Subgroups — C₅₃×#62136 #27269648

Order 13568.

1812 conjugacy classes of subgroups.

The subgroup lattice has 894 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×#3483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3385	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3366	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3347	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3341	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3309	C₂	1	4	yes	maximal, complemented
8	C₅₃×#3305	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3253	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3245	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3235	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3115	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3076	C₂	1	2	yes	maximal, complemented
17	C₅₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈²×C₅₃	C₂²	1	1	yes	characteristic
19	C₅₃×#556	—	2	1	no	—
20	C₅₃×#555	—	2	1	no	—
21	C₅₃×#555	—	2	2	no	—
22	C₅₃×#555	C₂²	1	1	yes	characteristic
23	C₅₃×#555	C₂²	1	2	yes	—
24	C₅₃×#555	C₂²	1	2	yes	—
25	C₅₃×#554	C₂²	1	2	yes	—
26	C₅₃×#553	C₂²	1	4	yes	—
27	C₅₃×#550	—	2	1	no	—
28	C₅₃×#550	C₂²	1	1	yes	characteristic
29	C₅₃×#550	C₂²	1	2	yes	—
30	C₅₃×#550	C₂²	1	1	yes	characteristic
31	C₅₃×#548	—	2	2	no	—
32	C₅₃×#547	—	2	1	no	—
33	C₅₃×#542	—	2	2	no	—
34	C₅₃×#537	—	2	1	no	—
35	C₅₃×#533	C₂²	1	2	yes	—
36	C₅₃×#532	—	2	1	no	—
37	C₅₃×#532	—	2	2	no	—
38	C₅₃×#532	C₂²	1	1	yes	characteristic
39	C₅₃×#532	C₂²	1	2	yes	—
40	C₅₃×#532	C₂²	1	2	yes	—
41	C₅₃×#532	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#520	—	2	1	no	—
44	C₄×#41×C₅₃	—	2	1	no	—
45	C₄×#41×C₅₃	C₂²	1	2	yes	—
46	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
47	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
48	C₅₃×#501	C₂²	1	4	yes	—
49	C₅₃×#500	C₂²	1	2	yes	—
50	C₅₃×#490	C₂²	1	4	yes	—
51	C₅₃×#486	C₂²	1	2	yes	—
52	C₅₃×#482	C₂²	1	4	yes	—
53	C₅₃×#482	C₂²	1	4	yes	—
54	C₅₃×#482	C₂²	1	4	yes	—
55	C₅₃×#482	C₂²	1	2	yes	—
56	C₅₃×#480	C₂²	1	4	yes	—
57	C₅₃×#479	C₂²	1	4	yes	—
58	C₅₃×#478	C₂²	1	4	yes	—
59	C₅₃×#477	C₂²	1	2	yes	—
60	C₅₃×#477	C₂²	1	1	yes	characteristic
61	C₅₃×#476	C₂²	1	1	yes	characteristic
62	C₅₃×#476	C₂²	1	2	yes	—
63	C₅₃×#476	C₂²	1	2	yes	—
64	C₅₃×#476	C₂²	1	2	yes	—
65	C₅₃×#475	C₂²	1	2	yes	—
66	C₅₃×#474	C₂²	1	2	yes	—
67	C₅₃×#474	C₂²	1	2	yes	—
68	C₅₃×#474	C₂²	1	2	yes	—
69	C₅₃×#474	C₂²	1	4	yes	—
70	C₅₃×#469	C₂²	1	4	yes	—
71	C₅₃×#466	C₂²	1	4	yes	—
72	C₅₃×#466	C₂²	1	4	yes	—
73	C₅₃×#460	C₂²	1	1	yes	characteristic
74	C₅₃×#459	C₂²	1	1	yes	characteristic
75	C₅₃×#459	C₂²	1	2	yes	—
76	C₅₃×#459	C₂²	1	4	yes	—
77	C₅₃×#459	C₂²	1	2	yes	—
78	C₅₃×#449	C₂²	1	4	yes	—
79	C₅₃×#449	C₂²	1	2	yes	—
80	C₅₃×#446	C₂²	1	2	yes	—
81	C₅₃×#442	C₂²	1	4	yes	—
82	C₅₃×#440	C₂²	1	4	yes	—
83	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
84	C₄×D₈×C₅₃	C₂²	1	2	yes	—
85	C₅₃×#435	C₂²	1	4	yes	—
86	C₈×D₄×C₅₃	C₂²	1	2	yes	—
87	C₅₃×#432	C₂²	1	2	yes	—
88	C₅₃×#431	C₂²	1	1	yes	characteristic
89	C₅₃×#428	C₂²	1	2	yes	—
90	C₅₃×#427	C₂²	1	4	yes	—
91	C₅₃×#423	C₂²	1	1	yes	characteristic
92	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
