Subgroups — D₅₃×#1300 #27274282

Order 13568.

786 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#432×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₄×M₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#376×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20272609	C₂	1	1	yes	maximal, characteristic, complemented
5	#20272608	C₂	1	1	yes	maximal, characteristic, complemented
6	#20272607	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1300	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₅₃	—	2	1	no	—
9	C₂×C₄²×D₅₃	—	2	1	no	—
10	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
11	#16810680	C₂²	1	1	yes	characteristic
12	#16810679	C₄	1	2	yes	complemented
13	#16810678	—	2	1	no	—
14	#16810677	—	2	1	no	—
15	C₄⋊C₈×D₅₃	C₄	1	2	yes	complemented
16	C₂²⋊C₈×D₅₃	—	2	1	no	—
17	C₄×#11719917	C₂²	1	1	yes	characteristic
18	#16810575	C₄	1	2	yes	complemented
19	M₁₆×Dic₅₃	—	2	1	no	—
20	C₄×#11719912	—	2	1	no	—
21	#97×D₅₃	—	2	1	no	—
22	#97×D₅₃	C₄	1	2	yes	complemented
23	C₄×C₈×D₅₃	—	2	1	no	—
24	#16810469	—	2	1	no	—
25	#16810469	C₂²	1	1	yes	characteristic
26	#16810468	—	2	1	no	—
27	#16810468	C₄	1	2	yes	—
28	#95×D₅₃	—	2	1	no	—
29	#95×D₅₃	C₄	1	2	yes	—
30	C₅₃×#432	C₂²	1	1	yes	characteristic
31	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
32	C₅₃×#376	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₅₃	—	2	2	no	—
34	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
37	C₂×#11719917	—	2	1	no	—
38	C₂×#11719912	—	2	2	no	—
39	M₁₆×D₅₃	—	2	8	no	—
40	C₂×C₈×D₅₃	—	2	2	no	—
41	C₂×C₈×D₅₃	—	2	2	no	—
42	C₂×C₄×Dic₅₃	—	2	1	no	—
43	C₂×C₄×Dic₅₃	—	2	2	no	—
44	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
46	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
47	C₄²×D₅₃	—	2	8	no	—
48	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
51	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₅₃	D₄	1	1	yes	characteristic
53	C₄²×D₅₃	D₄	1	1	yes	characteristic
54	C₄²×D₅₃	Q₈	1	1	yes	characteristic
55	C₄²×D₅₃	Q₈	1	1	yes	characteristic
56	C₄⋊#88322	C₂×C₄	1	2	yes	complemented
57	#13133146	—	2	2	no	—
58	C₂²⋊#88322	—	2	1	no	—
59	#13133129	—	2	2	no	—
60	#13133128	—	2	1	no	—
61	#13133128	C₂×C₄	1	2	yes	complemented
62	#13133127	—	2	2	no	—
63	#13133127	—	2	2	no	—
64	C₄×#88322	—	2	1	no	—
65	C₈×Dic₅₃	—	2	2	no	—
66	#13133124	—	2	1	no	—
67	#13133124	—	2	2	no	—
68	#13133124	—	2	2	no	—
69	#13133124	C₂×C₄	1	2	yes	—
70	C₂×M₁₆×C₅₃	—	2	1	no	—
71	C₂×C₄²×C₅₃	—	2	1	no	—
72	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₅₃	C₂×C₄	1	2	yes	complemented
74	C₂²⋊C₈×C₅₃	—	2	1	no	—
75	#97×C₅₃	—	2	1	no	—
76	#97×C₅₃	C₂×C₄	1	2	yes	complemented
77	C₄×C₈×C₅₃	—	2	1	no	—
78	#95×C₅₃	—	2	1	no	—
79	#95×C₅₃	C₂×C₄	1	2	yes	—
80	C₂³×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	—	2	2	no	—
82	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×Dic₅₃	—	2	2	no	—
86	C₂²×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₅₃	—	2	4	no	—
90	C₂×C₄×D₅₃	—	2	4	no	—
91	C₂×C₄×D₅₃	—	2	8	no	—
92	C₂×C₄×D₅₃	—	4	2	no	—
93	C₂×C₄×D₅₃	—	4	4	no	—
94	C₂×C₄×D₅₃	—	4	4	no	—
95	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
