Subgroups — #27367322

Order 13568.

678 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20286030	C₂	1	2	yes	maximal, complemented
2	#20285144	C₂	1	1	yes	maximal, characteristic
3	#20283644	C₂	1	1	yes	maximal, characteristic, complemented
4	#20274190	C₂	1	2	yes	maximal, complemented
5	#20274189	C₂	1	2	yes	maximal, complemented
6	#20274082	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274076	C₂	1	1	yes	maximal, characteristic, complemented
8	#20274075	C₂	1	1	yes	maximal, characteristic, complemented
9	#335×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273391	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1670	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133240	—	2	1	no	—
13	C₂×#13133240	—	2	1	no	—
14	#16811177	C₂²	1	1	yes	characteristic
15	#16811174	C₂²	1	2	yes	—
16	#16811008	—	2	1	no	—
17	#16811008	—	2	1	no	—
18	#16811000	C₂²	1	1	yes	characteristic
19	#16810997	C₂²	1	2	yes	—
20	#16810912	—	2	2	no	—
21	#16810905	C₂²	1	2	yes	—
22	#16810855	—	2	2	no	—
23	#16810853	—	2	2	no	—
24	#16810827	—	2	2	no	—
25	#16810824	C₂²	1	2	yes	—
26	#16810823	C₂²	1	2	yes	—
27	#16810754	C₂²	1	1	yes	characteristic
28	#16810752	—	2	1	no	—
29	#16810750	C₂²	1	1	yes	characteristic
30	C₈×Dic₁₀₆	—	2	1	no	—
31	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
32	#16810648	—	2	1	no	—
33	#16810645	C₂²	1	1	yes	characteristic
34	C₄⋊C₈×D₅₃	C₂²	1	2	yes	—
35	#16810577	—	2	1	no	—
36	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
37	#16810376	C₂²	1	1	yes	characteristic
38	#16810375	C₂²	1	2	yes	—
39	#16810369	C₂²	1	2	yes	—
40	#16810366	C₂²	1	2	yes	—
41	#16810366	C₂²	1	2	yes	—
42	C₅₃×#494	C₂²	1	1	yes	characteristic
43	C₅₃×#475	C₂²	1	2	yes	—
44	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#335	C₂²	1	1	yes	characteristic
46	C₅₃×#332	C₂²	1	2	yes	—
47	C₂×#11719949	—	2	2	no	—
48	#13133240	—	4	4	no	—
49	#13133240	—	4	4	no	—
50	C₂×#11719913	—	2	2	no	—
51	C₂×#11719924	—	2	2	no	—
52	C₂×#11719924	—	2	2	no	—
53	C₂×#11719924	—	2	2	no	—
54	C₂×D₄₂₄	—	2	1	no	—
55	C₂×D₄₂₄	—	2	1	no	—
56	C₂×#11719912	—	2	1	no	—
57	C₂×C₈×D₅₃	—	2	2	no	—
58	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
59	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
60	#13133216	D₄	1	1	yes	characteristic
61	#13133215	D₄	1	1	yes	characteristic
62	#13133214	C₂³	1	2	yes	—
63	#13133207	—	2	1	no	—
64	#13133206	—	2	2	no	—
65	#13133197	D₄	1	1	yes	characteristic
66	#13133195	—	2	1	no	—
67	#13133193	D₄	1	1	yes	characteristic
68	#13133192	—	2	2	no	—
69	#13133192	—	2	2	no	—
70	C₄×Dic₁₀₆	—	2	1	no	—
71	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
