Subgroups — C₅₃×#61633 #27269145

Order 13568.

2146 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3320	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3301	C₂	1	4	yes	maximal, complemented
5	D₄×SD₁₆×C₅₃	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3265	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3221	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3200	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3188	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3126	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3010	C₂	1	2	yes	maximal, complemented
12	C₂×C₅₃×#448	C₂	1	2	yes	maximal, complemented
13	C₅₃×#2977	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic, complemented
15	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
16	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
17	C₂²×SD₁₆×C₅₃	C₂²	1	4	yes	complemented
18	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
19	C₅₃×#560	—	2	2	no	—
20	C₅₃×#553	C₂²	1	4	yes	—
21	D₄×Q₈×C₅₃	—	2	2	no	—
22	D₄×Q₈×C₅₃	C₂²	1	4	yes	complemented
23	C₅₃×#548	—	2	2	no	—
24	C₅₃×#548	C₂²	1	4	yes	complemented
25	D₄²×C₅₃	—	2	2	no	—
26	D₄²×C₅₃	C₂²	1	4	yes	—
27	C₅₃×#540	C₂²	1	2	yes	—
28	C₅₃×#538	—	2	2	no	—
29	C₅₃×#536	—	2	2	no	—
30	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
32	C₅₃×#535	C₂²	1	2	yes	—
33	C₅₃×#534	—	2	2	no	—
34	C₅₃×#525	—	2	2	no	—
35	C₅₃×#525	C₂²	1	1	yes	characteristic
36	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
37	C₂×#121×C₅₃	C₂²	1	2	yes	—
38	C₅₃×#519	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#496	C₂²	1	2	yes	complemented
40	C₅₃×#492	C₂²	1	2	yes	complemented
41	C₅₃×#491	C₂²	1	2	yes	complemented
42	C₅₃×#488	C₂²	1	2	yes	complemented
43	C₅₃×#485	C₂²	1	4	yes	complemented
44	C₅₃×#484	C₂²	1	2	yes	complemented
45	C₅₃×#482	C₂²	1	4	yes	complemented
46	C₅₃×#481	C₂²	1	2	yes	complemented
47	C₅₃×#479	C₂²	1	4	yes	complemented
48	C₅₃×#468	C₂²	1	4	yes	complemented
49	C₅₃×#466	C₂²	1	4	yes	complemented
50	C₅₃×#465	C₂²	1	4	yes	complemented
51	C₅₃×#465	C₂²	1	4	yes	complemented
52	C₅₃×#463	C₂²	1	4	yes	complemented
53	C₅₃×#461	C₂²	1	4	yes	complemented
54	C₅₃×#460	C₂²	1	4	yes	complemented
55	C₅₃×#450	C₂²	1	4	yes	complemented
56	C₅₃×#450	C₂²	1	2	yes	complemented
57	C₅₃×#449	C₂²	1	4	yes	complemented
58	C₅₃×#449	C₂²	1	4	yes	complemented
59	C₅₃×#448	C₂²	1	4	yes	complemented
60	C₅₃×#448	C₂²	1	4	yes	complemented
61	C₅₃×#448	C₂²	1	4	yes	complemented
62	C₅₃×#448	C₂²	1	4	yes	complemented
63	C₅₃×#448	C₂²	1	4	yes	complemented
64	C₅₃×#447	C₂²	1	2	yes	complemented
65	C₅₃×#440	C₂²	1	4	yes	complemented
66	C₄×SD₁₆×C₅₃	C₂²	1	4	yes	complemented
67	C₅₃×#435	C₂²	1	4	yes	complemented
68	C₈×D₄×C₅₃	C₂²	1	4	yes	complemented
69	C₅₃×#433	C₂²	1	2	yes	complemented
70	C₅₃×#419	C₂²	1	2	yes	complemented
71	C₅₃×#416	C₂²	1	2	yes	complemented
72	C₂×#103×C₅₃	C₂²	1	4	yes	complemented
73	C₅₃×#408	C₂²	1	2	yes	complemented
74	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	complemented
75	2₋¹⁺⁴×C₅₃	—	4	4	no	—
76	C₂×#41×C₅₃	—	2	2	no	—
77	C₂×#41×C₅₃	—	2	1	no	—
78	C₂×#41×C₅₃	C₂³	1	2	yes	—
79	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
80	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₅₃	—	2	1	no	—
82	C₂²×Q₈×C₅₃	—	2	1	no	—
83	C₂²×Q₈×C₅₃	—	2	2	no	—
