Subgroups — C₅₃×#34736 #27242248

Order 13568.

5758 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#525	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2409	C₂	1	2	yes	maximal, complemented
5	C₅₃×#2408	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2407	C₂	1	4	yes	maximal, complemented
7	C₅₃×#2406	C₂	1	2	yes	maximal, complemented
8	C₅₃×#2405	C₂	1	2	yes	maximal, complemented
9	C₅₃×#2404	C₂	1	2	yes	maximal, complemented
10	C₅₃×#2403	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2388	C₂	1	4	yes	maximal, complemented
12	C₄×#120×C₅₃	C₂	1	4	yes	maximal, complemented
13	C₅₃×#2297	C₂	1	2	yes	maximal, complemented
14	C₅₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₅₃	—	2	16	no	—
16	C₂²×#41×C₅₃	—	2	8	no	—
17	C₂²×#41×C₅₃	C₂²	1	2	yes	—
18	C₂²×#41×C₅₃	C₂²	1	2	yes	—
19	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
20	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
21	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂³×D₄×C₅₃	C₂²	1	2	yes	—
23	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
24	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
25	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₅₃	C₂²	1	2	yes	complemented
27	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₅₃×#525	—	2	16	no	—
29	C₂×#123×C₅₃	C₂²	1	4	yes	complemented
30	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	complemented
31	C₂×#121×C₅₃	C₂²	1	4	yes	complemented
32	C₂×#120×C₅₃	C₂²	1	4	yes	—
33	C₂×#120×C₅₃	C₂²	1	4	yes	complemented
34	C₂×C₄×D₄×C₅₃	—	2	8	no	—
35	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₅₃	C₂²	1	8	yes	complemented
38	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
39	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
40	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
41	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#395	C₂²	1	4	yes	complemented
46	C₅₃×#394	C₂²	1	8	yes	complemented
47	C₅₃×#394	C₂²	1	4	yes	complemented
48	C₅₃×#393	C₂²	1	4	yes	complemented
49	C₅₃×#392	C₂²	1	8	yes	complemented
50	C₅₃×#392	C₂²	1	4	yes	complemented
51	C₅₃×#391	C₂²	1	4	yes	complemented
52	C₅₃×#390	C₂²	1	4	yes	complemented
53	C₅₃×#386	C₂²	1	4	yes	—
54	C₅₃×#386	C₂²	1	4	yes	complemented
55	C₅₃×#386	C₂²	1	4	yes	complemented
56	C₅₃×#386	C₂²	1	8	yes	complemented
57	C₅₃×#385	C₂²	1	4	yes	complemented
58	C₅₃×#385	C₂²	1	8	yes	complemented
59	C₅₃×#381	C₂²	1	2	yes	complemented
60	C₅₃×#380	C₂²	1	2	yes	complemented
61	C₅₃×#380	C₂²	1	2	yes	complemented
62	C₅₃×#379	C₂²	1	2	yes	—
63	C₅₃×#379	C₂²	1	4	yes	complemented
64	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊C₄×C₅₃	C₂²	1	8	yes	complemented
67	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
68	C₂⁵×C₅₃	C₂³	1	2	yes	—
69	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
70	C₂×#41×C₅₃	—	2	128	no	—
71	C₂×#41×C₅₃	—	2	8	no	—
72	C₂×#41×C₅₃	—	2	16	no	—
73	C₂×#41×C₅₃	—	2	8	no	—
74	C₂×#41×C₅₃	—	2	8	no	—
75	C₂×#41×C₅₃	—	2	8	no	—
76	C₂×#41×C₅₃	—	2	8	no	—
77	C₂×#41×C₅₃	—	2	8	no	—
78	C₂×#41×C₅₃	—	2	8	no	—
79	C₂×#41×C₅₃	—	2	16	no	—
80	C₂×#41×C₅₃	D₄	1	16	yes	complemented
81	C₂²×Q₈×C₅₃	—	2	8	no	—
82	C₂²×Q₈×C₅₃	—	2	4	no	—
83	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
84	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
85	C₂²×D₄×C₅₃	—	2	4	no	—
86	C₂²×D₄×C₅₃	—	2	8	no	—
87	C₂²×D₄×C₅₃	—	2	16	no	—
88	C₂²×D₄×C₅₃	—	2	8	no	—
89	C₂²×D₄×C₅₃	—	2	8	no	—
90	C₂²×D₄×C₅₃	—	2	4	no	—
91	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
