Subgroups — C₅₃×#24456 #27231968

Order 13568.

1410 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₃×#453	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3008	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2045	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2011	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2002	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#1876	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#1866	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#1792	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
18	C₅₃×#576	—	2	4	no	—
19	C₅₃×#576	—	2	4	no	—
20	C₂×AGL(1,ℤ/8)×C₅₃	—	2	1	no	—
21	C₂×AGL(1,ℤ/8)×C₅₃	—	2	1	no	—
22	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×#135×C₅₃	—	2	1	no	—
27	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
28	C₂²×D₈×C₅₃	—	2	1	no	—
29	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
30	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
34	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#472	—	2	4	no	—
37	C₅₃×#464	—	2	1	no	—
38	C₅₃×#463	—	2	1	no	—
39	C₅₃×#460	—	2	1	no	—
40	C₅₃×#459	—	2	1	no	—
41	C₅₃×#453	—	2	4	no	—
42	C₅₃×#449	—	2	1	no	—
43	C₅₃×#449	—	2	1	no	—
44	C₅₃×#447	—	2	1	no	—
45	C₅₃×#447	—	2	1	no	—
46	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
48	C₂×#104×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×#104×C₅₃	C₂²	1	1	yes	characteristic, complemented
50	C₂×#104×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#418	—	2	1	no	—
52	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#417	—	2	1	no	—
55	C₅₃×#417	C₂²	1	1	yes	characteristic
56	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#416	—	2	1	no	—
58	C₅₃×#416	C₂²	1	1	yes	characteristic
59	C₂×#102×C₅₃	—	2	1	no	—
60	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂×#100×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	C₂×#100×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	C₂×#100×C₅₃	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#343	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#341	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#339	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
71	H(5,𝔽₂)×C₅₃	—	2	2	no	—
72	H(5,𝔽₂)×C₅₃	—	2	2	no	—
73	H(5,𝔽₂)×C₅₃	—	2	2	no	—
74	H(5,𝔽₂)×C₅₃	—	2	2	no	—
75	H(5,𝔽₂)×C₅₃	—	2	2	no	—
76	H(5,𝔽₂)×C₅₃	—	4	1	no	—
77	H(5,𝔽₂)×C₅₃	—	4	1	no	—
78	H(5,𝔽₂)×C₅₃	D₄	1	4	yes	complemented
79	C₂×#41×C₅₃	—	2	1	no	—
80	C₂×#41×C₅₃	—	2	1	no	—
81	C₂×#41×C₅₃	—	2	1	no	—
82	C₂×#41×C₅₃	—	2	1	no	—
83	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
84	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
85	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₅₃	—	2	1	no	—
87	C₂²×D₄×C₅₃	—	2	1	no	—
88	C₂²×D₄×C₅₃	—	2	1	no	—
89	C₂²×D₄×C₅₃	—	2	1	no	—
90	C₂²×D₄×C₅₃	—	4	1	no	—
91	C₂²×D₄×C₅₃	—	4	1	no	—
92	C₂²×D₄×C₅₃	—	4	1	no	—
93	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
96	AGL(1,ℤ/8)×C₅₃	—	2	8	no	—
97	AGL(1,ℤ/8)×C₅₃	—	2	8	no	—
98	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
99	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
100	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
101	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
102	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
103	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
104	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
105	AGL(1,ℤ/8)×C₅₃	D₄	1	4	yes	complemented
106	#135×C₅₃	—	2	8	no	—
107	#135×C₅₃	—	2	2	no	—
108	#135×C₅₃	—	2	2	no	—
109	C₂×Q₁₆×C₅₃	D₄	1	1	yes	characteristic, complemented
110	C₂×SD₁₆×C₅₃	—	2	1	no	—
111	C₂×SD₁₆×C₅₃	—	2	1	no	—
