232	#97×C₅₃	C₂³	1	4	yes	—
233	C₄×C₈×C₅₃	C₂³	1	4	yes	—
234	C₂⁴×C₅₃	—	2	1	no	—
235	C₂⁴×C₅₃	—	2	4	no	—
236	C₂⁴×C₅₃	—	2	2	no	—
237	#41×C₅₃	—	2	2	no	—
238	#41×C₅₃	—	2	2	no	—
239	#41×C₅₃	—	2	2	no	—
240	#41×C₅₃	—	2	4	no	—
241	#41×C₅₃	—	2	2	no	—
242	#41×C₅₃	—	2	4	no	—
243	#41×C₅₃	—	4	4	no	—
244	#41×C₅₃	—	4	4	no	—
245	#41×C₅₃	—	4	8	no	—
246	#41×C₅₃	—	8	4	no	—
247	C₂×Q₈×C₅₃	—	2	2	no	—
248	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
249	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
250	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
251	C₂×D₄×C₅₃	—	2	1	no	—
252	C₂×D₄×C₅₃	—	2	4	no	—
253	C₂×D₄×C₅₃	—	2	2	no	—
254	C₂×D₄×C₅₃	—	2	2	no	—
255	C₂×D₄×C₅₃	—	2	2	no	—
256	C₂×D₄×C₅₃	—	2	2	no	—
257	C₂×D₄×C₅₃	—	2	1	no	—
258	C₂×D₄×C₅₃	—	2	1	no	—
259	C₂×D₄×C₅₃	—	2	2	no	—
260	C₂×D₄×C₅₃	—	2	1	no	—
261	C₂×D₄×C₅₃	—	2	2	no	—
262	C₂×D₄×C₅₃	—	2	4	no	—
263	C₂×D₄×C₅₃	—	2	2	no	—
264	C₂×D₄×C₅₃	—	2	2	no	—
265	C₂×D₄×C₅₃	—	2	2	no	—
266	C₂×D₄×C₅₃	—	2	2	no	—
267	C₂×D₄×C₅₃	—	2	4	no	—
268	C₂×D₄×C₅₃	—	2	4	no	—
269	C₂×D₄×C₅₃	—	2	2	no	—
270	C₂×D₄×C₅₃	—	2	2	no	—
271	C₂×D₄×C₅₃	—	2	4	no	—
272	C₂×D₄×C₅₃	—	2	2	no	—
273	C₂×D₄×C₅₃	—	2	4	no	—
274	C₂×D₄×C₅₃	—	4	4	no	—
275	C₂×D₄×C₅₃	—	4	4	no	—
276	C₂×D₄×C₅₃	—	4	16	no	—
277	C₂×D₄×C₅₃	—	4	8	no	—
278	C₂×D₄×C₅₃	—	8	2	no	—
279	C₂×D₄×C₅₃	—	8	4	no	—
280	C₂×D₄×C₅₃	—	8	2	no	—
281	C₂×D₄×C₅₃	—	8	4	no	—
282	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
283	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
284	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
285	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
286	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
287	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₅₃	—	2	1	no	—
289	C₂²×C₄×C₅₃	—	2	1	no	—
290	C₂²×C₄×C₅₃	—	2	1	no	—
291	C₂²×C₄×C₅₃	—	2	2	no	—
292	C₂²×C₄×C₅₃	—	2	4	no	—
293	C₂²×C₄×C₅₃	—	2	2	no	—
294	C₂²×C₄×C₅₃	—	2	1	no	—
295	C₂²×C₄×C₅₃	—	2	2	no	—
296	C₂²×C₄×C₅₃	—	8	2	no	—
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	1	yes	characteristic
300	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
301	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
303	Q₁₆×C₅₃	—	4	2	no	—
304	SD₁₆×C₅₃	—	4	2	no	—
305	SD₁₆×C₅₃	—	4	2	no	—
306	SD₁₆×C₅₃	—	4	4	no	—
307	SD₁₆×C₅₃	—	4	4	no	—
308	D₈×C₅₃	—	4	4	no	—
309	D₈×C₅₃	—	4	4	no	—
310	D₈×C₅₃	—	4	2	no	—
311	D₈×C₅₃	—	4	4	no	—
312	D₈×C₅₃	—	4	4	no	—
313	M₁₆×C₅₃	—	2	4	no	—
314	C₂×C₈×C₅₃	—	2	4	no	—
315	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
316	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
317	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
318	C₄⋊C₄×C₅₃	—	2	1	no	—
319	C₄⋊C₄×C₅₃	—	2	1	no	—
320	C₄⋊C₄×C₅₃	—	2	1	no	—
321	C₄⋊C₄×C₅₃	—	2	2	no	—
322	C₄⋊C₄×C₅₃	—	2	2	no	—
323	C₄⋊C₄×C₅₃	—	2	1	no	—
324	C₄⋊C₄×C₅₃	—	2	1	no	—
325	C₄⋊C₄×C₅₃	—	2	2	no	—
326	C₄⋊C₄×C₅₃	—	2	2	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	C₂×D₄	1	2	yes	—
331	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
332	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
333	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
334	C₂²⋊C₄×C₅₃	—	2	1	no	—
335	C₂²⋊C₄×C₅₃	—	2	2	no	—
336	C₂²⋊C₄×C₅₃	—	2	2	no	—
337	C₂²⋊C₄×C₅₃	—	2	2	no	—
338	C₂²⋊C₄×C₅₃	—	2	1	no	—
339	C₂²⋊C₄×C₅₃	—	2	1	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	2	no	—
344	C₂²⋊C₄×C₅₃	—	2	4	no	—
345	C₂²⋊C₄×C₅₃	—	2	4	no	—
