Subgroups — #20291213

Order 6784.

476 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811574	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811574	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811573	C₂	1	1	yes	maximal, characteristic
4	#16811573	C₂	1	1	yes	maximal, characteristic
5	#16811573	C₂	1	1	yes	maximal, characteristic
6	#16811572	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811572	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811572	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811570	C₂	1	1	yes	maximal, characteristic
10	#16811570	C₂	1	1	yes	maximal, characteristic
11	#16811567	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄⋊C₄×#6157	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₄⋊#6157	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₄×#6157	C₂	1	1	yes	maximal, characteristic
15	#126×D₅₃	C₂	1	1	yes	maximal, characteristic
16	C₂³×#6157	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊#6157	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊#6157	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊#6157	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#6157	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#6157	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#6157	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊#6157	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊#6157	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊#6157	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊#6157	C₂²	1	1	yes	characteristic
27	C₂×C₄×#6157	C₂²	1	1	yes	characteristic
28	C₂×C₄×#6157	C₂²	1	1	yes	characteristic
29	C₂×C₄×#6157	C₂²	1	1	yes	characteristic
30	C₂×C₄×#6157	C₂²	1	1	yes	characteristic
31	C₂×C₄×#6157	C₂²	1	1	yes	characteristic
32	(C₂×#6157)⋊C₄	C₂²	1	1	yes	characteristic
33	(C₂×#6157)⋊C₄	C₂²	1	1	yes	characteristic
34	(C₂×#6157)⋊C₄	C₂²	1	1	yes	characteristic
35	(C₂×#6157)⋊C₄	C₂²	1	1	yes	characteristic
36	(C₂×#6157)⋊C₄	C₂²	1	1	yes	characteristic
37	(C₂×#6157)⋊C₄	C₂²	1	1	yes	characteristic
38	(C₂×#6157)⋊C₄	C₂²	1	1	yes	characteristic
39	(C₂×#6157)⋊C₄	C₂²	1	1	yes	characteristic
40	(C₂×#6157)⋊C₄	C₂²	1	1	yes	characteristic
41	(C₂×#6157)⋊C₄	C₂²	1	1	yes	characteristic
42	(C₂×#6157)⋊C₄	C₂²	1	1	yes	characteristic
43	(C₂×#6157)⋊C₄	C₂²	1	1	yes	characteristic
44	#13133212	C₄	1	1	yes	characteristic, complemented
45	#13133212	C₄	1	1	yes	characteristic, complemented
46	#13133212	C₄	1	1	yes	characteristic, complemented
47	#13133211	C₄	1	1	yes	characteristic, complemented
48	#13133210	C₄	1	1	yes	characteristic, complemented
49	#13133210	C₄	1	1	yes	characteristic, complemented
50	#13133210	C₄	1	1	yes	characteristic, complemented
51	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
52	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
53	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
54	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
55	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
56	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
