Subgroups — #27394287

Order 13568.

670 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20275330	C₂	1	1	yes	maximal, characteristic
2	#20275330	C₂	1	1	yes	maximal, characteristic
3	#20275323	C₂	1	1	yes	maximal, characteristic
4	#20275323	C₂	1	1	yes	maximal, characteristic
5	#20275281	C₂	1	1	yes	maximal, characteristic, complemented
6	#20275281	C₂	1	1	yes	maximal, characteristic, complemented
7	#20275274	C₂	1	1	yes	maximal, characteristic, complemented
8	#20275274	C₂	1	1	yes	maximal, characteristic, complemented
9	#20274869	C₂	1	1	yes	maximal, characteristic, complemented
10	#20274835	C₂	1	1	yes	maximal, characteristic, complemented
11	#20274695	C₂	1	1	yes	maximal, characteristic
12	#20274695	C₂	1	1	yes	maximal, characteristic
13	#20274572	C₂	1	1	yes	maximal, characteristic, complemented
14	#20274572	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2283	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊#88322	C₂²	1	1	yes	characteristic
28	C₂×#13133128	C₂²	1	1	yes	characteristic
29	C₂×#13133128	C₂²	1	1	yes	characteristic
30	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
31	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
32	#16810378	C₂²	1	1	yes	characteristic
33	#16810378	C₂²	1	1	yes	characteristic
34	#16810378	C₂²	1	1	yes	characteristic
35	#16810378	C₂²	1	1	yes	characteristic
36	#16810378	C₂²	1	1	yes	characteristic
37	#16810378	C₂²	1	1	yes	characteristic
38	#16810378	C₂²	1	1	yes	characteristic
39	#16810378	C₂²	1	1	yes	characteristic
40	#16810378	C₂²	1	1	yes	characteristic
41	#16810378	C₂²	1	1	yes	characteristic
42	#16810378	C₂²	1	1	yes	characteristic
43	#16810378	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#383	C₄	1	1	yes	characteristic
46	C₅₃×#383	C₄	1	1	yes	characteristic
47	C₅₃×#382	C₄	1	1	yes	characteristic
48	C₅₃×#382	C₄	1	1	yes	characteristic
49	C₅₃×#381	C₄	1	1	yes	characteristic
50	C₅₃×#381	C₄	1	1	yes	characteristic
51	C₅₃×#380	C₄	1	1	yes	characteristic
52	C₅₃×#380	C₄	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#376	C₂²	1	1	yes	characteristic
58	C₅₃×#376	C₂²	1	1	yes	characteristic
59	C₂²×#88322	C₂³	1	1	yes	characteristic
60	C₂²×#88322	C₂³	1	1	yes	characteristic
61	C₂²×#88322	C₂³	1	1	yes	characteristic
62	C₂²×#88322	C₂³	1	1	yes	characteristic
63	C₂²×#88322	C₂³	1	1	yes	characteristic
64	C₂²×#88322	C₂³	1	1	yes	characteristic
65	C₂²×#88322	C₂³	1	1	yes	characteristic
66	C₂²×#88322	C₂³	1	1	yes	characteristic
67	C₄⋊#88322	—	2	2	no	—
68	C₄⋊#88322	—	2	2	no	—
69	C₄⋊#88322	—	2	2	no	—
70	C₄⋊#88322	—	2	2	no	—
71	C₄⋊#88322	—	4	1	no	—
72	C₄⋊#88322	—	4	1	no	—
73	C₄⋊#88322	—	4	1	no	—
74	C₄⋊#88322	—	4	1	no	—
75	C₂²⋊#88322	—	4	1	no	—
76	C₂²⋊#88322	—	4	1	no	—
77	C₂²⋊#88322	—	4	1	no	—
