Subgroups — C₅₃×#62116 #27269628

Order 13568.

1716 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3475	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3388	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3377	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3352	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3349	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3348	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3323	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3315	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3311	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3255	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3252	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3248	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3239	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#557	—	2	1	no	—
25	C₅₃×#557	C₂²	1	2	yes	complemented
26	C₅₃×#556	—	2	1	no	—
27	C₅₃×#556	C₂²	1	1	yes	characteristic
28	C₅₃×#556	C₂²	1	2	yes	—
29	C₅₃×#555	C₂²	1	1	yes	characteristic
30	C₅₃×#554	C₂²	1	1	yes	characteristic
31	C₅₃×#553	—	2	1	no	—
32	C₅₃×#552	—	2	1	no	—
33	C₅₃×#552	—	2	1	no	—
34	C₅₃×#552	—	2	1	no	—
35	C₅₃×#552	C₂²	1	1	yes	characteristic
36	C₅₃×#552	C₂²	1	1	yes	characteristic
37	C₅₃×#552	C₂²	1	2	yes	—
38	C₅₃×#552	C₂²	1	2	yes	complemented
39	C₅₃×#551	—	2	1	no	—
40	C₅₃×#551	—	2	1	no	—
41	C₅₃×#547	C₂²	1	1	yes	characteristic
42	C₅₃×#546	C₂²	1	1	yes	characteristic
43	C₅₃×#546	C₂²	1	1	yes	characteristic
44	C₅₃×#541	—	2	1	no	—
45	C₅₃×#541	—	2	1	no	—
46	C₅₃×#536	—	2	1	no	—
47	C₅₃×#533	C₂²	1	1	yes	characteristic
48	C₅₃×#533	C₂²	1	1	yes	characteristic
49	C₅₃×#533	C₂²	1	1	yes	characteristic
50	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#533	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	—	2	1	no	—
56	C₅₃×#529	C₂²	1	1	yes	characteristic
57	C₅₃×#529	C₂²	1	1	yes	characteristic
58	C₅₃×#525	—	2	1	no	—
59	C₅₃×#519	—	2	1	no	—
60	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
61	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
62	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
63	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×#117×C₅₃	—	2	1	no	—
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×#491	C₂²	1	2	yes	complemented
69	C₅₃×#489	C₂²	1	2	yes	—
70	C₅₃×#488	C₂²	1	2	yes	—
71	C₅₃×#485	C₂²	1	2	yes	—
72	C₅₃×#485	C₂²	1	2	yes	—
73	C₅₃×#485	C₂²	1	2	yes	complemented
74	C₅₃×#485	C₂²	1	2	yes	complemented
75	C₅₃×#485	C₂²	1	2	yes	complemented
76	C₅₃×#484	C₂²	1	2	yes	—
77	C₅₃×#484	C₂²	1	2	yes	complemented
78	C₅₃×#482	C₂²	1	2	yes	—
79	C₅₃×#481	C₂²	1	2	yes	—
80	C₅₃×#479	C₂²	1	2	yes	complemented
81	C₅₃×#479	C₂²	1	2	yes	complemented
82	C₅₃×#479	C₂²	1	2	yes	complemented
83	C₅₃×#478	C₂²	1	2	yes	—
84	C₅₃×#478	C₂²	1	2	yes	—
85	C₅₃×#478	C₂²	1	2	yes	—
86	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#477	C₂²	1	2	yes	complemented
89	C₅₃×#476	C₂²	1	1	yes	characteristic
90	C₅₃×#476	C₂²	1	2	yes	—
91	C₅₃×#476	C₂²	1	1	yes	characteristic
92	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#475	C₂²	1	2	yes	complemented
97	C₅₃×#474	C₂²	1	1	yes	characteristic
98	C₅₃×#474	C₂²	1	1	yes	characteristic
99	C₅₃×#474	C₂²	1	1	yes	characteristic
100	C₅₃×#474	C₂²	1	1	yes	characteristic
101	C₅₃×#470	C₂²	1	2	yes	—
102	C₅₃×#470	C₂²	1	2	yes	—
103	C₅₃×#470	C₂²	1	2	yes	complemented
104	C₅₃×#468	C₂²	1	2	yes	—
105	C₅₃×#467	C₂²	1	2	yes	complemented
106	C₅₃×#465	C₂²	1	2	yes	—
107	C₅₃×#464	C₂²	1	2	yes	—
108	C₅₃×#464	C₂²	1	2	yes	—
109	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#462	C₂²	1	2	yes	complemented
112	C₅₃×#461	C₂²	1	1	yes	characteristic
113	C₅₃×#461	C₂²	1	1	yes	characteristic
114	C₅₃×#452	C₂²	1	2	yes	—
115	C₅₃×#452	C₂²	1	2	yes	—
116	C₅₃×#450	C₂²	1	2	yes	—
117	C₅₃×#446	C₂²	1	2	yes	complemented
118	C₅₃×#441	C₂²	1	2	yes	complemented
119	C₅₃×#440	C₂²	1	2	yes	—
120	C₅₃×#440	C₂²	1	2	yes	—
121	C₅₃×#440	C₂²	1	2	yes	—
122	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
123	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
124	C₅₃×#436	C₂²	1	2	yes	—
125	C₅₃×#435	C₂²	1	2	yes	—
126	C₅₃×#435	C₂²	1	2	yes	complemented
127	C₅₃×#432	C₂²	1	1	yes	characteristic
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	—
131	C₅₃×#428	C₂²	1	2	yes	complemented
132	C₅₃×#427	C₂²	1	2	yes	complemented
133	C₅₃×#423	C₂²	1	1	yes	characteristic
134	C₅₃×#423	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×#417	C₂²	1	2	yes	—
138	C₅₃×#416	C₂²	1	2	yes	—
139	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
140	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
141	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₅₃	—	2	1	no	—
143	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₅₃	—	2	1	no	—
145	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