57	C₄²×D₅₃	C₂²	1	1	yes	characteristic
58	#126×C₅₃	C₄	1	1	yes	characteristic, complemented
59	C₂³×D₅₃	C₂³	1	1	yes	characteristic
60	C₂²×#6157	—	2	2	no	—
61	C₂²×#6157	—	4	1	no	—
62	C₂²×#6157	—	4	1	no	—
63	C₂²×#6157	C₂³	1	1	yes	characteristic
64	C₂²×#6157	C₂³	1	1	yes	characteristic
65	C₂²×#6157	C₂³	1	1	yes	characteristic
66	C₂²×#6157	C₂³	1	1	yes	characteristic
67	C₂²×#6157	C₂³	1	1	yes	characteristic
68	C₂²×#6157	C₂³	1	1	yes	characteristic
69	C₂²×#6157	C₂³	1	1	yes	characteristic
70	C₂²×#6157	C₂³	1	1	yes	characteristic
71	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
72	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
73	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
74	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
75	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
76	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
77	C₂²⋊#6157	—	2	2	no	—
78	C₂²⋊#6157	—	4	1	no	—
79	C₂²⋊#6157	—	4	1	no	—
80	C₄⋊#6157	—	2	2	no	—
81	C₄⋊#6157	—	2	2	no	—
82	C₄⋊#6157	—	2	2	no	—
83	C₄⋊#6157	—	4	1	no	—
84	C₄⋊#6157	—	4	1	no	—
85	C₄⋊#6157	—	4	1	no	—
86	C₄⋊#6157	—	4	1	no	—
87	C₄×#6157	—	2	2	no	—
88	C₄×#6157	—	4	1	no	—
89	C₄×#6157	—	4	1	no	—
90	C₄×#6157	—	4	1	no	—
91	C₄×#6157	—	4	1	no	—
92	C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
93	C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
94	C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
95	C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
97	C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
98	C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
99	C₂²⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
102	#11719921	C₂×C₄	1	1	yes	characteristic
103	#11719921	C₂×C₄	1	1	yes	characteristic
104	#11719921	C₂×C₄	1	1	yes	characteristic
105	#11719921	C₂×C₄	1	1	yes	characteristic
106	#11719921	C₂×C₄	1	1	yes	characteristic
107	#11719921	C₂×C₄	1	1	yes	characteristic
108	C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic, complemented
109	C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic, complemented
110	C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic, complemented
111	#11719919	C₂×C₄	1	1	yes	characteristic, complemented
112	#11719919	C₂×C₄	1	1	yes	characteristic, complemented
113	#11719919	C₂×C₄	1	1	yes	characteristic, complemented
114	#11719919	C₂×C₄	1	1	yes	characteristic, complemented
115	#11719919	C₂×C₄	1	1	yes	characteristic, complemented
116	#11719919	C₂×C₄	1	1	yes	characteristic, complemented
117	C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic, complemented
118	C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic, complemented
119	C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic, complemented
120	C₂³×C₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×D₅₃	—	2	1	no	—
122	C₂²×D₅₃	—	2	1	no	—
123	C₂²×D₅₃	—	2	1	no	—
124	C₂²×D₅₃	—	2	1	no	—
125	C₂²×D₅₃	—	2	1	no	—
126	C₂²×D₅₃	—	2	1	no	—
127	C₂²×D₅₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
129	C₂×#6157	—	2	1	no	—
130	C₂×#6157	—	2	1	no	—
131	C₂×#6157	—	2	1	no	—
