Subgroups — #28313963

Order 13568.

688 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291523	C₂	1	1	yes	maximal, characteristic
2	#20291400	C₂	1	1	yes	maximal, characteristic
3	#20289939	C₂	1	1	yes	maximal, characteristic, complemented
4	#20289937	C₂	1	1	yes	maximal, characteristic, complemented
5	#20289937	C₂	1	1	yes	maximal, characteristic, complemented
6	#20289935	C₂	1	1	yes	maximal, characteristic, complemented
7	#20289933	C₂	1	1	yes	maximal, characteristic, complemented
8	#20289933	C₂	1	1	yes	maximal, characteristic, complemented
9	#20289931	C₂	1	1	yes	maximal, characteristic, complemented
10	#20289929	C₂	1	1	yes	maximal, characteristic, complemented
11	#20289927	C₂	1	1	yes	maximal, characteristic, complemented
12	#20289925	C₂	1	1	yes	maximal, characteristic, complemented
13	#20289923	C₂	1	1	yes	maximal, characteristic, complemented
14	#20289923	C₂	1	1	yes	maximal, characteristic, complemented
15	#20283680	C₂	1	1	yes	maximal, characteristic
16	#16811674	C₄	1	2	yes	—
17	#16811657	C₄	1	2	yes	—
18	#16811653	C₄	1	2	yes	—
19	#16811653	C₄	1	2	yes	—
20	#16811648	C₄	1	2	yes	—
21	#16811648	C₄	1	2	yes	—
22	#16811642	C₂²	1	1	yes	characteristic
23	#16811642	C₂²	1	1	yes	characteristic
24	#16811642	C₂²	1	1	yes	characteristic
25	#16811641	C₂²	1	1	yes	characteristic
26	#16811641	C₂²	1	1	yes	characteristic
27	#16811641	C₂²	1	1	yes	characteristic
28	#16811641	C₂²	1	1	yes	characteristic
29	#16811630	C₄	1	2	yes	—
30	#16811598	C₄	1	2	yes	—
31	C₄×#11719936	C₂²	1	1	yes	characteristic
32	C₄×#11719936	C₂²	1	1	yes	characteristic
33	C₄×#11719936	C₂²	1	1	yes	characteristic
34	C₄×D₅₃⋊C₈	C₂²	1	1	yes	characteristic
35	C₄×D₅₃⋊C₈	C₂²	1	1	yes	characteristic
36	#88324⋊C₈	C₂²	1	1	yes	characteristic
37	#88324⋊C₈	C₂²	1	1	yes	characteristic
38	#88324⋊C₈	C₂²	1	1	yes	characteristic
39	#88324⋊C₈	C₂²	1	1	yes	characteristic
40	#88324⋊C₈	C₂²	1	1	yes	characteristic
41	#88324⋊C₈	C₂²	1	1	yes	characteristic
42	#88324⋊C₈	C₂²	1	1	yes	characteristic
43	#88324⋊C₈	C₂²	1	1	yes	characteristic
44	#88324⋊C₈	C₂²	1	1	yes	characteristic
45	#88324⋊C₈	C₂²	1	1	yes	characteristic
46	#16811464	C₂²	1	1	yes	characteristic
47	#16811464	C₂²	1	1	yes	characteristic
48	#16811464	C₂²	1	1	yes	characteristic
49	#16811464	C₂²	1	1	yes	characteristic
50	C₈×#88324	C₂²	1	1	yes	characteristic
51	C₈×#88324	C₂²	1	1	yes	characteristic
52	C₄×#11719949	C₂²	1	1	yes	characteristic
53	#16810754	C₄	1	1	yes	characteristic
54	#16810702	C₄	1	1	yes	characteristic
55	#16810700	C₄	1	1	yes	characteristic
56	#16810696	C₄	1	1	yes	characteristic
57	#16810696	C₄	1	1	yes	characteristic
58	#16810693	C₄	1	1	yes	characteristic
