Subgroups — #28319504

Order 13568.

810 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20291394	C₂	1	2	yes	maximal
2	#20290655	C₂	1	2	yes	maximal, complemented
3	#20290640	C₂	1	2	yes	maximal, complemented
4	#20290595	C₂	1	2	yes	maximal
5	#20290594	C₂	1	2	yes	maximal
6	C₄×#13133288	C₂	1	2	yes	maximal, complemented
7	C₄×#13133287	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
9	#16811646	—	2	2	no	—
10	#16811643	—	2	2	no	—
11	#16811641	—	2	2	no	—
12	#16811640	—	2	2	no	—
13	C₂×#13133288	C₂²	1	4	yes	—
14	C₂×#13133287	C₂²	1	4	yes	—
15	#16811628	C₂²	1	4	yes	—
16	#16811594	C₂²	1	4	yes	—
17	C₄×#11719936	C₂²	1	4	yes	—
18	#16811499	C₂²	1	4	yes	—
19	#16811499	C₂²	1	4	yes	—
20	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
21	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×#88322	C₄	1	1	yes	characteristic
24	C₂×C₈×Dic₅₃	C₄	1	1	yes	characteristic
25	C₂×C₈×Dic₅₃	C₄	1	1	yes	characteristic
26	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
27	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
28	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
29	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
30	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
32	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₅₃	C₄	1	1	yes	characteristic
35	C₂×#11719936	C₂³	1	8	yes	—
36	#13133288	—	2	8	no	—
37	#13133287	—	2	8	no	—
38	#13133284	—	2	4	no	—
39	#13133284	—	2	4	no	—
40	#13133274	—	2	4	no	—
41	C₂²⋊#88324	—	2	4	no	—
42	#13133272	—	2	4	no	—
43	C₄×#88324	—	2	4	no	—
44	C₂²×C₄×D₅₃	Q₈	1	1	yes	characteristic
45	C₂²×C₄×D₅₃	Q₈	1	1	yes	characteristic
46	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
47	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
48	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₅₃	—	2	4	no	—
50	C₂×C₈×D₅₃	—	2	4	no	—
51	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
61	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
62	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₅₃	D₄	1	1	yes	characteristic
65	C₄²×D₅₃	D₄	1	1	yes	characteristic
66	C₄²×D₅₃	Q₈	1	1	yes	characteristic
67	C₄²×D₅₃	Q₈	1	1	yes	characteristic
68	C₄²×D₅₃	C₂³	1	1	yes	characteristic
69	C₄²×D₅₃	C₂³	1	1	yes	characteristic
70	C₄×#88322	C₂×C₄	1	1	yes	characteristic
71	C₄×#88322	C₂×C₄	1	1	yes	characteristic
72	C₄×#88322	C₂×C₄	1	1	yes	characteristic
73	C₄×#88322	C₂×C₄	1	1	yes	characteristic
74	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
75	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
76	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
77	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
78	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
85	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
86	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
87	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
88	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
89	C₂³×D₅₃	C₂×Q₈	1	1	yes	characteristic
90	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
96	C₂×C₄×D₅₃	—	2	4	no	—
97	C₂×C₄×D₅₃	—	2	4	no	—
98	C₂×C₄×D₅₃	—	2	2	no	—
99	C₂×C₄×D₅₃	—	2	2	no	—
