Subgroups — C₂×#20289045 #28291682

Order 13568.

8814 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289045	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16811364	C₂	1	4	yes	maximal, complemented
3	C₂×#16811358	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16811295	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16811294	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16811269	C₂	1	2	yes	maximal, complemented
7	C₂×#16811264	C₂	1	2	yes	maximal, complemented
8	C₂×D₄×D₂₁₂	C₂	1	2	yes	maximal, complemented
9	C₂×D₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16811257	C₂	1	2	yes	maximal, complemented
11	C₂×#16811229	C₂	1	2	yes	maximal, complemented
12	C₂×#16811228	C₂	1	2	yes	maximal, complemented
13	C₂×#16811192	C₂	1	2	yes	maximal, complemented
14	C₂×#16811191	C₂	1	2	yes	maximal, complemented
15	C₂×#16811184	C₂	1	4	yes	maximal, complemented
16	C₂²×#13133214	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#16811157	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#11719949	C₂²	1	2	yes	complemented
20	C₂²×#11719945	C₂²	1	2	yes	complemented
21	C₂³×D₂₁₂	C₂²	1	2	yes	complemented
22	C₂³×D₂₁₂	C₂²	1	2	yes	complemented
23	C₂³×D₂₁₂	C₂²	1	2	yes	complemented
24	C₂³×D₂₁₂	C₂²	1	2	yes	complemented
25	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
26	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
27	#16811364	C₂²	1	64	yes	complemented
28	#16811358	C₂²	1	16	yes	complemented
29	#16811295	C₂²	1	16	yes	complemented
30	#16811294	C₂²	1	16	yes	complemented
31	#16811269	C₂²	1	32	yes	complemented
32	#16811264	C₂²	1	32	yes	complemented
33	D₄×D₂₁₂	C₂²	1	32	yes	complemented
34	D₄×D₂₁₂	C₂²	1	16	yes	complemented
35	#16811257	C₂²	1	32	yes	complemented
36	#16811229	C₂²	1	32	yes	complemented
37	#16811228	C₂²	1	32	yes	complemented
38	#16811192	C₂²	1	32	yes	complemented
39	#16811191	C₂²	1	32	yes	complemented
40	#16811184	C₂²	1	64	yes	complemented
41	C₂×#13133214	C₂²	1	1	yes	characteristic
42	C₂×#13133214	C₂²	1	2	yes	complemented
43	C₂×#13133214	C₂²	1	2	yes	complemented
44	C₂×#13133214	C₂²	1	2	yes	complemented
45	C₂×#13133214	C₂²	1	2	yes	complemented
46	C₂×#13133214	C₂²	1	1	yes	characteristic, complemented
47	C₂×#13133214	C₂²	1	16	yes	complemented
48	C₂×#13133213	C₂²	1	2	yes	complemented
49	#16811157	C₂²	1	16	yes	complemented
50	C₂×#13133211	C₂²	1	2	yes	complemented
51	C₂×#13133209	C₂²	1	1	yes	characteristic, complemented
52	C₂×#13133206	C₂²	1	2	yes	complemented
53	C₂×#13133205	C₂²	1	1	yes	characteristic, complemented
54	C₂×#13133205	C₂²	1	2	yes	complemented
55	C₂×#13133202	C₂²	1	4	yes	complemented
56	C₂×#13133202	C₂²	1	4	yes	complemented
57	C₂×#13133202	C₂²	1	4	yes	complemented
58	C₂×#13133202	C₂²	1	4	yes	complemented
59	C₂×#13133200	C₂²	1	2	yes	complemented
60	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
61	C₂×#13133192	C₂²	1	4	yes	complemented
62	C₂×#13133192	C₂²	1	4	yes	complemented
63	C₂×#13133192	C₂²	1	4	yes	complemented
64	C₂×#13133192	C₂²	1	4	yes	complemented
65	C₂×#13133192	C₂²	1	2	yes	complemented
66	C₂×#13133192	C₂²	1	2	yes	complemented
67	C₂×#13133191	C₂²	1	1	yes	characteristic
68	C₂×#13133191	C₂²	1	2	yes	complemented
69	C₂×#13133191	C₂²	1	2	yes	complemented
70	C₂×#13133190	C₂²	1	4	yes	complemented
71	C₂×#13133190	C₂²	1	4	yes	complemented
72	C₂×#13133190	C₂²	1	4	yes	complemented
73	C₂×#13133190	C₂²	1	4	yes	complemented
74	C₂×#13133187	C₂²	1	4	yes	complemented
75	C₂×#13133187	C₂²	1	4	yes	complemented
76	C₂×#13133187	C₂²	1	4	yes	complemented
77	C₂×#13133187	C₂²	1	4	yes	complemented
78	C₂×#13133187	C₂²	1	4	yes	complemented
79	C₂×#13133185	C₂²	1	4	yes	complemented
80	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
82	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
83	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
84	C₂×#13133179	C₂²	1	2	yes	complemented
85	C₂×#13133179	C₂²	1	2	yes	complemented
86	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
87	C₂×#13133174	C₂²	1	2	yes	complemented
88	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
89	C₅₃×#529	C₂²	1	16	yes	complemented
90	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
91	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
92	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
93	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
94	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
95	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
96	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
97	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
98	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
99	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
100	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
101	C₂⁴×D₅₃	C₂³	1	4	yes	—
102	C₂⁴×D₅₃	C₂³	1	4	yes	—
