Subgroups — C₅₃×#63061 #27270573

Order 13568.

6384 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3565	C₂	1	6	yes	maximal, complemented
2	C₅₃×#3563	C₂	1	3	yes	maximal, complemented
3	C₅₃×#3559	C₂	1	3	yes	maximal, complemented
4	C₅₃×#3557	C₂	1	6	yes	maximal, complemented
5	C₅₃×#3554	C₂	1	6	yes	maximal, complemented
6	C₅₃×#3552	C₂	1	6	yes	maximal, complemented
7	C₅₃×#3550	C₂	1	3	yes	maximal, complemented
8	C₅₃×#3547	C₂	1	6	yes	maximal, complemented
9	C₅₃×#3544	C₂	1	6	yes	maximal, complemented
10	C₅₃×#3531	C₂	1	3	yes	maximal, complemented
11	C₅₃×#3524	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3524	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3522	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3517	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3516	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3503	C₂	1	2	yes	maximal, complemented
19	C₅₃×#3502	C₂	1	2	yes	maximal, complemented
20	C₅₃×#564	C₂²	1	3	yes	—
21	C₅₃×#563	C₂²	1	1	yes	characteristic
22	C₅₃×#563	C₂²	1	6	yes	—
23	C₅₃×#563	C₂²	1	3	yes	—
24	C₅₃×#563	C₂²	1	6	yes	—
25	C₅₃×#563	C₂²	1	6	yes	—
26	C₅₃×#563	C₂²	1	6	yes	—
27	C₅₃×#563	C₂²	1	12	yes	—
28	C₅₃×#563	C₂²	1	6	yes	—
29	C₅₃×#562	C₂²	1	6	yes	—
30	C₅₃×#562	C₂²	1	6	yes	—
31	C₅₃×#562	C₂²	1	3	yes	—
32	C₅₃×#562	C₂²	1	12	yes	—
33	C₅₃×#559	C₂²	1	6	yes	—
34	C₅₃×#559	C₂²	1	6	yes	—
35	C₅₃×#559	C₂²	1	6	yes	—
36	Q₈²×C₅₃	C₂²	1	2	yes	—
37	Q₈²×C₅₃	C₂²	1	6	yes	—
38	Q₈²×C₅₃	C₂²	1	1	yes	characteristic
39	C₅₃×#557	C₂²	1	1	yes	characteristic
40	C₅₃×#557	C₂²	1	2	yes	—
41	C₅₃×#557	C₂²	1	2	yes	—
42	C₅₃×#557	C₂²	1	6	yes	—
43	C₅₃×#557	C₂²	1	6	yes	—
44	C₅₃×#557	C₂²	1	6	yes	—
45	C₅₃×#557	C₂²	1	2	yes	—
46	C₅₃×#556	C₂²	1	6	yes	—
47	C₅₃×#556	C₂²	1	6	yes	—
48	C₅₃×#556	C₂²	1	3	yes	—
49	C₅₃×#556	C₂²	1	6	yes	—
50	C₅₃×#555	C₂²	1	3	yes	—
51	C₅₃×#555	C₂²	1	6	yes	—
52	C₅₃×#555	C₂²	1	6	yes	—
53	C₅₃×#554	C₂²	1	6	yes	—
54	C₅₃×#554	C₂²	1	6	yes	—
55	C₅₃×#554	C₂²	1	6	yes	—
56	C₅₃×#554	C₂²	1	6	yes	—
57	C₅₃×#554	C₂²	1	6	yes	—
58	C₅₃×#554	C₂²	1	6	yes	—
59	C₅₃×#553	C₂²	1	6	yes	—
60	C₅₃×#553	C₂²	1	6	yes	—
61	C₅₃×#553	C₂²	1	6	yes	—
62	C₅₃×#553	C₂²	1	6	yes	—
63	C₅₃×#552	C₂²	1	6	yes	—
64	C₅₃×#552	C₂²	1	6	yes	—
65	C₅₃×#552	C₂²	1	6	yes	—
66	C₅₃×#552	C₂²	1	12	yes	—
67	C₅₃×#552	C₂²	1	12	yes	—
68	C₅₃×#550	C₂²	1	2	yes	—
69	C₅₃×#550	C₂²	1	1	yes	characteristic
70	C₅₃×#550	C₂²	1	3	yes	—
71	D₄×Q₈×C₅₃	C₂²	1	6	yes	—
72	D₄×Q₈×C₅₃	C₂²	1	6	yes	—
73	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
74	D₄×Q₈×C₅₃	C₂²	1	6	yes	—
75	C₅₃×#548	C₂²	1	2	yes	—
76	C₅₃×#548	C₂²	1	2	yes	—
77	C₅₃×#548	C₂²	1	2	yes	—
78	C₅₃×#548	C₂²	1	12	yes	—
79	C₅₃×#547	C₂²	1	3	yes	—
80	C₅₃×#547	C₂²	1	6	yes	—
81	C₅₃×#547	C₂²	1	6	yes	—
82	C₅₃×#547	C₂²	1	12	yes	—
83	C₅₃×#544	C₂²	1	6	yes	—
84	C₅₃×#544	C₂²	1	6	yes	—
85	C₅₃×#544	C₂²	1	6	yes	—
86	C₅₃×#544	C₂²	1	6	yes	—
87	C₅₃×#544	C₂²	1	3	yes	—
88	C₅₃×#544	C₂²	1	3	yes	—
89	C₅₃×#544	C₂²	1	6	yes	—
90	C₅₃×#542	C₂²	1	6	yes	—
91	C₅₃×#542	C₂²	1	6	yes	—
92	C₅₃×#542	C₂²	1	6	yes	—
93	C₅₃×#542	C₂²	1	6	yes	—
94	C₅₃×#542	C₂²	1	6	yes	—
95	C₅₃×#542	C₂²	1	6	yes	—
96	C₅₃×#542	C₂²	1	12	yes	—
97	C₅₃×#542	C₂²	1	12	yes	—
98	C₅₃×#542	C₂²	1	12	yes	—
99	C₅₃×#541	C₂²	1	6	yes	—
100	C₅₃×#541	C₂²	1	12	yes	—
101	C₅₃×#540	C₂²	1	6	yes	—
102	C₅₃×#540	C₂²	1	6	yes	—
103	C₅₃×#540	C₂²	1	6	yes	—
104	C₅₃×#539	C₂²	1	12	yes	—
105	C₅₃×#539	C₂²	1	12	yes	—
106	C₅₃×#539	C₂²	1	6	yes	—
107	C₅₃×#539	C₂²	1	6	yes	—
108	C₅₃×#537	C₂²	1	6	yes	—
109	C₅₃×#536	C₂²	1	12	yes	—
110	C₅₃×#536	C₂²	1	12	yes	—
111	C₅₃×#533	C₂²	1	6	yes	—
112	C₅₃×#533	C₂²	1	6	yes	—
113	C₅₃×#533	C₂²	1	6	yes	—
114	C₅₃×#533	C₂²	1	3	yes	—
115	C₅₃×#533	C₂²	1	3	yes	—
116	C₅₃×#532	C₂²	1	3	yes	—
117	C₅₃×#532	C₂²	1	6	yes	—
118	C₂×C₄⋊Q₈×C₅₃	C₂²	1	6	yes	—
119	C₅₃×#529	C₂²	1	6	yes	—
120	C₅₃×#529	C₂²	1	6	yes	—
121	C₅₃×#529	C₂²	1	3	yes	—
122	C₅₃×#529	C₂²	1	3	yes	—
123	C₅₃×#529	C₂²	1	6	yes	—
124	C₅₃×#529	C₂²	1	6	yes	—
125	C₅₃×#529	C₂²	1	6	yes	—
126	C₅₃×#529	C₂²	1	6	yes	—
127	C₅₃×#529	C₂²	1	6	yes	—
128	C₂×#125×C₅₃	C₂²	1	3	yes	—
129	C₅₃×#520	C₂²	1	2	yes	—
130	C₅₃×#520	C₂²	1	2	yes	—
131	C₅₃×#520	C₂²	1	1	yes	characteristic
132	C₅₃×#520	C₂²	1	1	yes	characteristic
133	C₅₃×#519	C₂²	1	2	yes	—
134	C₅₃×#519	C₂²	1	2	yes	—
135	C₄×#41×C₅₃	C₂²	1	2	yes	—
136	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
137	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
138	C₂×#41×C₅₃	C₂³	1	2	yes	—
139	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
140	C₂×#41×C₅₃	C₂³	1	6	yes	—
141	C₂×#41×C₅₃	C₂³	1	12	yes	—
142	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
143	C₂²×Q₈×C₅₃	C₂³	1	12	yes	—
144	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
145	C₄⋊Q₈×C₅₃	C₂³	1	12	yes	—
146	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
147	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
148	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
149	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
150	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	—
151	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
152	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
153	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
154	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	—
155	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
156	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
