Subgroups — C₅₃×#60836 #27268348

Order 13568.

2072 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3225	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3221	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3218	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3214	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3212	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3206	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3154	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3137	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3013	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3010	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	2	yes	—
19	C₂×#137×C₅₃	C₂²	1	2	yes	—
20	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
21	C₂×#135×C₅₃	C₂²	1	2	yes	—
22	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	—
23	D₄×Q₈×C₅₃	—	2	1	no	—
24	D₄×Q₈×C₅₃	—	2	1	no	—
25	C₅₃×#547	—	2	2	no	—
26	C₅₃×#547	—	2	2	no	—
27	C₅₃×#547	—	2	1	no	—
28	C₅₃×#547	—	2	1	no	—
29	C₅₃×#544	C₂²	1	1	yes	characteristic
30	C₅₃×#542	—	2	1	no	—
31	C₅₃×#542	C₂²	1	2	yes	—
32	C₅₃×#540	—	2	1	no	—
33	C₅₃×#540	C₂²	1	2	yes	—
34	C₅₃×#538	—	2	2	no	—
35	C₅₃×#537	C₂²	1	1	yes	characteristic
36	C₅₃×#536	C₂²	1	2	yes	—
37	C₅₃×#536	C₂²	1	4	yes	complemented
38	C₅₃×#535	C₂²	1	1	yes	characteristic
39	C₅₃×#535	C₂²	1	1	yes	characteristic
40	C₅₃×#532	—	2	1	no	—
41	C₅₃×#532	C₂²	1	1	yes	characteristic
42	C₅₃×#532	C₂²	1	2	yes	—
43	C₅₃×#532	C₂²	1	2	yes	complemented
44	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
46	C₅₃×#529	—	2	1	no	—
47	C₅₃×#529	C₂²	1	2	yes	—
48	C₅₃×#525	—	2	2	no	—
49	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
50	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
52	C₅₃×#497	C₂²	1	4	yes	—
53	C₅₃×#496	C₂²	1	4	yes	—
54	C₅₃×#495	C₂²	1	4	yes	—
55	C₅₃×#492	C₂²	1	4	yes	—
56	C₅₃×#491	C₂²	1	4	yes	complemented
57	C₅₃×#489	C₂²	1	4	yes	complemented
58	C₅₃×#488	C₂²	1	4	yes	complemented
59	C₅₃×#487	C₂²	1	4	yes	complemented
60	C₅₃×#464	C₂²	1	2	yes	complemented
61	C₅₃×#463	C₂²	1	4	yes	—
62	C₅₃×#463	C₂²	1	2	yes	complemented
63	C₅₃×#462	C₂²	1	2	yes	complemented
64	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#462	C₂²	1	2	yes	complemented
66	C₅₃×#461	C₂²	1	2	yes	—
67	C₅₃×#461	C₂²	1	2	yes	—
68	C₅₃×#461	C₂²	1	2	yes	—
69	C₅₃×#461	C₂²	1	4	yes	—
70	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#461	C₂²	1	2	yes	complemented
72	C₅₃×#461	C₂²	1	2	yes	complemented
73	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
74	C₅₃×#459	C₂²	1	2	yes	—
75	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#452	C₂²	1	4	yes	complemented
77	C₅₃×#451	C₂²	1	4	yes	complemented
78	C₅₃×#449	C₂²	1	4	yes	—
79	C₅₃×#449	C₂²	1	4	yes	—
80	C₅₃×#449	C₂²	1	4	yes	complemented
81	C₅₃×#448	C₂²	1	4	yes	—
82	C₅₃×#448	C₂²	1	4	yes	—
83	C₅₃×#448	C₂²	1	4	yes	complemented
84	C₅₃×#433	C₂²	1	4	yes	complemented
85	C₅₃×#432	C₂²	1	2	yes	complemented
86	C₅₃×#431	C₂²	1	2	yes	complemented
87	C₅₃×#423	C₂²	1	1	yes	characteristic
88	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
89	C₅₃×#419	C₂²	1	2	yes	—
90	C₅₃×#417	C₂²	1	2	yes	—
91	C₅₃×#416	C₂²	1	2	yes	—
92	C₂×#103×C₅₃	C₂²	1	2	yes	—
93	C₅₃×#408	C₂²	1	2	yes	—
94	C₅₃×#405	C₂²	1	2	yes	—
95	2₋¹⁺⁴×C₅₃	—	4	4	no	—
96	2₋¹⁺⁴×C₅₃	—	4	4	no	—
97	C₂×#41×C₅₃	—	2	4	no	—
98	C₂×#41×C₅₃	—	2	2	no	—
99	C₂×#41×C₅₃	—	2	2	no	—
100	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
101	C₂×#41×C₅₃	C₂³	1	2	yes	—
102	C₂×#41×C₅₃	C₂³	1	4	yes	—
103	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
104	C₂²×Q₈×C₅₃	—	2	2	no	—
105	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
106	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
107	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₅₃	—	2	1	no	—
109	#137×C₅₃	—	4	4	no	—
110	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
111	#135×C₅₃	—	4	4	no	—
112	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
