Subgroups — #28328258

Order 13568.

590 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291082	C₂	1	2	yes	maximal, complemented
2	#20291081	C₂	1	2	yes	maximal, complemented
3	#20291079	C₂	1	1	yes	maximal, characteristic, complemented
4	#20291076	C₂	1	1	yes	maximal, characteristic, complemented
5	#20291075	C₂	1	1	yes	maximal, characteristic, complemented
6	#20291072	C₂	1	1	yes	maximal, characteristic, complemented
7	#20291048	C₂	1	1	yes	maximal, characteristic, complemented
8	D₅₃⋊(C₄⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
9	#20290946	C₂	1	2	yes	maximal
10	#20290925	C₂	1	2	yes	maximal, complemented
11	C₄×#13133225	C₂	1	1	yes	maximal, characteristic
12	C₂×#13133292	C₂²	1	2	yes	—
13	C₂×D₅₃⋊C₁₆	C₂²	1	2	yes	—
14	#16811544	C₂²	1	2	yes	—
15	#16811544	C₂²	1	2	yes	—
16	C₄⋊#11719910	C₂²	1	1	yes	characteristic
17	C₄⋊#11719910	C₂²	1	1	yes	characteristic
18	C₄⋊#11719910	C₂²	1	1	yes	characteristic
19	C₄⋊#11719910	C₂²	1	1	yes	characteristic
20	#16811518	C₂²	1	2	yes	—
21	#16811518	C₂²	1	2	yes	—
22	C₂²⋊#11719910	C₂²	1	2	yes	—
23	C₂²⋊#11719910	C₂²	1	2	yes	—
24	#16811512	C₂²	1	2	yes	—
25	#16811511	C₂²	1	2	yes	—
26	#16811509	C₂²	1	2	yes	—
27	C₄×#11719910	C₂²	1	2	yes	—
28	C₂×#13133225	C₄	1	1	yes	characteristic
29	C₂×#13133225	C₂²	1	1	yes	characteristic
30	C₄×#11719945	C₄	1	1	yes	characteristic
31	#16810581	C₄	1	1	yes	characteristic
32	#16810581	C₂²	1	1	yes	characteristic
33	#16810580	C₄	1	1	yes	characteristic
34	#16810580	C₄	1	1	yes	characteristic
35	#16810580	C₂²	1	1	yes	characteristic
36	#16810580	C₂²	1	1	yes	characteristic
37	C₄×#11719912	C₄	1	1	yes	characteristic
38	C₄×#11719912	C₄	1	1	yes	characteristic
39	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
42	C₄×M₁₆×C₅₃	C₄	1	1	yes	characteristic
43	#13133292	—	2	4	no	—
44	D₅₃⋊C₁₆	—	2	4	no	—
45	C₂×#11719910	C₂³	1	2	yes	—
46	C₂×#11719910	C₂³	1	2	yes	—
47	C₂×#11719910	C₂³	1	2	yes	—
48	C₂×#11719910	C₂³	1	2	yes	—
49	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
50	#13133225	—	2	4	no	—
51	#13133225	—	2	2	no	—
52	#13133225	—	2	2	no	—
53	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
54	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
55	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
56	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
57	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
58	C₂²×#88322	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
63	C₄×Dic₁₀₆	C₈	1	1	yes	characteristic
64	C₄×Dic₁₀₆	C₈	1	1	yes	characteristic
65	C₄×D₂₁₂	C₈	1	1	yes	characteristic
66	C₄×D₂₁₂	C₈	1	1	yes	characteristic
67	C₄×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
68	C₄×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
69	C₄×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
70	C₄×C₂²⋊D₅₃	C₈	1	1	yes	characteristic
