Subgroups — C₂×C₅₃×#3475 #27270220

Order 13568.

7954 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3475	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₅₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#553	C₂	1	2	yes	maximal, complemented
6	C₂×C₅₃×#552	C₂	1	2	yes	maximal, complemented
7	C₂×C₅₃×#552	C₂	1	2	yes	maximal, complemented
8	C₂×C₅₃×#551	C₂	1	4	yes	maximal, complemented
9	C₂×C₅₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#546	C₂	1	2	yes	maximal, complemented
11	C₂×C₅₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#529	C₂	1	4	yes	maximal, complemented
13	C₂×C₅₃×#529	C₂	1	2	yes	maximal, complemented
14	C₂×C₅₃×#525	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×#41×C₅₃	C₂	1	2	yes	maximal, complemented
17	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#117×C₅₃	C₂	1	2	yes	maximal, complemented
19	C₂²×#41×C₅₃	C₂²	1	2	yes	—
20	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₅₃	C₂²	1	2	yes	—
23	C₅₃×#556	C₂²	1	16	yes	complemented
24	C₅₃×#555	C₂²	1	16	yes	complemented
25	C₅₃×#554	C₂²	1	16	yes	complemented
26	C₅₃×#553	C₂²	1	32	yes	complemented
27	C₅₃×#552	C₂²	1	32	yes	complemented
28	C₅₃×#552	C₂²	1	32	yes	complemented
29	C₅₃×#551	C₂²	1	64	yes	complemented
30	C₅₃×#547	C₂²	1	16	yes	complemented
31	C₅₃×#546	C₂²	1	32	yes	complemented
32	C₅₃×#533	C₂²	1	16	yes	complemented
33	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₅₃×#529	C₂²	1	64	yes	complemented
36	C₅₃×#529	C₂²	1	32	yes	complemented
37	C₂×#126×C₅₃	C₂²	1	4	yes	complemented
38	C₂×#126×C₅₃	C₂²	1	4	yes	complemented
39	C₂×#126×C₅₃	C₂²	1	4	yes	complemented
40	C₂×#125×C₅₃	C₂²	1	4	yes	complemented
41	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
42	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
43	C₂×#124×C₅₃	C₂²	1	2	yes	—
44	C₂×#124×C₅₃	C₂²	1	4	yes	complemented
45	C₅₃×#525	C₂²	1	32	yes	complemented
46	C₂×#123×C₅₃	C₂²	1	4	yes	—
47	C₂×#123×C₅₃	C₂²	1	4	yes	—
48	C₂×#123×C₅₃	C₂²	1	4	yes	complemented
49	C₂×#123×C₅₃	C₂²	1	4	yes	complemented
50	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
51	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
52	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
53	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	complemented
54	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
55	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
56	C₂×#121×C₅₃	C₂²	1	4	yes	—
57	C₂×#121×C₅₃	C₂²	1	2	yes	—
58	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
59	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
60	C₂×#120×C₅₃	C₂²	1	4	yes	—
61	C₄×#41×C₅₃	C₂²	1	16	yes	complemented
62	C₄×#41×C₅₃	C₂²	1	32	yes	complemented
63	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
65	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
67	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
68	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
69	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
70	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
71	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
72	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
73	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
74	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
75	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
76	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
77	C₂×C₄×D₄×C₅₃	C₂²	1	16	yes	complemented
78	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
80	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
82	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
83	C₂×#117×C₅₃	C₂²	1	4	yes	—
84	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
85	C₂×#117×C₅₃	C₂²	1	2	yes	—
86	C₂×#117×C₅₃	C₂²	1	4	yes	complemented
87	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
88	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
89	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
90	C₂×#117×C₅₃	C₂²	1	4	yes	complemented
91	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
92	C₂×#117×C₅₃	C₂²	1	32	yes	complemented
93	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
94	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
95	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
96	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	4	yes	—
97	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
98	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
99	C₂²×C₄²×C₅₃	C₂²	1	4	yes	complemented
100	C₂²×C₄²×C₅₃	C₂²	1	2	yes	complemented
101	C₂⁵×C₅₃	C₂³	1	2	yes	—
102	C₂×#41×C₅₃	—	2	16	no	—
103	C₂×#41×C₅₃	—	2	8	no	—
104	C₂×#41×C₅₃	C₂³	1	8	yes	—
105	C₂×#41×C₅₃	C₂³	1	16	yes	—
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×D₄×C₅₃	—	2	8	no	—
110	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
114	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₅₃	C₂³	1	8	yes	—
116	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
117	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₅₃	—	2	16	no	—
119	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
121	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
122	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₅₃	C₂³	1	16	yes	—
126	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
131	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
133	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
