Subgroups — #28306908

Order 13568.

774 conjugacy classes of subgroups.

The subgroup lattice has 464 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×#13133285	C₂	1	1	yes	maximal, characteristic
3	C₂×#16811502	C₂	1	2	yes	maximal
4	#20290404	C₂	1	2	yes	maximal
5	#405×D₅₃	C₂	1	1	yes	maximal, characteristic
6	C₂×D₅₃⋊M₁₆	C₂²	1	2	yes	—
7	C₂²×C₄⋊#6157	C₂²	1	2	yes	—
8	C₂×#13133288	—	2	1	no	—
9	D₅₃⋊#108	—	2	2	no	—
10	D₅₃⋊#108	C₄	1	4	yes	complemented
11	C₂×#13133287	—	2	1	no	—
12	C₂×#13133285	—	2	2	no	—
13	C₂×#13133285	—	2	1	no	—
14	C₂×#13133285	—	2	1	no	—
15	C₂×#13133285	C₄	1	4	yes	complemented
16	#16811502	—	2	4	no	—
17	#16811496	—	2	4	no	—
18	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
20	#117×D₅₃	C₂²	1	1	yes	characteristic
21	#16810581	C₄	1	1	yes	characteristic, complemented
22	#16810580	—	2	1	no	—
23	#16810579	C₄	1	1	yes	characteristic, complemented
24	#16810578	C₄	1	1	yes	characteristic, complemented
25	#16810577	—	2	1	no	—
26	#97×D₅₃	—	2	1	no	—
27	C₄×C₈×D₅₃	—	2	1	no	—
28	C₅₃×#405	C₄	1	1	yes	characteristic, complemented
29	C₂³×#6157	—	2	2	no	—
30	C₂×#11719936	—	2	2	no	—
31	D₅₃⋊M₁₆	—	2	2	no	—
32	D₅₃⋊M₁₆	—	2	2	no	—
33	D₅₃⋊M₁₆	—	2	2	no	—
34	D₅₃⋊M₁₆	C₂×C₄	1	4	yes	—
35	C₂×#11719940	—	2	2	no	—
36	C₂×D₅₃⋊C₈	—	2	2	no	—
37	C₂×C₄⋊#6157	—	2	2	no	—
38	C₂×C₄⋊#6157	—	2	2	no	—
39	C₂×C₄⋊#6157	—	2	2	no	—
40	C₂×C₄⋊#6157	—	2	2	no	—
41	C₂×C₄⋊#6157	—	2	2	no	—
42	C₂×C₄⋊#6157	C₂×C₄	1	4	yes	—
43	#13133288	—	2	4	no	—
44	#13133287	—	2	4	no	—
45	#13133285	—	2	4	no	—
46	#13133285	—	2	4	no	—
47	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
48	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
49	C₂×#11719912	—	2	1	no	—
50	M₁₆×D₅₃	—	2	1	no	—
51	M₁₆×D₅₃	—	2	1	no	—
52	M₁₆×D₅₃	D₄	1	2	yes	—
53	M₁₆×D₅₃	Q₈	1	2	yes	—
54	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₅₃	—	2	1	no	—
56	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
57	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
58	C₂×C₈×D₅₃	D₄	1	2	yes	—
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	D₄	1	1	yes	characteristic
63	C₂×C₈×D₅₃	Q₈	1	2	yes	—
64	#13133176	C₂×C₄	1	1	yes	characteristic
65	#13133175	Q₈	1	2	yes	—
66	#13133174	—	2	1	no	—
67	#13133173	—	2	1	no	—
68	C₄⋊C₄×D₅₃	D₄	1	2	yes	—
69	C₂²⋊C₄×D₅₃	—	2	1	no	—
70	C₄²×D₅₃	—	2	1	no	—
71	#13133128	—	2	1	no	—
72	#13133127	—	2	1	no	—
73	#13133127	—	2	1	no	—
74	C₄×#88322	—	2	1	no	—
75	C₈×Dic₅₃	—	2	1	no	—
76	C₈×Dic₅₃	—	2	1	no	—
77	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
79	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
80	#97×C₅₃	—	2	1	no	—
81	C₄×C₈×C₅₃	—	2	1	no	—
82	C₂³×D₅₃	#41	1	1	yes	characteristic
83	C₂²×#6157	—	2	4	no	—
84	C₂²×#6157	—	4	2	no	—
85	C₂²×#6157	—	4	2	no	—
86	C₂²×#6157	—	8	4	no	—
87	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×Dic₅₃	#41	1	1	yes	characteristic
89	C₂×C₄×D₅₃	—	2	2	no	—
