Subgroups — D₅₃⋊#1569 #28316119

Order 13568.

758 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₃⋊#432	C₂	1	1	yes	maximal, characteristic
2	D₅₃⋊#423	C₂	1	1	yes	maximal, characteristic
3	#20290281	C₂	1	2	yes	maximal, complemented
4	#20290280	C₂	1	2	yes	maximal, complemented
5	#20290279	C₂	1	4	yes	maximal, complemented
6	D₅₃⋊#335	C₂	1	2	yes	maximal, complemented
7	D₅₃⋊#334	C₂	1	2	yes	maximal, complemented
8	C₄×M₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
9	C₂×D₅₃⋊M₁₆	—	2	1	no	—
10	#16811646	—	2	1	no	—
11	#16811645	C₂²	1	2	yes	—
12	#16811644	C₂²	1	2	yes	—
13	#16811643	—	2	1	no	—
14	#16811628	—	2	1	no	—
15	#16811627	C₂²	1	2	yes	—
16	#16811626	—	2	1	no	—
17	#16811626	C₂²	1	2	yes	—
18	D₅₃⋊(C₄⋊C₈)	—	2	1	no	—
19	D₅₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
20	D₅₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
21	D₅₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
22	D₅₃⋊(C₂²⋊C₈)	—	2	1	no	—
23	#16811582	—	2	1	no	—
24	#16811487	C₂²	1	4	yes	complemented
25	#16811486	C₂²	1	4	yes	complemented
26	#16811485	C₂²	1	4	yes	complemented
27	#16811484	C₂²	1	4	yes	complemented
28	C₂×M₁₆×D₅₃	C₄	1	2	yes	—
29	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
30	C₄×#11719917	C₄	1	1	yes	characteristic
31	#16810575	C₂²	1	1	yes	characteristic
32	#16810575	C₂²	1	1	yes	characteristic
33	M₁₆×Dic₅₃	C₂²	1	2	yes	—
34	C₄×#11719912	C₄	1	2	yes	—
35	#97×D₅₃	C₄	1	1	yes	characteristic
36	#97×D₅₃	C₄	1	1	yes	characteristic
37	C₄×C₈×D₅₃	C₂²	1	2	yes	—
38	C₄×M₁₆×C₅₃	C₄	1	1	yes	characteristic
39	C₂×#11719936	—	2	2	no	—
40	D₅₃⋊M₁₆	—	4	4	no	—
41	C₂×#11719940	—	2	2	no	—
42	C₂×D₅₃⋊C₈	—	2	1	no	—
43	C₂×D₅₃⋊C₈	—	2	1	no	—
44	C₂×D₅₃⋊C₈	—	2	2	no	—
45	#13133284	—	2	2	no	—
46	#13133284	—	2	2	no	—
47	#13133284	—	2	1	no	—
48	#13133284	—	2	1	no	—
49	C₄⋊#88324	—	2	2	no	—
50	C₄⋊#88324	C₂³	1	4	yes	—
51	C₄⋊#88324	C₂³	1	2	yes	—
52	C₄⋊#88324	C₂³	1	2	yes	—
53	#13133274	—	2	2	no	—
54	C₂²⋊#88324	—	2	2	no	—
55	#13133272	—	2	2	no	—
56	#13133272	—	2	2	no	—
57	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
59	C₂²×C₄×D₅₃	Q₈	1	1	yes	characteristic
60	C₂×#11719917	C₂×C₄	1	2	yes	—
61	C₂×#11719912	C₂×C₄	1	2	yes	—
62	C₂×#11719912	C₂×C₄	1	2	yes	—
63	M₁₆×D₅₃	—	2	8	no	—
64	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
65	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
66	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
67	C₂×C₄×Dic₅₃	Q₈	1	1	yes	characteristic
68	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
69	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₅₃	D₄	1	1	yes	characteristic
72	C₄²×D₅₃	D₄	1	1	yes	characteristic