59	#16810693	C₄	1	1	yes	characteristic
60	#16810675	C₂²	1	1	yes	characteristic
61	#16810675	C₂²	1	1	yes	characteristic
62	#16810675	C₂²	1	1	yes	characteristic
63	#16810575	C₂²	1	1	yes	characteristic
64	#16810575	C₂²	1	1	yes	characteristic
65	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
66	C₅₃×#446	C₄	1	1	yes	characteristic
67	C₂×#11719936	C₂×C₄	1	2	yes	—
68	C₂×#11719936	C₂×C₄	1	2	yes	—
69	C₂×#11719936	C₂×C₄	1	2	yes	—
70	C₂×D₅₃⋊C₈	C₂×C₄	1	2	yes	—
71	C₂×D₅₃⋊C₈	C₂×C₄	1	2	yes	—
72	#13133284	C₂×C₄	1	2	yes	—
73	#13133284	C₂×C₄	1	2	yes	—
74	#13133284	C₂×C₄	1	2	yes	—
75	#13133284	C₂×C₄	1	2	yes	—
76	C₄⋊#88324	C₂×C₄	1	2	yes	—
77	C₄⋊#88324	C₂×C₄	1	2	yes	—
78	C₄⋊#88324	C₂×C₄	1	2	yes	—
79	#13133274	C₂×C₄	1	2	yes	—
80	#13133274	C₂×C₄	1	2	yes	—
81	#13133274	C₂×C₄	1	2	yes	—
82	#13133274	C₂×C₄	1	2	yes	—
83	#13133274	C₂×C₄	1	2	yes	—
84	#13133274	C₂×C₄	1	2	yes	—
85	#13133274	C₂×C₄	1	2	yes	—
86	#13133272	C₂×C₄	1	2	yes	—
87	#13133272	C₂×C₄	1	2	yes	—
88	#13133272	C₂×C₄	1	2	yes	—
89	C₄×#88324	C₂×C₄	1	2	yes	—
90	C₄×#88324	C₂×C₄	1	2	yes	—
91	C₄×#88324	C₂³	1	1	yes	characteristic
92	C₄×#88324	C₂³	1	1	yes	characteristic
93	C₄×#88324	C₂³	1	1	yes	characteristic
94	C₄×#88324	C₂³	1	1	yes	characteristic
95	C₄×#88324	C₂³	1	1	yes	characteristic
96	C₄×#88324	C₂³	1	1	yes	characteristic
97	C₄×#88324	C₂³	1	1	yes	characteristic
98	C₄×#88324	C₂³	1	1	yes	characteristic
99	C₂×#11719949	C₂×C₄	1	1	yes	characteristic
100	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
101	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
102	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
103	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
104	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
105	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
106	Q₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
107	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
108	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
109	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
110	#13133179	C₂×C₄	1	1	yes	characteristic
111	#13133179	C₂×C₄	1	1	yes	characteristic
112	#13133179	C₂×C₄	1	1	yes	characteristic
113	#13133175	C₂×C₄	1	1	yes	characteristic
114	#13133175	C₂×C₄	1	1	yes	characteristic
115	#13133175	C₂×C₄	1	1	yes	characteristic
116	C₄²×D₅₃	C₂³	1	1	yes	characteristic
117	C₄²×D₅₃	C₂³	1	1	yes	characteristic
118	C₄²×D₅₃	C₂³	1	1	yes	characteristic
119	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
120	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
121	C₄⋊#88322	C₂×C₄	1	1	yes	characteristic
122	#13133129	C₂×C₄	1	1	yes	characteristic
