Subgroups — C₁₉×#13323 #18019282

Order 4864.

534 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3067	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#472	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#361	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2143	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2115	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1388	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#575	—	2	1	no	—
9	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
10	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
11	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
13	C₁₉×#509	—	2	2	no	—
14	C₁₉×#509	—	2	2	no	—
15	C₂×C₁₉×SD₃₂	—	2	1	no	—
16	C₂×C₁₉×D₁₆	—	2	1	no	—
17	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
19	C₁₉×#473	—	2	1	no	—
20	C₁₉×#472	—	2	2	no	—
21	C₁₉×#472	—	2	2	no	—
22	C₁₉×#472	—	2	1	no	—
23	C₁₉×#471	—	2	2	no	—
24	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
26	C₁₉×#413	—	2	1	no	—
27	C₂×C₁₉×#100	—	2	1	no	—
28	C₁₉×#361	—	2	2	no	—
29	C₁₉×#359	—	2	2	no	—
30	C₁₉×#349	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₁₉×#137	—	2	2	no	—
35	C₁₉×#137	—	4	1	no	—
36	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
37	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
38	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
39	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
40	C₁₉×#135	—	2	1	no	—
41	C₁₉×#135	—	2	1	no	—
42	C₁₉×#135	—	2	1	no	—
43	C₁₉×#135	—	2	1	no	—
44	C₁₉×#135	—	4	2	no	—
45	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
46	C₂×SD₁₆×C₁₉	—	2	1	no	—
47	C₂×SD₁₆×C₁₉	—	4	1	no	—
48	C₂×D₈×C₁₉	—	2	1	no	—
49	C₂×D₈×C₁₉	—	2	1	no	—
50	C₂×D₈×C₁₉	—	2	1	no	—
51	C₂×D₈×C₁₉	—	2	1	no	—
52	C₂×D₈×C₁₉	—	2	1	no	—
53	C₂×D₈×C₁₉	—	4	1	no	—
54	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
55	C₂×D₈×C₁₉	D₄	1	2	yes	—
56	C₁₉×#131	—	2	1	no	—
57	C₁₉×#131	—	2	1	no	—
58	C₁₉×#131	—	2	1	no	—
59	C₁₉×#131	—	2	1	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₂×M₁₆×C₁₉	—	2	1	no	—
62	C₂×M₁₆×C₁₉	—	2	1	no	—
63	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₉	—	2	1	no	—
65	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₁₉×SD₃₂	—	2	4	no	—
67	C₁₉×D₁₆	—	2	4	no	—
68	C₁₉×M₃₂	—	2	1	no	—
69	C₁₉×M₃₂	—	2	1	no	—
70	C₁₉×M₃₂	—	2	1	no	—
71	C₁₉×M₃₂	D₄	1	2	yes	—
72	C₂×C₁₆×C₁₉	—	2	1	no	—
73	C₂×C₁₆×C₁₉	—	2	1	no	—
74	C₁₉×#108	—	2	1	no	—
75	C₁₉×#108	—	2	1	no	—
76	C₁₉×#108	D₄	1	2	yes	—
77	C₁₉×#108	D₄	1	2	yes	—
78	C₁₉×#101	—	2	2	no	—
79	C₁₉×#100	—	2	4	no	—
80	C₁₉×#100	—	2	2	no	—
81	C₂⁴×C₁₉	—	4	1	no	—
82	#41×C₁₉	—	2	1	no	—
83	#41×C₁₉	—	2	1	no	—
84	#41×C₁₉	—	2	1	no	—
85	#41×C₁₉	—	2	1	no	—
86	#41×C₁₉	—	4	1	no	—
87	#41×C₁₉	—	4	1	no	—
88	#41×C₁₉	—	4	1	no	—
89	#41×C₁₉	—	4	1	no	—
90	C₂×Q₈×C₁₉	—	2	1	no	—
91	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	2	2	no	—
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	—	4	1	no	—