100	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
107	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
108	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
110	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
111	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
112	C₂×#88324	—	2	8	no	—
113	#11719936	—	2	8	no	—
114	#11719936	—	2	8	no	—
115	C₂×C₈×C₅₃	—	2	2	no	—
116	C₂×C₈×C₅₃	—	2	2	no	—
117	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
122	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
123	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
134	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
135	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
136	C₄×Dic₅₃	C₂×D₄	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	C₂²×C₄	1	1	yes	characteristic
143	C₈×D₅₃	—	2	2	no	—
144	C₈×D₅₃	—	2	2	no	—
145	C₈×D₅₃	—	2	2	no	—
146	C₈×D₅₃	—	2	2	no	—
147	C₈×D₅₃	—	2	2	no	—
148	C₈×D₅₃	—	2	2	no	—
149	C₈×D₅₃	#41	1	4	yes	—
150	C₈×D₅₃	#41	1	4	yes	—
151	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂²×D₅₃	—	2	2	no	—
153	C₂²×D₅₃	—	2	2	no	—
154	C₂²×D₅₃	—	2	2	no	—
155	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂²×D₅₃	C₂²×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₅₃	—	2	2	no	—
158	C₂×C₄×C₅₃	—	2	1	no	—
159	C₂×C₄×C₅₃	—	2	1	no	—
160	C₂×C₄×C₅₃	—	2	2	no	—
161	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×Dic₅₃	—	2	2	no	—
168	C₂×Dic₅₃	—	2	2	no	—
169	C₂×Dic₅₃	#108	1	4	yes	complemented
170	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
176	C₄×D₅₃	—	2	2	no	—
177	C₄×D₅₃	—	2	2	no	—
178	C₄×D₅₃	—	2	1	no	—
179	C₄×D₅₃	—	2	1	no	—
180	C₄×D₅₃	—	2	2	no	—
181	C₄×D₅₃	—	2	2	no	—
182	C₄×D₅₃	—	2	2	no	—
183	C₄×D₅₃	—	2	2	no	—
184	C₄×D₅₃	—	2	2	no	—
185	C₄×D₅₃	—	2	2	no	—
186	C₄×D₅₃	—	2	2	no	—
187	C₄×D₅₃	#108	1	4	yes	complemented
188	C₄×D₅₃	C₂×#41	1	2	yes	—
189	C₄×D₅₃	C₂×#41	1	2	yes	—
190	#88324	—	4	8	no	—
191	C₈×C₅₃	—	2	1	no	—
192	C₈×C₅₃	—	2	1	no	—
193	C₈×C₅₃	#117	1	2	yes	—
194	C₈×C₅₃	#117	1	2	yes	—
195	#88322	—	2	1	no	—
196	#88322	—	2	1	no	—
197	#88322	#117	1	2	yes	—
198	#88322	#117	1	2	yes	—
199	#20826	—	53	1	no	maximal, Sylow
200	C₂²×C₅₃	—	2	1	no	—
201	C₂²×C₅₃	—	2	1	no	—
202	C₂²×C₅₃	C₂×#108	1	2	yes	—
203	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
204	C₂×D₅₃	—	2	8	no	—
205	C₂×D₅₃	—	2	1	no	—
206	C₂×D₅₃	—	2	1	no	—
207	C₂×D₅₃	—	2	1	no	—
208	C₂×D₅₃	—	2	1	no	—
209	C₂×D₅₃	C₂×#108	1	2	yes	—
210	C₂×D₅₃	#533	1	2	yes	—
211	C₄×C₅₃	—	2	1	no	—
212	C₄×C₅₃	—	2	1	no	—
213	C₄×C₅₃	—	2	1	no	—
214	C₄×C₅₃	—	2	1	no	—
215	C₄×C₅₃	C₂×#108	1	2	yes	—
216	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
217	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
218	Dic₅₃	—	2	1	no	—
219	Dic₅₃	—	2	1	no	—
220	Dic₅₃	C₂×#108	1	2	yes	—
221	Dic₅₃	C₂×#108	1	2	yes	—
222	Dic₅₃	C₂×#108	1	2	yes	—
223	Dic₅₃	#532	1	2	yes	—
224	#2920	—	53	2	no	—
225	C₂²×C₄×C₈	—	53	1	no	—
226	#1848	—	53	2	no	—
227	#1837	—	53	2	no	—
228	#1810	—	53	2	no	—
229	#1810	—	53	2	no	—
230	C₄×#108	—	53	2	no	—
231	C₄×#108	—	53	2	no	—
232	C₂×C₅₃	—	2	2	no	—
233	C₂×C₅₃	#2285	1	1	yes	characteristic
234	C₂×C₅₃	C₂²×#108	1	1	yes	characteristic
