Subgroups — #28328598

Order 13568.

484 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291132	C₂	1	1	yes	maximal, characteristic, complemented
2	#20291131	C₂	1	1	yes	maximal, characteristic, complemented
3	#20291101	C₂	1	1	yes	maximal, characteristic, complemented
4	#20291100	C₂	1	1	yes	maximal, characteristic, complemented
5	#20291098	C₂	1	1	yes	maximal, characteristic, complemented
6	#20291097	C₂	1	1	yes	maximal, characteristic, complemented
7	#20291097	C₂	1	1	yes	maximal, characteristic, complemented
8	#20291096	C₂	1	1	yes	maximal, characteristic, complemented
9	#20291083	C₂	1	1	yes	maximal, characteristic, complemented
10	#20291080	C₂	1	1	yes	maximal, characteristic, complemented
11	#20291079	C₂	1	1	yes	maximal, characteristic, complemented
12	#20291051	C₂	1	1	yes	maximal, characteristic, complemented
13	#20291050	C₂	1	1	yes	maximal, characteristic, complemented
14	#20291048	C₂	1	1	yes	maximal, characteristic, complemented
15	#20283688	C₂	1	1	yes	maximal, characteristic
16	C₂×#13133292	C₂²	1	1	yes	characteristic
17	C₂×#13133292	C₂²	1	1	yes	characteristic
18	C₂×#13133292	C₂²	1	1	yes	characteristic
19	C₂×#13133291	C₂²	1	1	yes	characteristic
20	C₂×D₅₃⋊C₁₆	C₂²	1	1	yes	characteristic
21	C₂²×#11719910	C₂²	1	1	yes	characteristic
22	#16811544	C₂²	1	1	yes	characteristic
23	#16811544	C₂²	1	1	yes	characteristic
24	#16811544	C₂²	1	1	yes	characteristic
25	#16811544	C₂²	1	1	yes	characteristic
26	C₄⋊#11719910	C₂²	1	1	yes	characteristic
27	C₄⋊#11719910	C₂²	1	1	yes	characteristic
28	C₄⋊#11719910	C₂²	1	1	yes	characteristic
29	C₄⋊#11719910	C₂²	1	1	yes	characteristic
30	C₄⋊#11719910	C₂²	1	1	yes	characteristic
31	C₄⋊#11719910	C₂²	1	1	yes	characteristic
32	#16811518	C₂²	1	1	yes	characteristic
33	#16811518	C₂²	1	1	yes	characteristic
34	#16811518	C₂²	1	1	yes	characteristic
35	#16811518	C₂²	1	1	yes	characteristic
36	C₂²⋊#11719910	C₂²	1	1	yes	characteristic
37	C₂²⋊#11719910	C₂²	1	1	yes	characteristic
38	#16811512	C₂²	1	1	yes	characteristic
39	#16811512	C₂²	1	1	yes	characteristic
40	#16811512	C₂²	1	1	yes	characteristic
41	#16811511	C₂²	1	1	yes	characteristic
42	#16811509	C₂²	1	1	yes	characteristic
43	C₄×#11719910	C₂²	1	1	yes	characteristic
44	#16811151	C₄	1	1	yes	characteristic
45	#16810752	C₄	1	1	yes	characteristic
46	#16810747	C₂²	1	1	yes	characteristic
47	#16810698	C₄	1	1	yes	characteristic
48	#16810697	C₄	1	1	yes	characteristic
49	#16810693	C₄	1	1	yes	characteristic
50	#16810688	C₂²	1	1	yes	characteristic
51	#16810686	C₂²	1	1	yes	characteristic
52	#16810686	C₂²	1	1	yes	characteristic
53	#16810682	C₄	1	1	yes	characteristic
54	#16810678	C₄	1	1	yes	characteristic
55	#16810580	C₂²	1	1	yes	characteristic
56	#16810579	C₂²	1	1	yes	characteristic
57	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
