Subgroups — #27398012

Order 13568.

772 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20285209	C₂	1	1	yes	maximal, characteristic
2	#20283633	C₂	1	1	yes	maximal, characteristic
3	#20283584	C₂	1	1	yes	maximal, characteristic, complemented
4	#20275630	C₂	1	1	yes	maximal, characteristic, complemented
5	#20275613	C₂	1	1	yes	maximal, characteristic
6	#20275251	C₂	1	2	yes	maximal, complemented
7	#20275236	C₂	1	2	yes	maximal, complemented
8	#20275210	C₂	1	2	yes	maximal, complemented
9	#20275189	C₂	1	2	yes	maximal, complemented
10	#20274839	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1747	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13133250	C₂²	1	2	yes	—
13	C₂×#13133239	C₂²	1	1	yes	characteristic
14	C₂²×Dic₂₁₂	C₂²	1	1	yes	characteristic
15	#16811389	C₂²	1	2	yes	—
16	#16811199	C₂²	1	2	yes	—
17	#16811100	C₂²	1	2	yes	—
18	#16811017	C₄	1	4	yes	complemented
19	#16811007	C₄	1	2	yes	complemented
20	#16811003	C₄	1	2	yes	complemented
21	#16810746	—	2	2	no	—
22	#16810741	—	2	2	no	—
23	#16810731	—	2	2	no	—
24	C₄×Dic₂₁₂	—	2	2	no	—
25	C₂×#13133153	C₂²	1	1	yes	characteristic
26	#16810661	C₂²	1	1	yes	characteristic
27	#16810641	C₂²	1	2	yes	—
28	#16810639	C₂²	1	2	yes	—
29	#16810633	C₂²	1	2	yes	—
30	#16810631	C₂²	1	2	yes	—
31	C₂×#13133135	C₂²	1	2	yes	—
32	#16810596	C₂²	1	2	yes	—
33	#16810394	C₂²	1	2	yes	—
34	#16810379	C₂²	1	2	yes	—
35	C₅₃×#405	C₂²	1	1	yes	characteristic
36	C₅₃×#405	C₂²	1	1	yes	characteristic
37	C₅₃×#405	C₂²	1	1	yes	characteristic
38	C₅₃×#338	C₂²	1	1	yes	characteristic
39	C₅₃×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
40	C₅₃×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
41	C₅₃×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
42	C₂×#11719945	C₂³	1	2	yes	—
43	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
44	#13133250	—	4	2	no	—
45	#13133250	—	4	2	no	—
46	#13133239	—	2	1	no	—
47	#13133239	—	2	1	no	—
48	#13133239	—	2	1	no	—
49	#13133239	—	2	1	no	—
50	C₂×Dic₂₁₂	—	2	1	no	—
51	C₂×Dic₂₁₂	—	2	1	no	—
52	C₂×Dic₂₁₂	—	2	1	no	—
53	C₂×Dic₂₁₂	—	2	1	no	—
54	C₂×Dic₂₁₂	C₂×C₄	1	2	yes	—
55	C₂×Dic₂₁₂	C₂×C₄	1	2	yes	—
56	C₂×Dic₂₁₂	C₂×C₄	1	1	yes	characteristic
57	C₂×Dic₂₁₂	C₂×C₄	1	4	yes	—
58	C₂×#11719913	C₂×C₄	1	2	yes	—
59	C₂×#11719913	C₂×C₄	1	4	yes	—
60	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic
61	#13133225	—	4	2	no	—
62	#13133223	—	2	4	no	—
63	C₂×#11719917	C₂³	1	2	yes	—
64	M₁₆×D₅₃	—	4	2	no	—
65	#13133217	C₂×C₄	1	4	yes	—
66	#13133205	C₂×C₄	1	4	yes	—
67	#13133201	—	4	2	no	—
68	#13133197	—	4	2	no	—
69	C₄×Dic₁₀₆	—	2	4	no	—
70	#13133182	—	4	2	no	—
71	#13133176	C₂³	1	2	yes	—
72	#13133173	—	4	2	no	—
