Subgroups — C₁₉×#19155 #18025114

Order 4864.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3131	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3104	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3103	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1704	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1702	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1700	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1698	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1540	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#488	—	2	1	no	—
16	C₁₉×#488	—	2	1	no	—
17	C₁₉×#487	C₂²	1	1	yes	characteristic
18	C₁₉×#487	C₂²	1	1	yes	characteristic
19	C₁₉×#486	C₂²	1	1	yes	characteristic
20	C₁₉×#486	C₂²	1	1	yes	characteristic
21	C₁₉×#484	—	2	1	no	—
22	C₁₉×#481	—	2	1	no	—
23	C₁₉×#477	C₂²	1	2	yes	—
24	C₁₉×#475	C₂²	1	2	yes	—
25	C₁₉×#462	C₂²	1	2	yes	—
26	C₁₉×#460	C₂²	1	2	yes	—
27	C₁₉×#451	—	2	1	no	—
28	C₁₉×#448	—	2	1	no	—
29	C₁₉×#446	—	2	1	no	—
30	C₁₉×#446	—	2	1	no	—
31	C₁₉×#446	C₂²	1	2	yes	—
32	C₁₉×#446	C₂²	1	2	yes	—
33	C₄×Q₁₆×C₁₉	—	2	2	no	—
34	C₄×SD₁₆×C₁₉	—	2	2	no	—
35	C₁₉×#431	C₂²	1	1	yes	characteristic
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
38	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₉×#416	—	2	1	no	—
40	C₁₉×#416	—	2	1	no	—
41	C₂×C₁₉×#97	—	2	1	no	—
42	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#335	C₂²	1	2	yes	—
44	C₁₉×#334	C₂²	1	2	yes	—
45	C₁₉×#333	C₂²	1	2	yes	—
46	C₁₉×#332	C₂²	1	2	yes	—
47	C₁₉×#332	C₂²	1	2	yes	—
48	C₁₉×#331	C₂²	1	2	yes	—
49	C₂×#41×C₁₉	—	2	1	no	—
50	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
51	C₂×Q₁₆×C₁₉	—	2	2	no	—
52	C₂×SD₁₆×C₁₉	—	2	2	no	—
53	C₂²×C₈×C₁₉	—	2	1	no	—
54	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
58	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₁₉×#127	C₂³	1	1	yes	characteristic
60	C₁₉×#125	—	2	1	no	—
61	C₁₉×#124	—	2	1	no	—
62	C₁₉×C₂²⋊Q₈	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×#121	—	2	1	no	—
65	C₁₉×#121	—	2	1	no	—
66	C₄×Q₈×C₁₉	—	2	1	no	—
67	C₄×Q₈×C₁₉	—	2	1	no	—
68	C₄×Q₈×C₁₉	—	2	1	no	—
69	C₄×Q₈×C₁₉	—	2	1	no	—
70	C₄×Q₈×C₁₉	D₄	1	2	yes	—
71	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	—	2	1	no	—
74	C₁₉×#117	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₉	—	2	1	no	—
78	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
79	C₁₉×#107	—	2	2	no	—
80	C₁₉×#106	—	2	2	no	—
81	C₁₉×C₄⋊C₈	—	2	2	no	—
82	C₁₉×C₄⋊C₈	—	2	2	no	—
83	C₁₉×C₄⋊C₈	—	2	1	no	—
84	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
85	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
86	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
87	C₁₉×#103	—	2	2	no	—
88	C₁₉×#103	—	2	2	no	—
89	C₁₉×#103	—	2	1	no	—
90	C₁₉×#103	—	2	1	no	—
91	C₁₉×#103	—	2	1	no	—
92	C₁₉×#103	—	2	1	no	—
93	C₁₉×#103	—	2	2	no	—
94	C₁₉×#102	—	2	1	no	—
95	C₁₉×#102	—	2	1	no	—
96	C₁₉×#102	—	2	1	no	—
97	C₁₉×#102	—	2	1	no	—
98	C₁₉×#102	—	2	2	no	—
99	C₁₉×C₂²⋊C₈	—	2	1	no	—
100	C₁₉×C₂²⋊C₈	—	2	1	no	—
101	C₁₉×#97	—	2	2	no	—
102	C₁₉×#97	—	2	2	no	—
103	C₄×C₈×C₁₉	—	2	1	no	—
104	C₄×C₈×C₁₉	—	2	1	no	—
105	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
106	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
109	#41×C₁₉	—	4	2	no	—
110	#41×C₁₉	—	4	2	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	4	2	no	—
116	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	—	2	1	no	—
119	C₂×D₄×C₁₉	—	2	1	no	—
120	C₂×D₄×C₁₉	—	4	1	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
127	Q₁₆×C₁₉	—	4	4	no	—
128	SD₁₆×C₁₉	—	4	4	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	4	2	no	—
135	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	4	1	no	—
149	C₄⋊C₄×C₁₉	—	4	1	no	—
150	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂²⋊C₄×C₁₉	—	4	1	no	—
152	C₂²⋊C₄×C₁₉	—	4	1	no	—
153	C₂²⋊C₄×C₁₉	—	4	1	no	—
154	C₄²×C₁₉	—	2	2	no	—
