Subgroups — #28319492

Order 13568.

982 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291164	C₂	1	2	yes	maximal
2	#20290650	C₂	1	2	yes	maximal, complemented
3	#20290636	C₂	1	2	yes	maximal, complemented
4	#20290591	C₂	1	4	yes	maximal
5	C₄×#13133285	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
7	C₂×#13133296	—	2	2	no	—
8	C₂×#13133285	C₂²	1	8	yes	—
9	#16811569	C₂²	1	4	yes	—
10	#16811567	—	2	2	no	—
11	#16811565	—	2	2	no	—
12	#16811565	C₂²	1	4	yes	—
13	C₄×C₄⋊#6157	—	2	2	no	—
14	C₄×C₄⋊#6157	C₂²	1	4	yes	—
15	#16811497	C₂²	1	8	yes	—
16	C₂²×C₈×D₅₃	C₂²	1	2	yes	—
17	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×#88322	C₄	1	1	yes	characteristic, complemented
19	C₂×C₈×Dic₅₃	C₄	1	2	yes	complemented
20	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic, complemented
21	C₄×C₈×D₅₃	C₄	1	2	yes	complemented
22	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic, complemented
23	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
24	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
25	C₄×C₈×D₅₃	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₅₃	C₄	1	1	yes	characteristic, complemented
27	#13133296	—	4	8	no	—
28	C₂×C₄⋊#6157	—	2	4	no	—
29	C₂×C₄⋊#6157	—	2	4	no	—
30	C₂×C₄⋊#6157	C₂³	1	8	yes	—
31	C₂×C₂²⋊#6157	—	2	4	no	—
32	C₂×C₄×#6157	—	2	4	no	—
33	#13133285	—	2	16	no	—
34	(C₂×#6157)⋊C₄	—	2	4	no	—
35	(C₂×#6157)⋊C₄	—	2	4	no	—
36	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
37	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
38	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
39	C₂²×#88322	C₂×C₄	1	2	yes	—
40	C₂×C₈×D₅₃	—	2	8	no	—
41	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
42	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
43	C₂×C₈×D₅₃	C₂³	1	2	yes	—
44	C₂×C₈×D₅₃	C₂³	1	2	yes	—
45	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₅₃	Q₈	1	1	yes	characteristic
47	C₂×C₄×Dic₅₃	Q₈	1	1	yes	characteristic
48	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₅₃	D₄	1	1	yes	characteristic
51	C₄²×D₅₃	D₄	1	1	yes	characteristic
52	C₄²×D₅₃	Q₈	1	1	yes	characteristic
53	C₄²×D₅₃	Q₈	1	1	yes	characteristic
54	C₄²×D₅₃	C₂³	1	1	yes	characteristic
55	C₄²×D₅₃	C₂³	1	1	yes	characteristic
56	C₄×#88322	C₂×C₄	1	1	yes	characteristic
57	C₄×#88322	C₂×C₄	1	2	yes	—
58	C₄×#88322	C₂×C₄	1	1	yes	characteristic
59	C₈×Dic₅₃	C₂×C₄	1	2	yes	—
60	C₈×Dic₅₃	C₂×C₄	1	2	yes	—
61	C₈×Dic₅₃	C₂×C₄	1	2	yes	—
62	C₈×Dic₅₃	C₂×C₄	1	2	yes	—
63	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
65	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
66	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	—
67	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
68	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×#6157	—	2	8	no	—
70	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
76	C₂×C₄×D₅₃	—	2	4	no	—
77	C₂×C₄×D₅₃	—	2	4	no	—
78	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₅₃	SD₁₆	1	8	yes	—
83	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
84	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
