Subgroups — C₅₃×#61163 #27268675

Order 13568.

2124 conjugacy classes of subgroups.

The subgroup lattice has 1436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3327	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3323	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3317	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3315	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3312	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3310	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3300	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3296	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3092	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3056	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3056	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#137×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×M₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₅₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#552	—	2	1	no	—
32	C₅₃×#552	—	2	1	no	—
33	C₅₃×#552	—	2	1	no	—
34	C₅₃×#552	—	2	1	no	—
35	C₅₃×#552	C₂²	1	2	yes	—
36	C₅₃×#552	C₂²	1	2	yes	complemented
37	C₅₃×#552	C₂²	1	2	yes	complemented
38	C₅₃×#552	C₂²	1	2	yes	complemented
39	C₅₃×#550	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#548	C₂²	1	1	yes	characteristic
42	C₅₃×#548	C₂²	1	1	yes	characteristic
43	C₅₃×#547	—	2	1	no	—
44	C₅₃×#547	C₂²	1	1	yes	characteristic
45	C₅₃×#546	—	2	1	no	—
46	C₅₃×#546	—	2	1	no	—
47	C₅₃×#546	C₂²	1	1	yes	characteristic
48	C₅₃×#546	C₂²	1	1	yes	characteristic
49	D₄²×C₅₃	—	2	1	no	—
50	D₄²×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#532	—	2	1	no	—
52	C₅₃×#532	C₂²	1	1	yes	characteristic
53	C₂×#126×C₅₃	—	2	1	no	—
54	C₂×#125×C₅₃	—	2	1	no	—
55	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#525	—	2	1	no	—
57	C₅₃×#525	—	2	1	no	—
58	C₅₃×#525	C₂²	1	1	yes	characteristic
59	C₅₃×#525	C₂²	1	1	yes	characteristic
60	C₂×#123×C₅₃	—	2	1	no	—
61	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×D₄×C₅₃	—	2	1	no	—
66	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
67	C₂×#117×C₅₃	—	2	1	no	—
68	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
69	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#491	C₂²	1	2	yes	complemented
71	C₅₃×#490	C₂²	1	2	yes	complemented
72	C₅₃×#488	C₂²	1	2	yes	complemented
73	C₅₃×#488	C₂²	1	2	yes	complemented
74	C₅₃×#485	C₂²	1	2	yes	complemented
75	C₅₃×#485	C₂²	1	2	yes	complemented
76	C₅₃×#484	C₂²	1	2	yes	complemented
77	C₅₃×#483	C₂²	1	2	yes	complemented
78	C₅₃×#482	C₂²	1	2	yes	complemented
79	C₅₃×#482	C₂²	1	2	yes	complemented
80	C₅₃×#481	C₂²	1	2	yes	complemented
81	C₅₃×#480	C₂²	1	2	yes	complemented
82	C₅₃×#479	C₂²	1	2	yes	complemented
83	C₅₃×#479	C₂²	1	2	yes	complemented
84	C₅₃×#478	C₂²	1	2	yes	complemented
85	C₅₃×#478	C₂²	1	2	yes	complemented
86	C₅₃×#470	C₂²	1	2	yes	complemented
87	C₅₃×#470	C₂²	1	2	yes	complemented
88	C₅₃×#468	C₂²	1	2	yes	complemented
89	C₅₃×#468	C₂²	1	2	yes	complemented
90	C₅₃×#467	C₂²	1	2	yes	complemented
91	C₅₃×#467	C₂²	1	2	yes	complemented
92	C₅₃×#465	C₂²	1	2	yes	complemented
93	C₅₃×#465	C₂²	1	2	yes	complemented
94	C₅₃×#464	C₂²	1	2	yes	complemented
95	C₅₃×#464	C₂²	1	2	yes	complemented
96	C₅₃×#462	C₂²	1	2	yes	complemented
97	C₅₃×#460	C₂²	1	2	yes	complemented
98	C₅₃×#452	C₂²	1	2	yes	complemented
99	C₅₃×#452	C₂²	1	2	yes	complemented
100	C₅₃×#452	C₂²	1	2	yes	complemented
101	C₅₃×#452	C₂²	1	2	yes	complemented
102	C₅₃×#451	C₂²	1	2	yes	complemented
103	C₅₃×#451	C₂²	1	2	yes	complemented
104	C₅₃×#450	C₂²	1	2	yes	complemented
105	C₅₃×#450	C₂²	1	2	yes	complemented
106	C₅₃×#441	C₂²	1	2	yes	complemented
107	C₅₃×#440	C₂²	1	2	yes	complemented
108	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
110	C₅₃×#436	C₂²	1	2	yes	complemented
111	C₅₃×#435	C₂²	1	2	yes	—
112	C₅₃×#435	C₂²	1	2	yes	complemented
113	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
114	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#419	C₂²	1	2	yes	complemented
120	C₅₃×#418	C₂²	1	2	yes	complemented
121	C₅₃×#417	C₂²	1	1	yes	characteristic
122	C₅₃×#417	C₂²	1	1	yes	characteristic
123	C₅₃×#417	C₂²	1	1	yes	characteristic
124	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#417	C₂²	1	2	yes	complemented
131	C₅₃×#417	C₂²	1	2	yes	complemented
132	C₅₃×#416	C₂²	1	2	yes	complemented
133	C₅₃×#416	C₂²	1	2	yes	complemented
134	C₂×#103×C₅₃	C₂²	1	2	yes	complemented
135	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
136	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
138	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
139	C₂×#41×C₅₃	—	2	1	no	—
140	C₂×#41×C₅₃	—	2	1	no	—
141	C₂×#41×C₅₃	—	2	1	no	—
142	C₂×#41×C₅₃	—	2	1	no	—
143	C₂×#41×C₅₃	—	2	4	no	—
144	C₂×#41×C₅₃	—	2	4	no	—
145	C₂×#41×C₅₃	—	4	2	no	—
146	C₂×#41×C₅₃	—	4	2	no	—
147	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
149	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
150	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
151	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
152	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
153	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
154	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
155	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
156	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
157	C₂²×D₄×C₅₃	—	2	1	no	—
158	C₂²×D₄×C₅₃	—	2	1	no	—
159	C₂²×D₄×C₅₃	—	2	1	no	—
160	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
161	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
162	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
163	C₂³×C₄×C₅₃	—	2	1	no	—
164	C₂³×C₄×C₅₃	—	2	1	no	—
165	C₂³×C₄×C₅₃	—	2	1	no	—
166	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
167	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
168	#137×C₅₃	—	2	4	no	—
169	#137×C₅₃	—	4	2	no	—
170	#137×C₅₃	—	4	2	no	—
171	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
172	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
173	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
174	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
175	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
176	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
177	C₂×M₁₆×C₅₃	—	4	2	no	—
178	C₂×M₁₆×C₅₃	—	4	2	no	—
179	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
180	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
181	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
182	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
183	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
184	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
185	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
186	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
187	C₄⋊Q₈×C₅₃	—	2	1	no	—
