Subgroups — C₅₃×#60825 #27268337

Order 13568.

2146 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3221	C₂	1	4	yes	maximal, complemented
4	C₅₃×#3220	C₂	1	4	yes	maximal, complemented
5	C₅₃×#3214	C₂	1	4	yes	maximal, complemented
6	C₅₃×#3213	C₂	1	4	yes	maximal, complemented
7	C₅₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3042	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3041	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3010	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3008	C₂	1	2	yes	maximal, complemented
15	C₅₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
18	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
20	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
21	C₂²×D₈×C₅₃	C₂²	1	2	yes	—
22	C₅₃×#559	—	2	2	no	—
23	C₅₃×#550	—	2	2	no	—
24	C₅₃×#548	—	2	2	no	—
25	C₅₃×#546	—	2	4	no	—
26	C₅₃×#546	—	2	2	no	—
27	C₅₃×#546	—	2	4	no	—
28	C₅₃×#540	C₂²	1	4	yes	complemented
29	C₅₃×#536	C₂²	1	1	yes	characteristic
30	C₅₃×#536	C₂²	1	2	yes	complemented
31	C₅₃×#535	C₂²	1	1	yes	characteristic
32	C₅₃×#535	C₂²	1	2	yes	—
33	C₅₃×#535	C₂²	1	2	yes	complemented
34	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
35	C₅₃×#532	C₂²	1	1	yes	characteristic
36	C₅₃×#532	C₂²	1	2	yes	complemented
37	C₅₃×#532	C₂²	1	4	yes	complemented
38	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
41	C₅₃×#518	C₂²	1	2	yes	complemented
42	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#496	C₂²	1	2	yes	complemented
44	C₅₃×#496	C₂²	1	4	yes	complemented
45	C₅₃×#496	C₂²	1	2	yes	complemented
46	C₅₃×#496	C₂²	1	4	yes	complemented
47	C₅₃×#493	C₂²	1	2	yes	complemented
48	C₅₃×#492	C₂²	1	2	yes	complemented
49	C₅₃×#491	C₂²	1	2	yes	complemented
50	C₅₃×#490	C₂²	1	2	yes	complemented
51	C₅₃×#489	C₂²	1	2	yes	complemented
52	C₅₃×#489	C₂²	1	4	yes	complemented
53	C₅₃×#489	C₂²	1	2	yes	complemented
54	C₅₃×#488	C₂²	1	4	yes	complemented
55	C₅₃×#463	C₂²	1	8	yes	complemented
56	C₅₃×#463	C₂²	1	8	yes	complemented
57	C₅₃×#461	C₂²	1	8	yes	complemented
58	C₅₃×#459	C₂²	1	8	yes	complemented
59	C₅₃×#449	C₂²	1	8	yes	complemented
60	C₅₃×#449	C₂²	1	8	yes	complemented
61	C₅₃×#448	C₂²	1	8	yes	complemented
62	C₅₃×#447	C₂²	1	8	yes	complemented
63	C₅₃×#433	C₂²	1	4	yes	complemented
64	C₅₃×#432	C₂²	1	4	yes	complemented
65	C₅₃×#424	C₂²	1	2	yes	complemented
66	C₅₃×#419	C₂²	1	2	yes	complemented
67	C₅₃×#418	C₂²	1	2	yes	—
68	C₅₃×#416	C₂²	1	2	yes	—
69	C₅₃×#416	C₂²	1	2	yes	complemented
70	C₅₃×#408	C₂²	1	2	yes	—
71	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
72	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic, complemented
73	2₋¹⁺⁴×C₅₃	—	4	4	no	—
74	H(5,𝔽₂)×C₅₃	—	4	4	no	—
75	C₂×#41×C₅₃	—	2	1	no	—
76	C₂×#41×C₅₃	—	2	2	no	—
77	C₂×#41×C₅₃	—	2	1	no	—
78	C₂×#41×C₅₃	—	2	4	no	—
79	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
80	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
81	C₂×#41×C₅₃	C₂³	1	2	yes	—
82	C₂×#41×C₅₃	C₂³	1	2	yes	—
83	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₅₃	—	2	1	no	—
85	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
87	C₂²×D₄×C₅₃	—	2	2	no	—
88	C₂²×D₄×C₅₃	—	2	1	no	—
89	C₂²×D₄×C₅₃	—	2	2	no	—
