Subgroups — C₅₃×#19909 #27227421

Order 13568.

638 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	C₅₃×#3391	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3333	C₂	1	2	yes	maximal, complemented
4	C₅₃×#1706	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#1697	C₂	1	2	yes	maximal, complemented
6	C₅₃×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1668	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#1631	C₂	1	2	yes	maximal, complemented
9	C₅₃×#1622	C₂	1	2	yes	maximal, complemented
10	C₅₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×Q₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#554	C₂²	1	2	yes	—
13	C₅₃×#550	C₂²	1	2	yes	—
14	C₅₃×#500	C₂²	1	1	yes	characteristic
15	C₅₃×#499	—	2	1	no	—
16	C₅₃×#493	—	2	1	no	—
17	C₅₃×#493	C₂²	1	1	yes	characteristic
18	C₅₃×#492	C₂²	1	2	yes	—
19	C₅₃×#486	C₂²	1	2	yes	—
20	C₅₃×#480	—	2	2	no	—
21	C₅₃×#478	—	2	2	no	—
22	C₅₃×#477	C₂²	1	2	yes	—
23	C₅₃×#476	C₂²	1	2	yes	—
24	C₅₃×#468	—	2	2	no	—
25	C₅₃×#460	C₂²	1	2	yes	—
26	C₅₃×#459	—	2	2	no	—
27	C₅₃×#459	C₂²	1	2	yes	—
28	C₅₃×#452	—	2	2	no	—
29	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
31	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
32	C₄×D₈×C₅₃	—	2	1	no	—
33	C₄×D₈×C₅₃	—	2	1	no	—
34	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
35	C₅₃×#436	C₂²	1	2	yes	—
36	C₅₃×#417	—	2	2	no	—
37	C₅₃×#335	C₂²	1	1	yes	characteristic
38	C₅₃×#335	C₂²	1	1	yes	characteristic
39	C₅₃×#333	C₂²	1	2	yes	—
40	C₅₃×#331	C₂²	1	2	yes	—
41	C₅₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₅₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₅₃×D₄⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×#41×C₅₃	—	2	2	no	—
46	C₂×Q₁₆×C₅₃	D₄	1	1	yes	characteristic
47	C₂×SD₁₆×C₅₃	—	2	2	no	—
48	C₂×SD₁₆×C₅₃	—	4	2	no	—
49	C₂×D₈×C₅₃	—	2	1	no	—
50	C₂×D₈×C₅₃	—	2	1	no	—
51	C₂×D₈×C₅₃	—	2	2	no	—
52	C₂×D₈×C₅₃	D₄	1	1	yes	characteristic
53	C₂×M₁₆×C₅₃	—	2	2	no	—
54	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
55	#127×C₅₃	—	2	2	no	—
56	#127×C₅₃	C₂³	1	2	yes	—
57	#125×C₅₃	—	2	2	no	—
58	C₂²⋊Q₈×C₅₃	—	2	2	no	—
59	C₂²⋊Q₈×C₅₃	—	4	2	no	—
60	#121×C₅₃	—	2	2	no	—
61	#121×C₅₃	—	4	2	no	—
62	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₅₃	—	2	2	no	—
65	C₄×D₄×C₅₃	—	2	2	no	—
66	C₄×D₄×C₅₃	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
68	#107×C₅₃	—	2	1	no	—
69	#107×C₅₃	—	2	1	no	—
70	#107×C₅₃	—	2	2	no	—
71	#107×C₅₃	D₄	1	1	yes	characteristic
72	#107×C₅₃	D₄	1	1	yes	characteristic
73	#106×C₅₃	—	2	2	no	—
74	C₄⋊C₈×C₅₃	—	2	1	no	—
75	C₄⋊C₈×C₅₃	—	2	1	no	—
76	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
77	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
79	#103×C₅₃	—	2	2	no	—
80	#103×C₅₃	D₄	1	1	yes	characteristic
81	#103×C₅₃	D₄	1	1	yes	characteristic
82	#102×C₅₃	—	2	2	no	—
83	#102×C₅₃	—	2	2	no	—
84	#102×C₅₃	—	2	2	no	—
85	#102×C₅₃	—	2	2	no	—
86	#102×C₅₃	—	2	2	no	—
87	#102×C₅₃	D₄	1	2	yes	—
88	C₂²⋊C₈×C₅₃	—	2	2	no	—
89	C₄×C₈×C₅₃	—	2	1	no	—
