Subgroups — #20289231

Order 6784.

1160 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811371	C₂	1	2	yes	maximal, complemented
2	#16811365	C₂	1	2	yes	maximal, complemented
3	#16811358	C₂	1	2	yes	maximal, complemented
4	#16811282	C₂	1	2	yes	maximal, complemented
5	#16811269	C₂	1	2	yes	maximal, complemented
6	#16811265	C₂	1	4	yes	maximal, complemented
7	D₄×D₂₁₂	C₂	1	2	yes	maximal, complemented
8	#16811244	C₂	1	2	yes	maximal, complemented
9	#16811213	C₂	1	2	yes	maximal, complemented
10	#16811212	C₂	1	4	yes	maximal, complemented
11	#16811192	C₂	1	2	yes	maximal, complemented
12	#16811181	C₂	1	2	yes	maximal, complemented
13	#16811173	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13133205	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11719945	C₂²	1	2	yes	complemented
17	C₂×#11719945	C₂²	1	2	yes	complemented
18	C₂²×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic
20	C₂²×D₂₁₂	C₂²	1	2	yes	complemented
21	C₂×D₄×D₅₃	C₂²	1	4	yes	complemented
22	#13133217	C₂²	1	1	yes	characteristic, complemented
23	#13133214	C₂²	1	2	yes	—
24	#13133214	C₂²	1	1	yes	characteristic, complemented
25	#13133212	C₂²	1	4	yes	complemented
26	#13133206	C₂²	1	4	yes	complemented
27	#13133205	C₂²	1	2	yes	complemented
28	#13133205	C₂²	1	2	yes	complemented
29	#13133205	C₂²	1	2	yes	complemented
30	#13133205	C₂²	1	2	yes	complemented
31	#13133205	C₂²	1	2	yes	complemented
32	#13133205	C₂²	1	2	yes	complemented
33	#13133203	C₂²	1	4	yes	complemented
34	#13133203	C₂²	1	4	yes	complemented
35	#13133202	C₂²	1	4	yes	complemented
36	#13133202	C₂²	1	4	yes	complemented
37	#13133202	C₂²	1	4	yes	complemented
38	#13133199	C₂²	1	4	yes	complemented
39	#13133196	C₂²	1	2	yes	complemented
40	#13133195	C₂²	1	4	yes	complemented
41	#13133195	C₂²	1	4	yes	complemented
42	#13133192	C₂²	1	4	yes	complemented
43	#13133192	C₂²	1	4	yes	complemented
44	#13133192	C₂²	1	4	yes	complemented
45	#13133191	C₂²	1	2	yes	—
46	#13133191	C₂²	1	2	yes	complemented
47	#13133191	C₂²	1	2	yes	complemented
48	#13133190	C₂²	1	4	yes	complemented
49	#13133189	C₂²	1	4	yes	complemented
50	#13133187	C₂²	1	4	yes	complemented
51	#13133187	C₂²	1	4	yes	complemented
52	#13133187	C₂²	1	4	yes	complemented
53	#13133187	C₂²	1	4	yes	complemented
54	#13133185	C₂²	1	4	yes	complemented
55	C₄×Dic₁₀₆	C₂²	1	2	yes	complemented
56	C₄×D₂₁₂	C₂²	1	2	yes	complemented
57	C₄×D₂₁₂	C₂²	1	2	yes	complemented
58	C₄×D₂₁₂	C₂²	1	2	yes	complemented
59	#13133179	C₂²	1	4	yes	complemented
60	#13133177	C₂²	1	4	yes	complemented
61	C₂×#11719921	C₂²	1	2	yes	complemented
62	C₂×#11719921	C₂²	1	2	yes	complemented
