Subgroups — C₂×#20276594 #27537490

Order 13568.

662 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	C₂×#16811053	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810741	C₂	1	1	yes	maximal, characteristic, complemented
3	#20276594	C₂	1	8	yes	maximal, direct product factor
4	C₂×#16810452	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16810430	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16810429	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×#11719908	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13133239	C₂²	1	1	yes	characteristic
10	C₂×#13133223	—	2	1	no	—
11	#16811053	C₄	1	4	yes	complemented
12	#16811053	C₂²	1	4	yes	—
13	C₂×#13133163	C₄	1	1	yes	characteristic, complemented
14	C₂×#13133161	C₄	1	1	yes	characteristic, complemented
15	C₂×#13133160	C₄	1	1	yes	characteristic, complemented
16	C₂×#13133158	C₄	1	1	yes	characteristic, complemented
17	C₂²×#11719908	C₂²	1	1	yes	characteristic
18	C₂²×#11719908	C₂²	1	1	yes	characteristic
19	#16810741	—	2	2	no	—
20	#16810741	C₂²	1	4	yes	complemented
21	C₂×#13133153	C₂²	1	1	yes	characteristic
22	C₂×#13133145	—	2	1	no	—
23	#16810452	C₂²	1	4	yes	complemented
24	#16810430	C₂²	1	4	yes	complemented
25	#16810429	C₂²	1	4	yes	complemented
26	C₄×#11719908	C₂²	1	4	yes	complemented
27	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×#131×C₅₃	—	2	1	no	—
29	C₅₃×#443	—	2	2	no	—
30	C₅₃×#443	C₂²	1	4	yes	complemented
31	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×#104×C₅₃	—	2	1	no	—
33	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#11719945	—	2	1	no	—
35	#13133239	—	2	1	no	—
36	#13133239	—	2	1	no	—
37	#13133239	C₂×C₄	1	2	yes	—
38	#13133239	C₂³	1	2	yes	—
39	C₂×Dic₂₁₂	C₂×C₄	1	1	yes	characteristic
40	C₂×#11719913	—	2	1	no	—
41	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic
42	#13133223	—	2	4	no	—
43	#13133223	—	4	2	no	—
44	C₂×#11719917	—	2	1	no	—
45	C₂×#11719912	—	4	1	no	—
46	C₂×C₈×D₅₃	—	4	1	no	—
47	#13133163	C₂×C₄	1	4	yes	complemented
48	#13133161	C₂×C₄	1	4	yes	complemented
49	#13133160	C₂×C₄	1	4	yes	complemented
50	#13133158	C₂×C₄	1	4	yes	complemented
51	C₂×#11719908	—	2	1	no	—
52	C₂×#11719908	—	2	1	no	—
53	C₂×#11719908	C₂×C₄	1	1	yes	characteristic
54	C₂×#11719908	C₂×C₄	1	1	yes	characteristic
55	C₂×#11719908	C₂×C₄	1	2	yes	—
56	C₂×#11719908	C₂³	1	2	yes	—
57	C₂×#11719908	C₂³	1	2	yes	—
58	#13133153	—	2	1	no	—
59	#13133153	C₂³	1	2	yes	—
60	#13133145	—	2	4	no	—
61	C₂×#41×C₅₃	—	2	1	no	—
62	#135×C₅₃	—	2	1	no	—
63	#135×C₅₃	—	2	1	no	—
64	#135×C₅₃	C₂×C₄	1	2	yes	—
65	#135×C₅₃	C₂³	1	2	yes	—
66	C₂×Q₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
