Subgroups — C₂×C₅₃×#2640 #27242127

Order 13568.

2806 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#124×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#2640	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅₃×#397	C₂	1	4	yes	maximal, complemented
5	C₂×C₅₃×#393	C₂	1	4	yes	maximal, complemented
6	C₂×C₅₃×#391	C₂	1	2	yes	maximal, complemented
7	C₂×C₅₃×#390	C₂	1	2	yes	maximal
8	C₂×C₅₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₅₃	C₂²	1	2	yes	—
11	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₅₃	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₅₃	C₂²	1	8	yes	complemented
14	C₂×#124×C₅₃	—	2	8	no	—
15	C₂×#124×C₅₃	C₂²	1	8	yes	—
16	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	8	yes	—
21	C₂²×C₄²×C₅₃	C₂²	1	2	yes	—
22	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
23	C₅₃×#397	C₂²	1	32	yes	complemented
24	C₅₃×#393	C₂²	1	32	yes	complemented
25	C₅₃×#391	C₂²	1	16	yes	complemented
26	C₅₃×#390	C₂²	1	16	yes	—
27	C₅₃×#376	C₂²	1	8	yes	complemented
28	C₂×#95×C₅₃	C₂²	1	2	yes	—
29	C₂×#95×C₅₃	C₂²	1	2	yes	—
30	C₂×#95×C₅₃	C₂²	1	8	yes	—
31	C₂⁵×C₅₃	C₂³	1	2	yes	—
32	C₂²×Q₈×C₅₃	—	2	4	no	—
33	C₂²×Q₈×C₅₃	—	2	8	no	—
34	C₂²×Q₈×C₅₃	—	2	8	no	—
35	C₂²×Q₈×C₅₃	—	4	8	no	—
36	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
37	C₂²×Q₈×C₅₃	C₂³	1	8	yes	—
38	C₂²×D₄×C₅₃	—	2	4	no	—
39	C₂²×D₄×C₅₃	—	2	8	no	—
40	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
41	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
42	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
43	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
47	C₄⋊Q₈×C₅₃	—	2	32	no	—
48	#124×C₅₃	—	2	32	no	—
49	C₂×C₄⋊C₄×C₅₃	—	2	8	no	—
50	C₂×C₄⋊C₄×C₅₃	—	2	8	no	—
51	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	—
52	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	—
53	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
54	C₂×C₂²⋊C₄×C₅₃	—	2	8	no	—
55	C₂×C₂²⋊C₄×C₅₃	—	4	16	no	—
56	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
57	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
58	C₂×C₂²⋊C₄×C₅₃	C₂³	1	32	yes	—
59	C₂×C₄²×C₅₃	—	2	8	no	—
60	C₂×C₄²×C₅₃	D₄	1	8	yes	—
61	C₂×C₄²×C₅₃	C₂³	1	8	yes	—
62	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
63	#95×C₅₃	C₂³	1	8	yes	—
64	#95×C₅₃	C₂³	1	8	yes	—
65	#95×C₅₃	C₂³	1	32	yes	—
66	C₂⁴×C₅₃	—	2	4	no	—
67	C₂⁴×C₅₃	—	2	8	no	—
68	C₂⁴×C₅₃	—	2	8	no	—
69	C₂⁴×C₅₃	—	2	8	no	—
70	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
71	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
72	C₂×Q₈×C₅₃	—	2	8	no	—
73	C₂×Q₈×C₅₃	—	2	16	no	—
74	C₂×Q₈×C₅₃	—	2	16	no	—
75	C₂×Q₈×C₅₃	—	4	16	no	—
76	C₂×Q₈×C₅₃	—	4	32	no	—
77	C₂×Q₈×C₅₃	—	4	16	no	—
78	C₂×D₄×C₅₃	—	2	8	no	—
79	C₂×D₄×C₅₃	—	2	16	no	—
80	C₂×D₄×C₅₃	—	4	16	no	—
81	C₂²×C₄×C₅₃	—	2	4	no	—
82	C₂²×C₄×C₅₃	—	2	4	no	—
83	C₂²×C₄×C₅₃	—	2	4	no	—
84	C₂²×C₄×C₅₃	—	2	8	no	—
85	C₂²×C₄×C₅₃	—	2	8	no	—
86	C₂²×C₄×C₅₃	—	2	8	no	—
87	C₂²×C₄×C₅₃	—	2	8	no	—
88	C₂²×C₄×C₅₃	—	2	16	no	—
89	C₂²×C₄×C₅₃	—	2	8	no	—
90	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
91	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₅₃	#41	1	8	yes	—
