Subgroups — C₁₉×#33862 #18039821

Order 4864.

622 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3338	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2240	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2233	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2226	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2217	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2207	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2187	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₉×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#357	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₁₉	C₂²	1	2	yes	—
13	C₁₉×#554	—	2	1	no	—
14	D₄²×C₁₉	—	2	1	no	—
15	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×SD₃₂	C₂²	1	2	yes	complemented
17	C₂²×C₁₆×C₁₉	C₂²	1	2	yes	complemented
18	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
19	C₁₉×#493	C₂²	1	1	yes	characteristic
20	C₁₉×#484	—	2	2	no	—
21	C₁₉×#477	—	2	1	no	—
22	C₁₉×#467	C₂²	1	2	yes	complemented
23	C₁₉×#466	C₂²	1	2	yes	—
24	C₁₉×#459	—	2	1	no	—
25	C₁₉×#447	—	2	2	no	—
26	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
27	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
30	C₁₉×#367	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#367	C₂²	1	2	yes	complemented
32	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#358	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#357	C₂²	1	1	yes	characteristic
35	C₁₉×#357	C₂²	1	2	yes	—
36	C₁₉×#357	C₂²	1	2	yes	complemented
37	C₁₉×#357	C₂²	1	2	yes	complemented
38	C₁₉×#357	C₂²	1	2	yes	complemented
39	C₁₉×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
40	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
41	C₂²×D₄×C₁₉	—	2	2	no	—
42	C₂²×D₄×C₁₉	—	4	1	no	—
43	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×D₈×C₁₉	—	2	4	no	—
45	C₂×D₈×C₁₉	—	2	2	no	—
46	C₂×D₈×C₁₉	—	2	1	no	—
47	C₂×D₈×C₁₉	—	4	2	no	—
48	C₂×D₈×C₁₉	C₂³	1	2	yes	—
49	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×#127	—	2	1	no	—
53	C₁₉×#125	—	4	1	no	—
54	C₁₉×C₂²⋊Q₈	—	2	2	no	—
55	C₁₉×C₂²⋊Q₈	—	4	2	no	—
56	C₁₉×#121	—	2	2	no	—
57	C₁₉×#121	—	4	1	no	—
58	C₁₉×#120	—	4	2	no	—
59	C₄×Q₈×C₁₉	—	2	1	no	—
60	C₄×D₄×C₁₉	—	2	1	no	—
61	C₄×D₄×C₁₉	—	4	1	no	—
62	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₁₉×SD₃₂	—	2	2	no	—
65	C₁₉×SD₃₂	—	4	2	no	—
66	C₂×C₁₆×C₁₉	—	4	2	no	—
67	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₁₆×C₁₉	C₂³	1	2	yes	—
70	C₁₉×#107	—	2	2	no	—
71	C₁₉×#107	—	2	1	no	—
72	C₁₉×#107	C₂³	1	1	yes	characteristic
73	C₁₉×#107	C₂³	1	2	yes	—
74	C₁₉×#107	C₂³	1	1	yes	characteristic
75	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
76	C₁₉×#103	—	2	1	no	—
77	C₁₉×#103	—	2	2	no	—
78	C₁₉×#102	—	2	1	no	—
79	C₁₉×#102	—	2	2	no	—
80	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
81	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
82	C₂⁴×C₁₉	—	4	2	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	4	4	no	—
88	C₂×D₄×C₁₉	—	4	2	no	—
89	C₂×D₄×C₁₉	—	4	2	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	4	1	no	—
92	C₂×D₄×C₁₉	—	8	2	no	—
93	C₂×D₄×C₁₉	—	8	4	no	—
94	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
98	Q₁₆×C₁₉	—	2	1	no	—
99	Q₁₆×C₁₉	—	2	1	no	—
100	D₈×C₁₉	—	2	2	no	—
