Subgroups — C₅₃×#60811 #27268323

Order 13568.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3224	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3220	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3217	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3213	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3211	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3205	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3155	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3045	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3041	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
21	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
22	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
23	C₂²×D₈×C₅₃	C₂²	1	2	yes	complemented
24	C₅₃×#555	—	2	1	no	—
25	C₅₃×#553	—	2	1	no	—
26	C₅₃×#553	—	2	1	no	—
27	C₅₃×#551	—	2	2	no	—
28	C₅₃×#547	—	2	1	no	—
29	C₅₃×#546	—	2	2	no	—
30	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#542	C₂²	1	2	yes	complemented
32	C₅₃×#540	C₂²	1	2	yes	complemented
33	C₅₃×#535	—	2	2	no	—
34	C₅₃×#535	—	2	1	no	—
35	C₅₃×#535	—	2	1	no	—
36	C₅₃×#535	C₂²	1	2	yes	—
37	C₅₃×#535	C₂²	1	2	yes	—
38	C₅₃×#535	C₂²	1	4	yes	complemented
39	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#532	C₂²	1	2	yes	complemented
41	C₂×#127×C₅₃	C₂²	1	2	yes	complemented
42	C₅₃×#529	C₂²	1	2	yes	complemented
43	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
44	C₅₃×#525	C₂²	1	1	yes	characteristic
45	C₂×#121×C₅₃	—	2	1	no	—
46	C₂×#121×C₅₃	—	2	1	no	—
47	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×#120×C₅₃	—	2	2	no	—
49	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
51	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
52	C₅₃×#496	C₂²	1	4	yes	complemented
53	C₅₃×#496	C₂²	1	4	yes	complemented
54	C₅₃×#495	C₂²	1	4	yes	complemented
55	C₅₃×#493	C₂²	1	4	yes	complemented
56	C₅₃×#490	C₂²	1	4	yes	complemented
57	C₅₃×#489	C₂²	1	4	yes	complemented
58	C₅₃×#488	C₂²	1	4	yes	complemented
59	C₅₃×#486	C₂²	1	4	yes	complemented
60	C₅₃×#464	C₂²	1	4	yes	complemented
61	C₅₃×#463	C₂²	1	4	yes	complemented
62	C₅₃×#463	C₂²	1	4	yes	complemented
63	C₅₃×#463	C₂²	1	4	yes	complemented
64	C₅₃×#460	C₂²	1	4	yes	complemented
65	C₅₃×#459	C₂²	1	4	yes	complemented
66	C₅₃×#459	C₂²	1	4	yes	complemented
67	C₅₃×#459	C₂²	1	4	yes	complemented
68	C₅₃×#452	C₂²	1	2	yes	complemented
69	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#450	C₂²	1	2	yes	complemented
71	C₅₃×#450	C₂²	1	2	yes	complemented
72	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#449	C₂²	1	2	yes	complemented
74	C₅₃×#449	C₂²	1	4	yes	complemented
75	C₅₃×#448	C₂²	1	2	yes	complemented
76	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#447	C₂²	1	2	yes	—
78	C₅₃×#447	C₂²	1	2	yes	—
79	C₅₃×#447	C₂²	1	2	yes	complemented
80	C₅₃×#447	C₂²	1	2	yes	complemented
81	C₅₃×#447	C₂²	1	4	yes	complemented
82	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#447	C₂²	1	2	yes	complemented
84	C₅₃×#433	C₂²	1	4	yes	complemented
85	C₅₃×#432	C₂²	1	2	yes	complemented
86	C₅₃×#431	C₂²	1	2	yes	complemented
87	C₅₃×#424	C₂²	1	2	yes	complemented
88	C₅₃×#418	C₂²	1	2	yes	complemented
89	C₅₃×#417	C₂²	1	2	yes	complemented
90	C₅₃×#416	C₂²	1	2	yes	complemented
91	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
92	C₅₃×#407	C₂²	1	1	yes	characteristic
93	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
94	C₅₃×#405	C₂²	1	2	yes	complemented
95	C₂⁵×C₅₃	—	2	1	no	—
96	C₂×#41×C₅₃	—	2	1	no	—
97	C₂×#41×C₅₃	—	2	1	no	—
98	C₂×#41×C₅₃	—	2	2	no	—
99	C₂×#41×C₅₃	—	4	4	no	—
100	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
101	C₂×#41×C₅₃	C₂³	1	2	yes	—
102	C₂×#41×C₅₃	C₂³	1	2	yes	—
103	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₅₃	—	2	1	no	—
105	C₂²×D₄×C₅₃	—	2	1	no	—
106	C₂²×D₄×C₅₃	—	2	1	no	—
107	C₂²×D₄×C₅₃	—	2	1	no	—
108	C₂²×D₄×C₅₃	—	2	1	no	—
109	C₂²×D₄×C₅₃	—	2	2	no	—
110	C₂²×D₄×C₅₃	—	2	2	no	—
111	C₂²×D₄×C₅₃	—	4	4	no	—
112	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
117	C₂³×C₄×C₅₃	—	2	1	no	—
118	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
119	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
120	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
121	#135×C₅₃	—	4	4	no	—
122	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	complemented
123	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
124	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	complemented
125	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	complemented
126	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	complemented
127	C₂×D₈×C₅₃	—	4	4	no	—
128	C₂×D₈×C₅₃	C₂³	1	4	yes	—
129	C₂×D₈×C₅₃	C₂³	1	4	yes	—