123	#13133129	C₂×C₄	1	1	yes	characteristic
124	#13133129	C₂×C₄	1	1	yes	characteristic
125	#13133129	C₂×C₄	1	1	yes	characteristic
126	#13133129	C₂×C₄	1	1	yes	characteristic
127	#13133129	C₂×C₄	1	1	yes	characteristic
128	#13133128	C₂×C₄	1	1	yes	characteristic
129	#13133128	C₂×C₄	1	1	yes	characteristic
130	C₄×#88322	C₂×C₄	1	1	yes	characteristic
131	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
132	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
133	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
134	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
135	C₄×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
136	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
137	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
138	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
139	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
140	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
141	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
142	C₂×Q₈×C₅₃	C₄²	1	1	yes	characteristic
143	#11719949	—	4	2	no	—
144	C₂×D₂₁₂	C₄²	1	1	yes	characteristic
145	C₂×D₂₁₂	C₄²	1	1	yes	characteristic
146	C₂×D₂₁₂	C₄²	1	1	yes	characteristic
147	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×#88324	C₂²×C₄	1	2	yes	—
157	C₂×#88324	C₂²×C₄	1	2	yes	—
158	C₂×#88324	C₂²×C₄	1	2	yes	—
159	C₂×#88324	C₂²×C₄	1	2	yes	—
160	C₂×#88324	C₂²×C₄	1	2	yes	—
161	C₂×#88324	C₂²×C₄	1	2	yes	—
162	C₂×#88324	C₂²×C₄	1	2	yes	—
163	C₂×#88324	C₂²×C₄	1	2	yes	—
164	#11719936	—	4	2	no	—
165	#11719936	—	4	2	no	—
166	#11719936	—	4	2	no	—
167	D₅₃⋊C₈	—	4	2	no	—
168	D₅₃⋊C₈	—	4	2	no	—
169	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
173	C₄⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
174	C₄⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
175	C₄⋊C₄×C₅₃	C₄²	1	1	yes	characteristic
176	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
179	#11719921	C₄²	1	1	yes	characteristic
180	#11719921	C₄²	1	1	yes	characteristic
181	#11719921	C₄²	1	1	yes	characteristic
182	#11719921	C₄²	1	1	yes	characteristic
183	#11719921	C₄²	1	1	yes	characteristic
184	#11719921	C₄²	1	1	yes	characteristic
185	C₄⋊Dic₅₃	C₄²	1	1	yes	characteristic
186	C₄⋊Dic₅₃	C₄²	1	1	yes	characteristic
187	C₄⋊Dic₅₃	C₄²	1	1	yes	characteristic
188	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
189	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
190	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
191	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
192	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
193	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
