Subgroups — C₂×#20290634 #28319336

Order 13568.

786 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₃⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#16811633	C₂	1	1	yes	maximal, characteristic
3	#20290634	C₂	1	8	yes	maximal, direct product factor
4	C₂×#16811505	C₂	1	2	yes	maximal
5	C₂×#16811490	C₂	1	2	yes	maximal
6	C₂×#16810577	C₂	1	1	yes	maximal, characteristic
7	C₂×D₅₃⋊M₁₆	C₂²	1	2	yes	—
8	C₂×#13133296	C₂²	1	2	yes	—
9	C₂×#13133288	—	2	1	no	—
10	D₅₃⋊#108	—	2	2	no	—
11	D₅₃⋊#108	C₂²	1	4	yes	—
12	C₂×#13133287	—	2	1	no	—
13	#16811633	—	2	2	no	—
14	#16811633	C₂²	1	4	yes	—
15	C₂×#13133286	—	2	1	no	—
16	C₂×#13133285	—	2	1	no	—
17	#16811505	C₂²	1	8	yes	—
18	#16811490	C₂²	1	8	yes	—
19	C₂²×#11719912	C₂²	1	1	yes	characteristic
20	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
21	C₂×#13133174	C₂²	1	1	yes	characteristic
22	#16810577	C₄	1	4	yes	complemented
23	#16810577	C₂²	1	4	yes	—
24	C₂×#13133128	C₄	1	1	yes	characteristic, complemented
25	C₂×#13133127	C₄	1	1	yes	characteristic, complemented
26	C₂×C₈×Dic₅₃	C₄	1	1	yes	characteristic, complemented
27	C₂×C₄×C₈×C₅₃	C₄	1	1	yes	characteristic, complemented
28	C₂×#11719936	—	2	2	no	—
29	D₅₃⋊M₁₆	—	2	2	no	—
30	D₅₃⋊M₁₆	—	2	2	no	—
31	D₅₃⋊M₁₆	—	2	2	no	—
32	D₅₃⋊M₁₆	C₂³	1	4	yes	—
33	C₂×#11719940	—	2	2	no	—
34	C₂×D₅₃⋊C₈	—	2	2	no	—
35	#13133296	—	2	2	no	—
36	#13133296	—	2	2	no	—
37	#13133296	—	2	2	no	—
38	#13133296	C₂³	1	4	yes	—
39	C₂×C₄⋊#6157	—	2	2	no	—
40	C₂×C₂²⋊#6157	—	2	2	no	—
41	C₂×C₄×#6157	—	2	2	no	—
42	#13133288	—	2	4	no	—
43	#13133287	—	2	4	no	—
44	#13133286	—	2	4	no	—
45	#13133285	—	2	4	no	—
46	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
47	C₂×#11719912	—	2	1	no	—
48	C₂×#11719912	—	2	1	no	—
49	C₂×#11719912	—	2	1	no	—
50	C₂×#11719912	—	2	1	no	—
51	C₂×#11719912	C₂×C₄	1	2	yes	—
52	C₂×#11719912	C₂³	1	2	yes	—
53	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
54	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
56	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
57	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
58	C₂×C₈×D₅₃	D₄	1	2	yes	—
59	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
60	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
61	C₂×C₈×D₅₃	Q₈	1	2	yes	—
62	C₂×C₈×D₅₃	C₂³	1	2	yes	—
63	#13133174	—	2	1	no	—
64	#13133174	—	2	1	no	—
65	#13133174	C₂×C₄	1	2	yes	—
66	#13133174	C₂³	1	2	yes	—
67	C₂×#11719919	—	2	1	no	—
68	C₂×#11719921	—	2	1	no	—
69	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
70	#13133128	C₂×C₄	1	4	yes	complemented
71	#13133127	C₂×C₄	1	4	yes	complemented
72	C₈×Dic₅₃	C₂×C₄	1	4	yes	complemented
73	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	complemented
77	C₂³×D₅₃	#41	1	1	yes	characteristic
78	C₂²×#6157	—	4	2	no	—
79	C₂²×C₄×C₅₃	—	2	1	no	—
80	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×Dic₅₃	—	2	1	no	—
82	C₂²×Dic₅₃	#41	1	1	yes	characteristic
83	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
