Subgroups — C₄×C₅₃×#552 #27241675

Order 13568.

2376 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#552	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2373	C₂	1	2	yes	maximal, complemented
3	C₅₃×#2371	C₂	1	2	yes	maximal, complemented
4	C₅₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2359	C₂	1	2	yes	maximal
8	C₅₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2352	C₂	1	1	yes	maximal, characteristic
10	C₅₃×#2346	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2344	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2343	C₂	1	2	yes	maximal, complemented
13	C₄×#125×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#125×C₅₃	C₂	1	2	yes	maximal, complemented
15	C₄×#126×C₅₃	C₂	1	2	yes	maximal, complemented
16	C₄×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#123×C₅₃	C₂	1	2	yes	maximal
19	C₄²×Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄²×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic
21	C₄×#117×C₅₃	C₂	1	2	yes	maximal, complemented
22	C₄×#117×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#552	C₄	1	16	yes	direct product factor
25	C₂×#126×C₅₃	C₂²	1	2	yes	—
26	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×#125×C₅₃	C₂²	1	2	yes	—
28	C₂×#123×C₅₃	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#117×C₅₃	C₂²	1	2	yes	—
38	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#117×C₅₃	C₂²	1	2	yes	—
40	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₅₃	C₂²	1	2	yes	—
44	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
46	C₅₃×#391	C₂²	1	1	yes	characteristic
47	C₅₃×#391	C₂²	1	1	yes	characteristic
48	C₅₃×#389	C₂²	1	1	yes	characteristic
49	C₅₃×#389	C₂²	1	1	yes	characteristic
50	C₅₃×#389	C₂²	1	1	yes	characteristic
51	C₅₃×#389	C₂²	1	1	yes	characteristic
52	C₅₃×#389	C₂²	1	2	yes	—
53	C₅₃×#389	C₂²	1	2	yes	—
54	C₅₃×#388	C₂²	1	2	yes	—
55	C₅₃×#388	C₂²	1	2	yes	—
56	C₅₃×#388	C₂²	1	2	yes	—
57	C₅₃×#388	C₂²	1	2	yes	—
58	C₅₃×#388	C₂²	1	2	yes	—
59	C₅₃×#387	C₂²	1	2	yes	—
60	C₅₃×#387	C₂²	1	2	yes	—
61	C₅₃×#387	C₂²	1	2	yes	—
62	C₅₃×#387	C₂²	1	2	yes	—
63	C₅₃×#387	C₂²	1	2	yes	—
64	C₅₃×#387	C₂²	1	2	yes	—
65	C₅₃×#387	C₂²	1	2	yes	—
66	C₅₃×#387	C₂²	1	2	yes	—
67	C₅₃×#387	C₂²	1	2	yes	—
68	C₅₃×#387	C₂²	1	2	yes	—
69	C₅₃×#387	C₂²	1	2	yes	—
70	C₅₃×#387	C₂²	1	2	yes	—
71	C₅₃×#387	C₂²	1	2	yes	—
72	C₅₃×#386	C₂²	1	2	yes	—
73	C₅₃×#385	C₂²	1	2	yes	—
74	C₅₃×#385	C₂²	1	2	yes	—
75	C₅₃×#385	C₂²	1	2	yes	—
76	C₅₃×#383	C₂²	1	2	yes	—
77	C₅₃×#382	C₂²	1	2	yes	—
78	C₅₃×#382	C₂²	1	1	yes	characteristic
79	C₅₃×#381	C₂²	1	2	yes	—
80	C₅₃×#380	C₂²	1	1	yes	characteristic
81	C₅₃×#380	C₂²	1	1	yes	characteristic
82	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
83	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
84	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
85	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
86	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
87	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
88	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
89	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
90	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
92	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
103	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
106	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
107	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
108	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
109	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
110	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
111	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
112	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
117	C₅₃×#376	C₂²	1	2	yes	—
118	C₅₃×#376	C₂²	1	2	yes	—
119	C₅₃×#376	C₂²	1	2	yes	—
120	C₂×#95×C₅₃	C₂²	1	2	yes	—
121	C₄³×C₅₃	C₂²	1	2	yes	—
122	C₄³×C₅₃	C₂²	1	2	yes	—
123	C₄³×C₅₃	C₂²	1	1	yes	characteristic