112	C₂×SD₁₆×C₅₃	—	2	1	no	—
113	C₂×SD₁₆×C₅₃	—	2	1	no	—
114	C₂×SD₁₆×C₅₃	D₄	1	1	yes	characteristic, complemented
115	C₂×SD₁₆×C₅₃	D₄	1	1	yes	characteristic, complemented
116	C₂×D₈×C₅₃	—	2	8	no	—
117	C₂×D₈×C₅₃	—	2	1	no	—
118	C₂×D₈×C₅₃	—	2	1	no	—
119	C₂×D₈×C₅₃	—	2	1	no	—
120	C₂×D₈×C₅₃	—	2	1	no	—
121	C₂×D₈×C₅₃	—	2	1	no	—
122	C₂×D₈×C₅₃	—	2	1	no	—
123	C₂×D₈×C₅₃	—	2	2	no	—
124	C₂×D₈×C₅₃	—	2	2	no	—
125	C₂×D₈×C₅₃	—	2	2	no	—
126	C₂×D₈×C₅₃	—	2	1	no	—
127	C₂×D₈×C₅₃	—	2	1	no	—
128	C₂×D₈×C₅₃	—	4	1	no	—
129	C₂×D₈×C₅₃	D₄	1	1	yes	characteristic, complemented
130	#131×C₅₃	—	2	2	no	—
131	#131×C₅₃	—	2	2	no	—
132	#131×C₅₃	—	2	2	no	—
133	#131×C₅₃	—	4	1	no	—
134	C₂×M₁₆×C₅₃	—	2	1	no	—
135	C₂×M₁₆×C₅₃	—	2	1	no	—
136	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₅₃	—	2	1	no	—
141	C₂²×C₈×C₅₃	—	2	1	no	—
142	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
144	#127×C₅₃	—	2	2	no	—
145	#127×C₅₃	—	2	1	no	—
146	#127×C₅₃	—	4	1	no	—
147	#124×C₅₃	—	2	1	no	—
148	#121×C₅₃	—	2	1	no	—
149	#121×C₅₃	—	2	1	no	—
150	#120×C₅₃	—	4	1	no	—
151	C₄×Q₈×C₅₃	—	2	1	no	—
152	C₄×D₄×C₅₃	—	2	1	no	—
153	C₄×D₄×C₅₃	—	4	1	no	—
154	#117×C₅₃	—	2	1	no	—
155	#117×C₅₃	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
157	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₅₃	—	4	1	no	—
159	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
160	#108×C₅₃	—	2	2	no	—
161	C₄⋊C₈×C₅₃	—	2	1	no	—
162	C₄⋊C₈×C₅₃	—	2	1	no	—
163	#104×C₅₃	—	2	2	no	—
164	#104×C₅₃	—	2	2	no	—
165	#104×C₅₃	—	4	1	no	—
166	#103×C₅₃	—	2	1	no	—
167	#103×C₅₃	—	2	1	no	—
168	#103×C₅₃	D₄	1	1	yes	characteristic, complemented
169	#103×C₅₃	D₄	1	1	yes	characteristic, complemented
170	#102×C₅₃	—	2	1	no	—
171	#102×C₅₃	—	2	1	no	—
172	#102×C₅₃	—	2	1	no	—
173	#102×C₅₃	—	2	1	no	—
174	#102×C₅₃	—	2	1	no	—
175	#102×C₅₃	—	2	1	no	—
176	#102×C₅₃	—	2	1	no	—
177	#102×C₅₃	—	2	1	no	—
178	#102×C₅₃	—	2	1	no	—
179	#102×C₅₃	—	2	1	no	—
180	#102×C₅₃	D₄	1	1	yes	characteristic, complemented
181	#102×C₅₃	D₄	1	1	yes	characteristic, complemented
182	#100×C₅₃	—	2	2	no	—
183	#100×C₅₃	—	2	2	no	—
184	#100×C₅₃	—	2	2	no	—
185	C₂²⋊C₈×C₅₃	—	2	1	no	—
186	C₂²⋊C₈×C₅₃	—	2	1	no	—
187	C₂⁴×C₅₃	—	2	1	no	—
188	C₂⁴×C₅₃	—	2	1	no	—
189	C₂⁴×C₅₃	—	2	1	no	—
190	C₂⁴×C₅₃	—	4	1	no	—
191	C₂⁴×C₅₃	—	4	1	no	—
192	#41×C₅₃	—	2	1	no	—
193	#41×C₅₃	—	2	1	no	—
194	#41×C₅₃	—	2	1	no	—
195	#41×C₅₃	—	2	1	no	—
196	#41×C₅₃	—	2	4	no	—
197	#41×C₅₃	—	2	4	no	—
198	#41×C₅₃	—	2	4	no	—
199	#41×C₅₃	—	2	1	no	—
200	#41×C₅₃	—	2	1	no	—
201	#41×C₅₃	—	2	1	no	—
202	#41×C₅₃	—	2	1	no	—
203	#41×C₅₃	—	4	2	no	—
204	#41×C₅₃	—	4	2	no	—
205	#41×C₅₃	—	4	2	no	—
206	#41×C₅₃	—	4	2	no	—
207	#41×C₅₃	—	4	2	no	—
208	#41×C₅₃	C₂×D₄	1	2	yes	—
209	#41×C₅₃	C₂×D₄	1	2	yes	—
210	#41×C₅₃	C₂×D₄	1	2	yes	—
211	#41×C₅₃	#41	1	2	yes	—
212	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
213	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
214	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
215	C₂×D₄×C₅₃	—	2	1	no	—
216	C₂×D₄×C₅₃	—	2	1	no	—
217	C₂×D₄×C₅₃	—	2	4	no	—
218	C₂×D₄×C₅₃	—	2	4	no	—
219	C₂×D₄×C₅₃	—	2	4	no	—
220	C₂×D₄×C₅₃	—	2	1	no	—
221	C₂×D₄×C₅₃	—	2	1	no	—
222	C₂×D₄×C₅₃	—	2	1	no	—
223	C₂×D₄×C₅₃	—	2	1	no	—
224	C₂×D₄×C₅₃	—	2	1	no	—
225	C₂×D₄×C₅₃	—	2	1	no	—
226	C₂×D₄×C₅₃	—	2	1	no	—
227	C₂×D₄×C₅₃	—	2	1	no	—
228	C₂×D₄×C₅₃	—	2	1	no	—
229	C₂×D₄×C₅₃	—	2	1	no	—
230	C₂×D₄×C₅₃	—	2	1	no	—
231	C₂×D₄×C₅₃	—	2	1	no	—
232	C₂×D₄×C₅₃	—	2	1	no	—
233	C₂×D₄×C₅₃	—	2	1	no	—
234	C₂×D₄×C₅₃	—	2	1	no	—
235	C₂×D₄×C₅₃	—	2	1	no	—
236	C₂×D₄×C₅₃	—	2	1	no	—
237	C₂×D₄×C₅₃	—	4	2	no	—
238	C₂×D₄×C₅₃	—	4	2	no	—
239	C₂×D₄×C₅₃	—	4	2	no	—
240	C₂×D₄×C₅₃	—	4	1	no	—
241	C₂×D₄×C₅₃	—	4	1	no	—
242	C₂×D₄×C₅₃	—	4	1	no	—
243	C₂×D₄×C₅₃	—	4	1	no	—
