Subgroups — #20289411

Order 6784.

958 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811377	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811377	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811373	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811365	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811345	C₂	1	2	yes	maximal, complemented
6	#16811341	C₂	1	2	yes	maximal, complemented
7	#16811340	C₂	1	2	yes	maximal, complemented
8	#16811302	C₂	1	2	yes	maximal, complemented
9	#16811298	C₂	1	2	yes	maximal, complemented
10	#16811297	C₂	1	2	yes	maximal, complemented
11	#16811243	C₂	1	2	yes	maximal, complemented
12	#16811241	C₂	1	2	yes	maximal, complemented
13	#16811238	C₂	1	2	yes	maximal, complemented
14	#16811209	C₂	1	2	yes	maximal, complemented
15	#16811206	C₂	1	2	yes	maximal, complemented
16	#16811205	C₂	1	2	yes	maximal, complemented
17	#16811157	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811157	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	#13133216	C₂²	1	2	yes	complemented
21	#13133216	C₂²	1	2	yes	complemented
22	#13133215	C₂²	1	2	yes	complemented
23	#13133212	C₂²	1	2	yes	complemented
24	#13133212	C₂²	1	2	yes	complemented
25	#13133212	C₂²	1	2	yes	complemented
26	#13133212	C₂²	1	2	yes	complemented
27	#13133212	C₂²	1	2	yes	complemented
28	#13133211	C₂²	1	2	yes	complemented
29	#13133211	C₂²	1	2	yes	complemented
30	#13133211	C₂²	1	2	yes	complemented
31	#13133210	C₂²	1	2	yes	complemented
32	#13133210	C₂²	1	2	yes	complemented
33	#13133210	C₂²	1	2	yes	complemented
34	#13133210	C₂²	1	2	yes	complemented
35	#13133209	C₂²	1	1	yes	characteristic, complemented
36	#13133209	C₂²	1	1	yes	characteristic, complemented
37	#13133206	C₂²	1	2	yes	—
38	#13133205	C₂²	1	2	yes	—
39	#13133205	C₂²	1	1	yes	characteristic
40	#13133205	C₂²	1	1	yes	characteristic
41	#13133204	C₂²	1	2	yes	complemented
42	#13133203	C₂²	1	2	yes	—
43	#13133203	C₂²	1	2	yes	—
44	#13133203	C₂²	1	2	yes	—
45	#13133203	C₂²	1	2	yes	—
46	#13133203	C₂²	1	2	yes	complemented
47	#13133203	C₂²	1	2	yes	complemented
48	#13133202	C₂²	1	2	yes	—
49	#13133202	C₂²	1	2	yes	—
50	#13133202	C₂²	1	2	yes	—
51	#13133200	C₂²	1	2	yes	—
52	#13133200	C₂²	1	2	yes	complemented
53	#13133200	C₂²	1	2	yes	complemented
54	#13133199	C₂²	1	2	yes	—
55	#13133198	C₂²	1	2	yes	—
56	#13133197	C₂²	1	2	yes	complemented
57	#13133197	C₂²	1	2	yes	complemented
58	#13133196	C₂²	1	2	yes	complemented
59	#13133196	C₂²	1	1	yes	characteristic, complemented
60	#13133196	C₂²	1	1	yes	characteristic, complemented
61	#13133195	C₂²	1	2	yes	complemented
62	#13133195	C₂²	1	2	yes	complemented
63	#13133195	C₂²	1	2	yes	complemented
64	#13133195	C₂²	1	2	yes	complemented
65	#13133194	C₂²	1	2	yes	complemented
66	#13133194	C₂²	1	2	yes	complemented
67	#13133191	C₂²	1	1	yes	characteristic