84	C₂²×Q₈×C₅₃	—	4	4	no	—
85	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
87	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
88	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₅₃	—	2	2	no	—
90	C₂²×D₄×C₅₃	—	2	4	no	—
91	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
92	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₅₃	—	2	1	no	—
94	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
95	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
96	C₂×SD₁₆×C₅₃	—	4	8	no	—
97	C₂×SD₁₆×C₅₃	—	4	4	no	—
98	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
103	C₂×D₈×C₅₃	C₂³	1	4	yes	—
104	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
105	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
106	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
107	C₄⋊Q₈×C₅₃	—	2	4	no	—
108	C₄⋊Q₈×C₅₃	—	2	1	no	—
109	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
110	#127×C₅₃	—	2	2	no	—
111	#127×C₅₃	C₂³	1	2	yes	—
112	#126×C₅₃	—	2	4	no	—
113	#125×C₅₃	C₂³	1	2	yes	—
114	#124×C₅₃	—	2	4	no	—
115	#124×C₅₃	—	2	2	no	—
116	#124×C₅₃	—	2	1	no	—
117	#124×C₅₃	C₂³	1	2	yes	—
118	#123×C₅₃	—	2	4	no	—
119	#123×C₅₃	—	2	2	no	—
120	#123×C₅₃	—	2	4	no	—
121	#123×C₅₃	—	2	2	no	—
122	#123×C₅₃	—	2	1	no	—
123	#123×C₅₃	D₄	1	2	yes	—
124	C₂²⋊Q₈×C₅₃	—	2	4	no	—
125	C₂²⋊Q₈×C₅₃	—	2	2	no	—
126	C₂²⋊Q₈×C₅₃	—	2	4	no	—
127	C₂²⋊Q₈×C₅₃	—	2	4	no	—
128	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
129	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
130	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
131	#121×C₅₃	—	2	4	no	—
132	#121×C₅₃	—	2	4	no	—
133	#121×C₅₃	—	2	4	no	—
134	#121×C₅₃	—	2	4	no	—
135	#121×C₅₃	—	2	2	no	—
136	#121×C₅₃	—	2	2	no	—
137	#121×C₅₃	D₄	1	2	yes	—
138	#121×C₅₃	C₂³	1	4	yes	—
139	#121×C₅₃	C₂³	1	4	yes	—
140	#121×C₅₃	C₂³	1	2	yes	—
141	#121×C₅₃	C₂³	1	4	yes	—
142	#120×C₅₃	—	2	4	no	—
143	#120×C₅₃	—	2	4	no	—
144	#120×C₅₃	—	2	1	no	—
145	#120×C₅₃	—	2	2	no	—
146	#120×C₅₃	—	2	2	no	—
147	#120×C₅₃	D₄	1	2	yes	—
148	C₄×Q₈×C₅₃	—	2	2	no	—
149	C₄×Q₈×C₅₃	C₂³	1	4	yes	—
150	C₄×D₄×C₅₃	—	2	4	no	—
151	C₄×D₄×C₅₃	—	2	4	no	—
152	C₄×D₄×C₅₃	—	2	4	no	—
153	C₄×D₄×C₅₃	—	2	2	no	—
154	C₄×D₄×C₅₃	C₂³	1	4	yes	—
155	C₄×D₄×C₅₃	C₂³	1	4	yes	—
156	#117×C₅₃	—	2	2	no	—
157	#117×C₅₃	C₂³	1	2	yes	—
158	#117×C₅₃	C₂³	1	1	yes	characteristic
159	#117×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
162	#107×C₅₃	C₂³	1	4	yes	—
163	#106×C₅₃	C₂³	1	4	yes	—
164	C₄⋊C₈×C₅₃	C₂³	1	4	yes	—
165	#103×C₅₃	C₂³	1	4	yes	—
166	#103×C₅₃	C₂³	1	4	yes	—
167	#103×C₅₃	C₂³	1	4	yes	—
168	#103×C₅₃	C₂³	1	4	yes	—
169	#103×C₅₃	C₂³	1	4	yes	—
170	#102×C₅₃	C₂³	1	4	yes	—
171	#102×C₅₃	C₂³	1	4	yes	—
172	#102×C₅₃	C₂³	1	4	yes	—
173	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
174	C₂²⋊C₈×C₅₃	C₂³	1	4	yes	—
175	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
176	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
177	#97×C₅₃	C₂³	1	2	yes	—
178	C₄×C₈×C₅₃	C₂³	1	2	yes	—
179	C₂⁴×C₅₃	—	2	2	no	—
180	C₂⁴×C₅₃	—	2	2	no	—
181	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
182	#41×C₅₃	—	2	4	no	—
183	#41×C₅₃	—	4	2	no	—
184	#41×C₅₃	—	4	2	no	—
185	#41×C₅₃	—	4	2	no	—
186	#41×C₅₃	—	4	8	no	—
187	#41×C₅₃	—	4	4	no	—
188	C₂×Q₈×C₅₃	—	2	4	no	—
189	C₂×Q₈×C₅₃	—	2	1	no	—
190	C₂×Q₈×C₅₃	—	2	4	no	—