134	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
135	#126×C₅₃	C₂³	1	32	yes	complemented
136	#126×C₅₃	C₂³	1	32	yes	complemented
137	#126×C₅₃	C₂³	1	32	yes	complemented
138	#125×C₅₃	C₂³	1	32	yes	complemented
139	#125×C₅₃	C₂³	1	16	yes	complemented
140	#125×C₅₃	C₂³	1	16	yes	complemented
141	#124×C₅₃	C₂³	1	16	yes	—
142	#124×C₅₃	C₂³	1	32	yes	complemented
143	#123×C₅₃	C₂³	1	32	yes	—
144	#123×C₅₃	C₂³	1	32	yes	—
145	#123×C₅₃	C₂³	1	32	yes	complemented
146	#123×C₅₃	C₂³	1	32	yes	complemented
147	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
148	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
149	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
150	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
151	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
152	C₂²⋊Q₈×C₅₃	C₂³	1	32	yes	complemented
153	#121×C₅₃	C₂³	1	32	yes	—
154	#121×C₅₃	C₂³	1	16	yes	—
155	#121×C₅₃	C₂³	1	16	yes	complemented
156	#121×C₅₃	C₂³	1	16	yes	complemented
157	#120×C₅₃	C₂³	1	32	yes	—
158	C₄×Q₈×C₅₃	C₂³	1	16	yes	complemented
159	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
160	C₄×Q₈×C₅₃	C₂³	1	16	yes	complemented
161	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
162	C₄×Q₈×C₅₃	C₂³	1	16	yes	complemented
163	C₄×D₄×C₅₃	C₂³	1	8	yes	—
164	C₄×D₄×C₅₃	C₂³	1	16	yes	—
165	C₄×D₄×C₅₃	C₂³	1	8	yes	—
166	C₄×D₄×C₅₃	C₂³	1	8	yes	—
167	C₄×D₄×C₅₃	C₂³	1	16	yes	—
168	C₄×D₄×C₅₃	C₂³	1	8	yes	—
169	C₄×D₄×C₅₃	C₂³	1	16	yes	—
170	C₄×D₄×C₅₃	C₂³	1	16	yes	—
171	C₄×D₄×C₅₃	C₂³	1	16	yes	—
172	C₄×D₄×C₅₃	C₂³	1	32	yes	complemented
173	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
174	C₄×D₄×C₅₃	C₂³	1	32	yes	complemented
175	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
176	C₄×D₄×C₅₃	C₂³	1	32	yes	complemented
177	#117×C₅₃	C₂³	1	8	yes	—
178	#117×C₅₃	C₂³	1	16	yes	—
179	#117×C₅₃	C₂³	1	32	yes	—
180	#117×C₅₃	C₂³	1	32	yes	complemented
181	#117×C₅₃	C₂³	1	16	yes	complemented
182	#117×C₅₃	C₂³	1	16	yes	complemented
183	#117×C₅₃	C₂³	1	16	yes	complemented
184	#117×C₅₃	C₂³	1	32	yes	complemented
185	#117×C₅₃	C₂³	1	16	yes	complemented
186	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	—
190	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
195	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
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	4	yes	—
200	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
201	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
202	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
203	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
204	C₂×C₄⋊C₄×C₅₃	C₂³	1	16	yes	complemented
205	C₂×C₄⋊C₄×C₅₃	C₂³	1	16	yes	complemented
206	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
208	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
210	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
211	C₂×C₂²⋊C₄×C₅₃	C₂³	1	32	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	16	yes	—
216	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
217	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
220	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
222	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₅₃	C₂³	1	8	yes	—
225	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
226	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
227	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
228	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
229	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
232	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
233	C₂×C₄²×C₅₃	C₂³	1	32	yes	complemented
234	C₂×C₄²×C₅₃	C₂³	1	16	yes	complemented
235	C₂⁴×C₅₃	—	2	8	no	—
236	C₂⁴×C₅₃	—	2	8	no	—
237	C₂⁴×C₅₃	—	4	4	no	—
238	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
239	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
240	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
241	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
242	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
243	#41×C₅₃	—	2	64	no	—
244	#41×C₅₃	—	2	32	no	—
245	C₂×Q₈×C₅₃	—	2	4	no	—
246	C₂×Q₈×C₅₃	—	2	8	no	—
247	C₂×Q₈×C₅₃	—	4	4	no	—
248	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
249	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
250	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
251	C₂×D₄×C₅₃	—	2	8	no	—
252	C₂×D₄×C₅₃	—	2	8	no	—
253	C₂×D₄×C₅₃	—	2	16	no	—
254	C₂×D₄×C₅₃	—	2	32	no	—
255	C₂×D₄×C₅₃	—	2	4	no	—
256	C₂×D₄×C₅₃	—	2	4	no	—
257	C₂×D₄×C₅₃	—	4	8	no	—
258	C₂×D₄×C₅₃	#41	1	8	yes	complemented
259	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
260	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
261	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
262	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
263	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
264	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
265	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
266	C₂²×C₄×C₅₃	—	2	8	no	—
267	C₂²×C₄×C₅₃	—	2	16	no	—
268	C₂²×C₄×C₅₃	—	2	8	no	—
269	C₂²×C₄×C₅₃	—	2	8	no	—
270	C₂²×C₄×C₅₃	—	2	8	no	—
271	C₂²×C₄×C₅₃	—	2	8	no	—
272	C₂²×C₄×C₅₃	—	2	4	no	—
273	C₂²×C₄×C₅₃	—	2	8	no	—
274	C₂²×C₄×C₅₃	—	2	8	no	—
275	C₂²×C₄×C₅₃	—	2	64	no	—
276	C₂²×C₄×C₅₃	—	4	4	no	—
277	C₂²×C₄×C₅₃	—	4	8	no	—
278	C₂²×C₄×C₅₃	—	4	2	no	—
279	C₂²×C₄×C₅₃	#41	1	8	yes	complemented
