Subgroups — #28318616

Order 13568.

998 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₃⋊#443	C₂	1	1	yes	maximal, characteristic
2	#135×#6157	C₂	1	1	yes	maximal, characteristic
3	#20291285	C₂	1	2	yes	maximal, complemented
4	#108×#6157	C₂	1	1	yes	maximal, characteristic, complemented
5	#20290520	C₂	1	1	yes	maximal, characteristic, complemented
6	#20290517	C₂	1	1	yes	maximal, characteristic, complemented
7	#20290495	C₂	1	2	yes	maximal, complemented
8	#20290493	C₂	1	2	yes	maximal, complemented
9	#20290480	C₂	1	2	yes	maximal, complemented
10	#20290371	C₂	1	1	yes	maximal, characteristic, complemented
11	#443×D₅₃	C₂	1	1	yes	maximal, characteristic
12	D₅₃⋊#131	C₂²	1	2	yes	—
13	#41×#6157	C₂²	1	2	yes	—
14	#16811667	C₄	1	2	yes	complemented
15	#16811666	C₄	1	4	yes	complemented
16	#16811665	C₄	1	2	yes	complemented
17	Q₁₆×#6157	C₄	1	2	yes	complemented
18	SD₁₆×#6157	C₄	1	4	yes	complemented
19	D₈×#6157	C₄	1	2	yes	complemented
20	D₅₃⋊#108	C₂²	1	1	yes	characteristic
21	#16811633	C₂²	1	1	yes	characteristic
22	D₅₃⋊#104	C₂²	1	2	yes	—
23	#16811613	C₂²	1	2	yes	—
24	#16811589	—	2	2	no	—
25	#16811589	C₂²	1	2	yes	—
26	#16811586	—	2	2	no	—
27	#16811586	C₂²	1	2	yes	—
28	M₁₆×#6157	—	2	2	no	—
29	M₁₆×#6157	C₂²	1	2	yes	—
30	#16811582	C₂²	1	1	yes	characteristic
31	C₂×#13133271	—	2	2	no	—
32	C₂×#13133271	C₂²	1	1	yes	characteristic
33	C₂×#13133271	C₂²	1	1	yes	characteristic
34	C₂×C₈×#6157	C₂²	1	1	yes	characteristic
35	C₂×C₈×#6157	C₂²	1	1	yes	characteristic
36	#16811559	C₂²	1	1	yes	characteristic
37	#16811498	C₂²	1	2	yes	—
38	#16811495	C₂²	1	2	yes	—
39	#16811494	C₂²	1	2	yes	—
40	#135×D₅₃	C₂²	1	1	yes	characteristic
41	#131×D₅₃	C₂²	1	2	yes	—
42	#16810741	C₄	1	1	yes	characteristic, complemented
43	#16810740	C₄	1	1	yes	characteristic, complemented
44	#16810739	C₄	1	1	yes	characteristic, complemented
45	#16810738	C₄	1	2	yes	complemented
46	#16810737	C₄	1	2	yes	complemented
47	#108×D₅₃	C₂²	1	1	yes	characteristic
48	#104×D₅₃	C₂²	1	2	yes	—
49	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
50	C₅₃×#443	C₄	1	1	yes	characteristic, complemented
51	#13133305	C₂×C₄	1	4	yes	complemented
52	#13133304	—	2	4	no	—
53	#13133304	C₂×C₄	1	4	yes	complemented
54	D₅₃⋊M₁₆	—	2	2	no	—
55	D₅₃⋊M₁₆	C₂³	1	2	yes	—
56	C₂×D₅₃⋊C₈	—	2	2	no	—
