Subgroups — D₅₃×#3585 #28297927

Order 13568.

11138 conjugacy classes of subgroups.

The subgroup lattice has 1252 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	1	yes	maximal, characteristic, complemented
2	C₂×H(5,𝔽₂)×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20289496	C₂	1	1	yes	maximal, characteristic, complemented
4	#20289495	C₂	1	1	yes	maximal, characteristic, complemented
5	#20289494	C₂	1	1	yes	maximal, characteristic, complemented
6	#20289493	C₂	1	8	yes	maximal, complemented
7	#20289492	C₂	1	6	yes	maximal, complemented
8	#20289491	C₂	1	6	yes	maximal, complemented
9	#20289490	C₂	1	8	yes	maximal, complemented
10	#577×D₅₃	C₂	1	8	yes	maximal, complemented
11	#576×D₅₃	C₂	1	8	yes	maximal, complemented
12	#575×D₅₃	C₂	1	6	yes	maximal, complemented
13	C₂×AGL(1,ℤ/8)×D₅₃	C₂	1	6	yes	maximal, complemented
14	#568×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3585	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811460	—	2	1	no	—
17	#16811460	C₂²	1	4	yes	complemented
18	#16811459	—	2	4	no	—
19	#16811459	C₂²	1	1	yes	characteristic, complemented
20	#16811459	C₂²	1	6	yes	complemented
21	#16811458	—	2	3	no	—
22	#16811458	C₂²	1	4	yes	complemented
23	2₋¹⁺⁴×D₅₃	—	2	1	no	—
24	2₋¹⁺⁴×D₅₃	C₂²	1	4	yes	complemented
25	C₂×#13133263	—	2	1	no	—
26	C₂×#13133263	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13133263	C₂²	1	3	yes	complemented
28	C₂×#13133262	—	2	3	no	—
29	C₂×#13133262	C₂²	1	3	yes	complemented
30	H(5,𝔽₂)×D₅₃	—	2	4	no	—
31	H(5,𝔽₂)×D₅₃	—	2	4	no	—
32	H(5,𝔽₂)×D₅₃	—	2	3	no	—
33	H(5,𝔽₂)×D₅₃	C₂²	1	8	yes	complemented
34	H(5,𝔽₂)×D₅₃	C₂²	1	4	yes	complemented
35	H(5,𝔽₂)×D₅₃	C₂²	1	8	yes	complemented
36	C₂×#41×D₅₃	—	2	4	no	—
37	C₂×#41×D₅₃	—	2	1	no	—
38	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
39	C₂×#41×D₅₃	C₂²	1	3	yes	complemented
40	C₂×#41×D₅₃	C₂²	1	6	yes	complemented
41	C₂²×D₄×D₅₃	—	2	3	no	—
42	C₂²×D₄×D₅₃	C₂²	1	3	yes	complemented
43	#16811435	C₂²	1	8	yes	complemented
44	#16811434	C₂²	1	8	yes	complemented
45	#16811433	C₂²	1	24	yes	complemented
46	#16811432	C₂²	1	24	yes	complemented
47	#16811431	C₂²	1	8	yes	complemented
48	#16811430	C₂²	1	24	yes	complemented
49	#16811429	C₂²	1	24	yes	complemented
50	#16811428	C₂²	1	8	yes	complemented
51	#16811427	C₂²	1	24	yes	complemented
52	#16811427	C₂²	1	24	yes	complemented
53	#16811426	C₂²	1	8	yes	complemented
54	#16811426	C₂²	1	8	yes	complemented
55	#16811425	C₂²	1	24	yes	complemented
56	#16811424	C₂²	1	24	yes	complemented
57	#16811423	C₂²	1	6	yes	complemented
58	#16811422	C₂²	1	12	yes	complemented
59	#16811422	C₂²	1	12	yes	complemented
60	#16811421	C₂²	1	6	yes	complemented
61	#16811421	C₂²	1	6	yes	complemented
62	#16811420	C₂²	1	24	yes	complemented
63	#16811419	C₂²	1	12	yes	complemented
64	#16811419	C₂²	1	12	yes	complemented
65	#137×D₅₃	C₂²	1	4	yes	complemented
66	#137×D₅₃	C₂²	1	12	yes	complemented
67	C₂×#13133245	C₂²	1	6	yes	complemented
68	C₂×#13133244	C₂²	1	12	yes	complemented
69	C₂×#13133243	C₂²	1	6	yes	complemented
70	C₂×#13133242	C₂²	1	6	yes	complemented
71	C₂×#13133241	C₂²	1	12	yes	complemented
72	AGL(1,ℤ/8)×D₅₃	C₂²	1	12	yes	complemented
73	AGL(1,ℤ/8)×D₅₃	C₂²	1	24	yes	complemented
74	AGL(1,ℤ/8)×D₅₃	C₂²	1	12	yes	complemented
75	AGL(1,ℤ/8)×D₅₃	C₂²	1	24	yes	complemented
76	AGL(1,ℤ/8)×D₅₃	C₂²	1	24	yes	complemented
77	#135×D₅₃	C₂²	1	24	yes	complemented
78	C₂×SD₁₆×D₅₃	C₂²	1	12	yes	complemented
79	C₂×D₈×D₅₃	C₂²	1	12	yes	complemented
80	#16811390	C₂²	1	1	yes	characteristic, complemented
81	#16811389	C₂²	1	6	yes	complemented
82	#16811388	C₂²	1	8	yes	complemented
83	#131×D₅₃	C₂²	1	8	yes	complemented
84	C₂×M₁₆×D₅₃	C₂²	1	6	yes	complemented
85	C₅₃×#585	C₂²	1	1	yes	characteristic, complemented
86	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#577	C₂²	1	8	yes	complemented
88	C₅₃×#576	C₂²	1	8	yes	complemented
89	C₅₃×#575	C₂²	1	6	yes	complemented
90	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	6	yes	complemented
91	C₅₃×#568	C₂²	1	1	yes	characteristic, complemented
92	C₂⁴×D₅₃	—	2	3	no	—
93	#13133265	—	2	1	no	—
94	#13133265	—	2	4	no	—
95	#13133265	—	2	4	no	—
96	#13133265	C₂³	1	12	yes	complemented
97	#13133264	—	2	4	no	—
98	#13133264	—	2	12	no	—
99	#13133264	—	2	6	no	—
100	#13133264	C₂³	1	12	yes	complemented
101	#13133264	C₂³	1	4	yes	complemented
102	#13133263	—	2	4	no	—
103	#13133263	—	2	8	no	—
104	#13133263	—	2	8	no	—
105	#13133263	—	2	4	no	—
106	#13133263	—	2	12	no	—
107	#13133263	—	2	12	no	—
108	#13133263	—	2	6	no	—
109	#13133263	C₂³	1	24	yes	complemented
110	#13133263	C₂³	1	12	yes	complemented
111	#13133263	C₂³	1	8	yes	complemented
112	#13133263	C₂³	1	4	yes	complemented
113	#13133262	—	2	3	no	—
114	#13133262	—	2	12	no	—
115	#13133262	—	2	24	no	—
116	#13133262	—	2	24	no	—
117	#13133262	—	2	12	no	—
118	#13133262	—	2	12	no	—
119	#13133262	—	2	12	no	—
120	#13133262	C₂³	1	24	yes	complemented
121	#13133262	C₂³	1	12	yes	complemented
122	C₂×#11719949	—	2	1	no	—
123	C₂×#11719949	—	2	4	no	—
124	C₂×#11719949	D₄	1	1	yes	characteristic
125	C₂×#11719949	C₂³	1	3	yes	complemented
126	C₂×#11719949	C₂³	1	6	yes	complemented
127	C₂×#11719945	—	2	12	no	—
128	C₂×#11719945	—	2	3	no	—
129	C₂×#11719945	—	2	6	no	—
130	C₂×#11719945	—	2	3	no	—
131	C₂×#11719945	C₂³	1	3	yes	—
132	C₂×#11719945	C₂³	1	3	yes	complemented
133	C₂×#11719945	C₂³	1	6	yes	complemented
134	C₂×#11719947	—	2	3	no	—
135	C₂×#11719947	—	2	6	no	—
136	C₂×#11719947	—	2	12	no	—
137	C₂×#11719947	—	2	3	no	—
138	C₂×#11719947	D₄	1	3	yes	—
139	C₂×#11719947	C₂³	1	3	yes	complemented
