Subgroups — C₁₉×#10480 #18016439

Order 4864.

474 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#476	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1802	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#333	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#476	—	2	2	no	—
11	C₁₉×#476	—	2	2	no	—
12	C₂×C₁₉×#106	—	2	1	no	—
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#102	—	2	1	no	—
17	C₂×C₁₉×#102	—	2	1	no	—
18	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
19	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#384	C₂²	1	1	yes	characteristic
22	C₁₉×#340	—	2	1	no	—
23	C₁₉×#340	—	2	1	no	—
24	C₁₉×#340	—	2	1	no	—
25	C₁₉×#334	—	2	2	no	—
26	C₁₉×#333	—	2	2	no	—
27	C₂²×Q₈×C₁₉	—	2	1	no	—
28	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	—	2	1	no	—
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
39	C₄×D₄×C₁₉	—	2	1	no	—
40	C₄×D₄×C₁₉	—	2	1	no	—
41	C₄×D₄×C₁₉	—	2	1	no	—
42	C₄×D₄×C₁₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
51	C₁₉×#106	—	2	4	no	—
52	C₁₉×C₄⋊C₈	—	2	1	no	—
53	C₁₉×C₄⋊C₈	—	2	1	no	—
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₄⋊C₈	—	2	1	no	—
57	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
58	C₁₉×#102	—	2	4	no	—
59	C₁₉×#102	—	4	2	no	—
60	C₁₉×C₂²⋊C₈	—	4	2	no	—
61	C₁₉×C₂²⋊C₈	—	4	2	no	—
62	C₄×C₈×C₁₉	—	2	1	no	—
63	C₄×C₈×C₁₉	—	2	1	no	—
64	C₂⁴×C₁₉	—	2	1	no	—
65	C₂×Q₈×C₁₉	—	2	2	no	—
66	C₂×Q₈×C₁₉	—	4	1	no	—
67	C₂×Q₈×C₁₉	—	8	1	no	—
68	C₂×Q₈×C₁₉	—	8	1	no	—
69	C₂×D₄×C₁₉	—	2	1	no	—
70	C₂×D₄×C₁₉	—	2	1	no	—
71	C₂×D₄×C₁₉	—	2	1	no	—
72	C₂×D₄×C₁₉	—	2	1	no	—
73	C₂×D₄×C₁₉	—	2	1	no	—
74	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
87	C₂×C₈×C₁₉	—	2	1	no	—
88	C₂×C₈×C₁₉	—	2	1	no	—
89	C₂×C₈×C₁₉	—	2	2	no	—
90	C₂×C₈×C₁₉	—	2	1	no	—
91	C₂×C₈×C₁₉	—	2	1	no	—
92	C₂×C₈×C₁₉	—	2	1	no	—
93	C₂×C₈×C₁₉	—	4	1	no	—
94	C₂×C₈×C₁₉	—	4	1	no	—
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₂×C₈×C₁₉	—	4	1	no	—
99	C₂×C₈×C₁₉	—	4	1	no	—
100	C₂×C₈×C₁₉	—	4	1	no	—
101	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
102	C₄⋊C₄×C₁₉	—	2	2	no	—
103	C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₄⋊C₄×C₁₉	—	2	2	no	—
105	C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₄⋊C₄×C₁₉	—	4	1	no	—
107	C₄⋊C₄×C₁₉	—	4	1	no	—
108	C₄⋊C₄×C₁₉	—	4	1	no	—
109	C₄⋊C₄×C₁₉	—	4	1	no	—
110	C₄⋊C₄×C₁₉	—	4	1	no	—
111	C₄⋊C₄×C₁₉	—	4	1	no	—
112	C₄⋊C₄×C₁₉	—	8	1	no	—
113	C₂²⋊C₄×C₁₉	—	4	1	no	—
114	C₂²⋊C₄×C₁₉	—	4	1	no	—
115	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₁₉	#41	1	1	yes	characteristic
118	C₄²×C₁₉	#41	1	1	yes	characteristic
119	#10480	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₁₉	—	2	2	no	—
121	C₂³×C₁₉	—	4	1	no	—
122	C₂³×C₁₉	—	4	1	no	—
123	C₂³×C₁₉	—	4	1	no	—
124	C₂³×C₁₉	—	4	1	no	—
125	C₂³×C₁₉	—	4	1	no	—
126	C₂³×C₁₉	—	4	1	no	—
127	C₂³×C₁₉	#121	1	1	yes	characteristic
128	Q₈×C₁₉	—	8	2	no	—
129	Q₈×C₁₉	—	8	2	no	—
130	D₄×C₁₉	—	2	2	no	—
131	D₄×C₁₉	—	2	2	no	—
132	D₄×C₁₉	—	4	1	no	—
133	D₄×C₁₉	—	4	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	—	4	2	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	4	1	no	—
140	C₂×C₄×C₁₉	—	8	1	no	—
141	C₂×C₄×C₁₉	—	8	1	no	—
142	C₂×C₄×C₁₉	—	8	1	no	—
143	C₂×C₄×C₁₉	—	8	1	no	—
144	C₂×C₄×C₁₉	—	8	1	no	—
145	C₂×C₄×C₁₉	—	8	1	no	—
146	C₂×C₄×C₁₉	—	8	1	no	—
147	C₂×C₄×C₁₉	—	8	1	no	—
148	C₂×C₄×C₁₉	—	8	1	no	—
149	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