244	C₂×D₄×C₅₃	—	4	1	no	—
245	C₂×D₄×C₅₃	—	4	1	no	—
246	C₂×D₄×C₅₃	—	4	4	no	—
247	C₂×D₄×C₅₃	—	4	2	no	—
248	C₂×D₄×C₅₃	—	4	4	no	—
249	C₂×D₄×C₅₃	—	4	4	no	—
250	C₂×D₄×C₅₃	—	4	4	no	—
251	C₂×D₄×C₅₃	—	4	2	no	—
252	C₂×D₄×C₅₃	—	4	4	no	—
253	C₂×D₄×C₅₃	—	8	2	no	—
254	C₂×D₄×C₅₃	—	8	2	no	—
255	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
258	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
259	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₅₃	—	2	1	no	—
261	C₂²×C₄×C₅₃	—	2	1	no	—
262	C₂²×C₄×C₅₃	—	2	1	no	—
263	C₂²×C₄×C₅₃	—	2	1	no	—
264	C₂²×C₄×C₅₃	—	2	1	no	—
265	C₂²×C₄×C₅₃	—	4	1	no	—
266	C₂²×C₄×C₅₃	—	4	1	no	—
267	C₂²×C₄×C₅₃	—	4	1	no	—
268	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
269	Q₁₆×C₅₃	—	2	2	no	—
270	SD₁₆×C₅₃	—	2	4	no	—
271	SD₁₆×C₅₃	—	2	4	no	—
272	SD₁₆×C₅₃	—	2	2	no	—
273	SD₁₆×C₅₃	—	2	2	no	—
274	SD₁₆×C₅₃	—	4	2	no	—
275	SD₁₆×C₅₃	—	4	2	no	—
276	D₈×C₅₃	—	2	4	no	—
277	D₈×C₅₃	—	2	4	no	—
278	D₈×C₅₃	—	2	4	no	—
279	D₈×C₅₃	—	2	2	no	—
280	D₈×C₅₃	—	2	4	no	—
281	D₈×C₅₃	—	4	2	no	—
282	D₈×C₅₃	—	4	2	no	—
283	D₈×C₅₃	—	4	2	no	—
284	D₈×C₅₃	—	4	2	no	—
285	M₁₆×C₅₃	—	2	4	no	—
286	M₁₆×C₅₃	—	2	1	no	—
287	M₁₆×C₅₃	—	2	1	no	—
288	M₁₆×C₅₃	—	2	1	no	—
289	M₁₆×C₅₃	—	2	1	no	—
290	M₁₆×C₅₃	—	2	1	no	—
291	M₁₆×C₅₃	—	2	1	no	—
292	M₁₆×C₅₃	—	2	1	no	—
293	M₁₆×C₅₃	—	4	2	no	—
294	M₁₆×C₅₃	C₂×D₄	1	2	yes	—
295	C₂×C₈×C₅₃	—	2	4	no	—
296	C₂×C₈×C₅₃	—	2	1	no	—
297	C₂×C₈×C₅₃	—	2	1	no	—
298	C₂×C₈×C₅₃	—	2	1	no	—
299	C₂×C₈×C₅₃	—	2	1	no	—
300	C₂×C₈×C₅₃	—	2	1	no	—
301	C₂×C₈×C₅₃	—	2	1	no	—
302	C₂×C₈×C₅₃	—	2	1	no	—
303	C₂×C₈×C₅₃	—	2	1	no	—
304	C₂×C₈×C₅₃	—	4	2	no	—
305	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
306	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
307	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
308	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₅₃	—	2	1	no	—
310	C₄⋊C₄×C₅₃	—	2	1	no	—
311	C₄⋊C₄×C₅₃	—	4	1	no	—
312	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
313	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
314	C₂²⋊C₄×C₅₃	—	2	1	no	—
315	C₂²⋊C₄×C₅₃	—	4	1	no	—
316	C₂²⋊C₄×C₅₃	—	4	1	no	—
317	C₂²⋊C₄×C₅₃	—	4	1	no	—
318	C₂²⋊C₄×C₅₃	—	8	2	no	—
319	C₄²×C₅₃	—	2	1	no	—
320	C₄²×C₅₃	—	2	1	no	—
321	C₄²×C₅₃	—	2	1	no	—
322	C₄²×C₅₃	—	4	1	no	—
323	C₂³×C₅₃	—	2	1	no	—
324	C₂³×C₅₃	—	2	1	no	—
325	C₂³×C₅₃	—	2	1	no	—
326	C₂³×C₅₃	—	2	2	no	—
327	C₂³×C₅₃	—	2	2	no	—
328	C₂³×C₅₃	—	4	4	no	—
329	C₂³×C₅₃	—	4	4	no	—
330	C₂³×C₅₃	—	4	1	no	—
331	C₂³×C₅₃	—	4	1	no	—
332	C₂³×C₅₃	—	4	1	no	—
333	C₂³×C₅₃	—	4	1	no	—
334	C₂³×C₅₃	—	4	1	no	—
335	C₂³×C₅₃	—	4	1	no	—
336	C₂³×C₅₃	—	4	1	no	—
337	C₂³×C₅₃	—	8	1	no	—
338	C₂³×C₅₃	—	8	1	no	—
339	C₂³×C₅₃	—	8	1	no	—
340	C₂³×C₅₃	—	8	1	no	—
341	C₂³×C₅₃	—	8	1	no	—
342	C₂³×C₅₃	—	8	1	no	—
343	C₂³×C₅₃	—	16	1	no	—
344	C₂³×C₅₃	—	16	1	no	—
345	C₂³×C₅₃	—	16	1	no	—
346	C₂³×C₅₃	—	16	1	no	—
347	C₂³×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
348	Q₈×C₅₃	—	2	1	no	—
349	Q₈×C₅₃	—	2	1	no	—
350	Q₈×C₅₃	—	2	1	no	—
351	Q₈×C₅₃	—	2	1	no	—
352	Q₈×C₅₃	#120	1	2	yes	—
353	Q₈×C₅₃	#121	1	2	yes	—
354	D₄×C₅₃	—	2	2	no	—
355	D₄×C₅₃	—	2	2	no	—
356	D₄×C₅₃	—	2	2	no	—
357	D₄×C₅₃	—	2	2	no	—
358	D₄×C₅₃	—	2	1	no	—
359	D₄×C₅₃	—	2	2	no	—
360	D₄×C₅₃	—	2	2	no	—
361	D₄×C₅₃	—	2	2	no	—
362	D₄×C₅₃	—	2	1	no	—
363	D₄×C₅₃	—	2	2	no	—
364	D₄×C₅₃	—	2	1	no	—
365	D₄×C₅₃	—	2	1	no	—
366	D₄×C₅₃	—	4	4	no	—
367	D₄×C₅₃	—	4	4	no	—
368	D₄×C₅₃	—	4	4	no	—
369	D₄×C₅₃	—	4	4	no	—
370	D₄×C₅₃	—	4	1	no	—
371	D₄×C₅₃	—	4	1	no	—
372	D₄×C₅₃	—	4	1	no	—
373	D₄×C₅₃	—	4	1	no	—
374	D₄×C₅₃	—	4	1	no	—
375	D₄×C₅₃	—	4	1	no	—
376	D₄×C₅₃	—	4	1	no	—
377	D₄×C₅₃	—	4	1	no	—
378	D₄×C₅₃	—	4	1	no	—
379	D₄×C₅₃	—	4	1	no	—
380	D₄×C₅₃	—	8	8	no	—
381	D₄×C₅₃	—	16	1	no	—
