Subgroups — #28328252

Order 13568.

600 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291083	C₂	1	2	yes	maximal, complemented
2	#20291082	C₂	1	2	yes	maximal, complemented
3	#20291077	C₂	1	1	yes	maximal, characteristic, complemented
4	#20291076	C₂	1	1	yes	maximal, characteristic, complemented
5	#20291073	C₂	1	1	yes	maximal, characteristic, complemented
6	#20291072	C₂	1	1	yes	maximal, characteristic, complemented
7	#20291051	C₂	1	2	yes	maximal, complemented
8	#20290943	C₂	1	1	yes	maximal, characteristic
9	D₅₃⋊(C₂²⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
10	#20290925	C₂	1	2	yes	maximal, complemented
11	C₂×#16810580	C₂	1	1	yes	maximal, characteristic
12	C₂×#13133292	C₂²	1	2	yes	—
13	C₂×D₅₃⋊C₁₆	C₂²	1	2	yes	—
14	#16811544	C₂²	1	2	yes	complemented
15	#16811544	C₂²	1	2	yes	complemented
16	C₄⋊#11719910	C₂²	1	2	yes	complemented
17	C₄⋊#11719910	C₂²	1	2	yes	complemented
18	#16811518	C₂²	1	2	yes	—
19	#16811518	C₂²	1	2	yes	—
20	C₂²⋊#11719910	C₂²	1	1	yes	characteristic
21	C₂²⋊#11719910	C₂²	1	1	yes	characteristic
22	C₂²⋊#11719910	C₂²	1	1	yes	characteristic
23	C₂²⋊#11719910	C₂²	1	1	yes	characteristic
24	#16811512	C₂²	1	2	yes	complemented
25	#16811511	C₂²	1	2	yes	complemented
26	#16811509	C₂²	1	2	yes	complemented
27	C₄×#11719910	C₂²	1	2	yes	complemented
28	C₂²×#11719912	C₄	1	1	yes	characteristic
29	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
30	C₂×#13133174	C₄	1	1	yes	characteristic
31	#16810580	C₄	1	1	yes	characteristic
32	#16810580	C₄	1	1	yes	characteristic
33	#16810580	C₄	1	1	yes	characteristic
34	#16810580	C₄	1	1	yes	characteristic
35	#16810580	C₂²	1	1	yes	characteristic
36	#16810580	C₂²	1	1	yes	characteristic
37	#16810580	C₂²	1	1	yes	characteristic
38	#16810580	C₂²	1	1	yes	characteristic
39	C₂×#13133127	C₄	1	1	yes	characteristic
40	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
41	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
42	C₂×#97×C₅₃	C₄	1	1	yes	characteristic
43	#13133292	—	2	4	no	—
44	D₅₃⋊C₁₆	—	2	4	no	—
45	C₂×#11719910	C₂³	1	2	yes	—
46	C₂×#11719910	C₂³	1	2	yes	—
47	C₂×#11719910	C₂³	1	2	yes	—
48	C₂×#11719910	C₂³	1	2	yes	—
49	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
50	C₂×#11719912	—	2	4	no	—
51	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
52	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
53	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
54	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
55	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
56	C₂²×#88322	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₅₃	—	2	4	no	—
58	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
62	#13133174	C₈	1	1	yes	characteristic
63	#13133174	C₈	1	1	yes	characteristic
64	#13133174	C₈	1	1	yes	characteristic
65	#13133174	C₈	1	1	yes	characteristic
66	#13133174	C₂×C₄	1	1	yes	characteristic
