Subgroups — #27537516

Order 13568.

642 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#508×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#20283627	C₂	1	2	yes	maximal, complemented
3	#20276602	C₂	1	1	yes	maximal, characteristic, complemented
4	#20276601	C₂	1	1	yes	maximal, characteristic, complemented
5	#20276600	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276594	C₂	1	2	yes	maximal, complemented
7	#20276593	C₂	1	2	yes	maximal, complemented
8	#368×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#20276441	C₂	1	2	yes	maximal, complemented
10	#20276313	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2179	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₅₃	C₂²	1	2	yes	—
13	#16811388	—	2	2	no	—
14	#16811056	C₄	1	1	yes	characteristic, complemented
15	#16811055	C₂²	1	1	yes	characteristic
16	#16811054	C₄	1	2	yes	complemented
17	#16811053	C₂²	1	2	yes	—
18	#16811052	C₄	1	1	yes	characteristic, complemented
19	Q₃₂×D₅₃	C₄	1	1	yes	characteristic, complemented
20	SD₃₂×D₅₃	C₄	1	2	yes	complemented
21	D₁₆×D₅₃	C₄	1	1	yes	characteristic, complemented
22	C₂×#13133156	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic
24	#16810743	—	2	2	no	—
25	#16810742	—	2	2	no	—
26	#16810741	C₂²	1	2	yes	complemented
27	#16810740	C₂²	1	2	yes	complemented
28	#16810739	C₂²	1	2	yes	complemented
29	#108×D₅₃	C₂²	1	2	yes	—
30	#16810638	—	2	2	no	—
31	#16810577	C₂²	1	1	yes	characteristic
32	#16810453	C₂²	1	1	yes	characteristic, complemented
33	#16810452	C₂²	1	2	yes	complemented
34	#16810431	C₂²	1	2	yes	complemented
35	#16810430	C₂²	1	2	yes	complemented
36	#16810429	C₂²	1	2	yes	complemented
37	#16810398	C₂²	1	1	yes	characteristic, complemented
38	C₄×#11719908	C₂²	1	1	yes	characteristic, complemented
39	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#508	C₂²	1	1	yes	characteristic
41	C₅₃×#443	C₂²	1	2	yes	complemented
42	C₅₃×#368	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#359	C₂²	1	2	yes	complemented
44	C₅₃×#346	C₂²	1	1	yes	characteristic, complemented
45	#41×D₅₃	—	2	2	no	—
46	#13133240	C₂×C₄	1	2	yes	—
47	#13133239	C₂³	1	2	yes	—
48	#13133238	—	2	2	no	—
49	#13133237	—	2	2	no	—
50	#13133236	C₂×C₄	1	2	yes	—
51	Q₁₆×D₅₃	C₂×C₄	1	2	yes	—
52	SD₁₆×D₅₃	—	2	2	no	—
53	D₈×D₅₃	C₂×C₄	1	2	yes	—
54	#13133225	—	2	2	no	—
55	#13133225	—	4	2	no	—
56	#13133224	—	2	2	no	—
57	#13133223	—	2	2	no	—
58	#13133223	—	4	2	no	—
59	C₂×#11719912	—	4	2	no	—
60	C₂×#11719912	D₄	1	1	yes	characteristic
61	M₁₆×D₅₃	—	2	2	no	—
62	M₁₆×D₅₃	—	4	2	no	—
63	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
64	#13133174	D₄	1	1	yes	characteristic
65	Dic₄₂₄	C₂×C₄	1	1	yes	characteristic
66	#13133163	C₂×C₄	1	2	yes	—
67	#13133162	C₂×C₄	1	2	yes	—
68	#13133161	C₂×C₄	1	2	yes	—
69	#13133160	C₂×C₄	1	2	yes	—
70	D₈₄₈	C₂×C₄	1	1	yes	characteristic
