Subgroups — #28316140

Order 13568.

666 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291637	C₂	1	2	yes	maximal
2	#20290280	C₂	1	2	yes	maximal, complemented
3	#20290279	C₂	1	2	yes	maximal, complemented
4	#20290278	C₂	1	1	yes	maximal, characteristic, complemented
5	#20290277	C₂	1	1	yes	maximal, characteristic, complemented
6	#20290271	C₂	1	1	yes	maximal, characteristic, complemented
7	#20290269	C₂	1	1	yes	maximal, characteristic, complemented
8	#20290267	C₂	1	2	yes	maximal, complemented
9	#20290265	C₂	1	1	yes	maximal, characteristic, complemented
10	D₅₃⋊#334	C₂	1	1	yes	maximal, characteristic, complemented
11	#20283137	C₂	1	1	yes	maximal, characteristic
12	#16811675	—	2	2	no	—
13	#16811656	—	2	2	no	—
14	#16811655	—	2	2	no	—
15	#16811653	—	2	2	no	—
16	#16811645	C₂²	1	2	yes	—
17	#16811644	C₂²	1	2	yes	—
18	#16811642	C₂²	1	2	yes	—
19	#16811627	C₂²	1	2	yes	—
20	#16811626	C₂²	1	2	yes	—
21	D₅₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
22	#16811487	C₂²	1	2	yes	—
23	#16811486	C₂²	1	2	yes	—
24	#16811486	C₂²	1	2	yes	—
25	#16811485	C₂²	1	1	yes	characteristic
26	#16811485	C₂²	1	1	yes	characteristic
27	#16811485	C₂²	1	1	yes	characteristic
28	#16811485	C₂²	1	1	yes	characteristic
29	#16811485	C₂²	1	2	yes	—
30	#16811484	C₂²	1	2	yes	—
31	#16811484	C₂²	1	2	yes	—
32	C₂×#13133225	C₄	1	1	yes	characteristic
33	C₂×#13133223	C₄	1	1	yes	characteristic
34	#16811091	C₂²	1	1	yes	characteristic
35	#16810580	C₄	1	1	yes	characteristic
36	#16810580	C₄	1	1	yes	characteristic
37	#16810579	C₄	1	1	yes	characteristic
38	#16810577	C₄	1	1	yes	characteristic
39	#16810577	C₄	1	1	yes	characteristic
40	#16810575	C₂²	1	1	yes	characteristic
41	#16810575	C₂²	1	1	yes	characteristic
42	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
46	C₅₃×#405	C₄	1	1	yes	characteristic
47	C₂×#11719936	—	2	2	no	—
48	C₂×#11719940	—	2	2	no	—
49	C₂×D₅₃⋊C₈	—	2	2	no	—
50	#13133284	—	2	2	no	—
51	#13133284	—	2	2	no	—
52	C₄⋊#88324	—	2	2	no	—
53	C₄⋊#88324	C₂³	1	2	yes	—
54	C₄⋊#88324	C₂³	1	2	yes	—
55	C₄⋊#88324	C₂³	1	2	yes	—
56	C₄⋊#88324	C₂³	1	2	yes	—
57	#13133274	—	2	2	no	—
58	#13133274	—	2	2	no	—
59	C₂²⋊#88324	—	2	2	no	—
60	#13133272	—	2	2	no	—
61	#13133272	—	2	2	no	—
62	C₄×#88324	—	2	2	no	—
63	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
64	#13133225	—	2	4	no	—
65	#13133223	—	2	4	no	—
66	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
67	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
68	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
69	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
70	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
71	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
76	#13133182	D₄	1	1	yes	characteristic
77	#13133182	Q₈	1	1	yes	characteristic
78	#13133179	D₄	1	1	yes	characteristic
79	#13133179	Q₈	1	1	yes	characteristic
80	#13133177	D₄	1	1	yes	characteristic
81	#13133177	D₄	1	1	yes	characteristic
82	#13133177	Q₈	1	1	yes	characteristic
83	#13133177	Q₈	1	1	yes	characteristic
84	#13133174	C₂×C₄	1	1	yes	characteristic