382	D₄×C₅₃	—	16	1	no	—
383	D₄×C₅₃	#120	1	2	yes	—
384	D₄×C₅₃	#121	1	2	yes	—
385	C₂×C₄×C₅₃	—	2	1	no	—
386	C₂×C₄×C₅₃	—	2	1	no	—
387	C₂×C₄×C₅₃	—	2	2	no	—
388	C₂×C₄×C₅₃	—	2	2	no	—
389	C₂×C₄×C₅₃	—	2	2	no	—
390	C₂×C₄×C₅₃	—	2	2	no	—
391	C₂×C₄×C₅₃	—	2	2	no	—
392	C₂×C₄×C₅₃	—	2	1	no	—
393	C₂×C₄×C₅₃	—	2	1	no	—
394	C₂×C₄×C₅₃	—	2	1	no	—
395	C₂×C₄×C₅₃	—	4	4	no	—
396	C₂×C₄×C₅₃	—	4	4	no	—
397	C₂×C₄×C₅₃	—	4	1	no	—
398	C₂×C₄×C₅₃	—	4	1	no	—
399	C₂×C₄×C₅₃	—	4	1	no	—
400	C₂×C₄×C₅₃	—	4	1	no	—
401	C₂×C₄×C₅₃	—	4	1	no	—
402	C₂×C₄×C₅₃	—	8	1	no	—
403	C₂×C₄×C₅₃	—	16	1	no	—
404	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
409	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
410	C₈×C₅₃	—	2	1	no	—
411	C₈×C₅₃	—	2	2	no	—
412	C₈×C₅₃	—	2	1	no	—
413	C₈×C₅₃	—	2	1	no	—
414	C₈×C₅₃	—	2	1	no	—
415	C₈×C₅₃	—	4	1	no	—
416	C₈×C₅₃	—	4	1	no	—
417	C₈×C₅₃	—	4	1	no	—
418	#24456	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
419	C₂²×C₅₃	—	2	1	no	—
420	C₂²×C₅₃	—	2	1	no	—
421	C₂²×C₅₃	—	2	2	no	—
422	C₂²×C₅₃	—	2	2	no	—
423	C₂²×C₅₃	—	4	1	no	—
424	C₂²×C₅₃	—	4	1	no	—
425	C₂²×C₅₃	—	4	1	no	—
426	C₂²×C₅₃	—	4	1	no	—
427	C₂²×C₅₃	—	4	1	no	—
428	C₂²×C₅₃	—	4	2	no	—
429	C₂²×C₅₃	—	4	2	no	—
430	C₂²×C₅₃	—	4	1	no	—
431	C₂²×C₅₃	—	4	1	no	—
432	C₂²×C₅₃	—	8	2	no	—
433	C₂²×C₅₃	—	8	2	no	—
434	C₂²×C₅₃	—	8	2	no	—
435	C₂²×C₅₃	—	8	1	no	—
436	C₂²×C₅₃	—	8	1	no	—
437	C₂²×C₅₃	—	8	1	no	—
438	C₂²×C₅₃	—	8	1	no	—
439	C₂²×C₅₃	—	8	1	no	—
440	C₂²×C₅₃	—	8	1	no	—
441	C₂²×C₅₃	—	8	1	no	—
442	C₂²×C₅₃	—	16	1	no	—
443	C₂²×C₅₃	—	16	1	no	—
444	C₂²×C₅₃	—	16	1	no	—
445	C₂²×C₅₃	—	16	4	no	—
446	C₂²×C₅₃	—	16	4	no	—
447	C₂²×C₅₃	#534	1	1	yes	characteristic
448	C₂²×C₅₃	D₄²	1	1	yes	characteristic
449	C₂²×C₅₃	#546	1	1	yes	characteristic
450	C₄×C₅₃	—	2	2	no	—
451	C₄×C₅₃	—	2	2	no	—
452	C₄×C₅₃	—	4	2	no	—
453	C₄×C₅₃	—	4	1	no	—
454	C₄×C₅₃	—	4	1	no	—
455	C₄×C₅₃	—	4	1	no	—
456	C₄×C₅₃	—	8	1	no	—
457	C₄×C₅₃	C₂×#120	1	1	yes	characteristic
458	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
459	C₄×C₅₃	D₄²	1	1	yes	characteristic
460	C₄×C₅₃	#546	1	1	yes	characteristic
461	C₂×#576	C₂×C₅₃	1	1	yes	characteristic, complemented
462	C₂×#472	C₂×C₅₃	1	1	yes	characteristic, complemented
463	#3045	C₂×C₅₃	1	1	yes	characteristic, complemented
464	C₂×#453	C₂×C₅₃	1	1	yes	characteristic, complemented
465	#3008	C₂×C₅₃	1	1	yes	characteristic, complemented
466	#2897	C₂×C₅₃	1	1	yes	characteristic, complemented
467	#2051	C₂×C₅₃	1	1	yes	characteristic, complemented
468	#2045	C₂×C₅₃	1	1	yes	characteristic, complemented
469	#2011	C₂×C₅₃	1	1	yes	characteristic, complemented
470	#2002	C₂×C₅₃	1	1	yes	characteristic, complemented
471	#1907	C₂×C₅₃	1	1	yes	characteristic, complemented
472	#1883	C₂×C₅₃	1	1	yes	characteristic, complemented
473	#1876	C₂×C₅₃	1	1	yes	characteristic, complemented
474	#1866	C₂×C₅₃	1	1	yes	characteristic, complemented
475	#1792	C₂×C₅₃	1	1	yes	characteristic, complemented
476	C₂×C₅₃	—	2	1	no	—
477	C₂×C₅₃	—	2	1	no	—
478	C₂×C₅₃	—	4	2	no	—
479	C₂×C₅₃	—	4	2	no	—
480	C₂×C₅₃	—	8	1	no	—
481	C₂×C₅₃	—	8	2	no	—
482	C₂×C₅₃	—	8	2	no	—
483	C₂×C₅₃	—	16	1	no	—
484	C₂×C₅₃	#2410	1	1	yes	characteristic
485	C₂×C₅₃	#3288	1	1	yes	characteristic
486	C₂×C₅₃	#3292	1	1	yes	characteristic
487	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
488	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
489	#576	—	2	4	no	—
490	#576	—	2	4	no	—
491	C₂×AGL(1,ℤ/8)	—	2	1	no	—
492	C₂×AGL(1,ℤ/8)	—	2	1	no	—
493	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
494	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
495	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
496	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
