Subgroups — C₅₃×#61984 #27269496

Order 13568.

1820 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3482	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3398	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3374	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3312	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3298	C₂	1	2	yes	maximal, complemented
7	D₄×Q₁₆×C₅₃	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3270	C₂	1	4	yes	maximal, complemented
9	C₅₃×#3255	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3248	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3218	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3113	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#462	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₅₃	C₂²	1	2	yes	—
19	C₂²×Q₁₆×C₅₃	C₂²	1	4	yes	—
20	Q₈²×C₅₃	—	2	1	no	—
21	C₅₃×#557	C₂²	1	2	yes	—
22	C₅₃×#557	C₂²	1	1	yes	characteristic
23	C₅₃×#556	—	2	1	no	—
24	C₅₃×#556	C₂²	1	1	yes	characteristic
25	C₅₃×#554	—	2	1	no	—
26	C₅₃×#554	—	2	2	no	—
27	C₅₃×#552	—	2	2	no	—
28	C₅₃×#552	C₂²	1	2	yes	—
29	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
30	D₄×Q₈×C₅₃	C₂²	1	4	yes	—
31	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
32	C₅₃×#548	C₂²	1	2	yes	—
33	C₅₃×#547	—	2	1	no	—
34	C₅₃×#547	C₂²	1	1	yes	characteristic
35	C₅₃×#544	—	2	2	no	—
36	C₅₃×#544	—	2	1	no	—
37	C₅₃×#533	—	2	1	no	—
38	C₅₃×#533	C₂²	1	1	yes	characteristic
39	C₅₃×#533	C₂²	1	2	yes	—
40	C₅₃×#533	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	—
43	C₅₃×#529	—	2	2	no	—
44	C₅₃×#529	C₂²	1	2	yes	—
45	C₅₃×#520	—	2	1	no	—
46	C₄×#41×C₅₃	—	2	1	no	—
47	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
48	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
50	C₅₃×#497	C₂²	1	4	yes	—
51	C₅₃×#494	C₂²	1	2	yes	—
52	C₅₃×#491	C₂²	1	4	yes	—
53	C₅₃×#487	C₂²	1	2	yes	—
54	C₅₃×#485	C₂²	1	2	yes	—
55	C₅₃×#483	C₂²	1	4	yes	—
56	C₅₃×#479	C₂²	1	4	yes	—
57	C₅₃×#475	C₂²	1	2	yes	—
58	C₅₃×#475	C₂²	1	2	yes	—
59	C₅₃×#475	C₂²	1	1	yes	characteristic
60	C₅₃×#474	C₂²	1	1	yes	characteristic
61	C₅₃×#470	C₂²	1	4	yes	—
62	C₅₃×#467	C₂²	1	4	yes	—
63	C₅₃×#465	C₂²	1	4	yes	—
64	C₅₃×#464	C₂²	1	4	yes	—
65	C₅₃×#462	C₂²	1	2	yes	—
66	C₅₃×#462	C₂²	1	2	yes	—
67	C₅₃×#462	C₂²	1	2	yes	—
68	C₅₃×#462	C₂²	1	2	yes	—
69	C₅₃×#462	C₂²	1	4	yes	—
70	C₅₃×#462	C₂²	1	2	yes	—
71	C₅₃×#462	C₂²	1	1	yes	characteristic
72	C₅₃×#462	C₂²	1	2	yes	—
73	C₅₃×#462	C₂²	1	4	yes	—
74	C₅₃×#461	C₂²	1	1	yes	characteristic
75	C₅₃×#461	C₂²	1	2	yes	—
76	C₅₃×#461	C₂²	1	2	yes	—
77	C₅₃×#452	C₂²	1	2	yes	—
78	C₅₃×#451	C₂²	1	4	yes	—
79	C₅₃×#451	C₂²	1	4	yes	—
80	C₅₃×#451	C₂²	1	4	yes	—
81	C₅₃×#448	C₂²	1	4	yes	—
82	C₅₃×#446	C₂²	1	2	yes	—
83	C₅₃×#441	C₂²	1	4	yes	—
84	C₅₃×#441	C₂²	1	4	yes	—
85	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
86	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
87	C₅₃×#435	C₂²	1	4	yes	—
88	C₈×D₄×C₅₃	C₂²	1	2	yes	—
89	C₅₃×#432	C₂²	1	2	yes	—
90	C₅₃×#431	C₂²	1	1	yes	characteristic
91	C₅₃×#423	C₂²	1	1	yes	characteristic
92	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
93	C₅₃×#419	C₂²	1	2	yes	—
94	C₂×#103×C₅₃	C₂²	1	4	yes	—
95	C₂×#41×C₅₃	—	2	1	no	—
96	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
97	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
