Subgroups — C₅₃×#60835 #27268347

Order 13568.

2040 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3225	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3224	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3223	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3222	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3219	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3215	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3211	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3210	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3154	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3011	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
32	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
34	C₅₃×#548	—	2	1	no	—
35	C₅₃×#548	—	2	1	no	—
36	C₅₃×#546	—	2	2	no	—
37	C₅₃×#546	—	2	1	no	—
38	C₅₃×#546	—	2	2	no	—
39	C₅₃×#546	—	2	1	no	—
40	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#542	—	2	1	no	—
42	C₅₃×#542	C₂²	1	2	yes	complemented
43	C₅₃×#541	—	2	1	no	—
44	C₅₃×#541	C₂²	1	2	yes	complemented
45	C₅₃×#539	—	2	2	no	—
46	C₅₃×#537	C₂²	1	1	yes	characteristic
47	C₅₃×#536	C₂²	1	2	yes	—
48	C₅₃×#536	C₂²	1	1	yes	characteristic
49	C₅₃×#536	C₂²	1	1	yes	characteristic
50	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#535	C₂²	1	2	yes	—
52	C₅₃×#535	C₂²	1	1	yes	characteristic
53	C₅₃×#533	—	2	1	no	—
54	C₅₃×#533	C₂²	1	2	yes	complemented
55	C₅₃×#532	C₂²	1	2	yes	—
56	C₅₃×#532	C₂²	1	1	yes	characteristic
57	C₅₃×#529	—	2	1	no	—
58	C₅₃×#529	—	2	2	no	—
59	C₅₃×#529	C₂²	1	2	yes	complemented
60	C₂×#124×C₅₃	C₂²	1	2	yes	—
61	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
62	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
63	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#497	C₂²	1	2	yes	complemented
66	C₅₃×#497	C₂²	1	2	yes	complemented
67	C₅₃×#497	C₂²	1	2	yes	complemented
68	C₅₃×#496	C₂²	1	2	yes	complemented
69	C₅₃×#495	C₂²	1	2	yes	complemented
70	C₅₃×#495	C₂²	1	2	yes	complemented
71	C₅₃×#494	C₂²	1	2	yes	complemented
72	C₅₃×#492	C₂²	1	2	yes	complemented
73	C₅₃×#491	C₂²	1	2	yes	complemented
74	C₅₃×#490	C₂²	1	2	yes	complemented
75	C₅₃×#489	C₂²	1	2	yes	complemented
76	C₅₃×#489	C₂²	1	2	yes	complemented
77	C₅₃×#488	C₂²	1	2	yes	complemented
78	C₅₃×#488	C₂²	1	2	yes	complemented
79	C₅₃×#487	C₂²	1	2	yes	complemented
80	C₅₃×#486	C₂²	1	2	yes	complemented
81	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#464	C₂²	1	2	yes	complemented
83	C₅₃×#464	C₂²	1	2	yes	complemented
84	C₅₃×#464	C₂²	1	2	yes	complemented
85	C₅₃×#464	C₂²	1	2	yes	complemented
86	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#464	C₂²	1	2	yes	complemented
88	C₅₃×#464	C₂²	1	2	yes	complemented
89	C₅₃×#464	C₂²	1	2	yes	complemented
90	C₅₃×#464	C₂²	1	2	yes	complemented
91	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#463	C₂²	1	2	yes	complemented
93	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#463	C₂²	1	2	yes	complemented
95	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#462	C₂²	1	2	yes	complemented
97	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#460	C₂²	1	2	yes	complemented
100	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#452	C₂²	1	2	yes	—
102	C₅₃×#452	C₂²	1	2	yes	—
103	C₅₃×#452	C₂²	1	2	yes	—
104	C₅₃×#452	C₂²	1	2	yes	complemented
105	C₅₃×#452	C₂²	1	2	yes	complemented
106	C₅₃×#452	C₂²	1	2	yes	complemented
107	C₅₃×#451	C₂²	1	2	yes	complemented
108	C₅₃×#451	C₂²	1	2	yes	complemented
109	C₅₃×#451	C₂²	1	2	yes	complemented
110	C₅₃×#450	C₂²	1	2	yes	—
111	C₅₃×#450	C₂²	1	2	yes	—
112	C₅₃×#450	C₂²	1	2	yes	—
113	C₅₃×#449	C₂²	1	2	yes	—
114	C₅₃×#449	C₂²	1	2	yes	complemented
115	C₅₃×#448	C₂²	1	2	yes	complemented
116	C₅₃×#447	C₂²	1	2	yes	—
117	C₅₃×#433	C₂²	1	2	yes	complemented
118	C₅₃×#433	C₂²	1	2	yes	complemented
119	C₅₃×#432	C₂²	1	2	yes	complemented
120	C₅₃×#431	C₂²	1	2	yes	complemented
121	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#418	C₂²	1	1	yes	characteristic
125	C₅₃×#417	C₂²	1	1	yes	characteristic
126	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#416	C₂²	1	1	yes	characteristic
128	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
129	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
131	C₅₃×#408	C₂²	1	1	yes	characteristic
132	C₅₃×#408	C₂²	1	1	yes	characteristic
133	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
135	2₋¹⁺⁴×C₅₃	—	4	2	no	—
136	2₋¹⁺⁴×C₅₃	—	4	2	no	—
137	H(5,𝔽₂)×C₅₃	—	4	2	no	—
138	H(5,𝔽₂)×C₅₃	—	4	2	no	—
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	2	2	no	—
141	C₂×#41×C₅₃	—	2	1	no	—
142	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×#41×C₅₃	C₂³	1	2	yes	—
146	C₂×#41×C₅₃	C₂³	1	2	yes	—
147	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₅₃	—	2	1	no	—
149	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
151	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
152	C₂²×D₄×C₅₃	—	2	2	no	—
153	C₂²×D₄×C₅₃	—	2	1	no	—
154	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
155	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
156	#137×C₅₃	—	4	2	no	—
157	#137×C₅₃	—	4	2	no	—
158	#137×C₅₃	—	4	2	no	—
159	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
160	#135×C₅₃	—	4	2	no	—
161	#135×C₅₃	—	4	2	no	—
162	C₂×Q₁₆×C₅₃	—	4	2	no	—
163	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
164	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
165	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
166	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
167	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
168	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
169	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
170	C₂×SD₁₆×C₅₃	—	4	2	no	—
171	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