73	#13133153	—	2	1	no	—
74	#13133153	—	2	1	no	—
75	#13133151	—	2	1	no	—
76	#13133149	—	2	1	no	—
77	#13133145	—	2	4	no	—
78	#13133143	—	4	2	no	—
79	#13133142	—	2	4	no	—
80	#13133140	—	4	2	no	—
81	#13133135	—	4	2	no	—
82	#13133131	—	4	2	no	—
83	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
87	#117×C₅₃	C₂³	1	1	yes	characteristic
88	#117×C₅₃	C₂³	1	1	yes	characteristic
89	#117×C₅₃	C₂³	1	1	yes	characteristic
90	#97×C₅₃	—	2	1	no	—
91	#97×C₅₃	C₂×C₄	1	2	yes	—
92	#97×C₅₃	D₄	1	2	yes	—
93	C₄×C₈×C₅₃	—	2	1	no	—
94	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₅₃	D₄	1	2	yes	—
96	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
97	C₂×C₂²⋊D₅₃	—	2	2	no	—
98	C₂²×Dic₅₃	—	2	2	no	—
99	#11719945	—	2	2	no	—
100	#11719945	—	2	2	no	—
101	#11719945	—	2	2	no	—
102	#11719945	—	2	2	no	—
103	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₅₃	—	2	2	no	—
105	C₂×Dic₁₀₆	—	2	2	no	—
106	C₂×Dic₁₀₆	—	2	2	no	—
107	C₂×Dic₁₀₆	—	2	2	no	—
108	C₂×Dic₁₀₆	—	2	2	no	—
109	C₂×Dic₁₀₆	—	2	2	no	—
110	C₂×Dic₁₀₆	C₂²×C₄	1	4	yes	—
111	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
112	M₁₆×C₅₃	—	2	1	no	—
113	M₁₆×C₅₃	—	2	1	no	—
114	M₁₆×C₅₃	—	2	1	no	—
115	M₁₆×C₅₃	—	2	1	no	—
116	M₁₆×C₅₃	—	2	1	no	—
117	M₁₆×C₅₃	—	2	1	no	—
118	C₂×C₈×C₅₃	—	2	1	no	—
119	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
126	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
127	C₄⋊C₄×C₅₃	—	2	1	no	—
128	C₄⋊C₄×C₅₃	—	2	1	no	—
129	C₄⋊C₄×C₅₃	—	2	1	no	—
130	C₂²⋊C₄×C₅₃	—	2	1	no	—
131	C₂²⋊C₄×C₅₃	—	2	1	no	—
132	C₂²⋊C₄×C₅₃	—	2	1	no	—
133	C₄²×C₅₃	—	2	1	no	—
134	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
135	C₄²×C₅₃	C₂×D₄	1	2	yes	—
136	C₂²⋊Dic₅₃	—	2	2	no	—
137	#11719921	—	4	4	no	—
138	C₄⋊Dic₅₃	—	2	2	no	—
139	C₄⋊Dic₅₃	—	4	4	no	—
140	#11719919	—	4	4	no	—
141	C₄×Dic₅₃	—	2	2	no	—
142	C₄×Dic₅₃	—	4	4	no	—
143	#11719917	—	2	2	no	—
144	#11719917	—	2	2	no	—
145	C₂×#88322	—	2	2	no	—
146	Dic₂₁₂	—	2	2	no	—
147	Dic₂₁₂	—	2	2	no	—
148	Dic₂₁₂	—	2	2	no	—
149	Dic₂₁₂	—	2	2	no	—
150	Dic₂₁₂	—	2	1	no	—
151	Dic₂₁₂	—	2	1	no	—
152	Dic₂₁₂	—	4	4	no	—
153	D₄₂₄	—	2	1	no	—
154	D₄₂₄	—	2	1	no	—
155	#11719913	—	2	2	no	—
156	#11719913	—	2	2	no	—
157	#11719913	—	4	4	no	—
158	#11719912	—	4	4	no	—
159	C₈×D₅₃	—	4	4	no	—
160	C₂³×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₅₃	—	2	2	no	—
162	C₂×C₄×C₅₃	—	2	2	no	—
163	C₂×C₄×C₅₃	—	2	2	no	—
164	C₂×C₄×C₅₃	—	4	1	no	—
165	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂²⋊D₅₃	—	4	2	no	—
172	C₂²⋊D₅₃	—	4	2	no	—
173	C₂×Dic₅₃	—	2	4	no	—
174	C₂×Dic₅₃	—	2	2	no	—
175	C₂×Dic₅₃	—	4	2	no	—
176	C₂×Dic₅₃	—	4	2	no	—
177	C₂×Dic₅₃	—	4	2	no	—
178	D₂₁₂	—	2	2	no	—
179	D₂₁₂	—	2	2	no	—