92	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
93	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₅₃	C₂³	1	8	yes	—
95	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
96	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
98	C₂³×C₄×C₅₃	—	2	8	no	—
99	C₂³×C₄×C₅₃	—	2	8	no	—
100	C₂³×C₄×C₅₃	—	2	16	no	—
101	C₂³×C₄×C₅₃	—	2	4	no	—
102	C₂³×C₄×C₅₃	—	2	8	no	—
103	C₂³×C₄×C₅₃	D₄	1	8	yes	complemented
104	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
107	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
108	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
109	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
116	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
118	#123×C₅₃	—	2	16	no	—
119	C₂²⋊Q₈×C₅₃	—	2	16	no	—
120	#121×C₅₃	—	2	16	no	—
121	#120×C₅₃	—	2	16	no	—
122	#120×C₅₃	—	2	16	no	—
123	C₄×D₄×C₅₃	—	2	8	no	—
124	C₄×D₄×C₅₃	—	2	8	no	—
125	C₄×D₄×C₅₃	—	2	8	no	—
126	C₄×D₄×C₅₃	—	2	8	no	—
127	C₄×D₄×C₅₃	—	2	32	no	—
128	#117×C₅₃	—	2	8	no	—
129	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
130	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	—
134	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
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	4	yes	—
141	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
142	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
143	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
145	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
147	C₂×C₄²×C₅₃	—	2	4	no	—
148	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
149	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
150	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
151	#95×C₅₃	C₂³	1	4	yes	—
152	#95×C₅₃	C₂³	1	4	yes	—
153	#95×C₅₃	C₂³	1	8	yes	—
154	#95×C₅₃	C₂³	1	8	yes	—
155	C₂⁴×C₅₃	—	2	2	no	—
156	C₂⁴×C₅₃	—	2	8	no	—
157	C₂⁴×C₅₃	—	2	4	no	—
158	C₂⁴×C₅₃	—	2	4	no	—
159	C₂⁴×C₅₃	—	2	4	no	—
160	C₂⁴×C₅₃	—	2	4	no	—
161	C₂⁴×C₅₃	—	2	4	no	—
162	C₂⁴×C₅₃	—	2	8	no	—
163	C₂⁴×C₅₃	—	4	2	no	—
164	C₂⁴×C₅₃	—	4	2	no	—
165	C₂⁴×C₅₃	—	4	4	no	—
166	C₂⁴×C₅₃	C₂×D₄	1	4	yes	—
167	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
168	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
169	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
170	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
171	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
172	#41×C₅₃	—	2	64	no	—
173	#41×C₅₃	—	2	64	no	—
174	#41×C₅₃	—	2	64	no	—
175	#41×C₅₃	—	2	64	no	—
176	C₂×Q₈×C₅₃	—	2	32	no	—
177	C₂×Q₈×C₅₃	—	2	8	no	—
178	C₂×Q₈×C₅₃	—	2	4	no	—
179	C₂×Q₈×C₅₃	—	2	4	no	—
180	C₂×Q₈×C₅₃	—	2	4	no	—
181	C₂×Q₈×C₅₃	C₂×D₄	1	8	yes	complemented
182	C₂×D₄×C₅₃	—	2	32	no	—
183	C₂×D₄×C₅₃	—	2	64	no	—
184	C₂×D₄×C₅₃	—	2	32	no	—
185	C₂×D₄×C₅₃	—	2	4	no	—
186	C₂×D₄×C₅₃	—	2	4	no	—
187	C₂×D₄×C₅₃	—	2	8	no	—
188	C₂×D₄×C₅₃	—	2	8	no	—
189	C₂×D₄×C₅₃	—	2	8	no	—
190	C₂×D₄×C₅₃	—	2	8	no	—
191	C₂×D₄×C₅₃	—	2	8	no	—
192	C₂×D₄×C₅₃	—	2	4	no	—
193	C₂×D₄×C₅₃	—	2	4	no	—
194	C₂×D₄×C₅₃	—	2	16	no	—
195	C₂×D₄×C₅₃	—	2	16	no	—
196	C₂×D₄×C₅₃	—	2	8	no	—
197	C₂×D₄×C₅₃	—	2	4	no	—
198	C₂×D₄×C₅₃	—	2	4	no	—
199	C₂×D₄×C₅₃	—	2	4	no	—
200	C₂×D₄×C₅₃	—	2	4	no	—
201	C₂×D₄×C₅₃	—	4	8	no	—
202	C₂×D₄×C₅₃	C₂×D₄	1	16	yes	—
203	C₂×D₄×C₅₃	C₂×D₄	1	8	yes	complemented
204	C₂×D₄×C₅₃	#41	1	8	yes	complemented
205	C₂²×C₄×C₅₃	—	2	64	no	—
206	C₂²×C₄×C₅₃	—	2	2	no	—
207	C₂²×C₄×C₅₃	—	2	4	no	—
208	C₂²×C₄×C₅₃	—	2	8	no	—
209	C₂²×C₄×C₅₃	—	2	4	no	—
210	C₂²×C₄×C₅₃	—	2	32	no	—