78	C₂²⋊#88322	—	4	1	no	—
79	#13133128	—	4	1	no	—
80	#13133128	—	4	1	no	—
81	C₄×#88322	—	4	1	no	—
82	C₄×#88322	—	4	1	no	—
83	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
85	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₅₃	—	2	2	no	—
95	C₂×C₄²×C₅₃	—	2	2	no	—
96	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
104	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
105	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
106	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
107	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
108	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
109	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
110	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
111	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
112	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
113	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
114	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
115	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
116	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
117	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
118	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
119	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
120	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅₃	—	2	2	no	—
122	C₂²×C₄×C₅₃	—	2	2	no	—
123	C₂²×C₄×C₅₃	—	2	2	no	—
124	C₂²×C₄×C₅₃	—	2	2	no	—
125	C₂²×C₄×C₅₃	—	2	1	no	—
126	C₂²×C₄×C₅₃	—	2	1	no	—
127	C₂²×C₄×C₅₃	—	2	1	no	—
128	C₂²×C₄×C₅₃	—	2	1	no	—
129	C₂²×C₄×C₅₃	—	2	1	no	—
130	C₂²×C₄×C₅₃	—	2	1	no	—
131	C₂²×C₄×C₅₃	—	4	1	no	—
132	C₂²×C₄×C₅₃	—	4	1	no	—
133	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
147	C₄⋊C₄×C₅₃	—	2	2	no	—
148	C₄⋊C₄×C₅₃	—	2	2	no	—
149	C₄⋊C₄×C₅₃	—	4	1	no	—
150	C₄⋊C₄×C₅₃	—	4	1	no	—
151	C₂²⋊C₄×C₅₃	—	2	2	no	—
152	C₂²⋊C₄×C₅₃	—	2	2	no	—
153	C₂²⋊C₄×C₅₃	—	4	1	no	—
154	C₂²⋊C₄×C₅₃	—	4	1	no	—
155	C₄²×C₅₃	—	2	2	no	—
156	C₄²×C₅₃	—	2	2	no	—
157	C₄²×C₅₃	—	2	1	no	—
158	C₄²×C₅₃	—	2	1	no	—
159	C₄²×C₅₃	—	2	1	no	—
160	C₄²×C₅₃	—	2	1	no	—
161	C₄²×C₅₃	—	2	1	no	—
162	C₄²×C₅₃	—	2	1	no	—
163	C₄²×C₅₃	—	2	1	no	—
164	C₄²×C₅₃	—	2	1	no	—
165	C₄²×C₅₃	—	2	1	no	—
166	C₄²×C₅₃	—	2	1	no	—
167	C₄²×C₅₃	#41	1	2	yes	—
168	C₄²×C₅₃	#41	1	2	yes	—
169	C₂×#88322	—	2	1	no	—
170	C₂×#88322	—	2	1	no	—
171	C₂×#88322	—	2	1	no	—
172	C₂×#88322	—	2	1	no	—
173	C₂×#88322	—	2	1	no	—
174	C₂×#88322	—	2	1	no	—
175	C₂×#88322	—	2	1	no	—
176	C₂×#88322	—	2	1	no	—
177	C₂×#88322	—	2	1	no	—
178	C₂×#88322	—	2	1	no	—
179	C₂×#88322	—	2	1	no	—
180	C₂×#88322	—	2	1	no	—
181	C₂×#88322	—	2	1	no	—
182	C₂×#88322	—	2	1	no	—
183	C₂×#88322	—	2	1	no	—
184	C₂×#88322	—	2	1	no	—
185	C₂×#88322	—	2	1	no	—
186	C₂×#88322	—	2	1	no	—
187	C₂×#88322	—	2	1	no	—
