Subgroups — C₂×C₅₃×#3555 #27270263

Order 13568.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3555	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₅₃×#563	C₂	1	4	yes	maximal, complemented
3	C₂×Q₈²×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₃×#557	C₂	1	2	yes	maximal, complemented
5	C₂×C₅₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×#556	C₂	1	2	yes	maximal, complemented
7	C₂×C₅₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#556	C₂	1	2	yes	maximal, complemented
9	C₂×C₅₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#552	C₂	1	2	yes	maximal, complemented
11	C₂×C₅₃×#544	C₂	1	2	yes	maximal, complemented
12	C₂×C₅₃×#542	C₂	1	2	yes	maximal
13	C₂×C₅₃×#541	C₂	1	2	yes	maximal, complemented
14	C₂×C₅₃×#541	C₂	1	2	yes	maximal, complemented
15	C₂×C₅₃×#541	C₂	1	4	yes	maximal, complemented
16	C₂×C₅₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic
19	C₅₃×#563	C₂²	1	64	yes	complemented
20	Q₈²×C₅₃	C₂²	1	16	yes	complemented
21	C₅₃×#557	C₂²	1	16	yes	complemented
22	C₅₃×#557	C₂²	1	32	yes	complemented
23	C₅₃×#556	C₂²	1	32	yes	complemented
24	C₅₃×#556	C₂²	1	32	yes	complemented
25	C₅₃×#556	C₂²	1	16	yes	complemented
26	C₅₃×#554	C₂²	1	16	yes	complemented
27	C₅₃×#552	C₂²	1	32	yes	complemented
28	C₅₃×#544	C₂²	1	32	yes	complemented
29	C₅₃×#542	C₂²	1	32	yes	—
30	C₅₃×#541	C₂²	1	32	yes	complemented
31	C₅₃×#541	C₂²	1	32	yes	complemented
32	C₅₃×#541	C₂²	1	64	yes	complemented
33	C₅₃×#533	C₂²	1	16	yes	complemented
34	C₅₃×#533	C₂²	1	16	yes	complemented
35	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	—
37	C₂×C₄⋊Q₈×C₅₃	C₂²	1	4	yes	—
38	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	—
39	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	—
41	C₂×C₄⋊Q₈×C₅₃	C₂²	1	4	yes	—
42	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
44	C₅₃×#529	C₂²	1	16	yes	—
45	C₂×#126×C₅₃	C₂²	1	4	yes	—
46	C₂×#126×C₅₃	C₂²	1	2	yes	—
47	C₂×#126×C₅₃	C₂²	1	4	yes	—
48	C₂×#126×C₅₃	C₂²	1	4	yes	—
49	C₂×#126×C₅₃	C₂²	1	4	yes	—
50	C₂×#126×C₅₃	C₂²	1	4	yes	—
51	C₂×#126×C₅₃	C₂²	1	4	yes	—
52	C₂×#125×C₅₃	C₂²	1	4	yes	—
53	C₂×#125×C₅₃	C₂²	1	4	yes	—
54	C₂×#125×C₅₃	C₂²	1	2	yes	—
55	C₂×#125×C₅₃	C₂²	1	2	yes	—
56	C₂×#125×C₅₃	C₂²	1	4	yes	—
57	C₂×#125×C₅₃	C₂²	1	2	yes	—
58	C₂×#125×C₅₃	C₂²	1	4	yes	—
59	C₂×#125×C₅₃	C₂²	1	4	yes	—
60	C₂×#125×C₅₃	C₂²	1	2	yes	—
61	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
62	C₂×#124×C₅₃	C₂²	1	2	yes	—
63	C₂×#124×C₅₃	C₂²	1	4	yes	—
64	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
65	C₂×#123×C₅₃	C₂²	1	4	yes	—
66	C₂×#123×C₅₃	C₂²	1	2	yes	—
67	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
68	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
69	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
70	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
71	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
72	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
73	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
74	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
75	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
76	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
77	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
78	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
79	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
80	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
81	C₂×C₄×Q₈×C₅₃	C₂²	1	4	yes	—
82	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
83	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
84	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
85	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
86	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
87	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
88	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
89	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
90	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
91	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
92	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
93	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
94	C₂×#117×C₅₃	C₂²	1	2	yes	—