58	C₅₃×#433	C₄	1	1	yes	characteristic
59	#13133292	—	4	1	no	—
60	#13133292	—	4	1	no	—
61	#13133292	—	4	1	no	—
62	#13133291	—	4	1	no	—
63	D₅₃⋊C₁₆	—	4	1	no	—
64	C₂×#11719910	—	4	1	no	—
65	C₂×#11719910	C₂³	1	1	yes	characteristic
66	C₂×#11719910	C₂³	1	1	yes	characteristic
67	C₂×#11719910	C₂³	1	1	yes	characteristic
68	C₂×#11719910	C₂³	1	1	yes	characteristic
69	C₂×#11719910	C₂³	1	1	yes	characteristic
70	C₂×#11719910	C₂³	1	1	yes	characteristic
71	C₂×#11719910	C₂³	1	1	yes	characteristic
72	C₂×#11719910	C₂³	1	1	yes	characteristic
73	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
74	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
75	C₂²×#88322	C₂³	1	1	yes	characteristic
76	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
78	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
79	#13133212	C₈	1	1	yes	characteristic
80	#13133210	C₈	1	1	yes	characteristic
81	#13133207	C₈	1	1	yes	characteristic
82	#13133203	C₈	1	1	yes	characteristic
83	#13133202	C₈	1	1	yes	characteristic
84	#13133199	C₈	1	1	yes	characteristic
85	#13133195	C₈	1	1	yes	characteristic
86	#13133190	C₈	1	1	yes	characteristic
87	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
88	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
89	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
90	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
91	#13133174	C₂×C₄	1	1	yes	characteristic
92	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
93	#13133146	C₂×C₄	1	1	yes	characteristic
94	#13133146	C₂×C₄	1	1	yes	characteristic
95	#13133146	C₂×C₄	1	1	yes	characteristic
96	#13133146	C₂×C₄	1	1	yes	characteristic
97	#13133129	C₂×C₄	1	1	yes	characteristic
98	#13133129	C₂×C₄	1	1	yes	characteristic
99	#13133129	C₂×C₄	1	1	yes	characteristic
100	#13133129	C₂×C₄	1	1	yes	characteristic
101	#13133128	C₂×C₄	1	1	yes	characteristic
102	#13133128	C₂×C₄	1	1	yes	characteristic
103	#13133127	C₂×C₄	1	1	yes	characteristic
104	C₄×#88322	C₂³	1	1	yes	characteristic
105	C₄×#88322	C₂³	1	1	yes	characteristic
106	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
107	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
108	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
109	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
110	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
111	C₄⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
114	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
115	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
118	C₂×C₂²⋊D₅₃	C₂×C₈	1	1	yes	characteristic
119	C₂×D₂₁₂	C₂×C₈	1	1	yes	characteristic
120	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
121	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
122	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×Dic₁₀₆	C₂×C₈	1	1	yes	characteristic
