Subgroups — #27537311

Order 13568.

682 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811041	C₂	1	1	yes	maximal, characteristic, complemented
2	#20283425	C₂	1	1	yes	maximal, characteristic
3	#20276545	C₂	1	2	yes	maximal, complemented
4	#20276540	C₂	1	2	yes	maximal, complemented
5	#20276538	C₂	1	2	yes	maximal, complemented
6	C₁₆×C₂²⋊D₅₃	C₂	1	2	yes	maximal, complemented
7	C₂×#16810441	C₂	1	1	yes	maximal, characteristic, complemented
8	#20276329	C₂	1	1	yes	maximal, characteristic, complemented
9	#20276328	C₂	1	1	yes	maximal, characteristic, complemented
10	M₃₂×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133223	C₂²	1	1	yes	characteristic
13	#16811169	C₄	1	1	yes	characteristic
14	#16811041	—	2	4	no	—
15	C₂×#13133157	C₂²	1	1	yes	characteristic
16	C₂×#13133156	C₂²	1	2	yes	—
17	C₂²×#11719908	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×D₅₃	C₂²	1	2	yes	—
19	#16810699	C₄	1	2	yes	—
20	#16810699	C₄	1	2	yes	—
21	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	—
22	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	—
23	#16810646	C₄	1	1	yes	characteristic
24	#16810591	C₄	1	1	yes	characteristic
25	#16810590	C₄	1	1	yes	characteristic
26	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
27	#16810441	C₂²	1	1	yes	characteristic
28	#16810441	C₂²	1	1	yes	characteristic
29	#16810441	C₂²	1	1	yes	characteristic
30	#16810441	C₂²	1	1	yes	characteristic
31	C₂²⋊#11719908	C₂²	1	2	yes	—
32	C₂²⋊#11719908	C₂²	1	2	yes	—
33	#16810402	C₂²	1	2	yes	—
34	#16810402	C₂²	1	2	yes	—
35	#16810398	C₂²	1	2	yes	—
36	C₁₆×Dic₅₃	C₂²	1	2	yes	—
37	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
38	C₅₃×#504	—	2	4	no	—
39	C₂×M₃₂×C₅₃	C₂²	1	2	yes	—
40	C₂×M₃₂×C₅₃	C₂²	1	1	yes	characteristic
41	C₂²×C₁₆×C₅₃	C₂²	1	2	yes	—
42	C₂²×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
44	#13133223	—	2	2	no	—
45	#13133223	—	2	2	no	—
46	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
47	C₂×#11719912	C₂×C₄	1	2	yes	—
48	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₅₃	C₂³	1	2	yes	—
50	#13133215	C₈	1	1	yes	characteristic
51	#13133213	C₈	1	1	yes	characteristic
52	#13133206	C₈	1	1	yes	characteristic
53	#13133204	C₈	1	1	yes	characteristic
54	#13133189	C₈	1	2	yes	—
55	#13133189	C₈	1	2	yes	—
56	C₄×C₂²⋊D₅₃	C₂×C₄	1	2	yes	—
57	C₄×C₂²⋊D₅₃	C₂×C₄	1	2	yes	—
58	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
59	#13133157	—	2	2	no	—
60	#13133156	—	2	4	no	—
61	C₂×#11719908	—	2	2	no	—
62	C₂×#11719908	C₂³	1	1	yes	characteristic
63	C₂×#11719908	C₂³	1	1	yes	characteristic
64	C₂×#11719908	C₂³	1	2	yes	—
65	C₁₆×D₅₃	—	2	4	no	—
66	#13133146	C₂×C₄	1	2	yes	—
67	#13133146	C₂×C₄	1	2	yes	—
68	C₂²⋊#88322	C₂×C₄	1	2	yes	—
