Subgroups — C₁₉×#10239 #18016198

Order 4864.

610 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3226	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3036	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2547	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1502	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1478	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1303	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
9	C₁₉×#532	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#124	—	2	1	no	—
12	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#500	—	2	1	no	—
14	C₁₉×#486	—	2	1	no	—
15	C₁₉×#480	—	2	2	no	—
16	C₁₉×#474	—	2	2	no	—
17	C₁₉×#463	—	2	2	no	—
18	C₁₉×#461	—	2	1	no	—
19	C₁₉×#459	—	2	1	no	—
20	C₁₉×#431	C₂²	1	1	yes	characteristic
21	C₁₉×#431	C₂²	1	1	yes	characteristic
22	C₁₉×#423	C₂²	1	1	yes	characteristic
23	C₁₉×#417	—	2	1	no	—
24	C₁₉×#397	—	2	2	no	—
25	C₁₉×#391	—	2	1	no	—
26	C₁₉×#380	—	2	2	no	—
27	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#332	—	2	2	no	—
29	C₁₉×#327	—	2	2	no	—
30	C₁₉×D₄⋊C₈	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	—	2	1	no	—
35	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
36	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
37	C₂×SD₁₆×C₁₉	—	2	2	no	—
38	C₂×D₈×C₁₉	—	2	2	no	—
39	C₂×M₁₆×C₁₉	—	2	1	no	—
40	C₁₉×C₄⋊Q₈	—	2	1	no	—
41	C₁₉×C₄⋊Q₈	—	2	1	no	—
42	C₁₉×C₄⋊Q₈	—	2	1	no	—
43	C₁₉×C₄⋊Q₈	—	2	1	no	—
44	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
45	C₁₉×#127	D₄	1	1	yes	characteristic
46	C₁₉×#124	—	2	1	no	—
47	C₁₉×#124	—	4	2	no	—
48	C₁₉×#124	—	4	2	no	—
49	C₁₉×#121	—	2	1	no	—
50	C₁₉×#121	—	2	1	no	—
51	C₄×D₄×C₁₉	—	2	1	no	—
52	C₄×D₄×C₁₉	—	2	1	no	—
53	C₄×D₄×C₁₉	—	2	1	no	—
54	C₄×D₄×C₁₉	—	2	1	no	—
55	C₄×D₄×C₁₉	—	2	1	no	—
56	C₄×D₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄²×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
65	C₁₉×#107	—	2	4	no	—
66	C₁₉×C₄⋊C₈	—	2	1	no	—
67	C₁₉×C₄⋊C₈	—	2	1	no	—
68	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
69	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
70	C₁₉×#103	—	2	2	no	—
71	C₁₉×#102	—	2	2	no	—
72	C₁₉×#102	—	2	4	no	—
73	C₁₉×C₂²⋊C₈	—	2	1	no	—
74	C₁₉×C₂²⋊C₈	—	2	1	no	—
75	C₄×C₈×C₁₉	—	2	1	no	—
76	C₄×C₈×C₁₉	—	2	1	no	—
77	C₁₉×#95	—	2	4	no	—
78	C₁₉×#95	D₄	1	2	yes	—
79	C₂⁴×C₁₉	—	2	1	no	—
80	#41×C₁₉	—	4	1	no	—
81	#41×C₁₉	—	4	1	no	—
82	#41×C₁₉	—	4	1	no	—
83	#41×C₁₉	—	4	1	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	4	1	no	—
86	C₂×Q₈×C₁₉	—	4	1	no	—
87	C₂×Q₈×C₁₉	—	4	1	no	—
88	C₂×Q₈×C₁₉	—	4	1	no	—
89	C₂×Q₈×C₁₉	—	4	1	no	—
90	C₂×Q₈×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	2	1	no	—
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	—	2	1	no	—
96	C₂×D₄×C₁₉	—	2	1	no	—
97	C₂×D₄×C₁₉	—	2	1	no	—
98	C₂×D₄×C₁₉	—	2	1	no	—
99	C₂×D₄×C₁₉	—	4	1	no	—
100	C₂×D₄×C₁₉	D₈	1	2	yes	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	4	4	no	—
105	C₂²×C₄×C₁₉	—	4	1	no	—
106	C₂²×C₄×C₁₉	—	4	1	no	—
107	C₂²×C₄×C₁₉	—	4	1	no	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	SD₁₆×C₁₉	—	4	4	no	—
112	D₈×C₁₉	—	4	4	no	—
113	M₁₆×C₁₉	—	4	1	no	—
114	M₁₆×C₁₉	—	4	1	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	4	1	no	—
118	C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₄⋊C₄×C₁₉	—	4	2	no	—
125	C₄⋊C₄×C₁₉	—	4	1	no	—
126	C₄⋊C₄×C₁₉	—	4	1	no	—
127	C₂²⋊C₄×C₁₉	—	4	8	no	—
128	C₂²⋊C₄×C₁₉	—	4	1	no	—
129	C₂²⋊C₄×C₁₉	—	4	1	no	—
130	C₂²⋊C₄×C₁₉	—	4	1	no	—
131	C₂²⋊C₄×C₁₉	—	4	1	no	—
132	C₄²×C₁₉	—	4	1	no	—
133	C₄²×C₁₉	—	4	1	no	—
134	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₉	#41	1	1	yes	characteristic
