Subgroups — #27353712

Order 13568.

662 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#11719945	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810753	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13133250	C₂	1	1	yes	maximal, characteristic
4	#20273588	C₂	1	2	yes	maximal, complemented
5	#20273574	C₂	1	2	yes	maximal, complemented
6	#20273567	C₂	1	2	yes	maximal, complemented
7	#20273553	C₂	1	2	yes	maximal, complemented
8	#20273467	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273111	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273103	C₂	1	1	yes	maximal, characteristic
11	C₅₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133250	C₄	1	1	yes	characteristic
13	C₄×#11719945	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
15	#16810753	—	2	1	no	—
16	#16810753	—	2	1	no	—
17	#16810753	C₂²	1	2	yes	—
18	#16810753	C₂²	1	2	yes	—
19	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
20	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
21	#16810731	C₄	1	2	yes	—
22	#16810725	C₄	1	2	yes	—
23	C₄×Dic₂₁₂	C₂²	1	2	yes	—
24	C₄×#11719913	C₂²	1	2	yes	—
25	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
26	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
27	C₈×C₂²⋊D₅₃	—	2	1	no	—
28	C₈×C₂²⋊D₅₃	—	2	1	no	—
29	#16810676	C₂²	1	1	yes	characteristic
30	#16810674	—	2	1	no	—
31	#16810665	C₄	1	1	yes	characteristic
32	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
33	C₂×#13133146	—	2	1	no	—
34	#16810633	C₄	1	1	yes	characteristic
35	#16810625	C₄	1	1	yes	characteristic
36	C₂×#13133127	—	2	1	no	—
37	C₄×C₈×D₅₃	—	2	1	no	—
38	#16810376	C₂²	1	2	yes	—
39	#16810374	C₂²	1	2	yes	—
40	#16810355	C₂²	1	2	yes	—
41	#16810355	C₂²	1	2	yes	—
42	#16810355	C₂²	1	2	yes	—
43	#16810352	C₂²	1	2	yes	—
44	C₅₃×#431	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
47	C₅₃×#322	C₂²	1	2	yes	—
48	C₅₃×#322	C₂²	1	2	yes	—
49	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
50	C₂²×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
51	#13133250	—	2	4	no	—
52	C₂×Dic₂₁₂	C₂×C₄	1	2	yes	—
53	C₂×#11719913	C₂×C₄	1	2	yes	—
54	C₂²×#88322	—	2	1	no	—
55	C₂×C₈×D₅₃	—	2	1	no	—
56	C₂×C₈×D₅₃	—	2	1	no	—
57	C₄×Dic₁₀₆	—	2	1	no	—
58	C₄×Dic₁₀₆	—	2	1	no	—
59	C₄×Dic₁₀₆	C₂×C₄	1	2	yes	—
60	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₁₀₆	C₂³	1	2	yes	—
62	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
63	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
64	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
65	C₄×C₂²⋊D₅₃	—	2	1	no	—
66	C₄×C₂²⋊D₅₃	—	2	1	no	—
67	#13133176	C₂×C₄	1	1	yes	characteristic
68	#13133174	—	2	1	no	—
69	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
70	C₂×#11719919	—	2	1	no	—
71	C₂×C₄×Dic₅₃	—	2	1	no	—
72	C₄²×D₅₃	—	2	1	no	—
73	#13133151	C₂×C₄	1	2	yes	—
74	#13133149	C₂×C₄	1	2	yes	—
75	C₄⋊#88322	—	2	1	no	—