73	C₄²×D₅₃	Q₈	1	1	yes	characteristic
74	C₄²×D₅₃	Q₈	1	1	yes	characteristic
75	C₄²×D₅₃	C₂³	1	1	yes	characteristic
76	C₄²×D₅₃	C₂³	1	1	yes	characteristic
77	#13133128	C₂×C₄	1	1	yes	characteristic
78	#13133128	C₂×C₄	1	1	yes	characteristic
79	#13133127	C₂×C₄	1	2	yes	—
80	#13133127	C₂×C₄	1	2	yes	—
81	C₄×#88322	C₂×C₄	1	2	yes	—
82	C₈×Dic₅₃	C₂³	1	2	yes	—
83	C₈×Dic₅₃	C₂³	1	2	yes	—
84	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
85	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
86	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
87	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
88	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	—
89	C₂³×D₅₃	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
96	C₂×C₄×D₅₃	—	2	4	no	—
97	C₂×C₄×D₅₃	—	2	2	no	—
98	C₂×C₄×D₅₃	—	2	2	no	—
99	C₂×C₄×D₅₃	—	4	2	no	—
100	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
111	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
112	#11719940	—	4	4	no	—
113	C₂×#88324	—	2	2	no	—
114	C₂×#88324	—	2	2	no	—
115	C₂×#88324	—	2	4	no	—
116	#11719936	—	4	4	no	—
117	D₅₃⋊C₈	—	4	2	no	—
118	D₅₃⋊C₈	—	4	4	no	—
119	D₅₃⋊C₈	—	4	2	no	—
120	M₁₆×C₅₃	—	2	4	no	—
121	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
123	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
124	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
125	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
133	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
134	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
135	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
136	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
137	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
138	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
139	#11719917	—	2	4	no	—
140	C₂×#88322	C₂²×C₄	1	2	yes	—
141	C₂×#88322	C₂²×C₄	1	2	yes	—
142	#11719912	—	2	4	no	—
143	#11719912	—	2	4	no	—
144	C₈×D₅₃	—	2	4	no	—
145	C₈×D₅₃	M₁₆	1	8	yes	complemented
146	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂²×D₅₃	—	2	2	no	—
148	C₂²×D₅₃	—	2	2	no	—
149	C₂²×D₅₃	—	2	2	no	—
150	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₅₃	—	2	2	no	—
153	C₂×C₄×C₅₃	—	2	2	no	—
154	C₂×C₄×C₅₃	—	4	1	no	—
155	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×Dic₅₃	—	2	1	no	—
162	C₂×Dic₅₃	—	2	1	no	—
163	C₂×Dic₅₃	—	2	2	no	—
164	C₂×Dic₅₃	—	4	1	no	—
165	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×Dic₅₃	C₂²×Q₈	1	1	yes	characteristic
171	C₄×D₅₃	—	2	2	no	—
172	C₄×D₅₃	—	2	2	no	—
173	C₄×D₅₃	—	2	2	no	—
174	C₄×D₅₃	—	2	2	no	—
175	C₄×D₅₃	—	2	2	no	—
176	C₄×D₅₃	—	2	2	no	—