130	C₂×D₈×C₅₃	C₂³	1	4	yes	—
131	C₂×D₈×C₅₃	C₂³	1	2	yes	complemented
132	C₂×D₈×C₅₃	C₂³	1	4	yes	complemented
133	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
134	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₅₃	—	2	1	no	—
136	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
137	#127×C₅₃	—	2	2	no	—
138	#127×C₅₃	—	2	2	no	—
139	#127×C₅₃	C₂³	1	4	yes	—
140	#127×C₅₃	C₂³	1	4	yes	—
141	#127×C₅₃	C₂³	1	2	yes	complemented
142	#126×C₅₃	—	2	2	no	—
143	#126×C₅₃	—	2	2	no	—
144	#125×C₅₃	—	2	1	no	—
145	#125×C₅₃	C₂³	1	2	yes	complemented
146	#124×C₅₃	—	2	2	no	—
147	#124×C₅₃	—	2	2	no	—
148	#124×C₅₃	—	2	2	no	—
149	#124×C₅₃	—	2	2	no	—
150	#124×C₅₃	C₂³	1	4	yes	—
151	#124×C₅₃	C₂³	1	4	yes	—
152	#124×C₅₃	C₂³	1	2	yes	complemented
153	#123×C₅₃	—	2	2	no	—
154	#123×C₅₃	—	2	2	no	—
155	#123×C₅₃	—	2	2	no	—
156	#123×C₅₃	—	2	1	no	—
157	#123×C₅₃	—	2	2	no	—
158	C₂²⋊Q₈×C₅₃	—	2	2	no	—
159	C₂²⋊Q₈×C₅₃	—	2	2	no	—
160	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
161	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
162	#121×C₅₃	—	2	2	no	—
163	#121×C₅₃	—	2	2	no	—
164	#121×C₅₃	—	2	2	no	—
165	#121×C₅₃	—	2	2	no	—
166	#121×C₅₃	—	2	4	no	—
167	#121×C₅₃	—	2	4	no	—
168	#121×C₅₃	—	2	1	no	—
169	#121×C₅₃	—	2	1	no	—
170	#121×C₅₃	—	2	2	no	—
171	#121×C₅₃	—	2	2	no	—
172	#121×C₅₃	—	2	1	no	—
173	#121×C₅₃	—	2	1	no	—
174	#121×C₅₃	—	2	2	no	—
175	#121×C₅₃	C₂³	1	2	yes	—
176	#121×C₅₃	C₂³	1	2	yes	—
177	#121×C₅₃	C₂³	1	1	yes	characteristic
178	#121×C₅₃	C₂³	1	1	yes	characteristic
179	#120×C₅₃	—	2	4	no	—
180	#120×C₅₃	—	2	4	no	—
181	#120×C₅₃	—	2	4	no	—
182	#120×C₅₃	—	2	4	no	—
183	#120×C₅₃	—	2	2	no	—
184	#120×C₅₃	—	2	1	no	—
185	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
186	C₄×D₄×C₅₃	—	2	1	no	—
187	C₄×D₄×C₅₃	—	2	1	no	—
188	C₄×D₄×C₅₃	—	2	2	no	—
189	C₄×D₄×C₅₃	—	2	2	no	—
190	C₄×D₄×C₅₃	—	2	1	no	—
191	C₄×D₄×C₅₃	—	2	1	no	—
192	C₄×D₄×C₅₃	—	2	2	no	—
193	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
194	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
195	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
196	#117×C₅₃	—	2	1	no	—
197	#117×C₅₃	—	2	2	no	—
198	#117×C₅₃	D₄	1	2	yes	—
199	#117×C₅₃	D₄	1	1	yes	characteristic
200	#117×C₅₃	D₄	1	1	yes	characteristic
201	#117×C₅₃	C₂³	1	1	yes	characteristic
202	#117×C₅₃	C₂³	1	1	yes	characteristic
203	#117×C₅₃	C₂³	1	1	yes	characteristic
204	#117×C₅₃	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
206	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
207	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
208	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
210	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
211	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
212	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
213	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
214	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
215	C₄⋊C₈×C₅₃	C₂³	1	4	yes	complemented
216	C₄⋊C₈×C₅₃	C₂³	1	4	yes	complemented
217	#103×C₅₃	C₂³	1	2	yes	complemented
218	#103×C₅₃	C₂³	1	4	yes	complemented
219	#103×C₅₃	C₂³	1	2	yes	complemented
220	#102×C₅₃	C₂³	1	4	yes	—
221	#102×C₅₃	C₂³	1	4	yes	—
222	#102×C₅₃	C₂³	1	4	yes	—
223	#102×C₅₃	C₂³	1	4	yes	—
224	#102×C₅₃	C₂³	1	2	yes	complemented
225	#102×C₅₃	C₂³	1	4	yes	complemented
226	#102×C₅₃	C₂³	1	2	yes	complemented
227	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
230	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
231	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
232	#97×C₅₃	C₂³	1	4	yes	complemented
233	C₄×C₈×C₅₃	C₂³	1	4	yes	complemented
234	C₂⁴×C₅₃	—	2	2	no	—
235	C₂⁴×C₅₃	—	2	1	no	—
236	C₂⁴×C₅₃	—	2	1	no	—
237	C₂⁴×C₅₃	—	2	2	no	—
238	C₂⁴×C₅₃	—	2	2	no	—
239	C₂⁴×C₅₃	—	4	4	no	—
240	C₂⁴×C₅₃	—	8	2	no	—
241	C₂⁴×C₅₃	—	8	2	no	—
242	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
243	#41×C₅₃	—	2	4	no	—
244	#41×C₅₃	—	2	4	no	—
245	#41×C₅₃	—	2	4	no	—
246	#41×C₅₃	—	4	2	no	—
247	#41×C₅₃	—	4	2	no	—
248	#41×C₅₃	—	4	4	no	—
249	#41×C₅₃	—	4	4	no	—
250	#41×C₅₃	—	8	4	no	—
251	C₂×Q₈×C₅₃	—	2	1	no	—
252	C₂×Q₈×C₅₃	—	2	2	no	—
253	C₂×Q₈×C₅₃	—	4	2	no	—
254	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
255	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
256	C₂×D₄×C₅₃	—	2	1	no	—
257	C₂×D₄×C₅₃	—	2	1	no	—
258	C₂×D₄×C₅₃	—	2	2	no	—
259	C₂×D₄×C₅₃	—	2	2	no	—
260	C₂×D₄×C₅₃	—	2	2	no	—
261	C₂×D₄×C₅₃	—	2	1	no	—
262	C₂×D₄×C₅₃	—	2	2	no	—
263	C₂×D₄×C₅₃	—	2	1	no	—
264	C₂×D₄×C₅₃	—	2	2	no	—
265	C₂×D₄×C₅₃	—	2	2	no	—
266	C₂×D₄×C₅₃	—	2	2	no	—
267	C₂×D₄×C₅₃	—	2	1	no	—
268	C₂×D₄×C₅₃	—	2	2	no	—
269	C₂×D₄×C₅₃	—	2	4	no	—
270	C₂×D₄×C₅₃	—	2	4	no	—
271	C₂×D₄×C₅₃	—	2	4	no	—
272	C₂×D₄×C₅₃	—	2	4	no	—
273	C₂×D₄×C₅₃	—	2	2	no	—