99	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
100	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
101	#137×C₅₃	—	4	4	no	—
102	C₂×Q₁₆×C₅₃	—	4	8	no	—
103	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
104	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
105	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
106	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
107	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
110	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
111	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
112	C₄⋊Q₈×C₅₃	—	2	1	no	—
113	C₄⋊Q₈×C₅₃	—	2	4	no	—
114	C₄⋊Q₈×C₅₃	—	2	2	no	—
115	C₄⋊Q₈×C₅₃	—	2	1	no	—
116	C₄⋊Q₈×C₅₃	—	2	2	no	—
117	C₄⋊Q₈×C₅₃	—	2	1	no	—
118	C₄⋊Q₈×C₅₃	—	2	2	no	—
119	C₄⋊Q₈×C₅₃	—	2	1	no	—
120	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
122	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
123	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
124	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
125	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
126	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
127	#126×C₅₃	—	2	2	no	—
128	#126×C₅₃	—	2	2	no	—
129	#126×C₅₃	—	2	2	no	—
130	#125×C₅₃	—	2	2	no	—
131	#125×C₅₃	—	2	2	no	—
132	#125×C₅₃	—	2	2	no	—
133	#125×C₅₃	—	2	4	no	—
134	#125×C₅₃	—	2	1	no	—
135	#125×C₅₃	—	2	2	no	—
136	#125×C₅₃	—	2	1	no	—
137	#125×C₅₃	C₂³	1	2	yes	—
138	#124×C₅₃	—	2	2	no	—
139	#124×C₅₃	C₂³	1	2	yes	—
140	#123×C₅₃	—	2	2	no	—
141	#123×C₅₃	—	2	2	no	—
142	#123×C₅₃	—	2	2	no	—
143	C₂²⋊Q₈×C₅₃	—	2	1	no	—
144	C₂²⋊Q₈×C₅₃	—	2	2	no	—
145	C₂²⋊Q₈×C₅₃	—	2	2	no	—
146	C₂²⋊Q₈×C₅₃	—	2	4	no	—
147	C₂²⋊Q₈×C₅₃	—	2	4	no	—
148	C₂²⋊Q₈×C₅₃	—	2	4	no	—
149	C₂²⋊Q₈×C₅₃	—	2	1	no	—
150	C₂²⋊Q₈×C₅₃	—	2	1	no	—
151	C₂²⋊Q₈×C₅₃	—	2	2	no	—
152	C₂²⋊Q₈×C₅₃	—	2	1	no	—
153	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
154	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
155	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
156	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
157	#121×C₅₃	—	2	2	no	—
158	#121×C₅₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₅₃	—	2	1	no	—
160	C₄×Q₈×C₅₃	—	2	2	no	—
161	C₄×Q₈×C₅₃	—	2	2	no	—
162	C₄×Q₈×C₅₃	—	2	1	no	—
163	C₄×Q₈×C₅₃	—	2	1	no	—
164	C₄×Q₈×C₅₃	—	2	2	no	—
165	C₄×Q₈×C₅₃	—	2	2	no	—
166	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
171	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
172	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
174	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
175	C₄×D₄×C₅₃	—	2	2	no	—
176	C₄×D₄×C₅₃	—	2	1	no	—
177	C₄×D₄×C₅₃	—	2	4	no	—
178	C₄×D₄×C₅₃	—	2	2	no	—
179	C₄×D₄×C₅₃	—	2	2	no	—
180	C₄×D₄×C₅₃	—	2	1	no	—
181	C₄×D₄×C₅₃	—	2	1	no	—
182	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
183	C₄×D₄×C₅₃	D₄	1	2	yes	—
184	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₅₃	C₂³	1	2	yes	—
188	#117×C₅₃	—	2	1	no	—
189	#117×C₅₃	—	2	2	no	—
190	#117×C₅₃	—	2	1	no	—
191	#117×C₅₃	—	2	2	no	—
192	#117×C₅₃	—	2	2	no	—
193	#117×C₅₃	—	2	1	no	—
194	#117×C₅₃	—	2	1	no	—
195	#117×C₅₃	D₄	1	2	yes	—
196	#117×C₅₃	D₄	1	1	yes	characteristic
197	#117×C₅₃	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
199	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
