Subgroups — #28306922

Order 13568.

714 conjugacy classes of subgroups.

The subgroup lattice has 510 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	C₂×D₅₃⋊#108	C₂	1	1	yes	maximal, characteristic
3	#20290423	C₂	1	2	yes	maximal
4	#20290408	C₂	1	2	yes	maximal
5	#405×D₅₃	C₂	1	1	yes	maximal, characteristic
6	C₂×D₅₃⋊M₁₆	C₂²	1	2	yes	—
7	C₂×D₅₃⋊M₁₆	C₂²	1	2	yes	—
8	C₂×#13133288	—	2	1	no	—
9	C₂×#13133288	C₄	1	2	yes	complemented
10	D₅₃⋊#108	—	2	1	no	—
11	D₅₃⋊#108	—	2	1	no	—
12	D₅₃⋊#108	—	2	1	no	—
13	D₅₃⋊#108	—	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	C₄	1	2	yes	complemented
18	C₂×#13133287	—	2	1	no	—
19	C₂×#13133287	C₄	1	2	yes	complemented
20	#16811504	—	2	4	no	—
21	#16811498	—	2	4	no	—
22	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
23	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
24	#117×D₅₃	C₂²	1	1	yes	characteristic
25	#16810581	C₄	1	1	yes	characteristic
26	#16810580	—	2	1	no	—
27	#16810579	C₄	1	1	yes	characteristic
28	#16810578	C₄	1	1	yes	characteristic
29	#16810577	—	2	1	no	—
30	#97×D₅₃	—	2	1	no	—
31	C₄×C₈×D₅₃	—	2	1	no	—
32	C₅₃×#405	C₄	1	1	yes	characteristic
33	C₂×#11719936	—	2	2	no	—
34	C₂×#11719936	C₂×C₄	1	4	yes	—
35	D₅₃⋊M₁₆	—	2	2	no	—
36	D₅₃⋊M₁₆	—	2	2	no	—
37	D₅₃⋊M₁₆	—	2	2	no	—
38	D₅₃⋊M₁₆	—	2	2	no	—
39	D₅₃⋊M₁₆	—	2	2	no	—
40	D₅₃⋊M₁₆	—	2	2	no	—
41	D₅₃⋊M₁₆	—	2	2	no	—
42	D₅₃⋊M₁₆	C₂×C₄	1	4	yes	—
43	C₂×#11719940	—	2	2	no	—
44	C₂×#11719940	—	2	2	no	—
45	C₂×D₅₃⋊C₈	—	2	2	no	—
46	C₂×D₅₃⋊C₈	—	2	2	no	—
47	#13133288	—	2	2	no	—
48	#13133288	—	2	2	no	—
49	#13133288	—	2	2	no	—
50	#13133288	—	2	2	no	—
51	#13133287	—	2	2	no	—
52	#13133287	—	2	2	no	—
53	#13133287	—	2	2	no	—
54	#13133287	—	2	2	no	—
55	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
56	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
57	C₂×#11719912	—	2	1	no	—
58	M₁₆×D₅₃	—	2	1	no	—
59	M₁₆×D₅₃	—	2	1	no	—
60	M₁₆×D₅₃	D₄	1	2	yes	—
61	M₁₆×D₅₃	Q₈	1	2	yes	—
62	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₅₃	—	2	1	no	—
64	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
69	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
70	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
71	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
72	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
73	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
74	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
75	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
76	#13133176	C₂×C₄	1	1	yes	characteristic
77	#13133175	—	2	1	no	—
78	#13133174	—	2	1	no	—
79	#13133173	D₄	1	2	yes	—
80	C₄⋊C₄×D₅₃	—	2	1	no	—
81	C₂²⋊C₄×D₅₃	Q₈	1	2	yes	—
82	C₄²×D₅₃	—	2	1	no	—
83	#13133128	—	2	1	no	—