346	C₂²⋊C₄×C₅₃	—	2	2	no	—
347	C₂²⋊C₄×C₅₃	—	2	2	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	C₄²×C₅₃	—	2	1	no	—
353	C₄²×C₅₃	—	2	1	no	—
354	C₄²×C₅₃	—	2	1	no	—
355	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
356	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
357	C₄²×C₅₃	C₂×D₄	1	2	yes	—
358	C₄²×C₅₃	C₂×D₄	1	2	yes	—
359	C₄²×C₅₃	C₂⁴	1	2	yes	—
360	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₂³×C₅₃	—	2	1	no	—
363	C₂³×C₅₃	—	2	2	no	—
364	C₂³×C₅₃	—	2	4	no	—
365	C₂³×C₅₃	—	2	2	no	—
366	C₂³×C₅₃	—	4	8	no	—
367	C₂³×C₅₃	—	4	2	no	—
368	C₂³×C₅₃	—	4	4	no	—
369	C₂³×C₅₃	—	8	1	no	—
370	C₂³×C₅₃	—	8	1	no	—
371	C₂³×C₅₃	—	8	2	no	—
372	C₂³×C₅₃	—	8	2	no	—
373	C₂³×C₅₃	—	8	4	no	—
374	C₂³×C₅₃	—	8	4	no	—
375	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
376	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
377	Q₈×C₅₃	—	2	2	no	—
378	Q₈×C₅₃	—	2	2	no	—
379	Q₈×C₅₃	—	2	2	no	—
380	Q₈×C₅₃	—	2	1	no	—
381	Q₈×C₅₃	—	2	1	no	—
382	Q₈×C₅₃	—	8	2	no	—
383	D₄×C₅₃	—	2	4	no	—
384	D₄×C₅₃	—	2	2	no	—
385	D₄×C₅₃	—	2	4	no	—
386	D₄×C₅₃	—	2	4	no	—
387	D₄×C₅₃	—	2	2	no	—
388	D₄×C₅₃	—	2	2	no	—
389	D₄×C₅₃	—	2	2	no	—
390	D₄×C₅₃	—	2	2	no	—
391	D₄×C₅₃	—	2	1	no	—
392	D₄×C₅₃	—	2	1	no	—
393	D₄×C₅₃	—	4	8	no	—
394	D₄×C₅₃	—	4	2	no	—
395	D₄×C₅₃	—	4	4	no	—
396	D₄×C₅₃	—	4	8	no	—
397	D₄×C₅₃	—	4	4	no	—
398	D₄×C₅₃	—	4	2	no	—
399	D₄×C₅₃	—	4	2	no	—
400	D₄×C₅₃	—	4	4	no	—
401	D₄×C₅₃	—	4	2	no	—
402	D₄×C₅₃	—	4	4	no	—
403	D₄×C₅₃	—	8	2	no	—
404	D₄×C₅₃	—	8	2	no	—
405	D₄×C₅₃	—	8	4	no	—
406	D₄×C₅₃	—	8	2	no	—
407	D₄×C₅₃	—	8	4	no	—
408	D₄×C₅₃	—	8	2	no	—
409	D₄×C₅₃	—	8	2	no	—
410	D₄×C₅₃	—	8	2	no	—
411	D₄×C₅₃	—	8	2	no	—
412	C₂×C₄×C₅₃	—	2	2	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	1	no	—
419	C₂×C₄×C₅₃	—	2	1	no	—
420	C₂×C₄×C₅₃	—	2	1	no	—
421	C₂×C₄×C₅₃	—	4	1	no	—
422	C₂×C₄×C₅₃	—	4	2	no	—
423	C₂×C₄×C₅₃	—	4	8	no	—
424	C₂×C₄×C₅₃	—	4	4	no	—
425	C₂×C₄×C₅₃	—	4	2	no	—
426	C₂×C₄×C₅₃	—	4	4	no	—
427	C₂×C₄×C₅₃	—	4	2	no	—
428	C₂×C₄×C₅₃	—	8	1	no	—
429	C₂×C₄×C₅₃	—	8	2	no	—
430	C₂×C₄×C₅₃	—	8	1	no	—
431	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
437	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
440	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
441	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
442	C₈×C₅₃	—	2	2	no	—
443	C₈×C₅₃	—	2	2	no	—
444	C₈×C₅₃	—	2	4	no	—
445	#60832	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
446	C₂²×C₅₃	—	2	1	no	—
447	C₂²×C₅₃	—	2	1	no	—
448	C₂²×C₅₃	—	2	2	no	—
449	C₂²×C₅₃	—	2	2	no	—
450	C₂²×C₅₃	—	2	2	no	—
451	C₂²×C₅₃	—	4	1	no	—
452	C₂²×C₅₃	—	4	4	no	—
453	C₂²×C₅₃	—	4	2	no	—
454	C₂²×C₅₃	—	4	2	no	—
455	C₂²×C₅₃	—	4	4	no	—
456	C₂²×C₅₃	—	4	2	no	—
457	C₂²×C₅₃	—	4	1	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	2	no	—
463	C₂²×C₅₃	—	8	4	no	—
464	C₂²×C₅₃	—	16	4	no	—
465	C₂²×C₅₃	—	16	8	no	—
466	C₂²×C₅₃	#535	1	2	yes	—
467	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
468	C₄×C₅₃	—	2	1	no	—
469	C₄×C₅₃	—	2	1	no	—
470	C₄×C₅₃	—	2	2	no	—
471	C₄×C₅₃	—	2	2	no	—
472	C₄×C₅₃	—	2	1	no	—
473	C₄×C₅₃	—	2	2	no	—
474	C₄×C₅₃	—	4	1	no	—
475	C₄×C₅₃	—	4	2	no	—
476	C₄×C₅₃	—	4	1	no	—
477	C₄×C₅₃	—	4	2	no	—
478	C₄×C₅₃	—	4	1	no	—
479	C₄×C₅₃	#535	1	2	yes	—
480	C₄×C₅₃	#576	1	2	yes	—
481	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
482	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
