Subgroups — C₅₃×#61978 #27269490

Order 13568.

1916 conjugacy classes of subgroups.

The subgroup lattice has 1344 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×#3401	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3376	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3316	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3307	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3301	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3282	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3267	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3265	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3252	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
25	C₂×#135×C₅₃	C₂²	1	2	yes	—
26	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	—
27	C₅₃×#559	C₂²	1	1	yes	characteristic
28	C₅₃×#556	C₂²	1	2	yes	complemented
29	C₅₃×#555	—	2	1	no	—
30	C₅₃×#554	—	2	1	no	—
31	C₅₃×#554	C₂²	1	1	yes	characteristic
32	C₅₃×#554	C₂²	1	1	yes	characteristic
33	C₅₃×#553	—	2	1	no	—
34	C₅₃×#553	—	2	1	no	—
35	C₅₃×#553	—	2	1	no	—
36	C₅₃×#553	C₂²	1	1	yes	characteristic
37	C₅₃×#553	C₂²	1	1	yes	characteristic
38	C₅₃×#551	—	2	1	no	—
39	C₅₃×#551	—	2	1	no	—
40	C₅₃×#548	C₂²	1	2	yes	—
41	C₅₃×#548	C₂²	1	2	yes	complemented
42	C₅₃×#547	C₂²	1	2	yes	complemented
43	C₅₃×#546	—	2	1	no	—
44	C₅₃×#546	C₂²	1	1	yes	characteristic
45	C₅₃×#546	C₂²	1	1	yes	characteristic
46	D₄²×C₅₃	C₂²	1	1	yes	characteristic
47	C₅₃×#542	—	2	1	no	—
48	C₅₃×#542	—	2	1	no	—
49	C₅₃×#537	—	2	1	no	—
50	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#532	C₂²	1	1	yes	characteristic
53	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#529	—	2	1	no	—
58	C₅₃×#529	C₂²	1	1	yes	characteristic
59	C₅₃×#529	C₂²	1	1	yes	characteristic
60	C₅₃×#525	—	2	1	no	—
61	C₅₃×#525	—	2	1	no	—
62	C₅₃×#520	—	2	1	no	—
63	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
64	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
65	C₂×C₄×D₄×C₅₃	—	2	1	no	—
66	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
67	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
68	C₅₃×#497	C₂²	1	2	yes	complemented
69	C₅₃×#496	C₂²	1	2	yes	—
70	C₅₃×#495	C₂²	1	2	yes	complemented
71	C₅₃×#491	C₂²	1	2	yes	complemented
72	C₅₃×#489	C₂²	1	2	yes	complemented
73	C₅₃×#488	C₂²	1	2	yes	complemented
74	C₅₃×#485	C₂²	1	2	yes	complemented
75	C₅₃×#483	C₂²	1	2	yes	complemented
76	C₅₃×#481	C₂²	1	2	yes	complemented
77	C₅₃×#479	C₂²	1	2	yes	complemented
78	C₅₃×#478	C₂²	1	2	yes	complemented
79	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#476	C₂²	1	1	yes	characteristic
81	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#475	C₂²	1	2	yes	complemented
84	C₅₃×#470	C₂²	1	2	yes	complemented
85	C₅₃×#468	C₂²	1	2	yes	—
86	C₅₃×#466	C₂²	1	2	yes	—
87	C₅₃×#465	C₂²	1	2	yes	complemented
88	C₅₃×#465	C₂²	1	2	yes	complemented
89	C₅₃×#465	C₂²	1	2	yes	complemented
90	C₅₃×#464	C₂²	1	2	yes	complemented
91	C₅₃×#464	C₂²	1	2	yes	complemented
92	C₅₃×#463	C₂²	1	2	yes	—
93	C₅₃×#463	C₂²	1	2	yes	—
94	C₅₃×#463	C₂²	1	2	yes	complemented
95	C₅₃×#463	C₂²	1	2	yes	complemented
96	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#461	C₂²	1	2	yes	—
99	C₅₃×#461	C₂²	1	1	yes	characteristic
100	C₅₃×#461	C₂²	1	1	yes	characteristic
101	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#461	C₂²	1	2	yes	complemented
106	C₅₃×#460	C₂²	1	2	yes	—
107	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#459	C₂²	1	1	yes	characteristic
109	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#452	C₂²	1	2	yes	—
112	C₅₃×#452	C₂²	1	2	yes	complemented
113	C₅₃×#451	C₂²	1	2	yes	complemented
114	C₅₃×#450	C₂²	1	2	yes	—
115	C₅₃×#449	C₂²	1	2	yes	—
116	C₅₃×#449	C₂²	1	2	yes	complemented
117	C₅₃×#449	C₂²	1	2	yes	complemented
118	C₅₃×#448	C₂²	1	2	yes	—
119	C₅₃×#447	C₂²	1	2	yes	—
120	C₅₃×#446	C₂²	1	2	yes	complemented
121	C₅₃×#442	C₂²	1	2	yes	—
122	C₅₃×#442	C₂²	1	2	yes	complemented
123	C₅₃×#441	C₂²	1	2	yes	complemented
124	C₅₃×#440	C₂²	1	2	yes	—
125	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
126	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
127	C₅₃×#435	C₂²	1	2	yes	—
128	C₅₃×#435	C₂²	1	2	yes	complemented
129	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
130	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#431	C₂²	1	1	yes	characteristic, 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×#417	C₂²	1	2	yes	complemented
137	C₅₃×#416	C₂²	1	2	yes	complemented
138	C₂×#103×C₅₃	C₂²	1	2	yes	complemented
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	2	1	no	—
141	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
142	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×#41×C₅₃	C₂³	1	2	yes	—
144	C₂×#41×C₅₃	C₂³	1	2	yes	—
145	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
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	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
152	#135×C₅₃	—	4	4	no	—
153	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₅₃	—	4	4	no	—
156	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
162	C₂×SD₁₆×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×M₁₆×C₅₃	C₂³	1	2	yes	—
167	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
168	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
169	C₄⋊Q₈×C₅₃	—	2	1	no	—
170	C₄⋊Q₈×C₅₃	—	2	1	no	—
171	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
172	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
173	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
174	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
175	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
176	#127×C₅₃	C₂³	1	1	yes	characteristic
177	#127×C₅₃	C₂³	1	1	yes	characteristic
178	#126×C₅₃	—	2	1	no	—
179	#126×C₅₃	—	2	1	no	—
180	#126×C₅₃	—	2	2	no	—
181	#126×C₅₃	—	2	2	no	—
182	#126×C₅₃	—	2	1	no	—
183	#126×C₅₃	—	2	1	no	—
184	#125×C₅₃	—	2	1	no	—
185	#125×C₅₃	—	2	1	no	—
186	#125×C₅₃	—	2	1	no	—
187	#125×C₅₃	C₂³	1	1	yes	characteristic
188	#125×C₅₃	C₂³	1	1	yes	characteristic
189	#124×C₅₃	—	2	2	no	—
190	#124×C₅₃	—	2	2	no	—
191	#124×C₅₃	—	2	1	no	—
192	#124×C₅₃	—	2	1	no	—
193	#124×C₅₃	—	2	1	no	—