113	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₅₃	—	4	4	no	—
115	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
120	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
121	C₂×D₈×C₅₃	C₂³	1	4	yes	—
122	C₂×D₈×C₅₃	C₂³	1	2	yes	—
123	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
124	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
125	C₄⋊Q₈×C₅₃	—	2	1	no	—
126	C₄⋊Q₈×C₅₃	—	2	1	no	—
127	C₄⋊Q₈×C₅₃	—	2	1	no	—
128	C₄⋊Q₈×C₅₃	—	2	2	no	—
129	C₄⋊Q₈×C₅₃	—	2	2	no	—
130	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
131	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	—
132	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
135	#127×C₅₃	—	2	1	no	—
136	#127×C₅₃	C₂³	1	2	yes	—
137	#127×C₅₃	C₂³	1	1	yes	characteristic
138	#126×C₅₃	—	2	2	no	—
139	#126×C₅₃	—	2	2	no	—
140	#125×C₅₃	—	2	1	no	—
141	#125×C₅₃	C₂³	1	2	yes	—
142	#124×C₅₃	—	2	2	no	—
143	#124×C₅₃	—	2	2	no	—
144	#124×C₅₃	—	2	1	no	—
145	#124×C₅₃	C₂³	1	4	yes	—
146	#124×C₅₃	C₂³	1	2	yes	—
147	#124×C₅₃	C₂³	1	2	yes	—
148	#123×C₅₃	—	2	2	no	—
149	#123×C₅₃	—	2	2	no	—
150	#123×C₅₃	—	2	2	no	—
151	#123×C₅₃	—	2	4	no	—
152	#123×C₅₃	—	2	4	no	—
153	#123×C₅₃	—	2	4	no	—
154	#123×C₅₃	—	2	2	no	—
155	C₂²⋊Q₈×C₅₃	—	2	2	no	—
156	C₂²⋊Q₈×C₅₃	—	2	2	no	—
157	C₂²⋊Q₈×C₅₃	—	2	2	no	—
158	C₂²⋊Q₈×C₅₃	—	2	4	no	—
159	C₂²⋊Q₈×C₅₃	—	2	4	no	—
160	C₂²⋊Q₈×C₅₃	—	2	2	no	—
161	C₂²⋊Q₈×C₅₃	—	2	1	no	—
162	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
163	#121×C₅₃	—	2	1	no	—
164	#121×C₅₃	—	2	1	no	—
165	#121×C₅₃	—	2	2	no	—
166	#121×C₅₃	—	2	2	no	—
167	#121×C₅₃	—	2	2	no	—
168	#121×C₅₃	—	2	1	no	—
169	#121×C₅₃	—	2	2	no	—
170	#121×C₅₃	—	2	1	no	—
171	#121×C₅₃	—	2	1	no	—
172	#121×C₅₃	—	2	2	no	—
173	#121×C₅₃	—	2	2	no	—
174	#121×C₅₃	C₂³	1	2	yes	—
175	#121×C₅₃	C₂³	1	2	yes	—
176	#121×C₅₃	C₂³	1	2	yes	—
177	#120×C₅₃	—	2	2	no	—
178	#120×C₅₃	—	2	2	no	—
179	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
180	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
181	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
182	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₅₃	—	2	1	no	—
184	C₄×D₄×C₅₃	—	2	1	no	—
185	C₄×D₄×C₅₃	—	2	2	no	—
186	C₄×D₄×C₅₃	—	2	1	no	—
187	C₄×D₄×C₅₃	—	2	1	no	—
188	C₄×D₄×C₅₃	—	2	2	no	—
189	C₄×D₄×C₅₃	—	2	2	no	—
190	C₄×D₄×C₅₃	—	2	1	no	—
191	C₄×D₄×C₅₃	—	2	1	no	—
192	C₄×D₄×C₅₃	—	2	2	no	—
193	C₄×D₄×C₅₃	D₄	1	2	yes	—
194	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
195	C₄×D₄×C₅₃	D₄	1	2	yes	—
196	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
197	C₄×D₄×C₅₃	C₂³	1	2	yes	—
198	C₄×D₄×C₅₃	C₂³	1	2	yes	—
199	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
201	#117×C₅₃	—	2	1	no	—
202	#117×C₅₃	—	2	2	no	—
203	#117×C₅₃	C₂³	1	1	yes	characteristic
204	#117×C₅₃	C₂³	1	1	yes	characteristic
205	#117×C₅₃	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
207	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
208	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
209	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
210	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
212	C₂×C₄²×C₅₃	—	2	1	no	—
213	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
215	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
216	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
217	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
218	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
219	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
220	#103×C₅₃	C₂³	1	2	yes	—
221	#103×C₅₃	C₂³	1	4	yes	—
222	#103×C₅₃	C₂³	1	4	yes	—
223	#103×C₅₃	C₂³	1	4	yes	—
224	#103×C₅₃	C₂³	1	4	yes	—
225	#103×C₅₃	C₂³	1	4	yes	—
226	#103×C₅₃	C₂³	1	2	yes	—
227	#102×C₅₃	C₂³	1	2	yes	—
228	#102×C₅₃	C₂³	1	4	yes	—
229	#102×C₅₃	C₂³	1	2	yes	—
230	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
231	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
232	#97×C₅₃	C₂³	1	4	yes	—
233	C₄×C₈×C₅₃	C₂³	1	4	yes	—
234	C₂⁴×C₅₃	—	2	1	no	—
235	#41×C₅₃	—	2	2	no	—
236	#41×C₅₃	—	2	2	no	—