96	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
97	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₅₃	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
107	M₁₆×C₅₃	—	2	4	no	—
108	C₂×C₈×C₅₃	—	2	2	no	—
109	C₂×C₈×C₅₃	—	2	2	no	—
110	C₄²×C₅₃	—	2	4	no	—
111	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₅₃	C₂×Q₈	1	1	yes	characteristic
115	C₄×Dic₅₃	—	2	8	no	—
116	C₄×Dic₅₃	—	2	4	no	—
117	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
118	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
119	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₅₃	C₄⋊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	#11719917	—	2	4	no	—
130	C₂×#88322	—	2	2	no	—
131	C₂×#88322	—	2	2	no	—
132	#11719912	—	2	8	no	—
133	C₈×D₅₃	—	2	8	no	—
134	C₈×D₅₃	—	4	4	no	—
135	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×D₅₃	—	2	2	no	—
137	C₂²×D₅₃	—	2	2	no	—
138	C₂²×D₅₃	#95	1	1	yes	characteristic
139	C₂²×D₅₃	#95	1	1	yes	characteristic
140	C₂²×D₅₃	#104	1	4	yes	—
141	C₂×C₄×C₅₃	—	2	2	no	—
142	C₂×C₄×C₅₃	—	2	2	no	—
143	C₂×C₄×C₅₃	—	2	4	no	—
144	C₂×C₄×C₅₃	—	4	1	no	—
145	C₂×C₄×C₅₃	—	4	2	no	—
146	C₂×C₄×C₅₃	—	4	2	no	—
147	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×Dic₅₃	—	2	2	no	—
154	C₂×Dic₅₃	—	2	2	no	—
155	C₂×Dic₅₃	—	2	4	no	—
156	C₂×Dic₅₃	—	4	1	no	—
157	C₂×Dic₅₃	—	4	2	no	—
158	C₂×Dic₅₃	—	4	2	no	—
159	C₂×Dic₅₃	#95	1	1	yes	characteristic
160	C₂×Dic₅₃	#95	1	1	yes	characteristic
161	C₂×Dic₅₃	#95	1	1	yes	characteristic
162	C₂×Dic₅₃	#95	1	1	yes	characteristic
163	C₂×Dic₅₃	#95	1	1	yes	characteristic
164	C₂×Dic₅₃	#95	1	1	yes	characteristic
165	C₄×D₅₃	—	2	2	no	—
166	C₄×D₅₃	—	2	2	no	—
167	C₄×D₅₃	—	2	2	no	—
168	C₄×D₅₃	—	2	2	no	—
169	C₄×D₅₃	—	2	2	no	—
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	16	no	—
177	C₄×D₅₃	#104	1	4	yes	—
178	C₈×C₅₃	—	2	4	no	—
179	C₈×C₅₃	—	4	2	no	—
180	#88322	—	2	4	no	—
181	#88322	—	4	2	no	—
182	C₂×#1300	—	53	1	no	maximal, Sylow
183	C₂²×C₅₃	—	2	1	no	—
184	C₂²×C₅₃	—	2	1	no	—
185	C₂²×C₅₃	C₂×#95	1	1	yes	characteristic
186	C₂²×C₅₃	C₂×#104	1	2	yes	—
187	C₂×D₅₃	—	2	1	no	—
188	C₂×D₅₃	—	2	1	no	—
189	C₂×D₅₃	—	2	8	no	—
190	C₂×D₅₃	#339	1	2	yes	—
191	C₂×D₅₃	#339	1	2	yes	—
192	C₂×D₅₃	#339	1	2	yes	—
193	C₂×D₅₃	#344	1	2	yes	—
194	C₄×C₅₃	—	2	1	no	—
195	C₄×C₅₃	—	2	1	no	—
196	C₄×C₅₃	—	2	1	no	—
197	C₄×C₅₃	—	2	1	no	—
198	C₄×C₅₃	—	2	1	no	—
199	C₄×C₅₃	—	4	4	no	—
200	C₄×C₅₃	C₂×#104	1	2	yes	—
201	Dic₅₃	—	2	1	no	—
202	Dic₅₃	—	2	1	no	—
203	Dic₅₃	—	2	1	no	—
204	Dic₅₃	—	2	1	no	—
205	Dic₅₃	—	2	1	no	—
206	Dic₅₃	—	4	4	no	—
207	Dic₅₃	#339	1	2	yes	—
208	C₂×#432	—	53	1	no	—
209	C₂×C₄×M₁₆	—	53	1	no	—
210	C₂×#376	—	53	1	no	—
211	#1300	—	53	1	no	—
212	#1300	—	53	1	no	—
213	#1300	—	53	1	no	—
214	#1300	D₅₃	1	1	yes	characteristic, direct product factor
215	C₂×C₅₃	—	2	2	no	—
216	C₂×C₅₃	C₂×#339	1	1	yes	characteristic
217	C₂×C₅₃	C₂×#339	1	1	yes	characteristic
218	C₂×C₅₃	C₂×#344	1	1	yes	characteristic
219	D₅₃	—	2	2	no	—
220	D₅₃	#1300	1	4	yes	direct product factor
221	C₂²×M₁₆	—	106	1	no	—
222	C₂²×C₄²	—	53	1	no	—
223	C₂²×C₄²	—	106	1	no	—
224	#432	—	53	1	no	—
225	#432	—	53	2	no	—
