Subgroups — C₁₉×#13311 #18019270

Order 4864.

520 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3067	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3059	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#362	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2145	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2117	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1389	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#575	—	2	1	no	—
9	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
10	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
12	C₁₉×#536	—	2	1	no	—
13	C₁₉×#510	—	2	2	no	—
14	C₁₉×#510	—	2	2	no	—
15	C₂×C₁₉×Q₃₂	—	2	1	no	—
16	C₂×C₁₉×SD₃₂	—	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	1	no	—
21	C₁₉×#471	—	2	2	no	—
22	C₁₉×#470	—	2	2	no	—
23	C₁₉×#467	—	2	2	no	—
24	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
25	C₁₉×#427	C₂²	1	1	yes	characteristic
26	C₁₉×#419	—	2	1	no	—
27	C₁₉×#413	—	2	1	no	—
28	C₁₉×#362	—	2	2	no	—
29	C₁₉×#360	—	2	2	no	—
30	C₁₉×#350	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×Q₈×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)	—	4	1	no	—
38	C₁₉×#135	—	2	1	no	—
39	C₁₉×#135	—	2	1	no	—
40	C₁₉×#135	—	2	1	no	—
41	C₁₉×#135	—	2	1	no	—
42	C₁₉×#135	—	4	2	no	—
43	C₂×Q₁₆×C₁₉	—	2	1	no	—
44	C₂×Q₁₆×C₁₉	—	2	1	no	—
45	C₂×Q₁₆×C₁₉	—	2	1	no	—
46	C₂×Q₁₆×C₁₉	—	2	1	no	—
47	C₂×Q₁₆×C₁₉	—	2	1	no	—
48	C₂×Q₁₆×C₁₉	D₄	1	2	yes	—
49	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
50	C₂×SD₁₆×C₁₉	—	2	1	no	—
51	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
52	C₁₉×#131	—	2	1	no	—
53	C₁₉×#131	—	2	1	no	—
54	C₁₉×#131	—	2	1	no	—
55	C₁₉×#131	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
59	C₂²×C₈×C₁₉	—	2	1	no	—
60	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	—	4	1	no	—
62	C₁₉×#124	—	4	1	no	—
63	C₁₉×#123	—	4	2	no	—
64	C₁₉×C₂²⋊Q₈	—	2	4	no	—
65	C₁₉×#117	—	2	1	no	—
66	C₁₉×Q₃₂	—	2	4	no	—
67	C₁₉×SD₃₂	—	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	D₄	1	2	yes	—
76	C₁₉×#107	—	2	1	no	—
77	C₁₉×#106	D₄	1	2	yes	—
78	C₁₉×#103	—	2	4	no	—
79	C₁₉×#101	—	2	2	no	—
80	C₁₉×#100	—	2	2	no	—
81	#41×C₁₉	—	2	1	no	—
82	#41×C₁₉	—	2	1	no	—
83	#41×C₁₉	—	2	1	no	—
84	#41×C₁₉	—	2	1	no	—
85	#41×C₁₉	—	4	1	no	—
86	#41×C₁₉	—	4	1	no	—
87	#41×C₁₉	—	4	1	no	—
88	#41×C₁₉	—	4	1	no	—
89	C₂×Q₈×C₁₉	—	2	2	no	—
90	C₂×Q₈×C₁₉	—	2	1	no	—
91	C₂×Q₈×C₁₉	—	4	1	no	—
92	C₂×Q₈×C₁₉	—	4	1	no	—
93	C₂×Q₈×C₁₉	—	4	1	no	—
94	C₂×Q₈×C₁₉	—	4	1	no	—
95	C₂×Q₈×C₁₉	—	4	1	no	—
96	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
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	1	yes	characteristic
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	Q₁₆×C₁₉	—	2	2	no	—
