Subgroups — C₂×C₅₃×#3552 #27270257

Order 13568.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3552	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₅₃×#563	C₂	1	4	yes	maximal, complemented
3	C₂×C₅₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#554	C₂	1	2	yes	maximal, complemented
6	C₂×C₅₃×#553	C₂	1	2	yes	maximal, complemented
7	C₂×D₄×Q₈×C₅₃	C₂	1	2	yes	maximal, complemented
8	C₂×D₄×Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#548	C₂	1	2	yes	maximal, complemented
10	C₂×C₅₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#544	C₂	1	2	yes	maximal, complemented
12	C₂×C₅₃×#542	C₂	1	2	yes	maximal, complemented
13	C₂×C₅₃×#541	C₂	1	2	yes	maximal, complemented
14	C₂×C₅₃×#539	C₂	1	4	yes	maximal, complemented
15	C₂×C₅₃×#536	C₂	1	2	yes	maximal, complemented
16	C₂²×C₄⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41×C₅₃	C₂²	1	2	yes	—
20	C₂³×Q₈×C₅₃	C₂²	1	2	yes	—
21	C₂³×Q₈×C₅₃	C₂²	1	2	yes	—
22	C₅₃×#563	C₂²	1	64	yes	complemented
23	C₅₃×#557	C₂²	1	16	yes	complemented
24	C₅₃×#556	C₂²	1	16	yes	complemented
25	C₅₃×#554	C₂²	1	32	yes	complemented
26	C₅₃×#553	C₂²	1	32	yes	complemented
27	D₄×Q₈×C₅₃	C₂²	1	16	yes	complemented
28	D₄×Q₈×C₅₃	C₂²	1	32	yes	complemented
29	C₅₃×#548	C₂²	1	32	yes	complemented
30	C₅₃×#547	C₂²	1	16	yes	complemented
31	C₅₃×#544	C₂²	1	32	yes	complemented
32	C₅₃×#542	C₂²	1	32	yes	complemented
33	C₅₃×#541	C₂²	1	32	yes	complemented
34	C₅₃×#539	C₂²	1	64	yes	complemented
35	C₅₃×#536	C₂²	1	32	yes	complemented
36	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	—
37	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	—
38	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	—
39	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	—
40	C₂×C₄⋊Q₈×C₅₃	C₂²	1	4	yes	—
41	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	—
44	C₂×C₄⋊Q₈×C₅₃	C₂²	1	16	yes	complemented
45	C₅₃×#529	C₂²	1	16	yes	complemented
46	C₅₃×#529	C₂²	1	16	yes	complemented
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	2	yes	—
51	C₂×#126×C₅₃	C₂²	1	2	yes	—
52	C₂×#125×C₅₃	C₂²	1	4	yes	—
53	C₂×#125×C₅₃	C₂²	1	4	yes	—
54	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
55	C₂×#125×C₅₃	C₂²	1	4	yes	—
56	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
57	C₂×#125×C₅₃	C₂²	1	2	yes	—
58	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
59	C₂×#124×C₅₃	C₂²	1	2	yes	—
60	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
61	C₂×#124×C₅₃	C₂²	1	4	yes	—
62	C₂×#123×C₅₃	C₂²	1	4	yes	—
63	C₂×#123×C₅₃	C₂²	1	4	yes	—
64	C₂×#123×C₅₃	C₂²	1	2	yes	—
65	C₂×#123×C₅₃	C₂²	1	2	yes	—
66	C₂×#123×C₅₃	C₂²	1	4	yes	—
67	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
68	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
69	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
70	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
71	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
72	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
73	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
74	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
75	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
76	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
77	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
78	C₂×#121×C₅₃	C₂²	1	4	yes	—
79	C₂×#121×C₅₃	C₂²	1	2	yes	—
80	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
81	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
86	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
87	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	—
88	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	—
89	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
90	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
91	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
92	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
93	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
94	C₂×#117×C₅₃	C₂²	1	2	yes	—
95	C₂×#117×C₅₃	C₂²	1	2	yes	—
96	C₂×#117×C₅₃	C₂²	1	2	yes	—
97	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
98	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
99	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
100	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
101	C₂×#41×C₅₃	—	4	8	no	—
102	C₂×#41×C₅₃	C₂³	1	16	yes	—
103	C₂²×Q₈×C₅₃	—	4	8	no	—