71	#13133176	C₂×C₄	1	1	yes	characteristic
72	#13133174	C₂×C₄	1	1	yes	characteristic
73	#13133174	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
75	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
76	#13133127	C₂×C₄	1	1	yes	characteristic
77	#13133127	C₂×C₄	1	1	yes	characteristic
78	#13133127	C₂×C₄	1	1	yes	characteristic
79	#13133127	C₂×C₄	1	1	yes	characteristic
80	C₄×#88322	C₂×C₄	1	1	yes	characteristic
81	C₄×#88322	C₂×C₄	1	1	yes	characteristic
82	C₄×#88322	C₂³	1	1	yes	characteristic
83	C₄×#88322	C₂³	1	1	yes	characteristic
84	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
87	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
89	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
91	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
92	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
93	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
94	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
97	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
99	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
100	#11719945	—	2	2	no	—
101	#11719945	—	2	2	no	—
102	C₂×D₂₁₂	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
107	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×Dic₁₀₆	C₂×C₈	1	1	yes	characteristic
110	M₁₆×C₅₃	—	2	2	no	—
111	M₁₆×C₅₃	—	2	2	no	—
112	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₅₃	C₂×C₈	1	1	yes	characteristic
117	C₄²×C₅₃	C₂×C₈	1	1	yes	characteristic
118	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
121	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
122	#11719921	C₂×C₈	1	1	yes	characteristic
123	#11719921	C₂×C₈	1	1	yes	characteristic
124	#11719921	C₂×C₈	1	1	yes	characteristic
125	#11719921	C₂×C₈	1	1	yes	characteristic
126	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
127	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
128	#11719919	C₂×C₈	1	1	yes	characteristic
129	#11719919	C₂×C₈	1	1	yes	characteristic
130	#11719919	C₂×C₈	1	1	yes	characteristic
131	#11719919	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
136	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×#88322	—	2	2	no	—
139	C₂×#88322	—	2	1	no	—
140	C₂×#88322	—	2	1	no	—
141	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
142	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
143	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
144	C₂×#88322	C₂⁴	1	1	yes	characteristic
145	#11719912	—	2	2	no	—
146	#11719912	—	2	2	no	—
147	#11719912	—	2	2	no	—
148	#11719912	M₁₆	1	4	yes	—
149	C₈×D₅₃	—	2	2	no	—
150	C₈×D₅₃	—	2	2	no	—
151	C₈×D₅₃	—	2	1	no	—
152	C₈×D₅₃	—	2	1	no	—
153	C₈×D₅₃	#41	1	2	yes	—
154	C₈×D₅₃	#41	1	2	yes	—
155	#11719910	—	2	2	no	—
156	#11719910	—	2	2	no	—
157	#11719910	—	2	2	no	—
158	#11719910	—	2	2	no	—
159	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