95	C₂×#117×C₅₃	C₂²	1	2	yes	—
96	C₂×#117×C₅₃	C₂²	1	4	yes	—
97	C₂×#117×C₅₃	C₂²	1	2	yes	—
98	C₂×#117×C₅₃	C₂²	1	2	yes	—
99	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
100	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
101	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
104	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
105	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
106	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
107	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
108	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
113	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
115	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	—
116	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	—
117	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	—
118	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	—
119	C₄⋊Q₈×C₅₃	C₂³	1	16	yes	—
120	C₄⋊Q₈×C₅₃	C₂³	1	32	yes	—
121	C₄⋊Q₈×C₅₃	C₂³	1	16	yes	—
122	C₄⋊Q₈×C₅₃	C₂³	1	16	yes	—
123	C₄⋊Q₈×C₅₃	C₂³	1	32	yes	—
124	#126×C₅₃	C₂³	1	16	yes	—
125	#126×C₅₃	C₂³	1	32	yes	—
126	#126×C₅₃	C₂³	1	32	yes	—
127	#126×C₅₃	C₂³	1	32	yes	—
128	#126×C₅₃	C₂³	1	32	yes	—
129	#126×C₅₃	C₂³	1	32	yes	—
130	#126×C₅₃	C₂³	1	32	yes	—
131	#125×C₅₃	C₂³	1	8	yes	—
132	#125×C₅₃	C₂³	1	16	yes	—
133	#125×C₅₃	C₂³	1	16	yes	—
134	#125×C₅₃	C₂³	1	32	yes	—
135	#125×C₅₃	C₂³	1	32	yes	—
136	#125×C₅₃	C₂³	1	32	yes	—
137	#125×C₅₃	C₂³	1	16	yes	—
138	#125×C₅₃	C₂³	1	32	yes	—
139	#125×C₅₃	C₂³	1	32	yes	—
140	#125×C₅₃	C₂³	1	16	yes	—
141	#124×C₅₃	C₂³	1	8	yes	—
142	#124×C₅₃	C₂³	1	16	yes	—
143	#124×C₅₃	C₂³	1	32	yes	—
144	#123×C₅₃	C₂³	1	16	yes	—
145	#123×C₅₃	C₂³	1	32	yes	—
146	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
147	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
148	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
149	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
150	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
151	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
152	C₂²⋊Q₈×C₅₃	C₂³	1	32	yes	—
153	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
154	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
155	C₂²⋊Q₈×C₅₃	C₂³	1	32	yes	—
156	C₂²⋊Q₈×C₅₃	C₂³	1	32	yes	—
157	#121×C₅₃	C₂³	1	8	yes	—
158	C₄×Q₈×C₅₃	C₂³	1	8	yes	—
159	C₄×Q₈×C₅₃	C₂³	1	16	yes	—
160	C₄×Q₈×C₅₃	C₂³	1	8	yes	—
161	C₄×Q₈×C₅₃	C₂³	1	16	yes	—
162	C₄×Q₈×C₅₃	C₂³	1	16	yes	—
163	C₄×Q₈×C₅₃	C₂³	1	8	yes	—
164	C₄×Q₈×C₅₃	C₂³	1	16	yes	—
165	C₄×Q₈×C₅₃	C₂³	1	16	yes	—
166	C₄×Q₈×C₅₃	C₂³	1	16	yes	—
167	C₄×Q₈×C₅₃	C₂³	1	32	yes	—
168	C₄×Q₈×C₅₃	C₂³	1	16	yes	—
169	C₄×Q₈×C₅₃	C₂³	1	16	yes	—
170	C₄×D₄×C₅₃	C₂³	1	16	yes	—
171	C₄×D₄×C₅₃	C₂³	1	8	yes	—
172	C₄×D₄×C₅₃	C₂³	1	16	yes	—
173	#117×C₅₃	C₂³	1	16	yes	—
174	#117×C₅₃	C₂³	1	16	yes	—
175	#117×C₅₃	C₂³	1	16	yes	—
176	#117×C₅₃	C₂³	1	32	yes	—
177	#117×C₅₃	C₂³	1	16	yes	—
178	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
181	C₂×C₄⋊C₄×C₅₃	C₂³	1	16	yes	—
182	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
188	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
197	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
198	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
199	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
200	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
201	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
204	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
206	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
207	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
208	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
213	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
215	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
216	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
218	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
219	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₅₃	C₂³	1	8	yes	—
224	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
225	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
226	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
227	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