149	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
150	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₅₃	—	2	1	no	—
153	C₄⋊Q₈×C₅₃	—	2	1	no	—
154	C₄⋊Q₈×C₅₃	—	2	2	no	—
155	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
162	#126×C₅₃	—	2	1	no	—
163	#126×C₅₃	—	2	1	no	—
164	#126×C₅₃	—	2	1	no	—
165	#126×C₅₃	—	2	1	no	—
166	#126×C₅₃	—	2	2	no	—
167	#126×C₅₃	—	2	2	no	—
168	#126×C₅₃	—	2	2	no	—
169	#126×C₅₃	—	2	2	no	—
170	#126×C₅₃	—	2	1	no	—
171	#126×C₅₃	—	2	1	no	—
172	#125×C₅₃	—	2	1	no	—
173	#125×C₅₃	—	2	1	no	—
174	#125×C₅₃	—	2	2	no	—
175	#125×C₅₃	—	2	2	no	—
176	#125×C₅₃	—	2	2	no	—
177	#125×C₅₃	—	2	2	no	—
178	#125×C₅₃	—	2	1	no	—
179	#125×C₅₃	—	2	1	no	—
180	#125×C₅₃	—	2	1	no	—
181	#125×C₅₃	—	2	1	no	—
182	#125×C₅₃	C₂³	1	2	yes	—
183	#125×C₅₃	C₂³	1	2	yes	—
184	#125×C₅₃	C₂³	1	1	yes	characteristic
185	#125×C₅₃	C₂³	1	1	yes	characteristic
186	#124×C₅₃	—	2	1	no	—
187	#124×C₅₃	—	2	1	no	—
188	#124×C₅₃	—	2	2	no	—
189	#124×C₅₃	C₂³	1	1	yes	characteristic
190	#124×C₅₃	C₂³	1	1	yes	characteristic
191	#123×C₅₃	—	2	1	no	—
192	#123×C₅₃	—	2	1	no	—
193	#123×C₅₃	—	2	1	no	—
194	#123×C₅₃	—	2	1	no	—
195	#123×C₅₃	—	2	1	no	—
196	#123×C₅₃	—	2	1	no	—
197	#123×C₅₃	—	2	2	no	—
198	#123×C₅₃	—	2	2	no	—
199	#123×C₅₃	—	2	1	no	—
200	#123×C₅₃	—	2	1	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	1	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	—	2	1	no	—
210	C₂²⋊Q₈×C₅₃	—	2	1	no	—
211	C₂²⋊Q₈×C₅₃	—	2	1	no	—
212	C₂²⋊Q₈×C₅₃	—	2	1	no	—
213	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
214	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
215	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
216	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
219	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
220	#121×C₅₃	—	2	1	no	—
221	#121×C₅₃	—	2	1	no	—
222	#121×C₅₃	—	2	1	no	—
223	#121×C₅₃	—	2	1	no	—
224	#121×C₅₃	C₂³	1	1	yes	characteristic
225	#121×C₅₃	C₂³	1	1	yes	characteristic
226	#120×C₅₃	—	2	1	no	—
227	#120×C₅₃	—	2	1	no	—
228	C₄×Q₈×C₅₃	—	2	2	no	—
229	C₄×Q₈×C₅₃	—	2	2	no	—
230	C₄×Q₈×C₅₃	—	2	1	no	—
231	C₄×Q₈×C₅₃	—	2	1	no	—
232	C₄×Q₈×C₅₃	—	2	1	no	—
233	C₄×Q₈×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×Q₈×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
245	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
246	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
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	D₄	1	1	yes	characteristic
256	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
257	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
258	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₅₃	C₂³	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	#117×C₅₃	—	2	1	no	—
268	#117×C₅₃	—	2	1	no	—
269	#117×C₅₃	—	2	1	no	—
270	#117×C₅₃	—	2	1	no	—
271	#117×C₅₃	—	2	2	no	—
272	#117×C₅₃	—	2	2	no	—
273	#117×C₅₃	—	2	1	no	—
274	#117×C₅₃	—	2	1	no	—
275	#117×C₅₃	—	2	1	no	—
276	#117×C₅₃	—	2	1	no	—
277	#117×C₅₃	—	2	1	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	1	yes	characteristic
287	#117×C₅₃	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
289	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
290	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
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×C₄²×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	#106×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	2	yes	—
316	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
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	#103×C₅₃	C₂³	1	2	yes	—
324	#103×C₅₃	C₂³	1	2	yes	—
325	#103×C₅₃	C₂³	1	2	yes	—
326	#103×C₅₃	C₂³	1	2	yes	—
327	#103×C₅₃	C₂³	1	2	yes	—
328	#103×C₅₃	C₂³	1	2	yes	—
329	#103×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	#41×C₅₃	—	2	2	no	—
344	#41×C₅₃	—	2	2	no	—
345	#41×C₅₃	—	4	2	no	—
346	#41×C₅₃	—	4	1	no	—
347	#41×C₅₃	—	4	1	no	—
348	C₂×Q₈×C₅₃	—	2	1	no	—
349	C₂×Q₈×C₅₃	—	2	1	no	—
350	C₂×Q₈×C₅₃	—	2	1	no	—
351	C₂×Q₈×C₅₃	—	2	2	no	—
352	C₂×Q₈×C₅₃	—	2	1	no	—
353	C₂×Q₈×C₅₃	—	4	4	no	—
354	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
355	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
358	C₂×D₄×C₅₃	—	2	2	no	—
359	C₂×D₄×C₅₃	—	2	1	no	—
360	C₂×D₄×C₅₃	—	2	1	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	—	4	1	no	—
365	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
368	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₅₃	—	2	1	no	—
371	C₂²×C₄×C₅₃	—	2	2	no	—
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	1	no	—
380	C₂²×C₄×C₅₃	—	4	4	no	—
381	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	Q₁₆×C₅₃	—	4	2	no	—
391	Q₁₆×C₅₃	—	4	2	no	—
392	SD₁₆×C₅₃	—	2	4	no	—
393	SD₁₆×C₅₃	—	4	2	no	—
394	M₁₆×C₅₃	—	4	2	no	—
395	M₁₆×C₅₃	—	4	2	no	—
396	C₂×C₈×C₅₃	—	4	2	no	—
397	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