57	C₂×D₅₃⋊C₈	C₂³	1	1	yes	characteristic
58	C₂×D₅₃⋊C₈	C₂³	1	1	yes	characteristic
59	Q₈×#6157	C₂×C₄	1	4	yes	—
60	D₄×#6157	—	2	4	no	—
61	D₄×#6157	C₂×C₄	1	4	yes	—
62	#13133296	—	2	2	no	—
63	#13133296	C₂³	1	2	yes	—
64	C₂×C₄×#6157	—	2	2	no	—
65	C₂×C₄×#6157	C₂³	1	1	yes	characteristic
66	C₂×C₄×#6157	C₂³	1	1	yes	characteristic
67	#13133288	C₂×C₄	1	2	yes	complemented
68	#13133287	C₂×C₄	1	2	yes	complemented
69	#13133286	C₂×C₄	1	2	yes	—
70	#13133285	C₂×C₄	1	2	yes	—
71	#13133282	C₂×C₄	1	4	yes	complemented
72	#13133281	C₂×C₄	1	4	yes	complemented
73	#13133280	C₂×C₄	1	4	yes	—
74	#13133279	C₂×C₄	1	4	yes	—
75	#13133272	—	2	2	no	—
76	#13133271	—	2	2	no	—
77	#13133271	—	2	2	no	—
78	#13133271	—	2	1	no	—
79	#13133271	—	2	1	no	—
80	#13133271	—	2	2	no	—
81	#13133271	D₄	1	1	yes	characteristic
82	#13133271	D₄	1	1	yes	characteristic
83	#13133271	D₄	1	1	yes	characteristic
84	#13133271	D₄	1	1	yes	characteristic
85	C₈×#6157	—	2	2	no	—
86	C₈×#6157	—	2	2	no	—
87	C₈×#6157	—	2	2	no	—
88	C₈×#6157	C₂×C₄	1	2	yes	—
89	C₈×#6157	C₂×C₄	1	2	yes	—
90	C₈×#6157	C₂×C₄	1	2	yes	complemented
91	C₈×#6157	C₂×C₄	1	2	yes	complemented
92	(C₂×#6157)⋊C₄	—	2	2	no	—
93	#41×D₅₃	C₂³	1	2	yes	—
94	#13133240	C₂×C₄	1	1	yes	characteristic
95	#13133239	C₂×C₄	1	1	yes	characteristic
96	#13133238	C₂×C₄	1	2	yes	—
97	#13133237	C₂×C₄	1	2	yes	—
98	#13133236	C₂×C₄	1	1	yes	characteristic
99	Q₁₆×D₅₃	C₂×C₄	1	1	yes	characteristic
100	SD₁₆×D₅₃	C₂×C₄	1	2	yes	—
101	D₈×D₅₃	C₂×C₄	1	1	yes	characteristic
102	#13133225	—	2	2	no	—
103	#13133225	C₂×C₄	1	2	yes	complemented
104	#13133224	C₂×C₄	1	2	yes	complemented
105	#13133223	—	2	2	no	—
106	#13133223	C₂×C₄	1	2	yes	complemented
107	M₁₆×D₅₃	—	2	2	no	—
108	M₁₆×D₅₃	C₂³	1	2	yes	—
109	C₂×C₈×D₅₃	—	2	2	no	—
110	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
111	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
112	C₄²×D₅₃	C₂³	1	1	yes	characteristic
113	#13133153	C₂×C₄	1	1	yes	characteristic, complemented
114	#13133152	C₂×C₄	1	2	yes	complemented
115	#13133145	C₂×C₄	1	2	yes	complemented
116	#13133144	C₂×C₄	1	2	yes	complemented
117	#13133143	C₂×C₄	1	2	yes	complemented
118	C₄×#88322	C₂×C₄	1	1	yes	characteristic, complemented
119	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic, complemented
120	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic, complemented