228	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
229	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
230	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
231	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
232	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
233	C₂×Q₈×C₅₃	—	2	4	no	—
234	C₂×Q₈×C₅₃	—	2	4	no	—
235	C₂×Q₈×C₅₃	—	2	8	no	—
236	C₂×Q₈×C₅₃	—	2	4	no	—
237	C₂×Q₈×C₅₃	—	4	4	no	—
238	C₂×Q₈×C₅₃	—	4	4	no	—
239	C₂×Q₈×C₅₃	—	4	8	no	—
240	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
241	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
242	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
243	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
244	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
245	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
246	C₂×Q₈×C₅₃	C₂⁴	1	16	yes	—
247	C₂×D₄×C₅₃	—	2	4	no	—
248	C₂×D₄×C₅₃	—	4	4	no	—
249	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
250	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
251	C₂²×C₄×C₅₃	—	2	4	no	—
252	C₂²×C₄×C₅₃	—	2	8	no	—
253	C₂²×C₄×C₅₃	—	2	4	no	—
254	C₂²×C₄×C₅₃	—	4	8	no	—
255	C₂²×C₄×C₅₃	—	4	2	no	—
256	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
257	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
258	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
259	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
271	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
273	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
274	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
276	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
278	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
279	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
280	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
281	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
282	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
283	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
284	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
285	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
286	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
287	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
288	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
289	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
290	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
291	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
292	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
293	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
294	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
295	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
296	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
297	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
298	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
299	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
300	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
301	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
302	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
303	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
304	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
305	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
306	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
307	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
308	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
309	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
310	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
311	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
312	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
313	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
314	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
315	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
316	C₄²×C₅₃	C₂⁴	1	4	yes	—
317	C₄²×C₅₃	C₂⁴	1	4	yes	—
318	C₄²×C₅₃	C₂⁴	1	4	yes	—
319	C₄²×C₅₃	C₂⁴	1	4	yes	—
320	C₄²×C₅₃	C₂⁴	1	16	yes	—
321	C₄²×C₅₃	C₂⁴	1	8	yes	—
322	C₄²×C₅₃	C₂⁴	1	8	yes	—
323	C₄²×C₅₃	C₂⁴	1	8	yes	—
324	C₄²×C₅₃	C₂⁴	1	16	yes	—
