Subgroups — #27390947

Order 13568.

938 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810745	C₂	1	1	yes	maximal, characteristic, complemented
2	#20283419	C₂	1	2	yes	maximal, complemented
3	C₂×M₁₆×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#20275604	C₂	1	1	yes	maximal, characteristic, complemented
5	#20275464	C₂	1	1	yes	maximal, characteristic, complemented
6	#20275428	C₂	1	2	yes	maximal, complemented
7	#20275159	C₂	1	2	yes	maximal, complemented
8	#20274757	C₂	1	1	yes	maximal, characteristic, complemented
9	#20274601	C₂	1	1	yes	maximal, characteristic, complemented
10	#20274555	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3054	C₂	1	1	yes	maximal, characteristic
12	C₂×#13133224	C₂²	1	2	yes	—
13	C₂²×#11719917	C₂²	1	1	yes	characteristic
14	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
15	#16810745	—	2	4	no	—
16	#16810701	—	2	4	no	—
17	#16810695	—	2	4	no	—
18	C₂×#13133153	C₂²	1	1	yes	characteristic
19	C₂×#13133153	C₂²	1	1	yes	characteristic
20	#16810650	C₂²	1	2	yes	—
21	C₂×#13133144	C₂²	1	2	yes	—
22	C₂×#13133144	C₂²	1	2	yes	—
23	#16810590	C₂²	1	2	yes	—
24	#16810587	C₂²	1	2	yes	—
25	#16810579	C₂²	1	2	yes	—
26	M₁₆×Dic₅₃	—	2	4	no	—
27	C₂×#13133127	C₂²	1	1	yes	characteristic
28	C₂×#13133127	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
31	#16810388	C₂²	1	2	yes	—
32	#16810382	C₂²	1	2	yes	—
33	#16810382	C₂²	1	2	yes	—
34	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
35	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
36	C₅₃×#525	C₂²	1	2	yes	—
37	C₅₃×#470	C₄	1	2	yes	complemented
38	C₅₃×#469	C₄	1	2	yes	complemented
39	C₅₃×#468	C₄	1	4	yes	complemented
40	C₅₃×#427	C₂²	1	1	yes	characteristic
41	C₅₃×#416	C₂²	1	2	yes	—
42	C₂³×Dic₅₃	—	2	1	no	—
43	#13133224	—	2	4	no	—
44	#13133224	—	2	4	no	—
45	C₂×#11719917	—	2	2	no	—
46	C₂×#11719917	—	2	2	no	—
47	C₂×#11719917	—	2	2	no	—
48	C₂×#11719917	D₄	1	4	yes	—
49	C₂×#11719917	C₂³	1	2	yes	—
50	C₂×#11719917	C₂³	1	2	yes	—
51	C₂²×#88322	—	2	2	no	—
52	C₂²×#88322	C₂³	1	1	yes	characteristic
53	C₂²×#88322	C₂³	1	1	yes	characteristic
54	C₂×C₄×Dic₅₃	—	2	2	no	—
55	C₂×C₄×Dic₅₃	—	2	2	no	—
56	C₂×C₄×Dic₅₃	—	2	1	no	—
57	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
59	#13133153	—	2	2	no	—
60	#13133153	—	2	2	no	—
61	C₄⋊#88322	—	2	4	no	—
62	#13133144	—	2	4	no	—
63	#13133144	—	2	4	no	—
64	C₂²⋊#88322	—	2	4	no	—
65	C₂²⋊#88322	—	2	4	no	—
66	#13133128	—	2	2	no	—
67	#13133127	—	2	2	no	—
68	#13133127	D₄	1	4	yes	complemented
69	C₄×#88322	—	2	2	no	—
70	C₈×Dic₅₃	—	2	2	no	—
71	C₈×Dic₅₃	—	2	2	no	—
72	C₂×#41×C₅₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
74	#135×C₅₃	—	2	2	no	—
75	#135×C₅₃	—	2	2	no	—
76	C₂×Q₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
