Subgroups — C₅₃×#34877 #27242389

Order 13568.

2646 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2611	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2610	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2601	C₂	1	4	yes	maximal, complemented
6	C₅₃×#2591	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2583	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2561	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2539	C₂	1	1	yes	maximal, characteristic
10	C₅₃×#2413	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2411	C₂	1	2	yes	maximal, complemented
12	C₅₃×#2396	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2392	C₂	1	2	yes	maximal, complemented
14	C₄×#123×C₅₃	C₂	1	2	yes	maximal, complemented
15	C₄×#120×C₅₃	C₂	1	2	yes	maximal, complemented
16	C₅₃×#2293	C₂	1	4	yes	maximal, complemented
17	C₄×#117×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
19	C₅₃×#529	—	2	8	no	—
20	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
21	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×#123×C₅₃	C₂²	1	2	yes	—
24	C₂×#123×C₅₃	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#120×C₅₃	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#117×C₅₃	—	2	8	no	—
33	C₂×#117×C₅₃	C₂²	1	2	yes	—
34	C₂×#117×C₅₃	C₂²	1	2	yes	—
35	C₂×#117×C₅₃	C₂²	1	2	yes	—
36	C₂×#117×C₅₃	C₂²	1	2	yes	—
37	C₂×#117×C₅₃	C₂²	1	2	yes	—
38	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
39	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#400	C₂²	1	2	yes	complemented
46	C₅₃×#399	C₂²	1	2	yes	—
47	C₅₃×#398	C₂²	1	2	yes	complemented
48	C₅₃×#398	C₂²	1	4	yes	complemented
49	C₅₃×#397	C₂²	1	2	yes	—
50	C₅₃×#396	C₂²	1	4	yes	—
51	C₅₃×#396	C₂²	1	4	yes	complemented
52	C₅₃×#395	C₂²	1	2	yes	complemented
53	C₅₃×#394	C₂²	1	4	yes	—
54	C₅₃×#394	C₂²	1	2	yes	complemented
55	C₅₃×#393	C₂²	1	2	yes	—
56	C₅₃×#392	C₂²	1	2	yes	—
57	C₅₃×#390	C₂²	1	4	yes	—
58	C₅₃×#390	C₂²	1	4	yes	—
59	C₅₃×#389	C₂²	1	4	yes	complemented
60	C₅₃×#389	C₂²	1	4	yes	complemented
61	C₅₃×#388	C₂²	1	4	yes	—
62	C₅₃×#388	C₂²	1	4	yes	—
63	C₅₃×#388	C₂²	1	4	yes	complemented
64	C₅₃×#388	C₂²	1	4	yes	complemented
65	C₅₃×#388	C₂²	1	4	yes	complemented
66	C₅₃×#387	C₂²	1	4	yes	complemented
67	C₅₃×#386	C₂²	1	2	yes	—
68	C₅₃×#386	C₂²	1	4	yes	—
69	C₅₃×#386	C₂²	1	2	yes	—
70	C₅₃×#385	C₂²	1	2	yes	—
71	C₅₃×#385	C₂²	1	4	yes	—
72	C₅₃×#385	C₂²	1	2	yes	—
73	C₅₃×#381	C₂²	1	2	yes	—
74	C₅₃×#379	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
76	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
77	C₄×C₄⋊C₄×C₅₃	C₂²	1	4	yes	complemented
78	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
79	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	—
82	C₄×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	complemented
83	C₅₃×#376	C₂²	1	2	yes	complemented
84	C₄³×C₅₃	C₂²	1	2	yes	complemented
85	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
89	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₅₃	—	2	4	no	—
91	C₂³×C₄×C₅₃	—	2	8	no	—
92	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
96	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
