Subgroups — C₂×C₅₃×#3184 #27268203

Order 13568.

2514 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#532	C₂	1	2	yes	maximal, complemented
2	C₅₃×#3184	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#486	C₂	1	2	yes	maximal, complemented
6	C₂×C₅₃×#469	C₂	1	4	yes	maximal, complemented
7	C₂×C₅₃×#442	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×M₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₅₃	—	2	2	no	—
10	C₂²×D₈×C₅₃	C₂²	1	4	yes	—
11	C₂²×M₁₆×C₅₃	C₂²	1	2	yes	—
12	C₅₃×#532	—	2	8	no	—
13	C₅₃×#532	C₂²	1	16	yes	complemented
14	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	—
15	C₂×#127×C₅₃	C₂²	1	2	yes	—
16	C₂×#124×C₅₃	—	2	2	no	—
17	C₂×#121×C₅₃	—	2	2	no	—
18	C₂×#121×C₅₃	C₂²	1	4	yes	—
19	C₂×C₄×D₄×C₅₃	—	2	2	no	—
20	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	—
21	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
22	C₅₃×#498	C₂²	1	8	yes	complemented
23	C₅₃×#493	C₂²	1	8	yes	complemented
24	C₅₃×#486	C₂²	1	16	yes	complemented
25	C₅₃×#469	C₂²	1	32	yes	complemented
26	C₅₃×#442	C₂²	1	32	yes	complemented
27	C₂×#106×C₅₃	C₂²	1	4	yes	—
28	C₂×#102×C₅₃	C₂²	1	8	yes	—
29	C₄×M₁₆×C₅₃	C₂²	1	8	yes	complemented
30	C₂×#97×C₅₃	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#41×C₅₃	—	2	16	no	—
34	C₂×#41×C₅₃	—	4	16	no	—
35	C₂²×Q₈×C₅₃	—	2	2	no	—
36	C₂²×D₄×C₅₃	—	2	4	no	—
37	C₂²×D₄×C₅₃	—	2	2	no	—
38	C₂²×D₄×C₅₃	—	2	2	no	—
39	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
40	C₂³×C₄×C₅₃	—	2	4	no	—
41	C₂³×C₄×C₅₃	D₄	1	2	yes	—
42	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
43	C₂×D₈×C₅₃	—	2	16	no	—
44	C₂×D₈×C₅₃	C₂³	1	16	yes	—
45	C₂×M₁₆×C₅₃	—	2	8	no	—
46	C₂×M₁₆×C₅₃	C₂³	1	8	yes	—
47	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₅₃	—	2	4	no	—
50	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	—
51	#127×C₅₃	—	2	4	no	—
52	#127×C₅₃	C₂³	1	8	yes	—
53	#124×C₅₃	—	2	16	no	—
54	#121×C₅₃	—	2	16	no	—
55	#121×C₅₃	—	2	8	no	—
56	#121×C₅₃	C₂³	1	16	yes	—
57	C₄×D₄×C₅₃	—	2	16	no	—
58	C₄×D₄×C₅₃	—	2	8	no	—
59	C₄×D₄×C₅₃	C₂³	1	16	yes	—
60	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
62	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
64	C₂×C₄²×C₅₃	D₄	1	2	yes	—
65	C₂×C₄²×C₅₃	D₄	1	4	yes	—
66	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
69	#106×C₅₃	C₂³	1	16	yes	—
70	#102×C₅₃	C₂³	1	32	yes	—
71	#97×C₅₃	C₂³	1	8	yes	—
72	C₄×C₈×C₅₃	C₂³	1	4	yes	—
73	C₄×C₈×C₅₃	C₂³	1	4	yes	—
74	C₂⁴×C₅₃	—	2	4	no	—
75	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
76	#41×C₅₃	—	4	64	no	—
77	C₂×Q₈×C₅₃	—	2	8	no	—
78	C₂×Q₈×C₅₃	—	4	8	no	—
79	C₂×D₄×C₅₃	—	2	16	no	—
80	C₂×D₄×C₅₃	—	2	4	no	—
81	C₂×D₄×C₅₃	—	2	8	no	—
82	C₂×D₄×C₅₃	—	2	8	no	—
83	C₂×D₄×C₅₃	—	2	16	no	—
84	C₂×D₄×C₅₃	—	4	16	no	—
85	C₂×D₄×C₅₃	—	4	8	no	—
86	C₂×D₄×C₅₃	—	4	8	no	—
87	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
88	C₂²×C₄×C₅₃	—	2	8	no	—
89	C₂²×C₄×C₅₃	—	2	4	no	—
90	C₂²×C₄×C₅₃	—	2	4	no	—
91	C₂²×C₄×C₅₃	—	2	16	no	—
92	C₂²×C₄×C₅₃	—	4	16	no	—
93	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	—
95	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