103	C₂×#11719949	—	4	8	no	—
104	C₂×#11719949	C₂³	1	16	yes	complemented
105	C₂×#11719945	—	4	8	no	—
106	C₂×#11719945	C₂³	1	16	yes	complemented
107	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
108	C₂²×D₂₁₂	—	4	8	no	—
109	C₂²×D₂₁₂	—	4	8	no	—
110	C₂²×D₂₁₂	—	4	8	no	—
111	C₂²×D₂₁₂	—	4	8	no	—
112	C₂²×D₂₁₂	C₂³	1	2	yes	—
113	C₂²×D₂₁₂	C₂³	1	2	yes	—
114	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
115	C₂²×D₂₁₂	C₂³	1	2	yes	—
116	C₂²×D₂₁₂	C₂³	1	2	yes	—
117	C₂²×D₂₁₂	C₂³	1	4	yes	—
118	C₂²×D₂₁₂	C₂³	1	4	yes	—
119	C₂²×D₂₁₂	C₂³	1	2	yes	—
120	C₂²×D₂₁₂	C₂³	1	4	yes	—
121	C₂²×D₂₁₂	C₂³	1	4	yes	—
122	C₂²×D₂₁₂	C₂³	1	4	yes	—
123	C₂²×D₂₁₂	C₂³	1	4	yes	—
124	C₂²×D₂₁₂	C₂³	1	2	yes	—
125	C₂²×D₂₁₂	C₂³	1	16	yes	complemented
126	C₂²×D₂₁₂	C₂³	1	16	yes	complemented
127	C₂²×D₂₁₂	C₂³	1	16	yes	complemented
128	C₂²×D₂₁₂	C₂³	1	16	yes	complemented
129	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
130	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
131	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
132	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
133	C₂×D₄×D₅₃	—	4	8	no	—
134	C₂×D₄×D₅₃	—	4	16	no	—
135	C₂×D₄×D₅₃	C₂³	1	32	yes	complemented
136	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
137	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
138	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
139	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
140	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
141	#13133214	C₂³	1	8	yes	—
142	#13133214	C₂³	1	8	yes	complemented
143	#13133214	C₂³	1	16	yes	complemented
144	#13133214	C₂³	1	16	yes	complemented
145	#13133214	C₂³	1	16	yes	complemented
146	#13133214	C₂³	1	16	yes	complemented
147	#13133213	C₂³	1	16	yes	complemented
148	#13133211	C₂³	1	16	yes	complemented
149	#13133209	C₂³	1	8	yes	complemented
150	#13133206	C₂³	1	16	yes	complemented
151	#13133205	C₂³	1	16	yes	complemented
152	#13133205	C₂³	1	8	yes	complemented
153	#13133202	C₂³	1	32	yes	complemented
154	#13133202	C₂³	1	32	yes	complemented
155	#13133202	C₂³	1	32	yes	complemented
156	#13133202	C₂³	1	32	yes	complemented
157	#13133200	C₂³	1	16	yes	complemented
158	#13133196	C₂³	1	8	yes	complemented
159	#13133192	C₂³	1	32	yes	complemented
160	#13133192	C₂³	1	16	yes	complemented
161	#13133192	C₂³	1	32	yes	complemented
162	#13133192	C₂³	1	16	yes	complemented
163	#13133192	C₂³	1	32	yes	complemented
164	#13133192	C₂³	1	32	yes	complemented
165	#13133191	C₂³	1	8	yes	—
166	#13133191	C₂³	1	16	yes	complemented
167	#13133191	C₂³	1	16	yes	complemented
168	#13133190	C₂³	1	32	yes	complemented
169	#13133190	C₂³	1	32	yes	complemented
170	#13133190	C₂³	1	32	yes	complemented
171	#13133190	C₂³	1	32	yes	complemented
172	#13133187	C₂³	1	32	yes	complemented
173	#13133187	C₂³	1	32	yes	complemented
174	#13133187	C₂³	1	32	yes	complemented
175	#13133187	C₂³	1	32	yes	complemented
176	#13133187	C₂³	1	32	yes	complemented
177	#13133185	C₂³	1	32	yes	complemented
178	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
179	C₄×D₂₁₂	C₂³	1	16	yes	complemented
180	C₄×D₂₁₂	C₂³	1	8	yes	complemented
181	C₄×D₂₁₂	C₂³	1	16	yes	complemented
182	#13133179	C₂³	1	16	yes	complemented
183	#13133179	C₂³	1	16	yes	complemented
184	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
185	#13133174	C₂³	1	16	yes	complemented
186	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
188	C₂×#11719919	C₂³	1	2	yes	—
189	C₂×#11719919	C₂³	1	2	yes	—
190	C₂×#11719919	C₂³	1	2	yes	—
191	C₂×#11719919	C₂³	1	2	yes	—
192	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
193	C₂×#11719921	C₂³	1	4	yes	—
194	C₂×#11719921	C₂³	1	4	yes	—
195	C₂×#11719921	C₂³	1	2	yes	—
196	C₂×#11719921	C₂³	1	2	yes	—
197	C₂×#11719921	C₂³	1	2	yes	—
198	C₂×#11719921	C₂³	1	4	yes	—
199	C₂×#11719921	C₂³	1	4	yes	—
200	C₂×#11719921	C₂³	1	4	yes	—
201	C₂×#11719921	C₂³	1	4	yes	—
202	C₂×#11719921	C₂³	1	2	yes	—
203	C₂²⋊C₄×D₅₃	C₂³	1	32	yes	complemented
204	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
205	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
206	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
207	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
212	#126×C₅₃	C₂³	1	16	yes	complemented
213	#125×C₅₃	C₂³	1	8	yes	complemented
214	#124×C₅₃	C₂³	1	8	yes	complemented
215	#123×C₅₃	C₂³	1	16	yes	complemented
216	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
217	#121×C₅₃	C₂³	1	8	yes	—
218	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
219	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
220	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
221	#117×C₅₃	C₂³	1	16	yes	complemented
222	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
223	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
224	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
