Subgroups — C₅₃×#61872 #27269384

Order 13568.

1722 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3389	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3388	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3384	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3384	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3373	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3370	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3370	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3366	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3244	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3241	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3122	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3118	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#562	—	2	2	no	—
21	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
22	C₅₃×#559	C₂²	1	2	yes	complemented
23	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
24	C₅₃×#554	—	2	1	no	—
25	C₅₃×#554	—	2	2	no	—
26	C₅₃×#554	C₂²	1	2	yes	—
27	C₅₃×#554	C₂²	1	2	yes	—
28	C₅₃×#554	C₂²	1	2	yes	—
29	C₅₃×#554	C₂²	1	2	yes	complemented
30	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
31	D₄×Q₈×C₅₃	—	2	1	no	—
32	D₄×Q₈×C₅₃	C₂²	1	2	yes	—
33	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₅₃×#548	—	2	1	no	—
35	C₅₃×#547	—	2	1	no	—
36	C₅₃×#544	C₂²	1	2	yes	—
37	C₅₃×#543	—	2	1	no	—
38	C₅₃×#543	—	2	1	no	—
39	C₅₃×#542	—	2	1	no	—
40	C₅₃×#542	C₂²	1	2	yes	—
41	C₅₃×#540	C₂²	1	2	yes	—
42	C₅₃×#539	—	2	2	no	—
43	C₅₃×#536	—	2	1	no	—
44	C₅₃×#533	C₂²	1	1	yes	characteristic
45	C₅₃×#533	C₂²	1	1	yes	characteristic
46	C₅₃×#532	C₂²	1	1	yes	characteristic
47	C₅₃×#529	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊Q₈×C₅₃	—	2	2	no	—
49	C₅₃×#518	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#501	C₂²	1	2	yes	complemented
52	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#501	C₂²	1	2	yes	complemented
55	C₅₃×#501	C₂²	1	2	yes	complemented
56	C₅₃×#499	C₂²	1	2	yes	complemented
57	C₅₃×#498	C₂²	1	2	yes	complemented
58	C₅₃×#490	C₂²	1	2	yes	complemented
59	C₅₃×#490	C₂²	1	2	yes	complemented
60	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#489	C₂²	1	2	yes	complemented
63	C₅₃×#488	C₂²	1	2	yes	complemented
64	C₅₃×#486	C₂²	1	2	yes	complemented
65	C₅₃×#485	C₂²	1	2	yes	—
66	C₅₃×#483	C₂²	1	1	yes	characteristic
67	C₅₃×#482	C₂²	1	2	yes	—
68	C₅₃×#482	C₂²	1	2	yes	—
69	C₅₃×#482	C₂²	1	2	yes	—
70	C₅₃×#481	C₂²	1	2	yes	—
71	C₅₃×#480	C₂²	1	1	yes	characteristic
72	C₅₃×#479	C₂²	1	2	yes	complemented
73	C₅₃×#479	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	2	yes	—
75	C₅₃×#478	C₂²	1	2	yes	—
76	C₅₃×#478	C₂²	1	2	yes	—
77	C₅₃×#478	C₂²	1	2	yes	complemented
78	C₅₃×#478	C₂²	1	2	yes	complemented
79	C₅₃×#478	C₂²	1	2	yes	complemented
80	C₅₃×#478	C₂²	1	2	yes	complemented
81	C₅₃×#476	C₂²	1	2	yes	—
82	C₅₃×#476	C₂²	1	2	yes	—
83	C₅₃×#476	C₂²	1	2	yes	complemented
84	C₅₃×#476	C₂²	1	2	yes	complemented
85	C₅₃×#476	C₂²	1	2	yes	complemented
86	C₅₃×#475	C₂²	1	2	yes	complemented
87	C₅₃×#474	C₂²	1	2	yes	—
88	C₅₃×#474	C₂²	1	2	yes	complemented
89	C₅₃×#474	C₂²	1	2	yes	complemented
90	C₅₃×#463	C₂²	1	2	yes	—
91	C₅₃×#463	C₂²	1	2	yes	—
92	C₅₃×#463	C₂²	1	2	yes	—
93	C₅₃×#459	C₂²	1	2	yes	—
94	C₅₃×#459	C₂²	1	2	yes	—
95	C₅₃×#459	C₂²	1	2	yes	—
96	C₅₃×#450	C₂²	1	1	yes	characteristic
97	C₅₃×#447	C₂²	1	2	yes	—
98	C₅₃×#447	C₂²	1	1	yes	characteristic
99	C₅₃×#446	C₂²	1	2	yes	complemented
100	C₅₃×#446	C₂²	1	2	yes	complemented
101	C₅₃×#446	C₂²	1	2	yes	complemented
102	C₅₃×#446	C₂²	1	2	yes	complemented
103	C₅₃×#442	C₂²	1	2	yes	—
104	C₅₃×#442	C₂²	1	2	yes	—
105	C₅₃×#442	C₂²	1	2	yes	—
106	C₅₃×#442	C₂²	1	2	yes	—
107	C₅₃×#442	C₂²	1	2	yes	—
108	C₅₃×#442	C₂²	1	2	yes	—
109	C₅₃×#440	C₂²	1	2	yes	—
110	C₅₃×#440	C₂²	1	2	yes	—
111	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
112	C₄×D₈×C₅₃	C₂²	1	2	yes	—
113	C₄×D₈×C₅₃	C₂²	1	2	yes	—
114	C₄×D₈×C₅₃	C₂²	1	2	yes	—
115	C₅₃×#433	C₂²	1	2	yes	—
116	C₅₃×#433	C₂²	1	2	yes	—
117	C₅₃×#432	C₂²	1	1	yes	characteristic
118	C₅₃×#432	C₂²	1	1	yes	characteristic
119	C₂×#41×C₅₃	—	2	1	no	—
120	C₂×#41×C₅₃	—	2	1	no	—
121	C₂²×Q₈×C₅₃	—	2	2	no	—
122	C₂²×Q₈×C₅₃	—	2	1	no	—