72	#13133179	—	2	2	no	—
73	#13133179	—	2	2	no	—
74	#13133174	—	2	1	no	—
75	C₄²×D₅₃	C₂³	1	1	yes	characteristic
76	#13133148	—	2	2	no	—
77	C₄⋊#88322	—	2	1	no	—
78	C₄⋊#88322	C₂³	1	1	yes	characteristic
79	C₄⋊#88322	C₂³	1	2	yes	—
80	#13133146	—	2	1	no	—
81	#13133146	—	2	1	no	—
82	#13133146	—	2	2	no	—
83	#13133146	—	2	1	no	—
84	#13133140	—	2	2	no	—
85	#13133139	—	2	2	no	—
86	#13133137	—	2	2	no	—
87	#13133128	—	2	1	no	—
88	#13133127	—	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	2	yes	—
100	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
101	#103×C₅₃	—	2	2	no	—
102	C₄×C₈×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	—	4	4	no	—
107	#11719949	—	4	4	no	—
108	C₂×D₂₁₂	—	2	2	no	—
109	C₂×D₂₁₂	—	2	2	no	—
110	C₂×D₂₁₂	—	2	2	no	—
111	C₂×D₂₁₂	—	4	2	no	—
112	C₂×C₄×D₅₃	—	4	2	no	—
113	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
116	C₂×Dic₁₀₆	—	2	1	no	—
117	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
118	Q₁₆×C₅₃	—	4	2	no	—
119	Q₁₆×C₅₃	—	4	2	no	—
120	C₂×C₈×C₅₃	—	2	1	no	—
121	C₂×C₈×C₅₃	—	2	2	no	—
122	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
124	C₄⋊C₄×C₅₃	—	2	1	no	—
125	C₄⋊C₄×C₅₃	—	2	2	no	—
126	C₄⋊C₄×C₅₃	—	2	2	no	—
127	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₅₃	—	2	1	no	—
129	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
130	#11719924	—	4	4	no	—
131	#11719924	—	4	4	no	—
132	#11719924	—	8	2	no	—
133	#11719921	—	2	1	no	—
134	#11719921	—	2	1	no	—
135	#11719921	—	4	2	no	—
136	#11719921	—	4	2	no	—
137	C₄⋊Dic₅₃	—	2	1	no	—
138	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
139	#11719919	—	2	1	no	—
140	#11719919	—	2	1	no	—
141	#11719919	—	2	1	no	—
142	#11719919	—	2	1	no	—
143	#11719919	—	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	D₄₂₄	—	4	2	no	—
153	D₄₂₄	—	4	2	no	—
154	#11719913	—	8	2	no	—
155	#11719912	—	4	2	no	—
156	C₈×D₅₃	—	2	2	no	—
157	C₈×D₅₃	—	8	2	no	—
158	C₈×D₅₃	SD₁₆	1	4	yes	complemented
159	C₂²×D₅₃	—	4	2	no	—
160	C₂²×D₅₃	#121	1	1	yes	characteristic
161	Q₈×C₅₃	—	2	1	no	—
162	Q₈×C₅₃	—	2	1	no	—
163	Q₈×C₅₃	—	4	2	no	—
164	Q₈×C₅₃	—	4	2	no	—
165	C₂×C₄×C₅₃	—	2	1	no	—
166	C₂×C₄×C₅₃	—	2	1	no	—
167	C₂×C₄×C₅₃	—	4	2	no	—
168	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
171	C₂×Dic₅₃	—	2	1	no	—
172	C₂×Dic₅₃	—	2	1	no	—
173	C₂×Dic₅₃	#121	1	1	yes	characteristic
174	C₂×Dic₅₃	#121	1	1	yes	characteristic
175	C₂×Dic₅₃	#121	1	1	yes	characteristic
176	D₂₁₂	—	4	2	no	—
177	D₂₁₂	—	4	2	no	—
178	D₂₁₂	—	4	2	no	—
179	D₂₁₂	—	4	2	no	—
180	D₂₁₂	—	8	2	no	—
181	D₂₁₂	—	8	4	no	—
182	C₄×D₅₃	—	2	1	no	—
183	C₄×D₅₃	—	2	1	no	—
184	C₄×D₅₃	—	4	1	no	—