85	#13133174	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
87	C₄²×D₅₃	C₂³	1	1	yes	characteristic
88	C₄²×D₅₃	C₂³	1	1	yes	characteristic
89	#13133128	C₂×C₄	1	1	yes	characteristic
90	#13133128	C₂×C₄	1	1	yes	characteristic
91	#13133127	C₂×C₄	1	1	yes	characteristic
92	#13133127	C₂×C₄	1	1	yes	characteristic
93	C₄×#88322	C₂×C₄	1	1	yes	characteristic
94	C₄×#88322	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
98	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
99	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
100	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
102	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
103	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
104	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
105	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
106	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
107	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊D₅₃	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₅₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
113	#11719945	—	2	2	no	—
114	#11719945	—	2	2	no	—
115	C₂×D₂₁₂	C₄⋊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	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
121	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
122	C₂×Dic₁₀₆	C₄⋊C₄	1	1	yes	characteristic
123	#11719940	—	8	2	no	—
124	C₂×#88324	—	2	2	no	—
125	C₂×#88324	—	2	2	no	—
126	C₂×#88324	—	2	2	no	—
127	C₂×#88324	—	2	2	no	—
128	#11719936	—	8	2	no	—
129	D₅₃⋊C₈	—	8	2	no	—
130	M₁₆×C₅₃	—	2	2	no	—
131	C₂×C₈×C₅₃	—	2	2	no	—
132	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
136	C₄⋊C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
137	C₄⋊C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
138	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
139	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
140	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
142	#11719921	C₄⋊C₄	1	1	yes	characteristic
143	#11719921	C₄⋊C₄	1	1	yes	characteristic
144	#11719921	C₄⋊C₄	1	1	yes	characteristic
145	#11719921	C₄⋊C₄	1	1	yes	characteristic
146	#11719919	C₄⋊C₄	1	1	yes	characteristic
147	#11719919	C₄⋊C₄	1	1	yes	characteristic
148	#11719919	C₄⋊C₄	1	1	yes	characteristic
149	#11719919	C₄⋊C₄	1	1	yes	characteristic
150	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
152	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
153	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
154	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
155	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
156	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
157	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
158	#11719917	—	2	2	no	—
159	C₂×#88322	—	2	2	no	—
160	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
161	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
162	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
163	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
164	#11719912	—	2	2	no	—