104	C₂²×Q₈×C₅₃	—	4	8	no	—
105	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
106	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
107	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
109	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
110	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
111	C₂²×Q₈×C₅₃	C₂³	1	16	yes	—
112	C₂²×Q₈×C₅₃	C₂³	1	16	yes	—
113	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
118	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
122	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
124	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
125	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
126	C₄⋊Q₈×C₅₃	C₂³	1	16	yes	—
127	C₄⋊Q₈×C₅₃	C₂³	1	16	yes	—
128	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	—
129	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	—
130	C₄⋊Q₈×C₅₃	C₂³	1	16	yes	—
131	C₄⋊Q₈×C₅₃	C₂³	1	16	yes	—
132	C₄⋊Q₈×C₅₃	C₂³	1	16	yes	—
133	C₄⋊Q₈×C₅₃	C₂³	1	32	yes	—
134	#126×C₅₃	C₂³	1	16	yes	—
135	#126×C₅₃	C₂³	1	16	yes	—
136	#126×C₅₃	C₂³	1	32	yes	—
137	#126×C₅₃	C₂³	1	32	yes	—
138	#126×C₅₃	C₂³	1	32	yes	—
139	#125×C₅₃	C₂³	1	8	yes	—
140	#125×C₅₃	C₂³	1	8	yes	—
141	#125×C₅₃	C₂³	1	32	yes	—
142	#125×C₅₃	C₂³	1	32	yes	—
143	#125×C₅₃	C₂³	1	32	yes	—
144	#125×C₅₃	C₂³	1	16	yes	—
145	#124×C₅₃	C₂³	1	8	yes	—
146	#124×C₅₃	C₂³	1	8	yes	—
147	#124×C₅₃	C₂³	1	16	yes	—
148	#124×C₅₃	C₂³	1	32	yes	—
149	#123×C₅₃	C₂³	1	16	yes	—
150	#123×C₅₃	C₂³	1	16	yes	—
151	#123×C₅₃	C₂³	1	32	yes	—
152	#123×C₅₃	C₂³	1	32	yes	—
153	#123×C₅₃	C₂³	1	32	yes	—
154	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
155	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
156	C₂²⋊Q₈×C₅₃	C₂³	1	32	yes	—
157	C₂²⋊Q₈×C₅₃	C₂³	1	32	yes	—
158	C₂²⋊Q₈×C₅₃	C₂³	1	32	yes	—
159	C₂²⋊Q₈×C₅₃	C₂³	1	32	yes	—
160	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
161	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
162	C₂²⋊Q₈×C₅₃	C₂³	1	32	yes	—
163	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
164	C₂²⋊Q₈×C₅₃	C₂³	1	32	yes	—
165	#121×C₅₃	C₂³	1	8	yes	—
166	#121×C₅₃	C₂³	1	8	yes	—
167	#121×C₅₃	C₂³	1	32	yes	—
168	#121×C₅₃	C₂³	1	16	yes	—
169	C₄×Q₈×C₅₃	C₂³	1	8	yes	—
170	C₄×Q₈×C₅₃	C₂³	1	8	yes	—
171	C₄×Q₈×C₅₃	C₂³	1	16	yes	—
172	C₄×Q₈×C₅₃	C₂³	1	16	yes	—
173	C₄×Q₈×C₅₃	C₂³	1	16	yes	—
174	C₄×D₄×C₅₃	C₂³	1	8	yes	—
175	C₄×D₄×C₅₃	C₂³	1	8	yes	—
176	C₄×D₄×C₅₃	C₂³	1	16	yes	—
177	C₄×D₄×C₅₃	C₂³	1	16	yes	—
178	C₄×D₄×C₅₃	C₂³	1	32	yes	—
179	C₄×D₄×C₅₃	C₂³	1	32	yes	—
180	C₄×D₄×C₅₃	C₂³	1	16	yes	—
181	#117×C₅₃	C₂³	1	16	yes	—
182	#117×C₅₃	C₂³	1	16	yes	—
183	#117×C₅₃	C₂³	1	16	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	4	yes	—
190	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
191	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₅₃	C₂³	1	16	yes	—
193	C₂×C₄⋊C₄×C₅₃	C₂³	1	16	yes	—
194	C₂×C₄⋊C₄×C₅₃	C₂³	1	16	yes	—
195	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	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	1	yes	characteristic
206	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
207	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
208	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
209	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
210	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
212	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
219	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
220	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
223	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
225	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₅₃	C₂³	1	8	yes	—
230	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
231	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
232	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
233	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
234	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
235	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
236	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
237	#41×C₅₃	—	4	32	no	—
238	C₂×Q₈×C₅₃	—	2	8	no	—
239	C₂×Q₈×C₅₃	—	2	4	no	—
240	C₂×Q₈×C₅₃	—	2	8	no	—
241	C₂×Q₈×C₅₃	—	2	4	no	—
242	C₂×Q₈×C₅₃	—	4	8	no	—
243	C₂×Q₈×C₅₃	—	4	8	no	—
244	C₂×Q₈×C₅₃	—	4	32	no	—
245	C₂×Q₈×C₅₃	—	4	32	no	—
246	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