237	#41×C₅₃	—	2	2	no	—
238	#41×C₅₃	—	2	4	no	—
239	#41×C₅₃	—	2	4	no	—
240	#41×C₅₃	—	2	2	no	—
241	#41×C₅₃	—	4	4	no	—
242	#41×C₅₃	—	4	4	no	—
243	#41×C₅₃	—	4	16	no	—
244	#41×C₅₃	—	4	8	no	—
245	#41×C₅₃	—	8	4	no	—
246	C₂×Q₈×C₅₃	—	2	4	no	—
247	C₂×Q₈×C₅₃	—	2	2	no	—
248	C₂×Q₈×C₅₃	—	2	2	no	—
249	C₂×Q₈×C₅₃	—	2	4	no	—
250	C₂×Q₈×C₅₃	—	2	4	no	—
251	C₂×Q₈×C₅₃	—	4	4	no	—
252	C₂×Q₈×C₅₃	—	4	4	no	—
253	C₂×Q₈×C₅₃	—	4	8	no	—
254	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
255	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
256	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
257	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
258	C₂×D₄×C₅₃	—	2	1	no	—
259	C₂×D₄×C₅₃	—	2	4	no	—
260	C₂×D₄×C₅₃	—	2	2	no	—
261	C₂×D₄×C₅₃	—	2	2	no	—
262	C₂×D₄×C₅₃	—	2	2	no	—
263	C₂×D₄×C₅₃	—	2	2	no	—
264	C₂×D₄×C₅₃	—	2	1	no	—
265	C₂×D₄×C₅₃	—	2	1	no	—
266	C₂×D₄×C₅₃	—	2	1	no	—
267	C₂×D₄×C₅₃	—	2	2	no	—
268	C₂×D₄×C₅₃	—	2	2	no	—
269	C₂×D₄×C₅₃	—	2	2	no	—
270	C₂×D₄×C₅₃	—	2	2	no	—
271	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
272	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
273	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
274	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
275	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₅₃	—	2	4	no	—
277	C₂²×C₄×C₅₃	—	2	2	no	—
278	C₂²×C₄×C₅₃	—	2	1	no	—
279	C₂²×C₄×C₅₃	—	2	1	no	—
280	C₂²×C₄×C₅₃	—	2	1	no	—
281	C₂²×C₄×C₅₃	—	2	2	no	—
282	C₂²×C₄×C₅₃	—	2	4	no	—
283	C₂²×C₄×C₅₃	—	2	2	no	—
284	C₂²×C₄×C₅₃	—	2	1	no	—
285	C₂²×C₄×C₅₃	—	2	2	no	—
286	C₂²×C₄×C₅₃	—	8	2	no	—
287	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
291	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
293	Q₁₆×C₅₃	—	4	2	no	—
294	Q₁₆×C₅₃	—	4	4	no	—
295	SD₁₆×C₅₃	—	4	4	no	—
296	SD₁₆×C₅₃	—	4	4	no	—
297	SD₁₆×C₅₃	—	4	2	no	—
298	SD₁₆×C₅₃	—	4	2	no	—
299	SD₁₆×C₅₃	—	4	4	no	—
300	SD₁₆×C₅₃	—	4	4	no	—
301	D₈×C₅₃	—	4	2	no	—
302	D₈×C₅₃	—	4	4	no	—
303	M₁₆×C₅₃	—	2	4	no	—
304	C₂×C₈×C₅₃	—	2	4	no	—
305	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
306	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
307	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₅₃	—	2	2	no	—
309	C₄⋊C₄×C₅₃	—	2	1	no	—
310	C₄⋊C₄×C₅₃	—	2	2	no	—
311	C₄⋊C₄×C₅₃	—	2	1	no	—
312	C₄⋊C₄×C₅₃	—	2	2	no	—
313	C₄⋊C₄×C₅₃	—	2	2	no	—
314	C₄⋊C₄×C₅₃	—	2	4	no	—
315	C₄⋊C₄×C₅₃	—	2	4	no	—
316	C₄⋊C₄×C₅₃	—	2	1	no	—
317	C₄⋊C₄×C₅₃	—	2	1	no	—
318	C₄⋊C₄×C₅₃	—	2	1	no	—
319	C₄⋊C₄×C₅₃	—	2	2	no	—
320	C₄⋊C₄×C₅₃	—	2	2	no	—
321	C₄⋊C₄×C₅₃	—	2	2	no	—
322	C₄⋊C₄×C₅₃	—	2	2	no	—
323	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
324	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
325	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
326	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
327	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
328	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
329	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₂²⋊C₄×C₅₃	—	2	1	no	—
331	C₂²⋊C₄×C₅₃	—	2	2	no	—
332	C₂²⋊C₄×C₅₃	—	2	2	no	—
333	C₂²⋊C₄×C₅₃	—	2	2	no	—
334	C₂²⋊C₄×C₅₃	—	2	1	no	—
335	C₂²⋊C₄×C₅₃	—	2	1	no	—
336	C₂²⋊C₄×C₅₃	—	2	2	no	—
337	C₂²⋊C₄×C₅₃	—	2	2	no	—
338	C₂²⋊C₄×C₅₃	—	2	2	no	—
339	C₂²⋊C₄×C₅₃	—	2	2	no	—
340	C₂²⋊C₄×C₅₃	—	2	2	no	—
341	C₂²⋊C₄×C₅₃	—	2	2	no	—
342	C₂²⋊C₄×C₅₃	—	2	2	no	—
343	C₂²⋊C₄×C₅₃	—	2	4	no	—
344	C₂²⋊C₄×C₅₃	—	2	4	no	—
345	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
346	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
347	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
348	C₄²×C₅₃	—	2	1	no	—
349	C₄²×C₅₃	—	2	1	no	—
350	C₄²×C₅₃	—	2	1	no	—
351	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
352	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
353	C₄²×C₅₃	C₂×D₄	1	2	yes	—
354	C₄²×C₅₃	C₂×D₄	1	2	yes	—
355	C₄²×C₅₃	C₂⁴	1	2	yes	—
356	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂³×C₅₃	—	2	1	no	—
359	C₂³×C₅₃	—	2	2	no	—
360	C₂³×C₅₃	—	2	2	no	—
361	C₂³×C₅₃	—	4	2	no	—
362	C₂³×C₅₃	—	8	1	no	—
