Subgroups — C₂×D₄×#41×C₅₃ #27270213

Order 13568.

12314 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₅₃	C₂	1	2	yes	maximal, complemented
2	D₄×#41×C₅₃	C₂	1	32	yes	maximal, direct product factor
3	C₂×C₅₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#548	C₂	1	2	yes	maximal, complemented
6	C₂×C₅₃×#547	C₂	1	3	yes	maximal, complemented
7	C₂×C₅₃×#546	C₂	1	6	yes	maximal, complemented
8	C₂×D₄²×C₅₃	C₂	1	3	yes	maximal, complemented
9	C₂×C₅₃×#532	C₂	1	3	yes	maximal, complemented
10	C₂×C₅₃×#525	C₂	1	6	yes	maximal, complemented
11	C₂×C₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×D₄×C₅₃	C₂	1	3	yes	maximal, complemented
13	C₂²×#41×C₅₃	—	2	32	no	—
14	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
15	C₂²×#41×C₅₃	C₂²	1	6	yes	complemented
16	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
17	C₂²×#41×C₅₃	C₂²	1	6	yes	complemented
18	C₂²×#41×C₅₃	C₂²	1	32	yes	complemented
19	C₂³×Q₈×C₅₃	C₂²	1	2	yes	complemented
20	C₂³×D₄×C₅₃	C₂²	1	3	yes	—
21	C₂³×D₄×C₅₃	C₂²	1	6	yes	complemented
22	C₂⁴×C₄×C₅₃	C₂²	1	6	yes	complemented
23	C₅₃×#550	C₂²	1	16	yes	complemented
24	D₄×Q₈×C₅₃	C₂²	1	16	yes	complemented
25	C₅₃×#548	C₂²	1	32	yes	complemented
26	C₅₃×#547	C₂²	1	48	yes	complemented
27	C₅₃×#546	C₂²	1	96	yes	complemented
28	D₄²×C₅₃	C₂²	1	48	yes	complemented
29	C₅₃×#532	C₂²	1	48	yes	complemented
30	C₂×C₄⋊Q₈×C₅₃	C₂²	1	3	yes	complemented
31	C₂×#127×C₅₃	C₂²	1	3	yes	complemented
32	C₂×#124×C₅₃	C₂²	1	6	yes	complemented
33	C₅₃×#525	C₂²	1	96	yes	complemented
34	C₂×#123×C₅₃	C₂²	1	12	yes	complemented
35	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	6	yes	complemented
36	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	6	yes	complemented
37	C₂×#121×C₅₃	C₂²	1	6	yes	complemented
38	C₂×#121×C₅₃	C₂²	1	6	yes	complemented
39	C₂×#121×C₅₃	C₂²	1	6	yes	complemented
40	C₂×#121×C₅₃	C₂²	1	6	yes	complemented
41	C₂×#120×C₅₃	C₂²	1	12	yes	complemented
42	C₄×#41×C₅₃	C₂²	1	16	yes	complemented
43	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×D₄×C₅₃	C₂²	1	3	yes	—
46	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₅₃	C₂²	1	3	yes	complemented
48	C₂×C₄×D₄×C₅₃	C₂²	1	3	yes	complemented
49	C₂×C₄×D₄×C₅₃	C₂²	1	6	yes	complemented
50	C₂×C₄×D₄×C₅₃	C₂²	1	3	yes	complemented
51	C₂×C₄×D₄×C₅₃	C₂²	1	6	yes	complemented
52	C₂×C₄×D₄×C₅₃	C₂²	1	3	yes	complemented
53	C₂×C₄×D₄×C₅₃	C₂²	1	6	yes	complemented
54	C₂×C₄×D₄×C₅₃	C₂²	1	48	yes	complemented
55	C₂×#117×C₅₃	C₂²	1	3	yes	complemented
56	C₂²×C₄⋊C₄×C₅₃	C₂²	1	3	yes	complemented
57	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	6	yes	complemented
58	C₂²×C₄²×C₅₃	C₂²	1	3	yes	complemented
59	C₂⁵×C₅₃	C₂³	1	6	yes	—
60	C₂×#41×C₅₃	—	2	256	no	—
61	C₂×#41×C₅₃	—	2	16	no	—
62	C₂×#41×C₅₃	—	2	48	no	—
63	C₂×#41×C₅₃	—	2	48	no	—
64	C₂×#41×C₅₃	D₄	1	16	yes	direct product factor
65	C₂×#41×C₅₃	C₂³	1	8	yes	—
66	C₂×#41×C₅₃	C₂³	1	48	yes	complemented
67	C₂×#41×C₅₃	C₂³	1	48	yes	complemented
68	C₂×#41×C₅₃	C₂³	1	16	yes	complemented
69	C₂²×Q₈×C₅₃	—	2	16	no	—
70	C₂²×Q₈×C₅₃	C₂³	1	6	yes	—
71	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₅₃	C₂³	1	16	yes	complemented
73	C₂²×D₄×C₅₃	—	2	48	no	—
74	C₂²×D₄×C₅₃	—	2	24	no	—
75	C₂²×D₄×C₅₃	C₂³	1	6	yes	—
76	C₂²×D₄×C₅₃	C₂³	1	3	yes	—
77	C₂²×D₄×C₅₃	C₂³	1	24	yes	—
78	C₂²×D₄×C₅₃	C₂³	1	12	yes	—
79	C₂²×D₄×C₅₃	C₂³	1	6	yes	—
80	C₂²×D₄×C₅₃	C₂³	1	6	yes	—
81	C₂²×D₄×C₅₃	C₂³	1	3	yes	—
82	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₅₃	C₂³	1	48	yes	complemented
84	C₂³×C₄×C₅₃	—	2	48	no	—
85	C₂³×C₄×C₅₃	C₂³	1	3	yes	—
86	C₂³×C₄×C₅₃	C₂³	1	6	yes	—
87	C₂³×C₄×C₅₃	C₂³	1	6	yes	—
88	C₂³×C₄×C₅₃	C₂³	1	6	yes	—