160	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
161	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₅₃	—	2	1	no	—
163	C₂×C₄×C₅₃	—	2	1	no	—
164	C₂×C₄×C₅₃	—	2	2	no	—
165	C₂×C₄×C₅₃	—	4	1	no	—
166	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
172	C₂²⋊D₅₃	—	2	2	no	—
173	C₂²⋊D₅₃	—	2	2	no	—
174	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
175	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
176	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
177	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
180	D₂₁₂	—	2	2	no	—
181	C₄×D₅₃	—	2	1	no	—
182	C₄×D₅₃	—	2	1	no	—
183	C₄×D₅₃	—	2	2	no	—
184	C₄×D₅₃	—	2	2	no	—
185	C₄×D₅₃	—	4	1	no	—
186	C₄×D₅₃	—	4	1	no	—
187	C₄×D₅₃	#117	1	2	yes	—
188	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
189	Dic₁₀₆	—	2	2	no	—
190	C₈×C₅₃	—	2	1	no	—
191	C₈×C₅₃	—	2	1	no	—
192	C₈×C₅₃	#117	1	2	yes	—
193	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
194	#88322	—	2	1	no	—
195	#88322	—	2	1	no	—
196	#88322	C₂×M₁₆	1	2	yes	—
197	#88322	C₂×#41	1	1	yes	characteristic
198	#88322	C₂×#41	1	1	yes	characteristic
199	#33423	—	53	1	no	maximal, Sylow
200	C₂²×C₅₃	—	2	1	no	—
201	C₂²×C₅₃	—	2	1	no	—
202	C₂²×C₅₃	—	2	1	no	—
203	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
204	C₂×D₅₃	—	2	1	no	—
205	C₂×D₅₃	—	2	1	no	—
206	C₂×D₅₃	—	2	1	no	—
207	C₂×D₅₃	—	2	1	no	—
208	C₂×D₅₃	—	2	1	no	—
209	C₂×D₅₃	#431	1	2	yes	—
210	C₄×C₅₃	—	2	1	no	—
211	C₄×C₅₃	—	2	1	no	—
212	C₄×C₅₃	—	2	1	no	—
213	C₄×C₅₃	—	2	1	no	—
214	C₄×C₅₃	#504	1	2	yes	—
215	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
216	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
217	Dic₅₃	—	2	1	no	—
218	Dic₅₃	—	2	1	no	—
219	Dic₅₃	—	2	1	no	—
220	Dic₅₃	—	2	1	no	—
221	Dic₅₃	—	2	1	no	—
222	Dic₅₃	#431	1	2	yes	—
223	C₄×#131	—	53	1	no	—
224	#2164	—	53	2	no	—
225	#2164	—	53	2	no	—
226	#2163	—	53	1	no	—
227	#2163	—	53	1	no	—
228	#2162	—	53	1	no	—
229	#2162	—	53	1	no	—
230	#2150	—	53	1	no	—
231	C₂×C₄⋊C₁₆	—	53	1	no	—
232	#2113	—	53	2	no	—
233	#2108	—	53	2	no	—
234	C₂×C₅₃	—	4	1	no	—
235	C₂×C₅₃	C₂×#431	1	1	yes	characteristic
236	C₂×C₅₃	C₂×#504	1	1	yes	characteristic
237	C₂×C₅₃	#3407	1	1	yes	characteristic
238	D₅₃	—	2	2	no	—
239	D₅₃	—	4	1	no	—
240	C₂×#131	—	53	1	no	—
241	C₂×#131	—	53	1	no	—
242	C₄×#41	—	53	1	no	—
243	C₂×M₃₂	—	53	2	no	—
244	C₂²×C₁₆	—	53	2	no	—
245	#405	—	53	1	no	—
246	#405	—	53	1	no	—
247	#405	—	53	1	no	—
248	#405	—	53	1	no	—
249	#405	—	53	1	no	—
250	#405	—	53	1	no	—
251	C₄×M₁₆	—	53	1	no	—
252	C₄×M₁₆	—	53	1	no	—
253	C₄×M₁₆	#6157	1	1	yes	characteristic
254	C₂×C₄×C₈	—	53	1	no	—
255	C₂×C₄×C₈	—	53	1	no	—
256	C₂×C₄×C₈	—	53	1	no	—
257	C₄⋊C₁₆	—	53	1	no	—
258	C₄⋊C₁₆	—	53	1	no	—
259	C₄⋊C₁₆	—	53	1	no	—
260	C₄⋊C₁₆	—	53	1	no	—
261	C₄⋊C₁₆	—	53	2	no	—
262	C₄⋊C₁₆	—	53	2	no	—
263	C₂²⋊C₁₆	—	53	2	no	—