398	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
399	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
400	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₅₃	—	2	1	no	—
402	C₄⋊C₄×C₅₃	—	2	1	no	—
403	C₄⋊C₄×C₅₃	—	2	1	no	—
404	C₄⋊C₄×C₅₃	—	2	1	no	—
405	C₄⋊C₄×C₅₃	—	2	1	no	—
406	C₄⋊C₄×C₅₃	—	2	1	no	—
407	C₄⋊C₄×C₅₃	—	2	1	no	—
408	C₄⋊C₄×C₅₃	—	2	1	no	—
409	C₄⋊C₄×C₅₃	—	2	2	no	—
410	C₄⋊C₄×C₅₃	—	2	1	no	—
411	C₄⋊C₄×C₅₃	—	2	2	no	—
412	C₄⋊C₄×C₅₃	—	2	1	no	—
413	C₄⋊C₄×C₅₃	—	2	1	no	—
414	C₄⋊C₄×C₅₃	—	2	1	no	—
415	C₄⋊C₄×C₅₃	—	2	1	no	—
416	C₄⋊C₄×C₅₃	—	2	1	no	—
417	C₄⋊C₄×C₅₃	—	2	1	no	—
418	C₄⋊C₄×C₅₃	—	2	1	no	—
419	C₄⋊C₄×C₅₃	—	2	2	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	—	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	2	no	—
431	C₄⋊C₄×C₅₃	—	2	2	no	—
432	C₄⋊C₄×C₅₃	—	2	2	no	—
433	C₄⋊C₄×C₅₃	—	2	2	no	—
434	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
441	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
442	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
443	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
445	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
447	C₂²⋊C₄×C₅₃	—	2	1	no	—
448	C₂²⋊C₄×C₅₃	—	2	1	no	—
449	C₂²⋊C₄×C₅₃	—	2	2	no	—
450	C₂²⋊C₄×C₅₃	—	2	2	no	—
451	C₂²⋊C₄×C₅₃	—	2	2	no	—
452	C₂²⋊C₄×C₅₃	—	2	1	no	—
453	C₂²⋊C₄×C₅₃	—	2	1	no	—
454	C₂²⋊C₄×C₅₃	—	2	2	no	—
455	C₂²⋊C₄×C₅₃	—	2	2	no	—
456	C₂²⋊C₄×C₅₃	—	2	1	no	—
457	C₂²⋊C₄×C₅₃	—	2	1	no	—
458	C₂²⋊C₄×C₅₃	—	2	1	no	—
459	C₂²⋊C₄×C₅₃	—	2	1	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	C₂×D₄	1	1	yes	characteristic
471	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
472	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
473	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
474	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
475	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
476	C₄²×C₅₃	—	2	1	no	—
477	C₄²×C₅₃	—	2	1	no	—
478	C₄²×C₅₃	—	2	1	no	—
479	C₄²×C₅₃	—	2	1	no	—
480	C₄²×C₅₃	—	2	1	no	—
481	C₄²×C₅₃	—	2	1	no	—
482	C₄²×C₅₃	—	2	2	no	—
483	C₄²×C₅₃	—	2	2	no	—
484	C₄²×C₅₃	—	2	2	no	—
485	C₄²×C₅₃	—	2	2	no	—
486	C₄²×C₅₃	—	2	2	no	—
487	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
488	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
489	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
490	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
494	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
495	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
496	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
497	C₂³×C₅₃	—	2	1	no	—
498	C₂³×C₅₃	—	2	1	no	—
499	C₂³×C₅₃	—	4	2	no	—
500	C₂³×C₅₃	—	4	2	no	—
501	C₂³×C₅₃	—	8	1	no	—
502	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
503	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
504	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
505	Q₈×C₅₃	—	2	1	no	—
506	Q₈×C₅₃	—	2	1	no	—
507	Q₈×C₅₃	—	2	2	no	—
508	Q₈×C₅₃	—	2	1	no	—
509	Q₈×C₅₃	—	2	1	no	—
510	Q₈×C₅₃	—	2	2	no	—
511	Q₈×C₅₃	—	4	1	no	—
512	Q₈×C₅₃	—	4	2	no	—
513	Q₈×C₅₃	—	4	4	no	—
514	Q₈×C₅₃	—	4	2	no	—
515	Q₈×C₅₃	—	4	2	no	—
516	Q₈×C₅₃	—	8	1	no	—
517	D₄×C₅₃	—	2	1	no	—
518	D₄×C₅₃	—	2	1	no	—
519	D₄×C₅₃	—	2	1	no	—
520	D₄×C₅₃	—	4	1	no	—
521	D₄×C₅₃	—	4	1	no	—
522	D₄×C₅₃	—	4	1	no	—
523	D₄×C₅₃	—	4	2	no	—
524	D₄×C₅₃	—	4	2	no	—
525	D₄×C₅₃	—	4	2	no	—
526	D₄×C₅₃	—	8	1	no	—
527	D₄×C₅₃	—	8	1	no	—
528	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
529	C₂×C₄×C₅₃	—	2	2	no	—
530	C₂×C₄×C₅₃	—	2	2	no	—
531	C₂×C₄×C₅₃	—	2	2	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	1	no	—
537	C₂×C₄×C₅₃	—	2	1	no	—
538	C₂×C₄×C₅₃	—	2	1	no	—
539	C₂×C₄×C₅₃	—	2	1	no	—
540	C₂×C₄×C₅₃	—	2	1	no	—
541	C₂×C₄×C₅₃	—	2	1	no	—
542	C₂×C₄×C₅₃	—	2	1	no	—
543	C₂×C₄×C₅₃	—	2	1	no	—
544	C₂×C₄×C₅₃	—	2	2	no	—
545	C₂×C₄×C₅₃	—	2	2	no	—
546	C₂×C₄×C₅₃	—	2	2	no	—
547	C₂×C₄×C₅₃	—	2	2	no	—
548	C₂×C₄×C₅₃	—	4	1	no	—
549	C₂×C₄×C₅₃	—	4	1	no	—
550	C₂×C₄×C₅₃	—	4	1	no	—
551	C₂×C₄×C₅₃	—	4	2	no	—
552	C₂×C₄×C₅₃	—	4	2	no	—
553	C₂×C₄×C₅₃	—	4	2	no	—
554	C₂×C₄×C₅₃	—	4	2	no	—
555	C₂×C₄×C₅₃	—	4	2	no	—
556	C₂×C₄×C₅₃	—	4	4	no	—
557	C₂×C₄×C₅₃	—	4	2	no	—
558	C₂×C₄×C₅₃	—	4	2	no	—
559	C₂×C₄×C₅₃	—	8	1	no	—
560	C₂×C₄×C₅₃	—	8	1	no	—
561	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
573	C₈×C₅₃	—	2	2	no	—
574	C₈×C₅₃	—	2	2	no	—
575	C₈×C₅₃	—	2	2	no	—
576	C₈×C₅₃	—	2	2	no	—
577	#62116	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
578	C₂²×C₅₃	—	2	1	no	—
579	C₂²×C₅₃	—	2	1	no	—
580	C₂²×C₅₃	—	2	1	no	—
581	C₂²×C₅₃	—	2	1	no	—
582	C₂²×C₅₃	—	2	1	no	—
583	C₂²×C₅₃	—	2	1	no	—
584	C₂²×C₅₃	—	2	2	no	—
585	C₂²×C₅₃	—	2	1	no	—
586	C₂²×C₅₃	—	2	1	no	—
587	C₂²×C₅₃	—	2	1	no	—
588	C₂²×C₅₃	—	4	1	no	—
589	C₂²×C₅₃	—	4	1	no	—
590	C₂²×C₅₃	—	4	1	no	—
591	C₂²×C₅₃	—	4	1	no	—
592	C₂²×C₅₃	—	4	1	no	—
593	C₂²×C₅₃	—	8	4	no	—
594	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
595	C₄×C₅₃	—	2	1	no	—