89	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
90	C₂³×C₄×C₅₃	C₂³	1	6	yes	—
91	C₂³×C₄×C₅₃	C₂³	1	3	yes	—
92	C₂³×C₄×C₅₃	C₂³	1	3	yes	—
93	C₂³×C₄×C₅₃	C₂³	1	48	yes	complemented
94	C₄⋊Q₈×C₅₃	C₂³	1	24	yes	complemented
95	#127×C₅₃	C₂³	1	24	yes	complemented
96	#124×C₅₃	C₂³	1	48	yes	complemented
97	#123×C₅₃	C₂³	1	96	yes	complemented
98	C₂²⋊Q₈×C₅₃	C₂³	1	48	yes	complemented
99	C₂²⋊Q₈×C₅₃	C₂³	1	48	yes	complemented
100	#121×C₅₃	C₂³	1	48	yes	complemented
101	#121×C₅₃	C₂³	1	48	yes	complemented
102	#121×C₅₃	C₂³	1	48	yes	complemented
103	#121×C₅₃	C₂³	1	48	yes	complemented
104	#120×C₅₃	C₂³	1	96	yes	complemented
105	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
106	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
107	C₄×D₄×C₅₃	C₂³	1	8	yes	—
108	C₄×D₄×C₅₃	C₂³	1	24	yes	—
109	C₄×D₄×C₅₃	C₂³	1	48	yes	complemented
110	C₄×D₄×C₅₃	C₂³	1	24	yes	complemented
111	C₄×D₄×C₅₃	C₂³	1	48	yes	complemented
112	C₄×D₄×C₅₃	C₂³	1	24	yes	complemented
113	C₄×D₄×C₅₃	C₂³	1	24	yes	complemented
114	C₄×D₄×C₅₃	C₂³	1	24	yes	complemented
115	C₄×D₄×C₅₃	C₂³	1	48	yes	complemented
116	#117×C₅₃	C₂³	1	24	yes	complemented
117	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₅₃	C₂³	1	3	yes	—
119	C₂×C₄⋊C₄×C₅₃	C₂³	1	6	yes	—
120	C₂×C₄⋊C₄×C₅₃	C₂³	1	3	yes	—
121	C₂×C₄⋊C₄×C₅₃	C₂³	1	3	yes	—
122	C₂×C₄⋊C₄×C₅₃	C₂³	1	6	yes	—
123	C₂×C₄⋊C₄×C₅₃	C₂³	1	24	yes	complemented
124	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	—
126	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	—
127	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	—
128	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	—
129	C₂×C₂²⋊C₄×C₅₃	C₂³	1	12	yes	—
130	C₂×C₂²⋊C₄×C₅₃	C₂³	1	48	yes	complemented
131	C₂×C₄²×C₅₃	C₂³	1	3	yes	—
132	C₂×C₄²×C₅₃	C₂³	1	3	yes	—
133	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₅₃	C₂³	1	3	yes	—
135	C₂×C₄²×C₅₃	C₂³	1	24	yes	complemented
136	C₂⁴×C₅₃	—	2	24	no	—
137	C₂⁴×C₅₃	—	2	24	no	—
138	C₂⁴×C₅₃	—	4	12	no	—
139	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
140	C₂⁴×C₅₃	C₂⁴	1	24	yes	—
141	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
142	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
143	#41×C₅₃	—	2	64	no	—
144	#41×C₅₃	—	2	192	no	—
145	#41×C₅₃	—	2	192	no	—
146	#41×C₅₃	C₂×D₄	1	64	yes	direct product factor
147	C₂×Q₈×C₅₃	—	2	64	no	—
148	C₂×Q₈×C₅₃	—	2	24	no	—
149	C₂×Q₈×C₅₃	C₂×D₄	1	8	yes	complemented
150	C₂×Q₈×C₅₃	C₂⁴	1	24	yes	—
151	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
152	C₂×D₄×C₅₃	—	2	48	no	—
153	C₂×D₄×C₅₃	—	2	24	no	—
154	C₂×D₄×C₅₃	—	2	192	no	—
155	C₂×D₄×C₅₃	—	2	96	no	—
156	C₂×D₄×C₅₃	—	2	24	no	—
157	C₂×D₄×C₅₃	—	2	12	no	—
158	C₂×D₄×C₅₃	—	4	12	no	—
159	C₂×D₄×C₅₃	C₂×D₄	1	24	yes	complemented
160	C₂×D₄×C₅₃	#41	1	8	yes	direct product factor
161	C₂×D₄×C₅₃	C₂⁴	1	24	yes	—
162	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
163	C₂×D₄×C₅₃	C₂⁴	1	48	yes	—
164	C₂×D₄×C₅₃	C₂⁴	1	24	yes	—
165	C₂×D₄×C₅₃	C₂⁴	1	24	yes	—
166	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
167	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₅₃	—	2	24	no	—
169	C₂²×C₄×C₅₃	—	2	8	no	—
170	C₂²×C₄×C₅₃	—	2	24	no	—
171	C₂²×C₄×C₅₃	—	2	24	no	—
172	C₂²×C₄×C₅₃	—	2	24	no	—
173	C₂²×C₄×C₅₃	—	2	192	no	—
174	C₂²×C₄×C₅₃	—	2	12	no	—
175	C₂²×C₄×C₅₃	—	4	6	no	—
176	C₂²×C₄×C₅₃	C₂×D₄	1	24	yes	complemented
177	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
179	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
180	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
181	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
183	C₂²×C₄×C₅₃	C₂⁴	1	24	yes	—
