Subgroups — C₅₃×#62200 #27269712

Order 13568.

1808 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3345	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3341	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3337	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3310	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3294	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3257	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3241	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3118	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3081	C₂	1	2	yes	maximal, complemented
22	C₂×C₅₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#563	—	2	2	no	—
25	Q₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₅₃×#555	C₂²	1	1	yes	characteristic
27	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
28	C₅₃×#554	C₂²	1	1	yes	characteristic
29	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#553	—	2	1	no	—
32	C₅₃×#553	C₂²	1	2	yes	—
33	C₅₃×#552	—	2	1	no	—
34	C₅₃×#552	C₂²	1	2	yes	complemented
35	C₅₃×#550	C₂²	1	1	yes	characteristic
36	C₅₃×#547	—	2	1	no	—
37	C₅₃×#547	C₂²	1	2	yes	complemented
38	C₅₃×#546	—	2	1	no	—
39	C₅₃×#546	—	2	2	no	—
40	D₄²×C₅₃	C₂²	1	2	yes	—
41	D₄²×C₅₃	C₂²	1	1	yes	characteristic
42	C₅₃×#544	—	2	1	no	—
43	C₅₃×#544	C₂²	1	2	yes	complemented
44	C₅₃×#542	—	2	1	no	—
45	C₅₃×#542	C₂²	1	2	yes	complemented
46	C₅₃×#540	C₂²	1	2	yes	—
47	C₅₃×#538	—	2	2	no	—
48	C₅₃×#536	—	2	2	no	—
49	C₅₃×#532	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#529	C₂²	1	1	yes	characteristic
52	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#525	—	2	1	no	—
54	C₂×#121×C₅₃	—	2	1	no	—
55	C₅₃×#518	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#501	C₂²	1	2	yes	complemented
58	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#499	C₂²	1	2	yes	complemented
61	C₅₃×#490	C₂²	1	2	yes	complemented
62	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#486	C₂²	1	2	yes	complemented
65	C₅₃×#485	C₂²	1	2	yes	complemented
66	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#482	C₂²	1	2	yes	complemented
68	C₅₃×#482	C₂²	1	2	yes	complemented
69	C₅₃×#482	C₂²	1	2	yes	complemented
70	C₅₃×#481	C₂²	1	2	yes	complemented
71	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#480	C₂²	1	2	yes	complemented
73	C₅₃×#480	C₂²	1	2	yes	complemented
74	C₅₃×#480	C₂²	1	2	yes	complemented
75	C₅₃×#479	C₂²	1	2	yes	complemented
76	C₅₃×#478	C₂²	1	2	yes	—
77	C₅₃×#478	C₂²	1	1	yes	characteristic
78	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#478	C₂²	1	2	yes	complemented
80	C₅₃×#478	C₂²	1	2	yes	complemented
81	C₅₃×#478	C₂²	1	2	yes	complemented
82	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#476	C₂²	1	1	yes	characteristic
84	C₅₃×#476	C₂²	1	1	yes	characteristic
85	C₅₃×#476	C₂²	1	2	yes	—
86	C₅₃×#476	C₂²	1	2	yes	complemented
87	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#476	C₂²	1	2	yes	complemented
91	C₅₃×#474	C₂²	1	2	yes	—
92	C₅₃×#474	C₂²	1	2	yes	complemented
93	C₅₃×#474	C₂²	1	2	yes	complemented
94	C₅₃×#469	C₂²	1	2	yes	complemented
95	C₅₃×#468	C₂²	1	2	yes	complemented
96	C₅₃×#466	C₂²	1	2	yes	complemented
97	C₅₃×#466	C₂²	1	2	yes	complemented
98	C₅₃×#465	C₂²	1	2	yes	complemented
99	C₅₃×#465	C₂²	1	2	yes	complemented
100	C₅₃×#463	C₂²	1	1	yes	characteristic
101	C₅₃×#463	C₂²	1	2	yes	complemented
102	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#460	C₂²	1	2	yes	complemented
105	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#459	C₂²	1	2	yes	complemented
107	C₅₃×#450	C₂²	1	2	yes	—
108	C₅₃×#450	C₂²	1	1	yes	characteristic
109	C₅₃×#447	C₂²	1	1	yes	characteristic
110	C₅₃×#447	C₂²	1	2	yes	—
111	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#442	C₂²	1	2	yes	complemented
114	C₅₃×#440	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₅₃	C₂²	1	2	yes	—
119	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
124	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#433	C₂²	1	2	yes	complemented
126	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#428	C₂²	1	2	yes	complemented
128	C₅₃×#427	C₂²	1	2	yes	complemented
129	C₂×#106×C₅₃	C₂²	1	2	yes	complemented
130	C₅₃×#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#418	C₂²	1	2	yes	—
133	C₂×#102×C₅₃	C₂²	1	2	yes	—
134	C₂×#102×C₅₃	C₂²	1	2	yes	—
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	2	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂²×Q₈×C₅₃	—	2	1	no	—
139	C₂²×D₄×C₅₃	—	2	1	no	—
140	C₂²×D₄×C₅₃	—	2	2	no	—
141	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₅₃	—	2	1	no	—
144	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