596	C₄×C₅₃	—	2	1	no	—
597	C₄×C₅₃	—	2	1	no	—
598	C₄×C₅₃	—	2	1	no	—
599	C₄×C₅₃	—	2	1	no	—
600	C₄×C₅₃	—	2	1	no	—
601	C₄×C₅₃	—	2	1	no	—
602	C₄×C₅₃	—	2	1	no	—
603	C₄×C₅₃	—	2	1	no	—
604	C₄×C₅₃	—	2	1	no	—
605	C₄×C₅₃	—	4	1	no	—
606	C₄×C₅₃	—	4	1	no	—
607	C₄×C₅₃	—	4	2	no	—
608	C₄×C₅₃	—	4	1	no	—
609	C₄×C₅₃	—	4	1	no	—
610	C₄×C₅₃	—	4	2	no	—
611	C₄×C₅₃	—	4	1	no	—
612	C₄×C₅₃	—	4	1	no	—
613	C₄×C₅₃	—	4	2	no	—
614	C₄×C₅₃	—	4	2	no	—
615	C₄×C₅₃	#575	1	2	yes	—
616	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
617	C₄×C₅₃	#585	1	1	yes	characteristic
618	#3509	C₂×C₅₃	1	1	yes	characteristic, complemented
619	#3475	C₂×C₅₃	1	1	yes	characteristic
620	#3388	C₂×C₅₃	1	2	yes	complemented
621	#3377	C₂×C₅₃	1	2	yes	complemented
622	#3352	C₂×C₅₃	1	2	yes	complemented
623	#3349	C₂×C₅₃	1	2	yes	complemented
624	#3348	C₂×C₅₃	1	2	yes	complemented
625	#3323	C₂×C₅₃	1	2	yes	complemented
626	#3315	C₂×C₅₃	1	2	yes	complemented
627	#3311	C₂×C₅₃	1	2	yes	complemented
628	#3255	C₂×C₅₃	1	1	yes	characteristic, complemented
629	#3252	C₂×C₅₃	1	1	yes	characteristic, complemented
630	#3248	C₂×C₅₃	1	1	yes	characteristic, complemented
631	#3239	C₂×C₅₃	1	1	yes	characteristic, complemented
632	#3237	C₂×C₅₃	1	1	yes	characteristic, complemented
633	#3233	C₂×C₅₃	1	1	yes	characteristic, complemented
634	#3116	C₂×C₅₃	1	1	yes	characteristic, complemented
635	#3110	C₂×C₅₃	1	1	yes	characteristic, complemented
636	#3107	C₂×C₅₃	1	1	yes	characteristic, complemented
637	#3079	C₂×C₅₃	1	1	yes	characteristic, complemented
638	#3077	C₂×C₅₃	1	1	yes	characteristic, complemented
639	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
640	#2989	C₂×C₅₃	1	1	yes	characteristic, complemented
641	C₂×C₅₃	—	4	1	no	—
642	C₂×C₅₃	—	4	1	no	—
643	C₂×C₅₃	—	4	1	no	—
644	C₂×C₅₃	—	4	2	no	—
645	C₂×C₅₃	—	8	1	no	—
646	C₂×C₅₃	#3489	1	1	yes	characteristic
647	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
648	C₂×C₅₃	#3586	1	1	yes	characteristic
649	#557	—	2	1	no	—
650	#557	C₂²×C₅₃	1	2	yes	complemented
651	#556	—	2	1	no	—
652	#556	C₂²×C₅₃	1	1	yes	characteristic
653	#556	C₂²×C₅₃	1	2	yes	—
654	#555	C₂²×C₅₃	1	1	yes	characteristic
655	#554	C₂²×C₅₃	1	1	yes	characteristic
656	#553	—	2	1	no	—
657	#552	—	2	1	no	—
658	#552	—	2	1	no	—
659	#552	—	2	1	no	—
660	#552	C₂²×C₅₃	1	1	yes	characteristic
661	#552	C₂²×C₅₃	1	1	yes	characteristic
662	#552	C₂²×C₅₃	1	2	yes	—
663	#552	C₂²×C₅₃	1	2	yes	complemented
664	#551	—	2	1	no	—
665	#551	—	2	1	no	—
666	#547	C₂²×C₅₃	1	1	yes	characteristic
667	#546	C₂²×C₅₃	1	1	yes	characteristic
668	#546	C₂²×C₅₃	1	1	yes	characteristic
669	#541	—	2	1	no	—
670	#541	—	2	1	no	—
671	#536	—	2	1	no	—
672	#533	C₂²×C₅₃	1	1	yes	characteristic
673	#533	C₂²×C₅₃	1	1	yes	characteristic
674	#533	C₂²×C₅₃	1	1	yes	characteristic
675	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
676	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
677	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
678	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
679	#529	—	2	1	no	—
680	#529	—	2	1	no	—
681	#529	C₂²×C₅₃	1	1	yes	characteristic
682	#529	C₂²×C₅₃	1	1	yes	characteristic
683	#525	—	2	1	no	—
684	#519	—	2	1	no	—
685	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
686	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
687	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
688	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
689	C₂×#117	—	2	1	no	—
690	#501	C₂²×C₅₃	1	2	yes	complemented
691	#501	C₂²×C₅₃	1	2	yes	complemented
692	#499	C₂²×C₅₃	1	2	yes	complemented
693	#491	C₂²×C₅₃	1	2	yes	complemented
694	#489	C₂²×C₅₃	1	2	yes	—
695	#488	C₂²×C₅₃	1	2	yes	—
696	#485	C₂²×C₅₃	1	2	yes	—
697	#485	C₂²×C₅₃	1	2	yes	—
698	#485	C₂²×C₅₃	1	2	yes	complemented
699	#485	C₂²×C₅₃	1	2	yes	complemented
700	#485	C₂²×C₅₃	1	2	yes	complemented
701	#484	C₂²×C₅₃	1	2	yes	—
702	#484	C₂²×C₅₃	1	2	yes	complemented
703	#482	C₂²×C₅₃	1	2	yes	—
704	#481	C₂²×C₅₃	1	2	yes	—
705	#479	C₂²×C₅₃	1	2	yes	complemented
706	#479	C₂²×C₅₃	1	2	yes	complemented
707	#479	C₂²×C₅₃	1	2	yes	complemented
708	#478	C₂²×C₅₃	1	2	yes	—
709	#478	C₂²×C₅₃	1	2	yes	—
710	#478	C₂²×C₅₃	1	2	yes	—
711	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	#477	C₂²×C₅₃	1	2	yes	complemented
713	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
714	#476	C₂²×C₅₃	1	1	yes	characteristic
715	#476	C₂²×C₅₃	1	1	yes	characteristic
716	#476	C₂²×C₅₃	1	2	yes	—
717	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
718	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
719	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
720	#475	C₂²×C₅₃	1	2	yes	complemented
721	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	#474	C₂²×C₅₃	1	1	yes	characteristic
723	#474	C₂²×C₅₃	1	1	yes	characteristic
724	#474	C₂²×C₅₃	1	1	yes	characteristic
725	#474	C₂²×C₅₃	1	1	yes	characteristic
