Subgroups — C₁₉×#23060 #18029019

Order 4864.

854 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#474	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2354	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1947	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1934	C₂	1	2	yes	maximal
7	C₁₉×#1925	C₂	1	2	yes	maximal
8	C₁₉×#1918	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₉×#107	C₂	1	2	yes	maximal, complemented
10	C₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₉×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
14	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	—	2	1	no	—
16	C₁₉×#474	C₄	1	8	yes	complemented
17	C₂×C₁₉×#107	C₂²	1	2	yes	—
18	C₂×C₁₉×#107	C₂²	1	2	yes	—
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#102	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#391	—	2	1	no	—
26	C₁₉×#390	C₂²	1	2	yes	—
27	C₁₉×#389	C₂²	1	2	yes	—
28	C₁₉×#388	—	2	2	no	—
29	C₁₉×#387	—	2	2	no	—
30	C₁₉×#384	C₂²	1	1	yes	characteristic
31	C₁₉×#380	—	2	1	no	—
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#340	C₂²	1	1	yes	characteristic
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	1	yes	characteristic
41	C₁₉×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₁₉×C₄⋊Q₈	—	2	2	no	—
49	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
50	C₄×Q₈×C₁₉	—	4	4	no	—
51	C₄×D₄×C₁₉	—	2	2	no	—
52	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
53	C₁₉×#117	—	4	4	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₄²×C₁₉	—	2	2	no	—
69	C₂×C₄²×C₁₉	—	2	2	no	—
70	C₂×C₄²×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×#107	—	2	4	no	—
74	C₁₉×#107	C₂×C₄	1	8	yes	—
75	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
76	C₁₉×#102	—	2	2	no	—
77	C₁₉×#102	—	2	2	no	—
78	C₁₉×#102	C₂×C₄	1	8	yes	—
79	C₄×C₈×C₁₉	—	2	4	no	—
80	C₄×C₈×C₁₉	—	2	2	no	—
81	C₁₉×#95	—	2	2	no	—
82	C₁₉×#95	—	2	1	no	—
83	C₁₉×#95	—	2	2	no	—
84	C₁₉×#95	—	2	2	no	—
85	C₁₉×#95	D₄	1	2	yes	—
86	C₂⁴×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	4	no	—
88	C₂×Q₈×C₁₉	—	4	2	no	—
89	C₂×Q₈×C₁₉	—	4	2	no	—
90	C₂×D₄×C₁₉	—	2	1	no	—
91	C₂×D₄×C₁₉	—	2	1	no	—
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
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	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	4	2	no	—
103	C₂²×C₄×C₁₉	—	4	2	no	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	1	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	1	no	—
113	C₂×C₈×C₁₉	—	2	1	no	—
114	C₂×C₈×C₁₉	—	2	1	no	—
115	C₂×C₈×C₁₉	—	2	1	no	—
116	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
117	C₂×C₈×C₁₉	#41	1	2	yes	—
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	4	2	no	—
128	C₄⋊C₄×C₁₉	—	4	4	no	—
129	C₄⋊C₄×C₁₉	—	8	1	no	—
130	C₄⋊C₄×C₁₉	D₈	1	4	yes	—
131	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
132	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
133	C₄⋊C₄×C₁₉	#41	1	2	yes	—
134	C₂²⋊C₄×C₁₉	—	2	4	no	—
135	C₂²⋊C₄×C₁₉	—	4	4	no	—
136	C₂²⋊C₄×C₁₉	—	8	2	no	—
137	C₄²×C₁₉	—	2	2	no	—
138	C₄²×C₁₉	—	2	2	no	—
139	C₄²×C₁₉	—	4	4	no	—
140	C₄²×C₁₉	—	4	4	no	—
141	C₄²×C₁₉	—	4	2	no	—
142	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
143	C₄²×C₁₉	#41	1	2	yes	—
144	#23060	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	4	1	no	—
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₁₉	—	4	8	no	—
154	D₄×C₁₉	—	2	2	no	—
155	D₄×C₁₉	—	2	2	no	—
156	D₄×C₁₉	—	4	1	no	—
157	D₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	8	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
183	C₂×C₄×C₁₉	C₂×D₈	1	4	yes	—
184	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