194	#124×C₅₃	C₂³	1	2	yes	—
195	#124×C₅₃	C₂³	1	2	yes	—
196	#124×C₅₃	C₂³	1	1	yes	characteristic
197	#124×C₅₃	C₂³	1	1	yes	characteristic
198	#123×C₅₃	—	2	1	no	—
199	#123×C₅₃	—	2	1	no	—
200	#123×C₅₃	—	2	1	no	—
201	#123×C₅₃	—	2	1	no	—
202	#123×C₅₃	—	2	1	no	—
203	#123×C₅₃	—	2	1	no	—
204	#123×C₅₃	—	2	2	no	—
205	#123×C₅₃	—	2	2	no	—
206	#123×C₅₃	—	2	1	no	—
207	#123×C₅₃	—	2	1	no	—
208	C₂²⋊Q₈×C₅₃	—	2	1	no	—
209	C₂²⋊Q₈×C₅₃	—	2	1	no	—
210	C₂²⋊Q₈×C₅₃	—	2	2	no	—
211	C₂²⋊Q₈×C₅₃	—	2	2	no	—
212	C₂²⋊Q₈×C₅₃	—	2	1	no	—
213	C₂²⋊Q₈×C₅₃	—	2	1	no	—
214	C₂²⋊Q₈×C₅₃	—	2	1	no	—
215	C₂²⋊Q₈×C₅₃	—	2	2	no	—
216	C₂²⋊Q₈×C₅₃	—	2	1	no	—
217	C₂²⋊Q₈×C₅₃	—	2	1	no	—
218	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
219	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
220	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
221	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
222	#121×C₅₃	—	2	1	no	—
223	#121×C₅₃	—	2	1	no	—
224	#121×C₅₃	—	2	1	no	—
225	#121×C₅₃	—	2	1	no	—
226	#121×C₅₃	—	2	1	no	—
227	#121×C₅₃	—	2	2	no	—
228	#121×C₅₃	—	2	2	no	—
229	#121×C₅₃	—	2	2	no	—
230	#121×C₅₃	—	2	1	no	—
231	#121×C₅₃	—	2	1	no	—
232	#121×C₅₃	—	2	1	no	—
233	#121×C₅₃	—	2	1	no	—
234	#121×C₅₃	—	2	1	no	—
235	#121×C₅₃	—	2	1	no	—
236	#121×C₅₃	C₂³	1	1	yes	characteristic
237	#121×C₅₃	C₂³	1	1	yes	characteristic
238	#121×C₅₃	C₂³	1	1	yes	characteristic
239	#121×C₅₃	C₂³	1	1	yes	characteristic
240	#121×C₅₃	C₂³	1	2	yes	—
241	#120×C₅₃	—	2	1	no	—
242	#120×C₅₃	—	2	1	no	—
243	#120×C₅₃	—	2	1	no	—
244	#120×C₅₃	—	2	1	no	—
245	C₄×Q₈×C₅₃	—	2	1	no	—
246	C₄×Q₈×C₅₃	—	2	1	no	—
247	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
248	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
251	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
252	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
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	2	no	—
257	C₄×D₄×C₅₃	—	2	2	no	—
258	C₄×D₄×C₅₃	—	2	1	no	—
259	C₄×D₄×C₅₃	—	2	1	no	—
260	C₄×D₄×C₅₃	—	2	1	no	—
261	C₄×D₄×C₅₃	—	2	1	no	—
262	C₄×D₄×C₅₃	—	2	1	no	—
263	C₄×D₄×C₅₃	—	2	1	no	—
264	C₄×D₄×C₅₃	—	2	1	no	—
265	C₄×D₄×C₅₃	—	2	1	no	—
266	C₄×D₄×C₅₃	—	2	1	no	—
267	C₄×D₄×C₅₃	—	2	1	no	—
268	C₄×D₄×C₅₃	—	2	1	no	—
269	C₄×D₄×C₅₃	—	2	1	no	—
270	C₄×D₄×C₅₃	—	2	1	no	—
271	C₄×D₄×C₅₃	—	2	1	no	—
272	C₄×D₄×C₅₃	—	2	1	no	—
273	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
274	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
275	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
276	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
277	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
278	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
282	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₄×D₄×C₅₃	C₂³	1	2	yes	—
285	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
288	#117×C₅₃	—	2	2	no	—
289	#117×C₅₃	—	2	1	no	—
290	#117×C₅₃	—	2	1	no	—
291	#117×C₅₃	—	2	1	no	—
292	#117×C₅₃	—	2	1	no	—
293	#117×C₅₃	—	2	1	no	—
294	#117×C₅₃	D₄	1	1	yes	characteristic
295	#117×C₅₃	D₄	1	1	yes	characteristic
296	#117×C₅₃	D₄	1	1	yes	characteristic
297	#117×C₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
299	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
300	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
301	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
302	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
305	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
306	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
307	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
308	C₂×C₄²×C₅₃	—	2	1	no	—
309	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
312	#107×C₅₃	C₂³	1	2	yes	—
313	#106×C₅₃	C₂³	1	2	yes	—
314	#106×C₅₃	C₂³	1	2	yes	—
315	#106×C₅₃	C₂³	1	2	yes	—
316	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
318	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
319	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
320	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
321	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
322	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
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	#103×C₅₃	C₂³	1	2	yes	—
331	#103×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	#102×C₅₃	C₂³	1	2	yes	—
337	#102×C₅₃	C₂³	1	2	yes	—
338	#102×C₅₃	C₂³	1	2	yes	—
339	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
340	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
341	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
342	#97×C₅₃	C₂³	1	2	yes	—
343	#97×C₅₃	C₂³	1	2	yes	—
344	C₄×C₈×C₅₃	C₂³	1	2	yes	—
345	C₂⁴×C₅₃	—	2	1	no	—
346	C₂⁴×C₅₃	—	2	1	no	—
347	#41×C₅₃	—	2	2	no	—
348	#41×C₅₃	—	4	2	no	—
349	#41×C₅₃	—	4	1	no	—
350	#41×C₅₃	—	4	4	no	—
351	#41×C₅₃	—	4	2	no	—
352	#41×C₅₃	—	4	2	no	—
353	#41×C₅₃	—	4	2	no	—
354	#41×C₅₃	—	4	2	no	—
355	#41×C₅₃	—	8	2	no	—
356	C₂×Q₈×C₅₃	—	2	1	no	—
357	C₂×Q₈×C₅₃	—	2	1	no	—
358	C₂×Q₈×C₅₃	—	2	2	no	—
359	C₂×Q₈×C₅₃	—	4	2	no	—
360	C₂×Q₈×C₅₃	—	4	2	no	—
361	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
362	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
363	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
364	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂×D₄×C₅₃	—	2	2	no	—
366	C₂×D₄×C₅₃	—	2	2	no	—
367	C₂×D₄×C₅₃	—	2	1	no	—
368	C₂×D₄×C₅₃	—	2	1	no	—
369	C₂×D₄×C₅₃	—	2	1	no	—
370	C₂×D₄×C₅₃	—	2	2	no	—
371	C₂×D₄×C₅₃	—	2	1	no	—
372	C₂×D₄×C₅₃	—	2	1	no	—
373	C₂×D₄×C₅₃	—	2	2	no	—
374	C₂×D₄×C₅₃	—	2	2	no	—
375	C₂×D₄×C₅₃	—	2	1	no	—
376	C₂×D₄×C₅₃	—	2	1	no	—
377	C₂×D₄×C₅₃	—	2	1	no	—
378	C₂×D₄×C₅₃	—	2	1	no	—
379	C₂×D₄×C₅₃	—	2	1	no	—
380	C₂×D₄×C₅₃	—	2	1	no	—
381	C₂×D₄×C₅₃	—	4	1	no	—
382	C₂×D₄×C₅₃	—	4	1	no	—
383	C₂×D₄×C₅₃	—	4	4	no	—
384	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
385	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
386	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
387	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
388	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₅₃	—	2	1	no	—
392	C₂²×C₄×C₅₃	—	2	1	no	—
393	C₂²×C₄×C₅₃	—	2	2	no	—
394	C₂²×C₄×C₅₃	—	2	1	no	—
395	C₂²×C₄×C₅₃	—	2	1	no	—
