Subgroups — C₂×C₅₃×#1962 #27228719

Order 13568.

1878 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#104×C₅₃	C₂	1	4	yes	maximal, complemented
4	C₂×C₄³×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#1962	C₂	1	8	yes	maximal, direct product factor
6	C₂²×#41×C₅₃	C₂²	1	2	yes	—
7	C₂²×M₁₆×C₅₃	C₂²	1	2	yes	—
8	C₅₃×#532	—	2	2	no	—
9	C₅₃×#532	—	2	2	no	—
10	C₅₃×#532	C₄	1	4	yes	complemented
11	C₅₃×#532	C₂²	1	4	yes	—
12	C₂×C₄⋊Q₈×C₅₃	C₄	1	1	yes	characteristic, complemented
13	C₂×#127×C₅₃	C₄	1	1	yes	characteristic, complemented
14	C₂×#124×C₅₃	C₄	1	2	yes	complemented
15	C₂×#121×C₅₃	—	2	2	no	—
16	C₂×C₄×D₄×C₅₃	—	2	2	no	—
17	C₂²×C₄²×C₅₃	—	2	2	no	—
18	C₂²×C₄²×C₅₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
20	C₅₃×#423	—	2	2	no	—
21	C₅₃×#423	C₂²	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₅₃	—	2	2	no	—
23	C₂×#104×C₅₃	—	2	16	no	—
24	C₂×#104×C₅₃	C₂²	1	16	yes	complemented
25	C₄³×C₅₃	—	2	2	no	—
26	C₄³×C₅₃	C₂²	1	4	yes	complemented
27	C₂×#41×C₅₃	—	2	2	no	—
28	C₂×#41×C₅₃	—	2	2	no	—
29	C₂×#41×C₅₃	—	2	8	no	—
30	C₂×#41×C₅₃	—	2	8	no	—
31	C₂×#41×C₅₃	C₂×C₄	1	4	yes	—
32	C₂×#41×C₅₃	C₂³	1	4	yes	—
33	C₂²×Q₈×C₅₃	C₂×C₄	1	2	yes	—
34	C₂²×D₄×C₅₃	—	2	2	no	—
35	C₂²×D₄×C₅₃	—	2	2	no	—
36	C₂²×D₄×C₅₃	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₅₃	—	2	2	no	—
38	C₂³×C₄×C₅₃	—	2	2	no	—
39	C₂³×C₄×C₅₃	D₄	1	2	yes	—
40	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
41	C₂×M₁₆×C₅₃	—	2	2	no	—
42	C₂×M₁₆×C₅₃	—	2	8	no	—
43	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
44	C₂²×C₈×C₅₃	—	2	2	no	—
45	C₄⋊Q₈×C₅₃	—	2	2	no	—
46	C₄⋊Q₈×C₅₃	C₂×C₄	1	4	yes	complemented
47	#127×C₅₃	—	2	2	no	—
48	#127×C₅₃	C₂×C₄	1	4	yes	complemented
49	#124×C₅₃	—	2	4	no	—
50	#124×C₅₃	C₂×C₄	1	8	yes	complemented
51	#121×C₅₃	—	2	8	no	—
52	#121×C₅₃	—	2	8	no	—
53	C₄×D₄×C₅₃	—	2	8	no	—
54	C₄×D₄×C₅₃	—	2	8	no	—
55	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
57	C₂×C₄²×C₅₃	—	2	16	no	—
58	C₂×C₄²×C₅₃	—	2	8	no	—
59	C₂×C₄²×C₅₃	—	2	2	no	—
60	C₂×C₄²×C₅₃	—	2	4	no	—
61	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₅₃	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₅₃	D₄	1	2	yes	—
65	C₂×C₄²×C₅₃	D₄	1	2	yes	—
66	C₂×C₄²×C₅₃	D₄	1	2	yes	—
67	C₂×C₄²×C₅₃	D₄	1	8	yes	complemented
68	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
69	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
70	C₄⋊C₈×C₅₃	—	2	8	no	—
71	#104×C₅₃	—	2	32	no	—
72	C₂⁴×C₅₃	—	2	2	no	—
73	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
74	#41×C₅₃	—	2	16	no	—
75	#41×C₅₃	—	2	8	no	—
76	#41×C₅₃	—	2	8	no	—
77	#41×C₅₃	—	4	8	no	—
78	#41×C₅₃	—	4	4	no	—
79	#41×C₅₃	—	4	4	no	—
80	C₂×Q₈×C₅₃	—	2	2	no	—
81	C₂×Q₈×C₅₃	—	2	8	no	—
