Subgroups — #28316088

Order 13568.

778 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811642	C₂	1	1	yes	maximal, characteristic
2	D₅₃⋊#431	C₂	1	1	yes	maximal, characteristic
3	#20290268	C₂	1	2	yes	maximal, complemented
4	#20290267	C₂	1	4	yes	maximal, complemented
5	#20290266	C₂	1	2	yes	maximal, complemented
6	#20290265	C₂	1	2	yes	maximal, complemented
7	#20290263	C₂	1	2	yes	maximal, complemented
8	C₄×M₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
9	#16811642	—	2	1	no	—
10	#16811642	—	2	1	no	—
11	#16811642	C₂²	1	1	yes	characteristic
12	#16811642	C₂²	1	1	yes	characteristic
13	#16811642	C₂²	1	2	yes	—
14	#16811642	C₂²	1	2	yes	—
15	#16811641	—	2	1	no	—
16	#16811640	—	2	1	no	—
17	#16811639	C₂²	1	2	yes	—
18	D₅₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₄⋊#88324	C₂²	1	2	yes	—
20	C₂×#13133274	—	2	1	no	—
21	D₅₃⋊(C₂²⋊C₈)	—	2	1	no	—
22	C₄×D₅₃⋊C₈	—	2	1	no	—
23	C₂×C₄×#88324	—	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	1	yes	characteristic
29	C₂×M₁₆×D₅₃	C₄	1	1	yes	characteristic
30	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
31	C₄×#11719917	C₄	1	1	yes	characteristic
32	#16810575	C₂²	1	2	yes	—
33	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
34	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
35	C₄×#11719912	C₄	1	2	yes	—
36	#97×D₅₃	C₄	1	2	yes	—
37	C₄×C₈×D₅₃	C₂²	1	2	yes	—
38	C₄×M₁₆×C₅₃	C₄	1	1	yes	characteristic
39	C₂×D₅₃⋊C₈	—	2	2	no	—
40	C₂²×#88324	—	2	2	no	—
41	#13133284	—	2	2	no	—
42	C₄⋊#88324	—	2	2	no	—
43	C₄⋊#88324	C₂³	1	4	yes	—
44	C₄⋊#88324	C₂³	1	2	yes	—
45	C₄⋊#88324	C₂³	1	2	yes	—
46	#13133274	—	2	1	no	—
47	#13133274	—	2	1	no	—
48	#13133274	—	2	2	no	—
49	#13133274	—	2	2	no	—
50	C₂²⋊#88324	—	2	2	no	—
51	C₄×#88324	—	2	2	no	—
52	C₄×#88324	—	2	2	no	—
53	C₄×#88324	—	2	2	no	—
54	C₄×#88324	—	2	1	no	—
55	C₄×#88324	—	2	1	no	—
56	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
58	C₂²×C₄×D₅₃	Q₈	1	1	yes	characteristic
59	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
60	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
61	C₂×#11719912	C₂×C₄	1	2	yes	—
62	C₂×#11719912	C₂×C₄	1	2	yes	—
63	M₁₆×D₅₃	—	2	4	no	—
64	M₁₆×D₅₃	C₈	1	8	yes	complemented
65	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
66	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
67	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
68	C₂×C₄×Dic₅₃	Q₈	1	1	yes	characteristic
69	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
70	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₅₃	D₄	1	1	yes	characteristic
73	C₄²×D₅₃	D₄	1	1	yes	characteristic
74	C₄²×D₅₃	Q₈	1	1	yes	characteristic
75	C₄²×D₅₃	Q₈	1	1	yes	characteristic
76	C₄²×D₅₃	C₂³	1	1	yes	characteristic
77	C₄²×D₅₃	C₂³	1	1	yes	characteristic
78	#13133128	C₂×C₄	1	2	yes	—
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	1	yes	characteristic
85	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
87	#97×C₅₃	C₂×C₄	1	2	yes	—
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	—	4	2	no	—
97	C₂×C₄×D₅₃	—	4	2	no	—
98	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
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	C₂×C₈	1	4	yes	—
