Subgroups — C₂×#365×D₅₃ #27537097

Order 13568.

702 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#108×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#106×D₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#16810447	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16810446	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16810445	C₂	1	1	yes	maximal, characteristic, complemented
7	#365×D₅₃	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₅₃×#365	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×M₁₆×D₅₃	—	2	1	no	—
10	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×D₅₃	—	2	1	no	—
12	C₂×#13133157	C₂²	1	1	yes	characteristic
13	C₂×#13133156	C₄	1	2	yes	complemented
14	M₃₂×D₅₃	C₄	1	4	yes	complemented
15	M₃₂×D₅₃	C₂²	1	4	yes	—
16	C₂×C₁₆×D₅₃	C₄	1	2	yes	complemented
17	C₂×#13133153	C₂²	1	1	yes	characteristic
18	C₂×#13133152	—	2	1	no	—
19	#108×D₅₃	—	2	2	no	—
20	#108×D₅₃	C₂²	1	4	yes	—
21	C₂×#13133149	C₂²	1	1	yes	characteristic
22	C₂×#13133148	—	2	1	no	—
23	#106×D₅₃	—	2	2	no	—
24	#106×D₅₃	C₂²	1	4	yes	—
25	#16810447	C₂²	1	4	yes	complemented
26	#16810446	C₂²	1	4	yes	complemented
27	#16810445	C₂²	1	4	yes	complemented
28	C₂×M₃₂×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic
31	C₅₃×#365	C₂²	1	4	yes	complemented
32	C₂²×C₄×D₅₃	—	4	1	no	—
33	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
34	C₂×#11719917	—	2	1	no	—
35	C₂×#11719912	—	4	1	no	—
36	M₁₆×D₅₃	—	2	4	no	—
37	M₁₆×D₅₃	—	4	2	no	—
38	C₂²×#88322	D₄	1	1	yes	characteristic
39	C₂×C₈×D₅₃	—	4	1	no	—
40	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
42	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×D₅₃	D₄	1	2	yes	—
44	C₂×C₈×D₅₃	Q₈	1	2	yes	—
45	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
46	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
47	C₂×C₈×D₅₃	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₅₃	—	2	1	no	—
49	C₂×#11719919	—	4	1	no	—
50	C₄⋊C₄×D₅₃	—	2	4	no	—
51	C₄⋊C₄×D₅₃	—	4	2	no	—
52	#13133157	C₂×C₄	1	2	yes	complemented
53	#13133157	C₂³	1	2	yes	—
54	#13133156	C₂×C₄	1	8	yes	complemented
55	C₂×#11719908	C₂×C₄	1	2	yes	complemented
56	C₁₆×D₅₃	C₂×C₄	1	8	yes	complemented
57	#13133153	—	2	1	no	—
58	#13133153	C₂³	1	2	yes	—
59	#13133152	—	2	4	no	—
60	#13133149	—	2	1	no	—
61	#13133149	C₂³	1	2	yes	—
62	#13133148	—	2	4	no	—
63	C₂×M₁₆×C₅₃	—	2	1	no	—
64	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
66	M₃₂×C₅₃	C₂×C₄	1	2	yes	complemented
67	M₃₂×C₅₃	C₂³	1	2	yes	—
68	C₂×C₁₆×C₅₃	C₂×C₄	1	2	yes	complemented
69	#108×C₅₃	—	2	1	no	—
70	#108×C₅₃	C₂³	1	2	yes	—
71	#106×C₅₃	—	2	1	no	—
72	#106×C₅₃	C₂³	1	2	yes	—
