Subgroups — C₂×C₁₉×#1927 #18027014

Order 4864.

1238 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#391	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1927	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₉	—	2	1	no	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#106	—	2	4	no	—
18	C₂×C₁₉×#106	C₂²	1	4	yes	—
19	C₂×C₁₉×#103	—	2	4	no	—
20	C₂×C₁₉×#103	C₄	1	8	yes	complemented
21	C₂×C₁₉×#103	C₂²	1	4	yes	—
22	C₂×C₁₉×#103	C₂²	1	4	yes	—
23	C₁₉×#391	—	2	2	no	—
24	C₁₉×#391	C₂²	1	4	yes	—
25	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
27	C₂×C₁₉×#95	—	2	1	no	—
28	C₂×C₁₉×#95	—	2	1	no	—
29	C₂×C₁₉×#95	—	2	1	no	—
30	C₁₉×#340	C₂²	1	4	yes	—
31	C₁₉×#336	C₂²	1	4	yes	—
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	—	2	2	no	—
34	C₂²×Q₈×C₁₉	—	2	2	no	—
35	C₂²×Q₈×C₁₉	—	2	2	no	—
36	C₂²×Q₈×C₁₉	—	2	2	no	—
37	C₂²×Q₈×C₁₉	—	2	2	no	—
38	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
39	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₉	—	2	1	no	—
41	C₂³×C₄×C₁₉	—	2	1	no	—
42	C₂³×C₄×C₁₉	—	2	1	no	—
43	C₂³×C₄×C₁₉	—	2	1	no	—
44	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₉	—	2	2	no	—
48	C₂²×C₈×C₁₉	—	2	2	no	—
49	C₂²×C₈×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₂²×C₈×C₁₉	—	2	2	no	—
52	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
53	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₉	—	2	2	no	—
68	C₂×C₄²×C₁₉	—	2	2	no	—
69	C₂×C₄²×C₁₉	—	2	4	no	—
70	C₂×C₄²×C₁₉	—	4	4	no	—
71	C₂×C₄²×C₁₉	D₄	1	2	yes	—
72	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
73	C₁₉×#106	—	2	8	no	—
74	C₁₉×#103	—	2	8	no	—
75	C₁₉×#103	C₂×C₄	1	16	yes	complemented
76	C₁₉×#95	—	2	4	no	—
77	C₁₉×#95	—	2	4	no	—
78	C₁₉×#95	—	2	4	no	—
79	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂×Q₈×C₁₉	—	2	4	no	—
81	C₂×Q₈×C₁₉	—	2	2	no	—
82	C₂×Q₈×C₁₉	—	2	8	no	—
83	C₂×Q₈×C₁₉	—	2	8	no	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	2	2	no	—
87	C₂×Q₈×C₁₉	—	2	2	no	—
88	C₂×Q₈×C₁₉	—	4	2	no	—
89	C₂×Q₈×C₁₉	—	4	2	no	—
90	C₂×Q₈×C₁₉	—	4	4	no	—
91	C₂×Q₈×C₁₉	—	4	4	no	—
92	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	4	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	4	2	no	—
106	C₂²×C₄×C₁₉	—	4	2	no	—
107	C₂²×C₄×C₁₉	—	4	2	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	—	4	2	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	—	4	2	no	—
113	C₂²×C₄×C₁₉	—	4	2	no	—
114	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	—
115	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₉	#41	1	2	yes	—
121	C₂²×C₄×C₁₉	#41	1	2	yes	—
122	C₂²×C₄×C₁₉	#41	1	2	yes	—
123	C₂²×C₄×C₁₉	#41	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
125	C₂×C₈×C₁₉	—	2	8	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	—	2	2	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	4	4	no	—
132	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
133	C₄⋊C₄×C₁₉	—	2	4	no	—
134	C₄⋊C₄×C₁₉	—	2	4	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	4	2	no	—
140	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
141	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
142	C₄²×C₁₉	—	2	4	no	—
143	C₄²×C₁₉	—	2	2	no	—
144	C₄²×C₁₉	—	2	2	no	—
145	C₄²×C₁₉	—	4	8	no	—
146	C₂×#1927	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂³×C₁₉	C₄×D₄	1	2	yes	—
148	C₂³×C₁₉	#121	1	2	yes	—
149	C₂³×C₁₉	#123	1	2	yes	—
150	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
151	C₂³×C₁₉	#135	1	2	yes	—
152	C₂³×C₁₉	#137	1	2	yes	—
153	C₂³×C₁₉	#137	1	2	yes	—
154	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₁₉	—	2	4	no	—
156	Q₈×C₁₉	—	2	4	no	—
157	Q₈×C₁₉	—	4	2	no	—
158	Q₈×C₁₉	—	4	2	no	—
159	Q₈×C₁₉	—	4	8	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	8	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	8	no	—
176	C₂×C₄×C₁₉	—	4	8	no	—
177	C₂×C₄×C₁₉	—	4	8	no	—
178	C₂×C₄×C₁₉	—	4	4	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	8	4	no	—
