Subgroups — C₂×#20290835 #28320265

Order 13568.

858 conjugacy classes of subgroups.

The subgroup lattice has 448 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×#13133288	C₂	1	1	yes	maximal, characteristic
3	C₂×#16811586	C₂	1	1	yes	maximal, characteristic
4	#20290835	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×#13133288	—	2	1	no	—
14	C₂×#13133288	—	2	1	no	—
15	C₂×#13133288	—	2	2	no	—
16	C₂×#13133288	C₂²	1	4	yes	—
17	C₂×#13133287	—	2	2	no	—
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	1	yes	characteristic
36	C₂×#11719936	D₄	1	1	yes	characteristic
37	C₂×#11719936	C₂³	1	4	yes	—
38	D₅₃⋊M₁₆	—	2	1	no	—
39	D₅₃⋊M₁₆	—	2	1	no	—
40	D₅₃⋊M₁₆	D₄	1	2	yes	—
41	D₅₃⋊M₁₆	C₂³	1	2	yes	—
42	C₂×#11719940	—	2	1	no	—
43	C₂×D₅₃⋊C₈	—	2	1	no	—
44	C₂²×#88324	—	2	2	no	—
45	#13133296	—	2	1	no	—
46	#13133296	—	2	1	no	—
47	#13133296	Q₈	1	2	yes	—
48	#13133296	C₂³	1	2	yes	—
49	C₂×C₄⋊#6157	—	2	1	no	—
50	C₂×C₂²⋊#6157	Q₈	1	2	yes	—
51	C₂×C₄×#6157	—	2	1	no	—
52	#13133288	—	2	4	no	—
53	#13133288	—	2	4	no	—
54	#13133288	—	2	8	no	—
55	#13133287	—	2	8	no	—
56	#13133271	—	2	4	no	—
57	C₈×#6157	—	2	4	no	—
58	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
59	C₂×#11719917	C₂×C₄	1	2	yes	—
60	C₂×#11719912	—	2	2	no	—
61	M₁₆×D₅₃	—	2	2	no	—
62	M₁₆×D₅₃	—	2	2	no	—
63	M₁₆×D₅₃	C₂×C₄	1	4	yes	—
64	M₁₆×D₅₃	C₂³	1	4	yes	—
65	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₅₃	—	2	2	no	—
67	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
68	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
69	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
70	C₂×C₈×D₅₃	D₄	1	2	yes	—
71	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
72	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
73	C₂×C₈×D₅₃	Q₈	1	2	yes	—
74	C₂×C₈×D₅₃	C₂³	1	2	yes	—
75	#13133153	C₂×C₄	1	4	yes	complemented
76	#13133152	C₂×C₄	1	8	yes	complemented
77	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
78	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
79	#108×C₅₃	C₂×C₄	1	4	yes	complemented
80	C₂³×D₅₃	C₂×Q₈	1	1	yes	characteristic
81	C₂²×#6157	—	2	2	no	—
82	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×Dic₅₃	#41	1	1	yes	characteristic
84	C₂×C₄×D₅₃	C₂²×C₄	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×D₄	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	C₂×Q₈	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	#41	1	1	yes	characteristic
95	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
96	C₂²⋊#6157	—	2	2	no	—
97	C₂²⋊#6157	C₂×Q₈	1	4	yes	—
98	#11719940	—	2	2	no	—
99	#11719940	—	2	2	no	—
100	C₂×#88324	—	2	1	no	—
101	C₂×#88324	—	2	1	no	—
102	C₂×#88324	—	2	4	no	—
103	C₂×#88324	—	4	2	no	—
104	C₂×#88324	—	4	2	no	—
105	C₄⋊#6157	—	2	2	no	—
106	C₄⋊#6157	—	2	2	no	—
107	C₄×#6157	—	2	2	no	—
108	C₄×#6157	—	2	2	no	—
109	#11719936	—	2	1	no	—
110	#11719936	—	2	1	no	—
111	#11719936	—	2	4	no	—
112	#11719936	—	2	4	no	—
113	#11719936	—	4	2	no	—
114	#11719936	—	4	2	no	—
115	#11719936	C₂×D₄	1	2	yes	—
116	#11719936	C₂×D₄	1	2	yes	—