325	C₄²×C₅₃	C₂⁴	1	16	yes	—
326	C₄²×C₅₃	C₂⁴	1	16	yes	—
327	C₂³×C₅₃	—	2	2	no	—
328	C₂³×C₅₃	—	2	2	no	—
329	C₂³×C₅₃	—	2	4	no	—
330	C₂³×C₅₃	—	2	4	no	—
331	C₂³×C₅₃	—	2	4	no	—
332	C₂³×C₅₃	—	2	2	no	—
333	C₂³×C₅₃	C₂⁵	1	2	yes	—
334	C₂³×C₅₃	C₂⁵	1	4	yes	—
335	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
336	Q₈×C₅₃	—	2	8	no	—
337	Q₈×C₅₃	—	2	8	no	—
338	Q₈×C₅₃	—	2	8	no	—
339	Q₈×C₅₃	—	2	16	no	—
340	Q₈×C₅₃	—	4	8	no	—
341	Q₈×C₅₃	—	4	8	no	—
342	Q₈×C₅₃	—	4	16	no	—
343	D₄×C₅₃	—	2	8	no	—
344	D₄×C₅₃	—	4	8	no	—
345	C₂×C₄×C₅₃	—	2	2	no	—
346	C₂×C₄×C₅₃	—	2	4	no	—
347	C₂×C₄×C₅₃	—	2	2	no	—
348	C₂×C₄×C₅₃	—	2	4	no	—
349	C₂×C₄×C₅₃	—	2	4	no	—
350	C₂×C₄×C₅₃	—	2	8	no	—
351	C₂×C₄×C₅₃	—	2	4	no	—
352	C₂×C₄×C₅₃	—	2	4	no	—
353	C₂×C₄×C₅₃	—	2	8	no	—
354	C₂×C₄×C₅₃	—	2	2	no	—
355	C₂×C₄×C₅₃	—	2	2	no	—
356	C₂×C₄×C₅₃	—	2	4	no	—
357	C₂×C₄×C₅₃	—	2	4	no	—
358	C₂×C₄×C₅₃	—	2	8	no	—
359	C₂×C₄×C₅₃	—	2	16	no	—
360	C₂×C₄×C₅₃	—	2	8	no	—
361	C₂×C₄×C₅₃	—	4	16	no	—
362	C₂×C₄×C₅₃	—	4	4	no	—
363	C₂×C₄×C₅₃	2₋¹⁺⁴	1	4	yes	—
364	C₂×C₄×C₅₃	2₋¹⁺⁴	1	4	yes	—
365	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
366	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
367	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
368	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
369	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
370	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
371	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
372	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
373	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
374	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
375	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
376	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
377	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
378	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
379	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
380	C₂×#3555	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
381	C₂²×C₅₃	—	2	2	no	—
382	C₂²×C₅₃	—	2	2	no	—
383	C₂²×C₅₃	—	2	4	no	—
384	C₂²×C₅₃	—	2	4	no	—
385	C₂²×C₅₃	—	2	4	no	—
386	C₂²×C₅₃	—	2	2	no	—
387	C₂²×C₅₃	—	4	4	no	—
388	C₂²×C₅₃	—	4	8	no	—
389	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
390	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
391	C₂²×C₅₃	#585	1	2	yes	—
392	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
393	C₄×C₅₃	—	2	2	no	—
394	C₄×C₅₃	—	2	4	no	—
395	C₄×C₅₃	—	2	2	no	—
396	C₄×C₅₃	—	2	4	no	—
397	C₄×C₅₃	—	2	4	no	—
398	C₄×C₅₃	—	2	8	no	—
399	C₄×C₅₃	—	2	4	no	—
400	C₄×C₅₃	—	2	4	no	—
401	C₄×C₅₃	—	2	8	no	—
402	C₄×C₅₃	—	2	2	no	—
403	C₄×C₅₃	—	2	2	no	—
404	C₄×C₅₃	—	2	4	no	—
405	C₄×C₅₃	—	2	4	no	—
406	C₄×C₅₃	C₂×2₋¹⁺⁴	1	4	yes	—
407	C₄×C₅₃	C₂×2₋¹⁺⁴	1	4	yes	—
408	#3555	C₂×C₅₃	1	32	yes	direct product factor
409	C₂×#563	C₂×C₅₃	1	4	yes	complemented
410	C₂×Q₈²	C₂×C₅₃	1	1	yes	characteristic, complemented
411	C₂×#557	C₂×C₅₃	1	1	yes	characteristic, complemented
412	C₂×#557	C₂×C₅₃	1	2	yes	complemented
413	C₂×#556	C₂×C₅₃	1	2	yes	complemented
414	C₂×#556	C₂×C₅₃	1	2	yes	complemented
415	C₂×#556	C₂×C₅₃	1	1	yes	characteristic, complemented
416	C₂×#554	C₂×C₅₃	1	1	yes	characteristic, complemented
417	C₂×#552	C₂×C₅₃	1	2	yes	complemented
418	C₂×#544	C₂×C₅₃	1	2	yes	complemented
419	C₂×#542	C₂×C₅₃	1	2	yes	—
420	C₂×#541	C₂×C₅₃	1	2	yes	complemented
421	C₂×#541	C₂×C₅₃	1	2	yes	complemented
422	C₂×#541	C₂×C₅₃	1	4	yes	complemented
423	C₂×#533	C₂×C₅₃	1	1	yes	characteristic, complemented
424	C₂×#533	C₂×C₅₃	1	1	yes	characteristic, complemented
425	C₂×#529	C₂×C₅₃	1	1	yes	characteristic
426	C₂×C₅₃	—	4	2	no	—
427	C₂×C₅₃	—	4	4	no	—
428	C₂×C₅₃	#3555	1	4	yes	direct product factor
429	C₂×C₅₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
430	C₂×C₅₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
431	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
432	#563	C₂²×C₅₃	1	64	yes	complemented
433	Q₈²	C₂²×C₅₃	1	16	yes	complemented
434	#557	C₂²×C₅₃	1	16	yes	complemented
435	#557	C₂²×C₅₃	1	32	yes	complemented
436	#556	C₂²×C₅₃	1	32	yes	complemented
437	#556	C₂²×C₅₃	1	32	yes	complemented
438	#556	C₂²×C₅₃	1	16	yes	complemented