76	C₄⋊#88322	C₂³	1	2	yes	—
77	C₄⋊#88322	C₂³	1	1	yes	characteristic
78	C₄⋊#88322	C₂³	1	1	yes	characteristic
79	#13133146	—	2	2	no	—
80	#13133146	—	2	2	no	—
81	#13133146	—	2	1	no	—
82	#13133146	—	2	1	no	—
83	#13133142	C₂×C₄	1	2	yes	—
84	#13133142	C₂×C₄	1	2	yes	—
85	#13133142	C₂×C₄	1	2	yes	—
86	#13133139	C₂×C₄	1	2	yes	—
87	C₂²⋊#88322	—	2	1	no	—
88	#13133129	—	2	1	no	—
89	#13133129	—	2	1	no	—
90	#13133127	—	2	2	no	—
91	#13133127	—	2	2	no	—
92	C₄×#88322	—	2	1	no	—
93	C₈×Dic₅₃	—	2	1	no	—
94	C₈×Dic₅₃	—	2	1	no	—
95	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
96	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
97	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
98	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₅₃	—	2	1	no	—
101	C₂²⋊C₈×C₅₃	—	2	1	no	—
102	#97×C₅₃	C₂×C₄	1	2	yes	—
103	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
104	C₄×C₈×C₅₃	D₄	1	1	yes	characteristic
105	C₄×C₈×C₅₃	C₂³	1	2	yes	—
106	C₄×C₈×C₅₃	C₂³	1	2	yes	—
107	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₅₃	—	2	1	no	—
113	C₂²×Dic₅₃	—	2	1	no	—
114	C₂²×Dic₅₃	—	2	1	no	—
115	#11719945	—	2	2	no	—
116	#11719945	M₁₆	1	4	yes	—
117	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₅₃	—	2	1	no	—
119	C₂×C₄×D₅₃	—	2	1	no	—
120	C₂×C₄×D₅₃	—	2	1	no	—
121	C₂×Dic₁₀₆	—	2	2	no	—
122	C₂×Dic₁₀₆	—	2	2	no	—
123	C₂×Dic₁₀₆	—	2	1	no	—
124	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
125	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
126	M₁₆×C₅₃	—	2	2	no	—
127	M₁₆×C₅₃	—	2	2	no	—
128	C₂×C₈×C₅₃	—	2	2	no	—
129	C₂×C₈×C₅₃	—	2	2	no	—
130	C₂×C₈×C₅₃	—	4	1	no	—
131	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₅₃	#41	1	1	yes	characteristic
140	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
141	C₂²⋊Dic₅₃	—	2	1	no	—
142	#11719921	—	2	1	no	—
143	#11719921	—	2	1	no	—
144	C₄⋊Dic₅₃	—	2	1	no	—
145	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
146	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
147	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
148	#11719919	—	2	2	no	—
149	#11719919	—	2	1	no	—
150	#11719919	—	2	2	no	—
151	#11719919	—	2	1	no	—
152	C₄×Dic₅₃	—	2	1	no	—
153	C₄×Dic₅₃	—	2	1	no	—
154	C₄×Dic₅₃	—	2	2	no	—
155	C₄×Dic₅₃	—	2	1	no	—
156	C₄×Dic₅₃	—	2	2	no	—
157	C₂×#88322	—	2	1	no	—
158	C₂×#88322	—	2	1	no	—
159	C₂×#88322	—	2	2	no	—
160	C₂×#88322	—	4	2	no	—
161	Dic₂₁₂	—	2	4	no	—
162	#11719913	—	2	4	no	—
163	C₈×D₅₃	—	4	2	no	—
164	C₈×D₅₃	—	4	2	no	—
165	C₂³×C₅₃	C₄×D₄	1	1	yes	characteristic
166	C₂²×D₅₃	—	2	1	no	—
167	C₂×C₄×C₅₃	—	2	1	no	—
168	C₂×C₄×C₅₃	—	2	1	no	—
169	C₂×C₄×C₅₃	—	4	1	no	—
170	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₅₃	C₂×M₁₆	1	2	yes	—
174	C₂×C₄×C₅₃	#131	1	2	yes	—
175	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
178	C₂²⋊D₅₃	—	2	4	no	—
179	C₂×Dic₅₃	—	2	1	no	—
180	C₂×Dic₅₃	—	2	2	no	—
