Subgroups — C₁₉×#23175 #18029134

Order 4864.

1116 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#435	C₂	1	4	yes	maximal, complemented
2	C₄×C₁₉×#127	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1955	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1870	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1869	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1767	C₂	1	2	yes	maximal, complemented
7	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
9	C₂×C₁₉×#127	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
11	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#435	—	2	16	no	—
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
17	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
18	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₉×#97	C₂²	1	4	yes	—
21	C₁₉×#390	C₄	1	1	yes	characteristic
22	C₁₉×#390	C₄	1	1	yes	characteristic
23	C₁₉×#390	C₄	1	4	yes	—
24	C₁₉×#384	C₄	1	1	yes	characteristic
25	C₄³×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#336	C₂²	1	4	yes	—
27	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
28	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
31	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
32	C₂×M₁₆×C₁₉	—	2	8	no	—
33	C₂×M₁₆×C₁₉	—	4	2	no	—
34	C₂²×C₈×C₁₉	—	2	8	no	—
35	C₂²×C₈×C₁₉	—	4	2	no	—
36	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
37	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
38	C₁₉×#127	—	2	4	no	—
39	C₄×D₄×C₁₉	—	2	8	no	—
40	C₄×D₄×C₁₉	—	2	8	no	—
41	C₄×D₄×C₁₉	—	4	1	no	—
42	C₄×D₄×C₁₉	—	4	1	no	—
43	C₄×D₄×C₁₉	—	4	1	no	—
44	C₄×D₄×C₁₉	—	4	1	no	—
45	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
49	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
50	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
57	C₁₉×C₄⋊C₈	—	2	4	no	—
58	C₁₉×C₄⋊C₈	D₄	1	8	yes	complemented
59	C₁₉×C₂²⋊C₈	—	2	8	no	—
60	C₁₉×C₂²⋊C₈	—	2	8	no	—
61	C₁₉×C₂²⋊C₈	—	4	2	no	—
62	C₁₉×C₂²⋊C₈	—	4	2	no	—
63	C₁₉×#97	—	2	8	no	—
64	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
65	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
66	C₂×D₄×C₁₉	—	2	8	no	—
67	C₂×D₄×C₁₉	—	2	8	no	—
68	C₂×D₄×C₁₉	—	2	2	no	—
69	C₂×D₄×C₁₉	—	4	1	no	—
70	C₂×D₄×C₁₉	—	4	1	no	—
71	C₂×D₄×C₁₉	—	4	1	no	—
72	C₂×D₄×C₁₉	—	4	4	no	—
73	C₂×D₄×C₁₉	—	4	1	no	—
74	C₂×D₄×C₁₉	M₁₆	1	4	yes	complemented
75	C₂²×C₄×C₁₉	—	2	4	no	—
76	C₂²×C₄×C₁₉	—	2	4	no	—
77	C₂²×C₄×C₁₉	—	2	4	no	—
78	C₂²×C₄×C₁₉	—	2	4	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
90	M₁₆×C₁₉	—	4	8	no	—
91	C₂×C₈×C₁₉	—	2	4	no	—
92	C₂×C₈×C₁₉	—	2	4	no	—
93	C₂×C₈×C₁₉	—	2	4	no	—
94	C₂×C₈×C₁₉	—	2	4	no	—
95	C₂×C₈×C₁₉	—	2	4	no	—
96	C₂×C₈×C₁₉	—	4	8	no	—
97	C₂×C₈×C₁₉	C₂×D₄	1	8	yes	—
98	C₄⋊C₄×C₁₉	—	2	8	no	—
99	C₄⋊C₄×C₁₉	—	4	1	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₂²⋊C₄×C₁₉	—	2	8	no	—
102	C₂²⋊C₄×C₁₉	—	2	8	no	—
103	C₂²⋊C₄×C₁₉	—	4	2	no	—
104	C₂²⋊C₄×C₁₉	—	4	2	no	—
105	C₄²×C₁₉	—	2	2	no	—
106	C₄²×C₁₉	—	2	1	no	—
107	C₄²×C₁₉	—	2	1	no	—
108	C₄²×C₁₉	—	4	1	no	—
109	C₄²×C₁₉	—	4	2	no	—
110	C₄²×C₁₉	C₂×D₄	1	4	yes	—
111	C₄²×C₁₉	#41	1	4	yes	—
112	#23175	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₁₉	—	2	4	no	—
114	C₂³×C₁₉	—	2	2	no	—
115	C₂³×C₁₉	—	2	4	no	—
116	C₂³×C₁₉	—	2	2	no	—
117	C₂³×C₁₉	—	2	4	no	—
118	C₂³×C₁₉	—	2	2	no	—
119	C₂³×C₁₉	—	2	2	no	—
120	C₂³×C₁₉	—	2	2	no	—
121	C₂³×C₁₉	—	2	4	no	—
122	C₂³×C₁₉	C₂×M₁₆	1	4	yes	—
123	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
124	D₄×C₁₉	—	4	4	no	—
125	D₄×C₁₉	—	4	16	no	—
126	D₄×C₁₉	—	4	4	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	2	no	—
129	C₂×C₄×C₁₉	—	2	2	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	4	no	—
134	C₂×C₄×C₁₉	—	2	4	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	2	no	—