157	C₄⋊Q₈×C₅₃	C₂³	1	6	yes	—
158	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	—
159	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	—
160	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	—
161	C₄⋊Q₈×C₅₃	C₂³	1	12	yes	—
162	C₄⋊Q₈×C₅₃	C₂³	1	12	yes	—
163	#127×C₅₃	C₂³	1	3	yes	—
164	#127×C₅₃	C₂³	1	6	yes	—
165	#126×C₅₃	C₂³	1	2	yes	—
166	#126×C₅₃	C₂³	1	2	yes	—
167	#126×C₅₃	C₂³	1	6	yes	—
168	#126×C₅₃	C₂³	1	6	yes	—
169	#126×C₅₃	C₂³	1	12	yes	—
170	#126×C₅₃	C₂³	1	6	yes	—
171	#126×C₅₃	C₂³	1	6	yes	—
172	#126×C₅₃	C₂³	1	6	yes	—
173	#126×C₅₃	C₂³	1	6	yes	—
174	#126×C₅₃	C₂³	1	6	yes	—
175	#126×C₅₃	C₂³	1	6	yes	—
176	#126×C₅₃	C₂³	1	12	yes	—
177	#126×C₅₃	C₂³	1	12	yes	—
178	#126×C₅₃	C₂³	1	12	yes	—
179	#126×C₅₃	C₂³	1	12	yes	—
180	#125×C₅₃	C₂³	1	3	yes	—
181	#125×C₅₃	C₂³	1	6	yes	—
182	#125×C₅₃	C₂³	1	6	yes	—
183	#125×C₅₃	C₂³	1	6	yes	—
184	#125×C₅₃	C₂³	1	1	yes	characteristic
185	#125×C₅₃	C₂³	1	3	yes	—
186	#125×C₅₃	C₂³	1	6	yes	—
187	#125×C₅₃	C₂³	1	6	yes	—
188	#125×C₅₃	C₂³	1	6	yes	—
189	#125×C₅₃	C₂³	1	6	yes	—
190	#125×C₅₃	C₂³	1	6	yes	—
191	#125×C₅₃	C₂³	1	6	yes	—
192	#125×C₅₃	C₂³	1	6	yes	—
193	#125×C₅₃	C₂³	1	1	yes	characteristic
194	#125×C₅₃	C₂³	1	6	yes	—
195	#125×C₅₃	C₂³	1	6	yes	—
196	#125×C₅₃	C₂³	1	6	yes	—
197	#125×C₅₃	C₂³	1	6	yes	—
198	#125×C₅₃	C₂³	1	6	yes	—
199	#125×C₅₃	C₂³	1	6	yes	—
200	#125×C₅₃	C₂³	1	12	yes	—
201	#125×C₅₃	C₂³	1	12	yes	—
202	#125×C₅₃	C₂³	1	12	yes	—
203	#124×C₅₃	C₂³	1	1	yes	characteristic
204	#124×C₅₃	C₂³	1	3	yes	—
205	#124×C₅₃	C₂³	1	6	yes	—
206	#124×C₅₃	C₂³	1	6	yes	—
207	#124×C₅₃	C₂³	1	6	yes	—
208	#124×C₅₃	C₂³	1	6	yes	—
209	#124×C₅₃	C₂³	1	6	yes	—
210	#124×C₅₃	C₂³	1	6	yes	—
211	#124×C₅₃	C₂³	1	6	yes	—
212	#124×C₅₃	C₂³	1	12	yes	—
213	#124×C₅₃	C₂³	1	12	yes	—
214	#124×C₅₃	C₂³	1	12	yes	—
215	#124×C₅₃	C₂³	1	12	yes	—
216	#123×C₅₃	C₂³	1	2	yes	—
217	#123×C₅₃	C₂³	1	6	yes	—
218	#123×C₅₃	C₂³	1	12	yes	—
219	#123×C₅₃	C₂³	1	6	yes	—
220	#123×C₅₃	C₂³	1	6	yes	—
221	#123×C₅₃	C₂³	1	12	yes	—
222	#123×C₅₃	C₂³	1	6	yes	—
223	#123×C₅₃	C₂³	1	6	yes	—
224	#123×C₅₃	C₂³	1	6	yes	—
225	#123×C₅₃	C₂³	1	6	yes	—
226	#123×C₅₃	C₂³	1	6	yes	—
227	#123×C₅₃	C₂³	1	6	yes	—
228	#123×C₅₃	C₂³	1	12	yes	—
229	#123×C₅₃	C₂³	1	12	yes	—
230	#123×C₅₃	C₂³	1	12	yes	—
231	#123×C₅₃	C₂³	1	12	yes	—
232	#123×C₅₃	C₂³	1	12	yes	—
233	#123×C₅₃	C₂³	1	12	yes	—
234	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
235	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
236	C₂²⋊Q₈×C₅₃	C₂³	1	3	yes	—
237	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
238	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
239	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
240	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
241	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
242	C₂²⋊Q₈×C₅₃	C₂³	1	3	yes	—
243	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
244	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
245	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
246	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
247	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
248	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
249	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
250	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
251	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
252	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
253	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
254	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
255	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	—
256	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
257	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
258	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
259	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
260	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
261	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
262	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
263	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
264	C₂²⋊Q₈×C₅₃	C₂³	1	12	yes	—
265	#121×C₅₃	C₂³	1	6	yes	—
266	#121×C₅₃	C₂³	1	6	yes	—
267	#121×C₅₃	C₂³	1	3	yes	—
268	#121×C₅₃	C₂³	1	3	yes	—
269	#121×C₅₃	C₂³	1	6	yes	—
270	#121×C₅₃	C₂³	1	6	yes	—
271	#121×C₅₃	C₂³	1	6	yes	—
272	#121×C₅₃	C₂³	1	6	yes	—
273	#121×C₅₃	C₂³	1	6	yes	—
274	#121×C₅₃	C₂³	1	6	yes	—
275	#121×C₅₃	C₂³	1	6	yes	—
276	#121×C₅₃	C₂³	1	6	yes	—
277	#121×C₅₃	C₂³	1	6	yes	—
278	#121×C₅₃	C₂³	1	12	yes	—
279	#121×C₅₃	C₂³	1	12	yes	—
280	#121×C₅₃	C₂³	1	12	yes	—
281	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
282	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
283	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
284	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
285	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
287	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
288	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
289	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
290	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
291	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
292	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
293	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
294	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
295	C₄×Q₈×C₅₃	C₂³	1	3	yes	—