99	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
101	#126×C₅₃	—	2	8	no	—
102	#125×C₅₃	—	2	4	no	—
103	#124×C₅₃	—	2	4	no	—
104	#123×C₅₃	—	2	8	no	—
105	#123×C₅₃	—	2	8	no	—
106	C₂²⋊Q₈×C₅₃	—	2	4	no	—
107	#121×C₅₃	—	2	4	no	—
108	#120×C₅₃	—	2	8	no	—
109	C₄×Q₈×C₅₃	—	2	4	no	—
110	C₄×D₄×C₅₃	—	2	4	no	—
111	C₄×D₄×C₅₃	—	2	8	no	—
112	C₄×D₄×C₅₃	—	2	16	no	—
113	#117×C₅₃	—	2	8	no	—
114	#117×C₅₃	—	2	8	no	—
115	#117×C₅₃	—	2	8	no	—
116	#117×C₅₃	—	2	8	no	—
117	#117×C₅₃	—	2	8	no	—
118	#117×C₅₃	—	2	8	no	—
119	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
120	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
121	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
136	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
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	2	yes	—
142	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	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	2	yes	—
149	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
154	C₂×C₄²×C₅₃	—	2	4	no	—
155	C₂×C₄²×C₅₃	D₄	1	8	yes	complemented
156	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
157	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
158	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
159	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
160	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
165	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
167	#95×C₅₃	C₂³	1	4	yes	—
168	#95×C₅₃	C₂³	1	2	yes	—
169	#95×C₅₃	C₂³	1	2	yes	—
170	#95×C₅₃	C₂³	1	4	yes	—
171	#95×C₅₃	C₂³	1	4	yes	—
172	#95×C₅₃	C₂³	1	4	yes	—
173	#95×C₅₃	C₂³	1	4	yes	—
174	#95×C₅₃	C₂³	1	4	yes	—
175	#95×C₅₃	C₂³	1	4	yes	—
176	C₂⁴×C₅₃	—	2	2	no	—
177	C₂⁴×C₅₃	—	2	4	no	—
178	C₂⁴×C₅₃	—	2	4	no	—
179	C₂⁴×C₅₃	—	4	2	no	—
180	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
181	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
182	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
183	C₂×Q₈×C₅₃	—	2	2	no	—
184	C₂×Q₈×C₅₃	—	4	2	no	—
185	C₂×D₄×C₅₃	—	2	4	no	—
186	C₂×D₄×C₅₃	—	2	8	no	—
187	C₂×D₄×C₅₃	—	2	4	no	—
188	C₂×D₄×C₅₃	—	2	4	no	—
189	C₂×D₄×C₅₃	—	2	2	no	—
190	C₂×D₄×C₅₃	—	2	8	no	—
191	C₂×D₄×C₅₃	—	4	2	no	—
192	C₂×D₄×C₅₃	—	4	4	no	—
193	C₂²×C₄×C₅₃	—	2	32	no	—
194	C₂²×C₄×C₅₃	—	2	2	no	—
195	C₂²×C₄×C₅₃	—	2	4	no	—
196	C₂²×C₄×C₅₃	—	2	4	no	—
197	C₂²×C₄×C₅₃	—	2	4	no	—
198	C₂²×C₄×C₅₃	—	2	4	no	—
199	C₂²×C₄×C₅₃	—	2	4	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	—	2	2	no	—
204	C₂²×C₄×C₅₃	—	2	2	no	—
205	C₂²×C₄×C₅₃	—	2	4	no	—
206	C₂²×C₄×C₅₃	—	2	4	no	—
207	C₂²×C₄×C₅₃	—	2	8	no	—
208	C₂²×C₄×C₅₃	—	4	2	no	—
209	C₂²×C₄×C₅₃	—	4	2	no	—
210	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₅₃	#41	1	8	yes	—
214	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
226	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	4	no	—
233	C₄⋊C₄×C₅₃	—	2	4	no	—
234	C₄⋊C₄×C₅₃	—	2	2	no	—
235	C₄⋊C₄×C₅₃	—	2	4	no	—
236	C₄⋊C₄×C₅₃	—	2	2	no	—
237	C₄⋊C₄×C₅₃	—	2	4	no	—
238	C₄⋊C₄×C₅₃	—	2	8	no	—
239	C₄⋊C₄×C₅₃	—	2	8	no	—
240	C₄⋊C₄×C₅₃	—	2	8	no	—
241	C₄⋊C₄×C₅₃	—	4	4	no	—
242	C₂²⋊C₄×C₅₃	—	2	4	no	—
243	C₂²⋊C₄×C₅₃	—	2	4	no	—
244	C₂²⋊C₄×C₅₃	—	2	8	no	—
245	C₂²⋊C₄×C₅₃	—	2	4	no	—