123	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₅₃	—	2	1	no	—
125	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
126	C₂×D₈×C₅₃	C₂³	1	2	yes	—
127	C₂×D₈×C₅₃	C₂³	1	2	yes	—
128	C₂×D₈×C₅₃	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₅₃	—	2	2	no	—
130	C₄⋊Q₈×C₅₃	—	2	1	no	—
131	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
132	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
133	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
137	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
138	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
139	#127×C₅₃	C₂³	1	2	yes	—
140	#127×C₅₃	C₂³	1	1	yes	characteristic
141	#126×C₅₃	—	2	2	no	—
142	#126×C₅₃	—	2	1	no	—
143	#125×C₅₃	—	2	2	no	—
144	#125×C₅₃	—	2	2	no	—
145	#125×C₅₃	D₄	1	2	yes	—
146	#125×C₅₃	C₂³	1	2	yes	—
147	#125×C₅₃	C₂³	1	2	yes	—
148	#125×C₅₃	C₂³	1	2	yes	—
149	#125×C₅₃	C₂³	1	2	yes	—
150	#125×C₅₃	C₂³	1	1	yes	characteristic
151	#124×C₅₃	—	2	2	no	—
152	#124×C₅₃	—	2	1	no	—
153	#124×C₅₃	—	2	1	no	—
154	#124×C₅₃	—	2	2	no	—
155	#124×C₅₃	C₂³	1	2	yes	—
156	#124×C₅₃	C₂³	1	1	yes	characteristic
157	#123×C₅₃	—	2	2	no	—
158	#123×C₅₃	—	2	2	no	—
159	#123×C₅₃	—	2	2	no	—
160	#123×C₅₃	—	2	2	no	—
161	#123×C₅₃	—	2	2	no	—
162	#123×C₅₃	—	2	2	no	—
163	#123×C₅₃	—	2	1	no	—
164	C₂²⋊Q₈×C₅₃	—	2	2	no	—
165	C₂²⋊Q₈×C₅₃	—	2	2	no	—
166	C₂²⋊Q₈×C₅₃	—	2	2	no	—
167	C₂²⋊Q₈×C₅₃	—	2	2	no	—
168	C₂²⋊Q₈×C₅₃	—	2	2	no	—
169	C₂²⋊Q₈×C₅₃	—	2	2	no	—
170	C₂²⋊Q₈×C₅₃	—	2	2	no	—
171	C₂²⋊Q₈×C₅₃	—	2	1	no	—
172	C₂²⋊Q₈×C₅₃	—	2	2	no	—
173	C₂²⋊Q₈×C₅₃	—	2	2	no	—
174	C₂²⋊Q₈×C₅₃	—	2	2	no	—
175	C₂²⋊Q₈×C₅₃	—	2	2	no	—
176	C₂²⋊Q₈×C₅₃	—	2	2	no	—
177	C₂²⋊Q₈×C₅₃	—	2	2	no	—
178	C₂²⋊Q₈×C₅₃	—	2	2	no	—
179	C₂²⋊Q₈×C₅₃	—	2	2	no	—
180	C₂²⋊Q₈×C₅₃	—	2	2	no	—
181	C₂²⋊Q₈×C₅₃	—	2	2	no	—
182	C₂²⋊Q₈×C₅₃	—	2	2	no	—
183	C₂²⋊Q₈×C₅₃	—	2	2	no	—
184	C₂²⋊Q₈×C₅₃	—	2	1	no	—
185	C₂²⋊Q₈×C₅₃	—	2	1	no	—
186	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
187	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
188	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
189	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
190	#121×C₅₃	—	2	2	no	—
191	#121×C₅₃	—	2	1	no	—
192	#121×C₅₃	—	2	2	no	—
193	#121×C₅₃	—	2	2	no	—
194	#121×C₅₃	—	2	1	no	—
195	#121×C₅₃	C₂³	1	1	yes	characteristic
196	#121×C₅₃	C₂³	1	2	yes	—
197	C₄×Q₈×C₅₃	—	2	1	no	—
198	C₄×Q₈×C₅₃	—	2	1	no	—
199	C₄×Q₈×C₅₃	—	2	1	no	—
200	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
201	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
202	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
203	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
204	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
205	C₄×D₄×C₅₃	—	2	2	no	—
206	C₄×D₄×C₅₃	—	2	2	no	—
207	C₄×D₄×C₅₃	—	2	2	no	—
208	C₄×D₄×C₅₃	—	2	1	no	—
209	C₄×D₄×C₅₃	—	2	1	no	—
210	C₄×D₄×C₅₃	—	2	1	no	—
211	C₄×D₄×C₅₃	—	2	1	no	—
212	C₄×D₄×C₅₃	—	2	1	no	—
213	C₄×D₄×C₅₃	C₂³	1	2	yes	—
214	C₄×D₄×C₅₃	C₂³	1	2	yes	—
215	C₄×D₄×C₅₃	C₂³	1	2	yes	—
216	C₄×D₄×C₅₃	C₂³	1	2	yes	—
217	C₄×D₄×C₅₃	C₂³	1	2	yes	—
218	C₄×D₄×C₅₃	C₂³	1	2	yes	—
219	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₅₃	C₂³	1	2	yes	—
221	C₄×D₄×C₅₃	C₂³	1	2	yes	—
222	C₄×D₄×C₅₃	C₂³	1	2	yes	—
223	C₄×D₄×C₅₃	C₂³	1	2	yes	—
224	#117×C₅₃	—	2	1	no	—
225	#117×C₅₃	C₂³	1	2	yes	—
226	#117×C₅₃	C₂³	1	2	yes	—
227	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
228	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
229	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
230	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
231	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
233	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
234	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
235	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
236	#107×C₅₃	C₂³	1	2	yes	—
237	#107×C₅₃	C₂³	1	2	yes	—
238	#107×C₅₃	C₂³	1	2	yes	—
239	#107×C₅₃	C₂³	1	2	yes	—
240	#107×C₅₃	C₂³	1	2	yes	—
241	#106×C₅₃	C₂³	1	2	yes	—
242	#106×C₅₃	C₂³	1	2	yes	—
243	#106×C₅₃	C₂³	1	2	yes	—
244	#106×C₅₃	C₂³	1	2	yes	—
245	#106×C₅₃	C₂³	1	2	yes	—
246	#106×C₅₃	C₂³	1	2	yes	—
247	#106×C₅₃	C₂³	1	2	yes	—
248	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