280	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
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	4	yes	—
286	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
288	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
290	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
291	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
292	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
293	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
294	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
296	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
297	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
298	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
299	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₅₃	C₂⁴	1	16	yes	—
301	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
302	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
305	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
307	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
308	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
309	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
310	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
311	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
312	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
313	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
314	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
315	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
316	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
317	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
318	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
319	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
320	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
321	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
322	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
323	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
324	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
325	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
326	C₂²⋊C₄×C₅₃	C₂⁴	1	16	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	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
331	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
332	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
333	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
334	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
335	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
336	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
337	C₄²×C₅₃	C₂⁴	1	4	yes	—
338	C₄²×C₅₃	C₂⁴	1	4	yes	—
339	C₄²×C₅₃	C₂⁴	1	4	yes	—
340	C₄²×C₅₃	C₂⁴	1	4	yes	—
341	C₄²×C₅₃	C₂⁴	1	8	yes	—
342	C₄²×C₅₃	C₂⁴	1	16	yes	—
343	C₄²×C₅₃	C₂⁴	1	16	yes	—
344	C₄²×C₅₃	C₂⁴	1	16	yes	—
345	C₄²×C₅₃	C₂⁴	1	8	yes	—
346	C₄²×C₅₃	C₂⁴	1	8	yes	—
347	C₂³×C₅₃	—	2	4	no	—
348	C₂³×C₅₃	—	2	2	no	—
349	C₂³×C₅₃	—	2	4	no	—
350	C₂³×C₅₃	—	2	2	no	—
351	C₂³×C₅₃	—	2	16	no	—
352	C₂³×C₅₃	—	2	4	no	—
353	C₂³×C₅₃	—	2	4	no	—
354	C₂³×C₅₃	—	2	4	no	—
355	C₂³×C₅₃	—	2	16	no	—
356	C₂³×C₅₃	—	2	4	no	—
357	C₂³×C₅₃	—	2	4	no	—
358	C₂³×C₅₃	—	2	4	no	—
359	C₂³×C₅₃	—	4	8	no	—
360	C₂³×C₅₃	—	4	32	no	—
361	C₂³×C₅₃	C₂×#41	1	4	yes	—
362	C₂³×C₅₃	C₂×#41	1	8	yes	—
363	C₂³×C₅₃	C₂⁵	1	4	yes	—
364	C₂³×C₅₃	C₂⁵	1	4	yes	—
365	C₂³×C₅₃	C₂⁵	1	4	yes	—
366	C₂³×C₅₃	C₂⁵	1	2	yes	—
367	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
368	Q₈×C₅₃	—	2	8	no	—
369	Q₈×C₅₃	—	2	16	no	—
370	Q₈×C₅₃	—	4	8	no	—
371	D₄×C₅₃	—	2	16	no	—
372	D₄×C₅₃	—	2	16	no	—
373	D₄×C₅₃	—	2	32	no	—
374	D₄×C₅₃	—	2	8	no	—
375	D₄×C₅₃	—	2	8	no	—
376	D₄×C₅₃	—	4	16	no	—
377	D₄×C₅₃	C₂×#41	1	16	yes	complemented
378	C₂×C₄×C₅₃	—	2	16	no	—
379	C₂×C₄×C₅₃	—	2	4	no	—
380	C₂×C₄×C₅₃	—	2	4	no	—
381	C₂×C₄×C₅₃	—	2	4	no	—
382	C₂×C₄×C₅₃	—	2	2	no	—
383	C₂×C₄×C₅₃	—	2	8	no	—
384	C₂×C₄×C₅₃	—	2	4	no	—
385	C₂×C₄×C₅₃	—	2	32	no	—
386	C₂×C₄×C₅₃	—	2	2	no	—
387	C₂×C₄×C₅₃	—	2	4	no	—
388	C₂×C₄×C₅₃	—	2	8	no	—
389	C₂×C₄×C₅₃	—	2	2	no	—
390	C₂×C₄×C₅₃	—	2	16	no	—
391	C₂×C₄×C₅₃	—	2	16	no	—
392	C₂×C₄×C₅₃	—	2	16	no	—
393	C₂×C₄×C₅₃	—	2	16	no	—
394	C₂×C₄×C₅₃	—	2	8	no	—
395	C₂×C₄×C₅₃	—	2	16	no	—
396	C₂×C₄×C₅₃	—	2	16	no	—
397	C₂×C₄×C₅₃	—	4	8	no	—
398	C₂×C₄×C₅₃	—	4	16	no	—
399	C₂×C₄×C₅₃	—	4	4	no	—
400	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
401	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
402	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
403	C₂×C₄×C₅₃	C₂×#41	1	16	yes	complemented
404	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
405	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
406	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
407	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
408	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
409	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
410	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
411	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
412	C₂×C₄×C₅₃	C₂⁵	1	8	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×#3475	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
418	C₂²×C₅₃	—	2	4	no	—
419	C₂²×C₅₃	—	2	2	no	—
420	C₂²×C₅₃	—	2	4	no	—
421	C₂²×C₅₃	—	2	2	no	—
422	C₂²×C₅₃	—	2	8	no	—
423	C₂²×C₅₃	—	2	16	no	—
424	C₂²×C₅₃	—	2	4	no	—
425	C₂²×C₅₃	—	2	4	no	—
426	C₂²×C₅₃	—	2	4	no	—
427	C₂²×C₅₃	—	2	4	no	—
428	C₂²×C₅₃	—	2	4	no	—
429	C₂²×C₅₃	—	2	4	no	—
430	C₂²×C₅₃	—	4	32	no	—