67	C₂×SD₁₆×C₅₃	—	2	1	no	—
68	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic
69	#131×C₅₃	—	2	4	no	—
70	#131×C₅₃	—	4	2	no	—
71	C₂×M₁₆×C₅₃	—	2	1	no	—
72	C₂×M₁₆×C₅₃	—	4	1	no	—
73	C₂²×C₈×C₅₃	—	4	1	no	—
74	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
77	#108×C₅₃	—	2	1	no	—
78	#108×C₅₃	C₂³	1	2	yes	—
79	#104×C₅₃	—	2	4	no	—
80	C₄×C₈×C₅₃	D₄	1	2	yes	—
81	C₄×C₈×C₅₃	C₂³	1	2	yes	—
82	#41×C₅₃	—	2	2	no	—
83	#41×C₅₃	—	2	2	no	—
84	#41×C₅₃	—	4	1	no	—
85	#41×C₅₃	—	4	1	no	—
86	C₂×Q₈×C₅₃	—	2	1	no	—
87	C₂×D₄×C₅₃	—	2	1	no	—
88	C₂×D₄×C₅₃	—	4	1	no	—
89	C₂²×C₄×C₅₃	—	2	1	no	—
90	C₂²×C₄×C₅₃	—	4	1	no	—
91	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
92	C₂×C₂²⋊D₅₃	—	4	1	no	—
93	#11719945	—	2	2	no	—
94	#11719945	—	2	2	no	—
95	#11719945	—	4	1	no	—
96	#11719945	—	4	1	no	—
97	C₂×D₂₁₂	—	2	1	no	—
98	C₂×C₄×D₅₃	—	4	1	no	—
99	C₂×Dic₁₀₆	—	2	1	no	—
100	Q₁₆×C₅₃	—	2	1	no	—
101	Q₁₆×C₅₃	C₂²×C₄	1	2	yes	—
102	SD₁₆×C₅₃	—	2	2	no	—
103	SD₁₆×C₅₃	—	2	2	no	—
104	D₈×C₅₃	—	2	1	no	—
105	D₈×C₅₃	C₂²×C₄	1	2	yes	—
106	M₁₆×C₅₃	—	2	2	no	—
107	M₁₆×C₅₃	—	4	1	no	—
108	M₁₆×C₅₃	—	4	4	no	—
109	C₂×C₈×C₅₃	—	4	1	no	—
110	C₂×C₈×C₅₃	—	4	4	no	—
111	C₂×C₈×C₅₃	D₈	1	1	yes	characteristic
112	C₂×C₈×C₅₃	D₈	1	2	yes	—
113	C₂×C₈×C₅₃	D₈	1	1	yes	characteristic
114	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
119	C₂×C₈×C₅₃	#41	1	1	yes	characteristic
120	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
121	C₄²×C₅₃	—	2	1	no	—
122	C₄²×C₅₃	C₂×D₄	1	2	yes	—
123	#11719917	—	2	2	no	—
124	#11719917	—	4	1	no	—
125	C₂×#88322	—	4	1	no	—
126	Dic₂₁₂	—	2	1	no	—
127	Dic₂₁₂	C₂²×C₄	1	2	yes	—
128	D₄₂₄	—	2	1	no	—
129	D₄₂₄	C₂²×C₄	1	2	yes	—
130	#11719913	—	2	2	no	—
131	#11719913	—	2	2	no	—
132	#11719912	—	4	4	no	—
133	C₈×D₅₃	—	4	4	no	—
134	#11719908	—	2	2	no	—
135	#11719908	C₂²×C₄	1	2	yes	—
136	#11719908	C₂²×C₄	1	2	yes	—
137	C₂³×C₅₃	—	4	1	no	—
138	C₂³×C₅₃	#135	1	1	yes	characteristic
139	C₂²×D₅₃	—	4	1	no	—
140	Q₈×C₅₃	—	2	2	no	—
141	Q₈×C₅₃	—	4	1	no	—
142	D₄×C₅₃	—	2	2	no	—
143	D₄×C₅₃	—	4	2	no	—
144	D₄×C₅₃	—	4	2	no	—
145	D₄×C₅₃	—	4	1	no	—
146	C₂×C₄×C₅₃	—	2	4	no	—
147	C₂×C₄×C₅₃	—	2	2	no	—
148	C₂×C₄×C₅₃	—	4	1	no	—
149	C₂×C₄×C₅₃	—	4	2	no	—
150	C₂×C₄×C₅₃	—	4	2	no	—
151	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₅₃	#135	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
157	C₂²⋊D₅₃	—	4	2	no	—
158	C₂²⋊D₅₃	—	4	2	no	—
159	C₂×Dic₅₃	—	4	1	no	—
160	D₂₁₂	—	2	2	no	—
161	D₂₁₂	—	4	1	no	—
162	C₄×D₅₃	—	4	2	no	—
163	C₄×D₅₃	—	4	2	no	—
164	Dic₁₀₆	—	2	2	no	—
165	Dic₁₀₆	—	4	1	no	—
166	C₈×C₅₃	—	4	2	no	—
167	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