73	C₂³×D₅₃	SD₁₆	1	1	yes	characteristic
74	C₂²×C₄×C₅₃	—	4	1	no	—
75	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×Dic₅₃	—	4	1	no	—
77	C₂²×Dic₅₃	SD₁₆	1	1	yes	characteristic
78	C₂×C₄×D₅₃	—	4	4	no	—
79	C₂×C₄×D₅₃	—	8	4	no	—
80	C₂×C₄×D₅₃	C₄⋊C₄	1	2	yes	—
81	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₅₃	SD₁₆	1	2	yes	—
84	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
85	C₂×C₄×D₅₃	SD₁₆	1	2	yes	—
86	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
87	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
88	M₁₆×C₅₃	—	2	2	no	—
89	M₁₆×C₅₃	—	4	1	no	—
90	C₂×C₈×C₅₃	—	4	1	no	—
91	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
94	C₂×C₈×C₅₃	C₂×Q₈	1	1	yes	characteristic
95	C₂×C₈×C₅₃	C₂×Q₈	1	1	yes	characteristic
96	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
97	C₄⋊C₄×C₅₃	—	2	2	no	—
98	C₄⋊C₄×C₅₃	—	4	1	no	—
99	C₄⋊Dic₅₃	—	2	2	no	—
100	C₄⋊Dic₅₃	—	4	1	no	—
101	#11719919	—	4	4	no	—
102	#11719917	—	2	2	no	—
103	#11719917	—	4	1	no	—
104	C₂×#88322	—	4	1	no	—
105	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
106	C₂×#88322	C₄⋊C₄	1	2	yes	—
107	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
108	C₂×#88322	C₂×D₄	1	2	yes	—
109	#11719912	—	4	4	no	—
110	C₈×D₅₃	—	4	4	no	—
111	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
112	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
113	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
114	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
115	C₈×D₅₃	C₂²×C₄	1	2	yes	—
116	C₈×D₅₃	C₂²×C₄	1	2	yes	—
117	C₈×D₅₃	C₂×Q₈	1	2	yes	—
118	C₈×D₅₃	C₂×Q₈	1	2	yes	—
119	C₁₆×C₅₃	C₂²×C₄	1	4	yes	complemented
120	#11719908	C₂²×C₄	1	4	yes	complemented
121	C₂³×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
122	C₂²×D₅₃	—	2	4	no	—
123	C₂²×D₅₃	#106	1	2	yes	—
124	C₂²×D₅₃	#106	1	1	yes	characteristic
125	C₂²×D₅₃	#106	1	1	yes	characteristic
126	C₂²×D₅₃	C₂×SD₁₆	1	2	yes	—
127	C₂×C₄×C₅₃	—	4	2	no	—
128	C₂×C₄×C₅₃	—	8	2	no	—
129	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
132	C₂×C₄×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
133	C₂×C₄×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
134	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
135	C₂×Dic₅₃	—	4	2	no	—
136	C₂×Dic₅₃	—	8	2	no	—
137	C₂×Dic₅₃	#106	1	2	yes	—
138	C₂×Dic₅₃	#106	1	1	yes	characteristic
139	C₂×Dic₅₃	#106	1	1	yes	characteristic
140	C₂×Dic₅₃	C₂×SD₁₆	1	2	yes	—
141	C₄×D₅₃	—	8	8	no	—
142	C₄×D₅₃	#106	1	2	yes	—
143	C₄×D₅₃	#106	1	2	yes	—
144	C₄×D₅₃	#106	1	2	yes	—
145	C₄×D₅₃	#106	1	2	yes	—
146	C₄×D₅₃	C₂×C₄⋊C₄	1	2	yes	—
147	C₄×D₅₃	C₂×C₄⋊C₄	1	2	yes	—