90	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
91	C₂²⋊#6157	—	4	8	no	—
92	C₄⋊#6157	—	2	16	no	—
93	C₄⋊#6157	—	4	8	no	—
94	C₄⋊#6157	—	4	8	no	—
95	C₄×#6157	—	4	8	no	—
96	C₂×C₈×C₅₃	—	2	4	no	—
97	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
99	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
103	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
104	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
105	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
106	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
107	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
108	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
109	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
111	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
112	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
113	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
114	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
115	C₂×#88322	—	2	4	no	—
116	C₂×#88322	C₂²×C₄	1	2	yes	—
117	C₂×#88322	C₂²×C₄	1	2	yes	—
118	C₈×D₅₃	—	2	4	no	—
119	C₈×D₅₃	—	2	4	no	—
120	C₈×D₅₃	—	2	4	no	—
121	C₈×D₅₃	#41	1	8	yes	—
122	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂²×D₅₃	—	2	2	no	—
124	C₂²×D₅₃	—	2	2	no	—
125	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂²×D₅₃	C₂×SD₁₆	1	4	yes	—
127	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
128	C₂×#6157	—	4	8	no	—
129	C₂×#6157	—	4	8	no	—
130	C₂×#6157	—	4	8	no	—
131	C₂×C₄×C₅₃	—	2	2	no	—
132	C₂×C₄×C₅₃	—	2	2	no	—
133	C₂×C₄×C₅₃	#106	1	4	yes	complemented
134	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
140	C₂×Dic₅₃	—	2	2	no	—
141	C₂×Dic₅₃	—	2	2	no	—
142	C₂×Dic₅₃	#106	1	4	yes	complemented
143	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×Dic₅₃	C₂²×Q₈	1	1	yes	characteristic
149	C₄×D₅₃	—	2	2	no	—
150	C₄×D₅₃	—	2	2	no	—
151	C₄×D₅₃	—	2	2	no	—
152	C₄×D₅₃	—	2	2	no	—
153	C₄×D₅₃	—	2	2	no	—
154	C₄×D₅₃	—	2	2	no	—
155	C₄×D₅₃	#106	1	4	yes	complemented
156	C₄×D₅₃	#106	1	4	yes	complemented
157	C₄×D₅₃	C₂×SD₁₆	1	4	yes	—
158	C₄×D₅₃	C₂×SD₁₆	1	4	yes	—
159	C₄×D₅₃	#135	1	4	yes	—
160	C₄×D₅₃	C₂×#41	1	4	yes	—
161	C₈×C₅₃	—	2	2	no	—
162	C₈×C₅₃	#117	1	4	yes	complemented
163	#88322	—	2	2	no	—
164	#88322	#117	1	4	yes	complemented
165	#20816	—	53	1	no	maximal, Sylow
166	C₂²×C₅₃	—	2	1	no	—
167	C₂²×C₅₃	—	2	1	no	—
168	C₂²×C₅₃	C₂×#106	1	2	yes	—
169	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
170	C₂×D₅₃	—	2	1	no	—
171	C₂×D₅₃	—	2	1	no	—
172	C₂×D₅₃	—	2	8	no	—
173	C₂×D₅₃	C₂×#106	1	2	yes	—
174	C₂×D₅₃	#532	1	2	yes	—
175	C₂×D₅₃	C₂²×SD₁₆	1	2	yes	—
176	C₂×D₅₃	C₂×#135	1	2	yes	—
177	#6157	—	8	8	no	—
178	C₄×C₅₃	—	2	1	no	—
179	C₄×C₅₃	—	2	1	no	—
180	C₄×C₅₃	C₂×#106	1	2	yes	—
181	C₄×C₅₃	C₂×#106	1	2	yes	—
182	C₄×C₅₃	#427	1	2	yes	—
183	C₄×C₅₃	C₂×#117	1	2	yes	—
184	Dic₅₃	—	2	1	no	—
185	Dic₅₃	—	2	1	no	—
186	Dic₅₃	C₂×#106	1	2	yes	—
187	Dic₅₃	C₂×#106	1	2	yes	—
188	Dic₅₃	#427	1	2	yes	—
189	Dic₅₃	#533	1	2	yes	—
190	C₂²×C₄×C₈	—	53	1	no	—
191	#2285	—	53	2	no	—
192	#1844	—	53	2	no	—
193	#1834	—	53	2	no	—
194	#1807	—	53	4	no	—
195	C₄×#106	—	53	4	no	—
