Subgroups — C₂×C₅₃×#3140 #27268127

Order 13568.

2246 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#124×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3140	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅₃×#489	C₂	1	4	yes	maximal, complemented
5	C₂×C₅₃×#488	C₂	1	4	yes	maximal, complemented
6	C₂×C₅₃×#419	C₂	1	2	yes	maximal, complemented
7	C₂×C₅₃×#418	C₂	1	2	yes	maximal
8	C₂×C₄×M₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₅₃	C₂²	1	2	yes	—
12	C₅₃×#533	—	2	4	no	—
13	C₅₃×#533	C₂²	1	8	yes	complemented
14	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
15	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
16	C₂×#124×C₅₃	—	2	2	no	—
17	C₂×#124×C₅₃	—	2	4	no	—
18	C₂×#124×C₅₃	C₂²	1	2	yes	—
19	C₂×#124×C₅₃	C₂²	1	2	yes	—
20	C₂×#124×C₅₃	C₂²	1	8	yes	—
21	C₂×C₂²⋊Q₈×C₅₃	—	2	2	no	—
22	C₂×C₄×Q₈×C₅₃	—	2	2	no	—
23	C₂×#117×C₅₃	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₅₃	—	2	2	no	—
25	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
26	C₅₃×#489	C₂²	1	32	yes	complemented
27	C₅₃×#488	C₂²	1	32	yes	complemented
28	C₅₃×#419	C₂²	1	16	yes	complemented
29	C₅₃×#418	C₂²	1	16	yes	—
30	C₂×#103×C₅₃	C₂²	1	8	yes	complemented
31	C₂×#102×C₅₃	C₂²	1	8	yes	—
32	C₄×M₁₆×C₅₃	C₂²	1	8	yes	complemented
33	C₂×#97×C₅₃	C₂²	1	2	yes	complemented
34	C₂×C₄×C₈×C₅₃	C₂²	1	2	yes	complemented
35	C₂⁵×C₅₃	—	2	1	no	—
36	C₂²×Q₈×C₅₃	—	2	2	no	—
37	C₂²×Q₈×C₅₃	—	2	2	no	—
38	C₂²×Q₈×C₅₃	—	2	1	no	—
39	C₂²×Q₈×C₅₃	—	2	8	no	—
40	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
41	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
42	C₂²×D₄×C₅₃	—	2	2	no	—
43	C₂²×D₄×C₅₃	—	2	1	no	—
44	C₂²×D₄×C₅₃	—	2	8	no	—
45	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
46	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
47	C₂³×C₄×C₅₃	—	2	1	no	—
48	C₂³×C₄×C₅₃	D₄	1	2	yes	—
49	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₅₃	—	2	8	no	—
51	C₂×M₁₆×C₅₃	C₂³	1	8	yes	—
52	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
53	C₄⋊Q₈×C₅₃	—	2	4	no	—
54	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
55	#125×C₅₃	—	2	4	no	—
56	#125×C₅₃	C₂³	1	8	yes	complemented
57	#124×C₅₃	—	2	16	no	—
58	#124×C₅₃	—	2	4	no	—
59	#124×C₅₃	—	2	4	no	—
60	#124×C₅₃	C₂³	1	8	yes	—
61	#124×C₅₃	C₂³	1	8	yes	—
62	C₂²⋊Q₈×C₅₃	—	2	16	no	—
63	C₄×Q₈×C₅₃	—	2	16	no	—
64	#117×C₅₃	—	2	4	no	—
65	#117×C₅₃	C₂³	1	8	yes	—
66	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
67	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
69	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₅₃	—	2	16	no	—
71	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
73	C₂×C₄²×C₅₃	—	2	2	no	—
74	C₂×C₄²×C₅₃	D₄	1	2	yes	—
75	C₂×C₄²×C₅₃	D₄	1	4	yes	—
