Subgroups — C₁₉×#12990 #18018949

Order 4864.

518 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3050	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#108	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#359	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1382	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₉	—	2	1	no	—
8	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#525	—	2	1	no	—
10	C₂²×C₁₆×C₁₉	C₂²	1	2	yes	—
11	C₁₉×#467	C₄	1	1	yes	characteristic
12	C₁₉×#467	C₄	1	1	yes	characteristic
13	C₁₉×#466	C₄	1	1	yes	characteristic
14	C₁₉×#466	C₄	1	1	yes	characteristic
15	C₁₉×#465	—	2	1	no	—
16	C₁₉×#465	—	2	1	no	—
17	C₂×C₁₉×#108	—	2	4	no	—
18	C₂×C₁₉×#108	—	2	1	no	—
19	C₂×C₁₉×#108	C₂²	1	2	yes	—
20	C₁₉×#427	C₂²	1	1	yes	characteristic
21	C₁₉×#416	—	2	1	no	—
22	C₁₉×#359	—	2	4	no	—
23	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
24	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
25	C₂×#41×C₁₉	—	2	1	no	—
26	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₁₉×#135	—	2	2	no	—
28	C₁₉×#135	—	2	2	no	—
29	C₂×Q₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂×SD₁₆×C₁₉	—	2	1	no	—
31	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×M₁₆×C₁₉	—	2	4	no	—
33	C₂×M₁₆×C₁₉	—	2	2	no	—
34	C₂×M₁₆×C₁₉	—	4	2	no	—
35	C₂×M₁₆×C₁₉	—	4	1	no	—
36	C₂²×C₈×C₁₉	—	2	2	no	—
37	C₂²×C₈×C₁₉	—	2	2	no	—
38	C₂²×C₈×C₁₉	—	4	1	no	—
39	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₁₉×#123	—	4	1	no	—
46	C₁₉×C₂²⋊Q₈	—	2	1	no	—
47	C₁₉×C₂²⋊Q₈	—	2	1	no	—
48	C₁₉×#121	—	2	1	no	—
49	C₁₉×#121	—	2	1	no	—
50	C₁₉×#120	—	4	1	no	—
51	C₄×D₄×C₁₉	—	4	1	no	—
52	C₄×D₄×C₁₉	—	4	1	no	—
53	C₁₉×#117	—	2	1	no	—
54	C₂×C₁₆×C₁₉	—	2	2	no	—
55	C₂×C₁₆×C₁₉	—	2	2	no	—
56	C₂×C₁₆×C₁₉	—	2	2	no	—
57	C₁₉×#108	—	2	4	no	—
58	C₁₉×#108	—	2	2	no	—
59	C₁₉×#108	D₄	1	4	yes	complemented
60	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
61	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
62	C₁₉×#106	—	2	1	no	—
63	C₁₉×#103	—	2	1	no	—
64	C₁₉×#103	—	2	1	no	—
65	C₁₉×#102	—	2	1	no	—
66	C₁₉×#102	—	2	1	no	—
67	C₂⁴×C₁₉	SD₁₆	1	1	yes	characteristic
68	#41×C₁₉	—	4	1	no	—
69	#41×C₁₉	—	4	1	no	—
70	#41×C₁₉	—	4	1	no	—
71	#41×C₁₉	—	4	1	no	—
72	C₂×Q₈×C₁₉	—	2	1	no	—
73	C₂×D₄×C₁₉	—	2	1	no	—
74	C₂×D₄×C₁₉	—	4	1	no	—
75	C₂×D₄×C₁₉	—	4	1	no	—
76	C₂×D₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	Q₁₆×C₁₉	—	2	2	no	—
89	SD₁₆×C₁₉	—	4	2	no	—
90	D₈×C₁₉	—	2	2	no	—
91	M₁₆×C₁₉	—	2	4	no	—
92	M₁₆×C₁₉	—	4	4	no	—
93	M₁₆×C₁₉	—	4	2	no	—
94	C₂×C₈×C₁₉	—	2	1	no	—
95	C₂×C₈×C₁₉	—	2	1	no	—
96	C₂×C₈×C₁₉	—	2	2	no	—
97	C₂×C₈×C₁₉	—	2	2	no	—
98	C₂×C₈×C₁₉	—	2	2	no	—
99	C₂×C₈×C₁₉	—	2	2	no	—
100	C₂×C₈×C₁₉	—	4	4	no	—
101	C₂×C₈×C₁₉	—	4	2	no	—
102	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₁₉	#41	1	2	yes	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	4	1	no	—
111	C₄⋊C₄×C₁₉	—	4	1	no	—
112	C₂²⋊C₄×C₁₉	—	4	1	no	—
113	C₂²⋊C₄×C₁₉	—	4	1	no	—
114	C₂²⋊C₄×C₁₉	—	4	1	no	—
115	C₂²⋊C₄×C₁₉	—	4	1	no	—
116	C₂²⋊C₄×C₁₉	—	4	1	no	—
117	C₄²×C₁₉	—	4	1	no	—
118	C₁₆×C₁₉	—	4	2	no	—
119	#12990	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₁₉	—	2	2	no	—
121	C₂³×C₁₉	—	2	1	no	—
122	C₂³×C₁₉	—	2	1	no	—
123	C₂³×C₁₉	—	4	1	no	—
124	C₂³×C₁₉	—	4	1	no	—
125	C₂³×C₁₉	#102	1	1	yes	characteristic
126	C₂³×C₁₉	#102	1	1	yes	characteristic
127	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
128	Q₈×C₁₉	—	4	1	no	—
129	Q₈×C₁₉	—	4	1	no	—
130	D₄×C₁₉	—	4	1	no	—
131	D₄×C₁₉	—	4	1	no	—
132	D₄×C₁₉	—	8	2	no	—
133	D₄×C₁₉	—	8	2	no	—
134	D₄×C₁₉	—	8	1	no	—
