Subgroups — C₁₉×#19476 #18025435

Order 4864.

608 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3230	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3113	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#462	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2984	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1700	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1694	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1680	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1674	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1573	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1552	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₁₉	—	2	1	no	—
13	C₁₉×#533	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#500	C₂²	1	2	yes	—
17	C₁₉×#487	C₂²	1	2	yes	—
18	C₁₉×#484	—	2	1	no	—
19	C₁₉×#484	—	2	1	no	—
20	C₁₉×#483	—	2	1	no	—
21	C₁₉×#477	—	2	2	no	—
22	C₁₉×#475	C₂²	1	1	yes	characteristic
23	C₁₉×#475	C₂²	1	1	yes	characteristic
24	C₁₉×#462	—	2	1	no	—
25	C₁₉×#462	—	2	1	no	—
26	C₁₉×#462	C₂²	1	1	yes	characteristic
27	C₁₉×#462	C₂²	1	2	yes	—
28	C₁₉×#462	C₂²	1	1	yes	characteristic
29	C₁₉×#462	C₂²	1	2	yes	—
30	C₁₉×#451	—	2	1	no	—
31	C₁₉×#446	—	2	2	no	—
32	C₁₉×#446	C₂²	1	2	yes	—
33	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#441	—	2	1	no	—
35	C₁₉×#441	—	2	1	no	—
36	C₁₉×#432	—	2	1	no	—
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#432	C₂²	1	1	yes	characteristic
39	C₁₉×#431	—	2	1	no	—
40	C₁₉×#431	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#103	—	2	1	no	—
43	C₁₉×#335	C₂²	1	2	yes	—
44	C₁₉×#334	C₂²	1	2	yes	—
45	C₁₉×#332	C₂²	1	2	yes	—
46	C₁₉×#332	C₂²	1	2	yes	—
47	C₁₉×#332	C₂²	1	2	yes	—
48	C₁₉×#332	C₂²	1	2	yes	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
51	C₂×Q₁₆×C₁₉	—	2	1	no	—
52	C₂×Q₁₆×C₁₉	—	2	1	no	—
53	C₂×Q₁₆×C₁₉	—	2	2	no	—
54	C₂×Q₁₆×C₁₉	—	2	2	no	—
55	C₂×Q₁₆×C₁₉	—	4	4	no	—
56	C₂²×C₈×C₁₉	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₁₉×#125	—	2	1	no	—
64	C₁₉×C₂²⋊Q₈	—	2	1	no	—
65	C₁₉×C₂²⋊Q₈	—	2	1	no	—
66	C₄×Q₈×C₁₉	—	2	1	no	—
67	C₄×Q₈×C₁₉	—	2	1	no	—
68	C₄×Q₈×C₁₉	—	2	1	no	—
69	C₄×Q₈×C₁₉	—	2	1	no	—
70	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
71	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
72	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×#117	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₉	—	2	1	no	—
80	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
81	C₁₉×#107	—	2	2	no	—
82	C₁₉×#107	—	2	2	no	—
83	C₁₉×#106	—	2	1	no	—
84	C₁₉×#106	—	2	1	no	—
85	C₁₉×C₄⋊C₈	—	2	2	no	—
86	C₁₉×C₄⋊C₈	—	2	2	no	—
87	C₁₉×C₄⋊C₈	—	2	1	no	—
88	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
89	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
90	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
91	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
92	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
93	C₁₉×#103	—	2	1	no	—
94	C₁₉×#103	—	2	1	no	—
95	C₁₉×#103	—	2	2	no	—
96	C₁₉×#103	—	2	2	no	—
97	C₁₉×#103	—	2	2	no	—
98	C₁₉×#103	—	2	2	no	—
99	C₁₉×#103	—	2	1	no	—
100	C₁₉×#103	—	2	1	no	—
101	C₁₉×C₂²⋊C₈	—	2	1	no	—
102	C₁₉×C₂²⋊C₈	—	2	1	no	—
103	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
104	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
105	C₁₉×#97	—	2	2	no	—
106	C₁₉×#97	—	2	1	no	—
107	C₁₉×#97	—	2	1	no	—
108	C₄×C₈×C₁₉	—	2	2	no	—