84	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
87	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
88	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
89	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
90	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
91	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
92	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
93	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
94	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
95	C₂²⋊#6157	—	2	4	no	—
96	C₂²⋊#6157	—	4	2	no	—
97	#11719940	—	2	4	no	—
98	#11719940	—	4	2	no	—
99	C₂×#88324	—	4	2	no	—
100	C₄⋊#6157	—	2	4	no	—
101	C₄⋊#6157	—	4	2	no	—
102	C₄×#6157	—	2	4	no	—
103	C₄×#6157	—	4	2	no	—
104	#11719936	—	2	4	no	—
105	#11719936	—	4	2	no	—
106	D₅₃⋊C₈	—	2	4	no	—
107	D₅₃⋊C₈	—	4	2	no	—
108	C₂×C₈×C₅₃	—	2	1	no	—
109	C₂×C₈×C₅₃	—	2	1	no	—
110	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₈×C₅₃	C₄⋊C₄	1	2	yes	—
113	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
115	C₄²×C₅₃	—	2	1	no	—
116	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
117	#11719921	—	2	2	no	—
118	#11719921	—	2	2	no	—
119	#11719919	—	2	2	no	—
120	#11719919	—	2	2	no	—
121	C₄×Dic₅₃	—	2	1	no	—
122	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
123	C₂×#88322	—	2	1	no	—
124	C₂×#88322	—	2	1	no	—
125	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
126	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
127	C₂×#88322	C₄⋊C₄	1	2	yes	—
128	C₂×#88322	C₂²×C₄	1	2	yes	—
129	C₂×#88322	C₂²×C₄	1	2	yes	—
130	#11719912	—	2	2	no	—
131	#11719912	—	2	2	no	—
132	#11719912	—	2	2	no	—
133	#11719912	—	2	2	no	—
134	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
135	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
136	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
137	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
138	C₈×D₅₃	C₂×D₄	1	2	yes	—
139	C₈×D₅₃	C₂×D₄	1	2	yes	—
140	C₈×D₅₃	C₂×Q₈	1	2	yes	—
141	C₈×D₅₃	C₂×Q₈	1	2	yes	—
142	C₂³×C₅₃	#117	1	1	yes	characteristic
143	C₂²×D₅₃	—	4	2	no	—
144	C₂²×D₅₃	#117	1	1	yes	characteristic
145	C₂²×D₅₃	#124	1	1	yes	characteristic
146	C₂²×D₅₃	#124	1	1	yes	characteristic
147	C₂²×D₅₃	#125	1	1	yes	characteristic
148	C₂²×D₅₃	#125	1	1	yes	characteristic
149	C₂²×D₅₃	C₂×#41	1	1	yes	characteristic
150	C₂×#6157	—	4	4	no	—
151	C₂×#6157	—	8	4	no	—
152	C₂×C₄×C₅₃	—	2	2	no	—
153	C₂×C₄×C₅₃	—	4	2	no	—
154	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
157	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
158	C₂×C₄×C₅₃	#117	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×Dic₅₃	—	2	2	no	—
161	C₂×Dic₅₃	—	4	2	no	—
162	C₂×Dic₅₃	#117	1	1	yes	characteristic
163	C₂×Dic₅₃	#124	1	1	yes	characteristic
164	C₂×Dic₅₃	#124	1	1	yes	characteristic
165	C₂×Dic₅₃	#125	1	1	yes	characteristic
166	C₂×Dic₅₃	#125	1	1	yes	characteristic
167	C₂×Dic₅₃	C₂×#41	1	1	yes	characteristic