132	C₂×#6157	—	2	1	no	—
133	C₂×#6157	—	2	1	no	—
134	C₂×#6157	—	2	1	no	—
135	C₂×#6157	—	2	1	no	—
136	C₂×#6157	—	2	1	no	—
137	C₂×#6157	—	2	1	no	—
138	C₂×#6157	—	2	1	no	—
139	C₂×#6157	—	2	1	no	—
140	C₂×#6157	—	2	1	no	—
141	C₂×#6157	—	2	1	no	—
142	C₂×#6157	—	2	1	no	—
143	C₂×#6157	—	2	1	no	—
144	C₂×#6157	—	2	1	no	—
145	C₂×#6157	—	2	1	no	—
146	C₂×#6157	—	2	1	no	—
147	C₂×#6157	—	2	1	no	—
148	C₂×#6157	—	2	1	no	—
149	C₂×#6157	—	2	1	no	—
150	C₂×#6157	—	2	1	no	—
151	C₂×#6157	—	4	4	no	—
152	C₂×#6157	#41	1	2	yes	—
153	C₂×#6157	#41	1	2	yes	—
154	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
162	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
163	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
164	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
165	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
166	C₄×D₅₃	—	2	1	no	—
167	C₄×D₅₃	—	2	1	no	—
168	C₄×D₅₃	—	2	1	no	—
169	C₄×D₅₃	—	2	1	no	—
170	C₄×D₅₃	—	2	1	no	—
171	C₄×D₅₃	—	2	1	no	—
172	C₄×D₅₃	—	2	1	no	—
173	C₄×D₅₃	—	2	1	no	—
174	C₄×D₅₃	—	2	1	no	—
175	C₄×D₅₃	—	2	1	no	—
176	C₄×D₅₃	—	2	1	no	—
177	C₄×D₅₃	—	2	1	no	—
178	C₂²×C₅₃	—	2	1	no	—
179	C₂²×C₅₃	—	2	1	no	—
180	C₂²×C₅₃	—	2	1	no	—
181	C₂²×C₅₃	C₂³×C₄	1	1	yes	characteristic
182	C₂×D₅₃	—	2	1	no	—
183	C₂×D₅₃	—	2	1	no	—
184	C₂×D₅₃	—	2	1	no	—
185	C₂×D₅₃	—	4	1	no	—
186	C₂×D₅₃	—	4	1	no	—
187	C₂×D₅₃	—	4	1	no	—
188	C₂×D₅₃	—	4	1	no	—
189	C₂×D₅₃	C₂×#41	1	1	yes	characteristic
190	C₂×D₅₃	C₂×#41	1	1	yes	characteristic
191	C₂×D₅₃	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×D₅₃	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂×D₅₃	2₋¹⁺⁴	1	1	yes	characteristic
194	C₂×D₅₃	2₋¹⁺⁴	1	1	yes	characteristic
195	#6157	—	2	2	no	—
196	#6157	—	2	2	no	—
197	#6157	—	4	1	no	—
198	#6157	—	4	1	no	—
199	#6157	—	4	1	no	—
200	#6157	—	4	1	no	—
201	#6157	—	4	1	no	—
202	#6157	—	4	1	no	—
203	C₄×C₅₃	—	2	1	no	—
204	C₄×C₅₃	—	2	1	no	—
205	C₄×C₅₃	—	2	1	no	—
206	C₄×C₅₃	—	2	1	no	—
207	C₄×C₅₃	—	2	1	no	—
208	C₄×C₅₃	—	2	1	no	—
209	Dic₅₃	—	2	1	no	—
210	Dic₅₃	—	2	1	no	—
211	Dic₅₃	—	2	1	no	—
212	Dic₅₃	—	2	1	no	—
213	Dic₅₃	—	2	1	no	—
214	Dic₅₃	—	2	1	no	—
215	#2334	—	53	1	no	maximal, Sylow
216	C₂×C₅₃	—	4	1	no	—
217	C₂×C₅₃	C₄×#41	1	1	yes	characteristic
218	C₂×C₅₃	#520	1	1	yes	characteristic
219	C₂×C₅₃	#520	1	1	yes	characteristic
220	D₅₃	—	4	1	no	—
221	D₅₃	#538	1	1	yes	characteristic
222	D₅₃	#539	1	1	yes	characteristic
223	D₅₃	#541	1	1	yes	characteristic
224	D₅₃	#542	1	1	yes	characteristic
225	C₂×#126	—	53	1	no	—
226	#389	—	53	1	no	—
227	#389	—	53	1	no	—
228	#388	—	53	1	no	—
229	#388	—	53	1	no	—
230	#388	—	53	1	no	—
231	#387	—	53	1	no	—
232	#387	—	53	1	no	—
233	#387	—	53	1	no	—
234	#385	—	53	1	no	—
235	#385	—	53	1	no	—
236	#382	—	53	1	no	—
237	C₄×C₄⋊C₄	—	53	1	no	—
238	C₄×C₄⋊C₄	—	53	1	no	—
239	C₄×C₂²⋊C₄	—	53	1	no	—
240	C₅₃	#2334	1	1	yes	characteristic, complemented, Sylow
241	C₂³×C₄	—	53	1	no	—
242	#126	—	53	1	no	—
243	#126	—	53	1	no	—
244	#126	—	53	1	no	—
245	#126	—	53	1	no	—
246	#126	—	53	1	no	—
247	#126	—	53	1	no	—
248	#126	—	53	1	no	—