726	#470	C₂²×C₅₃	1	2	yes	—
727	#470	C₂²×C₅₃	1	2	yes	—
728	#470	C₂²×C₅₃	1	2	yes	complemented
729	#468	C₂²×C₅₃	1	2	yes	—
730	#467	C₂²×C₅₃	1	2	yes	complemented
731	#465	C₂²×C₅₃	1	2	yes	—
732	#464	C₂²×C₅₃	1	2	yes	—
733	#464	C₂²×C₅₃	1	2	yes	—
734	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
735	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
736	#462	C₂²×C₅₃	1	2	yes	complemented
737	#461	C₂²×C₅₃	1	1	yes	characteristic
738	#461	C₂²×C₅₃	1	1	yes	characteristic
739	#452	C₂²×C₅₃	1	2	yes	—
740	#452	C₂²×C₅₃	1	2	yes	—
741	#450	C₂²×C₅₃	1	2	yes	—
742	#446	C₂²×C₅₃	1	2	yes	complemented
743	#441	C₂²×C₅₃	1	2	yes	complemented
744	#440	C₂²×C₅₃	1	2	yes	—
745	#440	C₂²×C₅₃	1	2	yes	—
746	#440	C₂²×C₅₃	1	2	yes	—
747	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
748	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
749	#436	C₂²×C₅₃	1	2	yes	—
750	#435	C₂²×C₅₃	1	2	yes	—
751	#435	C₂²×C₅₃	1	2	yes	complemented
752	#432	C₂²×C₅₃	1	1	yes	characteristic
753	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
754	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
755	#428	C₂²×C₅₃	1	2	yes	—
756	#428	C₂²×C₅₃	1	2	yes	complemented
757	#427	C₂²×C₅₃	1	2	yes	complemented
758	#423	C₂²×C₅₃	1	1	yes	characteristic
759	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
760	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
761	#418	C₂²×C₅₃	1	2	yes	—
762	#417	C₂²×C₅₃	1	2	yes	—
763	#416	C₂²×C₅₃	1	2	yes	—
764	C₅₃	#62116	1	1	yes	characteristic, direct product factor, Sylow
765	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
766	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
767	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
768	C₂²×Q₈	—	2	1	no	—
769	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
770	C₂³×C₄	—	2	1	no	—
771	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
772	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
773	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
775	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
776	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
777	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
778	C₄⋊Q₈	—	2	2	no	—
779	C₄⋊Q₈	—	2	1	no	—
780	C₄⋊Q₈	—	2	1	no	—
781	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
782	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
783	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
784	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
785	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
786	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
787	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
788	#126	—	2	1	no	—
789	#126	—	2	1	no	—
790	#126	—	2	1	no	—
791	#126	—	2	1	no	—
792	#126	—	2	2	no	—
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#126	—	2	2	no	—
796	#126	—	2	1	no	—
797	#126	—	2	1	no	—
798	#125	—	2	1	no	—
799	#125	—	2	1	no	—
800	#125	—	2	2	no	—
801	#125	—	2	2	no	—
802	#125	—	2	2	no	—
803	#125	—	2	2	no	—
804	#125	—	2	1	no	—
805	#125	—	2	1	no	—
806	#125	—	2	1	no	—
807	#125	—	2	1	no	—
808	#125	C₂³×C₅₃	1	1	yes	characteristic
809	#125	C₂³×C₅₃	1	1	yes	characteristic
810	#125	C₂³×C₅₃	1	2	yes	—
811	#125	C₂³×C₅₃	1	2	yes	—
812	#124	—	2	2	no	—
813	#124	—	2	1	no	—
814	#124	—	2	1	no	—
815	#124	C₂³×C₅₃	1	1	yes	characteristic
816	#124	C₂³×C₅₃	1	1	yes	characteristic
817	#123	—	2	1	no	—
818	#123	—	2	1	no	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	1	no	—
822	#123	—	2	1	no	—
823	#123	—	2	1	no	—
824	#123	—	2	1	no	—
825	#123	—	2	1	no	—
826	#123	—	2	1	no	—
827	C₂²⋊Q₈	—	2	1	no	—
828	C₂²⋊Q₈	—	2	1	no	—
829	C₂²⋊Q₈	—	2	1	no	—
830	C₂²⋊Q₈	—	2	1	no	—
831	C₂²⋊Q₈	—	2	1	no	—
832	C₂²⋊Q₈	—	2	1	no	—
833	C₂²⋊Q₈	—	2	1	no	—
834	C₂²⋊Q₈	—	2	1	no	—
835	C₂²⋊Q₈	—	2	1	no	—
836	C₂²⋊Q₈	—	2	1	no	—
837	C₂²⋊Q₈	—	2	1	no	—
838	C₂²⋊Q₈	—	2	1	no	—
839	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
840	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
841	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
842	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
843	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
844	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
845	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
846	#121	—	2	1	no	—
847	#121	—	2	1	no	—
848	#121	—	2	1	no	—
849	#121	—	2	1	no	—
850	#121	C₂³×C₅₃	1	1	yes	characteristic
851	#121	C₂³×C₅₃	1	1	yes	characteristic
852	#120	—	2	1	no	—
853	#120	—	2	1	no	—
854	C₄×Q₈	—	2	2	no	—
855	C₄×Q₈	—	2	2	no	—
856	C₄×Q₈	—	2	1	no	—
857	C₄×Q₈	—	2	1	no	—
858	C₄×Q₈	—	2	1	no	—
859	C₄×Q₈	—	2	1	no	—
860	C₄×Q₈	—	2	1	no	—
861	C₄×Q₈	—	2	1	no	—
862	C₄×Q₈	—	2	1	no	—
863	C₄×Q₈	—	2	1	no	—
864	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
865	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
866	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