248	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
249	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
250	C₂×Q₈×C₅₃	C₂⁴	1	16	yes	—
251	C₂×Q₈×C₅₃	C₂⁴	1	16	yes	—
252	C₂×D₄×C₅₃	—	2	8	no	—
253	C₂×D₄×C₅₃	—	2	8	no	—
254	C₂×D₄×C₅₃	—	2	4	no	—
255	C₂×D₄×C₅₃	—	2	4	no	—
256	C₂×D₄×C₅₃	—	4	8	no	—
257	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
258	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
259	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
260	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
261	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
262	C₂²×C₄×C₅₃	—	2	4	no	—
263	C₂²×C₄×C₅₃	—	2	4	no	—
264	C₂²×C₄×C₅₃	—	2	8	no	—
265	C₂²×C₄×C₅₃	—	2	4	no	—
266	C₂²×C₄×C₅₃	—	2	8	no	—
267	C₂²×C₄×C₅₃	—	4	8	no	—
268	C₂²×C₄×C₅₃	—	4	8	no	—
269	C₂²×C₄×C₅₃	—	4	8	no	—
270	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
271	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
272	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
273	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
274	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
275	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
285	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
286	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
288	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
289	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
290	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
292	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
293	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
294	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
295	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
296	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
297	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
298	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
299	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
300	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
301	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
302	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
303	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
304	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
305	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
306	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
307	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
308	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
309	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
310	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
311	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
312	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
313	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
314	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
315	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
316	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
317	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
318	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
319	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
320	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
321	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
322	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
323	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
324	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
325	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
326	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
327	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
328	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
329	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
330	C₄²×C₅₃	C₂⁴	1	4	yes	—
331	C₄²×C₅₃	C₂⁴	1	4	yes	—
332	C₄²×C₅₃	C₂⁴	1	4	yes	—
333	C₄²×C₅₃	C₂⁴	1	4	yes	—
334	C₄²×C₅₃	C₂⁴	1	8	yes	—
335	C₄²×C₅₃	C₂⁴	1	8	yes	—
336	C₄²×C₅₃	C₂⁴	1	16	yes	—
337	C₄²×C₅₃	C₂⁴	1	16	yes	—
338	C₂³×C₅₃	—	2	2	no	—
339	C₂³×C₅₃	—	2	2	no	—
340	C₂³×C₅₃	—	2	4	no	—
341	C₂³×C₅₃	—	2	4	no	—
342	C₂³×C₅₃	—	2	4	no	—
343	C₂³×C₅₃	—	2	4	no	—
344	C₂³×C₅₃	—	2	4	no	—
345	C₂³×C₅₃	—	2	4	no	—
346	C₂³×C₅₃	2₋¹⁺⁴	1	4	yes	—
347	C₂³×C₅₃	C₂⁵	1	4	yes	—
348	C₂³×C₅₃	C₂⁵	1	4	yes	—
349	C₂³×C₅₃	C₂⁵	1	2	yes	—
350	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
351	Q₈×C₅₃	—	2	16	no	—