181	C₂×Dic₅₃	—	2	1	no	—
182	C₂×Dic₅₃	—	2	1	no	—
183	C₂×Dic₅₃	—	2	2	no	—
184	C₂×Dic₅₃	—	4	2	no	—
185	C₂×Dic₅₃	—	4	2	no	—
186	D₂₁₂	—	2	1	no	—
187	D₂₁₂	C₂×M₁₆	1	2	yes	—
188	C₄×D₅₃	—	2	4	no	—
189	C₄×D₅₃	—	4	2	no	—
190	C₄×D₅₃	—	4	1	no	—
191	C₄×D₅₃	—	4	1	no	—
192	Dic₁₀₆	—	2	1	no	—
193	Dic₁₀₆	—	2	2	no	—
194	Dic₁₀₆	—	2	2	no	—
195	Dic₁₀₆	—	4	2	no	—
196	Dic₁₀₆	C₂×M₁₆	1	2	yes	—
197	C₈×C₅₃	—	2	2	no	—
198	C₈×C₅₃	—	2	2	no	—
199	C₈×C₅₃	—	2	1	no	—
200	C₈×C₅₃	—	2	1	no	—
201	C₈×C₅₃	—	2	1	no	—
202	C₈×C₅₃	—	4	2	no	—
203	C₈×C₅₃	#137	1	2	yes	complemented
204	#88322	—	4	1	no	—
205	#88322	—	4	1	no	—
206	#88322	—	4	2	no	—
207	#17872	—	53	1	no	maximal, Sylow
208	C₂²×C₅₃	—	2	1	no	—
209	C₂²×C₅₃	—	2	1	no	—
210	C₂²×C₅₃	#435	1	2	yes	—
211	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂×D₅₃	—	2	2	no	—
213	C₂×D₅₃	—	4	1	no	—
214	C₂×D₅₃	—	4	1	no	—
215	C₄×C₅₃	—	2	1	no	—
216	C₄×C₅₃	—	2	1	no	—
217	C₄×C₅₃	—	2	1	no	—
218	C₄×C₅₃	#435	1	2	yes	—
219	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
220	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
221	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
222	C₄×C₅₃	#575	1	1	yes	characteristic
223	Dic₅₃	—	2	2	no	—
224	Dic₅₃	—	4	2	no	—
225	Dic₅₃	—	4	1	no	—
226	Dic₅₃	—	4	1	no	—
227	Dic₅₃	—	4	2	no	—
228	C₈×#41	—	53	1	no	—
229	C₂×#446	—	53	1	no	—
230	C₄×#137	—	53	1	no	—
231	#1587	—	53	2	no	—
232	#1585	—	53	2	no	—
233	#1584	—	53	2	no	—
234	#1582	—	53	2	no	—
235	#1565	—	53	1	no	—
236	#1479	—	53	1	no	—
237	#1477	—	53	1	no	—
238	#1451	D₅₃	1	1	yes	characteristic, complemented
239	C₂×C₅₃	—	2	2	no	—
240	C₂×C₅₃	C₂×#435	1	1	yes	characteristic
241	C₂×C₅₃	C₄×#137	1	1	yes	characteristic
242	C₂×C₅₃	#2955	1	1	yes	characteristic
243	D₅₃	—	4	2	no	—
244	C₂×#137	—	53	1	no	—
245	C₄×#41	—	53	1	no	—
246	C₂×C₄×Q₈	—	53	1	no	—
247	#446	—	53	2	no	—
248	#446	—	53	2	no	—
249	#446	—	106	1	no	—
250	#446	—	106	1	no	—
251	C₈×Q₈	—	53	1	no	—
252	C₈×Q₈	—	53	1	no	—
253	#441	—	53	2	no	—
254	#440	—	53	2	no	—
255	C₄×Q₁₆	—	53	2	no	—
256	C₄×SD₁₆	—	53	2	no	—
257	C₈×D₄	—	53	1	no	—
258	C₈×D₄	—	53	1	no	—
259	C₈×D₄	—	106	1	no	—
260	C₈×D₄	—	106	1	no	—
261	#431	—	53	1	no	—
262	#431	—	106	1	no	—
263	#431	C₂×D₅₃	1	1	yes	characteristic
264	#428	—	53	1	no	—
265	C₂×C₄⋊C₈	—	53	1	no	—
266	C₂×C₄⋊C₈	—	106	1	no	—
267	#419	—	53	1	no	—
268	#417	—	53	1	no	—
269	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic
270	C₂×#97	—	106	1	no	—
271	C₂×C₄×C₈	—	106	1	no	—
272	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
273	#335	—	53	2	no	—
274	#334	—	53	2	no	—
275	Q₈⋊C₈	—	53	2	no	—
276	Q₈⋊C₈	—	53	2	no	—
277	Q₈⋊C₈	—	53	2	no	—
278	D₄⋊C₈	—	53	2	no	—
279	#322	C₂×D₅₃	1	2	yes	—
280	#322	C₂×D₅₃	1	2	yes	—
281	C₅₃	#17872	1	1	yes	characteristic, complemented, Sylow
282	C₂×#41	—	53	1	no	—
283	C₂²×Q₈	—	53	1	no	—
284	#137	—	106	4	no	—
285	C₂×Q₁₆	—	53	2	no	—
286	C₂×SD₁₆	—	53	2	no	—