148	C₄×D₅₃	C₂×SD₁₆	1	2	yes	—
149	C₄×D₅₃	C₂×SD₁₆	1	2	yes	—
150	C₈×C₅₃	—	4	2	no	—
151	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
154	C₈×C₅₃	C₂²×Q₈	1	1	yes	characteristic
155	#88322	—	4	2	no	—
156	#88322	C₂×C₄⋊C₄	1	2	yes	—
157	#88322	C₂×C₄⋊C₄	1	2	yes	—
158	C₂²×#365	—	53	1	no	maximal, Sylow
159	C₂²×C₅₃	—	2	2	no	—
160	C₂²×C₅₃	C₂×#106	1	1	yes	characteristic
161	C₂²×C₅₃	C₂×#106	1	1	yes	characteristic
162	C₂²×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
163	C₂×D₅₃	—	2	2	no	—
164	C₂×D₅₃	—	2	4	no	—
165	C₂×D₅₃	—	2	4	no	—
166	C₂×D₅₃	#365	1	4	yes	direct product factor
167	C₂×D₅₃	C₂×#106	1	2	yes	—
168	C₂×D₅₃	C₂×#106	1	2	yes	—
169	C₄×C₅₃	—	8	2	no	—
170	C₄×C₅₃	C₂×#106	1	1	yes	characteristic
171	C₄×C₅₃	C₂×#106	1	1	yes	characteristic
172	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
173	C₄×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
174	Dic₅₃	—	8	2	no	—
175	Dic₅₃	C₂×#106	1	2	yes	—
176	Dic₅₃	C₂×#106	1	2	yes	—
177	C₂²×M₃₂	—	53	1	no	—
178	C₂²×#108	—	53	1	no	—
179	C₂²×#106	—	53	1	no	—
180	C₂×#365	—	53	1	no	—
181	C₂×#365	—	53	1	no	—
182	C₂×#365	—	53	1	no	—
183	C₂×#365	—	53	8	no	—
184	C₂×#365	D₅₃	1	1	yes	characteristic, direct product factor
185	C₂×C₅₃	—	2	1	no	—
186	C₂×C₅₃	—	2	1	no	—
187	C₂×C₅₃	C₂×#365	1	2	yes	complemented
188	C₂×C₅₃	C₂²×#106	1	1	yes	characteristic
189	D₅₃	—	2	2	no	—
190	D₅₃	C₂×#365	1	4	yes	direct product factor
191	C₂²×M₁₆	—	106	1	no	—
192	C₂³×C₈	—	53	1	no	—
193	C₂²×C₄⋊C₄	—	106	1	no	—
194	C₂×M₃₂	—	53	1	no	—
195	C₂×M₃₂	—	53	4	no	—
196	C₂×M₃₂	—	53	4	no	—
197	C₂×M₃₂	—	53	2	no	—
198	C₂×M₃₂	C₂×D₅₃	1	1	yes	characteristic
199	C₂²×C₁₆	—	53	2	no	—
200	C₂×#108	—	53	1	no	—
201	C₂×#108	—	53	4	no	—
202	C₂×#108	—	106	2	no	—
203	C₂×#108	—	106	1	no	—
204	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
205	C₂×#106	—	53	1	no	—
206	C₂×#106	—	53	4	no	—
207	C₂×#106	—	106	2	no	—
208	C₂×#106	—	106	1	no	—
209	C₂×#106	C₂×D₅₃	1	1	yes	characteristic
210	#365	—	53	4	no	—
211	#365	—	53	4	no	—
212	#365	—	53	4	no	—
213	#365	C₂×D₅₃	1	4	yes	direct product factor
214	C₅₃	C₂²×#365	1	1	yes	characteristic, complemented, Sylow
215	C₂³×C₄	—	53	1	no	—
216	C₂³×C₄	—	212	1	no	—
217	C₂×M₁₆	—	2	1	no	—
218	C₂×M₁₆	—	106	4	no	—
219	C₂×M₁₆	—	106	1	no	—
220	C₂×M₁₆	—	212	1	no	—
221	C₂×M₁₆	—	212	2	no	—
222	C₂²×C₈	—	53	1	no	—
223	C₂²×C₈	—	53	1	no	—
224	C₂²×C₈	—	53	2	no	—
225	C₂²×C₈	—	53	1	no	—
226	C₂²×C₈	—	53	2	no	—
227	C₂²×C₈	—	53	2	no	—
228	C₂²×C₈	—	53	1	no	—
229	C₂²×C₈	—	53	1	no	—
230	C₂²×C₈	—	53	2	no	—
231	C₂²×C₈	—	212	1	no	—
232	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	106	4	no	—
235	C₂×C₄⋊C₄	—	106	1	no	—