77	C₂×SD₁₆×C₅₃	C₂×C₄	1	2	yes	complemented
78	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
79	C₂×M₁₆×C₅₃	—	2	2	no	—
80	C₂×M₁₆×C₅₃	—	2	2	no	—
81	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
82	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
83	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
85	#123×C₅₃	—	2	2	no	—
86	C₂²⋊Q₈×C₅₃	C₂×C₄	1	4	yes	—
87	#121×C₅₃	C₂×C₄	1	4	yes	—
88	#120×C₅₃	—	2	2	no	—
89	C₄×D₄×C₅₃	—	2	4	no	—
90	#117×C₅₃	C₂³	1	2	yes	—
91	#107×C₅₃	C₂×C₄	1	2	yes	complemented
92	#106×C₅₃	C₂×C₄	1	2	yes	complemented
93	#103×C₅₃	C₂×C₄	1	4	yes	complemented
94	#102×C₅₃	C₂×C₄	1	4	yes	complemented
95	C₂⁴×C₅₃	#41	1	1	yes	characteristic
96	#41×C₅₃	—	2	2	no	—
97	#41×C₅₃	—	2	2	no	—
98	#41×C₅₃	—	2	2	no	—
99	#41×C₅₃	—	2	2	no	—
100	C₂×Q₈×C₅₃	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₅₃	—	2	2	no	—
102	C₂×D₄×C₅₃	—	2	4	no	—
103	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₅₃	—	2	1	no	—
105	C₂²×C₄×C₅₃	—	2	1	no	—
106	C₂²×C₄×C₅₃	—	2	1	no	—
107	C₂²×C₄×C₅₃	—	2	1	no	—
108	C₂²×C₄×C₅₃	—	2	2	no	—
109	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
112	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
113	C₂²×Dic₅₃	—	2	1	no	—
114	C₂²×Dic₅₃	—	2	4	no	—
115	C₂²×Dic₅₃	—	2	1	no	—
116	C₂²×Dic₅₃	—	4	4	no	—
117	Q₁₆×C₅₃	—	2	2	no	—
118	SD₁₆×C₅₃	—	2	4	no	—
119	D₈×C₅₃	—	2	2	no	—
120	M₁₆×C₅₃	—	2	4	no	—
121	M₁₆×C₅₃	—	2	4	no	—
122	C₂×C₈×C₅₃	—	2	1	no	—
123	C₂×C₈×C₅₃	—	2	1	no	—
124	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₅₃	#41	1	2	yes	—
129	C₄⋊C₄×C₅₃	—	2	4	no	—
130	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
131	C₂²⋊C₄×C₅₃	—	2	4	no	—
132	C₂²⋊C₄×C₅₃	—	2	2	no	—
133	C₂²⋊C₄×C₅₃	—	2	4	no	—
134	C₄²×C₅₃	—	2	2	no	—
135	C₄×Dic₅₃	—	2	4	no	—
136	C₄×Dic₅₃	—	2	1	no	—
137	C₄×Dic₅₃	—	2	1	no	—
138	C₄×Dic₅₃	C₂×D₄	1	2	yes	—
139	C₄×Dic₅₃	#41	1	2	yes	—
140	#11719917	—	2	8	no	—
141	#11719917	—	2	2	no	—
142	#11719917	—	2	2	no	—
143	#11719917	—	2	2	no	—
144	#11719917	—	2	2	no	—
145	#11719917	—	4	4	no	—
146	C₂×#88322	—	2	1	no	—
147	C₂×#88322	—	2	1	no	—
148	C₂×#88322	—	2	2	no	—
149	C₂×#88322	—	2	2	no	—
150	C₂×#88322	—	4	4	no	—
151	C₂×#88322	C₂×D₄	1	2	yes	—
152	C₂×#88322	C₂×D₄	1	2	yes	—
153	C₂×#88322	C₂×D₄	1	2	yes	—
154	C₂×#88322	#41	1	2	yes	—
155	C₂³×C₅₃	—	2	1	no	—
156	C₂³×C₅₃	—	2	1	no	—
157	C₂³×C₅₃	—	2	2	no	—
158	C₂³×C₅₃	—	4	2	no	—
159	C₂³×C₅₃	C₄×D₄	1	2	yes	—
160	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
161	Q₈×C₅₃	—	2	2	no	—
162	Q₈×C₅₃	—	2	2	no	—
163	D₄×C₅₃	—	2	2	no	—
164	D₄×C₅₃	—	2	2	no	—
165	D₄×C₅₃	—	4	2	no	—
166	D₄×C₅₃	—	4	2	no	—
167	D₄×C₅₃	—	8	4	no	—
168	C₂×C₄×C₅₃	—	2	1	no	—
169	C₂×C₄×C₅₃	—	2	1	no	—
170	C₂×C₄×C₅₃	—	2	2	no	—
171	C₂×C₄×C₅₃	—	2	2	no	—
172	C₂×C₄×C₅₃	—	2	2	no	—
173	C₂×C₄×C₅₃	—	2	2	no	—