867	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
868	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
869	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
870	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
871	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
872	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
873	C₄×D₄	—	2	1	no	—
874	C₄×D₄	—	2	1	no	—
875	C₄×D₄	—	2	1	no	—
876	C₄×D₄	—	2	1	no	—
877	C₄×D₄	—	2	1	no	—
878	C₄×D₄	—	2	1	no	—
879	C₄×D₄	—	2	1	no	—
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
882	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
883	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
884	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
885	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
886	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
887	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
888	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
889	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
890	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
891	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
892	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
893	#117	—	2	1	no	—
894	#117	—	2	1	no	—
895	#117	—	2	1	no	—
896	#117	—	2	1	no	—
897	#117	—	2	1	no	—
898	#117	—	2	1	no	—
899	#117	—	2	1	no	—
900	#117	—	2	1	no	—
901	#117	—	2	2	no	—
902	#117	—	2	2	no	—
903	#117	—	2	1	no	—
904	#117	—	2	1	no	—
905	#117	—	2	1	no	—
906	#117	—	2	1	no	—
907	#117	D₄×C₅₃	1	1	yes	characteristic
908	#117	D₄×C₅₃	1	1	yes	characteristic
909	#117	D₄×C₅₃	1	1	yes	characteristic
910	#117	C₂³×C₅₃	1	1	yes	characteristic
911	#117	C₂³×C₅₃	1	1	yes	characteristic
912	#117	C₂³×C₅₃	1	2	yes	—
913	#117	C₂³×C₅₃	1	2	yes	—
914	C₂×C₄⋊C₄	—	2	1	no	—
915	C₂×C₄⋊C₄	—	2	1	no	—
916	C₂×C₄⋊C₄	—	2	1	no	—
917	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
918	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
919	C₂×C₂²⋊C₄	—	2	1	no	—
920	C₂×C₂²⋊C₄	—	2	1	no	—
921	C₂×C₂²⋊C₄	—	2	1	no	—
922	C₂×C₄²	—	2	1	no	—
923	C₂×C₄²	—	2	1	no	—
924	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
925	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
926	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
927	#107	C₂³×C₅₃	1	2	yes	—
928	#107	C₂³×C₅₃	1	2	yes	—
929	#107	C₂³×C₅₃	1	2	yes	—
930	#107	C₂³×C₅₃	1	2	yes	—
931	#107	C₂³×C₅₃	1	2	yes	—
932	#107	C₂³×C₅₃	1	2	yes	—
933	#106	C₂³×C₅₃	1	2	yes	—
934	#106	C₂³×C₅₃	1	2	yes	—
935	#106	C₂³×C₅₃	1	2	yes	—
936	#106	C₂³×C₅₃	1	2	yes	—
937	#106	C₂³×C₅₃	1	2	yes	—
938	#106	C₂³×C₅₃	1	2	yes	—
939	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
940	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
941	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
942	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
943	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
944	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
945	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
946	#103	C₂³×C₅₃	1	2	yes	—
947	#103	C₂³×C₅₃	1	2	yes	—
948	#103	C₂³×C₅₃	1	2	yes	—
949	#103	C₂³×C₅₃	1	2	yes	—
950	#103	C₂³×C₅₃	1	2	yes	—
951	#103	C₂³×C₅₃	1	2	yes	—
952	#103	C₂³×C₅₃	1	2	yes	—
953	#103	C₂³×C₅₃	1	2	yes	—
954	#103	C₂³×C₅₃	1	2	yes	—
955	#103	C₂³×C₅₃	1	2	yes	—
956	#102	C₂³×C₅₃	1	2	yes	—
957	#102	C₂³×C₅₃	1	2	yes	—
958	#102	C₂³×C₅₃	1	2	yes	—
959	#102	C₂³×C₅₃	1	2	yes	—
960	#102	C₂³×C₅₃	1	2	yes	—
961	#102	C₂³×C₅₃	1	2	yes	—
962	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
963	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
964	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
965	#97	C₂³×C₅₃	1	2	yes	—
966	#97	C₂³×C₅₃	1	2	yes	—
967	C₄×C₈	C₂³×C₅₃	1	2	yes	—
968	C₂⁴	—	2	1	no	—
969	#41	—	2	2	no	—
970	#41	—	2	2	no	—
971	#41	—	4	2	no	—
972	#41	—	4	1	no	—
973	#41	—	4	1	no	—
974	C₂×Q₈	—	2	1	no	—
975	C₂×Q₈	—	2	1	no	—
976	C₂×Q₈	—	2	1	no	—
977	C₂×Q₈	—	2	2	no	—
978	C₂×Q₈	—	2	1	no	—
979	C₂×Q₈	—	4	4	no	—
980	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
981	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
982	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
983	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	1	no	—
987	C₂×D₄	—	2	1	no	—
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	—	2	1	no	—
990	C₂×D₄	—	4	1	no	—
991	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
992	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
993	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
994	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
995	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	1	no	—
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	—	4	4	no	—
