Subgroups — #27368218

Order 13568.

680 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#494×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#20284525	C₂	1	2	yes	maximal
3	#20283680	C₂	1	1	yes	maximal, characteristic
4	#20274209	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274207	C₂	1	2	yes	maximal, complemented
6	#20274205	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274203	C₂	1	2	yes	maximal, complemented
8	#20274201	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273469	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273398	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1690	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₅₃	—	2	1	no	—
13	C₂×Q₁₆×D₅₃	—	2	1	no	—
14	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	—
15	C₄×#11719949	C₂²	1	1	yes	characteristic
16	#16811003	C₂²	1	1	yes	characteristic
17	#16811002	C₂²	1	2	yes	—
18	#16811001	—	2	1	no	—
19	#16811001	—	2	1	no	—
20	#16810916	—	2	2	no	—
21	#16810912	—	2	2	no	—
22	#16810908	C₂²	1	2	yes	—
23	#16810904	C₂²	1	2	yes	—
24	#16810900	C₂²	1	2	yes	—
25	#16810754	C₂²	1	1	yes	characteristic
26	#16810702	C₂²	1	1	yes	characteristic
27	#16810700	C₂²	1	1	yes	characteristic
28	#16810696	—	2	1	no	—
29	#16810693	—	2	1	no	—
30	#16810675	—	2	1	no	—
31	#16810675	C₂²	1	1	yes	characteristic
32	#16810662	—	2	2	no	—
33	#16810645	C₂²	1	2	yes	—
34	#16810623	—	2	2	no	—
35	#16810575	—	2	1	no	—
36	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
37	#16810374	C₂²	1	1	yes	characteristic
38	#16810373	C₂²	1	2	yes	—
39	#16810370	C₂²	1	2	yes	—
40	#16810369	C₂²	1	2	yes	—
41	#16810368	C₂²	1	2	yes	—
42	C₅₃×#494	C₂²	1	1	yes	characteristic
43	C₅₃×#475	C₂²	1	2	yes	—
44	C₅₃×#446	C₂²	1	1	yes	characteristic
45	C₅₃×#334	C₂²	1	1	yes	characteristic
46	C₅₃×#332	C₂²	1	2	yes	—
47	C₂×#11719949	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₅₃	—	2	2	no	—
49	C₂×Dic₂₁₂	—	2	1	no	—
50	C₂×Dic₂₁₂	—	2	1	no	—
51	C₂×#11719925	—	2	2	no	—
52	C₂×#11719925	—	2	2	no	—
53	Q₁₆×D₅₃	—	4	4	no	—
54	Q₁₆×D₅₃	—	4	4	no	—
55	C₂×#11719912	—	2	1	no	—
56	C₂×#11719912	—	2	1	no	—
57	C₂×#11719912	—	2	2	no	—
58	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
59	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
60	#13133217	C₂³	1	2	yes	—
61	#13133216	—	2	2	no	—
62	#13133216	—	2	2	no	—
63	#13133215	—	2	2	no	—
64	Q₈×Dic₅₃	D₄	1	1	yes	characteristic
65	C₄×D₂₁₂	—	2	1	no	—
66	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
67	#13133179	—	2	1	no	—
68	#13133179	D₄	1	1	yes	characteristic
69	#13133175	—	2	1	no	—
70	#13133175	D₄	1	1	yes	characteristic
71	C₄⋊C₄×D₅₃	—	2	2	no	—
72	C₄⋊C₄×D₅₃	—	2	2	no	—
73	C₄²×D₅₃	—	2	1	no	—