211	C₂²×C₄×C₅₃	—	2	4	no	—
212	C₂²×C₄×C₅₃	—	2	8	no	—
213	C₂²×C₄×C₅₃	—	2	4	no	—
214	C₂²×C₄×C₅₃	—	2	8	no	—
215	C₂²×C₄×C₅₃	—	2	8	no	—
216	C₂²×C₄×C₅₃	—	2	4	no	—
217	C₂²×C₄×C₅₃	—	2	4	no	—
218	C₂²×C₄×C₅₃	—	2	8	no	—
219	C₂²×C₄×C₅₃	—	2	8	no	—
220	C₂²×C₄×C₅₃	—	2	4	no	—
221	C₂²×C₄×C₅₃	—	2	2	no	—
222	C₂²×C₄×C₅₃	—	2	2	no	—
223	C₂²×C₄×C₅₃	—	2	4	no	—
224	C₂²×C₄×C₅₃	—	2	4	no	—
225	C₂²×C₄×C₅₃	—	2	8	no	—
226	C₂²×C₄×C₅₃	—	2	4	no	—
227	C₂²×C₄×C₅₃	—	2	8	no	—
228	C₂²×C₄×C₅₃	—	4	2	no	—
229	C₂²×C₄×C₅₃	—	4	16	no	—
230	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
231	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
233	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
234	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
235	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
236	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	—
237	C₂²×C₄×C₅₃	C₂×D₄	1	16	yes	complemented
238	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
240	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
247	C₄⋊C₄×C₅₃	—	2	4	no	—
248	C₄⋊C₄×C₅₃	—	2	4	no	—
249	C₄⋊C₄×C₅₃	—	2	8	no	—
250	C₄⋊C₄×C₅₃	—	2	16	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	16	no	—
255	C₂²⋊C₄×C₅₃	—	2	8	no	—
256	C₂²⋊C₄×C₅₃	—	2	4	no	—
257	C₂²⋊C₄×C₅₃	—	2	4	no	—
258	C₂²⋊C₄×C₅₃	—	2	16	no	—
259	C₂²⋊C₄×C₅₃	—	2	16	no	—
260	C₂²⋊C₄×C₅₃	—	4	8	no	—
261	C₂²⋊C₄×C₅₃	—	4	4	no	—
262	C₄²×C₅₃	—	2	4	no	—
263	C₄²×C₅₃	—	2	4	no	—
264	C₄²×C₅₃	—	2	8	no	—
265	C₂³×C₅₃	—	2	2	no	—
266	C₂³×C₅₃	—	2	2	no	—
267	C₂³×C₅₃	—	2	2	no	—
268	C₂³×C₅₃	—	2	2	no	—
269	C₂³×C₅₃	—	2	16	no	—
270	C₂³×C₅₃	—	2	8	no	—
271	C₂³×C₅₃	—	2	8	no	—
272	C₂³×C₅₃	—	2	8	no	—
273	C₂³×C₅₃	—	2	4	no	—
274	C₂³×C₅₃	—	2	4	no	—
275	C₂³×C₅₃	—	2	2	no	—
276	C₂³×C₅₃	—	2	2	no	—
277	C₂³×C₅₃	—	2	4	no	—
278	C₂³×C₅₃	—	2	2	no	—
279	C₂³×C₅₃	—	2	2	no	—
280	C₂³×C₅₃	—	2	8	no	—
281	C₂³×C₅₃	—	2	4	no	—
282	C₂³×C₅₃	—	2	8	no	—
283	C₂³×C₅₃	—	2	2	no	—
284	C₂³×C₅₃	—	4	4	no	—
285	C₂³×C₅₃	—	4	16	no	—
286	C₂³×C₅₃	—	4	32	no	—
287	C₂³×C₅₃	—	4	16	no	—
288	C₂³×C₅₃	—	4	4	no	—
289	C₂³×C₅₃	—	4	8	no	—
290	C₂³×C₅₃	—	4	4	no	—
291	C₂³×C₅₃	—	4	8	no	—
292	C₂³×C₅₃	C₂²×D₄	1	8	yes	—
293	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
294	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
295	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
296	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
297	C₂³×C₅₃	C₂×#41	1	4	yes	—
298	C₂³×C₅₃	C₂×#41	1	4	yes	complemented
299	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
300	Q₈×C₅₃	—	2	16	no	—
301	Q₈×C₅₃	—	2	16	no	—
302	D₄×C₅₃	—	2	16	no	—
303	D₄×C₅₃	—	2	32	no	—
304	D₄×C₅₃	—	2	16	no	—
305	D₄×C₅₃	—	2	32	no	—
306	D₄×C₅₃	—	2	16	no	—
307	D₄×C₅₃	—	2	16	no	—
308	D₄×C₅₃	—	4	32	no	—
309	C₂×C₄×C₅₃	—	2	16	no	—
310	C₂×C₄×C₅₃	—	2	32	no	—
311	C₂×C₄×C₅₃	—	2	8	no	—
312	C₂×C₄×C₅₃	—	2	8	no	—
313	C₂×C₄×C₅₃	—	2	2	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	2	no	—
318	C₂×C₄×C₅₃	—	2	2	no	—
319	C₂×C₄×C₅₃	—	2	8	no	—
320	C₂×C₄×C₅₃	—	2	8	no	—
321	C₂×C₄×C₅₃	—	2	8	no	—
322	C₂×C₄×C₅₃	—	2	8	no	—
323	C₂×C₄×C₅₃	—	2	32	no	—
324	C₂×C₄×C₅₃	—	2	2	no	—
325	C₂×C₄×C₅₃	—	2	4	no	—
326	C₂×C₄×C₅₃	—	2	2	no	—
327	C₂×C₄×C₅₃	—	2	8	no	—
328	C₂×C₄×C₅₃	—	2	8	no	—
329	C₂×C₄×C₅₃	—	2	4	no	—
330	C₂×C₄×C₅₃	—	2	8	no	—
331	C₂×C₄×C₅₃	—	4	4	no	—
332	C₂×C₄×C₅₃	—	4	4	no	—
333	C₂×C₄×C₅₃	—	4	8	no	—
334	C₂×C₄×C₅₃	—	4	8	no	—
335	C₂×C₄×C₅₃	#120	1	16	yes	complemented
336	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₅₃	C₂²×D₄	1	8	yes	—