226	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
233	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
238	C₂×C₄²×C₅₃	C₂³	1	8	yes	complemented
239	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
240	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
241	C₂³×D₅₃	—	2	16	no	—
242	C₂³×D₅₃	—	4	8	no	—
243	C₂³×D₅₃	—	4	8	no	—
244	C₂³×D₅₃	—	4	8	no	—
245	C₂³×D₅₃	—	4	8	no	—
246	C₂³×D₅₃	—	4	8	no	—
247	C₂³×D₅₃	C₂⁴	1	2	yes	—
248	C₂³×D₅₃	C₂⁴	1	4	yes	—
249	C₂³×D₅₃	C₂⁴	1	4	yes	—
250	C₂³×D₅₃	C₂⁴	1	16	yes	—
251	C₂³×D₅₃	C₂⁴	1	16	yes	—
252	C₂×Q₈×C₅₃	—	2	4	no	—
253	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
254	C₂×D₄×C₅₃	—	2	8	no	—
255	C₂×D₄×C₅₃	—	2	4	no	—
256	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
257	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
258	C₂²×C₄×C₅₃	—	2	4	no	—
259	C₂²×C₄×C₅₃	—	2	4	no	—
260	C₂²×C₄×C₅₃	—	2	4	no	—
261	C₂²×C₄×C₅₃	—	2	8	no	—
262	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
269	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
271	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
273	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
275	C₂×C₂²⋊D₅₃	—	2	8	no	—
276	C₂×C₂²⋊D₅₃	—	4	8	no	—
277	C₂×C₂²⋊D₅₃	—	4	8	no	—
278	C₂×C₂²⋊D₅₃	—	4	8	no	—
279	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
280	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
281	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
282	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
283	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
284	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
285	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
286	#11719949	—	4	32	no	—
287	D₄×D₅₃	—	4	32	no	—
288	D₄×D₅₃	—	4	64	no	—
289	#11719945	—	4	32	no	—
290	C₂×D₂₁₂	—	2	8	no	—
291	C₂×D₂₁₂	—	2	4	no	—
292	C₂×D₂₁₂	—	2	8	no	—
293	C₂×D₂₁₂	—	2	8	no	—
294	C₂×D₂₁₂	—	2	8	no	—
295	C₂×D₂₁₂	—	4	32	no	—
296	C₂×D₂₁₂	—	4	32	no	—
297	C₂×D₂₁₂	—	4	32	no	—
298	C₂×D₂₁₂	—	4	8	no	—
299	C₂×D₂₁₂	—	4	8	no	—
300	C₂×D₂₁₂	—	4	8	no	—
301	C₂×D₂₁₂	—	4	8	no	—
302	C₂×D₂₁₂	—	4	4	no	—
303	C₂×D₂₁₂	—	4	8	no	—
304	C₂×D₂₁₂	—	4	4	no	—
305	C₂×D₂₁₂	—	4	32	no	—
306	C₂×D₂₁₂	—	4	8	no	—
307	C₂×D₂₁₂	C₂⁴	1	8	yes	—
308	C₂×D₂₁₂	C₂⁴	1	8	yes	—
309	C₂×D₂₁₂	C₂⁴	1	4	yes	—
310	C₂×D₂₁₂	C₂⁴	1	8	yes	—
311	C₂×D₂₁₂	C₂⁴	1	8	yes	—
312	C₂×D₂₁₂	C₂⁴	1	16	yes	—
313	C₂×D₂₁₂	C₂⁴	1	16	yes	—
314	C₂×D₂₁₂	C₂⁴	1	8	yes	—
315	C₂×D₂₁₂	C₂⁴	1	16	yes	—
316	C₂×D₂₁₂	C₂⁴	1	16	yes	—
317	C₂×D₂₁₂	C₂⁴	1	16	yes	—
318	C₂×D₂₁₂	C₂⁴	1	16	yes	—
319	C₂×D₂₁₂	C₂⁴	1	8	yes	—
320	C₂×C₄×D₅₃	—	2	8	no	—
321	C₂×C₄×D₅₃	—	4	8	no	—
322	C₂×C₄×D₅₃	—	4	8	no	—
323	C₂×C₄×D₅₃	—	4	8	no	—
324	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
325	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
326	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
327	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
328	C₂×Dic₁₀₆	—	2	4	no	—
329	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
330	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
331	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
332	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
333	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
334	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
335	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
336	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
337	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
338	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
339	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
340	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
341	C₄²×C₅₃	C₂⁴	1	4	yes	—
342	C₄²×C₅₃	C₂⁴	1	4	yes	—
343	C₄²×C₅₃	C₂⁴	1	4	yes	—
344	C₄²×C₅₃	C₂⁴	1	4	yes	—
345	C₄²×C₅₃	C₂⁴	1	8	yes	—
346	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
347	#11719921	C₂⁴	1	16	yes	—
348	#11719921	C₂⁴	1	16	yes	—
349	#11719921	C₂⁴	1	8	yes	—
350	#11719921	C₂⁴	1	8	yes	—
351	#11719921	C₂⁴	1	8	yes	—
352	#11719921	C₂⁴	1	16	yes	—
353	#11719921	C₂⁴	1	16	yes	—
354	#11719921	C₂⁴	1	16	yes	—
355	#11719921	C₂⁴	1	16	yes	—
356	#11719921	C₂⁴	1	8	yes	—
357	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
358	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
359	#11719919	C₂⁴	1	8	yes	—
360	#11719919	C₂⁴	1	8	yes	—
361	#11719919	C₂⁴	1	8	yes	—
362	#11719919	C₂⁴	1	8	yes	—
363	C₄×Dic₅₃	C₂⁴	1	8	yes	—
364	C₂³×C₅₃	—	2	2	no	—
365	C₂³×C₅₃	—	2	2	no	—
366	C₂³×C₅₃	—	2	4	no	—
367	C₂³×C₅₃	—	2	4	no	—
368	C₂³×C₅₃	—	2	4	no	—
369	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
370	C₂³×C₅₃	C₂⁵	1	4	yes	—
371	C₂³×C₅₃	C₂⁵	1	2	yes	—
372	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
373	C₂²×D₅₃	—	2	4	no	—
374	C₂²×D₅₃	—	2	8	no	—
375	C₂²×D₅₃	—	2	8	no	—
376	C₂²×D₅₃	—	2	8	no	—
377	C₂²×D₅₃	—	2	4	no	—
378	C₂²×D₅₃	—	2	8	no	—