249	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
250	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
251	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
252	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
253	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
254	#103×C₅₃	C₂³	1	2	yes	—
255	#103×C₅₃	C₂³	1	2	yes	—
256	#103×C₅₃	C₂³	1	2	yes	—
257	#102×C₅₃	C₂³	1	2	yes	—
258	#102×C₅₃	C₂³	1	2	yes	—
259	#102×C₅₃	C₂³	1	2	yes	—
260	#102×C₅₃	C₂³	1	2	yes	—
261	#102×C₅₃	C₂³	1	2	yes	—
262	#102×C₅₃	C₂³	1	2	yes	—
263	#102×C₅₃	C₂³	1	2	yes	—
264	#102×C₅₃	C₂³	1	2	yes	—
265	#102×C₅₃	C₂³	1	2	yes	—
266	#102×C₅₃	C₂³	1	2	yes	—
267	#102×C₅₃	C₂³	1	2	yes	—
268	#102×C₅₃	C₂³	1	2	yes	—
269	#102×C₅₃	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
271	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
272	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
273	#97×C₅₃	C₂³	1	1	yes	characteristic
274	#97×C₅₃	C₂³	1	1	yes	characteristic
275	#97×C₅₃	C₂³	1	2	yes	—
276	#97×C₅₃	C₂³	1	2	yes	—
277	#97×C₅₃	C₂³	1	2	yes	—
278	C₄×C₈×C₅₃	C₂³	1	2	yes	—
279	C₄×C₈×C₅₃	C₂³	1	2	yes	—
280	C₂⁴×C₅₃	—	2	1	no	—
281	#41×C₅₃	—	8	2	no	—
282	#41×C₅₃	—	8	2	no	—
283	C₂×Q₈×C₅₃	—	2	1	no	—
284	C₂×Q₈×C₅₃	—	2	1	no	—
285	C₂×Q₈×C₅₃	—	2	1	no	—
286	C₂×Q₈×C₅₃	—	2	2	no	—
287	C₂×Q₈×C₅₃	—	2	2	no	—
288	C₂×Q₈×C₅₃	—	2	2	no	—
289	C₂×Q₈×C₅₃	—	8	4	no	—
290	C₂×Q₈×C₅₃	—	8	2	no	—
291	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
292	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
294	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
295	C₂×D₄×C₅₃	—	2	4	no	—
296	C₂×D₄×C₅₃	—	2	1	no	—
297	C₂×D₄×C₅₃	—	2	2	no	—
298	C₂×D₄×C₅₃	—	2	1	no	—
299	C₂×D₄×C₅₃	—	2	1	no	—
300	C₂×D₄×C₅₃	—	2	1	no	—
301	C₂×D₄×C₅₃	—	2	2	no	—
302	C₂×D₄×C₅₃	—	2	2	no	—
303	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
304	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
305	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₅₃	—	2	1	no	—
307	C₂²×C₄×C₅₃	—	2	2	no	—
308	C₂²×C₄×C₅₃	—	2	1	no	—
309	C₂²×C₄×C₅₃	—	2	2	no	—
310	C₂²×C₄×C₅₃	—	2	2	no	—
311	C₂²×C₄×C₅₃	—	2	2	no	—
312	C₂²×C₄×C₅₃	—	2	2	no	—
313	C₂²×C₄×C₅₃	—	2	2	no	—
314	C₂²×C₄×C₅₃	—	2	2	no	—
315	C₂²×C₄×C₅₃	—	2	2	no	—
316	C₂²×C₄×C₅₃	—	2	2	no	—
317	C₂²×C₄×C₅₃	—	2	2	no	—
318	C₂²×C₄×C₅₃	—	8	2	no	—
319	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
322	SD₁₆×C₅₃	—	2	4	no	—
323	D₈×C₅₃	—	2	4	no	—
324	D₈×C₅₃	—	2	4	no	—
325	D₈×C₅₃	—	2	4	no	—
326	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
327	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
328	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
329	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
330	C₄⋊C₄×C₅₃	—	2	1	no	—
331	C₄⋊C₄×C₅₃	—	2	2	no	—
332	C₄⋊C₄×C₅₃	—	2	1	no	—
333	C₄⋊C₄×C₅₃	—	2	2	no	—
334	C₄⋊C₄×C₅₃	—	2	2	no	—
335	C₄⋊C₄×C₅₃	—	2	2	no	—
336	C₄⋊C₄×C₅₃	—	2	2	no	—
337	C₄⋊C₄×C₅₃	—	2	2	no	—
338	C₄⋊C₄×C₅₃	—	2	2	no	—
339	C₄⋊C₄×C₅₃	—	2	2	no	—
340	C₄⋊C₄×C₅₃	—	2	2	no	—
341	C₄⋊C₄×C₅₃	—	2	1	no	—
342	C₄⋊C₄×C₅₃	—	2	1	no	—
343	C₄⋊C₄×C₅₃	—	2	1	no	—
344	C₄⋊C₄×C₅₃	—	2	1	no	—
345	C₄⋊C₄×C₅₃	—	2	2	no	—
346	C₄⋊C₄×C₅₃	—	2	2	no	—
347	C₄⋊C₄×C₅₃	—	2	1	no	—
348	C₄⋊C₄×C₅₃	—	2	2	no	—
349	C₄⋊C₄×C₅₃	—	2	1	no	—
350	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
351	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
352	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
353	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
354	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
355	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
358	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
361	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂²⋊C₄×C₅₃	—	2	2	no	—
366	C₂²⋊C₄×C₅₃	—	2	1	no	—
367	C₂²⋊C₄×C₅₃	—	2	2	no	—
368	C₂²⋊C₄×C₅₃	—	2	2	no	—
369	C₂²⋊C₄×C₅₃	—	2	2	no	—
370	C₂²⋊C₄×C₅₃	—	2	2	no	—
371	C₂²⋊C₄×C₅₃	—	2	2	no	—
372	C₂²⋊C₄×C₅₃	—	2	2	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	2	no	—
377	C₂²⋊C₄×C₅₃	—	2	2	no	—
378	C₂²⋊C₄×C₅₃	—	2	2	no	—
379	C₂²⋊C₄×C₅₃	—	2	1	no	—
380	C₂²⋊C₄×C₅₃	—	2	2	no	—
381	C₂²⋊C₄×C₅₃	—	2	2	no	—
382	C₂²⋊C₄×C₅₃	—	2	2	no	—
383	C₂²⋊C₄×C₅₃	—	2	2	no	—
384	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
