Subgroups — #20288871

Order 6784.

1336 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811365	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811364	C₂	1	2	yes	maximal, complemented
3	#16811363	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811297	C₂	1	2	yes	maximal, complemented
5	#16811265	C₂	1	2	yes	maximal, complemented
6	#16811264	C₂	1	2	yes	maximal, complemented
7	#16811263	C₂	1	2	yes	maximal, complemented
8	D₄×D₂₁₂	C₂	1	2	yes	maximal, complemented
9	#16811255	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811213	C₂	1	2	yes	maximal, complemented
11	#16811212	C₂	1	2	yes	maximal, complemented
12	#16811206	C₂	1	2	yes	maximal, complemented
13	#16811192	C₂	1	2	yes	maximal, complemented
14	#16811191	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811184	C₂	1	2	yes	maximal, complemented
16	#16811184	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#13133187	C₂	1	2	yes	maximal, complemented
18	#120×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₅₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×#11719949	C₂²	1	1	yes	characteristic, complemented
22	C₂×#11719945	C₂²	1	2	yes	complemented
23	C₂²×D₂₁₂	C₂²	1	2	yes	complemented
24	C₂²×D₂₁₂	C₂²	1	2	yes	complemented
25	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
27	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
28	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₅₃	C₂²	1	2	yes	complemented
30	#13133214	C₂²	1	2	yes	complemented
31	#13133214	C₂²	1	1	yes	characteristic, complemented
32	#13133213	C₂²	1	1	yes	characteristic, complemented
33	#13133212	C₂²	1	2	yes	complemented
34	#13133212	C₂²	1	2	yes	complemented
35	#13133211	C₂²	1	2	yes	complemented
36	#13133206	C₂²	1	2	yes	complemented
37	#13133206	C₂²	1	1	yes	characteristic, complemented
38	#13133205	C₂²	1	2	yes	complemented
39	#13133205	C₂²	1	2	yes	complemented
40	#13133203	C₂²	1	2	yes	complemented
41	#13133203	C₂²	1	2	yes	complemented
42	#13133202	C₂²	1	2	yes	complemented
43	#13133202	C₂²	1	2	yes	complemented
44	#13133202	C₂²	1	2	yes	complemented
45	#13133202	C₂²	1	2	yes	complemented
46	#13133202	C₂²	1	2	yes	complemented
47	#13133200	C₂²	1	2	yes	complemented
48	#13133200	C₂²	1	1	yes	characteristic, complemented
49	#13133199	C₂²	1	2	yes	complemented
50	#13133195	C₂²	1	2	yes	complemented
51	#13133194	C₂²	1	2	yes	complemented
52	#13133192	C₂²	1	2	yes	complemented
53	#13133192	C₂²	1	2	yes	complemented
54	#13133192	C₂²	1	2	yes	complemented
55	#13133192	C₂²	1	2	yes	complemented
56	#13133192	C₂²	1	2	yes	complemented
57	#13133192	C₂²	1	2	yes	complemented
58	#13133192	C₂²	1	2	yes	complemented
59	#13133191	C₂²	1	2	yes	complemented
60	#13133191	C₂²	1	2	yes	complemented
61	#13133190	C₂²	1	2	yes	complemented
62	#13133190	C₂²	1	2	yes	complemented
63	#13133190	C₂²	1	2	yes	complemented
64	#13133190	C₂²	1	2	yes	complemented
65	#13133190	C₂²	1	2	yes	complemented
66	#13133189	C₂²	1	2	yes	complemented
67	#13133187	C₂²	1	2	yes	—
68	#13133187	C₂²	1	2	yes	complemented