90	C₄×C₈×C₅₃	—	2	1	no	—
91	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	#41×C₅₃	—	4	4	no	—
95	#41×C₅₃	—	8	2	no	—
96	C₂×Q₈×C₅₃	—	2	2	no	—
97	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
99	C₂×D₄×C₅₃	—	2	2	no	—
100	C₂×D₄×C₅₃	—	2	2	no	—
101	C₂×D₄×C₅₃	—	2	2	no	—
102	C₂×D₄×C₅₃	—	4	2	no	—
103	C₂×D₄×C₅₃	—	4	2	no	—
104	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₅₃	—	2	2	no	—
106	C₂²×C₄×C₅₃	—	4	2	no	—
107	C₂²×C₄×C₅₃	—	4	2	no	—
108	Q₁₆×C₅₃	—	2	2	no	—
109	SD₁₆×C₅₃	—	8	4	no	—
110	SD₁₆×C₅₃	—	8	2	no	—
111	D₈×C₅₃	—	2	2	no	—
112	D₈×C₅₃	—	4	2	no	—
113	D₈×C₅₃	—	8	1	no	—
114	D₈×C₅₃	—	8	2	no	—
115	M₁₆×C₅₃	—	8	2	no	—
116	C₂×C₈×C₅₃	—	2	1	no	—
117	C₂×C₈×C₅₃	—	2	1	no	—
118	C₂×C₈×C₅₃	—	2	1	no	—
119	C₂×C₈×C₅₃	—	2	2	no	—
120	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
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	1	no	—
126	C₄⋊C₄×C₅₃	—	2	2	no	—
127	C₄⋊C₄×C₅₃	—	2	2	no	—
128	C₄⋊C₄×C₅₃	—	4	2	no	—
129	C₄⋊C₄×C₅₃	—	4	2	no	—
130	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
131	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
133	C₂²⋊C₄×C₅₃	—	2	2	no	—
134	C₂²⋊C₄×C₅₃	—	4	2	no	—
135	C₂²⋊C₄×C₅₃	—	4	2	no	—
136	C₄²×C₅₃	—	2	1	no	—
137	C₄²×C₅₃	—	2	1	no	—
138	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
139	C₂³×C₅₃	—	2	2	no	—
140	C₂³×C₅₃	—	4	2	no	—
141	Q₈×C₅₃	—	2	1	no	—
142	Q₈×C₅₃	—	2	1	no	—
143	Q₈×C₅₃	—	2	1	no	—
144	Q₈×C₅₃	—	8	2	no	—
145	Q₈×C₅₃	#135	1	2	yes	—
146	D₄×C₅₃	—	2	2	no	—
147	D₄×C₅₃	—	2	2	no	—
148	D₄×C₅₃	—	4	2	no	—
149	D₄×C₅₃	—	4	2	no	—
150	D₄×C₅₃	—	4	2	no	—
151	D₄×C₅₃	—	4	2	no	—
152	D₄×C₅₃	—	8	4	no	—
153	D₄×C₅₃	—	8	2	no	—
154	D₄×C₅₃	—	16	2	no	—
155	C₂×C₄×C₅₃	—	2	1	no	—
156	C₂×C₄×C₅₃	—	2	2	no	—
157	C₂×C₄×C₅₃	—	2	1	no	—
158	C₂×C₄×C₅₃	—	2	1	no	—
159	C₂×C₄×C₅₃	—	2	1	no	—
160	C₂×C₄×C₅₃	—	4	2	no	—
161	C₂×C₄×C₅₃	—	4	2	no	—
162	C₂×C₄×C₅₃	—	4	2	no	—
163	C₂×C₄×C₅₃	—	8	4	no	—
164	C₂×C₄×C₅₃	—	16	2	no	—
165	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
168	C₈×C₅₃	—	2	2	no	—
169	C₈×C₅₃	—	2	1	no	—
170	C₈×C₅₃	—	2	1	no	—
171	C₈×C₅₃	—	2	1	no	—
172	C₈×C₅₃	—	4	2	no	—
173	C₈×C₅₃	—	4	1	no	—
174	C₈×C₅₃	—	4	1	no	—
175	C₈×C₅₃	#137	1	2	yes	—
176	#19909	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂²×C₅₃	—	4	2	no	—
178	C₂²×C₅₃	—	4	2	no	—
179	C₂²×C₅₃	—	4	2	no	—
180	C₂²×C₅₃	—	8	2	no	—
181	C₂²×C₅₃	—	8	2	no	—
182	C₂²×C₅₃	—	8	2	no	—
183	C₂²×C₅₃	D₄²	1	1	yes	characteristic
184	C₄×C₅₃	—	2	2	no	—
185	C₄×C₅₃	—	2	1	no	—
186	C₄×C₅₃	—	4	2	no	—
187	C₄×C₅₃	—	4	1	no	—
188	C₄×C₅₃	—	4	1	no	—
189	C₄×C₅₃	—	4	1	no	—
190	C₄×C₅₃	—	8	2	no	—
191	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
192	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
193	C₄×C₅₃	#576	1	1	yes	characteristic
194	C₄×C₅₃	#577	1	1	yes	characteristic
195	#3391	C₂×C₅₃	1	1	yes	characteristic
196	#3380	C₂×C₅₃	1	1	yes	characteristic, complemented
197	#3333	C₂×C₅₃	1	2	yes	complemented
198	#1706	C₂×C₅₃	1	1	yes	characteristic, complemented