439	#554	C₂²×C₅₃	1	16	yes	complemented
440	#552	C₂²×C₅₃	1	32	yes	complemented
441	#544	C₂²×C₅₃	1	32	yes	complemented
442	#542	C₂²×C₅₃	1	32	yes	—
443	#541	C₂²×C₅₃	1	32	yes	complemented
444	#541	C₂²×C₅₃	1	32	yes	complemented
445	#541	C₂²×C₅₃	1	64	yes	complemented
446	#533	C₂²×C₅₃	1	16	yes	complemented
447	#533	C₂²×C₅₃	1	16	yes	complemented
448	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
449	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
450	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
451	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
452	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	—
453	C₂×C₄⋊Q₈	C₂²×C₅₃	1	4	yes	—
454	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	—
455	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	—
456	C₂×C₄⋊Q₈	C₂²×C₅₃	1	4	yes	—
457	#529	C₂²×C₅₃	1	16	yes	—
458	C₂×#126	C₂²×C₅₃	1	2	yes	—
459	C₂×#126	C₂²×C₅₃	1	4	yes	—
460	C₂×#126	C₂²×C₅₃	1	4	yes	—
461	C₂×#126	C₂²×C₅₃	1	4	yes	—
462	C₂×#126	C₂²×C₅₃	1	4	yes	—
463	C₂×#126	C₂²×C₅₃	1	4	yes	—
464	C₂×#126	C₂²×C₅₃	1	4	yes	—
465	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
466	C₂×#125	C₂²×C₅₃	1	2	yes	—
467	C₂×#125	C₂²×C₅₃	1	2	yes	—
468	C₂×#125	C₂²×C₅₃	1	4	yes	—
469	C₂×#125	C₂²×C₅₃	1	4	yes	—
470	C₂×#125	C₂²×C₅₃	1	4	yes	—
471	C₂×#125	C₂²×C₅₃	1	2	yes	—
472	C₂×#125	C₂²×C₅₃	1	4	yes	—
473	C₂×#125	C₂²×C₅₃	1	4	yes	—
474	C₂×#125	C₂²×C₅₃	1	2	yes	—
475	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
476	C₂×#124	C₂²×C₅₃	1	2	yes	—
477	C₂×#124	C₂²×C₅₃	1	4	yes	—
478	C₂×#123	C₂²×C₅₃	1	2	yes	—
479	C₂×#123	C₂²×C₅₃	1	4	yes	—
480	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
481	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
482	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
483	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
484	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
485	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
486	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
487	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
488	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
489	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
490	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
491	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
492	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
493	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
494	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
495	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
496	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
497	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
498	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
499	C₂×C₄×Q₈	C₂²×C₅₃	1	4	yes	—
500	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
501	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
502	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
503	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
504	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
505	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
506	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
507	C₂×#117	C₂²×C₅₃	1	2	yes	—
508	C₂×#117	C₂²×C₅₃	1	2	yes	—
509	C₂×#117	C₂²×C₅₃	1	2	yes	—
510	C₂×#117	C₂²×C₅₃	1	4	yes	—
511	C₂×#117	C₂²×C₅₃	1	2	yes	—
512	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
513	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
514	C₅₃	C₂×#3555	1	1	yes	characteristic, direct product factor, Sylow
515	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
516	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
517	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
518	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
519	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
520	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
521	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
522	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
523	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
524	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