249	#126	#6157	1	1	yes	characteristic, complemented
250	C₂×C₄⋊C₄	—	53	1	no	—
251	C₂×C₄⋊C₄	—	53	1	no	—
252	C₂×C₄⋊C₄	—	53	1	no	—
253	C₂×C₄⋊C₄	—	53	1	no	—
254	C₂×C₄⋊C₄	—	53	1	no	—
255	C₂×C₄⋊C₄	—	53	1	no	—
256	C₂×C₄⋊C₄	—	53	1	no	—
257	C₂×C₄⋊C₄	—	53	1	no	—
258	C₂×C₄⋊C₄	—	53	1	no	—
259	C₂×C₄⋊C₄	—	53	1	no	—
260	C₂×C₂²⋊C₄	—	53	1	no	—
261	C₂×C₂²⋊C₄	—	53	1	no	—
262	C₂×C₂²⋊C₄	—	53	1	no	—
263	C₂×C₂²⋊C₄	—	53	1	no	—
264	C₂×C₂²⋊C₄	—	53	1	no	—
265	C₂×C₂²⋊C₄	—	53	1	no	—
266	C₂×C₄²	—	53	1	no	—
267	C₂×C₄²	—	53	1	no	—
268	C₂×C₄²	—	53	1	no	—
269	C₂×C₄²	—	53	1	no	—
270	C₂×C₄²	—	53	1	no	—
271	C₂×C₄²	—	53	1	no	—
272	#95	—	53	1	no	—
273	#95	—	53	1	no	—
274	#95	—	53	1	no	—
275	#95	—	53	1	no	—
276	#95	—	53	1	no	—
277	#95	—	53	1	no	—
278	#95	—	53	1	no	—
279	#95	—	53	1	no	—
280	#95	—	53	1	no	—
281	#95	—	53	1	no	—
282	#95	—	53	1	no	—
283	#95	—	53	1	no	—
284	C₂⁴	—	53	1	no	—
285	C₂²×C₄	—	53	1	no	—
286	C₂²×C₄	—	53	1	no	—
287	C₂²×C₄	—	53	1	no	—
288	C₂²×C₄	—	53	1	no	—
289	C₂²×C₄	—	53	1	no	—
290	C₂²×C₄	—	53	1	no	—
291	C₂²×C₄	—	53	1	no	—
292	C₂²×C₄	—	53	1	no	—
293	C₂²×C₄	—	53	1	no	—
294	C₂²×C₄	—	53	1	no	—
295	C₂²×C₄	—	53	1	no	—
296	C₂²×C₄	—	53	1	no	—
297	C₂²×C₄	—	53	1	no	—
298	C₂²×C₄	—	53	1	no	—
299	C₂²×C₄	—	106	2	no	—
300	C₂²×C₄	—	212	1	no	—
301	C₂²×C₄	—	212	1	no	—
302	C₄⋊C₄	—	53	1	no	—
303	C₄⋊C₄	—	53	1	no	—
304	C₄⋊C₄	—	53	1	no	—
305	C₄⋊C₄	—	53	1	no	—
306	C₄⋊C₄	—	53	1	no	—
307	C₄⋊C₄	—	53	1	no	—
308	C₄⋊C₄	—	53	1	no	—
309	C₄⋊C₄	—	53	1	no	—
310	C₄⋊C₄	—	53	1	no	—
311	C₄⋊C₄	—	106	2	no	—
312	C₄⋊C₄	—	106	2	no	—
313	C₄⋊C₄	—	106	2	no	—
314	C₄⋊C₄	—	212	1	no	—
315	C₄⋊C₄	—	212	1	no	—
316	C₄⋊C₄	—	212	1	no	—
317	C₄⋊C₄	—	212	1	no	—
318	C₄⋊C₄	C₂×#6157	1	1	yes	characteristic, complemented
319	C₄⋊C₄	C₂×#6157	1	1	yes	characteristic, complemented
320	C₄⋊C₄	C₂×#6157	1	1	yes	characteristic, complemented
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	—	106	2	no	—
331	C₂²⋊C₄	—	212	1	no	—
332	C₂²⋊C₄	—	212	1	no	—
333	C₂²⋊C₄	C₂×#6157	1	1	yes	characteristic
334	C₂²⋊C₄	C₂×#6157	1	1	yes	characteristic
335	C₂²⋊C₄	C₂×#6157	1	1	yes	characteristic
336	C₄²	—	53	1	no	—
337	C₄²	—	53	1	no	—
338	C₄²	—	53	1	no	—
339	C₄²	—	106	2	no	—
340	C₄²	—	212	1	no	—
341	C₄²	—	212	1	no	—
342	C₄²	—	212	1	no	—
343	C₄²	—	212	1	no	—
344	C₄²	C₂×#6157	1	1	yes	characteristic, complemented
345	C₂³	—	53	1	no	—
346	C₂³	—	53	1	no	—
347	C₂³	—	106	1	no	—
348	C₂³	—	106	1	no	—
349	C₂³	—	106	1	no	—
350	C₂³	—	106	1	no	—
351	C₂³	—	106	1	no	—
352	C₂³	—	106	1	no	—
353	C₂³	C₂²×#6157	1	1	yes	characteristic
354	C₂×C₄	—	53	2	no	—
355	C₂×C₄	—	53	2	no	—
356	C₂×C₄	—	53	1	no	—
357	C₂×C₄	—	53	1	no	—
358	C₂×C₄	—	53	1	no	—
359	C₂×C₄	—	53	1	no	—
360	C₂×C₄	—	53	1	no	—
361	C₂×C₄	—	53	1	no	—
362	C₂×C₄	—	106	1	no	—
363	C₂×C₄	—	106	1	no	—
364	C₂×C₄	—	106	1	no	—
365	C₂×C₄	—	106	1	no	—
366	C₂×C₄	—	106	1	no	—
367	C₂×C₄	—	106	1	no	—
368	C₂×C₄	—	106	1	no	—
369	C₂×C₄	—	106	1	no	—
370	C₂×C₄	—	106	1	no	—
371	C₂×C₄	—	106	1	no	—
372	C₂×C₄	—	106	1	no	—
373	C₂×C₄	—	106	1	no	—
374	C₂×C₄	—	106	1	no	—
375	C₂×C₄	—	106	1	no	—
376	C₂×C₄	—	106	1	no	—
377	C₂×C₄	—	106	1	no	—
378	C₂×C₄	—	106	1	no	—