68	#13133191	C₂²	1	1	yes	characteristic
69	#13133190	C₂²	1	2	yes	—
70	#13133189	C₂²	1	2	yes	—
71	#13133188	C₂²	1	2	yes	—
72	#13133187	C₂²	1	2	yes	—
73	#13133187	C₂²	1	2	yes	—
74	#13133185	C₂²	1	2	yes	—
75	#13133185	C₂²	1	2	yes	complemented
76	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
78	C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
79	#13133182	C₂²	1	2	yes	complemented
80	#13133182	C₂²	1	2	yes	complemented
81	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
82	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
83	#13133179	C₂²	1	2	yes	—
84	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
85	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
87	#13133177	C₂²	1	2	yes	—
88	#13133175	C₂²	1	2	yes	complemented
89	#13133174	C₂²	1	2	yes	complemented
90	#13133174	C₂²	1	2	yes	complemented
91	#13133174	C₂²	1	2	yes	complemented
92	#13133173	C₂²	1	2	yes	complemented
93	C₂×#11719921	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
96	#126×C₅₃	C₂²	1	2	yes	complemented
97	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
98	#124×C₅₃	C₂²	1	1	yes	characteristic
99	#123×C₅₃	C₂²	1	2	yes	complemented
100	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
101	#121×C₅₃	C₂²	1	1	yes	characteristic
102	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
103	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
104	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
105	#117×C₅₃	C₂²	1	2	yes	complemented
106	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₅₃	C₂³	1	2	yes	—
108	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₅₃	C₂³	1	2	yes	—
111	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
115	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
119	C₂²×Dic₅₃	C₂³	1	2	yes	—
120	C₂×D₂₁₂	C₂³	1	2	yes	—
121	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
122	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
123	C₂×C₄×D₅₃	C₂³	1	2	yes	—
124	C₂×C₄×D₅₃	C₂³	1	2	yes	—
125	C₂×C₄×D₅₃	C₂³	1	2	yes	—
126	C₂×C₄×D₅₃	C₂³	1	2	yes	—
127	C₂×Dic₁₀₆	C₂³	1	2	yes	—
128	C₂×Dic₁₀₆	C₂³	1	2	yes	—
129	C₂×Dic₁₀₆	C₂³	1	2	yes	—
130	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
131	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
132	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
133	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
134	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
135	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
136	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
137	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
138	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
139	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
140	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
141	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