264	C₂²⋊C₁₆	—	53	2	no	—
265	C₂²⋊C₁₆	—	53	2	no	—
266	C₂²⋊C₁₆	—	53	2	no	—
267	#346	—	53	2	no	—
268	#346	—	53	2	no	—
269	C₄×C₁₆	—	53	2	no	—
270	C₄×C₁₆	—	53	2	no	—
271	C₅₃	#33423	1	1	yes	characteristic, complemented, Sylow
272	C₂×#41	—	53	1	no	—
273	#131	—	106	2	no	—
274	#131	—	106	2	no	—
275	#131	—	106	4	no	—
276	C₂×M₁₆	—	53	1	no	—
277	C₂×M₁₆	—	53	1	no	—
278	C₂×M₁₆	—	53	1	no	—
279	C₂×M₁₆	—	53	1	no	—
280	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
281	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
282	C₂²×C₈	—	53	1	no	—
283	C₂²×C₈	—	53	1	no	—
284	C₂²×C₈	—	53	1	no	—
285	C₂²×C₈	—	53	1	no	—
286	C₂²×C₈	—	53	1	no	—
287	C₂²×C₈	—	53	1	no	—
288	C₄×Q₈	—	53	1	no	—
289	C₄×Q₈	—	53	1	no	—
290	C₄×D₄	—	53	1	no	—
291	C₄×D₄	—	53	1	no	—
292	C₄×D₄	—	53	1	no	—
293	C₄×D₄	—	53	1	no	—
294	C₄×D₄	—	53	1	no	—
295	C₄×D₄	—	53	1	no	—
296	#117	—	53	1	no	—
297	#117	—	53	1	no	—
298	#117	—	53	1	no	—
299	C₂×C₄²	—	53	1	no	—
300	C₂×C₄²	—	53	1	no	—
301	C₂×C₄²	C₂×#6157	1	1	yes	characteristic
302	M₃₂	—	106	4	no	—
303	C₂×C₁₆	—	53	2	no	—
304	C₂×C₁₆	—	53	2	no	—
305	C₂×C₁₆	—	53	2	no	—
306	C₂×C₁₆	—	53	2	no	—
307	C₂×C₁₆	—	106	4	no	—
308	#97	—	53	1	no	—
309	#97	—	53	1	no	—
310	#97	—	53	1	no	—
311	#97	—	53	1	no	—
312	#97	C₂×#6157	1	1	yes	characteristic
313	#97	C₂×#6157	1	1	yes	characteristic
314	C₄×C₈	—	53	1	no	—
315	C₄×C₈	—	53	1	no	—
316	C₄×C₈	—	53	1	no	—
317	C₄×C₈	—	53	1	no	—
318	C₄×C₈	—	53	1	no	—
319	C₄×C₈	—	53	1	no	—
320	C₄×C₈	—	53	1	no	—
321	C₄×C₈	—	53	1	no	—
322	C₄×C₈	C₂×#6157	1	1	yes	characteristic
323	C₄×C₈	C₂×#6157	1	1	yes	characteristic
324	#41	—	106	2	no	—
325	#41	—	106	2	no	—
326	C₂×Q₈	—	53	1	no	—
327	C₂×D₄	—	53	1	no	—
328	C₂×D₄	—	53	1	no	—
329	C₂×D₄	—	53	1	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	D₅₃⋊C₈	1	1	yes	characteristic
337	C₂²×C₄	D₅₃⋊C₈	1	1	yes	characteristic
338	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
339	M₁₆	—	2	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	53	4	no	—
342	M₁₆	—	106	2	no	—
343	M₁₆	—	106	2	no	—
344	M₁₆	—	106	2	no	—
345	C₂×C₈	—	53	1	no	—
346	C₂×C₈	—	53	1	no	—
347	C₂×C₈	—	53	2	no	—
348	C₂×C₈	—	53	2	no	—
349	C₂×C₈	—	53	1	no	—
350	C₂×C₈	—	53	1	no	—
351	C₂×C₈	—	106	1	no	—
352	C₂×C₈	—	106	1	no	—
353	C₂×C₈	—	106	2	no	—
354	C₂×C₈	—	106	1	no	—
355	C₂×C₈	—	106	1	no	—
356	C₂×C₈	—	106	2	no	—
357	C₂×C₈	—	106	2	no	—
358	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
359	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
360	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
361	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
362	C₄⋊C₄	—	53	1	no	—
363	C₄⋊C₄	—	53	1	no	—
364	C₄⋊C₄	—	53	1	no	—
365	C₄⋊C₄	—	53	1	no	—
366	C₄⋊C₄	—	53	1	no	—
367	C₄⋊C₄	—	53	1	no	—
368	C₂²⋊C₄	—	53	1	no	—
369	C₂²⋊C₄	—	53	1	no	—
370	C₂²⋊C₄	—	53	1	no	—
371	C₂²⋊C₄	—	53	1	no	—
372	C₂²⋊C₄	—	53	1	no	—
373	C₂²⋊C₄	—	53	1	no	—