338	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
341	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
342	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₅₃	C₂×#41	1	4	yes	complemented
344	#34736	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂²×C₅₃	—	2	2	no	—
346	C₂²×C₅₃	—	2	2	no	—
347	C₂²×C₅₃	—	2	2	no	—
348	C₂²×C₅₃	—	2	2	no	—
349	C₂²×C₅₃	—	2	8	no	—
350	C₂²×C₅₃	—	2	8	no	—
351	C₂²×C₅₃	—	2	8	no	—
352	C₂²×C₅₃	—	2	2	no	—
353	C₂²×C₅₃	—	2	2	no	—
354	C₂²×C₅₃	—	2	4	no	—
355	C₂²×C₅₃	—	2	2	no	—
356	C₂²×C₅₃	—	2	8	no	—
357	C₂²×C₅₃	—	2	16	no	—
358	C₂²×C₅₃	—	4	16	no	—
359	C₂²×C₅₃	—	4	32	no	—
360	C₂²×C₅₃	—	4	16	no	—
361	C₂²×C₅₃	—	4	2	no	—
362	C₂²×C₅₃	—	4	4	no	—
363	C₂²×C₅₃	—	4	4	no	—
364	C₂²×C₅₃	—	4	2	no	—
365	C₂²×C₅₃	—	4	4	no	—
366	C₂²×C₅₃	—	4	8	no	—
367	C₂²×C₅₃	—	4	4	no	—
368	C₂²×C₅₃	C₂×#120	1	4	yes	—
369	C₂²×C₅₃	#525	1	4	yes	complemented
370	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
371	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
372	C₂²×C₅₃	C₂²×#41	1	2	yes	—
373	C₂²×C₅₃	#585	1	2	yes	—
374	C₄×C₅₃	—	2	2	no	—
375	C₄×C₅₃	—	2	8	no	—
376	C₄×C₅₃	—	2	2	no	—
377	C₄×C₅₃	—	2	4	no	—
378	C₄×C₅₃	—	4	2	no	—
379	C₄×C₅₃	—	4	2	no	—
380	C₄×C₅₃	—	4	8	no	—
381	C₄×C₅₃	C₂×#120	1	4	yes	—
382	C₄×C₅₃	C₂×#120	1	4	yes	—
383	C₂³×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
384	C₂×#525	C₂×C₅₃	1	2	yes	complemented
385	C₂²×C₄×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
386	#2409	C₂×C₅₃	1	2	yes	complemented
387	#2408	C₂×C₅₃	1	2	yes	complemented
388	#2407	C₂×C₅₃	1	4	yes	complemented
389	#2406	C₂×C₅₃	1	2	yes	complemented
390	#2405	C₂×C₅₃	1	2	yes	complemented
391	#2404	C₂×C₅₃	1	2	yes	complemented
392	#2403	C₂×C₅₃	1	2	yes	complemented
393	#2388	C₂×C₅₃	1	4	yes	complemented
394	C₄×#120	C₂×C₅₃	1	4	yes	complemented
395	#2297	C₂×C₅₃	1	2	yes	complemented
396	#2280	C₂×C₅₃	1	1	yes	characteristic, complemented
397	C₂×C₅₃	—	2	4	no	—
398	C₂×C₅₃	—	2	4	no	—
399	C₂×C₅₃	—	4	2	no	—
400	C₂×C₅₃	—	4	8	no	—
401	C₂×C₅₃	—	4	4	no	—
402	C₂×C₅₃	C₂²×#120	1	1	yes	characteristic
403	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
404	C₂×C₅₃	#3449	1	1	yes	characteristic
405	C₂×C₅₃	D₄×#41	1	4	yes	—
406	C₂²×#41	—	2	16	no	—
407	C₂²×#41	—	2	8	no	—
408	C₂²×#41	C₂²×C₅₃	1	2	yes	—
409	C₂²×#41	C₂²×C₅₃	1	2	yes	—
410	C₂²×#41	C₂²×C₅₃	1	2	yes	complemented
411	C₂²×#41	C₂²×C₅₃	1	2	yes	complemented
412	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
413	C₂³×D₄	C₂²×C₅₃	1	2	yes	—
414	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
415	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
416	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
417	C₂⁴×C₄	C₂²×C₅₃	1	2	yes	complemented
418	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
419	#525	—	2	16	no	—
420	C₂×#123	C₂²×C₅₃	1	4	yes	complemented
421	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	complemented
422	C₂×#121	C₂²×C₅₃	1	4	yes	complemented
423	C₂×#120	C₂²×C₅₃	1	4	yes	—
424	C₂×#120	C₂²×C₅₃	1	4	yes	complemented
425	C₂×C₄×D₄	—	2	8	no	—
426	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
427	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
428	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
429	C₂×C₄×D₄	C₂²×C₅₃	1	8	yes	complemented
430	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
431	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
432	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
433	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