236	C₂×C₄⋊C₄	—	212	2	no	—
237	C₂×C₄⋊C₄	—	212	1	no	—
238	M₃₂	—	53	2	no	—
239	M₃₂	—	53	2	no	—
240	M₃₂	—	53	8	no	—
241	M₃₂	C₄×D₅₃	1	2	yes	complemented
242	M₃₂	C₂²×D₅₃	1	2	yes	—
243	C₂×C₁₆	—	53	2	no	—
244	C₂×C₁₆	—	53	8	no	—
245	C₂×C₁₆	C₄×D₅₃	1	2	yes	complemented
246	#108	—	2	1	no	—
247	#108	—	53	2	no	—
248	#108	—	106	4	no	—
249	#108	—	106	1	no	—
250	#108	C₂²×D₅₃	1	2	yes	—
251	#106	—	2	1	no	—
252	#106	—	53	2	no	—
253	#106	—	106	4	no	—
254	#106	—	106	1	no	—
255	#106	C₂²×D₅₃	1	2	yes	—
256	C₂⁴	—	53	1	no	—
257	C₂²×C₄	—	4	1	no	—
258	C₂²×C₄	—	53	1	no	—
259	C₂²×C₄	—	53	2	no	—
260	C₂²×C₄	—	53	1	no	—
261	C₂²×C₄	—	53	1	no	—
262	C₂²×C₄	—	53	2	no	—
263	C₂²×C₄	—	53	1	no	—
264	C₂²×C₄	—	53	2	no	—
265	C₂²×C₄	—	53	1	no	—
266	C₂²×C₄	—	53	2	no	—
267	C₂²×C₄	—	424	4	no	—
268	C₂²×C₄	—	212	4	no	—
269	C₂²×C₄	—	212	1	no	—
270	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
271	M₁₆	—	2	2	no	—
272	M₁₆	—	4	1	no	—
273	M₁₆	—	106	2	no	—
274	M₁₆	—	212	4	no	—
275	M₁₆	—	212	1	no	—
276	C₂×C₈	—	4	1	no	—
277	C₂×C₈	—	53	2	no	—
278	C₂×C₈	—	53	1	no	—
279	C₂×C₈	—	53	1	no	—
280	C₂×C₈	—	53	2	no	—
281	C₂×C₈	—	53	2	no	—
282	C₂×C₈	—	53	2	no	—
283	C₂×C₈	—	53	2	no	—
284	C₂×C₈	—	53	2	no	—
285	C₂×C₈	—	53	2	no	—
286	C₂×C₈	—	53	2	no	—
287	C₂×C₈	—	53	2	no	—
288	C₂×C₈	—	53	2	no	—
289	C₂×C₈	—	212	4	no	—
290	C₂×C₈	—	212	1	no	—
291	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
292	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
293	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
294	C₂×C₈	Q₈×D₅₃	1	1	yes	characteristic
295	C₂×C₈	Q₈×D₅₃	1	1	yes	characteristic
296	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	4	1	no	—
299	C₄⋊C₄	—	106	2	no	—
300	C₄⋊C₄	—	212	4	no	—
301	C₄⋊C₄	—	212	1	no	—
302	C₁₆	—	53	4	no	—
303	C₁₆	C₂×C₄×D₅₃	1	4	yes	complemented
304	C₂³	—	53	1	no	—
305	C₂³	—	53	2	no	—
306	C₂³	—	53	2	no	—
307	C₂³	—	53	1	no	—
308	C₂³	—	106	4	no	—
309	C₂³	SD₁₆×D₅₃	1	1	yes	characteristic
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	8	2	no	—
312	C₂×C₄	—	53	2	no	—
313	C₂×C₄	—	53	2	no	—
314	C₂×C₄	—	53	1	no	—
315	C₂×C₄	—	53	1	no	—
316	C₂×C₄	—	53	2	no	—
317	C₂×C₄	—	53	2	no	—
318	C₂×C₄	—	53	2	no	—
319	C₂×C₄	—	53	2	no	—
320	C₂×C₄	—	53	2	no	—
321	C₂×C₄	—	53	2	no	—
322	C₂×C₄	—	53	2	no	—
323	C₂×C₄	—	53	2	no	—
324	C₂×C₄	—	424	8	no	—
325	C₂×C₄	—	424	2	no	—
326	C₂×C₄	—	212	2	no	—
327	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
328	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
329	C₂×C₄	SD₁₆×D₅₃	1	1	yes	characteristic
330	C₂×C₄	SD₁₆×D₅₃	1	1	yes	characteristic
331	C₂×C₄	SD₁₆×D₅₃	1	1	yes	characteristic
