Subgroups — C₁₉×#21941 #18027900

Order 4864.

1194 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2280	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1854	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1853	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1852	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1808	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1807	C₂	1	2	yes	maximal, complemented
9	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
11	C₂×C₁₉×#117	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
14	C₂×C₁₉×#107	C₂²	1	4	yes	complemented
15	C₂×C₁₉×#106	C₂²	1	4	yes	complemented
16	C₂×C₁₉×C₂²⋊C₈	C₄	1	8	yes	complemented
17	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₁₉×#381	—	2	1	no	—
21	C₁₉×#380	—	2	1	no	—
22	C₁₉×#380	—	2	1	no	—
23	C₁₉×#380	C₂²	1	2	yes	—
24	C₁₉×#380	C₂²	1	2	yes	—
25	C₁₉×#380	C₂²	1	1	yes	characteristic
26	C₁₉×#380	C₂²	1	1	yes	characteristic
27	C₁₉×#380	C₂²	1	2	yes	—
28	C₁₉×#379	—	2	1	no	—
29	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
30	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₁₉×#95	—	2	1	no	—
32	C₁₉×#340	C₂²	1	4	yes	complemented
33	C₁₉×#340	C₂²	1	4	yes	complemented
34	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	—	2	2	no	—
36	C₂³×C₄×C₁₉	—	4	4	no	—
37	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
38	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	Q₈	1	4	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₉	—	4	4	no	—
46	C₂²×C₈×C₁₉	C₂×C₄	1	8	yes	complemented
47	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
49	C₁₉×#117	—	4	4	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
52	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
62	C₂×C₄²×C₁₉	—	2	2	no	—
63	C₁₉×#107	—	4	4	no	—
64	C₁₉×#106	—	4	4	no	—
65	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	—
66	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	—
67	C₁₉×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
68	C₁₉×#95	—	2	2	no	—
69	C₁₉×#95	—	2	2	no	—
70	C₁₉×#95	—	2	2	no	—
71	C₁₉×#95	—	2	1	no	—
72	C₁₉×#95	—	2	1	no	—
73	C₂⁴×C₁₉	—	2	4	no	—
74	C₂⁴×C₁₉	—	2	2	no	—
75	C₂⁴×C₁₉	—	2	2	no	—
76	C₂⁴×C₁₉	—	4	2	no	—
77	C₂⁴×C₁₉	C₄⋊C₄	1	4	yes	—
78	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	—	2	4	no	—
82	C₂²×C₄×C₁₉	—	2	4	no	—
83	C₂²×C₄×C₁₉	—	2	4	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	4	no	—
87	C₂²×C₄×C₁₉	—	4	8	no	—
88	C₂²×C₄×C₁₉	—	4	8	no	—
89	C₂²×C₄×C₁₉	—	4	2	no	—
90	C₂²×C₄×C₁₉	—	4	2	no	—
91	C₂²×C₄×C₁₉	—	4	2	no	—
92	C₂²×C₄×C₁₉	—	4	4	no	—
93	C₂²×C₄×C₁₉	—	4	4	no	—
94	C₂²×C₄×C₁₉	—	4	4	no	—
95	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
96	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
97	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
98	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₁₉	—	2	4	no	—
109	C₂×C₈×C₁₉	—	2	4	no	—
110	C₂×C₈×C₁₉	—	4	8	no	—
111	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
112	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
113	C₄⋊C₄×C₁₉	—	2	4	no	—
114	C₄⋊C₄×C₁₉	—	2	4	no	—
115	C₄⋊C₄×C₁₉	—	2	4	no	—
116	C₄⋊C₄×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	4	4	no	—
118	C₂²⋊C₄×C₁₉	—	4	4	no	—
119	C₂²⋊C₄×C₁₉	—	4	4	no	—
120	C₂²⋊C₄×C₁₉	—	4	4	no	—
121	C₂²⋊C₄×C₁₉	—	4	2	no	—
122	C₂²⋊C₄×C₁₉	—	4	4	no	—
123	C₂²⋊C₄×C₁₉	—	4	2	no	—
124	C₄²×C₁₉	—	4	4	no	—
125	#21941	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₁₉	—	2	2	no	—
127	C₂³×C₁₉	—	2	2	no	—
128	C₂³×C₁₉	—	2	2	no	—
129	C₂³×C₁₉	—	2	1	no	—
130	C₂³×C₁₉	—	2	1	no	—
131	C₂³×C₁₉	—	2	2	no	—
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	2	1	no	—
134	C₂³×C₁₉	—	2	1	no	—
135	C₂³×C₁₉	—	2	8	no	—
136	C₂³×C₁₉	—	2	8	no	—
137	C₂³×C₁₉	—	4	4	no	—
138	C₂³×C₁₉	—	4	8	no	—
139	C₂³×C₁₉	—	4	8	no	—
140	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
141	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
142	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
143	C₂³×C₁₉	#135	1	4	yes	—
144	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