196	C₂×C₅₃	—	2	2	no	—
197	C₂×C₅₃	#2285	1	1	yes	characteristic
198	C₂×C₅₃	C₂²×#106	1	1	yes	characteristic
199	C₂×C₅₃	C₂×#427	1	1	yes	characteristic
200	D₅₃	—	2	2	no	—
201	D₅₃	#3167	1	4	yes	—
202	C₂³×C₈	—	53	2	no	—
203	C₂×#117	—	106	2	no	—
204	C₂²×C₄²	—	53	1	no	—
205	C₂×#106	—	53	8	no	—
206	C₂×C₄×C₈	—	53	2	no	—
207	C₂×C₄×C₈	—	53	1	no	—
208	C₂×C₄×C₈	—	53	1	no	—
209	C₂×C₄×C₈	—	53	1	no	—
210	C₂×C₄×C₈	—	53	1	no	—
211	C₂×C₄×C₈	—	53	2	no	—
212	C₂×C₄×C₈	—	53	1	no	—
213	C₂×C₄×C₈	—	53	2	no	—
214	C₂×C₄×C₈	#6157	1	1	yes	characteristic, complemented
215	#384	—	53	4	no	—
216	#382	—	106	2	no	—
217	#380	—	53	4	no	—
218	#380	—	106	2	no	—
219	C₄×C₄⋊C₄	—	53	4	no	—
220	C₄×C₄⋊C₄	—	106	2	no	—
221	#340	—	53	8	no	—
222	C₅₃	#20816	1	1	yes	characteristic, complemented, Sylow
223	C₂³×C₄	—	53	1	no	—
224	C₂³×C₄	—	53	1	no	—
225	C₂³×C₄	—	53	1	no	—
226	C₂²×C₈	—	53	2	no	—
227	C₂²×C₈	—	53	2	no	—
228	C₂²×C₈	—	53	2	no	—
229	C₂²×C₈	—	53	2	no	—
230	C₂²×C₈	—	53	2	no	—
231	C₂²×C₈	—	106	8	no	—
232	C₂²×C₈	C₂×#6157	1	2	yes	—
233	#117	—	212	8	no	—
234	C₂×C₄⋊C₄	—	53	8	no	—
235	C₂×C₄⋊C₄	—	106	4	no	—
236	C₂×C₄⋊C₄	—	106	4	no	—
237	C₂×C₂²⋊C₄	—	106	4	no	—
238	C₂×C₄²	—	53	1	no	—
239	C₂×C₄²	—	53	1	no	—
240	C₂×C₄²	—	53	1	no	—
241	C₂×C₄²	—	53	1	no	—
242	C₂×C₄²	—	53	1	no	—
243	C₂×C₄²	—	53	1	no	—
244	C₂×C₄²	—	53	1	no	—
245	C₂×C₄²	—	53	1	no	—
246	C₂×C₄²	—	53	1	no	—
247	C₂×C₄²	—	53	1	no	—
248	C₂×C₄²	—	53	1	no	—
249	C₂×C₄²	—	106	4	no	—
250	C₂×C₄²	C₂×#6157	1	1	yes	characteristic
251	#106	—	106	16	no	—
252	C₄×C₈	—	53	2	no	—
253	C₄×C₈	—	53	2	no	—
254	C₄×C₈	—	53	2	no	—
255	C₄×C₈	—	53	2	no	—
256	C₄×C₈	—	53	1	no	—
257	C₄×C₈	—	53	1	no	—
258	C₄×C₈	—	53	2	no	—
259	C₄×C₈	C₂×#6157	1	1	yes	characteristic
260	C₄×C₈	C₂×#6157	1	1	yes	characteristic
261	C₄×C₈	C₂×#6157	1	2	yes	—
262	#95	—	106	4	no	—
263	#95	—	106	4	no	—
264	C₂⁴	—	53	1	no	—
265	C₂²×C₄	—	53	1	no	—
266	C₂²×C₄	—	53	8	no	—
267	C₂²×C₄	—	53	1	no	—
268	C₂²×C₄	—	53	1	no	—
269	C₂²×C₄	—	53	1	no	—
270	C₂²×C₄	—	53	1	no	—
271	C₂²×C₄	—	53	1	no	—
272	C₂²×C₄	—	53	1	no	—
273	C₂²×C₄	—	53	1	no	—
274	C₂²×C₄	—	53	1	no	—
275	C₂²×C₄	—	53	1	no	—
276	C₂²×C₄	—	53	1	no	—
277	C₂²×C₄	—	53	1	no	—
278	C₂²×C₄	—	53	1	no	—
279	C₂²×C₄	—	53	1	no	—
280	C₂²×C₄	—	53	1	no	—
281	C₂²×C₄	—	106	4	no	—
282	C₂²×C₄	—	106	4	no	—
283	C₂²×C₄	—	106	8	no	—
284	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
285	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
286	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	53	2	no	—
289	C₂×C₈	—	53	8	no	—
290	C₂×C₈	—	53	2	no	—
291	C₂×C₈	—	106	4	no	—
292	C₂×C₈	—	106	4	no	—
293	C₂×C₈	—	106	4	no	—
294	C₂×C₈	—	106	4	no	—
295	C₂×C₈	C₂²×#6157	1	2	yes	—
296	C₂×C₈	C₂²×#6157	1	2	yes	—
297	C₄⋊C₄	—	106	16	no	—
298	C₄⋊C₄	—	212	8	no	—
299	C₄⋊C₄	—	212	8	no	—
300	C₂²⋊C₄	—	212	8	no	—
301	C₄²	—	53	1	no	—
302	C₄²	—	53	1	no	—
303	C₄²	—	53	1	no	—
304	C₄²	—	53	1	no	—
305	C₄²	—	53	1	no	—
306	C₄²	—	53	1	no	—
307	C₄²	—	53	1	no	—
308	C₄²	—	53	1	no	—
309	C₄²	—	53	1	no	—
310	C₄²	—	53	1	no	—
311	C₄²	—	53	1	no	—
312	C₄²	—	53	1	no	—
313	C₄²	—	212	8	no	—
314	C₄²	C₄⋊#6157	1	1	yes	characteristic
