Subgroups — C₁₉×#60333 #18066292

Order 4864.

1926 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2991	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2989	C₂	1	6	yes	maximal, complemented
4	C₁₉×#2984	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2982	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2971	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2965	C₂	1	6	yes	maximal, complemented
8	Q₈×M₁₆×C₁₉	C₂	1	4	yes	maximal, complemented
9	C₂×C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×2₋¹⁺⁴	C₄	1	1	yes	characteristic
11	C₁₉×#520	C₄	1	4	yes	—
12	C₁₉×#520	C₄	1	6	yes	—
13	C₁₉×#519	C₄	1	4	yes	—
14	C₁₉×#519	C₄	1	1	yes	characteristic
15	C₄×#41×C₁₉	C₂²	1	6	yes	—
16	C₄×#41×C₁₉	C₂²	1	4	yes	—
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
19	C₁₉×#446	C₂²	1	6	yes	—
20	C₁₉×#446	C₂²	1	12	yes	—
21	C₁₉×#446	C₂²	1	6	yes	—
22	C₈×Q₈×C₁₉	C₂²	1	4	yes	—
23	C₈×Q₈×C₁₉	C₂²	1	4	yes	—
24	C₈×Q₈×C₁₉	C₂²	1	4	yes	—
25	C₈×Q₈×C₁₉	C₂²	1	4	yes	—
26	C₁₉×#436	C₂²	1	6	yes	—
27	C₁₉×#436	C₂²	1	6	yes	—
28	C₁₉×#436	C₂²	1	12	yes	—
29	C₁₉×#435	C₂²	1	4	yes	—
30	C₁₉×#435	C₂²	1	12	yes	—
31	C₁₉×#432	C₂²	1	12	yes	—
32	C₁₉×#431	C₂²	1	6	yes	—
33	C₁₉×#431	C₂²	1	12	yes	—
34	C₁₉×#423	C₂²	1	12	yes	—
35	C₂×C₁₉×C₄⋊C₈	C₂²	1	3	yes	—
36	C₄×M₁₆×C₁₉	C₂²	1	12	yes	—
37	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
38	C₁₉×2₋¹⁺⁴	—	2	8	no	—
39	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
40	C₂×#41×C₁₉	C₂×C₄	1	6	yes	—
41	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
42	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
44	C₂×M₁₆×C₁₉	C₂³	1	12	yes	—
45	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
47	C₄×Q₈×C₁₉	C₂×C₄	1	12	yes	—
48	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
49	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
50	C₄×Q₈×C₁₉	C₂×C₄	1	6	yes	—
51	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
52	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
53	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
54	C₄×D₄×C₁₉	C₂×C₄	1	12	yes	—
55	C₄×D₄×C₁₉	C₂×C₄	1	6	yes	—
56	C₄×D₄×C₁₉	C₂×C₄	1	12	yes	—
57	C₄×D₄×C₁₉	C₂³	1	4	yes	—
58	C₄×D₄×C₁₉	C₂³	1	6	yes	—
59	C₁₉×#117	C₂×C₄	1	12	yes	—
60	C₁₉×#117	C₂×C₄	1	12	yes	—
61	C₁₉×#117	C₂×C₄	1	6	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	12	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	3	yes	—
64	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
65	C₂×C₄²×C₁₉	C₂³	1	12	yes	—
66	C₁₉×C₄⋊C₈	C₂³	1	12	yes	—
67	C₁₉×C₄⋊C₈	C₂³	1	12	yes	—
68	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
69	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
70	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
71	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
72	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
73	C₁₉×C₂²⋊C₈	C₂³	1	12	yes	—
74	C₁₉×#97	C₂³	1	4	yes	—
75	C₁₉×#97	C₂³	1	12	yes	—
76	C₄×C₈×C₁₉	C₂³	1	6	yes	—
77	C₄×C₈×C₁₉	C₂³	1	6	yes	—
78	C₄×C₈×C₁₉	C₂³	1	12	yes	—
79	#41×C₁₉	—	2	16	no	—
80	#41×C₁₉	—	2	24	no	—
81	C₂×Q₈×C₁₉	—	2	16	no	—
82	C₂×Q₈×C₁₉	M₁₆	1	8	yes	complemented
83	C₂×Q₈×C₁₉	C₂²×C₄	1	6	yes	—
84	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
85	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
86	C₂×D₄×C₁₉	C₂²×C₄	1	6	yes	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