106	Q₁₆×C₁₉	—	2	1	no	—
107	Q₁₆×C₁₉	—	2	2	no	—
108	Q₁₆×C₁₉	—	2	1	no	—
109	Q₁₆×C₁₉	—	4	2	no	—
110	Q₁₆×C₁₉	—	4	1	no	—
111	Q₁₆×C₁₉	—	4	1	no	—
112	SD₁₆×C₁₉	—	4	2	no	—
113	SD₁₆×C₁₉	—	4	2	no	—
114	SD₁₆×C₁₉	—	4	1	no	—
115	SD₁₆×C₁₉	—	4	1	no	—
116	D₈×C₁₉	—	2	1	no	—
117	D₈×C₁₉	—	2	1	no	—
118	D₈×C₁₉	—	4	2	no	—
119	M₁₆×C₁₉	—	2	2	no	—
120	M₁₆×C₁₉	—	2	1	no	—
121	M₁₆×C₁₉	—	2	1	no	—
122	M₁₆×C₁₉	—	4	1	no	—
123	M₁₆×C₁₉	—	4	1	no	—
124	M₁₆×C₁₉	—	4	1	no	—
125	C₂×C₈×C₁₉	—	2	1	no	—
126	C₂×C₈×C₁₉	—	4	1	no	—
127	C₂×C₈×C₁₉	—	4	1	no	—
128	C₂×C₈×C₁₉	—	4	1	no	—
129	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	4	4	no	—
137	C₂²⋊C₄×C₁₉	—	4	4	no	—
138	C₂²⋊C₄×C₁₉	—	4	1	no	—
139	C₄²×C₁₉	—	4	1	no	—
140	C₁₆×C₁₉	—	2	2	no	—
141	C₁₆×C₁₉	—	4	1	no	—
142	#13311	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	AGL(1,ℤ/8)	1	1	yes	characteristic
146	Q₈×C₁₉	—	2	1	no	—
147	Q₈×C₁₉	—	2	1	no	—
148	Q₈×C₁₉	—	4	1	no	—
149	Q₈×C₁₉	—	4	2	no	—
150	Q₈×C₁₉	—	4	1	no	—
151	Q₈×C₁₉	—	4	2	no	—
152	Q₈×C₁₉	—	8	1	no	—
153	Q₈×C₁₉	—	8	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	1	no	—
159	D₄×C₁₉	—	4	1	no	—
160	D₄×C₁₉	—	8	1	no	—
161	D₄×C₁₉	—	8	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	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	—	8	1	no	—
169	C₂×C₄×C₁₉	—	8	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	#135	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	#120	1	1	yes	characteristic
181	C₈×C₁₉	#121	1	1	yes	characteristic
182	C₈×C₁₉	#121	1	1	yes	characteristic
183	C₈×C₁₉	#127	1	1	yes	characteristic
184	C₂×#510	C₂×C₁₉	1	1	yes	characteristic, complemented
185	#3067	C₂×C₁₉	1	1	yes	characteristic
186	#3059	C₂×C₁₉	1	1	yes	characteristic, complemented
187	C₂×#362	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#2145	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#2117	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#1389	C₂×C₁₉	1	1	yes	characteristic, complemented
191	C₂²×C₁₉	—	4	1	no	—
192	C₂²×C₁₉	—	4	2	no	—
193	C₂²×C₁₉	—	4	1	no	—
194	C₂²×C₁₉	—	8	1	no	—
195	C₂²×C₁₉	—	16	1	no	—
196	C₂²×C₁₉	#447	1	1	yes	characteristic
197	C₂²×C₁₉	#449	1	1	yes	characteristic
198	C₂²×C₁₉	#469	1	1	yes	characteristic
199	C₄×C₁₉	—	4	1	no	—
200	C₄×C₁₉	—	8	2	no	—
201	C₄×C₁₉	—	8	1	no	—
202	C₄×C₁₉	—	8	2	no	—
203	C₄×C₁₉	#392	1	1	yes	characteristic
204	C₄×C₁₉	#447	1	1	yes	characteristic
205	C₄×C₁₉	#449	1	1	yes	characteristic
206	C₄×C₁₉	#466	1	1	yes	characteristic
207	#575	—	2	1	no	—
208	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
209	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
210	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
211	#536	—	2	1	no	—