140	C₂×#11719947	C₂³	1	6	yes	complemented
141	#41×D₅₃	—	2	4	no	—
142	#41×D₅₃	—	2	4	no	—
143	#41×D₅₃	—	2	8	no	—
144	#41×D₅₃	—	2	8	no	—
145	#41×D₅₃	—	2	4	no	—
146	#41×D₅₃	—	2	12	no	—
147	#41×D₅₃	—	2	12	no	—
148	#41×D₅₃	—	2	12	no	—
149	#41×D₅₃	—	2	6	no	—
150	#41×D₅₃	—	2	6	no	—
151	#41×D₅₃	—	2	6	no	—
152	#41×D₅₃	—	2	6	no	—
153	#41×D₅₃	—	2	6	no	—
154	#41×D₅₃	—	2	6	no	—
155	#41×D₅₃	D₄	1	4	yes	—
156	#41×D₅₃	D₄	1	4	yes	—
157	#41×D₅₃	C₂³	1	12	yes	—
158	#41×D₅₃	C₂³	1	4	yes	—
159	#41×D₅₃	C₂³	1	4	yes	—
160	#41×D₅₃	C₂³	1	4	yes	—
161	#41×D₅₃	C₂³	1	12	yes	complemented
162	#41×D₅₃	C₂³	1	12	yes	complemented
163	#41×D₅₃	C₂³	1	12	yes	complemented
164	#41×D₅₃	C₂³	1	12	yes	complemented
165	C₂×Q₈×D₅₃	—	2	4	no	—
166	C₂×Q₈×D₅₃	D₄	1	1	yes	characteristic
167	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
168	C₂×Q₈×D₅₃	C₂³	1	6	yes	complemented
169	C₂²×D₂₁₂	—	2	3	no	—
170	C₂²×D₂₁₂	C₂³	1	3	yes	complemented
171	C₂²×C₂²⋊D₅₃	—	2	6	no	—
172	C₂²×C₂²⋊D₅₃	—	2	3	no	—
173	C₂×D₄×D₅₃	—	2	3	no	—
174	C₂×D₄×D₅₃	—	2	6	no	—
175	C₂×D₄×D₅₃	—	2	3	no	—
176	C₂×D₄×D₅₃	—	2	6	no	—
177	C₂×D₄×D₅₃	—	2	24	no	—
178	C₂×D₄×D₅₃	—	2	24	no	—
179	C₂×D₄×D₅₃	—	2	12	no	—
180	C₂×D₄×D₅₃	—	2	3	no	—
181	C₂×D₄×D₅₃	—	2	3	no	—
182	C₂×D₄×D₅₃	—	2	6	no	—
183	C₂×D₄×D₅₃	—	2	6	no	—
184	C₂×D₄×D₅₃	—	2	3	no	—
185	C₂×D₄×D₅₃	D₄	1	3	yes	—
186	C₂×D₄×D₅₃	C₂³	1	12	yes	—
187	C₂×D₄×D₅₃	C₂³	1	3	yes	—
188	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
189	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
190	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
191	C₂²×C₄×D₅₃	—	2	3	no	—
192	C₂²×C₄×D₅₃	—	2	6	no	—
193	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
194	#13133250	C₂³	1	4	yes	complemented
195	#13133250	C₂³	1	12	yes	complemented
196	#13133249	C₂³	1	8	yes	complemented
197	#13133249	C₂³	1	24	yes	complemented
198	#13133248	C₂³	1	4	yes	complemented
199	#13133248	C₂³	1	12	yes	complemented
200	#13133247	C₂³	1	4	yes	complemented
201	#13133247	C₂³	1	12	yes	complemented
202	#13133246	C₂³	1	8	yes	complemented
203	#13133246	C₂³	1	24	yes	complemented
204	#13133245	C₂³	1	12	yes	complemented
205	#13133245	C₂³	1	24	yes	complemented
206	#13133245	C₂³	1	12	yes	complemented
207	#13133244	C₂³	1	24	yes	complemented
208	#13133244	C₂³	1	48	yes	complemented
209	#13133244	C₂³	1	24	yes	complemented
210	#13133243	C₂³	1	12	yes	complemented
211	#13133243	C₂³	1	12	yes	complemented
212	#13133243	C₂³	1	24	yes	complemented
213	#13133242	C₂³	1	12	yes	complemented
214	#13133242	C₂³	1	24	yes	complemented
215	#13133242	C₂³	1	12	yes	complemented
216	#13133241	C₂³	1	24	yes	complemented
217	#13133241	C₂³	1	48	yes	complemented
218	#13133241	C₂³	1	24	yes	complemented
219	#13133240	C₂³	1	24	yes	complemented
220	#13133239	C₂³	1	24	yes	complemented
221	#13133238	C₂³	1	24	yes	complemented
222	#13133238	C₂³	1	24	yes	complemented
223	#13133237	C₂³	1	24	yes	complemented
224	#13133237	C₂³	1	24	yes	complemented
225	#13133236	C₂³	1	24	yes	complemented
226	Q₁₆×D₅₃	C₂³	1	8	yes	complemented
227	C₂×#11719913	C₂³	1	12	yes	complemented
228	C₂×#11719923	C₂³	1	12	yes	complemented
229	C₂×#11719924	C₂³	1	12	yes	complemented
230	SD₁₆×D₅₃	C₂³	1	24	yes	complemented
231	SD₁₆×D₅₃	C₂³	1	8	yes	complemented
232	SD₁₆×D₅₃	C₂³	1	48	yes	complemented
233	C₂×D₄₂₄	C₂³	1	12	yes	complemented
234	C₂×#11719922	C₂³	1	12	yes	complemented
235	C₂×#11719922	C₂³	1	12	yes	complemented
236	D₈×D₅₃	C₂³	1	24	yes	complemented
237	D₈×D₅₃	C₂³	1	48	yes	complemented
238	#13133225	C₂³	1	24	yes	complemented
239	#13133224	C₂³	1	8	yes	complemented
240	#13133223	C₂³	1	24	yes	complemented
241	C₂×#11719917	C₂³	1	6	yes	complemented
242	C₂×#11719912	C₂³	1	12	yes	complemented
243	M₁₆×D₅₃	C₂³	1	4	yes	—
244	M₁₆×D₅₃	C₂³	1	12	yes	complemented
245	M₁₆×D₅₃	C₂³	1	12	yes	complemented
246	M₁₆×D₅₃	C₂³	1	12	yes	complemented
247	C₂×C₈×D₅₃	C₂³	1	12	yes	complemented
248	2₋¹⁺⁴×C₅₃	—	2	1	no	—
249	2₋¹⁺⁴×C₅₃	C₂³	1	4	yes	complemented
250	H(5,𝔽₂)×C₅₃	—	2	4	no	—
251	H(5,𝔽₂)×C₅₃	—	2	3	no	—
252	H(5,𝔽₂)×C₅₃	C₂³	1	8	yes	complemented
253	H(5,𝔽₂)×C₅₃	C₂³	1	4	yes	complemented
254	C₂×#41×C₅₃	—	2	4	no	—
255	C₂×#41×C₅₃	—	2	1	no	—
256	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×#41×C₅₃	C₂³	1	3	yes	complemented
258	C₂×#41×C₅₃	C₂³	1	6	yes	complemented
259	C₂²×D₄×C₅₃	—	2	3	no	—
260	C₂²×D₄×C₅₃	C₂³	1	3	yes	complemented
261	#137×C₅₃	C₂³	1	4	yes	complemented
262	#137×C₅₃	C₂³	1	12	yes	complemented
263	AGL(1,ℤ/8)×C₅₃	C₂³	1	12	yes	complemented
264	AGL(1,ℤ/8)×C₅₃	C₂³	1	24	yes	complemented
265	AGL(1,ℤ/8)×C₅₃	C₂³	1	12	yes	complemented
266	#135×C₅₃	C₂³	1	24	yes	complemented
267	C₂×SD₁₆×C₅₃	C₂³	1	12	yes	complemented
268	C₂×D₈×C₅₃	C₂³	1	12	yes	complemented
269	#131×C₅₃	C₂³	1	8	yes	complemented
270	C₂×M₁₆×C₅₃	C₂³	1	6	yes	complemented
271	C₂⁴×C₅₃	—	2	3	no	—
272	C₂³×D₅₃	—	2	3	no	—
273	C₂³×D₅₃	—	2	3	no	—
274	C₂³×D₅₃	—	2	6	no	—
275	C₂³×D₅₃	—	2	12	no	—
276	C₂³×D₅₃	—	2	12	no	—
277	C₂³×D₅₃	—	2	6	no	—
278	C₂³×D₅₃	—	8	12	no	—
279	C₂³×D₅₃	C₂×D₄	1	3	yes	—
280	#41×C₅₃	—	2	8	no	—
281	#41×C₅₃	—	2	4	no	—
282	#41×C₅₃	—	2	12	no	—
283	#41×C₅₃	—	2	6	no	—
284	#41×C₅₃	—	2	6	no	—
285	#41×C₅₃	—	2	6	no	—
286	#41×C₅₃	C₂×D₄	1	4	yes	—
287	#41×C₅₃	C₂⁴	1	12	yes	—
288	#41×C₅₃	C₂⁴	1	4	yes	—
289	#41×C₅₃	C₂⁴	1	4	yes	—
290	#41×C₅₃	C₂⁴	1	12	yes	complemented
291	C₂×Q₈×C₅₃	—	2	4	no	—
292	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
294	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	complemented
295	C₂×D₄×C₅₃	—	2	3	no	—
296	C₂×D₄×C₅₃	—	2	6	no	—
297	C₂×D₄×C₅₃	—	2	24	no	—
298	C₂×D₄×C₅₃	—	2	12	no	—
299	C₂×D₄×C₅₃	—	2	3	no	—
300	C₂×D₄×C₅₃	—	2	6	no	—