296	C₄×Q₈×C₅₃	C₂³	1	3	yes	—
297	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
298	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
299	C₄×Q₈×C₅₃	C₂³	1	6	yes	—
300	C₄×Q₈×C₅₃	C₂³	1	12	yes	—
301	C₄×Q₈×C₅₃	C₂³	1	12	yes	—
302	C₄×D₄×C₅₃	C₂³	1	3	yes	—
303	C₄×D₄×C₅₃	C₂³	1	6	yes	—
304	C₄×D₄×C₅₃	C₂³	1	6	yes	—
305	C₄×D₄×C₅₃	C₂³	1	3	yes	—
306	C₄×D₄×C₅₃	C₂³	1	6	yes	—
307	C₄×D₄×C₅₃	C₂³	1	6	yes	—
308	C₄×D₄×C₅₃	C₂³	1	6	yes	—
309	C₄×D₄×C₅₃	C₂³	1	6	yes	—
310	C₄×D₄×C₅₃	C₂³	1	6	yes	—
311	C₄×D₄×C₅₃	C₂³	1	6	yes	—
312	C₄×D₄×C₅₃	C₂³	1	6	yes	—
313	C₄×D₄×C₅₃	C₂³	1	6	yes	—
314	C₄×D₄×C₅₃	C₂³	1	3	yes	—
315	C₄×D₄×C₅₃	C₂³	1	6	yes	—
316	C₄×D₄×C₅₃	C₂³	1	3	yes	—
317	C₄×D₄×C₅₃	C₂³	1	6	yes	—
318	C₄×D₄×C₅₃	C₂³	1	12	yes	—
319	C₄×D₄×C₅₃	C₂³	1	12	yes	—
320	C₄×D₄×C₅₃	C₂³	1	12	yes	—
321	C₄×D₄×C₅₃	C₂³	1	12	yes	—
322	C₄×D₄×C₅₃	C₂³	1	6	yes	—
323	#117×C₅₃	C₂³	1	6	yes	—
324	#117×C₅₃	C₂³	1	3	yes	—
325	#117×C₅₃	C₂³	1	6	yes	—
326	#117×C₅₃	C₂³	1	6	yes	—
327	#117×C₅₃	C₂³	1	6	yes	—
328	#117×C₅₃	C₂³	1	6	yes	—
329	#117×C₅₃	C₂³	1	6	yes	—
330	#117×C₅₃	C₂³	1	6	yes	—
331	#117×C₅₃	C₂³	1	3	yes	—
332	#117×C₅₃	C₂³	1	3	yes	—
333	#117×C₅₃	C₂³	1	12	yes	—
334	#117×C₅₃	C₂³	1	12	yes	—
335	#117×C₅₃	C₂³	1	12	yes	—
336	#117×C₅₃	C₂³	1	6	yes	—
337	C₂×C₄⋊C₄×C₅₃	C₂³	1	6	yes	—
338	C₂×C₄⋊C₄×C₅₃	C₂³	1	3	yes	—
339	C₂×C₄⋊C₄×C₅₃	C₂³	1	3	yes	—
340	C₂×C₄⋊C₄×C₅₃	C₂³	1	6	yes	—
341	C₂×C₄⋊C₄×C₅₃	C₂³	1	6	yes	—
342	C₂×C₄⋊C₄×C₅₃	C₂³	1	6	yes	—
343	C₂×C₄⋊C₄×C₅₃	C₂³	1	6	yes	—
344	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	—
345	C₂×C₄²×C₅₃	C₂³	1	6	yes	—
346	C₂×C₄²×C₅₃	C₂³	1	3	yes	—
347	C₂×C₄²×C₅₃	C₂³	1	6	yes	—
348	#41×C₅₃	—	2	8	no	—
349	#41×C₅₃	—	2	4	no	—
350	#41×C₅₃	—	8	6	no	—
351	#41×C₅₃	—	8	12	no	—
352	C₂×Q₈×C₅₃	—	2	8	no	—
353	C₂×Q₈×C₅₃	—	8	12	no	—
354	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
355	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
357	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
358	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
359	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
360	C₂×Q₈×C₅₃	C₂⁴	1	12	yes	—
361	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
362	C₂×Q₈×C₅₃	C₂⁴	1	3	yes	—
363	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
365	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
366	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
367	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
369	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
370	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
371	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
372	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
373	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
374	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
375	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
376	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
377	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
379	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
380	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
381	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
382	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
383	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
384	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
385	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
386	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
387	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
388	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
389	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
390	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
391	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
392	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
393	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
394	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
395	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
396	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
397	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
398	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
399	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
400	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
401	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
402	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
403	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
404	C₄⋊C₄×C₅₃	C₂⁴	1	3	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	2	yes	—
409	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
410	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
411	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
412	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
413	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
414	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
415	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
416	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
417	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
418	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
419	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
422	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
423	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