96	C₂×D₄×C₁₉	—	4	1	no	—
97	C₂×D₄×C₁₉	—	4	1	no	—
98	C₂×D₄×C₁₉	—	4	1	no	—
99	C₂×D₄×C₁₉	—	4	1	no	—
100	C₂×D₄×C₁₉	—	4	1	no	—
101	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	Q₁₆×C₁₉	—	2	1	no	—
106	Q₁₆×C₁₉	—	2	1	no	—
107	Q₁₆×C₁₉	—	4	2	no	—
108	SD₁₆×C₁₉	—	4	2	no	—
109	SD₁₆×C₁₉	—	4	4	no	—
110	SD₁₆×C₁₉	—	4	2	no	—
111	SD₁₆×C₁₉	—	4	1	no	—
112	SD₁₆×C₁₉	—	4	1	no	—
113	D₈×C₁₉	—	2	2	no	—
114	D₈×C₁₉	—	2	1	no	—
115	D₈×C₁₉	—	2	2	no	—
116	D₈×C₁₉	—	2	1	no	—
117	D₈×C₁₉	—	4	4	no	—
118	D₈×C₁₉	—	4	2	no	—
119	D₈×C₁₉	—	4	1	no	—
120	D₈×C₁₉	—	4	1	no	—
121	M₁₆×C₁₉	—	2	2	no	—
122	M₁₆×C₁₉	—	2	2	no	—
123	M₁₆×C₁₉	—	2	1	no	—
124	M₁₆×C₁₉	—	2	1	no	—
125	M₁₆×C₁₉	—	4	1	no	—
126	M₁₆×C₁₉	—	4	1	no	—
127	M₁₆×C₁₉	—	4	1	no	—
128	M₁₆×C₁₉	—	4	1	no	—
129	C₂×C₈×C₁₉	—	2	1	no	—
130	C₂×C₈×C₁₉	—	4	1	no	—
131	C₂×C₈×C₁₉	—	4	1	no	—
132	C₂×C₈×C₁₉	—	4	1	no	—
133	C₂×C₈×C₁₉	—	4	1	no	—
134	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
140	C₁₆×C₁₉	—	2	2	no	—
141	C₁₆×C₁₉	—	4	1	no	—
142	#13323	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂³×C₁₉	—	2	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	2	no	—
146	C₂³×C₁₉	—	8	1	no	—
147	C₂³×C₁₉	—	8	1	no	—
148	C₂³×C₁₉	—	16	2	no	—
149	C₂³×C₁₉	#135	1	1	yes	characteristic
150	Q₈×C₁₉	—	2	1	no	—
151	Q₈×C₁₉	—	2	1	no	—
152	Q₈×C₁₉	—	4	1	no	—
153	Q₈×C₁₉	—	4	1	no	—
154	D₄×C₁₉	—	2	1	no	—
155	D₄×C₁₉	—	2	1	no	—
156	D₄×C₁₉	—	4	1	no	—
157	D₄×C₁₉	—	4	1	no	—
158	D₄×C₁₉	—	4	2	no	—
159	D₄×C₁₉	—	4	1	no	—
160	D₄×C₁₉	—	4	2	no	—
161	D₄×C₁₉	—	4	1	no	—
162	D₄×C₁₉	—	8	1	no	—
163	D₄×C₁₉	—	8	1	no	—
164	D₄×C₁₉	—	8	1	no	—
165	D₄×C₁₉	—	8	1	no	—
166	C₂×C₄×C₁₉	—	2	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	—	8	1	no	—
171	C₂×C₄×C₁₉	—	8	1	no	—
172	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
176	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
178	C₈×C₁₉	—	4	1	no	—
179	C₈×C₁₉	—	4	2	no	—
180	C₈×C₁₉	—	4	2	no	—
181	C₈×C₁₉	#120	1	1	yes	characteristic
182	C₈×C₁₉	#121	1	1	yes	characteristic
183	C₈×C₁₉	#121	1	1	yes	characteristic
184	C₈×C₁₉	#127	1	1	yes	characteristic
185	C₂×#509	C₂×C₁₉	1	1	yes	characteristic, complemented
186	#3067	C₂×C₁₉	1	1	yes	characteristic, complemented
187	C₂×#472	C₂×C₁₉	1	1	yes	characteristic, complemented
188	C₂×#361	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#2143	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#2115	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#1388	C₂×C₁₉	1	1	yes	characteristic, complemented
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	—	4	1	no	—
194	C₂²×C₁₉	—	8	1	no	—
195	C₂²×C₁₉	—	8	1	no	—
196	C₂²×C₁₉	—	8	2	no	—
197	C₂²×C₁₉	—	16	1	no	—
198	C₂²×C₁₉	—	16	2	no	—
199	C₂²×C₁₉	—	16	2	no	—
200	C₂²×C₁₉	—	16	2	no	—
201	C₂²×C₁₉	#449	1	1	yes	characteristic
202	C₂²×C₁₉	#449	1	1	yes	characteristic
203	C₂²×C₁₉	#466	1	1	yes	characteristic
204	C₄×C₁₉	—	4	1	no	—
205	C₄×C₁₉	—	8	1	no	—
