Subgroups — C₂×C₅₃×#3154 #27268152

Order 13568.

3342 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×AGL(1,ℤ/8)×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#135×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3154	C₂	1	16	yes	maximal, direct product factor
8	C₂×C₅₃×#497	C₂	1	2	yes	maximal, complemented
9	C₂×C₅₃×#496	C₂	1	2	yes	maximal, complemented
10	C₂×C₅₃×#495	C₂	1	2	yes	maximal, complemented
11	C₂×C₅₃×#492	C₂	1	2	yes	maximal, complemented
12	C₂×C₅₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
14	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
15	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×#137×C₅₃	—	2	8	no	—
18	C₂×#137×C₅₃	C₂²	1	8	yes	complemented
19	C₂×AGL(1,ℤ/8)×C₅₃	—	2	8	no	—
20	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	8	yes	complemented
21	C₂×#135×C₅₃	—	2	8	no	—
22	C₂×#135×C₅₃	C₂²	1	8	yes	complemented
23	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
25	C₂²×SD₁₆×C₅₃	—	2	8	no	—
26	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	—
27	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	—
28	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	—
29	C₂²×SD₁₆×C₅₃	C₂²	1	8	yes	complemented
30	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
32	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
33	C₂²×D₈×C₅₃	C₂²	1	2	yes	—
34	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
36	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
37	C₅₃×#536	—	2	4	no	—
38	C₅₃×#536	C₂²	1	8	yes	complemented
39	C₅₃×#535	—	2	4	no	—
40	C₅₃×#535	C₂²	1	8	yes	complemented
41	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
42	C₂×#127×C₅₃	C₂²	1	2	yes	—
43	C₂×#124×C₅₃	C₂²	1	2	yes	—
44	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
45	C₂×#123×C₅₃	—	2	2	no	—
46	C₂×C₂²⋊Q₈×C₅₃	—	2	2	no	—
47	C₂×#121×C₅₃	—	2	2	no	—
48	C₂×#120×C₅₃	—	2	2	no	—
49	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
50	C₅₃×#497	C₂²	1	16	yes	complemented
51	C₅₃×#496	C₂²	1	16	yes	complemented
52	C₅₃×#495	C₂²	1	16	yes	complemented
53	C₅₃×#492	C₂²	1	16	yes	complemented
54	C₅₃×#405	C₂²	1	8	yes	complemented
55	C₂×#97×C₅₃	C₂²	1	2	yes	complemented
56	C₂×C₄×C₈×C₅₃	C₂²	1	2	yes	complemented
57	C₂⁵×C₅₃	—	2	1	no	—
58	C₂×#41×C₅₃	—	2	2	no	—
59	C₂×#41×C₅₃	—	2	2	no	—
60	C₂×#41×C₅₃	—	2	4	no	—
61	C₂×#41×C₅₃	—	2	4	no	—
62	C₂×#41×C₅₃	—	2	4	no	—
63	C₂×#41×C₅₃	—	2	4	no	—
64	C₂×#41×C₅₃	C₂³	1	4	yes	—
65	C₂×#41×C₅₃	C₂³	1	4	yes	—
66	C₂²×Q₈×C₅₃	—	2	1	no	—
67	C₂²×Q₈×C₅₃	—	2	2	no	—
68	C₂²×Q₈×C₅₃	—	2	4	no	—
69	C₂²×Q₈×C₅₃	—	2	4	no	—
70	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
72	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
73	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
74	C₂²×D₄×C₅₃	—	2	1	no	—
75	C₂²×D₄×C₅₃	—	2	1	no	—
76	C₂²×D₄×C₅₃	—	2	4	no	—
77	C₂²×D₄×C₅₃	—	2	4	no	—
78	C₂²×D₄×C₅₃	—	2	1	no	—
79	C₂²×D₄×C₅₃	—	2	2	no	—
80	C₂²×D₄×C₅₃	—	2	4	no	—
81	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
82	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
85	C₂³×C₄×C₅₃	—	2	1	no	—
