Subgroups — C₅₃×#61617 #27269129

Order 13568.

2224 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3322	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3318	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3309	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3301	C₂	1	2	yes	maximal, complemented
7	D₄×D₈×C₅₃	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3274	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3265	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3264	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3220	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3198	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3192	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3186	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3119	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3008	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2976	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
25	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₈×C₅₃	C₂²	1	2	yes	complemented
28	C₅₃×#560	—	2	2	no	—
29	C₅₃×#553	C₂²	1	2	yes	complemented
30	C₅₃×#553	C₂²	1	2	yes	complemented
31	C₅₃×#550	C₂²	1	2	yes	complemented
32	C₅₃×#548	C₂²	1	2	yes	complemented
33	C₅₃×#546	—	2	2	no	—
34	C₅₃×#546	C₂²	1	2	yes	complemented
35	D₄²×C₅₃	—	2	2	no	—
36	D₄²×C₅₃	—	2	2	no	—
37	D₄²×C₅₃	C₂²	1	2	yes	complemented
38	D₄²×C₅₃	C₂²	1	2	yes	complemented
39	D₄²×C₅₃	C₂²	1	2	yes	complemented
40	C₅₃×#540	C₂²	1	2	yes	complemented
41	C₅₃×#538	—	2	1	no	—
42	C₅₃×#538	—	2	1	no	—
43	C₅₃×#537	—	2	1	no	—
44	C₅₃×#537	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#535	—	2	1	no	—
46	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#535	C₂²	1	2	yes	complemented
48	C₅₃×#534	—	2	1	no	—
49	C₅₃×#534	—	2	1	no	—
50	C₅₃×#525	—	2	1	no	—
51	C₅₃×#525	C₂²	1	1	yes	characteristic
52	C₂×#121×C₅₃	—	2	1	no	—
53	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#496	C₂²	1	2	yes	complemented
58	C₅₃×#493	C₂²	1	2	yes	complemented
59	C₅₃×#490	C₂²	1	2	yes	complemented
60	C₅₃×#488	C₂²	1	2	yes	complemented
61	C₅₃×#485	C₂²	1	2	yes	complemented
62	C₅₃×#482	C₂²	1	2	yes	complemented
63	C₅₃×#481	C₂²	1	2	yes	complemented
64	C₅₃×#481	C₂²	1	2	yes	complemented
65	C₅₃×#480	C₂²	1	2	yes	complemented
66	C₅₃×#480	C₂²	1	2	yes	complemented
67	C₅₃×#479	C₂²	1	2	yes	complemented
68	C₅₃×#478	C₂²	1	2	yes	complemented
69	C₅₃×#469	C₂²	1	2	yes	complemented
70	C₅₃×#469	C₂²	1	2	yes	complemented
71	C₅₃×#469	C₂²	1	2	yes	complemented
72	C₅₃×#468	C₂²	1	2	yes	complemented
73	C₅₃×#466	C₂²	1	2	yes	complemented
74	C₅₃×#466	C₂²	1	2	yes	complemented
75	C₅₃×#466	C₂²	1	2	yes	complemented
76	C₅₃×#465	C₂²	1	2	yes	complemented
77	C₅₃×#463	C₂²	1	2	yes	complemented
78	C₅₃×#463	C₂²	1	2	yes	complemented
79	C₅₃×#460	C₂²	1	2	yes	complemented
80	C₅₃×#459	C₂²	1	2	yes	complemented
81	C₅₃×#459	C₂²	1	2	yes	complemented
82	C₅₃×#459	C₂²	1	2	yes	complemented
83	C₅₃×#450	C₂²	1	2	yes	complemented
84	C₅₃×#449	C₂²	1	2	yes	complemented
85	C₅₃×#449	C₂²	1	2	yes	complemented
86	C₅₃×#449	C₂²	1	2	yes	complemented
87	C₅₃×#449	C₂²	1	2	yes	complemented
88	C₅₃×#449	C₂²	1	2	yes	complemented
89	C₅₃×#449	C₂²	1	2	yes	complemented
90	C₅₃×#449	C₂²	1	2	yes	complemented
91	C₅₃×#449	C₂²	1	2	yes	complemented
92	C₅₃×#448	C₂²	1	2	yes	complemented
93	C₅₃×#447	C₂²	1	2	yes	complemented
94	C₅₃×#447	C₂²	1	2	yes	complemented
95	C₅₃×#447	C₂²	1	2	yes	complemented
96	C₅₃×#447	C₂²	1	2	yes	complemented
97	C₅₃×#447	C₂²	1	2	yes	complemented
98	C₅₃×#447	C₂²	1	2	yes	complemented
99	C₅₃×#447	C₂²	1	2	yes	complemented
100	C₅₃×#447	C₂²	1	2	yes	complemented
101	C₅₃×#442	C₂²	1	2	yes	complemented
102	C₅₃×#440	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
104	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
105	C₅₃×#436	C₂²	1	2	yes	complemented
106	C₅₃×#435	C₂²	1	2	yes	complemented
107	C₅₃×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
109	C₅₃×#433	C₂²	1	2	yes	complemented
110	C₅₃×#418	C₂²	1	2	yes	complemented
111	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#416	C₂²	1	2	yes	complemented
114	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#408	C₂²	1	2	yes	complemented
117	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	H(5,𝔽₂)×C₅₃	—	4	2	no	—
120	H(5,𝔽₂)×C₅₃	—	4	2	no	—
121	C₂×#41×C₅₃	—	2	1	no	—
122	C₂×#41×C₅₃	—	2	1	no	—
123	C₂×#41×C₅₃	—	2	1	no	—
124	C₂×#41×C₅₃	—	4	2	no	—
125	C₂×#41×C₅₃	—	4	2	no	—
126	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
127	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
128	C₂×#41×C₅₃	C₂³	1	2	yes	—
129	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
130	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
131	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₅₃	—	2	1	no	—
134	C₂²×D₄×C₅₃	—	2	1	no	—
135	C₂²×D₄×C₅₃	—	2	1	no	—
136	C₂²×D₄×C₅₃	—	2	1	no	—
137	C₂²×D₄×C₅₃	—	2	1	no	—
138	C₂²×D₄×C₅₃	—	2	2	no	—
139	C₂²×D₄×C₅₃	—	2	2	no	—
140	C₂²×D₄×C₅₃	—	2	2	no	—
141	C₂²×D₄×C₅₃	—	2	2	no	—
142	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
144	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
147	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
148	C₂³×C₄×C₅₃	—	2	1	no	—
149	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
150	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
151	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
152	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
153	C₂×SD₁₆×C₅₃	—	4	2	no	—