212	#510	—	2	2	no	—
213	#510	—	2	2	no	—
214	C₂×Q₃₂	—	2	1	no	—
215	C₂×SD₃₂	—	2	1	no	—
216	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
218	#473	—	2	1	no	—
219	#472	—	2	1	no	—
220	#471	—	2	2	no	—
221	#470	—	2	2	no	—
222	#467	—	2	2	no	—
223	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
224	#427	C₂²×C₁₉	1	1	yes	characteristic
225	#419	—	2	1	no	—
226	#413	—	2	1	no	—
227	#362	—	2	2	no	—
228	#360	—	2	2	no	—
229	#350	—	2	2	no	—
230	C₂×C₁₉	—	2	1	no	—
231	C₂×C₁₉	—	2	1	no	—
232	C₂×C₁₉	—	2	1	no	—
233	C₂×C₁₉	—	8	1	no	—
234	C₂×C₁₉	—	16	1	no	—
235	C₂×C₁₉	#1999	1	1	yes	characteristic
236	C₂×#41	—	2	1	no	—
237	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
238	C₂²×Q₈	—	2	1	no	—
239	#137	—	2	2	no	—
240	#137	—	4	1	no	—
241	AGL(1,ℤ/8)	—	2	2	no	—
242	AGL(1,ℤ/8)	—	4	1	no	—
243	#135	—	2	1	no	—
244	#135	—	2	1	no	—
245	#135	—	2	1	no	—
246	#135	—	2	1	no	—
247	#135	—	4	2	no	—
248	C₂×Q₁₆	—	2	1	no	—
249	C₂×Q₁₆	—	2	1	no	—
250	C₂×Q₁₆	—	2	1	no	—
251	C₂×Q₁₆	—	2	1	no	—
252	C₂×Q₁₆	—	2	1	no	—
253	C₂×Q₁₆	D₄×C₁₉	1	2	yes	—
254	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
255	C₂×SD₁₆	—	2	1	no	—
256	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
257	#131	—	2	1	no	—
258	#131	—	2	1	no	—
259	#131	—	2	1	no	—
260	#131	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	—	2	1	no	—
263	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
266	C₄⋊Q₈	—	4	1	no	—
267	#124	—	4	1	no	—
268	#123	—	4	2	no	—
269	C₂²⋊Q₈	—	2	4	no	—
270	#117	—	2	1	no	—
271	Q₃₂	—	2	4	no	—
272	SD₃₂	—	2	4	no	—
273	M₃₂	—	2	1	no	—
274	M₃₂	—	2	1	no	—
275	M₃₂	—	2	1	no	—
276	M₃₂	D₄×C₁₉	1	2	yes	—
277	C₂×C₁₆	—	2	1	no	—
278	C₂×C₁₆	—	2	1	no	—
279	#108	—	2	1	no	—
280	#108	D₄×C₁₉	1	2	yes	—
281	#107	—	2	1	no	—
282	#106	D₄×C₁₉	1	2	yes	—
283	#103	—	2	4	no	—
284	#101	—	2	2	no	—
285	#100	—	2	2	no	—
286	C₁₉	#13311	1	1	yes	characteristic, direct product factor, Sylow
287	#41	—	2	1	no	—
288	#41	—	2	1	no	—
289	#41	—	2	1	no	—
290	#41	—	2	1	no	—
291	#41	—	4	1	no	—
292	#41	—	4	1	no	—
293	#41	—	4	1	no	—
294	#41	—	4	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
311	Q₁₆	—	2	2	no	—
312	Q₁₆	—	2	1	no	—
313	Q₁₆	—	2	2	no	—
314	Q₁₆	—	2	1	no	—
315	Q₁₆	—	4	2	no	—
316	Q₁₆	—	4	1	no	—
317	Q₁₆	—	4	1	no	—
318	SD₁₆	—	4	2	no	—
319	SD₁₆	—	4	2	no	—
320	SD₁₆	—	4	1	no	—
321	SD₁₆	—	4	1	no	—
322	D₈	—	2	1	no	—
323	D₈	—	2	1	no	—
324	D₈	—	4	2	no	—
325	M₁₆	—	2	1	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	1	no	—
328	M₁₆	—	4	1	no	—
329	M₁₆	—	4	1	no	—
330	M₁₆	—	4	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
336	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
338	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
