Subgroups — C₄×SD₁₆×D₅₃ #20283468

Order 6784.

552 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#16810714	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#11719913	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#11719924	C₂	1	1	yes	maximal, characteristic, complemented
8	#16810710	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#11719923	C₂	1	1	yes	maximal, characteristic, complemented
10	#16810708	C₂	1	1	yes	maximal, characteristic, complemented
11	#106×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#103×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#102×D₅₃	C₂	1	1	yes	maximal, characteristic
14	C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₅₃	—	2	1	no	—
19	C₂×#11719913	C₂²	1	1	yes	characteristic
20	C₂×#11719923	C₂²	1	1	yes	characteristic
21	C₂×#11719924	C₂²	1	1	yes	characteristic
22	SD₁₆×D₅₃	C₄	1	8	yes	direct product factor
23	C₂×C₈×D₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₈×D₅₃	C₂²	1	1	yes	characteristic
25	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
26	C₄×Dic₁₀₆	—	2	1	no	—
27	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
28	#13133182	—	2	1	no	—
29	#13133182	C₂²	1	1	yes	characteristic, complemented
30	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
31	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
32	#13133179	C₂²	1	1	yes	characteristic
33	C₄×C₂²⋊D₅₃	—	2	1	no	—
34	#13133177	—	2	1	no	—
35	C₄⋊C₄×D₅₃	—	2	1	no	—
36	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
37	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
38	C₂²⋊C₄×D₅₃	—	2	1	no	—
39	C₄²×D₅₃	—	2	1	no	—
40	C₄²×D₅₃	C₂²	1	1	yes	characteristic
41	#13133149	C₂²	1	1	yes	characteristic, complemented
42	#13133148	C₂²	1	1	yes	characteristic, complemented
43	#13133148	C₂²	1	1	yes	characteristic, complemented
44	#13133142	C₂²	1	1	yes	characteristic, complemented
45	#13133141	C₂²	1	1	yes	characteristic, complemented
46	#13133140	C₂²	1	1	yes	characteristic, complemented
47	#13133139	C₂²	1	1	yes	characteristic
48	#13133138	C₂²	1	1	yes	characteristic
49	#13133137	C₂²	1	1	yes	characteristic
50	C₄×#88322	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
54	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
56	#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
58	#102×C₅₃	C₂²	1	1	yes	characteristic
59	C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₅₃	—	2	1	no	—
61	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₅₃	—	2	1	no	—
64	C₂×C₂²⋊D₅₃	—	2	1	no	—
65	C₂²×Dic₅₃	—	2	1	no	—
66	Q₈×D₅₃	—	2	2	no	—
67	Q₈×D₅₃	C₂×C₄	1	4	yes	complemented
68	D₄×D₅₃	—	2	2	no	—
69	D₄×D₅₃	C₂×C₄	1	4	yes	—
