Subgroups — #27384359

Order 13568.

684 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283132	C₂	1	1	yes	maximal, characteristic
2	#20274865	C₂	1	1	yes	maximal, characteristic, complemented
3	#20274864	C₂	1	1	yes	maximal, characteristic, complemented
4	#20274863	C₂	1	2	yes	maximal, complemented
5	#20274862	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274861	C₂	1	2	yes	maximal, complemented
7	#344×D₅₃	C₂	1	2	yes	maximal
8	#20274423	C₂	1	2	yes	maximal
9	#338×D₅₃	C₂	1	1	yes	maximal, characteristic
10	H(3,ℤ/4)×D₅₃	C₂	1	1	yes	maximal, characteristic
11	C₅₃×#1841	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₅₃	C₂²	1	2	yes	—
13	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
15	C₂×#13133174	C₂²	1	1	yes	characteristic
16	#117×D₅₃	C₂²	1	2	yes	—
17	#16810580	C₄	1	2	yes	complemented
18	#16810580	C₄	1	2	yes	complemented
19	#16810577	C₄	1	2	yes	complemented
20	#16810577	C₄	1	2	yes	complemented
21	C₄×#11719917	C₂²	1	1	yes	characteristic
22	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
23	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
24	#16810395	C₂²	1	2	yes	—
25	#16810394	C₂²	1	2	yes	—
26	#16810393	C₂²	1	2	yes	—
27	#16810384	C₂²	1	2	yes	—
28	#16810383	C₂²	1	2	yes	—
29	#16810382	C₂²	1	2	yes	—
30	#16810381	C₂²	1	2	yes	—
31	#16810381	C₂²	1	1	yes	characteristic
32	#16810380	C₂²	1	1	yes	characteristic
33	#16810379	C₂²	1	2	yes	—
34	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
35	C₅₃×#344	C₂²	1	2	yes	—
36	C₅₃×#339	C₂²	1	2	yes	—
37	C₅₃×#338	C₂²	1	1	yes	characteristic
38	C₅₃×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
39	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
40	C₂×#11719917	C₂³	1	2	yes	—
41	C₂×#11719917	C₂³	1	1	yes	characteristic
42	C₂×#11719917	C₂³	1	1	yes	characteristic
43	C₂×#11719912	—	2	2	no	—
44	C₂×#11719912	C₂×C₄	1	2	yes	—
45	C₂×#11719912	C₂×C₄	1	2	yes	—
46	M₁₆×D₅₃	—	2	2	no	—
47	M₁₆×D₅₃	—	2	2	no	—
48	M₁₆×D₅₃	—	2	2	no	—
49	M₁₆×D₅₃	—	2	2	no	—
50	M₁₆×D₅₃	—	2	2	no	—
51	M₁₆×D₅₃	—	2	2	no	—
52	M₁₆×D₅₃	—	2	2	no	—
53	M₁₆×D₅₃	—	2	2	no	—
54	C₂×C₈×D₅₃	—	2	2	no	—
55	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
56	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
57	#13133176	C₂³	1	2	yes	—
58	#13133175	—	2	2	no	—
59	#13133174	—	2	1	no	—
60	#13133174	—	2	1	no	—
61	#13133174	—	2	2	no	—
62	#13133174	C₂×C₄	1	1	yes	characteristic
63	#13133174	C₂×C₄	1	1	yes	characteristic
64	#13133174	C₂×C₄	1	1	yes	characteristic
65	#13133174	C₂×C₄	1	1	yes	characteristic
66	#13133173	—	2	2	no	—
67	C₂×#11719919	—	2	1	no	—
68	C₄⋊C₄×D₅₃	—	2	2	no	—
69	C₂×#11719921	—	2	1	no	—
70	C₂²⋊C₄×D₅₃	—	2	2	no	—
71	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
72	C₄²×D₅₃	—	2	2	no	—
73	#13133128	C₂×C₄	1	2	yes	complemented