71	#13133158	C₂×C₄	1	2	yes	—
72	#13133156	—	2	1	no	—
73	#13133156	—	2	1	no	—
74	C₂×#11719908	C₂³	1	1	yes	characteristic
75	C₂×#11719908	C₂³	1	1	yes	characteristic
76	C₁₆×D₅₃	C₂×C₄	1	1	yes	characteristic
77	C₁₆×D₅₃	C₂×C₄	1	1	yes	characteristic
78	C₁₆×D₅₃	C₂×C₄	1	1	yes	characteristic
79	C₁₆×D₅₃	C₂×C₄	1	1	yes	characteristic
80	#13133153	C₂³	1	2	yes	—
81	#13133152	—	2	2	no	—
82	#13133145	—	2	2	no	—
83	#13133144	—	2	2	no	—
84	#13133143	—	2	2	no	—
85	#13133128	D₄	1	1	yes	characteristic
86	#13133127	D₄	1	1	yes	characteristic
87	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
88	#135×C₅₃	C₂³	1	2	yes	—
89	#131×C₅₃	—	2	2	no	—
90	Q₃₂×C₅₃	C₂×C₄	1	1	yes	characteristic
91	SD₃₂×C₅₃	C₂×C₄	1	2	yes	—
92	D₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
94	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
95	#108×C₅₃	C₂³	1	2	yes	—
96	#104×C₅₃	—	2	2	no	—
97	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
98	#41×C₅₃	—	2	2	no	—
99	#11719949	—	2	2	no	—
100	Q₈×D₅₃	—	2	2	no	—
101	#11719947	—	2	2	no	—
102	#11719947	—	4	2	no	—
103	D₄×D₅₃	—	2	2	no	—
104	D₄×D₅₃	—	4	2	no	—
105	#11719945	—	2	2	no	—
106	#11719945	—	4	2	no	—
107	C₂×C₄×D₅₃	—	4	2	no	—
108	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
109	Q₁₆×C₅₃	C₂²×C₄	1	2	yes	—
110	SD₁₆×C₅₃	—	2	2	no	—
111	D₈×C₅₃	C₂²×C₄	1	2	yes	—
112	M₁₆×C₅₃	—	2	2	no	—
113	M₁₆×C₅₃	—	4	2	no	—
114	C₂×C₈×C₅₃	—	4	2	no	—
115	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
117	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
118	#11719925	—	2	2	no	—
119	#11719924	—	2	2	no	—
120	#11719923	—	2	2	no	—
121	#11719922	—	2	2	no	—
122	#11719921	—	2	1	no	—
123	#11719919	—	2	1	no	—
124	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
125	#11719917	—	2	2	no	—
126	#11719917	—	4	2	no	—
127	C₂×#88322	—	4	2	no	—
128	C₂×#88322	C₂×D₄	1	1	yes	characteristic
129	C₂×#88322	C₂×D₄	1	1	yes	characteristic
130	Dic₂₁₂	C₂²×C₄	1	2	yes	—
131	D₄₂₄	C₂²×C₄	1	2	yes	—
132	#11719913	—	2	2	no	—
133	#11719912	—	4	2	no	—
134	#11719912	—	4	2	no	—
135	#11719912	—	4	2	no	—
136	#11719912	D₈	1	2	yes	—
137	#11719912	D₈	1	2	yes	—
138	C₈×D₅₃	—	4	2	no	—
139	C₈×D₅₃	—	4	2	no	—
140	C₈×D₅₃	—	4	2	no	—
141	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
142	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
143	C₈×D₅₃	#41	1	1	yes	characteristic
144	C₈×D₅₃	#41	1	1	yes	characteristic
145	C₁₆×C₅₃	—	2	1	no	—
146	C₁₆×C₅₃	C₂²×C₄	1	1	yes	characteristic
147	C₁₆×C₅₃	C₂²×C₄	1	1	yes	characteristic
148	#11719908	—	2	1	no	—
149	#11719908	C₂²×C₄	1	1	yes	characteristic
150	#11719908	C₂²×C₄	1	1	yes	characteristic
151	C₂²×D₅₃	—	4	2	no	—
152	C₂²×D₅₃	#135	1	1	yes	characteristic
153	Q₈×C₅₃	—	2	2	no	—
154	D₄×C₅₃	—	2	2	no	—
155	D₄×C₅₃	—	4	2	no	—
156	C₂×C₄×C₅₃	—	2	1	no	—
157	C₂×C₄×C₅₃	—	4	2	no	—