200	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
201	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
202	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
203	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
204	C₂×C₄²×C₅₃	—	2	1	no	—
205	C₂×C₄²×C₅₃	—	2	2	no	—
206	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
207	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
208	#107×C₅₃	C₂³	1	2	yes	—
209	#106×C₅₃	C₂³	1	2	yes	—
210	#106×C₅₃	C₂³	1	4	yes	—
211	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
212	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
213	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
214	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
215	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
216	#103×C₅₃	C₂³	1	2	yes	—
217	#103×C₅₃	C₂³	1	2	yes	—
218	#103×C₅₃	C₂³	1	4	yes	—
219	#103×C₅₃	C₂³	1	4	yes	—
220	#103×C₅₃	C₂³	1	4	yes	—
221	#103×C₅₃	C₂³	1	4	yes	—
222	#103×C₅₃	C₂³	1	4	yes	—
223	#103×C₅₃	C₂³	1	2	yes	—
224	#103×C₅₃	C₂³	1	4	yes	—
225	#102×C₅₃	C₂³	1	2	yes	—
226	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
228	#97×C₅₃	C₂³	1	4	yes	—
229	C₄×C₈×C₅₃	C₂³	1	2	yes	—
230	#41×C₅₃	—	2	4	no	—
231	#41×C₅₃	—	2	2	no	—
232	#41×C₅₃	—	4	1	no	—
233	#41×C₅₃	—	4	4	no	—
234	C₂×Q₈×C₅₃	—	2	1	no	—
235	C₂×Q₈×C₅₃	—	2	2	no	—
236	C₂×Q₈×C₅₃	—	2	1	no	—
237	C₂×Q₈×C₅₃	—	2	2	no	—
238	C₂×Q₈×C₅₃	—	2	4	no	—
239	C₂×Q₈×C₅₃	—	2	4	no	—
240	C₂×Q₈×C₅₃	—	4	2	no	—
241	C₂×Q₈×C₅₃	—	4	4	no	—
242	C₂×Q₈×C₅₃	—	4	2	no	—
243	C₂×Q₈×C₅₃	—	4	4	no	—
244	C₂×Q₈×C₅₃	—	4	2	no	—
245	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
248	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
249	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
250	C₂×D₄×C₅₃	—	2	1	no	—
251	C₂×D₄×C₅₃	—	2	2	no	—
252	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
254	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₅₃	—	2	2	no	—
256	C₂²×C₄×C₅₃	—	2	2	no	—
257	C₂²×C₄×C₅₃	—	2	2	no	—
258	C₂²×C₄×C₅₃	—	2	4	no	—
259	C₂²×C₄×C₅₃	—	2	1	no	—
260	C₂²×C₄×C₅₃	—	2	1	no	—
261	C₂²×C₄×C₅₃	—	2	1	no	—
262	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
268	Q₁₆×C₅₃	—	2	4	no	—
269	Q₁₆×C₅₃	—	2	8	no	—
270	Q₁₆×C₅₃	—	4	4	no	—
271	Q₁₆×C₅₃	—	4	4	no	—
272	Q₁₆×C₅₃	—	4	4	no	—
273	SD₁₆×C₅₃	—	4	2	no	—
274	SD₁₆×C₅₃	—	4	4	no	—
275	M₁₆×C₅₃	—	4	2	no	—
276	C₂×C₈×C₅₃	—	4	4	no	—
277	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
278	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
279	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
280	C₄⋊C₄×C₅₃	—	2	1	no	—
281	C₄⋊C₄×C₅₃	—	2	1	no	—
282	C₄⋊C₄×C₅₃	—	2	2	no	—
283	C₄⋊C₄×C₅₃	—	2	1	no	—
284	C₄⋊C₄×C₅₃	—	2	2	no	—
285	C₄⋊C₄×C₅₃	—	2	4	no	—
286	C₄⋊C₄×C₅₃	—	2	2	no	—
287	C₄⋊C₄×C₅₃	—	2	2	no	—
288	C₄⋊C₄×C₅₃	—	2	2	no	—
289	C₄⋊C₄×C₅₃	—	2	2	no	—
290	C₄⋊C₄×C₅₃	—	2	4	no	—
291	C₄⋊C₄×C₅₃	—	2	2	no	—
292	C₄⋊C₄×C₅₃	—	2	2	no	—
293	C₄⋊C₄×C₅₃	—	2	1	no	—
294	C₄⋊C₄×C₅₃	—	2	1	no	—
295	C₄⋊C₄×C₅₃	—	2	2	no	—
296	C₄⋊C₄×C₅₃	—	2	2	no	—
297	C₄⋊C₄×C₅₃	—	2	1	no	—
298	C₄⋊C₄×C₅₃	—	2	1	no	—
299	C₄⋊C₄×C₅₃	—	2	2	no	—
300	C₄⋊C₄×C₅₃	—	2	1	no	—
301	C₄⋊C₄×C₅₃	—	2	2	no	—
302	C₄⋊C₄×C₅₃	—	2	2	no	—
303	C₄⋊C₄×C₅₃	—	2	4	no	—
304	C₄⋊C₄×C₅₃	—	2	4	no	—
305	C₄⋊C₄×C₅₃	—	2	2	no	—
306	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
307	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