155	C₄²×C₁₉	—	2	2	no	—
156	C₄²×C₁₉	—	4	1	no	—
157	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₉	#41	1	1	yes	characteristic
160	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
161	#19155	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂³×C₁₉	—	4	1	no	—
163	C₂³×C₁₉	#121	1	1	yes	characteristic
164	Q₈×C₁₉	—	2	2	no	—
165	Q₈×C₁₉	—	2	2	no	—
166	Q₈×C₁₉	—	4	2	no	—
167	Q₈×C₁₉	—	4	1	no	—
168	Q₈×C₁₉	—	4	1	no	—
169	Q₈×C₁₉	—	4	2	no	—
170	Q₈×C₁₉	—	8	1	no	—
171	D₄×C₁₉	—	4	1	no	—
172	D₄×C₁₉	—	4	1	no	—
173	D₄×C₁₉	—	4	2	no	—
174	D₄×C₁₉	—	8	1	no	—
175	D₄×C₁₉	—	8	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	8	2	no	—
186	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#135	1	2	yes	—
190	C₂×C₄×C₁₉	#137	1	2	yes	—
191	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
194	C₈×C₁₉	—	2	1	no	—
195	C₈×C₁₉	—	2	1	no	—
196	C₈×C₁₉	—	2	1	no	—
197	C₈×C₁₉	—	2	1	no	—
198	C₈×C₁₉	—	4	2	no	—
199	C₈×C₁₉	—	4	2	no	—
200	C₈×C₁₉	—	4	2	no	—
201	#3131	C₂×C₁₉	1	1	yes	characteristic
202	#3104	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#3103	C₂×C₁₉	1	1	yes	characteristic
204	C₂×#446	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#1704	C₂×C₁₉	1	2	yes	complemented
206	#1702	C₂×C₁₉	1	2	yes	complemented
207	#1700	C₂×C₁₉	1	2	yes	complemented
208	#1698	C₂×C₁₉	1	2	yes	complemented
209	#1564	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#1542	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#1540	C₂×C₁₉	1	1	yes	characteristic
212	C₂²×C₁₉	—	2	1	no	—
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	8	1	no	—
215	C₂²×C₁₉	—	8	1	no	—
216	C₂²×C₁₉	—	8	1	no	—
217	C₂²×C₁₉	#464	1	2	yes	—
218	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	4	2	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	—	8	1	no	—
225	C₄×C₁₉	—	8	1	no	—
226	C₄×C₁₉	—	8	1	no	—
227	C₄×C₁₉	#464	1	2	yes	—
228	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
229	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
230	C₄×C₁₉	#575	1	2	yes	—
231	#533	C₂²×C₁₉	1	1	yes	characteristic
232	#532	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
234	#488	—	2	1	no	—
235	#488	—	2	1	no	—
236	#487	C₂²×C₁₉	1	1	yes	characteristic
237	#487	C₂²×C₁₉	1	1	yes	characteristic
238	#486	C₂²×C₁₉	1	1	yes	characteristic
239	#486	C₂²×C₁₉	1	1	yes	characteristic
240	#484	—	2	1	no	—
241	#481	—	2	1	no	—
242	#477	C₂²×C₁₉	1	2	yes	—
243	#475	C₂²×C₁₉	1	2	yes	—
244	#462	C₂²×C₁₉	1	2	yes	—
245	#460	C₂²×C₁₉	1	2	yes	—
246	#451	—	2	1	no	—
247	#448	—	2	1	no	—
248	#446	—	2	1	no	—
249	#446	—	2	1	no	—
250	#446	C₂²×C₁₉	1	2	yes	—
251	#446	C₂²×C₁₉	1	2	yes	—
252	C₄×Q₁₆	—	2	2	no	—
253	C₄×SD₁₆	—	2	2	no	—
254	#431	C₂²×C₁₉	1	1	yes	characteristic
255	#431	C₂²×C₁₉	1	1	yes	characteristic
256	C₂×C₄⋊C₈	—	2	1	no	—
257	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
258	#416	—	2	1	no	—
259	#416	—	2	1	no	—
260	C₂×#97	—	2	1	no	—
261	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
262	#335	C₂²×C₁₉	1	2	yes	—
263	#334	C₂²×C₁₉	1	2	yes	—
264	#333	C₂²×C₁₉	1	2	yes	—
265	#332	C₂²×C₁₉	1	2	yes	—
266	#332	C₂²×C₁₉	1	2	yes	—
267	#331	C₂²×C₁₉	1	2	yes	—
268	C₂×C₁₉	—	2	2	no	—
269	C₂×C₁₉	—	16	1	no	—
270	C₂×C₁₉	C₂×#464	1	1	yes	characteristic
271	C₂×C₁₉	#3054	1	1	yes	characteristic
272	C₂×C₁₉	#3067	1	1	yes	characteristic
273	C₂×#41	—	2	1	no	—
274	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
275	C₂×Q₁₆	—	2	2	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
279	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
280	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
281	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
282	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
283	#127	C₂³×C₁₉	1	1	yes	characteristic
284	#125	—	2	1	no	—
285	#124	—	2	1	no	—
286	C₂²⋊Q₈	—	2	1	no	—
287	C₂²⋊Q₈	—	2	1	no	—
288	#121	—	2	1	no	—