483	#3498	C₂×C₅₃	1	1	yes	characteristic, complemented
484	#3460	C₂×C₅₃	1	1	yes	characteristic, complemented
485	#3224	C₂×C₅₃	1	4	yes	complemented
486	#3220	C₂×C₅₃	1	4	yes	complemented
487	#3217	C₂×C₅₃	1	2	yes	complemented
488	#3214	C₂×C₅₃	1	2	yes	complemented
489	#3212	C₂×C₅₃	1	2	yes	complemented
490	#3205	C₂×C₅₃	1	2	yes	complemented
491	#3155	C₂×C₅₃	1	2	yes	complemented
492	#3136	C₂×C₅₃	1	2	yes	complemented
493	#3038	C₂×C₅₃	1	1	yes	characteristic, complemented
494	#3036	C₂×C₅₃	1	1	yes	characteristic, complemented
495	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
496	C₂×#459	C₂×C₅₃	1	1	yes	characteristic, complemented
497	#3012	C₂×C₅₃	1	2	yes	complemented
498	#3008	C₂×C₅₃	1	2	yes	complemented
499	#2925	C₂×C₅₃	1	1	yes	characteristic, complemented
500	C₂×C₅₃	—	2	2	no	—
501	C₂×C₅₃	—	4	2	no	—
502	C₂×C₅₃	—	8	1	no	—
503	C₂×C₅₃	—	8	2	no	—
504	C₂×C₅₃	—	8	4	no	—
505	C₂×C₅₃	—	8	2	no	—
506	C₂×C₅₃	C₂×#535	1	1	yes	characteristic
507	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
508	C₂×C₅₃	#3585	1	1	yes	characteristic
509	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	2	yes	—
510	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
511	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
512	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
513	C₂²×D₈	C₂²×C₅₃	1	2	yes	complemented
514	#550	—	2	1	no	—
515	#550	—	2	1	no	—
516	D₄²	—	2	1	no	—
517	D₄²	—	2	1	no	—
518	D₄²	—	2	2	no	—
519	D₄²	—	2	2	no	—
520	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
521	#542	—	2	1	no	—
522	#542	C₂²×C₅₃	1	2	yes	complemented
523	#540	—	2	1	no	—
524	#540	C₂²×C₅₃	1	2	yes	complemented
525	#538	—	2	2	no	—
526	#537	C₂²×C₅₃	1	1	yes	characteristic
527	#535	C₂²×C₅₃	1	2	yes	—
528	#535	C₂²×C₅₃	1	1	yes	characteristic
529	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
530	#535	C₂²×C₅₃	1	4	yes	complemented
531	#532	—	2	1	no	—
532	#532	C₂²×C₅₃	1	1	yes	characteristic
533	#532	C₂²×C₅₃	1	2	yes	complemented
534	#532	C₂²×C₅₃	1	2	yes	complemented
535	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
536	C₂×#127	C₂²×C₅₃	1	2	yes	complemented
537	#529	—	2	1	no	—
538	#529	C₂²×C₅₃	1	2	yes	complemented
539	#525	—	2	2	no	—
540	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
541	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
542	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
543	#496	C₂²×C₅₃	1	4	yes	complemented
544	#496	C₂²×C₅₃	1	4	yes	complemented
545	#495	C₂²×C₅₃	1	4	yes	complemented
546	#493	C₂²×C₅₃	1	4	yes	complemented
547	#490	C₂²×C₅₃	1	4	yes	complemented
548	#489	C₂²×C₅₃	1	4	yes	complemented
549	#488	C₂²×C₅₃	1	4	yes	complemented
550	#486	C₂²×C₅₃	1	4	yes	complemented
551	#464	C₂²×C₅₃	1	2	yes	complemented
552	#463	C₂²×C₅₃	1	2	yes	complemented
553	#463	C₂²×C₅₃	1	4	yes	complemented
554	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
555	#461	C₂²×C₅₃	1	2	yes	complemented
556	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
557	#460	C₂²×C₅₃	1	2	yes	complemented
558	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
559	#460	C₂²×C₅₃	1	2	yes	complemented
560	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
561	#459	C₂²×C₅₃	1	2	yes	complemented
562	#459	C₂²×C₅₃	1	2	yes	complemented
563	#459	C₂²×C₅₃	1	2	yes	complemented
564	#459	C₂²×C₅₃	1	2	yes	complemented
565	#459	C₂²×C₅₃	1	2	yes	complemented