93	C₅₃×#417	C₂²	1	2	yes	—
94	C₅₃×#416	C₂²	1	4	yes	—
95	C₂×#41×C₅₃	—	2	1	no	—
96	C₂×#41×C₅₃	—	2	1	no	—
97	C₂×#41×C₅₃	—	2	1	no	—
98	C₂×#41×C₅₃	—	2	2	no	—
99	C₂×#41×C₅₃	—	2	2	no	—
100	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
101	C₂×#41×C₅₃	C₂³	1	2	yes	—
102	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₅₃	—	2	1	no	—
104	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
105	C₂×D₈×C₅₃	C₂³	1	2	yes	—
106	C₂×D₈×C₅₃	C₂³	1	4	yes	—
107	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
109	C₄⋊Q₈×C₅₃	—	2	1	no	—
110	C₄⋊Q₈×C₅₃	—	2	2	no	—
111	C₄⋊Q₈×C₅₃	—	2	1	no	—
112	C₄⋊Q₈×C₅₃	—	2	1	no	—
113	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
116	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
117	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
118	#127×C₅₃	—	2	1	no	—
119	#127×C₅₃	—	2	2	no	—
120	#127×C₅₃	C₂³	1	1	yes	characteristic
121	#127×C₅₃	C₂³	1	2	yes	—
122	#127×C₅₃	C₂³	1	1	yes	characteristic
123	#126×C₅₃	—	2	4	no	—
124	#125×C₅₃	C₂³	1	4	yes	—
125	#124×C₅₃	—	2	2	no	—
126	#124×C₅₃	—	2	2	no	—
127	#124×C₅₃	—	2	2	no	—
128	#124×C₅₃	—	2	4	no	—
129	#124×C₅₃	—	2	1	no	—
130	#124×C₅₃	—	2	2	no	—
131	#124×C₅₃	—	2	2	no	—
132	#124×C₅₃	—	2	1	no	—
133	#123×C₅₃	—	2	4	no	—
134	C₂²⋊Q₈×C₅₃	—	2	4	no	—
135	C₂²⋊Q₈×C₅₃	—	2	2	no	—
136	C₂²⋊Q₈×C₅₃	—	2	2	no	—
137	C₂²⋊Q₈×C₅₃	—	2	2	no	—
138	#121×C₅₃	—	2	1	no	—
139	#121×C₅₃	—	2	2	no	—
140	#121×C₅₃	—	2	2	no	—
141	#121×C₅₃	—	2	2	no	—
142	#121×C₅₃	—	2	2	no	—
143	#121×C₅₃	—	2	1	no	—
144	#121×C₅₃	—	2	2	no	—
145	#121×C₅₃	—	2	2	no	—
146	#121×C₅₃	—	2	4	no	—
147	#121×C₅₃	—	2	2	no	—
148	#121×C₅₃	—	2	1	no	—
149	#121×C₅₃	—	2	1	no	—
150	#121×C₅₃	—	2	2	no	—
151	#121×C₅₃	C₂³	1	2	yes	—
152	#121×C₅₃	C₂³	1	2	yes	—
153	#121×C₅₃	C₂³	1	2	yes	—
154	#121×C₅₃	C₂³	1	2	yes	—
155	#121×C₅₃	C₂³	1	4	yes	—
156	C₄×Q₈×C₅₃	—	2	2	no	—
157	C₄×Q₈×C₅₃	—	2	2	no	—
158	C₄×Q₈×C₅₃	—	2	1	no	—
159	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
160	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
164	C₄×D₄×C₅₃	—	2	1	no	—
165	C₄×D₄×C₅₃	—	2	2	no	—
166	C₄×D₄×C₅₃	—	2	4	no	—
167	C₄×D₄×C₅₃	—	2	1	no	—
168	C₄×D₄×C₅₃	—	2	2	no	—
169	C₄×D₄×C₅₃	—	2	2	no	—
170	C₄×D₄×C₅₃	—	2	1	no	—
171	C₄×D₄×C₅₃	—	2	1	no	—
172	C₄×D₄×C₅₃	—	2	2	no	—
173	C₄×D₄×C₅₃	—	2	1	no	—
174	C₄×D₄×C₅₃	—	2	2	no	—
175	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
176	C₄×D₄×C₅₃	D₄	1	2	yes	—
177	C₄×D₄×C₅₃	C₂³	1	2	yes	—
178	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₅₃	C₂³	1	2	yes	—
181	C₄×D₄×C₅₃	C₂³	1	4	yes	—
182	C₄×D₄×C₅₃	C₂³	1	2	yes	—
183	C₄×D₄×C₅₃	C₂³	1	2	yes	—
184	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
185	#117×C₅₃	—	2	1	no	—
186	#117×C₅₃	—	2	2	no	—
187	#117×C₅₃	—	2	2	no	—
188	#117×C₅₃	—	2	2	no	—
189	#117×C₅₃	—	2	1	no	—
190	#117×C₅₃	D₄	1	1	yes	characteristic
191	#117×C₅₃	D₄	1	2	yes	—
192	#117×C₅₃	C₂³	1	2	yes	—
193	#117×C₅₃	C₂³	1	1	yes	characteristic
194	#117×C₅₃	C₂³	1	4	yes	—
195	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
196	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
197	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₅₃	—	2	1	no	—
199	C₂×C₄²×C₅₃	—	2	2	no	—
