Subgroups — #554×D₅₃ #20288242

Order 6784.

1200 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811334	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811333	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811332	C₂	1	2	yes	maximal, complemented
4	#16811331	C₂	1	2	yes	maximal, complemented
5	#16811330	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811329	C₂	1	2	yes	maximal, complemented
7	#16811328	C₂	1	2	yes	maximal, complemented
8	#16811327	C₂	1	4	yes	maximal, complemented
9	C₄⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#125×D₅₃	C₂	1	2	yes	maximal, complemented
11	C₂²⋊Q₈×D₅₃	C₂	1	4	yes	maximal, complemented
12	C₂²⋊Q₈×D₅₃	C₂	1	2	yes	maximal, complemented
13	C₄×Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
15	C₄×D₄×D₅₃	C₂	1	2	yes	maximal
16	C₂×C₄⋊C₄×D₅₃	C₂	1	2	yes	maximal, complemented
17	C₅₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic
19	C₂×Q₈×D₅₃	C₂²	1	2	yes	—
20	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₅₃	C₂²	1	2	yes	—
22	C₂²×C₄×D₅₃	C₂²	1	4	yes	—
23	#13133217	C₂²	1	1	yes	characteristic, complemented
24	#13133216	C₂²	1	2	yes	complemented
25	#13133216	C₂²	1	2	yes	complemented
26	#13133215	C₂²	1	2	yes	complemented
27	#13133209	C₂²	1	2	yes	complemented
28	#13133208	C₂²	1	2	yes	complemented
29	#13133208	C₂²	1	2	yes	complemented
30	#13133207	C₂²	1	4	yes	complemented
31	#13133207	C₂²	1	4	yes	complemented
32	#13133197	C₂²	1	2	yes	complemented
33	#13133197	C₂²	1	4	yes	complemented
34	#13133196	C₂²	1	2	yes	complemented
35	#13133196	C₂²	1	4	yes	complemented
36	#13133195	C₂²	1	4	yes	complemented
37	#13133195	C₂²	1	4	yes	complemented
38	#13133195	C₂²	1	4	yes	complemented
39	#13133194	C₂²	1	4	yes	complemented
40	#13133194	C₂²	1	4	yes	complemented
41	#13133194	C₂²	1	4	yes	complemented
42	#13133193	C₂²	1	4	yes	complemented
43	#13133193	C₂²	1	2	yes	complemented
44	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
46	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
47	#13133182	C₂²	1	2	yes	complemented
48	#13133182	C₂²	1	1	yes	characteristic, complemented
49	C₄×D₂₁₂	C₂²	1	2	yes	—
50	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
51	D₄×Dic₅₃	C₂²	1	2	yes	—
52	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
53	#13133179	C₂²	1	1	yes	characteristic
54	#13133179	C₂²	1	2	yes	—
55	C₄×C₂²⋊D₅₃	C₂²	1	4	yes	—
56	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
57	#13133177	C₂²	1	2	yes	—
58	#13133177	C₂²	1	4	yes	—
59	C₂×C₄⋊Dic₅₃	C₂²	1	2	yes	complemented
60	C₂×#11719919	C₂²	1	4	yes	complemented
61	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
62	C₄⋊C₄×D₅₃	C₂²	1	4	yes	—
63	C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