206	C₄×C₁₉	#392	1	1	yes	characteristic
207	C₄×C₁₉	#447	1	1	yes	characteristic
208	C₄×C₁₉	#447	1	1	yes	characteristic
209	C₄×C₁₉	#469	1	1	yes	characteristic
210	#575	—	2	1	no	—
211	C₂×AGL(1,ℤ/8)	—	2	1	no	—
212	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
213	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
214	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
215	#509	—	2	2	no	—
216	#509	—	2	2	no	—
217	C₂×SD₃₂	—	2	1	no	—
218	C₂×D₁₆	—	2	1	no	—
219	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
220	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
221	#473	—	2	1	no	—
222	#472	—	2	2	no	—
223	#472	—	2	1	no	—
224	#472	—	2	2	no	—
225	#471	—	2	2	no	—
226	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
228	#413	—	2	1	no	—
229	C₂×#100	—	2	1	no	—
230	#361	—	2	2	no	—
231	#359	—	2	2	no	—
232	#349	—	2	2	no	—
233	C₂×C₁₉	—	2	1	no	—
234	C₂×C₁₉	—	2	1	no	—
235	C₂×C₁₉	—	2	1	no	—
236	C₂×C₁₉	—	8	1	no	—
237	C₂×C₁₉	—	16	1	no	—
238	C₂×C₁₉	—	16	2	no	—
239	C₂×C₁₉	#1999	1	1	yes	characteristic
240	C₂×#41	—	2	1	no	—
241	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
242	C₂²×D₄	—	2	1	no	—
243	#137	—	2	2	no	—
244	#137	—	4	1	no	—
245	AGL(1,ℤ/8)	—	2	4	no	—
246	AGL(1,ℤ/8)	—	2	2	no	—
247	AGL(1,ℤ/8)	—	4	2	no	—
248	AGL(1,ℤ/8)	—	4	1	no	—
249	#135	—	2	1	no	—
250	#135	—	2	1	no	—
251	#135	—	2	1	no	—
252	#135	—	2	1	no	—
253	#135	—	4	2	no	—
254	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
255	C₂×SD₁₆	—	2	1	no	—
256	C₂×SD₁₆	—	4	1	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	—	2	1	no	—
259	C₂×D₈	—	2	1	no	—
260	C₂×D₈	—	2	1	no	—
261	C₂×D₈	—	2	1	no	—
262	C₂×D₈	—	4	1	no	—
263	C₂×D₈	D₄×C₁₉	1	2	yes	—
264	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
265	#131	—	2	1	no	—
266	#131	—	2	1	no	—
267	#131	—	2	1	no	—
268	#131	—	2	1	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
275	SD₃₂	—	2	4	no	—
276	D₁₆	—	2	4	no	—
277	M₃₂	—	2	1	no	—
278	M₃₂	—	2	1	no	—
279	M₃₂	—	2	1	no	—
280	M₃₂	D₄×C₁₉	1	2	yes	—
281	C₂×C₁₆	—	2	1	no	—
282	C₂×C₁₆	—	2	1	no	—
283	#108	—	2	1	no	—
284	#108	—	2	1	no	—
285	#108	D₄×C₁₉	1	2	yes	—
286	#108	D₄×C₁₉	1	2	yes	—
287	#101	—	2	2	no	—
288	#100	—	2	4	no	—
289	#100	—	2	2	no	—
290	C₁₉	#13323	1	1	yes	characteristic, direct product factor, Sylow
291	C₂⁴	—	4	1	no	—
292	#41	—	2	1	no	—
293	#41	—	2	1	no	—
294	#41	—	2	1	no	—
295	#41	—	2	1	no	—
296	#41	—	4	1	no	—
297	#41	—	4	1	no	—
298	#41	—	4	1	no	—
299	#41	—	4	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
315	Q₁₆	—	2	1	no	—
316	Q₁₆	—	2	1	no	—
317	Q₁₆	—	4	2	no	—
318	SD₁₆	—	4	2	no	—
319	SD₁₆	—	4	4	no	—
320	SD₁₆	—	4	2	no	—
321	SD₁₆	—	4	1	no	—
322	SD₁₆	—	4	1	no	—
323	D₈	—	2	1	no	—
324	D₈	—	2	2	no	—
325	D₈	—	2	2	no	—
326	D₈	—	2	1	no	—
327	D₈	—	4	4	no	—
328	D₈	—	4	2	no	—
329	D₈	—	4	1	no	—
330	D₈	—	4	1	no	—
331	M₁₆	—	2	1	no	—
332	M₁₆	—	2	1	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	—	4	1	no	—
