Subgroups — C₅₃×#62125 #27269637

Order 13568.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3389	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3370	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3347	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3346	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3339	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3319	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3318	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3297	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3239	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#559	C₂²	1	1	yes	characteristic
25	C₅₃×#556	—	2	1	no	—
26	C₅₃×#555	C₂²	1	2	yes	complemented
27	C₅₃×#554	C₂²	1	1	yes	characteristic
28	C₅₃×#554	C₂²	1	1	yes	characteristic
29	C₅₃×#554	C₂²	1	2	yes	complemented
30	C₅₃×#553	—	2	1	no	—
31	C₅₃×#553	C₂²	1	1	yes	characteristic
32	C₅₃×#553	C₂²	1	1	yes	characteristic
33	C₅₃×#553	C₂²	1	2	yes	—
34	C₅₃×#553	C₂²	1	2	yes	complemented
35	C₅₃×#551	—	2	1	no	—
36	C₅₃×#551	—	2	1	no	—
37	C₅₃×#548	—	2	1	no	—
38	C₅₃×#548	—	2	1	no	—
39	C₅₃×#547	—	2	1	no	—
40	C₅₃×#546	—	2	1	no	—
41	C₅₃×#546	C₂²	1	1	yes	characteristic
42	C₅₃×#546	C₂²	1	1	yes	characteristic
43	D₄²×C₅₃	C₂²	1	1	yes	characteristic
44	C₅₃×#542	—	2	1	no	—
45	C₅₃×#542	—	2	1	no	—
46	C₅₃×#537	—	2	1	no	—
47	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#532	C₂²	1	1	yes	characteristic
50	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#529	—	2	1	no	—
55	C₅₃×#529	C₂²	1	1	yes	characteristic
56	C₅₃×#529	C₂²	1	1	yes	characteristic
57	C₅₃×#525	—	2	1	no	—
58	C₅₃×#525	—	2	1	no	—
59	C₅₃×#520	—	2	1	no	—
60	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
61	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄×C₅₃	—	2	1	no	—
63	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
65	C₅₃×#501	C₂²	1	2	yes	complemented
66	C₅₃×#501	C₂²	1	2	yes	complemented
67	C₅₃×#499	C₂²	1	2	yes	complemented
68	C₅₃×#490	C₂²	1	2	yes	—
69	C₅₃×#489	C₂²	1	2	yes	complemented
70	C₅₃×#488	C₂²	1	2	yes	complemented
71	C₅₃×#485	C₂²	1	2	yes	complemented
72	C₅₃×#484	C₂²	1	2	yes	complemented
73	C₅₃×#482	C₂²	1	2	yes	—
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	—
78	C₅₃×#481	C₂²	1	2	yes	complemented
79	C₅₃×#480	C₂²	1	2	yes	complemented
80	C₅₃×#479	C₂²	1	2	yes	complemented
81	C₅₃×#478	C₂²	1	2	yes	—
82	C₅₃×#478	C₂²	1	2	yes	—
83	C₅₃×#478	C₂²	1	2	yes	complemented
84	C₅₃×#478	C₂²	1	2	yes	complemented
85	C₅₃×#478	C₂²	1	2	yes	complemented
86	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#476	C₂²	1	1	yes	characteristic
88	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#474	C₂²	1	2	yes	—
93	C₅₃×#474	C₂²	1	1	yes	characteristic
94	C₅₃×#474	C₂²	1	1	yes	characteristic
95	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#474	C₂²	1	2	yes	complemented
100	C₅₃×#474	C₂²	1	2	yes	complemented
101	C₅₃×#469	C₂²	1	2	yes	—
102	C₅₃×#468	C₂²	1	2	yes	complemented
103	C₅₃×#466	C₂²	1	2	yes	—
104	C₅₃×#466	C₂²	1	2	yes	complemented
105	C₅₃×#466	C₂²	1	2	yes	complemented
106	C₅₃×#465	C₂²	1	2	yes	complemented
107	C₅₃×#463	C₂²	1	2	yes	complemented
108	C₅₃×#463	C₂²	1	2	yes	complemented
109	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#459	C₂²	1	2	yes	—
111	C₅₃×#459	C₂²	1	1	yes	characteristic
112	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#449	C₂²	1	2	yes	—
115	C₅₃×#447	C₂²	1	2	yes	—
116	C₅₃×#447	C₂²	1	2	yes	—
117	C₅₃×#446	C₂²	1	2	yes	complemented
118	C₅₃×#442	C₂²	1	2	yes	—
119	C₅₃×#442	C₂²	1	2	yes	—
120	C₅₃×#442	C₂²	1	2	yes	complemented
121	C₅₃×#440	C₂²	1	2	yes	complemented
122	C₄×D₈×C₅₃	C₂²	1	2	yes	—
123	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
124	C₅₃×#435	C₂²	1	2	yes	—
125	C₅₃×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
127	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#428	C₂²	1	2	yes	complemented
131	C₅₃×#427	C₂²	1	2	yes	complemented
132	C₂×#107×C₅₃	C₂²	1	2	yes	complemented
133	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#418	C₂²	1	2	yes	—
137	C₅₃×#416	C₂²	1	2	yes	—
138	C₂×#102×C₅₃	C₂²	1	2	yes	—
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	2	1	no	—
141	C₂×#41×C₅₃	—	2	1	no	—
142	C₂×#41×C₅₃	—	2	1	no	—
143	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
144	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
145	C₂²×Q₈×C₅₃	—	2	1	no	—
146	C₂²×D₄×C₅₃	—	2	1	no	—
147	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
148	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₅₃	—	2	1	no	—
150	C₂³×C₄×C₅₃	—	2	1	no	—
151	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
152	C₂×D₈×C₅₃	C₂³	1	2	yes	—
153	C₂×D₈×C₅₃	C₂³	1	2	yes	—
154	C₂×D₈×C₅₃	C₂³	1	2	yes	—
155	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
156	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
157	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₅₃	—	2	1	no	—
159	C₄⋊Q₈×C₅₃	—	2	1	no	—
160	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
165	#127×C₅₃	C₂³	1	1	yes	characteristic
166	#127×C₅₃	C₂³	1	1	yes	characteristic
167	#126×C₅₃	—	2	1	no	—
168	#126×C₅₃	—	2	1	no	—
169	#126×C₅₃	—	2	2	no	—
170	#126×C₅₃	—	2	2	no	—
171	#126×C₅₃	—	2	1	no	—
172	#126×C₅₃	—	2	1	no	—
173	#125×C₅₃	—	2	1	no	—
174	#125×C₅₃	C₂³	1	2	yes	—
175	#125×C₅₃	C₂³	1	2	yes	—
176	#125×C₅₃	C₂³	1	1	yes	characteristic
177	#125×C₅₃	C₂³	1	1	yes	characteristic
178	#124×C₅₃	—	2	2	no	—
179	#124×C₅₃	—	2	2	no	—
180	#124×C₅₃	—	2	1	no	—
181	#124×C₅₃	—	2	1	no	—
182	#124×C₅₃	—	2	1	no	—
183	#124×C₅₃	—	2	1	no	—
184	#124×C₅₃	—	2	1	no	—
185	#124×C₅₃	C₂³	1	1	yes	characteristic
186	#124×C₅₃	C₂³	1	1	yes	characteristic
187	#123×C₅₃	—	2	1	no	—
188	#123×C₅₃	—	2	1	no	—
189	#123×C₅₃	—	2	1	no	—
190	#123×C₅₃	—	2	1	no	—
