Subgroups — C₂×#20289793 #28310322

Order 13568.

554 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₃⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13133287	C₂	1	1	yes	maximal, characteristic
3	#20289793	C₂	1	4	yes	maximal, direct product factor
4	C₂×M₃₂×D₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11719936	—	2	1	no	—
6	C₂×D₅₃⋊M₁₆	—	2	1	no	—
7	C₂×#13133288	C₄	1	2	yes	—
8	D₅₃⋊#108	—	2	1	no	—
9	D₅₃⋊#108	—	2	1	no	—
10	D₅₃⋊#108	C₄	1	2	yes	—
11	D₅₃⋊#108	C₂²	1	2	yes	—
12	C₂×#13133287	—	2	1	no	—
13	C₂×#13133287	—	2	1	no	—
14	C₂×#13133287	—	2	1	no	—
15	C₂×#13133287	—	2	1	no	—
16	C₂×#13133287	C₄	1	2	yes	—
17	C₂×#13133287	C₄	1	2	yes	—
18	C₂×#13133287	C₂²	1	2	yes	—
19	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
20	C₂×#13133157	C₄	1	1	yes	characteristic
21	C₂×#13133156	—	2	1	no	—
22	M₃₂×D₅₃	—	2	1	no	—
23	M₃₂×D₅₃	—	2	1	no	—
24	M₃₂×D₅₃	C₄	1	2	yes	—
25	M₃₂×D₅₃	C₂²	1	2	yes	—
26	C₂×C₁₆×D₅₃	—	2	1	no	—
27	C₂×M₃₂×C₅₃	C₄	1	1	yes	characteristic
28	C₂×#11719936	—	2	2	no	—
29	C₂×#11719936	—	2	2	no	—
30	C₂×#11719936	—	2	2	no	—
31	C₂×#11719936	—	2	2	no	—
32	C₂×#11719936	—	4	1	no	—
33	C₂×#11719936	—	4	1	no	—
34	C₂×#11719936	—	4	1	no	—
35	D₅₃⋊M₁₆	—	2	2	no	—
36	D₅₃⋊M₁₆	—	2	2	no	—
37	D₅₃⋊M₁₆	—	4	1	no	—
38	D₅₃⋊M₁₆	—	4	1	no	—
39	C₂×#11719940	—	4	1	no	—
40	C₂×D₅₃⋊C₈	—	4	1	no	—
41	C₂²×#88324	—	4	1	no	—
42	#13133288	—	2	2	no	—
43	#13133288	C₂×C₄	1	4	yes	—
44	#13133287	—	2	2	no	—
45	#13133287	—	2	2	no	—
46	#13133287	—	2	2	no	—
47	#13133287	—	2	2	no	—
48	#13133287	—	2	2	no	—
49	#13133287	C₂×C₄	1	4	yes	—
50	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
51	C₂²×#88322	Q₈	1	1	yes	characteristic
52	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
58	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
59	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
60	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
61	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
62	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
63	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
64	#13133157	—	2	1	no	—
65	#13133157	C₂×C₄	1	2	yes	—
66	#13133156	—	2	2	no	—
67	#13133156	—	2	2	no	—
68	C₂×#11719908	—	2	1	no	—
69	C₁₆×D₅₃	—	2	2	no	—
70	C₁₆×D₅₃	—	2	2	no	—
71	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
72	M₃₂×C₅₃	—	2	1	no	—
73	M₃₂×C₅₃	C₂×C₄	1	2	yes	—
74	C₂×C₁₆×C₅₃	—	2	1	no	—
75	C₂³×D₅₃	Q₁₆	1	1	yes	characteristic
76	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₅₃	D₈	1	1	yes	characteristic
78	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₅₃	D₈	1	1	yes	characteristic
84	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
85	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