154	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
158	C₂×D₈×C₅₃	—	4	2	no	—
159	C₂×D₈×C₅₃	—	4	4	no	—
160	C₂×D₈×C₅₃	C₂³	1	2	yes	—
161	C₂×D₈×C₅₃	C₂³	1	2	yes	—
162	C₂×D₈×C₅₃	C₂³	1	2	yes	—
163	C₂×D₈×C₅₃	C₂³	1	2	yes	—
164	C₂×D₈×C₅₃	C₂³	1	2	yes	—
165	C₂×D₈×C₅₃	C₂³	1	2	yes	—
166	C₂×D₈×C₅₃	C₂³	1	2	yes	—
167	C₂×D₈×C₅₃	C₂³	1	2	yes	—
168	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
171	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
172	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
173	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
174	#127×C₅₃	—	2	2	no	—
175	#127×C₅₃	—	2	2	no	—
176	#127×C₅₃	C₂³	1	2	yes	—
177	#127×C₅₃	C₂³	1	2	yes	—
178	#126×C₅₃	—	2	2	no	—
179	#126×C₅₃	—	2	2	no	—
180	#125×C₅₃	C₂³	1	2	yes	—
181	#124×C₅₃	—	2	2	no	—
182	#124×C₅₃	—	2	2	no	—
183	#124×C₅₃	C₂³	1	2	yes	—
184	#123×C₅₃	—	2	2	no	—
185	#123×C₅₃	—	2	2	no	—
186	#123×C₅₃	—	2	2	no	—
187	#123×C₅₃	—	2	2	no	—
188	#123×C₅₃	—	2	2	no	—
189	#123×C₅₃	D₄	1	2	yes	—
190	C₂²⋊Q₈×C₅₃	—	2	2	no	—
191	C₂²⋊Q₈×C₅₃	—	2	1	no	—
192	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
193	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
194	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
195	#121×C₅₃	—	2	1	no	—
196	#121×C₅₃	—	2	1	no	—
197	#121×C₅₃	—	2	2	no	—
198	#121×C₅₃	—	2	2	no	—
199	#121×C₅₃	—	2	2	no	—
200	#121×C₅₃	—	2	2	no	—
201	#121×C₅₃	—	2	2	no	—
202	#121×C₅₃	—	2	2	no	—
203	#121×C₅₃	—	2	2	no	—
204	#121×C₅₃	—	2	2	no	—
205	#121×C₅₃	—	2	1	no	—
206	#121×C₅₃	—	2	2	no	—
207	#121×C₅₃	—	2	2	no	—
208	#121×C₅₃	—	2	2	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	—	2	1	no	—
211	#121×C₅₃	—	2	1	no	—
212	#121×C₅₃	—	2	1	no	—
213	#121×C₅₃	—	2	1	no	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	—	2	1	no	—
216	#121×C₅₃	D₄	1	1	yes	characteristic
217	#121×C₅₃	D₄	1	1	yes	characteristic
218	#121×C₅₃	C₂³	1	2	yes	—
219	#121×C₅₃	C₂³	1	2	yes	—
220	#121×C₅₃	C₂³	1	2	yes	—
221	#121×C₅₃	C₂³	1	2	yes	—
222	#121×C₅₃	C₂³	1	2	yes	—
223	#121×C₅₃	C₂³	1	2	yes	—
224	#121×C₅₃	C₂³	1	2	yes	—
225	#121×C₅₃	C₂³	1	2	yes	—
226	#121×C₅₃	C₂³	1	2	yes	—
227	#120×C₅₃	—	2	2	no	—
228	#120×C₅₃	—	2	2	no	—
229	#120×C₅₃	—	2	2	no	—
230	#120×C₅₃	—	2	2	no	—
231	#120×C₅₃	—	2	2	no	—
232	#120×C₅₃	—	2	2	no	—
233	#120×C₅₃	—	2	2	no	—
234	#120×C₅₃	—	2	2	no	—
235	#120×C₅₃	—	2	2	no	—
236	#120×C₅₃	—	2	2	no	—
237	#120×C₅₃	D₄	1	2	yes	—
238	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
239	C₄×D₄×C₅₃	—	2	2	no	—
240	C₄×D₄×C₅₃	—	2	2	no	—
241	C₄×D₄×C₅₃	—	2	2	no	—
242	C₄×D₄×C₅₃	—	2	2	no	—
243	C₄×D₄×C₅₃	—	2	2	no	—
244	C₄×D₄×C₅₃	C₂³	1	2	yes	—
245	C₄×D₄×C₅₃	C₂³	1	2	yes	—
246	C₄×D₄×C₅₃	C₂³	1	2	yes	—
247	C₄×D₄×C₅₃	C₂³	1	2	yes	—
248	C₄×D₄×C₅₃	C₂³	1	2	yes	—
249	#117×C₅₃	—	2	1	no	—
250	#117×C₅₃	C₂³	1	2	yes	—
251	#117×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
253	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
257	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
258	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
259	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
260	#107×C₅₃	C₂³	1	2	yes	—
261	#107×C₅₃	C₂³	1	2	yes	—
262	#106×C₅₃	C₂³	1	2	yes	—
263	#106×C₅₃	C₂³	1	2	yes	—
264	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
265	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
266	#103×C₅₃	C₂³	1	2	yes	—
267	#103×C₅₃	C₂³	1	2	yes	—
268	#103×C₅₃	C₂³	1	2	yes	—
269	#103×C₅₃	C₂³	1	2	yes	—
270	#102×C₅₃	C₂³	1	2	yes	—
271	#102×C₅₃	C₂³	1	2	yes	—
272	#102×C₅₃	C₂³	1	2	yes	—
273	#102×C₅₃	C₂³	1	2	yes	—
274	#102×C₅₃	C₂³	1	2	yes	—
275	#102×C₅₃	C₂³	1	2	yes	—
276	#102×C₅₃	C₂³	1	2	yes	—
277	#102×C₅₃	C₂³	1	2	yes	—
278	#102×C₅₃	C₂³	1	2	yes	—
279	#102×C₅₃	C₂³	1	2	yes	—
280	#102×C₅₃	C₂³	1	2	yes	—
281	#102×C₅₃	C₂³	1	2	yes	—
282	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
284	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
285	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
286	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
287	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
288	#97×C₅₃	C₂³	1	2	yes	—
289	C₄×C₈×C₅₃	C₂³	1	2	yes	—
290	C₂⁴×C₅₃	—	2	1	no	—
291	C₂⁴×C₅₃	—	2	2	no	—
292	C₂⁴×C₅₃	—	2	1	no	—
293	C₂⁴×C₅₃	—	2	1	no	—
294	C₂⁴×C₅₃	—	2	1	no	—
295	C₂⁴×C₅₃	—	2	2	no	—
296	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
297	#41×C₅₃	—	2	2	no	—
298	#41×C₅₃	—	2	2	no	—
299	#41×C₅₃	—	2	2	no	—
300	#41×C₅₃	—	2	4	no	—
301	#41×C₅₃	—	2	2	no	—
302	#41×C₅₃	—	4	1	no	—
303	#41×C₅₃	—	4	1	no	—
304	#41×C₅₃	—	4	1	no	—
305	#41×C₅₃	—	4	1	no	—
306	#41×C₅₃	—	4	1	no	—
307	#41×C₅₃	—	4	1	no	—
308	#41×C₅₃	—	4	2	no	—
309	#41×C₅₃	—	4	4	no	—
310	#41×C₅₃	—	4	4	no	—
311	#41×C₅₃	—	4	4	no	—
312	C₂×Q₈×C₅₃	—	2	1	no	—
313	C₂×Q₈×C₅₃	—	2	2	no	—
314	C₂×Q₈×C₅₃	—	4	1	no	—
315	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
316	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
317	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
318	C₂×D₄×C₅₃	—	2	1	no	—
319	C₂×D₄×C₅₃	—	2	2	no	—
320	C₂×D₄×C₅₃	—	2	4	no	—
321	C₂×D₄×C₅₃	—	2	2	no	—
322	C₂×D₄×C₅₃	—	2	2	no	—
323	C₂×D₄×C₅₃	—	2	2	no	—
324	C₂×D₄×C₅₃	—	2	1	no	—
325	C₂×D₄×C₅₃	—	2	1	no	—
326	C₂×D₄×C₅₃	—	2	2	no	—
327	C₂×D₄×C₅₃	—	2	1	no	—
328	C₂×D₄×C₅₃	—	2	2	no	—
329	C₂×D₄×C₅₃	—	2	2	no	—
330	C₂×D₄×C₅₃	—	2	2	no	—
331	C₂×D₄×C₅₃	—	2	2	no	—
332	C₂×D₄×C₅₃	—	2	2	no	—
333	C₂×D₄×C₅₃	—	2	2	no	—
334	C₂×D₄×C₅₃	—	2	1	no	—
335	C₂×D₄×C₅₃	—	2	2	no	—
336	C₂×D₄×C₅₃	—	2	1	no	—
337	C₂×D₄×C₅₃	—	2	2	no	—
338	C₂×D₄×C₅₃	—	2	1	no	—
339	C₂×D₄×C₅₃	—	2	1	no	—
340	C₂×D₄×C₅₃	—	2	2	no	—
