Subgroups — C₁₉×#21182 #18027141

Order 4864.

882 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#430	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2911	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2873	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1952	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1951	C₂	1	4	yes	maximal, complemented
8	C₁₉×#1742	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#430	C₄	1	8	yes	complemented
18	C₂×C₁₉×#108	C₂²	1	4	yes	—
19	C₁₉×#428	—	2	2	no	—
20	C₁₉×#428	—	2	2	no	—
21	C₁₉×#428	—	2	2	no	—
22	C₁₉×#428	—	2	1	no	—
23	C₁₉×#428	—	2	1	no	—
24	C₁₉×#428	C₂²	1	2	yes	—
25	C₁₉×#428	C₂²	1	2	yes	—
26	C₁₉×#428	C₂²	1	4	yes	—
27	C₁₉×#427	—	2	2	no	—
28	C₂×C₁₉×#107	—	2	1	no	—
29	C₂×C₁₉×#107	C₂²	1	2	yes	—
30	C₂×C₁₉×#106	—	2	1	no	—
31	C₂×C₁₉×#106	C₂²	1	2	yes	—
32	C₁₉×#405	—	2	2	no	—
33	C₁₉×#405	C₂²	1	4	yes	—
34	C₄×M₁₆×C₁₉	—	2	2	no	—
35	C₁₉×#343	C₂²	1	2	yes	—
36	C₁₉×#343	C₂²	1	4	yes	—
37	C₁₉×#343	C₂²	1	2	yes	—
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×M₁₆×C₁₉	—	2	1	no	—
41	C₂×M₁₆×C₁₉	—	2	1	no	—
42	C₂×M₁₆×C₁₉	—	2	1	no	—
43	C₂×M₁₆×C₁₉	—	2	2	no	—
44	C₂×M₁₆×C₁₉	—	2	2	no	—
45	C₂×M₁₆×C₁₉	—	2	2	no	—
46	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
47	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
48	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
49	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
50	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
51	C₂×M₁₆×C₁₉	Q₈	1	4	yes	—
52	C₂×M₁₆×C₁₉	Q₈	1	4	yes	—
53	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
54	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
55	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₉	—	2	1	no	—
57	C₂²×C₈×C₁₉	—	2	1	no	—
58	C₂²×C₈×C₁₉	—	2	1	no	—
59	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
60	C₁₉×#117	—	2	1	no	—
61	C₁₉×#117	—	2	1	no	—
62	C₁₉×#117	—	2	1	no	—
63	C₁₉×#117	—	2	1	no	—
64	C₁₉×#117	—	2	1	no	—
65	C₁₉×#117	—	2	1	no	—
66	C₁₉×#117	D₄	1	2	yes	—
67	C₁₉×#117	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄²×C₁₉	—	2	1	no	—
81	C₂×C₄²×C₁₉	—	2	1	no	—
82	C₁₉×#108	C₂×C₄	1	16	yes	complemented
83	C₁₉×#107	—	2	4	no	—
84	C₁₉×#107	—	2	4	no	—
85	C₁₉×#107	—	2	2	no	—
86	C₁₉×#107	—	2	2	no	—
87	C₁₉×#106	—	2	4	no	—
88	C₁₉×#106	—	2	4	no	—
89	C₁₉×#106	—	2	2	no	—
90	C₁₉×#106	—	2	2	no	—
91	C₁₉×#97	—	2	4	no	—
92	C₄×C₈×C₁₉	—	2	4	no	—
93	C₂⁴×C₁₉	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	8	2	no	—
102	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₁₉	#41	1	2	yes	—
110	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
112	M₁₆×C₁₉	—	2	4	no	—
113	M₁₆×C₁₉	—	2	4	no	—
114	M₁₆×C₁₉	—	2	4	no	—
115	M₁₆×C₁₉	—	2	2	no	—
116	M₁₆×C₁₉	—	2	2	no	—
117	M₁₆×C₁₉	—	2	2	no	—
118	M₁₆×C₁₉	C₄⋊C₄	1	8	yes	—
119	M₁₆×C₁₉	C₄⋊C₄	1	8	yes	—
120	M₁₆×C₁₉	C₂²×C₄	1	4	yes	—
121	M₁₆×C₁₉	C₂²×C₄	1	4	yes	—
122	M₁₆×C₁₉	C₂×Q₈	1	4	yes	—
123	C₂×C₈×C₁₉	—	2	4	no	—
124	C₂×C₈×C₁₉	—	2	4	no	—
125	C₂×C₈×C₁₉	—	2	4	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	C₂²×C₄	1	4	yes	—
130	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
131	C₂×C₈×C₁₉	C₂×Q₈	1	4	yes	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	4	1	no	—
141	C₄⋊C₄×C₁₉	—	4	1	no	—
142	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
143	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²⋊C₄×C₁₉	—	2	2	no	—
145	C₂²⋊C₄×C₁₉	—	2	2	no	—
146	C₂²⋊C₄×C₁₉	—	4	1	no	—
147	C₂²⋊C₄×C₁₉	—	4	1	no	—
148	C₄²×C₁₉	—	2	2	no	—
149	C₄²×C₁₉	—	2	2	no	—
150	C₄²×C₁₉	—	4	1	no	—
151	C₄²×C₁₉	—	4	1	no	—
152	#21182	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂³×C₁₉	—	4	1	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	C₄×Q₈	1	2	yes	—
156	C₂³×C₁₉	#121	1	1	yes	characteristic
157	C₂³×C₁₉	#121	1	1	yes	characteristic
158	C₂³×C₁₉	#125	1	2	yes	—
159	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	8	1	no	—
166	C₂×C₄×C₁₉	—	8	1	no	—
167	C₂×C₄×C₁₉	—	8	2	no	—
168	C₂×C₄×C₁₉	—	8	2	no	—
