Subgroups — C₅₃×#60767 #27268279

Order 13568.

2208 conjugacy classes of subgroups.

The subgroup lattice has 1358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3488	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3201	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3200	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3199	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3198	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3197	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3194	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3191	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3188	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3061	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3060	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₅₃×#550	—	2	1	no	—
34	C₅₃×#548	—	2	1	no	—
35	C₅₃×#546	—	2	2	no	—
36	C₅₃×#546	—	2	1	no	—
37	D₄²×C₅₃	—	2	1	no	—
38	D₄²×C₅₃	—	2	2	no	—
39	C₅₃×#537	C₂²	1	1	yes	characteristic
40	C₅₃×#537	C₂²	1	1	yes	characteristic
41	C₅₃×#537	C₂²	1	2	yes	—
42	C₅₃×#537	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#537	C₂²	1	1	yes	characteristic, complemented
44	C₅₃×#537	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#536	—	2	1	no	—
46	C₅₃×#536	C₂²	1	2	yes	complemented
47	C₅₃×#535	—	2	1	no	—
48	C₅₃×#535	C₂²	1	2	yes	—
49	C₅₃×#535	C₂²	1	2	yes	complemented
50	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#534	—	2	2	no	—
52	C₅₃×#532	—	2	2	no	—
53	C₅₃×#525	—	2	1	no	—
54	C₅₃×#525	—	2	1	no	—
55	C₅₃×#525	C₂²	1	1	yes	characteristic
56	C₅₃×#525	C₂²	1	2	yes	complemented
57	C₅₃×#525	C₂²	1	2	yes	complemented
58	C₅₃×#525	C₂²	1	2	yes	complemented
59	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
60	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
61	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
62	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#485	C₂²	1	2	yes	complemented
64	C₅₃×#485	C₂²	1	2	yes	complemented
65	C₅₃×#485	C₂²	1	2	yes	complemented
66	C₅₃×#485	C₂²	1	2	yes	complemented
67	C₅₃×#484	C₂²	1	2	yes	complemented
68	C₅₃×#483	C₂²	1	2	yes	complemented
69	C₅₃×#482	C₂²	1	2	yes	complemented
70	C₅₃×#482	C₂²	1	2	yes	complemented
71	C₅₃×#482	C₂²	1	2	yes	complemented
72	C₅₃×#482	C₂²	1	2	yes	complemented
73	C₅₃×#482	C₂²	1	2	yes	complemented
74	C₅₃×#482	C₂²	1	2	yes	complemented
75	C₅₃×#482	C₂²	1	2	yes	complemented
76	C₅₃×#482	C₂²	1	2	yes	complemented
77	C₅₃×#481	C₂²	1	2	yes	complemented
78	C₅₃×#480	C₂²	1	2	yes	complemented
79	C₅₃×#470	C₂²	1	2	yes	complemented
80	C₅₃×#469	C₂²	1	2	yes	complemented
81	C₅₃×#469	C₂²	1	2	yes	complemented
82	C₅₃×#469	C₂²	1	2	yes	complemented
83	C₅₃×#468	C₂²	1	2	yes	complemented
84	C₅₃×#468	C₂²	1	2	yes	complemented
85	C₅₃×#468	C₂²	1	2	yes	complemented
86	C₅₃×#468	C₂²	1	2	yes	complemented
87	C₅₃×#467	C₂²	1	2	yes	complemented
88	C₅₃×#466	C₂²	1	2	yes	complemented
89	C₅₃×#466	C₂²	1	2	yes	complemented
90	C₅₃×#466	C₂²	1	2	yes	complemented
91	C₅₃×#465	C₂²	1	2	yes	complemented
92	C₅₃×#465	C₂²	1	2	yes	complemented
93	C₅₃×#465	C₂²	1	2	yes	complemented
94	C₅₃×#465	C₂²	1	2	yes	complemented
95	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#452	C₂²	1	2	yes	complemented
97	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#452	C₂²	1	2	yes	complemented
99	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#450	C₂²	1	2	yes	complemented
101	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#450	C₂²	1	2	yes	complemented
103	C₅₃×#449	C₂²	1	2	yes	complemented
104	C₅₃×#449	C₂²	1	2	yes	complemented
105	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#449	C₂²	1	2	yes	complemented
107	C₅₃×#449	C₂²	1	2	yes	complemented
108	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#448	C₂²	1	2	yes	complemented
111	C₅₃×#447	C₂²	1	2	yes	complemented
112	C₅₃×#447	C₂²	1	2	yes	complemented
113	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#447	C₂²	1	2	yes	complemented
115	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
117	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
125	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
126	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#408	C₂²	1	2	yes	complemented
128	C₅₃×#408	C₂²	1	2	yes	complemented
129	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#407	C₂²	1	2	yes	complemented
132	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
135	H(5,𝔽₂)×C₅₃	—	4	2	no	—
136	H(5,𝔽₂)×C₅₃	—	4	2	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	—	2	1	no	—
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	4	2	no	—
141	C₂×#41×C₅₃	—	4	2	no	—
142	C₂×#41×C₅₃	—	4	2	no	—
143	C₂×#41×C₅₃	—	4	2	no	—
144	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
145	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
146	C₂×#41×C₅₃	D₄	1	2	yes	—
147	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
149	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
150	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
151	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
152	C₂×#41×C₅₃	C₂³	1	2	yes	—
153	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
154	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
155	C₂×#41×C₅₃	C₂³	1	2	yes	—
156	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
157	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₂²×D₄×C₅₃	—	2	1	no	—
159	C₂²×D₄×C₅₃	—	2	1	no	—
160	C₂²×D₄×C₅₃	—	2	2	no	—
161	C₂²×D₄×C₅₃	—	2	2	no	—
162	C₂²×D₄×C₅₃	—	2	1	no	—
163	C₂²×D₄×C₅₃	D₄	1	2	yes	—
164	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
165	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
166	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
167	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
168	C₂³×C₄×C₅₃	—	2	1	no	—
169	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
170	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
171	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
172	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
173	#135×C₅₃	—	4	2	no	—
174	#135×C₅₃	—	4	2	no	—
175	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
176	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
177	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
178	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
179	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
180	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