70	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
71	C₂×C₄×D₅₃	—	2	1	no	—
72	C₂×C₄×D₅₃	—	2	1	no	—
73	C₂×C₄×D₅₃	—	2	1	no	—
74	C₂×C₄×D₅₃	—	2	1	no	—
75	C₂×C₄×D₅₃	—	2	1	no	—
76	C₂×C₄×D₅₃	—	4	4	no	—
77	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
78	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
79	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
80	C₂×Dic₁₀₆	—	2	1	no	—
81	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
82	SD₁₆×C₅₃	C₂×C₄	1	4	yes	complemented
83	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
84	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
85	C₄⋊C₄×C₅₃	—	2	1	no	—
86	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
87	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
88	C₂²⋊C₄×C₅₃	—	2	1	no	—
89	C₄²×C₅₃	—	2	1	no	—
90	C₄²×C₅₃	C₂³	1	1	yes	characteristic
91	C₂²⋊Dic₅₃	—	2	1	no	—
92	#11719924	C₂×C₄	1	4	yes	complemented
93	#11719923	C₂×C₄	1	4	yes	complemented
94	#11719921	—	2	1	no	—
95	#11719921	—	2	1	no	—
96	C₄⋊Dic₅₃	—	2	1	no	—
97	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
99	#11719919	—	2	1	no	—
100	#11719919	—	2	1	no	—
101	#11719919	—	2	1	no	—
102	#11719919	—	2	1	no	—
103	C₄×Dic₅₃	—	2	1	no	—
104	C₄×Dic₅₃	—	2	1	no	—
105	C₄×Dic₅₃	—	2	1	no	—
106	C₄×Dic₅₃	D₄	1	1	yes	characteristic
107	C₄×Dic₅₃	D₄	1	1	yes	characteristic
108	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
109	C₂×#88322	C₂³	1	1	yes	characteristic
110	C₂×#88322	C₂³	1	1	yes	characteristic
111	#11719913	C₂×C₄	1	4	yes	complemented
112	C₈×D₅₃	—	2	2	no	—
113	C₈×D₅₃	C₂×C₄	1	4	yes	complemented
114	C₂³×C₅₃	—	2	1	no	—
115	C₂²×D₅₃	—	2	1	no	—
116	C₂²×D₅₃	—	2	4	no	—
117	C₂²×D₅₃	—	4	2	no	—
118	C₂²×D₅₃	—	4	2	no	—
119	C₂²×D₅₃	C₂×D₄	1	1	yes	characteristic
120	Q₈×C₅₃	—	2	1	no	—
121	Q₈×C₅₃	C₂²×C₄	1	2	yes	complemented
122	D₄×C₅₃	—	2	1	no	—
123	D₄×C₅₃	C₂²×C₄	1	2	yes	—
124	C₂×C₄×C₅₃	—	2	1	no	—
125	C₂×C₄×C₅₃	—	2	1	no	—
126	C₂×C₄×C₅₃	—	2	1	no	—
127	C₂×C₄×C₅₃	—	4	2	no	—
128	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
131	C₂²⋊D₅₃	—	2	4	no	—
132	C₂×Dic₅₃	—	2	1	no	—
133	C₂×Dic₅₃	—	2	1	no	—
134	C₂×Dic₅₃	—	2	1	no	—
135	C₂×Dic₅₃	—	4	2	no	—
136	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
137	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
138	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
139	D₂₁₂	—	2	1	no	—
140	D₂₁₂	C₂²×C₄	1	2	yes	—
141	C₄×D₅₃	—	2	4	no	—
142	C₄×D₅₃	—	2	2	no	—
143	C₄×D₅₃	—	4	2	no	—
144	C₄×D₅₃	—	4	2	no	—
145	C₄×D₅₃	—	4	2	no	—
146	C₄×D₅₃	—	4	2	no	—
147	C₄×D₅₃	SD₁₆	1	4	yes	direct product factor
148	C₄×D₅₃	C₂²×C₄	1	2	yes	—
149	C₄×D₅₃	#41	1	2	yes	—
150	Dic₁₀₆	—	2	1	no	—
151	Dic₁₀₆	—	2	4	no	—
152	Dic₁₀₆	C₂²×C₄	1	2	yes	complemented