177	C₄×D₅₃	—	2	1	no	—
178	C₄×D₅₃	—	2	1	no	—
179	C₄×D₅₃	—	2	2	no	—
180	C₄×D₅₃	—	4	1	no	—
181	C₄×D₅₃	—	4	1	no	—
182	C₄×D₅₃	C₂×M₁₆	1	4	yes	—
183	C₄×D₅₃	AGL(1,ℤ/8)	1	2	yes	—
184	C₄×D₅₃	#137	1	2	yes	—
185	#88324	—	4	4	no	—
186	#88324	—	4	2	no	—
187	#88324	—	4	2	no	—
188	C₈×C₅₃	—	2	2	no	—
189	C₈×C₅₃	C₂×M₁₆	1	4	yes	complemented
190	#88322	—	2	2	no	—
191	#88322	C₂×M₁₆	1	4	yes	complemented
192	C₂×#1569	—	53	1	no	maximal, Sylow
193	C₂²×C₅₃	—	2	1	no	—
194	C₂²×C₅₃	—	2	1	no	—
195	C₂²×C₅₃	—	2	1	no	—
196	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
197	C₂×D₅₃	—	2	1	no	—
198	C₂×D₅₃	—	2	1	no	—
199	C₂×D₅₃	—	2	1	no	—
200	C₂×D₅₃	—	4	4	no	—
201	C₂×D₅₃	#423	1	2	yes	—
202	C₂×D₅₃	#428	1	2	yes	—
203	C₂×D₅₃	#430	1	2	yes	—
204	C₄×C₅₃	—	2	1	no	—
205	C₄×C₅₃	—	2	1	no	—
206	C₄×C₅₃	—	2	1	no	—
207	C₄×C₅₃	—	2	1	no	—
208	C₄×C₅₃	#428	1	2	yes	—
209	C₄×C₅₃	C₂²×M₁₆	1	2	yes	—
210	Dic₅₃	—	2	1	no	—
211	Dic₅₃	—	2	1	no	—
212	Dic₅₃	—	2	1	no	—
213	Dic₅₃	—	2	1	no	—
214	Dic₅₃	#423	1	2	yes	—
215	Dic₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
216	Dic₅₃	C₂×#137	1	1	yes	characteristic
217	C₂×#432	—	53	1	no	—
218	C₂×#423	—	53	1	no	—
219	C₂×C₄×M₁₆	—	53	1	no	—
220	#1569	—	53	4	no	—
221	#1569	—	53	2	no	—
222	#1569	—	53	2	no	—
223	C₂×#335	—	53	2	no	—
224	C₂×#334	—	53	2	no	—
225	C₂×C₅₃	—	4	1	no	—
226	C₂×C₅₃	C₂×#423	1	1	yes	characteristic
227	C₂×C₅₃	C₂×#428	1	1	yes	characteristic
228	C₂×C₅₃	C₂×#430	1	1	yes	characteristic
229	D₅₃	—	4	1	no	—
230	D₅₃	#1569	1	4	yes	complemented
231	C₂²×M₁₆	—	53	2	no	—
232	C₂²×M₁₆	—	106	1	no	—
233	C₂²×C₄²	—	53	1	no	—
234	#432	—	53	2	no	—
235	#432	—	53	2	no	—
236	#432	—	106	1	no	—
237	#432	—	106	1	no	—
238	#423	—	53	2	no	—
239	#423	—	53	2	no	—
240	#423	—	106	1	no	—
241	#423	—	106	1	no	—
242	C₂×C₄⋊C₈	—	53	1	no	—
243	C₂×C₄⋊C₈	—	53	2	no	—
244	C₂×C₄⋊C₈	—	53	1	no	—
245	C₂×C₄⋊C₈	—	106	1	no	—
246	C₂×C₂²⋊C₈	—	106	1	no	—
247	C₄×M₁₆	—	53	2	no	—
248	C₄×M₁₆	—	53	1	no	—
249	C₄×M₁₆	—	53	1	no	—
250	C₄×M₁₆	—	53	1	no	—
251	C₄×M₁₆	—	53	2	no	—
252	C₄×M₁₆	#6157	1	1	yes	characteristic
253	C₂×#97	—	53	1	no	—
254	C₂×#97	—	53	1	no	—
255	C₂×#97	—	106	1	no	—
256	C₂×C₄×C₈	—	53	2	no	—
257	#335	—	53	4	no	—
258	#335	—	53	4	no	—
259	#334	—	53	4	no	—
260	#334	—	53	4	no	—
261	C₅₃	C₂×#1569	1	1	yes	characteristic, complemented, Sylow
262	C₂³×C₄	—	53	1	no	—
263	C₂³×C₄	—	53	1	no	—
264	C₂³×C₄	—	53	1	no	—
265	C₂×M₁₆	—	53	2	no	—
266	C₂×M₁₆	—	53	2	no	—
267	C₂×M₁₆	—	53	2	no	—
268	C₂×M₁₆	—	106	8	no	—
269	C₂×M₁₆	—	106	2	no	—
270	C₂×M₁₆	—	106	2	no	—
271	C₂×M₁₆	—	212	4	no	—
272	C₂×M₁₆	C₂×#6157	1	2	yes	—
273	C₂²×C₈	—	53	2	no	—
274	C₂²×C₈	—	53	2	no	—