191	#123×C₅₃	—	2	1	no	—
192	#123×C₅₃	—	2	1	no	—
193	#123×C₅₃	—	2	2	no	—
194	#123×C₅₃	—	2	2	no	—
195	#123×C₅₃	—	2	1	no	—
196	#123×C₅₃	—	2	1	no	—
197	C₂²⋊Q₈×C₅₃	—	2	1	no	—
198	C₂²⋊Q₈×C₅₃	—	2	1	no	—
199	C₂²⋊Q₈×C₅₃	—	2	2	no	—
200	C₂²⋊Q₈×C₅₃	—	2	2	no	—
201	C₂²⋊Q₈×C₅₃	—	2	1	no	—
202	C₂²⋊Q₈×C₅₃	—	2	1	no	—
203	C₂²⋊Q₈×C₅₃	—	2	1	no	—
204	C₂²⋊Q₈×C₅₃	—	2	2	no	—
205	C₂²⋊Q₈×C₅₃	—	2	1	no	—
206	C₂²⋊Q₈×C₅₃	—	2	1	no	—
207	C₂²⋊Q₈×C₅₃	—	2	1	no	—
208	C₂²⋊Q₈×C₅₃	—	2	1	no	—
209	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
210	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
217	#121×C₅₃	—	2	2	no	—
218	#121×C₅₃	—	2	2	no	—
219	#121×C₅₃	—	2	1	no	—
220	#121×C₅₃	—	2	1	no	—
221	#121×C₅₃	—	2	1	no	—
222	#121×C₅₃	—	2	1	no	—
223	#121×C₅₃	C₂³	1	1	yes	characteristic
224	#121×C₅₃	C₂³	1	1	yes	characteristic
225	#121×C₅₃	C₂³	1	1	yes	characteristic
226	#121×C₅₃	C₂³	1	1	yes	characteristic
227	#121×C₅₃	C₂³	1	2	yes	—
228	#121×C₅₃	C₂³	1	2	yes	—
229	#121×C₅₃	C₂³	1	2	yes	—
230	#120×C₅₃	—	2	1	no	—
231	#120×C₅₃	—	2	1	no	—
232	#120×C₅₃	—	2	1	no	—
233	#120×C₅₃	—	2	1	no	—
234	C₄×Q₈×C₅₃	—	2	1	no	—
235	C₄×Q₈×C₅₃	—	2	1	no	—
236	C₄×Q₈×C₅₃	—	2	1	no	—
237	C₄×Q₈×C₅₃	—	2	1	no	—
238	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
239	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₅₃	—	2	1	no	—
243	C₄×D₄×C₅₃	—	2	1	no	—
244	C₄×D₄×C₅₃	—	2	1	no	—
245	C₄×D₄×C₅₃	—	2	2	no	—
246	C₄×D₄×C₅₃	—	2	2	no	—
247	C₄×D₄×C₅₃	—	2	1	no	—
248	C₄×D₄×C₅₃	—	2	1	no	—
249	C₄×D₄×C₅₃	—	2	1	no	—
250	C₄×D₄×C₅₃	—	2	1	no	—
251	C₄×D₄×C₅₃	—	2	1	no	—
252	C₄×D₄×C₅₃	—	2	1	no	—
253	C₄×D₄×C₅₃	—	2	1	no	—
254	C₄×D₄×C₅₃	—	2	1	no	—
255	C₄×D₄×C₅₃	—	2	1	no	—
256	C₄×D₄×C₅₃	—	2	1	no	—
257	C₄×D₄×C₅₃	—	2	1	no	—
258	C₄×D₄×C₅₃	—	2	1	no	—
259	C₄×D₄×C₅₃	—	2	1	no	—
260	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
261	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
262	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
263	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₄×D₄×C₅₃	C₂³	1	2	yes	—
272	C₄×D₄×C₅₃	C₂³	1	2	yes	—
273	C₄×D₄×C₅₃	C₂³	1	2	yes	—
274	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
277	#117×C₅₃	—	2	2	no	—
278	#117×C₅₃	—	2	1	no	—
279	#117×C₅₃	—	2	1	no	—
280	#117×C₅₃	—	2	1	no	—
281	#117×C₅₃	D₄	1	1	yes	characteristic
282	#117×C₅₃	D₄	1	1	yes	characteristic
283	#117×C₅₃	D₄	1	1	yes	characteristic
284	#117×C₅₃	C₂³	1	2	yes	—
285	#117×C₅₃	C₂³	1	1	yes	characteristic
286	#117×C₅₃	C₂³	1	2	yes	—
287	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
288	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
289	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
290	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
293	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
294	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
297	C₂×C₄²×C₅₃	—	2	1	no	—
298	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
301	#107×C₅₃	C₂³	1	2	yes	—
302	#107×C₅₃	C₂³	1	2	yes	—
303	#107×C₅₃	C₂³	1	2	yes	—
304	#107×C₅₃	C₂³	1	2	yes	—
305	#107×C₅₃	C₂³	1	2	yes	—
306	#107×C₅₃	C₂³	1	2	yes	—
307	#107×C₅₃	C₂³	1	2	yes	—
308	#106×C₅₃	C₂³	1	2	yes	—
309	#106×C₅₃	C₂³	1	2	yes	—
310	#106×C₅₃	C₂³	1	2	yes	—
311	#106×C₅₃	C₂³	1	2	yes	—
312	#106×C₅₃	C₂³	1	2	yes	—
313	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
315	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
316	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
317	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
318	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
319	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
320	#103×C₅₃	C₂³	1	2	yes	—
321	#103×C₅₃	C₂³	1	2	yes	—
322	#103×C₅₃	C₂³	1	2	yes	—
323	#102×C₅₃	C₂³	1	2	yes	—
324	#102×C₅₃	C₂³	1	2	yes	—
325	#102×C₅₃	C₂³	1	2	yes	—
326	#102×C₅₃	C₂³	1	2	yes	—
327	#102×C₅₃	C₂³	1	2	yes	—
328	#102×C₅₃	C₂³	1	2	yes	—
329	#102×C₅₃	C₂³	1	2	yes	—
330	#102×C₅₃	C₂³	1	2	yes	—
331	#102×C₅₃	C₂³	1	2	yes	—
332	#102×C₅₃	C₂³	1	2	yes	—
333	#102×C₅₃	C₂³	1	2	yes	—
334	#102×C₅₃	C₂³	1	2	yes	—
335	#102×C₅₃	C₂³	1	2	yes	—
336	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
337	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
338	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
339	#97×C₅₃	C₂³	1	2	yes	—
340	#97×C₅₃	C₂³	1	2	yes	—
341	C₄×C₈×C₅₃	C₂³	1	2	yes	—
342	C₂⁴×C₅₃	—	2	1	no	—
343	C₂⁴×C₅₃	—	2	1	no	—
344	#41×C₅₃	—	2	2	no	—
345	#41×C₅₃	—	4	2	no	—
346	#41×C₅₃	—	4	1	no	—
347	#41×C₅₃	—	4	4	no	—
348	#41×C₅₃	—	8	2	no	—
349	#41×C₅₃	—	8	2	no	—
350	#41×C₅₃	—	8	2	no	—
351	C₂×Q₈×C₅₃	—	2	1	no	—
352	C₂×Q₈×C₅₃	—	2	1	no	—
353	C₂×Q₈×C₅₃	—	2	1	no	—
354	C₂×Q₈×C₅₃	—	2	1	no	—
355	C₂×Q₈×C₅₃	—	2	2	no	—
356	C₂×Q₈×C₅₃	—	8	2	no	—
357	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
358	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₅₃	—	2	2	no	—
360	C₂×D₄×C₅₃	—	2	2	no	—
361	C₂×D₄×C₅₃	—	2	1	no	—
362	C₂×D₄×C₅₃	—	2	1	no	—
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	2	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	1	no	—
373	C₂×D₄×C₅₃	—	2	1	no	—
374	C₂×D₄×C₅₃	—	2	1	no	—
375	C₂×D₄×C₅₃	—	4	1	no	—
376	C₂×D₄×C₅₃	—	4	1	no	—
377	C₂×D₄×C₅₃	—	4	4	no	—
378	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
379	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
380	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
381	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
384	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₅₃	—	2	1	no	—
386	C₂²×C₄×C₅₃	—	2	1	no	—
387	C₂²×C₄×C₅₃	—	2	2	no	—
388	C₂²×C₄×C₅₃	—	2	1	no	—
389	C₂²×C₄×C₅₃	—	2	1	no	—
390	C₂²×C₄×C₅₃	—	2	1	no	—
391	C₂²×C₄×C₅₃	—	2	2	no	—
392	C₂²×C₄×C₅₃	—	2	1	no	—
393	C₂²×C₄×C₅₃	—	2	1	no	—
394	C₂²×C₄×C₅₃	—	2	1	no	—
395	C₂²×C₄×C₅₃	—	2	1	no	—
396	C₂²×C₄×C₅₃	—	2	2	no	—
