Subgroups — C₂×#20276614 #27537534

Order 13568.

710 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810745	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16810735	C₂	1	1	yes	maximal, characteristic, complemented
3	#20276614	C₂	1	8	yes	maximal, direct product factor
4	C₂×#16810446	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16810436	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16810433	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16810400	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#509	C₂	1	1	yes	maximal, characteristic
9	C₂×#13133224	—	2	1	no	—
10	C₂×D₄×Dic₅₃	—	2	1	no	—
11	C₂×#13133157	C₂²	1	1	yes	characteristic
12	#16810745	—	2	2	no	—
13	#16810745	C₂²	1	4	yes	complemented
14	#16810735	—	2	2	no	—
15	#16810735	C₂²	1	4	yes	complemented
16	C₂×#13133153	C₂²	1	1	yes	characteristic
17	C₂×#13133149	C₂²	1	1	yes	characteristic
18	C₂×#13133144	—	2	1	no	—
19	C₂×#13133138	—	2	1	no	—
20	C₂×#13133127	C₂²	1	1	yes	characteristic
21	#16810446	C₂²	1	4	yes	complemented
22	#16810436	C₂²	1	4	yes	complemented
23	#16810433	C₂²	1	4	yes	complemented
24	#16810400	C₂²	1	4	yes	complemented
25	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
27	C₅₃×#509	C₄	1	4	yes	complemented
28	C₅₃×#509	C₂²	1	4	yes	—
29	C₂×SD₃₂×C₅₃	C₄	1	2	yes	complemented
30	C₂×D₁₆×C₅₃	C₄	1	2	yes	complemented
31	C₂×M₃₂×C₅₃	C₂²	1	1	yes	characteristic
32	C₂³×Dic₅₃	—	4	1	no	—
33	#13133224	—	2	4	no	—
34	#13133224	—	4	2	no	—
35	C₂×#11719917	—	2	1	no	—
36	C₂×#11719917	—	4	1	no	—
37	C₂²×#88322	—	4	1	no	—
38	C₂²×#88322	D₄	1	1	yes	characteristic
39	D₄×Dic₅₃	—	2	4	no	—
40	D₄×Dic₅₃	—	4	2	no	—
41	C₂×C₄⋊Dic₅₃	—	2	1	no	—
42	C₂×C₂²⋊Dic₅₃	—	4	1	no	—
43	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
44	#13133157	—	2	1	no	—
45	#13133157	C₂³	1	2	yes	—
46	C₂×#11719908	—	2	1	no	—
47	#13133153	—	2	1	no	—
48	#13133153	C₂³	1	2	yes	—
49	#13133149	—	2	1	no	—
50	#13133149	C₂³	1	2	yes	—
51	#13133144	—	2	4	no	—
52	#13133138	—	2	4	no	—
53	#13133127	D₄	1	2	yes	—
54	#13133127	C₂³	1	2	yes	—
55	C₂×#41×C₅₃	—	2	1	no	—
56	C₂²×D₄×C₅₃	—	2	1	no	—
57	#135×C₅₃	—	2	1	no	—
58	#135×C₅₃	—	2	1	no	—
59	#135×C₅₃	C₂×C₄	1	2	yes	complemented
60	#135×C₅₃	C₂³	1	2	yes	—
61	C₂×Q₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
62	C₂×SD₁₆×C₅₃	—	2	1	no	—
63	C₂×D₈×C₅₃	—	2	1	no	—
64	C₂×D₈×C₅₃	—	2	1	no	—
65	C₂×D₈×C₅₃	—	2	1	no	—
66	C₂×D₈×C₅₃	C₂×C₄	1	2	yes	—
67	C₂×D₈×C₅₃	C₂×C₄	1	2	yes	—
68	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
69	C₂×D₈×C₅₃	C₂³	1	2	yes	—
70	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
71	SD₃₂×C₅₃	C₂×C₄	1	8	yes	complemented