145	C₂³×C₁₉	#137	1	2	yes	—
146	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	4	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	4	4	no	—
157	C₂×C₄×C₁₉	—	4	4	no	—
158	C₂×C₄×C₁₉	—	4	4	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	4	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	4	no	—
165	C₂×C₄×C₁₉	—	4	4	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	8	8	no	—
169	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
170	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
175	C₈×C₁₉	—	2	4	no	—
176	C₈×C₁₉	—	2	4	no	—
177	C₂²×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic
178	#2280	C₂×C₁₉	1	1	yes	characteristic
179	C₂×#380	C₂×C₁₉	1	1	yes	characteristic
180	#1854	C₂×C₁₉	1	4	yes	complemented
181	#1853	C₂×C₁₉	1	2	yes	complemented
182	#1852	C₂×C₁₉	1	2	yes	complemented
183	#1808	C₂×C₁₉	1	2	yes	complemented
184	#1807	C₂×C₁₉	1	2	yes	complemented
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	—	2	4	no	—
190	C₂²×C₁₉	—	2	4	no	—
191	C₂²×C₁₉	—	2	4	no	—
192	C₂²×C₁₉	—	2	4	no	—
193	C₂²×C₁₉	—	2	2	no	—
194	C₂²×C₁₉	—	2	2	no	—
195	C₂²×C₁₉	—	2	2	no	—
196	C₂²×C₁₉	—	4	16	no	—
197	C₂²×C₁₉	—	4	2	no	—
198	C₂²×C₁₉	—	4	2	no	—
199	C₂²×C₁₉	#427	1	4	yes	—
200	C₂²×C₁₉	#428	1	4	yes	—
201	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
202	C₂²×C₁₉	#534	1	2	yes	—
203	C₂²×C₁₉	C₂×#135	1	2	yes	—
204	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
205	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
206	C₄×C₁₉	—	2	2	no	—
207	C₄×C₁₉	—	2	2	no	—
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	8	2	no	—
210	C₄×C₁₉	—	8	4	no	—
211	C₄×C₁₉	—	8	2	no	—
212	C₄×C₁₉	#518	1	2	yes	—
213	C₄×C₁₉	#543	1	2	yes	—
214	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
215	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
216	C₂×#117	C₂²×C₁₉	1	2	yes	—
217	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
218	C₂²×C₂²⋊C₄	—	2	1	no	—
219	C₂×#107	C₂²×C₁₉	1	4	yes	complemented
220	C₂×#106	C₂²×C₁₉	1	4	yes	complemented
221	C₂×C₂²⋊C₈	C₄×C₁₉	1	8	yes	complemented
222	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
223	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
225	#381	—	2	1	no	—
226	#380	—	2	1	no	—
227	#380	—	2	1	no	—
228	#380	C₂²×C₁₉	1	1	yes	characteristic
229	#380	C₂²×C₁₉	1	2	yes	—
230	#380	C₂²×C₁₉	1	1	yes	characteristic
231	#380	C₂²×C₁₉	1	2	yes	—
232	#380	C₂²×C₁₉	1	2	yes	—
233	#379	—	2	1	no	—
234	C₄×C₂²⋊C₄	—	2	1	no	—
235	C₄×C₂²⋊C₄	—	2	1	no	—
236	C₂×#95	—	2	1	no	—
237	#340	C₂²×C₁₉	1	4	yes	complemented
238	#340	C₂²×C₁₉	1	4	yes	complemented
239	C₂×C₁₉	—	2	4	no	—
240	C₂×C₁₉	—	2	4	no	—
241	C₂×C₁₉	—	4	2	no	—
242	C₂×C₁₉	#2315	1	1	yes	characteristic
243	C₂×C₁₉	C₂×#427	1	1	yes	characteristic
244	C₂×C₁₉	C₂×#428	1	1	yes	characteristic
245	C₂×C₁₉	#3188	1	2	yes	—
246	C₂×C₁₉	#3190	1	2	yes	—
247	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
248	C₂³×C₄	—	2	2	no	—
249	C₂³×C₄	—	4	4	no	—
250	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
251	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
252	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
253	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
254	C₂³×C₄	Q₈×C₁₉	1	4	yes	—
255	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
256	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
258	C₂²×C₈	—	4	4	no	—
259	C₂²×C₈	C₂×C₄×C₁₉	1	8	yes	complemented
260	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
261	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
262	#117	—	4	4	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	4	4	no	—
265	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₂²⋊C₄	—	4	4	no	—
275	C₂×C₄²	—	2	2	no	—
276	#107	—	4	4	no	—
277	#106	—	4	4	no	—
278	C₂²⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
279	C₂²⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
280	C₂²⋊C₈	C₂×C₄×C₁₉	1	8	yes	complemented
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	1	no	—
284	#95	—	2	1	no	—
285	#95	—	2	2	no	—
