Subgroups — C₂×#535×D₅₃ #28290843

Order 13568.

14414 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#535	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×#535	D₅₃
hypocenter	C₅₃	C₂²×#535
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#535

Complements

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

N	H ≅ G/N	type
1. C₂²×#41×D₅₃	C₂	semidirect
2. C₂³×D₄×D₅₃	C₂	semidirect
3. C₂×#16811192	C₂	semidirect
4. C₂×#16811191	C₂	semidirect
5. C₂×#16811190	C₂	semidirect
6. C₂×#16811189	C₂	semidirect
7. C₂×#16811188	C₂	semidirect
8. C₂×#16811187	C₂	semidirect
9. C₂×#16811186	C₂	semidirect
10. #535×D₅₃	C₂	direct (N × H)
11. C₂×#127×D₅₃	C₂	semidirect
12. C₂×#124×D₅₃	C₂	semidirect
13. C₂×#121×D₅₃	C₂	semidirect
14. C₂×#120×D₅₃	C₂	semidirect
15. C₂×#117×D₅₃	C₂	semidirect
16. C₂×C₅₃×#535	C₂	semidirect
18. C₂²×#11719949	C₂²	semidirect
19. C₂²×#11719945	C₂²	semidirect
20. C₂²×#11719945	C₂²	semidirect
21. C₂²×#11719947	C₂²	semidirect
22. C₂²×#11719947	C₂²	semidirect
24. C₂×#41×D₅₃	C₂²	semidirect
25. C₂²×Q₈×D₅₃	C₂²	semidirect
26. C₂³×D₂₁₂	C₂²	semidirect
27. C₂³×C₂²⋊D₅₃	C₂²	semidirect
32. C₂²×D₄×D₅₃	C₂²	semidirect
33. C₂²×D₄×D₅₃	C₂²	semidirect
34. C₂²×D₄×D₅₃	C₂²	semidirect
35. C₂²×D₄×D₅₃	C₂²	semidirect
36. C₂²×D₄×D₅₃	C₂²	semidirect
38. C₂³×C₄×D₅₃	C₂²	semidirect
39. #16811192	C₂²	semidirect
40. #16811191	C₂²	semidirect
41. #16811190	C₂²	semidirect
42. #16811189	C₂²	semidirect
43. #16811188	C₂²	semidirect
44. #16811187	C₂²	semidirect
45. #16811186	C₂²	semidirect
46. C₂×#13133214	C₂²	semidirect
47. C₂×#13133213	C₂²	semidirect
48. C₂×#13133213	C₂²	semidirect
49. C₂×#13133213	C₂²	semidirect
50. #127×D₅₃	C₂²	semidirect
51. C₂×#13133206	C₂²	semidirect
52. C₂×#13133205	C₂²	semidirect
53. C₂×#13133204	C₂²	semidirect
54. C₂×#13133203	C₂²	semidirect
55. #124×D₅₃	C₂²	semidirect
56. C₂×#13133192	C₂²	semidirect
57. C₂×#13133191	C₂²	semidirect
58. C₂×#13133190	C₂²	semidirect
59. C₂×#13133189	C₂²	semidirect
60. C₂×#13133188	C₂²	semidirect
61. #121×D₅₃	C₂²	semidirect
62. C₂×#13133187	C₂²	semidirect
63. C₂×#13133187	C₂²	semidirect
64. C₂×#13133186	C₂²	semidirect
65. C₂×#13133185	C₂²	semidirect
66. C₂×#13133185	C₂²	semidirect
67. #120×D₅₃	C₂²	semidirect
68. C₂×#13133176	C₂²	semidirect
69. C₂×#13133175	C₂²	semidirect
70. C₂×#13133174	C₂²	semidirect
71. C₂×#13133173	C₂²	semidirect
72. #117×D₅₃	C₂²	semidirect
73. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
75. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
76. C₂×C₄²×D₅₃	C₂²	semidirect
77. C₂²×#41×C₅₃	C₂²	semidirect
78. C₂³×D₄×C₅₃	C₂²	semidirect
