Subgroups — #27349698

Order 13568.

834 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810674	C₂	1	1	yes	maximal, characteristic
2	#431×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20273006	C₂	1	2	yes	maximal, complemented
5	#20273006	C₂	1	2	yes	maximal, complemented
6	#20273005	C₂	1	1	yes	maximal, characteristic, complemented
7	#20273004	C₂	1	1	yes	maximal, characteristic, complemented
8	#20273003	C₂	1	2	yes	maximal, complemented
9	#20273002	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273001	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₅₃	C₄	1	2	yes	—
13	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
14	#16810676	C₂²	1	1	yes	characteristic
15	#16810675	C₄	1	2	yes	—
16	#16810674	C₄	1	2	yes	—
17	#16810674	C₄	1	2	yes	—
18	#16810674	C₂²	1	1	yes	characteristic
19	#16810674	C₂²	1	1	yes	characteristic
20	#16810674	C₂²	1	2	yes	—
21	#16810674	C₂²	1	1	yes	characteristic
22	#16810674	C₂²	1	1	yes	characteristic
23	#16810673	C₄	1	2	yes	—
24	C₂×#13133146	C₄	1	2	yes	—
25	C₄⋊C₈×D₅₃	C₄	1	2	yes	—
26	C₂×#13133129	C₄	1	2	yes	—
27	C₂²⋊C₈×D₅₃	C₄	1	2	yes	—
28	C₄×#11719917	C₂²	1	1	yes	characteristic
29	#16810575	C₄	1	2	yes	—
30	M₁₆×Dic₅₃	C₄	1	2	yes	—
31	C₄×#11719912	C₂²	1	2	yes	—
32	#97×D₅₃	C₄	1	2	yes	—
33	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₅₃	C₂²	1	2	yes	—
35	C₄×C₈×D₅₃	C₂²	1	2	yes	—
36	#16810345	C₂²	1	2	yes	complemented
37	#16810345	C₂²	1	2	yes	complemented
38	#16810345	C₂²	1	2	yes	complemented
39	#16810345	C₂²	1	2	yes	complemented
40	#16810344	C₂²	1	2	yes	complemented
41	#16810344	C₂²	1	2	yes	complemented
42	C₅₃×#431	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#322	C₂²	1	2	yes	complemented
46	C₅₃×#322	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
50	C₂×#11719917	C₂×C₄	1	2	yes	—
51	C₂×#11719912	C₂×C₄	1	4	yes	—
52	M₁₆×D₅₃	—	2	8	no	—
53	C₂²×#88322	C₂×C₄	1	2	yes	—
54	C₂×C₈×D₅₃	C₂×C₄	1	4	yes	—
55	C₂×C₈×D₅₃	C₂×C₄	1	4	yes	—
56	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₅₃	C₂³	1	1	yes	characteristic
66	C₄²×D₅₃	C₂³	1	1	yes	characteristic
67	C₄⋊#88322	C₂×C₄	1	2	yes	—
68	#13133146	C₂×C₄	1	4	yes	—
69	#13133146	C₂×C₄	1	2	yes	—
70	#13133146	C₂×C₄	1	2	yes	—
71	#13133146	C₂×C₄	1	2	yes	—
72	#13133146	C₂×C₄	1	2	yes	—
73	C₂²⋊#88322	C₂×C₄	1	2	yes	—
74	#13133129	C₂×C₄	1	4	yes	—
75	#13133129	C₂×C₄	1	2	yes	—
76	#13133129	C₂×C₄	1	2	yes	—
77	#13133129	C₂×C₄	1	2	yes	—
78	#13133129	C₂×C₄	1	2	yes	—
79	#13133128	C₂×C₄	1	2	yes	—
80	#13133127	C₂×C₄	1	4	yes	—
81	C₄×#88322	C₂×C₄	1	2	yes	—
82	C₄×#88322	C₂³	1	2	yes	—
83	C₄×#88322	C₂³	1	2	yes	—
84	C₄×#88322	C₂³	1	1	yes	characteristic
85	C₄×#88322	C₂³	1	1	yes	characteristic
86	C₈×Dic₅₃	C₂×C₄	1	4	yes	—
87	C₈×Dic₅₃	C₂×C₄	1	4	yes	—