169	C₂×C₄×C₁₉	—	8	1	no	—
170	C₂×C₄×C₁₉	—	8	1	no	—
171	C₂×C₄×C₁₉	—	8	2	no	—
172	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
173	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
177	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
180	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
181	C₂×C₄×C₁₉	#125	1	2	yes	—
182	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
183	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
184	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
190	C₈×C₁₉	—	2	4	no	—
191	C₈×C₁₉	—	2	4	no	—
192	C₈×C₁₉	—	2	4	no	—
193	C₈×C₁₉	C₂×C₄⋊C₄	1	8	yes	—
194	C₂×#430	C₂×C₁₉	1	1	yes	characteristic
195	#2911	C₂×C₁₉	1	1	yes	characteristic
196	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
197	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
198	#2873	C₂×C₁₉	1	1	yes	characteristic
199	#1952	C₂×C₁₉	1	4	yes	complemented
200	#1951	C₂×C₁₉	1	4	yes	complemented
201	#1742	C₂×C₁₉	1	1	yes	characteristic
202	C₂×#343	C₂×C₁₉	1	1	yes	characteristic
203	C₂²×C₁₉	—	2	1	no	—
204	C₂²×C₁₉	—	2	1	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	2	1	no	—
207	C₂²×C₁₉	—	2	1	no	—
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	#389	1	2	yes	—
212	C₂²×C₁₉	#389	1	2	yes	—
213	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
214	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
215	C₂²×C₁₉	C₂×#125	1	1	yes	characteristic
216	C₄×C₁₉	—	4	2	no	—
217	C₄×C₁₉	—	4	2	no	—
218	C₄×C₁₉	—	8	1	no	—
219	C₄×C₁₉	—	8	2	no	—
220	C₄×C₁₉	—	8	1	no	—
221	C₄×C₁₉	#389	1	2	yes	—
222	C₄×C₁₉	#389	1	2	yes	—
223	C₄×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
224	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
225	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
226	C₄×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
227	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
228	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
229	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
230	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
231	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
232	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
233	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
234	#430	C₄×C₁₉	1	8	yes	complemented
235	C₂×#108	C₂²×C₁₉	1	4	yes	—
236	#428	—	2	2	no	—
237	#428	—	2	2	no	—
238	#428	—	2	2	no	—
239	#428	—	2	1	no	—
240	#428	—	2	1	no	—
241	#428	C₂²×C₁₉	1	4	yes	—
242	#428	C₂²×C₁₉	1	2	yes	—
243	#428	C₂²×C₁₉	1	2	yes	—
244	#427	—	2	2	no	—
245	C₂×#107	—	2	1	no	—
246	C₂×#107	C₂²×C₁₉	1	2	yes	—
247	C₂×#106	—	2	1	no	—
248	C₂×#106	C₂²×C₁₉	1	2	yes	—
249	#405	—	2	2	no	—
250	#405	C₂²×C₁₉	1	4	yes	—
251	C₄×M₁₆	—	2	2	no	—
252	#343	C₂²×C₁₉	1	2	yes	—
253	#343	C₂²×C₁₉	1	4	yes	—
254	#343	C₂²×C₁₉	1	2	yes	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	—	2	1	no	—
257	C₂×C₁₉	—	2	2	no	—
258	C₂×C₁₉	—	2	2	no	—
259	C₂×C₁₉	C₂×#389	1	1	yes	characteristic
260	C₂×C₁₉	#3068	1	1	yes	characteristic
261	C₂×C₁₉	#3069	1	1	yes	characteristic
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
271	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
272	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
273	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
274	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
275	C₂×M₁₆	Q₈×C₁₉	1	4	yes	—
276	C₂×M₁₆	Q₈×C₁₉	1	4	yes	—
277	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
278	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
279	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
284	#117	—	2	1	no	—
285	#117	—	2	1	no	—
286	#117	—	2	1	no	—
287	#117	—	2	1	no	—
288	#117	—	2	1	no	—
289	#117	—	2	1	no	—
290	#117	D₄×C₁₉	1	2	yes	—
291	#117	C₂³×C₁₉	1	2	yes	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
298	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	—	2	1	no	—
306	#108	C₂×C₄×C₁₉	1	16	yes	complemented
307	#107	—	2	4	no	—
308	#107	—	2	4	no	—
309	#107	—	2	2	no	—