172	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
173	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
174	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
175	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
176	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
177	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
178	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
179	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
180	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
181	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
182	C₂×D₈×C₅₃	C₂³	1	2	yes	—
183	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
184	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
185	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
186	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
187	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
188	C₄⋊Q₈×C₅₃	—	2	1	no	—
189	C₄⋊Q₈×C₅₃	—	2	1	no	—
190	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
191	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
192	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
193	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
194	#127×C₅₃	C₂³	1	2	yes	—
195	#127×C₅₃	C₂³	1	1	yes	characteristic
196	#126×C₅₃	—	2	2	no	—
197	#126×C₅₃	—	2	2	no	—
198	#126×C₅₃	—	2	2	no	—
199	#126×C₅₃	—	2	2	no	—
200	#125×C₅₃	—	2	2	no	—
201	#125×C₅₃	—	2	1	no	—
202	#125×C₅₃	—	2	2	no	—
203	#125×C₅₃	—	2	2	no	—
204	#125×C₅₃	C₂³	1	2	yes	—
205	#124×C₅₃	—	2	2	no	—
206	#124×C₅₃	—	2	1	no	—
207	#124×C₅₃	—	2	2	no	—
208	#124×C₅₃	—	2	1	no	—
209	#124×C₅₃	—	2	2	no	—
210	#124×C₅₃	—	2	1	no	—
211	#124×C₅₃	C₂³	1	2	yes	—
212	#124×C₅₃	C₂³	1	2	yes	—
213	#124×C₅₃	C₂³	1	2	yes	—
214	#124×C₅₃	C₂³	1	1	yes	characteristic
215	#124×C₅₃	C₂³	1	2	yes	—
216	#124×C₅₃	C₂³	1	2	yes	—
217	#124×C₅₃	C₂³	1	1	yes	characteristic
218	#123×C₅₃	—	2	2	no	—
219	#123×C₅₃	—	2	2	no	—
220	#123×C₅₃	—	2	2	no	—
221	#123×C₅₃	—	2	2	no	—
222	#123×C₅₃	—	2	2	no	—
223	#123×C₅₃	—	2	2	no	—
224	#123×C₅₃	—	2	2	no	—
225	C₂²⋊Q₈×C₅₃	—	2	1	no	—
226	C₂²⋊Q₈×C₅₃	—	2	1	no	—
227	C₂²⋊Q₈×C₅₃	—	2	2	no	—
228	C₂²⋊Q₈×C₅₃	—	2	2	no	—
229	C₂²⋊Q₈×C₅₃	—	2	1	no	—
230	C₂²⋊Q₈×C₅₃	—	2	1	no	—
231	C₂²⋊Q₈×C₅₃	—	2	2	no	—
232	C₂²⋊Q₈×C₅₃	—	2	2	no	—
233	C₂²⋊Q₈×C₅₃	—	2	1	no	—
234	C₂²⋊Q₈×C₅₃	—	2	2	no	—
235	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
236	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
237	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
238	#121×C₅₃	—	2	2	no	—
239	#121×C₅₃	—	2	1	no	—
240	#121×C₅₃	—	2	1	no	—
241	#121×C₅₃	—	2	2	no	—
242	#121×C₅₃	—	2	2	no	—
243	#121×C₅₃	—	2	1	no	—
244	#121×C₅₃	—	2	1	no	—
245	#121×C₅₃	—	2	1	no	—
246	#121×C₅₃	—	2	2	no	—
247	#121×C₅₃	—	2	2	no	—
248	#121×C₅₃	C₂³	1	2	yes	—
249	#120×C₅₃	—	2	2	no	—
250	#120×C₅₃	—	2	2	no	—
251	#120×C₅₃	—	2	2	no	—
252	C₄×Q₈×C₅₃	—	2	1	no	—
253	C₄×Q₈×C₅₃	—	2	1	no	—
254	C₄×Q₈×C₅₃	—	2	2	no	—
255	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
256	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
257	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
258	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
259	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
260	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₅₃	—	2	1	no	—
262	C₄×D₄×C₅₃	—	2	2	no	—
263	C₄×D₄×C₅₃	—	2	1	no	—
264	C₄×D₄×C₅₃	—	2	2	no	—
265	C₄×D₄×C₅₃	—	2	1	no	—
266	C₄×D₄×C₅₃	—	2	1	no	—
267	C₄×D₄×C₅₃	—	2	2	no	—
268	C₄×D₄×C₅₃	D₄	1	2	yes	—
269	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
270	C₄×D₄×C₅₃	D₄	1	2	yes	—
271	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
272	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
274	#117×C₅₃	—	2	1	no	—
275	#117×C₅₃	—	2	2	no	—
276	#117×C₅₃	—	2	2	no	—
277	#117×C₅₃	C₂³	1	1	yes	characteristic
278	#117×C₅₃	C₂³	1	1	yes	characteristic
279	#117×C₅₃	C₂³	1	2	yes	—
280	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
281	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
283	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
284	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
285	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
286	C₂×C₄²×C₅₃	—	2	1	no	—
287	C₂×C₄²×C₅₃	—	2	1	no	—
288	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
290	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
291	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
292	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
293	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
294	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
295	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
296	#103×C₅₃	C₂³	1	1	yes	characteristic
297	#103×C₅₃	C₂³	1	2	yes	—
298	#103×C₅₃	C₂³	1	2	yes	—
299	#103×C₅₃	C₂³	1	2	yes	—
300	#103×C₅₃	C₂³	1	1	yes	characteristic
301	#103×C₅₃	C₂³	1	2	yes	—
302	#103×C₅₃	C₂³	1	2	yes	—
303	#103×C₅₃	C₂³	1	1	yes	characteristic
304	#103×C₅₃	C₂³	1	2	yes	—
305	#103×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	1	yes	characteristic
307	#102×C₅₃	C₂³	1	2	yes	—
308	#102×C₅₃	C₂³	1	2	yes	—
309	#102×C₅₃	C₂³	1	2	yes	—
310	#102×C₅₃	C₂³	1	1	yes	characteristic
311	#102×C₅₃	C₂³	1	2	yes	—
312	#102×C₅₃	C₂³	1	2	yes	—
313	#102×C₅₃	C₂³	1	1	yes	characteristic
314	#102×C₅₃	C₂³	1	2	yes	—
315	#102×C₅₃	C₂³	1	1	yes	characteristic
316	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
317	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
319	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
320	#97×C₅₃	C₂³	1	2	yes	—
321	#97×C₅₃	C₂³	1	2	yes	—
322	C₄×C₈×C₅₃	C₂³	1	2	yes	—
323	C₄×C₈×C₅₃	C₂³	1	2	yes	—
324	C₂⁴×C₅₃	—	2	2	no	—
325	C₂⁴×C₅₃	—	2	1	no	—
326	#41×C₅₃	—	2	2	no	—
327	#41×C₅₃	—	2	2	no	—
328	#41×C₅₃	—	2	2	no	—
329	#41×C₅₃	—	2	2	no	—
330	#41×C₅₃	—	2	2	no	—
331	#41×C₅₃	—	2	2	no	—
332	#41×C₅₃	—	2	2	no	—