180	C₄×D₅₃	—	4	2	no	—
181	C₄×D₅₃	—	4	2	no	—
182	Dic₁₀₆	—	2	4	no	—
183	Dic₁₀₆	—	2	2	no	—
184	Dic₁₀₆	—	2	4	no	—
185	Dic₁₀₆	—	2	2	no	—
186	Dic₁₀₆	—	4	2	no	—
187	Dic₁₀₆	—	4	2	no	—
188	C₈×C₅₃	—	2	2	no	—
189	C₈×C₅₃	—	2	2	no	—
190	C₈×C₅₃	—	4	1	no	—
191	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
192	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
193	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
194	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
195	#88322	—	4	2	no	—
196	#22285	—	53	1	no	maximal, Sylow
197	C₂²×C₅₃	—	4	1	no	—
198	C₂²×C₅₃	#518	1	1	yes	characteristic
199	C₂²×C₅₃	#535	1	1	yes	characteristic
200	C₂²×C₅₃	#540	1	1	yes	characteristic
201	C₂×D₅₃	—	4	2	no	—
202	C₂×D₅₃	—	8	2	no	—
203	C₄×C₅₃	—	4	2	no	—
204	C₄×C₅₃	—	4	2	no	—
205	C₄×C₅₃	—	8	1	no	—
206	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
207	C₄×C₅₃	#518	1	1	yes	characteristic
208	C₄×C₅₃	#535	1	1	yes	characteristic
209	C₄×C₅₃	#540	1	1	yes	characteristic
210	Dic₅₃	—	4	4	no	—
211	Dic₅₃	—	4	2	no	—
212	Dic₅₃	—	8	2	no	—
213	#3156	—	53	1	no	—
214	#2957	—	53	1	no	—
215	#2950	—	53	1	no	—
216	#1979	—	53	1	no	—
217	#1976	—	53	1	no	—
218	#1912	—	53	2	no	—
219	#1909	—	53	2	no	—
220	#1905	—	53	2	no	—
221	#1902	—	53	2	no	—
222	#1833	—	53	1	no	—
223	#1747	D₅₃	1	1	yes	characteristic, complemented
224	C₂×C₅₃	—	2	1	no	—
225	C₂×C₅₃	—	2	1	no	—
226	C₂×C₅₃	—	2	1	no	—
227	C₂×C₅₃	#2328	1	1	yes	characteristic
228	D₅₃	—	8	2	no	—
229	C₂×#137	—	53	2	no	—
230	C₂×#135	—	53	1	no	—
231	C₂²×Q₁₆	—	53	1	no	—
232	#568	—	53	2	no	—
233	#536	—	53	2	no	—
234	#519	—	53	2	no	—
235	#497	—	53	4	no	—
236	#495	—	53	2	no	—
237	#494	—	53	2	no	—
238	#444	—	106	2	no	—
239	#443	—	106	2	no	—
240	#441	—	106	2	no	—
241	C₄×Q₁₆	—	106	2	no	—
242	C₂×#108	—	53	1	no	—
243	#427	—	53	1	no	—
244	#421	—	53	2	no	—
245	#421	—	53	2	no	—
246	#419	—	53	2	no	—
247	#419	—	53	2	no	—
248	C₂×#101	—	53	2	no	—
249	#410	—	53	2	no	—
250	#405	C₂×D₅₃	1	1	yes	characteristic
251	#405	C₂×D₅₃	1	1	yes	characteristic
252	#405	C₂×D₅₃	1	1	yes	characteristic
253	#344	—	53	2	no	—
254	#338	C₂×D₅₃	1	1	yes	characteristic
255	H(3,ℤ/4)	—	53	2	no	—
256	H(3,ℤ/4)	C₂×D₅₃	1	1	yes	characteristic
257	H(3,ℤ/4)	C₂×D₅₃	1	1	yes	characteristic
258	H(3,ℤ/4)	C₂×D₅₃	1	1	yes	characteristic
259	C₅₃	#22285	1	1	yes	characteristic, complemented, Sylow
260	C₂×#41	—	53	2	no	—
261	C₂²×Q₈	—	53	2	no	—
262	#137	—	212	2	no	—
263	#137	—	212	2	no	—
264	#135	—	106	1	no	—
265	#135	—	106	1	no	—
266	#135	—	106	1	no	—
267	#135	—	106	1	no	—
268	C₂×Q₁₆	—	53	2	no	—
269	C₂×Q₁₆	—	53	2	no	—
270	C₂×Q₁₆	—	53	1	no	—
271	C₂×Q₁₆	—	53	4	no	—
272	C₂×Q₁₆	—	106	1	no	—