76	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
79	#103×C₅₃	C₂³	1	32	yes	complemented
80	#102×C₅₃	C₂³	1	32	yes	—
81	#97×C₅₃	C₂³	1	8	yes	complemented
82	C₄×C₈×C₅₃	C₂³	1	8	yes	complemented
83	C₂⁴×C₅₃	—	2	4	no	—
84	C₂⁴×C₅₃	—	2	2	no	—
85	C₂⁴×C₅₃	—	4	8	no	—
86	C₂⁴×C₅₃	—	4	4	no	—
87	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
88	C₂×Q₈×C₅₃	—	2	8	no	—
89	C₂×Q₈×C₅₃	—	2	4	no	—
90	C₂×Q₈×C₅₃	—	2	2	no	—
91	C₂×Q₈×C₅₃	—	2	8	no	—
92	C₂×Q₈×C₅₃	—	2	16	no	—
93	C₂×Q₈×C₅₃	—	4	8	no	—
94	C₂×Q₈×C₅₃	—	4	8	no	—
95	C₂×Q₈×C₅₃	—	4	4	no	—
96	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
97	C₂×D₄×C₅₃	—	2	4	no	—
98	C₂×D₄×C₅₃	—	2	2	no	—
99	C₂×D₄×C₅₃	—	2	8	no	—
100	C₂×D₄×C₅₃	—	2	16	no	—
101	C₂×D₄×C₅₃	—	4	8	no	—
102	C₂×D₄×C₅₃	—	4	4	no	—
103	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
104	C₂²×C₄×C₅₃	—	2	4	no	—
105	C₂²×C₄×C₅₃	—	2	4	no	—
106	C₂²×C₄×C₅₃	—	2	2	no	—
107	C₂²×C₄×C₅₃	—	4	4	no	—
108	C₂²×C₄×C₅₃	—	4	4	no	—
109	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	—
112	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅₃	#41	1	8	yes	—
115	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
117	M₁₆×C₅₃	—	2	16	no	—
118	C₂×C₈×C₅₃	—	2	8	no	—
119	C₂×C₈×C₅₃	C₂⁴	1	8	yes	—
120	C₄⋊C₄×C₅₃	—	2	16	no	—
121	C₄⋊C₄×C₅₃	—	2	8	no	—
122	C₄⋊C₄×C₅₃	—	2	4	no	—
123	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
124	C₂²⋊C₄×C₅₃	—	2	8	no	—
125	C₂²⋊C₄×C₅₃	—	2	16	no	—
126	C₂²⋊C₄×C₅₃	—	2	16	no	—
127	C₄²×C₅₃	—	2	8	no	—
128	C₄²×C₅₃	C₂×D₄	1	8	yes	—
129	C₄²×C₅₃	C₂×D₄	1	2	yes	—
130	C₄²×C₅₃	C₂×D₄	1	2	yes	—
131	C₄²×C₅₃	C₂⁴	1	2	yes	—
132	C₄²×C₅₃	C₂⁴	1	2	yes	—
133	C₂³×C₅₃	—	2	4	no	—
134	C₂³×C₅₃	—	2	4	no	—
135	C₂³×C₅₃	—	4	16	no	—
136	C₂³×C₅₃	—	4	8	no	—
137	C₂³×C₅₃	—	4	4	no	—
138	C₂³×C₅₃	—	4	8	no	—
139	C₂³×C₅₃	—	8	16	no	—
140	C₂³×C₅₃	#124	1	4	yes	—
141	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
142	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₅₃	—	2	8	no	—
144	Q₈×C₅₃	—	4	16	no	—
145	Q₈×C₅₃	—	4	8	no	—
146	Q₈×C₅₃	—	4	4	no	—
147	D₄×C₅₃	—	2	8	no	—
148	D₄×C₅₃	—	4	8	no	—
149	D₄×C₅₃	—	4	4	no	—
150	C₂×C₄×C₅₃	—	2	4	no	—
151	C₂×C₄×C₅₃	—	2	4	no	—
152	C₂×C₄×C₅₃	—	2	4	no	—
153	C₂×C₄×C₅₃	—	2	8	no	—
154	C₂×C₄×C₅₃	—	4	8	no	—
155	C₂×C₄×C₅₃	—	4	8	no	—
156	C₂×C₄×C₅₃	—	4	4	no	—
157	C₂×C₄×C₅₃	—	4	8	no	—
158	C₂×C₄×C₅₃	#124	1	8	yes	—
159	C₂×C₄×C₅₃	#124	1	4	yes	—
160	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
161	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
162	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
163	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
165	C₂×C₄×C₅₃	C₂×#41	1	8	yes	—
166	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
167	C₈×C₅₃	—	2	8	no	—