397	C₂²×C₄×C₅₃	—	2	2	no	—
398	C₂²×C₄×C₅₃	—	2	1	no	—
399	C₂²×C₄×C₅₃	—	2	1	no	—
400	C₂²×C₄×C₅₃	—	8	2	no	—
401	C₂²×C₄×C₅₃	—	8	2	no	—
402	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
404	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
405	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
406	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
407	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
411	SD₁₆×C₅₃	—	4	2	no	—
412	D₈×C₅₃	—	2	4	no	—
413	D₈×C₅₃	—	4	2	no	—
414	D₈×C₅₃	—	4	2	no	—
415	M₁₆×C₅₃	—	4	2	no	—
416	C₂×C₈×C₅₃	—	4	2	no	—
417	C₂×C₈×C₅₃	—	4	2	no	—
418	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
419	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
420	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
421	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₅₃	—	2	2	no	—
423	C₄⋊C₄×C₅₃	—	2	1	no	—
424	C₄⋊C₄×C₅₃	—	2	1	no	—
425	C₄⋊C₄×C₅₃	—	2	1	no	—
426	C₄⋊C₄×C₅₃	—	2	1	no	—
427	C₄⋊C₄×C₅₃	—	2	1	no	—
428	C₄⋊C₄×C₅₃	—	2	2	no	—
429	C₄⋊C₄×C₅₃	—	2	2	no	—
430	C₄⋊C₄×C₅₃	—	2	1	no	—
431	C₄⋊C₄×C₅₃	—	2	1	no	—
432	C₄⋊C₄×C₅₃	—	2	2	no	—
433	C₄⋊C₄×C₅₃	—	2	1	no	—
434	C₄⋊C₄×C₅₃	—	2	1	no	—
435	C₄⋊C₄×C₅₃	—	2	1	no	—
436	C₄⋊C₄×C₅₃	—	2	1	no	—
437	C₄⋊C₄×C₅₃	—	2	1	no	—
438	C₄⋊C₄×C₅₃	—	2	1	no	—
439	C₄⋊C₄×C₅₃	—	2	1	no	—
440	C₄⋊C₄×C₅₃	—	2	2	no	—
441	C₄⋊C₄×C₅₃	—	2	2	no	—
442	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
449	C₄⋊C₄×C₅₃	C₂⁴	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	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
455	C₂²⋊C₄×C₅₃	—	2	1	no	—
456	C₂²⋊C₄×C₅₃	—	2	1	no	—
457	C₂²⋊C₄×C₅₃	—	2	1	no	—
458	C₂²⋊C₄×C₅₃	—	2	2	no	—
459	C₂²⋊C₄×C₅₃	—	2	2	no	—
460	C₂²⋊C₄×C₅₃	—	2	1	no	—
461	C₂²⋊C₄×C₅₃	—	2	1	no	—
462	C₂²⋊C₄×C₅₃	—	2	1	no	—
463	C₂²⋊C₄×C₅₃	—	2	1	no	—
464	C₂²⋊C₄×C₅₃	—	2	1	no	—
465	C₂²⋊C₄×C₅₃	—	2	1	no	—
466	C₂²⋊C₄×C₅₃	—	2	1	no	—
467	C₂²⋊C₄×C₅₃	—	2	1	no	—
468	C₂²⋊C₄×C₅₃	—	2	1	no	—
469	C₂²⋊C₄×C₅₃	—	2	1	no	—
470	C₂²⋊C₄×C₅₃	—	2	1	no	—
471	C₂²⋊C₄×C₅₃	—	2	2	no	—
472	C₂²⋊C₄×C₅₃	—	2	2	no	—
473	C₂²⋊C₄×C₅₃	—	2	1	no	—
474	C₂²⋊C₄×C₅₃	—	2	1	no	—
475	C₂²⋊C₄×C₅₃	—	2	1	no	—
476	C₂²⋊C₄×C₅₃	—	2	1	no	—
477	C₂²⋊C₄×C₅₃	—	2	1	no	—
478	C₂²⋊C₄×C₅₃	—	2	2	no	—
479	C₂²⋊C₄×C₅₃	—	2	2	no	—
480	C₂²⋊C₄×C₅₃	—	2	2	no	—
481	C₂²⋊C₄×C₅₃	—	2	2	no	—
482	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
484	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
485	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
486	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
487	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
488	C₄²×C₅₃	—	2	1	no	—
489	C₄²×C₅₃	—	2	1	no	—
490	C₄²×C₅₃	—	2	1	no	—
491	C₄²×C₅₃	—	2	2	no	—
492	C₄²×C₅₃	—	2	2	no	—
493	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
497	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
498	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
499	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
500	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
501	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
502	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
503	C₂³×C₅₃	—	2	1	no	—
504	C₂³×C₅₃	—	2	2	no	—
505	C₂³×C₅₃	—	2	1	no	—
506	C₂³×C₅₃	—	2	1	no	—
507	C₂³×C₅₃	—	4	2	no	—
508	C₂³×C₅₃	—	4	2	no	—
509	C₂³×C₅₃	—	4	2	no	—
510	C₂³×C₅₃	—	4	2	no	—
511	C₂³×C₅₃	—	8	1	no	—
512	C₂³×C₅₃	—	8	1	no	—
513	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
514	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
515	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
516	Q₈×C₅₃	—	2	1	no	—
517	Q₈×C₅₃	—	2	1	no	—
518	Q₈×C₅₃	—	4	1	no	—
519	Q₈×C₅₃	—	4	2	no	—
520	Q₈×C₅₃	—	4	2	no	—
521	Q₈×C₅₃	—	4	2	no	—
522	Q₈×C₅₃	—	8	2	no	—
523	Q₈×C₅₃	—	8	1	no	—
524	D₄×C₅₃	—	2	2	no	—
525	D₄×C₅₃	—	2	2	no	—
526	D₄×C₅₃	—	2	1	no	—
527	D₄×C₅₃	—	2	1	no	—
528	D₄×C₅₃	—	2	2	no	—
529	D₄×C₅₃	—	2	1	no	—
530	D₄×C₅₃	—	2	1	no	—
531	D₄×C₅₃	—	2	1	no	—
532	D₄×C₅₃	—	2	2	no	—
533	D₄×C₅₃	—	4	1	no	—
534	D₄×C₅₃	—	4	2	no	—
535	D₄×C₅₃	—	4	2	no	—
536	D₄×C₅₃	—	4	2	no	—
537	D₄×C₅₃	—	4	2	no	—
538	D₄×C₅₃	—	4	2	no	—
539	D₄×C₅₃	—	4	2	no	—
540	D₄×C₅₃	—	4	2	no	—
541	D₄×C₅₃	—	4	4	no	—
542	D₄×C₅₃	—	4	2	no	—
543	D₄×C₅₃	—	8	1	no	—
544	D₄×C₅₃	—	8	1	no	—
545	D₄×C₅₃	—	8	1	no	—
546	D₄×C₅₃	—	8	2	no	—
547	D₄×C₅₃	—	8	2	no	—
548	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
549	C₂×C₄×C₅₃	—	2	2	no	—
550	C₂×C₄×C₅₃	—	2	2	no	—
551	C₂×C₄×C₅₃	—	2	2	no	—
552	C₂×C₄×C₅₃	—	2	2	no	—
553	C₂×C₄×C₅₃	—	2	1	no	—
554	C₂×C₄×C₅₃	—	2	1	no	—
555	C₂×C₄×C₅₃	—	2	1	no	—
556	C₂×C₄×C₅₃	—	2	1	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	1	no	—
559	C₂×C₄×C₅₃	—	2	1	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	2	1	no	—
562	C₂×C₄×C₅₃	—	2	2	no	—
563	C₂×C₄×C₅₃	—	2	2	no	—
564	C₂×C₄×C₅₃	—	2	1	no	—
565	C₂×C₄×C₅₃	—	2	2	no	—
566	C₂×C₄×C₅₃	—	2	1	no	—
567	C₂×C₄×C₅₃	—	4	1	no	—
568	C₂×C₄×C₅₃	—	4	1	no	—
569	C₂×C₄×C₅₃	—	4	2	no	—
570	C₂×C₄×C₅₃	—	4	2	no	—
571	C₂×C₄×C₅₃	—	4	4	no	—
572	C₂×C₄×C₅₃	—	4	2	no	—
573	C₂×C₄×C₅₃	—	4	2	no	—
574	C₂×C₄×C₅₃	—	4	2	no	—
575	C₂×C₄×C₅₃	—	8	1	no	—
576	C₂×C₄×C₅₃	—	8	1	no	—
577	C₂×C₄×C₅₃	—	8	1	no	—
578	C₂×C₄×C₅₃	—	8	1	no	—
579	C₂×C₄×C₅₃	—	8	2	no	—
580	C₂×C₄×C₅₃	—	8	2	no	—
581	C₂×C₄×C₅₃	—	8	1	no	—
582	C₂×C₄×C₅₃	—	8	1	no	—
583	C₂×C₄×C₅₃	—	8	2	no	—
584	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
587	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
588	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
592	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
593	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
594	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
595	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
596	C₈×C₅₃	—	2	2	no	—
597	C₈×C₅₃	—	2	2	no	—
598	C₈×C₅₃	—	2	2	no	—
599	C₈×C₅₃	—	2	2	no	—