138	#10239	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₁₉	—	2	2	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	#120	1	1	yes	characteristic
146	Q₈×C₁₉	—	4	1	no	—
147	Q₈×C₁₉	—	4	1	no	—
148	Q₈×C₁₉	—	8	1	no	—
149	Q₈×C₁₉	—	8	1	no	—
150	Q₈×C₁₉	—	8	1	no	—
151	Q₈×C₁₉	—	8	1	no	—
152	D₄×C₁₉	—	2	2	no	—
153	D₄×C₁₉	—	2	2	no	—
154	D₄×C₁₉	—	4	1	no	—
155	D₄×C₁₉	—	4	1	no	—
156	D₄×C₁₉	—	4	1	no	—
157	D₄×C₁₉	—	4	2	no	—
158	D₄×C₁₉	—	4	1	no	—
159	D₄×C₁₉	—	8	1	no	—
160	D₄×C₁₉	—	8	1	no	—
161	D₄×C₁₉	—	8	1	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	8	2	no	—
174	C₂×C₄×C₁₉	—	8	2	no	—
175	C₂×C₄×C₁₉	—	8	1	no	—
176	C₂×C₄×C₁₉	—	8	1	no	—
177	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
185	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₈×C₁₉	—	4	2	no	—
188	C₈×C₁₉	—	4	2	no	—
189	C₈×C₁₉	—	8	1	no	—
190	#3226	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#3036	C₂×C₁₉	1	1	yes	characteristic
192	#2547	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#1546	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#1502	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#1478	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#1303	C₂×C₁₉	1	1	yes	characteristic, complemented
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	4	4	no	—
200	C₂²×C₁₉	—	4	2	no	—
201	C₂²×C₁₉	—	8	2	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	#392	1	1	yes	characteristic
208	C₂²×C₁₉	#447	1	1	yes	characteristic
209	C₂²×C₁₉	#449	1	1	yes	characteristic
210	C₄×C₁₉	—	2	1	no	—
211	C₄×C₁₉	—	2	1	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	8	2	no	—
214	C₄×C₁₉	—	8	2	no	—
215	C₄×C₁₉	—	8	1	no	—
216	C₄×C₁₉	—	8	1	no	—
217	C₄×C₁₉	#447	1	1	yes	characteristic
218	C₄×C₁₉	#449	1	1	yes	characteristic
219	C₄×C₁₉	#454	1	2	yes	—
220	C₄×C₁₉	#466	1	1	yes	characteristic
221	C₄×C₁₉	#469	1	1	yes	characteristic
222	C₂×AGL(1,ℤ/8)	—	2	1	no	—
223	#532	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×#124	—	2	1	no	—
226	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
227	#500	—	2	1	no	—
228	#486	—	2	1	no	—
229	#480	—	2	2	no	—
230	#474	—	2	2	no	—
231	#463	—	2	2	no	—
232	#461	—	2	1	no	—
233	#459	—	2	1	no	—
234	#431	C₂²×C₁₉	1	1	yes	characteristic
235	#431	C₂²×C₁₉	1	1	yes	characteristic
236	#423	C₂²×C₁₉	1	1	yes	characteristic
237	#417	—	2	1	no	—
238	#397	—	2	2	no	—
239	#391	—	2	1	no	—
240	#380	—	2	2	no	—
241	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
242	#332	—	2	2	no	—
243	#327	—	2	2	no	—
244	D₄⋊C₈	—	2	2	no	—
245	C₂×C₁₉	—	2	1	no	—
246	C₂×C₁₉	—	2	1	no	—
247	C₂×C₁₉	—	8	2	no	—
248	C₂×C₁₉	—	16	1	no	—
249	C₂×C₁₉	#1999	1	1	yes	characteristic
250	C₂×C₁₉	#2003	1	1	yes	characteristic
251	C₂×C₁₉	#2009	1	1	yes	characteristic
252	C₂×#41	—	2	1	no	—
253	C₂²×Q₈	—	2	1	no	—
254	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
255	C₂³×C₄	—	2	1	no	—
256	AGL(1,ℤ/8)	—	4	2	no	—
257	AGL(1,ℤ/8)	—	4	2	no	—
258	C₂×SD₁₆	—	2	2	no	—
259	C₂×D₈	—	2	2	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₄⋊Q₈	—	2	1	no	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
266	#127	D₄×C₁₉	1	1	yes	characteristic
267	#124	—	2	1	no	—
268	#124	—	4	2	no	—
269	#124	—	4	2	no	—
270	#121	—	2	1	no	—
271	#121	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
281	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
286	#107	—	2	4	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
290	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
291	#103	—	2	2	no	—
292	#102	—	2	2	no	—
293	#102	—	2	4	no	—
294	C₂²⋊C₈	—	2	1	no	—