188	C₂×#88322	—	2	1	no	—
189	C₂×#88322	—	2	1	no	—
190	C₂×#88322	—	2	1	no	—
191	C₂×#88322	—	2	1	no	—
192	C₂×#88322	—	2	1	no	—
193	C₂³×C₅₃	—	2	1	no	—
194	C₂³×C₅₃	—	2	1	no	—
195	C₂³×C₅₃	—	2	1	no	—
196	C₂³×C₅₃	—	2	1	no	—
197	C₂³×C₅₃	—	2	1	no	—
198	C₂³×C₅₃	—	2	1	no	—
199	C₂³×C₅₃	#131	1	2	yes	—
200	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₅₃	—	2	1	no	—
202	C₂×C₄×C₅₃	—	2	1	no	—
203	C₂×C₄×C₅₃	—	2	1	no	—
204	C₂×C₄×C₅₃	—	2	1	no	—
205	C₂×C₄×C₅₃	—	2	1	no	—
206	C₂×C₄×C₅₃	—	2	1	no	—
207	C₂×C₄×C₅₃	—	2	1	no	—
208	C₂×C₄×C₅₃	—	2	1	no	—
209	C₂×C₄×C₅₃	—	2	1	no	—
210	C₂×C₄×C₅₃	—	2	1	no	—
211	C₂×C₄×C₅₃	—	2	1	no	—
212	C₂×C₄×C₅₃	—	2	1	no	—
213	C₂×C₄×C₅₃	—	2	1	no	—
214	C₂×C₄×C₅₃	—	2	1	no	—
215	C₂×C₄×C₅₃	—	2	1	no	—
216	C₂×C₄×C₅₃	—	2	1	no	—
217	C₂×C₄×C₅₃	—	2	1	no	—
218	C₂×C₄×C₅₃	—	2	1	no	—
219	C₂×C₄×C₅₃	—	2	1	no	—
220	C₂×C₄×C₅₃	—	2	1	no	—
221	C₂×C₄×C₅₃	—	2	1	no	—
222	C₂×C₄×C₅₃	—	2	1	no	—
223	C₂×C₄×C₅₃	—	2	1	no	—
224	C₂×C₄×C₅₃	—	2	1	no	—
225	C₂×C₄×C₅₃	—	2	1	no	—
226	C₂×C₄×C₅₃	—	2	1	no	—
227	C₂×C₄×C₅₃	—	2	1	no	—
228	C₂×C₄×C₅₃	—	2	1	no	—
229	C₂×C₄×C₅₃	—	2	1	no	—
230	C₂×C₄×C₅₃	—	2	1	no	—
231	C₂×C₄×C₅₃	—	2	1	no	—
232	C₂×C₄×C₅₃	—	2	1	no	—
233	C₂×C₄×C₅₃	—	2	1	no	—
234	C₂×C₄×C₅₃	—	2	1	no	—
235	C₂×C₄×C₅₃	—	2	1	no	—
236	C₂×C₄×C₅₃	—	2	1	no	—
237	C₂×C₄×C₅₃	—	4	4	no	—
238	C₂×C₄×C₅₃	—	4	4	no	—
239	C₂×C₄×C₅₃	—	4	1	no	—
240	C₂×C₄×C₅₃	—	4	1	no	—
241	C₂×C₄×C₅₃	—	4	1	no	—
242	C₂×C₄×C₅₃	—	4	1	no	—
243	C₂×C₄×C₅₃	#117	1	2	yes	—
244	C₂×C₄×C₅₃	#117	1	2	yes	—
245	C₂×C₄×C₅₃	#131	1	2	yes	—
246	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
249	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂×C₄×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
251	C₂×C₄×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
252	#88322	—	4	1	no	—
253	#88322	—	4	1	no	—
254	#88322	—	4	1	no	—
255	#88322	—	4	1	no	—
256	#88322	—	4	1	no	—
257	#88322	—	4	1	no	—
258	#88322	—	4	1	no	—
259	#88322	—	4	1	no	—
260	#21928	—	53	1	no	maximal, Sylow
261	C₂²×C₅₃	—	2	2	no	—
262	C₂²×C₅₃	—	2	2	no	—
263	C₂²×C₅₃	—	2	2	no	—
264	C₂²×C₅₃	—	4	1	no	—
265	C₂²×C₅₃	—	4	1	no	—
266	C₂²×C₅₃	—	4	1	no	—
267	C₂²×C₅₃	—	4	1	no	—
268	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
269	C₂²×C₅₃	#520	1	1	yes	characteristic
270	C₂²×C₅₃	#520	1	1	yes	characteristic
271	C₂²×C₅₃	C₂×#131	1	1	yes	characteristic
272	C₂²×C₅₃	C₂×#131	1	1	yes	characteristic
273	C₂²×C₅₃	#568	1	1	yes	characteristic
274	C₂²×C₅₃	#568	1	1	yes	characteristic
275	C₄×C₅₃	—	2	2	no	—
276	C₄×C₅₃	—	2	2	no	—
277	C₄×C₅₃	—	2	2	no	—
278	C₄×C₅₃	—	4	1	no	—
279	C₄×C₅₃	—	4	1	no	—
280	C₄×C₅₃	—	4	1	no	—
281	C₄×C₅₃	—	4	1	no	—
282	C₄×C₅₃	—	4	1	no	—
283	C₄×C₅₃	—	4	1	no	—
284	C₄×C₅₃	—	4	1	no	—
285	C₄×C₅₃	—	4	1	no	—
286	C₄×C₅₃	—	4	1	no	—
287	C₄×C₅₃	—	4	1	no	—
