Subgroups — C₁₉×#13336 #18019295

Order 4864.

586 conjugacy classes of subgroups.

The subgroup lattice has 414 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	C₂²×C₁₉×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3155	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#361	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#359	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1978	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1379	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
9	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
10	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#535	—	2	1	no	—
13	C₁₉×#509	—	2	2	no	—
14	C₁₉×#509	—	2	2	no	—
15	C₂×C₁₉×SD₃₂	—	2	1	no	—
16	C₂×C₁₉×D₁₆	—	2	2	no	—
17	C₂×C₁₉×D₁₆	—	2	2	no	—
18	C₂×C₁₉×D₁₆	—	2	1	no	—
19	C₂×C₁₉×D₁₆	—	2	2	no	—
20	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
21	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#496	—	2	2	no	—
23	C₁₉×#495	—	2	1	no	—
24	C₁₉×#493	—	2	1	no	—
25	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
26	C₁₉×#418	—	2	1	no	—
27	C₂×C₁₉×#100	—	2	1	no	—
28	C₁₉×#405	C₂²	1	1	yes	characteristic
29	C₁₉×#361	—	2	2	no	—
30	C₁₉×#359	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
35	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
36	C₁₉×#135	—	2	1	no	—
37	C₁₉×#135	—	2	1	no	—
38	C₁₉×#135	—	2	1	no	—
39	C₁₉×#135	—	2	1	no	—
40	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
41	C₂×SD₁₆×C₁₉	—	2	2	no	—
42	C₂×SD₁₆×C₁₉	—	2	1	no	—
43	C₂×D₈×C₁₉	—	2	2	no	—
44	C₂×D₈×C₁₉	—	2	1	no	—
45	C₂×D₈×C₁₉	—	2	1	no	—
46	C₂×D₈×C₁₉	—	2	1	no	—
47	C₂×D₈×C₁₉	—	2	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	—	2	1	no	—
54	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
55	C₂×D₈×C₁₉	D₄	1	2	yes	—
56	C₂×D₈×C₁₉	D₄	1	2	yes	complemented
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
59	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₁₉×#127	—	2	2	no	—
61	C₁₉×#124	—	2	2	no	—
62	C₁₉×#121	—	4	2	no	—
63	C₁₉×#120	—	4	2	no	—
64	C₁₉×#117	D₄	1	1	yes	characteristic
65	C₁₉×SD₃₂	—	2	4	no	—
66	C₁₉×D₁₆	—	2	8	no	—
67	C₁₉×D₁₆	—	2	4	no	—
68	C₁₉×M₃₂	—	2	1	no	—
69	C₁₉×M₃₂	D₄	1	2	yes	complemented
70	C₂×C₁₆×C₁₉	—	2	1	no	—
71	C₂×C₁₆×C₁₉	—	2	1	no	—
72	C₂×C₁₆×C₁₉	—	2	1	no	—
73	C₂×C₁₆×C₁₉	D₄	1	2	yes	complemented
74	C₁₉×#108	—	2	1	no	—
75	C₁₉×#108	—	2	1	no	—
76	C₁₉×#102	—	4	2	no	—
77	C₁₉×#100	—	4	2	no	—
78	C₁₉×#97	—	2	1	no	—
79	C₄×C₈×C₁₉	—	2	1	no	—
80	C₂⁴×C₁₉	—	4	1	no	—
81	C₂⁴×C₁₉	—	4	1	no	—
82	#41×C₁₉	—	4	1	no	—
83	#41×C₁₉	—	4	1	no	—
84	#41×C₁₉	—	4	1	no	—
85	#41×C₁₉	—	4	1	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	2	1	no	—
89	C₂×D₄×C₁₉	—	2	2	no	—
90	C₂×D₄×C₁₉	—	4	4	no	—
91	C₂×D₄×C₁₉	—	4	1	no	—
92	C₂×D₄×C₁₉	—	4	1	no	—
93	C₂×D₄×C₁₉	—	4	1	no	—
94	C₂×D₄×C₁₉	—	4	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	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	Q₁₆×C₁₉	—	2	1	no	—
