Subgroups — #28297944

Order 13568.

10836 conjugacy classes of subgroups.

The subgroup lattice has 876 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	#20289500	C₂	1	8	yes	maximal, complemented
3	#20289497	C₂	1	8	yes	maximal, complemented
4	#20289493	C₂	1	8	yes	maximal, complemented
5	#20289490	C₂	1	8	yes	maximal, complemented
6	#20289489	C₂	1	1	yes	maximal, characteristic, complemented
7	#20289488	C₂	1	6	yes	maximal, complemented
8	#20289486	C₂	1	2	yes	maximal, complemented
9	#20289484	C₂	1	6	yes	maximal, complemented
10	C₂×#16811420	C₂	1	6	yes	maximal, complemented
11	#575×D₅₃	C₂	1	6	yes	maximal, complemented
12	C₂×#16811388	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3584	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811460	—	2	2	no	—
15	#16811460	C₂²	1	8	yes	complemented
16	#16811459	—	2	8	no	—
17	#16811459	C₂²	1	2	yes	complemented
18	#16811459	C₂²	1	12	yes	complemented
19	#16811458	—	2	6	no	—
20	#16811458	C₂²	1	8	yes	complemented
21	2₋¹⁺⁴×D₅₃	—	2	2	no	—
22	2₋¹⁺⁴×D₅₃	C₂²	1	8	yes	complemented
23	H(5,𝔽₂)×D₅₃	—	2	6	no	—
24	H(5,𝔽₂)×D₅₃	C₂²	1	8	yes	complemented
25	C₂×#41×D₅₃	—	2	8	no	—
26	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
27	C₂×#41×D₅₃	C₂²	1	12	yes	complemented
28	#16811440	C₂²	1	4	yes	complemented
29	#16811439	C₂²	1	24	yes	complemented
30	#16811438	C₂²	1	8	yes	complemented
31	#16811437	C₂²	1	12	yes	complemented
32	#16811436	C₂²	1	12	yes	complemented
33	#16811435	C₂²	1	8	yes	complemented
34	#16811434	C₂²	1	8	yes	complemented
35	#16811433	C₂²	1	24	yes	complemented
36	#16811432	C₂²	1	24	yes	complemented
37	#16811431	C₂²	1	8	yes	complemented
38	#16811430	C₂²	1	24	yes	complemented
39	#16811429	C₂²	1	24	yes	complemented
40	#16811428	C₂²	1	4	yes	complemented
41	#16811427	C₂²	1	24	yes	complemented
42	#16811426	C₂²	1	8	yes	complemented
43	#16811425	C₂²	1	12	yes	complemented
44	#16811424	C₂²	1	12	yes	complemented
45	#16811423	C₂²	1	6	yes	complemented
46	#16811422	C₂²	1	24	yes	complemented
47	#16811421	C₂²	1	12	yes	complemented
48	#16811420	C₂²	1	12	yes	complemented
49	#16811420	C₂²	1	4	yes	complemented
50	#16811420	C₂²	1	24	yes	complemented
51	#16811420	C₂²	1	24	yes	complemented
52	#16811420	C₂²	1	12	yes	complemented
53	#16811420	C₂²	1	12	yes	complemented
54	#16811419	C₂²	1	24	yes	complemented
55	C₂×#13133249	C₂²	1	12	yes	complemented
56	C₂×#13133246	C₂²	1	12	yes	complemented
57	#137×D₅₃	C₂²	1	24	yes	complemented
58	C₂×#13133244	C₂²	1	12	yes	complemented
59	C₂×#13133241	C₂²	1	12	yes	complemented
60	AGL(1,ℤ/8)×D₅₃	C₂²	1	24	yes	complemented
61	C₂×#13133239	C₂²	1	6	yes	complemented
62	C₂×#13133237	C₂²	1	12	yes	complemented
63	#135×D₅₃	C₂²	1	24	yes	complemented
64	#16811388	C₂²	1	8	yes	complemented
65	#16811388	C₂²	1	8	yes	complemented
66	C₂×#13133225	C₂²	1	3	yes	complemented
67	C₂×#13133224	C₂²	1	1	yes	characteristic, complemented
68	C₂×#13133223	C₂²	1	3	yes	complemented
69	C₂²×#11719912	C₂²	1	3	yes	complemented
70	C₂×M₁₆×D₅₃	C₂²	1	3	yes	complemented
71	C₅₃×#585	C₂²	1	2	yes	complemented
72	C₅₃×#578	C₂²	1	4	yes	complemented
73	C₅₃×#577	C₂²	1	8	yes	complemented
74	C₅₃×#576	C₂²	1	4	yes	complemented
75	C₅₃×#575	C₂²	1	6	yes	complemented
76	C₂×#135×C₅₃	C₂²	1	6	yes	complemented
77	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic, complemented
78	#13133265	—	2	2	no	—
79	#13133265	—	2	8	no	—
80	#13133265	—	2	8	no	—
81	#13133265	C₂³	1	24	yes	complemented
82	#13133264	—	2	8	no	—
83	#13133264	—	2	24	no	—
84	#13133264	—	2	12	no	—
85	#13133264	C₂³	1	24	yes	complemented
86	#13133264	C₂³	1	8	yes	complemented
87	#13133263	—	2	8	no	—
88	#13133263	—	2	24	no	—
89	#13133263	—	2	12	no	—
90	#13133263	C₂³	1	24	yes	complemented
91	#13133263	C₂³	1	8	yes	complemented
92	#13133262	—	2	6	no	—
93	#13133262	—	2	24	no	—
94	#13133262	—	2	24	no	—
95	#13133262	—	2	24	no	—
96	#13133262	C₂³	1	24	yes	complemented
97	C₂×#11719949	—	2	8	no	—