396	C₂²×C₄×C₅₃	—	2	1	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	—	2	1	no	—
401	C₂²×C₄×C₅₃	—	2	1	no	—
402	C₂²×C₄×C₅₃	—	2	2	no	—
403	C₂²×C₄×C₅₃	—	2	2	no	—
404	C₂²×C₄×C₅₃	—	2	1	no	—
405	C₂²×C₄×C₅₃	—	2	1	no	—
406	C₂²×C₄×C₅₃	—	8	2	no	—
407	C₂²×C₄×C₅₃	—	8	2	no	—
408	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
409	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
410	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
412	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
413	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
414	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	Q₁₆×C₅₃	—	4	2	no	—
418	Q₁₆×C₅₃	—	4	2	no	—
419	SD₁₆×C₅₃	—	2	4	no	—
420	SD₁₆×C₅₃	—	2	4	no	—
421	SD₁₆×C₅₃	—	4	2	no	—
422	SD₁₆×C₅₃	—	4	2	no	—
423	SD₁₆×C₅₃	—	4	2	no	—
424	SD₁₆×C₅₃	—	4	2	no	—
425	SD₁₆×C₅₃	—	4	2	no	—
426	D₈×C₅₃	—	2	4	no	—
427	D₈×C₅₃	—	4	2	no	—
428	D₈×C₅₃	—	4	2	no	—
429	M₁₆×C₅₃	—	4	2	no	—
430	C₂×C₈×C₅₃	—	4	2	no	—
431	C₂×C₈×C₅₃	—	4	2	no	—
432	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
433	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
434	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
435	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
436	C₄⋊C₄×C₅₃	—	2	2	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	1	no	—
441	C₄⋊C₄×C₅₃	—	2	1	no	—
442	C₄⋊C₄×C₅₃	—	2	1	no	—
443	C₄⋊C₄×C₅₃	—	2	1	no	—
444	C₄⋊C₄×C₅₃	—	2	2	no	—
445	C₄⋊C₄×C₅₃	—	2	2	no	—
446	C₄⋊C₄×C₅₃	—	2	2	no	—
447	C₄⋊C₄×C₅₃	—	2	1	no	—
448	C₄⋊C₄×C₅₃	—	2	1	no	—
449	C₄⋊C₄×C₅₃	—	2	1	no	—
450	C₄⋊C₄×C₅₃	—	2	1	no	—
451	C₄⋊C₄×C₅₃	—	2	1	no	—
452	C₄⋊C₄×C₅₃	—	2	1	no	—
453	C₄⋊C₄×C₅₃	—	2	1	no	—
454	C₄⋊C₄×C₅₃	—	2	1	no	—
455	C₄⋊C₄×C₅₃	—	2	1	no	—
456	C₄⋊C₄×C₅₃	—	2	2	no	—
457	C₄⋊C₄×C₅₃	—	2	2	no	—
458	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
459	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
460	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
461	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
462	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
463	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
464	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
465	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
466	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
467	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
468	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
479	C₂²⋊C₄×C₅₃	—	2	1	no	—
480	C₂²⋊C₄×C₅₃	—	2	1	no	—
481	C₂²⋊C₄×C₅₃	—	2	1	no	—
482	C₂²⋊C₄×C₅₃	—	2	1	no	—
483	C₂²⋊C₄×C₅₃	—	2	1	no	—
484	C₂²⋊C₄×C₅₃	—	2	1	no	—
485	C₂²⋊C₄×C₅₃	—	2	2	no	—
486	C₂²⋊C₄×C₅₃	—	2	2	no	—
487	C₂²⋊C₄×C₅₃	—	2	1	no	—
488	C₂²⋊C₄×C₅₃	—	2	1	no	—
489	C₂²⋊C₄×C₅₃	—	2	1	no	—
490	C₂²⋊C₄×C₅₃	—	2	1	no	—
491	C₂²⋊C₄×C₅₃	—	2	1	no	—
492	C₂²⋊C₄×C₅₃	—	2	2	no	—
493	C₂²⋊C₄×C₅₃	—	2	2	no	—
494	C₂²⋊C₄×C₅₃	—	2	2	no	—
495	C₂²⋊C₄×C₅₃	—	2	2	no	—
496	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
497	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
498	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
499	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
500	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
501	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
502	C₄²×C₅₃	—	2	1	no	—
503	C₄²×C₅₃	—	2	1	no	—
504	C₄²×C₅₃	—	2	1	no	—
505	C₄²×C₅₃	—	2	2	no	—
506	C₄²×C₅₃	—	2	2	no	—
507	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
508	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
509	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
510	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
511	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
512	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
513	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
514	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
515	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
516	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
517	C₂³×C₅₃	—	2	1	no	—
518	C₂³×C₅₃	—	2	2	no	—
519	C₂³×C₅₃	—	2	1	no	—
520	C₂³×C₅₃	—	2	1	no	—
521	C₂³×C₅₃	—	4	2	no	—
522	C₂³×C₅₃	—	4	2	no	—
523	C₂³×C₅₃	—	4	2	no	—
524	C₂³×C₅₃	—	4	2	no	—
525	C₂³×C₅₃	—	8	1	no	—
526	C₂³×C₅₃	—	8	1	no	—
527	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
528	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
529	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
530	Q₈×C₅₃	—	2	2	no	—
531	Q₈×C₅₃	—	2	2	no	—
532	Q₈×C₅₃	—	2	1	no	—
533	Q₈×C₅₃	—	2	2	no	—
534	Q₈×C₅₃	—	2	2	no	—
535	Q₈×C₅₃	—	2	1	no	—
536	Q₈×C₅₃	—	4	1	no	—
537	Q₈×C₅₃	—	4	2	no	—
538	Q₈×C₅₃	—	8	2	no	—
539	Q₈×C₅₃	—	8	1	no	—
540	D₄×C₅₃	—	2	2	no	—
541	D₄×C₅₃	—	2	2	no	—
542	D₄×C₅₃	—	2	1	no	—
543	D₄×C₅₃	—	2	1	no	—
544	D₄×C₅₃	—	2	2	no	—
545	D₄×C₅₃	—	2	1	no	—
546	D₄×C₅₃	—	2	1	no	—
547	D₄×C₅₃	—	2	1	no	—
548	D₄×C₅₃	—	2	2	no	—
549	D₄×C₅₃	—	4	1	no	—
550	D₄×C₅₃	—	4	2	no	—
551	D₄×C₅₃	—	4	2	no	—
552	D₄×C₅₃	—	4	2	no	—
553	D₄×C₅₃	—	4	2	no	—
554	D₄×C₅₃	—	4	2	no	—
555	D₄×C₅₃	—	4	2	no	—
556	D₄×C₅₃	—	4	2	no	—
557	D₄×C₅₃	—	4	4	no	—
558	D₄×C₅₃	—	4	2	no	—
559	D₄×C₅₃	—	8	1	no	—
560	D₄×C₅₃	—	8	2	no	—
561	D₄×C₅₃	—	8	2	no	—
562	D₄×C₅₃	—	8	1	no	—
563	D₄×C₅₃	—	8	1	no	—
564	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
565	C₂×C₄×C₅₃	—	2	2	no	—
566	C₂×C₄×C₅₃	—	2	2	no	—
567	C₂×C₄×C₅₃	—	2	2	no	—
568	C₂×C₄×C₅₃	—	2	2	no	—
569	C₂×C₄×C₅₃	—	2	1	no	—
570	C₂×C₄×C₅₃	—	2	1	no	—
571	C₂×C₄×C₅₃	—	2	1	no	—
572	C₂×C₄×C₅₃	—	2	1	no	—
573	C₂×C₄×C₅₃	—	2	1	no	—
574	C₂×C₄×C₅₃	—	2	1	no	—
575	C₂×C₄×C₅₃	—	2	1	no	—
576	C₂×C₄×C₅₃	—	2	1	no	—
577	C₂×C₄×C₅₃	—	2	1	no	—
578	C₂×C₄×C₅₃	—	2	2	no	—
579	C₂×C₄×C₅₃	—	2	2	no	—
580	C₂×C₄×C₅₃	—	2	1	no	—
581	C₂×C₄×C₅₃	—	2	2	no	—
582	C₂×C₄×C₅₃	—	2	1	no	—
583	C₂×C₄×C₅₃	—	4	1	no	—
584	C₂×C₄×C₅₃	—	4	1	no	—
585	C₂×C₄×C₅₃	—	4	2	no	—
586	C₂×C₄×C₅₃	—	4	2	no	—
587	C₂×C₄×C₅₃	—	4	4	no	—
588	C₂×C₄×C₅₃	—	4	2	no	—
589	C₂×C₄×C₅₃	—	4	2	no	—
590	C₂×C₄×C₅₃	—	4	2	no	—
591	C₂×C₄×C₅₃	—	8	1	no	—
592	C₂×C₄×C₅₃	—	8	1	no	—
593	C₂×C₄×C₅₃	—	8	1	no	—
594	C₂×C₄×C₅₃	—	8	1	no	—
595	C₂×C₄×C₅₃	—	8	2	no	—
596	C₂×C₄×C₅₃	—	8	2	no	—
597	C₂×C₄×C₅₃	—	8	1	no	—
598	C₂×C₄×C₅₃	—	8	1	no	—
599	C₂×C₄×C₅₃	—	8	2	no	—
600	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