74	C₄²×D₅₃	C₂³	1	1	yes	characteristic
75	#13133151	—	2	2	no	—
76	#13133150	—	2	2	no	—
77	#13133148	—	2	2	no	—
78	C₄⋊#88322	—	2	1	no	—
79	C₄⋊#88322	C₂³	1	1	yes	characteristic
80	C₄⋊#88322	C₂³	1	2	yes	—
81	#13133146	—	2	2	no	—
82	#13133141	—	2	2	no	—
83	#13133139	—	2	2	no	—
84	#13133137	—	2	2	no	—
85	#13133129	—	2	1	no	—
86	#13133129	—	2	1	no	—
87	#13133129	—	2	1	no	—
88	#13133128	—	2	1	no	—
89	C₄×#88322	C₂³	1	1	yes	characteristic
90	C₈×Dic₅₃	—	2	1	no	—
91	C₈×Dic₅₃	D₄	1	1	yes	characteristic
92	C₈×Dic₅₃	D₄	1	1	yes	characteristic
93	C₂×Q₁₆×C₅₃	—	2	1	no	—
94	C₂×Q₁₆×C₅₃	—	2	1	no	—
95	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
96	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
97	#106×C₅₃	—	2	2	no	—
98	C₄⋊C₈×C₅₃	—	2	1	no	—
99	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
101	#103×C₅₃	—	2	2	no	—
102	#97×C₅₃	—	2	1	no	—
103	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₂×Q₈×C₅₃	—	2	2	no	—
105	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
106	#11719949	—	2	4	no	—
107	Q₈×D₅₃	—	4	4	no	—
108	Q₈×D₅₃	—	4	4	no	—
109	C₂×D₂₁₂	—	2	1	no	—
110	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₅₃	—	2	1	no	—
112	C₂×C₄×D₅₃	—	2	1	no	—
113	C₂×C₄×D₅₃	—	2	1	no	—
114	C₂×C₄×D₅₃	—	4	2	no	—
115	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
118	C₂×Dic₁₀₆	—	2	2	no	—
119	C₂×Dic₁₀₆	—	4	2	no	—
120	Q₁₆×C₅₃	—	4	2	no	—
121	Q₁₆×C₅₃	—	4	2	no	—
122	C₂×C₈×C₅₃	—	2	1	no	—
123	C₂×C₈×C₅₃	—	2	2	no	—
124	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
126	C₄⋊C₄×C₅₃	—	2	1	no	—
127	C₄⋊C₄×C₅₃	—	2	2	no	—
128	C₄⋊C₄×C₅₃	—	2	2	no	—
129	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₅₃	—	2	1	no	—
131	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
132	#11719925	—	4	4	no	—
133	#11719925	—	4	4	no	—
134	#11719921	—	2	1	no	—
135	#11719921	—	2	1	no	—
136	#11719921	—	2	1	no	—
137	C₄⋊Dic₅₃	—	2	1	no	—
138	C₄⋊Dic₅₃	—	2	2	no	—
139	C₄⋊Dic₅₃	—	2	2	no	—
140	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
141	#11719919	—	4	2	no	—
142	#11719919	—	4	2	no	—
143	C₄×Dic₅₃	—	2	1	no	—
144	C₄×Dic₅₃	—	2	1	no	—
145	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
146	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
147	C₄×Dic₅₃	#41	1	1	yes	characteristic
148	C₂×#88322	—	2	1	no	—
149	C₂×#88322	—	2	2	no	—
150	C₂×#88322	C₂×D₄	1	1	yes	characteristic
151	C₂×#88322	C₂×D₄	1	1	yes	characteristic
152	Dic₂₁₂	—	4	2	no	—
153	Dic₂₁₂	—	4	2	no	—
154	#11719912	—	4	4	no	—
155	#11719912	—	4	2	no	—
156	#11719912	—	4	2	no	—
157	C₈×D₅₃	—	2	2	no	—
158	C₈×D₅₃	—	2	2	no	—
159	C₂²×D₅₃	—	2	1	no	—
160	C₂²×D₅₃	#121	1	1	yes	characteristic
161	Q₈×C₅₃	—	2	2	no	—
162	Q₈×C₅₃	—	4	2	no	—
