Subgroups — C₅₃×#61164 #27268676

Order 13568.

2188 conjugacy classes of subgroups.

The subgroup lattice has 1466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3326	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3322	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3320	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3318	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3309	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3307	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3301	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3297	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×#3055	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×AGL(1,ℤ/8)×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×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×AGL(1,ℤ/8)×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×#553	—	2	1	no	—
32	C₅₃×#553	—	2	1	no	—
33	C₅₃×#553	—	2	1	no	—
34	C₅₃×#553	—	2	1	no	—
35	C₅₃×#553	C₂²	1	2	yes	—
36	C₅₃×#553	C₂²	1	2	yes	complemented
37	C₅₃×#553	C₂²	1	2	yes	complemented
38	C₅₃×#553	C₂²	1	2	yes	complemented
39	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
40	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#547	—	2	1	no	—
44	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#546	—	2	1	no	—
46	C₅₃×#546	—	2	1	no	—
47	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
49	D₄²×C₅₃	—	2	1	no	—
50	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
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	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#525	—	2	1	no	—
56	C₅₃×#525	—	2	1	no	—
57	C₅₃×#525	C₂²	1	1	yes	characteristic
58	C₅₃×#525	C₂²	1	1	yes	characteristic
59	C₂×#123×C₅₃	—	2	1	no	—
60	C₂×#121×C₅₃	—	2	1	no	—
61	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×C₄×D₄×C₅₃	—	2	1	no	—
65	C₂×C₄×D₄×C₅₃	—	2	1	no	—
66	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
67	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
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×#469	C₂²	1	2	yes	complemented
87	C₅₃×#469	C₂²	1	2	yes	complemented
88	C₅₃×#468	C₂²	1	2	yes	complemented
89	C₅₃×#468	C₂²	1	2	yes	complemented
90	C₅₃×#466	C₂²	1	2	yes	complemented
91	C₅₃×#466	C₂²	1	2	yes	complemented
92	C₅₃×#465	C₂²	1	2	yes	complemented
93	C₅₃×#465	C₂²	1	2	yes	complemented
94	C₅₃×#463	C₂²	1	2	yes	complemented
95	C₅₃×#463	C₂²	1	2	yes	complemented
96	C₅₃×#461	C₂²	1	2	yes	complemented
97	C₅₃×#459	C₂²	1	2	yes	complemented
98	C₅₃×#449	C₂²	1	2	yes	complemented
99	C₅₃×#449	C₂²	1	2	yes	complemented
100	C₅₃×#449	C₂²	1	2	yes	complemented
101	C₅₃×#449	C₂²	1	2	yes	complemented
102	C₅₃×#448	C₂²	1	2	yes	complemented
103	C₅₃×#448	C₂²	1	2	yes	complemented
104	C₅₃×#447	C₂²	1	2	yes	complemented
105	C₅₃×#447	C₂²	1	2	yes	complemented
106	C₅₃×#442	C₂²	1	2	yes	complemented
107	C₅₃×#440	C₂²	1	2	yes	complemented
108	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
109	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
110	C₅₃×#436	C₂²	1	2	yes	complemented
111	C₅₃×#435	C₂²	1	2	yes	complemented
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	2	yes	complemented
119	C₅₃×#418	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
129	C₅₃×#417	C₂²	1	2	yes	complemented
130	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#417	C₂²	1	1	yes	characteristic, 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×D₄×C₅₃	—	2	1	no	—
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	—	2	1	no	—
161	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
162	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
163	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
164	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
165	C₂³×C₄×C₅₃	—	2	1	no	—
166	C₂³×C₄×C₅₃	—	2	1	no	—
167	C₂³×C₄×C₅₃	—	2	1	no	—
168	C₂³×C₄×C₅₃	—	2	1	no	—
169	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
170	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
171	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
172	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
173	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
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×D₈×C₅₃	C₂³	1	2	yes	—
178	C₂×D₈×C₅₃	C₂³	1	2	yes	—
179	C₂×D₈×C₅₃	C₂³	1	2	yes	—
180	C₂×M₁₆×C₅₃	—	4	2	no	—
181	C₂×M₁₆×C₅₃	—	4	2	no	—
182	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
183	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
184	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
185	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
186	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
187	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
188	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
189	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
190	C₄⋊Q₈×C₅₃	—	2	1	no	—
191	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
192	#127×C₅₃	—	2	1	no	—
193	#127×C₅₃	C₂³	1	1	yes	characteristic
194	#126×C₅₃	—	2	2	no	—
195	#126×C₅₃	—	2	2	no	—
196	#126×C₅₃	—	2	2	no	—
197	#126×C₅₃	—	2	2	no	—
198	#125×C₅₃	—	2	1	no	—
199	#125×C₅₃	—	2	1	no	—
200	#125×C₅₃	C₂³	1	2	yes	—
201	#125×C₅₃	C₂³	1	2	yes	—
202	#124×C₅₃	—	2	1	no	—
203	#124×C₅₃	—	2	1	no	—
204	#124×C₅₃	C₂³	1	1	yes	characteristic
205	#124×C₅₃	C₂³	1	1	yes	characteristic
206	#123×C₅₃	—	2	1	no	—
207	#123×C₅₃	—	2	1	no	—
208	#123×C₅₃	—	2	2	no	—
209	#123×C₅₃	—	2	2	no	—
210	#123×C₅₃	—	2	2	no	—
211	#123×C₅₃	—	2	2	no	—
212	#123×C₅₃	—	2	1	no	—
213	#123×C₅₃	—	2	1	no	—
214	#123×C₅₃	—	2	1	no	—
215	#123×C₅₃	—	2	1	no	—
216	C₂²⋊Q₈×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	C₂³	1	1	yes	characteristic
221	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
222	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
223	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
224	#121×C₅₃	—	2	1	no	—
225	#121×C₅₃	—	2	1	no	—
226	#121×C₅₃	—	2	1	no	—
227	#121×C₅₃	—	2	1	no	—
228	#121×C₅₃	—	2	1	no	—
229	#121×C₅₃	—	2	2	no	—
230	#121×C₅₃	—	2	2	no	—
231	#121×C₅₃	—	2	2	no	—
232	#121×C₅₃	—	2	2	no	—
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	C₂³	1	2	yes	—
243	#121×C₅₃	C₂³	1	2	yes	—