105	Q₁₆×C₁₉	—	2	1	no	—
106	SD₁₆×C₁₉	—	4	4	no	—
107	SD₁₆×C₁₉	—	4	1	no	—
108	SD₁₆×C₁₉	—	4	1	no	—
109	D₈×C₁₉	—	2	2	no	—
110	D₈×C₁₉	—	2	2	no	—
111	D₈×C₁₉	—	2	2	no	—
112	D₈×C₁₉	—	2	1	no	—
113	D₈×C₁₉	—	2	2	no	—
114	D₈×C₁₉	—	2	1	no	—
115	D₈×C₁₉	—	4	4	no	—
116	D₈×C₁₉	—	4	1	no	—
117	D₈×C₁₉	—	4	1	no	—
118	D₈×C₁₉	—	4	1	no	—
119	D₈×C₁₉	—	4	1	no	—
120	M₁₆×C₁₉	—	2	1	no	—
121	M₁₆×C₁₉	—	4	1	no	—
122	M₁₆×C₁₉	—	4	1	no	—
123	M₁₆×C₁₉	D₈	1	2	yes	—
124	C₂×C₈×C₁₉	—	2	1	no	—
125	C₂×C₈×C₁₉	—	4	1	no	—
126	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
132	C₄⋊C₄×C₁₉	D₈	1	2	yes	—
133	C₂²⋊C₄×C₁₉	—	2	1	no	—
134	C₂²⋊C₄×C₁₉	—	4	4	no	—
135	C₄²×C₁₉	—	2	1	no	—
136	C₁₆×C₁₉	—	2	2	no	—
137	C₁₆×C₁₉	—	2	2	no	—
138	#13336	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	—	8	1	no	—
143	C₂³×C₁₉	—	8	1	no	—
144	C₂³×C₁₉	—	8	1	no	—
145	C₂³×C₁₉	—	8	1	no	—
146	C₂³×C₁₉	—	16	2	no	—
147	C₂³×C₁₉	—	16	2	no	—
148	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
149	Q₈×C₁₉	—	4	1	no	—
150	Q₈×C₁₉	—	4	1	no	—
151	D₄×C₁₉	—	4	2	no	—
152	D₄×C₁₉	—	4	2	no	—
153	D₄×C₁₉	—	4	1	no	—
154	D₄×C₁₉	—	4	1	no	—
155	D₄×C₁₉	—	4	2	no	—
156	D₄×C₁₉	—	4	2	no	—
157	D₄×C₁₉	—	8	1	no	—
158	D₄×C₁₉	—	8	1	no	—
159	D₄×C₁₉	—	8	1	no	—
160	D₄×C₁₉	—	8	1	no	—
161	D₄×C₁₉	—	8	1	no	—
162	D₄×C₁₉	—	8	1	no	—
163	D₄×C₁₉	—	16	4	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	8	1	no	—
167	C₂×C₄×C₁₉	—	8	1	no	—
168	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₈×C₁₉	—	2	2	no	—
175	C₈×C₁₉	—	8	1	no	—
176	C₈×C₁₉	#120	1	1	yes	characteristic
177	C₈×C₁₉	#120	1	1	yes	characteristic
178	C₈×C₁₉	#121	1	1	yes	characteristic
179	C₈×C₁₉	#121	1	1	yes	characteristic
180	C₂×#509	C₂×C₁₉	1	1	yes	characteristic, complemented
181	C₂²×D₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
182	#3155	C₂×C₁₉	1	1	yes	characteristic, complemented
183	C₂×#361	C₂×C₁₉	1	1	yes	characteristic, complemented
184	C₂×#359	C₂×C₁₉	1	1	yes	characteristic, complemented
185	#1978	C₂×C₁₉	1	1	yes	characteristic, complemented
186	#1379	C₂×C₁₉	1	1	yes	characteristic, complemented
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	8	2	no	—
189	C₂²×C₁₉	—	8	4	no	—
190	C₂²×C₁₉	—	8	1	no	—
191	C₂²×C₁₉	—	8	2	no	—
192	C₂²×C₁₉	—	8	2	no	—
193	C₂²×C₁₉	—	16	2	no	—
194	C₂²×C₁₉	—	16	2	no	—
195	C₂²×C₁₉	—	16	2	no	—
196	C₂²×C₁₉	—	16	2	no	—
197	C₂²×C₁₉	—	16	2	no	—
198	C₂²×C₁₉	#447	1	1	yes	characteristic
199	C₂²×C₁₉	#459	1	1	yes	characteristic
200	C₂²×C₁₉	#496	1	1	yes	characteristic
201	C₄×C₁₉	—	4	2	no	—
202	C₄×C₁₉	—	8	1	no	—
203	C₄×C₁₉	#392	1	1	yes	characteristic
204	C₄×C₁₉	#447	1	1	yes	characteristic
205	C₄×C₁₉	#459	1	1	yes	characteristic
206	C₄×C₁₉	#493	1	1	yes	characteristic
207	C₂×AGL(1,ℤ/8)	—	2	1	no	—
208	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
209	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