98	C₂×#11719949	D₄	1	1	yes	characteristic
99	C₂×#11719949	C₂³	1	12	yes	—
100	C₂×#11719945	—	2	24	no	—
101	C₂×#11719945	—	2	12	no	—
102	C₂×#11719945	C₂³	1	3	yes	—
103	C₂×#11719945	C₂³	1	12	yes	complemented
104	C₂×#11719947	—	2	12	no	—
105	C₂×#11719947	—	2	24	no	—
106	C₂×#11719947	D₄	1	3	yes	—
107	C₂×#11719947	C₂³	1	12	yes	—
108	#41×D₅₃	—	2	8	no	—
109	#41×D₅₃	—	2	8	no	—
110	#41×D₅₃	—	2	8	no	—
111	#41×D₅₃	—	2	24	no	—
112	#41×D₅₃	—	2	24	no	—
113	#41×D₅₃	—	2	24	no	—
114	#41×D₅₃	—	2	12	no	—
115	#41×D₅₃	—	2	12	no	—
116	#41×D₅₃	—	2	12	no	—
117	#41×D₅₃	—	2	12	no	—
118	#41×D₅₃	D₄	1	8	yes	—
119	#41×D₅₃	C₂³	1	24	yes	—
120	#41×D₅₃	C₂³	1	8	yes	—
121	#41×D₅₃	C₂³	1	8	yes	—
122	#41×D₅₃	C₂³	1	24	yes	complemented
123	#41×D₅₃	C₂³	1	24	yes	complemented
124	C₂×Q₈×D₅₃	—	2	8	no	—
125	C₂×Q₈×D₅₃	D₄	1	1	yes	characteristic
126	C₂×Q₈×D₅₃	C₂³	1	12	yes	complemented
127	C₂×D₄×D₅₃	—	2	12	no	—
128	C₂×D₄×D₅₃	—	2	24	no	—
129	C₂×D₄×D₅₃	D₄	1	3	yes	—
130	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
131	C₂²×C₄×D₅₃	—	2	12	no	—
132	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
133	#13133250	C₂³	1	24	yes	complemented
134	#13133249	C₂³	1	24	yes	complemented
135	#13133249	C₂³	1	8	yes	complemented
136	#13133249	C₂³	1	24	yes	complemented
137	#13133249	C₂³	1	24	yes	complemented
138	#13133248	C₂³	1	24	yes	complemented
139	#13133247	C₂³	1	24	yes	complemented
140	#13133246	C₂³	1	24	yes	complemented
141	#13133246	C₂³	1	8	yes	complemented
142	#13133246	C₂³	1	24	yes	complemented
143	#13133246	C₂³	1	24	yes	complemented
144	#13133245	C₂³	1	24	yes	complemented
145	#13133244	C₂³	1	24	yes	complemented
146	#13133244	C₂³	1	8	yes	complemented
147	#13133244	C₂³	1	24	yes	complemented
148	#13133244	C₂³	1	24	yes	complemented
149	#13133243	C₂³	1	24	yes	complemented
150	#13133242	C₂³	1	24	yes	complemented
151	#13133241	C₂³	1	24	yes	complemented
152	#13133241	C₂³	1	8	yes	complemented
153	#13133241	C₂³	1	24	yes	complemented
154	#13133241	C₂³	1	24	yes	complemented
155	#13133240	C₂³	1	24	yes	complemented
156	#13133239	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	#13133238	C₂³	1	48	yes	complemented
161	#13133237	C₂³	1	24	yes	complemented
162	#13133237	C₂³	1	8	yes	complemented
163	#13133237	C₂³	1	24	yes	complemented
164	#13133237	C₂³	1	24	yes	complemented
165	#13133236	C₂³	1	24	yes	complemented
166	C₂×Dic₂₁₂	C₂³	1	6	yes	complemented
167	C₂×#11719925	C₂³	1	12	yes	complemented
168	Q₁₆×D₅₃	C₂³	1	24	yes	complemented
169	C₂×#11719913	C₂³	1	12	yes	complemented
170	C₂×#11719923	C₂³	1	12	yes	complemented
171	C₂×#11719924	C₂³	1	12	yes	complemented
172	SD₁₆×D₅₃	C₂³	1	48	yes	complemented
173	C₂×D₄₂₄	C₂³	1	6	yes	complemented
174	C₂×#11719922	C₂³	1	12	yes	complemented
175	D₈×D₅₃	C₂³	1	24	yes	complemented
176	#13133225	C₂³	1	24	yes	complemented
177	#13133224	C₂³	1	8	yes	complemented
178	#13133223	C₂³	1	12	yes	complemented
179	#13133223	C₂³	1	12	yes	complemented
180	C₂×#11719917	C₂³	1	3	yes	complemented
181	C₂×#11719912	C₂³	1	3	yes	—
182	C₂×#11719912	C₂³	1	1	yes	characteristic
183	C₂×#11719912	C₂³	1	3	yes	complemented
184	C₂×#11719912	C₂³	1	3	yes	complemented
185	C₂×#11719912	C₂³	1	12	yes	complemented
186	C₂×#11719912	C₂³	1	12	yes	complemented
187	M₁₆×D₅₃	C₂³	1	24	yes	complemented
188	C₂²×#88322	C₂³	1	3	yes	complemented
189	C₂×C₈×D₅₃	C₂³	1	6	yes	complemented
190	2₋¹⁺⁴×C₅₃	—	2	2	no	—
191	2₋¹⁺⁴×C₅₃	C₂³	1	8	yes	complemented
192	H(5,𝔽₂)×C₅₃	—	2	6	no	—
193	H(5,𝔽₂)×C₅₃	C₂³	1	8	yes	complemented
194	C₂×#41×C₅₃	—	2	8	no	—
195	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×#41×C₅₃	C₂³	1	12	yes	complemented
197	#137×C₅₃	C₂³	1	24	yes	complemented
198	AGL(1,ℤ/8)×C₅₃	C₂³	1	24	yes	complemented
199	#135×C₅₃	C₂³	1	4	yes	complemented
200	#135×C₅₃	C₂³	1	12	yes	complemented
201	#135×C₅₃	C₂³	1	12	yes	complemented
202	#135×C₅₃	C₂³	1	12	yes	complemented
203	C₂×Q₁₆×C₅₃	C₂³	1	6	yes	complemented
204	C₂×SD₁₆×C₅₃	C₂³	1	12	yes	complemented