191	C₂×Q₈×C₅₃	—	2	1	no	—
192	C₂×Q₈×C₅₃	—	2	2	no	—
193	C₂×Q₈×C₅₃	—	2	8	no	—
194	C₂×Q₈×C₅₃	—	2	4	no	—
195	C₂×Q₈×C₅₃	—	4	4	no	—
196	C₂×Q₈×C₅₃	—	4	2	no	—
197	C₂×Q₈×C₅₃	—	4	2	no	—
198	C₂×Q₈×C₅₃	—	4	4	no	—
199	C₂×Q₈×C₅₃	—	4	8	no	—
200	C₂×Q₈×C₅₃	—	4	4	no	—
201	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
202	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
203	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
204	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
205	C₂×D₄×C₅₃	—	2	2	no	—
206	C₂×D₄×C₅₃	—	2	4	no	—
207	C₂×D₄×C₅₃	—	2	1	no	—
208	C₂×D₄×C₅₃	—	2	2	no	—
209	C₂×D₄×C₅₃	—	2	4	no	—
210	C₂×D₄×C₅₃	—	2	4	no	—
211	C₂×D₄×C₅₃	—	2	2	no	—
212	C₂×D₄×C₅₃	—	2	4	no	—
213	C₂×D₄×C₅₃	—	2	2	no	—
214	C₂×D₄×C₅₃	—	4	4	no	—
215	C₂×D₄×C₅₃	—	4	2	no	—
216	C₂×D₄×C₅₃	—	4	2	no	—
217	C₂×D₄×C₅₃	—	8	8	no	—
218	C₂×D₄×C₅₃	—	8	4	no	—
219	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
220	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
221	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
222	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
223	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₅₃	—	2	1	no	—
225	C₂²×C₄×C₅₃	—	2	4	no	—
226	C₂²×C₄×C₅₃	—	2	2	no	—
227	C₂²×C₄×C₅₃	—	2	1	no	—
228	C₂²×C₄×C₅₃	—	2	2	no	—
229	C₂²×C₄×C₅₃	—	2	2	no	—
230	C₂²×C₄×C₅₃	—	2	1	no	—
231	C₂²×C₄×C₅₃	—	2	4	no	—
232	C₂²×C₄×C₅₃	—	4	2	no	—
233	C₂²×C₄×C₅₃	—	4	4	no	—
234	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
239	SD₁₆×C₅₃	—	2	8	no	—
240	SD₁₆×C₅₃	—	2	8	no	—
241	SD₁₆×C₅₃	—	4	4	no	—
242	SD₁₆×C₅₃	—	4	4	no	—
243	SD₁₆×C₅₃	—	4	4	no	—
244	D₈×C₅₃	—	4	4	no	—
245	M₁₆×C₅₃	—	4	2	no	—
246	C₂×C₈×C₅₃	—	4	2	no	—
247	C₂×C₈×C₅₃	—	4	4	no	—
248	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
249	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
250	C₄⋊C₄×C₅₃	—	2	2	no	—
251	C₄⋊C₄×C₅₃	—	2	4	no	—
252	C₄⋊C₄×C₅₃	—	2	4	no	—
253	C₄⋊C₄×C₅₃	—	2	4	no	—
254	C₄⋊C₄×C₅₃	—	2	2	no	—
255	C₄⋊C₄×C₅₃	—	2	4	no	—
256	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
258	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
260	C₂²⋊C₄×C₅₃	—	2	1	no	—
261	C₂²⋊C₄×C₅₃	—	2	2	no	—
262	C₂²⋊C₄×C₅₃	—	2	2	no	—
263	C₂²⋊C₄×C₅₃	—	2	4	no	—
264	C₂²⋊C₄×C₅₃	—	2	4	no	—
265	C₂²⋊C₄×C₅₃	—	2	4	no	—
266	C₂²⋊C₄×C₅₃	—	2	4	no	—
267	C₂²⋊C₄×C₅₃	—	2	4	no	—
268	C₂²⋊C₄×C₅₃	—	2	2	no	—
269	C₂²⋊C₄×C₅₃	—	2	4	no	—
270	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
271	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
272	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
273	C₄²×C₅₃	—	2	4	no	—
274	C₄²×C₅₃	—	2	1	no	—
275	C₄²×C₅₃	—	2	2	no	—
276	C₄²×C₅₃	C₂⁴	1	2	yes	—
277	C₂³×C₅₃	—	2	4	no	—
278	C₂³×C₅₃	—	2	1	no	—
279	C₂³×C₅₃	—	2	4	no	—
280	C₂³×C₅₃	—	4	1	no	—
281	C₂³×C₅₃	—	4	4	no	—
282	C₂³×C₅₃	—	8	2	no	—
283	C₂³×C₅₃	—	8	2	no	—
284	C₂³×C₅₃	—	8	2	no	—
285	C₂³×C₅₃	—	8	4	no	—
286	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
287	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
288	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
289	Q₈×C₅₃	—	2	4	no	—
290	Q₈×C₅₃	—	2	2	no	—
291	Q₈×C₅₃	—	2	4	no	—
292	Q₈×C₅₃	—	2	2	no	—
293	Q₈×C₅₃	—	4	1	no	—
294	Q₈×C₅₃	—	4	8	no	—
295	Q₈×C₅₃	—	4	4	no	—
296	Q₈×C₅₃	—	4	2	no	—
297	Q₈×C₅₃	H(5,𝔽₂)	1	4	yes	—
298	D₄×C₅₃	—	2	8	no	—
299	D₄×C₅₃	—	2	4	no	—
300	D₄×C₅₃	—	2	4	no	—