246	C₂²⋊C₄×C₅₃	—	2	4	no	—
247	C₂²⋊C₄×C₅₃	—	2	4	no	—
248	C₂²⋊C₄×C₅₃	—	2	4	no	—
249	C₂²⋊C₄×C₅₃	—	2	4	no	—
250	C₂²⋊C₄×C₅₃	—	2	4	no	—
251	C₂²⋊C₄×C₅₃	—	2	4	no	—
252	C₂²⋊C₄×C₅₃	—	2	4	no	—
253	C₂²⋊C₄×C₅₃	—	2	8	no	—
254	C₂²⋊C₄×C₅₃	—	2	8	no	—
255	C₂²⋊C₄×C₅₃	—	2	8	no	—
256	C₂²⋊C₄×C₅₃	—	4	4	no	—
257	C₂²⋊C₄×C₅₃	—	4	4	no	—
258	C₂²⋊C₄×C₅₃	#41	1	8	yes	—
259	C₄²×C₅₃	—	2	4	no	—
260	C₄²×C₅₃	—	2	4	no	—
261	C₄²×C₅₃	—	2	4	no	—
262	C₄²×C₅₃	—	2	8	no	—
263	C₄²×C₅₃	—	2	8	no	—
264	C₄²×C₅₃	—	4	2	no	—
265	C₄²×C₅₃	—	4	2	no	—
266	C₄²×C₅₃	C₂×D₄	1	4	yes	—
267	C₄²×C₅₃	C₂×D₄	1	4	yes	—
268	C₄²×C₅₃	C₂×D₄	1	4	yes	—
269	C₄²×C₅₃	C₂×D₄	1	4	yes	—
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	4	no	—
277	C₂³×C₅₃	—	2	2	no	—
278	C₂³×C₅₃	—	2	4	no	—
279	C₂³×C₅₃	—	2	2	no	—
280	C₂³×C₅₃	—	2	2	no	—
281	C₂³×C₅₃	—	2	4	no	—
282	C₂³×C₅₃	—	4	16	no	—
283	C₂³×C₅₃	—	4	4	no	—
284	C₂³×C₅₃	—	4	4	no	—
285	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
286	C₂³×C₅₃	C₂×#41	1	4	yes	—
287	C₂³×C₅₃	C₂×#41	1	4	yes	—
288	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
289	Q₈×C₅₃	—	4	4	no	—
290	D₄×C₅₃	—	4	16	no	—
291	D₄×C₅₃	—	4	4	no	—
292	D₄×C₅₃	—	4	8	no	—
293	C₂×C₄×C₅₃	—	2	16	no	—
294	C₂×C₄×C₅₃	—	2	8	no	—
295	C₂×C₄×C₅₃	—	2	8	no	—
296	C₂×C₄×C₅₃	—	2	2	no	—
297	C₂×C₄×C₅₃	—	2	2	no	—
298	C₂×C₄×C₅₃	—	2	2	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	4	no	—
305	C₂×C₄×C₅₃	—	2	8	no	—
306	C₂×C₄×C₅₃	—	2	16	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	2	no	—
312	C₂×C₄×C₅₃	—	2	4	no	—
313	C₂×C₄×C₅₃	—	2	4	no	—
314	C₂×C₄×C₅₃	—	2	2	no	—
315	C₂×C₄×C₅₃	—	2	2	no	—
316	C₂×C₄×C₅₃	—	2	4	no	—
317	C₂×C₄×C₅₃	—	2	4	no	—
318	C₂×C₄×C₅₃	—	2	4	no	—
319	C₂×C₄×C₅₃	—	2	4	no	—
320	C₂×C₄×C₅₃	—	2	4	no	—
321	C₂×C₄×C₅₃	—	4	4	no	—
322	C₂×C₄×C₅₃	—	4	4	no	—
323	C₂×C₄×C₅₃	—	4	4	no	—
324	C₂×C₄×C₅₃	—	4	8	no	—
325	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
332	C₂×C₄×C₅₃	C₂×#41	1	8	yes	—
333	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
334	#34877	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₂²×C₅₃	—	2	2	no	—
336	C₂²×C₅₃	—	2	2	no	—
337	C₂²×C₅₃	—	2	8	no	—
338	C₂²×C₅₃	—	2	4	no	—
339	C₂²×C₅₃	—	2	8	no	—
340	C₂²×C₅₃	—	4	16	no	—
341	C₂²×C₅₃	—	4	2	no	—
342	C₂²×C₅₃	—	4	2	no	—
343	C₂²×C₅₃	—	4	4	no	—
344	C₂²×C₅₃	—	4	2	no	—
345	C₂²×C₅₃	—	4	2	no	—
346	C₂²×C₅₃	—	4	2	no	—
347	C₂²×C₅₃	—	4	4	no	—
348	C₂²×C₅₃	—	4	4	no	—
349	C₂²×C₅₃	#532	1	4	yes	—
350	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
351	C₂²×C₅₃	C₂²×#41	1	2	yes	—
352	C₂²×C₅₃	C₂²×#41	1	2	yes	—
353	C₂²×C₅₃	#585	1	2	yes	—
354	C₄×C₅₃	—	2	2	no	—
355	C₄×C₅₃	—	2	4	no	—
356	C₄×C₅₃	—	2	2	no	—
357	C₄×C₅₃	—	2	2	no	—
358	C₄×C₅₃	—	2	2	no	—
359	C₄×C₅₃	—	2	2	no	—
360	C₄×C₅₃	—	2	8	no	—
361	C₄×C₅₃	—	4	2	no	—
362	C₄×C₅₃	—	4	2	no	—
363	C₄×C₅₃	—	4	2	no	—
364	C₄×C₅₃	—	4	2	no	—
365	C₄×C₅₃	—	4	2	no	—
366	C₄×C₅₃	—	4	4	no	—
367	C₄×C₅₃	#525	1	4	yes	—
368	C₂×#529	C₂×C₅₃	1	1	yes	characteristic, complemented
369	C₂²×#117	C₂×C₅₃	1	1	yes	characteristic, complemented
370	#2611	C₂×C₅₃	1	2	yes	complemented
371	#2610	C₂×C₅₃	1	2	yes	complemented
372	#2601	C₂×C₅₃	1	4	yes	complemented
373	#2591	C₂×C₅₃	1	1	yes	characteristic, complemented