84	#13133127	—	2	1	no	—
85	#13133127	—	2	1	no	—
86	C₄×#88322	—	2	1	no	—
87	C₈×Dic₅₃	—	2	1	no	—
88	C₈×Dic₅₃	—	2	1	no	—
89	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
91	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
92	#97×C₅₃	—	2	1	no	—
93	C₄×C₈×C₅₃	—	2	1	no	—
94	C₂³×D₅₃	C₂×Q₈	1	1	yes	characteristic
95	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×D₅₃	—	2	2	no	—
98	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
101	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
105	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
106	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
107	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
108	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
109	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
110	#11719940	—	2	4	no	—
111	#11719940	—	4	2	no	—
112	#11719940	—	4	2	no	—
113	#11719940	—	4	2	no	—
114	C₂×#88324	—	2	4	no	—
115	C₂×#88324	—	4	2	no	—
116	#11719936	—	2	4	no	—
117	#11719936	—	2	4	no	—
118	#11719936	—	2	4	no	—
119	#11719936	—	4	2	no	—
120	D₅₃⋊C₈	—	2	4	no	—
121	D₅₃⋊C₈	—	4	2	no	—
122	D₅₃⋊C₈	—	4	2	no	—
123	D₅₃⋊C₈	—	4	2	no	—
124	M₁₆×C₅₃	—	2	1	no	—
125	M₁₆×C₅₃	C₄⋊C₄	1	2	yes	—
126	C₂×C₈×C₅₃	—	2	1	no	—
127	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
128	C₂×C₈×C₅₃	C₄²	1	1	yes	characteristic
129	C₂×C₈×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₈×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
133	C₄⋊C₄×C₅₃	—	2	1	no	—
134	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	2	yes	—
135	C₄²×C₅₃	—	2	1	no	—
136	C₂²⋊Dic₅₃	C₄⋊C₄	1	2	yes	—
137	#11719921	—	2	2	no	—
138	C₄⋊Dic₅₃	—	2	1	no	—
139	#11719919	—	2	2	no	—
140	C₄×Dic₅₃	—	2	1	no	—
141	C₄×Dic₅₃	—	2	2	no	—
142	#11719917	—	2	1	no	—
143	#11719917	C₄⋊C₄	1	2	yes	—
144	C₂×#88322	—	2	1	no	—
145	C₂×#88322	C₄²	1	1	yes	characteristic
146	C₂×#88322	C₄²	1	1	yes	characteristic
147	C₂×#88322	C₂²⋊C₄	1	1	yes	characteristic
148	C₂×#88322	C₂²⋊C₄	1	1	yes	characteristic
149	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
150	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
151	#11719912	—	2	2	no	—
152	#11719912	—	2	2	no	—
153	C₈×D₅₃	—	2	2	no	—
154	C₈×D₅₃	—	2	2	no	—
155	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
156	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
157	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
158	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
159	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
160	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
161	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
162	C₈×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