89	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
90	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
91	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
93	M₁₆×C₁₉	—	2	8	no	—
94	M₁₆×C₁₉	—	4	12	no	—
95	C₂×C₈×C₁₉	—	2	2	no	—
96	C₂×C₈×C₁₉	—	4	3	no	—
97	C₂×C₈×C₁₉	C₂⁴	1	6	yes	—
98	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
100	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
101	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
102	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
103	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
104	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
105	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
106	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
107	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
108	C₂²⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
109	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
110	C₄²×C₁₉	C₂²×C₄	1	12	yes	—
111	C₄²×C₁₉	C₂²×C₄	1	6	yes	—
112	C₄²×C₁₉	C₂²×C₄	1	12	yes	—
113	C₄²×C₁₉	C₂⁴	1	6	yes	—
114	C₄²×C₁₉	C₂⁴	1	4	yes	—
115	#60333	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
117	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
118	Q₈×C₁₉	—	2	12	no	—
119	Q₈×C₁₉	C₂×M₁₆	1	16	yes	—
120	D₄×C₁₉	—	2	8	no	—
121	D₄×C₁₉	—	2	12	no	—
122	C₂×C₄×C₁₉	—	2	24	no	—
123	C₂×C₄×C₁₉	—	2	1	no	—
124	C₂×C₄×C₁₉	—	2	4	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	2	4	no	—
127	C₂×C₄×C₁₉	—	4	3	no	—
128	C₂×C₄×C₁₉	—	4	12	no	—
129	C₂×C₄×C₁₉	C₂×M₁₆	1	12	yes	—
130	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
132	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
133	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
134	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
135	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
136	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
137	C₈×C₁₉	—	2	1	no	—
138	C₈×C₁₉	—	2	4	no	—
139	C₈×C₁₉	—	2	6	no	—
140	C₈×C₁₉	—	2	4	no	—
141	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	complemented
142	C₄×2₋¹⁺⁴	C₂×C₁₉	1	1	yes	characteristic
143	#2991	C₂×C₁₉	1	4	yes	complemented
144	#2989	C₂×C₁₉	1	6	yes	complemented
145	#2984	C₂×C₁₉	1	4	yes	complemented
146	#2982	C₂×C₁₉	1	1	yes	characteristic, complemented
147	#2971	C₂×C₁₉	1	4	yes	complemented
148	#2965	C₂×C₁₉	1	6	yes	complemented
149	Q₈×M₁₆	C₂×C₁₉	1	4	yes	complemented
150	C₂×C₈×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
151	C₂²×C₁₉	—	2	1	no	—
152	C₂²×C₁₉	—	2	1	no	—
153	C₂²×C₁₉	—	2	4	no	—
154	C₂²×C₁₉	—	2	4	no	—
155	C₂²×C₁₉	—	2	4	no	—
156	C₂²×C₁₉	C₂²×M₁₆	1	2	yes	—
157	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
158	C₄×C₁₉	—	2	1	no	—
159	C₄×C₁₉	—	2	4	no	—
160	C₄×C₁₉	—	2	4	no	—
161	C₄×C₁₉	—	2	6	no	—
162	C₄×C₁₉	—	2	4	no	—
163	C₄×C₁₉	C₂²×M₁₆	1	12	yes	—
164	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
165	C₄×C₁₉	#585	1	1	yes	characteristic
166	C₂×2₋¹⁺⁴	C₄×C₁₉	1	1	yes	characteristic
167	#520	C₄×C₁₉	1	4	yes	—
168	#520	C₄×C₁₉	1	6	yes	—
169	#519	C₄×C₁₉	1	4	yes	—
170	#519	C₄×C₁₉	1	1	yes	characteristic
171	C₄×#41	C₂²×C₁₉	1	6	yes	—
172	C₄×#41	C₂²×C₁₉	1	4	yes	—
173	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
174	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
175	#446	C₂²×C₁₉	1	6	yes	—
176	#446	C₂²×C₁₉	1	12	yes	—
177	#446	C₂²×C₁₉	1	6	yes	—