210	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
211	#535	—	2	1	no	—
212	#509	—	2	2	no	—
213	#509	—	2	2	no	—
214	C₂×SD₃₂	—	2	1	no	—
215	C₂×D₁₆	—	2	2	no	—
216	C₂×D₁₆	—	2	1	no	—
217	C₂×D₁₆	—	2	2	no	—
218	C₂×D₁₆	—	2	2	no	—
219	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
220	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
221	#496	—	2	2	no	—
222	#495	—	2	1	no	—
223	#493	—	2	1	no	—
224	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
225	#418	—	2	1	no	—
226	C₂×#100	—	2	1	no	—
227	#405	C₂²×C₁₉	1	1	yes	characteristic
228	#361	—	2	2	no	—
229	#359	—	2	2	no	—
230	C₂×C₁₉	—	2	1	no	—
231	C₂×C₁₉	—	2	1	no	—
232	C₂×C₁₉	—	16	1	no	—
233	C₂×C₁₉	—	16	2	no	—
234	C₂×C₁₉	—	16	2	no	—
235	C₂×C₁₉	#2011	1	1	yes	characteristic
236	C₂×C₁₉	#2192	1	2	yes	—
237	C₂×#41	—	2	1	no	—
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	AGL(1,ℤ/8)	—	4	2	no	—
241	AGL(1,ℤ/8)	—	4	2	no	—
242	#135	—	2	1	no	—
243	#135	—	2	1	no	—
244	#135	—	2	1	no	—
245	#135	—	2	1	no	—
246	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
247	C₂×SD₁₆	—	2	2	no	—
248	C₂×SD₁₆	—	2	1	no	—
249	C₂×D₈	—	2	2	no	—
250	C₂×D₈	—	2	1	no	—
251	C₂×D₈	—	2	1	no	—
252	C₂×D₈	—	2	1	no	—
253	C₂×D₈	—	2	1	no	—
254	C₂×D₈	—	2	1	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	—	2	1	no	—
259	C₂×D₈	—	2	1	no	—
260	C₂×D₈	D₄×C₁₉	1	2	yes	—
261	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
262	C₂×D₈	D₄×C₁₉	1	2	yes	complemented
263	C₂×M₁₆	—	2	1	no	—
264	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
266	#127	—	2	2	no	—
267	#124	—	2	2	no	—
268	#121	—	4	2	no	—
269	#120	—	4	2	no	—
270	#117	D₄×C₁₉	1	1	yes	characteristic
271	SD₃₂	—	2	4	no	—
272	D₁₆	—	2	8	no	—
273	D₁₆	—	2	4	no	—
274	M₃₂	—	2	1	no	—
275	M₃₂	D₄×C₁₉	1	2	yes	complemented
276	C₂×C₁₆	—	2	1	no	—
277	C₂×C₁₆	—	2	1	no	—
278	C₂×C₁₆	—	2	1	no	—
279	C₂×C₁₆	D₄×C₁₉	1	2	yes	complemented
280	#108	—	2	1	no	—
281	#108	—	2	1	no	—
282	#102	—	4	2	no	—
283	#100	—	4	2	no	—
284	#97	—	2	1	no	—
285	C₄×C₈	—	2	1	no	—
286	C₁₉	#13336	1	1	yes	characteristic, direct product factor, Sylow
287	C₂⁴	—	4	1	no	—
288	C₂⁴	—	4	1	no	—
289	#41	—	4	1	no	—
290	#41	—	4	1	no	—
291	#41	—	4	1	no	—
292	#41	—	4	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	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	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
311	Q₁₆	—	2	1	no	—
312	Q₁₆	—	2	1	no	—
313	SD₁₆	—	4	4	no	—
314	SD₁₆	—	4	1	no	—
315	SD₁₆	—	4	1	no	—
316	D₈	—	2	2	no	—
317	D₈	—	2	2	no	—
318	D₈	—	2	1	no	—
319	D₈	—	2	2	no	—
320	D₈	—	2	2	no	—
321	D₈	—	2	1	no	—
322	D₈	—	4	4	no	—
323	D₈	—	4	1	no	—
324	D₈	—	4	1	no	—
325	D₈	—	4	1	no	—
326	D₈	—	4	1	no	—
327	M₁₆	—	2	1	no	—
328	M₁₆	—	4	1	no	—
329	M₁₆	—	4	1	no	—
330	M₁₆	D₈×C₁₉	1	2	yes	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