63	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
64	#126×C₅₃	C₂²	1	2	yes	complemented
65	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
66	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	#123×C₅₃	C₂²	1	2	yes	complemented
68	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
69	#121×C₅₃	C₂²	1	1	yes	characteristic
70	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
71	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
72	C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
73	#117×C₅₃	C₂²	1	2	yes	complemented
74	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₅₃	C₂³	1	2	yes	—
76	C₂³×D₅₃	C₂³	1	4	yes	—
77	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
78	C₂×D₄×C₅₃	C₂³	1	2	yes	—
79	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
83	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
85	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
86	C₂×C₂²⋊D₅₃	C₂³	1	4	yes	—
87	C₂²×Dic₅₃	C₂³	1	2	yes	—
88	D₄×D₅₃	—	4	8	no	—
89	#11719945	—	4	4	no	—
90	#11719945	—	4	4	no	—
91	C₂×D₂₁₂	—	4	2	no	—
92	C₂×D₂₁₂	—	4	4	no	—
93	C₂×D₂₁₂	C₂³	1	2	yes	—
94	C₂×D₂₁₂	C₂³	1	2	yes	—
95	C₂×D₂₁₂	C₂³	1	4	yes	—
96	C₂×D₂₁₂	C₂³	1	2	yes	—
97	C₂×D₂₁₂	C₂³	1	2	yes	—
98	C₂×D₂₁₂	C₂³	1	2	yes	—
99	C₂×D₂₁₂	C₂³	1	4	yes	—
100	C₂×D₂₁₂	C₂³	1	4	yes	—
101	C₂×C₄×D₅₃	C₂³	1	4	yes	—
102	C₂×C₄×D₅₃	C₂³	1	4	yes	—
103	C₂×C₄×D₅₃	C₂³	1	4	yes	—
104	C₂×Dic₁₀₆	—	4	2	no	—
105	C₂×Dic₁₀₆	C₂³	1	2	yes	—
106	C₂×Dic₁₀₆	C₂³	1	2	yes	—
107	C₂×Dic₁₀₆	C₂³	1	2	yes	—
108	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
109	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
110	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
111	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
112	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
114	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
115	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
116	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
119	C₄²×C₅₃	C₂³	1	1	yes	characteristic
120	C₄²×C₅₃	C₂³	1	1	yes	characteristic
121	C₄²×C₅₃	C₂³	1	1	yes	characteristic
122	C₄²×C₅₃	C₂³	1	1	yes	characteristic
123	C₄²×C₅₃	C₂³	1	2	yes	—
124	C₂²⋊Dic₅₃	C₂³	1	4	yes	—
125	#11719921	C₂³	1	4	yes	—
126	#11719921	C₂³	1	4	yes	—
127	#11719921	C₂³	1	4	yes	—
128	#11719921	C₂³	1	4	yes	—
129	#11719921	C₂³	1	4	yes	—
130	#11719921	C₂³	1	4	yes	—
131	#11719921	C₂³	1	4	yes	—
132	#11719921	C₂³	1	4	yes	—
133	#11719921	C₂³	1	4	yes	—
134	#11719921	C₂³	1	4	yes	—
135	C₄⋊Dic₅₃	C₂³	1	2	yes	—
136	C₄⋊Dic₅₃	C₂³	1	2	yes	—
137	#11719919	C₂³	1	4	yes	—
138	#11719919	C₂³	1	4	yes	—
139	C₄×Dic₅₃	C₂³	1	4	yes	—
140	C₂³×C₅₃	C₂⁴	1	2	yes	—
