Subgroups — D₅₃×#3498 #28292407

Order 13568.

12982 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×H(5,𝔽₂)×D₅₃	C₂	1	2	yes	maximal, complemented
2	#20288493	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288492	C₂	1	4	yes	maximal, complemented
4	#20288491	C₂	1	3	yes	maximal, complemented
5	#20288490	C₂	1	6	yes	maximal, complemented
6	#20288489	C₂	1	2	yes	maximal, complemented
7	#20288488	C₂	1	3	yes	maximal, complemented
8	#20288487	C₂	1	12	yes	maximal, complemented
9	#550×D₅₃	C₂	1	4	yes	maximal, complemented
10	D₄²×D₅₃	C₂	1	12	yes	maximal, complemented
11	#535×D₅₃	C₂	1	6	yes	maximal, complemented
12	#532×D₅₃	C₂	1	3	yes	maximal, complemented
13	C₂×#127×D₅₃	C₂	1	3	yes	maximal, complemented
14	C₄×#41×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13133263	C₂²	1	2	yes	complemented
17	C₂×#13133263	C₂²	1	6	yes	complemented
18	C₂×#13133263	C₂²	1	4	yes	complemented
19	C₂×#13133262	C₂²	1	12	yes	complemented
20	C₂×#13133262	C₂²	1	6	yes	complemented
21	H(5,𝔽₂)×D₅₃	—	2	32	no	—
22	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
23	C₂×#41×D₅₃	C₂²	1	6	yes	complemented
24	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
25	C₂²×D₄×D₅₃	C₂²	1	6	yes	complemented
26	C₂²×D₄×D₅₃	C₂²	1	12	yes	complemented
27	C₂²×D₄×D₅₃	C₂²	1	12	yes	complemented
28	#16811295	C₂²	1	4	yes	complemented
29	#16811294	C₂²	1	12	yes	complemented
30	#16811293	C₂²	1	12	yes	complemented
31	#16811292	C₂²	1	8	yes	complemented
32	#16811291	C₂²	1	24	yes	complemented
33	D₄×D₂₁₂	C₂²	1	12	yes	complemented
34	D₄×D₂₁₂	C₂²	1	12	yes	complemented
35	#16811258	C₂²	1	12	yes	complemented
36	#16811257	C₂²	1	24	yes	complemented
37	#16811257	C₂²	1	24	yes	complemented
38	D₄×C₂²⋊D₅₃	C₂²	1	24	yes	complemented
39	D₄×C₂²⋊D₅₃	C₂²	1	24	yes	complemented
40	#16811255	C₂²	1	48	yes	complemented
41	#16811192	C₂²	1	6	yes	complemented
42	#16811191	C₂²	1	12	yes	complemented
43	#16811190	C₂²	1	6	yes	complemented
44	#16811189	C₂²	1	24	yes	complemented
45	#16811188	C₂²	1	24	yes	complemented
46	#16811187	C₂²	1	6	yes	complemented
47	#16811186	C₂²	1	12	yes	complemented
48	#16811174	C₂²	1	3	yes	complemented
49	#16811173	C₂²	1	3	yes	complemented
50	#16811172	C₂²	1	6	yes	complemented
51	#16811171	C₂²	1	3	yes	complemented
52	#16811170	C₂²	1	12	yes	complemented
53	#16811169	C₂²	1	6	yes	complemented
54	#16811168	C₂²	1	12	yes	complemented
55	C₄⋊Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₂×#13133214	C₂²	1	3	yes	complemented
57	C₂×#13133213	C₂²	1	12	yes	complemented
58	C₂×#13133213	C₂²	1	6	yes	complemented
59	#127×D₅₃	C₂²	1	6	yes	complemented
60	#127×D₅₃	C₂²	1	12	yes	complemented
61	#127×D₅₃	C₂²	1	3	yes	complemented
62	#127×D₅₃	C₂²	1	12	yes	complemented
63	#127×D₅₃	C₂²	1	6	yes	complemented
64	#127×D₅₃	C₂²	1	6	yes	complemented
65	#124×D₅₃	C₂²	1	6	yes	complemented
66	#121×D₅₃	C₂²	1	24	yes	complemented
67	#121×D₅₃	C₂²	1	12	yes	complemented
68	#120×D₅₃	C₂²	1	24	yes	complemented
69	#41×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
70	C₄×#11719949	C₂²	1	2	yes	complemented
71	C₄×#11719945	C₂²	1	3	yes	complemented
72	#16811091	C₂²	1	3	yes	complemented
73	C₄×#11719947	C₂²	1	6	yes	complemented
74	C₄×Q₈×D₅₃	C₂²	1	2	yes	complemented
75	C₄×D₄×D₅₃	C₂²	1	6	yes	complemented
76	C₄×D₄×D₅₃	C₂²	1	12	yes	complemented
77	#117×D₅₃	C₂²	1	3	yes	complemented
78	C₂×C₄²×D₅₃	C₂²	1	3	yes	complemented
79	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	2	yes	complemented
80	C₅₃×#550	C₂²	1	4	yes	complemented
81	D₄²×C₅₃	C₂²	1	12	yes	complemented
82	C₅₃×#535	C₂²	1	6	yes	complemented
83	C₅₃×#532	C₂²	1	3	yes	complemented
84	C₂×#127×C₅₃	C₂²	1	3	yes	complemented
85	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
86	C₂⁴×D₅₃	C₂³	1	12	yes	—
87	#13133263	—	2	16	no	—
88	#13133263	—	2	32	no	—
89	#13133263	—	2	48	no	—
90	#13133262	—	2	96	no	—
91	#13133262	—	2	48	no	—
92	C₂×#11719949	C₂³	1	1	yes	characteristic
93	C₂×#11719949	C₂³	1	4	yes	complemented
94	C₂×#11719949	C₂³	1	6	yes	complemented
95	C₂×#11719945	C₂³	1	3	yes	—
96	C₂×#11719945	C₂³	1	12	yes	complemented
97	C₂×#11719945	C₂³	1	6	yes	complemented
98	C₂×#11719945	C₂³	1	12	yes	complemented
99	C₂×#11719947	C₂³	1	3	yes	—
100	C₂×#11719947	C₂³	1	12	yes	complemented
101	C₂×#11719947	C₂³	1	12	yes	complemented
102	C₂×#11719947	C₂³	1	6	yes	complemented
103	#41×D₅₃	—	2	32	no	—
104	#41×D₅₃	—	2	48	no	—
105	#41×D₅₃	D₄	1	16	yes	complemented