308	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
311	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
314	C₂²⋊C₄×C₅₃	—	2	2	no	—
315	C₂²⋊C₄×C₅₃	—	2	4	no	—
316	C₂²⋊C₄×C₅₃	—	2	2	no	—
317	C₂²⋊C₄×C₅₃	—	2	2	no	—
318	C₂²⋊C₄×C₅₃	—	2	1	no	—
319	C₂²⋊C₄×C₅₃	—	2	2	no	—
320	C₂²⋊C₄×C₅₃	—	2	1	no	—
321	C₂²⋊C₄×C₅₃	—	2	1	no	—
322	C₂²⋊C₄×C₅₃	—	2	2	no	—
323	C₂²⋊C₄×C₅₃	—	2	2	no	—
324	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
327	C₄²×C₅₃	—	2	1	no	—
328	C₄²×C₅₃	—	2	1	no	—
329	C₄²×C₅₃	—	2	2	no	—
330	C₄²×C₅₃	—	2	2	no	—
331	C₄²×C₅₃	—	2	1	no	—
332	C₄²×C₅₃	—	2	2	no	—
333	C₄²×C₅₃	—	2	4	no	—
334	C₄²×C₅₃	—	2	2	no	—
335	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₅₃	C₂×D₄	1	2	yes	—
338	C₄²×C₅₃	C₂×D₄	1	2	yes	—
339	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₄²×C₅₃	C₂⁴	1	2	yes	—
341	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
342	C₂³×C₅₃	—	2	1	no	—
343	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
344	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
345	Q₈×C₅₃	—	2	2	no	—
346	Q₈×C₅₃	—	2	1	no	—
347	Q₈×C₅₃	—	2	2	no	—
348	Q₈×C₅₃	—	2	4	no	—
349	Q₈×C₅₃	—	2	2	no	—
350	Q₈×C₅₃	—	2	2	no	—
351	Q₈×C₅₃	—	2	4	no	—
352	Q₈×C₅₃	—	2	2	no	—
353	Q₈×C₅₃	—	4	4	no	—
354	Q₈×C₅₃	—	4	2	no	—
355	Q₈×C₅₃	—	4	2	no	—
356	Q₈×C₅₃	—	8	2	no	—
357	Q₈×C₅₃	—	8	4	no	—
358	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
359	D₄×C₅₃	—	2	4	no	—
360	D₄×C₅₃	—	2	1	no	—
361	D₄×C₅₃	—	2	1	no	—
362	D₄×C₅₃	—	4	2	no	—
363	D₄×C₅₃	—	4	4	no	—
364	D₄×C₅₃	#137	1	4	yes	complemented
365	C₂×C₄×C₅₃	—	2	4	no	—
366	C₂×C₄×C₅₃	—	2	1	no	—
367	C₂×C₄×C₅₃	—	2	2	no	—
368	C₂×C₄×C₅₃	—	2	4	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	2	2	no	—
371	C₂×C₄×C₅₃	—	2	1	no	—
372	C₂×C₄×C₅₃	—	2	2	no	—
373	C₂×C₄×C₅₃	—	2	1	no	—
374	C₂×C₄×C₅₃	—	2	1	no	—
375	C₂×C₄×C₅₃	—	2	4	no	—
376	C₂×C₄×C₅₃	—	2	2	no	—
377	C₂×C₄×C₅₃	—	2	2	no	—
378	C₂×C₄×C₅₃	—	2	2	no	—
379	C₂×C₄×C₅₃	—	2	1	no	—
380	C₂×C₄×C₅₃	—	2	2	no	—
381	C₂×C₄×C₅₃	—	4	2	no	—
382	C₂×C₄×C₅₃	—	4	4	no	—
383	C₂×C₄×C₅₃	—	4	4	no	—
384	C₂×C₄×C₅₃	—	4	2	no	—
385	C₂×C₄×C₅₃	—	4	2	no	—
386	C₂×C₄×C₅₃	—	8	4	no	—
387	C₂×C₄×C₅₃	—	8	2	no	—
388	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
397	C₈×C₅₃	—	2	2	no	—
398	C₈×C₅₃	—	2	4	no	—
399	C₈×C₅₃	—	2	2	no	—
400	#61984	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
401	C₂²×C₅₃	—	2	2	no	—
402	C₂²×C₅₃	—	2	2	no	—
403	C₂²×C₅₃	—	2	1	no	—
404	C₂²×C₅₃	—	2	1	no	—
405	C₂²×C₅₃	—	2	1	no	—
406	C₂²×C₅₃	—	4	1	no	—
407	C₂²×C₅₃	—	4	1	no	—
408	C₂²×C₅₃	—	4	1	no	—
409	C₂²×C₅₃	C₂×#137	1	4	yes	—
410	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
411	C₄×C₅₃	—	2	1	no	—
412	C₄×C₅₃	—	2	2	no	—
413	C₄×C₅₃	—	2	2	no	—
414	C₄×C₅₃	—	2	1	no	—
415	C₄×C₅₃	—	2	2	no	—
416	C₄×C₅₃	—	2	2	no	—
417	C₄×C₅₃	—	2	1	no	—
418	C₄×C₅₃	—	4	2	no	—
419	C₄×C₅₃	—	4	4	no	—
420	C₄×C₅₃	—	4	2	no	—
421	C₄×C₅₃	—	4	1	no	—
422	C₄×C₅₃	—	4	2	no	—
423	C₄×C₅₃	—	4	1	no	—
424	C₄×C₅₃	—	4	2	no	—
425	C₄×C₅₃	C₂×#137	1	2	yes	—
426	C₄×C₅₃	#578	1	2	yes	—
427	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
428	C₄×C₅₃	#585	1	1	yes	characteristic
429	#3503	C₂×C₅₃	1	1	yes	characteristic, complemented
430	#3482	C₂×C₅₃	1	1	yes	characteristic
431	#3398	C₂×C₅₃	1	2	yes	complemented
432	#3374	C₂×C₅₃	1	2	yes	complemented
433	#3312	C₂×C₅₃	1	4	yes	complemented