158	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
159	C₂²⋊D₅₃	—	4	2	no	—
160	C₂²⋊D₅₃	—	4	2	no	—
161	C₂²⋊D₅₃	—	4	2	no	—
162	C₂×Dic₅₃	—	2	1	no	—
163	C₂×Dic₅₃	—	4	2	no	—
164	C₂×Dic₅₃	#135	1	1	yes	characteristic
165	D₂₁₂	—	2	2	no	—
166	D₂₁₂	—	4	2	no	—
167	C₄×D₅₃	—	4	2	no	—
168	C₄×D₅₃	—	4	2	no	—
169	C₄×D₅₃	—	4	2	no	—
170	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
171	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
172	C₄×D₅₃	C₂×D₈	1	1	yes	characteristic
173	C₄×D₅₃	C₂×D₈	1	1	yes	characteristic
174	Dic₁₀₆	—	2	2	no	—
175	Dic₁₀₆	—	4	2	no	—
176	C₈×C₅₃	—	4	2	no	—
177	C₈×C₅₃	C₂×D₈	1	2	yes	—
178	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
179	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
180	#88322	—	4	2	no	—
181	#88322	C₄×D₄	1	1	yes	characteristic
182	#88322	C₄×D₄	1	1	yes	characteristic
183	#88322	C₂×D₈	1	2	yes	—
184	#33465	—	53	1	no	maximal, Sylow
185	C₂²×C₅₃	—	4	2	no	—
186	C₂²×C₅₃	C₂×#135	1	1	yes	characteristic
187	C₂×D₅₃	—	4	1	no	—
188	C₂×D₅₃	—	4	2	no	—
189	C₂×D₅₃	—	16	2	no	—
190	C₂×D₅₃	C₄×D₈	1	1	yes	characteristic
191	C₂×D₅₃	C₄×D₈	1	1	yes	characteristic
192	C₄×C₅₃	—	4	1	no	—
193	C₄×C₅₃	—	4	2	no	—
194	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
195	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
196	Dic₅₃	—	4	1	no	—
197	Dic₅₃	—	4	2	no	—
198	Dic₅₃	C₄×D₈	1	1	yes	characteristic
199	Dic₅₃	C₄×D₈	1	1	yes	characteristic
200	C₂×#508	—	53	1	no	—
201	#2957	—	53	2	no	—
202	#2179	—	53	1	no	—
203	#2179	—	53	1	no	—
204	#2179	—	53	1	no	—
205	#2179	D₅₃	1	1	yes	characteristic, complemented
206	#2178	—	53	2	no	—
207	#2178	—	53	2	no	—
208	C₂×#368	—	53	1	no	—
209	#2143	—	53	2	no	—
210	#2108	—	53	1	no	—
211	C₂×C₅₃	—	2	1	no	—
212	C₂×C₅₃	—	8	2	no	—
213	C₂×C₅₃	C₂×C₄×D₈	1	1	yes	characteristic
214	D₅₃	—	2	1	no	—
215	D₅₃	—	2	1	no	—
216	D₅₃	—	8	2	no	—
217	C₂×#135	—	53	2	no	—
218	#568	—	106	2	no	—
219	#508	—	53	2	no	—
220	#508	—	53	1	no	—
221	#508	—	53	2	no	—
222	#508	—	53	1	no	—
223	#508	—	53	1	no	—
224	#508	C₂×D₅₃	1	1	yes	characteristic
225	C₂×Q₃₂	—	53	1	no	—
226	C₂×SD₃₂	—	53	2	no	—
227	C₂×D₁₆	—	53	1	no	—
228	C₂×M₃₂	—	53	1	no	—
229	C₂²×C₁₆	—	53	1	no	—
230	#444	—	106	2	no	—
231	#444	—	106	2	no	—
232	#443	—	53	2	no	—
233	#443	—	53	2	no	—
234	#443	—	53	2	no	—
235	#443	C₂×D₅₃	1	2	yes	complemented
236	C₂×#108	—	53	2	no	—
237	#421	—	106	2	no	—
238	#405	—	53	1	no	—
239	#368	—	53	1	no	—
240	#368	—	53	2	no	—
241	#368	C₂×D₅₃	1	1	yes	characteristic, complemented
242	#359	—	53	2	no	—
243	#359	—	53	2	no	—
244	#359	—	53	2	no	—
245	#359	C₂×D₅₃	1	2	yes	complemented
246	#346	—	53	1	no	—
247	#346	C₂×D₅₃	1	1	yes	characteristic, complemented
248	C₄×C₁₆	—	53	1	no	—
249	C₄×C₁₆	—	53	1	no	—
250	C₅₃	#33465	1	1	yes	characteristic, complemented, Sylow
251	C₂×#41	—	106	2	no	—
252	#135	—	53	2	no	—
253	#135	—	53	2	no	—