601	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
602	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
603	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
604	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
605	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
606	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
607	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
608	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
609	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
610	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
611	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
612	C₈×C₅₃	—	2	2	no	—
613	C₈×C₅₃	—	2	2	no	—
614	C₈×C₅₃	—	2	2	no	—
615	C₈×C₅₃	—	2	2	no	—
616	#61978	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
617	C₂²×C₅₃	—	2	1	no	—
618	C₂²×C₅₃	—	2	1	no	—
619	C₂²×C₅₃	—	2	1	no	—
620	C₂²×C₅₃	—	2	1	no	—
621	C₂²×C₅₃	—	2	2	no	—
622	C₂²×C₅₃	—	2	1	no	—
623	C₂²×C₅₃	—	2	1	no	—
624	C₂²×C₅₃	—	2	1	no	—
625	C₂²×C₅₃	—	2	1	no	—
626	C₂²×C₅₃	—	4	1	no	—
627	C₂²×C₅₃	—	4	1	no	—
628	C₂²×C₅₃	—	4	2	no	—
629	C₂²×C₅₃	—	4	1	no	—
630	C₂²×C₅₃	—	4	1	no	—
631	C₂²×C₅₃	—	4	2	no	—
632	C₂²×C₅₃	—	4	1	no	—
633	C₂²×C₅₃	—	4	1	no	—
634	C₂²×C₅₃	—	4	1	no	—
635	C₂²×C₅₃	—	4	1	no	—
636	C₂²×C₅₃	—	4	2	no	—
637	C₂²×C₅₃	—	8	4	no	—
638	C₂²×C₅₃	—	8	4	no	—
639	C₂²×C₅₃	#575	1	2	yes	—
640	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
641	C₄×C₅₃	—	2	1	no	—
642	C₄×C₅₃	—	2	1	no	—
643	C₄×C₅₃	—	2	1	no	—
644	C₄×C₅₃	—	2	1	no	—
645	C₄×C₅₃	—	2	1	no	—
646	C₄×C₅₃	—	2	1	no	—
647	C₄×C₅₃	—	2	1	no	—
648	C₄×C₅₃	—	2	1	no	—
649	C₄×C₅₃	—	2	1	no	—
650	C₄×C₅₃	—	2	1	no	—
651	C₄×C₅₃	—	4	1	no	—
652	C₄×C₅₃	—	4	2	no	—
653	C₄×C₅₃	—	4	2	no	—
654	C₄×C₅₃	—	4	1	no	—
655	C₄×C₅₃	—	4	2	no	—
656	C₄×C₅₃	—	4	1	no	—
657	C₄×C₅₃	—	4	1	no	—
658	C₄×C₅₃	—	4	1	no	—
659	C₄×C₅₃	#577	1	2	yes	—
660	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
661	C₄×C₅₃	#585	1	1	yes	characteristic
662	#3511	C₂×C₅₃	1	1	yes	characteristic, complemented
663	#3481	C₂×C₅₃	1	1	yes	characteristic, complemented
664	#3401	C₂×C₅₃	1	2	yes	complemented
665	#3376	C₂×C₅₃	1	2	yes	complemented
666	#3316	C₂×C₅₃	1	2	yes	complemented
667	#3307	C₂×C₅₃	1	2	yes	complemented
668	#3301	C₂×C₅₃	1	2	yes	complemented
669	#3282	C₂×C₅₃	1	2	yes	complemented
670	#3267	C₂×C₅₃	1	2	yes	complemented
671	#3265	C₂×C₅₃	1	2	yes	complemented
672	#3252	C₂×C₅₃	1	1	yes	characteristic, complemented
673	#3247	C₂×C₅₃	1	1	yes	characteristic, complemented
674	#3246	C₂×C₅₃	1	1	yes	characteristic, complemented
675	#3218	C₂×C₅₃	1	1	yes	characteristic, complemented
676	#3214	C₂×C₅₃	1	1	yes	characteristic, complemented
677	#3212	C₂×C₅₃	1	1	yes	characteristic, complemented
678	#3116	C₂×C₅₃	1	1	yes	characteristic, complemented
679	#3109	C₂×C₅₃	1	1	yes	characteristic, complemented
680	#3101	C₂×C₅₃	1	1	yes	characteristic, complemented
681	#3036	C₂×C₅₃	1	1	yes	characteristic, complemented
682	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
683	C₂×#461	C₂×C₅₃	1	1	yes	characteristic, complemented
684	#2990	C₂×C₅₃	1	1	yes	characteristic, complemented
685	C₂×C₅₃	—	2	2	no	—
686	C₂×C₅₃	—	4	1	no	—
687	C₂×C₅₃	—	4	1	no	—
688	C₂×C₅₃	—	4	2	no	—
689	C₂×C₅₃	—	8	2	no	—
690	C₂×C₅₃	—	8	1	no	—
691	C₂×C₅₃	—	8	1	no	—
692	C₂×C₅₃	#3488	1	1	yes	characteristic
693	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
694	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
695	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
696	C₂×#135	C₂²×C₅₃	1	2	yes	—
697	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	—
698	#559	C₂²×C₅₃	1	1	yes	characteristic
699	#556	C₂²×C₅₃	1	2	yes	complemented
700	#555	—	2	1	no	—
701	#554	—	2	1	no	—
702	#554	C₂²×C₅₃	1	1	yes	characteristic
703	#554	C₂²×C₅₃	1	1	yes	characteristic
704	#553	—	2	1	no	—
705	#553	—	2	1	no	—
706	#553	—	2	1	no	—
707	#553	C₂²×C₅₃	1	1	yes	characteristic
708	#553	C₂²×C₅₃	1	1	yes	characteristic
709	#551	—	2	1	no	—
710	#551	—	2	1	no	—
711	#548	C₂²×C₅₃	1	2	yes	—
712	#548	C₂²×C₅₃	1	2	yes	complemented
713	#547	C₂²×C₅₃	1	2	yes	complemented
714	#546	—	2	1	no	—
715	#546	C₂²×C₅₃	1	1	yes	characteristic
716	#546	C₂²×C₅₃	1	1	yes	characteristic
717	D₄²	C₂²×C₅₃	1	1	yes	characteristic
718	#542	—	2	1	no	—
719	#542	—	2	1	no	—
720	#537	—	2	1	no	—
721	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
723	#532	C₂²×C₅₃	1	1	yes	characteristic
724	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
725	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
726	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
727	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
728	#529	—	2	1	no	—
729	#529	C₂²×C₅₃	1	1	yes	characteristic
730	#529	C₂²×C₅₃	1	1	yes	characteristic
731	#525	—	2	1	no	—
732	#525	—	2	1	no	—
733	#520	—	2	1	no	—
734	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
735	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
736	C₂×C₄×D₄	—	2	1	no	—
737	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
738	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
739	#497	C₂²×C₅₃	1	2	yes	complemented
740	#496	C₂²×C₅₃	1	2	yes	—
741	#495	C₂²×C₅₃	1	2	yes	complemented
742	#491	C₂²×C₅₃	1	2	yes	complemented
743	#489	C₂²×C₅₃	1	2	yes	complemented
744	#488	C₂²×C₅₃	1	2	yes	complemented
745	#485	C₂²×C₅₃	1	2	yes	complemented
746	#483	C₂²×C₅₃	1	2	yes	complemented
747	#481	C₂²×C₅₃	1	2	yes	complemented
748	#479	C₂²×C₅₃	1	2	yes	complemented
749	#478	C₂²×C₅₃	1	2	yes	complemented
750	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
751	#476	C₂²×C₅₃	1	1	yes	characteristic
752	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
753	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
754	#475	C₂²×C₅₃	1	2	yes	complemented
755	#470	C₂²×C₅₃	1	2	yes	complemented
756	#468	C₂²×C₅₃	1	2	yes	—
757	#466	C₂²×C₅₃	1	2	yes	—
758	#465	C₂²×C₅₃	1	2	yes	complemented
759	#465	C₂²×C₅₃	1	2	yes	complemented
760	#465	C₂²×C₅₃	1	2	yes	complemented
761	#464	C₂²×C₅₃	1	2	yes	complemented
762	#464	C₂²×C₅₃	1	2	yes	complemented
763	#463	C₂²×C₅₃	1	2	yes	—
764	#463	C₂²×C₅₃	1	2	yes	—
765	#463	C₂²×C₅₃	1	2	yes	complemented