99	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
100	D₈×C₅₃	—	2	32	no	—
101	M₁₆×C₅₃	—	2	16	no	—
102	C₂×C₈×C₅₃	—	2	4	no	—
103	C₂×C₈×C₅₃	#41	1	8	yes	complemented
104	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
105	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
106	C₄⋊C₄×C₅₃	—	2	8	no	—
107	C₄⋊C₄×C₅₃	—	2	4	no	—
108	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
109	C₂²⋊C₄×C₅₃	—	2	16	no	—
110	C₂²⋊C₄×C₅₃	—	2	16	no	—
111	C₄²×C₅₃	C₂×D₄	1	2	yes	—
112	C₄²×C₅₃	C₂×D₄	1	8	yes	—
113	C₄²×C₅₃	C₂×D₄	1	2	yes	—
114	C₄²×C₅₃	C₂⁴	1	2	yes	—
115	C₄²×C₅₃	C₂⁴	1	2	yes	—
116	C₂³×C₅₃	—	2	2	no	—
117	C₂³×C₅₃	—	2	4	no	—
118	C₂³×C₅₃	—	2	8	no	—
119	C₂³×C₅₃	—	4	8	no	—
120	C₂³×C₅₃	—	4	8	no	—
121	C₂³×C₅₃	—	4	8	no	—
122	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
123	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
124	Q₈×C₅₃	—	4	16	no	—
125	D₄×C₅₃	—	2	16	no	—
126	D₄×C₅₃	—	4	32	no	—
127	D₄×C₅₃	—	4	8	no	—
128	D₄×C₅₃	—	4	16	no	—
129	D₄×C₅₃	—	4	16	no	—
130	C₂×C₄×C₅₃	—	2	2	no	—
131	C₂×C₄×C₅₃	—	2	4	no	—
132	C₂×C₄×C₅₃	—	2	4	no	—
133	C₂×C₄×C₅₃	—	2	16	no	—
134	C₂×C₄×C₅₃	—	2	4	no	—
135	C₂×C₄×C₅₃	—	2	8	no	—
136	C₂×C₄×C₅₃	—	4	32	no	—
137	C₂×C₄×C₅₃	—	4	8	no	—
138	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	8	yes	—
139	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
140	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
141	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
143	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
144	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
145	C₈×C₅₃	—	2	4	no	—
146	C₈×C₅₃	C₂×#41	1	8	yes	complemented
147	C₂×#3184	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂²×C₅₃	—	2	2	no	—
149	C₂²×C₅₃	—	2	4	no	—
150	C₂²×C₅₃	—	4	4	no	—
151	C₂²×C₅₃	—	4	8	no	—
152	C₂²×C₅₃	—	4	8	no	—
153	C₂²×C₅₃	—	4	8	no	—
154	C₂²×C₅₃	—	8	16	no	—
155	C₂²×C₅₃	#532	1	2	yes	—
156	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
157	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
158	C₄×C₅₃	—	2	2	no	—
159	C₄×C₅₃	—	2	4	no	—
160	C₄×C₅₃	—	4	8	no	—
161	C₄×C₅₃	#532	1	2	yes	—
162	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	8	yes	—
163	C₄×C₅₃	C₂²×#41	1	2	yes	—
164	C₂×#532	C₂×C₅₃	1	2	yes	complemented
165	#3184	C₂×C₅₃	1	16	yes	direct product factor
166	C₂×#498	C₂×C₅₃	1	1	yes	characteristic, complemented
167	C₂×#493	C₂×C₅₃	1	1	yes	characteristic, complemented
168	C₂×#486	C₂×C₅₃	1	2	yes	complemented
169	C₂×#469	C₂×C₅₃	1	4	yes	complemented
170	C₂×#442	C₂×C₅₃	1	4	yes	complemented
171	C₂×C₄×M₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
172	C₂×C₅₃	—	4	2	no	—
173	C₂×C₅₃	—	8	8	no	—
174	C₂×C₅₃	#3184	1	4	yes	direct product factor
175	C₂×C₅₃	C₂×#532	1	1	yes	characteristic
176	C₂×C₅₃	C₂²×AGL(1,ℤ/8)	1	2	yes	—
177	C₂²×#41	—	2	2	no	—
178	C₂²×D₈	C₂²×C₅₃	1	4	yes	—
179	C₂²×M₁₆	C₂²×C₅₃	1	2	yes	—
180	#532	—	2	8	no	—
181	#532	C₂²×C₅₃	1	16	yes	complemented
182	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	—
183	C₂×#127	C₂²×C₅₃	1	2	yes	—
184	C₂×#124	—	2	2	no	—
185	C₂×#121	—	2	2	no	—
186	C₂×#121	C₂²×C₅₃	1	4	yes	—