86	C₂³×C₄×C₅₃	—	2	1	no	—
87	C₂³×C₄×C₅₃	—	2	1	no	—
88	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
89	#137×C₅₃	—	2	32	no	—
90	AGL(1,ℤ/8)×C₅₃	—	2	32	no	—
91	#135×C₅₃	—	2	32	no	—
92	C₂×Q₁₆×C₅₃	—	2	4	no	—
93	C₂×Q₁₆×C₅₃	—	2	8	no	—
94	C₂×Q₁₆×C₅₃	C₂³	1	8	yes	complemented
95	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	complemented
96	C₂×SD₁₆×C₅₃	—	2	8	no	—
97	C₂×SD₁₆×C₅₃	—	2	8	no	—
98	C₂×SD₁₆×C₅₃	—	2	8	no	—
99	C₂×SD₁₆×C₅₃	—	2	4	no	—
100	C₂×SD₁₆×C₅₃	—	2	4	no	—
101	C₂×SD₁₆×C₅₃	—	2	8	no	—
102	C₂×SD₁₆×C₅₃	—	2	32	no	—
103	C₂×SD₁₆×C₅₃	C₂³	1	8	yes	—
104	C₂×SD₁₆×C₅₃	C₂³	1	8	yes	—
105	C₂×SD₁₆×C₅₃	C₂³	1	8	yes	—
106	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	complemented
107	C₂×SD₁₆×C₅₃	C₂³	1	8	yes	complemented
108	C₂×SD₁₆×C₅₃	C₂³	1	4	yes	complemented
109	C₂×D₈×C₅₃	—	2	8	no	—
110	C₂×D₈×C₅₃	—	2	4	no	—
111	C₂×D₈×C₅₃	C₂³	1	8	yes	—
112	C₂×D₈×C₅₃	C₂³	1	4	yes	complemented
113	C₂×M₁₆×C₅₃	D₄	1	8	yes	complemented
114	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
115	C₂²×C₈×C₅₃	D₄	1	8	yes	complemented
116	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
119	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
120	C₄⋊Q₈×C₅₃	—	2	4	no	—
121	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
122	#127×C₅₃	—	2	4	no	—
123	#127×C₅₃	C₂³	1	8	yes	—
124	#124×C₅₃	—	2	4	no	—
125	#124×C₅₃	—	2	4	no	—
126	#124×C₅₃	C₂³	1	8	yes	—
127	#124×C₅₃	C₂³	1	8	yes	complemented
128	#123×C₅₃	—	2	16	no	—
129	C₂²⋊Q₈×C₅₃	—	2	16	no	—
130	#121×C₅₃	—	2	16	no	—
131	#120×C₅₃	—	2	16	no	—
132	#117×C₅₃	D₄	1	4	yes	—
133	#117×C₅₃	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
135	C₂×C₄⋊C₄×C₅₃	D₄	1	2	yes	—
136	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
137	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
138	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
139	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
140	#97×C₅₃	C₂³	1	8	yes	complemented
141	C₄×C₈×C₅₃	C₂³	1	8	yes	complemented
142	C₂⁴×C₅₃	—	2	1	no	—
143	C₂⁴×C₅₃	—	2	2	no	—
144	C₂⁴×C₅₃	—	2	1	no	—
145	C₂⁴×C₅₃	—	2	4	no	—
146	C₂⁴×C₅₃	—	4	4	no	—
147	C₂⁴×C₅₃	—	8	4	no	—
148	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
149	#41×C₅₃	—	2	8	no	—
150	#41×C₅₃	—	2	8	no	—
151	#41×C₅₃	—	2	8	no	—
152	#41×C₅₃	—	2	8	no	—
153	#41×C₅₃	—	4	8	no	—
154	#41×C₅₃	—	4	8	no	—
155	C₂×Q₈×C₅₃	—	2	4	no	—
156	C₂×Q₈×C₅₃	—	2	1	no	—
157	C₂×Q₈×C₅₃	—	2	2	no	—
158	C₂×Q₈×C₅₃	—	2	1	no	—
159	C₂×Q₈×C₅₃	—	2	4	no	—
160	C₂×Q₈×C₅₃	—	2	8	no	—
161	C₂×Q₈×C₅₃	—	2	2	no	—
162	C₂×Q₈×C₅₃	—	2	4	no	—
163	C₂×Q₈×C₅₃	—	2	2	no	—
164	C₂×Q₈×C₅₃	—	2	2	no	—
165	C₂×Q₈×C₅₃	—	2	2	no	—
166	C₂×Q₈×C₅₃	—	2	8	no	—
167	C₂×Q₈×C₅₃	—	4	4	no	—
168	C₂×Q₈×C₅₃	—	4	8	no	—
169	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
170	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
171	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
172	C₂×D₄×C₅₃	—	2	4	no	—
173	C₂×D₄×C₅₃	—	2	4	no	—
174	C₂×D₄×C₅₃	—	2	2	no	—
175	C₂×D₄×C₅₃	—	2	4	no	—
176	C₂×D₄×C₅₃	—	2	2	no	—
177	C₂×D₄×C₅₃	—	2	2	no	—
178	C₂×D₄×C₅₃	—	2	4	no	—
179	C₂×D₄×C₅₃	—	2	8	no	—