121	#135×C₅₃	C₂×C₄	1	1	yes	characteristic
122	#131×C₅₃	C₂×C₄	1	2	yes	complemented
123	#108×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
124	#104×C₅₃	C₂×C₄	1	2	yes	complemented
125	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
126	C₂²×#6157	—	2	1	no	—
127	C₂²×#6157	—	2	4	no	—
128	C₂²×#6157	#41	1	2	yes	—
129	#41×C₅₃	C₂²×C₄	1	2	yes	—
130	#11719949	C₂²×C₄	1	2	yes	—
131	Q₈×D₅₃	C₂²×C₄	1	2	yes	—
132	#11719947	—	2	2	no	—
133	#11719947	C₂²×C₄	1	2	yes	—
134	D₄×D₅₃	—	2	2	no	—
135	D₄×D₅₃	C₂²×C₄	1	2	yes	—
136	#11719945	—	2	2	no	—
137	#11719945	C₂²×C₄	1	2	yes	—
138	C₂×C₄×D₅₃	—	2	2	no	—
139	C₂×C₄×D₅₃	—	2	1	no	—
140	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
141	C₂²⋊#6157	—	2	2	no	—
142	C₂²⋊#6157	—	2	4	no	—
143	#11719940	—	2	2	no	—
144	#11719940	—	2	4	no	—
145	C₂×#88324	—	2	1	no	—
146	C₂×#88324	—	2	4	no	—
147	C₂×#88324	#41	1	2	yes	—
148	C₄⋊#6157	—	2	4	no	—
149	C₄⋊#6157	C₂²×C₄	1	4	yes	—
150	C₄×#6157	—	2	4	no	—
151	C₄×#6157	—	2	2	no	—
152	C₄×#6157	—	2	1	no	—
153	C₄×#6157	C₂²×C₄	1	2	yes	—
154	C₄×#6157	C₂²×C₄	1	2	yes	—
155	C₄×#6157	C₂×D₄	1	1	yes	characteristic
156	C₄×#6157	C₂×D₄	1	1	yes	characteristic
157	#11719936	—	2	4	no	—
158	#11719936	C₂²×C₄	1	4	yes	—
159	D₅₃⋊C₈	—	2	2	no	—
160	D₅₃⋊C₈	—	2	1	no	—
161	D₅₃⋊C₈	—	2	4	no	—
162	D₅₃⋊C₈	C₂²×C₄	1	2	yes	—
163	D₅₃⋊C₈	C₂²×C₄	1	2	yes	—
164	D₅₃⋊C₈	C₂×D₄	1	1	yes	characteristic
165	D₅₃⋊C₈	C₂×D₄	1	1	yes	characteristic
166	Q₁₆×C₅₃	C₄²	1	1	yes	characteristic
167	SD₁₆×C₅₃	C₄²	1	2	yes	—
168	D₈×C₅₃	C₄²	1	1	yes	characteristic
169	M₁₆×C₅₃	—	2	2	no	—
170	M₁₆×C₅₃	C₂²×C₄	1	2	yes	—
171	C₂×C₈×C₅₃	—	2	2	no	—
172	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
175	#11719925	C₄²	1	2	yes	—
176	#11719924	C₄²	1	2	yes	—
177	#11719923	C₄²	1	2	yes	—
178	#11719922	C₄²	1	2	yes	—
179	C₄×Dic₅₃	—	2	1	no	—
180	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
181	#11719917	—	2	2	no	—
182	#11719917	C₂²×C₄	1	2	yes	—
183	C₂×#88322	—	2	2	no	—
184	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
185	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
186	Dic₂₁₂	C₄²	1	1	yes	characteristic
187	D₄₂₄	C₄²	1	1	yes	characteristic
188	#11719913	C₄²	1	2	yes	—
189	#11719912	—	2	2	no	—
190	#11719912	—	2	2	no	—
191	#11719912	—	2	2	no	—
192	C₈×D₅₃	—	2	2	no	—
193	C₈×D₅₃	—	2	2	no	—
