Subgroups — C₂×#20289779 #28310288

Order 13568.

614 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₃⋊M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×D₅₃⋊#108	C₂	1	1	yes	maximal, characteristic
3	#20289779	C₂	1	4	yes	maximal, direct product factor
4	C₂×#106×D₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂×D₅₃⋊M₁₆	—	2	1	no	—
6	C₂×#13133292	—	2	1	no	—
7	D₅₃⋊M₃₂	—	2	1	no	—
8	D₅₃⋊M₃₂	—	2	1	no	—
9	D₅₃⋊M₃₂	C₄	1	2	yes	complemented
10	D₅₃⋊M₃₂	C₂²	1	2	yes	—
11	C₂×#13133291	—	2	1	no	—
12	C₂×D₅₃⋊C₁₆	C₄	1	2	yes	complemented
13	C₂×#13133288	—	2	1	no	—
14	D₅₃⋊#108	—	2	1	no	—
15	D₅₃⋊#108	—	2	1	no	—
16	D₅₃⋊#108	C₄	1	2	yes	complemented
17	D₅₃⋊#108	C₂²	1	2	yes	—
18	C₂×#13133287	C₄	1	2	yes	complemented
19	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×D₅₃	—	2	1	no	—
21	C₂×#13133149	C₄	1	1	yes	characteristic
22	C₂×#13133148	—	2	1	no	—
23	#106×D₅₃	—	2	1	no	—
24	#106×D₅₃	—	2	1	no	—
25	#106×D₅₃	C₄	1	2	yes	—
26	#106×D₅₃	C₂²	1	2	yes	—
27	C₂×#106×C₅₃	C₄	1	1	yes	characteristic
28	C₂×#11719936	—	2	2	no	—
29	D₅₃⋊M₁₆	—	2	2	no	—
30	D₅₃⋊M₁₆	—	2	2	no	—
31	D₅₃⋊M₁₆	—	4	1	no	—
32	D₅₃⋊M₁₆	—	4	1	no	—
33	C₂×#11719940	—	4	1	no	—
34	C₂×D₅₃⋊C₈	—	4	1	no	—
35	#13133292	—	2	2	no	—
36	#13133292	—	2	2	no	—
37	#13133291	—	2	2	no	—
38	#13133291	—	2	2	no	—
39	D₅₃⋊C₁₆	—	2	2	no	—
40	D₅₃⋊C₁₆	C₂×C₄	1	4	yes	complemented
41	C₂×#11719910	—	2	2	no	—
42	#13133288	—	2	2	no	—
43	#13133288	—	2	2	no	—
44	#13133287	—	2	2	no	—
45	#13133287	C₂×C₄	1	4	yes	complemented
46	C₂²×C₄×D₅₃	—	4	1	no	—
47	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
48	C₂²×#88322	D₄	1	1	yes	characteristic
49	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₅₃	C₂×C₄	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	D₄	1	1	yes	characteristic
55	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
56	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
57	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
58	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
59	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
60	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊Dic₅₃	—	2	1	no	—
62	C₂×#11719919	—	4	1	no	—
63	C₄⋊C₄×D₅₃	—	2	2	no	—
64	C₄⋊C₄×D₅₃	—	2	2	no	—
65	C₄⋊C₄×D₅₃	—	4	1	no	—
66	C₄⋊C₄×D₅₃	—	4	1	no	—
67	#13133149	—	2	1	no	—
68	#13133149	C₂×C₄	1	2	yes	—
69	#13133148	—	2	2	no	—
70	#13133148	—	2	2	no	—
71	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
73	#106×C₅₃	—	2	1	no	—
74	#106×C₅₃	C₂×C₄	1	2	yes	—
75	C₂³×D₅₃	SD₁₆	1	1	yes	characteristic
76	C₂²×C₄×C₅₃	—	4	1	no	—
77	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₅₃	—	4	1	no	—
79	C₂²×Dic₅₃	D₈	1	1	yes	characteristic
80	C₂×C₄×D₅₃	—	4	2	no	—
81	C₂×C₄×D₅₃	—	4	2	no	—
82	C₂×C₄×D₅₃	—	8	4	no	—