88	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
89	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
90	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
92	C₂²⋊C₈×C₅₃	C₂×C₄	1	2	yes	—
93	#97×C₅₃	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₅₃	C₂³	1	2	yes	—
96	C₄×C₈×C₅₃	C₂³	1	2	yes	—
97	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
99	C₂³×D₅₃	C₄²	1	1	yes	characteristic
100	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×Dic₅₃	C₄²	1	1	yes	characteristic
104	C₂²×Dic₅₃	C₄²	1	1	yes	characteristic
105	C₂²×Dic₅₃	C₄²	1	1	yes	characteristic
106	C₂×C₄×D₅₃	—	4	2	no	—
107	C₂×C₄×D₅₃	—	4	2	no	—
108	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
109	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
110	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
111	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
112	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
113	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
114	C₂×C₄×D₅₃	M₁₆	1	8	yes	—
115	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
121	M₁₆×C₅₃	—	2	4	no	—
122	C₂×C₈×C₅₃	—	4	2	no	—
123	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
126	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
127	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
131	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
132	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
133	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
134	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
135	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
136	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
137	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
143	#11719917	—	2	4	no	—
144	C₂×#88322	—	4	2	no	—
145	C₂×#88322	C₂²×C₄	1	4	yes	—
146	C₂×#88322	C₂²×C₄	1	4	yes	—
147	C₂×#88322	C₂²×C₄	1	2	yes	—
148	C₂×#88322	C₂²×C₄	1	2	yes	—
149	#11719912	—	2	8	no	—
150	C₈×D₅₃	—	2	8	no	—
151	C₈×D₅₃	—	4	4	no	—
152	C₂³×C₅₃	C₂×C₄²	1	1	yes	characteristic
153	C₂²×D₅₃	—	4	1	no	—
154	C₂²×D₅₃	—	4	1	no	—
155	C₂²×D₅₃	#97	1	4	yes	—
156	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
157	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₅₃	—	2	2	no	—
159	C₂×C₄×C₅₃	—	2	2	no	—
160	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂×M₁₆	1	4	yes	—
164	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×Dic₅₃	—	4	1	no	—
168	C₂×Dic₅₃	—	4	1	no	—
169	C₂×Dic₅₃	#97	1	4	yes	—
170	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
171	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
172	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
173	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
174	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