379	C₂²×D₅₃	—	2	8	no	—
380	C₂²×D₅₃	—	2	8	no	—
381	C₂²×D₅₃	—	2	4	no	—
382	C₂²×D₅₃	—	2	32	no	—
383	C₂²×D₅₃	—	4	16	no	—
384	C₂²×D₅₃	—	4	16	no	—
385	C₂²×D₅₃	—	4	16	no	—
386	C₂²×D₅₃	—	4	16	no	—
387	C₂²×D₅₃	—	4	16	no	—
388	C₂²×D₅₃	—	8	32	no	—
389	C₂²×D₅₃	—	8	32	no	—
390	C₂²×D₅₃	C₂⁵	1	8	yes	—
391	C₂²×D₅₃	C₂⁵	1	4	yes	—
392	C₂²×D₅₃	C₂⁵	1	8	yes	—
393	Q₈×C₅₃	—	2	8	no	—
394	D₄×C₅₃	—	2	16	no	—
395	D₄×C₅₃	—	2	8	no	—
396	C₂×C₄×C₅₃	—	2	4	no	—
397	C₂×C₄×C₅₃	—	2	4	no	—
398	C₂×C₄×C₅₃	—	2	4	no	—
399	C₂×C₄×C₅₃	—	2	8	no	—
400	C₂×C₄×C₅₃	—	2	2	no	—
401	C₂×C₄×C₅₃	—	2	2	no	—
402	C₂×C₄×C₅₃	—	2	2	no	—
403	C₂×C₄×C₅₃	—	2	2	no	—
404	C₂×C₄×C₅₃	—	2	8	no	—
405	C₂×C₄×C₅₃	—	2	8	no	—
406	C₂×C₄×C₅₃	—	2	16	no	—
407	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
408	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
409	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
410	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
411	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
412	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
413	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
414	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
415	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
416	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
417	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
418	C₂²⋊D₅₃	—	2	16	no	—
419	C₂²⋊D₅₃	—	4	16	no	—
420	C₂²⋊D₅₃	—	4	16	no	—
421	C₂²⋊D₅₃	—	4	16	no	—
422	C₂×Dic₅₃	—	2	4	no	—
423	C₂×Dic₅₃	—	2	4	no	—
424	C₂×Dic₅₃	—	2	4	no	—
425	C₂×Dic₅₃	C₂⁵	1	4	yes	—
426	C₂×Dic₅₃	C₂⁵	1	4	yes	—
427	C₂×Dic₅₃	C₂⁵	1	4	yes	—
428	D₂₁₂	—	2	8	no	—
429	D₂₁₂	—	2	16	no	—
430	D₂₁₂	—	2	16	no	—
431	D₂₁₂	—	2	16	no	—
432	D₂₁₂	—	2	16	no	—
433	D₂₁₂	—	4	16	no	—
434	D₂₁₂	—	4	16	no	—
435	D₂₁₂	—	4	16	no	—
436	D₂₁₂	—	4	8	no	—
437	D₂₁₂	—	4	16	no	—
438	D₂₁₂	—	4	8	no	—
439	D₂₁₂	—	4	16	no	—
440	D₂₁₂	—	4	16	no	—
441	C₄×D₅₃	—	2	16	no	—
442	C₄×D₅₃	—	4	16	no	—
443	C₄×D₅₃	—	4	16	no	—
444	C₄×D₅₃	—	4	16	no	—
445	Dic₁₀₆	—	2	8	no	—
446	C₂×#3543	—	53	1	no	maximal, Sylow
447	C₂²×C₅₃	—	2	2	no	—
448	C₂²×C₅₃	—	2	2	no	—
449	C₂²×C₅₃	—	2	8	no	—
450	C₂²×C₅₃	—	2	4	no	—
451	C₂²×C₅₃	—	2	4	no	—
452	C₂²×C₅₃	—	2	4	no	—
453	C₂²×C₅₃	—	4	8	no	—
454	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
455	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
456	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
457	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
458	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
459	C₂×D₅₃	—	2	4	no	—
460	C₂×D₅₃	—	2	8	no	—
461	C₂×D₅₃	—	2	8	no	—
462	C₂×D₅₃	—	2	8	no	—
463	C₂×D₅₃	—	2	4	no	—
464	C₂×D₅₃	—	2	8	no	—
465	C₂×D₅₃	—	2	8	no	—
466	C₂×D₅₃	—	2	8	no	—
467	C₂×D₅₃	—	2	4	no	—
468	C₂×D₅₃	—	4	16	no	—
469	C₂×D₅₃	—	4	8	no	—
470	C₂×D₅₃	—	4	16	no	—
471	C₂×D₅₃	—	8	32	no	—
472	C₂×D₅₃	—	8	32	no	—
473	C₄×C₅₃	—	2	4	no	—
474	C₄×C₅₃	—	2	4	no	—
475	C₄×C₅₃	—	2	4	no	—
476	C₄×C₅₃	—	2	2	no	—
477	C₄×C₅₃	—	2	2	no	—
478	C₄×C₅₃	—	2	2	no	—
479	C₄×C₅₃	—	2	2	no	—
480	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
481	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
482	Dic₅₃	—	2	4	no	—
483	Dic₅₃	—	2	4	no	—
484	Dic₅₃	—	2	4	no	—
485	#3543	—	53	32	no	—
486	C₂×#560	—	53	4	no	—
487	C₂×#559	—	53	1	no	—
488	C₂×#550	—	53	1	no	—
489	C₂×#550	—	53	1	no	—
490	C₂×#546	—	53	2	no	—
491	C₂×#546	—	53	2	no	—
492	C₂×D₄²	—	53	2	no	—
493	C₂×D₄²	—	53	1	no	—
494	C₂×D₄²	—	53	2	no	—
495	C₂×#540	—	53	2	no	—
496	C₂×#540	—	53	2	no	—
497	C₂×#535	—	53	2	no	—
498	C₂×#535	—	53	2	no	—
499	C₂×#534	—	53	4	no	—
500	C₂²×#127	—	53	1	no	—
501	C₂×#529	—	53	1	no	—
502	C₂×#529	D₅₃	1	1	yes	characteristic, complemented
503	C₂×C₅₃	—	2	4	no	—
504	C₂×C₅₃	—	4	4	no	—
505	C₂×C₅₃	#3543	1	4	yes	complemented
506	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
507	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
508	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
509	D₅₃	—	4	8	no	—
510	D₅₃	—	4	4	no	—
511	D₅₃	—	4	8	no	—
512	C₂²×#41	—	53	2	no	—
513	C₂²×#41	—	53	2	no	—
514	C₂³×D₄	—	53	4	no	—
515	C₂³×D₄	—	53	2	no	—
516	C₂³×D₄	—	53	2	no	—
517	C₂³×D₄	—	53	2	no	—
518	C₂³×D₄	—	53	2	no	—
519	C₂³×D₄	—	53	2	no	—
520	#560	—	53	64	no	—
521	#559	—	53	16	no	—
522	#550	—	53	16	no	—
523	#550	—	53	16	no	—
524	#546	—	53	32	no	—
525	#546	—	53	32	no	—
526	D₄²	—	53	32	no	—
527	D₄²	—	53	16	no	—
528	D₄²	—	53	32	no	—
529	#540	—	53	32	no	—
530	#540	—	53	32	no	—
531	#535	—	53	32	no	—
532	#535	—	53	32	no	—
533	#534	—	53	64	no	—
534	C₂×#127	—	53	2	no	—
535	C₂×#127	—	53	2	no	—
536	C₂×#127	—	53	2	no	—
537	C₂×#127	—	53	1	no	—
538	C₂×#127	—	53	1	no	—
539	C₂×#127	—	53	2	no	—
540	C₂×#127	—	53	2	no	—
541	C₂×#127	—	53	16	no	—
542	#529	—	53	16	no	—
543	#529	C₂×D₅₃	1	16	yes	complemented
544	C₂×#126	—	53	2	no	—
545	C₂×#126	C₂×D₅₃	1	2	yes	complemented