205	C₂×D₈×C₅₃	C₂³	1	6	yes	complemented
206	#131×C₅₃	C₂³	1	4	yes	complemented
207	#131×C₅₃	C₂³	1	4	yes	complemented
208	C₂×M₁₆×C₅₃	C₂³	1	3	yes	complemented
209	C₂²×C₈×C₅₃	C₂³	1	3	yes	complemented
210	C₂³×D₅₃	—	2	12	no	—
211	C₂³×D₅₃	C₂×D₄	1	3	yes	—
212	#41×C₅₃	—	2	8	no	—
213	#41×C₅₃	—	2	24	no	—
214	#41×C₅₃	—	2	12	no	—
215	#41×C₅₃	—	2	12	no	—
216	#41×C₅₃	C₂×D₄	1	4	yes	—
217	#41×C₅₃	C₂⁴	1	8	yes	—
218	#41×C₅₃	C₂⁴	1	24	yes	—
219	#41×C₅₃	C₂⁴	1	4	yes	—
220	C₂×Q₈×C₅₃	—	2	8	no	—
221	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
222	C₂×Q₈×C₅₃	C₂⁴	1	12	yes	—
223	C₂×D₄×C₅₃	—	2	12	no	—
224	C₂×D₄×C₅₃	—	2	24	no	—
225	C₂×D₄×C₅₃	C₂×D₄	1	3	yes	—
226	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
227	C₂²×C₄×C₅₃	—	2	12	no	—
228	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
229	C₂×C₂²⋊D₅₃	—	2	12	no	—
230	C₂×C₂²⋊D₅₃	—	2	12	no	—
231	C₂×C₂²⋊D₅₃	—	2	48	no	—
232	C₂×C₂²⋊D₅₃	—	2	12	no	—
233	C₂×C₂²⋊D₅₃	C₂×D₄	1	6	yes	—
234	C₂²×Dic₅₃	—	2	12	no	—
235	C₂²×Dic₅₃	C₂×D₄	1	3	yes	—
236	#11719949	—	2	8	no	—
237	#11719949	—	2	24	no	—
238	#11719949	—	2	12	no	—
239	#11719949	—	2	12	no	—
240	#11719949	C₂×D₄	1	8	yes	—
241	#11719949	C₂⁴	1	24	yes	—
242	#11719949	C₂⁴	1	8	yes	—
243	Q₈×D₅₃	—	2	8	no	—
244	Q₈×D₅₃	—	2	12	no	—
245	Q₈×D₅₃	—	2	12	no	—
246	Q₈×D₅₃	—	2	24	no	—
247	Q₈×D₅₃	C₂×D₄	1	8	yes	—
248	Q₈×D₅₃	C₂⁴	1	24	yes	—
249	Q₈×D₅₃	C₂⁴	1	8	yes	—
250	#11719947	—	2	24	no	—
251	#11719947	—	2	48	no	—
252	#11719947	—	2	24	no	—
253	#11719947	—	2	8	no	—
254	#11719947	—	2	24	no	—
255	#11719947	—	2	24	no	—
256	#11719947	—	2	12	no	—
257	#11719947	—	2	12	no	—
258	#11719947	—	2	24	no	—
259	#11719947	C₂×D₄	1	24	yes	—
260	#11719947	C₂⁴	1	24	yes	—
261	#11719947	C₂⁴	1	8	yes	—
262	D₄×D₅₃	—	2	8	no	—
263	D₄×D₅₃	—	2	24	no	—
264	D₄×D₅₃	—	2	24	no	—
265	D₄×D₅₃	—	2	24	no	—
266	D₄×D₅₃	—	2	24	no	—
267	D₄×D₅₃	—	2	48	no	—
268	D₄×D₅₃	—	2	24	no	—
269	D₄×D₅₃	—	2	12	no	—
270	D₄×D₅₃	—	2	12	no	—
271	D₄×D₅₃	C₂×D₄	1	24	yes	—
272	D₄×D₅₃	C₂⁴	1	24	yes	—
273	D₄×D₅₃	C₂⁴	1	8	yes	—
274	#11719945	—	2	12	no	—
275	#11719945	—	2	12	no	—
276	#11719945	—	2	48	no	—
277	#11719945	—	2	24	no	—
278	#11719945	—	2	8	no	—
279	#11719945	—	2	24	no	—
280	#11719945	—	2	24	no	—
281	#11719945	—	2	24	no	—
282	#11719945	—	2	24	no	—
283	#11719945	C₂×D₄	1	12	yes	—
284	#11719945	C₂⁴	1	12	yes	—
285	#11719945	C₂⁴	1	8	yes	—
286	#11719945	C₂⁴	1	24	yes	—
287	C₂×D₂₁₂	—	2	12	no	—
288	C₂×D₂₁₂	—	2	24	no	—
289	C₂×D₂₁₂	C₂×D₄	1	3	yes	—
290	C₂×D₂₁₂	C₂⁴	1	12	yes	—
291	C₂×C₄×D₅₃	—	2	12	no	—
292	C₂×C₄×D₅₃	—	2	12	no	—
293	C₂×C₄×D₅₃	—	2	12	no	—
294	C₂×C₄×D₅₃	—	2	8	no	—
295	C₂×C₄×D₅₃	—	2	24	no	—
296	C₂×C₄×D₅₃	—	2	24	no	—
297	C₂×C₄×D₅₃	—	2	24	no	—
298	C₂×C₄×D₅₃	C₂×D₄	1	12	yes	—
299	C₂×C₄×D₅₃	C₂×D₄	1	3	yes	—
300	C₂×C₄×D₅₃	C₂×D₄	1	3	yes	—
301	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
302	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
303	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
304	C₂×Dic₁₀₆	—	2	12	no	—
305	C₂×Dic₁₀₆	—	2	24	no	—
306	C₂×Dic₁₀₆	C₂×D₄	1	3	yes	—
307	C₂×Dic₁₀₆	C₂⁴	1	12	yes	—
308	Q₁₆×C₅₃	C₂⁴	1	4	yes	—
309	Q₁₆×C₅₃	C₂⁴	1	12	yes	—
310	SD₁₆×C₅₃	C₂⁴	1	8	yes	—
311	SD₁₆×C₅₃	C₂⁴	1	24	yes	—
312	D₈×C₅₃	C₂⁴	1	4	yes	—
313	D₈×C₅₃	C₂⁴	1	12	yes	—
314	M₁₆×C₅₃	C₂⁴	1	12	yes	—
315	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
316	C₂×C₈×C₅₃	C₂⁴	1	3	yes	—
317	C₂×C₈×C₅₃	C₂⁴	1	6	yes	—
318	C₂×C₈×C₅₃	C₂⁴	1	6	yes	—
319	#11719925	C₂⁴	1	24	yes	—
320	#11719925	C₂⁴	1	8	yes	—
321	#11719924	C₂⁴	1	24	yes	—
322	#11719924	C₂⁴	1	8	yes	—
323	#11719923	C₂⁴	1	24	yes	—
324	#11719923	C₂⁴	1	8	yes	—
325	#11719922	C₂⁴	1	24	yes	—
326	#11719922	C₂⁴	1	8	yes	—
327	#11719917	C₂⁴	1	12	yes	—
328	C₂×#88322	C₂⁴	1	3	yes	—
329	C₂×#88322	C₂⁴	1	1	yes	characteristic
330	C₂×#88322	C₂⁴	1	12	yes	—
331	Dic₂₁₂	C₂⁴	1	12	yes	—
332	Dic₂₁₂	C₂⁴	1	4	yes	—
333	D₄₂₄	C₂⁴	1	12	yes	—
334	D₄₂₄	C₂⁴	1	4	yes	—
335	#11719913	C₂⁴	1	24	yes	—
336	#11719913	C₂⁴	1	8	yes	—
337	#11719912	C₂⁴	1	12	yes	—
