Subgroups — #27398015

Order 13568.

772 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20285204	C₂	1	1	yes	maximal, characteristic
2	#20283631	C₂	1	1	yes	maximal, characteristic
3	#20283583	C₂	1	1	yes	maximal, characteristic, complemented
4	#20275613	C₂	1	1	yes	maximal, characteristic
5	#20275250	C₂	1	2	yes	maximal, complemented
6	#20275234	C₂	1	2	yes	maximal, complemented
7	#20275207	C₂	1	2	yes	maximal, complemented
8	#20275191	C₂	1	2	yes	maximal, complemented
9	#20274840	C₂	1	1	yes	maximal, characteristic, complemented
10	#20274470	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1979	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133248	C₂²	1	2	yes	—
13	C₂×#13133239	C₂²	1	1	yes	characteristic
14	#16811389	C₂²	1	2	yes	—
15	#16811197	C₂²	1	2	yes	—
16	#16811101	C₂²	1	2	yes	—
17	#16811016	C₄	1	4	yes	complemented
18	#16811008	C₄	1	2	yes	complemented
19	#16811001	C₄	1	2	yes	complemented
20	#16810744	—	2	2	no	—
21	#16810739	—	2	2	no	—
22	#16810730	—	2	2	no	—
23	Q₁₆×Dic₅₃	—	2	2	no	—
24	#16810661	C₂²	1	1	yes	characteristic
25	#16810639	C₂²	1	2	yes	—
26	#16810639	C₂²	1	2	yes	—
27	#16810632	C₂²	1	2	yes	—
28	#16810596	C₂²	1	2	yes	—
29	#16810578	C₂²	1	1	yes	characteristic
30	#16810578	C₂²	1	1	yes	characteristic
31	#16810395	C₂²	1	2	yes	—
32	#16810381	C₂²	1	1	yes	characteristic
33	#16810380	C₂²	1	2	yes	—
34	#16810380	C₂²	1	1	yes	characteristic
35	#16810379	C₂²	1	1	yes	characteristic
36	#16810379	C₂²	1	1	yes	characteristic
37	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
39	C₅₃×#419	C₂²	1	2	yes	—
40	C₂×#101×C₅₃	C₂²	1	2	yes	—
41	C₅₃×#405	C₂²	1	1	yes	characteristic
42	C₂×#11719945	C₂³	1	2	yes	—
43	#13133248	—	4	2	no	—
44	#13133248	—	4	2	no	—
45	#13133239	—	2	1	no	—
46	#13133239	—	2	1	no	—
47	#13133239	—	2	1	no	—
48	#13133239	—	2	1	no	—
49	C₂×Dic₂₁₂	C₂×C₄	1	1	yes	characteristic
50	C₂×#11719925	C₂×C₄	1	4	yes	—
51	C₂×#11719913	C₂×C₄	1	2	yes	—
52	C₂×#11719924	C₂×C₄	1	4	yes	—
53	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic
54	#13133225	—	2	4	no	—
55	#13133223	—	4	2	no	—
56	C₂×#11719917	C₂³	1	1	yes	characteristic
57	C₂×#11719917	C₂³	1	1	yes	characteristic
58	M₁₆×D₅₃	—	4	2	no	—
59	#13133215	C₂×C₄	1	4	yes	—
60	#13133206	C₂×C₄	1	4	yes	—
61	#13133200	—	4	2	no	—
62	#13133193	—	4	2	no	—
63	Q₈×Dic₅₃	—	2	4	no	—
64	Q₈×Dic₅₃	—	4	2	no	—
65	#13133176	—	4	2	no	—
66	#13133176	C₂³	1	2	yes	—
67	#13133176	C₂³	1	1	yes	characteristic
68	#13133176	C₂³	1	1	yes	characteristic
69	#13133151	—	2	1	no	—
70	#13133149	—	2	1	no	—
71	#13133143	—	2	4	no	—
72	#13133143	—	4	2	no	—
73	#13133141	—	2	4	no	—
74	#13133131	—	4	2	no	—
75	#13133127	C₂×C₄	1	2	yes	—