274	C₂×D₄×C₅₃	—	2	4	no	—
275	C₂×D₄×C₅₃	—	2	4	no	—
276	C₂×D₄×C₅₃	—	2	4	no	—
277	C₂×D₄×C₅₃	—	4	4	no	—
278	C₂×D₄×C₅₃	—	4	4	no	—
279	C₂×D₄×C₅₃	—	4	2	no	—
280	C₂×D₄×C₅₃	—	4	4	no	—
281	C₂×D₄×C₅₃	—	4	4	no	—
282	C₂×D₄×C₅₃	—	4	4	no	—
283	C₂×D₄×C₅₃	—	4	4	no	—
284	C₂×D₄×C₅₃	—	8	4	no	—
285	C₂×D₄×C₅₃	—	8	4	no	—
286	C₂×D₄×C₅₃	—	8	2	no	—
287	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
288	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
289	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
290	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅₃	—	2	4	no	—
292	C₂²×C₄×C₅₃	—	2	1	no	—
293	C₂²×C₄×C₅₃	—	2	1	no	—
294	C₂²×C₄×C₅₃	—	2	1	no	—
295	C₂²×C₄×C₅₃	—	2	2	no	—
296	C₂²×C₄×C₅₃	—	2	2	no	—
297	C₂²×C₄×C₅₃	—	2	2	no	—
298	C₂²×C₄×C₅₃	—	2	2	no	—
299	C₂²×C₄×C₅₃	—	2	2	no	—
300	C₂²×C₄×C₅₃	—	4	4	no	—
301	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
302	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
306	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
309	Q₁₆×C₅₃	—	4	2	no	—
310	SD₁₆×C₅₃	—	4	4	no	—
311	SD₁₆×C₅₃	—	4	2	no	—
312	SD₁₆×C₅₃	—	4	2	no	—
313	SD₁₆×C₅₃	—	4	4	no	—
314	D₈×C₅₃	—	4	4	no	—
315	D₈×C₅₃	—	4	4	no	—
316	D₈×C₅₃	—	4	4	no	—
317	D₈×C₅₃	—	4	2	no	—
318	D₈×C₅₃	—	4	4	no	—
319	M₁₆×C₅₃	—	2	4	no	—
320	C₂×C₈×C₅₃	—	2	4	no	—
321	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
322	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
323	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
324	C₄⋊C₄×C₅₃	—	2	1	no	—
325	C₄⋊C₄×C₅₃	—	2	2	no	—
326	C₄⋊C₄×C₅₃	—	2	1	no	—
327	C₄⋊C₄×C₅₃	—	2	2	no	—
328	C₄⋊C₄×C₅₃	—	2	2	no	—
329	C₄⋊C₄×C₅₃	—	2	2	no	—
330	C₄⋊C₄×C₅₃	—	2	1	no	—
331	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
332	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
333	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
334	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
335	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
336	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
337	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₂²⋊C₄×C₅₃	—	2	1	no	—
341	C₂²⋊C₄×C₅₃	—	2	1	no	—
342	C₂²⋊C₄×C₅₃	—	2	1	no	—
343	C₂²⋊C₄×C₅₃	—	2	2	no	—
344	C₂²⋊C₄×C₅₃	—	2	2	no	—
345	C₂²⋊C₄×C₅₃	—	2	2	no	—
346	C₂²⋊C₄×C₅₃	—	2	4	no	—
347	C₂²⋊C₄×C₅₃	—	2	4	no	—
348	C₂²⋊C₄×C₅₃	—	2	4	no	—
349	C₂²⋊C₄×C₅₃	—	2	4	no	—
350	C₂²⋊C₄×C₅₃	—	2	2	no	—
351	C₂²⋊C₄×C₅₃	—	2	2	no	—
352	C₂²⋊C₄×C₅₃	—	2	2	no	—
353	C₂²⋊C₄×C₅₃	—	2	1	no	—
354	C₂²⋊C₄×C₅₃	—	2	2	no	—
355	C₂²⋊C₄×C₅₃	—	2	1	no	—
356	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
357	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
358	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
359	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
360	C₄²×C₅₃	—	2	2	no	—
361	C₄²×C₅₃	—	2	1	no	—
362	C₄²×C₅₃	C₂×D₄	1	2	yes	—
363	C₄²×C₅₃	C₂×D₄	1	2	yes	—
364	C₄²×C₅₃	C₂⁴	1	2	yes	—
365	C₄²×C₅₃	C₂⁴	1	2	yes	—
366	C₂³×C₅₃	—	2	2	no	—
367	C₂³×C₅₃	—	2	2	no	—
368	C₂³×C₅₃	—	2	1	no	—
369	C₂³×C₅₃	—	2	2	no	—
370	C₂³×C₅₃	—	2	2	no	—
371	C₂³×C₅₃	—	2	4	no	—
372	C₂³×C₅₃	—	4	1	no	—
373	C₂³×C₅₃	—	4	2	no	—
374	C₂³×C₅₃	—	4	4	no	—
375	C₂³×C₅₃	—	4	4	no	—
376	C₂³×C₅₃	—	4	2	no	—
377	C₂³×C₅₃	—	4	4	no	—
378	C₂³×C₅₃	—	4	4	no	—
379	C₂³×C₅₃	—	4	2	no	—
380	C₂³×C₅₃	—	4	4	no	—
381	C₂³×C₅₃	—	4	2	no	—
382	C₂³×C₅₃	—	8	2	no	—
383	C₂³×C₅₃	—	8	2	no	—
384	C₂³×C₅₃	—	8	2	no	—
385	C₂³×C₅₃	—	8	2	no	—
386	C₂³×C₅₃	—	8	1	no	—
387	C₂³×C₅₃	—	8	1	no	—
388	C₂³×C₅₃	—	8	16	no	—
389	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
390	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
391	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
392	Q₈×C₅₃	—	2	2	no	—
393	Q₈×C₅₃	—	2	2	no	—
394	Q₈×C₅₃	—	2	2	no	—
395	Q₈×C₅₃	—	4	2	no	—
396	Q₈×C₅₃	—	8	2	no	—
397	D₄×C₅₃	—	2	4	no	—
398	D₄×C₅₃	—	2	4	no	—
399	D₄×C₅₃	—	2	4	no	—
400	D₄×C₅₃	—	2	2	no	—
401	D₄×C₅₃	—	2	2	no	—
402	D₄×C₅₃	—	2	2	no	—
403	D₄×C₅₃	—	4	4	no	—
404	D₄×C₅₃	—	4	4	no	—
405	D₄×C₅₃	—	4	2	no	—
406	D₄×C₅₃	—	4	4	no	—
407	D₄×C₅₃	—	4	4	no	—
408	D₄×C₅₃	—	4	2	no	—
409	D₄×C₅₃	—	4	4	no	—
410	D₄×C₅₃	—	4	2	no	—
411	D₄×C₅₃	—	4	2	no	—
412	D₄×C₅₃	—	4	4	no	—
413	D₄×C₅₃	—	8	2	no	—
414	D₄×C₅₃	—	8	4	no	—
415	D₄×C₅₃	—	8	4	no	—
416	D₄×C₅₃	—	8	4	no	—
417	D₄×C₅₃	—	8	4	no	—
418	D₄×C₅₃	—	8	2	no	—
419	D₄×C₅₃	—	8	1	no	—
420	D₄×C₅₃	—	8	2	no	—
421	C₂×C₄×C₅₃	—	2	2	no	—
422	C₂×C₄×C₅₃	—	2	4	no	—
423	C₂×C₄×C₅₃	—	2	2	no	—
424	C₂×C₄×C₅₃	—	2	2	no	—
425	C₂×C₄×C₅₃	—	2	2	no	—
426	C₂×C₄×C₅₃	—	2	2	no	—
427	C₂×C₄×C₅₃	—	2	2	no	—
428	C₂×C₄×C₅₃	—	2	2	no	—
429	C₂×C₄×C₅₃	—	2	1	no	—
430	C₂×C₄×C₅₃	—	2	1	no	—
431	C₂×C₄×C₅₃	—	2	1	no	—
432	C₂×C₄×C₅₃	—	4	2	no	—
433	C₂×C₄×C₅₃	—	4	4	no	—
434	C₂×C₄×C₅₃	—	4	2	no	—
435	C₂×C₄×C₅₃	—	4	4	no	—
436	C₂×C₄×C₅₃	—	4	2	no	—