74	#13133127	C₂×C₄	1	2	yes	complemented
75	#13133127	C₂×C₄	1	2	yes	complemented
76	C₄×#88322	C₂×C₄	1	2	yes	complemented
77	C₈×Dic₅₃	C₂×C₄	1	2	yes	complemented
78	C₈×Dic₅₃	C₂×C₄	1	2	yes	complemented
79	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
80	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
81	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
82	#117×C₅₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
84	#97×C₅₃	C₂×C₄	1	2	yes	complemented
85	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	complemented
86	C₂³×D₅₃	#41	1	1	yes	characteristic
87	C₂²×C₄×C₅₃	—	2	1	no	—
88	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
89	C₂²×Dic₅₃	—	2	1	no	—
90	C₂²×Dic₅₃	#41	1	1	yes	characteristic
91	C₂×C₄×D₅₃	—	4	2	no	—
92	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₄×D₅₃	#41	1	2	yes	—
95	C₂×C₄×D₅₃	#41	1	2	yes	—
96	C₂×C₄×D₅₃	#41	1	2	yes	—
97	C₂×C₄×D₅₃	#41	1	2	yes	—
98	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
99	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
100	M₁₆×C₅₃	—	2	2	no	—
101	M₁₆×C₅₃	—	2	2	no	—
102	M₁₆×C₅₃	—	2	2	no	—
103	M₁₆×C₅₃	—	2	2	no	—
104	C₂×C₈×C₅₃	—	2	2	no	—
105	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
107	C₄⋊C₄×C₅₃	—	2	2	no	—
108	C₂²⋊C₄×C₅₃	—	2	2	no	—
109	C₄²×C₅₃	—	2	1	no	—
110	C₄²×C₅₃	—	2	2	no	—
111	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²⋊Dic₅₃	—	2	2	no	—
114	#11719921	—	2	1	no	—
115	#11719921	—	2	1	no	—
116	#11719921	—	2	1	no	—
117	#11719921	—	2	1	no	—
118	#11719921	—	4	2	no	—
119	C₄⋊Dic₅₃	—	2	2	no	—
120	#11719919	—	2	1	no	—
121	#11719919	—	2	1	no	—
122	#11719919	—	2	1	no	—
123	#11719919	—	2	1	no	—
124	#11719919	—	4	2	no	—
125	C₄×Dic₅₃	—	2	1	no	—
126	C₄×Dic₅₃	—	2	2	no	—
127	C₄×Dic₅₃	—	4	2	no	—
128	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
130	#11719917	—	2	2	no	—
131	#11719917	—	2	2	no	—
132	#11719917	—	2	2	no	—
133	#11719917	—	2	2	no	—
134	C₂×#88322	—	2	2	no	—
135	C₂×#88322	C₂²×C₄	1	2	yes	—
136	C₂×#88322	C₂²×C₄	1	2	yes	—
137	#11719912	—	2	4	no	—
138	#11719912	—	2	2	no	—
139	#11719912	—	2	2	no	—
140	#11719912	—	4	2	no	—
141	#11719912	—	4	2	no	—
142	C₈×D₅₃	—	2	2	no	—
143	C₈×D₅₃	—	2	2	no	—
144	C₈×D₅₃	—	2	4	no	—
145	C₈×D₅₃	—	4	2	no	—
146	C₈×D₅₃	—	4	2	no	—
147	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
148	C₂²×D₅₃	—	8	1	no	—
149	C₂²×D₅₃	#117	1	1	yes	characteristic
150	C₂²×D₅₃	#117	1	1	yes	characteristic
151	C₂²×D₅₃	#126	1	2	yes	—
152	C₂²×D₅₃	#126	1	2	yes	—
153	C₂×C₄×C₅₃	—	2	1	no	—
154	C₂×C₄×C₅₃	—	2	1	no	—
155	C₂×C₄×C₅₃	—	4	2	no	—
156	C₂×C₄×C₅₃	—	8	1	no	—
157	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
159	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
160	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