165	#11719912	—	2	2	no	—
166	#11719912	—	2	2	no	—
167	#11719912	M₁₆	1	4	yes	complemented
168	C₈×D₅₃	—	2	2	no	—
169	C₈×D₅₃	—	2	2	no	—
170	C₈×D₅₃	—	2	2	no	—
171	C₈×D₅₃	M₁₆	1	4	yes	complemented
172	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₅₃	—	2	1	no	—
176	C₂×C₄×C₅₃	—	2	1	no	—
177	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
183	C₂²⋊D₅₃	—	2	2	no	—
184	C₂²⋊D₅₃	—	2	2	no	—
185	C₂×Dic₅₃	—	2	2	no	—
186	C₂×Dic₅₃	—	4	1	no	—
187	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×Dic₅₃	C₂²×Q₈	1	1	yes	characteristic
193	D₂₁₂	—	2	2	no	—
194	C₄×D₅₃	—	2	1	no	—
195	C₄×D₅₃	—	2	1	no	—
196	C₄×D₅₃	—	2	2	no	—
197	C₄×D₅₃	—	2	2	no	—
198	C₄×D₅₃	—	4	1	no	—
199	C₄×D₅₃	—	4	1	no	—
200	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
201	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
202	Dic₁₀₆	—	2	2	no	—
203	#88324	—	4	2	no	—
204	#88324	—	4	2	no	—
205	#88324	—	4	2	no	—
206	#88324	—	4	2	no	—
207	C₈×C₅₃	—	2	1	no	—
208	C₈×C₅₃	—	2	1	no	—
209	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
210	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
211	#88322	—	2	1	no	—
212	#88322	—	2	1	no	—
213	#88322	C₂×M₁₆	1	2	yes	—
214	#88322	C₂×M₁₆	1	2	yes	—
215	#17798	—	53	1	no	maximal, Sylow
216	C₂²×C₅₃	—	2	1	no	—
217	C₂²×C₅₃	—	2	1	no	—
218	C₂²×C₅₃	—	2	1	no	—
219	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
220	C₂×D₅₃	—	2	1	no	—
221	C₂×D₅₃	—	2	1	no	—
222	C₂×D₅₃	—	2	1	no	—
223	C₂×D₅₃	—	2	1	no	—
224	C₂×D₅₃	—	2	1	no	—
225	C₂×D₅₃	#423	1	2	yes	—
226	C₄×C₅₃	—	2	1	no	—
227	C₄×C₅₃	—	2	1	no	—
228	C₄×C₅₃	—	2	1	no	—
229	C₄×C₅₃	—	2	1	no	—
230	C₄×C₅₃	—	2	1	no	—
231	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
232	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
233	Dic₅₃	—	2	1	no	—
234	Dic₅₃	—	2	1	no	—
235	Dic₅₃	—	2	1	no	—
236	Dic₅₃	—	2	1	no	—
237	Dic₅₃	#423	1	2	yes	—
238	Dic₅₃	#577	1	2	yes	—
239	#2989	—	53	2	no	—
240	C₄×#131	—	53	1	no	—
241	#1569	—	53	2	no	—
242	#1569	—	53	2	no	—
243	#1568	—	53	1	no	—
244	#1568	—	53	1	no	—
245	#1566	—	53	1	no	—
246	#1566	—	53	1	no	—
247	#1565	—	53	2	no	—
248	#1564	—	53	1	no	—
249	C₂×#334	—	53	1	no	—
250	C₂×C₅₃	—	4	1	no	—
251	C₂×C₅₃	C₂×#423	1	1	yes	characteristic
252	C₂×C₅₃	#2912	1	1	yes	characteristic
253	C₂×C₅₃	#2916	1	1	yes	characteristic
254	D₅₃	—	2	2	no	—
255	D₅₃	—	4	1	no	—
256	C₂×#131	—	53	1	no	—
257	C₂×#131	—	53	1	no	—
258	C₄×#41	—	53	1	no	—
259	#446	—	106	2	no	—
260	#436	—	106	2	no	—
261	#435	—	106	2	no	—
262	#435	—	106	2	no	—
263	#432	—	53	2	no	—
264	#432	—	53	2	no	—
265	#431	—	53	2	no	—
266	#423	—	53	2	no	—
267	#423	—	53	2	no	—
268	C₂×C₄⋊C₈	—	53	2	no	—
269	#405	—	53	1	no	—
270	#405	—	53	1	no	—
271	#405	—	53	1	no	—
272	#405	—	53	1	no	—
273	#405	—	53	1	no	—
274	#405	#6157	1	1	yes	characteristic
275	C₄×M₁₆	—	53	1	no	—
276	C₄×M₁₆	—	53	1	no	—
277	C₄×M₁₆	—	53	1	no	—
278	C₂×C₄×C₈	—	53	1	no	—
279	C₂×C₄×C₈	—	53	1	no	—
280	C₂×C₄×C₈	—	53	1	no	—
281	#335	—	53	2	no	—
282	#335	—	53	2	no	—
283	#335	—	53	2	no	—
284	#334	—	53	1	no	—
285	#334	—	53	1	no	—
286	#334	—	53	2	no	—
287	#334	—	53	1	no	—