600	#62125	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
601	C₂²×C₅₃	—	2	1	no	—
602	C₂²×C₅₃	—	2	1	no	—
603	C₂²×C₅₃	—	2	1	no	—
604	C₂²×C₅₃	—	2	1	no	—
605	C₂²×C₅₃	—	2	2	no	—
606	C₂²×C₅₃	—	2	1	no	—
607	C₂²×C₅₃	—	2	1	no	—
608	C₂²×C₅₃	—	2	1	no	—
609	C₂²×C₅₃	—	2	1	no	—
610	C₂²×C₅₃	—	4	1	no	—
611	C₂²×C₅₃	—	4	1	no	—
612	C₂²×C₅₃	—	4	1	no	—
613	C₂²×C₅₃	—	4	1	no	—
614	C₂²×C₅₃	—	4	2	no	—
615	C₂²×C₅₃	—	4	2	no	—
616	C₂²×C₅₃	—	4	1	no	—
617	C₂²×C₅₃	—	4	1	no	—
618	C₂²×C₅₃	—	4	1	no	—
619	C₂²×C₅₃	—	4	1	no	—
620	C₂²×C₅₃	—	4	2	no	—
621	C₂²×C₅₃	—	8	4	no	—
622	C₂²×C₅₃	—	8	4	no	—
623	C₂²×C₅₃	#575	1	2	yes	—
624	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
625	C₄×C₅₃	—	2	1	no	—
626	C₄×C₅₃	—	2	1	no	—
627	C₄×C₅₃	—	2	1	no	—
628	C₄×C₅₃	—	2	1	no	—
629	C₄×C₅₃	—	2	1	no	—
630	C₄×C₅₃	—	2	1	no	—
631	C₄×C₅₃	—	2	1	no	—
632	C₄×C₅₃	—	2	1	no	—
633	C₄×C₅₃	—	2	1	no	—
634	C₄×C₅₃	—	2	1	no	—
635	C₄×C₅₃	—	4	1	no	—
636	C₄×C₅₃	—	4	1	no	—
637	C₄×C₅₃	—	4	2	no	—
638	C₄×C₅₃	—	4	1	no	—
639	C₄×C₅₃	—	4	1	no	—
640	C₄×C₅₃	—	4	1	no	—
641	C₄×C₅₃	—	4	2	no	—
642	C₄×C₅₃	—	4	2	no	—
643	C₄×C₅₃	#576	1	2	yes	—
644	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
645	C₄×C₅₃	#585	1	1	yes	characteristic
646	#3511	C₂×C₅₃	1	1	yes	characteristic, complemented
647	#3481	C₂×C₅₃	1	1	yes	characteristic, complemented
648	#3389	C₂×C₅₃	1	2	yes	complemented
649	#3370	C₂×C₅₃	1	2	yes	complemented
650	#3347	C₂×C₅₃	1	2	yes	complemented
651	#3346	C₂×C₅₃	1	2	yes	complemented
652	#3339	C₂×C₅₃	1	2	yes	complemented
653	#3319	C₂×C₅₃	1	2	yes	complemented
654	#3318	C₂×C₅₃	1	2	yes	complemented
655	#3297	C₂×C₅₃	1	2	yes	complemented
656	#3251	C₂×C₅₃	1	1	yes	characteristic, complemented
657	#3247	C₂×C₅₃	1	1	yes	characteristic, complemented
658	#3245	C₂×C₅₃	1	1	yes	characteristic, complemented
659	#3239	C₂×C₅₃	1	1	yes	characteristic, complemented
660	#3235	C₂×C₅₃	1	1	yes	characteristic, complemented
661	#3233	C₂×C₅₃	1	1	yes	characteristic, complemented
662	#3115	C₂×C₅₃	1	1	yes	characteristic, complemented
663	#3109	C₂×C₅₃	1	1	yes	characteristic, complemented
664	#3100	C₂×C₅₃	1	1	yes	characteristic, complemented
665	#3077	C₂×C₅₃	1	1	yes	characteristic, complemented
666	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
667	C₂×#474	C₂×C₅₃	1	1	yes	characteristic, complemented
668	#2990	C₂×C₅₃	1	1	yes	characteristic, complemented
669	C₂×C₅₃	—	2	2	no	—
670	C₂×C₅₃	—	4	1	no	—
671	C₂×C₅₃	—	4	1	no	—
672	C₂×C₅₃	—	4	2	no	—
673	C₂×C₅₃	—	8	2	no	—
674	C₂×C₅₃	—	8	1	no	—
675	C₂×C₅₃	—	8	1	no	—
676	C₂×C₅₃	#3489	1	1	yes	characteristic
677	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
678	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
679	#559	C₂²×C₅₃	1	1	yes	characteristic
680	#556	—	2	1	no	—
681	#555	C₂²×C₅₃	1	2	yes	complemented
682	#554	C₂²×C₅₃	1	1	yes	characteristic
683	#554	C₂²×C₅₃	1	1	yes	characteristic
684	#554	C₂²×C₅₃	1	2	yes	complemented
685	#553	—	2	1	no	—
686	#553	C₂²×C₅₃	1	1	yes	characteristic
687	#553	C₂²×C₅₃	1	2	yes	—
688	#553	C₂²×C₅₃	1	1	yes	characteristic
689	#553	C₂²×C₅₃	1	2	yes	complemented
690	#551	—	2	1	no	—
691	#551	—	2	1	no	—
692	#548	—	2	1	no	—
693	#548	—	2	1	no	—
694	#547	—	2	1	no	—
695	#546	—	2	1	no	—
696	#546	C₂²×C₅₃	1	1	yes	characteristic
697	#546	C₂²×C₅₃	1	1	yes	characteristic
698	D₄²	C₂²×C₅₃	1	1	yes	characteristic
699	#542	—	2	1	no	—
700	#542	—	2	1	no	—
701	#537	—	2	1	no	—
702	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
703	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
704	#532	C₂²×C₅₃	1	1	yes	characteristic
705	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
706	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
708	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#529	—	2	1	no	—
710	#529	C₂²×C₅₃	1	1	yes	characteristic
711	#529	C₂²×C₅₃	1	1	yes	characteristic
712	#525	—	2	1	no	—
713	#525	—	2	1	no	—
714	#520	—	2	1	no	—
715	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
716	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
717	C₂×C₄×D₄	—	2	1	no	—
718	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
719	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
720	#501	C₂²×C₅₃	1	2	yes	complemented
721	#501	C₂²×C₅₃	1	2	yes	complemented
722	#499	C₂²×C₅₃	1	2	yes	complemented
723	#490	C₂²×C₅₃	1	2	yes	—
724	#489	C₂²×C₅₃	1	2	yes	complemented
725	#488	C₂²×C₅₃	1	2	yes	complemented
726	#485	C₂²×C₅₃	1	2	yes	complemented
727	#484	C₂²×C₅₃	1	2	yes	complemented
728	#482	C₂²×C₅₃	1	2	yes	—
729	#482	C₂²×C₅₃	1	2	yes	complemented
730	#482	C₂²×C₅₃	1	2	yes	complemented
731	#482	C₂²×C₅₃	1	2	yes	complemented
732	#481	C₂²×C₅₃	1	2	yes	—
733	#481	C₂²×C₅₃	1	2	yes	complemented
734	#480	C₂²×C₅₃	1	2	yes	complemented
735	#479	C₂²×C₅₃	1	2	yes	complemented
736	#478	C₂²×C₅₃	1	2	yes	—
737	#478	C₂²×C₅₃	1	2	yes	—
738	#478	C₂²×C₅₃	1	2	yes	complemented
739	#478	C₂²×C₅₃	1	2	yes	complemented
740	#478	C₂²×C₅₃	1	2	yes	complemented
741	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
742	#476	C₂²×C₅₃	1	1	yes	characteristic
743	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
744	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
745	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
746	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
747	#474	C₂²×C₅₃	1	1	yes	characteristic
748	#474	C₂²×C₅₃	1	1	yes	characteristic
749	#474	C₂²×C₅₃	1	2	yes	—
750	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
751	#474	C₂²×C₅₃	1	2	yes	complemented
752	#474	C₂²×C₅₃	1	2	yes	complemented
753	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
754	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
755	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
756	#469	C₂²×C₅₃	1	2	yes	—