109	C₄×C₈×C₁₉	C₂³	1	2	yes	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	4	1	no	—
116	C₂×Q₈×C₁₉	—	4	2	no	—
117	C₂×Q₈×C₁₉	—	4	2	no	—
118	C₂×Q₈×C₁₉	—	4	1	no	—
119	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
127	Q₁₆×C₁₉	—	4	2	no	—
128	Q₁₆×C₁₉	—	4	4	no	—
129	Q₁₆×C₁₉	—	4	2	no	—
130	Q₁₆×C₁₉	—	4	4	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	1	no	—
133	C₂×C₈×C₁₉	—	2	1	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	4	2	no	—
136	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	4	1	no	—
150	C₄⋊C₄×C₁₉	—	4	1	no	—
151	C₄⋊C₄×C₁₉	—	4	1	no	—
152	C₄⋊C₄×C₁₉	—	4	1	no	—
153	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²⋊C₄×C₁₉	—	4	1	no	—
156	C₄²×C₁₉	—	2	1	no	—
157	C₄²×C₁₉	—	2	1	no	—
158	C₄²×C₁₉	—	2	1	no	—
159	C₄²×C₁₉	—	2	1	no	—
160	C₄²×C₁₉	—	4	1	no	—
161	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₉	#41	1	1	yes	characteristic
164	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
165	#19476	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₁₉	#121	1	1	yes	characteristic
167	Q₈×C₁₉	—	2	1	no	—
168	Q₈×C₁₉	—	2	1	no	—
169	Q₈×C₁₉	—	2	1	no	—
170	Q₈×C₁₉	—	4	2	no	—
171	Q₈×C₁₉	—	4	2	no	—
172	Q₈×C₁₉	—	4	1	no	—
173	Q₈×C₁₉	—	4	1	no	—
174	Q₈×C₁₉	—	4	2	no	—
175	Q₈×C₁₉	—	4	2	no	—
176	Q₈×C₁₉	—	8	2	no	—
177	Q₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	2	1	no	—
185	C₂×C₄×C₁₉	—	2	1	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	8	2	no	—
192	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
198	C₈×C₁₉	—	2	2	no	—
199	C₈×C₁₉	—	2	2	no	—
200	C₈×C₁₉	—	4	2	no	—
201	C₈×C₁₉	—	4	1	no	—
202	C₈×C₁₉	—	4	1	no	—
203	C₈×C₁₉	—	4	2	no	—
204	#3230	C₂×C₁₉	1	1	yes	characteristic
205	#3113	C₂×C₁₉	1	1	yes	characteristic
206	C₂×#462	C₂×C₁₉	1	1	yes	characteristic
207	#2984	C₂×C₁₉	1	1	yes	characteristic
208	#1700	C₂×C₁₉	1	2	yes	complemented
209	#1694	C₂×C₁₉	1	2	yes	complemented
210	#1680	C₂×C₁₉	1	2	yes	complemented
211	#1674	C₂×C₁₉	1	2	yes	complemented
212	#1573	C₂×C₁₉	1	1	yes	characteristic
213	#1556	C₂×C₁₉	1	1	yes	characteristic
214	#1552	C₂×C₁₉	1	1	yes	characteristic
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	#473	1	2	yes	—
218	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	2	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	4	1	no	—
225	C₄×C₁₉	—	4	1	no	—
226	C₄×C₁₉	—	4	1	no	—
227	C₄×C₁₉	—	8	1	no	—
228	C₄×C₁₉	—	8	2	no	—
229	C₄×C₁₉	—	8	1	no	—
230	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
231	C₄×C₁₉	#575	1	1	yes	characteristic
232	C₄×C₁₉	#578	1	2	yes	—
233	C₂²×Q₁₆	—	2	1	no	—
234	#533	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
237	#500	C₂²×C₁₉	1	2	yes	—
238	#487	C₂²×C₁₉	1	2	yes	—
239	#484	—	2	1	no	—
240	#484	—	2	1	no	—
241	#483	—	2	1	no	—
242	#477	—	2	2	no	—
243	#475	C₂²×C₁₉	1	1	yes	characteristic
244	#475	C₂²×C₁₉	1	1	yes	characteristic
245	#462	—	2	1	no	—
246	#462	—	2	1	no	—
247	#462	C₂²×C₁₉	1	1	yes	characteristic
248	#462	C₂²×C₁₉	1	1	yes	characteristic
249	#462	C₂²×C₁₉	1	2	yes	—
250	#462	C₂²×C₁₉	1	2	yes	—
251	#451	—	2	1	no	—
252	#446	—	2	2	no	—
253	#446	C₂²×C₁₉	1	2	yes	—
254	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
255	#441	—	2	1	no	—
256	#441	—	2	1	no	—
257	#432	—	2	1	no	—
258	#432	C₂²×C₁₉	1	1	yes	characteristic
259	#432	C₂²×C₁₉	1	1	yes	characteristic
260	#431	—	2	1	no	—
261	#431	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
263	C₂×#103	—	2	1	no	—
264	#335	C₂²×C₁₉	1	2	yes	—
265	#334	C₂²×C₁₉	1	2	yes	—
266	#332	C₂²×C₁₉	1	2	yes	—