163	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
164	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
165	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
166	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
167	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
168	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
169	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
170	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
171	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂²×D₅₃	—	4	2	no	—
173	C₂²×D₅₃	C₄×Q₈	1	1	yes	characteristic
174	C₂²×D₅₃	C₄×Q₈	1	1	yes	characteristic
175	C₂²×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
176	C₂²×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
177	C₂²×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
178	C₂²×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
179	C₂×C₄×C₅₃	—	2	2	no	—
180	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
181	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
185	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
186	C₂×Dic₅₃	—	2	2	no	—
187	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
188	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
189	C₂×Dic₅₃	#121	1	1	yes	characteristic
190	C₂×Dic₅₃	#121	1	1	yes	characteristic
191	C₂×Dic₅₃	#127	1	1	yes	characteristic
192	C₂×Dic₅₃	C₄⋊Q₈	1	1	yes	characteristic
193	C₄×D₅₃	—	4	4	no	—
194	C₄×D₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₄×D₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
199	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
200	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
201	C₄×D₅₃	C₄×Q₈	1	1	yes	characteristic
202	C₄×D₅₃	#121	1	1	yes	characteristic
203	C₄×D₅₃	#121	1	1	yes	characteristic
204	C₄×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
205	C₄×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
206	C₄×D₅₃	#124	1	1	yes	characteristic
207	C₄×D₅₃	#124	1	1	yes	characteristic
208	C₄×D₅₃	#125	1	1	yes	characteristic
209	C₄×D₅₃	#125	1	1	yes	characteristic
210	#88324	—	4	4	no	—
211	#88324	—	4	4	no	—
212	C₈×C₅₃	—	2	2	no	—
213	C₈×C₅₃	#95	1	1	yes	characteristic
214	C₈×C₅₃	#95	1	1	yes	characteristic
215	C₈×C₅₃	#95	1	1	yes	characteristic
216	C₈×C₅₃	#95	1	1	yes	characteristic
217	#88322	—	2	2	no	—
218	#88322	#95	1	1	yes	characteristic
219	#88322	#95	1	1	yes	characteristic
220	#88322	#95	1	1	yes	characteristic
221	#88322	#95	1	1	yes	characteristic
222	#10873	—	53	1	no	maximal, Sylow
223	C₂²×C₅₃	—	4	1	no	—
224	C₂²×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
225	C₂²×C₅₃	#380	1	1	yes	characteristic
226	C₂²×C₅₃	#384	1	1	yes	characteristic