90	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
93	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
94	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
95	C₂×SD₁₆×C₅₃	—	4	4	no	—
96	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
97	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₅₃	C₂³	1	8	yes	—
99	C₂×D₈×C₅₃	—	4	4	no	—
100	C₂×D₈×C₅₃	C₂³	1	4	yes	—
101	C₂×D₈×C₅₃	C₂³	1	4	yes	—
102	C₂×D₈×C₅₃	C₂³	1	8	yes	—
103	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
104	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
105	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
106	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
108	#127×C₅₃	—	2	2	no	—
109	#127×C₅₃	—	2	2	no	—
110	#127×C₅₃	C₂³	1	1	yes	characteristic
111	#127×C₅₃	C₂³	1	2	yes	—
112	#127×C₅₃	C₂³	1	2	yes	—
113	#127×C₅₃	C₂³	1	2	yes	—
114	#125×C₅₃	C₂³	1	2	yes	—
115	#124×C₅₃	—	2	2	no	—
116	#124×C₅₃	—	2	4	no	—
117	#124×C₅₃	—	2	4	no	—
118	#124×C₅₃	—	2	2	no	—
119	#124×C₅₃	C₂³	1	2	yes	—
120	#124×C₅₃	C₂³	1	2	yes	—
121	#124×C₅₃	C₂³	1	1	yes	characteristic
122	#124×C₅₃	C₂³	1	1	yes	characteristic
123	#124×C₅₃	C₂³	1	2	yes	—
124	#124×C₅₃	C₂³	1	2	yes	—
125	#123×C₅₃	—	2	8	no	—
126	#123×C₅₃	—	2	2	no	—
127	#123×C₅₃	—	2	4	no	—
128	C₂²⋊Q₈×C₅₃	—	2	2	no	—
129	C₂²⋊Q₈×C₅₃	—	2	4	no	—
130	C₂²⋊Q₈×C₅₃	—	2	2	no	—
131	#121×C₅₃	—	2	2	no	—
132	#121×C₅₃	—	2	4	no	—
133	#121×C₅₃	—	2	8	no	—
134	#121×C₅₃	—	2	2	no	—
135	#121×C₅₃	—	2	4	no	—
136	#121×C₅₃	—	2	4	no	—
137	#121×C₅₃	C₂³	1	8	yes	—
138	#120×C₅₃	—	2	2	no	—
139	#120×C₅₃	—	2	4	no	—
140	#120×C₅₃	—	2	4	no	—
141	C₄×Q₈×C₅₃	—	2	2	no	—
142	C₄×Q₈×C₅₃	D₄	1	2	yes	—
143	C₄×D₄×C₅₃	—	2	4	no	—
144	C₄×D₄×C₅₃	—	2	2	no	—
145	C₄×D₄×C₅₃	—	2	4	no	—
146	C₄×D₄×C₅₃	—	2	4	no	—
147	C₄×D₄×C₅₃	D₄	1	4	yes	—
148	C₄×D₄×C₅₃	D₄	1	2	yes	—
149	C₄×D₄×C₅₃	C₂³	1	8	yes	—
150	#117×C₅₃	C₂³	1	2	yes	—
151	#117×C₅₃	C₂³	1	1	yes	characteristic
152	#117×C₅₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
154	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
155	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
156	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
158	C₄⋊C₈×C₅₃	C₂³	1	8	yes	—
159	#103×C₅₃	C₂³	1	8	yes	—
160	#103×C₅₃	C₂³	1	4	yes	—
161	#103×C₅₃	C₂³	1	4	yes	—
162	#102×C₅₃	C₂³	1	8	yes	—
163	#102×C₅₃	C₂³	1	4	yes	—
164	#102×C₅₃	C₂³	1	4	yes	—
165	C₂²⋊C₈×C₅₃	C₂³	1	8	yes	—
166	#97×C₅₃	C₂³	1	2	yes	—
167	#97×C₅₃	C₂³	1	2	yes	—
168	#97×C₅₃	C₂³	1	2	yes	—
169	C₄×C₈×C₅₃	C₂³	1	2	yes	—
170	C₂⁴×C₅₃	—	2	2	no	—
171	C₂⁴×C₅₃	—	2	2	no	—
172	C₂⁴×C₅₃	—	2	1	no	—
173	#41×C₅₃	—	2	4	no	—
174	#41×C₅₃	—	2	4	no	—
175	#41×C₅₃	—	2	4	no	—
176	#41×C₅₃	—	4	4	no	—
177	#41×C₅₃	—	4	4	no	—
178	#41×C₅₃	—	4	8	no	—
179	#41×C₅₃	—	4	4	no	—
180	#41×C₅₃	—	4	4	no	—
181	#41×C₅₃	—	8	8	no	—
182	C₂×Q₈×C₅₃	—	2	2	no	—
183	C₂×Q₈×C₅₃	—	2	2	no	—
184	C₂×Q₈×C₅₃	—	2	1	no	—
185	C₂×Q₈×C₅₃	—	2	4	no	—
186	C₂×Q₈×C₅₃	—	4	4	no	—
187	C₂×Q₈×C₅₃	—	4	4	no	—
188	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
189	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
190	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
191	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