301	D₄×C₅₃	—	2	2	no	—
302	D₄×C₅₃	—	4	1	no	—
303	D₄×C₅₃	—	4	2	no	—
304	D₄×C₅₃	—	4	4	no	—
305	D₄×C₅₃	—	4	2	no	—
306	D₄×C₅₃	—	4	4	no	—
307	D₄×C₅₃	—	4	8	no	—
308	D₄×C₅₃	—	8	2	no	—
309	D₄×C₅₃	—	8	2	no	—
310	D₄×C₅₃	—	8	4	no	—
311	D₄×C₅₃	—	8	4	no	—
312	D₄×C₅₃	—	8	4	no	—
313	C₂×C₄×C₅₃	—	2	4	no	—
314	C₂×C₄×C₅₃	—	2	2	no	—
315	C₂×C₄×C₅₃	—	2	4	no	—
316	C₂×C₄×C₅₃	—	2	2	no	—
317	C₂×C₄×C₅₃	—	2	2	no	—
318	C₂×C₄×C₅₃	—	2	2	no	—
319	C₂×C₄×C₅₃	—	2	1	no	—
320	C₂×C₄×C₅₃	—	2	2	no	—
321	C₂×C₄×C₅₃	—	2	4	no	—
322	C₂×C₄×C₅₃	—	2	2	no	—
323	C₂×C₄×C₅₃	—	4	2	no	—
324	C₂×C₄×C₅₃	—	4	1	no	—
325	C₂×C₄×C₅₃	—	4	4	no	—
326	C₂×C₄×C₅₃	—	4	8	no	—
327	C₂×C₄×C₅₃	—	4	4	no	—
328	C₂×C₄×C₅₃	—	4	2	no	—
329	C₂×C₄×C₅₃	—	4	2	no	—
330	C₂×C₄×C₅₃	—	8	4	no	—
331	C₂×C₄×C₅₃	—	8	2	no	—
332	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
335	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
337	C₈×C₅₃	—	2	4	no	—
338	C₈×C₅₃	—	2	4	no	—
339	#61633	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂²×C₅₃	—	2	2	no	—
341	C₂²×C₅₃	—	2	2	no	—
342	C₂²×C₅₃	—	2	1	no	—
343	C₂²×C₅₃	—	2	2	no	—
344	C₂²×C₅₃	—	2	4	no	—
345	C₂²×C₅₃	—	2	2	no	—
346	C₂²×C₅₃	—	4	4	no	—
347	C₂²×C₅₃	—	4	1	no	—
348	C₂²×C₅₃	—	4	4	no	—
349	C₂²×C₅₃	—	4	4	no	—
350	C₂²×C₅₃	—	4	4	no	—
351	C₂²×C₅₃	—	4	2	no	—
352	C₂²×C₅₃	—	16	4	no	—
353	C₂²×C₅₃	—	16	4	no	—
354	C₂²×C₅₃	#577	1	4	yes	—
355	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
356	C₄×C₅₃	—	2	4	no	—
357	C₄×C₅₃	—	2	1	no	—
358	C₄×C₅₃	—	2	2	no	—
359	C₄×C₅₃	—	2	2	no	—
360	C₄×C₅₃	—	2	4	no	—
361	C₄×C₅₃	—	4	1	no	—
362	C₄×C₅₃	—	4	2	no	—
363	C₄×C₅₃	—	4	4	no	—
364	C₄×C₅₃	—	4	2	no	—
365	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
366	#3537	C₂×C₅₃	1	1	yes	characteristic, complemented
367	#3486	C₂×C₅₃	1	1	yes	characteristic, complemented
368	#3320	C₂×C₅₃	1	4	yes	complemented
369	#3301	C₂×C₅₃	1	4	yes	complemented
370	D₄×SD₁₆	C₂×C₅₃	1	4	yes	complemented
371	#3265	C₂×C₅₃	1	4	yes	complemented
372	#3221	C₂×C₅₃	1	2	yes	complemented
373	#3200	C₂×C₅₃	1	2	yes	complemented
374	#3188	C₂×C₅₃	1	2	yes	complemented
375	#3126	C₂×C₅₃	1	2	yes	complemented
376	#3010	C₂×C₅₃	1	2	yes	complemented
377	C₂×#448	C₂×C₅₃	1	2	yes	complemented
378	#2977	C₂×C₅₃	1	1	yes	characteristic, complemented
379	C₂×C₅₃	—	2	4	no	—
380	C₂×C₅₃	—	4	1	no	—
381	C₂×C₅₃	—	4	2	no	—
382	C₂×C₅₃	—	8	1	no	—
383	C₂×C₅₃	—	8	4	no	—
384	C₂×C₅₃	#3484	1	1	yes	characteristic
385	C₂×C₅₃	C₂×#577	1	2	yes	—
386	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic, complemented
387	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
388	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
389	C₂²×SD₁₆	C₂²×C₅₃	1	4	yes	complemented
390	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
391	#560	—	2	2	no	—
392	#553	C₂²×C₅₃	1	4	yes	—
393	D₄×Q₈	—	2	2	no	—
394	D₄×Q₈	C₂²×C₅₃	1	4	yes	complemented
395	#548	—	2	2	no	—
396	#548	C₂²×C₅₃	1	4	yes	complemented
397	D₄²	—	2	2	no	—
398	D₄²	C₂²×C₅₃	1	4	yes	—
399	#540	C₂²×C₅₃	1	2	yes	—
400	#538	—	2	2	no	—
401	#536	—	2	2	no	—
402	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
403	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
404	#535	C₂²×C₅₃	1	2	yes	—
405	#534	—	2	2	no	—
406	#525	—	2	2	no	—
407	#525	C₂²×C₅₃	1	1	yes	characteristic
408	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