341	C₂×D₄×C₅₃	—	2	2	no	—
342	C₂×D₄×C₅₃	—	2	2	no	—
343	C₂×D₄×C₅₃	—	2	2	no	—
344	C₂×D₄×C₅₃	—	4	1	no	—
345	C₂×D₄×C₅₃	—	4	1	no	—
346	C₂×D₄×C₅₃	—	4	1	no	—
347	C₂×D₄×C₅₃	—	4	2	no	—
348	C₂×D₄×C₅₃	—	4	1	no	—
349	C₂×D₄×C₅₃	—	4	2	no	—
350	C₂×D₄×C₅₃	—	4	1	no	—
351	C₂×D₄×C₅₃	—	4	1	no	—
352	C₂×D₄×C₅₃	—	4	1	no	—
353	C₂×D₄×C₅₃	—	4	2	no	—
354	C₂×D₄×C₅₃	—	4	4	no	—
355	C₂×D₄×C₅₃	—	4	4	no	—
356	C₂×D₄×C₅₃	—	4	8	no	—
357	C₂×D₄×C₅₃	—	8	4	no	—
358	C₂×D₄×C₅₃	—	8	4	no	—
359	C₂×D₄×C₅₃	—	8	2	no	—
360	C₂×D₄×C₅₃	—	8	2	no	—
361	C₂×D₄×C₅₃	—	8	4	no	—
362	C₂×D₄×C₅₃	—	8	2	no	—
363	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
364	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
365	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
367	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
368	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
370	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
371	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅₃	—	2	1	no	—
373	C₂²×C₄×C₅₃	—	2	1	no	—
374	C₂²×C₄×C₅₃	—	2	1	no	—
375	C₂²×C₄×C₅₃	—	2	1	no	—
376	C₂²×C₄×C₅₃	—	2	1	no	—
377	C₂²×C₄×C₅₃	—	2	1	no	—
378	C₂²×C₄×C₅₃	—	2	1	no	—
379	C₂²×C₄×C₅₃	—	2	2	no	—
380	C₂²×C₄×C₅₃	—	2	1	no	—
381	C₂²×C₄×C₅₃	—	2	2	no	—
382	C₂²×C₄×C₅₃	—	2	2	no	—
383	C₂²×C₄×C₅₃	—	2	2	no	—
384	C₂²×C₄×C₅₃	—	4	1	no	—
385	C₂²×C₄×C₅₃	—	4	1	no	—
386	C₂²×C₄×C₅₃	—	4	4	no	—
387	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
394	SD₁₆×C₅₃	—	2	4	no	—
395	SD₁₆×C₅₃	—	2	4	no	—
396	SD₁₆×C₅₃	—	4	2	no	—
397	SD₁₆×C₅₃	—	4	2	no	—
398	D₈×C₅₃	—	2	4	no	—
399	D₈×C₅₃	—	2	4	no	—
400	D₈×C₅₃	—	4	2	no	—
401	D₈×C₅₃	—	4	2	no	—
402	D₈×C₅₃	—	4	2	no	—
403	D₈×C₅₃	—	4	2	no	—
404	D₈×C₅₃	—	4	2	no	—
405	D₈×C₅₃	—	4	2	no	—
406	M₁₆×C₅₃	—	4	1	no	—
407	M₁₆×C₅₃	—	4	2	no	—
408	M₁₆×C₅₃	—	4	1	no	—
409	C₂×C₈×C₅₃	—	4	1	no	—
410	C₂×C₈×C₅₃	—	4	2	no	—
411	C₂×C₈×C₅₃	—	4	1	no	—
412	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
413	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
414	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
415	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₅₃	—	2	1	no	—
417	C₄⋊C₄×C₅₃	—	2	2	no	—
418	C₄⋊C₄×C₅₃	—	2	1	no	—
419	C₄⋊C₄×C₅₃	—	2	1	no	—
420	C₄⋊C₄×C₅₃	—	2	2	no	—
421	C₄⋊C₄×C₅₃	—	2	2	no	—
422	C₄⋊C₄×C₅₃	—	2	2	no	—
423	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
424	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
425	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
426	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
427	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
428	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
429	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
430	C₂²⋊C₄×C₅₃	—	2	2	no	—
431	C₂²⋊C₄×C₅₃	—	2	2	no	—
432	C₂²⋊C₄×C₅₃	—	2	2	no	—
433	C₂²⋊C₄×C₅₃	—	2	2	no	—
434	C₂²⋊C₄×C₅₃	—	2	2	no	—
435	C₂²⋊C₄×C₅₃	—	2	2	no	—
436	C₂²⋊C₄×C₅₃	—	2	2	no	—
437	C₂²⋊C₄×C₅₃	—	2	2	no	—
438	C₂²⋊C₄×C₅₃	—	2	2	no	—
439	C₂²⋊C₄×C₅₃	—	2	2	no	—
440	C₂²⋊C₄×C₅₃	—	2	2	no	—
441	C₂²⋊C₄×C₅₃	—	2	2	no	—
442	C₂²⋊C₄×C₅₃	—	2	2	no	—
443	C₂²⋊C₄×C₅₃	—	2	2	no	—
444	C₂²⋊C₄×C₅₃	—	2	2	no	—
445	C₂²⋊C₄×C₅₃	—	2	2	no	—
446	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
451	C₄²×C₅₃	—	2	2	no	—
452	C₄²×C₅₃	—	2	2	no	—
453	C₄²×C₅₃	C₂⁴	1	2	yes	—
454	C₂³×C₅₃	—	2	1	no	—
455	C₂³×C₅₃	—	2	2	no	—
456	C₂³×C₅₃	—	2	1	no	—
457	C₂³×C₅₃	—	2	2	no	—
458	C₂³×C₅₃	—	2	2	no	—
459	C₂³×C₅₃	—	2	2	no	—
460	C₂³×C₅₃	—	4	1	no	—
461	C₂³×C₅₃	—	4	1	no	—
462	C₂³×C₅₃	—	4	2	no	—
463	C₂³×C₅₃	—	4	4	no	—
464	C₂³×C₅₃	—	4	2	no	—
465	C₂³×C₅₃	—	4	2	no	—
466	C₂³×C₅₃	—	4	2	no	—
467	C₂³×C₅₃	—	4	2	no	—
468	C₂³×C₅₃	—	8	1	no	—
469	C₂³×C₅₃	—	8	1	no	—
470	C₂³×C₅₃	—	8	1	no	—
471	C₂³×C₅₃	—	8	2	no	—
472	C₂³×C₅₃	—	8	1	no	—
473	C₂³×C₅₃	—	8	2	no	—
474	C₂³×C₅₃	—	8	1	no	—
475	C₂³×C₅₃	—	8	1	no	—
476	C₂³×C₅₃	—	8	2	no	—
477	C₂³×C₅₃	—	8	2	no	—
478	C₂³×C₅₃	—	8	2	no	—
479	C₂³×C₅₃	—	8	1	no	—
480	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
481	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
482	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
483	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
484	Q₈×C₅₃	—	2	1	no	—
485	Q₈×C₅₃	—	2	1	no	—
486	Q₈×C₅₃	—	2	1	no	—
487	Q₈×C₅₃	—	4	1	no	—
488	Q₈×C₅₃	—	4	2	no	—
489	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
490	D₄×C₅₃	—	2	4	no	—
491	D₄×C₅₃	—	2	4	no	—
492	D₄×C₅₃	—	2	1	no	—
493	D₄×C₅₃	—	2	2	no	—
494	D₄×C₅₃	—	2	1	no	—
495	D₄×C₅₃	—	2	2	no	—
496	D₄×C₅₃	—	2	2	no	—
497	D₄×C₅₃	—	2	2	no	—
498	D₄×C₅₃	—	2	2	no	—
499	D₄×C₅₃	—	2	2	no	—
500	D₄×C₅₃	—	2	1	no	—
501	D₄×C₅₃	—	4	1	no	—
502	D₄×C₅₃	—	4	2	no	—
503	D₄×C₅₃	—	4	2	no	—
504	D₄×C₅₃	—	4	4	no	—
505	D₄×C₅₃	—	4	2	no	—
506	D₄×C₅₃	—	4	4	no	—
507	D₄×C₅₃	—	4	2	no	—
508	D₄×C₅₃	—	4	2	no	—
509	D₄×C₅₃	—	4	2	no	—
510	D₄×C₅₃	—	4	2	no	—
511	D₄×C₅₃	—	4	4	no	—
512	D₄×C₅₃	—	4	4	no	—
513	D₄×C₅₃	—	4	4	no	—
514	D₄×C₅₃	—	8	2	no	—
515	D₄×C₅₃	—	8	1	no	—
516	D₄×C₅₃	—	8	2	no	—
517	D₄×C₅₃	—	8	1	no	—
518	D₄×C₅₃	—	8	2	no	—
519	D₄×C₅₃	—	8	2	no	—
520	D₄×C₅₃	—	8	2	no	—
521	D₄×C₅₃	—	8	2	no	—
522	D₄×C₅₃	—	8	2	no	—
523	D₄×C₅₃	—	8	2	no	—
524	D₄×C₅₃	—	8	2	no	—
525	D₄×C₅₃	—	8	2	no	—
526	D₄×C₅₃	—	8	2	no	—
527	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
528	C₂×C₄×C₅₃	—	2	4	no	—
529	C₂×C₄×C₅₃	—	2	1	no	—
530	C₂×C₄×C₅₃	—	2	1	no	—
531	C₂×C₄×C₅₃	—	2	1	no	—
532	C₂×C₄×C₅₃	—	2	1	no	—
533	C₂×C₄×C₅₃	—	2	1	no	—
534	C₂×C₄×C₅₃	—	2	1	no	—
535	C₂×C₄×C₅₃	—	2	1	no	—
536	C₂×C₄×C₅₃	—	2	2	no	—
537	C₂×C₄×C₅₃	—	2	2	no	—
538	C₂×C₄×C₅₃	—	2	1	no	—
539	C₂×C₄×C₅₃	—	2	2	no	—
540	C₂×C₄×C₅₃	—	2	2	no	—