149	C₂×D₈×C₅₃	C₂³	1	2	yes	—
150	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
152	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
153	C₄⋊Q₈×C₅₃	—	2	2	no	—
154	C₄⋊Q₈×C₅₃	—	2	2	no	—
155	C₄⋊Q₈×C₅₃	—	2	1	no	—
156	C₄⋊Q₈×C₅₃	—	2	1	no	—
157	C₄⋊Q₈×C₅₃	—	2	1	no	—
158	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
163	#127×C₅₃	C₂³	1	1	yes	characteristic
164	#127×C₅₃	C₂³	1	2	yes	—
165	#126×C₅₃	—	2	2	no	—
166	#126×C₅₃	—	2	2	no	—
167	#126×C₅₃	—	2	2	no	—
168	#126×C₅₃	—	2	1	no	—
169	#126×C₅₃	D₄	1	2	yes	—
170	#125×C₅₃	—	2	1	no	—
171	#125×C₅₃	—	2	2	no	—
172	#125×C₅₃	—	2	2	no	—
173	#125×C₅₃	D₄	1	1	yes	characteristic
174	#125×C₅₃	C₂³	1	2	yes	—
175	#125×C₅₃	C₂³	1	2	yes	—
176	#125×C₅₃	C₂³	1	1	yes	characteristic
177	#124×C₅₃	—	2	2	no	—
178	#124×C₅₃	—	2	2	no	—
179	#124×C₅₃	—	2	2	no	—
180	#124×C₅₃	—	2	1	no	—
181	#124×C₅₃	D₄	1	1	yes	characteristic
182	#124×C₅₃	C₂³	1	1	yes	characteristic
183	#123×C₅₃	—	2	2	no	—
184	#123×C₅₃	—	2	2	no	—
185	#123×C₅₃	—	2	2	no	—
186	#123×C₅₃	—	2	2	no	—
187	#123×C₅₃	—	2	2	no	—
188	#123×C₅₃	—	2	2	no	—
189	#123×C₅₃	—	2	2	no	—
190	#123×C₅₃	—	2	1	no	—
191	#123×C₅₃	D₄	1	2	yes	—
192	C₂²⋊Q₈×C₅₃	—	2	2	no	—
193	C₂²⋊Q₈×C₅₃	—	2	2	no	—
194	C₂²⋊Q₈×C₅₃	—	2	2	no	—
195	C₂²⋊Q₈×C₅₃	—	2	2	no	—
196	C₂²⋊Q₈×C₅₃	—	2	2	no	—
197	C₂²⋊Q₈×C₅₃	—	2	2	no	—
198	C₂²⋊Q₈×C₅₃	—	2	2	no	—
199	C₂²⋊Q₈×C₅₃	—	2	1	no	—
200	C₂²⋊Q₈×C₅₃	—	2	1	no	—
201	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
202	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
203	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
204	#121×C₅₃	—	2	1	no	—
205	#121×C₅₃	—	2	1	no	—
206	#121×C₅₃	—	2	2	no	—
207	#121×C₅₃	—	2	2	no	—
208	#121×C₅₃	—	2	2	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	—	2	2	no	—
211	#121×C₅₃	—	2	1	no	—
212	#121×C₅₃	—	2	1	no	—
213	#121×C₅₃	—	2	1	no	—
214	#121×C₅₃	D₄	1	1	yes	characteristic
215	#121×C₅₃	C₂³	1	1	yes	characteristic
216	#121×C₅₃	C₂³	1	2	yes	—
217	#121×C₅₃	C₂³	1	2	yes	—
218	#121×C₅₃	C₂³	1	2	yes	—
219	#121×C₅₃	C₂³	1	2	yes	—
220	#120×C₅₃	—	2	2	no	—
221	#120×C₅₃	—	2	2	no	—
222	#120×C₅₃	—	2	2	no	—
223	C₄×Q₈×C₅₃	—	2	1	no	—
224	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	—	2	2	no	—
229	C₄×D₄×C₅₃	—	2	2	no	—
230	C₄×D₄×C₅₃	—	2	1	no	—
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	1	no	—
233	C₄×D₄×C₅₃	—	2	1	no	—
234	C₄×D₄×C₅₃	—	2	1	no	—
235	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₅₃	C₂³	1	2	yes	—
240	C₄×D₄×C₅₃	C₂³	1	2	yes	—
241	C₄×D₄×C₅₃	C₂³	1	2	yes	—
242	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₅₃	C₂³	1	2	yes	—
244	C₄×D₄×C₅₃	C₂³	1	2	yes	—
245	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
246	#117×C₅₃	—	2	1	no	—
247	#117×C₅₃	—	2	1	no	—
248	#117×C₅₃	—	2	2	no	—
249	#117×C₅₃	—	2	1	no	—
250	#117×C₅₃	C₂³	1	2	yes	—
251	#117×C₅₃	C₂³	1	2	yes	—
252	#117×C₅₃	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
254	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
255	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
256	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
259	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
261	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
262	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
263	#107×C₅₃	C₂³	1	2	yes	—
264	#107×C₅₃	C₂³	1	1	yes	characteristic
265	#107×C₅₃	C₂³	1	2	yes	—
266	#107×C₅₃	C₂³	1	2	yes	—
267	#107×C₅₃	C₂³	1	2	yes	—
268	#107×C₅₃	C₂³	1	2	yes	—
269	#107×C₅₃	C₂³	1	1	yes	characteristic
270	#106×C₅₃	C₂³	1	2	yes	—
271	#106×C₅₃	C₂³	1	2	yes	—
272	#106×C₅₃	C₂³	1	2	yes	—
273	#106×C₅₃	C₂³	1	1	yes	characteristic
274	#106×C₅₃	C₂³	1	2	yes	—
275	#106×C₅₃	C₂³	1	2	yes	—
276	#106×C₅₃	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
278	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
282	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	#103×C₅₃	C₂³	1	1	yes	characteristic
285	#103×C₅₃	C₂³	1	2	yes	—
286	#103×C₅₃	C₂³	1	1	yes	characteristic
287	#102×C₅₃	C₂³	1	2	yes	—
288	#102×C₅₃	C₂³	1	1	yes	characteristic
289	#102×C₅₃	C₂³	1	2	yes	—
290	#102×C₅₃	C₂³	1	2	yes	—
291	#102×C₅₃	C₂³	1	2	yes	—
292	#102×C₅₃	C₂³	1	2	yes	—
293	#102×C₅₃	C₂³	1	2	yes	—
294	#102×C₅₃	C₂³	1	1	yes	characteristic
295	#102×C₅₃	C₂³	1	2	yes	—
296	#102×C₅₃	C₂³	1	2	yes	—
297	#102×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	1	yes	characteristic
299	#102×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
308	#97×C₅₃	C₂³	1	2	yes	—
309	C₄×C₈×C₅₃	C₂³	1	2	yes	—
310	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
312	C₂⁴×C₅₃	—	2	1	no	—
313	C₂⁴×C₅₃	—	2	2	no	—
314	#41×C₅₃	—	8	2	no	—
315	#41×C₅₃	—	8	4	no	—