339	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
340	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₄²	—	4	1	no	—
346	C₁₆	—	2	2	no	—
347	C₁₆	—	4	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	4	1	no	—
350	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
351	Q₈	—	2	1	no	—
352	Q₈	—	2	1	no	—
353	Q₈	—	4	1	no	—
354	Q₈	—	4	2	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	4	2	no	—
357	Q₈	—	8	1	no	—
358	Q₈	—	8	1	no	—
359	D₄	—	2	1	no	—
360	D₄	—	2	1	no	—
361	D₄	—	4	1	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	1	no	—
364	D₄	—	4	1	no	—
365	D₄	—	8	1	no	—
366	D₄	—	8	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	8	1	no	—
374	C₂×C₄	—	8	1	no	—
375	C₂×C₄	—	8	1	no	—
376	C₂×C₄	—	8	1	no	—
377	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
378	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
379	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
380	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
381	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
382	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
383	C₈	—	4	1	no	—
384	C₈	—	4	2	no	—
385	C₈	C₁₉×#120	1	1	yes	characteristic
386	C₈	C₁₉×#121	1	1	yes	characteristic
387	C₈	C₁₉×#121	1	1	yes	characteristic
388	C₈	C₁₉×#127	1	1	yes	characteristic
389	C₂²	—	4	1	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	8	1	no	—
393	C₂²	—	16	1	no	—
394	C₂²	C₁₉×#447	1	1	yes	characteristic
395	C₂²	C₁₉×#449	1	1	yes	characteristic
396	C₂²	C₁₉×#469	1	1	yes	characteristic
397	C₄	—	4	1	no	—
398	C₄	—	8	2	no	—
399	C₄	—	8	1	no	—
400	C₄	—	8	2	no	—
401	C₄	C₁₉×#392	1	1	yes	characteristic
402	C₄	C₁₉×#447	1	1	yes	characteristic
403	C₄	C₁₉×#449	1	1	yes	characteristic
404	C₄	C₁₉×#466	1	1	yes	characteristic
405	C₂	—	2	1	no	—
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	8	1	no	—
409	C₂	—	16	1	no	—
410	C₂	C₁₉×#1999	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#1999
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₁₉×#3067	C₂
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×#510	C₂	semidirect
3. C₁₉×#3059	C₂	semidirect
4. C₂×C₁₉×#362	C₂	semidirect
5. C₁₉×#2145	C₂	semidirect
6. C₁₉×#2117	C₂	semidirect
7. C₁₉×#1389	C₂	semidirect
142. #13311	C₁₉	direct (N × H)
184. C₂×#510	C₂×C₁₉	semidirect
186. #3059	C₂×C₁₉	semidirect
187. C₂×#362	C₂×C₁₉	semidirect
188. #2145	C₂×C₁₉	semidirect
189. #2117	C₂×C₁₉	semidirect
190. #1389	C₂×C₁₉	semidirect
286. C₁₉	#13311	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×#510	2
C₁₉×#3067	2
C₁₉×#3059	2
C₂×C₁₉×#362	2
C₁₉×#2145	2
C₁₉×#2117	2
C₁₉×#1389	2
#13311	19

Subgroups — C19×#13311 #18019270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13311 #18019270