Subgroups — C₅₃×#24282 #27231794

Order 13568.

1308 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₃×#473	C₂	1	2	yes	maximal, complemented
3	C₅₃×#3004	C₂	1	2	yes	maximal
4	C₅₃×#2929	C₂	1	1	yes	maximal, characteristic
5	C₅₃×#2047	C₂	1	2	yes	maximal, complemented
6	C₅₃×#2020	C₂	1	2	yes	maximal, complemented
7	C₅₃×#1979	C₂	1	2	yes	maximal, complemented
8	C₅₃×#1810	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#1784	C₂	1	2	yes	maximal, complemented
10	C₂³×Q₈×C₅₃	C₂²	1	2	yes	—
11	C₂×#137×C₅₃	C₂²	1	4	yes	—
12	C₂²×Q₁₆×C₅₃	—	2	8	no	—
13	C₂²×Q₁₆×C₅₃	—	2	2	no	—
14	C₂²×Q₁₆×C₅₃	—	2	2	no	—
15	C₂²×Q₁₆×C₅₃	C₂²	1	2	yes	—
16	C₂²×Q₁₆×C₅₃	C₂²	1	2	yes	—
17	C₂×#131×C₅₃	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
19	C₅₃×#525	C₂²	1	1	yes	characteristic
20	C₅₃×#473	—	2	8	no	—
21	C₅₃×#451	—	2	4	no	—
22	C₅₃×#448	—	2	4	no	—
23	C₅₃×#435	—	2	2	no	—
24	C₈×D₄×C₅₃	—	2	2	no	—
25	C₂×#108×C₅₃	C₂²	1	2	yes	—
26	C₅₃×#424	C₂²	1	1	yes	characteristic
27	C₅₃×#419	C₂²	1	4	yes	—
28	C₂×#101×C₅₃	C₂²	1	4	yes	—
29	C₂×#101×C₅₃	C₂²	1	4	yes	—
30	C₅₃×#408	C₂²	1	1	yes	characteristic
31	C₅₃×#407	C₂²	1	2	yes	—
32	C₅₃×#407	C₂²	1	1	yes	characteristic
33	C₅₃×#405	C₂²	1	1	yes	characteristic
34	C₅₃×#341	C₂²	1	2	yes	—
35	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
36	C₂²×Q₈×C₅₃	—	2	2	no	—
37	C₂²×Q₈×C₅₃	—	2	8	no	—
38	C₂²×Q₈×C₅₃	—	2	4	no	—
39	C₂²×Q₈×C₅₃	—	2	4	no	—
40	C₂²×Q₈×C₅₃	—	4	4	no	—
41	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
42	C₂³×C₄×C₅₃	—	2	2	no	—
43	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
44	#137×C₅₃	—	2	8	no	—
45	#137×C₅₃	—	4	4	no	—
46	C₂×Q₁₆×C₅₃	—	2	16	no	—
47	C₂×Q₁₆×C₅₃	—	2	16	no	—
48	C₂×Q₁₆×C₅₃	—	2	4	no	—
49	C₂×Q₁₆×C₅₃	—	2	2	no	—
50	C₂×Q₁₆×C₅₃	—	2	2	no	—
51	C₂×Q₁₆×C₅₃	—	2	4	no	—
52	C₂×Q₁₆×C₅₃	—	2	8	no	—
53	C₂×Q₁₆×C₅₃	—	2	4	no	—
54	C₂×Q₁₆×C₅₃	D₄	1	8	yes	complemented
55	C₂×SD₁₆×C₅₃	—	2	4	no	—
56	#131×C₅₃	—	2	4	no	—
57	C₂×M₁₆×C₅₃	—	2	1	no	—
58	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
60	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₅₃	—	2	4	no	—
62	C₂²×C₈×C₅₃	—	2	1	no	—
63	C₂²×C₈×C₅₃	D₄	1	2	yes	—
64	C₂²×C₈×C₅₃	D₄	1	2	yes	—
65	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
67	#123×C₅₃	—	2	1	no	—
68	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
69	#121×C₅₃	D₄	1	2	yes	—
70	#120×C₅₃	—	2	1	no	—
71	C₄×D₄×C₅₃	—	2	2	no	—