333	#41×C₅₃	—	2	2	no	—
334	#41×C₅₃	—	4	2	no	—
335	#41×C₅₃	—	4	2	no	—
336	#41×C₅₃	—	4	2	no	—
337	#41×C₅₃	—	4	2	no	—
338	#41×C₅₃	—	4	8	no	—
339	#41×C₅₃	—	4	4	no	—
340	#41×C₅₃	—	4	4	no	—
341	C₂×Q₈×C₅₃	—	2	1	no	—
342	C₂×Q₈×C₅₃	—	2	2	no	—
343	C₂×Q₈×C₅₃	—	2	1	no	—
344	C₂×Q₈×C₅₃	—	2	2	no	—
345	C₂×Q₈×C₅₃	—	2	2	no	—
346	C₂×Q₈×C₅₃	—	2	2	no	—
347	C₂×Q₈×C₅₃	—	2	2	no	—
348	C₂×Q₈×C₅₃	—	2	2	no	—
349	C₂×Q₈×C₅₃	—	4	2	no	—
350	C₂×Q₈×C₅₃	—	4	2	no	—
351	C₂×Q₈×C₅₃	—	4	4	no	—
352	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
353	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
354	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
357	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₅₃	—	2	1	no	—
359	C₂×D₄×C₅₃	—	2	2	no	—
360	C₂×D₄×C₅₃	—	2	1	no	—
361	C₂×D₄×C₅₃	—	2	2	no	—
362	C₂×D₄×C₅₃	—	2	1	no	—
363	C₂×D₄×C₅₃	—	2	2	no	—
364	C₂×D₄×C₅₃	—	2	2	no	—
365	C₂×D₄×C₅₃	—	2	1	no	—
366	C₂×D₄×C₅₃	—	2	1	no	—
367	C₂×D₄×C₅₃	—	2	2	no	—
368	C₂×D₄×C₅₃	—	2	1	no	—
369	C₂×D₄×C₅₃	—	2	2	no	—
370	C₂×D₄×C₅₃	—	2	2	no	—
371	C₂×D₄×C₅₃	—	2	2	no	—
372	C₂×D₄×C₅₃	—	4	2	no	—
373	C₂×D₄×C₅₃	—	4	2	no	—
374	C₂×D₄×C₅₃	—	4	8	no	—
375	C₂×D₄×C₅₃	—	4	4	no	—
376	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
377	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
378	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
379	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₅₃	—	2	1	no	—
383	C₂²×C₄×C₅₃	—	2	2	no	—
384	C₂²×C₄×C₅₃	—	2	1	no	—
385	C₂²×C₄×C₅₃	—	2	1	no	—
386	C₂²×C₄×C₅₃	—	2	1	no	—
387	C₂²×C₄×C₅₃	—	2	1	no	—
388	C₂²×C₄×C₅₃	—	2	2	no	—
389	C₂²×C₄×C₅₃	—	2	1	no	—
390	C₂²×C₄×C₅₃	—	2	2	no	—
391	C₂²×C₄×C₅₃	—	2	1	no	—
392	C₂²×C₄×C₅₃	—	2	1	no	—
393	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
396	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
397	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
398	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	Q₁₆×C₅₃	—	4	2	no	—
400	Q₁₆×C₅₃	—	4	2	no	—
401	Q₁₆×C₅₃	—	4	1	no	—
402	Q₁₆×C₅₃	—	4	1	no	—
403	Q₁₆×C₅₃	—	4	2	no	—
404	Q₁₆×C₅₃	—	4	2	no	—
405	Q₁₆×C₅₃	—	4	2	no	—
406	SD₁₆×C₅₃	—	4	2	no	—
407	SD₁₆×C₅₃	—	4	2	no	—
408	SD₁₆×C₅₃	—	4	1	no	—
409	SD₁₆×C₅₃	—	4	1	no	—
410	SD₁₆×C₅₃	—	4	1	no	—
411	SD₁₆×C₅₃	—	4	1	no	—
412	SD₁₆×C₅₃	—	4	2	no	—
413	SD₁₆×C₅₃	—	4	2	no	—
414	SD₁₆×C₅₃	—	4	2	no	—
415	SD₁₆×C₅₃	—	4	2	no	—
416	D₈×C₅₃	—	4	1	no	—
417	D₈×C₅₃	—	4	1	no	—
418	D₈×C₅₃	—	4	2	no	—
419	M₁₆×C₅₃	—	2	2	no	—
420	M₁₆×C₅₃	—	2	2	no	—
421	C₂×C₈×C₅₃	—	2	2	no	—
422	C₂×C₈×C₅₃	—	2	2	no	—
423	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
426	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
427	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
428	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
429	C₄⋊C₄×C₅₃	—	2	2	no	—
430	C₄⋊C₄×C₅₃	—	2	2	no	—
431	C₄⋊C₄×C₅₃	—	2	1	no	—
432	C₄⋊C₄×C₅₃	—	2	1	no	—
433	C₄⋊C₄×C₅₃	—	2	1	no	—
434	C₄⋊C₄×C₅₃	—	2	2	no	—
435	C₄⋊C₄×C₅₃	—	2	2	no	—
436	C₄⋊C₄×C₅₃	—	2	2	no	—
437	C₄⋊C₄×C₅₃	—	2	2	no	—
438	C₄⋊C₄×C₅₃	—	2	1	no	—
439	C₄⋊C₄×C₅₃	—	2	2	no	—
440	C₄⋊C₄×C₅₃	—	2	1	no	—
441	C₄⋊C₄×C₅₃	—	2	2	no	—
442	C₄⋊C₄×C₅₃	—	2	2	no	—
443	C₄⋊C₄×C₅₃	—	2	2	no	—
444	C₄⋊C₄×C₅₃	—	2	2	no	—
445	C₄⋊C₄×C₅₃	—	2	2	no	—
446	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
447	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
450	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
451	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
453	C₂²⋊C₄×C₅₃	—	2	2	no	—
454	C₂²⋊C₄×C₅₃	—	2	2	no	—
455	C₂²⋊C₄×C₅₃	—	2	1	no	—
456	C₂²⋊C₄×C₅₃	—	2	2	no	—
457	C₂²⋊C₄×C₅₃	—	2	2	no	—
458	C₂²⋊C₄×C₅₃	—	2	1	no	—
459	C₂²⋊C₄×C₅₃	—	2	2	no	—
460	C₂²⋊C₄×C₅₃	—	2	1	no	—
461	C₂²⋊C₄×C₅₃	—	2	2	no	—
462	C₂²⋊C₄×C₅₃	—	2	2	no	—
463	C₂²⋊C₄×C₅₃	—	2	2	no	—
464	C₂²⋊C₄×C₅₃	—	2	2	no	—
465	C₂²⋊C₄×C₅₃	—	2	2	no	—
466	C₂²⋊C₄×C₅₃	—	2	2	no	—
467	C₂²⋊C₄×C₅₃	—	2	1	no	—
468	C₂²⋊C₄×C₅₃	—	2	1	no	—
469	C₂²⋊C₄×C₅₃	—	2	2	no	—
470	C₂²⋊C₄×C₅₃	—	2	2	no	—
471	C₂²⋊C₄×C₅₃	—	2	1	no	—
472	C₂²⋊C₄×C₅₃	—	2	1	no	—
473	C₂²⋊C₄×C₅₃	—	2	2	no	—
474	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
475	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
476	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
477	C₄²×C₅₃	—	2	2	no	—
478	C₄²×C₅₃	—	2	1	no	—
479	C₄²×C₅₃	—	2	1	no	—
480	C₄²×C₅₃	—	2	1	no	—
481	C₄²×C₅₃	—	2	2	no	—
482	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
483	C₄²×C₅₃	C₂×D₄	1	2	yes	—
484	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
485	C₄²×C₅₃	C₂×D₄	1	2	yes	—
486	C₄²×C₅₃	C₂⁴	1	2	yes	—
487	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
488	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
489	C₂³×C₅₃	—	2	1	no	—
490	C₂³×C₅₃	—	2	1	no	—
491	C₂³×C₅₃	—	2	2	no	—
492	C₂³×C₅₃	—	2	1	no	—
493	C₂³×C₅₃	—	4	4	no	—
494	C₂³×C₅₃	—	4	2	no	—
495	C₂³×C₅₃	—	8	1	no	—
496	C₂³×C₅₃	—	8	1	no	—
497	C₂³×C₅₃	—	8	2	no	—
498	C₂³×C₅₃	—	8	2	no	—
499	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
500	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
501	Q₈×C₅₃	—	2	2	no	—
502	Q₈×C₅₃	—	2	2	no	—
503	Q₈×C₅₃	—	2	2	no	—
504	Q₈×C₅₃	—	2	2	no	—
505	Q₈×C₅₃	—	2	2	no	—
506	Q₈×C₅₃	—	2	1	no	—
507	Q₈×C₅₃	—	2	1	no	—
508	Q₈×C₅₃	—	2	1	no	—
509	Q₈×C₅₃	—	2	1	no	—
510	Q₈×C₅₃	—	2	1	no	—
511	Q₈×C₅₃	—	2	1	no	—
512	Q₈×C₅₃	—	4	4	no	—
513	Q₈×C₅₃	—	4	2	no	—
514	Q₈×C₅₃	—	4	2	no	—
515	Q₈×C₅₃	—	8	2	no	—
516	D₄×C₅₃	—	2	4	no	—
517	D₄×C₅₃	—	2	2	no	—
518	D₄×C₅₃	—	2	2	no	—
519	D₄×C₅₃	—	2	2	no	—
520	D₄×C₅₃	—	2	1	no	—
521	D₄×C₅₃	—	2	1	no	—
522	D₄×C₅₃	—	2	1	no	—
523	D₄×C₅₃	—	2	1	no	—
524	D₄×C₅₃	—	2	1	no	—
525	D₄×C₅₃	—	2	1	no	—
526	D₄×C₅₃	—	4	4	no	—
527	D₄×C₅₃	—	4	4	no	—
528	D₄×C₅₃	—	4	4	no	—
529	D₄×C₅₃	—	4	2	no	—
530	D₄×C₅₃	—	4	2	no	—
531	D₄×C₅₃	—	4	2	no	—
532	D₄×C₅₃	—	4	2	no	—
533	D₄×C₅₃	—	8	1	no	—
534	D₄×C₅₃	—	8	2	no	—
535	D₄×C₅₃	—	8	1	no	—
536	D₄×C₅₃	—	8	2	no	—
537	D₄×C₅₃	—	8	2	no	—