141	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
142	C₂²×D₅₃	—	2	4	no	—
143	C₂²×D₅₃	—	4	4	no	—
144	C₂²×D₅₃	—	4	2	no	—
145	C₂²×D₅₃	—	4	4	no	—
146	C₂²×D₅₃	—	4	4	no	—
147	C₂²×D₅₃	—	4	2	no	—
148	C₂²×D₅₃	C₂⁴	1	4	yes	—
149	C₂²×D₅₃	C₂⁴	1	4	yes	—
150	Q₈×C₅₃	—	4	1	no	—
151	D₄×C₅₃	—	2	4	no	—
152	D₄×C₅₃	—	4	1	no	—
153	C₂×C₄×C₅₃	—	2	2	no	—
154	C₂×C₄×C₅₃	—	2	2	no	—
155	C₂×C₄×C₅₃	—	2	4	no	—
156	C₂×C₄×C₅₃	—	4	1	no	—
157	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
158	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
160	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
161	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
162	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
164	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
166	C₂²⋊D₅₃	—	2	8	no	—
167	C₂²⋊D₅₃	—	4	4	no	—
168	C₂²⋊D₅₃	—	4	4	no	—
169	C₂×Dic₅₃	—	4	2	no	—
170	C₂×Dic₅₃	C₂⁴	1	4	yes	—
171	C₂×Dic₅₃	C₂⁴	1	4	yes	—
172	D₂₁₂	—	2	4	no	—
173	D₂₁₂	—	2	4	no	—
174	D₂₁₂	—	4	2	no	—
175	D₂₁₂	—	4	4	no	—
176	D₂₁₂	—	4	2	no	—
177	D₂₁₂	—	4	4	no	—
178	D₂₁₂	—	4	2	no	—
179	D₂₁₂	—	4	4	no	—
180	C₄×D₅₃	—	4	4	no	—
181	C₄×D₅₃	—	4	4	no	—
182	C₄×D₅₃	—	4	4	no	—
183	Dic₁₀₆	—	2	4	no	—
184	Dic₁₀₆	—	4	2	no	—
185	Dic₁₀₆	—	4	2	no	—
186	C₂²×C₅₃	—	2	1	no	—
187	C₂²×C₅₃	—	2	1	no	—
188	C₂²×C₅₃	—	2	2	no	—
189	C₂²×C₅₃	—	2	2	no	—
190	C₂²×C₅₃	—	2	2	no	—
191	C₂²×C₅₃	H(5,𝔽₂)	1	2	yes	—
192	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
193	C₂×D₅₃	—	2	4	no	—
194	C₂×D₅₃	—	2	4	no	—
195	C₂×D₅₃	—	2	4	no	—
196	C₂×D₅₃	—	2	4	no	—
197	C₂×D₅₃	—	2	4	no	—
198	C₂×D₅₃	—	2	4	no	—
199	C₂×D₅₃	—	8	4	no	—
200	C₂×D₅₃	—	8	8	no	—
201	C₄×C₅₃	—	2	1	no	—
202	C₄×C₅₃	—	2	1	no	—
203	C₄×C₅₃	—	2	1	no	—
204	C₄×C₅₃	—	2	2	no	—
205	C₄×C₅₃	—	2	2	no	—
206	C₄×C₅₃	—	2	1	no	—
207	C₄×C₅₃	—	2	2	no	—
208	C₄×C₅₃	—	2	1	no	—
209	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
210	Dic₅₃	—	2	4	no	—
211	Dic₅₃	—	2	4	no	—
212	#3558	—	53	1	no	maximal, Sylow
213	C₂×C₅₃	—	2	2	no	—
214	C₂×C₅₃	—	4	2	no	—
215	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₅₃	#585	1	1	yes	characteristic
218	D₅₃	—	4	4	no	—
219	D₅₃	—	4	4	no	—
220	#562	—	53	2	no	—
221	H(3,𝔽₄)	—	53	2	no	—
222	#559	—	53	2	no	—
223	#548	—	53	2	no	—
224	#546	—	53	4	no	—
225	#546	—	53	2	no	—
226	D₄²	—	53	2	no	—
227	#542	—	53	2	no	—
228	#538	—	53	4	no	—
229	#538	—	53	2	no	—
230	#535	—	53	2	no	—
231	#534	—	53	2	no	—
232	#532	—	53	1	no	—
233	#529	D₅₃	1	1	yes	characteristic, complemented
234	C₂×#124	—	53	1	no	—
235	C₅₃	#3558	1	1	yes	characteristic, complemented, Sylow
236	C₂×#41	—	53	2	no	—
237	C₂×#41	—	53	2	no	—
238	C₂²×Q₈	—	53	1	no	—
