Subgroups — C₅₃×#36709 #27244221

Order 13568.

2630 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#123×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2847	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2695	C₂	1	4	yes	maximal, complemented
6	C₅₃×#2693	C₂	1	4	yes	maximal, complemented
7	C₅₃×#2672	C₂	1	4	yes	maximal, complemented
8	C₅₃×#2671	C₂	1	4	yes	maximal, complemented
9	C₅₃×#2627	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2618	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2534	C₂	1	2	yes	maximal, complemented
12	C₅₃×#2487	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2412	C₂	1	2	yes	maximal, complemented
14	C₅₃×#2410	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
18	C₅₃×#538	—	2	8	no	—
19	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
20	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
21	C₂×#123×C₅₃	—	2	8	no	—
22	C₂×#123×C₅₃	C₂²	1	4	yes	—
23	C₂×#123×C₅₃	C₂²	1	4	yes	—
24	C₂×#123×C₅₃	C₂²	1	2	yes	—
25	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
26	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
28	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#121×C₅₃	C₂²	1	4	yes	—
30	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
31	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
32	C₂×#120×C₅₃	C₂²	1	2	yes	—
33	C₂×#120×C₅₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
35	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
40	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#400	C₂²	1	2	yes	complemented
42	C₅₃×#400	C₂²	1	4	yes	complemented
43	C₅₃×#399	C₂²	1	4	yes	complemented
44	C₅₃×#398	C₂²	1	2	yes	complemented
45	C₅₃×#398	C₂²	1	4	yes	complemented
46	C₅₃×#397	C₂²	1	4	yes	complemented
47	C₅₃×#396	C₂²	1	4	yes	complemented
48	C₅₃×#396	C₂²	1	4	yes	complemented
49	C₅₃×#395	C₂²	1	2	yes	complemented
50	C₅₃×#394	C₂²	1	4	yes	—
51	C₅₃×#394	C₂²	1	4	yes	complemented
52	C₅₃×#394	C₂²	1	2	yes	complemented
53	C₅₃×#394	C₂²	1	4	yes	complemented
54	C₅₃×#392	C₂²	1	4	yes	—
55	C₅₃×#389	C₂²	1	4	yes	complemented
56	C₅₃×#388	C₂²	1	4	yes	complemented
57	C₅₃×#386	C₂²	1	4	yes	—
58	C₅₃×#386	C₂²	1	2	yes	—
59	C₅₃×#386	C₂²	1	2	yes	—
60	C₅₃×#386	C₂²	1	4	yes	complemented
61	C₅₃×#386	C₂²	1	4	yes	complemented
62	C₅₃×#386	C₂²	1	4	yes	complemented
63	C₅₃×#385	C₂²	1	2	yes	—
64	C₅₃×#385	C₂²	1	2	yes	—
65	C₅₃×#385	C₂²	1	4	yes	complemented
66	C₅₃×#385	C₂²	1	4	yes	complemented
67	C₅₃×#385	C₂²	1	4	yes	complemented
68	C₅₃×#381	C₂²	1	2	yes	—
69	C₅₃×#380	C₂²	1	2	yes	—
70	C₅₃×#380	C₂²	1	1	yes	characteristic
71	C₅₃×#380	C₂²	1	1	yes	characteristic
72	C₅₃×#380	C₂²	1	2	yes	complemented
73	C₅₃×#380	C₂²	1	4	yes	complemented
74	C₅₃×#380	C₂²	1	2	yes	complemented
75	C₅₃×#380	C₂²	1	4	yes	complemented
76	C₅₃×#379	C₂²	1	2	yes	—
77	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