525	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
527	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
528	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
529	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	—
530	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	—
531	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	—
532	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	—
533	C₄⋊Q₈	C₂³×C₅₃	1	16	yes	—
534	C₄⋊Q₈	C₂³×C₅₃	1	32	yes	—
535	C₄⋊Q₈	C₂³×C₅₃	1	16	yes	—
536	C₄⋊Q₈	C₂³×C₅₃	1	16	yes	—
537	C₄⋊Q₈	C₂³×C₅₃	1	32	yes	—
538	#126	C₂³×C₅₃	1	16	yes	—
539	#126	C₂³×C₅₃	1	32	yes	—
540	#126	C₂³×C₅₃	1	32	yes	—
541	#126	C₂³×C₅₃	1	32	yes	—
542	#126	C₂³×C₅₃	1	32	yes	—
543	#126	C₂³×C₅₃	1	32	yes	—
544	#126	C₂³×C₅₃	1	32	yes	—
545	#125	C₂³×C₅₃	1	8	yes	—
546	#125	C₂³×C₅₃	1	16	yes	—
547	#125	C₂³×C₅₃	1	16	yes	—
548	#125	C₂³×C₅₃	1	32	yes	—
549	#125	C₂³×C₅₃	1	32	yes	—
550	#125	C₂³×C₅₃	1	32	yes	—
551	#125	C₂³×C₅₃	1	16	yes	—
552	#125	C₂³×C₅₃	1	32	yes	—
553	#125	C₂³×C₅₃	1	32	yes	—
554	#125	C₂³×C₅₃	1	16	yes	—
555	#124	C₂³×C₅₃	1	8	yes	—
556	#124	C₂³×C₅₃	1	16	yes	—
557	#124	C₂³×C₅₃	1	32	yes	—
558	#123	C₂³×C₅₃	1	16	yes	—
559	#123	C₂³×C₅₃	1	32	yes	—
560	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
561	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
562	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
563	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
564	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
565	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
566	C₂²⋊Q₈	C₂³×C₅₃	1	32	yes	—
567	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
568	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
569	C₂²⋊Q₈	C₂³×C₅₃	1	32	yes	—
570	C₂²⋊Q₈	C₂³×C₅₃	1	32	yes	—
571	#121	C₂³×C₅₃	1	8	yes	—
572	C₄×Q₈	C₂³×C₅₃	1	8	yes	—
573	C₄×Q₈	C₂³×C₅₃	1	16	yes	—
574	C₄×Q₈	C₂³×C₅₃	1	8	yes	—
575	C₄×Q₈	C₂³×C₅₃	1	16	yes	—
576	C₄×Q₈	C₂³×C₅₃	1	16	yes	—
577	C₄×Q₈	C₂³×C₅₃	1	8	yes	—
578	C₄×Q₈	C₂³×C₅₃	1	16	yes	—
579	C₄×Q₈	C₂³×C₅₃	1	32	yes	—
580	C₄×Q₈	C₂³×C₅₃	1	16	yes	—
581	C₄×Q₈	C₂³×C₅₃	1	16	yes	—
582	C₄×Q₈	C₂³×C₅₃	1	16	yes	—
583	C₄×Q₈	C₂³×C₅₃	1	16	yes	—
584	C₄×D₄	C₂³×C₅₃	1	16	yes	—
585	C₄×D₄	C₂³×C₅₃	1	8	yes	—
586	C₄×D₄	C₂³×C₅₃	1	16	yes	—
587	#117	C₂³×C₅₃	1	16	yes	—
588	#117	C₂³×C₅₃	1	16	yes	—
589	#117	C₂³×C₅₃	1	16	yes	—
590	#117	C₂³×C₅₃	1	32	yes	—
591	#117	C₂³×C₅₃	1	16	yes	—
592	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
595	C₂×C₄⋊C₄	C₂³×C₅₃	1	16	yes	—
596	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
602	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
611	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
612	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
613	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
614	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
615	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
619	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
621	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
633	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
634	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
636	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
637	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
638	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
639	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
640	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
643	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₅₃	1	8	yes	—
645	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
646	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
647	C₂×Q₈	—	2	4	no	—
648	C₂×Q₈	—	2	4	no	—
649	C₂×Q₈	—	2	4	no	—
650	C₂×Q₈	—	2	8	no	—
651	C₂×Q₈	—	4	4	no	—
652	C₂×Q₈	—	4	4	no	—
653	C₂×Q₈	—	4	8	no	—
654	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
655	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
656	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
657	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
658	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
659	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
660	C₂×Q₈	C₂⁴×C₅₃	1	16	yes	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	4	4	no	—