301	C₂×D₄×C₅₃	C₂×D₄	1	3	yes	—
302	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
303	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
304	C₂×D₄×C₅₃	C₂⁴	1	6	yes	complemented
305	C₂²×C₄×C₅₃	—	2	3	no	—
306	C₂²×C₄×C₅₃	—	2	6	no	—
307	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
308	C₂×C₂²⋊D₅₃	—	2	3	no	—
309	C₂×C₂²⋊D₅₃	—	2	6	no	—
310	C₂×C₂²⋊D₅₃	—	2	3	no	—
311	C₂×C₂²⋊D₅₃	—	2	6	no	—
312	C₂×C₂²⋊D₅₃	—	2	48	no	—
313	C₂×C₂²⋊D₅₃	—	2	24	no	—
314	C₂×C₂²⋊D₅₃	—	2	3	no	—
315	C₂×C₂²⋊D₅₃	—	2	6	no	—
316	C₂×C₂²⋊D₅₃	—	2	12	no	—
317	C₂×C₂²⋊D₅₃	—	2	12	no	—
318	C₂×C₂²⋊D₅₃	—	2	6	no	—
319	C₂×C₂²⋊D₅₃	C₂×D₄	1	6	yes	—
320	C₂²×Dic₅₃	—	2	3	no	—
321	C₂²×Dic₅₃	—	2	6	no	—
322	C₂²×Dic₅₃	C₂×D₄	1	3	yes	—
323	#11719949	—	2	8	no	—
324	#11719949	—	2	4	no	—
325	#11719949	—	2	12	no	—
326	#11719949	—	2	6	no	—
327	#11719949	—	2	6	no	—
328	#11719949	—	2	6	no	—
329	#11719949	C₂×D₄	1	4	yes	—
330	#11719949	C₂×D₄	1	4	yes	—
331	#11719949	C₂⁴	1	12	yes	—
332	#11719949	C₂⁴	1	4	yes	—
333	#11719949	C₂⁴	1	12	yes	complemented
334	Q₈×D₅₃	—	2	4	no	—
335	Q₈×D₅₃	—	2	6	no	—
336	Q₈×D₅₃	—	2	1	no	—
337	Q₈×D₅₃	—	2	1	no	—
338	Q₈×D₅₃	—	2	6	no	—
339	Q₈×D₅₃	—	2	12	no	—
340	Q₈×D₅₃	C₂×D₄	1	4	yes	—
341	Q₈×D₅₃	C₂×D₄	1	4	yes	—
342	Q₈×D₅₃	C₂⁴	1	4	yes	—
343	Q₈×D₅₃	C₂⁴	1	2	yes	—
344	Q₈×D₅₃	C₂⁴	1	2	yes	—
345	Q₈×D₅₃	C₂⁴	1	12	yes	complemented
346	#11719947	—	2	12	no	—
347	#11719947	—	2	24	no	—
348	#11719947	—	2	4	no	—
349	#11719947	—	2	12	no	—
350	#11719947	—	2	12	no	—
351	#11719947	—	2	12	no	—
352	#11719947	—	2	12	no	—
353	#11719947	—	2	12	no	—
354	#11719947	—	2	6	no	—
355	#11719947	—	2	6	no	—
356	#11719947	—	2	6	no	—
357	#11719947	—	2	24	no	—
358	#11719947	—	2	12	no	—
359	#11719947	C₂×D₄	1	12	yes	—
360	#11719947	C₂×D₄	1	12	yes	—
361	#11719947	C₂⁴	1	12	yes	—
362	#11719947	C₂⁴	1	4	yes	—
363	#11719947	C₂⁴	1	12	yes	complemented
364	D₄×D₅₃	—	2	12	no	—
365	D₄×D₅₃	—	2	12	no	—
366	D₄×D₅₃	—	2	4	no	—
367	D₄×D₅₃	—	2	12	no	—
368	D₄×D₅₃	—	2	12	no	—
369	D₄×D₅₃	—	2	12	no	—
370	D₄×D₅₃	—	2	24	no	—
371	D₄×D₅₃	—	2	12	no	—
372	D₄×D₅₃	—	2	48	no	—
373	D₄×D₅₃	—	2	24	no	—
374	D₄×D₅₃	—	2	24	no	—
375	D₄×D₅₃	—	2	12	no	—
376	D₄×D₅₃	—	2	3	no	—
377	D₄×D₅₃	—	2	12	no	—
378	D₄×D₅₃	—	2	3	no	—
379	D₄×D₅₃	—	2	12	no	—
380	D₄×D₅₃	—	2	12	no	—
381	D₄×D₅₃	—	2	6	no	—
382	D₄×D₅₃	—	2	12	no	—
383	D₄×D₅₃	—	2	12	no	—
384	D₄×D₅₃	—	2	6	no	—
385	D₄×D₅₃	C₂×D₄	1	12	yes	—
386	D₄×D₅₃	C₂×D₄	1	12	yes	—
387	D₄×D₅₃	C₂⁴	1	4	yes	—
388	D₄×D₅₃	C₂⁴	1	6	yes	—
389	D₄×D₅₃	C₂⁴	1	24	yes	—
390	D₄×D₅₃	C₂⁴	1	6	yes	—
391	D₄×D₅₃	C₂⁴	1	12	yes	complemented
392	#11719945	—	2	6	no	—
393	#11719945	—	2	6	no	—
394	#11719945	—	2	6	no	—
395	#11719945	—	2	24	no	—
396	#11719945	—	2	12	no	—
397	#11719945	—	2	4	no	—
398	#11719945	—	2	12	no	—
399	#11719945	—	2	12	no	—
400	#11719945	—	2	12	no	—
401	#11719945	—	2	12	no	—
402	#11719945	—	2	12	no	—
403	#11719945	—	2	24	no	—
404	#11719945	—	2	12	no	—
405	#11719945	C₂×D₄	1	12	yes	—
406	#11719945	C₂⁴	1	12	yes	—
407	#11719945	C₂⁴	1	12	yes	—
408	#11719945	C₂⁴	1	4	yes	—
409	#11719945	C₂⁴	1	12	yes	complemented
410	C₂×D₂₁₂	—	2	3	no	—
411	C₂×D₂₁₂	—	2	6	no	—
412	C₂×D₂₁₂	—	2	3	no	—
413	C₂×D₂₁₂	—	2	6	no	—
414	C₂×D₂₁₂	—	2	24	no	—
415	C₂×D₂₁₂	—	2	12	no	—
416	C₂×D₂₁₂	C₂×D₄	1	3	yes	—
417	C₂×D₂₁₂	C₂⁴	1	12	yes	—
418	C₂×D₂₁₂	C₂⁴	1	3	yes	—
419	C₂×D₂₁₂	C₂⁴	1	6	yes	complemented
420	C₂×C₄×D₅₃	—	2	1	no	—
421	C₂×C₄×D₅₃	—	2	6	no	—
422	C₂×C₄×D₅₃	—	2	3	no	—
423	C₂×C₄×D₅₃	—	2	6	no	—
424	C₂×C₄×D₅₃	—	2	3	no	—
425	C₂×C₄×D₅₃	—	2	6	no	—
426	C₂×C₄×D₅₃	—	2	4	no	—
427	C₂×C₄×D₅₃	—	2	12	no	—
428	C₂×C₄×D₅₃	—	2	12	no	—
429	C₂×C₄×D₅₃	—	2	12	no	—
430	C₂×C₄×D₅₃	—	2	12	no	—
431	C₂×C₄×D₅₃	—	2	12	no	—
432	C₂×C₄×D₅₃	C₂×D₄	1	3	yes	—
433	C₂×C₄×D₅₃	C₂×D₄	1	6	yes	—
434	C₂×C₄×D₅₃	C₂×D₄	1	6	yes	—
435	C₂×C₄×D₅₃	C₂×D₄	1	3	yes	—
436	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
437	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
438	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
439	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
440	C₂×Dic₁₀₆	—	2	1	no	—
441	C₂×Dic₁₀₆	—	2	6	no	—
442	C₂×Dic₁₀₆	—	2	12	no	—
443	C₂×Dic₁₀₆	C₂×D₄	1	3	yes	—
444	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
445	C₂×Dic₁₀₆	C₂⁴	1	6	yes	complemented
446	Q₁₆×C₅₃	C₂⁴	1	8	yes	complemented
447	SD₁₆×C₅₃	C₂⁴	1	24	yes	complemented
448	SD₁₆×C₅₃	C₂⁴	1	8	yes	complemented
449	D₈×C₅₃	C₂⁴	1	24	yes	complemented
450	M₁₆×C₅₃	C₂⁴	1	4	yes	—
451	M₁₆×C₅₃	C₂⁴	1	12	yes	complemented
452	C₂×C₈×C₅₃	C₂⁴	1	12	yes	complemented
453	#11719925	C₂⁴	1	8	yes	complemented
454	#11719925	C₂⁴	1	8	yes	complemented
455	#11719924	C₂⁴	1	24	yes	complemented
456	#11719924	C₂⁴	1	8	yes	complemented
457	#11719923	C₂⁴	1	24	yes	complemented
458	#11719923	C₂⁴	1	8	yes	complemented
459	#11719922	C₂⁴	1	24	yes	complemented
460	#11719922	C₂⁴	1	24	yes	complemented
461	#11719917	C₂⁴	1	4	yes	—
462	#11719917	C₂⁴	1	12	yes	complemented
463	C₂×#88322	C₂⁴	1	12	yes	complemented
464	Dic₂₁₂	C₂⁴	1	8	yes	complemented
465	D₄₂₄	C₂⁴	1	24	yes	complemented
466	#11719913	C₂⁴	1	24	yes	complemented
467	#11719913	C₂⁴	1	8	yes	complemented
468	#11719912	C₂⁴	1	8	yes	—
469	#11719912	C₂⁴	1	24	yes	complemented
470	C₈×D₅₃	C₂⁴	1	8	yes	—
471	C₈×D₅₃	C₂⁴	1	24	yes	complemented
472	C₂³×C₅₃	—	2	3	no	—
473	C₂³×C₅₃	—	2	6	no	—
474	C₂³×C₅₃	—	2	12	no	—
475	C₂³×C₅₃	—	8	6	no	—
476	C₂³×C₅₃	C₂²×D₄	1	3	yes	—
477	C₂²×D₅₃	—	2	3	no	—
478	C₂²×D₅₃	—	2	6	no	—
479	C₂²×D₅₃	—	2	12	no	—
480	C₂²×D₅₃	—	2	4	no	—
481	C₂²×D₅₃	—	2	6	no	—
482	C₂²×D₅₃	—	2	6	no	—
483	C₂²×D₅₃	—	2	12	no	—
484	C₂²×D₅₃	—	2	24	no	—
485	C₂²×D₅₃	—	4	6	no	—
486	C₂²×D₅₃	—	4	12	no	—