200	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
202	#107×C₅₃	C₂³	1	4	yes	—
203	#107×C₅₃	C₂³	1	4	yes	—
204	#107×C₅₃	C₂³	1	4	yes	—
205	#107×C₅₃	C₂³	1	2	yes	—
206	#106×C₅₃	C₂³	1	2	yes	—
207	#106×C₅₃	C₂³	1	4	yes	—
208	#106×C₅₃	C₂³	1	4	yes	—
209	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
210	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
211	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
212	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
213	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
214	#103×C₅₃	C₂³	1	2	yes	—
215	#103×C₅₃	C₂³	1	4	yes	—
216	#102×C₅₃	C₂³	1	4	yes	—
217	#102×C₅₃	C₂³	1	4	yes	—
218	#102×C₅₃	C₂³	1	2	yes	—
219	#102×C₅₃	C₂³	1	4	yes	—
220	#102×C₅₃	C₂³	1	4	yes	—
221	#102×C₅₃	C₂³	1	2	yes	—
222	#102×C₅₃	C₂³	1	2	yes	—
223	#102×C₅₃	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
225	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
226	#97×C₅₃	C₂³	1	4	yes	—
227	C₄×C₈×C₅₃	C₂³	1	2	yes	—
228	#41×C₅₃	—	2	4	no	—
229	#41×C₅₃	—	2	2	no	—
230	#41×C₅₃	—	4	2	no	—
231	#41×C₅₃	—	4	2	no	—
232	#41×C₅₃	—	4	1	no	—
233	#41×C₅₃	—	4	4	no	—
234	#41×C₅₃	—	4	4	no	—
235	#41×C₅₃	—	8	2	no	—
236	#41×C₅₃	—	8	4	no	—
237	#41×C₅₃	—	8	4	no	—
238	C₂×Q₈×C₅₃	—	2	1	no	—
239	C₂×Q₈×C₅₃	—	2	2	no	—
240	C₂×Q₈×C₅₃	—	2	2	no	—
241	C₂×Q₈×C₅₃	—	2	2	no	—
242	C₂×Q₈×C₅₃	—	2	1	no	—
243	C₂×Q₈×C₅₃	—	8	2	no	—
244	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
246	C₂×D₄×C₅₃	—	2	2	no	—
247	C₂×D₄×C₅₃	—	2	1	no	—
248	C₂×D₄×C₅₃	—	2	2	no	—
249	C₂×D₄×C₅₃	—	2	4	no	—
250	C₂×D₄×C₅₃	—	2	2	no	—
251	C₂×D₄×C₅₃	—	2	2	no	—
252	C₂×D₄×C₅₃	—	2	2	no	—
253	C₂×D₄×C₅₃	—	2	1	no	—
254	C₂×D₄×C₅₃	—	2	2	no	—
255	C₂×D₄×C₅₃	—	2	1	no	—
256	C₂×D₄×C₅₃	—	2	1	no	—
257	C₂×D₄×C₅₃	—	2	2	no	—
258	C₂×D₄×C₅₃	—	2	1	no	—
259	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
260	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
262	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₅₃	—	2	2	no	—
265	C₂²×C₄×C₅₃	—	2	2	no	—
266	C₂²×C₄×C₅₃	—	2	1	no	—
267	C₂²×C₄×C₅₃	—	2	2	no	—
268	C₂²×C₄×C₅₃	—	2	1	no	—
269	C₂²×C₄×C₅₃	—	2	1	no	—
270	C₂²×C₄×C₅₃	—	2	2	no	—
271	C₂²×C₄×C₅₃	—	2	2	no	—
272	C₂²×C₄×C₅₃	—	2	4	no	—
273	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
279	SD₁₆×C₅₃	—	2	4	no	—
280	D₈×C₅₃	—	4	2	no	—
281	D₈×C₅₃	—	4	4	no	—
282	M₁₆×C₅₃	—	4	2	no	—
283	C₂×C₈×C₅₃	—	4	4	no	—
284	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
285	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
286	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
287	C₄⋊C₄×C₅₃	—	2	2	no	—
288	C₄⋊C₄×C₅₃	—	2	2	no	—
289	C₄⋊C₄×C₅₃	—	2	4	no	—
290	C₄⋊C₄×C₅₃	—	2	2	no	—
291	C₄⋊C₄×C₅₃	—	2	1	no	—
292	C₄⋊C₄×C₅₃	—	2	2	no	—
293	C₄⋊C₄×C₅₃	—	2	1	no	—
294	C₄⋊C₄×C₅₃	—	2	2	no	—
295	C₄⋊C₄×C₅₃	—	2	1	no	—
296	C₄⋊C₄×C₅₃	—	2	1	no	—
297	C₄⋊C₄×C₅₃	—	2	4	no	—
298	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
307	C₂²⋊C₄×C₅₃	—	2	1	no	—
308	C₂²⋊C₄×C₅₃	—	2	2	no	—
309	C₂²⋊C₄×C₅₃	—	2	4	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	4	no	—
314	C₂²⋊C₄×C₅₃	—	2	2	no	—
315	C₂²⋊C₄×C₅₃	—	2	1	no	—
316	C₂²⋊C₄×C₅₃	—	2	2	no	—
317	C₂²⋊C₄×C₅₃	—	2	1	no	—