174	C₂×C₄×C₅₃	—	2	2	no	—
175	C₂×C₄×C₅₃	—	2	4	no	—
176	C₂×C₄×C₅₃	—	4	2	no	—
177	C₂×C₄×C₅₃	—	4	2	no	—
178	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
185	C₂×Dic₅₃	—	2	4	no	—
186	C₂×Dic₅₃	—	2	2	no	—
187	C₂×Dic₅₃	—	2	2	no	—
188	C₂×Dic₅₃	—	4	8	no	—
189	C₂×Dic₅₃	—	4	2	no	—
190	C₈×C₅₃	—	2	2	no	—
191	C₈×C₅₃	C₄×D₄	1	2	yes	—
192	C₈×C₅₃	C₄×D₄	1	2	yes	—
193	#88322	—	2	2	no	—
194	#88322	—	4	2	no	—
195	#88322	—	4	2	no	—
196	#88322	#121	1	4	yes	—
197	#21551	—	53	1	no	maximal, Sylow
198	C₂²×C₅₃	—	2	2	no	—
199	C₂²×C₅₃	—	2	4	no	—
200	C₂²×C₅₃	—	2	2	no	—
201	C₂²×C₅₃	—	4	2	no	—
202	C₂²×C₅₃	—	4	2	no	—
203	C₂²×C₅₃	—	4	4	no	—
204	C₂²×C₅₃	—	4	2	no	—
205	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
206	C₂²×C₅₃	#525	1	1	yes	characteristic
207	C₂²×C₅₃	#529	1	1	yes	characteristic
208	C₄×C₅₃	—	2	2	no	—
209	C₄×C₅₃	—	4	4	no	—
210	C₄×C₅₃	—	4	2	no	—
211	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
212	C₄×C₅₃	C₄×#41	1	1	yes	characteristic
213	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
214	C₄×C₅₃	#532	1	1	yes	characteristic
215	Dic₅₃	—	2	4	no	—
216	Dic₅₃	—	4	2	no	—
217	#3054	D₅₃	1	1	yes	characteristic
218	C₂×#444	—	53	1	no	—
219	#2930	—	53	2	no	—
220	C₂×C₄×M₁₆	—	53	1	no	—
221	#1974	—	53	1	no	—
222	#1945	—	53	1	no	—
223	#1938	—	53	2	no	—
224	#1896	—	53	2	no	—
225	#1811	—	53	1	no	—
226	#1773	—	53	1	no	—
227	#1764	—	53	2	no	—
228	C₂×C₅₃	—	2	1	no	—
229	C₂×C₅₃	—	2	1	no	—
230	C₂×C₅₃	—	4	2	no	—
231	C₂×C₅₃	—	8	2	no	—
232	C₂×C₅₃	C₄×#121	1	1	yes	characteristic
233	C₂×C₅₃	#2956	1	2	yes	—
234	C₂×#135	C₂×D₅₃	1	1	yes	characteristic
235	C₂×#131	—	53	2	no	—
236	C₂²×M₁₆	—	53	1	no	—
237	C₂²×M₁₆	C₂×D₅₃	1	1	yes	characteristic
238	#525	C₂×D₅₃	1	2	yes	—
239	C₂²×C₄²	—	53	1	no	—
240	#470	Dic₅₃	1	2	yes	complemented
241	#469	Dic₅₃	1	2	yes	complemented
242	#468	Dic₅₃	1	4	yes	complemented
243	#444	—	106	4	no	—
244	#436	—	106	4	no	—
245	#435	—	106	4	no	—
246	C₂×#108	—	53	1	no	—
247	C₂×#108	—	53	1	no	—
248	#427	C₂×D₅₃	1	1	yes	characteristic
249	#424	—	53	2	no	—
250	C₂×#104	—	53	2	no	—
251	C₂×#104	—	53	2	no	—
252	#416	C₂×D₅₃	1	2	yes	—
253	#408	—	53	2	no	—
254	#407	—	53	2	no	—
255	#405	—	53	2	no	—
256	C₄×M₁₆	—	106	4	no	—
257	C₂×#97	—	53	1	no	—
258	C₂×#97	—	53	1	no	—
259	C₂×C₄×C₈	—	53	1	no	—
260	C₂×C₄×C₈	—	53	1	no	—
261	#341	—	53	2	no	—
262	#339	—	53	2	no	—
263	#339	—	53	2	no	—
264	C₅₃	#21551	1	1	yes	characteristic, complemented, Sylow
265	C₂×#41	C₂²×D₅₃	1	2	yes	—
266	C₂³×C₄	—	106	1	no	—
267	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
268	#135	—	2	2	no	—
269	#135	—	2	2	no	—
270	C₂×Q₁₆	C₂×Dic₅₃	1	1	yes	characteristic, complemented
271	C₂×SD₁₆	C₂×Dic₅₃	1	2	yes	complemented
272	C₂×D₈	C₂×Dic₅₃	1	1	yes	characteristic, complemented
273	#131	—	106	4	no	—