168	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₄×D₅₃	#117	1	1	yes	characteristic
171	C₄×D₅₃	#117	1	1	yes	characteristic
172	C₄×D₅₃	#124	1	1	yes	characteristic
173	C₄×D₅₃	#124	1	1	yes	characteristic
174	C₄×D₅₃	#124	1	1	yes	characteristic
175	C₄×D₅₃	#124	1	1	yes	characteristic
176	C₄×D₅₃	#125	1	1	yes	characteristic
177	C₄×D₅₃	#125	1	1	yes	characteristic
178	C₄×D₅₃	#125	1	1	yes	characteristic
179	C₄×D₅₃	#125	1	1	yes	characteristic
180	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
181	C₄×D₅₃	C₂²×Q₈	1	1	yes	characteristic
182	C₄×D₅₃	C₂×#41	1	1	yes	characteristic
183	C₄×D₅₃	C₂×#41	1	1	yes	characteristic
184	#88324	—	4	4	no	—
185	C₈×C₅₃	—	2	2	no	—
186	C₈×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
187	C₈×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
188	#88322	—	2	2	no	—
189	#88322	C₂×C₄⋊C₄	1	2	yes	—
190	#88322	C₂×C₄⋊C₄	1	2	yes	—
191	C₂×#1833	—	53	1	no	maximal, Sylow
192	C₂²×C₅₃	—	2	2	no	—
193	C₂²×C₅₃	#382	1	1	yes	characteristic
194	C₂²×C₅₃	#382	1	1	yes	characteristic
195	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
196	C₂×D₅₃	—	2	2	no	—
197	C₂×D₅₃	—	2	2	no	—
198	C₂×D₅₃	—	4	1	no	—
199	C₂×D₅₃	—	4	1	no	—
200	C₂×D₅₃	—	4	1	no	—
201	C₂×D₅₃	—	4	1	no	—
202	C₂×D₅₃	#382	1	1	yes	characteristic
203	C₂×D₅₃	#382	1	1	yes	characteristic
204	C₂×D₅₃	C₂×#124	1	1	yes	characteristic
205	C₂×D₅₃	C₂×#125	1	1	yes	characteristic
206	#6157	—	8	4	no	—
207	C₄×C₅₃	—	4	2	no	—
208	C₄×C₅₃	#382	1	1	yes	characteristic
209	C₄×C₅₃	#382	1	1	yes	characteristic
210	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
211	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
212	Dic₅₃	—	4	2	no	—
213	Dic₅₃	#382	1	1	yes	characteristic
214	Dic₅₃	#382	1	1	yes	characteristic
215	Dic₅₃	C₂×#124	1	1	yes	characteristic
216	Dic₅₃	C₂×#125	1	1	yes	characteristic
217	C₂²×#108	—	53	1	no	—
218	C₂×#427	—	53	1	no	—
219	C₂×#405	—	53	1	no	—
220	#1833	—	53	8	no	—
221	C₂×#344	—	53	2	no	—
222	C₂×H(3,ℤ/4)	—	53	2	no	—
223	C₂×C₅₃	—	2	1	no	—
224	C₂×C₅₃	—	2	1	no	—
225	C₂×C₅₃	#1833	1	2	yes	complemented
226	C₂×C₅₃	C₂×#382	1	1	yes	characteristic
227	D₅₃	—	2	1	no	—
228	D₅₃	—	2	1	no	—
229	D₅₃	—	2	1	no	—
230	D₅₃	—	2	1	no	—
231	C₂²×M₁₆	—	53	1	no	—
232	C₂²×M₁₆	—	53	2	no	—
233	C₂³×C₈	—	53	1	no	—
234	C₂×#117	—	53	1	no	—
235	C₂×#117	—	53	2	no	—
236	C₂×#108	—	53	4	no	—
237	C₂×#108	—	106	1	no	—
238	C₂×#108	—	106	2	no	—
239	C₂×#108	—	106	1	no	—
240	#427	—	53	4	no	—
241	#427	—	106	2	no	—
242	C₂×#107	—	106	1	no	—
243	C₂×#106	—	106	1	no	—
244	#405	—	53	4	no	—
245	#405	—	53	4	no	—
246	C₂×#97	—	53	1	no	—
247	C₂×#97	—	53	1	no	—
248	C₂×C₄×C₈	—	53	1	no	—
249	C₂×C₄×C₈	#6157	1	1	yes	characteristic, complemented
250	#344	—	53	8	no	—
251	H(3,ℤ/4)	—	53	8	no	—
252	C₅₃	C₂×#1833	1	1	yes	characteristic, complemented, Sylow
253	C₂³×C₄	—	53	1	no	—
254	C₂×M₁₆	—	53	2	no	—
255	C₂×M₁₆	—	53	2	no	—
256	C₂×M₁₆	—	53	4	no	—
257	C₂×M₁₆	—	106	1	no	—
258	C₂×M₁₆	—	106	1	no	—
259	C₂×M₁₆	—	106	1	no	—