352	Q₈×C₅₃	—	2	8	no	—
353	Q₈×C₅₃	—	2	16	no	—
354	Q₈×C₅₃	—	2	8	no	—
355	Q₈×C₅₃	—	4	16	no	—
356	Q₈×C₅₃	—	4	16	no	—
357	D₄×C₅₃	—	2	16	no	—
358	D₄×C₅₃	—	2	16	no	—
359	D₄×C₅₃	—	2	8	no	—
360	D₄×C₅₃	—	2	8	no	—
361	D₄×C₅₃	—	4	16	no	—
362	C₂×C₄×C₅₃	—	2	4	no	—
363	C₂×C₄×C₅₃	—	2	2	no	—
364	C₂×C₄×C₅₃	—	2	8	no	—
365	C₂×C₄×C₅₃	—	2	8	no	—
366	C₂×C₄×C₅₃	—	2	4	no	—
367	C₂×C₄×C₅₃	—	2	8	no	—
368	C₂×C₄×C₅₃	—	2	2	no	—
369	C₂×C₄×C₅₃	—	2	2	no	—
370	C₂×C₄×C₅₃	—	2	2	no	—
371	C₂×C₄×C₅₃	—	2	4	no	—
372	C₂×C₄×C₅₃	—	2	4	no	—
373	C₂×C₄×C₅₃	—	2	4	no	—
374	C₂×C₄×C₅₃	—	2	4	no	—
375	C₂×C₄×C₅₃	—	2	8	no	—
376	C₂×C₄×C₅₃	—	2	16	no	—
377	C₂×C₄×C₅₃	—	2	8	no	—
378	C₂×C₄×C₅₃	—	2	16	no	—
379	C₂×C₄×C₅₃	—	4	16	no	—
380	C₂×C₄×C₅₃	—	4	16	no	—
381	C₂×C₄×C₅₃	—	4	16	no	—
382	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
383	C₂×C₄×C₅₃	2₋¹⁺⁴	1	4	yes	—
384	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
385	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
386	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
387	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
388	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
389	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
390	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
391	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
392	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
393	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
394	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
395	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
396	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
397	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
398	C₂×#3552	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
399	C₂²×C₅₃	—	2	2	no	—
400	C₂²×C₅₃	—	2	2	no	—
401	C₂²×C₅₃	—	2	8	no	—
402	C₂²×C₅₃	—	2	4	no	—
403	C₂²×C₅₃	—	2	4	no	—
404	C₂²×C₅₃	—	2	4	no	—
405	C₂²×C₅₃	—	2	4	no	—
406	C₂²×C₅₃	—	2	4	no	—
407	C₂²×C₅₃	—	2	4	no	—
408	C₂²×C₅₃	—	4	8	no	—
409	C₂²×C₅₃	—	4	8	no	—
410	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
411	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	4	yes	—
412	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
413	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
414	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
415	C₄×C₅₃	—	2	4	no	—
416	C₄×C₅₃	—	2	2	no	—
417	C₄×C₅₃	—	2	8	no	—
418	C₄×C₅₃	—	2	8	no	—
419	C₄×C₅₃	—	2	4	no	—
420	C₄×C₅₃	—	2	2	no	—
421	C₄×C₅₃	—	2	2	no	—
422	C₄×C₅₃	—	2	2	no	—
423	C₄×C₅₃	—	2	4	no	—
424	C₄×C₅₃	—	2	4	no	—
425	C₄×C₅₃	—	2	4	no	—
426	C₄×C₅₃	—	2	4	no	—
427	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
428	C₄×C₅₃	C₂×2₋¹⁺⁴	1	4	yes	—
429	#3552	C₂×C₅₃	1	32	yes	direct product factor
430	C₂×#563	C₂×C₅₃	1	4	yes	complemented
431	C₂×#557	C₂×C₅₃	1	1	yes	characteristic, complemented
432	C₂×#556	C₂×C₅₃	1	1	yes	characteristic, complemented
433	C₂×#554	C₂×C₅₃	1	2	yes	complemented
434	C₂×#553	C₂×C₅₃	1	2	yes	complemented
435	C₂×D₄×Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
436	C₂×D₄×Q₈	C₂×C₅₃	1	2	yes	complemented
437	C₂×#548	C₂×C₅₃	1	2	yes	complemented
438	C₂×#547	C₂×C₅₃	1	1	yes	characteristic, complemented
439	C₂×#544	C₂×C₅₃	1	2	yes	complemented
440	C₂×#542	C₂×C₅₃	1	2	yes	complemented
441	C₂×#541	C₂×C₅₃	1	2	yes	complemented
442	C₂×#539	C₂×C₅₃	1	4	yes	complemented
443	C₂×#536	C₂×C₅₃	1	2	yes	complemented
444	C₂²×C₄⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
445	C₂×#529	C₂×C₅₃	1	1	yes	characteristic, complemented
446	C₂×#529	C₂×C₅₃	1	1	yes	characteristic, complemented
447	C₂×C₅₃	—	2	4	no	—
448	C₂×C₅₃	—	4	4	no	—
449	C₂×C₅₃	—	4	4	no	—
450	C₂×C₅₃	#3552	1	4	yes	direct product factor
451	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂×C₅₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
453	C₂×C₅₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
454	C₂²×#41	C₂²×C₅₃	1	2	yes	—
455	C₂³×Q₈	C₂²×C₅₃	1	2	yes	—
456	C₂³×Q₈	C₂²×C₅₃	1	2	yes	—
457	#563	C₂²×C₅₃	1	64	yes	complemented
458	#557	C₂²×C₅₃	1	16	yes	complemented
459	#556	C₂²×C₅₃	1	16	yes	complemented
460	#554	C₂²×C₅₃	1	32	yes	complemented
461	#553	C₂²×C₅₃	1	32	yes	complemented
462	D₄×Q₈	C₂²×C₅₃	1	16	yes	complemented
463	D₄×Q₈	C₂²×C₅₃	1	32	yes	complemented
464	#548	C₂²×C₅₃	1	32	yes	complemented
465	#547	C₂²×C₅₃	1	16	yes	complemented