180	C₂×D₄×C₅₃	—	2	2	no	—
181	C₂×D₄×C₅₃	—	2	8	no	—
182	C₂×D₄×C₅₃	—	2	4	no	—
183	C₂×D₄×C₅₃	—	2	1	no	—
184	C₂×D₄×C₅₃	—	2	2	no	—
185	C₂×D₄×C₅₃	—	2	1	no	—
186	C₂×D₄×C₅₃	—	2	16	no	—
187	C₂×D₄×C₅₃	—	4	4	no	—
188	C₂×D₄×C₅₃	—	4	4	no	—
189	C₂×D₄×C₅₃	—	4	4	no	—
190	C₂×D₄×C₅₃	—	4	8	no	—
191	C₂×D₄×C₅₃	—	8	8	no	—
192	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
193	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
194	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₅₃	—	2	4	no	—
196	C₂²×C₄×C₅₃	—	2	1	no	—
197	C₂²×C₄×C₅₃	—	2	2	no	—
198	C₂²×C₄×C₅₃	—	2	1	no	—
199	C₂²×C₄×C₅₃	—	2	4	no	—
200	C₂²×C₄×C₅₃	—	2	4	no	—
201	C₂²×C₄×C₅₃	—	4	4	no	—
202	C₂²×C₄×C₅₃	—	4	4	no	—
203	C₂²×C₄×C₅₃	—	4	4	no	—
204	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
208	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
209	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
211	Q₁₆×C₅₃	—	2	8	no	—
212	Q₁₆×C₅₃	—	2	16	no	—
213	SD₁₆×C₅₃	—	2	16	no	—
214	SD₁₆×C₅₃	—	2	16	no	—
215	SD₁₆×C₅₃	—	2	16	no	—
216	SD₁₆×C₅₃	—	2	8	no	—
217	SD₁₆×C₅₃	—	2	8	no	—
218	SD₁₆×C₅₃	—	2	16	no	—
219	D₈×C₅₃	—	2	16	no	—
220	D₈×C₅₃	—	2	8	no	—
221	M₁₆×C₅₃	C₂×D₄	1	16	yes	complemented
222	C₂×C₈×C₅₃	C₂×D₄	1	4	yes	—
223	C₂×C₈×C₅₃	C₂×D₄	1	4	yes	—
224	C₂×C₈×C₅₃	C₂×D₄	1	8	yes	—
225	C₂×C₈×C₅₃	C₂×D₄	1	16	yes	complemented
226	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
227	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
228	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
229	C₄⋊C₄×C₅₃	—	2	16	no	—
230	C₄⋊C₄×C₅₃	C₂×D₄	1	8	yes	—
231	C₂²⋊C₄×C₅₃	—	2	16	no	—
232	C₂²⋊C₄×C₅₃	—	2	16	no	—
233	C₂²⋊C₄×C₅₃	C₂×D₄	1	8	yes	—
234	C₄²×C₅₃	C₂×D₄	1	4	yes	—
235	C₄²×C₅₃	C₂⁴	1	4	yes	—
236	C₂³×C₅₃	—	2	4	no	—
237	C₂³×C₅₃	—	2	2	no	—
238	C₂³×C₅₃	—	2	2	no	—
239	C₂³×C₅₃	—	2	4	no	—
240	C₂³×C₅₃	—	4	2	no	—
241	C₂³×C₅₃	—	4	2	no	—
242	C₂³×C₅₃	—	4	8	no	—
243	C₂³×C₅₃	—	4	4	no	—
244	C₂³×C₅₃	—	4	4	no	—
245	C₂³×C₅₃	—	4	8	no	—
246	C₂³×C₅₃	—	4	4	no	—
247	C₂³×C₅₃	—	8	8	no	—
248	C₂³×C₅₃	—	8	16	no	—
249	C₂³×C₅₃	#127	1	4	yes	—
250	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
251	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
252	Q₈×C₅₃	—	2	4	no	—
253	Q₈×C₅₃	—	2	4	no	—
254	Q₈×C₅₃	—	2	2	no	—
255	Q₈×C₅₃	—	2	2	no	—
256	Q₈×C₅₃	—	2	2	no	—
257	Q₈×C₅₃	—	2	2	no	—
258	Q₈×C₅₃	—	4	8	no	—
259	Q₈×C₅₃	—	4	4	no	—
260	Q₈×C₅₃	—	4	2	no	—
261	Q₈×C₅₃	—	4	2	no	—
262	D₄×C₅₃	—	2	4	no	—
263	D₄×C₅₃	—	2	4	no	—
264	D₄×C₅₃	—	2	2	no	—
265	D₄×C₅₃	—	2	2	no	—
266	D₄×C₅₃	—	2	2	no	—
267	D₄×C₅₃	—	2	2	no	—
268	D₄×C₅₃	—	4	8	no	—
269	D₄×C₅₃	—	4	8	no	—
270	D₄×C₅₃	—	4	8	no	—
271	D₄×C₅₃	—	4	4	no	—
272	D₄×C₅₃	—	4	2	no	—
273	D₄×C₅₃	—	4	2	no	—
274	D₄×C₅₃	—	8	16	no	—
275	C₂×C₄×C₅₃	—	2	8	no	—
276	C₂×C₄×C₅₃	—	2	2	no	—
277	C₂×C₄×C₅₃	—	2	2	no	—
278	C₂×C₄×C₅₃	—	2	4	no	—
279	C₂×C₄×C₅₃	—	4	2	no	—
280	C₂×C₄×C₅₃	—	4	2	no	—
281	C₂×C₄×C₅₃	—	4	8	no	—
282	C₂×C₄×C₅₃	—	4	4	no	—
283	C₂×C₄×C₅₃	—	4	8	no	—
284	C₂×C₄×C₅₃	—	4	8	no	—
285	C₂×C₄×C₅₃	#127	1	4	yes	—
286	C₂×C₄×C₅₃	#127	1	8	yes	—
287	C₂×C₄×C₅₃	C₂²×D₄	1	8	yes	—
288	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