153	C₈×C₅₃	—	2	1	no	—
154	C₈×C₅₃	C₂²×C₄	1	2	yes	complemented
155	#88322	—	2	1	no	—
156	#88322	C₂²×C₄	1	2	yes	complemented
157	C₂²×C₅₃	—	2	2	no	—
158	C₂²×C₅₃	—	4	1	no	—
159	C₂²×C₅₃	—	4	1	no	—
160	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
161	C₂×D₅₃	—	2	2	no	—
162	C₂×D₅₃	—	4	1	no	—
163	C₂×D₅₃	—	4	1	no	—
164	C₂×D₅₃	—	4	8	no	—
165	C₂×D₅₃	C₄×D₄	1	2	yes	—
166	C₂×D₅₃	C₂×SD₁₆	1	2	yes	—
167	C₂×D₅₃	#135	1	2	yes	—
168	C₄×C₅₃	—	2	2	no	—
169	C₄×C₅₃	—	2	1	no	—
170	C₄×C₅₃	—	4	1	no	—
171	C₄×C₅₃	—	4	1	no	—
172	C₄×C₅₃	C₂×SD₁₆	1	2	yes	complemented
173	C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
174	C₄×C₅₃	C₂×#41	1	1	yes	characteristic
175	Dic₅₃	—	2	2	no	—
176	Dic₅₃	—	2	1	no	—
177	Dic₅₃	—	4	1	no	—
178	Dic₅₃	—	4	1	no	—
179	Dic₅₃	C₄×D₄	1	2	yes	—
180	Dic₅₃	C₂×SD₁₆	1	2	yes	complemented
181	C₂×C₄×SD₁₆	—	53	1	no	maximal, Sylow
182	C₂×C₅₃	—	4	2	no	—
183	C₂×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
184	C₂×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
185	C₂×C₅₃	C₂×#135	1	1	yes	characteristic
186	D₅₃	—	4	2	no	—
187	D₅₃	C₄×SD₁₆	1	4	yes	direct product factor
188	C₂²×SD₁₆	—	53	1	no	—
189	C₂×C₄×Q₈	—	53	1	no	—
190	C₂×C₄×D₄	—	53	1	no	—
191	C₄×SD₁₆	—	53	1	no	—
192	C₄×SD₁₆	—	53	1	no	—
193	C₄×SD₁₆	—	53	1	no	—
194	C₄×SD₁₆	—	53	1	no	—
195	C₄×SD₁₆	—	53	1	no	—
196	C₄×SD₁₆	—	53	1	no	—
197	C₄×SD₁₆	—	53	1	no	—
198	C₄×SD₁₆	D₅₃	1	1	yes	characteristic, direct product factor
199	C₂×#106	—	53	1	no	—
200	C₂×#103	—	53	1	no	—
201	C₂×#102	—	53	1	no	—
202	C₂×C₄×C₈	—	53	1	no	—
203	C₅₃	C₂×C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
204	C₂²×Q₈	—	53	1	no	—
205	C₂²×D₄	—	53	1	no	—
206	C₂³×C₄	—	106	1	no	—
207	C₂×SD₁₆	—	53	1	no	—
208	C₂×SD₁₆	—	53	1	no	—
209	C₂×SD₁₆	—	53	8	no	—
210	C₂×SD₁₆	—	53	1	no	—
211	C₂×SD₁₆	C₂×D₅₃	1	1	yes	characteristic
212	C₂²×C₈	—	53	1	no	—
213	C₂²×C₈	—	53	1	no	—
214	C₄×Q₈	—	53	1	no	—
215	C₄×Q₈	—	53	1	no	—
216	C₄×Q₈	—	53	1	no	—
217	C₄×Q₈	—	106	1	no	—
218	C₄×Q₈	—	106	1	no	—
219	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
220	C₄×D₄	—	53	1	no	—
221	C₄×D₄	—	53	1	no	—
222	C₄×D₄	—	53	1	no	—
223	C₄×D₄	—	106	1	no	—
224	C₄×D₄	—	106	1	no	—
225	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
226	C₂×C₄⋊C₄	—	53	1	no	—
227	C₂×C₄⋊C₄	—	53	1	no	—
228	C₂×C₄⋊C₄	—	106	1	no	—
229	C₂×C₂²⋊C₄	—	106	1	no	—
230	C₂×C₄²	—	53	1	no	—
231	C₂×C₄²	—	106	1	no	—
232	#106	—	53	1	no	—
233	#106	—	53	1	no	—
234	#106	—	53	1	no	—
235	#106	C₂×D₅₃	1	1	yes	characteristic, complemented
236	#103	—	53	1	no	—
237	#103	—	53	1	no	—
238	#103	—	53	1	no	—
239	#103	C₂×D₅₃	1	1	yes	characteristic, complemented
240	#102	—	53	1	no	—
241	#102	—	53	1	no	—
242	#102	—	53	1	no	—