78	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₅₃	—	2	4	no	—
81	C₂²×D₄×C₅₃	—	4	4	no	—
82	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
84	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
85	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
86	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
87	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₅₃	—	2	4	no	—
89	C₂³×C₄×C₅₃	—	4	4	no	—
90	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
96	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
97	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
99	#126×C₅₃	—	2	8	no	—
100	#124×C₅₃	—	2	8	no	—
101	#123×C₅₃	—	2	16	no	—
102	#123×C₅₃	—	2	16	no	—
103	#123×C₅₃	—	2	8	no	—
104	#123×C₅₃	—	4	4	no	—
105	C₂²⋊Q₈×C₅₃	—	2	4	no	—
106	C₂²⋊Q₈×C₅₃	—	4	4	no	—
107	#121×C₅₃	—	2	8	no	—
108	#121×C₅₃	—	2	4	no	—
109	#121×C₅₃	—	4	4	no	—
110	#121×C₅₃	—	4	8	no	—
111	#120×C₅₃	—	2	8	no	—
112	#120×C₅₃	—	4	4	no	—
113	C₄×D₄×C₅₃	—	2	8	no	—
114	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
115	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
116	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
130	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
131	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
132	C₂×C₂²⋊C₄×C₅₃	D₄	1	8	yes	complemented
133	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
151	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
152	#95×C₅₃	C₂³	1	2	yes	—
153	#95×C₅₃	C₂³	1	2	yes	—
154	#95×C₅₃	C₂³	1	4	yes	—
155	#95×C₅₃	C₂³	1	4	yes	—
156	#95×C₅₃	C₂³	1	4	yes	—
157	#95×C₅₃	C₂³	1	4	yes	—
158	#95×C₅₃	C₂³	1	4	yes	—
159	#95×C₅₃	C₂³	1	4	yes	—
160	#95×C₅₃	C₂³	1	4	yes	—
161	C₂⁴×C₅₃	—	2	2	no	—
162	C₂⁴×C₅₃	—	2	4	no	—
163	C₂⁴×C₅₃	—	2	2	no	—
164	C₂⁴×C₅₃	—	2	2	no	—
165	C₂⁴×C₅₃	—	2	2	no	—
166	C₂⁴×C₅₃	—	2	2	no	—
167	C₂⁴×C₅₃	—	4	2	no	—
168	C₂⁴×C₅₃	—	4	2	no	—
169	C₂⁴×C₅₃	—	4	2	no	—
170	C₂⁴×C₅₃	C₂×D₄	1	4	yes	—
171	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
172	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
173	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
174	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
175	C₂×Q₈×C₅₃	—	2	2	no	—
176	C₂×Q₈×C₅₃	—	4	2	no	—
177	C₂×D₄×C₅₃	—	2	4	no	—
178	C₂×D₄×C₅₃	—	2	8	no	—
179	C₂×D₄×C₅₃	—	2	4	no	—
180	C₂×D₄×C₅₃	—	2	8	no	—
181	C₂×D₄×C₅₃	—	2	4	no	—
182	C₂×D₄×C₅₃	—	2	4	no	—
183	C₂×D₄×C₅₃	—	2	4	no	—
184	C₂×D₄×C₅₃	—	2	8	no	—
185	C₂×D₄×C₅₃	—	2	2	no	—
186	C₂×D₄×C₅₃	—	4	4	no	—
187	C₂×D₄×C₅₃	—	4	4	no	—
188	C₂×D₄×C₅₃	—	4	2	no	—
189	C₂×D₄×C₅₃	—	4	4	no	—
190	C₂×D₄×C₅₃	—	4	4	no	—
191	C₂×D₄×C₅₃	—	4	4	no	—
192	C₂×D₄×C₅₃	—	4	16	no	—
193	C₂²×C₄×C₅₃	—	2	2	no	—
194	C₂²×C₄×C₅₃	—	2	2	no	—
195	C₂²×C₄×C₅₃	—	2	2	no	—
196	C₂²×C₄×C₅₃	—	2	4	no	—
197	C₂²×C₄×C₅₃	—	2	4	no	—
198	C₂²×C₄×C₅₃	—	2	2	no	—
199	C₂²×C₄×C₅₃	—	2	2	no	—
200	C₂²×C₄×C₅₃	—	2	4	no	—
201	C₂²×C₄×C₅₃	—	2	4	no	—