175	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
176	C₄×D₅₃	—	2	2	no	—
177	C₄×D₅₃	—	2	2	no	—
178	C₄×D₅₃	—	2	2	no	—
179	C₄×D₅₃	—	2	2	no	—
180	C₄×D₅₃	—	4	1	no	—
181	C₄×D₅₃	—	4	1	no	—
182	C₄×D₅₃	—	4	1	no	—
183	C₄×D₅₃	—	4	1	no	—
184	C₄×D₅₃	#97	1	4	yes	—
185	C₄×D₅₃	#97	1	4	yes	—
186	C₄×D₅₃	C₂×M₁₆	1	4	yes	—
187	C₄×D₅₃	C₂×M₁₆	1	4	yes	—
188	C₈×C₅₃	—	2	4	no	—
189	C₈×C₅₃	—	2	4	no	—
190	C₈×C₅₃	—	2	2	no	—
191	C₈×C₅₃	—	2	2	no	—
192	#88322	—	2	4	no	—
193	#88322	—	2	4	no	—
194	#88322	—	2	2	no	—
195	#88322	—	2	2	no	—
196	#17319	—	53	1	no	maximal, Sylow
197	C₂²×C₅₃	—	2	1	no	—
198	C₂²×C₅₃	—	2	1	no	—
199	C₂²×C₅₃	C₂×#97	1	2	yes	—
200	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
201	C₂×D₅₃	—	2	1	no	—
202	C₂×D₅₃	—	2	1	no	—
203	C₂×D₅₃	—	2	1	no	—
204	C₂×D₅₃	—	2	1	no	—
205	C₂×D₅₃	—	4	4	no	—
206	C₂×D₅₃	C₂×#97	1	2	yes	—
207	C₂×D₅₃	C₂×#97	1	2	yes	—
208	C₄×C₅₃	—	2	1	no	—
209	C₄×C₅₃	—	2	1	no	—
210	C₄×C₅₃	C₂×#97	1	2	yes	—
211	C₄×C₅₃	C₂²×M₁₆	1	2	yes	—
212	C₄×C₅₃	#568	1	2	yes	—
213	C₄×C₅₃	#568	1	2	yes	—
214	Dic₅₃	—	2	1	no	—
215	Dic₅₃	—	2	1	no	—
216	Dic₅₃	—	2	1	no	—
217	Dic₅₃	—	2	1	no	—
218	Dic₅₃	C₂×#97	1	2	yes	—
219	Dic₅₃	C₂×#97	1	2	yes	—
220	C₂×#431	—	53	1	no	—
221	C₂×#431	—	53	1	no	—
222	C₂×C₄×M₁₆	—	53	1	no	—
223	#1452	—	53	2	no	—
224	#1452	—	53	2	no	—
225	#1451	—	53	1	no	—
226	#1451	—	53	1	no	—
227	#1451	—	53	1	no	—
228	#1451	—	53	2	no	—
229	#1451	—	53	2	no	—
230	#1451	D₅₃	1	1	yes	characteristic, complemented
231	C₂×C₅₃	—	2	2	no	—
232	C₂×C₅₃	C₂²×#97	1	1	yes	characteristic
233	C₂×C₅₃	#2873	1	1	yes	characteristic
234	C₂×C₅₃	#2873	1	1	yes	characteristic
235	D₅₃	—	2	2	no	—
236	D₅₃	—	2	2	no	—
237	C₂²×M₁₆	—	53	2	no	—
238	C₂²×C₄²	—	53	1	no	—
239	#431	—	53	1	no	—
240	#431	—	53	2	no	—
241	#431	—	53	2	no	—
242	#431	—	53	2	no	—
243	#431	—	53	2	no	—
244	#431	—	53	1	no	—
245	#431	—	53	1	no	—
246	#431	—	53	2	no	—
247	#431	—	53	1	no	—
248	#431	—	53	1	no	—
249	#431	C₂×D₅₃	1	1	yes	characteristic
250	C₂×C₄⋊C₈	—	53	2	no	—
251	C₂×C₄⋊C₈	—	53	2	no	—
252	C₂×C₂²⋊C₈	—	53	2	no	—
253	C₂×C₂²⋊C₈	—	53	2	no	—
254	C₄×M₁₆	—	53	2	no	—
255	C₄×M₁₆	—	53	1	no	—
256	C₄×M₁₆	—	53	2	no	—
257	C₄×M₁₆	—	53	2	no	—
258	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic
259	C₂×#97	—	53	2	no	—
260	C₂×C₄×C₈	—	53	1	no	—
261	C₂×C₄×C₈	—	53	2	no	—
262	C₂×C₄×C₈	—	53	2	no	—
263	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
264	#322	—	53	2	no	—
265	#322	—	53	2	no	—
266	#322	—	53	2	no	—
267	#322	—	53	2	no	—
268	#322	—	53	2	no	—
269	#322	—	53	2	no	—
270	#322	C₂×D₅₃	1	2	yes	complemented
271	#322	C₂×D₅₃	1	2	yes	complemented
272	C₅₃	#17319	1	1	yes	characteristic, complemented, Sylow
273	C₂³×C₄	—	53	1	no	—
274	C₂³×C₄	—	53	1	no	—
275	C₂³×C₄	—	53	1	no	—
276	C₂×M₁₆	—	53	2	no	—
277	C₂×M₁₆	—	53	4	no	—