235	C₂×C₅₃	C₂²×#108	1	1	yes	characteristic
236	D₅₃	—	2	2	no	—
237	D₅₃	—	2	2	no	—
238	C₂³×C₈	—	53	1	no	—
239	C₂³×C₈	—	53	1	no	—
240	C₂²×C₄²	—	53	1	no	—
241	#432	—	106	2	no	—
242	#432	—	106	2	no	—
243	#431	—	106	2	no	—
244	#431	—	106	2	no	—
245	C₂×#108	—	53	4	no	—
246	C₂×#108	—	53	4	no	—
247	#423	—	53	4	no	—
248	#407	—	53	4	no	—
249	C₄×M₁₆	—	53	4	no	—
250	C₂×C₄×C₈	—	53	1	no	—
251	C₂×C₄×C₈	—	53	1	no	—
252	C₂×C₄×C₈	—	53	1	no	—
253	C₂×C₄×C₈	—	53	1	no	—
254	C₂×C₄×C₈	—	53	1	no	—
255	C₂×C₄×C₈	—	53	1	no	—
256	C₂×C₄×C₈	—	53	1	no	—
257	C₂×C₄×C₈	—	53	1	no	—
258	C₂×C₄×C₈	—	53	1	no	—
259	C₂×C₄×C₈	—	53	1	no	—
260	C₂×C₄×C₈	—	53	1	no	—
261	C₂×C₄×C₈	#6157	1	1	yes	characteristic
262	#341	—	53	4	no	—
263	#341	—	53	4	no	—
264	C₅₃	#20826	1	1	yes	characteristic, complemented, Sylow
265	C₂³×C₄	—	53	1	no	—
266	C₂³×C₄	—	53	1	no	—
267	C₂³×C₄	—	53	1	no	—
268	C₂×M₁₆	—	53	8	no	—
269	C₂²×C₈	—	53	1	no	—
270	C₂²×C₈	—	53	1	no	—
271	C₂²×C₈	—	53	1	no	—
272	C₂²×C₈	—	53	1	no	—
273	C₂²×C₈	—	53	1	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	—	106	4	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	C₂×C₄²	—	53	1	no	—
284	C₂×C₄²	—	53	1	no	—
285	C₂×C₄²	—	53	1	no	—
286	C₂×C₄²	—	53	1	no	—
287	C₂×C₄²	—	53	1	no	—
288	C₂×C₄²	—	53	1	no	—
289	C₂×C₄²	—	53	1	no	—
290	C₂×C₄²	—	53	1	no	—
291	C₂×C₄²	—	53	1	no	—
292	C₂×C₄²	—	53	1	no	—
293	C₂×C₄²	—	53	1	no	—
294	C₂×C₄²	C₂×#6157	1	1	yes	characteristic
295	#108	—	106	8	no	—
296	#108	—	106	8	no	—
297	C₄⋊C₈	—	106	4	no	—
298	C₄⋊C₈	—	106	4	no	—
299	C₂²⋊C₈	—	106	4	no	—
300	C₂²⋊C₈	—	106	4	no	—
301	#97	—	106	4	no	—
302	C₄×C₈	—	53	1	no	—
303	C₄×C₈	—	53	1	no	—
304	C₄×C₈	—	53	1	no	—
305	C₄×C₈	—	53	1	no	—
306	C₄×C₈	—	53	1	no	—
307	C₄×C₈	—	53	1	no	—
308	C₄×C₈	—	53	1	no	—
309	C₄×C₈	—	53	1	no	—
310	C₄×C₈	—	53	1	no	—
311	C₄×C₈	—	53	1	no	—
312	C₄×C₈	—	53	1	no	—
313	C₄×C₈	—	53	1	no	—
314	C₄×C₈	—	106	4	no	—
315	C₄×C₈	C₂×#6157	1	1	yes	characteristic
316	C₄×C₈	C₂×#6157	1	1	yes	characteristic
317	C₄×C₈	C₂×#6157	1	1	yes	characteristic
318	C₄×C₈	C₂×#6157	1	1	yes	characteristic
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	—	53	1	no	—
328	C₂²×C₄	—	53	1	no	—
329	C₂²×C₄	—	53	1	no	—
330	C₂²×C₄	—	53	1	no	—
331	C₂²×C₄	—	53	1	no	—
332	C₂²×C₄	—	53	1	no	—
333	C₂²×C₄	—	53	1	no	—
334	C₂²×C₄	—	53	1	no	—
335	C₂²×C₄	—	106	2	no	—
336	C₂²×C₄	—	106	2	no	—
337	C₂²×C₄	—	106	4	no	—
338	C₂²×C₄	—	106	4	no	—
339	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
340	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
341	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
342	M₁₆	—	106	8	no	—
343	M₁₆	—	106	8	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	53	1	no	—
347	C₂×C₈	—	53	1	no	—
348	C₂×C₈	—	53	4	no	—
349	C₂×C₈	—	53	4	no	—
350	C₂×C₈	—	53	1	no	—
351	C₂×C₈	—	53	1	no	—
352	C₂×C₈	—	106	2	no	—
353	C₂×C₈	—	106	2	no	—
354	C₂×C₈	—	106	2	no	—
355	C₂×C₈	—	106	2	no	—
356	C₂×C₈	—	106	2	no	—
357	C₂×C₈	—	106	2	no	—
358	C₂×C₈	—	106	2	no	—
359	C₂×C₈	—	106	2	no	—
360	C₂×C₈	—	106	8	no	—
361	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
362	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