316	#41×C₅₃	—	8	2	no	—
317	C₂×Q₈×C₅₃	—	2	1	no	—
318	C₂×Q₈×C₅₃	—	2	1	no	—
319	C₂×Q₈×C₅₃	—	2	2	no	—
320	C₂×Q₈×C₅₃	—	2	2	no	—
321	C₂×Q₈×C₅₃	—	2	1	no	—
322	C₂×Q₈×C₅₃	—	8	2	no	—
323	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₅₃	—	2	2	no	—
326	C₂×D₄×C₅₃	—	2	4	no	—
327	C₂×D₄×C₅₃	—	2	2	no	—
328	C₂×D₄×C₅₃	—	2	1	no	—
329	C₂×D₄×C₅₃	—	2	2	no	—
330	C₂×D₄×C₅₃	—	2	2	no	—
331	C₂×D₄×C₅₃	—	2	2	no	—
332	C₂×D₄×C₅₃	—	2	2	no	—
333	C₂×D₄×C₅₃	—	2	1	no	—
334	C₂×D₄×C₅₃	—	2	1	no	—
335	C₂×D₄×C₅₃	—	2	2	no	—
336	C₂×D₄×C₅₃	—	2	1	no	—
337	C₂×D₄×C₅₃	—	2	2	no	—
338	C₂×D₄×C₅₃	—	4	1	no	—
339	C₂×D₄×C₅₃	—	4	2	no	—
340	C₂×D₄×C₅₃	—	8	2	no	—
341	C₂×D₄×C₅₃	—	8	4	no	—
342	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
343	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
345	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₅₃	—	2	2	no	—
349	C₂²×C₄×C₅₃	—	2	1	no	—
350	C₂²×C₄×C₅₃	—	2	2	no	—
351	C₂²×C₄×C₅₃	—	2	1	no	—
352	C₂²×C₄×C₅₃	—	2	1	no	—
353	C₂²×C₄×C₅₃	—	2	1	no	—
354	C₂²×C₄×C₅₃	—	2	1	no	—
355	C₂²×C₄×C₅₃	—	2	2	no	—
356	C₂²×C₄×C₅₃	—	2	2	no	—
357	C₂²×C₄×C₅₃	—	2	2	no	—
358	C₂²×C₄×C₅₃	—	2	2	no	—
359	C₂²×C₄×C₅₃	—	2	1	no	—
360	C₂²×C₄×C₅₃	—	8	2	no	—
361	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
365	SD₁₆×C₅₃	—	2	2	no	—
366	SD₁₆×C₅₃	—	4	2	no	—
367	SD₁₆×C₅₃	—	4	1	no	—
368	D₈×C₅₃	—	2	2	no	—
369	D₈×C₅₃	—	4	1	no	—
370	D₈×C₅₃	—	4	2	no	—
371	M₁₆×C₅₃	—	4	2	no	—
372	C₂×C₈×C₅₃	—	4	2	no	—
373	C₂×C₈×C₅₃	—	4	2	no	—
374	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
377	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
380	C₄⋊C₄×C₅₃	—	2	1	no	—
381	C₄⋊C₄×C₅₃	—	2	1	no	—
382	C₄⋊C₄×C₅₃	—	2	1	no	—
383	C₄⋊C₄×C₅₃	—	2	2	no	—
384	C₄⋊C₄×C₅₃	—	2	2	no	—
385	C₄⋊C₄×C₅₃	—	2	2	no	—
386	C₄⋊C₄×C₅₃	—	2	1	no	—
387	C₄⋊C₄×C₅₃	—	2	2	no	—
388	C₄⋊C₄×C₅₃	—	2	2	no	—
389	C₄⋊C₄×C₅₃	—	2	2	no	—
390	C₄⋊C₄×C₅₃	—	2	2	no	—
391	C₄⋊C₄×C₅₃	—	2	1	no	—
392	C₄⋊C₄×C₅₃	—	2	1	no	—
393	C₄⋊C₄×C₅₃	—	2	2	no	—
394	C₄⋊C₄×C₅₃	—	2	1	no	—
395	C₄⋊C₄×C₅₃	—	2	2	no	—
396	C₄⋊C₄×C₅₃	—	2	1	no	—
397	C₄⋊C₄×C₅₃	—	2	2	no	—
398	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
411	C₂²⋊C₄×C₅₃	—	2	2	no	—
412	C₂²⋊C₄×C₅₃	—	2	1	no	—
413	C₂²⋊C₄×C₅₃	—	2	2	no	—
414	C₂²⋊C₄×C₅₃	—	2	2	no	—
415	C₂²⋊C₄×C₅₃	—	2	1	no	—
416	C₂²⋊C₄×C₅₃	—	2	1	no	—
417	C₂²⋊C₄×C₅₃	—	2	2	no	—
418	C₂²⋊C₄×C₅₃	—	2	2	no	—
419	C₂²⋊C₄×C₅₃	—	2	1	no	—
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	1	no	—
422	C₂²⋊C₄×C₅₃	—	2	2	no	—
423	C₂²⋊C₄×C₅₃	—	2	1	no	—
424	C₂²⋊C₄×C₅₃	—	2	2	no	—
425	C₂²⋊C₄×C₅₃	—	2	1	no	—
426	C₂²⋊C₄×C₅₃	—	2	2	no	—
427	C₂²⋊C₄×C₅₃	—	2	2	no	—
428	C₂²⋊C₄×C₅₃	—	2	1	no	—
429	C₂²⋊C₄×C₅₃	—	2	2	no	—
430	C₂²⋊C₄×C₅₃	—	2	1	no	—
431	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
436	C₄²×C₅₃	—	2	2	no	—
437	C₄²×C₅₃	—	2	2	no	—
438	C₄²×C₅₃	—	2	1	no	—
439	C₄²×C₅₃	—	2	2	no	—
440	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₄²×C₅₃	C₂⁴	1	2	yes	—
444	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
445	C₂³×C₅₃	—	2	1	no	—
446	C₂³×C₅₃	—	2	1	no	—
447	C₂³×C₅₃	—	2	2	no	—
448	C₂³×C₅₃	—	2	1	no	—
449	C₂³×C₅₃	—	4	2	no	—
450	C₂³×C₅₃	—	4	4	no	—
451	C₂³×C₅₃	—	4	2	no	—
452	C₂³×C₅₃	—	8	1	no	—
453	C₂³×C₅₃	—	8	2	no	—
454	C₂³×C₅₃	—	8	2	no	—
455	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
456	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
457	Q₈×C₅₃	—	2	2	no	—
458	Q₈×C₅₃	—	2	1	no	—
459	Q₈×C₅₃	—	2	1	no	—
460	Q₈×C₅₃	—	8	2	no	—
461	Q₈×C₅₃	—	8	1	no	—
462	Q₈×C₅₃	—	8	1	no	—
463	Q₈×C₅₃	—	8	1	no	—
464	Q₈×C₅₃	—	8	2	no	—
465	D₄×C₅₃	—	2	4	no	—
466	D₄×C₅₃	—	2	2	no	—
467	D₄×C₅₃	—	2	1	no	—
468	D₄×C₅₃	—	2	2	no	—
469	D₄×C₅₃	—	2	1	no	—
470	D₄×C₅₃	—	2	1	no	—
471	D₄×C₅₃	—	2	1	no	—
472	D₄×C₅₃	—	2	2	no	—
473	D₄×C₅₃	—	2	1	no	—
474	D₄×C₅₃	—	4	2	no	—
475	D₄×C₅₃	—	4	4	no	—
476	D₄×C₅₃	—	4	4	no	—
477	D₄×C₅₃	—	4	2	no	—
478	D₄×C₅₃	—	4	2	no	—
479	D₄×C₅₃	—	8	2	no	—
480	D₄×C₅₃	—	8	1	no	—
481	D₄×C₅₃	—	8	2	no	—
482	D₄×C₅₃	—	8	2	no	—
483	D₄×C₅₃	—	8	2	no	—
484	D₄×C₅₃	—	8	2	no	—
485	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
486	C₂×C₄×C₅₃	—	2	2	no	—
487	C₂×C₄×C₅₃	—	2	2	no	—
488	C₂×C₄×C₅₃	—	2	1	no	—
489	C₂×C₄×C₅₃	—	2	2	no	—
490	C₂×C₄×C₅₃	—	2	1	no	—
491	C₂×C₄×C₅₃	—	2	2	no	—
492	C₂×C₄×C₅₃	—	2	1	no	—
493	C₂×C₄×C₅₃	—	2	1	no	—
494	C₂×C₄×C₅₃	—	2	2	no	—
495	C₂×C₄×C₅₃	—	2	2	no	—
496	C₂×C₄×C₅₃	—	2	1	no	—
497	C₂×C₄×C₅₃	—	2	2	no	—
498	C₂×C₄×C₅₃	—	2	1	no	—
499	C₂×C₄×C₅₃	—	2	1	no	—
500	C₂×C₄×C₅₃	—	4	4	no	—
501	C₂×C₄×C₅₃	—	4	2	no	—
502	C₂×C₄×C₅₃	—	4	2	no	—
503	C₂×C₄×C₅₃	—	4	2	no	—
504	C₂×C₄×C₅₃	—	8	1	no	—
505	C₂×C₄×C₅₃	—	8	1	no	—
506	C₂×C₄×C₅₃	—	8	2	no	—
507	C₂×C₄×C₅₃	—	8	2	no	—
508	C₂×C₄×C₅₃	—	8	2	no	—
509	C₂×C₄×C₅₃	—	8	2	no	—
510	C₂×C₄×C₅₃	—	8	1	no	—