424	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
425	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
426	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
428	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
429	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
430	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
431	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
432	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
433	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
434	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
435	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
436	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
437	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
438	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
439	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
440	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
441	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
442	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
443	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
444	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
445	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
446	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
447	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
448	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
449	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
450	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
451	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
452	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
453	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
454	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
455	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
456	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
457	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
458	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
459	C₄²×C₅₃	C₂⁴	1	2	yes	—
460	C₄²×C₅₃	C₂⁴	1	6	yes	—
461	C₄²×C₅₃	C₂⁴	1	3	yes	—
462	C₄²×C₅₃	C₂⁴	1	6	yes	—
463	C₄²×C₅₃	C₂⁴	1	6	yes	—
464	C₄²×C₅₃	C₂⁴	1	6	yes	—
465	C₄²×C₅₃	C₂⁴	1	3	yes	—
466	C₄²×C₅₃	C₂⁴	1	6	yes	—
467	C₄²×C₅₃	C₂⁴	1	3	yes	—
468	C₄²×C₅₃	C₂⁴	1	6	yes	—
469	C₄²×C₅₃	C₂⁴	1	6	yes	—
470	C₄²×C₅₃	C₂⁴	1	12	yes	—
471	C₄²×C₅₃	C₂⁴	1	12	yes	—
472	C₂³×C₅₃	C₂⁵	1	2	yes	—
473	C₂³×C₅₃	C₂⁵	1	6	yes	—
474	C₂³×C₅₃	C₂⁵	1	3	yes	—
475	Q₈×C₅₃	—	2	12	no	—
476	Q₈×C₅₃	—	4	6	no	—
477	Q₈×C₅₃	—	4	6	no	—
478	Q₈×C₅₃	—	4	6	no	—
479	Q₈×C₅₃	—	4	12	no	—
480	Q₈×C₅₃	—	4	1	no	—
481	Q₈×C₅₃	—	4	6	no	—
482	Q₈×C₅₃	—	4	2	no	—
483	Q₈×C₅₃	—	4	3	no	—
484	Q₈×C₅₃	2₋¹⁺⁴	1	4	yes	—
485	D₄×C₅₃	—	2	6	no	—
486	D₄×C₅₃	—	2	12	no	—
487	D₄×C₅₃	—	4	6	no	—
488	D₄×C₅₃	—	4	1	no	—
489	D₄×C₅₃	—	4	6	no	—
490	D₄×C₅₃	—	4	6	no	—
491	D₄×C₅₃	—	4	6	no	—
492	D₄×C₅₃	—	4	3	no	—
493	D₄×C₅₃	—	4	12	no	—
494	D₄×C₅₃	—	4	6	no	—
495	C₂×C₄×C₅₃	—	2	12	no	—
496	C₂×C₄×C₅₃	—	2	6	no	—
497	C₂×C₄×C₅₃	—	2	12	no	—
498	C₂×C₄×C₅₃	—	4	6	no	—
499	C₂×C₄×C₅₃	—	4	6	no	—
500	C₂×C₄×C₅₃	—	4	3	no	—
501	C₂×C₄×C₅₃	—	4	2	no	—
502	C₂×C₄×C₅₃	—	4	6	no	—
503	C₂×C₄×C₅₃	—	4	12	no	—
504	C₂×C₄×C₅₃	—	4	12	no	—
505	C₂×C₄×C₅₃	—	4	6	no	—
506	C₂×C₄×C₅₃	—	4	6	no	—
507	C₂×C₄×C₅₃	—	4	3	no	—
508	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
509	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
510	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
511	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
512	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
513	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
514	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
515	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
516	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
517	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
518	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
519	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
520	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
521	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
522	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
523	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
524	#63061	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
525	C₂²×C₅₃	—	2	2	no	—
526	C₂²×C₅₃	—	2	6	no	—
527	C₂²×C₅₃	—	2	3	no	—
528	C₂²×C₅₃	—	2	6	no	—
529	C₂²×C₅₃	—	2	2	no	—
530	C₂²×C₅₃	—	2	3	no	—
531	C₂²×C₅₃	—	2	3	no	—
532	C₂²×C₅₃	—	2	2	no	—
533	C₂²×C₅₃	—	2	6	no	—
534	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
535	C₄×C₅₃	—	2	1	no	—
536	C₄×C₅₃	—	2	2	no	—
537	C₄×C₅₃	—	2	6	no	—
538	C₄×C₅₃	—	2	6	no	—
539	C₄×C₅₃	—	2	3	no	—
540	C₄×C₅₃	—	2	1	no	—
541	C₄×C₅₃	—	2	6	no	—
542	C₄×C₅₃	—	2	6	no	—
543	C₄×C₅₃	—	2	2	no	—
544	C₄×C₅₃	—	2	6	no	—
545	C₄×C₅₃	—	2	1	no	—
546	C₄×C₅₃	—	2	2	no	—
547	C₄×C₅₃	—	2	2	no	—
548	C₄×C₅₃	—	2	3	no	—
549	C₄×C₅₃	—	2	2	no	—
550	C₄×C₅₃	C₂×2₋¹⁺⁴	1	6	yes	—
551	#3565	C₂×C₅₃	1	6	yes	complemented
552	#3563	C₂×C₅₃	1	3	yes	complemented
553	#3559	C₂×C₅₃	1	3	yes	complemented
554	#3557	C₂×C₅₃	1	6	yes	complemented
555	#3554	C₂×C₅₃	1	6	yes	complemented
556	#3552	C₂×C₅₃	1	6	yes	complemented
557	#3550	C₂×C₅₃	1	3	yes	complemented
558	#3547	C₂×C₅₃	1	6	yes	complemented
559	#3544	C₂×C₅₃	1	6	yes	complemented
560	#3531	C₂×C₅₃	1	3	yes	complemented
561	#3524	C₂×C₅₃	1	2	yes	complemented