466	#544	C₂²×C₅₃	1	32	yes	complemented
467	#542	C₂²×C₅₃	1	32	yes	complemented
468	#541	C₂²×C₅₃	1	32	yes	complemented
469	#539	C₂²×C₅₃	1	64	yes	complemented
470	#536	C₂²×C₅₃	1	32	yes	complemented
471	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	—
472	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	—
473	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
474	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
475	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	—
476	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	—
477	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	—
478	C₂×C₄⋊Q₈	C₂²×C₅₃	1	4	yes	—
479	C₂×C₄⋊Q₈	C₂²×C₅₃	1	16	yes	complemented
480	#529	C₂²×C₅₃	1	16	yes	complemented
481	#529	C₂²×C₅₃	1	16	yes	complemented
482	C₂×#126	C₂²×C₅₃	1	2	yes	—
483	C₂×#126	C₂²×C₅₃	1	2	yes	—
484	C₂×#126	C₂²×C₅₃	1	4	yes	—
485	C₂×#126	C₂²×C₅₃	1	4	yes	—
486	C₂×#126	C₂²×C₅₃	1	4	yes	—
487	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
488	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
489	C₂×#125	C₂²×C₅₃	1	4	yes	—
490	C₂×#125	C₂²×C₅₃	1	4	yes	—
491	C₂×#125	C₂²×C₅₃	1	4	yes	—
492	C₂×#125	C₂²×C₅₃	1	2	yes	—
493	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
494	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
495	C₂×#124	C₂²×C₅₃	1	2	yes	—
496	C₂×#124	C₂²×C₅₃	1	4	yes	—
497	C₂×#123	C₂²×C₅₃	1	2	yes	—
498	C₂×#123	C₂²×C₅₃	1	2	yes	—
499	C₂×#123	C₂²×C₅₃	1	4	yes	—
500	C₂×#123	C₂²×C₅₃	1	4	yes	—
501	C₂×#123	C₂²×C₅₃	1	4	yes	—
502	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
503	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
504	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
505	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
506	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
507	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
508	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
509	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
510	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
511	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
512	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
513	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
514	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
515	C₂×#121	C₂²×C₅₃	1	4	yes	—
516	C₂×#121	C₂²×C₅₃	1	2	yes	—
517	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
518	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
519	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
520	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
521	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
522	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
523	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
524	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
525	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
526	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	—
527	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	—
528	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
529	C₂×#117	C₂²×C₅₃	1	2	yes	—
530	C₂×#117	C₂²×C₅₃	1	2	yes	—
531	C₂×#117	C₂²×C₅₃	1	2	yes	—
532	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
533	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
534	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
535	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
536	C₅₃	C₂×#3552	1	1	yes	characteristic, direct product factor, Sylow
537	C₂×#41	—	4	8	no	—
538	C₂×#41	C₂³×C₅₃	1	16	yes	—
539	C₂²×Q₈	—	4	8	no	—
540	C₂²×Q₈	—	4	8	no	—
541	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
542	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
543	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
544	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
545	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
546	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
547	C₂²×Q₈	C₂³×C₅₃	1	16	yes	—
548	C₂²×Q₈	C₂³×C₅₃	1	16	yes	—
549	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
550	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
551	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
553	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
554	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
557	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