437	C₂×C₄×C₅₃	—	8	2	no	—
438	C₂×C₄×C₅₃	—	8	2	no	—
439	C₂×C₄×C₅₃	—	8	2	no	—
440	C₂×C₄×C₅₃	—	8	1	no	—
441	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
443	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
446	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
447	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
449	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
450	C₈×C₅₃	—	2	2	no	—
451	C₈×C₅₃	—	2	2	no	—
452	C₈×C₅₃	—	2	4	no	—
453	#60811	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
454	C₂²×C₅₃	—	2	1	no	—
455	C₂²×C₅₃	—	2	1	no	—
456	C₂²×C₅₃	—	2	1	no	—
457	C₂²×C₅₃	—	2	1	no	—
458	C₂²×C₅₃	—	2	1	no	—
459	C₂²×C₅₃	—	2	1	no	—
460	C₂²×C₅₃	—	2	1	no	—
461	C₂²×C₅₃	—	4	4	no	—
462	C₂²×C₅₃	—	4	2	no	—
463	C₂²×C₅₃	—	4	2	no	—
464	C₂²×C₅₃	—	4	1	no	—
465	C₂²×C₅₃	—	4	4	no	—
466	C₂²×C₅₃	—	4	2	no	—
467	C₂²×C₅₃	—	4	1	no	—
468	C₂²×C₅₃	—	4	4	no	—
469	C₂²×C₅₃	—	4	2	no	—
470	C₂²×C₅₃	—	4	1	no	—
471	C₂²×C₅₃	—	4	2	no	—
472	C₂²×C₅₃	—	4	2	no	—
473	C₂²×C₅₃	—	4	4	no	—
474	C₂²×C₅₃	—	8	4	no	—
475	C₂²×C₅₃	—	8	8	no	—
476	C₂²×C₅₃	—	8	8	no	—
477	C₂²×C₅₃	—	8	8	no	—
478	C₂²×C₅₃	—	16	2	no	—
479	C₂²×C₅₃	#535	1	2	yes	—
480	C₂²×C₅₃	#576	1	2	yes	—
481	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
482	C₄×C₅₃	—	2	2	no	—
483	C₄×C₅₃	—	2	2	no	—
484	C₄×C₅₃	—	2	1	no	—
485	C₄×C₅₃	—	2	1	no	—
486	C₄×C₅₃	—	2	2	no	—
487	C₄×C₅₃	—	2	2	no	—
488	C₄×C₅₃	—	4	1	no	—
489	C₄×C₅₃	—	4	2	no	—
490	C₄×C₅₃	—	4	1	no	—
491	C₄×C₅₃	—	4	2	no	—
492	C₄×C₅₃	—	4	1	no	—
493	C₄×C₅₃	#535	1	2	yes	—
494	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
495	#3494	C₂×C₅₃	1	1	yes	characteristic, complemented
496	C₂×#535	C₂×C₅₃	1	1	yes	characteristic, complemented
497	#3224	C₂×C₅₃	1	4	yes	complemented
498	#3220	C₂×C₅₃	1	4	yes	complemented
499	#3217	C₂×C₅₃	1	2	yes	complemented
500	#3213	C₂×C₅₃	1	2	yes	complemented
501	#3211	C₂×C₅₃	1	2	yes	complemented
502	#3205	C₂×C₅₃	1	2	yes	complemented
503	#3155	C₂×C₅₃	1	2	yes	complemented
504	#3136	C₂×C₅₃	1	2	yes	complemented
505	#3045	C₂×C₅₃	1	2	yes	complemented
506	#3041	C₂×C₅₃	1	2	yes	complemented
507	#3006	C₂×C₅₃	1	1	yes	characteristic, complemented
508	#3003	C₂×C₅₃	1	1	yes	characteristic, complemented
509	#3002	C₂×C₅₃	1	1	yes	characteristic, complemented
510	C₂×#447	C₂×C₅₃	1	1	yes	characteristic, complemented
511	#2924	C₂×C₅₃	1	1	yes	characteristic, complemented
512	C₂×C₅₃	—	2	2	no	—
513	C₂×C₅₃	—	2	2	no	—
514	C₂×C₅₃	—	4	1	no	—
515	C₂×C₅₃	—	8	1	no	—
516	C₂×C₅₃	—	8	2	no	—
517	C₂×C₅₃	—	8	4	no	—
518	C₂×C₅₃	—	8	2	no	—
519	C₂×C₅₃	C₂×#535	1	1	yes	characteristic
520	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
521	C₂×C₅₃	#3585	1	1	yes	characteristic
522	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
523	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
524	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
525	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
526	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
527	C₂²×D₈	C₂²×C₅₃	1	2	yes	complemented
528	#555	—	2	1	no	—
529	#553	—	2	1	no	—
530	#553	—	2	1	no	—
531	#551	—	2	2	no	—
532	#547	—	2	1	no	—
533	#546	—	2	2	no	—
534	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
535	#542	C₂²×C₅₃	1	2	yes	complemented
536	#540	C₂²×C₅₃	1	2	yes	complemented
537	#535	—	2	2	no	—
538	#535	—	2	1	no	—
539	#535	—	2	1	no	—
540	#535	C₂²×C₅₃	1	2	yes	—
541	#535	C₂²×C₅₃	1	2	yes	—
542	#535	C₂²×C₅₃	1	4	yes	complemented
543	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
544	#532	C₂²×C₅₃	1	2	yes	complemented
545	C₂×#127	C₂²×C₅₃	1	2	yes	complemented
546	#529	C₂²×C₅₃	1	2	yes	complemented
547	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
548	#525	C₂²×C₅₃	1	1	yes	characteristic
549	C₂×#121	—	2	1	no	—
550	C₂×#121	—	2	1	no	—
551	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
552	C₂×#120	—	2	2	no	—
553	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
554	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
555	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
556	#496	C₂²×C₅₃	1	4	yes	complemented
557	#496	C₂²×C₅₃	1	4	yes	complemented
558	#495	C₂²×C₅₃	1	4	yes	complemented
559	#493	C₂²×C₅₃	1	4	yes	complemented
560	#490	C₂²×C₅₃	1	4	yes	complemented
561	#489	C₂²×C₅₃	1	4	yes	complemented
562	#488	C₂²×C₅₃	1	4	yes	complemented
563	#486	C₂²×C₅₃	1	4	yes	complemented
564	#464	C₂²×C₅₃	1	4	yes	complemented
565	#463	C₂²×C₅₃	1	4	yes	complemented
566	#463	C₂²×C₅₃	1	4	yes	complemented
567	#463	C₂²×C₅₃	1	4	yes	complemented
568	#460	C₂²×C₅₃	1	4	yes	complemented
569	#459	C₂²×C₅₃	1	4	yes	complemented
570	#459	C₂²×C₅₃	1	4	yes	complemented
571	#459	C₂²×C₅₃	1	4	yes	complemented
572	#452	C₂²×C₅₃	1	2	yes	complemented