79. C₅₃×#535	C₂²	semidirect
80. C₂×#127×C₅₃	C₂²	semidirect
81. C₂×#124×C₅₃	C₂²	semidirect
82. C₂×#121×C₅₃	C₂²	semidirect
83. C₂×#120×C₅₃	C₂²	semidirect
84. C₂×#117×C₅₃	C₂²	semidirect
94. C₂×#11719949	C₂³	semidirect
97. C₂×#11719945	C₂³	semidirect
98. C₂×#11719945	C₂³	semidirect
101. C₂×#11719947	C₂³	semidirect
102. C₂×#11719947	C₂³	semidirect
104. C₂²×Dic₁₀₆	C₂³	semidirect
105. C₂²×Dic₁₀₆	C₂³	semidirect
107. C₂×Q₈×D₅₃	C₂³	semidirect
112. C₂²×D₂₁₂	C₂³	semidirect
113. C₂²×D₂₁₂	C₂³	semidirect
114. C₂²×D₂₁₂	C₂³	semidirect
120. C₂²×C₂²⋊D₅₃	C₂³	semidirect
121. C₂²×C₂²⋊D₅₃	C₂³	semidirect
122. C₂²×C₂²⋊D₅₃	C₂³	semidirect
123. C₂²×C₂²⋊D₅₃	C₂³	semidirect
135. C₂×D₄×D₅₃	C₂³	semidirect
136. C₂×D₄×D₅₃	C₂³	semidirect
137. C₂×D₄×D₅₃	C₂³	semidirect
138. C₂×D₄×D₅₃	C₂³	semidirect
140. C₂³×Dic₅₃	C₂³	semidirect
142. C₂²×C₄×D₅₃	D₄	semidirect
150. C₂²×C₄×D₅₃	C₂³	semidirect
151. C₂²×C₄×D₅₃	C₂³	semidirect
152. C₂²×C₄×D₅₃	C₂³	semidirect
153. #13133214	C₂³	semidirect
154. #13133213	C₂³	semidirect
155. #13133213	C₂³	semidirect
156. #13133213	C₂³	semidirect
157. #13133206	C₂³	semidirect
158. #13133205	C₂³	semidirect
159. #13133204	C₂³	semidirect
160. #13133203	C₂³	semidirect
161. #13133192	C₂³	semidirect
162. #13133191	C₂³	semidirect
163. #13133190	C₂³	semidirect
164. #13133189	C₂³	semidirect
165. #13133188	C₂³	semidirect
166. #13133187	C₂³	semidirect
167. #13133187	C₂³	semidirect
168. #13133186	C₂³	semidirect
169. #13133185	C₂³	semidirect
170. #13133185	C₂³	semidirect
171. #13133176	C₂³	semidirect
172. #13133175	C₂³	semidirect
173. #13133174	C₂³	semidirect
174. #13133173	C₂³	semidirect
175. C₂×C₄⋊Dic₅₃	C₂³	semidirect
176. C₂×#11719919	C₂³	semidirect
177. C₄⋊C₄×D₅₃	C₂³	semidirect
179. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
181. C₂×#11719921	C₂³	semidirect
182. C₂×#11719921	C₂³	semidirect
184. C₂²⋊C₄×D₅₃	C₂³	semidirect
185. C₂×C₄×Dic₅₃	C₂³	semidirect
186. C₂×C₄×Dic₅₃	C₂³	semidirect
187. C₄²×D₅₃	C₂³	semidirect
190. C₂×#41×C₅₃	C₂³	semidirect
191. C₂²×Q₈×C₅₃	C₂³	semidirect
196. C₂²×D₄×C₅₃	C₂³	semidirect
197. C₂²×D₄×C₅₃	C₂³	semidirect
198. C₂²×D₄×C₅₃	C₂³	semidirect
200. C₂³×C₄×C₅₃	C₂³	semidirect
201. #127×C₅₃	C₂³	semidirect
202. #124×C₅₃	C₂³	semidirect
203. #121×C₅₃	C₂³	semidirect
204. #120×C₅₃	C₂³	semidirect
205. #117×C₅₃	C₂³	semidirect
206. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
208. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
209. C₂×C₄²×C₅₃	C₂³	semidirect
240. C₂×Q₈×C₅₃	C₂⁴	semidirect
250. C₂×D₄×C₅₃	C₂⁴	semidirect
251. C₂×D₄×C₅₃	C₂⁴	semidirect
253. C₂²×C₄×C₅₃	C₂×D₄	semidirect