168	C₂×#3140	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂²×C₅₃	—	2	8	no	—
170	C₂²×C₅₃	—	2	4	no	—
171	C₂²×C₅₃	—	4	4	no	—
172	C₂²×C₅₃	—	4	8	no	—
173	C₂²×C₅₃	—	8	16	no	—
174	C₂²×C₅₃	—	8	8	no	—
175	C₂²×C₅₃	C₂×#124	1	4	yes	—
176	C₂²×C₅₃	C₂×#124	1	2	yes	—
177	C₂²×C₅₃	#575	1	4	yes	—
178	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
179	C₄×C₅₃	—	2	4	no	—
180	C₄×C₅₃	—	2	4	no	—
181	C₄×C₅₃	—	4	4	no	—
182	C₄×C₅₃	—	4	8	no	—
183	C₄×C₅₃	C₂×#124	1	4	yes	—
184	C₄×C₅₃	C₂×#124	1	2	yes	—
185	C₄×C₅₃	C₂²×#41	1	2	yes	—
186	C₂×#533	C₂×C₅₃	1	1	yes	characteristic, complemented
187	C₂²×#124	C₂×C₅₃	1	1	yes	characteristic
188	#3140	C₂×C₅₃	1	16	yes	direct product factor
189	C₂×#489	C₂×C₅₃	1	4	yes	complemented
190	C₂×#488	C₂×C₅₃	1	4	yes	complemented
191	C₂×#419	C₂×C₅₃	1	2	yes	complemented
192	C₂×#418	C₂×C₅₃	1	2	yes	—
193	C₂×C₄×M₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
194	C₂×C₅₃	—	2	4	no	—
195	C₂×C₅₃	—	8	4	no	—
196	C₂×C₅₃	#3140	1	4	yes	direct product factor
197	C₂×C₅₃	C₂²×#124	1	1	yes	characteristic
198	C₂×C₅₃	C₂×#575	1	2	yes	—
199	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic
200	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
201	C₂²×M₁₆	C₂²×C₅₃	1	2	yes	—
202	#533	—	2	4	no	—
203	#533	C₂²×C₅₃	1	8	yes	complemented
204	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
205	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
206	C₂×#124	—	2	2	no	—
207	C₂×#124	—	2	4	no	—
208	C₂×#124	C₂²×C₅₃	1	2	yes	—
209	C₂×#124	C₂²×C₅₃	1	2	yes	—
210	C₂×#124	C₂²×C₅₃	1	8	yes	—
211	C₂×C₂²⋊Q₈	—	2	2	no	—
212	C₂×C₄×Q₈	—	2	2	no	—
213	C₂×#117	C₂²×C₅₃	1	2	yes	—
214	C₂²×C₂²⋊C₄	—	2	2	no	—
215	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
216	#489	C₂²×C₅₃	1	32	yes	complemented
217	#488	C₂²×C₅₃	1	32	yes	complemented
218	#419	C₂²×C₅₃	1	16	yes	complemented
219	#418	C₂²×C₅₃	1	16	yes	—
220	C₂×#103	C₂²×C₅₃	1	8	yes	complemented
221	C₂×#102	C₂²×C₅₃	1	8	yes	—
222	C₄×M₁₆	C₂²×C₅₃	1	8	yes	complemented
223	C₂×#97	C₂²×C₅₃	1	2	yes	complemented
224	C₂×C₄×C₈	C₂²×C₅₃	1	2	yes	complemented
225	C₅₃	C₂×#3140	1	1	yes	characteristic, direct product factor, Sylow
226	C₂⁵	—	2	1	no	—
227	C₂²×Q₈	—	2	2	no	—
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×Q₈	—	2	2	no	—
230	C₂²×Q₈	—	2	8	no	—
231	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
232	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	—	2	2	no	—
235	C₂²×D₄	—	2	8	no	—
236	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
237	C₂²×D₄	C₂³×C₅₃	1	4	yes	—
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	D₄×C₅₃	1	2	yes	—
240	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
241	C₂×M₁₆	—	2	8	no	—
242	C₂×M₁₆	C₂³×C₅₃	1	8	yes	—