86	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
87	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
88	C₂×C₄×D₅₃	Q₁₆	1	1	yes	characteristic
89	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
90	#11719940	—	4	2	no	—
91	#11719940	—	4	2	no	—
92	C₂×#88324	—	4	2	no	—
93	C₂×#88324	—	4	2	no	—
94	C₂×#88324	—	4	2	no	—
95	C₂×#88324	—	4	2	no	—
96	#11719936	—	2	4	no	—
97	#11719936	—	2	4	no	—
98	#11719936	—	4	2	no	—
99	#11719936	—	4	2	no	—
100	#11719936	—	4	2	no	—
101	#11719936	—	4	2	no	—
102	D₅₃⋊C₈	—	4	2	no	—
103	D₅₃⋊C₈	—	4	2	no	—
104	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
105	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
106	C₂×C₈×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₈×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
111	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
112	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
113	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
114	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
115	C₂×#88322	C₂×Q₈	1	1	yes	characteristic
116	C₈×D₅₃	C₄²	1	1	yes	characteristic
117	C₈×D₅₃	C₄²	1	1	yes	characteristic
118	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
125	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
126	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
127	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
128	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
129	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
130	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
131	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
132	C₁₆×C₅₃	—	2	2	no	—
133	#11719908	—	2	2	no	—
134	C₂³×C₅₃	#107	1	1	yes	characteristic
135	C₂²×D₅₃	—	4	2	no	—
136	C₂²×D₅₃	#103	1	1	yes	characteristic
137	C₂²×D₅₃	#103	1	1	yes	characteristic
138	C₂²×D₅₃	#103	1	1	yes	characteristic
139	C₂²×D₅₃	#103	1	1	yes	characteristic
140	C₂²×D₅₃	#107	1	1	yes	characteristic
141	C₂²×D₅₃	C₂×Q₁₆	1	1	yes	characteristic
142	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
143	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
144	C₂×C₄×C₅₃	#106	1	1	yes	characteristic
145	C₂×C₄×C₅₃	#106	1	1	yes	characteristic
146	C₂×C₄×C₅₃	#107	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×Dic₅₃	#102	1	1	yes	characteristic
149	C₂×Dic₅₃	#102	1	1	yes	characteristic
150	C₂×Dic₅₃	#102	1	1	yes	characteristic
151	C₂×Dic₅₃	#102	1	1	yes	characteristic
152	C₂×Dic₅₃	#107	1	1	yes	characteristic
153	C₂×Dic₅₃	C₂×D₈	1	1	yes	characteristic
154	C₄×D₅₃	#95	1	1	yes	characteristic
155	C₄×D₅₃	#95	1	1	yes	characteristic
156	C₄×D₅₃	#102	1	1	yes	characteristic
157	C₄×D₅₃	#102	1	1	yes	characteristic