194	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
195	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
196	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
197	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
198	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
199	#11719912	—	4	1	no	—
200	#11719912	—	4	1	no	—
201	#11719912	—	4	1	no	—
202	#11719912	—	4	1	no	—
203	C₈×D₅₃	—	4	1	no	—
204	C₈×D₅₃	—	4	1	no	—
205	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
206	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
207	C₂²×D₅₃	C₂×C₄²	1	1	yes	characteristic
208	Q₈×C₅₃	—	4	1	no	—
209	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
210	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
211	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
212	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
213	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
214	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
215	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
216	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
217	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
218	C₂×Dic₅₃	C₂×C₄²	1	1	yes	characteristic
219	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
220	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
221	D₂₁₂	—	4	1	no	—
222	D₂₁₂	—	4	1	no	—
223	D₂₁₂	—	4	1	no	—
224	C₄×D₅₃	—	2	1	no	—
225	C₄×D₅₃	—	2	1	no	—
226	C₄×D₅₃	—	2	1	no	—
227	C₄×D₅₃	—	2	1	no	—
228	C₄×D₅₃	—	2	1	no	—
229	C₄×D₅₃	—	2	1	no	—
230	C₄×D₅₃	—	2	2	no	—
231	C₄×D₅₃	—	2	2	no	—
232	C₄×D₅₃	—	2	2	no	—
233	C₄×D₅₃	—	2	2	no	—
234	C₄×D₅₃	—	2	2	no	—
235	C₄×D₅₃	—	2	2	no	—
236	#88324	—	2	2	no	—
237	#88324	—	2	2	no	—
238	#88324	—	2	2	no	—
239	#88324	—	2	2	no	—
240	#88324	—	2	2	no	—
241	#88324	—	2	2	no	—
242	#88324	—	2	2	no	—
243	#88324	—	2	2	no	—
244	C₈×C₅₃	—	2	1	no	—
245	C₈×C₅₃	—	2	1	no	—
246	C₈×C₅₃	—	2	1	no	—
247	C₈×C₅₃	—	2	1	no	—
248	#88322	—	2	1	no	—
249	#88322	—	2	1	no	—
250	#88322	—	2	1	no	—
251	#88322	—	2	1	no	—
252	#17342	—	53	1	no	maximal, Sylow
253	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
254	C₂×D₅₃	—	2	1	no	—
255	C₂×D₅₃	—	2	1	no	—
256	C₂×D₅₃	—	2	1	no	—
257	C₂×D₅₃	—	2	1	no	—
258	C₂×D₅₃	—	2	1	no	—
259	C₂×D₅₃	—	2	1	no	—
260	C₂×D₅₃	—	2	1	no	—
261	C₂×D₅₃	—	2	1	no	—
262	C₂×D₅₃	—	2	1	no	—
263	C₄×C₅₃	—	2	1	no	—
264	C₄×C₅₃	—	2	1	no	—
265	C₄×C₅₃	—	2	1	no	—
266	C₄×C₅₃	—	2	1	no	—
267	C₄×C₅₃	—	2	1	no	—
268	C₄×C₅₃	—	2	1	no	—
269	C₄×C₅₃	#568	1	1	yes	characteristic
270	C₄×C₅₃	#568	1	1	yes	characteristic
271	Dic₅₃	—	2	1	no	—
272	Dic₅₃	—	2	1	no	—
273	Dic₅₃	—	2	1	no	—
274	Dic₅₃	#568	1	2	yes	—