409	C₂×#121	C₂²×C₅₃	1	2	yes	—
410	#519	C₂²×C₅₃	1	1	yes	characteristic, complemented
411	#496	C₂²×C₅₃	1	2	yes	complemented
412	#492	C₂²×C₅₃	1	2	yes	complemented
413	#491	C₂²×C₅₃	1	2	yes	complemented
414	#488	C₂²×C₅₃	1	2	yes	complemented
415	#485	C₂²×C₅₃	1	4	yes	complemented
416	#484	C₂²×C₅₃	1	2	yes	complemented
417	#482	C₂²×C₅₃	1	4	yes	complemented
418	#481	C₂²×C₅₃	1	2	yes	complemented
419	#479	C₂²×C₅₃	1	4	yes	complemented
420	#468	C₂²×C₅₃	1	4	yes	complemented
421	#466	C₂²×C₅₃	1	4	yes	complemented
422	#465	C₂²×C₅₃	1	4	yes	complemented
423	#465	C₂²×C₅₃	1	4	yes	complemented
424	#463	C₂²×C₅₃	1	4	yes	complemented
425	#461	C₂²×C₅₃	1	4	yes	complemented
426	#460	C₂²×C₅₃	1	4	yes	complemented
427	#450	C₂²×C₅₃	1	2	yes	complemented
428	#450	C₂²×C₅₃	1	4	yes	complemented
429	#449	C₂²×C₅₃	1	4	yes	complemented
430	#449	C₂²×C₅₃	1	4	yes	complemented
431	#448	C₂²×C₅₃	1	4	yes	complemented
432	#448	C₂²×C₅₃	1	4	yes	complemented
433	#448	C₂²×C₅₃	1	4	yes	complemented
434	#448	C₂²×C₅₃	1	4	yes	complemented
435	#448	C₂²×C₅₃	1	4	yes	complemented
436	#447	C₂²×C₅₃	1	2	yes	complemented
437	#440	C₂²×C₅₃	1	4	yes	complemented
438	C₄×SD₁₆	C₂²×C₅₃	1	4	yes	complemented
439	#435	C₂²×C₅₃	1	4	yes	complemented
440	C₈×D₄	C₂²×C₅₃	1	4	yes	complemented
441	#433	C₂²×C₅₃	1	2	yes	complemented
442	#419	C₂²×C₅₃	1	2	yes	complemented
443	#416	C₂²×C₅₃	1	2	yes	complemented
444	C₂×#103	C₂²×C₅₃	1	4	yes	complemented
445	#408	C₂²×C₅₃	1	2	yes	complemented
446	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	complemented
447	C₅₃	#61633	1	1	yes	characteristic, direct product factor, Sylow
448	2₋¹⁺⁴	—	4	4	no	—
449	C₂×#41	—	2	2	no	—
450	C₂×#41	—	2	1	no	—
451	C₂×#41	C₂³×C₅₃	1	2	yes	—
452	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
453	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
454	C₂²×Q₈	—	2	1	no	—
455	C₂²×Q₈	—	2	1	no	—
456	C₂²×Q₈	—	2	2	no	—
457	C₂²×Q₈	—	4	4	no	—
458	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
459	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
460	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
461	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
462	C₂²×D₄	—	2	2	no	—
463	C₂²×D₄	—	2	4	no	—
464	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
465	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
466	C₂³×C₄	—	2	1	no	—
467	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
468	AGL(1,ℤ/8)	—	4	4	no	—
469	C₂×SD₁₆	—	4	4	no	—
470	C₂×SD₁₆	—	4	8	no	—
471	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
472	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
473	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
474	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
475	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
476	C₂×D₈	C₂³×C₅₃	1	4	yes	—
477	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
478	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
479	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
480	C₄⋊Q₈	—	2	1	no	—
481	C₄⋊Q₈	—	2	4	no	—
482	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
483	#127	—	2	2	no	—
484	#127	C₂³×C₅₃	1	2	yes	—
485	#126	—	2	4	no	—
486	#125	C₂³×C₅₃	1	2	yes	—
487	#124	—	2	2	no	—
488	#124	—	2	1	no	—
489	#124	—	2	4	no	—
490	#124	C₂³×C₅₃	1	2	yes	—