227	C₂×D₅₃	—	2	2	no	—
228	C₂×D₅₃	—	2	2	no	—
229	C₂×D₅₃	—	2	2	no	—
230	C₂×D₅₃	—	4	1	no	—
231	C₂×D₅₃	—	4	1	no	—
232	C₂×D₅₃	—	4	1	no	—
233	C₂×D₅₃	#389	1	1	yes	characteristic
234	C₂×D₅₃	#389	1	1	yes	characteristic
235	C₂×D₅₃	#391	1	1	yes	characteristic
236	C₂×D₅₃	#391	1	1	yes	characteristic
237	C₄×C₅₃	—	4	2	no	—
238	C₄×C₅₃	C₂×#95	1	1	yes	characteristic
239	C₄×C₅₃	C₄×C₄⋊C₄	1	1	yes	characteristic
240	C₄×C₅₃	#380	1	1	yes	characteristic
241	C₄×C₅₃	#382	1	1	yes	characteristic
242	Dic₅₃	—	4	2	no	—
243	Dic₅₃	#389	1	1	yes	characteristic
244	Dic₅₃	#389	1	1	yes	characteristic
245	Dic₅₃	#390	1	1	yes	characteristic
246	Dic₅₃	#390	1	1	yes	characteristic
247	C₂²×#108	—	53	1	no	—
248	C₂²×#108	—	53	1	no	—
249	C₂×#405	—	53	1	no	—
250	C₂×#344	—	53	2	no	—
251	#1738	—	53	2	no	—
252	C₂×C₅₃	—	2	1	no	—
253	C₂×C₅₃	—	2	1	no	—
254	C₂×C₅₃	—	2	1	no	—
255	C₂×C₅₃	C₄⋊#95	1	1	yes	characteristic
256	D₅₃	—	2	1	no	—
257	D₅₃	—	2	1	no	—
258	D₅₃	—	2	1	no	—
259	D₅₃	#1953	1	2	yes	—
260	C₂²×M₁₆	—	53	1	no	—
261	C₂²×M₁₆	—	53	2	no	—
262	C₂²×M₁₆	—	53	2	no	—
263	C₂³×C₈	—	53	1	no	—
264	C₂×#117	—	53	1	no	—
265	C₂×#108	—	53	2	no	—
266	C₂×#108	—	53	2	no	—
267	C₂×#108	—	53	2	no	—
268	C₂×#108	—	53	2	no	—
269	C₂×#108	—	106	1	no	—
270	C₂×#108	—	106	1	no	—
271	C₂×#108	—	106	1	no	—
272	C₂×#108	—	106	1	no	—
273	C₂×#108	—	106	1	no	—
274	C₂×#108	—	106	1	no	—
275	C₂×#108	—	106	1	no	—
276	C₂×#108	—	106	1	no	—
277	#405	—	53	1	no	—
278	#405	—	53	1	no	—
279	#405	—	53	1	no	—
280	#405	—	106	1	no	—
281	#405	—	106	1	no	—
282	#405	#6157	1	1	yes	characteristic
283	C₂×#97	—	106	1	no	—
284	C₂×C₄×C₈	—	106	1	no	—
285	#344	—	106	4	no	—
286	#341	—	106	4	no	—
287	C₅₃	#10873	1	1	yes	characteristic, complemented, Sylow
288	C₂³×C₄	—	53	1	no	—
289	C₂×M₁₆	—	53	1	no	—
290	C₂×M₁₆	—	53	2	no	—
291	C₂×M₁₆	—	53	2	no	—
292	C₂×M₁₆	—	53	4	no	—
293	C₂×M₁₆	—	53	4	no	—
294	C₂×M₁₆	—	106	1	no	—
295	C₂×M₁₆	—	106	1	no	—
296	C₂×M₁₆	—	106	1	no	—
297	C₂×M₁₆	—	106	2	no	—
298	C₂×M₁₆	—	106	2	no	—
299	C₂×M₁₆	—	106	2	no	—
300	C₂×M₁₆	—	106	2	no	—
301	C₂×M₁₆	—	106	2	no	—
302	C₂×M₁₆	—	106	2	no	—
303	C₂×M₁₆	—	106	2	no	—
304	C₂×M₁₆	—	106	2	no	—
305	C₂×M₁₆	—	106	2	no	—
306	C₂×M₁₆	—	106	2	no	—
307	C₂×M₁₆	C₂×#6157	1	1	yes	characteristic
308	C₂²×C₈	—	53	1	no	—
309	C₂²×C₈	—	53	1	no	—
310	C₂²×C₈	—	53	1	no	—
311	C₂²×C₈	—	53	1	no	—
312	C₂²×C₈	—	53	1	no	—
313	C₂²×C₈	—	53	1	no	—
314	C₂²×C₈	—	53	1	no	—
315	C₂²×C₈	—	53	1	no	—
316	C₂²×C₈	—	53	1	no	—
317	C₂²×C₈	—	53	1	no	—
318	C₂²×C₈	—	53	1	no	—
319	C₂²×C₈	—	53	1	no	—
320	C₂²×C₈	—	53	1	no	—
321	C₂²×C₈	—	106	1	no	—
322	C₂²×C₈	—	106	2	no	—
323	C₂²×C₈	—	106	2	no	—
324	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