184	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
185	C₂²×C₄×C₅₃	C₂⁴	1	24	yes	—
186	C₂²×C₄×C₅₃	C₂⁴	1	24	yes	—
187	C₂²×C₄×C₅₃	C₂⁴	1	24	yes	—
188	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
189	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
190	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
191	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
193	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
194	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
195	C₄⋊C₄×C₅₃	C₂⁴	1	24	yes	—
196	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
197	C₄⋊C₄×C₅₃	C₂⁴	1	12	yes	—
198	C₄⋊C₄×C₅₃	C₂⁴	1	24	yes	—
199	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
200	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
201	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
202	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
203	C₂²⋊C₄×C₅₃	C₂⁴	1	24	yes	—
204	C₂²⋊C₄×C₅₃	C₂⁴	1	48	yes	—
205	C₄²×C₅₃	C₂⁴	1	4	yes	—
206	C₄²×C₅₃	C₂⁴	1	12	yes	—
207	C₄²×C₅₃	C₂⁴	1	12	yes	—
208	C₄²×C₅₃	C₂⁴	1	12	yes	—
209	C₂³×C₅₃	—	2	4	no	—
210	C₂³×C₅₃	—	2	6	no	—
211	C₂³×C₅₃	—	2	6	no	—
212	C₂³×C₅₃	—	2	4	no	—
213	C₂³×C₅₃	—	2	48	no	—
214	C₂³×C₅₃	—	2	12	no	—
215	C₂³×C₅₃	—	2	12	no	—
216	C₂³×C₅₃	—	2	48	no	—
217	C₂³×C₅₃	—	2	12	no	—
218	C₂³×C₅₃	—	4	24	no	—
219	C₂³×C₅₃	—	4	96	no	—
220	C₂³×C₅₃	C₂²×D₄	1	12	yes	—
221	C₂³×C₅₃	C₂×#41	1	8	yes	complemented
222	C₂³×C₅₃	C₂⁵	1	12	yes	—
223	C₂³×C₅₃	C₂⁵	1	6	yes	—
224	C₂³×C₅₃	C₂⁵	1	4	yes	—
225	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
226	Q₈×C₅₃	—	2	48	no	—
227	Q₈×C₅₃	C₂²×D₄	1	16	yes	complemented
228	D₄×C₅₃	—	2	96	no	—
229	D₄×C₅₃	—	2	48	no	—
230	D₄×C₅₃	—	2	48	no	—
231	D₄×C₅₃	—	2	24	no	—
232	D₄×C₅₃	—	4	24	no	—
233	D₄×C₅₃	C₂²×D₄	1	48	yes	complemented
234	D₄×C₅₃	C₂×#41	1	16	yes	direct product factor
235	C₂×C₄×C₅₃	—	2	4	no	—
236	C₂×C₄×C₅₃	—	2	12	no	—
237	C₂×C₄×C₅₃	—	2	48	no	—
238	C₂×C₄×C₅₃	—	2	6	no	—
239	C₂×C₄×C₅₃	—	2	2	no	—
240	C₂×C₄×C₅₃	—	2	6	no	—
241	C₂×C₄×C₅₃	—	2	16	no	—
242	C₂×C₄×C₅₃	—	2	48	no	—
243	C₂×C₄×C₅₃	—	2	48	no	—
244	C₂×C₄×C₅₃	—	2	48	no	—
245	C₂×C₄×C₅₃	—	2	24	no	—
246	C₂×C₄×C₅₃	—	4	12	no	—
247	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
248	C₂×C₄×C₅₃	C₂²×D₄	1	12	yes	—
249	C₂×C₄×C₅₃	C₂²×D₄	1	48	yes	complemented
250	C₂×C₄×C₅₃	C₂×#41	1	4	yes	complemented
251	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
252	C₂×C₄×C₅₃	C₂⁵	1	12	yes	—
253	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
254	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
255	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
256	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
257	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
258	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
259	C₂×D₄×#41	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₂²×C₅₃	—	2	4	no	—
261	C₂²×C₅₃	—	2	6	no	—
262	C₂²×C₅₃	—	2	6	no	—
263	C₂²×C₅₃	—	2	4	no	—
264	C₂²×C₅₃	—	2	16	no	—
265	C₂²×C₅₃	—	2	24	no	—
266	C₂²×C₅₃	—	2	12	no	—
267	C₂²×C₅₃	—	2	12	no	—
268	C₂²×C₅₃	—	2	12	no	—
269	C₂²×C₅₃	—	4	96	no	—
270	C₂²×C₅₃	—	4	24	no	—
271	C₂²×C₅₃	C₂³×D₄	1	12	yes	—
272	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
273	C₂²×C₅₃	C₂²×#41	1	2	yes	—
274	C₂²×C₅₃	C₂²×#41	1	8	yes	complemented
275	C₂²×C₅₃	#585	1	2	yes	—
276	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
277	C₄×C₅₃	—	2	4	no	—
278	C₄×C₅₃	—	2	12	no	—
279	C₄×C₅₃	—	2	6	no	—
280	C₄×C₅₃	—	2	2	no	—
281	C₄×C₅₃	—	2	6	no	—
282	C₄×C₅₃	C₂³×D₄	1	4	yes	—
283	C₄×C₅₃	C₂³×D₄	1	12	yes	—
284	C₄×C₅₃	C₂²×#41	1	4	yes	complemented