573	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
574	#450	C₂²×C₅₃	1	2	yes	complemented
575	#450	C₂²×C₅₃	1	2	yes	complemented
576	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
577	#449	C₂²×C₅₃	1	2	yes	complemented
578	#449	C₂²×C₅₃	1	4	yes	complemented
579	#448	C₂²×C₅₃	1	2	yes	complemented
580	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
581	#447	C₂²×C₅₃	1	2	yes	—
582	#447	C₂²×C₅₃	1	2	yes	—
583	#447	C₂²×C₅₃	1	2	yes	complemented
584	#447	C₂²×C₅₃	1	2	yes	complemented
585	#447	C₂²×C₅₃	1	4	yes	complemented
586	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
587	#447	C₂²×C₅₃	1	2	yes	complemented
588	#433	C₂²×C₅₃	1	4	yes	complemented
589	#432	C₂²×C₅₃	1	2	yes	complemented
590	#431	C₂²×C₅₃	1	2	yes	complemented
591	#424	C₂²×C₅₃	1	2	yes	complemented
592	#418	C₂²×C₅₃	1	2	yes	complemented
593	#417	C₂²×C₅₃	1	2	yes	complemented
594	#416	C₂²×C₅₃	1	2	yes	complemented
595	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
596	#407	C₂²×C₅₃	1	1	yes	characteristic
597	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
598	#405	C₂²×C₅₃	1	2	yes	complemented
599	C₅₃	#60811	1	1	yes	characteristic, direct product factor, Sylow
600	C₂⁵	—	2	1	no	—
601	C₂×#41	—	2	1	no	—
602	C₂×#41	—	2	1	no	—
603	C₂×#41	—	2	2	no	—
604	C₂×#41	—	4	4	no	—
605	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
606	C₂×#41	C₂³×C₅₃	1	2	yes	—
607	C₂×#41	C₂³×C₅₃	1	2	yes	—
608	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
609	C₂²×D₄	—	2	1	no	—
610	C₂²×D₄	—	2	1	no	—
611	C₂²×D₄	—	2	1	no	—
612	C₂²×D₄	—	2	1	no	—
613	C₂²×D₄	—	2	1	no	—
614	C₂²×D₄	—	2	2	no	—
615	C₂²×D₄	—	2	2	no	—
616	C₂²×D₄	—	4	4	no	—
617	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
618	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
619	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
620	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
621	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
622	C₂³×C₄	—	2	1	no	—
623	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
624	AGL(1,ℤ/8)	—	4	4	no	—
625	AGL(1,ℤ/8)	—	4	4	no	—
626	#135	—	4	4	no	—
627	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	complemented
628	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
629	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	complemented
630	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	complemented
631	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	complemented
632	C₂×D₈	—	4	4	no	—
633	C₂×D₈	C₂³×C₅₃	1	4	yes	—
634	C₂×D₈	C₂³×C₅₃	1	4	yes	—
635	C₂×D₈	C₂³×C₅₃	1	4	yes	—
636	C₂×D₈	C₂³×C₅₃	1	2	yes	complemented
637	C₂×D₈	C₂³×C₅₃	1	4	yes	complemented
638	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
639	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
640	C₄⋊Q₈	—	2	1	no	—
641	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	complemented
642	#127	—	2	2	no	—
643	#127	—	2	2	no	—
644	#127	C₂³×C₅₃	1	4	yes	—
645	#127	C₂³×C₅₃	1	4	yes	—
646	#127	C₂³×C₅₃	1	2	yes	complemented
647	#126	—	2	2	no	—
648	#126	—	2	2	no	—
649	#125	—	2	1	no	—
650	#125	C₂³×C₅₃	1	2	yes	complemented
651	#124	—	2	2	no	—
652	#124	—	2	2	no	—
653	#124	—	2	2	no	—
654	#124	—	2	2	no	—
655	#124	C₂³×C₅₃	1	4	yes	—
656	#124	C₂³×C₅₃	1	4	yes	—
657	#124	C₂³×C₅₃	1	2	yes	complemented
658	#123	—	2	1	no	—
659	#123	—	2	2	no	—
660	#123	—	2	2	no	—
661	#123	—	2	2	no	—
662	#123	—	2	2	no	—
663	C₂²⋊Q₈	—	2	2	no	—
664	C₂²⋊Q₈	—	2	2	no	—
665	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
666	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
667	#121	—	2	1	no	—
668	#121	—	2	1	no	—
669	#121	—	2	2	no	—
670	#121	—	2	2	no	—
671	#121	—	2	2	no	—
672	#121	—	2	2	no	—
673	#121	—	2	2	no	—
674	#121	—	2	4	no	—
675	#121	—	2	4	no	—
676	#121	—	2	1	no	—
677	#121	—	2	1	no	—
678	#121	—	2	2	no	—
679	#121	—	2	2	no	—
680	#121	C₂³×C₅₃	1	2	yes	—
681	#121	C₂³×C₅₃	1	2	yes	—
682	#121	C₂³×C₅₃	1	1	yes	characteristic
683	#121	C₂³×C₅₃	1	1	yes	characteristic
684	#120	—	2	1	no	—
685	#120	—	2	4	no	—
686	#120	—	2	4	no	—
687	#120	—	2	4	no	—
688	#120	—	2	4	no	—
689	#120	—	2	2	no	—
690	C₄×Q₈	C₂³×C₅₃	1	2	yes	complemented
691	C₄×D₄	—	2	1	no	—
692	C₄×D₄	—	2	1	no	—
693	C₄×D₄	—	2	2	no	—
694	C₄×D₄	—	2	1	no	—
695	C₄×D₄	—	2	1	no	—
696	C₄×D₄	—	2	2	no	—
697	C₄×D₄	—	2	2	no	—
698	C₄×D₄	C₂³×C₅₃	1	2	yes	complemented
699	C₄×D₄	C₂³×C₅₃	1	2	yes	complemented
700	C₄×D₄	C₂³×C₅₃	1	2	yes	complemented
701	#117	—	2	1	no	—
702	#117	—	2	2	no	—
703	#117	D₄×C₅₃	1	2	yes	—
704	#117	D₄×C₅₃	1	1	yes	characteristic
705	#117	D₄×C₅₃	1	1	yes	characteristic
706	#117	C₂³×C₅₃	1	1	yes	characteristic
707	#117	C₂³×C₅₃	1	1	yes	characteristic
708	#117	C₂³×C₅₃	1	1	yes	characteristic
709	#117	C₂³×C₅₃	1	2	yes	—