67	#13133174	C₂×C₄	1	1	yes	characteristic
68	#13133174	C₂×C₄	1	1	yes	characteristic
69	#13133174	C₂×C₄	1	1	yes	characteristic
70	C₂×#11719919	C₈	1	1	yes	characteristic
71	C₂×#11719919	C₈	1	1	yes	characteristic
72	C₂×#11719921	C₈	1	1	yes	characteristic
73	C₂×#11719921	C₈	1	1	yes	characteristic
74	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
75	#13133127	C₂×C₄	1	1	yes	characteristic
76	#13133127	C₂×C₄	1	1	yes	characteristic
77	#13133127	C₂×C₄	1	1	yes	characteristic
78	#13133127	C₂×C₄	1	1	yes	characteristic
79	C₄×#88322	C₂×C₄	1	1	yes	characteristic
80	C₄×#88322	C₂×C₄	1	1	yes	characteristic
81	C₄×#88322	C₂³	1	1	yes	characteristic
82	C₄×#88322	C₂³	1	1	yes	characteristic
83	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
86	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
88	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
90	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
91	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
92	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
93	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
94	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
97	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
99	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
100	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₅₃	—	2	2	no	—
102	C₂×C₄×D₅₃	—	2	2	no	—
103	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₅₃	—	2	2	no	—
108	C₂×C₈×C₅₃	—	2	2	no	—
109	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₅₃	C₂×C₈	1	1	yes	characteristic
114	C₄²×C₅₃	C₂×C₈	1	1	yes	characteristic
115	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
117	#11719921	C₂×C₈	1	1	yes	characteristic
118	#11719921	C₂×C₈	1	1	yes	characteristic
119	#11719921	C₂×C₈	1	1	yes	characteristic
120	#11719921	C₂×C₈	1	1	yes	characteristic
121	#11719921	C₂×C₈	1	1	yes	characteristic
122	#11719921	C₂×C₈	1	1	yes	characteristic
123	#11719921	C₂×C₈	1	1	yes	characteristic
124	#11719921	C₂×C₈	1	1	yes	characteristic
125	#11719919	C₂×C₈	1	1	yes	characteristic
126	#11719919	C₂×C₈	1	1	yes	characteristic
127	#11719919	C₂×C₈	1	1	yes	characteristic
128	#11719919	C₂×C₈	1	1	yes	characteristic
129	#11719919	C₂×C₈	1	1	yes	characteristic
130	#11719919	C₂×C₈	1	1	yes	characteristic
131	#11719919	C₂×C₈	1	1	yes	characteristic
132	#11719919	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₅₃	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×#88322	—	2	2	no	—
138	C₂×#88322	—	2	2	no	—
139	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
140	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
141	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
142	C₂×#88322	C₂⁴	1	1	yes	characteristic
143	#11719912	—	2	2	no	—
144	#11719912	—	2	2	no	—
145	#11719912	—	2	2	no	—
146	#11719912	M₁₆	1	4	yes	—
147	C₈×D₅₃	—	2	2	no	—
148	C₈×D₅₃	—	2	2	no	—