766	#463	C₂²×C₅₃	1	2	yes	complemented
767	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
768	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
769	#461	C₂²×C₅₃	1	1	yes	characteristic
770	#461	C₂²×C₅₃	1	1	yes	characteristic
771	#461	C₂²×C₅₃	1	2	yes	—
772	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
773	#461	C₂²×C₅₃	1	2	yes	complemented
774	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
775	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
776	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
777	#460	C₂²×C₅₃	1	2	yes	—
778	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
779	#459	C₂²×C₅₃	1	1	yes	characteristic
780	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
781	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
782	#452	C₂²×C₅₃	1	2	yes	—
783	#452	C₂²×C₅₃	1	2	yes	complemented
784	#451	C₂²×C₅₃	1	2	yes	complemented
785	#450	C₂²×C₅₃	1	2	yes	—
786	#449	C₂²×C₅₃	1	2	yes	—
787	#449	C₂²×C₅₃	1	2	yes	complemented
788	#449	C₂²×C₅₃	1	2	yes	complemented
789	#448	C₂²×C₅₃	1	2	yes	—
790	#447	C₂²×C₅₃	1	2	yes	—
791	#446	C₂²×C₅₃	1	2	yes	complemented
792	#442	C₂²×C₅₃	1	2	yes	—
793	#442	C₂²×C₅₃	1	2	yes	complemented
794	#441	C₂²×C₅₃	1	2	yes	complemented
795	#440	C₂²×C₅₃	1	2	yes	—
796	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
797	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
798	#435	C₂²×C₅₃	1	2	yes	—
799	#435	C₂²×C₅₃	1	2	yes	complemented
800	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
801	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
802	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
803	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
804	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
805	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
806	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
807	#417	C₂²×C₅₃	1	2	yes	complemented
808	#416	C₂²×C₅₃	1	2	yes	complemented
809	C₂×#103	C₂²×C₅₃	1	2	yes	complemented
810	C₅₃	#61978	1	1	yes	characteristic, direct product factor, Sylow
811	C₂×#41	—	2	1	no	—
812	C₂×#41	—	2	1	no	—
813	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
814	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
815	C₂×#41	C₂³×C₅₃	1	2	yes	—
816	C₂×#41	C₂³×C₅₃	1	2	yes	—
817	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
818	C₂²×D₄	—	2	1	no	—
819	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
820	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
821	C₂³×C₄	—	2	1	no	—
822	C₂³×C₄	—	2	1	no	—
823	AGL(1,ℤ/8)	—	4	4	no	—
824	#135	—	4	4	no	—
825	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
826	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
827	C₂×SD₁₆	—	4	4	no	—
828	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
829	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
830	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
831	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
832	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
833	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
834	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
835	C₂×D₈	C₂³×C₅₃	1	2	yes	—
836	C₂×D₈	C₂³×C₅₃	1	2	yes	—
837	C₂×D₈	C₂³×C₅₃	1	2	yes	—
838	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
839	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
840	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
841	C₄⋊Q₈	—	2	1	no	—
842	C₄⋊Q₈	—	2	1	no	—
843	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
844	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
845	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
846	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
847	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
848	#127	C₂³×C₅₃	1	1	yes	characteristic
849	#127	C₂³×C₅₃	1	1	yes	characteristic
850	#126	—	2	1	no	—
851	#126	—	2	1	no	—
852	#126	—	2	2	no	—
853	#126	—	2	2	no	—
854	#126	—	2	1	no	—
855	#126	—	2	1	no	—
856	#125	—	2	1	no	—
857	#125	—	2	1	no	—
858	#125	—	2	1	no	—
859	#125	C₂³×C₅₃	1	1	yes	characteristic
860	#125	C₂³×C₅₃	1	1	yes	characteristic
861	#124	—	2	1	no	—
862	#124	—	2	2	no	—
863	#124	—	2	2	no	—
864	#124	—	2	1	no	—
865	#124	—	2	1	no	—
866	#124	C₂³×C₅₃	1	1	yes	characteristic
867	#124	C₂³×C₅₃	1	1	yes	characteristic
868	#124	C₂³×C₅₃	1	2	yes	—
869	#124	C₂³×C₅₃	1	2	yes	—
870	#123	—	2	1	no	—
871	#123	—	2	1	no	—
872	#123	—	2	1	no	—
873	#123	—	2	1	no	—
874	#123	—	2	1	no	—
875	#123	—	2	1	no	—
876	#123	—	2	1	no	—
877	#123	—	2	1	no	—
878	#123	—	2	2	no	—
879	#123	—	2	2	no	—
880	C₂²⋊Q₈	—	2	1	no	—
881	C₂²⋊Q₈	—	2	2	no	—
882	C₂²⋊Q₈	—	2	1	no	—
883	C₂²⋊Q₈	—	2	1	no	—
884	C₂²⋊Q₈	—	2	1	no	—
885	C₂²⋊Q₈	—	2	1	no	—
886	C₂²⋊Q₈	—	2	2	no	—
887	C₂²⋊Q₈	—	2	2	no	—
888	C₂²⋊Q₈	—	2	1	no	—
889	C₂²⋊Q₈	—	2	1	no	—
890	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
891	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
892	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
893	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
894	#121	—	2	1	no	—
895	#121	—	2	1	no	—
896	#121	—	2	2	no	—
897	#121	—	2	2	no	—
898	#121	—	2	2	no	—
899	#121	—	2	1	no	—
900	#121	—	2	1	no	—
901	#121	—	2	1	no	—
902	#121	—	2	1	no	—
903	#121	—	2	1	no	—
904	#121	—	2	1	no	—
905	#121	—	2	1	no	—
906	#121	—	2	1	no	—
907	#121	—	2	1	no	—
908	#121	C₂³×C₅₃	1	1	yes	characteristic
909	#121	C₂³×C₅₃	1	1	yes	characteristic
910	#121	C₂³×C₅₃	1	1	yes	characteristic
911	#121	C₂³×C₅₃	1	1	yes	characteristic
912	#121	C₂³×C₅₃	1	2	yes	—
913	#120	—	2	1	no	—
914	#120	—	2	1	no	—
915	#120	—	2	1	no	—
916	#120	—	2	1	no	—
917	C₄×Q₈	—	2	1	no	—
918	C₄×Q₈	—	2	1	no	—
919	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
920	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
921	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
922	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
923	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
924	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
925	C₄×D₄	—	2	1	no	—
926	C₄×D₄	—	2	1	no	—
927	C₄×D₄	—	2	1	no	—
928	C₄×D₄	—	2	1	no	—
929	C₄×D₄	—	2	1	no	—
930	C₄×D₄	—	2	1	no	—
931	C₄×D₄	—	2	1	no	—
932	C₄×D₄	—	2	1	no	—