562	#3524	C₂×C₅₃	1	2	yes	complemented
563	#3522	C₂×C₅₃	1	2	yes	complemented
564	#3518	C₂×C₅₃	1	1	yes	characteristic, complemented
565	#3517	C₂×C₅₃	1	1	yes	characteristic, complemented
566	#3516	C₂×C₅₃	1	2	yes	complemented
567	#3504	C₂×C₅₃	1	1	yes	characteristic, complemented
568	#3503	C₂×C₅₃	1	2	yes	complemented
569	#3502	C₂×C₅₃	1	2	yes	complemented
570	C₂×C₅₃	—	4	2	no	—
571	C₂×C₅₃	—	4	6	no	—
572	C₂×C₅₃	—	4	3	no	—
573	C₂×C₅₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
574	C₂×C₅₃	H(7,𝔽₂)	1	1	yes	characteristic
575	C₂×C₅₃	2₋¹⁺⁶	1	1	yes	characteristic
576	#564	C₂²×C₅₃	1	3	yes	—
577	#563	C₂²×C₅₃	1	1	yes	characteristic
578	#563	C₂²×C₅₃	1	6	yes	—
579	#563	C₂²×C₅₃	1	3	yes	—
580	#563	C₂²×C₅₃	1	6	yes	—
581	#563	C₂²×C₅₃	1	6	yes	—
582	#563	C₂²×C₅₃	1	6	yes	—
583	#563	C₂²×C₅₃	1	12	yes	—
584	#563	C₂²×C₅₃	1	6	yes	—
585	#562	C₂²×C₅₃	1	6	yes	—
586	#562	C₂²×C₅₃	1	6	yes	—
587	#562	C₂²×C₅₃	1	3	yes	—
588	#562	C₂²×C₅₃	1	12	yes	—
589	#559	C₂²×C₅₃	1	6	yes	—
590	#559	C₂²×C₅₃	1	6	yes	—
591	#559	C₂²×C₅₃	1	6	yes	—
592	Q₈²	C₂²×C₅₃	1	2	yes	—
593	Q₈²	C₂²×C₅₃	1	6	yes	—
594	Q₈²	C₂²×C₅₃	1	1	yes	characteristic
595	#557	C₂²×C₅₃	1	1	yes	characteristic
596	#557	C₂²×C₅₃	1	2	yes	—
597	#557	C₂²×C₅₃	1	2	yes	—
598	#557	C₂²×C₅₃	1	6	yes	—
599	#557	C₂²×C₅₃	1	6	yes	—
600	#557	C₂²×C₅₃	1	6	yes	—
601	#557	C₂²×C₅₃	1	2	yes	—
602	#556	C₂²×C₅₃	1	6	yes	—
603	#556	C₂²×C₅₃	1	6	yes	—
604	#556	C₂²×C₅₃	1	3	yes	—
605	#556	C₂²×C₅₃	1	6	yes	—
606	#555	C₂²×C₅₃	1	3	yes	—
607	#555	C₂²×C₅₃	1	6	yes	—
608	#555	C₂²×C₅₃	1	6	yes	—
609	#554	C₂²×C₅₃	1	6	yes	—
610	#554	C₂²×C₅₃	1	6	yes	—
611	#554	C₂²×C₅₃	1	6	yes	—
612	#554	C₂²×C₅₃	1	6	yes	—
613	#554	C₂²×C₅₃	1	6	yes	—
614	#554	C₂²×C₅₃	1	6	yes	—
615	#553	C₂²×C₅₃	1	6	yes	—
616	#553	C₂²×C₅₃	1	6	yes	—
617	#553	C₂²×C₅₃	1	6	yes	—
618	#553	C₂²×C₅₃	1	6	yes	—
619	#552	C₂²×C₅₃	1	6	yes	—
620	#552	C₂²×C₅₃	1	6	yes	—
621	#552	C₂²×C₅₃	1	6	yes	—
622	#552	C₂²×C₅₃	1	12	yes	—
623	#552	C₂²×C₅₃	1	12	yes	—
624	#550	C₂²×C₅₃	1	2	yes	—
625	#550	C₂²×C₅₃	1	1	yes	characteristic
626	#550	C₂²×C₅₃	1	3	yes	—
627	D₄×Q₈	C₂²×C₅₃	1	6	yes	—
628	D₄×Q₈	C₂²×C₅₃	1	6	yes	—
629	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
630	D₄×Q₈	C₂²×C₅₃	1	6	yes	—
631	#548	C₂²×C₅₃	1	2	yes	—
632	#548	C₂²×C₅₃	1	2	yes	—
633	#548	C₂²×C₅₃	1	2	yes	—
634	#548	C₂²×C₅₃	1	12	yes	—
635	#547	C₂²×C₅₃	1	3	yes	—
636	#547	C₂²×C₅₃	1	6	yes	—
637	#547	C₂²×C₅₃	1	6	yes	—
638	#547	C₂²×C₅₃	1	12	yes	—
639	#544	C₂²×C₅₃	1	6	yes	—
640	#544	C₂²×C₅₃	1	6	yes	—
641	#544	C₂²×C₅₃	1	6	yes	—
642	#544	C₂²×C₅₃	1	6	yes	—
643	#544	C₂²×C₅₃	1	3	yes	—
644	#544	C₂²×C₅₃	1	3	yes	—
645	#544	C₂²×C₅₃	1	6	yes	—
646	#542	C₂²×C₅₃	1	6	yes	—
647	#542	C₂²×C₅₃	1	6	yes	—
648	#542	C₂²×C₅₃	1	6	yes	—
649	#542	C₂²×C₅₃	1	6	yes	—
650	#542	C₂²×C₅₃	1	6	yes	—
651	#542	C₂²×C₅₃	1	6	yes	—
652	#542	C₂²×C₅₃	1	12	yes	—
653	#542	C₂²×C₅₃	1	12	yes	—
654	#542	C₂²×C₅₃	1	12	yes	—
655	#541	C₂²×C₅₃	1	6	yes	—
656	#541	C₂²×C₅₃	1	12	yes	—
657	#540	C₂²×C₅₃	1	6	yes	—
658	#540	C₂²×C₅₃	1	6	yes	—
659	#540	C₂²×C₅₃	1	6	yes	—
660	#539	C₂²×C₅₃	1	12	yes	—
661	#539	C₂²×C₅₃	1	12	yes	—
662	#539	C₂²×C₅₃	1	6	yes	—
663	#539	C₂²×C₅₃	1	6	yes	—
664	#537	C₂²×C₅₃	1	6	yes	—
665	#536	C₂²×C₅₃	1	12	yes	—
666	#536	C₂²×C₅₃	1	12	yes	—
667	#533	C₂²×C₅₃	1	6	yes	—
668	#533	C₂²×C₅₃	1	6	yes	—
669	#533	C₂²×C₅₃	1	6	yes	—
670	#533	C₂²×C₅₃	1	3	yes	—
671	#533	C₂²×C₅₃	1	3	yes	—
672	#532	C₂²×C₅₃	1	3	yes	—
673	#532	C₂²×C₅₃	1	6	yes	—
674	C₂×C₄⋊Q₈	C₂²×C₅₃	1	6	yes	—
675	#529	C₂²×C₅₃	1	6	yes	—
676	#529	C₂²×C₅₃	1	6	yes	—
677	#529	C₂²×C₅₃	1	3	yes	—
678	#529	C₂²×C₅₃	1	3	yes	—
679	#529	C₂²×C₅₃	1	6	yes	—
680	#529	C₂²×C₅₃	1	6	yes	—
681	#529	C₂²×C₅₃	1	6	yes	—
682	#529	C₂²×C₅₃	1	6	yes	—
683	#529	C₂²×C₅₃	1	6	yes	—
684	C₂×#125	C₂²×C₅₃	1	3	yes	—
685	#520	C₂²×C₅₃	1	2	yes	—
686	#520	C₂²×C₅₃	1	2	yes	—
687	#520	C₂²×C₅₃	1	1	yes	characteristic
688	#520	C₂²×C₅₃	1	1	yes	characteristic
689	#519	C₂²×C₅₃	1	2	yes	—
690	#519	C₂²×C₅₃	1	2	yes	—
691	C₄×#41	C₂²×C₅₃	1	2	yes	—
692	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
693	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
694	C₅₃	#63061	1	1	yes	characteristic, direct product factor, Sylow
695	C₂×#41	C₂³×C₅₃	1	2	yes	—
696	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
697	C₂×#41	C₂³×C₅₃	1	6	yes	—
698	C₂×#41	C₂³×C₅₃	1	12	yes	—
699	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
700	C₂²×Q₈	C₂³×C₅₃	1	12	yes	—
701	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
702	C₄⋊Q₈	C₂³×C₅₃	1	12	yes	—
703	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
704	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
705	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
706	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
707	C₄⋊Q₈	C₂³×C₅₃	1	3	yes	—
708	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
709	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
710	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
711	C₄⋊Q₈	C₂³×C₅₃	1	3	yes	—
712	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
713	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
714	C₄⋊Q₈	C₂³×C₅₃	1	6	yes	—
715	C₄⋊Q₈	C₂³×C₅₃	1	3	yes	—
716	C₄⋊Q₈	C₂³×C₅₃	1	3	yes	—
717	C₄⋊Q₈	C₂³×C₅₃	1	3	yes	—
718	C₄⋊Q₈	C₂³×C₅₃	1	12	yes	—
719	C₄⋊Q₈	C₂³×C₅₃	1	12	yes	—
720	#127	C₂³×C₅₃	1	3	yes	—
721	#127	C₂³×C₅₃	1	6	yes	—
722	#126	C₂³×C₅₃	1	2	yes	—