254	#135	—	53	2	no	—
255	#135	—	106	2	no	—
256	#135	—	106	2	no	—
257	#135	C₂²×D₅₃	1	2	yes	—
258	C₂×Q₁₆	—	53	2	no	—
259	C₂×SD₁₆	—	106	2	no	—
260	C₂×D₈	—	53	2	no	—
261	#131	—	2	2	no	—
262	#131	—	106	2	no	—
263	#131	—	106	2	no	—
264	#131	—	106	2	no	—
265	#131	—	212	2	no	—
266	#131	—	212	2	no	—
267	C₂×M₁₆	—	53	1	no	—
268	C₂×M₁₆	—	106	2	no	—
269	C₂×M₁₆	—	212	2	no	—
270	C₂×M₁₆	—	212	2	no	—
271	C₂²×C₈	—	53	1	no	—
272	#117	—	53	1	no	—
273	Q₃₂	—	53	2	no	—
274	Q₃₂	—	53	1	no	—
275	Q₃₂	C₄×D₅₃	1	1	yes	characteristic
276	SD₃₂	—	53	2	no	—
277	SD₃₂	—	53	2	no	—
278	SD₃₂	—	53	2	no	—
279	SD₃₂	C₄×D₅₃	1	2	yes	—
280	D₁₆	—	53	2	no	—
281	D₁₆	—	53	1	no	—
282	D₁₆	C₄×D₅₃	1	1	yes	characteristic
283	M₃₂	—	106	1	no	—
284	M₃₂	—	106	1	no	—
285	C₂×C₁₆	—	53	1	no	—
286	C₂×C₁₆	—	53	1	no	—
287	C₂×C₁₆	—	53	1	no	—
288	C₂×C₁₆	—	53	1	no	—
289	C₂×C₁₆	—	53	1	no	—
290	C₂×C₁₆	—	53	1	no	—
291	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
292	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
293	#108	—	53	2	no	—
294	#108	—	106	2	no	—
295	#108	C₂²×D₅₃	1	2	yes	—
296	#104	—	2	2	no	—
297	#104	—	106	2	no	—
298	#104	—	106	2	no	—
299	#104	—	106	2	no	—
300	#97	—	53	1	no	—
301	#97	—	53	1	no	—
302	C₄×C₈	—	53	1	no	—
303	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
304	#41	—	2	2	no	—
305	#41	—	106	2	no	—
306	#41	—	106	2	no	—
307	#41	—	106	2	no	—
308	#41	—	212	2	no	—
309	#41	—	212	2	no	—
310	C₂×Q₈	—	106	2	no	—
311	C₂×D₄	—	106	2	no	—
312	C₂×D₄	—	212	2	no	—
313	C₂²×C₄	—	53	1	no	—
314	C₂²×C₄	—	212	2	no	—
315	Q₁₆	—	53	2	no	—
316	Q₁₆	—	106	2	no	—
317	Q₁₆	C₂×C₄×D₅₃	1	2	yes	—
318	SD₁₆	—	2	2	no	—
319	SD₁₆	—	106	2	no	—
320	SD₁₆	—	106	2	no	—
321	SD₁₆	—	106	2	no	—
322	D₈	—	53	2	no	—
323	D₈	—	106	2	no	—
324	D₈	C₂×C₄×D₅₃	1	2	yes	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	4	2	no	—
327	M₁₆	—	53	2	no	—
328	M₁₆	—	53	2	no	—
329	M₁₆	—	106	2	no	—
330	M₁₆	—	212	2	no	—
331	M₁₆	—	212	2	no	—
332	M₁₆	—	212	2	no	—
333	M₁₆	—	212	2	no	—
334	C₂×C₈	—	4	2	no	—
335	C₂×C₈	—	53	1	no	—
336	C₂×C₈	—	53	1	no	—
337	C₂×C₈	—	53	1	no	—
338	C₂×C₈	—	53	1	no	—
339	C₂×C₈	—	53	1	no	—
340	C₂×C₈	—	53	1	no	—
341	C₂×C₈	—	212	2	no	—
342	C₂×C₈	—	212	2	no	—
343	C₂×C₈	—	212	2	no	—
344	C₂×C₈	—	212	2	no	—
345	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
346	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
347	C₄⋊C₄	—	106	1	no	—
348	C₂²⋊C₄	—	106	1	no	—
349	C₄²	—	53	1	no	—
350	C₄²	D₄×D₅₃	1	1	yes	characteristic
351	C₁₆	—	2	1	no	—
352	C₁₆	—	53	1	no	—
353	C₁₆	—	53	1	no	—
354	C₁₆	—	106	1	no	—
355	C₁₆	C₂×C₄×D₅₃	1	1	yes	characteristic
356	C₁₆	C₂×C₄×D₅₃	1	1	yes	characteristic
357	C₂³	—	53	1	no	—
358	C₂³	—	212	2	no	—
359	Q₈	—	2	2	no	—
360	Q₈	—	106	2	no	—
361	Q₈	—	212	2	no	—
362	D₄	—	2	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	106	2	no	—
365	D₄	—	212	2	no	—