194	C₈×D₅₃	—	2	2	no	—
195	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
196	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
197	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
198	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
199	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
200	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
201	C₈×D₅₃	#41	1	1	yes	characteristic
202	C₈×D₅₃	#41	1	1	yes	characteristic
203	C₂²×D₅₃	—	2	2	no	—
204	C₂²×D₅₃	C₂×#41	1	1	yes	characteristic
205	C₂×#6157	—	2	4	no	—
206	C₂×#6157	—	2	2	no	—
207	C₂×#6157	—	4	2	no	—
208	C₂×#6157	—	4	2	no	—
209	C₂×#6157	—	8	4	no	—
210	C₂×#6157	C₄×D₄	1	2	yes	—
211	C₂×#6157	C₄×D₄	1	2	yes	—
212	Q₈×C₅₃	C₂×C₄²	1	2	yes	—
213	D₄×C₅₃	—	2	2	no	—
214	D₄×C₅₃	C₂×C₄²	1	2	yes	—
215	C₂×C₄×C₅₃	—	2	2	no	—
216	C₂×C₄×C₅₃	—	2	1	no	—
217	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
218	C₂²⋊D₅₃	—	2	2	no	—
219	C₂²⋊D₅₃	—	2	2	no	—
220	C₂²⋊D₅₃	—	2	2	no	—
221	C₂×Dic₅₃	—	2	2	no	—
222	C₂×Dic₅₃	—	2	1	no	—
223	C₂×Dic₅₃	C₂×#41	1	1	yes	characteristic
224	D₂₁₂	—	2	2	no	—
225	D₂₁₂	C₂×C₄²	1	2	yes	—
226	C₄×D₅₃	—	2	2	no	—
227	C₄×D₅₃	—	2	2	no	—
228	C₄×D₅₃	—	2	2	no	—
229	C₄×D₅₃	—	4	2	no	—
230	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
231	C₄×D₅₃	C₂³×C₄	1	1	yes	characteristic
232	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
233	C₄×D₅₃	C₂×#41	1	1	yes	characteristic
234	Dic₁₀₆	—	2	2	no	—
235	Dic₁₀₆	C₂×C₄²	1	2	yes	—
236	#88324	—	2	4	no	—
237	#88324	—	2	2	no	—
238	#88324	C₄×D₄	1	2	yes	—
239	#88324	C₄×D₄	1	2	yes	—
240	C₈×C₅₃	—	2	2	no	—
241	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
242	C₈×C₅₃	C₂×C₄²	1	1	yes	characteristic
243	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
244	C₈×C₅₃	C₄×D₄	1	1	yes	characteristic
245	#88322	—	2	2	no	—
246	#88322	C₂×C₄²	1	1	yes	characteristic
247	#88322	C₂×C₄²	1	1	yes	characteristic
248	#88322	C₄×D₄	1	1	yes	characteristic
249	#88322	C₄×D₄	1	1	yes	characteristic
250	#20514	—	53	1	no	maximal, Sylow
251	C₂²×C₅₃	—	2	2	no	—
252	C₂²×C₅₃	C₄×#41	1	1	yes	characteristic
253	C₂×D₅₃	—	2	2	no	—
254	C₂×D₅₃	—	2	2	no	—
255	C₂×D₅₃	—	4	4	no	—
256	C₂×D₅₃	C₂×C₄×D₄	1	1	yes	characteristic
257	C₂×D₅₃	C₄×#41	1	1	yes	characteristic
258	#6157	—	2	2	no	—
259	#6157	—	2	2	no	—
260	#6157	—	4	2	no	—