318	C₂²⋊C₄×C₅₃	—	2	2	no	—
319	C₂²⋊C₄×C₅₃	—	2	4	no	—
320	C₂²⋊C₄×C₅₃	—	2	2	no	—
321	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
322	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
324	C₄²×C₅₃	—	2	1	no	—
325	C₄²×C₅₃	—	2	2	no	—
326	C₄²×C₅₃	—	2	1	no	—
327	C₄²×C₅₃	—	2	2	no	—
328	C₄²×C₅₃	—	2	1	no	—
329	C₄²×C₅₃	—	2	4	no	—
330	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₅₃	C₂×D₄	1	2	yes	—
332	C₄²×C₅₃	C₂×D₄	1	2	yes	—
333	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
335	C₄²×C₅₃	C₂⁴	1	2	yes	—
336	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
337	C₂³×C₅₃	—	2	2	no	—
338	C₂³×C₅₃	—	2	1	no	—
339	C₂³×C₅₃	—	2	2	no	—
340	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
341	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
342	Q₈×C₅₃	—	2	2	no	—
343	Q₈×C₅₃	—	2	1	no	—
344	Q₈×C₅₃	—	4	2	no	—
345	Q₈×C₅₃	—	4	4	no	—
346	Q₈×C₅₃	—	8	2	no	—
347	Q₈×C₅₃	—	8	2	no	—
348	Q₈×C₅₃	—	8	1	no	—
349	Q₈×C₅₃	2₋¹⁺⁴	1	2	yes	—
350	D₄×C₅₃	—	2	2	no	—
351	D₄×C₅₃	—	2	2	no	—
352	D₄×C₅₃	—	2	1	no	—
353	D₄×C₅₃	—	2	2	no	—
354	D₄×C₅₃	—	2	2	no	—
355	D₄×C₅₃	—	2	1	no	—
356	D₄×C₅₃	—	2	2	no	—
357	D₄×C₅₃	—	4	2	no	—
358	D₄×C₅₃	—	4	4	no	—
359	D₄×C₅₃	—	4	2	no	—
360	D₄×C₅₃	—	4	2	no	—
361	D₄×C₅₃	—	4	4	no	—
362	D₄×C₅₃	—	4	4	no	—
363	D₄×C₅₃	—	4	2	no	—
364	D₄×C₅₃	—	4	2	no	—
365	D₄×C₅₃	—	8	2	no	—
366	D₄×C₅₃	—	8	1	no	—
367	D₄×C₅₃	—	8	2	no	—
368	D₄×C₅₃	—	8	2	no	—
369	D₄×C₅₃	—	8	2	no	—
370	D₄×C₅₃	—	8	4	no	—
371	C₂×C₄×C₅₃	—	2	1	no	—
372	C₂×C₄×C₅₃	—	2	2	no	—
373	C₂×C₄×C₅₃	—	2	2	no	—
374	C₂×C₄×C₅₃	—	2	4	no	—
375	C₂×C₄×C₅₃	—	2	1	no	—
376	C₂×C₄×C₅₃	—	2	2	no	—
377	C₂×C₄×C₅₃	—	2	2	no	—
378	C₂×C₄×C₅₃	—	2	1	no	—
379	C₂×C₄×C₅₃	—	2	1	no	—
380	C₂×C₄×C₅₃	—	2	4	no	—
381	C₂×C₄×C₅₃	—	2	2	no	—
382	C₂×C₄×C₅₃	—	2	1	no	—
383	C₂×C₄×C₅₃	—	2	2	no	—
384	C₂×C₄×C₅₃	—	4	2	no	—
385	C₂×C₄×C₅₃	—	4	4	no	—
386	C₂×C₄×C₅₃	—	4	2	no	—
387	C₂×C₄×C₅₃	—	4	4	no	—
388	C₂×C₄×C₅₃	—	4	2	no	—
389	C₂×C₄×C₅₃	—	4	4	no	—
390	C₂×C₄×C₅₃	—	4	4	no	—
391	C₂×C₄×C₅₃	—	4	2	no	—
392	C₂×C₄×C₅₃	—	8	4	no	—
393	C₂×C₄×C₅₃	—	8	2	no	—
394	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
403	C₈×C₅₃	—	2	2	no	—
404	C₈×C₅₃	—	2	2	no	—
405	C₈×C₅₃	—	2	4	no	—
406	#62136	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
407	C₂²×C₅₃	—	2	2	no	—
408	C₂²×C₅₃	—	2	1	no	—
409	C₂²×C₅₃	—	2	1	no	—
410	C₂²×C₅₃	—	2	2	no	—
411	C₂²×C₅₃	—	2	1	no	—
412	C₂²×C₅₃	—	2	2	no	—
413	C₂²×C₅₃	—	4	2	no	—
414	C₂²×C₅₃	—	4	1	no	—
415	C₂²×C₅₃	—	4	2	no	—
416	C₂²×C₅₃	—	4	2	no	—
417	C₂²×C₅₃	—	4	1	no	—
418	C₂²×C₅₃	—	4	2	no	—
419	C₂²×C₅₃	—	4	1	no	—
420	C₂²×C₅₃	—	4	2	no	—
421	C₂²×C₅₃	—	4	2	no	—
422	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
423	C₄×C₅₃	—	2	2	no	—
424	C₄×C₅₃	—	2	1	no	—
425	C₄×C₅₃	—	2	2	no	—
426	C₄×C₅₃	—	2	1	no	—
427	C₄×C₅₃	—	2	2	no	—
428	C₄×C₅₃	—	2	2	no	—
429	C₄×C₅₃	—	2	1	no	—
430	C₄×C₅₃	—	4	1	no	—
431	C₄×C₅₃	—	4	2	no	—
432	C₄×C₅₃	—	4	2	no	—
433	C₄×C₅₃	—	4	1	no	—
434	C₄×C₅₃	—	4	4	no	—
435	C₄×C₅₃	#575	1	2	yes	—
436	C₄×C₅₃	#576	1	2	yes	—
437	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
438	C₄×C₅₃	#585	1	1	yes	characteristic
439	#3511	C₂×C₅₃	1	1	yes	characteristic, complemented