538	C₂×C₄×C₅₃	—	2	2	no	—
539	C₂×C₄×C₅₃	—	2	2	no	—
540	C₂×C₄×C₅₃	—	2	1	no	—
541	C₂×C₄×C₅₃	—	2	2	no	—
542	C₂×C₄×C₅₃	—	2	1	no	—
543	C₂×C₄×C₅₃	—	2	2	no	—
544	C₂×C₄×C₅₃	—	2	1	no	—
545	C₂×C₄×C₅₃	—	2	1	no	—
546	C₂×C₄×C₅₃	—	2	2	no	—
547	C₂×C₄×C₅₃	—	2	1	no	—
548	C₂×C₄×C₅₃	—	4	1	no	—
549	C₂×C₄×C₅₃	—	4	2	no	—
550	C₂×C₄×C₅₃	—	4	1	no	—
551	C₂×C₄×C₅₃	—	4	2	no	—
552	C₂×C₄×C₅₃	—	4	2	no	—
553	C₂×C₄×C₅₃	—	4	4	no	—
554	C₂×C₄×C₅₃	—	4	4	no	—
555	C₂×C₄×C₅₃	—	4	4	no	—
556	C₂×C₄×C₅₃	—	4	2	no	—
557	C₂×C₄×C₅₃	—	4	2	no	—
558	C₂×C₄×C₅₃	—	4	2	no	—
559	C₂×C₄×C₅₃	—	4	2	no	—
560	C₂×C₄×C₅₃	—	4	2	no	—
561	C₂×C₄×C₅₃	—	8	1	no	—
562	C₂×C₄×C₅₃	—	8	1	no	—
563	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
564	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
568	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
570	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
572	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
573	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
574	C₈×C₅₃	—	2	1	no	—
575	C₈×C₅₃	—	2	1	no	—
576	C₈×C₅₃	—	2	1	no	—
577	C₈×C₅₃	—	2	1	no	—
578	C₈×C₅₃	—	2	2	no	—
579	C₈×C₅₃	—	2	2	no	—
580	#60835	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
581	C₂²×C₅₃	—	2	1	no	—
582	C₂²×C₅₃	—	2	1	no	—
583	C₂²×C₅₃	—	2	2	no	—
584	C₂²×C₅₃	—	2	2	no	—
585	C₂²×C₅₃	—	2	2	no	—
586	C₂²×C₅₃	—	4	1	no	—
587	C₂²×C₅₃	—	4	1	no	—
588	C₂²×C₅₃	—	4	2	no	—
589	C₂²×C₅₃	—	4	1	no	—
590	C₂²×C₅₃	—	4	1	no	—
591	C₂²×C₅₃	—	4	1	no	—
592	C₂²×C₅₃	—	4	2	no	—
593	C₂²×C₅₃	—	4	1	no	—
594	C₂²×C₅₃	—	4	1	no	—
595	C₂²×C₅₃	—	4	2	no	—
596	C₂²×C₅₃	—	4	1	no	—
597	C₂²×C₅₃	—	4	1	no	—
598	C₂²×C₅₃	—	16	2	no	—
599	C₂²×C₅₃	—	16	4	no	—
600	C₂²×C₅₃	#535	1	2	yes	—
601	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
602	C₄×C₅₃	—	2	1	no	—
603	C₄×C₅₃	—	2	1	no	—
604	C₄×C₅₃	—	2	2	no	—
605	C₄×C₅₃	—	2	1	no	—
606	C₄×C₅₃	—	2	1	no	—
607	C₄×C₅₃	—	2	2	no	—
608	C₄×C₅₃	—	2	2	no	—
609	C₄×C₅₃	—	4	2	no	—
610	C₄×C₅₃	—	4	1	no	—
611	C₄×C₅₃	—	4	1	no	—
612	C₄×C₅₃	—	4	1	no	—
613	C₄×C₅₃	—	4	2	no	—
614	C₄×C₅₃	—	4	1	no	—
615	C₄×C₅₃	—	4	1	no	—
616	C₄×C₅₃	—	4	2	no	—
617	C₄×C₅₃	#535	1	2	yes	—
618	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
619	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
620	#3500	C₂×C₅₃	1	1	yes	characteristic, complemented
621	#3461	C₂×C₅₃	1	1	yes	characteristic, complemented
622	#3225	C₂×C₅₃	1	2	yes	complemented
623	#3224	C₂×C₅₃	1	2	yes	complemented
624	#3223	C₂×C₅₃	1	2	yes	complemented
625	#3222	C₂×C₅₃	1	2	yes	complemented
626	#3219	C₂×C₅₃	1	2	yes	complemented
627	#3215	C₂×C₅₃	1	2	yes	complemented
628	#3211	C₂×C₅₃	1	2	yes	complemented
629	#3210	C₂×C₅₃	1	2	yes	complemented
630	#3156	C₂×C₅₃	1	1	yes	characteristic, complemented
631	#3154	C₂×C₅₃	1	1	yes	characteristic, complemented
632	#3137	C₂×C₅₃	1	1	yes	characteristic, complemented
633	#3136	C₂×C₅₃	1	1	yes	characteristic, complemented
634	#3040	C₂×C₅₃	1	1	yes	characteristic, complemented
635	#3037	C₂×C₅₃	1	1	yes	characteristic, complemented
636	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
637	C₂×#464	C₂×C₅₃	1	1	yes	characteristic, complemented
638	#3013	C₂×C₅₃	1	1	yes	characteristic, complemented
639	#3012	C₂×C₅₃	1	1	yes	characteristic, complemented
640	#3011	C₂×C₅₃	1	1	yes	characteristic, complemented
641	#3009	C₂×C₅₃	1	1	yes	characteristic, complemented
642	#2925	C₂×C₅₃	1	1	yes	characteristic, complemented
643	C₂×C₅₃	—	2	2	no	—
644	C₂×C₅₃	—	4	2	no	—
645	C₂×C₅₃	—	8	1	no	—
646	C₂×C₅₃	—	8	1	no	—
647	C₂×C₅₃	—	8	2	no	—
648	C₂×C₅₃	—	8	1	no	—
649	C₂×C₅₃	C₂×#535	1	1	yes	characteristic
650	C₂×C₅₃	#3584	1	1	yes	characteristic
651	C₂×C₅₃	#3586	1	1	yes	characteristic
652	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic
653	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
654	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
655	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
656	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
657	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
658	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
659	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
660	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
661	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
662	#548	—	2	1	no	—
663	#548	—	2	1	no	—
664	#546	—	2	2	no	—
665	#546	—	2	1	no	—
666	#546	—	2	2	no	—
667	#546	—	2	1	no	—
668	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
669	#542	—	2	1	no	—
670	#542	C₂²×C₅₃	1	2	yes	complemented
671	#541	—	2	1	no	—
672	#541	C₂²×C₅₃	1	2	yes	complemented
673	#539	—	2	2	no	—
674	#537	C₂²×C₅₃	1	1	yes	characteristic
675	#536	C₂²×C₅₃	1	1	yes	characteristic
676	#536	C₂²×C₅₃	1	2	yes	—
677	#536	C₂²×C₅₃	1	1	yes	characteristic
678	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
679	#535	C₂²×C₅₃	1	1	yes	characteristic
680	#535	C₂²×C₅₃	1	2	yes	—
681	#533	—	2	1	no	—
682	#533	C₂²×C₅₃	1	2	yes	complemented
683	#532	C₂²×C₅₃	1	2	yes	—
684	#532	C₂²×C₅₃	1	1	yes	characteristic
685	#529	—	2	2	no	—
686	#529	—	2	1	no	—
687	#529	C₂²×C₅₃	1	2	yes	complemented
688	C₂×#124	C₂²×C₅₃	1	2	yes	—
689	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
690	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
691	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
692	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	#497	C₂²×C₅₃	1	2	yes	complemented
694	#497	C₂²×C₅₃	1	2	yes	complemented
695	#497	C₂²×C₅₃	1	2	yes	complemented
696	#496	C₂²×C₅₃	1	2	yes	complemented
697	#495	C₂²×C₅₃	1	2	yes	complemented
698	#495	C₂²×C₅₃	1	2	yes	complemented
699	#494	C₂²×C₅₃	1	2	yes	complemented
700	#492	C₂²×C₅₃	1	2	yes	complemented
701	#491	C₂²×C₅₃	1	2	yes	complemented
702	#490	C₂²×C₅₃	1	2	yes	complemented
703	#489	C₂²×C₅₃	1	2	yes	complemented
704	#489	C₂²×C₅₃	1	2	yes	complemented