663	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
664	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
665	C₂²×C₄	—	2	8	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	4	8	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
672	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
680	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
683	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
684	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
686	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
687	C₂²×C₄	C₂⁴×C₅₃	1	16	yes	—
688	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
690	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
691	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
692	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
693	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
694	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
695	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
696	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
697	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
698	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
699	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
700	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
701	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
702	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
703	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
704	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
705	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
706	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
707	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
708	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
709	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
710	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
711	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
712	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
713	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
714	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
715	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
716	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
717	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
718	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
719	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
720	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
721	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
722	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
723	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
724	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
725	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
726	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
727	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
728	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
729	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
730	C₄²	C₂⁴×C₅₃	1	4	yes	—
731	C₄²	C₂⁴×C₅₃	1	4	yes	—
732	C₄²	C₂⁴×C₅₃	1	4	yes	—
733	C₄²	C₂⁴×C₅₃	1	4	yes	—
734	C₄²	C₂⁴×C₅₃	1	16	yes	—
735	C₄²	C₂⁴×C₅₃	1	8	yes	—
736	C₄²	C₂⁴×C₅₃	1	8	yes	—
737	C₄²	C₂⁴×C₅₃	1	8	yes	—
738	C₄²	C₂⁴×C₅₃	1	16	yes	—
739	C₄²	C₂⁴×C₅₃	1	16	yes	—
740	C₄²	C₂⁴×C₅₃	1	16	yes	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	4	no	—
744	C₂³	—	2	4	no	—
745	C₂³	—	2	4	no	—
746	C₂³	—	2	2	no	—
747	C₂³	C₂⁵×C₅₃	1	2	yes	—
748	C₂³	C₂⁵×C₅₃	1	4	yes	—
749	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
750	Q₈	—	2	8	no	—
751	Q₈	—	2	8	no	—
752	Q₈	—	2	8	no	—
753	Q₈	—	2	16	no	—
754	Q₈	—	4	8	no	—
755	Q₈	—	4	8	no	—
756	Q₈	—	4	16	no	—
757	D₄	—	2	8	no	—
758	D₄	—	4	8	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	8	no	—
765	C₂×C₄	—	2	4	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	8	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	4	no	—
771	C₂×C₄	—	2	4	no	—
772	C₂×C₄	—	2	8	no	—
773	C₂×C₄	—	2	16	no	—
774	C₂×C₄	—	2	8	no	—
775	C₂×C₄	—	4	16	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	2₋¹⁺⁴×C₅₃	1	4	yes	—