558	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
559	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
560	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
561	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
562	C₄⋊Q₈	C₂³×C₅₃	1	16	yes	—
563	C₄⋊Q₈	C₂³×C₅₃	1	16	yes	—
564	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	—
565	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	—
566	C₄⋊Q₈	C₂³×C₅₃	1	16	yes	—
567	C₄⋊Q₈	C₂³×C₅₃	1	16	yes	—
568	C₄⋊Q₈	C₂³×C₅₃	1	16	yes	—
569	C₄⋊Q₈	C₂³×C₅₃	1	32	yes	—
570	#126	C₂³×C₅₃	1	16	yes	—
571	#126	C₂³×C₅₃	1	16	yes	—
572	#126	C₂³×C₅₃	1	32	yes	—
573	#126	C₂³×C₅₃	1	32	yes	—
574	#126	C₂³×C₅₃	1	32	yes	—
575	#125	C₂³×C₅₃	1	8	yes	—
576	#125	C₂³×C₅₃	1	8	yes	—
577	#125	C₂³×C₅₃	1	32	yes	—
578	#125	C₂³×C₅₃	1	32	yes	—
579	#125	C₂³×C₅₃	1	32	yes	—
580	#125	C₂³×C₅₃	1	16	yes	—
581	#124	C₂³×C₅₃	1	8	yes	—
582	#124	C₂³×C₅₃	1	8	yes	—
583	#124	C₂³×C₅₃	1	16	yes	—
584	#124	C₂³×C₅₃	1	32	yes	—
585	#123	C₂³×C₅₃	1	16	yes	—
586	#123	C₂³×C₅₃	1	16	yes	—
587	#123	C₂³×C₅₃	1	32	yes	—
588	#123	C₂³×C₅₃	1	32	yes	—
589	#123	C₂³×C₅₃	1	32	yes	—
590	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
591	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
592	C₂²⋊Q₈	C₂³×C₅₃	1	32	yes	—
593	C₂²⋊Q₈	C₂³×C₅₃	1	32	yes	—
594	C₂²⋊Q₈	C₂³×C₅₃	1	32	yes	—
595	C₂²⋊Q₈	C₂³×C₅₃	1	32	yes	—
596	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
597	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
598	C₂²⋊Q₈	C₂³×C₅₃	1	32	yes	—
599	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
600	C₂²⋊Q₈	C₂³×C₅₃	1	32	yes	—
601	#121	C₂³×C₅₃	1	8	yes	—
602	#121	C₂³×C₅₃	1	8	yes	—
603	#121	C₂³×C₅₃	1	32	yes	—
604	#121	C₂³×C₅₃	1	16	yes	—
605	C₄×Q₈	C₂³×C₅₃	1	8	yes	—
606	C₄×Q₈	C₂³×C₅₃	1	8	yes	—
607	C₄×Q₈	C₂³×C₅₃	1	16	yes	—
608	C₄×Q₈	C₂³×C₅₃	1	16	yes	—
609	C₄×Q₈	C₂³×C₅₃	1	16	yes	—
610	C₄×D₄	C₂³×C₅₃	1	8	yes	—
611	C₄×D₄	C₂³×C₅₃	1	8	yes	—
612	C₄×D₄	C₂³×C₅₃	1	16	yes	—
613	C₄×D₄	C₂³×C₅₃	1	16	yes	—
614	C₄×D₄	C₂³×C₅₃	1	32	yes	—
615	C₄×D₄	C₂³×C₅₃	1	32	yes	—
616	C₄×D₄	C₂³×C₅₃	1	16	yes	—
617	#117	C₂³×C₅₃	1	16	yes	—
618	#117	C₂³×C₅₃	1	16	yes	—
619	#117	C₂³×C₅₃	1	16	yes	—
620	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
624	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
626	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
627	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₅₃	1	16	yes	—
629	C₂×C₄⋊C₄	C₂³×C₅₃	1	16	yes	—
630	C₂×C₄⋊C₄	C₂³×C₅₃	1	16	yes	—
631	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
638	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
640	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
643	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
644	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
645	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
661	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
664	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
665	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
666	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
668	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₅₃	1	8	yes	—
670	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
671	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
672	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
673	#41	—	4	32	no	—
674	C₂×Q₈	—	2	8	no	—
675	C₂×Q₈	—	2	4	no	—
676	C₂×Q₈	—	2	8	no	—
677	C₂×Q₈	—	2	4	no	—
678	C₂×Q₈	—	4	8	no	—
679	C₂×Q₈	—	4	8	no	—
680	C₂×Q₈	—	4	32	no	—
681	C₂×Q₈	—	4	32	no	—
682	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
683	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
684	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
685	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
686	C₂×Q₈	C₂⁴×C₅₃	1	16	yes	—
687	C₂×Q₈	C₂⁴×C₅₃	1	16	yes	—
688	C₂×D₄	—	2	8	no	—
689	C₂×D₄	—	2	8	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	4	8	no	—
693	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
694	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
695	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
696	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
697	C₂×D₄	C₂⁴×C₅₃	1	16	yes	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	8	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	8	no	—