244	#121×C₅₃	C₂³	1	2	yes	—
245	#121×C₅₃	C₂³	1	2	yes	—
246	#121×C₅₃	C₂³	1	1	yes	characteristic
247	#121×C₅₃	C₂³	1	1	yes	characteristic
248	#121×C₅₃	C₂³	1	1	yes	characteristic
249	#121×C₅₃	C₂³	1	1	yes	characteristic
250	#120×C₅₃	—	2	1	no	—
251	#120×C₅₃	—	2	1	no	—
252	#120×C₅₃	—	2	1	no	—
253	#120×C₅₃	—	2	1	no	—
254	#120×C₅₃	—	2	1	no	—
255	#120×C₅₃	—	2	1	no	—
256	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
257	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₅₃	—	2	1	no	—
259	C₄×D₄×C₅₃	—	2	1	no	—
260	C₄×D₄×C₅₃	—	2	1	no	—
261	C₄×D₄×C₅₃	—	2	2	no	—
262	C₄×D₄×C₅₃	—	2	2	no	—
263	C₄×D₄×C₅₃	—	2	2	no	—
264	C₄×D₄×C₅₃	—	2	2	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	—	2	1	no	—
272	C₄×D₄×C₅₃	—	2	1	no	—
273	C₄×D₄×C₅₃	—	2	1	no	—
274	C₄×D₄×C₅₃	—	2	1	no	—
275	C₄×D₄×C₅₃	—	2	1	no	—
276	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
277	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
278	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
279	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
280	C₄×D₄×C₅₃	C₂³	1	2	yes	—
281	C₄×D₄×C₅₃	C₂³	1	2	yes	—
282	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
285	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
288	#117×C₅₃	—	2	1	no	—
289	#117×C₅₃	—	2	1	no	—
290	#117×C₅₃	—	2	1	no	—
291	#117×C₅₃	C₂³	1	2	yes	—
292	#117×C₅₃	C₂³	1	2	yes	—
293	#117×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
312	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
313	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
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	#102×C₅₃	C₂³	1	2	yes	—
335	#102×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	—	2	1	no	—
354	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
355	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
365	#41×C₅₃	—	4	4	no	—
366	#41×C₅₃	—	4	4	no	—
367	#41×C₅₃	—	4	1	no	—
368	#41×C₅₃	—	4	1	no	—
369	#41×C₅₃	—	4	1	no	—
370	#41×C₅₃	—	4	1	no	—
371	#41×C₅₃	—	4	4	no	—
372	#41×C₅₃	—	4	4	no	—
373	#41×C₅₃	#41	1	4	yes	—
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	—	4	1	no	—
379	C₂×Q₈×C₅₃	—	4	1	no	—
380	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂×D₄×C₅₃	—	2	1	no	—
384	C₂×D₄×C₅₃	—	2	2	no	—
385	C₂×D₄×C₅₃	—	2	2	no	—
386	C₂×D₄×C₅₃	—	2	1	no	—
387	C₂×D₄×C₅₃	—	2	1	no	—
388	C₂×D₄×C₅₃	—	2	2	no	—
389	C₂×D₄×C₅₃	—	2	2	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	2	no	—
399	C₂×D₄×C₅₃	—	2	2	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	—	2	1	no	—
404	C₂×D₄×C₅₃	—	2	1	no	—
405	C₂×D₄×C₅₃	—	2	2	no	—
406	C₂×D₄×C₅₃	—	2	2	no	—
407	C₂×D₄×C₅₃	—	4	1	no	—
408	C₂×D₄×C₅₃	—	4	1	no	—
409	C₂×D₄×C₅₃	—	4	2	no	—
410	C₂×D₄×C₅₃	—	4	4	no	—
411	C₂×D₄×C₅₃	—	4	4	no	—
412	C₂×D₄×C₅₃	—	4	4	no	—
413	C₂×D₄×C₅₃	—	4	4	no	—
414	C₂×D₄×C₅₃	—	8	2	no	—
415	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
416	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
417	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
418	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
419	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
422	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄×C₅₃	—	2	1	no	—
424	C₂²×C₄×C₅₃	—	2	2	no	—
425	C₂²×C₄×C₅₃	—	2	2	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	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	2	no	—
434	C₂²×C₄×C₅₃	—	2	2	no	—
435	C₂²×C₄×C₅₃	—	2	1	no	—
436	C₂²×C₄×C₅₃	—	2	1	no	—
437	C₂²×C₄×C₅₃	—	2	1	no	—
438	C₂²×C₄×C₅₃	—	2	1	no	—
439	C₂²×C₄×C₅₃	—	2	1	no	—
440	C₂²×C₄×C₅₃	—	2	1	no	—
441	C₂²×C₄×C₅₃	—	2	1	no	—
442	C₂²×C₄×C₅₃	—	2	1	no	—
443	C₂²×C₄×C₅₃	—	2	2	no	—
444	C₂²×C₄×C₅₃	—	2	2	no	—
445	C₂²×C₄×C₅₃	—	4	4	no	—
446	C₂²×C₄×C₅₃	—	4	4	no	—
447	C₂²×C₄×C₅₃	—	8	2	no	—
448	C₂²×C₄×C₅₃	—	8	2	no	—
449	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
450	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
451	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
452	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
453	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
454	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
455	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
456	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
457	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
458	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
459	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
460	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
461	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
462	SD₁₆×C₅₃	—	2	4	no	—
463	SD₁₆×C₅₃	—	4	2	no	—
464	SD₁₆×C₅₃	—	4	2	no	—
465	D₈×C₅₃	—	2	4	no	—
466	D₈×C₅₃	—	4	2	no	—
467	D₈×C₅₃	—	4	2	no	—
468	M₁₆×C₅₃	—	2	2	no	—
469	M₁₆×C₅₃	—	2	2	no	—
470	M₁₆×C₅₃	—	2	2	no	—
471	M₁₆×C₅₃	—	2	2	no	—
472	M₁₆×C₅₃	—	4	2	no	—
473	M₁₆×C₅₃	—	4	2	no	—
474	C₂×C₈×C₅₃	—	4	2	no	—
475	C₂×C₈×C₅₃	—	4	2	no	—
476	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
477	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
478	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
479	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
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	1	no	—
485	C₄⋊C₄×C₅₃	—	2	1	no	—
486	C₄⋊C₄×C₅₃	—	2	1	no	—
487	C₄⋊C₄×C₅₃	—	2	2	no	—
488	C₄⋊C₄×C₅₃	—	2	2	no	—
489	C₄⋊C₄×C₅₃	—	2	2	no	—
490	C₄⋊C₄×C₅₃	—	2	2	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	—	2	1	no	—
495	C₄⋊C₄×C₅₃	—	2	1	no	—
496	C₄⋊C₄×C₅₃	—	2	1	no	—
497	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
498	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
499	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
500	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
501	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
502	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
503	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
504	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
505	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
506	C₂²⋊C₄×C₅₃	—	2	2	no	—
507	C₂²⋊C₄×C₅₃	—	2	2	no	—
508	C₂²⋊C₄×C₅₃	—	2	1	no	—
509	C₂²⋊C₄×C₅₃	—	2	1	no	—
510	C₂²⋊C₄×C₅₃	—	2	1	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	2	no	—
518	C₂²⋊C₄×C₅₃	—	2	2	no	—