192	C₂×D₄×C₅₃	—	2	2	no	—
193	C₂×D₄×C₅₃	—	2	1	no	—
194	C₂×D₄×C₅₃	—	2	2	no	—
195	C₂×D₄×C₅₃	—	2	1	no	—
196	C₂×D₄×C₅₃	—	2	8	no	—
197	C₂×D₄×C₅₃	—	2	2	no	—
198	C₂×D₄×C₅₃	—	2	4	no	—
199	C₂×D₄×C₅₃	—	2	2	no	—
200	C₂×D₄×C₅₃	—	2	1	no	—
201	C₂×D₄×C₅₃	—	2	4	no	—
202	C₂×D₄×C₅₃	—	2	2	no	—
203	C₂×D₄×C₅₃	—	2	4	no	—
204	C₂×D₄×C₅₃	—	2	4	no	—
205	C₂×D₄×C₅₃	—	2	4	no	—
206	C₂×D₄×C₅₃	—	2	4	no	—
207	C₂×D₄×C₅₃	—	4	4	no	—
208	C₂×D₄×C₅₃	—	4	8	no	—
209	C₂×D₄×C₅₃	—	4	4	no	—
210	C₂×D₄×C₅₃	—	8	4	no	—
211	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
212	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
213	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
214	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
215	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
216	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₅₃	—	2	2	no	—
218	C₂²×C₄×C₅₃	—	2	1	no	—
219	C₂²×C₄×C₅₃	—	2	2	no	—
220	C₂²×C₄×C₅₃	—	2	1	no	—
221	C₂²×C₄×C₅₃	—	2	2	no	—
222	C₂²×C₄×C₅₃	—	2	1	no	—
223	C₂²×C₄×C₅₃	—	2	8	no	—
224	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
225	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
228	SD₁₆×C₅₃	—	4	8	no	—
229	SD₁₆×C₅₃	—	4	4	no	—
230	SD₁₆×C₅₃	—	4	4	no	—
231	D₈×C₅₃	—	4	8	no	—
232	D₈×C₅₃	—	4	4	no	—
233	D₈×C₅₃	—	4	4	no	—
234	M₁₆×C₅₃	—	2	4	no	—
235	C₂×C₈×C₅₃	—	2	4	no	—
236	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
237	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
238	C₄⋊C₄×C₅₃	—	2	2	no	—
239	C₄⋊C₄×C₅₃	—	2	4	no	—
240	C₄⋊C₄×C₅₃	—	2	2	no	—
241	C₄⋊C₄×C₅₃	—	2	4	no	—
242	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
243	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
244	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
245	C₂²⋊C₄×C₅₃	—	2	2	no	—
246	C₂²⋊C₄×C₅₃	—	2	4	no	—
247	C₂²⋊C₄×C₅₃	—	2	2	no	—
248	C₂²⋊C₄×C₅₃	—	2	8	no	—
249	C₂²⋊C₄×C₅₃	—	2	4	no	—
250	C₂²⋊C₄×C₅₃	—	2	4	no	—
251	C₂²⋊C₄×C₅₃	—	2	4	no	—
252	C₂²⋊C₄×C₅₃	—	2	2	no	—
253	C₂²⋊C₄×C₅₃	—	2	8	no	—
254	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
255	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
256	C₄²×C₅₃	—	2	2	no	—
257	C₄²×C₅₃	C₂×D₄	1	4	yes	—
258	C₄²×C₅₃	C₂×D₄	1	2	yes	—
259	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
260	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
261	C₄²×C₅₃	C₂⁴	1	2	yes	—
262	C₂³×C₅₃	—	2	1	no	—
263	C₂³×C₅₃	—	2	4	no	—
264	C₂³×C₅₃	—	2	2	no	—
265	C₂³×C₅₃	—	2	1	no	—
266	C₂³×C₅₃	—	4	4	no	—
267	C₂³×C₅₃	—	4	2	no	—
268	C₂³×C₅₃	—	4	4	no	—
269	C₂³×C₅₃	—	8	4	no	—
270	C₂³×C₅₃	—	8	2	no	—
271	C₂³×C₅₃	—	8	4	no	—
272	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
273	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
274	Q₈×C₅₃	—	2	2	no	—
275	Q₈×C₅₃	—	2	4	no	—
276	Q₈×C₅₃	—	2	2	no	—
277	Q₈×C₅₃	—	2	2	no	—
278	Q₈×C₅₃	—	4	4	no	—
279	Q₈×C₅₃	—	4	4	no	—
280	Q₈×C₅₃	—	4	2	no	—
281	D₄×C₅₃	—	2	4	no	—
282	D₄×C₅₃	—	2	2	no	—
283	D₄×C₅₃	—	2	4	no	—
284	D₄×C₅₃	—	2	4	no	—
285	D₄×C₅₃	—	2	4	no	—
286	D₄×C₅₃	—	2	2	no	—
287	D₄×C₅₃	—	2	2	no	—
288	D₄×C₅₃	—	4	4	no	—
289	D₄×C₅₃	—	4	8	no	—
290	D₄×C₅₃	—	4	4	no	—
291	D₄×C₅₃	—	4	4	no	—
292	D₄×C₅₃	—	4	2	no	—
293	D₄×C₅₃	—	4	2	no	—
294	D₄×C₅₃	—	4	4	no	—
295	D₄×C₅₃	—	4	2	no	—