168	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
169	C₈×C₅₃	C₂×D₈	1	2	yes	—
170	C₈×C₅₃	C₂×D₈	1	2	yes	—
171	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
172	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
173	#88322	—	4	2	no	—
174	C₂×#2178	—	53	1	no	maximal, Sylow
175	C₂²×C₅₃	—	2	2	no	—
176	C₂²×C₅₃	—	4	2	no	—
177	C₂²×C₅₃	—	8	2	no	—
178	C₂²×C₅₃	C₄×D₈	1	1	yes	characteristic
179	C₂²×C₅₃	C₄×D₈	1	1	yes	characteristic
180	C₂²×C₅₃	C₂×#135	1	1	yes	characteristic
181	C₂×D₅₃	—	4	2	no	—
182	C₂×D₅₃	—	8	2	no	—
183	C₄×C₅₃	—	2	4	no	—
184	C₄×C₅₃	—	4	2	no	—
185	C₄×C₅₃	C₄×D₈	1	1	yes	characteristic
186	C₄×C₅₃	C₄×D₈	1	1	yes	characteristic
187	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
188	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
189	Dic₅₃	—	4	2	no	—
190	C₂×#508	—	53	1	no	—
191	C₂×#443	—	53	1	no	—
192	C₂×#443	D₅₃	1	1	yes	characteristic, complemented
193	#2178	—	53	8	no	—
194	C₂×#368	—	53	1	no	—
195	C₂×#359	—	53	1	no	—
196	C₂×#359	—	53	1	no	—
197	C₂×C₄×C₁₆	—	53	1	no	—
198	C₂×C₅₃	—	2	1	no	—
199	C₂×C₅₃	—	2	1	no	—
200	C₂×C₅₃	—	8	2	no	—
201	C₂×C₅₃	#2178	1	2	yes	complemented
202	C₂×C₅₃	C₂×C₄×D₈	1	1	yes	characteristic
203	D₅₃	—	8	2	no	—
204	C₂×#135	—	53	1	no	—
205	C₂×#135	C₂×D₅₃	1	1	yes	characteristic
206	C₂×#131	—	2	1	no	—
207	C₂×#131	—	106	1	no	—
208	#508	—	53	4	no	—
209	#508	—	53	4	no	—
210	C₂×Q₃₂	—	53	1	no	—
211	C₂×SD₃₂	—	53	1	no	—
212	C₂×SD₃₂	—	53	1	no	—
213	C₂×D₁₆	—	53	1	no	—
214	C₂²×C₁₆	—	53	1	no	—
215	C₂²×C₁₆	—	53	1	no	—
216	#443	—	2	2	no	—
217	#443	—	53	4	no	—
218	#443	—	106	2	no	—
219	#443	C₂×D₅₃	1	4	yes	complemented
220	C₂×#108	—	53	1	no	—
221	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
222	C₂×#104	—	2	1	no	—
223	C₂×#104	—	106	1	no	—
224	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
225	#368	—	53	4	no	—
226	#359	—	53	4	no	—
227	#359	—	53	4	no	—
228	C₄×C₁₆	—	53	4	no	—
229	C₅₃	C₂×#2178	1	1	yes	characteristic, complemented, Sylow
230	C₂×#41	—	2	1	no	—
231	C₂×#41	—	106	1	no	—
232	#135	—	2	1	no	—
233	#135	—	2	1	no	—
234	#135	—	53	2	no	—
235	#135	—	53	2	no	—
236	#135	—	106	1	no	—
237	#135	—	106	1	no	—
238	#135	C₄×D₅₃	1	2	yes	—
239	#135	C₂²×D₅₃	1	2	yes	—
240	C₂×Q₁₆	—	53	1	no	—
241	C₂×Q₁₆	C₄×D₅₃	1	1	yes	characteristic
242	C₂×SD₁₆	—	2	1	no	—
243	C₂×SD₁₆	—	106	1	no	—
244	C₂×D₈	—	53	1	no	—
245	C₂×D₈	C₄×D₅₃	1	1	yes	characteristic
246	#131	—	2	4	no	—
247	#131	—	4	2	no	—
248	#131	—	106	4	no	—
249	#131	—	212	2	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	4	1	no	—
252	C₂×M₁₆	—	106	1	no	—
253	C₂×M₁₆	—	212	1	no	—
254	C₂²×C₈	—	4	1	no	—
255	C₂²×C₈	—	212	1	no	—