374	#2583	C₂×C₅₃	1	1	yes	characteristic, complemented
375	#2561	C₂×C₅₃	1	1	yes	characteristic, complemented
376	#2539	C₂×C₅₃	1	1	yes	characteristic
377	#2413	C₂×C₅₃	1	2	yes	complemented
378	#2411	C₂×C₅₃	1	2	yes	complemented
379	#2396	C₂×C₅₃	1	2	yes	complemented
380	#2392	C₂×C₅₃	1	2	yes	complemented
381	C₄×#123	C₂×C₅₃	1	2	yes	complemented
382	C₄×#120	C₂×C₅₃	1	2	yes	complemented
383	#2293	C₂×C₅₃	1	4	yes	complemented
384	C₄×#117	C₂×C₅₃	1	1	yes	characteristic, complemented
385	C₂×C₅₃	—	2	4	no	—
386	C₂×C₅₃	—	4	4	no	—
387	C₂×C₅₃	—	8	2	no	—
388	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
389	C₂×C₅₃	C₂×#532	1	1	yes	characteristic
390	C₂×C₅₃	#3449	1	1	yes	characteristic
391	C₂×C₅₃	#3475	1	4	yes	—
392	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
393	#529	—	2	8	no	—
394	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
395	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
396	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
397	C₂×#123	C₂²×C₅₃	1	2	yes	—
398	C₂×#123	C₂²×C₅₃	1	2	yes	—
399	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
400	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
401	C₂×#120	C₂²×C₅₃	1	2	yes	—
402	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
403	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	—
404	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
405	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
406	C₂×#117	—	2	8	no	—
407	C₂×#117	C₂²×C₅₃	1	2	yes	—
408	C₂×#117	C₂²×C₅₃	1	2	yes	—
409	C₂×#117	C₂²×C₅₃	1	2	yes	—
410	C₂×#117	C₂²×C₅₃	1	2	yes	—
411	C₂×#117	C₂²×C₅₃	1	2	yes	—
412	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
413	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
414	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
415	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
416	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
417	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
418	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
419	#400	C₂²×C₅₃	1	2	yes	complemented
420	#399	C₂²×C₅₃	1	2	yes	—
421	#398	C₂²×C₅₃	1	2	yes	complemented
422	#398	C₂²×C₅₃	1	4	yes	complemented
423	#397	C₂²×C₅₃	1	2	yes	—
424	#396	C₂²×C₅₃	1	4	yes	—
425	#396	C₂²×C₅₃	1	4	yes	complemented
426	#395	C₂²×C₅₃	1	2	yes	complemented
427	#394	C₂²×C₅₃	1	4	yes	—
428	#394	C₂²×C₅₃	1	2	yes	complemented
429	#393	C₂²×C₅₃	1	2	yes	—
430	#392	C₂²×C₅₃	1	2	yes	—
431	#390	C₂²×C₅₃	1	4	yes	—
432	#390	C₂²×C₅₃	1	4	yes	—
433	#389	C₂²×C₅₃	1	4	yes	complemented
434	#389	C₂²×C₅₃	1	4	yes	complemented
435	#388	C₂²×C₅₃	1	4	yes	—
436	#388	C₂²×C₅₃	1	4	yes	—
437	#388	C₂²×C₅₃	1	4	yes	complemented
438	#388	C₂²×C₅₃	1	4	yes	complemented
439	#388	C₂²×C₅₃	1	4	yes	complemented
440	#387	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	#385	C₂²×C₅₃	1	2	yes	—
445	#385	C₂²×C₅₃	1	2	yes	—
446	#385	C₂²×C₅₃	1	4	yes	—
447	#381	C₂²×C₅₃	1	2	yes	—
448	#379	C₂²×C₅₃	1	2	yes	—
449	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
450	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
451	C₄×C₄⋊C₄	C₂²×C₅₃	1	4	yes	complemented
452	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
