Subgroups — #18078869

Order 4864.

478 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	#14572293	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563734	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562151	C₂	1	1	yes	maximal, characteristic
4	#14561995	C₂	1	1	yes	maximal, characteristic
5	#14561512	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#482	C₂	1	1	yes	maximal, characteristic
8	#11926605	—	2	2	no	—
9	#11926601	—	2	1	no	—
10	#11926597	—	2	1	no	—
11	#11926571	—	2	1	no	—
12	#11926508	C₂²	1	1	yes	characteristic
13	#11926508	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	#11926500	—	2	1	no	—
16	C₄×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
17	#11926303	—	2	1	no	—
18	#11926303	—	2	1	no	—
19	#11926278	—	2	2	no	—
20	#11926268	—	2	1	no	—
21	#11926268	—	2	1	no	—
22	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₁₉×#482	—	2	1	no	—
25	C₁₉×#482	—	2	1	no	—
26	C₁₉×#482	—	2	1	no	—
27	C₁₉×#482	—	2	1	no	—
28	C₂×C₁₉×#107	C₄	1	1	yes	characteristic, complemented
29	C₂×C₁₉×#106	C₄	1	1	yes	characteristic, complemented
30	C₂×C₁₉×#102	C₄	1	1	yes	characteristic, complemented
31	C₂×C₁₉×#102	C₄	1	1	yes	characteristic, complemented
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₁₉×#121	—	2	1	no	—
39	C₁₉×#121	—	2	1	no	—
40	C₁₉×#121	—	2	1	no	—
41	C₁₉×#121	—	2	1	no	—
42	C₁₉×#117	—	2	1	no	—
43	C₁₉×#117	—	2	1	no	—
44	C₁₉×#117	D₄	1	1	yes	characteristic
45	C₁₉×#117	D₄	1	1	yes	characteristic
46	C₁₉×#117	D₄	1	1	yes	characteristic
47	C₁₉×#117	D₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	—	2	1	no	—
54	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
55	C₂×C₄×Dic₁₉	—	2	1	no	—
56	C₂×#64520	—	2	1	no	—
57	C₂×#64520	—	2	1	no	—
58	C₂²×C₁₉⋊C₈	—	2	1	no	—
59	C₁₉×#107	—	2	1	no	—
60	C₁₉×#107	—	2	1	no	—
61	C₁₉×#106	—	2	1	no	—
62	C₁₉×#106	—	2	1	no	—
63	C₁₉×#102	—	2	1	no	—
64	C₁₉×#102	—	2	1	no	—
65	C₁₉×#102	—	2	1	no	—
66	C₁₉×#102	—	2	1	no	—
67	C₁₉×C₂²⋊C₈	—	2	1	no	—
68	C₁₉×C₂²⋊C₈	—	2	1	no	—
69	C₁₉⋊#95	—	2	1	no	—
70	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
73	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
74	C₂²⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
75	C₂²⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
76	C₂²⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
77	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
78	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
79	#10597260	—	2	2	no	—
80	C₄×C₁₉⋊C₈	—	2	2	no	—
81	C₂⁴×C₁₉	—	2	1	no	—
82	C₂⁴×C₁₉	#41	1	1	yes	characteristic
83	C₂×D₄×C₁₉	—	2	1	no	—
84	C₂×D₄×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	8	2	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
101	C₂²×Dic₁₉	—	4	1	no	—
102	C₂×C₈×C₁₉	—	2	1	no	—
103	C₂×C₈×C₁₉	—	2	1	no	—
104	C₂×C₈×C₁₉	—	4	1	no	—
105	C₂×C₈×C₁₉	—	4	1	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
111	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂²⋊C₄×C₁₉	—	2	1	no	—
117	C₂²⋊C₄×C₁₉	—	2	1	no	—
118	C₂²⋊C₄×C₁₉	—	4	1	no	—
119	C₂²⋊C₄×C₁₉	—	4	1	no	—
120	C₄²×C₁₉	—	2	1	no	—
121	C₄²×C₁₉	—	2	1	no	—
122	C₄²×C₁₉	—	2	1	no	—
123	C₄²×C₁₉	—	2	1	no	—
124	C₂²⋊Dic₁₉	—	2	2	no	—
125	C₂²⋊Dic₁₉	—	4	1	no	—
126	C₄×Dic₁₉	—	4	1	no	—
127	C₄×Dic₁₉	—	4	1	no	—
128	#64520	—	4	1	no	—
129	#64520	—	4	1	no	—
130	#64520	—	4	1	no	—
131	#64520	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	2	1	no	—
133	C₂×C₁₉⋊C₈	—	2	2	no	—
134	C₂×C₁₉⋊C₈	—	2	1	no	—
135	C₂×C₁₉⋊C₈	—	4	1	no	—
136	C₂×C₁₉⋊C₈	—	4	1	no	—
137	C₂×C₁₉⋊C₈	—	4	1	no	—
138	#9242	—	19	1	no	maximal, Sylow
139	C₂³×C₁₉	—	2	1	no	—