106	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
107	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
108	C₂²×D₂₁₂	C₂³	1	6	yes	complemented
109	C₂²×D₂₁₂	C₂³	1	12	yes	complemented
110	C₂²×D₂₁₂	C₂³	1	12	yes	complemented
111	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
112	C₂²×C₂²⋊D₅₃	C₂³	1	24	yes	complemented
113	C₂²×C₂²⋊D₅₃	C₂³	1	24	yes	complemented
114	C₂×D₄×D₅₃	—	2	96	no	—
115	C₂×D₄×D₅₃	—	2	48	no	—
116	C₂×D₄×D₅₃	—	4	48	no	—
117	C₂×D₄×D₅₃	C₂³	1	12	yes	—
118	C₂×D₄×D₅₃	C₂³	1	12	yes	—
119	C₂×D₄×D₅₃	C₂³	1	12	yes	—
120	C₂×D₄×D₅₃	C₂³	1	6	yes	—
121	C₂×D₄×D₅₃	C₂³	1	24	yes	—
122	C₂×D₄×D₅₃	C₂³	1	3	yes	—
123	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
124	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
125	C₂×D₄×D₅₃	C₂³	1	24	yes	complemented
126	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
127	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
128	C₂×D₄×D₅₃	C₂³	1	24	yes	complemented
129	C₂×D₄×D₅₃	C₂³	1	24	yes	complemented
130	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
131	C₂²×C₄×D₅₃	C₂³	1	12	yes	—
132	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
133	#13133217	C₂³	1	1	yes	characteristic, complemented
134	#13133216	C₂³	1	4	yes	complemented
135	#13133215	C₂³	1	2	yes	complemented
136	#13133214	C₂³	1	12	yes	complemented
137	#13133214	C₂³	1	3	yes	complemented
138	#13133214	C₂³	1	6	yes	complemented
139	#13133213	C₂³	1	24	yes	complemented
140	#13133213	C₂³	1	24	yes	complemented
141	#13133213	C₂³	1	24	yes	complemented
142	#13133213	C₂³	1	12	yes	complemented
143	#13133213	C₂³	1	6	yes	complemented
144	#13133213	C₂³	1	12	yes	complemented
145	#13133213	C₂³	1	24	yes	complemented
146	#13133206	C₂³	1	6	yes	complemented
147	#13133205	C₂³	1	6	yes	complemented
148	#13133204	C₂³	1	6	yes	complemented
149	#13133203	C₂³	1	24	yes	complemented
150	#13133192	C₂³	1	24	yes	complemented
151	#13133192	C₂³	1	12	yes	complemented
152	#13133191	C₂³	1	24	yes	complemented
153	#13133191	C₂³	1	12	yes	complemented
154	#13133190	C₂³	1	48	yes	complemented
155	#13133190	C₂³	1	24	yes	complemented
156	#13133189	C₂³	1	48	yes	complemented
157	#13133189	C₂³	1	24	yes	complemented
158	#13133188	C₂³	1	24	yes	complemented
159	#13133188	C₂³	1	12	yes	complemented
160	#13133187	C₂³	1	24	yes	complemented
161	#13133187	C₂³	1	48	yes	complemented
162	#13133186	C₂³	1	24	yes	complemented
163	#13133185	C₂³	1	48	yes	complemented
164	#13133185	C₂³	1	24	yes	complemented
165	Q₈×Dic₅₃	C₂³	1	2	yes	complemented
166	C₄×Dic₁₀₆	C₂³	1	6	yes	complemented
167	#13133182	C₂³	1	6	yes	complemented
168	C₄×D₂₁₂	C₂³	1	12	yes	complemented
169	C₄×D₂₁₂	C₂³	1	6	yes	complemented
170	D₄×Dic₅₃	C₂³	1	12	yes	complemented
171	D₄×Dic₅₃	C₂³	1	6	yes	complemented
172	#13133179	C₂³	1	12	yes	complemented
173	#13133179	C₂³	1	6	yes	complemented
174	C₄×C₂²⋊D₅₃	C₂³	1	24	yes	complemented
175	C₄×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
176	#13133177	C₂³	1	24	yes	complemented
177	#13133177	C₂³	1	12	yes	complemented
178	#13133176	C₂³	1	3	yes	complemented
179	#13133175	C₂³	1	6	yes	complemented
180	#13133174	C₂³	1	6	yes	complemented
181	#13133173	C₂³	1	6	yes	complemented
182	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
183	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
184	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
185	C₂²⋊C₄×D₅₃	C₂³	1	24	yes	—
186	C₂×C₄×Dic₅₃	C₂³	1	6	yes	complemented
187	C₂×C₄×Dic₅₃	C₂³	1	3	yes	complemented
188	C₄²×D₅₃	C₂³	1	1	yes	characteristic
189	C₄²×D₅₃	C₂³	1	3	yes	—
190	C₄²×D₅₃	C₂³	1	6	yes	—
191	C₄²×D₅₃	C₂³	1	6	yes	complemented
192	C₄²×D₅₃	C₂³	1	3	yes	complemented
193	C₄²×D₅₃	C₂³	1	3	yes	complemented
194	H(5,𝔽₂)×C₅₃	—	2	16	no	—
195	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
197	C₂×#41×C₅₃	C₂³	1	6	yes	complemented
198	C₂²×D₄×C₅₃	C₂³	1	6	yes	complemented
199	C₂²×D₄×C₅₃	C₂³	1	12	yes	complemented
200	C₂²×D₄×C₅₃	C₂³	1	12	yes	complemented
201	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
202	#127×C₅₃	C₂³	1	12	yes	complemented
203	#127×C₅₃	C₂³	1	3	yes	complemented
204	#127×C₅₃	C₂³	1	6	yes	complemented
205	#124×C₅₃	C₂³	1	6	yes	complemented
206	#121×C₅₃	C₂³	1	24	yes	complemented
207	#121×C₅₃	C₂³	1	12	yes	complemented
208	#120×C₅₃	C₂³	1	24	yes	complemented
209	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
210	C₄×D₄×C₅₃	C₂³	1	12	yes	complemented
211	C₄×D₄×C₅₃	C₂³	1	6	yes	complemented