181	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
182	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
183	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
184	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
185	C₂×D₈×C₅₃	C₂³	1	2	yes	—
186	C₂×D₈×C₅₃	C₂³	1	2	yes	—
187	#131×C₅₃	—	4	2	no	—
188	#131×C₅₃	—	4	2	no	—
189	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
190	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
191	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
192	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
193	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
194	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
195	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
196	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
197	C₄⋊Q₈×C₅₃	—	2	2	no	—
198	#127×C₅₃	—	2	2	no	—
199	#127×C₅₃	—	2	2	no	—
200	#127×C₅₃	—	2	1	no	—
201	#124×C₅₃	—	2	2	no	—
202	#124×C₅₃	—	2	2	no	—
203	#124×C₅₃	—	2	1	no	—
204	#124×C₅₃	—	2	2	no	—
205	#123×C₅₃	—	2	2	no	—
206	#123×C₅₃	—	2	2	no	—
207	#123×C₅₃	—	2	1	no	—
208	#123×C₅₃	—	2	2	no	—
209	#123×C₅₃	—	2	2	no	—
210	#123×C₅₃	—	2	2	no	—
211	C₂²⋊Q₈×C₅₃	—	2	1	no	—
212	C₂²⋊Q₈×C₅₃	—	2	1	no	—
213	C₂²⋊Q₈×C₅₃	—	2	1	no	—
214	C₂²⋊Q₈×C₅₃	—	2	1	no	—
215	C₂²⋊Q₈×C₅₃	—	2	2	no	—
216	C₂²⋊Q₈×C₅₃	—	2	1	no	—
217	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
218	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
219	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
220	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
221	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
222	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
223	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
224	#121×C₅₃	—	2	1	no	—
225	#121×C₅₃	—	2	1	no	—
226	#121×C₅₃	—	2	1	no	—
227	#121×C₅₃	—	2	1	no	—
228	#121×C₅₃	—	2	2	no	—
229	#121×C₅₃	—	2	2	no	—
230	#121×C₅₃	—	2	2	no	—
231	#121×C₅₃	—	2	2	no	—
232	#121×C₅₃	—	2	2	no	—
233	#121×C₅₃	—	2	2	no	—
234	#121×C₅₃	—	2	2	no	—
235	#121×C₅₃	—	2	2	no	—
236	#121×C₅₃	—	2	1	no	—
237	#121×C₅₃	—	2	1	no	—
238	#121×C₅₃	—	2	1	no	—
239	#121×C₅₃	—	2	2	no	—
240	#121×C₅₃	—	2	2	no	—
241	#121×C₅₃	C₂³	1	2	yes	—
242	#121×C₅₃	C₂³	1	2	yes	—
243	#121×C₅₃	C₂³	1	1	yes	characteristic
244	#121×C₅₃	C₂³	1	2	yes	—
245	#121×C₅₃	C₂³	1	2	yes	—
246	#121×C₅₃	C₂³	1	1	yes	characteristic
247	#121×C₅₃	C₂³	1	2	yes	—
248	#121×C₅₃	C₂³	1	2	yes	—
249	#121×C₅₃	C₂³	1	2	yes	—
250	#121×C₅₃	C₂³	1	2	yes	—
251	#121×C₅₃	C₂³	1	2	yes	—
252	#120×C₅₃	—	2	1	no	—
253	#120×C₅₃	—	2	2	no	—
254	#120×C₅₃	—	2	2	no	—
255	#120×C₅₃	—	2	2	no	—
256	#120×C₅₃	—	2	2	no	—
257	#120×C₅₃	—	2	2	no	—
258	#120×C₅₃	—	2	2	no	—
259	#120×C₅₃	—	2	2	no	—
260	#120×C₅₃	—	2	2	no	—
261	C₄×Q₈×C₅₃	—	2	1	no	—
262	C₄×D₄×C₅₃	—	2	1	no	—
263	C₄×D₄×C₅₃	—	2	2	no	—
264	C₄×D₄×C₅₃	—	2	2	no	—
265	C₄×D₄×C₅₃	—	2	2	no	—
266	C₄×D₄×C₅₃	—	2	2	no	—
267	C₄×D₄×C₅₃	—	2	2	no	—
268	C₄×D₄×C₅₃	—	2	1	no	—
269	C₄×D₄×C₅₃	—	2	1	no	—
270	C₄×D₄×C₅₃	—	2	2	no	—
271	C₄×D₄×C₅₃	—	2	2	no	—
272	#117×C₅₃	—	2	1	no	—
273	#117×C₅₃	—	2	1	no	—
274	#117×C₅₃	C₂³	1	2	yes	—
275	#117×C₅₃	C₂³	1	2	yes	—
276	#117×C₅₃	C₂³	1	2	yes	—
277	#117×C₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
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×C₄²×C₅₃	—	2	1	no	—
286	#107×C₅₃	C₂³	1	2	yes	—
287	#107×C₅₃	C₂³	1	2	yes	—
288	#107×C₅₃	C₂³	1	2	yes	—
289	#107×C₅₃	C₂³	1	2	yes	—
290	#106×C₅₃	C₂³	1	2	yes	—
291	#106×C₅₃	C₂³	1	2	yes	—
292	#106×C₅₃	C₂³	1	2	yes	—
293	#106×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	1	yes	characteristic
295	#103×C₅₃	C₂³	1	1	yes	characteristic
296	#103×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
302	#102×C₅₃	C₂³	1	2	yes	—
303	#102×C₅₃	C₂³	1	2	yes	—
304	#102×C₅₃	C₂³	1	2	yes	—
305	#102×C₅₃	C₂³	1	2	yes	—
306	#102×C₅₃	C₂³	1	1	yes	characteristic
307	#102×C₅₃	C₂³	1	1	yes	characteristic
308	#102×C₅₃	C₂³	1	1	yes	characteristic
309	#102×C₅₃	C₂³	1	1	yes	characteristic
310	#102×C₅₃	C₂³	1	2	yes	—
311	#102×C₅₃	C₂³	1	2	yes	—
312	#102×C₅₃	C₂³	1	2	yes	—
313	#102×C₅₃	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
315	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
316	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
317	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
319	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
320	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
321	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
322	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
323	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
324	C₂⁴×C₅₃	—	2	2	no	—
325	C₂⁴×C₅₃	—	2	1	no	—
326	C₂⁴×C₅₃	—	2	1	no	—
327	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
328	C₂⁴×C₅₃	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
335	#41×C₅₃	—	2	2	no	—
336	#41×C₅₃	—	2	2	no	—
337	#41×C₅₃	—	2	2	no	—
338	#41×C₅₃	—	2	2	no	—
339	#41×C₅₃	—	4	2	no	—
340	#41×C₅₃	—	4	2	no	—
341	#41×C₅₃	—	4	4	no	—
342	#41×C₅₃	—	4	2	no	—
343	#41×C₅₃	—	4	2	no	—
344	#41×C₅₃	—	4	1	no	—
345	#41×C₅₃	—	4	1	no	—
346	#41×C₅₃	—	4	1	no	—
347	#41×C₅₃	—	4	1	no	—
348	#41×C₅₃	—	4	2	no	—
349	#41×C₅₃	—	4	2	no	—
350	#41×C₅₃	—	4	4	no	—
351	#41×C₅₃	—	4	4	no	—
352	#41×C₅₃	—	4	4	no	—
353	C₂×Q₈×C₅₃	—	2	1	no	—
354	C₂×Q₈×C₅₃	—	4	2	no	—
355	C₂×Q₈×C₅₃	—	4	1	no	—
356	C₂×Q₈×C₅₃	—	4	1	no	—
357	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
358	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
359	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
360	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₅₃	—	2	1	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	1	no	—
370	C₂×D₄×C₅₃	—	2	1	no	—
371	C₂×D₄×C₅₃	—	2	1	no	—
372	C₂×D₄×C₅₃	—	2	2	no	—
373	C₂×D₄×C₅₃	—	2	2	no	—
374	C₂×D₄×C₅₃	—	2	2	no	—
375	C₂×D₄×C₅₃	—	2	2	no	—
376	C₂×D₄×C₅₃	—	2	2	no	—
377	C₂×D₄×C₅₃	—	2	2	no	—
378	C₂×D₄×C₅₃	—	2	2	no	—
379	C₂×D₄×C₅₃	—	2	2	no	—
380	C₂×D₄×C₅₃	—	2	2	no	—
381	C₂×D₄×C₅₃	—	2	1	no	—
382	C₂×D₄×C₅₃	—	2	1	no	—
383	C₂×D₄×C₅₃	—	2	2	no	—
384	C₂×D₄×C₅₃	—	2	2	no	—
385	C₂×D₄×C₅₃	—	4	2	no	—
386	C₂×D₄×C₅₃	—	4	1	no	—
387	C₂×D₄×C₅₃	—	4	1	no	—
388	C₂×D₄×C₅₃	—	4	2	no	—
389	C₂×D₄×C₅₃	—	4	2	no	—
390	C₂×D₄×C₅₃	—	4	4	no	—
391	C₂×D₄×C₅₃	—	4	8	no	—
392	C₂×D₄×C₅₃	—	4	4	no	—
393	C₂×D₄×C₅₃	—	4	4	no	—
394	C₂×D₄×C₅₃	—	8	2	no	—
395	C₂×D₄×C₅₃	—	8	4	no	—
396	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
397	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