140	C₂³×C₁₉	—	2	1	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	8	1	no	—
147	C₂³×C₁₉	—	8	1	no	—
148	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
149	C₂³×C₁₉	#121	1	1	yes	characteristic
150	C₂³×C₁₉	#123	1	1	yes	characteristic
151	D₄×C₁₉	—	4	1	no	—
152	D₄×C₁₉	—	4	1	no	—
153	D₄×C₁₉	—	8	1	no	—
154	D₄×C₁₉	—	8	2	no	—
155	D₄×C₁₉	—	8	2	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	8	1	no	—
173	C₂×C₄×C₁₉	—	8	1	no	—
174	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
178	C₂×Dic₁₉	—	4	2	no	—
179	C₂×Dic₁₉	—	8	1	no	—
180	C₂×Dic₁₉	—	8	1	no	—
181	C₈×C₁₉	—	4	1	no	—
182	C₈×C₁₉	—	4	1	no	—
183	C₁₉⋊C₈	—	4	1	no	—
184	C₁₉⋊C₈	—	4	1	no	—
185	C₁₉⋊C₈	—	4	2	no	—
186	C₁₉⋊C₈	—	8	1	no	—
187	C₂×#482	D₁₉	1	1	yes	characteristic
188	#2924	—	19	1	no	—
189	#1826	—	19	1	no	—
190	#1507	—	19	1	no	—
191	#1471	—	19	1	no	—
192	#1293	—	19	1	no	—
193	#1282	—	19	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	8	1	no	—
203	C₂²×C₁₉	—	8	1	no	—
204	C₂²×C₁₉	—	8	1	no	—
205	C₂²×C₁₉	—	8	1	no	—
206	C₂²×C₁₉	—	8	1	no	—
207	C₂²×C₁₉	—	16	1	no	—
208	C₂²×C₁₉	—	16	1	no	—
209	C₂²×C₁₉	#386	1	1	yes	characteristic
210	C₂²×C₁₉	#443	1	1	yes	characteristic
211	C₂²×C₁₉	#444	1	1	yes	characteristic
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	2	1	no	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	4	1	no	—
216	C₄×C₁₉	—	4	1	no	—
217	C₄×C₁₉	—	4	1	no	—
218	C₄×C₁₉	—	4	1	no	—
219	C₄×C₁₉	—	8	1	no	—
220	C₄×C₁₉	#410	1	1	yes	characteristic
221	C₄×C₁₉	#410	1	1	yes	characteristic
222	Dic₁₉	—	8	2	no	—
223	C₂×#121	C₂×D₁₉	1	1	yes	characteristic
224	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
225	#482	—	2	1	no	—
226	#482	—	2	1	no	—
227	#482	—	2	1	no	—
228	#482	—	2	1	no	—
229	#433	—	38	2	no	—
230	#432	—	38	1	no	—
231	#431	—	38	1	no	—
232	C₂×#107	Dic₁₉	1	1	yes	characteristic, complemented
233	C₂×#106	Dic₁₉	1	1	yes	characteristic, complemented
234	#424	—	38	1	no	—
235	C₂×#102	Dic₁₉	1	1	yes	characteristic, complemented
236	C₂×#102	Dic₁₉	1	1	yes	characteristic, complemented
237	#407	—	19	1	no	—
238	#407	—	19	1	no	—
239	C₂×C₂²⋊C₈	—	19	1	no	—
240	C₂×C₂²⋊C₈	C₂×D₁₉	1	1	yes	characteristic
241	#405	—	38	1	no	—
242	C₄×C₂²⋊C₄	—	19	1	no	—
243	#339	—	38	1	no	—
244	#339	—	38	1	no	—
245	#327	—	38	2	no	—
246	#323	—	38	1	no	—
247	#323	—	38	1	no	—
248	C₂×C₁₉	—	2	1	no	—
249	C₂×C₁₉	—	2	1	no	—
250	C₂×C₁₉	—	4	1	no	—
251	C₂×C₁₉	—	4	1	no	—
252	C₂×C₁₉	—	16	1	no	—
253	C₂×C₁₉	#1876	1	1	yes	characteristic
254	C₂×C₁₉	#1899	1	1	yes	characteristic
255	C₂×C₁₉	#1903	1	1	yes	characteristic
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
258	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
259	C₂×M₁₆	—	38	1	no	—
260	C₂×M₁₆	—	38	1	no	—
261	C₂²×C₈	—	38	1	no	—
262	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
263	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
264	#121	—	2	1	no	—
265	#121	—	2	1	no	—
266	#121	—	2	1	no	—
267	#121	—	2	1	no	—
268	#117	—	2	1	no	—
269	#117	—	2	1	no	—
270	#117	C₂²⋊D₁₉	1	1	yes	characteristic
271	#117	C₂²⋊D₁₉	1	1	yes	characteristic
272	#117	C₂²⋊D₁₉	1	1	yes	characteristic
273	#117	C₂²⋊D₁₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₂²⋊C₄	—	38	1	no	—
280	C₂×C₄²	—	2	1	no	—
281	C₂×C₄²	—	38	1	no	—
282	#107	—	2	1	no	—
283	#107	—	2	1	no	—
284	#106	—	2	1	no	—
285	#106	—	2	1	no	—
286	C₄⋊C₈	—	38	2	no	—
287	C₄⋊C₈	—	38	2	no	—
288	#102	—	2	1	no	—
289	#102	—	2	1	no	—
290	#102	—	2	1	no	—
291	#102	—	2	1	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	—	2	1	no	—
294	C₂²⋊C₈	—	19	1	no	—
295	C₂²⋊C₈	—	19	1	no	—
296	C₂²⋊C₈	—	19	2	no	—
297	C₂²⋊C₈	—	38	1	no	—