76	#13133127	D₄	1	2	yes	—
77	C₈×Dic₅₃	C₂×C₄	1	2	yes	—
78	C₈×Dic₅₃	D₄	1	2	yes	—
79	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
80	C₂×Q₁₆×C₅₃	—	2	1	no	—
81	C₂×Q₁₆×C₅₃	—	2	1	no	—
82	C₂×Q₁₆×C₅₃	—	2	1	no	—
83	C₂×Q₁₆×C₅₃	—	2	1	no	—
84	C₂×Q₁₆×C₅₃	C₂×C₄	1	2	yes	—
85	C₂×Q₁₆×C₅₃	C₂×C₄	1	2	yes	—
86	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
87	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
89	#117×C₅₃	C₂³	1	1	yes	characteristic
90	#108×C₅₃	—	2	1	no	—
91	#108×C₅₃	—	2	1	no	—
92	#103×C₅₃	—	4	2	no	—
93	#101×C₅₃	—	4	2	no	—
94	#97×C₅₃	—	2	1	no	—
95	C₄×C₈×C₅₃	—	2	1	no	—
96	C₂×Q₈×C₅₃	—	2	2	no	—
97	C₂×Q₈×C₅₃	—	2	2	no	—
98	C₂×Q₈×C₅₃	—	2	2	no	—
99	C₂×Q₈×C₅₃	—	2	2	no	—
100	C₂×Q₈×C₅₃	—	2	2	no	—
101	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₅₃	—	2	2	no	—
103	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
104	C₂×C₂²⋊D₅₃	—	2	2	no	—
105	#11719945	—	2	2	no	—
106	#11719945	—	2	2	no	—
107	#11719945	—	2	2	no	—
108	#11719945	—	2	2	no	—
109	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
110	C₂×C₄×D₅₃	—	2	2	no	—
111	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
112	Q₁₆×C₅₃	—	2	2	no	—
113	Q₁₆×C₅₃	—	2	2	no	—
114	Q₁₆×C₅₃	—	2	2	no	—
115	Q₁₆×C₅₃	—	2	2	no	—
116	M₁₆×C₅₃	—	2	2	no	—
117	M₁₆×C₅₃	—	2	1	no	—
118	M₁₆×C₅₃	—	2	2	no	—
119	M₁₆×C₅₃	—	2	1	no	—
120	C₂×C₈×C₅₃	—	2	1	no	—
121	C₂×C₈×C₅₃	—	2	2	no	—
122	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
127	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
128	C₄⋊C₄×C₅₃	—	2	1	no	—
129	C₂²⋊C₄×C₅₃	—	2	1	no	—
130	C₄²×C₅₃	—	2	1	no	—
131	C₂²⋊Dic₅₃	—	2	1	no	—
132	C₂²⋊Dic₅₃	—	2	1	no	—
133	C₂²⋊Dic₅₃	—	2	2	no	—
134	#11719925	—	4	4	no	—
135	#11719924	—	4	4	no	—
136	#11719921	—	4	4	no	—
137	C₄⋊Dic₅₃	—	2	1	no	—
138	C₄⋊Dic₅₃	—	2	1	no	—
139	C₄⋊Dic₅₃	—	2	2	no	—
140	C₄⋊Dic₅₃	—	4	4	no	—
141	#11719919	—	4	4	no	—
142	C₄×Dic₅₃	—	2	2	no	—
143	C₄×Dic₅₃	—	4	4	no	—
144	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
145	C₄×Dic₅₃	C₂×D₄	1	2	yes	—
146	#11719917	—	2	1	no	—
147	#11719917	—	2	1	no	—
148	#11719917	—	2	1	no	—
149	#11719917	—	2	1	no	—
150	C₂×#88322	C₂²×C₄	1	2	yes	—
151	C₂×#88322	C₂×D₄	1	2	yes	—
152	Dic₂₁₂	—	2	1	no	—
153	Dic₂₁₂	—	2	1	no	—
154	D₄₂₄	—	2	1	no	—
155	D₄₂₄	—	2	1	no	—
156	#11719913	—	2	2	no	—
157	#11719913	—	2	2	no	—
158	#11719912	—	4	4	no	—
159	C₈×D₅₃	—	4	4	no	—
160	C₂³×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₅₃	—	2	2	no	—
162	Q₈×C₅₃	—	2	4	no	—
163	Q₈×C₅₃	—	2	4	no	—
164	Q₈×C₅₃	—	4	2	no	—
165	Q₈×C₅₃	—	4	2	no	—
166	C₂×C₄×C₅₃	—	2	4	no	—
167	C₂×C₄×C₅₃	—	4	2	no	—
168	C₂×C₄×C₅₃	—	4	2	no	—
169	C₂×C₄×C₅₃	—	4	1	no	—
170	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂²⋊D₅₃	—	4	2	no	—