398	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
399	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
400	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
401	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
402	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
403	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
406	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₅₃	—	2	2	no	—
408	C₂²×C₄×C₅₃	—	2	2	no	—
409	C₂²×C₄×C₅₃	—	2	1	no	—
410	C₂²×C₄×C₅₃	—	2	1	no	—
411	C₂²×C₄×C₅₃	—	2	1	no	—
412	C₂²×C₄×C₅₃	—	2	2	no	—
413	C₂²×C₄×C₅₃	—	2	1	no	—
414	C₂²×C₄×C₅₃	—	2	1	no	—
415	C₂²×C₄×C₅₃	—	2	1	no	—
416	C₂²×C₄×C₅₃	—	2	2	no	—
417	C₂²×C₄×C₅₃	—	2	1	no	—
418	C₂²×C₄×C₅₃	—	2	1	no	—
419	C₂²×C₄×C₅₃	—	2	1	no	—
420	C₂²×C₄×C₅₃	—	4	2	no	—
421	C₂²×C₄×C₅₃	—	4	2	no	—
422	C₂²×C₄×C₅₃	—	4	4	no	—
423	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
424	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
425	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
426	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
427	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
428	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
429	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
430	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
433	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
434	Q₁₆×C₅₃	—	4	1	no	—
435	Q₁₆×C₅₃	—	4	1	no	—
436	SD₁₆×C₅₃	—	4	1	no	—
437	SD₁₆×C₅₃	—	4	1	no	—
438	SD₁₆×C₅₃	—	4	1	no	—
439	SD₁₆×C₅₃	—	4	1	no	—
440	SD₁₆×C₅₃	—	4	2	no	—
441	SD₁₆×C₅₃	—	4	2	no	—
442	D₈×C₅₃	—	4	1	no	—
443	D₈×C₅₃	—	4	1	no	—
444	D₈×C₅₃	—	4	2	no	—
445	D₈×C₅₃	—	4	2	no	—
446	M₁₆×C₅₃	—	2	2	no	—
447	M₁₆×C₅₃	—	2	2	no	—
448	M₁₆×C₅₃	—	4	2	no	—
449	M₁₆×C₅₃	—	4	2	no	—
450	C₂×C₈×C₅₃	—	2	2	no	—
451	C₂×C₈×C₅₃	—	2	2	no	—
452	C₂×C₈×C₅₃	—	4	2	no	—
453	C₂×C₈×C₅₃	—	4	2	no	—
454	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
455	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
456	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
457	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
458	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
459	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
460	C₄⋊C₄×C₅₃	—	2	1	no	—
461	C₄⋊C₄×C₅₃	—	2	1	no	—
462	C₄⋊C₄×C₅₃	—	2	2	no	—
463	C₄⋊C₄×C₅₃	—	2	1	no	—
464	C₄⋊C₄×C₅₃	—	2	1	no	—
465	C₄⋊C₄×C₅₃	—	2	1	no	—
466	C₄⋊C₄×C₅₃	—	2	2	no	—
467	C₄⋊C₄×C₅₃	—	2	2	no	—
468	C₄⋊C₄×C₅₃	—	2	2	no	—
469	C₄⋊C₄×C₅₃	—	2	2	no	—
470	C₄⋊C₄×C₅₃	—	2	2	no	—
471	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
472	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
473	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
474	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
475	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
476	C₂²⋊C₄×C₅₃	—	2	2	no	—
477	C₂²⋊C₄×C₅₃	—	2	2	no	—
478	C₂²⋊C₄×C₅₃	—	2	2	no	—
479	C₂²⋊C₄×C₅₃	—	2	1	no	—
480	C₂²⋊C₄×C₅₃	—	2	1	no	—
481	C₂²⋊C₄×C₅₃	—	2	1	no	—
482	C₂²⋊C₄×C₅₃	—	2	2	no	—
483	C₂²⋊C₄×C₅₃	—	2	2	no	—
484	C₂²⋊C₄×C₅₃	—	2	2	no	—
485	C₂²⋊C₄×C₅₃	—	2	2	no	—
486	C₂²⋊C₄×C₅₃	—	2	2	no	—
487	C₂²⋊C₄×C₅₃	—	2	2	no	—
488	C₂²⋊C₄×C₅₃	—	2	1	no	—
489	C₂²⋊C₄×C₅₃	—	2	2	no	—
490	C₂²⋊C₄×C₅₃	—	2	2	no	—
491	C₂²⋊C₄×C₅₃	—	2	2	no	—
492	C₂²⋊C₄×C₅₃	—	2	1	no	—
493	C₂²⋊C₄×C₅₃	—	2	2	no	—
494	C₂²⋊C₄×C₅₃	—	2	2	no	—
495	C₂²⋊C₄×C₅₃	—	2	2	no	—
496	C₂²⋊C₄×C₅₃	—	2	2	no	—
497	C₂²⋊C₄×C₅₃	—	2	2	no	—
498	C₄²×C₅₃	—	2	2	no	—
499	C₄²×C₅₃	—	2	2	no	—
500	C₄²×C₅₃	—	2	2	no	—
501	C₄²×C₅₃	—	2	1	no	—
502	C₂³×C₅₃	—	2	2	no	—
503	C₂³×C₅₃	—	2	1	no	—
504	C₂³×C₅₃	—	2	1	no	—
505	C₂³×C₅₃	—	2	2	no	—
506	C₂³×C₅₃	—	2	1	no	—
507	C₂³×C₅₃	—	4	2	no	—
508	C₂³×C₅₃	—	4	1	no	—
509	C₂³×C₅₃	—	4	2	no	—
510	C₂³×C₅₃	—	4	1	no	—
511	C₂³×C₅₃	—	4	2	no	—
512	C₂³×C₅₃	—	4	2	no	—
513	C₂³×C₅₃	—	4	4	no	—
514	C₂³×C₅₃	—	4	2	no	—
515	C₂³×C₅₃	—	8	1	no	—
516	C₂³×C₅₃	—	8	1	no	—
517	C₂³×C₅₃	—	8	1	no	—
518	C₂³×C₅₃	—	8	2	no	—
519	C₂³×C₅₃	—	8	1	no	—
520	C₂³×C₅₃	—	8	2	no	—
521	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
522	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
523	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
524	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
525	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
526	Q₈×C₅₃	—	2	2	no	—
527	Q₈×C₅₃	—	2	2	no	—
528	Q₈×C₅₃	—	2	1	no	—
529	Q₈×C₅₃	—	2	1	no	—
530	Q₈×C₅₃	—	2	1	no	—
531	Q₈×C₅₃	—	2	1	no	—
532	Q₈×C₅₃	—	2	1	no	—
533	Q₈×C₅₃	—	2	1	no	—
534	Q₈×C₅₃	—	4	2	no	—
535	Q₈×C₅₃	—	4	2	no	—
536	D₄×C₅₃	—	2	4	no	—
537	D₄×C₅₃	—	2	4	no	—
538	D₄×C₅₃	—	2	2	no	—
539	D₄×C₅₃	—	2	2	no	—
540	D₄×C₅₃	—	2	2	no	—
541	D₄×C₅₃	—	2	2	no	—
542	D₄×C₅₃	—	2	1	no	—
543	D₄×C₅₃	—	2	1	no	—
544	D₄×C₅₃	—	2	1	no	—
545	D₄×C₅₃	—	2	1	no	—
546	D₄×C₅₃	—	2	1	no	—
547	D₄×C₅₃	—	2	1	no	—
548	D₄×C₅₃	—	4	2	no	—
549	D₄×C₅₃	—	4	2	no	—
550	D₄×C₅₃	—	4	2	no	—
551	D₄×C₅₃	—	4	4	no	—
552	D₄×C₅₃	—	4	2	no	—
553	D₄×C₅₃	—	4	4	no	—
554	D₄×C₅₃	—	4	2	no	—
555	D₄×C₅₃	—	4	2	no	—
556	D₄×C₅₃	—	4	2	no	—
557	D₄×C₅₃	—	4	4	no	—
558	D₄×C₅₃	—	4	2	no	—
559	D₄×C₅₃	—	4	2	no	—
560	D₄×C₅₃	—	4	2	no	—
561	D₄×C₅₃	—	4	2	no	—
562	D₄×C₅₃	—	8	2	no	—
563	D₄×C₅₃	—	8	2	no	—
564	D₄×C₅₃	—	8	2	no	—
565	D₄×C₅₃	—	8	1	no	—
566	D₄×C₅₃	—	8	2	no	—
567	D₄×C₅₃	—	8	2	no	—
568	D₄×C₅₃	—	8	2	no	—
569	D₄×C₅₃	—	8	2	no	—
570	D₄×C₅₃	—	8	2	no	—
571	C₂×C₄×C₅₃	—	2	2	no	—
572	C₂×C₄×C₅₃	—	2	2	no	—
573	C₂×C₄×C₅₃	—	2	2	no	—
574	C₂×C₄×C₅₃	—	2	1	no	—
575	C₂×C₄×C₅₃	—	2	1	no	—
576	C₂×C₄×C₅₃	—	2	1	no	—
577	C₂×C₄×C₅₃	—	2	1	no	—
578	C₂×C₄×C₅₃	—	2	2	no	—
579	C₂×C₄×C₅₃	—	2	2	no	—
580	C₂×C₄×C₅₃	—	2	2	no	—
581	C₂×C₄×C₅₃	—	2	2	no	—
582	C₂×C₄×C₅₃	—	2	1	no	—
583	C₂×C₄×C₅₃	—	2	1	no	—
584	C₂×C₄×C₅₃	—	2	1	no	—
585	C₂×C₄×C₅₃	—	2	1	no	—
586	C₂×C₄×C₅₃	—	2	2	no	—
587	C₂×C₄×C₅₃	—	2	2	no	—
588	C₂×C₄×C₅₃	—	2	2	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
590	C₂×C₄×C₅₃	—	4	2	no	—
591	C₂×C₄×C₅₃	—	4	2	no	—
592	C₂×C₄×C₅₃	—	4	2	no	—
593	C₂×C₄×C₅₃	—	4	2	no	—
594	C₂×C₄×C₅₃	—	4	2	no	—
595	C₂×C₄×C₅₃	—	4	4	no	—
596	C₂×C₄×C₅₃	—	4	2	no	—
597	C₂×C₄×C₅₃	—	4	2	no	—
598	C₂×C₄×C₅₃	—	4	2	no	—
599	C₂×C₄×C₅₃	—	4	2	no	—
600	C₂×C₄×C₅₃	—	8	1	no	—
601	C₂×C₄×C₅₃	—	8	1	no	—
602	C₂×C₄×C₅₃	—	8	1	no	—
603	C₂×C₄×C₅₃	—	8	2	no	—
604	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
605	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
606	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
607	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
608	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
609	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