64	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
65	C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
66	C₄⋊C₄×D₅₃	C₂²	1	2	yes	—
67	C₄⋊C₄×D₅₃	C₂²	1	4	yes	—
68	C₄⋊C₄×D₅₃	C₂²	1	4	yes	complemented
69	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
71	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	—
72	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
73	C₄²×D₅₃	C₂²	1	2	yes	—
74	C₄²×D₅₃	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
76	#125×C₅₃	C₂²	1	2	yes	complemented
77	C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	complemented
78	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
79	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
81	C₄×D₄×C₅₃	C₂²	1	2	yes	—
82	C₂×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
83	C₂³×D₅₃	C₂³	1	2	yes	—
84	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
86	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
88	C₂²×C₄×C₅₃	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
90	C₂²×Dic₅₃	C₂³	1	2	yes	—
91	C₂²×Dic₅₃	C₂³	1	4	yes	—
92	Q₈×D₅₃	—	2	4	no	—
93	Q₈×D₅₃	—	4	4	no	—
94	D₄×D₅₃	Q₈	1	8	yes	complemented
95	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
96	C₂×C₄×D₅₃	—	2	8	no	—
97	C₂×C₄×D₅₃	—	4	8	no	—
98	C₂×C₄×D₅₃	C₂³	1	2	yes	—
99	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₅₃	C₂³	1	2	yes	—
101	C₂×C₄×D₅₃	C₂³	1	2	yes	—
102	C₂×C₄×D₅₃	C₂³	1	4	yes	—
103	C₂×C₄×D₅₃	C₂³	1	2	yes	—
104	C₂×C₄×D₅₃	C₂³	1	2	yes	—
105	C₂×C₄×D₅₃	C₂³	1	4	yes	—
106	C₂×C₄×D₅₃	C₂³	1	4	yes	—
107	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
109	C₂×Dic₁₀₆	C₂³	1	2	yes	—
110	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
111	C₂×Dic₁₀₆	C₂³	1	2	yes	—
112	C₂×Dic₁₀₆	C₂³	1	4	yes	—
113	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
114	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
115	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
116	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
118	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
119	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
120	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
121	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
122	C₄²×C₅₃	C₂³	1	2	yes	—
123	C₄²×C₅₃	C₂³	1	1	yes	characteristic
124	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
125	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
126	#11719921	C₂³	1	2	yes	—
127	#11719921	C₂³	1	4	yes	—
128	#11719921	C₂³	1	4	yes	—
129	#11719921	C₂³	1	2	yes	—
130	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
131	C₄⋊Dic₅₃	C₂³	1	2	yes	—
132	C₄⋊Dic₅₃	C₂³	1	4	yes	—
133	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
134	C₄⋊Dic₅₃	C₂³	1	2	yes	—
135	C₄⋊Dic₅₃	C₂³	1	2	yes	—