199	#1697	C₂×C₅₃	1	2	yes	complemented
200	#1676	C₂×C₅₃	1	1	yes	characteristic, complemented
201	#1668	C₂×C₅₃	1	1	yes	characteristic, complemented
202	#1631	C₂×C₅₃	1	2	yes	complemented
203	#1622	C₂×C₅₃	1	2	yes	complemented
204	#1589	C₂×C₅₃	1	1	yes	characteristic, complemented
205	C₈×Q₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
206	C₂×C₅₃	—	8	2	no	—
207	C₂×C₅₃	—	16	2	no	—
208	C₂×C₅₃	#3278	1	1	yes	characteristic
209	C₂×C₅₃	#3280	1	1	yes	characteristic
210	C₂×C₅₃	#3292	1	1	yes	characteristic
211	#554	C₂²×C₅₃	1	2	yes	—
212	#550	C₂²×C₅₃	1	2	yes	—
213	#500	C₂²×C₅₃	1	1	yes	characteristic
214	#499	—	2	1	no	—
215	#493	—	2	1	no	—
216	#493	C₂²×C₅₃	1	1	yes	characteristic
217	#492	C₂²×C₅₃	1	2	yes	—
218	#486	C₂²×C₅₃	1	2	yes	—
219	#480	—	2	2	no	—
220	#478	—	2	2	no	—
221	#477	C₂²×C₅₃	1	2	yes	—
222	#476	C₂²×C₅₃	1	2	yes	—
223	#468	—	2	2	no	—
224	#460	C₂²×C₅₃	1	2	yes	—
225	#459	—	2	2	no	—
226	#459	C₂²×C₅₃	1	2	yes	—
227	#452	—	2	2	no	—
228	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic
229	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic
230	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
231	C₄×D₈	—	2	1	no	—
232	C₄×D₈	—	2	1	no	—
233	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
234	#436	C₂²×C₅₃	1	2	yes	—
235	#417	—	2	2	no	—
236	#335	C₂²×C₅₃	1	1	yes	characteristic
237	#335	C₂²×C₅₃	1	1	yes	characteristic
238	#333	C₂²×C₅₃	1	2	yes	—
239	#331	C₂²×C₅₃	1	2	yes	—
240	Q₈⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
241	Q₈⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
242	D₄⋊C₈	C₂²×C₅₃	1	2	yes	—
243	C₈²	C₂²×C₅₃	1	1	yes	characteristic
244	C₅₃	#19909	1	1	yes	characteristic, direct product factor, Sylow
245	C₂×#41	—	2	2	no	—
246	C₂×Q₁₆	D₄×C₅₃	1	1	yes	characteristic
247	C₂×SD₁₆	—	2	2	no	—
248	C₂×SD₁₆	—	4	2	no	—
249	C₂×D₈	—	2	2	no	—
250	C₂×D₈	—	2	1	no	—
251	C₂×D₈	—	2	1	no	—
252	C₂×D₈	D₄×C₅₃	1	1	yes	characteristic
253	C₂×M₁₆	—	2	2	no	—
254	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
255	#127	—	2	2	no	—
256	#127	C₂³×C₅₃	1	2	yes	—
257	#125	—	2	2	no	—
258	C₂²⋊Q₈	—	2	2	no	—
259	C₂²⋊Q₈	—	4	2	no	—
260	#121	—	2	2	no	—
261	#121	—	4	2	no	—
262	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
263	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	C₂³×C₅₃	1	2	yes	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	#107	—	2	1	no	—
269	#107	—	2	1	no	—
270	#107	—	2	2	no	—
271	#107	D₄×C₅₃	1	1	yes	characteristic
272	#107	D₄×C₅₃	1	1	yes	characteristic
273	#106	—	2	2	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
277	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
278	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
279	#103	—	2	2	no	—
280	#103	D₄×C₅₃	1	1	yes	characteristic
281	#103	D₄×C₅₃	1	1	yes	characteristic
282	#102	—	2	2	no	—
283	#102	—	2	2	no	—
284	#102	—	2	2	no	—
285	#102	—	2	2	no	—
286	#102	—	2	2	no	—
287	#102	D₄×C₅₃	1	2	yes	—
288	C₂²⋊C₈	—	2	2	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