260	C₂×M₁₆	—	106	1	no	—
261	C₂×M₁₆	—	106	2	no	—
262	C₂×M₁₆	—	106	2	no	—
263	C₂×M₁₆	—	106	2	no	—
264	C₂×M₁₆	—	106	2	no	—
265	C₂×M₁₆	—	106	2	no	—
266	C₂²×C₈	—	53	1	no	—
267	C₂²×C₈	—	53	1	no	—
268	C₂²×C₈	—	53	1	no	—
269	C₂²×C₈	—	53	2	no	—
270	C₂²×C₈	—	53	1	no	—
271	C₂²×C₈	—	53	1	no	—
272	C₂²×C₈	—	53	2	no	—
273	C₂²×C₈	—	53	2	no	—
274	C₂²×C₈	—	53	2	no	—
275	C₂²×C₈	—	53	1	no	—
276	C₂²×C₈	—	106	2	no	—
277	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
278	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
279	#117	—	53	2	no	—
280	#117	—	53	2	no	—
281	#117	—	53	4	no	—
282	#117	—	106	1	no	—
283	#117	—	106	1	no	—
284	#117	—	106	2	no	—
285	#117	—	106	2	no	—
286	#117	—	106	2	no	—
287	C₂×C₄⋊C₄	—	106	1	no	—
288	C₂×C₄⋊C₄	—	106	2	no	—
289	C₂×C₂²⋊C₄	—	106	1	no	—
290	C₂×C₂²⋊C₄	—	106	2	no	—
291	C₂×C₄²	—	53	1	no	—
292	C₂×C₄²	—	106	2	no	—
293	C₂×C₄²	C₂×#6157	1	1	yes	characteristic
294	#108	—	106	4	no	—
295	#108	—	106	4	no	—
296	#107	—	106	4	no	—
297	#106	—	106	4	no	—
298	#97	—	53	4	no	—
299	#97	—	53	4	no	—
300	C₄×C₈	—	53	4	no	—
301	C₄×C₈	C₂×#6157	1	4	yes	complemented
302	C₂⁴	—	53	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	53	1	no	—
305	C₂²×C₄	—	53	1	no	—
306	C₂²×C₄	—	53	1	no	—
307	C₂²×C₄	—	53	1	no	—
308	C₂²×C₄	—	53	1	no	—
309	C₂²×C₄	—	53	1	no	—
310	C₂²×C₄	—	53	1	no	—
311	C₂²×C₄	—	53	1	no	—
312	C₂²×C₄	—	53	1	no	—
313	C₂²×C₄	—	53	1	no	—
314	C₂²×C₄	—	53	1	no	—
315	C₂²×C₄	—	53	1	no	—
316	C₂²×C₄	—	53	1	no	—
317	C₂²×C₄	—	106	1	no	—
318	C₂²×C₄	—	212	2	no	—
319	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
320	M₁₆	—	106	2	no	—
321	M₁₆	—	106	2	no	—
322	M₁₆	—	106	2	no	—
323	M₁₆	—	106	2	no	—
324	M₁₆	—	106	4	no	—
325	M₁₆	—	106	4	no	—
326	M₁₆	—	212	2	no	—
327	M₁₆	—	212	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	53	1	no	—
331	C₂×C₈	—	53	1	no	—
332	C₂×C₈	—	53	2	no	—
333	C₂×C₈	—	53	2	no	—
334	C₂×C₈	—	53	2	no	—
335	C₂×C₈	—	53	2	no	—
336	C₂×C₈	—	53	2	no	—
337	C₂×C₈	—	53	2	no	—
338	C₂×C₈	—	53	2	no	—
339	C₂×C₈	—	53	2	no	—
340	C₂×C₈	—	53	2	no	—
341	C₂×C₈	—	53	2	no	—
342	C₂×C₈	—	53	2	no	—
343	C₂×C₈	—	106	1	no	—
344	C₂×C₈	—	106	1	no	—
345	C₂×C₈	—	106	4	no	—
346	C₂×C₈	—	212	2	no	—
347	C₂×C₈	—	212	2	no	—
348	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
349	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
350	C₂×C₈	C₄⋊#6157	1	2	yes	—
351	C₂×C₈	C₂²×#6157	1	2	yes	—
352	C₂×C₈	C₂²×#6157	1	2	yes	—
353	C₄⋊C₄	—	106	2	no	—
354	C₄⋊C₄	—	106	2	no	—
355	C₄⋊C₄	—	106	4	no	—
356	C₄⋊C₄	—	212	2	no	—
357	C₂²⋊C₄	—	106	2	no	—
358	C₂²⋊C₄	—	106	2	no	—
359	C₂²⋊C₄	—	106	4	no	—
360	C₂²⋊C₄	—	212	2	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	53	2	no	—
363	C₄²	—	106	4	no	—
364	C₄²	—	106	1	no	—
365	C₄²	—	212	2	no	—
366	C₄²	C₂²×#6157	1	2	yes	—
367	C₂³	—	53	1	no	—
368	C₂³	—	53	1	no	—
369	C₂³	—	53	1	no	—
370	C₂³	—	53	1	no	—
371	C₂³	—	53	1	no	—
372	C₂³	—	53	1	no	—
373	C₂³	—	212	2	no	—
374	C₂³	#13133296	1	1	yes	characteristic