723	#126	C₂³×C₅₃	1	2	yes	—
724	#126	C₂³×C₅₃	1	6	yes	—
725	#126	C₂³×C₅₃	1	6	yes	—
726	#126	C₂³×C₅₃	1	12	yes	—
727	#126	C₂³×C₅₃	1	6	yes	—
728	#126	C₂³×C₅₃	1	6	yes	—
729	#126	C₂³×C₅₃	1	6	yes	—
730	#126	C₂³×C₅₃	1	6	yes	—
731	#126	C₂³×C₅₃	1	6	yes	—
732	#126	C₂³×C₅₃	1	6	yes	—
733	#126	C₂³×C₅₃	1	12	yes	—
734	#126	C₂³×C₅₃	1	12	yes	—
735	#126	C₂³×C₅₃	1	12	yes	—
736	#126	C₂³×C₅₃	1	12	yes	—
737	#125	C₂³×C₅₃	1	3	yes	—
738	#125	C₂³×C₅₃	1	6	yes	—
739	#125	C₂³×C₅₃	1	6	yes	—
740	#125	C₂³×C₅₃	1	6	yes	—
741	#125	C₂³×C₅₃	1	1	yes	characteristic
742	#125	C₂³×C₅₃	1	3	yes	—
743	#125	C₂³×C₅₃	1	6	yes	—
744	#125	C₂³×C₅₃	1	6	yes	—
745	#125	C₂³×C₅₃	1	6	yes	—
746	#125	C₂³×C₅₃	1	6	yes	—
747	#125	C₂³×C₅₃	1	6	yes	—
748	#125	C₂³×C₅₃	1	6	yes	—
749	#125	C₂³×C₅₃	1	6	yes	—
750	#125	C₂³×C₅₃	1	1	yes	characteristic
751	#125	C₂³×C₅₃	1	6	yes	—
752	#125	C₂³×C₅₃	1	6	yes	—
753	#125	C₂³×C₅₃	1	6	yes	—
754	#125	C₂³×C₅₃	1	6	yes	—
755	#125	C₂³×C₅₃	1	6	yes	—
756	#125	C₂³×C₅₃	1	6	yes	—
757	#125	C₂³×C₅₃	1	12	yes	—
758	#125	C₂³×C₅₃	1	12	yes	—
759	#125	C₂³×C₅₃	1	12	yes	—
760	#124	C₂³×C₅₃	1	1	yes	characteristic
761	#124	C₂³×C₅₃	1	3	yes	—
762	#124	C₂³×C₅₃	1	6	yes	—
763	#124	C₂³×C₅₃	1	6	yes	—
764	#124	C₂³×C₅₃	1	6	yes	—
765	#124	C₂³×C₅₃	1	6	yes	—
766	#124	C₂³×C₅₃	1	6	yes	—
767	#124	C₂³×C₅₃	1	6	yes	—
768	#124	C₂³×C₅₃	1	6	yes	—
769	#124	C₂³×C₅₃	1	12	yes	—
770	#124	C₂³×C₅₃	1	12	yes	—
771	#124	C₂³×C₅₃	1	12	yes	—
772	#124	C₂³×C₅₃	1	12	yes	—
773	#123	C₂³×C₅₃	1	2	yes	—
774	#123	C₂³×C₅₃	1	6	yes	—
775	#123	C₂³×C₅₃	1	12	yes	—
776	#123	C₂³×C₅₃	1	6	yes	—
777	#123	C₂³×C₅₃	1	6	yes	—
778	#123	C₂³×C₅₃	1	12	yes	—
779	#123	C₂³×C₅₃	1	6	yes	—
780	#123	C₂³×C₅₃	1	6	yes	—
781	#123	C₂³×C₅₃	1	6	yes	—
782	#123	C₂³×C₅₃	1	6	yes	—
783	#123	C₂³×C₅₃	1	6	yes	—
784	#123	C₂³×C₅₃	1	6	yes	—
785	#123	C₂³×C₅₃	1	12	yes	—
786	#123	C₂³×C₅₃	1	12	yes	—
787	#123	C₂³×C₅₃	1	12	yes	—
788	#123	C₂³×C₅₃	1	12	yes	—
789	#123	C₂³×C₅₃	1	12	yes	—
790	#123	C₂³×C₅₃	1	12	yes	—
791	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
792	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
793	C₂²⋊Q₈	C₂³×C₅₃	1	3	yes	—
794	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
795	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
796	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
797	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
798	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
799	C₂²⋊Q₈	C₂³×C₅₃	1	3	yes	—
800	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
802	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
803	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
804	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
805	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
806	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
807	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
808	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
809	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
810	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
811	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
812	C₂²⋊Q₈	C₂³×C₅₃	1	6	yes	—
813	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
814	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
815	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
816	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
817	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
818	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
819	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
820	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
821	C₂²⋊Q₈	C₂³×C₅₃	1	12	yes	—
822	#121	C₂³×C₅₃	1	6	yes	—
823	#121	C₂³×C₅₃	1	6	yes	—
824	#121	C₂³×C₅₃	1	3	yes	—
825	#121	C₂³×C₅₃	1	3	yes	—
826	#121	C₂³×C₅₃	1	6	yes	—
827	#121	C₂³×C₅₃	1	6	yes	—
828	#121	C₂³×C₅₃	1	6	yes	—
829	#121	C₂³×C₅₃	1	6	yes	—
830	#121	C₂³×C₅₃	1	6	yes	—
831	#121	C₂³×C₅₃	1	6	yes	—
832	#121	C₂³×C₅₃	1	6	yes	—
833	#121	C₂³×C₅₃	1	6	yes	—
834	#121	C₂³×C₅₃	1	6	yes	—
835	#121	C₂³×C₅₃	1	12	yes	—
836	#121	C₂³×C₅₃	1	12	yes	—
837	#121	C₂³×C₅₃	1	12	yes	—
838	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
839	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
840	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
841	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
842	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
843	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
844	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
845	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
846	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
847	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
848	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
849	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
850	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
851	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
852	C₄×Q₈	C₂³×C₅₃	1	3	yes	—
853	C₄×Q₈	C₂³×C₅₃	1	3	yes	—
854	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
855	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
856	C₄×Q₈	C₂³×C₅₃	1	6	yes	—
857	C₄×Q₈	C₂³×C₅₃	1	12	yes	—
858	C₄×Q₈	C₂³×C₅₃	1	12	yes	—
859	C₄×D₄	C₂³×C₅₃	1	3	yes	—
860	C₄×D₄	C₂³×C₅₃	1	6	yes	—
861	C₄×D₄	C₂³×C₅₃	1	6	yes	—
862	C₄×D₄	C₂³×C₅₃	1	3	yes	—
863	C₄×D₄	C₂³×C₅₃	1	6	yes	—
864	C₄×D₄	C₂³×C₅₃	1	6	yes	—