83	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₅₃	D₈	1	1	yes	characteristic
89	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
90	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
91	C₂×C₄×D₅₃	SD₁₆	1	1	yes	characteristic
92	C₂×C₄×D₅₃	Q₁₆	1	1	yes	characteristic
93	C₂×C₄×D₅₃	Q₁₆	1	1	yes	characteristic
94	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
95	#11719940	—	4	2	no	—
96	#11719940	—	4	2	no	—
97	C₂×#88324	—	4	2	no	—
98	#11719936	—	2	4	no	—
99	#11719936	—	4	2	no	—
100	D₅₃⋊C₈	—	4	2	no	—
101	D₅₃⋊C₈	—	4	2	no	—
102	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
103	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
104	C₂×C₈×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₄⋊C₄×C₅₃	—	2	2	no	—
109	C₄⋊C₄×C₅₃	—	4	1	no	—
110	C₄⋊Dic₅₃	—	2	2	no	—
111	C₄⋊Dic₅₃	—	4	1	no	—
112	#11719919	—	4	2	no	—
113	#11719919	—	4	2	no	—
114	C₂×#88322	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×#88322	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×#88322	C₂²⋊C₄	1	1	yes	characteristic
117	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
118	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
119	C₂×#88322	C₂×D₄	1	1	yes	characteristic
120	C₈×D₅₃	C₄²	1	1	yes	characteristic
121	C₈×D₅₃	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
125	C₈×D₅₃	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
129	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
130	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
131	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
132	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
134	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
135	C₈×D₅₃	C₂×Q₈	1	1	yes	characteristic
136	#11719910	—	2	4	no	—
137	C₂³×C₅₃	#102	1	1	yes	characteristic
138	C₂²×D₅₃	—	2	4	no	—
139	C₂²×D₅₃	#102	1	1	yes	characteristic
140	C₂²×D₅₃	#103	1	1	yes	characteristic
141	C₂²×D₅₃	#103	1	1	yes	characteristic
142	C₂²×D₅₃	#106	1	1	yes	characteristic
143	C₂²×D₅₃	#106	1	1	yes	characteristic
144	C₂²×D₅₃	C₂×SD₁₆	1	1	yes	characteristic
145	C₂×C₄×C₅₃	—	4	2	no	—
146	C₂×C₄×C₅₃	—	8	2	no	—
147	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
148	C₂×C₄×C₅₃	#95	1	1	yes	characteristic
149	C₂×C₄×C₅₃	#102	1	1	yes	characteristic
150	C₂×C₄×C₅₃	#103	1	1	yes	characteristic
151	C₂×C₄×C₅₃	#103	1	1	yes	characteristic
152	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×Dic₅₃	—	4	2	no	—
154	C₂×Dic₅₃	—	8	2	no	—
155	C₂×Dic₅₃	#102	1	1	yes	characteristic
156	C₂×Dic₅₃	#102	1	1	yes	characteristic
157	C₂×Dic₅₃	#102	1	1	yes	characteristic
158	C₂×Dic₅₃	#107	1	1	yes	characteristic
159	C₂×Dic₅₃	#107	1	1	yes	characteristic
160	C₂×Dic₅₃	C₂×D₈	1	1	yes	characteristic
161	C₄×D₅₃	—	8	4	no	—
162	C₄×D₅₃	—	8	4	no	—
163	C₄×D₅₃	#95	1	1	yes	characteristic