261	#6157	—	4	4	no	—
262	C₄×C₅₃	—	2	2	no	—
263	C₄×C₅₃	—	4	1	no	—
264	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
265	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
266	Dic₅₃	—	2	2	no	—
267	Dic₅₃	—	4	1	no	—
268	Dic₅₃	C₂×C₄×D₄	1	1	yes	characteristic
269	Dic₅₃	C₄×#41	1	1	yes	characteristic
270	C₂×#443	—	53	1	no	—
271	C₂×#443	—	53	1	no	—
272	C₄×#135	—	53	1	no	—
273	#2875	—	53	2	no	—
274	C₄×#108	—	53	1	no	—
275	#1772	—	53	1	no	—
276	#1772	—	53	1	no	—
277	#1765	—	53	2	no	—
278	#1765	—	53	2	no	—
279	#1759	—	53	2	no	—
280	#1726	—	53	1	no	—
281	C₂×C₅₃	—	2	1	no	—
282	C₂×C₅₃	—	4	2	no	—
283	C₂×C₅₃	C₄²×D₄	1	1	yes	characteristic
284	D₅₃	—	2	1	no	—
285	D₅₃	—	4	2	no	—
286	D₅₃	#2957	1	2	yes	—
287	C₂×#135	—	53	1	no	—
288	C₂×#131	—	53	2	no	—
289	C₂×#131	—	53	2	no	—
290	C₄×#41	—	53	2	no	—
291	#443	—	53	2	no	—
292	#443	—	53	4	no	—
293	#443	—	53	2	no	—
294	#443	—	53	1	no	—
295	#443	—	53	2	no	—
296	#443	—	53	1	no	—
297	#443	—	53	2	no	—
298	#443	—	53	1	no	—
299	#443	#6157	1	1	yes	characteristic, complemented
300	C₄×Q₁₆	—	53	2	no	—
301	C₄×SD₁₆	—	53	4	no	—
302	C₄×D₈	—	53	2	no	—
303	C₂×#108	—	53	1	no	—
304	C₂×#108	—	53	1	no	—
305	#427	—	53	1	no	—
306	C₂×#104	—	53	2	no	—
307	C₂×#104	—	53	2	no	—
308	#416	—	53	2	no	—
309	#405	—	53	2	no	—
310	#405	—	53	2	no	—
311	#405	—	106	2	no	—
312	#405	—	106	2	no	—
313	C₄×M₁₆	—	53	2	no	—
314	C₄×M₁₆	—	106	2	no	—
315	C₂×#97	—	53	1	no	—
316	C₂×#97	—	53	1	no	—
317	C₂×#97	—	53	1	no	—
318	C₂×#97	—	106	2	no	—
319	C₂×C₄×C₈	—	53	1	no	—
320	C₂×C₄×C₈	—	53	1	no	—
321	C₂×C₄×C₈	—	53	1	no	—
322	#376	—	53	1	no	—
323	#341	—	53	2	no	—
324	#339	—	53	2	no	—
325	#339	—	53	2	no	—
326	C₅₃	#20514	1	1	yes	characteristic, complemented, Sylow
327	C₂×#41	—	53	2	no	—
328	#135	—	53	2	no	—
329	#135	—	53	1	no	—
330	#135	—	53	2	no	—
331	#135	—	53	1	no	—
332	#135	—	53	1	no	—
333	#135	C₂×#6157	1	1	yes	characteristic
334	C₂×Q₁₆	—	53	1	no	—
335	C₂×SD₁₆	—	53	2	no	—
336	C₂×D₈	—	53	1	no	—
337	#131	—	53	4	no	—
338	#131	—	53	4	no	—
339	#131	—	53	2	no	—
340	#131	—	53	2	no	—
341	#131	—	53	2	no	—
342	#131	—	106	2	no	—
343	#131	—	106	2	no	—
344	#131	—	106	4	no	—
345	#131	C₂×#6157	1	2	yes	complemented
346	C₂×M₁₆	—	53	2	no	—
347	C₂×M₁₆	—	53	2	no	—
348	C₂×M₁₆	—	106	2	no	—
349	C₂×M₁₆	—	106	2	no	—
350	C₂²×C₈	—	53	1	no	—