159	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
163	C₈×C₁₉	—	2	2	no	—
164	C₈×C₁₉	—	4	2	no	—
165	C₈×C₁₉	—	4	1	no	—
166	C₈×C₁₉	—	8	1	no	—
167	C₈×C₁₉	—	8	1	no	—
168	C₂×#476	C₂×C₁₉	1	1	yes	characteristic
169	#1990	C₂×C₁₉	1	1	yes	characteristic, complemented
170	#1954	C₂×C₁₉	1	1	yes	characteristic
171	#1802	C₂×C₁₉	1	1	yes	characteristic
172	C₂×#334	C₂×C₁₉	1	1	yes	characteristic, complemented
173	C₂×#333	C₂×C₁₉	1	1	yes	characteristic, complemented
174	#1296	C₂×C₁₉	1	1	yes	characteristic, complemented
175	C₂²×C₁₉	—	4	2	no	—
176	C₂²×C₁₉	—	4	2	no	—
177	C₂²×C₁₉	—	4	2	no	—
178	C₂²×C₁₉	—	8	1	no	—
179	C₂²×C₁₉	—	8	1	no	—
180	C₂²×C₁₉	—	8	1	no	—
181	C₂²×C₁₉	—	8	1	no	—
182	C₂²×C₁₉	#394	1	1	yes	characteristic
183	C₂²×C₁₉	#461	1	1	yes	characteristic
184	C₂²×C₁₉	#463	1	1	yes	characteristic
185	C₂²×C₁₉	#465	1	1	yes	characteristic
186	C₂²×C₁₉	#470	1	1	yes	characteristic
187	C₂²×C₁₉	#471	1	1	yes	characteristic
188	C₂²×C₁₉	#472	1	1	yes	characteristic
189	C₄×C₁₉	—	2	1	no	—
190	C₄×C₁₉	—	2	1	no	—
191	C₄×C₁₉	—	8	2	no	—
192	C₄×C₁₉	—	8	1	no	—
193	C₄×C₁₉	—	16	1	no	—
194	C₄×C₁₉	#448	1	1	yes	characteristic
195	C₄×C₁₉	#452	1	1	yes	characteristic
196	C₄×C₁₉	#460	1	1	yes	characteristic
197	C₄×C₁₉	#464	1	1	yes	characteristic
198	C₄×C₁₉	#465	1	1	yes	characteristic
199	C₄×C₁₉	#468	1	1	yes	characteristic
200	C₄×C₁₉	#483	1	1	yes	characteristic
201	C₄×C₁₉	#485	1	1	yes	characteristic
202	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
203	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
204	#476	—	2	2	no	—
205	#476	—	2	2	no	—
206	C₂×#106	—	2	1	no	—
207	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
208	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
209	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
210	C₂×#102	—	2	1	no	—
211	C₂×#102	—	2	1	no	—
212	C₂×C₂²⋊C₈	—	2	1	no	—
213	C₂×C₂²⋊C₈	—	2	1	no	—
214	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
215	#384	C₂²×C₁₉	1	1	yes	characteristic
216	#340	—	2	1	no	—
217	#340	—	2	1	no	—
218	#340	—	2	1	no	—
219	#334	—	2	2	no	—
220	#333	—	2	2	no	—
221	C₂×C₁₉	—	8	2	no	—
222	C₂×C₁₉	#1671	1	1	yes	characteristic
223	C₂×C₁₉	#1677	1	1	yes	characteristic
224	C₂×C₁₉	#1695	1	1	yes	characteristic
225	C₂×C₁₉	#1703	1	1	yes	characteristic
226	C₂×C₁₉	#2035	1	1	yes	characteristic
227	C₂×C₁₉	#2051	1	1	yes	characteristic
228	C₂×C₁₉	#2055	1	1	yes	characteristic
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
231	C₂³×C₄	—	2	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₂²×C₈	—	2	1	no	—
235	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
236	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
253	#106	—	2	4	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
260	#102	—	2	4	no	—
261	#102	—	4	2	no	—
262	C₂²⋊C₈	—	4	2	no	—
263	C₂²⋊C₈	—	4	2	no	—
264	C₄×C₈	—	2	1	no	—
265	C₄×C₈	—	2	1	no	—
266	C₁₉	#10480	1	1	yes	characteristic, direct product factor, Sylow
267	C₂⁴	—	2	1	no	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	4	1	no	—
270	C₂×Q₈	—	8	1	no	—
271	C₂×Q₈	—	8	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	SD₁₆×C₁₉	1	2	yes	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
289	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	4	1	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	4	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	SD₁₆×C₁₉	1	2	yes	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	8	1	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₂²⋊C₄	—	4	1	no	—