566	#459	C₂²×C₅₃	1	4	yes	complemented
567	#452	C₂²×C₅₃	1	4	yes	complemented
568	#450	C₂²×C₅₃	1	4	yes	complemented
569	#449	C₂²×C₅₃	1	4	yes	complemented
570	#449	C₂²×C₅₃	1	4	yes	complemented
571	#449	C₂²×C₅₃	1	4	yes	complemented
572	#447	C₂²×C₅₃	1	4	yes	complemented
573	#447	C₂²×C₅₃	1	4	yes	complemented
574	#447	C₂²×C₅₃	1	4	yes	complemented
575	#433	C₂²×C₅₃	1	4	yes	complemented
576	#432	C₂²×C₅₃	1	2	yes	complemented
577	#431	C₂²×C₅₃	1	2	yes	complemented
578	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
579	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
580	#418	C₂²×C₅₃	1	2	yes	complemented
581	#417	C₂²×C₅₃	1	2	yes	complemented
582	#416	C₂²×C₅₃	1	2	yes	complemented
583	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
584	#408	C₂²×C₅₃	1	2	yes	—
585	#405	C₂²×C₅₃	1	2	yes	complemented
586	C₅₃	#60832	1	1	yes	characteristic, direct product factor, Sylow
587	H(5,𝔽₂)	—	4	4	no	—
588	H(5,𝔽₂)	—	4	4	no	—
589	C₂×#41	—	2	2	no	—
590	C₂×#41	—	2	2	no	—
591	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
592	C₂×#41	C₂³×C₅₃	1	2	yes	—
593	C₂×#41	C₂³×C₅₃	1	4	yes	—
594	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
595	C₂²×D₄	—	2	4	no	—
596	C₂²×D₄	—	2	2	no	—
597	C₂²×D₄	—	2	1	no	—
598	C₂²×D₄	—	2	1	no	—
599	C₂²×D₄	—	2	2	no	—
600	C₂²×D₄	—	2	2	no	—
601	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
602	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
603	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
604	C₂³×C₄	—	2	1	no	—
605	AGL(1,ℤ/8)	—	4	4	no	—
606	AGL(1,ℤ/8)	—	4	4	no	—
607	#135	—	4	4	no	—
608	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
609	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
610	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
611	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
612	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
613	C₂×D₈	—	4	4	no	—
614	C₂×D₈	C₂³×C₅₃	1	4	yes	—
615	C₂×D₈	C₂³×C₅₃	1	4	yes	—
616	C₂×D₈	C₂³×C₅₃	1	2	yes	—
617	C₂×D₈	C₂³×C₅₃	1	4	yes	—
618	C₂×D₈	C₂³×C₅₃	1	4	yes	—
619	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
620	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
621	C₄⋊Q₈	—	2	1	no	—
622	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
623	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
624	#127	—	2	1	no	—
625	#127	—	2	1	no	—
626	#127	—	2	1	no	—
627	#127	—	2	2	no	—
628	#127	—	2	2	no	—
629	#127	C₂³×C₅₃	1	2	yes	—
630	#127	C₂³×C₅₃	1	2	yes	—
631	#127	C₂³×C₅₃	1	1	yes	characteristic
632	#127	C₂³×C₅₃	1	4	yes	—
633	#127	C₂³×C₅₃	1	2	yes	—
634	#126	—	2	2	no	—
635	#126	—	2	2	no	—
636	#125	—	2	1	no	—
637	#125	C₂³×C₅₃	1	2	yes	—
638	#124	—	2	1	no	—
639	#124	—	2	2	no	—
640	#124	—	2	2	no	—
641	#124	C₂³×C₅₃	1	2	yes	—
642	#124	C₂³×C₅₃	1	2	yes	—
643	#124	C₂³×C₅₃	1	4	yes	—
644	#123	—	2	2	no	—
645	#123	—	2	2	no	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	C₂²⋊Q₈	—	2	1	no	—
649	C₂²⋊Q₈	—	2	2	no	—
650	C₂²⋊Q₈	—	2	2	no	—
651	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
652	#121	—	2	2	no	—
653	#121	—	2	1	no	—
654	#121	—	2	1	no	—
655	#121	—	2	1	no	—
656	#121	—	2	2	no	—
657	#121	—	2	2	no	—
658	#121	—	2	2	no	—
659	#121	—	2	1	no	—
660	#121	—	2	1	no	—
661	#121	—	2	2	no	—
662	#121	—	2	2	no	—
663	#121	—	2	4	no	—
664	#121	—	2	4	no	—
665	#121	—	2	2	no	—
666	#121	—	2	2	no	—
667	#121	C₂³×C₅₃	1	2	yes	—
668	#121	C₂³×C₅₃	1	2	yes	—