188	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
189	#127×C₅₃	—	2	1	no	—
190	#127×C₅₃	C₂³	1	1	yes	characteristic
191	#126×C₅₃	—	2	2	no	—
192	#126×C₅₃	—	2	2	no	—
193	#126×C₅₃	—	2	2	no	—
194	#126×C₅₃	—	2	2	no	—
195	#125×C₅₃	—	2	2	no	—
196	#125×C₅₃	—	2	2	no	—
197	#125×C₅₃	—	2	2	no	—
198	#125×C₅₃	—	2	2	no	—
199	#125×C₅₃	—	2	1	no	—
200	#125×C₅₃	—	2	1	no	—
201	#125×C₅₃	C₂³	1	2	yes	—
202	#125×C₅₃	C₂³	1	2	yes	—
203	#124×C₅₃	—	2	1	no	—
204	#124×C₅₃	—	2	1	no	—
205	#124×C₅₃	C₂³	1	1	yes	characteristic
206	#124×C₅₃	C₂³	1	1	yes	characteristic
207	#123×C₅₃	—	2	1	no	—
208	#123×C₅₃	—	2	1	no	—
209	#123×C₅₃	—	2	1	no	—
210	#123×C₅₃	—	2	1	no	—
211	#123×C₅₃	—	2	2	no	—
212	#123×C₅₃	—	2	2	no	—
213	#123×C₅₃	—	2	2	no	—
214	#123×C₅₃	—	2	2	no	—
215	#123×C₅₃	—	2	1	no	—
216	#123×C₅₃	—	2	1	no	—
217	C₂²⋊Q₈×C₅₃	—	2	1	no	—
218	C₂²⋊Q₈×C₅₃	—	2	1	no	—
219	C₂²⋊Q₈×C₅₃	—	2	1	no	—
220	C₂²⋊Q₈×C₅₃	—	2	1	no	—
221	C₂²⋊Q₈×C₅₃	—	2	1	no	—
222	C₂²⋊Q₈×C₅₃	—	2	1	no	—
223	C₂²⋊Q₈×C₅₃	—	2	1	no	—
224	C₂²⋊Q₈×C₅₃	—	2	1	no	—
225	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
228	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
229	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
230	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
231	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
232	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
233	#121×C₅₃	—	2	1	no	—
234	#121×C₅₃	—	2	1	no	—
235	#121×C₅₃	—	2	1	no	—
236	#121×C₅₃	—	2	1	no	—
237	#121×C₅₃	—	2	1	no	—
238	#121×C₅₃	—	2	1	no	—
239	#121×C₅₃	—	2	1	no	—
240	#121×C₅₃	—	2	1	no	—
241	#121×C₅₃	—	2	1	no	—
242	#121×C₅₃	—	2	1	no	—
243	#121×C₅₃	C₂³	1	1	yes	characteristic
244	#121×C₅₃	C₂³	1	1	yes	characteristic
245	#121×C₅₃	C₂³	1	1	yes	characteristic
246	#121×C₅₃	C₂³	1	1	yes	characteristic
247	#120×C₅₃	—	2	1	no	—
248	#120×C₅₃	—	2	1	no	—
249	#120×C₅₃	—	2	1	no	—
250	#120×C₅₃	—	2	1	no	—
251	#120×C₅₃	—	2	1	no	—
252	#120×C₅₃	—	2	1	no	—
253	C₄×Q₈×C₅₃	—	2	1	no	—
254	C₄×Q₈×C₅₃	—	2	1	no	—
255	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
256	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
257	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
258	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₅₃	—	2	1	no	—
260	C₄×D₄×C₅₃	—	2	1	no	—
261	C₄×D₄×C₅₃	—	2	1	no	—
262	C₄×D₄×C₅₃	—	2	1	no	—
263	C₄×D₄×C₅₃	—	2	1	no	—
264	C₄×D₄×C₅₃	—	2	1	no	—
265	C₄×D₄×C₅₃	—	2	1	no	—
266	C₄×D₄×C₅₃	—	2	1	no	—
267	C₄×D₄×C₅₃	—	2	1	no	—
268	C₄×D₄×C₅₃	—	2	1	no	—
269	C₄×D₄×C₅₃	—	2	1	no	—
270	C₄×D₄×C₅₃	—	2	1	no	—
271	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
272	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
273	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
274	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
275	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
277	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
278	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
281	#117×C₅₃	—	2	2	no	—
282	#117×C₅₃	—	2	2	no	—
283	#117×C₅₃	—	2	2	no	—
284	#117×C₅₃	—	2	2	no	—
285	#117×C₅₃	—	2	1	no	—
286	#117×C₅₃	—	2	1	no	—
287	#117×C₅₃	—	2	1	no	—
288	#117×C₅₃	C₂³	1	2	yes	—
289	#117×C₅₃	C₂³	1	2	yes	—
290	#117×C₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
292	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
293	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
294	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
295	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
296	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
297	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
298	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
299	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
300	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
301	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
304	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
305	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
307	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
308	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
309	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
310	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
311	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
312	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
313	C₂×C₄²×C₅₃	—	2	1	no	—
314	C₂×C₄²×C₅₃	—	2	1	no	—
315	C₂×C₄²×C₅₃	—	2	1	no	—
316	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
317	#107×C₅₃	C₂³	1	2	yes	—
318	#107×C₅₃	C₂³	1	2	yes	—
319	#107×C₅₃	C₂³	1	2	yes	—
320	#106×C₅₃	C₂³	1	2	yes	—
321	#106×C₅₃	C₂³	1	2	yes	—
322	#106×C₅₃	C₂³	1	2	yes	—
323	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
324	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
325	#103×C₅₃	C₂³	1	2	yes	—
326	#103×C₅₃	C₂³	1	2	yes	—
327	#103×C₅₃	C₂³	1	2	yes	—
328	#103×C₅₃	C₂³	1	2	yes	—
329	#103×C₅₃	C₂³	1	2	yes	—
330	#103×C₅₃	C₂³	1	2	yes	—
331	#103×C₅₃	C₂³	1	2	yes	—
332	#103×C₅₃	C₂³	1	2	yes	—
333	#103×C₅₃	C₂³	1	2	yes	—
334	#103×C₅₃	C₂³	1	2	yes	—
335	#103×C₅₃	C₂³	1	2	yes	—
336	#102×C₅₃	C₂³	1	2	yes	—
337	#102×C₅₃	C₂³	1	2	yes	—
338	#102×C₅₃	C₂³	1	2	yes	—
339	#102×C₅₃	C₂³	1	2	yes	—
340	#102×C₅₃	C₂³	1	2	yes	—
341	#102×C₅₃	C₂³	1	2	yes	—
342	#102×C₅₃	C₂³	1	2	yes	—
343	#102×C₅₃	C₂³	1	2	yes	—
344	#102×C₅₃	C₂³	1	2	yes	—
345	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
346	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
347	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
348	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
349	#97×C₅₃	C₂³	1	2	yes	—
350	C₄×C₈×C₅₃	C₂³	1	2	yes	—
351	C₂⁴×C₅₃	—	2	1	no	—
352	C₂⁴×C₅₃	—	2	1	no	—
353	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
354	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
355	#41×C₅₃	—	2	2	no	—
356	#41×C₅₃	—	2	2	no	—
357	#41×C₅₃	—	2	2	no	—
358	#41×C₅₃	—	2	2	no	—
359	#41×C₅₃	—	2	2	no	—
360	#41×C₅₃	—	2	2	no	—
361	#41×C₅₃	—	2	2	no	—
362	#41×C₅₃	—	2	2	no	—
363	#41×C₅₃	—	2	2	no	—
364	#41×C₅₃	—	4	4	no	—
365	#41×C₅₃	—	4	4	no	—
366	#41×C₅₃	—	4	1	no	—
367	#41×C₅₃	—	4	1	no	—
368	#41×C₅₃	—	4	1	no	—
369	#41×C₅₃	—	4	1	no	—
370	#41×C₅₃	—	4	4	no	—
371	#41×C₅₃	—	4	4	no	—
372	#41×C₅₃	#41	1	4	yes	—
373	C₂×Q₈×C₅₃	—	2	1	no	—
374	C₂×Q₈×C₅₃	—	2	1	no	—
375	C₂×Q₈×C₅₃	—	2	1	no	—
376	C₂×Q₈×C₅₃	—	2	2	no	—
377	C₂×Q₈×C₅₃	—	2	2	no	—
378	C₂×Q₈×C₅₃	—	2	2	no	—
379	C₂×Q₈×C₅₃	—	2	2	no	—
380	C₂×Q₈×C₅₃	—	4	1	no	—
381	C₂×Q₈×C₅₃	—	4	1	no	—
382	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
385	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂×D₄×C₅₃	—	2	1	no	—
387	C₂×D₄×C₅₃	—	2	2	no	—
388	C₂×D₄×C₅₃	—	2	2	no	—
389	C₂×D₄×C₅₃	—	2	1	no	—
390	C₂×D₄×C₅₃	—	2	1	no	—
391	C₂×D₄×C₅₃	—	2	1	no	—
392	C₂×D₄×C₅₃	—	2	1	no	—
393	C₂×D₄×C₅₃	—	2	1	no	—
394	C₂×D₄×C₅₃	—	2	1	no	—
395	C₂×D₄×C₅₃	—	2	1	no	—
396	C₂×D₄×C₅₃	—	2	1	no	—
397	C₂×D₄×C₅₃	—	2	1	no	—