363	C₂³×C₅₃	—	8	1	no	—
364	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
365	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
366	Q₈×C₅₃	—	2	2	no	—
367	Q₈×C₅₃	—	2	4	no	—
368	Q₈×C₅₃	—	2	4	no	—
369	Q₈×C₅₃	—	2	2	no	—
370	Q₈×C₅₃	—	2	2	no	—
371	Q₈×C₅₃	—	2	1	no	—
372	Q₈×C₅₃	—	2	1	no	—
373	Q₈×C₅₃	—	4	8	no	—
374	Q₈×C₅₃	—	4	4	no	—
375	Q₈×C₅₃	—	8	2	no	—
376	D₄×C₅₃	—	2	4	no	—
377	D₄×C₅₃	—	2	2	no	—
378	D₄×C₅₃	—	2	2	no	—
379	D₄×C₅₃	—	2	2	no	—
380	D₄×C₅₃	—	2	2	no	—
381	D₄×C₅₃	—	2	2	no	—
382	D₄×C₅₃	—	2	1	no	—
383	D₄×C₅₃	—	2	1	no	—
384	D₄×C₅₃	—	4	2	no	—
385	D₄×C₅₃	—	4	8	no	—
386	D₄×C₅₃	—	4	2	no	—
387	D₄×C₅₃	—	4	4	no	—
388	D₄×C₅₃	—	4	2	no	—
389	D₄×C₅₃	—	4	2	no	—
390	D₄×C₅₃	—	8	2	no	—
391	D₄×C₅₃	—	8	2	no	—
392	D₄×C₅₃	—	8	2	no	—
393	D₄×C₅₃	—	8	2	no	—
394	D₄×C₅₃	—	8	2	no	—
395	C₂×C₄×C₅₃	—	2	2	no	—
396	C₂×C₄×C₅₃	—	2	4	no	—
397	C₂×C₄×C₅₃	—	2	2	no	—
398	C₂×C₄×C₅₃	—	2	2	no	—
399	C₂×C₄×C₅₃	—	2	4	no	—
400	C₂×C₄×C₅₃	—	2	2	no	—
401	C₂×C₄×C₅₃	—	2	2	no	—
402	C₂×C₄×C₅₃	—	2	1	no	—
403	C₂×C₄×C₅₃	—	2	1	no	—
404	C₂×C₄×C₅₃	—	2	1	no	—
405	C₂×C₄×C₅₃	—	4	1	no	—
406	C₂×C₄×C₅₃	—	4	2	no	—
407	C₂×C₄×C₅₃	—	4	8	no	—
408	C₂×C₄×C₅₃	—	4	8	no	—
409	C₂×C₄×C₅₃	—	4	4	no	—
410	C₂×C₄×C₅₃	—	4	4	no	—
411	C₂×C₄×C₅₃	—	4	2	no	—
412	C₂×C₄×C₅₃	—	4	4	no	—
413	C₂×C₄×C₅₃	—	4	2	no	—
414	C₂×C₄×C₅₃	—	8	1	no	—
415	C₂×C₄×C₅₃	—	8	2	no	—
416	C₂×C₄×C₅₃	—	8	1	no	—
417	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
423	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
426	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
427	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
428	C₈×C₅₃	—	2	2	no	—
429	C₈×C₅₃	—	2	2	no	—
430	C₈×C₅₃	—	2	4	no	—
431	#60836	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
432	C₂²×C₅₃	—	2	1	no	—
433	C₂²×C₅₃	—	2	1	no	—
434	C₂²×C₅₃	—	2	2	no	—
435	C₂²×C₅₃	—	2	2	no	—
436	C₂²×C₅₃	—	2	2	no	—
437	C₂²×C₅₃	—	4	1	no	—
438	C₂²×C₅₃	—	4	2	no	—
439	C₂²×C₅₃	—	4	2	no	—
440	C₂²×C₅₃	—	4	2	no	—
441	C₂²×C₅₃	—	4	1	no	—
442	C₂²×C₅₃	—	4	2	no	—
443	C₂²×C₅₃	—	4	2	no	—
444	C₂²×C₅₃	—	4	1	no	—
445	C₂²×C₅₃	—	4	2	no	—
446	C₂²×C₅₃	—	8	4	no	—
447	C₂²×C₅₃	#535	1	2	yes	—
448	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
449	C₄×C₅₃	—	2	1	no	—
450	C₄×C₅₃	—	2	1	no	—
451	C₄×C₅₃	—	2	2	no	—
452	C₄×C₅₃	—	2	2	no	—
453	C₄×C₅₃	—	2	1	no	—
454	C₄×C₅₃	—	2	2	no	—
455	C₄×C₅₃	—	4	1	no	—
456	C₄×C₅₃	—	4	4	no	—
457	C₄×C₅₃	—	4	2	no	—
458	C₄×C₅₃	—	4	1	no	—
459	C₄×C₅₃	—	4	2	no	—
460	C₄×C₅₃	—	4	1	no	—
461	C₄×C₅₃	#535	1	2	yes	—
462	C₄×C₅₃	#577	1	2	yes	—
463	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
464	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
465	#3499	C₂×C₅₃	1	1	yes	characteristic, complemented
466	#3460	C₂×C₅₃	1	1	yes	characteristic, complemented
467	#3225	C₂×C₅₃	1	4	yes	complemented
468	#3221	C₂×C₅₃	1	4	yes	complemented
469	#3218	C₂×C₅₃	1	2	yes	complemented
470	#3214	C₂×C₅₃	1	2	yes	complemented
471	#3212	C₂×C₅₃	1	2	yes	complemented
472	#3206	C₂×C₅₃	1	2	yes	complemented
473	#3154	C₂×C₅₃	1	2	yes	complemented
474	#3137	C₂×C₅₃	1	2	yes	complemented
475	#3039	C₂×C₅₃	1	1	yes	characteristic, complemented
476	#3036	C₂×C₅₃	1	1	yes	characteristic, complemented
477	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
478	C₂×#461	C₂×C₅₃	1	1	yes	characteristic, complemented
479	#3013	C₂×C₅₃	1	2	yes	complemented
480	#3010	C₂×C₅₃	1	2	yes	complemented
481	#2925	C₂×C₅₃	1	1	yes	characteristic, complemented
482	C₂×C₅₃	—	2	2	no	—
483	C₂×C₅₃	—	4	2	no	—
484	C₂×C₅₃	—	8	1	no	—
485	C₂×C₅₃	—	8	2	no	—
486	C₂×C₅₃	—	8	2	no	—
487	C₂×C₅₃	C₂×#535	1	1	yes	characteristic
488	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
489	C₂×C₅₃	#3586	1	1	yes	characteristic
490	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	2	yes	—
491	C₂×#137	C₂²×C₅₃	1	2	yes	—
492	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
493	C₂×#135	C₂²×C₅₃	1	2	yes	—
494	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	—
495	D₄×Q₈	—	2	1	no	—
496	D₄×Q₈	—	2	1	no	—
497	#547	—	2	2	no	—