497	C₂×#135	—	2	1	no	—
498	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
499	C₂²×D₈	—	2	1	no	—
500	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
501	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
502	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
503	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic, complemented
504	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
505	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic, complemented
506	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
507	#472	—	2	4	no	—
508	#464	—	2	1	no	—
509	#463	—	2	1	no	—
510	#460	—	2	1	no	—
511	#459	—	2	1	no	—
512	#453	—	2	4	no	—
513	#449	—	2	1	no	—
514	#449	—	2	1	no	—
515	#447	—	2	1	no	—
516	#447	—	2	1	no	—
517	C₂×#108	C₂²×C₅₃	1	1	yes	characteristic, complemented
518	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
519	C₂×#104	C₂²×C₅₃	1	1	yes	characteristic
520	C₂×#104	C₂²×C₅₃	1	1	yes	characteristic, complemented
521	C₂×#104	C₂²×C₅₃	1	1	yes	characteristic, complemented
522	#418	—	2	1	no	—
523	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
524	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
525	#417	—	2	1	no	—
526	#417	C₂²×C₅₃	1	1	yes	characteristic
527	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
528	#416	—	2	1	no	—
529	#416	C₂²×C₅₃	1	1	yes	characteristic
530	C₂×#102	—	2	1	no	—
531	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
532	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
533	C₂×#100	C₂²×C₅₃	1	1	yes	characteristic, complemented
534	C₂×#100	C₂²×C₅₃	1	1	yes	characteristic, complemented
535	C₂×#100	C₂²×C₅₃	1	1	yes	characteristic, complemented
536	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
537	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
538	#343	C₂²×C₅₃	1	1	yes	characteristic, complemented
539	#341	C₂²×C₅₃	1	1	yes	characteristic, complemented
540	#339	C₂²×C₅₃	1	1	yes	characteristic, complemented
541	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
542	C₅₃	#24456	1	1	yes	characteristic, direct product factor, Sylow
543	H(5,𝔽₂)	—	2	2	no	—
544	H(5,𝔽₂)	—	2	2	no	—
545	H(5,𝔽₂)	—	2	2	no	—
546	H(5,𝔽₂)	—	2	2	no	—
547	H(5,𝔽₂)	—	2	2	no	—
548	H(5,𝔽₂)	—	4	1	no	—
549	H(5,𝔽₂)	—	4	1	no	—
550	H(5,𝔽₂)	D₄×C₅₃	1	4	yes	complemented
551	C₂×#41	—	2	1	no	—
552	C₂×#41	—	2	1	no	—
553	C₂×#41	—	2	1	no	—
554	C₂×#41	—	2	1	no	—
555	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
556	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
557	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
558	C₂²×D₄	—	2	1	no	—
559	C₂²×D₄	—	2	1	no	—
560	C₂²×D₄	—	2	1	no	—
561	C₂²×D₄	—	2	1	no	—
562	C₂²×D₄	—	4	1	no	—
563	C₂²×D₄	—	4	1	no	—
564	C₂²×D₄	—	4	1	no	—
565	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
568	AGL(1,ℤ/8)	—	2	8	no	—
569	AGL(1,ℤ/8)	—	2	8	no	—
570	AGL(1,ℤ/8)	—	2	2	no	—
571	AGL(1,ℤ/8)	—	2	2	no	—
572	AGL(1,ℤ/8)	—	2	2	no	—
573	AGL(1,ℤ/8)	—	2	2	no	—
574	AGL(1,ℤ/8)	—	2	2	no	—
575	AGL(1,ℤ/8)	—	2	2	no	—
576	AGL(1,ℤ/8)	—	2	2	no	—
577	AGL(1,ℤ/8)	D₄×C₅₃	1	4	yes	complemented
578	#135	—	2	8	no	—
579	#135	—	2	2	no	—
580	#135	—	2	2	no	—
581	C₂×Q₁₆	D₄×C₅₃	1	1	yes	characteristic, complemented
582	C₂×SD₁₆	—	2	1	no	—
583	C₂×SD₁₆	—	2	1	no	—
584	C₂×SD₁₆	—	2	1	no	—
585	C₂×SD₁₆	—	2	1	no	—
586	C₂×SD₁₆	D₄×C₅₃	1	1	yes	characteristic, complemented
587	C₂×SD₁₆	D₄×C₅₃	1	1	yes	characteristic, complemented
588	C₂×D₈	—	2	8	no	—
589	C₂×D₈	—	2	1	no	—
590	C₂×D₈	—	2	1	no	—
591	C₂×D₈	—	2	2	no	—
592	C₂×D₈	—	2	2	no	—
593	C₂×D₈	—	2	2	no	—
594	C₂×D₈	—	2	1	no	—
595	C₂×D₈	—	2	1	no	—
596	C₂×D₈	—	2	1	no	—
597	C₂×D₈	—	2	1	no	—
598	C₂×D₈	—	2	1	no	—
599	C₂×D₈	—	2	1	no	—