334	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	#41×C₁₉	1	1	yes	characteristic
339	C₄⋊C₄	D₈×C₁₉	1	2	yes	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₄²	—	2	1	no	—
343	C₁₆	—	2	2	no	—
344	C₁₆	—	2	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	8	1	no	—
350	C₂³	—	8	1	no	—
351	C₂³	—	8	1	no	—
352	C₂³	—	16	2	no	—
353	C₂³	—	16	2	no	—
354	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
355	Q₈	—	4	1	no	—
356	Q₈	—	4	1	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	8	1	no	—
364	D₄	—	8	1	no	—
365	D₄	—	8	1	no	—
366	D₄	—	8	1	no	—
367	D₄	—	8	1	no	—
368	D₄	—	8	1	no	—
369	D₄	—	16	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	8	1	no	—
373	C₂×C₄	—	8	1	no	—
374	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
375	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
376	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
377	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
378	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
379	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
380	C₈	—	2	2	no	—
381	C₈	—	8	1	no	—
382	C₈	C₁₉×#120	1	1	yes	characteristic
383	C₈	C₁₉×#120	1	1	yes	characteristic
384	C₈	C₁₉×#121	1	1	yes	characteristic
385	C₈	C₁₉×#121	1	1	yes	characteristic
386	C₂²	—	2	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	4	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	16	2	no	—
393	C₂²	—	16	2	no	—
394	C₂²	—	16	2	no	—
395	C₂²	—	16	2	no	—
396	C₂²	—	16	2	no	—
397	C₂²	C₁₉×#447	1	1	yes	characteristic
398	C₂²	C₁₉×#459	1	1	yes	characteristic
399	C₂²	C₁₉×#496	1	1	yes	characteristic
400	C₄	—	4	2	no	—
401	C₄	—	8	1	no	—
402	C₄	C₁₉×#392	1	1	yes	characteristic
403	C₄	C₁₉×#447	1	1	yes	characteristic
404	C₄	C₁₉×#459	1	1	yes	characteristic
405	C₄	C₁₉×#493	1	1	yes	characteristic
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	16	2	no	—
409	C₂	—	16	1	no	—
410	C₂	—	16	2	no	—
411	C₂	C₁₉×#2011	1	1	yes	characteristic
412	C₂	C₁₉×#2192	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#509	C₂	semidirect
2. C₂²×C₁₉×D₁₆	C₂	semidirect
3. C₁₉×#3155	C₂	semidirect
4. C₂×C₁₉×#361	C₂	semidirect
5. C₂×C₁₉×#359	C₂	semidirect
6. C₁₉×#1978	C₂	semidirect
7. C₁₉×#1379	C₂	semidirect
56. C₂×D₈×C₁₉	D₄	semidirect
69. C₁₉×M₃₂	D₄	semidirect
73. C₂×C₁₆×C₁₉	D₄	semidirect
138. #13336	C₁₉	direct (N × H)
180. C₂×#509	C₂×C₁₉	semidirect
181. C₂²×D₁₆	C₂×C₁₉	semidirect
182. #3155	C₂×C₁₉	semidirect
183. C₂×#361	C₂×C₁₉	semidirect
184. C₂×#359	C₂×C₁₉	semidirect
185. #1978	C₂×C₁₉	semidirect
186. #1379	C₂×C₁₉	semidirect
262. C₂×D₈	D₄×C₁₉	semidirect
275. M₃₂	D₄×C₁₉	semidirect
279. C₂×C₁₆	D₄×C₁₉	semidirect
286. C₁₉	#13336	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
C₂²×C₁₉×D₁₆	2
C₁₉×#3155	2
C₂×C₁₉×#361	2
C₂×C₁₉×#359	2
C₁₉×#1978	2
C₁₉×#1379	2
#13336	19

Subgroups — C19×#13336 #18019295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13336 #18019295