434	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
435	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
436	#395	C₂²×C₅₃	1	4	yes	complemented
437	#394	C₂²×C₅₃	1	8	yes	complemented
438	#394	C₂²×C₅₃	1	4	yes	complemented
439	#393	C₂²×C₅₃	1	4	yes	complemented
440	#392	C₂²×C₅₃	1	8	yes	complemented
441	#392	C₂²×C₅₃	1	4	yes	complemented
442	#391	C₂²×C₅₃	1	4	yes	complemented
443	#390	C₂²×C₅₃	1	4	yes	complemented
444	#386	C₂²×C₅₃	1	4	yes	—
445	#386	C₂²×C₅₃	1	4	yes	complemented
446	#386	C₂²×C₅₃	1	4	yes	complemented
447	#386	C₂²×C₅₃	1	8	yes	complemented
448	#385	C₂²×C₅₃	1	4	yes	complemented
449	#385	C₂²×C₅₃	1	8	yes	complemented
450	#381	C₂²×C₅₃	1	2	yes	complemented
451	#380	C₂²×C₅₃	1	2	yes	complemented
452	#380	C₂²×C₅₃	1	2	yes	complemented
453	#379	C₂²×C₅₃	1	2	yes	—
454	#379	C₂²×C₅₃	1	4	yes	complemented
455	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
456	C₄×C₂²⋊C₄	C₂²×C₅₃	1	8	yes	complemented
457	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	complemented
458	C₅₃	#34736	1	1	yes	characteristic, direct product factor, Sylow
459	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
460	C₂⁵	C₂³×C₅₃	1	2	yes	—
461	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
462	C₂×#41	—	2	128	no	—
463	C₂×#41	—	2	8	no	—
464	C₂×#41	—	2	16	no	—
465	C₂×#41	—	2	8	no	—
466	C₂×#41	—	2	8	no	—
467	C₂×#41	—	2	8	no	—
468	C₂×#41	—	2	8	no	—
469	C₂×#41	—	2	8	no	—
470	C₂×#41	—	2	8	no	—
471	C₂×#41	—	2	16	no	—
472	C₂×#41	D₄×C₅₃	1	16	yes	complemented
473	C₂²×Q₈	—	2	8	no	—
474	C₂²×Q₈	—	2	4	no	—
475	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
476	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
477	C₂²×D₄	—	2	4	no	—
478	C₂²×D₄	—	2	8	no	—
479	C₂²×D₄	—	2	16	no	—
480	C₂²×D₄	—	2	8	no	—
481	C₂²×D₄	—	2	8	no	—
482	C₂²×D₄	—	2	4	no	—
483	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
484	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
485	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
486	C₂²×D₄	C₂³×C₅₃	1	8	yes	—
487	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
488	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
489	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
490	C₂³×C₄	—	2	8	no	—
491	C₂³×C₄	—	2	8	no	—
492	C₂³×C₄	—	2	16	no	—
493	C₂³×C₄	—	2	4	no	—
494	C₂³×C₄	—	2	8	no	—
495	C₂³×C₄	D₄×C₅₃	1	8	yes	complemented
496	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
498	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
499	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
500	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
501	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
502	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
508	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
510	#123	—	2	16	no	—
511	C₂²⋊Q₈	—	2	16	no	—
512	#121	—	2	16	no	—
513	#120	—	2	16	no	—
514	#120	—	2	16	no	—
515	C₄×D₄	—	2	8	no	—
516	C₄×D₄	—	2	8	no	—
517	C₄×D₄	—	2	8	no	—
518	C₄×D₄	—	2	8	no	—
519	C₄×D₄	—	2	32	no	—
520	#117	—	2	8	no	—
521	C₂×C₄⋊C₄	—	2	4	no	—
522	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
525	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	—
526	C₂×C₂²⋊C₄	—	2	4	no	—
527	C₂×C₂²⋊C₄	—	2	4	no	—
528	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
539	C₂×C₄²	—	2	4	no	—
540	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
541	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
542	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
543	#95	C₂³×C₅₃	1	4	yes	—