275	Dic₅₃	#568	1	2	yes	—
276	#2965	—	53	1	no	—
277	#2965	—	53	1	no	—
278	#2922	—	53	1	no	—
279	#1455	—	53	1	no	—
280	#1454	—	53	1	no	—
281	#1454	—	53	1	no	—
282	#1453	—	53	1	no	—
283	#1453	—	53	1	no	—
284	#1453	—	53	1	no	—
285	#1452	—	53	1	no	—
286	#1452	—	53	1	no	—
287	#1451	—	53	1	no	—
288	#1451	—	53	1	no	—
289	#1451	—	53	1	no	—
290	#1451	—	53	1	no	—
291	C₂×C₅₃	#2873	1	1	yes	characteristic
292	C₂×C₅₃	#2875	1	1	yes	characteristic
293	C₂×C₅₃	#2875	1	1	yes	characteristic
294	D₅₃	—	4	1	no	—
295	D₅₃	—	4	1	no	—
296	D₅₃	—	4	1	no	—
297	C₄×#41	—	53	1	no	—
298	#446	—	53	2	no	—
299	#446	—	53	1	no	—
300	#446	#6157	1	1	yes	characteristic
301	#436	—	53	2	no	—
302	#436	—	53	1	no	—
303	#436	—	53	1	no	—
304	#435	—	53	2	no	—
305	#435	—	53	2	no	—
306	#435	—	53	1	no	—
307	#435	—	53	1	no	—
308	#435	—	53	1	no	—
309	#435	—	53	1	no	—
310	#433	—	53	2	no	—
311	#433	—	53	2	no	—
312	#431	—	53	1	no	—
313	#431	—	53	1	no	—
314	#431	—	53	1	no	—
315	#431	—	53	1	no	—
316	#431	—	53	1	no	—
317	#431	—	53	1	no	—
318	#431	—	53	1	no	—
319	#431	—	53	1	no	—
320	#431	—	53	1	no	—
321	#431	—	53	1	no	—
322	#424	—	53	2	no	—
323	#408	—	53	2	no	—
324	C₄×M₁₆	—	53	1	no	—
325	C₄×M₁₆	—	53	1	no	—
326	C₄×M₁₆	—	53	1	no	—
327	C₄×M₁₆	—	53	1	no	—
328	C₄×M₁₆	—	53	1	no	—
329	C₂×C₄×C₈	—	53	1	no	—
330	C₂×C₄×C₈	—	53	1	no	—
331	C₂×C₄×C₈	—	53	1	no	—
332	#322	—	53	1	no	—
333	#322	—	53	1	no	—
334	#322	—	53	1	no	—
335	#322	—	53	1	no	—
336	#322	—	53	1	no	—
337	#322	—	53	1	no	—
338	#322	—	53	1	no	—
339	#322	—	53	1	no	—
340	#322	—	53	1	no	—
341	#322	—	53	1	no	—
342	#322	—	53	1	no	—
343	#322	—	53	1	no	—
344	#322	—	53	1	no	—
345	#322	—	53	1	no	—
346	C₈²	—	53	1	no	—
347	C₈²	—	53	1	no	—
348	C₅₃	#17342	1	1	yes	characteristic, complemented, Sylow
349	C₂×#41	—	53	1	no	—
350	C₂×M₁₆	—	53	2	no	—
351	C₂×M₁₆	—	53	2	no	—
352	C₂×M₁₆	—	53	2	no	—
353	C₂×M₁₆	—	53	1	no	—
354	C₂×M₁₆	—	53	1	no	—
355	C₂×M₁₆	—	53	1	no	—
356	C₂×M₁₆	—	53	1	no	—
357	C₂²×C₈	—	53	2	no	—
358	C₂²×C₈	—	53	2	no	—
359	C₂²×C₈	—	53	1	no	—
360	C₂²×C₈	—	53	1	no	—
361	C₄×Q₈	—	53	1	no	—
362	C₄×Q₈	C₂×#6157	1	1	yes	characteristic
363	C₄×D₄	—	53	1	no	—
364	C₄×D₄	—	53	1	no	—
365	C₄×D₄	—	53	1	no	—
366	C₄×D₄	—	53	1	no	—
367	C₄×D₄	—	53	1	no	—
368	C₄×D₄	—	53	1	no	—
369	#117	—	53	1	no	—
370	#117	—	53	1	no	—
371	#117	—	53	1	no	—
372	C₂×C₄²	—	53	1	no	—
373	C₂×C₄²	—	53	1	no	—
374	C₂×C₄²	—	53	1	no	—
375	C₄⋊C₈	—	53	2	no	—
376	C₄⋊C₈	—	53	2	no	—
377	C₄⋊C₈	—	53	2	no	—
378	C₄⋊C₈	—	53	2	no	—
379	C₄⋊C₈	—	53	2	no	—
380	C₄⋊C₈	—	53	2	no	—
381	C₄⋊C₈	—	53	2	no	—
382	C₄⋊C₈	—	53	1	no	—
383	C₄⋊C₈	—	53	1	no	—
384	C₄⋊C₈	—	53	1	no	—
385	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic
386	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic
387	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic
388	C₂²⋊C₈	—	53	2	no	—
389	C₂²⋊C₈	—	53	2	no	—
390	C₂²⋊C₈	—	53	2	no	—
391	C₂²⋊C₈	—	53	2	no	—
392	C₂²⋊C₈	—	53	2	no	—
393	C₂²⋊C₈	—	53	2	no	—
394	C₂²⋊C₈	—	53	2	no	—
395	C₂²⋊C₈	—	53	1	no	—
396	C₂²⋊C₈	—	53	1	no	—
397	C₂²⋊C₈	—	53	1	no	—
398	C₂²⋊C₈	—	53	1	no	—
399	C₂²⋊C₈	—	53	1	no	—
400	C₂²⋊C₈	—	53	1	no	—
401	#97	—	53	2	no	—
402	#97	—	53	2	no	—
403	#97	—	53	2	no	—
404	#97	—	53	1	no	—
405	#97	—	53	1	no	—
406	#97	C₂×#6157	1	1	yes	characteristic
407	#97	C₂×#6157	1	1	yes	characteristic
408	C₄×C₈	—	53	1	no	—
409	C₄×C₈	—	53	1	no	—
410	C₄×C₈	—	53	1	no	—
411	C₄×C₈	—	53	1	no	—
412	C₄×C₈	—	53	1	no	—
413	C₄×C₈	—	53	1	no	—
414	C₄×C₈	—	53	1	no	—
415	C₄×C₈	—	53	1	no	—
416	C₄×C₈	—	53	2	no	—
417	C₄×C₈	—	53	2	no	—
418	C₄×C₈	—	53	1	no	—
419	C₄×C₈	—	53	1	no	—
420	C₄×C₈	—	53	1	no	—
421	C₄×C₈	—	53	1	no	—
422	C₄×C₈	—	53	1	no	—
423	C₄×C₈	C₂×#6157	1	1	yes	characteristic
424	#41	—	212	2	no	—
425	C₂×Q₈	C₄×#6157	1	1	yes	characteristic
426	C₂×D₄	—	53	1	no	—
427	C₂×D₄	—	53	1	no	—
428	C₂×D₄	—	53	1	no	—
429	C₂²×C₄	—	53	1	no	—
430	C₂²×C₄	—	53	1	no	—
431	C₂²×C₄	—	53	1	no	—
432	C₂²×C₄	—	53	1	no	—
433	C₂²×C₄	—	53	1	no	—
434	C₂²×C₄	—	53	1	no	—
435	C₂²×C₄	—	53	1	no	—
436	C₂²×C₄	—	53	1	no	—
437	C₂²×C₄	—	53	1	no	—
438	M₁₆	—	212	1	no	—
439	M₁₆	—	212	1	no	—
440	M₁₆	—	212	1	no	—
441	M₁₆	—	212	1	no	—
442	M₁₆	—	212	2	no	—
443	M₁₆	—	212	2	no	—
444	M₁₆	—	212	2	no	—
445	C₂×C₈	—	53	2	no	—
446	C₂×C₈	—	53	2	no	—
447	C₂×C₈	—	53	2	no	—
448	C₂×C₈	—	53	2	no	—
449	C₂×C₈	—	53	2	no	—
450	C₂×C₈	—	53	2	no	—
451	C₂×C₈	—	53	2	no	—
452	C₂×C₈	—	53	2	no	—
453	C₂×C₈	—	53	1	no	—
454	C₂×C₈	—	53	1	no	—
455	C₂×C₈	—	53	1	no	—
456	C₂×C₈	—	53	1	no	—
457	C₂×C₈	—	212	1	no	—
458	C₂×C₈	—	212	1	no	—
459	C₂×C₈	—	212	2	no	—
460	C₂×C₈	—	212	2	no	—
461	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
462	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
463	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
464	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
465	C₄⋊C₄	—	53	1	no	—
466	C₄⋊C₄	—	53	1	no	—
467	C₄⋊C₄	—	53	1	no	—
468	C₄⋊C₄	C₄×#6157	1	1	yes	characteristic
469	C₄⋊C₄	C₄×#6157	1	1	yes	characteristic
470	C₄⋊C₄	C₄×#6157	1	1	yes	characteristic
471	C₂²⋊C₄	—	53	1	no	—
472	C₂²⋊C₄	—	53	1	no	—
473	C₂²⋊C₄	—	53	1	no	—
474	C₂²⋊C₄	—	53	1	no	—
475	C₂²⋊C₄	—	53	1	no	—
476	C₂²⋊C₄	—	53	1	no	—
477	C₄²	—	53	1	no	—
478	C₄²	—	53	1	no	—
479	C₄²	—	53	1	no	—
480	C₄²	—	53	1	no	—
481	C₄²	—	53	1	no	—
482	C₄²	—	53	1	no	—
483	C₄²	—	53	1	no	—
484	C₄²	C₂²×#6157	1	1	yes	characteristic