398	C₂×D₄×C₅₃	—	2	1	no	—
399	C₂×D₄×C₅₃	—	2	1	no	—
400	C₂×D₄×C₅₃	—	2	1	no	—
401	C₂×D₄×C₅₃	—	2	1	no	—
402	C₂×D₄×C₅₃	—	2	1	no	—
403	C₂×D₄×C₅₃	—	4	1	no	—
404	C₂×D₄×C₅₃	—	4	1	no	—
405	C₂×D₄×C₅₃	—	4	2	no	—
406	C₂×D₄×C₅₃	—	4	4	no	—
407	C₂×D₄×C₅₃	—	4	4	no	—
408	C₂×D₄×C₅₃	—	4	4	no	—
409	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
410	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
411	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
412	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
413	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	2	no	—
420	C₂²×C₄×C₅₃	—	2	2	no	—
421	C₂²×C₄×C₅₃	—	2	1	no	—
422	C₂²×C₄×C₅₃	—	2	1	no	—
423	C₂²×C₄×C₅₃	—	2	1	no	—
424	C₂²×C₄×C₅₃	—	2	1	no	—
425	C₂²×C₄×C₅₃	—	2	2	no	—
426	C₂²×C₄×C₅₃	—	2	2	no	—
427	C₂²×C₄×C₅₃	—	2	1	no	—
428	C₂²×C₄×C₅₃	—	2	1	no	—
429	C₂²×C₄×C₅₃	—	2	1	no	—
430	C₂²×C₄×C₅₃	—	2	1	no	—
431	C₂²×C₄×C₅₃	—	2	1	no	—
432	C₂²×C₄×C₅₃	—	2	1	no	—
433	C₂²×C₄×C₅₃	—	2	1	no	—
434	C₂²×C₄×C₅₃	—	2	1	no	—
435	C₂²×C₄×C₅₃	—	2	1	no	—
436	C₂²×C₄×C₅₃	—	2	1	no	—
437	C₂²×C₄×C₅₃	—	4	4	no	—
438	C₂²×C₄×C₅₃	—	4	4	no	—
439	C₂²×C₄×C₅₃	—	4	4	no	—
440	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
441	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
442	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
443	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
444	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
445	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
446	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
447	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
448	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
452	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
453	Q₁₆×C₅₃	—	2	4	no	—
454	Q₁₆×C₅₃	—	4	2	no	—
455	Q₁₆×C₅₃	—	4	2	no	—
456	SD₁₆×C₅₃	—	2	4	no	—
457	SD₁₆×C₅₃	—	4	2	no	—
458	SD₁₆×C₅₃	—	4	2	no	—
459	M₁₆×C₅₃	—	2	2	no	—
460	M₁₆×C₅₃	—	2	2	no	—
461	M₁₆×C₅₃	—	2	2	no	—
462	M₁₆×C₅₃	—	2	2	no	—
463	M₁₆×C₅₃	—	4	2	no	—
464	M₁₆×C₅₃	—	4	2	no	—
465	C₂×C₈×C₅₃	—	4	2	no	—
466	C₂×C₈×C₅₃	—	4	2	no	—
467	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
468	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
469	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
470	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
471	C₄⋊C₄×C₅₃	—	2	1	no	—
472	C₄⋊C₄×C₅₃	—	2	1	no	—
473	C₄⋊C₄×C₅₃	—	2	2	no	—
474	C₄⋊C₄×C₅₃	—	2	2	no	—
475	C₄⋊C₄×C₅₃	—	2	2	no	—
476	C₄⋊C₄×C₅₃	—	2	2	no	—
477	C₄⋊C₄×C₅₃	—	2	2	no	—
478	C₄⋊C₄×C₅₃	—	2	2	no	—
479	C₄⋊C₄×C₅₃	—	2	1	no	—
480	C₄⋊C₄×C₅₃	—	2	1	no	—
481	C₄⋊C₄×C₅₃	—	2	1	no	—
482	C₄⋊C₄×C₅₃	—	2	2	no	—
483	C₄⋊C₄×C₅₃	—	2	2	no	—
484	C₄⋊C₄×C₅₃	—	2	2	no	—
485	C₄⋊C₄×C₅₃	—	2	2	no	—
486	C₄⋊C₄×C₅₃	—	2	2	no	—
487	C₄⋊C₄×C₅₃	—	2	2	no	—
488	C₄⋊C₄×C₅₃	—	2	1	no	—
489	C₄⋊C₄×C₅₃	—	2	1	no	—
490	C₄⋊C₄×C₅₃	—	2	1	no	—
491	C₄⋊C₄×C₅₃	—	2	1	no	—
492	C₄⋊C₄×C₅₃	—	2	1	no	—
493	C₄⋊C₄×C₅₃	—	2	1	no	—
494	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
495	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
496	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
497	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
498	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
499	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
500	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
501	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
502	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
503	C₂²⋊C₄×C₅₃	—	2	2	no	—
504	C₂²⋊C₄×C₅₃	—	2	2	no	—
505	C₂²⋊C₄×C₅₃	—	2	2	no	—
506	C₂²⋊C₄×C₅₃	—	2	2	no	—
507	C₂²⋊C₄×C₅₃	—	2	1	no	—
508	C₂²⋊C₄×C₅₃	—	2	1	no	—
509	C₂²⋊C₄×C₅₃	—	2	2	no	—
510	C₂²⋊C₄×C₅₃	—	2	2	no	—
511	C₂²⋊C₄×C₅₃	—	2	1	no	—
512	C₂²⋊C₄×C₅₃	—	2	1	no	—
513	C₂²⋊C₄×C₅₃	—	2	1	no	—
514	C₂²⋊C₄×C₅₃	—	2	1	no	—
515	C₂²⋊C₄×C₅₃	—	2	1	no	—
516	C₂²⋊C₄×C₅₃	—	2	1	no	—
517	C₂²⋊C₄×C₅₃	—	2	1	no	—
518	C₂²⋊C₄×C₅₃	—	2	1	no	—
519	C₂²⋊C₄×C₅₃	—	2	1	no	—
520	C₂²⋊C₄×C₅₃	—	2	1	no	—
521	C₂²⋊C₄×C₅₃	—	2	1	no	—
522	C₂²⋊C₄×C₅₃	—	2	1	no	—
523	C₂²⋊C₄×C₅₃	—	2	1	no	—
524	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
525	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
526	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
527	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
528	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
529	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
530	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
531	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
532	C₄²×C₅₃	—	2	2	no	—
533	C₄²×C₅₃	—	2	2	no	—
534	C₄²×C₅₃	—	2	2	no	—
535	C₄²×C₅₃	—	2	2	no	—
536	C₄²×C₅₃	—	2	1	no	—
537	C₄²×C₅₃	—	2	1	no	—
538	C₄²×C₅₃	—	2	1	no	—
539	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
540	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
541	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
542	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
543	C₂³×C₅₃	—	2	2	no	—
544	C₂³×C₅₃	—	2	2	no	—
545	C₂³×C₅₃	—	2	1	no	—
546	C₂³×C₅₃	—	2	2	no	—
547	C₂³×C₅₃	—	2	1	no	—
548	C₂³×C₅₃	—	2	1	no	—
549	C₂³×C₅₃	—	4	1	no	—
550	C₂³×C₅₃	—	4	1	no	—
551	C₂³×C₅₃	—	4	1	no	—
552	C₂³×C₅₃	—	4	2	no	—
553	C₂³×C₅₃	—	4	2	no	—
554	C₂³×C₅₃	—	4	2	no	—
555	C₂³×C₅₃	—	4	2	no	—
556	C₂³×C₅₃	—	8	1	no	—
557	C₂³×C₅₃	—	8	1	no	—
558	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
559	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
560	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
561	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
562	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
563	Q₈×C₅₃	—	2	1	no	—
564	Q₈×C₅₃	—	2	1	no	—
565	Q₈×C₅₃	—	2	1	no	—
566	Q₈×C₅₃	—	2	2	no	—
567	Q₈×C₅₃	—	2	2	no	—
568	Q₈×C₅₃	—	2	1	no	—
569	Q₈×C₅₃	—	2	1	no	—
570	Q₈×C₅₃	—	4	2	no	—
571	Q₈×C₅₃	—	4	2	no	—
572	Q₈×C₅₃	—	4	2	no	—
573	Q₈×C₅₃	C₂×#41	1	2	yes	—
574	D₄×C₅₃	—	2	4	no	—
575	D₄×C₅₃	—	2	2	no	—
576	D₄×C₅₃	—	2	2	no	—
577	D₄×C₅₃	—	2	1	no	—
578	D₄×C₅₃	—	2	1	no	—
579	D₄×C₅₃	—	2	1	no	—
580	D₄×C₅₃	—	2	1	no	—
581	D₄×C₅₃	—	2	1	no	—
582	D₄×C₅₃	—	4	1	no	—
583	D₄×C₅₃	—	4	1	no	—
584	D₄×C₅₃	—	4	2	no	—
585	D₄×C₅₃	—	4	2	no	—
586	D₄×C₅₃	—	4	2	no	—
587	D₄×C₅₃	—	4	2	no	—
588	D₄×C₅₃	—	4	2	no	—
589	D₄×C₅₃	—	4	2	no	—
590	D₄×C₅₃	—	4	2	no	—
591	D₄×C₅₃	—	4	2	no	—
592	D₄×C₅₃	—	4	2	no	—
593	D₄×C₅₃	—	4	2	no	—
594	D₄×C₅₃	—	4	2	no	—
595	D₄×C₅₃	—	8	1	no	—
596	D₄×C₅₃	—	8	1	no	—
597	D₄×C₅₃	—	8	1	no	—
598	D₄×C₅₃	C₂×#41	1	2	yes	—
599	C₂×C₄×C₅₃	—	2	2	no	—
600	C₂×C₄×C₅₃	—	2	2	no	—
601	C₂×C₄×C₅₃	—	2	1	no	—
602	C₂×C₄×C₅₃	—	2	2	no	—
603	C₂×C₄×C₅₃	—	2	2	no	—
604	C₂×C₄×C₅₃	—	2	2	no	—
605	C₂×C₄×C₅₃	—	2	2	no	—
606	C₂×C₄×C₅₃	—	2	4	no	—
607	C₂×C₄×C₅₃	—	2	1	no	—
608	C₂×C₄×C₅₃	—	2	1	no	—
609	C₂×C₄×C₅₃	—	2	1	no	—
610	C₂×C₄×C₅₃	—	2	1	no	—
611	C₂×C₄×C₅₃	—	2	1	no	—
612	C₂×C₄×C₅₃	—	2	1	no	—
613	C₂×C₄×C₅₃	—	2	1	no	—
614	C₂×C₄×C₅₃	—	2	1	no	—
615	C₂×C₄×C₅₃	—	2	1	no	—