94	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
95	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
96	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
97	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
98	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
99	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
100	C₄⋊C₄×C₅₃	—	2	16	no	—
101	C₄⋊C₄×C₅₃	—	2	16	no	—
102	C₂²⋊C₄×C₅₃	—	2	16	no	—
103	C₂²⋊C₄×C₅₃	—	2	16	no	—
104	C₂²⋊C₄×C₅₃	—	4	32	no	—
105	C₄²×C₅₃	—	2	16	no	—
106	C₄²×C₅₃	C₂×D₄	1	16	yes	—
107	C₂³×C₅₃	—	2	4	no	—
108	C₂³×C₅₃	—	2	8	no	—
109	C₂³×C₅₃	—	2	8	no	—
110	C₂³×C₅₃	—	2	8	no	—
111	C₂³×C₅₃	—	4	8	no	—
112	C₂³×C₅₃	—	4	8	no	—
113	C₂³×C₅₃	—	4	8	no	—
114	C₂³×C₅₃	—	4	32	no	—
115	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
116	C₂³×C₅₃	C₂×#41	1	4	yes	—
117	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
118	C₂³×C₅₃	2₋¹⁺⁴	1	4	yes	—
119	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
120	Q₈×C₅₃	—	4	32	no	—
121	Q₈×C₅₃	—	4	16	no	—
122	D₄×C₅₃	—	4	16	no	—
123	C₂×C₄×C₅₃	—	2	8	no	—
124	C₂×C₄×C₅₃	—	2	8	no	—
125	C₂×C₄×C₅₃	—	2	4	no	—
126	C₂×C₄×C₅₃	—	2	4	no	—
127	C₂×C₄×C₅₃	—	2	4	no	—
128	C₂×C₄×C₅₃	—	2	8	no	—
129	C₂×C₄×C₅₃	—	2	8	no	—
130	C₂×C₄×C₅₃	—	2	8	no	—
131	C₂×C₄×C₅₃	—	2	16	no	—
132	C₂×C₄×C₅₃	—	2	8	no	—
133	C₂×C₄×C₅₃	—	2	8	no	—
134	C₂×C₄×C₅₃	—	4	8	no	—
135	C₂×C₄×C₅₃	—	4	16	no	—
136	C₂×C₄×C₅₃	—	4	16	no	—
137	C₂×C₄×C₅₃	#124	1	16	yes	—
138	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
139	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
140	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
141	C₂×C₄×C₅₃	C₂×#41	1	8	yes	—
142	C₂×#2640	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂²×C₅₃	—	4	4	no	—
144	C₂²×C₅₃	—	4	4	no	—
145	C₂²×C₅₃	—	4	4	no	—
146	C₂²×C₅₃	—	4	16	no	—
147	C₂²×C₅₃	—	8	16	no	—
148	C₂²×C₅₃	C₂×#124	1	4	yes	—
149	C₂²×C₅₃	#535	1	4	yes	—
150	C₂²×C₅₃	#536	1	4	yes	—
151	C₂²×C₅₃	#542	1	16	yes	—
152	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
153	C₂²×C₅₃	C₂²×#41	1	2	yes	—
154	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
155	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
156	C₄×C₅₃	—	2	4	no	—
157	C₄×C₅₃	—	2	4	no	—
158	C₄×C₅₃	—	4	4	no	—
159	C₄×C₅₃	—	4	8	no	—
160	C₄×C₅₃	—	4	8	no	—
161	C₄×C₅₃	C₂×#124	1	8	yes	—
162	C₂²×C₄⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
163	C₂²×#124	C₂×C₅₃	1	1	yes	characteristic
164	#2640	C₂×C₅₃	1	16	yes	direct product factor
165	C₂×#397	C₂×C₅₃	1	4	yes	complemented
166	C₂×#393	C₂×C₅₃	1	4	yes	complemented
167	C₂×#391	C₂×C₅₃	1	2	yes	complemented
168	C₂×#390	C₂×C₅₃	1	2	yes	—
169	C₂×#376	C₂×C₅₃	1	1	yes	characteristic, complemented
170	C₂×C₅₃	—	8	4	no	—
171	C₂×C₅₃	#2640	1	8	yes	direct product factor
172	C₂×C₅₃	C₂²×#124	1	1	yes	characteristic
173	C₂×C₅₃	C₂×#535	1	1	yes	characteristic
174	C₂×C₅₃	C₂×#536	1	1	yes	characteristic
175	C₂×C₅₃	C₂×#542	1	4	yes	—
176	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic
177	C₂³×Q₈	C₂²×C₅₃	1	2	yes	—
178	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