600	C₂×D₈	—	4	1	no	—
601	C₂×D₈	D₄×C₅₃	1	1	yes	characteristic, complemented
602	#131	—	2	2	no	—
603	#131	—	2	2	no	—
604	#131	—	2	2	no	—
605	#131	—	4	1	no	—
606	C₂×M₁₆	—	2	1	no	—
607	C₂×M₁₆	—	2	1	no	—
608	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
609	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
610	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
611	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
612	C₂²×C₈	—	2	1	no	—
613	C₂²×C₈	—	2	1	no	—
614	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
615	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
616	#127	—	2	2	no	—
617	#127	—	2	1	no	—
618	#127	—	4	1	no	—
619	#124	—	2	1	no	—
620	#121	—	2	1	no	—
621	#121	—	2	1	no	—
622	#120	—	4	1	no	—
623	C₄×Q₈	—	2	1	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	4	1	no	—
626	#117	—	2	1	no	—
627	#117	C₂³×C₅₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	—	4	1	no	—
631	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
632	#108	—	2	2	no	—
633	C₄⋊C₈	—	2	1	no	—
634	C₄⋊C₈	—	2	1	no	—
635	#104	—	2	2	no	—
636	#104	—	2	2	no	—
637	#104	—	4	1	no	—
638	#103	—	2	1	no	—
639	#103	—	2	1	no	—
640	#103	D₄×C₅₃	1	1	yes	characteristic, complemented
641	#103	D₄×C₅₃	1	1	yes	characteristic, complemented
642	#102	—	2	1	no	—
643	#102	—	2	1	no	—
644	#102	—	2	1	no	—
645	#102	—	2	1	no	—
646	#102	—	2	1	no	—
647	#102	—	2	1	no	—
648	#102	—	2	1	no	—
649	#102	—	2	1	no	—
650	#102	—	2	1	no	—
651	#102	—	2	1	no	—
652	#102	D₄×C₅₃	1	1	yes	characteristic, complemented
653	#102	D₄×C₅₃	1	1	yes	characteristic, complemented
654	#100	—	2	2	no	—
655	#100	—	2	2	no	—
656	#100	—	2	2	no	—
657	C₂²⋊C₈	—	2	1	no	—
658	C₂²⋊C₈	—	2	1	no	—
659	C₂⁴	—	2	1	no	—
660	C₂⁴	—	2	1	no	—
661	C₂⁴	—	2	1	no	—
662	C₂⁴	—	4	1	no	—
663	C₂⁴	—	4	1	no	—
664	#41	—	2	1	no	—
665	#41	—	2	1	no	—
666	#41	—	2	1	no	—
667	#41	—	2	1	no	—
668	#41	—	2	4	no	—
669	#41	—	2	4	no	—
670	#41	—	2	4	no	—
671	#41	—	2	1	no	—
672	#41	—	2	1	no	—
673	#41	—	2	1	no	—
674	#41	—	2	1	no	—
675	#41	—	4	2	no	—
676	#41	—	4	2	no	—
677	#41	—	4	2	no	—
678	#41	—	4	2	no	—
679	#41	—	4	2	no	—
680	#41	C₂×D₄×C₅₃	1	2	yes	—
681	#41	C₂×D₄×C₅₃	1	2	yes	—
682	#41	C₂×D₄×C₅₃	1	2	yes	—
683	#41	#41×C₅₃	1	2	yes	—
684	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
685	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
686	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	2	1	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	1	no	—
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	1	no	—
713	C₂×D₄	—	4	1	no	—
714	C₂×D₄	—	4	1	no	—
715	C₂×D₄	—	4	1	no	—
716	C₂×D₄	—	4	1	no	—
717	C₂×D₄	—	4	1	no	—
718	C₂×D₄	—	4	4	no	—
719	C₂×D₄	—	4	2	no	—
720	C₂×D₄	—	4	4	no	—
721	C₂×D₄	—	4	4	no	—
722	C₂×D₄	—	4	4	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	4	no	—
725	C₂×D₄	—	8	2	no	—
726	C₂×D₄	—	8	2	no	—
727	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
728	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
729	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
730	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
731	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	4	1	no	—
738	C₂²×C₄	—	4	1	no	—
739	C₂²×C₄	—	4	1	no	—
740	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
741	Q₁₆	—	2	2	no	—
742	SD₁₆	—	2	4	no	—
743	SD₁₆	—	2	4	no	—
744	SD₁₆	—	2	2	no	—
745	SD₁₆	—	2	2	no	—
746	SD₁₆	—	4	2	no	—
747	SD₁₆	—	4	2	no	—
748	D₈	—	2	4	no	—
749	D₈	—	2	4	no	—
750	D₈	—	2	4	no	—
751	D₈	—	2	2	no	—
752	D₈	—	2	4	no	—
753	D₈	—	4	2	no	—
754	D₈	—	4	2	no	—
755	D₈	—	4	2	no	—
756	D₈	—	4	2	no	—
757	M₁₆	—	2	4	no	—
758	M₁₆	—	2	1	no	—
759	M₁₆	—	2	1	no	—
760	M₁₆	—	2	1	no	—
761	M₁₆	—	2	1	no	—