933	C₄×D₄	—	2	2	no	—
934	C₄×D₄	—	2	2	no	—
935	C₄×D₄	—	2	1	no	—
936	C₄×D₄	—	2	1	no	—
937	C₄×D₄	—	2	1	no	—
938	C₄×D₄	—	2	1	no	—
939	C₄×D₄	—	2	1	no	—
940	C₄×D₄	—	2	1	no	—
941	C₄×D₄	—	2	1	no	—
942	C₄×D₄	—	2	1	no	—
943	C₄×D₄	—	2	1	no	—
944	C₄×D₄	—	2	1	no	—
945	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
946	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
947	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
948	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
949	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
950	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
951	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
952	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
953	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
954	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
955	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
956	C₄×D₄	C₂³×C₅₃	1	2	yes	—
957	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
958	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
959	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
960	#117	—	2	1	no	—
961	#117	—	2	1	no	—
962	#117	—	2	2	no	—
963	#117	—	2	1	no	—
964	#117	—	2	1	no	—
965	#117	—	2	1	no	—
966	#117	D₄×C₅₃	1	1	yes	characteristic
967	#117	D₄×C₅₃	1	1	yes	characteristic
968	#117	D₄×C₅₃	1	1	yes	characteristic
969	#117	C₂³×C₅₃	1	1	yes	characteristic
970	C₂×C₄⋊C₄	—	2	1	no	—
971	C₂×C₄⋊C₄	—	2	1	no	—
972	C₂×C₄⋊C₄	—	2	1	no	—
973	C₂×C₄⋊C₄	—	2	2	no	—
974	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
975	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
976	C₂×C₂²⋊C₄	—	2	1	no	—
977	C₂×C₂²⋊C₄	—	2	1	no	—
978	C₂×C₂²⋊C₄	—	2	1	no	—
979	C₂×C₂²⋊C₄	—	2	1	no	—
980	C₂×C₄²	—	2	1	no	—
981	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
982	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
983	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
984	#107	C₂³×C₅₃	1	2	yes	—
985	#106	C₂³×C₅₃	1	2	yes	—
986	#106	C₂³×C₅₃	1	2	yes	—
987	#106	C₂³×C₅₃	1	2	yes	—
988	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
989	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
990	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
991	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
992	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
993	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
994	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
995	#103	C₂³×C₅₃	1	2	yes	—
996	#103	C₂³×C₅₃	1	2	yes	—
997	#103	C₂³×C₅₃	1	2	yes	—
998	#103	C₂³×C₅₃	1	2	yes	—
999	#103	C₂³×C₅₃	1	2	yes	—
1000	#103	C₂³×C₅₃	1	2	yes	—
1001	#103	C₂³×C₅₃	1	2	yes	—
1002	#103	C₂³×C₅₃	1	2	yes	—
1003	#103	C₂³×C₅₃	1	2	yes	—
1004	#102	C₂³×C₅₃	1	2	yes	—
1005	#102	C₂³×C₅₃	1	2	yes	—
1006	#102	C₂³×C₅₃	1	2	yes	—
1007	#102	C₂³×C₅₃	1	2	yes	—
1008	#102	C₂³×C₅₃	1	2	yes	—
1009	#102	C₂³×C₅₃	1	2	yes	—
1010	#102	C₂³×C₅₃	1	2	yes	—
1011	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1012	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1013	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1014	#97	C₂³×C₅₃	1	2	yes	—
1015	#97	C₂³×C₅₃	1	2	yes	—
1016	C₄×C₈	C₂³×C₅₃	1	2	yes	—
1017	C₂⁴	—	2	1	no	—
1018	C₂⁴	—	2	1	no	—
1019	#41	—	2	2	no	—
1020	#41	—	4	2	no	—
1021	#41	—	4	1	no	—
1022	#41	—	4	4	no	—
1023	#41	—	4	2	no	—
1024	#41	—	4	2	no	—
1025	#41	—	4	2	no	—
1026	#41	—	4	2	no	—
1027	#41	—	8	2	no	—
1028	C₂×Q₈	—	2	1	no	—
1029	C₂×Q₈	—	2	1	no	—
1030	C₂×Q₈	—	2	2	no	—
1031	C₂×Q₈	—	4	2	no	—
1032	C₂×Q₈	—	4	2	no	—
1033	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1034	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1035	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1036	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1037	C₂×D₄	—	2	2	no	—
1038	C₂×D₄	—	2	2	no	—
1039	C₂×D₄	—	2	1	no	—
1040	C₂×D₄	—	2	1	no	—
1041	C₂×D₄	—	2	1	no	—
1042	C₂×D₄	—	2	2	no	—
1043	C₂×D₄	—	2	1	no	—
1044	C₂×D₄	—	2	1	no	—
1045	C₂×D₄	—	2	2	no	—
1046	C₂×D₄	—	2	2	no	—
1047	C₂×D₄	—	2	1	no	—
1048	C₂×D₄	—	2	1	no	—
1049	C₂×D₄	—	2	1	no	—
1050	C₂×D₄	—	2	1	no	—
1051	C₂×D₄	—	2	1	no	—
1052	C₂×D₄	—	2	1	no	—
1053	C₂×D₄	—	4	1	no	—
1054	C₂×D₄	—	4	1	no	—
1055	C₂×D₄	—	4	4	no	—
1056	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1057	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1058	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1059	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1060	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1061	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1062	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1063	C₂²×C₄	—	2	1	no	—
1064	C₂²×C₄	—	2	1	no	—
1065	C₂²×C₄	—	2	2	no	—
1066	C₂²×C₄	—	2	1	no	—
1067	C₂²×C₄	—	2	1	no	—
1068	C₂²×C₄	—	2	1	no	—
1069	C₂²×C₄	—	2	2	no	—
1070	C₂²×C₄	—	2	1	no	—
1071	C₂²×C₄	—	2	1	no	—
1072	C₂²×C₄	—	2	1	no	—
1073	C₂²×C₄	—	2	1	no	—
1074	C₂²×C₄	—	2	2	no	—
1075	C₂²×C₄	—	2	2	no	—
1076	C₂²×C₄	—	2	1	no	—
1077	C₂²×C₄	—	2	1	no	—
1078	C₂²×C₄	—	8	2	no	—
1079	C₂²×C₄	—	8	2	no	—
1080	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1081	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1082	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1083	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1084	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1085	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1086	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1087	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1088	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1089	Q₁₆	—	4	2	no	—
1090	Q₁₆	—	4	2	no	—
1091	SD₁₆	—	2	4	no	—
1092	SD₁₆	—	2	4	no	—
1093	SD₁₆	—	4	2	no	—
1094	SD₁₆	—	4	2	no	—
1095	SD₁₆	—	4	2	no	—
1096	SD₁₆	—	4	2	no	—
1097	SD₁₆	—	4	2	no	—
1098	D₈	—	2	4	no	—
1099	D₈	—	4	2	no	—
1100	D₈	—	4	2	no	—
1101	M₁₆	—	4	2	no	—
1102	C₂×C₈	—	4	2	no	—
1103	C₂×C₈	—	4	2	no	—
1104	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1105	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1106	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1107	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1108	C₄⋊C₄	—	2	2	no	—