136	C₄⋊Dic₅₃	C₂³	1	4	yes	—
137	#11719919	C₂³	1	2	yes	—
138	#11719919	C₂³	1	4	yes	—
139	#11719919	C₂³	1	4	yes	—
140	#11719919	C₂³	1	4	yes	—
141	#11719919	C₂³	1	2	yes	—
142	#11719919	C₂³	1	4	yes	—
143	#11719919	C₂³	1	2	yes	—
144	#11719919	C₂³	1	2	yes	—
145	#11719919	C₂³	1	4	yes	—
146	#11719919	C₂³	1	4	yes	—
147	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
148	C₄×Dic₅₃	C₂³	1	2	yes	—
149	C₄×Dic₅₃	C₂³	1	2	yes	—
150	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
151	C₄×Dic₅₃	C₂³	1	2	yes	—
152	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
153	C₂³×C₅₃	C₂⁴	1	2	yes	—
154	C₂²×D₅₃	—	2	4	no	—
155	C₂²×D₅₃	—	2	4	no	—
156	C₂²×D₅₃	C₂×Q₈	1	8	yes	—
157	C₂²×D₅₃	C₂⁴	1	2	yes	—
158	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
159	Q₈×C₅₃	—	2	2	no	—
160	Q₈×C₅₃	—	4	2	no	—
161	D₄×C₅₃	C₂×Q₈	1	4	yes	complemented
162	C₂×C₄×C₅₃	—	2	4	no	—
163	C₂×C₄×C₅₃	—	4	4	no	—
164	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
166	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
171	C₂²⋊D₅₃	C₂×Q₈	1	8	yes	complemented
172	C₂×Dic₅₃	—	2	4	no	—
173	C₂×Dic₅₃	—	4	4	no	—
174	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
175	C₂×Dic₅₃	C₂⁴	1	4	yes	—
176	C₂×Dic₅₃	C₂⁴	1	2	yes	—
177	C₂×Dic₅₃	C₂⁴	1	2	yes	—
178	C₂×Dic₅₃	C₂⁴	1	2	yes	—
179	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
180	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
181	D₂₁₂	C₂×Q₈	1	4	yes	complemented
182	C₄×D₅₃	—	2	4	no	—
183	C₄×D₅₃	—	2	4	no	—
184	C₄×D₅₃	—	2	4	no	—
185	C₄×D₅₃	—	2	8	no	—
186	C₄×D₅₃	—	2	2	no	—
187	C₄×D₅₃	—	2	4	no	—
188	C₄×D₅₃	—	2	4	no	—
189	C₄×D₅₃	—	4	4	no	—
190	C₄×D₅₃	—	4	4	no	—
191	C₄×D₅₃	C₂×Q₈	1	4	yes	—
192	C₄×D₅₃	#41	1	4	yes	—
193	Dic₁₀₆	—	2	2	no	—
194	Dic₁₀₆	—	2	4	no	—
195	Dic₁₀₆	—	4	4	no	—
196	Dic₁₀₆	—	4	2	no	—
197	C₂²×C₅₃	—	2	2	no	—
198	C₂²×C₅₃	—	2	2	no	—
199	C₂²×C₅₃	C₂²×Q₈	1	4	yes	—
200	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
201	C₂×D₅₃	—	2	2	no	—
202	C₂×D₅₃	—	2	2	no	—
203	C₂×D₅₃	—	2	16	no	—
204	C₂×D₅₃	C₂²×Q₈	1	4	yes	—
205	C₂×D₅₃	C₂²×Q₈	1	2	yes	—
206	C₂×D₅₃	C₂×#41	1	2	yes	—
207	C₂×D₅₃	H(5,𝔽₂)	1	2	yes	—
208	C₄×C₅₃	—	2	2	no	—
209	C₄×C₅₃	—	2	2	no	—
210	C₄×C₅₃	—	2	1	no	—
211	C₄×C₅₃	—	2	4	no	—
212	C₄×C₅₃	—	2	2	no	—
213	C₄×C₅₃	C₂²×Q₈	1	2	yes	—
214	C₄×C₅₃	C₂×#41	1	2	yes	—
215	Dic₅₃	—	2	2	no	—
216	Dic₅₃	—	2	2	no	—
217	Dic₅₃	—	2	1	no	—
218	Dic₅₃	—	2	4	no	—
219	Dic₅₃	—	2	2	no	—
220	Dic₅₃	C₂²×Q₈	1	2	yes	—
221	Dic₅₃	C₂×#41	1	2	yes	—
222	C₂×#554	—	53	1	no	maximal, Sylow
223	C₂×C₅₃	—	2	4	no	—
224	C₂×C₅₃	C₂³×Q₈	1	1	yes	characteristic
225	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
226	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
227	D₅₃	—	2	4	no	—
228	D₅₃	#554	1	4	yes	direct product factor