298	C₂²⋊C₈	—	38	1	no	—
299	C₂²⋊C₈	—	38	1	no	—
300	C₂²⋊C₈	—	38	1	no	—
301	#97	—	38	2	no	—
302	C₄×C₈	—	38	2	no	—
303	#95	—	38	1	no	—
304	C₁₉	#9242	1	1	yes	characteristic, complemented, Sylow
305	C₂⁴	—	2	1	no	—
306	C₂⁴	#64543	1	1	yes	characteristic
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	76	1	no	—
320	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
321	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
322	C₂²×C₄	#64543	1	1	yes	characteristic
323	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
326	M₁₆	—	76	1	no	—
327	M₁₆	—	76	1	no	—
328	M₁₆	—	76	1	no	—
329	M₁₆	—	76	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	38	1	no	—
335	C₂×C₈	—	38	2	no	—
336	C₂×C₈	—	38	1	no	—
337	C₂×C₈	—	76	1	no	—
338	C₂×C₈	—	76	1	no	—
339	C₂×C₈	—	76	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
345	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
346	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
347	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
348	C₂²⋊C₄	—	2	1	no	—
349	C₂²⋊C₄	—	2	1	no	—
350	C₂²⋊C₄	—	2	1	no	—
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	4	1	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	38	2	no	—
355	C₂²⋊C₄	—	76	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	76	1	no	—
361	C₄²	—	76	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	8	1	no	—
370	C₂³	—	8	1	no	—
371	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
372	C₂³	#10597381	1	1	yes	characteristic
373	C₂³	#10597385	1	1	yes	characteristic
374	D₄	—	4	1	no	—
375	D₄	—	4	1	no	—
376	D₄	—	8	1	no	—
377	D₄	—	8	2	no	—
378	D₄	—	8	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	8	1	no	—
396	C₂×C₄	—	8	1	no	—
397	C₂×C₄	—	76	2	no	—
398	C₂×C₄	—	152	1	no	—
399	C₂×C₄	—	152	1	no	—
400	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
401	C₂×C₄	#10597383	1	1	yes	characteristic
402	C₂×C₄	#10597385	1	1	yes	characteristic
403	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
404	C₈	—	4	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	76	1	no	—
407	C₈	—	76	1	no	—
408	C₈	—	76	2	no	—
409	C₈	—	152	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	16	1	no	—
424	C₂²	—	16	1	no	—
425	C₂²	#11926424	1	1	yes	characteristic
426	C₂²	#11926661	1	1	yes	characteristic
427	C₂²	#11926666	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	8	1	no	—
436	C₄	—	152	2	no	—
437	C₄	#11926518	1	1	yes	characteristic
438	C₄	#11926518	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	4	1	no	—
442	C₂	—	4	1	no	—
443	C₂	—	16	1	no	—
444	C₂	#14563964	1	1	yes	characteristic
445	C₂	#14564094	1	1	yes	characteristic
446	C₂	#14564117	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#482	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂×C₁₉×#121	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#482	D₁₉
hypocenter	C₁₉	#9242
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#482

Complements

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

N	H ≅ G/N	type
1. #14572293	C₂	semidirect
2. #14563734	C₂	semidirect
5. #14561512	C₂	semidirect
6. #14561482	C₂	semidirect
28. C₂×C₁₉×#107	C₄	semidirect
29. C₂×C₁₉×#106	C₄	semidirect
30. C₂×C₁₉×#102	C₄	semidirect
31. C₂×C₁₉×#102	C₄	semidirect
232. C₂×#107	Dic₁₉	semidirect
233. C₂×#106	Dic₁₉	semidirect
235. C₂×#102	Dic₁₉	semidirect
236. C₂×#102	Dic₁₉	semidirect
304. C₁₉	#9242	semidirect

Maximal subgroups

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

subgroup	index
#14572293	2
#14563734	2
#14562151	2
#14561995	2
#14561512	2
#14561482	2
C₂×C₁₉×#482	2
#9242	19