338	#11719912	C₂⁴	1	2	yes	—
339	#11719912	C₂⁴	1	2	yes	—
340	#11719912	C₂⁴	1	6	yes	—
341	#11719912	C₂⁴	1	6	yes	—
342	#11719912	C₂⁴	1	12	yes	—
343	C₈×D₅₃	C₂⁴	1	24	yes	—
344	C₂³×C₅₃	—	2	12	no	—
345	C₂³×C₅₃	C₂²×D₄	1	3	yes	—
346	C₂²×D₅₃	—	2	12	no	—
347	C₂²×D₅₃	—	2	8	no	—
348	C₂²×D₅₃	—	2	24	no	—
349	C₂²×D₅₃	—	8	3	no	—
350	C₂²×D₅₃	—	8	24	no	—
351	C₂²×D₅₃	C₂²×D₄	1	12	yes	—
352	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
353	C₂²×D₅₃	C₂²×D₄	1	3	yes	—
354	Q₈×C₅₃	—	2	12	no	—
355	Q₈×C₅₃	C₂²×D₄	1	4	yes	—
356	Q₈×C₅₃	C₂⁵	1	8	yes	—
357	D₄×C₅₃	—	2	24	no	—
358	D₄×C₅₃	—	2	8	no	—
359	D₄×C₅₃	—	2	12	no	—
360	D₄×C₅₃	C₂²×D₄	1	12	yes	—
361	D₄×C₅₃	C₂⁵	1	8	yes	—
362	C₂×C₄×C₅₃	—	2	12	no	—
363	C₂×C₄×C₅₃	—	2	24	no	—
364	C₂×C₄×C₅₃	—	2	8	no	—
365	C₂×C₄×C₅₃	C₂²×D₄	1	3	yes	—
366	C₂×C₄×C₅₃	C₂²×D₄	1	6	yes	—
367	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
368	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
369	C₂²⋊D₅₃	—	2	24	no	—
370	C₂²⋊D₅₃	—	2	8	no	—
371	C₂²⋊D₅₃	—	2	8	no	—
372	C₂²⋊D₅₃	—	2	24	no	—
373	C₂²⋊D₅₃	—	2	24	no	—
374	C₂²⋊D₅₃	—	2	8	no	—
375	C₂²⋊D₅₃	C₂²×D₄	1	24	yes	—
376	C₂×Dic₅₃	—	2	12	no	—
377	C₂×Dic₅₃	—	2	24	no	—
378	C₂×Dic₅₃	—	2	8	no	—
379	C₂×Dic₅₃	C₂²×D₄	1	12	yes	—
380	C₂×Dic₅₃	C₂²×D₄	1	3	yes	—
381	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
382	D₂₁₂	—	2	8	no	—
383	D₂₁₂	—	2	24	no	—
384	D₂₁₂	—	2	12	no	—
385	D₂₁₂	C₂²×D₄	1	12	yes	—
386	D₂₁₂	C₂⁵	1	8	yes	—
387	C₄×D₅₃	—	2	8	no	—
388	C₄×D₅₃	—	2	24	no	—
389	C₄×D₅₃	—	2	8	no	—
390	C₄×D₅₃	—	2	24	no	—
391	C₄×D₅₃	—	2	8	no	—
392	C₄×D₅₃	—	2	24	no	—
393	C₄×D₅₃	C₂²×D₄	1	2	yes	—
394	C₄×D₅₃	C₂²×D₄	1	6	yes	—
395	C₄×D₅₃	C₂²×D₄	1	12	yes	—
396	C₄×D₅₃	C₂²×D₄	1	12	yes	—
397	C₄×D₅₃	C₂⁵	1	2	yes	—
398	C₄×D₅₃	C₂⁵	1	6	yes	—
399	Dic₁₀₆	—	2	12	no	—
400	Dic₁₀₆	—	2	24	no	—
401	Dic₁₀₆	—	2	8	no	—
402	Dic₁₀₆	C₂²×D₄	1	12	yes	—
403	Dic₁₀₆	C₂⁵	1	8	yes	—
404	C₈×C₅₃	C₂⁵	1	6	yes	—
405	C₈×C₅₃	C₂⁵	1	1	yes	characteristic
406	C₈×C₅₃	C₂⁵	1	1	yes	characteristic
407	#88322	C₂⁵	1	6	yes	—
408	#88322	C₂⁵	1	2	yes	—
409	#63090	—	53	1	no	maximal, Sylow
410	C₂²×C₅₃	—	2	8	no	—
411	C₂²×C₅₃	—	4	3	no	—
412	C₂²×C₅₃	—	8	12	no	—
413	C₂²×C₅₃	C₂³×D₄	1	6	yes	—
414	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
415	C₂×D₅₃	—	2	8	no	—
416	C₂×D₅₃	—	4	1	no	—
417	C₂×D₅₃	—	4	12	no	—
418	C₂×D₅₃	—	4	3	no	—
419	C₂×D₅₃	—	4	16	no	—
420	C₂×D₅₃	—	8	24	no	—
421	C₂×D₅₃	—	8	12	no	—
422	C₂×D₅₃	C₂³×D₄	1	2	yes	—
423	C₂×D₅₃	C₂³×D₄	1	6	yes	—
424	C₄×C₅₃	—	2	8	no	—
425	C₄×C₅₃	C₂³×D₄	1	6	yes	—
426	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
427	C₄×C₅₃	C₂⁶	1	1	yes	characteristic
428	Dic₅₃	—	2	8	no	—
429	Dic₅₃	C₂³×D₄	1	6	yes	—
430	Dic₅₃	C₂³×D₄	1	2	yes	—
431	C₂×#585	—	53	2	no	—
432	#3586	—	53	8	no	—
433	#3586	—	53	8	no	—
434	#3585	—	53	8	no	—
435	#3585	—	53	8	no	—
436	#3584	—	53	2	no	—
437	#3584	—	53	6	no	—
438	#3584	—	53	6	no	—
439	#3584	—	53	1	no	—
440	#3584	D₅₃	1	1	yes	characteristic, complemented
441	C₂×#575	—	53	6	no	—
442	C₂×#575	—	53	6	no	—
443	C₂×#568	—	53	1	no	—
444	C₂×C₅₃	—	2	1	no	—
445	C₂×C₅₃	—	2	6	no	—
446	C₂×C₅₃	—	4	8	no	—
447	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
448	D₅₃	—	2	2	no	—
449	D₅₃	—	2	6	no	—
450	D₅₃	—	4	8	no	—
451	#585	—	53	8	no	—
452	#585	—	53	8	no	—
453	#585	—	53	2	no	—
454	#585	—	53	12	no	—
455	#585	—	106	8	no	—
456	#585	—	106	6	no	—
457	#585	—	106	2	no	—
458	#585	C₂×D₅₃	1	2	yes	complemented
459	C₂×2₋¹⁺⁴	—	53	8	no	—
460	C₂×2₋¹⁺⁴	—	106	2	no	—
461	C₂×H(5,𝔽₂)	—	53	8	no	—
462	C₂×H(5,𝔽₂)	—	106	6	no	—
463	C₂²×#41	—	53	1	no	—
464	C₂²×#41	—	53	12	no	—
465	C₂²×#41	—	106	8	no	—
466	#578	—	53	8	no	—
467	#578	—	53	24	no	—
468	#578	—	53	12	no	—
469	#578	—	53	12	no	—
470	#578	—	53	4	no	—
471	#578	C₂×D₅₃	1	4	yes	complemented
472	#577	—	53	8	no	—
473	#577	—	53	8	no	—
474	#577	—	53	24	no	—
475	#577	—	53	24	no	—
476	#577	—	53	24	no	—
477	#577	—	53	24	no	—
478	#577	—	53	8	no	—
479	#577	C₂×D₅₃	1	8	yes	complemented
480	#576	—	53	8	no	—