541	C₂×C₄×C₅₃	—	2	2	no	—
542	C₂×C₄×C₅₃	—	4	1	no	—
543	C₂×C₄×C₅₃	—	4	1	no	—
544	C₂×C₄×C₅₃	—	4	1	no	—
545	C₂×C₄×C₅₃	—	4	2	no	—
546	C₂×C₄×C₅₃	—	4	4	no	—
547	C₂×C₄×C₅₃	—	4	2	no	—
548	C₂×C₄×C₅₃	—	4	2	no	—
549	C₂×C₄×C₅₃	—	4	2	no	—
550	C₂×C₄×C₅₃	—	8	2	no	—
551	C₂×C₄×C₅₃	—	8	2	no	—
552	C₂×C₄×C₅₃	—	8	2	no	—
553	C₂×C₄×C₅₃	—	8	1	no	—
554	C₂×C₄×C₅₃	—	8	1	no	—
555	C₂×C₄×C₅₃	—	8	1	no	—
556	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
559	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
560	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
561	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
563	C₈×C₅₃	—	2	2	no	—
564	C₈×C₅₃	—	2	2	no	—
565	C₈×C₅₃	—	2	2	no	—
566	C₈×C₅₃	—	2	2	no	—
567	#61617	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
568	C₂²×C₅₃	—	2	1	no	—
569	C₂²×C₅₃	—	2	1	no	—
570	C₂²×C₅₃	—	2	1	no	—
571	C₂²×C₅₃	—	2	2	no	—
572	C₂²×C₅₃	—	2	1	no	—
573	C₂²×C₅₃	—	2	1	no	—
574	C₂²×C₅₃	—	2	2	no	—
575	C₂²×C₅₃	—	2	1	no	—
576	C₂²×C₅₃	—	2	2	no	—
577	C₂²×C₅₃	—	2	1	no	—
578	C₂²×C₅₃	—	2	1	no	—
579	C₂²×C₅₃	—	2	2	no	—
580	C₂²×C₅₃	—	4	1	no	—
581	C₂²×C₅₃	—	4	1	no	—
582	C₂²×C₅₃	—	4	2	no	—
583	C₂²×C₅₃	—	4	2	no	—
584	C₂²×C₅₃	—	4	1	no	—
585	C₂²×C₅₃	—	4	2	no	—
586	C₂²×C₅₃	—	4	1	no	—
587	C₂²×C₅₃	—	4	2	no	—
588	C₂²×C₅₃	—	4	2	no	—
589	C₂²×C₅₃	—	4	2	no	—
590	C₂²×C₅₃	—	4	2	no	—
591	C₂²×C₅₃	—	4	2	no	—
592	C₂²×C₅₃	—	4	2	no	—
593	C₂²×C₅₃	—	4	1	no	—
594	C₂²×C₅₃	—	8	2	no	—
595	C₂²×C₅₃	—	8	4	no	—
596	C₂²×C₅₃	—	16	2	no	—
597	C₂²×C₅₃	—	16	4	no	—
598	C₂²×C₅₃	—	16	2	no	—
599	C₂²×C₅₃	—	16	2	no	—
600	C₂²×C₅₃	—	16	4	no	—
601	C₂²×C₅₃	#576	1	2	yes	—
602	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
603	C₄×C₅₃	—	2	2	no	—
604	C₄×C₅₃	—	2	1	no	—
605	C₄×C₅₃	—	2	2	no	—
606	C₄×C₅₃	—	2	1	no	—
607	C₄×C₅₃	—	2	2	no	—
608	C₄×C₅₃	—	2	1	no	—
609	C₄×C₅₃	—	2	2	no	—
610	C₄×C₅₃	—	4	2	no	—
611	C₄×C₅₃	—	4	1	no	—
612	C₄×C₅₃	—	4	2	no	—
613	C₄×C₅₃	—	4	2	no	—
614	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
615	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
616	#3537	C₂×C₅₃	1	1	yes	characteristic, complemented
617	#3488	C₂×C₅₃	1	1	yes	characteristic, complemented
618	#3322	C₂×C₅₃	1	2	yes	complemented
619	#3318	C₂×C₅₃	1	2	yes	complemented
620	#3309	C₂×C₅₃	1	2	yes	complemented
621	#3301	C₂×C₅₃	1	2	yes	complemented
622	D₄×D₈	C₂×C₅₃	1	2	yes	complemented
623	#3274	C₂×C₅₃	1	2	yes	complemented
624	#3265	C₂×C₅₃	1	2	yes	complemented
625	#3264	C₂×C₅₃	1	2	yes	complemented
626	#3220	C₂×C₅₃	1	2	yes	complemented
627	#3198	C₂×C₅₃	1	2	yes	complemented
628	#3192	C₂×C₅₃	1	1	yes	characteristic, complemented
629	#3186	C₂×C₅₃	1	1	yes	characteristic, complemented
630	#3119	C₂×C₅₃	1	2	yes	complemented
631	#3008	C₂×C₅₃	1	2	yes	complemented
632	#3006	C₂×C₅₃	1	1	yes	characteristic, complemented
633	C₂×#449	C₂×C₅₃	1	1	yes	characteristic, complemented
634	#2976	C₂×C₅₃	1	1	yes	characteristic, complemented
635	C₂×C₅₃	—	2	2	no	—
636	C₂×C₅₃	—	4	1	no	—
637	C₂×C₅₃	—	4	1	no	—
638	C₂×C₅₃	—	4	2	no	—
639	C₂×C₅₃	—	4	2	no	—
640	C₂×C₅₃	—	8	1	no	—
641	C₂×C₅₃	—	8	2	no	—
642	C₂×C₅₃	—	8	2	no	—
643	C₂×C₅₃	—	8	2	no	—
644	C₂×C₅₃	#3484	1	1	yes	characteristic
645	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
646	C₂×C₅₃	#3585	1	1	yes	characteristic
647	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic, complemented
648	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
649	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
650	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
651	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
652	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
653	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
654	C₂²×D₈	C₂²×C₅₃	1	2	yes	complemented
655	#560	—	2	2	no	—
656	#553	C₂²×C₅₃	1	2	yes	complemented
657	#553	C₂²×C₅₃	1	2	yes	complemented
658	#550	C₂²×C₅₃	1	2	yes	complemented
659	#548	C₂²×C₅₃	1	2	yes	complemented
660	#546	—	2	2	no	—
661	#546	C₂²×C₅₃	1	2	yes	complemented
662	D₄²	—	2	2	no	—
663	D₄²	—	2	2	no	—
664	D₄²	C₂²×C₅₃	1	2	yes	complemented
665	D₄²	C₂²×C₅₃	1	2	yes	complemented
666	D₄²	C₂²×C₅₃	1	2	yes	complemented
667	#540	C₂²×C₅₃	1	2	yes	complemented
668	#538	—	2	1	no	—
669	#538	—	2	1	no	—
670	#537	—	2	1	no	—
671	#537	C₂²×C₅₃	1	1	yes	characteristic, complemented
672	#535	—	2	1	no	—
673	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
674	#535	C₂²×C₅₃	1	2	yes	complemented
675	#534	—	2	1	no	—
676	#534	—	2	1	no	—
677	#525	—	2	1	no	—
678	#525	C₂²×C₅₃	1	1	yes	characteristic
679	C₂×#121	—	2	1	no	—
680	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
681	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
682	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
683	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
684	#496	C₂²×C₅₃	1	2	yes	complemented
685	#493	C₂²×C₅₃	1	2	yes	complemented
686	#490	C₂²×C₅₃	1	2	yes	complemented
687	#488	C₂²×C₅₃	1	2	yes	complemented
688	#485	C₂²×C₅₃	1	2	yes	complemented
689	#482	C₂²×C₅₃	1	2	yes	complemented
690	#481	C₂²×C₅₃	1	2	yes	complemented
691	#481	C₂²×C₅₃	1	2	yes	complemented
692	#480	C₂²×C₅₃	1	2	yes	complemented
693	#480	C₂²×C₅₃	1	2	yes	complemented
694	#479	C₂²×C₅₃	1	2	yes	complemented
695	#478	C₂²×C₅₃	1	2	yes	complemented
696	#469	C₂²×C₅₃	1	2	yes	complemented
697	#469	C₂²×C₅₃	1	2	yes	complemented
698	#469	C₂²×C₅₃	1	2	yes	complemented
699	#468	C₂²×C₅₃	1	2	yes	complemented
700	#466	C₂²×C₅₃	1	2	yes	complemented
701	#466	C₂²×C₅₃	1	2	yes	complemented
702	#466	C₂²×C₅₃	1	2	yes	complemented