101	D₈×C₁₉	—	2	1	no	—
102	D₈×C₁₉	—	2	2	no	—
103	D₈×C₁₉	—	4	4	no	—
104	D₈×C₁₉	—	8	1	no	—
105	D₈×C₁₉	#41	1	2	yes	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
111	C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	4	2	no	—
115	C₄⋊C₄×C₁₉	—	4	1	no	—
116	C₄⋊C₄×C₁₉	—	4	1	no	—
117	C₄⋊C₄×C₁₉	—	4	2	no	—
118	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
119	C₂²⋊C₄×C₁₉	—	4	2	no	—
120	C₂²⋊C₄×C₁₉	—	4	1	no	—
121	C₂²⋊C₄×C₁₉	—	4	2	no	—
122	C₂²⋊C₄×C₁₉	D₈	1	2	yes	—
123	C₄²×C₁₉	—	4	1	no	—
124	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₁₆×C₁₉	—	2	1	no	—
126	C₁₆×C₁₉	—	2	1	no	—
127	C₁₆×C₁₉	—	2	2	no	—
128	#33862	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₁₉	—	4	1	no	—
130	C₂³×C₁₉	—	4	2	no	—
131	C₂³×C₁₉	—	8	4	no	—
132	C₂³×C₁₉	—	8	4	no	—
133	C₂³×C₁₉	—	16	2	no	—
134	C₂³×C₁₉	C₂×D₈	1	2	yes	—
135	Q₈×C₁₉	—	4	1	no	—
136	Q₈×C₁₉	—	4	1	no	—
137	Q₈×C₁₉	—	16	1	no	—
138	D₄×C₁₉	—	2	2	no	—
139	D₄×C₁₉	—	4	2	no	—
140	D₄×C₁₉	—	4	1	no	—
141	D₄×C₁₉	—	4	2	no	—
142	D₄×C₁₉	—	8	4	no	—
143	D₄×C₁₉	—	8	4	no	—
144	D₄×C₁₉	—	8	2	no	—
145	D₄×C₁₉	—	16	1	no	—
146	D₄×C₁₉	SD₃₂	1	4	yes	complemented
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	8	2	no	—
154	C₂×C₄×C₁₉	—	16	2	no	—
155	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
157	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
159	C₈×C₁₉	—	2	2	no	—
160	C₈×C₁₉	—	2	1	no	—
161	C₈×C₁₉	C₂×#41	1	1	yes	characteristic
162	C₈×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
163	#3338	C₂×C₁₉	1	1	yes	characteristic, complemented
164	D₄×D₈	C₂×C₁₉	1	1	yes	characteristic
165	#2240	C₂×C₁₉	1	1	yes	characteristic, complemented
166	#2233	C₂×C₁₉	1	2	yes	complemented
167	#2226	C₂×C₁₉	1	1	yes	characteristic, complemented
168	#2217	C₂×C₁₉	1	2	yes	complemented
169	#2207	C₂×C₁₉	1	1	yes	characteristic, complemented
170	#2187	C₂×C₁₉	1	2	yes	complemented
171	C₄×SD₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
172	D₄×C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
173	C₂×#357	C₂×C₁₉	1	2	yes	complemented
174	C₂²×C₁₉	—	2	2	no	—
175	C₂²×C₁₉	—	2	2	no	—
176	C₂²×C₁₉	—	4	2	no	—
177	C₂²×C₁₉	—	8	1	no	—
178	C₂²×C₁₉	—	8	1	no	—
179	C₂²×C₁₉	—	8	2	no	—
180	C₂²×C₁₉	—	8	2	no	—
181	C₂²×C₁₉	—	8	2	no	—
182	C₂²×C₁₉	—	16	8	no	—
183	C₂²×C₁₉	C₂×SD₃₂	1	4	yes	—
184	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
185	C₄×C₁₉	—	2	1	no	—
186	C₄×C₁₉	—	2	2	no	—
187	C₄×C₁₉	—	8	1	no	—
188	C₄×C₁₉	—	8	1	no	—
189	C₄×C₁₉	—	8	2	no	—
190	C₄×C₁₉	—	8	1	no	—
191	C₄×C₁₉	C₂×SD₃₂	1	2	yes	—
192	C₄×C₁₉	#546	1	1	yes	characteristic
193	C₄×C₁₉	#577	1	1	yes	characteristic
194	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
195	#554	—	2	1	no	—
196	D₄²	—	2	1	no	—
197	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
198	C₂×SD₃₂	C₂²×C₁₉	1	2	yes	complemented
199	C₂²×C₁₆	C₂²×C₁₉	1	2	yes	complemented
200	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
201	#493	C₂²×C₁₉	1	1	yes	characteristic
202	#484	—	2	2	no	—
203	#477	—	2	1	no	—
204	#467	C₂²×C₁₉	1	2	yes	complemented
205	#466	C₂²×C₁₉	1	2	yes	—
206	#459	—	2	1	no	—
207	#447	—	2	2	no	—
208	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
209	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
