Subgroups — C₁₉×#22996 #18028955

Order 4864.

1030 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#461	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₁₉	C₂	1	2	yes	maximal
3	C₁₉×#2365	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1933	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1877	C₂	1	2	yes	maximal
9	C₁₉×#1865	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	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
18	C₁₉×#461	C₄	1	8	yes	complemented
19	C₄×SD₁₆×C₁₉	—	2	8	no	—
20	C₂×C₁₉×#106	C₂²	1	2	yes	—
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#103	C₂²	1	2	yes	—
23	C₂×C₁₉×#103	C₂²	1	2	yes	—
24	C₂×C₁₉×#103	C₂²	1	2	yes	—
25	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#391	C₂²	1	2	yes	—
30	C₁₉×#389	—	2	1	no	—
31	C₁₉×#389	C₂²	1	2	yes	—
32	C₁₉×#387	—	2	2	no	—
33	C₁₉×#385	—	2	2	no	—
34	C₁₉×#384	C₂²	1	1	yes	characteristic
35	C₁₉×#380	—	2	1	no	—
36	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	1	yes	characteristic
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	1	yes	characteristic
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	—	2	2	no	—
47	C₂×SD₁₆×C₁₉	—	2	4	no	—
48	C₂×SD₁₆×C₁₉	—	2	4	no	—
49	C₂×SD₁₆×C₁₉	C₂×C₄	1	8	yes	—
50	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₁₉×C₄⋊Q₈	—	2	2	no	—
54	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
55	C₄×Q₈×C₁₉	—	2	4	no	—
56	C₄×Q₈×C₁₉	—	4	2	no	—
57	C₄×D₄×C₁₉	—	2	4	no	—
58	C₄×D₄×C₁₉	—	2	2	no	—
59	C₄×D₄×C₁₉	—	4	2	no	—
60	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
68	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄²×C₁₉	—	2	1	no	—
77	C₂×C₄²×C₁₉	—	2	2	no	—
78	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×#106	—	2	4	no	—
81	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
82	C₁₉×#103	—	2	4	no	—
83	C₁₉×#103	—	4	2	no	—
84	C₁₉×#103	C₂×C₄	1	8	yes	complemented
85	C₁₉×#102	—	2	2	no	—
86	C₁₉×#102	D₄	1	4	yes	—
87	C₄×C₈×C₁₉	—	2	4	no	—
88	C₄×C₈×C₁₉	—	2	2	no	—
89	C₁₉×#95	—	2	2	no	—
90	C₁₉×#95	—	2	1	no	—
91	C₁₉×#95	—	2	2	no	—
92	C₁₉×#95	—	2	2	no	—
93	C₁₉×#95	D₄	1	2	yes	—
94	C₂⁴×C₁₉	—	2	1	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
101	C₂×D₄×C₁₉	—	2	1	no	—
102	C₂×D₄×C₁₉	—	2	1	no	—
103	C₂×D₄×C₁₉	—	2	1	no	—
104	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
105	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₁₉	#41	1	2	yes	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	4	no	—
111	C₂²×C₄×C₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	4	4	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	—	4	2	no	—
116	C₂²×C₄×C₁₉	—	4	4	no	—
117	C₂²×C₄×C₁₉	—	8	2	no	—
118	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
123	SD₁₆×C₁₉	—	2	16	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	1	no	—
127	C₂×C₈×C₁₉	—	2	1	no	—
128	C₂×C₈×C₁₉	—	2	1	no	—
129	C₂×C₈×C₁₉	—	2	1	no	—
130	C₂×C₈×C₁₉	—	2	1	no	—
131	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
132	C₂×C₈×C₁₉	C₂×D₄	1	2	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	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	4	4	no	—
143	C₄⋊C₄×C₁₉	—	4	4	no	—
144	C₄⋊C₄×C₁₉	—	4	2	no	—
145	C₄⋊C₄×C₁₉	—	8	1	no	—
146	C₄⋊C₄×C₁₉	SD₁₆	1	4	yes	complemented
147	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
148	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
149	C₂²⋊C₄×C₁₉	—	2	4	no	—
150	C₂²⋊C₄×C₁₉	—	4	4	no	—
151	C₄²×C₁₉	—	2	2	no	—
152	C₄²×C₁₉	—	2	2	no	—
153	C₄²×C₁₉	—	4	4	no	—
154	C₄²×C₁₉	—	4	2	no	—
155	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
156	C₄²×C₁₉	#41	1	2	yes	—
157	#22996	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	—	2	2	no	—
161	C₂³×C₁₉	—	4	1	no	—
162	C₂³×C₁₉	—	4	1	no	—
163	C₂³×C₁₉	—	4	1	no	—
164	C₂³×C₁₉	—	4	1	no	—
165	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₁₉	—	2	4	no	—
167	Q₈×C₁₉	—	2	4	no	—
168	Q₈×C₁₉	—	4	2	no	—
169	Q₈×C₁₉	—	4	2	no	—
170	D₄×C₁₉	—	2	2	no	—
171	D₄×C₁₉	—	2	2	no	—
172	D₄×C₁₉	—	2	2	no	—
173	D₄×C₁₉	C₄×D₄	1	4	yes	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	8	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	8	8	no	—
198	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