124	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
134	#126×C₅₃	C₂×C₄	1	16	yes	complemented
135	#125×C₅₃	C₂×C₄	1	16	yes	complemented
136	#125×C₅₃	C₂×C₄	1	8	yes	complemented
137	#123×C₅₃	C₂×C₄	1	16	yes	—
138	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
139	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
140	C₄×Q₈×C₅₃	—	2	4	no	—
141	C₄×Q₈×C₅₃	—	2	4	no	—
142	C₄×Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
143	C₄×D₄×C₅₃	—	2	4	no	—
144	C₄×D₄×C₅₃	—	2	4	no	—
145	C₄×D₄×C₅₃	C₂×C₄	1	8	yes	—
146	#117×C₅₃	—	2	4	no	—
147	#117×C₅₃	—	2	8	no	—
148	#117×C₅₃	C₂×C₄	1	16	yes	complemented
149	#117×C₅₃	C₂×C₄	1	8	yes	complemented
150	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
151	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	8	yes	complemented
152	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₅₃	—	2	4	no	—
188	C₂×C₄²×C₅₃	—	2	4	no	—
189	C₂×C₄²×C₅₃	—	2	8	no	—
190	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
192	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
197	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
199	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
204	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
205	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
206	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
207	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
209	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
211	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
214	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
216	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
217	#95×C₅₃	C₂³	1	2	yes	—
218	#95×C₅₃	C₂³	1	2	yes	—
219	#95×C₅₃	C₂³	1	2	yes	—
220	#95×C₅₃	C₂³	1	2	yes	—
221	#95×C₅₃	C₂³	1	1	yes	characteristic
222	#95×C₅₃	C₂³	1	1	yes	characteristic
223	#95×C₅₃	C₂³	1	2	yes	—
224	#95×C₅₃	C₂³	1	2	yes	—
225	#95×C₅₃	C₂³	1	2	yes	—
226	#95×C₅₃	C₂³	1	2	yes	—
227	#95×C₅₃	C₂³	1	2	yes	—
228	#95×C₅₃	C₂³	1	2	yes	—
229	#95×C₅₃	C₂³	1	2	yes	—
230	#95×C₅₃	C₂³	1	2	yes	—
231	#95×C₅₃	C₂³	1	2	yes	—
232	#95×C₅₃	C₂³	1	1	yes	characteristic
233	#95×C₅₃	C₂³	1	1	yes	characteristic
234	#95×C₅₃	C₂³	1	1	yes	characteristic
235	#95×C₅₃	C₂³	1	1	yes	characteristic
236	#95×C₅₃	C₂³	1	2	yes	—
237	#95×C₅₃	C₂³	1	2	yes	—
238	#95×C₅₃	C₂³	1	2	yes	—
239	#95×C₅₃	C₂³	1	2	yes	—
240	#95×C₅₃	C₂³	1	2	yes	—
241	#95×C₅₃	C₂³	1	2	yes	—
242	#95×C₅₃	C₂³	1	2	yes	—
243	#95×C₅₃	C₂³	1	2	yes	—
244	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
245	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈×C₅₃	—	2	2	no	—
247	C₂×Q₈×C₅₃	—	2	2	no	—
248	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
249	C₂×D₄×C₅₃	—	2	2	no	—
250	C₂×D₄×C₅₃	—	2	2	no	—
251	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
252	C₂²×C₄×C₅₃	—	2	4	no	—
253	C₂²×C₄×C₅₃	—	2	4	no	—
254	C₂²×C₄×C₅₃	—	2	2	no	—
255	C₂²×C₄×C₅₃	—	2	2	no	—
256	C₂²×C₄×C₅₃	—	2	2	no	—
257	C₂²×C₄×C₅₃	—	2	2	no	—
258	C₂²×C₄×C₅₃	—	2	2	no	—
259	C₂²×C₄×C₅₃	—	2	2	no	—
260	C₂²×C₄×C₅₃	—	2	4	no	—
261	C₂²×C₄×C₅₃	—	2	2	no	—
262	C₂²×C₄×C₅₃	—	2	2	no	—
263	C₂²×C₄×C₅₃	—	2	2	no	—
264	C₂²×C₄×C₅₃	—	2	2	no	—
265	C₂²×C₄×C₅₃	—	2	4	no	—
266	C₂²×C₄×C₅₃	—	2	2	no	—
267	C₂²×C₄×C₅₃	—	2	2	no	—
268	C₂²×C₄×C₅₃	—	2	2	no	—
269	C₂²×C₄×C₅₃	—	4	1	no	—
270	C₂²×C₄×C₅₃	—	4	1	no	—
271	C₂²×C₄×C₅₃	—	4	2	no	—
272	C₂²×C₄×C₅₃	C₂²×C₄	1	8	yes	—
273	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
274	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
275	C₂²×C₄×C₅₃	#41	1	4	yes	—
276	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
285	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
297	C₄⋊C₄×C₅₃	—	2	4	no	—
298	C₄⋊C₄×C₅₃	—	2	2	no	—
299	C₄⋊C₄×C₅₃	—	2	4	no	—
300	C₄⋊C₄×C₅₃	—	2	4	no	—
301	C₄⋊C₄×C₅₃	—	2	2	no	—
302	C₄⋊C₄×C₅₃	—	2	2	no	—
303	C₄⋊C₄×C₅₃	—	2	2	no	—
304	C₄⋊C₄×C₅₃	—	2	4	no	—
305	C₄⋊C₄×C₅₃	—	2	4	no	—
306	C₄⋊C₄×C₅₃	—	2	2	no	—
307	C₄⋊C₄×C₅₃	—	4	2	no	—