498	#547	—	2	2	no	—
499	#547	—	2	1	no	—
500	#547	—	2	1	no	—
501	#544	C₂²×C₅₃	1	1	yes	characteristic
502	#542	—	2	1	no	—
503	#542	C₂²×C₅₃	1	2	yes	—
504	#540	—	2	1	no	—
505	#540	C₂²×C₅₃	1	2	yes	—
506	#538	—	2	2	no	—
507	#537	C₂²×C₅₃	1	1	yes	characteristic
508	#536	C₂²×C₅₃	1	2	yes	—
509	#536	C₂²×C₅₃	1	4	yes	complemented
510	#535	C₂²×C₅₃	1	1	yes	characteristic
511	#535	C₂²×C₅₃	1	1	yes	characteristic
512	#532	—	2	1	no	—
513	#532	C₂²×C₅₃	1	1	yes	characteristic
514	#532	C₂²×C₅₃	1	2	yes	—
515	#532	C₂²×C₅₃	1	2	yes	complemented
516	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
517	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
518	#529	—	2	1	no	—
519	#529	C₂²×C₅₃	1	2	yes	—
520	#525	—	2	2	no	—
521	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
522	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
523	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
524	#497	C₂²×C₅₃	1	4	yes	—
525	#496	C₂²×C₅₃	1	4	yes	—
526	#495	C₂²×C₅₃	1	4	yes	—
527	#492	C₂²×C₅₃	1	4	yes	—
528	#491	C₂²×C₅₃	1	4	yes	complemented
529	#489	C₂²×C₅₃	1	4	yes	complemented
530	#488	C₂²×C₅₃	1	4	yes	complemented
531	#487	C₂²×C₅₃	1	4	yes	complemented
532	#464	C₂²×C₅₃	1	2	yes	complemented
533	#463	C₂²×C₅₃	1	4	yes	—
534	#463	C₂²×C₅₃	1	2	yes	complemented
535	#462	C₂²×C₅₃	1	2	yes	complemented
536	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
537	#462	C₂²×C₅₃	1	2	yes	complemented
538	#461	C₂²×C₅₃	1	2	yes	—
539	#461	C₂²×C₅₃	1	2	yes	—
540	#461	C₂²×C₅₃	1	2	yes	—
541	#461	C₂²×C₅₃	1	4	yes	—
542	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
543	#461	C₂²×C₅₃	1	2	yes	complemented
544	#461	C₂²×C₅₃	1	2	yes	complemented
545	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
546	#459	C₂²×C₅₃	1	2	yes	—
547	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
548	#452	C₂²×C₅₃	1	4	yes	complemented
549	#451	C₂²×C₅₃	1	4	yes	complemented
550	#449	C₂²×C₅₃	1	4	yes	—
551	#449	C₂²×C₅₃	1	4	yes	—
552	#449	C₂²×C₅₃	1	4	yes	complemented
553	#448	C₂²×C₅₃	1	4	yes	—
554	#448	C₂²×C₅₃	1	4	yes	—
555	#448	C₂²×C₅₃	1	4	yes	complemented
556	#433	C₂²×C₅₃	1	4	yes	complemented
557	#432	C₂²×C₅₃	1	2	yes	complemented
558	#431	C₂²×C₅₃	1	2	yes	complemented
559	#423	C₂²×C₅₃	1	1	yes	characteristic
560	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
561	#419	C₂²×C₅₃	1	2	yes	—
562	#417	C₂²×C₅₃	1	2	yes	—
563	#416	C₂²×C₅₃	1	2	yes	—
564	C₂×#103	C₂²×C₅₃	1	2	yes	—
565	#408	C₂²×C₅₃	1	2	yes	—
566	#405	C₂²×C₅₃	1	2	yes	—
567	C₅₃	#60836	1	1	yes	characteristic, direct product factor, Sylow
568	2₋¹⁺⁴	—	4	4	no	—
569	2₋¹⁺⁴	—	4	4	no	—
570	C₂×#41	—	2	4	no	—
571	C₂×#41	—	2	2	no	—
572	C₂×#41	—	2	2	no	—
573	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
574	C₂×#41	C₂³×C₅₃	1	2	yes	—
575	C₂×#41	C₂³×C₅₃	1	4	yes	—
576	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
577	C₂²×Q₈	—	2	2	no	—
578	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
579	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
580	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
581	C₂³×C₄	—	2	1	no	—
582	#137	—	4	4	no	—
583	AGL(1,ℤ/8)	—	4	4	no	—
584	#135	—	4	4	no	—
585	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
586	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	—
587	C₂×SD₁₆	—	4	4	no	—
588	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
589	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
590	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
591	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
592	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
593	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
594	C₂×D₈	C₂³×C₅₃	1	2	yes	—
595	C₂×D₈	C₂³×C₅₃	1	4	yes	—
596	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
597	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
598	C₄⋊Q₈	—	2	1	no	—
599	C₄⋊Q₈	—	2	1	no	—
600	C₄⋊Q₈	—	2	1	no	—
601	C₄⋊Q₈	—	2	2	no	—
602	C₄⋊Q₈	—	2	2	no	—
603	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