610	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
611	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
612	C₈×C₅₃	—	2	1	no	—
613	C₈×C₅₃	—	2	1	no	—
614	C₈×C₅₃	—	2	1	no	—
615	C₈×C₅₃	—	2	1	no	—
616	C₈×C₅₃	—	2	2	no	—
617	C₈×C₅₃	—	2	2	no	—
618	#60767	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
619	C₂²×C₅₃	—	2	1	no	—
620	C₂²×C₅₃	—	2	1	no	—
621	C₂²×C₅₃	—	2	2	no	—
622	C₂²×C₅₃	—	2	1	no	—
623	C₂²×C₅₃	—	2	2	no	—
624	C₂²×C₅₃	—	2	1	no	—
625	C₂²×C₅₃	—	2	2	no	—
626	C₂²×C₅₃	—	2	1	no	—
627	C₂²×C₅₃	—	2	2	no	—
628	C₂²×C₅₃	—	2	1	no	—
629	C₂²×C₅₃	—	2	1	no	—
630	C₂²×C₅₃	—	2	1	no	—
631	C₂²×C₅₃	—	2	2	no	—
632	C₂²×C₅₃	—	2	2	no	—
633	C₂²×C₅₃	—	4	1	no	—
634	C₂²×C₅₃	—	4	1	no	—
635	C₂²×C₅₃	—	4	2	no	—
636	C₂²×C₅₃	—	4	1	no	—
637	C₂²×C₅₃	—	4	2	no	—
638	C₂²×C₅₃	—	4	1	no	—
639	C₂²×C₅₃	—	4	1	no	—
640	C₂²×C₅₃	—	4	1	no	—
641	C₂²×C₅₃	—	4	1	no	—
642	C₂²×C₅₃	—	4	1	no	—
643	C₂²×C₅₃	—	4	2	no	—
644	C₂²×C₅₃	—	4	1	no	—
645	C₂²×C₅₃	—	8	2	no	—
646	C₂²×C₅₃	—	8	4	no	—
647	C₂²×C₅₃	—	8	4	no	—
648	C₂²×C₅₃	—	16	2	no	—
649	C₂²×C₅₃	—	16	4	no	—
650	C₂²×C₅₃	#534	1	2	yes	—
651	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
652	C₄×C₅₃	—	2	1	no	—
653	C₄×C₅₃	—	2	1	no	—
654	C₄×C₅₃	—	2	2	no	—
655	C₄×C₅₃	—	2	2	no	—
656	C₄×C₅₃	—	4	2	no	—
657	C₄×C₅₃	—	4	1	no	—
658	C₄×C₅₃	—	4	2	no	—
659	C₄×C₅₃	—	4	1	no	—
660	C₄×C₅₃	—	4	2	no	—
661	C₄×C₅₃	—	4	1	no	—
662	C₄×C₅₃	—	4	1	no	—
663	C₄×C₅₃	—	4	1	no	—
664	C₄×C₅₃	#534	1	2	yes	—
665	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
666	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
667	#3488	C₂×C₅₃	1	1	yes	characteristic, complemented
668	#3449	C₂×C₅₃	1	1	yes	characteristic, complemented
669	#3201	C₂×C₅₃	1	2	yes	complemented
670	#3200	C₂×C₅₃	1	2	yes	complemented
671	#3199	C₂×C₅₃	1	2	yes	complemented
672	#3198	C₂×C₅₃	1	2	yes	complemented
673	#3197	C₂×C₅₃	1	2	yes	complemented
674	#3194	C₂×C₅₃	1	2	yes	complemented
675	#3191	C₂×C₅₃	1	2	yes	complemented
676	#3188	C₂×C₅₃	1	2	yes	complemented
677	#3099	C₂×C₅₃	1	1	yes	characteristic, complemented
678	#3098	C₂×C₅₃	1	1	yes	characteristic, complemented
679	#3093	C₂×C₅₃	1	1	yes	characteristic, complemented
680	C₂×#482	C₂×C₅₃	1	1	yes	characteristic, complemented
681	#3062	C₂×C₅₃	1	1	yes	characteristic, complemented
682	#3062	C₂×C₅₃	1	1	yes	characteristic, complemented
683	#3061	C₂×C₅₃	1	1	yes	characteristic, complemented
684	#3060	C₂×C₅₃	1	1	yes	characteristic, complemented
685	#3012	C₂×C₅₃	1	1	yes	characteristic, complemented
686	#3012	C₂×C₅₃	1	1	yes	characteristic, complemented
687	#3006	C₂×C₅₃	1	1	yes	characteristic, complemented
688	#3002	C₂×C₅₃	1	1	yes	characteristic, complemented
689	#2880	C₂×C₅₃	1	1	yes	characteristic, complemented
690	C₂×C₅₃	—	2	2	no	—
691	C₂×C₅₃	—	4	2	no	—
692	C₂×C₅₃	—	4	1	no	—
693	C₂×C₅₃	—	4	1	no	—
694	C₂×C₅₃	—	4	2	no	—
695	C₂×C₅₃	—	8	1	no	—
696	C₂×C₅₃	—	8	1	no	—
697	C₂×C₅₃	—	8	2	no	—
698	C₂×C₅₃	—	8	1	no	—
699	C₂×C₅₃	C₂×#534	1	1	yes	characteristic
700	C₂×C₅₃	#3584	1	1	yes	characteristic
701	C₂×C₅₃	#3585	1	1	yes	characteristic
702	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic, complemented
703	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
704	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
705	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
706	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
708	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic, complemented
710	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic, complemented
711	#550	—	2	1	no	—
712	#548	—	2	1	no	—
713	#546	—	2	2	no	—
714	#546	—	2	1	no	—
715	D₄²	—	2	1	no	—
716	D₄²	—	2	2	no	—
717	#537	C₂²×C₅₃	1	1	yes	characteristic
718	#537	C₂²×C₅₃	1	1	yes	characteristic
719	#537	C₂²×C₅₃	1	2	yes	—
720	#537	C₂²×C₅₃	1	1	yes	characteristic, complemented
721	#537	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	#537	C₂²×C₅₃	1	1	yes	characteristic, complemented
723	#536	—	2	1	no	—
724	#536	C₂²×C₅₃	1	2	yes	complemented
725	#535	—	2	1	no	—
726	#535	C₂²×C₅₃	1	2	yes	—
727	#535	C₂²×C₅₃	1	2	yes	complemented
728	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
729	#534	—	2	2	no	—
730	#532	—	2	2	no	—
731	#525	—	2	1	no	—
732	#525	—	2	1	no	—
733	#525	C₂²×C₅₃	1	1	yes	characteristic
734	#525	C₂²×C₅₃	1	2	yes	complemented
735	#525	C₂²×C₅₃	1	2	yes	complemented
736	#525	C₂²×C₅₃	1	2	yes	complemented
737	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
738	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
739	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
740	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
741	#485	C₂²×C₅₃	1	2	yes	complemented
742	#485	C₂²×C₅₃	1	2	yes	complemented
743	#485	C₂²×C₅₃	1	2	yes	complemented
744	#485	C₂²×C₅₃	1	2	yes	complemented
745	#484	C₂²×C₅₃	1	2	yes	complemented
746	#483	C₂²×C₅₃	1	2	yes	complemented
747	#482	C₂²×C₅₃	1	2	yes	complemented
748	#482	C₂²×C₅₃	1	2	yes	complemented
749	#482	C₂²×C₅₃	1	2	yes	complemented
750	#482	C₂²×C₅₃	1	2	yes	complemented
751	#482	C₂²×C₅₃	1	2	yes	complemented
752	#482	C₂²×C₅₃	1	2	yes	complemented
753	#482	C₂²×C₅₃	1	2	yes	complemented
754	#482	C₂²×C₅₃	1	2	yes	complemented
755	#481	C₂²×C₅₃	1	2	yes	complemented
756	#480	C₂²×C₅₃	1	2	yes	complemented
757	#470	C₂²×C₅₃	1	2	yes	complemented
758	#469	C₂²×C₅₃	1	2	yes	complemented
759	#469	C₂²×C₅₃	1	2	yes	complemented
760	#469	C₂²×C₅₃	1	2	yes	complemented
761	#468	C₂²×C₅₃	1	2	yes	complemented
762	#468	C₂²×C₅₃	1	2	yes	complemented
763	#468	C₂²×C₅₃	1	2	yes	complemented
764	#468	C₂²×C₅₃	1	2	yes	complemented
765	#467	C₂²×C₅₃	1	2	yes	complemented
766	#466	C₂²×C₅₃	1	2	yes	complemented
767	#466	C₂²×C₅₃	1	2	yes	complemented
768	#466	C₂²×C₅₃	1	2	yes	complemented
769	#465	C₂²×C₅₃	1	2	yes	complemented
770	#465	C₂²×C₅₃	1	2	yes	complemented
771	#465	C₂²×C₅₃	1	2	yes	complemented
772	#465	C₂²×C₅₃	1	2	yes	complemented
773	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
774	#452	C₂²×C₅₃	1	2	yes	complemented
775	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
776	#452	C₂²×C₅₃	1	2	yes	complemented
777	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
778	#450	C₂²×C₅₃	1	2	yes	complemented
779	#450	C₂²×C₅₃	1	2	yes	complemented
780	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
781	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
782	#449	C₂²×C₅₃	1	2	yes	complemented
783	#449	C₂²×C₅₃	1	2	yes	complemented
784	#449	C₂²×C₅₃	1	2	yes	complemented