296	D₄×C₅₃	—	8	4	no	—
297	D₄×C₅₃	—	8	2	no	—
298	D₄×C₅₃	—	8	4	no	—
299	D₄×C₅₃	—	8	8	no	—
300	C₂×C₄×C₅₃	—	2	4	no	—
301	C₂×C₄×C₅₃	—	2	1	no	—
302	C₂×C₄×C₅₃	—	2	2	no	—
303	C₂×C₄×C₅₃	—	2	1	no	—
304	C₂×C₄×C₅₃	—	2	4	no	—
305	C₂×C₄×C₅₃	—	4	2	no	—
306	C₂×C₄×C₅₃	—	4	4	no	—
307	C₂×C₄×C₅₃	—	4	4	no	—
308	C₂×C₄×C₅₃	—	4	4	no	—
309	C₂×C₄×C₅₃	—	4	4	no	—
310	C₂×C₄×C₅₃	—	4	2	no	—
311	C₂×C₄×C₅₃	—	4	2	no	—
312	C₂×C₄×C₅₃	—	4	2	no	—
313	C₂×C₄×C₅₃	—	8	8	no	—
314	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
315	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
320	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
321	C₈×C₅₃	—	2	4	no	—
322	C₈×C₅₃	—	2	4	no	—
323	#60825	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
324	C₂²×C₅₃	—	2	2	no	—
325	C₂²×C₅₃	—	2	4	no	—
326	C₂²×C₅₃	—	2	2	no	—
327	C₂²×C₅₃	—	4	8	no	—
328	C₂²×C₅₃	—	4	2	no	—
329	C₂²×C₅₃	—	4	4	no	—
330	C₂²×C₅₃	—	4	2	no	—
331	C₂²×C₅₃	—	4	1	no	—
332	C₂²×C₅₃	—	4	2	no	—
333	C₂²×C₅₃	—	4	1	no	—
334	C₂²×C₅₃	—	4	4	no	—
335	C₂²×C₅₃	—	16	4	no	—
336	C₂²×C₅₃	—	16	2	no	—
337	C₂²×C₅₃	—	16	4	no	—
338	C₂²×C₅₃	#535	1	2	yes	—
339	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
340	C₄×C₅₃	—	2	2	no	—
341	C₄×C₅₃	—	2	4	no	—
342	C₄×C₅₃	—	2	2	no	—
343	C₄×C₅₃	—	2	2	no	—
344	C₄×C₅₃	—	4	4	no	—
345	C₄×C₅₃	—	4	1	no	—
346	C₄×C₅₃	—	4	2	no	—
347	C₄×C₅₃	—	4	1	no	—
348	C₄×C₅₃	#535	1	2	yes	—
349	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
350	#3508	C₂×C₅₃	1	1	yes	characteristic, complemented
351	#3500	C₂×C₅₃	1	1	yes	characteristic, complemented
352	#3221	C₂×C₅₃	1	4	yes	complemented
353	#3220	C₂×C₅₃	1	4	yes	complemented
354	#3214	C₂×C₅₃	1	4	yes	complemented
355	#3213	C₂×C₅₃	1	4	yes	complemented
356	#3151	C₂×C₅₃	1	1	yes	characteristic, complemented
357	C₂×#496	C₂×C₅₃	1	1	yes	characteristic, complemented
358	#3140	C₂×C₅₃	1	1	yes	characteristic, complemented
359	#3135	C₂×C₅₃	1	1	yes	characteristic, complemented
360	#3042	C₂×C₅₃	1	2	yes	complemented
361	#3041	C₂×C₅₃	1	2	yes	complemented
362	#3010	C₂×C₅₃	1	2	yes	complemented
363	#3008	C₂×C₅₃	1	2	yes	complemented
364	#2923	C₂×C₅₃	1	1	yes	characteristic, complemented
365	C₂×C₅₃	—	2	2	no	—
366	C₂×C₅₃	—	4	2	no	—
367	C₂×C₅₃	—	8	1	no	—
368	C₂×C₅₃	—	8	4	no	—
369	C₂×C₅₃	—	8	2	no	—
370	C₂×C₅₃	—	8	1	no	—
371	C₂×C₅₃	C₂×#535	1	1	yes	characteristic
372	C₂×C₅₃	#3585	1	2	yes	—
373	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic
374	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
375	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
376	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
377	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
378	C₂²×D₈	C₂²×C₅₃	1	2	yes	—
379	#559	—	2	2	no	—
380	#550	—	2	2	no	—
381	#548	—	2	2	no	—
382	#546	—	2	4	no	—
383	#546	—	2	2	no	—
384	#546	—	2	4	no	—
385	#540	C₂²×C₅₃	1	4	yes	complemented
386	#536	C₂²×C₅₃	1	1	yes	characteristic
387	#536	C₂²×C₅₃	1	2	yes	complemented
388	#535	C₂²×C₅₃	1	1	yes	characteristic
389	#535	C₂²×C₅₃	1	2	yes	—
390	#535	C₂²×C₅₃	1	2	yes	complemented
391	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
392	#532	C₂²×C₅₃	1	1	yes	characteristic
393	#532	C₂²×C₅₃	1	2	yes	complemented