546	C₂×#125	—	53	1	no	—
547	C₂×#125	C₂×D₅₃	1	1	yes	characteristic, complemented
548	C₂×#124	—	53	2	no	—
549	C₂×#124	—	53	1	no	—
550	C₂×#124	—	53	2	no	—
551	C₂×#124	C₂×D₅₃	1	1	yes	characteristic, complemented
552	C₂×#123	—	53	2	no	—
553	C₂×#123	—	53	4	no	—
554	C₂×#123	—	53	4	no	—
555	C₂×#123	—	53	4	no	—
556	C₂×#123	—	53	4	no	—
557	C₂×#123	C₂×D₅₃	1	2	yes	complemented
558	C₂×C₂²⋊Q₈	—	53	1	no	—
559	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
560	C₂×#121	—	53	1	no	—
561	C₂×#121	—	53	2	no	—
562	C₂×#121	—	53	2	no	—
563	C₂×#121	—	53	4	no	—
564	C₂×#121	—	53	4	no	—
565	C₂×#121	—	53	4	no	—
566	C₂×#121	—	53	2	no	—
567	C₂×#121	—	53	2	no	—
568	C₂×#121	—	53	4	no	—
569	C₂×#121	—	53	4	no	—
570	C₂×#121	—	53	4	no	—
571	C₂×#121	—	53	4	no	—
572	C₂×#121	—	53	4	no	—
573	C₂×#121	C₂×D₅₃	1	1	yes	characteristic
574	C₂×#120	—	53	4	no	—
575	C₂×#120	—	53	4	no	—
576	C₂×#120	—	53	4	no	—
577	C₂×#120	—	53	4	no	—
578	C₂×#120	—	53	4	no	—
579	C₂×#120	—	53	4	no	—
580	C₂×C₄×Q₈	—	53	1	no	—
581	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
582	C₂×C₄×D₄	—	53	2	no	—
583	C₂×C₄×D₄	—	53	2	no	—
584	C₂×C₄×D₄	—	53	2	no	—
585	C₂×C₄×D₄	—	53	1	no	—
586	C₂×C₄×D₄	—	53	2	no	—
587	C₂×C₄×D₄	—	53	2	no	—
588	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
589	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
590	C₂×#117	—	53	2	no	—
591	C₂×#117	C₂×D₅₃	1	2	yes	complemented
592	C₂²×C₂²⋊C₄	—	53	4	no	—
593	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
594	C₅₃	C₂×#3543	1	1	yes	characteristic, complemented, Sylow
595	C₂⁵	—	53	4	no	—
596	C₂⁵	—	53	4	no	—
597	C₂×#41	—	53	16	no	—
598	C₂×#41	—	53	16	no	—
599	C₂×#41	—	212	8	no	—
600	C₂×#41	—	212	8	no	—
601	C₂²×Q₈	—	53	1	no	—
602	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
603	C₂²×D₄	—	53	2	no	—
604	C₂²×D₄	—	53	4	no	—
605	C₂²×D₄	—	53	4	no	—
606	C₂²×D₄	—	53	4	no	—
607	C₂²×D₄	—	53	32	no	—
608	C₂²×D₄	—	53	16	no	—
609	C₂²×D₄	—	53	2	no	—
610	C₂²×D₄	—	53	1	no	—
611	C₂²×D₄	—	53	2	no	—
612	C₂²×D₄	—	53	2	no	—
613	C₂²×D₄	—	53	2	no	—
614	C₂²×D₄	—	53	4	no	—
615	C₂²×D₄	—	53	4	no	—
616	C₂²×D₄	—	53	2	no	—
617	C₂²×D₄	—	53	4	no	—
618	C₂²×D₄	—	53	4	no	—
619	C₂²×D₄	—	53	4	no	—
620	C₂²×D₄	—	53	4	no	—
621	C₂²×D₄	—	53	2	no	—
622	C₂²×D₄	—	53	16	no	—
623	C₂²×D₄	—	53	16	no	—
624	C₂²×D₄	—	53	16	no	—
625	C₂²×D₄	—	53	16	no	—
626	C₂²×D₄	—	212	8	no	—
627	C₂²×D₄	—	212	8	no	—
628	C₂²×D₄	—	212	8	no	—
629	C₂²×D₄	—	212	8	no	—
630	C₂²×D₄	—	212	8	no	—
631	C₂²×D₄	—	212	16	no	—
632	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
633	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
634	C₂³×C₄	—	53	2	no	—
635	C₂³×C₄	—	53	4	no	—
636	C₂³×C₄	—	53	4	no	—
637	C₂³×C₄	—	53	4	no	—
638	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
639	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
640	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
641	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
642	#127	—	53	16	no	—
643	#127	—	53	16	no	—
644	#127	—	53	16	no	—
645	#127	—	53	8	no	—
646	#127	—	53	8	no	—
647	#127	—	53	16	no	—
648	#127	—	53	16	no	—
649	#126	—	53	16	no	—
650	#126	C₂²×D₅₃	1	16	yes	complemented
651	#125	—	53	8	no	—
652	#125	C₂²×D₅₃	1	8	yes	complemented
653	#124	—	53	16	no	—
654	#124	—	53	8	no	—
655	#124	—	53	16	no	—
656	#124	C₂²×D₅₃	1	8	yes	complemented
657	#123	—	53	16	no	—
658	#123	—	53	32	no	—
659	#123	—	53	32	no	—
660	#123	—	53	32	no	—
661	#123	—	53	32	no	—
662	#123	C₂²×D₅₃	1	16	yes	complemented
663	C₂²⋊Q₈	—	53	8	no	—
664	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
665	#121	—	53	8	no	—
666	#121	—	53	16	no	—
667	#121	—	53	16	no	—
668	#121	—	53	32	no	—
669	#121	—	53	32	no	—
670	#121	—	53	32	no	—
671	#121	—	53	16	no	—
672	#121	—	53	16	no	—
673	#121	—	53	32	no	—
674	#121	—	53	32	no	—
675	#121	—	53	32	no	—
676	#121	—	53	32	no	—
677	#121	—	53	32	no	—
678	#121	C₂²×D₅₃	1	8	yes	—
679	#120	—	53	32	no	—
680	#120	—	53	32	no	—
681	#120	—	53	32	no	—
682	#120	—	53	32	no	—
683	#120	—	53	32	no	—
684	#120	—	53	32	no	—
685	C₄×Q₈	—	53	8	no	—
686	C₄×Q₈	C₂²×D₅₃	1	8	yes	complemented
687	C₄×D₄	—	53	16	no	—
688	C₄×D₄	—	53	16	no	—
689	C₄×D₄	—	53	16	no	—
690	C₄×D₄	—	53	8	no	—
691	C₄×D₄	—	53	16	no	—
692	C₄×D₄	—	53	16	no	—
693	C₄×D₄	C₂²×D₅₃	1	16	yes	complemented
694	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
695	#117	—	53	16	no	—
696	#117	C₂²×D₅₃	1	16	yes	complemented
697	C₂×C₄⋊C₄	—	53	2	no	—
698	C₂×C₄⋊C₄	—	53	2	no	—
699	C₂×C₄⋊C₄	—	53	1	no	—
700	C₂×C₄⋊C₄	—	53	1	no	—
701	C₂×C₄⋊C₄	—	53	2	no	—
702	C₂×C₄⋊C₄	—	53	2	no	—
703	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
704	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
705	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
708	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
709	C₂×C₂²⋊C₄	—	53	2	no	—
710	C₂×C₂²⋊C₄	—	53	4	no	—