481	#576	—	53	24	no	—
482	#576	—	53	12	no	—
483	#576	—	53	12	no	—
484	#576	—	53	4	no	—
485	#576	C₂×D₅₃	1	4	yes	complemented
486	#575	—	53	12	no	—
487	#575	—	53	24	no	—
488	#575	—	53	24	no	—
489	#575	—	53	12	no	—
490	#575	—	53	12	no	—
491	#575	—	53	24	no	—
492	#575	—	53	24	no	—
493	#575	—	53	12	no	—
494	#575	—	53	4	no	—
495	#575	—	53	6	no	—
496	#575	C₂×D₅₃	1	6	yes	complemented
497	C₂×#137	—	53	24	no	—
498	C₂×#137	—	53	12	no	—
499	C₂×#137	—	53	12	no	—
500	C₂×AGL(1,ℤ/8)	—	53	24	no	—
501	C₂×AGL(1,ℤ/8)	—	53	12	no	—
502	C₂×AGL(1,ℤ/8)	—	53	12	no	—
503	C₂×#135	—	53	12	no	—
504	C₂×#135	—	53	24	no	—
505	C₂×#135	—	53	6	no	—
506	C₂×#135	C₂×D₅₃	1	6	yes	complemented
507	#568	—	53	8	no	—
508	#568	—	53	8	no	—
509	C₂×#131	—	53	1	no	—
510	C₂×#131	—	53	3	no	—
511	C₂×#131	—	53	3	no	—
512	C₂×#131	C₂×D₅₃	1	1	yes	characteristic, complemented
513	C₂²×M₁₆	—	53	3	no	—
514	C₂²×M₁₆	—	53	3	no	—
515	C₅₃	#63090	1	1	yes	characteristic, complemented, Sylow
516	2₋¹⁺⁴	—	2	2	no	—
517	2₋¹⁺⁴	—	53	24	no	—
518	2₋¹⁺⁴	—	53	8	no	—
519	2₋¹⁺⁴	—	53	24	no	—
520	2₋¹⁺⁴	—	106	8	no	—
521	2₋¹⁺⁴	—	106	8	no	—
522	2₋¹⁺⁴	—	106	8	no	—
523	2₋¹⁺⁴	—	106	12	no	—
524	2₋¹⁺⁴	—	106	24	no	—
525	2₋¹⁺⁴	—	106	2	no	—
526	2₋¹⁺⁴	C₂²×D₅₃	1	8	yes	complemented
527	H(5,𝔽₂)	—	2	6	no	—
528	H(5,𝔽₂)	—	53	24	no	—
529	H(5,𝔽₂)	—	53	8	no	—
530	H(5,𝔽₂)	—	53	24	no	—
531	H(5,𝔽₂)	—	106	24	no	—
532	H(5,𝔽₂)	—	106	24	no	—
533	H(5,𝔽₂)	—	106	24	no	—
534	H(5,𝔽₂)	—	106	24	no	—
535	H(5,𝔽₂)	—	106	12	no	—
536	H(5,𝔽₂)	—	106	8	no	—
537	H(5,𝔽₂)	—	106	6	no	—
538	H(5,𝔽₂)	C₂²×D₅₃	1	8	yes	complemented
539	C₂×#41	—	2	8	no	—
540	C₂×#41	—	53	8	no	—
541	C₂×#41	—	53	8	no	—
542	C₂×#41	—	53	1	no	—
543	C₂×#41	—	53	3	no	—
544	C₂×#41	—	53	3	no	—
545	C₂×#41	—	53	24	no	—
546	C₂×#41	—	53	24	no	—
547	C₂×#41	—	53	8	no	—
548	C₂×#41	—	53	24	no	—
549	C₂×#41	—	53	12	no	—
550	C₂×#41	—	53	12	no	—
551	C₂×#41	—	53	12	no	—
552	C₂×#41	—	106	12	no	—
553	C₂×#41	—	106	24	no	—
554	C₂×#41	—	106	12	no	—
555	C₂×#41	—	106	12	no	—
556	C₂×#41	—	106	12	no	—
557	C₂×#41	—	106	12	no	—
558	C₂×#41	—	106	12	no	—
559	C₂×#41	—	106	24	no	—
560	C₂×#41	—	106	24	no	—
561	C₂×#41	—	106	8	no	—
562	C₂×#41	—	106	8	no	—
563	C₂×#41	—	106	8	no	—
564	C₂×#41	—	106	24	no	—
565	C₂×#41	—	106	24	no	—
566	C₂×#41	—	106	8	no	—
567	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
568	C₂×#41	C₂²×D₅₃	1	12	yes	complemented
569	C₂²×Q₈	—	53	1	no	—
570	C₂²×Q₈	—	53	12	no	—
571	C₂²×Q₈	—	106	8	no	—
572	C₂²×D₄	—	53	3	no	—
573	C₂²×D₄	—	53	12	no	—
574	C₂²×D₄	—	106	24	no	—
575	C₂²×D₄	—	106	12	no	—
576	C₂³×C₄	—	53	3	no	—
577	C₂³×C₄	—	106	12	no	—
578	#137	—	53	24	no	—
579	#137	—	53	24	no	—
580	#137	—	53	24	no	—
581	#137	—	53	8	no	—
582	#137	—	53	24	no	—
583	#137	—	53	24	no	—
584	#137	—	53	24	no	—
585	#137	—	53	8	no	—
586	#137	—	53	24	no	—
587	#137	—	53	24	no	—
588	#137	—	53	24	no	—
589	#137	C₂²×D₅₃	1	24	yes	complemented
590	AGL(1,ℤ/8)	—	53	24	no	—
591	AGL(1,ℤ/8)	—	53	24	no	—
592	AGL(1,ℤ/8)	—	53	24	no	—
593	AGL(1,ℤ/8)	—	53	8	no	—
594	AGL(1,ℤ/8)	—	53	24	no	—
595	AGL(1,ℤ/8)	—	53	24	no	—
596	AGL(1,ℤ/8)	—	53	24	no	—
597	AGL(1,ℤ/8)	—	53	8	no	—
598	AGL(1,ℤ/8)	—	53	24	no	—
599	AGL(1,ℤ/8)	—	53	24	no	—
600	AGL(1,ℤ/8)	—	53	24	no	—
601	AGL(1,ℤ/8)	C₂²×D₅₃	1	24	yes	complemented
602	#135	—	53	8	no	—
603	#135	—	53	24	no	—
604	#135	—	53	24	no	—
605	#135	—	53	24	no	—
606	#135	—	53	24	no	—
607	#135	—	53	48	no	—
608	#135	—	53	24	no	—
609	#135	—	53	12	no	—
610	#135	—	53	4	no	—
611	#135	—	53	12	no	—
612	#135	—	53	12	no	—
613	#135	C₂²×D₅₃	1	12	yes	complemented
614	#135	C₂²×D₅₃	1	4	yes	complemented
615	#135	C₂²×D₅₃	1	12	yes	complemented
616	#135	C₂²×D₅₃	1	12	yes	complemented
617	C₂×Q₁₆	—	53	12	no	—
618	C₂×Q₁₆	—	53	24	no	—
619	C₂×Q₁₆	—	53	6	no	—
620	C₂×Q₁₆	C₂²×D₅₃	1	6	yes	complemented
621	C₂×SD₁₆	—	53	12	no	—
622	C₂×SD₁₆	—	53	12	no	—
623	C₂×SD₁₆	—	53	48	no	—
624	C₂×SD₁₆	—	53	12	no	—
625	C₂×SD₁₆	C₂²×D₅₃	1	12	yes	complemented
626	C₂×D₈	—	53	12	no	—