69	#13133187	C₂²	1	1	yes	characteristic, complemented
70	#13133187	C₂²	1	2	yes	complemented
71	#13133187	C₂²	1	2	yes	complemented
72	#13133187	C₂²	1	2	yes	complemented
73	#13133187	C₂²	1	2	yes	complemented
74	#13133187	C₂²	1	2	yes	complemented
75	#13133187	C₂²	1	2	yes	complemented
76	#13133187	C₂²	1	2	yes	complemented
77	#13133187	C₂²	1	2	yes	complemented
78	#13133187	C₂²	1	1	yes	characteristic, complemented
79	#13133187	C₂²	1	2	yes	complemented
80	#13133187	C₂²	1	2	yes	complemented
81	#13133187	C₂²	1	2	yes	complemented
82	#13133186	C₂²	1	1	yes	characteristic, complemented
83	#13133185	C₂²	1	1	yes	characteristic, complemented
84	#13133185	C₂²	1	2	yes	complemented
85	#13133185	C₂²	1	1	yes	characteristic, complemented
86	C₄×D₂₁₂	C₂²	1	2	yes	complemented
87	#13133179	C₂²	1	2	yes	complemented
88	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
89	#13133177	C₂²	1	2	yes	complemented
90	#13133177	C₂²	1	2	yes	complemented
91	#13133174	C₂²	1	1	yes	characteristic, complemented
92	C₂×#11719921	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	1	yes	characteristic, complemented
96	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
97	C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
98	#126×C₅₃	C₂²	1	2	yes	complemented
99	#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
100	#123×C₅₃	C₂²	1	2	yes	complemented
101	#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
102	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
103	#120×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×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
107	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
108	C₂³×D₅₃	—	4	2	no	—
109	C₂³×D₅₃	—	4	4	no	—
110	C₂³×D₅₃	C₂³	1	2	yes	—
111	C₂³×D₅₃	C₂³	1	1	yes	characteristic
112	C₂³×D₅₃	C₂³	1	1	yes	characteristic
113	C₂³×D₅₃	C₂³	1	2	yes	—
114	C₂³×D₅₃	C₂³	1	2	yes	—
115	C₂³×D₅₃	C₂³	1	1	yes	characteristic
116	C₂³×D₅₃	C₂³	1	1	yes	characteristic, complemented
117	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
118	C₂×D₄×C₅₃	C₂³	1	2	yes	—
119	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
121	C₂²×C₄×C₅₃	C₂³	1	2	yes	—
122	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
123	C₂×C₂²⋊D₅₃	—	4	4	no	—
124	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
133	C₂²×Dic₅₃	C₂³	1	2	yes	—
134	#11719949	—	4	2	no	—
135	D₄×D₅₃	—	4	2	no	—
136	D₄×D₅₃	—	4	4	no	—
137	D₄×D₅₃	—	4	4	no	—
138	#11719945	—	4	4	no	—
139	C₂×D₂₁₂	—	4	2	no	—
140	C₂×D₂₁₂	—	4	4	no	—
141	C₂×D₂₁₂	—	4	4	no	—
142	C₂×D₂₁₂	C₂³	1	2	yes	—
143	C₂×D₂₁₂	C₂³	1	2	yes	—
144	C₂×D₂₁₂	C₂³	1	2	yes	—
145	C₂×D₂₁₂	C₂³	1	2	yes	—
146	C₂×D₂₁₂	C₂³	1	2	yes	—
147	C₂×D₂₁₂	C₂³	1	2	yes	—
148	C₂×D₂₁₂	C₂³	1	2	yes	—
149	C₂×D₂₁₂	C₂³	1	2	yes	—
150	C₂×D₂₁₂	C₂³	1	2	yes	—
151	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
152	C₂×D₂₁₂	C₂³	1	2	yes	complemented
153	C₂×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
154	C₂×D₂₁₂	C₂³	1	2	yes	complemented
155	C₂×D₂₁₂	C₂³	1	2	yes	complemented