757	#468	C₂²×C₅₃	1	2	yes	complemented
758	#466	C₂²×C₅₃	1	2	yes	—
759	#466	C₂²×C₅₃	1	2	yes	complemented
760	#466	C₂²×C₅₃	1	2	yes	complemented
761	#465	C₂²×C₅₃	1	2	yes	complemented
762	#463	C₂²×C₅₃	1	2	yes	complemented
763	#463	C₂²×C₅₃	1	2	yes	complemented
764	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
765	#459	C₂²×C₅₃	1	1	yes	characteristic
766	#459	C₂²×C₅₃	1	2	yes	—
767	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
768	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
769	#449	C₂²×C₅₃	1	2	yes	—
770	#447	C₂²×C₅₃	1	2	yes	—
771	#447	C₂²×C₅₃	1	2	yes	—
772	#446	C₂²×C₅₃	1	2	yes	complemented
773	#442	C₂²×C₅₃	1	2	yes	—
774	#442	C₂²×C₅₃	1	2	yes	—
775	#442	C₂²×C₅₃	1	2	yes	complemented
776	#440	C₂²×C₅₃	1	2	yes	complemented
777	C₄×D₈	C₂²×C₅₃	1	2	yes	—
778	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
779	#435	C₂²×C₅₃	1	2	yes	—
780	#435	C₂²×C₅₃	1	2	yes	complemented
781	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
782	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
783	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
784	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
785	#428	C₂²×C₅₃	1	2	yes	complemented
786	#427	C₂²×C₅₃	1	2	yes	complemented
787	C₂×#107	C₂²×C₅₃	1	2	yes	complemented
788	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
789	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
790	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
791	#418	C₂²×C₅₃	1	2	yes	—
792	#416	C₂²×C₅₃	1	2	yes	—
793	C₂×#102	C₂²×C₅₃	1	2	yes	—
794	C₅₃	#62125	1	1	yes	characteristic, direct product factor, Sylow
795	C₂×#41	—	2	1	no	—
796	C₂×#41	—	2	1	no	—
797	C₂×#41	—	2	1	no	—
798	C₂×#41	—	2	1	no	—
799	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
800	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
801	C₂²×Q₈	—	2	1	no	—
802	C₂²×D₄	—	2	1	no	—
803	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
804	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
805	C₂³×C₄	—	2	1	no	—
806	C₂³×C₄	—	2	1	no	—
807	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
808	C₂×D₈	C₂³×C₅₃	1	2	yes	—
809	C₂×D₈	C₂³×C₅₃	1	2	yes	—
810	C₂×D₈	C₂³×C₅₃	1	2	yes	—
811	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
812	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
813	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
814	C₄⋊Q₈	—	2	1	no	—
815	C₄⋊Q₈	—	2	1	no	—
816	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
817	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
818	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
819	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
820	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
821	#127	C₂³×C₅₃	1	1	yes	characteristic
822	#127	C₂³×C₅₃	1	1	yes	characteristic
823	#126	—	2	1	no	—
824	#126	—	2	1	no	—
825	#126	—	2	2	no	—
826	#126	—	2	2	no	—
827	#126	—	2	1	no	—
828	#126	—	2	1	no	—
829	#125	—	2	1	no	—
830	#125	C₂³×C₅₃	1	1	yes	characteristic
831	#125	C₂³×C₅₃	1	1	yes	characteristic
832	#125	C₂³×C₅₃	1	2	yes	—
833	#125	C₂³×C₅₃	1	2	yes	—
834	#124	—	2	1	no	—
835	#124	—	2	2	no	—
836	#124	—	2	2	no	—
837	#124	—	2	1	no	—
838	#124	—	2	1	no	—
839	#124	—	2	1	no	—
840	#124	—	2	1	no	—
841	#124	C₂³×C₅₃	1	1	yes	characteristic
842	#124	C₂³×C₅₃	1	1	yes	characteristic
843	#123	—	2	1	no	—
844	#123	—	2	1	no	—
845	#123	—	2	1	no	—
846	#123	—	2	1	no	—
847	#123	—	2	1	no	—
848	#123	—	2	1	no	—
849	#123	—	2	1	no	—
850	#123	—	2	1	no	—
851	#123	—	2	2	no	—
852	#123	—	2	2	no	—
853	C₂²⋊Q₈	—	2	1	no	—
854	C₂²⋊Q₈	—	2	2	no	—
855	C₂²⋊Q₈	—	2	1	no	—
856	C₂²⋊Q₈	—	2	1	no	—
857	C₂²⋊Q₈	—	2	1	no	—
858	C₂²⋊Q₈	—	2	1	no	—
859	C₂²⋊Q₈	—	2	1	no	—
860	C₂²⋊Q₈	—	2	1	no	—
861	C₂²⋊Q₈	—	2	2	no	—
862	C₂²⋊Q₈	—	2	2	no	—
863	C₂²⋊Q₈	—	2	1	no	—
864	C₂²⋊Q₈	—	2	1	no	—
865	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
866	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
867	#121	—	2	1	no	—
868	#121	—	2	1	no	—
869	#121	—	2	2	no	—
870	#121	—	2	2	no	—
871	#121	—	2	2	no	—
872	#121	—	2	1	no	—
873	#121	—	2	1	no	—
874	#121	—	2	1	no	—
875	#121	—	2	1	no	—
876	#121	—	2	1	no	—
877	#121	—	2	1	no	—
878	#121	—	2	1	no	—
879	#121	C₂³×C₅₃	1	1	yes	characteristic
880	#121	C₂³×C₅₃	1	1	yes	characteristic
881	#121	C₂³×C₅₃	1	1	yes	characteristic
882	#121	C₂³×C₅₃	1	1	yes	characteristic
883	#121	C₂³×C₅₃	1	2	yes	—
884	#121	C₂³×C₅₃	1	2	yes	—
885	#121	C₂³×C₅₃	1	2	yes	—
886	#120	—	2	1	no	—
887	#120	—	2	1	no	—
888	#120	—	2	1	no	—
889	#120	—	2	1	no	—
890	C₄×Q₈	—	2	1	no	—
891	C₄×Q₈	—	2	1	no	—
892	C₄×Q₈	—	2	1	no	—
893	C₄×Q₈	—	2	1	no	—
894	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
895	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
896	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
897	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
898	C₄×D₄	—	2	1	no	—
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	—	2	1	no	—
903	C₄×D₄	—	2	1	no	—
904	C₄×D₄	—	2	1	no	—
905	C₄×D₄	—	2	1	no	—
906	C₄×D₄	—	2	2	no	—
907	C₄×D₄	—	2	2	no	—
908	C₄×D₄	—	2	1	no	—
909	C₄×D₄	—	2	1	no	—
910	C₄×D₄	—	2	1	no	—
911	C₄×D₄	—	2	1	no	—
912	C₄×D₄	—	2	1	no	—
913	C₄×D₄	—	2	1	no	—
914	C₄×D₄	—	2	1	no	—
915	C₄×D₄	—	2	1	no	—
916	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
917	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
918	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
919	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
920	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
921	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
922	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
923	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
924	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
925	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