487	C₂²×D₅₃	—	8	12	no	—
488	C₂²×D₅₃	—	8	24	no	—
489	C₂²×D₅₃	—	8	24	no	—
490	C₂²×D₅₃	—	8	12	no	—
491	C₂²×D₅₃	—	8	6	no	—
492	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
493	C₂²×D₅₃	C₂²×D₄	1	6	yes	—
494	C₂²×D₅₃	C₂²×D₄	1	3	yes	—
495	C₂²×D₅₃	C₂²×D₄	1	6	yes	—
496	Q₈×C₅₃	—	2	6	no	—
497	Q₈×C₅₃	—	2	1	no	—
498	Q₈×C₅₃	C₂²×D₄	1	4	yes	—
499	Q₈×C₅₃	C₂⁵	1	2	yes	—
500	Q₈×C₅₃	C₂⁵	1	4	yes	—
501	D₄×C₅₃	—	2	12	no	—
502	D₄×C₅₃	—	2	4	no	—
503	D₄×C₅₃	—	2	12	no	—
504	D₄×C₅₃	—	2	12	no	—
505	D₄×C₅₃	—	2	3	no	—
506	D₄×C₅₃	—	2	6	no	—
507	D₄×C₅₃	C₂²×D₄	1	12	yes	—
508	D₄×C₅₃	C₂⁵	1	6	yes	—
509	D₄×C₅₃	C₂⁵	1	4	yes	—
510	C₂×C₄×C₅₃	—	2	1	no	—
511	C₂×C₄×C₅₃	—	2	6	no	—
512	C₂×C₄×C₅₃	—	2	12	no	—
513	C₂×C₄×C₅₃	—	2	4	no	—
514	C₂×C₄×C₅₃	—	2	12	no	—
515	C₂×C₄×C₅₃	C₂²×D₄	1	3	yes	—
516	C₂×C₄×C₅₃	C₂²×D₄	1	6	yes	—
517	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
518	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
519	C₂²⋊D₅₃	—	2	4	no	—
520	C₂²⋊D₅₃	—	2	12	no	—
521	C₂²⋊D₅₃	—	2	12	no	—
522	C₂²⋊D₅₃	—	2	4	no	—
523	C₂²⋊D₅₃	—	2	12	no	—
524	C₂²⋊D₅₃	—	2	12	no	—
525	C₂²⋊D₅₃	—	2	4	no	—
526	C₂²⋊D₅₃	—	2	12	no	—
527	C₂²⋊D₅₃	—	2	6	no	—
528	C₂²⋊D₅₃	—	2	24	no	—
529	C₂²⋊D₅₃	—	2	6	no	—
530	C₂²⋊D₅₃	C₂²×D₄	1	24	yes	—
531	C₂×Dic₅₃	—	2	1	no	—
532	C₂×Dic₅₃	—	2	6	no	—
533	C₂×Dic₅₃	—	2	12	no	—
534	C₂×Dic₅₃	—	2	4	no	—
535	C₂×Dic₅₃	—	2	12	no	—
536	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
537	C₂×Dic₅₃	C₂²×D₄	1	6	yes	—
538	C₂×Dic₅₃	C₂²×D₄	1	3	yes	—
539	C₂×Dic₅₃	C₂²×D₄	1	6	yes	—
540	D₂₁₂	—	2	12	no	—
541	D₂₁₂	—	2	4	no	—
542	D₂₁₂	—	2	12	no	—
543	D₂₁₂	—	2	12	no	—
544	D₂₁₂	—	2	3	no	—
545	D₂₁₂	—	2	6	no	—
546	D₂₁₂	C₂²×D₄	1	12	yes	—
547	D₂₁₂	C₂⁵	1	6	yes	—
548	D₂₁₂	C₂⁵	1	4	yes	—
549	C₄×D₅₃	—	2	2	no	—
550	C₄×D₅₃	—	2	2	no	—
551	C₄×D₅₃	—	2	4	no	—
552	C₄×D₅₃	—	2	12	no	—
553	C₄×D₅₃	—	2	4	no	—
554	C₄×D₅₃	—	2	12	no	—
555	C₄×D₅₃	—	2	12	no	—
556	C₄×D₅₃	—	2	4	no	—
557	C₄×D₅₃	—	2	12	no	—
558	C₄×D₅₃	—	2	12	no	—
559	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
560	C₄×D₅₃	C₂²×D₄	1	6	yes	—
561	C₄×D₅₃	C₂²×D₄	1	6	yes	—
562	C₄×D₅₃	C₂²×D₄	1	6	yes	—
563	C₄×D₅₃	C₂²×D₄	1	6	yes	—
564	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
565	C₄×D₅₃	C₂²×D₄	1	6	yes	—
566	C₄×D₅₃	C₂⁵	1	1	yes	characteristic
567	C₄×D₅₃	C₂⁵	1	1	yes	characteristic
568	C₄×D₅₃	C₂⁵	1	6	yes	—
569	Dic₁₀₆	—	2	6	no	—
570	Dic₁₀₆	—	2	1	no	—
571	Dic₁₀₆	—	2	4	no	—
572	Dic₁₀₆	—	2	12	no	—
573	Dic₁₀₆	—	2	2	no	—
574	Dic₁₀₆	—	2	2	no	—
575	Dic₁₀₆	C₂²×D₄	1	12	yes	—
576	Dic₁₀₆	C₂⁵	1	2	yes	—
577	Dic₁₀₆	C₂⁵	1	4	yes	—
578	C₈×C₅₃	C₂⁵	1	8	yes	—
579	#88322	C₂⁵	1	8	yes	—
580	C₂×#3585	—	53	1	no	maximal, Sylow
581	C₂²×C₅₃	—	2	4	no	—
582	C₂²×C₅₃	—	2	6	no	—
583	C₂²×C₅₃	—	4	3	no	—
584	C₂²×C₅₃	—	4	6	no	—
585	C₂²×C₅₃	—	8	12	no	—
586	C₂²×C₅₃	—	8	6	no	—
587	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
588	C₂²×C₅₃	C₂³×D₄	1	6	yes	—
589	C₂×D₅₃	—	2	2	no	—
590	C₂×D₅₃	—	2	12	no	—
591	C₂×D₅₃	—	2	4	no	—
592	C₂×D₅₃	—	2	6	no	—
593	C₂×D₅₃	—	4	6	no	—
594	C₂×D₅₃	—	4	3	no	—
595	C₂×D₅₃	—	4	12	no	—
596	C₂×D₅₃	—	4	6	no	—
597	C₂×D₅₃	—	4	12	no	—
598	C₂×D₅₃	—	4	8	no	—
599	C₂×D₅₃	—	8	12	no	—
600	C₂×D₅₃	—	8	24	no	—
601	C₂×D₅₃	—	8	6	no	—
602	C₂×D₅₃	—	8	12	no	—
603	C₂×D₅₃	C₂³×D₄	1	1	yes	characteristic
604	C₂×D₅₃	C₂³×D₄	1	6	yes	—
605	C₂×D₅₃	C₂³×D₄	1	1	yes	characteristic
606	C₄×C₅₃	—	2	4	no	—
607	C₄×C₅₃	—	2	2	no	—
608	C₄×C₅₃	C₂³×D₄	1	6	yes	—
609	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
610	C₄×C₅₃	C₂⁶	1	1	yes	characteristic
611	Dic₅₃	—	2	4	no	—
612	Dic₅₃	—	2	2	no	—
613	Dic₅₃	C₂³×D₄	1	1	yes	characteristic
614	Dic₅₃	C₂³×D₄	1	6	yes	—
615	Dic₅₃	C₂³×D₄	1	1	yes	characteristic
616	C₂×#585	—	53	1	no	—
617	C₂²×H(5,𝔽₂)	—	53	1	no	—
618	#3585	—	53	1	no	—
619	#3585	—	53	1	no	—
620	#3585	—	53	8	no	—
621	#3585	—	53	8	no	—
622	#3585	—	53	6	no	—
623	#3585	—	53	6	no	—
624	#3585	—	53	1	no	—
625	#3585	D₅₃	1	1	yes	characteristic, direct product factor
626	C₂×#577	—	53	8	no	—
627	C₂×#576	—	53	8	no	—
628	C₂×#575	—	53	6	no	—
629	C₂²×AGL(1,ℤ/8)	—	53	6	no	—
630	C₂×#568	—	53	1	no	—
631	C₂×C₅₃	—	2	1	no	—
632	C₂×C₅₃	—	2	6	no	—
633	C₂×C₅₃	—	4	6	no	—
634	C₂×C₅₃	—	4	4	no	—
635	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
636	D₅₃	—	2	1	no	—
637	D₅₃	—	2	6	no	—
638	D₅₃	—	4	6	no	—
639	D₅₃	—	4	4	no	—
640	D₅₃	#3585	1	2	yes	direct product factor
641	#585	—	53	4	no	—
642	#585	—	53	4	no	—
643	#585	—	53	1	no	—
644	#585	—	53	6	no	—
645	#585	—	106	4	no	—
646	#585	—	106	3	no	—
647	#585	—	106	1	no	—
648	#585	C₂×D₅₃	1	1	yes	characteristic, complemented
649	C₂×2₋¹⁺⁴	—	53	4	no	—
650	C₂×2₋¹⁺⁴	—	106	1	no	—
651	C₂×H(5,𝔽₂)	—	53	8	no	—
652	C₂×H(5,𝔽₂)	—	53	8	no	—
653	C₂×H(5,𝔽₂)	—	53	4	no	—
654	C₂×H(5,𝔽₂)	—	53	1	no	—
655	C₂×H(5,𝔽₂)	—	53	3	no	—
656	C₂×H(5,𝔽₂)	—	53	3	no	—
657	C₂×H(5,𝔽₂)	—	106	3	no	—
658	C₂×H(5,𝔽₂)	—	106	3	no	—
659	C₂×H(5,𝔽₂)	—	106	1	no	—
660	C₂×H(5,𝔽₂)	—	106	4	no	—
661	C₂×H(5,𝔽₂)	—	106	4	no	—
662	C₂×H(5,𝔽₂)	C₂×D₅₃	1	1	yes	characteristic, complemented
663	C₂²×#41	—	53	1	no	—
664	C₂²×#41	—	53	3	no	—
665	C₂²×#41	—	53	6	no	—
666	C₂²×#41	—	106	1	no	—
667	C₂²×#41	—	106	4	no	—
668	C₂³×D₄	—	53	3	no	—
669	C₂³×D₄	—	106	3	no	—
670	#577	—	53	8	no	—
671	#577	—	53	8	no	—
672	#577	—	53	24	no	—
673	#577	—	53	24	no	—
674	#577	—	53	24	no	—
675	#577	—	53	24	no	—
676	#577	—	53	8	no	—
677	#577	C₂×D₅₃	1	8	yes	complemented
678	#576	—	53	8	no	—
679	#576	—	53	8	no	—
680	#576	—	53	24	no	—
681	#576	—	53	24	no	—
682	#576	—	53	24	no	—
683	#576	—	53	24	no	—
684	#576	—	53	8	no	—
685	#576	C₂×D₅₃	1	8	yes	complemented
686	#575	—	53	6	no	—
687	#575	—	53	6	no	—
688	#575	—	53	12	no	—