202	C₂²×C₄×C₅₃	—	2	4	no	—
203	C₂²×C₄×C₅₃	—	4	2	no	—
204	C₂²×C₄×C₅₃	—	4	2	no	—
205	C₂²×C₄×C₅₃	—	4	2	no	—
206	C₂²×C₄×C₅₃	—	4	2	no	—
207	C₂²×C₄×C₅₃	—	4	2	no	—
208	C₂²×C₄×C₅₃	—	4	2	no	—
209	C₂²×C₄×C₅₃	—	4	4	no	—
210	C₂²×C₄×C₅₃	—	4	4	no	—
211	C₂²×C₄×C₅₃	—	4	4	no	—
212	C₂²×C₄×C₅₃	—	4	4	no	—
213	C₂²×C₄×C₅₃	—	4	16	no	—
214	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
215	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
216	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
227	C₄⋊C₄×C₅₃	—	2	8	no	—
228	C₄⋊C₄×C₅₃	—	2	4	no	—
229	C₄⋊C₄×C₅₃	—	2	4	no	—
230	C₄⋊C₄×C₅₃	—	2	4	no	—
231	C₄⋊C₄×C₅₃	—	2	4	no	—
232	C₄⋊C₄×C₅₃	—	2	2	no	—
233	C₄⋊C₄×C₅₃	—	2	2	no	—
234	C₄⋊C₄×C₅₃	—	4	4	no	—
235	C₄⋊C₄×C₅₃	—	4	2	no	—
236	C₄⋊C₄×C₅₃	—	4	4	no	—
237	C₄⋊C₄×C₅₃	—	4	2	no	—
238	C₄⋊C₄×C₅₃	—	4	4	no	—
239	C₄⋊C₄×C₅₃	—	4	4	no	—
240	C₂²⋊C₄×C₅₃	—	2	8	no	—
241	C₂²⋊C₄×C₅₃	—	2	4	no	—
242	C₂²⋊C₄×C₅₃	—	2	4	no	—
243	C₂²⋊C₄×C₅₃	—	2	4	no	—
244	C₂²⋊C₄×C₅₃	—	2	4	no	—
245	C₂²⋊C₄×C₅₃	—	2	4	no	—
246	C₂²⋊C₄×C₅₃	—	2	8	no	—
247	C₂²⋊C₄×C₅₃	—	2	8	no	—
248	C₂²⋊C₄×C₅₃	—	2	4	no	—
249	C₂²⋊C₄×C₅₃	—	2	4	no	—
250	C₂²⋊C₄×C₅₃	—	4	4	no	—
251	C₂²⋊C₄×C₅₃	—	4	4	no	—
252	C₂²⋊C₄×C₅₃	—	4	4	no	—
253	C₂²⋊C₄×C₅₃	—	4	4	no	—
254	C₂²⋊C₄×C₅₃	—	4	4	no	—
255	C₂²⋊C₄×C₅₃	—	4	4	no	—
256	C₂²⋊C₄×C₅₃	C₂×D₄	1	8	yes	—
257	C₂²⋊C₄×C₅₃	C₂×D₄	1	8	yes	—
258	C₄²×C₅₃	—	2	4	no	—
259	C₂³×C₅₃	—	2	2	no	—
260	C₂³×C₅₃	—	2	2	no	—
261	C₂³×C₅₃	—	2	8	no	—
262	C₂³×C₅₃	—	2	2	no	—
263	C₂³×C₅₃	—	2	2	no	—
264	C₂³×C₅₃	—	2	2	no	—
265	C₂³×C₅₃	—	2	4	no	—
266	C₂³×C₅₃	—	2	2	no	—
267	C₂³×C₅₃	—	2	2	no	—
268	C₂³×C₅₃	—	2	2	no	—
269	C₂³×C₅₃	—	2	4	no	—
270	C₂³×C₅₃	—	2	2	no	—
271	C₂³×C₅₃	—	2	2	no	—
272	C₂³×C₅₃	—	2	8	no	—
273	C₂³×C₅₃	—	2	2	no	—
274	C₂³×C₅₃	—	2	2	no	—
275	C₂³×C₅₃	—	2	4	no	—
276	C₂³×C₅₃	—	2	2	no	—
277	C₂³×C₅₃	—	2	4	no	—
278	C₂³×C₅₃	—	4	4	no	—
279	C₂³×C₅₃	—	4	4	no	—
280	C₂³×C₅₃	—	4	8	no	—
281	C₂³×C₅₃	—	4	8	no	—
282	C₂³×C₅₃	—	4	4	no	—
283	C₂³×C₅₃	—	4	4	no	—
284	C₂³×C₅₃	—	8	4	no	—
285	C₂³×C₅₃	—	8	4	no	—
286	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
287	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
288	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
289	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
290	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
291	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
292	Q₈×C₅₃	—	8	2	no	—
293	D₄×C₅₃	—	4	16	no	—
294	D₄×C₅₃	—	4	8	no	—
295	D₄×C₅₃	—	8	2	no	—
296	D₄×C₅₃	—	8	4	no	—
297	D₄×C₅₃	—	8	4	no	—
298	D₄×C₅₃	—	8	8	no	—
299	C₂×C₄×C₅₃	—	2	2	no	—
300	C₂×C₄×C₅₃	—	2	2	no	—
301	C₂×C₄×C₅₃	—	2	4	no	—
302	C₂×C₄×C₅₃	—	2	2	no	—
303	C₂×C₄×C₅₃	—	2	2	no	—
304	C₂×C₄×C₅₃	—	2	2	no	—
305	C₂×C₄×C₅₃	—	2	2	no	—
306	C₂×C₄×C₅₃	—	2	2	no	—
307	C₂×C₄×C₅₃	—	2	2	no	—
308	C₂×C₄×C₅₃	—	2	2	no	—
309	C₂×C₄×C₅₃	—	2	2	no	—
310	C₂×C₄×C₅₃	—	2	2	no	—
311	C₂×C₄×C₅₃	—	2	4	no	—
312	C₂×C₄×C₅₃	—	2	4	no	—
