Subgroups — D₅₃×#3584 #28297919

Order 13568.

10858 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#585×D₅₃	C₂	1	2	yes	maximal, complemented
2	#20289489	C₂	1	1	yes	maximal, characteristic, complemented
3	#20289488	C₂	1	6	yes	maximal, complemented
4	#20289487	C₂	1	8	yes	maximal, complemented
5	#20289486	C₂	1	2	yes	maximal, complemented
6	#20289485	C₂	1	4	yes	maximal, complemented
7	#20289484	C₂	1	6	yes	maximal, complemented
8	#20289483	C₂	1	4	yes	maximal, complemented
9	#578×D₅₃	C₂	1	4	yes	maximal, complemented
10	#577×D₅₃	C₂	1	8	yes	maximal, complemented
11	#576×D₅₃	C₂	1	4	yes	maximal, complemented
12	#575×D₅₃	C₂	1	6	yes	maximal, complemented
13	C₂×#135×D₅₃	C₂	1	6	yes	maximal, complemented
14	C₂×#131×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3584	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811460	—	2	2	no	—
17	#16811460	C₂²	1	8	yes	complemented
18	#16811459	—	2	8	no	—
19	#16811459	C₂²	1	2	yes	complemented
20	#16811459	C₂²	1	12	yes	complemented
21	#16811458	—	2	6	no	—
22	#16811458	C₂²	1	8	yes	complemented
23	2₋¹⁺⁴×D₅₃	—	2	2	no	—
24	2₋¹⁺⁴×D₅₃	C₂²	1	8	yes	complemented
25	H(5,𝔽₂)×D₅₃	—	2	6	no	—
26	H(5,𝔽₂)×D₅₃	C₂²	1	8	yes	complemented
27	C₂×#41×D₅₃	—	2	8	no	—
28	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
29	C₂×#41×D₅₃	C₂²	1	12	yes	complemented
30	#16811440	C₂²	1	4	yes	complemented
31	#16811439	C₂²	1	24	yes	complemented
32	#16811438	C₂²	1	8	yes	complemented
33	#16811437	C₂²	1	12	yes	complemented
34	#16811436	C₂²	1	12	yes	complemented
35	#16811435	C₂²	1	8	yes	complemented
36	#16811434	C₂²	1	8	yes	complemented
37	#16811433	C₂²	1	24	yes	complemented
38	#16811432	C₂²	1	24	yes	complemented
39	#16811431	C₂²	1	8	yes	complemented
40	#16811430	C₂²	1	24	yes	complemented
41	#16811429	C₂²	1	24	yes	complemented
42	#16811428	C₂²	1	4	yes	complemented
43	#16811427	C₂²	1	24	yes	complemented
44	#16811426	C₂²	1	8	yes	complemented
45	#16811425	C₂²	1	12	yes	complemented
46	#16811424	C₂²	1	12	yes	complemented
47	#16811423	C₂²	1	6	yes	complemented
48	#16811422	C₂²	1	24	yes	complemented
49	#16811421	C₂²	1	12	yes	complemented
50	#16811420	C₂²	1	24	yes	complemented
51	#16811419	C₂²	1	24	yes	complemented
52	#137×D₅₃	C₂²	1	24	yes	complemented
53	AGL(1,ℤ/8)×D₅₃	C₂²	1	24	yes	complemented
54	C₂×#13133240	C₂²	1	6	yes	complemented
55	C₂×#13133239	C₂²	1	6	yes	complemented
56	C₂×#13133238	C₂²	1	12	yes	complemented
57	C₂×#13133237	C₂²	1	12	yes	complemented
58	C₂×#13133236	C₂²	1	6	yes	complemented
59	#135×D₅₃	C₂²	1	4	yes	complemented
60	#135×D₅₃	C₂²	1	12	yes	complemented
61	#135×D₅₃	C₂²	1	12	yes	complemented
62	#135×D₅₃	C₂²	1	12	yes	complemented
63	#135×D₅₃	C₂²	1	12	yes	complemented
64	#135×D₅₃	C₂²	1	12	yes	complemented
65	#135×D₅₃	C₂²	1	12	yes	complemented
66	#135×D₅₃	C₂²	1	12	yes	complemented
67	C₂×Q₁₆×D₅₃	C₂²	1	6	yes	complemented
68	C₂×SD₁₆×D₅₃	C₂²	1	12	yes	complemented
69	C₂×D₈×D₅₃	C₂²	1	6	yes	complemented
70	C₂×#13133225	C₂²	1	3	yes	complemented
71	C₂×#13133224	C₂²	1	1	yes	characteristic, complemented
72	C₂×#13133223	C₂²	1	3	yes	complemented
73	#131×D₅₃	C₂²	1	4	yes	complemented
74	#131×D₅₃	C₂²	1	4	yes	complemented
75	#131×D₅₃	C₂²	1	4	yes	complemented
76	#131×D₅₃	C₂²	1	4	yes	complemented
77	C₂×M₁₆×D₅₃	C₂²	1	3	yes	complemented
78	C₂²×C₈×D₅₃	C₂²	1	3	yes	complemented
79	C₅₃×#585	C₂²	1	2	yes	complemented
80	C₅₃×#578	C₂²	1	4	yes	complemented
81	C₅₃×#577	C₂²	1	8	yes	complemented
82	C₅₃×#576	C₂²	1	4	yes	complemented
83	C₅₃×#575	C₂²	1	6	yes	complemented
84	C₂×#135×C₅₃	C₂²	1	6	yes	complemented
85	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic, complemented
86	#13133265	—	2	2	no	—
87	#13133265	—	2	8	no	—
88	#13133265	—	2	8	no	—
89	#13133265	C₂³	1	24	yes	complemented
90	#13133264	—	2	8	no	—
91	#13133264	—	2	24	no	—
92	#13133264	—	2	12	no	—
93	#13133264	C₂³	1	24	yes	complemented
94	#13133264	C₂³	1	8	yes	complemented
95	#13133263	—	2	8	no	—
96	#13133263	—	2	24	no	—
97	#13133263	—	2	12	no	—
98	#13133263	C₂³	1	24	yes	complemented
99	#13133263	C₂³	1	8	yes	complemented
100	#13133262	—	2	6	no	—
101	#13133262	—	2	24	no	—
102	#13133262	—	2	24	no	—
103	#13133262	—	2	24	no	—
104	#13133262	C₂³	1	24	yes	complemented
105	C₂×#11719949	—	2	8	no	—
106	C₂×#11719949	D₄	1	1	yes	characteristic
107	C₂×#11719949	C₂³	1	12	yes	complemented
108	C₂×#11719945	—	2	24	no	—