275	C₂²×C₈	—	106	2	no	—
276	C₂²×C₈	—	106	1	no	—
277	C₂²×C₈	—	106	1	no	—
278	C₂×C₄²	—	53	1	no	—
279	C₂×C₄²	—	53	1	no	—
280	C₂×C₄²	—	53	1	no	—
281	C₂×C₄²	—	53	1	no	—
282	C₂×C₄²	—	53	1	no	—
283	C₂×C₄²	—	53	1	no	—
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	C₂×#6157	1	1	yes	characteristic
290	C₄⋊C₈	—	53	2	no	—
291	C₄⋊C₈	—	53	4	no	—
292	C₄⋊C₈	—	53	2	no	—
293	C₄⋊C₈	—	106	2	no	—
294	C₄⋊C₈	—	106	1	no	—
295	C₄⋊C₈	—	106	1	no	—
296	C₄⋊C₈	—	106	2	no	—
297	C₄⋊C₈	—	106	2	no	—
298	C₂²⋊C₈	—	106	2	no	—
299	C₂²⋊C₈	—	106	2	no	—
300	#97	—	53	2	no	—
301	#97	—	53	2	no	—
302	#97	—	53	1	no	—
303	#97	—	53	1	no	—
304	#97	—	106	2	no	—
305	#97	—	106	2	no	—
306	#97	C₂×#6157	1	1	yes	characteristic
307	#97	C₂×#6157	1	1	yes	characteristic
308	C₄×C₈	—	53	2	no	—
309	C₄×C₈	—	53	2	no	—
310	C₄×C₈	—	53	2	no	—
311	C₄×C₈	C₂×#6157	1	2	yes	—
312	C₂⁴	—	53	1	no	—
313	C₂²×C₄	—	53	1	no	—
314	C₂²×C₄	—	53	1	no	—
315	C₂²×C₄	—	53	1	no	—
316	C₂²×C₄	—	53	1	no	—
317	C₂²×C₄	—	53	1	no	—
318	C₂²×C₄	—	53	1	no	—
319	C₂²×C₄	—	53	1	no	—
320	C₂²×C₄	—	53	1	no	—
321	C₂²×C₄	—	53	1	no	—
322	C₂²×C₄	—	53	1	no	—
323	C₂²×C₄	—	53	1	no	—
324	C₂²×C₄	—	53	1	no	—
325	C₂²×C₄	—	53	1	no	—
326	C₂²×C₄	—	53	1	no	—
327	C₂²×C₄	—	53	1	no	—
328	C₂²×C₄	—	106	4	no	—
329	C₂²×C₄	—	106	2	no	—
330	C₂²×C₄	—	106	2	no	—
331	C₂²×C₄	—	212	2	no	—
332	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
333	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
334	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
335	M₁₆	—	2	4	no	—
336	M₁₆	—	106	4	no	—
337	M₁₆	—	106	4	no	—
338	M₁₆	—	106	4	no	—
339	M₁₆	—	212	4	no	—
340	M₁₆	—	212	4	no	—
341	C₂×C₈	—	53	2	no	—
342	C₂×C₈	—	53	8	no	—
343	C₂×C₈	—	53	2	no	—
344	C₂×C₈	—	106	4	no	—
345	C₂×C₈	—	106	2	no	—
346	C₂×C₈	—	106	2	no	—
347	C₂×C₈	—	106	4	no	—
348	C₂×C₈	—	212	4	no	—
349	C₂×C₈	—	212	2	no	—
350	C₂×C₈	—	212	2	no	—
351	C₂×C₈	C₂²×#6157	1	2	yes	—
352	C₂×C₈	C₂²×#6157	1	2	yes	—
353	C₄²	—	53	1	no	—
354	C₄²	—	53	1	no	—
355	C₄²	—	53	1	no	—
356	C₄²	—	53	1	no	—
357	C₄²	—	53	1	no	—
358	C₄²	—	53	1	no	—
359	C₄²	—	53	1	no	—
360	C₄²	—	53	1	no	—
361	C₄²	—	53	1	no	—
362	C₄²	—	53	1	no	—
363	C₄²	—	53	1	no	—
364	C₄²	—	53	1	no	—
365	C₄²	C₄⋊#6157	1	1	yes	characteristic
366	C₄²	C₄⋊#6157	1	1	yes	characteristic
367	C₄²	C₂²×#6157	1	1	yes	characteristic
368	C₄²	C₂²×#6157	1	1	yes	characteristic
369	C₂³	—	53	1	no	—
370	C₂³	—	53	1	no	—
371	C₂³	—	106	2	no	—
372	C₂³	—	106	2	no	—
373	C₂³	—	106	2	no	—
374	C₂³	C₂×C₄⋊#6157	1	1	yes	characteristic
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	53	1	no	—
379	C₂×C₄	—	53	1	no	—
380	C₂×C₄	—	53	2	no	—
381	C₂×C₄	—	53	2	no	—