105	C₂×C₄×D₅₃	M₁₆	1	4	yes	—
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	C₂×#88324	—	2	2	no	—
113	C₂×#88324	—	2	2	no	—
114	C₂×#88324	—	2	4	no	—
115	C₂×#88324	—	4	4	no	—
116	D₅₃⋊C₈	—	4	4	no	—
117	M₁₆×C₅₃	—	2	2	no	—
118	M₁₆×C₅₃	C₂×C₈	1	4	yes	complemented
119	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
121	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
122	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
123	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₅₃	C₄⋊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	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
131	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
132	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
133	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
134	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
135	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
136	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
137	#11719917	—	2	2	no	—
138	#11719917	C₂×C₈	1	4	yes	complemented
139	C₂×#88322	C₂²×C₄	1	2	yes	—
140	C₂×#88322	C₂²×C₄	1	2	yes	—
141	#11719912	—	2	4	no	—
142	#11719912	C₂×C₈	1	8	yes	complemented
143	C₈×D₅₃	—	2	4	no	—
144	C₈×D₅₃	C₂×C₈	1	8	yes	complemented
145	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂²×D₅₃	—	4	1	no	—
147	C₂²×D₅₃	—	4	1	no	—
148	C₂²×D₅₃	C₄⋊C₈	1	4	yes	—
149	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₅₃	—	2	2	no	—
152	C₂×C₄×C₅₃	—	4	1	no	—
153	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
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	C₂²×C₈	1	2	yes	—
159	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
160	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×Dic₅₃	—	2	2	no	—
162	C₂×Dic₅₃	—	4	1	no	—
163	C₂×Dic₅₃	C₄⋊C₈	1	4	yes	—
164	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
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	C₂²×D₄	1	1	yes	characteristic
169	C₂×Dic₅₃	C₂²×Q₈	1	1	yes	characteristic
170	C₄×D₅₃	—	2	2	no	—
171	C₄×D₅₃	—	2	2	no	—
172	C₄×D₅₃	—	2	2	no	—
173	C₄×D₅₃	—	2	2	no	—
174	C₄×D₅₃	—	4	1	no	—
175	C₄×D₅₃	—	4	1	no	—
176	C₄×D₅₃	—	4	1	no	—
177	C₄×D₅₃	—	4	1	no	—
178	C₄×D₅₃	C₄⋊C₈	1	4	yes	—
179	C₄×D₅₃	C₄⋊C₈	1	4	yes	—
180	C₄×D₅₃	C₂²×C₈	1	2	yes	—
181	C₄×D₅₃	C₂²×C₈	1	2	yes	—
182	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
183	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
184	#88324	—	4	4	no	—
185	#88324	—	4	2	no	—
186	#88324	—	4	2	no	—
187	C₈×C₅₃	—	2	2	no	—
188	C₈×C₅₃	C₂²×C₈	1	4	yes	—
189	#88322	—	2	2	no	—
190	#88322	C₂²×C₈	1	4	yes	—
191	#17787	—	53	1	no	maximal, Sylow
192	C₂²×C₅₃	—	2	1	no	—
193	C₂²×C₅₃	—	2	1	no	—
194	C₂²×C₅₃	C₂×C₄⋊C₈	1	2	yes	—
195	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
196	C₂×D₅₃	—	2	1	no	—
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	C₂×C₄⋊C₈	1	2	yes	—
202	C₂×D₅₃	C₂×C₄⋊C₈	1	2	yes	—
203	C₄×C₅₃	—	2	1	no	—
204	C₄×C₅₃	—	2	1	no	—
205	C₄×C₅₃	—	2	1	no	—
206	C₄×C₅₃	C₂×C₄⋊C₈	1	2	yes	—
207	C₄×C₅₃	#430	1	2	yes	—
208	C₄×C₅₃	C₂³×C₈	1	1	yes	characteristic
209	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
210	Dic₅₃	—	2	1	no	—
211	Dic₅₃	—	2	1	no	—