703	#465	C₂²×C₅₃	1	2	yes	complemented
704	#463	C₂²×C₅₃	1	2	yes	complemented
705	#463	C₂²×C₅₃	1	2	yes	complemented
706	#460	C₂²×C₅₃	1	2	yes	complemented
707	#459	C₂²×C₅₃	1	2	yes	complemented
708	#459	C₂²×C₅₃	1	2	yes	complemented
709	#459	C₂²×C₅₃	1	2	yes	complemented
710	#450	C₂²×C₅₃	1	2	yes	complemented
711	#449	C₂²×C₅₃	1	2	yes	complemented
712	#449	C₂²×C₅₃	1	2	yes	complemented
713	#449	C₂²×C₅₃	1	2	yes	complemented
714	#449	C₂²×C₅₃	1	2	yes	complemented
715	#449	C₂²×C₅₃	1	2	yes	complemented
716	#449	C₂²×C₅₃	1	2	yes	complemented
717	#449	C₂²×C₅₃	1	2	yes	complemented
718	#449	C₂²×C₅₃	1	2	yes	complemented
719	#448	C₂²×C₅₃	1	2	yes	complemented
720	#447	C₂²×C₅₃	1	2	yes	complemented
721	#447	C₂²×C₅₃	1	2	yes	complemented
722	#447	C₂²×C₅₃	1	2	yes	complemented
723	#447	C₂²×C₅₃	1	2	yes	complemented
724	#447	C₂²×C₅₃	1	2	yes	complemented
725	#447	C₂²×C₅₃	1	2	yes	complemented
726	#447	C₂²×C₅₃	1	2	yes	complemented
727	#447	C₂²×C₅₃	1	2	yes	complemented
728	#442	C₂²×C₅₃	1	2	yes	complemented
729	#440	C₂²×C₅₃	1	2	yes	complemented
730	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
731	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
732	#436	C₂²×C₅₃	1	2	yes	complemented
733	#435	C₂²×C₅₃	1	2	yes	complemented
734	#435	C₂²×C₅₃	1	2	yes	complemented
735	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
736	#433	C₂²×C₅₃	1	2	yes	complemented
737	#418	C₂²×C₅₃	1	2	yes	complemented
738	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
739	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
740	#416	C₂²×C₅₃	1	2	yes	complemented
741	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
742	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
743	#408	C₂²×C₅₃	1	2	yes	complemented
744	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
745	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
746	C₅₃	#61617	1	1	yes	characteristic, direct product factor, Sylow
747	H(5,𝔽₂)	—	4	2	no	—
748	H(5,𝔽₂)	—	4	2	no	—
749	C₂×#41	—	2	1	no	—
750	C₂×#41	—	2	1	no	—
751	C₂×#41	—	2	1	no	—
752	C₂×#41	—	4	2	no	—
753	C₂×#41	—	4	2	no	—
754	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
755	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
756	C₂×#41	C₂³×C₅₃	1	2	yes	—
757	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
758	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
759	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
760	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
761	C₂²×D₄	—	2	1	no	—
762	C₂²×D₄	—	2	1	no	—
763	C₂²×D₄	—	2	1	no	—
764	C₂²×D₄	—	2	1	no	—
765	C₂²×D₄	—	2	1	no	—
766	C₂²×D₄	—	2	2	no	—
767	C₂²×D₄	—	2	2	no	—
768	C₂²×D₄	—	2	2	no	—
769	C₂²×D₄	—	2	2	no	—
770	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
771	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
772	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
773	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
774	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
775	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
776	C₂³×C₄	—	2	1	no	—
777	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
778	AGL(1,ℤ/8)	—	4	2	no	—
779	AGL(1,ℤ/8)	—	4	4	no	—
780	AGL(1,ℤ/8)	—	4	2	no	—
781	C₂×SD₁₆	—	4	2	no	—
782	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
783	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
785	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
786	C₂×D₈	—	4	2	no	—
787	C₂×D₈	—	4	4	no	—
788	C₂×D₈	C₂³×C₅₃	1	2	yes	—
789	C₂×D₈	C₂³×C₅₃	1	2	yes	—
790	C₂×D₈	C₂³×C₅₃	1	2	yes	—
791	C₂×D₈	C₂³×C₅₃	1	2	yes	—
792	C₂×D₈	C₂³×C₅₃	1	2	yes	—
793	C₂×D₈	C₂³×C₅₃	1	2	yes	—
794	C₂×D₈	C₂³×C₅₃	1	2	yes	—
795	C₂×D₈	C₂³×C₅₃	1	2	yes	—
796	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
797	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
798	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
799	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
800	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
801	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
802	#127	—	2	2	no	—
803	#127	—	2	2	no	—
804	#127	C₂³×C₅₃	1	2	yes	—
805	#127	C₂³×C₅₃	1	2	yes	—
806	#126	—	2	2	no	—
807	#126	—	2	2	no	—
808	#125	C₂³×C₅₃	1	2	yes	—
809	#124	—	2	2	no	—
810	#124	—	2	2	no	—
811	#124	C₂³×C₅₃	1	2	yes	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	#123	D₄×C₅₃	1	2	yes	—
818	C₂²⋊Q₈	—	2	1	no	—
819	C₂²⋊Q₈	—	2	2	no	—
820	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
821	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
822	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
823	#121	—	2	1	no	—
824	#121	—	2	2	no	—
825	#121	—	2	2	no	—
826	#121	—	2	2	no	—
827	#121	—	2	2	no	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	1	no	—
833	#121	—	2	1	no	—
834	#121	—	2	1	no	—
835	#121	—	2	1	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	2	no	—
841	#121	—	2	2	no	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#121	D₄×C₅₃	1	1	yes	characteristic
845	#121	D₄×C₅₃	1	1	yes	characteristic
846	#121	C₂³×C₅₃	1	2	yes	—
847	#121	C₂³×C₅₃	1	2	yes	—
848	#121	C₂³×C₅₃	1	2	yes	—
849	#121	C₂³×C₅₃	1	2	yes	—
850	#121	C₂³×C₅₃	1	2	yes	—
851	#121	C₂³×C₅₃	1	2	yes	—
852	#121	C₂³×C₅₃	1	2	yes	—
853	#121	C₂³×C₅₃	1	2	yes	—
854	#121	C₂³×C₅₃	1	2	yes	—
855	#120	—	2	2	no	—
856	#120	—	2	2	no	—
857	#120	—	2	2	no	—
858	#120	—	2	2	no	—
859	#120	—	2	2	no	—
860	#120	—	2	2	no	—
861	#120	—	2	2	no	—
862	#120	—	2	2	no	—
863	#120	—	2	2	no	—
864	#120	—	2	2	no	—