285	C₂³×#41	C₂×C₅₃	1	2	yes	complemented
286	D₄×#41	C₂×C₅₃	1	32	yes	direct product factor
287	C₂×#550	C₂×C₅₃	1	1	yes	characteristic, complemented
288	C₂×D₄×Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
289	C₂×#548	C₂×C₅₃	1	2	yes	complemented
290	C₂×#547	C₂×C₅₃	1	3	yes	complemented
291	C₂×#546	C₂×C₅₃	1	6	yes	complemented
292	C₂×D₄²	C₂×C₅₃	1	3	yes	complemented
293	C₂×#532	C₂×C₅₃	1	3	yes	complemented
294	C₂×#525	C₂×C₅₃	1	6	yes	complemented
295	C₂×C₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
296	C₂²×C₄×D₄	C₂×C₅₃	1	3	yes	complemented
297	C₂×C₅₃	—	2	8	no	—
298	C₂×C₅₃	—	2	12	no	—
299	C₂×C₅₃	—	4	12	no	—
300	C₂×C₅₃	D₄×#41	1	4	yes	direct product factor
301	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
302	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
303	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
304	C₂²×#41	—	2	32	no	—
305	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
306	C₂²×#41	C₂²×C₅₃	1	6	yes	complemented
307	C₂²×#41	C₂²×C₅₃	1	6	yes	complemented
308	C₂²×#41	C₂²×C₅₃	1	2	yes	complemented
309	C₂²×#41	C₂²×C₅₃	1	32	yes	complemented
310	C₂³×Q₈	C₂²×C₅₃	1	2	yes	complemented
311	C₂³×D₄	C₂²×C₅₃	1	3	yes	—
312	C₂³×D₄	C₂²×C₅₃	1	6	yes	complemented
313	C₂⁴×C₄	C₂²×C₅₃	1	6	yes	complemented
314	#550	C₂²×C₅₃	1	16	yes	complemented
315	D₄×Q₈	C₂²×C₅₃	1	16	yes	complemented
316	#548	C₂²×C₅₃	1	32	yes	complemented
317	#547	C₂²×C₅₃	1	48	yes	complemented
318	#546	C₂²×C₅₃	1	96	yes	complemented
319	D₄²	C₂²×C₅₃	1	48	yes	complemented
320	#532	C₂²×C₅₃	1	48	yes	complemented
321	C₂×C₄⋊Q₈	C₂²×C₅₃	1	3	yes	complemented
322	C₂×#127	C₂²×C₅₃	1	3	yes	complemented
323	C₂×#124	C₂²×C₅₃	1	6	yes	complemented
324	#525	C₂²×C₅₃	1	96	yes	complemented
325	C₂×#123	C₂²×C₅₃	1	12	yes	complemented
326	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	6	yes	complemented
327	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	6	yes	complemented
328	C₂×#121	C₂²×C₅₃	1	6	yes	complemented
329	C₂×#121	C₂²×C₅₃	1	6	yes	complemented
330	C₂×#121	C₂²×C₅₃	1	6	yes	complemented
331	C₂×#121	C₂²×C₅₃	1	6	yes	complemented
332	C₂×#120	C₂²×C₅₃	1	12	yes	complemented
333	C₄×#41	C₂²×C₅₃	1	16	yes	complemented
334	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
335	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
336	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
337	C₂×C₄×D₄	C₂²×C₅₃	1	3	yes	—
338	C₂×C₄×D₄	C₂²×C₅₃	1	6	yes	complemented
339	C₂×C₄×D₄	C₂²×C₅₃	1	3	yes	complemented
340	C₂×C₄×D₄	C₂²×C₅₃	1	6	yes	complemented
341	C₂×C₄×D₄	C₂²×C₅₃	1	3	yes	complemented
342	C₂×C₄×D₄	C₂²×C₅₃	1	3	yes	complemented
343	C₂×C₄×D₄	C₂²×C₅₃	1	3	yes	complemented
344	C₂×C₄×D₄	C₂²×C₅₃	1	6	yes	complemented
345	C₂×C₄×D₄	C₂²×C₅₃	1	48	yes	complemented
346	C₂×#117	C₂²×C₅₃	1	3	yes	complemented
347	C₂²×C₄⋊C₄	C₂²×C₅₃	1	3	yes	complemented
348	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	6	yes	complemented
349	C₂²×C₄²	C₂²×C₅₃	1	3	yes	complemented
350	C₅₃	C₂×D₄×#41	1	1	yes	characteristic, direct product factor, Sylow
351	C₂⁵	C₂³×C₅₃	1	6	yes	—
352	C₂×#41	—	2	256	no	—
353	C₂×#41	—	2	16	no	—
354	C₂×#41	—	2	48	no	—
355	C₂×#41	—	2	48	no	—
356	C₂×#41	D₄×C₅₃	1	16	yes	direct product factor
357	C₂×#41	C₂³×C₅₃	1	8	yes	—
358	C₂×#41	C₂³×C₅₃	1	48	yes	complemented
359	C₂×#41	C₂³×C₅₃	1	48	yes	complemented
360	C₂×#41	C₂³×C₅₃	1	16	yes	complemented
361	C₂²×Q₈	—	2	16	no	—
362	C₂²×Q₈	C₂³×C₅₃	1	6	yes	—
363	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
364	C₂²×Q₈	C₂³×C₅₃	1	16	yes	complemented
365	C₂²×D₄	—	2	48	no	—
366	C₂²×D₄	—	2	24	no	—
367	C₂²×D₄	C₂³×C₅₃	1	6	yes	—
368	C₂²×D₄	C₂³×C₅₃	1	3	yes	—
