Subgroups — C₂×#20290834 #28320263

Order 13568.

858 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811638	C₂	1	2	yes	maximal
2	C₂²×#13133287	C₂	1	1	yes	maximal, characteristic
3	C₂×#16811586	C₂	1	1	yes	maximal, characteristic
4	#20290834	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16811506	C₂	1	2	yes	maximal
6	C₂×#108×D₅₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×#11719936	C₂²	1	2	yes	—
8	C₂×D₅₃⋊M₁₆	C₂²	1	1	yes	characteristic
9	C₂×#13133296	C₂²	1	1	yes	characteristic
10	#16811638	—	2	4	no	—
11	#16811638	C₂²	1	8	yes	—
12	C₂×#13133288	—	2	2	no	—
13	C₂×#13133287	—	2	2	no	—
14	C₂×#13133287	—	2	1	no	—
15	C₂×#13133287	—	2	1	no	—
16	C₂×#13133287	—	2	2	no	—
17	C₂×#13133287	C₂²	1	4	yes	—
18	#16811586	—	2	2	no	—
19	#16811586	C₂²	1	4	yes	—
20	C₂×#13133271	—	2	1	no	—
21	C₂×C₈×#6157	—	2	1	no	—
22	#16811506	C₂²	1	8	yes	—
23	C₂×M₁₆×D₅₃	C₂²	1	2	yes	—
24	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
25	C₂×#13133153	C₄	1	1	yes	characteristic, complemented
26	C₂×#13133152	C₄	1	2	yes	complemented
27	#108×D₅₃	C₄	1	4	yes	complemented
28	#108×D₅₃	C₂²	1	4	yes	—
29	C₂×#108×C₅₃	C₄	1	1	yes	characteristic, complemented
30	C₂×#11719936	—	2	2	no	—
31	C₂×#11719936	—	2	2	no	—
32	C₂×#11719936	—	2	2	no	—
33	C₂×#11719936	—	2	2	no	—
34	C₂×#11719936	—	2	2	no	—
35	C₂×#11719936	D₄	1	2	yes	—
36	C₂×#11719936	C₂³	1	4	yes	—
37	D₅₃⋊M₁₆	—	2	1	no	—
38	D₅₃⋊M₁₆	—	2	1	no	—
39	D₅₃⋊M₁₆	D₄	1	2	yes	—
40	D₅₃⋊M₁₆	C₂³	1	2	yes	—
41	C₂×#11719940	—	2	1	no	—
42	C₂×D₅₃⋊C₈	—	2	1	no	—
43	C₂²×#88324	—	2	2	no	—
44	#13133296	—	2	1	no	—
45	#13133296	—	2	1	no	—
46	#13133296	Q₈	1	2	yes	—
47	#13133296	C₂³	1	2	yes	—
48	C₂×C₄⋊#6157	—	2	1	no	—
49	C₂×C₂²⋊#6157	Q₈	1	2	yes	—
50	C₂×C₄×#6157	—	2	1	no	—
51	#13133288	—	2	8	no	—
52	#13133287	—	2	4	no	—
53	#13133287	—	2	4	no	—
54	#13133287	—	2	8	no	—
55	#13133271	—	2	4	no	—
56	C₈×#6157	—	2	4	no	—
57	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
58	C₂×#11719917	C₂×C₄	1	2	yes	—
59	C₂×#11719912	—	2	2	no	—
60	M₁₆×D₅₃	—	2	2	no	—
61	M₁₆×D₅₃	—	2	2	no	—
62	M₁₆×D₅₃	C₂×C₄	1	4	yes	—
63	M₁₆×D₅₃	C₂³	1	4	yes	—
64	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₅₃	—	2	2	no	—
66	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
67	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
68	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
69	C₂×C₈×D₅₃	D₄	1	2	yes	—
70	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
71	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
72	C₂×C₈×D₅₃	Q₈	1	2	yes	—
73	C₂×C₈×D₅₃	C₂³	1	2	yes	—
74	#13133153	C₂×C₄	1	4	yes	complemented
75	#13133152	C₂×C₄	1	8	yes	complemented