229	#554	—	53	1	no	—
230	#554	—	53	2	no	—
231	#554	—	53	4	no	—
232	#554	—	53	2	no	—
233	#554	—	53	1	no	—
234	#554	—	53	1	no	—
235	#554	—	53	2	no	—
236	#554	—	53	2	no	—
237	#554	D₅₃	1	1	yes	characteristic, direct product factor
238	C₂×C₄⋊Q₈	—	53	1	no	—
239	C₂×#125	—	53	2	no	—
240	C₂×C₂²⋊Q₈	—	53	4	no	—
241	C₂×C₂²⋊Q₈	—	53	2	no	—
242	C₂×C₄×Q₈	—	53	1	no	—
243	C₂×C₄×D₄	—	53	2	no	—
244	C₂×C₄×D₄	—	53	1	no	—
245	C₂²×C₄⋊C₄	—	53	2	no	—
246	C₅₃	C₂×#554	1	1	yes	characteristic, complemented, Sylow
247	C₂²×Q₈	—	53	1	no	—
248	C₂²×Q₈	—	53	2	no	—
249	C₂²×D₄	—	53	1	no	—
250	C₂³×C₄	—	53	2	no	—
251	C₂³×C₄	—	53	4	no	—
252	C₄⋊Q₈	—	53	2	no	—
253	C₄⋊Q₈	—	53	2	no	—
254	C₄⋊Q₈	—	53	2	no	—
255	C₄⋊Q₈	—	53	1	no	—
256	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
257	#125	—	53	4	no	—
258	#125	—	53	4	no	—
259	#125	—	53	2	no	—
260	#125	—	53	2	no	—
261	#125	—	53	2	no	—
262	#125	C₂×D₅₃	1	2	yes	complemented
263	C₂²⋊Q₈	—	53	4	no	—
264	C₂²⋊Q₈	—	53	2	no	—
265	C₂²⋊Q₈	—	53	4	no	—
266	C₂²⋊Q₈	—	53	2	no	—
267	C₂²⋊Q₈	—	53	4	no	—
268	C₂²⋊Q₈	—	53	4	no	—
269	C₂²⋊Q₈	—	53	4	no	—
270	C₂²⋊Q₈	—	53	4	no	—
271	C₂²⋊Q₈	—	53	2	no	—
272	C₂²⋊Q₈	—	53	4	no	—
273	C₂²⋊Q₈	—	53	4	no	—
274	C₂²⋊Q₈	—	53	4	no	—
275	C₂²⋊Q₈	C₂×D₅₃	1	4	yes	complemented
276	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
277	C₄×Q₈	—	53	1	no	—
278	C₄×Q₈	—	53	2	no	—
279	C₄×Q₈	—	53	1	no	—
280	C₄×Q₈	—	53	1	no	—
281	C₄×Q₈	—	53	2	no	—
282	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
283	C₄×D₄	—	53	2	no	—
284	C₄×D₄	—	53	1	no	—
285	C₄×D₄	—	53	4	no	—
286	C₄×D₄	—	53	2	no	—
287	C₄×D₄	—	53	2	no	—
288	C₄×D₄	—	53	1	no	—
289	C₄×D₄	—	53	4	no	—
290	C₄×D₄	—	53	2	no	—
291	C₄×D₄	—	53	2	no	—
292	C₄×D₄	—	53	1	no	—
293	C₄×D₄	C₂×D₅₃	1	2	yes	—
294	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
295	C₂×C₄⋊C₄	—	53	4	no	—
296	C₂×C₄⋊C₄	—	53	2	no	—
297	C₂×C₄⋊C₄	—	53	1	no	—
298	C₂×C₄⋊C₄	—	53	4	no	—
299	C₂×C₄⋊C₄	—	53	2	no	—
300	C₂×C₄⋊C₄	—	53	4	no	—
301	C₂×C₄⋊C₄	—	53	2	no	—
302	C₂×C₄⋊C₄	—	53	2	no	—
303	C₂×C₄⋊C₄	—	53	1	no	—
304	C₂×C₄⋊C₄	—	53	2	no	—
305	C₂×C₄⋊C₄	—	53	2	no	—
306	C₂×C₄⋊C₄	—	53	4	no	—
307	C₂×C₄⋊C₄	C₂×D₅₃	1	2	yes	complemented
308	C₂×C₂²⋊C₄	—	53	4	no	—
309	C₂×C₂²⋊C₄	—	53	2	no	—
310	C₂×C₄²	—	53	2	no	—
311	C₂×C₄²	—	53	1	no	—
312	C₂⁴	—	53	2	no	—
313	C₂×Q₈	—	53	2	no	—
314	C₂×Q₈	—	53	1	no	—
315	C₂×Q₈	—	53	4	no	—
316	C₂×Q₈	—	53	2	no	—
317	C₂×Q₈	—	106	4	no	—
318	C₂×Q₈	—	212	4	no	—
319	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
320	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
321	C₂×D₄	—	53	2	no	—
322	C₂×D₄	—	53	8	no	—
323	C₂×D₄	—	53	1	no	—
324	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
325	C₂²×C₄	—	53	1	no	—
326	C₂²×C₄	—	53	1	no	—
327	C₂²×C₄	—	53	2	no	—