163	Q₈×C₅₃	—	4	2	no	—
164	C₂×C₄×C₅₃	—	2	1	no	—
165	C₂×C₄×C₅₃	—	2	1	no	—
166	C₂×C₄×C₅₃	—	4	2	no	—
167	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
170	C₂×Dic₅₃	—	2	1	no	—
171	C₂×Dic₅₃	—	4	2	no	—
172	C₂×Dic₅₃	#121	1	1	yes	characteristic
173	C₂×Dic₅₃	#121	1	1	yes	characteristic
174	C₂×Dic₅₃	#121	1	1	yes	characteristic
175	D₂₁₂	—	2	2	no	—
176	D₂₁₂	—	4	2	no	—
177	C₄×D₅₃	—	2	1	no	—
178	C₄×D₅₃	—	2	1	no	—
179	C₄×D₅₃	—	2	2	no	—
180	C₄×D₅₃	—	4	1	no	—
181	C₄×D₅₃	—	4	1	no	—
182	C₄×D₅₃	—	4	2	no	—
183	C₄×D₅₃	—	4	2	no	—
184	C₄×D₅₃	—	8	4	no	—
185	C₄×D₅₃	#137	1	4	yes	—
186	Dic₁₀₆	—	4	2	no	—
187	Dic₁₀₆	—	4	2	no	—
188	Dic₁₀₆	—	8	4	no	—
189	C₈×C₅₃	—	2	1	no	—
190	C₈×C₅₃	—	4	1	no	—
191	C₈×C₅₃	—	4	2	no	—
192	C₈×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
193	#88322	—	2	1	no	—
194	#88322	—	4	1	no	—
195	#88322	—	4	2	no	—
196	#88322	AGL(1,ℤ/8)	1	2	yes	—
197	#19293	—	53	1	no	maximal, Sylow
198	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
199	C₂×D₅₃	—	2	1	no	—
200	C₂×D₅₃	—	2	1	no	—
201	C₂×D₅₃	—	4	1	no	—
202	C₂×D₅₃	—	4	1	no	—
203	C₂×D₅₃	—	4	1	no	—
204	C₂×D₅₃	#470	1	2	yes	—
205	C₄×C₅₃	—	2	1	no	—
206	C₄×C₅₃	—	4	1	no	—
207	C₄×C₅₃	—	4	1	no	—
208	C₄×C₅₃	—	8	2	no	—
209	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
210	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₄×C₅₃	C₂×#137	1	2	yes	—
212	Dic₅₃	—	2	1	no	—
213	Dic₅₃	—	4	1	no	—
214	Dic₅₃	—	8	2	no	—
215	Dic₅₃	#470	1	2	yes	—
216	Dic₅₃	#473	1	2	yes	—
217	C₂×#494	—	53	1	no	—
218	#3079	—	53	2	no	—
219	#2965	—	53	1	no	—
220	#1690	—	53	2	no	—
221	#1690	—	53	1	no	—
222	#1690	D₅₃	1	1	yes	characteristic, complemented
223	#1689	—	53	1	no	—
224	#1689	—	53	1	no	—
225	#1689	—	53	2	no	—
226	#1566	—	53	1	no	—
227	#1549	—	53	2	no	—
228	C₂×C₅₃	#3038	1	1	yes	characteristic
229	C₂×C₅₃	C₂×#470	1	1	yes	characteristic
230	C₂×C₅₃	C₂×#473	1	1	yes	characteristic
231	D₅₃	—	2	2	no	—
232	D₅₃	—	8	1	no	—
233	C₂²×Q₁₆	—	106	1	no	—
234	C₂²×Q₁₆	—	106	1	no	—
235	C₂×C₄⋊Q₈	—	53	2	no	—
236	C₄×#41	—	53	1	no	—
237	#494	—	53	2	no	—
238	#494	—	53	1	no	—
239	#494	—	106	1	no	—
240	#494	—	106	1	no	—
241	#494	C₂×D₅₃	1	1	yes	characteristic
242	#477	—	106	2	no	—
243	#476	—	106	2	no	—
244	#475	—	53	2	no	—
245	#475	C₂×D₅₃	1	2	yes	—
246	#474	—	53	2	no	—
247	#474	—	53	2	no	—
248	#446	—	53	1	no	—
249	#446	C₂×D₅₃	1	1	yes	characteristic
250	#436	—	53	1	no	—
251	#436	—	53	1	no	—
252	#435	—	106	1	no	—
253	#435	—	106	1	no	—
254	#431	—	53	1	no	—
255	#431	—	106	1	no	—
256	#428	—	106	2	no	—
257	#423	—	53	2	no	—
258	#417	—	106	2	no	—
259	C₄×M₁₆	—	106	1	no	—
260	C₂×C₄×C₈	—	53	1	no	—
261	#334	—	53	2	no	—
262	#334	—	53	1	no	—
263	#334	C₂×D₅₃	1	1	yes	characteristic