76	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
77	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
78	#108×C₅₃	C₂×C₄	1	4	yes	complemented
79	C₂³×D₅₃	C₂×Q₈	1	1	yes	characteristic
80	C₂²×#6157	—	2	2	no	—
81	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
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×D₄	1	1	yes	characteristic
87	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
89	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
90	C₂×C₄×D₅₃	C₂×Q₈	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	2	no	—
96	C₂²⋊#6157	C₂×Q₈	1	4	yes	—
97	#11719940	—	2	2	no	—
98	#11719940	—	2	2	no	—
99	C₂×#88324	—	2	2	no	—
100	C₂×#88324	—	2	4	no	—
101	C₂×#88324	—	4	2	no	—
102	C₂×#88324	—	4	2	no	—
103	C₄⋊#6157	—	2	2	no	—
104	C₄⋊#6157	—	2	2	no	—
105	C₄×#6157	—	2	2	no	—
106	C₄×#6157	—	2	2	no	—
107	#11719936	—	2	2	no	—
108	#11719936	—	2	4	no	—
109	#11719936	—	2	4	no	—
110	#11719936	—	4	2	no	—
111	#11719936	—	4	2	no	—
112	#11719936	C₂×D₄	1	4	yes	—
113	D₅₃⋊C₈	—	2	2	no	—
114	D₅₃⋊C₈	—	2	2	no	—
115	M₁₆×C₅₃	—	2	2	no	—
116	M₁₆×C₅₃	C₂²×C₄	1	4	yes	—
117	C₂×C₈×C₅₃	—	2	2	no	—
118	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₈×C₅₃	C₄⋊C₄	1	2	yes	—
121	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
122	#11719917	—	2	2	no	—
123	#11719917	C₂²×C₄	1	4	yes	—
124	C₂×#88322	—	2	2	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	#11719912	—	2	4	no	—
130	#11719912	—	2	4	no	—
131	C₈×D₅₃	—	2	4	no	—
132	C₈×D₅₃	—	2	4	no	—
133	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
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	C₂×D₄	1	2	yes	—
138	C₈×D₅₃	C₂×D₄	1	2	yes	—
139	C₈×D₅₃	C₂×Q₈	1	2	yes	—
140	C₈×D₅₃	C₂×Q₈	1	2	yes	—
141	C₂³×C₅₃	C₄×Q₈	1	1	yes	characteristic
142	C₂²×D₅₃	—	4	2	no	—
143	C₂²×D₅₃	C₄×Q₈	1	1	yes	characteristic
144	C₂²×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
145	C₂²×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
146	C₂²×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
147	C₂²×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
148	C₂²×D₅₃	C₂²×Q₈	1	1	yes	characteristic
149	C₂×#6157	—	2	4	no	—
150	C₂×#6157	—	4	4	no	—
151	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
157	C₂×Dic₅₃	C₄×Q₈	1	1	yes	characteristic
158	C₂×Dic₅₃	#121	1	1	yes	characteristic
159	C₂×Dic₅₃	#121	1	1	yes	characteristic
160	C₂×Dic₅₃	#125	1	1	yes	characteristic
161	C₂×Dic₅₃	#125	1	1	yes	characteristic
162	C₂×Dic₅₃	C₂×#41	1	1	yes	characteristic
163	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
166	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
167	C₄×D₅₃	#121	1	1	yes	characteristic