135	D₄×C₁₉	—	8	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	8	1	no	—
150	C₂×C₄×C₁₉	—	8	1	no	—
151	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
159	C₈×C₁₉	—	2	1	no	—
160	C₈×C₁₉	—	2	1	no	—
161	C₈×C₁₉	—	4	4	no	—
162	C₈×C₁₉	C₄×D₄	1	2	yes	—
163	C₈×C₁₉	#121	1	2	yes	—
164	#3050	C₂×C₁₉	1	1	yes	characteristic
165	C₂²×#108	C₂×C₁₉	1	1	yes	characteristic, complemented
166	C₂×#359	C₂×C₁₉	1	2	yes	complemented
167	C₂×C₂²⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
168	#1382	C₂×C₁₉	1	2	yes	complemented
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	2	1	no	—
171	C₂²×C₁₉	—	2	1	no	—
172	C₂²×C₁₉	—	2	1	no	—
173	C₂²×C₁₉	—	2	1	no	—
174	C₂²×C₁₉	—	2	1	no	—
175	C₂²×C₁₉	—	2	1	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	#359	1	2	yes	complemented
182	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
183	C₂²×C₁₉	#448	1	1	yes	characteristic
184	C₂²×C₁₉	#481	1	1	yes	characteristic
185	C₄×C₁₉	—	2	1	no	—
186	C₄×C₁₉	—	2	1	no	—
187	C₄×C₁₉	—	8	1	no	—
188	C₄×C₁₉	—	8	1	no	—
189	C₄×C₁₉	—	8	1	no	—
190	C₄×C₁₉	#386	1	1	yes	characteristic
191	C₄×C₁₉	#417	1	1	yes	characteristic
192	C₄×C₁₉	#447	1	1	yes	characteristic
193	C₄×C₁₉	#480	1	1	yes	characteristic
194	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
195	C₂²×M₁₆	—	2	1	no	—
196	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
197	#525	—	2	1	no	—
198	C₂²×C₁₆	C₂²×C₁₉	1	2	yes	—
199	#467	C₄×C₁₉	1	1	yes	characteristic
200	#467	C₄×C₁₉	1	1	yes	characteristic
201	#466	C₄×C₁₉	1	1	yes	characteristic
202	#466	C₄×C₁₉	1	1	yes	characteristic
203	#465	—	2	1	no	—
204	#465	—	2	1	no	—
205	C₂×#108	—	2	1	no	—
206	C₂×#108	—	2	4	no	—
207	C₂×#108	C₂²×C₁₉	1	2	yes	—
208	#427	C₂²×C₁₉	1	1	yes	characteristic
209	#416	—	2	1	no	—
210	#359	—	2	4	no	—
211	C₂²⋊C₁₆	—	2	1	no	—
212	C₂²⋊C₁₆	—	2	1	no	—
213	C₂×C₁₉	—	2	2	no	—
214	C₂×C₁₉	—	2	1	no	—
215	C₂×C₁₉	—	2	1	no	—
216	C₂×C₁₉	—	4	1	no	—
217	C₂×C₁₉	—	16	1	no	—
218	C₂×C₁₉	#1874	1	1	yes	characteristic
219	C₂×C₁₉	C₂×#359	1	1	yes	characteristic
220	C₂×C₁₉	#2143	1	1	yes	characteristic
221	C₂×#41	—	2	1	no	—
222	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
223	#135	—	2	2	no	—
224	#135	—	2	2	no	—
225	C₂×Q₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
226	C₂×SD₁₆	—	2	1	no	—
227	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
228	C₂×M₁₆	—	2	4	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	—	4	2	no	—
231	C₂×M₁₆	—	4	1	no	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	—	2	2	no	—
234	C₂²×C₈	—	4	1	no	—
235	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
236	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
237	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
238	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
239	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
241	#123	—	4	1	no	—
242	C₂²⋊Q₈	—	2	1	no	—
243	C₂²⋊Q₈	—	2	1	no	—
244	#121	—	2	1	no	—
245	#121	—	2	1	no	—
246	#120	—	4	1	no	—
247	C₄×D₄	—	4	1	no	—
248	C₄×D₄	—	4	1	no	—
249	#117	—	2	1	no	—
250	C₂×C₁₆	—	2	2	no	—
251	C₂×C₁₆	—	2	2	no	—
252	C₂×C₁₆	—	2	2	no	—
253	#108	—	2	4	no	—
254	#108	—	2	2	no	—
255	#108	D₄×C₁₉	1	4	yes	complemented
256	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
257	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
258	#106	—	2	1	no	—
259	#103	—	2	1	no	—
260	#103	—	2	1	no	—
261	#102	—	2	1	no	—
262	#102	—	2	1	no	—
263	C₁₉	#12990	1	1	yes	characteristic, direct product factor, Sylow
264	C₂⁴	SD₁₆×C₁₉	1	1	yes	characteristic
265	#41	—	4	1	no	—
266	#41	—	4	1	no	—
267	#41	—	4	1	no	—