616	C₂×C₄×C₅₃	—	2	1	no	—
617	C₂×C₄×C₅₃	—	2	2	no	—
618	C₂×C₄×C₅₃	—	2	2	no	—
619	C₂×C₄×C₅₃	—	2	1	no	—
620	C₂×C₄×C₅₃	—	2	1	no	—
621	C₂×C₄×C₅₃	—	2	2	no	—
622	C₂×C₄×C₅₃	—	2	2	no	—
623	C₂×C₄×C₅₃	—	4	1	no	—
624	C₂×C₄×C₅₃	—	4	1	no	—
625	C₂×C₄×C₅₃	—	4	2	no	—
626	C₂×C₄×C₅₃	—	4	2	no	—
627	C₂×C₄×C₅₃	—	4	2	no	—
628	C₂×C₄×C₅₃	—	4	2	no	—
629	C₂×C₄×C₅₃	—	4	2	no	—
630	C₂×C₄×C₅₃	—	4	2	no	—
631	C₂×C₄×C₅₃	—	4	2	no	—
632	C₂×C₄×C₅₃	—	4	2	no	—
633	C₂×C₄×C₅₃	—	4	2	no	—
634	C₂×C₄×C₅₃	—	4	2	no	—
635	C₂×C₄×C₅₃	—	4	4	no	—
636	C₂×C₄×C₅₃	—	4	2	no	—
637	C₂×C₄×C₅₃	—	4	4	no	—
638	C₂×C₄×C₅₃	—	4	2	no	—
639	C₂×C₄×C₅₃	—	4	2	no	—
640	C₂×C₄×C₅₃	—	8	1	no	—
641	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
642	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
643	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
644	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
645	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
646	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
647	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
648	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
649	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
650	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
651	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
652	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
653	C₈×C₅₃	—	2	2	no	—
654	C₈×C₅₃	—	2	2	no	—
655	C₈×C₅₃	—	2	2	no	—
656	C₈×C₅₃	—	2	2	no	—
657	#61163	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
658	C₂²×C₅₃	—	2	1	no	—
659	C₂²×C₅₃	—	2	1	no	—
660	C₂²×C₅₃	—	2	1	no	—
661	C₂²×C₅₃	—	2	1	no	—
662	C₂²×C₅₃	—	2	1	no	—
663	C₂²×C₅₃	—	2	1	no	—
664	C₂²×C₅₃	—	2	1	no	—
665	C₂²×C₅₃	—	2	1	no	—
666	C₂²×C₅₃	—	2	1	no	—
667	C₂²×C₅₃	—	2	1	no	—
668	C₂²×C₅₃	—	2	2	no	—
669	C₂²×C₅₃	—	2	1	no	—
670	C₂²×C₅₃	—	2	1	no	—
671	C₂²×C₅₃	—	2	1	no	—
672	C₂²×C₅₃	—	4	4	no	—
673	C₂²×C₅₃	—	4	1	no	—
674	C₂²×C₅₃	—	4	1	no	—
675	C₂²×C₅₃	—	4	1	no	—
676	C₂²×C₅₃	—	4	1	no	—
677	C₂²×C₅₃	—	4	1	no	—
678	C₂²×C₅₃	—	4	1	no	—
679	C₂²×C₅₃	—	4	1	no	—
680	C₂²×C₅₃	—	4	1	no	—
681	C₂²×C₅₃	—	8	2	no	—
682	C₂²×C₅₃	—	8	4	no	—
683	C₂²×C₅₃	—	8	4	no	—
684	C₂²×C₅₃	#546	1	2	yes	—
685	C₂²×C₅₃	#575	1	2	yes	—
686	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
687	C₄×C₅₃	—	2	1	no	—
688	C₄×C₅₃	—	2	1	no	—
689	C₄×C₅₃	—	2	1	no	—
690	C₄×C₅₃	—	2	1	no	—
691	C₄×C₅₃	—	2	1	no	—
692	C₄×C₅₃	—	2	1	no	—
693	C₄×C₅₃	—	2	2	no	—
694	C₄×C₅₃	—	2	1	no	—
695	C₄×C₅₃	—	2	1	no	—
696	C₄×C₅₃	—	4	2	no	—
697	C₄×C₅₃	—	4	1	no	—
698	C₄×C₅₃	—	4	1	no	—
699	C₄×C₅₃	—	4	1	no	—
700	C₄×C₅₃	—	4	2	no	—
701	C₄×C₅₃	—	4	2	no	—
702	C₄×C₅₃	—	4	2	no	—
703	C₄×C₅₃	—	4	1	no	—
704	C₄×C₅₃	#546	1	2	yes	—
705	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
706	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
707	C₂×#552	C₂×C₅₃	1	1	yes	characteristic, complemented
708	D₄×#41	C₂×C₅₃	1	1	yes	characteristic
709	#3327	C₂×C₅₃	1	2	yes	complemented
710	#3323	C₂×C₅₃	1	2	yes	complemented
711	#3317	C₂×C₅₃	1	2	yes	complemented
712	#3315	C₂×C₅₃	1	2	yes	complemented
713	#3312	C₂×C₅₃	1	2	yes	complemented
714	#3310	C₂×C₅₃	1	2	yes	complemented
715	#3300	C₂×C₅₃	1	2	yes	complemented
716	#3296	C₂×C₅₃	1	2	yes	complemented
717	#3142	C₂×C₅₃	1	1	yes	characteristic, complemented
718	#3093	C₂×C₅₃	1	1	yes	characteristic, complemented
719	#3092	C₂×C₅₃	1	1	yes	characteristic, complemented
720	#3080	C₂×C₅₃	1	1	yes	characteristic, complemented
721	#3056	C₂×C₅₃	1	1	yes	characteristic, complemented
722	#3056	C₂×C₅₃	1	1	yes	characteristic, complemented
723	#3037	C₂×C₅₃	1	1	yes	characteristic, complemented
724	#3007	C₂×C₅₃	1	1	yes	characteristic, complemented
725	#3007	C₂×C₅₃	1	1	yes	characteristic, complemented
726	C₄×#137	C₂×C₅₃	1	1	yes	characteristic, complemented
727	D₄×M₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
728	#2896	C₂×C₅₃	1	1	yes	characteristic, complemented
729	C₂×#417	C₂×C₅₃	1	1	yes	characteristic, complemented
730	C₂×C₅₃	—	2	2	no	—
731	C₂×C₅₃	—	2	2	no	—
732	C₂×C₅₃	—	4	1	no	—
733	C₂×C₅₃	—	4	1	no	—
734	C₂×C₅₃	—	4	1	no	—
735	C₂×C₅₃	—	4	2	no	—
736	C₂×C₅₃	—	8	1	no	—
737	C₂×C₅₃	—	8	1	no	—
738	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
739	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
740	C₂×C₅₃	#3586	1	1	yes	characteristic
741	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
742	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
743	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
744	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
745	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
746	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
747	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
748	#552	—	2	1	no	—
749	#552	—	2	1	no	—
750	#552	—	2	1	no	—
751	#552	—	2	1	no	—
752	#552	C₂²×C₅₃	1	2	yes	—
753	#552	C₂²×C₅₃	1	2	yes	complemented
754	#552	C₂²×C₅₃	1	2	yes	complemented
755	#552	C₂²×C₅₃	1	2	yes	complemented
756	#550	C₂²×C₅₃	1	1	yes	characteristic
757	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
758	#548	C₂²×C₅₃	1	1	yes	characteristic
759	#548	C₂²×C₅₃	1	1	yes	characteristic
760	#547	—	2	1	no	—
761	#547	C₂²×C₅₃	1	1	yes	characteristic
762	#546	—	2	1	no	—
763	#546	—	2	1	no	—
764	#546	C₂²×C₅₃	1	1	yes	characteristic
765	#546	C₂²×C₅₃	1	1	yes	characteristic
766	D₄²	—	2	1	no	—
767	D₄²	C₂²×C₅₃	1	1	yes	characteristic
768	#532	—	2	1	no	—
769	#532	C₂²×C₅₃	1	1	yes	characteristic
770	C₂×#126	—	2	1	no	—
771	C₂×#125	—	2	1	no	—
772	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
773	#525	—	2	1	no	—
774	#525	—	2	1	no	—
775	#525	C₂²×C₅₃	1	1	yes	characteristic
776	#525	C₂²×C₅₃	1	1	yes	characteristic
777	C₂×#123	—	2	1	no	—
778	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
779	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
780	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
781	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
782	C₂×C₄×D₄	—	2	1	no	—
783	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
784	C₂×#117	—	2	1	no	—
785	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
786	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
787	#491	C₂²×C₅₃	1	2	yes	complemented
788	#490	C₂²×C₅₃	1	2	yes	complemented
789	#488	C₂²×C₅₃	1	2	yes	complemented
790	#488	C₂²×C₅₃	1	2	yes	complemented
791	#485	C₂²×C₅₃	1	2	yes	complemented
792	#485	C₂²×C₅₃	1	2	yes	complemented
793	#484	C₂²×C₅₃	1	2	yes	complemented
794	#483	C₂²×C₅₃	1	2	yes	complemented
795	#482	C₂²×C₅₃	1	2	yes	complemented
796	#482	C₂²×C₅₃	1	2	yes	complemented
797	#481	C₂²×C₅₃	1	2	yes	complemented
798	#480	C₂²×C₅₃	1	2	yes	complemented
799	#479	C₂²×C₅₃	1	2	yes	complemented
800	#479	C₂²×C₅₃	1	2	yes	complemented
801	#478	C₂²×C₅₃	1	2	yes	complemented
802	#478	C₂²×C₅₃	1	2	yes	complemented
803	#470	C₂²×C₅₃	1	2	yes	complemented
804	#470	C₂²×C₅₃	1	2	yes	complemented