313	C₂×C₄×C₅₃	—	2	4	no	—
314	C₂×C₄×C₅₃	—	2	4	no	—
315	C₂×C₄×C₅₃	—	2	4	no	—
316	C₂×C₄×C₅₃	—	2	2	no	—
317	C₂×C₄×C₅₃	—	2	4	no	—
318	C₂×C₄×C₅₃	—	2	2	no	—
319	C₂×C₄×C₅₃	—	2	2	no	—
320	C₂×C₄×C₅₃	—	2	4	no	—
321	C₂×C₄×C₅₃	—	2	4	no	—
322	C₂×C₄×C₅₃	—	2	4	no	—
323	C₂×C₄×C₅₃	—	4	4	no	—
324	C₂×C₄×C₅₃	—	4	4	no	—
325	C₂×C₄×C₅₃	—	4	8	no	—
326	C₂×C₄×C₅₃	—	4	8	no	—
327	C₂×C₄×C₅₃	—	4	4	no	—
328	C₂×C₄×C₅₃	—	4	4	no	—
329	C₂×C₄×C₅₃	—	4	4	no	—
330	C₂×C₄×C₅₃	—	8	4	no	—
331	C₂×C₄×C₅₃	—	8	8	no	—
332	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
335	#36709	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂²×C₅₃	—	2	2	no	—
337	C₂²×C₅₃	—	2	2	no	—
338	C₂²×C₅₃	—	2	4	no	—
339	C₂²×C₅₃	—	2	4	no	—
340	C₂²×C₅₃	—	2	4	no	—
341	C₂²×C₅₃	—	2	4	no	—
342	C₂²×C₅₃	—	2	4	no	—
343	C₂²×C₅₃	—	2	4	no	—
344	C₂²×C₅₃	—	2	4	no	—
345	C₂²×C₅₃	—	2	4	no	—
346	C₂²×C₅₃	—	4	16	no	—
347	C₂²×C₅₃	—	4	2	no	—
348	C₂²×C₅₃	—	4	2	no	—
349	C₂²×C₅₃	—	4	4	no	—
350	C₂²×C₅₃	—	4	2	no	—
351	C₂²×C₅₃	—	4	2	no	—
352	C₂²×C₅₃	—	4	4	no	—
353	C₂²×C₅₃	—	4	2	no	—
354	C₂²×C₅₃	—	4	2	no	—
355	C₂²×C₅₃	—	4	2	no	—
356	C₂²×C₅₃	—	4	4	no	—
357	C₂²×C₅₃	—	4	4	no	—
358	C₂²×C₅₃	—	8	8	no	—
359	C₂²×C₅₃	#537	1	4	yes	—
360	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
361	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
363	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
364	C₂²×C₅₃	#585	1	2	yes	—
365	C₄×C₅₃	—	2	2	no	—
366	C₄×C₅₃	—	2	2	no	—
367	C₄×C₅₃	—	2	4	no	—
368	C₄×C₅₃	—	4	2	no	—
369	C₄×C₅₃	—	4	2	no	—
370	C₄×C₅₃	—	4	2	no	—
371	C₄×C₅₃	—	4	2	no	—
372	C₄×C₅₃	—	4	2	no	—
373	C₄×C₅₃	—	4	2	no	—
374	C₄×C₅₃	—	4	4	no	—
375	C₄×C₅₃	—	4	4	no	—
376	C₂×#538	C₂×C₅₃	1	1	yes	characteristic, complemented
377	C₂²×#123	C₂×C₅₃	1	1	yes	characteristic, complemented
378	#2848	C₂×C₅₃	1	1	yes	characteristic, complemented
379	#2847	C₂×C₅₃	1	1	yes	characteristic, complemented
380	#2695	C₂×C₅₃	1	4	yes	complemented
381	#2693	C₂×C₅₃	1	4	yes	complemented
382	#2672	C₂×C₅₃	1	4	yes	complemented
383	#2671	C₂×C₅₃	1	4	yes	complemented
384	#2627	C₂×C₅₃	1	1	yes	characteristic, complemented
385	#2618	C₂×C₅₃	1	1	yes	characteristic, complemented
386	#2534	C₂×C₅₃	1	2	yes	complemented
387	#2487	C₂×C₅₃	1	2	yes	complemented
388	#2412	C₂×C₅₃	1	2	yes	complemented
389	#2410	C₂×C₅₃	1	2	yes	complemented
390	#2315	C₂×C₅₃	1	1	yes	characteristic, complemented
391	C₂×C₅₃	—	2	4	no	—
392	C₂×C₅₃	—	4	4	no	—
393	C₂×C₅₃	—	4	4	no	—
394	C₂×C₅₃	—	8	2	no	—
395	C₂×C₅₃	C₂×#537	1	1	yes	characteristic
396	C₂×C₅₃	#3484	1	1	yes	characteristic
397	C₂×C₅₃	#3485	1	1	yes	characteristic
398	C₂×C₅₃	#3534	1	2	yes	—
399	C₂×C₅₃	#3535	1	2	yes	—
400	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
401	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
402	#538	—	2	8	no	—
403	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
404	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