440	#3483	C₂×C₅₃	1	1	yes	characteristic, complemented
441	#3385	C₂×C₅₃	1	2	yes	complemented
442	#3366	C₂×C₅₃	1	2	yes	complemented
443	#3347	C₂×C₅₃	1	4	yes	complemented
444	#3341	C₂×C₅₃	1	2	yes	complemented
445	#3309	C₂×C₅₃	1	4	yes	complemented
446	#3305	C₂×C₅₃	1	2	yes	complemented
447	#3253	C₂×C₅₃	1	1	yes	characteristic, complemented
448	#3245	C₂×C₅₃	1	2	yes	complemented
449	#3235	C₂×C₅₃	1	2	yes	complemented
450	#3226	C₂×C₅₃	1	1	yes	characteristic, complemented
451	#3115	C₂×C₅₃	1	2	yes	complemented
452	#3106	C₂×C₅₃	1	1	yes	characteristic, complemented
453	#3079	C₂×C₅₃	1	1	yes	characteristic, complemented
454	#3076	C₂×C₅₃	1	2	yes	complemented
455	#2990	C₂×C₅₃	1	1	yes	characteristic, complemented
456	C₂×C₅₃	—	4	1	no	—
457	C₂×C₅₃	—	4	2	no	—
458	C₂×C₅₃	—	8	2	no	—
459	C₂×C₅₃	—	8	1	no	—
460	C₂×C₅₃	—	8	2	no	—
461	C₂×C₅₃	#3489	1	1	yes	characteristic
462	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
463	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
464	Q₈²	C₂²×C₅₃	1	1	yes	characteristic
465	#556	—	2	1	no	—
466	#555	—	2	1	no	—
467	#555	—	2	2	no	—
468	#555	C₂²×C₅₃	1	1	yes	characteristic
469	#555	C₂²×C₅₃	1	2	yes	—
470	#555	C₂²×C₅₃	1	2	yes	—
471	#554	C₂²×C₅₃	1	2	yes	—
472	#553	C₂²×C₅₃	1	4	yes	—
473	#550	—	2	1	no	—
474	#550	C₂²×C₅₃	1	1	yes	characteristic
475	#550	C₂²×C₅₃	1	2	yes	—
476	#550	C₂²×C₅₃	1	1	yes	characteristic
477	#548	—	2	2	no	—
478	#547	—	2	1	no	—
479	#542	—	2	2	no	—
480	#537	—	2	1	no	—
481	#533	C₂²×C₅₃	1	2	yes	—
482	#532	—	2	1	no	—
483	#532	—	2	2	no	—
484	#532	C₂²×C₅₃	1	1	yes	characteristic
485	#532	C₂²×C₅₃	1	2	yes	—
486	#532	C₂²×C₅₃	1	1	yes	characteristic
487	#532	C₂²×C₅₃	1	2	yes	—
488	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
489	#520	—	2	1	no	—
490	C₄×#41	—	2	1	no	—
491	C₄×#41	C₂²×C₅₃	1	2	yes	—
492	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
493	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
494	#501	C₂²×C₅₃	1	4	yes	—
495	#500	C₂²×C₅₃	1	2	yes	—
496	#490	C₂²×C₅₃	1	4	yes	—
497	#486	C₂²×C₅₃	1	2	yes	—
498	#482	C₂²×C₅₃	1	4	yes	—
499	#482	C₂²×C₅₃	1	4	yes	—
500	#482	C₂²×C₅₃	1	2	yes	—
501	#482	C₂²×C₅₃	1	4	yes	—
502	#480	C₂²×C₅₃	1	4	yes	—
503	#479	C₂²×C₅₃	1	4	yes	—
504	#478	C₂²×C₅₃	1	4	yes	—
505	#477	C₂²×C₅₃	1	1	yes	characteristic
506	#477	C₂²×C₅₃	1	2	yes	—
507	#476	C₂²×C₅₃	1	2	yes	—
508	#476	C₂²×C₅₃	1	2	yes	—
509	#476	C₂²×C₅₃	1	2	yes	—
510	#476	C₂²×C₅₃	1	1	yes	characteristic
511	#475	C₂²×C₅₃	1	2	yes	—
512	#474	C₂²×C₅₃	1	2	yes	—
513	#474	C₂²×C₅₃	1	2	yes	—
514	#474	C₂²×C₅₃	1	4	yes	—
515	#474	C₂²×C₅₃	1	2	yes	—
516	#469	C₂²×C₅₃	1	4	yes	—
517	#466	C₂²×C₅₃	1	4	yes	—
518	#466	C₂²×C₅₃	1	4	yes	—
519	#460	C₂²×C₅₃	1	1	yes	characteristic
520	#459	C₂²×C₅₃	1	1	yes	characteristic
521	#459	C₂²×C₅₃	1	4	yes	—
522	#459	C₂²×C₅₃	1	2	yes	—
523	#459	C₂²×C₅₃	1	2	yes	—
524	#449	C₂²×C₅₃	1	2	yes	—
525	#449	C₂²×C₅₃	1	4	yes	—
526	#446	C₂²×C₅₃	1	2	yes	—
527	#442	C₂²×C₅₃	1	4	yes	—
528	#440	C₂²×C₅₃	1	4	yes	—
529	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
530	C₄×D₈	C₂²×C₅₃	1	2	yes	—
531	#435	C₂²×C₅₃	1	4	yes	—
532	C₈×D₄	C₂²×C₅₃	1	2	yes	—
533	#432	C₂²×C₅₃	1	2	yes	—
534	#431	C₂²×C₅₃	1	1	yes	characteristic