90	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
93	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
94	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
96	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
98	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
100	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
101	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
102	#11719940	—	2	4	no	—
103	#11719940	—	4	2	no	—
104	C₂×#88324	—	4	2	no	—
105	C₄⋊#6157	—	2	4	no	—
106	C₄⋊#6157	—	2	4	no	—
107	C₄⋊#6157	—	4	2	no	—
108	C₄⋊#6157	—	4	2	no	—
109	#11719936	—	2	4	no	—
110	#11719936	—	4	2	no	—
111	D₅₃⋊C₈	—	2	4	no	—
112	D₅₃⋊C₈	—	4	2	no	—
113	M₁₆×C₅₃	—	2	1	no	—
114	M₁₆×C₅₃	C₄⋊C₄	1	2	yes	—
115	C₂×C₈×C₅₃	—	2	1	no	—
116	C₂×C₈×C₅₃	C₄²	1	2	yes	—
117	C₂×C₈×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₈×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₈×C₅₃	C₄⋊C₄	1	2	yes	—
120	C₄⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
121	C₂²⋊C₄×C₅₃	—	2	1	no	—
122	C₄²×C₅₃	—	2	1	no	—
123	C₂²⋊Dic₅₃	—	2	1	no	—
124	#11719921	—	2	2	no	—
125	C₄⋊Dic₅₃	C₄⋊C₄	1	2	yes	—
126	#11719919	—	2	2	no	—
127	C₄×Dic₅₃	—	2	1	no	—
128	C₄×Dic₅₃	—	2	2	no	—
129	#11719917	—	2	1	no	—
130	#11719917	C₄⋊C₄	1	2	yes	—
131	C₂×#88322	—	2	1	no	—
132	C₂×#88322	C₄²	1	2	yes	—
133	C₂×#88322	C₂²⋊C₄	1	1	yes	characteristic
134	C₂×#88322	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×#88322	C₄⋊C₄	1	2	yes	—
136	#11719912	—	2	2	no	—
137	#11719912	—	2	2	no	—
138	C₈×D₅₃	—	2	2	no	—
139	C₈×D₅₃	—	2	2	no	—
140	C₈×D₅₃	C₂²⋊C₄	1	2	yes	—
141	C₈×D₅₃	C₂²⋊C₄	1	2	yes	—
142	C₈×D₅₃	C₂²⋊C₄	1	2	yes	—
143	C₈×D₅₃	C₂²⋊C₄	1	2	yes	—
144	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
145	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
146	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
147	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
148	C₂³×C₅₃	#117	1	1	yes	characteristic
149	C₂²×D₅₃	—	2	4	no	—
150	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
151	C₂²×D₅₃	C₄×Q₈	1	1	yes	characteristic
152	C₂²×D₅₃	#121	1	1	yes	characteristic
153	C₂²×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂²×D₅₃	#124	1	1	yes	characteristic
155	C₂²×D₅₃	#125	1	1	yes	characteristic
156	C₂×#6157	—	4	4	no	—
157	C₂×#6157	—	8	4	no	—
158	C₂×#6157	—	8	4	no	—
159	C₂×#6157	—	8	4	no	—
160	C₂×C₄×C₅₃	—	2	2	no	—
161	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
167	C₂×Dic₅₃	—	2	2	no	—
168	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
169	C₂×Dic₅₃	C₄×Q₈	1	1	yes	characteristic
170	C₂×Dic₅₃	#121	1	1	yes	characteristic
171	C₂×Dic₅₃	C₂²⋊Q₈	1	1	yes	characteristic
172	C₂×Dic₅₃	#124	1	1	yes	characteristic
173	C₂×Dic₅₃	#125	1	1	yes	characteristic
174	C₄×D₅₃	—	4	4	no	—
175	C₄×D₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₄×D₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