72	#117×C₅₃	C₂³	1	1	yes	characteristic
73	#108×C₅₃	—	2	4	no	—
74	C₄⋊C₈×C₅₃	—	2	2	no	—
75	#103×C₅₃	—	2	8	no	—
76	#101×C₅₃	—	2	8	no	—
77	#101×C₅₃	—	4	4	no	—
78	C₂²⋊C₈×C₅₃	—	2	2	no	—
79	C₂²⋊C₈×C₅₃	—	2	2	no	—
80	C₂²⋊C₈×C₅₃	—	2	4	no	—
81	#97×C₅₃	—	2	1	no	—
82	C₄×C₈×C₅₃	—	2	1	no	—
83	C₂⁴×C₅₃	#41	1	1	yes	characteristic
84	#41×C₅₃	—	2	2	no	—
85	#41×C₅₃	—	2	2	no	—
86	C₂×Q₈×C₅₃	—	2	4	no	—
87	C₂×Q₈×C₅₃	—	2	16	no	—
88	C₂×Q₈×C₅₃	—	2	4	no	—
89	C₂×Q₈×C₅₃	—	2	4	no	—
90	C₂×Q₈×C₅₃	—	2	4	no	—
91	C₂×Q₈×C₅₃	—	2	4	no	—
92	C₂×Q₈×C₅₃	—	4	8	no	—
93	C₂×Q₈×C₅₃	—	4	16	no	—
94	C₂×Q₈×C₅₃	—	4	8	no	—
95	C₂×Q₈×C₅₃	—	4	4	no	—
96	C₂×Q₈×C₅₃	C₂×D₄	1	8	yes	—
97	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₅₃	—	2	2	no	—
99	C₂×D₄×C₅₃	—	2	1	no	—
100	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₅₃	—	2	2	no	—
102	C₂²×C₄×C₅₃	—	2	2	no	—
103	C₂²×C₄×C₅₃	—	2	4	no	—
104	C₂²×C₄×C₅₃	—	2	1	no	—
105	C₂²×C₄×C₅₃	—	4	8	no	—
106	C₂²×C₄×C₅₃	—	4	4	no	—
107	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
110	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
111	Q₁₆×C₅₃	—	2	16	no	—
112	Q₁₆×C₅₃	—	2	8	no	—
113	Q₁₆×C₅₃	—	2	8	no	—
114	Q₁₆×C₅₃	—	4	8	no	—
115	SD₁₆×C₅₃	—	4	8	no	—
116	M₁₆×C₅₃	—	2	2	no	—
117	M₁₆×C₅₃	—	2	4	no	—
118	M₁₆×C₅₃	—	2	2	no	—
119	M₁₆×C₅₃	—	2	4	no	—
120	M₁₆×C₅₃	—	4	2	no	—
121	C₂×C₈×C₅₃	—	2	2	no	—
122	C₂×C₈×C₅₃	—	2	4	no	—
123	C₂×C₈×C₅₃	—	2	4	no	—
124	C₂×C₈×C₅₃	—	2	1	no	—
125	C₂×C₈×C₅₃	—	2	4	no	—
126	C₂×C₈×C₅₃	—	2	1	no	—
127	C₂×C₈×C₅₃	—	4	2	no	—
128	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₅₃	C₂×D₄	1	4	yes	—
132	C₄⋊C₄×C₅₃	—	2	2	no	—
133	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
134	C₂²⋊C₄×C₅₃	—	2	2	no	—
135	C₂²⋊C₄×C₅₃	—	2	1	no	—
136	C₂²⋊C₄×C₅₃	—	2	2	no	—
137	C₄²×C₅₃	—	2	1	no	—
138	C₂³×C₅₃	—	2	2	no	—
139	C₂³×C₅₃	—	2	4	no	—
140	C₂³×C₅₃	—	2	1	no	—
141	C₂³×C₅₃	#121	1	2	yes	—
142	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
143	Q₈×C₅₃	—	2	8	no	—
144	Q₈×C₅₃	—	2	8	no	—
145	Q₈×C₅₃	—	2	2	no	—
146	Q₈×C₅₃	—	4	16	no	—
147	Q₈×C₅₃	—	4	4	no	—
148	Q₈×C₅₃	—	4	4	no	—
149	D₄×C₅₃	—	2	2	no	—
150	D₄×C₅₃	—	4	2	no	—
151	D₄×C₅₃	—	4	4	no	—
152	C₂×C₄×C₅₃	—	2	2	no	—
153	C₂×C₄×C₅₃	—	2	2	no	—
154	C₂×C₄×C₅₃	—	2	2	no	—
155	C₂×C₄×C₅₃	—	2	4	no	—
156	C₂×C₄×C₅₃	—	2	1	no	—
157	C₂×C₄×C₅₃	—	2	2	no	—
158	C₂×C₄×C₅₃	—	2	8	no	—
159	C₂×C₄×C₅₃	—	4	16	no	—
160	C₂×C₄×C₅₃	—	4	4	no	—