72	D₁₆×C₅₃	C₂×C₄	1	8	yes	complemented
73	M₃₂×C₅₃	C₂×C₄	1	2	yes	complemented
74	M₃₂×C₅₃	C₂³	1	2	yes	—
75	C₂×C₁₆×C₅₃	C₂×C₄	1	2	yes	complemented
76	C₂⁴×C₅₃	—	4	1	no	—
77	#41×C₅₃	—	2	2	no	—
78	#41×C₅₃	—	2	2	no	—
79	#41×C₅₃	—	4	1	no	—
80	#41×C₅₃	—	4	1	no	—
81	C₂×Q₈×C₅₃	—	2	1	no	—
82	C₂×D₄×C₅₃	—	2	2	no	—
83	C₂×D₄×C₅₃	—	2	2	no	—
84	C₂×D₄×C₅₃	—	2	1	no	—
85	C₂×D₄×C₅₃	—	2	2	no	—
86	C₂×D₄×C₅₃	—	4	1	no	—
87	C₂×D₄×C₅₃	—	4	1	no	—
88	C₂×D₄×C₅₃	—	4	1	no	—
89	C₂×D₄×C₅₃	—	4	1	no	—
90	C₂²×C₄×C₅₃	—	4	1	no	—
91	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×Dic₅₃	—	2	1	no	—
93	C₂²×Dic₅₃	—	4	4	no	—
94	C₂²×Dic₅₃	—	4	1	no	—
95	C₂²×Dic₅₃	—	8	4	no	—
96	Q₁₆×C₅₃	—	2	1	no	—
97	Q₁₆×C₅₃	C₂²×C₄	1	2	yes	complemented
98	SD₁₆×C₅₃	—	2	2	no	—
99	SD₁₆×C₅₃	—	2	2	no	—
100	D₈×C₅₃	—	2	2	no	—
101	D₈×C₅₃	—	2	2	no	—
102	D₈×C₅₃	—	2	1	no	—
103	D₈×C₅₃	—	2	2	no	—
104	D₈×C₅₃	C₂²×C₄	1	4	yes	—
105	D₈×C₅₃	C₂²×C₄	1	2	yes	complemented
106	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
110	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
111	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
112	C₂²⋊Dic₅₃	—	4	4	no	—
113	C₄⋊Dic₅₃	—	2	2	no	—
114	C₄⋊Dic₅₃	—	4	1	no	—
115	C₄×Dic₅₃	—	2	1	no	—
116	C₄×Dic₅₃	C₂×D₄	1	2	yes	—
117	#11719917	—	2	2	no	—
118	#11719917	—	4	4	no	—
119	#11719917	—	4	1	no	—
120	C₂×#88322	—	2	1	no	—
121	C₂×#88322	—	2	1	no	—
122	C₂×#88322	—	4	4	no	—
123	C₂×#88322	—	4	1	no	—
124	C₂×#88322	C₂×D₄	1	2	yes	—
125	C₁₆×C₅₃	C₂²×C₄	1	4	yes	complemented
126	#11719908	—	2	2	no	—
127	C₂³×C₅₃	—	4	2	no	—
128	C₂³×C₅₃	—	4	1	no	—
129	C₂³×C₅₃	—	4	2	no	—
130	C₂³×C₅₃	—	4	2	no	—
131	C₂³×C₅₃	—	8	2	no	—
132	C₂³×C₅₃	—	8	2	no	—
133	C₂³×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
134	Q₈×C₅₃	—	2	2	no	—
135	Q₈×C₅₃	—	4	1	no	—
136	D₄×C₅₃	—	2	4	no	—
137	D₄×C₅₃	—	2	2	no	—
138	D₄×C₅₃	—	4	2	no	—
139	D₄×C₅₃	—	4	2	no	—
140	D₄×C₅₃	—	4	2	no	—
141	D₄×C₅₃	—	4	2	no	—
142	D₄×C₅₃	—	4	2	no	—
143	D₄×C₅₃	—	4	1	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	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
153	C₂×Dic₅₃	—	2	2	no	—
154	C₂×Dic₅₃	—	4	2	no	—
155	C₂×Dic₅₃	—	4	2	no	—
156	C₂×Dic₅₃	—	8	8	no	—
157	C₂×Dic₅₃	—	8	2	no	—
158	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
159	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
160	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
161	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
162	#88322	—	2	2	no	—
163	#88322	—	4	2	no	—
164	C₂×AGL(1,ℤ/16)	—	53	1	no	maximal, Sylow
165	C₂²×C₅₃	—	2	2	no	—
166	C₂²×C₅₃	—	4	2	no	—
167	C₂²×C₅₃	—	4	4	no	—
168	C₂²×C₅₃	—	8	2	no	—