434	#3298	C₂×C₅₃	1	2	yes	complemented
435	D₄×Q₁₆	C₂×C₅₃	1	2	yes	complemented
436	#3270	C₂×C₅₃	1	4	yes	complemented
437	#3255	C₂×C₅₃	1	1	yes	characteristic, complemented
438	#3248	C₂×C₅₃	1	2	yes	complemented
439	#3218	C₂×C₅₃	1	2	yes	complemented
440	#3209	C₂×C₅₃	1	1	yes	characteristic, complemented
441	#3113	C₂×C₅₃	1	2	yes	complemented
442	#3107	C₂×C₅₃	1	1	yes	characteristic, complemented
443	#3039	C₂×C₅₃	1	1	yes	characteristic, complemented
444	C₂×#462	C₂×C₅₃	1	2	yes	complemented
445	#2990	C₂×C₅₃	1	1	yes	characteristic, complemented
446	C₂×C₅₃	—	2	4	no	—
447	C₂×C₅₃	—	4	1	no	—
448	C₂×C₅₃	—	8	1	no	—
449	C₂×C₅₃	#3488	1	1	yes	characteristic
450	C₂×C₅₃	C₂²×#137	1	1	yes	characteristic
451	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
452	C₂×#137	C₂²×C₅₃	1	2	yes	—
453	C₂²×Q₁₆	C₂²×C₅₃	1	4	yes	—
454	Q₈²	—	2	1	no	—
455	#557	C₂²×C₅₃	1	2	yes	—
456	#557	C₂²×C₅₃	1	1	yes	characteristic
457	#556	—	2	1	no	—
458	#556	C₂²×C₅₃	1	1	yes	characteristic
459	#554	—	2	1	no	—
460	#554	—	2	2	no	—
461	#552	—	2	2	no	—
462	#552	C₂²×C₅₃	1	2	yes	—
463	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
464	D₄×Q₈	C₂²×C₅₃	1	4	yes	—
465	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
466	#548	C₂²×C₅₃	1	2	yes	—
467	#547	—	2	1	no	—
468	#547	C₂²×C₅₃	1	1	yes	characteristic
469	#544	—	2	2	no	—
470	#544	—	2	1	no	—
471	#533	—	2	1	no	—
472	#533	C₂²×C₅₃	1	1	yes	characteristic
473	#533	C₂²×C₅₃	1	2	yes	—
474	#533	C₂²×C₅₃	1	1	yes	characteristic
475	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
476	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	—
477	#529	—	2	2	no	—
478	#529	C₂²×C₅₃	1	2	yes	—
479	#520	—	2	1	no	—
480	C₄×#41	—	2	1	no	—
481	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
482	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
483	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
484	#497	C₂²×C₅₃	1	4	yes	—
485	#494	C₂²×C₅₃	1	2	yes	—
486	#491	C₂²×C₅₃	1	4	yes	—
487	#487	C₂²×C₅₃	1	2	yes	—
488	#485	C₂²×C₅₃	1	2	yes	—
489	#483	C₂²×C₅₃	1	4	yes	—
490	#479	C₂²×C₅₃	1	4	yes	—
491	#475	C₂²×C₅₃	1	1	yes	characteristic
492	#475	C₂²×C₅₃	1	2	yes	—
493	#475	C₂²×C₅₃	1	2	yes	—
494	#474	C₂²×C₅₃	1	1	yes	characteristic
495	#470	C₂²×C₅₃	1	4	yes	—
496	#467	C₂²×C₅₃	1	4	yes	—
497	#465	C₂²×C₅₃	1	4	yes	—
498	#464	C₂²×C₅₃	1	4	yes	—
499	#462	C₂²×C₅₃	1	1	yes	characteristic
500	#462	C₂²×C₅₃	1	2	yes	—
501	#462	C₂²×C₅₃	1	2	yes	—
502	#462	C₂²×C₅₃	1	4	yes	—
503	#462	C₂²×C₅₃	1	2	yes	—
504	#462	C₂²×C₅₃	1	2	yes	—
505	#462	C₂²×C₅₃	1	4	yes	—
506	#462	C₂²×C₅₃	1	2	yes	—
507	#462	C₂²×C₅₃	1	2	yes	—
508	#461	C₂²×C₅₃	1	1	yes	characteristic
509	#461	C₂²×C₅₃	1	2	yes	—
510	#461	C₂²×C₅₃	1	2	yes	—
511	#452	C₂²×C₅₃	1	2	yes	—
512	#451	C₂²×C₅₃	1	4	yes	—
513	#451	C₂²×C₅₃	1	4	yes	—
514	#451	C₂²×C₅₃	1	4	yes	—
515	#448	C₂²×C₅₃	1	4	yes	—
516	#446	C₂²×C₅₃	1	2	yes	—
517	#441	C₂²×C₅₃	1	4	yes	—
518	#441	C₂²×C₅₃	1	4	yes	—
519	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
520	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
521	#435	C₂²×C₅₃	1	4	yes	—
522	C₈×D₄	C₂²×C₅₃	1	2	yes	—
523	#432	C₂²×C₅₃	1	2	yes	—
524	#431	C₂²×C₅₃	1	1	yes	characteristic
525	#423	C₂²×C₅₃	1	1	yes	characteristic
526	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	—
527	#419	C₂²×C₅₃	1	2	yes	—