519	C₂²⋊C₄×C₅₃	—	2	2	no	—
520	C₂²⋊C₄×C₅₃	—	2	2	no	—
521	C₂²⋊C₄×C₅₃	—	2	2	no	—
522	C₂²⋊C₄×C₅₃	—	2	2	no	—
523	C₂²⋊C₄×C₅₃	—	2	1	no	—
524	C₂²⋊C₄×C₅₃	—	2	1	no	—
525	C₂²⋊C₄×C₅₃	—	2	1	no	—
526	C₂²⋊C₄×C₅₃	—	2	1	no	—
527	C₂²⋊C₄×C₅₃	—	2	1	no	—
528	C₂²⋊C₄×C₅₃	—	2	1	no	—
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	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
533	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
534	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
535	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
536	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
537	C₄²×C₅₃	—	2	1	no	—
538	C₄²×C₅₃	—	2	2	no	—
539	C₄²×C₅₃	—	2	2	no	—
540	C₄²×C₅₃	—	2	1	no	—
541	C₄²×C₅₃	—	2	1	no	—
542	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
543	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
544	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
545	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
546	C₂³×C₅₃	—	2	2	no	—
547	C₂³×C₅₃	—	2	2	no	—
548	C₂³×C₅₃	—	2	1	no	—
549	C₂³×C₅₃	—	2	2	no	—
550	C₂³×C₅₃	—	2	1	no	—
551	C₂³×C₅₃	—	2	1	no	—
552	C₂³×C₅₃	—	2	2	no	—
553	C₂³×C₅₃	—	4	1	no	—
554	C₂³×C₅₃	—	4	1	no	—
555	C₂³×C₅₃	—	4	1	no	—
556	C₂³×C₅₃	—	4	2	no	—
557	C₂³×C₅₃	—	4	2	no	—
558	C₂³×C₅₃	—	4	2	no	—
559	C₂³×C₅₃	—	4	2	no	—
560	C₂³×C₅₃	—	4	2	no	—
561	C₂³×C₅₃	—	4	2	no	—
562	C₂³×C₅₃	—	4	2	no	—
563	C₂³×C₅₃	—	8	1	no	—
564	C₂³×C₅₃	—	8	1	no	—
565	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
566	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
567	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
568	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
569	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
570	Q₈×C₅₃	—	2	1	no	—
571	Q₈×C₅₃	—	2	1	no	—
572	Q₈×C₅₃	—	2	1	no	—
573	Q₈×C₅₃	—	2	1	no	—
574	Q₈×C₅₃	—	2	1	no	—
575	Q₈×C₅₃	—	4	2	no	—
576	Q₈×C₅₃	—	4	2	no	—
577	Q₈×C₅₃	C₂×#41	1	2	yes	—
578	D₄×C₅₃	—	2	4	no	—
579	D₄×C₅₃	—	2	2	no	—
580	D₄×C₅₃	—	2	2	no	—
581	D₄×C₅₃	—	2	1	no	—
582	D₄×C₅₃	—	2	1	no	—
583	D₄×C₅₃	—	2	2	no	—
584	D₄×C₅₃	—	2	1	no	—
585	D₄×C₅₃	—	2	2	no	—
586	D₄×C₅₃	—	2	1	no	—
587	D₄×C₅₃	—	2	1	no	—
588	D₄×C₅₃	—	4	1	no	—
589	D₄×C₅₃	—	4	1	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	—	4	2	no	—
596	D₄×C₅₃	—	4	2	no	—
597	D₄×C₅₃	—	4	2	no	—
598	D₄×C₅₃	—	4	4	no	—
599	D₄×C₅₃	—	4	2	no	—
600	D₄×C₅₃	—	4	2	no	—
601	D₄×C₅₃	—	4	2	no	—
602	D₄×C₅₃	—	4	4	no	—
603	D₄×C₅₃	—	4	2	no	—
604	D₄×C₅₃	—	8	1	no	—
605	D₄×C₅₃	—	8	1	no	—
606	D₄×C₅₃	—	8	1	no	—
607	D₄×C₅₃	—	8	2	no	—
608	D₄×C₅₃	—	8	2	no	—
609	D₄×C₅₃	C₂×#41	1	2	yes	—
610	C₂×C₄×C₅₃	—	2	2	no	—
611	C₂×C₄×C₅₃	—	2	2	no	—
612	C₂×C₄×C₅₃	—	2	1	no	—
613	C₂×C₄×C₅₃	—	2	2	no	—
614	C₂×C₄×C₅₃	—	2	2	no	—
615	C₂×C₄×C₅₃	—	2	2	no	—
616	C₂×C₄×C₅₃	—	2	2	no	—
617	C₂×C₄×C₅₃	—	2	4	no	—
618	C₂×C₄×C₅₃	—	2	1	no	—
619	C₂×C₄×C₅₃	—	2	1	no	—
620	C₂×C₄×C₅₃	—	2	1	no	—
621	C₂×C₄×C₅₃	—	2	1	no	—
622	C₂×C₄×C₅₃	—	2	1	no	—
623	C₂×C₄×C₅₃	—	2	1	no	—
624	C₂×C₄×C₅₃	—	2	1	no	—
625	C₂×C₄×C₅₃	—	2	1	no	—
626	C₂×C₄×C₅₃	—	2	2	no	—
627	C₂×C₄×C₅₃	—	2	1	no	—
628	C₂×C₄×C₅₃	—	2	1	no	—
629	C₂×C₄×C₅₃	—	2	2	no	—
630	C₂×C₄×C₅₃	—	2	1	no	—
631	C₂×C₄×C₅₃	—	2	1	no	—
632	C₂×C₄×C₅₃	—	2	2	no	—
633	C₂×C₄×C₅₃	—	4	1	no	—
634	C₂×C₄×C₅₃	—	4	1	no	—
635	C₂×C₄×C₅₃	—	4	2	no	—
636	C₂×C₄×C₅₃	—	4	2	no	—
637	C₂×C₄×C₅₃	—	4	2	no	—
638	C₂×C₄×C₅₃	—	4	2	no	—
639	C₂×C₄×C₅₃	—	4	2	no	—
640	C₂×C₄×C₅₃	—	4	2	no	—
641	C₂×C₄×C₅₃	—	4	2	no	—
642	C₂×C₄×C₅₃	—	4	2	no	—
643	C₂×C₄×C₅₃	—	4	2	no	—
644	C₂×C₄×C₅₃	—	4	2	no	—
645	C₂×C₄×C₅₃	—	4	2	no	—
646	C₂×C₄×C₅₃	—	4	2	no	—
647	C₂×C₄×C₅₃	—	8	1	no	—
648	C₂×C₄×C₅₃	—	8	2	no	—
649	C₂×C₄×C₅₃	—	8	2	no	—
650	C₂×C₄×C₅₃	—	8	2	no	—
651	C₂×C₄×C₅₃	—	8	2	no	—
652	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
653	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
654	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
655	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
656	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
657	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
658	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
659	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
660	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
661	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
662	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
663	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
664	C₈×C₅₃	—	2	2	no	—
665	C₈×C₅₃	—	2	2	no	—
666	C₈×C₅₃	—	2	2	no	—
667	C₈×C₅₃	—	2	2	no	—
668	#61164	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
669	C₂²×C₅₃	—	2	1	no	—
670	C₂²×C₅₃	—	2	1	no	—
671	C₂²×C₅₃	—	2	1	no	—
672	C₂²×C₅₃	—	2	1	no	—
673	C₂²×C₅₃	—	2	1	no	—
674	C₂²×C₅₃	—	2	1	no	—
675	C₂²×C₅₃	—	2	1	no	—
676	C₂²×C₅₃	—	2	1	no	—
677	C₂²×C₅₃	—	2	1	no	—
678	C₂²×C₅₃	—	2	1	no	—
679	C₂²×C₅₃	—	2	2	no	—
680	C₂²×C₅₃	—	2	1	no	—
681	C₂²×C₅₃	—	2	1	no	—
682	C₂²×C₅₃	—	2	1	no	—
683	C₂²×C₅₃	—	4	4	no	—
684	C₂²×C₅₃	—	4	1	no	—
685	C₂²×C₅₃	—	4	1	no	—
686	C₂²×C₅₃	—	4	2	no	—
687	C₂²×C₅₃	—	4	1	no	—
688	C₂²×C₅₃	—	4	1	no	—
689	C₂²×C₅₃	—	4	1	no	—
690	C₂²×C₅₃	—	4	1	no	—
691	C₂²×C₅₃	—	4	2	no	—
692	C₂²×C₅₃	—	4	1	no	—
693	C₂²×C₅₃	—	4	1	no	—
694	C₂²×C₅₃	—	4	2	no	—
695	C₂²×C₅₃	—	8	2	no	—
696	C₂²×C₅₃	—	8	4	no	—
697	C₂²×C₅₃	—	8	4	no	—
698	C₂²×C₅₃	—	8	4	no	—
699	C₂²×C₅₃	#546	1	2	yes	—
700	C₂²×C₅₃	#575	1	2	yes	—
701	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
702	C₄×C₅₃	—	2	1	no	—
703	C₄×C₅₃	—	2	1	no	—
704	C₄×C₅₃	—	2	1	no	—
705	C₄×C₅₃	—	2	1	no	—
706	C₄×C₅₃	—	2	1	no	—
707	C₄×C₅₃	—	2	1	no	—
708	C₄×C₅₃	—	2	2	no	—
709	C₄×C₅₃	—	2	1	no	—
710	C₄×C₅₃	—	2	1	no	—
711	C₄×C₅₃	—	4	2	no	—
712	C₄×C₅₃	—	4	2	no	—
713	C₄×C₅₃	—	4	1	no	—
714	C₄×C₅₃	—	4	1	no	—
715	C₄×C₅₃	—	4	1	no	—
716	C₄×C₅₃	—	4	1	no	—
717	C₄×C₅₃	—	4	2	no	—
718	C₄×C₅₃	#546	1	2	yes	—
719	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
720	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
721	C₂×#553	C₂×C₅₃	1	1	yes	characteristic, complemented
722	D₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
723	#3326	C₂×C₅₃	1	2	yes	complemented
724	#3322	C₂×C₅₃	1	2	yes	complemented
725	#3320	C₂×C₅₃	1	2	yes	complemented
726	#3318	C₂×C₅₃	1	2	yes	complemented