310	#107	—	2	2	no	—
311	#106	—	2	4	no	—
312	#106	—	2	4	no	—
313	#106	—	2	2	no	—
314	#106	—	2	2	no	—
315	#97	—	2	4	no	—
316	C₄×C₈	—	2	4	no	—
317	C₁₉	#21182	1	1	yes	characteristic, direct product factor, Sylow
318	C₂⁴	#41×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	8	2	no	—
327	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
333	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
334	C₂²×C₄	#41×C₁₉	1	2	yes	—
335	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
337	M₁₆	—	2	4	no	—
338	M₁₆	—	2	4	no	—
339	M₁₆	—	2	4	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	C₄⋊C₄×C₁₉	1	8	yes	—
344	M₁₆	C₄⋊C₄×C₁₉	1	8	yes	—
345	M₁₆	C₂²×C₄×C₁₉	1	4	yes	—
346	M₁₆	C₂²×C₄×C₁₉	1	4	yes	—
347	M₁₆	C₂×Q₈×C₁₉	1	4	yes	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	4	no	—
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
355	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
356	C₂×C₈	C₂×Q₈×C₁₉	1	4	yes	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
368	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	4	1	no	—
372	C₂²⋊C₄	—	4	1	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	4	1	no	—
376	C₄²	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	C₄×Q₈×C₁₉	1	2	yes	—
380	C₂³	C₁₉×#121	1	1	yes	characteristic
381	C₂³	C₁₉×#121	1	1	yes	characteristic
382	C₂³	C₁₉×#125	1	2	yes	—
383	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	8	1	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	—	8	2	no	—
394	C₂×C₄	—	8	1	no	—
395	C₂×C₄	—	8	1	no	—
396	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
397	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
398	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
399	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
400	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
401	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
402	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
403	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
404	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
405	C₂×C₄	C₁₉×#125	1	2	yes	—
406	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
407	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
408	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
410	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
411	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
412	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
414	C₈	—	2	4	no	—
415	C₈	—	2	4	no	—
416	C₈	—	2	4	no	—
417	C₈	C₂×C₄⋊C₄×C₁₉	1	8	yes	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	C₁₉×#389	1	2	yes	—
427	C₂²	C₁₉×#389	1	2	yes	—
428	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
429	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
430	C₂²	C₂×C₁₉×#125	1	1	yes	characteristic
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	1	no	—
435	C₄	—	8	1	no	—
436	C₄	C₁₉×#389	1	2	yes	—
437	C₄	C₁₉×#389	1	2	yes	—
438	C₄	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
439	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
440	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
441	C₄	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
442	C₂	—	2	2	no	—
443	C₂	—	2	2	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	C₂×C₁₉×#389	1	1	yes	characteristic
447	C₂	C₁₉×#3068	1	1	yes	characteristic
448	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₁₉×#1952	C₂	semidirect
7. C₁₉×#1951	C₂	semidirect
17. C₁₉×#430	C₄	semidirect
82. C₁₉×#108	C₂×C₄	semidirect
152. #21182	C₁₉	direct (N × H)
199. #1952	C₂×C₁₉	semidirect
200. #1951	C₂×C₁₉	semidirect
234. #430	C₄×C₁₉	semidirect
306. #108	C₂×C₄×C₁₉	semidirect
317. C₁₉	#21182	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#430	2
C₁₉×#2911	2
C₂×C₁₉×#428	2
C₁₉×#2873	2
C₁₉×#1952	2
C₁₉×#1951	2
C₁₉×#1742	2
C₂×C₁₉×#343	2
#21182	19

Subgroups — C19×#21182 #18027141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21182 #18027141