382	C₂×C₄	—	53	4	no	—
383	C₂×C₄	—	53	1	no	—
384	C₂×C₄	—	53	1	no	—
385	C₂×C₄	—	53	1	no	—
386	C₂×C₄	—	53	1	no	—
387	C₂×C₄	—	106	1	no	—
388	C₂×C₄	—	106	2	no	—
389	C₂×C₄	—	106	1	no	—
390	C₂×C₄	—	106	2	no	—
391	C₂×C₄	—	106	2	no	—
392	C₂×C₄	—	106	2	no	—
393	C₂×C₄	—	106	2	no	—
394	C₂×C₄	—	106	1	no	—
395	C₂×C₄	—	106	2	no	—
396	C₂×C₄	—	106	1	no	—
397	C₂×C₄	—	106	2	no	—
398	C₂×C₄	—	106	2	no	—
399	C₂×C₄	—	212	1	no	—
400	C₂×C₄	—	212	1	no	—
401	C₂×C₄	—	212	1	no	—
402	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
403	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
404	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
405	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
406	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
407	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	53	4	no	—
410	C₈	—	106	2	no	—
411	C₈	—	212	2	no	—
412	C₈	—	212	2	no	—
413	C₈	—	212	4	no	—
414	C₈	D₅₃⋊M₁₆	1	4	yes	complemented
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	53	2	no	—
419	C₂²	—	53	2	no	—
420	C₂²	—	53	2	no	—
421	C₂²	—	106	1	no	—
422	C₂²	—	106	1	no	—
423	C₂²	—	106	1	no	—
424	C₂²	—	212	4	no	—
425	C₂²	C₂²×C₄⋊#6157	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	53	2	no	—
431	C₄	—	53	1	no	—
432	C₄	—	53	1	no	—
433	C₄	—	106	1	no	—
434	C₄	—	106	1	no	—
435	C₄	—	106	1	no	—
436	C₄	—	106	1	no	—
437	C₄	#16811634	1	2	yes	—
438	C₄	C₂×D₅₃⋊M₁₆	1	2	yes	—
439	C₂	—	4	1	no	—
440	C₂	—	53	4	no	—
441	C₂	—	212	1	no	—
442	C₂	D₅₃⋊#423	1	1	yes	characteristic
443	C₂	C₂×#16811634	1	1	yes	characteristic
444	C₂	D₅₃⋊#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#6157
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₄×M₁₆×C₅₃	C₄
socle	C₂²×C₅₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₅₃	C₄⋊C₄
cosocle	C₄×Dic₅₃	C₂⁴
hypercenter	C₄×M₁₆	#6157
hypocenter	C₅₃	C₂×#1569
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #20290281	C₂	semidirect
4. #20290280	C₂	semidirect
5. #20290279	C₂	semidirect
6. D₅₃⋊#335	C₂	semidirect
7. D₅₃⋊#334	C₂	semidirect
24. #16811487	C₂²	semidirect
25. #16811486	C₂²	semidirect
26. #16811485	C₂²	semidirect
27. #16811484	C₂²	semidirect
145. C₈×D₅₃	M₁₆	semidirect
189. C₈×C₅₃	C₂×M₁₆	semidirect
191. #88322	C₂×M₁₆	semidirect
230. D₅₃	#1569	semidirect
261. C₅₃	C₂×#1569	semidirect
414. C₈	D₅₃⋊M₁₆	semidirect

Maximal subgroups

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

subgroup	index
D₅₃⋊#432	2
D₅₃⋊#423	2
#20290281	2
#20290280	2
#20290279	2
D₅₃⋊#335	2
D₅₃⋊#334	2
C₄×M₁₆×D₅₃	2
C₂×#1569	53

Subgroups — D53⋊#1569 #28316119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃⋊#1569 #28316119