239	C₂²×D₄	—	53	4	no	—
240	C₂²×D₄	—	53	1	no	—
241	C₂²×D₄	—	53	2	no	—
242	C₄⋊Q₈	—	53	1	no	—
243	#127	—	53	1	no	—
244	#127	—	53	2	no	—
245	#126	—	53	4	no	—
246	#126	C₂×D₅₃	1	2	yes	complemented
247	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
248	#124	—	53	4	no	—
249	#124	—	53	4	no	—
250	#124	—	53	4	no	—
251	#124	—	53	2	no	—
252	#124	—	53	2	no	—
253	#124	—	53	2	no	—
254	#124	—	53	2	no	—
255	#124	—	53	2	no	—
256	#124	—	53	2	no	—
257	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
258	#123	—	53	4	no	—
259	#123	—	53	4	no	—
260	#123	—	53	4	no	—
261	#123	—	53	4	no	—
262	#123	C₂×D₅₃	1	2	yes	complemented
263	C₂²⋊Q₈	—	53	2	no	—
264	C₂²⋊Q₈	—	53	4	no	—
265	C₂²⋊Q₈	—	53	4	no	—
266	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
267	#121	—	53	4	no	—
268	#121	—	53	2	no	—
269	#121	—	53	2	no	—
270	#121	—	53	2	no	—
271	#121	—	53	4	no	—
272	#121	—	53	4	no	—
273	#121	—	53	4	no	—
274	#121	—	53	4	no	—
275	#121	C₂×D₅₃	1	1	yes	characteristic
276	#120	—	53	4	no	—
277	#120	—	53	4	no	—
278	#120	—	53	4	no	—
279	#120	—	53	4	no	—
280	#120	—	53	4	no	—
281	C₄×Q₈	—	53	2	no	—
282	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
283	C₄×D₄	—	53	4	no	—
284	C₄×D₄	—	53	4	no	—
285	C₄×D₄	—	53	2	no	—
286	C₄×D₄	—	53	2	no	—
287	C₄×D₄	—	53	2	no	—
288	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
289	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
290	#117	C₂×D₅₃	1	2	yes	complemented
291	C₂×C₂²⋊C₄	—	53	2	no	—
292	C₂×C₂²⋊C₄	—	53	2	no	—
293	C₂×C₂²⋊C₄	—	53	4	no	—
294	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
295	C₂⁴	—	53	2	no	—
296	C₂⁴	—	53	4	no	—
297	#41	—	212	4	no	—
298	#41	—	212	4	no	—
299	C₂×Q₈	—	53	2	no	—
300	C₂×Q₈	—	53	2	no	—
301	C₂×Q₈	—	53	2	no	—
302	C₂×Q₈	—	212	2	no	—
303	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
304	C₂×D₄	—	53	4	no	—
305	C₂×D₄	—	53	4	no	—
306	C₂×D₄	—	53	4	no	—
307	C₂×D₄	—	53	2	no	—
308	C₂×D₄	—	53	2	no	—
309	C₂×D₄	—	53	4	no	—
310	C₂×D₄	—	53	2	no	—
311	C₂×D₄	—	53	2	no	—
312	C₂×D₄	—	53	2	no	—
313	C₂×D₄	—	53	4	no	—
314	C₂×D₄	—	53	4	no	—
315	C₂×D₄	—	212	2	no	—
316	C₂×D₄	—	212	4	no	—
317	C₂×D₄	—	212	8	no	—
318	C₂×D₄	C₂²×D₅₃	1	2	yes	—
319	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
320	C₂²×C₄	—	53	2	no	—
321	C₂²×C₄	—	53	4	no	—
322	C₂²×C₄	—	53	4	no	—
323	C₂²×C₄	—	53	4	no	—
324	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
325	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
326	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
327	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
328	C₄⋊C₄	—	53	2	no	—
329	C₄⋊C₄	—	53	4	no	—
330	C₄⋊C₄	—	53	2	no	—