125	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
129	C₄⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
130	C₄⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
131	C₂²⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
132	C₂²⋊C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
133	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
136	C₂²⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
137	#11719921	C₂×C₈	1	1	yes	characteristic
138	#11719921	C₂×C₈	1	1	yes	characteristic
139	#11719921	C₂×C₈	1	1	yes	characteristic
140	#11719921	C₂×C₈	1	1	yes	characteristic
141	#11719921	C₂×C₈	1	1	yes	characteristic
142	#11719921	C₂×C₈	1	1	yes	characteristic
143	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
144	C₄⋊Dic₅₃	C₂×C₈	1	1	yes	characteristic
145	#11719919	C₂×C₈	1	1	yes	characteristic
146	#11719919	C₂×C₈	1	1	yes	characteristic
147	#11719919	C₂×C₈	1	1	yes	characteristic
148	#11719919	C₂×C₈	1	1	yes	characteristic
149	#11719919	C₂×C₈	1	1	yes	characteristic
150	#11719919	C₂×C₈	1	1	yes	characteristic
151	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
152	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
153	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
154	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
155	#11719917	—	4	1	no	—
156	C₂×#88322	—	2	1	no	—
157	C₂×#88322	—	2	1	no	—
158	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
159	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
160	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
161	C₂×#88322	C₂⁴	1	1	yes	characteristic
162	#11719912	—	4	1	no	—
163	C₈×D₅₃	—	2	1	no	—
164	C₈×D₅₃	—	2	1	no	—
165	C₈×D₅₃	—	2	1	no	—
166	C₈×D₅₃	—	2	1	no	—
167	C₈×D₅₃	—	4	1	no	—
168	#11719910	—	2	1	no	—
169	#11719910	—	2	1	no	—
170	#11719910	—	2	1	no	—
171	#11719910	—	2	1	no	—
172	#11719910	—	2	1	no	—
173	#11719910	—	2	1	no	—
174	#11719910	—	2	1	no	—
175	#11719910	—	2	1	no	—
176	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
177	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
178	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
179	C₂×C₄×C₅₃	—	2	1	no	—
180	C₂×C₄×C₅₃	—	2	1	no	—
181	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
182	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
183	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
184	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
185	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
186	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
187	C₂²⋊D₅₃	—	4	1	no	—
188	C₂²⋊D₅₃	—	4	1	no	—
189	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
190	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
191	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
192	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