156	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₅₃	C₂³	1	2	yes	—
158	C₂×C₄×D₅₃	C₂³	1	2	yes	complemented
159	C₂×C₄×D₅₃	C₂³	1	2	yes	complemented
160	C₂×C₄×D₅₃	C₂³	1	2	yes	complemented
161	C₂×C₄×D₅₃	C₂³	1	2	yes	complemented
162	C₂×Dic₁₀₆	C₂³	1	2	yes	complemented
163	C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
164	C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
165	C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
166	C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
167	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
173	C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
174	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
175	C₄²×C₅₃	C₂³	1	1	yes	characteristic, complemented
176	C₄²×C₅₃	C₂³	1	2	yes	complemented
177	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
180	#11719921	C₂³	1	2	yes	—
181	#11719921	C₂³	1	2	yes	—
182	#11719921	C₂³	1	2	yes	—
183	#11719921	C₂³	1	2	yes	—
184	#11719921	C₂³	1	2	yes	—
185	#11719921	C₂³	1	2	yes	—
186	#11719921	C₂³	1	2	yes	—
187	#11719921	C₂³	1	2	yes	—
188	#11719921	C₂³	1	2	yes	—
189	#11719921	C₂³	1	2	yes	—
190	#11719921	C₂³	1	2	yes	—
191	#11719921	C₂³	1	2	yes	complemented
192	#11719921	C₂³	1	2	yes	complemented
193	#11719921	C₂³	1	2	yes	complemented
194	#11719921	C₂³	1	2	yes	complemented
195	#11719921	C₂³	1	2	yes	complemented
196	#11719921	C₂³	1	2	yes	complemented
197	#11719921	C₂³	1	2	yes	complemented
198	C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
199	#11719919	C₂³	1	2	yes	complemented
200	#11719919	C₂³	1	2	yes	complemented
201	#11719919	C₂³	1	2	yes	complemented
202	#11719919	C₂³	1	2	yes	complemented
203	C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
204	C₄×Dic₅₃	C₂³	1	2	yes	complemented
205	C₂³×C₅₃	—	2	4	no	—
206	C₂³×C₅₃	—	4	1	no	—
207	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
208	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
209	C₂³×C₅₃	C₂⁴	1	2	yes	—
210	C₂²×D₅₃	—	2	4	no	—
211	C₂²×D₅₃	—	2	4	no	—
212	C₂²×D₅₃	—	2	4	no	—
213	C₂²×D₅₃	—	2	4	no	—
214	C₂²×D₅₃	—	2	2	no	—
215	C₂²×D₅₃	—	2	2	no	—
216	C₂²×D₅₃	—	4	2	no	—
217	C₂²×D₅₃	—	4	2	no	—
218	C₂²×D₅₃	—	4	1	no	—
219	C₂²×D₅₃	—	4	2	no	—
220	C₂²×D₅₃	—	4	2	no	—
221	C₂²×D₅₃	—	4	2	no	—
222	C₂²×D₅₃	—	4	2	no	—
223	C₂²×D₅₃	—	4	1	no	—
224	C₂²×D₅₃	—	4	2	no	—
225	C₂²×D₅₃	—	4	2	no	—
226	C₂²×D₅₃	—	4	2	no	—
227	C₂²×D₅₃	—	4	16	no	—
228	C₂²×D₅₃	C₂⁴	1	2	yes	—
229	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
230	C₂²×D₅₃	C₂⁴	1	2	yes	—
231	C₂²×D₅₃	C₂⁴	1	2	yes	—
232	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
233	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
234	Q₈×C₅₃	—	4	1	no	—
235	D₄×C₅₃	—	2	4	no	—
236	D₄×C₅₃	—	4	1	no	—
237	C₂×C₄×C₅₃	—	2	4	no	—
238	C₂×C₄×C₅₃	—	4	2	no	—
239	C₂×C₄×C₅₃	—	4	1	no	—
240	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
241	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
242	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
244	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
245	C₂×C₄×C₅₃	C₂⁴	1	2	yes	—