273	C₂×Q₁₆	—	106	1	no	—
274	C₂×Q₁₆	—	106	1	no	—
275	C₂×Q₁₆	—	106	1	no	—
276	C₂×SD₁₆	—	53	2	no	—
277	C₂×SD₁₆	—	53	4	no	—
278	C₂×D₈	—	53	1	no	—
279	#131	—	106	4	no	—
280	#131	—	212	2	no	—
281	C₂×M₁₆	—	53	2	no	—
282	C₂×M₁₆	—	212	2	no	—
283	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
284	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
285	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
286	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
287	C₄⋊Q₈	—	53	4	no	—
288	#124	—	53	4	no	—
289	#123	—	212	2	no	—
290	C₂²⋊Q₈	—	212	2	no	—
291	C₄×Q₈	—	106	4	no	—
292	C₄×Q₈	—	212	2	no	—
293	#117	—	53	2	no	—
294	#117	—	212	2	no	—
295	#117	C₂²×D₅₃	1	1	yes	characteristic
296	#117	C₂²×D₅₃	1	1	yes	characteristic
297	#117	C₂²×D₅₃	1	1	yes	characteristic
298	#108	—	106	1	no	—
299	#108	—	106	1	no	—
300	#107	—	106	1	no	—
301	#106	—	106	1	no	—
302	#104	—	106	4	no	—
303	#104	—	212	2	no	—
304	#103	—	106	4	no	—
305	#103	—	212	2	no	—
306	#101	—	212	2	no	—
307	#99	—	212	2	no	—
308	#97	—	2	1	no	—
309	#97	C₄×D₅₃	1	2	yes	—
310	#97	D₂₁₂	1	2	yes	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	C₄×D₅₃	1	2	yes	—
313	C₄×C₈	D₂₁₂	1	2	yes	—
314	#41	—	106	2	no	—
315	#41	—	106	2	no	—
316	#41	—	106	2	no	—
317	#41	—	106	2	no	—
318	C₂×Q₈	—	53	4	no	—
319	C₂×Q₈	—	53	2	no	—
320	C₂×Q₈	—	106	2	no	—
321	C₂×Q₈	—	106	2	no	—
322	C₂×Q₈	—	106	2	no	—
323	C₂×Q₈	—	106	2	no	—
324	C₂×Q₈	—	106	2	no	—
325	C₂×D₄	—	53	2	no	—
326	C₂×D₄	—	106	2	no	—
327	C₂²×C₄	—	106	2	no	—
328	C₂²×C₄	—	106	2	no	—
329	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
330	Q₁₆	—	106	2	no	—
331	Q₁₆	—	106	2	no	—
332	Q₁₆	—	106	2	no	—
333	Q₁₆	—	106	2	no	—
334	Q₁₆	—	106	1	no	—
335	Q₁₆	—	106	1	no	—
336	Q₁₆	—	212	4	no	—
337	SD₁₆	—	106	2	no	—
338	SD₁₆	—	106	2	no	—
339	SD₁₆	—	212	4	no	—
340	D₈	—	106	1	no	—
341	D₈	—	106	1	no	—
342	M₁₆	—	2	1	no	—
343	M₁₆	—	2	1	no	—
344	M₁₆	—	2	1	no	—
345	M₁₆	—	2	1	no	—
346	M₁₆	—	2	1	no	—
347	M₁₆	—	2	1	no	—
348	M₁₆	—	106	2	no	—
349	M₁₆	—	106	2	no	—
350	M₁₆	—	212	4	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	106	2	no	—
353	C₂×C₈	—	212	4	no	—
354	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
355	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
356	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
357	C₂×C₈	C₂×D₂₁₂	1	2	yes	—
358	C₂×C₈	C₂×D₂₁₂	1	1	yes	characteristic
359	C₂×C₈	C₂×D₂₁₂	1	1	yes	characteristic
360	C₂×C₈	#11719945	1	1	yes	characteristic
361	C₂×C₈	#11719945	1	1	yes	characteristic
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	106	2	no	—
366	C₄⋊C₄	—	212	4	no	—
367	C₄⋊C₄	—	212	4	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	106	2	no	—