394	#532	C₂²×C₅₃	1	4	yes	complemented
395	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic, complemented
396	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
397	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
398	#518	C₂²×C₅₃	1	2	yes	complemented
399	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
400	#496	C₂²×C₅₃	1	4	yes	complemented
401	#496	C₂²×C₅₃	1	4	yes	complemented
402	#496	C₂²×C₅₃	1	2	yes	complemented
403	#496	C₂²×C₅₃	1	2	yes	complemented
404	#493	C₂²×C₅₃	1	2	yes	complemented
405	#492	C₂²×C₅₃	1	2	yes	complemented
406	#491	C₂²×C₅₃	1	2	yes	complemented
407	#490	C₂²×C₅₃	1	2	yes	complemented
408	#489	C₂²×C₅₃	1	2	yes	complemented
409	#489	C₂²×C₅₃	1	2	yes	complemented
410	#489	C₂²×C₅₃	1	4	yes	complemented
411	#488	C₂²×C₅₃	1	4	yes	complemented
412	#463	C₂²×C₅₃	1	8	yes	complemented
413	#463	C₂²×C₅₃	1	8	yes	complemented
414	#461	C₂²×C₅₃	1	8	yes	complemented
415	#459	C₂²×C₅₃	1	8	yes	complemented
416	#449	C₂²×C₅₃	1	8	yes	complemented
417	#449	C₂²×C₅₃	1	8	yes	complemented
418	#448	C₂²×C₅₃	1	8	yes	complemented
419	#447	C₂²×C₅₃	1	8	yes	complemented
420	#433	C₂²×C₅₃	1	4	yes	complemented
421	#432	C₂²×C₅₃	1	4	yes	complemented
422	#424	C₂²×C₅₃	1	2	yes	complemented
423	#419	C₂²×C₅₃	1	2	yes	complemented
424	#418	C₂²×C₅₃	1	2	yes	—
425	#416	C₂²×C₅₃	1	2	yes	—
426	#416	C₂²×C₅₃	1	2	yes	complemented
427	#408	C₂²×C₅₃	1	2	yes	—
428	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
429	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic, complemented
430	C₅₃	#60825	1	1	yes	characteristic, direct product factor, Sylow
431	2₋¹⁺⁴	—	4	4	no	—
432	H(5,𝔽₂)	—	4	4	no	—
433	C₂×#41	—	2	1	no	—
434	C₂×#41	—	2	2	no	—
435	C₂×#41	—	2	1	no	—
436	C₂×#41	—	2	4	no	—
437	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
438	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
439	C₂×#41	C₂³×C₅₃	1	2	yes	—
440	C₂×#41	C₂³×C₅₃	1	2	yes	—
441	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
442	C₂²×Q₈	—	2	1	no	—
443	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
444	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
445	C₂²×D₄	—	2	2	no	—
446	C₂²×D₄	—	2	1	no	—
447	C₂²×D₄	—	2	2	no	—
448	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
449	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
450	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
451	AGL(1,ℤ/8)	—	4	4	no	—
452	AGL(1,ℤ/8)	—	4	4	no	—
453	C₂×SD₁₆	—	4	4	no	—
454	C₂×SD₁₆	C₂³×C₅₃	1	8	yes	—
455	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
456	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	—
457	C₂×D₈	—	4	4	no	—
458	C₂×D₈	C₂³×C₅₃	1	8	yes	—
459	C₂×D₈	C₂³×C₅₃	1	4	yes	—
460	C₂×D₈	C₂³×C₅₃	1	4	yes	—
461	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
462	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
463	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
465	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
466	#127	—	2	2	no	—
467	#127	—	2	2	no	—
468	#127	C₂³×C₅₃	1	2	yes	—
469	#127	C₂³×C₅₃	1	2	yes	—
470	#127	C₂³×C₅₃	1	1	yes	characteristic
471	#127	C₂³×C₅₃	1	2	yes	—
472	#125	C₂³×C₅₃	1	2	yes	—
473	#124	—	2	2	no	—