363	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
364	C₂×C₈	C₂²×#6157	1	1	yes	characteristic
365	C₄²	—	53	1	no	—
366	C₄²	—	53	1	no	—
367	C₄²	—	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	—	53	1	no	—
373	C₄²	—	53	1	no	—
374	C₄²	—	53	1	no	—
375	C₄²	—	53	1	no	—
376	C₄²	—	53	1	no	—
377	C₄²	C₄⋊#6157	1	1	yes	characteristic
378	C₄²	C₄⋊#6157	1	1	yes	characteristic
379	C₄²	C₂²×#6157	1	1	yes	characteristic
380	C₄²	C₂²×#6157	1	1	yes	characteristic
381	C₂³	—	53	1	no	—
382	C₂³	—	53	1	no	—
383	C₂³	—	106	2	no	—
384	C₂³	—	106	2	no	—
385	C₂³	—	106	2	no	—
386	C₂³	C₂×C₄⋊#6157	1	1	yes	characteristic
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	53	4	no	—
392	C₂×C₄	—	53	1	no	—
393	C₂×C₄	—	53	1	no	—
394	C₂×C₄	—	53	1	no	—
395	C₂×C₄	—	53	1	no	—
396	C₂×C₄	—	53	4	no	—
397	C₂×C₄	—	53	2	no	—
398	C₂×C₄	—	53	2	no	—
399	C₂×C₄	—	53	1	no	—
400	C₂×C₄	—	53	1	no	—
401	C₂×C₄	—	106	2	no	—
402	C₂×C₄	—	106	2	no	—
403	C₂×C₄	—	106	2	no	—
404	C₂×C₄	—	106	2	no	—
405	C₂×C₄	—	106	2	no	—
406	C₂×C₄	—	106	2	no	—
407	C₂×C₄	—	106	2	no	—
408	C₂×C₄	—	106	2	no	—
409	C₂×C₄	—	106	2	no	—
410	C₂×C₄	—	106	2	no	—
411	C₂×C₄	—	106	2	no	—
412	C₂×C₄	—	106	1	no	—
413	C₂×C₄	—	106	1	no	—
414	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
415	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
416	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
417	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
418	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
419	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	53	2	no	—
423	C₈	—	53	2	no	—
424	C₈	—	106	1	no	—
425	C₈	—	106	1	no	—
426	C₈	—	212	8	no	—
427	C₈	#13133296	1	2	yes	—
428	C₈	#13133296	1	2	yes	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	53	2	no	—
432	C₂²	—	53	2	no	—
433	C₂²	—	106	8	no	—
434	C₂²	—	106	1	no	—
435	C₂²	—	106	1	no	—
436	C₂²	—	106	1	no	—
437	C₂²	—	106	1	no	—
438	C₂²	D₅₃⋊#108	1	2	yes	—
439	C₂²	C₂²×C₄⋊#6157	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	53	2	no	—
445	C₄	—	53	2	no	—
446	C₄	—	53	2	no	—
447	C₄	—	53	2	no	—
448	C₄	—	106	1	no	—
449	C₄	—	106	1	no	—
450	C₄	D₅₃⋊#108	1	2	yes	—
451	C₄	C₂×#13133296	1	1	yes	characteristic
452	C₄	C₂×#13133296	1	1	yes	characteristic
453	C₂	—	2	2	no	—
454	C₂	—	106	2	no	—
455	C₂	—	106	2	no	—
456	C₂	#20291164	1	1	yes	characteristic
457	C₂	C₂×D₅₃⋊#108	1	1	yes	characteristic
458	C₂	C₂×D₅₃⋊#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#6157
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₂×C₄×C₈×C₅₃	C₄
socle	C₂²×C₅₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₅₃	C₂×Q₈
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	C₂×C₄×C₈	#6157
hypocenter	C₅₃	#20826
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #20290655	C₂	semidirect
3. #20290640	C₂	semidirect
6. C₄×#13133288	C₂	semidirect
7. C₄×#13133287	C₂	semidirect
169. C₂×Dic₅₃	#108	semidirect
187. C₄×D₅₃	#108	semidirect
264. C₅₃	#20826	semidirect

Maximal subgroups

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

subgroup	index
#20291394	2
#20290655	2
#20290640	2
#20290595	2
#20290594	2
C₄×#13133288	2
C₄×#13133287	2
C₂×C₄×C₈×D₅₃	2
#20826	53