109	C₂×#11719945	—	2	12	no	—
110	C₂×#11719945	C₂³	1	3	yes	—
111	C₂×#11719945	C₂³	1	12	yes	complemented
112	C₂×#11719947	—	2	12	no	—
113	C₂×#11719947	—	2	24	no	—
114	C₂×#11719947	D₄	1	3	yes	—
115	C₂×#11719947	C₂³	1	12	yes	complemented
116	#41×D₅₃	—	2	8	no	—
117	#41×D₅₃	—	2	8	no	—
118	#41×D₅₃	—	2	8	no	—
119	#41×D₅₃	—	2	24	no	—
120	#41×D₅₃	—	2	24	no	—
121	#41×D₅₃	—	2	24	no	—
122	#41×D₅₃	—	2	12	no	—
123	#41×D₅₃	—	2	12	no	—
124	#41×D₅₃	—	2	12	no	—
125	#41×D₅₃	—	2	12	no	—
126	#41×D₅₃	D₄	1	4	yes	—
127	#41×D₅₃	D₄	1	4	yes	—
128	#41×D₅₃	C₂³	1	8	yes	—
129	#41×D₅₃	C₂³	1	24	yes	—
130	#41×D₅₃	C₂³	1	4	yes	—
131	#41×D₅₃	C₂³	1	4	yes	—
132	#41×D₅₃	C₂³	1	24	yes	complemented
133	#41×D₅₃	C₂³	1	24	yes	complemented
134	C₂×Q₈×D₅₃	—	2	8	no	—
135	C₂×Q₈×D₅₃	D₄	1	1	yes	characteristic
136	C₂×Q₈×D₅₃	C₂³	1	12	yes	—
137	C₂×D₄×D₅₃	—	2	12	no	—
138	C₂×D₄×D₅₃	—	2	24	no	—
139	C₂×D₄×D₅₃	D₄	1	3	yes	—
140	C₂×D₄×D₅₃	C₂³	1	12	yes	—
141	C₂²×C₄×D₅₃	—	2	12	no	—
142	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
143	#13133250	C₂³	1	24	yes	complemented
144	#13133249	C₂³	1	48	yes	complemented
145	#13133248	C₂³	1	24	yes	complemented
146	#13133247	C₂³	1	24	yes	complemented
147	#13133246	C₂³	1	48	yes	complemented
148	#13133245	C₂³	1	24	yes	complemented
149	#13133244	C₂³	1	48	yes	complemented
150	#13133243	C₂³	1	24	yes	complemented
151	#13133242	C₂³	1	24	yes	complemented
152	#13133241	C₂³	1	48	yes	complemented
153	#13133240	C₂³	1	4	yes	complemented
154	#13133240	C₂³	1	12	yes	complemented
155	#13133240	C₂³	1	12	yes	complemented
156	#13133240	C₂³	1	12	yes	complemented
157	#13133239	C₂³	1	4	yes	complemented
158	#13133239	C₂³	1	12	yes	complemented
159	#13133239	C₂³	1	12	yes	complemented
160	#13133239	C₂³	1	12	yes	complemented
161	#13133238	C₂³	1	8	yes	complemented
162	#13133238	C₂³	1	24	yes	complemented
163	#13133238	C₂³	1	24	yes	complemented
164	#13133238	C₂³	1	24	yes	complemented
165	#13133237	C₂³	1	8	yes	complemented
166	#13133237	C₂³	1	24	yes	complemented
167	#13133237	C₂³	1	24	yes	complemented
168	#13133237	C₂³	1	24	yes	complemented
169	#13133236	C₂³	1	4	yes	complemented
170	#13133236	C₂³	1	12	yes	complemented
171	#13133236	C₂³	1	12	yes	complemented
172	#13133236	C₂³	1	12	yes	complemented
173	C₂×Dic₂₁₂	C₂³	1	6	yes	complemented
174	C₂×#11719925	C₂³	1	12	yes	complemented
175	Q₁₆×D₅₃	C₂³	1	4	yes	—
176	Q₁₆×D₅₃	C₂³	1	12	yes	—
177	Q₁₆×D₅₃	C₂³	1	12	yes	complemented
178	Q₁₆×D₅₃	C₂³	1	12	yes	complemented
179	C₂×#11719913	C₂³	1	12	yes	complemented
180	C₂×#11719923	C₂³	1	12	yes	complemented
181	C₂×#11719924	C₂³	1	12	yes	complemented
182	SD₁₆×D₅₃	C₂³	1	8	yes	—
183	SD₁₆×D₅₃	C₂³	1	24	yes	—
184	SD₁₆×D₅₃	C₂³	1	24	yes	complemented
185	SD₁₆×D₅₃	C₂³	1	24	yes	complemented
186	C₂×D₄₂₄	C₂³	1	6	yes	complemented
187	C₂×#11719922	C₂³	1	12	yes	complemented
188	D₈×D₅₃	C₂³	1	4	yes	—
189	D₈×D₅₃	C₂³	1	12	yes	—
190	D₈×D₅₃	C₂³	1	12	yes	complemented
191	D₈×D₅₃	C₂³	1	12	yes	complemented
192	#13133225	C₂³	1	12	yes	complemented
193	#13133225	C₂³	1	12	yes	complemented
194	#13133224	C₂³	1	4	yes	complemented
195	#13133224	C₂³	1	4	yes	complemented
196	#13133223	C₂³	1	12	yes	complemented
197	#13133223	C₂³	1	12	yes	complemented
198	C₂×#11719917	C₂³	1	3	yes	complemented
199	C₂×#11719912	C₂³	1	6	yes	complemented
200	M₁₆×D₅₃	C₂³	1	12	yes	—
201	M₁₆×D₅₃	C₂³	1	12	yes	complemented
202	C₂²×#88322	C₂³	1	3	yes	complemented
203	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₈×D₅₃	C₂³	1	3	yes	—
205	C₂×C₈×D₅₃	C₂³	1	6	yes	—
206	C₂×C₈×D₅₃	C₂³	1	6	yes	—
207	C₂×C₈×D₅₃	C₂³	1	6	yes	complemented
208	C₂×C₈×D₅₃	C₂³	1	6	yes	complemented
209	C₂×C₈×D₅₃	C₂³	1	3	yes	complemented
210	C₂×C₈×D₅₃	C₂³	1	3	yes	complemented
211	2₋¹⁺⁴×C₅₃	—	2	2	no	—
212	2₋¹⁺⁴×C₅₃	C₂³	1	8	yes	complemented
213	H(5,𝔽₂)×C₅₃	—	2	6	no	—
214	H(5,𝔽₂)×C₅₃	C₂³	1	8	yes	complemented
215	C₂×#41×C₅₃	—	2	8	no	—
216	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×#41×C₅₃	C₂³	1	12	yes	complemented
218	#137×C₅₃	C₂³	1	24	yes	complemented
219	AGL(1,ℤ/8)×C₅₃	C₂³	1	24	yes	complemented
220	#135×C₅₃	C₂³	1	4	yes	complemented
221	#135×C₅₃	C₂³	1	12	yes	complemented
222	#135×C₅₃	C₂³	1	12	yes	complemented
223	#135×C₅₃	C₂³	1	12	yes	complemented
224	C₂×Q₁₆×C₅₃	C₂³	1	6	yes	complemented
225	C₂×SD₁₆×C₅₃	C₂³	1	12	yes	complemented
226	C₂×D₈×C₅₃	C₂³	1	6	yes	complemented
227	#131×C₅₃	C₂³	1	4	yes	complemented