431	C₂²×C₅₃	—	4	8	no	—
432	C₂²×C₅₃	—	4	8	no	—
433	C₂²×C₅₃	C₂²×#41	1	4	yes	—
434	C₂²×C₅₃	C₂²×#41	1	8	yes	—
435	C₂²×C₅₃	C₂²×#41	1	2	yes	—
436	C₂²×C₅₃	C₂²×#41	1	2	yes	—
437	C₂²×C₅₃	#585	1	2	yes	—
438	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
439	C₄×C₅₃	—	2	4	no	—
440	C₄×C₅₃	—	2	4	no	—
441	C₄×C₅₃	—	2	4	no	—
442	C₄×C₅₃	—	2	2	no	—
443	C₄×C₅₃	—	2	8	no	—
444	C₄×C₅₃	—	2	4	no	—
445	C₄×C₅₃	—	2	2	no	—
446	C₄×C₅₃	—	2	4	no	—
447	C₄×C₅₃	—	2	8	no	—
448	C₄×C₅₃	—	2	2	no	—
449	C₄×C₅₃	C₂²×#41	1	4	yes	—
450	C₄×C₅₃	C₂²×#41	1	4	yes	—
451	C₄×C₅₃	C₂²×#41	1	4	yes	—
452	#3475	C₂×C₅₃	1	32	yes	direct product factor
453	C₂×#556	C₂×C₅₃	1	1	yes	characteristic, complemented
454	C₂×#555	C₂×C₅₃	1	1	yes	characteristic, complemented
455	C₂×#554	C₂×C₅₃	1	1	yes	characteristic, complemented
456	C₂×#553	C₂×C₅₃	1	2	yes	complemented
457	C₂×#552	C₂×C₅₃	1	2	yes	complemented
458	C₂×#552	C₂×C₅₃	1	2	yes	complemented
459	C₂×#551	C₂×C₅₃	1	4	yes	complemented
460	C₂×#547	C₂×C₅₃	1	1	yes	characteristic, complemented
461	C₂×#546	C₂×C₅₃	1	2	yes	complemented
462	C₂×#533	C₂×C₅₃	1	1	yes	characteristic, complemented
463	C₂×#529	C₂×C₅₃	1	4	yes	complemented
464	C₂×#529	C₂×C₅₃	1	2	yes	complemented
465	C₂×#525	C₂×C₅₃	1	2	yes	complemented
466	C₂×C₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
467	C₂×C₄×#41	C₂×C₅₃	1	2	yes	complemented
468	C₂²×C₄×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
469	C₂²×#117	C₂×C₅₃	1	2	yes	complemented
470	C₂×C₅₃	—	2	4	no	—
471	C₂×C₅₃	—	2	8	no	—
472	C₂×C₅₃	—	4	4	no	—
473	C₂×C₅₃	—	4	4	no	—
474	C₂×C₅₃	#3475	1	4	yes	direct product factor
475	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
476	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
477	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
478	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
479	C₂²×#41	C₂²×C₅₃	1	2	yes	—
480	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
481	C₂⁴×C₄	C₂²×C₅₃	1	2	yes	—
482	#556	C₂²×C₅₃	1	16	yes	complemented
483	#555	C₂²×C₅₃	1	16	yes	complemented
484	#554	C₂²×C₅₃	1	16	yes	complemented
485	#553	C₂²×C₅₃	1	32	yes	complemented
486	#552	C₂²×C₅₃	1	32	yes	complemented
487	#552	C₂²×C₅₃	1	32	yes	complemented
488	#551	C₂²×C₅₃	1	64	yes	complemented
489	#547	C₂²×C₅₃	1	16	yes	complemented
490	#546	C₂²×C₅₃	1	32	yes	complemented
491	#533	C₂²×C₅₃	1	16	yes	complemented
492	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
493	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
494	#529	C₂²×C₅₃	1	64	yes	complemented
495	#529	C₂²×C₅₃	1	32	yes	complemented
496	C₂×#126	C₂²×C₅₃	1	4	yes	complemented
497	C₂×#126	C₂²×C₅₃	1	4	yes	complemented
498	C₂×#126	C₂²×C₅₃	1	4	yes	complemented
499	C₂×#125	C₂²×C₅₃	1	4	yes	complemented
500	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
501	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
502	C₂×#124	C₂²×C₅₃	1	2	yes	—
503	C₂×#124	C₂²×C₅₃	1	4	yes	complemented
504	#525	C₂²×C₅₃	1	32	yes	complemented
505	C₂×#123	C₂²×C₅₃	1	4	yes	—
506	C₂×#123	C₂²×C₅₃	1	4	yes	—
507	C₂×#123	C₂²×C₅₃	1	4	yes	complemented
508	C₂×#123	C₂²×C₅₃	1	4	yes	complemented
509	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
510	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
511	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
512	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
513	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
514	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	complemented
515	C₂×#121	C₂²×C₅₃	1	4	yes	—
516	C₂×#121	C₂²×C₅₃	1	2	yes	—
517	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
518	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
519	C₂×#120	C₂²×C₅₃	1	4	yes	—
520	C₄×#41	C₂²×C₅₃	1	16	yes	complemented
521	C₄×#41	C₂²×C₅₃	1	32	yes	complemented
522	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
523	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
524	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
525	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
526	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
527	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
528	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
529	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
530	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
531	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
532	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
533	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
534	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
535	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
536	C₂×C₄×D₄	C₂²×C₅₃	1	16	yes	complemented
537	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	complemented
538	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
539	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	complemented
540	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
541	C₂×C₄×D₄	C₂²×C₅₃	1	4	yes	complemented
542	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
543	C₂×#117	C₂²×C₅₃	1	2	yes	—
544	C₂×#117	C₂²×C₅₃	1	4	yes	—
545	C₂×#117	C₂²×C₅₃	1	4	yes	complemented
546	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
547	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
548	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
549	C₂×#117	C₂²×C₅₃	1	4	yes	complemented
550	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