727	#3309	C₂×C₅₃	1	2	yes	complemented
728	#3307	C₂×C₅₃	1	2	yes	complemented
729	#3301	C₂×C₅₃	1	2	yes	complemented
730	#3297	C₂×C₅₃	1	2	yes	complemented
731	#3142	C₂×C₅₃	1	1	yes	characteristic, complemented
732	#3093	C₂×C₅₃	1	1	yes	characteristic, complemented
733	#3092	C₂×C₅₃	1	1	yes	characteristic, complemented
734	#3080	C₂×C₅₃	1	1	yes	characteristic, complemented
735	#3055	C₂×C₅₃	1	1	yes	characteristic, complemented
736	#3055	C₂×C₅₃	1	1	yes	characteristic, complemented
737	#3036	C₂×C₅₃	1	1	yes	characteristic, complemented
738	#3006	C₂×C₅₃	1	1	yes	characteristic, complemented
739	#3006	C₂×C₅₃	1	1	yes	characteristic, complemented
740	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	1	yes	characteristic, complemented
741	D₄×M₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
742	#2896	C₂×C₅₃	1	1	yes	characteristic, complemented
743	C₂×#417	C₂×C₅₃	1	1	yes	characteristic, complemented
744	C₂×C₅₃	—	2	2	no	—
745	C₂×C₅₃	—	2	2	no	—
746	C₂×C₅₃	—	4	1	no	—
747	C₂×C₅₃	—	4	1	no	—
748	C₂×C₅₃	—	4	1	no	—
749	C₂×C₅₃	—	4	2	no	—
750	C₂×C₅₃	—	8	2	no	—
751	C₂×C₅₃	—	8	1	no	—
752	C₂×C₅₃	—	8	1	no	—
753	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
754	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
755	C₂×C₅₃	#3585	1	1	yes	characteristic
756	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
757	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
758	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
759	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
760	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
761	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
762	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
763	#553	—	2	1	no	—
764	#553	—	2	1	no	—
765	#553	—	2	1	no	—
766	#553	—	2	1	no	—
767	#553	C₂²×C₅₃	1	2	yes	—
768	#553	C₂²×C₅₃	1	2	yes	complemented
769	#553	C₂²×C₅₃	1	2	yes	complemented
770	#553	C₂²×C₅₃	1	2	yes	complemented
771	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
772	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
773	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
774	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
775	#547	—	2	1	no	—
776	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
777	#546	—	2	1	no	—
778	#546	—	2	1	no	—
779	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
780	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
781	D₄²	—	2	1	no	—
782	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
783	#532	—	2	1	no	—
784	#532	C₂²×C₅₃	1	1	yes	characteristic
785	C₂×#126	—	2	1	no	—
786	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
787	#525	—	2	1	no	—
788	#525	—	2	1	no	—
789	#525	C₂²×C₅₃	1	1	yes	characteristic
790	#525	C₂²×C₅₃	1	1	yes	characteristic
791	C₂×#123	—	2	1	no	—
792	C₂×#121	—	2	1	no	—
793	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
794	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
795	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
796	C₂×C₄×D₄	—	2	1	no	—
797	C₂×C₄×D₄	—	2	1	no	—
798	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
799	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
800	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
801	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
802	#491	C₂²×C₅₃	1	2	yes	complemented
803	#490	C₂²×C₅₃	1	2	yes	complemented
804	#488	C₂²×C₅₃	1	2	yes	complemented
805	#488	C₂²×C₅₃	1	2	yes	complemented
806	#485	C₂²×C₅₃	1	2	yes	complemented
807	#485	C₂²×C₅₃	1	2	yes	complemented
808	#484	C₂²×C₅₃	1	2	yes	complemented
809	#483	C₂²×C₅₃	1	2	yes	complemented
810	#482	C₂²×C₅₃	1	2	yes	complemented
811	#482	C₂²×C₅₃	1	2	yes	complemented
812	#481	C₂²×C₅₃	1	2	yes	complemented
813	#480	C₂²×C₅₃	1	2	yes	complemented
814	#479	C₂²×C₅₃	1	2	yes	complemented
815	#479	C₂²×C₅₃	1	2	yes	complemented
816	#478	C₂²×C₅₃	1	2	yes	complemented
817	#478	C₂²×C₅₃	1	2	yes	complemented
818	#469	C₂²×C₅₃	1	2	yes	complemented
819	#469	C₂²×C₅₃	1	2	yes	complemented
820	#468	C₂²×C₅₃	1	2	yes	complemented
821	#468	C₂²×C₅₃	1	2	yes	complemented
822	#466	C₂²×C₅₃	1	2	yes	complemented
823	#466	C₂²×C₅₃	1	2	yes	complemented
824	#465	C₂²×C₅₃	1	2	yes	complemented
825	#465	C₂²×C₅₃	1	2	yes	complemented
826	#463	C₂²×C₅₃	1	2	yes	complemented
827	#463	C₂²×C₅₃	1	2	yes	complemented
828	#461	C₂²×C₅₃	1	2	yes	complemented
829	#459	C₂²×C₅₃	1	2	yes	complemented
830	#449	C₂²×C₅₃	1	2	yes	complemented
831	#449	C₂²×C₅₃	1	2	yes	complemented
832	#449	C₂²×C₅₃	1	2	yes	complemented
833	#449	C₂²×C₅₃	1	2	yes	complemented
834	#448	C₂²×C₅₃	1	2	yes	complemented
835	#448	C₂²×C₅₃	1	2	yes	complemented
836	#447	C₂²×C₅₃	1	2	yes	complemented
837	#447	C₂²×C₅₃	1	2	yes	complemented
838	#442	C₂²×C₅₃	1	2	yes	complemented
839	#440	C₂²×C₅₃	1	2	yes	complemented
840	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
841	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
842	#436	C₂²×C₅₃	1	2	yes	complemented
843	#435	C₂²×C₅₃	1	2	yes	complemented
844	#435	C₂²×C₅₃	1	2	yes	complemented
845	C₈×D₄	C₂²×C₅₃	1	2	yes	complemented
846	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
847	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
848	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
849	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
850	#419	C₂²×C₅₃	1	2	yes	complemented
851	#418	C₂²×C₅₃	1	2	yes	complemented
852	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
853	#417	C₂²×C₅₃	1	1	yes	characteristic
854	#417	C₂²×C₅₃	1	1	yes	characteristic
855	#417	C₂²×C₅₃	1	1	yes	characteristic
856	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
857	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
858	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
859	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
860	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
861	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
862	#417	C₂²×C₅₃	1	2	yes	complemented
863	#417	C₂²×C₅₃	1	2	yes	complemented
864	#416	C₂²×C₅₃	1	2	yes	complemented
865	#416	C₂²×C₅₃	1	2	yes	complemented
866	C₂×#103	C₂²×C₅₃	1	2	yes	complemented
867	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