604	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
605	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
606	C₄⋊Q₈	C₂³×C₅₃	1	4	yes	—
607	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
608	#127	—	2	1	no	—
609	#127	C₂³×C₅₃	1	1	yes	characteristic
610	#127	C₂³×C₅₃	1	2	yes	—
611	#126	—	2	2	no	—
612	#126	—	2	2	no	—
613	#125	—	2	1	no	—
614	#125	C₂³×C₅₃	1	2	yes	—
615	#124	—	2	1	no	—
616	#124	—	2	2	no	—
617	#124	—	2	2	no	—
618	#124	C₂³×C₅₃	1	2	yes	—
619	#124	C₂³×C₅₃	1	2	yes	—
620	#124	C₂³×C₅₃	1	4	yes	—
621	#123	—	2	2	no	—
622	#123	—	2	2	no	—
623	#123	—	2	2	no	—
624	#123	—	2	2	no	—
625	#123	—	2	4	no	—
626	#123	—	2	4	no	—
627	#123	—	2	4	no	—
628	C₂²⋊Q₈	—	2	1	no	—
629	C₂²⋊Q₈	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	4	no	—
633	C₂²⋊Q₈	—	2	4	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
636	#121	—	2	2	no	—
637	#121	—	2	1	no	—
638	#121	—	2	2	no	—
639	#121	—	2	1	no	—
640	#121	—	2	1	no	—
641	#121	—	2	2	no	—
642	#121	—	2	2	no	—
643	#121	—	2	1	no	—
644	#121	—	2	1	no	—
645	#121	—	2	2	no	—
646	#121	—	2	2	no	—
647	#121	C₂³×C₅₃	1	2	yes	—
648	#121	C₂³×C₅₃	1	2	yes	—
649	#121	C₂³×C₅₃	1	2	yes	—
650	#120	—	2	2	no	—
651	#120	—	2	2	no	—
652	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
653	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
654	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
655	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
656	C₄×D₄	—	2	1	no	—
657	C₄×D₄	—	2	1	no	—
658	C₄×D₄	—	2	2	no	—
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	—	2	1	no	—
661	C₄×D₄	—	2	2	no	—
662	C₄×D₄	—	2	1	no	—
663	C₄×D₄	—	2	1	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	D₄×C₅₃	1	2	yes	—
667	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
668	C₄×D₄	D₄×C₅₃	1	2	yes	—
669	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
670	C₄×D₄	C₂³×C₅₃	1	2	yes	—
671	C₄×D₄	C₂³×C₅₃	1	2	yes	—
672	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
673	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
674	#117	—	2	1	no	—
675	#117	—	2	2	no	—
676	#117	C₂³×C₅₃	1	1	yes	characteristic
677	#117	C₂³×C₅₃	1	1	yes	characteristic
678	#117	C₂³×C₅₃	1	2	yes	—
679	C₂×C₄⋊C₄	—	2	1	no	—
680	C₂×C₄⋊C₄	—	2	1	no	—
681	C₂×C₄⋊C₄	—	2	2	no	—
682	C₂×C₄⋊C₄	—	2	2	no	—
683	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	—	2	1	no	—
685	C₂×C₄²	—	2	1	no	—
686	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
688	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
689	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
690	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
691	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
692	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
693	#103	C₂³×C₅₃	1	4	yes	—
694	#103	C₂³×C₅₃	1	4	yes	—
695	#103	C₂³×C₅₃	1	2	yes	—
696	#103	C₂³×C₅₃	1	2	yes	—
697	#103	C₂³×C₅₃	1	4	yes	—
698	#103	C₂³×C₅₃	1	4	yes	—
699	#103	C₂³×C₅₃	1	4	yes	—
700	#102	C₂³×C₅₃	1	2	yes	—
701	#102	C₂³×C₅₃	1	2	yes	—
702	#102	C₂³×C₅₃	1	4	yes	—
703	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
704	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
705	#97	C₂³×C₅₃	1	4	yes	—
706	C₄×C₈	C₂³×C₅₃	1	4	yes	—
707	C₂⁴	—	2	1	no	—
708	#41	—	2	2	no	—
709	#41	—	2	2	no	—
710	#41	—	2	2	no	—
711	#41	—	2	4	no	—
712	#41	—	2	4	no	—
713	#41	—	2	2	no	—
714	#41	—	4	4	no	—
715	#41	—	4	4	no	—
716	#41	—	4	16	no	—
717	#41	—	4	8	no	—
718	#41	—	8	4	no	—
719	C₂×Q₈	—	2	4	no	—
720	C₂×Q₈	—	2	2	no	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	—	2	4	no	—
723	C₂×Q₈	—	2	4	no	—
724	C₂×Q₈	—	4	4	no	—
725	C₂×Q₈	—	4	4	no	—
726	C₂×Q₈	—	4	8	no	—
727	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
728	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
729	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
730	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
731	C₂×D₄	—	2	1	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	1	no	—
738	C₂×D₄	—	2	1	no	—