259. C₂²×C₄×C₅₃	C₂⁴	semidirect
272. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
273. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
274. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
276. C₂²×Dic₅₃	C₂×D₄	semidirect
282. C₂²×Dic₅₃	C₂⁴	semidirect
305. C₂×D₂₁₂	C₂⁴	semidirect
306. C₂×D₂₁₂	C₂⁴	semidirect
314. C₂×C₄×D₅₃	C₂×D₄	semidirect
315. C₂×C₄×D₅₃	C₂×D₄	semidirect
316. C₂×C₄×D₅₃	C₂×D₄	semidirect
323. C₂×C₄×D₅₃	C₂⁴	semidirect
324. C₂×C₄×D₅₃	C₂⁴	semidirect
327. C₂×Dic₁₀₆	C₂⁴	semidirect
328. C₂×Dic₁₀₆	C₂⁴	semidirect
329. C₄⋊C₄×C₅₃	C₂⁴	semidirect
331. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
332. C₄²×C₅₃	C₂⁴	semidirect
334. C₂²⋊Dic₅₃	C₂⁴	semidirect
336. #11719921	C₂⁴	semidirect
337. #11719921	C₂⁴	semidirect
338. C₄⋊Dic₅₃	C₂⁴	semidirect
339. #11719919	C₂⁴	semidirect
340. C₄×Dic₅₃	C₂⁴	semidirect
341. C₄×Dic₅₃	C₂⁴	semidirect
394. C₂×C₄×C₅₃	C₂²×D₄	semidirect
411. C₂×Dic₅₃	C₂²×D₄	semidirect
427. C₄×D₅₃	C₂²×D₄	semidirect
428. C₄×D₅₃	C₂²×D₄	semidirect
458. C₂×D₅₃	#535	direct (N × H)
480. C₂×#535	D₅₃	direct (N × H)
489. C₂×C₅₃	C₂×#535	semidirect
495. D₅₃	C₂×#535	direct (N × H)
504. C₂²×#41	C₂×D₅₃	semidirect
517. C₂³×D₄	C₂×D₅₃	semidirect
527. #535	C₂×D₅₃	direct (N × H)
533. C₂×#127	C₂×D₅₃	semidirect
539. C₂×#124	C₂×D₅₃	semidirect
546. C₂×#121	C₂×D₅₃	semidirect
553. C₂×#120	C₂×D₅₃	semidirect
559. C₂×#117	C₂×D₅₃	semidirect
564. C₅₃	C₂²×#535	semidirect
586. C₂×#41	C₂²×D₅₃	semidirect
591. C₂²×Q₈	C₂²×D₅₃	semidirect
627. C₂²×D₄	C₂²×D₅₃	semidirect
628. C₂²×D₄	C₂²×D₅₃	semidirect
629. C₂²×D₄	C₂²×D₅₃	semidirect
645. C₂³×C₄	C₂²×D₅₃	semidirect
650. #127	C₂²×D₅₃	semidirect
655. #124	C₂²×D₅₃	semidirect
661. #121	C₂²×D₅₃	semidirect
667. #120	C₂²×D₅₃	semidirect
672. #117	C₂²×D₅₃	semidirect
676. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
685. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
689. C₂×C₄²	C₂²×D₅₃	semidirect
730. C₂×Q₈	C₂³×D₅₃	semidirect
773. C₂×D₄	C₂³×D₅₃	semidirect
774. C₂×D₄	C₂³×D₅₃	semidirect
802. C₂²×C₄	D₄×D₅₃	semidirect
808. C₂²×C₄	C₂³×D₅₃	semidirect
811. C₄⋊C₄	C₂³×D₅₃	semidirect
818. C₂²⋊C₄	C₂³×D₅₃	semidirect
821. C₄²	C₂³×D₅₃	semidirect
906. C₂×C₄	C₂×D₄×D₅₃	semidirect
956. C₂	#535×D₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#41×D₅₃	2
C₂³×D₄×D₅₃	2
C₂×#16811192	2
C₂×#16811191	2
C₂×#16811190	2
C₂×#16811189	2
C₂×#16811188	2
C₂×#16811187	2
C₂×#16811186	2
#535×D₅₃	2
C₂×#127×D₅₃	2
C₂×#124×D₅₃	2
C₂×#121×D₅₃	2
C₂×#120×D₅₃	2
C₂×#117×D₅₃	2
C₂×C₅₃×#535	2
C₂²×#535	53

Subgroups — C2×#535×D53 #28290843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#535×D₅₃ #28290843