711	C₂×C₂²⋊C₄	—	53	4	no	—
712	C₂×C₂²⋊C₄	—	53	2	no	—
713	C₂×C₂²⋊C₄	—	53	2	no	—
714	C₂×C₂²⋊C₄	—	53	2	no	—
715	C₂×C₂²⋊C₄	—	53	2	no	—
716	C₂×C₂²⋊C₄	—	53	4	no	—
717	C₂×C₂²⋊C₄	—	53	4	no	—
718	C₂×C₂²⋊C₄	—	53	4	no	—
719	C₂×C₂²⋊C₄	—	53	4	no	—
720	C₂×C₂²⋊C₄	—	53	32	no	—
721	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
726	C₂×C₄²	—	53	2	no	—
727	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
728	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
729	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
730	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
731	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
732	C₂×C₄²	C₂²×D₅₃	1	8	yes	complemented
733	C₂⁴	—	53	2	no	—
734	C₂⁴	—	53	4	no	—
735	C₂⁴	—	53	4	no	—
736	C₂⁴	—	53	16	no	—
737	C₂⁴	—	53	16	no	—
738	C₂⁴	—	106	16	no	—
739	C₂⁴	—	212	8	no	—
740	C₂⁴	—	212	8	no	—
741	C₂⁴	—	212	8	no	—
742	C₂⁴	—	212	8	no	—
743	C₂⁴	—	212	8	no	—
744	C₂⁴	C₂³×D₅₃	1	2	yes	—
745	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
746	#41	—	212	32	no	—
747	#41	—	212	32	no	—
748	C₂×Q₈	—	2	4	no	—
749	C₂×Q₈	—	53	4	no	—
750	C₂×Q₈	—	106	4	no	—
751	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
752	C₂×D₄	—	2	8	no	—
753	C₂×D₄	—	2	4	no	—
754	C₂×D₄	—	53	8	no	—
755	C₂×D₄	—	53	16	no	—
756	C₂×D₄	—	53	16	no	—
757	C₂×D₄	—	53	16	no	—
758	C₂×D₄	—	53	8	no	—
759	C₂×D₄	—	53	4	no	—
760	C₂×D₄	—	53	8	no	—
761	C₂×D₄	—	53	8	no	—
762	C₂×D₄	—	53	8	no	—
763	C₂×D₄	—	53	16	no	—
764	C₂×D₄	—	53	16	no	—
765	C₂×D₄	—	53	8	no	—
766	C₂×D₄	—	53	16	no	—
767	C₂×D₄	—	53	16	no	—
768	C₂×D₄	—	53	16	no	—
769	C₂×D₄	—	53	16	no	—
770	C₂×D₄	—	53	8	no	—
771	C₂×D₄	—	106	8	no	—
772	C₂×D₄	—	106	4	no	—
773	C₂×D₄	—	106	8	no	—
774	C₂×D₄	—	106	8	no	—
775	C₂×D₄	—	106	8	no	—
776	C₂×D₄	—	106	8	no	—
777	C₂×D₄	—	212	32	no	—
778	C₂×D₄	—	212	32	no	—
779	C₂×D₄	—	212	32	no	—
780	C₂×D₄	—	212	8	no	—
781	C₂×D₄	—	212	32	no	—
782	C₂×D₄	—	212	8	no	—
783	C₂×D₄	—	212	8	no	—
784	C₂×D₄	—	212	4	no	—
785	C₂×D₄	—	212	8	no	—
786	C₂×D₄	—	212	4	no	—
787	C₂×D₄	—	212	8	no	—
788	C₂×D₄	—	212	8	no	—
789	C₂×D₄	—	212	32	no	—
790	C₂×D₄	—	212	8	no	—
791	C₂×D₄	—	212	8	no	—
792	C₂×D₄	—	212	8	no	—
793	C₂×D₄	—	212	64	no	—
794	C₂×D₄	C₂³×D₅₃	1	8	yes	—
795	C₂×D₄	C₂³×D₅₃	1	4	yes	—
796	C₂²×C₄	—	2	4	no	—
797	C₂²×C₄	—	2	4	no	—
798	C₂²×C₄	—	2	4	no	—
799	C₂²×C₄	—	2	8	no	—
800	C₂²×C₄	—	53	2	no	—
801	C₂²×C₄	—	53	2	no	—
802	C₂²×C₄	—	53	2	no	—
803	C₂²×C₄	—	53	8	no	—
804	C₂²×C₄	—	53	16	no	—
805	C₂²×C₄	—	53	16	no	—
806	C₂²×C₄	—	53	16	no	—
807	C₂²×C₄	—	106	8	no	—
808	C₂²×C₄	—	212	8	no	—
809	C₂²×C₄	—	212	8	no	—
810	C₂²×C₄	—	212	8	no	—
811	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
812	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
813	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
814	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
815	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
816	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
817	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
818	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
819	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
820	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
821	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
822	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
823	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
824	C₄⋊C₄	—	53	8	no	—
825	C₄⋊C₄	—	53	8	no	—
826	C₄⋊C₄	—	53	4	no	—
827	C₄⋊C₄	—	53	4	no	—
828	C₄⋊C₄	—	53	8	no	—
829	C₄⋊C₄	—	53	8	no	—
830	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
831	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
832	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
833	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
834	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
835	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
836	C₂²⋊C₄	—	53	8	no	—
837	C₂²⋊C₄	—	53	16	no	—
838	C₂²⋊C₄	—	53	16	no	—
839	C₂²⋊C₄	—	53	8	no	—
840	C₂²⋊C₄	—	53	8	no	—
841	C₂²⋊C₄	—	53	8	no	—
842	C₂²⋊C₄	—	53	8	no	—
843	C₂²⋊C₄	—	53	16	no	—
844	C₂²⋊C₄	—	53	16	no	—
845	C₂²⋊C₄	—	53	16	no	—
846	C₂²⋊C₄	—	53	16	no	—
847	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
848	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
849	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
850	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
851	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
852	C₄²	—	53	8	no	—
853	C₄²	C₂³×D₅₃	1	4	yes	—
854	C₄²	C₂³×D₅₃	1	4	yes	—
855	C₄²	C₂³×D₅₃	1	4	yes	—
856	C₄²	C₂³×D₅₃	1	4	yes	—
857	C₄²	C₂³×D₅₃	1	8	yes	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	4	no	—
861	C₂³	—	2	4	no	—
862	C₂³	—	2	4	no	—
863	C₂³	—	53	4	no	—
864	C₂³	—	53	8	no	—
865	C₂³	—	53	8	no	—
866	C₂³	—	106	32	no	—
867	C₂³	—	106	4	no	—
868	C₂³	—	106	8	no	—
869	C₂³	—	106	8	no	—