551	C₂×#117	C₂²×C₅₃	1	32	yes	complemented
552	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
553	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
554	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
555	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	4	yes	—
556	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
557	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
558	C₂²×C₄²	C₂²×C₅₃	1	4	yes	complemented
559	C₂²×C₄²	C₂²×C₅₃	1	2	yes	complemented
560	C₅₃	C₂×#3475	1	1	yes	characteristic, direct product factor, Sylow
561	C₂⁵	C₂³×C₅₃	1	2	yes	—
562	C₂×#41	—	2	16	no	—
563	C₂×#41	—	2	8	no	—
564	C₂×#41	C₂³×C₅₃	1	8	yes	—
565	C₂×#41	C₂³×C₅₃	1	16	yes	—
566	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
567	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
568	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
569	C₂²×D₄	—	2	8	no	—
570	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
571	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
572	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
573	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
574	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
575	C₂²×D₄	C₂³×C₅₃	1	8	yes	—
576	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
577	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
578	C₂³×C₄	—	2	16	no	—
579	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
580	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
581	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
583	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
584	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
585	C₂³×C₄	C₂³×C₅₃	1	16	yes	—
586	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
587	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
588	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
589	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
591	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
592	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
593	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
594	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
595	#126	C₂³×C₅₃	1	32	yes	complemented
596	#126	C₂³×C₅₃	1	32	yes	complemented
597	#126	C₂³×C₅₃	1	32	yes	complemented
598	#125	C₂³×C₅₃	1	32	yes	complemented
599	#125	C₂³×C₅₃	1	16	yes	complemented
600	#125	C₂³×C₅₃	1	16	yes	complemented
601	#124	C₂³×C₅₃	1	16	yes	—
602	#124	C₂³×C₅₃	1	32	yes	complemented
603	#123	C₂³×C₅₃	1	32	yes	—
604	#123	C₂³×C₅₃	1	32	yes	—
605	#123	C₂³×C₅₃	1	32	yes	complemented
606	#123	C₂³×C₅₃	1	32	yes	complemented
607	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
608	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
609	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
610	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
611	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
612	C₂²⋊Q₈	C₂³×C₅₃	1	32	yes	complemented
613	#121	C₂³×C₅₃	1	32	yes	—
614	#121	C₂³×C₅₃	1	16	yes	—
615	#121	C₂³×C₅₃	1	16	yes	complemented
616	#121	C₂³×C₅₃	1	16	yes	complemented
617	#120	C₂³×C₅₃	1	32	yes	—
618	C₄×Q₈	C₂³×C₅₃	1	16	yes	complemented
619	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
620	C₄×Q₈	C₂³×C₅₃	1	16	yes	complemented
621	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
622	C₄×Q₈	C₂³×C₅₃	1	16	yes	complemented
623	C₄×D₄	C₂³×C₅₃	1	8	yes	—
624	C₄×D₄	C₂³×C₅₃	1	8	yes	—
625	C₄×D₄	C₂³×C₅₃	1	16	yes	—
626	C₄×D₄	C₂³×C₅₃	1	8	yes	—
627	C₄×D₄	C₂³×C₅₃	1	16	yes	—
628	C₄×D₄	C₂³×C₅₃	1	8	yes	—
629	C₄×D₄	C₂³×C₅₃	1	16	yes	—
630	C₄×D₄	C₂³×C₅₃	1	16	yes	—
631	C₄×D₄	C₂³×C₅₃	1	16	yes	—
632	C₄×D₄	C₂³×C₅₃	1	32	yes	complemented
633	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
634	C₄×D₄	C₂³×C₅₃	1	32	yes	complemented
635	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
636	C₄×D₄	C₂³×C₅₃	1	32	yes	complemented
637	#117	C₂³×C₅₃	1	8	yes	—
638	#117	C₂³×C₅₃	1	16	yes	—
639	#117	C₂³×C₅₃	1	32	yes	—
640	#117	C₂³×C₅₃	1	32	yes	complemented
641	#117	C₂³×C₅₃	1	16	yes	complemented
642	#117	C₂³×C₅₃	1	16	yes	complemented
643	#117	C₂³×C₅₃	1	16	yes	complemented
644	#117	C₂³×C₅₃	1	32	yes	complemented
645	#117	C₂³×C₅₃	1	16	yes	complemented
646	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	—
650	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
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	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
655	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
656	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
660	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
661	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
662	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
663	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₅₃	1	16	yes	complemented
665	C₂×C₄⋊C₄	C₂³×C₅₃	1	16	yes	complemented
666	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₅₃	1	32	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₅₃	1	16	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₅₃	1	4	yes	—
682	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
683	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
684	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
685	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
686	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