287	C₂×M₁₆	C₄×D₅₃	1	1	yes	characteristic
288	C₂×M₁₆	C₄×D₅₃	1	1	yes	characteristic
289	C₂²×C₈	—	106	1	no	—
290	C₂²×C₈	—	106	1	no	—
291	C₂²×C₈	—	106	1	no	—
292	C₂²×C₈	D₂₁₂	1	1	yes	characteristic
293	C₂²×C₈	D₂₁₂	1	1	yes	characteristic
294	C₄×Q₈	—	53	2	no	—
295	C₄×Q₈	—	53	1	no	—
296	C₄×Q₈	—	53	2	no	—
297	C₄×Q₈	—	53	1	no	—
298	C₄×Q₈	—	106	1	no	—
299	C₄×Q₈	—	106	1	no	—
300	C₄×D₄	—	53	1	no	—
301	C₄×D₄	—	53	1	no	—
302	C₄×D₄	—	106	1	no	—
303	C₄×D₄	—	106	1	no	—
304	#117	—	53	1	no	—
305	#117	—	106	1	no	—
306	C₂×C₄⋊C₄	—	53	1	no	—
307	C₂×C₄⋊C₄	—	106	1	no	—
308	C₂×C₄²	—	106	1	no	—
309	C₂×C₄²	—	106	1	no	—
310	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
311	#107	—	53	2	no	—
312	#106	—	53	2	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	53	2	no	—
315	C₄⋊C₈	—	53	1	no	—
316	C₄⋊C₈	—	53	1	no	—
317	C₄⋊C₈	—	106	2	no	—
318	C₄⋊C₈	—	106	2	no	—
319	C₄⋊C₈	—	106	1	no	—
320	C₄⋊C₈	—	106	1	no	—
321	C₄⋊C₈	—	106	1	no	—
322	#103	—	53	2	no	—
323	#103	—	53	2	no	—
324	#103	—	53	2	no	—
325	#102	—	53	2	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	106	1	no	—
328	C₂²⋊C₈	—	106	1	no	—
329	C₂²⋊C₈	—	106	1	no	—
330	#97	—	106	2	no	—
331	#97	—	106	2	no	—
332	#97	C₄×D₅₃	1	2	yes	—
333	C₄×C₈	—	106	1	no	—
334	C₄×C₈	—	106	1	no	—
335	C₄×C₈	—	106	1	no	—
336	C₄×C₈	D₂₁₂	1	1	yes	characteristic
337	C₄×C₈	D₂₁₂	1	1	yes	characteristic
338	C₄×C₈	C₂²×D₅₃	1	2	yes	—
339	C₄×C₈	C₂²×D₅₃	1	2	yes	—
340	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
341	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
342	#41	—	53	4	no	—
343	#41	—	106	2	no	—
344	C₂×Q₈	—	53	1	no	—
345	C₂×Q₈	—	53	2	no	—
346	C₂×Q₈	—	106	1	no	—
347	C₂×Q₈	—	106	2	no	—
348	C₂×Q₈	—	106	2	no	—
349	C₂×D₄	—	53	1	no	—
350	C₂×D₄	—	106	1	no	—
351	C₂²×C₄	—	106	1	no	—
352	C₂²×C₄	—	106	1	no	—
353	C₂²×C₄	—	106	1	no	—
354	C₂²×C₄	—	106	1	no	—
355	C₂²×C₄	—	106	1	no	—
356	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
358	C₂²×C₄	#11719945	1	1	yes	characteristic
359	Q₁₆	—	106	4	no	—
360	SD₁₆	—	106	4	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	106	1	no	—
367	C₂×C₈	—	106	1	no	—
368	C₂×C₈	—	106	2	no	—
369	C₂×C₈	—	212	2	no	—
370	C₂×C₈	—	212	2	no	—
371	C₂×C₈	—	212	2	no	—
372	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
373	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
374	C₂×C₈	C₂×D₂₁₂	1	1	yes	characteristic
375	C₂×C₈	C₂×D₂₁₂	1	1	yes	characteristic
376	C₂×C₈	C₂×D₂₁₂	1	1	yes	characteristic
377	C₂×C₈	C₂×D₂₁₂	1	1	yes	characteristic
378	C₄⋊C₄	—	53	2	no	—
379	C₄⋊C₄	—	53	1	no	—
380	C₄⋊C₄	—	53	1	no	—
381	C₄⋊C₄	—	106	1	no	—
382	C₄⋊C₄	—	106	2	no	—
383	C₄⋊C₄	—	106	1	no	—
384	C₄⋊C₄	—	106	2	no	—
385	C₄⋊C₄	—	106	1	no	—
386	C₂²⋊C₄	—	106	1	no	—
387	C₂²⋊C₄	—	106	1	no	—
388	C₂²⋊C₄	—	106	1	no	—
389	C₄²	—	106	1	no	—
390	C₄²	—	106	1	no	—
391	C₄²	—	106	2	no	—
392	C₄²	—	106	1	no	—
393	C₄²	—	106	2	no	—