164	C₄×D₅₃	#95	1	1	yes	characteristic
165	C₄×D₅₃	#102	1	1	yes	characteristic
166	C₄×D₅₃	#102	1	1	yes	characteristic
167	C₄×D₅₃	#103	1	1	yes	characteristic
168	C₄×D₅₃	#103	1	1	yes	characteristic
169	C₄×D₅₃	#103	1	1	yes	characteristic
170	C₄×D₅₃	#103	1	1	yes	characteristic
171	C₄×D₅₃	#106	1	1	yes	characteristic
172	C₄×D₅₃	#106	1	1	yes	characteristic
173	C₄×D₅₃	#107	1	1	yes	characteristic
174	C₄×D₅₃	#107	1	1	yes	characteristic
175	C₄×D₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₄×D₅₃	C₂×SD₁₆	1	1	yes	characteristic
178	C₄×D₅₃	C₂×Q₁₆	1	1	yes	characteristic
179	#88324	—	4	4	no	—
180	C₈×C₅₃	#95	1	1	yes	characteristic
181	C₈×C₅₃	#95	1	1	yes	characteristic
182	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
183	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	#88322	#95	1	1	yes	characteristic
185	#88322	#95	1	1	yes	characteristic
186	#88322	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	#88322	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×#1383	—	53	1	no	maximal, Sylow
189	C₂²×C₅₃	—	2	2	no	—
190	C₂²×C₅₃	#340	1	1	yes	characteristic
191	C₂²×C₅₃	#340	1	1	yes	characteristic
192	C₂²×C₅₃	C₂×#102	1	1	yes	characteristic
193	C₂×D₅₃	—	2	2	no	—
194	C₂×D₅₃	—	2	2	no	—
195	C₂×D₅₃	—	2	2	no	—
196	C₂×D₅₃	—	2	2	no	—
197	C₂×D₅₃	—	2	2	no	—
198	C₂×D₅₃	#340	1	1	yes	characteristic
199	C₂×D₅₃	#340	1	1	yes	characteristic
200	C₂×D₅₃	#365	1	4	yes	—
201	C₂×D₅₃	C₂×#103	1	1	yes	characteristic
202	C₂×D₅₃	C₂×#106	1	1	yes	characteristic
203	C₄×C₅₃	—	8	2	no	—
204	C₄×C₅₃	#340	1	1	yes	characteristic
205	C₄×C₅₃	#340	1	1	yes	characteristic
206	C₄×C₅₃	C₂×#95	1	1	yes	characteristic
207	C₄×C₅₃	C₂×#103	1	1	yes	characteristic
208	Dic₅₃	—	8	2	no	—
209	Dic₅₃	#340	1	1	yes	characteristic
210	Dic₅₃	#340	1	1	yes	characteristic
211	Dic₅₃	C₂×#102	1	1	yes	characteristic
212	Dic₅₃	C₂×#107	1	1	yes	characteristic
213	C₂²×M₃₂	—	53	1	no	—
214	C₂²×#108	—	53	1	no	—
215	C₂²×#106	—	53	1	no	—
216	#1383	—	53	4	no	—
217	C₂×C₅₃	—	2	1	no	—
218	C₂×C₅₃	—	2	1	no	—
219	C₂×C₅₃	#1383	1	2	yes	complemented
220	C₂×C₅₃	C₂×#340	1	1	yes	characteristic
221	D₅₃	—	2	1	no	—
222	D₅₃	—	2	1	no	—
223	D₅₃	#1383	1	2	yes	complemented
224	D₅₃	C₂×#365	1	2	yes	—
225	C₂²×M₁₆	—	106	1	no	—
226	C₂³×C₈	—	53	1	no	—
227	C₂²×C₄⋊C₄	—	106	1	no	—
228	C₂×M₃₂	—	53	2	no	—
229	C₂×M₃₂	—	53	2	no	—
230	C₂×M₃₂	—	106	1	no	—
231	C₂×M₃₂	—	106	1	no	—
232	C₂×M₃₂	—	106	1	no	—
233	C₂×M₃₂	—	106	1	no	—
234	C₂²×C₁₆	—	53	2	no	—
235	C₂×#108	—	53	2	no	—
236	C₂×#108	—	53	2	no	—
237	C₂×#108	—	53	2	no	—
238	C₂×#108	—	106	1	no	—
239	C₂×#108	—	106	1	no	—
240	C₂×#108	—	106	1	no	—
241	C₂×#106	—	53	1	no	—
242	C₂×#106	—	53	2	no	—
243	C₂×#106	—	53	2	no	—
244	C₂×#106	—	106	1	no	—
245	C₂×#106	—	106	1	no	—
246	C₂×#106	—	106	1	no	—