739	C₂×D₄	—	2	1	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
745	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
746	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
747	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
748	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	1	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	4	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	1	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	8	2	no	—
760	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
761	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
762	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
763	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
766	Q₁₆	—	4	2	no	—
767	Q₁₆	—	4	4	no	—
768	SD₁₆	—	4	4	no	—
769	SD₁₆	—	4	4	no	—
770	SD₁₆	—	4	2	no	—
771	SD₁₆	—	4	2	no	—
772	SD₁₆	—	4	4	no	—
773	SD₁₆	—	4	4	no	—
774	D₈	—	4	2	no	—
775	D₈	—	4	4	no	—
776	M₁₆	—	2	4	no	—
777	C₂×C₈	—	2	4	no	—
778	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
779	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
780	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	4	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	4	no	—
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	—	2	1	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
797	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
798	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
799	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
800	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
801	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
802	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
803	C₂²⋊C₄	—	2	1	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	1	no	—
808	C₂²⋊C₄	—	2	1	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
819	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
820	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
821	C₄²	—	2	1	no	—
822	C₄²	—	2	1	no	—
823	C₄²	—	2	1	no	—
824	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
825	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
826	C₄²	C₂×D₄×C₅₃	1	2	yes	—
827	C₄²	C₂×D₄×C₅₃	1	2	yes	—
828	C₄²	C₂⁴×C₅₃	1	2	yes	—
829	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
830	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	8	1	no	—
836	C₂³	—	8	1	no	—
837	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
838	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
839	Q₈	—	2	2	no	—
840	Q₈	—	2	1	no	—
841	Q₈	—	2	4	no	—
842	Q₈	—	2	2	no	—
843	Q₈	—	2	4	no	—
844	Q₈	—	2	2	no	—
845	Q₈	—	2	1	no	—
846	Q₈	—	4	8	no	—
847	Q₈	—	4	4	no	—
848	Q₈	—	8	2	no	—
849	D₄	—	2	4	no	—
850	D₄	—	2	2	no	—
851	D₄	—	2	2	no	—
852	D₄	—	2	1	no	—
853	D₄	—	2	2	no	—
854	D₄	—	2	2	no	—
855	D₄	—	2	2	no	—
856	D₄	—	2	1	no	—
857	D₄	—	4	2	no	—
858	D₄	—	4	8	no	—
859	D₄	—	4	2	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	2	no	—
862	D₄	—	4	2	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	2	no	—
865	D₄	—	8	2	no	—
866	D₄	—	8	2	no	—
867	D₄	—	8	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	4	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	4	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	2	no	—
880	C₂×C₄	—	4	8	no	—
881	C₂×C₄	—	4	8	no	—
882	C₂×C₄	—	4	4	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	4	2	no	—
885	C₂×C₄	—	4	4	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	8	1	no	—
888	C₂×C₄	—	8	2	no	—
889	C₂×C₄	—	8	1	no	—
890	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
891	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
892	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
893	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
894	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
895	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
896	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
897	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