177	C₂²⋊D₅₃	—	4	2	no	—
178	C₂×Dic₅₃	—	2	2	no	—
179	C₂×Dic₅₃	—	2	2	no	—
180	C₂×Dic₅₃	—	2	2	no	—
181	C₂×Dic₅₃	—	4	2	no	—
182	D₂₁₂	—	2	2	no	—
183	D₂₁₂	—	2	2	no	—
184	C₄×D₅₃	—	4	2	no	—
185	C₄×D₅₃	—	4	2	no	—
186	Dic₁₀₆	—	2	2	no	—
187	Dic₁₀₆	—	2	2	no	—
188	C₈×C₅₃	—	4	2	no	—
189	C₈×C₅₃	—	4	1	no	—
190	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
191	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
192	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
193	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
194	#88322	—	2	2	no	—
195	#88322	—	2	2	no	—
196	#22285	—	53	1	no	maximal, Sylow
197	C₂²×C₅₃	—	4	1	no	—
198	C₂²×C₅₃	#518	1	1	yes	characteristic
199	C₂²×C₅₃	#535	1	1	yes	characteristic
200	C₂²×C₅₃	#540	1	1	yes	characteristic
201	C₂×D₅₃	—	4	2	no	—
202	C₂×D₅₃	—	8	2	no	—
203	C₄×C₅₃	—	4	4	no	—
204	C₄×C₅₃	—	8	1	no	—
205	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₅₃	#518	1	1	yes	characteristic
207	C₄×C₅₃	#535	1	1	yes	characteristic
208	C₄×C₅₃	#540	1	1	yes	characteristic
209	Dic₅₃	—	4	2	no	—
210	Dic₅₃	—	4	2	no	—
211	Dic₅₃	—	4	2	no	—
212	Dic₅₃	—	8	2	no	—
213	#3156	—	53	1	no	—
214	#2957	—	53	1	no	—
215	#2950	—	53	1	no	—
216	#1979	D₅₃	1	1	yes	characteristic, complemented
217	#1976	—	53	1	no	—
218	#1912	—	53	2	no	—
219	#1909	—	53	2	no	—
220	#1905	—	53	2	no	—
221	#1902	—	53	2	no	—
222	#1833	—	53	1	no	—
223	#1747	—	53	1	no	—
224	C₂×C₅₃	—	2	1	no	—
225	C₂×C₅₃	—	2	1	no	—
226	C₂×C₅₃	—	2	1	no	—
227	C₂×C₅₃	#2328	1	1	yes	characteristic
228	D₅₃	—	8	2	no	—
229	C₂×#137	—	53	2	no	—
230	C₂×#135	—	53	1	no	—
231	C₂²×Q₁₆	C₂×D₅₃	1	1	yes	characteristic
232	#568	—	53	2	no	—
233	#536	—	53	2	no	—
234	#519	—	53	2	no	—
235	#497	—	53	4	no	—
236	#495	—	53	2	no	—
237	#494	—	53	2	no	—
238	#444	—	106	2	no	—
239	#443	—	106	2	no	—
240	#441	—	106	2	no	—
241	C₄×Q₁₆	—	106	2	no	—
242	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
243	#427	—	53	1	no	—
244	#421	—	53	2	no	—
245	#421	—	53	2	no	—
246	#419	—	53	2	no	—
247	#419	C₂×D₅₃	1	2	yes	—
248	C₂×#101	C₂×D₅₃	1	2	yes	—
249	#410	—	53	2	no	—
250	#405	—	53	1	no	—
251	#405	—	53	1	no	—
252	#405	C₂×D₅₃	1	1	yes	characteristic
253	#344	—	53	2	no	—
254	#338	—	53	1	no	—
255	H(3,ℤ/4)	—	53	2	no	—
256	H(3,ℤ/4)	—	53	1	no	—
257	H(3,ℤ/4)	—	53	1	no	—
258	H(3,ℤ/4)	—	53	1	no	—
259	C₅₃	#22285	1	1	yes	characteristic, complemented, Sylow
260	C₂×#41	—	53	2	no	—
261	C₂²×Q₈	C₂²×D₅₃	1	2	yes	—
262	#137	—	212	2	no	—
263	#137	—	212	2	no	—
264	#135	—	106	1	no	—
265	#135	—	106	1	no	—
266	#135	—	106	1	no	—
267	#135	—	106	1	no	—
268	C₂×Q₁₆	—	2	1	no	—
269	C₂×Q₁₆	—	2	1	no	—
270	C₂×Q₁₆	—	2	1	no	—
271	C₂×Q₁₆	—	2	1	no	—