528	C₂×#103	C₂²×C₅₃	1	4	yes	—
529	C₅₃	#61984	1	1	yes	characteristic, direct product factor, Sylow
530	C₂×#41	—	2	1	no	—
531	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
532	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
533	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
534	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
535	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
536	#137	—	4	4	no	—
537	C₂×Q₁₆	—	4	8	no	—
538	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
539	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
540	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
541	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
542	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
543	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
544	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
545	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
546	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
547	C₄⋊Q₈	—	2	1	no	—
548	C₄⋊Q₈	—	2	1	no	—
549	C₄⋊Q₈	—	2	4	no	—
550	C₄⋊Q₈	—	2	2	no	—
551	C₄⋊Q₈	—	2	1	no	—
552	C₄⋊Q₈	—	2	2	no	—
553	C₄⋊Q₈	—	2	1	no	—
554	C₄⋊Q₈	—	2	2	no	—
555	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
556	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
557	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
558	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
559	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
560	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
561	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
562	#126	—	2	2	no	—
563	#126	—	2	2	no	—
564	#126	—	2	2	no	—
565	#125	—	2	2	no	—
566	#125	—	2	2	no	—
567	#125	—	2	2	no	—
568	#125	—	2	4	no	—
569	#125	—	2	1	no	—
570	#125	—	2	2	no	—
571	#125	—	2	1	no	—
572	#125	C₂³×C₅₃	1	2	yes	—
573	#124	—	2	2	no	—
574	#124	C₂³×C₅₃	1	2	yes	—
575	#123	—	2	2	no	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	1	no	—
582	C₂²⋊Q₈	—	2	1	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	4	no	—
586	C₂²⋊Q₈	—	2	4	no	—
587	C₂²⋊Q₈	—	2	4	no	—
588	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
589	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
590	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
591	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
592	#121	—	2	2	no	—
593	#121	C₂³×C₅₃	1	2	yes	—
594	C₄×Q₈	—	2	2	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	—	2	2	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	—	2	1	no	—
600	C₄×Q₈	—	2	2	no	—
601	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
603	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
604	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
605	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
606	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
608	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
609	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	4	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
618	C₄×D₄	D₄×C₅₃	1	2	yes	—
619	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
620	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
621	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
622	C₄×D₄	C₂³×C₅₃	1	2	yes	—
623	#117	—	2	2	no	—
624	#117	—	2	1	no	—