865	#120	D₄×C₅₃	1	2	yes	—
866	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
867	C₄×D₄	—	2	2	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	—	2	2	no	—
871	C₄×D₄	—	2	2	no	—
872	C₄×D₄	C₂³×C₅₃	1	2	yes	—
873	C₄×D₄	C₂³×C₅₃	1	2	yes	—
874	C₄×D₄	C₂³×C₅₃	1	2	yes	—
875	C₄×D₄	C₂³×C₅₃	1	2	yes	—
876	C₄×D₄	C₂³×C₅₃	1	2	yes	—
877	#117	—	2	1	no	—
878	#117	C₂³×C₅₃	1	2	yes	—
879	#117	C₂³×C₅₃	1	1	yes	characteristic
880	C₂×C₄⋊C₄	—	2	1	no	—
881	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
884	C₂×C₂²⋊C₄	—	2	1	no	—
885	C₂×C₂²⋊C₄	—	2	1	no	—
886	C₂×C₂²⋊C₄	—	2	1	no	—
887	C₂×C₂²⋊C₄	—	2	2	no	—
888	#107	C₂³×C₅₃	1	2	yes	—
889	#107	C₂³×C₅₃	1	2	yes	—
890	#106	C₂³×C₅₃	1	2	yes	—
891	#106	C₂³×C₅₃	1	2	yes	—
892	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
893	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
894	#103	C₂³×C₅₃	1	2	yes	—
895	#103	C₂³×C₅₃	1	2	yes	—
896	#103	C₂³×C₅₃	1	2	yes	—
897	#103	C₂³×C₅₃	1	2	yes	—
898	#102	C₂³×C₅₃	1	2	yes	—
899	#102	C₂³×C₅₃	1	2	yes	—
900	#102	C₂³×C₅₃	1	2	yes	—
901	#102	C₂³×C₅₃	1	2	yes	—
902	#102	C₂³×C₅₃	1	2	yes	—
903	#102	C₂³×C₅₃	1	2	yes	—
904	#102	C₂³×C₅₃	1	2	yes	—
905	#102	C₂³×C₅₃	1	2	yes	—
906	#102	C₂³×C₅₃	1	2	yes	—
907	#102	C₂³×C₅₃	1	2	yes	—
908	#102	C₂³×C₅₃	1	2	yes	—
909	#102	C₂³×C₅₃	1	2	yes	—
910	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
911	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
912	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
913	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
914	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
915	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
916	#97	C₂³×C₅₃	1	2	yes	—
917	C₄×C₈	C₂³×C₅₃	1	2	yes	—
918	C₂⁴	—	2	1	no	—
919	C₂⁴	—	2	2	no	—
920	C₂⁴	—	2	1	no	—
921	C₂⁴	—	2	1	no	—
922	C₂⁴	—	2	1	no	—
923	C₂⁴	—	2	2	no	—
924	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
925	#41	—	2	2	no	—
926	#41	—	2	2	no	—
927	#41	—	2	2	no	—
928	#41	—	2	4	no	—
929	#41	—	2	2	no	—
930	#41	—	4	1	no	—
931	#41	—	4	1	no	—
932	#41	—	4	1	no	—
933	#41	—	4	1	no	—
934	#41	—	4	1	no	—
935	#41	—	4	1	no	—
936	#41	—	4	2	no	—
937	#41	—	4	4	no	—
938	#41	—	4	4	no	—
939	#41	—	4	4	no	—
940	C₂×Q₈	—	2	1	no	—
941	C₂×Q₈	—	2	2	no	—
942	C₂×Q₈	—	4	1	no	—
943	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
944	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
945	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
946	C₂×D₄	—	2	1	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	4	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	1	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	1	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	1	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	1	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	4	1	no	—
973	C₂×D₄	—	4	2	no	—
974	C₂×D₄	—	4	1	no	—
975	C₂×D₄	—	4	1	no	—
976	C₂×D₄	—	4	1	no	—
977	C₂×D₄	—	4	2	no	—
978	C₂×D₄	—	4	1	no	—
979	C₂×D₄	—	4	1	no	—
980	C₂×D₄	—	4	1	no	—
981	C₂×D₄	—	4	2	no	—
982	C₂×D₄	—	4	4	no	—
983	C₂×D₄	—	4	4	no	—
984	C₂×D₄	—	4	8	no	—
985	C₂×D₄	—	8	4	no	—
986	C₂×D₄	—	8	4	no	—
987	C₂×D₄	—	8	2	no	—
988	C₂×D₄	—	8	2	no	—
989	C₂×D₄	—	8	4	no	—
990	C₂×D₄	—	8	2	no	—
991	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
992	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
993	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
994	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
995	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
996	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
997	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
998	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
999	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	4	1	no	—
1013	C₂²×C₄	—	4	1	no	—
1014	C₂²×C₄	—	4	4	no	—
1015	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1016	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1017	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1019	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1020	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1021	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1022	SD₁₆	—	2	4	no	—
1023	SD₁₆	—	2	4	no	—
1024	SD₁₆	—	4	2	no	—
1025	SD₁₆	—	4	2	no	—
1026	D₈	—	2	4	no	—
1027	D₈	—	2	4	no	—
1028	D₈	—	4	2	no	—
1029	D₈	—	4	2	no	—
1030	D₈	—	4	2	no	—
1031	D₈	—	4	2	no	—
1032	D₈	—	4	2	no	—
1033	D₈	—	4	2	no	—
1034	M₁₆	—	4	1	no	—
1035	M₁₆	—	4	2	no	—
1036	M₁₆	—	4	1	no	—
1037	C₂×C₈	—	4	1	no	—
1038	C₂×C₈	—	4	2	no	—
1039	C₂×C₈	—	4	1	no	—
1040	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1041	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1042	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1043	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1052	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1053	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1054	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1055	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1056	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1057	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1076	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1077	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1078	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1079	C₄²	—	2	2	no	—
1080	C₄²	—	2	2	no	—
1081	C₄²	C₂⁴×C₅₃	1	2	yes	—
1082	C₂³	—	2	1	no	—
1083	C₂³	—	2	2	no	—
1084	C₂³	—	2	2	no	—
1085	C₂³	—	2	2	no	—
1086	C₂³	—	2	2	no	—
1087	C₂³	—	2	1	no	—
1088	C₂³	—	4	1	no	—
1089	C₂³	—	4	1	no	—