169	C₂²×C₅₃	—	8	2	no	—
170	C₂²×C₅₃	—	8	4	no	—
171	C₂²×C₅₃	—	8	2	no	—
172	C₂²×C₅₃	—	8	4	no	—
173	C₂²×C₅₃	#442	1	1	yes	characteristic
174	C₂²×C₅₃	#442	1	1	yes	characteristic
175	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₄×C₅₃	—	4	2	no	—
177	C₄×C₅₃	#442	1	1	yes	characteristic
178	C₄×C₅₃	#442	1	1	yes	characteristic
179	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
180	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
181	Dic₅₃	—	4	2	no	—
182	Dic₅₃	—	8	2	no	—
183	C₂×#509	D₅₃	1	1	yes	characteristic
184	C₂×#444	—	53	1	no	—
185	C₂×#442	—	53	1	no	—
186	AGL(1,ℤ/16)	—	53	8	no	—
187	C₂×#365	—	53	1	no	—
188	C₂×#361	—	53	1	no	—
189	C₂×#360	—	53	1	no	—
190	C₂×#347	—	53	1	no	—
191	C₂×C₅₃	—	2	1	no	—
192	C₂×C₅₃	—	2	1	no	—
193	C₂×C₅₃	—	8	2	no	—
194	C₂×C₅₃	—	8	4	no	—
195	C₂×C₅₃	AGL(1,ℤ/16)	1	2	yes	complemented
196	C₂×C₅₃	C₂×#442	1	1	yes	characteristic
197	C₂×#135	C₂×D₅₃	1	1	yes	characteristic
198	C₂²×D₈	C₂×D₅₃	1	1	yes	characteristic
199	C₂×#131	—	106	1	no	—
200	C₂×C₄×D₄	—	106	1	no	—
201	#509	Dic₅₃	1	4	yes	complemented
202	#509	C₂×D₅₃	1	4	yes	—
203	C₂×SD₃₂	Dic₅₃	1	2	yes	complemented
204	C₂×D₁₆	Dic₅₃	1	2	yes	complemented
205	C₂×M₃₂	—	53	1	no	—
206	C₂×M₃₂	C₂×D₅₃	1	1	yes	characteristic
207	#444	—	53	4	no	—
208	#444	—	106	2	no	—
209	#442	—	53	4	no	—
210	#442	—	106	2	no	—
211	C₂×#108	—	53	1	no	—
212	C₂×#106	—	53	1	no	—
213	C₂×#104	—	106	1	no	—
214	C₂×#102	—	106	1	no	—
215	C₂×#97	—	53	1	no	—
216	#365	—	53	4	no	—
217	#361	—	53	4	no	—
218	#360	—	53	4	no	—
219	#347	—	53	4	no	—
220	C₅₃	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic, complemented, Sylow
221	C₂×#41	—	2	1	no	—
222	C₂²×D₄	—	2	1	no	—
223	C₂³×C₄	—	212	1	no	—
224	#135	—	2	1	no	—
225	#135	—	2	1	no	—
226	#135	C₂×Dic₅₃	1	2	yes	complemented
227	#135	C₂²×D₅₃	1	2	yes	—
228	C₂×Q₁₆	C₂×Dic₅₃	1	1	yes	characteristic, complemented
229	C₂×SD₁₆	—	2	1	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	—	2	1	no	—
232	C₂×D₈	—	2	1	no	—
233	C₂×D₈	C₂×Dic₅₃	1	2	yes	—
234	C₂×D₈	C₂×Dic₅₃	1	2	yes	—
235	C₂×D₈	C₂×Dic₅₃	1	1	yes	characteristic, complemented
236	C₂×D₈	C₂²×D₅₃	1	2	yes	—
237	#131	—	106	4	no	—
238	#131	—	212	2	no	—
239	C₂×M₁₆	—	106	1	no	—
240	C₂×M₁₆	—	212	1	no	—
241	C₂²×C₈	—	53	1	no	—
242	C₂²×C₈	—	212	1	no	—
243	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
244	C₄×D₄	—	106	4	no	—
245	C₄×D₄	—	212	2	no	—
246	C₂×C₄⋊C₄	—	106	1	no	—
247	C₂×C₂²⋊C₄	—	212	1	no	—
248	C₂×C₄²	—	53	1	no	—
249	SD₃₂	C₂×Dic₅₃	1	8	yes	complemented
250	D₁₆	C₂×Dic₅₃	1	8	yes	complemented
251	M₃₂	—	53	2	no	—
252	M₃₂	—	106	1	no	—
253	M₃₂	C₂×Dic₅₃	1	2	yes	complemented
254	M₃₂	C₂²×D₅₃	1	2	yes	—