69	C₂²⋊#88322	C₂×C₄	1	2	yes	—
70	#13133129	C₂×C₄	1	2	yes	—
71	#13133129	C₂×C₄	1	2	yes	—
72	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
73	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
74	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
75	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
76	C₂×#41×C₅₃	C₂×C₄	1	1	yes	characteristic
77	#131×C₅₃	—	2	2	no	—
78	#131×C₅₃	—	2	2	no	—
79	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
80	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
81	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
82	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
83	M₃₂×C₅₃	—	2	4	no	—
84	M₃₂×C₅₃	D₄	1	4	yes	complemented
85	C₂×C₁₆×C₅₃	—	2	2	no	—
86	C₂×C₁₆×C₅₃	—	2	4	no	—
87	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
88	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
89	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
90	#41×C₅₃	—	2	2	no	—
91	#41×C₅₃	—	2	2	no	—
92	C₂×Q₈×C₅₃	C₂×C₈	1	1	yes	characteristic
93	C₂×D₄×C₅₃	C₂×C₈	1	2	yes	—
94	C₂×D₄×C₅₃	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊D₅₃	C₂×C₈	1	2	yes	—
98	C₂×C₂²⋊D₅₃	C₂×C₈	1	2	yes	—
99	C₂×C₂²⋊D₅₃	C₂×C₈	1	2	yes	—
100	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
101	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
102	#11719945	—	2	2	no	—
103	#11719945	—	2	2	no	—
104	C₂×D₂₁₂	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
106	C₂×Dic₁₀₆	C₂×C₈	1	1	yes	characteristic
107	M₁₆×C₅₃	—	2	2	no	—
108	M₁₆×C₅₃	—	2	4	no	—
109	C₂×C₈×C₅₃	—	2	2	no	—
110	C₂×C₈×C₅₃	—	2	2	no	—
111	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₅₃	#41	1	2	yes	—
115	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
116	C₂²⋊Dic₅₃	C₂×C₈	1	2	yes	—
117	C₂²⋊Dic₅₃	C₂×C₈	1	2	yes	—
118	#11719921	C₂×C₈	1	2	yes	—
119	#11719921	C₂×C₈	1	2	yes	—
120	#11719919	C₂×C₈	1	2	yes	—
121	#11719919	C₂×C₈	1	2	yes	—
122	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
123	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
124	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
126	#11719917	—	2	2	no	—
127	C₂×#88322	—	2	2	no	—
128	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
129	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
130	C₂×#88322	C₂²×C₄	1	2	yes	—
131	#11719912	—	2	4	no	—
132	C₈×D₅₃	—	2	2	no	—
133	C₈×D₅₃	—	2	2	no	—
134	C₁₆×C₅₃	—	2	1	no	—
135	C₁₆×C₅₃	—	2	1	no	—
136	C₁₆×C₅₃	C₂×D₄	1	4	yes	—
137	#11719908	—	2	1	no	—
138	#11719908	—	2	1	no	—
139	#11719908	—	2	2	no	—
140	C₂³×C₅₃	C₂²×C₈	1	2	yes	—
141	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
142	C₂²×D₅₃	C₂²×C₈	1	2	yes	—
143	Q₈×C₅₃	—	2	2	no	—
144	D₄×C₅₃	—	2	4	no	—