289	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
292	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
293	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
294	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
295	C₈×C₅₃	C₂²×D₄	1	4	yes	—
296	C₈×C₅₃	C₂²×D₄	1	4	yes	—
297	C₈×C₅₃	C₂²×D₄	1	8	yes	—
298	C₂×#3154	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
299	C₂²×C₅₃	—	2	8	no	—
300	C₂²×C₅₃	—	2	4	no	—
301	C₂²×C₅₃	—	4	2	no	—
302	C₂²×C₅₃	—	4	2	no	—
303	C₂²×C₅₃	—	4	4	no	—
304	C₂²×C₅₃	—	4	4	no	—
305	C₂²×C₅₃	—	4	8	no	—
306	C₂²×C₅₃	—	4	4	no	—
307	C₂²×C₅₃	—	8	16	no	—
308	C₂²×C₅₃	—	8	4	no	—
309	C₂²×C₅₃	—	8	4	no	—
310	C₂²×C₅₃	—	8	8	no	—
311	C₂²×C₅₃	C₂×#127	1	4	yes	—
312	C₂²×C₅₃	C₂×#127	1	2	yes	—
313	C₂²×C₅₃	#577	1	4	yes	—
314	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
315	C₄×C₅₃	—	2	8	no	—
316	C₄×C₅₃	—	4	2	no	—
317	C₄×C₅₃	—	4	2	no	—
318	C₄×C₅₃	—	4	4	no	—
319	C₄×C₅₃	C₂×#127	1	4	yes	—
320	C₄×C₅₃	C₂×#127	1	2	yes	—
321	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
322	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
323	C₂²×#137	C₂×C₅₃	1	1	yes	characteristic, complemented
324	C₂²×AGL(1,ℤ/8)	C₂×C₅₃	1	1	yes	characteristic, complemented
325	C₂²×#135	C₂×C₅₃	1	1	yes	characteristic, complemented
326	C₂³×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
327	C₂×#536	C₂×C₅₃	1	1	yes	characteristic, complemented
328	C₂×#535	C₂×C₅₃	1	1	yes	characteristic, complemented
329	#3154	C₂×C₅₃	1	16	yes	direct product factor
330	C₂×#497	C₂×C₅₃	1	2	yes	complemented
331	C₂×#496	C₂×C₅₃	1	2	yes	complemented
332	C₂×#495	C₂×C₅₃	1	2	yes	complemented
333	C₂×#492	C₂×C₅₃	1	2	yes	complemented
334	C₂×#405	C₂×C₅₃	1	1	yes	characteristic, complemented
335	C₂×C₅₃	—	2	4	no	—
336	C₂×C₅₃	—	8	2	no	—
337	C₂×C₅₃	—	8	2	no	—
338	C₂×C₅₃	—	8	4	no	—
339	C₂×C₅₃	#3154	1	4	yes	direct product factor
340	C₂×C₅₃	C₂²×#127	1	1	yes	characteristic
341	C₂×C₅₃	C₂×#577	1	2	yes	—
342	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
343	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
344	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic
345	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
346	C₂×#137	—	2	8	no	—
347	C₂×#137	C₂²×C₅₃	1	8	yes	complemented
348	C₂×AGL(1,ℤ/8)	—	2	8	no	—
349	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	8	yes	complemented
350	C₂×#135	—	2	8	no	—
351	C₂×#135	C₂²×C₅₃	1	8	yes	complemented
352	C₂²×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
353	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
354	C₂²×SD₁₆	—	2	8	no	—
355	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	—
356	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	—
357	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	—
358	C₂²×SD₁₆	C₂²×C₅₃	1	8	yes	complemented
359	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
360	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
361	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
362	C₂²×D₈	C₂²×C₅₃	1	2	yes	—
363	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