161	C₂×Dic₅₃	—	2	1	no	—
162	C₂×Dic₅₃	—	2	1	no	—
163	C₂×Dic₅₃	—	4	2	no	—
164	C₂×Dic₅₃	—	8	1	no	—
165	C₂×Dic₅₃	#117	1	1	yes	characteristic
166	C₂×Dic₅₃	#117	1	1	yes	characteristic
167	C₂×Dic₅₃	#126	1	2	yes	—
168	C₂×Dic₅₃	#126	1	2	yes	—
169	C₄×D₅₃	—	8	4	no	—
170	C₄×D₅₃	#117	1	1	yes	characteristic
171	C₄×D₅₃	#117	1	1	yes	characteristic
172	C₄×D₅₃	#117	1	2	yes	—
173	C₄×D₅₃	#117	1	2	yes	—
174	C₄×D₅₃	#117	1	1	yes	characteristic
175	C₄×D₅₃	#117	1	1	yes	characteristic
176	C₄×D₅₃	#126	1	2	yes	—
177	C₄×D₅₃	#126	1	2	yes	—
178	C₄×D₅₃	#126	1	2	yes	—
179	C₄×D₅₃	#126	1	2	yes	—
180	C₈×C₅₃	—	2	2	no	—
181	C₈×C₅₃	—	2	2	no	—
182	C₈×C₅₃	—	4	2	no	—
183	#88322	—	2	2	no	—
184	#88322	—	2	2	no	—
185	#88322	—	4	2	no	—
186	#20776	—	53	1	no	maximal, Sylow
187	C₂²×C₅₃	—	4	1	no	—
188	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
189	C₂²×C₅₃	C₂×#126	1	2	yes	—
190	C₂×D₅₃	—	4	2	no	—
191	C₂×D₅₃	—	4	1	no	—
192	C₂×D₅₃	—	4	1	no	—
193	C₂×D₅₃	—	4	2	no	—
194	C₂×D₅₃	#383	1	1	yes	characteristic
195	C₂×D₅₃	#383	1	2	yes	—
196	C₂×D₅₃	#383	1	1	yes	characteristic
197	C₄×C₅₃	—	4	1	no	—
198	C₄×C₅₃	—	4	1	no	—
199	C₄×C₅₃	—	8	2	no	—
200	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
201	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
202	C₄×C₅₃	C₂×#126	1	2	yes	—
203	Dic₅₃	—	4	1	no	—
204	Dic₅₃	—	4	1	no	—
205	Dic₅₃	—	8	2	no	—
206	Dic₅₃	#383	1	1	yes	characteristic
207	Dic₅₃	#383	1	2	yes	—
208	Dic₅₃	#383	1	1	yes	characteristic
209	#2873	—	53	1	no	—
210	#1841	—	53	1	no	—
211	#1841	—	53	2	no	—
212	#1841	—	53	2	no	—
213	#1841	—	53	1	no	—
214	#1841	—	53	1	no	—
215	#1841	D₅₃	1	1	yes	characteristic, complemented
216	C₂×#344	—	53	2	no	—
217	#1733	—	53	2	no	—
218	C₂×#338	—	53	1	no	—
219	C₂×H(3,ℤ/4)	—	53	1	no	—
220	C₂×C₅₃	—	2	1	no	—
221	C₂×C₅₃	—	2	2	no	—
222	C₂×C₅₃	C₂×#383	1	1	yes	characteristic
223	D₅₃	—	2	1	no	—
224	D₅₃	—	2	2	no	—
225	D₅₃	—	2	1	no	—
226	C₂²×M₁₆	—	53	1	no	—
227	C₂²×M₁₆	—	53	1	no	—
228	C₂²×M₁₆	—	53	2	no	—
229	C₂×#117	—	53	1	no	—
230	C₂×#117	—	53	2	no	—
231	#405	—	53	2	no	—
232	#405	—	53	2	no	—
233	#405	—	53	2	no	—
234	#405	—	53	2	no	—
235	C₄×M₁₆	—	53	1	no	—
236	C₄×M₁₆	—	53	1	no	—
237	C₄×M₁₆	—	53	1	no	—
238	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic
239	#344	—	53	2	no	—
240	#344	—	53	2	no	—
241	#344	—	53	2	no	—
242	#344	C₂×D₅₃	1	2	yes	—
243	#339	—	53	2	no	—
244	#339	—	53	2	no	—
245	#339	—	53	2	no	—
246	#339	C₂×D₅₃	1	2	yes	—
247	#338	—	53	2	no	—
248	#338	—	53	1	no	—
249	#338	C₂×D₅₃	1	1	yes	characteristic
250	H(3,ℤ/4)	—	53	1	no	—
251	H(3,ℤ/4)	—	53	2	no	—
252	H(3,ℤ/4)	C₂×D₅₃	1	1	yes	characteristic
253	C₅₃	#20776	1	1	yes	characteristic, complemented, Sylow
254	C₂³×C₄	—	53	1	no	—
255	C₂×M₁₆	—	53	1	no	—
256	C₂×M₁₆	—	53	1	no	—