168	C₄×D₅₃	#121	1	1	yes	characteristic
169	C₄×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
170	C₄×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
171	C₄×D₅₃	#125	1	1	yes	characteristic
172	C₄×D₅₃	#125	1	1	yes	characteristic
173	C₄×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
174	C₄×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
175	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
176	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
177	C₄×D₅₃	C₂²×Q₈	1	1	yes	characteristic
178	C₄×D₅₃	C₂×#41	1	1	yes	characteristic
179	#88324	—	2	4	no	—
180	#88324	—	4	4	no	—
181	C₈×C₅₃	—	2	4	no	—
182	C₈×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
183	C₈×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
184	#88322	—	2	4	no	—
185	#88322	C₂×C₄⋊C₄	1	2	yes	—
186	#88322	C₂×C₄⋊C₄	1	2	yes	—
187	C₂×#1953	—	53	1	no	maximal, Sylow
188	C₂²×C₅₃	—	2	2	no	—
189	C₂²×C₅₃	#389	1	1	yes	characteristic
190	C₂²×C₅₃	#389	1	1	yes	characteristic
191	C₂²×C₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
192	C₂×D₅₃	—	2	2	no	—
193	C₂×D₅₃	—	2	2	no	—
194	C₂×D₅₃	—	4	1	no	—
195	C₂×D₅₃	—	4	1	no	—
196	C₂×D₅₃	—	4	1	no	—
197	C₂×D₅₃	—	4	1	no	—
198	C₂×D₅₃	#389	1	1	yes	characteristic
199	C₂×D₅₃	#389	1	1	yes	characteristic
200	C₂×D₅₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
201	C₂×D₅₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
202	#6157	—	4	4	no	—
203	C₄×C₅₃	#389	1	1	yes	characteristic
204	C₄×C₅₃	#389	1	1	yes	characteristic
205	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
206	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
207	Dic₅₃	#389	1	1	yes	characteristic
208	Dic₅₃	#389	1	1	yes	characteristic
209	Dic₅₃	C₂×#121	1	1	yes	characteristic
210	Dic₅₃	C₂×#125	1	1	yes	characteristic
211	C₂×#430	—	53	2	no	—
212	C₂²×#108	—	53	1	no	—
213	C₂²×#108	—	53	1	no	—
214	C₂×#405	—	53	1	no	—
215	#1953	—	53	8	no	—
216	C₂×#344	—	53	2	no	—
217	C₂×C₅₃	—	2	1	no	—
218	C₂×C₅₃	—	2	1	no	—
219	C₂×C₅₃	#1953	1	2	yes	complemented
220	C₂×C₅₃	C₂×#389	1	1	yes	characteristic
221	D₅₃	—	2	1	no	—
222	D₅₃	—	2	1	no	—
223	D₅₃	—	2	1	no	—
224	D₅₃	—	2	1	no	—
225	C₂²×M₁₆	—	53	1	no	—
226	C₂²×M₁₆	—	53	2	no	—
227	C₂²×M₁₆	—	53	2	no	—
228	C₂³×C₈	—	53	1	no	—
229	C₂×#117	—	53	1	no	—
230	#430	—	53	8	no	—
231	#430	—	106	4	no	—
232	C₂×#108	—	53	2	no	—
233	C₂×#108	—	53	1	no	—
234	C₂×#108	—	53	4	no	—
235	C₂×#108	—	53	4	no	—
236	C₂×#108	—	53	4	no	—
237	C₂×#108	—	106	1	no	—
238	C₂×#108	—	106	1	no	—
239	C₂×#108	—	106	2	no	—
240	C₂×#108	—	106	2	no	—
241	C₂×#108	—	106	2	no	—
242	C₂×#108	#6157	1	1	yes	characteristic, complemented
243	#405	—	53	4	no	—