243	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
244	C₄⋊Q₈	—	2	4	no	—
245	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
246	#125	—	2	4	no	—
247	#125	C₂³×C₅₃	1	8	yes	complemented
248	#124	—	2	16	no	—
249	#124	—	2	4	no	—
250	#124	—	2	4	no	—
251	#124	C₂³×C₅₃	1	8	yes	—
252	#124	C₂³×C₅₃	1	8	yes	—
253	C₂²⋊Q₈	—	2	16	no	—
254	C₄×Q₈	—	2	16	no	—
255	#117	—	2	4	no	—
256	#117	C₂³×C₅₃	1	8	yes	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	4	no	—
262	C₂×C₂²⋊C₄	—	2	4	no	—
263	C₂×C₂²⋊C₄	—	2	16	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	D₄×C₅₃	1	2	yes	—
266	C₂×C₄²	D₄×C₅₃	1	4	yes	—
267	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
270	#103	C₂³×C₅₃	1	32	yes	complemented
271	#102	C₂³×C₅₃	1	32	yes	—
272	#97	C₂³×C₅₃	1	8	yes	complemented
273	C₄×C₈	C₂³×C₅₃	1	8	yes	complemented
274	C₂⁴	—	2	4	no	—
275	C₂⁴	—	2	2	no	—
276	C₂⁴	—	4	8	no	—
277	C₂⁴	—	4	4	no	—
278	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
279	C₂×Q₈	—	2	8	no	—
280	C₂×Q₈	—	2	4	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	8	no	—
283	C₂×Q₈	—	2	16	no	—
284	C₂×Q₈	—	4	8	no	—
285	C₂×Q₈	—	4	8	no	—
286	C₂×Q₈	—	4	4	no	—
287	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	8	no	—
291	C₂×D₄	—	2	16	no	—
292	C₂×D₄	—	4	8	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₅₃	1	8	yes	—
303	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
305	C₂²×C₄	#41×C₅₃	1	8	yes	—
306	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
308	M₁₆	—	2	16	no	—
309	C₂×C₈	—	2	8	no	—
310	C₂×C₈	C₂⁴×C₅₃	1	8	yes	—
311	C₄⋊C₄	—	2	16	no	—
312	C₄⋊C₄	—	2	8	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₂²⋊C₄	—	2	16	no	—
317	C₂²⋊C₄	—	2	16	no	—
318	C₄²	—	2	8	no	—
319	C₄²	C₂×D₄×C₅₃	1	8	yes	—
320	C₄²	C₂×D₄×C₅₃	1	2	yes	—
321	C₄²	C₂×D₄×C₅₃	1	2	yes	—
322	C₄²	C₂⁴×C₅₃	1	2	yes	—
323	C₄²	C₂⁴×C₅₃	1	2	yes	—
324	C₂³	—	2	4	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	4	16	no	—
327	C₂³	—	4	8	no	—
328	C₂³	—	4	4	no	—
329	C₂³	—	4	8	no	—
330	C₂³	—	8	16	no	—
331	C₂³	#124×C₅₃	1	4	yes	—
332	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
333	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
334	Q₈	—	2	8	no	—
335	Q₈	—	4	16	no	—
336	Q₈	—	4	8	no	—
337	Q₈	—	4	4	no	—
338	D₄	—	2	8	no	—
339	D₄	—	4	8	no	—
340	D₄	—	4	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	8	no	—
346	C₂×C₄	—	4	8	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	#124×C₅₃	1	8	yes	—
350	C₂×C₄	#124×C₅₃	1	4	yes	—
351	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
352	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
353	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
354	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