295	C₂²⋊C₈	—	2	1	no	—
296	C₄×C₈	—	2	1	no	—
297	C₄×C₈	—	2	1	no	—
298	#95	—	2	4	no	—
299	#95	D₄×C₁₉	1	2	yes	—
300	C₁₉	#10239	1	1	yes	characteristic, direct product factor, Sylow
301	C₂⁴	—	2	1	no	—
302	#41	—	4	1	no	—
303	#41	—	4	1	no	—
304	#41	—	4	1	no	—
305	#41	—	4	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	4	1	no	—
308	C₂×Q₈	—	4	1	no	—
309	C₂×Q₈	—	4	1	no	—
310	C₂×Q₈	—	4	1	no	—
311	C₂×Q₈	—	4	1	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	D₈×C₁₉	1	2	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	4	4	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
333	SD₁₆	—	4	4	no	—
334	D₈	—	4	4	no	—
335	M₁₆	—	4	1	no	—
336	M₁₆	—	4	1	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	—	4	8	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₂²⋊C₄	—	4	1	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₄²	—	4	1	no	—
355	C₄²	—	4	1	no	—
356	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
357	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₄²	#41×C₁₉	1	1	yes	characteristic
360	C₂³	—	2	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	C₁₉×#120	1	1	yes	characteristic
367	Q₈	—	4	1	no	—
368	Q₈	—	4	1	no	—
369	Q₈	—	8	1	no	—
370	Q₈	—	8	1	no	—
371	Q₈	—	8	1	no	—
372	Q₈	—	8	1	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	1	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	1	no	—
380	D₄	—	8	1	no	—
381	D₄	—	8	1	no	—
382	D₄	—	8	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	—	8	2	no	—
396	C₂×C₄	—	8	1	no	—
397	C₂×C₄	—	8	1	no	—
398	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
399	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
400	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
401	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
402	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
403	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
404	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
405	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
406	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
407	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
408	C₈	—	4	2	no	—
409	C₈	—	4	2	no	—
410	C₈	—	8	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	4	4	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	C₁₉×#392	1	1	yes	characteristic
422	C₂²	C₁₉×#447	1	1	yes	characteristic
423	C₂²	C₁₉×#449	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	1	no	—
431	C₄	C₁₉×#447	1	1	yes	characteristic
432	C₄	C₁₉×#449	1	1	yes	characteristic
433	C₄	C₁₉×#454	1	2	yes	—
434	C₄	C₁₉×#466	1	1	yes	characteristic
435	C₄	C₁₉×#469	1	1	yes	characteristic
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	8	2	no	—
439	C₂	—	16	1	no	—
440	C₂	C₁₉×#1999	1	1	yes	characteristic
441	C₂	C₁₉×#2003	1	1	yes	characteristic
442	C₂	C₁₉×#2009	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3036	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3226	C₂	semidirect
3. C₁₉×#2547	C₂	semidirect
4. C₁₉×#1546	C₂	semidirect
5. C₁₉×#1502	C₂	semidirect
6. C₁₉×#1478	C₂	semidirect
7. C₁₉×#1303	C₂	semidirect
138. #10239	C₁₉	direct (N × H)
190. #3226	C₂×C₁₉	semidirect
192. #2547	C₂×C₁₉	semidirect
193. #1546	C₂×C₁₉	semidirect
194. #1502	C₂×C₁₉	semidirect
195. #1478	C₂×C₁₉	semidirect
196. #1303	C₂×C₁₉	semidirect
300. C₁₉	#10239	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3226	2
C₁₉×#3036	2
C₁₉×#2547	2
C₁₉×#1546	2
C₁₉×#1502	2
C₁₉×#1478	2
C₁₉×#1303	2
#10239	19

Subgroups — C19×#10239 #18016198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10239 #18016198