149	C₈×D₅₃	—	2	2	no	—
150	C₈×D₅₃	#41	1	4	yes	—
151	#11719910	—	2	2	no	—
152	#11719910	—	2	2	no	—
153	#11719910	—	2	2	no	—
154	#11719910	—	2	2	no	—
155	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
156	C₂²×D₅₃	—	2	2	no	—
157	C₂²×D₅₃	—	2	2	no	—
158	C₂²×D₅₃	—	4	1	no	—
159	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
160	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
161	C₂×C₄×C₅₃	—	2	2	no	—
162	C₂×C₄×C₅₃	—	2	1	no	—
163	C₂×C₄×C₅₃	—	2	1	no	—
164	C₂×C₄×C₅₃	—	4	1	no	—
165	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
171	C₂×Dic₅₃	—	2	2	no	—
172	C₂×Dic₅₃	—	2	2	no	—
173	C₂×Dic₅₃	—	4	1	no	—
174	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
175	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
176	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
177	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
180	C₄×D₅₃	—	2	2	no	—
181	C₄×D₅₃	—	2	1	no	—
182	C₄×D₅₃	—	2	1	no	—
183	C₄×D₅₃	—	2	2	no	—
184	C₄×D₅₃	#117	1	2	yes	—
185	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
186	C₈×C₅₃	—	2	1	no	—
187	C₈×C₅₃	—	2	1	no	—
188	C₈×C₅₃	#117	1	2	yes	—
189	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
190	#88322	—	2	1	no	—
191	#88322	—	2	1	no	—
192	#88322	C₂×M₁₆	1	2	yes	—
193	#88322	C₂×#41	1	2	yes	—
194	#33422	—	53	1	no	maximal, Sylow
195	C₂²×C₅₃	—	2	1	no	—
196	C₂²×C₅₃	—	2	1	no	—
197	C₂²×C₅₃	#504	1	2	yes	—
198	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
199	C₂×D₅₃	—	2	1	no	—
200	C₂×D₅₃	—	2	1	no	—
201	C₂×D₅₃	—	2	1	no	—
202	C₂×D₅₃	—	2	1	no	—
203	C₂×D₅₃	—	2	1	no	—
204	C₂×D₅₃	—	4	4	no	—
205	C₂×D₅₃	#431	1	2	yes	—
206	C₄×C₅₃	—	2	1	no	—
207	C₄×C₅₃	—	2	1	no	—
208	C₄×C₅₃	—	2	1	no	—
209	C₄×C₅₃	—	2	1	no	—
210	C₄×C₅₃	—	2	1	no	—
211	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
212	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
213	Dic₅₃	—	2	1	no	—
214	Dic₅₃	—	2	1	no	—
215	Dic₅₃	—	2	1	no	—
216	Dic₅₃	—	2	1	no	—
217	Dic₅₃	—	2	1	no	—
218	Dic₅₃	#431	1	2	yes	—
219	C₂×#405	—	53	1	no	—
220	#2164	—	53	2	no	—
221	#2164	—	53	2	no	—
222	#2163	—	53	1	no	—
223	#2163	—	53	1	no	—
224	#2162	—	53	1	no	—
225	#2162	—	53	1	no	—
226	#2151	—	53	2	no	—
227	#2112	—	53	1	no	—
228	C₂×C₂²⋊C₁₆	—	53	1	no	—
229	#2108	—	53	2	no	—
230	C₂×C₅₃	—	2	2	no	—
231	C₂×C₅₃	C₂×#431	1	1	yes	characteristic
232	C₂×C₅₃	C₂×#504	1	1	yes	characteristic
233	C₂×C₅₃	#3407	1	1	yes	characteristic
234	D₅₃	—	2	2	no	—
235	D₅₃	—	4	1	no	—
236	C₂²×M₁₆	—	53	1	no	—
237	C₂³×C₈	—	53	1	no	—
238	C₂×#117	—	53	1	no	—
239	C₂×M₃₂	—	53	2	no	—
240	C₂²×C₁₆	—	53	2	no	—
241	#405	—	53	1	no	—
242	#405	—	53	1	no	—
243	#405	—	53	1	no	—
244	#405	—	53	1	no	—
245	#405	—	53	1	no	—
246	#405	—	53	1	no	—
247	#405	—	53	1	no	—
248	#405	—	53	1	no	—
249	C₂×#97	—	53	1	no	—
250	C₂×#97	#6157	1	1	yes	characteristic
251	C₂×C₄×C₈	—	53	1	no	—
252	C₂×C₄×C₈	—	53	1	no	—
253	C₄⋊C₁₆	—	53	2	no	—
254	C₄⋊C₁₆	—	53	2	no	—