180	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
181	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
182	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
183	C₄×D₅₃	#121	1	1	yes	characteristic
184	C₄×D₅₃	#121	1	1	yes	characteristic
185	C₄×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
186	C₄×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
187	C₄×D₅₃	#127	1	1	yes	characteristic
188	C₄×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
189	C₄×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
190	C₄×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
191	#88324	—	4	4	no	—
192	C₈×C₅₃	—	2	2	no	—
193	C₈×C₅₃	#95	1	2	yes	—
194	C₈×C₅₃	#95	1	2	yes	—
195	#88322	—	2	2	no	—
196	#88322	#95	1	2	yes	—
197	#88322	#95	1	2	yes	—
198	#10869	—	53	1	no	maximal, Sylow
199	C₂²×C₅₃	—	2	2	no	—
200	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
201	C₂²×C₅₃	#380	1	1	yes	characteristic
202	C₂²×C₅₃	#382	1	1	yes	characteristic
203	C₂×D₅₃	—	2	2	no	—
204	C₂×D₅₃	—	2	2	no	—
205	C₂×D₅₃	—	2	2	no	—
206	C₂×D₅₃	—	2	2	no	—
207	C₂×D₅₃	—	2	2	no	—
208	C₂×D₅₃	#389	1	1	yes	characteristic
209	C₂×D₅₃	#389	1	1	yes	characteristic
210	C₂×D₅₃	#390	1	1	yes	characteristic
211	C₂×D₅₃	#391	1	1	yes	characteristic
212	C₂×D₅₃	#471	1	4	yes	—
213	#6157	—	8	4	no	—
214	C₄×C₅₃	—	4	2	no	—
215	C₄×C₅₃	C₂×#95	1	1	yes	characteristic
216	C₄×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
217	C₄×C₅₃	#380	1	1	yes	characteristic
218	C₄×C₅₃	#384	1	1	yes	characteristic
219	Dic₅₃	—	4	2	no	—
220	Dic₅₃	#389	1	1	yes	characteristic
221	Dic₅₃	#389	1	1	yes	characteristic
222	Dic₅₃	#390	1	1	yes	characteristic
223	Dic₅₃	#391	1	1	yes	characteristic
224	C₂²×#108	—	53	1	no	—
225	C₂²×#106	—	53	1	no	—
226	C₂×#405	—	53	1	no	—
227	C₂×#343	—	53	2	no	—
228	#1736	—	53	2	no	—
229	C₂×C₅₃	—	2	1	no	—
230	C₂×C₅₃	—	2	1	no	—
231	C₂×C₅₃	C₄⋊#95	1	1	yes	characteristic
232	C₂×C₅₃	#1815	1	2	yes	—
233	D₅₃	—	2	1	no	—
234	D₅₃	—	2	1	no	—
235	D₅₃	#1951	1	2	yes	—
236	D₅₃	#1977	1	2	yes	—
237	C₂²×M₁₆	—	53	1	no	—
238	C₂²×M₁₆	—	53	2	no	—
239	C₂³×C₈	—	53	1	no	—
240	C₂×#117	—	53	1	no	—
241	C₂²×C₄⋊C₄	—	53	2	no	—
242	C₂×#108	—	53	4	no	—
243	C₂×#108	—	106	1	no	—
244	C₂×#108	—	106	2	no	—
245	C₂×#108	—	106	1	no	—
246	C₂×#106	—	53	4	no	—
247	C₂×#106	—	106	2	no	—
248	C₂×#106	—	106	1	no	—
249	C₂×#106	—	106	1	no	—
250	#405	—	53	1	no	—
251	#405	—	53	1	no	—
252	#405	—	53	1	no	—
253	#405	—	106	1	no	—
254	#405	—	106	1	no	—
255	#405	#6157	1	1	yes	characteristic, complemented
256	C₂×#97	—	106	1	no	—
257	C₂×C₄×C₈	—	106	1	no	—
258	#343	—	106	4	no	—
259	#340	—	106	4	no	—
260	C₅₃	#10869	1	1	yes	characteristic, complemented, Sylow
261	C₂³×C₄	—	53	1	no	—
262	C₂³×C₄	—	106	2	no	—
263	C₂×M₁₆	—	53	1	no	—
264	C₂×M₁₆	—	53	2	no	—
265	C₂×M₁₆	—	53	2	no	—
266	C₂×M₁₆	—	53	4	no	—