185	C₂×C₄×C₁₉	#135	1	2	yes	—
186	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
191	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
192	C₈×C₁₉	—	2	4	no	—
193	C₈×C₁₉	—	2	2	no	—
194	C₈×C₁₉	—	4	1	no	—
195	C₂×#474	C₂×C₁₉	1	1	yes	characteristic
196	#2365	C₂×C₁₉	1	1	yes	characteristic, complemented
197	#2354	C₂×C₁₉	1	1	yes	characteristic
198	#1990	C₂×C₁₉	1	1	yes	characteristic, complemented
199	#1947	C₂×C₁₉	1	1	yes	characteristic, complemented
200	#1934	C₂×C₁₉	1	2	yes	—
201	#1925	C₂×C₁₉	1	2	yes	—
202	#1918	C₂×C₁₉	1	2	yes	complemented
203	C₄×#107	C₂×C₁₉	1	2	yes	complemented
204	C₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
205	C₄×#102	C₂×C₁₉	1	1	yes	characteristic
206	C₂²×C₁₉	—	4	2	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	4	2	no	—
209	C₂²×C₁₉	—	8	1	no	—
210	C₂²×C₁₉	—	8	1	no	—
211	C₂²×C₁₉	—	8	1	no	—
212	C₂²×C₁₉	—	8	1	no	—
213	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
214	C₂²×C₁₉	#547	1	1	yes	characteristic
215	C₂²×C₁₉	#548	1	1	yes	characteristic
216	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
217	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
218	C₂²×C₁₉	#577	1	1	yes	characteristic
219	C₂²×C₁₉	#578	1	1	yes	characteristic
220	C₄×C₁₉	—	2	4	no	—
221	C₄×C₁₉	—	2	2	no	—
222	C₄×C₁₉	—	4	2	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	—	4	4	no	—
226	C₄×C₁₉	—	8	1	no	—
227	C₄×C₁₉	—	8	2	no	—
228	C₄×C₁₉	C₄×D₈	1	4	yes	—
229	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
230	C₄×C₁₉	#519	1	1	yes	characteristic
231	C₄×C₁₉	#552	1	1	yes	characteristic
232	C₄×C₁₉	#556	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×C₄×Q₈	—	2	1	no	—
235	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×#117	—	2	1	no	—
237	#474	C₄×C₁₉	1	8	yes	complemented
238	C₂×#107	C₂²×C₁₉	1	2	yes	—
239	C₂×#107	C₂²×C₁₉	1	2	yes	—
240	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
241	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
242	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
243	C₂×#102	C₂²×C₁₉	1	2	yes	—
244	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
245	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
246	#391	—	2	1	no	—
247	#390	C₂²×C₁₉	1	2	yes	—
248	#389	C₂²×C₁₉	1	2	yes	—
249	#388	—	2	2	no	—
250	#387	—	2	2	no	—
251	#384	C₂²×C₁₉	1	1	yes	characteristic
252	#380	—	2	1	no	—
253	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
254	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
255	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
256	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
257	#340	C₂²×C₁₉	1	1	yes	characteristic
258	#340	C₂²×C₁₉	1	2	yes	—
259	#340	C₂²×C₁₉	1	2	yes	—
260	#340	C₂²×C₁₉	1	2	yes	—
261	#340	C₂²×C₁₉	1	1	yes	characteristic
262	#336	C₂²×C₁₉	1	2	yes	—
263	C₂×C₁₉	—	8	2	no	—
264	C₂×C₁₉	#2362	1	1	yes	characteristic
265	C₂×C₁₉	C₂×C₄×D₈	1	1	yes	characteristic
266	C₂×C₁₉	#2947	1	1	yes	characteristic
267	C₂×C₁₉	#3334	1	1	yes	characteristic
268	C₂×C₁₉	#3340	1	1	yes	characteristic
269	C₂×C₁₉	#3358	1	1	yes	characteristic
270	C₂×C₁₉	#3364	1	1	yes	characteristic
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
273	C₂³×C₄	—	2	1	no	—
274	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
276	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
279	C₄×Q₈	—	4	4	no	—
280	C₄×D₄	—	2	2	no	—
281	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
282	#117	—	4	4	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
288	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
301	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
302	#107	—	2	4	no	—