243	#102	C₂×D₅₃	1	1	yes	characteristic
244	C₄×C₈	—	53	1	no	—
245	C₄×C₈	—	53	1	no	—
246	C₄×C₈	—	53	1	no	—
247	C₄×C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
248	C₂⁴	—	106	1	no	—
249	C₂×Q₈	—	53	4	no	—
250	C₂×Q₈	—	53	1	no	—
251	C₂×Q₈	—	106	1	no	—
252	C₂×Q₈	—	106	2	no	—
253	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
254	C₂×D₄	—	53	4	no	—
255	C₂×D₄	—	53	1	no	—
256	C₂×D₄	—	106	2	no	—
257	C₂×D₄	—	106	1	no	—
258	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	53	1	no	—
261	C₂²×C₄	—	53	1	no	—
262	C₂²×C₄	—	53	1	no	—
263	C₂²×C₄	—	106	1	no	—
264	C₂²×C₄	—	106	1	no	—
265	C₂²×C₄	—	106	1	no	—
266	C₂²×C₄	—	106	1	no	—
267	C₂²×C₄	—	106	1	no	—
268	C₂²×C₄	—	106	1	no	—
269	C₂²×C₄	—	212	4	no	—
270	SD₁₆	—	53	4	no	—
271	SD₁₆	—	53	4	no	—
272	SD₁₆	—	53	4	no	—
273	SD₁₆	C₄×D₅₃	1	4	yes	direct product factor
274	C₂×C₈	—	53	1	no	—
275	C₂×C₈	—	53	4	no	—
276	C₂×C₈	—	53	1	no	—
277	C₂×C₈	—	106	2	no	—
278	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
279	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	53	1	no	—
282	C₄⋊C₄	—	53	1	no	—
283	C₄⋊C₄	—	106	1	no	—
284	C₄⋊C₄	—	106	1	no	—
285	C₄⋊C₄	—	106	1	no	—
286	C₄⋊C₄	—	106	1	no	—
287	C₄⋊C₄	—	106	1	no	—
288	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
289	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	106	1	no	—
292	C₂²⋊C₄	—	106	1	no	—
293	C₂²⋊C₄	—	106	1	no	—
294	C₄²	—	2	1	no	—
295	C₄²	—	53	1	no	—
296	C₄²	—	53	1	no	—
297	C₄²	—	53	1	no	—
298	C₄²	—	106	1	no	—
299	C₄²	—	106	1	no	—
300	C₄²	—	106	1	no	—
301	C₄²	C₂²×D₅₃	1	1	yes	characteristic
302	C₂³	—	2	1	no	—
303	C₂³	—	53	1	no	—
304	C₂³	—	106	4	no	—
305	C₂³	—	106	1	no	—
306	C₂³	—	212	2	no	—
307	C₂³	—	212	2	no	—
308	Q₈	—	2	1	no	—
309	Q₈	—	53	2	no	—
310	Q₈	—	106	4	no	—
311	Q₈	—	106	1	no	—
312	Q₈	C₂×C₄×D₅₃	1	2	yes	complemented
313	D₄	—	2	1	no	—
314	D₄	—	53	2	no	—
315	D₄	—	106	4	no	—
316	D₄	—	106	1	no	—
317	D₄	C₂×C₄×D₅₃	1	2	yes	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	53	1	no	—
323	C₂×C₄	—	53	1	no	—
324	C₂×C₄	—	53	4	no	—
325	C₂×C₄	—	53	2	no	—
326	C₂×C₄	—	53	2	no	—
327	C₂×C₄	—	53	1	no	—
328	C₂×C₄	—	106	2	no	—
329	C₂×C₄	—	106	4	no	—
330	C₂×C₄	—	106	1	no	—
331	C₂×C₄	—	106	1	no	—
332	C₂×C₄	—	106	1	no	—
333	C₂×C₄	—	212	2	no	—
334	C₂×C₄	—	212	2	no	—
335	C₂×C₄	—	212	2	no	—
336	C₂×C₄	—	212	2	no	—
337	C₂×C₄	—	212	2	no	—
338	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
339	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
340	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
341	C₈	—	2	1	no	—
342	C₈	—	53	2	no	—
343	C₈	—	106	1	no	—
344	C₈	C₂×C₄×D₅₃	1	2	yes	complemented
345	C₂²	—	2	2	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	53	2	no	—