805	#468	C₂²×C₅₃	1	2	yes	complemented
806	#468	C₂²×C₅₃	1	2	yes	complemented
807	#467	C₂²×C₅₃	1	2	yes	complemented
808	#467	C₂²×C₅₃	1	2	yes	complemented
809	#465	C₂²×C₅₃	1	2	yes	complemented
810	#465	C₂²×C₅₃	1	2	yes	complemented
811	#464	C₂²×C₅₃	1	2	yes	complemented
812	#464	C₂²×C₅₃	1	2	yes	complemented
813	#462	C₂²×C₅₃	1	2	yes	complemented
814	#460	C₂²×C₅₃	1	2	yes	complemented
815	#452	C₂²×C₅₃	1	2	yes	complemented
816	#452	C₂²×C₅₃	1	2	yes	complemented
817	#452	C₂²×C₅₃	1	2	yes	complemented
818	#452	C₂²×C₅₃	1	2	yes	complemented
819	#451	C₂²×C₅₃	1	2	yes	complemented
820	#451	C₂²×C₅₃	1	2	yes	complemented
821	#450	C₂²×C₅₃	1	2	yes	complemented
822	#450	C₂²×C₅₃	1	2	yes	complemented
823	#441	C₂²×C₅₃	1	2	yes	complemented
824	#440	C₂²×C₅₃	1	2	yes	complemented
825	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
826	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
827	#436	C₂²×C₅₃	1	2	yes	complemented
828	#435	C₂²×C₅₃	1	2	yes	—
829	#435	C₂²×C₅₃	1	2	yes	complemented
830	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
831	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
832	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
833	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
834	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
835	#419	C₂²×C₅₃	1	2	yes	complemented
836	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
837	#418	C₂²×C₅₃	1	2	yes	complemented
838	#417	C₂²×C₅₃	1	1	yes	characteristic
839	#417	C₂²×C₅₃	1	1	yes	characteristic
840	#417	C₂²×C₅₃	1	1	yes	characteristic
841	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
842	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
843	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
844	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
845	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
846	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
847	#417	C₂²×C₅₃	1	2	yes	complemented
848	#417	C₂²×C₅₃	1	2	yes	complemented
849	#416	C₂²×C₅₃	1	2	yes	complemented
850	#416	C₂²×C₅₃	1	2	yes	complemented
851	C₂×#103	C₂²×C₅₃	1	2	yes	complemented
852	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
853	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
854	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
855	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
856	C₅₃	#61163	1	1	yes	characteristic, direct product factor, Sylow
857	C₂×#41	—	2	1	no	—
858	C₂×#41	—	2	1	no	—
859	C₂×#41	—	2	1	no	—
860	C₂×#41	—	2	1	no	—
861	C₂×#41	—	2	4	no	—
862	C₂×#41	—	2	4	no	—
863	C₂×#41	—	4	2	no	—
864	C₂×#41	—	4	2	no	—
865	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
866	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
867	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
868	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
869	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
870	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
871	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
872	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
873	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
874	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
875	C₂²×D₄	—	2	1	no	—
876	C₂²×D₄	—	2	1	no	—
877	C₂²×D₄	—	2	1	no	—
878	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
879	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
880	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
881	C₂³×C₄	—	2	1	no	—
882	C₂³×C₄	—	2	1	no	—
883	C₂³×C₄	—	2	1	no	—
884	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
885	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
886	#137	—	2	4	no	—
887	#137	—	4	2	no	—
888	#137	—	4	2	no	—
889	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
890	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
891	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
892	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
893	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
894	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
895	C₂×M₁₆	—	4	2	no	—
896	C₂×M₁₆	—	4	2	no	—
897	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
898	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
899	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
900	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
901	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
902	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
903	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
904	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
905	C₄⋊Q₈	—	2	1	no	—
906	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
907	#127	—	2	1	no	—
908	#127	C₂³×C₅₃	1	1	yes	characteristic
909	#126	—	2	2	no	—
910	#126	—	2	2	no	—
911	#126	—	2	2	no	—
912	#126	—	2	2	no	—
913	#125	—	2	2	no	—
914	#125	—	2	2	no	—
915	#125	—	2	2	no	—
916	#125	—	2	2	no	—
917	#125	—	2	1	no	—
918	#125	—	2	1	no	—
919	#125	C₂³×C₅₃	1	2	yes	—
920	#125	C₂³×C₅₃	1	2	yes	—
921	#124	—	2	1	no	—
922	#124	—	2	1	no	—
923	#124	C₂³×C₅₃	1	1	yes	characteristic
924	#124	C₂³×C₅₃	1	1	yes	characteristic
925	#123	—	2	2	no	—
926	#123	—	2	2	no	—
927	#123	—	2	2	no	—
928	#123	—	2	2	no	—
929	#123	—	2	1	no	—
930	#123	—	2	1	no	—
931	#123	—	2	1	no	—
932	#123	—	2	1	no	—
933	#123	—	2	1	no	—
934	#123	—	2	1	no	—
935	C₂²⋊Q₈	—	2	1	no	—
936	C₂²⋊Q₈	—	2	1	no	—
937	C₂²⋊Q₈	—	2	1	no	—
938	C₂²⋊Q₈	—	2	1	no	—
939	C₂²⋊Q₈	—	2	1	no	—
940	C₂²⋊Q₈	—	2	1	no	—
941	C₂²⋊Q₈	—	2	1	no	—
942	C₂²⋊Q₈	—	2	1	no	—
943	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
944	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
945	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
946	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
947	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
948	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
949	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
950	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
951	#121	—	2	1	no	—
952	#121	—	2	1	no	—
953	#121	—	2	1	no	—
954	#121	—	2	1	no	—
955	#121	—	2	1	no	—
956	#121	—	2	1	no	—
957	#121	—	2	1	no	—
958	#121	—	2	1	no	—
959	#121	—	2	1	no	—
960	#121	—	2	1	no	—
961	#121	C₂³×C₅₃	1	1	yes	characteristic
962	#121	C₂³×C₅₃	1	1	yes	characteristic
963	#121	C₂³×C₅₃	1	1	yes	characteristic
964	#121	C₂³×C₅₃	1	1	yes	characteristic
965	#120	—	2	1	no	—
966	#120	—	2	1	no	—
967	#120	—	2	1	no	—
968	#120	—	2	1	no	—
969	#120	—	2	1	no	—
970	#120	—	2	1	no	—
971	C₄×Q₈	—	2	1	no	—
972	C₄×Q₈	—	2	1	no	—
973	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
974	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
975	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
976	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
977	C₄×D₄	—	2	1	no	—
978	C₄×D₄	—	2	1	no	—