325	#117	—	53	1	no	—
326	#117	—	53	2	no	—
327	#117	—	106	1	no	—
328	#117	—	106	1	no	—
329	#117	C₂×#6157	1	1	yes	characteristic
330	C₂×C₄⋊C₄	—	106	1	no	—
331	C₂×C₂²⋊C₄	—	53	2	no	—
332	C₂×C₄²	—	106	1	no	—
333	#108	—	106	2	no	—
334	#108	—	106	2	no	—
335	#108	—	106	2	no	—
336	#108	—	106	2	no	—
337	#108	—	106	2	no	—
338	#108	—	106	2	no	—
339	#108	—	106	2	no	—
340	#108	—	106	2	no	—
341	#97	—	2	1	no	—
342	#97	—	106	1	no	—
343	#97	—	106	1	no	—
344	#97	—	106	1	no	—
345	C₄×C₈	—	2	1	no	—
346	C₄×C₈	—	106	1	no	—
347	C₄×C₈	—	106	1	no	—
348	C₄×C₈	—	106	1	no	—
349	C₂⁴	—	53	1	no	—
350	C₂²×C₄	—	53	1	no	—
351	C₂²×C₄	—	53	1	no	—
352	C₂²×C₄	—	53	1	no	—
353	C₂²×C₄	—	53	1	no	—
354	C₂²×C₄	—	53	1	no	—
355	C₂²×C₄	—	53	1	no	—
356	C₂²×C₄	—	53	1	no	—
357	C₂²×C₄	—	53	1	no	—
358	C₂²×C₄	—	53	1	no	—
359	C₂²×C₄	—	53	1	no	—
360	C₂²×C₄	—	53	1	no	—
361	C₂²×C₄	—	53	1	no	—
362	C₂²×C₄	—	53	1	no	—
363	C₂²×C₄	—	106	2	no	—
364	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
365	M₁₆	—	2	1	no	—
366	M₁₆	—	53	2	no	—
367	M₁₆	—	106	2	no	—
368	M₁₆	—	106	2	no	—
369	M₁₆	—	106	1	no	—
370	M₁₆	—	106	4	no	—
371	M₁₆	—	106	4	no	—
372	M₁₆	—	106	4	no	—
373	M₁₆	—	106	4	no	—
374	M₁₆	—	212	2	no	—
375	M₁₆	—	212	2	no	—
376	M₁₆	—	212	2	no	—
377	M₁₆	—	212	2	no	—
378	M₁₆	C₄⋊#6157	1	2	yes	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	53	1	no	—
381	C₂×C₈	—	53	1	no	—
382	C₂×C₈	—	53	1	no	—
383	C₂×C₈	—	53	1	no	—
384	C₂×C₈	—	53	1	no	—
385	C₂×C₈	—	53	1	no	—
386	C₂×C₈	—	53	1	no	—
387	C₂×C₈	—	53	1	no	—
388	C₂×C₈	—	53	1	no	—
389	C₂×C₈	—	53	1	no	—
390	C₂×C₈	—	53	1	no	—
391	C₂×C₈	—	53	1	no	—
392	C₂×C₈	—	53	1	no	—
393	C₂×C₈	—	53	1	no	—
394	C₂×C₈	—	53	1	no	—
395	C₂×C₈	—	53	1	no	—
396	C₂×C₈	—	53	1	no	—
397	C₂×C₈	—	53	1	no	—
398	C₂×C₈	—	53	1	no	—
399	C₂×C₈	—	53	1	no	—
400	C₂×C₈	—	53	1	no	—
401	C₂×C₈	—	53	1	no	—
402	C₂×C₈	—	106	2	no	—
403	C₂×C₈	—	106	2	no	—
404	C₂×C₈	—	106	1	no	—
405	C₂×C₈	—	106	4	no	—
406	C₂×C₈	—	106	4	no	—
407	C₂×C₈	—	212	2	no	—
408	C₂×C₈	—	212	2	no	—
409	C₂×C₈	—	212	2	no	—
410	C₂×C₈	—	212	2	no	—
411	C₂×C₈	C₄×#6157	1	1	yes	characteristic
412	C₂×C₈	C₄×#6157	1	1	yes	characteristic
413	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
414	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
415	C₂×C₈	C₂²⋊#6157	1	1	yes	characteristic
416	C₂×C₈	C₂²⋊#6157	1	1	yes	characteristic
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	106	2	no	—
419	C₄⋊C₄	—	106	1	no	—
420	C₂²⋊C₄	—	53	2	no	—
421	C₂²⋊C₄	—	106	2	no	—
422	C₂²⋊C₄	C₄⋊#6157	1	2	yes	—
423	C₄²	—	2	1	no	—
424	C₄²	—	106	2	no	—
425	C₄²	—	106	1	no	—
426	C₂³	—	53	1	no	—
427	C₂³	—	53	1	no	—
428	C₂³	—	53	1	no	—
429	C₂³	—	53	1	no	—
430	C₂³	—	53	1	no	—
431	C₂³	—	53	1	no	—
432	C₂³	—	212	2	no	—