142	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
143	C₄²×C₅₃	C₂³	1	1	yes	characteristic
144	C₄²×C₅₃	C₂³	1	1	yes	characteristic
145	C₄²×C₅₃	C₂³	1	1	yes	characteristic
146	C₄²×C₅₃	C₂³	1	1	yes	characteristic
147	C₄²×C₅₃	C₂³	1	2	yes	—
148	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
149	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
150	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
151	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
152	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
153	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
154	#11719921	C₂³	1	2	yes	—
155	#11719921	C₂³	1	2	yes	—
156	#11719921	C₂³	1	2	yes	—
157	#11719921	C₂³	1	2	yes	—
158	#11719921	C₂³	1	2	yes	—
159	#11719921	C₂³	1	2	yes	—
160	#11719921	C₂³	1	2	yes	—
161	#11719921	C₂³	1	2	yes	—
162	#11719921	C₂³	1	2	yes	—
163	#11719921	C₂³	1	2	yes	—
164	#11719921	C₂³	1	2	yes	—
165	#11719921	C₂³	1	2	yes	—
166	#11719921	C₂³	1	2	yes	—
167	#11719921	C₂³	1	2	yes	—
168	#11719921	C₂³	1	2	yes	—
169	#11719921	C₂³	1	2	yes	—
170	C₄⋊Dic₅₃	C₂³	1	2	yes	—
171	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
172	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
173	C₄⋊Dic₅₃	C₂³	1	2	yes	—
174	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
175	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
176	#11719919	C₂³	1	2	yes	—
177	#11719919	C₂³	1	2	yes	—
178	#11719919	C₂³	1	2	yes	—
179	#11719919	C₂³	1	2	yes	—
180	#11719919	C₂³	1	2	yes	—
181	#11719919	C₂³	1	2	yes	—
182	#11719919	C₂³	1	2	yes	—
183	#11719919	C₂³	1	2	yes	—
184	#11719919	C₂³	1	2	yes	—
185	#11719919	C₂³	1	2	yes	—
186	#11719919	C₂³	1	2	yes	—
187	#11719919	C₂³	1	2	yes	—
188	C₄×Dic₅₃	C₂³	1	2	yes	—
189	C₄×Dic₅₃	C₂³	1	2	yes	—
190	C₄×Dic₅₃	C₂³	1	2	yes	—
191	C₄×Dic₅₃	C₂³	1	2	yes	—
192	C₄×Dic₅₃	C₂³	1	2	yes	—
193	C₄×Dic₅₃	C₂³	1	2	yes	—
194	C₂³×C₅₃	C₂⁴	1	2	yes	—
195	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
196	C₂²×D₅₃	—	4	2	no	—
197	C₂²×D₅₃	—	4	2	no	—
198	C₂²×D₅₃	—	4	2	no	—
199	C₂²×D₅₃	C₂⁴	1	2	yes	—
200	C₂²×D₅₃	C₂⁴	1	2	yes	—
201	Q₈×C₅₃	—	4	1	no	—
202	D₄×C₅₃	—	4	2	no	—
203	D₄×C₅₃	—	4	1	no	—
204	C₂×C₄×C₅₃	—	4	2	no	—
205	C₂×C₄×C₅₃	—	4	1	no	—
206	C₂×C₄×C₅₃	—	4	1	no	—
207	C₂×C₄×C₅₃	—	4	1	no	—
208	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
209	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
210	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
211	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
212	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
213	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
214	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
215	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
216	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
217	C₂²⋊D₅₃	—	4	2	no	—
218	C₂²⋊D₅₃	—	4	2	no	—