228	#131×C₅₃	C₂³	1	4	yes	complemented
229	C₂×M₁₆×C₅₃	C₂³	1	3	yes	complemented
230	C₂²×C₈×C₅₃	C₂³	1	3	yes	complemented
231	C₂³×D₅₃	—	2	12	no	—
232	C₂³×D₅₃	C₂×D₄	1	3	yes	—
233	#41×C₅₃	—	2	8	no	—
234	#41×C₅₃	—	2	24	no	—
235	#41×C₅₃	—	2	12	no	—
236	#41×C₅₃	—	2	12	no	—
237	#41×C₅₃	C₂×D₄	1	4	yes	—
238	#41×C₅₃	C₂⁴	1	8	yes	—
239	#41×C₅₃	C₂⁴	1	24	yes	—
240	#41×C₅₃	C₂⁴	1	4	yes	—
241	C₂×Q₈×C₅₃	—	2	8	no	—
242	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₅₃	C₂⁴	1	12	yes	—
244	C₂×D₄×C₅₃	—	2	12	no	—
245	C₂×D₄×C₅₃	—	2	24	no	—
246	C₂×D₄×C₅₃	C₂×D₄	1	3	yes	—
247	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
248	C₂²×C₄×C₅₃	—	2	12	no	—
249	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
250	C₂×C₂²⋊D₅₃	—	2	12	no	—
251	C₂×C₂²⋊D₅₃	—	2	12	no	—
252	C₂×C₂²⋊D₅₃	—	2	48	no	—
253	C₂×C₂²⋊D₅₃	—	2	12	no	—
254	C₂×C₂²⋊D₅₃	C₂×D₄	1	6	yes	—
255	C₂²×Dic₅₃	—	2	12	no	—
256	C₂²×Dic₅₃	C₂×D₄	1	3	yes	—
257	#11719949	—	2	8	no	—
258	#11719949	—	2	24	no	—
259	#11719949	—	2	12	no	—
260	#11719949	—	2	12	no	—
261	#11719949	C₂×D₄	1	4	yes	—
262	#11719949	C₂×D₄	1	4	yes	—
263	#11719949	C₂⁴	1	8	yes	—
264	#11719949	C₂⁴	1	24	yes	—
265	Q₈×D₅₃	—	2	8	no	—
266	Q₈×D₅₃	—	2	12	no	—
267	Q₈×D₅₃	—	2	12	no	—
268	Q₈×D₅₃	—	2	24	no	—
269	Q₈×D₅₃	C₂×D₄	1	4	yes	—
270	Q₈×D₅₃	C₂×D₄	1	4	yes	—
271	Q₈×D₅₃	C₂⁴	1	8	yes	—
272	Q₈×D₅₃	C₂⁴	1	24	yes	—
273	#11719947	—	2	24	no	—
274	#11719947	—	2	48	no	—
275	#11719947	—	2	8	no	—
276	#11719947	—	2	24	no	—
277	#11719947	—	2	24	no	—
278	#11719947	—	2	24	no	—
279	#11719947	—	2	12	no	—
280	#11719947	—	2	12	no	—
281	#11719947	—	2	24	no	—
282	#11719947	C₂×D₄	1	12	yes	—
283	#11719947	C₂×D₄	1	12	yes	—
284	#11719947	C₂⁴	1	8	yes	—
285	#11719947	C₂⁴	1	24	yes	—
286	D₄×D₅₃	—	2	24	no	—
287	D₄×D₅₃	—	2	8	no	—
288	D₄×D₅₃	—	2	24	no	—
289	D₄×D₅₃	—	2	24	no	—
290	D₄×D₅₃	—	2	24	no	—
291	D₄×D₅₃	—	2	48	no	—
292	D₄×D₅₃	—	2	24	no	—
293	D₄×D₅₃	—	2	12	no	—
294	D₄×D₅₃	—	2	12	no	—
295	D₄×D₅₃	C₂×D₄	1	12	yes	—
296	D₄×D₅₃	C₂×D₄	1	12	yes	—
297	D₄×D₅₃	C₂⁴	1	8	yes	—
298	D₄×D₅₃	C₂⁴	1	24	yes	—
299	#11719945	—	2	12	no	—
300	#11719945	—	2	12	no	—
301	#11719945	—	2	48	no	—
302	#11719945	—	2	24	no	—
303	#11719945	—	2	8	no	—
304	#11719945	—	2	24	no	—
305	#11719945	—	2	24	no	—
306	#11719945	—	2	24	no	—
307	#11719945	—	2	24	no	—
308	#11719945	C₂×D₄	1	12	yes	—
309	#11719945	C₂⁴	1	12	yes	—
310	#11719945	C₂⁴	1	8	yes	—
311	#11719945	C₂⁴	1	24	yes	—
312	C₂×D₂₁₂	—	2	12	no	—
313	C₂×D₂₁₂	—	2	24	no	—
314	C₂×D₂₁₂	C₂×D₄	1	3	yes	—
315	C₂×D₂₁₂	C₂⁴	1	12	yes	—
316	C₂×C₄×D₅₃	—	2	12	no	—
317	C₂×C₄×D₅₃	—	2	12	no	—
318	C₂×C₄×D₅₃	—	2	12	no	—
319	C₂×C₄×D₅₃	—	2	8	no	—
320	C₂×C₄×D₅₃	—	2	24	no	—
321	C₂×C₄×D₅₃	—	2	24	no	—
322	C₂×C₄×D₅₃	—	2	24	no	—
323	C₂×C₄×D₅₃	C₂×D₄	1	6	yes	—
324	C₂×C₄×D₅₃	C₂×D₄	1	3	yes	—
325	C₂×C₄×D₅₃	C₂×D₄	1	3	yes	—
326	C₂×C₄×D₅₃	C₂×D₄	1	6	yes	—
327	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
328	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
329	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
330	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
331	C₂×Dic₁₀₆	—	2	12	no	—
332	C₂×Dic₁₀₆	—	2	24	no	—
333	C₂×Dic₁₀₆	C₂×D₄	1	3	yes	—
334	C₂×Dic₁₀₆	C₂⁴	1	12	yes	—
335	Q₁₆×C₅₃	C₂⁴	1	4	yes	—
336	Q₁₆×C₅₃	C₂⁴	1	12	yes	—
337	SD₁₆×C₅₃	C₂⁴	1	8	yes	—
338	SD₁₆×C₅₃	C₂⁴	1	24	yes	—
339	D₈×C₅₃	C₂⁴	1	4	yes	—
340	D₈×C₅₃	C₂⁴	1	12	yes	—
341	M₁₆×C₅₃	C₂⁴	1	12	yes	—
342	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
343	C₂×C₈×C₅₃	C₂⁴	1	3	yes	—
344	C₂×C₈×C₅₃	C₂⁴	1	6	yes	—
345	C₂×C₈×C₅₃	C₂⁴	1	6	yes	—
346	#11719925	C₂⁴	1	8	yes	—
347	#11719925	C₂⁴	1	24	yes	—
348	#11719924	C₂⁴	1	8	yes	—
349	#11719924	C₂⁴	1	24	yes	—
350	#11719923	C₂⁴	1	8	yes	—
351	#11719923	C₂⁴	1	24	yes	—
352	#11719922	C₂⁴	1	8	yes	—
353	#11719922	C₂⁴	1	24	yes	—
354	#11719917	C₂⁴	1	12	yes	—
355	C₂×#88322	C₂⁴	1	1	yes	characteristic
356	C₂×#88322	C₂⁴	1	3	yes	—
357	C₂×#88322	C₂⁴	1	6	yes	—
358	C₂×#88322	C₂⁴	1	6	yes	—
359	Dic₂₁₂	C₂⁴	1	4	yes	—
360	Dic₂₁₂	C₂⁴	1	12	yes	—
361	D₄₂₄	C₂⁴	1	4	yes	—
362	D₄₂₄	C₂⁴	1	12	yes	—
363	#11719913	C₂⁴	1	8	yes	—
364	#11719913	C₂⁴	1	24	yes	—
365	#11719912	C₂⁴	1	24	yes	—
366	C₈×D₅₃	C₂⁴	1	1	yes	characteristic
367	C₈×D₅₃	C₂⁴	1	1	yes	characteristic
368	C₈×D₅₃	C₂⁴	1	6	yes	—
369	C₈×D₅₃	C₂⁴	1	1	yes	characteristic
370	C₈×D₅₃	C₂⁴	1	1	yes	characteristic
371	C₈×D₅₃	C₂⁴	1	6	yes	—
372	C₈×D₅₃	C₂⁴	1	6	yes	—
373	C₈×D₅₃	C₂⁴	1	6	yes	—