785	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
786	#449	C₂²×C₅₃	1	2	yes	complemented
787	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
788	#448	C₂²×C₅₃	1	2	yes	complemented
789	#447	C₂²×C₅₃	1	2	yes	complemented
790	#447	C₂²×C₅₃	1	2	yes	complemented
791	#447	C₂²×C₅₃	1	2	yes	complemented
792	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
793	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
794	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
795	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
796	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
797	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
798	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
799	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
800	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
801	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
802	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
803	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
804	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
805	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
806	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
807	#408	C₂²×C₅₃	1	2	yes	complemented
808	#408	C₂²×C₅₃	1	2	yes	complemented
809	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
810	#407	C₂²×C₅₃	1	2	yes	complemented
811	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
812	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	complemented
813	C₅₃	#60767	1	1	yes	characteristic, direct product factor, Sylow
814	H(5,𝔽₂)	—	4	2	no	—
815	H(5,𝔽₂)	—	4	2	no	—
816	C₂×#41	—	2	1	no	—
817	C₂×#41	—	2	1	no	—
818	C₂×#41	—	2	1	no	—
819	C₂×#41	—	4	2	no	—
820	C₂×#41	—	4	2	no	—
821	C₂×#41	—	4	2	no	—
822	C₂×#41	—	4	2	no	—
823	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
824	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
825	C₂×#41	D₄×C₅₃	1	2	yes	—
826	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
827	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
828	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
829	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
830	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
831	C₂×#41	C₂³×C₅₃	1	2	yes	—
832	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
833	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
834	C₂×#41	C₂³×C₅₃	1	2	yes	—
835	C₂²×Q₈	D₄×C₅₃	1	1	yes	characteristic
836	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
837	C₂²×D₄	—	2	1	no	—
838	C₂²×D₄	—	2	1	no	—
839	C₂²×D₄	—	2	2	no	—
840	C₂²×D₄	—	2	2	no	—
841	C₂²×D₄	—	2	1	no	—
842	C₂²×D₄	D₄×C₅₃	1	2	yes	—
843	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
844	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
845	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
846	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
847	C₂³×C₄	—	2	1	no	—
848	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
849	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
850	AGL(1,ℤ/8)	—	4	2	no	—
851	AGL(1,ℤ/8)	—	4	2	no	—
852	#135	—	4	2	no	—
853	#135	—	4	2	no	—
854	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
855	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
856	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
857	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
858	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
859	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
860	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
861	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
862	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
863	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
864	C₂×D₈	C₂³×C₅₃	1	2	yes	—
865	C₂×D₈	C₂³×C₅₃	1	2	yes	—
866	#131	—	4	2	no	—
867	#131	—	4	2	no	—
868	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
869	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
870	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
871	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
872	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
873	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
874	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
875	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
876	C₄⋊Q₈	—	2	2	no	—
877	#127	—	2	2	no	—
878	#127	—	2	2	no	—
879	#127	—	2	1	no	—
880	#124	—	2	2	no	—
881	#124	—	2	2	no	—
882	#124	—	2	1	no	—
883	#124	—	2	2	no	—
884	#123	—	2	2	no	—
885	#123	—	2	2	no	—
886	#123	—	2	1	no	—
887	#123	—	2	2	no	—
888	#123	—	2	2	no	—
889	#123	—	2	2	no	—
890	C₂²⋊Q₈	—	2	1	no	—
891	C₂²⋊Q₈	—	2	1	no	—
892	C₂²⋊Q₈	—	2	1	no	—
893	C₂²⋊Q₈	—	2	1	no	—
894	C₂²⋊Q₈	—	2	2	no	—
895	C₂²⋊Q₈	—	2	1	no	—
896	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
897	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
898	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
899	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
900	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
901	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
902	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
903	#121	—	2	1	no	—
904	#121	—	2	1	no	—
905	#121	—	2	1	no	—
906	#121	—	2	1	no	—
907	#121	—	2	2	no	—
908	#121	—	2	2	no	—
909	#121	—	2	2	no	—
910	#121	—	2	2	no	—
911	#121	—	2	2	no	—
912	#121	—	2	2	no	—
913	#121	—	2	2	no	—
914	#121	—	2	2	no	—
915	#121	—	2	1	no	—
916	#121	—	2	1	no	—
917	#121	—	2	1	no	—
918	#121	—	2	2	no	—
919	#121	—	2	2	no	—
920	#121	C₂³×C₅₃	1	2	yes	—
921	#121	C₂³×C₅₃	1	2	yes	—
922	#121	C₂³×C₅₃	1	1	yes	characteristic
923	#121	C₂³×C₅₃	1	2	yes	—
924	#121	C₂³×C₅₃	1	2	yes	—
925	#121	C₂³×C₅₃	1	1	yes	characteristic
926	#121	C₂³×C₅₃	1	2	yes	—
927	#121	C₂³×C₅₃	1	2	yes	—
928	#121	C₂³×C₅₃	1	2	yes	—
929	#121	C₂³×C₅₃	1	2	yes	—
930	#121	C₂³×C₅₃	1	2	yes	—
931	#120	—	2	1	no	—
932	#120	—	2	2	no	—
933	#120	—	2	2	no	—
934	#120	—	2	2	no	—
935	#120	—	2	2	no	—
936	#120	—	2	2	no	—
937	#120	—	2	2	no	—
938	#120	—	2	2	no	—
939	#120	—	2	2	no	—
940	C₄×Q₈	—	2	1	no	—
941	C₄×D₄	—	2	2	no	—
942	C₄×D₄	—	2	1	no	—
943	C₄×D₄	—	2	2	no	—
944	C₄×D₄	—	2	2	no	—
945	C₄×D₄	—	2	2	no	—
946	C₄×D₄	—	2	2	no	—
947	C₄×D₄	—	2	1	no	—
948	C₄×D₄	—	2	1	no	—
949	C₄×D₄	—	2	2	no	—
950	C₄×D₄	—	2	2	no	—
951	#117	—	2	1	no	—
952	#117	—	2	1	no	—
953	#117	C₂³×C₅₃	1	2	yes	—
954	#117	C₂³×C₅₃	1	2	yes	—
955	#117	C₂³×C₅₃	1	1	yes	characteristic