246	C₂²⋊D₅₃	—	2	4	no	—
247	C₂²⋊D₅₃	—	2	4	no	—
248	C₂²⋊D₅₃	—	2	4	no	—
249	C₂²⋊D₅₃	—	4	2	no	—
250	C₂²⋊D₅₃	—	4	1	no	—
251	C₂²⋊D₅₃	—	4	1	no	—
252	C₂²⋊D₅₃	—	4	2	no	—
253	C₂²⋊D₅₃	—	4	2	no	—
254	C₂²⋊D₅₃	—	4	2	no	—
255	C₂×Dic₅₃	—	4	2	no	—
256	C₂×Dic₅₃	C₂⁴	1	2	yes	—
257	C₂×Dic₅₃	C₂⁴	1	2	yes	—
258	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₅₃	C₂⁴	1	2	yes	—
260	D₂₁₂	—	2	4	no	—
261	D₂₁₂	—	2	4	no	—
262	D₂₁₂	—	4	2	no	—
263	D₂₁₂	—	4	2	no	—
264	D₂₁₂	—	4	2	no	—
265	D₂₁₂	—	4	2	no	—
266	D₂₁₂	—	4	2	no	—
267	D₂₁₂	—	4	2	no	—
268	D₂₁₂	—	4	2	no	—
269	D₂₁₂	—	4	1	no	—
270	D₂₁₂	—	4	2	no	—
271	D₂₁₂	—	4	2	no	—
272	D₂₁₂	—	4	2	no	—
273	D₂₁₂	—	4	1	no	—
274	C₄×D₅₃	—	2	2	no	—
275	C₄×D₅₃	—	4	2	no	—
276	C₄×D₅₃	—	4	2	no	—
277	C₄×D₅₃	—	4	2	no	—
278	C₄×D₅₃	—	4	2	no	—
279	C₄×D₅₃	—	4	2	no	—
280	Dic₁₀₆	—	4	2	no	—
281	C₂²×C₅₃	—	2	2	no	—
282	C₂²×C₅₃	—	2	2	no	—
283	C₂²×C₅₃	—	2	2	no	—
284	C₂²×C₅₃	—	2	2	no	—
285	C₂²×C₅₃	—	2	1	no	—
286	C₂²×C₅₃	—	2	1	no	—
287	C₂²×C₅₃	—	4	4	no	—
288	C₂²×C₅₃	H(5,𝔽₂)	1	4	yes	—
289	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
290	C₂×D₅₃	—	2	2	no	—
291	C₂×D₅₃	—	2	2	no	—
292	C₂×D₅₃	—	2	2	no	—
293	C₂×D₅₃	—	2	2	no	—
294	C₂×D₅₃	—	2	2	no	—
295	C₂×D₅₃	—	2	2	no	—
296	C₂×D₅₃	—	2	1	no	—
297	C₂×D₅₃	—	2	2	no	—
298	C₂×D₅₃	—	2	2	no	—
299	C₂×D₅₃	—	2	2	no	—
300	C₂×D₅₃	—	2	2	no	—
301	C₂×D₅₃	—	2	2	no	—
302	C₂×D₅₃	—	2	1	no	—
303	C₂×D₅₃	—	2	2	no	—
304	C₂×D₅₃	—	4	8	no	—
305	C₂×D₅₃	—	4	4	no	—
306	C₂×D₅₃	—	4	8	no	—
307	C₂×D₅₃	—	4	4	no	—
308	C₂×D₅₃	—	8	2	no	—
309	C₂×D₅₃	—	8	4	no	—
310	C₂×D₅₃	—	8	2	no	—
311	C₂×D₅₃	H(5,𝔽₂)	1	2	yes	—
312	C₄×C₅₃	—	2	2	no	—
313	C₄×C₅₃	—	2	1	no	—
314	C₄×C₅₃	—	2	2	no	—
315	C₄×C₅₃	—	2	2	no	—
316	C₄×C₅₃	—	2	2	no	—
317	C₄×C₅₃	—	2	2	no	—
318	Dic₅₃	—	2	2	no	—
319	Dic₅₃	—	2	2	no	—
320	Dic₅₃	—	2	1	no	—
321	Dic₅₃	—	2	2	no	—
322	#3532	—	53	1	no	maximal, Sylow
323	C₂×C₅₃	—	2	4	no	—
324	C₂×C₅₃	—	4	1	no	—
325	C₂×C₅₃	—	4	1	no	—
326	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
327	C₂×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
328	D₅₃	—	2	2	no	—
329	D₅₃	—	4	2	no	—
330	D₅₃	—	4	1	no	—
331	D₅₃	—	4	2	no	—
332	D₅₃	—	4	1	no	—
333	D₅₃	—	4	2	no	—
334	H(3,𝔽₄)	—	53	1	no	—
335	#560	—	53	2	no	—
336	#560	—	53	1	no	—
337	#551	—	53	2	no	—
338	#551	D₅₃	1	1	yes	characteristic, complemented
339	#546	—	53	2	no	—
340	#546	—	53	2	no	—
341	#546	—	53	2	no	—
342	D₄²	—	53	1	no	—
343	D₄²	—	53	2	no	—
344	#538	—	53	2	no	—
345	#538	—	53	2	no	—
346	#538	—	53	2	no	—
347	#535	—	53	1	no	—
348	#535	—	53	2	no	—
349	#534	—	53	2	no	—
350	#534	—	53	1	no	—
351	C₂×#120	—	53	1	no	—
352	C₂×#120	—	53	2	no	—
353	C₅₃	#3532	1	1	yes	characteristic, complemented, Sylow
354	C₂⁵	—	53	1	no	—
355	C₂×#41	—	53	1	no	—
356	C₂×#41	—	53	2	no	—
357	C₂²×D₄	—	53	2	no	—
358	C₂²×D₄	—	53	1	no	—
359	C₂²×D₄	—	53	2	no	—
360	C₂²×D₄	—	53	2	no	—
361	C₂²×D₄	—	53	2	no	—
362	C₂²×D₄	—	53	2	no	—
363	C₂²×D₄	—	53	1	no	—
364	#127	—	53	1	no	—
365	#127	—	53	1	no	—
366	#127	—	53	2	no	—
367	#126	—	53	2	no	—
368	#126	—	53	2	no	—
369	#126	—	53	2	no	—