688	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
691	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₅₃	1	8	yes	—
693	C₂×C₄²	C₂³×C₅₃	1	32	yes	complemented
694	C₂×C₄²	C₂³×C₅₃	1	16	yes	complemented
695	C₂⁴	—	2	8	no	—
696	C₂⁴	—	2	8	no	—
697	C₂⁴	—	4	4	no	—
698	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
699	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
700	C₂⁴	C₂⁴×C₅₃	1	8	yes	—
701	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
702	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
703	#41	—	2	64	no	—
704	#41	—	2	32	no	—
705	C₂×Q₈	—	2	4	no	—
706	C₂×Q₈	—	2	8	no	—
707	C₂×Q₈	—	4	4	no	—
708	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
709	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
710	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
711	C₂×D₄	—	2	8	no	—
712	C₂×D₄	—	2	8	no	—
713	C₂×D₄	—	2	16	no	—
714	C₂×D₄	—	2	32	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	4	8	no	—
718	C₂×D₄	#41×C₅₃	1	8	yes	complemented
719	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
720	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
721	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
722	C₂×D₄	C₂⁴×C₅₃	1	16	yes	—
723	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
724	C₂×D₄	C₂⁴×C₅₃	1	16	yes	—
725	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
726	C₂²×C₄	—	2	8	no	—
727	C₂²×C₄	—	2	16	no	—
728	C₂²×C₄	—	2	8	no	—
729	C₂²×C₄	—	2	8	no	—
730	C₂²×C₄	—	2	8	no	—
731	C₂²×C₄	—	2	8	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	2	8	no	—
734	C₂²×C₄	—	2	8	no	—
735	C₂²×C₄	—	2	64	no	—
736	C₂²×C₄	—	4	4	no	—
737	C₂²×C₄	—	4	8	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	#41×C₅₃	1	8	yes	complemented
740	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
746	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
748	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
750	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
751	C₂²×C₄	C₂⁴×C₅₃	1	16	yes	—
752	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
753	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
754	C₂²×C₄	C₂⁴×C₅₃	1	2	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	4	yes	—
760	C₂²×C₄	C₂⁴×C₅₃	1	16	yes	—
761	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
762	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
766	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
767	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
768	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
769	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
770	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
771	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
772	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
773	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
774	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
775	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
776	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
777	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
778	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
779	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
780	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
781	C₄⋊C₄	C₂⁴×C₅₃	1	16	yes	—
782	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
783	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
784	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
785	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
786	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
787	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
788	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
789	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
790	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
791	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
792	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
793	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
794	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
795	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
796	C₂²⋊C₄	C₂⁴×C₅₃	1	16	yes	—
797	C₄²	C₂⁴×C₅₃	1	4	yes	—
798	C₄²	C₂⁴×C₅₃	1	4	yes	—
799	C₄²	C₂⁴×C₅₃	1	4	yes	—
800	C₄²	C₂⁴×C₅₃	1	4	yes	—
801	C₄²	C₂⁴×C₅₃	1	8	yes	—
802	C₄²	C₂⁴×C₅₃	1	16	yes	—
803	C₄²	C₂⁴×C₅₃	1	16	yes	—
804	C₄²	C₂⁴×C₅₃	1	16	yes	—
805	C₄²	C₂⁴×C₅₃	1	8	yes	—
806	C₄²	C₂⁴×C₅₃	1	8	yes	—
807	C₂³	—	2	4	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	4	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	16	no	—
812	C₂³	—	2	4	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	4	no	—
815	C₂³	—	2	16	no	—
816	C₂³	—	2	4	no	—
817	C₂³	—	2	4	no	—
818	C₂³	—	2	4	no	—
819	C₂³	—	4	8	no	—
820	C₂³	—	4	32	no	—
821	C₂³	C₂×#41×C₅₃	1	4	yes	—
822	C₂³	C₂×#41×C₅₃	1	8	yes	—
823	C₂³	C₂⁵×C₅₃	1	4	yes	—
824	C₂³	C₂⁵×C₅₃	1	4	yes	—
825	C₂³	C₂⁵×C₅₃	1	2	yes	—
826	C₂³	C₂⁵×C₅₃	1	4	yes	—
827	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
828	Q₈	—	2	8	no	—
829	Q₈	—	2	16	no	—
830	Q₈	—	4	8	no	—
831	D₄	—	2	16	no	—
832	D₄	—	2	16	no	—
833	D₄	—	2	32	no	—
834	D₄	—	2	8	no	—
835	D₄	—	2	8	no	—
836	D₄	—	4	16	no	—
837	D₄	C₂×#41×C₅₃	1	16	yes	complemented
838	C₂×C₄	—	2	16	no	—