1007	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1008	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1009	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1010	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1011	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1012	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1014	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1015	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1016	Q₁₆	—	4	2	no	—
1017	Q₁₆	—	4	2	no	—
1018	SD₁₆	—	2	4	no	—
1019	SD₁₆	—	4	2	no	—
1020	M₁₆	—	4	2	no	—
1021	M₁₆	—	4	2	no	—
1022	C₂×C₈	—	4	2	no	—
1023	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1024	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1025	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1026	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1061	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1062	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1063	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1064	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1065	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1067	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1068	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1069	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1070	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1071	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1072	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1097	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1098	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1099	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1100	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1101	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1102	C₄²	—	2	1	no	—
1103	C₄²	—	2	1	no	—
1104	C₄²	—	2	1	no	—
1105	C₄²	—	2	1	no	—
1106	C₄²	—	2	1	no	—
1107	C₄²	—	2	1	no	—
1108	C₄²	—	2	2	no	—
1109	C₄²	—	2	2	no	—
1110	C₄²	—	2	2	no	—
1111	C₄²	—	2	2	no	—
1112	C₄²	—	2	2	no	—
1113	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1114	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1115	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1116	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1117	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1118	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1119	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1120	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1121	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1122	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1123	C₂³	—	2	1	no	—
1124	C₂³	—	2	1	no	—
1125	C₂³	—	4	2	no	—
1126	C₂³	—	4	2	no	—
1127	C₂³	—	8	1	no	—
1128	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1129	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1130	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1131	Q₈	—	2	2	no	—
1132	Q₈	—	2	1	no	—
1133	Q₈	—	2	1	no	—
1134	Q₈	—	2	2	no	—
1135	Q₈	—	2	1	no	—
1136	Q₈	—	2	1	no	—
1137	Q₈	—	4	1	no	—
1138	Q₈	—	4	2	no	—
1139	Q₈	—	4	4	no	—
1140	Q₈	—	4	2	no	—
1141	Q₈	—	4	2	no	—
1142	Q₈	—	8	1	no	—
1143	D₄	—	2	1	no	—
1144	D₄	—	2	1	no	—
1145	D₄	—	2	1	no	—
1146	D₄	—	4	1	no	—
1147	D₄	—	4	1	no	—
1148	D₄	—	4	1	no	—
1149	D₄	—	4	2	no	—
1150	D₄	—	4	2	no	—
1151	D₄	—	4	2	no	—
1152	D₄	—	8	1	no	—
1153	D₄	—	8	1	no	—
1154	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	2	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	2	no	—
1178	C₂×C₄	—	4	2	no	—
1179	C₂×C₄	—	4	2	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	4	2	no	—
1182	C₂×C₄	—	4	4	no	—
1183	C₂×C₄	—	4	2	no	—
1184	C₂×C₄	—	4	2	no	—
1185	C₂×C₄	—	8	1	no	—
1186	C₂×C₄	—	8	1	no	—
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	C₂²×D₄×C₅₃	1	1	yes	characteristic
1191	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1192	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1193	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1194	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1195	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1196	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1197	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1198	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1199	C₈	—	2	2	no	—
1200	C₈	—	2	2	no	—
1201	C₈	—	2	2	no	—
1202	C₈	—	2	2	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	1	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	2	no	—
1207	C₂²	—	2	1	no	—
1208	C₂²	—	2	1	no	—
1209	C₂²	—	2	1	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	1	no	—
1212	C₂²	—	2	1	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	8	4	no	—
1219	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1220	C₄	—	2	1	no	—
1221	C₄	—	2	1	no	—
1222	C₄	—	2	1	no	—
1223	C₄	—	2	1	no	—
1224	C₄	—	2	1	no	—
1225	C₄	—	2	1	no	—
1226	C₄	—	2	1	no	—
1227	C₄	—	2	1	no	—
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	2	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	2	no	—