710	C₂×C₄⋊C₄	—	2	1	no	—
711	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
712	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
713	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
714	C₂×C₂²⋊C₄	—	2	2	no	—
715	C₂×C₂²⋊C₄	—	2	2	no	—
716	C₂×C₂²⋊C₄	—	2	1	no	—
717	C₂×C₂²⋊C₄	—	2	2	no	—
718	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
719	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
720	C₄⋊C₈	C₂³×C₅₃	1	4	yes	complemented
721	C₄⋊C₈	C₂³×C₅₃	1	4	yes	complemented
722	#103	C₂³×C₅₃	1	2	yes	complemented
723	#103	C₂³×C₅₃	1	2	yes	complemented
724	#103	C₂³×C₅₃	1	4	yes	complemented
725	#102	C₂³×C₅₃	1	4	yes	—
726	#102	C₂³×C₅₃	1	4	yes	—
727	#102	C₂³×C₅₃	1	4	yes	—
728	#102	C₂³×C₅₃	1	4	yes	—
729	#102	C₂³×C₅₃	1	2	yes	complemented
730	#102	C₂³×C₅₃	1	2	yes	complemented
731	#102	C₂³×C₅₃	1	4	yes	complemented
732	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
733	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
734	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
735	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
736	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
737	#97	C₂³×C₅₃	1	4	yes	complemented
738	C₄×C₈	C₂³×C₅₃	1	4	yes	complemented
739	C₂⁴	—	2	2	no	—
740	C₂⁴	—	2	1	no	—
741	C₂⁴	—	2	1	no	—
742	C₂⁴	—	2	2	no	—
743	C₂⁴	—	2	2	no	—
744	C₂⁴	—	4	4	no	—
745	C₂⁴	—	8	2	no	—
746	C₂⁴	—	8	2	no	—
747	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
748	#41	—	2	4	no	—
749	#41	—	2	4	no	—
750	#41	—	2	4	no	—
751	#41	—	4	2	no	—
752	#41	—	4	2	no	—
753	#41	—	4	4	no	—
754	#41	—	4	4	no	—
755	#41	—	8	4	no	—
756	C₂×Q₈	—	2	1	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	—	4	2	no	—
759	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
760	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
761	C₂×D₄	—	2	1	no	—
762	C₂×D₄	—	2	1	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	1	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	1	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	1	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	2	4	no	—
776	C₂×D₄	—	2	4	no	—
777	C₂×D₄	—	2	4	no	—
778	C₂×D₄	—	2	2	no	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	4	4	no	—
783	C₂×D₄	—	4	4	no	—
784	C₂×D₄	—	4	2	no	—
785	C₂×D₄	—	4	4	no	—
786	C₂×D₄	—	4	4	no	—
787	C₂×D₄	—	4	4	no	—
788	C₂×D₄	—	4	4	no	—
789	C₂×D₄	—	8	4	no	—
790	C₂×D₄	—	8	4	no	—
791	C₂×D₄	—	8	2	no	—
792	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
793	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
794	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
795	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
796	C₂²×C₄	—	2	4	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	2	1	no	—
799	C₂²×C₄	—	2	1	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	4	4	no	—
806	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
807	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
808	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
809	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
810	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
811	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
814	Q₁₆	—	4	2	no	—
815	SD₁₆	—	4	4	no	—
816	SD₁₆	—	4	2	no	—
817	SD₁₆	—	4	2	no	—
818	SD₁₆	—	4	4	no	—
819	D₈	—	4	4	no	—
820	D₈	—	4	4	no	—
821	D₈	—	4	4	no	—
822	D₈	—	4	2	no	—
823	D₈	—	4	4	no	—
824	M₁₆	—	2	4	no	—
825	C₂×C₈	—	2	4	no	—
826	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
827	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
828	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
837	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
838	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
839	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
840	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
841	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
842	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
843	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
844	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
845	C₂²⋊C₄	—	2	1	no	—
846	C₂²⋊C₄	—	2	1	no	—
847	C₂²⋊C₄	—	2	1	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	1	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	1	no	—
861	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
862	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
863	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
864	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	1	no	—
867	C₄²	C₂×D₄×C₅₃	1	2	yes	—
868	C₄²	C₂×D₄×C₅₃	1	2	yes	—
869	C₄²	C₂⁴×C₅₃	1	2	yes	—
870	C₄²	C₂⁴×C₅₃	1	2	yes	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	4	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	4	1	no	—