405	C₂×#123	—	2	8	no	—
406	C₂×#123	C₂²×C₅₃	1	4	yes	—
407	C₂×#123	C₂²×C₅₃	1	4	yes	—
408	C₂×#123	C₂²×C₅₃	1	2	yes	—
409	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
410	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
411	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
412	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
413	C₂×#121	C₂²×C₅₃	1	4	yes	—
414	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
415	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
416	C₂×#120	C₂²×C₅₃	1	2	yes	—
417	C₂×#120	C₂²×C₅₃	1	2	yes	—
418	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
419	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
420	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
421	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
422	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
423	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
424	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
425	#400	C₂²×C₅₃	1	2	yes	complemented
426	#400	C₂²×C₅₃	1	4	yes	complemented
427	#399	C₂²×C₅₃	1	4	yes	complemented
428	#398	C₂²×C₅₃	1	2	yes	complemented
429	#398	C₂²×C₅₃	1	4	yes	complemented
430	#397	C₂²×C₅₃	1	4	yes	complemented
431	#396	C₂²×C₅₃	1	4	yes	complemented
432	#396	C₂²×C₅₃	1	4	yes	complemented
433	#395	C₂²×C₅₃	1	2	yes	complemented
434	#394	C₂²×C₅₃	1	4	yes	—
435	#394	C₂²×C₅₃	1	2	yes	complemented
436	#394	C₂²×C₅₃	1	4	yes	complemented
437	#394	C₂²×C₅₃	1	4	yes	complemented
438	#392	C₂²×C₅₃	1	4	yes	—
439	#389	C₂²×C₅₃	1	4	yes	complemented
440	#388	C₂²×C₅₃	1	4	yes	complemented
441	#386	C₂²×C₅₃	1	2	yes	—
442	#386	C₂²×C₅₃	1	2	yes	—
443	#386	C₂²×C₅₃	1	4	yes	—
444	#386	C₂²×C₅₃	1	4	yes	complemented
445	#386	C₂²×C₅₃	1	4	yes	complemented
446	#386	C₂²×C₅₃	1	4	yes	complemented
447	#385	C₂²×C₅₃	1	2	yes	—
448	#385	C₂²×C₅₃	1	2	yes	—
449	#385	C₂²×C₅₃	1	4	yes	complemented
450	#385	C₂²×C₅₃	1	4	yes	complemented
451	#385	C₂²×C₅₃	1	4	yes	complemented
452	#381	C₂²×C₅₃	1	2	yes	—
453	#380	C₂²×C₅₃	1	1	yes	characteristic
454	#380	C₂²×C₅₃	1	1	yes	characteristic
455	#380	C₂²×C₅₃	1	2	yes	—
456	#380	C₂²×C₅₃	1	2	yes	complemented
457	#380	C₂²×C₅₃	1	2	yes	complemented
458	#380	C₂²×C₅₃	1	4	yes	complemented
459	#380	C₂²×C₅₃	1	4	yes	complemented
460	#379	C₂²×C₅₃	1	2	yes	—
461	C₅₃	#36709	1	1	yes	characteristic, direct product factor, Sylow
462	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
463	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
464	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
465	C₂²×D₄	—	2	4	no	—
466	C₂²×D₄	—	4	4	no	—
467	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
468	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
469	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
470	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
471	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