385	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
386	C₄²×C₅₃	—	2	1	no	—
387	C₄²×C₅₃	—	2	2	no	—
388	C₄²×C₅₃	—	2	2	no	—
389	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₅₃	C₂⁴	1	2	yes	—
392	C₄²×C₅₃	C₂⁴	1	2	yes	—
393	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂³×C₅₃	—	2	4	no	—
396	C₂³×C₅₃	—	2	2	no	—
397	C₂³×C₅₃	—	2	1	no	—
398	C₂³×C₅₃	—	2	2	no	—
399	C₂³×C₅₃	—	8	1	no	—
400	C₂³×C₅₃	—	8	1	no	—
401	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
402	Q₈×C₅₃	—	2	2	no	—
403	Q₈×C₅₃	—	4	2	no	—
404	Q₈×C₅₃	—	4	1	no	—
405	Q₈×C₅₃	—	4	1	no	—
406	Q₈×C₅₃	—	4	2	no	—
407	Q₈×C₅₃	—	4	2	no	—
408	Q₈×C₅₃	—	8	1	no	—
409	Q₈×C₅₃	—	8	2	no	—
410	Q₈×C₅₃	—	8	2	no	—
411	Q₈×C₅₃	—	8	2	no	—
412	D₄×C₅₃	—	2	4	no	—
413	D₄×C₅₃	—	2	2	no	—
414	D₄×C₅₃	—	2	2	no	—
415	D₄×C₅₃	—	2	2	no	—
416	D₄×C₅₃	—	2	2	no	—
417	D₄×C₅₃	—	4	2	no	—
418	D₄×C₅₃	—	8	1	no	—
419	D₄×C₅₃	—	8	2	no	—
420	D₄×C₅₃	—	8	2	no	—
421	D₄×C₅₃	—	8	1	no	—
422	D₄×C₅₃	—	8	2	no	—
423	D₄×C₅₃	2₋¹⁺⁴	1	4	yes	—
424	C₂×C₄×C₅₃	—	2	2	no	—
425	C₂×C₄×C₅₃	—	2	1	no	—
426	C₂×C₄×C₅₃	—	2	2	no	—
427	C₂×C₄×C₅₃	—	2	2	no	—
428	C₂×C₄×C₅₃	—	2	1	no	—
429	C₂×C₄×C₅₃	—	2	2	no	—
430	C₂×C₄×C₅₃	—	2	2	no	—
431	C₂×C₄×C₅₃	—	2	1	no	—
432	C₂×C₄×C₅₃	—	4	1	no	—
433	C₂×C₄×C₅₃	—	4	1	no	—
434	C₂×C₄×C₅₃	—	4	4	no	—
435	C₂×C₄×C₅₃	—	4	2	no	—
436	C₂×C₄×C₅₃	—	8	2	no	—
437	C₂×C₄×C₅₃	—	8	2	no	—
438	C₂×C₄×C₅₃	—	8	2	no	—
439	C₂×C₄×C₅₃	—	8	2	no	—
440	C₂×C₄×C₅₃	—	8	2	no	—
441	C₂×C₄×C₅₃	—	8	2	no	—
442	C₂×C₄×C₅₃	—	8	2	no	—
443	C₂×C₄×C₅₃	—	8	2	no	—
444	C₂×C₄×C₅₃	—	8	2	no	—
445	C₂×C₄×C₅₃	—	8	1	no	—
446	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
450	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
451	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
456	C₈×C₅₃	—	2	2	no	—
457	C₈×C₅₃	—	2	2	no	—
458	C₈×C₅₃	—	2	2	no	—
459	C₈×C₅₃	—	2	2	no	—
460	#61872	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂²×C₅₃	—	2	1	no	—
462	C₂²×C₅₃	—	2	1	no	—
463	C₂²×C₅₃	—	2	1	no	—
464	C₂²×C₅₃	—	2	4	no	—
465	C₂²×C₅₃	—	4	2	no	—
466	C₂²×C₅₃	—	4	2	no	—
467	C₂²×C₅₃	—	4	1	no	—
468	C₂²×C₅₃	—	4	2	no	—
469	C₂²×C₅₃	—	4	2	no	—
470	C₂²×C₅₃	—	4	1	no	—
471	C₂²×C₅₃	—	4	1	no	—
472	C₂²×C₅₃	—	4	2	no	—
473	C₂²×C₅₃	—	8	4	no	—
474	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
475	C₄×C₅₃	—	2	1	no	—
476	C₄×C₅₃	—	2	1	no	—
477	C₄×C₅₃	—	2	1	no	—
478	C₄×C₅₃	—	2	1	no	—
479	C₄×C₅₃	—	2	2	no	—
480	C₄×C₅₃	—	2	2	no	—
481	C₄×C₅₃	—	2	2	no	—
482	C₄×C₅₃	—	2	2	no	—
483	C₄×C₅₃	—	2	1	no	—
484	C₄×C₅₃	—	4	1	no	—
485	C₄×C₅₃	—	4	2	no	—
486	C₄×C₅₃	—	4	1	no	—
487	C₄×C₅₃	—	4	2	no	—
488	C₄×C₅₃	—	4	2	no	—
489	C₄×C₅₃	—	4	2	no	—
490	C₄×C₅₃	—	4	1	no	—
491	C₄×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
492	#3554	C₂×C₅₃	1	1	yes	characteristic, complemented
493	#3501	C₂×C₅₃	1	1	yes	characteristic, complemented
494	#3389	C₂×C₅₃	1	2	yes	complemented
495	#3388	C₂×C₅₃	1	2	yes	complemented
496	#3384	C₂×C₅₃	1	2	yes	complemented
497	#3384	C₂×C₅₃	1	2	yes	complemented
498	#3373	C₂×C₅₃	1	2	yes	complemented
499	#3370	C₂×C₅₃	1	2	yes	complemented
500	#3370	C₂×C₅₃	1	2	yes	complemented
501	#3366	C₂×C₅₃	1	2	yes	complemented
502	#3244	C₂×C₅₃	1	2	yes	complemented
503	#3241	C₂×C₅₃	1	2	yes	complemented
504	#3240	C₂×C₅₃	1	1	yes	characteristic, complemented
505	#3235	C₂×C₅₃	1	1	yes	characteristic, complemented
506	#3122	C₂×C₅₃	1	2	yes	complemented
507	#3118	C₂×C₅₃	1	2	yes	complemented
508	#3114	C₂×C₅₃	1	1	yes	characteristic, complemented
509	#3109	C₂×C₅₃	1	1	yes	characteristic, complemented
510	#2987	C₂×C₅₃	1	1	yes	characteristic, complemented
511	C₂×C₅₃	—	4	1	no	—
512	C₂×C₅₃	—	4	4	no	—
513	C₂×C₅₃	—	8	1	no	—
514	C₂×C₅₃	—	8	2	no	—
515	C₂×C₅₃	#3486	1	1	yes	characteristic
516	C₂×C₅₃	#3585	1	1	yes	characteristic
517	C₂×C₅₃	#3585	1	1	yes	characteristic
518	#562	—	2	2	no	—
519	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
520	#559	C₂²×C₅₃	1	2	yes	complemented
521	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
522	#554	—	2	1	no	—
523	#554	—	2	2	no	—
524	#554	C₂²×C₅₃	1	2	yes	—
525	#554	C₂²×C₅₃	1	2	yes	—
526	#554	C₂²×C₅₃	1	2	yes	—
527	#554	C₂²×C₅₃	1	2	yes	complemented
528	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
529	D₄×Q₈	—	2	1	no	—
530	D₄×Q₈	C₂²×C₅₃	1	2	yes	—