272	C₂×Q₁₆	—	53	4	no	—
273	C₂×Q₁₆	—	53	1	no	—
274	C₂×Q₁₆	C₄×D₅₃	1	2	yes	—
275	C₂×Q₁₆	C₄×D₅₃	1	2	yes	—
276	C₂×SD₁₆	—	53	4	no	—
277	C₂×SD₁₆	—	53	2	no	—
278	C₂×D₈	—	53	1	no	—
279	#131	—	106	4	no	—
280	#131	—	212	2	no	—
281	C₂×M₁₆	—	53	1	no	—
282	C₂×M₁₆	—	53	1	no	—
283	C₂×M₁₆	—	212	2	no	—
284	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
285	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
286	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
287	C₄⋊Q₈	—	53	4	no	—
288	#124	—	53	4	no	—
289	#123	—	212	2	no	—
290	C₂²⋊Q₈	—	212	2	no	—
291	C₄×Q₈	—	106	4	no	—
292	C₄×Q₈	—	212	2	no	—
293	#117	—	53	1	no	—
294	#117	—	53	1	no	—
295	#117	—	53	2	no	—
296	#117	—	212	2	no	—
297	#117	C₂²×D₅₃	1	1	yes	characteristic
298	#108	—	2	1	no	—
299	#108	—	2	1	no	—
300	#107	—	106	1	no	—
301	#106	—	106	1	no	—
302	#104	—	106	4	no	—
303	#104	—	212	2	no	—
304	#103	—	4	2	no	—
305	#103	—	106	4	no	—
306	#101	—	4	2	no	—
307	#99	—	212	2	no	—
308	#97	—	2	1	no	—
309	#97	—	53	2	no	—
310	#97	—	53	2	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	53	2	no	—
313	C₄×C₈	—	53	2	no	—
314	#41	—	106	2	no	—
315	#41	—	106	2	no	—
316	#41	—	106	2	no	—
317	#41	—	106	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	53	2	no	—
324	C₂×Q₈	C₂×C₄×D₅₃	1	4	yes	—
325	C₂×D₄	—	53	2	no	—
326	C₂×D₄	—	106	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	106	2	no	—
329	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
330	Q₁₆	—	2	2	no	—
331	Q₁₆	—	2	2	no	—
332	Q₁₆	—	2	2	no	—
333	Q₁₆	—	2	2	no	—
334	Q₁₆	—	106	1	no	—
335	Q₁₆	—	106	1	no	—
336	Q₁₆	—	212	4	no	—
337	SD₁₆	—	106	2	no	—
338	SD₁₆	—	106	2	no	—
339	SD₁₆	—	212	4	no	—
340	D₈	—	106	1	no	—
341	D₈	—	106	1	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	2	1	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	1	no	—
346	M₁₆	—	106	1	no	—
347	M₁₆	—	106	1	no	—
348	M₁₆	—	106	1	no	—
349	M₁₆	—	106	1	no	—
350	M₁₆	—	212	4	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	53	2	no	—
354	C₂×C₈	—	53	2	no	—
355	C₂×C₈	—	212	4	no	—
356	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
357	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
358	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
359	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
360	C₂×C₈	#11719947	1	1	yes	characteristic
361	C₂×C₈	#11719947	1	1	yes	characteristic
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	106	1	no	—
364	C₄⋊C₄	—	106	1	no	—
365	C₄⋊C₄	—	106	2	no	—
366	C₄⋊C₄	—	212	4	no	—
367	C₄⋊C₄	—	212	4	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	106	1	no	—
370	C₂²⋊C₄	—	106	1	no	—
371	C₂²⋊C₄	—	106	2	no	—