491	#123	—	2	2	no	—
492	#123	—	2	1	no	—
493	#123	—	2	4	no	—
494	#123	—	2	2	no	—
495	#123	—	2	4	no	—
496	#123	D₄×C₅₃	1	2	yes	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	—	2	2	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
502	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
503	C₂²⋊Q₈	C₂³×C₅₃	1	4	yes	—
504	#121	—	2	4	no	—
505	#121	—	2	4	no	—
506	#121	—	2	2	no	—
507	#121	—	2	2	no	—
508	#121	—	2	4	no	—
509	#121	—	2	4	no	—
510	#121	D₄×C₅₃	1	2	yes	—
511	#121	C₂³×C₅₃	1	4	yes	—
512	#121	C₂³×C₅₃	1	4	yes	—
513	#121	C₂³×C₅₃	1	2	yes	—
514	#121	C₂³×C₅₃	1	4	yes	—
515	#120	—	2	1	no	—
516	#120	—	2	2	no	—
517	#120	—	2	2	no	—
518	#120	—	2	4	no	—
519	#120	—	2	4	no	—
520	#120	D₄×C₅₃	1	2	yes	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	C₂³×C₅₃	1	4	yes	—
523	C₄×D₄	—	2	4	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	—	2	4	no	—
527	C₄×D₄	C₂³×C₅₃	1	4	yes	—
528	C₄×D₄	C₂³×C₅₃	1	4	yes	—
529	#117	—	2	2	no	—
530	#117	C₂³×C₅₃	1	1	yes	characteristic
531	#117	C₂³×C₅₃	1	2	yes	—
532	#117	C₂³×C₅₃	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
534	C₂×C₂²⋊C₄	—	2	2	no	—
535	#107	C₂³×C₅₃	1	4	yes	—
536	#106	C₂³×C₅₃	1	4	yes	—
537	C₄⋊C₈	C₂³×C₅₃	1	4	yes	—
538	#103	C₂³×C₅₃	1	4	yes	—
539	#103	C₂³×C₅₃	1	4	yes	—
540	#103	C₂³×C₅₃	1	4	yes	—
541	#103	C₂³×C₅₃	1	4	yes	—
542	#103	C₂³×C₅₃	1	4	yes	—
543	#102	C₂³×C₅₃	1	4	yes	—
544	#102	C₂³×C₅₃	1	4	yes	—
545	#102	C₂³×C₅₃	1	4	yes	—
546	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
547	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
548	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
549	C₂²⋊C₈	C₂³×C₅₃	1	4	yes	—
550	#97	C₂³×C₅₃	1	2	yes	—
551	C₄×C₈	C₂³×C₅₃	1	2	yes	—
552	C₂⁴	—	2	2	no	—
553	C₂⁴	—	2	2	no	—
554	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
555	#41	—	2	4	no	—
556	#41	—	4	2	no	—
557	#41	—	4	2	no	—
558	#41	—	4	2	no	—
559	#41	—	4	8	no	—
560	#41	—	4	4	no	—
561	C₂×Q₈	—	2	4	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	4	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	2	8	no	—
567	C₂×Q₈	—	2	4	no	—
568	C₂×Q₈	—	4	4	no	—
569	C₂×Q₈	—	4	2	no	—
570	C₂×Q₈	—	4	2	no	—
571	C₂×Q₈	—	4	4	no	—
572	C₂×Q₈	—	4	8	no	—
573	C₂×Q₈	—	4	4	no	—
574	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
575	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
576	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
577	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	4	4	no	—
588	C₂×D₄	—	4	2	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	—	8	8	no	—
591	C₂×D₄	—	8	4	no	—
592	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
593	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
594	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
595	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
596	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	—	4	4	no	—
607	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
608	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
612	SD₁₆	—	2	8	no	—
613	SD₁₆	—	2	8	no	—
614	SD₁₆	—	4	4	no	—
615	SD₁₆	—	4	4	no	—
616	SD₁₆	—	4	4	no	—
617	D₈	—	4	4	no	—
618	M₁₆	—	4	2	no	—
619	C₂×C₈	—	4	2	no	—
620	C₂×C₈	—	4	4	no	—
621	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
622	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