193	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
194	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
195	D₂₁₂	—	4	1	no	—
196	C₄×D₅₃	—	2	1	no	—
197	C₄×D₅₃	—	2	1	no	—
198	C₄×D₅₃	—	2	1	no	—
199	C₄×D₅₃	—	2	1	no	—
200	C₄×D₅₃	—	4	1	no	—
201	C₄×D₅₃	—	4	1	no	—
202	Dic₁₀₆	—	4	1	no	—
203	C₈×C₅₃	—	2	1	no	—
204	C₈×C₅₃	—	2	1	no	—
205	C₈×C₅₃	—	2	1	no	—
206	C₈×C₅₃	—	2	1	no	—
207	#88322	—	2	1	no	—
208	#88322	—	2	1	no	—
209	#88322	—	2	1	no	—
210	#88322	H(5,𝔽₂)	1	1	yes	characteristic
211	#88322	2₋¹⁺⁴	1	1	yes	characteristic
212	#33509	—	53	1	no	maximal, Sylow
213	C₂²×C₅₃	—	2	1	no	—
214	C₂²×C₅₃	—	2	1	no	—
215	C₂²×C₅₃	—	2	1	no	—
216	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
217	C₂×D₅₃	—	2	1	no	—
218	C₂×D₅₃	—	2	1	no	—
219	C₂×D₅₃	—	2	1	no	—
220	C₂×D₅₃	—	2	1	no	—
221	C₂×D₅₃	—	2	1	no	—
222	C₂×D₅₃	—	2	1	no	—
223	C₄×C₅₃	—	2	1	no	—
224	C₄×C₅₃	—	2	1	no	—
225	C₄×C₅₃	—	2	1	no	—
226	C₄×C₅₃	—	2	1	no	—
227	C₄×C₅₃	—	2	1	no	—
228	C₄×C₅₃	#520	1	1	yes	characteristic
229	C₄×C₅₃	#568	1	1	yes	characteristic
230	Dic₅₃	—	2	1	no	—
231	Dic₅₃	—	2	1	no	—
232	Dic₅₃	—	2	1	no	—
233	Dic₅₃	—	2	1	no	—
234	Dic₅₃	—	2	1	no	—
235	Dic₅₃	—	2	1	no	—
236	#2966	—	53	1	no	—
237	#2183	—	53	1	no	—
238	#2183	—	53	1	no	—
239	#2169	—	53	1	no	—
240	#2169	—	53	1	no	—
241	#2168	—	53	1	no	—
242	#2168	—	53	1	no	—
243	#2168	—	53	1	no	—
244	#2168	—	53	1	no	—
245	#2164	—	53	1	no	—
246	#2164	—	53	1	no	—
247	#2163	—	53	1	no	—
248	#2151	—	53	1	no	—
249	#2151	—	53	1	no	—
250	#2150	—	53	1	no	—
251	C₂×C₅₃	—	4	1	no	—
252	C₂×C₅₃	#2988	1	1	yes	characteristic
253	C₂×C₅₃	#3407	1	1	yes	characteristic
254	C₂×C₅₃	#3407	1	1	yes	characteristic
255	D₅₃	—	4	1	no	—
256	D₅₃	—	4	1	no	—
257	#529	—	53	1	no	—
258	C₂×M₃₂	—	53	1	no	—
259	C₂×M₃₂	—	53	1	no	—
260	C₂×M₃₂	—	53	1	no	—
261	C₂×M₃₂	—	53	1	no	—
262	C₂²×C₁₆	—	53	1	no	—
263	C₂²×C₁₆	—	53	1	no	—
264	#446	—	53	1	no	—
265	C₈×Q₈	—	53	1	no	—
266	#436	—	53	1	no	—
267	#435	—	53	1	no	—
268	#435	—	53	1	no	—
269	C₈×D₄	—	53	1	no	—
270	C₈×D₄	—	53	1	no	—
271	C₈×D₄	—	53	1	no	—
272	#433	—	53	1	no	—
273	#433	#6157	1	1	yes	characteristic
274	#432	—	53	1	no	—
275	#405	—	53	1	no	—
276	#405	—	53	1	no	—
277	C₂×C₄×C₈	—	53	1	no	—
278	C₄⋊C₁₆	—	53	1	no	—
279	C₄⋊C₁₆	—	53	1	no	—
280	C₄⋊C₁₆	—	53	1	no	—
281	C₄⋊C₁₆	—	53	1	no	—
282	C₄⋊C₁₆	—	53	1	no	—
283	C₄⋊C₁₆	—	53	1	no	—
284	C₄⋊C₁₆	—	53	1	no	—
285	C₄⋊C₁₆	—	53	1	no	—
286	C₄⋊C₁₆	—	53	1	no	—
287	C₄⋊C₁₆	—	53	1	no	—
288	C₂²⋊C₁₆	—	53	1	no	—
289	C₂²⋊C₁₆	—	53	1	no	—
290	C₂²⋊C₁₆	—	53	1	no	—
291	C₂²⋊C₁₆	—	53	1	no	—
292	C₂²⋊C₁₆	—	53	1	no	—
293	C₂²⋊C₁₆	—	53	1	no	—
294	#346	—	53	1	no	—
295	#346	—	53	1	no	—
296	#346	—	53	1	no	—
297	#346	—	53	1	no	—
298	C₄×C₁₆	—	53	1	no	—
299	C₄×C₁₆	—	53	1	no	—
300	C₅₃	#33509	1	1	yes	characteristic, complemented, Sylow
301	C₂×M₁₆	—	53	1	no	—
302	C₂×M₁₆	—	53	1	no	—
303	C₂²×C₈	—	53	1	no	—