82	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
83	C₂×D₄×C₅₃	—	2	4	no	—
84	C₂×D₄×C₅₃	—	2	4	no	—
85	C₂×D₄×C₅₃	—	2	8	no	—
86	C₂×D₄×C₅₃	—	2	2	no	—
87	C₂×D₄×C₅₃	—	2	8	no	—
88	C₂×D₄×C₅₃	—	4	8	no	—
89	C₂×D₄×C₅₃	—	4	8	no	—
90	C₂×D₄×C₅₃	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₅₃	—	2	16	no	—
92	C₂²×C₄×C₅₃	—	2	8	no	—
93	C₂²×C₄×C₅₃	—	2	4	no	—
94	C₂²×C₄×C₅₃	—	2	8	no	—
95	C₂²×C₄×C₅₃	—	2	2	no	—
96	C₂²×C₄×C₅₃	—	2	4	no	—
97	C₂²×C₄×C₅₃	—	2	4	no	—
98	C₂²×C₄×C₅₃	—	4	4	no	—
99	C₂²×C₄×C₅₃	—	4	4	no	—
100	C₂²×C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₅₃	C₂²⋊C₄	1	4	yes	—
102	C₂²×C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₅₃	#41	1	4	yes	—
111	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
112	M₁₆×C₅₃	—	2	8	no	—
113	M₁₆×C₅₃	—	4	4	no	—
114	C₂×C₈×C₅₃	—	2	4	no	—
115	C₂×C₈×C₅₃	—	4	4	no	—
116	C₄⋊C₄×C₅₃	—	2	8	no	—
117	C₂²⋊C₄×C₅₃	—	2	16	no	—
118	C₄²×C₅₃	—	2	32	no	—
119	C₄²×C₅₃	—	2	8	no	—
120	C₄²×C₅₃	—	2	4	no	—
121	C₄²×C₅₃	C₂²⋊C₄	1	4	yes	—
122	C₄²×C₅₃	C₂²⋊C₄	1	2	yes	—
123	C₄²×C₅₃	C₂²⋊C₄	1	2	yes	—
124	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
125	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₅₃	C₂×D₄	1	4	yes	—
127	C₄²×C₅₃	C₂×D₄	1	8	yes	complemented
128	C₂³×C₅₃	—	2	4	no	—
129	C₂³×C₅₃	—	2	4	no	—
130	C₂³×C₅₃	—	4	4	no	—
131	C₂³×C₅₃	—	4	8	no	—
132	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂³×C₅₃	#121	1	4	yes	—
135	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₅₃	—	2	8	no	—
137	Q₈×C₅₃	—	4	4	no	—
138	D₄×C₅₃	—	2	8	no	—
139	D₄×C₅₃	—	4	8	no	—
140	D₄×C₅₃	—	4	8	no	—
141	D₄×C₅₃	—	4	4	no	—
142	D₄×C₅₃	—	4	16	no	—
143	C₂×C₄×C₅₃	—	2	32	no	—
144	C₂×C₄×C₅₃	—	2	16	no	—
145	C₂×C₄×C₅₃	—	2	8	no	—
146	C₂×C₄×C₅₃	—	2	4	no	—
147	C₂×C₄×C₅₃	—	2	8	no	—
148	C₂×C₄×C₅₃	—	2	8	no	—
149	C₂×C₄×C₅₃	—	2	4	no	—
150	C₂×C₄×C₅₃	—	4	4	no	—
151	C₂×C₄×C₅₃	—	4	4	no	—
152	C₂×C₄×C₅₃	—	4	4	no	—
153	C₂×C₄×C₅₃	—	4	8	no	—
154	C₂×C₄×C₅₃	#104	1	8	yes	complemented
155	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	4	yes	—
156	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	4	yes	—
159	C₂×C₄×C₅₃	C₄×D₄	1	4	yes	—
160	C₂×C₄×C₅₃	C₄×D₄	1	4	yes	—
161	C₂×C₄×C₅₃	#121	1	4	yes	—
162	C₂×C₄×C₅₃	#124	1	2	yes	—
163	C₂×C₄×C₅₃	#124	1	2	yes	—
164	C₂×C₄×C₅₃	#127	1	2	yes	—
165	C₂×C₄×C₅₃	#127	1	2	yes	—
166	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
168	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
170	C₈×C₅₃	—	4	4	no	—
171	C₂×#1962	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₅₃	—	2	2	no	—
173	C₂²×C₅₃	—	2	2	no	—
174	C₂²×C₅₃	—	2	8	no	—
175	C₂²×C₅₃	—	4	8	no	—
176	C₂²×C₅₃	—	4	4	no	—
177	C₂²×C₅₃	—	8	8	no	—
178	C₂²×C₅₃	#390	1	2	yes	—
179	C₂²×C₅₃	#390	1	2	yes	—