256	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
257	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
258	C₂×C₄²	C₂²⋊D₅₃	1	1	yes	characteristic
259	Q₃₂	—	53	4	no	—
260	SD₃₂	—	53	4	no	—
261	SD₃₂	—	53	4	no	—
262	D₁₆	—	53	4	no	—
263	C₂×C₁₆	—	53	1	no	—
264	C₂×C₁₆	—	53	1	no	—
265	C₂×C₁₆	—	53	2	no	—
266	C₂×C₁₆	—	53	2	no	—
267	C₂×C₁₆	—	53	2	no	—
268	C₂×C₁₆	—	106	1	no	—
269	C₂×C₁₆	—	106	1	no	—
270	#108	—	2	1	no	—
271	#108	—	53	2	no	—
272	#108	—	106	1	no	—
273	#108	C₂²×D₅₃	1	2	yes	—
274	#104	—	2	4	no	—
275	#104	—	106	4	no	—
276	C₄×C₈	C₂²⋊D₅₃	1	2	yes	—
277	C₄×C₈	C₂²×D₅₃	1	2	yes	—
278	#41	—	2	2	no	—
279	#41	—	2	2	no	—
280	#41	—	4	1	no	—
281	#41	—	4	1	no	—
282	#41	—	106	2	no	—
283	#41	—	106	2	no	—
284	#41	—	212	1	no	—
285	#41	—	212	1	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	106	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	106	1	no	—
291	C₂×D₄	—	212	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	212	1	no	—
295	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
296	Q₁₆	—	2	1	no	—
297	Q₁₆	—	53	2	no	—
298	Q₁₆	—	106	1	no	—
299	Q₁₆	C₂×C₄×D₅₃	1	2	yes	—
300	SD₁₆	—	2	2	no	—
301	SD₁₆	—	2	2	no	—
302	SD₁₆	—	106	2	no	—
303	SD₁₆	—	106	2	no	—
304	D₈	—	2	1	no	—
305	D₈	—	53	2	no	—
306	D₈	—	106	1	no	—
307	D₈	C₂×C₄×D₅₃	1	2	yes	—
308	M₁₆	—	2	2	no	—
309	M₁₆	—	4	1	no	—
310	M₁₆	—	4	4	no	—
311	M₁₆	—	106	2	no	—
312	M₁₆	—	212	1	no	—
313	M₁₆	—	212	4	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	4	no	—
316	C₂×C₈	—	212	1	no	—
317	C₂×C₈	—	212	4	no	—
318	C₂×C₈	#11719922	1	1	yes	characteristic
319	C₂×C₈	#11719922	1	2	yes	—
320	C₂×C₈	#11719922	1	1	yes	characteristic
321	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
322	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
323	C₂×C₈	#11719945	1	1	yes	characteristic
324	C₂×C₈	#11719945	1	1	yes	characteristic
325	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
326	C₂×C₈	C₂×C₂²⋊D₅₃	1	2	yes	—
327	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
328	C₄²	—	2	1	no	—
329	C₄²	C₂×C₂²⋊D₅₃	1	2	yes	—
330	C₁₆	—	53	2	no	—
331	C₁₆	—	53	2	no	—
332	C₁₆	—	106	2	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	212	1	no	—
335	C₂³	#13133237	1	1	yes	characteristic
336	Q₈	—	2	2	no	—
337	Q₈	—	4	1	no	—
338	Q₈	—	106	2	no	—
339	Q₈	—	212	1	no	—
340	D₄	—	2	2	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	1	no	—
344	D₄	—	106	2	no	—
345	D₄	—	212	2	no	—
346	D₄	—	212	2	no	—
347	D₄	—	212	1	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	212	1	no	—
354	C₂×C₄	—	212	2	no	—
355	C₂×C₄	—	212	2	no	—
356	C₂×C₄	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