366	D₄	—	212	2	no	—
367	D₄	—	212	2	no	—
368	D₄	—	212	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	53	1	no	—
372	C₂×C₄	—	53	1	no	—
373	C₂×C₄	—	53	1	no	—
374	C₂×C₄	—	53	1	no	—
375	C₂×C₄	—	53	1	no	—
376	C₂×C₄	—	106	1	no	—
377	C₂×C₄	—	212	2	no	—
378	C₂×C₄	—	212	2	no	—
379	C₂×C₄	—	212	2	no	—
380	C₂×C₄	—	212	2	no	—
381	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
382	C₈	—	4	2	no	—
383	C₈	—	53	1	no	—
384	C₈	—	53	1	no	—
385	C₈	—	53	2	no	—
386	C₈	—	212	2	no	—
387	C₈	D₈×D₅₃	1	2	yes	—
388	C₈	C₂²×C₄×D₅₃	1	1	yes	characteristic
389	C₈	#41×D₅₃	1	1	yes	characteristic
390	C₂²	—	4	2	no	—
391	C₂²	—	53	1	no	—
392	C₂²	—	53	1	no	—
393	C₂²	—	848	2	no	—
394	C₂²	—	212	1	no	—
395	C₂²	—	212	2	no	—
396	C₂²	#135×D₅₃	1	1	yes	characteristic
397	C₄	—	4	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	53	1	no	—
400	C₄	—	53	1	no	—
401	C₄	—	212	1	no	—
402	C₄	—	212	2	no	—
403	C₄	C₄×D₄×D₅₃	1	1	yes	characteristic
404	C₄	C₂×D₈×D₅₃	1	1	yes	characteristic
405	C₂	—	2	1	no	—
406	C₂	—	8	2	no	—
407	C₂	—	106	1	no	—
408	C₂	—	106	1	no	—
409	C₂	—	424	2	no	—
410	C₂	C₄×D₈×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₈×D₅₃
commutator	C₈×C₅₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₅₃×#2179	C₂
socle	C₂×C₅₃	C₂×C₄×D₈
prime radical	#508×D₅₃	C₂
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	#2179	D₅₃
hypocenter	C₅₃	#33465
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #2179

Complements

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

N	H ≅ G/N	type
2. #20283627	C₂	semidirect
3. #20276602	C₂	semidirect
4. #20276601	C₂	semidirect
5. #20276600	C₂	semidirect
6. #20276594	C₂	semidirect
7. #20276593	C₂	semidirect
8. #368×D₅₃	C₂	semidirect
9. #20276441	C₂	semidirect
10. #20276313	C₂	semidirect
11. C₅₃×#2179	C₂	semidirect
14. #16811056	C₄	semidirect
16. #16811054	C₄	semidirect
18. #16811052	C₄	semidirect
19. Q₃₂×D₅₃	C₄	semidirect
20. SD₃₂×D₅₃	C₄	semidirect
21. D₁₆×D₅₃	C₄	semidirect
26. #16810741	C₂²	semidirect
27. #16810740	C₂²	semidirect
28. #16810739	C₂²	semidirect
32. #16810453	C₂²	semidirect
33. #16810452	C₂²	semidirect
34. #16810431	C₂²	semidirect
35. #16810430	C₂²	semidirect
36. #16810429	C₂²	semidirect
37. #16810398	C₂²	semidirect
38. C₄×#11719908	C₂²	semidirect
39. C₁₆×Dic₅₃	C₂²	semidirect
41. C₅₃×#443	C₂²	semidirect
42. C₅₃×#368	C₂²	semidirect
43. C₅₃×#359	C₂²	semidirect
44. C₅₃×#346	C₂²	semidirect
205. #2179	D₅₃	semidirect
235. #443	C₂×D₅₃	semidirect
241. #368	C₂×D₅₃	semidirect
245. #359	C₂×D₅₃	semidirect
247. #346	C₂×D₅₃	semidirect
250. C₅₃	#33465	semidirect

Maximal subgroups

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

subgroup	index
#508×D₅₃	2
#20283627	2
#20276602	2
#20276601	2
#20276600	2
#20276594	2
#20276593	2
#368×D₅₃	2
#20276441	2
#20276313	2
C₅₃×#2179	2
#33465	53