308	C₄⋊C₄×C₅₃	—	4	2	no	—
309	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
310	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
311	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
312	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
313	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
314	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
315	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
316	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
317	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
318	C₄⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
319	C₄⋊C₄×C₅₃	#41	1	4	yes	—
320	C₂²⋊C₄×C₅₃	—	2	4	no	—
321	C₂²⋊C₄×C₅₃	—	2	2	no	—
322	C₂²⋊C₄×C₅₃	—	2	4	no	—
323	C₂²⋊C₄×C₅₃	—	2	2	no	—
324	C₂²⋊C₄×C₅₃	—	2	2	no	—
325	C₂²⋊C₄×C₅₃	—	4	2	no	—
326	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
327	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
328	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
329	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
330	C₂²⋊C₄×C₅₃	C₂²×C₄	1	8	yes	—
331	C₂²⋊C₄×C₅₃	#41	1	4	yes	—
332	C₄²×C₅₃	—	2	2	no	—
333	C₄²×C₅₃	—	2	4	no	—
334	C₄²×C₅₃	—	2	2	no	—
335	C₄²×C₅₃	—	2	4	no	—
336	C₄²×C₅₃	—	2	2	no	—
337	C₄²×C₅₃	—	2	4	no	—
338	C₄²×C₅₃	—	2	2	no	—
339	C₄²×C₅₃	—	2	2	no	—
340	C₄²×C₅₃	—	2	2	no	—
341	C₄²×C₅₃	—	2	4	no	—
342	C₄²×C₅₃	—	2	4	no	—
343	C₄²×C₅₃	—	2	4	no	—
344	C₄²×C₅₃	—	2	4	no	—
345	C₄²×C₅₃	—	2	2	no	—
346	C₄²×C₅₃	—	2	2	no	—
347	C₄²×C₅₃	—	2	4	no	—
348	C₄²×C₅₃	—	2	4	no	—
349	C₄²×C₅₃	—	2	2	no	—
350	C₄²×C₅₃	—	2	2	no	—
351	C₄²×C₅₃	—	2	4	no	—
352	C₄²×C₅₃	—	4	1	no	—
353	C₄²×C₅₃	—	4	2	no	—
354	C₄²×C₅₃	—	4	2	no	—
355	C₄²×C₅₃	C₂²×C₄	1	8	yes	—
356	C₄²×C₅₃	C₂²×C₄	1	8	yes	—
357	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
358	C₄²×C₅₃	#41	1	4	yes	—
359	C₂³×C₅₃	—	2	1	no	—
360	C₂³×C₅₃	—	2	1	no	—
361	C₂³×C₅₃	—	2	1	no	—
362	C₂³×C₅₃	—	2	1	no	—
363	C₂³×C₅₃	—	2	1	no	—
364	C₂³×C₅₃	—	2	1	no	—
365	C₂³×C₅₃	—	2	1	no	—
366	C₂³×C₅₃	—	2	1	no	—
367	C₂³×C₅₃	—	2	1	no	—
368	C₂³×C₅₃	—	2	1	no	—
369	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
370	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
371	C₂³×C₅₃	C₂×#41	1	2	yes	—
372	C₂³×C₅₃	C₂×#41	1	2	yes	—
373	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
374	Q₈×C₅₃	—	2	8	no	—
375	D₄×C₅₃	—	2	8	no	—
376	C₂×C₄×C₅₃	—	2	16	no	—
377	C₂×C₄×C₅₃	—	2	1	no	—
378	C₂×C₄×C₅₃	—	2	2	no	—
379	C₂×C₄×C₅₃	—	2	2	no	—
380	C₂×C₄×C₅₃	—	2	1	no	—
381	C₂×C₄×C₅₃	—	2	1	no	—
382	C₂×C₄×C₅₃	—	2	2	no	—
383	C₂×C₄×C₅₃	—	2	1	no	—
384	C₂×C₄×C₅₃	—	2	1	no	—
385	C₂×C₄×C₅₃	—	2	2	no	—
386	C₂×C₄×C₅₃	—	2	1	no	—
387	C₂×C₄×C₅₃	—	2	2	no	—
388	C₂×C₄×C₅₃	—	2	1	no	—
389	C₂×C₄×C₅₃	—	2	1	no	—
390	C₂×C₄×C₅₃	—	2	1	no	—
391	C₂×C₄×C₅₃	—	2	2	no	—
392	C₂×C₄×C₅₃	—	2	2	no	—
393	C₂×C₄×C₅₃	—	2	1	no	—
394	C₂×C₄×C₅₃	—	2	1	no	—
395	C₂×C₄×C₅₃	—	2	1	no	—
396	C₂×C₄×C₅₃	—	2	2	no	—
397	C₂×C₄×C₅₃	—	2	1	no	—
398	C₂×C₄×C₅₃	—	2	1	no	—
399	C₂×C₄×C₅₃	—	2	1	no	—
400	C₂×C₄×C₅₃	—	2	2	no	—
401	C₂×C₄×C₅₃	—	2	1	no	—
402	C₂×C₄×C₅₃	—	2	2	no	—
403	C₂×C₄×C₅₃	—	2	8	no	—
404	C₂×C₄×C₅₃	—	2	8	no	—
405	C₂×C₄×C₅₃	—	2	8	no	—
406	C₂×C₄×C₅₃	—	2	1	no	—
407	C₂×C₄×C₅₃	—	2	2	no	—
408	C₂×C₄×C₅₃	—	2	1	no	—
409	C₂×C₄×C₅₃	—	2	1	no	—
410	C₂×C₄×C₅₃	—	2	1	no	—
411	C₂×C₄×C₅₃	—	2	2	no	—
412	C₂×C₄×C₅₃	—	2	1	no	—
413	C₂×C₄×C₅₃	—	2	2	no	—
414	C₂×C₄×C₅₃	—	2	2	no	—
415	C₂×C₄×C₅₃	—	2	2	no	—
416	C₂×C₄×C₅₃	—	2	2	no	—
417	C₂×C₄×C₅₃	—	2	1	no	—
418	C₂×C₄×C₅₃	—	2	1	no	—
419	C₂×C₄×C₅₃	—	2	2	no	—
420	C₂×C₄×C₅₃	—	2	2	no	—
421	C₂×C₄×C₅₃	—	2	1	no	—
422	C₂×C₄×C₅₃	—	2	2	no	—
423	C₂×C₄×C₅₃	—	2	1	no	—
424	C₂×C₄×C₅₃	—	4	4	no	—
425	C₂×C₄×C₅₃	—	4	4	no	—
426	C₂×C₄×C₅₃	—	4	8	no	—
427	C₂×C₄×C₅₃	—	4	4	no	—
428	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
429	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
430	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
431	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