349	C₂²	—	53	2	no	—
350	C₂²	—	53	2	no	—
351	C₂²	—	106	2	no	—
352	C₂²	—	212	8	no	—
353	C₂²	—	212	1	no	—
354	C₂²	—	212	1	no	—
355	C₂²	C₂×D₄×D₅₃	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	1	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	53	2	no	—
361	C₄	—	53	2	no	—
362	C₄	—	106	2	no	—
363	C₄	—	106	1	no	—
364	C₄	—	212	1	no	—
365	C₄	—	212	1	no	—
366	C₄	SD₁₆×D₅₃	1	2	yes	direct product factor
367	C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
368	C₄	#41×D₅₃	1	1	yes	characteristic
369	C₂	—	4	2	no	—
370	C₂	—	53	4	no	—
371	C₂	—	212	2	no	—
372	C₂	C₄×D₄×D₅₃	1	1	yes	characteristic
373	C₂	C₂×SD₁₆×D₅₃	1	1	yes	characteristic
374	C₂	#135×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₅₃
commutator	C₄×C₅₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₅₃
Fitting	C₄×SD₁₆×C₅₃	C₂
socle	C₂²×C₅₃	C₂²×D₄
hypercenter	C₄×SD₁₆	D₅₃
hypocenter	C₅₃	C₂×C₄×SD₁₆
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈×D₅₃	C₂	semidirect
4. #16810714	C₂	semidirect
5. C₄×#11719913	C₂	semidirect
6. SD₁₆×Dic₅₃	C₂	semidirect
7. C₄×#11719924	C₂	semidirect
8. #16810710	C₂	semidirect
9. C₄×#11719923	C₂	semidirect
10. #16810708	C₂	semidirect
11. #106×D₅₃	C₂	semidirect
12. #103×D₅₃	C₂	semidirect
14. C₄×C₈×D₅₃	C₂	semidirect
15. C₄×SD₁₆×C₅₃	C₂	semidirect
22. SD₁₆×D₅₃	C₄	direct (N × H)
25. Q₈×Dic₅₃	C₂²	semidirect
27. C₄×Dic₁₀₆	C₂²	semidirect
29. #13133182	C₂²	semidirect
41. #13133149	C₂²	semidirect
42. #13133148	C₂²	semidirect
43. #13133148	C₂²	semidirect
44. #13133142	C₂²	semidirect
45. #13133141	C₂²	semidirect
46. #13133140	C₂²	semidirect
50. C₄×#88322	C₂²	semidirect
51. C₈×Dic₅₃	C₂²	semidirect
52. C₈×Dic₅₃	C₂²	semidirect
54. C₄×Q₈×C₅₃	C₂²	semidirect
56. #106×C₅₃	C₂²	semidirect
57. #103×C₅₃	C₂²	semidirect
59. C₄×C₈×C₅₃	C₂²	semidirect
67. Q₈×D₅₃	C₂×C₄	semidirect
82. SD₁₆×C₅₃	C₂×C₄	semidirect
92. #11719924	C₂×C₄	semidirect
93. #11719923	C₂×C₄	semidirect
111. #11719913	C₂×C₄	semidirect
113. C₈×D₅₃	C₂×C₄	semidirect
121. Q₈×C₅₃	C₂²×C₄	semidirect
147. C₄×D₅₃	SD₁₆	direct (N × H)
152. Dic₁₀₆	C₂²×C₄	semidirect
154. C₈×C₅₃	C₂²×C₄	semidirect
156. #88322	C₂²×C₄	semidirect
172. C₄×C₅₃	C₂×SD₁₆	semidirect
180. Dic₅₃	C₂×SD₁₆	semidirect
187. D₅₃	C₄×SD₁₆	direct (N × H)
198. C₄×SD₁₆	D₅₃	direct (N × H)
203. C₅₃	C₂×C₄×SD₁₆	semidirect
219. C₄×Q₈	C₂×D₅₃	semidirect
235. #106	C₂×D₅₃	semidirect
239. #103	C₂×D₅₃	semidirect
247. C₄×C₈	C₂×D₅₃	semidirect
273. SD₁₆	C₄×D₅₃	direct (N × H)
312. Q₈	C₂×C₄×D₅₃	semidirect
344. C₈	C₂×C₄×D₅₃	semidirect
366. C₄	SD₁₆×D₅₃	direct (N × H)

Subgroups — C4×SD16×D53 #20283468

Conjugacy classes of subgroups

Complements

Subgroups — C₄×SD₁₆×D₅₃ #20283468