630	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
631	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
632	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
644	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
645	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
646	C₄²	—	2	4	no	—
647	C₄²	—	2	1	no	—
648	C₄²	—	2	2	no	—
649	C₄²	C₂⁴×C₅₃	1	2	yes	—
650	C₂³	—	2	4	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	4	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	4	no	—
655	C₂³	—	8	2	no	—
656	C₂³	—	8	2	no	—
657	C₂³	—	8	2	no	—
658	C₂³	—	8	4	no	—
659	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
660	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
661	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
662	Q₈	—	2	4	no	—
663	Q₈	—	2	2	no	—
664	Q₈	—	2	4	no	—
665	Q₈	—	2	2	no	—
666	Q₈	—	4	1	no	—
667	Q₈	—	4	8	no	—
668	Q₈	—	4	4	no	—
669	Q₈	—	4	2	no	—
670	Q₈	H(5,𝔽₂)×C₅₃	1	4	yes	—
671	D₄	—	2	8	no	—
672	D₄	—	2	2	no	—
673	D₄	—	2	4	no	—
674	D₄	—	2	4	no	—
675	D₄	—	4	1	no	—
676	D₄	—	4	2	no	—
677	D₄	—	4	4	no	—
678	D₄	—	4	2	no	—
679	D₄	—	4	4	no	—
680	D₄	—	4	8	no	—
681	D₄	—	8	2	no	—
682	D₄	—	8	2	no	—
683	D₄	—	8	4	no	—
684	D₄	—	8	4	no	—
685	D₄	—	8	4	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	4	2	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	8	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	2	no	—
702	C₂×C₄	—	4	2	no	—
703	C₂×C₄	—	8	4	no	—
704	C₂×C₄	—	8	2	no	—
705	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
706	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
708	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
709	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
710	C₈	—	2	4	no	—
711	C₈	—	2	4	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	4	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	4	4	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	4	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	16	4	no	—
725	C₂²	—	16	4	no	—
726	C₂²	C₅₃×#577	1	4	yes	—
727	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
728	C₄	—	2	4	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	4	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	4	no	—
736	C₄	—	4	2	no	—
737	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
738	C₂	—	2	4	no	—
739	C₂	—	4	1	no	—
740	C₂	—	4	2	no	—
741	C₂	—	8	4	no	—
742	C₂	—	8	1	no	—
743	C₂	C₅₃×#3484	1	1	yes	characteristic
744	C₂	C₂×C₅₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3537	C₂	semidirect
2. C₅₃×#3486	C₂	semidirect
3. C₅₃×#3320	C₂	semidirect
4. C₅₃×#3301	C₂	semidirect
5. D₄×SD₁₆×C₅₃	C₂	semidirect
6. C₅₃×#3265	C₂	semidirect
7. C₅₃×#3221	C₂	semidirect
8. C₅₃×#3200	C₂	semidirect
9. C₅₃×#3188	C₂	semidirect
10. C₅₃×#3126	C₂	semidirect
11. C₅₃×#3010	C₂	semidirect
12. C₂×C₅₃×#448	C₂	semidirect
13. C₅₃×#2977	C₂	semidirect
14. C₂×2₋¹⁺⁴×C₅₃	C₂²	semidirect
15. C₂³×Q₈×C₅₃	C₂²	semidirect
16. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
17. C₂²×SD₁₆×C₅₃	C₂²	semidirect
18. C₂²×SD₁₆×C₅₃	C₂²	semidirect
22. D₄×Q₈×C₅₃	C₂²	semidirect
24. C₅₃×#548	C₂²	semidirect
30. C₅₃×#536	C₂²	semidirect
31. C₅₃×#536	C₂²	semidirect
36. C₅₃×#525	C₂²	semidirect
38. C₅₃×#519	C₂²	semidirect
39. C₅₃×#496	C₂²	semidirect
40. C₅₃×#492	C₂²	semidirect