544	#95	C₂³×C₅₃	1	4	yes	—
545	#95	C₂³×C₅₃	1	8	yes	—
546	#95	C₂³×C₅₃	1	8	yes	—
547	C₂⁴	—	2	2	no	—
548	C₂⁴	—	2	8	no	—
549	C₂⁴	—	2	4	no	—
550	C₂⁴	—	2	4	no	—
551	C₂⁴	—	2	4	no	—
552	C₂⁴	—	2	4	no	—
553	C₂⁴	—	2	4	no	—
554	C₂⁴	—	2	8	no	—
555	C₂⁴	—	4	2	no	—
556	C₂⁴	—	4	2	no	—
557	C₂⁴	—	4	4	no	—
558	C₂⁴	C₂×D₄×C₅₃	1	4	yes	—
559	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
560	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
561	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
562	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
563	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
564	#41	—	2	64	no	—
565	#41	—	2	64	no	—
566	#41	—	2	64	no	—
567	#41	—	2	64	no	—
568	C₂×Q₈	—	2	32	no	—
569	C₂×Q₈	—	2	8	no	—
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	—	2	4	no	—
573	C₂×Q₈	C₂×D₄×C₅₃	1	8	yes	complemented
574	C₂×D₄	—	2	32	no	—
575	C₂×D₄	—	2	64	no	—
576	C₂×D₄	—	2	32	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	8	no	—
580	C₂×D₄	—	2	8	no	—
581	C₂×D₄	—	2	8	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	8	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	16	no	—
587	C₂×D₄	—	2	16	no	—
588	C₂×D₄	—	2	8	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	4	8	no	—
594	C₂×D₄	C₂×D₄×C₅₃	1	16	yes	—
595	C₂×D₄	C₂×D₄×C₅₃	1	8	yes	complemented
596	C₂×D₄	#41×C₅₃	1	8	yes	complemented
597	C₂²×C₄	—	2	64	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	8	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	32	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	8	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	8	no	—
607	C₂²×C₄	—	2	8	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	8	no	—
611	C₂²×C₄	—	2	8	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	8	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	8	no	—
620	C₂²×C₄	—	4	2	no	—
621	C₂²×C₄	—	4	16	no	—
622	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
623	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
624	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
625	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
626	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
627	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
628	C₂²×C₄	C₂×D₄×C₅₃	1	8	yes	—
629	C₂²×C₄	C₂×D₄×C₅₃	1	16	yes	complemented
630	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
632	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
635	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	8	no	—
642	C₄⋊C₄	—	2	16	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	8	no	—
646	C₂²⋊C₄	—	2	16	no	—
647	C₂²⋊C₄	—	2	8	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	16	no	—
651	C₂²⋊C₄	—	2	16	no	—
652	C₂²⋊C₄	—	4	8	no	—
653	C₂²⋊C₄	—	4	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	8	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	16	no	—
662	C₂³	—	2	8	no	—
663	C₂³	—	2	8	no	—
664	C₂³	—	2	8	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	8	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	8	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	4	4	no	—
677	C₂³	—	4	16	no	—
678	C₂³	—	4	32	no	—
679	C₂³	—	4	16	no	—
680	C₂³	—	4	4	no	—
681	C₂³	—	4	8	no	—
682	C₂³	—	4	4	no	—
683	C₂³	—	4	8	no	—
684	C₂³	C₂²×D₄×C₅₃	1	8	yes	—
685	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
686	C₂³	C₂²×D₄×C₅₃	1	4	yes	—
687	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
688	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