304	C₂²×C₈	—	53	1	no	—
305	C₂²×C₈	—	53	1	no	—
306	C₂²×C₈	—	53	1	no	—
307	#126	—	53	1	no	—
308	#126	—	53	1	no	—
309	#125	—	53	1	no	—
310	#124	—	53	1	no	—
311	#123	—	53	1	no	—
312	#123	—	53	1	no	—
313	C₂²⋊Q₈	—	53	1	no	—
314	#121	—	53	1	no	—
315	C₄×Q₈	—	53	1	no	—
316	C₄×D₄	—	53	1	no	—
317	C₄×D₄	—	53	1	no	—
318	C₄×D₄	—	53	1	no	—
319	#117	—	53	1	no	—
320	#117	C₂×#6157	1	1	yes	characteristic
321	C₂×C₄²	—	53	1	no	—
322	M₃₂	—	212	1	no	—
323	M₃₂	—	212	1	no	—
324	M₃₂	—	212	1	no	—
325	M₃₂	—	212	1	no	—
326	C₂×C₁₆	—	53	1	no	—
327	C₂×C₁₆	—	53	1	no	—
328	C₂×C₁₆	—	53	1	no	—
329	C₂×C₁₆	—	53	1	no	—
330	C₂×C₁₆	—	53	1	no	—
331	C₂×C₁₆	—	53	1	no	—
332	C₂×C₁₆	—	53	1	no	—
333	C₂×C₁₆	—	53	1	no	—
334	C₂×C₁₆	—	212	1	no	—
335	C₂×C₁₆	—	212	1	no	—
336	C₄⋊C₈	—	53	1	no	—
337	C₄⋊C₈	—	53	1	no	—
338	C₄⋊C₈	—	53	1	no	—
339	C₄⋊C₈	—	53	1	no	—
340	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic
341	C₄⋊C₈	C₂×#6157	1	1	yes	characteristic
342	C₂²⋊C₈	—	53	1	no	—
343	C₂²⋊C₈	—	53	1	no	—
344	C₂²⋊C₈	—	53	1	no	—
345	C₂²⋊C₈	—	53	1	no	—
346	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
347	C₂²⋊C₈	C₂×#6157	1	1	yes	characteristic
348	#97	—	53	1	no	—
349	#97	—	53	1	no	—
350	#97	—	53	1	no	—
351	#97	C₂×#6157	1	1	yes	characteristic
352	C₄×C₈	—	53	1	no	—
353	C₄×C₈	—	53	1	no	—
354	C₄×C₈	—	53	1	no	—
355	C₄×C₈	—	53	1	no	—
356	C₄×C₈	—	53	1	no	—
357	C₄×C₈	C₂×#6157	1	1	yes	characteristic
358	C₂×Q₈	—	53	1	no	—
359	C₂×D₄	—	53	1	no	—
360	C₂×D₄	—	53	1	no	—
361	C₂×D₄	—	53	1	no	—
362	C₂²×C₄	—	53	1	no	—
363	C₂²×C₄	—	53	1	no	—
364	C₂²×C₄	—	53	1	no	—
365	C₂²×C₄	—	53	1	no	—
366	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
367	M₁₆	—	212	1	no	—
368	M₁₆	—	212	1	no	—
369	C₂×C₈	—	53	1	no	—
370	C₂×C₈	—	53	1	no	—
371	C₂×C₈	—	53	1	no	—
372	C₂×C₈	—	53	1	no	—
373	C₂×C₈	—	106	1	no	—
374	C₂×C₈	—	106	1	no	—
375	C₂×C₈	—	106	1	no	—
376	C₂×C₈	—	106	1	no	—
377	C₂×C₈	—	106	1	no	—
378	C₂×C₈	—	106	1	no	—
379	C₂×C₈	—	212	1	no	—
380	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
381	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
382	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
383	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
384	C₄⋊C₄	—	53	1	no	—
385	C₄⋊C₄	—	53	1	no	—
386	C₄⋊C₄	—	53	1	no	—
387	C₄⋊C₄	—	53	1	no	—
388	C₄⋊C₄	—	53	1	no	—
389	C₄⋊C₄	—	53	1	no	—
390	C₄⋊C₄	—	53	1	no	—
391	C₄⋊C₄	—	53	1	no	—
392	C₄⋊C₄	D₅₃⋊C₈	1	1	yes	characteristic
393	C₄⋊C₄	D₅₃⋊C₈	1	1	yes	characteristic
394	C₂²⋊C₄	—	53	1	no	—
395	C₂²⋊C₄	—	53	1	no	—
396	C₂²⋊C₄	—	53	1	no	—
397	C₂²⋊C₄	—	53	1	no	—
398	C₂²⋊C₄	—	53	1	no	—
399	C₂²⋊C₄	—	53	1	no	—
400	C₂²⋊C₄	—	53	1	no	—
401	C₂²⋊C₄	—	53	1	no	—
402	C₂²⋊C₄	D₅₃⋊C₈	1	1	yes	characteristic
403	C₂²⋊C₄	D₅₃⋊C₈	1	1	yes	characteristic
404	C₄²	—	53	1	no	—
405	C₄²	—	53	1	no	—
406	C₄²	—	53	1	no	—
407	C₄²	—	53	1	no	—