286	C₁₉	#21941	1	1	yes	characteristic, direct product factor, Sylow
287	C₂⁴	—	2	4	no	—
288	C₂⁴	—	2	2	no	—
289	C₂⁴	—	2	2	no	—
290	C₂⁴	—	4	2	no	—
291	C₂⁴	C₄⋊C₄×C₁₉	1	4	yes	—
292	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
293	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
294	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	4	8	no	—
302	C₂²×C₄	—	4	8	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
310	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
311	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
312	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
314	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
319	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
320	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
321	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	4	no	—
324	C₂×C₈	—	4	8	no	—
325	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
326	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₂²⋊C₄	—	4	4	no	—
333	C₂²⋊C₄	—	4	4	no	—
334	C₂²⋊C₄	—	4	4	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	4	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₄²	—	4	4	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	8	no	—
345	C₂³	—	2	8	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	4	4	no	—
351	C₂³	—	4	8	no	—
352	C₂³	—	4	8	no	—
353	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
354	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
355	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
356	C₂³	C₁₉×#135	1	4	yes	—
357	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
358	C₂³	C₁₉×#137	1	2	yes	—
359	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	8	8	no	—
382	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
383	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
384	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
385	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
386	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
387	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
388	C₈	—	2	4	no	—
389	C₈	—	2	4	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	2	4	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	16	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	C₁₉×#427	1	4	yes	—
405	C₂²	C₁₉×#428	1	4	yes	—
406	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
407	C₂²	C₁₉×#534	1	2	yes	—
408	C₂²	C₂×C₁₉×#135	1	2	yes	—
409	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
410	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	8	4	no	—
415	C₄	—	8	2	no	—
416	C₄	—	8	2	no	—
417	C₄	C₁₉×#518	1	2	yes	—
418	C₄	C₁₉×#543	1	2	yes	—
419	C₂	—	2	4	no	—
420	C₂	—	2	4	no	—
421	C₂	—	4	2	no	—
422	C₂	C₁₉×#2315	1	1	yes	characteristic
423	C₂	C₂×C₁₉×#427	1	1	yes	characteristic
424	C₂	C₂×C₁₉×#428	1	1	yes	characteristic
425	C₂	C₁₉×#3188	1	2	yes	—
426	C₂	C₁₉×#3190	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	C₂⁵×C₁₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1854	C₂	semidirect
5. C₁₉×#1853	C₂	semidirect
6. C₁₉×#1852	C₂	semidirect
7. C₁₉×#1808	C₂	semidirect
8. C₁₉×#1807	C₂	semidirect
14. C₂×C₁₉×#107	C₂²	semidirect
15. C₂×C₁₉×#106	C₂²	semidirect
16. C₂×C₁₉×C₂²⋊C₈	C₄	semidirect
32. C₁₉×#340	C₂²	semidirect
33. C₁₉×#340	C₂²	semidirect
46. C₂²×C₈×C₁₉	C₂×C₄	semidirect
67. C₁₉×C₂²⋊C₈	C₂×C₄	semidirect
125. #21941	C₁₉	direct (N × H)
180. #1854	C₂×C₁₉	semidirect
181. #1853	C₂×C₁₉	semidirect
182. #1852	C₂×C₁₉	semidirect
183. #1808	C₂×C₁₉	semidirect
184. #1807	C₂×C₁₉	semidirect
219. C₂×#107	C₂²×C₁₉	semidirect
220. C₂×#106	C₂²×C₁₉	semidirect
221. C₂×C₂²⋊C₈	C₄×C₁₉	semidirect
237. #340	C₂²×C₁₉	semidirect
238. #340	C₂²×C₁₉	semidirect
259. C₂²×C₈	C₂×C₄×C₁₉	semidirect
280. C₂²⋊C₈	C₂×C₄×C₁₉	semidirect
286. C₁₉	#21941	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₂²⋊C₈	2
C₁₉×#2280	2
C₂×C₁₉×#380	2
C₁₉×#1854	2
C₁₉×#1853	2
C₁₉×#1852	2
C₁₉×#1808	2
C₁₉×#1807	2
#21941	19

Subgroups — C19×#21941 #18027900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21941 #18027900