212	Dic₅₃	—	2	1	no	—
213	Dic₅₃	C₂×C₄⋊C₈	1	2	yes	—
214	Dic₅₃	C₂×C₄⋊C₈	1	2	yes	—
215	Dic₅₃	#575	1	2	yes	—
216	C₂×#431	—	53	1	no	—
217	C₂×#431	—	53	1	no	—
218	C₂×C₄×M₁₆	—	53	1	no	—
219	#1565	—	53	2	no	—
220	#1565	—	53	4	no	—
221	#1565	—	53	2	no	—
222	#1564	—	53	2	no	—
223	#1564	—	53	2	no	—
224	C₂×C₅₃	—	2	2	no	—
225	C₂×C₅₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
226	C₂×C₅₃	#2911	1	1	yes	characteristic
227	C₂×C₅₃	C₂×#430	1	1	yes	characteristic
228	D₅₃	—	2	2	no	—
229	D₅₃	—	2	2	no	—
230	C₂²×M₁₆	—	53	1	no	—
231	C₂²×M₁₆	—	53	1	no	—
232	C₂²×C₄²	—	53	1	no	—
233	#431	—	53	1	no	—
234	#431	—	53	2	no	—
235	#431	—	53	1	no	—
236	#431	—	53	2	no	—
237	#431	—	53	2	no	—
238	#431	—	106	1	no	—
239	#431	—	106	1	no	—
240	#431	—	106	1	no	—
241	#431	—	106	1	no	—
242	C₂×C₄⋊C₈	—	53	2	no	—
243	C₂×C₄⋊C₈	—	53	2	no	—
244	C₂×C₂²⋊C₈	—	106	1	no	—
245	C₂×C₂²⋊C₈	—	106	1	no	—
246	C₄×M₁₆	—	53	1	no	—
247	C₄×M₁₆	—	53	1	no	—
248	C₄×M₁₆	—	53	1	no	—
249	C₄×M₁₆	—	53	2	no	—
250	C₄×M₁₆	—	53	2	no	—
251	C₄×M₁₆	#6157	1	1	yes	characteristic
252	C₂×#97	—	53	2	no	—
253	C₂×C₄×C₈	—	53	2	no	—
254	C₂×C₄×C₈	—	106	1	no	—
255	C₂×C₄×C₈	—	106	1	no	—
256	#335	—	53	4	no	—
257	#335	—	53	4	no	—
258	#334	—	53	4	no	—
259	#334	—	53	4	no	—
260	C₅₃	#17787	1	1	yes	characteristic, complemented, Sylow
261	C₂³×C₄	—	53	1	no	—
262	C₂³×C₄	—	53	1	no	—
263	C₂³×C₄	—	53	1	no	—
264	C₂×M₁₆	—	53	1	no	—
265	C₂×M₁₆	—	53	8	no	—
266	C₂×M₁₆	—	53	1	no	—
267	C₂×M₁₆	—	53	2	no	—
268	C₂×M₁₆	—	53	2	no	—
269	C₂×M₁₆	—	106	4	no	—
270	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
271	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
272	C₂²×C₈	—	53	2	no	—
273	C₂²×C₈	—	53	2	no	—
274	C₂²×C₈	—	106	2	no	—
275	C₂²×C₈	—	106	2	no	—
276	C₂×C₄²	—	53	1	no	—
277	C₂×C₄²	—	53	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	C₂×#6157	1	1	yes	characteristic
288	C₄⋊C₈	—	53	2	no	—
289	C₄⋊C₈	—	53	4	no	—
290	C₄⋊C₈	—	53	2	no	—
291	C₄⋊C₈	—	106	2	no	—
292	C₄⋊C₈	—	106	2	no	—
293	C₂²⋊C₈	—	106	2	no	—
294	C₂²⋊C₈	—	106	1	no	—
295	C₂²⋊C₈	—	106	1	no	—
296	C₂²⋊C₈	—	106	2	no	—
297	C₂²⋊C₈	—	106	2	no	—
298	#97	—	53	2	no	—
299	#97	—	53	2	no	—
300	#97	—	53	2	no	—
301	#97	C₂×#6157	1	2	yes	—
302	C₄×C₈	—	53	2	no	—
303	C₄×C₈	—	53	2	no	—
304	C₄×C₈	—	53	2	no	—
305	C₄×C₈	—	106	2	no	—
306	C₄×C₈	—	106	2	no	—
307	C₄×C₈	—	106	2	no	—
308	C₄×C₈	—	106	1	no	—
309	C₄×C₈	—	106	1	no	—
310	C₄×C₈	C₂×#6157	1	2	yes	—
311	C₂⁴	—	53	1	no	—
312	C₂²×C₄	—	53	1	no	—
313	C₂²×C₄	—	53	1	no	—
314	C₂²×C₄	—	53	1	no	—
315	C₂²×C₄	—	53	4	no	—
316	C₂²×C₄	—	53	4	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	—	53	1	no	—
329	C₂²×C₄	—	212	2	no	—
330	C₂²×C₄	—	212	2	no	—
331	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
332	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
333	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
334	M₁₆	—	2	2	no	—
335	M₁₆	—	53	4	no	—
336	M₁₆	—	53	8	no	—
337	M₁₆	—	106	4	no	—
338	M₁₆	—	106	2	no	—
339	M₁₆	D₅₃⋊C₈	1	4	yes	complemented
340	C₂×C₈	—	53	2	no	—
341	C₂×C₈	—	53	8	no	—
342	C₂×C₈	—	53	2	no	—
343	C₂×C₈	—	106	4	no	—
344	C₂×C₈	—	106	2	no	—
345	C₂×C₈	—	106	2	no	—
346	C₂×C₈	—	106	4	no	—
347	C₂×C₈	—	212	4	no	—