535	#428	C₂²×C₅₃	1	2	yes	—
536	#427	C₂²×C₅₃	1	4	yes	—
537	#423	C₂²×C₅₃	1	1	yes	characteristic
538	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	—
539	#417	C₂²×C₅₃	1	2	yes	—
540	#416	C₂²×C₅₃	1	4	yes	—
541	C₅₃	#62136	1	1	yes	characteristic, direct product factor, Sylow
542	C₂×#41	—	2	1	no	—
543	C₂×#41	—	2	1	no	—
544	C₂×#41	—	2	1	no	—
545	C₂×#41	—	2	2	no	—
546	C₂×#41	—	2	2	no	—
547	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
548	C₂×#41	C₂³×C₅₃	1	2	yes	—
549	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
550	C₂²×Q₈	—	2	1	no	—
551	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
552	C₂×D₈	C₂³×C₅₃	1	2	yes	—
553	C₂×D₈	C₂³×C₅₃	1	4	yes	—
554	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
555	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
556	C₄⋊Q₈	—	2	1	no	—
557	C₄⋊Q₈	—	2	2	no	—
558	C₄⋊Q₈	—	2	1	no	—
559	C₄⋊Q₈	—	2	1	no	—
560	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
561	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
562	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
563	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
564	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
565	#127	—	2	1	no	—
566	#127	—	2	2	no	—
567	#127	C₂³×C₅₃	1	1	yes	characteristic
568	#127	C₂³×C₅₃	1	1	yes	characteristic
569	#127	C₂³×C₅₃	1	2	yes	—
570	#126	—	2	4	no	—
571	#125	C₂³×C₅₃	1	4	yes	—
572	#124	—	2	2	no	—
573	#124	—	2	2	no	—
574	#124	—	2	2	no	—
575	#124	—	2	4	no	—
576	#124	—	2	1	no	—
577	#124	—	2	2	no	—
578	#124	—	2	2	no	—
579	#124	—	2	1	no	—
580	#123	—	2	4	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	4	no	—
585	#121	—	2	1	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	4	no	—
589	#121	—	2	2	no	—
590	#121	—	2	1	no	—
591	#121	—	2	1	no	—
592	#121	—	2	2	no	—
593	#121	—	2	1	no	—
594	#121	—	2	2	no	—
595	#121	—	2	2	no	—
596	#121	—	2	2	no	—
597	#121	—	2	2	no	—
598	#121	C₂³×C₅₃	1	2	yes	—
599	#121	C₂³×C₅₃	1	2	yes	—
600	#121	C₂³×C₅₃	1	2	yes	—
601	#121	C₂³×C₅₃	1	2	yes	—
602	#121	C₂³×C₅₃	1	4	yes	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	—	2	2	no	—
605	C₄×Q₈	—	2	2	no	—
606	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
609	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
610	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	4	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
623	C₄×D₄	D₄×C₅₃	1	2	yes	—
624	C₄×D₄	C₂³×C₅₃	1	2	yes	—
625	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
626	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
627	C₄×D₄	C₂³×C₅₃	1	2	yes	—
628	C₄×D₄	C₂³×C₅₃	1	4	yes	—
629	C₄×D₄	C₂³×C₅₃	1	2	yes	—
630	C₄×D₄	C₂³×C₅₃	1	2	yes	—
631	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
632	#117	—	2	1	no	—
633	#117	—	2	2	no	—
634	#117	—	2	2	no	—
635	#117	—	2	2	no	—
636	#117	—	2	1	no	—
637	#117	D₄×C₅₃	1	1	yes	characteristic
638	#117	D₄×C₅₃	1	2	yes	—
639	#117	C₂³×C₅₃	1	2	yes	—
640	#117	C₂³×C₅₃	1	1	yes	characteristic
641	#117	C₂³×C₅₃	1	4	yes	—
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	—	2	2	no	—
644	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
645	C₂×C₄²	—	2	1	no	—
646	C₂×C₄²	—	2	2	no	—
