Subgroups — C₁₉×#60183 #18066142

Order 4864.

2612 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3584	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3573	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2957	C₂	1	6	yes	maximal, complemented
4	C₁₉×#2956	C₂	1	6	yes	maximal, complemented
5	C₁₉×#2955	C₂	1	6	yes	maximal, complemented
6	C₂×C₁₉×#443	C₂	1	6	yes	maximal, complemented
7	C₁₉×#2916	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2901	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#585	C₂²	1	2	yes	—
11	C₁₉×#578	C₄	1	4	yes	complemented
12	C₁₉×#577	C₄	1	8	yes	complemented
13	C₁₉×#576	C₄	1	4	yes	complemented
14	C₁₉×#575	C₂²	1	6	yes	—
15	C₂×C₁₉×#135	C₂²	1	6	yes	—
16	C₁₉×#568	—	2	8	no	—
17	C₁₉×#568	C₂²	1	2	yes	—
18	C₁₉×#568	C₂²	1	12	yes	complemented
19	C₂×C₁₉×#131	—	2	8	no	—
20	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#131	C₂²	1	12	yes	complemented
23	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#444	C₂²	1	24	yes	complemented
25	C₁₉×#443	C₂²	1	4	yes	complemented
26	C₁₉×#443	C₂²	1	12	yes	complemented
27	C₁₉×#443	C₂²	1	12	yes	complemented
28	C₁₉×#443	C₂²	1	12	yes	complemented
29	C₁₉×#430	C₂²	1	6	yes	complemented
30	C₂×C₁₉×#108	C₂²	1	6	yes	complemented
31	C₁₉×#421	C₂²	1	12	yes	complemented
32	C₂×C₁₉×#104	C₂²	1	12	yes	complemented
33	C₁₉×#405	C₂²	1	3	yes	complemented
34	C₁₉×#405	C₂²	1	3	yes	complemented
35	C₄×M₁₆×C₁₉	C₂²	1	3	yes	complemented
36	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	complemented
37	C₁₉×2₋¹⁺⁴	—	2	2	no	—
38	C₁₉×2₋¹⁺⁴	C₂×C₄	1	8	yes	—
39	C₁₉×H(5,𝔽₂)	—	2	6	no	—
40	C₁₉×H(5,𝔽₂)	C₂×C₄	1	8	yes	—
41	C₂×#41×C₁₉	—	2	8	no	—
42	C₂×#41×C₁₉	C₂³	1	12	yes	—
43	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
44	C₁₉×#137	C₂×C₄	1	24	yes	complemented
45	C₁₉×AGL(1,ℤ/8)	C₂×C₄	1	24	yes	complemented
46	C₁₉×#135	C₂×C₄	1	12	yes	complemented
47	C₁₉×#135	C₂×C₄	1	12	yes	complemented
48	C₁₉×#135	C₂³	1	4	yes	—
49	C₁₉×#135	C₂³	1	12	yes	—
50	C₂×Q₁₆×C₁₉	C₂×C₄	1	6	yes	complemented
51	C₂×SD₁₆×C₁₉	C₂×C₄	1	12	yes	complemented
52	C₂×D₈×C₁₉	C₂×C₄	1	6	yes	complemented
53	C₁₉×#131	—	2	8	no	—
54	C₁₉×#131	—	2	24	no	—
55	C₁₉×#131	—	2	12	no	—
56	C₁₉×#131	—	2	12	no	—
57	C₁₉×#131	C₂×C₄	1	4	yes	—
58	C₁₉×#131	C₂×C₄	1	4	yes	—
59	C₁₉×#131	D₄	1	4	yes	—
60	C₁₉×#131	D₄	1	4	yes	—
61	C₁₉×#131	C₂³	1	8	yes	—
62	C₁₉×#131	C₂³	1	24	yes	—