865	C₄×D₄	C₂³×C₅₃	1	6	yes	—
866	C₄×D₄	C₂³×C₅₃	1	6	yes	—
867	C₄×D₄	C₂³×C₅₃	1	6	yes	—
868	C₄×D₄	C₂³×C₅₃	1	6	yes	—
869	C₄×D₄	C₂³×C₅₃	1	6	yes	—
870	C₄×D₄	C₂³×C₅₃	1	6	yes	—
871	C₄×D₄	C₂³×C₅₃	1	3	yes	—
872	C₄×D₄	C₂³×C₅₃	1	6	yes	—
873	C₄×D₄	C₂³×C₅₃	1	3	yes	—
874	C₄×D₄	C₂³×C₅₃	1	6	yes	—
875	C₄×D₄	C₂³×C₅₃	1	12	yes	—
876	C₄×D₄	C₂³×C₅₃	1	12	yes	—
877	C₄×D₄	C₂³×C₅₃	1	12	yes	—
878	C₄×D₄	C₂³×C₅₃	1	12	yes	—
879	C₄×D₄	C₂³×C₅₃	1	6	yes	—
880	#117	C₂³×C₅₃	1	6	yes	—
881	#117	C₂³×C₅₃	1	3	yes	—
882	#117	C₂³×C₅₃	1	6	yes	—
883	#117	C₂³×C₅₃	1	6	yes	—
884	#117	C₂³×C₅₃	1	6	yes	—
885	#117	C₂³×C₅₃	1	6	yes	—
886	#117	C₂³×C₅₃	1	6	yes	—
887	#117	C₂³×C₅₃	1	6	yes	—
888	#117	C₂³×C₅₃	1	3	yes	—
889	#117	C₂³×C₅₃	1	3	yes	—
890	#117	C₂³×C₅₃	1	12	yes	—
891	#117	C₂³×C₅₃	1	12	yes	—
892	#117	C₂³×C₅₃	1	12	yes	—
893	#117	C₂³×C₅₃	1	6	yes	—
894	C₂×C₄⋊C₄	C₂³×C₅₃	1	6	yes	—
895	C₂×C₄⋊C₄	C₂³×C₅₃	1	3	yes	—
896	C₂×C₄⋊C₄	C₂³×C₅₃	1	3	yes	—
897	C₂×C₄⋊C₄	C₂³×C₅₃	1	6	yes	—
898	C₂×C₄⋊C₄	C₂³×C₅₃	1	6	yes	—
899	C₂×C₄⋊C₄	C₂³×C₅₃	1	6	yes	—
900	C₂×C₄⋊C₄	C₂³×C₅₃	1	6	yes	—
901	C₂×C₄⋊C₄	C₂³×C₅₃	1	12	yes	—
902	C₂×C₄²	C₂³×C₅₃	1	6	yes	—
903	C₂×C₄²	C₂³×C₅₃	1	3	yes	—
904	C₂×C₄²	C₂³×C₅₃	1	6	yes	—
905	#41	—	2	8	no	—
906	#41	—	2	4	no	—
907	#41	—	8	6	no	—
908	#41	—	8	12	no	—
909	C₂×Q₈	—	2	8	no	—
910	C₂×Q₈	—	8	12	no	—
911	C₂×Q₈	C₂⁴×C₅₃	1	6	yes	—
912	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₅₃	1	6	yes	—
914	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₅₃	1	6	yes	—
916	C₂×Q₈	C₂⁴×C₅₃	1	6	yes	—
917	C₂×Q₈	C₂⁴×C₅₃	1	12	yes	—
918	C₂×Q₈	C₂⁴×C₅₃	1	6	yes	—
919	C₂×Q₈	C₂⁴×C₅₃	1	3	yes	—
920	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
921	C₂×D₄	C₂⁴×C₅₃	1	3	yes	—
922	C₂×D₄	C₂⁴×C₅₃	1	6	yes	—
923	C₂×D₄	C₂⁴×C₅₃	1	6	yes	—
924	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
925	C₂×D₄	C₂⁴×C₅₃	1	6	yes	—
926	C₂×D₄	C₂⁴×C₅₃	1	6	yes	—
927	C₂×D₄	C₂⁴×C₅₃	1	6	yes	—
928	C₂×D₄	C₂⁴×C₅₃	1	6	yes	—
929	C₂×D₄	C₂⁴×C₅₃	1	12	yes	—
930	C₂×D₄	C₂⁴×C₅₃	1	3	yes	—
931	C₂²×C₄	C₂⁴×C₅₃	1	3	yes	—
932	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
933	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
934	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
935	C₂²×C₄	C₂⁴×C₅₃	1	3	yes	—
936	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
937	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
938	C₂²×C₄	C₂⁴×C₅₃	1	3	yes	—
939	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
940	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
941	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
942	C₂²×C₄	C₂⁴×C₅₃	1	12	yes	—
943	C₂²×C₄	C₂⁴×C₅₃	1	12	yes	—
944	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
945	C₄⋊C₄	C₂⁴×C₅₃	1	3	yes	—
946	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
947	C₄⋊C₄	C₂⁴×C₅₃	1	3	yes	—
948	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
949	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
950	C₄⋊C₄	C₂⁴×C₅₃	1	3	yes	—
951	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
952	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
953	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
954	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
955	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
956	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
957	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
958	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
959	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
960	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
961	C₄⋊C₄	C₂⁴×C₅₃	1	3	yes	—
962	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
964	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
967	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
968	C₄⋊C₄	C₂⁴×C₅₃	1	3	yes	—
969	C₄⋊C₄	C₂⁴×C₅₃	1	3	yes	—
970	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
971	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
972	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
973	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
974	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
975	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
976	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
978	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
979	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
980	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
981	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
982	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
983	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
985	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
986	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
987	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
988	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
989	C₄⋊C₄	C₂⁴×C₅₃	1	6	yes	—
990	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
991	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
992	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
993	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
994	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
995	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
996	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
997	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