257	C₂×M₁₆	—	53	2	no	—
258	C₂×M₁₆	—	53	2	no	—
259	C₂×M₁₆	—	53	2	no	—
260	C₂×M₁₆	—	106	2	no	—
261	C₂×M₁₆	—	106	2	no	—
262	C₂×M₁₆	—	106	2	no	—
263	C₂×M₁₆	—	106	2	no	—
264	C₂×M₁₆	—	106	2	no	—
265	C₂×M₁₆	—	106	2	no	—
266	C₂×M₁₆	—	106	2	no	—
267	C₂×M₁₆	—	106	2	no	—
268	C₂×M₁₆	—	106	2	no	—
269	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
270	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
271	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
272	C₂²×C₈	—	53	2	no	—
273	C₂²×C₈	—	53	2	no	—
274	C₂²×C₈	—	106	2	no	—
275	#117	—	53	1	no	—
276	#117	—	53	1	no	—
277	#117	—	53	1	no	—
278	#117	—	53	1	no	—
279	#117	—	53	2	no	—
280	#117	—	106	1	no	—
281	#117	—	106	1	no	—
282	#117	—	106	2	no	—
283	#117	—	106	2	no	—
284	#117	—	106	2	no	—
285	#117	C₂²×D₅₃	1	2	yes	—
286	C₂×C₄⋊C₄	—	106	2	no	—
287	C₂×C₄⋊C₄	—	106	1	no	—
288	C₂×C₂²⋊C₄	—	106	2	no	—
289	C₂×C₂²⋊C₄	—	106	1	no	—
290	C₂×C₄²	—	53	1	no	—
291	C₂×C₄²	—	106	2	no	—
292	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
293	#97	—	53	2	no	—
294	#97	—	53	2	no	—
295	#97	—	53	2	no	—
296	#97	C₄×D₅₃	1	2	yes	complemented
297	C₄×C₈	—	53	2	no	—
298	C₄×C₈	—	53	2	no	—
299	C₄×C₈	—	53	2	no	—
300	C₄×C₈	C₄×D₅₃	1	2	yes	complemented
301	C₂⁴	—	53	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	53	1	no	—
304	C₂²×C₄	—	53	1	no	—
305	C₂²×C₄	—	53	1	no	—
306	C₂²×C₄	—	53	2	no	—
307	C₂²×C₄	—	53	2	no	—
308	C₂²×C₄	—	53	2	no	—
309	C₂²×C₄	—	53	1	no	—
310	C₂²×C₄	—	53	1	no	—
311	C₂²×C₄	—	53	2	no	—
312	C₂²×C₄	—	106	1	no	—
313	C₂²×C₄	—	212	2	no	—
314	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
315	M₁₆	—	2	2	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	106	4	no	—
320	M₁₆	—	106	2	no	—
321	M₁₆	—	106	2	no	—
322	M₁₆	—	106	2	no	—
323	M₁₆	—	106	2	no	—
324	M₁₆	—	106	2	no	—
325	M₁₆	—	106	2	no	—
326	M₁₆	—	212	2	no	—
327	M₁₆	—	212	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	53	2	no	—
330	C₂×C₈	—	53	2	no	—
331	C₂×C₈	—	106	2	no	—
332	C₂×C₈	—	106	2	no	—
333	C₂×C₈	—	106	4	no	—
334	C₂×C₈	—	106	2	no	—
335	C₂×C₈	—	212	2	no	—
336	C₂×C₈	—	212	2	no	—
337	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
338	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	106	1	no	—
341	C₄⋊C₄	—	106	1	no	—
342	C₄⋊C₄	—	106	1	no	—
343	C₄⋊C₄	—	106	1	no	—
344	C₄⋊C₄	—	106	2	no	—
345	C₄⋊C₄	—	212	2	no	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₂²⋊C₄	—	106	1	no	—
348	C₂²⋊C₄	—	106	1	no	—
349	C₂²⋊C₄	—	106	1	no	—
350	C₂²⋊C₄	—	106	1	no	—
351	C₂²⋊C₄	—	106	2	no	—
352	C₂²⋊C₄	—	212	2	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	53	1	no	—
356	C₄²	—	53	1	no	—
357	C₄²	—	106	1	no	—
358	C₄²	—	106	2	no	—
359	C₄²	—	212	2	no	—
360	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
361	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