472	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
473	C₂³×C₄	—	2	4	no	—
474	C₂³×C₄	—	4	4	no	—
475	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
477	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
478	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
481	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
482	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
484	#126	—	2	8	no	—
485	#124	—	2	8	no	—
486	#123	—	2	16	no	—
487	#123	—	2	16	no	—
488	#123	—	2	8	no	—
489	#123	—	4	4	no	—
490	C₂²⋊Q₈	—	2	4	no	—
491	C₂²⋊Q₈	—	4	4	no	—
492	#121	—	2	4	no	—
493	#121	—	2	8	no	—
494	#121	—	4	8	no	—
495	#121	—	4	4	no	—
496	#120	—	2	8	no	—
497	#120	—	4	4	no	—
498	C₄×D₄	—	2	8	no	—
499	C₂×C₄⋊C₄	—	2	4	no	—
500	C₂×C₄⋊C₄	—	2	4	no	—
501	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
502	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
509	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
512	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
513	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
514	C₂×C₂²⋊C₄	—	2	4	no	—
515	C₂×C₂²⋊C₄	—	2	4	no	—
516	C₂×C₂²⋊C₄	—	4	4	no	—
517	C₂×C₂²⋊C₄	D₄×C₅₃	1	8	yes	complemented
518	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
536	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
537	#95	C₂³×C₅₃	1	2	yes	—
538	#95	C₂³×C₅₃	1	2	yes	—
539	#95	C₂³×C₅₃	1	4	yes	—
540	#95	C₂³×C₅₃	1	4	yes	—
541	#95	C₂³×C₅₃	1	4	yes	—
542	#95	C₂³×C₅₃	1	4	yes	—
543	#95	C₂³×C₅₃	1	4	yes	—
544	#95	C₂³×C₅₃	1	4	yes	—
545	#95	C₂³×C₅₃	1	4	yes	—
546	C₂⁴	—	2	2	no	—
547	C₂⁴	—	2	4	no	—
548	C₂⁴	—	2	2	no	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	2	no	—
552	C₂⁴	—	4	2	no	—
553	C₂⁴	—	4	2	no	—
554	C₂⁴	—	4	2	no	—
555	C₂⁴	C₂×D₄×C₅₃	1	4	yes	—
556	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
557	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
558	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
559	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
560	C₂×Q₈	—	2	2	no	—
561	C₂×Q₈	—	4	2	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	8	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	8	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	8	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	—	4	4	no	—
573	C₂×D₄	—	4	2	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂×D₄	—	4	4	no	—
577	C₂×D₄	—	4	16	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	4	no	—
595	C₂²×C₄	—	4	4	no	—
596	C₂²×C₄	—	4	4	no	—
597	C₂²×C₄	—	4	4	no	—
598	C₂²×C₄	—	4	16	no	—
599	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
600	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
601	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
603	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