511	C₂×C₄×C₅₃	—	8	2	no	—
512	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
521	C₈×C₅₃	—	2	1	no	—
522	C₈×C₅₃	—	2	1	no	—
523	C₈×C₅₃	—	2	1	no	—
524	C₈×C₅₃	—	2	2	no	—
525	C₈×C₅₃	—	2	2	no	—
526	C₈×C₅₃	—	2	1	no	—
527	#62200	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
528	C₂²×C₅₃	—	2	1	no	—
529	C₂²×C₅₃	—	2	1	no	—
530	C₂²×C₅₃	—	2	2	no	—
531	C₂²×C₅₃	—	2	2	no	—
532	C₂²×C₅₃	—	2	2	no	—
533	C₂²×C₅₃	—	2	2	no	—
534	C₂²×C₅₃	—	4	1	no	—
535	C₂²×C₅₃	—	4	1	no	—
536	C₂²×C₅₃	—	4	1	no	—
537	C₂²×C₅₃	—	4	2	no	—
538	C₂²×C₅₃	—	4	1	no	—
539	C₂²×C₅₃	—	4	1	no	—
540	C₂²×C₅₃	—	4	2	no	—
541	C₂²×C₅₃	—	4	1	no	—
542	C₂²×C₅₃	—	4	1	no	—
543	C₂²×C₅₃	—	4	1	no	—
544	C₂²×C₅₃	—	4	2	no	—
545	C₂²×C₅₃	—	8	4	no	—
546	C₂²×C₅₃	—	16	4	no	—
547	C₂²×C₅₃	#576	1	2	yes	—
548	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
549	C₄×C₅₃	—	2	1	no	—
550	C₄×C₅₃	—	2	2	no	—
551	C₄×C₅₃	—	2	1	no	—
552	C₄×C₅₃	—	2	1	no	—
553	C₄×C₅₃	—	2	2	no	—
554	C₄×C₅₃	—	2	1	no	—
555	C₄×C₅₃	—	2	2	no	—
556	C₄×C₅₃	—	4	1	no	—
557	C₄×C₅₃	—	4	2	no	—
558	C₄×C₅₃	—	4	2	no	—
559	C₄×C₅₃	—	4	2	no	—
560	C₄×C₅₃	—	4	1	no	—
561	C₄×C₅₃	—	4	1	no	—
562	C₄×C₅₃	—	4	1	no	—
563	C₄×C₅₃	—	4	1	no	—
564	C₄×C₅₃	#577	1	2	yes	—
565	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
566	C₄×C₅₃	#585	1	1	yes	characteristic
567	#3544	C₂×C₅₃	1	1	yes	characteristic, complemented
568	#3519	C₂×C₅₃	1	1	yes	characteristic, complemented
569	#3385	C₂×C₅₃	1	1	yes	characteristic, complemented
570	#3380	C₂×C₅₃	1	1	yes	characteristic, complemented
571	#3366	C₂×C₅₃	1	1	yes	characteristic, complemented
572	#3362	C₂×C₅₃	1	1	yes	characteristic, complemented
573	#3357	C₂×C₅₃	1	1	yes	characteristic, complemented
574	#3345	C₂×C₅₃	1	2	yes	complemented
575	#3341	C₂×C₅₃	1	1	yes	characteristic, complemented
576	#3337	C₂×C₅₃	1	2	yes	complemented
577	#3325	C₂×C₅₃	1	1	yes	characteristic, complemented
578	#3310	C₂×C₅₃	1	2	yes	complemented
579	#3295	C₂×C₅₃	1	1	yes	characteristic, complemented
580	#3294	C₂×C₅₃	1	2	yes	complemented
581	#3257	C₂×C₅₃	1	2	yes	complemented
582	#3247	C₂×C₅₃	1	1	yes	characteristic, complemented
583	#3241	C₂×C₅₃	1	2	yes	complemented
584	#3226	C₂×C₅₃	1	1	yes	characteristic, complemented
585	#3118	C₂×C₅₃	1	2	yes	complemented
586	#3105	C₂×C₅₃	1	1	yes	characteristic, complemented
587	#3081	C₂×C₅₃	1	2	yes	complemented
588	C₂×#476	C₂×C₅₃	1	1	yes	characteristic, complemented
589	#2994	C₂×C₅₃	1	1	yes	characteristic, complemented
590	C₂×C₅₃	—	2	2	no	—
591	C₂×C₅₃	—	4	2	no	—
592	C₂×C₅₃	—	4	2	no	—
593	C₂×C₅₃	—	8	1	no	—
594	C₂×C₅₃	—	8	1	no	—
595	C₂×C₅₃	—	8	2	no	—
596	C₂×C₅₃	#3489	1	1	yes	characteristic
597	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
598	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
599	#563	—	2	2	no	—
600	Q₈²	C₂²×C₅₃	1	1	yes	characteristic, complemented
601	#555	C₂²×C₅₃	1	1	yes	characteristic
602	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
603	#554	C₂²×C₅₃	1	1	yes	characteristic
604	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
605	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
606	#553	—	2	1	no	—
607	#553	C₂²×C₅₃	1	2	yes	—
608	#552	—	2	1	no	—
609	#552	C₂²×C₅₃	1	2	yes	complemented
610	#550	C₂²×C₅₃	1	1	yes	characteristic
611	#547	—	2	1	no	—
612	#547	C₂²×C₅₃	1	2	yes	complemented
613	#546	—	2	1	no	—
614	#546	—	2	2	no	—
615	D₄²	C₂²×C₅₃	1	2	yes	—
616	D₄²	C₂²×C₅₃	1	1	yes	characteristic
617	#544	—	2	1	no	—
618	#544	C₂²×C₅₃	1	2	yes	complemented
619	#542	—	2	1	no	—
620	#542	C₂²×C₅₃	1	2	yes	complemented
621	#540	C₂²×C₅₃	1	2	yes	—
622	#538	—	2	2	no	—
623	#536	—	2	2	no	—
624	#532	C₂²×C₅₃	1	1	yes	characteristic
625	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
626	#529	C₂²×C₅₃	1	1	yes	characteristic
627	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
628	#525	—	2	1	no	—
629	C₂×#121	—	2	1	no	—
630	#518	C₂²×C₅₃	1	2	yes	—
631	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
632	#501	C₂²×C₅₃	1	2	yes	complemented
633	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
634	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
635	#499	C₂²×C₅₃	1	2	yes	complemented
636	#490	C₂²×C₅₃	1	2	yes	complemented
637	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
638	#486	C₂²×C₅₃	1	2	yes	complemented
639	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
640	#485	C₂²×C₅₃	1	2	yes	complemented
641	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
642	#482	C₂²×C₅₃	1	2	yes	complemented
643	#482	C₂²×C₅₃	1	2	yes	complemented
644	#482	C₂²×C₅₃	1	2	yes	complemented
645	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
646	#481	C₂²×C₅₃	1	2	yes	complemented