161	C₂×C₄×C₅₃	—	4	4	no	—
162	C₂×C₄×C₅₃	—	4	1	no	—
163	C₂×C₄×C₅₃	—	4	1	no	—
164	C₂×C₄×C₅₃	#121	1	2	yes	—
165	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
167	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
169	C₈×C₅₃	—	2	2	no	—
170	C₈×C₅₃	—	4	1	no	—
171	C₈×C₅₃	—	4	1	no	—
172	C₈×C₅₃	—	4	4	no	—
173	C₈×C₅₃	#120	1	2	yes	—
174	C₈×C₅₃	#120	1	2	yes	—
175	#24282	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂²×C₅₃	—	2	8	no	—
177	C₂²×C₅₃	—	2	2	no	—
178	C₂²×C₅₃	—	2	2	no	—
179	C₂²×C₅₃	—	2	2	no	—
180	C₂²×C₅₃	—	4	1	no	—
181	C₂²×C₅₃	—	4	2	no	—
182	C₂²×C₅₃	#473	1	4	yes	complemented
183	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
184	C₂²×C₅₃	#546	1	2	yes	—
185	C₄×C₅₃	—	2	2	no	—
186	C₄×C₅₃	—	4	8	no	—
187	C₄×C₅₃	—	4	1	no	—
188	C₄×C₅₃	—	4	2	no	—
189	C₄×C₅₃	C₂×#120	1	1	yes	characteristic
190	C₄×C₅₃	#535	1	1	yes	characteristic
191	C₄×C₅₃	D₄²	1	2	yes	—
192	C₂³×Q₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
193	C₂×#473	C₂×C₅₃	1	2	yes	complemented
194	#3004	C₂×C₅₃	1	2	yes	—
195	#2929	C₂×C₅₃	1	1	yes	characteristic
196	#2047	C₂×C₅₃	1	2	yes	complemented
197	#2020	C₂×C₅₃	1	2	yes	complemented
198	#1979	C₂×C₅₃	1	2	yes	complemented
199	#1810	C₂×C₅₃	1	1	yes	characteristic, complemented
200	#1784	C₂×C₅₃	1	2	yes	complemented
201	C₂×C₅₃	—	2	2	no	—
202	C₂×C₅₃	—	2	4	no	—
203	C₂×C₅₃	—	8	1	no	—
204	C₂×C₅₃	#2408	1	1	yes	characteristic
205	C₂×C₅₃	C₂×#473	1	2	yes	—
206	C₂³×Q₈	C₂²×C₅₃	1	2	yes	—
207	C₂×#137	C₂²×C₅₃	1	4	yes	—
208	C₂²×Q₁₆	—	2	8	no	—
209	C₂²×Q₁₆	—	2	2	no	—
210	C₂²×Q₁₆	—	2	2	no	—
211	C₂²×Q₁₆	C₂²×C₅₃	1	2	yes	—
212	C₂²×Q₁₆	C₂²×C₅₃	1	2	yes	—
213	C₂×#131	C₂²×C₅₃	1	1	yes	characteristic
214	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
215	#525	C₂²×C₅₃	1	1	yes	characteristic
216	#473	—	2	8	no	—
217	#451	—	2	4	no	—
218	#448	—	2	4	no	—
219	#435	—	2	2	no	—
220	C₈×D₄	—	2	2	no	—
221	C₂×#108	C₂²×C₅₃	1	2	yes	—
222	#424	C₂²×C₅₃	1	1	yes	characteristic
223	#419	C₂²×C₅₃	1	4	yes	—
224	C₂×#101	C₂²×C₅₃	1	4	yes	—
225	C₂×#101	C₂²×C₅₃	1	4	yes	—
226	#408	C₂²×C₅₃	1	1	yes	characteristic
227	#407	C₂²×C₅₃	1	2	yes	—
228	#407	C₂²×C₅₃	1	1	yes	characteristic
229	#405	C₂²×C₅₃	1	1	yes	characteristic
230	#341	C₂²×C₅₃	1	2	yes	—
231	C₅₃	#24282	1	1	yes	characteristic, direct product factor, Sylow
232	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	—	2	8	no	—