364	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
365	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
366	#536	—	2	4	no	—
367	#536	C₂²×C₅₃	1	8	yes	complemented
368	#535	—	2	4	no	—
369	#535	C₂²×C₅₃	1	8	yes	complemented
370	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
371	C₂×#127	C₂²×C₅₃	1	2	yes	—
372	C₂×#124	C₂²×C₅₃	1	2	yes	—
373	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
374	C₂×#123	—	2	2	no	—
375	C₂×C₂²⋊Q₈	—	2	2	no	—
376	C₂×#121	—	2	2	no	—
377	C₂×#120	—	2	2	no	—
378	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
379	#497	C₂²×C₅₃	1	16	yes	complemented
380	#496	C₂²×C₅₃	1	16	yes	complemented
381	#495	C₂²×C₅₃	1	16	yes	complemented
382	#492	C₂²×C₅₃	1	16	yes	complemented
383	#405	C₂²×C₅₃	1	8	yes	complemented
384	C₂×#97	C₂²×C₅₃	1	2	yes	complemented
385	C₂×C₄×C₈	C₂²×C₅₃	1	2	yes	complemented
386	C₅₃	C₂×#3154	1	1	yes	characteristic, direct product factor, Sylow
387	C₂⁵	—	2	1	no	—
388	C₂×#41	—	2	2	no	—
389	C₂×#41	—	2	2	no	—
390	C₂×#41	—	2	4	no	—
391	C₂×#41	—	2	4	no	—
392	C₂×#41	—	2	4	no	—
393	C₂×#41	—	2	4	no	—
394	C₂×#41	C₂³×C₅₃	1	4	yes	—
395	C₂×#41	C₂³×C₅₃	1	4	yes	—
396	C₂²×Q₈	—	2	1	no	—
397	C₂²×Q₈	—	2	2	no	—
398	C₂²×Q₈	—	2	4	no	—
399	C₂²×Q₈	—	2	4	no	—
400	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
401	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
402	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
403	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
404	C₂²×D₄	—	2	1	no	—
405	C₂²×D₄	—	2	1	no	—
406	C₂²×D₄	—	2	4	no	—
407	C₂²×D₄	—	2	4	no	—
408	C₂²×D₄	—	2	1	no	—
409	C₂²×D₄	—	2	2	no	—
410	C₂²×D₄	—	2	4	no	—
411	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
412	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
413	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
414	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
415	C₂³×C₄	—	2	1	no	—
416	C₂³×C₄	—	2	1	no	—
417	C₂³×C₄	—	2	1	no	—
418	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
419	#137	—	2	32	no	—
420	AGL(1,ℤ/8)	—	2	32	no	—
421	#135	—	2	32	no	—
422	C₂×Q₁₆	—	2	4	no	—
423	C₂×Q₁₆	—	2	8	no	—
424	C₂×Q₁₆	C₂³×C₅₃	1	4	yes	complemented
425	C₂×Q₁₆	C₂³×C₅₃	1	8	yes	complemented
426	C₂×SD₁₆	—	2	8	no	—
427	C₂×SD₁₆	—	2	8	no	—
428	C₂×SD₁₆	—	2	8	no	—
429	C₂×SD₁₆	—	2	4	no	—
430	C₂×SD₁₆	—	2	4	no	—
431	C₂×SD₁₆	—	2	8	no	—
432	C₂×SD₁₆	—	2	32	no	—
433	C₂×SD₁₆	C₂³×C₅₃	1	8	yes	—
434	C₂×SD₁₆	C₂³×C₅₃	1	8	yes	—
435	C₂×SD₁₆	C₂³×C₅₃	1	8	yes	—
436	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	complemented
437	C₂×SD₁₆	C₂³×C₅₃	1	4	yes	complemented
438	C₂×SD₁₆	C₂³×C₅₃	1	8	yes	complemented
439	C₂×D₈	—	2	8	no	—
440	C₂×D₈	—	2	4	no	—
441	C₂×D₈	C₂³×C₅₃	1	8	yes	—
442	C₂×D₈	C₂³×C₅₃	1	4	yes	complemented
443	C₂×M₁₆	D₄×C₅₃	1	8	yes	complemented
444	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
445	C₂²×C₈	D₄×C₅₃	1	8	yes	complemented
446	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
449	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
450	C₄⋊Q₈	—	2	4	no	—