199	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₁₉	C₂×SD₁₆	1	4	yes	—
201	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
202	C₂×C₄×C₁₉	#135	1	2	yes	—
203	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
209	C₈×C₁₉	—	2	4	no	—
210	C₈×C₁₉	—	2	2	no	—
211	C₈×C₁₉	—	4	1	no	—
212	C₂×#461	C₂×C₁₉	1	1	yes	characteristic
213	C₂×C₄×SD₁₆	C₂×C₁₉	1	2	yes	—
214	#2365	C₂×C₁₉	1	1	yes	characteristic, complemented
215	D₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
216	#1956	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#1948	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#1933	C₂×C₁₉	1	2	yes	complemented
219	#1877	C₂×C₁₉	1	2	yes	—
220	#1865	C₂×C₁₉	1	2	yes	complemented
221	C₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
222	C₄×#102	C₂×C₁₉	1	1	yes	characteristic
223	C₂²×C₁₉	—	2	4	no	—
224	C₂²×C₁₉	—	4	2	no	—
225	C₂²×C₁₉	—	4	2	no	—
226	C₂²×C₁₉	—	4	2	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	—	4	2	no	—
230	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
231	C₂²×C₁₉	D₄²	1	1	yes	characteristic
232	C₂²×C₁₉	#548	1	1	yes	characteristic
233	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
234	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
235	C₂²×C₁₉	#577	1	1	yes	characteristic
236	C₂²×C₁₉	#578	1	1	yes	characteristic
237	C₄×C₁₉	—	2	2	no	—
238	C₄×C₁₉	—	2	4	no	—
239	C₄×C₁₉	—	4	4	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	4	2	no	—
242	C₄×C₁₉	—	4	2	no	—
243	C₄×C₁₉	—	8	1	no	—
244	C₄×C₁₉	—	8	2	no	—
245	C₄×C₁₉	C₄×SD₁₆	1	4	yes	complemented
246	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
247	C₄×C₁₉	#520	1	1	yes	characteristic
248	C₄×C₁₉	#547	1	1	yes	characteristic
249	C₄×C₁₉	#553	1	1	yes	characteristic
250	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
251	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
253	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
254	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	—	2	1	no	—
256	#461	C₄×C₁₉	1	8	yes	complemented
257	C₄×SD₁₆	—	2	8	no	—
258	C₂×#106	C₂²×C₁₉	1	2	yes	—
259	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
260	C₂×#103	C₂²×C₁₉	1	2	yes	—
261	C₂×#103	C₂²×C₁₉	1	2	yes	—
262	C₂×#103	C₂²×C₁₉	1	2	yes	—
263	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
264	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
266	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
267	#391	C₂²×C₁₉	1	2	yes	—
268	#389	—	2	1	no	—
269	#389	C₂²×C₁₉	1	2	yes	—
270	#387	—	2	2	no	—
271	#385	—	2	2	no	—
272	#384	C₂²×C₁₉	1	1	yes	characteristic
273	#380	—	2	1	no	—
274	C₄×C₄⋊C₄	—	2	1	no	—
275	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
276	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
277	#340	C₂²×C₁₉	1	1	yes	characteristic
278	#340	C₂²×C₁₉	1	2	yes	—
279	#340	C₂²×C₁₉	1	1	yes	characteristic
280	#336	C₂²×C₁₉	1	2	yes	—
281	C₂×C₁₉	—	4	4	no	—
282	C₂×C₁₉	#2361	1	1	yes	characteristic
283	C₂×C₁₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
284	C₂×C₁₉	#2947	1	1	yes	characteristic
285	C₂×C₁₉	D₄×SD₁₆	1	1	yes	characteristic
286	C₂×C₁₉	#3283	1	1	yes	characteristic
287	C₂×C₁₉	#3359	1	1	yes	characteristic
288	C₂×C₁₉	#3360	1	1	yes	characteristic
289	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
290	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
291	C₂³×C₄	—	2	1	no	—
292	C₂³×C₄	—	2	2	no	—
293	C₂×SD₁₆	—	2	4	no	—
294	C₂×SD₁₆	—	2	4	no	—
295	C₂×SD₁₆	C₂×C₄×C₁₉	1	8	yes	—
296	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
298	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
301	C₄×Q₈	—	2	4	no	—
302	C₄×Q₈	—	4	2	no	—
303	C₄×D₄	—	2	4	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	—	4	2	no	—
306	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	4	4	no	—
314	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
315	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₄²	—	2	2	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
325	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
326	#106	—	2	4	no	—
327	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	complemented
328	#103	—	2	4	no	—
329	#103	—	4	2	no	—
330	#103	C₂×C₄×C₁₉	1	8	yes	complemented