432	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
433	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
434	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
435	C₂×C₄×C₅₃	C₂³×C₄	1	4	yes	—
436	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
437	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
438	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
439	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
440	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
441	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
442	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
443	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
444	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
445	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
446	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
447	C₄×#552	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
448	C₂²×C₅₃	—	2	2	no	—
449	C₂²×C₅₃	—	2	2	no	—
450	C₂²×C₅₃	—	2	2	no	—
451	C₂²×C₅₃	—	2	2	no	—
452	C₂²×C₅₃	—	2	2	no	—
453	C₂²×C₅₃	—	2	2	no	—
454	C₂²×C₅₃	—	2	2	no	—
455	C₂²×C₅₃	—	2	2	no	—
456	C₂²×C₅₃	—	2	2	no	—
457	C₂²×C₅₃	—	4	1	no	—
458	C₂²×C₅₃	—	4	1	no	—
459	C₂²×C₅₃	—	4	1	no	—
460	C₂²×C₅₃	—	4	1	no	—
461	C₂²×C₅₃	C₄×#41	1	4	yes	—
462	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
463	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
464	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
465	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
466	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
467	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
468	C₂²×C₅₃	#585	1	1	yes	characteristic
469	C₄×C₅₃	—	2	4	no	—
470	C₄×C₅₃	—	2	4	no	—
471	C₄×C₅₃	—	2	2	no	—
472	C₄×C₅₃	—	2	2	no	—
473	C₄×C₅₃	—	2	2	no	—
474	C₄×C₅₃	—	2	4	no	—
475	C₄×C₅₃	—	2	2	no	—
476	C₄×C₅₃	—	2	4	no	—
477	C₄×C₅₃	—	2	2	no	—
478	C₄×C₅₃	—	2	2	no	—
479	C₄×C₅₃	—	2	2	no	—
480	C₄×C₅₃	—	2	4	no	—
481	C₄×C₅₃	—	2	2	no	—
482	C₄×C₅₃	—	4	1	no	—
483	C₄×C₅₃	—	4	1	no	—
484	C₄×C₅₃	—	4	2	no	—
485	C₄×C₅₃	—	4	1	no	—
486	C₄×C₅₃	—	4	2	no	—
487	C₄×C₅₃	—	4	2	no	—
488	C₄×C₅₃	C₄×#41	1	4	yes	—
489	C₄×C₅₃	#552	1	4	yes	direct product factor
490	C₂×#552	C₂×C₅₃	1	1	yes	characteristic
491	#2373	C₂×C₅₃	1	2	yes	complemented
492	#2371	C₂×C₅₃	1	2	yes	complemented
493	#2370	C₂×C₅₃	1	1	yes	characteristic, complemented
494	#2362	C₂×C₅₃	1	1	yes	characteristic, complemented
495	#2360	C₂×C₅₃	1	1	yes	characteristic, complemented
496	#2359	C₂×C₅₃	1	2	yes	—
497	#2356	C₂×C₅₃	1	1	yes	characteristic, complemented
498	#2352	C₂×C₅₃	1	1	yes	characteristic
499	#2346	C₂×C₅₃	1	1	yes	characteristic, complemented
500	#2344	C₂×C₅₃	1	1	yes	characteristic, complemented
501	#2343	C₂×C₅₃	1	2	yes	complemented
502	C₄×#125	C₂×C₅₃	1	1	yes	characteristic, complemented
503	C₄×#125	C₂×C₅₃	1	2	yes	complemented
504	C₄×#126	C₂×C₅₃	1	2	yes	complemented
505	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
506	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
507	C₄×#123	C₂×C₅₃	1	2	yes	—
508	C₄²×Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
509	C₄²×D₄	C₂×C₅₃	1	1	yes	characteristic
510	C₄×#117	C₂×C₅₃	1	2	yes	complemented
511	C₄×#117	C₂×C₅₃	1	1	yes	characteristic, complemented
512	C₂×C₄×C₄⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
513	C₂×C₅₃	—	2	4	no	—
514	C₂×C₅₃	—	4	2	no	—
515	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
516	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
517	C₂×C₅₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
518	C₂×C₅₃	C₂×#552	1	1	yes	characteristic
519	C₂×C₅₃	#3475	1	1	yes	characteristic
520	C₂×C₅₃	#3475	1	1	yes	characteristic
521	C₂×C₅₃	#3482	1	1	yes	characteristic
522	#552	C₄×C₅₃	1	16	yes	direct product factor
523	C₂×#126	C₂²×C₅₃	1	2	yes	—
524	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
525	C₂×#125	C₂²×C₅₃	1	2	yes	—
526	C₂×#123	C₂²×C₅₃	1	2	yes	—