179	C₂×C₄⋊Q₈	—	2	8	no	—
180	C₂×C₄⋊Q₈	C₂²×C₅₃	1	8	yes	complemented
181	C₂×#124	—	2	8	no	—
182	C₂×#124	C₂²×C₅₃	1	8	yes	—
183	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
184	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
185	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
186	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
187	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	8	yes	—
188	C₂²×C₄²	C₂²×C₅₃	1	2	yes	—
189	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
190	#397	C₂²×C₅₃	1	32	yes	complemented
191	#393	C₂²×C₅₃	1	32	yes	complemented
192	#391	C₂²×C₅₃	1	16	yes	complemented
193	#390	C₂²×C₅₃	1	16	yes	—
194	#376	C₂²×C₅₃	1	8	yes	complemented
195	C₂×#95	C₂²×C₅₃	1	2	yes	—
196	C₂×#95	C₂²×C₅₃	1	8	yes	—
197	C₂×#95	C₂²×C₅₃	1	2	yes	—
198	C₅₃	C₂×#2640	1	1	yes	characteristic, direct product factor, Sylow
199	C₂⁵	C₂³×C₅₃	1	2	yes	—
200	C₂²×Q₈	—	2	4	no	—
201	C₂²×Q₈	—	2	8	no	—
202	C₂²×Q₈	—	2	8	no	—
203	C₂²×Q₈	—	4	8	no	—
204	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
205	C₂²×Q₈	C₂³×C₅₃	1	8	yes	—
206	C₂²×D₄	—	2	4	no	—
207	C₂²×D₄	—	2	8	no	—
208	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
209	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
210	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
211	C₂³×C₄	C₂³×C₅₃	1	4	yes	—
212	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
213	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
214	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
215	C₄⋊Q₈	—	2	32	no	—
216	#124	—	2	32	no	—
217	C₂×C₄⋊C₄	—	2	8	no	—
218	C₂×C₄⋊C₄	—	2	8	no	—
219	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	—
220	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	—
221	C₂×C₂²⋊C₄	—	2	8	no	—
222	C₂×C₂²⋊C₄	—	2	8	no	—
223	C₂×C₂²⋊C₄	—	4	16	no	—
224	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
225	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
226	C₂×C₂²⋊C₄	C₂³×C₅₃	1	32	yes	—
227	C₂×C₄²	—	2	8	no	—
228	C₂×C₄²	D₄×C₅₃	1	8	yes	—
229	C₂×C₄²	C₂³×C₅₃	1	8	yes	—
230	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
231	#95	C₂³×C₅₃	1	8	yes	—
232	#95	C₂³×C₅₃	1	8	yes	—
233	#95	C₂³×C₅₃	1	32	yes	—
234	C₂⁴	—	2	4	no	—
235	C₂⁴	—	2	8	no	—
236	C₂⁴	—	2	8	no	—
237	C₂⁴	—	2	8	no	—
238	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
239	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
240	C₂×Q₈	—	2	8	no	—
241	C₂×Q₈	—	2	16	no	—
242	C₂×Q₈	—	2	16	no	—
243	C₂×Q₈	—	4	16	no	—
244	C₂×Q₈	—	4	32	no	—
245	C₂×Q₈	—	4	16	no	—
246	C₂×D₄	—	2	8	no	—
247	C₂×D₄	—	2	16	no	—
248	C₂×D₄	—	4	16	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	8	no	—
256	C₂²×C₄	—	2	16	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
259	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
260	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
261	C₂²×C₄	#41×C₅₃	1	8	yes	—
262	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
263	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
264	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
265	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