187	C₂×C₄×D₄	—	2	2	no	—
188	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	—
189	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
190	#498	C₂²×C₅₃	1	8	yes	complemented
191	#493	C₂²×C₅₃	1	8	yes	complemented
192	#486	C₂²×C₅₃	1	16	yes	complemented
193	#469	C₂²×C₅₃	1	32	yes	complemented
194	#442	C₂²×C₅₃	1	32	yes	complemented
195	C₂×#106	C₂²×C₅₃	1	4	yes	—
196	C₂×#102	C₂²×C₅₃	1	8	yes	—
197	C₄×M₁₆	C₂²×C₅₃	1	8	yes	complemented
198	C₂×#97	C₂²×C₅₃	1	2	yes	—
199	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
200	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
201	C₅₃	C₂×#3184	1	1	yes	characteristic, direct product factor, Sylow
202	C₂×#41	—	2	16	no	—
203	C₂×#41	—	4	16	no	—
204	C₂²×Q₈	—	2	2	no	—
205	C₂²×D₄	—	2	4	no	—
206	C₂²×D₄	—	2	2	no	—
207	C₂²×D₄	—	2	2	no	—
208	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
209	C₂³×C₄	—	2	4	no	—
210	C₂³×C₄	D₄×C₅₃	1	2	yes	—
211	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
212	C₂×D₈	—	2	16	no	—
213	C₂×D₈	C₂³×C₅₃	1	16	yes	—
214	C₂×M₁₆	—	2	8	no	—
215	C₂×M₁₆	C₂³×C₅₃	1	8	yes	—
216	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
217	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
218	C₄⋊Q₈	—	2	4	no	—
219	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	—
220	#127	—	2	4	no	—
221	#127	C₂³×C₅₃	1	8	yes	—
222	#124	—	2	16	no	—
223	#121	—	2	16	no	—
224	#121	—	2	8	no	—
225	#121	C₂³×C₅₃	1	16	yes	—
226	C₄×D₄	—	2	16	no	—
227	C₄×D₄	—	2	8	no	—
228	C₄×D₄	C₂³×C₅₃	1	16	yes	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
231	C₂×C₂²⋊C₄	—	2	4	no	—
232	C₂×C₂²⋊C₄	—	2	4	no	—
233	C₂×C₄²	D₄×C₅₃	1	2	yes	—
234	C₂×C₄²	D₄×C₅₃	1	4	yes	—
235	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
238	#106	C₂³×C₅₃	1	16	yes	—
239	#102	C₂³×C₅₃	1	32	yes	—
240	#97	C₂³×C₅₃	1	8	yes	—
241	C₄×C₈	C₂³×C₅₃	1	4	yes	—
242	C₄×C₈	C₂³×C₅₃	1	4	yes	—
243	C₂⁴	—	2	4	no	—
244	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
245	#41	—	4	64	no	—
246	C₂×Q₈	—	2	8	no	—
247	C₂×Q₈	—	4	8	no	—
248	C₂×D₄	—	2	16	no	—
249	C₂×D₄	—	2	4	no	—
250	C₂×D₄	—	2	8	no	—
251	C₂×D₄	—	2	8	no	—
252	C₂×D₄	—	2	16	no	—
253	C₂×D₄	—	4	16	no	—
254	C₂×D₄	—	4	8	no	—
255	C₂×D₄	—	4	8	no	—
256	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	16	no	—
261	C₂²×C₄	—	4	16	no	—
262	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
265	C₂²×C₄	C₂×D₄×C₅₃	1	8	yes	—
266	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
267	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
268	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
269	D₈	—	2	32	no	—
270	M₁₆	—	2	16	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	#41×C₅₃	1	8	yes	complemented
273	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
274	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
275	C₄⋊C₄	—	2	8	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
278	C₂²⋊C₄	—	2	16	no	—
279	C₂²⋊C₄	—	2	16	no	—
280	C₄²	C₂×D₄×C₅₃	1	2	yes	—
281	C₄²	C₂×D₄×C₅₃	1	8	yes	—
282	C₄²	C₂×D₄×C₅₃	1	2	yes	—
283	C₄²	C₂⁴×C₅₃	1	2	yes	—
284	C₄²	C₂⁴×C₅₃	1	2	yes	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	2	8	no	—