180	C₂²×C₅₃	C₂×#104	1	4	yes	—
181	C₂²×C₅₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
182	C₂²×C₅₃	C₂×#121	1	2	yes	—
183	C₄×C₅₃	—	2	16	no	—
184	C₄×C₅₃	—	2	4	no	—
185	C₄×C₅₃	—	4	4	no	—
186	C₄×C₅₃	#390	1	2	yes	—
187	C₄×C₅₃	#390	1	2	yes	—
188	C₄×C₅₃	C₂×#104	1	8	yes	complemented
189	C₄×C₅₃	C₂×C₄×D₄	1	2	yes	—
190	C₄×C₅₃	C₂×#124	1	1	yes	characteristic
191	C₄×C₅₃	C₂×#127	1	1	yes	characteristic
192	C₂×#532	C₂×C₅₃	1	1	yes	characteristic
193	C₂×#423	C₂×C₅₃	1	1	yes	characteristic, complemented
194	C₂²×#104	C₂×C₅₃	1	4	yes	complemented
195	C₂×C₄³	C₂×C₅₃	1	1	yes	characteristic, complemented
196	#1962	C₂×C₅₃	1	8	yes	direct product factor
197	C₂×C₅₃	—	2	2	no	—
198	C₂×C₅₃	—	2	2	no	—
199	C₂×C₅₃	—	8	4	no	—
200	C₂×C₅₃	#1962	1	4	yes	direct product factor
201	C₂×C₅₃	C₂×#390	1	1	yes	characteristic
202	C₂×C₅₃	C₂²×#104	1	2	yes	—
203	C₂²×#41	C₂²×C₅₃	1	2	yes	—
204	C₂²×M₁₆	C₂²×C₅₃	1	2	yes	—
205	#532	—	2	2	no	—
206	#532	—	2	2	no	—
207	#532	C₄×C₅₃	1	4	yes	complemented
208	#532	C₂²×C₅₃	1	4	yes	—
209	C₂×C₄⋊Q₈	C₄×C₅₃	1	1	yes	characteristic, complemented
210	C₂×#127	C₄×C₅₃	1	1	yes	characteristic, complemented
211	C₂×#124	C₄×C₅₃	1	2	yes	complemented
212	C₂×#121	—	2	2	no	—
213	C₂×C₄×D₄	—	2	2	no	—
214	C₂²×C₄²	—	2	2	no	—
215	C₂²×C₄²	C₂²×C₅₃	1	2	yes	—
216	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
217	#423	—	2	2	no	—
218	#423	C₂²×C₅₃	1	4	yes	complemented
219	C₂×C₄⋊C₈	—	2	2	no	—
220	C₂×#104	—	2	16	no	—
221	C₂×#104	C₂²×C₅₃	1	16	yes	complemented
222	C₄³	—	2	2	no	—
223	C₄³	C₂²×C₅₃	1	4	yes	complemented
224	C₅₃	C₂×#1962	1	1	yes	characteristic, direct product factor, Sylow
225	C₂×#41	—	2	2	no	—
226	C₂×#41	—	2	2	no	—
227	C₂×#41	—	2	8	no	—
228	C₂×#41	—	2	8	no	—
229	C₂×#41	C₂×C₄×C₅₃	1	4	yes	—
230	C₂×#41	C₂³×C₅₃	1	4	yes	—
231	C₂²×Q₈	C₂×C₄×C₅₃	1	2	yes	—
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	—	2	2	no	—
234	C₂²×D₄	C₂×C₄×C₅₃	1	2	yes	—
235	C₂³×C₄	—	2	2	no	—
236	C₂³×C₄	—	2	2	no	—
237	C₂³×C₄	D₄×C₅₃	1	2	yes	—
238	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	2	8	no	—
241	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
242	C₂²×C₈	—	2	2	no	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	C₂×C₄×C₅₃	1	4	yes	complemented
245	#127	—	2	2	no	—
246	#127	C₂×C₄×C₅₃	1	4	yes	complemented
247	#124	—	2	4	no	—
248	#124	C₂×C₄×C₅₃	1	8	yes	complemented
249	#121	—	2	8	no	—
250	#121	—	2	8	no	—
251	C₄×D₄	—	2	8	no	—
252	C₄×D₄	—	2	8	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	4	no	—
255	C₂×C₄²	—	2	16	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	2	8	no	—
258	C₂×C₄²	—	2	4	no	—
259	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
260	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