212	#117×C₅₃	C₂³	1	3	yes	complemented
213	C₂×C₄²×C₅₃	C₂³	1	3	yes	complemented
214	C₂⁴×C₅₃	C₂⁴	1	12	yes	—
215	C₂³×D₅₃	—	2	48	no	—
216	C₂³×D₅₃	—	4	48	no	—
217	C₂³×D₅₃	C₂⁴	1	12	yes	—
218	C₂³×D₅₃	C₂⁴	1	3	yes	—
219	C₂³×D₅₃	C₂⁴	1	24	yes	—
220	C₂³×D₅₃	C₂⁴	1	12	yes	—
221	#41×C₅₃	—	2	16	no	—
222	#41×C₅₃	—	2	24	no	—
223	#41×C₅₃	C₂×D₄	1	8	yes	complemented
224	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
225	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
226	C₂×D₄×C₅₃	—	2	48	no	—
227	C₂×D₄×C₅₃	—	2	24	no	—
228	C₂×D₄×C₅₃	—	4	24	no	—
229	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
230	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
231	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
232	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
233	C₂×D₄×C₅₃	C₂⁴	1	24	yes	—
234	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
235	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
236	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
237	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
238	C₂×C₂²⋊D₅₃	—	2	96	no	—
239	C₂×C₂²⋊D₅₃	—	2	48	no	—
240	C₂×C₂²⋊D₅₃	—	4	48	no	—
241	C₂×C₂²⋊D₅₃	C₂⁴	1	24	yes	—
242	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
243	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
244	C₂×C₂²⋊D₅₃	C₂⁴	1	24	yes	—
245	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
246	C₂×C₂²⋊D₅₃	C₂⁴	1	48	yes	—
247	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
248	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
249	C₂²×Dic₅₃	C₂⁴	1	12	yes	—
250	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
251	#11719949	—	2	16	no	—
252	#11719949	—	2	24	no	—
253	#11719949	C₂×D₄	1	8	yes	complemented
254	Q₈×D₅₃	—	2	8	no	—
255	Q₈×D₅₃	C₂×D₄	1	8	yes	complemented
256	#11719947	—	2	48	no	—
257	#11719947	—	2	24	no	—
258	#11719947	—	2	48	no	—
259	#11719947	C₂×D₄	1	24	yes	complemented
260	D₄×D₅₃	—	2	48	no	—
261	D₄×D₅₃	—	2	48	no	—
262	D₄×D₅₃	—	2	96	no	—
263	D₄×D₅₃	—	2	48	no	—
264	D₄×D₅₃	—	2	48	no	—
265	D₄×D₅₃	—	2	24	no	—
266	D₄×D₅₃	—	2	48	no	—
267	D₄×D₅₃	—	2	48	no	—
268	D₄×D₅₃	—	2	48	no	—
269	D₄×D₅₃	—	4	48	no	—
270	D₄×D₅₃	—	4	48	no	—
271	D₄×D₅₃	—	4	48	no	—
272	D₄×D₅₃	C₂×D₄	1	24	yes	complemented
273	#11719945	—	2	24	no	—
274	#11719945	—	2	48	no	—
275	#11719945	—	2	48	no	—
276	#11719945	C₂×D₄	1	24	yes	complemented
277	C₂×D₂₁₂	—	2	24	no	—
278	C₂×D₂₁₂	—	2	48	no	—
279	C₂×D₂₁₂	—	4	24	no	—
280	C₂×D₂₁₂	C₂⁴	1	12	yes	—
281	C₂×D₂₁₂	C₂⁴	1	12	yes	—
282	C₂×D₂₁₂	C₂⁴	1	12	yes	—
283	C₂×D₂₁₂	C₂⁴	1	6	yes	—
284	C₂×D₂₁₂	C₂⁴	1	24	yes	—
285	C₂×D₂₁₂	C₂⁴	1	3	yes	—
286	C₂×C₄×D₅₃	—	2	48	no	—
287	C₂×C₄×D₅₃	—	2	24	no	—
288	C₂×C₄×D₅₃	C₂×D₄	1	24	yes	complemented
289	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
290	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
291	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
292	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
293	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
294	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
295	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
296	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
297	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
298	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
299	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
300	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
301	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
302	C₂×Dic₁₀₆	C₂⁴	1	3	yes	—
303	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
304	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
305	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
306	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
307	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
308	C₄²×C₅₃	C₂⁴	1	3	yes	—
309	C₄²×C₅₃	C₂⁴	1	6	yes	—
310	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
311	C₂²⋊Dic₅₃	C₂⁴	1	24	yes	—
312	#11719921	C₂⁴	1	12	yes	—
313	#11719921	C₂⁴	1	24	yes	—
314	#11719921	C₂⁴	1	24	yes	—
315	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
316	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
317	#11719919	C₂⁴	1	12	yes	—
318	#11719919	C₂⁴	1	8	yes	—
319	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
320	C₄×Dic₅₃	C₂⁴	1	2	yes	—
321	C₄×Dic₅₃	C₂⁴	1	6	yes	—
322	C₄×Dic₅₃	C₂⁴	1	3	yes	—
323	C₄×Dic₅₃	C₂⁴	1	6	yes	—
324	C₄×Dic₅₃	C₂⁴	1	6	yes	—
325	C₄×Dic₅₃	C₂⁴	1	6	yes	—