394	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
395	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
396	C₄²	#11719945	1	1	yes	characteristic
397	C₄²	C₂³×D₅₃	1	1	yes	characteristic
398	C₂³	—	106	1	no	—
399	C₂³	C₄×D₂₁₂	1	1	yes	characteristic
400	Q₈	—	53	2	no	—
401	Q₈	—	106	1	no	—
402	Q₈	—	106	2	no	—
403	Q₈	—	106	2	no	—
404	Q₈	—	212	2	no	—
405	D₄	—	53	2	no	—
406	D₄	—	106	4	no	—
407	D₄	—	106	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	106	1	no	—
412	C₂×C₄	—	106	4	no	—
413	C₂×C₄	—	106	1	no	—
414	C₂×C₄	—	106	1	no	—
415	C₂×C₄	—	106	2	no	—
416	C₂×C₄	—	106	2	no	—
417	C₂×C₄	—	212	2	no	—
418	C₂×C₄	—	212	2	no	—
419	C₂×C₄	—	212	2	no	—
420	C₂×C₄	—	212	1	no	—
421	C₂×C₄	—	212	1	no	—
422	C₂×C₄	C₄×D₂₁₂	1	1	yes	characteristic
423	C₂×C₄	C₄×D₂₁₂	1	1	yes	characteristic
424	C₂×C₄	C₄×D₂₁₂	1	1	yes	characteristic
425	C₂×C₄	M₁₆×D₅₃	1	2	yes	—
426	C₂×C₄	#13133225	1	2	yes	—
427	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
429	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	2	2	no	—
432	C₈	—	2	1	no	—
433	C₈	—	2	1	no	—
434	C₈	—	2	1	no	—
435	C₈	—	4	2	no	—
436	C₈	—	212	1	no	—
437	C₈	—	212	1	no	—
438	C₈	—	212	2	no	—
439	C₈	#13133250	1	2	yes	complemented
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	106	2	no	—
443	C₂²	—	212	1	no	—
444	C₂²	—	212	1	no	—
445	C₂²	#16810696	1	2	yes	—
446	C₂²	C₂×C₄×D₂₁₂	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	106	2	no	—
451	C₄	—	212	2	no	—
452	C₄	—	212	1	no	—
453	C₄	—	212	1	no	—
454	C₄	—	212	2	no	—
455	C₄	#16810696	1	2	yes	—
456	C₄	C₂×M₁₆×D₅₃	1	1	yes	characteristic
457	C₄	C₂×#13133225	1	1	yes	characteristic
458	C₄	C₂×#13133250	1	1	yes	characteristic
459	C₄	#16811423	1	1	yes	characteristic
460	C₂	—	2	2	no	—
461	C₂	—	212	2	no	—
462	C₂	C₂×#16810696	1	1	yes	characteristic
463	C₂	C₄×#13133250	1	1	yes	characteristic
464	C₂	#20283619	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₁₂
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1451	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂×#11719945	C₂×C₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	#1451	D₅₃
hypocenter	C₅₃	#17872
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1451

Complements

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

N	H ≅ G/N	type
2. C₂×#16810753	C₂	semidirect
4. #20273588	C₂	semidirect
5. #20273574	C₂	semidirect
6. #20273567	C₂	semidirect
7. #20273553	C₂	semidirect
8. #20273467	C₂	semidirect
9. #20273111	C₂	semidirect
11. C₅₃×#1451	C₂	semidirect
203. C₈×C₅₃	#137	semidirect
238. #1451	D₅₃	semidirect
281. C₅₃	#17872	semidirect
439. C₈	#13133250	semidirect

Maximal subgroups

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

subgroup	index
C₈×#11719945	2
C₂×#16810753	2
C₄×#13133250	2
#20273588	2
#20273574	2
#20273567	2
#20273553	2
#20273467	2
#20273111	2
#20273103	2
C₅₃×#1451	2
#17872	53