288	C₄×C₅₃	#540	1	1	yes	characteristic
289	C₄×C₅₃	#541	1	1	yes	characteristic
290	C₄×C₅₃	#542	1	1	yes	characteristic
291	C₄×C₅₃	#542	1	1	yes	characteristic
292	#2283	D₅₃	1	1	yes	characteristic
293	#1924	—	53	1	no	—
294	#1924	—	53	1	no	—
295	#1923	—	53	1	no	—
296	#1923	—	53	1	no	—
297	#1917	—	53	1	no	—
298	#1917	—	53	1	no	—
299	#1916	—	53	1	no	—
300	#1916	—	53	1	no	—
301	#1843	—	53	1	no	—
302	#1832	—	53	1	no	—
303	#1797	—	53	1	no	—
304	#1797	—	53	1	no	—
305	#1768	—	53	1	no	—
306	#1768	—	53	1	no	—
307	C₂×C₅₃	—	4	2	no	—
308	C₂×C₅₃	#2314	1	1	yes	characteristic
309	C₂×C₅₃	#2924	1	1	yes	characteristic
310	C₂×C₅₃	#2924	1	1	yes	characteristic
311	C₂×C₅₃	#2992	1	1	yes	characteristic
312	C₂×C₅₃	#2993	1	1	yes	characteristic
313	C₂×C₅₃	#2994	1	1	yes	characteristic
314	C₂×C₅₃	#2995	1	1	yes	characteristic
315	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic
316	C₂×C₄⋊C₈	—	53	1	no	—
317	C₂×C₄⋊C₈	—	53	1	no	—
318	C₂×C₄⋊C₈	—	53	1	no	—
319	C₂×C₄⋊C₈	—	53	1	no	—
320	C₂×C₄⋊C₈	—	53	1	no	—
321	C₂×C₄⋊C₈	—	53	1	no	—
322	C₂×C₄⋊C₈	—	53	1	no	—
323	C₂×C₄⋊C₈	—	53	1	no	—
324	C₂×C₂²⋊C₈	—	53	1	no	—
325	C₂×C₂²⋊C₈	—	53	1	no	—
326	C₂×C₂²⋊C₈	—	53	1	no	—
327	C₂×C₂²⋊C₈	—	53	1	no	—
328	C₂×#97	—	53	1	no	—
329	C₂×#97	—	53	1	no	—
330	C₂×C₄×C₈	—	53	1	no	—
331	C₂×C₄×C₈	—	53	1	no	—
332	#383	Dic₅₃	1	1	yes	characteristic
333	#383	Dic₅₃	1	1	yes	characteristic
334	#382	Dic₅₃	1	1	yes	characteristic
335	#382	Dic₅₃	1	1	yes	characteristic
336	#381	Dic₅₃	1	1	yes	characteristic
337	#381	Dic₅₃	1	1	yes	characteristic
338	#380	Dic₅₃	1	1	yes	characteristic
339	#380	Dic₅₃	1	1	yes	characteristic
340	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
341	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
342	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
343	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
344	#376	C₂×D₅₃	1	1	yes	characteristic
345	#376	C₂×D₅₃	1	1	yes	characteristic
346	#336	—	53	1	no	—
347	#336	—	53	1	no	—
348	#336	—	53	1	no	—
349	#336	—	53	1	no	—
350	#336	—	53	1	no	—
351	#336	—	53	1	no	—
352	#336	—	53	1	no	—
353	#336	—	53	1	no	—
354	#336	—	53	1	no	—
355	#336	—	53	1	no	—
356	#336	—	53	1	no	—
357	#336	—	53	1	no	—
358	C₅₃	#21928	1	1	yes	characteristic, complemented, Sylow
359	C₂³×C₄	C₂×Dic₅₃	1	1	yes	characteristic
360	C₂³×C₄	C₂×Dic₅₃	1	1	yes	characteristic
361	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
362	C₂²×C₈	—	53	1	no	—
363	C₂²×C₈	—	53	1	no	—
364	C₂²×C₈	—	53	1	no	—
365	C₂²×C₈	—	53	1	no	—
366	C₂²×C₈	—	53	1	no	—
367	C₂²×C₈	—	53	1	no	—
368	C₂²×C₈	—	53	1	no	—
369	C₂²×C₈	—	53	1	no	—
370	C₂×C₄⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	C₂×Dic₅₃	1	1	yes	characteristic
378	C₂×C₄²	—	2	2	no	—
379	C₂×C₄²	—	2	2	no	—