255	C₄⋊C₁₆	—	53	2	no	—
256	C₄⋊C₁₆	—	53	2	no	—
257	C₂²⋊C₁₆	—	53	1	no	—
258	C₂²⋊C₁₆	—	53	1	no	—
259	C₂²⋊C₁₆	—	53	2	no	—
260	C₂²⋊C₁₆	—	53	1	no	—
261	C₂²⋊C₁₆	—	53	1	no	—
262	C₂²⋊C₁₆	—	53	2	no	—
263	#346	—	53	2	no	—
264	#346	—	53	2	no	—
265	C₄×C₁₆	—	53	2	no	—
266	C₄×C₁₆	—	53	2	no	—
267	C₅₃	#33422	1	1	yes	characteristic, complemented, Sylow
268	C₂³×C₄	—	53	1	no	—
269	C₂×M₁₆	—	53	1	no	—
270	C₂×M₁₆	—	53	1	no	—
271	C₂×M₁₆	—	53	1	no	—
272	C₂×M₁₆	—	53	1	no	—
273	C₂×M₁₆	—	106	4	no	—
274	C₂²×C₈	—	53	1	no	—
275	C₂²×C₈	—	53	1	no	—
276	C₂²×C₈	—	53	1	no	—
277	C₂²×C₈	—	53	1	no	—
278	C₂²×C₈	—	53	1	no	—
279	C₂²×C₈	—	53	1	no	—
280	C₂²×C₈	—	106	4	no	—
281	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
282	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
283	#117	—	53	1	no	—
284	#117	—	53	1	no	—
285	#117	—	53	1	no	—
286	#117	—	53	1	no	—
287	#117	—	53	1	no	—
288	#117	—	53	1	no	—
289	#117	—	53	1	no	—
290	#117	—	53	1	no	—
291	C₂×C₄⋊C₄	—	53	1	no	—
292	C₂×C₄⋊C₄	—	53	1	no	—
293	C₂×C₂²⋊C₄	—	53	1	no	—
294	C₂×C₂²⋊C₄	—	53	1	no	—
295	C₂×C₄²	—	53	1	no	—
296	C₂×C₄²	C₂×#6157	1	1	yes	characteristic
297	M₃₂	—	106	4	no	—
298	C₂×C₁₆	—	53	2	no	—
299	C₂×C₁₆	—	53	2	no	—
300	C₂×C₁₆	—	53	2	no	—
301	C₂×C₁₆	—	53	2	no	—
302	C₂×C₁₆	—	106	4	no	—
303	#97	—	53	1	no	—
304	#97	—	53	1	no	—
305	#97	—	53	1	no	—
306	#97	—	53	1	no	—
307	#97	C₂×#6157	1	1	yes	characteristic
308	#97	C₂×#6157	1	1	yes	characteristic
309	#97	C₂×#6157	1	1	yes	characteristic
310	#97	C₂×#6157	1	1	yes	characteristic
311	C₄×C₈	—	53	1	no	—
312	C₄×C₈	—	53	1	no	—
313	C₄×C₈	—	53	1	no	—
314	C₄×C₈	—	53	1	no	—
315	C₄×C₈	—	53	1	no	—
316	C₄×C₈	—	53	1	no	—
317	C₄×C₈	—	53	1	no	—
318	C₄×C₈	—	53	1	no	—
319	C₂⁴	—	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	—	106	2	no	—
328	C₂²×C₄	—	106	2	no	—
329	C₂²×C₄	D₅₃⋊C₈	1	1	yes	characteristic
330	C₂²×C₄	D₅₃⋊C₈	1	1	yes	characteristic
331	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
332	M₁₆	—	53	4	no	—
333	M₁₆	—	106	2	no	—
334	M₁₆	—	106	2	no	—
335	M₁₆	—	106	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	53	1	no	—
339	C₂×C₈	—	53	1	no	—
340	C₂×C₈	—	53	4	no	—
341	C₂×C₈	—	53	1	no	—
342	C₂×C₈	—	53	1	no	—
343	C₂×C₈	—	106	2	no	—
344	C₂×C₈	—	106	2	no	—
345	C₂×C₈	—	106	2	no	—
346	C₂×C₈	—	106	2	no	—
347	C₂×C₈	—	106	2	no	—
348	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
349	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
350	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
351	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
352	C₄⋊C₄	—	53	1	no	—
353	C₄⋊C₄	—	53	1	no	—
354	C₄⋊C₄	—	53	1	no	—
355	C₄⋊C₄	—	53	1	no	—
356	C₄⋊C₄	—	53	1	no	—
357	C₄⋊C₄	—	53	1	no	—
358	C₄⋊C₄	—	53	1	no	—
359	C₄⋊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	—	53	1	no	—
364	C₂²⋊C₄	—	53	1	no	—
365	C₂²⋊C₄	—	53	1	no	—
366	C₂²⋊C₄	—	53	1	no	—
367	C₂²⋊C₄	—	53	1	no	—
368	C₄²	—	53	1	no	—
369	C₄²	—	53	1	no	—