63	C₂×M₁₆×C₁₉	—	2	24	no	—
64	C₂×M₁₆×C₁₉	—	2	12	no	—
65	C₂×M₁₆×C₁₉	C₂³	1	12	yes	—
66	C₂×M₁₆×C₁₉	C₂³	1	3	yes	—
67	C₂×M₁₆×C₁₉	C₂³	1	3	yes	—
68	C₂²×C₈×C₁₉	—	2	12	no	—
69	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
70	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
71	C₄×Q₈×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	—	2	3	no	—
73	C₁₉×#117	C₂³	1	3	yes	—
74	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
75	C₁₉×#108	C₂³	1	4	yes	—
76	C₁₉×#108	C₂³	1	12	yes	—
77	C₁₉×#104	C₂³	1	8	yes	—
78	C₁₉×#104	C₂³	1	24	yes	—
79	C₁₉×#97	C₂³	1	6	yes	—
80	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₉	C₂³	1	3	yes	—
82	C₄×C₈×C₁₉	C₂³	1	3	yes	—
83	C₄×C₈×C₁₉	C₂³	1	3	yes	—
84	#41×C₁₉	—	2	8	no	—
85	#41×C₁₉	—	2	24	no	—
86	#41×C₁₉	—	2	12	no	—
87	#41×C₁₉	—	2	12	no	—
88	#41×C₁₉	C₂²×C₄	1	24	yes	—
89	#41×C₁₉	C₂²×C₄	1	4	yes	—
90	#41×C₁₉	C₂×D₄	1	4	yes	—
91	#41×C₁₉	C₂⁴	1	8	yes	—
92	C₂×Q₈×C₁₉	—	2	8	no	—
93	C₂×Q₈×C₁₉	C₂²×C₄	1	12	yes	—
94	C₂×Q₈×C₁₉	#41	1	1	yes	characteristic
95	C₂×D₄×C₁₉	—	2	12	no	—
96	C₂×D₄×C₁₉	—	2	24	no	—
97	C₂×D₄×C₁₉	C₂²×C₄	1	12	yes	—
98	C₂×D₄×C₁₉	#41	1	3	yes	—
99	C₂²×C₄×C₁₉	—	2	12	no	—
100	C₂²×C₄×C₁₉	—	2	3	no	—
101	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
102	Q₁₆×C₁₉	C₂²×C₄	1	4	yes	—
103	Q₁₆×C₁₉	C₂²×C₄	1	12	yes	—
104	SD₁₆×C₁₉	C₂²×C₄	1	8	yes	—
105	SD₁₆×C₁₉	C₂²×C₄	1	24	yes	—
106	D₈×C₁₉	C₂²×C₄	1	4	yes	—
107	D₈×C₁₉	C₂²×C₄	1	12	yes	—
108	M₁₆×C₁₉	—	2	12	no	—
109	M₁₆×C₁₉	—	2	24	no	—
110	M₁₆×C₁₉	—	2	8	no	—
111	M₁₆×C₁₉	C₂²×C₄	1	12	yes	—
112	M₁₆×C₁₉	C₂×D₄	1	12	yes	—
113	M₁₆×C₁₉	C₂⁴	1	8	yes	—
114	C₂×C₈×C₁₉	—	2	12	no	—
115	C₂×C₈×C₁₉	—	2	24	no	—
116	C₂×C₈×C₁₉	—	2	8	no	—
117	C₂×C₈×C₁₉	C₂²×C₄	1	6	yes	—
118	C₂×C₈×C₁₉	C₂²×C₄	1	6	yes	—
119	C₂×C₈×C₁₉	C₂×D₄	1	6	yes	—
120	C₂×C₈×C₁₉	C₂×D₄	1	6	yes	—
121	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
122	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
123	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
124	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
125	C₄⋊C₄×C₁₉	—	2	3	no	—
126	C₂²⋊C₄×C₁₉	—	2	3	no	—
127	C₄²×C₁₉	—	2	3	no	—
128	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
129	C₄²×C₁₉	C₂⁴	1	3	yes	—
130	#60183	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₁₉	—	2	12	no	—
132	C₂³×C₁₉	C₂×#41	1	3	yes	—
133	Q₈×C₁₉	—	2	12	no	—
134	Q₈×C₁₉	C₄×D₄	1	4	yes	—
135	Q₈×C₁₉	C₂³×C₄	1	8	yes	—