474	#124	—	2	2	no	—
475	#124	—	2	4	no	—
476	#124	—	2	4	no	—
477	#124	C₂³×C₅₃	1	2	yes	—
478	#124	C₂³×C₅₃	1	2	yes	—
479	#124	C₂³×C₅₃	1	1	yes	characteristic
480	#124	C₂³×C₅₃	1	2	yes	—
481	#124	C₂³×C₅₃	1	2	yes	—
482	#124	C₂³×C₅₃	1	1	yes	characteristic
483	#123	—	2	8	no	—
484	#123	—	2	2	no	—
485	#123	—	2	4	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	4	no	—
489	#121	—	2	2	no	—
490	#121	—	2	4	no	—
491	#121	—	2	4	no	—
492	#121	—	2	2	no	—
493	#121	—	2	4	no	—
494	#121	—	2	8	no	—
495	#121	C₂³×C₅₃	1	8	yes	—
496	#120	—	2	4	no	—
497	#120	—	2	2	no	—
498	#120	—	2	4	no	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	D₄×C₅₃	1	2	yes	—
501	C₄×D₄	—	2	4	no	—
502	C₄×D₄	—	2	2	no	—
503	C₄×D₄	—	2	4	no	—
504	C₄×D₄	—	2	4	no	—
505	C₄×D₄	D₄×C₅₃	1	4	yes	—
506	C₄×D₄	D₄×C₅₃	1	2	yes	—
507	C₄×D₄	C₂³×C₅₃	1	8	yes	—
508	#117	C₂³×C₅₃	1	2	yes	—
509	#117	C₂³×C₅₃	1	1	yes	characteristic
510	#117	C₂³×C₅₃	1	2	yes	—
511	C₂×C₂²⋊C₄	—	2	2	no	—
512	C₂×C₂²⋊C₄	—	2	4	no	—
513	C₂×C₂²⋊C₄	—	2	4	no	—
514	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
515	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
516	C₄⋊C₈	C₂³×C₅₃	1	8	yes	—
517	#103	C₂³×C₅₃	1	4	yes	—
518	#103	C₂³×C₅₃	1	4	yes	—
519	#103	C₂³×C₅₃	1	8	yes	—
520	#102	C₂³×C₅₃	1	4	yes	—
521	#102	C₂³×C₅₃	1	4	yes	—
522	#102	C₂³×C₅₃	1	8	yes	—
523	C₂²⋊C₈	C₂³×C₅₃	1	8	yes	—
524	#97	C₂³×C₅₃	1	2	yes	—
525	#97	C₂³×C₅₃	1	2	yes	—
526	#97	C₂³×C₅₃	1	2	yes	—
527	C₄×C₈	C₂³×C₅₃	1	2	yes	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	2	1	no	—
530	C₂⁴	—	2	2	no	—
531	#41	—	2	4	no	—
532	#41	—	2	4	no	—
533	#41	—	2	4	no	—
534	#41	—	4	4	no	—
535	#41	—	4	4	no	—
536	#41	—	4	8	no	—
537	#41	—	4	4	no	—
538	#41	—	4	4	no	—
539	#41	—	8	8	no	—
540	C₂×Q₈	—	2	2	no	—
541	C₂×Q₈	—	2	2	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	4	no	—
544	C₂×Q₈	—	4	4	no	—
545	C₂×Q₈	—	4	4	no	—
546	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
547	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
548	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
549	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	8	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	4	4	no	—
566	C₂×D₄	—	4	8	no	—
567	C₂×D₄	—	4	4	no	—
568	C₂×D₄	—	8	4	no	—
569	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
570	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
571	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
572	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
573	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
574	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	8	no	—
582	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
583	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
586	SD₁₆	—	4	8	no	—
587	SD₁₆	—	4	4	no	—
588	SD₁₆	—	4	4	no	—
589	D₈	—	4	8	no	—
590	D₈	—	4	4	no	—
591	D₈	—	4	4	no	—
592	M₁₆	—	2	4	no	—
593	C₂×C₈	—	2	4	no	—
594	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
595	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
601	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
602	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	8	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	8	no	—