956	#117	C₂³×C₅₃	1	2	yes	—
957	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
958	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
959	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
960	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
961	C₂×C₂²⋊C₄	—	2	1	no	—
962	C₂×C₂²⋊C₄	—	2	1	no	—
963	C₂×C₂²⋊C₄	—	2	2	no	—
964	C₂×C₄²	—	2	1	no	—
965	#107	C₂³×C₅₃	1	2	yes	—
966	#107	C₂³×C₅₃	1	2	yes	—
967	#107	C₂³×C₅₃	1	2	yes	—
968	#107	C₂³×C₅₃	1	2	yes	—
969	#106	C₂³×C₅₃	1	2	yes	—
970	#106	C₂³×C₅₃	1	2	yes	—
971	#106	C₂³×C₅₃	1	2	yes	—
972	#106	C₂³×C₅₃	1	2	yes	—
973	#103	C₂³×C₅₃	1	1	yes	characteristic
974	#103	C₂³×C₅₃	1	1	yes	characteristic
975	#103	C₂³×C₅₃	1	1	yes	characteristic
976	#103	C₂³×C₅₃	1	1	yes	characteristic
977	#103	C₂³×C₅₃	1	2	yes	—
978	#103	C₂³×C₅₃	1	2	yes	—
979	#103	C₂³×C₅₃	1	2	yes	—
980	#103	C₂³×C₅₃	1	2	yes	—
981	#102	C₂³×C₅₃	1	2	yes	—
982	#102	C₂³×C₅₃	1	2	yes	—
983	#102	C₂³×C₅₃	1	2	yes	—
984	#102	C₂³×C₅₃	1	2	yes	—
985	#102	C₂³×C₅₃	1	1	yes	characteristic
986	#102	C₂³×C₅₃	1	1	yes	characteristic
987	#102	C₂³×C₅₃	1	1	yes	characteristic
988	#102	C₂³×C₅₃	1	1	yes	characteristic
989	#102	C₂³×C₅₃	1	2	yes	—
990	#102	C₂³×C₅₃	1	2	yes	—
991	#102	C₂³×C₅₃	1	2	yes	—
992	#102	C₂³×C₅₃	1	2	yes	—
993	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
994	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
995	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
996	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
997	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
998	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
999	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1000	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1001	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1002	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1003	C₂⁴	—	2	2	no	—
1004	C₂⁴	—	2	1	no	—
1005	C₂⁴	—	2	1	no	—
1006	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1007	C₂⁴	C₂×D₄×C₅₃	1	2	yes	—
1008	#41	—	2	2	no	—
1009	#41	—	2	2	no	—
1010	#41	—	2	2	no	—
1011	#41	—	2	2	no	—
1012	#41	—	2	2	no	—
1013	#41	—	2	2	no	—
1014	#41	—	2	2	no	—
1015	#41	—	2	2	no	—
1016	#41	—	2	2	no	—
1017	#41	—	2	2	no	—
1018	#41	—	4	2	no	—
1019	#41	—	4	2	no	—
1020	#41	—	4	4	no	—
1021	#41	—	4	2	no	—
1022	#41	—	4	2	no	—
1023	#41	—	4	1	no	—
1024	#41	—	4	1	no	—
1025	#41	—	4	1	no	—
1026	#41	—	4	1	no	—
1027	#41	—	4	2	no	—
1028	#41	—	4	2	no	—
1029	#41	—	4	4	no	—
1030	#41	—	4	4	no	—
1031	#41	—	4	4	no	—
1032	C₂×Q₈	—	2	1	no	—
1033	C₂×Q₈	—	4	2	no	—
1034	C₂×Q₈	—	4	1	no	—
1035	C₂×Q₈	—	4	1	no	—
1036	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1037	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1038	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
1039	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1040	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1041	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1042	C₂×D₄	—	2	1	no	—
1043	C₂×D₄	—	2	2	no	—
1044	C₂×D₄	—	2	1	no	—
1045	C₂×D₄	—	2	1	no	—
1046	C₂×D₄	—	2	2	no	—
1047	C₂×D₄	—	2	1	no	—
1048	C₂×D₄	—	2	1	no	—
1049	C₂×D₄	—	2	1	no	—
1050	C₂×D₄	—	2	1	no	—
1051	C₂×D₄	—	2	2	no	—
1052	C₂×D₄	—	2	2	no	—
1053	C₂×D₄	—	2	2	no	—
1054	C₂×D₄	—	2	2	no	—
1055	C₂×D₄	—	2	2	no	—
1056	C₂×D₄	—	2	2	no	—
1057	C₂×D₄	—	2	2	no	—
1058	C₂×D₄	—	2	2	no	—
1059	C₂×D₄	—	2	2	no	—
1060	C₂×D₄	—	2	1	no	—
1061	C₂×D₄	—	2	1	no	—
1062	C₂×D₄	—	2	2	no	—
1063	C₂×D₄	—	2	2	no	—
1064	C₂×D₄	—	4	2	no	—
1065	C₂×D₄	—	4	1	no	—
1066	C₂×D₄	—	4	1	no	—
1067	C₂×D₄	—	4	2	no	—
1068	C₂×D₄	—	4	2	no	—
1069	C₂×D₄	—	4	4	no	—
1070	C₂×D₄	—	4	8	no	—
1071	C₂×D₄	—	4	4	no	—
1072	C₂×D₄	—	4	4	no	—
1073	C₂×D₄	—	8	2	no	—
1074	C₂×D₄	—	8	4	no	—
1075	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1076	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1077	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1078	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1079	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1080	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1081	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
1082	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1083	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1084	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1085	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1086	C₂²×C₄	—	2	2	no	—
1087	C₂²×C₄	—	2	2	no	—
1088	C₂²×C₄	—	2	1	no	—
1089	C₂²×C₄	—	2	1	no	—
1090	C₂²×C₄	—	2	1	no	—
1091	C₂²×C₄	—	2	2	no	—
1092	C₂²×C₄	—	2	1	no	—
1093	C₂²×C₄	—	2	1	no	—
1094	C₂²×C₄	—	2	1	no	—
1095	C₂²×C₄	—	2	2	no	—
1096	C₂²×C₄	—	2	1	no	—
1097	C₂²×C₄	—	2	1	no	—
1098	C₂²×C₄	—	2	1	no	—
1099	C₂²×C₄	—	4	2	no	—
1100	C₂²×C₄	—	4	2	no	—
1101	C₂²×C₄	—	4	4	no	—
1102	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1103	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1104	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1105	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1106	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1107	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
1108	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1109	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1110	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1111	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1112	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1113	Q₁₆	—	4	1	no	—
1114	Q₁₆	—	4	1	no	—
1115	SD₁₆	—	4	1	no	—
1116	SD₁₆	—	4	1	no	—
1117	SD₁₆	—	4	1	no	—
1118	SD₁₆	—	4	1	no	—
1119	SD₁₆	—	4	2	no	—
1120	SD₁₆	—	4	2	no	—
1121	D₈	—	4	1	no	—
1122	D₈	—	4	1	no	—
1123	D₈	—	4	2	no	—
1124	D₈	—	4	2	no	—
1125	M₁₆	—	2	2	no	—
1126	M₁₆	—	2	2	no	—
1127	M₁₆	—	4	2	no	—
1128	M₁₆	—	4	2	no	—
1129	C₂×C₈	—	2	2	no	—
1130	C₂×C₈	—	2	2	no	—
1131	C₂×C₈	—	4	2	no	—
1132	C₂×C₈	—	4	2	no	—
1133	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1134	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1135	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1136	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1137	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1138	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1139	C₄⋊C₄	—	2	1	no	—
1140	C₄⋊C₄	—	2	1	no	—
1141	C₄⋊C₄	—	2	2	no	—
1142	C₄⋊C₄	—	2	1	no	—
1143	C₄⋊C₄	—	2	1	no	—
1144	C₄⋊C₄	—	2	1	no	—
1145	C₄⋊C₄	—	2	2	no	—
1146	C₄⋊C₄	—	2	2	no	—
1147	C₄⋊C₄	—	2	2	no	—
1148	C₄⋊C₄	—	2	2	no	—
1149	C₄⋊C₄	—	2	2	no	—