268	#41	—	4	1	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂×D₄	—	4	1	no	—
273	C₂×D₄	—	4	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
281	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
282	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
283	C₂²×C₄	SD₁₆×C₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
285	Q₁₆	—	2	2	no	—
286	SD₁₆	—	4	2	no	—
287	D₈	—	2	2	no	—
288	M₁₆	—	2	4	no	—
289	M₁₆	—	4	4	no	—
290	M₁₆	—	4	2	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	4	4	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
300	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
301	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
302	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
303	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
304	C₂×C₈	#41×C₁₉	1	2	yes	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	4	1	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₂²⋊C₄	—	4	1	no	—
313	C₂²⋊C₄	—	4	1	no	—
314	C₄²	—	4	1	no	—
315	C₁₆	—	4	2	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	4	1	no	—
320	C₂³	—	4	1	no	—
321	C₂³	C₁₉×#102	1	1	yes	characteristic
322	C₂³	C₁₉×#102	1	1	yes	characteristic
323	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
324	Q₈	—	4	1	no	—
325	Q₈	—	4	1	no	—
326	D₄	—	4	1	no	—
327	D₄	—	4	1	no	—
328	D₄	—	8	2	no	—
329	D₄	—	8	2	no	—
330	D₄	—	8	1	no	—
331	D₄	—	8	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	8	1	no	—
346	C₂×C₄	—	8	1	no	—
347	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
348	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
349	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
350	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
351	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
352	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
353	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
354	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	4	4	no	—
358	C₈	C₄×D₄×C₁₉	1	2	yes	—
359	C₈	C₁₉×#121	1	2	yes	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	1	no	—
371	C₂²	—	8	1	no	—
372	C₂²	C₁₉×#359	1	2	yes	complemented
373	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
374	C₂²	C₁₉×#448	1	1	yes	characteristic
375	C₂²	C₁₉×#481	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	8	1	no	—
379	C₄	—	8	1	no	—
380	C₄	—	8	1	no	—
381	C₄	C₁₉×#386	1	1	yes	characteristic
382	C₄	C₁₉×#417	1	1	yes	characteristic
383	C₄	C₁₉×#447	1	1	yes	characteristic
384	C₄	C₁₉×#480	1	1	yes	characteristic
385	C₂	—	2	2	no	—
386	C₂	—	2	1	no	—
387	C₂	—	2	1	no	—
388	C₂	—	4	1	no	—
389	C₂	—	16	1	no	—
390	C₂	C₁₉×#1874	1	1	yes	characteristic
391	C₂	C₂×C₁₉×#359	1	1	yes	characteristic
392	C₂	C₁₉×#2143	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×#102
prime radical	C₁₉×#3050	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ C₂³×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#108	C₂	semidirect
3. C₂×C₁₉×#359	C₂	semidirect
4. C₂×C₁₉×C₂²⋊C₁₆	C₂	semidirect
5. C₁₉×#1382	C₂	semidirect
59. C₁₉×#108	D₄	semidirect
119. #12990	C₁₉	direct (N × H)
165. C₂²×#108	C₂×C₁₉	semidirect
166. C₂×#359	C₂×C₁₉	semidirect
167. C₂×C₂²⋊C₁₆	C₂×C₁₉	semidirect
168. #1382	C₂×C₁₉	semidirect
181. C₂²×C₁₉	#359	semidirect
255. #108	D₄×C₁₉	semidirect
263. C₁₉	#12990	direct (N × H)
372. C₂²	C₁₉×#359	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3050	2
C₂²×C₁₉×#108	2
C₂×C₁₉×#359	2
C₂×C₁₉×C₂²⋊C₁₆	2
C₁₉×#1382	2
#12990	19

Subgroups — C19×#12990 #18018949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12990 #18018949