370	#126	C₂×D₅₃	1	2	yes	complemented
371	#124	—	53	1	no	—
372	#124	—	53	2	no	—
373	#124	—	53	2	no	—
374	#124	—	53	2	no	—
375	#124	—	53	2	no	—
376	#124	—	53	2	no	—
377	#124	C₂×D₅₃	1	1	yes	characteristic, complemented
378	#123	—	53	2	no	—
379	#123	—	53	1	no	—
380	#123	—	53	2	no	—
381	#123	—	53	2	no	—
382	#123	—	53	2	no	—
383	#123	—	53	2	no	—
384	#123	—	53	2	no	—
385	#123	—	53	2	no	—
386	#123	C₂×D₅₃	1	1	yes	characteristic, complemented
387	#123	C₂×D₅₃	1	2	yes	complemented
388	C₂²⋊Q₈	—	53	2	no	—
389	C₂²⋊Q₈	—	53	2	no	—
390	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
391	#121	—	53	2	no	—
392	#121	—	53	2	no	—
393	#121	—	53	2	no	—
394	#121	—	53	2	no	—
395	#121	—	53	2	no	—
396	#121	—	53	2	no	—
397	#121	—	53	2	no	—
398	#121	—	53	2	no	—
399	#121	—	53	2	no	—
400	#121	—	53	2	no	—
401	#121	—	53	2	no	—
402	#121	—	53	2	no	—
403	#121	—	53	2	no	—
404	#121	—	53	2	no	—
405	#121	—	53	2	no	—
406	#120	—	53	1	no	—
407	#120	—	53	2	no	—
408	#120	—	53	1	no	—
409	#120	—	53	1	no	—
410	#120	—	53	2	no	—
411	#120	—	53	2	no	—
412	#120	—	53	2	no	—
413	#120	—	53	2	no	—
414	#120	—	53	2	no	—
415	#120	—	53	2	no	—
416	#120	—	53	2	no	—
417	#120	—	53	2	no	—
418	#120	—	53	1	no	—
419	#120	—	53	2	no	—
420	#120	—	53	2	no	—
421	#120	—	53	2	no	—
422	#120	—	53	1	no	—
423	#120	—	53	2	no	—
424	#120	—	53	2	no	—
425	#120	C₂×D₅₃	1	1	yes	characteristic
426	C₄×D₄	—	53	2	no	—
427	C₄×D₄	—	53	2	no	—
428	C₄×D₄	—	53	2	no	—
429	C₄×D₄	—	53	2	no	—
430	C₄×D₄	—	53	2	no	—
431	C₄×D₄	C₂×D₅₃	1	2	yes	complemented
432	#117	—	53	1	no	—
433	#117	C₂×D₅₃	1	2	yes	complemented
434	C₂×C₂²⋊C₄	—	53	2	no	—
435	C₂×C₂²⋊C₄	—	53	2	no	—
436	C₂×C₂²⋊C₄	—	53	1	no	—
437	C₂×C₂²⋊C₄	—	53	2	no	—
438	C₂×C₂²⋊C₄	—	53	2	no	—
439	C₂×C₂²⋊C₄	—	53	1	no	—
440	C₂×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
441	C₂⁴	—	53	2	no	—
442	C₂⁴	—	53	1	no	—
443	C₂⁴	—	53	2	no	—
444	C₂⁴	—	53	1	no	—
445	C₂⁴	—	53	2	no	—
446	C₂⁴	—	53	1	no	—
447	C₂⁴	—	53	1	no	—
448	C₂⁴	—	212	4	no	—
449	C₂⁴	—	212	2	no	—
450	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
451	#41	—	212	4	no	—
452	#41	—	212	2	no	—
453	C₂×Q₈	—	53	2	no	—
454	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
455	C₂×D₄	—	53	2	no	—
456	C₂×D₄	—	53	2	no	—
457	C₂×D₄	—	53	2	no	—
458	C₂×D₄	—	53	1	no	—
459	C₂×D₄	—	53	2	no	—
460	C₂×D₄	—	53	2	no	—
461	C₂×D₄	—	53	1	no	—
462	C₂×D₄	—	53	2	no	—
463	C₂×D₄	—	53	2	no	—
464	C₂×D₄	—	53	2	no	—
465	C₂×D₄	—	53	2	no	—
466	C₂×D₄	—	53	2	no	—
467	C₂×D₄	—	53	2	no	—
468	C₂×D₄	—	53	2	no	—
469	C₂×D₄	—	53	2	no	—
470	C₂×D₄	—	53	2	no	—
471	C₂×D₄	—	53	2	no	—
472	C₂×D₄	—	53	1	no	—
473	C₂×D₄	—	53	2	no	—
474	C₂×D₄	—	53	1	no	—
475	C₂×D₄	—	53	2	no	—
476	C₂×D₄	—	53	2	no	—
477	C₂×D₄	—	53	2	no	—
478	C₂×D₄	—	212	4	no	—
479	C₂×D₄	—	212	4	no	—
480	C₂×D₄	—	212	2	no	—
481	C₂×D₄	—	212	2	no	—
482	C₂×D₄	—	212	4	no	—
483	C₂×D₄	—	212	4	no	—
484	C₂×D₄	—	212	4	no	—
485	C₂×D₄	C₂²×D₅₃	1	2	yes	—
486	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
487	C₂²×C₄	—	53	2	no	—
488	C₂²×C₄	—	53	1	no	—
489	C₂²×C₄	—	53	2	no	—
490	C₂²×C₄	—	53	2	no	—