331	C₄⋊C₄	—	53	4	no	—
332	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
333	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
334	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
335	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
336	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
337	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
338	C₂²⋊C₄	—	53	4	no	—
339	C₂²⋊C₄	—	53	4	no	—
340	C₂²⋊C₄	—	53	4	no	—
341	C₂²⋊C₄	—	53	4	no	—
342	C₂²⋊C₄	—	53	4	no	—
343	C₂²⋊C₄	—	53	4	no	—
344	C₂²⋊C₄	—	53	4	no	—
345	C₂²⋊C₄	—	53	4	no	—
346	C₂²⋊C₄	—	53	4	no	—
347	C₂²⋊C₄	—	53	4	no	—
348	C₂²⋊C₄	—	53	4	no	—
349	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
350	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
351	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
352	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
353	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
354	C₄²	—	53	4	no	—
355	C₄²	C₂²×D₅₃	1	1	yes	characteristic
356	C₄²	C₂²×D₅₃	1	1	yes	characteristic
357	C₄²	C₂²×D₅₃	1	1	yes	characteristic
358	C₄²	C₂²×D₅₃	1	1	yes	characteristic
359	C₄²	C₂²×D₅₃	1	2	yes	—
360	C₂³	—	53	4	no	—
361	C₂³	—	53	4	no	—
362	C₂³	—	106	4	no	—
363	C₂³	—	212	2	no	—
364	C₂³	—	212	4	no	—
365	C₂³	—	212	4	no	—
366	C₂³	—	212	2	no	—
367	C₂³	—	212	4	no	—
368	C₂³	C₂³×D₅₃	1	2	yes	—
369	C₂³	C₂³×D₅₃	1	1	yes	characteristic
370	Q₈	—	4	1	no	—
371	Q₈	—	106	4	no	—
372	Q₈	—	212	2	no	—
373	Q₈	—	212	2	no	—
374	D₄	—	2	4	no	—
375	D₄	—	4	1	no	—
376	D₄	—	106	8	no	—
377	D₄	—	106	4	no	—
378	D₄	—	106	4	no	—
379	D₄	—	212	2	no	—
380	D₄	—	212	4	no	—
381	D₄	—	212	4	no	—
382	D₄	—	212	2	no	—
383	D₄	—	212	4	no	—
384	D₄	—	212	2	no	—
385	D₄	—	212	4	no	—
386	D₄	—	212	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	53	4	no	—
392	C₂×C₄	—	53	4	no	—
393	C₂×C₄	—	212	4	no	—
394	C₂×C₄	—	212	4	no	—
395	C₂×C₄	—	212	4	no	—
396	C₂×C₄	—	212	2	no	—
397	C₂×C₄	C₂³×D₅₃	1	2	yes	—
398	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
399	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
400	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
403	C₂×C₄	C₂³×D₅₃	1	2	yes	—
404	C₂×C₄	C₂³×D₅₃	1	2	yes	—
405	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	106	4	no	—
412	C₂²	—	106	4	no	—
413	C₂²	—	106	4	no	—
414	C₂²	—	106	4	no	—
415	C₂²	—	106	4	no	—
416	C₂²	—	106	4	no	—
417	C₂²	—	424	4	no	—
418	C₂²	—	424	8	no	—
419	C₂²	#13133263	1	2	yes	—
420	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	2	no	—
429	C₄	—	106	4	no	—
430	C₄	—	106	4	no	—
431	C₄	#13133263	1	2	yes	—
432	C₂	—	2	2	no	—
433	C₂	—	4	2	no	—
434	C₂	—	212	4	no	—
435	C₂	—	212	4	no	—