219	C₂²⋊D₅₃	—	4	2	no	—
220	C₂²⋊D₅₃	—	4	2	no	—
221	C₂×Dic₅₃	—	4	2	no	—
222	C₂×Dic₅₃	C₂⁴	1	2	yes	—
223	C₂×Dic₅₃	C₂⁴	1	2	yes	—
224	C₂×Dic₅₃	C₂⁴	1	2	yes	—
225	C₂×Dic₅₃	C₂⁴	1	2	yes	—
226	C₂×Dic₅₃	C₂⁴	1	2	yes	—
227	C₂×Dic₅₃	C₂⁴	1	2	yes	—
228	D₂₁₂	—	4	1	no	—
229	D₂₁₂	—	4	1	no	—
230	D₂₁₂	—	4	2	no	—
231	C₄×D₅₃	—	4	2	no	—
232	C₄×D₅₃	—	4	2	no	—
233	C₄×D₅₃	—	4	2	no	—
234	C₄×D₅₃	—	4	2	no	—
235	Dic₁₀₆	—	4	1	no	—
236	Dic₁₀₆	—	4	1	no	—
237	Dic₁₀₆	—	4	2	no	—
238	Dic₁₀₆	—	4	2	no	—
239	Dic₁₀₆	—	4	2	no	—
240	C₂²×C₅₃	—	2	2	no	—
241	C₂²×C₅₃	—	2	1	no	—
242	C₂²×C₅₃	—	2	1	no	—
243	C₂²×C₅₃	—	2	2	no	—
244	C₂²×C₅₃	—	2	2	no	—
245	C₂²×C₅₃	—	2	1	no	—
246	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
247	C₂×D₅₃	—	2	2	no	—
248	C₂×D₅₃	—	2	2	no	—
249	C₂×D₅₃	—	2	2	no	—
250	C₂×D₅₃	—	2	2	no	—
251	C₂×D₅₃	—	2	2	no	—
252	C₂×D₅₃	—	2	2	no	—
253	C₂×D₅₃	—	8	4	no	—
254	C₄×C₅₃	—	2	2	no	—
255	C₄×C₅₃	—	2	2	no	—
256	C₄×C₅₃	—	2	1	no	—
257	C₄×C₅₃	—	2	1	no	—
258	C₄×C₅₃	—	2	2	no	—
259	C₄×C₅₃	—	2	1	no	—
260	C₄×C₅₃	—	2	1	no	—
261	C₄×C₅₃	—	2	1	no	—
262	C₄×C₅₃	—	2	1	no	—
263	Dic₅₃	—	2	2	no	—
264	Dic₅₃	—	2	2	no	—
265	Dic₅₃	—	2	2	no	—
266	Dic₅₃	—	2	2	no	—
267	Dic₅₃	—	2	2	no	—
268	Dic₅₃	—	2	2	no	—
269	#3568	—	53	1	no	maximal, Sylow
270	C₂×C₅₃	—	4	2	no	—
271	C₂×C₅₃	—	4	1	no	—
272	C₂×C₅₃	#585	1	1	yes	characteristic
273	C₂×C₅₃	#585	1	1	yes	characteristic
274	C₂×C₅₃	#585	1	1	yes	characteristic
275	D₅₃	—	4	2	no	—
276	D₅₃	—	4	2	no	—
277	#563	—	53	1	no	—
278	#563	—	53	1	no	—
279	#563	—	53	1	no	—
280	H(3,𝔽₄)	—	53	1	no	—
281	#556	—	53	2	no	—
282	#556	—	53	2	no	—
283	#556	—	53	2	no	—
284	#551	—	53	2	no	—
285	#551	—	53	2	no	—
286	#551	—	53	2	no	—
287	#542	—	53	2	no	—
288	#542	—	53	2	no	—
289	#542	—	53	2	no	—
290	#538	—	53	2	no	—
291	#538	—	53	2	no	—
292	#538	—	53	2	no	—
293	#529	—	53	1	no	—
294	#529	—	53	1	no	—
295	#529	D₅₃	1	1	yes	characteristic, complemented
296	C₅₃	#3568	1	1	yes	characteristic, complemented, Sylow
297	C₄⋊Q₈	—	53	2	no	—
298	C₄⋊Q₈	—	53	2	no	—
299	C₄⋊Q₈	—	53	2	no	—
300	#126	—	53	2	no	—
301	#126	—	53	2	no	—
302	#126	—	53	2	no	—
303	#126	—	53	2	no	—
304	#126	—	53	2	no	—
305	#126	—	53	2	no	—
306	#126	—	53	2	no	—
307	#126	—	53	2	no	—
308	#126	—	53	2	no	—
309	#126	—	53	2	no	—
310	#126	—	53	2	no	—
311	#126	—	53	2	no	—
312	#126	C₂×D₅₃	1	2	yes	complemented
313	#125	—	53	1	no	—
314	#125	—	53	1	no	—
315	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
316	#124	—	53	2	no	—
317	#124	—	53	2	no	—
318	#124	—	53	2	no	—
319	#124	—	53	2	no	—
320	#124	—	53	2	no	—
321	#124	—	53	2	no	—
322	#124	—	53	2	no	—
323	#124	—	53	2	no	—
324	#124	—	53	1	no	—
325	#124	—	53	1	no	—
326	#124	—	53	2	no	—
327	#124	C₂×D₅₃	1	1	yes	characteristic
328	#123	—	53	2	no	—
329	#123	—	53	2	no	—
330	#123	—	53	2	no	—
331	#123	—	53	2	no	—
332	#123	—	53	2	no	—
333	#123	—	53	2	no	—
334	#123	—	53	2	no	—