839	C₂×C₄	—	2	4	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	4	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	8	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	2	32	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	2	8	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	16	no	—
851	C₂×C₄	—	2	16	no	—
852	C₂×C₄	—	2	16	no	—
853	C₂×C₄	—	2	16	no	—
854	C₂×C₄	—	2	8	no	—
855	C₂×C₄	—	2	16	no	—
856	C₂×C₄	—	2	16	no	—
857	C₂×C₄	—	4	8	no	—
858	C₂×C₄	—	4	16	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
861	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
862	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
863	C₂×C₄	C₂×#41×C₅₃	1	16	yes	complemented
864	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
865	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
866	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
867	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
868	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
869	C₂×C₄	C₂⁵×C₅₃	1	8	yes	—
870	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
871	C₂×C₄	C₂⁵×C₅₃	1	8	yes	—
872	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
873	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
874	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
875	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
876	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
877	C₂²	—	2	8	no	—
878	C₂²	—	2	16	no	—
879	C₂²	—	2	4	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	4	no	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	4	32	no	—
890	C₂²	—	4	8	no	—
891	C₂²	—	4	8	no	—
892	C₂²	C₂²×#41×C₅₃	1	4	yes	—
893	C₂²	C₂²×#41×C₅₃	1	8	yes	—
894	C₂²	C₂²×#41×C₅₃	1	2	yes	—
895	C₂²	C₂²×#41×C₅₃	1	2	yes	—
896	C₂²	C₅₃×#585	1	2	yes	—
897	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
898	C₄	—	2	4	no	—
899	C₄	—	2	4	no	—
900	C₄	—	2	4	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	8	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	4	no	—
906	C₄	—	2	8	no	—
907	C₄	—	2	2	no	—
908	C₄	C₂²×#41×C₅₃	1	4	yes	—
909	C₄	C₂²×#41×C₅₃	1	4	yes	—
910	C₄	C₂²×#41×C₅₃	1	4	yes	—
911	C₂	—	2	4	no	—
912	C₂	—	2	8	no	—
913	C₂	—	4	4	no	—
914	C₂	—	4	4	no	—
915	C₂	C₅₃×#3475	1	4	yes	direct product factor
916	C₂	C₂³×#41×C₅₃	1	1	yes	characteristic
917	C₂	C₂³×#41×C₅₃	1	1	yes	characteristic
918	C₂	C₂×C₅₃×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅₃
socle	C₂³×C₅₃	C₂⁵
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
1. C₅₃×#3475	C₂	direct (N × H)
2. C₂×C₅₃×#556	C₂	semidirect
3. C₂×C₅₃×#555	C₂	semidirect
4. C₂×C₅₃×#554	C₂	semidirect
5. C₂×C₅₃×#553	C₂	semidirect
6. C₂×C₅₃×#552	C₂	semidirect
7. C₂×C₅₃×#552	C₂	semidirect
8. C₂×C₅₃×#551	C₂	semidirect
9. C₂×C₅₃×#547	C₂	semidirect
10. C₂×C₅₃×#546	C₂	semidirect
11. C₂×C₅₃×#533	C₂	semidirect
12. C₂×C₅₃×#529	C₂	semidirect
13. C₂×C₅₃×#529	C₂	semidirect
14. C₂×C₅₃×#525	C₂	semidirect
15. C₂×C₄×#41×C₅₃	C₂	semidirect
16. C₂×C₄×#41×C₅₃	C₂	semidirect
17. C₂²×C₄×D₄×C₅₃	C₂	semidirect
18. C₂²×#117×C₅₃	C₂	semidirect
23. C₅₃×#556	C₂²	semidirect
24. C₅₃×#555	C₂²	semidirect
25. C₅₃×#554	C₂²	semidirect
26. C₅₃×#553	C₂²	semidirect
27. C₅₃×#552	C₂²	semidirect
28. C₅₃×#552	C₂²	semidirect
29. C₅₃×#551	C₂²	semidirect
30. C₅₃×#547	C₂²	semidirect
31. C₅₃×#546	C₂²	semidirect
32. C₅₃×#533	C₂²	semidirect
33. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
34. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
35. C₅₃×#529	C₂²	semidirect
36. C₅₃×#529	C₂²	semidirect
37. C₂×#126×C₅₃	C₂²	semidirect
38. C₂×#126×C₅₃	C₂²	semidirect
39. C₂×#126×C₅₃	C₂²	semidirect
40. C₂×#125×C₅₃	C₂²	semidirect
41. C₂×#125×C₅₃	C₂²	semidirect
42. C₂×#125×C₅₃	C₂²	semidirect
44. C₂×#124×C₅₃	C₂²	semidirect
45. C₅₃×#525	C₂²	semidirect
48. C₂×#123×C₅₃	C₂²	semidirect
49. C₂×#123×C₅₃	C₂²	semidirect
52. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
53. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
54. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
55. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
58. C₂×#121×C₅₃	C₂²	semidirect
59. C₂×#121×C₅₃	C₂²	semidirect
61. C₄×#41×C₅₃	C₂²	semidirect
62. C₄×#41×C₅₃	C₂²	semidirect
63. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
64. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
65. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
66. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
67. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
77. C₂×C₄×D₄×C₅₃	C₂²	semidirect
78. C₂×C₄×D₄×C₅₃	C₂²	semidirect
79. C₂×C₄×D₄×C₅₃	C₂²	semidirect
80. C₂×C₄×D₄×C₅₃	C₂²	semidirect
81. C₂×C₄×D₄×C₅₃	C₂²	semidirect
82. C₂×C₄×D₄×C₅₃	C₂²	semidirect
86. C₂×#117×C₅₃	C₂²	semidirect
87. C₂×#117×C₅₃	C₂²	semidirect
88. C₂×#117×C₅₃	C₂²	semidirect
89. C₂×#117×C₅₃	C₂²	semidirect
90. C₂×#117×C₅₃	C₂²	semidirect
91. C₂×#117×C₅₃	C₂²	semidirect
92. C₂×#117×C₅₃	C₂²	semidirect
94. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
95. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
99. C₂²×C₄²×C₅₃	C₂²	semidirect
100. C₂²×C₄²×C₅₃	C₂²	semidirect
133. C₄⋊Q₈×C₅₃	C₂³	semidirect
134. C₄⋊Q₈×C₅₃	C₂³	semidirect
135. #126×C₅₃	C₂³	semidirect
136. #126×C₅₃	C₂³	semidirect
137. #126×C₅₃	C₂³	semidirect
138. #125×C₅₃	C₂³	semidirect
139. #125×C₅₃	C₂³	semidirect
140. #125×C₅₃	C₂³	semidirect
142. #124×C₅₃	C₂³	semidirect
145. #123×C₅₃	C₂³	semidirect
146. #123×C₅₃	C₂³	semidirect
149. C₂²⋊Q₈×C₅₃	C₂³	semidirect
150. C₂²⋊Q₈×C₅₃	C₂³	semidirect
151. C₂²⋊Q₈×C₅₃	C₂³	semidirect