274	#131	—	106	4	no	—
275	C₂×M₁₆	—	2	2	no	—
276	C₂×M₁₆	—	2	2	no	—
277	C₂×M₁₆	—	53	4	no	—
278	C₂×M₁₆	—	53	2	no	—
279	C₂×M₁₆	—	53	2	no	—
280	C₂×M₁₆	—	106	2	no	—
281	C₂×M₁₆	—	106	2	no	—
282	C₂×M₁₆	—	106	2	no	—
283	C₂×M₁₆	C₂×Dic₅₃	1	2	yes	—
284	C₂×M₁₆	C₂×Dic₅₃	1	2	yes	—
285	C₂²×C₈	—	53	1	no	—
286	C₂²×C₈	—	53	1	no	—
287	C₂²×C₈	—	106	2	no	—
288	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
289	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
290	#123	—	2	2	no	—
291	C₂²⋊Q₈	C₂×Dic₅₃	1	4	yes	—
292	#121	C₂×Dic₅₃	1	4	yes	—
293	#120	—	2	2	no	—
294	C₄×D₄	—	2	4	no	—
295	#117	C₂²×D₅₃	1	2	yes	—
296	C₂×C₄²	—	53	1	no	—
297	C₂×C₄²	—	53	1	no	—
298	C₂×C₄²	—	106	2	no	—
299	C₂×C₄²	—	106	2	no	—
300	C₂×C₄²	—	106	1	no	—
301	#108	—	106	2	no	—
302	#108	—	106	2	no	—
303	#107	C₂×Dic₅₃	1	2	yes	complemented
304	#106	C₂×Dic₅₃	1	2	yes	complemented
305	C₄⋊C₈	—	106	4	no	—
306	#104	—	106	4	no	—
307	#104	—	106	4	no	—
308	#103	C₂×Dic₅₃	1	4	yes	complemented
309	#102	C₂×Dic₅₃	1	4	yes	complemented
310	C₂²⋊C₈	—	106	4	no	—
311	C₂²⋊C₈	—	106	4	no	—
312	#97	—	53	4	no	—
313	#97	—	106	2	no	—
314	#97	—	106	2	no	—
315	C₄×C₈	—	106	2	no	—
316	C₄×C₈	—	106	2	no	—
317	C₄×C₈	—	106	2	no	—
318	C₂⁴	#11719947	1	1	yes	characteristic
319	#41	—	2	2	no	—
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	C₂×Q₈	C₂²×Dic₅₃	1	2	yes	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	C₂²×Dic₅₃	1	2	yes	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	106	1	no	—
333	C₂²×C₄	—	106	4	no	—
334	C₂²×C₄	—	106	1	no	—
335	C₂²×C₄	—	212	4	no	—
336	C₂²×C₄	D₄×D₅₃	1	2	yes	—
337	C₂²×C₄	#11719947	1	1	yes	characteristic
338	C₂²×C₄	C₂²×Dic₅₃	1	2	yes	—
339	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
340	Q₁₆	—	2	2	no	—
341	SD₁₆	—	2	4	no	—
342	D₈	—	2	2	no	—
343	M₁₆	—	2	4	no	—
344	M₁₆	—	2	4	no	—
345	M₁₆	—	106	8	no	—
346	M₁₆	—	106	2	no	—
347	M₁₆	—	106	2	no	—
348	M₁₆	—	106	2	no	—
349	M₁₆	—	106	2	no	—
350	M₁₆	—	212	4	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	53	2	no	—
354	C₂×C₈	—	53	2	no	—
355	C₂×C₈	—	53	2	no	—
356	C₂×C₈	—	53	2	no	—
357	C₂×C₈	—	106	1	no	—
358	C₂×C₈	—	106	1	no	—
359	C₂×C₈	—	106	2	no	—
360	C₂×C₈	—	106	2	no	—
361	C₂×C₈	—	212	4	no	—
362	C₂×C₈	D₄×D₅₃	1	2	yes	—
363	C₂×C₈	#11719947	1	2	yes	—
364	C₂×C₈	C₂²×Dic₅₃	1	2	yes	—
365	C₂×C₈	C₂²×Dic₅₃	1	1	yes	characteristic
366	C₂×C₈	C₂²×Dic₅₃	1	1	yes	characteristic
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	C₂²×Dic₅₃	1	4	yes	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	53	2	no	—
374	C₄²	—	53	2	no	—
375	C₄²	—	106	4	no	—
376	C₄²	—	106	1	no	—
377	C₄²	—	106	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	D₄×Dic₅₃	1	2	yes	—
383	C₂³	C₂×#11719947	1	1	yes	characteristic
384	Q₈	—	2	2	no	—
385	Q₈	—	2	2	no	—