267	C₂×M₁₆	—	106	1	no	—
268	C₂×M₁₆	—	106	1	no	—
269	C₂×M₁₆	—	106	1	no	—
270	C₂×M₁₆	—	106	2	no	—
271	C₂×M₁₆	—	106	2	no	—
272	C₂×M₁₆	—	106	2	no	—
273	C₂×M₁₆	—	106	2	no	—
274	C₂×M₁₆	—	106	2	no	—
275	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
276	C₂²×C₈	—	53	1	no	—
277	C₂²×C₈	—	53	2	no	—
278	C₂²×C₈	—	53	2	no	—
279	C₂²×C₈	—	53	2	no	—
280	C₂²×C₈	—	53	2	no	—
281	C₂²×C₈	—	53	1	no	—
282	C₂²×C₈	—	53	1	no	—
283	C₂²×C₈	—	53	1	no	—
284	C₂²×C₈	—	53	1	no	—
285	C₂²×C₈	—	106	1	no	—
286	C₂²×C₈	—	106	2	no	—
287	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
288	#117	—	53	1	no	—
289	#117	—	53	2	no	—
290	#117	—	106	1	no	—
291	#117	—	106	1	no	—
292	#117	C₂×#6157	1	1	yes	characteristic
293	C₂×C₄⋊C₄	—	53	2	no	—
294	C₂×C₄⋊C₄	—	53	4	no	—
295	C₂×C₄⋊C₄	—	106	2	no	—
296	C₂×C₄⋊C₄	—	106	2	no	—
297	C₂×C₄⋊C₄	—	106	2	no	—
298	C₂×C₄⋊C₄	—	106	2	no	—
299	C₂×C₄⋊C₄	—	106	2	no	—
300	C₂×C₂²⋊C₄	—	106	1	no	—
301	C₂×C₄²	—	106	1	no	—
302	#108	—	106	4	no	—
303	#108	—	106	4	no	—
304	#106	—	106	4	no	—
305	#106	—	106	4	no	—
306	#97	—	2	1	no	—
307	#97	—	106	1	no	—
308	#97	—	106	1	no	—
309	#97	—	106	1	no	—
310	C₄×C₈	—	2	1	no	—
311	C₄×C₈	—	106	1	no	—
312	C₄×C₈	—	106	1	no	—
313	C₄×C₈	—	106	1	no	—
314	C₂⁴	—	53	1	no	—
315	C₂²×C₄	—	53	1	no	—
316	C₂²×C₄	—	53	1	no	—
317	C₂²×C₄	—	53	1	no	—
318	C₂²×C₄	—	53	1	no	—
319	C₂²×C₄	—	53	1	no	—
320	C₂²×C₄	—	53	1	no	—
321	C₂²×C₄	—	53	1	no	—
322	C₂²×C₄	—	53	1	no	—
323	C₂²×C₄	—	53	1	no	—
324	C₂²×C₄	—	53	1	no	—
325	C₂²×C₄	—	53	1	no	—
326	C₂²×C₄	—	53	1	no	—
327	C₂²×C₄	—	53	1	no	—
328	C₂²×C₄	—	106	2	no	—
329	C₂²×C₄	—	106	4	no	—
330	C₂²×C₄	—	424	4	no	—
331	C₂²×C₄	—	212	2	no	—
332	C₂²×C₄	—	212	2	no	—
333	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
334	M₁₆	—	2	1	no	—
335	M₁₆	—	53	2	no	—
336	M₁₆	—	106	2	no	—
337	M₁₆	—	106	2	no	—
338	M₁₆	—	106	1	no	—
339	M₁₆	—	106	4	no	—
340	M₁₆	—	106	4	no	—
341	M₁₆	—	212	2	no	—
342	M₁₆	—	212	2	no	—
343	M₁₆	C₄⋊#6157	1	2	yes	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	53	2	no	—
346	C₂×C₈	—	53	1	no	—
347	C₂×C₈	—	53	1	no	—
348	C₂×C₈	—	53	2	no	—
349	C₂×C₈	—	53	2	no	—
350	C₂×C₈	—	53	2	no	—
351	C₂×C₈	—	53	2	no	—
352	C₂×C₈	—	53	2	no	—
353	C₂×C₈	—	53	2	no	—
354	C₂×C₈	—	53	2	no	—
355	C₂×C₈	—	53	2	no	—
356	C₂×C₈	—	53	2	no	—
357	C₂×C₈	—	106	2	no	—
358	C₂×C₈	—	106	2	no	—
359	C₂×C₈	—	106	1	no	—
360	C₂×C₈	—	106	4	no	—
361	C₂×C₈	—	212	2	no	—
362	C₂×C₈	—	212	2	no	—
363	C₂×C₈	C₄×#6157	1	2	yes	—
364	C₂×C₈	C₄⋊#6157	1	2	yes	—
365	C₂×C₈	C₂²⋊#6157	1	1	yes	characteristic
366	C₂×C₈	C₂²⋊#6157	1	1	yes	characteristic
367	C₄⋊C₄	—	53	2	no	—
368	C₄⋊C₄	—	106	2	no	—
369	C₄⋊C₄	—	106	4	no	—
370	C₄⋊C₄	—	106	4	no	—
371	C₄⋊C₄	—	212	2	no	—
372	C₄⋊C₄	—	212	2	no	—
373	C₄⋊C₄	C₄⋊#6157	1	2	yes	—
374	C₂²⋊C₄	—	2	1	no	—
375	C₂²⋊C₄	—	106	2	no	—
376	C₂²⋊C₄	—	106	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	106	2	no	—
379	C₄²	—	106	1	no	—