303	#107	C₂×C₄×C₁₉	1	8	yes	—
304	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
305	#102	—	2	2	no	—
306	#102	—	2	2	no	—
307	#102	C₂×C₄×C₁₉	1	8	yes	—
308	C₄×C₈	—	2	4	no	—
309	C₄×C₈	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	1	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	#95	D₄×C₁₉	1	2	yes	—
315	C₁₉	#23060	1	1	yes	characteristic, direct product factor, Sylow
316	C₂⁴	—	2	1	no	—
317	C₂×Q₈	—	2	4	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
347	C₂×C₈	#41×C₁₉	1	2	yes	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	4	no	—
359	C₄⋊C₄	—	8	1	no	—
360	C₄⋊C₄	D₈×C₁₉	1	4	yes	—
361	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
362	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
363	C₄⋊C₄	#41×C₁₉	1	2	yes	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	4	4	no	—
366	C₂²⋊C₄	—	8	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	4	4	no	—
370	C₄²	—	4	4	no	—
371	C₄²	—	4	2	no	—
372	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
373	C₄²	#41×C₁₉	1	2	yes	—
374	C₂³	—	2	2	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
382	Q₈	—	4	8	no	—
383	D₄	—	2	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	1	no	—
386	D₄	—	4	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	8	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
411	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
412	C₂×C₄	C₂×D₈×C₁₉	1	4	yes	—
413	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
414	C₂×C₄	C₁₉×#135	1	2	yes	—
415	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
418	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
419	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
420	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
421	C₈	—	2	4	no	—
422	C₈	—	2	2	no	—
423	C₈	—	4	1	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
432	C₂²	C₁₉×#547	1	1	yes	characteristic
433	C₂²	C₁₉×#548	1	1	yes	characteristic
434	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
435	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
436	C₂²	C₁₉×#577	1	1	yes	characteristic
437	C₂²	C₁₉×#578	1	1	yes	characteristic
438	C₄	—	2	2	no	—
439	C₄	—	2	4	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	4	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	2	no	—
446	C₄	C₄×D₈×C₁₉	1	4	yes	—
447	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
448	C₄	C₁₉×#519	1	1	yes	characteristic
449	C₄	C₁₉×#552	1	1	yes	characteristic
450	C₄	C₁₉×#556	1	1	yes	characteristic
451	C₂	—	8	2	no	—
452	C₂	C₁₉×#2362	1	1	yes	characteristic
453	C₂	C₂×C₄×D₈×C₁₉	1	1	yes	characteristic
454	C₂	C₁₉×#2947	1	1	yes	characteristic
455	C₂	C₁₉×#3334	1	1	yes	characteristic
456	C₂	C₁₉×#3340	1	1	yes	characteristic
457	C₂	C₁₉×#3358	1	1	yes	characteristic
458	C₂	C₁₉×#3364	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2365	C₂	semidirect
4. C₁₉×#1990	C₂	semidirect
5. C₁₉×#1947	C₂	semidirect
8. C₁₉×#1918	C₂	semidirect
9. C₄×C₁₉×#107	C₂	semidirect
10. C₈×C₄⋊C₄×C₁₉	C₂	semidirect
16. C₁₉×#474	C₄	semidirect
144. #23060	C₁₉	direct (N × H)
196. #2365	C₂×C₁₉	semidirect
198. #1990	C₂×C₁₉	semidirect
199. #1947	C₂×C₁₉	semidirect
202. #1918	C₂×C₁₉	semidirect
203. C₄×#107	C₂×C₁₉	semidirect
204. C₈×C₄⋊C₄	C₂×C₁₉	semidirect
237. #474	C₄×C₁₉	semidirect
315. C₁₉	#23060	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×#474	2
C₁₉×#2365	2
C₁₉×#2354	2
C₁₉×#1990	2
C₁₉×#1947	2
C₁₉×#1934	2
C₁₉×#1925	2
C₁₉×#1918	2
C₄×C₁₉×#107	2
C₈×C₄⋊C₄×C₁₉	2
C₄×C₁₉×#102	2
#23060	19

Subgroups — C19×#23060 #18029019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23060 #18029019