705	#488	C₂²×C₅₃	1	2	yes	complemented
706	#488	C₂²×C₅₃	1	2	yes	complemented
707	#487	C₂²×C₅₃	1	2	yes	complemented
708	#486	C₂²×C₅₃	1	2	yes	complemented
709	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
710	#464	C₂²×C₅₃	1	2	yes	complemented
711	#464	C₂²×C₅₃	1	2	yes	complemented
712	#464	C₂²×C₅₃	1	2	yes	complemented
713	#464	C₂²×C₅₃	1	2	yes	complemented
714	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
715	#464	C₂²×C₅₃	1	2	yes	complemented
716	#464	C₂²×C₅₃	1	2	yes	complemented
717	#464	C₂²×C₅₃	1	2	yes	complemented
718	#464	C₂²×C₅₃	1	2	yes	complemented
719	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
720	#463	C₂²×C₅₃	1	2	yes	complemented
721	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	#463	C₂²×C₅₃	1	2	yes	complemented
723	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
724	#462	C₂²×C₅₃	1	2	yes	complemented
725	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
726	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
727	#460	C₂²×C₅₃	1	2	yes	complemented
728	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
729	#452	C₂²×C₅₃	1	2	yes	—
730	#452	C₂²×C₅₃	1	2	yes	—
731	#452	C₂²×C₅₃	1	2	yes	—
732	#452	C₂²×C₅₃	1	2	yes	complemented
733	#452	C₂²×C₅₃	1	2	yes	complemented
734	#452	C₂²×C₅₃	1	2	yes	complemented
735	#451	C₂²×C₅₃	1	2	yes	complemented
736	#451	C₂²×C₅₃	1	2	yes	complemented
737	#451	C₂²×C₅₃	1	2	yes	complemented
738	#450	C₂²×C₅₃	1	2	yes	—
739	#450	C₂²×C₅₃	1	2	yes	—
740	#450	C₂²×C₅₃	1	2	yes	—
741	#449	C₂²×C₅₃	1	2	yes	—
742	#449	C₂²×C₅₃	1	2	yes	complemented
743	#448	C₂²×C₅₃	1	2	yes	complemented
744	#447	C₂²×C₅₃	1	2	yes	—
745	#433	C₂²×C₅₃	1	2	yes	complemented
746	#433	C₂²×C₅₃	1	2	yes	complemented
747	#432	C₂²×C₅₃	1	2	yes	complemented
748	#431	C₂²×C₅₃	1	2	yes	complemented
749	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
750	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
751	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
752	#418	C₂²×C₅₃	1	1	yes	characteristic
753	#417	C₂²×C₅₃	1	1	yes	characteristic
754	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
755	#416	C₂²×C₅₃	1	1	yes	characteristic
756	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
757	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
758	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
759	#408	C₂²×C₅₃	1	1	yes	characteristic
760	#408	C₂²×C₅₃	1	1	yes	characteristic
761	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
762	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
763	C₅₃	#60835	1	1	yes	characteristic, direct product factor, Sylow
764	2₋¹⁺⁴	—	4	2	no	—
765	2₋¹⁺⁴	—	4	2	no	—
766	H(5,𝔽₂)	—	4	2	no	—
767	H(5,𝔽₂)	—	4	2	no	—
768	C₂×#41	—	2	1	no	—
769	C₂×#41	—	2	2	no	—
770	C₂×#41	—	2	1	no	—
771	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
772	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
773	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
774	C₂×#41	C₂³×C₅₃	1	2	yes	—
775	C₂×#41	C₂³×C₅₃	1	2	yes	—
776	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
777	C₂²×Q₈	—	2	1	no	—
778	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
779	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
780	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
781	C₂²×D₄	—	2	2	no	—
782	C₂²×D₄	—	2	1	no	—
783	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
784	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
785	#137	—	4	2	no	—
786	#137	—	4	2	no	—
787	#137	—	4	2	no	—
788	AGL(1,ℤ/8)	—	4	2	no	—
789	#135	—	4	2	no	—
790	#135	—	4	2	no	—
791	C₂×Q₁₆	—	4	2	no	—
792	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
793	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
794	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
795	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
796	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
797	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
798	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
799	C₂×SD₁₆	—	4	2	no	—
800	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
801	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
802	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
803	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
804	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
805	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
806	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
807	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
808	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
809	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
810	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
811	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
812	C₂×D₈	C₂³×C₅₃	1	2	yes	—
813	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
814	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
815	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
816	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
817	C₄⋊Q₈	—	2	1	no	—
818	C₄⋊Q₈	—	2	1	no	—
819	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
820	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
821	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
822	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
823	#127	C₂³×C₅₃	1	1	yes	characteristic
824	#127	C₂³×C₅₃	1	2	yes	—
825	#126	—	2	2	no	—
826	#126	—	2	2	no	—
827	#126	—	2	2	no	—
828	#126	—	2	2	no	—
829	#125	—	2	2	no	—
830	#125	—	2	1	no	—
831	#125	—	2	2	no	—
832	#125	—	2	2	no	—
833	#125	C₂³×C₅₃	1	2	yes	—
834	#124	—	2	1	no	—
835	#124	—	2	2	no	—
836	#124	—	2	1	no	—
837	#124	—	2	2	no	—
838	#124	—	2	1	no	—
839	#124	—	2	2	no	—
840	#124	C₂³×C₅₃	1	1	yes	characteristic
841	#124	C₂³×C₅₃	1	2	yes	—
842	#124	C₂³×C₅₃	1	2	yes	—
843	#124	C₂³×C₅₃	1	2	yes	—