348	C₂×C₈	—	212	4	no	—
349	C₂×C₈	C₂²×#6157	1	2	yes	—
350	C₂×C₈	C₂²×#6157	1	2	yes	—
351	C₄²	—	53	1	no	—
352	C₄²	—	53	1	no	—
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	C₄⋊#6157	1	1	yes	characteristic
364	C₄²	C₄⋊#6157	1	1	yes	characteristic
365	C₄²	C₂²×#6157	1	1	yes	characteristic
366	C₄²	C₂²×#6157	1	1	yes	characteristic
367	C₂³	—	53	1	no	—
368	C₂³	—	53	1	no	—
369	C₂³	—	53	4	no	—
370	C₂³	—	212	1	no	—
371	C₂³	—	212	1	no	—
372	C₂³	C₂×C₄⋊#6157	1	1	yes	characteristic
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	53	4	no	—
376	C₂×C₄	—	53	1	no	—
377	C₂×C₄	—	53	1	no	—
378	C₂×C₄	—	53	1	no	—
379	C₂×C₄	—	53	4	no	—
380	C₂×C₄	—	53	4	no	—
381	C₂×C₄	—	53	2	no	—
382	C₂×C₄	—	53	2	no	—
383	C₂×C₄	—	53	2	no	—
384	C₂×C₄	—	53	2	no	—
385	C₂×C₄	—	53	1	no	—
386	C₂×C₄	—	53	1	no	—
387	C₂×C₄	—	53	1	no	—
388	C₂×C₄	—	106	2	no	—
389	C₂×C₄	—	106	2	no	—
390	C₂×C₄	—	106	2	no	—
391	C₂×C₄	—	106	2	no	—
392	C₂×C₄	—	106	2	no	—
393	C₂×C₄	—	212	1	no	—
394	C₂×C₄	—	212	1	no	—
395	C₂×C₄	—	212	1	no	—
396	C₂×C₄	—	212	1	no	—
397	C₂×C₄	—	212	1	no	—
398	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
399	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
400	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
401	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
402	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
403	C₂×C₄	C₂×D₅₃⋊C₈	1	2	yes	—
404	C₂×C₄	D₅₃⋊M₁₆	1	2	yes	—
405	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	53	4	no	—
408	C₈	—	106	2	no	—
409	C₈	—	212	4	no	—
410	C₈	—	212	2	no	—
411	C₈	—	212	2	no	—
412	C₈	C₂×D₅₃⋊C₈	1	4	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	53	2	no	—
416	C₂²	—	53	2	no	—
417	C₂²	—	106	1	no	—
418	C₂²	—	106	1	no	—
419	C₂²	—	106	1	no	—
420	C₂²	—	106	1	no	—
421	C₂²	—	212	4	no	—
422	C₂²	D₅₃⋊(C₄⋊C₈)	1	2	yes	—
423	C₂²	C₂²×C₄⋊#6157	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	53	2	no	—
428	C₄	—	53	2	no	—
429	C₄	—	53	2	no	—
430	C₄	—	106	1	no	—
431	C₄	—	106	1	no	—
432	C₄	—	106	1	no	—
433	C₄	D₅₃⋊(C₄⋊C₈)	1	2	yes	—
434	C₄	#16811638	1	2	yes	—
435	C₄	C₂²×D₅₃⋊C₈	1	1	yes	characteristic
436	C₄	C₂×D₅₃⋊M₁₆	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	106	2	no	—
439	C₂	—	106	2	no	—
440	C₂	C₂×D₅₃⋊(C₄⋊C₈)	1	1	yes	characteristic
441	C₂	#20291368	1	1	yes	characteristic
442	C₂	C₂×#16811638	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#6157
commutator	C₄×C₅₃	C₂³×C₈
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	#17787
LCS	G ▷ 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. #20290268	C₂	semidirect
4. #20290267	C₂	semidirect
5. #20290266	C₂	semidirect
6. #20290265	C₂	semidirect
7. #20290263	C₂	semidirect
24. #16811487	C₂²	semidirect
25. #16811486	C₂²	semidirect
26. #16811485	C₂²	semidirect
27. #16811484	C₂²	semidirect
64. M₁₆×D₅₃	C₈	semidirect
118. M₁₆×C₅₃	C₂×C₈	semidirect
138. #11719917	C₂×C₈	semidirect
142. #11719912	C₂×C₈	semidirect
144. C₈×D₅₃	C₂×C₈	semidirect
260. C₅₃	#17787	semidirect
339. M₁₆	D₅₃⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811642	2
D₅₃⋊#431	2
#20290268	2
#20290267	2
#20290266	2
#20290265	2
#20290263	2
C₄×M₁₆×D₅₃	2
#17787	53