491	C₂²×C₄	—	53	2	no	—
492	C₂²×C₄	—	53	2	no	—
493	C₂²×C₄	—	53	2	no	—
494	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
495	C₂²×C₄	C₂²×D₅₃	1	2	yes	—
496	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
497	C₄⋊C₄	—	53	2	no	—
498	C₄⋊C₄	—	53	2	no	—
499	C₄⋊C₄	—	53	2	no	—
500	C₄⋊C₄	—	53	2	no	—
501	C₄⋊C₄	—	53	2	no	—
502	C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
503	C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
504	C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
505	C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
506	C₂²⋊C₄	—	53	2	no	—
507	C₂²⋊C₄	—	53	1	no	—
508	C₂²⋊C₄	—	53	1	no	—
509	C₂²⋊C₄	—	53	2	no	—
510	C₂²⋊C₄	—	53	2	no	—
511	C₂²⋊C₄	—	53	2	no	—
512	C₂²⋊C₄	—	53	2	no	—
513	C₂²⋊C₄	—	53	2	no	—
514	C₂²⋊C₄	—	53	2	no	—
515	C₂²⋊C₄	—	53	2	no	—
516	C₂²⋊C₄	—	53	2	no	—
517	C₂²⋊C₄	—	53	2	no	—
518	C₂²⋊C₄	—	53	2	no	—
519	C₂²⋊C₄	—	53	2	no	—
520	C₂²⋊C₄	—	53	2	no	—
521	C₂²⋊C₄	—	53	2	no	—
522	C₂²⋊C₄	—	53	2	no	—
523	C₂²⋊C₄	—	53	2	no	—
524	C₂²⋊C₄	—	53	2	no	—
525	C₂²⋊C₄	—	53	2	no	—
526	C₂²⋊C₄	—	53	2	no	—
527	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
529	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
530	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
534	C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
535	C₄²	—	53	1	no	—
536	C₄²	—	53	2	no	—
537	C₄²	C₂²×D₅₃	1	1	yes	characteristic, complemented
538	C₄²	C₂²×D₅₃	1	2	yes	complemented
539	C₂³	—	2	4	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	53	1	no	—
542	C₂³	—	53	2	no	—
543	C₂³	—	53	1	no	—
544	C₂³	—	53	2	no	—
545	C₂³	—	53	2	no	—
546	C₂³	—	53	1	no	—
547	C₂³	—	106	2	no	—
548	C₂³	—	106	4	no	—
549	C₂³	—	106	2	no	—
550	C₂³	—	106	4	no	—
551	C₂³	—	106	4	no	—
552	C₂³	—	106	4	no	—
553	C₂³	—	212	2	no	—
554	C₂³	—	212	2	no	—
555	C₂³	—	212	1	no	—
556	C₂³	—	212	2	no	—
557	C₂³	—	212	2	no	—
558	C₂³	—	212	2	no	—
559	C₂³	—	212	2	no	—
560	C₂³	—	212	2	no	—
561	C₂³	—	212	1	no	—
562	C₂³	—	212	2	no	—
563	C₂³	—	212	2	no	—
564	C₂³	—	212	16	no	—
565	C₂³	C₂³×D₅₃	1	1	yes	characteristic
566	C₂³	C₂³×D₅₃	1	1	yes	characteristic
567	C₂³	C₂³×D₅₃	1	2	yes	—
568	Q₈	—	4	1	no	—
569	Q₈	—	212	2	no	—
570	D₄	—	2	4	no	—
571	D₄	—	4	1	no	—
572	D₄	—	106	4	no	—
573	D₄	—	106	4	no	—
574	D₄	—	106	4	no	—
575	D₄	—	106	4	no	—
576	D₄	—	106	4	no	—
577	D₄	—	212	2	no	—
578	D₄	—	212	2	no	—
579	D₄	—	212	2	no	—
580	D₄	—	212	1	no	—
581	D₄	—	212	2	no	—
582	D₄	—	212	2	no	—
583	D₄	—	212	2	no	—
584	D₄	—	212	2	no	—
585	D₄	—	212	2	no	—
586	D₄	—	212	2	no	—
587	D₄	—	212	1	no	—
588	D₄	—	212	2	no	—
589	D₄	—	212	1	no	—
590	D₄	—	212	1	no	—
591	D₄	—	212	2	no	—
592	D₄	—	212	2	no	—
593	D₄	—	212	2	no	—
594	D₄	—	212	2	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	53	2	no	—
599	C₂×C₄	—	53	2	no	—
600	C₂×C₄	—	53	2	no	—
601	C₂×C₄	—	53	1	no	—
602	C₂×C₄	—	106	2	no	—
603	C₂×C₄	—	212	2	no	—
604	C₂×C₄	—	212	2	no	—
605	C₂×C₄	—	212	2	no	—
606	C₂×C₄	—	212	2	no	—
607	C₂×C₄	—	212	2	no	—
608	C₂×C₄	—	212	2	no	—
609	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₅₃	1	2	yes	—