627	C₂×D₈	—	53	24	no	—
628	C₂×D₈	—	53	6	no	—
629	C₂×D₈	C₂²×D₅₃	1	6	yes	complemented
630	#131	—	53	8	no	—
631	#131	—	53	24	no	—
632	#131	—	53	12	no	—
633	#131	—	53	12	no	—
634	#131	C₂²×D₅₃	1	4	yes	complemented
635	#131	C₂²×D₅₃	1	4	yes	complemented
636	C₂×M₁₆	—	53	3	no	—
637	C₂×M₁₆	—	53	24	no	—
638	C₂×M₁₆	—	53	3	no	—
639	C₂×M₁₆	—	53	1	no	—
640	C₂×M₁₆	—	53	3	no	—
641	C₂×M₁₆	—	53	3	no	—
642	C₂×M₁₆	—	53	12	no	—
643	C₂×M₁₆	—	53	12	no	—
644	C₂×M₁₆	C₂²×D₅₃	1	3	yes	complemented
645	C₂²×C₈	—	53	3	no	—
646	C₂²×C₈	—	53	6	no	—
647	C₂²×C₈	C₂²×D₅₃	1	3	yes	complemented
648	C₂⁴	—	53	3	no	—
649	C₂⁴	—	106	12	no	—
650	#41	—	2	8	no	—
651	#41	—	2	24	no	—
652	#41	—	2	12	no	—
653	#41	—	2	12	no	—
654	#41	—	53	8	no	—
655	#41	—	53	24	no	—
656	#41	—	53	12	no	—
657	#41	—	53	12	no	—
658	#41	—	53	24	no	—
659	#41	—	53	8	no	—
660	#41	—	53	24	no	—
661	#41	—	53	8	no	—
662	#41	—	53	8	no	—
663	#41	—	53	24	no	—
664	#41	—	106	8	no	—
665	#41	—	106	24	no	—
666	#41	—	106	24	no	—
667	#41	—	106	24	no	—
668	#41	—	106	48	no	—
669	#41	—	106	24	no	—
670	#41	—	106	24	no	—
671	#41	—	106	8	no	—
672	#41	—	106	24	no	—
673	#41	—	106	12	no	—
674	#41	—	106	24	no	—
675	#41	—	106	24	no	—
676	#41	—	106	12	no	—
677	#41	—	106	12	no	—
678	#41	—	106	12	no	—
679	#41	—	106	48	no	—
680	#41	—	106	24	no	—
681	#41	—	106	24	no	—
682	#41	—	106	8	no	—
683	#41	—	106	24	no	—
684	#41	—	106	12	no	—
685	#41	—	106	12	no	—
686	#41	D₄×D₅₃	1	4	yes	—
687	#41	C₂³×D₅₃	1	8	yes	—
688	#41	C₂³×D₅₃	1	24	yes	—
689	#41	C₂³×D₅₃	1	4	yes	—
690	C₂×Q₈	—	2	8	no	—
691	C₂×Q₈	—	53	8	no	—
692	C₂×Q₈	—	53	3	no	—
693	C₂×Q₈	—	53	24	no	—
694	C₂×Q₈	—	53	8	no	—
695	C₂×Q₈	—	53	12	no	—
696	C₂×Q₈	—	106	12	no	—
697	C₂×Q₈	—	106	24	no	—
698	C₂×Q₈	—	106	12	no	—
699	C₂×Q₈	—	106	12	no	—
700	C₂×Q₈	—	106	24	no	—
701	C₂×Q₈	—	106	8	no	—
702	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
703	C₂×Q₈	C₂³×D₅₃	1	12	yes	—
704	C₂×D₄	—	2	12	no	—
705	C₂×D₄	—	2	24	no	—
706	C₂×D₄	—	53	6	no	—
707	C₂×D₄	—	53	24	no	—
708	C₂×D₄	—	53	24	no	—
709	C₂×D₄	—	53	8	no	—
710	C₂×D₄	—	53	3	no	—
711	C₂×D₄	—	53	12	no	—
712	C₂×D₄	—	106	24	no	—
713	C₂×D₄	—	106	12	no	—
714	C₂×D₄	—	106	12	no	—
715	C₂×D₄	—	106	12	no	—
716	C₂×D₄	—	106	12	no	—
717	C₂×D₄	—	106	48	no	—
718	C₂×D₄	—	106	24	no	—
719	C₂×D₄	—	106	8	no	—
720	C₂×D₄	—	106	24	no	—
721	C₂×D₄	—	106	24	no	—
722	C₂×D₄	—	106	24	no	—
723	C₂×D₄	—	106	48	no	—
724	C₂×D₄	—	106	12	no	—
725	C₂×D₄	—	106	12	no	—
726	C₂×D₄	—	106	24	no	—
727	C₂×D₄	D₄×D₅₃	1	3	yes	—
728	C₂×D₄	C₂³×D₅₃	1	12	yes	—
729	C₂²×C₄	—	2	12	no	—
730	C₂²×C₄	—	53	3	no	—
731	C₂²×C₄	—	53	12	no	—
732	C₂²×C₄	—	53	3	no	—
733	C₂²×C₄	—	53	3	no	—
734	C₂²×C₄	—	53	3	no	—
735	C₂²×C₄	—	53	1	no	—
736	C₂²×C₄	—	53	12	no	—
737	C₂²×C₄	—	106	8	no	—
738	C₂²×C₄	—	106	24	no	—
739	C₂²×C₄	—	106	12	no	—
740	C₂²×C₄	—	106	24	no	—
741	C₂²×C₄	—	106	24	no	—
742	C₂²×C₄	—	106	12	no	—
743	C₂²×C₄	—	106	12	no	—
744	C₂²×C₄	—	106	12	no	—
745	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
746	Q₁₆	—	53	8	no	—
747	Q₁₆	—	53	24	no	—
748	Q₁₆	—	53	12	no	—
749	Q₁₆	—	53	4	no	—
750	Q₁₆	C₂³×D₅₃	1	12	yes	—
751	Q₁₆	C₂³×D₅₃	1	4	yes	—
752	SD₁₆	—	53	8	no	—
753	SD₁₆	—	53	24	no	—
754	SD₁₆	—	53	8	no	—
755	SD₁₆	—	53	24	no	—
756	SD₁₆	—	53	24	no	—
757	SD₁₆	—	53	8	no	—
758	SD₁₆	C₂³×D₅₃	1	24	yes	—
759	SD₁₆	C₂³×D₅₃	1	8	yes	—
760	D₈	—	53	8	no	—
761	D₈	—	53	24	no	—
762	D₈	—	53	12	no	—
763	D₈	—	53	4	no	—
764	D₈	C₂³×D₅₃	1	12	yes	—
765	D₈	C₂³×D₅₃	1	4	yes	—
766	M₁₆	—	53	12	no	—
767	M₁₆	—	53	12	no	—
768	M₁₆	—	53	2	no	—
769	M₁₆	—	53	2	no	—
770	M₁₆	—	53	12	no	—
771	M₁₆	—	53	6	no	—
772	M₁₆	—	53	6	no	—
773	M₁₆	C₂³×D₅₃	1	12	yes	—
774	C₂×C₈	—	53	1	no	—
775	C₂×C₈	—	53	3	no	—
776	C₂×C₈	—	53	12	no	—
777	C₂×C₈	—	53	24	no	—
778	C₂×C₈	C₂³×D₅₃	1	3	yes	—
779	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
780	C₂×C₈	C₂³×D₅₃	1	6	yes	—
781	C₂×C₈	C₂³×D₅₃	1	6	yes	—
782	C₂³	—	2	12	no	—
783	C₂³	—	53	1	no	—
784	C₂³	—	53	12	no	—
785	C₂³	—	53	3	no	—