369	C₂²×D₄	C₂³×C₅₃	1	24	yes	—
370	C₂²×D₄	C₂³×C₅₃	1	12	yes	—
371	C₂²×D₄	C₂³×C₅₃	1	6	yes	—
372	C₂²×D₄	C₂³×C₅₃	1	6	yes	—
373	C₂²×D₄	C₂³×C₅₃	1	3	yes	—
374	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
375	C₂²×D₄	C₂³×C₅₃	1	48	yes	complemented
376	C₂³×C₄	—	2	48	no	—
377	C₂³×C₄	C₂³×C₅₃	1	6	yes	—
378	C₂³×C₄	C₂³×C₅₃	1	3	yes	—
379	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
380	C₂³×C₄	C₂³×C₅₃	1	6	yes	—
381	C₂³×C₄	C₂³×C₅₃	1	6	yes	—
382	C₂³×C₄	C₂³×C₅₃	1	6	yes	—
383	C₂³×C₄	C₂³×C₅₃	1	3	yes	—
384	C₂³×C₄	C₂³×C₅₃	1	3	yes	—
385	C₂³×C₄	C₂³×C₅₃	1	48	yes	complemented
386	C₄⋊Q₈	C₂³×C₅₃	1	24	yes	complemented
387	#127	C₂³×C₅₃	1	24	yes	complemented
388	#124	C₂³×C₅₃	1	48	yes	complemented
389	#123	C₂³×C₅₃	1	96	yes	complemented
390	C₂²⋊Q₈	C₂³×C₅₃	1	48	yes	complemented
391	C₂²⋊Q₈	C₂³×C₅₃	1	48	yes	complemented
392	#121	C₂³×C₅₃	1	48	yes	complemented
393	#121	C₂³×C₅₃	1	48	yes	complemented
394	#121	C₂³×C₅₃	1	48	yes	complemented
395	#121	C₂³×C₅₃	1	48	yes	complemented
396	#120	C₂³×C₅₃	1	96	yes	complemented
397	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
398	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
399	C₄×D₄	C₂³×C₅₃	1	8	yes	—
400	C₄×D₄	C₂³×C₅₃	1	24	yes	—
401	C₄×D₄	C₂³×C₅₃	1	48	yes	complemented
402	C₄×D₄	C₂³×C₅₃	1	24	yes	complemented
403	C₄×D₄	C₂³×C₅₃	1	48	yes	complemented
404	C₄×D₄	C₂³×C₅₃	1	24	yes	complemented
405	C₄×D₄	C₂³×C₅₃	1	24	yes	complemented
406	C₄×D₄	C₂³×C₅₃	1	24	yes	complemented
407	C₄×D₄	C₂³×C₅₃	1	48	yes	complemented
408	#117	C₂³×C₅₃	1	24	yes	complemented
409	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₅₃	1	3	yes	—
411	C₂×C₄⋊C₄	C₂³×C₅₃	1	6	yes	—
412	C₂×C₄⋊C₄	C₂³×C₅₃	1	3	yes	—
413	C₂×C₄⋊C₄	C₂³×C₅₃	1	3	yes	—
414	C₂×C₄⋊C₄	C₂³×C₅₃	1	6	yes	—
415	C₂×C₄⋊C₄	C₂³×C₅₃	1	24	yes	complemented
416	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₅₃	1	6	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₅₃	1	6	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₅₃	1	6	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₅₃	1	6	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₅₃	1	12	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₅₃	1	48	yes	complemented
423	C₂×C₄²	C₂³×C₅₃	1	3	yes	—
424	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₅₃	1	3	yes	—
426	C₂×C₄²	C₂³×C₅₃	1	3	yes	—
427	C₂×C₄²	C₂³×C₅₃	1	24	yes	complemented
428	C₂⁴	—	2	24	no	—
429	C₂⁴	—	2	24	no	—
430	C₂⁴	—	4	12	no	—
431	C₂⁴	C₂⁴×C₅₃	1	6	yes	—
432	C₂⁴	C₂⁴×C₅₃	1	24	yes	—
433	C₂⁴	C₂⁴×C₅₃	1	3	yes	—
434	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
435	#41	—	2	64	no	—
436	#41	—	2	192	no	—
437	#41	—	2	192	no	—
438	#41	C₂×D₄×C₅₃	1	64	yes	direct product factor
439	C₂×Q₈	—	2	64	no	—
440	C₂×Q₈	—	2	24	no	—
441	C₂×Q₈	C₂×D₄×C₅₃	1	8	yes	complemented
442	C₂×Q₈	C₂⁴×C₅₃	1	24	yes	—
443	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
444	C₂×D₄	—	2	48	no	—
445	C₂×D₄	—	2	24	no	—
446	C₂×D₄	—	2	192	no	—
447	C₂×D₄	—	2	96	no	—
448	C₂×D₄	—	2	24	no	—
449	C₂×D₄	—	2	12	no	—
450	C₂×D₄	—	4	12	no	—
451	C₂×D₄	C₂×D₄×C₅₃	1	24	yes	complemented
452	C₂×D₄	#41×C₅₃	1	8	yes	direct product factor
453	C₂×D₄	C₂⁴×C₅₃	1	24	yes	—
454	C₂×D₄	C₂⁴×C₅₃	1	12	yes	—
455	C₂×D₄	C₂⁴×C₅₃	1	48	yes	—
456	C₂×D₄	C₂⁴×C₅₃	1	24	yes	—
457	C₂×D₄	C₂⁴×C₅₃	1	24	yes	—
458	C₂×D₄	C₂⁴×C₅₃	1	12	yes	—
459	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
460	C₂²×C₄	—	2	24	no	—
461	C₂²×C₄	—	2	8	no	—
462	C₂²×C₄	—	2	24	no	—
463	C₂²×C₄	—	2	24	no	—
464	C₂²×C₄	—	2	24	no	—
465	C₂²×C₄	—	2	192	no	—
466	C₂²×C₄	—	2	12	no	—
467	C₂²×C₄	—	4	6	no	—
468	C₂²×C₄	C₂×D₄×C₅₃	1	24	yes	complemented