335	#123	—	53	2	no	—
336	#123	C₂×D₅₃	1	2	yes	complemented
337	C₂²⋊Q₈	—	53	1	no	—
338	C₂²⋊Q₈	—	53	1	no	—
339	C₂²⋊Q₈	—	53	2	no	—
340	C₂²⋊Q₈	—	53	2	no	—
341	C₂²⋊Q₈	—	53	2	no	—
342	C₂²⋊Q₈	—	53	2	no	—
343	C₂²⋊Q₈	—	53	2	no	—
344	C₂²⋊Q₈	—	53	2	no	—
345	C₂²⋊Q₈	—	53	2	no	—
346	C₂²⋊Q₈	—	53	2	no	—
347	C₂²⋊Q₈	—	53	2	no	—
348	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
349	#121	—	53	2	no	—
350	#121	—	53	2	no	—
351	#121	—	53	1	no	—
352	#121	—	53	1	no	—
353	#121	—	53	2	no	—
354	#121	C₂×D₅₃	1	1	yes	characteristic
355	#120	—	53	2	no	—
356	#120	—	53	2	no	—
357	#120	—	53	2	no	—
358	#120	—	53	2	no	—
359	C₄×Q₈	—	53	2	no	—
360	C₄×Q₈	—	53	2	no	—
361	C₄×Q₈	—	53	1	no	—
362	C₄×Q₈	—	53	1	no	—
363	C₄×Q₈	—	53	2	no	—
364	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
365	C₄×D₄	—	53	2	no	—
366	C₄×D₄	—	53	2	no	—
367	C₄×D₄	—	53	2	no	—
368	C₄×D₄	—	53	2	no	—
369	C₄×D₄	—	53	2	no	—
370	C₄×D₄	—	53	1	no	—
371	C₄×D₄	—	53	1	no	—
372	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
373	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
374	#117	—	53	2	no	—
375	#117	—	53	2	no	—
376	#117	—	53	2	no	—
377	#117	—	53	2	no	—
378	#117	—	53	2	no	—
379	#117	C₂×D₅₃	1	2	yes	complemented
380	C₂×C₂²⋊C₄	—	53	2	no	—
381	C₂×C₂²⋊C₄	—	53	2	no	—
382	C₂×C₂²⋊C₄	—	53	2	no	—
383	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
384	C₂⁴	—	53	2	no	—
385	C₂×Q₈	—	53	2	no	—
386	C₂×Q₈	—	53	2	no	—
387	C₂×Q₈	—	53	2	no	—
388	C₂×Q₈	—	53	1	no	—
389	C₂×Q₈	—	53	1	no	—
390	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
391	C₂×D₄	—	53	2	no	—
392	C₂×D₄	—	53	2	no	—
393	C₂×D₄	—	53	2	no	—
394	C₂×D₄	—	53	2	no	—
395	C₂×D₄	—	53	1	no	—
396	C₂×D₄	—	53	1	no	—
397	C₂×D₄	—	53	2	no	—
398	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
399	C₂×D₄	C₂²×D₅₃	1	2	yes	—
400	C₂²×C₄	—	53	2	no	—
401	C₂²×C₄	—	53	2	no	—
402	C₂²×C₄	—	53	2	no	—
403	C₂²×C₄	—	53	2	no	—
404	C₂²×C₄	—	53	2	no	—
405	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
406	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
407	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
408	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
409	C₄⋊C₄	—	53	2	no	—
410	C₄⋊C₄	—	53	2	no	—
411	C₄⋊C₄	—	53	2	no	—
412	C₄⋊C₄	—	53	2	no	—
413	C₄⋊C₄	—	53	2	no	—
414	C₄⋊C₄	—	53	2	no	—
415	C₄⋊C₄	—	53	2	no	—
416	C₄⋊C₄	—	53	2	no	—
417	C₄⋊C₄	—	53	2	no	—
418	C₄⋊C₄	—	53	1	no	—
419	C₄⋊C₄	—	53	1	no	—
420	C₄⋊C₄	—	53	2	no	—
421	C₄⋊C₄	—	53	2	no	—
422	C₄⋊C₄	—	53	1	no	—
423	C₄⋊C₄	—	53	1	no	—
424	C₄⋊C₄	—	53	2	no	—
425	C₄⋊C₄	—	53	2	no	—
426	C₄⋊C₄	—	53	2	no	—
427	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
428	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
429	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
430	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
431	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