374	C₈×D₅₃	C₂⁴	1	6	yes	—
375	C₈×D₅₃	C₂⁴	1	6	yes	—
376	C₂³×C₅₃	—	2	12	no	—
377	C₂³×C₅₃	C₂²×D₄	1	3	yes	—
378	C₂²×D₅₃	—	2	12	no	—
379	C₂²×D₅₃	—	2	8	no	—
380	C₂²×D₅₃	—	2	24	no	—
381	C₂²×D₅₃	—	4	6	no	—
382	C₂²×D₅₃	—	8	24	no	—
383	C₂²×D₅₃	C₂²×D₄	1	6	yes	—
384	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
385	C₂²×D₅₃	C₂²×D₄	1	6	yes	—
386	C₂²×D₅₃	C₂²×D₄	1	3	yes	—
387	Q₈×C₅₃	—	2	12	no	—
388	Q₈×C₅₃	C₂²×D₄	1	4	yes	—
389	Q₈×C₅₃	C₂⁵	1	8	yes	—
390	D₄×C₅₃	—	2	24	no	—
391	D₄×C₅₃	—	2	8	no	—
392	D₄×C₅₃	—	2	12	no	—
393	D₄×C₅₃	C₂²×D₄	1	12	yes	—
394	D₄×C₅₃	C₂⁵	1	8	yes	—
395	C₂×C₄×C₅₃	—	2	12	no	—
396	C₂×C₄×C₅₃	—	2	24	no	—
397	C₂×C₄×C₅₃	—	2	8	no	—
398	C₂×C₄×C₅₃	C₂²×D₄	1	3	yes	—
399	C₂×C₄×C₅₃	C₂²×D₄	1	6	yes	—
400	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
401	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
402	C₂²⋊D₅₃	—	2	24	no	—
403	C₂²⋊D₅₃	—	2	8	no	—
404	C₂²⋊D₅₃	—	2	24	no	—
405	C₂²⋊D₅₃	—	2	8	no	—
406	C₂²⋊D₅₃	—	2	8	no	—
407	C₂²⋊D₅₃	—	2	24	no	—
408	C₂²⋊D₅₃	C₂²×D₄	1	24	yes	—
409	C₂×Dic₅₃	—	2	12	no	—
410	C₂×Dic₅₃	—	2	24	no	—
411	C₂×Dic₅₃	—	2	8	no	—
412	C₂×Dic₅₃	C₂²×D₄	1	6	yes	—
413	C₂×Dic₅₃	C₂²×D₄	1	3	yes	—
414	C₂×Dic₅₃	C₂²×D₄	1	6	yes	—
415	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
416	D₂₁₂	—	2	24	no	—
417	D₂₁₂	—	2	8	no	—
418	D₂₁₂	—	2	12	no	—
419	D₂₁₂	C₂²×D₄	1	12	yes	—
420	D₂₁₂	C₂⁵	1	8	yes	—
421	C₄×D₅₃	—	2	8	no	—
422	C₄×D₅₃	—	2	24	no	—
423	C₄×D₅₃	—	2	8	no	—
424	C₄×D₅₃	—	2	24	no	—
425	C₄×D₅₃	—	2	8	no	—
426	C₄×D₅₃	—	2	24	no	—
427	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
428	C₄×D₅₃	C₂²×D₄	1	6	yes	—
429	C₄×D₅₃	C₂²×D₄	1	6	yes	—
430	C₄×D₅₃	C₂²×D₄	1	6	yes	—
431	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
432	C₄×D₅₃	C₂²×D₄	1	6	yes	—
433	C₄×D₅₃	C₂²×D₄	1	6	yes	—
434	C₄×D₅₃	C₂⁵	1	1	yes	characteristic
435	C₄×D₅₃	C₂⁵	1	1	yes	characteristic
436	C₄×D₅₃	C₂⁵	1	6	yes	—
437	Dic₁₀₆	—	2	12	no	—
438	Dic₁₀₆	—	2	8	no	—
439	Dic₁₀₆	—	2	24	no	—
440	Dic₁₀₆	C₂²×D₄	1	12	yes	—
441	Dic₁₀₆	C₂⁵	1	8	yes	—
442	C₈×C₅₃	C₂⁵	1	1	yes	characteristic
443	C₈×C₅₃	C₂⁵	1	1	yes	characteristic
444	C₈×C₅₃	C₂⁵	1	6	yes	—
445	#88322	C₂⁵	1	1	yes	characteristic
446	#88322	C₂⁵	1	1	yes	characteristic
447	#88322	C₂⁵	1	6	yes	—
448	C₂×#3584	—	53	1	no	maximal, Sylow
449	C₂²×C₅₃	—	2	8	no	—
450	C₂²×C₅₃	—	4	3	no	—
451	C₂²×C₅₃	—	8	12	no	—
452	C₂²×C₅₃	C₂³×D₄	1	6	yes	—
453	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
454	C₂×D₅₃	—	2	2	no	—
455	C₂×D₅₃	—	2	12	no	—
456	C₂×D₅₃	—	2	8	no	—
457	C₂×D₅₃	—	4	6	no	—
458	C₂×D₅₃	—	4	3	no	—
459	C₂×D₅₃	—	4	16	no	—
460	C₂×D₅₃	—	8	24	no	—
461	C₂×D₅₃	—	8	12	no	—
462	C₂×D₅₃	C₂³×D₄	1	6	yes	—
463	C₂×D₅₃	C₂³×D₄	1	1	yes	characteristic
464	C₂×D₅₃	C₂³×D₄	1	1	yes	characteristic
465	C₄×C₅₃	—	2	8	no	—
466	C₄×C₅₃	C₂³×D₄	1	6	yes	—
467	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
468	C₄×C₅₃	C₂⁶	1	1	yes	characteristic
469	Dic₅₃	—	2	8	no	—
470	Dic₅₃	C₂³×D₄	1	1	yes	characteristic
471	Dic₅₃	C₂³×D₄	1	6	yes	—
472	Dic₅₃	C₂³×D₄	1	1	yes	characteristic
473	C₂×#585	—	53	2	no	—
474	#3584	—	53	2	no	—
475	#3584	—	53	4	no	—
476	#3584	—	53	8	no	—
477	#3584	—	53	4	no	—
478	#3584	—	53	6	no	—
479	#3584	—	53	6	no	—
480	#3584	—	53	1	no	—
481	#3584	D₅₃	1	1	yes	characteristic, direct product factor
482	C₂×#578	—	53	4	no	—
483	C₂×#577	—	53	8	no	—
484	C₂×#576	—	53	4	no	—
485	C₂×#575	—	53	6	no	—
486	C₂²×#135	—	53	6	no	—
487	C₂²×#131	—	53	1	no	—
488	C₂×C₅₃	—	2	1	no	—
489	C₂×C₅₃	—	2	6	no	—
490	C₂×C₅₃	—	4	8	no	—
491	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
492	D₅₃	—	2	1	no	—
493	D₅₃	—	2	6	no	—
494	D₅₃	—	4	8	no	—
495	D₅₃	#3584	1	2	yes	direct product factor
496	#585	—	53	8	no	—
497	#585	—	53	8	no	—
498	#585	—	53	2	no	—
499	#585	—	53	12	no	—
500	#585	—	106	8	no	—
501	#585	—	106	6	no	—
502	#585	—	106	2	no	—
503	#585	C₂×D₅₃	1	2	yes	complemented
504	C₂×2₋¹⁺⁴	—	53	8	no	—
505	C₂×2₋¹⁺⁴	—	106	2	no	—
506	C₂×H(5,𝔽₂)	—	53	8	no	—
507	C₂×H(5,𝔽₂)	—	106	6	no	—
508	C₂²×#41	—	53	1	no	—
509	C₂²×#41	—	53	12	no	—
510	C₂²×#41	—	106	8	no	—
511	#578	—	53	8	no	—
512	#578	—	53	24	no	—
513	#578	—	53	12	no	—
514	#578	—	53	12	no	—
515	#578	—	53	4	no	—
516	#578	C₂×D₅₃	1	4	yes	complemented
517	#577	—	53	8	no	—
518	#577	—	53	8	no	—
519	#577	—	53	24	no	—
520	#577	—	53	24	no	—
521	#577	—	53	24	no	—
522	#577	—	53	24	no	—
523	#577	—	53	8	no	—
524	#577	C₂×D₅₃	1	8	yes	complemented