436	C₂	C₂×#13133263	1	1	yes	characteristic
437	C₂	C₂×#13133263	1	1	yes	characteristic
438	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	#3558
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. #16811371	C₂	semidirect
2. #16811365	C₂	semidirect
3. #16811358	C₂	semidirect
4. #16811282	C₂	semidirect
5. #16811269	C₂	semidirect
6. #16811265	C₂	semidirect
7. D₄×D₂₁₂	C₂	semidirect
8. #16811244	C₂	semidirect
9. #16811213	C₂	semidirect
10. #16811212	C₂	semidirect
11. #16811192	C₂	semidirect
12. #16811181	C₂	semidirect
13. #16811173	C₂	semidirect
14. C₂×#13133205	C₂	semidirect
15. C₅₃×#529	C₂	semidirect
16. C₂×#11719945	C₂²	semidirect
17. C₂×#11719945	C₂²	semidirect
18. C₂²×Dic₁₀₆	C₂²	semidirect
20. C₂²×D₂₁₂	C₂²	semidirect
21. C₂×D₄×D₅₃	C₂²	semidirect
22. #13133217	C₂²	semidirect
24. #13133214	C₂²	semidirect
25. #13133212	C₂²	semidirect
26. #13133206	C₂²	semidirect
27. #13133205	C₂²	semidirect
28. #13133205	C₂²	semidirect
29. #13133205	C₂²	semidirect
30. #13133205	C₂²	semidirect
31. #13133205	C₂²	semidirect
32. #13133205	C₂²	semidirect
33. #13133203	C₂²	semidirect
34. #13133203	C₂²	semidirect
35. #13133202	C₂²	semidirect
36. #13133202	C₂²	semidirect
37. #13133202	C₂²	semidirect
38. #13133199	C₂²	semidirect
39. #13133196	C₂²	semidirect
40. #13133195	C₂²	semidirect
41. #13133195	C₂²	semidirect
42. #13133192	C₂²	semidirect
43. #13133192	C₂²	semidirect
44. #13133192	C₂²	semidirect
46. #13133191	C₂²	semidirect
47. #13133191	C₂²	semidirect
48. #13133190	C₂²	semidirect
49. #13133189	C₂²	semidirect
50. #13133187	C₂²	semidirect
51. #13133187	C₂²	semidirect
52. #13133187	C₂²	semidirect
53. #13133187	C₂²	semidirect
54. #13133185	C₂²	semidirect
55. C₄×Dic₁₀₆	C₂²	semidirect
56. C₄×D₂₁₂	C₂²	semidirect
57. C₄×D₂₁₂	C₂²	semidirect
58. C₄×D₂₁₂	C₂²	semidirect
59. #13133179	C₂²	semidirect
60. #13133177	C₂²	semidirect
61. C₂×#11719921	C₂²	semidirect
62. C₂×#11719921	C₂²	semidirect
63. C₂²⋊C₄×D₅₃	C₂²	semidirect
64. #126×C₅₃	C₂²	semidirect
65. #125×C₅₃	C₂²	semidirect
66. #124×C₅₃	C₂²	semidirect
67. #123×C₅₃	C₂²	semidirect
68. C₂²⋊Q₈×C₅₃	C₂²	semidirect
70. C₄×Q₈×C₅₃	C₂²	semidirect
71. C₄×D₄×C₅₃	C₂²	semidirect
72. C₄×D₄×C₅₃	C₂²	semidirect
73. #117×C₅₃	C₂²	semidirect
74. C₂×C₄²×C₅₃	C₂²	semidirect
233. #529	D₅₃	semidirect
235. C₅₃	#3558	semidirect
246. #126	C₂×D₅₃	semidirect
247. #125	C₂×D₅₃	semidirect
257. #124	C₂×D₅₃	semidirect
262. #123	C₂×D₅₃	semidirect
266. C₂²⋊Q₈	C₂×D₅₃	semidirect
282. C₄×Q₈	C₂×D₅₃	semidirect
288. C₄×D₄	C₂×D₅₃	semidirect
289. C₄×D₄	C₂×D₅₃	semidirect
290. #117	C₂×D₅₃	semidirect
294. C₂×C₄²	C₂×D₅₃	semidirect