998	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
999	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
1000	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
1001	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
1002	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
1003	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
1004	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
1005	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
1006	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
1007	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
1008	C₂²⋊C₄	C₂⁴×C₅₃	1	12	yes	—
1009	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
1010	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1011	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
1012	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1013	C₂²⋊C₄	C₂⁴×C₅₃	1	6	yes	—
1014	C₂²⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1015	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1016	C₄²	C₂⁴×C₅₃	1	2	yes	—
1017	C₄²	C₂⁴×C₅₃	1	6	yes	—
1018	C₄²	C₂⁴×C₅₃	1	3	yes	—
1019	C₄²	C₂⁴×C₅₃	1	6	yes	—
1020	C₄²	C₂⁴×C₅₃	1	6	yes	—
1021	C₄²	C₂⁴×C₅₃	1	6	yes	—
1022	C₄²	C₂⁴×C₅₃	1	3	yes	—
1023	C₄²	C₂⁴×C₅₃	1	6	yes	—
1024	C₄²	C₂⁴×C₅₃	1	3	yes	—
1025	C₄²	C₂⁴×C₅₃	1	6	yes	—
1026	C₄²	C₂⁴×C₅₃	1	6	yes	—
1027	C₄²	C₂⁴×C₅₃	1	12	yes	—
1028	C₄²	C₂⁴×C₅₃	1	12	yes	—
1029	C₂³	C₂⁵×C₅₃	1	2	yes	—
1030	C₂³	C₂⁵×C₅₃	1	6	yes	—
1031	C₂³	C₂⁵×C₅₃	1	3	yes	—
1032	Q₈	—	2	12	no	—
1033	Q₈	—	4	6	no	—
1034	Q₈	—	4	6	no	—
1035	Q₈	—	4	6	no	—
1036	Q₈	—	4	12	no	—
1037	Q₈	—	4	1	no	—
1038	Q₈	—	4	6	no	—
1039	Q₈	—	4	2	no	—
1040	Q₈	—	4	3	no	—
1041	Q₈	2₋¹⁺⁴×C₅₃	1	4	yes	—
1042	D₄	—	2	6	no	—
1043	D₄	—	2	12	no	—
1044	D₄	—	4	6	no	—
1045	D₄	—	4	1	no	—
1046	D₄	—	4	6	no	—
1047	D₄	—	4	6	no	—
1048	D₄	—	4	6	no	—
1049	D₄	—	4	3	no	—
1050	D₄	—	4	12	no	—
1051	D₄	—	4	6	no	—
1052	C₂×C₄	—	2	12	no	—
1053	C₂×C₄	—	2	6	no	—
1054	C₂×C₄	—	2	12	no	—
1055	C₂×C₄	—	4	6	no	—
1056	C₂×C₄	—	4	6	no	—
1057	C₂×C₄	—	4	3	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	6	no	—
1060	C₂×C₄	—	4	12	no	—
1061	C₂×C₄	—	4	12	no	—
1062	C₂×C₄	—	4	6	no	—
1063	C₂×C₄	—	4	6	no	—
1064	C₂×C₄	—	4	3	no	—
1065	C₂×C₄	C₂⁵×C₅₃	1	6	yes	—
1066	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1067	C₂×C₄	C₂⁵×C₅₃	1	3	yes	—
1068	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1069	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1070	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1071	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1072	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1073	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1074	C₂×C₄	C₂⁵×C₅₃	1	6	yes	—
1075	C₂×C₄	C₂⁵×C₅₃	1	6	yes	—
1076	C₂×C₄	C₂⁵×C₅₃	1	6	yes	—
1077	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1078	C₂×C₄	C₂⁵×C₅₃	1	3	yes	—
1079	C₂×C₄	C₂⁵×C₅₃	1	6	yes	—
1080	C₂×C₄	C₂⁵×C₅₃	1	3	yes	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	6	no	—
1083	C₂²	—	2	3	no	—
1084	C₂²	—	2	6	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	3	no	—
1087	C₂²	—	2	3	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	6	no	—
1090	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
1091	C₄	—	2	1	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	2	6	no	—
1094	C₄	—	2	6	no	—
1095	C₄	—	2	3	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	6	no	—
1098	C₄	—	2	6	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	6	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	3	no	—
1105	C₄	—	2	2	no	—
1106	C₄	C₂×2₋¹⁺⁴×C₅₃	1	6	yes	—
1107	C₂	—	4	2	no	—
1108	C₂	—	4	6	no	—
1109	C₂	—	4	3	no	—
1110	C₂	C₂²×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1111	C₂	C₅₃×H(7,𝔽₂)	1	1	yes	characteristic
1112	C₂	C₅₃×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3565	C₂	semidirect
2. C₅₃×#3563	C₂	semidirect
3. C₅₃×#3559	C₂	semidirect
4. C₅₃×#3557	C₂	semidirect
5. C₅₃×#3554	C₂	semidirect
6. C₅₃×#3552	C₂	semidirect
7. C₅₃×#3550	C₂	semidirect
8. C₅₃×#3547	C₂	semidirect
9. C₅₃×#3544	C₂	semidirect
10. C₅₃×#3531	C₂	semidirect
11. C₅₃×#3524	C₂	semidirect
12. C₅₃×#3524	C₂	semidirect
13. C₅₃×#3522	C₂	semidirect
14. C₅₃×#3518	C₂	semidirect
15. C₅₃×#3517	C₂	semidirect
16. C₅₃×#3516	C₂	semidirect
17. C₅₃×#3504	C₂	semidirect
18. C₅₃×#3503	C₂	semidirect
19. C₅₃×#3502	C₂	semidirect
524. #63061	C₅₃	direct (N × H)
551. #3565	C₂×C₅₃	semidirect
552. #3563	C₂×C₅₃	semidirect
553. #3559	C₂×C₅₃	semidirect
554. #3557	C₂×C₅₃	semidirect
555. #3554	C₂×C₅₃	semidirect
556. #3552	C₂×C₅₃	semidirect
557. #3550	C₂×C₅₃	semidirect
558. #3547	C₂×C₅₃	semidirect
559. #3544	C₂×C₅₃	semidirect
560. #3531	C₂×C₅₃	semidirect
561. #3524	C₂×C₅₃	semidirect
562. #3524	C₂×C₅₃	semidirect
563. #3522	C₂×C₅₃	semidirect
564. #3518	C₂×C₅₃	semidirect
565. #3517	C₂×C₅₃	semidirect
566. #3516	C₂×C₅₃	semidirect
567. #3504	C₂×C₅₃	semidirect
568. #3503	C₂×C₅₃	semidirect
569. #3502	C₂×C₅₃	semidirect
694. C₅₃	#63061	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×#3565	2
C₅₃×#3563	2
C₅₃×#3559	2
C₅₃×#3557	2
C₅₃×#3554	2
C₅₃×#3552	2
C₅₃×#3550	2
C₅₃×#3547	2
C₅₃×#3544	2
C₅₃×#3531	2
C₅₃×#3524	2
C₅₃×#3522	2
C₅₃×#3518	2
C₅₃×#3517	2
C₅₃×#3516	2
C₅₃×#3504	2
C₅₃×#3503	2
C₅₃×#3502	2
#63061	53

Subgroups — C53×#63061 #27270573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#63061 #27270573