611	C₂×C₄	C₂³×D₅₃	1	2	yes	—
612	C₂×C₄	C₂³×D₅₃	1	2	yes	—
613	C₂×C₄	C₂³×D₅₃	1	2	yes	—
614	C₂×C₄	C₂³×D₅₃	1	2	yes	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	4	4	no	—
622	C₂²	—	53	2	no	—
623	C₂²	—	106	2	no	—
624	C₂²	—	106	2	no	—
625	C₂²	—	106	2	no	—
626	C₂²	—	106	1	no	—
627	C₂²	—	106	2	no	—
628	C₂²	—	106	1	no	—
629	C₂²	—	106	2	no	—
630	C₂²	—	106	2	no	—
631	C₂²	—	106	2	no	—
632	C₂²	—	106	2	no	—
633	C₂²	—	106	2	no	—
634	C₂²	—	106	2	no	—
635	C₂²	—	106	2	no	—
636	C₂²	—	106	2	no	—
637	C₂²	—	424	4	no	—
638	C₂²	—	424	2	no	—
639	C₂²	—	424	2	no	—
640	C₂²	—	212	8	no	—
641	C₂²	—	212	8	no	—
642	C₂²	—	212	4	no	—
643	C₂²	—	212	4	no	—
644	C₂²	#13133263	1	4	yes	—
645	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	106	1	no	—
653	C₄	—	106	2	no	—
654	C₄	—	106	2	no	—
655	C₄	—	106	2	no	—
656	C₂	—	2	4	no	—
657	C₂	—	4	1	no	—
658	C₂	—	4	1	no	—
659	C₂	—	106	2	no	—
660	C₂	—	212	2	no	—
661	C₂	—	212	2	no	—
662	C₂	—	212	1	no	—
663	C₂	—	212	2	no	—
664	C₂	—	212	1	no	—
665	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
666	C₂	C₂×#13133263	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#551	C₂
hypercenter	#551	D₅₃
hypocenter	C₅₃	#3532
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #16811365	C₂	semidirect
2. #16811364	C₂	semidirect
3. #16811363	C₂	semidirect
4. #16811297	C₂	semidirect
5. #16811265	C₂	semidirect
6. #16811264	C₂	semidirect
7. #16811263	C₂	semidirect
8. D₄×D₂₁₂	C₂	semidirect
9. #16811255	C₂	semidirect
10. #16811213	C₂	semidirect
11. #16811212	C₂	semidirect
12. #16811206	C₂	semidirect
13. #16811192	C₂	semidirect
14. #16811191	C₂	semidirect
15. #16811184	C₂	semidirect
16. #16811184	C₂	semidirect
17. C₂×#13133187	C₂	semidirect
18. #120×D₅₃	C₂	semidirect
19. C₅₃×#551	C₂	semidirect
20. C₂⁴×D₅₃	C₂²	semidirect
21. C₂×#11719949	C₂²	semidirect
22. C₂×#11719945	C₂²	semidirect
23. C₂²×D₂₁₂	C₂²	semidirect
24. C₂²×D₂₁₂	C₂²	semidirect
25. C₂²×D₂₁₂	C₂²	semidirect
26. C₂²×C₂²⋊D₅₃	C₂²	semidirect
27. C₂×D₄×D₅₃	C₂²	semidirect
28. C₂×D₄×D₅₃	C₂²	semidirect
29. C₂×D₄×D₅₃	C₂²	semidirect
30. #13133214	C₂²	semidirect
31. #13133214	C₂²	semidirect
32. #13133213	C₂²	semidirect
33. #13133212	C₂²	semidirect
34. #13133212	C₂²	semidirect
35. #13133211	C₂²	semidirect
36. #13133206	C₂²	semidirect
37. #13133206	C₂²	semidirect
38. #13133205	C₂²	semidirect
39. #13133205	C₂²	semidirect
40. #13133203	C₂²	semidirect
41. #13133203	C₂²	semidirect
42. #13133202	C₂²	semidirect
43. #13133202	C₂²	semidirect
44. #13133202	C₂²	semidirect
45. #13133202	C₂²	semidirect
46. #13133202	C₂²	semidirect
47. #13133200	C₂²	semidirect
48. #13133200	C₂²	semidirect
49. #13133199	C₂²	semidirect
50. #13133195	C₂²	semidirect
51. #13133194	C₂²	semidirect
52. #13133192	C₂²	semidirect
53. #13133192	C₂²	semidirect
54. #13133192	C₂²	semidirect
55. #13133192	C₂²	semidirect
56. #13133192	C₂²	semidirect
57. #13133192	C₂²	semidirect
58. #13133192	C₂²	semidirect
59. #13133191	C₂²	semidirect
60. #13133191	C₂²	semidirect
61. #13133190	C₂²	semidirect