289	#121	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	D₄×C₁₉	1	2	yes	—
295	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	2	1	no	—
298	#117	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
303	#107	—	2	2	no	—
304	#106	—	2	2	no	—
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
309	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
310	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
311	#103	—	2	2	no	—
312	#103	—	2	2	no	—
313	#103	—	2	1	no	—
314	#103	—	2	1	no	—
315	#103	—	2	1	no	—
316	#103	—	2	1	no	—
317	#103	—	2	2	no	—
318	#102	—	2	1	no	—
319	#102	—	2	1	no	—
320	#102	—	2	1	no	—
321	#102	—	2	1	no	—
322	#102	—	2	2	no	—
323	C₂²⋊C₈	—	2	1	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	#97	—	2	2	no	—
326	#97	—	2	2	no	—
327	C₄×C₈	—	2	1	no	—
328	C₄×C₈	—	2	1	no	—
329	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
330	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
331	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
332	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
333	C₁₉	#19155	1	1	yes	characteristic, direct product factor, Sylow
334	#41	—	4	2	no	—
335	#41	—	4	2	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	4	2	no	—
341	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
352	Q₁₆	—	4	4	no	—
353	SD₁₆	—	4	4	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	2	no	—
360	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
362	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
363	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	4	1	no	—
378	C₂²⋊C₄	—	4	1	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	4	1	no	—
382	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
383	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₄²	#41×C₁₉	1	1	yes	characteristic
385	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
386	C₂³	—	4	1	no	—
387	C₂³	C₁₉×#121	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	4	1	no	—
392	Q₈	—	4	1	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	8	1	no	—
395	D₄	—	4	1	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	2	no	—
398	D₄	—	8	1	no	—
399	D₄	—	8	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
411	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
412	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
413	C₂×C₄	C₁₉×#135	1	2	yes	—
414	C₂×C₄	C₁₉×#137	1	2	yes	—
415	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	4	2	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	C₁₉×#464	1	2	yes	—
431	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	8	1	no	—
438	C₄	—	8	1	no	—
439	C₄	—	8	1	no	—
440	C₄	C₁₉×#464	1	2	yes	—
441	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
442	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
443	C₄	C₁₉×#575	1	2	yes	—
444	C₂	—	2	2	no	—
445	C₂	—	16	1	no	—
446	C₂	C₂×C₁₉×#464	1	1	yes	characteristic
447	C₂	C₁₉×#3054	1	1	yes	characteristic
448	C₂	C₁₉×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#121
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3104	C₂	semidirect
4. C₂×C₁₉×#446	C₂	semidirect
5. C₁₉×#1704	C₂	semidirect
6. C₁₉×#1702	C₂	semidirect
7. C₁₉×#1700	C₂	semidirect
8. C₁₉×#1698	C₂	semidirect
9. C₁₉×#1564	C₂	semidirect
10. C₁₉×#1542	C₂	semidirect
161. #19155	C₁₉	direct (N × H)
202. #3104	C₂×C₁₉	semidirect
204. C₂×#446	C₂×C₁₉	semidirect
205. #1704	C₂×C₁₉	semidirect
206. #1702	C₂×C₁₉	semidirect
207. #1700	C₂×C₁₉	semidirect
208. #1698	C₂×C₁₉	semidirect
209. #1564	C₂×C₁₉	semidirect
210. #1542	C₂×C₁₉	semidirect
333. C₁₉	#19155	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×#3131	2
C₁₉×#3104	2
C₁₉×#3103	2
C₂×C₁₉×#446	2
C₁₉×#1704	2
C₁₉×#1702	2
C₁₉×#1700	2
C₁₉×#1698	2
C₁₉×#1564	2
C₁₉×#1542	2
C₁₉×#1540	2
#19155	19

Subgroups — C19×#19155 #18025114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19155 #18025114