226	#432	—	106	1	no	—
227	#432	—	106	1	no	—
228	#432	C₂×D₅₃	1	1	yes	characteristic
229	C₂×C₄⋊C₈	—	53	2	no	—
230	C₂×C₂²⋊C₈	—	106	1	no	—
231	C₄×M₁₆	—	53	1	no	—
232	C₄×M₁₆	—	53	2	no	—
233	C₄×M₁₆	—	106	1	no	—
234	C₄×M₁₆	—	106	1	no	—
235	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic
236	C₂×#97	—	53	2	no	—
237	C₂×#97	—	106	1	no	—
238	C₂×C₄×C₈	—	106	1	no	—
239	#376	—	53	1	no	—
240	#376	—	53	2	no	—
241	#376	—	106	1	no	—
242	#376	—	106	1	no	—
243	#376	C₂×D₅₃	1	1	yes	characteristic
244	C₂×#95	—	53	2	no	—
245	C₂×#95	—	106	1	no	—
246	C₅₃	C₂×#1300	1	1	yes	characteristic, complemented, Sylow
247	C₂³×C₄	—	53	1	no	—
248	C₂³×C₄	—	53	1	no	—
249	C₂³×C₄	—	53	1	no	—
250	C₂³×C₄	—	106	2	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	106	2	no	—
253	C₂×M₁₆	—	106	8	no	—
254	C₂×M₁₆	—	106	1	no	—
255	C₂²×C₈	—	106	2	no	—
256	C₂²×C₈	—	106	2	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	—	53	1	no	—
259	C₂×C₄²	—	53	1	no	—
260	C₂×C₄²	—	53	1	no	—
261	C₂×C₄²	—	53	1	no	—
262	C₂×C₄²	—	53	1	no	—
263	C₂×C₄²	—	53	1	no	—
264	C₂×C₄²	—	53	1	no	—
265	C₂×C₄²	—	53	1	no	—
266	C₂×C₄²	—	53	1	no	—
267	C₂×C₄²	—	53	1	no	—
268	C₂×C₄²	—	53	1	no	—
269	C₂×C₄²	—	106	8	no	—
270	C₂×C₄²	—	106	2	no	—
271	C₂×C₄²	—	106	1	no	—
272	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
273	C₄⋊C₈	—	53	2	no	—
274	C₄⋊C₈	—	106	2	no	—
275	C₄⋊C₈	C₄×D₅₃	1	2	yes	complemented
276	C₂²⋊C₈	—	2	1	no	—
277	C₂²⋊C₈	—	106	2	no	—
278	C₂²⋊C₈	—	106	1	no	—
279	#97	—	2	1	no	—
280	#97	—	53	2	no	—
281	#97	—	106	2	no	—
282	#97	—	106	2	no	—
283	#97	—	106	1	no	—
284	#97	C₄×D₅₃	1	2	yes	complemented
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	—	106	2	no	—
287	C₄×C₈	—	106	1	no	—
288	#95	—	2	1	no	—
289	#95	—	53	2	no	—
290	#95	—	106	2	no	—
291	#95	—	106	2	no	—
292	#95	—	106	1	no	—
293	#95	C₄×D₅₃	1	2	yes	—
294	C₂⁴	—	53	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	53	1	no	—
297	C₂²×C₄	—	53	1	no	—
298	C₂²×C₄	—	53	1	no	—
299	C₂²×C₄	—	53	1	no	—
300	C₂²×C₄	—	53	1	no	—
301	C₂²×C₄	—	53	1	no	—
302	C₂²×C₄	—	53	1	no	—
303	C₂²×C₄	—	53	1	no	—
304	C₂²×C₄	—	53	1	no	—
305	C₂²×C₄	—	53	1	no	—
306	C₂²×C₄	—	53	1	no	—
307	C₂²×C₄	—	53	1	no	—
308	C₂²×C₄	—	53	1	no	—
309	C₂²×C₄	—	53	1	no	—
310	C₂²×C₄	—	53	1	no	—
311	C₂²×C₄	—	106	4	no	—
312	C₂²×C₄	—	106	4	no	—
313	C₂²×C₄	—	106	8	no	—
314	C₂²×C₄	—	106	2	no	—
315	C₂²×C₄	—	212	2	no	—
316	C₂²×C₄	—	212	4	no	—
317	C₂²×C₄	—	212	4	no	—
318	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
319	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
320	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
321	M₁₆	—	2	4	no	—
322	M₁₆	—	106	8	no	—
323	M₁₆	—	106	4	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	106	8	no	—
327	C₂×C₈	—	106	2	no	—
328	C₂×C₈	—	106	2	no	—
329	C₂×C₈	—	212	4	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	53	1	no	—
332	C₄²	—	53	1	no	—
333	C₄²	—	53	1	no	—
334	C₄²	—	53	1	no	—
335	C₄²	—	53	1	no	—
336	C₄²	—	53	1	no	—
337	C₄²	—	53	1	no	—
338	C₄²	—	53	1	no	—
339	C₄²	—	53	1	no	—
340	C₄²	—	53	1	no	—
341	C₄²	—	53	1	no	—
342	C₄²	—	53	1	no	—
343	C₄²	—	106	4	no	—