244	#405	—	106	2	no	—
245	C₂×#97	—	106	1	no	—
246	C₂×C₄×C₈	—	106	1	no	—
247	#344	—	53	8	no	—
248	C₅₃	C₂×#1953	1	1	yes	characteristic, complemented, Sylow
249	C₂³×C₄	—	53	1	no	—
250	C₂×M₁₆	—	53	2	no	—
251	C₂×M₁₆	—	53	2	no	—
252	C₂×M₁₆	—	53	2	no	—
253	C₂×M₁₆	—	53	2	no	—
254	C₂×M₁₆	—	53	4	no	—
255	C₂×M₁₆	—	53	4	no	—
256	C₂×M₁₆	—	53	4	no	—
257	C₂×M₁₆	—	106	2	no	—
258	C₂×M₁₆	—	106	2	no	—
259	C₂×M₁₆	—	106	2	no	—
260	C₂×M₁₆	—	106	1	no	—
261	C₂×M₁₆	—	106	1	no	—
262	C₂×M₁₆	—	106	1	no	—
263	C₂×M₁₆	—	106	2	no	—
264	C₂×M₁₆	—	106	2	no	—
265	C₂×M₁₆	—	106	2	no	—
266	C₂×M₁₆	—	106	2	no	—
267	C₂×M₁₆	—	106	2	no	—
268	C₂×M₁₆	C₂×#6157	1	2	yes	—
269	C₂²×C₈	—	53	1	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	1	no	—
275	C₂²×C₈	—	53	1	no	—
276	C₂²×C₈	—	53	2	no	—
277	C₂²×C₈	—	53	2	no	—
278	C₂²×C₈	—	106	2	no	—
279	C₂²×C₈	—	106	1	no	—
280	C₂²×C₈	—	106	2	no	—
281	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
282	#117	—	53	2	no	—
283	#117	—	53	2	no	—
284	#117	—	106	1	no	—
285	#117	—	106	1	no	—
286	C₂×C₄⋊C₄	—	106	1	no	—
287	C₂×C₂²⋊C₄	—	53	2	no	—
288	C₂×C₄²	—	106	1	no	—
289	#108	—	53	8	no	—
290	#108	—	53	4	no	—
291	#108	—	106	4	no	—
292	#108	—	106	4	no	—
293	#108	—	106	8	no	—
294	#108	—	106	8	no	—
295	#108	C₂×#6157	1	4	yes	complemented
296	#97	—	106	4	no	—
297	C₄×C₈	—	106	4	no	—
298	C₂⁴	—	53	1	no	—
299	C₂²×C₄	—	53	1	no	—
300	C₂²×C₄	—	53	1	no	—
301	C₂²×C₄	—	53	1	no	—
302	C₂²×C₄	—	53	1	no	—
303	C₂²×C₄	—	53	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	—	106	2	no	—
313	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
314	M₁₆	—	2	2	no	—
315	M₁₆	—	53	4	no	—
316	M₁₆	—	53	4	no	—
317	M₁₆	—	106	4	no	—
318	M₁₆	—	106	4	no	—
319	M₁₆	—	106	2	no	—
320	M₁₆	—	106	2	no	—
321	M₁₆	—	106	2	no	—
322	M₁₆	—	106	2	no	—
323	M₁₆	—	106	4	no	—
324	M₁₆	—	106	4	no	—
325	M₁₆	—	212	2	no	—
326	M₁₆	—	212	2	no	—
327	M₁₆	C₂²×#6157	1	4	yes	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	53	2	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	—	106	4	no	—
342	C₂×C₈	—	106	4	no	—
343	C₂×C₈	—	106	2	no	—
344	C₂×C₈	—	106	2	no	—
345	C₂×C₈	—	106	2	no	—
346	C₂×C₈	—	106	2	no	—
347	C₂×C₈	—	106	4	no	—
348	C₂×C₈	—	212	2	no	—
349	C₂×C₈	—	212	2	no	—
350	C₂×C₈	C₄⋊#6157	1	2	yes	—
351	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
352	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
353	C₂×C₈	C₂²×#6157	1	2	yes	—
354	C₄⋊C₄	—	106	2	no	—
355	C₄⋊C₄	—	106	2	no	—
356	C₂²⋊C₄	—	53	4	no	—
357	C₂²⋊C₄	—	106	2	no	—
358	C₄²	—	106	2	no	—
359	C₄²	—	106	2	no	—
360	C₂³	—	53	1	no	—
361	C₂³	—	53	1	no	—
362	C₂³	—	53	1	no	—
363	C₂³	—	53	1	no	—
364	C₂³	—	53	1	no	—
365	C₂³	—	53	1	no	—