647	#480	C₂²×C₅₃	1	2	yes	complemented
648	#480	C₂²×C₅₃	1	2	yes	complemented
649	#480	C₂²×C₅₃	1	2	yes	complemented
650	#479	C₂²×C₅₃	1	2	yes	complemented
651	#478	C₂²×C₅₃	1	1	yes	characteristic
652	#478	C₂²×C₅₃	1	2	yes	—
653	#478	C₂²×C₅₃	1	2	yes	complemented
654	#478	C₂²×C₅₃	1	2	yes	complemented
655	#478	C₂²×C₅₃	1	2	yes	complemented
656	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
657	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
658	#476	C₂²×C₅₃	1	2	yes	—
659	#476	C₂²×C₅₃	1	1	yes	characteristic
660	#476	C₂²×C₅₃	1	1	yes	characteristic
661	#476	C₂²×C₅₃	1	2	yes	complemented
662	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
664	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
665	#476	C₂²×C₅₃	1	2	yes	complemented
666	#474	C₂²×C₅₃	1	2	yes	—
667	#474	C₂²×C₅₃	1	2	yes	complemented
668	#474	C₂²×C₅₃	1	2	yes	complemented
669	#469	C₂²×C₅₃	1	2	yes	complemented
670	#468	C₂²×C₅₃	1	2	yes	complemented
671	#466	C₂²×C₅₃	1	2	yes	complemented
672	#466	C₂²×C₅₃	1	2	yes	complemented
673	#465	C₂²×C₅₃	1	2	yes	complemented
674	#465	C₂²×C₅₃	1	2	yes	complemented
675	#463	C₂²×C₅₃	1	1	yes	characteristic
676	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
677	#463	C₂²×C₅₃	1	2	yes	complemented
678	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
679	#460	C₂²×C₅₃	1	2	yes	complemented
680	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
681	#459	C₂²×C₅₃	1	2	yes	complemented
682	#450	C₂²×C₅₃	1	1	yes	characteristic
683	#450	C₂²×C₅₃	1	2	yes	—
684	#447	C₂²×C₅₃	1	1	yes	characteristic
685	#447	C₂²×C₅₃	1	2	yes	—
686	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
688	#442	C₂²×C₅₃	1	2	yes	complemented
689	#440	C₂²×C₅₃	1	2	yes	—
690	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
691	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
694	C₄×D₈	C₂²×C₅₃	1	2	yes	—
695	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
696	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
697	#435	C₂²×C₅₃	1	2	yes	complemented
698	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
699	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
700	#433	C₂²×C₅₃	1	2	yes	complemented
701	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
702	#428	C₂²×C₅₃	1	2	yes	complemented
703	#427	C₂²×C₅₃	1	2	yes	complemented
704	C₂×#106	C₂²×C₅₃	1	2	yes	complemented
705	#424	C₂²×C₅₃	1	2	yes	complemented
706	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	#418	C₂²×C₅₃	1	2	yes	—
708	C₂×#102	C₂²×C₅₃	1	2	yes	—
709	C₂×#102	C₂²×C₅₃	1	2	yes	—
710	C₅₃	#62200	1	1	yes	characteristic, direct product factor, Sylow
711	C₂×#41	—	2	1	no	—
712	C₂×#41	—	2	2	no	—
713	C₂×#41	—	2	1	no	—
714	C₂²×Q₈	—	2	1	no	—
715	C₂²×D₄	—	2	1	no	—
716	C₂²×D₄	—	2	2	no	—
717	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
718	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
719	C₂³×C₄	—	2	1	no	—
720	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
721	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
723	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
724	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
725	C₂×D₈	C₂³×C₅₃	1	2	yes	—
726	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
727	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
728	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
729	C₄⋊Q₈	—	2	2	no	—
730	C₄⋊Q₈	—	2	2	no	—
731	C₄⋊Q₈	—	2	1	no	—
732	C₄⋊Q₈	—	2	1	no	—
733	C₄⋊Q₈	—	2	1	no	—
734	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
735	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
738	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
739	#127	C₂³×C₅₃	1	1	yes	characteristic
740	#127	C₂³×C₅₃	1	2	yes	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	1	no	—
745	#126	D₄×C₅₃	1	2	yes	—
746	#125	—	2	1	no	—
747	#125	—	2	2	no	—
748	#125	—	2	2	no	—
749	#125	D₄×C₅₃	1	1	yes	characteristic
750	#125	C₂³×C₅₃	1	1	yes	characteristic
751	#125	C₂³×C₅₃	1	2	yes	—
752	#125	C₂³×C₅₃	1	2	yes	—
753	#124	—	2	2	no	—
754	#124	—	2	2	no	—
755	#124	—	2	2	no	—
756	#124	—	2	1	no	—
757	#124	D₄×C₅₃	1	1	yes	characteristic
758	#124	C₂³×C₅₃	1	1	yes	characteristic
759	#123	—	2	2	no	—
760	#123	—	2	1	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	D₄×C₅₃	1	2	yes	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
778	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
779	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
780	#121	—	2	2	no	—
781	#121	—	2	1	no	—
782	#121	—	2	1	no	—
783	#121	—	2	1	no	—
784	#121	—	2	1	no	—
785	#121	—	2	1	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	D₄×C₅₃	1	1	yes	characteristic