235	C₂²×Q₈	—	2	4	no	—
236	C₂²×Q₈	—	2	4	no	—
237	C₂²×Q₈	—	4	4	no	—
238	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
239	C₂³×C₄	—	2	2	no	—
240	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
241	#137	—	2	8	no	—
242	#137	—	4	4	no	—
243	C₂×Q₁₆	—	2	16	no	—
244	C₂×Q₁₆	—	2	16	no	—
245	C₂×Q₁₆	—	2	8	no	—
246	C₂×Q₁₆	—	2	4	no	—
247	C₂×Q₁₆	—	2	4	no	—
248	C₂×Q₁₆	—	2	2	no	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×Q₁₆	—	2	4	no	—
251	C₂×Q₁₆	D₄×C₅₃	1	8	yes	complemented
252	C₂×SD₁₆	—	2	4	no	—
253	#131	—	2	4	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
256	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
257	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
258	C₂²×C₈	—	2	4	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	D₄×C₅₃	1	2	yes	—
261	C₂²×C₈	D₄×C₅₃	1	2	yes	—
262	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
264	#123	—	2	1	no	—
265	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
266	#121	D₄×C₅₃	1	2	yes	—
267	#120	—	2	1	no	—
268	C₄×D₄	—	2	2	no	—
269	#117	C₂³×C₅₃	1	1	yes	characteristic
270	#108	—	2	4	no	—
271	C₄⋊C₈	—	2	2	no	—
272	#103	—	2	8	no	—
273	#101	—	2	8	no	—
274	#101	—	4	4	no	—
275	C₂²⋊C₈	—	2	2	no	—
276	C₂²⋊C₈	—	2	4	no	—
277	C₂²⋊C₈	—	2	2	no	—
278	#97	—	2	1	no	—
279	C₄×C₈	—	2	1	no	—
280	C₂⁴	#41×C₅₃	1	1	yes	characteristic
281	#41	—	2	2	no	—
282	#41	—	2	2	no	—
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	2	16	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	4	8	no	—
290	C₂×Q₈	—	4	16	no	—
291	C₂×Q₈	—	4	8	no	—
292	C₂×Q₈	—	4	4	no	—
293	C₂×Q₈	C₂×D₄×C₅₃	1	8	yes	—
294	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	4	8	no	—
303	C₂²×C₄	—	4	4	no	—
304	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
306	C₂²×C₄	#41×C₅₃	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
308	Q₁₆	—	2	16	no	—
309	Q₁₆	—	2	8	no	—
310	Q₁₆	—	2	8	no	—
311	Q₁₆	—	4	8	no	—
312	SD₁₆	—	4	8	no	—
313	M₁₆	—	2	2	no	—
314	M₁₆	—	2	4	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	2	4	no	—
317	M₁₆	—	4	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	4	2	no	—
325	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
326	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
327	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₅₃	1	4	yes	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₄²	—	2	1	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	1	no	—