408	C₄²	C₂²×#6157	1	1	yes	characteristic
409	C₄²	C₂²×#6157	1	1	yes	characteristic
410	C₁₆	—	106	1	no	—
411	C₁₆	—	106	1	no	—
412	C₁₆	—	106	1	no	—
413	C₁₆	—	106	1	no	—
414	C₁₆	—	106	1	no	—
415	C₁₆	—	106	1	no	—
416	C₁₆	—	106	1	no	—
417	C₁₆	—	106	1	no	—
418	C₂³	—	53	1	no	—
419	C₂³	—	53	1	no	—
420	C₂³	C₂×D₅₃⋊C₈	1	1	yes	characteristic
421	Q₈	—	212	1	no	—
422	D₄	—	212	1	no	—
423	D₄	—	212	1	no	—
424	D₄	—	212	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	53	1	no	—
428	C₂×C₄	—	53	1	no	—
429	C₂×C₄	—	53	1	no	—
430	C₂×C₄	—	53	1	no	—
431	C₂×C₄	—	53	1	no	—
432	C₂×C₄	—	53	1	no	—
433	C₂×C₄	—	106	1	no	—
434	C₂×C₄	—	106	1	no	—
435	C₂×C₄	—	106	1	no	—
436	C₂×C₄	—	106	1	no	—
437	C₂×C₄	—	212	1	no	—
438	C₂×C₄	—	212	1	no	—
439	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
440	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
441	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
442	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
443	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
444	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	53	1	no	—
450	C₈	—	53	1	no	—
451	C₈	—	106	1	no	—
452	C₈	—	106	1	no	—
453	C₈	—	106	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	106	1	no	—
458	C₂²	—	106	1	no	—
459	C₂²	—	106	1	no	—
460	C₂²	—	106	1	no	—
461	C₂²	—	106	1	no	—
462	C₂²	—	106	1	no	—
463	C₂²	C₂²×D₅₃⋊C₈	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	106	1	no	—
470	C₄	—	106	1	no	—
471	C₄	—	106	1	no	—
472	C₄	—	106	1	no	—
473	C₄	—	106	1	no	—
474	C₄	—	106	1	no	—
475	C₄	#16811692	1	1	yes	characteristic
476	C₄	#16811702	1	1	yes	characteristic
477	C₂	—	4	1	no	—
478	C₂	—	212	1	no	—
479	C₂	—	212	1	no	—
480	C₂	#20291632	1	1	yes	characteristic
481	C₂	#20291683	1	1	yes	characteristic
482	C₂	#20291683	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6157
commutator, socle	C₂²×C₅₃	C₂³×C₈
Fitting	C₅₃×#433	C₄
prime radical	#13133190	C₈
cosocle	C₂×#88322	C₂⁴
hypercenter	#433	#6157
hypocenter	C₅₃	#33509
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #433

Complements

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

N	H ≅ G/N	type
1. #20291132	C₂	semidirect
2. #20291131	C₂	semidirect
3. #20291101	C₂	semidirect
4. #20291100	C₂	semidirect
5. #20291098	C₂	semidirect
6. #20291097	C₂	semidirect
7. #20291097	C₂	semidirect
8. #20291096	C₂	semidirect
9. #20291083	C₂	semidirect
10. #20291080	C₂	semidirect
11. #20291079	C₂	semidirect
12. #20291051	C₂	semidirect
13. #20291050	C₂	semidirect
14. #20291048	C₂	semidirect
300. C₅₃	#33509	semidirect

Maximal subgroups

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

subgroup	index
#20291132	2
#20291131	2
#20291101	2
#20291100	2
#20291098	2
#20291097	2
#20291096	2
#20291083	2
#20291080	2
#20291079	2
#20291051	2
#20291050	2
#20291048	2
#20283688	2
#33509	53