451	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
452	#127	—	2	4	no	—
453	#127	C₂³×C₅₃	1	8	yes	—
454	#124	—	2	4	no	—
455	#124	—	2	4	no	—
456	#124	C₂³×C₅₃	1	8	yes	—
457	#124	C₂³×C₅₃	1	8	yes	complemented
458	#123	—	2	16	no	—
459	C₂²⋊Q₈	—	2	16	no	—
460	#121	—	2	16	no	—
461	#120	—	2	16	no	—
462	#117	D₄×C₅₃	1	4	yes	—
463	#117	C₂³×C₅₃	1	4	yes	—
464	C₂×C₄⋊C₄	—	2	4	no	—
465	C₂×C₄⋊C₄	D₄×C₅₃	1	2	yes	—
466	C₂×C₂²⋊C₄	—	2	4	no	—
467	C₂×C₂²⋊C₄	—	2	4	no	—
468	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
469	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
470	#97	C₂³×C₅₃	1	8	yes	complemented
471	C₄×C₈	C₂³×C₅₃	1	8	yes	complemented
472	C₂⁴	—	2	1	no	—
473	C₂⁴	—	2	2	no	—
474	C₂⁴	—	2	1	no	—
475	C₂⁴	—	2	4	no	—
476	C₂⁴	—	4	4	no	—
477	C₂⁴	—	8	4	no	—
478	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
479	#41	—	2	8	no	—
480	#41	—	2	8	no	—
481	#41	—	2	8	no	—
482	#41	—	2	8	no	—
483	#41	—	4	8	no	—
484	#41	—	4	8	no	—
485	C₂×Q₈	—	2	4	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	2	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	4	no	—
490	C₂×Q₈	—	2	8	no	—
491	C₂×Q₈	—	2	2	no	—
492	C₂×Q₈	—	2	4	no	—
493	C₂×Q₈	—	2	2	no	—
494	C₂×Q₈	—	2	2	no	—
495	C₂×Q₈	—	2	2	no	—
496	C₂×Q₈	—	2	8	no	—
497	C₂×Q₈	—	4	4	no	—
498	C₂×Q₈	—	4	8	no	—
499	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
500	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
501	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
502	C₂×D₄	—	2	4	no	—
503	C₂×D₄	—	2	4	no	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	2	4	no	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	2	4	no	—
509	C₂×D₄	—	2	8	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	8	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	16	no	—
517	C₂×D₄	—	4	4	no	—
518	C₂×D₄	—	4	4	no	—
519	C₂×D₄	—	4	4	no	—
520	C₂×D₄	—	4	8	no	—
521	C₂×D₄	—	8	8	no	—
522	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
523	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
524	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	4	no	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	—	4	4	no	—
533	C₂²×C₄	—	4	4	no	—
534	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
535	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
537	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
538	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
541	Q₁₆	—	2	8	no	—
542	Q₁₆	—	2	16	no	—
543	SD₁₆	—	2	16	no	—
544	SD₁₆	—	2	16	no	—
545	SD₁₆	—	2	16	no	—
546	SD₁₆	—	2	8	no	—
547	SD₁₆	—	2	8	no	—
548	SD₁₆	—	2	16	no	—
549	D₈	—	2	16	no	—
550	D₈	—	2	8	no	—
551	M₁₆	C₂×D₄×C₅₃	1	16	yes	complemented
552	C₂×C₈	C₂×D₄×C₅₃	1	4	yes	—
553	C₂×C₈	C₂×D₄×C₅₃	1	4	yes	—
554	C₂×C₈	C₂×D₄×C₅₃	1	8	yes	—
555	C₂×C₈	C₂×D₄×C₅₃	1	16	yes	complemented
556	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
557	C₂×C₈	C₂⁴×C₅₃	1	4	yes	—
558	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
559	C₄⋊C₄	—	2	16	no	—
560	C₄⋊C₄	C₂×D₄×C₅₃	1	8	yes	—
561	C₂²⋊C₄	—	2	16	no	—
562	C₂²⋊C₄	—	2	16	no	—
563	C₂²⋊C₄	C₂×D₄×C₅₃	1	8	yes	—
564	C₄²	C₂×D₄×C₅₃	1	4	yes	—