355	C₂×C₄	C₂×#41×C₅₃	1	4	yes	—
356	C₂×C₄	C₂×#41×C₅₃	1	8	yes	—
357	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
358	C₈	—	2	8	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	2	8	no	—
361	C₂²	—	4	8	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	8	16	no	—
364	C₂²	—	8	8	no	—
365	C₂²	C₂×#124×C₅₃	1	4	yes	—
366	C₂²	C₂×#124×C₅₃	1	2	yes	—
367	C₂²	C₅₃×#575	1	4	yes	—
368	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
369	C₄	—	2	4	no	—
370	C₄	—	2	4	no	—
371	C₄	—	4	8	no	—
372	C₄	—	4	4	no	—
373	C₄	C₂×#124×C₅₃	1	4	yes	—
374	C₄	C₂×#124×C₅₃	1	2	yes	—
375	C₄	C₂²×#41×C₅₃	1	2	yes	—
376	C₂	—	2	4	no	—
377	C₂	—	8	4	no	—
378	C₂	C₅₃×#3140	1	4	yes	direct product factor
379	C₂	C₂²×#124×C₅₃	1	1	yes	characteristic
380	C₂	C₂×C₅₃×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₂³×D₄×C₅₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂²×C₄²×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#533	C₂	semidirect
3. C₅₃×#3140	C₂	direct (N × H)
4. C₂×C₅₃×#489	C₂	semidirect
5. C₂×C₅₃×#488	C₂	semidirect
6. C₂×C₅₃×#419	C₂	semidirect
8. C₂×C₄×M₁₆×C₅₃	C₂	semidirect
13. C₅₃×#533	C₂²	semidirect
14. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
15. C₂×#125×C₅₃	C₂²	semidirect
26. C₅₃×#489	C₂²	semidirect
27. C₅₃×#488	C₂²	semidirect
28. C₅₃×#419	C₂²	semidirect
30. C₂×#103×C₅₃	C₂²	semidirect
32. C₄×M₁₆×C₅₃	C₂²	semidirect
33. C₂×#97×C₅₃	C₂²	semidirect
34. C₂×C₄×C₈×C₅₃	C₂²	semidirect
54. C₄⋊Q₈×C₅₃	C₂³	semidirect
56. #125×C₅₃	C₂³	semidirect
79. #103×C₅₃	C₂³	semidirect
81. #97×C₅₃	C₂³	semidirect
82. C₄×C₈×C₅₃	C₂³	semidirect
168. C₂×#3140	C₅₃	direct (N × H)
186. C₂×#533	C₂×C₅₃	semidirect
188. #3140	C₂×C₅₃	direct (N × H)
189. C₂×#489	C₂×C₅₃	semidirect
190. C₂×#488	C₂×C₅₃	semidirect
191. C₂×#419	C₂×C₅₃	semidirect
193. C₂×C₄×M₁₆	C₂×C₅₃	semidirect
196. C₂×C₅₃	#3140	direct (N × H)
203. #533	C₂²×C₅₃	semidirect
204. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
205. C₂×#125	C₂²×C₅₃	semidirect
216. #489	C₂²×C₅₃	semidirect
217. #488	C₂²×C₅₃	semidirect
218. #419	C₂²×C₅₃	semidirect
220. C₂×#103	C₂²×C₅₃	semidirect
222. C₄×M₁₆	C₂²×C₅₃	semidirect
223. C₂×#97	C₂²×C₅₃	semidirect
224. C₂×C₄×C₈	C₂²×C₅₃	semidirect
225. C₅₃	C₂×#3140	direct (N × H)
245. C₄⋊Q₈	C₂³×C₅₃	semidirect
247. #125	C₂³×C₅₃	semidirect
270. #103	C₂³×C₅₃	semidirect
272. #97	C₂³×C₅₃	semidirect
273. C₄×C₈	C₂³×C₅₃	semidirect
378. C₂	C₅₃×#3140	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×#533	2
C₂²×#124×C₅₃	2
C₅₃×#3140	2
C₂×C₅₃×#489	2
C₂×C₅₃×#488	2
C₂×C₅₃×#419	2
C₂×C₅₃×#418	2
C₂×C₄×M₁₆×C₅₃	2
C₂×#3140	53

Subgroups — C2×C53×#3140 #27268127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3140 #27268127