926	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
927	C₄×D₄	C₂³×C₅₃	1	2	yes	—
928	C₄×D₄	C₂³×C₅₃	1	2	yes	—
929	C₄×D₄	C₂³×C₅₃	1	2	yes	—
930	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
931	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
932	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
933	#117	—	2	2	no	—
934	#117	—	2	1	no	—
935	#117	—	2	1	no	—
936	#117	—	2	1	no	—
937	#117	D₄×C₅₃	1	1	yes	characteristic
938	#117	D₄×C₅₃	1	1	yes	characteristic
939	#117	D₄×C₅₃	1	1	yes	characteristic
940	#117	C₂³×C₅₃	1	1	yes	characteristic
941	#117	C₂³×C₅₃	1	2	yes	—
942	#117	C₂³×C₅₃	1	2	yes	—
943	C₂×C₄⋊C₄	—	2	1	no	—
944	C₂×C₄⋊C₄	—	2	1	no	—
945	C₂×C₄⋊C₄	—	2	2	no	—
946	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
947	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
948	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
949	C₂×C₂²⋊C₄	—	2	1	no	—
950	C₂×C₂²⋊C₄	—	2	1	no	—
951	C₂×C₂²⋊C₄	—	2	1	no	—
952	C₂×C₂²⋊C₄	—	2	1	no	—
953	C₂×C₄²	—	2	1	no	—
954	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
955	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
956	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
957	#107	C₂³×C₅₃	1	2	yes	—
958	#107	C₂³×C₅₃	1	2	yes	—
959	#107	C₂³×C₅₃	1	2	yes	—
960	#107	C₂³×C₅₃	1	2	yes	—
961	#107	C₂³×C₅₃	1	2	yes	—
962	#107	C₂³×C₅₃	1	2	yes	—
963	#107	C₂³×C₅₃	1	2	yes	—
964	#106	C₂³×C₅₃	1	2	yes	—
965	#106	C₂³×C₅₃	1	2	yes	—
966	#106	C₂³×C₅₃	1	2	yes	—
967	#106	C₂³×C₅₃	1	2	yes	—
968	#106	C₂³×C₅₃	1	2	yes	—
969	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
970	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
971	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
972	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
973	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
974	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
975	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
976	#103	C₂³×C₅₃	1	2	yes	—
977	#103	C₂³×C₅₃	1	2	yes	—
978	#103	C₂³×C₅₃	1	2	yes	—
979	#102	C₂³×C₅₃	1	2	yes	—
980	#102	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	2	yes	—
986	#102	C₂³×C₅₃	1	2	yes	—
987	#102	C₂³×C₅₃	1	2	yes	—
988	#102	C₂³×C₅₃	1	2	yes	—
989	#102	C₂³×C₅₃	1	2	yes	—
990	#102	C₂³×C₅₃	1	2	yes	—
991	#102	C₂³×C₅₃	1	2	yes	—
992	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
993	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
994	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
995	#97	C₂³×C₅₃	1	2	yes	—
996	#97	C₂³×C₅₃	1	2	yes	—
997	C₄×C₈	C₂³×C₅₃	1	2	yes	—
998	C₂⁴	—	2	1	no	—
999	C₂⁴	—	2	1	no	—
1000	#41	—	2	2	no	—
1001	#41	—	4	2	no	—
1002	#41	—	4	1	no	—
1003	#41	—	4	4	no	—
1004	#41	—	8	2	no	—
1005	#41	—	8	2	no	—
1006	#41	—	8	2	no	—
1007	C₂×Q₈	—	2	1	no	—
1008	C₂×Q₈	—	2	1	no	—
1009	C₂×Q₈	—	2	1	no	—
1010	C₂×Q₈	—	2	1	no	—
1011	C₂×Q₈	—	2	2	no	—
1012	C₂×Q₈	—	8	2	no	—
1013	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1014	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	2	2	no	—
1017	C₂×D₄	—	2	1	no	—
1018	C₂×D₄	—	2	1	no	—
1019	C₂×D₄	—	2	1	no	—
1020	C₂×D₄	—	2	2	no	—
1021	C₂×D₄	—	2	1	no	—
1022	C₂×D₄	—	2	1	no	—
1023	C₂×D₄	—	2	2	no	—
1024	C₂×D₄	—	2	2	no	—
1025	C₂×D₄	—	2	1	no	—
1026	C₂×D₄	—	2	1	no	—
1027	C₂×D₄	—	2	1	no	—
1028	C₂×D₄	—	2	1	no	—
1029	C₂×D₄	—	2	1	no	—
1030	C₂×D₄	—	2	1	no	—
1031	C₂×D₄	—	4	1	no	—
1032	C₂×D₄	—	4	1	no	—
1033	C₂×D₄	—	4	4	no	—
1034	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1035	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1036	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1037	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1038	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1039	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1040	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1041	C₂²×C₄	—	2	1	no	—
1042	C₂²×C₄	—	2	1	no	—
1043	C₂²×C₄	—	2	2	no	—
1044	C₂²×C₄	—	2	1	no	—
1045	C₂²×C₄	—	2	1	no	—
1046	C₂²×C₄	—	2	1	no	—
1047	C₂²×C₄	—	2	2	no	—
1048	C₂²×C₄	—	2	1	no	—
1049	C₂²×C₄	—	2	1	no	—
1050	C₂²×C₄	—	2	1	no	—
1051	C₂²×C₄	—	2	1	no	—
1052	C₂²×C₄	—	2	2	no	—
1053	C₂²×C₄	—	2	2	no	—
1054	C₂²×C₄	—	2	1	no	—
1055	C₂²×C₄	—	2	1	no	—
1056	C₂²×C₄	—	8	2	no	—
1057	C₂²×C₄	—	8	2	no	—
1058	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1059	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1060	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1061	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1062	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1063	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1064	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1065	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1066	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1067	SD₁₆	—	4	2	no	—
1068	D₈	—	2	4	no	—
1069	D₈	—	4	2	no	—
1070	D₈	—	4	2	no	—
1071	M₁₆	—	4	2	no	—
1072	C₂×C₈	—	4	2	no	—
1073	C₂×C₈	—	4	2	no	—
1074	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1075	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1076	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1077	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1078	C₄⋊C₄	—	2	2	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	1	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	—	2	1	no	—
1094	C₄⋊C₄	—	2	1	no	—
1095	C₄⋊C₄	—	2	1	no	—
1096	C₄⋊C₄	—	2	2	no	—
1097	C₄⋊C₄	—	2	2	no	—