326	C₂³×C₅₃	—	2	24	no	—
327	C₂³×C₅₃	—	4	24	no	—
328	C₂³×C₅₃	C₂⁵	1	12	yes	—
329	C₂³×C₅₃	C₂⁵	1	3	yes	—
330	C₂²×D₅₃	—	2	12	no	—
331	C₂²×D₅₃	—	2	24	no	—
332	C₂²×D₅₃	—	2	24	no	—
333	C₂²×D₅₃	—	2	48	no	—
334	C₂²×D₅₃	—	2	48	no	—
335	C₂²×D₅₃	—	4	24	no	—
336	C₂²×D₅₃	—	4	48	no	—
337	C₂²×D₅₃	—	8	96	no	—
338	C₂²×D₅₃	C₂²×D₄	1	12	yes	—
339	C₂²×D₅₃	C₂⁵	1	12	yes	—
340	C₂²×D₅₃	C₂⁵	1	3	yes	—
341	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
342	Q₈×C₅₃	—	2	4	no	—
343	Q₈×C₅₃	C₂²×D₄	1	4	yes	complemented
344	D₄×C₅₃	—	2	24	no	—
345	D₄×C₅₃	—	2	12	no	—
346	D₄×C₅₃	—	2	24	no	—
347	D₄×C₅₃	—	2	24	no	—
348	D₄×C₅₃	—	4	24	no	—
349	D₄×C₅₃	C₂²×D₄	1	12	yes	complemented
350	C₂×C₄×C₅₃	—	2	24	no	—
351	C₂×C₄×C₅₃	—	2	12	no	—
352	C₂×C₄×C₅₃	C₂²×D₄	1	12	yes	complemented
353	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
354	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
355	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
356	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
357	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
358	C₂²⋊D₅₃	—	2	24	no	—
359	C₂²⋊D₅₃	—	2	24	no	—
360	C₂²⋊D₅₃	—	2	24	no	—
361	C₂²⋊D₅₃	—	2	48	no	—
362	C₂²⋊D₅₃	—	2	48	no	—
363	C₂²⋊D₅₃	—	4	48	no	—
364	C₂²⋊D₅₃	C₂²×D₄	1	24	yes	complemented
365	C₂×Dic₅₃	—	2	24	no	—
366	C₂×Dic₅₃	—	2	12	no	—
367	C₂×Dic₅₃	C₂²×D₄	1	12	yes	complemented
368	C₂×Dic₅₃	C₂⁵	1	4	yes	—
369	C₂×Dic₅₃	C₂⁵	1	6	yes	—
370	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
371	C₂×Dic₅₃	C₂⁵	1	3	yes	—
372	C₂×Dic₅₃	C₂⁵	1	2	yes	—
373	D₂₁₂	—	2	24	no	—
374	D₂₁₂	—	2	12	no	—
375	D₂₁₂	—	2	24	no	—
376	D₂₁₂	—	2	24	no	—
377	D₂₁₂	—	4	24	no	—
378	D₂₁₂	C₂²×D₄	1	12	yes	complemented
379	C₄×D₅₃	—	2	8	no	—
380	C₄×D₅₃	—	2	12	no	—
381	C₄×D₅₃	—	2	24	no	—
382	C₄×D₅₃	—	2	12	no	—
383	C₄×D₅₃	—	2	24	no	—
384	C₄×D₅₃	—	2	12	no	—
385	C₄×D₅₃	C₂²×D₄	1	12	yes	—
386	C₄×D₅₃	C₂²×D₄	1	4	yes	—
387	C₄×D₅₃	C₂²×D₄	1	12	yes	complemented
388	C₄×D₅₃	C₂²×D₄	1	12	yes	complemented
389	C₄×D₅₃	H(5,𝔽₂)	1	8	yes	complemented
390	Dic₁₀₆	—	2	4	no	—
391	Dic₁₀₆	—	2	8	no	—
392	Dic₁₀₆	C₂²×D₄	1	12	yes	complemented
393	C₂×#3498	—	53	1	no	maximal, Sylow
394	C₂²×C₅₃	—	2	6	no	—
395	C₂²×C₅₃	—	2	12	no	—
396	C₂²×C₅₃	—	2	24	no	—
397	C₂²×C₅₃	—	8	24	no	—
398	C₂²×C₅₃	C₂³×D₄	1	6	yes	—
399	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
400	C₂×D₅₃	—	2	6	no	—
401	C₂×D₅₃	—	2	24	no	—
402	C₂×D₅₃	—	2	12	no	—
403	C₂×D₅₃	—	2	24	no	—
404	C₂×D₅₃	—	4	48	no	—
405	C₂×D₅₃	—	8	48	no	—
406	C₂×D₅₃	—	8	24	no	—
407	C₂×D₅₃	C₂³×D₄	1	6	yes	—
408	C₂×D₅₃	C₂³×D₄	1	2	yes	—
409	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
410	C₄×C₅₃	—	2	4	no	—
411	C₄×C₅₃	—	2	6	no	—
412	C₄×C₅₃	C₂³×D₄	1	2	yes	—
413	C₄×C₅₃	C₂³×D₄	1	6	yes	—
414	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	complemented
415	Dic₅₃	—	2	4	no	—
416	Dic₅₃	—	2	6	no	—
417	Dic₅₃	C₂³×D₄	1	2	yes	—
418	Dic₅₃	C₂³×D₄	1	6	yes	—
419	Dic₅₃	C₂×H(5,𝔽₂)	1	4	yes	complemented
420	C₂²×H(5,𝔽₂)	—	53	2	no	—
421	#3498	—	53	2	no	—
422	#3498	—	53	4	no	—
423	#3498	—	53	12	no	—
424	#3498	—	53	6	no	—
425	#3498	—	53	3	no	—
426	#3498	—	53	3	no	—
427	#3498	—	53	1	no	—
428	#3498	D₅₃	1	1	yes	characteristic, direct product factor
429	C₂×#550	—	53	4	no	—
430	C₂×D₄²	—	53	12	no	—
431	C₂×#535	—	53	6	no	—
432	C₂×#532	—	53	3	no	—
433	C₂²×#127	—	53	3	no	—
434	C₂×C₄×#41	—	53	1	no	—
435	C₂×C₅₃	—	2	6	no	—
436	C₂×C₅₃	—	4	12	no	—
437	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
438	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	2	yes	—
439	D₅₃	—	2	6	no	—
440	D₅₃	—	4	12	no	—
441	D₅₃	#3498	1	4	yes	direct product factor
442	C₂×H(5,𝔽₂)	—	53	2	no	—
443	C₂×H(5,𝔽₂)	—	53	4	no	—
444	C₂×H(5,𝔽₂)	—	53	6	no	—
445	C₂×H(5,𝔽₂)	—	53	12	no	—
446	C₂×H(5,𝔽₂)	—	53	6	no	—
447	C₂×H(5,𝔽₂)	—	106	32	no	—
448	C₂×H(5,𝔽₂)	C₂×D₅₃	1	2	yes	complemented
449	C₂²×#41	—	53	1	no	—
450	C₂²×#41	—	53	6	no	—
451	C₂²×#41	—	53	4	no	—
452	C₂³×D₄	—	53	6	no	—
453	C₂³×D₄	—	53	12	no	—
454	C₂³×D₄	—	53	12	no	—
455	#550	—	53	8	no	—
456	#550	—	53	12	no	—
457	#550	—	53	24	no	—
458	#550	—	53	4	no	—
459	#550	—	53	12	no	—
460	#550	C₂×D₅₃	1	4	yes	complemented
461	D₄²	—	53	24	no	—
462	D₄²	—	53	24	no	—
463	D₄²	—	53	12	no	—
464	D₄²	—	53	24	no	—
465	D₄²	—	53	24	no	—
466	D₄²	—	53	48	no	—
467	D₄²	—	53	12	no	—
468	D₄²	—	53	12	no	—
469	D₄²	C₂×D₅₃	1	12	yes	complemented
470	#535	—	53	6	no	—
471	#535	—	53	6	no	—
472	#535	—	53	12	no	—
473	#535	—	53	12	no	—
474	#535	—	53	24	no	—