266	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
267	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
268	C₄⋊C₄	—	2	16	no	—
269	C₄⋊C₄	—	2	16	no	—
270	C₂²⋊C₄	—	2	16	no	—
271	C₂²⋊C₄	—	2	16	no	—
272	C₂²⋊C₄	—	4	32	no	—
273	C₄²	—	2	16	no	—
274	C₄²	C₂×D₄×C₅₃	1	16	yes	—
275	C₂³	—	2	4	no	—
276	C₂³	—	2	8	no	—
277	C₂³	—	2	8	no	—
278	C₂³	—	2	8	no	—
279	C₂³	—	4	8	no	—
280	C₂³	—	4	8	no	—
281	C₂³	—	4	8	no	—
282	C₂³	—	4	32	no	—
283	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
284	C₂³	C₂×#41×C₅₃	1	4	yes	—
285	C₂³	H(5,𝔽₂)×C₅₃	1	4	yes	—
286	C₂³	2₋¹⁺⁴×C₅₃	1	4	yes	—
287	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
288	Q₈	—	4	32	no	—
289	Q₈	—	4	16	no	—
290	D₄	—	4	16	no	—
291	C₂×C₄	—	2	8	no	—
292	C₂×C₄	—	2	8	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	16	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	4	8	no	—
303	C₂×C₄	—	4	16	no	—
304	C₂×C₄	—	4	16	no	—
305	C₂×C₄	#124×C₅₃	1	16	yes	—
306	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
307	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
308	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
309	C₂×C₄	C₂×#41×C₅₃	1	8	yes	—
310	C₂²	—	4	4	no	—
311	C₂²	—	4	16	no	—
312	C₂²	—	4	4	no	—
313	C₂²	—	4	4	no	—
314	C₂²	—	8	16	no	—
315	C₂²	C₂×#124×C₅₃	1	4	yes	—
316	C₂²	C₅₃×#535	1	4	yes	—
317	C₂²	C₅₃×#536	1	4	yes	—
318	C₂²	C₅₃×#542	1	16	yes	—
319	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
320	C₂²	C₂²×#41×C₅₃	1	2	yes	—
321	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
322	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	2	yes	—
323	C₄	—	2	4	no	—
324	C₄	—	2	4	no	—
325	C₄	—	4	8	no	—
326	C₄	—	4	4	no	—
327	C₄	—	4	8	no	—
328	C₄	C₂×#124×C₅₃	1	8	yes	—
329	C₂	—	8	4	no	—
330	C₂	C₅₃×#2640	1	8	yes	direct product factor
331	C₂	C₂²×#124×C₅₃	1	1	yes	characteristic
332	C₂	C₂×C₅₃×#535	1	1	yes	characteristic
333	C₂	C₂×C₅₃×#536	1	1	yes	characteristic
334	C₂	C₂×C₅₃×#542	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄⋊Q₈×C₅₃	C₂	semidirect
3. C₅₃×#2640	C₂	direct (N × H)
4. C₂×C₅₃×#397	C₂	semidirect
5. C₂×C₅₃×#393	C₂	semidirect
6. C₂×C₅₃×#391	C₂	semidirect
8. C₂×C₅₃×#376	C₂	semidirect
13. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
23. C₅₃×#397	C₂²	semidirect
24. C₅₃×#393	C₂²	semidirect
25. C₅₃×#391	C₂²	semidirect
27. C₅₃×#376	C₂²	semidirect
142. C₂×#2640	C₅₃	direct (N × H)
162. C₂²×C₄⋊Q₈	C₂×C₅₃	semidirect
164. #2640	C₂×C₅₃	direct (N × H)
165. C₂×#397	C₂×C₅₃	semidirect
166. C₂×#393	C₂×C₅₃	semidirect
167. C₂×#391	C₂×C₅₃	semidirect
169. C₂×#376	C₂×C₅₃	semidirect
171. C₂×C₅₃	#2640	direct (N × H)
180. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
190. #397	C₂²×C₅₃	semidirect
191. #393	C₂²×C₅₃	semidirect
192. #391	C₂²×C₅₃	semidirect
194. #376	C₂²×C₅₃	semidirect
198. C₅₃	C₂×#2640	direct (N × H)
330. C₂	C₅₃×#2640	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₅₃	2
C₂²×#124×C₅₃	2
C₅₃×#2640	2
C₂×C₅₃×#397	2
C₂×C₅₃×#393	2
C₂×C₅₃×#391	2
C₂×C₅₃×#390	2
C₂×C₅₃×#376	2
C₂×#2640	53

Subgroups — C2×C53×#2640 #27242127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#2640 #27242127