979	C₄×D₄	—	2	1	no	—
980	C₄×D₄	—	2	1	no	—
981	C₄×D₄	—	2	1	no	—
982	C₄×D₄	—	2	1	no	—
983	C₄×D₄	—	2	1	no	—
984	C₄×D₄	—	2	1	no	—
985	C₄×D₄	—	2	1	no	—
986	C₄×D₄	—	2	1	no	—
987	C₄×D₄	—	2	1	no	—
988	C₄×D₄	—	2	1	no	—
989	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
990	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
991	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
992	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
993	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
994	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
995	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
996	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
997	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
998	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
999	#117	—	2	1	no	—
1000	#117	—	2	1	no	—
1001	#117	—	2	2	no	—
1002	#117	—	2	2	no	—
1003	#117	—	2	2	no	—
1004	#117	—	2	2	no	—
1005	#117	—	2	1	no	—
1006	#117	C₂³×C₅₃	1	2	yes	—
1007	#117	C₂³×C₅₃	1	2	yes	—
1008	#117	C₂³×C₅₃	1	1	yes	characteristic
1009	C₂×C₄⋊C₄	—	2	1	no	—
1010	C₂×C₄⋊C₄	—	2	1	no	—
1011	C₂×C₄⋊C₄	—	2	1	no	—
1012	C₂×C₄⋊C₄	—	2	1	no	—
1013	C₂×C₄⋊C₄	—	2	1	no	—
1014	C₂×C₄⋊C₄	—	2	1	no	—
1015	C₂×C₄⋊C₄	—	2	1	no	—
1016	C₂×C₄⋊C₄	—	2	1	no	—
1017	C₂×C₄⋊C₄	—	2	1	no	—
1018	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1019	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1020	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1021	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1022	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1023	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1024	C₂×C₂²⋊C₄	—	2	1	no	—
1025	C₂×C₂²⋊C₄	—	2	1	no	—
1026	C₂×C₂²⋊C₄	—	2	1	no	—
1027	C₂×C₂²⋊C₄	—	2	1	no	—
1028	C₂×C₂²⋊C₄	—	2	1	no	—
1029	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1031	C₂×C₄²	—	2	1	no	—
1032	C₂×C₄²	—	2	1	no	—
1033	C₂×C₄²	—	2	1	no	—
1034	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1035	#107	C₂³×C₅₃	1	2	yes	—
1036	#107	C₂³×C₅₃	1	2	yes	—
1037	#107	C₂³×C₅₃	1	2	yes	—
1038	#106	C₂³×C₅₃	1	2	yes	—
1039	#106	C₂³×C₅₃	1	2	yes	—
1040	#106	C₂³×C₅₃	1	2	yes	—
1041	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
1042	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
1043	#103	C₂³×C₅₃	1	2	yes	—
1044	#103	C₂³×C₅₃	1	2	yes	—
1045	#103	C₂³×C₅₃	1	2	yes	—
1046	#103	C₂³×C₅₃	1	2	yes	—
1047	#103	C₂³×C₅₃	1	2	yes	—
1048	#103	C₂³×C₅₃	1	2	yes	—
1049	#103	C₂³×C₅₃	1	2	yes	—
1050	#103	C₂³×C₅₃	1	2	yes	—
1051	#103	C₂³×C₅₃	1	2	yes	—
1052	#103	C₂³×C₅₃	1	2	yes	—
1053	#103	C₂³×C₅₃	1	2	yes	—
1054	#102	C₂³×C₅₃	1	2	yes	—
1055	#102	C₂³×C₅₃	1	2	yes	—
1056	#102	C₂³×C₅₃	1	2	yes	—
1057	#102	C₂³×C₅₃	1	2	yes	—
1058	#102	C₂³×C₅₃	1	2	yes	—
1059	#102	C₂³×C₅₃	1	2	yes	—
1060	#102	C₂³×C₅₃	1	2	yes	—
1061	#102	C₂³×C₅₃	1	2	yes	—
1062	#102	C₂³×C₅₃	1	2	yes	—
1063	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1064	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1065	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1066	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1067	#97	C₂³×C₅₃	1	2	yes	—
1068	C₄×C₈	C₂³×C₅₃	1	2	yes	—
1069	C₂⁴	—	2	1	no	—
1070	C₂⁴	—	2	1	no	—
1071	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1072	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1073	#41	—	2	2	no	—
1074	#41	—	2	2	no	—
1075	#41	—	2	2	no	—
1076	#41	—	2	2	no	—
1077	#41	—	2	2	no	—
1078	#41	—	2	2	no	—
1079	#41	—	2	2	no	—
1080	#41	—	2	2	no	—
1081	#41	—	2	2	no	—
1082	#41	—	4	4	no	—
1083	#41	—	4	4	no	—
1084	#41	—	4	1	no	—
1085	#41	—	4	1	no	—
1086	#41	—	4	1	no	—
1087	#41	—	4	1	no	—
1088	#41	—	4	4	no	—
1089	#41	—	4	4	no	—
1090	#41	#41×C₅₃	1	4	yes	—
1091	C₂×Q₈	—	2	1	no	—
1092	C₂×Q₈	—	2	1	no	—
1093	C₂×Q₈	—	2	1	no	—
1094	C₂×Q₈	—	2	2	no	—
1095	C₂×Q₈	—	2	2	no	—
1096	C₂×Q₈	—	2	2	no	—
1097	C₂×Q₈	—	2	2	no	—
1098	C₂×Q₈	—	4	1	no	—
1099	C₂×Q₈	—	4	1	no	—
1100	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1101	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1102	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
1103	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1104	C₂×D₄	—	2	1	no	—
1105	C₂×D₄	—	2	2	no	—
1106	C₂×D₄	—	2	2	no	—
1107	C₂×D₄	—	2	1	no	—
1108	C₂×D₄	—	2	1	no	—
1109	C₂×D₄	—	2	1	no	—
1110	C₂×D₄	—	2	1	no	—
1111	C₂×D₄	—	2	1	no	—
1112	C₂×D₄	—	2	1	no	—
1113	C₂×D₄	—	2	1	no	—
1114	C₂×D₄	—	2	1	no	—
1115	C₂×D₄	—	2	1	no	—
1116	C₂×D₄	—	2	1	no	—
1117	C₂×D₄	—	2	1	no	—
1118	C₂×D₄	—	2	1	no	—
1119	C₂×D₄	—	2	1	no	—
1120	C₂×D₄	—	2	1	no	—
1121	C₂×D₄	—	4	1	no	—
1122	C₂×D₄	—	4	1	no	—
1123	C₂×D₄	—	4	2	no	—
1124	C₂×D₄	—	4	4	no	—
1125	C₂×D₄	—	4	4	no	—
1126	C₂×D₄	—	4	4	no	—
1127	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1128	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1129	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1130	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1131	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1132	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1133	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1134	C₂²×C₄	—	2	1	no	—
1135	C₂²×C₄	—	2	2	no	—
1136	C₂²×C₄	—	2	2	no	—
1137	C₂²×C₄	—	2	2	no	—
1138	C₂²×C₄	—	2	2	no	—
1139	C₂²×C₄	—	2	1	no	—
1140	C₂²×C₄	—	2	1	no	—
1141	C₂²×C₄	—	2	1	no	—
1142	C₂²×C₄	—	2	1	no	—
1143	C₂²×C₄	—	2	2	no	—
1144	C₂²×C₄	—	2	2	no	—
1145	C₂²×C₄	—	2	1	no	—
1146	C₂²×C₄	—	2	1	no	—
1147	C₂²×C₄	—	2	1	no	—
1148	C₂²×C₄	—	2	1	no	—
1149	C₂²×C₄	—	2	1	no	—
1150	C₂²×C₄	—	2	1	no	—
1151	C₂²×C₄	—	2	1	no	—
1152	C₂²×C₄	—	2	1	no	—
1153	C₂²×C₄	—	2	1	no	—
1154	C₂²×C₄	—	2	1	no	—
1155	C₂²×C₄	—	4	4	no	—
1156	C₂²×C₄	—	4	4	no	—
1157	C₂²×C₄	—	4	4	no	—
1158	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1159	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1160	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1161	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1162	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1163	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1164	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1165	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1166	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1167	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1168	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1169	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1170	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1171	Q₁₆	—	2	4	no	—
1172	Q₁₆	—	4	2	no	—
1173	Q₁₆	—	4	2	no	—
1174	SD₁₆	—	2	4	no	—
1175	SD₁₆	—	4	2	no	—
1176	SD₁₆	—	4	2	no	—
1177	M₁₆	—	2	2	no	—
1178	M₁₆	—	2	2	no	—
1179	M₁₆	—	2	2	no	—
1180	M₁₆	—	2	2	no	—
1181	M₁₆	—	4	2	no	—
1182	M₁₆	—	4	2	no	—
1183	C₂×C₈	—	4	2	no	—
1184	C₂×C₈	—	4	2	no	—