288	#334	—	53	1	no	—
289	#334	—	53	2	no	—
290	#334	—	53	2	no	—
291	C₅₃	#17798	1	1	yes	characteristic, complemented, Sylow
292	C₂×#41	—	53	1	no	—
293	#131	—	106	4	no	—
294	#131	—	106	4	no	—
295	C₂×M₁₆	—	53	1	no	—
296	C₂×M₁₆	—	53	1	no	—
297	C₂×M₁₆	—	53	1	no	—
298	C₂×M₁₆	—	53	1	no	—
299	C₂×M₁₆	—	53	1	no	—
300	C₂×M₁₆	—	106	2	no	—
301	C₂×M₁₆	—	106	2	no	—
302	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
303	C₂²×C₈	—	53	1	no	—
304	C₂²×C₈	—	53	1	no	—
305	C₂²×C₈	—	53	1	no	—
306	C₂²×C₈	—	53	1	no	—
307	C₂²×C₈	—	53	1	no	—
308	C₂²×C₈	—	106	2	no	—
309	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
310	C₄×Q₈	—	53	1	no	—
311	C₄×Q₈	—	53	1	no	—
312	C₄×D₄	—	53	1	no	—
313	C₄×D₄	—	53	1	no	—
314	C₄×D₄	—	53	1	no	—
315	C₄×D₄	—	53	1	no	—
316	C₄×D₄	—	53	1	no	—
317	C₄×D₄	—	53	1	no	—
318	#117	—	53	1	no	—
319	#117	—	53	1	no	—
320	#117	C₂×#6157	1	1	yes	characteristic
321	C₂×C₄²	—	53	1	no	—
322	C₂×C₄²	—	53	1	no	—
323	C₂×C₄²	—	53	1	no	—
324	C₄⋊C₈	—	53	2	no	—
325	C₄⋊C₈	—	53	2	no	—
326	C₄⋊C₈	—	53	2	no	—
327	C₄⋊C₈	—	53	2	no	—
328	C₄⋊C₈	—	106	2	no	—
329	C₄⋊C₈	—	106	2	no	—
330	C₄⋊C₈	—	106	2	no	—
331	C₂²⋊C₈	—	106	2	no	—
332	C₂²⋊C₈	—	106	2	no	—
333	C₂²⋊C₈	—	106	2	no	—
334	#97	—	53	1	no	—
335	#97	—	53	1	no	—
336	#97	—	53	1	no	—
337	#97	—	53	1	no	—
338	#97	—	106	2	no	—
339	#97	—	106	2	no	—
340	#97	C₂×#6157	1	1	yes	characteristic
341	#97	C₂×#6157	1	1	yes	characteristic
342	C₄×C₈	—	53	1	no	—
343	C₄×C₈	—	53	1	no	—
344	C₄×C₈	—	53	1	no	—
345	C₄×C₈	—	53	1	no	—
346	C₄×C₈	—	53	1	no	—
347	C₄×C₈	—	53	1	no	—
348	C₄×C₈	—	53	1	no	—
349	C₄×C₈	—	53	1	no	—
350	C₄×C₈	—	106	2	no	—
351	C₄×C₈	C₂×#6157	1	1	yes	characteristic
352	C₄×C₈	C₂×#6157	1	1	yes	characteristic
353	#41	—	106	2	no	—
354	#41	—	106	2	no	—
355	C₂×Q₈	—	53	1	no	—
356	C₂×D₄	—	53	1	no	—
357	C₂×D₄	—	53	1	no	—
358	C₂×D₄	—	53	1	no	—
359	C₂²×C₄	—	53	1	no	—
360	C₂²×C₄	—	53	1	no	—
361	C₂²×C₄	—	53	1	no	—
362	C₂²×C₄	—	53	1	no	—
363	C₂²×C₄	—	53	1	no	—
364	C₂²×C₄	—	53	1	no	—
365	C₂²×C₄	—	53	1	no	—
366	C₂²×C₄	—	53	1	no	—
367	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
368	M₁₆	—	2	2	no	—
369	M₁₆	—	53	4	no	—
370	M₁₆	—	106	2	no	—
371	M₁₆	—	106	2	no	—
372	M₁₆	—	106	2	no	—
373	M₁₆	—	106	2	no	—
374	M₁₆	—	424	2	no	—
375	M₁₆	—	424	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	53	1	no	—
378	C₂×C₈	—	53	1	no	—
379	C₂×C₈	—	53	4	no	—
380	C₂×C₈	—	53	1	no	—
381	C₂×C₈	—	53	1	no	—
382	C₂×C₈	—	106	2	no	—
383	C₂×C₈	—	106	2	no	—
384	C₂×C₈	—	106	2	no	—
385	C₂×C₈	—	106	2	no	—
386	C₂×C₈	—	106	2	no	—
387	C₂×C₈	—	106	2	no	—
388	C₂×C₈	—	106	2	no	—
389	C₂×C₈	—	106	2	no	—
390	C₂×C₈	—	424	2	no	—
391	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
392	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
393	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
394	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
395	C₄⋊C₄	—	53	1	no	—
396	C₄⋊C₄	—	53	1	no	—
397	C₄⋊C₄	—	53	1	no	—
398	C₄⋊C₄	—	53	1	no	—
399	C₄⋊C₄	C₄⋊#6157	1	1	yes	characteristic
400	C₄⋊C₄	C₄⋊#6157	1	1	yes	characteristic
401	C₂²⋊C₄	—	53	1	no	—
402	C₂²⋊C₄	—	53	1	no	—