1109	C₄⋊C₄	—	2	1	no	—
1110	C₄⋊C₄	—	2	1	no	—
1111	C₄⋊C₄	—	2	1	no	—
1112	C₄⋊C₄	—	2	1	no	—
1113	C₄⋊C₄	—	2	1	no	—
1114	C₄⋊C₄	—	2	1	no	—
1115	C₄⋊C₄	—	2	1	no	—
1116	C₄⋊C₄	—	2	2	no	—
1117	C₄⋊C₄	—	2	2	no	—
1118	C₄⋊C₄	—	2	2	no	—
1119	C₄⋊C₄	—	2	1	no	—
1120	C₄⋊C₄	—	2	1	no	—
1121	C₄⋊C₄	—	2	1	no	—
1122	C₄⋊C₄	—	2	1	no	—
1123	C₄⋊C₄	—	2	1	no	—
1124	C₄⋊C₄	—	2	1	no	—
1125	C₄⋊C₄	—	2	1	no	—
1126	C₄⋊C₄	—	2	1	no	—
1127	C₄⋊C₄	—	2	1	no	—
1128	C₄⋊C₄	—	2	2	no	—
1129	C₄⋊C₄	—	2	2	no	—
1130	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1131	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1132	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1133	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1134	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1135	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1136	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1137	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1138	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1139	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1140	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1141	C₂²⋊C₄	—	2	1	no	—
1142	C₂²⋊C₄	—	2	1	no	—
1143	C₂²⋊C₄	—	2	2	no	—
1144	C₂²⋊C₄	—	2	2	no	—
1145	C₂²⋊C₄	—	2	1	no	—
1146	C₂²⋊C₄	—	2	1	no	—
1147	C₂²⋊C₄	—	2	1	no	—
1148	C₂²⋊C₄	—	2	1	no	—
1149	C₂²⋊C₄	—	2	1	no	—
1150	C₂²⋊C₄	—	2	1	no	—
1151	C₂²⋊C₄	—	2	1	no	—
1152	C₂²⋊C₄	—	2	1	no	—
1153	C₂²⋊C₄	—	2	1	no	—
1154	C₂²⋊C₄	—	2	1	no	—
1155	C₂²⋊C₄	—	2	1	no	—
1156	C₂²⋊C₄	—	2	1	no	—
1157	C₂²⋊C₄	—	2	2	no	—
1158	C₂²⋊C₄	—	2	2	no	—
1159	C₂²⋊C₄	—	2	1	no	—
1160	C₂²⋊C₄	—	2	1	no	—
1161	C₂²⋊C₄	—	2	1	no	—
1162	C₂²⋊C₄	—	2	1	no	—
1163	C₂²⋊C₄	—	2	1	no	—
1164	C₂²⋊C₄	—	2	2	no	—
1165	C₂²⋊C₄	—	2	2	no	—
1166	C₂²⋊C₄	—	2	2	no	—
1167	C₂²⋊C₄	—	2	2	no	—
1168	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1169	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1170	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1171	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1172	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1173	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1174	C₄²	—	2	1	no	—
1175	C₄²	—	2	1	no	—
1176	C₄²	—	2	1	no	—
1177	C₄²	—	2	2	no	—
1178	C₄²	—	2	2	no	—
1179	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1180	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1181	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1182	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1183	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1184	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1185	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1186	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1187	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1188	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1189	C₂³	—	2	1	no	—
1190	C₂³	—	2	2	no	—
1191	C₂³	—	2	1	no	—
1192	C₂³	—	2	1	no	—
1193	C₂³	—	4	2	no	—
1194	C₂³	—	4	2	no	—
1195	C₂³	—	4	2	no	—
1196	C₂³	—	4	2	no	—
1197	C₂³	—	8	1	no	—
1198	C₂³	—	8	1	no	—
1199	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1200	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1201	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1202	Q₈	—	2	2	no	—
1203	Q₈	—	2	2	no	—
1204	Q₈	—	2	1	no	—
1205	Q₈	—	2	2	no	—
1206	Q₈	—	2	1	no	—
1207	Q₈	—	2	2	no	—
1208	Q₈	—	4	1	no	—
1209	Q₈	—	4	2	no	—
1210	Q₈	—	8	2	no	—
1211	Q₈	—	8	1	no	—
1212	D₄	—	2	2	no	—
1213	D₄	—	2	2	no	—
1214	D₄	—	2	2	no	—
1215	D₄	—	2	1	no	—
1216	D₄	—	2	1	no	—
1217	D₄	—	2	1	no	—
1218	D₄	—	2	1	no	—
1219	D₄	—	2	2	no	—
1220	D₄	—	2	1	no	—
1221	D₄	—	4	1	no	—
1222	D₄	—	4	2	no	—
1223	D₄	—	4	2	no	—
1224	D₄	—	4	2	no	—
1225	D₄	—	4	2	no	—
1226	D₄	—	4	2	no	—
1227	D₄	—	4	2	no	—
1228	D₄	—	4	2	no	—
1229	D₄	—	4	4	no	—
1230	D₄	—	4	2	no	—
1231	D₄	—	8	1	no	—
1232	D₄	—	8	2	no	—
1233	D₄	—	8	2	no	—
1234	D₄	—	8	1	no	—
1235	D₄	—	8	1	no	—
1236	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1237	C₂×C₄	—	2	2	no	—
1238	C₂×C₄	—	2	2	no	—
1239	C₂×C₄	—	2	2	no	—
1240	C₂×C₄	—	2	2	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	1	no	—
1249	C₂×C₄	—	2	2	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	2	no	—
1252	C₂×C₄	—	2	2	no	—
1253	C₂×C₄	—	2	1	no	—
1254	C₂×C₄	—	2	1	no	—
1255	C₂×C₄	—	4	1	no	—
1256	C₂×C₄	—	4	1	no	—
1257	C₂×C₄	—	4	2	no	—
1258	C₂×C₄	—	4	2	no	—
1259	C₂×C₄	—	4	4	no	—
1260	C₂×C₄	—	4	2	no	—
1261	C₂×C₄	—	4	2	no	—
1262	C₂×C₄	—	4	2	no	—
1263	C₂×C₄	—	8	1	no	—
1264	C₂×C₄	—	8	1	no	—
1265	C₂×C₄	—	8	1	no	—
1266	C₂×C₄	—	8	1	no	—
1267	C₂×C₄	—	8	2	no	—
1268	C₂×C₄	—	8	2	no	—
1269	C₂×C₄	—	8	1	no	—
1270	C₂×C₄	—	8	1	no	—
1271	C₂×C₄	—	8	2	no	—
1272	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1273	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1274	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1275	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1276	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1277	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1278	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1279	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1280	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1281	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1282	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1283	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1284	C₈	—	2	2	no	—
1285	C₈	—	2	2	no	—
1286	C₈	—	2	2	no	—
1287	C₈	—	2	2	no	—
1288	C₂²	—	2	1	no	—
1289	C₂²	—	2	1	no	—
1290	C₂²	—	2	1	no	—
1291	C₂²	—	2	1	no	—
1292	C₂²	—	2	2	no	—
1293	C₂²	—	2	1	no	—
1294	C₂²	—	2	1	no	—
1295	C₂²	—	2	1	no	—
1296	C₂²	—	2	1	no	—
1297	C₂²	—	4	1	no	—
1298	C₂²	—	4	1	no	—
1299	C₂²	—	4	2	no	—
1300	C₂²	—	4	1	no	—
1301	C₂²	—	4	1	no	—
1302	C₂²	—	4	2	no	—
1303	C₂²	—	4	1	no	—
1304	C₂²	—	4	1	no	—
1305	C₂²	—	4	1	no	—
1306	C₂²	—	4	1	no	—
1307	C₂²	—	4	2	no	—
1308	C₂²	—	8	4	no	—
1309	C₂²	—	8	4	no	—
1310	C₂²	C₅₃×#575	1	2	yes	—
1311	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1312	C₄	—	2	1	no	—
1313	C₄	—	2	1	no	—
1314	C₄	—	2	1	no	—
1315	C₄	—	2	1	no	—
1316	C₄	—	2	1	no	—
1317	C₄	—	2	1	no	—
1318	C₄	—	2	1	no	—
1319	C₄	—	2	1	no	—