1150	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1151	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1152	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1153	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1154	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1155	C₂²⋊C₄	—	2	2	no	—
1156	C₂²⋊C₄	—	2	2	no	—
1157	C₂²⋊C₄	—	2	2	no	—
1158	C₂²⋊C₄	—	2	1	no	—
1159	C₂²⋊C₄	—	2	1	no	—
1160	C₂²⋊C₄	—	2	1	no	—
1161	C₂²⋊C₄	—	2	2	no	—
1162	C₂²⋊C₄	—	2	2	no	—
1163	C₂²⋊C₄	—	2	2	no	—
1164	C₂²⋊C₄	—	2	2	no	—
1165	C₂²⋊C₄	—	2	2	no	—
1166	C₂²⋊C₄	—	2	2	no	—
1167	C₂²⋊C₄	—	2	1	no	—
1168	C₂²⋊C₄	—	2	2	no	—
1169	C₂²⋊C₄	—	2	2	no	—
1170	C₂²⋊C₄	—	2	2	no	—
1171	C₂²⋊C₄	—	2	1	no	—
1172	C₂²⋊C₄	—	2	2	no	—
1173	C₂²⋊C₄	—	2	2	no	—
1174	C₂²⋊C₄	—	2	2	no	—
1175	C₂²⋊C₄	—	2	2	no	—
1176	C₂²⋊C₄	—	2	2	no	—
1177	C₄²	—	2	2	no	—
1178	C₄²	—	2	2	no	—
1179	C₄²	—	2	2	no	—
1180	C₄²	—	2	1	no	—
1181	C₂³	—	2	2	no	—
1182	C₂³	—	2	1	no	—
1183	C₂³	—	2	1	no	—
1184	C₂³	—	2	2	no	—
1185	C₂³	—	2	1	no	—
1186	C₂³	—	4	2	no	—
1187	C₂³	—	4	1	no	—
1188	C₂³	—	4	2	no	—
1189	C₂³	—	4	1	no	—
1190	C₂³	—	4	2	no	—
1191	C₂³	—	4	2	no	—
1192	C₂³	—	4	4	no	—
1193	C₂³	—	4	2	no	—
1194	C₂³	—	8	1	no	—
1195	C₂³	—	8	1	no	—
1196	C₂³	—	8	1	no	—
1197	C₂³	—	8	2	no	—
1198	C₂³	—	8	1	no	—
1199	C₂³	—	8	2	no	—
1200	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1201	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1202	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1203	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1204	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1205	Q₈	—	2	2	no	—
1206	Q₈	—	2	2	no	—
1207	Q₈	—	2	1	no	—
1208	Q₈	—	2	1	no	—
1209	Q₈	—	2	1	no	—
1210	Q₈	—	2	1	no	—
1211	Q₈	—	2	1	no	—
1212	Q₈	—	2	1	no	—
1213	Q₈	—	4	2	no	—
1214	Q₈	—	4	2	no	—
1215	D₄	—	2	4	no	—
1216	D₄	—	2	4	no	—
1217	D₄	—	2	2	no	—
1218	D₄	—	2	2	no	—
1219	D₄	—	2	1	no	—
1220	D₄	—	2	1	no	—
1221	D₄	—	2	2	no	—
1222	D₄	—	2	2	no	—
1223	D₄	—	2	1	no	—
1224	D₄	—	2	1	no	—
1225	D₄	—	2	1	no	—
1226	D₄	—	2	1	no	—
1227	D₄	—	4	2	no	—
1228	D₄	—	4	2	no	—
1229	D₄	—	4	2	no	—
1230	D₄	—	4	4	no	—
1231	D₄	—	4	2	no	—
1232	D₄	—	4	4	no	—
1233	D₄	—	4	2	no	—
1234	D₄	—	4	2	no	—
1235	D₄	—	4	2	no	—
1236	D₄	—	4	4	no	—
1237	D₄	—	4	2	no	—
1238	D₄	—	4	2	no	—
1239	D₄	—	4	2	no	—
1240	D₄	—	4	2	no	—
1241	D₄	—	8	2	no	—
1242	D₄	—	8	2	no	—
1243	D₄	—	8	2	no	—
1244	D₄	—	8	1	no	—
1245	D₄	—	8	2	no	—
1246	D₄	—	8	2	no	—
1247	D₄	—	8	2	no	—
1248	D₄	—	8	2	no	—
1249	D₄	—	8	2	no	—
1250	C₂×C₄	—	2	2	no	—
1251	C₂×C₄	—	2	2	no	—
1252	C₂×C₄	—	2	2	no	—
1253	C₂×C₄	—	2	2	no	—
1254	C₂×C₄	—	2	2	no	—
1255	C₂×C₄	—	2	1	no	—
1256	C₂×C₄	—	2	1	no	—
1257	C₂×C₄	—	2	1	no	—
1258	C₂×C₄	—	2	1	no	—
1259	C₂×C₄	—	2	2	no	—
1260	C₂×C₄	—	2	2	no	—
1261	C₂×C₄	—	2	1	no	—
1262	C₂×C₄	—	2	2	no	—
1263	C₂×C₄	—	2	2	no	—
1264	C₂×C₄	—	2	2	no	—
1265	C₂×C₄	—	2	1	no	—
1266	C₂×C₄	—	2	1	no	—
1267	C₂×C₄	—	2	1	no	—
1268	C₂×C₄	—	2	1	no	—
1269	C₂×C₄	—	4	2	no	—
1270	C₂×C₄	—	4	2	no	—
1271	C₂×C₄	—	4	2	no	—
1272	C₂×C₄	—	4	2	no	—
1273	C₂×C₄	—	4	2	no	—
1274	C₂×C₄	—	4	4	no	—
1275	C₂×C₄	—	4	2	no	—
1276	C₂×C₄	—	4	2	no	—
1277	C₂×C₄	—	4	2	no	—
1278	C₂×C₄	—	4	2	no	—
1279	C₂×C₄	—	8	1	no	—
1280	C₂×C₄	—	8	1	no	—
1281	C₂×C₄	—	8	1	no	—
1282	C₂×C₄	—	8	2	no	—
1283	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1284	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1285	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1286	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1287	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1288	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1289	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1290	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1291	C₈	—	2	1	no	—
1292	C₈	—	2	1	no	—
1293	C₈	—	2	1	no	—
1294	C₈	—	2	1	no	—
1295	C₈	—	2	2	no	—
1296	C₈	—	2	2	no	—
1297	C₂²	—	2	1	no	—
1298	C₂²	—	2	1	no	—
1299	C₂²	—	2	2	no	—
1300	C₂²	—	2	1	no	—
1301	C₂²	—	2	2	no	—
1302	C₂²	—	2	1	no	—
1303	C₂²	—	2	2	no	—
1304	C₂²	—	2	1	no	—
1305	C₂²	—	2	2	no	—
1306	C₂²	—	2	1	no	—
1307	C₂²	—	2	1	no	—
1308	C₂²	—	2	1	no	—
1309	C₂²	—	2	2	no	—
1310	C₂²	—	2	2	no	—
1311	C₂²	—	4	1	no	—
1312	C₂²	—	4	1	no	—
1313	C₂²	—	4	2	no	—
1314	C₂²	—	4	1	no	—
1315	C₂²	—	4	2	no	—
1316	C₂²	—	4	1	no	—
1317	C₂²	—	4	1	no	—
1318	C₂²	—	4	1	no	—
1319	C₂²	—	4	1	no	—
1320	C₂²	—	4	1	no	—
1321	C₂²	—	4	2	no	—
1322	C₂²	—	4	1	no	—
1323	C₂²	—	8	2	no	—
1324	C₂²	—	8	4	no	—
1325	C₂²	—	8	4	no	—
1326	C₂²	—	16	2	no	—
1327	C₂²	—	16	4	no	—
1328	C₂²	C₅₃×#534	1	2	yes	—
1329	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1330	C₄	—	2	1	no	—
1331	C₄	—	2	1	no	—
1332	C₄	—	2	2	no	—
1333	C₄	—	2	2	no	—
1334	C₄	—	4	2	no	—
1335	C₄	—	4	1	no	—
1336	C₄	—	4	2	no	—
1337	C₄	—	4	1	no	—
1338	C₄	—	4	2	no	—
1339	C₄	—	4	1	no	—
1340	C₄	—	4	1	no	—
1341	C₄	—	4	1	no	—
1342	C₄	C₅₃×#534	1	2	yes	—
1343	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1344	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1345	C₂	—	2	2	no	—
1346	C₂	—	4	1	no	—
1347	C₂	—	4	1	no	—
1348	C₂	—	4	2	no	—
1349	C₂	—	4	2	no	—
1350	C₂	—	8	1	no	—
1351	C₂	—	8	1	no	—
1352	C₂	—	8	2	no	—
1353	C₂	—	8	1	no	—
1354	C₂	C₂×C₅₃×#534	1	1	yes	characteristic
1355	C₂	C₅₃×#3584	1	1	yes	characteristic
1356	C₂	C₅₃×#3585	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 ◁ C₂²×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3488	C₂	semidirect
2. C₅₃×#3449	C₂	semidirect
3. C₅₃×#3201	C₂	semidirect
4. C₅₃×#3200	C₂	semidirect
5. C₅₃×#3199	C₂	semidirect
6. C₅₃×#3198	C₂	semidirect
7. C₅₃×#3197	C₂	semidirect
8. C₅₃×#3194	C₂	semidirect
9. C₅₃×#3191	C₂	semidirect
10. C₅₃×#3188	C₂	semidirect
11. C₅₃×#3099	C₂	semidirect
12. C₅₃×#3098	C₂	semidirect
13. C₅₃×#3093	C₂	semidirect
14. C₂×C₅₃×#482	C₂	semidirect
15. C₅₃×#3062	C₂	semidirect
16. C₅₃×#3062	C₂	semidirect
17. C₅₃×#3061	C₂	semidirect
18. C₅₃×#3060	C₂	semidirect
19. C₅₃×#3012	C₂	semidirect
20. C₅₃×#3012	C₂	semidirect
21. C₅₃×#3006	C₂	semidirect
22. C₅₃×#3002	C₂	semidirect
23. C₅₃×#2880	C₂	semidirect
24. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
26. C₂²×#41×C₅₃	C₂²	semidirect
27. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
28. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
29. C₂×#135×C₅₃	C₂²	semidirect
30. C₂×#135×C₅₃	C₂²	semidirect
31. C₂×#131×C₅₃	C₂²	semidirect
32. C₂×#131×C₅₃	C₂²	semidirect
42. C₅₃×#537	C₂²	semidirect
43. C₅₃×#537	C₂²	semidirect
44. C₅₃×#537	C₂²	semidirect
46. C₅₃×#536	C₂²	semidirect
49. C₅₃×#535	C₂²	semidirect