606	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	8	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	—	4	4	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	4	no	—
623	C₄⋊C₄	—	4	4	no	—
624	C₄⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	2	8	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	8	no	—
632	C₂²⋊C₄	—	2	8	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	4	4	no	—
636	C₂²⋊C₄	—	4	4	no	—
637	C₂²⋊C₄	—	4	4	no	—
638	C₂²⋊C₄	—	4	4	no	—
639	C₂²⋊C₄	—	4	4	no	—
640	C₂²⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	C₂×D₄×C₅₃	1	8	yes	—
642	C₂²⋊C₄	C₂×D₄×C₅₃	1	8	yes	—
643	C₄²	—	2	4	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	8	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	8	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	4	no	—
663	C₂³	—	4	4	no	—
664	C₂³	—	4	4	no	—
665	C₂³	—	4	8	no	—
666	C₂³	—	4	8	no	—
667	C₂³	—	4	4	no	—
668	C₂³	—	4	4	no	—
669	C₂³	—	8	4	no	—
670	C₂³	—	8	4	no	—
671	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
672	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
673	C₂³	H(5,𝔽₂)×C₅₃	1	4	yes	—
674	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
675	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
676	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
677	Q₈	—	8	2	no	—
678	D₄	—	4	16	no	—
679	D₄	—	4	8	no	—
680	D₄	—	8	2	no	—
681	D₄	—	8	4	no	—
682	D₄	—	8	4	no	—
683	D₄	—	8	8	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	4	4	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	8	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	—	8	4	no	—
716	C₂×C₄	—	8	8	no	—
717	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
718	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	4	16	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	4	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	4	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	4	no	—
742	C₂²	—	8	8	no	—
743	C₂²	C₅₃×#537	1	4	yes	—
744	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
745	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
746	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
747	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
748	C₂²	C₅₃×#585	1	2	yes	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	4	no	—
759	C₄	—	4	4	no	—
760	C₂	—	2	4	no	—
761	C₂	—	4	4	no	—
762	C₂	—	4	4	no	—
763	C₂	—	8	2	no	—
764	C₂	C₂×C₅₃×#537	1	1	yes	characteristic
765	C₂	C₅₃×#3484	1	1	yes	characteristic
766	C₂	C₅₃×#3485	1	1	yes	characteristic
767	C₂	C₅₃×#3534	1	2	yes	—
768	C₂	C₅₃×#3535	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#538	C₂	semidirect
2. C₂²×#123×C₅₃	C₂	semidirect
3. C₅₃×#2848	C₂	semidirect
4. C₅₃×#2847	C₂	semidirect
5. C₅₃×#2695	C₂	semidirect
6. C₅₃×#2693	C₂	semidirect
7. C₅₃×#2672	C₂	semidirect
8. C₅₃×#2671	C₂	semidirect
9. C₅₃×#2627	C₂	semidirect
10. C₅₃×#2618	C₂	semidirect
11. C₅₃×#2534	C₂	semidirect