366	C₂³	—	212	2	no	—
367	C₂³	Q₈×#6157	1	1	yes	characteristic
368	C₂×C₄	—	53	1	no	—
369	C₂×C₄	—	53	1	no	—
370	C₂×C₄	—	53	1	no	—
371	C₂×C₄	—	53	1	no	—
372	C₂×C₄	—	53	1	no	—
373	C₂×C₄	—	53	1	no	—
374	C₂×C₄	—	53	1	no	—
375	C₂×C₄	—	53	1	no	—
376	C₂×C₄	—	53	1	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	—	106	4	no	—
391	C₂×C₄	—	212	4	no	—
392	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
393	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
394	C₂×C₄	D₄×#6157	1	1	yes	characteristic
395	C₂×C₄	D₄×#6157	1	1	yes	characteristic
396	C₂×C₄	Q₈×#6157	1	1	yes	characteristic
397	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
398	C₈	—	2	4	no	—
399	C₈	—	53	2	no	—
400	C₈	—	53	2	no	—
401	C₈	—	106	4	no	—
402	C₈	—	106	4	no	—
403	C₈	—	212	4	no	—
404	C₈	C₂×C₄⋊#6157	1	2	yes	—
405	C₈	C₂×C₄⋊#6157	1	2	yes	—
406	C₂²	—	2	2	no	—
407	C₂²	—	53	1	no	—
408	C₂²	—	53	1	no	—
409	C₂²	—	53	1	no	—
410	C₂²	—	53	1	no	—
411	C₂²	—	106	2	no	—
412	C₂²	—	106	2	no	—
413	C₂²	—	212	1	no	—
414	C₂²	—	212	1	no	—
415	C₂²	—	212	1	no	—
416	C₂²	—	212	1	no	—
417	C₂²	#16811574	1	1	yes	characteristic
418	C₂²	#16811574	1	1	yes	characteristic
419	C₂²	C₂×Q₈×#6157	1	1	yes	characteristic
420	C₄	—	53	1	no	—
421	C₄	—	53	1	no	—
422	C₄	—	53	1	no	—
423	C₄	—	53	1	no	—
424	C₄	—	212	4	no	—
425	C₄	#16811574	1	1	yes	characteristic
426	C₄	#16811574	1	1	yes	characteristic
427	C₄	C₂²×C₄⋊#6157	1	1	yes	characteristic
428	C₄	C₂×D₄×#6157	1	1	yes	characteristic
429	C₂	—	2	1	no	—
430	C₂	—	2	1	no	—
431	C₂	—	106	1	no	—
432	C₂	—	106	1	no	—
433	C₂	—	106	1	no	—
434	C₂	—	106	1	no	—
435	C₂	#20290834	1	2	yes	direct product factor
436	C₂	C₂×#16811574	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16811574
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₂×#108×C₅₃	C₄
socle	C₂²×C₅₃	#389
prime radical	C₂³×D₅₃	C₂×Q₈
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	C₂×#108	#6157
hypocenter	C₅₃	C₂×#1953
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
4. #20290834	C₂	direct (N × H)
25. C₂×#13133153	C₄	semidirect
26. C₂×#13133152	C₄	semidirect
27. #108×D₅₃	C₄	semidirect
29. C₂×#108×C₅₃	C₄	semidirect
74. #13133153	C₂×C₄	semidirect
75. #13133152	C₂×C₄	semidirect
78. #108×C₅₃	C₂×C₄	semidirect
219. C₂×C₅₃	#1953	semidirect
242. C₂×#108	#6157	semidirect
248. C₅₃	C₂×#1953	semidirect
295. #108	C₂×#6157	semidirect
435. C₂	#20290834	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×#16811638	2
C₂²×#13133287	2
C₂×#16811586	2
#20290834	2
C₂×#16811506	2
C₂×#108×D₅₃	2
C₂×#1953	53

Subgroups — C2×#20290834 #28320263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20290834 #28320263