669	#121	C₂³×C₅₃	1	2	yes	—
670	#120	—	2	2	no	—
671	#120	—	2	2	no	—
672	#120	—	2	4	no	—
673	#120	—	2	4	no	—
674	#120	—	2	4	no	—
675	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
676	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
677	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
678	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
679	C₄×D₄	—	2	1	no	—
680	C₄×D₄	—	2	1	no	—
681	C₄×D₄	—	2	2	no	—
682	C₄×D₄	—	2	1	no	—
683	C₄×D₄	—	2	1	no	—
684	C₄×D₄	—	2	2	no	—
685	C₄×D₄	—	2	1	no	—
686	C₄×D₄	—	2	1	no	—
687	C₄×D₄	—	2	2	no	—
688	C₄×D₄	—	2	2	no	—
689	C₄×D₄	D₄×C₅₃	1	2	yes	—
690	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
691	C₄×D₄	D₄×C₅₃	1	2	yes	—
692	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
693	C₄×D₄	C₂³×C₅₃	1	2	yes	—
694	C₄×D₄	C₂³×C₅₃	1	2	yes	—
695	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
696	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
697	#117	—	2	1	no	—
698	#117	—	2	2	no	—
699	#117	C₂³×C₅₃	1	1	yes	characteristic
700	#117	C₂³×C₅₃	1	1	yes	characteristic
701	#117	C₂³×C₅₃	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
703	C₂×C₂²⋊C₄	—	2	1	no	—
704	C₂×C₄²	—	2	1	no	—
705	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
707	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
708	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
709	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
710	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
711	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
712	#103	C₂³×C₅₃	1	2	yes	—
713	#103	C₂³×C₅₃	1	2	yes	—
714	#103	C₂³×C₅₃	1	4	yes	—
715	#102	C₂³×C₅₃	1	4	yes	—
716	#102	C₂³×C₅₃	1	4	yes	—
717	#102	C₂³×C₅₃	1	2	yes	—
718	#102	C₂³×C₅₃	1	2	yes	—
719	#102	C₂³×C₅₃	1	4	yes	—
720	#102	C₂³×C₅₃	1	4	yes	—
721	#102	C₂³×C₅₃	1	4	yes	—
722	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
723	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
724	#97	C₂³×C₅₃	1	4	yes	—
725	C₄×C₈	C₂³×C₅₃	1	4	yes	—
726	C₂⁴	—	2	1	no	—
727	C₂⁴	—	2	4	no	—
728	C₂⁴	—	2	2	no	—
729	#41	—	2	2	no	—
730	#41	—	2	2	no	—
731	#41	—	2	2	no	—
732	#41	—	2	4	no	—
733	#41	—	2	2	no	—
734	#41	—	2	4	no	—
735	#41	—	4	4	no	—
736	#41	—	4	4	no	—
737	#41	—	4	8	no	—
738	#41	—	8	4	no	—
739	C₂×Q₈	—	2	2	no	—
740	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
741	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
742	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
743	C₂×D₄	—	2	1	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	1	no	—
750	C₂×D₄	—	2	1	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	2	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	4	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	4	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	4	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	4	no	—
766	C₂×D₄	—	4	4	no	—
767	C₂×D₄	—	4	4	no	—
768	C₂×D₄	—	4	16	no	—
769	C₂×D₄	—	4	8	no	—
770	C₂×D₄	—	8	2	no	—
771	C₂×D₄	—	8	4	no	—
772	C₂×D₄	—	8	2	no	—
773	C₂×D₄	—	8	4	no	—
774	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
775	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
776	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
777	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
778	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
779	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