531	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
532	#548	—	2	1	no	—
533	#547	—	2	1	no	—
534	#544	C₂²×C₅₃	1	2	yes	—
535	#543	—	2	1	no	—
536	#543	—	2	1	no	—
537	#542	—	2	1	no	—
538	#542	C₂²×C₅₃	1	2	yes	—
539	#540	C₂²×C₅₃	1	2	yes	—
540	#539	—	2	2	no	—
541	#536	—	2	1	no	—
542	#533	C₂²×C₅₃	1	1	yes	characteristic
543	#533	C₂²×C₅₃	1	1	yes	characteristic
544	#532	C₂²×C₅₃	1	1	yes	characteristic
545	#529	C₂²×C₅₃	1	1	yes	characteristic
546	C₂×C₂²⋊Q₈	—	2	2	no	—
547	#518	C₂²×C₅₃	1	2	yes	—
548	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
549	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
550	#501	C₂²×C₅₃	1	2	yes	complemented
551	#501	C₂²×C₅₃	1	2	yes	complemented
552	#501	C₂²×C₅₃	1	2	yes	complemented
553	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
554	#499	C₂²×C₅₃	1	2	yes	complemented
555	#498	C₂²×C₅₃	1	2	yes	complemented
556	#490	C₂²×C₅₃	1	2	yes	complemented
557	#490	C₂²×C₅₃	1	2	yes	complemented
558	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
559	#489	C₂²×C₅₃	1	2	yes	complemented
560	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
561	#488	C₂²×C₅₃	1	2	yes	complemented
562	#486	C₂²×C₅₃	1	2	yes	complemented
563	#485	C₂²×C₅₃	1	2	yes	—
564	#483	C₂²×C₅₃	1	1	yes	characteristic
565	#482	C₂²×C₅₃	1	2	yes	—
566	#482	C₂²×C₅₃	1	2	yes	—
567	#482	C₂²×C₅₃	1	2	yes	—
568	#481	C₂²×C₅₃	1	2	yes	—
569	#480	C₂²×C₅₃	1	1	yes	characteristic
570	#479	C₂²×C₅₃	1	2	yes	complemented
571	#479	C₂²×C₅₃	1	2	yes	complemented
572	#478	C₂²×C₅₃	1	2	yes	—
573	#478	C₂²×C₅₃	1	2	yes	—
574	#478	C₂²×C₅₃	1	2	yes	—
575	#478	C₂²×C₅₃	1	2	yes	complemented
576	#478	C₂²×C₅₃	1	2	yes	complemented
577	#478	C₂²×C₅₃	1	2	yes	complemented
578	#478	C₂²×C₅₃	1	2	yes	complemented
579	#476	C₂²×C₅₃	1	2	yes	—
580	#476	C₂²×C₅₃	1	2	yes	—
581	#476	C₂²×C₅₃	1	2	yes	complemented
582	#476	C₂²×C₅₃	1	2	yes	complemented
583	#476	C₂²×C₅₃	1	2	yes	complemented
584	#475	C₂²×C₅₃	1	2	yes	complemented
585	#474	C₂²×C₅₃	1	2	yes	—
586	#474	C₂²×C₅₃	1	2	yes	complemented
587	#474	C₂²×C₅₃	1	2	yes	complemented
588	#463	C₂²×C₅₃	1	2	yes	—
589	#463	C₂²×C₅₃	1	2	yes	—
590	#463	C₂²×C₅₃	1	2	yes	—
591	#459	C₂²×C₅₃	1	2	yes	—
592	#459	C₂²×C₅₃	1	2	yes	—
593	#459	C₂²×C₅₃	1	2	yes	—
594	#450	C₂²×C₅₃	1	1	yes	characteristic
595	#447	C₂²×C₅₃	1	2	yes	—
596	#447	C₂²×C₅₃	1	1	yes	characteristic
597	#446	C₂²×C₅₃	1	2	yes	complemented
598	#446	C₂²×C₅₃	1	2	yes	complemented
599	#446	C₂²×C₅₃	1	2	yes	complemented
600	#446	C₂²×C₅₃	1	2	yes	complemented
601	#442	C₂²×C₅₃	1	2	yes	—
602	#442	C₂²×C₅₃	1	2	yes	—
603	#442	C₂²×C₅₃	1	2	yes	—
604	#442	C₂²×C₅₃	1	2	yes	—
605	#442	C₂²×C₅₃	1	2	yes	—
606	#442	C₂²×C₅₃	1	2	yes	—
607	#440	C₂²×C₅₃	1	2	yes	—
608	#440	C₂²×C₅₃	1	2	yes	—
609	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
610	C₄×D₈	C₂²×C₅₃	1	2	yes	—
611	C₄×D₈	C₂²×C₅₃	1	2	yes	—
612	C₄×D₈	C₂²×C₅₃	1	2	yes	—
613	#433	C₂²×C₅₃	1	2	yes	—
614	#433	C₂²×C₅₃	1	2	yes	—
615	#432	C₂²×C₅₃	1	1	yes	characteristic
616	#432	C₂²×C₅₃	1	1	yes	characteristic
617	C₅₃	#61872	1	1	yes	characteristic, direct product factor, Sylow
618	C₂×#41	—	2	1	no	—
619	C₂×#41	—	2	1	no	—
620	C₂²×Q₈	—	2	2	no	—
621	C₂²×Q₈	—	2	1	no	—
622	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
623	C₂³×C₄	—	2	1	no	—
624	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
625	C₂×D₈	C₂³×C₅₃	1	2	yes	—
626	C₂×D₈	C₂³×C₅₃	1	2	yes	—
627	C₂×D₈	C₂³×C₅₃	1	2	yes	—
628	C₄⋊Q₈	—	2	1	no	—
629	C₄⋊Q₈	—	2	2	no	—
630	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
631	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
632	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
633	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
634	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
635	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
636	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
637	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
638	#127	C₂³×C₅₃	1	1	yes	characteristic
639	#127	C₂³×C₅₃	1	2	yes	—
640	#126	—	2	2	no	—
641	#126	—	2	1	no	—
642	#125	—	2	2	no	—
643	#125	—	2	2	no	—
644	#125	D₄×C₅₃	1	2	yes	—
645	#125	C₂³×C₅₃	1	1	yes	characteristic
646	#125	C₂³×C₅₃	1	2	yes	—
647	#125	C₂³×C₅₃	1	2	yes	—