336	M₁₆	—	4	1	no	—
337	M₁₆	—	4	1	no	—
338	M₁₆	—	4	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
347	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
348	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
349	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
350	C₁₆	—	2	2	no	—
351	C₁₆	—	4	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	8	1	no	—
356	C₂³	—	8	1	no	—
357	C₂³	—	16	2	no	—
358	C₂³	C₁₉×#135	1	1	yes	characteristic
359	Q₈	—	2	1	no	—
360	Q₈	—	2	1	no	—
361	Q₈	—	4	1	no	—
362	Q₈	—	4	1	no	—
363	D₄	—	2	1	no	—
364	D₄	—	2	1	no	—
365	D₄	—	4	1	no	—
366	D₄	—	4	1	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	1	no	—
371	D₄	—	8	1	no	—
372	D₄	—	8	1	no	—
373	D₄	—	8	1	no	—
374	D₄	—	8	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	8	1	no	—
380	C₂×C₄	—	8	1	no	—
381	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
382	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
383	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
384	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
385	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
386	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
387	C₈	—	4	1	no	—
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₈	C₁₉×#120	1	1	yes	characteristic
391	C₈	C₁₉×#121	1	1	yes	characteristic
392	C₈	C₁₉×#121	1	1	yes	characteristic
393	C₈	C₁₉×#127	1	1	yes	characteristic
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	8	1	no	—
397	C₂²	—	8	1	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	16	2	no	—
400	C₂²	—	16	1	no	—
401	C₂²	—	16	2	no	—
402	C₂²	—	16	2	no	—
403	C₂²	C₁₉×#449	1	1	yes	characteristic
404	C₂²	C₁₉×#449	1	1	yes	characteristic
405	C₂²	C₁₉×#466	1	1	yes	characteristic
406	C₄	—	4	1	no	—
407	C₄	—	8	1	no	—
408	C₄	C₁₉×#392	1	1	yes	characteristic
409	C₄	C₁₉×#447	1	1	yes	characteristic
410	C₄	C₁₉×#447	1	1	yes	characteristic
411	C₄	C₁₉×#469	1	1	yes	characteristic
412	C₂	—	2	1	no	—
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	—	8	1	no	—
416	C₂	—	16	2	no	—
417	C₂	—	16	1	no	—
418	C₂	C₁₉×#1999	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#1999
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#509	C₂	semidirect
2. C₁₉×#3067	C₂	semidirect
3. C₂×C₁₉×#472	C₂	semidirect
4. C₂×C₁₉×#361	C₂	semidirect
5. C₁₉×#2143	C₂	semidirect
6. C₁₉×#2115	C₂	semidirect
7. C₁₉×#1388	C₂	semidirect
142. #13323	C₁₉	direct (N × H)
185. C₂×#509	C₂×C₁₉	semidirect
186. #3067	C₂×C₁₉	semidirect
187. C₂×#472	C₂×C₁₉	semidirect
188. C₂×#361	C₂×C₁₉	semidirect
189. #2143	C₂×C₁₉	semidirect
190. #2115	C₂×C₁₉	semidirect
191. #1388	C₂×C₁₉	semidirect
290. C₁₉	#13323	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×#509	2
C₁₉×#3067	2
C₂×C₁₉×#472	2
C₂×C₁₉×#361	2
C₁₉×#2143	2
C₁₉×#2115	2
C₁₉×#1388	2
#13323	19

Subgroups — C19×#13323 #18019282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13323 #18019282