370	C₄²	—	53	1	no	—
371	C₄²	—	53	1	no	—
372	C₄²	D₅₃⋊C₈	1	1	yes	characteristic
373	C₄²	D₅₃⋊C₈	1	1	yes	characteristic
374	C₄²	C₂²×#6157	1	1	yes	characteristic
375	C₄²	C₂²×#6157	1	1	yes	characteristic
376	C₁₆	—	106	2	no	—
377	C₁₆	—	106	2	no	—
378	C₁₆	—	106	2	no	—
379	C₁₆	—	106	2	no	—
380	C₂³	—	53	1	no	—
381	C₂³	—	53	1	no	—
382	C₂³	—	106	2	no	—
383	C₂³	—	106	2	no	—
384	C₂³	—	212	1	no	—
385	C₂³	C₂×D₅₃⋊C₈	1	1	yes	characteristic
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	53	1	no	—
391	C₂×C₄	—	53	2	no	—
392	C₂×C₄	—	53	2	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	—	106	2	no	—
399	C₂×C₄	—	106	2	no	—
400	C₂×C₄	—	106	2	no	—
401	C₂×C₄	—	106	2	no	—
402	C₂×C₄	—	106	1	no	—
403	C₂×C₄	—	106	1	no	—
404	C₂×C₄	—	212	1	no	—
405	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
406	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
407	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
408	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
409	C₂×C₄	C₂×D₅₃⋊C₈	1	1	yes	characteristic
410	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	53	2	no	—
414	C₈	—	53	2	no	—
415	C₈	—	106	1	no	—
416	C₈	—	106	1	no	—
417	C₈	#13133296	1	2	yes	—
418	C₈	D₅₃⋊M₁₆	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	53	2	no	—
422	C₂²	—	106	1	no	—
423	C₂²	—	106	1	no	—
424	C₂²	—	106	1	no	—
425	C₂²	—	106	1	no	—
426	C₂²	—	106	1	no	—
427	C₂²	—	212	4	no	—
428	C₂²	#16811682	1	2	yes	—
429	C₂²	C₂²×D₅₃⋊C₈	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	53	2	no	—
436	C₄	—	106	1	no	—
437	C₄	—	106	1	no	—
438	C₄	—	106	1	no	—
439	C₄	—	106	1	no	—
440	C₄	—	106	1	no	—
441	C₄	C₂×#13133296	1	1	yes	characteristic
442	C₄	C₂×D₅₃⋊M₁₆	1	1	yes	characteristic
443	C₂	—	2	2	no	—
444	C₂	—	106	2	no	—
445	C₂	—	212	1	no	—
446	C₂	D₅₃⋊#431	1	1	yes	characteristic
447	C₂	C₂×#16811682	1	1	yes	characteristic
448	C₂	#20291684	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6157
commutator, socle	C₂²×C₅₃	C₂³×C₈
Fitting	C₂×#97×C₅₃	C₄
prime radical	C₂³×D₅₃	C₂×C₈
cosocle	C₂×#88322	C₂⁴
hypercenter	C₂×#97	#6157
hypocenter	C₅₃	#33422
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
1. #20291083	C₂	semidirect
2. #20291082	C₂	semidirect
3. #20291077	C₂	semidirect
4. #20291076	C₂	semidirect
5. #20291073	C₂	semidirect
6. #20291072	C₂	semidirect
7. #20291051	C₂	semidirect
10. #20290925	C₂	semidirect
14. #16811544	C₂²	semidirect
15. #16811544	C₂²	semidirect
16. C₄⋊#11719910	C₂²	semidirect
17. C₄⋊#11719910	C₂²	semidirect
24. #16811512	C₂²	semidirect
25. #16811511	C₂²	semidirect
26. #16811509	C₂²	semidirect
27. C₄×#11719910	C₂²	semidirect
267. C₅₃	#33422	semidirect

Maximal subgroups

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

subgroup	index
#20291083	2
#20291082	2
#20291077	2
#20291076	2
#20291073	2
#20291072	2
#20291051	2
#20290943	2
D₅₃⋊(C₂²⋊C₁₆)	2
#20290925	2
C₂×#16810580	2
#33422	53