117	D₅₃⋊C₈	—	2	2	no	—
118	D₅₃⋊C₈	—	2	2	no	—
119	M₁₆×C₅₃	—	2	2	no	—
120	M₁₆×C₅₃	C₂²×C₄	1	4	yes	—
121	C₂×C₈×C₅₃	—	2	2	no	—
122	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₈×C₅₃	C₄⋊C₄	1	2	yes	—
125	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
126	#11719917	—	2	2	no	—
127	#11719917	C₂²×C₄	1	4	yes	—
128	C₂×#88322	—	2	2	no	—
129	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
130	C₂×#88322	C₄⋊C₄	1	1	yes	characteristic
131	C₂×#88322	C₄⋊C₄	1	2	yes	—
132	C₂×#88322	C₂²×C₄	1	2	yes	—
133	#11719912	—	2	4	no	—
134	#11719912	—	2	4	no	—
135	C₈×D₅₃	—	2	4	no	—
136	C₈×D₅₃	—	2	4	no	—
137	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
138	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
139	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
140	C₈×D₅₃	C₄⋊C₄	1	2	yes	—
141	C₈×D₅₃	C₂×D₄	1	2	yes	—
142	C₈×D₅₃	C₂×D₄	1	2	yes	—
143	C₈×D₅₃	C₂×Q₈	1	2	yes	—
144	C₈×D₅₃	C₂×Q₈	1	2	yes	—
145	C₂³×C₅₃	C₄×Q₈	1	1	yes	characteristic
146	C₂²×D₅₃	—	4	2	no	—
147	C₂²×D₅₃	C₄×Q₈	1	1	yes	characteristic
148	C₂²×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
149	C₂²×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂²×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
151	C₂²×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
152	C₂²×D₅₃	C₂²×Q₈	1	1	yes	characteristic
153	C₂×#6157	—	2	4	no	—
154	C₂×#6157	—	4	4	no	—
155	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₄×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×Dic₅₃	C₄×Q₈	1	1	yes	characteristic
162	C₂×Dic₅₃	#121	1	1	yes	characteristic
163	C₂×Dic₅₃	#121	1	1	yes	characteristic
164	C₂×Dic₅₃	#125	1	1	yes	characteristic
165	C₂×Dic₅₃	#125	1	1	yes	characteristic
166	C₂×Dic₅₃	C₂×#41	1	1	yes	characteristic
167	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
170	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
171	C₄×D₅₃	#121	1	1	yes	characteristic
172	C₄×D₅₃	#121	1	1	yes	characteristic
173	C₄×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
174	C₄×D₅₃	C₂²⋊Q₈	1	1	yes	characteristic
175	C₄×D₅₃	#125	1	1	yes	characteristic
176	C₄×D₅₃	#125	1	1	yes	characteristic
177	C₄×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
178	C₄×D₅₃	C₄⋊Q₈	1	1	yes	characteristic
179	C₄×D₅₃	C₂²×D₄	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	#88324	—	2	2	no	—
184	#88324	—	2	2	no	—
185	#88324	—	4	4	no	—
186	C₈×C₅₃	—	2	4	no	—
187	C₈×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
188	C₈×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
189	#88322	—	2	4	no	—
190	#88322	C₂×C₄⋊C₄	1	2	yes	—
191	#88322	C₂×C₄⋊C₄	1	2	yes	—
192	C₂×#1953	—	53	1	no	maximal, Sylow
193	C₂²×C₅₃	—	2	2	no	—
194	C₂²×C₅₃	#389	1	1	yes	characteristic
195	C₂²×C₅₃	#389	1	1	yes	characteristic
196	C₂²×C₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
197	C₂×D₅₃	—	2	2	no	—
198	C₂×D₅₃	—	2	2	no	—
199	C₂×D₅₃	—	4	1	no	—
200	C₂×D₅₃	—	4	1	no	—
201	C₂×D₅₃	—	4	1	no	—
202	C₂×D₅₃	—	4	1	no	—
203	C₂×D₅₃	#389	1	1	yes	characteristic
204	C₂×D₅₃	#389	1	1	yes	characteristic