878	C₂³	—	4	2	no	—
879	C₂³	—	4	4	no	—
880	C₂³	—	4	4	no	—
881	C₂³	—	4	2	no	—
882	C₂³	—	4	4	no	—
883	C₂³	—	4	4	no	—
884	C₂³	—	4	2	no	—
885	C₂³	—	4	4	no	—
886	C₂³	—	4	2	no	—
887	C₂³	—	8	2	no	—
888	C₂³	—	8	2	no	—
889	C₂³	—	8	2	no	—
890	C₂³	—	8	2	no	—
891	C₂³	—	8	1	no	—
892	C₂³	—	8	1	no	—
893	C₂³	—	8	16	no	—
894	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
895	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
896	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
897	Q₈	—	2	2	no	—
898	Q₈	—	2	2	no	—
899	Q₈	—	2	2	no	—
900	Q₈	—	4	2	no	—
901	Q₈	—	8	2	no	—
902	D₄	—	2	4	no	—
903	D₄	—	2	2	no	—
904	D₄	—	2	4	no	—
905	D₄	—	2	2	no	—
906	D₄	—	2	4	no	—
907	D₄	—	2	2	no	—
908	D₄	—	4	4	no	—
909	D₄	—	4	4	no	—
910	D₄	—	4	2	no	—
911	D₄	—	4	4	no	—
912	D₄	—	4	4	no	—
913	D₄	—	4	2	no	—
914	D₄	—	4	4	no	—
915	D₄	—	4	2	no	—
916	D₄	—	4	2	no	—
917	D₄	—	4	4	no	—
918	D₄	—	8	2	no	—
919	D₄	—	8	4	no	—
920	D₄	—	8	4	no	—
921	D₄	—	8	4	no	—
922	D₄	—	8	4	no	—
923	D₄	—	8	2	no	—
924	D₄	—	8	1	no	—
925	D₄	—	8	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	4	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	4	2	no	—
938	C₂×C₄	—	4	4	no	—
939	C₂×C₄	—	4	2	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	4	2	no	—
942	C₂×C₄	—	8	2	no	—
943	C₂×C₄	—	8	2	no	—
944	C₂×C₄	—	8	2	no	—
945	C₂×C₄	—	8	1	no	—
946	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
947	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
948	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
949	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
950	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
951	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
952	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
953	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
954	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
955	C₈	—	2	2	no	—
956	C₈	—	2	2	no	—
957	C₈	—	2	4	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	1	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	1	no	—
965	C₂²	—	4	4	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	4	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	1	no	—
973	C₂²	—	4	4	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	4	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	8	8	no	—
979	C₂²	—	8	4	no	—
980	C₂²	—	8	8	no	—
981	C₂²	—	8	8	no	—
982	C₂²	—	16	2	no	—
983	C₂²	C₅₃×#535	1	2	yes	—
984	C₂²	C₅₃×#576	1	2	yes	—
985	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
986	C₄	—	2	2	no	—
987	C₄	—	2	2	no	—
988	C₄	—	2	2	no	—
989	C₄	—	2	2	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	1	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	1	no	—
997	C₄	C₅₃×#535	1	2	yes	—
998	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
999	C₂	—	2	2	no	—
1000	C₂	—	2	2	no	—
1001	C₂	—	4	1	no	—
1002	C₂	—	8	4	no	—
1003	C₂	—	8	2	no	—
1004	C₂	—	8	2	no	—
1005	C₂	—	8	1	no	—
1006	C₂	C₂×C₅₃×#535	1	1	yes	characteristic
1007	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1008	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×#117×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3494	C₂	semidirect
2. C₂×C₅₃×#535	C₂	semidirect
3. C₅₃×#3224	C₂	semidirect
4. C₅₃×#3220	C₂	semidirect
5. C₅₃×#3217	C₂	semidirect
6. C₅₃×#3213	C₂	semidirect
7. C₅₃×#3211	C₂	semidirect
8. C₅₃×#3205	C₂	semidirect
9. C₅₃×#3155	C₂	semidirect
10. C₅₃×#3136	C₂	semidirect
11. C₅₃×#3045	C₂	semidirect
12. C₅₃×#3041	C₂	semidirect
13. C₅₃×#3006	C₂	semidirect
14. C₅₃×#3003	C₂	semidirect
15. C₅₃×#3002	C₂	semidirect
16. C₂×C₅₃×#447	C₂	semidirect
17. C₅₃×#2924	C₂	semidirect
20. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
21. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
22. C₂×#135×C₅₃	C₂²	semidirect
23. C₂²×D₈×C₅₃	C₂²	semidirect
30. C₅₃×#544	C₂²	semidirect
31. C₅₃×#542	C₂²	semidirect
32. C₅₃×#540	C₂²	semidirect
38. C₅₃×#535	C₂²	semidirect
39. C₅₃×#535	C₂²	semidirect
40. C₅₃×#532	C₂²	semidirect
41. C₂×#127×C₅₃	C₂²	semidirect
42. C₅₃×#529	C₂²	semidirect
43. C₂×#124×C₅₃	C₂²	semidirect
49. C₅₃×#520	C₂²	semidirect
50. C₅₃×#518	C₂²	semidirect
52. C₅₃×#496	C₂²	semidirect
53. C₅₃×#496	C₂²	semidirect
54. C₅₃×#495	C₂²	semidirect
55. C₅₃×#493	C₂²	semidirect
56. C₅₃×#490	C₂²	semidirect
57. C₅₃×#489	C₂²	semidirect
58. C₅₃×#488	C₂²	semidirect
59. C₅₃×#486	C₂²	semidirect
60. C₅₃×#464	C₂²	semidirect
61. C₅₃×#463	C₂²	semidirect
62. C₅₃×#463	C₂²	semidirect
63. C₅₃×#463	C₂²	semidirect
64. C₅₃×#460	C₂²	semidirect
65. C₅₃×#459	C₂²	semidirect
66. C₅₃×#459	C₂²	semidirect
67. C₅₃×#459	C₂²	semidirect
68. C₅₃×#452	C₂²	semidirect
69. C₅₃×#451	C₂²	semidirect
70. C₅₃×#450	C₂²	semidirect