648	#125	C₂³×C₅₃	1	2	yes	—
649	#125	C₂³×C₅₃	1	2	yes	—
650	#124	—	2	1	no	—
651	#124	—	2	2	no	—
652	#124	—	2	2	no	—
653	#124	—	2	1	no	—
654	#124	C₂³×C₅₃	1	1	yes	characteristic
655	#124	C₂³×C₅₃	1	2	yes	—
656	#123	—	2	1	no	—
657	#123	—	2	2	no	—
658	#123	—	2	2	no	—
659	#123	—	2	2	no	—
660	#123	—	2	2	no	—
661	#123	—	2	2	no	—
662	#123	—	2	2	no	—
663	C₂²⋊Q₈	—	2	2	no	—
664	C₂²⋊Q₈	—	2	2	no	—
665	C₂²⋊Q₈	—	2	2	no	—
666	C₂²⋊Q₈	—	2	2	no	—
667	C₂²⋊Q₈	—	2	1	no	—
668	C₂²⋊Q₈	—	2	1	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	2	no	—
672	C₂²⋊Q₈	—	2	2	no	—
673	C₂²⋊Q₈	—	2	2	no	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	—	2	1	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
686	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
687	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
688	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
689	#121	—	2	1	no	—
690	#121	—	2	2	no	—
691	#121	—	2	1	no	—
692	#121	—	2	2	no	—
693	#121	—	2	2	no	—
694	#121	C₂³×C₅₃	1	1	yes	characteristic
695	#121	C₂³×C₅₃	1	2	yes	—
696	C₄×Q₈	—	2	1	no	—
697	C₄×Q₈	—	2	1	no	—
698	C₄×Q₈	—	2	1	no	—
699	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
700	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
701	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
702	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
703	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
704	C₄×D₄	—	2	1	no	—
705	C₄×D₄	—	2	2	no	—
706	C₄×D₄	—	2	2	no	—
707	C₄×D₄	—	2	2	no	—
708	C₄×D₄	—	2	1	no	—
709	C₄×D₄	—	2	1	no	—
710	C₄×D₄	—	2	1	no	—
711	C₄×D₄	—	2	1	no	—
712	C₄×D₄	C₂³×C₅₃	1	2	yes	—
713	C₄×D₄	C₂³×C₅₃	1	2	yes	—
714	C₄×D₄	C₂³×C₅₃	1	2	yes	—
715	C₄×D₄	C₂³×C₅₃	1	2	yes	—
716	C₄×D₄	C₂³×C₅₃	1	2	yes	—
717	C₄×D₄	C₂³×C₅₃	1	2	yes	—
718	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
719	C₄×D₄	C₂³×C₅₃	1	2	yes	—
720	C₄×D₄	C₂³×C₅₃	1	2	yes	—
721	C₄×D₄	C₂³×C₅₃	1	2	yes	—
722	C₄×D₄	C₂³×C₅₃	1	2	yes	—
723	#117	—	2	1	no	—
724	#117	C₂³×C₅₃	1	2	yes	—
725	#117	C₂³×C₅₃	1	2	yes	—
726	C₂×C₄⋊C₄	—	2	2	no	—
727	C₂×C₄⋊C₄	—	2	2	no	—
728	C₂×C₄⋊C₄	—	2	2	no	—
729	C₂×C₄⋊C₄	—	2	2	no	—
730	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
731	C₂×C₂²⋊C₄	—	2	1	no	—
732	C₂×C₂²⋊C₄	—	2	2	no	—
733	C₂×C₂²⋊C₄	—	2	2	no	—
734	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
735	#107	C₂³×C₅₃	1	2	yes	—
736	#107	C₂³×C₅₃	1	2	yes	—
737	#107	C₂³×C₅₃	1	2	yes	—
738	#107	C₂³×C₅₃	1	2	yes	—
739	#107	C₂³×C₅₃	1	2	yes	—
740	#106	C₂³×C₅₃	1	2	yes	—
741	#106	C₂³×C₅₃	1	2	yes	—
742	#106	C₂³×C₅₃	1	2	yes	—
743	#106	C₂³×C₅₃	1	2	yes	—
744	#106	C₂³×C₅₃	1	2	yes	—
745	#106	C₂³×C₅₃	1	2	yes	—
746	#106	C₂³×C₅₃	1	2	yes	—
747	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
748	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
749	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
750	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
751	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
752	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
753	#103	C₂³×C₅₃	1	2	yes	—
754	#103	C₂³×C₅₃	1	2	yes	—
755	#103	C₂³×C₅₃	1	2	yes	—
756	#102	C₂³×C₅₃	1	2	yes	—
757	#102	C₂³×C₅₃	1	2	yes	—
758	#102	C₂³×C₅₃	1	2	yes	—
759	#102	C₂³×C₅₃	1	2	yes	—
760	#102	C₂³×C₅₃	1	2	yes	—
761	#102	C₂³×C₅₃	1	2	yes	—
762	#102	C₂³×C₅₃	1	2	yes	—
763	#102	C₂³×C₅₃	1	2	yes	—
764	#102	C₂³×C₅₃	1	2	yes	—
765	#102	C₂³×C₅₃	1	2	yes	—
766	#102	C₂³×C₅₃	1	2	yes	—
767	#102	C₂³×C₅₃	1	2	yes	—
768	#102	C₂³×C₅₃	1	2	yes	—
769	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
770	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
771	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
772	#97	C₂³×C₅₃	1	2	yes	—
773	#97	C₂³×C₅₃	1	1	yes	characteristic
774	#97	C₂³×C₅₃	1	1	yes	characteristic
775	#97	C₂³×C₅₃	1	2	yes	—
776	#97	C₂³×C₅₃	1	2	yes	—
777	C₄×C₈	C₂³×C₅₃	1	2	yes	—
778	C₄×C₈	C₂³×C₅₃	1	2	yes	—
779	C₂⁴	—	2	1	no	—
780	#41	—	8	2	no	—
781	#41	—	8	2	no	—
782	C₂×Q₈	—	2	1	no	—
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	2	2	no	—
786	C₂×Q₈	—	2	2	no	—
787	C₂×Q₈	—	2	2	no	—
788	C₂×Q₈	—	8	4	no	—
789	C₂×Q₈	—	8	2	no	—
790	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
791	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