647	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
649	#107	C₂³×C₅₃	1	2	yes	—
650	#107	C₂³×C₅₃	1	4	yes	—
651	#107	C₂³×C₅₃	1	4	yes	—
652	#107	C₂³×C₅₃	1	4	yes	—
653	#106	C₂³×C₅₃	1	4	yes	—
654	#106	C₂³×C₅₃	1	4	yes	—
655	#106	C₂³×C₅₃	1	2	yes	—
656	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
657	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
658	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
659	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
660	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
661	#103	C₂³×C₅₃	1	2	yes	—
662	#103	C₂³×C₅₃	1	4	yes	—
663	#102	C₂³×C₅₃	1	4	yes	—
664	#102	C₂³×C₅₃	1	4	yes	—
665	#102	C₂³×C₅₃	1	4	yes	—
666	#102	C₂³×C₅₃	1	2	yes	—
667	#102	C₂³×C₅₃	1	2	yes	—
668	#102	C₂³×C₅₃	1	2	yes	—
669	#102	C₂³×C₅₃	1	4	yes	—
670	#102	C₂³×C₅₃	1	4	yes	—
671	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
672	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
673	#97	C₂³×C₅₃	1	4	yes	—
674	C₄×C₈	C₂³×C₅₃	1	2	yes	—
675	#41	—	2	4	no	—
676	#41	—	2	2	no	—
677	#41	—	4	2	no	—
678	#41	—	4	2	no	—
679	#41	—	4	1	no	—
680	#41	—	4	4	no	—
681	#41	—	4	4	no	—
682	#41	—	8	2	no	—
683	#41	—	8	4	no	—
684	#41	—	8	4	no	—
685	C₂×Q₈	—	2	1	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	2	2	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	8	2	no	—
691	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
692	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
707	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
708	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
709	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
710	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
721	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
722	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
723	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
726	SD₁₆	—	2	4	no	—
727	D₈	—	4	2	no	—
728	D₈	—	4	4	no	—
729	M₁₆	—	4	2	no	—
730	C₂×C₈	—	4	4	no	—
731	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
732	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
733	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
746	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
747	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
748	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
749	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
751	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
752	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	1	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
769	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
770	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
771	C₄²	—	2	1	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	1	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	4	no	—
777	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
778	C₄²	C₂×D₄×C₅₃	1	2	yes	—
779	C₄²	C₂×D₄×C₅₃	1	2	yes	—
780	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
781	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
782	C₄²	C₂⁴×C₅₃	1	2	yes	—
783	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	1	no	—