264	#332	—	53	2	no	—
265	#332	—	53	2	no	—
266	#332	—	53	2	no	—
267	#332	C₂×D₅₃	1	2	yes	—
268	C₅₃	#19293	1	1	yes	characteristic, complemented, Sylow
269	C₂×#41	—	53	1	no	—
270	C₂²×Q₈	—	106	2	no	—
271	C₂×Q₁₆	—	2	1	no	—
272	C₂×Q₁₆	—	2	1	no	—
273	C₂×Q₁₆	—	106	2	no	—
274	C₂×Q₁₆	—	106	2	no	—
275	C₂×Q₁₆	—	106	1	no	—
276	C₂×Q₁₆	—	106	1	no	—
277	C₂×Q₁₆	—	212	4	no	—
278	C₂×Q₁₆	—	212	4	no	—
279	C₂×M₁₆	—	106	1	no	—
280	C₂×M₁₆	—	106	2	no	—
281	C₂×M₁₆	—	106	1	no	—
282	C₂²×C₈	—	53	1	no	—
283	C₂²×C₈	—	53	1	no	—
284	C₄⋊Q₈	—	53	2	no	—
285	C₄⋊Q₈	—	106	2	no	—
286	C₄⋊Q₈	—	106	2	no	—
287	C₄⋊Q₈	—	106	2	no	—
288	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
289	C₄×Q₈	—	53	1	no	—
290	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
291	C₄×D₄	—	53	1	no	—
292	C₄×D₄	—	53	1	no	—
293	C₄×D₄	—	106	1	no	—
294	C₄×D₄	—	106	1	no	—
295	#117	—	53	1	no	—
296	#117	—	106	1	no	—
297	C₂×C₄⋊C₄	—	106	2	no	—
298	C₂×C₄⋊C₄	—	106	2	no	—
299	C₂×C₄²	—	53	1	no	—
300	C₂×C₄²	—	106	1	no	—
301	#107	—	106	2	no	—
302	#107	—	106	2	no	—
303	#106	—	2	2	no	—
304	#106	—	106	2	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	—	53	1	no	—
307	C₄⋊C₈	—	53	2	no	—
308	C₄⋊C₈	—	106	1	no	—
309	C₄⋊C₈	—	106	2	no	—
310	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
311	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
312	#103	—	2	2	no	—
313	#103	—	106	2	no	—
314	#102	—	106	2	no	—
315	#102	—	106	2	no	—
316	C₂²⋊C₈	—	106	1	no	—
317	C₂²⋊C₈	—	106	1	no	—
318	C₂²⋊C₈	—	106	1	no	—
319	#97	—	2	1	no	—
320	#97	—	106	1	no	—
321	C₄×C₈	—	53	1	no	—
322	C₄×C₈	—	53	1	no	—
323	C₄×C₈	—	53	1	no	—
324	C₄×C₈	—	106	1	no	—
325	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
326	#41	—	106	4	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	106	2	no	—
329	C₂×Q₈	—	212	2	no	—
330	C₂×Q₈	—	212	4	no	—
331	C₂×Q₈	—	212	4	no	—
332	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
333	C₂×D₄	—	53	1	no	—
334	C₂×D₄	—	106	1	no	—
335	C₂²×C₄	—	53	1	no	—
336	C₂²×C₄	—	53	1	no	—
337	C₂²×C₄	—	53	1	no	—
338	C₂²×C₄	—	106	1	no	—
339	C₂²×C₄	—	106	1	no	—
340	C₂²×C₄	—	106	1	no	—
341	C₂²×C₄	—	212	2	no	—
342	Q₁₆	—	4	2	no	—
343	Q₁₆	—	4	2	no	—
344	Q₁₆	—	212	2	no	—
345	Q₁₆	—	212	4	no	—
346	Q₁₆	—	212	4	no	—
347	Q₁₆	—	212	2	no	—
348	M₁₆	—	212	2	no	—
349	M₁₆	—	212	4	no	—
350	M₁₆	—	212	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	53	1	no	—
354	C₂×C₈	—	53	1	no	—
355	C₂×C₈	—	106	2	no	—
356	C₂×C₈	—	106	2	no	—
357	C₂×C₈	—	106	1	no	—
358	C₂×C₈	—	106	2	no	—
359	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
360	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	53	1	no	—
365	C₄⋊C₄	—	106	1	no	—
366	C₄⋊C₄	—	106	2	no	—
367	C₄⋊C₄	—	106	2	no	—