1098	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1099	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1100	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1101	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1102	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1103	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1104	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1105	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1106	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1107	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1108	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1109	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1110	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	—	2	1	no	—
1120	C₂²⋊C₄	—	2	1	no	—
1121	C₂²⋊C₄	—	2	1	no	—
1122	C₂²⋊C₄	—	2	1	no	—
1123	C₂²⋊C₄	—	2	1	no	—
1124	C₂²⋊C₄	—	2	1	no	—
1125	C₂²⋊C₄	—	2	1	no	—
1126	C₂²⋊C₄	—	2	1	no	—
1127	C₂²⋊C₄	—	2	2	no	—
1128	C₂²⋊C₄	—	2	2	no	—
1129	C₂²⋊C₄	—	2	1	no	—
1130	C₂²⋊C₄	—	2	1	no	—
1131	C₂²⋊C₄	—	2	1	no	—
1132	C₂²⋊C₄	—	2	1	no	—
1133	C₂²⋊C₄	—	2	1	no	—
1134	C₂²⋊C₄	—	2	2	no	—
1135	C₂²⋊C₄	—	2	2	no	—
1136	C₂²⋊C₄	—	2	2	no	—
1137	C₂²⋊C₄	—	2	2	no	—
1138	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1139	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1140	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1141	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1142	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1143	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1144	C₄²	—	2	1	no	—
1145	C₄²	—	2	1	no	—
1146	C₄²	—	2	1	no	—
1147	C₄²	—	2	2	no	—
1148	C₄²	—	2	2	no	—
1149	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1150	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1151	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1152	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1153	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1154	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1155	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1156	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1157	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1158	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1159	C₂³	—	2	1	no	—
1160	C₂³	—	2	2	no	—
1161	C₂³	—	2	1	no	—
1162	C₂³	—	2	1	no	—
1163	C₂³	—	4	2	no	—
1164	C₂³	—	4	2	no	—
1165	C₂³	—	4	2	no	—
1166	C₂³	—	4	2	no	—
1167	C₂³	—	8	1	no	—
1168	C₂³	—	8	1	no	—
1169	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1170	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1171	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1172	Q₈	—	2	1	no	—
1173	Q₈	—	2	1	no	—
1174	Q₈	—	4	1	no	—
1175	Q₈	—	4	2	no	—
1176	Q₈	—	4	2	no	—
1177	Q₈	—	4	2	no	—
1178	Q₈	—	8	2	no	—
1179	Q₈	—	8	1	no	—
1180	D₄	—	2	2	no	—
1181	D₄	—	2	2	no	—
1182	D₄	—	2	2	no	—
1183	D₄	—	2	1	no	—
1184	D₄	—	2	1	no	—
1185	D₄	—	2	1	no	—
1186	D₄	—	2	2	no	—
1187	D₄	—	2	1	no	—
1188	D₄	—	2	1	no	—
1189	D₄	—	4	1	no	—
1190	D₄	—	4	2	no	—
1191	D₄	—	4	2	no	—
1192	D₄	—	4	2	no	—
1193	D₄	—	4	2	no	—
1194	D₄	—	4	2	no	—
1195	D₄	—	4	2	no	—
1196	D₄	—	4	2	no	—
1197	D₄	—	4	4	no	—
1198	D₄	—	4	2	no	—
1199	D₄	—	8	1	no	—
1200	D₄	—	8	1	no	—
1201	D₄	—	8	1	no	—
1202	D₄	—	8	2	no	—
1203	D₄	—	8	2	no	—
1204	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1205	C₂×C₄	—	2	2	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	2	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	1	no	—
1215	C₂×C₄	—	2	1	no	—
1216	C₂×C₄	—	2	1	no	—
1217	C₂×C₄	—	2	2	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	2	no	—
1220	C₂×C₄	—	2	2	no	—
1221	C₂×C₄	—	2	1	no	—
1222	C₂×C₄	—	2	1	no	—
1223	C₂×C₄	—	4	1	no	—
1224	C₂×C₄	—	4	1	no	—
1225	C₂×C₄	—	4	2	no	—
1226	C₂×C₄	—	4	2	no	—
1227	C₂×C₄	—	4	4	no	—
1228	C₂×C₄	—	4	2	no	—
1229	C₂×C₄	—	4	2	no	—
1230	C₂×C₄	—	4	2	no	—
1231	C₂×C₄	—	8	1	no	—
1232	C₂×C₄	—	8	1	no	—
1233	C₂×C₄	—	8	1	no	—
1234	C₂×C₄	—	8	1	no	—
1235	C₂×C₄	—	8	2	no	—
1236	C₂×C₄	—	8	2	no	—
1237	C₂×C₄	—	8	1	no	—
1238	C₂×C₄	—	8	1	no	—
1239	C₂×C₄	—	8	2	no	—
1240	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1241	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1242	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1243	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1244	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1245	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1246	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1247	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1248	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1249	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1250	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1251	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1252	C₈	—	2	2	no	—
1253	C₈	—	2	2	no	—
1254	C₈	—	2	2	no	—
1255	C₈	—	2	2	no	—
1256	C₂²	—	2	1	no	—
1257	C₂²	—	2	1	no	—
1258	C₂²	—	2	1	no	—
1259	C₂²	—	2	1	no	—
1260	C₂²	—	2	2	no	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	1	no	—
1263	C₂²	—	2	1	no	—
1264	C₂²	—	2	1	no	—
1265	C₂²	—	4	1	no	—
1266	C₂²	—	4	1	no	—
1267	C₂²	—	4	1	no	—
1268	C₂²	—	4	1	no	—
1269	C₂²	—	4	2	no	—
1270	C₂²	—	4	2	no	—
1271	C₂²	—	4	1	no	—
1272	C₂²	—	4	1	no	—
1273	C₂²	—	4	1	no	—
1274	C₂²	—	4	1	no	—
1275	C₂²	—	4	2	no	—
1276	C₂²	—	8	4	no	—
1277	C₂²	—	8	4	no	—
1278	C₂²	C₅₃×#575	1	2	yes	—
1279	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1280	C₄	—	2	1	no	—
1281	C₄	—	2	1	no	—
1282	C₄	—	2	1	no	—
1283	C₄	—	2	1	no	—
1284	C₄	—	2	1	no	—
1285	C₄	—	2	1	no	—
1286	C₄	—	2	1	no	—
1287	C₄	—	2	1	no	—
1288	C₄	—	2	1	no	—
1289	C₄	—	2	1	no	—
1290	C₄	—	4	1	no	—
1291	C₄	—	4	1	no	—
1292	C₄	—	4	2	no	—
1293	C₄	—	4	1	no	—
1294	C₄	—	4	1	no	—
1295	C₄	—	4	1	no	—
1296	C₄	—	4	2	no	—
1297	C₄	—	4	2	no	—
1298	C₄	C₅₃×#576	1	2	yes	—
1299	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1300	C₄	C₅₃×#585	1	1	yes	characteristic
1301	C₂	—	2	2	no	—
1302	C₂	—	4	1	no	—
1303	C₂	—	4	1	no	—
1304	C₂	—	4	2	no	—
1305	C₂	—	8	1	no	—
1306	C₂	—	8	1	no	—
1307	C₂	—	8	2	no	—
1308	C₂	C₅₃×#3489	1	1	yes	characteristic
