Subgroups — C₁₉×#21171 #18027130

Order 4864.

1110 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#428	C₂	1	2	yes	maximal
2	C₂×C₁₉×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#384	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1948	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1947	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1736	C₂	1	2	yes	maximal
8	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
9	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₉	—	2	2	no	—
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#428	—	2	8	no	—
15	C₂×C₁₉×#107	C₂²	1	4	yes	—
16	C₂×C₁₉×#106	C₂²	1	4	yes	—
17	C₁₉×#423	C₄	1	8	yes	complemented
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
19	C₁₉×#384	—	2	1	no	—
20	C₁₉×#384	—	2	1	no	—
21	C₁₉×#384	C₂²	1	4	yes	—
22	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
25	C₁₉×#376	—	2	1	no	—
26	C₄³×C₁₉	—	2	1	no	—
27	C₁₉×#340	C₂²	1	8	yes	—
28	C₂³×C₄×C₁₉	—	2	2	no	—
29	C₂³×C₄×C₁₉	D₄	1	2	yes	—
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×M₁₆×C₁₉	—	2	4	no	—
32	C₂×M₁₆×C₁₉	—	2	4	no	—
33	C₂×M₁₆×C₁₉	C₂×C₄	1	8	yes	—
34	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
35	C₁₉×#117	—	2	2	no	—
36	C₁₉×#117	—	2	2	no	—
37	C₁₉×#117	D₄	1	4	yes	—
38	C₁₉×#117	Q₈	1	4	yes	—
39	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₉	—	4	8	no	—
45	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	—	2	1	no	—
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	—	2	2	no	—
54	C₂×C₄²×C₁₉	—	2	2	no	—
55	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
56	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₉	Q₈	1	4	yes	—
59	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
60	C₁₉×#107	—	2	8	no	—
61	C₁₉×#106	—	2	8	no	—
62	C₁₉×C₄⋊C₈	C₂×C₄	1	16	yes	complemented
63	C₁₉×#95	—	2	2	no	—
64	C₁₉×#95	—	2	2	no	—
65	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	—	2	4	no	—
67	C₂²×C₄×C₁₉	—	2	4	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	—	2	4	no	—
72	C₂²×C₄×C₁₉	—	4	8	no	—
73	C₂²×C₄×C₁₉	—	4	4	no	—
74	C₂²×C₄×C₁₉	C₄⋊C₄	1	8	yes	—
75	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
80	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
81	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₁₉	#41	1	2	yes	—
83	C₂²×C₄×C₁₉	#41	1	2	yes	—
84	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
85	M₁₆×C₁₉	—	2	16	no	—
86	C₂×C₈×C₁₉	—	2	4	no	—
87	C₂×C₈×C₁₉	—	2	4	no	—
88	C₂×C₈×C₁₉	C₂²×C₄	1	8	yes	—
89	C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₄⋊C₄×C₁₉	—	2	2	no	—
92	C₄⋊C₄×C₁₉	—	2	4	no	—
93	C₄⋊C₄×C₁₉	—	2	4	no	—
94	C₄⋊C₄×C₁₉	—	4	8	no	—
95	C₄⋊C₄×C₁₉	—	4	4	no	—
96	C₄⋊C₄×C₁₉	—	4	8	no	—
97	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
98	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
99	C₄⋊C₄×C₁₉	C₂×Q₈	1	4	yes	—
100	C₂²⋊C₄×C₁₉	—	2	4	no	—
101	C₂²⋊C₄×C₁₉	—	2	4	no	—
102	C₄²×C₁₉	—	2	4	no	—
103	C₄²×C₁₉	—	2	4	no	—
104	C₄²×C₁₉	—	4	4	no	—
105	C₄²×C₁₉	—	4	4	no	—
106	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
107	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
108	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
109	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
110	#21171	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂³×C₁₉	—	2	2	no	—
112	C₂³×C₁₉	—	2	2	no	—
113	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
114	C₂³×C₁₉	#121	1	2	yes	—
115	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
116	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
117	C₂×C₄×C₁₉	—	2	2	no	—
118	C₂×C₄×C₁₉	—	2	2	no	—
119	C₂×C₄×C₁₉	—	2	16	no	—
120	C₂×C₄×C₁₉	—	2	2	no	—
121	C₂×C₄×C₁₉	—	2	2	no	—
122	C₂×C₄×C₁₉	—	2	4	no	—
123	C₂×C₄×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	—	4	2	no	—
125	C₂×C₄×C₁₉	—	4	2	no	—
126	C₂×C₄×C₁₉	—	4	2	no	—
127	C₂×C₄×C₁₉	—	4	4	no	—
128	C₂×C₄×C₁₉	—	4	8	no	—
129	C₂×C₄×C₁₉	—	8	8	no	—
130	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
131	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
132	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