183	C₂×C₄×C₁₉	#117	1	4	yes	—
184	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
185	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₁₉	#121	1	2	yes	—
187	C₂×C₄×C₁₉	#123	1	2	yes	—
188	C₂×C₄×C₁₉	#124	1	4	yes	—
189	C₂×C₄×C₁₉	#126	1	4	yes	—
190	C₂×C₄×C₁₉	C₂×SD₁₆	1	4	yes	—
191	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
197	C₈×C₁₉	—	2	4	no	—
198	C₈×C₁₉	—	4	2	no	—
199	C₂²×#106	C₂×C₁₉	1	1	yes	characteristic
200	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic
201	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic
202	C₂×#391	C₂×C₁₉	1	1	yes	characteristic
203	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
204	#1927	C₂×C₁₉	1	8	yes	direct product factor
205	C₂×#340	C₂×C₁₉	1	1	yes	characteristic
206	C₂×#336	C₂×C₁₉	1	1	yes	characteristic
207	C₂²×C₁₉	#388	1	4	yes	—
208	C₂²×C₁₉	C₄×SD₁₆	1	4	yes	—
209	C₂²×C₁₉	#441	1	4	yes	—
210	C₂²×C₁₉	#461	1	4	yes	—
211	C₂²×C₁₉	#464	1	4	yes	—
212	C₂²×C₁₉	#483	1	4	yes	—
213	C₂²×C₁₉	#485	1	4	yes	—
214	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
215	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
216	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
217	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
218	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
219	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
220	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
221	C₄×C₁₉	—	2	4	no	—
222	C₄×C₁₉	—	4	2	no	—
223	C₄×C₁₉	—	4	4	no	—
224	C₄×C₁₉	—	4	4	no	—
225	C₄×C₁₉	—	4	4	no	—
226	C₄×C₁₉	—	8	2	no	—
227	C₄×C₁₉	#388	1	4	yes	—
228	C₄×C₁₉	C₂×#117	1	1	yes	characteristic
229	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
230	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
231	C₄×C₁₉	C₂×#126	1	1	yes	characteristic
232	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
233	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
234	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
238	C₂²×C₄²	—	2	1	no	—
239	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
240	C₂×#106	—	2	4	no	—
241	C₂×#106	C₂²×C₁₉	1	4	yes	—
242	C₂×#103	—	2	4	no	—
243	C₂×#103	C₄×C₁₉	1	8	yes	complemented
244	C₂×#103	C₂²×C₁₉	1	4	yes	—
245	C₂×#103	C₂²×C₁₉	1	4	yes	—
246	#391	—	2	2	no	—
247	#391	C₂²×C₁₉	1	4	yes	—
248	C₄×C₄⋊C₄	—	2	2	no	—
249	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
250	C₂×#95	—	2	1	no	—
251	C₂×#95	—	2	1	no	—
252	C₂×#95	—	2	1	no	—
253	#340	C₂²×C₁₉	1	4	yes	—
254	#336	C₂²×C₁₉	1	4	yes	—
255	C₂×C₁₉	#1927	1	8	yes	direct product factor
256	C₂×C₁₉	C₂×#388	1	1	yes	characteristic
257	C₂×C₁₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
258	C₂×C₁₉	C₂×#441	1	1	yes	characteristic
259	C₂×C₁₉	C₂×#461	1	1	yes	characteristic
260	C₂×C₁₉	C₂×#464	1	1	yes	characteristic
261	C₂×C₁₉	C₂×#483	1	1	yes	characteristic
262	C₂×C₁₉	C₂×#485	1	1	yes	characteristic
263	C₂²×Q₈	—	2	1	no	—
264	C₂²×Q₈	—	2	2	no	—
265	C₂²×Q₈	—	2	2	no	—
266	C₂²×Q₈	—	2	2	no	—
267	C₂²×Q₈	—	2	2	no	—
268	C₂²×Q₈	—	2	2	no	—
269	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
270	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
271	C₂³×C₄	—	2	1	no	—
272	C₂³×C₄	—	2	1	no	—
273	C₂³×C₄	—	2	1	no	—
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
276	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
277	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	—
284	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
285	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
294	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	4	no	—
301	C₂×C₄²	—	4	4	no	—
302	C₂×C₄²	D₄×C₁₉	1	2	yes	—
303	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
304	#106	—	2	8	no	—
305	#103	—	2	8	no	—
306	#103	C₂×C₄×C₁₉	1	16	yes	complemented
307	#95	—	2	4	no	—
308	#95	—	2	4	no	—
309	#95	—	2	4	no	—
310	C₁₉	C₂×#1927	1	1	yes	characteristic, direct product factor, Sylow