185	C₄×D₅₃	—	8	4	no	—
186	C₄×D₅₃	C₂×SD₁₆	1	2	yes	—
187	C₄×D₅₃	AGL(1,ℤ/8)	1	2	yes	—
188	Dic₁₀₆	—	2	1	no	—
189	Dic₁₀₆	—	2	1	no	—
190	Dic₁₀₆	—	4	2	no	—
191	C₈×C₅₃	—	2	1	no	—
192	C₈×C₅₃	—	4	1	no	—
193	C₈×C₅₃	—	4	2	no	—
194	C₈×C₅₃	C₂×SD₁₆	1	2	yes	—
195	#88322	—	2	1	no	—
196	#88322	—	4	1	no	—
197	#88322	—	4	2	no	—
198	#88322	C₂×SD₁₆	1	2	yes	—
199	#19206	—	53	1	no	maximal, Sylow
200	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
201	C₂×D₅₃	—	2	1	no	—
202	C₂×D₅₃	—	2	1	no	—
203	C₂×D₅₃	—	8	2	no	—
204	C₂×D₅₃	—	8	2	no	—
205	C₂×D₅₃	—	8	2	no	—
206	C₂×D₅₃	#460	1	2	yes	—
207	C₄×C₅₃	—	2	1	no	—
208	C₄×C₅₃	—	4	1	no	—
209	C₄×C₅₃	—	4	1	no	—
210	C₄×C₅₃	—	8	2	no	—
211	C₄×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
212	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₄×C₅₃	#576	1	1	yes	characteristic
214	C₄×C₅₃	#578	1	1	yes	characteristic
215	Dic₅₃	—	2	1	no	—
216	Dic₅₃	—	2	1	no	—
217	Dic₅₃	—	4	1	no	—
218	Dic₅₃	—	4	1	no	—
219	Dic₅₃	#460	1	2	yes	—
220	#3246	—	53	2	no	—
221	#3147	—	53	1	no	—
222	#2960	—	53	1	no	—
223	#1686	—	53	2	no	—
224	#1686	—	53	2	no	—
225	#1670	—	53	1	no	—
226	#1670	D₅₃	1	1	yes	characteristic, complemented
227	#1668	—	53	1	no	—
228	#1668	—	53	1	no	—
229	C₂×#335	—	53	1	no	—
230	#1547	—	53	2	no	—
231	C₂×C₅₃	C₂×#460	1	1	yes	characteristic
232	C₂×C₅₃	#3061	1	1	yes	characteristic
233	C₂×C₅₃	#3067	1	1	yes	characteristic
234	D₅₃	—	2	2	no	—
235	D₅₃	—	16	2	no	—
236	C₂×#135	—	106	1	no	—
237	C₂×#135	—	106	1	no	—
238	#533	—	53	1	no	—
239	#532	—	53	2	no	—
240	#495	—	106	1	no	—
241	#495	—	106	1	no	—
242	#494	C₂×D₅₃	1	1	yes	characteristic
243	#493	—	53	1	no	—
244	#492	—	53	2	no	—
245	#476	—	106	2	no	—
246	#475	—	53	2	no	—
247	#475	C₂×D₅₃	1	2	yes	—
248	#465	—	106	2	no	—
249	#465	—	106	2	no	—
250	#461	—	106	2	no	—
251	#460	—	53	2	no	—
252	#460	—	53	2	no	—
253	#446	—	53	1	no	—
254	#446	—	53	1	no	—
255	#446	—	106	1	no	—
256	C₈×Q₈	—	53	1	no	—
257	C₈×Q₈	—	106	1	no	—
258	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic
259	#424	—	106	1	no	—
260	#423	—	53	1	no	—
261	C₂×C₄⋊C₈	—	53	2	no	—
262	#405	—	106	1	no	—
263	C₂×C₄×C₈	—	53	1	no	—
264	#335	—	53	2	no	—
265	#335	—	53	1	no	—
266	#335	C₂×D₅₃	1	1	yes	characteristic
267	#332	—	53	2	no	—
268	#332	C₂×D₅₃	1	2	yes	—
269	#331	—	53	2	no	—
270	#331	—	53	2	no	—
271	C₅₃	#19206	1	1	yes	characteristic, complemented, Sylow
272	C₂×#41	—	106	2	no	—
273	#135	—	212	4	no	—
274	#135	—	212	4	no	—
275	C₂×Q₁₆	—	2	1	no	—
276	C₂×Q₁₆	—	2	1	no	—
277	C₂×SD₁₆	—	106	2	no	—
278	C₂×SD₁₆	—	106	2	no	—
279	C₂×SD₁₆	—	106	2	no	—
280	C₂×SD₁₆	—	106	2	no	—
281	C₂×D₈	—	106	1	no	—