525	#576	—	53	8	no	—
526	#576	—	53	24	no	—
527	#576	—	53	12	no	—
528	#576	—	53	12	no	—
529	#576	—	53	4	no	—
530	#576	C₂×D₅₃	1	4	yes	complemented
531	#575	—	53	12	no	—
532	#575	—	53	24	no	—
533	#575	—	53	24	no	—
534	#575	—	53	24	no	—
535	#575	—	53	6	no	—
536	#575	C₂×D₅₃	1	6	yes	complemented
537	C₂×#137	—	53	24	no	—
538	C₂×AGL(1,ℤ/8)	—	53	24	no	—
539	C₂×#135	—	53	12	no	—
540	C₂×#135	—	53	12	no	—
541	C₂×#135	—	53	12	no	—
542	C₂×#135	—	53	12	no	—
543	C₂×#135	—	53	12	no	—
544	C₂×#135	—	53	4	no	—
545	C₂×#135	—	53	12	no	—
546	C₂×#135	—	53	12	no	—
547	C₂×#135	—	53	12	no	—
548	C₂×#135	—	53	6	no	—
549	C₂×#135	—	53	12	no	—
550	C₂×#135	—	53	6	no	—
551	C₂×#135	—	53	6	no	—
552	C₂×#135	C₂×D₅₃	1	6	yes	complemented
553	C₂²×Q₁₆	—	53	6	no	—
554	C₂²×SD₁₆	—	53	12	no	—
555	C₂²×D₈	—	53	6	no	—
556	C₂×#131	—	53	1	no	—
557	C₂×#131	—	53	4	no	—
558	C₂×#131	—	53	4	no	—
559	C₂×#131	—	53	4	no	—
560	C₂×#131	—	53	4	no	—
561	C₂×#131	—	53	3	no	—
562	C₂×#131	—	53	3	no	—
563	C₂×#131	C₂×D₅₃	1	1	yes	characteristic, complemented
564	C₂²×M₁₆	—	53	3	no	—
565	C₂³×C₈	—	53	3	no	—
566	C₅₃	C₂×#3584	1	1	yes	characteristic, complemented, Sylow
567	2₋¹⁺⁴	—	2	2	no	—
568	2₋¹⁺⁴	—	53	24	no	—
569	2₋¹⁺⁴	—	53	8	no	—
570	2₋¹⁺⁴	—	53	24	no	—
571	2₋¹⁺⁴	—	106	8	no	—
572	2₋¹⁺⁴	—	106	8	no	—
573	2₋¹⁺⁴	—	106	8	no	—
574	2₋¹⁺⁴	—	106	12	no	—
575	2₋¹⁺⁴	—	106	24	no	—
576	2₋¹⁺⁴	—	106	2	no	—
577	2₋¹⁺⁴	C₂²×D₅₃	1	8	yes	complemented
578	H(5,𝔽₂)	—	2	6	no	—
579	H(5,𝔽₂)	—	53	24	no	—
580	H(5,𝔽₂)	—	53	8	no	—
581	H(5,𝔽₂)	—	53	24	no	—
582	H(5,𝔽₂)	—	106	24	no	—
583	H(5,𝔽₂)	—	106	24	no	—
584	H(5,𝔽₂)	—	106	24	no	—
585	H(5,𝔽₂)	—	106	24	no	—
586	H(5,𝔽₂)	—	106	12	no	—
587	H(5,𝔽₂)	—	106	8	no	—
588	H(5,𝔽₂)	—	106	6	no	—
589	H(5,𝔽₂)	C₂²×D₅₃	1	8	yes	complemented
590	C₂×#41	—	2	8	no	—
591	C₂×#41	—	53	4	no	—
592	C₂×#41	—	53	4	no	—
593	C₂×#41	—	53	4	no	—
594	C₂×#41	—	53	4	no	—
595	C₂×#41	—	53	1	no	—
596	C₂×#41	—	53	3	no	—
597	C₂×#41	—	53	3	no	—
598	C₂×#41	—	53	8	no	—
599	C₂×#41	—	53	24	no	—
600	C₂×#41	—	53	24	no	—
601	C₂×#41	—	53	24	no	—
602	C₂×#41	—	53	12	no	—
603	C₂×#41	—	53	12	no	—
604	C₂×#41	—	53	12	no	—
605	C₂×#41	—	106	12	no	—
606	C₂×#41	—	106	24	no	—
607	C₂×#41	—	106	12	no	—
608	C₂×#41	—	106	12	no	—
609	C₂×#41	—	106	12	no	—
610	C₂×#41	—	106	12	no	—
611	C₂×#41	—	106	12	no	—
612	C₂×#41	—	106	24	no	—
613	C₂×#41	—	106	24	no	—
614	C₂×#41	—	106	8	no	—
615	C₂×#41	—	106	8	no	—
616	C₂×#41	—	106	8	no	—
617	C₂×#41	—	106	24	no	—
618	C₂×#41	—	106	24	no	—
619	C₂×#41	—	106	8	no	—
620	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
621	C₂×#41	C₂²×D₅₃	1	12	yes	complemented
622	C₂²×Q₈	—	53	1	no	—
623	C₂²×Q₈	—	53	12	no	—
624	C₂²×Q₈	—	106	8	no	—
625	C₂²×D₄	—	53	3	no	—
626	C₂²×D₄	—	53	12	no	—
627	C₂²×D₄	—	106	24	no	—
628	C₂²×D₄	—	106	12	no	—
629	C₂³×C₄	—	53	3	no	—
630	C₂³×C₄	—	106	12	no	—
631	#137	—	53	24	no	—
632	#137	—	53	24	no	—
633	#137	—	53	48	no	—
634	#137	—	53	48	no	—
635	#137	—	53	24	no	—
636	#137	C₂²×D₅₃	1	24	yes	complemented
637	AGL(1,ℤ/8)	—	53	24	no	—
638	AGL(1,ℤ/8)	—	53	24	no	—
639	AGL(1,ℤ/8)	—	53	48	no	—
640	AGL(1,ℤ/8)	—	53	48	no	—
641	AGL(1,ℤ/8)	—	53	24	no	—
642	AGL(1,ℤ/8)	C₂²×D₅₃	1	24	yes	complemented
643	#135	—	53	8	no	—
644	#135	—	53	24	no	—
645	#135	—	53	24	no	—
646	#135	—	53	24	no	—
647	#135	—	53	4	no	—
648	#135	—	53	12	no	—
649	#135	—	53	12	no	—
650	#135	—	53	12	no	—
651	#135	—	53	8	no	—
652	#135	—	53	24	no	—
653	#135	—	53	24	no	—
654	#135	—	53	24	no	—
655	#135	—	53	4	no	—
656	#135	—	53	12	no	—
657	#135	—	53	12	no	—
658	#135	—	53	12	no	—
659	#135	—	53	4	no	—
660	#135	—	53	12	no	—
661	#135	—	53	12	no	—
662	#135	—	53	12	no	—
663	#135	C₂²×D₅₃	1	4	yes	complemented
664	#135	C₂²×D₅₃	1	12	yes	complemented
665	#135	C₂²×D₅₃	1	12	yes	complemented
666	#135	C₂²×D₅₃	1	12	yes	complemented
667	C₂×Q₁₆	—	53	12	no	—
668	C₂×Q₁₆	—	53	4	no	—
669	C₂×Q₁₆	—	53	12	no	—
670	C₂×Q₁₆	—	53	12	no	—
671	C₂×Q₁₆	—	53	12	no	—
672	C₂×Q₁₆	—	53	6	no	—
673	C₂×Q₁₆	C₂²×D₅₃	1	6	yes	complemented
674	C₂×SD₁₆	—	53	12	no	—
675	C₂×SD₁₆	—	53	12	no	—
676	C₂×SD₁₆	—	53	8	no	—
677	C₂×SD₁₆	—	53	24	no	—
678	C₂×SD₁₆	—	53	24	no	—
679	C₂×SD₁₆	—	53	24	no	—
680	C₂×SD₁₆	—	53	12	no	—
681	C₂×SD₁₆	C₂²×D₅₃	1	12	yes	complemented
682	C₂×D₈	—	53	12	no	—
683	C₂×D₈	—	53	4	no	—
684	C₂×D₈	—	53	12	no	—
685	C₂×D₈	—	53	12	no	—
686	C₂×D₈	—	53	12	no	—
687	C₂×D₈	—	53	6	no	—
688	C₂×D₈	C₂²×D₅₃	1	6	yes	complemented