485	C₄²	C₂²×#6157	1	1	yes	characteristic
486	C₄²	C₂²×#6157	1	1	yes	characteristic
487	C₂³	—	53	1	no	—
488	C₂³	—	53	1	no	—
489	C₂³	—	53	1	no	—
490	Q₈	—	4	1	no	—
491	D₄	—	212	1	no	—
492	D₄	—	212	1	no	—
493	D₄	—	212	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	1	no	—
499	C₂×C₄	—	106	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	1	no	—
506	C₂×C₄	—	106	1	no	—
507	C₂×C₄	—	106	1	no	—
508	C₂×C₄	—	106	1	no	—
509	C₂×C₄	—	106	1	no	—
510	C₂×C₄	—	106	1	no	—
511	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
512	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
513	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
514	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
515	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
516	C₂×C₄	C₂×C₄×#6157	1	1	yes	characteristic
517	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	106	2	no	—
523	C₈	—	106	2	no	—
524	C₈	—	106	2	no	—
525	C₈	—	106	2	no	—
526	C₈	—	106	2	no	—
527	C₈	—	106	2	no	—
528	C₈	—	106	2	no	—
529	C₈	—	106	2	no	—
530	C₈	—	106	1	no	—
531	C₈	—	106	1	no	—
532	C₈	—	106	1	no	—
533	C₈	—	106	1	no	—
534	C₂²	—	106	1	no	—
535	C₂²	—	106	1	no	—
536	C₂²	—	106	1	no	—
537	C₂²	—	106	1	no	—
538	C₂²	—	106	1	no	—
539	C₂²	—	106	1	no	—
540	C₂²	—	106	1	no	—
541	C₂²	—	106	1	no	—
542	C₂²	—	106	1	no	—
543	C₂²	C₂²×C₄×#6157	1	1	yes	characteristic
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	53	2	no	—
551	C₄	—	53	2	no	—
552	C₄	—	106	1	no	—
553	C₄	—	106	1	no	—
554	C₄	—	106	1	no	—
555	C₄	#16811702	1	1	yes	characteristic
556	C₄	#16811703	1	1	yes	characteristic
557	C₂	—	212	1	no	—
558	C₂	—	212	1	no	—
559	C₂	—	212	1	no	—
560	C₂	#20291278	1	1	yes	characteristic
561	C₂	#20291285	1	1	yes	characteristic
562	C₂	#20291287	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6157
commutator, socle	C₂²×C₅₃	C₂²×C₄²
Fitting	C₅₃×#446	C₄
prime radical	C₂×#11719949	C₂×C₄
cosocle	C₄×Dic₅₃	C₂⁴
hypercenter	#446	#6157
hypocenter	C₅₃	#17342
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
3. #20289939	C₂	semidirect
4. #20289937	C₂	semidirect
5. #20289937	C₂	semidirect
6. #20289935	C₂	semidirect
7. #20289933	C₂	semidirect
8. #20289933	C₂	semidirect
9. #20289931	C₂	semidirect
10. #20289929	C₂	semidirect
11. #20289927	C₂	semidirect
12. #20289925	C₂	semidirect
13. #20289923	C₂	semidirect
14. #20289923	C₂	semidirect
348. C₅₃	#17342	semidirect

Maximal subgroups

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

subgroup	index
#20291523	2
#20291400	2
#20289939	2
#20289937	2
#20289935	2
#20289933	2
#20289931	2
#20289929	2
#20289927	2
#20289925	2
#20289923	2
#20283680	2
#17342	53