133	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
134	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
135	C₂×C₄×C₁₉	#121	1	2	yes	—
136	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
137	C₂×C₄×C₁₉	#125	1	4	yes	—
138	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
139	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
140	C₂×C₄×C₁₉	#137	1	4	yes	—
141	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
147	C₈×C₁₉	—	2	8	no	—
148	C₂×#428	C₂×C₁₉	1	2	yes	—
149	C₂×#423	C₂×C₁₉	1	1	yes	characteristic
150	C₂×#384	C₂×C₁₉	1	1	yes	characteristic
151	C₄×#117	C₂×C₁₉	1	1	yes	characteristic
152	#1948	C₂×C₁₉	1	4	yes	complemented
153	#1947	C₂×C₁₉	1	4	yes	complemented
154	#1736	C₂×C₁₉	1	2	yes	—
155	C₂²×C₁₉	—	2	4	no	—
156	C₂²×C₁₉	—	2	4	no	—
157	C₂²×C₁₉	—	2	2	no	—
158	C₂²×C₁₉	—	2	2	no	—
159	C₂²×C₁₉	#389	1	4	yes	—
160	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
161	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
162	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
163	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
164	C₂²×C₁₉	C₂×#137	1	2	yes	—
165	C₄×C₁₉	—	2	4	no	—
166	C₄×C₁₉	—	4	4	no	—
167	C₄×C₁₉	—	4	2	no	—
168	C₄×C₁₉	—	4	2	no	—
169	C₄×C₁₉	—	8	4	no	—
170	C₄×C₁₉	#389	1	4	yes	—
171	C₄×C₁₉	#428	1	8	yes	complemented
172	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
173	C₄×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
174	C₄×C₁₉	C₂×#125	1	1	yes	characteristic
175	C₄×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
176	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
177	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
178	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
179	C₂²×C₄⋊C₄	—	2	2	no	—
180	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
181	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
182	#428	—	2	8	no	—
183	C₂×#107	C₂²×C₁₉	1	4	yes	—
184	C₂×#106	C₂²×C₁₉	1	4	yes	—
185	#423	C₄×C₁₉	1	8	yes	complemented
186	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	—
187	#384	—	2	1	no	—
188	#384	—	2	1	no	—
189	#384	C₂²×C₁₉	1	4	yes	—
190	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
191	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
192	C₄×C₂²⋊C₄	—	2	2	no	—
193	#376	—	2	1	no	—
194	C₄³	—	2	1	no	—
195	#340	C₂²×C₁₉	1	8	yes	—
196	C₂×C₁₉	—	2	4	no	—
197	C₂×C₁₉	C₂×#389	1	1	yes	characteristic
198	C₂×C₁₉	C₂×#428	1	2	yes	—
199	C₂×C₁₉	#3038	1	1	yes	characteristic
200	C₂×C₁₉	#3039	1	1	yes	characteristic
201	C₂×C₁₉	#3079	1	2	yes	—
202	C₂³×C₄	—	2	2	no	—
203	C₂³×C₄	D₄×C₁₉	1	2	yes	—
204	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
205	C₂×M₁₆	—	2	4	no	—
206	C₂×M₁₆	—	2	4	no	—
207	C₂×M₁₆	C₂×C₄×C₁₉	1	8	yes	—
208	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
209	#117	—	2	2	no	—
210	#117	—	2	2	no	—
211	#117	D₄×C₁₉	1	4	yes	—
212	#117	Q₈×C₁₉	1	4	yes	—
213	C₂×C₄⋊C₄	—	2	4	no	—
214	C₂×C₄⋊C₄	—	2	4	no	—
215	C₂×C₄⋊C₄	—	2	4	no	—
216	C₂×C₄⋊C₄	—	2	4	no	—
217	C₂×C₄⋊C₄	—	2	2	no	—
218	C₂×C₄⋊C₄	—	4	8	no	—
219	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
220	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
221	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
222	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
223	C₂×C₂²⋊C₄	—	2	1	no	—
224	C₂×C₂²⋊C₄	—	2	1	no	—
225	C₂×C₄²	—	2	1	no	—
226	C₂×C₄²	—	2	1	no	—
227	C₂×C₄²	—	2	2	no	—
228	C₂×C₄²	—	2	2	no	—
229	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
230	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
231	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
232	C₂×C₄²	Q₈×C₁₉	1	4	yes	—
233	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
234	#107	—	2	8	no	—
235	#106	—	2	8	no	—
236	C₄⋊C₈	C₂×C₄×C₁₉	1	16	yes	complemented
237	#95	—	2	2	no	—
238	#95	—	2	2	no	—
239	C₁₉	#21171	1	1	yes	characteristic, direct product factor, Sylow
240	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	2	4	no	—
243	C₂²×C₄	—	2	1	no	—
244	C₂²×C₄	—	2	1	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	4	8	no	—
248	C₂²×C₄	—	4	4	no	—
249	C₂²×C₄	C₄⋊C₄×C₁₉	1	8	yes	—
250	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