791	#121	C₂³×C₅₃	1	1	yes	characteristic
792	#121	C₂³×C₅₃	1	2	yes	—
793	#121	C₂³×C₅₃	1	2	yes	—
794	#121	C₂³×C₅₃	1	2	yes	—
795	#121	C₂³×C₅₃	1	2	yes	—
796	#120	—	2	2	no	—
797	#120	—	2	2	no	—
798	#120	—	2	2	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
802	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₅₃	1	2	yes	—
816	C₄×D₄	C₂³×C₅₃	1	2	yes	—
817	C₄×D₄	C₂³×C₅₃	1	2	yes	—
818	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₅₃	1	2	yes	—
820	C₄×D₄	C₂³×C₅₃	1	2	yes	—
821	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
822	#117	—	2	1	no	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	—	2	1	no	—
826	#117	C₂³×C₅₃	1	2	yes	—
827	#117	C₂³×C₅₃	1	2	yes	—
828	#117	C₂³×C₅₃	1	2	yes	—
829	C₂×C₄⋊C₄	—	2	1	no	—
830	C₂×C₄⋊C₄	—	2	1	no	—
831	C₂×C₄⋊C₄	—	2	1	no	—
832	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
833	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
834	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
835	C₂×C₂²⋊C₄	—	2	1	no	—
836	C₂×C₂²⋊C₄	—	2	2	no	—
837	C₂×C₂²⋊C₄	—	2	2	no	—
838	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
839	#107	C₂³×C₅₃	1	1	yes	characteristic
840	#107	C₂³×C₅₃	1	2	yes	—
841	#107	C₂³×C₅₃	1	2	yes	—
842	#107	C₂³×C₅₃	1	2	yes	—
843	#107	C₂³×C₅₃	1	2	yes	—
844	#107	C₂³×C₅₃	1	1	yes	characteristic
845	#107	C₂³×C₅₃	1	2	yes	—
846	#106	C₂³×C₅₃	1	2	yes	—
847	#106	C₂³×C₅₃	1	2	yes	—
848	#106	C₂³×C₅₃	1	2	yes	—
849	#106	C₂³×C₅₃	1	2	yes	—
850	#106	C₂³×C₅₃	1	2	yes	—
851	#106	C₂³×C₅₃	1	1	yes	characteristic
852	#106	C₂³×C₅₃	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
854	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
856	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
857	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
858	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
859	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
860	#103	C₂³×C₅₃	1	1	yes	characteristic
861	#103	C₂³×C₅₃	1	1	yes	characteristic
862	#103	C₂³×C₅₃	1	2	yes	—
863	#102	C₂³×C₅₃	1	2	yes	—
864	#102	C₂³×C₅₃	1	1	yes	characteristic
865	#102	C₂³×C₅₃	1	2	yes	—
866	#102	C₂³×C₅₃	1	2	yes	—
867	#102	C₂³×C₅₃	1	2	yes	—
868	#102	C₂³×C₅₃	1	2	yes	—
869	#102	C₂³×C₅₃	1	2	yes	—
870	#102	C₂³×C₅₃	1	1	yes	characteristic
871	#102	C₂³×C₅₃	1	2	yes	—
872	#102	C₂³×C₅₃	1	2	yes	—
873	#102	C₂³×C₅₃	1	2	yes	—
874	#102	C₂³×C₅₃	1	1	yes	characteristic
875	#102	C₂³×C₅₃	1	1	yes	characteristic
876	#102	C₂³×C₅₃	1	1	yes	characteristic
877	#102	C₂³×C₅₃	1	2	yes	—
878	#102	C₂³×C₅₃	1	1	yes	characteristic
879	#102	C₂³×C₅₃	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
881	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
882	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
884	#97	C₂³×C₅₃	1	2	yes	—
885	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
886	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
887	C₄×C₈	C₂³×C₅₃	1	2	yes	—
888	C₂⁴	—	2	1	no	—
889	C₂⁴	—	2	2	no	—
890	#41	—	8	2	no	—
891	#41	—	8	4	no	—
892	#41	—	8	2	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	2	no	—
896	C₂×Q₈	—	2	2	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	8	2	no	—
899	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
900	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	4	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	4	1	no	—
915	C₂×D₄	—	4	2	no	—
916	C₂×D₄	—	8	2	no	—
917	C₂×D₄	—	8	4	no	—
918	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
919	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
920	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
921	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
922	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
923	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	8	2	no	—
937	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
938	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
939	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
941	SD₁₆	—	2	2	no	—
942	SD₁₆	—	4	2	no	—
943	SD₁₆	—	4	1	no	—
944	D₈	—	2	2	no	—
945	D₈	—	4	1	no	—
946	D₈	—	4	2	no	—
947	M₁₆	—	4	2	no	—
948	C₂×C₈	—	4	2	no	—
949	C₂×C₈	—	4	2	no	—
950	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
953	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
954	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
955	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
975	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
976	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
977	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
978	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