868	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
869	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
870	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
871	C₅₃	#61164	1	1	yes	characteristic, direct product factor, Sylow
872	C₂×#41	—	2	1	no	—
873	C₂×#41	—	2	1	no	—
874	C₂×#41	—	2	1	no	—
875	C₂×#41	—	2	1	no	—
876	C₂×#41	—	2	4	no	—
877	C₂×#41	—	2	4	no	—
878	C₂×#41	—	4	2	no	—
879	C₂×#41	—	4	2	no	—
880	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
881	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
882	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
883	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
884	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
885	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
886	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
887	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
888	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
889	C₂²×D₄	—	2	1	no	—
890	C₂²×D₄	—	2	1	no	—
891	C₂²×D₄	—	2	1	no	—
892	C₂²×D₄	—	2	1	no	—
893	C₂²×D₄	—	2	1	no	—
894	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
895	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
896	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
897	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
898	C₂³×C₄	—	2	1	no	—
899	C₂³×C₄	—	2	1	no	—
900	C₂³×C₄	—	2	1	no	—
901	C₂³×C₄	—	2	1	no	—
902	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
903	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
904	AGL(1,ℤ/8)	—	2	4	no	—
905	AGL(1,ℤ/8)	—	4	2	no	—
906	AGL(1,ℤ/8)	—	4	2	no	—
907	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
908	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
909	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
910	C₂×D₈	C₂³×C₅₃	1	2	yes	—
911	C₂×D₈	C₂³×C₅₃	1	2	yes	—
912	C₂×D₈	C₂³×C₅₃	1	2	yes	—
913	C₂×M₁₆	—	4	2	no	—
914	C₂×M₁₆	—	4	2	no	—
915	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
916	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
917	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
918	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
919	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
920	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
921	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
922	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
923	C₄⋊Q₈	—	2	1	no	—
924	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
925	#127	—	2	1	no	—
926	#127	C₂³×C₅₃	1	1	yes	characteristic
927	#126	—	2	2	no	—
928	#126	—	2	2	no	—
929	#126	—	2	2	no	—
930	#126	—	2	2	no	—
931	#125	—	2	1	no	—
932	#125	—	2	1	no	—
933	#125	C₂³×C₅₃	1	2	yes	—
934	#125	C₂³×C₅₃	1	2	yes	—
935	#124	—	2	1	no	—
936	#124	—	2	1	no	—
937	#124	C₂³×C₅₃	1	1	yes	characteristic
938	#124	C₂³×C₅₃	1	1	yes	characteristic
939	#123	—	2	1	no	—
940	#123	—	2	1	no	—
941	#123	—	2	1	no	—
942	#123	—	2	1	no	—
943	#123	—	2	2	no	—
944	#123	—	2	2	no	—
945	#123	—	2	2	no	—
946	#123	—	2	2	no	—
947	#123	—	2	1	no	—
948	#123	—	2	1	no	—
949	C₂²⋊Q₈	—	2	1	no	—
950	C₂²⋊Q₈	—	2	1	no	—
951	C₂²⋊Q₈	—	2	1	no	—
952	C₂²⋊Q₈	—	2	1	no	—
953	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
954	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
955	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
956	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
957	#121	—	2	2	no	—
958	#121	—	2	2	no	—
959	#121	—	2	2	no	—
960	#121	—	2	2	no	—
961	#121	—	2	1	no	—
962	#121	—	2	1	no	—
963	#121	—	2	1	no	—
964	#121	—	2	1	no	—
965	#121	—	2	1	no	—
966	#121	—	2	1	no	—
967	#121	—	2	1	no	—
968	#121	—	2	1	no	—
969	#121	—	2	1	no	—
970	#121	—	2	1	no	—
971	#121	—	2	1	no	—
972	#121	—	2	1	no	—
973	#121	—	2	1	no	—
974	#121	—	2	1	no	—
975	#121	C₂³×C₅₃	1	2	yes	—
976	#121	C₂³×C₅₃	1	2	yes	—
977	#121	C₂³×C₅₃	1	2	yes	—
978	#121	C₂³×C₅₃	1	2	yes	—
979	#121	C₂³×C₅₃	1	1	yes	characteristic
980	#121	C₂³×C₅₃	1	1	yes	characteristic
981	#121	C₂³×C₅₃	1	1	yes	characteristic
982	#121	C₂³×C₅₃	1	1	yes	characteristic
983	#120	—	2	1	no	—
984	#120	—	2	1	no	—
985	#120	—	2	1	no	—
986	#120	—	2	1	no	—
987	#120	—	2	1	no	—
988	#120	—	2	1	no	—
989	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
990	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
991	C₄×D₄	—	2	1	no	—
992	C₄×D₄	—	2	1	no	—
993	C₄×D₄	—	2	1	no	—
994	C₄×D₄	—	2	1	no	—
995	C₄×D₄	—	2	1	no	—
996	C₄×D₄	—	2	1	no	—
997	C₄×D₄	—	2	1	no	—
998	C₄×D₄	—	2	1	no	—
999	C₄×D₄	—	2	1	no	—
1000	C₄×D₄	—	2	1	no	—
1001	C₄×D₄	—	2	2	no	—
1002	C₄×D₄	—	2	2	no	—
1003	C₄×D₄	—	2	2	no	—
1004	C₄×D₄	—	2	2	no	—
1005	C₄×D₄	—	2	1	no	—
1006	C₄×D₄	—	2	1	no	—
1007	C₄×D₄	—	2	1	no	—
1008	C₄×D₄	—	2	1	no	—
1009	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1010	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1011	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1012	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1013	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1014	C₄×D₄	C₂³×C₅₃	1	2	yes	—
1015	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1016	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1017	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1018	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1019	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1020	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1021	#117	—	2	1	no	—
1022	#117	—	2	1	no	—
1023	#117	—	2	1	no	—
1024	#117	C₂³×C₅₃	1	2	yes	—
1025	#117	C₂³×C₅₃	1	2	yes	—
1026	#117	C₂³×C₅₃	1	1	yes	characteristic
1027	C₂×C₄⋊C₄	—	2	1	no	—
1028	C₂×C₄⋊C₄	—	2	1	no	—
1029	C₂×C₄⋊C₄	—	2	1	no	—
1030	C₂×C₄⋊C₄	—	2	1	no	—
1031	C₂×C₄⋊C₄	—	2	1	no	—
1032	C₂×C₄⋊C₄	—	2	1	no	—
1033	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1034	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1035	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1036	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1037	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
1038	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1039	C₂×C₂²⋊C₄	—	2	1	no	—
1040	C₂×C₂²⋊C₄	—	2	1	no	—
1041	C₂×C₂²⋊C₄	—	2	1	no	—
1042	C₂×C₂²⋊C₄	—	2	1	no	—
1043	C₂×C₂²⋊C₄	—	2	1	no	—
1044	C₂×C₂²⋊C₄	—	2	1	no	—