1185	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1186	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1187	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1188	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1189	C₄⋊C₄	—	2	1	no	—
1190	C₄⋊C₄	—	2	1	no	—
1191	C₄⋊C₄	—	2	2	no	—
1192	C₄⋊C₄	—	2	2	no	—
1193	C₄⋊C₄	—	2	2	no	—
1194	C₄⋊C₄	—	2	2	no	—
1195	C₄⋊C₄	—	2	2	no	—
1196	C₄⋊C₄	—	2	2	no	—
1197	C₄⋊C₄	—	2	1	no	—
1198	C₄⋊C₄	—	2	1	no	—
1199	C₄⋊C₄	—	2	1	no	—
1200	C₄⋊C₄	—	2	2	no	—
1201	C₄⋊C₄	—	2	2	no	—
1202	C₄⋊C₄	—	2	2	no	—
1203	C₄⋊C₄	—	2	2	no	—
1204	C₄⋊C₄	—	2	2	no	—
1205	C₄⋊C₄	—	2	2	no	—
1206	C₄⋊C₄	—	2	1	no	—
1207	C₄⋊C₄	—	2	1	no	—
1208	C₄⋊C₄	—	2	1	no	—
1209	C₄⋊C₄	—	2	1	no	—
1210	C₄⋊C₄	—	2	1	no	—
1211	C₄⋊C₄	—	2	1	no	—
1212	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1213	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1214	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1215	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1216	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1217	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1218	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1219	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1220	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1221	C₂²⋊C₄	—	2	2	no	—
1222	C₂²⋊C₄	—	2	2	no	—
1223	C₂²⋊C₄	—	2	2	no	—
1224	C₂²⋊C₄	—	2	2	no	—
1225	C₂²⋊C₄	—	2	1	no	—
1226	C₂²⋊C₄	—	2	1	no	—
1227	C₂²⋊C₄	—	2	2	no	—
1228	C₂²⋊C₄	—	2	2	no	—
1229	C₂²⋊C₄	—	2	1	no	—
1230	C₂²⋊C₄	—	2	1	no	—
1231	C₂²⋊C₄	—	2	1	no	—
1232	C₂²⋊C₄	—	2	1	no	—
1233	C₂²⋊C₄	—	2	1	no	—
1234	C₂²⋊C₄	—	2	1	no	—
1235	C₂²⋊C₄	—	2	1	no	—
1236	C₂²⋊C₄	—	2	1	no	—
1237	C₂²⋊C₄	—	2	1	no	—
1238	C₂²⋊C₄	—	2	1	no	—
1239	C₂²⋊C₄	—	2	1	no	—
1240	C₂²⋊C₄	—	2	1	no	—
1241	C₂²⋊C₄	—	2	1	no	—
1242	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1243	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1244	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1245	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1246	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1247	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1248	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1249	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1250	C₄²	—	2	2	no	—
1251	C₄²	—	2	2	no	—
1252	C₄²	—	2	2	no	—
1253	C₄²	—	2	2	no	—
1254	C₄²	—	2	1	no	—
1255	C₄²	—	2	1	no	—
1256	C₄²	—	2	1	no	—
1257	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1258	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1259	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1260	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1261	C₂³	—	2	2	no	—
1262	C₂³	—	2	2	no	—
1263	C₂³	—	2	1	no	—
1264	C₂³	—	2	2	no	—
1265	C₂³	—	2	1	no	—
1266	C₂³	—	2	1	no	—
1267	C₂³	—	4	1	no	—
1268	C₂³	—	4	1	no	—
1269	C₂³	—	4	1	no	—
1270	C₂³	—	4	2	no	—
1271	C₂³	—	4	2	no	—
1272	C₂³	—	4	2	no	—
1273	C₂³	—	4	2	no	—
1274	C₂³	—	8	1	no	—
1275	C₂³	—	8	1	no	—
1276	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1277	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1278	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1279	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1280	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1281	Q₈	—	2	1	no	—
1282	Q₈	—	2	2	no	—
1283	Q₈	—	2	1	no	—
1284	Q₈	—	2	1	no	—
1285	Q₈	—	2	2	no	—
1286	Q₈	—	2	1	no	—
1287	Q₈	—	2	1	no	—
1288	Q₈	—	4	2	no	—
1289	Q₈	—	4	2	no	—
1290	Q₈	—	4	2	no	—
1291	Q₈	C₂×#41×C₅₃	1	2	yes	—
1292	D₄	—	2	4	no	—
1293	D₄	—	2	2	no	—
1294	D₄	—	2	2	no	—
1295	D₄	—	2	1	no	—
1296	D₄	—	2	1	no	—
1297	D₄	—	2	1	no	—
1298	D₄	—	2	1	no	—
1299	D₄	—	2	1	no	—
1300	D₄	—	4	1	no	—
1301	D₄	—	4	1	no	—
1302	D₄	—	4	2	no	—
1303	D₄	—	4	2	no	—
1304	D₄	—	4	2	no	—
1305	D₄	—	4	2	no	—
1306	D₄	—	4	2	no	—
1307	D₄	—	4	2	no	—
1308	D₄	—	4	2	no	—
1309	D₄	—	4	2	no	—
1310	D₄	—	4	2	no	—
1311	D₄	—	4	2	no	—
1312	D₄	—	4	2	no	—
1313	D₄	—	8	1	no	—
1314	D₄	—	8	1	no	—
1315	D₄	—	8	1	no	—
1316	D₄	C₂×#41×C₅₃	1	2	yes	—
1317	C₂×C₄	—	2	2	no	—
1318	C₂×C₄	—	2	2	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	2	no	—
1321	C₂×C₄	—	2	2	no	—
1322	C₂×C₄	—	2	2	no	—
1323	C₂×C₄	—	2	2	no	—
1324	C₂×C₄	—	2	4	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	2	2	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	2	no	—
1337	C₂×C₄	—	2	2	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	2	no	—
1341	C₂×C₄	—	4	1	no	—
1342	C₂×C₄	—	4	1	no	—
1343	C₂×C₄	—	4	2	no	—
1344	C₂×C₄	—	4	2	no	—
1345	C₂×C₄	—	4	2	no	—
1346	C₂×C₄	—	4	2	no	—
1347	C₂×C₄	—	4	2	no	—
1348	C₂×C₄	—	4	2	no	—
1349	C₂×C₄	—	4	2	no	—
1350	C₂×C₄	—	4	2	no	—
1351	C₂×C₄	—	4	2	no	—
1352	C₂×C₄	—	4	2	no	—
1353	C₂×C₄	—	4	4	no	—
1354	C₂×C₄	—	4	2	no	—
1355	C₂×C₄	—	4	4	no	—
1356	C₂×C₄	—	4	2	no	—
1357	C₂×C₄	—	4	2	no	—
1358	C₂×C₄	—	8	1	no	—
1359	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1360	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1361	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1362	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1363	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1364	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1365	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1366	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1367	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1368	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1369	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1370	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1371	C₈	—	2	2	no	—
1372	C₈	—	2	2	no	—
1373	C₈	—	2	2	no	—
1374	C₈	—	2	2	no	—
1375	C₂²	—	2	1	no	—
1376	C₂²	—	2	1	no	—
1377	C₂²	—	2	1	no	—
1378	C₂²	—	2	1	no	—
1379	C₂²	—	2	1	no	—
1380	C₂²	—	2	1	no	—
1381	C₂²	—	2	1	no	—
1382	C₂²	—	2	2	no	—
1383	C₂²	—	2	1	no	—
1384	C₂²	—	2	1	no	—
1385	C₂²	—	2	1	no	—
1386	C₂²	—	2	1	no	—
1387	C₂²	—	2	1	no	—
1388	C₂²	—	2	1	no	—
1389	C₂²	—	4	4	no	—
1390	C₂²	—	4	1	no	—
1391	C₂²	—	4	1	no	—
1392	C₂²	—	4	1	no	—
1393	C₂²	—	4	1	no	—
1394	C₂²	—	4	1	no	—
1395	C₂²	—	4	1	no	—
1396	C₂²	—	4	1	no	—
1397	C₂²	—	4	1	no	—
1398	C₂²	—	8	2	no	—
1399	C₂²	—	8	4	no	—
1400	C₂²	—	8	4	no	—
1401	C₂²	C₅₃×#546	1	2	yes	—
1402	C₂²	C₅₃×#575	1	2	yes	—
1403	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1404	C₄	—	2	1	no	—
1405	C₄	—	2	1	no	—
1406	C₄	—	2	1	no	—
1407	C₄	—	2	1	no	—
1408	C₄	—	2	2	no	—
1409	C₄	—	2	1	no	—
1410	C₄	—	2	1	no	—
1411	C₄	—	2	1	no	—
1412	C₄	—	2	1	no	—
1413	C₄	—	4	1	no	—
1414	C₄	—	4	1	no	—
1415	C₄	—	4	2	no	—
1416	C₄	—	4	2	no	—
1417	C₄	—	4	2	no	—
1418	C₄	—	4	1	no	—
1419	C₄	—	4	2	no	—
1420	C₄	—	4	1	no	—
1421	C₄	C₅₃×#546	1	2	yes	—
1422	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1423	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1424	C₂	—	2	2	no	—
1425	C₂	—	2	2	no	—
1426	C₂	—	4	1	no	—
1427	C₂	—	4	1	no	—
1428	C₂	—	4	1	no	—
1429	C₂	—	4	2	no	—
1430	C₂	—	8	1	no	—
1431	C₂	—	8	1	no	—
1432	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