1090	C₂³	—	4	2	no	—
1091	C₂³	—	4	4	no	—
1092	C₂³	—	4	2	no	—
1093	C₂³	—	4	2	no	—
1094	C₂³	—	4	2	no	—
1095	C₂³	—	4	2	no	—
1096	C₂³	—	8	1	no	—
1097	C₂³	—	8	1	no	—
1098	C₂³	—	8	1	no	—
1099	C₂³	—	8	2	no	—
1100	C₂³	—	8	1	no	—
1101	C₂³	—	8	1	no	—
1102	C₂³	—	8	1	no	—
1103	C₂³	—	8	2	no	—
1104	C₂³	—	8	2	no	—
1105	C₂³	—	8	2	no	—
1106	C₂³	—	8	2	no	—
1107	C₂³	—	8	1	no	—
1108	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1109	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1110	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1111	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1112	Q₈	—	2	1	no	—
1113	Q₈	—	2	1	no	—
1114	Q₈	—	2	1	no	—
1115	Q₈	—	4	1	no	—
1116	Q₈	—	4	2	no	—
1117	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1118	D₄	—	2	4	no	—
1119	D₄	—	2	4	no	—
1120	D₄	—	2	1	no	—
1121	D₄	—	2	2	no	—
1122	D₄	—	2	2	no	—
1123	D₄	—	2	2	no	—
1124	D₄	—	2	2	no	—
1125	D₄	—	2	1	no	—
1126	D₄	—	2	2	no	—
1127	D₄	—	2	1	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	4	1	no	—
1130	D₄	—	4	2	no	—
1131	D₄	—	4	2	no	—
1132	D₄	—	4	4	no	—
1133	D₄	—	4	2	no	—
1134	D₄	—	4	4	no	—
1135	D₄	—	4	2	no	—
1136	D₄	—	4	2	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	2	no	—
1139	D₄	—	4	4	no	—
1140	D₄	—	4	4	no	—
1141	D₄	—	4	4	no	—
1142	D₄	—	8	2	no	—
1143	D₄	—	8	1	no	—
1144	D₄	—	8	2	no	—
1145	D₄	—	8	1	no	—
1146	D₄	—	8	2	no	—
1147	D₄	—	8	2	no	—
1148	D₄	—	8	2	no	—
1149	D₄	—	8	2	no	—
1150	D₄	—	8	2	no	—
1151	D₄	—	8	2	no	—
1152	D₄	—	8	2	no	—
1153	D₄	—	8	2	no	—
1154	D₄	—	8	2	no	—
1155	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1156	C₂×C₄	—	2	4	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	4	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	4	1	no	—
1173	C₂×C₄	—	4	2	no	—
1174	C₂×C₄	—	4	4	no	—
1175	C₂×C₄	—	4	2	no	—
1176	C₂×C₄	—	4	2	no	—
1177	C₂×C₄	—	4	2	no	—
1178	C₂×C₄	—	8	2	no	—
1179	C₂×C₄	—	8	2	no	—
1180	C₂×C₄	—	8	2	no	—
1181	C₂×C₄	—	8	1	no	—
1182	C₂×C₄	—	8	1	no	—
1183	C₂×C₄	—	8	1	no	—
1184	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1185	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1186	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1187	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1188	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1189	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1190	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1191	C₈	—	2	2	no	—
1192	C₈	—	2	2	no	—
1193	C₈	—	2	2	no	—
1194	C₈	—	2	2	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	1	no	—
1197	C₂²	—	2	1	no	—
1198	C₂²	—	2	2	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	1	no	—
1203	C₂²	—	2	2	no	—
1204	C₂²	—	2	1	no	—
1205	C₂²	—	2	2	no	—
1206	C₂²	—	2	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	2	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	2	no	—
1213	C₂²	—	4	2	no	—
1214	C₂²	—	4	2	no	—
1215	C₂²	—	4	2	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	2	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	2	no	—
1221	C₂²	—	8	2	no	—
1222	C₂²	—	8	4	no	—
1223	C₂²	—	16	2	no	—
1224	C₂²	—	16	4	no	—
1225	C₂²	—	16	2	no	—
1226	C₂²	—	16	2	no	—
1227	C₂²	—	16	4	no	—
1228	C₂²	C₅₃×#576	1	2	yes	—
1229	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1230	C₄	—	2	1	no	—
1231	C₄	—	2	2	no	—
1232	C₄	—	2	1	no	—
1233	C₄	—	2	2	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	2	no	—
1236	C₄	—	2	2	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	2	no	—
1239	C₄	—	4	2	no	—
1240	C₄	—	4	2	no	—
1241	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1242	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1243	C₂	—	2	2	no	—
1244	C₂	—	4	1	no	—
1245	C₂	—	4	1	no	—
1246	C₂	—	4	2	no	—
1247	C₂	—	4	2	no	—
1248	C₂	—	8	1	no	—
1249	C₂	—	8	2	no	—
1250	C₂	—	8	2	no	—
1251	C₂	—	8	2	no	—
1252	C₂	C₅₃×#3484	1	1	yes	characteristic
1253	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1254	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 ◁ C₅₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3537	C₂	semidirect
2. C₅₃×#3488	C₂	semidirect
3. C₅₃×#3322	C₂	semidirect
4. C₅₃×#3318	C₂	semidirect
5. C₅₃×#3309	C₂	semidirect
6. C₅₃×#3301	C₂	semidirect
7. D₄×D₈×C₅₃	C₂	semidirect
8. C₅₃×#3274	C₂	semidirect
9. C₅₃×#3265	C₂	semidirect
10. C₅₃×#3264	C₂	semidirect
11. C₅₃×#3220	C₂	semidirect
12. C₅₃×#3198	C₂	semidirect
13. C₅₃×#3192	C₂	semidirect
14. C₅₃×#3186	C₂	semidirect
15. C₅₃×#3119	C₂	semidirect
16. C₅₃×#3008	C₂	semidirect
17. C₅₃×#3006	C₂	semidirect
18. C₂×C₅₃×#449	C₂	semidirect
19. C₅₃×#2976	C₂	semidirect
20. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
21. C₂²×#41×C₅₃	C₂²	semidirect
22. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
23. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
24. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
25. C₂²×SD₁₆×C₅₃	C₂²	semidirect
26. C₂²×D₈×C₅₃	C₂²	semidirect
27. C₂²×D₈×C₅₃	C₂²	semidirect
29. C₅₃×#553	C₂²	semidirect
30. C₅₃×#553	C₂²	semidirect
31. C₅₃×#550	C₂²	semidirect
32. C₅₃×#548	C₂²	semidirect
34. C₅₃×#546	C₂²	semidirect
37. D₄²×C₅₃	C₂²	semidirect
38. D₄²×C₅₃	C₂²	semidirect
39. D₄²×C₅₃	C₂²	semidirect
40. C₅₃×#540	C₂²	semidirect
44. C₅₃×#537	C₂²	semidirect
46. C₅₃×#535	C₂²	semidirect
47. C₅₃×#535	C₂²	semidirect
53. C₂×#121×C₅₃	C₂²	semidirect
54. C₂×#121×C₅₃	C₂²	semidirect
55. C₂×#121×C₅₃	C₂²	semidirect
56. C₅₃×#520	C₂²	semidirect
57. C₅₃×#496	C₂²	semidirect
58. C₅₃×#493	C₂²	semidirect
59. C₅₃×#490	C₂²	semidirect
60. C₅₃×#488	C₂²	semidirect