357	C₂×C₄	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
358	C₂×C₄	C₂×#11719922	1	1	yes	characteristic
359	C₂×C₄	C₂×#11719922	1	1	yes	characteristic
360	C₂×C₄	#13133237	1	1	yes	characteristic
361	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
362	C₈	—	4	2	no	—
363	C₈	—	212	2	no	—
364	C₈	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
365	C₈	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
366	C₈	C₂×#11719922	1	2	yes	—
367	C₈	C₂×#11719922	1	2	yes	—
368	C₈	C₂²×C₄×D₅₃	1	1	yes	characteristic
369	C₈	C₂×#11719945	1	1	yes	characteristic
370	C₂²	—	2	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	424	2	no	—
374	C₂²	—	212	2	no	—
375	C₂²	C₄×#11719922	1	1	yes	characteristic
376	C₂²	C₄×#11719922	1	1	yes	characteristic
377	C₂²	C₂×#13133237	1	1	yes	characteristic
378	C₄	—	2	4	no	—
379	C₄	—	4	2	no	—
380	C₄	—	212	2	no	—
381	C₄	C₄×#11719922	1	1	yes	characteristic
382	C₄	C₄×#11719922	1	1	yes	characteristic
383	C₄	C₂×C₄×C₂²⋊D₅₃	1	1	yes	characteristic
384	C₄	C₂²×#11719922	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	8	2	no	—
388	C₂	—	424	2	no	—
389	C₂	#20276594	1	2	yes	direct product factor
390	C₂	C₂×C₄×#11719922	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	#11719922
commutator	C₈×C₅₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₂×C₅₃×#443	C₂
socle	C₂²×C₅₃	C₄×D₈
prime radical	C₂×#16811053	C₂
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	C₂×#443	D₅₃
hypocenter	C₅₃	C₂×#2178
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
2. C₂×#16810741	C₂	semidirect
3. #20276594	C₂	direct (N × H)
4. C₂×#16810452	C₂	semidirect
5. C₂×#16810430	C₂	semidirect
6. C₂×#16810429	C₂	semidirect
7. C₂×C₄×#11719908	C₂	semidirect
8. C₂×C₅₃×#443	C₂	semidirect
11. #16811053	C₄	semidirect
13. C₂×#13133163	C₄	semidirect
14. C₂×#13133161	C₄	semidirect
15. C₂×#13133160	C₄	semidirect
16. C₂×#13133158	C₄	semidirect
20. #16810741	C₂²	semidirect
23. #16810452	C₂²	semidirect
24. #16810430	C₂²	semidirect
25. #16810429	C₂²	semidirect
26. C₄×#11719908	C₂²	semidirect
30. C₅₃×#443	C₂²	semidirect
47. #13133163	C₂×C₄	semidirect
48. #13133161	C₂×C₄	semidirect
49. #13133160	C₂×C₄	semidirect
50. #13133158	C₂×C₄	semidirect
192. C₂×#443	D₅₃	semidirect
201. C₂×C₅₃	#2178	semidirect
219. #443	C₂×D₅₃	semidirect
229. C₅₃	C₂×#2178	semidirect
389. C₂	#20276594	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×#16811053	2
C₂×#16810741	2
#20276594	2
C₂×#16810452	2
C₂×#16810430	2
C₂×#16810429	2
C₂×C₄×#11719908	2
C₂×C₅₃×#443	2
C₂×#2178	53

Subgroups — C2×#20276594 #27537490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20276594 #27537490