386	D₄	—	2	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	8	4	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	106	4	no	—
402	C₂×C₄	—	106	2	no	—
403	C₂×C₄	—	106	2	no	—
404	C₂×C₄	—	212	8	no	—
405	C₂×C₄	—	212	2	no	—
406	C₂×C₄	D₄×Dic₅₃	1	2	yes	—
407	C₂×C₄	C₂³×Dic₅₃	1	1	yes	characteristic
408	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
409	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
410	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
411	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
412	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	53	4	no	—
415	C₈	—	106	2	no	—
416	C₈	—	212	2	no	—
417	C₈	—	212	2	no	—
418	C₈	D₄×Dic₅₃	1	2	yes	—
419	C₈	D₄×Dic₅₃	1	2	yes	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	2	no	—
427	C₂²	C₂×D₄×Dic₅₃	1	1	yes	characteristic
428	C₂²	#16811133	1	1	yes	characteristic
429	C₂²	#16811154	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	4	4	no	—
432	C₄	—	4	2	no	—
433	C₄	—	106	4	no	—
434	C₄	—	212	2	no	—
435	C₄	C₂×D₄×Dic₅₃	1	1	yes	characteristic
436	C₄	#41×Dic₅₃	1	1	yes	characteristic
437	C₄	#121×D₅₃	1	1	yes	characteristic
438	C₄	#16811168	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	4	2	no	—
442	C₂	—	8	2	no	—
443	C₂	#121×Dic₅₃	1	1	yes	characteristic
444	C₂	#20283625	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting, prime radical	C₅₃×#3054	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#3054	D₅₃
hypocenter	C₅₃	#21551
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3054

Complements

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

N	H ≅ G/N	type
1. C₂×#16810745	C₂	semidirect
2. #20283419	C₂	semidirect
3. C₂×M₁₆×Dic₅₃	C₂	semidirect
4. #20275604	C₂	semidirect
5. #20275464	C₂	semidirect
6. #20275428	C₂	semidirect
7. #20275159	C₂	semidirect
8. #20274757	C₂	semidirect
9. #20274601	C₂	semidirect
10. #20274555	C₂	semidirect
37. C₅₃×#470	C₄	semidirect
38. C₅₃×#469	C₄	semidirect
39. C₅₃×#468	C₄	semidirect
68. #13133127	D₄	semidirect
76. C₂×Q₁₆×C₅₃	C₂×C₄	semidirect
77. C₂×SD₁₆×C₅₃	C₂×C₄	semidirect
78. C₂×D₈×C₅₃	C₂×C₄	semidirect
91. #107×C₅₃	C₂×C₄	semidirect
92. #106×C₅₃	C₂×C₄	semidirect
93. #103×C₅₃	C₂×C₄	semidirect
94. #102×C₅₃	C₂×C₄	semidirect
240. #470	Dic₅₃	semidirect
241. #469	Dic₅₃	semidirect
242. #468	Dic₅₃	semidirect
264. C₅₃	#21551	semidirect
270. C₂×Q₁₆	C₂×Dic₅₃	semidirect
271. C₂×SD₁₆	C₂×Dic₅₃	semidirect
272. C₂×D₈	C₂×Dic₅₃	semidirect
303. #107	C₂×Dic₅₃	semidirect
304. #106	C₂×Dic₅₃	semidirect
308. #103	C₂×Dic₅₃	semidirect
309. #102	C₂×Dic₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16810745	2
#20283419	2
C₂×M₁₆×Dic₅₃	2
#20275604	2
#20275464	2
#20275428	2
#20275159	2
#20274757	2
#20274601	2
#20274555	2
C₅₃×#3054	2
#21551	53