432	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
433	C₂²⋊C₄	—	53	2	no	—
434	C₂²⋊C₄	—	53	2	no	—
435	C₂²⋊C₄	—	53	2	no	—
436	C₂²⋊C₄	—	53	2	no	—
437	C₂²⋊C₄	—	53	2	no	—
438	C₂²⋊C₄	—	53	2	no	—
439	C₂²⋊C₄	—	53	2	no	—
440	C₂²⋊C₄	—	53	2	no	—
441	C₂²⋊C₄	—	53	2	no	—
442	C₂²⋊C₄	—	53	2	no	—
443	C₂²⋊C₄	—	53	2	no	—
444	C₂²⋊C₄	—	53	2	no	—
445	C₂²⋊C₄	—	53	2	no	—
446	C₂²⋊C₄	—	53	2	no	—
447	C₂²⋊C₄	—	53	2	no	—
448	C₂²⋊C₄	—	53	2	no	—
449	C₂²⋊C₄	—	53	2	no	—
450	C₂²⋊C₄	—	53	2	no	—
451	C₂²⋊C₄	—	53	2	no	—
452	C₂²⋊C₄	—	53	2	no	—
453	C₂²⋊C₄	—	53	2	no	—
454	C₂²⋊C₄	—	53	2	no	—
455	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
456	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
457	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
458	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
459	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
460	C₄²	—	53	2	no	—
461	C₄²	—	53	2	no	—
462	C₄²	—	53	2	no	—
463	C₄²	—	53	2	no	—
464	C₄²	—	53	2	no	—
465	C₄²	—	53	2	no	—
466	C₄²	C₂²×D₅₃	1	1	yes	characteristic
467	C₄²	C₂²×D₅₃	1	1	yes	characteristic
468	C₄²	C₂²×D₅₃	1	1	yes	characteristic
469	C₄²	C₂²×D₅₃	1	1	yes	characteristic
470	C₄²	C₂²×D₅₃	1	2	yes	—
471	C₂³	—	53	2	no	—
472	C₂³	—	53	2	no	—
473	C₂³	—	212	2	no	—
474	C₂³	—	212	2	no	—
475	C₂³	—	212	2	no	—
476	C₂³	C₂³×D₅₃	1	2	yes	—
477	C₂³	C₂³×D₅₃	1	1	yes	characteristic
478	Q₈	—	4	1	no	—
479	Q₈	—	212	2	no	—
480	Q₈	—	212	1	no	—
481	Q₈	—	212	1	no	—
482	Q₈	—	212	2	no	—
483	Q₈	—	212	2	no	—
484	D₄	—	4	1	no	—
485	D₄	—	4	2	no	—
486	D₄	—	212	1	no	—
487	D₄	—	212	1	no	—
488	D₄	—	212	2	no	—
489	D₄	—	212	2	no	—
490	D₄	—	212	2	no	—
491	D₄	—	212	2	no	—
492	D₄	—	212	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	53	2	no	—
498	C₂×C₄	—	53	2	no	—
499	C₂×C₄	—	53	2	no	—
500	C₂×C₄	—	53	2	no	—
501	C₂×C₄	—	53	2	no	—
502	C₂×C₄	—	53	2	no	—
503	C₂×C₄	—	212	2	no	—
504	C₂×C₄	—	212	2	no	—
505	C₂×C₄	—	212	2	no	—
506	C₂×C₄	—	212	2	no	—
507	C₂×C₄	—	212	2	no	—
508	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
509	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
510	C₂×C₄	C₂³×D₅₃	1	2	yes	—
511	C₂×C₄	C₂³×D₅₃	1	2	yes	—
512	C₂×C₄	C₂³×D₅₃	1	2	yes	—
513	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
514	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
515	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
516	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
517	C₂²	—	2	1	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	106	2	no	—
524	C₂²	—	106	2	no	—
525	C₂²	—	106	2	no	—
526	C₂²	—	106	2	no	—
527	C₂²	—	106	2	no	—
528	C₂²	—	106	2	no	—
529	C₂²	—	424	4	no	—
530	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	2	no	—
539	C₄	—	2	2	no	—
540	C₄	—	106	2	no	—
541	C₄	—	106	2	no	—
542	C₄	—	106	2	no	—
543	C₄	—	106	2	no	—
544	C₄	—	106	2	no	—
545	C₄	—	106	2	no	—
546	C₂	—	4	2	no	—