278	C₂×M₁₆	—	106	8	no	—
279	C₂×M₁₆	C₄×D₅₃	1	2	yes	—
280	C₂²×C₈	—	53	2	no	—
281	C₂²×C₈	—	53	4	no	—
282	C₂²×C₈	—	53	4	no	—
283	C₂²×C₈	C₄×D₅₃	1	2	yes	—
284	C₂×C₄²	—	53	1	no	—
285	C₂×C₄²	—	53	1	no	—
286	C₂×C₄²	—	53	1	no	—
287	C₂×C₄²	—	53	1	no	—
288	C₂×C₄²	—	53	1	no	—
289	C₂×C₄²	—	53	1	no	—
290	C₂×C₄²	—	53	1	no	—
291	C₂×C₄²	—	53	1	no	—
292	C₂×C₄²	—	53	1	no	—
293	C₂×C₄²	—	53	1	no	—
294	C₂×C₄²	—	53	1	no	—
295	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
296	C₄⋊C₈	—	53	4	no	—
297	C₄⋊C₈	—	53	2	no	—
298	C₄⋊C₈	—	53	2	no	—
299	C₄⋊C₈	—	53	2	no	—
300	C₄⋊C₈	—	53	2	no	—
301	C₄⋊C₈	—	53	2	no	—
302	C₄⋊C₈	C₄×D₅₃	1	2	yes	—
303	C₂²⋊C₈	—	53	2	no	—
304	C₂²⋊C₈	—	53	4	no	—
305	C₂²⋊C₈	—	53	2	no	—
306	C₂²⋊C₈	—	53	2	no	—
307	C₂²⋊C₈	—	53	2	no	—
308	C₂²⋊C₈	—	53	2	no	—
309	C₂²⋊C₈	C₄×D₅₃	1	2	yes	—
310	#97	—	53	4	no	—
311	#97	—	53	2	no	—
312	#97	C₄×D₅₃	1	2	yes	—
313	C₄×C₈	—	53	4	no	—
314	C₄×C₈	—	53	4	no	—
315	C₄×C₈	—	53	2	no	—
316	C₄×C₈	—	53	2	no	—
317	C₄×C₈	—	53	1	no	—
318	C₄×C₈	—	53	2	no	—
319	C₄×C₈	—	53	1	no	—
320	C₄×C₈	C₄×D₅₃	1	2	yes	—
321	C₄×C₈	C₂²×D₅₃	1	2	yes	—
322	C₄×C₈	C₂²×D₅₃	1	2	yes	—
323	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
324	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
325	C₂⁴	—	53	1	no	—
326	C₂²×C₄	—	53	1	no	—
327	C₂²×C₄	—	53	1	no	—
328	C₂²×C₄	—	53	1	no	—
329	C₂²×C₄	—	53	8	no	—
330	C₂²×C₄	—	53	1	no	—
331	C₂²×C₄	—	53	1	no	—
332	C₂²×C₄	—	53	1	no	—
333	C₂²×C₄	—	53	1	no	—
334	C₂²×C₄	—	53	1	no	—
335	C₂²×C₄	—	53	1	no	—
336	C₂²×C₄	—	53	1	no	—
337	C₂²×C₄	—	53	1	no	—
338	C₂²×C₄	—	53	1	no	—
339	C₂²×C₄	—	53	1	no	—
340	C₂²×C₄	—	53	1	no	—
341	C₂²×C₄	—	53	1	no	—
342	C₂²×C₄	—	212	2	no	—
343	C₂²×C₄	—	212	2	no	—
344	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
347	M₁₆	—	2	4	no	—
348	M₁₆	—	106	8	no	—
349	M₁₆	—	106	4	no	—
350	C₂×C₈	—	4	2	no	—
351	C₂×C₈	—	53	4	no	—
352	C₂×C₈	—	53	4	no	—
353	C₂×C₈	—	53	2	no	—
354	C₂×C₈	—	53	2	no	—
355	C₂×C₈	—	106	8	no	—
356	C₂×C₈	—	212	4	no	—
357	C₂×C₈	—	212	2	no	—
358	C₂×C₈	C₂×C₄×D₅₃	1	4	yes	—
359	C₂×C₈	C₂×C₄×D₅₃	1	4	yes	—
360	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
361	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
362	C₄²	—	53	1	no	—
363	C₄²	—	53	1	no	—
364	C₄²	—	53	1	no	—
365	C₄²	—	53	1	no	—
366	C₄²	—	53	1	no	—
367	C₄²	—	53	1	no	—
368	C₄²	—	53	1	no	—
369	C₄²	—	53	1	no	—
370	C₄²	—	53	1	no	—
371	C₄²	—	53	1	no	—
372	C₄²	—	53	1	no	—
373	C₄²	—	53	1	no	—
374	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
375	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
376	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
377	C₄²	C₂³×D₅₃	1	1	yes	characteristic
378	C₂³	—	53	1	no	—
379	C₂³	—	53	1	no	—
380	C₂³	—	53	4	no	—
381	C₂³	—	212	1	no	—
382	C₂³	—	212	1	no	—