178	C₈×Q₈	C₂²×C₁₉	1	4	yes	—
179	C₈×Q₈	C₂²×C₁₉	1	4	yes	—
180	C₈×Q₈	C₂²×C₁₉	1	4	yes	—
181	C₈×Q₈	C₂²×C₁₉	1	4	yes	—
182	#436	C₂²×C₁₉	1	6	yes	—
183	#436	C₂²×C₁₉	1	6	yes	—
184	#436	C₂²×C₁₉	1	12	yes	—
185	#435	C₂²×C₁₉	1	4	yes	—
186	#435	C₂²×C₁₉	1	12	yes	—
187	#432	C₂²×C₁₉	1	12	yes	—
188	#431	C₂²×C₁₉	1	6	yes	—
189	#431	C₂²×C₁₉	1	12	yes	—
190	#423	C₂²×C₁₉	1	12	yes	—
191	C₂×C₄⋊C₈	C₂²×C₁₉	1	3	yes	—
192	C₄×M₁₆	C₂²×C₁₉	1	12	yes	—
193	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	—
194	C₂×C₁₉	—	2	2	no	—
195	C₂×C₁₉	—	4	4	no	—
196	C₂×C₁₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
197	C₂×C₁₉	C₂³×M₁₆	1	1	yes	characteristic
198	C₂×C₁₉	#3573	1	1	yes	characteristic
199	2₋¹⁺⁴	—	2	8	no	—
200	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
201	C₂×#41	C₂×C₄×C₁₉	1	6	yes	—
202	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
203	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
204	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
205	C₂×M₁₆	C₂³×C₁₉	1	12	yes	—
206	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
207	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
208	C₄×Q₈	C₂×C₄×C₁₉	1	12	yes	—
209	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
210	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
211	C₄×Q₈	C₂×C₄×C₁₉	1	6	yes	—
212	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
213	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
214	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
215	C₄×D₄	C₂×C₄×C₁₉	1	12	yes	—
216	C₄×D₄	C₂×C₄×C₁₉	1	6	yes	—
217	C₄×D₄	C₂×C₄×C₁₉	1	12	yes	—
218	C₄×D₄	C₂³×C₁₉	1	4	yes	—
219	C₄×D₄	C₂³×C₁₉	1	6	yes	—
220	#117	C₂×C₄×C₁₉	1	12	yes	—
221	#117	C₂×C₄×C₁₉	1	12	yes	—
222	#117	C₂×C₄×C₁₉	1	6	yes	—
223	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	12	yes	—
224	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	3	yes	—
225	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
226	C₂×C₄²	C₂³×C₁₉	1	12	yes	—
227	C₄⋊C₈	C₂³×C₁₉	1	12	yes	—
228	C₄⋊C₈	C₂³×C₁₉	1	12	yes	—
229	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
230	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
231	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
232	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
233	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
234	C₂²⋊C₈	C₂³×C₁₉	1	12	yes	—
235	#97	C₂³×C₁₉	1	4	yes	—
236	#97	C₂³×C₁₉	1	12	yes	—
237	C₄×C₈	C₂³×C₁₉	1	6	yes	—
238	C₄×C₈	C₂³×C₁₉	1	6	yes	—
239	C₄×C₈	C₂³×C₁₉	1	12	yes	—
240	C₁₉	#60333	1	1	yes	characteristic, direct product factor, Sylow
241	#41	—	2	16	no	—
242	#41	—	2	24	no	—
243	C₂×Q₈	—	2	16	no	—
244	C₂×Q₈	M₁₆×C₁₉	1	8	yes	complemented
245	C₂×Q₈	C₂²×C₄×C₁₉	1	6	yes	—
246	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
247	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
248	C₂×D₄	C₂²×C₄×C₁₉	1	6	yes	—
249	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
250	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
251	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
252	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
253	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
254	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
255	M₁₆	—	2	8	no	—
256	M₁₆	—	4	12	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	4	3	no	—
259	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