136	D₄×C₁₉	—	2	24	no	—
137	D₄×C₁₉	—	2	8	no	—
138	D₄×C₁₉	—	2	12	no	—
139	D₄×C₁₉	C₄×D₄	1	12	yes	—
140	D₄×C₁₉	C₂³×C₄	1	8	yes	—
141	C₂×C₄×C₁₉	—	2	12	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	24	no	—
144	C₂×C₄×C₁₉	—	2	8	no	—
145	C₂×C₄×C₁₉	—	2	3	no	—
146	C₂×C₄×C₁₉	—	4	6	no	—
147	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
148	C₂×C₄×C₁₉	C₂²×D₄	1	6	yes	—
149	C₂×C₄×C₁₉	C₂×#41	1	3	yes	—
150	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
151	C₈×C₁₉	—	2	8	no	—
152	C₈×C₁₉	C₂³×C₄	1	1	yes	characteristic
153	C₈×C₁₉	C₂³×C₄	1	1	yes	characteristic
154	C₈×C₁₉	C₂³×C₄	1	6	yes	—
155	C₈×C₁₉	C₂²×D₄	1	6	yes	—
156	C₈×C₁₉	C₂²×D₄	1	1	yes	characteristic
157	C₈×C₁₉	C₂²×D₄	1	1	yes	characteristic
158	#3584	C₂×C₁₉	1	1	yes	characteristic
159	#3573	C₂×C₁₉	1	2	yes	complemented
160	#2957	C₂×C₁₉	1	6	yes	complemented
161	#2956	C₂×C₁₉	1	6	yes	complemented
162	#2955	C₂×C₁₉	1	6	yes	complemented
163	C₂×#443	C₂×C₁₉	1	6	yes	complemented
164	#2916	C₂×C₁₉	1	1	yes	characteristic, complemented
165	#2901	C₂×C₁₉	1	2	yes	complemented
166	C₄×#131	C₂×C₁₉	1	1	yes	characteristic, complemented
167	C₂²×C₁₉	—	2	8	no	—
168	C₂²×C₁₉	—	4	3	no	—
169	C₂²×C₁₉	—	8	12	no	—
170	C₂²×C₁₉	C₂×C₄×D₄	1	6	yes	—
171	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
172	C₄×C₁₉	—	2	2	no	—
173	C₄×C₁₉	—	2	8	no	—
174	C₄×C₁₉	—	4	3	no	—
175	C₄×C₁₉	C₂×C₄×D₄	1	6	yes	—
176	C₄×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
177	C₄×C₁₉	C₂³×D₄	1	1	yes	characteristic
178	#585	C₂²×C₁₉	1	2	yes	—
179	#578	C₄×C₁₉	1	4	yes	complemented
180	#577	C₄×C₁₉	1	8	yes	complemented
181	#576	C₄×C₁₉	1	4	yes	complemented
182	#575	C₂²×C₁₉	1	6	yes	—
183	C₂×#135	C₂²×C₁₉	1	6	yes	—
184	#568	—	2	8	no	—
185	#568	C₂²×C₁₉	1	2	yes	—
186	#568	C₂²×C₁₉	1	12	yes	complemented
187	C₂×#131	—	2	8	no	—
188	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
189	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
190	C₂×#131	C₂²×C₁₉	1	12	yes	complemented
191	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
192	#444	C₂²×C₁₉	1	24	yes	complemented
193	#443	C₂²×C₁₉	1	4	yes	complemented
194	#443	C₂²×C₁₉	1	12	yes	complemented
195	#443	C₂²×C₁₉	1	12	yes	complemented
196	#443	C₂²×C₁₉	1	12	yes	complemented
197	#430	C₂²×C₁₉	1	6	yes	complemented
198	C₂×#108	C₂²×C₁₉	1	6	yes	complemented
199	#421	C₂²×C₁₉	1	12	yes	complemented
200	C₂×#104	C₂²×C₁₉	1	12	yes	complemented