1045	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1046	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1047	C₂×C₄²	—	2	1	no	—
1048	C₂×C₄²	—	2	1	no	—
1049	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1050	#107	C₂³×C₅₃	1	2	yes	—
1051	#107	C₂³×C₅₃	1	2	yes	—
1052	#107	C₂³×C₅₃	1	2	yes	—
1053	#106	C₂³×C₅₃	1	2	yes	—
1054	#106	C₂³×C₅₃	1	2	yes	—
1055	#106	C₂³×C₅₃	1	2	yes	—
1056	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
1057	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
1058	#103	C₂³×C₅₃	1	2	yes	—
1059	#103	C₂³×C₅₃	1	2	yes	—
1060	#103	C₂³×C₅₃	1	2	yes	—
1061	#103	C₂³×C₅₃	1	2	yes	—
1062	#103	C₂³×C₅₃	1	2	yes	—
1063	#103	C₂³×C₅₃	1	2	yes	—
1064	#103	C₂³×C₅₃	1	2	yes	—
1065	#103	C₂³×C₅₃	1	2	yes	—
1066	#103	C₂³×C₅₃	1	2	yes	—
1067	#102	C₂³×C₅₃	1	2	yes	—
1068	#102	C₂³×C₅₃	1	2	yes	—
1069	#102	C₂³×C₅₃	1	2	yes	—
1070	#102	C₂³×C₅₃	1	2	yes	—
1071	#102	C₂³×C₅₃	1	2	yes	—
1072	#102	C₂³×C₅₃	1	2	yes	—
1073	#102	C₂³×C₅₃	1	2	yes	—
1074	#102	C₂³×C₅₃	1	2	yes	—
1075	#102	C₂³×C₅₃	1	2	yes	—
1076	#102	C₂³×C₅₃	1	2	yes	—
1077	#102	C₂³×C₅₃	1	2	yes	—
1078	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1079	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1080	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1081	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
1082	#97	C₂³×C₅₃	1	2	yes	—
1083	C₄×C₈	C₂³×C₅₃	1	2	yes	—
1084	C₂⁴	—	2	1	no	—
1085	C₂⁴	—	2	1	no	—
1086	C₂⁴	—	2	1	no	—
1087	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1088	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1089	#41	—	2	2	no	—
1090	#41	—	2	2	no	—
1091	#41	—	2	2	no	—
1092	#41	—	2	2	no	—
1093	#41	—	2	2	no	—
1094	#41	—	2	2	no	—
1095	#41	—	2	2	no	—
1096	#41	—	2	2	no	—
1097	#41	—	2	2	no	—
1098	#41	—	4	4	no	—
1099	#41	—	4	4	no	—
1100	#41	—	4	1	no	—
1101	#41	—	4	1	no	—
1102	#41	—	4	1	no	—
1103	#41	—	4	1	no	—
1104	#41	—	4	4	no	—
1105	#41	—	4	4	no	—
1106	#41	#41×C₅₃	1	4	yes	—
1107	C₂×Q₈	—	2	1	no	—
1108	C₂×Q₈	—	2	1	no	—
1109	C₂×Q₈	—	2	2	no	—
1110	C₂×Q₈	—	2	2	no	—
1111	C₂×Q₈	—	4	1	no	—
1112	C₂×Q₈	—	4	1	no	—
1113	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1114	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1115	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1116	C₂×D₄	—	2	1	no	—
1117	C₂×D₄	—	2	2	no	—
1118	C₂×D₄	—	2	2	no	—
1119	C₂×D₄	—	2	1	no	—
1120	C₂×D₄	—	2	1	no	—
1121	C₂×D₄	—	2	2	no	—
1122	C₂×D₄	—	2	2	no	—
1123	C₂×D₄	—	2	1	no	—
1124	C₂×D₄	—	2	1	no	—
1125	C₂×D₄	—	2	1	no	—
1126	C₂×D₄	—	2	1	no	—
1127	C₂×D₄	—	2	1	no	—
1128	C₂×D₄	—	2	1	no	—
1129	C₂×D₄	—	2	1	no	—
1130	C₂×D₄	—	2	1	no	—
1131	C₂×D₄	—	2	2	no	—
1132	C₂×D₄	—	2	2	no	—
1133	C₂×D₄	—	2	1	no	—
1134	C₂×D₄	—	2	1	no	—
1135	C₂×D₄	—	2	1	no	—
1136	C₂×D₄	—	2	1	no	—
1137	C₂×D₄	—	2	1	no	—
1138	C₂×D₄	—	2	2	no	—
1139	C₂×D₄	—	2	2	no	—
1140	C₂×D₄	—	4	1	no	—
1141	C₂×D₄	—	4	1	no	—
1142	C₂×D₄	—	4	2	no	—
1143	C₂×D₄	—	4	4	no	—
1144	C₂×D₄	—	4	4	no	—
1145	C₂×D₄	—	4	4	no	—
1146	C₂×D₄	—	4	4	no	—
1147	C₂×D₄	—	8	2	no	—
1148	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1149	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1150	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1151	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1152	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1153	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1154	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
1155	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1156	C₂²×C₄	—	2	1	no	—
1157	C₂²×C₄	—	2	2	no	—
1158	C₂²×C₄	—	2	2	no	—
1159	C₂²×C₄	—	2	2	no	—
1160	C₂²×C₄	—	2	2	no	—
1161	C₂²×C₄	—	2	1	no	—
1162	C₂²×C₄	—	2	1	no	—
1163	C₂²×C₄	—	2	1	no	—
1164	C₂²×C₄	—	2	1	no	—
1165	C₂²×C₄	—	2	1	no	—
1166	C₂²×C₄	—	2	2	no	—
1167	C₂²×C₄	—	2	2	no	—
1168	C₂²×C₄	—	2	1	no	—
1169	C₂²×C₄	—	2	1	no	—
1170	C₂²×C₄	—	2	1	no	—
1171	C₂²×C₄	—	2	1	no	—
1172	C₂²×C₄	—	2	1	no	—
1173	C₂²×C₄	—	2	1	no	—
1174	C₂²×C₄	—	2	1	no	—
1175	C₂²×C₄	—	2	1	no	—
1176	C₂²×C₄	—	2	2	no	—
1177	C₂²×C₄	—	2	2	no	—
1178	C₂²×C₄	—	4	4	no	—
1179	C₂²×C₄	—	4	4	no	—
1180	C₂²×C₄	—	8	2	no	—
1181	C₂²×C₄	—	8	2	no	—
1182	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1183	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1184	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1185	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1186	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1187	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1188	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1189	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1190	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1191	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1192	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1193	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1194	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1195	SD₁₆	—	2	4	no	—
1196	SD₁₆	—	4	2	no	—
1197	SD₁₆	—	4	2	no	—
1198	D₈	—	2	4	no	—
1199	D₈	—	4	2	no	—
1200	D₈	—	4	2	no	—
1201	M₁₆	—	2	2	no	—
1202	M₁₆	—	2	2	no	—
1203	M₁₆	—	2	2	no	—
1204	M₁₆	—	2	2	no	—
1205	M₁₆	—	4	2	no	—
1206	M₁₆	—	4	2	no	—
1207	C₂×C₈	—	4	2	no	—
1208	C₂×C₈	—	4	2	no	—
1209	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1210	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1211	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1212	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1213	C₄⋊C₄	—	2	1	no	—
1214	C₄⋊C₄	—	2	1	no	—
1215	C₄⋊C₄	—	2	2	no	—
1216	C₄⋊C₄	—	2	2	no	—
1217	C₄⋊C₄	—	2	1	no	—
1218	C₄⋊C₄	—	2	1	no	—
1219	C₄⋊C₄	—	2	1	no	—
1220	C₄⋊C₄	—	2	2	no	—
1221	C₄⋊C₄	—	2	2	no	—
1222	C₄⋊C₄	—	2	2	no	—
1223	C₄⋊C₄	—	2	2	no	—
1224	C₄⋊C₄	—	2	1	no	—
1225	C₄⋊C₄	—	2	1	no	—
1226	C₄⋊C₄	—	2	1	no	—
1227	C₄⋊C₄	—	2	1	no	—
1228	C₄⋊C₄	—	2	1	no	—
1229	C₄⋊C₄	—	2	1	no	—
1230	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1231	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1232	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1233	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1234	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1235	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1236	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1237	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1238	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1239	C₂²⋊C₄	—	2	2	no	—