689	#575	—	53	12	no	—
690	#575	—	53	12	no	—
691	#575	—	53	12	no	—
692	#575	—	53	24	no	—
693	#575	—	53	6	no	—
694	#575	C₂×D₅₃	1	6	yes	complemented
695	C₂×#137	—	53	4	no	—
696	C₂×#137	—	53	12	no	—
697	C₂×AGL(1,ℤ/8)	—	53	6	no	—
698	C₂×AGL(1,ℤ/8)	—	53	6	no	—
699	C₂×AGL(1,ℤ/8)	—	53	24	no	—
700	C₂×AGL(1,ℤ/8)	—	53	24	no	—
701	C₂×AGL(1,ℤ/8)	—	53	12	no	—
702	C₂×AGL(1,ℤ/8)	—	53	24	no	—
703	C₂×AGL(1,ℤ/8)	—	53	12	no	—
704	C₂×AGL(1,ℤ/8)	—	53	12	no	—
705	C₂×AGL(1,ℤ/8)	—	53	12	no	—
706	C₂×AGL(1,ℤ/8)	—	53	6	no	—
707	C₂×AGL(1,ℤ/8)	C₂×D₅₃	1	6	yes	complemented
708	C₂×#135	—	53	24	no	—
709	C₂²×SD₁₆	—	53	12	no	—
710	C₂²×D₈	—	53	12	no	—
711	#568	—	53	1	no	—
712	#568	—	53	8	no	—
713	#568	—	53	6	no	—
714	#568	C₂×D₅₃	1	1	yes	characteristic, complemented
715	C₂×#131	—	53	8	no	—
716	C₂²×M₁₆	—	53	6	no	—
717	C₅₃	C₂×#3585	1	1	yes	characteristic, complemented, Sylow
718	C₂⁵	—	106	3	no	—
719	2₋¹⁺⁴	—	2	1	no	—
720	2₋¹⁺⁴	—	53	4	no	—
721	2₋¹⁺⁴	—	53	12	no	—
722	2₋¹⁺⁴	—	53	12	no	—
723	2₋¹⁺⁴	—	106	4	no	—
724	2₋¹⁺⁴	—	106	4	no	—
725	2₋¹⁺⁴	—	106	4	no	—
726	2₋¹⁺⁴	—	106	6	no	—
727	2₋¹⁺⁴	—	106	12	no	—
728	2₋¹⁺⁴	—	106	1	no	—
729	2₋¹⁺⁴	C₂²×D₅₃	1	4	yes	complemented
730	H(5,𝔽₂)	—	2	4	no	—
731	H(5,𝔽₂)	—	2	3	no	—
732	H(5,𝔽₂)	—	53	4	no	—
733	H(5,𝔽₂)	—	53	24	no	—
734	H(5,𝔽₂)	—	53	8	no	—
735	H(5,𝔽₂)	—	53	12	no	—
736	H(5,𝔽₂)	—	53	24	no	—
737	H(5,𝔽₂)	—	53	12	no	—
738	H(5,𝔽₂)	—	106	12	no	—
739	H(5,𝔽₂)	—	106	12	no	—
740	H(5,𝔽₂)	—	106	24	no	—
741	H(5,𝔽₂)	—	106	24	no	—
742	H(5,𝔽₂)	—	106	12	no	—
743	H(5,𝔽₂)	—	106	12	no	—
744	H(5,𝔽₂)	—	106	12	no	—
745	H(5,𝔽₂)	—	106	6	no	—
746	H(5,𝔽₂)	—	106	8	no	—
747	H(5,𝔽₂)	—	106	8	no	—
748	H(5,𝔽₂)	—	106	12	no	—
749	H(5,𝔽₂)	—	106	4	no	—
750	H(5,𝔽₂)	—	106	4	no	—
751	H(5,𝔽₂)	—	106	3	no	—
752	H(5,𝔽₂)	C₂²×D₅₃	1	8	yes	complemented
753	H(5,𝔽₂)	C₂²×D₅₃	1	4	yes	complemented
754	C₂×#41	—	2	4	no	—
755	C₂×#41	—	2	1	no	—
756	C₂×#41	—	53	4	no	—
757	C₂×#41	—	53	4	no	—
758	C₂×#41	—	53	4	no	—
759	C₂×#41	—	53	4	no	—
760	C₂×#41	—	53	1	no	—
761	C₂×#41	—	53	3	no	—
762	C₂×#41	—	53	3	no	—
763	C₂×#41	—	53	12	no	—
764	C₂×#41	—	53	4	no	—
765	C₂×#41	—	53	12	no	—
766	C₂×#41	—	53	12	no	—
767	C₂×#41	—	53	12	no	—
768	C₂×#41	—	53	12	no	—
769	C₂×#41	—	53	3	no	—
770	C₂×#41	—	53	6	no	—
771	C₂×#41	—	53	3	no	—
772	C₂×#41	—	53	6	no	—
773	C₂×#41	—	53	6	no	—
774	C₂×#41	—	53	3	no	—
775	C₂×#41	—	106	3	no	—
776	C₂×#41	—	106	6	no	—
777	C₂×#41	—	106	3	no	—
778	C₂×#41	—	106	12	no	—
779	C₂×#41	—	106	3	no	—
780	C₂×#41	—	106	6	no	—
781	C₂×#41	—	106	6	no	—
782	C₂×#41	—	106	6	no	—
783	C₂×#41	—	106	6	no	—
784	C₂×#41	—	106	6	no	—
785	C₂×#41	—	106	6	no	—
786	C₂×#41	—	106	6	no	—
787	C₂×#41	—	106	3	no	—
788	C₂×#41	—	106	12	no	—
789	C₂×#41	—	106	12	no	—
790	C₂×#41	—	106	4	no	—
791	C₂×#41	—	106	8	no	—
792	C₂×#41	—	106	8	no	—
793	C₂×#41	—	106	4	no	—
794	C₂×#41	—	106	4	no	—
795	C₂×#41	—	106	12	no	—
796	C₂×#41	—	106	12	no	—
797	C₂×#41	—	106	4	no	—
798	C₂×#41	—	106	1	no	—
799	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
800	C₂×#41	C₂²×D₅₃	1	3	yes	complemented
801	C₂×#41	C₂²×D₅₃	1	6	yes	complemented
802	C₂²×Q₈	—	53	1	no	—
803	C₂²×Q₈	—	53	1	no	—
804	C₂²×Q₈	—	53	6	no	—
805	C₂²×Q₈	—	106	4	no	—
806	C₂²×D₄	—	2	3	no	—
807	C₂²×D₄	—	53	3	no	—
808	C₂²×D₄	—	53	12	no	—
809	C₂²×D₄	—	53	3	no	—
810	C₂²×D₄	—	53	6	no	—
811	C₂²×D₄	—	53	12	no	—
812	C₂²×D₄	—	53	6	no	—
813	C₂²×D₄	—	53	3	no	—
814	C₂²×D₄	—	106	3	no	—
815	C₂²×D₄	—	106	3	no	—
816	C₂²×D₄	—	106	6	no	—
817	C₂²×D₄	—	106	3	no	—
818	C₂²×D₄	—	106	6	no	—
819	C₂²×D₄	—	106	3	no	—
820	C₂²×D₄	—	106	6	no	—
821	C₂²×D₄	—	106	24	no	—
822	C₂²×D₄	—	106	24	no	—
823	C₂²×D₄	—	106	3	no	—
824	C₂²×D₄	—	106	12	no	—
825	C₂²×D₄	—	106	3	no	—
826	C₂²×D₄	—	106	6	no	—
827	C₂²×D₄	—	106	6	no	—
828	C₂²×D₄	—	106	3	no	—
829	C₂²×D₄	C₂²×D₅₃	1	3	yes	complemented
830	C₂³×C₄	—	53	3	no	—
831	C₂³×C₄	—	106	3	no	—
832	C₂³×C₄	—	106	6	no	—
833	#137	—	53	4	no	—
834	#137	—	53	12	no	—
835	#137	—	53	4	no	—
836	#137	—	53	12	no	—
837	#137	—	53	8	no	—
838	#137	—	53	24	no	—
839	#137	—	53	8	no	—
840	#137	—	53	24	no	—
841	#137	—	53	4	no	—
842	#137	—	53	12	no	—
843	#137	C₂²×D₅₃	1	4	yes	complemented
844	#137	C₂²×D₅₃	1	12	yes	complemented
845	AGL(1,ℤ/8)	—	53	12	no	—
846	AGL(1,ℤ/8)	—	53	12	no	—
847	AGL(1,ℤ/8)	—	53	24	no	—
848	AGL(1,ℤ/8)	—	53	12	no	—
849	AGL(1,ℤ/8)	—	53	24	no	—
850	AGL(1,ℤ/8)	—	53	12	no	—
851	AGL(1,ℤ/8)	—	53	24	no	—
852	AGL(1,ℤ/8)	—	53	48	no	—
853	AGL(1,ℤ/8)	—	53	24	no	—
854	AGL(1,ℤ/8)	—	53	24	no	—
855	AGL(1,ℤ/8)	—	53	48	no	—
856	AGL(1,ℤ/8)	—	53	24	no	—
857	AGL(1,ℤ/8)	—	53	12	no	—
858	AGL(1,ℤ/8)	—	53	24	no	—
859	AGL(1,ℤ/8)	—	53	12	no	—
860	AGL(1,ℤ/8)	C₂²×D₅₃	1	12	yes	complemented
861	AGL(1,ℤ/8)	C₂²×D₅₃	1	24	yes	complemented
862	AGL(1,ℤ/8)	C₂²×D₅₃	1	12	yes	complemented
863	#135	—	53	24	no	—
864	#135	—	53	24	no	—
865	#135	—	53	24	no	—
866	#135	—	53	24	no	—
867	#135	—	53	24	no	—
868	#135	—	53	24	no	—
869	#135	—	53	24	no	—
870	#135	C₂²×D₅₃	1	24	yes	complemented
871	C₂×Q₁₆	—	53	8	no	—
872	C₂×SD₁₆	—	53	12	no	—
873	C₂×SD₁₆	—	53	12	no	—
874	C₂×SD₁₆	—	53	24	no	—
875	C₂×SD₁₆	—	53	48	no	—
876	C₂×SD₁₆	—	53	8	no	—
877	C₂×SD₁₆	—	53	12	no	—
878	C₂×SD₁₆	C₂²×D₅₃	1	12	yes	complemented
879	C₂×D₈	—	53	12	no	—
880	C₂×D₈	—	53	12	no	—
881	C₂×D₈	—	53	24	no	—
882	C₂×D₈	—	53	48	no	—
883	C₂×D₈	—	53	12	no	—
884	C₂×D₈	C₂²×D₅₃	1	12	yes	complemented
885	#131	—	53	8	no	—
886	#131	—	53	24	no	—
887	#131	—	53	24	no	—
888	#131	C₂²×D₅₃	1	8	yes	complemented
889	C₂×M₁₆	—	53	6	no	—
890	C₂×M₁₆	—	53	4	no	—
891	C₂×M₁₆	—	53	12	no	—
892	C₂×M₁₆	—	53	12	no	—
893	C₂×M₁₆	—	53	12	no	—
894	C₂×M₁₆	—	53	12	no	—