61. C₅₃×#485	C₂²	semidirect
62. C₅₃×#482	C₂²	semidirect
63. C₅₃×#481	C₂²	semidirect
64. C₅₃×#481	C₂²	semidirect
65. C₅₃×#480	C₂²	semidirect
66. C₅₃×#480	C₂²	semidirect
67. C₅₃×#479	C₂²	semidirect
68. C₅₃×#478	C₂²	semidirect
69. C₅₃×#469	C₂²	semidirect
70. C₅₃×#469	C₂²	semidirect
71. C₅₃×#469	C₂²	semidirect
72. C₅₃×#468	C₂²	semidirect
73. C₅₃×#466	C₂²	semidirect
74. C₅₃×#466	C₂²	semidirect
75. C₅₃×#466	C₂²	semidirect
76. C₅₃×#465	C₂²	semidirect
77. C₅₃×#463	C₂²	semidirect
78. C₅₃×#463	C₂²	semidirect
79. C₅₃×#460	C₂²	semidirect
80. C₅₃×#459	C₂²	semidirect
81. C₅₃×#459	C₂²	semidirect
82. C₅₃×#459	C₂²	semidirect
83. C₅₃×#450	C₂²	semidirect
84. C₅₃×#449	C₂²	semidirect
85. C₅₃×#449	C₂²	semidirect
86. C₅₃×#449	C₂²	semidirect
87. C₅₃×#449	C₂²	semidirect
88. C₅₃×#449	C₂²	semidirect
89. C₅₃×#449	C₂²	semidirect
90. C₅₃×#449	C₂²	semidirect
91. C₅₃×#449	C₂²	semidirect
92. C₅₃×#448	C₂²	semidirect
93. C₅₃×#447	C₂²	semidirect
94. C₅₃×#447	C₂²	semidirect
95. C₅₃×#447	C₂²	semidirect
96. C₅₃×#447	C₂²	semidirect
97. C₅₃×#447	C₂²	semidirect
98. C₅₃×#447	C₂²	semidirect
99. C₅₃×#447	C₂²	semidirect
100. C₅₃×#447	C₂²	semidirect
101. C₅₃×#442	C₂²	semidirect
102. C₅₃×#440	C₂²	semidirect
103. C₄×SD₁₆×C₅₃	C₂²	semidirect
104. C₄×D₈×C₅₃	C₂²	semidirect
105. C₅₃×#436	C₂²	semidirect
106. C₅₃×#435	C₂²	semidirect
107. C₅₃×#435	C₂²	semidirect
108. C₈×D₄×C₅₃	C₂²	semidirect
109. C₅₃×#433	C₂²	semidirect
110. C₅₃×#418	C₂²	semidirect
111. C₅₃×#417	C₂²	semidirect
112. C₅₃×#417	C₂²	semidirect
113. C₅₃×#416	C₂²	semidirect
114. C₂×#103×C₅₃	C₂²	semidirect
115. C₂×#102×C₅₃	C₂²	semidirect
116. C₅₃×#408	C₂²	semidirect
117. C₅₃×#407	C₂²	semidirect
118. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
567. #61617	C₅₃	direct (N × H)
616. #3537	C₂×C₅₃	semidirect
617. #3488	C₂×C₅₃	semidirect
618. #3322	C₂×C₅₃	semidirect
619. #3318	C₂×C₅₃	semidirect
620. #3309	C₂×C₅₃	semidirect
621. #3301	C₂×C₅₃	semidirect
622. D₄×D₈	C₂×C₅₃	semidirect
623. #3274	C₂×C₅₃	semidirect
624. #3265	C₂×C₅₃	semidirect
625. #3264	C₂×C₅₃	semidirect
626. #3220	C₂×C₅₃	semidirect
627. #3198	C₂×C₅₃	semidirect
628. #3192	C₂×C₅₃	semidirect
629. #3186	C₂×C₅₃	semidirect
630. #3119	C₂×C₅₃	semidirect
631. #3008	C₂×C₅₃	semidirect
632. #3006	C₂×C₅₃	semidirect
633. C₂×#449	C₂×C₅₃	semidirect
634. #2976	C₂×C₅₃	semidirect
647. C₂×H(5,𝔽₂)	C₂²×C₅₃	semidirect
648. C₂²×#41	C₂²×C₅₃	semidirect
649. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
650. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
651. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
652. C₂²×SD₁₆	C₂²×C₅₃	semidirect
653. C₂²×D₈	C₂²×C₅₃	semidirect
654. C₂²×D₈	C₂²×C₅₃	semidirect
656. #553	C₂²×C₅₃	semidirect
657. #553	C₂²×C₅₃	semidirect
658. #550	C₂²×C₅₃	semidirect
659. #548	C₂²×C₅₃	semidirect
661. #546	C₂²×C₅₃	semidirect
664. D₄²	C₂²×C₅₃	semidirect
665. D₄²	C₂²×C₅₃	semidirect
666. D₄²	C₂²×C₅₃	semidirect
667. #540	C₂²×C₅₃	semidirect
671. #537	C₂²×C₅₃	semidirect
673. #535	C₂²×C₅₃	semidirect
674. #535	C₂²×C₅₃	semidirect
680. C₂×#121	C₂²×C₅₃	semidirect
681. C₂×#121	C₂²×C₅₃	semidirect
682. C₂×#121	C₂²×C₅₃	semidirect
683. #520	C₂²×C₅₃	semidirect
684. #496	C₂²×C₅₃	semidirect
685. #493	C₂²×C₅₃	semidirect
686. #490	C₂²×C₅₃	semidirect
687. #488	C₂²×C₅₃	semidirect
688. #485	C₂²×C₅₃	semidirect
689. #482	C₂²×C₅₃	semidirect
690. #481	C₂²×C₅₃	semidirect
691. #481	C₂²×C₅₃	semidirect
692. #480	C₂²×C₅₃	semidirect
693. #480	C₂²×C₅₃	semidirect
694. #479	C₂²×C₅₃	semidirect
695. #478	C₂²×C₅₃	semidirect
696. #469	C₂²×C₅₃	semidirect
697. #469	C₂²×C₅₃	semidirect
698. #469	C₂²×C₅₃	semidirect
699. #468	C₂²×C₅₃	semidirect
700. #466	C₂²×C₅₃	semidirect
701. #466	C₂²×C₅₃	semidirect
702. #466	C₂²×C₅₃	semidirect
703. #465	C₂²×C₅₃	semidirect
704. #463	C₂²×C₅₃	semidirect
705. #463	C₂²×C₅₃	semidirect
706. #460	C₂²×C₅₃	semidirect
707. #459	C₂²×C₅₃	semidirect
708. #459	C₂²×C₅₃	semidirect
709. #459	C₂²×C₅₃	semidirect
710. #450	C₂²×C₅₃	semidirect
711. #449	C₂²×C₅₃	semidirect
712. #449	C₂²×C₅₃	semidirect
713. #449	C₂²×C₅₃	semidirect
714. #449	C₂²×C₅₃	semidirect
715. #449	C₂²×C₅₃	semidirect
716. #449	C₂²×C₅₃	semidirect
717. #449	C₂²×C₅₃	semidirect
718. #449	C₂²×C₅₃	semidirect
719. #448	C₂²×C₅₃	semidirect
720. #447	C₂²×C₅₃	semidirect
721. #447	C₂²×C₅₃	semidirect
722. #447	C₂²×C₅₃	semidirect
723. #447	C₂²×C₅₃	semidirect
724. #447	C₂²×C₅₃	semidirect
725. #447	C₂²×C₅₃	semidirect
726. #447	C₂²×C₅₃	semidirect
727. #447	C₂²×C₅₃	semidirect
728. #442	C₂²×C₅₃	semidirect
729. #440	C₂²×C₅₃	semidirect
730. C₄×SD₁₆	C₂²×C₅₃	semidirect
731. C₄×D₈	C₂²×C₅₃	semidirect
732. #436	C₂²×C₅₃	semidirect
733. #435	C₂²×C₅₃	semidirect
734. #435	C₂²×C₅₃	semidirect
735. C₈×D₄	C₂²×C₅₃	semidirect
736. #433	C₂²×C₅₃	semidirect
737. #418	C₂²×C₅₃	semidirect
738. #417	C₂²×C₅₃	semidirect
739. #417	C₂²×C₅₃	semidirect
740. #416	C₂²×C₅₃	semidirect
741. C₂×#103	C₂²×C₅₃	semidirect
742. C₂×#102	C₂²×C₅₃	semidirect
743. #408	C₂²×C₅₃	semidirect
744. #407	C₂²×C₅₃	semidirect
745. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
746. C₅₃	#61617	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×#3537	2
C₅₃×#3488	2
C₅₃×#3322	2
C₅₃×#3318	2
C₅₃×#3309	2
C₅₃×#3301	2
D₄×D₈×C₅₃	2
C₅₃×#3274	2
C₅₃×#3265	2
C₅₃×#3264	2
C₅₃×#3220	2
C₅₃×#3198	2
C₅₃×#3192	2
C₅₃×#3186	2
C₅₃×#3119	2
C₅₃×#3008	2
C₅₃×#3006	2
C₂×C₅₃×#449	2
C₅₃×#2976	2
#61617	53

Subgroups — C53×#61617 #27269129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61617 #27269129