453	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
454	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	—
455	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
456	C₄×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	complemented
457	#376	C₂²×C₅₃	1	2	yes	complemented
458	C₄³	C₂²×C₅₃	1	2	yes	complemented
459	C₅₃	#34877	1	1	yes	characteristic, direct product factor, Sylow
460	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
461	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
462	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
463	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
464	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
465	C₂³×C₄	—	2	4	no	—
466	C₂³×C₄	—	2	8	no	—
467	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
470	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
471	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
474	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
476	#126	—	2	8	no	—
477	#125	—	2	4	no	—
478	#124	—	2	4	no	—
479	#123	—	2	8	no	—
480	#123	—	2	8	no	—
481	C₂²⋊Q₈	—	2	4	no	—
482	#121	—	2	4	no	—
483	#120	—	2	8	no	—
484	C₄×Q₈	—	2	4	no	—
485	C₄×D₄	—	2	8	no	—
486	C₄×D₄	—	2	16	no	—
487	C₄×D₄	—	2	4	no	—
488	#117	—	2	8	no	—
489	#117	—	2	8	no	—
490	#117	—	2	8	no	—
491	#117	—	2	8	no	—
492	#117	—	2	8	no	—
493	#117	—	2	8	no	—
494	C₂×C₄⋊C₄	—	2	4	no	—
495	C₂×C₄⋊C₄	—	2	4	no	—
496	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
501	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	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	4	yes	—
505	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
509	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
510	C₂×C₂²⋊C₄	—	2	4	no	—
511	C₂×C₂²⋊C₄	—	2	4	no	—
512	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
529	C₂×C₄²	—	2	4	no	—
530	C₂×C₄²	D₄×C₅₃	1	8	yes	complemented
531	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
532	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
533	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
534	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
535	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
536	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
537	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
538	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
542	#95	C₂³×C₅₃	1	4	yes	—
543	#95	C₂³×C₅₃	1	2	yes	—
544	#95	C₂³×C₅₃	1	2	yes	—
545	#95	C₂³×C₅₃	1	4	yes	—
546	#95	C₂³×C₅₃	1	4	yes	—
547	#95	C₂³×C₅₃	1	4	yes	—
548	#95	C₂³×C₅₃	1	4	yes	—
549	#95	C₂³×C₅₃	1	4	yes	—
550	#95	C₂³×C₅₃	1	4	yes	—
551	C₂⁴	—	2	2	no	—
552	C₂⁴	—	2	4	no	—
553	C₂⁴	—	2	4	no	—
554	C₂⁴	—	4	2	no	—
555	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
556	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
557	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	4	2	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	8	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	8	no	—
566	C₂×D₄	—	4	4	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂²×C₄	—	2	32	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	8	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