152. C₂²⋊Q₈×C₅₃	C₂³	semidirect
155. #121×C₅₃	C₂³	semidirect
156. #121×C₅₃	C₂³	semidirect
158. C₄×Q₈×C₅₃	C₂³	semidirect
159. C₄×Q₈×C₅₃	C₂³	semidirect
160. C₄×Q₈×C₅₃	C₂³	semidirect
161. C₄×Q₈×C₅₃	C₂³	semidirect
162. C₄×Q₈×C₅₃	C₂³	semidirect
172. C₄×D₄×C₅₃	C₂³	semidirect
173. C₄×D₄×C₅₃	C₂³	semidirect
174. C₄×D₄×C₅₃	C₂³	semidirect
175. C₄×D₄×C₅₃	C₂³	semidirect
176. C₄×D₄×C₅₃	C₂³	semidirect
180. #117×C₅₃	C₂³	semidirect
181. #117×C₅₃	C₂³	semidirect
182. #117×C₅₃	C₂³	semidirect
183. #117×C₅₃	C₂³	semidirect
184. #117×C₅₃	C₂³	semidirect
185. #117×C₅₃	C₂³	semidirect
204. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
205. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
233. C₂×C₄²×C₅₃	C₂³	semidirect
234. C₂×C₄²×C₅₃	C₂³	semidirect
258. C₂×D₄×C₅₃	#41	semidirect
279. C₂²×C₄×C₅₃	#41	semidirect
377. D₄×C₅₃	C₂×#41	semidirect
403. C₂×C₄×C₅₃	C₂×#41	semidirect
417. C₂×#3475	C₅₃	direct (N × H)
452. #3475	C₂×C₅₃	direct (N × H)
453. C₂×#556	C₂×C₅₃	semidirect
454. C₂×#555	C₂×C₅₃	semidirect
455. C₂×#554	C₂×C₅₃	semidirect
456. C₂×#553	C₂×C₅₃	semidirect
457. C₂×#552	C₂×C₅₃	semidirect
458. C₂×#552	C₂×C₅₃	semidirect
459. C₂×#551	C₂×C₅₃	semidirect
460. C₂×#547	C₂×C₅₃	semidirect
461. C₂×#546	C₂×C₅₃	semidirect
462. C₂×#533	C₂×C₅₃	semidirect
463. C₂×#529	C₂×C₅₃	semidirect
464. C₂×#529	C₂×C₅₃	semidirect
465. C₂×#525	C₂×C₅₃	semidirect
466. C₂×C₄×#41	C₂×C₅₃	semidirect
467. C₂×C₄×#41	C₂×C₅₃	semidirect
468. C₂²×C₄×D₄	C₂×C₅₃	semidirect
469. C₂²×#117	C₂×C₅₃	semidirect
474. C₂×C₅₃	#3475	direct (N × H)
482. #556	C₂²×C₅₃	semidirect
483. #555	C₂²×C₅₃	semidirect
484. #554	C₂²×C₅₃	semidirect
485. #553	C₂²×C₅₃	semidirect
486. #552	C₂²×C₅₃	semidirect
487. #552	C₂²×C₅₃	semidirect
488. #551	C₂²×C₅₃	semidirect
489. #547	C₂²×C₅₃	semidirect
490. #546	C₂²×C₅₃	semidirect
491. #533	C₂²×C₅₃	semidirect
492. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
493. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
494. #529	C₂²×C₅₃	semidirect
495. #529	C₂²×C₅₃	semidirect
496. C₂×#126	C₂²×C₅₃	semidirect
497. C₂×#126	C₂²×C₅₃	semidirect
498. C₂×#126	C₂²×C₅₃	semidirect
499. C₂×#125	C₂²×C₅₃	semidirect
500. C₂×#125	C₂²×C₅₃	semidirect
501. C₂×#125	C₂²×C₅₃	semidirect
503. C₂×#124	C₂²×C₅₃	semidirect
504. #525	C₂²×C₅₃	semidirect
507. C₂×#123	C₂²×C₅₃	semidirect
508. C₂×#123	C₂²×C₅₃	semidirect
511. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
512. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
513. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
514. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
517. C₂×#121	C₂²×C₅₃	semidirect
518. C₂×#121	C₂²×C₅₃	semidirect
520. C₄×#41	C₂²×C₅₃	semidirect
521. C₄×#41	C₂²×C₅₃	semidirect
522. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
523. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
524. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
525. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
526. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
536. C₂×C₄×D₄	C₂²×C₅₃	semidirect
537. C₂×C₄×D₄	C₂²×C₅₃	semidirect
538. C₂×C₄×D₄	C₂²×C₅₃	semidirect
539. C₂×C₄×D₄	C₂²×C₅₃	semidirect
540. C₂×C₄×D₄	C₂²×C₅₃	semidirect
541. C₂×C₄×D₄	C₂²×C₅₃	semidirect
545. C₂×#117	C₂²×C₅₃	semidirect
546. C₂×#117	C₂²×C₅₃	semidirect
547. C₂×#117	C₂²×C₅₃	semidirect
548. C₂×#117	C₂²×C₅₃	semidirect
549. C₂×#117	C₂²×C₅₃	semidirect
550. C₂×#117	C₂²×C₅₃	semidirect
551. C₂×#117	C₂²×C₅₃	semidirect
553. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
554. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
558. C₂²×C₄²	C₂²×C₅₃	semidirect
559. C₂²×C₄²	C₂²×C₅₃	semidirect
560. C₅₃	C₂×#3475	direct (N × H)
593. C₄⋊Q₈	C₂³×C₅₃	semidirect
594. C₄⋊Q₈	C₂³×C₅₃	semidirect
595. #126	C₂³×C₅₃	semidirect
596. #126	C₂³×C₅₃	semidirect
597. #126	C₂³×C₅₃	semidirect
598. #125	C₂³×C₅₃	semidirect
599. #125	C₂³×C₅₃	semidirect
600. #125	C₂³×C₅₃	semidirect
602. #124	C₂³×C₅₃	semidirect
605. #123	C₂³×C₅₃	semidirect
606. #123	C₂³×C₅₃	semidirect
609. C₂²⋊Q₈	C₂³×C₅₃	semidirect
610. C₂²⋊Q₈	C₂³×C₅₃	semidirect
611. C₂²⋊Q₈	C₂³×C₅₃	semidirect
612. C₂²⋊Q₈	C₂³×C₅₃	semidirect
615. #121	C₂³×C₅₃	semidirect
616. #121	C₂³×C₅₃	semidirect
618. C₄×Q₈	C₂³×C₅₃	semidirect
619. C₄×Q₈	C₂³×C₅₃	semidirect
620. C₄×Q₈	C₂³×C₅₃	semidirect
621. C₄×Q₈	C₂³×C₅₃	semidirect
622. C₄×Q₈	C₂³×C₅₃	semidirect
632. C₄×D₄	C₂³×C₅₃	semidirect
633. C₄×D₄	C₂³×C₅₃	semidirect
634. C₄×D₄	C₂³×C₅₃	semidirect
635. C₄×D₄	C₂³×C₅₃	semidirect
636. C₄×D₄	C₂³×C₅₃	semidirect
640. #117	C₂³×C₅₃	semidirect
641. #117	C₂³×C₅₃	semidirect
642. #117	C₂³×C₅₃	semidirect
643. #117	C₂³×C₅₃	semidirect
644. #117	C₂³×C₅₃	semidirect
645. #117	C₂³×C₅₃	semidirect
664. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
665. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
693. C₂×C₄²	C₂³×C₅₃	semidirect
694. C₂×C₄²	C₂³×C₅₃	semidirect
718. C₂×D₄	#41×C₅₃	semidirect
739. C₂²×C₄	#41×C₅₃	semidirect
837. D₄	C₂×#41×C₅₃	semidirect
863. C₂×C₄	C₂×#41×C₅₃	semidirect
915. C₂	C₅₃×#3475	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×#3475	2
C₂×C₅₃×#556	2
C₂×C₅₃×#555	2
C₂×C₅₃×#554	2
C₂×C₅₃×#553	2
C₂×C₅₃×#552	2
C₂×C₅₃×#551	2
C₂×C₅₃×#547	2
C₂×C₅₃×#546	2
C₂×C₅₃×#533	2
C₂×C₅₃×#529	2
C₂×C₅₃×#525	2
C₂×C₄×#41×C₅₃	2
C₂²×C₄×D₄×C₅₃	2
C₂²×#117×C₅₃	2
C₂×#3475	53

Subgroups — C2×C53×#3475 #27270220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3475 #27270220