475	#535	—	53	24	no	—
476	#535	—	53	6	no	—
477	#535	C₂×D₅₃	1	6	yes	complemented
478	#532	—	53	6	no	—
479	#532	—	53	3	no	—
480	#532	—	53	3	no	—
481	#532	—	53	6	no	—
482	#532	—	53	12	no	—
483	#532	—	53	12	no	—
484	#532	—	53	3	no	—
485	#532	C₂×D₅₃	1	3	yes	complemented
486	C₂×C₄⋊Q₈	—	53	1	no	—
487	C₂×#127	—	53	12	no	—
488	C₂×#127	—	53	6	no	—
489	C₂×#127	—	53	3	no	—
490	C₂×#127	—	53	6	no	—
491	C₂×#127	—	53	12	no	—
492	C₂×#127	—	53	12	no	—
493	C₂×#127	—	53	6	no	—
494	C₂×#127	—	53	6	no	—
495	C₂×#127	—	53	3	no	—
496	C₂×#127	C₂×D₅₃	1	3	yes	complemented
497	C₂×#124	—	53	6	no	—
498	C₂×#121	—	53	12	no	—
499	C₂×#121	—	53	24	no	—
500	C₂×#120	—	53	24	no	—
501	C₄×#41	—	53	1	no	—
502	C₄×#41	—	53	2	no	—
503	C₄×#41	—	53	6	no	—
504	C₄×#41	—	53	3	no	—
505	C₄×#41	—	53	3	no	—
506	C₄×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
507	C₂×C₄×Q₈	—	53	2	no	—
508	C₂×C₄×D₄	—	53	6	no	—
509	C₂×C₄×D₄	—	53	12	no	—
510	C₂×#117	—	53	3	no	—
511	C₂²×C₄²	—	53	3	no	—
512	C₅₃	C₂×#3498	1	1	yes	characteristic, complemented, Sylow
513	C₂⁵	—	53	12	no	—
514	H(5,𝔽₂)	—	2	16	no	—
515	H(5,𝔽₂)	—	106	96	no	—
516	H(5,𝔽₂)	—	106	48	no	—
517	H(5,𝔽₂)	—	106	32	no	—
518	H(5,𝔽₂)	—	106	48	no	—
519	H(5,𝔽₂)	—	106	16	no	—
520	C₂×#41	—	53	16	no	—
521	C₂×#41	—	53	1	no	—
522	C₂×#41	—	53	6	no	—
523	C₂×#41	—	53	4	no	—
524	C₂×#41	—	53	3	no	—
525	C₂×#41	—	53	12	no	—
526	C₂×#41	—	53	6	no	—
527	C₂×#41	—	53	12	no	—
528	C₂×#41	—	53	3	no	—
529	C₂×#41	—	53	12	no	—
530	C₂×#41	—	53	6	no	—
531	C₂×#41	—	53	12	no	—
532	C₂×#41	—	106	48	no	—
533	C₂×#41	—	106	32	no	—
534	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
535	C₂×#41	C₂²×D₅₃	1	6	yes	complemented
536	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
537	C₂²×Q₈	—	53	1	no	—
538	C₂²×Q₈	—	53	2	no	—
539	C₂²×D₄	—	53	3	no	—
540	C₂²×D₄	—	53	12	no	—
541	C₂²×D₄	—	53	24	no	—
542	C₂²×D₄	—	53	24	no	—
543	C₂²×D₄	—	53	12	no	—
544	C₂²×D₄	—	53	12	no	—
545	C₂²×D₄	—	53	12	no	—
546	C₂²×D₄	—	53	6	no	—
547	C₂²×D₄	—	53	12	no	—
548	C₂²×D₄	—	53	12	no	—
549	C₂²×D₄	—	53	24	no	—
550	C₂²×D₄	—	53	12	no	—
551	C₂²×D₄	—	53	12	no	—
552	C₂²×D₄	—	53	24	no	—
553	C₂²×D₄	—	53	24	no	—
554	C₂²×D₄	—	53	24	no	—
555	C₂²×D₄	—	53	6	no	—
556	C₂²×D₄	—	53	12	no	—
557	C₂²×D₄	—	53	12	no	—
558	C₂²×D₄	—	106	48	no	—
559	C₂²×D₄	—	106	96	no	—
560	C₂²×D₄	—	212	48	no	—
561	C₂²×D₄	C₂²×D₅₃	1	6	yes	complemented
562	C₂²×D₄	C₂²×D₅₃	1	12	yes	complemented
563	C₂²×D₄	C₂²×D₅₃	1	12	yes	complemented
564	C₂³×C₄	—	53	3	no	—
565	C₂³×C₄	—	53	6	no	—
566	C₂³×C₄	—	53	12	no	—
567	C₄⋊Q₈	—	53	2	no	—
568	C₄⋊Q₈	—	53	4	no	—
569	C₄⋊Q₈	—	53	1	no	—
570	C₄⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
571	#127	—	53	6	no	—
572	#127	—	53	12	no	—
573	#127	—	53	24	no	—
574	#127	—	53	12	no	—
575	#127	—	53	24	no	—
576	#127	—	53	24	no	—
577	#127	—	53	24	no	—
578	#127	—	53	3	no	—
579	#127	—	53	6	no	—
580	#127	—	53	12	no	—
581	#127	C₂²×D₅₃	1	3	yes	complemented
582	#127	C₂²×D₅₃	1	6	yes	complemented
583	#127	C₂²×D₅₃	1	12	yes	complemented
584	#124	—	53	6	no	—
585	#124	—	53	6	no	—
586	#124	—	53	24	no	—
587	#124	—	53	6	no	—
588	#124	C₂²×D₅₃	1	6	yes	complemented
589	#121	—	53	12	no	—
590	#121	—	53	24	no	—
591	#121	—	53	24	no	—
592	#121	—	53	48	no	—
593	#121	—	53	12	no	—
594	#121	—	53	24	no	—
595	#121	—	53	12	no	—
596	#121	—	53	24	no	—
597	#121	—	53	24	no	—
598	#121	—	53	48	no	—
599	#121	C₂²×D₅₃	1	12	yes	complemented
600	#121	C₂²×D₅₃	1	24	yes	complemented
601	#120	—	53	24	no	—
602	#120	—	53	24	no	—
603	#120	—	53	48	no	—
604	#120	—	53	48	no	—
605	#120	—	53	24	no	—
606	#120	C₂²×D₅₃	1	24	yes	complemented
607	C₄×Q₈	—	53	2	no	—
608	C₄×Q₈	—	53	6	no	—
609	C₄×Q₈	—	53	6	no	—
610	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
611	C₄×D₄	—	53	6	no	—
612	C₄×D₄	—	53	12	no	—
613	C₄×D₄	—	53	12	no	—
614	C₄×D₄	—	53	24	no	—
615	C₄×D₄	—	53	6	no	—
616	C₄×D₄	—	53	12	no	—
617	C₄×D₄	—	53	12	no	—
618	C₄×D₄	—	53	24	no	—
619	C₄×D₄	—	53	6	no	—
620	C₄×D₄	—	53	12	no	—
621	C₄×D₄	C₂²×D₅₃	1	6	yes	complemented
622	C₄×D₄	C₂²×D₅₃	1	12	yes	complemented
623	#117	—	53	3	no	—
624	#117	—	53	6	no	—
625	#117	—	53	6	no	—
626	#117	—	53	6	no	—
627	#117	C₂²×D₅₃	1	3	yes	complemented
628	C₂×C₄⋊C₄	—	53	6	no	—
629	C₂×C₄⋊C₄	—	53	4	no	—
630	C₂×C₂²⋊C₄	—	53	6	no	—
631	C₂×C₂²⋊C₄	—	53	24	no	—
632	C₂×C₄²	—	53	6	no	—
633	C₂×C₄²	—	53	3	no	—
634	C₂×C₄²	—	53	3	no	—
635	C₂×C₄²	—	53	6	no	—
636	C₂×C₄²	—	53	6	no	—
637	C₂×C₄²	—	53	3	no	—
638	C₂×C₄²	—	53	3	no	—