380	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
381	C₂×C₄²	C₂×Dic₅₃	1	1	yes	characteristic
382	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
383	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
384	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
385	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
386	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
387	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
388	C₄⋊C₈	—	106	2	no	—
389	C₄⋊C₈	—	106	2	no	—
390	C₄⋊C₈	—	106	2	no	—
391	C₄⋊C₈	—	106	2	no	—
392	C₄⋊C₈	—	212	1	no	—
393	C₄⋊C₈	—	212	1	no	—
394	C₄⋊C₈	—	212	1	no	—
395	C₄⋊C₈	—	212	1	no	—
396	C₂²⋊C₈	—	212	1	no	—
397	C₂²⋊C₈	—	212	1	no	—
398	C₂²⋊C₈	—	212	1	no	—
399	C₂²⋊C₈	—	212	1	no	—
400	#97	—	212	1	no	—
401	#97	—	212	1	no	—
402	C₄×C₈	—	212	1	no	—
403	C₄×C₈	—	212	1	no	—
404	#95	C₂×Dic₅₃	1	1	yes	characteristic
405	#95	C₂×Dic₅₃	1	1	yes	characteristic
406	#95	C₂×Dic₅₃	1	1	yes	characteristic
407	#95	C₂×Dic₅₃	1	1	yes	characteristic
408	#95	C₂×Dic₅₃	1	1	yes	characteristic
409	#95	C₂×Dic₅₃	1	1	yes	characteristic
410	#95	C₂×Dic₅₃	1	1	yes	characteristic
411	#95	C₂×Dic₅₃	1	1	yes	characteristic
412	#95	C₂×Dic₅₃	1	1	yes	characteristic
413	#95	C₂×Dic₅₃	1	1	yes	characteristic
414	#95	C₂×Dic₅₃	1	1	yes	characteristic
415	#95	C₂×Dic₅₃	1	1	yes	characteristic
416	#95	C₂×Dic₅₃	1	1	yes	characteristic
417	#95	C₂×Dic₅₃	1	1	yes	characteristic
418	#95	C₂×Dic₅₃	1	1	yes	characteristic
419	#95	C₂×Dic₅₃	1	1	yes	characteristic
420	C₂⁴	C₂²×Dic₅₃	1	1	yes	characteristic
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
434	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
435	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
436	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
437	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
438	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
439	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
440	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
441	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
442	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
443	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
444	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
445	C₂²×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
446	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
447	C₂×C₈	—	106	1	no	—
448	C₂×C₈	—	106	1	no	—
449	C₂×C₈	—	106	1	no	—
450	C₂×C₈	—	106	1	no	—
451	C₂×C₈	—	106	1	no	—
452	C₂×C₈	—	106	1	no	—
453	C₂×C₈	—	106	1	no	—
454	C₂×C₈	—	106	1	no	—
455	C₂×C₈	—	106	1	no	—
456	C₂×C₈	—	106	1	no	—
457	C₂×C₈	—	106	1	no	—
458	C₂×C₈	—	106	1	no	—
459	C₂×C₈	—	106	1	no	—
460	C₂×C₈	—	106	1	no	—
461	C₂×C₈	—	106	1	no	—
462	C₂×C₈	—	106	1	no	—
463	C₂×C₈	—	106	1	no	—