586	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
587	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
588	C₂²×C₄	#41×C₅₃	1	8	yes	—
589	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
590	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
601	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	8	no	—
614	C₄⋊C₄	—	2	8	no	—
615	C₄⋊C₄	—	2	8	no	—
616	C₄⋊C₄	—	4	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	8	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	8	no	—
629	C₂²⋊C₄	—	2	8	no	—
630	C₂²⋊C₄	—	2	8	no	—
631	C₂²⋊C₄	—	4	4	no	—
632	C₂²⋊C₄	—	4	4	no	—
633	C₂²⋊C₄	#41×C₅₃	1	8	yes	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	2	8	no	—
638	C₄²	—	2	8	no	—
639	C₄²	—	4	2	no	—
640	C₄²	—	4	2	no	—
641	C₄²	C₂×D₄×C₅₃	1	4	yes	—
642	C₄²	C₂×D₄×C₅₃	1	4	yes	—
643	C₄²	C₂×D₄×C₅₃	1	4	yes	—
644	C₄²	C₂×D₄×C₅₃	1	4	yes	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	8	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	4	no	—
657	C₂³	—	4	16	no	—
658	C₂³	—	4	4	no	—
659	C₂³	—	4	4	no	—
660	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
661	C₂³	C₂×#41×C₅₃	1	4	yes	—
662	C₂³	C₂×#41×C₅₃	1	4	yes	—
663	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
664	Q₈	—	4	4	no	—
665	D₄	—	4	16	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	8	no	—
668	C₂×C₄	—	2	16	no	—
669	C₂×C₄	—	2	8	no	—
670	C₂×C₄	—	2	8	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	8	no	—
681	C₂×C₄	—	2	16	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	4	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	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	8	no	—
700	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
704	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
705	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
706	C₂×C₄	C₂×#41×C₅₃	1	8	yes	—
707	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
708	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	8	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	8	no	—
713	C₂²	—	2	4	no	—
714	C₂²	—	4	16	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	4	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	4	no	—
720	C₂²	—	4	4	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	C₅₃×#532	1	4	yes	—
724	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
725	C₂²	C₂²×#41×C₅₃	1	2	yes	—
726	C₂²	C₂²×#41×C₅₃	1	2	yes	—
727	C₂²	C₅₃×#585	1	2	yes	—
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	8	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	4	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	4	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	C₅₃×#525	1	4	yes	—
742	C₂	—	2	4	no	—
743	C₂	—	4	4	no	—
744	C₂	—	8	2	no	—
745	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
746	C₂	C₂×C₅₃×#532	1	1	yes	characteristic
747	C₂	C₅₃×#3449	1	1	yes	characteristic
748	C₂	C₅₃×#3475	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
socle	C₂³×C₅₃	C₂⁵
prime radical	C₅₃×#2539	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#529	C₂	semidirect