331	#102	—	2	2	no	—
332	#102	D₄×C₁₉	1	4	yes	—
333	C₄×C₈	—	2	4	no	—
334	C₄×C₈	—	2	2	no	—
335	#95	—	2	2	no	—
336	#95	—	2	1	no	—
337	#95	—	2	2	no	—
338	#95	—	2	2	no	—
339	#95	D₄×C₁₉	1	2	yes	—
340	C₁₉	#22996	1	1	yes	characteristic, direct product factor, Sylow
341	C₂⁴	—	2	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
352	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
353	C₂×D₄	#41×C₁₉	1	2	yes	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	4	4	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	4	no	—
364	C₂²×C₄	—	8	2	no	—
365	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
370	SD₁₆	—	2	16	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
379	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	4	4	no	—
390	C₄⋊C₄	—	4	4	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	8	1	no	—
393	C₄⋊C₄	SD₁₆×C₁₉	1	4	yes	complemented
394	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
395	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	4	4	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	4	4	no	—
401	C₄²	—	4	2	no	—
402	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
403	C₄²	#41×C₁₉	1	2	yes	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
412	Q₈	—	2	4	no	—
413	Q₈	—	2	4	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	D₄	—	2	2	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	C₄×D₄×C₁₉	1	4	yes	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	8	8	no	—
444	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
445	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
446	C₂×C₄	C₂×SD₁₆×C₁₉	1	4	yes	—
447	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
448	C₂×C₄	C₁₉×#135	1	2	yes	—
449	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
451	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
453	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
454	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
455	C₈	—	2	4	no	—
456	C₈	—	2	2	no	—
457	C₈	—	4	1	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
466	C₂²	D₄²×C₁₉	1	1	yes	characteristic
467	C₂²	C₁₉×#548	1	1	yes	characteristic
468	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
469	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
470	C₂²	C₁₉×#577	1	1	yes	characteristic
471	C₂²	C₁₉×#578	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	2	4	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	4	no	—
478	C₄	—	8	2	no	—
479	C₄	—	8	1	no	—
480	C₄	C₄×SD₁₆×C₁₉	1	4	yes	complemented
481	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
482	C₄	C₁₉×#520	1	1	yes	characteristic
483	C₄	C₁₉×#547	1	1	yes	characteristic
484	C₄	C₁₉×#553	1	1	yes	characteristic
485	C₂	—	4	4	no	—
486	C₂	C₁₉×#2361	1	1	yes	characteristic
487	C₂	C₂×C₄×SD₁₆×C₁₉	1	1	yes	characteristic
488	C₂	C₁₉×#2947	1	1	yes	characteristic
489	C₂	D₄×SD₁₆×C₁₉	1	1	yes	characteristic
490	C₂	C₁₉×#3283	1	1	yes	characteristic
491	C₂	C₁₉×#3359	1	1	yes	characteristic
492	C₂	C₁₉×#3360	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
3. C₁₉×#2365	C₂	semidirect
5. C₁₉×#1956	C₂	semidirect
6. C₁₉×#1948	C₂	semidirect
7. C₁₉×#1933	C₂	semidirect
9. C₁₉×#1865	C₂	semidirect
10. C₈×C₄⋊C₄×C₁₉	C₂	semidirect
18. C₁₉×#461	C₄	semidirect
54. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
81. C₁₉×C₄⋊C₈	C₂×C₄	semidirect
84. C₁₉×#103	C₂×C₄	semidirect
146. C₄⋊C₄×C₁₉	SD₁₆	semidirect
157. #22996	C₁₉	direct (N × H)
214. #2365	C₂×C₁₉	semidirect
216. #1956	C₂×C₁₉	semidirect
217. #1948	C₂×C₁₉	semidirect
218. #1933	C₂×C₁₉	semidirect
220. #1865	C₂×C₁₉	semidirect
221. C₈×C₄⋊C₄	C₂×C₁₉	semidirect
245. C₄×C₁₉	C₄×SD₁₆	semidirect
256. #461	C₄×C₁₉	semidirect
300. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
327. C₄⋊C₈	C₂×C₄×C₁₉	semidirect
330. #103	C₂×C₄×C₁₉	semidirect
340. C₁₉	#22996	direct (N × H)
393. C₄⋊C₄	SD₁₆×C₁₉	semidirect
480. C₄	C₄×SD₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#461	2
C₂×C₄×SD₁₆×C₁₉	2
C₁₉×#2365	2
D₄×C₄⋊C₄×C₁₉	2
C₁₉×#1956	2
C₁₉×#1948	2
C₁₉×#1933	2
C₁₉×#1877	2
C₁₉×#1865	2
C₈×C₄⋊C₄×C₁₉	2
C₄×C₁₉×#102	2
#22996	19

Subgroups — C19×#22996 #18028955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22996 #18028955