1433	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1434	C₂	C₅₃×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#552	C₂	semidirect
3. C₅₃×#3327	C₂	semidirect
4. C₅₃×#3323	C₂	semidirect
5. C₅₃×#3317	C₂	semidirect
6. C₅₃×#3315	C₂	semidirect
7. C₅₃×#3312	C₂	semidirect
8. C₅₃×#3310	C₂	semidirect
9. C₅₃×#3300	C₂	semidirect
10. C₅₃×#3296	C₂	semidirect
11. C₅₃×#3142	C₂	semidirect
12. C₅₃×#3093	C₂	semidirect
13. C₅₃×#3092	C₂	semidirect
14. C₅₃×#3080	C₂	semidirect
15. C₅₃×#3056	C₂	semidirect
16. C₅₃×#3056	C₂	semidirect
17. C₅₃×#3037	C₂	semidirect
18. C₅₃×#3007	C₂	semidirect
19. C₅₃×#3007	C₂	semidirect
20. C₄×#137×C₅₃	C₂	semidirect
21. D₄×M₁₆×C₅₃	C₂	semidirect
22. C₅₃×#2896	C₂	semidirect
23. C₂×C₅₃×#417	C₂	semidirect
27. C₂×#137×C₅₃	C₂²	semidirect
28. C₂×#137×C₅₃	C₂²	semidirect
29. C₂²×M₁₆×C₅₃	C₂²	semidirect
30. C₂²×M₁₆×C₅₃	C₂²	semidirect
36. C₅₃×#552	C₂²	semidirect
37. C₅₃×#552	C₂²	semidirect
38. C₅₃×#552	C₂²	semidirect
55. C₂×#125×C₅₃	C₂²	semidirect
61. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
62. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
64. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
68. C₂×#117×C₅₃	C₂²	semidirect
69. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
70. C₅₃×#491	C₂²	semidirect
71. C₅₃×#490	C₂²	semidirect
72. C₅₃×#488	C₂²	semidirect
73. C₅₃×#488	C₂²	semidirect
74. C₅₃×#485	C₂²	semidirect
75. C₅₃×#485	C₂²	semidirect
76. C₅₃×#484	C₂²	semidirect
77. C₅₃×#483	C₂²	semidirect
78. C₅₃×#482	C₂²	semidirect
79. C₅₃×#482	C₂²	semidirect
80. C₅₃×#481	C₂²	semidirect
81. C₅₃×#480	C₂²	semidirect
82. C₅₃×#479	C₂²	semidirect
83. C₅₃×#479	C₂²	semidirect
84. C₅₃×#478	C₂²	semidirect
85. C₅₃×#478	C₂²	semidirect
86. C₅₃×#470	C₂²	semidirect
87. C₅₃×#470	C₂²	semidirect
88. C₅₃×#468	C₂²	semidirect
89. C₅₃×#468	C₂²	semidirect
90. C₅₃×#467	C₂²	semidirect
91. C₅₃×#467	C₂²	semidirect
92. C₅₃×#465	C₂²	semidirect
93. C₅₃×#465	C₂²	semidirect
94. C₅₃×#464	C₂²	semidirect
95. C₅₃×#464	C₂²	semidirect
96. C₅₃×#462	C₂²	semidirect
97. C₅₃×#460	C₂²	semidirect
98. C₅₃×#452	C₂²	semidirect
99. C₅₃×#452	C₂²	semidirect
100. C₅₃×#452	C₂²	semidirect
101. C₅₃×#452	C₂²	semidirect
102. C₅₃×#451	C₂²	semidirect
103. C₅₃×#451	C₂²	semidirect
104. C₅₃×#450	C₂²	semidirect
105. C₅₃×#450	C₂²	semidirect
106. C₅₃×#441	C₂²	semidirect
107. C₅₃×#440	C₂²	semidirect
108. C₄×Q₁₆×C₅₃	C₂²	semidirect
109. C₄×SD₁₆×C₅₃	C₂²	semidirect
110. C₅₃×#436	C₂²	semidirect
112. C₅₃×#435	C₂²	semidirect
113. C₈×D₄×C₅₃	C₂²	semidirect
114. C₅₃×#428	C₂²	semidirect
115. C₅₃×#428	C₂²	semidirect
116. C₅₃×#428	C₂²	semidirect
117. C₅₃×#423	C₂²	semidirect
118. C₅₃×#419	C₂²	semidirect
119. C₅₃×#419	C₂²	semidirect
120. C₅₃×#418	C₂²	semidirect
124. C₅₃×#417	C₂²	semidirect
125. C₅₃×#417	C₂²	semidirect
126. C₅₃×#417	C₂²	semidirect
127. C₅₃×#417	C₂²	semidirect
128. C₅₃×#417	C₂²	semidirect
129. C₅₃×#417	C₂²	semidirect
130. C₅₃×#417	C₂²	semidirect
131. C₅₃×#417	C₂²	semidirect
132. C₅₃×#416	C₂²	semidirect
133. C₅₃×#416	C₂²	semidirect
134. C₂×#103×C₅₃	C₂²	semidirect
135. C₂×#102×C₅₃	C₂²	semidirect
136. C₅₃×#407	C₂²	semidirect
137. C₅₃×#407	C₂²	semidirect
138. C₄×M₁₆×C₅₃	C₂²	semidirect
657. #61163	C₅₃	direct (N × H)
707. C₂×#552	C₂×C₅₃	semidirect
709. #3327	C₂×C₅₃	semidirect
710. #3323	C₂×C₅₃	semidirect
711. #3317	C₂×C₅₃	semidirect
712. #3315	C₂×C₅₃	semidirect
713. #3312	C₂×C₅₃	semidirect
714. #3310	C₂×C₅₃	semidirect
715. #3300	C₂×C₅₃	semidirect
716. #3296	C₂×C₅₃	semidirect
717. #3142	C₂×C₅₃	semidirect
718. #3093	C₂×C₅₃	semidirect
719. #3092	C₂×C₅₃	semidirect
720. #3080	C₂×C₅₃	semidirect
721. #3056	C₂×C₅₃	semidirect
722. #3056	C₂×C₅₃	semidirect
723. #3037	C₂×C₅₃	semidirect
724. #3007	C₂×C₅₃	semidirect
725. #3007	C₂×C₅₃	semidirect
726. C₄×#137	C₂×C₅₃	semidirect
727. D₄×M₁₆	C₂×C₅₃	semidirect
728. #2896	C₂×C₅₃	semidirect
729. C₂×#417	C₂×C₅₃	semidirect
744. C₂×#137	C₂²×C₅₃	semidirect
745. C₂×#137	C₂²×C₅₃	semidirect
746. C₂²×M₁₆	C₂²×C₅₃	semidirect
747. C₂²×M₁₆	C₂²×C₅₃	semidirect
753. #552	C₂²×C₅₃	semidirect
754. #552	C₂²×C₅₃	semidirect
755. #552	C₂²×C₅₃	semidirect
772. C₂×#125	C₂²×C₅₃	semidirect
778. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
779. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
781. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
785. C₂×#117	C₂²×C₅₃	semidirect
786. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
787. #491	C₂²×C₅₃	semidirect
788. #490	C₂²×C₅₃	semidirect
789. #488	C₂²×C₅₃	semidirect
790. #488	C₂²×C₅₃	semidirect
791. #485	C₂²×C₅₃	semidirect
792. #485	C₂²×C₅₃	semidirect
793. #484	C₂²×C₅₃	semidirect
794. #483	C₂²×C₅₃	semidirect
795. #482	C₂²×C₅₃	semidirect
796. #482	C₂²×C₅₃	semidirect
797. #481	C₂²×C₅₃	semidirect
798. #480	C₂²×C₅₃	semidirect
799. #479	C₂²×C₅₃	semidirect
800. #479	C₂²×C₅₃	semidirect
801. #478	C₂²×C₅₃	semidirect
802. #478	C₂²×C₅₃	semidirect
803. #470	C₂²×C₅₃	semidirect
804. #470	C₂²×C₅₃	semidirect
805. #468	C₂²×C₅₃	semidirect
806. #468	C₂²×C₅₃	semidirect
807. #467	C₂²×C₅₃	semidirect
808. #467	C₂²×C₅₃	semidirect
809. #465	C₂²×C₅₃	semidirect
810. #465	C₂²×C₅₃	semidirect
811. #464	C₂²×C₅₃	semidirect
812. #464	C₂²×C₅₃	semidirect
813. #462	C₂²×C₅₃	semidirect
814. #460	C₂²×C₅₃	semidirect
815. #452	C₂²×C₅₃	semidirect
816. #452	C₂²×C₅₃	semidirect
817. #452	C₂²×C₅₃	semidirect
818. #452	C₂²×C₅₃	semidirect
819. #451	C₂²×C₅₃	semidirect
820. #451	C₂²×C₅₃	semidirect
821. #450	C₂²×C₅₃	semidirect
822. #450	C₂²×C₅₃	semidirect
823. #441	C₂²×C₅₃	semidirect
824. #440	C₂²×C₅₃	semidirect
825. C₄×Q₁₆	C₂²×C₅₃	semidirect
826. C₄×SD₁₆	C₂²×C₅₃	semidirect
827. #436	C₂²×C₅₃	semidirect
829. #435	C₂²×C₅₃	semidirect
830. C₈×D₄	C₂²×C₅₃	semidirect
831. #428	C₂²×C₅₃	semidirect
832. #428	C₂²×C₅₃	semidirect
833. #428	C₂²×C₅₃	semidirect
834. #423	C₂²×C₅₃	semidirect
835. #419	C₂²×C₅₃	semidirect
836. #419	C₂²×C₅₃	semidirect
837. #418	C₂²×C₅₃	semidirect
841. #417	C₂²×C₅₃	semidirect
842. #417	C₂²×C₅₃	semidirect
843. #417	C₂²×C₅₃	semidirect
844. #417	C₂²×C₅₃	semidirect
845. #417	C₂²×C₅₃	semidirect
846. #417	C₂²×C₅₃	semidirect
847. #417	C₂²×C₅₃	semidirect
848. #417	C₂²×C₅₃	semidirect
849. #416	C₂²×C₅₃	semidirect
850. #416	C₂²×C₅₃	semidirect
851. C₂×#103	C₂²×C₅₃	semidirect
852. C₂×#102	C₂²×C₅₃	semidirect
853. #407	C₂²×C₅₃	semidirect
854. #407	C₂²×C₅₃	semidirect
855. C₄×M₁₆	C₂²×C₅₃	semidirect
856. C₅₃	#61163	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅₃×#552	2
D₄×#41×C₅₃	2
C₅₃×#3327	2
C₅₃×#3323	2
C₅₃×#3317	2
C₅₃×#3315	2
C₅₃×#3312	2
C₅₃×#3310	2
C₅₃×#3300	2
C₅₃×#3296	2
C₅₃×#3142	2
C₅₃×#3093	2
C₅₃×#3092	2
C₅₃×#3080	2
C₅₃×#3056	2
C₅₃×#3037	2
C₅₃×#3007	2
C₄×#137×C₅₃	2
D₄×M₁₆×C₅₃	2
C₅₃×#2896	2
C₂×C₅₃×#417	2
#61163	53

Subgroups — C53×#61163 #27268675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61163 #27268675