703	C₂²×C₄	—	4	8	no	—
704	C₂²×C₄	—	4	8	no	—
705	C₂²×C₄	—	4	8	no	—
706	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
715	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
716	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
717	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
719	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
720	C₂²×C₄	C₂⁴×C₅₃	1	2	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	16	yes	—
725	C₂²×C₄	C₂⁴×C₅₃	1	16	yes	—
726	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
728	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
729	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
730	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
731	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
732	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
733	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
734	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
735	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
736	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
737	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
738	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
739	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
740	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
741	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
742	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
743	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
744	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
745	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
746	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
747	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
748	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
749	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
750	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
751	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
752	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
753	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
754	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
755	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
756	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
757	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
758	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
759	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
760	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
761	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
762	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
763	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
764	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
765	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
766	C₄²	C₂⁴×C₅₃	1	4	yes	—
767	C₄²	C₂⁴×C₅₃	1	4	yes	—
768	C₄²	C₂⁴×C₅₃	1	4	yes	—
769	C₄²	C₂⁴×C₅₃	1	4	yes	—
770	C₄²	C₂⁴×C₅₃	1	8	yes	—
771	C₄²	C₂⁴×C₅₃	1	8	yes	—
772	C₄²	C₂⁴×C₅₃	1	16	yes	—
773	C₄²	C₂⁴×C₅₃	1	16	yes	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	4	no	—
777	C₂³	—	2	4	no	—
778	C₂³	—	2	4	no	—
779	C₂³	—	2	4	no	—
780	C₂³	—	2	4	no	—
781	C₂³	—	2	4	no	—
782	C₂³	2₋¹⁺⁴×C₅₃	1	4	yes	—
783	C₂³	C₂⁵×C₅₃	1	4	yes	—
784	C₂³	C₂⁵×C₅₃	1	4	yes	—
785	C₂³	C₂⁵×C₅₃	1	2	yes	—
786	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
787	Q₈	—	2	16	no	—
788	Q₈	—	2	8	no	—
789	Q₈	—	2	16	no	—
790	Q₈	—	2	8	no	—
791	Q₈	—	4	16	no	—
792	Q₈	—	4	16	no	—
793	D₄	—	2	16	no	—
794	D₄	—	2	16	no	—
795	D₄	—	2	8	no	—
796	D₄	—	2	8	no	—
797	D₄	—	4	16	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	8	no	—
801	C₂×C₄	—	2	8	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	8	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	4	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	4	no	—
811	C₂×C₄	—	2	8	no	—
812	C₂×C₄	—	2	16	no	—
813	C₂×C₄	—	2	8	no	—
814	C₂×C₄	—	2	16	no	—
815	C₂×C₄	—	4	16	no	—
816	C₂×C₄	—	4	16	no	—
817	C₂×C₄	—	4	16	no	—
818	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
819	C₂×C₄	2₋¹⁺⁴×C₅₃	1	4	yes	—
820	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
821	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
822	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
823	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