762	M₁₆	—	2	1	no	—
763	M₁₆	—	2	1	no	—
764	M₁₆	—	2	1	no	—
765	M₁₆	—	4	2	no	—
766	M₁₆	C₂×D₄×C₅₃	1	2	yes	—
767	C₂×C₈	—	2	4	no	—
768	C₂×C₈	—	2	1	no	—
769	C₂×C₈	—	2	1	no	—
770	C₂×C₈	—	2	1	no	—
771	C₂×C₈	—	2	1	no	—
772	C₂×C₈	—	2	1	no	—
773	C₂×C₈	—	2	1	no	—
774	C₂×C₈	—	2	1	no	—
775	C₂×C₈	—	2	1	no	—
776	C₂×C₈	—	4	2	no	—
777	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
778	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
779	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
780	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	4	1	no	—
784	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
785	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
786	C₂²⋊C₄	—	2	1	no	—
787	C₂²⋊C₄	—	4	1	no	—
788	C₂²⋊C₄	—	4	1	no	—
789	C₂²⋊C₄	—	4	1	no	—
790	C₂²⋊C₄	—	8	2	no	—
791	C₄²	—	2	1	no	—
792	C₄²	—	2	1	no	—
793	C₄²	—	2	1	no	—
794	C₄²	—	4	1	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	4	4	no	—
801	C₂³	—	4	4	no	—
802	C₂³	—	4	1	no	—
803	C₂³	—	4	1	no	—
804	C₂³	—	4	1	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	8	1	no	—
810	C₂³	—	8	1	no	—
811	C₂³	—	8	1	no	—
812	C₂³	—	8	1	no	—
813	C₂³	—	8	1	no	—
814	C₂³	—	8	1	no	—
815	C₂³	—	16	1	no	—
816	C₂³	—	16	1	no	—
817	C₂³	—	16	1	no	—
818	C₂³	—	16	1	no	—
819	C₂³	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
820	Q₈	—	2	1	no	—
821	Q₈	—	2	1	no	—
822	Q₈	—	2	1	no	—
823	Q₈	—	2	1	no	—
824	Q₈	#120×C₅₃	1	2	yes	—
825	Q₈	#121×C₅₃	1	2	yes	—
826	D₄	—	2	2	no	—
827	D₄	—	2	2	no	—
828	D₄	—	2	2	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	2	no	—
831	D₄	—	2	2	no	—
832	D₄	—	2	1	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	1	no	—
835	D₄	—	2	2	no	—
836	D₄	—	2	1	no	—
837	D₄	—	2	1	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	4	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	1	no	—
843	D₄	—	4	1	no	—
844	D₄	—	4	1	no	—
845	D₄	—	4	1	no	—
846	D₄	—	4	1	no	—
847	D₄	—	4	1	no	—
848	D₄	—	4	1	no	—
849	D₄	—	4	1	no	—
850	D₄	—	4	1	no	—
851	D₄	—	4	1	no	—
852	D₄	—	8	8	no	—
853	D₄	—	16	1	no	—
854	D₄	—	16	1	no	—
855	D₄	#120×C₅₃	1	2	yes	—
856	D₄	#121×C₅₃	1	2	yes	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	1	no	—
870	C₂×C₄	—	4	1	no	—
871	C₂×C₄	—	4	1	no	—
872	C₂×C₄	—	4	1	no	—
873	C₂×C₄	—	4	1	no	—
874	C₂×C₄	—	8	1	no	—
875	C₂×C₄	—	16	1	no	—
876	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
877	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
878	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
880	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
881	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
882	C₈	—	2	1	no	—
883	C₈	—	2	2	no	—
884	C₈	—	2	1	no	—
885	C₈	—	2	1	no	—
886	C₈	—	2	1	no	—
887	C₈	—	4	1	no	—
888	C₈	—	4	1	no	—
889	C₈	—	4	1	no	—
890	C₂²	—	2	1	no	—
891	C₂²	—	2	1	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	1	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	1	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	8	2	no	—
904	C₂²	—	8	2	no	—
905	C₂²	—	8	2	no	—
906	C₂²	—	8	1	no	—
907	C₂²	—	8	1	no	—
908	C₂²	—	8	1	no	—
909	C₂²	—	8	1	no	—
910	C₂²	—	8	1	no	—
911	C₂²	—	8	1	no	—
912	C₂²	—	8	1	no	—
913	C₂²	—	16	1	no	—
914	C₂²	—	16	1	no	—
915	C₂²	—	16	1	no	—
916	C₂²	—	16	4	no	—
917	C₂²	—	16	4	no	—
918	C₂²	C₅₃×#534	1	1	yes	characteristic
919	C₂²	D₄²×C₅₃	1	1	yes	characteristic
920	C₂²	C₅₃×#546	1	1	yes	characteristic
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	1	no	—
927	C₄	—	8	1	no	—
928	C₄	C₂×#120×C₅₃	1	1	yes	characteristic
929	C₄	C₂×#121×C₅₃	1	1	yes	characteristic
930	C₄	D₄²×C₅₃	1	1	yes	characteristic
931	C₄	C₅₃×#546	1	1	yes	characteristic
932	C₂	—	2	1	no	—
933	C₂	—	2	1	no	—
934	C₂	—	4	2	no	—
