Subgroups — C₁₉×#32760 #18038719

Order 4864.

952 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	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2856	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2072	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2071	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2014	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2013	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2000	C₂	1	4	yes	maximal, complemented
8	C₁₉×#1817	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×SD₁₆×C₁₉	C₂²	1	4	yes	—
10	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₁₉×#121	—	2	1	no	—
14	C₂×C₁₉×#121	—	2	1	no	—
15	C₂×C₁₉×#121	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#103	C₂²	1	4	yes	—
18	C₂×C₁₉×#102	C₂²	1	4	yes	—
19	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₁₉×#391	C₂²	1	2	yes	—
21	C₁₉×#390	—	2	1	no	—
22	C₁₉×#390	—	2	1	no	—
23	C₁₉×#390	C₂²	1	2	yes	—
24	C₁₉×#389	—	2	1	no	—
25	C₁₉×#389	—	2	1	no	—
26	C₁₉×#384	C₂²	1	1	yes	characteristic
27	C₁₉×#384	C₂²	1	1	yes	characteristic
28	C₁₉×#380	—	2	1	no	—
29	C₁₉×#380	—	2	1	no	—
30	C₁₉×#340	C₂²	1	4	yes	—
31	C₁₉×#336	C₂²	1	2	yes	—
32	C₁₉×#336	C₂²	1	2	yes	—
33	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
34	C₂²×D₄×C₁₉	—	2	2	no	—
35	C₂²×D₄×C₁₉	—	2	1	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂×SD₁₆×C₁₉	—	4	4	no	—
42	C₂×SD₁₆×C₁₉	—	4	4	no	—
43	C₂×SD₁₆×C₁₉	—	4	4	no	—
44	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
45	C₁₉×C₄⋊Q₈	—	4	2	no	—
46	C₁₉×#127	—	4	2	no	—
47	C₁₉×C₂²⋊Q₈	—	4	4	no	—
48	C₁₉×#121	—	4	4	no	—
49	C₁₉×#121	—	4	4	no	—
50	C₁₉×#121	—	4	4	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
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	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄²×C₁₉	—	4	2	no	—
65	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×#103	—	4	4	no	—
70	C₁₉×#102	—	4	4	no	—
71	C₁₉×C₂²⋊C₈	—	4	2	no	—
72	C₁₉×#95	—	2	2	no	—
73	C₁₉×#95	—	2	2	no	—
74	C₂⁴×C₁₉	—	2	2	no	—
75	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂×Q₈×C₁₉	—	2	4	no	—
77	C₂×Q₈×C₁₉	—	2	4	no	—
78	C₂×Q₈×C₁₉	—	2	2	no	—
79	C₂×Q₈×C₁₉	—	2	2	no	—
80	C₂×D₄×C₁₉	—	2	4	no	—
81	C₂×D₄×C₁₉	—	2	4	no	—
82	C₂×D₄×C₁₉	—	2	2	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	4	2	no	—
85	C₂×D₄×C₁₉	—	4	2	no	—
86	C₂×D₄×C₁₉	—	4	2	no	—
87	C₂×D₄×C₁₉	—	4	2	no	—
88	C₂×D₄×C₁₉	—	4	4	no	—
89	C₂×D₄×C₁₉	—	4	4	no	—
90	C₂×D₄×C₁₉	—	4	4	no	—
91	C₂×D₄×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	—	4	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	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	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	complemented
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×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
111	SD₁₆×C₁₉	—	4	16	no	—
112	C₂×C₈×C₁₉	—	2	4	no	—
113	C₂×C₈×C₁₉	—	2	4	no	—
114	C₂×C₈×C₁₉	—	2	4	no	—
115	C₄⋊C₄×C₁₉	—	2	4	no	—
116	C₄⋊C₄×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	4	2	no	—
118	C₄⋊C₄×C₁₉	—	4	2	no	—
119	C₄⋊C₄×C₁₉	—	4	4	no	—
120	C₄⋊C₄×C₁₉	—	4	2	no	—
121	C₄⋊C₄×C₁₉	—	4	2	no	—
122	C₄⋊C₄×C₁₉	—	4	2	no	—
123	C₄⋊C₄×C₁₉	—	4	2	no	—
124	C₂²⋊C₄×C₁₉	—	4	4	no	—
125	C₂²⋊C₄×C₁₉	—	4	4	no	—
126	C₂²⋊C₄×C₁₉	—	4	4	no	—
127	C₂²⋊C₄×C₁₉	—	4	4	no	—
128	C₄²×C₁₉	—	2	2	no	—
129	C₄²×C₁₉	—	2	2	no	—
130	C₄²×C₁₉	—	4	1	no	—
131	C₄²×C₁₉	—	4	1	no	—
132	#32760	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₁₉	—	2	1	no	—
134	C₂³×C₁₉	—	2	1	no	—