368	C₄⋊C₄	—	212	2	no	—
369	C₄⋊C₄	—	212	2	no	—
370	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
371	C₂²⋊C₄	—	106	1	no	—
372	C₂²⋊C₄	—	106	1	no	—
373	C₂²⋊C₄	—	106	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	53	1	no	—
376	C₄²	—	53	1	no	—
377	C₄²	—	53	1	no	—
378	C₄²	—	106	1	no	—
379	C₄²	—	106	1	no	—
380	C₄²	C₂³×D₅₃	1	1	yes	characteristic
381	C₂³	—	53	1	no	—
382	C₂³	—	106	1	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	424	4	no	—
387	Q₈	—	212	2	no	—
388	Q₈	—	212	2	no	—
389	D₄	—	106	2	no	—
390	D₄	—	212	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	53	1	no	—
395	C₂×C₄	—	53	1	no	—
396	C₂×C₄	—	53	4	no	—
397	C₂×C₄	—	53	1	no	—
398	C₂×C₄	—	106	2	no	—
399	C₂×C₄	—	106	1	no	—
400	C₂×C₄	—	106	1	no	—
401	C₂×C₄	—	106	1	no	—
402	C₂×C₄	—	424	4	no	—
403	C₂×C₄	—	212	2	no	—
404	C₂×C₄	—	212	2	no	—
405	C₂×C₄	—	212	2	no	—
406	C₂×C₄	—	212	1	no	—
407	C₂×C₄	—	212	1	no	—
408	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
409	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
410	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	4	2	no	—
414	C₈	—	53	2	no	—
415	C₈	—	106	1	no	—
416	C₈	—	212	1	no	—
417	C₈	—	212	2	no	—
418	C₈	#13133244	1	2	yes	—
419	C₂²	—	53	2	no	—
420	C₂²	—	106	1	no	—
421	C₂²	—	106	1	no	—
422	C₂²	—	212	1	no	—
423	C₂²	—	212	1	no	—
424	C₂²	—	212	1	no	—
425	C₂²	#121×D₅₃	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	53	2	no	—
431	C₄	—	53	2	no	—
432	C₄	—	106	1	no	—
433	C₄	—	424	2	no	—
434	C₄	—	212	1	no	—
435	C₄	AGL(1,ℤ/8)×D₅₃	1	1	yes	characteristic
436	C₄	C₂×#13133244	1	1	yes	characteristic
437	C₄	#137×D₅₃	1	2	yes	—
438	C₂	—	106	2	no	—
439	C₂	—	424	1	no	—
440	C₂	#20284192	1	1	yes	characteristic
441	C₂	#470×D₅₃	1	1	yes	characteristic
442	C₂	#473×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₅₃
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1690	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	C₂×#11719949	D₄
hypercenter	#1690	D₅₃
hypocenter	C₅₃	#19293
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1690

Complements

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

N	H ≅ G/N	type
1. #494×D₅₃	C₂	semidirect
4. #20274209	C₂	semidirect
5. #20274207	C₂	semidirect
6. #20274205	C₂	semidirect
7. #20274203	C₂	semidirect
8. #20274201	C₂	semidirect
9. #20273469	C₂	semidirect
10. #20273398	C₂	semidirect
11. C₅₃×#1690	C₂	semidirect
222. #1690	D₅₃	semidirect
268. C₅₃	#19293	semidirect

Maximal subgroups

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

subgroup	index
#494×D₅₃	2
#20284525	2
#20283680	2
#20274209	2
#20274207	2
#20274205	2
#20274203	2
#20274201	2
#20273469	2
#20273398	2
C₅₃×#1690	2
#19293	53