332	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
333	C₈	—	4	2	no	—
334	C₈	—	53	2	no	—
335	C₈	—	53	2	no	—
336	C₈	—	212	2	no	—
337	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
338	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
339	C₈	C₂²×C₄×D₅₃	1	1	yes	characteristic
340	C₈	C₂×Q₈×D₅₃	1	1	yes	characteristic
341	C₂²	—	2	2	no	—
342	C₂²	—	53	4	no	—
343	C₂²	—	53	2	no	—
344	C₂²	—	53	2	no	—
345	C₂²	—	106	4	no	—
346	C₂²	—	106	4	no	—
347	C₂²	—	106	2	no	—
348	C₂²	#106×D₅₃	1	1	yes	characteristic
349	C₂²	#106×D₅₃	1	1	yes	characteristic
350	C₂²	C₂×SD₁₆×D₅₃	1	1	yes	characteristic
351	C₄	—	8	2	no	—
352	C₄	—	53	2	no	—
353	C₄	—	53	2	no	—
354	C₄	—	424	2	no	—
355	C₄	#106×D₅₃	1	1	yes	characteristic
356	C₄	#106×D₅₃	1	1	yes	characteristic
357	C₄	C₂×C₄⋊C₄×D₅₃	1	1	yes	characteristic
358	C₄	C₂×SD₁₆×D₅₃	1	1	yes	characteristic
359	C₂	—	2	1	no	—
360	C₂	—	2	1	no	—
361	C₂	—	53	4	no	—
362	C₂	—	106	2	no	—
363	C₂	#365×D₅₃	1	2	yes	direct product factor
364	C₂	C₂×#106×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#106×D₅₃
commutator	C₈×C₅₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₂×C₅₃×#365	C₂
socle	C₂²×C₅₃	C₂×#106
prime radical	C₂³×D₅₃	SD₁₆
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	C₂×#365	D₅₃
hypocenter	C₅₃	C₂²×#365
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#365

Complements

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

N	H ≅ G/N	type
4. C₂×#16810447	C₂	semidirect
5. C₂×#16810446	C₂	semidirect
6. C₂×#16810445	C₂	semidirect
7. #365×D₅₃	C₂	direct (N × H)
8. C₂×C₅₃×#365	C₂	semidirect
13. C₂×#13133156	C₄	semidirect
14. M₃₂×D₅₃	C₄	semidirect
16. C₂×C₁₆×D₅₃	C₄	semidirect
25. #16810447	C₂²	semidirect
26. #16810446	C₂²	semidirect
27. #16810445	C₂²	semidirect
31. C₅₃×#365	C₂²	semidirect
52. #13133157	C₂×C₄	semidirect
54. #13133156	C₂×C₄	semidirect
55. C₂×#11719908	C₂×C₄	semidirect
56. C₁₆×D₅₃	C₂×C₄	semidirect
66. M₃₂×C₅₃	C₂×C₄	semidirect
68. C₂×C₁₆×C₅₃	C₂×C₄	semidirect
119. C₁₆×C₅₃	C₂²×C₄	semidirect
120. #11719908	C₂²×C₄	semidirect
166. C₂×D₅₃	#365	direct (N × H)
184. C₂×#365	D₅₃	direct (N × H)
187. C₂×C₅₃	C₂×#365	semidirect
190. D₅₃	C₂×#365	direct (N × H)
213. #365	C₂×D₅₃	direct (N × H)
214. C₅₃	C₂²×#365	semidirect
241. M₃₂	C₄×D₅₃	semidirect
245. C₂×C₁₆	C₄×D₅₃	semidirect
303. C₁₆	C₂×C₄×D₅₃	semidirect
363. C₂	#365×D₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₅₃	2
C₂×#108×D₅₃	2
C₂×#106×D₅₃	2
C₂×#16810447	2
C₂×#16810446	2
C₂×#16810445	2
#365×D₅₃	2
C₂×C₅₃×#365	2
C₂²×#365	53

Subgroups — C2×#365×D53 #27537097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#365×D₅₃ #27537097