639	C₂×C₄²	—	53	1	no	—
640	C₂×C₄²	C₂²×D₅₃	1	3	yes	complemented
641	C₂⁴	—	53	3	no	—
642	C₂⁴	—	53	12	no	—
643	C₂⁴	—	53	24	no	—
644	C₂⁴	—	53	12	no	—
645	C₂⁴	—	106	48	no	—
646	C₂⁴	—	212	48	no	—
647	C₂⁴	C₂³×D₅₃	1	12	yes	—
648	#41	—	2	16	no	—
649	#41	—	2	24	no	—
650	#41	—	53	8	no	—
651	#41	—	53	24	no	—
652	#41	—	53	24	no	—
653	#41	—	106	48	no	—
654	#41	—	106	48	no	—
655	#41	—	106	48	no	—
656	#41	—	106	24	no	—
657	#41	—	106	24	no	—
658	#41	—	106	48	no	—
659	#41	—	106	16	no	—
660	#41	—	106	24	no	—
661	#41	D₄×D₅₃	1	8	yes	complemented
662	C₂×Q₈	—	53	8	no	—
663	C₂×Q₈	—	53	3	no	—
664	C₂×Q₈	—	53	4	no	—
665	C₂×Q₈	—	53	2	no	—
666	C₂×Q₈	—	106	8	no	—
667	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
668	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
669	C₂×D₄	—	2	48	no	—
670	C₂×D₄	—	2	24	no	—
671	C₂×D₄	—	4	24	no	—
672	C₂×D₄	—	53	6	no	—
673	C₂×D₄	—	53	24	no	—
674	C₂×D₄	—	53	24	no	—
675	C₂×D₄	—	53	12	no	—
676	C₂×D₄	—	53	12	no	—
677	C₂×D₄	—	53	24	no	—
678	C₂×D₄	—	53	12	no	—
679	C₂×D₄	—	53	48	no	—
680	C₂×D₄	—	53	3	no	—
681	C₂×D₄	—	53	12	no	—
682	C₂×D₄	—	53	12	no	—
683	C₂×D₄	—	53	12	no	—
684	C₂×D₄	—	53	6	no	—
685	C₂×D₄	—	53	24	no	—
686	C₂×D₄	—	106	48	no	—
687	C₂×D₄	—	106	24	no	—
688	C₂×D₄	—	106	48	no	—
689	C₂×D₄	—	106	48	no	—
690	C₂×D₄	—	106	48	no	—
691	C₂×D₄	—	106	48	no	—
692	C₂×D₄	—	106	48	no	—
693	C₂×D₄	—	106	96	no	—
694	C₂×D₄	—	106	48	no	—
695	C₂×D₄	—	106	48	no	—
696	C₂×D₄	—	106	96	no	—
697	C₂×D₄	—	106	48	no	—
698	C₂×D₄	—	106	24	no	—
699	C₂×D₄	—	212	24	no	—
700	C₂×D₄	—	212	48	no	—
701	C₂×D₄	—	212	48	no	—
702	C₂×D₄	—	212	48	no	—
703	C₂×D₄	—	212	48	no	—
704	C₂×D₄	C₂³×D₅₃	1	12	yes	—
705	C₂×D₄	C₂³×D₅₃	1	12	yes	—
706	C₂×D₄	C₂³×D₅₃	1	12	yes	—
707	C₂×D₄	C₂³×D₅₃	1	6	yes	—
708	C₂×D₄	C₂³×D₅₃	1	24	yes	—
709	C₂×D₄	C₂³×D₅₃	1	3	yes	—
710	C₂²×C₄	—	53	3	no	—
711	C₂²×C₄	—	53	24	no	—
712	C₂²×C₄	—	53	2	no	—
713	C₂²×C₄	—	53	1	no	—
714	C₂²×C₄	—	53	3	no	—
715	C₂²×C₄	—	53	3	no	—
716	C₂²×C₄	—	53	3	no	—
717	C₂²×C₄	—	53	6	no	—
718	C₂²×C₄	—	53	12	no	—
719	C₂²×C₄	—	53	6	no	—
720	C₂²×C₄	—	53	6	no	—
721	C₂²×C₄	—	53	6	no	—
722	C₂²×C₄	—	53	4	no	—
723	C₂²×C₄	—	53	12	no	—
724	C₂²×C₄	—	53	12	no	—
725	C₂²×C₄	—	106	48	no	—
726	C₂²×C₄	—	106	24	no	—
727	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
728	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
729	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
730	C₄⋊C₄	—	53	12	no	—
731	C₄⋊C₄	—	53	6	no	—
732	C₄⋊C₄	—	53	8	no	—
733	C₄⋊C₄	—	53	4	no	—
734	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
735	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
736	C₂²⋊C₄	—	53	6	no	—
737	C₂²⋊C₄	—	53	24	no	—
738	C₂²⋊C₄	—	53	12	no	—
739	C₂²⋊C₄	—	53	24	no	—
740	C₂²⋊C₄	—	53	24	no	—
741	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
742	C₂²⋊C₄	C₂³×D₅₃	1	24	yes	—
743	C₄²	—	53	1	no	—
744	C₄²	—	53	2	no	—
745	C₄²	—	53	6	no	—
746	C₄²	—	53	3	no	—
747	C₄²	—	53	6	no	—
748	C₄²	—	53	6	no	—
749	C₄²	—	53	6	no	—
750	C₄²	C₂³×D₅₃	1	1	yes	characteristic
751	C₄²	C₂³×D₅₃	1	3	yes	—
752	C₄²	C₂³×D₅₃	1	6	yes	—
753	C₂³	—	2	24	no	—
754	C₂³	—	4	24	no	—
755	C₂³	—	53	1	no	—
756	C₂³	—	53	12	no	—
757	C₂³	—	53	3	no	—
758	C₂³	—	53	12	no	—
759	C₂³	—	106	12	no	—
760	C₂³	—	106	48	no	—
761	C₂³	—	106	24	no	—
762	C₂³	—	106	48	no	—
763	C₂³	—	106	24	no	—
764	C₂³	—	424	96	no	—
765	C₂³	—	212	24	no	—
766	C₂³	—	212	48	no	—
767	C₂³	C₂⁴×D₅₃	1	12	yes	—
768	C₂³	C₂⁴×D₅₃	1	3	yes	—
769	Q₈	—	2	4	no	—
770	Q₈	—	53	12	no	—
771	Q₈	—	106	8	no	—
772	Q₈	—	106	4	no	—
773	Q₈	C₂×D₄×D₅₃	1	4	yes	complemented
774	D₄	—	2	24	no	—
775	D₄	—	2	24	no	—
776	D₄	—	2	12	no	—
777	D₄	—	2	24	no	—
778	D₄	—	4	24	no	—
779	D₄	—	53	24	no	—
780	D₄	—	53	12	no	—
781	D₄	—	106	24	no	—
782	D₄	—	106	24	no	—
783	D₄	—	106	48	no	—
784	D₄	—	106	48	no	—
785	D₄	—	106	24	no	—
786	D₄	—	106	24	no	—
787	D₄	—	106	24	no	—
788	D₄	—	106	12	no	—
789	D₄	—	106	24	no	—
790	D₄	—	212	24	no	—
791	D₄	—	212	48	no	—
792	D₄	C₂×D₄×D₅₃	1	12	yes	complemented
793	C₂×C₄	—	2	24	no	—
794	C₂×C₄	—	2	12	no	—
795	C₂×C₄	—	53	12	no	—
796	C₂×C₄	—	53	2	no	—
797	C₂×C₄	—	53	1	no	—
798	C₂×C₄	—	53	3	no	—
799	C₂×C₄	—	53	4	no	—
800	C₂×C₄	—	53	12	no	—
801	C₂×C₄	—	53	12	no	—
802	C₂×C₄	—	53	12	no	—
803	C₂×C₄	—	53	8	no	—
804	C₂×C₄	—	53	6	no	—
805	C₂×C₄	—	53	4	no	—
806	C₂×C₄	—	106	24	no	—
807	C₂×C₄	—	106	12	no	—
808	C₂×C₄	—	106	8	no	—
809	C₂×C₄	—	106	12	no	—
810	C₂×C₄	—	106	24	no	—
811	C₂×C₄	—	106	12	no	—
812	C₂×C₄	—	106	24	no	—