12. C₅₃×#2487	C₂	semidirect
13. C₅₃×#2412	C₂	semidirect
14. C₅₃×#2410	C₂	semidirect
15. C₅₃×#2315	C₂	semidirect
19. C₂×#126×C₅₃	C₂²	semidirect
20. C₂×#124×C₅₃	C₂²	semidirect
25. C₂×#123×C₅₃	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
30. C₂×#121×C₅₃	C₂²	semidirect
31. C₂×#121×C₅₃	C₂²	semidirect
41. C₅₃×#400	C₂²	semidirect
42. C₅₃×#400	C₂²	semidirect
43. C₅₃×#399	C₂²	semidirect
44. C₅₃×#398	C₂²	semidirect
45. C₅₃×#398	C₂²	semidirect
46. C₅₃×#397	C₂²	semidirect
47. C₅₃×#396	C₂²	semidirect
48. C₅₃×#396	C₂²	semidirect
49. C₅₃×#395	C₂²	semidirect
51. C₅₃×#394	C₂²	semidirect
52. C₅₃×#394	C₂²	semidirect
53. C₅₃×#394	C₂²	semidirect
55. C₅₃×#389	C₂²	semidirect
56. C₅₃×#388	C₂²	semidirect
60. C₅₃×#386	C₂²	semidirect
61. C₅₃×#386	C₂²	semidirect
62. C₅₃×#386	C₂²	semidirect
65. C₅₃×#385	C₂²	semidirect
66. C₅₃×#385	C₂²	semidirect
67. C₅₃×#385	C₂²	semidirect
72. C₅₃×#380	C₂²	semidirect
73. C₅₃×#380	C₂²	semidirect
74. C₅₃×#380	C₂²	semidirect
75. C₅₃×#380	C₂²	semidirect
132. C₂×C₂²⋊C₄×C₅₃	D₄	semidirect
335. #36709	C₅₃	direct (N × H)
376. C₂×#538	C₂×C₅₃	semidirect
377. C₂²×#123	C₂×C₅₃	semidirect
378. #2848	C₂×C₅₃	semidirect
379. #2847	C₂×C₅₃	semidirect
380. #2695	C₂×C₅₃	semidirect
381. #2693	C₂×C₅₃	semidirect
382. #2672	C₂×C₅₃	semidirect
383. #2671	C₂×C₅₃	semidirect
384. #2627	C₂×C₅₃	semidirect
385. #2618	C₂×C₅₃	semidirect
386. #2534	C₂×C₅₃	semidirect
387. #2487	C₂×C₅₃	semidirect
388. #2412	C₂×C₅₃	semidirect
389. #2410	C₂×C₅₃	semidirect
390. #2315	C₂×C₅₃	semidirect
403. C₂×#126	C₂²×C₅₃	semidirect
404. C₂×#124	C₂²×C₅₃	semidirect
409. C₂×#123	C₂²×C₅₃	semidirect
411. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
414. C₂×#121	C₂²×C₅₃	semidirect
415. C₂×#121	C₂²×C₅₃	semidirect
425. #400	C₂²×C₅₃	semidirect
426. #400	C₂²×C₅₃	semidirect
427. #399	C₂²×C₅₃	semidirect
428. #398	C₂²×C₅₃	semidirect
429. #398	C₂²×C₅₃	semidirect
430. #397	C₂²×C₅₃	semidirect
431. #396	C₂²×C₅₃	semidirect
432. #396	C₂²×C₅₃	semidirect
433. #395	C₂²×C₅₃	semidirect
435. #394	C₂²×C₅₃	semidirect
436. #394	C₂²×C₅₃	semidirect
437. #394	C₂²×C₅₃	semidirect
439. #389	C₂²×C₅₃	semidirect
440. #388	C₂²×C₅₃	semidirect
444. #386	C₂²×C₅₃	semidirect
445. #386	C₂²×C₅₃	semidirect
446. #386	C₂²×C₅₃	semidirect
449. #385	C₂²×C₅₃	semidirect
450. #385	C₂²×C₅₃	semidirect
451. #385	C₂²×C₅₃	semidirect
456. #380	C₂²×C₅₃	semidirect
457. #380	C₂²×C₅₃	semidirect
458. #380	C₂²×C₅₃	semidirect
459. #380	C₂²×C₅₃	semidirect
461. C₅₃	#36709	direct (N × H)
517. C₂×C₂²⋊C₄	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×#538	2
C₂²×#123×C₅₃	2
C₅₃×#2848	2
C₅₃×#2847	2
C₅₃×#2695	2
C₅₃×#2693	2
C₅₃×#2672	2
C₅₃×#2671	2
C₅₃×#2627	2
C₅₃×#2618	2
C₅₃×#2534	2
C₅₃×#2487	2
C₅₃×#2412	2
C₅₃×#2410	2
C₅₃×#2315	2
#36709	53

Subgroups — C53×#36709 #27244221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36709 #27244221