403	C₂²⋊C₄	—	53	1	no	—
404	C₂²⋊C₄	—	53	1	no	—
405	C₂²⋊C₄	C₄⋊#6157	1	1	yes	characteristic
406	C₂²⋊C₄	C₄⋊#6157	1	1	yes	characteristic
407	C₄²	—	53	1	no	—
408	C₄²	—	53	1	no	—
409	C₄²	—	53	1	no	—
410	C₄²	—	53	1	no	—
411	C₄²	—	53	1	no	—
412	C₄²	—	53	1	no	—
413	C₄²	—	53	1	no	—
414	C₄²	—	53	1	no	—
415	C₄²	C₂²×#6157	1	1	yes	characteristic
416	C₄²	C₂²×#6157	1	1	yes	characteristic
417	C₂³	—	53	1	no	—
418	C₂³	—	53	1	no	—
419	C₂³	C₂×C₄⋊#6157	1	1	yes	characteristic
420	Q₈	—	106	2	no	—
421	D₄	—	106	2	no	—
422	D₄	—	106	2	no	—
423	D₄	—	106	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	53	1	no	—
427	C₂×C₄	—	53	1	no	—
428	C₂×C₄	—	53	2	no	—
429	C₂×C₄	—	53	2	no	—
430	C₂×C₄	—	53	1	no	—
431	C₂×C₄	—	53	1	no	—
432	C₂×C₄	—	53	1	no	—
433	C₂×C₄	—	53	1	no	—
434	C₂×C₄	—	106	2	no	—
435	C₂×C₄	—	106	2	no	—
436	C₂×C₄	—	106	2	no	—
437	C₂×C₄	—	106	1	no	—
438	C₂×C₄	—	106	1	no	—
439	C₂×C₄	—	212	1	no	—
440	C₂×C₄	—	212	1	no	—
441	C₂×C₄	—	212	1	no	—
442	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
443	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
444	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
445	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
446	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
447	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
448	C₈	—	2	1	no	—
449	C₈	—	2	1	no	—
450	C₈	—	53	2	no	—
451	C₈	—	53	2	no	—
452	C₈	—	106	1	no	—
453	C₈	—	106	1	no	—
454	C₈	—	212	2	no	—
455	C₈	—	212	2	no	—
456	C₈	—	212	2	no	—
457	C₈	—	212	2	no	—
458	C₈	D₅₃⋊M₁₆	1	2	yes	—
459	C₈	D₅₃⋊M₁₆	1	2	yes	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	53	2	no	—
464	C₂²	—	106	1	no	—
465	C₂²	—	106	1	no	—
466	C₂²	—	106	1	no	—
467	C₂²	—	106	1	no	—
468	C₂²	—	106	1	no	—
469	C₂²	C₂²×C₄⋊#6157	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	53	2	no	—
476	C₄	—	53	2	no	—
477	C₄	—	106	1	no	—
478	C₄	—	106	1	no	—
479	C₄	—	106	1	no	—
480	C₄	—	106	1	no	—
481	C₄	C₂×D₅₃⋊M₁₆	1	1	yes	characteristic
482	C₄	C₂×D₅₃⋊M₁₆	1	1	yes	characteristic
483	C₂	—	4	1	no	—
484	C₂	—	106	2	no	—
485	C₂	—	212	1	no	—
486	C₂	D₅₃⋊#423	1	1	yes	characteristic
487	C₂	#20291369	1	1	yes	characteristic
488	C₂	#20291377	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#6157
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₅₃×#405	C₄
socle	C₂²×C₅₃	C₂²×C₄⋊C₄
prime radical	C₂×#11719945	C₂×C₄
cosocle	C₄×Dic₅₃	C₂⁴
hypercenter	#405	#6157
hypocenter	C₅₃	#17798
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
2. #20290280	C₂	semidirect
3. #20290279	C₂	semidirect
4. #20290278	C₂	semidirect
5. #20290277	C₂	semidirect
6. #20290271	C₂	semidirect
7. #20290269	C₂	semidirect
8. #20290267	C₂	semidirect
9. #20290265	C₂	semidirect
10. D₅₃⋊#334	C₂	semidirect
167. #11719912	M₁₆	semidirect
171. C₈×D₅₃	M₁₆	semidirect
291. C₅₃	#17798	semidirect

Maximal subgroups

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

subgroup	index
#20291637	2
#20290280	2
#20290279	2
#20290278	2
#20290277	2
#20290271	2
#20290269	2
#20290267	2
#20290265	2
D₅₃⋊#334	2
#20283137	2
#17798	53