315	C₄²	C₄⋊#6157	1	1	yes	characteristic
316	C₄²	C₂²×#6157	1	1	yes	characteristic
317	C₄²	C₂²×#6157	1	1	yes	characteristic
318	C₂³	—	53	1	no	—
319	C₂³	—	53	4	no	—
320	C₂³	—	53	1	no	—
321	C₂³	—	106	2	no	—
322	C₂³	—	106	2	no	—
323	C₂³	C₂×C₄⋊#6157	1	1	yes	characteristic
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	53	4	no	—
327	C₂×C₄	—	53	1	no	—
328	C₂×C₄	—	53	1	no	—
329	C₂×C₄	—	53	1	no	—
330	C₂×C₄	—	53	1	no	—
331	C₂×C₄	—	53	4	no	—
332	C₂×C₄	—	53	4	no	—
333	C₂×C₄	—	53	4	no	—
334	C₂×C₄	—	53	4	no	—
335	C₂×C₄	—	53	4	no	—
336	C₂×C₄	—	53	4	no	—
337	C₂×C₄	—	53	1	no	—
338	C₂×C₄	—	53	1	no	—
339	C₂×C₄	—	106	2	no	—
340	C₂×C₄	—	106	2	no	—
341	C₂×C₄	—	106	2	no	—
342	C₂×C₄	—	106	2	no	—
343	C₂×C₄	—	106	2	no	—
344	C₂×C₄	—	106	2	no	—
345	C₂×C₄	—	106	2	no	—
346	C₂×C₄	—	106	2	no	—
347	C₂×C₄	—	212	8	no	—
348	C₂×C₄	—	212	8	no	—
349	C₂×C₄	—	212	8	no	—
350	C₂×C₄	#13133285	1	4	yes	complemented
351	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
353	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
354	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
355	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
356	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
357	C₈	—	2	2	no	—
358	C₈	—	53	4	no	—
359	C₈	—	106	2	no	—
360	C₈	#13133296	1	4	yes	complemented
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	53	2	no	—
364	C₂²	—	53	2	no	—
365	C₂²	—	53	2	no	—
366	C₂²	—	53	2	no	—
367	C₂²	—	106	8	no	—
368	C₂²	—	106	1	no	—
369	C₂²	—	106	1	no	—
370	C₂²	C₂×#13133285	1	2	yes	—
371	C₂²	C₂²×C₄⋊#6157	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	53	2	no	—
375	C₄	—	53	2	no	—
376	C₄	—	53	2	no	—
377	C₄	—	53	2	no	—
378	C₄	—	106	1	no	—
379	C₄	—	106	1	no	—
380	C₄	—	424	8	no	—
381	C₄	C₂×#13133285	1	2	yes	—
382	C₄	C₂×#13133285	1	2	yes	—
383	C₄	#16811633	1	2	yes	—
384	C₄	C₂×#13133296	1	2	yes	—
385	C₂	—	2	2	no	—
386	C₂	—	53	4	no	—
387	C₂	—	106	2	no	—
388	C₂	#20291164	1	1	yes	characteristic
389	C₂	C₂²×#13133285	1	1	yes	characteristic
390	C₂	C₂×#16811633	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	C₂×C₄×C₈×C₅₃	C₄
socle	C₂²×C₅₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₅₃	C₂×D₄
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	C₂×C₄×C₈	#6157
hypocenter	C₅₃	#20816
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #20290650	C₂	semidirect
3. #20290636	C₂	semidirect
5. C₄×#13133285	C₂	semidirect
18. C₂×C₄×#88322	C₄	semidirect
19. C₂×C₈×Dic₅₃	C₄	semidirect
20. C₄×C₈×D₅₃	C₄	semidirect
21. C₄×C₈×D₅₃	C₄	semidirect
22. C₄×C₈×D₅₃	C₄	semidirect
26. C₂×C₄×C₈×C₅₃	C₄	semidirect
133. C₂×C₄×C₅₃	#106	semidirect
142. C₂×Dic₅₃	#106	semidirect
155. C₄×D₅₃	#106	semidirect
156. C₄×D₅₃	#106	semidirect
162. C₈×C₅₃	#117	semidirect
164. #88322	#117	semidirect
214. C₂×C₄×C₈	#6157	semidirect
222. C₅₃	#20816	semidirect
350. C₂×C₄	#13133285	semidirect
360. C₈	#13133296	semidirect

Maximal subgroups

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

subgroup	index
#20291164	2
#20290650	2
#20290636	2
#20290591	2
C₄×#13133285	2
C₂×C₄×C₈×D₅₃	2
#20816	53