527	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
528	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
529	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
530	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
531	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
532	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
533	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
534	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
535	C₂×#117	C₂²×C₅₃	1	2	yes	—
536	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
537	C₂×#117	C₂²×C₅₃	1	2	yes	—
538	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
539	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
540	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
541	C₂²×C₄²	C₂²×C₅₃	1	2	yes	—
542	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
543	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
544	#391	C₂²×C₅₃	1	1	yes	characteristic
545	#391	C₂²×C₅₃	1	1	yes	characteristic
546	#389	C₂²×C₅₃	1	1	yes	characteristic
547	#389	C₂²×C₅₃	1	1	yes	characteristic
548	#389	C₂²×C₅₃	1	2	yes	—
549	#389	C₂²×C₅₃	1	2	yes	—
550	#389	C₂²×C₅₃	1	1	yes	characteristic
551	#389	C₂²×C₅₃	1	1	yes	characteristic
552	#388	C₂²×C₅₃	1	2	yes	—
553	#388	C₂²×C₅₃	1	2	yes	—
554	#388	C₂²×C₅₃	1	2	yes	—
555	#388	C₂²×C₅₃	1	2	yes	—
556	#388	C₂²×C₅₃	1	2	yes	—
557	#387	C₂²×C₅₃	1	2	yes	—
558	#387	C₂²×C₅₃	1	2	yes	—
559	#387	C₂²×C₅₃	1	2	yes	—
560	#387	C₂²×C₅₃	1	2	yes	—
561	#387	C₂²×C₅₃	1	2	yes	—
562	#387	C₂²×C₅₃	1	2	yes	—
563	#387	C₂²×C₅₃	1	2	yes	—
564	#387	C₂²×C₅₃	1	2	yes	—
565	#387	C₂²×C₅₃	1	2	yes	—
566	#387	C₂²×C₅₃	1	2	yes	—
567	#387	C₂²×C₅₃	1	2	yes	—
568	#387	C₂²×C₅₃	1	2	yes	—
569	#387	C₂²×C₅₃	1	2	yes	—
570	#386	C₂²×C₅₃	1	2	yes	—
571	#385	C₂²×C₅₃	1	2	yes	—
572	#385	C₂²×C₅₃	1	2	yes	—
573	#385	C₂²×C₅₃	1	2	yes	—
574	#383	C₂²×C₅₃	1	2	yes	—
575	#382	C₂²×C₅₃	1	2	yes	—
576	#382	C₂²×C₅₃	1	1	yes	characteristic
577	#381	C₂²×C₅₃	1	2	yes	—
578	#380	C₂²×C₅₃	1	1	yes	characteristic
579	#380	C₂²×C₅₃	1	1	yes	characteristic
580	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
581	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
582	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
583	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
584	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
585	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
586	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
587	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
588	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
589	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
590	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
591	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
592	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
593	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
594	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
595	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
596	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
597	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
598	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
599	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
600	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
601	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
602	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
603	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
604	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
605	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
606	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
607	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
608	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
609	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
610	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