625	#117	—	2	1	no	—
626	#117	—	2	1	no	—
627	#117	—	2	2	no	—
628	#117	—	2	1	no	—
629	#117	—	2	2	no	—
630	#117	D₄×C₅₃	1	2	yes	—
631	#117	D₄×C₅₃	1	1	yes	characteristic
632	#117	C₂³×C₅₃	1	1	yes	characteristic
633	C₂×C₄⋊C₄	—	2	2	no	—
634	C₂×C₄⋊C₄	—	2	2	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	2	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
639	C₂×C₄²	—	2	2	no	—
640	C₂×C₄²	—	2	1	no	—
641	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
642	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
643	#107	C₂³×C₅₃	1	2	yes	—
644	#106	C₂³×C₅₃	1	2	yes	—
645	#106	C₂³×C₅₃	1	4	yes	—
646	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
647	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
648	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
649	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
650	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
651	#103	C₂³×C₅₃	1	2	yes	—
652	#103	C₂³×C₅₃	1	4	yes	—
653	#103	C₂³×C₅₃	1	4	yes	—
654	#103	C₂³×C₅₃	1	4	yes	—
655	#103	C₂³×C₅₃	1	4	yes	—
656	#103	C₂³×C₅₃	1	2	yes	—
657	#103	C₂³×C₅₃	1	2	yes	—
658	#103	C₂³×C₅₃	1	4	yes	—
659	#103	C₂³×C₅₃	1	4	yes	—
660	#102	C₂³×C₅₃	1	2	yes	—
661	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
662	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
663	#97	C₂³×C₅₃	1	4	yes	—
664	C₄×C₈	C₂³×C₅₃	1	2	yes	—
665	#41	—	2	4	no	—
666	#41	—	2	2	no	—
667	#41	—	4	1	no	—
668	#41	—	4	4	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	4	no	—
674	C₂×Q₈	—	2	4	no	—
675	C₂×Q₈	—	4	2	no	—
676	C₂×Q₈	—	4	4	no	—
677	C₂×Q₈	—	4	2	no	—
678	C₂×Q₈	—	4	4	no	—
679	C₂×Q₈	—	4	2	no	—
680	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
681	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
682	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
683	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
684	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
688	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
689	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
698	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
699	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
703	Q₁₆	—	2	4	no	—
704	Q₁₆	—	2	8	no	—
705	Q₁₆	—	4	4	no	—
706	Q₁₆	—	4	4	no	—
707	Q₁₆	—	4	4	no	—
708	SD₁₆	—	4	4	no	—
709	SD₁₆	—	4	2	no	—
710	M₁₆	—	4	2	no	—
711	C₂×C₈	—	4	4	no	—
712	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
713	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
714	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
742	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
743	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
744	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
745	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
746	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
747	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
748	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
760	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
761	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
762	C₄²	—	2	1	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	4	no	—
769	C₄²	—	2	2	no	—
770	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
772	C₄²	C₂×D₄×C₅₃	1	2	yes	—
773	C₄²	C₂×D₄×C₅₃	1	2	yes	—