362	C₂³	—	53	1	no	—
363	C₂³	—	53	1	no	—
364	C₂³	—	53	2	no	—
365	C₂³	—	53	2	no	—
366	C₂³	—	424	1	no	—
367	C₂³	#41×D₅₃	1	1	yes	characteristic
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	—	53	1	no	—
373	C₂×C₄	—	53	1	no	—
374	C₂×C₄	—	53	2	no	—
375	C₂×C₄	—	53	2	no	—
376	C₂×C₄	—	53	1	no	—
377	C₂×C₄	—	53	1	no	—
378	C₂×C₄	—	53	2	no	—
379	C₂×C₄	—	53	2	no	—
380	C₂×C₄	—	53	1	no	—
381	C₂×C₄	—	53	1	no	—
382	C₂×C₄	—	53	2	no	—
383	C₂×C₄	—	53	2	no	—
384	C₂×C₄	—	53	2	no	—
385	C₂×C₄	—	53	2	no	—
386	C₂×C₄	—	106	1	no	—
387	C₂×C₄	—	106	1	no	—
388	C₂×C₄	—	424	4	no	—
389	C₂×C₄	—	424	1	no	—
390	C₂×C₄	—	212	2	no	—
391	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
392	C₂×C₄	#41×D₅₃	1	2	yes	—
393	C₂×C₄	#41×D₅₃	1	2	yes	—
394	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	106	2	no	—
399	C₈	—	106	2	no	—
400	C₈	—	212	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	53	1	no	—
403	C₂²	—	53	1	no	—
404	C₂²	—	53	2	no	—
405	C₂²	—	212	2	no	—
406	C₂²	—	212	1	no	—
407	C₂²	—	212	1	no	—
408	C₂²	—	212	2	no	—
409	C₂²	#117×D₅₃	1	1	yes	characteristic
410	C₂²	#126×D₅₃	1	2	yes	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	8	2	no	—
414	C₄	—	53	1	no	—
415	C₄	—	53	2	no	—
416	C₄	—	53	1	no	—
417	C₄	—	424	2	no	—
418	C₄	—	212	1	no	—
419	C₄	—	212	1	no	—
420	C₄	#117×D₅₃	1	1	yes	characteristic
421	C₄	#117×D₅₃	1	1	yes	characteristic
422	C₄	#126×D₅₃	1	2	yes	—
423	C₂	—	2	1	no	—
424	C₂	—	2	2	no	—
425	C₂	—	106	1	no	—
426	C₂	—	106	2	no	—
427	C₂	—	106	1	no	—
428	C₂	#383×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#117×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1841	C₂
socle	C₂×C₅₃	C₂×#383
prime radical	C₂³×D₅₃	#41
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1841	D₅₃
hypocenter	C₅₃	#20776
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #1841

Complements

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

N	H ≅ G/N	type
2. #20274865	C₂	semidirect
3. #20274864	C₂	semidirect
4. #20274863	C₂	semidirect
5. #20274862	C₂	semidirect
6. #20274861	C₂	semidirect
11. C₅₃×#1841	C₂	semidirect
17. #16810580	C₄	semidirect
18. #16810580	C₄	semidirect
19. #16810577	C₄	semidirect
20. #16810577	C₄	semidirect
73. #13133128	C₂×C₄	semidirect
74. #13133127	C₂×C₄	semidirect
75. #13133127	C₂×C₄	semidirect
76. C₄×#88322	C₂×C₄	semidirect
77. C₈×Dic₅₃	C₂×C₄	semidirect
78. C₈×Dic₅₃	C₂×C₄	semidirect
84. #97×C₅₃	C₂×C₄	semidirect
85. C₄×C₈×C₅₃	C₂×C₄	semidirect
215. #1841	D₅₃	semidirect
253. C₅₃	#20776	semidirect
296. #97	C₄×D₅₃	semidirect
300. C₄×C₈	C₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20283132	2
#20274865	2
#20274864	2
#20274863	2
#20274862	2
#20274861	2
#344×D₅₃	2
#20274423	2
#338×D₅₃	2
H(3,ℤ/4)×D₅₃	2
C₅₃×#1841	2
#20776	53