1240	C₂²⋊C₄	—	2	2	no	—
1241	C₂²⋊C₄	—	2	1	no	—
1242	C₂²⋊C₄	—	2	1	no	—
1243	C₂²⋊C₄	—	2	1	no	—
1244	C₂²⋊C₄	—	2	1	no	—
1245	C₂²⋊C₄	—	2	1	no	—
1246	C₂²⋊C₄	—	2	1	no	—
1247	C₂²⋊C₄	—	2	1	no	—
1248	C₂²⋊C₄	—	2	1	no	—
1249	C₂²⋊C₄	—	2	1	no	—
1250	C₂²⋊C₄	—	2	2	no	—
1251	C₂²⋊C₄	—	2	2	no	—
1252	C₂²⋊C₄	—	2	2	no	—
1253	C₂²⋊C₄	—	2	2	no	—
1254	C₂²⋊C₄	—	2	2	no	—
1255	C₂²⋊C₄	—	2	2	no	—
1256	C₂²⋊C₄	—	2	1	no	—
1257	C₂²⋊C₄	—	2	1	no	—
1258	C₂²⋊C₄	—	2	1	no	—
1259	C₂²⋊C₄	—	2	1	no	—
1260	C₂²⋊C₄	—	2	1	no	—
1261	C₂²⋊C₄	—	2	1	no	—
1262	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1263	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1264	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1265	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1266	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1267	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1268	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1269	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1270	C₄²	—	2	1	no	—
1271	C₄²	—	2	2	no	—
1272	C₄²	—	2	2	no	—
1273	C₄²	—	2	1	no	—
1274	C₄²	—	2	1	no	—
1275	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1276	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1277	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1278	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1279	C₂³	—	2	2	no	—
1280	C₂³	—	2	2	no	—
1281	C₂³	—	2	1	no	—
1282	C₂³	—	2	2	no	—
1283	C₂³	—	2	2	no	—
1284	C₂³	—	2	1	no	—
1285	C₂³	—	2	1	no	—
1286	C₂³	—	4	1	no	—
1287	C₂³	—	4	1	no	—
1288	C₂³	—	4	1	no	—
1289	C₂³	—	4	2	no	—
1290	C₂³	—	4	2	no	—
1291	C₂³	—	4	2	no	—
1292	C₂³	—	4	2	no	—
1293	C₂³	—	4	2	no	—
1294	C₂³	—	4	2	no	—
1295	C₂³	—	4	2	no	—
1296	C₂³	—	8	1	no	—
1297	C₂³	—	8	1	no	—
1298	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1299	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1300	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1301	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1302	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1303	Q₈	—	2	1	no	—
1304	Q₈	—	2	1	no	—
1305	Q₈	—	2	1	no	—
1306	Q₈	—	2	1	no	—
1307	Q₈	—	2	1	no	—
1308	Q₈	—	4	2	no	—
1309	Q₈	—	4	2	no	—
1310	Q₈	C₂×#41×C₅₃	1	2	yes	—
1311	D₄	—	2	4	no	—
1312	D₄	—	2	2	no	—
1313	D₄	—	2	2	no	—
1314	D₄	—	2	2	no	—
1315	D₄	—	2	1	no	—
1316	D₄	—	2	1	no	—
1317	D₄	—	2	1	no	—
1318	D₄	—	2	2	no	—
1319	D₄	—	2	1	no	—
1320	D₄	—	2	1	no	—
1321	D₄	—	4	1	no	—
1322	D₄	—	4	1	no	—
1323	D₄	—	4	2	no	—
1324	D₄	—	4	2	no	—
1325	D₄	—	4	2	no	—
1326	D₄	—	4	2	no	—
1327	D₄	—	4	2	no	—
1328	D₄	—	4	2	no	—
1329	D₄	—	4	2	no	—
1330	D₄	—	4	2	no	—
1331	D₄	—	4	4	no	—
1332	D₄	—	4	2	no	—
1333	D₄	—	4	2	no	—
1334	D₄	—	4	2	no	—
1335	D₄	—	4	4	no	—
1336	D₄	—	4	2	no	—
1337	D₄	—	8	1	no	—
1338	D₄	—	8	1	no	—
1339	D₄	—	8	1	no	—
1340	D₄	—	8	2	no	—
1341	D₄	—	8	2	no	—
1342	D₄	C₂×#41×C₅₃	1	2	yes	—
1343	C₂×C₄	—	2	2	no	—
1344	C₂×C₄	—	2	2	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	2	no	—
1347	C₂×C₄	—	2	2	no	—
1348	C₂×C₄	—	2	2	no	—
1349	C₂×C₄	—	2	2	no	—
1350	C₂×C₄	—	2	4	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	1	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	2	2	no	—
1362	C₂×C₄	—	2	2	no	—
1363	C₂×C₄	—	2	1	no	—
1364	C₂×C₄	—	2	1	no	—
1365	C₂×C₄	—	2	2	no	—
1366	C₂×C₄	—	4	1	no	—
1367	C₂×C₄	—	4	1	no	—
1368	C₂×C₄	—	4	2	no	—
1369	C₂×C₄	—	4	2	no	—
1370	C₂×C₄	—	4	2	no	—
1371	C₂×C₄	—	4	2	no	—
1372	C₂×C₄	—	4	2	no	—
1373	C₂×C₄	—	4	2	no	—
1374	C₂×C₄	—	4	2	no	—
1375	C₂×C₄	—	4	2	no	—
1376	C₂×C₄	—	4	2	no	—
1377	C₂×C₄	—	4	2	no	—
1378	C₂×C₄	—	4	2	no	—
1379	C₂×C₄	—	4	2	no	—
1380	C₂×C₄	—	8	1	no	—
1381	C₂×C₄	—	8	2	no	—
1382	C₂×C₄	—	8	2	no	—
1383	C₂×C₄	—	8	2	no	—
1384	C₂×C₄	—	8	2	no	—
1385	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1386	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1387	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1388	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1389	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1390	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1391	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1392	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1393	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1394	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1395	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1396	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1397	C₈	—	2	2	no	—
1398	C₈	—	2	2	no	—
1399	C₈	—	2	2	no	—
1400	C₈	—	2	2	no	—
1401	C₂²	—	2	1	no	—
1402	C₂²	—	2	1	no	—
1403	C₂²	—	2	1	no	—
1404	C₂²	—	2	1	no	—
1405	C₂²	—	2	1	no	—
1406	C₂²	—	2	1	no	—
1407	C₂²	—	2	1	no	—
1408	C₂²	—	2	2	no	—
1409	C₂²	—	2	1	no	—
1410	C₂²	—	2	1	no	—
1411	C₂²	—	2	1	no	—
1412	C₂²	—	2	1	no	—
1413	C₂²	—	2	1	no	—
1414	C₂²	—	2	1	no	—
1415	C₂²	—	4	4	no	—
1416	C₂²	—	4	1	no	—
1417	C₂²	—	4	1	no	—
1418	C₂²	—	4	1	no	—
1419	C₂²	—	4	1	no	—
1420	C₂²	—	4	2	no	—
1421	C₂²	—	4	1	no	—
1422	C₂²	—	4	1	no	—
1423	C₂²	—	4	2	no	—
1424	C₂²	—	4	2	no	—
1425	C₂²	—	4	1	no	—
1426	C₂²	—	4	1	no	—
1427	C₂²	—	8	2	no	—
1428	C₂²	—	8	4	no	—
1429	C₂²	—	8	4	no	—
1430	C₂²	—	8	4	no	—
1431	C₂²	C₅₃×#546	1	2	yes	—
1432	C₂²	C₅₃×#575	1	2	yes	—
1433	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1434	C₄	—	2	1	no	—
1435	C₄	—	2	1	no	—
1436	C₄	—	2	1	no	—
1437	C₄	—	2	1	no	—
1438	C₄	—	2	2	no	—
1439	C₄	—	2	1	no	—
1440	C₄	—	2	1	no	—
1441	C₄	—	2	1	no	—
1442	C₄	—	2	1	no	—
1443	C₄	—	4	1	no	—
1444	C₄	—	4	1	no	—
1445	C₄	—	4	1	no	—
1446	C₄	—	4	2	no	—
1447	C₄	—	4	2	no	—
1448	C₄	—	4	2	no	—
1449	C₄	—	4	1	no	—
1450	C₄	C₅₃×#546	1	2	yes	—
1451	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1452	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1453	C₂	—	2	2	no	—
1454	C₂	—	2	2	no	—
1455	C₂	—	4	1	no	—
1456	C₂	—	4	1	no	—
1457	C₂	—	4	1	no	—
1458	C₂	—	4	2	no	—
1459	C₂	—	8	1	no	—
1460	C₂	—	8	1	no	—
1461	C₂	—	8	2	no	—
1462	C₂	C₂×C₅₃×#546	1	1	yes	characteristic
1463	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1464	C₂	C₅₃×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#553	C₂	semidirect