201	#405	C₂²×C₁₉	1	3	yes	complemented
202	#405	C₂²×C₁₉	1	3	yes	complemented
203	C₄×M₁₆	C₂²×C₁₉	1	3	yes	complemented
204	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	complemented
205	C₂×C₁₉	—	2	1	no	—
206	C₂×C₁₉	—	2	6	no	—
207	C₂×C₁₉	—	4	8	no	—
208	C₂×C₁₉	C₂²×C₄×D₄	1	1	yes	characteristic
209	2₋¹⁺⁴	—	2	2	no	—
210	2₋¹⁺⁴	C₂×C₄×C₁₉	1	8	yes	—
211	H(5,𝔽₂)	—	2	6	no	—
212	H(5,𝔽₂)	C₂×C₄×C₁₉	1	8	yes	—
213	C₂×#41	—	2	8	no	—
214	C₂×#41	C₂³×C₁₉	1	12	yes	—
215	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
216	#137	C₂×C₄×C₁₉	1	24	yes	complemented
217	AGL(1,ℤ/8)	C₂×C₄×C₁₉	1	24	yes	complemented
218	#135	C₂×C₄×C₁₉	1	12	yes	complemented
219	#135	C₂×C₄×C₁₉	1	12	yes	complemented
220	#135	C₂³×C₁₉	1	4	yes	—
221	#135	C₂³×C₁₉	1	12	yes	—
222	C₂×Q₁₆	C₂×C₄×C₁₉	1	6	yes	complemented
223	C₂×SD₁₆	C₂×C₄×C₁₉	1	12	yes	complemented
224	C₂×D₈	C₂×C₄×C₁₉	1	6	yes	complemented
225	#131	—	2	8	no	—
226	#131	—	2	24	no	—
227	#131	—	2	12	no	—
228	#131	—	2	12	no	—
229	#131	C₂×C₄×C₁₉	1	4	yes	—
230	#131	C₂×C₄×C₁₉	1	4	yes	—
231	#131	D₄×C₁₉	1	4	yes	—
232	#131	D₄×C₁₉	1	4	yes	—
233	#131	C₂³×C₁₉	1	8	yes	—
234	#131	C₂³×C₁₉	1	24	yes	—
235	C₂×M₁₆	—	2	24	no	—
236	C₂×M₁₆	—	2	12	no	—
237	C₂×M₁₆	C₂³×C₁₉	1	12	yes	—
238	C₂×M₁₆	C₂³×C₁₉	1	3	yes	—
239	C₂×M₁₆	C₂³×C₁₉	1	3	yes	—
240	C₂²×C₈	—	2	12	no	—
241	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
242	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
243	C₄×Q₈	—	2	1	no	—
244	C₄×D₄	—	2	3	no	—
245	#117	C₂³×C₁₉	1	3	yes	—
246	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
247	#108	C₂³×C₁₉	1	4	yes	—
248	#108	C₂³×C₁₉	1	12	yes	—
249	#104	C₂³×C₁₉	1	8	yes	—
250	#104	C₂³×C₁₉	1	24	yes	—
251	#97	C₂³×C₁₉	1	6	yes	—
252	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
253	C₄×C₈	C₂³×C₁₉	1	3	yes	—
254	C₄×C₈	C₂³×C₁₉	1	3	yes	—
255	C₄×C₈	C₂³×C₁₉	1	3	yes	—
256	C₁₉	#60183	1	1	yes	characteristic, direct product factor, Sylow
257	#41	—	2	8	no	—
258	#41	—	2	24	no	—
259	#41	—	2	12	no	—
260	#41	—	2	12	no	—
261	#41	C₂²×C₄×C₁₉	1	24	yes	—
262	#41	C₂²×C₄×C₁₉	1	4	yes	—
263	#41	C₂×D₄×C₁₉	1	4	yes	—
264	#41	C₂⁴×C₁₉	1	8	yes	—
265	C₂×Q₈	—	2	8	no	—
266	C₂×Q₈	C₂²×C₄×C₁₉	1	12	yes	—
267	C₂×Q₈	#41×C₁₉	1	1	yes	characteristic
268	C₂×D₄	—	2	12	no	—
269	C₂×D₄	—	2	24	no	—
270	C₂×D₄	C₂²×C₄×C₁₉	1	12	yes	—
271	C₂×D₄	#41×C₁₉	1	3	yes	—
272	C₂²×C₄	—	2	12	no	—
273	C₂²×C₄	—	2	3	no	—