981	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
983	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
986	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1008	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1010	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1011	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1017	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1018	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1019	C₄²	C₂⁴×C₅₃	1	2	yes	—
1020	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	1	no	—
1023	C₂³	—	2	2	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	4	2	no	—
1026	C₂³	—	4	4	no	—
1027	C₂³	—	4	2	no	—
1028	C₂³	—	8	1	no	—
1029	C₂³	—	8	2	no	—
1030	C₂³	—	8	2	no	—
1031	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1032	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1033	Q₈	—	2	2	no	—
1034	Q₈	—	2	1	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	8	2	no	—
1037	Q₈	—	8	1	no	—
1038	Q₈	—	8	1	no	—
1039	Q₈	—	8	1	no	—
1040	Q₈	—	8	2	no	—
1041	D₄	—	2	4	no	—
1042	D₄	—	2	2	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	2	1	no	—
1045	D₄	—	2	2	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	4	no	—
1052	D₄	—	4	4	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	4	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	1	no	—
1057	D₄	—	8	2	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	2	no	—
1060	D₄	—	8	2	no	—
1061	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	4	4	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	2	no	—
1080	C₂×C₄	—	8	1	no	—
1081	C₂×C₄	—	8	1	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	—	8	1	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1090	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1091	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1092	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1093	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1094	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1095	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1096	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1097	C₈	—	2	1	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	1	no	—
1100	C₈	—	2	2	no	—
1101	C₈	—	2	2	no	—
1102	C₈	—	2	1	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	8	4	no	—
1121	C₂²	—	16	4	no	—
1122	C₂²	C₅₃×#576	1	2	yes	—
1123	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1124	C₄	—	2	1	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	2	1	no	—
1127	C₄	—	2	1	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	2	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	C₅₃×#577	1	2	yes	—
1140	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1141	C₄	C₅₃×#585	1	1	yes	characteristic
1142	C₂	—	2	2	no	—
1143	C₂	—	4	2	no	—
1144	C₂	—	4	2	no	—
1145	C₂	—	8	1	no	—
1146	C₂	—	8	2	no	—
1147	C₂	—	8	1	no	—
1148	C₂	C₅₃×#3489	1	1	yes	characteristic
1149	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1150	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 ◁ C₅₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3544	C₂	semidirect
2. C₅₃×#3519	C₂	semidirect
3. C₅₃×#3385	C₂	semidirect
4. C₅₃×#3380	C₂	semidirect
5. C₅₃×#3366	C₂	semidirect
6. C₅₃×#3362	C₂	semidirect
7. C₅₃×#3357	C₂	semidirect
8. C₅₃×#3345	C₂	semidirect
9. C₅₃×#3341	C₂	semidirect
10. C₅₃×#3337	C₂	semidirect
11. C₅₃×#3325	C₂	semidirect
12. C₅₃×#3310	C₂	semidirect
13. C₅₃×#3295	C₂	semidirect
14. C₅₃×#3294	C₂	semidirect
15. C₅₃×#3257	C₂	semidirect
16. C₅₃×#3247	C₂	semidirect
17. C₅₃×#3241	C₂	semidirect
18. C₅₃×#3226	C₂	semidirect
19. C₅₃×#3118	C₂	semidirect
20. C₅₃×#3105	C₂	semidirect
21. C₅₃×#3081	C₂	semidirect
22. C₂×C₅₃×#476	C₂	semidirect
23. C₅₃×#2994	C₂	semidirect
25. Q₈²×C₅₃	C₂²	semidirect
27. C₅₃×#555	C₂²	semidirect
29. C₅₃×#554	C₂²	semidirect
30. C₅₃×#554	C₂²	semidirect
34. C₅₃×#552	C₂²	semidirect
37. C₅₃×#547	C₂²	semidirect
43. C₅₃×#544	C₂²	semidirect
45. C₅₃×#542	C₂²	semidirect
50. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
52. C₅₃×#529	C₂²	semidirect
57. C₅₃×#501	C₂²	semidirect
58. C₅₃×#500	C₂²	semidirect
59. C₅₃×#500	C₂²	semidirect
60. C₅₃×#499	C₂²	semidirect
61. C₅₃×#490	C₂²	semidirect
62. C₅₃×#486	C₂²	semidirect
63. C₅₃×#486	C₂²	semidirect
64. C₅₃×#486	C₂²	semidirect
65. C₅₃×#485	C₂²	semidirect
66. C₅₃×#484	C₂²	semidirect
67. C₅₃×#482	C₂²	semidirect
68. C₅₃×#482	C₂²	semidirect
69. C₅₃×#482	C₂²	semidirect
70. C₅₃×#481	C₂²	semidirect
71. C₅₃×#481	C₂²	semidirect
72. C₅₃×#480	C₂²	semidirect
73. C₅₃×#480	C₂²	semidirect
74. C₅₃×#480	C₂²	semidirect