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	2	1	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	—	4	2	no	—
144	C₂³×C₁₉	—	4	2	no	—
145	C₂³×C₁₉	—	4	2	no	—
146	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
147	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₁₉	—	4	4	no	—
149	Q₈×C₁₉	—	4	4	no	—
150	D₄×C₁₉	—	4	4	no	—
151	D₄×C₁₉	—	4	4	no	—
152	D₄×C₁₉	—	8	4	no	—
153	D₄×C₁₉	—	8	4	no	—
154	D₄×C₁₉	—	8	8	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	4	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	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
179	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
180	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
181	C₂×C₄×C₁₉	#137	1	2	yes	—
182	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
183	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
184	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
185	C₈×C₁₉	—	4	4	no	—
186	#2857	C₂×C₁₉	1	1	yes	characteristic, complemented
187	#2856	C₂×C₁₉	1	1	yes	characteristic
188	#2072	C₂×C₁₉	1	2	yes	complemented
189	#2071	C₂×C₁₉	1	2	yes	complemented
190	#2014	C₂×C₁₉	1	2	yes	complemented
191	#2013	C₂×C₁₉	1	2	yes	complemented
192	#2000	C₂×C₁₉	1	4	yes	complemented
193	#1817	C₂×C₁₉	1	1	yes	characteristic, complemented
194	C₂²×C₁₉	—	2	2	no	—
195	C₂²×C₁₉	—	2	2	no	—
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	4	1	no	—
198	C₂²×C₁₉	—	4	1	no	—
199	C₂²×C₁₉	—	4	1	no	—
200	C₂²×C₁₉	—	4	1	no	—
201	C₂²×C₁₉	—	8	2	no	—
202	C₂²×C₁₉	—	8	2	no	—
203	C₂²×C₁₉	—	8	2	no	—
204	C₂²×C₁₉	—	8	2	no	—
205	C₂²×C₁₉	—	8	2	no	—
206	C₂²×C₁₉	—	8	2	no	—
207	C₂²×C₁₉	—	8	2	no	—
208	C₂²×C₁₉	#534	1	1	yes	characteristic
209	C₂²×C₁₉	#535	1	1	yes	characteristic
210	C₂²×C₁₉	#535	1	1	yes	characteristic
211	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
212	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
214	C₂²×C₁₉	#575	1	1	yes	characteristic
215	C₄×C₁₉	—	2	2	no	—
216	C₄×C₁₉	—	2	2	no	—
217	C₄×C₁₉	—	2	2	no	—
218	C₄×C₁₉	—	2	2	no	—
219	C₄×C₁₉	—	4	1	no	—
220	C₄×C₁₉	—	8	2	no	—
221	C₄×C₁₉	—	8	2	no	—
222	C₄×C₁₉	—	8	2	no	—
223	C₄×C₁₉	#560	1	4	yes	—
224	C₂²×SD₁₆	C₂²×C₁₉	1	4	yes	—
225	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
226	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
228	C₂×#121	—	2	1	no	—
229	C₂×#121	—	2	1	no	—
230	C₂×#121	C₂²×C₁₉	1	2	yes	—
231	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
232	C₂×#103	C₂²×C₁₉	1	4	yes	—
233	C₂×#102	C₂²×C₁₉	1	4	yes	—
234	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
235	#391	C₂²×C₁₉	1	2	yes	—
236	#390	—	2	1	no	—
237	#390	—	2	1	no	—
238	#390	C₂²×C₁₉	1	2	yes	—
239	#389	—	2	1	no	—
240	#389	—	2	1	no	—
241	#384	C₂²×C₁₉	1	1	yes	characteristic
242	#384	C₂²×C₁₉	1	1	yes	characteristic
243	#380	—	2	1	no	—
244	#380	—	2	1	no	—
245	#340	C₂²×C₁₉	1	4	yes	—
246	#336	C₂²×C₁₉	1	2	yes	—
247	#336	C₂²×C₁₉	1	2	yes	—
248	C₂×C₁₉	—	4	2	no	—
249	C₂×C₁₉	—	16	2	no	—
250	C₂×C₁₉	#2815	1	1	yes	characteristic
251	C₂×C₁₉	#3187	1	1	yes	characteristic
252	C₂×C₁₉	#3193	1	1	yes	characteristic
253	C₂×C₁₉	#3206	1	1	yes	characteristic
254	C₂×C₁₉	#3208	1	1	yes	characteristic
255	C₂×C₁₉	#3214	1	1	yes	characteristic
256	C₂×C₁₉	#3216	1	1	yes	characteristic
257	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
258	C₂²×D₄	—	2	2	no	—
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
262	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
263	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
264	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