158	C₄×D₅₃	#102	1	1	yes	characteristic
159	C₄×D₅₃	#102	1	1	yes	characteristic
160	C₄×D₅₃	#103	1	1	yes	characteristic
161	C₄×D₅₃	#103	1	1	yes	characteristic
162	C₄×D₅₃	#103	1	1	yes	characteristic
163	C₄×D₅₃	#103	1	1	yes	characteristic
164	C₄×D₅₃	#106	1	1	yes	characteristic
165	C₄×D₅₃	#106	1	1	yes	characteristic
166	C₄×D₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₄×D₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₄×D₅₃	C₂×SD₁₆	1	1	yes	characteristic
169	C₄×D₅₃	C₂×SD₁₆	1	1	yes	characteristic
170	#88324	—	4	4	no	—
171	#88324	—	4	4	no	—
172	C₈×C₅₃	#95	1	1	yes	characteristic
173	C₈×C₅₃	#95	1	1	yes	characteristic
174	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
175	C₈×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	#88322	#95	1	1	yes	characteristic
177	#88322	#95	1	1	yes	characteristic
178	#88322	C₂×C₄⋊C₄	1	1	yes	characteristic
179	#88322	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×#1388	—	53	1	no	maximal, Sylow
181	C₂²×C₅₃	—	2	2	no	—
182	C₂²×C₅₃	#340	1	1	yes	characteristic
183	C₂²×C₅₃	#340	1	1	yes	characteristic
184	C₂²×C₅₃	C₂×#107	1	1	yes	characteristic
185	C₂×D₅₃	—	2	2	no	—
186	C₂×D₅₃	—	2	2	no	—
187	C₂×D₅₃	—	4	1	no	—
188	C₂×D₅₃	—	4	1	no	—
189	C₂×D₅₃	—	4	1	no	—
190	C₂×D₅₃	—	4	1	no	—
191	C₂×D₅₃	#340	1	1	yes	characteristic
192	C₂×D₅₃	#340	1	1	yes	characteristic
193	C₂×D₅₃	C₂×#103	1	1	yes	characteristic
194	C₂×D₅₃	C₂×#103	1	1	yes	characteristic
195	C₄×C₅₃	#340	1	1	yes	characteristic
196	C₄×C₅₃	#340	1	1	yes	characteristic
197	C₄×C₅₃	C₂×#95	1	1	yes	characteristic
198	C₄×C₅₃	C₂×#106	1	1	yes	characteristic
199	Dic₅₃	#340	1	1	yes	characteristic
200	Dic₅₃	#340	1	1	yes	characteristic
201	Dic₅₃	C₂×#102	1	1	yes	characteristic
202	Dic₅₃	C₂×#102	1	1	yes	characteristic
203	C₂²×M₃₂	—	53	1	no	—
204	C₂²×#108	—	53	1	no	—
205	C₂²×#108	—	53	1	no	—
206	#1388	—	53	4	no	—
207	C₂×C₅₃	—	2	1	no	—
208	C₂×C₅₃	—	2	1	no	—
209	C₂×C₅₃	#1388	1	2	yes	complemented
210	C₂×C₅₃	C₂×#340	1	1	yes	characteristic
211	D₅₃	—	2	1	no	—
212	D₅₃	—	2	1	no	—
213	D₅₃	—	2	1	no	—
214	D₅₃	—	2	1	no	—
215	C₂²×M₁₆	—	106	1	no	—
216	C₂²×M₁₆	—	106	1	no	—
217	C₂³×C₈	—	53	1	no	—
218	C₂×M₃₂	—	53	1	no	—
219	C₂×M₃₂	—	53	2	no	—
220	C₂×M₃₂	—	53	2	no	—
221	C₂×M₃₂	—	106	1	no	—
222	C₂×M₃₂	—	106	1	no	—
223	C₂×M₃₂	—	106	1	no	—
224	C₂×M₃₂	#6157	1	1	yes	characteristic
225	C₂²×C₁₆	—	106	1	no	—
226	C₂×#108	—	53	2	no	—
227	C₂×#108	—	53	2	no	—
228	C₂×#108	—	53	2	no	—
229	C₂×#108	—	53	2	no	—
230	C₂×#108	—	53	2	no	—
231	C₂×#108	—	53	2	no	—
232	C₂×#108	—	106	1	no	—
233	C₂×#108	—	106	1	no	—
234	C₂×#108	—	106	1	no	—
235	C₂×#108	—	106	1	no	—
236	C₂×#108	—	106	1	no	—
237	C₂×#108	—	106	1	no	—
238	C₅₃	C₂×#1388	1	1	yes	characteristic, complemented, Sylow