813	C₂×C₄	—	106	12	no	—
814	C₂×C₄	C₂×D₄×D₅₃	1	12	yes	complemented
815	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
816	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
817	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
818	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
819	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
820	C₂²	—	2	6	no	—
821	C₂²	—	2	12	no	—
822	C₂²	—	2	24	no	—
823	C₂²	—	8	24	no	—
824	C₂²	—	53	2	no	—
825	C₂²	—	53	4	no	—
826	C₂²	—	53	6	no	—
827	C₂²	—	106	24	no	—
828	C₂²	—	106	6	no	—
829	C₂²	—	106	12	no	—
830	C₂²	—	106	24	no	—
831	C₂²	—	424	24	no	—
832	C₂²	—	424	48	no	—
833	C₂²	—	212	48	no	—
834	C₂²	C₂²×D₄×D₅₃	1	6	yes	—
835	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
836	C₄	—	2	4	no	—
837	C₄	—	2	6	no	—
838	C₄	—	53	2	no	—
839	C₄	—	53	6	no	—
840	C₄	—	53	4	no	—
841	C₄	—	106	4	no	—
842	C₄	—	106	6	no	—
843	C₄	C₂²×D₄×D₅₃	1	6	yes	—
844	C₄	C₂²×D₄×D₅₃	1	2	yes	—
845	C₄	H(5,𝔽₂)×D₅₃	1	4	yes	complemented
846	C₂	—	2	6	no	—
847	C₂	—	4	12	no	—
848	C₂	—	53	4	no	—
849	C₂	—	106	6	no	—
850	C₂	—	212	12	no	—
851	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
852	C₂	C₂×H(5,𝔽₂)×D₅₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3498	C₂
hypercenter	#3498	D₅₃
hypocenter	C₅₃	C₂×#3498
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3498

Complements

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

N	H ≅ G/N	type
1. C₂×H(5,𝔽₂)×D₅₃	C₂	semidirect
2. #20288493	C₂	semidirect
3. #20288492	C₂	semidirect
4. #20288491	C₂	semidirect
5. #20288490	C₂	semidirect
6. #20288489	C₂	semidirect
7. #20288488	C₂	semidirect
8. #20288487	C₂	semidirect
9. #550×D₅₃	C₂	semidirect
10. D₄²×D₅₃	C₂	semidirect
11. #535×D₅₃	C₂	semidirect
12. #532×D₅₃	C₂	semidirect
13. C₂×#127×D₅₃	C₂	semidirect
14. C₄×#41×D₅₃	C₂	semidirect
15. C₅₃×#3498	C₂	semidirect
16. C₂×#13133263	C₂²	semidirect
17. C₂×#13133263	C₂²	semidirect
18. C₂×#13133263	C₂²	semidirect
19. C₂×#13133262	C₂²	semidirect
20. C₂×#13133262	C₂²	semidirect
23. C₂×#41×D₅₃	C₂²	semidirect
24. C₂×#41×D₅₃	C₂²	semidirect
25. C₂²×D₄×D₅₃	C₂²	semidirect
26. C₂²×D₄×D₅₃	C₂²	semidirect
27. C₂²×D₄×D₅₃	C₂²	semidirect
28. #16811295	C₂²	semidirect
29. #16811294	C₂²	semidirect
30. #16811293	C₂²	semidirect
31. #16811292	C₂²	semidirect
32. #16811291	C₂²	semidirect
33. D₄×D₂₁₂	C₂²	semidirect
34. D₄×D₂₁₂	C₂²	semidirect
35. #16811258	C₂²	semidirect
36. #16811257	C₂²	semidirect
37. #16811257	C₂²	semidirect
38. D₄×C₂²⋊D₅₃	C₂²	semidirect
39. D₄×C₂²⋊D₅₃	C₂²	semidirect
40. #16811255	C₂²	semidirect
41. #16811192	C₂²	semidirect
42. #16811191	C₂²	semidirect
43. #16811190	C₂²	semidirect
44. #16811189	C₂²	semidirect
45. #16811188	C₂²	semidirect
46. #16811187	C₂²	semidirect
47. #16811186	C₂²	semidirect
48. #16811174	C₂²	semidirect
49. #16811173	C₂²	semidirect
50. #16811172	C₂²	semidirect
51. #16811171	C₂²	semidirect
52. #16811170	C₂²	semidirect
53. #16811169	C₂²	semidirect
54. #16811168	C₂²	semidirect
55. C₄⋊Q₈×D₅₃	C₂²	semidirect
56. C₂×#13133214	C₂²	semidirect
57. C₂×#13133213	C₂²	semidirect
58. C₂×#13133213	C₂²	semidirect
59. #127×D₅₃	C₂²	semidirect
60. #127×D₅₃	C₂²	semidirect
61. #127×D₅₃	C₂²	semidirect
62. #127×D₅₃	C₂²	semidirect
63. #127×D₅₃	C₂²	semidirect
64. #127×D₅₃	C₂²	semidirect
65. #124×D₅₃	C₂²	semidirect
66. #121×D₅₃	C₂²	semidirect
67. #121×D₅₃	C₂²	semidirect
68. #120×D₅₃	C₂²	semidirect
69. #41×Dic₅₃	C₂²	semidirect
70. C₄×#11719949	C₂²	semidirect
71. C₄×#11719945	C₂²	semidirect
72. #16811091	C₂²	semidirect
73. C₄×#11719947	C₂²	semidirect
74. C₄×Q₈×D₅₃	C₂²	semidirect
75. C₄×D₄×D₅₃	C₂²	semidirect
76. C₄×D₄×D₅₃	C₂²	semidirect
77. #117×D₅₃	C₂²	semidirect
78. C₂×C₄²×D₅₃	C₂²	semidirect
79. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
80. C₅₃×#550	C₂²	semidirect
81. D₄²×C₅₃	C₂²	semidirect
82. C₅₃×#535	C₂²	semidirect
83. C₅₃×#532	C₂²	semidirect
84. C₂×#127×C₅₃	C₂²	semidirect
85. C₄×#41×C₅₃	C₂²	semidirect
93. C₂×#11719949	C₂³	semidirect
94. C₂×#11719949	C₂³	semidirect
96. C₂×#11719945	C₂³	semidirect
97. C₂×#11719945	C₂³	semidirect
98. C₂×#11719945	C₂³	semidirect
100. C₂×#11719947	C₂³	semidirect
101. C₂×#11719947	C₂³	semidirect
102. C₂×#11719947	C₂³	semidirect
105. #41×D₅₃	D₄	semidirect
108. C₂²×D₂₁₂	C₂³	semidirect
109. C₂²×D₂₁₂	C₂³	semidirect
110. C₂²×D₂₁₂	C₂³	semidirect
111. C₂²×C₂²⋊D₅₃	C₂³	semidirect
112. C₂²×C₂²⋊D₅₃	C₂³	semidirect
113. C₂²×C₂²⋊D₅₃	C₂³	semidirect