292	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
293	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
294	#41	—	4	4	no	—
295	#41	—	8	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
298	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	Q₁₆	—	2	2	no	—
309	SD₁₆	—	8	4	no	—
310	SD₁₆	—	8	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	4	2	no	—
313	D₈	—	8	1	no	—
314	D₈	—	8	2	no	—
315	M₁₆	—	8	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
321	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
322	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
323	C₂×C₈	C₂×D₄×C₅₃	1	1	yes	characteristic
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
331	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
332	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
339	C₂³	—	2	2	no	—
340	C₂³	—	4	2	no	—
341	Q₈	—	2	1	no	—
342	Q₈	—	2	1	no	—
343	Q₈	—	2	1	no	—
344	Q₈	—	8	2	no	—
345	Q₈	#135×C₅₃	1	2	yes	—
346	D₄	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	8	4	no	—
353	D₄	—	8	2	no	—
354	D₄	—	16	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	8	4	no	—
364	C₂×C₄	—	16	2	no	—
365	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
367	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
368	C₈	—	2	2	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	1	no	—
374	C₈	—	4	1	no	—
375	C₈	#137×C₅₃	1	2	yes	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	D₄²×C₅₃	1	1	yes	characteristic
383	C₄	—	2	2	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	1	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	8	2	no	—
390	C₄	C₂×#135×C₅₃	1	1	yes	characteristic
391	C₄	C₂×#137×C₅₃	1	1	yes	characteristic
392	C₄	C₅₃×#576	1	1	yes	characteristic
393	C₄	C₅₃×#577	1	1	yes	characteristic
394	C₂	—	8	2	no	—
395	C₂	—	16	2	no	—
396	C₂	C₅₃×#3278	1	1	yes	characteristic
397	C₂	C₅₃×#3280	1	1	yes	characteristic
398	C₂	C₅₃×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₃
prime radical	C₅₃×#3391	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#3380	C₂	semidirect
3. C₅₃×#3333	C₂	semidirect
4. C₅₃×#1706	C₂	semidirect
5. C₅₃×#1697	C₂	semidirect
6. C₅₃×#1676	C₂	semidirect
7. C₅₃×#1668	C₂	semidirect
8. C₅₃×#1631	C₂	semidirect
9. C₅₃×#1622	C₂	semidirect
10. C₅₃×#1589	C₂	semidirect
11. C₈×Q₁₆×C₅₃	C₂	semidirect
176. #19909	C₅₃	direct (N × H)
196. #3380	C₂×C₅₃	semidirect
197. #3333	C₂×C₅₃	semidirect
198. #1706	C₂×C₅₃	semidirect
199. #1697	C₂×C₅₃	semidirect
200. #1676	C₂×C₅₃	semidirect
201. #1668	C₂×C₅₃	semidirect
202. #1631	C₂×C₅₃	semidirect
203. #1622	C₂×C₅₃	semidirect
204. #1589	C₂×C₅₃	semidirect
205. C₈×Q₁₆	C₂×C₅₃	semidirect
244. C₅₃	#19909	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3391	2
C₅₃×#3380	2
C₅₃×#3333	2
C₅₃×#1706	2
C₅₃×#1697	2
C₅₃×#1676	2
C₅₃×#1668	2
C₅₃×#1631	2
C₅₃×#1622	2
C₅₃×#1589	2
C₈×Q₁₆×C₅₃	2
#19909	53

Subgroups — C53×#19909 #27227421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#19909 #27227421