338	C₂³	#121×C₅₃	1	2	yes	—
339	C₂³	C₂×#41×C₅₃	1	1	yes	characteristic
340	Q₈	—	2	8	no	—
341	Q₈	—	2	8	no	—
342	Q₈	—	2	2	no	—
343	Q₈	—	4	16	no	—
344	Q₈	—	4	4	no	—
345	Q₈	—	4	4	no	—
346	D₄	—	2	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	4	16	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	#121×C₅₃	1	2	yes	—
362	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
363	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
364	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
365	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
366	C₈	—	2	2	no	—
367	C₈	—	4	1	no	—
368	C₈	—	4	1	no	—
369	C₈	—	4	4	no	—
370	C₈	#120×C₅₃	1	2	yes	—
371	C₈	#120×C₅₃	1	2	yes	—
372	C₂²	—	2	8	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	1	no	—
378	C₂²	C₅₃×#473	1	4	yes	complemented
379	C₂²	C₂×#121×C₅₃	1	1	yes	characteristic
380	C₂²	C₅₃×#546	1	2	yes	—
381	C₄	—	2	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	8	no	—
384	C₄	—	4	1	no	—
385	C₄	C₂×#120×C₅₃	1	1	yes	characteristic
386	C₄	C₅₃×#535	1	1	yes	characteristic
387	C₄	D₄²×C₅₃	1	2	yes	—
388	C₂	—	2	2	no	—
389	C₂	—	2	4	no	—
390	C₂	—	8	1	no	—
391	C₂	C₅₃×#2408	1	1	yes	characteristic
392	C₂	C₂×C₅₃×#473	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₅₃×#525	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂³×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₁₆×C₅₃	C₂	semidirect
2. C₂×C₅₃×#473	C₂	semidirect
5. C₅₃×#2047	C₂	semidirect
6. C₅₃×#2020	C₂	semidirect
7. C₅₃×#1979	C₂	semidirect
8. C₅₃×#1810	C₂	semidirect
9. C₅₃×#1784	C₂	semidirect
54. C₂×Q₁₆×C₅₃	D₄	semidirect
175. #24282	C₅₃	direct (N × H)
182. C₂²×C₅₃	#473	semidirect
192. C₂³×Q₁₆	C₂×C₅₃	semidirect
193. C₂×#473	C₂×C₅₃	semidirect
196. #2047	C₂×C₅₃	semidirect
197. #2020	C₂×C₅₃	semidirect
198. #1979	C₂×C₅₃	semidirect
199. #1810	C₂×C₅₃	semidirect
200. #1784	C₂×C₅₃	semidirect
231. C₅₃	#24282	direct (N × H)
251. C₂×Q₁₆	D₄×C₅₃	semidirect
378. C₂²	C₅₃×#473	semidirect

Maximal subgroups

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

subgroup	index
C₂³×Q₁₆×C₅₃	2
C₂×C₅₃×#473	2
C₅₃×#3004	2
C₅₃×#2929	2
C₅₃×#2047	2
C₅₃×#2020	2
C₅₃×#1979	2
C₅₃×#1810	2
C₅₃×#1784	2
#24282	53

Subgroups — C53×#24282 #27231794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#24282 #27231794