351	C₂²×C₈	—	53	1	no	—
352	C₂²×C₈	—	53	1	no	—
353	C₂²×C₈	—	53	1	no	—
354	C₂²×C₈	—	106	2	no	—
355	C₂²×C₈	—	106	2	no	—
356	C₄×Q₈	—	53	4	no	—
357	C₄×D₄	—	53	4	no	—
358	C₄×D₄	—	106	4	no	—
359	#117	—	53	2	no	—
360	#117	—	106	2	no	—
361	C₂×C₄²	—	53	1	no	—
362	C₂×C₄²	—	53	1	no	—
363	C₂×C₄²	—	53	1	no	—
364	C₂×C₄²	—	106	2	no	—
365	#108	—	53	2	no	—
366	#108	—	53	2	no	—
367	#108	—	53	2	no	—
368	#108	—	53	1	no	—
369	#108	C₂×#6157	1	1	yes	characteristic, complemented
370	#107	—	53	2	no	—
371	#106	—	53	2	no	—
372	#104	—	53	4	no	—
373	#104	—	53	4	no	—
374	#104	—	53	2	no	—
375	#104	—	53	2	no	—
376	#104	—	53	2	no	—
377	#104	C₂×#6157	1	2	yes	complemented
378	#103	—	53	4	no	—
379	#102	—	53	4	no	—
380	#97	—	53	1	no	—
381	#97	—	53	1	no	—
382	#97	—	53	1	no	—
383	#97	—	53	1	no	—
384	#97	—	106	2	no	—
385	#97	—	106	1	no	—
386	#97	—	106	1	no	—
387	#97	—	106	2	no	—
388	#97	—	106	2	no	—
389	#97	—	106	2	no	—
390	C₄×C₈	—	53	2	no	—
391	C₄×C₈	—	53	2	no	—
392	C₄×C₈	—	53	2	no	—
393	C₄×C₈	—	53	2	no	—
394	C₄×C₈	—	53	1	no	—
395	C₄×C₈	—	53	1	no	—
396	C₄×C₈	—	53	1	no	—
397	C₄×C₈	—	106	2	no	—
398	C₄×C₈	—	106	2	no	—
399	C₄×C₈	—	106	2	no	—
400	C₄×C₈	C₂×#6157	1	1	yes	characteristic, complemented
401	#95	—	106	2	no	—
402	#41	—	53	2	no	—
403	#41	—	53	2	no	—
404	#41	—	53	2	no	—
405	#41	—	106	2	no	—
406	#41	—	106	2	no	—
407	#41	C₂²×#6157	1	2	yes	—
408	C₂×Q₈	—	53	2	no	—
409	C₂×D₄	—	53	2	no	—
410	C₂×D₄	—	106	2	no	—
411	C₂²×C₄	—	53	1	no	—
412	C₂²×C₄	—	53	2	no	—
413	C₂²×C₄	—	106	2	no	—
414	C₂²×C₄	—	106	1	no	—
415	C₂²×C₄	—	106	4	no	—
416	C₂²×C₄	—	106	1	no	—
417	Q₁₆	—	53	2	no	—
418	Q₁₆	—	53	1	no	—
419	Q₁₆	C₄×#6157	1	1	yes	characteristic
420	SD₁₆	—	53	2	no	—
421	SD₁₆	—	53	2	no	—
422	SD₁₆	—	53	2	no	—
423	SD₁₆	C₄×#6157	1	2	yes	—
424	D₈	—	53	2	no	—
425	D₈	—	53	1	no	—
426	D₈	C₄×#6157	1	1	yes	characteristic
427	M₁₆	—	2	2	no	—
428	M₁₆	—	53	4	no	—
429	M₁₆	—	53	2	no	—
430	M₁₆	—	106	2	no	—
431	M₁₆	—	106	2	no	—
432	M₁₆	—	106	2	no	—
433	M₁₆	—	106	4	no	—
434	M₁₆	—	106	4	no	—
435	M₁₆	—	106	2	no	—
436	M₁₆	—	106	2	no	—
437	M₁₆	C₂²×#6157	1	2	yes	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	53	2	no	—
440	C₂×C₈	—	53	2	no	—
441	C₂×C₈	—	53	1	no	—
442	C₂×C₈	—	53	1	no	—
443	C₂×C₈	—	53	1	no	—
444	C₂×C₈	—	53	1	no	—
445	C₂×C₈	—	53	1	no	—
446	C₂×C₈	—	53	1	no	—
447	C₂×C₈	—	53	1	no	—