50. C₅₃×#535	C₂²	semidirect
56. C₅₃×#525	C₂²	semidirect
57. C₅₃×#525	C₂²	semidirect
58. C₅₃×#525	C₂²	semidirect
60. C₂×#121×C₅₃	C₂²	semidirect
61. C₅₃×#520	C₂²	semidirect
62. C₂×#117×C₅₃	C₂²	semidirect
63. C₅₃×#485	C₂²	semidirect
64. C₅₃×#485	C₂²	semidirect
65. C₅₃×#485	C₂²	semidirect
66. C₅₃×#485	C₂²	semidirect
67. C₅₃×#484	C₂²	semidirect
68. C₅₃×#483	C₂²	semidirect
69. C₅₃×#482	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#482	C₂²	semidirect
73. C₅₃×#482	C₂²	semidirect
74. C₅₃×#482	C₂²	semidirect
75. C₅₃×#482	C₂²	semidirect
76. C₅₃×#482	C₂²	semidirect
77. C₅₃×#481	C₂²	semidirect
78. C₅₃×#480	C₂²	semidirect
79. C₅₃×#470	C₂²	semidirect
80. C₅₃×#469	C₂²	semidirect
81. C₅₃×#469	C₂²	semidirect
82. C₅₃×#469	C₂²	semidirect
83. C₅₃×#468	C₂²	semidirect
84. C₅₃×#468	C₂²	semidirect
85. C₅₃×#468	C₂²	semidirect
86. C₅₃×#468	C₂²	semidirect
87. C₅₃×#467	C₂²	semidirect
88. C₅₃×#466	C₂²	semidirect
89. C₅₃×#466	C₂²	semidirect
90. C₅₃×#466	C₂²	semidirect
91. C₅₃×#465	C₂²	semidirect
92. C₅₃×#465	C₂²	semidirect
93. C₅₃×#465	C₂²	semidirect
94. C₅₃×#465	C₂²	semidirect
95. C₅₃×#452	C₂²	semidirect
96. C₅₃×#452	C₂²	semidirect
97. C₅₃×#452	C₂²	semidirect
98. C₅₃×#452	C₂²	semidirect
99. C₅₃×#451	C₂²	semidirect
100. C₅₃×#450	C₂²	semidirect
101. C₅₃×#450	C₂²	semidirect
102. C₅₃×#450	C₂²	semidirect
103. C₅₃×#449	C₂²	semidirect
104. C₅₃×#449	C₂²	semidirect
105. C₅₃×#449	C₂²	semidirect
106. C₅₃×#449	C₂²	semidirect
107. C₅₃×#449	C₂²	semidirect
108. C₅₃×#449	C₂²	semidirect
109. C₅₃×#448	C₂²	semidirect
110. C₅₃×#448	C₂²	semidirect
111. C₅₃×#447	C₂²	semidirect
112. C₅₃×#447	C₂²	semidirect
113. C₅₃×#447	C₂²	semidirect
114. C₅₃×#447	C₂²	semidirect
115. C₅₃×#428	C₂²	semidirect
116. C₅₃×#428	C₂²	semidirect
117. C₂×#107×C₅₃	C₂²	semidirect
118. C₂×#106×C₅₃	C₂²	semidirect
119. C₅₃×#417	C₂²	semidirect
120. C₅₃×#417	C₂²	semidirect
121. C₅₃×#417	C₂²	semidirect
122. C₅₃×#417	C₂²	semidirect
123. C₅₃×#416	C₂²	semidirect
124. C₅₃×#416	C₂²	semidirect
125. C₂×#102×C₅₃	C₂²	semidirect
126. C₂×#102×C₅₃	C₂²	semidirect
127. C₅₃×#408	C₂²	semidirect
128. C₅₃×#408	C₂²	semidirect
129. C₅₃×#408	C₂²	semidirect
130. C₅₃×#408	C₂²	semidirect
131. C₅₃×#407	C₂²	semidirect
132. C₅₃×#407	C₂²	semidirect
133. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
134. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
618. #60767	C₅₃	direct (N × H)
667. #3488	C₂×C₅₃	semidirect
668. #3449	C₂×C₅₃	semidirect
669. #3201	C₂×C₅₃	semidirect
670. #3200	C₂×C₅₃	semidirect
671. #3199	C₂×C₅₃	semidirect
672. #3198	C₂×C₅₃	semidirect
673. #3197	C₂×C₅₃	semidirect
674. #3194	C₂×C₅₃	semidirect
675. #3191	C₂×C₅₃	semidirect
676. #3188	C₂×C₅₃	semidirect
677. #3099	C₂×C₅₃	semidirect
678. #3098	C₂×C₅₃	semidirect
679. #3093	C₂×C₅₃	semidirect
680. C₂×#482	C₂×C₅₃	semidirect
681. #3062	C₂×C₅₃	semidirect
682. #3062	C₂×C₅₃	semidirect
683. #3061	C₂×C₅₃	semidirect
684. #3060	C₂×C₅₃	semidirect
685. #3012	C₂×C₅₃	semidirect
686. #3012	C₂×C₅₃	semidirect
687. #3006	C₂×C₅₃	semidirect
688. #3002	C₂×C₅₃	semidirect
689. #2880	C₂×C₅₃	semidirect
702. C₂×H(5,𝔽₂)	C₂²×C₅₃	semidirect
704. C₂²×#41	C₂²×C₅₃	semidirect
705. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
706. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
707. C₂×#135	C₂²×C₅₃	semidirect
708. C₂×#135	C₂²×C₅₃	semidirect
709. C₂×#131	C₂²×C₅₃	semidirect
710. C₂×#131	C₂²×C₅₃	semidirect
720. #537	C₂²×C₅₃	semidirect
721. #537	C₂²×C₅₃	semidirect
722. #537	C₂²×C₅₃	semidirect
724. #536	C₂²×C₅₃	semidirect
727. #535	C₂²×C₅₃	semidirect
728. #535	C₂²×C₅₃	semidirect
734. #525	C₂²×C₅₃	semidirect
735. #525	C₂²×C₅₃	semidirect
736. #525	C₂²×C₅₃	semidirect
738. C₂×#121	C₂²×C₅₃	semidirect
739. #520	C₂²×C₅₃	semidirect
740. C₂×#117	C₂²×C₅₃	semidirect
741. #485	C₂²×C₅₃	semidirect
742. #485	C₂²×C₅₃	semidirect
743. #485	C₂²×C₅₃	semidirect
744. #485	C₂²×C₅₃	semidirect
745. #484	C₂²×C₅₃	semidirect
746. #483	C₂²×C₅₃	semidirect
747. #482	C₂²×C₅₃	semidirect
748. #482	C₂²×C₅₃	semidirect
749. #482	C₂²×C₅₃	semidirect
750. #482	C₂²×C₅₃	semidirect
751. #482	C₂²×C₅₃	semidirect
752. #482	C₂²×C₅₃	semidirect
753. #482	C₂²×C₅₃	semidirect
754. #482	C₂²×C₅₃	semidirect
755. #481	C₂²×C₅₃	semidirect
756. #480	C₂²×C₅₃	semidirect
757. #470	C₂²×C₅₃	semidirect
758. #469	C₂²×C₅₃	semidirect
759. #469	C₂²×C₅₃	semidirect
760. #469	C₂²×C₅₃	semidirect
761. #468	C₂²×C₅₃	semidirect
762. #468	C₂²×C₅₃	semidirect
763. #468	C₂²×C₅₃	semidirect
764. #468	C₂²×C₅₃	semidirect
765. #467	C₂²×C₅₃	semidirect
766. #466	C₂²×C₅₃	semidirect
767. #466	C₂²×C₅₃	semidirect
768. #466	C₂²×C₅₃	semidirect
769. #465	C₂²×C₅₃	semidirect
770. #465	C₂²×C₅₃	semidirect
771. #465	C₂²×C₅₃	semidirect
772. #465	C₂²×C₅₃	semidirect
773. #452	C₂²×C₅₃	semidirect
774. #452	C₂²×C₅₃	semidirect
775. #452	C₂²×C₅₃	semidirect
776. #452	C₂²×C₅₃	semidirect
777. #451	C₂²×C₅₃	semidirect
778. #450	C₂²×C₅₃	semidirect
779. #450	C₂²×C₅₃	semidirect
780. #450	C₂²×C₅₃	semidirect
781. #449	C₂²×C₅₃	semidirect
782. #449	C₂²×C₅₃	semidirect
783. #449	C₂²×C₅₃	semidirect
784. #449	C₂²×C₅₃	semidirect
785. #449	C₂²×C₅₃	semidirect
786. #449	C₂²×C₅₃	semidirect
787. #448	C₂²×C₅₃	semidirect
788. #448	C₂²×C₅₃	semidirect
789. #447	C₂²×C₅₃	semidirect
790. #447	C₂²×C₅₃	semidirect
791. #447	C₂²×C₅₃	semidirect
792. #447	C₂²×C₅₃	semidirect
793. #428	C₂²×C₅₃	semidirect
794. #428	C₂²×C₅₃	semidirect
795. C₂×#107	C₂²×C₅₃	semidirect
796. C₂×#106	C₂²×C₅₃	semidirect
797. #417	C₂²×C₅₃	semidirect
798. #417	C₂²×C₅₃	semidirect
799. #417	C₂²×C₅₃	semidirect
800. #417	C₂²×C₅₃	semidirect
801. #416	C₂²×C₅₃	semidirect
802. #416	C₂²×C₅₃	semidirect
803. C₂×#102	C₂²×C₅₃	semidirect
804. C₂×#102	C₂²×C₅₃	semidirect
805. #408	C₂²×C₅₃	semidirect
806. #408	C₂²×C₅₃	semidirect
807. #408	C₂²×C₅₃	semidirect
808. #408	C₂²×C₅₃	semidirect
809. #407	C₂²×C₅₃	semidirect
810. #407	C₂²×C₅₃	semidirect
811. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
812. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
813. C₅₃	#60767	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×#3488	2
C₅₃×#3449	2
C₅₃×#3201	2
C₅₃×#3200	2
C₅₃×#3199	2
C₅₃×#3198	2
C₅₃×#3197	2
C₅₃×#3194	2
C₅₃×#3191	2
C₅₃×#3188	2
C₅₃×#3099	2
C₅₃×#3098	2
C₅₃×#3093	2
C₂×C₅₃×#482	2
C₅₃×#3062	2
C₅₃×#3061	2
C₅₃×#3060	2
C₅₃×#3012	2
C₅₃×#3006	2
C₅₃×#3002	2
C₅₃×#2880	2
#60767	53

Subgroups — C53×#60767 #27268279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60767 #27268279