205	C₂×D₅₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
206	C₂×D₅₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
207	#6157	—	4	4	no	—
208	C₄×C₅₃	#389	1	1	yes	characteristic
209	C₄×C₅₃	#389	1	1	yes	characteristic
210	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
211	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
212	Dic₅₃	#389	1	1	yes	characteristic
213	Dic₅₃	#389	1	1	yes	characteristic
214	Dic₅₃	C₂×#121	1	1	yes	characteristic
215	Dic₅₃	C₂×#125	1	1	yes	characteristic
216	C₂×#430	—	53	2	no	—
217	C₂²×#108	—	53	1	no	—
218	C₂²×#108	—	53	1	no	—
219	C₂×#405	—	53	1	no	—
220	#1953	—	53	8	no	—
221	C₂×#344	—	53	2	no	—
222	C₂×C₅₃	—	2	1	no	—
223	C₂×C₅₃	—	2	1	no	—
224	C₂×C₅₃	#1953	1	2	yes	complemented
225	C₂×C₅₃	C₂×#389	1	1	yes	characteristic
226	D₅₃	—	2	1	no	—
227	D₅₃	—	2	1	no	—
228	D₅₃	—	2	1	no	—
229	D₅₃	—	2	1	no	—
230	C₂²×M₁₆	—	53	1	no	—
231	C₂²×M₁₆	—	53	2	no	—
232	C₂²×M₁₆	—	53	2	no	—
233	C₂³×C₈	—	53	1	no	—
234	C₂×#117	—	53	1	no	—
235	#430	—	53	8	no	—
236	#430	—	106	4	no	—
237	C₂×#108	—	53	2	no	—
238	C₂×#108	—	53	1	no	—
239	C₂×#108	—	53	4	no	—
240	C₂×#108	—	53	4	no	—
241	C₂×#108	—	53	4	no	—
242	C₂×#108	—	106	1	no	—
243	C₂×#108	—	106	1	no	—
244	C₂×#108	—	106	2	no	—
245	C₂×#108	—	106	2	no	—
246	C₂×#108	—	106	2	no	—
247	C₂×#108	#6157	1	1	yes	characteristic, complemented
248	#405	—	53	4	no	—
249	#405	—	106	2	no	—
250	C₂×#97	—	106	1	no	—
251	C₂×C₄×C₈	—	106	1	no	—
252	#344	—	53	8	no	—
253	C₅₃	C₂×#1953	1	1	yes	characteristic, complemented, Sylow
254	C₂³×C₄	—	53	1	no	—
255	C₂×M₁₆	—	53	2	no	—
256	C₂×M₁₆	—	53	1	no	—
257	C₂×M₁₆	—	53	1	no	—
258	C₂×M₁₆	—	53	2	no	—
259	C₂×M₁₆	—	53	2	no	—
260	C₂×M₁₆	—	53	4	no	—
261	C₂×M₁₆	—	53	4	no	—
262	C₂×M₁₆	—	53	4	no	—
263	C₂×M₁₆	—	106	2	no	—
264	C₂×M₁₆	—	106	2	no	—
265	C₂×M₁₆	—	106	2	no	—
266	C₂×M₁₆	—	106	1	no	—
267	C₂×M₁₆	—	106	1	no	—
268	C₂×M₁₆	—	106	1	no	—
269	C₂×M₁₆	—	106	2	no	—
270	C₂×M₁₆	—	106	2	no	—
271	C₂×M₁₆	—	106	2	no	—
272	C₂×M₁₆	—	106	2	no	—
273	C₂×M₁₆	—	106	2	no	—
274	C₂×M₁₆	C₂×#6157	1	2	yes	—
275	C₂²×C₈	—	53	1	no	—
276	C₂²×C₈	—	53	1	no	—
277	C₂²×C₈	—	53	1	no	—
278	C₂²×C₈	—	53	2	no	—
279	C₂²×C₈	—	53	2	no	—
280	C₂²×C₈	—	53	1	no	—
281	C₂²×C₈	—	53	1	no	—
282	C₂²×C₈	—	53	2	no	—
283	C₂²×C₈	—	53	2	no	—
284	C₂²×C₈	—	106	2	no	—
285	C₂²×C₈	—	106	1	no	—
286	C₂²×C₈	—	106	2	no	—
287	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
288	#117	—	53	2	no	—
289	#117	—	53	2	no	—
290	#117	—	106	1	no	—
291	#117	—	106	1	no	—
292	C₂×C₄⋊C₄	—	106	1	no	—
293	C₂×C₂²⋊C₄	—	53	2	no	—
294	C₂×C₄²	—	106	1	no	—
295	#108	—	53	8	no	—
296	#108	—	53	4	no	—
297	#108	—	106	4	no	—
298	#108	—	106	4	no	—
299	#108	—	106	8	no	—
300	#108	—	106	8	no	—
301	#108	C₂×#6157	1	4	yes	complemented
302	#97	—	106	4	no	—
303	C₄×C₈	—	106	4	no	—
304	C₂⁴	—	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	—	53	1	no	—
318	C₂²×C₄	—	106	2	no	—
319	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
320	M₁₆	—	2	2	no	—
321	M₁₆	—	53	2	no	—
322	M₁₆	—	53	2	no	—
323	M₁₆	—	53	4	no	—