844	#124	C₂³×C₅₃	1	2	yes	—
845	#124	C₂³×C₅₃	1	2	yes	—
846	#124	C₂³×C₅₃	1	1	yes	characteristic
847	#123	—	2	2	no	—
848	#123	—	2	2	no	—
849	#123	—	2	2	no	—
850	#123	—	2	2	no	—
851	#123	—	2	2	no	—
852	#123	—	2	2	no	—
853	#123	—	2	2	no	—
854	C₂²⋊Q₈	—	2	1	no	—
855	C₂²⋊Q₈	—	2	2	no	—
856	C₂²⋊Q₈	—	2	1	no	—
857	C₂²⋊Q₈	—	2	1	no	—
858	C₂²⋊Q₈	—	2	2	no	—
859	C₂²⋊Q₈	—	2	1	no	—
860	C₂²⋊Q₈	—	2	2	no	—
861	C₂²⋊Q₈	—	2	1	no	—
862	C₂²⋊Q₈	—	2	2	no	—
863	C₂²⋊Q₈	—	2	2	no	—
864	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
865	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
866	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
867	#121	—	2	2	no	—
868	#121	—	2	1	no	—
869	#121	—	2	1	no	—
870	#121	—	2	1	no	—
871	#121	—	2	2	no	—
872	#121	—	2	2	no	—
873	#121	—	2	1	no	—
874	#121	—	2	2	no	—
875	#121	—	2	1	no	—
876	#121	—	2	2	no	—
877	#121	C₂³×C₅₃	1	2	yes	—
878	#120	—	2	2	no	—
879	#120	—	2	2	no	—
880	#120	—	2	2	no	—
881	C₄×Q₈	—	2	1	no	—
882	C₄×Q₈	—	2	1	no	—
883	C₄×Q₈	—	2	2	no	—
884	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
885	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
886	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
887	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
888	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
889	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	2	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	2	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	—	2	2	no	—
897	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
898	C₄×D₄	D₄×C₅₃	1	2	yes	—
899	C₄×D₄	D₄×C₅₃	1	2	yes	—
900	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
901	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
902	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
903	#117	—	2	2	no	—
904	#117	—	2	1	no	—
905	#117	—	2	2	no	—
906	#117	C₂³×C₅₃	1	1	yes	characteristic
907	#117	C₂³×C₅₃	1	1	yes	characteristic
908	#117	C₂³×C₅₃	1	2	yes	—
909	C₂×C₄⋊C₄	—	2	1	no	—
910	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
911	C₂×C₂²⋊C₄	—	2	1	no	—
912	C₂×C₂²⋊C₄	—	2	1	no	—
913	C₂×C₂²⋊C₄	—	2	2	no	—
914	C₂×C₂²⋊C₄	—	2	2	no	—
915	C₂×C₄²	—	2	1	no	—
916	C₂×C₄²	—	2	1	no	—
917	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
918	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
919	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
920	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
921	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
922	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
923	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
924	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
925	#103	C₂³×C₅₃	1	2	yes	—
926	#103	C₂³×C₅₃	1	2	yes	—
927	#103	C₂³×C₅₃	1	1	yes	characteristic
928	#103	C₂³×C₅₃	1	1	yes	characteristic
929	#103	C₂³×C₅₃	1	1	yes	characteristic
930	#103	C₂³×C₅₃	1	1	yes	characteristic
931	#103	C₂³×C₅₃	1	2	yes	—
932	#103	C₂³×C₅₃	1	2	yes	—
933	#103	C₂³×C₅₃	1	2	yes	—
934	#103	C₂³×C₅₃	1	2	yes	—
935	#102	C₂³×C₅₃	1	2	yes	—
936	#102	C₂³×C₅₃	1	2	yes	—
937	#102	C₂³×C₅₃	1	1	yes	characteristic
938	#102	C₂³×C₅₃	1	1	yes	characteristic
939	#102	C₂³×C₅₃	1	1	yes	characteristic
940	#102	C₂³×C₅₃	1	1	yes	characteristic
941	#102	C₂³×C₅₃	1	2	yes	—
942	#102	C₂³×C₅₃	1	2	yes	—
943	#102	C₂³×C₅₃	1	2	yes	—
944	#102	C₂³×C₅₃	1	2	yes	—
945	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
946	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
947	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
948	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
949	#97	C₂³×C₅₃	1	2	yes	—
950	#97	C₂³×C₅₃	1	2	yes	—
951	C₄×C₈	C₂³×C₅₃	1	2	yes	—
952	C₄×C₈	C₂³×C₅₃	1	2	yes	—
953	C₂⁴	—	2	2	no	—
954	C₂⁴	—	2	1	no	—
955	#41	—	2	2	no	—
956	#41	—	2	2	no	—
957	#41	—	2	2	no	—
958	#41	—	2	2	no	—
959	#41	—	2	2	no	—
960	#41	—	2	2	no	—
961	#41	—	2	2	no	—
962	#41	—	2	2	no	—
963	#41	—	4	2	no	—
964	#41	—	4	2	no	—
965	#41	—	4	2	no	—
966	#41	—	4	2	no	—
967	#41	—	4	8	no	—
968	#41	—	4	4	no	—
969	#41	—	4	4	no	—
970	C₂×Q₈	—	2	1	no	—
971	C₂×Q₈	—	2	2	no	—
972	C₂×Q₈	—	2	1	no	—
973	C₂×Q₈	—	2	2	no	—
974	C₂×Q₈	—	2	2	no	—
975	C₂×Q₈	—	2	2	no	—
976	C₂×Q₈	—	2	2	no	—
977	C₂×Q₈	—	2	2	no	—
978	C₂×Q₈	—	4	2	no	—
979	C₂×Q₈	—	4	2	no	—
980	C₂×Q₈	—	4	4	no	—
981	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
982	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
983	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
984	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
985	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
986	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
987	C₂×D₄	—	2	1	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	2	1	no	—
990	C₂×D₄	—	2	2	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	2	no	—
993	C₂×D₄	—	2	2	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	2	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	4	2	no	—
1002	C₂×D₄	—	4	2	no	—
1003	C₂×D₄	—	4	8	no	—
1004	C₂×D₄	—	4	4	no	—
1005	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1006	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1007	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1008	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1009	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1010	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	2	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	1	no	—
1015	C₂²×C₄	—	2	1	no	—
1016	C₂²×C₄	—	2	1	no	—
1017	C₂²×C₄	—	2	2	no	—
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	—	2	2	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1023	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1024	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1025	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1026	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1027	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1028	Q₁₆	—	4	2	no	—