780	C₂²×C₄	—	2	1	no	—
781	C₂²×C₄	—	2	1	no	—
782	C₂²×C₄	—	2	1	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	4	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	1	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	8	2	no	—
789	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
790	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
791	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
792	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
795	Q₁₆	—	4	2	no	—
796	SD₁₆	—	4	2	no	—
797	SD₁₆	—	4	2	no	—
798	SD₁₆	—	4	4	no	—
799	SD₁₆	—	4	4	no	—
800	D₈	—	4	4	no	—
801	D₈	—	4	4	no	—
802	D₈	—	4	2	no	—
803	D₈	—	4	4	no	—
804	D₈	—	4	4	no	—
805	M₁₆	—	2	4	no	—
806	C₂×C₈	—	2	4	no	—
807	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
808	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
809	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	1	no	—
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	1	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
820	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
821	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
822	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
823	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
824	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
825	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
826	C₂²⋊C₄	—	2	1	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	1	no	—
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	4	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	4	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
842	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
843	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
844	C₄²	—	2	1	no	—
845	C₄²	—	2	1	no	—
846	C₄²	—	2	1	no	—
847	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
848	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
849	C₄²	C₂×D₄×C₅₃	1	2	yes	—
850	C₄²	C₂×D₄×C₅₃	1	2	yes	—
851	C₄²	C₂⁴×C₅₃	1	2	yes	—
852	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
853	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
854	C₂³	—	2	2	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	4	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	4	8	no	—
859	C₂³	—	4	2	no	—
860	C₂³	—	4	4	no	—
861	C₂³	—	8	1	no	—
862	C₂³	—	8	1	no	—
863	C₂³	—	8	2	no	—
864	C₂³	—	8	2	no	—
865	C₂³	—	8	4	no	—
866	C₂³	—	8	4	no	—
867	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
868	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
869	Q₈	—	2	2	no	—
870	Q₈	—	2	1	no	—
871	Q₈	—	2	1	no	—
872	Q₈	—	2	2	no	—
873	Q₈	—	2	2	no	—
874	Q₈	—	8	2	no	—
875	D₄	—	2	4	no	—
876	D₄	—	2	2	no	—
877	D₄	—	2	2	no	—
878	D₄	—	2	1	no	—
879	D₄	—	2	2	no	—
880	D₄	—	2	1	no	—
881	D₄	—	2	4	no	—
882	D₄	—	2	2	no	—
883	D₄	—	2	4	no	—
884	D₄	—	2	2	no	—
885	D₄	—	4	8	no	—
886	D₄	—	4	2	no	—
887	D₄	—	4	4	no	—
888	D₄	—	4	8	no	—
889	D₄	—	4	4	no	—
890	D₄	—	4	2	no	—
891	D₄	—	4	2	no	—
892	D₄	—	4	4	no	—
893	D₄	—	4	2	no	—
894	D₄	—	4	4	no	—
895	D₄	—	8	2	no	—
896	D₄	—	8	2	no	—
897	D₄	—	8	4	no	—
898	D₄	—	8	2	no	—
899	D₄	—	8	4	no	—
900	D₄	—	8	2	no	—
901	D₄	—	8	2	no	—
902	D₄	—	8	2	no	—
903	D₄	—	8	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	4	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	2	no	—
915	C₂×C₄	—	4	8	no	—
916	C₂×C₄	—	4	4	no	—