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	53	1	no	—
378	C₂×C₄	—	53	1	no	—
379	C₂×C₄	—	53	1	no	—
380	C₂×C₄	—	53	1	no	—
381	C₂×C₄	—	53	1	no	—
382	C₂×C₄	—	53	1	no	—
383	C₂×C₄	—	53	1	no	—
384	C₂×C₄	—	53	1	no	—
385	C₂×C₄	—	53	1	no	—
386	C₂×C₄	—	53	1	no	—
387	C₂×C₄	—	53	1	no	—
388	C₂×C₄	—	53	1	no	—
389	C₂×C₄	—	53	1	no	—
390	C₂×C₄	—	53	1	no	—
391	C₂×C₄	—	53	1	no	—
392	C₂×C₄	—	53	1	no	—
393	C₂×C₄	—	53	1	no	—
394	C₂×C₄	—	53	1	no	—
395	C₂×C₄	—	53	1	no	—
396	C₂×C₄	—	53	1	no	—
397	C₂×C₄	—	53	1	no	—
398	C₂×C₄	—	53	1	no	—
399	C₂×C₄	—	106	2	no	—
400	C₂×C₄	—	424	4	no	—
401	C₂×C₄	—	212	4	no	—
402	C₂×C₄	—	212	2	no	—
403	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
404	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
405	C₂×C₄	#13133296	1	1	yes	characteristic
406	C₂×C₄	#13133296	1	1	yes	characteristic
407	C₂×C₄	#13133296	1	1	yes	characteristic
408	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	53	2	no	—
411	C₈	—	53	2	no	—
412	C₈	—	106	2	no	—
413	C₈	—	212	4	no	—
414	C₈	C₂×C₄⋊#6157	1	2	yes	—
415	C₈	C₂×C₄⋊#6157	1	2	yes	—
416	C₂²	—	2	2	no	—
417	C₂²	—	53	1	no	—
418	C₂²	—	53	1	no	—
419	C₂²	—	53	1	no	—
420	C₂²	—	53	1	no	—
421	C₂²	—	106	2	no	—
422	C₂²	—	106	2	no	—
423	C₂²	—	212	1	no	—
424	C₂²	—	212	1	no	—
425	C₂²	—	212	1	no	—
426	C₂²	—	212	1	no	—
427	C₂²	#16811567	1	1	yes	characteristic
428	C₂²	#16811567	1	1	yes	characteristic
429	C₂²	C₂×#13133296	1	1	yes	characteristic
430	C₄	—	4	2	no	—
431	C₄	—	53	1	no	—
432	C₄	—	53	1	no	—
433	C₄	—	53	1	no	—
434	C₄	—	53	1	no	—
435	C₄	—	424	4	no	—
436	C₄	—	212	2	no	—
437	C₄	#16811567	1	1	yes	characteristic
438	C₄	#16811567	1	1	yes	characteristic
439	C₄	C₂²×C₄⋊#6157	1	1	yes	characteristic
440	C₄	C₂×#13133296	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	106	1	no	—
444	C₂	—	106	1	no	—
445	C₂	—	106	1	no	—
446	C₂	—	106	1	no	—
447	C₂	#20290634	1	2	yes	direct product factor
448	C₂	C₂×#16811567	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13133296
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₂×C₄×C₈×C₅₃	C₄
socle	C₂²×C₅₃	#382
prime radical	C₂³×D₅₃	#41
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	C₂×C₄×C₈	#6157
hypocenter	C₅₃	C₂×#1833
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #20290634	C₂	direct (N × H)
22. #16810577	C₄	semidirect
24. C₂×#13133128	C₄	semidirect
25. C₂×#13133127	C₄	semidirect
26. C₂×C₈×Dic₅₃	C₄	semidirect
27. C₂×C₄×C₈×C₅₃	C₄	semidirect
70. #13133128	C₂×C₄	semidirect
71. #13133127	C₂×C₄	semidirect
72. C₈×Dic₅₃	C₂×C₄	semidirect
76. C₄×C₈×C₅₃	C₂×C₄	semidirect
225. C₂×C₅₃	#1833	semidirect
249. C₂×C₄×C₈	#6157	semidirect
252. C₅₃	C₂×#1833	semidirect
301. C₄×C₈	C₂×#6157	semidirect
447. C₂	#20290634	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×D₅₃⋊#108	2
C₂×#16811633	2
#20290634	2
C₂×#16811505	2
C₂×#16811490	2
C₂×#16810577	2
C₂×#1833	53

Subgroups — C2×#20290634 #28319336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20290634 #28319336