311	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
312	C₂×Q₈	—	2	4	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	8	no	—
315	C₂×Q₈	—	2	8	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×Q₈	—	4	4	no	—
323	C₂×Q₈	—	4	4	no	—
324	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	SD₁₆×C₁₉	1	4	yes	—
347	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
352	C₂²×C₄	#41×C₁₉	1	2	yes	—
353	C₂²×C₄	#41×C₁₉	1	2	yes	—
354	C₂²×C₄	#41×C₁₉	1	2	yes	—
355	C₂²×C₄	#41×C₁₉	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
357	C₂×C₈	—	2	8	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	4	no	—
364	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
373	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
374	C₄²	—	2	4	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	4	8	no	—
378	C₂³	C₄×D₄×C₁₉	1	2	yes	—
379	C₂³	C₁₉×#121	1	2	yes	—
380	C₂³	C₁₉×#123	1	2	yes	—
381	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
382	C₂³	C₁₉×#135	1	2	yes	—
383	C₂³	C₁₉×#137	1	2	yes	—
384	C₂³	C₁₉×#137	1	2	yes	—
385	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
386	Q₈	—	2	4	no	—
387	Q₈	—	2	4	no	—
388	Q₈	—	4	8	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	4	2	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	—	4	8	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	8	4	no	—
414	C₂×C₄	C₁₉×#117	1	4	yes	—
415	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
416	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
417	C₂×C₄	C₁₉×#121	1	2	yes	—
418	C₂×C₄	C₁₉×#123	1	2	yes	—
419	C₂×C₄	C₁₉×#124	1	4	yes	—
420	C₂×C₄	C₁₉×#126	1	4	yes	—
421	C₂×C₄	C₂×SD₁₆×C₁₉	1	4	yes	—
422	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
424	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
427	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
428	C₈	—	2	4	no	—
429	C₈	—	4	2	no	—
430	C₂²	C₁₉×#388	1	4	yes	—
431	C₂²	C₄×SD₁₆×C₁₉	1	4	yes	—
432	C₂²	C₁₉×#441	1	4	yes	—
433	C₂²	C₁₉×#461	1	4	yes	—
434	C₂²	C₁₉×#464	1	4	yes	—
435	C₂²	C₁₉×#483	1	4	yes	—
436	C₂²	C₁₉×#485	1	4	yes	—
437	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
438	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
439	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
440	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
441	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
442	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
443	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
444	C₄	—	2	4	no	—
445	C₄	—	4	4	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	4	no	—
448	C₄	—	4	2	no	—
449	C₄	—	8	2	no	—
450	C₄	C₁₉×#388	1	4	yes	—
451	C₄	C₂×C₁₉×#117	1	1	yes	characteristic
452	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
453	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
454	C₄	C₂×C₁₉×#126	1	1	yes	characteristic
455	C₂	C₁₉×#1927	1	8	yes	direct product factor
456	C₂	C₂×C₁₉×#388	1	1	yes	characteristic
457	C₂	C₂×C₄×SD₁₆×C₁₉	1	1	yes	characteristic
458	C₂	C₂×C₁₉×#441	1	1	yes	characteristic
459	C₂	C₂×C₁₉×#461	1	1	yes	characteristic
460	C₂	C₂×C₁₉×#464	1	1	yes	characteristic
461	C₂	C₂×C₁₉×#483	1	1	yes	characteristic
462	C₂	C₂×C₁₉×#485	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. C₁₉×#1927	C₂	direct (N × H)
20. C₂×C₁₉×#103	C₄	semidirect
75. C₁₉×#103	C₂×C₄	semidirect
146. C₂×#1927	C₁₉	direct (N × H)
204. #1927	C₂×C₁₉	direct (N × H)
243. C₂×#103	C₄×C₁₉	semidirect
255. C₂×C₁₉	#1927	direct (N × H)
306. #103	C₂×C₄×C₁₉	semidirect
310. C₁₉	C₂×#1927	direct (N × H)
455. C₂	C₁₉×#1927	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×#106	2
C₂²×C₁₉×#103	2
C₂×C₁₉×#391	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₁₉×#1927	2
C₂×C₁₉×#340	2
C₂×C₁₉×#336	2
C₂×#1927	19

Subgroups — C2×C19×#1927 #18027014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1927 #18027014