255	C₂×C₁₆	—	106	1	no	—
256	C₂×C₁₆	C₂×Dic₅₃	1	2	yes	complemented
257	#108	—	53	2	no	—
258	#108	—	106	1	no	—
259	#106	—	53	2	no	—
260	#106	—	106	1	no	—
261	#104	—	106	4	no	—
262	#102	—	106	4	no	—
263	#97	—	53	2	no	—
264	#97	—	53	2	no	—
265	C₂⁴	—	4	1	no	—
266	#41	—	2	2	no	—
267	#41	—	2	2	no	—
268	#41	—	4	1	no	—
269	#41	—	4	1	no	—
270	C₂×Q₈	—	2	1	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	4	1	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	—	4	1	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	106	1	no	—
281	C₂²×C₄	—	424	4	no	—
282	C₂²×C₄	—	212	4	no	—
283	C₂²×C₄	—	212	1	no	—
284	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
285	Q₁₆	—	2	1	no	—
286	Q₁₆	C₂²×Dic₅₃	1	2	yes	complemented
287	SD₁₆	—	2	2	no	—
288	SD₁₆	—	2	2	no	—
289	D₈	—	2	2	no	—
290	D₈	—	2	2	no	—
291	D₈	—	2	1	no	—
292	D₈	—	2	2	no	—
293	D₈	C₂²×Dic₅₃	1	4	yes	—
294	D₈	C₂²×Dic₅₃	1	2	yes	complemented
295	M₁₆	—	106	2	no	—
296	M₁₆	—	212	4	no	—
297	M₁₆	—	212	1	no	—
298	C₂×C₈	—	53	2	no	—
299	C₂×C₈	—	106	1	no	—
300	C₂×C₈	—	106	1	no	—
301	C₂×C₈	—	212	4	no	—
302	C₂×C₈	—	212	1	no	—
303	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
304	C₂×C₈	#11719947	1	1	yes	characteristic
305	C₂×C₈	#11719947	1	1	yes	characteristic
306	C₂×C₈	C₂²×Dic₅₃	1	1	yes	characteristic
307	C₂×C₈	C₂²×Dic₅₃	1	1	yes	characteristic
308	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
309	C₄⋊C₄	—	106	2	no	—
310	C₄⋊C₄	—	212	1	no	—
311	C₂²⋊C₄	—	212	4	no	—
312	C₄²	—	53	2	no	—
313	C₄²	—	106	1	no	—
314	C₁₆	—	106	2	no	—
315	C₁₆	C₂²×Dic₅₃	1	4	yes	complemented
316	C₂³	—	4	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	1	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	8	2	no	—
321	C₂³	—	8	2	no	—
322	C₂³	#13133241	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	Q₈	—	4	1	no	—
325	D₄	—	2	4	no	—
326	D₄	—	2	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	2	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	106	2	no	—
337	C₂×C₄	—	424	2	no	—
338	C₂×C₄	—	424	8	no	—
339	C₂×C₄	—	212	2	no	—
340	C₂×C₄	—	212	2	no	—
341	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
342	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
343	C₂×C₄	#13133241	1	1	yes	characteristic
344	C₂×C₄	#13133241	1	1	yes	characteristic
345	C₂×C₄	#13133241	1	1	yes	characteristic
346	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
347	C₈	—	106	2	no	—
348	C₈	—	212	2	no	—
349	C₈	D₄×Dic₅₃	1	1	yes	characteristic
350	C₈	D₄×Dic₅₃	1	1	yes	characteristic
351	C₈	C₂³×Dic₅₃	1	1	yes	characteristic
352	C₈	C₂×#11719947	1	1	yes	characteristic