274	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
275	Q₁₆	C₂²×C₄×C₁₉	1	4	yes	—
276	Q₁₆	C₂²×C₄×C₁₉	1	12	yes	—
277	SD₁₆	C₂²×C₄×C₁₉	1	8	yes	—
278	SD₁₆	C₂²×C₄×C₁₉	1	24	yes	—
279	D₈	C₂²×C₄×C₁₉	1	4	yes	—
280	D₈	C₂²×C₄×C₁₉	1	12	yes	—
281	M₁₆	—	2	12	no	—
282	M₁₆	—	2	24	no	—
283	M₁₆	—	2	8	no	—
284	M₁₆	C₂²×C₄×C₁₉	1	12	yes	—
285	M₁₆	C₂×D₄×C₁₉	1	12	yes	—
286	M₁₆	C₂⁴×C₁₉	1	8	yes	—
287	C₂×C₈	—	2	12	no	—
288	C₂×C₈	—	2	8	no	—
289	C₂×C₈	—	2	24	no	—
290	C₂×C₈	C₂²×C₄×C₁₉	1	6	yes	—
291	C₂×C₈	C₂²×C₄×C₁₉	1	6	yes	—
292	C₂×C₈	C₂×D₄×C₁₉	1	6	yes	—
293	C₂×C₈	C₂×D₄×C₁₉	1	6	yes	—
294	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
295	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
296	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
297	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
298	C₄⋊C₄	—	2	3	no	—
299	C₂²⋊C₄	—	2	3	no	—
300	C₄²	—	2	3	no	—
301	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
302	C₄²	C₂⁴×C₁₉	1	3	yes	—
303	C₂³	—	2	12	no	—
304	C₂³	C₂×#41×C₁₉	1	3	yes	—
305	Q₈	—	2	12	no	—
306	Q₈	C₄×D₄×C₁₉	1	4	yes	—
307	Q₈	C₂³×C₄×C₁₉	1	8	yes	—
308	D₄	—	2	24	no	—
309	D₄	—	2	8	no	—
310	D₄	—	2	12	no	—
311	D₄	C₄×D₄×C₁₉	1	12	yes	—
312	D₄	C₂³×C₄×C₁₉	1	8	yes	—
313	C₂×C₄	—	2	12	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	24	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	3	no	—
318	C₂×C₄	—	4	6	no	—
319	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
320	C₂×C₄	C₂²×D₄×C₁₉	1	6	yes	—
321	C₂×C₄	C₂×#41×C₁₉	1	3	yes	—
322	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
323	C₈	—	2	8	no	—
324	C₈	C₂³×C₄×C₁₉	1	1	yes	characteristic
325	C₈	C₂³×C₄×C₁₉	1	1	yes	characteristic
326	C₈	C₂³×C₄×C₁₉	1	6	yes	—
327	C₈	C₂²×D₄×C₁₉	1	1	yes	characteristic
328	C₈	C₂²×D₄×C₁₉	1	6	yes	—
329	C₈	C₂²×D₄×C₁₉	1	1	yes	characteristic
330	C₂²	—	2	8	no	—
331	C₂²	—	4	3	no	—
332	C₂²	—	8	12	no	—
333	C₂²	C₂×C₄×D₄×C₁₉	1	6	yes	—
334	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
335	C₄	—	2	2	no	—
336	C₄	—	2	8	no	—
337	C₄	—	4	3	no	—
338	C₄	C₂×C₄×D₄×C₁₉	1	6	yes	—
339	C₄	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
340	C₄	C₂³×D₄×C₁₉	1	1	yes	characteristic
341	C₂	—	2	1	no	—
342	C₂	—	2	6	no	—
343	C₂	—	4	8	no	—
344	C₂	C₂²×C₄×D₄×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₁₉	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂×C₁₉	C₂²×C₄×D₄