139	C₂×C₄×C₁₉	—	4	2	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	4	no	—
142	C₂×C₄×C₁₉	—	4	4	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
146	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
147	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
148	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
149	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
150	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
151	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
152	C₈×C₁₉	—	2	8	no	—
153	C₈×C₁₉	—	4	4	no	—
154	C₂×#435	C₂×C₁₉	1	4	yes	complemented
155	C₄×#127	C₂×C₁₉	1	1	yes	characteristic
156	#1955	C₂×C₁₉	1	4	yes	complemented
157	#1870	C₂×C₁₉	1	2	yes	complemented
158	#1869	C₂×C₁₉	1	2	yes	complemented
159	#1767	C₂×C₁₉	1	2	yes	complemented
160	C₂²×C₁₉	—	2	8	no	—
161	C₂²×C₁₉	—	2	4	no	—
162	C₂²×C₁₉	—	4	2	no	—
163	C₂²×C₁₉	—	4	4	no	—
164	C₂²×C₁₉	—	4	2	no	—
165	C₂²×C₁₉	—	4	2	no	—
166	C₂²×C₁₉	—	4	4	no	—
167	C₂²×C₁₉	—	4	4	no	—
168	C₂²×C₁₉	—	4	2	no	—
169	C₂²×C₁₉	—	4	2	no	—
170	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
171	C₂²×C₁₉	#518	1	1	yes	characteristic
172	C₂²×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
173	C₂²×C₁₉	#568	1	1	yes	characteristic
174	C₂²×C₁₉	#568	1	2	yes	—
175	C₄×C₁₉	—	2	4	no	—
176	C₄×C₁₉	—	2	4	no	—
177	C₄×C₁₉	—	2	2	no	—
178	C₄×C₁₉	—	4	2	no	—
179	C₄×C₁₉	—	4	2	no	—
180	C₄×C₁₉	—	4	1	no	—
181	C₄×C₁₉	D₄²	1	1	yes	characteristic
182	C₄×C₁₉	#550	1	2	yes	—
183	C₄×C₁₉	#559	1	1	yes	characteristic
184	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
185	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
186	C₂×#127	C₄×C₁₉	1	1	yes	characteristic
187	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
188	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
189	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
190	#435	—	2	16	no	—
191	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
192	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
193	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
194	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
195	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
196	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
197	C₂×#97	C₂²×C₁₉	1	4	yes	—
198	#390	C₄×C₁₉	1	1	yes	characteristic
199	#390	C₄×C₁₉	1	1	yes	characteristic
200	#390	C₄×C₁₉	1	4	yes	—
201	#384	C₄×C₁₉	1	1	yes	characteristic
202	C₄³	C₂²×C₁₉	1	1	yes	characteristic
203	#336	C₂²×C₁₉	1	4	yes	—
204	C₂×C₁₉	—	4	4	no	—
205	C₂×C₁₉	—	8	2	no	—
206	C₂×C₁₉	#2366	1	1	yes	characteristic
207	C₂×C₁₉	#2932	1	2	yes	—
208	C₂×C₁₉	D₄×M₁₆	1	2	yes	—
209	C₂×C₁₉	#2973	1	1	yes	characteristic
210	C₂×C₁₉	#2980	1	1	yes	characteristic
211	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
212	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
213	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
214	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
215	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
216	C₂×M₁₆	—	2	8	no	—
217	C₂×M₁₆	—	4	2	no	—
218	C₂²×C₈	—	2	8	no	—
219	C₂²×C₈	—	4	2	no	—
220	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
221	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
222	#127	—	2	4	no	—
223	C₄×D₄	—	2	8	no	—
224	C₄×D₄	—	2	8	no	—
225	C₄×D₄	—	4	1	no	—
226	C₄×D₄	—	4	1	no	—
227	C₄×D₄	—	4	1	no	—
228	C₄×D₄	—	4	1	no	—
229	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
230	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
232	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
233	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
234	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
235	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
236	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