787	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
788	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
789	Q₈	—	2	2	no	—
790	Q₈	—	2	1	no	—
791	Q₈	—	4	2	no	—
792	Q₈	—	4	4	no	—
793	Q₈	—	8	2	no	—
794	Q₈	—	8	2	no	—
795	Q₈	—	8	1	no	—
796	Q₈	2₋¹⁺⁴×C₅₃	1	2	yes	—
797	D₄	—	2	2	no	—
798	D₄	—	2	2	no	—
799	D₄	—	2	2	no	—
800	D₄	—	2	1	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	1	no	—
803	D₄	—	2	2	no	—
804	D₄	—	4	2	no	—
805	D₄	—	4	4	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	2	no	—
808	D₄	—	4	4	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	2	no	—
811	D₄	—	4	2	no	—
812	D₄	—	8	2	no	—
813	D₄	—	8	1	no	—
814	D₄	—	8	2	no	—
815	D₄	—	8	2	no	—
816	D₄	—	8	2	no	—
817	D₄	—	8	4	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	8	4	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
842	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
844	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
849	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
850	C₈	—	2	2	no	—
851	C₈	—	2	2	no	—
852	C₈	—	2	4	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
869	C₄	—	2	2	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	2	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	1	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	4	no	—
881	C₄	C₅₃×#575	1	2	yes	—
882	C₄	C₅₃×#576	1	2	yes	—
883	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
884	C₄	C₅₃×#585	1	1	yes	characteristic
885	C₂	—	4	1	no	—
886	C₂	—	4	2	no	—
887	C₂	—	8	2	no	—
888	C₂	—	8	1	no	—
889	C₂	—	8	2	no	—
890	C₂	C₅₃×#3489	1	1	yes	characteristic
891	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
892	C₂	C₂×C₅₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3511	C₂	semidirect
2. C₅₃×#3483	C₂	semidirect
3. C₅₃×#3385	C₂	semidirect
4. C₅₃×#3366	C₂	semidirect
5. C₅₃×#3347	C₂	semidirect
6. C₅₃×#3341	C₂	semidirect
7. C₅₃×#3309	C₂	semidirect
8. C₅₃×#3305	C₂	semidirect
9. C₅₃×#3253	C₂	semidirect
10. C₅₃×#3245	C₂	semidirect
11. C₅₃×#3235	C₂	semidirect
12. C₅₃×#3226	C₂	semidirect
13. C₅₃×#3115	C₂	semidirect
14. C₅₃×#3106	C₂	semidirect
15. C₅₃×#3079	C₂	semidirect
16. C₅₃×#3076	C₂	semidirect
17. C₅₃×#2990	C₂	semidirect
406. #62136	C₅₃	direct (N × H)
439. #3511	C₂×C₅₃	semidirect
440. #3483	C₂×C₅₃	semidirect
441. #3385	C₂×C₅₃	semidirect
442. #3366	C₂×C₅₃	semidirect
443. #3347	C₂×C₅₃	semidirect
444. #3341	C₂×C₅₃	semidirect
445. #3309	C₂×C₅₃	semidirect
446. #3305	C₂×C₅₃	semidirect
447. #3253	C₂×C₅₃	semidirect
448. #3245	C₂×C₅₃	semidirect
449. #3235	C₂×C₅₃	semidirect
450. #3226	C₂×C₅₃	semidirect
451. #3115	C₂×C₅₃	semidirect
452. #3106	C₂×C₅₃	semidirect
453. #3079	C₂×C₅₃	semidirect
454. #3076	C₂×C₅₃	semidirect
455. #2990	C₂×C₅₃	semidirect
541. C₅₃	#62136	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×#3483	2
C₅₃×#3385	2
C₅₃×#3366	2
C₅₃×#3347	2
C₅₃×#3341	2
C₅₃×#3309	2
C₅₃×#3305	2
C₅₃×#3253	2
C₅₃×#3245	2
C₅₃×#3235	2
C₅₃×#3226	2
C₅₃×#3115	2
C₅₃×#3106	2
C₅₃×#3079	2
C₅₃×#3076	2
C₅₃×#2990	2
#62136	53

Subgroups — C53×#62136 #27269648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62136 #27269648