prime radical	C₁₉×#3584	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3573	C₂	semidirect
3. C₁₉×#2957	C₂	semidirect
4. C₁₉×#2956	C₂	semidirect
5. C₁₉×#2955	C₂	semidirect
6. C₂×C₁₉×#443	C₂	semidirect
7. C₁₉×#2916	C₂	semidirect
8. C₁₉×#2901	C₂	semidirect
9. C₄×C₁₉×#131	C₂	semidirect
11. C₁₉×#578	C₄	semidirect
12. C₁₉×#577	C₄	semidirect
13. C₁₉×#576	C₄	semidirect
18. C₁₉×#568	C₂²	semidirect
22. C₂×C₁₉×#131	C₂²	semidirect
24. C₁₉×#444	C₂²	semidirect
25. C₁₉×#443	C₂²	semidirect
26. C₁₉×#443	C₂²	semidirect
27. C₁₉×#443	C₂²	semidirect
28. C₁₉×#443	C₂²	semidirect
29. C₁₉×#430	C₂²	semidirect
30. C₂×C₁₉×#108	C₂²	semidirect
31. C₁₉×#421	C₂²	semidirect
32. C₂×C₁₉×#104	C₂²	semidirect
33. C₁₉×#405	C₂²	semidirect
34. C₁₉×#405	C₂²	semidirect
35. C₄×M₁₆×C₁₉	C₂²	semidirect
36. C₂×C₄×C₈×C₁₉	C₂²	semidirect
44. C₁₉×#137	C₂×C₄	semidirect
45. C₁₉×AGL(1,ℤ/8)	C₂×C₄	semidirect
46. C₁₉×#135	C₂×C₄	semidirect
47. C₁₉×#135	C₂×C₄	semidirect
50. C₂×Q₁₆×C₁₉	C₂×C₄	semidirect
51. C₂×SD₁₆×C₁₉	C₂×C₄	semidirect
52. C₂×D₈×C₁₉	C₂×C₄	semidirect
130. #60183	C₁₉	direct (N × H)
159. #3573	C₂×C₁₉	semidirect
160. #2957	C₂×C₁₉	semidirect
161. #2956	C₂×C₁₉	semidirect
162. #2955	C₂×C₁₉	semidirect
163. C₂×#443	C₂×C₁₉	semidirect
164. #2916	C₂×C₁₉	semidirect
165. #2901	C₂×C₁₉	semidirect
166. C₄×#131	C₂×C₁₉	semidirect
179. #578	C₄×C₁₉	semidirect
180. #577	C₄×C₁₉	semidirect
181. #576	C₄×C₁₉	semidirect
186. #568	C₂²×C₁₉	semidirect
190. C₂×#131	C₂²×C₁₉	semidirect
192. #444	C₂²×C₁₉	semidirect
193. #443	C₂²×C₁₉	semidirect
194. #443	C₂²×C₁₉	semidirect
195. #443	C₂²×C₁₉	semidirect
196. #443	C₂²×C₁₉	semidirect
197. #430	C₂²×C₁₉	semidirect
198. C₂×#108	C₂²×C₁₉	semidirect
199. #421	C₂²×C₁₉	semidirect
200. C₂×#104	C₂²×C₁₉	semidirect
201. #405	C₂²×C₁₉	semidirect
202. #405	C₂²×C₁₉	semidirect
203. C₄×M₁₆	C₂²×C₁₉	semidirect
204. C₂×C₄×C₈	C₂²×C₁₉	semidirect
216. #137	C₂×C₄×C₁₉	semidirect
217. AGL(1,ℤ/8)	C₂×C₄×C₁₉	semidirect
218. #135	C₂×C₄×C₁₉	semidirect
219. #135	C₂×C₄×C₁₉	semidirect
222. C₂×Q₁₆	C₂×C₄×C₁₉	semidirect
223. C₂×SD₁₆	C₂×C₄×C₁₉	semidirect
224. C₂×D₈	C₂×C₄×C₁₉	semidirect
256. C₁₉	#60183	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3584	2
C₁₉×#3573	2
C₁₉×#2957	2
C₁₉×#2956	2
C₁₉×#2955	2
C₂×C₁₉×#443	2
C₁₉×#2916	2
C₁₉×#2901	2
C₄×C₁₉×#131	2
#60183	19

Subgroups — C19×#60183 #18066142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60183 #18066142