448	C₂×C₈	—	53	1	no	—
449	C₂×C₈	—	53	1	no	—
450	C₂×C₈	—	53	1	no	—
451	C₂×C₈	—	53	1	no	—
452	C₂×C₈	—	53	1	no	—
453	C₂×C₈	—	53	2	no	—
454	C₂×C₈	—	106	2	no	—
455	C₂×C₈	—	106	2	no	—
456	C₂×C₈	—	106	2	no	—
457	C₂×C₈	—	106	4	no	—
458	C₂×C₈	—	106	4	no	—
459	C₂×C₈	—	106	1	no	—
460	C₂×C₈	—	106	2	no	—
461	C₂×C₈	—	106	1	no	—
462	C₂×C₈	—	106	2	no	—
463	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
464	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
465	C₄⋊C₄	—	53	4	no	—
466	C₄⋊C₄	—	106	4	no	—
467	C₂²⋊C₄	—	106	4	no	—
468	C₂²⋊C₄	—	106	2	no	—
469	C₄²	—	53	2	no	—
470	C₄²	—	53	1	no	—
471	C₄²	—	53	1	no	—
472	C₄²	—	53	2	no	—
473	C₄²	—	53	1	no	—
474	C₄²	—	106	1	no	—
475	C₄²	—	106	2	no	—
476	C₄²	—	106	1	no	—
477	C₄²	—	106	4	no	—
478	C₄²	C₂²×#6157	1	1	yes	characteristic
479	C₂³	—	53	1	no	—
480	C₂³	—	106	2	no	—
481	Q₈	—	53	2	no	—
482	Q₈	—	106	2	no	—
483	Q₈	C₂×C₄×#6157	1	2	yes	—
484	D₄	—	2	2	no	—
485	D₄	—	53	2	no	—
486	D₄	—	106	2	no	—
487	D₄	—	106	2	no	—
488	D₄	—	106	2	no	—
489	D₄	—	106	2	no	—
490	D₄	C₂×C₄×#6157	1	2	yes	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	53	1	no	—
494	C₂×C₄	—	53	1	no	—
495	C₂×C₄	—	53	1	no	—
496	C₂×C₄	—	53	1	no	—
497	C₂×C₄	—	53	1	no	—
498	C₂×C₄	—	53	2	no	—
499	C₂×C₄	—	53	2	no	—
500	C₂×C₄	—	106	2	no	—
501	C₂×C₄	—	106	2	no	—
502	C₂×C₄	—	106	2	no	—
503	C₂×C₄	—	106	2	no	—
504	C₂×C₄	—	106	2	no	—
505	C₂×C₄	—	106	4	no	—
506	C₂×C₄	—	106	1	no	—
507	C₂×C₄	—	424	4	no	—
508	C₂×C₄	—	212	2	no	—
509	C₂×C₄	—	212	2	no	—
510	C₂×C₄	—	212	2	no	—
511	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
512	C₈	—	2	2	no	—
513	C₈	—	53	2	no	—
514	C₈	—	53	2	no	—
515	C₈	—	53	1	no	—
516	C₈	—	53	1	no	—
517	C₈	—	53	1	no	—
518	C₈	—	53	1	no	—
519	C₈	—	106	2	no	—
520	C₈	—	106	4	no	—
521	C₈	—	106	2	no	—
522	C₈	C₂×C₄×#6157	1	1	yes	characteristic
523	C₈	C₂×C₄×#6157	1	1	yes	characteristic
524	C₈	D₄×#6157	1	1	yes	characteristic
525	C₈	D₄×#6157	1	1	yes	characteristic
526	C₂²	—	2	2	no	—
527	C₂²	—	53	1	no	—
528	C₂²	—	53	1	no	—
529	C₂²	—	106	2	no	—
530	C₂²	—	106	2	no	—
531	C₂²	—	212	4	no	—
532	C₂²	#41×#6157	1	1	yes	characteristic
533	C₄	—	2	2	no	—
534	C₄	—	4	1	no	—
535	C₄	—	53	1	no	—
536	C₄	—	53	1	no	—
537	C₄	—	106	2	no	—
538	C₄	—	106	2	no	—
539	C₄	—	106	2	no	—
540	C₄	—	212	1	no	—
541	C₄	—	212	4	no	—