612	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
613	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
614	C₄²	—	2	2	no	—
615	C₄²	C₂×D₄×C₅₃	1	4	yes	—
616	C₄²	C₂×D₄×C₅₃	1	2	yes	—
617	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
618	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
619	C₄²	C₂⁴×C₅₃	1	2	yes	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	4	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	4	4	no	—
625	C₂³	—	4	2	no	—
626	C₂³	—	4	4	no	—
627	C₂³	—	8	4	no	—
628	C₂³	—	8	2	no	—
629	C₂³	—	8	4	no	—
630	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
631	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
632	Q₈	—	2	2	no	—
633	Q₈	—	2	4	no	—
634	Q₈	—	2	2	no	—
635	Q₈	—	2	2	no	—
636	Q₈	—	4	4	no	—
637	Q₈	—	4	4	no	—
638	Q₈	—	4	2	no	—
639	D₄	—	2	4	no	—
640	D₄	—	2	2	no	—
641	D₄	—	2	4	no	—
642	D₄	—	2	4	no	—
643	D₄	—	2	2	no	—
644	D₄	—	2	2	no	—
645	D₄	—	2	4	no	—
646	D₄	—	4	4	no	—
647	D₄	—	4	8	no	—
648	D₄	—	4	4	no	—
649	D₄	—	4	4	no	—
650	D₄	—	4	2	no	—
651	D₄	—	4	2	no	—
652	D₄	—	4	4	no	—
653	D₄	—	4	2	no	—
654	D₄	—	8	4	no	—
655	D₄	—	8	2	no	—
656	D₄	—	8	4	no	—
657	D₄	—	8	8	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	4	2	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	4	no	—
668	C₂×C₄	—	4	2	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	2	no	—
671	C₂×C₄	—	8	8	no	—
672	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
673	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
674	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
675	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
676	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
677	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
678	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
679	C₈	—	2	4	no	—
680	C₈	—	2	4	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	4	8	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	4	no	—
687	C₂²	—	4	2	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	4	no	—
692	C₂²	—	16	2	no	—
693	C₂²	—	16	4	no	—
694	C₂²	—	16	4	no	—
695	C₂²	C₅₃×#535	1	2	yes	—
696	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
697	C₄	—	2	2	no	—
698	C₄	—	2	4	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	2	no	—
701	C₄	—	4	4	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	1	no	—
705	C₄	C₅₃×#535	1	2	yes	—
706	C₄	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
707	C₂	—	2	2	no	—
708	C₂	—	4	2	no	—
709	C₂	—	8	2	no	—
710	C₂	—	8	1	no	—
711	C₂	—	8	4	no	—
712	C₂	—	8	1	no	—
713	C₂	C₂×C₅₃×#535	1	1	yes	characteristic
714	C₂	C₅₃×#3585	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 ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3508	C₂	semidirect
2. C₅₃×#3500	C₂	semidirect
3. C₅₃×#3221	C₂	semidirect
4. C₅₃×#3220	C₂	semidirect
5. C₅₃×#3214	C₂	semidirect
6. C₅₃×#3213	C₂	semidirect
7. C₅₃×#3151	C₂	semidirect
8. C₂×C₅₃×#496	C₂	semidirect
9. C₅₃×#3140	C₂	semidirect
10. C₅₃×#3135	C₂	semidirect
11. C₅₃×#3042	C₂	semidirect
12. C₅₃×#3041	C₂	semidirect
13. C₅₃×#3010	C₂	semidirect
14. C₅₃×#3008	C₂	semidirect
15. C₅₃×#2923	C₂	semidirect
19. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
20. C₂²×SD₁₆×C₅₃	C₂²	semidirect
28. C₅₃×#540	C₂²	semidirect
30. C₅₃×#536	C₂²	semidirect
33. C₅₃×#535	C₂²	semidirect
34. C₅₃×#533	C₂²	semidirect
36. C₅₃×#532	C₂²	semidirect
37. C₅₃×#532	C₂²	semidirect
38. C₂×#127×C₅₃	C₂²	semidirect
40. C₂×#124×C₅₃	C₂²	semidirect
41. C₅₃×#518	C₂²	semidirect
43. C₅₃×#496	C₂²	semidirect
44. C₅₃×#496	C₂²	semidirect
45. C₅₃×#496	C₂²	semidirect
46. C₅₃×#496	C₂²	semidirect
47. C₅₃×#493	C₂²	semidirect
48. C₅₃×#492	C₂²	semidirect
49. C₅₃×#491	C₂²	semidirect
50. C₅₃×#490	C₂²	semidirect
51. C₅₃×#489	C₂²	semidirect
52. C₅₃×#489	C₂²	semidirect
53. C₅₃×#489	C₂²	semidirect
54. C₅₃×#488	C₂²	semidirect
55. C₅₃×#463	C₂²	semidirect
56. C₅₃×#463	C₂²	semidirect
57. C₅₃×#461	C₂²	semidirect
58. C₅₃×#459	C₂²	semidirect
59. C₅₃×#449	C₂²	semidirect
60. C₅₃×#449	C₂²	semidirect
61. C₅₃×#448	C₂²	semidirect
62. C₅₃×#447	C₂²	semidirect
63. C₅₃×#433	C₂²	semidirect
64. C₅₃×#432	C₂²	semidirect
65. C₅₃×#424	C₂²	semidirect
66. C₅₃×#419	C₂²	semidirect
69. C₅₃×#416	C₂²	semidirect
71. C₄×M₁₆×C₅₃	C₂²	semidirect
72. C₂×#97×C₅₃	C₂²	semidirect
323. #60825	C₅₃	direct (N × H)
350. #3508	C₂×C₅₃	semidirect
351. #3500	C₂×C₅₃	semidirect
352. #3221	C₂×C₅₃	semidirect
353. #3220	C₂×C₅₃	semidirect
354. #3214	C₂×C₅₃	semidirect
355. #3213	C₂×C₅₃	semidirect
356. #3151	C₂×C₅₃	semidirect
357. C₂×#496	C₂×C₅₃	semidirect
358. #3140	C₂×C₅₃	semidirect
359. #3135	C₂×C₅₃	semidirect
360. #3042	C₂×C₅₃	semidirect
361. #3041	C₂×C₅₃	semidirect
362. #3010	C₂×C₅₃	semidirect
363. #3008	C₂×C₅₃	semidirect
364. #2923	C₂×C₅₃	semidirect
376. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
377. C₂²×SD₁₆	C₂²×C₅₃	semidirect
385. #540	C₂²×C₅₃	semidirect
387. #536	C₂²×C₅₃	semidirect
390. #535	C₂²×C₅₃	semidirect
391. #533	C₂²×C₅₃	semidirect
393. #532	C₂²×C₅₃	semidirect
394. #532	C₂²×C₅₃	semidirect
395. C₂×#127	C₂²×C₅₃	semidirect
397. C₂×#124	C₂²×C₅₃	semidirect
398. #518	C₂²×C₅₃	semidirect
400. #496	C₂²×C₅₃	semidirect
401. #496	C₂²×C₅₃	semidirect
402. #496	C₂²×C₅₃	semidirect
403. #496	C₂²×C₅₃	semidirect
404. #493	C₂²×C₅₃	semidirect
405. #492	C₂²×C₅₃	semidirect
406. #491	C₂²×C₅₃	semidirect
407. #490	C₂²×C₅₃	semidirect
408. #489	C₂²×C₅₃	semidirect
409. #489	C₂²×C₅₃	semidirect
410. #489	C₂²×C₅₃	semidirect
411. #488	C₂²×C₅₃	semidirect
412. #463	C₂²×C₅₃	semidirect
413. #463	C₂²×C₅₃	semidirect
414. #461	C₂²×C₅₃	semidirect
415. #459	C₂²×C₅₃	semidirect
416. #449	C₂²×C₅₃	semidirect
417. #449	C₂²×C₅₃	semidirect
418. #448	C₂²×C₅₃	semidirect
419. #447	C₂²×C₅₃	semidirect
420. #433	C₂²×C₅₃	semidirect
421. #432	C₂²×C₅₃	semidirect
422. #424	C₂²×C₅₃	semidirect
423. #419	C₂²×C₅₃	semidirect
426. #416	C₂²×C₅₃	semidirect
428. C₄×M₁₆	C₂²×C₅₃	semidirect
429. C₂×#97	C₂²×C₅₃	semidirect
430. C₅₃	#60825	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×#3508	2
C₅₃×#3500	2
C₅₃×#3221	2
C₅₃×#3220	2
C₅₃×#3214	2
C₅₃×#3213	2
C₅₃×#3151	2
C₂×C₅₃×#496	2
C₅₃×#3140	2
C₅₃×#3135	2
C₅₃×#3042	2
C₅₃×#3041	2
C₅₃×#3010	2
C₅₃×#3008	2
C₅₃×#2923	2
#60825	53

Subgroups — C53×#60825 #27268337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#60825 #27268337