145	D₄×C₅₃	—	2	2	no	—
146	C₂×C₄×C₅₃	—	2	2	no	—
147	C₂×C₄×C₅₃	—	2	2	no	—
148	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
150	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₅₃	#131	1	2	yes	—
152	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
153	C₂²⋊D₅₃	—	2	4	no	—
154	C₂²⋊D₅₃	—	2	4	no	—
155	C₂²⋊D₅₃	—	4	2	no	—
156	C₂×Dic₅₃	—	2	2	no	—
157	C₂×Dic₅₃	—	4	1	no	—
158	C₂×Dic₅₃	C₂²×C₈	1	2	yes	—
159	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
160	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
161	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
162	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
163	D₂₁₂	—	2	2	no	—
164	C₄×D₅₃	—	2	2	no	—
165	C₄×D₅₃	—	2	2	no	—
166	Dic₁₀₆	—	2	2	no	—
167	C₈×C₅₃	—	2	2	no	—
168	C₈×C₅₃	C₄×D₄	1	2	yes	—
169	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
170	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
171	#88322	—	2	2	no	—
172	#88322	—	2	1	no	—
173	#88322	—	2	1	no	—
174	#33438	—	53	1	no	maximal, Sylow
175	C₂²×C₅₃	—	2	1	no	—
176	C₂²×C₅₃	—	2	1	no	—
177	C₂²×C₅₃	—	2	2	no	—
178	C₂²×C₅₃	—	2	2	no	—
179	C₂²×C₅₃	—	2	2	no	—
180	C₂²×C₅₃	C₈×D₄	1	2	yes	—
181	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
182	C₂×D₅₃	—	2	2	no	—
183	C₂×D₅₃	—	2	2	no	—
184	C₂×D₅₃	—	2	2	no	—
185	C₄×C₅₃	—	2	2	no	—
186	C₄×C₅₃	C₈×D₄	1	2	yes	—
187	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
188	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
189	Dic₅₃	—	2	1	no	—
190	Dic₅₃	—	2	1	no	—
191	Dic₅₃	—	2	1	no	—
192	Dic₅₃	—	2	2	no	—
193	Dic₅₃	#504	1	2	yes	complemented
194	C₂×#504	—	53	1	no	—
195	C₂×#504	D₅₃	1	1	yes	characteristic, complemented
196	#2931	—	53	1	no	—
197	#2169	—	53	2	no	—
198	#2168	—	53	2	no	—
199	#2168	—	53	2	no	—
200	D₄×C₁₆	—	53	2	no	—
201	C₂×C₄⋊C₁₆	—	53	1	no	—
202	#2113	—	53	1	no	—
203	#2113	—	53	1	no	—
204	C₄×M₃₂	—	53	1	no	—
205	C₂×C₅₃	—	2	2	no	—
206	C₂×C₅₃	—	4	2	no	—
207	C₂×C₅₃	C₂×C₈×D₄	1	1	yes	characteristic
208	C₂×C₅₃	C₂×#504	1	1	yes	characteristic
209	C₂×C₅₃	#3407	1	1	yes	characteristic
210	D₅₃	—	4	2	no	—
211	C₂×#131	—	53	1	no	—
212	C₂×#131	C₂×D₅₃	1	1	yes	characteristic
213	#532	—	53	1	no	—
214	#504	—	2	4	no	—
215	#504	—	106	4	no	—
216	C₂×M₃₂	—	53	1	no	—
217	C₂×M₃₂	—	53	2	no	—
218	C₂×M₃₂	C₂×D₅₃	1	2	yes	—
219	C₂×M₃₂	C₂×D₅₃	1	1	yes	characteristic
220	C₂²×C₁₆	—	53	1	no	—
221	C₂²×C₁₆	—	53	2	no	—
222	C₂²×C₁₆	C₂×D₅₃	1	1	yes	characteristic
223	C₂²×C₁₆	C₂×D₅₃	1	2	yes	—
224	#436	—	53	2	no	—
225	#436	—	53	2	no	—
226	C₈×D₄	—	53	2	no	—
227	C₈×D₄	—	53	2	no	—
228	#423	—	53	1	no	—
229	#408	—	53	1	no	—
230	#408	—	53	1	no	—
231	C₂×C₄×C₈	—	53	1	no	—
232	C₄⋊C₁₆	—	53	1	no	—
233	C₄⋊C₁₆	—	53	1	no	—
234	C₄⋊C₁₆	—	53	1	no	—