380	C₂³	—	53	1	no	—
381	C₂³	—	53	1	no	—
382	C₂³	—	53	1	no	—
383	C₂³	—	53	1	no	—
384	C₂³	—	53	1	no	—
385	C₂³	—	53	1	no	—
386	C₂³	—	106	4	no	—
387	C₂³	#13133296	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	53	1	no	—
390	C₂×C₄	—	53	1	no	—
391	C₂×C₄	—	53	1	no	—
392	C₂×C₄	—	53	1	no	—
393	C₂×C₄	—	53	1	no	—
394	C₂×C₄	—	53	1	no	—
395	C₂×C₄	—	53	1	no	—
396	C₂×C₄	—	53	1	no	—
397	C₂×C₄	—	53	1	no	—
398	C₂×C₄	—	53	1	no	—
399	C₂×C₄	—	53	1	no	—
400	C₂×C₄	—	53	1	no	—
401	C₂×C₄	—	53	1	no	—
402	C₂×C₄	—	53	1	no	—
403	C₂×C₄	—	53	1	no	—
404	C₂×C₄	—	53	1	no	—
405	C₂×C₄	—	53	1	no	—
406	C₂×C₄	—	53	1	no	—
407	C₂×C₄	—	53	1	no	—
408	C₂×C₄	—	53	1	no	—
409	C₂×C₄	—	53	1	no	—
410	C₂×C₄	—	53	1	no	—
411	C₂×C₄	—	106	2	no	—
412	C₂×C₄	—	424	4	no	—
413	C₂×C₄	—	424	4	no	—
414	C₂×C₄	—	424	4	no	—
415	C₂×C₄	—	212	4	no	—
416	C₂×C₄	—	212	4	no	—
417	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
418	C₂×C₄	C₂×C₂²⋊#6157	1	1	yes	characteristic
419	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
420	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
421	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
422	C₂×C₄	#13133296	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	53	2	no	—
425	C₈	—	53	2	no	—
426	C₈	—	106	2	no	—
427	C₈	—	212	4	no	—
428	C₈	(C₂×#6157)⋊C₄	1	2	yes	—
429	C₈	(C₂×#6157)⋊C₄	1	2	yes	—
430	C₂²	—	2	2	no	—
431	C₂²	—	53	4	no	—
432	C₂²	—	53	1	no	—
433	C₂²	—	53	1	no	—
434	C₂²	—	53	1	no	—
435	C₂²	—	53	1	no	—
436	C₂²	—	106	2	no	—
437	C₂²	—	106	2	no	—
438	C₂²	—	106	2	no	—
439	C₂²	—	106	2	no	—
440	C₂²	—	106	2	no	—
441	C₂²	C₄×C₄⋊#6157	1	1	yes	characteristic
442	C₂²	#16811565	1	1	yes	characteristic
443	C₂²	#16811567	1	1	yes	characteristic
444	C₄	—	4	2	no	—
445	C₄	—	53	1	no	—
446	C₄	—	53	1	no	—
447	C₄	—	53	1	no	—
448	C₄	—	53	1	no	—
449	C₄	—	424	4	no	—
450	C₄	—	212	2	no	—
451	C₄	C₂×(C₂×#6157)⋊C₄	1	1	yes	characteristic
452	C₄	C₄×C₄⋊#6157	1	1	yes	characteristic
453	C₄	#16811565	1	1	yes	characteristic
454	C₄	#16811569	1	1	yes	characteristic
455	C₂	—	2	1	no	—
456	C₂	—	2	1	no	—
457	C₂	—	53	2	no	—
458	C₂	—	53	2	no	—
459	C₂	—	106	1	no	—
460	C₂	—	106	1	no	—
461	C₂	#20289893	1	1	yes	characteristic
462	C₂	#20290603	1	2	yes	—

	subgroup	G/H
center	C₂²	#16811565
commutator	C₂×C₄×C₅₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×#6157
Fitting	C₅₃×#405	C₄
socle	C₂²×C₅₃	#380
prime radical	C₂³×D₅₃	#41
cosocle	C₂²×C₄×D₅₃	C₂³
hypercenter	#405	#6157
hypocenter	C₅₃	#10869
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
10. D₅₃⋊#108	C₄	semidirect
15. C₂×#13133285	C₄	semidirect
21. #16810581	C₄	semidirect
23. #16810579	C₄	semidirect
24. #16810578	C₄	semidirect
28. C₅₃×#405	C₄	semidirect
255. #405	#6157	semidirect
260. C₅₃	#10869	semidirect

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×#13133285	2
C₂×#16811502	2
#20290404	2
#405×D₅₃	2
#10869	53