210	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
212	#367	C₂²×C₁₉	1	1	yes	characteristic, complemented
213	#367	C₂²×C₁₉	1	2	yes	complemented
214	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
215	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
216	#357	C₂²×C₁₉	1	1	yes	characteristic
217	#357	C₂²×C₁₉	1	2	yes	—
218	#357	C₂²×C₁₉	1	2	yes	complemented
219	#357	C₂²×C₁₉	1	2	yes	complemented
220	#357	C₂²×C₁₉	1	2	yes	complemented
221	C₂²⋊C₁₆	C₂²×C₁₉	1	2	yes	complemented
222	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
223	C₂×C₁₉	—	2	4	no	—
224	C₂×C₁₉	—	8	2	no	—
225	C₂×C₁₉	—	16	2	no	—
226	C₂×C₁₉	#3294	1	1	yes	characteristic
227	C₂×C₁₉	C₂²×SD₃₂	1	1	yes	characteristic
228	C₂×C₁₉	#3415	1	1	yes	characteristic
229	C₂²×D₄	—	2	2	no	—
230	C₂²×D₄	—	4	1	no	—
231	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
232	C₂×D₈	—	2	4	no	—
233	C₂×D₈	—	2	2	no	—
234	C₂×D₈	—	2	1	no	—
235	C₂×D₈	—	4	2	no	—
236	C₂×D₈	C₂³×C₁₉	1	2	yes	—
237	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
239	C₄⋊Q₈	—	2	1	no	—
240	#127	—	2	1	no	—
241	#125	—	4	1	no	—
242	C₂²⋊Q₈	—	2	2	no	—
243	C₂²⋊Q₈	—	4	2	no	—
244	#121	—	2	2	no	—
245	#121	—	4	1	no	—
246	#120	—	4	2	no	—
247	C₄×Q₈	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	4	1	no	—
250	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
251	C₂×C₄⋊C₄	—	2	2	no	—
252	SD₃₂	—	2	2	no	—
253	SD₃₂	—	4	2	no	—
254	C₂×C₁₆	—	4	2	no	—
255	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
256	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
257	C₂×C₁₆	C₂³×C₁₉	1	2	yes	—
258	#107	—	2	2	no	—
259	#107	—	2	1	no	—
260	#107	C₂³×C₁₉	1	1	yes	characteristic
261	#107	C₂³×C₁₉	1	2	yes	—
262	#107	C₂³×C₁₉	1	1	yes	characteristic
263	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
264	#103	—	2	1	no	—
265	#103	—	2	2	no	—
266	#102	—	2	1	no	—
267	#102	—	2	2	no	—
268	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
269	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
270	C₁₉	#33862	1	1	yes	characteristic, direct product factor, Sylow
271	C₂⁴	—	4	2	no	—
272	C₂×Q₈	—	2	1	no	—
273	C₂×Q₈	—	4	1	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	4	4	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	—	8	2	no	—
282	C₂×D₄	—	8	4	no	—
283	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
287	Q₁₆	—	2	1	no	—
288	Q₁₆	—	2	1	no	—
289	D₈	—	2	2	no	—
290	D₈	—	2	1	no	—
291	D₈	—	2	2	no	—
292	D₈	—	4	4	no	—
293	D₈	—	8	1	no	—
294	D₈	#41×C₁₉	1	2	yes	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
298	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
299	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
308	C₂²⋊C₄	—	4	2	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	D₈×C₁₉	1	2	yes	—
312	C₄²	—	4	1	no	—
313	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
314	C₁₆	—	2	1	no	—
315	C₁₆	—	2	1	no	—
316	C₁₆	—	2	2	no	—
317	C₂³	—	4	1	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	8	4	no	—
320	C₂³	—	8	4	no	—
321	C₂³	—	16	2	no	—
322	C₂³	C₂×D₈×C₁₉	1	2	yes	—
323	Q₈	—	4	1	no	—
324	Q₈	—	4	1	no	—
325	Q₈	—	16	1	no	—
326	D₄	—	2	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	1	no	—
329	D₄	—	4	2	no	—
330	D₄	—	8	4	no	—
331	D₄	—	8	4	no	—
332	D₄	—	8	2	no	—
333	D₄	—	16	1	no	—