611	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
612	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
613	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
614	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
615	#376	C₂²×C₅₃	1	2	yes	—
616	#376	C₂²×C₅₃	1	2	yes	—
617	#376	C₂²×C₅₃	1	2	yes	—
618	C₂×#95	C₂²×C₅₃	1	2	yes	—
619	C₄³	C₂²×C₅₃	1	2	yes	—
620	C₄³	C₂²×C₅₃	1	2	yes	—
621	C₄³	C₂²×C₅₃	1	1	yes	characteristic
622	C₅₃	C₄×#552	1	1	yes	characteristic, direct product factor, Sylow
623	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
624	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
626	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
627	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
628	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
629	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
630	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
631	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
632	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
633	#126	C₂×C₄×C₅₃	1	16	yes	complemented
634	#125	C₂×C₄×C₅₃	1	16	yes	complemented
635	#125	C₂×C₄×C₅₃	1	8	yes	complemented
636	#123	C₂×C₄×C₅₃	1	16	yes	—
637	C₂²⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
638	C₂²⋊Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
639	C₄×Q₈	—	2	4	no	—
640	C₄×Q₈	—	2	4	no	—
641	C₄×Q₈	C₂×C₄×C₅₃	1	8	yes	complemented
642	C₄×D₄	—	2	4	no	—
643	C₄×D₄	—	2	4	no	—
644	C₄×D₄	C₂×C₄×C₅₃	1	8	yes	—
645	#117	—	2	4	no	—
646	#117	—	2	8	no	—
647	#117	C₂×C₄×C₅₃	1	8	yes	complemented
648	#117	C₂×C₄×C₅₃	1	16	yes	complemented
649	C₂×C₄⋊C₄	—	2	4	no	—
650	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	8	yes	complemented
651	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
678	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
686	C₂×C₄²	—	2	8	no	—
687	C₂×C₄²	—	2	4	no	—
688	C₂×C₄²	—	2	4	no	—
689	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
690	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
691	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
692	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
695	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
697	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
699	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
701	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
703	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
705	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
708	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
709	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
710	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
711	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
712	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
713	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
714	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
716	#95	C₂³×C₅₃	1	2	yes	—
717	#95	C₂³×C₅₃	1	2	yes	—
718	#95	C₂³×C₅₃	1	2	yes	—
719	#95	C₂³×C₅₃	1	2	yes	—
720	#95	C₂³×C₅₃	1	1	yes	characteristic
721	#95	C₂³×C₅₃	1	1	yes	characteristic
722	#95	C₂³×C₅₃	1	2	yes	—
723	#95	C₂³×C₅₃	1	2	yes	—
724	#95	C₂³×C₅₃	1	2	yes	—
725	#95	C₂³×C₅₃	1	2	yes	—
726	#95	C₂³×C₅₃	1	2	yes	—
727	#95	C₂³×C₅₃	1	2	yes	—
728	#95	C₂³×C₅₃	1	2	yes	—
729	#95	C₂³×C₅₃	1	2	yes	—
730	#95	C₂³×C₅₃	1	2	yes	—
731	#95	C₂³×C₅₃	1	1	yes	characteristic
732	#95	C₂³×C₅₃	1	1	yes	characteristic
733	#95	C₂³×C₅₃	1	1	yes	characteristic
734	#95	C₂³×C₅₃	1	1	yes	characteristic
735	#95	C₂³×C₅₃	1	2	yes	—
736	#95	C₂³×C₅₃	1	2	yes	—
737	#95	C₂³×C₅₃	1	2	yes	—
738	#95	C₂³×C₅₃	1	2	yes	—
739	#95	C₂³×C₅₃	1	2	yes	—
740	#95	C₂³×C₅₃	1	2	yes	—
741	#95	C₂³×C₅₃	1	2	yes	—
742	#95	C₂³×C₅₃	1	2	yes	—
743	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
744	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
745	C₂×Q₈	—	2	2	no	—
746	C₂×Q₈	—	2	2	no	—