898	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
899	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
900	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
901	C₈	—	2	2	no	—
902	C₈	—	2	2	no	—
903	C₈	—	2	4	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	1	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	8	4	no	—
919	C₂²	C₅₃×#535	1	2	yes	—
920	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
921	C₄	—	2	1	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	1	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	4	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	1	no	—
933	C₄	C₅₃×#535	1	2	yes	—
934	C₄	C₅₃×#577	1	2	yes	—
935	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
936	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
937	C₂	—	2	2	no	—
938	C₂	—	4	2	no	—
939	C₂	—	8	2	no	—
940	C₂	—	8	1	no	—
941	C₂	—	8	2	no	—
942	C₂	C₂×C₅₃×#535	1	1	yes	characteristic
943	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
944	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
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×#3499	C₂	semidirect
2. C₅₃×#3460	C₂	semidirect
3. C₅₃×#3225	C₂	semidirect
4. C₅₃×#3221	C₂	semidirect
5. C₅₃×#3218	C₂	semidirect
6. C₅₃×#3214	C₂	semidirect
7. C₅₃×#3212	C₂	semidirect
8. C₅₃×#3206	C₂	semidirect
9. C₅₃×#3154	C₂	semidirect
10. C₅₃×#3137	C₂	semidirect
11. C₅₃×#3039	C₂	semidirect
12. C₅₃×#3036	C₂	semidirect
13. C₅₃×#3035	C₂	semidirect
14. C₂×C₅₃×#461	C₂	semidirect
15. C₅₃×#3013	C₂	semidirect
16. C₅₃×#3010	C₂	semidirect
17. C₅₃×#2925	C₂	semidirect
37. C₅₃×#536	C₂²	semidirect
43. C₅₃×#532	C₂²	semidirect
45. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
56. C₅₃×#491	C₂²	semidirect
57. C₅₃×#489	C₂²	semidirect
58. C₅₃×#488	C₂²	semidirect
59. C₅₃×#487	C₂²	semidirect
60. C₅₃×#464	C₂²	semidirect
62. C₅₃×#463	C₂²	semidirect
63. C₅₃×#462	C₂²	semidirect
64. C₅₃×#462	C₂²	semidirect
65. C₅₃×#462	C₂²	semidirect
70. C₅₃×#461	C₂²	semidirect
71. C₅₃×#461	C₂²	semidirect
72. C₅₃×#461	C₂²	semidirect
73. C₅₃×#460	C₂²	semidirect
75. C₅₃×#459	C₂²	semidirect
76. C₅₃×#452	C₂²	semidirect
77. C₅₃×#451	C₂²	semidirect
80. C₅₃×#449	C₂²	semidirect
83. C₅₃×#448	C₂²	semidirect
84. C₅₃×#433	C₂²	semidirect
85. C₅₃×#432	C₂²	semidirect
86. C₅₃×#431	C₂²	semidirect
431. #60836	C₅₃	direct (N × H)
465. #3499	C₂×C₅₃	semidirect
466. #3460	C₂×C₅₃	semidirect
467. #3225	C₂×C₅₃	semidirect
468. #3221	C₂×C₅₃	semidirect
469. #3218	C₂×C₅₃	semidirect
470. #3214	C₂×C₅₃	semidirect
471. #3212	C₂×C₅₃	semidirect
472. #3206	C₂×C₅₃	semidirect
473. #3154	C₂×C₅₃	semidirect
474. #3137	C₂×C₅₃	semidirect
475. #3039	C₂×C₅₃	semidirect
476. #3036	C₂×C₅₃	semidirect
477. #3035	C₂×C₅₃	semidirect
478. C₂×#461	C₂×C₅₃	semidirect
479. #3013	C₂×C₅₃	semidirect
480. #3010	C₂×C₅₃	semidirect
481. #2925	C₂×C₅₃	semidirect
509. #536	C₂²×C₅₃	semidirect
515. #532	C₂²×C₅₃	semidirect
517. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
528. #491	C₂²×C₅₃	semidirect
529. #489	C₂²×C₅₃	semidirect
530. #488	C₂²×C₅₃	semidirect
531. #487	C₂²×C₅₃	semidirect
532. #464	C₂²×C₅₃	semidirect
534. #463	C₂²×C₅₃	semidirect
535. #462	C₂²×C₅₃	semidirect
536. #462	C₂²×C₅₃	semidirect
537. #462	C₂²×C₅₃	semidirect
542. #461	C₂²×C₅₃	semidirect
543. #461	C₂²×C₅₃	semidirect
544. #461	C₂²×C₅₃	semidirect
545. #460	C₂²×C₅₃	semidirect
547. #459	C₂²×C₅₃	semidirect
548. #452	C₂²×C₅₃	semidirect
549. #451	C₂²×C₅₃	semidirect
552. #449	C₂²×C₅₃	semidirect
555. #448	C₂²×C₅₃	semidirect
556. #433	C₂²×C₅₃	semidirect
557. #432	C₂²×C₅₃	semidirect
558. #431	C₂²×C₅₃	semidirect
567. C₅₃	#60836	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3499	2
C₅₃×#3460	2
C₅₃×#3225	2
C₅₃×#3221	2
C₅₃×#3218	2
C₅₃×#3214	2
C₅₃×#3212	2
C₅₃×#3206	2
C₅₃×#3154	2
C₅₃×#3137	2
C₅₃×#3039	2
C₅₃×#3036	2
C₅₃×#3035	2
C₂×C₅₃×#461	2
C₅₃×#3013	2
C₅₃×#3010	2
C₅₃×#2925	2
#60836	53

Subgroups — C53×#60836 #27268348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60836 #27268348