260	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
261	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
262	C₂×C₈	C₂⁴×C₁₉	1	6	yes	—
263	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
264	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
265	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
266	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
267	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
268	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
269	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
270	C₂²⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
271	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
272	C₄²	C₂²×C₄×C₁₉	1	12	yes	—
273	C₄²	C₂²×C₄×C₁₉	1	6	yes	—
274	C₄²	C₂²×C₄×C₁₉	1	12	yes	—
275	C₄²	C₂⁴×C₁₉	1	6	yes	—
276	C₄²	C₂⁴×C₁₉	1	4	yes	—
277	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
278	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
279	Q₈	—	2	12	no	—
280	Q₈	C₂×M₁₆×C₁₉	1	16	yes	—
281	D₄	—	2	8	no	—
282	D₄	—	2	12	no	—
283	C₂×C₄	—	2	24	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	4	3	no	—
289	C₂×C₄	—	4	12	no	—
290	C₂×C₄	C₂×M₁₆×C₁₉	1	12	yes	—
291	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
292	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
293	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
294	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
295	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
296	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
297	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
298	C₈	—	2	1	no	—
299	C₈	—	2	4	no	—
300	C₈	—	2	6	no	—
301	C₈	—	2	4	no	—
302	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	complemented
303	C₂²	—	2	1	no	—
304	C₂²	—	2	1	no	—
305	C₂²	—	2	4	no	—
306	C₂²	—	2	4	no	—
307	C₂²	—	2	4	no	—
308	C₂²	C₂²×M₁₆×C₁₉	1	2	yes	—
309	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
310	C₄	—	2	1	no	—
311	C₄	—	2	4	no	—
312	C₄	—	2	4	no	—
313	C₄	—	2	6	no	—
314	C₄	—	2	4	no	—
315	C₄	C₂²×M₁₆×C₁₉	1	12	yes	—
316	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
317	C₄	C₁₉×#585	1	1	yes	characteristic
318	C₂	—	2	2	no	—
319	C₂	—	4	4	no	—
320	C₂	C₄×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
321	C₂	C₂³×M₁₆×C₁₉	1	1	yes	characteristic
322	C₂	C₁₉×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	C₂×C₁₉×2₋¹⁺⁴	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2991	C₂	semidirect
3. C₁₉×#2989	C₂	semidirect
4. C₁₉×#2984	C₂	semidirect
5. C₁₉×#2982	C₂	semidirect
6. C₁₉×#2971	C₂	semidirect
7. C₁₉×#2965	C₂	semidirect
8. Q₈×M₁₆×C₁₉	C₂	semidirect
9. C₂×C₈×Q₈×C₁₉	C₂	semidirect
82. C₂×Q₈×C₁₉	M₁₆	semidirect
115. #60333	C₁₉	direct (N × H)
141. C₈×C₁₉	2₋¹⁺⁴	semidirect
143. #2991	C₂×C₁₉	semidirect
144. #2989	C₂×C₁₉	semidirect
145. #2984	C₂×C₁₉	semidirect
146. #2982	C₂×C₁₉	semidirect
147. #2971	C₂×C₁₉	semidirect
148. #2965	C₂×C₁₉	semidirect
149. Q₈×M₁₆	C₂×C₁₉	semidirect
150. C₂×C₈×Q₈	C₂×C₁₉	semidirect
240. C₁₉	#60333	direct (N × H)
244. C₂×Q₈	M₁₆×C₁₉	semidirect
302. C₈	C₁₉×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₉×2₋¹⁺⁴	2
C₁₉×#2991	2
C₁₉×#2989	2
C₁₉×#2984	2
C₁₉×#2982	2
C₁₉×#2971	2
C₁₉×#2965	2
Q₈×M₁₆×C₁₉	2
C₂×C₈×Q₈×C₁₉	2
#60333	19

Subgroups — C19×#60333 #18066292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60333 #18066292