917	C₂×C₄	—	4	2	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	4	2	no	—
920	C₂×C₄	—	8	1	no	—
921	C₂×C₄	—	8	2	no	—
922	C₂×C₄	—	8	1	no	—
923	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
924	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
925	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
926	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
927	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
928	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
929	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
931	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
932	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
933	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
934	C₈	—	2	2	no	—
935	C₈	—	2	2	no	—
936	C₈	—	2	4	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	4	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	1	no	—
947	C₂²	—	4	4	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	4	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	8	4	no	—
955	C₂²	—	16	4	no	—
956	C₂²	—	16	8	no	—
957	C₂²	C₅₃×#535	1	2	yes	—
958	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
959	C₄	—	2	1	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	1	no	—
970	C₄	C₅₃×#535	1	2	yes	—
971	C₄	C₅₃×#576	1	2	yes	—
972	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
973	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
974	C₂	—	2	2	no	—
975	C₂	—	4	2	no	—
976	C₂	—	8	2	no	—
977	C₂	—	8	4	no	—
978	C₂	—	8	2	no	—
979	C₂	—	8	1	no	—
980	C₂	C₂×C₅₃×#535	1	1	yes	characteristic
981	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
982	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 ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3498	C₂	semidirect
2. C₅₃×#3460	C₂	semidirect
3. C₅₃×#3224	C₂	semidirect
4. C₅₃×#3220	C₂	semidirect
5. C₅₃×#3217	C₂	semidirect
6. C₅₃×#3214	C₂	semidirect
7. C₅₃×#3212	C₂	semidirect
8. C₅₃×#3205	C₂	semidirect
9. C₅₃×#3155	C₂	semidirect
10. C₅₃×#3136	C₂	semidirect
11. C₅₃×#3038	C₂	semidirect
12. C₅₃×#3036	C₂	semidirect
13. C₅₃×#3035	C₂	semidirect
14. C₂×C₅₃×#459	C₂	semidirect
15. C₅₃×#3012	C₂	semidirect
16. C₅₃×#3008	C₂	semidirect
17. C₅₃×#2925	C₂	semidirect
19. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
20. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
21. C₂×#135×C₅₃	C₂²	semidirect
22. C₂²×D₈×C₅₃	C₂²	semidirect
29. C₅₃×#544	C₂²	semidirect
31. C₅₃×#542	C₂²	semidirect
33. C₅₃×#540	C₂²	semidirect
38. C₅₃×#535	C₂²	semidirect
39. C₅₃×#535	C₂²	semidirect
42. C₅₃×#532	C₂²	semidirect
43. C₅₃×#532	C₂²	semidirect
45. C₂×#127×C₅₃	C₂²	semidirect
47. C₅₃×#529	C₂²	semidirect
50. C₄×#41×C₅₃	C₂²	semidirect
51. C₂×C₄×D₄×C₅₃	C₂²	semidirect
52. C₅₃×#496	C₂²	semidirect
53. C₅₃×#496	C₂²	semidirect
54. C₅₃×#495	C₂²	semidirect
55. C₅₃×#493	C₂²	semidirect
56. C₅₃×#490	C₂²	semidirect
57. C₅₃×#489	C₂²	semidirect
58. C₅₃×#488	C₂²	semidirect
59. C₅₃×#486	C₂²	semidirect
60. C₅₃×#464	C₂²	semidirect
61. C₅₃×#463	C₂²	semidirect
62. C₅₃×#463	C₂²	semidirect
63. C₅₃×#462	C₂²	semidirect
64. C₅₃×#461	C₂²	semidirect
65. C₅₃×#461	C₂²	semidirect
66. C₅₃×#460	C₂²	semidirect
67. C₅₃×#460	C₂²	semidirect
68. C₅₃×#460	C₂²	semidirect
69. C₅₃×#459	C₂²	semidirect
70. C₅₃×#459	C₂²	semidirect
71. C₅₃×#459	C₂²	semidirect
72. C₅₃×#459	C₂²	semidirect
73. C₅₃×#459	C₂²	semidirect