62. #13133190	C₂²	semidirect
63. #13133190	C₂²	semidirect
64. #13133190	C₂²	semidirect
65. #13133190	C₂²	semidirect
66. #13133189	C₂²	semidirect
68. #13133187	C₂²	semidirect
69. #13133187	C₂²	semidirect
70. #13133187	C₂²	semidirect
71. #13133187	C₂²	semidirect
72. #13133187	C₂²	semidirect
73. #13133187	C₂²	semidirect
74. #13133187	C₂²	semidirect
75. #13133187	C₂²	semidirect
76. #13133187	C₂²	semidirect
77. #13133187	C₂²	semidirect
78. #13133187	C₂²	semidirect
79. #13133187	C₂²	semidirect
80. #13133187	C₂²	semidirect
81. #13133187	C₂²	semidirect
82. #13133186	C₂²	semidirect
83. #13133185	C₂²	semidirect
84. #13133185	C₂²	semidirect
85. #13133185	C₂²	semidirect
86. C₄×D₂₁₂	C₂²	semidirect
87. #13133179	C₂²	semidirect
88. C₄×C₂²⋊D₅₃	C₂²	semidirect
89. #13133177	C₂²	semidirect
90. #13133177	C₂²	semidirect
91. #13133174	C₂²	semidirect
92. C₂×#11719921	C₂²	semidirect
93. C₂×#11719921	C₂²	semidirect
94. C₂²⋊C₄×D₅₃	C₂²	semidirect
95. C₂²⋊C₄×D₅₃	C₂²	semidirect
96. C₂²⋊C₄×D₅₃	C₂²	semidirect
97. C₂²⋊C₄×D₅₃	C₂²	semidirect
98. #126×C₅₃	C₂²	semidirect
99. #124×C₅₃	C₂²	semidirect
100. #123×C₅₃	C₂²	semidirect
101. #123×C₅₃	C₂²	semidirect
102. C₂²⋊Q₈×C₅₃	C₂²	semidirect
104. C₄×D₄×C₅₃	C₂²	semidirect
105. #117×C₅₃	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₅₃	C₂²	semidirect
116. C₂³×D₅₃	C₂³	semidirect
117. C₂×Q₈×C₅₃	C₂³	semidirect
122. C₂²×C₄×C₅₃	C₂³	semidirect
132. C₂×C₂²⋊D₅₃	C₂³	semidirect
152. C₂×D₂₁₂	C₂³	semidirect
153. C₂×D₂₁₂	C₂³	semidirect
154. C₂×D₂₁₂	C₂³	semidirect
155. C₂×D₂₁₂	C₂³	semidirect
158. C₂×C₄×D₅₃	C₂³	semidirect
159. C₂×C₄×D₅₃	C₂³	semidirect
160. C₂×C₄×D₅₃	C₂³	semidirect
161. C₂×C₄×D₅₃	C₂³	semidirect
162. C₂×Dic₁₀₆	C₂³	semidirect
163. C₄⋊C₄×C₅₃	C₂³	semidirect
164. C₄⋊C₄×C₅₃	C₂³	semidirect
165. C₄⋊C₄×C₅₃	C₂³	semidirect
166. C₄⋊C₄×C₅₃	C₂³	semidirect
173. C₂²⋊C₄×C₅₃	C₂³	semidirect
174. C₂²⋊C₄×C₅₃	C₂³	semidirect
175. C₄²×C₅₃	C₂³	semidirect
176. C₄²×C₅₃	C₂³	semidirect
179. C₂²⋊Dic₅₃	C₂³	semidirect
191. #11719921	C₂³	semidirect
192. #11719921	C₂³	semidirect
193. #11719921	C₂³	semidirect
194. #11719921	C₂³	semidirect
195. #11719921	C₂³	semidirect
196. #11719921	C₂³	semidirect
197. #11719921	C₂³	semidirect
198. C₄⋊Dic₅₃	C₂³	semidirect
199. #11719919	C₂³	semidirect
200. #11719919	C₂³	semidirect
201. #11719919	C₂³	semidirect
202. #11719919	C₂³	semidirect
203. C₄×Dic₅₃	C₂³	semidirect
204. C₄×Dic₅₃	C₂³	semidirect
338. #551	D₅₃	semidirect
353. C₅₃	#3532	semidirect
370. #126	C₂×D₅₃	semidirect
377. #124	C₂×D₅₃	semidirect
386. #123	C₂×D₅₃	semidirect
387. #123	C₂×D₅₃	semidirect
390. C₂²⋊Q₈	C₂×D₅₃	semidirect
431. C₄×D₄	C₂×D₅₃	semidirect
433. #117	C₂×D₅₃	semidirect
440. C₂×C₂²⋊C₄	C₂×D₅₃	semidirect
454. C₂×Q₈	C₂²×D₅₃	semidirect
496. C₂²×C₄	C₂²×D₅₃	semidirect
502. C₄⋊C₄	C₂²×D₅₃	semidirect
503. C₄⋊C₄	C₂²×D₅₃	semidirect
504. C₄⋊C₄	C₂²×D₅₃	semidirect
505. C₄⋊C₄	C₂²×D₅₃	semidirect
533. C₂²⋊C₄	C₂²×D₅₃	semidirect
534. C₂²⋊C₄	C₂²×D₅₃	semidirect
537. C₄²	C₂²×D₅₃	semidirect
538. C₄²	C₂²×D₅₃	semidirect