469	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
470	C₂²×C₄	C₂⁴×C₅₃	1	3	yes	—
471	C₂²×C₄	C₂⁴×C₅₃	1	3	yes	—
472	C₂²×C₄	C₂⁴×C₅₃	1	12	yes	—
473	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₅₃	1	6	yes	—
475	C₂²×C₄	C₂⁴×C₅₃	1	24	yes	—
476	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
477	C₂²×C₄	C₂⁴×C₅₃	1	24	yes	—
478	C₂²×C₄	C₂⁴×C₅₃	1	24	yes	—
479	C₂²×C₄	C₂⁴×C₅₃	1	24	yes	—
480	C₂²×C₄	C₂⁴×C₅₃	1	12	yes	—
481	C₂²×C₄	C₂⁴×C₅₃	1	3	yes	—
482	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₅₃	1	12	yes	—
484	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
485	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
486	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
487	C₄⋊C₄	C₂⁴×C₅₃	1	24	yes	—
488	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
489	C₄⋊C₄	C₂⁴×C₅₃	1	12	yes	—
490	C₄⋊C₄	C₂⁴×C₅₃	1	24	yes	—
491	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
492	C₂²⋊C₄	C₂⁴×C₅₃	1	24	yes	—
493	C₂²⋊C₄	C₂⁴×C₅₃	1	24	yes	—
494	C₂²⋊C₄	C₂⁴×C₅₃	1	24	yes	—
495	C₂²⋊C₄	C₂⁴×C₅₃	1	24	yes	—
496	C₂²⋊C₄	C₂⁴×C₅₃	1	48	yes	—
497	C₄²	C₂⁴×C₅₃	1	4	yes	—
498	C₄²	C₂⁴×C₅₃	1	12	yes	—
499	C₄²	C₂⁴×C₅₃	1	12	yes	—
500	C₄²	C₂⁴×C₅₃	1	12	yes	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	6	no	—
503	C₂³	—	2	6	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	2	48	no	—
506	C₂³	—	2	12	no	—
507	C₂³	—	2	12	no	—
508	C₂³	—	2	48	no	—
509	C₂³	—	2	12	no	—
510	C₂³	—	4	24	no	—
511	C₂³	—	4	96	no	—
512	C₂³	C₂²×D₄×C₅₃	1	12	yes	—
513	C₂³	C₂×#41×C₅₃	1	8	yes	complemented
514	C₂³	C₂⁵×C₅₃	1	12	yes	—
515	C₂³	C₂⁵×C₅₃	1	6	yes	—
516	C₂³	C₂⁵×C₅₃	1	4	yes	—
517	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
518	Q₈	—	2	48	no	—
519	Q₈	C₂²×D₄×C₅₃	1	16	yes	complemented
520	D₄	—	2	96	no	—
521	D₄	—	2	48	no	—
522	D₄	—	2	48	no	—
523	D₄	—	2	24	no	—
524	D₄	—	4	24	no	—
525	D₄	C₂²×D₄×C₅₃	1	48	yes	complemented
526	D₄	C₂×#41×C₅₃	1	16	yes	direct product factor
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	12	no	—
529	C₂×C₄	—	2	48	no	—
530	C₂×C₄	—	2	6	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	6	no	—
533	C₂×C₄	—	2	16	no	—
534	C₂×C₄	—	2	48	no	—
535	C₂×C₄	—	2	48	no	—
536	C₂×C₄	—	2	48	no	—
537	C₂×C₄	—	2	24	no	—
538	C₂×C₄	—	4	12	no	—
539	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
540	C₂×C₄	C₂²×D₄×C₅₃	1	12	yes	—
541	C₂×C₄	C₂²×D₄×C₅₃	1	48	yes	complemented
542	C₂×C₄	C₂×#41×C₅₃	1	4	yes	complemented
543	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
544	C₂×C₄	C₂⁵×C₅₃	1	6	yes	—
545	C₂×C₄	C₂⁵×C₅₃	1	6	yes	—
546	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
547	C₂×C₄	C₂⁵×C₅₃	1	12	yes	—
548	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
549	C₂×C₄	C₂⁵×C₅₃	1	6	yes	—
550	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
551	C₂²	—	2	16	no	—
552	C₂²	—	2	24	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	2	6	no	—
555	C₂²	—	2	6	no	—
556	C₂²	—	2	4	no	—
557	C₂²	—	2	12	no	—
558	C₂²	—	2	12	no	—
559	C₂²	—	2	12	no	—
560	C₂²	—	4	96	no	—
561	C₂²	—	4	24	no	—
562	C₂²	C₂³×D₄×C₅₃	1	12	yes	—
563	C₂²	C₂³×D₄×C₅₃	1	2	yes	—
564	C₂²	C₂²×#41×C₅₃	1	2	yes	—
565	C₂²	C₂²×#41×C₅₃	1	8	yes	complemented
566	C₂²	C₅₃×#585	1	2	yes	—
567	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
568	C₄	—	2	4	no	—
569	C₄	—	2	12	no	—
570	C₄	—	2	6	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	6	no	—
573	C₄	C₂³×D₄×C₅₃	1	4	yes	—
574	C₄	C₂³×D₄×C₅₃	1	12	yes	—
575	C₄	C₂²×#41×C₅₃	1	4	yes	complemented
576	C₂	—	2	8	no	—
577	C₂	—	2	12	no	—
578	C₂	—	4	12	no	—
579	C₂	D₄×#41×C₅₃	1	4	yes	direct product factor
580	C₂	C₂⁴×D₄×C₅₃	1	1	yes	characteristic