895	C₂×M₁₆	C₂²×D₅₃	1	6	yes	complemented
896	C₂²×C₈	—	53	12	no	—
897	C₂⁴	—	2	3	no	—
898	C₂⁴	—	53	3	no	—
899	C₂⁴	—	106	6	no	—
900	C₂⁴	—	106	6	no	—
901	C₂⁴	—	106	12	no	—
902	C₂⁴	—	106	12	no	—
903	C₂⁴	—	106	3	no	—
904	C₂⁴	—	106	3	no	—
905	C₂⁴	—	424	12	no	—
906	#41	—	2	8	no	—
907	#41	—	2	4	no	—
908	#41	—	2	12	no	—
909	#41	—	2	6	no	—
910	#41	—	2	6	no	—
911	#41	—	2	6	no	—
912	#41	—	53	4	no	—
913	#41	—	53	4	no	—
914	#41	—	53	12	no	—
915	#41	—	53	12	no	—
916	#41	—	53	12	no	—
917	#41	—	53	12	no	—
918	#41	—	53	12	no	—
919	#41	—	53	4	no	—
920	#41	—	53	12	no	—
921	#41	—	53	12	no	—
922	#41	—	53	4	no	—
923	#41	—	53	12	no	—
924	#41	—	53	12	no	—
925	#41	—	53	4	no	—
926	#41	—	53	12	no	—
927	#41	—	106	4	no	—
928	#41	—	106	12	no	—
929	#41	—	106	12	no	—
930	#41	—	106	12	no	—
931	#41	—	106	12	no	—
932	#41	—	106	12	no	—
933	#41	—	106	24	no	—
934	#41	—	106	12	no	—
935	#41	—	106	24	no	—
936	#41	—	106	12	no	—
937	#41	—	106	4	no	—
938	#41	—	106	12	no	—
939	#41	—	106	6	no	—
940	#41	—	106	12	no	—
941	#41	—	106	12	no	—
942	#41	—	106	6	no	—
943	#41	—	106	12	no	—
944	#41	—	106	12	no	—
945	#41	—	106	6	no	—
946	#41	—	106	6	no	—
947	#41	—	106	6	no	—
948	#41	—	106	6	no	—
949	#41	—	106	24	no	—
950	#41	—	106	24	no	—
951	#41	—	106	12	no	—
952	#41	—	106	12	no	—
953	#41	—	106	8	no	—
954	#41	—	106	4	no	—
955	#41	—	106	12	no	—
956	#41	—	106	6	no	—
957	#41	—	106	6	no	—
958	#41	—	106	6	no	—
959	#41	D₄×D₅₃	1	4	yes	—
960	#41	C₂³×D₅₃	1	12	yes	—
961	#41	C₂³×D₅₃	1	4	yes	—
962	#41	C₂³×D₅₃	1	4	yes	—
963	#41	C₂³×D₅₃	1	12	yes	complemented
964	C₂×Q₈	—	2	4	no	—
965	C₂×Q₈	—	53	4	no	—
966	C₂×Q₈	—	53	4	no	—
967	C₂×Q₈	—	53	3	no	—
968	C₂×Q₈	—	53	4	no	—
969	C₂×Q₈	—	53	2	no	—
970	C₂×Q₈	—	53	2	no	—
971	C₂×Q₈	—	53	12	no	—
972	C₂×Q₈	—	53	1	no	—
973	C₂×Q₈	—	53	6	no	—
974	C₂×Q₈	—	106	1	no	—
975	C₂×Q₈	—	106	6	no	—
976	C₂×Q₈	—	106	12	no	—
977	C₂×Q₈	—	106	6	no	—
978	C₂×Q₈	—	106	1	no	—
979	C₂×Q₈	—	106	1	no	—
980	C₂×Q₈	—	106	6	no	—
981	C₂×Q₈	—	106	12	no	—
982	C₂×Q₈	—	106	4	no	—
983	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
984	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
985	C₂×Q₈	C₂³×D₅₃	1	6	yes	complemented
986	C₂×D₄	—	2	3	no	—
987	C₂×D₄	—	2	6	no	—
988	C₂×D₄	—	2	24	no	—
989	C₂×D₄	—	2	12	no	—
990	C₂×D₄	—	2	3	no	—
991	C₂×D₄	—	2	6	no	—
992	C₂×D₄	—	53	6	no	—
993	C₂×D₄	—	53	12	no	—
994	C₂×D₄	—	53	12	no	—
995	C₂×D₄	—	53	4	no	—
996	C₂×D₄	—	53	6	no	—
997	C₂×D₄	—	53	24	no	—
998	C₂×D₄	—	53	6	no	—
999	C₂×D₄	—	53	12	no	—
1000	C₂×D₄	—	53	3	no	—
1001	C₂×D₄	—	53	12	no	—
1002	C₂×D₄	—	53	3	no	—
1003	C₂×D₄	—	53	6	no	—
1004	C₂×D₄	—	106	24	no	—
1005	C₂×D₄	—	106	12	no	—
1006	C₂×D₄	—	106	3	no	—
1007	C₂×D₄	—	106	6	no	—
1008	C₂×D₄	—	106	3	no	—
1009	C₂×D₄	—	106	3	no	—
1010	C₂×D₄	—	106	12	no	—
1011	C₂×D₄	—	106	12	no	—
1012	C₂×D₄	—	106	6	no	—
1013	C₂×D₄	—	106	12	no	—
1014	C₂×D₄	—	106	12	no	—
1015	C₂×D₄	—	106	12	no	—
1016	C₂×D₄	—	106	6	no	—
1017	C₂×D₄	—	106	3	no	—
1018	C₂×D₄	—	106	6	no	—
1019	C₂×D₄	—	106	12	no	—
1020	C₂×D₄	—	106	12	no	—
1021	C₂×D₄	—	106	6	no	—
1022	C₂×D₄	—	106	48	no	—
1023	C₂×D₄	—	106	24	no	—
1024	C₂×D₄	—	106	24	no	—
1025	C₂×D₄	—	106	12	no	—
1026	C₂×D₄	—	106	12	no	—
1027	C₂×D₄	—	106	12	no	—
1028	C₂×D₄	—	106	4	no	—
1029	C₂×D₄	—	106	12	no	—
1030	C₂×D₄	—	106	12	no	—
1031	C₂×D₄	—	106	12	no	—
1032	C₂×D₄	—	106	48	no	—
1033	C₂×D₄	—	106	24	no	—
1034	C₂×D₄	—	106	3	no	—
1035	C₂×D₄	—	106	6	no	—
1036	C₂×D₄	—	106	3	no	—
1037	C₂×D₄	—	106	6	no	—
1038	C₂×D₄	—	106	24	no	—
1039	C₂×D₄	—	106	12	no	—
1040	C₂×D₄	—	106	3	no	—
1041	C₂×D₄	—	106	6	no	—
1042	C₂×D₄	D₄×D₅₃	1	3	yes	—
1043	C₂×D₄	C₂³×D₅₃	1	12	yes	—
1044	C₂×D₄	C₂³×D₅₃	1	3	yes	—
1045	C₂×D₄	C₂³×D₅₃	1	6	yes	complemented
1046	C₂²×C₄	—	2	3	no	—
1047	C₂²×C₄	—	2	6	no	—
1048	C₂²×C₄	—	53	3	no	—
1049	C₂²×C₄	—	53	3	no	—
1050	C₂²×C₄	—	53	6	no	—
1051	C₂²×C₄	—	53	3	no	—
1052	C₂²×C₄	—	53	6	no	—
1053	C₂²×C₄	—	53	6	no	—
1054	C₂²×C₄	—	53	1	no	—
1055	C₂²×C₄	—	53	3	no	—
1056	C₂²×C₄	—	53	6	no	—
1057	C₂²×C₄	—	106	4	no	—
1058	C₂²×C₄	—	106	3	no	—
1059	C₂²×C₄	—	106	12	no	—
1060	C₂²×C₄	—	106	12	no	—
1061	C₂²×C₄	—	106	12	no	—
1062	C₂²×C₄	—	106	6	no	—
1063	C₂²×C₄	—	106	12	no	—
1064	C₂²×C₄	—	106	12	no	—
1065	C₂²×C₄	—	106	1	no	—
1066	C₂²×C₄	—	106	6	no	—
1067	C₂²×C₄	—	106	3	no	—
1068	C₂²×C₄	—	106	6	no	—
1069	C₂²×C₄	—	106	3	no	—
1070	C₂²×C₄	—	106	6	no	—
1071	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1072	Q₁₆	—	53	8	no	—
1073	Q₁₆	—	53	8	no	—
1074	Q₁₆	—	53	8	no	—
1075	Q₁₆	C₂³×D₅₃	1	8	yes	complemented
1076	SD₁₆	—	53	24	no	—
1077	SD₁₆	—	53	8	no	—
1078	SD₁₆	—	53	24	no	—
1079	SD₁₆	—	53	8	no	—
1080	SD₁₆	—	53	24	no	—
1081	SD₁₆	—	53	8	no	—
1082	SD₁₆	C₂³×D₅₃	1	24	yes	complemented
1083	SD₁₆	C₂³×D₅₃	1	8	yes	complemented
1084	D₈	—	53	24	no	—
1085	D₈	—	53	24	no	—
1086	D₈	—	53	24	no	—
1087	D₈	C₂³×D₅₃	1	24	yes	complemented
1088	M₁₆	—	53	4	no	—
1089	M₁₆	—	53	12	no	—
1090	M₁₆	—	53	8	no	—
1091	M₁₆	—	53	24	no	—
1092	M₁₆	C₂³×D₅₃	1	4	yes	—
1093	M₁₆	C₂³×D₅₃	1	12	yes	complemented
1094	C₂×C₈	—	53	12	no	—
1095	C₂×C₈	—	53	8	no	—
1096	C₂×C₈	—	53	24	no	—
1097	C₂×C₈	C₂³×D₅₃	1	12	yes	complemented
1098	C₂³	—	2	3	no	—
1099	C₂³	—	2	6	no	—
1100	C₂³	—	2	12	no	—
1101	C₂³	—	8	6	no	—
1102	C₂³	—	53	1	no	—
1103	C₂³	—	53	6	no	—
1104	C₂³	—	53	6	no	—
1105	C₂³	—	53	3	no	—
1106	C₂³	—	106	12	no	—
1107	C₂³	—	106	24	no	—
1108	C₂³	—	106	4	no	—
1109	C₂³	—	106	6	no	—
1110	C₂³	—	106	6	no	—
1111	C₂³	—	106	6	no	—
1112	C₂³	—	106	12	no	—
1113	C₂³	—	106	3	no	—
1114	C₂³	—	424	6	no	—
1115	C₂³	—	424	12	no	—
1116	C₂³	—	424	12	no	—
1117	C₂³	—	424	24	no	—
1118	C₂³	—	424	24	no	—
1119	C₂³	—	212	6	no	—
1120	C₂³	—	212	12	no	—