383	C₂³	C₄²×D₅₃	1	1	yes	characteristic
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	53	1	no	—
387	C₂×C₄	—	53	1	no	—
388	C₂×C₄	—	53	4	no	—
389	C₂×C₄	—	53	4	no	—
390	C₂×C₄	—	53	4	no	—
391	C₂×C₄	—	53	4	no	—
392	C₂×C₄	—	53	4	no	—
393	C₂×C₄	—	53	1	no	—
394	C₂×C₄	—	53	1	no	—
395	C₂×C₄	—	53	1	no	—
396	C₂×C₄	—	53	1	no	—
397	C₂×C₄	—	106	2	no	—
398	C₂×C₄	—	106	2	no	—
399	C₂×C₄	—	106	2	no	—
400	C₂×C₄	—	106	2	no	—
401	C₂×C₄	—	212	1	no	—
402	C₂×C₄	—	212	1	no	—
403	C₂×C₄	—	212	1	no	—
404	C₂×C₄	—	212	1	no	—
405	C₂×C₄	—	212	1	no	—
406	C₂×C₄	—	212	1	no	—
407	C₂×C₄	C₄²×D₅₃	1	1	yes	characteristic
408	C₂×C₄	C₄²×D₅₃	1	1	yes	characteristic
409	C₂×C₄	C₄²×D₅₃	1	1	yes	characteristic
410	C₂×C₄	M₁₆×D₅₃	1	4	yes	—
411	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
414	C₈	—	2	4	no	—
415	C₈	—	2	4	no	—
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	106	4	no	—
419	C₈	—	106	4	no	—
420	C₈	—	106	2	no	—
421	C₈	—	106	2	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	53	2	no	—
425	C₂²	—	53	2	no	—
426	C₂²	—	106	1	no	—
427	C₂²	—	106	1	no	—
428	C₂²	—	106	1	no	—
429	C₂²	—	106	1	no	—
430	C₂²	—	212	4	no	—
431	C₂²	#97×D₅₃	1	2	yes	—
432	C₂²	C₂×C₄²×D₅₃	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	53	2	no	—
436	C₄	—	53	2	no	—
437	C₄	—	106	1	no	—
438	C₄	—	106	1	no	—
439	C₄	—	106	1	no	—
440	C₄	—	106	1	no	—
441	C₄	#97×D₅₃	1	2	yes	—
442	C₄	C₂×M₁₆×D₅₃	1	2	yes	—
443	C₄	#16811388	1	2	yes	—
444	C₄	#16811389	1	2	yes	—
445	C₂	—	2	2	no	—
446	C₂	—	106	2	no	—
447	C₂	—	106	2	no	—
448	C₂	C₂×#97×D₅₃	1	1	yes	characteristic
449	C₂	#20283131	1	1	yes	characteristic
450	C₂	#20283132	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₅₃
commutator, socle	C₂²×C₅₃	C₂²×C₄²
Fitting	C₅₃×#1451	C₂
prime radical	C₂³×D₅₃	C₄²
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	#1451	D₅₃
hypocenter	C₅₃	#17319
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄² ◁ #1451

Complements

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

N	H ≅ G/N	type
4. #20273006	C₂	semidirect
5. #20273006	C₂	semidirect
6. #20273005	C₂	semidirect
7. #20273004	C₂	semidirect
8. #20273003	C₂	semidirect
9. #20273002	C₂	semidirect
10. #20273001	C₂	semidirect
11. C₅₃×#1451	C₂	semidirect
36. #16810345	C₂²	semidirect
37. #16810345	C₂²	semidirect
38. #16810345	C₂²	semidirect
39. #16810345	C₂²	semidirect
40. #16810344	C₂²	semidirect
41. #16810344	C₂²	semidirect
45. C₅₃×#322	C₂²	semidirect
46. C₅₃×#322	C₂²	semidirect
230. #1451	D₅₃	semidirect
270. #322	C₂×D₅₃	semidirect
271. #322	C₂×D₅₃	semidirect
272. C₅₃	#17319	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16810674	2
#431×D₅₃	2
C₄×M₁₆×D₅₃	2
#20273006	2
#20273005	2
#20273004	2
#20273003	2
#20273002	2
#20273001	2
C₅₃×#1451	2
#17319	53