379	C₂×C₄	—	106	1	no	—
380	C₂×C₄	—	106	1	no	—
381	C₂×C₄	—	106	1	no	—
382	C₂×C₄	—	106	1	no	—
383	C₂×C₄	—	106	1	no	—
384	C₂×C₄	—	106	1	no	—
385	C₂×C₄	—	106	1	no	—
386	C₂×C₄	—	106	1	no	—
387	C₂×C₄	—	106	1	no	—
388	C₂×C₄	—	106	1	no	—
389	C₂×C₄	—	106	1	no	—
390	C₂×C₄	—	106	1	no	—
391	C₂×C₄	—	106	1	no	—
392	C₂×C₄	—	106	1	no	—
393	C₂×C₄	—	106	1	no	—
394	C₂×C₄	—	106	1	no	—
395	C₂×C₄	—	106	1	no	—
396	C₂×C₄	—	212	4	no	—
397	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
398	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
399	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
400	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
401	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
402	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	53	1	no	—
407	C₂²	—	53	1	no	—
408	C₂²	—	53	1	no	—
409	C₂²	—	53	1	no	—
410	C₂²	—	53	1	no	—
411	C₂²	—	53	1	no	—
412	C₂²	—	106	1	no	—
413	C₂²	—	106	1	no	—
414	C₂²	—	106	1	no	—
415	C₂²	—	212	1	no	—
416	C₂²	—	212	1	no	—
417	C₂²	—	212	1	no	—
418	C₂²	—	212	1	no	—
419	C₂²	C₂³×#6157	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	106	2	no	—
427	C₄	—	106	2	no	—
428	C₄	—	106	1	no	—
429	C₄	—	106	1	no	—
430	C₄	—	106	1	no	—
431	C₄	—	106	1	no	—
432	C₄	—	106	1	no	—
433	C₄	—	106	1	no	—
434	C₄	—	212	1	no	—
435	C₄	—	212	1	no	—
436	C₄	—	212	1	no	—
437	C₄	—	212	1	no	—
438	C₄	—	212	1	no	—
439	C₄	—	212	1	no	—
440	C₂	—	4	1	no	—
441	C₂	—	53	1	no	—
442	C₂	—	53	1	no	—
443	C₂	—	53	1	no	—
444	C₂	—	53	1	no	—
445	C₂	—	212	1	no	—
446	C₂	#41×#6157	1	1	yes	characteristic
447	C₂	#16811692	1	1	yes	characteristic
448	C₂	#16811692	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#6157
commutator, socle	C₂²×C₅₃	C₂³×C₄
Fitting	#126×C₅₃	C₄
hypercenter	#126	#6157
hypocenter	C₅₃	#2334
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #126

Complements

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

N	H ≅ G/N	type
1. #16811574	C₂	semidirect
2. #16811574	C₂	semidirect
6. #16811572	C₂	semidirect
7. #16811572	C₂	semidirect
8. #16811572	C₂	semidirect
11. #16811567	C₂	semidirect
12. C₄⋊C₄×#6157	C₂	semidirect
13. C₄×C₄⋊#6157	C₂	semidirect
44. #13133212	C₄	semidirect
45. #13133212	C₄	semidirect
46. #13133212	C₄	semidirect
47. #13133211	C₄	semidirect
48. #13133210	C₄	semidirect
49. #13133210	C₄	semidirect
50. #13133210	C₄	semidirect
58. #126×C₅₃	C₄	semidirect
92. C₄⋊C₄×C₅₃	C₂×C₄	semidirect
93. C₄⋊C₄×C₅₃	C₂×C₄	semidirect
94. C₄⋊C₄×C₅₃	C₂×C₄	semidirect
98. C₄²×C₅₃	C₂×C₄	semidirect
108. C₄⋊Dic₅₃	C₂×C₄	semidirect
109. C₄⋊Dic₅₃	C₂×C₄	semidirect
110. C₄⋊Dic₅₃	C₂×C₄	semidirect
111. #11719919	C₂×C₄	semidirect
112. #11719919	C₂×C₄	semidirect
113. #11719919	C₂×C₄	semidirect
114. #11719919	C₂×C₄	semidirect
115. #11719919	C₂×C₄	semidirect
116. #11719919	C₂×C₄	semidirect
117. C₄×Dic₅₃	C₂×C₄	semidirect
118. C₄×Dic₅₃	C₂×C₄	semidirect
119. C₄×Dic₅₃	C₂×C₄	semidirect
240. C₅₃	#2334	semidirect
249. #126	#6157	semidirect
318. C₄⋊C₄	C₂×#6157	semidirect
319. C₄⋊C₄	C₂×#6157	semidirect
320. C₄⋊C₄	C₂×#6157	semidirect
344. C₄²	C₂×#6157	semidirect