689	C₂³	C₂×#41×C₅₃	1	4	yes	—
690	C₂³	C₂×#41×C₅₃	1	4	yes	complemented
691	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
692	Q₈	—	2	16	no	—
693	Q₈	—	2	16	no	—
694	D₄	—	2	16	no	—
695	D₄	—	2	32	no	—
696	D₄	—	2	16	no	—
697	D₄	—	2	32	no	—
698	D₄	—	2	16	no	—
699	D₄	—	2	16	no	—
700	D₄	—	4	32	no	—
701	C₂×C₄	—	2	16	no	—
702	C₂×C₄	—	2	32	no	—
703	C₂×C₄	—	2	8	no	—
704	C₂×C₄	—	2	8	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	8	no	—
712	C₂×C₄	—	2	8	no	—
713	C₂×C₄	—	2	8	no	—
714	C₂×C₄	—	2	8	no	—
715	C₂×C₄	—	2	32	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	8	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	8	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	8	no	—
723	C₂×C₄	—	4	4	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	4	8	no	—
726	C₂×C₄	—	4	8	no	—
727	C₂×C₄	#120×C₅₃	1	16	yes	complemented
728	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₅₃	1	8	yes	—
730	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
732	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
733	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
735	C₂×C₄	C₂×#41×C₅₃	1	4	yes	complemented
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	8	no	—
739	C₂²	—	2	8	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	8	no	—
744	C₂²	—	2	16	no	—
745	C₂²	—	2	8	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	2	4	no	—
749	C₂²	—	4	16	no	—
750	C₂²	—	4	32	no	—
751	C₂²	—	4	16	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	4	no	—
755	C₂²	—	4	8	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	4	no	—
759	C₂²	C₂×#120×C₅₃	1	4	yes	—
760	C₂²	C₅₃×#525	1	4	yes	complemented
761	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
762	C₂²	C₂³×D₄×C₅₃	1	2	yes	—
763	C₂²	C₂²×#41×C₅₃	1	2	yes	—
764	C₂²	C₅₃×#585	1	2	yes	—
765	C₄	—	2	2	no	—
766	C₄	—	2	8	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	4	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	8	no	—
771	C₄	—	4	2	no	—
772	C₄	C₂×#120×C₅₃	1	4	yes	—
773	C₄	C₂×#120×C₅₃	1	4	yes	—
774	C₂	—	2	4	no	—
775	C₂	—	2	4	no	—
776	C₂	—	4	2	no	—
777	C₂	—	4	4	no	—
778	C₂	—	4	8	no	—
779	C₂	C₂²×#120×C₅₃	1	1	yes	characteristic
780	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
781	C₂	C₅₃×#3449	1	1	yes	characteristic
782	C₂	D₄×#41×C₅₃	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
socle	C₂³×C₅₃	C₂⁵
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. C₂³×#41×C₅₃	C₂	semidirect
2. C₂×C₅₃×#525	C₂	semidirect
3. C₂²×C₄×D₄×C₅₃	C₂	semidirect
4. C₅₃×#2409	C₂	semidirect
5. C₅₃×#2408	C₂	semidirect
6. C₅₃×#2407	C₂	semidirect
7. C₅₃×#2406	C₂	semidirect
8. C₅₃×#2405	C₂	semidirect
9. C₅₃×#2404	C₂	semidirect
10. C₅₃×#2403	C₂	semidirect
11. C₅₃×#2388	C₂	semidirect
12. C₄×#120×C₅₃	C₂	semidirect
13. C₅₃×#2297	C₂	semidirect
14. C₅₃×#2280	C₂	semidirect
19. C₂²×#41×C₅₃	C₂²	semidirect
20. C₂²×#41×C₅₃	C₂²	semidirect
21. C₂³×Q₈×C₅₃	C₂²	semidirect
24. C₂³×D₄×C₅₃	C₂²	semidirect
26. C₂⁴×C₄×C₅₃	C₂²	semidirect
27. C₂⁴×C₄×C₅₃	C₂²	semidirect
29. C₂×#123×C₅₃	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
31. C₂×#121×C₅₃	C₂²	semidirect
33. C₂×#120×C₅₃	C₂²	semidirect
37. C₂×C₄×D₄×C₅₃	C₂²	semidirect
38. C₂×C₄×D₄×C₅₃	C₂²	semidirect
39. C₂×C₄×D₄×C₅₃	C₂²	semidirect
40. C₂×#117×C₅₃	C₂²	semidirect
41. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
43. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
44. C₂²×C₄²×C₅₃	C₂²	semidirect
45. C₅₃×#395	C₂²	semidirect