1236	C₄	—	4	2	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	2	no	—
1240	C₄	C₅₃×#575	1	2	yes	—
1241	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1242	C₄	C₅₃×#585	1	1	yes	characteristic
1243	C₂	—	4	1	no	—
1244	C₂	—	4	1	no	—
1245	C₂	—	4	1	no	—
1246	C₂	—	4	2	no	—
1247	C₂	—	8	1	no	—
1248	C₂	C₅₃×#3489	1	1	yes	characteristic
1249	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1250	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3475	C₂
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×#3509	C₂	semidirect
3. C₅₃×#3388	C₂	semidirect
4. C₅₃×#3377	C₂	semidirect
5. C₅₃×#3352	C₂	semidirect
6. C₅₃×#3349	C₂	semidirect
7. C₅₃×#3348	C₂	semidirect
8. C₅₃×#3323	C₂	semidirect
9. C₅₃×#3315	C₂	semidirect
10. C₅₃×#3311	C₂	semidirect
11. C₅₃×#3255	C₂	semidirect
12. C₅₃×#3252	C₂	semidirect
13. C₅₃×#3248	C₂	semidirect
14. C₅₃×#3239	C₂	semidirect
15. C₅₃×#3237	C₂	semidirect
16. C₅₃×#3233	C₂	semidirect
17. C₅₃×#3116	C₂	semidirect
18. C₅₃×#3110	C₂	semidirect
19. C₅₃×#3107	C₂	semidirect
20. C₅₃×#3079	C₂	semidirect
21. C₅₃×#3077	C₂	semidirect
22. C₅₃×#3076	C₂	semidirect
23. C₅₃×#2989	C₂	semidirect
25. C₅₃×#557	C₂²	semidirect
38. C₅₃×#552	C₂²	semidirect
50. C₅₃×#533	C₂²	semidirect
51. C₅₃×#533	C₂²	semidirect
52. C₅₃×#533	C₂²	semidirect
53. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
65. C₅₃×#501	C₂²	semidirect
66. C₅₃×#501	C₂²	semidirect
67. C₅₃×#499	C₂²	semidirect
68. C₅₃×#491	C₂²	semidirect
73. C₅₃×#485	C₂²	semidirect
74. C₅₃×#485	C₂²	semidirect
75. C₅₃×#485	C₂²	semidirect
77. C₅₃×#484	C₂²	semidirect
80. C₅₃×#479	C₂²	semidirect
81. C₅₃×#479	C₂²	semidirect
82. C₅₃×#479	C₂²	semidirect
86. C₅₃×#477	C₂²	semidirect
87. C₅₃×#477	C₂²	semidirect
88. C₅₃×#477	C₂²	semidirect
92. C₅₃×#475	C₂²	semidirect
93. C₅₃×#475	C₂²	semidirect
94. C₅₃×#475	C₂²	semidirect
95. C₅₃×#475	C₂²	semidirect
96. C₅₃×#475	C₂²	semidirect
103. C₅₃×#470	C₂²	semidirect
105. C₅₃×#467	C₂²	semidirect
109. C₅₃×#462	C₂²	semidirect
110. C₅₃×#462	C₂²	semidirect
111. C₅₃×#462	C₂²	semidirect
117. C₅₃×#446	C₂²	semidirect
118. C₅₃×#441	C₂²	semidirect
122. C₄×Q₁₆×C₅₃	C₂²	semidirect
126. C₅₃×#435	C₂²	semidirect
128. C₅₃×#432	C₂²	semidirect
129. C₅₃×#431	C₂²	semidirect
131. C₅₃×#428	C₂²	semidirect
132. C₅₃×#427	C₂²	semidirect
134. C₅₃×#423	C₂²	semidirect
135. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
577. #62116	C₅₃	direct (N × H)
618. #3509	C₂×C₅₃	semidirect
620. #3388	C₂×C₅₃	semidirect
621. #3377	C₂×C₅₃	semidirect
622. #3352	C₂×C₅₃	semidirect
623. #3349	C₂×C₅₃	semidirect
624. #3348	C₂×C₅₃	semidirect
625. #3323	C₂×C₅₃	semidirect
626. #3315	C₂×C₅₃	semidirect
627. #3311	C₂×C₅₃	semidirect
628. #3255	C₂×C₅₃	semidirect
629. #3252	C₂×C₅₃	semidirect
630. #3248	C₂×C₅₃	semidirect
631. #3239	C₂×C₅₃	semidirect
632. #3237	C₂×C₅₃	semidirect
633. #3233	C₂×C₅₃	semidirect
634. #3116	C₂×C₅₃	semidirect
635. #3110	C₂×C₅₃	semidirect
636. #3107	C₂×C₅₃	semidirect
637. #3079	C₂×C₅₃	semidirect
638. #3077	C₂×C₅₃	semidirect
639. #3076	C₂×C₅₃	semidirect
640. #2989	C₂×C₅₃	semidirect
650. #557	C₂²×C₅₃	semidirect
663. #552	C₂²×C₅₃	semidirect
675. #533	C₂²×C₅₃	semidirect
676. #533	C₂²×C₅₃	semidirect
677. #533	C₂²×C₅₃	semidirect
678. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
690. #501	C₂²×C₅₃	semidirect
691. #501	C₂²×C₅₃	semidirect
692. #499	C₂²×C₅₃	semidirect
693. #491	C₂²×C₅₃	semidirect
698. #485	C₂²×C₅₃	semidirect
699. #485	C₂²×C₅₃	semidirect
700. #485	C₂²×C₅₃	semidirect
702. #484	C₂²×C₅₃	semidirect
705. #479	C₂²×C₅₃	semidirect
706. #479	C₂²×C₅₃	semidirect
707. #479	C₂²×C₅₃	semidirect
711. #477	C₂²×C₅₃	semidirect
712. #477	C₂²×C₅₃	semidirect
713. #477	C₂²×C₅₃	semidirect
717. #475	C₂²×C₅₃	semidirect
718. #475	C₂²×C₅₃	semidirect
719. #475	C₂²×C₅₃	semidirect
720. #475	C₂²×C₅₃	semidirect
721. #475	C₂²×C₅₃	semidirect
728. #470	C₂²×C₅₃	semidirect
730. #467	C₂²×C₅₃	semidirect
734. #462	C₂²×C₅₃	semidirect
735. #462	C₂²×C₅₃	semidirect
736. #462	C₂²×C₅₃	semidirect
742. #446	C₂²×C₅₃	semidirect
743. #441	C₂²×C₅₃	semidirect
747. C₄×Q₁₆	C₂²×C₅₃	semidirect
751. #435	C₂²×C₅₃	semidirect
753. #432	C₂²×C₅₃	semidirect
754. #431	C₂²×C₅₃	semidirect
756. #428	C₂²×C₅₃	semidirect
757. #427	C₂²×C₅₃	semidirect
759. #423	C₂²×C₅₃	semidirect
760. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
764. C₅₃	#62116	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×#3509	2
C₅₃×#3475	2
C₅₃×#3388	2
C₅₃×#3377	2
C₅₃×#3352	2
C₅₃×#3349	2
C₅₃×#3348	2
C₅₃×#3323	2
C₅₃×#3315	2
C₅₃×#3311	2
C₅₃×#3255	2
C₅₃×#3252	2
C₅₃×#3248	2
C₅₃×#3239	2
C₅₃×#3237	2
C₅₃×#3233	2
C₅₃×#3116	2
C₅₃×#3110	2
C₅₃×#3107	2
C₅₃×#3079	2
C₅₃×#3077	2
C₅₃×#3076	2
C₅₃×#2989	2
#62116	53

Subgroups — C53×#62116 #27269628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62116 #27269628