237	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
238	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
240	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
241	C₄⋊C₈	—	2	4	no	—
242	C₄⋊C₈	D₄×C₁₉	1	8	yes	complemented
243	C₂²⋊C₈	—	2	8	no	—
244	C₂²⋊C₈	—	2	8	no	—
245	C₂²⋊C₈	—	4	2	no	—
246	C₂²⋊C₈	—	4	2	no	—
247	#97	—	2	8	no	—
248	C₁₉	#23175	1	1	yes	characteristic, direct product factor, Sylow
249	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
250	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
251	C₂×D₄	—	2	8	no	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	2	2	no	—
254	C₂×D₄	—	4	1	no	—
255	C₂×D₄	—	4	1	no	—
256	C₂×D₄	—	4	1	no	—
257	C₂×D₄	—	4	4	no	—
258	C₂×D₄	—	4	1	no	—
259	C₂×D₄	M₁₆×C₁₉	1	4	yes	complemented
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
270	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
272	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
274	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
275	M₁₆	—	4	8	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	4	8	no	—
282	C₂×C₈	C₂×D₄×C₁₉	1	8	yes	—
283	C₄⋊C₄	—	2	8	no	—
284	C₄⋊C₄	—	4	1	no	—
285	C₄⋊C₄	—	4	1	no	—
286	C₂²⋊C₄	—	2	8	no	—
287	C₂²⋊C₄	—	2	8	no	—
288	C₂²⋊C₄	—	4	2	no	—
289	C₂²⋊C₄	—	4	2	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	1	no	—
292	C₄²	—	2	1	no	—
293	C₄²	—	4	1	no	—
294	C₄²	—	4	2	no	—
295	C₄²	C₂×D₄×C₁₉	1	4	yes	—
296	C₄²	#41×C₁₉	1	4	yes	—
297	C₂³	—	2	4	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	4	no	—
306	C₂³	C₂×M₁₆×C₁₉	1	4	yes	—
307	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
308	D₄	—	4	4	no	—
309	D₄	—	4	16	no	—
310	D₄	—	4	4	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
330	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
331	C₂×C₄	C₂×M₁₆×C₁₉	1	2	yes	—
332	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
333	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
334	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
335	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
336	C₈	—	2	8	no	—
337	C₈	—	4	4	no	—
338	C₂²	—	2	8	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	4	4	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	4	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	4	2	no	—
348	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
349	C₂²	C₁₉×#518	1	1	yes	characteristic
350	C₂²	C₂²×M₁₆×C₁₉	1	1	yes	characteristic
351	C₂²	C₁₉×#568	1	1	yes	characteristic
352	C₂²	C₁₉×#568	1	2	yes	—
353	C₄	—	2	4	no	—
354	C₄	—	2	4	no	—
355	C₄	—	2	2	no	—
356	C₄	—	4	1	no	—
357	C₄	—	4	2	no	—
358	C₄	—	4	2	no	—
359	C₄	D₄²×C₁₉	1	1	yes	characteristic
360	C₄	C₁₉×#550	1	2	yes	—
361	C₄	C₁₉×#559	1	1	yes	characteristic
362	C₂	—	4	4	no	—
363	C₂	—	8	2	no	—
364	C₂	C₁₉×#2366	1	1	yes	characteristic
365	C₂	C₁₉×#2932	1	2	yes	—
366	C₂	D₄×M₁₆×C₁₉	1	2	yes	—
367	C₂	C₁₉×#2973	1	1	yes	characteristic
368	C₂	C₁₉×#2980	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂³×C₄
prime radical	C₂×C₁₉×#127	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#435	C₂	semidirect
3. C₁₉×#1955	C₂	semidirect
4. C₁₉×#1870	C₂	semidirect
5. C₁₉×#1869	C₂	semidirect
6. C₁₉×#1767	C₂	semidirect
58. C₁₉×C₄⋊C₈	D₄	semidirect
74. C₂×D₄×C₁₉	M₁₆	semidirect
112. #23175	C₁₉	direct (N × H)
154. C₂×#435	C₂×C₁₉	semidirect
156. #1955	C₂×C₁₉	semidirect
157. #1870	C₂×C₁₉	semidirect
158. #1869	C₂×C₁₉	semidirect
159. #1767	C₂×C₁₉	semidirect
242. C₄⋊C₈	D₄×C₁₉	semidirect
248. C₁₉	#23175	direct (N × H)
259. C₂×D₄	M₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#435	2
C₄×C₁₉×#127	2
C₁₉×#1955	2
C₁₉×#1870	2
C₁₉×#1869	2
C₁₉×#1767	2
#23175	19

Subgroups — C19×#23175 #18029134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23175 #18029134