46. C₅₃×#394	C₂²	semidirect
47. C₅₃×#394	C₂²	semidirect
48. C₅₃×#393	C₂²	semidirect
49. C₅₃×#392	C₂²	semidirect
50. C₅₃×#392	C₂²	semidirect
51. C₅₃×#391	C₂²	semidirect
52. C₅₃×#390	C₂²	semidirect
54. C₅₃×#386	C₂²	semidirect
55. C₅₃×#386	C₂²	semidirect
56. C₅₃×#386	C₂²	semidirect
57. C₅₃×#385	C₂²	semidirect
58. C₅₃×#385	C₂²	semidirect
59. C₅₃×#381	C₂²	semidirect
60. C₅₃×#380	C₂²	semidirect
61. C₅₃×#380	C₂²	semidirect
63. C₅₃×#379	C₂²	semidirect
64. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
65. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
66. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
80. C₂×#41×C₅₃	D₄	semidirect
103. C₂³×C₄×C₅₃	D₄	semidirect
181. C₂×Q₈×C₅₃	C₂×D₄	semidirect
203. C₂×D₄×C₅₃	C₂×D₄	semidirect
204. C₂×D₄×C₅₃	#41	semidirect
237. C₂²×C₄×C₅₃	C₂×D₄	semidirect
298. C₂³×C₅₃	C₂×#41	semidirect
335. C₂×C₄×C₅₃	#120	semidirect
343. C₂×C₄×C₅₃	C₂×#41	semidirect
344. #34736	C₅₃	direct (N × H)
369. C₂²×C₅₃	#525	semidirect
383. C₂³×#41	C₂×C₅₃	semidirect
384. C₂×#525	C₂×C₅₃	semidirect
385. C₂²×C₄×D₄	C₂×C₅₃	semidirect
386. #2409	C₂×C₅₃	semidirect
387. #2408	C₂×C₅₃	semidirect
388. #2407	C₂×C₅₃	semidirect
389. #2406	C₂×C₅₃	semidirect
390. #2405	C₂×C₅₃	semidirect
391. #2404	C₂×C₅₃	semidirect
392. #2403	C₂×C₅₃	semidirect
393. #2388	C₂×C₅₃	semidirect
394. C₄×#120	C₂×C₅₃	semidirect
395. #2297	C₂×C₅₃	semidirect
396. #2280	C₂×C₅₃	semidirect
410. C₂²×#41	C₂²×C₅₃	semidirect
411. C₂²×#41	C₂²×C₅₃	semidirect
412. C₂³×Q₈	C₂²×C₅₃	semidirect
415. C₂³×D₄	C₂²×C₅₃	semidirect
417. C₂⁴×C₄	C₂²×C₅₃	semidirect
418. C₂⁴×C₄	C₂²×C₅₃	semidirect
420. C₂×#123	C₂²×C₅₃	semidirect
421. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
422. C₂×#121	C₂²×C₅₃	semidirect
424. C₂×#120	C₂²×C₅₃	semidirect
428. C₂×C₄×D₄	C₂²×C₅₃	semidirect
429. C₂×C₄×D₄	C₂²×C₅₃	semidirect
430. C₂×C₄×D₄	C₂²×C₅₃	semidirect
431. C₂×#117	C₂²×C₅₃	semidirect
432. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
434. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
435. C₂²×C₄²	C₂²×C₅₃	semidirect
436. #395	C₂²×C₅₃	semidirect
437. #394	C₂²×C₅₃	semidirect
438. #394	C₂²×C₅₃	semidirect
439. #393	C₂²×C₅₃	semidirect
440. #392	C₂²×C₅₃	semidirect
441. #392	C₂²×C₅₃	semidirect
442. #391	C₂²×C₅₃	semidirect
443. #390	C₂²×C₅₃	semidirect
445. #386	C₂²×C₅₃	semidirect
446. #386	C₂²×C₅₃	semidirect
447. #386	C₂²×C₅₃	semidirect
448. #385	C₂²×C₅₃	semidirect
449. #385	C₂²×C₅₃	semidirect
450. #381	C₂²×C₅₃	semidirect
451. #380	C₂²×C₅₃	semidirect
452. #380	C₂²×C₅₃	semidirect
454. #379	C₂²×C₅₃	semidirect
455. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
456. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
457. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
458. C₅₃	#34736	direct (N × H)
472. C₂×#41	D₄×C₅₃	semidirect
495. C₂³×C₄	D₄×C₅₃	semidirect
573. C₂×Q₈	C₂×D₄×C₅₃	semidirect
595. C₂×D₄	C₂×D₄×C₅₃	semidirect
596. C₂×D₄	#41×C₅₃	semidirect
629. C₂²×C₄	C₂×D₄×C₅₃	semidirect
690. C₂³	C₂×#41×C₅₃	semidirect
727. C₂×C₄	#120×C₅₃	semidirect
735. C₂×C₄	C₂×#41×C₅₃	semidirect
760. C₂²	C₅₃×#525	semidirect

Maximal subgroups

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

subgroup	index
C₂³×#41×C₅₃	2
C₂×C₅₃×#525	2
C₂²×C₄×D₄×C₅₃	2
C₅₃×#2409	2
C₅₃×#2408	2
C₅₃×#2407	2
C₅₃×#2406	2
C₅₃×#2405	2
C₅₃×#2404	2
C₅₃×#2403	2
C₅₃×#2388	2
C₄×#120×C₅₃	2
C₅₃×#2297	2
C₅₃×#2280	2
#34736	53

Subgroups — C53×#34736 #27242248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34736 #27242248