464	C₂×C₈	—	106	1	no	—
465	C₂×C₈	—	106	1	no	—
466	C₂×C₈	—	106	1	no	—
467	C₂×C₈	—	106	1	no	—
468	C₂×C₈	—	106	1	no	—
469	C₂×C₈	—	106	1	no	—
470	C₂×C₈	—	106	1	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	2	2	no	—
477	C₂²⋊C₄	—	4	1	no	—
478	C₂²⋊C₄	—	4	1	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	#11719945	1	2	yes	—
492	C₄²	#11719945	1	2	yes	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	#13133224	1	2	yes	—
500	C₂³	C₂³×Dic₅₃	1	1	yes	characteristic
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	#13133176	1	2	yes	—
544	C₂×C₄	#13133176	1	2	yes	—
545	C₂×C₄	#13133224	1	2	yes	—
546	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
547	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
548	C₂×C₄	#13133263	1	1	yes	characteristic
549	C₂×C₄	#13133263	1	1	yes	characteristic
550	C₂×C₄	#13133264	1	1	yes	characteristic
551	C₂×C₄	#13133264	1	1	yes	characteristic
552	C₈	—	212	1	no	—
553	C₈	—	212	1	no	—
554	C₈	—	212	1	no	—
555	C₈	—	212	1	no	—
556	C₈	—	212	1	no	—
557	C₈	—	212	1	no	—
558	C₈	—	212	1	no	—
559	C₈	—	212	1	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	C₂×#13133176	1	1	yes	characteristic
568	C₂²	#16811106	1	1	yes	characteristic
569	C₂²	#16811106	1	1	yes	characteristic
570	C₂²	C₂×#13133224	1	1	yes	characteristic
571	C₂²	C₂×#13133224	1	1	yes	characteristic
572	C₂²	#16811390	1	1	yes	characteristic
573	C₂²	#16811390	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	#16811228	1	1	yes	characteristic
588	C₄	#16811235	1	1	yes	characteristic
589	C₄	#16811244	1	1	yes	characteristic
590	C₄	#16811244	1	1	yes	characteristic
591	C₂	—	4	2	no	—
592	C₂	#20277324	1	1	yes	characteristic
593	C₂	#20283373	1	1	yes	characteristic
594	C₂	#20283373	1	1	yes	characteristic
595	C₂	#20283854	1	1	yes	characteristic
596	C₂	#20283864	1	1	yes	characteristic
597	C₂	#20283875	1	1	yes	characteristic
598	C₂	#20283885	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅₃
commutator, socle	C₂³×C₅₃	C₂³×C₄
Fitting	C₅₃×#2283	C₂
prime radical	C₂⁴×C₅₃	C₂²×C₄
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#2283	D₅₃
hypocenter	C₅₃	#21928
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ #2283

Complements

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

N	H ≅ G/N	type
5. #20275281	C₂	semidirect
6. #20275281	C₂	semidirect
7. #20275274	C₂	semidirect
8. #20275274	C₂	semidirect
9. #20274869	C₂	semidirect
10. #20274835	C₂	semidirect
13. #20274572	C₂	semidirect
14. #20274572	C₂	semidirect
358. C₅₃	#21928	semidirect

Maximal subgroups

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

subgroup	index
#20275330	2
#20275323	2
#20275281	2
#20275274	2
#20274869	2
#20274835	2
#20274695	2
#20274572	2
C₅₃×#2283	2
#21928	53