689	#131	—	53	4	no	—
690	#131	—	53	4	no	—
691	#131	—	53	12	no	—
692	#131	—	53	12	no	—
693	#131	—	53	12	no	—
694	#131	—	53	12	no	—
695	#131	C₂²×D₅₃	1	4	yes	complemented
696	#131	C₂²×D₅₃	1	4	yes	complemented
697	C₂×M₁₆	—	53	3	no	—
698	C₂×M₁₆	—	53	12	no	—
699	C₂×M₁₆	—	53	12	no	—
700	C₂×M₁₆	—	53	6	no	—
701	C₂×M₁₆	C₂²×D₅₃	1	3	yes	complemented
702	C₂²×C₈	—	53	3	no	—
703	C₂²×C₈	—	53	1	no	—
704	C₂²×C₈	—	53	3	no	—
705	C₂²×C₈	—	53	6	no	—
706	C₂²×C₈	—	53	6	no	—
707	C₂²×C₈	—	53	3	no	—
708	C₂²×C₈	—	53	3	no	—
709	C₂²×C₈	—	53	6	no	—
710	C₂²×C₈	—	53	6	no	—
711	C₂²×C₈	C₂²×D₅₃	1	3	yes	complemented
712	C₂⁴	—	53	3	no	—
713	C₂⁴	—	106	12	no	—
714	#41	—	2	8	no	—
715	#41	—	2	24	no	—
716	#41	—	2	12	no	—
717	#41	—	2	12	no	—
718	#41	—	53	4	no	—
719	#41	—	53	4	no	—
720	#41	—	53	12	no	—
721	#41	—	53	12	no	—
722	#41	—	53	12	no	—
723	#41	—	53	12	no	—
724	#41	—	53	8	no	—
725	#41	—	53	24	no	—
726	#41	—	53	8	no	—
727	#41	—	53	24	no	—
728	#41	—	53	8	no	—
729	#41	—	53	24	no	—
730	#41	—	106	8	no	—
731	#41	—	106	24	no	—
732	#41	—	106	24	no	—
733	#41	—	106	24	no	—
734	#41	—	106	48	no	—
735	#41	—	106	24	no	—
736	#41	—	106	24	no	—
737	#41	—	106	8	no	—
738	#41	—	106	24	no	—
739	#41	—	106	12	no	—
740	#41	—	106	24	no	—
741	#41	—	106	24	no	—
742	#41	—	106	12	no	—
743	#41	—	106	12	no	—
744	#41	—	106	12	no	—
745	#41	—	106	48	no	—
746	#41	—	106	24	no	—
747	#41	—	106	24	no	—
748	#41	—	106	8	no	—
749	#41	—	106	24	no	—
750	#41	—	106	12	no	—
751	#41	—	106	12	no	—
752	#41	D₄×D₅₃	1	4	yes	—
753	#41	C₂³×D₅₃	1	8	yes	—
754	#41	C₂³×D₅₃	1	24	yes	—
755	#41	C₂³×D₅₃	1	4	yes	—
756	C₂×Q₈	—	2	8	no	—
757	C₂×Q₈	—	53	4	no	—
758	C₂×Q₈	—	53	4	no	—
759	C₂×Q₈	—	53	3	no	—
760	C₂×Q₈	—	53	8	no	—
761	C₂×Q₈	—	53	24	no	—
762	C₂×Q₈	—	53	12	no	—
763	C₂×Q₈	—	106	12	no	—
764	C₂×Q₈	—	106	24	no	—
765	C₂×Q₈	—	106	12	no	—
766	C₂×Q₈	—	106	12	no	—
767	C₂×Q₈	—	106	24	no	—
768	C₂×Q₈	—	106	8	no	—
769	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
770	C₂×Q₈	C₂³×D₅₃	1	12	yes	—
771	C₂×D₄	—	2	12	no	—
772	C₂×D₄	—	2	24	no	—
773	C₂×D₄	—	53	6	no	—
774	C₂×D₄	—	53	12	no	—
775	C₂×D₄	—	53	12	no	—
776	C₂×D₄	—	53	8	no	—
777	C₂×D₄	—	53	24	no	—
778	C₂×D₄	—	53	3	no	—
779	C₂×D₄	—	53	12	no	—
780	C₂×D₄	—	106	24	no	—
781	C₂×D₄	—	106	12	no	—
782	C₂×D₄	—	106	12	no	—
783	C₂×D₄	—	106	12	no	—
784	C₂×D₄	—	106	12	no	—
785	C₂×D₄	—	106	48	no	—
786	C₂×D₄	—	106	24	no	—
787	C₂×D₄	—	106	8	no	—
788	C₂×D₄	—	106	24	no	—
789	C₂×D₄	—	106	24	no	—
790	C₂×D₄	—	106	24	no	—
791	C₂×D₄	—	106	48	no	—
792	C₂×D₄	—	106	12	no	—
793	C₂×D₄	—	106	12	no	—
794	C₂×D₄	—	106	24	no	—
795	C₂×D₄	D₄×D₅₃	1	3	yes	—
796	C₂×D₄	C₂³×D₅₃	1	12	yes	—
797	C₂²×C₄	—	2	12	no	—
798	C₂²×C₄	—	53	3	no	—
799	C₂²×C₄	—	53	6	no	—
800	C₂²×C₄	—	53	3	no	—
801	C₂²×C₄	—	53	3	no	—
802	C₂²×C₄	—	53	6	no	—
803	C₂²×C₄	—	53	1	no	—
804	C₂²×C₄	—	53	6	no	—
805	C₂²×C₄	—	53	6	no	—
806	C₂²×C₄	—	53	3	no	—
807	C₂²×C₄	—	106	8	no	—
808	C₂²×C₄	—	106	24	no	—
809	C₂²×C₄	—	106	12	no	—
810	C₂²×C₄	—	106	24	no	—
811	C₂²×C₄	—	106	24	no	—
812	C₂²×C₄	—	106	12	no	—
813	C₂²×C₄	—	106	12	no	—
814	C₂²×C₄	—	106	12	no	—
815	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
816	Q₁₆	—	53	8	no	—
817	Q₁₆	—	53	24	no	—
818	Q₁₆	—	53	4	no	—
819	Q₁₆	—	53	12	no	—
820	Q₁₆	C₂³×D₅₃	1	4	yes	—
821	Q₁₆	C₂³×D₅₃	1	12	yes	—
822	SD₁₆	—	53	8	no	—
823	SD₁₆	—	53	24	no	—
824	SD₁₆	—	53	8	no	—
825	SD₁₆	—	53	24	no	—
826	SD₁₆	—	53	8	no	—
827	SD₁₆	—	53	24	no	—
828	SD₁₆	C₂³×D₅₃	1	8	yes	—
829	SD₁₆	C₂³×D₅₃	1	24	yes	—
830	D₈	—	53	8	no	—
831	D₈	—	53	24	no	—
832	D₈	—	53	4	no	—
833	D₈	—	53	12	no	—
834	D₈	C₂³×D₅₃	1	4	yes	—
835	D₈	C₂³×D₅₃	1	12	yes	—
836	M₁₆	—	53	12	no	—
837	M₁₆	—	53	24	no	—
838	M₁₆	C₂³×D₅₃	1	12	yes	—
839	C₂×C₈	—	53	1	no	—
840	C₂×C₈	—	53	3	no	—
841	C₂×C₈	—	53	6	no	—
842	C₂×C₈	—	53	6	no	—
843	C₂×C₈	—	53	1	no	—
844	C₂×C₈	—	53	1	no	—
845	C₂×C₈	—	53	1	no	—
846	C₂×C₈	—	53	1	no	—
847	C₂×C₈	—	53	6	no	—
848	C₂×C₈	—	53	6	no	—
849	C₂×C₈	—	53	6	no	—
850	C₂×C₈	—	53	6	no	—
851	C₂×C₈	—	53	6	no	—
852	C₂×C₈	—	53	6	no	—
853	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
854	C₂×C₈	C₂³×D₅₃	1	3	yes	—
855	C₂×C₈	C₂³×D₅₃	1	6	yes	—
856	C₂×C₈	C₂³×D₅₃	1	6	yes	—
857	C₂³	—	2	12	no	—
858	C₂³	—	53	1	no	—
859	C₂³	—	53	6	no	—
860	C₂³	—	53	6	no	—
861	C₂³	—	53	3	no	—
862	C₂³	—	106	24	no	—
863	C₂³	—	106	8	no	—
864	C₂³	—	106	12	no	—
865	C₂³	—	424	24	no	—
866	C₂³	—	212	6	no	—