235	C₄⋊C₁₆	—	53	1	no	—
236	C₂²⋊C₁₆	—	53	2	no	—
237	C₂²⋊C₁₆	—	53	2	no	—
238	C₂²⋊C₁₆	—	53	2	no	—
239	C₂²⋊C₁₆	—	53	2	no	—
240	#346	—	53	2	no	—
241	C₄×C₁₆	—	53	2	no	—
242	C₅₃	#33438	1	1	yes	characteristic, complemented, Sylow
243	C₂×#41	—	53	1	no	—
244	C₂×#41	C₄×D₅₃	1	1	yes	characteristic
245	#131	—	2	2	no	—
246	#131	—	2	2	no	—
247	#131	—	106	2	no	—
248	#131	—	106	2	no	—
249	C₂×M₁₆	—	53	1	no	—
250	C₂×M₁₆	—	53	2	no	—
251	C₂×M₁₆	C₄×D₅₃	1	1	yes	characteristic
252	C₂×M₁₆	C₄×D₅₃	1	2	yes	—
253	C₂²×C₈	—	53	1	no	—
254	C₂²×C₈	—	53	2	no	—
255	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
256	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
257	C₄⋊Q₈	—	53	1	no	—
258	#127	—	53	1	no	—
259	#124	—	53	1	no	—
260	#124	—	53	1	no	—
261	#121	—	53	2	no	—
262	#121	—	53	2	no	—
263	C₄×D₄	—	53	2	no	—
264	C₄×D₄	—	53	2	no	—
265	C₂×C₄²	—	53	1	no	—
266	M₃₂	—	2	4	no	—
267	M₃₂	—	106	2	no	—
268	M₃₂	—	106	4	no	—
269	M₃₂	C₂²⋊D₅₃	1	4	yes	complemented
270	C₂×C₁₆	—	2	2	no	—
271	C₂×C₁₆	—	2	4	no	—
272	C₂×C₁₆	—	53	2	no	—
273	C₂×C₁₆	—	53	1	no	—
274	C₂×C₁₆	—	53	1	no	—
275	C₂×C₁₆	—	106	2	no	—
276	C₂×C₁₆	—	106	4	no	—
277	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
278	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
279	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
280	C₄⋊C₈	—	53	2	no	—
281	C₄⋊C₈	—	53	2	no	—
282	C₂²⋊C₈	—	53	2	no	—
283	C₂²⋊C₈	—	53	2	no	—
284	C₂²⋊C₈	—	53	2	no	—
285	C₂²⋊C₈	—	53	2	no	—
286	C₄×C₈	—	53	1	no	—
287	C₄×C₈	—	53	1	no	—
288	C₄×C₈	—	53	1	no	—
289	C₄×C₈	—	53	1	no	—
290	#41	—	2	2	no	—
291	#41	—	2	2	no	—
292	#41	—	106	2	no	—
293	#41	—	106	2	no	—
294	C₂×Q₈	—	53	1	no	—
295	C₂×Q₈	C₈×D₅₃	1	1	yes	characteristic
296	C₂×D₄	—	53	2	no	—
297	C₂×D₄	—	53	2	no	—
298	C₂×D₄	—	53	2	no	—
299	C₂×D₄	—	53	1	no	—
300	C₂×D₄	C₈×D₅₃	1	2	yes	—
301	C₂×D₄	C₈×D₅₃	1	1	yes	characteristic
302	C₂²×C₄	—	53	1	no	—
303	C₂²×C₄	—	53	1	no	—
304	C₂²×C₄	—	53	2	no	—
305	C₂²×C₄	C₂×C₄×D₅₃	1	2	yes	—
306	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
307	M₁₆	—	2	2	no	—
308	M₁₆	—	2	4	no	—
309	M₁₆	—	106	2	no	—
310	M₁₆	—	106	4	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	53	1	no	—
314	C₂×C₈	—	53	1	no	—
315	C₂×C₈	—	53	2	no	—
316	C₂×C₈	—	106	2	no	—
317	C₂×C₈	—	106	2	no	—
318	C₂×C₈	—	106	2	no	—
319	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
320	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
321	C₂×C₈	#11719945	1	2	yes	—
322	C₂×C₈	C₂×C₂²⋊D₅₃	1	2	yes	—
323	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
324	C₄⋊C₄	—	53	2	no	—
325	C₄⋊C₄	—	53	2	no	—
326	C₂²⋊C₄	—	53	2	no	—
327	C₂²⋊C₄	—	53	2	no	—
328	C₂²⋊C₄	—	53	2	no	—
329	C₂²⋊C₄	—	53	2	no	—
330	C₄²	—	53	1	no	—
331	C₄²	—	53	1	no	—