792	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
793	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
794	C₂×D₄	—	2	4	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
803	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
804	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	8	2	no	—
818	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
819	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
821	SD₁₆	—	2	4	no	—
822	D₈	—	2	4	no	—
823	D₈	—	2	4	no	—
824	D₈	—	2	4	no	—
825	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
826	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
827	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
828	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	1	no	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	1	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
850	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
851	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
852	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
853	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
854	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
855	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
856	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
857	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
858	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
859	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
860	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
861	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
862	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
863	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	1	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	1	no	—
873	C₂²⋊C₄	—	2	1	no	—
874	C₂²⋊C₄	—	2	1	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	1	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
884	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
885	C₄²	—	2	1	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	2	2	no	—
888	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
889	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
890	C₄²	C₂⁴×C₅₃	1	2	yes	—
891	C₄²	C₂⁴×C₅₃	1	2	yes	—
892	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
893	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
894	C₂³	—	2	4	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	8	1	no	—
899	C₂³	—	8	1	no	—
900	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
901	Q₈	—	2	2	no	—
902	Q₈	—	4	2	no	—
903	Q₈	—	4	1	no	—
904	Q₈	—	4	1	no	—
905	Q₈	—	4	2	no	—
906	Q₈	—	4	2	no	—
907	Q₈	—	8	1	no	—
908	Q₈	—	8	2	no	—
909	Q₈	—	8	2	no	—
910	Q₈	—	8	2	no	—
911	D₄	—	2	4	no	—
912	D₄	—	2	2	no	—
913	D₄	—	2	2	no	—
914	D₄	—	2	2	no	—
915	D₄	—	2	2	no	—
916	D₄	—	4	2	no	—
917	D₄	—	8	1	no	—
918	D₄	—	8	2	no	—
919	D₄	—	8	2	no	—
920	D₄	—	8	1	no	—
921	D₄	—	8	2	no	—
922	D₄	2₋¹⁺⁴×C₅₃	1	4	yes	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	4	no	—
934	C₂×C₄	—	4	2	no	—
935	C₂×C₄	—	8	2	no	—
936	C₂×C₄	—	8	2	no	—
937	C₂×C₄	—	8	2	no	—
938	C₂×C₄	—	8	2	no	—
939	C₂×C₄	—	8	2	no	—
940	C₂×C₄	—	8	2	no	—
941	C₂×C₄	—	8	2	no	—
942	C₂×C₄	—	8	2	no	—
943	C₂×C₄	—	8	2	no	—
944	C₂×C₄	—	8	1	no	—
945	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
946	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
947	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
948	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
949	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
950	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
951	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
952	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
953	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
954	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
955	C₈	—	2	2	no	—
956	C₈	—	2	2	no	—
957	C₈	—	2	2	no	—
958	C₈	—	2	2	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	4	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	1	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	1	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	1	no	—
971	C₂²	—	8	4	no	—
972	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