581	C₂	C₂³×#41×C₅₃	1	1	yes	characteristic
582	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. C₂³×#41×C₅₃	C₂	semidirect
2. D₄×#41×C₅₃	C₂	direct (N × H)
3. C₂×C₅₃×#550	C₂	semidirect
4. C₂×D₄×Q₈×C₅₃	C₂	semidirect
5. C₂×C₅₃×#548	C₂	semidirect
6. C₂×C₅₃×#547	C₂	semidirect
7. C₂×C₅₃×#546	C₂	semidirect
8. C₂×D₄²×C₅₃	C₂	semidirect
9. C₂×C₅₃×#532	C₂	semidirect
10. C₂×C₅₃×#525	C₂	semidirect
11. C₂×C₄×#41×C₅₃	C₂	semidirect
12. C₂²×C₄×D₄×C₅₃	C₂	semidirect
15. C₂²×#41×C₅₃	C₂²	semidirect
16. C₂²×#41×C₅₃	C₂²	semidirect
17. C₂²×#41×C₅₃	C₂²	semidirect
18. C₂²×#41×C₅₃	C₂²	semidirect
19. C₂³×Q₈×C₅₃	C₂²	semidirect
21. C₂³×D₄×C₅₃	C₂²	semidirect
22. C₂⁴×C₄×C₅₃	C₂²	semidirect
23. C₅₃×#550	C₂²	semidirect
24. D₄×Q₈×C₅₃	C₂²	semidirect
25. C₅₃×#548	C₂²	semidirect
26. C₅₃×#547	C₂²	semidirect
27. C₅₃×#546	C₂²	semidirect
28. D₄²×C₅₃	C₂²	semidirect
29. C₅₃×#532	C₂²	semidirect
30. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
31. C₂×#127×C₅₃	C₂²	semidirect
32. C₂×#124×C₅₃	C₂²	semidirect
33. C₅₃×#525	C₂²	semidirect
34. C₂×#123×C₅₃	C₂²	semidirect
35. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
36. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
37. C₂×#121×C₅₃	C₂²	semidirect
38. C₂×#121×C₅₃	C₂²	semidirect
39. C₂×#121×C₅₃	C₂²	semidirect
40. C₂×#121×C₅₃	C₂²	semidirect
41. C₂×#120×C₅₃	C₂²	semidirect
42. C₄×#41×C₅₃	C₂²	semidirect
43. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
44. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
47. C₂×C₄×D₄×C₅₃	C₂²	semidirect
48. C₂×C₄×D₄×C₅₃	C₂²	semidirect
49. C₂×C₄×D₄×C₅₃	C₂²	semidirect
50. C₂×C₄×D₄×C₅₃	C₂²	semidirect
51. C₂×C₄×D₄×C₅₃	C₂²	semidirect
52. C₂×C₄×D₄×C₅₃	C₂²	semidirect
53. C₂×C₄×D₄×C₅₃	C₂²	semidirect
54. C₂×C₄×D₄×C₅₃	C₂²	semidirect
55. C₂×#117×C₅₃	C₂²	semidirect
56. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
57. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
58. C₂²×C₄²×C₅₃	C₂²	semidirect
64. C₂×#41×C₅₃	D₄	direct (N × H)
66. C₂×#41×C₅₃	C₂³	semidirect
67. C₂×#41×C₅₃	C₂³	semidirect
68. C₂×#41×C₅₃	C₂³	semidirect
72. C₂²×Q₈×C₅₃	C₂³	semidirect
83. C₂²×D₄×C₅₃	C₂³	semidirect
93. C₂³×C₄×C₅₃	C₂³	semidirect
94. C₄⋊Q₈×C₅₃	C₂³	semidirect
95. #127×C₅₃	C₂³	semidirect
96. #124×C₅₃	C₂³	semidirect
97. #123×C₅₃	C₂³	semidirect
98. C₂²⋊Q₈×C₅₃	C₂³	semidirect
99. C₂²⋊Q₈×C₅₃	C₂³	semidirect
100. #121×C₅₃	C₂³	semidirect
101. #121×C₅₃	C₂³	semidirect
102. #121×C₅₃	C₂³	semidirect
103. #121×C₅₃	C₂³	semidirect
104. #120×C₅₃	C₂³	semidirect
105. C₄×Q₈×C₅₃	C₂³	semidirect
106. C₄×Q₈×C₅₃	C₂³	semidirect
109. C₄×D₄×C₅₃	C₂³	semidirect
110. C₄×D₄×C₅₃	C₂³	semidirect
111. C₄×D₄×C₅₃	C₂³	semidirect
112. C₄×D₄×C₅₃	C₂³	semidirect
113. C₄×D₄×C₅₃	C₂³	semidirect
114. C₄×D₄×C₅₃	C₂³	semidirect
115. C₄×D₄×C₅₃	C₂³	semidirect
116. #117×C₅₃	C₂³	semidirect
123. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
130. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
135. C₂×C₄²×C₅₃	C₂³	semidirect
146. #41×C₅₃	C₂×D₄	direct (N × H)
149. C₂×Q₈×C₅₃	C₂×D₄	semidirect
159. C₂×D₄×C₅₃	C₂×D₄	semidirect
160. C₂×D₄×C₅₃	#41	direct (N × H)
176. C₂²×C₄×C₅₃	C₂×D₄	semidirect
221. C₂³×C₅₃	C₂×#41	semidirect
227. Q₈×C₅₃	C₂²×D₄	semidirect
233. D₄×C₅₃	C₂²×D₄	semidirect
234. D₄×C₅₃	C₂×#41	direct (N × H)
249. C₂×C₄×C₅₃	C₂²×D₄	semidirect
250. C₂×C₄×C₅₃	C₂×#41	semidirect
259. C₂×D₄×#41	C₅₃	direct (N × H)
274. C₂²×C₅₃	C₂²×#41	semidirect
284. C₄×C₅₃	C₂²×#41	semidirect
285. C₂³×#41	C₂×C₅₃	semidirect
286. D₄×#41	C₂×C₅₃	direct (N × H)
287. C₂×#550	C₂×C₅₃	semidirect
288. C₂×D₄×Q₈	C₂×C₅₃	semidirect
289. C₂×#548	C₂×C₅₃	semidirect