547	C₂	—	4	1	no	—
548	C₂	—	212	2	no	—
549	C₂	—	212	2	no	—
550	C₂	#16811459	1	1	yes	characteristic
551	C₂	#16811459	1	1	yes	characteristic
552	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#529	C₂
hypercenter	#529	D₅₃
hypocenter	C₅₃	#3568
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #16811377	C₂	semidirect
2. #16811377	C₂	semidirect
3. #16811373	C₂	semidirect
4. #16811365	C₂	semidirect
5. #16811345	C₂	semidirect
6. #16811341	C₂	semidirect
7. #16811340	C₂	semidirect
8. #16811302	C₂	semidirect
9. #16811298	C₂	semidirect
10. #16811297	C₂	semidirect
11. #16811243	C₂	semidirect
12. #16811241	C₂	semidirect
13. #16811238	C₂	semidirect
14. #16811209	C₂	semidirect
15. #16811206	C₂	semidirect
16. #16811205	C₂	semidirect
17. #16811157	C₂	semidirect
18. #16811157	C₂	semidirect
19. C₅₃×#529	C₂	semidirect
20. #13133216	C₂²	semidirect
21. #13133216	C₂²	semidirect
22. #13133215	C₂²	semidirect
23. #13133212	C₂²	semidirect
24. #13133212	C₂²	semidirect
25. #13133212	C₂²	semidirect
26. #13133212	C₂²	semidirect
27. #13133212	C₂²	semidirect
28. #13133211	C₂²	semidirect
29. #13133211	C₂²	semidirect
30. #13133211	C₂²	semidirect
31. #13133210	C₂²	semidirect
32. #13133210	C₂²	semidirect
33. #13133210	C₂²	semidirect
34. #13133210	C₂²	semidirect
35. #13133209	C₂²	semidirect
36. #13133209	C₂²	semidirect
41. #13133204	C₂²	semidirect
46. #13133203	C₂²	semidirect
47. #13133203	C₂²	semidirect
52. #13133200	C₂²	semidirect
53. #13133200	C₂²	semidirect
56. #13133197	C₂²	semidirect
57. #13133197	C₂²	semidirect
58. #13133196	C₂²	semidirect
59. #13133196	C₂²	semidirect
60. #13133196	C₂²	semidirect
61. #13133195	C₂²	semidirect
62. #13133195	C₂²	semidirect
63. #13133195	C₂²	semidirect
64. #13133195	C₂²	semidirect
65. #13133194	C₂²	semidirect
66. #13133194	C₂²	semidirect
75. #13133185	C₂²	semidirect
76. C₄×Dic₁₀₆	C₂²	semidirect
77. C₄×Dic₁₀₆	C₂²	semidirect
78. C₄×Dic₁₀₆	C₂²	semidirect
79. #13133182	C₂²	semidirect
80. #13133182	C₂²	semidirect
85. C₄×C₂²⋊D₅₃	C₂²	semidirect
86. C₄×C₂²⋊D₅₃	C₂²	semidirect
88. #13133175	C₂²	semidirect
89. #13133174	C₂²	semidirect
90. #13133174	C₂²	semidirect
91. #13133174	C₂²	semidirect
92. #13133173	C₂²	semidirect
93. C₂×#11719921	C₂²	semidirect
94. C₂²⋊C₄×D₅₃	C₂²	semidirect
95. C₂²⋊C₄×D₅₃	C₂²	semidirect
96. #126×C₅₃	C₂²	semidirect
97. #125×C₅₃	C₂²	semidirect
99. #123×C₅₃	C₂²	semidirect
100. C₂²⋊Q₈×C₅₃	C₂²	semidirect
102. C₄×Q₈×C₅₃	C₂²	semidirect
104. C₄×D₄×C₅₃	C₂²	semidirect
105. #117×C₅₃	C₂²	semidirect
106. C₂×C₄²×C₅₃	C₂²	semidirect
295. #529	D₅₃	semidirect
296. C₅₃	#3568	semidirect
312. #126	C₂×D₅₃	semidirect
315. #125	C₂×D₅₃	semidirect
336. #123	C₂×D₅₃	semidirect
348. C₂²⋊Q₈	C₂×D₅₃	semidirect
364. C₄×Q₈	C₂×D₅₃	semidirect
373. C₄×D₄	C₂×D₅₃	semidirect
379. #117	C₂×D₅₃	semidirect
383. C₂×C₄²	C₂×D₅₃	semidirect