565	C₄²	C₂⁴×C₅₃	1	4	yes	—
566	C₂³	—	2	4	no	—
567	C₂³	—	2	2	no	—
568	C₂³	—	2	4	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	4	2	no	—
571	C₂³	—	4	2	no	—
572	C₂³	—	4	8	no	—
573	C₂³	—	4	4	no	—
574	C₂³	—	4	4	no	—
575	C₂³	—	4	8	no	—
576	C₂³	—	4	4	no	—
577	C₂³	—	8	8	no	—
578	C₂³	—	8	16	no	—
579	C₂³	#127×C₅₃	1	4	yes	—
580	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
581	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
582	Q₈	—	2	4	no	—
583	Q₈	—	2	2	no	—
584	Q₈	—	2	4	no	—
585	Q₈	—	2	2	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	2	2	no	—
588	Q₈	—	4	8	no	—
589	Q₈	—	4	4	no	—
590	Q₈	—	4	2	no	—
591	Q₈	—	4	2	no	—
592	D₄	—	2	2	no	—
593	D₄	—	2	4	no	—
594	D₄	—	2	2	no	—
595	D₄	—	2	2	no	—
596	D₄	—	2	4	no	—
597	D₄	—	2	2	no	—
598	D₄	—	4	8	no	—
599	D₄	—	4	8	no	—
600	D₄	—	4	8	no	—
601	D₄	—	4	4	no	—
602	D₄	—	4	2	no	—
603	D₄	—	4	2	no	—
604	D₄	—	8	16	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	8	no	—
612	C₂×C₄	—	4	4	no	—
613	C₂×C₄	—	4	8	no	—
614	C₂×C₄	—	4	8	no	—
615	C₂×C₄	#127×C₅₃	1	4	yes	—
616	C₂×C₄	#127×C₅₃	1	8	yes	—
617	C₂×C₄	C₂²×D₄×C₅₃	1	8	yes	—
618	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
619	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
620	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
621	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
622	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
623	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
624	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
625	C₈	C₂²×D₄×C₅₃	1	4	yes	—
626	C₈	C₂²×D₄×C₅₃	1	4	yes	—
627	C₈	C₂²×D₄×C₅₃	1	8	yes	—
628	C₂²	—	2	4	no	—
629	C₂²	—	2	8	no	—
630	C₂²	—	4	4	no	—
631	C₂²	—	4	8	no	—
632	C₂²	—	4	4	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	4	no	—
636	C₂²	—	8	16	no	—
637	C₂²	—	8	8	no	—
638	C₂²	—	8	4	no	—
639	C₂²	—	8	4	no	—
640	C₂²	C₂×#127×C₅₃	1	4	yes	—
641	C₂²	C₂×#127×C₅₃	1	2	yes	—
642	C₂²	C₅₃×#577	1	4	yes	—
643	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
644	C₄	—	2	8	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	2	no	—
647	C₄	—	4	4	no	—
648	C₄	C₂×#127×C₅₃	1	4	yes	—
649	C₄	C₂×#127×C₅₃	1	2	yes	—
650	C₄	C₂³×D₄×C₅₃	1	1	yes	characteristic
651	C₄	C₂³×D₄×C₅₃	1	1	yes	characteristic
652	C₂	—	2	4	no	—
653	C₂	—	8	4	no	—
654	C₂	—	8	2	no	—
655	C₂	—	8	2	no	—
656	C₂	C₅₃×#3154	1	4	yes	direct product factor
657	C₂	C₂²×#127×C₅₃	1	1	yes	characteristic
658	C₂	C₂×C₅₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×#117×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#137×C₅₃	C₂	semidirect
2. C₂²×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
3. C₂²×#135×C₅₃	C₂	semidirect
4. C₂³×SD₁₆×C₅₃	C₂	semidirect
5. C₂×C₅₃×#536	C₂	semidirect
6. C₂×C₅₃×#535	C₂	semidirect
7. C₅₃×#3154	C₂	direct (N × H)
8. C₂×C₅₃×#497	C₂	semidirect
9. C₂×C₅₃×#496	C₂	semidirect
10. C₂×C₅₃×#495	C₂	semidirect
11. C₂×C₅₃×#492	C₂	semidirect
12. C₂×C₅₃×#405	C₂	semidirect
18. C₂×#137×C₅₃	C₂²	semidirect
20. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
22. C₂×#135×C₅₃	C₂²	semidirect