433	C₂³	C₂×C₄⋊#6157	1	1	yes	characteristic
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	53	1	no	—
436	C₂×C₄	—	53	1	no	—
437	C₂×C₄	—	53	1	no	—
438	C₂×C₄	—	53	1	no	—
439	C₂×C₄	—	53	1	no	—
440	C₂×C₄	—	53	1	no	—
441	C₂×C₄	—	53	1	no	—
442	C₂×C₄	—	53	1	no	—
443	C₂×C₄	—	53	1	no	—
444	C₂×C₄	—	53	1	no	—
445	C₂×C₄	—	53	1	no	—
446	C₂×C₄	—	53	1	no	—
447	C₂×C₄	—	53	1	no	—
448	C₂×C₄	—	53	1	no	—
449	C₂×C₄	—	53	1	no	—
450	C₂×C₄	—	53	1	no	—
451	C₂×C₄	—	53	1	no	—
452	C₂×C₄	—	53	1	no	—
453	C₂×C₄	—	53	1	no	—
454	C₂×C₄	—	53	1	no	—
455	C₂×C₄	—	53	1	no	—
456	C₂×C₄	—	53	1	no	—
457	C₂×C₄	—	106	2	no	—
458	C₂×C₄	—	212	4	no	—
459	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
460	C₂×C₄	C₂×C₂²⋊#6157	1	1	yes	characteristic
461	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
462	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
463	C₂×C₄	#13133296	1	1	yes	characteristic
464	C₂×C₄	#13133296	1	1	yes	characteristic
465	C₈	—	2	2	no	—
466	C₈	—	53	1	no	—
467	C₈	—	53	1	no	—
468	C₈	—	53	1	no	—
469	C₈	—	53	1	no	—
470	C₈	—	106	2	no	—
471	C₈	—	212	4	no	—
472	C₈	—	212	4	no	—
473	C₈	(C₂×#6157)⋊C₄	1	1	yes	characteristic
474	C₈	(C₂×#6157)⋊C₄	1	1	yes	characteristic
475	C₈	(C₂×#6157)⋊C₄	1	1	yes	characteristic
476	C₈	(C₂×#6157)⋊C₄	1	1	yes	characteristic
477	C₂²	—	4	1	no	—
478	C₂²	—	53	1	no	—
479	C₂²	—	53	1	no	—
480	C₂²	—	53	1	no	—
481	C₂²	—	53	1	no	—
482	C₂²	—	106	2	no	—
483	C₂²	—	106	2	no	—
484	C₂²	—	106	2	no	—
485	C₂²	—	212	1	no	—
486	C₂²	—	212	1	no	—
487	C₂²	—	212	1	no	—
488	C₂²	C₄×C₄⋊#6157	1	1	yes	characteristic
489	C₂²	#16811565	1	1	yes	characteristic
490	C₂²	#16811569	1	1	yes	characteristic
491	C₄	—	4	2	no	—
492	C₄	—	53	1	no	—
493	C₄	—	53	1	no	—
494	C₄	—	53	1	no	—
495	C₄	—	53	1	no	—
496	C₄	—	212	2	no	—
497	C₄	C₂×(C₂×#6157)⋊C₄	1	1	yes	characteristic
498	C₄	C₄×C₄⋊#6157	1	1	yes	characteristic
499	C₄	#16811565	1	1	yes	characteristic
500	C₄	#16811567	1	1	yes	characteristic
501	C₂	—	2	1	no	—
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	53	2	no	—
505	C₂	—	106	1	no	—
506	C₂	—	106	1	no	—
507	C₂	—	106	1	no	—
508	C₂	#20289893	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16811565
commutator	C₂×C₄×C₅₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×#6157
Fitting	C₅₃×#405	C₄
socle	C₂×C₅₃	C₄⋊#95
prime radical	C₂³×D₅₃	C₂×Q₈
cosocle	C₂²×C₄×D₅₃	C₂³
hypercenter	#405	#6157
hypocenter	C₅₃	#10873
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
9. C₂×#13133288	C₄	semidirect
16. D₅₃⋊#108	C₄	semidirect
17. D₅₃⋊#108	C₄	semidirect
19. C₂×#13133287	C₄	semidirect
287. C₅₃	#10873	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
#20290423	2
#20290408	2
#405×D₅₃	2
#10873	53