328	C₂²×C₄	—	53	4	no	—
329	C₂²×C₄	—	53	2	no	—
330	C₂²×C₄	—	53	1	no	—
331	C₂²×C₄	—	53	2	no	—
332	C₂²×C₄	—	53	2	no	—
333	C₂²×C₄	—	53	4	no	—
334	C₂²×C₄	—	53	2	no	—
335	C₂²×C₄	—	53	2	no	—
336	C₂²×C₄	—	53	4	no	—
337	C₂²×C₄	—	53	4	no	—
338	C₂²×C₄	—	106	8	no	—
339	C₂²×C₄	—	212	8	no	—
340	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
341	C₂²×C₄	C₂²×D₅₃	1	4	yes	—
342	C₄⋊C₄	—	53	2	no	—
343	C₄⋊C₄	—	53	1	no	—
344	C₄⋊C₄	—	53	4	no	—
345	C₄⋊C₄	—	53	4	no	—
346	C₄⋊C₄	—	53	4	no	—
347	C₄⋊C₄	—	53	4	no	—
348	C₄⋊C₄	—	53	2	no	—
349	C₄⋊C₄	—	53	2	no	—
350	C₄⋊C₄	—	53	1	no	—
351	C₄⋊C₄	—	53	4	no	—
352	C₄⋊C₄	—	53	2	no	—
353	C₄⋊C₄	—	53	2	no	—
354	C₄⋊C₄	—	53	2	no	—
355	C₄⋊C₄	—	53	2	no	—
356	C₄⋊C₄	—	53	4	no	—
357	C₄⋊C₄	—	53	4	no	—
358	C₄⋊C₄	—	53	4	no	—
359	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₅₃	1	4	yes	—
361	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
362	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
363	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
364	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
365	C₄⋊C₄	C₂²×D₅₃	1	4	yes	—
366	C₂²⋊C₄	—	53	4	no	—
367	C₂²⋊C₄	—	53	2	no	—
368	C₂²⋊C₄	—	53	4	no	—
369	C₂²⋊C₄	—	53	2	no	—
370	C₂²⋊C₄	—	53	2	no	—
371	C₂²⋊C₄	—	53	4	no	—
372	C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
373	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
374	C₄²	—	53	2	no	—
375	C₄²	—	53	2	no	—
376	C₄²	—	53	2	no	—
377	C₄²	—	53	1	no	—
378	C₄²	—	53	1	no	—
379	C₄²	—	53	1	no	—
380	C₄²	C₂²×D₅₃	1	2	yes	—
381	C₄²	C₂²×D₅₃	1	1	yes	characteristic
382	C₂³	—	53	1	no	—
383	C₂³	—	53	8	no	—
384	C₂³	—	53	2	no	—
385	C₂³	—	106	4	no	—
386	C₂³	—	106	4	no	—
387	C₂³	C₂³×D₅₃	1	2	yes	—
388	Q₈	—	2	2	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	106	4	no	—
391	Q₈	—	106	2	no	—
392	Q₈	—	212	4	no	—
393	Q₈	—	212	2	no	—
394	D₄	—	53	8	no	—
395	D₄	—	53	4	no	—
396	D₄	Q₈×D₅₃	1	4	yes	complemented
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	53	1	no	—
400	C₂×C₄	—	53	1	no	—
401	C₂×C₄	—	53	4	no	—
402	C₂×C₄	—	53	4	no	—
403	C₂×C₄	—	53	2	no	—
404	C₂×C₄	—	53	1	no	—
405	C₂×C₄	—	53	2	no	—
406	C₂×C₄	—	53	2	no	—
407	C₂×C₄	—	53	4	no	—
408	C₂×C₄	—	106	4	no	—
409	C₂×C₄	—	106	4	no	—
410	C₂×C₄	—	106	4	no	—
411	C₂×C₄	—	106	8	no	—
412	C₂×C₄	—	106	4	no	—
413	C₂×C₄	—	106	2	no	—
414	C₂×C₄	—	106	4	no	—
415	C₂×C₄	—	106	4	no	—
416	C₂×C₄	—	212	4	no	—
417	C₂×C₄	—	212	4	no	—
418	C₂×C₄	—	212	4	no	—
419	C₂×C₄	C₂³×D₅₃	1	2	yes	—
420	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₅₃	1	2	yes	—
422	C₂×C₄	C₂³×D₅₃	1	2	yes	—
423	C₂×C₄	C₂³×D₅₃	1	4	yes	—
424	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	53	2	no	—
429	C₂²	—	53	2	no	—
430	C₂²	—	53	2	no	—
431	C₂²	—	53	4	no	—
432	C₂²	—	106	16	no	—