251	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
252	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
253	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
254	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
255	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
256	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
257	C₂²×C₄	#41×C₁₉	1	2	yes	—
258	C₂²×C₄	#41×C₁₉	1	2	yes	—
259	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
260	M₁₆	—	2	16	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	C₂²×C₄×C₁₉	1	8	yes	—
264	C₄⋊C₄	—	2	1	no	—
265	C₄⋊C₄	—	2	1	no	—
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	—	2	4	no	—
268	C₄⋊C₄	—	2	4	no	—
269	C₄⋊C₄	—	4	8	no	—
270	C₄⋊C₄	—	4	4	no	—
271	C₄⋊C₄	—	4	8	no	—
272	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
273	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
274	C₄⋊C₄	C₂×Q₈×C₁₉	1	4	yes	—
275	C₂²⋊C₄	—	2	4	no	—
276	C₂²⋊C₄	—	2	4	no	—
277	C₄²	—	2	4	no	—
278	C₄²	—	2	4	no	—
279	C₄²	—	4	4	no	—
280	C₄²	—	4	4	no	—
281	C₄²	C₄⋊C₄×C₁₉	1	4	yes	—
282	C₄²	C₄⋊C₄×C₁₉	1	4	yes	—
283	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
284	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	2	no	—
287	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
288	C₂³	C₁₉×#121	1	2	yes	—
289	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
290	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	16	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	4	2	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	—	4	8	no	—
303	C₂×C₄	—	8	8	no	—
304	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
305	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
306	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
307	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
308	C₂×C₄	C₄×Q₈×C₁₉	1	4	yes	—
309	C₂×C₄	C₁₉×#121	1	2	yes	—
310	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
311	C₂×C₄	C₁₉×#125	1	4	yes	—
312	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
313	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
314	C₂×C₄	C₁₉×#137	1	4	yes	—
315	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
316	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
317	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
318	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
319	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
320	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
321	C₈	—	2	8	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	2	4	no	—
326	C₂²	C₁₉×#389	1	4	yes	—
327	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
328	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
329	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
330	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
331	C₂²	C₂×C₁₉×#137	1	2	yes	—
332	C₄	—	2	4	no	—
333	C₄	—	4	2	no	—
334	C₄	—	4	2	no	—
335	C₄	—	4	4	no	—
336	C₄	—	8	4	no	—
337	C₄	C₁₉×#389	1	4	yes	—
338	C₄	C₁₉×#428	1	8	yes	complemented
339	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
340	C₄	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
341	C₄	C₂×C₁₉×#125	1	1	yes	characteristic
342	C₄	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
343	C₂	—	2	4	no	—
344	C₂	C₂×C₁₉×#389	1	1	yes	characteristic
345	C₂	C₂×C₁₉×#428	1	2	yes	—
346	C₂	C₁₉×#3038	1	1	yes	characteristic
347	C₂	C₁₉×#3039	1	1	yes	characteristic
348	C₂	C₁₉×#3079	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₉×#1948	C₂	semidirect
6. C₁₉×#1947	C₂	semidirect
17. C₁₉×#423	C₄	semidirect
62. C₁₉×C₄⋊C₈	C₂×C₄	semidirect
110. #21171	C₁₉	direct (N × H)
152. #1948	C₂×C₁₉	semidirect
153. #1947	C₂×C₁₉	semidirect
171. C₄×C₁₉	#428	semidirect
185. #423	C₄×C₁₉	semidirect
236. C₄⋊C₈	C₂×C₄×C₁₉	semidirect
239. C₁₉	#21171	direct (N × H)
338. C₄	C₁₉×#428	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#428	2
C₂×C₁₉×#423	2
C₂×C₁₉×#384	2
C₄×C₁₉×#117	2
C₁₉×#1948	2
C₁₉×#1947	2
C₁₉×#1736	2
#21171	19

Subgroups — C19×#21171 #18027130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21171 #18027130