332	C₄²	—	53	1	no	—
333	C₄²	—	53	1	no	—
334	C₁₆	—	2	1	no	—
335	C₁₆	—	2	1	no	—
336	C₁₆	—	106	1	no	—
337	C₁₆	—	106	1	no	—
338	C₁₆	—	106	2	no	—
339	C₁₆	C₂×C₂²⋊D₅₃	1	4	yes	—
340	C₂³	—	53	2	no	—
341	C₂³	C₂×C₈×D₅₃	1	2	yes	—
342	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
343	Q₈	—	2	2	no	—
344	Q₈	—	106	2	no	—
345	D₄	—	2	4	no	—
346	D₄	—	2	2	no	—
347	D₄	—	106	4	no	—
348	D₄	—	106	4	no	—
349	D₄	—	106	2	no	—
350	D₄	—	212	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	53	1	no	—
354	C₂×C₄	—	53	1	no	—
355	C₂×C₄	—	53	1	no	—
356	C₂×C₄	—	53	1	no	—
357	C₂×C₄	—	53	2	no	—
358	C₂×C₄	—	106	2	no	—
359	C₂×C₄	—	106	2	no	—
360	C₂×C₄	—	106	2	no	—
361	C₂×C₄	—	212	1	no	—
362	C₂×C₄	C₄×C₂²⋊D₅₃	1	2	yes	—
363	C₂×C₄	C₂×C₈×D₅₃	1	2	yes	—
364	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
365	C₂×C₄	#13133223	1	2	yes	—
366	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
367	C₈	—	2	2	no	—
368	C₈	—	106	2	no	—
369	C₈	—	106	1	no	—
370	C₈	—	106	1	no	—
371	C₈	C₄×C₂²⋊D₅₃	1	2	yes	—
372	C₈	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
373	C₈	C₂×#11719945	1	1	yes	characteristic
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	106	2	no	—
380	C₂²	—	106	2	no	—
381	C₂²	—	106	2	no	—
382	C₂²	C₈×C₂²⋊D₅₃	1	2	yes	—
383	C₂²	C₂²×C₈×D₅₃	1	1	yes	characteristic
384	C₄	—	2	2	no	—
385	C₄	—	53	2	no	—
386	C₄	—	106	1	no	—
387	C₄	—	106	1	no	—
388	C₄	—	106	1	no	—
389	C₄	—	106	2	no	—
390	C₄	C₈×C₂²⋊D₅₃	1	2	yes	—
391	C₄	C₂×C₄×C₂²⋊D₅₃	1	1	yes	characteristic
392	C₄	C₂×#13133223	1	1	yes	characteristic
393	C₂	—	2	2	no	—
394	C₂	—	4	2	no	—
395	C₂	—	212	2	no	—
396	C₂	C₂×C₈×C₂²⋊D₅₃	1	1	yes	characteristic
397	C₂	#504×D₅₃	1	1	yes	characteristic
398	C₂	#20287816	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅₃
commutator, socle	C₂²×C₅₃	C₂³×C₈
Fitting	C₂×C₅₃×#504	C₂
prime radical	#16811169	C₄
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	C₂×#504	D₅₃
hypocenter	C₅₃	#33438
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#504

Complements

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

N	H ≅ G/N	type
1. C₂×#16811041	C₂	semidirect
3. #20276545	C₂	semidirect
4. #20276540	C₂	semidirect
5. #20276538	C₂	semidirect
6. C₁₆×C₂²⋊D₅₃	C₂	semidirect
7. C₂×#16810441	C₂	semidirect
8. #20276329	C₂	semidirect
9. #20276328	C₂	semidirect
10. M₃₂×Dic₅₃	C₂	semidirect
11. C₂×C₅₃×#504	C₂	semidirect
84. M₃₂×C₅₃	D₄	semidirect
193. Dic₅₃	#504	semidirect
195. C₂×#504	D₅₃	semidirect
242. C₅₃	#33438	semidirect
269. M₃₂	C₂²⋊D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811041	2
#20283425	2
#20276545	2
#20276540	2
#20276538	2
C₁₆×C₂²⋊D₅₃	2
C₂×#16810441	2
#20276329	2
#20276328	2
M₃₂×Dic₅₃	2
C₂×C₅₃×#504	2
#33438	53