824	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
825	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
826	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
827	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
828	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
829	C₂×C₄	C₂⁵×C₅₃	1	8	yes	—
830	C₂×C₄	C₂⁵×C₅₃	1	8	yes	—
831	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
832	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
833	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
834	C₂²	—	2	8	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	4	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	4	8	no	—
844	C₂²	—	4	8	no	—
845	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
846	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	4	yes	—
847	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	2	yes	—
848	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	2	yes	—
849	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
850	C₄	—	2	4	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	8	no	—
853	C₄	—	2	8	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	4	no	—
859	C₄	—	2	4	no	—
860	C₄	—	2	4	no	—
861	C₄	—	2	4	no	—
862	C₄	C₂×H(5,𝔽₂)×C₅₃	1	4	yes	—
863	C₄	C₂×2₋¹⁺⁴×C₅₃	1	4	yes	—
864	C₂	—	2	4	no	—
865	C₂	—	4	4	no	—
866	C₂	—	4	4	no	—
867	C₂	C₅₃×#3552	1	4	yes	direct product factor
868	C₂	C₂²×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
869	C₂	C₂²×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
870	C₂	C₂²×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅₃
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×#3552	C₂	direct (N × H)
2. C₂×C₅₃×#563	C₂	semidirect
3. C₂×C₅₃×#557	C₂	semidirect
4. C₂×C₅₃×#556	C₂	semidirect
5. C₂×C₅₃×#554	C₂	semidirect
6. C₂×C₅₃×#553	C₂	semidirect
7. C₂×D₄×Q₈×C₅₃	C₂	semidirect
8. C₂×D₄×Q₈×C₅₃	C₂	semidirect
9. C₂×C₅₃×#548	C₂	semidirect
10. C₂×C₅₃×#547	C₂	semidirect
11. C₂×C₅₃×#544	C₂	semidirect
12. C₂×C₅₃×#542	C₂	semidirect
13. C₂×C₅₃×#541	C₂	semidirect
14. C₂×C₅₃×#539	C₂	semidirect
15. C₂×C₅₃×#536	C₂	semidirect
16. C₂²×C₄⋊Q₈×C₅₃	C₂	semidirect
17. C₂×C₅₃×#529	C₂	semidirect
18. C₂×C₅₃×#529	C₂	semidirect
22. C₅₃×#563	C₂²	semidirect
23. C₅₃×#557	C₂²	semidirect
24. C₅₃×#556	C₂²	semidirect
25. C₅₃×#554	C₂²	semidirect
26. C₅₃×#553	C₂²	semidirect
27. D₄×Q₈×C₅₃	C₂²	semidirect
28. D₄×Q₈×C₅₃	C₂²	semidirect
29. C₅₃×#548	C₂²	semidirect
30. C₅₃×#547	C₂²	semidirect
31. C₅₃×#544	C₂²	semidirect
32. C₅₃×#542	C₂²	semidirect
33. C₅₃×#541	C₂²	semidirect
34. C₅₃×#539	C₂²	semidirect
35. C₅₃×#536	C₂²	semidirect
44. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
45. C₅₃×#529	C₂²	semidirect
46. C₅₃×#529	C₂²	semidirect
398. C₂×#3552	C₅₃	direct (N × H)
429. #3552	C₂×C₅₃	direct (N × H)
430. C₂×#563	C₂×C₅₃	semidirect
431. C₂×#557	C₂×C₅₃	semidirect
432. C₂×#556	C₂×C₅₃	semidirect
433. C₂×#554	C₂×C₅₃	semidirect
434. C₂×#553	C₂×C₅₃	semidirect
435. C₂×D₄×Q₈	C₂×C₅₃	semidirect
436. C₂×D₄×Q₈	C₂×C₅₃	semidirect
437. C₂×#548	C₂×C₅₃	semidirect
438. C₂×#547	C₂×C₅₃	semidirect
439. C₂×#544	C₂×C₅₃	semidirect
440. C₂×#542	C₂×C₅₃	semidirect
441. C₂×#541	C₂×C₅₃	semidirect
442. C₂×#539	C₂×C₅₃	semidirect
443. C₂×#536	C₂×C₅₃	semidirect
444. C₂²×C₄⋊Q₈	C₂×C₅₃	semidirect
445. C₂×#529	C₂×C₅₃	semidirect
446. C₂×#529	C₂×C₅₃	semidirect
450. C₂×C₅₃	#3552	direct (N × H)
457. #563	C₂²×C₅₃	semidirect
458. #557	C₂²×C₅₃	semidirect
459. #556	C₂²×C₅₃	semidirect
460. #554	C₂²×C₅₃	semidirect
461. #553	C₂²×C₅₃	semidirect
462. D₄×Q₈	C₂²×C₅₃	semidirect
463. D₄×Q₈	C₂²×C₅₃	semidirect
464. #548	C₂²×C₅₃	semidirect
465. #547	C₂²×C₅₃	semidirect
466. #544	C₂²×C₅₃	semidirect
467. #542	C₂²×C₅₃	semidirect
468. #541	C₂²×C₅₃	semidirect
469. #539	C₂²×C₅₃	semidirect
470. #536	C₂²×C₅₃	semidirect
479. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
480. #529	C₂²×C₅₃	semidirect
481. #529	C₂²×C₅₃	semidirect
536. C₅₃	C₂×#3552	direct (N × H)
867. C₂	C₅₃×#3552	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×#3552	2
C₂×C₅₃×#563	2
C₂×C₅₃×#557	2
C₂×C₅₃×#556	2
C₂×C₅₃×#554	2
C₂×C₅₃×#553	2
C₂×D₄×Q₈×C₅₃	2
C₂×C₅₃×#548	2
C₂×C₅₃×#547	2
C₂×C₅₃×#544	2
C₂×C₅₃×#542	2
C₂×C₅₃×#541	2
C₂×C₅₃×#539	2
C₂×C₅₃×#536	2
C₂²×C₄⋊Q₈×C₅₃	2
C₂×C₅₃×#529	2
C₂×#3552	53

Subgroups — C2×C53×#3552 #27270257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3552 #27270257