2. C₂²×#117×C₅₃	C₂	semidirect
3. C₅₃×#2611	C₂	semidirect
4. C₅₃×#2610	C₂	semidirect
5. C₅₃×#2601	C₂	semidirect
6. C₅₃×#2591	C₂	semidirect
7. C₅₃×#2583	C₂	semidirect
8. C₅₃×#2561	C₂	semidirect
10. C₅₃×#2413	C₂	semidirect
11. C₅₃×#2411	C₂	semidirect
12. C₅₃×#2396	C₂	semidirect
13. C₅₃×#2392	C₂	semidirect
14. C₄×#123×C₅₃	C₂	semidirect
15. C₄×#120×C₅₃	C₂	semidirect
16. C₅₃×#2293	C₂	semidirect
17. C₄×#117×C₅₃	C₂	semidirect
20. C₂×#126×C₅₃	C₂²	semidirect
21. C₂×#125×C₅₃	C₂²	semidirect
22. C₂×#124×C₅₃	C₂²	semidirect
28. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
31. C₂×C₄×D₄×C₅₃	C₂²	semidirect
38. C₂×#117×C₅₃	C₂²	semidirect
45. C₅₃×#400	C₂²	semidirect
47. C₅₃×#398	C₂²	semidirect
48. C₅₃×#398	C₂²	semidirect
51. C₅₃×#396	C₂²	semidirect
52. C₅₃×#395	C₂²	semidirect
54. C₅₃×#394	C₂²	semidirect
59. C₅₃×#389	C₂²	semidirect
60. C₅₃×#389	C₂²	semidirect
63. C₅₃×#388	C₂²	semidirect
64. C₅₃×#388	C₂²	semidirect
65. C₅₃×#388	C₂²	semidirect
66. C₅₃×#387	C₂²	semidirect
75. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
76. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
77. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
82. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
83. C₅₃×#376	C₂²	semidirect
84. C₄³×C₅₃	C₂²	semidirect
155. C₂×C₄²×C₅₃	D₄	semidirect
334. #34877	C₅₃	direct (N × H)
368. C₂×#529	C₂×C₅₃	semidirect
369. C₂²×#117	C₂×C₅₃	semidirect
370. #2611	C₂×C₅₃	semidirect
371. #2610	C₂×C₅₃	semidirect
372. #2601	C₂×C₅₃	semidirect
373. #2591	C₂×C₅₃	semidirect
374. #2583	C₂×C₅₃	semidirect
375. #2561	C₂×C₅₃	semidirect
377. #2413	C₂×C₅₃	semidirect
378. #2411	C₂×C₅₃	semidirect
379. #2396	C₂×C₅₃	semidirect
380. #2392	C₂×C₅₃	semidirect
381. C₄×#123	C₂×C₅₃	semidirect
382. C₄×#120	C₂×C₅₃	semidirect
383. #2293	C₂×C₅₃	semidirect
384. C₄×#117	C₂×C₅₃	semidirect
394. C₂×#126	C₂²×C₅₃	semidirect
395. C₂×#125	C₂²×C₅₃	semidirect
396. C₂×#124	C₂²×C₅₃	semidirect
402. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
405. C₂×C₄×D₄	C₂²×C₅₃	semidirect
412. C₂×#117	C₂²×C₅₃	semidirect
419. #400	C₂²×C₅₃	semidirect
421. #398	C₂²×C₅₃	semidirect
422. #398	C₂²×C₅₃	semidirect
425. #396	C₂²×C₅₃	semidirect
426. #395	C₂²×C₅₃	semidirect
428. #394	C₂²×C₅₃	semidirect
433. #389	C₂²×C₅₃	semidirect
434. #389	C₂²×C₅₃	semidirect
437. #388	C₂²×C₅₃	semidirect
438. #388	C₂²×C₅₃	semidirect
439. #388	C₂²×C₅₃	semidirect
440. #387	C₂²×C₅₃	semidirect
449. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
450. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
451. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
456. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
457. #376	C₂²×C₅₃	semidirect
458. C₄³	C₂²×C₅₃	semidirect
459. C₅₃	#34877	direct (N × H)
530. C₂×C₄²	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×#529	2
C₂²×#117×C₅₃	2
C₅₃×#2611	2
C₅₃×#2610	2
C₅₃×#2601	2
C₅₃×#2591	2
C₅₃×#2583	2
C₅₃×#2561	2
C₅₃×#2539	2
C₅₃×#2413	2
C₅₃×#2411	2
C₅₃×#2396	2
C₅₃×#2392	2
C₄×#123×C₅₃	2
C₄×#120×C₅₃	2
C₅₃×#2293	2
C₄×#117×C₅₃	2
#34877	53

Subgroups — C53×#34877 #27242389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34877 #27242389