1121	C₂³	C₂×D₄×D₅₃	1	3	yes	—
1122	Q₈	—	2	6	no	—
1123	Q₈	—	2	1	no	—
1124	Q₈	—	53	12	no	—
1125	Q₈	—	53	4	no	—
1126	Q₈	—	53	2	no	—
1127	Q₈	—	106	4	no	—
1128	Q₈	—	106	12	no	—
1129	Q₈	—	106	2	no	—
1130	Q₈	—	106	2	no	—
1131	Q₈	—	106	6	no	—
1132	Q₈	—	106	1	no	—
1133	Q₈	C₂×D₄×D₅₃	1	4	yes	—
1134	Q₈	C₂⁴×D₅₃	1	4	yes	—
1135	Q₈	C₂⁴×D₅₃	1	2	yes	—
1136	D₄	—	2	12	no	—
1137	D₄	—	2	4	no	—
1138	D₄	—	2	12	no	—
1139	D₄	—	2	3	no	—
1140	D₄	—	2	12	no	—
1141	D₄	—	2	6	no	—
1142	D₄	—	53	24	no	—
1143	D₄	—	53	12	no	—
1144	D₄	—	53	4	no	—
1145	D₄	—	53	6	no	—
1146	D₄	—	106	12	no	—
1147	D₄	—	106	4	no	—
1148	D₄	—	106	12	no	—
1149	D₄	—	106	6	no	—
1150	D₄	—	106	6	no	—
1151	D₄	—	106	24	no	—
1152	D₄	—	106	4	no	—
1153	D₄	—	106	12	no	—
1154	D₄	—	106	12	no	—
1155	D₄	—	106	4	no	—
1156	D₄	—	106	12	no	—
1157	D₄	—	106	12	no	—
1158	D₄	—	106	4	no	—
1159	D₄	—	106	12	no	—
1160	D₄	—	106	3	no	—
1161	D₄	—	106	12	no	—
1162	D₄	—	106	6	no	—
1163	D₄	C₂×D₄×D₅₃	1	12	yes	—
1164	D₄	C₂⁴×D₅₃	1	4	yes	—
1165	D₄	C₂⁴×D₅₃	1	6	yes	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	6	no	—
1168	C₂×C₄	—	2	4	no	—
1169	C₂×C₄	—	2	12	no	—
1170	C₂×C₄	—	2	12	no	—
1171	C₂×C₄	—	53	1	no	—
1172	C₂×C₄	—	53	3	no	—
1173	C₂×C₄	—	53	6	no	—
1174	C₂×C₄	—	53	6	no	—
1175	C₂×C₄	—	53	1	no	—
1176	C₂×C₄	—	53	1	no	—
1177	C₂×C₄	—	53	6	no	—
1178	C₂×C₄	—	53	6	no	—
1179	C₂×C₄	—	53	6	no	—
1180	C₂×C₄	—	53	6	no	—
1181	C₂×C₄	—	53	6	no	—
1182	C₂×C₄	—	53	1	no	—
1183	C₂×C₄	—	53	6	no	—
1184	C₂×C₄	—	53	1	no	—
1185	C₂×C₄	—	106	4	no	—
1186	C₂×C₄	—	106	12	no	—
1187	C₂×C₄	—	106	12	no	—
1188	C₂×C₄	—	106	2	no	—
1189	C₂×C₄	—	106	2	no	—
1190	C₂×C₄	—	106	4	no	—
1191	C₂×C₄	—	106	12	no	—
1192	C₂×C₄	—	106	4	no	—
1193	C₂×C₄	—	106	12	no	—
1194	C₂×C₄	—	106	12	no	—
1195	C₂×C₄	—	106	1	no	—
1196	C₂×C₄	—	106	6	no	—
1197	C₂×C₄	—	106	4	no	—
1198	C₂×C₄	—	106	12	no	—
1199	C₂×C₄	—	106	12	no	—
1200	C₂×C₄	C₂×D₄×D₅₃	1	3	yes	—
1201	C₂×C₄	C₂×D₄×D₅₃	1	6	yes	—
1202	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1203	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1204	C₈	—	53	8	no	—
1205	C₈	C₂⁴×D₅₃	1	8	yes	—
1206	C₂²	—	2	4	no	—
1207	C₂²	—	2	6	no	—
1208	C₂²	—	4	3	no	—
1209	C₂²	—	4	6	no	—
1210	C₂²	—	8	12	no	—
1211	C₂²	—	8	6	no	—
1212	C₂²	—	53	1	no	—
1213	C₂²	—	53	1	no	—
1214	C₂²	—	53	6	no	—
1215	C₂²	—	106	12	no	—
1216	C₂²	—	106	2	no	—
1217	C₂²	—	106	4	no	—
1218	C₂²	—	106	6	no	—
1219	C₂²	—	424	12	no	—
1220	C₂²	—	424	6	no	—
1221	C₂²	—	424	24	no	—
1222	C₂²	—	424	12	no	—
1223	C₂²	—	212	3	no	—
1224	C₂²	—	212	6	no	—
1225	C₂²	—	212	6	no	—
1226	C₂²	—	212	12	no	—
1227	C₂²	—	212	8	no	—
1228	C₂²	—	212	12	no	—
1229	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1230	C₂²	C₂²×D₄×D₅₃	1	6	yes	—
1231	C₄	—	2	2	no	—
1232	C₄	—	2	4	no	—
1233	C₄	—	53	1	no	—
1234	C₄	—	53	1	no	—
1235	C₄	—	53	6	no	—
1236	C₄	—	106	2	no	—
1237	C₄	—	106	4	no	—
1238	C₄	C₂²×D₄×D₅₃	1	1	yes	characteristic
1239	C₄	C₂²×D₄×D₅₃	1	6	yes	—
1240	C₄	C₂⁵×D₅₃	1	1	yes	characteristic
1241	C₂	—	2	1	no	—
1242	C₂	—	2	6	no	—
1243	C₂	—	4	6	no	—
1244	C₂	—	4	4	no	—
1245	C₂	—	53	2	no	—
1246	C₂	—	106	6	no	—
1247	C₂	—	106	1	no	—
1248	C₂	—	212	6	no	—
1249	C₂	—	212	4	no	—
1250	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂³×D₄×D₅₃
commutator, cosocle	C₄×C₅₃	C₂⁶
Frattini	C₄	C₂⁵×D₅₃
Fitting	C₅₃×#3585	C₂
socle	C₂×C₅₃	C₂⁴×D₄
hypercenter	#3585	D₅₃
hypocenter	C₅₃	C₂×#3585
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ #3585

Complements

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

N	H ≅ G/N	type
1. #585×D₅₃	C₂	semidirect
2. C₂×H(5,𝔽₂)×D₅₃	C₂	semidirect
3. #20289496	C₂	semidirect
4. #20289495	C₂	semidirect
5. #20289494	C₂	semidirect
6. #20289493	C₂	semidirect
7. #20289492	C₂	semidirect
8. #20289491	C₂	semidirect
9. #20289490	C₂	semidirect
10. #577×D₅₃	C₂	semidirect
11. #576×D₅₃	C₂	semidirect
12. #575×D₅₃	C₂	semidirect
13. C₂×AGL(1,ℤ/8)×D₅₃	C₂	semidirect
14. #568×D₅₃	C₂	semidirect
15. C₅₃×#3585	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. C₂×#13133263	C₂²	semidirect
27. C₂×#13133263	C₂²	semidirect
29. C₂×#13133262	C₂²	semidirect
33. H(5,𝔽₂)×D₅₃	C₂²	semidirect
34. H(5,𝔽₂)×D₅₃	C₂²	semidirect
35. H(5,𝔽₂)×D₅₃	C₂²	semidirect
39. C₂×#41×D₅₃	C₂²	semidirect
40. C₂×#41×D₅₃	C₂²	semidirect
42. C₂²×D₄×D₅₃	C₂²	semidirect
43. #16811435	C₂²	semidirect
44. #16811434	C₂²	semidirect
45. #16811433	C₂²	semidirect
46. #16811432	C₂²	semidirect
47. #16811431	C₂²	semidirect
48. #16811430	C₂²	semidirect
49. #16811429	C₂²	semidirect
50. #16811428	C₂²	semidirect
51. #16811427	C₂²	semidirect
52. #16811427	C₂²	semidirect
53. #16811426	C₂²	semidirect
54. #16811426	C₂²	semidirect
55. #16811425	C₂²	semidirect
56. #16811424	C₂²	semidirect
57. #16811423	C₂²	semidirect
58. #16811422	C₂²	semidirect
59. #16811422	C₂²	semidirect
60. #16811421	C₂²	semidirect
61. #16811421	C₂²	semidirect
62. #16811420	C₂²	semidirect
63. #16811419	C₂²	semidirect
64. #16811419	C₂²	semidirect
65. #137×D₅₃	C₂²	semidirect
66. #137×D₅₃	C₂²	semidirect
67. C₂×#13133245	C₂²	semidirect
68. C₂×#13133244	C₂²	semidirect
69. C₂×#13133243	C₂²	semidirect
70. C₂×#13133242	C₂²	semidirect
71. C₂×#13133241	C₂²	semidirect
72. AGL(1,ℤ/8)×D₅₃	C₂²	semidirect
73. AGL(1,ℤ/8)×D₅₃	C₂²	semidirect
74. AGL(1,ℤ/8)×D₅₃	C₂²	semidirect
75. AGL(1,ℤ/8)×D₅₃	C₂²	semidirect
76. AGL(1,ℤ/8)×D₅₃	C₂²	semidirect
77. #135×D₅₃	C₂²	semidirect
78. C₂×SD₁₆×D₅₃	C₂²	semidirect
79. C₂×D₈×D₅₃	C₂²	semidirect
80. #16811390	C₂²	semidirect
81. #16811389	C₂²	semidirect
82. #16811388	C₂²	semidirect
83. #131×D₅₃	C₂²	semidirect
84. C₂×M₁₆×D₅₃	C₂²	semidirect
85. C₅₃×#585	C₂²	semidirect
86. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
87. C₅₃×#577	C₂²	semidirect
88. C₅₃×#576	C₂²	semidirect
89. C₅₃×#575	C₂²	semidirect
90. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
91. C₅₃×#568	C₂²	semidirect
96. #13133265	C₂³	semidirect
100. #13133264	C₂³	semidirect
101. #13133264	C₂³	semidirect
109. #13133263	C₂³	semidirect
110. #13133263	C₂³	semidirect
111. #13133263	C₂³	semidirect
112. #13133263	C₂³	semidirect
120. #13133262	C₂³	semidirect
121. #13133262	C₂³	semidirect
125. C₂×#11719949	C₂³	semidirect
126. C₂×#11719949	C₂³	semidirect
132. C₂×#11719945	C₂³	semidirect
133. C₂×#11719945	C₂³	semidirect
139. C₂×#11719947	C₂³	semidirect
140. C₂×#11719947	C₂³	semidirect
161. #41×D₅₃	C₂³	semidirect
162. #41×D₅₃	C₂³	semidirect
163. #41×D₅₃	C₂³	semidirect
164. #41×D₅₃	C₂³	semidirect
168. C₂×Q₈×D₅₃	C₂³	semidirect
170. C₂²×D₂₁₂	C₂³	semidirect
188. C₂×D₄×D₅₃	C₂³	semidirect
189. C₂×D₄×D₅₃	C₂³	semidirect
190. C₂×D₄×D₅₃	C₂³	semidirect
194. #13133250	C₂³	semidirect
195. #13133250	C₂³	semidirect
196. #13133249	C₂³	semidirect
197. #13133249	C₂³	semidirect
198. #13133248	C₂³	semidirect
199. #13133248	C₂³	semidirect
200. #13133247	C₂³	semidirect
201. #13133247	C₂³	semidirect
202. #13133246	C₂³	semidirect
203. #13133246	C₂³	semidirect
204. #13133245	C₂³	semidirect
205. #13133245	C₂³	semidirect
206. #13133245	C₂³	semidirect
207. #13133244	C₂³	semidirect
208. #13133244	C₂³	semidirect
209. #13133244	C₂³	semidirect
210. #13133243	C₂³	semidirect
211. #13133243	C₂³	semidirect
212. #13133243	C₂³	semidirect
213. #13133242	C₂³	semidirect
214. #13133242	C₂³	semidirect
215. #13133242	C₂³	semidirect
216. #13133241	C₂³	semidirect
217. #13133241	C₂³	semidirect
218. #13133241	C₂³	semidirect
219. #13133240	C₂³	semidirect
220. #13133239	C₂³	semidirect
221. #13133238	C₂³	semidirect
222. #13133238	C₂³	semidirect
223. #13133237	C₂³	semidirect
224. #13133237	C₂³	semidirect
225. #13133236	C₂³	semidirect
226. Q₁₆×D₅₃	C₂³	semidirect
227. C₂×#11719913	C₂³	semidirect
228. C₂×#11719923	C₂³	semidirect
229. C₂×#11719924	C₂³	semidirect
230. SD₁₆×D₅₃	C₂³	semidirect
231. SD₁₆×D₅₃	C₂³	semidirect
232. SD₁₆×D₅₃	C₂³	semidirect
233. C₂×D₄₂₄	C₂³	semidirect
234. C₂×#11719922	C₂³	semidirect
235. C₂×#11719922	C₂³	semidirect
236. D₈×D₅₃	C₂³	semidirect
237. D₈×D₅₃	C₂³	semidirect
238. #13133225	C₂³	semidirect
239. #13133224	C₂³	semidirect
240. #13133223	C₂³	semidirect
241. C₂×#11719917	C₂³	semidirect
242. C₂×#11719912	C₂³	semidirect
244. M₁₆×D₅₃	C₂³	semidirect
245. M₁₆×D₅₃	C₂³	semidirect
246. M₁₆×D₅₃	C₂³	semidirect
247. C₂×C₈×D₅₃	C₂³	semidirect
249. 2₋¹⁺⁴×C₅₃	C₂³	semidirect
252. H(5,𝔽₂)×C₅₃	C₂³	semidirect
253. H(5,𝔽₂)×C₅₃	C₂³	semidirect
257. C₂×#41×C₅₃	C₂³	semidirect
258. C₂×#41×C₅₃	C₂³	semidirect
260. C₂²×D₄×C₅₃	C₂³	semidirect
261. #137×C₅₃	C₂³	semidirect
262. #137×C₅₃	C₂³	semidirect
263. AGL(1,ℤ/8)×C₅₃	C₂³	semidirect
264. AGL(1,ℤ/8)×C₅₃	C₂³	semidirect
265. AGL(1,ℤ/8)×C₅₃	C₂³	semidirect
266. #135×C₅₃	C₂³	semidirect
267. C₂×SD₁₆×C₅₃	C₂³	semidirect
268. C₂×D₈×C₅₃	C₂³	semidirect
269. #131×C₅₃	C₂³	semidirect
270. C₂×M₁₆×C₅₃	C₂³	semidirect
290. #41×C₅₃	C₂⁴	semidirect
294. C₂×Q₈×C₅₃	C₂⁴	semidirect
304. C₂×D₄×C₅₃	C₂⁴	semidirect
333. #11719949	C₂⁴	semidirect
345. Q₈×D₅₃	C₂⁴	semidirect
363. #11719947	C₂⁴	semidirect
391. D₄×D₅₃	C₂⁴	semidirect
409. #11719945	C₂⁴	semidirect
419. C₂×D₂₁₂	C₂⁴	semidirect
445. C₂×Dic₁₀₆	C₂⁴	semidirect
446. Q₁₆×C₅₃	C₂⁴	semidirect
447. SD₁₆×C₅₃	C₂⁴	semidirect
448. SD₁₆×C₅₃	C₂⁴	semidirect
449. D₈×C₅₃	C₂⁴	semidirect
451. M₁₆×C₅₃	C₂⁴	semidirect
452. C₂×C₈×C₅₃	C₂⁴	semidirect
453. #11719925	C₂⁴	semidirect
454. #11719925	C₂⁴	semidirect
455. #11719924	C₂⁴	semidirect
456. #11719924	C₂⁴	semidirect
457. #11719923	C₂⁴	semidirect
458. #11719923	C₂⁴	semidirect
459. #11719922	C₂⁴	semidirect
460. #11719922	C₂⁴	semidirect
462. #11719917	C₂⁴	semidirect
463. C₂×#88322	C₂⁴	semidirect
464. Dic₂₁₂	C₂⁴	semidirect
465. D₄₂₄	C₂⁴	semidirect
466. #11719913	C₂⁴	semidirect
467. #11719913	C₂⁴	semidirect
469. #11719912	C₂⁴	semidirect
471. C₈×D₅₃	C₂⁴	semidirect
625. #3585	D₅₃	direct (N × H)
640. D₅₃	#3585	direct (N × H)
648. #585	C₂×D₅₃	semidirect
662. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
677. #577	C₂×D₅₃	semidirect
685. #576	C₂×D₅₃	semidirect
694. #575	C₂×D₅₃	semidirect
707. C₂×AGL(1,ℤ/8)	C₂×D₅₃	semidirect
714. #568	C₂×D₅₃	semidirect
717. C₅₃	C₂×#3585	semidirect
729. 2₋¹⁺⁴	C₂²×D₅₃	semidirect
752. H(5,𝔽₂)	C₂²×D₅₃	semidirect
753. H(5,𝔽₂)	C₂²×D₅₃	semidirect
800. C₂×#41	C₂²×D₅₃	semidirect
801. C₂×#41	C₂²×D₅₃	semidirect
829. C₂²×D₄	C₂²×D₅₃	semidirect
843. #137	C₂²×D₅₃	semidirect
844. #137	C₂²×D₅₃	semidirect
860. AGL(1,ℤ/8)	C₂²×D₅₃	semidirect
861. AGL(1,ℤ/8)	C₂²×D₅₃	semidirect
862. AGL(1,ℤ/8)	C₂²×D₅₃	semidirect
870. #135	C₂²×D₅₃	semidirect
878. C₂×SD₁₆	C₂²×D₅₃	semidirect
884. C₂×D₈	C₂²×D₅₃	semidirect
888. #131	C₂²×D₅₃	semidirect
895. C₂×M₁₆	C₂²×D₅₃	semidirect
963. #41	C₂³×D₅₃	semidirect
985. C₂×Q₈	C₂³×D₅₃	semidirect
1045. C₂×D₄	C₂³×D₅₃	semidirect
1075. Q₁₆	C₂³×D₅₃	semidirect
1082. SD₁₆	C₂³×D₅₃	semidirect
1083. SD₁₆	C₂³×D₅₃	semidirect
1087. D₈	C₂³×D₅₃	semidirect
1093. M₁₆	C₂³×D₅₃	semidirect
1097. C₂×C₈	C₂³×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
C₂×H(5,𝔽₂)×D₅₃	2
#20289496	2
#20289495	2
#20289494	2
#20289493	2
#20289492	2
#20289491	2
#20289490	2
#577×D₅₃	2
#576×D₅₃	2
#575×D₅₃	2
C₂×AGL(1,ℤ/8)×D₅₃	2
#568×D₅₃	2
C₅₃×#3585	2
C₂×#3585	53

Subgroups — D53×#3585 #28297927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3585 #28297927