2. D₄×#41×C₅₃	C₂	semidirect
3. C₅₃×#3326	C₂	semidirect
4. C₅₃×#3322	C₂	semidirect
5. C₅₃×#3320	C₂	semidirect
6. C₅₃×#3318	C₂	semidirect
7. C₅₃×#3309	C₂	semidirect
8. C₅₃×#3307	C₂	semidirect
9. C₅₃×#3301	C₂	semidirect
10. C₅₃×#3297	C₂	semidirect
11. C₅₃×#3142	C₂	semidirect
12. C₅₃×#3093	C₂	semidirect
13. C₅₃×#3092	C₂	semidirect
14. C₅₃×#3080	C₂	semidirect
15. C₅₃×#3055	C₂	semidirect
16. C₅₃×#3055	C₂	semidirect
17. C₅₃×#3036	C₂	semidirect
18. C₅₃×#3006	C₂	semidirect
19. C₅₃×#3006	C₂	semidirect
20. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
21. D₄×M₁₆×C₅₃	C₂	semidirect
22. C₅₃×#2896	C₂	semidirect
23. C₂×C₅₃×#417	C₂	semidirect
27. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
28. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
29. C₂²×M₁₆×C₅₃	C₂²	semidirect
30. C₂²×M₁₆×C₅₃	C₂²	semidirect
36. C₅₃×#553	C₂²	semidirect
37. C₅₃×#553	C₂²	semidirect
38. C₅₃×#553	C₂²	semidirect
39. C₅₃×#550	C₂²	semidirect
40. D₄×Q₈×C₅₃	C₂²	semidirect
41. C₅₃×#548	C₂²	semidirect
42. C₅₃×#548	C₂²	semidirect
44. C₅₃×#547	C₂²	semidirect
47. C₅₃×#546	C₂²	semidirect
48. C₅₃×#546	C₂²	semidirect
50. D₄²×C₅₃	C₂²	semidirect
54. C₂×#125×C₅₃	C₂²	semidirect
61. C₂×#121×C₅₃	C₂²	semidirect
62. C₂×#121×C₅₃	C₂²	semidirect
67. C₂×C₄×D₄×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×#469	C₂²	semidirect
87. C₅₃×#469	C₂²	semidirect
88. C₅₃×#468	C₂²	semidirect
89. C₅₃×#468	C₂²	semidirect
90. C₅₃×#466	C₂²	semidirect
91. C₅₃×#466	C₂²	semidirect
92. C₅₃×#465	C₂²	semidirect
93. C₅₃×#465	C₂²	semidirect
94. C₅₃×#463	C₂²	semidirect
95. C₅₃×#463	C₂²	semidirect
96. C₅₃×#461	C₂²	semidirect
97. C₅₃×#459	C₂²	semidirect
98. C₅₃×#449	C₂²	semidirect
99. C₅₃×#449	C₂²	semidirect
100. C₅₃×#449	C₂²	semidirect
101. C₅₃×#449	C₂²	semidirect
102. C₅₃×#448	C₂²	semidirect
103. C₅₃×#448	C₂²	semidirect
104. C₅₃×#447	C₂²	semidirect
105. C₅₃×#447	C₂²	semidirect
106. C₅₃×#442	C₂²	semidirect
107. C₅₃×#440	C₂²	semidirect
108. C₄×SD₁₆×C₅₃	C₂²	semidirect
109. C₄×D₈×C₅₃	C₂²	semidirect
110. C₅₃×#436	C₂²	semidirect
111. C₅₃×#435	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×#418	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
668. #61164	C₅₃	direct (N × H)
721. C₂×#553	C₂×C₅₃	semidirect
722. D₄×#41	C₂×C₅₃	semidirect
723. #3326	C₂×C₅₃	semidirect
724. #3322	C₂×C₅₃	semidirect
725. #3320	C₂×C₅₃	semidirect
726. #3318	C₂×C₅₃	semidirect
727. #3309	C₂×C₅₃	semidirect
728. #3307	C₂×C₅₃	semidirect
729. #3301	C₂×C₅₃	semidirect
730. #3297	C₂×C₅₃	semidirect
731. #3142	C₂×C₅₃	semidirect
732. #3093	C₂×C₅₃	semidirect
733. #3092	C₂×C₅₃	semidirect
734. #3080	C₂×C₅₃	semidirect
735. #3055	C₂×C₅₃	semidirect
736. #3055	C₂×C₅₃	semidirect
737. #3036	C₂×C₅₃	semidirect
738. #3006	C₂×C₅₃	semidirect
739. #3006	C₂×C₅₃	semidirect
740. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
741. D₄×M₁₆	C₂×C₅₃	semidirect
742. #2896	C₂×C₅₃	semidirect
743. C₂×#417	C₂×C₅₃	semidirect
759. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
760. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
761. C₂²×M₁₆	C₂²×C₅₃	semidirect
762. C₂²×M₁₆	C₂²×C₅₃	semidirect
768. #553	C₂²×C₅₃	semidirect
769. #553	C₂²×C₅₃	semidirect
770. #553	C₂²×C₅₃	semidirect
771. #550	C₂²×C₅₃	semidirect
772. D₄×Q₈	C₂²×C₅₃	semidirect
773. #548	C₂²×C₅₃	semidirect
774. #548	C₂²×C₅₃	semidirect
776. #547	C₂²×C₅₃	semidirect
779. #546	C₂²×C₅₃	semidirect
780. #546	C₂²×C₅₃	semidirect
782. D₄²	C₂²×C₅₃	semidirect
786. C₂×#125	C₂²×C₅₃	semidirect
793. C₂×#121	C₂²×C₅₃	semidirect
794. C₂×#121	C₂²×C₅₃	semidirect
799. C₂×C₄×D₄	C₂²×C₅₃	semidirect
800. C₂×#117	C₂²×C₅₃	semidirect
801. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
802. #491	C₂²×C₅₃	semidirect
803. #490	C₂²×C₅₃	semidirect
804. #488	C₂²×C₅₃	semidirect
805. #488	C₂²×C₅₃	semidirect
806. #485	C₂²×C₅₃	semidirect
807. #485	C₂²×C₅₃	semidirect
808. #484	C₂²×C₅₃	semidirect
809. #483	C₂²×C₅₃	semidirect
810. #482	C₂²×C₅₃	semidirect
811. #482	C₂²×C₅₃	semidirect
812. #481	C₂²×C₅₃	semidirect
813. #480	C₂²×C₅₃	semidirect
814. #479	C₂²×C₅₃	semidirect
815. #479	C₂²×C₅₃	semidirect
816. #478	C₂²×C₅₃	semidirect
817. #478	C₂²×C₅₃	semidirect
818. #469	C₂²×C₅₃	semidirect
819. #469	C₂²×C₅₃	semidirect
820. #468	C₂²×C₅₃	semidirect
821. #468	C₂²×C₅₃	semidirect
822. #466	C₂²×C₅₃	semidirect
823. #466	C₂²×C₅₃	semidirect
824. #465	C₂²×C₅₃	semidirect
825. #465	C₂²×C₅₃	semidirect
826. #463	C₂²×C₅₃	semidirect
827. #463	C₂²×C₅₃	semidirect
828. #461	C₂²×C₅₃	semidirect
829. #459	C₂²×C₅₃	semidirect
830. #449	C₂²×C₅₃	semidirect
831. #449	C₂²×C₅₃	semidirect
832. #449	C₂²×C₅₃	semidirect
833. #449	C₂²×C₅₃	semidirect
834. #448	C₂²×C₅₃	semidirect
835. #448	C₂²×C₅₃	semidirect
836. #447	C₂²×C₅₃	semidirect
837. #447	C₂²×C₅₃	semidirect
838. #442	C₂²×C₅₃	semidirect
839. #440	C₂²×C₅₃	semidirect
840. C₄×SD₁₆	C₂²×C₅₃	semidirect
841. C₄×D₈	C₂²×C₅₃	semidirect
842. #436	C₂²×C₅₃	semidirect
843. #435	C₂²×C₅₃	semidirect
844. #435	C₂²×C₅₃	semidirect
845. C₈×D₄	C₂²×C₅₃	semidirect
846. #428	C₂²×C₅₃	semidirect
847. #428	C₂²×C₅₃	semidirect
848. #428	C₂²×C₅₃	semidirect
849. #423	C₂²×C₅₃	semidirect
850. #419	C₂²×C₅₃	semidirect
851. #418	C₂²×C₅₃	semidirect
852. #418	C₂²×C₅₃	semidirect
856. #417	C₂²×C₅₃	semidirect
857. #417	C₂²×C₅₃	semidirect
858. #417	C₂²×C₅₃	semidirect
859. #417	C₂²×C₅₃	semidirect
860. #417	C₂²×C₅₃	semidirect
861. #417	C₂²×C₅₃	semidirect
862. #417	C₂²×C₅₃	semidirect
863. #417	C₂²×C₅₃	semidirect
864. #416	C₂²×C₅₃	semidirect
865. #416	C₂²×C₅₃	semidirect
866. C₂×#103	C₂²×C₅₃	semidirect
867. C₂×#102	C₂²×C₅₃	semidirect
868. #407	C₂²×C₅₃	semidirect
869. #407	C₂²×C₅₃	semidirect
870. C₄×M₁₆	C₂²×C₅₃	semidirect
871. C₅₃	#61164	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×#553	2
D₄×#41×C₅₃	2
C₅₃×#3326	2
C₅₃×#3322	2
C₅₃×#3320	2
C₅₃×#3318	2
C₅₃×#3309	2
C₅₃×#3307	2
C₅₃×#3301	2
C₅₃×#3297	2
C₅₃×#3142	2
C₅₃×#3093	2
C₅₃×#3092	2
C₅₃×#3080	2
C₅₃×#3055	2
C₅₃×#3036	2
C₅₃×#3006	2
C₄×AGL(1,ℤ/8)×C₅₃	2
D₄×M₁₆×C₅₃	2
C₅₃×#2896	2
C₂×C₅₃×#417	2
#61164	53

Subgroups — C53×#61164 #27268676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61164 #27268676