324	M₁₆	—	106	4	no	—
325	M₁₆	—	106	4	no	—
326	M₁₆	—	106	1	no	—
327	M₁₆	—	106	1	no	—
328	M₁₆	—	106	2	no	—
329	M₁₆	—	106	2	no	—
330	M₁₆	—	106	2	no	—
331	M₁₆	—	106	4	no	—
332	M₁₆	—	106	4	no	—
333	M₁₆	—	212	2	no	—
334	M₁₆	—	212	2	no	—
335	M₁₆	C₂²×#6157	1	4	yes	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	53	2	no	—
338	C₂×C₈	—	53	1	no	—
339	C₂×C₈	—	53	1	no	—
340	C₂×C₈	—	53	2	no	—
341	C₂×C₈	—	53	2	no	—
342	C₂×C₈	—	53	2	no	—
343	C₂×C₈	—	53	2	no	—
344	C₂×C₈	—	53	2	no	—
345	C₂×C₈	—	53	2	no	—
346	C₂×C₈	—	53	2	no	—
347	C₂×C₈	—	53	2	no	—
348	C₂×C₈	—	53	2	no	—
349	C₂×C₈	—	106	4	no	—
350	C₂×C₈	—	106	4	no	—
351	C₂×C₈	—	106	1	no	—
352	C₂×C₈	—	106	1	no	—
353	C₂×C₈	—	106	2	no	—
354	C₂×C₈	—	106	2	no	—
355	C₂×C₈	—	106	2	no	—
356	C₂×C₈	—	106	4	no	—
357	C₂×C₈	—	212	2	no	—
358	C₂×C₈	—	212	2	no	—
359	C₂×C₈	C₄⋊#6157	1	2	yes	—
360	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
361	C₂×C₈	C₄⋊#6157	1	1	yes	characteristic
362	C₂×C₈	C₂²×#6157	1	2	yes	—
363	C₄⋊C₄	—	106	2	no	—
364	C₄⋊C₄	—	106	2	no	—
365	C₂²⋊C₄	—	53	4	no	—
366	C₂²⋊C₄	—	106	2	no	—
367	C₄²	—	106	2	no	—
368	C₄²	—	106	2	no	—
369	C₂³	—	53	1	no	—
370	C₂³	—	53	1	no	—
371	C₂³	—	53	1	no	—
372	C₂³	—	53	1	no	—
373	C₂³	—	53	1	no	—
374	C₂³	—	53	1	no	—
375	C₂³	—	212	2	no	—
376	C₂³	Q₈×#6157	1	1	yes	characteristic
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	4	no	—
400	C₂×C₄	—	212	4	no	—
401	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
402	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
403	C₂×C₄	D₄×#6157	1	1	yes	characteristic
404	C₂×C₄	D₄×#6157	1	1	yes	characteristic
405	C₂×C₄	Q₈×#6157	1	1	yes	characteristic
406	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
407	C₈	—	2	4	no	—
408	C₈	—	53	2	no	—
409	C₈	—	53	2	no	—
410	C₈	—	106	2	no	—
411	C₈	—	106	2	no	—
412	C₈	—	106	4	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	#16811574	1	1	yes	characteristic
428	C₂²	#16811574	1	1	yes	characteristic
429	C₂²	C₂×Q₈×#6157	1	1	yes	characteristic
430	C₄	—	53	1	no	—
431	C₄	—	53	1	no	—
432	C₄	—	53	1	no	—
433	C₄	—	53	1	no	—
434	C₄	—	212	4	no	—
435	C₄	#16811574	1	1	yes	characteristic
436	C₄	#16811574	1	1	yes	characteristic
437	C₄	C₂²×C₄⋊#6157	1	1	yes	characteristic
438	C₄	C₂×D₄×#6157	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	106	1	no	—
442	C₂	—	106	1	no	—
443	C₂	—	106	1	no	—
444	C₂	—	106	1	no	—
445	C₂	#20290835	1	2	yes	direct product factor
446	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. #20290835	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
75. #13133153	C₂×C₄	semidirect
76. #13133152	C₂×C₄	semidirect
79. #108×C₅₃	C₂×C₄	semidirect
224. C₂×C₅₃	#1953	semidirect
247. C₂×#108	#6157	semidirect
253. C₅₃	C₂×#1953	semidirect
301. #108	C₂×#6157	semidirect
445. C₂	#20290835	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×#13133288	2
C₂×#16811586	2
#20290835	2
C₂×#16811506	2
C₂×#108×D₅₃	2
C₂×#1953	53

Subgroups — C2×#20290835 #28320265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20290835 #28320265