374	C₄²	—	53	1	no	—
375	C₄²	—	53	1	no	—
376	C₄²	—	53	1	no	—
377	C₄²	—	53	1	no	—
378	C₄²	—	53	1	no	—
379	C₄²	—	53	1	no	—
380	C₄²	D₅₃⋊C₈	1	1	yes	characteristic
381	C₄²	D₅₃⋊C₈	1	1	yes	characteristic
382	C₄²	C₂²×#6157	1	1	yes	characteristic
383	C₄²	C₂²×#6157	1	1	yes	characteristic
384	C₁₆	—	106	2	no	—
385	C₁₆	—	106	2	no	—
386	C₁₆	—	106	2	no	—
387	C₁₆	—	106	2	no	—
388	C₂³	—	53	1	no	—
389	C₂³	—	53	1	no	—
390	C₂³	C₂×D₅₃⋊C₈	1	1	yes	characteristic
391	Q₈	—	106	2	no	—
392	D₄	—	106	2	no	—
393	D₄	—	106	2	no	—
394	D₄	—	106	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	53	1	no	—
400	C₂×C₄	—	53	2	no	—
401	C₂×C₄	—	53	2	no	—
402	C₂×C₄	—	53	1	no	—
403	C₂×C₄	—	53	1	no	—
404	C₂×C₄	—	53	1	no	—
405	C₂×C₄	—	53	1	no	—
406	C₂×C₄	—	53	1	no	—
407	C₂×C₄	—	106	2	no	—
408	C₂×C₄	—	106	2	no	—
409	C₂×C₄	—	106	1	no	—
410	C₂×C₄	—	106	1	no	—
411	C₂×C₄	—	212	1	no	—
412	C₂×C₄	—	212	1	no	—
413	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
414	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
415	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
416	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
417	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
418	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	53	1	no	—
422	C₈	—	53	1	no	—
423	C₈	—	53	2	no	—
424	C₈	—	106	1	no	—
425	C₈	—	106	1	no	—
426	C₈	#13133296	1	2	yes	—
427	C₈	D₅₃⋊M₁₆	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	53	2	no	—
432	C₂²	—	106	1	no	—
433	C₂²	—	106	1	no	—
434	C₂²	—	106	1	no	—
435	C₂²	—	106	1	no	—
436	C₂²	—	106	1	no	—
437	C₂²	C₂²×D₅₃⋊C₈	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	53	2	no	—
443	C₄	—	106	1	no	—
444	C₄	—	106	1	no	—
445	C₄	—	106	1	no	—
446	C₄	—	106	1	no	—
447	C₄	—	106	1	no	—
448	C₄	#16811682	1	2	yes	—
449	C₄	C₂×#13133296	1	1	yes	characteristic
450	C₄	C₂×D₅₃⋊M₁₆	1	1	yes	characteristic
451	C₂	—	4	1	no	—
452	C₂	—	106	2	no	—
453	C₂	—	212	1	no	—
454	C₂	D₅₃⋊#431	1	1	yes	characteristic
455	C₂	C₂×#16811682	1	1	yes	characteristic
456	C₂	#20291684	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6157
commutator, socle	C₂²×C₅₃	C₂³×C₈
Fitting	C₄×M₁₆×C₅₃	C₄
prime radical	C₂×#11719945	C₂×C₄
cosocle	C₂×#88322	C₂⁴
hypercenter	C₄×M₁₆	#6157
hypocenter	C₅₃	#33423
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
1. #20291082	C₂	semidirect
2. #20291081	C₂	semidirect
3. #20291079	C₂	semidirect
4. #20291076	C₂	semidirect
5. #20291075	C₂	semidirect
6. #20291072	C₂	semidirect
7. #20291048	C₂	semidirect
8. D₅₃⋊(C₄⋊C₁₆)	C₂	semidirect
10. #20290925	C₂	semidirect
271. C₅₃	#33423	semidirect

Maximal subgroups

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

subgroup	index
#20291082	2
#20291081	2
#20291079	2
#20291076	2
#20291075	2
#20291072	2
#20291048	2
D₅₃⋊(C₄⋊C₁₆)	2
#20290946	2
#20290925	2
C₄×#13133225	2
#33423	53