344	C₄²	—	106	8	no	—
345	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
346	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
347	C₄²	D₄×D₅₃	1	1	yes	characteristic
348	C₄²	Q₈×D₅₃	1	1	yes	characteristic
349	C₂³	—	53	1	no	—
350	C₂³	—	53	4	no	—
351	C₂³	—	53	1	no	—
352	C₂³	—	106	2	no	—
353	C₂³	—	106	2	no	—
354	C₂³	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	53	1	no	—
362	C₂×C₄	—	53	4	no	—
363	C₂×C₄	—	53	1	no	—
364	C₂×C₄	—	53	1	no	—
365	C₂×C₄	—	53	1	no	—
366	C₂×C₄	—	53	1	no	—
367	C₂×C₄	—	53	1	no	—
368	C₂×C₄	—	106	2	no	—
369	C₂×C₄	—	106	2	no	—
370	C₂×C₄	—	106	2	no	—
371	C₂×C₄	—	106	2	no	—
372	C₂×C₄	—	106	2	no	—
373	C₂×C₄	—	106	2	no	—
374	C₂×C₄	—	106	2	no	—
375	C₂×C₄	—	106	2	no	—
376	C₂×C₄	—	106	2	no	—
377	C₂×C₄	—	106	2	no	—
378	C₂×C₄	—	106	2	no	—
379	C₂×C₄	—	106	4	no	—
380	C₂×C₄	—	212	1	no	—
381	C₂×C₄	—	212	1	no	—
382	C₂×C₄	—	212	16	no	—
383	C₂×C₄	—	212	1	no	—
384	C₂×C₄	—	212	2	no	—
385	C₂×C₄	—	212	2	no	—
386	C₂×C₄	C₄²×D₅₃	1	1	yes	characteristic
387	C₂×C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
388	C₂×C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
389	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
390	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
391	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
392	C₈	—	2	4	no	—
393	C₈	—	4	2	no	—
394	C₈	—	106	4	no	—
395	C₈	—	212	2	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	53	2	no	—
399	C₂²	—	53	2	no	—
400	C₂²	—	53	2	no	—
401	C₂²	—	53	2	no	—
402	C₂²	—	106	8	no	—
403	C₂²	—	106	1	no	—
404	C₂²	—	106	1	no	—
405	C₂²	#95×D₅₃	1	1	yes	characteristic
406	C₂²	#104×D₅₃	1	2	yes	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	4	4	no	—
413	C₄	—	53	2	no	—
414	C₄	—	106	1	no	—
415	C₄	—	106	1	no	—
416	C₄	—	106	1	no	—
417	C₄	—	106	1	no	—
418	C₄	—	106	1	no	—
419	C₄	—	212	4	no	—
420	C₄	#104×D₅₃	1	2	yes	—
421	C₂	—	2	2	no	—
422	C₂	—	53	4	no	—
423	C₂	—	106	2	no	—
424	C₂	#339×D₅₃	1	1	yes	characteristic
425	C₂	#339×D₅₃	1	1	yes	characteristic
426	C₂	#344×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₅₃×#1300	C₂
socle	C₂²×C₅₃	C₂×#95
prime radical	C₂³×D₅₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	#1300	D₅₃
hypocenter	C₅₃	C₂×#1300
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1300

Complements

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

N	H ≅ G/N	type
4. #20272609	C₂	semidirect
5. #20272608	C₂	semidirect
6. #20272607	C₂	semidirect
7. C₅₃×#1300	C₂	semidirect
12. #16810679	C₄	semidirect
15. C₄⋊C₈×D₅₃	C₄	semidirect
18. #16810575	C₄	semidirect
22. #97×D₅₃	C₄	semidirect
56. C₄⋊#88322	C₂×C₄	semidirect
61. #13133128	C₂×C₄	semidirect
73. C₄⋊C₈×C₅₃	C₂×C₄	semidirect
76. #97×C₅₃	C₂×C₄	semidirect
214. #1300	D₅₃	direct (N × H)
220. D₅₃	#1300	direct (N × H)
246. C₅₃	C₂×#1300	semidirect
275. C₄⋊C₈	C₄×D₅₃	semidirect
284. #97	C₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#432×D₅₃	2
C₄×M₁₆×D₅₃	2
#376×D₅₃	2
#20272609	2
#20272608	2
#20272607	2
C₅₃×#1300	2
C₂×#1300	53

Subgroups — D53×#1300 #27274282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#1300 #27274282