75. C₅₃×#479	C₂²	semidirect
78. C₅₃×#478	C₂²	semidirect
79. C₅₃×#478	C₂²	semidirect
80. C₅₃×#478	C₂²	semidirect
81. C₅₃×#478	C₂²	semidirect
82. C₅₃×#477	C₂²	semidirect
86. C₅₃×#476	C₂²	semidirect
87. C₅₃×#476	C₂²	semidirect
88. C₅₃×#476	C₂²	semidirect
89. C₅₃×#476	C₂²	semidirect
90. C₅₃×#476	C₂²	semidirect
92. C₅₃×#474	C₂²	semidirect
93. C₅₃×#474	C₂²	semidirect
94. C₅₃×#469	C₂²	semidirect
95. C₅₃×#468	C₂²	semidirect
96. C₅₃×#466	C₂²	semidirect
97. C₅₃×#466	C₂²	semidirect
98. C₅₃×#465	C₂²	semidirect
99. C₅₃×#465	C₂²	semidirect
101. C₅₃×#463	C₂²	semidirect
102. C₅₃×#463	C₂²	semidirect
103. C₅₃×#460	C₂²	semidirect
104. C₅₃×#460	C₂²	semidirect
105. C₅₃×#459	C₂²	semidirect
106. C₅₃×#459	C₂²	semidirect
111. C₅₃×#446	C₂²	semidirect
112. C₈×Q₈×C₅₃	C₂²	semidirect
113. C₅₃×#442	C₂²	semidirect
116. C₄×SD₁₆×C₅₃	C₂²	semidirect
117. C₄×SD₁₆×C₅₃	C₂²	semidirect
120. C₄×D₈×C₅₃	C₂²	semidirect
121. C₅₃×#436	C₂²	semidirect
122. C₅₃×#435	C₂²	semidirect
123. C₈×D₄×C₅₃	C₂²	semidirect
124. C₈×D₄×C₅₃	C₂²	semidirect
125. C₅₃×#433	C₂²	semidirect
126. C₅₃×#431	C₂²	semidirect
127. C₅₃×#428	C₂²	semidirect
128. C₅₃×#427	C₂²	semidirect
129. C₂×#106×C₅₃	C₂²	semidirect
130. C₅₃×#424	C₂²	semidirect
131. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
527. #62200	C₅₃	direct (N × H)
567. #3544	C₂×C₅₃	semidirect
568. #3519	C₂×C₅₃	semidirect
569. #3385	C₂×C₅₃	semidirect
570. #3380	C₂×C₅₃	semidirect
571. #3366	C₂×C₅₃	semidirect
572. #3362	C₂×C₅₃	semidirect
573. #3357	C₂×C₅₃	semidirect
574. #3345	C₂×C₅₃	semidirect
575. #3341	C₂×C₅₃	semidirect
576. #3337	C₂×C₅₃	semidirect
577. #3325	C₂×C₅₃	semidirect
578. #3310	C₂×C₅₃	semidirect
579. #3295	C₂×C₅₃	semidirect
580. #3294	C₂×C₅₃	semidirect
581. #3257	C₂×C₅₃	semidirect
582. #3247	C₂×C₅₃	semidirect
583. #3241	C₂×C₅₃	semidirect
584. #3226	C₂×C₅₃	semidirect
585. #3118	C₂×C₅₃	semidirect
586. #3105	C₂×C₅₃	semidirect
587. #3081	C₂×C₅₃	semidirect
588. C₂×#476	C₂×C₅₃	semidirect
589. #2994	C₂×C₅₃	semidirect
600. Q₈²	C₂²×C₅₃	semidirect
602. #555	C₂²×C₅₃	semidirect
604. #554	C₂²×C₅₃	semidirect
605. #554	C₂²×C₅₃	semidirect
609. #552	C₂²×C₅₃	semidirect
612. #547	C₂²×C₅₃	semidirect
618. #544	C₂²×C₅₃	semidirect
620. #542	C₂²×C₅₃	semidirect
625. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
627. #529	C₂²×C₅₃	semidirect
632. #501	C₂²×C₅₃	semidirect
633. #500	C₂²×C₅₃	semidirect
634. #500	C₂²×C₅₃	semidirect
635. #499	C₂²×C₅₃	semidirect
636. #490	C₂²×C₅₃	semidirect
637. #486	C₂²×C₅₃	semidirect
638. #486	C₂²×C₅₃	semidirect
639. #486	C₂²×C₅₃	semidirect
640. #485	C₂²×C₅₃	semidirect
641. #484	C₂²×C₅₃	semidirect
642. #482	C₂²×C₅₃	semidirect
643. #482	C₂²×C₅₃	semidirect
644. #482	C₂²×C₅₃	semidirect
645. #481	C₂²×C₅₃	semidirect
646. #481	C₂²×C₅₃	semidirect
647. #480	C₂²×C₅₃	semidirect
648. #480	C₂²×C₅₃	semidirect
649. #480	C₂²×C₅₃	semidirect
650. #479	C₂²×C₅₃	semidirect
653. #478	C₂²×C₅₃	semidirect
654. #478	C₂²×C₅₃	semidirect
655. #478	C₂²×C₅₃	semidirect
656. #478	C₂²×C₅₃	semidirect
657. #477	C₂²×C₅₃	semidirect
661. #476	C₂²×C₅₃	semidirect
662. #476	C₂²×C₅₃	semidirect
663. #476	C₂²×C₅₃	semidirect
664. #476	C₂²×C₅₃	semidirect
665. #476	C₂²×C₅₃	semidirect
667. #474	C₂²×C₅₃	semidirect
668. #474	C₂²×C₅₃	semidirect
669. #469	C₂²×C₅₃	semidirect
670. #468	C₂²×C₅₃	semidirect
671. #466	C₂²×C₅₃	semidirect
672. #466	C₂²×C₅₃	semidirect
673. #465	C₂²×C₅₃	semidirect
674. #465	C₂²×C₅₃	semidirect
676. #463	C₂²×C₅₃	semidirect
677. #463	C₂²×C₅₃	semidirect
678. #460	C₂²×C₅₃	semidirect
679. #460	C₂²×C₅₃	semidirect
680. #459	C₂²×C₅₃	semidirect
681. #459	C₂²×C₅₃	semidirect
686. #446	C₂²×C₅₃	semidirect
687. C₈×Q₈	C₂²×C₅₃	semidirect
688. #442	C₂²×C₅₃	semidirect
691. C₄×SD₁₆	C₂²×C₅₃	semidirect
692. C₄×SD₁₆	C₂²×C₅₃	semidirect
695. C₄×D₈	C₂²×C₅₃	semidirect
696. #436	C₂²×C₅₃	semidirect
697. #435	C₂²×C₅₃	semidirect
698. C₈×D₄	C₂²×C₅₃	semidirect
699. C₈×D₄	C₂²×C₅₃	semidirect
700. #433	C₂²×C₅₃	semidirect
701. #431	C₂²×C₅₃	semidirect
702. #428	C₂²×C₅₃	semidirect
703. #427	C₂²×C₅₃	semidirect
704. C₂×#106	C₂²×C₅₃	semidirect
705. #424	C₂²×C₅₃	semidirect
706. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
710. C₅₃	#62200	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×#3544	2
C₅₃×#3519	2
C₅₃×#3385	2
C₅₃×#3380	2
C₅₃×#3366	2
C₅₃×#3362	2
C₅₃×#3357	2
C₅₃×#3345	2
C₅₃×#3341	2
C₅₃×#3337	2
C₅₃×#3325	2
C₅₃×#3310	2
C₅₃×#3295	2
C₅₃×#3294	2
C₅₃×#3257	2
C₅₃×#3247	2
C₅₃×#3241	2
C₅₃×#3226	2
C₅₃×#3118	2
C₅₃×#3105	2
C₅₃×#3081	2
C₂×C₅₃×#476	2
C₅₃×#2994	2
#62200	53

Subgroups — C53×#62200 #27269712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62200 #27269712