747	C₂×Q₈	C₂²×C₄×C₅₃	1	4	yes	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	4	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	4	1	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	1	no	—
771	C₂²×C₄	C₂²×C₄×C₅₃	1	8	yes	—
772	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
773	C₂²×C₄	C₂²×C₄×C₅₃	1	4	yes	—
774	C₂²×C₄	#41×C₅₃	1	4	yes	—
775	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
796	C₄⋊C₄	—	2	4	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	4	no	—
799	C₄⋊C₄	—	2	4	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	4	2	no	—
807	C₄⋊C₄	—	4	2	no	—
808	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
809	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
810	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
811	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
812	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
813	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
814	C₄⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
815	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
816	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
817	C₄⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
818	C₄⋊C₄	#41×C₅₃	1	4	yes	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	4	2	no	—
825	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
826	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
827	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
828	C₂²⋊C₄	C₂²×C₄×C₅₃	1	4	yes	—
829	C₂²⋊C₄	C₂²×C₄×C₅₃	1	8	yes	—
830	C₂²⋊C₄	#41×C₅₃	1	4	yes	—
831	C₄²	—	2	4	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	4	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	4	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	4	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	4	no	—
842	C₄²	—	2	4	no	—
843	C₄²	—	2	4	no	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	4	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	4	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	4	no	—
851	C₄²	—	4	2	no	—
852	C₄²	—	4	1	no	—
853	C₄²	—	4	2	no	—
854	C₄²	C₂²×C₄×C₅₃	1	8	yes	—
855	C₄²	C₂²×C₄×C₅₃	1	8	yes	—
856	C₄²	C₂²×C₄×C₅₃	1	4	yes	—
857	C₄²	#41×C₅₃	1	4	yes	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	1	no	—
867	C₂³	—	2	1	no	—
868	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
869	C₂³	C₂³×C₄×C₅₃	1	2	yes	—
870	C₂³	C₂×#41×C₅₃	1	2	yes	—
871	C₂³	C₂×#41×C₅₃	1	2	yes	—
872	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
873	Q₈	—	2	8	no	—
874	D₄	—	2	8	no	—
875	C₂×C₄	—	2	16	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	8	no	—
903	C₂×C₄	—	2	8	no	—
904	C₂×C₄	—	2	8	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	—	4	8	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
928	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
929	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
930	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
931	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
932	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
933	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
934	C₂×C₄	C₂³×C₄×C₅₃	1	4	yes	—
935	C₂×C₄	C₂³×C₄×C₅₃	1	2	yes	—
936	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
937	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
938	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
939	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
940	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
941	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
942	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
943	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
944	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
945	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	2	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	1	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	1	no	—
959	C₂²	C₄×#41×C₅₃	1	4	yes	—