973	C₄	—	2	1	no	—
974	C₄	—	2	1	no	—
975	C₄	—	2	1	no	—
976	C₄	—	2	1	no	—
977	C₄	—	2	1	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	2	2	no	—
981	C₄	—	2	2	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	1	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	C₂×2₋¹⁺⁴×C₅₃	1	2	yes	—
990	C₂	—	4	1	no	—
991	C₂	—	4	4	no	—
992	C₂	—	8	1	no	—
993	C₂	—	8	2	no	—
994	C₂	C₅₃×#3486	1	1	yes	characteristic
995	C₂	C₅₃×#3585	1	1	yes	characteristic
996	C₂	C₅₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3554	C₂	semidirect
2. C₅₃×#3501	C₂	semidirect
3. C₅₃×#3389	C₂	semidirect
4. C₅₃×#3388	C₂	semidirect
5. C₅₃×#3384	C₂	semidirect
6. C₅₃×#3384	C₂	semidirect
7. C₅₃×#3373	C₂	semidirect
8. C₅₃×#3370	C₂	semidirect
9. C₅₃×#3370	C₂	semidirect
10. C₅₃×#3366	C₂	semidirect
11. C₅₃×#3244	C₂	semidirect
12. C₅₃×#3241	C₂	semidirect
13. C₅₃×#3240	C₂	semidirect
14. C₅₃×#3235	C₂	semidirect
15. C₅₃×#3122	C₂	semidirect
16. C₅₃×#3118	C₂	semidirect
17. C₅₃×#3114	C₂	semidirect
18. C₅₃×#3109	C₂	semidirect
19. C₅₃×#2987	C₂	semidirect
21. C₅₃×#559	C₂²	semidirect
22. C₅₃×#559	C₂²	semidirect
23. C₅₃×#557	C₂²	semidirect
29. C₅₃×#554	C₂²	semidirect
30. C₅₃×#550	C₂²	semidirect
33. D₄×Q₈×C₅₃	C₂²	semidirect
51. C₅₃×#501	C₂²	semidirect
52. C₅₃×#501	C₂²	semidirect
53. C₅₃×#501	C₂²	semidirect
54. C₅₃×#501	C₂²	semidirect
55. C₅₃×#501	C₂²	semidirect
56. C₅₃×#499	C₂²	semidirect
57. C₅₃×#498	C₂²	semidirect
58. C₅₃×#490	C₂²	semidirect
59. C₅₃×#490	C₂²	semidirect
60. C₅₃×#489	C₂²	semidirect
61. C₅₃×#489	C₂²	semidirect
62. C₅₃×#489	C₂²	semidirect
63. C₅₃×#488	C₂²	semidirect
64. C₅₃×#486	C₂²	semidirect
72. C₅₃×#479	C₂²	semidirect
73. C₅₃×#479	C₂²	semidirect
77. C₅₃×#478	C₂²	semidirect
78. C₅₃×#478	C₂²	semidirect
79. C₅₃×#478	C₂²	semidirect
80. C₅₃×#478	C₂²	semidirect
83. C₅₃×#476	C₂²	semidirect
84. C₅₃×#476	C₂²	semidirect
85. C₅₃×#476	C₂²	semidirect
86. C₅₃×#475	C₂²	semidirect
88. C₅₃×#474	C₂²	semidirect
89. C₅₃×#474	C₂²	semidirect
99. C₅₃×#446	C₂²	semidirect
100. C₅₃×#446	C₂²	semidirect
101. C₅₃×#446	C₂²	semidirect
102. C₅₃×#446	C₂²	semidirect
460. #61872	C₅₃	direct (N × H)
492. #3554	C₂×C₅₃	semidirect
493. #3501	C₂×C₅₃	semidirect
494. #3389	C₂×C₅₃	semidirect
495. #3388	C₂×C₅₃	semidirect
496. #3384	C₂×C₅₃	semidirect
497. #3384	C₂×C₅₃	semidirect
498. #3373	C₂×C₅₃	semidirect
499. #3370	C₂×C₅₃	semidirect
500. #3370	C₂×C₅₃	semidirect
501. #3366	C₂×C₅₃	semidirect
502. #3244	C₂×C₅₃	semidirect
503. #3241	C₂×C₅₃	semidirect
504. #3240	C₂×C₅₃	semidirect
505. #3235	C₂×C₅₃	semidirect
506. #3122	C₂×C₅₃	semidirect
507. #3118	C₂×C₅₃	semidirect
508. #3114	C₂×C₅₃	semidirect
509. #3109	C₂×C₅₃	semidirect
510. #2987	C₂×C₅₃	semidirect
519. #559	C₂²×C₅₃	semidirect
520. #559	C₂²×C₅₃	semidirect
521. #557	C₂²×C₅₃	semidirect
527. #554	C₂²×C₅₃	semidirect
528. #550	C₂²×C₅₃	semidirect
531. D₄×Q₈	C₂²×C₅₃	semidirect
549. #501	C₂²×C₅₃	semidirect
550. #501	C₂²×C₅₃	semidirect
551. #501	C₂²×C₅₃	semidirect
552. #501	C₂²×C₅₃	semidirect
553. #501	C₂²×C₅₃	semidirect
554. #499	C₂²×C₅₃	semidirect
555. #498	C₂²×C₅₃	semidirect
556. #490	C₂²×C₅₃	semidirect
557. #490	C₂²×C₅₃	semidirect
558. #489	C₂²×C₅₃	semidirect
559. #489	C₂²×C₅₃	semidirect
560. #489	C₂²×C₅₃	semidirect
561. #488	C₂²×C₅₃	semidirect
562. #486	C₂²×C₅₃	semidirect
570. #479	C₂²×C₅₃	semidirect
571. #479	C₂²×C₅₃	semidirect
575. #478	C₂²×C₅₃	semidirect
576. #478	C₂²×C₅₃	semidirect
577. #478	C₂²×C₅₃	semidirect
578. #478	C₂²×C₅₃	semidirect
581. #476	C₂²×C₅₃	semidirect
582. #476	C₂²×C₅₃	semidirect
583. #476	C₂²×C₅₃	semidirect
584. #475	C₂²×C₅₃	semidirect
586. #474	C₂²×C₅₃	semidirect
587. #474	C₂²×C₅₃	semidirect
597. #446	C₂²×C₅₃	semidirect
598. #446	C₂²×C₅₃	semidirect
599. #446	C₂²×C₅₃	semidirect
600. #446	C₂²×C₅₃	semidirect
617. C₅₃	#61872	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×#3554	2
C₅₃×#3501	2
C₅₃×#3389	2
C₅₃×#3388	2
C₅₃×#3384	2
C₅₃×#3373	2
C₅₃×#3370	2
C₅₃×#3366	2
C₅₃×#3244	2
C₅₃×#3241	2
C₅₃×#3240	2
C₅₃×#3235	2
C₅₃×#3122	2
C₅₃×#3118	2
C₅₃×#3114	2
C₅₃×#3109	2
C₅₃×#2987	2
#61872	53

Subgroups — C53×#61872 #27269384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61872 #27269384