1309	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1310	C₂	C₂×C₅₃×#576	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×#3511	C₂	semidirect
2. C₅₃×#3481	C₂	semidirect
3. C₅₃×#3389	C₂	semidirect
4. C₅₃×#3370	C₂	semidirect
5. C₅₃×#3347	C₂	semidirect
6. C₅₃×#3346	C₂	semidirect
7. C₅₃×#3339	C₂	semidirect
8. C₅₃×#3319	C₂	semidirect
9. C₅₃×#3318	C₂	semidirect
10. C₅₃×#3297	C₂	semidirect
11. C₅₃×#3251	C₂	semidirect
12. C₅₃×#3247	C₂	semidirect
13. C₅₃×#3245	C₂	semidirect
14. C₅₃×#3239	C₂	semidirect
15. C₅₃×#3235	C₂	semidirect
16. C₅₃×#3233	C₂	semidirect
17. C₅₃×#3115	C₂	semidirect
18. C₅₃×#3109	C₂	semidirect
19. C₅₃×#3100	C₂	semidirect
20. C₅₃×#3077	C₂	semidirect
21. C₅₃×#3076	C₂	semidirect
22. C₂×C₅₃×#474	C₂	semidirect
23. C₅₃×#2990	C₂	semidirect
26. C₅₃×#555	C₂²	semidirect
29. C₅₃×#554	C₂²	semidirect
34. C₅₃×#553	C₂²	semidirect
47. C₅₃×#533	C₂²	semidirect
48. C₅₃×#533	C₂²	semidirect
50. C₅₃×#532	C₂²	semidirect
51. C₅₃×#532	C₂²	semidirect
52. C₅₃×#532	C₂²	semidirect
53. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
65. C₅₃×#501	C₂²	semidirect
66. C₅₃×#501	C₂²	semidirect
67. C₅₃×#499	C₂²	semidirect
69. C₅₃×#489	C₂²	semidirect
70. C₅₃×#488	C₂²	semidirect
71. C₅₃×#485	C₂²	semidirect
72. C₅₃×#484	C₂²	semidirect
74. C₅₃×#482	C₂²	semidirect
75. C₅₃×#482	C₂²	semidirect
76. C₅₃×#482	C₂²	semidirect
78. C₅₃×#481	C₂²	semidirect
79. C₅₃×#480	C₂²	semidirect
80. C₅₃×#479	C₂²	semidirect
83. C₅₃×#478	C₂²	semidirect
84. C₅₃×#478	C₂²	semidirect
85. C₅₃×#478	C₂²	semidirect
86. C₅₃×#477	C₂²	semidirect
88. C₅₃×#476	C₂²	semidirect
89. C₅₃×#476	C₂²	semidirect
90. C₅₃×#475	C₂²	semidirect
91. C₅₃×#475	C₂²	semidirect
95. C₅₃×#474	C₂²	semidirect
96. C₅₃×#474	C₂²	semidirect
97. C₅₃×#474	C₂²	semidirect
98. C₅₃×#474	C₂²	semidirect
99. C₅₃×#474	C₂²	semidirect
100. C₅₃×#474	C₂²	semidirect
102. C₅₃×#468	C₂²	semidirect
104. C₅₃×#466	C₂²	semidirect
105. C₅₃×#466	C₂²	semidirect
106. C₅₃×#465	C₂²	semidirect
107. C₅₃×#463	C₂²	semidirect
108. C₅₃×#463	C₂²	semidirect
109. C₅₃×#460	C₂²	semidirect
112. C₅₃×#459	C₂²	semidirect
113. C₅₃×#459	C₂²	semidirect
117. C₅₃×#446	C₂²	semidirect
120. C₅₃×#442	C₂²	semidirect
121. C₅₃×#440	C₂²	semidirect
123. C₄×D₈×C₅₃	C₂²	semidirect
125. C₅₃×#435	C₂²	semidirect
126. C₈×D₄×C₅₃	C₂²	semidirect
127. C₅₃×#432	C₂²	semidirect
128. C₅₃×#432	C₂²	semidirect
129. C₅₃×#431	C₂²	semidirect
130. C₅₃×#428	C₂²	semidirect
131. C₅₃×#427	C₂²	semidirect
132. C₂×#107×C₅₃	C₂²	semidirect
133. C₅₃×#423	C₂²	semidirect
134. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
135. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
600. #62125	C₅₃	direct (N × H)
646. #3511	C₂×C₅₃	semidirect
647. #3481	C₂×C₅₃	semidirect
648. #3389	C₂×C₅₃	semidirect
649. #3370	C₂×C₅₃	semidirect
650. #3347	C₂×C₅₃	semidirect
651. #3346	C₂×C₅₃	semidirect
652. #3339	C₂×C₅₃	semidirect
653. #3319	C₂×C₅₃	semidirect
654. #3318	C₂×C₅₃	semidirect
655. #3297	C₂×C₅₃	semidirect
656. #3251	C₂×C₅₃	semidirect
657. #3247	C₂×C₅₃	semidirect
658. #3245	C₂×C₅₃	semidirect
659. #3239	C₂×C₅₃	semidirect
660. #3235	C₂×C₅₃	semidirect
661. #3233	C₂×C₅₃	semidirect
662. #3115	C₂×C₅₃	semidirect
663. #3109	C₂×C₅₃	semidirect
664. #3100	C₂×C₅₃	semidirect
665. #3077	C₂×C₅₃	semidirect
666. #3076	C₂×C₅₃	semidirect
667. C₂×#474	C₂×C₅₃	semidirect
668. #2990	C₂×C₅₃	semidirect
681. #555	C₂²×C₅₃	semidirect
684. #554	C₂²×C₅₃	semidirect
689. #553	C₂²×C₅₃	semidirect
702. #533	C₂²×C₅₃	semidirect
703. #533	C₂²×C₅₃	semidirect
705. #532	C₂²×C₅₃	semidirect
706. #532	C₂²×C₅₃	semidirect
707. #532	C₂²×C₅₃	semidirect
708. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
720. #501	C₂²×C₅₃	semidirect
721. #501	C₂²×C₅₃	semidirect
722. #499	C₂²×C₅₃	semidirect
724. #489	C₂²×C₅₃	semidirect
725. #488	C₂²×C₅₃	semidirect
726. #485	C₂²×C₅₃	semidirect
727. #484	C₂²×C₅₃	semidirect
729. #482	C₂²×C₅₃	semidirect
730. #482	C₂²×C₅₃	semidirect
731. #482	C₂²×C₅₃	semidirect
733. #481	C₂²×C₅₃	semidirect
734. #480	C₂²×C₅₃	semidirect
735. #479	C₂²×C₅₃	semidirect
738. #478	C₂²×C₅₃	semidirect
739. #478	C₂²×C₅₃	semidirect
740. #478	C₂²×C₅₃	semidirect
741. #477	C₂²×C₅₃	semidirect
743. #476	C₂²×C₅₃	semidirect
744. #476	C₂²×C₅₃	semidirect
745. #475	C₂²×C₅₃	semidirect
746. #475	C₂²×C₅₃	semidirect
750. #474	C₂²×C₅₃	semidirect
751. #474	C₂²×C₅₃	semidirect
752. #474	C₂²×C₅₃	semidirect
753. #474	C₂²×C₅₃	semidirect
754. #474	C₂²×C₅₃	semidirect
755. #474	C₂²×C₅₃	semidirect
757. #468	C₂²×C₅₃	semidirect
759. #466	C₂²×C₅₃	semidirect
760. #466	C₂²×C₅₃	semidirect
761. #465	C₂²×C₅₃	semidirect
762. #463	C₂²×C₅₃	semidirect
763. #463	C₂²×C₅₃	semidirect
764. #460	C₂²×C₅₃	semidirect
767. #459	C₂²×C₅₃	semidirect
768. #459	C₂²×C₅₃	semidirect
772. #446	C₂²×C₅₃	semidirect
775. #442	C₂²×C₅₃	semidirect
776. #440	C₂²×C₅₃	semidirect
778. C₄×D₈	C₂²×C₅₃	semidirect
780. #435	C₂²×C₅₃	semidirect
781. C₈×D₄	C₂²×C₅₃	semidirect
782. #432	C₂²×C₅₃	semidirect
783. #432	C₂²×C₅₃	semidirect
784. #431	C₂²×C₅₃	semidirect
785. #428	C₂²×C₅₃	semidirect
786. #427	C₂²×C₅₃	semidirect
787. C₂×#107	C₂²×C₅₃	semidirect
788. #423	C₂²×C₅₃	semidirect
789. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
790. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
794. C₅₃	#62125	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×#3511	2
C₅₃×#3481	2
C₅₃×#3389	2
C₅₃×#3370	2
C₅₃×#3347	2
C₅₃×#3346	2
C₅₃×#3339	2
C₅₃×#3319	2
C₅₃×#3318	2
C₅₃×#3297	2
C₅₃×#3251	2
C₅₃×#3247	2
C₅₃×#3245	2
C₅₃×#3239	2
C₅₃×#3235	2
C₅₃×#3233	2
C₅₃×#3115	2
C₅₃×#3109	2
C₅₃×#3100	2
C₅₃×#3077	2
C₅₃×#3076	2
C₂×C₅₃×#474	2
C₅₃×#2990	2
#62125	53

Subgroups — C53×#62125 #27269637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62125 #27269637