353	C₂²	—	2	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	4	no	—
359	C₂²	—	8	4	no	—
360	C₂²	—	8	2	no	—
361	C₂²	#16810735	1	1	yes	characteristic
362	C₂²	#16810735	1	1	yes	characteristic
363	C₂²	C₂×#13133241	1	1	yes	characteristic
364	C₄	—	4	2	no	—
365	C₄	—	424	2	no	—
366	C₄	—	212	2	no	—
367	C₄	#16810735	1	1	yes	characteristic
368	C₄	#16810735	1	1	yes	characteristic
369	C₄	C₂×D₄×Dic₅₃	1	1	yes	characteristic
370	C₄	C₂×#13133241	1	1	yes	characteristic
371	C₂	—	2	1	no	—
372	C₂	—	2	1	no	—
373	C₂	—	8	4	no	—
374	C₂	—	8	2	no	—
375	C₂	#20276614	1	2	yes	direct product factor
376	C₂	C₂×#16810735	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16810735
commutator	C₈×C₅₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₅₃
Fitting, prime radical	C₂×C₅₃×#509	C₂
socle	C₂²×C₅₃	#442
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	C₂×#509	D₅₃
hypocenter	C₅₃	C₂×AGL(1,ℤ/16)
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#509

Complements

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

N	H ≅ G/N	type
1. C₂×#16810745	C₂	semidirect
2. C₂×#16810735	C₂	semidirect
3. #20276614	C₂	direct (N × H)
4. C₂×#16810446	C₂	semidirect
5. C₂×#16810436	C₂	semidirect
6. C₂×#16810433	C₂	semidirect
7. C₂×#16810400	C₂	semidirect
13. #16810745	C₂²	semidirect
15. #16810735	C₂²	semidirect
21. #16810446	C₂²	semidirect
22. #16810436	C₂²	semidirect
23. #16810433	C₂²	semidirect
24. #16810400	C₂²	semidirect
27. C₅₃×#509	C₄	semidirect
29. C₂×SD₃₂×C₅₃	C₄	semidirect
30. C₂×D₁₆×C₅₃	C₄	semidirect
59. #135×C₅₃	C₂×C₄	semidirect
61. C₂×Q₁₆×C₅₃	C₂×C₄	semidirect
68. C₂×D₈×C₅₃	C₂×C₄	semidirect
71. SD₃₂×C₅₃	C₂×C₄	semidirect
72. D₁₆×C₅₃	C₂×C₄	semidirect
73. M₃₂×C₅₃	C₂×C₄	semidirect
75. C₂×C₁₆×C₅₃	C₂×C₄	semidirect
97. Q₁₆×C₅₃	C₂²×C₄	semidirect
105. D₈×C₅₃	C₂²×C₄	semidirect
125. C₁₆×C₅₃	C₂²×C₄	semidirect
195. C₂×C₅₃	AGL(1,ℤ/16)	semidirect
201. #509	Dic₅₃	semidirect
203. C₂×SD₃₂	Dic₅₃	semidirect
204. C₂×D₁₆	Dic₅₃	semidirect
220. C₅₃	C₂×AGL(1,ℤ/16)	semidirect
226. #135	C₂×Dic₅₃	semidirect
228. C₂×Q₁₆	C₂×Dic₅₃	semidirect
235. C₂×D₈	C₂×Dic₅₃	semidirect
249. SD₃₂	C₂×Dic₅₃	semidirect
250. D₁₆	C₂×Dic₅₃	semidirect
253. M₃₂	C₂×Dic₅₃	semidirect
256. C₂×C₁₆	C₂×Dic₅₃	semidirect
286. Q₁₆	C₂²×Dic₅₃	semidirect
294. D₈	C₂²×Dic₅₃	semidirect
315. C₁₆	C₂²×Dic₅₃	semidirect
375. C₂	#20276614	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×#16810745	2
C₂×#16810735	2
#20276614	2
C₂×#16810446	2
C₂×#16810436	2
C₂×#16810433	2
C₂×#16810400	2
C₂×C₅₃×#509	2
C₂×AGL(1,ℤ/16)	53

Subgroups — C2×#20276614 #27537534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20276614 #27537534