372	C₂²⋊C₄	—	212	4	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	106	2	no	—
375	C₄²	—	212	4	no	—
376	C₄²	C₂×C₄×D₅₃	1	2	yes	—
377	C₄²	C₂×D₂₁₂	1	2	yes	—
378	C₂³	—	106	2	no	—
379	C₂³	#13133263	1	1	yes	characteristic
380	Q₈	—	106	2	no	—
381	Q₈	—	106	4	no	—
382	Q₈	—	106	4	no	—
383	Q₈	—	106	2	no	—
384	Q₈	—	212	2	no	—
385	Q₈	—	212	2	no	—
386	D₄	—	106	2	no	—
387	D₄	—	106	2	no	—
388	D₄	—	212	2	no	—
389	D₄	—	212	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	106	4	no	—
394	C₂×C₄	—	106	2	no	—
395	C₂×C₄	—	212	2	no	—
396	C₂×C₄	—	212	2	no	—
397	C₂×C₄	—	212	2	no	—
398	C₂×C₄	—	212	2	no	—
399	C₂×C₄	—	212	2	no	—
400	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
402	C₂×C₄	C₂×#11719945	1	1	yes	characteristic
403	C₂×C₄	#13133263	1	1	yes	characteristic
404	C₂×C₄	#13133263	1	1	yes	characteristic
405	C₂×C₄	#13133263	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	1	no	—
409	C₈	—	212	2	no	—
410	C₈	C₄×D₂₁₂	1	1	yes	characteristic
411	C₈	C₄×D₂₁₂	1	1	yes	characteristic
412	C₈	C₄×D₂₁₂	1	1	yes	characteristic
413	C₈	C₄×D₂₁₂	1	1	yes	characteristic
414	C₂²	—	4	1	no	—
415	C₂²	—	424	2	no	—
416	C₂²	—	212	2	no	—
417	C₂²	#16811097	1	1	yes	characteristic
418	C₂²	#16811192	1	1	yes	characteristic
419	C₂²	#16811228	1	1	yes	characteristic
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	8	1	no	—
423	C₄	—	424	2	no	—
424	C₄	—	212	2	no	—
425	C₄	—	212	4	no	—
426	C₄	C₂×C₄×D₂₁₂	1	1	yes	characteristic
427	C₄	#16811097	1	1	yes	characteristic
428	C₄	#16811192	1	1	yes	characteristic
429	C₄	#16811228	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	424	2	no	—
434	C₂	#20277440	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20277440
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1747	C₂
socle	C₂×C₅₃	#2328
prime radical	C₂×#13133239	C₂²
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1747	D₅₃
hypocenter	C₅₃	#22285
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1747

Complements

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

N	H ≅ G/N	type
3. #20283584	C₂	semidirect
4. #20275630	C₂	semidirect
6. #20275251	C₂	semidirect
7. #20275236	C₂	semidirect
8. #20275210	C₂	semidirect
9. #20275189	C₂	semidirect
10. #20274839	C₂	semidirect
11. C₅₃×#1747	C₂	semidirect
18. #16811017	C₄	semidirect
19. #16811007	C₄	semidirect
20. #16811003	C₄	semidirect
223. #1747	D₅₃	semidirect
259. C₅₃	#22285	semidirect

Maximal subgroups

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

subgroup	index
#20285209	2
#20283633	2
#20283584	2
#20275630	2
#20275613	2
#20275251	2
#20275236	2
#20275210	2
#20275189	2
#20274839	2
C₅₃×#1747	2
#22285	53