1029	Q₁₆	—	4	2	no	—
1030	Q₁₆	—	4	1	no	—
1031	Q₁₆	—	4	1	no	—
1032	Q₁₆	—	4	2	no	—
1033	Q₁₆	—	4	2	no	—
1034	Q₁₆	—	4	2	no	—
1035	SD₁₆	—	4	2	no	—
1036	SD₁₆	—	4	2	no	—
1037	SD₁₆	—	4	1	no	—
1038	SD₁₆	—	4	1	no	—
1039	SD₁₆	—	4	1	no	—
1040	SD₁₆	—	4	1	no	—
1041	SD₁₆	—	4	2	no	—
1042	SD₁₆	—	4	2	no	—
1043	SD₁₆	—	4	2	no	—
1044	SD₁₆	—	4	2	no	—
1045	D₈	—	4	1	no	—
1046	D₈	—	4	1	no	—
1047	D₈	—	4	2	no	—
1048	M₁₆	—	2	2	no	—
1049	M₁₆	—	2	2	no	—
1050	C₂×C₈	—	2	2	no	—
1051	C₂×C₈	—	2	2	no	—
1052	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1053	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1054	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1055	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1056	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1057	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	2	no	—
1065	C₄⋊C₄	—	2	2	no	—
1066	C₄⋊C₄	—	2	2	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	2	2	no	—
1071	C₄⋊C₄	—	2	2	no	—
1072	C₄⋊C₄	—	2	2	no	—
1073	C₄⋊C₄	—	2	2	no	—
1074	C₄⋊C₄	—	2	2	no	—
1075	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1076	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1077	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1078	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1079	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1080	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1081	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	1	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1104	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1105	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1106	C₄²	—	2	2	no	—
1107	C₄²	—	2	1	no	—
1108	C₄²	—	2	1	no	—
1109	C₄²	—	2	1	no	—
1110	C₄²	—	2	2	no	—
1111	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1112	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1113	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1114	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1115	C₄²	C₂⁴×C₅₃	1	2	yes	—
1116	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1117	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1118	C₂³	—	2	1	no	—
1119	C₂³	—	2	2	no	—
1120	C₂³	—	2	1	no	—
1121	C₂³	—	2	1	no	—
1122	C₂³	—	4	4	no	—
1123	C₂³	—	4	2	no	—
1124	C₂³	—	8	1	no	—
1125	C₂³	—	8	1	no	—
1126	C₂³	—	8	2	no	—
1127	C₂³	—	8	2	no	—
1128	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1129	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1130	Q₈	—	2	2	no	—
1131	Q₈	—	2	2	no	—
1132	Q₈	—	2	2	no	—
1133	Q₈	—	2	1	no	—
1134	Q₈	—	2	1	no	—
1135	Q₈	—	2	2	no	—
1136	Q₈	—	2	1	no	—
1137	Q₈	—	2	1	no	—
1138	Q₈	—	2	2	no	—
1139	Q₈	—	2	1	no	—
1140	Q₈	—	2	1	no	—
1141	Q₈	—	4	4	no	—
1142	Q₈	—	4	2	no	—
1143	Q₈	—	4	2	no	—
1144	Q₈	—	8	2	no	—
1145	D₄	—	2	4	no	—
1146	D₄	—	2	2	no	—
1147	D₄	—	2	1	no	—
1148	D₄	—	2	1	no	—
1149	D₄	—	2	2	no	—
1150	D₄	—	2	1	no	—
1151	D₄	—	2	1	no	—
1152	D₄	—	2	2	no	—
1153	D₄	—	2	1	no	—
1154	D₄	—	2	1	no	—
1155	D₄	—	4	4	no	—
1156	D₄	—	4	4	no	—
1157	D₄	—	4	4	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	8	1	no	—
1163	D₄	—	8	2	no	—
1164	D₄	—	8	1	no	—
1165	D₄	—	8	2	no	—
1166	D₄	—	8	2	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	4	2	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	4	2	no	—
1182	C₂×C₄	—	4	4	no	—
1183	C₂×C₄	—	4	4	no	—
1184	C₂×C₄	—	4	4	no	—
1185	C₂×C₄	—	4	2	no	—
1186	C₂×C₄	—	4	2	no	—
1187	C₂×C₄	—	4	2	no	—
1188	C₂×C₄	—	4	2	no	—
1189	C₂×C₄	—	4	2	no	—
1190	C₂×C₄	—	8	1	no	—
1191	C₂×C₄	—	8	1	no	—
1192	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1193	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1194	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1195	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1196	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1197	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1198	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1199	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1200	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1201	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1202	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1203	C₈	—	2	1	no	—
1204	C₈	—	2	1	no	—
1205	C₈	—	2	1	no	—
1206	C₈	—	2	1	no	—
1207	C₈	—	2	2	no	—
1208	C₈	—	2	2	no	—
1209	C₂²	—	2	1	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	2	no	—
1212	C₂²	—	2	2	no	—
1213	C₂²	—	2	2	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	2	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	2	no	—
1221	C₂²	—	4	1	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	2	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	16	2	no	—
1227	C₂²	—	16	4	no	—
1228	C₂²	C₅₃×#535	1	2	yes	—
1229	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1230	C₄	—	2	1	no	—
1231	C₄	—	2	1	no	—
1232	C₄	—	2	2	no	—
1233	C₄	—	2	1	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	2	no	—
1236	C₄	—	2	2	no	—
1237	C₄	—	4	2	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	2	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	2	no	—
1245	C₄	C₅₃×#535	1	2	yes	—
1246	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1247	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1248	C₂	—	2	2	no	—
1249	C₂	—	4	2	no	—
1250	C₂	—	8	2	no	—
1251	C₂	—	8	1	no	—
1252	C₂	—	8	1	no	—
1253	C₂	—	8	1	no	—
1254	C₂	C₂×C₅₃×#535	1	1	yes	characteristic
1255	C₂	C₅₃×#3584	1	1	yes	characteristic
1256	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×#3500	C₂	semidirect
2. C₅₃×#3461	C₂	semidirect
3. C₅₃×#3225	C₂	semidirect
4. C₅₃×#3224	C₂	semidirect
5. C₅₃×#3223	C₂	semidirect
6. C₅₃×#3222	C₂	semidirect
7. C₅₃×#3219	C₂	semidirect
8. C₅₃×#3215	C₂	semidirect