935	C₂	—	4	2	no	—
936	C₂	—	8	1	no	—
937	C₂	—	8	2	no	—
938	C₂	—	8	2	no	—
939	C₂	—	16	1	no	—
940	C₂	C₅₃×#2410	1	1	yes	characteristic
941	C₂	C₅₃×#3288	1	1	yes	characteristic
942	C₂	C₅₃×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#576	C₂	semidirect
2. C₂×C₅₃×#472	C₂	semidirect
3. C₅₃×#3045	C₂	semidirect
4. C₂×C₅₃×#453	C₂	semidirect
5. C₅₃×#3008	C₂	semidirect
6. C₅₃×#2897	C₂	semidirect
7. C₅₃×#2051	C₂	semidirect
8. C₅₃×#2045	C₂	semidirect
9. C₅₃×#2011	C₂	semidirect
10. C₅₃×#2002	C₂	semidirect
11. C₅₃×#1907	C₂	semidirect
12. C₅₃×#1883	C₂	semidirect
13. C₅₃×#1876	C₂	semidirect
14. C₅₃×#1866	C₂	semidirect
15. C₅₃×#1792	C₂	semidirect
25. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
30. C₂²×D₈×C₅₃	C₂²	semidirect
32. C₂×#131×C₅₃	C₂²	semidirect
33. C₅₃×#535	C₂²	semidirect
34. C₂×#127×C₅₃	C₂²	semidirect
35. C₅₃×#520	C₂²	semidirect
46. C₂×#108×C₅₃	C₂²	semidirect
47. C₅₃×#424	C₂²	semidirect
49. C₂×#104×C₅₃	C₂²	semidirect
50. C₂×#104×C₅₃	C₂²	semidirect
52. C₅₃×#418	C₂²	semidirect
53. C₅₃×#418	C₂²	semidirect
56. C₅₃×#417	C₂²	semidirect
60. C₂×#102×C₅₃	C₂²	semidirect
61. C₂×#102×C₅₃	C₂²	semidirect
62. C₂×#100×C₅₃	C₂²	semidirect
63. C₂×#100×C₅₃	C₂²	semidirect
64. C₂×#100×C₅₃	C₂²	semidirect
65. C₅₃×#408	C₂²	semidirect
66. C₅₃×#390	C₂²	semidirect
67. C₅₃×#343	C₂²	semidirect
68. C₅₃×#341	C₂²	semidirect
69. C₅₃×#339	C₂²	semidirect
70. C₅₃×#336	C₂²	semidirect
78. H(5,𝔽₂)×C₅₃	D₄	semidirect
105. AGL(1,ℤ/8)×C₅₃	D₄	semidirect
109. C₂×Q₁₆×C₅₃	D₄	semidirect
114. C₂×SD₁₆×C₅₃	D₄	semidirect
115. C₂×SD₁₆×C₅₃	D₄	semidirect
129. C₂×D₈×C₅₃	D₄	semidirect
168. #103×C₅₃	D₄	semidirect
169. #103×C₅₃	D₄	semidirect
180. #102×C₅₃	D₄	semidirect
181. #102×C₅₃	D₄	semidirect
418. #24456	C₅₃	direct (N × H)
461. C₂×#576	C₂×C₅₃	semidirect
462. C₂×#472	C₂×C₅₃	semidirect
463. #3045	C₂×C₅₃	semidirect
464. C₂×#453	C₂×C₅₃	semidirect
465. #3008	C₂×C₅₃	semidirect
466. #2897	C₂×C₅₃	semidirect
467. #2051	C₂×C₅₃	semidirect
468. #2045	C₂×C₅₃	semidirect
469. #2011	C₂×C₅₃	semidirect
470. #2002	C₂×C₅₃	semidirect
471. #1907	C₂×C₅₃	semidirect
472. #1883	C₂×C₅₃	semidirect
473. #1876	C₂×C₅₃	semidirect
474. #1866	C₂×C₅₃	semidirect
475. #1792	C₂×C₅₃	semidirect
496. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
501. C₂²×D₈	C₂²×C₅₃	semidirect
503. C₂×#131	C₂²×C₅₃	semidirect
504. #535	C₂²×C₅₃	semidirect
505. C₂×#127	C₂²×C₅₃	semidirect
506. #520	C₂²×C₅₃	semidirect
517. C₂×#108	C₂²×C₅₃	semidirect
518. #424	C₂²×C₅₃	semidirect
520. C₂×#104	C₂²×C₅₃	semidirect
521. C₂×#104	C₂²×C₅₃	semidirect
523. #418	C₂²×C₅₃	semidirect
524. #418	C₂²×C₅₃	semidirect
527. #417	C₂²×C₅₃	semidirect
531. C₂×#102	C₂²×C₅₃	semidirect
532. C₂×#102	C₂²×C₅₃	semidirect
533. C₂×#100	C₂²×C₅₃	semidirect
534. C₂×#100	C₂²×C₅₃	semidirect
535. C₂×#100	C₂²×C₅₃	semidirect
536. #408	C₂²×C₅₃	semidirect
537. #390	C₂²×C₅₃	semidirect
538. #343	C₂²×C₅₃	semidirect
539. #341	C₂²×C₅₃	semidirect
540. #339	C₂²×C₅₃	semidirect
541. #336	C₂²×C₅₃	semidirect
542. C₅₃	#24456	direct (N × H)
550. H(5,𝔽₂)	D₄×C₅₃	semidirect
577. AGL(1,ℤ/8)	D₄×C₅₃	semidirect
581. C₂×Q₁₆	D₄×C₅₃	semidirect
586. C₂×SD₁₆	D₄×C₅₃	semidirect
587. C₂×SD₁₆	D₄×C₅₃	semidirect
601. C₂×D₈	D₄×C₅₃	semidirect
640. #103	D₄×C₅₃	semidirect
641. #103	D₄×C₅₃	semidirect
652. #102	D₄×C₅₃	semidirect
653. #102	D₄×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#576	2
C₂×C₅₃×#472	2
C₅₃×#3045	2
C₂×C₅₃×#453	2
C₅₃×#3008	2
C₅₃×#2897	2
C₅₃×#2051	2
C₅₃×#2045	2
C₅₃×#2011	2
C₅₃×#2002	2
C₅₃×#1907	2
C₅₃×#1883	2
C₅₃×#1876	2
C₅₃×#1866	2
C₅₃×#1792	2
#24456	53

Subgroups — C53×#24456 #27231968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#24456 #27231968