261	C₂×C₄²	C₂×C₄×C₅₃	1	2	yes	—
262	C₂×C₄²	D₄×C₅₃	1	2	yes	—
263	C₂×C₄²	D₄×C₅₃	1	2	yes	—
264	C₂×C₄²	D₄×C₅₃	1	2	yes	—
265	C₂×C₄²	D₄×C₅₃	1	8	yes	complemented
266	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
267	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
268	C₄⋊C₈	—	2	8	no	—
269	#104	—	2	32	no	—
270	C₂⁴	—	2	2	no	—
271	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
272	#41	—	2	16	no	—
273	#41	—	2	8	no	—
274	#41	—	2	8	no	—
275	#41	—	4	8	no	—
276	#41	—	4	4	no	—
277	#41	—	4	4	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	8	no	—
280	C₂×Q₈	C₂²×C₄×C₅₃	1	4	yes	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	8	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	8	no	—
286	C₂×D₄	—	4	8	no	—
287	C₂×D₄	—	4	8	no	—
288	C₂×D₄	C₂²×C₄×C₅₃	1	4	yes	—
289	C₂²×C₄	—	2	16	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	4	4	no	—
297	C₂²×C₄	—	4	4	no	—
298	C₂²×C₄	C₂²⋊C₄×C₅₃	1	2	yes	—
299	C₂²×C₄	C₂²⋊C₄×C₅₃	1	4	yes	—
300	C₂²×C₄	C₂²⋊C₄×C₅₃	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
304	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
308	C₂²×C₄	#41×C₅₃	1	4	yes	—
309	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
310	M₁₆	—	2	8	no	—
311	M₁₆	—	4	4	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	4	4	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₂²⋊C₄	—	2	16	no	—
316	C₄²	—	2	32	no	—
317	C₄²	—	2	8	no	—
318	C₄²	—	2	4	no	—
319	C₄²	C₂²⋊C₄×C₅₃	1	4	yes	—
320	C₄²	C₂²⋊C₄×C₅₃	1	2	yes	—
321	C₄²	C₂²⋊C₄×C₅₃	1	2	yes	—
322	C₄²	C₂²×C₄×C₅₃	1	2	yes	—
323	C₄²	C₂²×C₄×C₅₃	1	2	yes	—
324	C₄²	C₂×D₄×C₅₃	1	4	yes	—
325	C₄²	C₂×D₄×C₅₃	1	8	yes	complemented
326	C₂³	—	2	4	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	4	4	no	—
329	C₂³	—	4	8	no	—
330	C₂³	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
331	C₂³	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
332	C₂³	#121×C₅₃	1	4	yes	—
333	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
334	Q₈	—	2	8	no	—
335	Q₈	—	4	4	no	—
336	D₄	—	2	8	no	—
337	D₄	—	4	8	no	—
338	D₄	—	4	8	no	—
339	D₄	—	4	4	no	—
340	D₄	—	4	16	no	—
341	C₂×C₄	—	2	16	no	—
342	C₂×C₄	—	2	32	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	8	no	—
352	C₂×C₄	#104×C₅₃	1	8	yes	complemented
353	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	4	yes	—
354	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
355	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
356	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	4	yes	—
357	C₂×C₄	C₄×D₄×C₅₃	1	4	yes	—
358	C₂×C₄	C₄×D₄×C₅₃	1	4	yes	—
359	C₂×C₄	#121×C₅₃	1	4	yes	—
360	C₂×C₄	#124×C₅₃	1	2	yes	—
361	C₂×C₄	#124×C₅₃	1	2	yes	—
362	C₂×C₄	#127×C₅₃	1	2	yes	—