774	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
775	C₄²	C₂⁴×C₅₃	1	2	yes	—
776	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
777	C₂³	—	2	1	no	—
778	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
779	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
780	Q₈	—	2	2	no	—
781	Q₈	—	2	1	no	—
782	Q₈	—	2	4	no	—
783	Q₈	—	2	2	no	—
784	Q₈	—	2	2	no	—
785	Q₈	—	2	2	no	—
786	Q₈	—	2	2	no	—
787	Q₈	—	2	4	no	—
788	Q₈	—	4	4	no	—
789	Q₈	—	4	2	no	—
790	Q₈	—	4	2	no	—
791	Q₈	—	8	2	no	—
792	Q₈	—	8	4	no	—
793	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
794	D₄	—	2	4	no	—
795	D₄	—	2	1	no	—
796	D₄	—	2	1	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	4	no	—
799	D₄	#137×C₅₃	1	4	yes	complemented
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	4	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	8	4	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
828	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
829	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
831	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
832	C₈	—	2	2	no	—
833	C₈	—	2	4	no	—
834	C₈	—	2	2	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	C₂×#137×C₅₃	1	4	yes	—
844	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
845	C₄	—	2	1	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	1	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	4	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	2	no	—
859	C₄	C₂×#137×C₅₃	1	2	yes	—
860	C₄	C₅₃×#578	1	2	yes	—
861	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
862	C₄	C₅₃×#585	1	1	yes	characteristic
863	C₂	—	2	4	no	—
864	C₂	—	4	1	no	—
865	C₂	—	8	1	no	—
866	C₂	C₅₃×#3488	1	1	yes	characteristic
867	C₂	C₂²×#137×C₅₃	1	1	yes	characteristic
868	C₂	C₂×C₅₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3482	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3503	C₂	semidirect
3. C₅₃×#3398	C₂	semidirect
4. C₅₃×#3374	C₂	semidirect
5. C₅₃×#3312	C₂	semidirect
6. C₅₃×#3298	C₂	semidirect
7. D₄×Q₁₆×C₅₃	C₂	semidirect
8. C₅₃×#3270	C₂	semidirect
9. C₅₃×#3255	C₂	semidirect
10. C₅₃×#3248	C₂	semidirect
11. C₅₃×#3218	C₂	semidirect
12. C₅₃×#3209	C₂	semidirect
13. C₅₃×#3113	C₂	semidirect
14. C₅₃×#3107	C₂	semidirect
15. C₅₃×#3039	C₂	semidirect
16. C₂×C₅₃×#462	C₂	semidirect
17. C₅₃×#2990	C₂	semidirect
364. D₄×C₅₃	#137	semidirect
400. #61984	C₅₃	direct (N × H)
429. #3503	C₂×C₅₃	semidirect
431. #3398	C₂×C₅₃	semidirect
432. #3374	C₂×C₅₃	semidirect
433. #3312	C₂×C₅₃	semidirect
434. #3298	C₂×C₅₃	semidirect
435. D₄×Q₁₆	C₂×C₅₃	semidirect
436. #3270	C₂×C₅₃	semidirect
437. #3255	C₂×C₅₃	semidirect
438. #3248	C₂×C₅₃	semidirect
439. #3218	C₂×C₅₃	semidirect
440. #3209	C₂×C₅₃	semidirect
441. #3113	C₂×C₅₃	semidirect
442. #3107	C₂×C₅₃	semidirect
443. #3039	C₂×C₅₃	semidirect
444. C₂×#462	C₂×C₅₃	semidirect
445. #2990	C₂×C₅₃	semidirect
529. C₅₃	#61984	direct (N × H)
799. D₄	#137×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3503	2
C₅₃×#3482	2
C₅₃×#3398	2
C₅₃×#3374	2
C₅₃×#3312	2
C₅₃×#3298	2
D₄×Q₁₆×C₅₃	2
C₅₃×#3270	2
C₅₃×#3255	2
C₅₃×#3248	2
C₅₃×#3218	2
C₅₃×#3209	2
C₅₃×#3113	2
C₅₃×#3107	2
C₅₃×#3039	2
C₂×C₅₃×#462	2
C₅₃×#2990	2
#61984	53

Subgroups — C53×#61984 #27269496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61984 #27269496