786	C₂³	—	106	24	no	—
787	C₂³	—	106	8	no	—
788	C₂³	—	106	12	no	—
789	C₂³	—	424	3	no	—
790	C₂³	—	424	24	no	—
791	C₂³	C₂×D₄×D₅₃	1	3	yes	—
792	Q₈	—	2	12	no	—
793	Q₈	—	53	12	no	—
794	Q₈	—	53	8	no	—
795	Q₈	—	106	8	no	—
796	Q₈	—	106	24	no	—
797	Q₈	—	106	12	no	—
798	Q₈	C₂×D₄×D₅₃	1	4	yes	—
799	Q₈	C₂⁴×D₅₃	1	8	yes	—
800	D₄	—	2	24	no	—
801	D₄	—	2	8	no	—
802	D₄	—	2	12	no	—
803	D₄	—	53	24	no	—
804	D₄	—	53	12	no	—
805	D₄	—	53	8	no	—
806	D₄	—	106	8	no	—
807	D₄	—	106	24	no	—
808	D₄	—	106	8	no	—
809	D₄	—	106	24	no	—
810	D₄	—	106	8	no	—
811	D₄	—	106	24	no	—
812	D₄	—	106	24	no	—
813	D₄	—	106	8	no	—
814	D₄	—	106	12	no	—
815	D₄	C₂×D₄×D₅₃	1	12	yes	—
816	D₄	C₂⁴×D₅₃	1	8	yes	—
817	C₂×C₄	—	2	12	no	—
818	C₂×C₄	—	2	24	no	—
819	C₂×C₄	—	2	8	no	—
820	C₂×C₄	—	53	1	no	—
821	C₂×C₄	—	53	12	no	—
822	C₂×C₄	—	53	3	no	—
823	C₂×C₄	—	53	12	no	—
824	C₂×C₄	—	53	12	no	—
825	C₂×C₄	—	53	2	no	—
826	C₂×C₄	—	53	6	no	—
827	C₂×C₄	—	53	6	no	—
828	C₂×C₄	—	53	2	no	—
829	C₂×C₄	—	106	8	no	—
830	C₂×C₄	—	106	24	no	—
831	C₂×C₄	—	106	8	no	—
832	C₂×C₄	—	106	24	no	—
833	C₂×C₄	—	106	8	no	—
834	C₂×C₄	—	106	24	no	—
835	C₂×C₄	—	106	12	no	—
836	C₂×C₄	—	106	24	no	—
837	C₂×C₄	—	106	8	no	—
838	C₂×C₄	C₂×D₄×D₅₃	1	3	yes	—
839	C₂×C₄	C₂×D₄×D₅₃	1	6	yes	—
840	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
841	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
842	C₈	—	53	6	no	—
843	C₈	—	53	2	no	—
844	C₈	C₂⁴×D₅₃	1	6	yes	—
845	C₈	C₂⁴×D₅₃	1	1	yes	characteristic
846	C₈	C₂⁴×D₅₃	1	1	yes	characteristic
847	C₂²	—	2	8	no	—
848	C₂²	—	4	3	no	—
849	C₂²	—	8	12	no	—
850	C₂²	—	53	2	no	—
851	C₂²	—	53	6	no	—
852	C₂²	—	106	8	no	—
853	C₂²	—	424	12	no	—
854	C₂²	—	424	24	no	—
855	C₂²	—	212	1	no	—
856	C₂²	—	212	12	no	—
857	C₂²	—	212	3	no	—
858	C₂²	—	212	16	no	—
859	C₂²	C₂²×D₄×D₅₃	1	6	yes	—
860	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
861	C₄	—	2	8	no	—
862	C₄	—	53	2	no	—
863	C₄	—	53	6	no	—
864	C₄	—	106	8	no	—
865	C₄	C₂²×D₄×D₅₃	1	6	yes	—
866	C₄	C₂²×D₄×D₅₃	1	1	yes	characteristic
867	C₄	C₂⁵×D₅₃	1	1	yes	characteristic
868	C₂	—	2	1	no	—
869	C₂	—	2	6	no	—
870	C₂	—	4	8	no	—
871	C₂	—	106	6	no	—
872	C₂	—	106	2	no	—
873	C₂	—	212	8	no	—
874	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	#63090
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. #20289500	C₂	semidirect
3. #20289497	C₂	semidirect
4. #20289493	C₂	semidirect
5. #20289490	C₂	semidirect
6. #20289489	C₂	semidirect
7. #20289488	C₂	semidirect
8. #20289486	C₂	semidirect
9. #20289484	C₂	semidirect
10. C₂×#16811420	C₂	semidirect
11. #575×D₅₃	C₂	semidirect
12. C₂×#16811388	C₂	semidirect
13. C₅₃×#3584	C₂	semidirect
15. #16811460	C₂²	semidirect
17. #16811459	C₂²	semidirect
18. #16811459	C₂²	semidirect
20. #16811458	C₂²	semidirect
22. 2₋¹⁺⁴×D₅₃	C₂²	semidirect
24. H(5,𝔽₂)×D₅₃	C₂²	semidirect
27. C₂×#41×D₅₃	C₂²	semidirect
28. #16811440	C₂²	semidirect
29. #16811439	C₂²	semidirect
30. #16811438	C₂²	semidirect
31. #16811437	C₂²	semidirect
32. #16811436	C₂²	semidirect
33. #16811435	C₂²	semidirect
34. #16811434	C₂²	semidirect
35. #16811433	C₂²	semidirect
36. #16811432	C₂²	semidirect
37. #16811431	C₂²	semidirect
38. #16811430	C₂²	semidirect
39. #16811429	C₂²	semidirect
40. #16811428	C₂²	semidirect
41. #16811427	C₂²	semidirect
42. #16811426	C₂²	semidirect
43. #16811425	C₂²	semidirect
44. #16811424	C₂²	semidirect
45. #16811423	C₂²	semidirect
46. #16811422	C₂²	semidirect
47. #16811421	C₂²	semidirect
48. #16811420	C₂²	semidirect
49. #16811420	C₂²	semidirect
50. #16811420	C₂²	semidirect
51. #16811420	C₂²	semidirect
52. #16811420	C₂²	semidirect
53. #16811420	C₂²	semidirect
54. #16811419	C₂²	semidirect
55. C₂×#13133249	C₂²	semidirect
56. C₂×#13133246	C₂²	semidirect
57. #137×D₅₃	C₂²	semidirect
58. C₂×#13133244	C₂²	semidirect
59. C₂×#13133241	C₂²	semidirect
60. AGL(1,ℤ/8)×D₅₃	C₂²	semidirect
61. C₂×#13133239	C₂²	semidirect
62. C₂×#13133237	C₂²	semidirect
63. #135×D₅₃	C₂²	semidirect