363	C₂×C₄	#127×C₅₃	1	2	yes	—
364	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
365	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
366	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
367	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
368	C₈	—	4	4	no	—
369	C₂²	—	2	8	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	4	8	no	—
374	C₂²	—	8	8	no	—
375	C₂²	C₅₃×#390	1	2	yes	—
376	C₂²	C₅₃×#390	1	2	yes	—
377	C₂²	C₂×#104×C₅₃	1	4	yes	—
378	C₂²	C₂²×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
379	C₂²	C₂×#121×C₅₃	1	2	yes	—
380	C₄	—	2	16	no	—
381	C₄	—	2	4	no	—
382	C₄	—	4	4	no	—
383	C₄	C₅₃×#390	1	2	yes	—
384	C₄	C₅₃×#390	1	2	yes	—
385	C₄	C₂×#104×C₅₃	1	8	yes	complemented
386	C₄	C₂×C₄×D₄×C₅₃	1	2	yes	—
387	C₄	C₂×#124×C₅₃	1	1	yes	characteristic
388	C₄	C₂×#127×C₅₃	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	2	2	no	—
391	C₂	—	8	4	no	—
392	C₂	C₅₃×#1962	1	4	yes	direct product factor
393	C₂	C₂×C₅₃×#390	1	1	yes	characteristic
394	C₂	C₂²×#104×C₅₃	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
socle	C₂³×C₅₃	C₂×C₂²⋊C₄
prime radical	C₂×C₅₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ C₂²×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₃×#423	C₂	semidirect
3. C₂²×#104×C₅₃	C₂	semidirect
4. C₂×C₄³×C₅₃	C₂	semidirect
5. C₅₃×#1962	C₂	direct (N × H)
10. C₅₃×#532	C₄	semidirect
12. C₂×C₄⋊Q₈×C₅₃	C₄	semidirect
13. C₂×#127×C₅₃	C₄	semidirect
14. C₂×#124×C₅₃	C₄	semidirect
21. C₅₃×#423	C₂²	semidirect
24. C₂×#104×C₅₃	C₂²	semidirect
26. C₄³×C₅₃	C₂²	semidirect
46. C₄⋊Q₈×C₅₃	C₂×C₄	semidirect
48. #127×C₅₃	C₂×C₄	semidirect
50. #124×C₅₃	C₂×C₄	semidirect
67. C₂×C₄²×C₅₃	D₄	semidirect
127. C₄²×C₅₃	C₂×D₄	semidirect
154. C₂×C₄×C₅₃	#104	semidirect
171. C₂×#1962	C₅₃	direct (N × H)
188. C₄×C₅₃	C₂×#104	semidirect
193. C₂×#423	C₂×C₅₃	semidirect
194. C₂²×#104	C₂×C₅₃	semidirect
195. C₂×C₄³	C₂×C₅₃	semidirect
196. #1962	C₂×C₅₃	direct (N × H)
200. C₂×C₅₃	#1962	direct (N × H)
207. #532	C₄×C₅₃	semidirect
209. C₂×C₄⋊Q₈	C₄×C₅₃	semidirect
210. C₂×#127	C₄×C₅₃	semidirect
211. C₂×#124	C₄×C₅₃	semidirect
218. #423	C₂²×C₅₃	semidirect
221. C₂×#104	C₂²×C₅₃	semidirect
223. C₄³	C₂²×C₅₃	semidirect
224. C₅₃	C₂×#1962	direct (N × H)
244. C₄⋊Q₈	C₂×C₄×C₅₃	semidirect
246. #127	C₂×C₄×C₅₃	semidirect
248. #124	C₂×C₄×C₅₃	semidirect
265. C₂×C₄²	D₄×C₅₃	semidirect
325. C₄²	C₂×D₄×C₅₃	semidirect
352. C₂×C₄	#104×C₅₃	semidirect
385. C₄	C₂×#104×C₅₃	semidirect
392. C₂	C₅₃×#1962	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#532	2
C₂×C₅₃×#423	2
C₂²×#104×C₅₃	2
C₂×C₄³×C₅₃	2
C₅₃×#1962	2
C₂×#1962	53

Subgroups — C2×C53×#1962 #27228719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#1962 #27228719