288	C₂³	—	4	8	no	—
289	C₂³	—	4	8	no	—
290	C₂³	—	4	8	no	—
291	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
292	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
293	Q₈	—	4	16	no	—
294	D₄	—	2	16	no	—
295	D₄	—	4	32	no	—
296	D₄	—	4	8	no	—
297	D₄	—	4	16	no	—
298	D₄	—	4	16	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	16	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	4	32	no	—
306	C₂×C₄	—	4	8	no	—
307	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	8	yes	—
308	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
309	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
310	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
311	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
312	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
313	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
314	C₈	—	2	4	no	—
315	C₈	C₂×#41×C₅₃	1	8	yes	complemented
316	C₂²	—	2	4	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	4	4	no	—
319	C₂²	—	4	8	no	—
320	C₂²	—	4	8	no	—
321	C₂²	—	4	8	no	—
322	C₂²	—	8	16	no	—
323	C₂²	C₅₃×#532	1	2	yes	—
324	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	4	yes	—
325	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
326	C₄	—	2	4	no	—
327	C₄	—	2	2	no	—
328	C₄	—	4	8	no	—
329	C₄	C₅₃×#532	1	2	yes	—
330	C₄	C₂×AGL(1,ℤ/8)×C₅₃	1	8	yes	—
331	C₄	C₂²×#41×C₅₃	1	2	yes	—
332	C₂	—	4	2	no	—
333	C₂	—	8	8	no	—
334	C₂	C₅₃×#3184	1	4	yes	direct product factor
335	C₂	C₂×C₅₃×#532	1	1	yes	characteristic
336	C₂	C₂²×AGL(1,ℤ/8)×C₅₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂²×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#532	C₂	semidirect
2. C₅₃×#3184	C₂	direct (N × H)
3. C₂×C₅₃×#498	C₂	semidirect
4. C₂×C₅₃×#493	C₂	semidirect
5. C₂×C₅₃×#486	C₂	semidirect
6. C₂×C₅₃×#469	C₂	semidirect
7. C₂×C₅₃×#442	C₂	semidirect
8. C₂×C₄×M₁₆×C₅₃	C₂	semidirect
13. C₅₃×#532	C₂²	semidirect
22. C₅₃×#498	C₂²	semidirect
23. C₅₃×#493	C₂²	semidirect
24. C₅₃×#486	C₂²	semidirect
25. C₅₃×#469	C₂²	semidirect
26. C₅₃×#442	C₂²	semidirect
29. C₄×M₁₆×C₅₃	C₂²	semidirect
103. C₂×C₈×C₅₃	#41	semidirect
146. C₈×C₅₃	C₂×#41	semidirect
147. C₂×#3184	C₅₃	direct (N × H)
164. C₂×#532	C₂×C₅₃	semidirect
165. #3184	C₂×C₅₃	direct (N × H)
166. C₂×#498	C₂×C₅₃	semidirect
167. C₂×#493	C₂×C₅₃	semidirect
168. C₂×#486	C₂×C₅₃	semidirect
169. C₂×#469	C₂×C₅₃	semidirect
170. C₂×#442	C₂×C₅₃	semidirect
171. C₂×C₄×M₁₆	C₂×C₅₃	semidirect
174. C₂×C₅₃	#3184	direct (N × H)
181. #532	C₂²×C₅₃	semidirect
190. #498	C₂²×C₅₃	semidirect
191. #493	C₂²×C₅₃	semidirect
192. #486	C₂²×C₅₃	semidirect
193. #469	C₂²×C₅₃	semidirect
194. #442	C₂²×C₅₃	semidirect
197. C₄×M₁₆	C₂²×C₅₃	semidirect
201. C₅₃	C₂×#3184	direct (N × H)
272. C₂×C₈	#41×C₅₃	semidirect
315. C₈	C₂×#41×C₅₃	semidirect
334. C₂	C₅₃×#3184	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#532	2
C₅₃×#3184	2
C₂×C₅₃×#498	2
C₂×C₅₃×#493	2
C₂×C₅₃×#486	2
C₂×C₅₃×#469	2
C₂×C₅₃×#442	2
C₂×C₄×M₁₆×C₅₃	2
C₂×#3184	53

Subgroups — C2×C53×#3184 #27268203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3184 #27268203