239	C₂³×C₄	—	53	1	no	—
240	C₂×M₁₆	—	106	2	no	—
241	C₂×M₁₆	—	106	2	no	—
242	C₂×M₁₆	—	106	2	no	—
243	C₂×M₁₆	—	106	2	no	—
244	C₂×M₁₆	—	106	2	no	—
245	C₂×M₁₆	—	106	2	no	—
246	C₂×M₁₆	—	212	1	no	—
247	C₂×M₁₆	—	212	1	no	—
248	C₂×M₁₆	—	212	1	no	—
249	C₂×M₁₆	—	212	1	no	—
250	C₂×M₁₆	—	212	1	no	—
251	C₂×M₁₆	—	212	1	no	—
252	C₂²×C₈	—	53	1	no	—
253	C₂²×C₈	—	53	1	no	—
254	C₂²×C₈	—	53	1	no	—
255	C₂²×C₈	—	53	1	no	—
256	C₂²×C₈	—	53	1	no	—
257	C₂²×C₈	—	53	1	no	—
258	C₂²×C₈	—	53	1	no	—
259	C₂²×C₈	—	53	1	no	—
260	C₂²×C₈	—	53	1	no	—
261	C₂²×C₈	—	53	1	no	—
262	C₂²×C₈	—	53	1	no	—
263	C₂²×C₈	—	53	1	no	—
264	C₂²×C₈	—	53	1	no	—
265	C₂²×C₈	—	212	1	no	—
266	C₂²×C₈	—	212	1	no	—
267	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
268	M₃₂	—	2	1	no	—
269	M₃₂	—	53	2	no	—
270	M₃₂	—	106	2	no	—
271	M₃₂	—	106	2	no	—
272	M₃₂	—	106	1	no	—
273	M₃₂	C₂×#6157	1	2	yes	—
274	C₂×C₁₆	—	2	1	no	—
275	C₂×C₁₆	—	106	2	no	—
276	C₂×C₁₆	—	106	2	no	—
277	C₂×C₁₆	—	106	1	no	—
278	#108	—	53	4	no	—
279	#108	—	53	4	no	—
280	#108	—	106	2	no	—
281	#108	—	106	2	no	—
282	#108	—	106	2	no	—
283	#108	—	106	2	no	—
284	#108	—	106	2	no	—
285	#108	—	106	2	no	—
286	C₂⁴	—	53	1	no	—
287	C₂²×C₄	—	53	1	no	—
288	C₂²×C₄	—	53	1	no	—
289	C₂²×C₄	—	53	1	no	—
290	C₂²×C₄	—	53	1	no	—
291	C₂²×C₄	—	53	1	no	—
292	C₂²×C₄	—	53	1	no	—
293	C₂²×C₄	—	53	1	no	—
294	C₂²×C₄	—	53	1	no	—
295	C₂²×C₄	—	53	1	no	—
296	C₂²×C₄	—	53	1	no	—
297	C₂²×C₄	—	53	1	no	—
298	C₂²×C₄	—	53	1	no	—
299	C₂²×C₄	—	53	1	no	—
300	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
301	M₁₆	—	106	4	no	—
302	M₁₆	—	106	4	no	—
303	M₁₆	—	212	2	no	—
304	M₁₆	—	212	2	no	—
305	M₁₆	—	212	2	no	—
306	M₁₆	—	212	2	no	—
307	M₁₆	—	212	2	no	—
308	M₁₆	—	212	2	no	—
309	C₂×C₈	—	53	1	no	—
310	C₂×C₈	—	53	1	no	—
311	C₂×C₈	—	53	1	no	—
312	C₂×C₈	—	53	1	no	—
313	C₂×C₈	—	53	1	no	—
314	C₂×C₈	—	53	1	no	—
315	C₂×C₈	—	53	1	no	—
316	C₂×C₈	—	53	1	no	—
317	C₂×C₈	—	53	1	no	—
318	C₂×C₈	—	53	1	no	—
319	C₂×C₈	—	53	1	no	—
320	C₂×C₈	—	53	1	no	—
321	C₂×C₈	—	53	1	no	—
322	C₂×C₈	—	53	1	no	—
323	C₂×C₈	—	53	1	no	—
324	C₂×C₈	—	53	1	no	—
325	C₂×C₈	—	53	1	no	—
326	C₂×C₈	—	53	1	no	—
327	C₂×C₈	—	53	1	no	—
328	C₂×C₈	—	53	1	no	—
329	C₂×C₈	—	53	1	no	—
330	C₂×C₈	—	53	1	no	—
331	C₂×C₈	—	212	2	no	—
332	C₂×C₈	—	212	2	no	—
333	C₂×C₈	—	212	2	no	—
334	C₂×C₈	—	212	2	no	—
335	C₂×C₈	—	212	2	no	—
336	C₂×C₈	—	212	2	no	—
337	C₂×C₈	C₄×#6157	1	1	yes	characteristic
338	C₂×C₈	C₄×#6157	1	1	yes	characteristic
339	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
340	C₂×C₈	C₂²⋊#6157	1	1	yes	characteristic
341	C₂×C₈	C₂²⋊#6157	1	1	yes	characteristic
342	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
343	C₁₆	—	2	2	no	—
344	C₁₆	—	106	2	no	—
345	C₂³	—	53	1	no	—