123. C₂×D₄×D₅₃	C₂³	semidirect
124. C₂×D₄×D₅₃	C₂³	semidirect
125. C₂×D₄×D₅₃	C₂³	semidirect
126. C₂×D₄×D₅₃	C₂³	semidirect
127. C₂×D₄×D₅₃	C₂³	semidirect
128. C₂×D₄×D₅₃	C₂³	semidirect
129. C₂×D₄×D₅₃	C₂³	semidirect
133. #13133217	C₂³	semidirect
134. #13133216	C₂³	semidirect
135. #13133215	C₂³	semidirect
136. #13133214	C₂³	semidirect
137. #13133214	C₂³	semidirect
138. #13133214	C₂³	semidirect
139. #13133213	C₂³	semidirect
140. #13133213	C₂³	semidirect
141. #13133213	C₂³	semidirect
142. #13133213	C₂³	semidirect
143. #13133213	C₂³	semidirect
144. #13133213	C₂³	semidirect
145. #13133213	C₂³	semidirect
146. #13133206	C₂³	semidirect
147. #13133205	C₂³	semidirect
148. #13133204	C₂³	semidirect
149. #13133203	C₂³	semidirect
150. #13133192	C₂³	semidirect
151. #13133192	C₂³	semidirect
152. #13133191	C₂³	semidirect
153. #13133191	C₂³	semidirect
154. #13133190	C₂³	semidirect
155. #13133190	C₂³	semidirect
156. #13133189	C₂³	semidirect
157. #13133189	C₂³	semidirect
158. #13133188	C₂³	semidirect
159. #13133188	C₂³	semidirect
160. #13133187	C₂³	semidirect
161. #13133187	C₂³	semidirect
162. #13133186	C₂³	semidirect
163. #13133185	C₂³	semidirect
164. #13133185	C₂³	semidirect
165. Q₈×Dic₅₃	C₂³	semidirect
166. C₄×Dic₁₀₆	C₂³	semidirect
167. #13133182	C₂³	semidirect
168. C₄×D₂₁₂	C₂³	semidirect
169. C₄×D₂₁₂	C₂³	semidirect
170. D₄×Dic₅₃	C₂³	semidirect
171. D₄×Dic₅₃	C₂³	semidirect
172. #13133179	C₂³	semidirect
173. #13133179	C₂³	semidirect
174. C₄×C₂²⋊D₅₃	C₂³	semidirect
175. C₄×C₂²⋊D₅₃	C₂³	semidirect
176. #13133177	C₂³	semidirect
177. #13133177	C₂³	semidirect
178. #13133176	C₂³	semidirect
179. #13133175	C₂³	semidirect
180. #13133174	C₂³	semidirect
181. #13133173	C₂³	semidirect
186. C₂×C₄×Dic₅₃	C₂³	semidirect
187. C₂×C₄×Dic₅₃	C₂³	semidirect
191. C₄²×D₅₃	C₂³	semidirect
192. C₄²×D₅₃	C₂³	semidirect
193. C₄²×D₅₃	C₂³	semidirect
196. C₂×#41×C₅₃	C₂³	semidirect
197. C₂×#41×C₅₃	C₂³	semidirect
198. C₂²×D₄×C₅₃	C₂³	semidirect
199. C₂²×D₄×C₅₃	C₂³	semidirect
200. C₂²×D₄×C₅₃	C₂³	semidirect
201. C₄⋊Q₈×C₅₃	C₂³	semidirect
202. #127×C₅₃	C₂³	semidirect
203. #127×C₅₃	C₂³	semidirect
204. #127×C₅₃	C₂³	semidirect
205. #124×C₅₃	C₂³	semidirect
206. #121×C₅₃	C₂³	semidirect
207. #121×C₅₃	C₂³	semidirect
208. #120×C₅₃	C₂³	semidirect
209. C₄×Q₈×C₅₃	C₂³	semidirect
210. C₄×D₄×C₅₃	C₂³	semidirect
211. C₄×D₄×C₅₃	C₂³	semidirect
212. #117×C₅₃	C₂³	semidirect
213. C₂×C₄²×C₅₃	C₂³	semidirect
223. #41×C₅₃	C₂×D₄	semidirect
253. #11719949	C₂×D₄	semidirect
255. Q₈×D₅₃	C₂×D₄	semidirect
259. #11719947	C₂×D₄	semidirect
272. D₄×D₅₃	C₂×D₄	semidirect
276. #11719945	C₂×D₄	semidirect
288. C₂×C₄×D₅₃	C₂×D₄	semidirect
343. Q₈×C₅₃	C₂²×D₄	semidirect
349. D₄×C₅₃	C₂²×D₄	semidirect
352. C₂×C₄×C₅₃	C₂²×D₄	semidirect
364. C₂²⋊D₅₃	C₂²×D₄	semidirect
367. C₂×Dic₅₃	C₂²×D₄	semidirect
378. D₂₁₂	C₂²×D₄	semidirect
387. C₄×D₅₃	C₂²×D₄	semidirect
388. C₄×D₅₃	C₂²×D₄	semidirect
389. C₄×D₅₃	H(5,𝔽₂)	semidirect
392. Dic₁₀₆	C₂²×D₄	semidirect
414. C₄×C₅₃	C₂×H(5,𝔽₂)	semidirect
419. Dic₅₃	C₂×H(5,𝔽₂)	semidirect
428. #3498	D₅₃	direct (N × H)
441. D₅₃	#3498	direct (N × H)
448. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
460. #550	C₂×D₅₃	semidirect
469. D₄²	C₂×D₅₃	semidirect
477. #535	C₂×D₅₃	semidirect
485. #532	C₂×D₅₃	semidirect
496. C₂×#127	C₂×D₅₃	semidirect
506. C₄×#41	C₂×D₅₃	semidirect
512. C₅₃	C₂×#3498	semidirect
535. C₂×#41	C₂²×D₅₃	semidirect
536. C₂×#41	C₂²×D₅₃	semidirect
561. C₂²×D₄	C₂²×D₅₃	semidirect
562. C₂²×D₄	C₂²×D₅₃	semidirect
563. C₂²×D₄	C₂²×D₅₃	semidirect
570. C₄⋊Q₈	C₂²×D₅₃	semidirect
581. #127	C₂²×D₅₃	semidirect
582. #127	C₂²×D₅₃	semidirect
583. #127	C₂²×D₅₃	semidirect
588. #124	C₂²×D₅₃	semidirect
599. #121	C₂²×D₅₃	semidirect
600. #121	C₂²×D₅₃	semidirect
606. #120	C₂²×D₅₃	semidirect
610. C₄×Q₈	C₂²×D₅₃	semidirect
621. C₄×D₄	C₂²×D₅₃	semidirect
622. C₄×D₄	C₂²×D₅₃	semidirect
627. #117	C₂²×D₅₃	semidirect
640. C₂×C₄²	C₂²×D₅₃	semidirect
661. #41	D₄×D₅₃	semidirect
773. Q₈	C₂×D₄×D₅₃	semidirect
792. D₄	C₂×D₄×D₅₃	semidirect
814. C₂×C₄	C₂×D₄×D₅₃	semidirect
845. C₄	H(5,𝔽₂)×D₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×H(5,𝔽₂)×D₅₃	2
#20288493	2
#20288492	2
#20288491	2
#20288490	2
#20288489	2
#20288488	2
#20288487	2
#550×D₅₃	2
D₄²×D₅₃	2
#535×D₅₃	2
#532×D₅₃	2
C₂×#127×D₅₃	2
C₄×#41×D₅₃	2
C₅₃×#3498	2
C₂×#3498	53

Subgroups — D53×#3498 #28292407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3498 #28292407