64. #16811388	C₂²	semidirect
65. #16811388	C₂²	semidirect
66. C₂×#13133225	C₂²	semidirect
67. C₂×#13133224	C₂²	semidirect
68. C₂×#13133223	C₂²	semidirect
69. C₂²×#11719912	C₂²	semidirect
70. C₂×M₁₆×D₅₃	C₂²	semidirect
71. C₅₃×#585	C₂²	semidirect
72. C₅₃×#578	C₂²	semidirect
73. C₅₃×#577	C₂²	semidirect
74. C₅₃×#576	C₂²	semidirect
75. C₅₃×#575	C₂²	semidirect
76. C₂×#135×C₅₃	C₂²	semidirect
77. C₂×#131×C₅₃	C₂²	semidirect
81. #13133265	C₂³	semidirect
85. #13133264	C₂³	semidirect
86. #13133264	C₂³	semidirect
90. #13133263	C₂³	semidirect
91. #13133263	C₂³	semidirect
96. #13133262	C₂³	semidirect
103. C₂×#11719945	C₂³	semidirect
122. #41×D₅₃	C₂³	semidirect
123. #41×D₅₃	C₂³	semidirect
126. C₂×Q₈×D₅₃	C₂³	semidirect
130. C₂×D₄×D₅₃	C₂³	semidirect
133. #13133250	C₂³	semidirect
134. #13133249	C₂³	semidirect
135. #13133249	C₂³	semidirect
136. #13133249	C₂³	semidirect
137. #13133249	C₂³	semidirect
138. #13133248	C₂³	semidirect
139. #13133247	C₂³	semidirect
140. #13133246	C₂³	semidirect
141. #13133246	C₂³	semidirect
142. #13133246	C₂³	semidirect
143. #13133246	C₂³	semidirect
144. #13133245	C₂³	semidirect
145. #13133244	C₂³	semidirect
146. #13133244	C₂³	semidirect
147. #13133244	C₂³	semidirect
148. #13133244	C₂³	semidirect
149. #13133243	C₂³	semidirect
150. #13133242	C₂³	semidirect
151. #13133241	C₂³	semidirect
152. #13133241	C₂³	semidirect
153. #13133241	C₂³	semidirect
154. #13133241	C₂³	semidirect
155. #13133240	C₂³	semidirect
156. #13133239	C₂³	semidirect
157. #13133239	C₂³	semidirect
158. #13133239	C₂³	semidirect
159. #13133239	C₂³	semidirect
160. #13133238	C₂³	semidirect
161. #13133237	C₂³	semidirect
162. #13133237	C₂³	semidirect
163. #13133237	C₂³	semidirect
164. #13133237	C₂³	semidirect
165. #13133236	C₂³	semidirect
166. C₂×Dic₂₁₂	C₂³	semidirect
167. C₂×#11719925	C₂³	semidirect
168. Q₁₆×D₅₃	C₂³	semidirect
169. C₂×#11719913	C₂³	semidirect
170. C₂×#11719923	C₂³	semidirect
171. C₂×#11719924	C₂³	semidirect
172. SD₁₆×D₅₃	C₂³	semidirect
173. C₂×D₄₂₄	C₂³	semidirect
174. C₂×#11719922	C₂³	semidirect
175. D₈×D₅₃	C₂³	semidirect
176. #13133225	C₂³	semidirect
177. #13133224	C₂³	semidirect
178. #13133223	C₂³	semidirect
179. #13133223	C₂³	semidirect
180. C₂×#11719917	C₂³	semidirect
183. C₂×#11719912	C₂³	semidirect
184. C₂×#11719912	C₂³	semidirect
185. C₂×#11719912	C₂³	semidirect
186. C₂×#11719912	C₂³	semidirect
187. M₁₆×D₅₃	C₂³	semidirect
188. C₂²×#88322	C₂³	semidirect
189. C₂×C₈×D₅₃	C₂³	semidirect
191. 2₋¹⁺⁴×C₅₃	C₂³	semidirect
193. H(5,𝔽₂)×C₅₃	C₂³	semidirect
196. C₂×#41×C₅₃	C₂³	semidirect
197. #137×C₅₃	C₂³	semidirect
198. AGL(1,ℤ/8)×C₅₃	C₂³	semidirect
199. #135×C₅₃	C₂³	semidirect
200. #135×C₅₃	C₂³	semidirect
201. #135×C₅₃	C₂³	semidirect
202. #135×C₅₃	C₂³	semidirect
203. C₂×Q₁₆×C₅₃	C₂³	semidirect
204. C₂×SD₁₆×C₅₃	C₂³	semidirect
205. C₂×D₈×C₅₃	C₂³	semidirect
206. #131×C₅₃	C₂³	semidirect
207. #131×C₅₃	C₂³	semidirect
208. C₂×M₁₆×C₅₃	C₂³	semidirect
209. C₂²×C₈×C₅₃	C₂³	semidirect
440. #3584	D₅₃	semidirect
458. #585	C₂×D₅₃	semidirect
471. #578	C₂×D₅₃	semidirect
479. #577	C₂×D₅₃	semidirect
485. #576	C₂×D₅₃	semidirect
496. #575	C₂×D₅₃	semidirect
506. C₂×#135	C₂×D₅₃	semidirect
512. C₂×#131	C₂×D₅₃	semidirect
515. C₅₃	#63090	semidirect
526. 2₋¹⁺⁴	C₂²×D₅₃	semidirect
538. H(5,𝔽₂)	C₂²×D₅₃	semidirect
568. C₂×#41	C₂²×D₅₃	semidirect
589. #137	C₂²×D₅₃	semidirect
601. AGL(1,ℤ/8)	C₂²×D₅₃	semidirect
613. #135	C₂²×D₅₃	semidirect
614. #135	C₂²×D₅₃	semidirect
615. #135	C₂²×D₅₃	semidirect
616. #135	C₂²×D₅₃	semidirect
620. C₂×Q₁₆	C₂²×D₅₃	semidirect
625. C₂×SD₁₆	C₂²×D₅₃	semidirect
629. C₂×D₈	C₂²×D₅₃	semidirect
634. #131	C₂²×D₅₃	semidirect
635. #131	C₂²×D₅₃	semidirect
644. C₂×M₁₆	C₂²×D₅₃	semidirect
647. 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
#20289500	2
#20289497	2
#20289493	2
#20289490	2
#20289489	2
#20289488	2
#20289486	2
#20289484	2
C₂×#16811420	2
#575×D₅₃	2
C₂×#16811388	2
C₅₃×#3584	2
#63090	53