867	C₂³	C₂×D₄×D₅₃	1	3	yes	—
868	Q₈	—	2	12	no	—
869	Q₈	—	53	12	no	—
870	Q₈	—	53	8	no	—
871	Q₈	—	106	8	no	—
872	Q₈	—	106	24	no	—
873	Q₈	—	106	12	no	—
874	Q₈	C₂×D₄×D₅₃	1	4	yes	—
875	Q₈	C₂⁴×D₅₃	1	8	yes	—
876	D₄	—	2	24	no	—
877	D₄	—	2	8	no	—
878	D₄	—	2	12	no	—
879	D₄	—	53	24	no	—
880	D₄	—	53	12	no	—
881	D₄	—	53	8	no	—
882	D₄	—	106	8	no	—
883	D₄	—	106	24	no	—
884	D₄	—	106	8	no	—
885	D₄	—	106	24	no	—
886	D₄	—	106	8	no	—
887	D₄	—	106	24	no	—
888	D₄	—	106	24	no	—
889	D₄	—	106	8	no	—
890	D₄	—	106	12	no	—
891	D₄	C₂×D₄×D₅₃	1	12	yes	—
892	D₄	C₂⁴×D₅₃	1	8	yes	—
893	C₂×C₄	—	2	12	no	—
894	C₂×C₄	—	2	24	no	—
895	C₂×C₄	—	2	8	no	—
896	C₂×C₄	—	53	1	no	—
897	C₂×C₄	—	53	6	no	—
898	C₂×C₄	—	53	3	no	—
899	C₂×C₄	—	53	6	no	—
900	C₂×C₄	—	53	6	no	—
901	C₂×C₄	—	53	6	no	—
902	C₂×C₄	—	53	6	no	—
903	C₂×C₄	—	53	6	no	—
904	C₂×C₄	—	53	1	no	—
905	C₂×C₄	—	53	1	no	—
906	C₂×C₄	—	53	6	no	—
907	C₂×C₄	—	53	1	no	—
908	C₂×C₄	—	53	1	no	—
909	C₂×C₄	—	53	6	no	—
910	C₂×C₄	—	106	8	no	—
911	C₂×C₄	—	106	24	no	—
912	C₂×C₄	—	106	8	no	—
913	C₂×C₄	—	106	24	no	—
914	C₂×C₄	—	106	8	no	—
915	C₂×C₄	—	106	24	no	—
916	C₂×C₄	—	106	12	no	—
917	C₂×C₄	—	106	24	no	—
918	C₂×C₄	—	106	8	no	—
919	C₂×C₄	C₂×D₄×D₅₃	1	3	yes	—
920	C₂×C₄	C₂×D₄×D₅₃	1	6	yes	—
921	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
922	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
923	C₈	—	53	1	no	—
924	C₈	—	53	1	no	—
925	C₈	—	53	6	no	—
926	C₈	C₂⁴×D₅₃	1	1	yes	characteristic
927	C₈	C₂⁴×D₅₃	1	1	yes	characteristic
928	C₈	C₂⁴×D₅₃	1	6	yes	—
929	C₂²	—	2	8	no	—
930	C₂²	—	4	3	no	—
931	C₂²	—	8	12	no	—
932	C₂²	—	53	1	no	—
933	C₂²	—	53	1	no	—
934	C₂²	—	53	6	no	—
935	C₂²	—	106	12	no	—
936	C₂²	—	106	2	no	—
937	C₂²	—	106	8	no	—
938	C₂²	—	424	12	no	—
939	C₂²	—	424	24	no	—
940	C₂²	—	212	3	no	—
941	C₂²	—	212	6	no	—
942	C₂²	—	212	16	no	—
943	C₂²	C₂²×D₄×D₅₃	1	6	yes	—
944	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
945	C₄	—	2	8	no	—
946	C₄	—	53	1	no	—
947	C₄	—	53	1	no	—
948	C₄	—	53	6	no	—
949	C₄	—	106	8	no	—
950	C₄	C₂²×D₄×D₅₃	1	6	yes	—
951	C₄	C₂²×D₄×D₅₃	1	1	yes	characteristic
952	C₄	C₂⁵×D₅₃	1	1	yes	characteristic
953	C₂	—	2	1	no	—
954	C₂	—	2	6	no	—
955	C₂	—	4	8	no	—
956	C₂	—	53	2	no	—
957	C₂	—	106	6	no	—
958	C₂	—	106	1	no	—
959	C₂	—	212	8	no	—
960	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₄×D₅₃
commutator, cosocle	C₄×C₅₃	C₂⁶
Frattini	C₄	C₂⁵×D₅₃
Fitting	C₅₃×#3584	C₂
socle	C₂×C₅₃	C₂⁴×D₄
hypercenter	#3584	D₅₃
hypocenter	C₅₃	C₂×#3584
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ C₂×#41 ◁ #3584

Complements

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

N	H ≅ G/N	type
1. #585×D₅₃	C₂	semidirect
2. #20289489	C₂	semidirect
3. #20289488	C₂	semidirect
4. #20289487	C₂	semidirect
5. #20289486	C₂	semidirect
6. #20289485	C₂	semidirect
7. #20289484	C₂	semidirect
8. #20289483	C₂	semidirect
9. #578×D₅₃	C₂	semidirect
10. #577×D₅₃	C₂	semidirect
11. #576×D₅₃	C₂	semidirect
12. #575×D₅₃	C₂	semidirect
13. C₂×#135×D₅₃	C₂	semidirect
14. C₂×#131×D₅₃	C₂	semidirect
15. C₅₃×#3584	C₂	semidirect
17. #16811460	C₂²	semidirect
19. #16811459	C₂²	semidirect
20. #16811459	C₂²	semidirect
22. #16811458	C₂²	semidirect
24. 2₋¹⁺⁴×D₅₃	C₂²	semidirect
26. H(5,𝔽₂)×D₅₃	C₂²	semidirect
29. C₂×#41×D₅₃	C₂²	semidirect
30. #16811440	C₂²	semidirect
31. #16811439	C₂²	semidirect
32. #16811438	C₂²	semidirect
33. #16811437	C₂²	semidirect
34. #16811436	C₂²	semidirect
35. #16811435	C₂²	semidirect
36. #16811434	C₂²	semidirect
37. #16811433	C₂²	semidirect
38. #16811432	C₂²	semidirect
39. #16811431	C₂²	semidirect
40. #16811430	C₂²	semidirect
41. #16811429	C₂²	semidirect
42. #16811428	C₂²	semidirect
43. #16811427	C₂²	semidirect
44. #16811426	C₂²	semidirect
45. #16811425	C₂²	semidirect
46. #16811424	C₂²	semidirect
47. #16811423	C₂²	semidirect
48. #16811422	C₂²	semidirect
49. #16811421	C₂²	semidirect
50. #16811420	C₂²	semidirect
51. #16811419	C₂²	semidirect
52. #137×D₅₃	C₂²	semidirect
53. AGL(1,ℤ/8)×D₅₃	C₂²	semidirect
54. C₂×#13133240	C₂²	semidirect
55. C₂×#13133239	C₂²	semidirect
56. C₂×#13133238	C₂²	semidirect
57. C₂×#13133237	C₂²	semidirect
58. C₂×#13133236	C₂²	semidirect
59. #135×D₅₃	C₂²	semidirect
60. #135×D₅₃	C₂²	semidirect
61. #135×D₅₃	C₂²	semidirect
62. #135×D₅₃	C₂²	semidirect
63. #135×D₅₃	C₂²	semidirect
64. #135×D₅₃	C₂²	semidirect
65. #135×D₅₃	C₂²	semidirect