778	C₂×C₄	2₋¹⁺⁴×C₅₃	1	4	yes	—
779	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
780	C₂×C₄	C₂⁵×C₅₃	1	8	yes	—
781	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
782	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
783	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
784	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
785	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
786	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
787	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
788	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
789	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
790	C₂×C₄	C₂⁵×C₅₃	1	8	yes	—
791	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
792	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
793	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	2	4	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	4	4	no	—
801	C₂²	—	4	8	no	—
802	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	2	yes	—
803	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	2	yes	—
804	C₂²	C₅₃×#585	1	2	yes	—
805	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
806	C₄	—	2	2	no	—
807	C₄	—	2	4	no	—
808	C₄	—	2	2	no	—
809	C₄	—	2	4	no	—
810	C₄	—	2	4	no	—
811	C₄	—	2	8	no	—
812	C₄	—	2	4	no	—
813	C₄	—	2	4	no	—
814	C₄	—	2	8	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	4	no	—
818	C₄	—	2	4	no	—
819	C₄	C₂×2₋¹⁺⁴×C₅₃	1	4	yes	—
820	C₄	C₂×2₋¹⁺⁴×C₅₃	1	4	yes	—
821	C₂	—	4	2	no	—
822	C₂	—	4	4	no	—
823	C₂	C₅₃×#3555	1	4	yes	direct product factor
824	C₂	C₂²×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
825	C₂	C₂²×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
826	C₂	C₂×C₅₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅₃
prime radical	C₂×#121×C₅₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3555	C₂	direct (N × H)
2. C₂×C₅₃×#563	C₂	semidirect
3. C₂×Q₈²×C₅₃	C₂	semidirect
4. C₂×C₅₃×#557	C₂	semidirect
5. C₂×C₅₃×#557	C₂	semidirect
6. C₂×C₅₃×#556	C₂	semidirect
7. C₂×C₅₃×#556	C₂	semidirect
8. C₂×C₅₃×#556	C₂	semidirect
9. C₂×C₅₃×#554	C₂	semidirect
10. C₂×C₅₃×#552	C₂	semidirect
11. C₂×C₅₃×#544	C₂	semidirect
13. C₂×C₅₃×#541	C₂	semidirect
14. C₂×C₅₃×#541	C₂	semidirect
15. C₂×C₅₃×#541	C₂	semidirect
16. C₂×C₅₃×#533	C₂	semidirect
17. C₂×C₅₃×#533	C₂	semidirect
19. C₅₃×#563	C₂²	semidirect
20. Q₈²×C₅₃	C₂²	semidirect
21. C₅₃×#557	C₂²	semidirect
22. C₅₃×#557	C₂²	semidirect
23. C₅₃×#556	C₂²	semidirect
24. C₅₃×#556	C₂²	semidirect
25. C₅₃×#556	C₂²	semidirect
26. C₅₃×#554	C₂²	semidirect
27. C₅₃×#552	C₂²	semidirect
28. C₅₃×#544	C₂²	semidirect
30. C₅₃×#541	C₂²	semidirect
31. C₅₃×#541	C₂²	semidirect
32. C₅₃×#541	C₂²	semidirect
33. C₅₃×#533	C₂²	semidirect
34. C₅₃×#533	C₂²	semidirect
380. C₂×#3555	C₅₃	direct (N × H)
408. #3555	C₂×C₅₃	direct (N × H)
409. C₂×#563	C₂×C₅₃	semidirect
410. C₂×Q₈²	C₂×C₅₃	semidirect
411. C₂×#557	C₂×C₅₃	semidirect
412. C₂×#557	C₂×C₅₃	semidirect
413. C₂×#556	C₂×C₅₃	semidirect
414. C₂×#556	C₂×C₅₃	semidirect
415. C₂×#556	C₂×C₅₃	semidirect
416. C₂×#554	C₂×C₅₃	semidirect
417. C₂×#552	C₂×C₅₃	semidirect
418. C₂×#544	C₂×C₅₃	semidirect
420. C₂×#541	C₂×C₅₃	semidirect
421. C₂×#541	C₂×C₅₃	semidirect
422. C₂×#541	C₂×C₅₃	semidirect
423. C₂×#533	C₂×C₅₃	semidirect
424. C₂×#533	C₂×C₅₃	semidirect
428. C₂×C₅₃	#3555	direct (N × H)
432. #563	C₂²×C₅₃	semidirect
433. Q₈²	C₂²×C₅₃	semidirect
434. #557	C₂²×C₅₃	semidirect
435. #557	C₂²×C₅₃	semidirect
436. #556	C₂²×C₅₃	semidirect
437. #556	C₂²×C₅₃	semidirect
438. #556	C₂²×C₅₃	semidirect
439. #554	C₂²×C₅₃	semidirect
440. #552	C₂²×C₅₃	semidirect
441. #544	C₂²×C₅₃	semidirect
443. #541	C₂²×C₅₃	semidirect
444. #541	C₂²×C₅₃	semidirect
445. #541	C₂²×C₅₃	semidirect
446. #533	C₂²×C₅₃	semidirect
447. #533	C₂²×C₅₃	semidirect
514. C₅₃	C₂×#3555	direct (N × H)
823. C₂	C₅₃×#3555	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3555	2
C₂×C₅₃×#563	2
C₂×Q₈²×C₅₃	2
C₂×C₅₃×#557	2
C₂×C₅₃×#556	2
C₂×C₅₃×#554	2
C₂×C₅₃×#552	2
C₂×C₅₃×#544	2
C₂×C₅₃×#542	2
C₂×C₅₃×#541	2
C₂×C₅₃×#533	2
C₂×C₅₃×#529	2
C₂×#3555	53

Subgroups — C2×C53×#3555 #27270263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3555 #27270263