870	C₂³	—	106	8	no	—
871	C₂³	—	106	4	no	—
872	C₂³	—	106	4	no	—
873	C₂³	—	106	8	no	—
874	C₂³	—	106	8	no	—
875	C₂³	—	106	8	no	—
876	C₂³	—	424	32	no	—
877	C₂³	—	424	32	no	—
878	C₂³	—	212	16	no	—
879	C₂³	—	212	16	no	—
880	C₂³	—	212	16	no	—
881	C₂³	—	212	16	no	—
882	C₂³	—	212	16	no	—
883	C₂³	#13133263	1	4	yes	—
884	C₂³	C₂⁴×D₅₃	1	4	yes	—
885	C₂³	C₂⁴×D₅₃	1	2	yes	—
886	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
887	Q₈	—	2	8	no	—
888	Q₈	—	106	8	no	—
889	D₄	—	2	16	no	—
890	D₄	—	2	8	no	—
891	D₄	—	106	16	no	—
892	D₄	—	106	8	no	—
893	D₄	—	106	16	no	—
894	D₄	—	106	16	no	—
895	D₄	—	106	16	no	—
896	D₄	—	106	16	no	—
897	D₄	—	212	16	no	—
898	D₄	—	212	16	no	—
899	D₄	—	212	16	no	—
900	D₄	—	212	8	no	—
901	D₄	—	212	16	no	—
902	D₄	—	212	8	no	—
903	D₄	—	212	16	no	—
904	D₄	—	212	16	no	—
905	D₄	—	212	16	no	—
906	D₄	—	212	16	no	—
907	D₄	—	212	16	no	—
908	C₂×C₄	—	2	4	no	—
909	C₂×C₄	—	2	8	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	4	no	—
915	C₂×C₄	—	2	4	no	—
916	C₂×C₄	—	2	8	no	—
917	C₂×C₄	—	2	8	no	—
918	C₂×C₄	—	2	16	no	—
919	C₂×C₄	—	53	4	no	—
920	C₂×C₄	—	53	4	no	—
921	C₂×C₄	—	53	4	no	—
922	C₂×C₄	—	106	4	no	—
923	C₂×C₄	—	106	4	no	—
924	C₂×C₄	—	106	4	no	—
925	C₂×C₄	—	106	16	no	—
926	C₂×C₄	—	212	16	no	—
927	C₂×C₄	—	212	16	no	—
928	C₂×C₄	—	212	16	no	—
929	C₂×C₄	#13133263	1	4	yes	—
930	C₂×C₄	#13133263	1	4	yes	—
931	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
932	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
933	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
934	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
935	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
936	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
937	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
938	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
939	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
940	C₂²	—	2	8	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	4	no	—
944	C₂²	—	2	4	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	4	8	no	—
947	C₂²	—	106	4	no	—
948	C₂²	—	106	8	no	—
949	C₂²	—	106	8	no	—
950	C₂²	—	106	8	no	—
951	C₂²	—	106	4	no	—
952	C₂²	—	106	4	no	—
953	C₂²	—	106	8	no	—
954	C₂²	—	106	8	no	—
955	C₂²	—	106	8	no	—
956	C₂²	—	424	32	no	—
957	C₂²	—	424	32	no	—
958	C₂²	—	212	8	no	—
959	C₂²	—	212	16	no	—
960	C₂²	—	212	16	no	—
961	C₂²	C₂×#13133263	1	4	yes	—
962	C₂²	C₂×#13133263	1	2	yes	—
963	C₂²	C₂×#13133263	1	2	yes	—
964	C₂²	C₂×#13133263	1	2	yes	—
965	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
966	C₄	—	2	4	no	—
967	C₄	—	2	2	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	2	no	—
970	C₄	—	2	2	no	—
971	C₄	—	2	4	no	—
972	C₄	—	2	4	no	—
973	C₄	—	106	4	no	—
974	C₄	—	106	4	no	—
975	C₄	—	106	4	no	—
976	C₄	C₂×#13133263	1	4	yes	—
977	C₄	C₂×#13133263	1	4	yes	—
978	C₂	—	2	4	no	—
979	C₂	—	4	4	no	—
980	C₂	—	212	4	no	—
981	C₂	—	212	8	no	—
982	C₂	—	212	8	no	—
983	C₂	#20289045	1	4	yes	direct product factor
984	C₂	C₂²×#13133263	1	1	yes	characteristic
985	C₂	C₂²×#13133263	1	1	yes	characteristic
986	C₂	C₂²×#13133263	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#529	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×#529	D₅₃
hypocenter	C₅₃	C₂×#3543
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #20289045	C₂	direct (N × H)
2. C₂×#16811364	C₂	semidirect
3. C₂×#16811358	C₂	semidirect
4. C₂×#16811295	C₂	semidirect
5. C₂×#16811294	C₂	semidirect
6. C₂×#16811269	C₂	semidirect
7. C₂×#16811264	C₂	semidirect
8. C₂×D₄×D₂₁₂	C₂	semidirect
9. C₂×D₄×D₂₁₂	C₂	semidirect
10. C₂×#16811257	C₂	semidirect
11. C₂×#16811229	C₂	semidirect
12. C₂×#16811228	C₂	semidirect
13. C₂×#16811192	C₂	semidirect
14. C₂×#16811191	C₂	semidirect
15. C₂×#16811184	C₂	semidirect
16. C₂²×#13133214	C₂	semidirect
17. C₂×#16811157	C₂	semidirect
18. C₂×C₅₃×#529	C₂	semidirect
19. C₂²×#11719949	C₂²	semidirect
20. C₂²×#11719945	C₂²	semidirect
21. C₂³×D₂₁₂	C₂²	semidirect
22. C₂³×D₂₁₂	C₂²	semidirect
23. C₂³×D₂₁₂	C₂²	semidirect
24. C₂³×D₂₁₂	C₂²	semidirect
25. C₂²×D₄×D₅₃	C₂²	semidirect
26. C₂²×D₄×D₅₃	C₂²	semidirect
27. #16811364	C₂²	semidirect
28. #16811358	C₂²	semidirect
29. #16811295	C₂²	semidirect
30. #16811294	C₂²	semidirect
31. #16811269	C₂²	semidirect
32. #16811264	C₂²	semidirect
33. D₄×D₂₁₂	C₂²	semidirect
34. D₄×D₂₁₂	C₂²	semidirect
35. #16811257	C₂²	semidirect
36. #16811229	C₂²	semidirect
37. #16811228	C₂²	semidirect
38. #16811192	C₂²	semidirect
39. #16811191	C₂²	semidirect
40. #16811184	C₂²	semidirect
42. C₂×#13133214	C₂²	semidirect
43. C₂×#13133214	C₂²	semidirect
44. C₂×#13133214	C₂²	semidirect
45. C₂×#13133214	C₂²	semidirect
46. C₂×#13133214	C₂²	semidirect
47. C₂×#13133214	C₂²	semidirect
48. C₂×#13133213	C₂²	semidirect
49. #16811157	C₂²	semidirect
50. C₂×#13133211	C₂²	semidirect
51. C₂×#13133209	C₂²	semidirect