74. C₅₃×#459	C₂²	semidirect
75. C₅₃×#459	C₂²	semidirect
76. C₅₃×#452	C₂²	semidirect
77. C₅₃×#450	C₂²	semidirect
78. C₅₃×#449	C₂²	semidirect
79. C₅₃×#449	C₂²	semidirect
80. C₅₃×#449	C₂²	semidirect
81. C₅₃×#447	C₂²	semidirect
82. C₅₃×#447	C₂²	semidirect
83. C₅₃×#447	C₂²	semidirect
84. C₅₃×#433	C₂²	semidirect
85. C₅₃×#432	C₂²	semidirect
86. C₅₃×#431	C₂²	semidirect
87. C₅₃×#423	C₂²	semidirect
88. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
89. C₅₃×#418	C₂²	semidirect
90. C₅₃×#417	C₂²	semidirect
91. C₅₃×#416	C₂²	semidirect
92. C₂×#102×C₅₃	C₂²	semidirect
94. C₅₃×#405	C₂²	semidirect
445. #60832	C₅₃	direct (N × H)
483. #3498	C₂×C₅₃	semidirect
484. #3460	C₂×C₅₃	semidirect
485. #3224	C₂×C₅₃	semidirect
486. #3220	C₂×C₅₃	semidirect
487. #3217	C₂×C₅₃	semidirect
488. #3214	C₂×C₅₃	semidirect
489. #3212	C₂×C₅₃	semidirect
490. #3205	C₂×C₅₃	semidirect
491. #3155	C₂×C₅₃	semidirect
492. #3136	C₂×C₅₃	semidirect
493. #3038	C₂×C₅₃	semidirect
494. #3036	C₂×C₅₃	semidirect
495. #3035	C₂×C₅₃	semidirect
496. C₂×#459	C₂×C₅₃	semidirect
497. #3012	C₂×C₅₃	semidirect
498. #3008	C₂×C₅₃	semidirect
499. #2925	C₂×C₅₃	semidirect
510. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
511. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
512. C₂×#135	C₂²×C₅₃	semidirect
513. C₂²×D₈	C₂²×C₅₃	semidirect
520. #544	C₂²×C₅₃	semidirect
522. #542	C₂²×C₅₃	semidirect
524. #540	C₂²×C₅₃	semidirect
529. #535	C₂²×C₅₃	semidirect
530. #535	C₂²×C₅₃	semidirect
533. #532	C₂²×C₅₃	semidirect
534. #532	C₂²×C₅₃	semidirect
536. C₂×#127	C₂²×C₅₃	semidirect
538. #529	C₂²×C₅₃	semidirect
541. C₄×#41	C₂²×C₅₃	semidirect
542. C₂×C₄×D₄	C₂²×C₅₃	semidirect
543. #496	C₂²×C₅₃	semidirect
544. #496	C₂²×C₅₃	semidirect
545. #495	C₂²×C₅₃	semidirect
546. #493	C₂²×C₅₃	semidirect
547. #490	C₂²×C₅₃	semidirect
548. #489	C₂²×C₅₃	semidirect
549. #488	C₂²×C₅₃	semidirect
550. #486	C₂²×C₅₃	semidirect
551. #464	C₂²×C₅₃	semidirect
552. #463	C₂²×C₅₃	semidirect
553. #463	C₂²×C₅₃	semidirect
554. #462	C₂²×C₅₃	semidirect
555. #461	C₂²×C₅₃	semidirect
556. #461	C₂²×C₅₃	semidirect
557. #460	C₂²×C₅₃	semidirect
558. #460	C₂²×C₅₃	semidirect
559. #460	C₂²×C₅₃	semidirect
560. #459	C₂²×C₅₃	semidirect
561. #459	C₂²×C₅₃	semidirect
562. #459	C₂²×C₅₃	semidirect
563. #459	C₂²×C₅₃	semidirect
564. #459	C₂²×C₅₃	semidirect
565. #459	C₂²×C₅₃	semidirect
566. #459	C₂²×C₅₃	semidirect
567. #452	C₂²×C₅₃	semidirect
568. #450	C₂²×C₅₃	semidirect
569. #449	C₂²×C₅₃	semidirect
570. #449	C₂²×C₅₃	semidirect
571. #449	C₂²×C₅₃	semidirect
572. #447	C₂²×C₅₃	semidirect
573. #447	C₂²×C₅₃	semidirect
574. #447	C₂²×C₅₃	semidirect
575. #433	C₂²×C₅₃	semidirect
576. #432	C₂²×C₅₃	semidirect
577. #431	C₂²×C₅₃	semidirect
578. #423	C₂²×C₅₃	semidirect
579. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
580. #418	C₂²×C₅₃	semidirect
581. #417	C₂²×C₅₃	semidirect
582. #416	C₂²×C₅₃	semidirect
583. C₂×#102	C₂²×C₅₃	semidirect
585. #405	C₂²×C₅₃	semidirect
586. C₅₃	#60832	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3498	2
C₅₃×#3460	2
C₅₃×#3224	2
C₅₃×#3220	2
C₅₃×#3217	2
C₅₃×#3214	2
C₅₃×#3212	2
C₅₃×#3205	2
C₅₃×#3155	2
C₅₃×#3136	2
C₅₃×#3038	2
C₅₃×#3036	2
C₅₃×#3035	2
C₂×C₅₃×#459	2
C₅₃×#3012	2
C₅₃×#3008	2
C₅₃×#2925	2
#60832	53

Subgroups — C53×#60832 #27268344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60832 #27268344