247	C₂×#106	#6157	1	1	yes	characteristic
248	C₅₃	C₂×#1383	1	1	yes	characteristic, complemented, Sylow
249	C₂³×C₄	—	53	1	no	—
250	C₂³×C₄	—	212	1	no	—
251	C₂×M₁₆	—	106	2	no	—
252	C₂×M₁₆	—	106	2	no	—
253	C₂×M₁₆	—	106	2	no	—
254	C₂×M₁₆	—	212	1	no	—
255	C₂×M₁₆	—	212	1	no	—
256	C₂×M₁₆	—	212	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	—	53	1	no	—
266	C₂²×C₈	—	53	1	no	—
267	C₂²×C₈	—	53	1	no	—
268	C₂²×C₈	—	53	1	no	—
269	C₂²×C₈	—	53	1	no	—
270	C₂²×C₈	—	212	1	no	—
271	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	106	2	no	—
274	C₂×C₄⋊C₄	—	106	2	no	—
275	C₂×C₄⋊C₄	—	106	1	no	—
276	C₂×C₄⋊C₄	—	212	1	no	—
277	C₂×C₄⋊C₄	—	212	1	no	—
278	C₂×C₄⋊C₄	—	212	1	no	—
279	M₃₂	—	106	2	no	—
280	M₃₂	—	106	2	no	—
281	M₃₂	—	106	2	no	—
282	M₃₂	—	106	2	no	—
283	C₂×C₁₆	—	53	4	no	—
284	C₂×C₁₆	—	106	2	no	—
285	C₂×C₁₆	—	106	2	no	—
286	#108	—	53	4	no	—
287	#108	—	106	2	no	—
288	#108	—	106	2	no	—
289	#108	—	106	2	no	—
290	#106	—	2	1	no	—
291	#106	—	53	2	no	—
292	#106	—	106	2	no	—
293	#106	—	106	2	no	—
294	#106	—	106	1	no	—
295	#106	C₂×#6157	1	2	yes	—
296	C₂⁴	—	53	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	53	1	no	—
299	C₂²×C₄	—	53	1	no	—
300	C₂²×C₄	—	53	1	no	—
301	C₂²×C₄	—	53	1	no	—
302	C₂²×C₄	—	53	1	no	—
303	C₂²×C₄	—	53	1	no	—
304	C₂²×C₄	—	53	1	no	—
305	C₂²×C₄	—	53	1	no	—
306	C₂²×C₄	—	53	1	no	—
307	C₂²×C₄	—	53	1	no	—
308	C₂²×C₄	—	53	1	no	—
309	C₂²×C₄	—	53	1	no	—
310	C₂²×C₄	—	53	1	no	—
311	C₂²×C₄	—	424	4	no	—
312	C₂²×C₄	—	212	2	no	—
313	C₂²×C₄	—	212	2	no	—
314	C₂²×C₄	—	212	1	no	—
315	C₂²×C₄	C₂²⋊#6157	1	1	yes	characteristic
316	M₁₆	—	106	4	no	—
317	M₁₆	—	212	2	no	—
318	M₁₆	—	212	2	no	—
319	M₁₆	—	212	2	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	—	53	1	no	—
332	C₂×C₈	—	53	1	no	—
333	C₂×C₈	—	53	1	no	—
334	C₂×C₈	—	53	1	no	—
335	C₂×C₈	—	53	1	no	—
336	C₂×C₈	—	53	1	no	—
337	C₂×C₈	—	53	1	no	—
338	C₂×C₈	—	53	1	no	—
339	C₂×C₈	—	53	1	no	—
340	C₂×C₈	—	53	1	no	—
341	C₂×C₈	—	53	1	no	—
342	C₂×C₈	—	212	2	no	—
343	C₂×C₈	—	212	2	no	—
344	C₂×C₈	—	212	2	no	—
345	C₂×C₈	C₄×#6157	1	1	yes	characteristic
346	C₂×C₈	C₄×#6157	1	1	yes	characteristic
347	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
348	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
349	C₂×C₈	C₂²⋊#6157	1	1	yes	characteristic
350	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	106	2	no	—
354	C₄⋊C₄	—	212	2	no	—
355	C₄⋊C₄	—	212	2	no	—
356	C₄⋊C₄	—	212	1	no	—
357	C₁₆	—	106	4	no	—
358	C₂³	—	53	1	no	—
359	C₂³	—	53	1	no	—
360	C₂³	—	53	1	no	—
361	C₂³	—	53	1	no	—
362	C₂³	—	53	1	no	—
363	C₂³	—	53	1	no	—
364	C₂³	—	106	4	no	—
365	C₂³	#13133279	1	1	yes	characteristic
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	8	2	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	—	53	1	no	—