290. C₂×#547	C₂×C₅₃	semidirect
291. C₂×#546	C₂×C₅₃	semidirect
292. C₂×D₄²	C₂×C₅₃	semidirect
293. C₂×#532	C₂×C₅₃	semidirect
294. C₂×#525	C₂×C₅₃	semidirect
295. C₂×C₄×#41	C₂×C₅₃	semidirect
296. C₂²×C₄×D₄	C₂×C₅₃	semidirect
300. C₂×C₅₃	D₄×#41	direct (N × H)
306. C₂²×#41	C₂²×C₅₃	semidirect
307. C₂²×#41	C₂²×C₅₃	semidirect
308. C₂²×#41	C₂²×C₅₃	semidirect
309. C₂²×#41	C₂²×C₅₃	semidirect
310. C₂³×Q₈	C₂²×C₅₃	semidirect
312. C₂³×D₄	C₂²×C₅₃	semidirect
313. C₂⁴×C₄	C₂²×C₅₃	semidirect
314. #550	C₂²×C₅₃	semidirect
315. D₄×Q₈	C₂²×C₅₃	semidirect
316. #548	C₂²×C₅₃	semidirect
317. #547	C₂²×C₅₃	semidirect
318. #546	C₂²×C₅₃	semidirect
319. D₄²	C₂²×C₅₃	semidirect
320. #532	C₂²×C₅₃	semidirect
321. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
322. C₂×#127	C₂²×C₅₃	semidirect
323. C₂×#124	C₂²×C₅₃	semidirect
324. #525	C₂²×C₅₃	semidirect
325. C₂×#123	C₂²×C₅₃	semidirect
326. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
327. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
328. C₂×#121	C₂²×C₅₃	semidirect
329. C₂×#121	C₂²×C₅₃	semidirect
330. C₂×#121	C₂²×C₅₃	semidirect
331. C₂×#121	C₂²×C₅₃	semidirect
332. C₂×#120	C₂²×C₅₃	semidirect
333. C₄×#41	C₂²×C₅₃	semidirect
334. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
335. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
338. C₂×C₄×D₄	C₂²×C₅₃	semidirect
339. C₂×C₄×D₄	C₂²×C₅₃	semidirect
340. C₂×C₄×D₄	C₂²×C₅₃	semidirect
341. C₂×C₄×D₄	C₂²×C₅₃	semidirect
342. C₂×C₄×D₄	C₂²×C₅₃	semidirect
343. C₂×C₄×D₄	C₂²×C₅₃	semidirect
344. C₂×C₄×D₄	C₂²×C₅₃	semidirect
345. C₂×C₄×D₄	C₂²×C₅₃	semidirect
346. C₂×#117	C₂²×C₅₃	semidirect
347. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
348. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
349. C₂²×C₄²	C₂²×C₅₃	semidirect
350. C₅₃	C₂×D₄×#41	direct (N × H)
356. C₂×#41	D₄×C₅₃	direct (N × H)
358. C₂×#41	C₂³×C₅₃	semidirect
359. C₂×#41	C₂³×C₅₃	semidirect
360. C₂×#41	C₂³×C₅₃	semidirect
364. C₂²×Q₈	C₂³×C₅₃	semidirect
375. C₂²×D₄	C₂³×C₅₃	semidirect
385. C₂³×C₄	C₂³×C₅₃	semidirect
386. C₄⋊Q₈	C₂³×C₅₃	semidirect
387. #127	C₂³×C₅₃	semidirect
388. #124	C₂³×C₅₃	semidirect
389. #123	C₂³×C₅₃	semidirect
390. C₂²⋊Q₈	C₂³×C₅₃	semidirect
391. C₂²⋊Q₈	C₂³×C₅₃	semidirect
392. #121	C₂³×C₅₃	semidirect
393. #121	C₂³×C₅₃	semidirect
394. #121	C₂³×C₅₃	semidirect
395. #121	C₂³×C₅₃	semidirect
396. #120	C₂³×C₅₃	semidirect
397. C₄×Q₈	C₂³×C₅₃	semidirect
398. C₄×Q₈	C₂³×C₅₃	semidirect
401. C₄×D₄	C₂³×C₅₃	semidirect
402. C₄×D₄	C₂³×C₅₃	semidirect
403. C₄×D₄	C₂³×C₅₃	semidirect
404. C₄×D₄	C₂³×C₅₃	semidirect
405. C₄×D₄	C₂³×C₅₃	semidirect
406. C₄×D₄	C₂³×C₅₃	semidirect
407. C₄×D₄	C₂³×C₅₃	semidirect
408. #117	C₂³×C₅₃	semidirect
415. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
422. C₂×C₂²⋊C₄	C₂³×C₅₃	semidirect
427. C₂×C₄²	C₂³×C₅₃	semidirect
438. #41	C₂×D₄×C₅₃	direct (N × H)
441. C₂×Q₈	C₂×D₄×C₅₃	semidirect
451. C₂×D₄	C₂×D₄×C₅₃	semidirect
452. C₂×D₄	#41×C₅₃	direct (N × H)
468. C₂²×C₄	C₂×D₄×C₅₃	semidirect
513. C₂³	C₂×#41×C₅₃	semidirect
519. Q₈	C₂²×D₄×C₅₃	semidirect
525. D₄	C₂²×D₄×C₅₃	semidirect
526. D₄	C₂×#41×C₅₃	direct (N × H)
541. C₂×C₄	C₂²×D₄×C₅₃	semidirect
542. C₂×C₄	C₂×#41×C₅₃	semidirect
565. C₂²	C₂²×#41×C₅₃	semidirect
575. C₄	C₂²×#41×C₅₃	semidirect
579. C₂	D₄×#41×C₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₅₃	2
D₄×#41×C₅₃	2
C₂×C₅₃×#550	2
C₂×D₄×Q₈×C₅₃	2
C₂×C₅₃×#548	2
C₂×C₅₃×#547	2
C₂×C₅₃×#546	2
C₂×D₄²×C₅₃	2
C₂×C₅₃×#532	2
C₂×C₅₃×#525	2
C₂×C₄×#41×C₅₃	2
C₂²×C₄×D₄×C₅₃	2
C₂×D₄×#41	53

Subgroups — C2×D4×#41×C53 #27270213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×#41×C₅₃ #27270213