71. C₅₃×#450	C₂²	semidirect
72. C₅₃×#450	C₂²	semidirect
73. C₅₃×#449	C₂²	semidirect
74. C₅₃×#449	C₂²	semidirect
75. C₅₃×#448	C₂²	semidirect
76. C₅₃×#448	C₂²	semidirect
79. C₅₃×#447	C₂²	semidirect
80. C₅₃×#447	C₂²	semidirect
81. C₅₃×#447	C₂²	semidirect
82. C₅₃×#447	C₂²	semidirect
83. C₅₃×#447	C₂²	semidirect
84. C₅₃×#433	C₂²	semidirect
85. C₅₃×#432	C₂²	semidirect
86. C₅₃×#431	C₂²	semidirect
87. C₅₃×#424	C₂²	semidirect
88. C₅₃×#418	C₂²	semidirect
89. C₅₃×#417	C₂²	semidirect
90. C₅₃×#416	C₂²	semidirect
91. C₂×#102×C₅₃	C₂²	semidirect
94. C₅₃×#405	C₂²	semidirect
122. C₂×Q₁₆×C₅₃	C₂³	semidirect
124. C₂×SD₁₆×C₅₃	C₂³	semidirect
125. C₂×SD₁₆×C₅₃	C₂³	semidirect
126. C₂×SD₁₆×C₅₃	C₂³	semidirect
131. C₂×D₈×C₅₃	C₂³	semidirect
132. C₂×D₈×C₅₃	C₂³	semidirect
136. C₄⋊Q₈×C₅₃	C₂³	semidirect
141. #127×C₅₃	C₂³	semidirect
145. #125×C₅₃	C₂³	semidirect
152. #124×C₅₃	C₂³	semidirect
185. C₄×Q₈×C₅₃	C₂³	semidirect
193. C₄×D₄×C₅₃	C₂³	semidirect
194. C₄×D₄×C₅₃	C₂³	semidirect
195. C₄×D₄×C₅₃	C₂³	semidirect
215. C₄⋊C₈×C₅₃	C₂³	semidirect
216. C₄⋊C₈×C₅₃	C₂³	semidirect
217. #103×C₅₃	C₂³	semidirect
218. #103×C₅₃	C₂³	semidirect
219. #103×C₅₃	C₂³	semidirect
224. #102×C₅₃	C₂³	semidirect
225. #102×C₅₃	C₂³	semidirect
226. #102×C₅₃	C₂³	semidirect
232. #97×C₅₃	C₂³	semidirect
233. C₄×C₈×C₅₃	C₂³	semidirect
453. #60811	C₅₃	direct (N × H)
495. #3494	C₂×C₅₃	semidirect
496. C₂×#535	C₂×C₅₃	semidirect
497. #3224	C₂×C₅₃	semidirect
498. #3220	C₂×C₅₃	semidirect
499. #3217	C₂×C₅₃	semidirect
500. #3213	C₂×C₅₃	semidirect
501. #3211	C₂×C₅₃	semidirect
502. #3205	C₂×C₅₃	semidirect
503. #3155	C₂×C₅₃	semidirect
504. #3136	C₂×C₅₃	semidirect
505. #3045	C₂×C₅₃	semidirect
506. #3041	C₂×C₅₃	semidirect
507. #3006	C₂×C₅₃	semidirect
508. #3003	C₂×C₅₃	semidirect
509. #3002	C₂×C₅₃	semidirect
510. C₂×#447	C₂×C₅₃	semidirect
511. #2924	C₂×C₅₃	semidirect
524. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
525. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
526. C₂×#135	C₂²×C₅₃	semidirect
527. C₂²×D₈	C₂²×C₅₃	semidirect
534. #544	C₂²×C₅₃	semidirect
535. #542	C₂²×C₅₃	semidirect
536. #540	C₂²×C₅₃	semidirect
542. #535	C₂²×C₅₃	semidirect
543. #535	C₂²×C₅₃	semidirect
544. #532	C₂²×C₅₃	semidirect
545. C₂×#127	C₂²×C₅₃	semidirect
546. #529	C₂²×C₅₃	semidirect
547. C₂×#124	C₂²×C₅₃	semidirect
553. #520	C₂²×C₅₃	semidirect
554. #518	C₂²×C₅₃	semidirect
556. #496	C₂²×C₅₃	semidirect
557. #496	C₂²×C₅₃	semidirect
558. #495	C₂²×C₅₃	semidirect
559. #493	C₂²×C₅₃	semidirect
560. #490	C₂²×C₅₃	semidirect
561. #489	C₂²×C₅₃	semidirect
562. #488	C₂²×C₅₃	semidirect
563. #486	C₂²×C₅₃	semidirect
564. #464	C₂²×C₅₃	semidirect
565. #463	C₂²×C₅₃	semidirect
566. #463	C₂²×C₅₃	semidirect
567. #463	C₂²×C₅₃	semidirect
568. #460	C₂²×C₅₃	semidirect
569. #459	C₂²×C₅₃	semidirect
570. #459	C₂²×C₅₃	semidirect
571. #459	C₂²×C₅₃	semidirect
572. #452	C₂²×C₅₃	semidirect
573. #451	C₂²×C₅₃	semidirect
574. #450	C₂²×C₅₃	semidirect
575. #450	C₂²×C₅₃	semidirect
576. #450	C₂²×C₅₃	semidirect
577. #449	C₂²×C₅₃	semidirect
578. #449	C₂²×C₅₃	semidirect
579. #448	C₂²×C₅₃	semidirect
580. #448	C₂²×C₅₃	semidirect
583. #447	C₂²×C₅₃	semidirect
584. #447	C₂²×C₅₃	semidirect
585. #447	C₂²×C₅₃	semidirect
586. #447	C₂²×C₅₃	semidirect
587. #447	C₂²×C₅₃	semidirect
588. #433	C₂²×C₅₃	semidirect
589. #432	C₂²×C₅₃	semidirect
590. #431	C₂²×C₅₃	semidirect
591. #424	C₂²×C₅₃	semidirect
592. #418	C₂²×C₅₃	semidirect
593. #417	C₂²×C₅₃	semidirect
594. #416	C₂²×C₅₃	semidirect
595. C₂×#102	C₂²×C₅₃	semidirect
598. #405	C₂²×C₅₃	semidirect
599. C₅₃	#60811	direct (N × H)
627. C₂×Q₁₆	C₂³×C₅₃	semidirect
629. C₂×SD₁₆	C₂³×C₅₃	semidirect
630. C₂×SD₁₆	C₂³×C₅₃	semidirect
631. C₂×SD₁₆	C₂³×C₅₃	semidirect
636. C₂×D₈	C₂³×C₅₃	semidirect
637. C₂×D₈	C₂³×C₅₃	semidirect
641. C₄⋊Q₈	C₂³×C₅₃	semidirect
646. #127	C₂³×C₅₃	semidirect
650. #125	C₂³×C₅₃	semidirect
657. #124	C₂³×C₅₃	semidirect
690. C₄×Q₈	C₂³×C₅₃	semidirect
698. C₄×D₄	C₂³×C₅₃	semidirect
699. C₄×D₄	C₂³×C₅₃	semidirect
700. C₄×D₄	C₂³×C₅₃	semidirect
720. C₄⋊C₈	C₂³×C₅₃	semidirect
721. C₄⋊C₈	C₂³×C₅₃	semidirect
722. #103	C₂³×C₅₃	semidirect
723. #103	C₂³×C₅₃	semidirect
724. #103	C₂³×C₅₃	semidirect
729. #102	C₂³×C₅₃	semidirect
730. #102	C₂³×C₅₃	semidirect
731. #102	C₂³×C₅₃	semidirect
737. #97	C₂³×C₅₃	semidirect
738. C₄×C₈	C₂³×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3494	2
C₂×C₅₃×#535	2
C₅₃×#3224	2
C₅₃×#3220	2
C₅₃×#3217	2
C₅₃×#3213	2
C₅₃×#3211	2
C₅₃×#3205	2
C₅₃×#3155	2
C₅₃×#3136	2
C₅₃×#3045	2
C₅₃×#3041	2
C₅₃×#3006	2
C₅₃×#3003	2
C₅₃×#3002	2
C₂×C₅₃×#447	2
C₅₃×#2924	2
#60811	53

Subgroups — C53×#60811 #27268323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60811 #27268323