542	C₄	—	212	2	no	—
543	C₄	C₂²×C₄×#6157	1	1	yes	characteristic
544	C₄	C₂×D₄×#6157	1	1	yes	characteristic
545	C₂	—	2	1	no	—
546	C₂	—	4	2	no	—
547	C₂	—	53	2	no	—
548	C₂	—	106	1	no	—
549	C₂	—	212	2	no	—
550	C₂	C₄×D₄×#6157	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×#6157
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₅₃×#443	C₄
socle	C₂×C₅₃	C₄²×D₄
prime radical	#135×D₅₃	C₂²
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	#443	#6157
hypocenter	C₅₃	#20514
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #443

Complements

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

N	H ≅ G/N	type
3. #20291285	C₂	semidirect
4. #108×#6157	C₂	semidirect
5. #20290520	C₂	semidirect
6. #20290517	C₂	semidirect
7. #20290495	C₂	semidirect
8. #20290493	C₂	semidirect
9. #20290480	C₂	semidirect
10. #20290371	C₂	semidirect
14. #16811667	C₄	semidirect
15. #16811666	C₄	semidirect
16. #16811665	C₄	semidirect
17. Q₁₆×#6157	C₄	semidirect
18. SD₁₆×#6157	C₄	semidirect
19. D₈×#6157	C₄	semidirect
42. #16810741	C₄	semidirect
43. #16810740	C₄	semidirect
44. #16810739	C₄	semidirect
45. #16810738	C₄	semidirect
46. #16810737	C₄	semidirect
50. C₅₃×#443	C₄	semidirect
51. #13133305	C₂×C₄	semidirect
53. #13133304	C₂×C₄	semidirect
67. #13133288	C₂×C₄	semidirect
68. #13133287	C₂×C₄	semidirect
71. #13133282	C₂×C₄	semidirect
72. #13133281	C₂×C₄	semidirect
90. C₈×#6157	C₂×C₄	semidirect
91. C₈×#6157	C₂×C₄	semidirect
103. #13133225	C₂×C₄	semidirect
104. #13133224	C₂×C₄	semidirect
106. #13133223	C₂×C₄	semidirect
113. #13133153	C₂×C₄	semidirect
114. #13133152	C₂×C₄	semidirect
115. #13133145	C₂×C₄	semidirect
116. #13133144	C₂×C₄	semidirect
117. #13133143	C₂×C₄	semidirect
118. C₄×#88322	C₂×C₄	semidirect
119. C₈×Dic₅₃	C₂×C₄	semidirect
120. C₈×Dic₅₃	C₂×C₄	semidirect
122. #131×C₅₃	C₂×C₄	semidirect
123. #108×C₅₃	C₂×C₄	semidirect
124. #104×C₅₃	C₂×C₄	semidirect
125. C₄×C₈×C₅₃	C₂×C₄	semidirect
299. #443	#6157	semidirect
326. C₅₃	#20514	semidirect
345. #131	C₂×#6157	semidirect
369. #108	C₂×#6157	semidirect
377. #104	C₂×#6157	semidirect
400. C₄×C₈	C₂×#6157	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₅₃⋊#443	2
#135×#6157	2
#20291285	2
#108×#6157	2
#20290520	2
#20290517	2
#20290495	2
#20290493	2
#20290480	2
#20290371	2
#443×D₅₃	2
#20514	53