23. C₂²×Q₁₆×C₅₃	C₂²	semidirect
24. C₂²×Q₁₆×C₅₃	C₂²	semidirect
29. C₂²×SD₁₆×C₅₃	C₂²	semidirect
30. C₂²×SD₁₆×C₅₃	C₂²	semidirect
31. C₂²×SD₁₆×C₅₃	C₂²	semidirect
32. C₂²×SD₁₆×C₅₃	C₂²	semidirect
34. C₂²×D₈×C₅₃	C₂²	semidirect
38. C₅₃×#536	C₂²	semidirect
40. C₅₃×#535	C₂²	semidirect
41. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
44. C₂×#124×C₅₃	C₂²	semidirect
50. C₅₃×#497	C₂²	semidirect
51. C₅₃×#496	C₂²	semidirect
52. C₅₃×#495	C₂²	semidirect
53. C₅₃×#492	C₂²	semidirect
54. C₅₃×#405	C₂²	semidirect
55. C₂×#97×C₅₃	C₂²	semidirect
56. C₂×C₄×C₈×C₅₃	C₂²	semidirect
94. C₂×Q₁₆×C₅₃	C₂³	semidirect
95. C₂×Q₁₆×C₅₃	C₂³	semidirect
106. C₂×SD₁₆×C₅₃	C₂³	semidirect
107. C₂×SD₁₆×C₅₃	C₂³	semidirect
108. C₂×SD₁₆×C₅₃	C₂³	semidirect
112. C₂×D₈×C₅₃	C₂³	semidirect
113. C₂×M₁₆×C₅₃	D₄	semidirect
115. C₂²×C₈×C₅₃	D₄	semidirect
121. C₄⋊Q₈×C₅₃	C₂³	semidirect
127. #124×C₅₃	C₂³	semidirect
140. #97×C₅₃	C₂³	semidirect
141. C₄×C₈×C₅₃	C₂³	semidirect
221. M₁₆×C₅₃	C₂×D₄	semidirect
225. C₂×C₈×C₅₃	C₂×D₄	semidirect
298. C₂×#3154	C₅₃	direct (N × H)
323. C₂²×#137	C₂×C₅₃	semidirect
324. C₂²×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
325. C₂²×#135	C₂×C₅₃	semidirect
326. C₂³×SD₁₆	C₂×C₅₃	semidirect
327. C₂×#536	C₂×C₅₃	semidirect
328. C₂×#535	C₂×C₅₃	semidirect
329. #3154	C₂×C₅₃	direct (N × H)
330. C₂×#497	C₂×C₅₃	semidirect
331. C₂×#496	C₂×C₅₃	semidirect
332. C₂×#495	C₂×C₅₃	semidirect
333. C₂×#492	C₂×C₅₃	semidirect
334. C₂×#405	C₂×C₅₃	semidirect
339. C₂×C₅₃	#3154	direct (N × H)
347. C₂×#137	C₂²×C₅₃	semidirect
349. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
351. C₂×#135	C₂²×C₅₃	semidirect
352. C₂²×Q₁₆	C₂²×C₅₃	semidirect
353. C₂²×Q₁₆	C₂²×C₅₃	semidirect
358. C₂²×SD₁₆	C₂²×C₅₃	semidirect
359. C₂²×SD₁₆	C₂²×C₅₃	semidirect
360. C₂²×SD₁₆	C₂²×C₅₃	semidirect
361. C₂²×SD₁₆	C₂²×C₅₃	semidirect
363. C₂²×D₈	C₂²×C₅₃	semidirect
367. #536	C₂²×C₅₃	semidirect
369. #535	C₂²×C₅₃	semidirect
370. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
373. C₂×#124	C₂²×C₅₃	semidirect
379. #497	C₂²×C₅₃	semidirect
380. #496	C₂²×C₅₃	semidirect
381. #495	C₂²×C₅₃	semidirect
382. #492	C₂²×C₅₃	semidirect
383. #405	C₂²×C₅₃	semidirect
384. C₂×#97	C₂²×C₅₃	semidirect
385. C₂×C₄×C₈	C₂²×C₅₃	semidirect
386. C₅₃	C₂×#3154	direct (N × H)
424. C₂×Q₁₆	C₂³×C₅₃	semidirect
425. C₂×Q₁₆	C₂³×C₅₃	semidirect
436. C₂×SD₁₆	C₂³×C₅₃	semidirect
437. C₂×SD₁₆	C₂³×C₅₃	semidirect
438. C₂×SD₁₆	C₂³×C₅₃	semidirect
442. C₂×D₈	C₂³×C₅₃	semidirect
443. C₂×M₁₆	D₄×C₅₃	semidirect
445. C₂²×C₈	D₄×C₅₃	semidirect
451. C₄⋊Q₈	C₂³×C₅₃	semidirect
457. #124	C₂³×C₅₃	semidirect
470. #97	C₂³×C₅₃	semidirect
471. C₄×C₈	C₂³×C₅₃	semidirect
551. M₁₆	C₂×D₄×C₅₃	semidirect
555. C₂×C₈	C₂×D₄×C₅₃	semidirect
656. C₂	C₅₃×#3154	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×#137×C₅₃	2
C₂²×AGL(1,ℤ/8)×C₅₃	2
C₂²×#135×C₅₃	2
C₂³×SD₁₆×C₅₃	2
C₂×C₅₃×#536	2
C₂×C₅₃×#535	2
C₅₃×#3154	2
C₂×C₅₃×#497	2
C₂×C₅₃×#496	2
C₂×C₅₃×#495	2
C₂×C₅₃×#492	2
C₂×C₅₃×#405	2
C₂×#3154	53

Subgroups — C2×C53×#3154 #27268152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3154 #27268152