372	C₂²⋊C₄	—	212	4	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	53	2	no	—
375	C₄²	—	53	2	no	—
376	C₄²	—	106	2	no	—
377	C₄²	—	212	4	no	—
378	C₂³	—	106	2	no	—
379	C₂³	#13133263	1	1	yes	characteristic
380	Q₈	—	2	4	no	—
381	Q₈	—	2	4	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	106	2	no	—
385	Q₈	—	106	2	no	—
386	D₄	—	106	2	no	—
387	D₄	—	106	2	no	—
388	D₄	—	212	2	no	—
389	D₄	—	212	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	106	2	no	—
395	C₂×C₄	—	106	2	no	—
396	C₂×C₄	—	106	2	no	—
397	C₂×C₄	—	212	2	no	—
398	C₂×C₄	—	212	2	no	—
399	C₂×C₄	—	212	2	no	—
400	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
401	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
402	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
403	C₂×C₄	#13133262	1	1	yes	characteristic
404	C₂×C₄	#13133262	1	1	yes	characteristic
405	C₂×C₄	#13133263	1	1	yes	characteristic
406	C₈	—	4	2	no	—
407	C₈	—	4	1	no	—
408	C₈	—	106	2	no	—
409	C₈	—	106	2	no	—
410	C₈	#13133177	1	1	yes	characteristic
411	C₈	#13133177	1	1	yes	characteristic
412	C₈	#13133177	1	1	yes	characteristic
413	C₈	#13133177	1	1	yes	characteristic
414	C₂²	—	4	1	no	—
415	C₂²	—	424	2	no	—
416	C₂²	—	212	2	no	—
417	C₂²	#16811095	1	1	yes	characteristic
418	C₂²	#16811191	1	1	yes	characteristic
419	C₂²	#16811226	1	1	yes	characteristic
420	C₄	—	4	4	no	—
421	C₄	—	8	1	no	—
422	C₄	—	424	2	no	—
423	C₄	—	212	2	no	—
424	C₄	—	212	2	no	—
425	C₄	—	212	2	no	—
426	C₄	C₂×#13133177	1	1	yes	characteristic
427	C₄	#16811095	1	1	yes	characteristic
428	C₄	#16811186	1	1	yes	characteristic
429	C₄	#16811226	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	424	2	no	—
434	C₂	#20277439	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20277439
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1979	C₂
socle	C₂×C₅₃	#2328
prime radical	C₂×#13133239	C₂²
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1979	D₅₃
hypocenter	C₅₃	#22285
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1979

Complements

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

N	H ≅ G/N	type
3. #20283583	C₂	semidirect
5. #20275250	C₂	semidirect
6. #20275234	C₂	semidirect
7. #20275207	C₂	semidirect
8. #20275191	C₂	semidirect
9. #20274840	C₂	semidirect
10. #20274470	C₂	semidirect
11. C₅₃×#1979	C₂	semidirect
17. #16811016	C₄	semidirect
18. #16811008	C₄	semidirect
19. #16811001	C₄	semidirect
216. #1979	D₅₃	semidirect
259. C₅₃	#22285	semidirect

Maximal subgroups

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

subgroup	index
#20285204	2
#20283631	2
#20283583	2
#20275613	2
#20275250	2
#20275234	2
#20275207	2
#20275191	2
#20274840	2
#20274470	2
C₅₃×#1979	2
#22285	53