265	C₂×SD₁₆	—	4	4	no	—
266	C₂×SD₁₆	—	4	4	no	—
267	C₂×SD₁₆	—	4	4	no	—
268	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
269	C₄⋊Q₈	—	4	2	no	—
270	#127	—	4	2	no	—
271	C₂²⋊Q₈	—	4	4	no	—
272	#121	—	4	4	no	—
273	#121	—	4	4	no	—
274	#121	—	4	4	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₄²	—	4	2	no	—
289	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
290	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
293	#103	—	4	4	no	—
294	#102	—	4	4	no	—
295	C₂²⋊C₈	—	4	2	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	C₁₉	#32760	1	1	yes	characteristic, direct product factor, Sylow
299	C₂⁴	—	2	2	no	—
300	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	4	no	—
314	C₂×D₄	—	4	4	no	—
315	C₂×D₄	—	4	4	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	SD₁₆×C₁₉	1	4	yes	complemented
330	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
336	SD₁₆	—	4	16	no	—
337	C₂×C₈	—	2	4	no	—
338	C₂×C₈	—	2	4	no	—
339	C₂×C₈	—	2	4	no	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₂²⋊C₄	—	4	4	no	—
352	C₂²⋊C₄	—	4	4	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	4	1	no	—
356	C₄²	—	4	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
371	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
372	Q₈	—	4	4	no	—
373	Q₈	—	4	4	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	4	no	—
376	D₄	—	8	4	no	—
377	D₄	—	8	4	no	—
378	D₄	—	8	8	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
403	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
404	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
405	C₂×C₄	C₁₉×#137	1	2	yes	—
406	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
407	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
408	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
409	C₈	—	4	4	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	C₁₉×#534	1	1	yes	characteristic
425	C₂²	C₁₉×#535	1	1	yes	characteristic
426	C₂²	C₁₉×#535	1	1	yes	characteristic
427	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
428	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
429	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
430	C₂²	C₁₉×#575	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	4	1	no	—
436	C₄	—	8	2	no	—
437	C₄	—	8	2	no	—
438	C₄	—	8	2	no	—
439	C₄	C₁₉×#560	1	4	yes	—
440	C₂	—	4	2	no	—
441	C₂	—	16	2	no	—
442	C₂	C₁₉×#2815	1	1	yes	characteristic
443	C₂	C₁₉×#3187	1	1	yes	characteristic
444	C₂	C₁₉×#3193	1	1	yes	characteristic
445	C₂	C₁₉×#3206	1	1	yes	characteristic
446	C₂	C₁₉×#3208	1	1	yes	characteristic
447	C₂	C₁₉×#3214	1	1	yes	characteristic
448	C₂	C₁₉×#3216	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2856	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2857	C₂	semidirect
3. C₁₉×#2072	C₂	semidirect
4. C₁₉×#2071	C₂	semidirect
5. C₁₉×#2014	C₂	semidirect
6. C₁₉×#2013	C₂	semidirect
7. C₁₉×#2000	C₂	semidirect
8. C₁₉×#1817	C₂	semidirect
104. C₂²×C₄×C₁₉	SD₁₆	semidirect
132. #32760	C₁₉	direct (N × H)
186. #2857	C₂×C₁₉	semidirect
188. #2072	C₂×C₁₉	semidirect
189. #2071	C₂×C₁₉	semidirect
190. #2014	C₂×C₁₉	semidirect
191. #2013	C₂×C₁₉	semidirect
192. #2000	C₂×C₁₉	semidirect
193. #1817	C₂×C₁₉	semidirect
298. C₁₉	#32760	direct (N × H)
329. C₂²×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
C₁₉×#2857	2
C₁₉×#2856	2
C₁₉×#2072	2
C₁₉×#2071	2
C₁₉×#2014	2
C₁₉×#2013	2
C₁₉×#2000	2
C₁₉×#1817	2
#32760	19

Subgroups — C19×#32760 #18038719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32760 #18038719