282	C₂×D₈	—	106	1	no	—
283	C₂×M₁₆	—	106	1	no	—
284	C₂²×C₈	—	53	1	no	—
285	C₂²×C₈	—	53	1	no	—
286	C₂²×C₈	—	106	2	no	—
287	C₄⋊Q₈	—	53	1	no	—
288	C₄⋊Q₈	—	53	1	no	—
289	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
290	#127	—	53	2	no	—
291	#125	—	106	1	no	—
292	#124	—	106	2	no	—
293	C₂²⋊Q₈	—	53	1	no	—
294	C₂²⋊Q₈	—	53	1	no	—
295	C₂²⋊Q₈	—	106	1	no	—
296	#121	—	106	2	no	—
297	#121	—	106	2	no	—
298	C₄×Q₈	—	53	1	no	—
299	C₄×Q₈	—	106	1	no	—
300	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
301	C₄×D₄	—	106	2	no	—
302	C₄×D₄	—	106	2	no	—
303	#117	—	106	1	no	—
304	C₂×C₄²	—	53	1	no	—
305	#106	—	2	2	no	—
306	#106	—	106	2	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	53	1	no	—
309	C₄⋊C₈	—	53	2	no	—
310	C₄⋊C₈	—	106	1	no	—
311	C₄⋊C₈	—	106	2	no	—
312	C₄⋊C₈	—	106	1	no	—
313	C₄⋊C₈	—	106	1	no	—
314	C₄⋊C₈	—	106	1	no	—
315	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
316	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
317	#103	—	2	2	no	—
318	#103	—	106	2	no	—
319	#102	—	106	2	no	—
320	#102	—	106	2	no	—
321	#97	—	106	1	no	—
322	#97	—	106	1	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	—	53	1	no	—
325	C₄×C₈	—	53	1	no	—
326	C₄×C₈	—	53	1	no	—
327	C₄×C₈	—	106	1	no	—
328	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
329	#41	—	212	4	no	—
330	#41	—	212	4	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	53	1	no	—
333	C₂×Q₈	—	106	1	no	—
334	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
335	C₂×D₄	—	106	2	no	—
336	C₂×D₄	—	106	2	no	—
337	C₂×D₄	—	106	2	no	—
338	C₂×D₄	—	212	2	no	—
339	C₂²×C₄	—	53	1	no	—
340	C₂²×C₄	—	53	1	no	—
341	C₂²×C₄	—	53	1	no	—
342	C₂²×C₄	—	212	2	no	—
343	Q₁₆	—	4	2	no	—
344	Q₁₆	—	4	2	no	—
345	SD₁₆	—	424	2	no	—
346	SD₁₆	—	424	2	no	—
347	SD₁₆	—	212	4	no	—
348	SD₁₆	—	212	4	no	—
349	D₈	—	212	2	no	—
350	D₈	—	212	2	no	—
351	M₁₆	—	212	2	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	53	1	no	—
355	C₂×C₈	—	53	4	no	—
356	C₂×C₈	—	53	1	no	—
357	C₂×C₈	—	106	2	no	—
358	C₂×C₈	—	106	1	no	—
359	C₂×C₈	—	106	2	no	—
360	C₂×C₈	—	424	2	no	—
361	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
362	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	53	1	no	—
367	C₄⋊C₄	—	106	1	no	—
368	C₄⋊C₄	—	106	1	no	—
369	C₄⋊C₄	—	106	1	no	—
370	C₄⋊C₄	—	106	1	no	—
371	C₄⋊C₄	—	106	1	no	—
372	C₄⋊C₄	—	106	1	no	—
373	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
374	C₂²⋊C₄	—	106	1	no	—
375	C₂²⋊C₄	—	106	1	no	—
376	C₂²⋊C₄	—	212	2	no	—
377	C₂²⋊C₄	—	212	2	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	53	1	no	—
380	C₄²	—	53	1	no	—
381	C₄²	—	53	1	no	—
382	C₄²	—	106	1	no	—