960	C₂²	C₂⁴×C₄×C₅₃	1	1	yes	characteristic
961	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
962	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
963	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
964	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
965	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
966	C₂²	C₅₃×#585	1	1	yes	characteristic
967	C₄	—	2	2	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	2	no	—
970	C₄	—	2	4	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	4	no	—
973	C₄	—	2	4	no	—
974	C₄	—	2	2	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	2	4	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	4	no	—
980	C₄	—	4	1	no	—
981	C₄	—	4	1	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	1	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	C₄×#41×C₅₃	1	4	yes	—
987	C₄	C₅₃×#552	1	4	yes	direct product factor
988	C₂	—	2	4	no	—
989	C₂	—	4	2	no	—
990	C₂	C₂×C₄×#41×C₅₃	1	1	yes	characteristic
991	C₂	C₂×C₄×#41×C₅₃	1	1	yes	characteristic
992	C₂	C₄×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
993	C₂	C₂×C₅₃×#552	1	1	yes	characteristic
994	C₂	C₅₃×#3475	1	1	yes	characteristic
995	C₂	C₅₃×#3475	1	1	yes	characteristic
996	C₂	C₅₃×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₅₃
Frattini, cosocle	C₂³	C₂⁵×C₅₃
socle	C₂³×C₅₃	C₂⁵
prime radical	C₂²×D₄×C₅₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#2373	C₂	semidirect
3. C₅₃×#2371	C₂	semidirect
4. C₅₃×#2370	C₂	semidirect
5. C₅₃×#2362	C₂	semidirect
6. C₅₃×#2360	C₂	semidirect
8. C₅₃×#2356	C₂	semidirect
10. C₅₃×#2346	C₂	semidirect
11. C₅₃×#2344	C₂	semidirect
12. C₅₃×#2343	C₂	semidirect
13. C₄×#125×C₅₃	C₂	semidirect
14. C₄×#125×C₅₃	C₂	semidirect
15. C₄×#126×C₅₃	C₂	semidirect
16. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
17. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
19. C₄²×Q₈×C₅₃	C₂	semidirect
21. C₄×#117×C₅₃	C₂	semidirect
22. C₄×#117×C₅₃	C₂	semidirect
23. C₂×C₄×C₄⋊C₄×C₅₃	C₂	semidirect
24. C₅₃×#552	C₄	direct (N × H)
134. #126×C₅₃	C₂×C₄	semidirect
135. #125×C₅₃	C₂×C₄	semidirect
136. #125×C₅₃	C₂×C₄	semidirect
138. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
139. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
142. C₄×Q₈×C₅₃	C₂×C₄	semidirect
148. #117×C₅₃	C₂×C₄	semidirect
149. #117×C₅₃	C₂×C₄	semidirect
151. C₂×C₄⋊C₄×C₅₃	C₂×C₄	semidirect
447. C₄×#552	C₅₃	direct (N × H)
489. C₄×C₅₃	#552	direct (N × H)
491. #2373	C₂×C₅₃	semidirect
492. #2371	C₂×C₅₃	semidirect
493. #2370	C₂×C₅₃	semidirect
494. #2362	C₂×C₅₃	semidirect
495. #2360	C₂×C₅₃	semidirect
497. #2356	C₂×C₅₃	semidirect
499. #2346	C₂×C₅₃	semidirect
500. #2344	C₂×C₅₃	semidirect
501. #2343	C₂×C₅₃	semidirect
502. C₄×#125	C₂×C₅₃	semidirect
503. C₄×#125	C₂×C₅₃	semidirect
504. C₄×#126	C₂×C₅₃	semidirect
505. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
506. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
508. C₄²×Q₈	C₂×C₅₃	semidirect
510. C₄×#117	C₂×C₅₃	semidirect
511. C₄×#117	C₂×C₅₃	semidirect
512. C₂×C₄×C₄⋊C₄	C₂×C₅₃	semidirect
522. #552	C₄×C₅₃	direct (N × H)
622. C₅₃	C₄×#552	direct (N × H)
633. #126	C₂×C₄×C₅₃	semidirect
634. #125	C₂×C₄×C₅₃	semidirect
635. #125	C₂×C₄×C₅₃	semidirect
637. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
638. C₂²⋊Q₈	C₂×C₄×C₅₃	semidirect
641. C₄×Q₈	C₂×C₄×C₅₃	semidirect
647. #117	C₂×C₄×C₅₃	semidirect
648. #117	C₂×C₄×C₅₃	semidirect
650. C₂×C₄⋊C₄	C₂×C₄×C₅₃	semidirect
987. C₄	C₅₃×#552	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#552	2
C₅₃×#2373	2
C₅₃×#2371	2
C₅₃×#2370	2
C₅₃×#2362	2
C₅₃×#2360	2
C₅₃×#2359	2
C₅₃×#2356	2
C₅₃×#2352	2
C₅₃×#2346	2
C₅₃×#2344	2
C₅₃×#2343	2
C₄×#125×C₅₃	2
C₄×#126×C₅₃	2
C₄×C₂²⋊Q₈×C₅₃	2
C₄×#123×C₅₃	2
C₄²×Q₈×C₅₃	2
C₄²×D₄×C₅₃	2
C₄×#117×C₅₃	2
C₂×C₄×C₄⋊C₄×C₅₃	2
C₄×#552	53

Subgroups — C4×C53×#552 #27241675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅₃×#552 #27241675