376	C₂×C₄	—	53	1	no	—
377	C₂×C₄	—	53	1	no	—
378	C₂×C₄	—	53	1	no	—
379	C₂×C₄	—	53	1	no	—
380	C₂×C₄	—	53	1	no	—
381	C₂×C₄	—	53	1	no	—
382	C₂×C₄	—	53	1	no	—
383	C₂×C₄	—	53	1	no	—
384	C₂×C₄	—	53	1	no	—
385	C₂×C₄	—	53	1	no	—
386	C₂×C₄	—	53	1	no	—
387	C₂×C₄	—	53	1	no	—
388	C₂×C₄	—	53	1	no	—
389	C₂×C₄	—	53	1	no	—
390	C₂×C₄	—	424	4	no	—
391	C₂×C₄	—	424	4	no	—
392	C₂×C₄	—	424	2	no	—
393	C₂×C₄	—	212	2	no	—
394	C₂×C₄	(C₂×#6157)⋊C₄	1	1	yes	characteristic
395	C₂×C₄	(C₂×#6157)⋊C₄	1	1	yes	characteristic
396	C₂×C₄	#13133279	1	1	yes	characteristic
397	C₂×C₄	#13133280	1	1	yes	characteristic
398	C₂×C₄	#13133280	1	1	yes	characteristic
399	C₂×C₄	C₂×C₂²⋊#6157	1	1	yes	characteristic
400	C₈	—	53	1	no	—
401	C₈	—	53	1	no	—
402	C₈	—	53	1	no	—
403	C₈	—	53	1	no	—
404	C₈	—	212	4	no	—
405	C₈	(C₂×#6157)⋊C₄	1	1	yes	characteristic
406	C₈	(C₂×#6157)⋊C₄	1	1	yes	characteristic
407	C₈	C₂×C₄×#6157	1	1	yes	characteristic
408	C₈	C₂×C₄⋊#6157	1	1	yes	characteristic
409	C₂²	—	2	2	no	—
410	C₂²	—	53	1	no	—
411	C₂²	—	53	1	no	—
412	C₂²	—	53	4	no	—
413	C₂²	—	53	1	no	—
414	C₂²	—	53	1	no	—
415	C₂²	—	106	2	no	—
416	C₂²	—	106	2	no	—
417	C₂²	—	106	2	no	—
418	C₂²	—	106	2	no	—
419	C₂²	—	106	2	no	—
420	C₂²	#16811496	1	1	yes	characteristic
421	C₂²	#16811496	1	1	yes	characteristic
422	C₂²	C₂×#13133279	1	1	yes	characteristic
423	C₄	—	8	2	no	—
424	C₄	—	53	1	no	—
425	C₄	—	53	1	no	—
426	C₄	—	53	1	no	—
427	C₄	—	53	1	no	—
428	C₄	—	424	2	no	—
429	C₄	#16811496	1	1	yes	characteristic
430	C₄	#16811496	1	1	yes	characteristic
431	C₄	C₂×(C₂×#6157)⋊C₄	1	1	yes	characteristic
432	C₄	C₂×#13133280	1	1	yes	characteristic
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	53	2	no	—
436	C₂	—	53	2	no	—
437	C₂	—	106	1	no	—
438	C₂	—	106	1	no	—
439	C₂	#20289779	1	2	yes	direct product factor
440	C₂	C₂×#16811496	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16811496
commutator	C₈×C₅₃	C₂×C₄²
Frattini	C₂×C₈	C₂²×#6157
Fitting	C₂×#106×C₅₃	C₄
socle	C₂²×C₅₃	#340
prime radical	C₂³×D₅₃	SD₁₆
cosocle	C₂×C₈×D₅₃	C₂³
hypercenter	C₂×#106	#6157
hypocenter	C₅₃	C₂×#1383
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#106

Complements

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

N	H ≅ G/N	type
3. #20289779	C₂	direct (N × H)
9. D₅₃⋊M₃₂	C₄	semidirect
12. C₂×D₅₃⋊C₁₆	C₄	semidirect
16. D₅₃⋊#108	C₄	semidirect
18. C₂×#13133287	C₄	semidirect
40. D₅₃⋊C₁₆	C₂×C₄	semidirect
45. #13133287	C₂×C₄	semidirect
219. C₂×C₅₃	#1383	semidirect
223. D₅₃	#1383	semidirect
248. C₅₃	C₂×#1383	semidirect
439. C₂	#20289779	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⋊M₃₂	2
C₂×D₅₃⋊#108	2
#20289779	2
C₂×#106×D₅₃	2
C₂×#1383	53

Subgroups — C2×#20289779 #28310288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20289779 #28310288