433	C₂²	—	106	2	no	—
434	C₂²	—	106	2	no	—
435	C₂²	C₂×Q₈×D₅₃	1	4	yes	—
436	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	4	no	—
441	C₄	—	2	1	no	—
442	C₄	—	53	2	no	—
443	C₄	—	53	2	no	—
444	C₄	—	106	2	no	—
445	C₄	—	106	2	no	—
446	C₄	—	106	2	no	—
447	C₄	—	106	4	no	—
448	C₄	—	106	1	no	—
449	C₄	C₂×Q₈×D₅₃	1	2	yes	—
450	C₄	#41×D₅₃	1	2	yes	—
451	C₂	—	2	4	no	—
452	C₂	—	53	4	no	—
453	C₂	—	106	4	no	—
454	C₂	C₂²×Q₈×D₅₃	1	1	yes	characteristic
455	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
456	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#554	C₂
hypercenter	#554	D₅₃
hypocenter	C₅₃	C₂×#554
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #16811334	C₂	semidirect
2. #16811333	C₂	semidirect
3. #16811332	C₂	semidirect
4. #16811331	C₂	semidirect
5. #16811330	C₂	semidirect
6. #16811329	C₂	semidirect
7. #16811328	C₂	semidirect
8. #16811327	C₂	semidirect
9. C₄⋊Q₈×D₅₃	C₂	semidirect
10. #125×D₅₃	C₂	semidirect
11. C₂²⋊Q₈×D₅₃	C₂	semidirect
12. C₂²⋊Q₈×D₅₃	C₂	semidirect
13. C₄×Q₈×D₅₃	C₂	semidirect
16. C₂×C₄⋊C₄×D₅₃	C₂	semidirect
17. C₅₃×#554	C₂	semidirect
23. #13133217	C₂²	semidirect
24. #13133216	C₂²	semidirect
25. #13133216	C₂²	semidirect
26. #13133215	C₂²	semidirect
27. #13133209	C₂²	semidirect
28. #13133208	C₂²	semidirect
29. #13133208	C₂²	semidirect
30. #13133207	C₂²	semidirect
31. #13133207	C₂²	semidirect
32. #13133197	C₂²	semidirect
33. #13133197	C₂²	semidirect
34. #13133196	C₂²	semidirect
35. #13133196	C₂²	semidirect
36. #13133195	C₂²	semidirect
37. #13133195	C₂²	semidirect
38. #13133195	C₂²	semidirect
39. #13133194	C₂²	semidirect
40. #13133194	C₂²	semidirect
41. #13133194	C₂²	semidirect
42. #13133193	C₂²	semidirect
43. #13133193	C₂²	semidirect
44. Q₈×Dic₅₃	C₂²	semidirect
45. C₄×Dic₁₀₆	C₂²	semidirect
46. C₄×Dic₁₀₆	C₂²	semidirect
47. #13133182	C₂²	semidirect
48. #13133182	C₂²	semidirect
59. C₂×C₄⋊Dic₅₃	C₂²	semidirect
60. C₂×#11719919	C₂²	semidirect
68. C₄⋊C₄×D₅₃	C₂²	semidirect
69. C₄⋊C₄×D₅₃	C₂²	semidirect
70. C₄⋊C₄×D₅₃	C₂²	semidirect
75. C₄⋊Q₈×C₅₃	C₂²	semidirect
76. #125×C₅₃	C₂²	semidirect
77. C₂²⋊Q₈×C₅₃	C₂²	semidirect
78. C₂²⋊Q₈×C₅₃	C₂²	semidirect
79. C₄×Q₈×C₅₃	C₂²	semidirect
82. C₂×C₄⋊C₄×C₅₃	C₂²	semidirect
94. D₄×D₅₃	Q₈	semidirect
161. D₄×C₅₃	C₂×Q₈	semidirect
171. C₂²⋊D₅₃	C₂×Q₈	semidirect
181. D₂₁₂	C₂×Q₈	semidirect
228. D₅₃	#554	direct (N × H)
237. #554	D₅₃	direct (N × H)
246. C₅₃	C₂×#554	semidirect
256. C₄⋊Q₈	C₂×D₅₃	semidirect
262. #125	C₂×D₅₃	semidirect
275. C₂²⋊Q₈	C₂×D₅₃	semidirect
276. C₂²⋊Q₈	C₂×D₅₃	semidirect
282. C₄×Q₈	C₂×D₅₃	semidirect
307. C₂×C₄⋊C₄	C₂×D₅₃	semidirect
396. D₄	Q₈×D₅₃	semidirect

Subgroups — #554×D53 #20288242

Conjugacy classes of subgroups

Complements

Subgroups — #554×D₅₃ #20288242