41. C₅₃×#491	C₂²	semidirect
42. C₅₃×#488	C₂²	semidirect
43. C₅₃×#485	C₂²	semidirect
44. C₅₃×#484	C₂²	semidirect
45. C₅₃×#482	C₂²	semidirect
46. C₅₃×#481	C₂²	semidirect
47. C₅₃×#479	C₂²	semidirect
48. C₅₃×#468	C₂²	semidirect
49. C₅₃×#466	C₂²	semidirect
50. C₅₃×#465	C₂²	semidirect
51. C₅₃×#465	C₂²	semidirect
52. C₅₃×#463	C₂²	semidirect
53. C₅₃×#461	C₂²	semidirect
54. C₅₃×#460	C₂²	semidirect
55. C₅₃×#450	C₂²	semidirect
56. C₅₃×#450	C₂²	semidirect
57. C₅₃×#449	C₂²	semidirect
58. C₅₃×#449	C₂²	semidirect
59. C₅₃×#448	C₂²	semidirect
60. C₅₃×#448	C₂²	semidirect
61. C₅₃×#448	C₂²	semidirect
62. C₅₃×#448	C₂²	semidirect
63. C₅₃×#448	C₂²	semidirect
64. C₅₃×#447	C₂²	semidirect
65. C₅₃×#440	C₂²	semidirect
66. C₄×SD₁₆×C₅₃	C₂²	semidirect
67. C₅₃×#435	C₂²	semidirect
68. C₈×D₄×C₅₃	C₂²	semidirect
69. C₅₃×#433	C₂²	semidirect
70. C₅₃×#419	C₂²	semidirect
71. C₅₃×#416	C₂²	semidirect
72. C₂×#103×C₅₃	C₂²	semidirect
73. C₅₃×#408	C₂²	semidirect
74. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
339. #61633	C₅₃	direct (N × H)
366. #3537	C₂×C₅₃	semidirect
367. #3486	C₂×C₅₃	semidirect
368. #3320	C₂×C₅₃	semidirect
369. #3301	C₂×C₅₃	semidirect
370. D₄×SD₁₆	C₂×C₅₃	semidirect
371. #3265	C₂×C₅₃	semidirect
372. #3221	C₂×C₅₃	semidirect
373. #3200	C₂×C₅₃	semidirect
374. #3188	C₂×C₅₃	semidirect
375. #3126	C₂×C₅₃	semidirect
376. #3010	C₂×C₅₃	semidirect
377. C₂×#448	C₂×C₅₃	semidirect
378. #2977	C₂×C₅₃	semidirect
386. C₂×2₋¹⁺⁴	C₂²×C₅₃	semidirect
387. C₂³×Q₈	C₂²×C₅₃	semidirect
388. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
389. C₂²×SD₁₆	C₂²×C₅₃	semidirect
390. C₂²×SD₁₆	C₂²×C₅₃	semidirect
394. D₄×Q₈	C₂²×C₅₃	semidirect
396. #548	C₂²×C₅₃	semidirect
402. #536	C₂²×C₅₃	semidirect
403. #536	C₂²×C₅₃	semidirect
408. #525	C₂²×C₅₃	semidirect
410. #519	C₂²×C₅₃	semidirect
411. #496	C₂²×C₅₃	semidirect
412. #492	C₂²×C₅₃	semidirect
413. #491	C₂²×C₅₃	semidirect
414. #488	C₂²×C₅₃	semidirect
415. #485	C₂²×C₅₃	semidirect
416. #484	C₂²×C₅₃	semidirect
417. #482	C₂²×C₅₃	semidirect
418. #481	C₂²×C₅₃	semidirect
419. #479	C₂²×C₅₃	semidirect
420. #468	C₂²×C₅₃	semidirect
421. #466	C₂²×C₅₃	semidirect
422. #465	C₂²×C₅₃	semidirect
423. #465	C₂²×C₅₃	semidirect
424. #463	C₂²×C₅₃	semidirect
425. #461	C₂²×C₅₃	semidirect
426. #460	C₂²×C₅₃	semidirect
427. #450	C₂²×C₅₃	semidirect
428. #450	C₂²×C₅₃	semidirect
429. #449	C₂²×C₅₃	semidirect
430. #449	C₂²×C₅₃	semidirect
431. #448	C₂²×C₅₃	semidirect
432. #448	C₂²×C₅₃	semidirect
433. #448	C₂²×C₅₃	semidirect
434. #448	C₂²×C₅₃	semidirect
435. #448	C₂²×C₅₃	semidirect
436. #447	C₂²×C₅₃	semidirect
437. #440	C₂²×C₅₃	semidirect
438. C₄×SD₁₆	C₂²×C₅₃	semidirect
439. #435	C₂²×C₅₃	semidirect
440. C₈×D₄	C₂²×C₅₃	semidirect
441. #433	C₂²×C₅₃	semidirect
442. #419	C₂²×C₅₃	semidirect
443. #416	C₂²×C₅₃	semidirect
444. C₂×#103	C₂²×C₅₃	semidirect
445. #408	C₂²×C₅₃	semidirect
446. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
447. C₅₃	#61633	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×#3537	2
C₅₃×#3486	2
C₅₃×#3320	2
C₅₃×#3301	2
D₄×SD₁₆×C₅₃	2
C₅₃×#3265	2
C₅₃×#3221	2
C₅₃×#3200	2
C₅₃×#3188	2
C₅₃×#3126	2
C₅₃×#3010	2
C₂×C₅₃×#448	2
C₅₃×#2977	2
#61633	53

Subgroups — C53×#61633 #27269145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61633 #27269145