334	D₄	C₁₉×SD₃₂	1	4	yes	complemented
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	8	2	no	—
342	C₂×C₄	—	16	2	no	—
343	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
344	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
345	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
346	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
347	C₈	—	2	2	no	—
348	C₈	—	2	1	no	—
349	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
350	C₈	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂²	—	2	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	8	1	no	—
355	C₂²	—	8	1	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	16	8	no	—
360	C₂²	C₂×C₁₉×SD₃₂	1	4	yes	—
361	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	2	1	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	1	no	—
366	C₄	—	8	1	no	—
367	C₄	—	8	2	no	—
368	C₄	C₂×C₁₉×SD₃₂	1	2	yes	—
369	C₄	C₁₉×#546	1	1	yes	characteristic
370	C₄	C₁₉×#577	1	1	yes	characteristic
371	C₂	—	2	4	no	—
372	C₂	—	8	2	no	—
373	C₂	—	16	2	no	—
374	C₂	C₁₉×#3294	1	1	yes	characteristic
375	C₂	C₂²×C₁₉×SD₃₂	1	1	yes	characteristic
376	C₂	C₁₉×#3415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	D₄×D₈×C₁₉	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×D₄×C₁₉ ◁ C₈×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3338	C₂	semidirect
3. C₁₉×#2240	C₂	semidirect
4. C₁₉×#2233	C₂	semidirect
5. C₁₉×#2226	C₂	semidirect
6. C₁₉×#2217	C₂	semidirect
7. C₁₉×#2207	C₂	semidirect
8. C₁₉×#2187	C₂	semidirect
9. C₄×C₁₉×SD₃₂	C₂	semidirect
10. D₄×C₁₆×C₁₉	C₂	semidirect
11. C₂×C₁₉×#357	C₂	semidirect
16. C₂×C₁₉×SD₃₂	C₂²	semidirect
17. C₂²×C₁₆×C₁₉	C₂²	semidirect
18. C₁₉×#500	C₂²	semidirect
22. C₁₉×#467	C₂²	semidirect
26. C₄×Q₁₆×C₁₉	C₂²	semidirect
29. C₂×C₁₉×#107	C₂²	semidirect
30. C₁₉×#367	C₂²	semidirect
31. C₁₉×#367	C₂²	semidirect
32. C₁₉×C₄⋊C₁₆	C₂²	semidirect
33. C₁₉×#358	C₂²	semidirect
36. C₁₉×#357	C₂²	semidirect
37. C₁₉×#357	C₂²	semidirect
38. C₁₉×#357	C₂²	semidirect
39. C₁₉×C₂²⋊C₁₆	C₂²	semidirect
40. C₄×C₁₆×C₁₉	C₂²	semidirect
128. #33862	C₁₉	direct (N × H)
146. D₄×C₁₉	SD₃₂	semidirect
163. #3338	C₂×C₁₉	semidirect
165. #2240	C₂×C₁₉	semidirect
166. #2233	C₂×C₁₉	semidirect
167. #2226	C₂×C₁₉	semidirect
168. #2217	C₂×C₁₉	semidirect
169. #2207	C₂×C₁₉	semidirect
170. #2187	C₂×C₁₉	semidirect
171. C₄×SD₃₂	C₂×C₁₉	semidirect
172. D₄×C₁₆	C₂×C₁₉	semidirect
173. C₂×#357	C₂×C₁₉	semidirect
198. C₂×SD₃₂	C₂²×C₁₉	semidirect
199. C₂²×C₁₆	C₂²×C₁₉	semidirect
200. #500	C₂²×C₁₉	semidirect
204. #467	C₂²×C₁₉	semidirect
208. C₄×Q₁₆	C₂²×C₁₉	semidirect
211. C₂×#107	C₂²×C₁₉	semidirect
212. #367	C₂²×C₁₉	semidirect
213. #367	C₂²×C₁₉	semidirect
214. C₄⋊C₁₆	C₂²×C₁₉	semidirect
215. #358	C₂²×C₁₉	semidirect
218. #357	C₂²×C₁₉	semidirect
219. #357	C₂²×C₁₉	semidirect
220. #357	C₂²×C₁₉	semidirect
221. C₂²⋊C₁₆	C₂²×C₁₉	semidirect
222. C₄×C₁₆	C₂²×C₁₉	semidirect
270. C₁₉	#33862	direct (N × H)
334. D₄	C₁₉×SD₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3338	2
D₄×D₈×C₁₉	2
C₁₉×#2240	2
C₁₉×#2233	2
C₁₉×#2226	2
C₁₉×#2217	2
C₁₉×#2207	2
C₁₉×#2187	2
C₄×C₁₉×SD₃₂	2
D₄×C₁₆×C₁₉	2
C₂×C₁₉×#357	2
#33862	19

Subgroups — C19×#33862 #18039821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33862 #18039821