1320	C₄	—	2	1	no	—
1321	C₄	—	2	1	no	—
1322	C₄	—	4	1	no	—
1323	C₄	—	4	2	no	—
1324	C₄	—	4	2	no	—
1325	C₄	—	4	1	no	—
1326	C₄	—	4	2	no	—
1327	C₄	—	4	1	no	—
1328	C₄	—	4	1	no	—
1329	C₄	—	4	1	no	—
1330	C₄	C₅₃×#577	1	2	yes	—
1331	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1332	C₄	C₅₃×#585	1	1	yes	characteristic
1333	C₂	—	2	2	no	—
1334	C₂	—	4	1	no	—
1335	C₂	—	4	1	no	—
1336	C₂	—	4	2	no	—
1337	C₂	—	8	1	no	—
1338	C₂	—	8	1	no	—
1339	C₂	—	8	2	no	—
1340	C₂	C₅₃×#3488	1	1	yes	characteristic
1341	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1342	C₂	C₂×C₅₃×#577	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×#3401	C₂	semidirect
4. C₅₃×#3376	C₂	semidirect
5. C₅₃×#3316	C₂	semidirect
6. C₅₃×#3307	C₂	semidirect
7. C₅₃×#3301	C₂	semidirect
8. C₅₃×#3282	C₂	semidirect
9. C₅₃×#3267	C₂	semidirect
10. C₅₃×#3265	C₂	semidirect
11. C₅₃×#3252	C₂	semidirect
12. C₅₃×#3247	C₂	semidirect
13. C₅₃×#3246	C₂	semidirect
14. C₅₃×#3218	C₂	semidirect
15. C₅₃×#3214	C₂	semidirect
16. C₅₃×#3212	C₂	semidirect
17. C₅₃×#3116	C₂	semidirect
18. C₅₃×#3109	C₂	semidirect
19. C₅₃×#3101	C₂	semidirect
20. C₅₃×#3036	C₂	semidirect
21. C₅₃×#3035	C₂	semidirect
22. C₂×C₅₃×#461	C₂	semidirect
23. C₅₃×#2990	C₂	semidirect
28. C₅₃×#556	C₂²	semidirect
41. C₅₃×#548	C₂²	semidirect
42. C₅₃×#547	C₂²	semidirect
50. C₅₃×#533	C₂²	semidirect
51. C₅₃×#533	C₂²	semidirect
53. C₅₃×#532	C₂²	semidirect
54. C₅₃×#532	C₂²	semidirect
55. C₅₃×#532	C₂²	semidirect
56. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
68. C₅₃×#497	C₂²	semidirect
70. C₅₃×#495	C₂²	semidirect
71. C₅₃×#491	C₂²	semidirect
72. C₅₃×#489	C₂²	semidirect
73. C₅₃×#488	C₂²	semidirect
74. C₅₃×#485	C₂²	semidirect
75. C₅₃×#483	C₂²	semidirect
76. C₅₃×#481	C₂²	semidirect
77. C₅₃×#479	C₂²	semidirect
78. C₅₃×#478	C₂²	semidirect
79. C₅₃×#477	C₂²	semidirect
81. C₅₃×#476	C₂²	semidirect
82. C₅₃×#476	C₂²	semidirect
83. C₅₃×#475	C₂²	semidirect
84. C₅₃×#470	C₂²	semidirect
87. C₅₃×#465	C₂²	semidirect
88. C₅₃×#465	C₂²	semidirect
89. C₅₃×#465	C₂²	semidirect
90. C₅₃×#464	C₂²	semidirect
91. C₅₃×#464	C₂²	semidirect
94. C₅₃×#463	C₂²	semidirect
95. C₅₃×#463	C₂²	semidirect
96. C₅₃×#462	C₂²	semidirect
97. C₅₃×#462	C₂²	semidirect
101. C₅₃×#461	C₂²	semidirect
102. C₅₃×#461	C₂²	semidirect
103. C₅₃×#461	C₂²	semidirect
104. C₅₃×#461	C₂²	semidirect
105. C₅₃×#461	C₂²	semidirect
107. C₅₃×#460	C₂²	semidirect
109. C₅₃×#459	C₂²	semidirect
110. C₅₃×#459	C₂²	semidirect
112. C₅₃×#452	C₂²	semidirect
113. C₅₃×#451	C₂²	semidirect
116. C₅₃×#449	C₂²	semidirect
117. C₅₃×#449	C₂²	semidirect
120. C₅₃×#446	C₂²	semidirect
122. C₅₃×#442	C₂²	semidirect
123. C₅₃×#441	C₂²	semidirect
126. C₄×SD₁₆×C₅₃	C₂²	semidirect
128. C₅₃×#435	C₂²	semidirect
129. C₈×D₄×C₅₃	C₂²	semidirect
130. C₅₃×#432	C₂²	semidirect
131. C₅₃×#432	C₂²	semidirect
132. C₅₃×#431	C₂²	semidirect
133. C₅₃×#423	C₂²	semidirect
134. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
135. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
136. C₅₃×#417	C₂²	semidirect
137. C₅₃×#416	C₂²	semidirect
138. C₂×#103×C₅₃	C₂²	semidirect
616. #61978	C₅₃	direct (N × H)
662. #3511	C₂×C₅₃	semidirect
663. #3481	C₂×C₅₃	semidirect
664. #3401	C₂×C₅₃	semidirect
665. #3376	C₂×C₅₃	semidirect
666. #3316	C₂×C₅₃	semidirect
667. #3307	C₂×C₅₃	semidirect
668. #3301	C₂×C₅₃	semidirect
669. #3282	C₂×C₅₃	semidirect
670. #3267	C₂×C₅₃	semidirect
671. #3265	C₂×C₅₃	semidirect
672. #3252	C₂×C₅₃	semidirect
673. #3247	C₂×C₅₃	semidirect
674. #3246	C₂×C₅₃	semidirect
675. #3218	C₂×C₅₃	semidirect
676. #3214	C₂×C₅₃	semidirect
677. #3212	C₂×C₅₃	semidirect
678. #3116	C₂×C₅₃	semidirect
679. #3109	C₂×C₅₃	semidirect
680. #3101	C₂×C₅₃	semidirect
681. #3036	C₂×C₅₃	semidirect
682. #3035	C₂×C₅₃	semidirect
683. C₂×#461	C₂×C₅₃	semidirect
684. #2990	C₂×C₅₃	semidirect
699. #556	C₂²×C₅₃	semidirect
712. #548	C₂²×C₅₃	semidirect
713. #547	C₂²×C₅₃	semidirect
721. #533	C₂²×C₅₃	semidirect
722. #533	C₂²×C₅₃	semidirect
724. #532	C₂²×C₅₃	semidirect
725. #532	C₂²×C₅₃	semidirect
726. #532	C₂²×C₅₃	semidirect
727. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
739. #497	C₂²×C₅₃	semidirect
741. #495	C₂²×C₅₃	semidirect
742. #491	C₂²×C₅₃	semidirect
743. #489	C₂²×C₅₃	semidirect
744. #488	C₂²×C₅₃	semidirect
745. #485	C₂²×C₅₃	semidirect
746. #483	C₂²×C₅₃	semidirect
747. #481	C₂²×C₅₃	semidirect
748. #479	C₂²×C₅₃	semidirect
749. #478	C₂²×C₅₃	semidirect
750. #477	C₂²×C₅₃	semidirect
752. #476	C₂²×C₅₃	semidirect
753. #476	C₂²×C₅₃	semidirect
754. #475	C₂²×C₅₃	semidirect
755. #470	C₂²×C₅₃	semidirect
758. #465	C₂²×C₅₃	semidirect
759. #465	C₂²×C₅₃	semidirect
760. #465	C₂²×C₅₃	semidirect
761. #464	C₂²×C₅₃	semidirect
762. #464	C₂²×C₅₃	semidirect
765. #463	C₂²×C₅₃	semidirect
766. #463	C₂²×C₅₃	semidirect
767. #462	C₂²×C₅₃	semidirect
768. #462	C₂²×C₅₃	semidirect
772. #461	C₂²×C₅₃	semidirect
773. #461	C₂²×C₅₃	semidirect
774. #461	C₂²×C₅₃	semidirect
775. #461	C₂²×C₅₃	semidirect
776. #461	C₂²×C₅₃	semidirect
778. #460	C₂²×C₅₃	semidirect
780. #459	C₂²×C₅₃	semidirect
781. #459	C₂²×C₅₃	semidirect
783. #452	C₂²×C₅₃	semidirect
784. #451	C₂²×C₅₃	semidirect
787. #449	C₂²×C₅₃	semidirect
788. #449	C₂²×C₅₃	semidirect
791. #446	C₂²×C₅₃	semidirect
793. #442	C₂²×C₅₃	semidirect
794. #441	C₂²×C₅₃	semidirect
797. C₄×SD₁₆	C₂²×C₅₃	semidirect
799. #435	C₂²×C₅₃	semidirect
800. C₈×D₄	C₂²×C₅₃	semidirect
801. #432	C₂²×C₅₃	semidirect
802. #432	C₂²×C₅₃	semidirect
803. #431	C₂²×C₅₃	semidirect
804. #423	C₂²×C₅₃	semidirect
805. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
806. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
807. #417	C₂²×C₅₃	semidirect
808. #416	C₂²×C₅₃	semidirect
809. C₂×#103	C₂²×C₅₃	semidirect
810. C₅₃	#61978	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×#3401	2
C₅₃×#3376	2
C₅₃×#3316	2
C₅₃×#3307	2
C₅₃×#3301	2
C₅₃×#3282	2
C₅₃×#3267	2
C₅₃×#3265	2
C₅₃×#3252	2
C₅₃×#3247	2
C₅₃×#3246	2
C₅₃×#3218	2
C₅₃×#3214	2
C₅₃×#3212	2
C₅₃×#3116	2
C₅₃×#3109	2
C₅₃×#3101	2
C₅₃×#3036	2
C₅₃×#3035	2
C₂×C₅₃×#461	2
C₅₃×#2990	2
#61978	53

Subgroups — C53×#61978 #27269490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61978 #27269490