9. C₅₃×#3211	C₂	semidirect
10. C₅₃×#3210	C₂	semidirect
11. C₅₃×#3156	C₂	semidirect
12. C₅₃×#3154	C₂	semidirect
13. C₅₃×#3137	C₂	semidirect
14. C₅₃×#3136	C₂	semidirect
15. C₅₃×#3040	C₂	semidirect
16. C₅₃×#3037	C₂	semidirect
17. C₅₃×#3035	C₂	semidirect
18. C₂×C₅₃×#464	C₂	semidirect
19. C₅₃×#3013	C₂	semidirect
20. C₅₃×#3012	C₂	semidirect
21. C₅₃×#3011	C₂	semidirect
22. C₅₃×#3009	C₂	semidirect
23. C₅₃×#2925	C₂	semidirect
27. C₂×#137×C₅₃	C₂²	semidirect
28. C₂×#137×C₅₃	C₂²	semidirect
31. C₂×#135×C₅₃	C₂²	semidirect
32. C₂²×Q₁₆×C₅₃	C₂²	semidirect
40. C₅₃×#544	C₂²	semidirect
42. C₅₃×#542	C₂²	semidirect
44. C₅₃×#541	C₂²	semidirect
50. C₅₃×#536	C₂²	semidirect
54. C₅₃×#533	C₂²	semidirect
59. C₅₃×#529	C₂²	semidirect
63. C₄×#41×C₅₃	C₂²	semidirect
64. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
65. C₅₃×#497	C₂²	semidirect
66. C₅₃×#497	C₂²	semidirect
67. C₅₃×#497	C₂²	semidirect
68. C₅₃×#496	C₂²	semidirect
69. C₅₃×#495	C₂²	semidirect
70. C₅₃×#495	C₂²	semidirect
71. C₅₃×#494	C₂²	semidirect
72. C₅₃×#492	C₂²	semidirect
73. C₅₃×#491	C₂²	semidirect
74. C₅₃×#490	C₂²	semidirect
75. C₅₃×#489	C₂²	semidirect
76. C₅₃×#489	C₂²	semidirect
77. C₅₃×#488	C₂²	semidirect
78. C₅₃×#488	C₂²	semidirect
79. C₅₃×#487	C₂²	semidirect
80. C₅₃×#486	C₂²	semidirect
81. C₅₃×#464	C₂²	semidirect
82. C₅₃×#464	C₂²	semidirect
83. C₅₃×#464	C₂²	semidirect
84. C₅₃×#464	C₂²	semidirect
85. C₅₃×#464	C₂²	semidirect
86. C₅₃×#464	C₂²	semidirect
87. C₅₃×#464	C₂²	semidirect
88. C₅₃×#464	C₂²	semidirect
89. C₅₃×#464	C₂²	semidirect
90. C₅₃×#464	C₂²	semidirect
91. C₅₃×#463	C₂²	semidirect
92. C₅₃×#463	C₂²	semidirect
93. C₅₃×#463	C₂²	semidirect
94. C₅₃×#463	C₂²	semidirect
95. C₅₃×#462	C₂²	semidirect
96. C₅₃×#462	C₂²	semidirect
97. C₅₃×#461	C₂²	semidirect
98. C₅₃×#460	C₂²	semidirect
99. C₅₃×#460	C₂²	semidirect
100. C₅₃×#459	C₂²	semidirect
104. C₅₃×#452	C₂²	semidirect
105. C₅₃×#452	C₂²	semidirect
106. C₅₃×#452	C₂²	semidirect
107. C₅₃×#451	C₂²	semidirect
108. C₅₃×#451	C₂²	semidirect
109. C₅₃×#451	C₂²	semidirect
114. C₅₃×#449	C₂²	semidirect
115. C₅₃×#448	C₂²	semidirect
117. C₅₃×#433	C₂²	semidirect
118. C₅₃×#433	C₂²	semidirect
119. C₅₃×#432	C₂²	semidirect
120. C₅₃×#431	C₂²	semidirect
121. C₅₃×#423	C₂²	semidirect
122. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
123. C₅₃×#419	C₂²	semidirect
126. C₅₃×#417	C₂²	semidirect
128. C₅₃×#416	C₂²	semidirect
129. C₂×#103×C₅₃	C₂²	semidirect
133. C₅₃×#405	C₂²	semidirect
134. C₅₃×#405	C₂²	semidirect
580. #60835	C₅₃	direct (N × H)
620. #3500	C₂×C₅₃	semidirect
621. #3461	C₂×C₅₃	semidirect
622. #3225	C₂×C₅₃	semidirect
623. #3224	C₂×C₅₃	semidirect
624. #3223	C₂×C₅₃	semidirect
625. #3222	C₂×C₅₃	semidirect
626. #3219	C₂×C₅₃	semidirect
627. #3215	C₂×C₅₃	semidirect
628. #3211	C₂×C₅₃	semidirect
629. #3210	C₂×C₅₃	semidirect
630. #3156	C₂×C₅₃	semidirect
631. #3154	C₂×C₅₃	semidirect
632. #3137	C₂×C₅₃	semidirect
633. #3136	C₂×C₅₃	semidirect
634. #3040	C₂×C₅₃	semidirect
635. #3037	C₂×C₅₃	semidirect
636. #3035	C₂×C₅₃	semidirect
637. C₂×#464	C₂×C₅₃	semidirect
638. #3013	C₂×C₅₃	semidirect
639. #3012	C₂×C₅₃	semidirect
640. #3011	C₂×C₅₃	semidirect
641. #3009	C₂×C₅₃	semidirect
642. #2925	C₂×C₅₃	semidirect
655. C₂×#137	C₂²×C₅₃	semidirect
656. C₂×#137	C₂²×C₅₃	semidirect
659. C₂×#135	C₂²×C₅₃	semidirect
660. C₂²×Q₁₆	C₂²×C₅₃	semidirect
668. #544	C₂²×C₅₃	semidirect
670. #542	C₂²×C₅₃	semidirect
672. #541	C₂²×C₅₃	semidirect
678. #536	C₂²×C₅₃	semidirect
682. #533	C₂²×C₅₃	semidirect
687. #529	C₂²×C₅₃	semidirect
691. C₄×#41	C₂²×C₅₃	semidirect
692. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
693. #497	C₂²×C₅₃	semidirect
694. #497	C₂²×C₅₃	semidirect
695. #497	C₂²×C₅₃	semidirect
696. #496	C₂²×C₅₃	semidirect
697. #495	C₂²×C₅₃	semidirect
698. #495	C₂²×C₅₃	semidirect
699. #494	C₂²×C₅₃	semidirect
700. #492	C₂²×C₅₃	semidirect
701. #491	C₂²×C₅₃	semidirect
702. #490	C₂²×C₅₃	semidirect
703. #489	C₂²×C₅₃	semidirect
704. #489	C₂²×C₅₃	semidirect
705. #488	C₂²×C₅₃	semidirect
706. #488	C₂²×C₅₃	semidirect
707. #487	C₂²×C₅₃	semidirect
708. #486	C₂²×C₅₃	semidirect
709. #464	C₂²×C₅₃	semidirect
710. #464	C₂²×C₅₃	semidirect
711. #464	C₂²×C₅₃	semidirect
712. #464	C₂²×C₅₃	semidirect
713. #464	C₂²×C₅₃	semidirect
714. #464	C₂²×C₅₃	semidirect
715. #464	C₂²×C₅₃	semidirect
716. #464	C₂²×C₅₃	semidirect
717. #464	C₂²×C₅₃	semidirect
718. #464	C₂²×C₅₃	semidirect
719. #463	C₂²×C₅₃	semidirect
720. #463	C₂²×C₅₃	semidirect
721. #463	C₂²×C₅₃	semidirect
722. #463	C₂²×C₅₃	semidirect
723. #462	C₂²×C₅₃	semidirect
724. #462	C₂²×C₅₃	semidirect
725. #461	C₂²×C₅₃	semidirect
726. #460	C₂²×C₅₃	semidirect
727. #460	C₂²×C₅₃	semidirect
728. #459	C₂²×C₅₃	semidirect
732. #452	C₂²×C₅₃	semidirect
733. #452	C₂²×C₅₃	semidirect
734. #452	C₂²×C₅₃	semidirect
735. #451	C₂²×C₅₃	semidirect
736. #451	C₂²×C₅₃	semidirect
737. #451	C₂²×C₅₃	semidirect
742. #449	C₂²×C₅₃	semidirect
743. #448	C₂²×C₅₃	semidirect
745. #433	C₂²×C₅₃	semidirect
746. #433	C₂²×C₅₃	semidirect
747. #432	C₂²×C₅₃	semidirect
748. #431	C₂²×C₅₃	semidirect
749. #423	C₂²×C₅₃	semidirect
750. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
751. #419	C₂²×C₅₃	semidirect
754. #417	C₂²×C₅₃	semidirect
756. #416	C₂²×C₅₃	semidirect
757. C₂×#103	C₂²×C₅₃	semidirect
761. #405	C₂²×C₅₃	semidirect
762. #405	C₂²×C₅₃	semidirect
763. C₅₃	#60835	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×#3500	2
C₅₃×#3461	2
C₅₃×#3225	2
C₅₃×#3224	2
C₅₃×#3223	2
C₅₃×#3222	2
C₅₃×#3219	2
C₅₃×#3215	2
C₅₃×#3211	2
C₅₃×#3210	2
C₅₃×#3156	2
C₅₃×#3154	2
C₅₃×#3137	2
C₅₃×#3136	2
C₅₃×#3040	2
C₅₃×#3037	2
C₅₃×#3035	2
C₂×C₅₃×#464	2
C₅₃×#3013	2
C₅₃×#3012	2
C₅₃×#3011	2
C₅₃×#3009	2
C₅₃×#2925	2
#60835	53

Subgroups — C53×#60835 #27268347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60835 #27268347