346	C₂³	—	53	1	no	—
347	C₂³	—	53	1	no	—
348	C₂³	—	53	1	no	—
349	C₂³	—	53	1	no	—
350	C₂³	—	53	1	no	—
351	C₂³	—	212	2	no	—
352	C₂³	#13133286	1	1	yes	characteristic
353	C₂×C₄	—	53	1	no	—
354	C₂×C₄	—	53	1	no	—
355	C₂×C₄	—	53	1	no	—
356	C₂×C₄	—	53	1	no	—
357	C₂×C₄	—	53	1	no	—
358	C₂×C₄	—	53	1	no	—
359	C₂×C₄	—	53	1	no	—
360	C₂×C₄	—	53	1	no	—
361	C₂×C₄	—	53	1	no	—
362	C₂×C₄	—	53	1	no	—
363	C₂×C₄	—	53	1	no	—
364	C₂×C₄	—	53	1	no	—
365	C₂×C₄	—	53	1	no	—
366	C₂×C₄	—	53	1	no	—
367	C₂×C₄	—	53	1	no	—
368	C₂×C₄	—	53	1	no	—
369	C₂×C₄	—	53	1	no	—
370	C₂×C₄	—	53	1	no	—
371	C₂×C₄	—	53	1	no	—
372	C₂×C₄	—	53	1	no	—
373	C₂×C₄	—	53	1	no	—
374	C₂×C₄	—	53	1	no	—
375	C₂×C₄	(C₂×#6157)⋊C₄	1	1	yes	characteristic
376	C₂×C₄	(C₂×#6157)⋊C₄	1	1	yes	characteristic
377	C₂×C₄	#13133285	1	1	yes	characteristic
378	C₂×C₄	#13133285	1	1	yes	characteristic
379	C₂×C₄	#13133286	1	1	yes	characteristic
380	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
381	C₈	—	53	1	no	—
382	C₈	—	53	1	no	—
383	C₈	—	53	1	no	—
384	C₈	—	53	1	no	—
385	C₈	—	212	4	no	—
386	C₈	—	212	4	no	—
387	C₈	(C₂×#6157)⋊C₄	1	1	yes	characteristic
388	C₈	(C₂×#6157)⋊C₄	1	1	yes	characteristic
389	C₈	C₂×C₄×#6157	1	1	yes	characteristic
390	C₈	C₂×C₂²⋊#6157	1	1	yes	characteristic
391	C₂²	—	2	2	no	—
392	C₂²	—	53	1	no	—
393	C₂²	—	53	1	no	—
394	C₂²	—	53	1	no	—
395	C₂²	—	53	1	no	—
396	C₂²	—	106	2	no	—
397	C₂²	—	106	2	no	—
398	C₂²	—	212	1	no	—
399	C₂²	—	212	1	no	—
400	C₂²	—	212	1	no	—
401	C₂²	—	212	1	no	—
402	C₂²	#16811497	1	1	yes	characteristic
403	C₂²	#16811497	1	1	yes	characteristic
404	C₂²	C₂×#13133286	1	1	yes	characteristic
405	C₄	—	53	1	no	—
406	C₄	—	53	1	no	—
407	C₄	—	53	1	no	—
408	C₄	—	53	1	no	—
409	C₄	#16811497	1	1	yes	characteristic
410	C₄	#16811497	1	1	yes	characteristic
411	C₄	C₂×(C₂×#6157)⋊C₄	1	1	yes	characteristic
412	C₄	C₂×#13133285	1	1	yes	characteristic
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	—	106	1	no	—
416	C₂	—	106	1	no	—
417	C₂	—	106	1	no	—
418	C₂	—	106	1	no	—
419	C₂	#20289793	1	2	yes	direct product factor
420	C₂	C₂×#16811497	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16811497
commutator	C₈×C₅₃	C₂×C₄²
Frattini	C₂×C₈	C₂²×#6157
Fitting	C₂×M₃₂×C₅₃	C₄
socle	C₂²×C₅₃	#340
prime radical	C₂³×D₅₃	Q₁₆
cosocle	C₂×C₈×D₅₃	C₂³
hypercenter	C₂×M₃₂	#6157
hypocenter	C₅₃	C₂×#1388
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #20289793	C₂	direct (N × H)
209. C₂×C₅₃	#1388	semidirect
238. C₅₃	C₂×#1388	semidirect
419. C₂	#20289793	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×D₅₃⋊#108	2
C₂²×#13133287	2
#20289793	2
C₂×M₃₂×D₅₃	2
C₂×#1388	53

Subgroups — C2×#20289793 #28310322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20289793 #28310322