383	C₄²	C₂³×D₅₃	1	1	yes	characteristic
384	C₂³	—	53	1	no	—
385	C₂³	—	212	2	no	—
386	Q₈	—	2	1	no	—
387	Q₈	—	2	1	no	—
388	Q₈	—	4	2	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	106	1	no	—
391	Q₈	—	106	1	no	—
392	Q₈	—	212	2	no	—
393	D₄	—	424	2	no	—
394	D₄	—	424	4	no	—
395	D₄	—	212	2	no	—
396	D₄	—	212	2	no	—
397	D₄	—	212	2	no	—
398	D₄	—	212	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	53	1	no	—
403	C₂×C₄	—	53	2	no	—
404	C₂×C₄	—	53	2	no	—
405	C₂×C₄	—	53	1	no	—
406	C₂×C₄	—	53	1	no	—
407	C₂×C₄	—	106	1	no	—
408	C₂×C₄	—	106	1	no	—
409	C₂×C₄	—	106	1	no	—
410	C₂×C₄	—	106	1	no	—
411	C₂×C₄	—	424	4	no	—
412	C₂×C₄	—	212	1	no	—
413	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
414	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
415	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
416	C₈	—	2	1	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	2	no	—
419	C₈	—	53	2	no	—
420	C₈	—	106	1	no	—
421	C₈	—	212	1	no	—
422	C₈	—	212	2	no	—
423	C₈	SD₁₆×D₅₃	1	2	yes	—
424	C₂²	—	53	2	no	—
425	C₂²	—	106	1	no	—
426	C₂²	—	106	1	no	—
427	C₂²	—	424	2	no	—
428	C₂²	—	424	2	no	—
429	C₂²	—	424	2	no	—
430	C₂²	#121×D₅₃	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	8	2	no	—
435	C₄	—	53	2	no	—
436	C₄	—	106	1	no	—
437	C₄	—	106	1	no	—
438	C₄	—	212	1	no	—
439	C₄	—	212	1	no	—
440	C₄	C₂×SD₁₆×D₅₃	1	1	yes	characteristic
441	C₄	AGL(1,ℤ/8)×D₅₃	1	1	yes	characteristic
442	C₄	#16811425	1	1	yes	characteristic
443	C₄	#16811436	1	1	yes	characteristic
444	C₂	—	848	2	no	—
445	C₂	—	106	2	no	—
446	C₂	#460×D₅₃	1	1	yes	characteristic
447	C₂	#20284386	1	1	yes	characteristic
448	C₂	#20284437	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₅₃
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1670	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	#20285144	C₂
hypercenter	#1670	D₅₃
hypocenter	C₅₃	#19206
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1670

Complements

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

N	H ≅ G/N	type
1. #20286030	C₂	semidirect
3. #20283644	C₂	semidirect
4. #20274190	C₂	semidirect
5. #20274189	C₂	semidirect
6. #20274082	C₂	semidirect
7. #20274076	C₂	semidirect
8. #20274075	C₂	semidirect
9. #335×D₅₃	C₂	semidirect
10. #20273391	C₂	semidirect
11. C₅₃×#1670	C₂	semidirect
158. C₈×D₅₃	SD₁₆	semidirect
226. #1670	D₅₃	semidirect
271. C₅₃	#19206	semidirect

Maximal subgroups

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

subgroup	index
#20286030	2
#20285144	2
#20283644	2
#20274190	2
#20274189	2
#20274082	2
#20274076	2
#20274075	2
#335×D₅₃	2
#20273391	2
C₅₃×#1670	2
#19206	53