318	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
319	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
320	C₄²	#41×C₁₉	1	1	yes	characteristic
321	C₄²	#41×C₁₉	1	1	yes	characteristic
322	C₂³	—	2	2	no	—
323	C₂³	—	4	1	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	1	no	—
329	C₂³	C₁₉×#121	1	1	yes	characteristic
330	Q₈	—	8	2	no	—
331	Q₈	—	8	2	no	—
332	D₄	—	2	2	no	—
333	D₄	—	2	2	no	—
334	D₄	—	4	1	no	—
335	D₄	—	4	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	8	1	no	—
343	C₂×C₄	—	8	1	no	—
344	C₂×C₄	—	8	1	no	—
345	C₂×C₄	—	8	1	no	—
346	C₂×C₄	—	8	1	no	—
347	C₂×C₄	—	8	1	no	—
348	C₂×C₄	—	8	1	no	—
349	C₂×C₄	—	8	1	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
352	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
353	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
354	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
355	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
356	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
357	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
358	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
359	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
360	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
361	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
362	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
363	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
364	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
365	C₈	—	2	2	no	—
366	C₈	—	4	2	no	—
367	C₈	—	4	1	no	—
368	C₈	—	8	1	no	—
369	C₈	—	8	1	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	8	1	no	—
374	C₂²	—	8	1	no	—
375	C₂²	—	8	1	no	—
376	C₂²	—	8	1	no	—
377	C₂²	C₁₉×#394	1	1	yes	characteristic
378	C₂²	C₁₉×#461	1	1	yes	characteristic
379	C₂²	C₁₉×#463	1	1	yes	characteristic
380	C₂²	C₁₉×#465	1	1	yes	characteristic
381	C₂²	C₁₉×#470	1	1	yes	characteristic
382	C₂²	C₁₉×#471	1	1	yes	characteristic
383	C₂²	C₁₉×#472	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	8	2	no	—
387	C₄	—	8	1	no	—
388	C₄	—	16	1	no	—
389	C₄	C₁₉×#448	1	1	yes	characteristic
390	C₄	C₁₉×#452	1	1	yes	characteristic
391	C₄	C₁₉×#460	1	1	yes	characteristic
392	C₄	C₁₉×#464	1	1	yes	characteristic
393	C₄	C₁₉×#465	1	1	yes	characteristic
394	C₄	C₁₉×#468	1	1	yes	characteristic
395	C₄	C₁₉×#483	1	1	yes	characteristic
396	C₄	C₁₉×#485	1	1	yes	characteristic
397	C₂	—	8	2	no	—
398	C₂	C₁₉×#1671	1	1	yes	characteristic
399	C₂	C₁₉×#1677	1	1	yes	characteristic
400	C₂	C₁₉×#1695	1	1	yes	characteristic
401	C₂	C₁₉×#1703	1	1	yes	characteristic
402	C₂	C₁₉×#2035	1	1	yes	characteristic
403	C₂	C₁₉×#2051	1	1	yes	characteristic
404	C₂	C₁₉×#2055	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1990	C₂	semidirect
5. C₂×C₁₉×#334	C₂	semidirect
6. C₂×C₁₉×#333	C₂	semidirect
7. C₁₉×#1296	C₂	semidirect
119. #10480	C₁₉	direct (N × H)
169. #1990	C₂×C₁₉	semidirect
172. C₂×#334	C₂×C₁₉	semidirect
173. C₂×#333	C₂×C₁₉	semidirect
174. #1296	C₂×C₁₉	semidirect
266. C₁₉	#10480	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×C₁₉×#476	2
C₁₉×#1990	2
C₁₉×#1954	2
C₁₉×#1802	2
C₂×C₁₉×#334	2
C₂×C₁₉×#333	2
C₁₉×#1296	2
#10480	19

Subgroups — C19×#10480 #18016439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10480 #18016439