52. C₂×#13133206	C₂²	semidirect
53. C₂×#13133205	C₂²	semidirect
54. C₂×#13133205	C₂²	semidirect
55. C₂×#13133202	C₂²	semidirect
56. C₂×#13133202	C₂²	semidirect
57. C₂×#13133202	C₂²	semidirect
58. C₂×#13133202	C₂²	semidirect
59. C₂×#13133200	C₂²	semidirect
60. C₂×#13133196	C₂²	semidirect
61. C₂×#13133192	C₂²	semidirect
62. C₂×#13133192	C₂²	semidirect
63. C₂×#13133192	C₂²	semidirect
64. C₂×#13133192	C₂²	semidirect
65. C₂×#13133192	C₂²	semidirect
66. C₂×#13133192	C₂²	semidirect
68. C₂×#13133191	C₂²	semidirect
69. C₂×#13133191	C₂²	semidirect
70. C₂×#13133190	C₂²	semidirect
71. C₂×#13133190	C₂²	semidirect
72. C₂×#13133190	C₂²	semidirect
73. C₂×#13133190	C₂²	semidirect
74. C₂×#13133187	C₂²	semidirect
75. C₂×#13133187	C₂²	semidirect
76. C₂×#13133187	C₂²	semidirect
77. C₂×#13133187	C₂²	semidirect
78. C₂×#13133187	C₂²	semidirect
79. C₂×#13133185	C₂²	semidirect
80. C₂×C₄×Dic₁₀₆	C₂²	semidirect
81. C₂×C₄×D₂₁₂	C₂²	semidirect
82. C₂×C₄×D₂₁₂	C₂²	semidirect
83. C₂×C₄×D₂₁₂	C₂²	semidirect
84. C₂×#13133179	C₂²	semidirect
85. C₂×#13133179	C₂²	semidirect
86. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
87. C₂×#13133174	C₂²	semidirect
88. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
89. C₅₃×#529	C₂²	semidirect
90. C₂×#126×C₅₃	C₂²	semidirect
91. C₂×#125×C₅₃	C₂²	semidirect
92. C₂×#124×C₅₃	C₂²	semidirect
93. C₂×#123×C₅₃	C₂²	semidirect
94. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
96. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
97. C₂×C₄×D₄×C₅₃	C₂²	semidirect
98. C₂×C₄×D₄×C₅₃	C₂²	semidirect
99. C₂×#117×C₅₃	C₂²	semidirect
100. C₂²×C₄²×C₅₃	C₂²	semidirect
104. C₂×#11719949	C₂³	semidirect
106. C₂×#11719945	C₂³	semidirect
125. C₂²×D₂₁₂	C₂³	semidirect
126. C₂²×D₂₁₂	C₂³	semidirect
127. C₂²×D₂₁₂	C₂³	semidirect
128. C₂²×D₂₁₂	C₂³	semidirect
135. C₂×D₄×D₅₃	C₂³	semidirect
136. C₂×D₄×D₅₃	C₂³	semidirect
142. #13133214	C₂³	semidirect
143. #13133214	C₂³	semidirect
144. #13133214	C₂³	semidirect
145. #13133214	C₂³	semidirect
146. #13133214	C₂³	semidirect
147. #13133213	C₂³	semidirect
148. #13133211	C₂³	semidirect
149. #13133209	C₂³	semidirect
150. #13133206	C₂³	semidirect
151. #13133205	C₂³	semidirect
152. #13133205	C₂³	semidirect
153. #13133202	C₂³	semidirect
154. #13133202	C₂³	semidirect
155. #13133202	C₂³	semidirect
156. #13133202	C₂³	semidirect
157. #13133200	C₂³	semidirect
158. #13133196	C₂³	semidirect
159. #13133192	C₂³	semidirect
160. #13133192	C₂³	semidirect
161. #13133192	C₂³	semidirect
162. #13133192	C₂³	semidirect
163. #13133192	C₂³	semidirect
164. #13133192	C₂³	semidirect
166. #13133191	C₂³	semidirect
167. #13133191	C₂³	semidirect
168. #13133190	C₂³	semidirect
169. #13133190	C₂³	semidirect
170. #13133190	C₂³	semidirect
171. #13133190	C₂³	semidirect
172. #13133187	C₂³	semidirect
173. #13133187	C₂³	semidirect
174. #13133187	C₂³	semidirect
175. #13133187	C₂³	semidirect
176. #13133187	C₂³	semidirect
177. #13133185	C₂³	semidirect
178. C₄×Dic₁₀₆	C₂³	semidirect
179. C₄×D₂₁₂	C₂³	semidirect
180. C₄×D₂₁₂	C₂³	semidirect
181. C₄×D₂₁₂	C₂³	semidirect
182. #13133179	C₂³	semidirect
183. #13133179	C₂³	semidirect
184. C₄×C₂²⋊D₅₃	C₂³	semidirect
185. #13133174	C₂³	semidirect
203. C₂²⋊C₄×D₅₃	C₂³	semidirect
212. #126×C₅₃	C₂³	semidirect
213. #125×C₅₃	C₂³	semidirect
214. #124×C₅₃	C₂³	semidirect
215. #123×C₅₃	C₂³	semidirect
216. C₂²⋊Q₈×C₅₃	C₂³	semidirect
218. C₄×Q₈×C₅₃	C₂³	semidirect
219. C₄×D₄×C₅₃	C₂³	semidirect
220. C₄×D₄×C₅₃	C₂³	semidirect
221. #117×C₅₃	C₂³	semidirect
238. C₂×C₄²×C₅₃	C₂³	semidirect
502. C₂×#529	D₅₃	semidirect
505. C₂×C₅₃	#3543	semidirect
543. #529	C₂×D₅₃	semidirect
545. C₂×#126	C₂×D₅₃	semidirect
547. C₂×#125	C₂×D₅₃	semidirect
551. C₂×#124	C₂×D₅₃	semidirect
557. C₂×#123	C₂×D₅₃	semidirect
559. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
581. C₂×C₄×Q₈	C₂×D₅₃	semidirect
588. C₂×C₄×D₄	C₂×D₅₃	semidirect
589. C₂×C₄×D₄	C₂×D₅₃	semidirect
591. C₂×#117	C₂×D₅₃	semidirect
593. C₂²×C₄²	C₂×D₅₃	semidirect
594. C₅₃	C₂×#3543	semidirect
650. #126	C₂²×D₅₃	semidirect
652. #125	C₂²×D₅₃	semidirect
656. #124	C₂²×D₅₃	semidirect
662. #123	C₂²×D₅₃	semidirect
664. C₂²⋊Q₈	C₂²×D₅₃	semidirect
686. C₄×Q₈	C₂²×D₅₃	semidirect
693. C₄×D₄	C₂²×D₅₃	semidirect
694. C₄×D₄	C₂²×D₅₃	semidirect
696. #117	C₂²×D₅₃	semidirect
732. C₂×C₄²	C₂²×D₅₃	semidirect
983. C₂	#20289045	direct (N × H)

Maximal subgroups

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

subgroup	index
#20289045	2
C₂×#16811364	2
C₂×#16811358	2
C₂×#16811295	2
C₂×#16811294	2
C₂×#16811269	2
C₂×#16811264	2
C₂×D₄×D₂₁₂	2
C₂×#16811257	2
C₂×#16811229	2
C₂×#16811228	2
C₂×#16811192	2
C₂×#16811191	2
C₂×#16811184	2
C₂²×#13133214	2
C₂×#16811157	2
C₂×C₅₃×#529	2
C₂×#3543	53

Subgroups — C2×#20289045 #28291682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20289045 #28291682