66. #135×D₅₃	C₂²	semidirect
67. C₂×Q₁₆×D₅₃	C₂²	semidirect
68. C₂×SD₁₆×D₅₃	C₂²	semidirect
69. C₂×D₈×D₅₃	C₂²	semidirect
70. C₂×#13133225	C₂²	semidirect
71. C₂×#13133224	C₂²	semidirect
72. C₂×#13133223	C₂²	semidirect
73. #131×D₅₃	C₂²	semidirect
74. #131×D₅₃	C₂²	semidirect
75. #131×D₅₃	C₂²	semidirect
76. #131×D₅₃	C₂²	semidirect
77. C₂×M₁₆×D₅₃	C₂²	semidirect
78. C₂²×C₈×D₅₃	C₂²	semidirect
79. C₅₃×#585	C₂²	semidirect
80. C₅₃×#578	C₂²	semidirect
81. C₅₃×#577	C₂²	semidirect
82. C₅₃×#576	C₂²	semidirect
83. C₅₃×#575	C₂²	semidirect
84. C₂×#135×C₅₃	C₂²	semidirect
85. C₂×#131×C₅₃	C₂²	semidirect
89. #13133265	C₂³	semidirect
93. #13133264	C₂³	semidirect
94. #13133264	C₂³	semidirect
98. #13133263	C₂³	semidirect
99. #13133263	C₂³	semidirect
104. #13133262	C₂³	semidirect
107. C₂×#11719949	C₂³	semidirect
111. C₂×#11719945	C₂³	semidirect
115. C₂×#11719947	C₂³	semidirect
132. #41×D₅₃	C₂³	semidirect
133. #41×D₅₃	C₂³	semidirect
143. #13133250	C₂³	semidirect
144. #13133249	C₂³	semidirect
145. #13133248	C₂³	semidirect
146. #13133247	C₂³	semidirect
147. #13133246	C₂³	semidirect
148. #13133245	C₂³	semidirect
149. #13133244	C₂³	semidirect
150. #13133243	C₂³	semidirect
151. #13133242	C₂³	semidirect
152. #13133241	C₂³	semidirect
153. #13133240	C₂³	semidirect
154. #13133240	C₂³	semidirect
155. #13133240	C₂³	semidirect
156. #13133240	C₂³	semidirect
157. #13133239	C₂³	semidirect
158. #13133239	C₂³	semidirect
159. #13133239	C₂³	semidirect
160. #13133239	C₂³	semidirect
161. #13133238	C₂³	semidirect
162. #13133238	C₂³	semidirect
163. #13133238	C₂³	semidirect
164. #13133238	C₂³	semidirect
165. #13133237	C₂³	semidirect
166. #13133237	C₂³	semidirect
167. #13133237	C₂³	semidirect
168. #13133237	C₂³	semidirect
169. #13133236	C₂³	semidirect
170. #13133236	C₂³	semidirect
171. #13133236	C₂³	semidirect
172. #13133236	C₂³	semidirect
173. C₂×Dic₂₁₂	C₂³	semidirect
174. C₂×#11719925	C₂³	semidirect
177. Q₁₆×D₅₃	C₂³	semidirect
178. Q₁₆×D₅₃	C₂³	semidirect
179. C₂×#11719913	C₂³	semidirect
180. C₂×#11719923	C₂³	semidirect
181. C₂×#11719924	C₂³	semidirect
184. SD₁₆×D₅₃	C₂³	semidirect
185. SD₁₆×D₅₃	C₂³	semidirect
186. C₂×D₄₂₄	C₂³	semidirect
187. C₂×#11719922	C₂³	semidirect
190. D₈×D₅₃	C₂³	semidirect
191. D₈×D₅₃	C₂³	semidirect
192. #13133225	C₂³	semidirect
193. #13133225	C₂³	semidirect
194. #13133224	C₂³	semidirect
195. #13133224	C₂³	semidirect
196. #13133223	C₂³	semidirect
197. #13133223	C₂³	semidirect
198. C₂×#11719917	C₂³	semidirect
199. C₂×#11719912	C₂³	semidirect
201. M₁₆×D₅₃	C₂³	semidirect
202. C₂²×#88322	C₂³	semidirect
207. C₂×C₈×D₅₃	C₂³	semidirect
208. C₂×C₈×D₅₃	C₂³	semidirect
209. C₂×C₈×D₅₃	C₂³	semidirect
210. C₂×C₈×D₅₃	C₂³	semidirect
212. 2₋¹⁺⁴×C₅₃	C₂³	semidirect
214. H(5,𝔽₂)×C₅₃	C₂³	semidirect
217. C₂×#41×C₅₃	C₂³	semidirect
218. #137×C₅₃	C₂³	semidirect
219. AGL(1,ℤ/8)×C₅₃	C₂³	semidirect
220. #135×C₅₃	C₂³	semidirect
221. #135×C₅₃	C₂³	semidirect
222. #135×C₅₃	C₂³	semidirect
223. #135×C₅₃	C₂³	semidirect
224. C₂×Q₁₆×C₅₃	C₂³	semidirect
225. C₂×SD₁₆×C₅₃	C₂³	semidirect
226. C₂×D₈×C₅₃	C₂³	semidirect
227. #131×C₅₃	C₂³	semidirect
228. #131×C₅₃	C₂³	semidirect
229. C₂×M₁₆×C₅₃	C₂³	semidirect
230. C₂²×C₈×C₅₃	C₂³	semidirect
481. #3584	D₅₃	direct (N × H)
495. D₅₃	#3584	direct (N × H)
503. #585	C₂×D₅₃	semidirect
516. #578	C₂×D₅₃	semidirect
524. #577	C₂×D₅₃	semidirect
530. #576	C₂×D₅₃	semidirect
536. #575	C₂×D₅₃	semidirect
552. C₂×#135	C₂×D₅₃	semidirect
563. C₂×#131	C₂×D₅₃	semidirect
566. C₅₃	C₂×#3584	semidirect
577. 2₋¹⁺⁴	C₂²×D₅₃	semidirect
589. H(5,𝔽₂)	C₂²×D₅₃	semidirect
621. C₂×#41	C₂²×D₅₃	semidirect
636. #137	C₂²×D₅₃	semidirect
642. AGL(1,ℤ/8)	C₂²×D₅₃	semidirect
663. #135	C₂²×D₅₃	semidirect
664. #135	C₂²×D₅₃	semidirect
665. #135	C₂²×D₅₃	semidirect
666. #135	C₂²×D₅₃	semidirect
673. C₂×Q₁₆	C₂²×D₅₃	semidirect
681. C₂×SD₁₆	C₂²×D₅₃	semidirect
688. C₂×D₈	C₂²×D₅₃	semidirect
695. #131	C₂²×D₅₃	semidirect
696. #131	C₂²×D₅₃	semidirect
701. C₂×M₁₆	C₂²×D₅₃	semidirect
711. C₂²×C₈	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#585×D₅₃	2
#20289489	2
#20289488	2
#20289487	2
#20289486	2
#20289485	2
#20289484	2
#20289483	2
#578×D₅₃	2
#577×D₅₃	2
#576×D₅₃	2
#575×D₅₃	2
C₂×#135×D₅₃	2
C₂×#131×D₅₃	2
C₅₃×#3584	2
C₂×#3584	53

Subgroups — D53×#3584 #28297919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3584 #28297919