267	#332	C₂²×C₁₉	1	2	yes	—
268	#332	C₂²×C₁₉	1	2	yes	—
269	#332	C₂²×C₁₉	1	2	yes	—
270	C₂×C₁₉	—	2	2	no	—
271	C₂×C₁₉	#3044	1	1	yes	characteristic
272	C₂×C₁₉	#3055	1	1	yes	characteristic
273	C₂×C₁₉	C₂×#473	1	1	yes	characteristic
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
276	C₂×Q₁₆	—	2	2	no	—
277	C₂×Q₁₆	—	2	2	no	—
278	C₂×Q₁₆	—	2	1	no	—
279	C₂×Q₁₆	—	2	1	no	—
280	C₂×Q₁₆	—	4	4	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
286	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
287	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
288	#125	—	2	1	no	—
289	C₂²⋊Q₈	—	2	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
296	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
297	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
298	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
299	#117	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
306	#107	—	2	2	no	—
307	#107	—	2	2	no	—
308	#106	—	2	1	no	—
309	#106	—	2	1	no	—
310	C₄⋊C₈	—	2	2	no	—
311	C₄⋊C₈	—	2	2	no	—
312	C₄⋊C₈	—	2	1	no	—
313	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
314	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
315	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
316	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
317	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
318	#103	—	2	1	no	—
319	#103	—	2	1	no	—
320	#103	—	2	2	no	—
321	#103	—	2	2	no	—
322	#103	—	2	2	no	—
323	#103	—	2	2	no	—
324	#103	—	2	1	no	—
325	#103	—	2	1	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
329	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
330	#97	—	2	2	no	—
331	#97	—	2	1	no	—
332	#97	—	2	1	no	—
333	C₄×C₈	—	2	2	no	—
334	C₄×C₈	C₂³×C₁₉	1	2	yes	—
335	C₁₉	#19476	1	1	yes	characteristic, direct product factor, Sylow
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	1	no	—
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×Q₈	—	4	1	no	—
345	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	4	1	no	—
350	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
352	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
353	Q₁₆	—	4	2	no	—
354	Q₁₆	—	4	4	no	—
355	Q₁₆	—	4	2	no	—
356	Q₁₆	—	4	4	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	4	2	no	—
362	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
363	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
380	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₂²⋊C₄	—	4	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	4	1	no	—
387	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
388	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₄²	#41×C₁₉	1	1	yes	characteristic
390	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
391	C₂³	C₁₉×#121	1	1	yes	characteristic
392	Q₈	—	2	1	no	—
393	Q₈	—	2	1	no	—
394	Q₈	—	2	1	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	4	1	no	—
398	Q₈	—	4	1	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	8	2	no	—
402	Q₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	8	2	no	—
417	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
418	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
419	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
420	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
421	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
422	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	2	2	no	—
425	C₈	—	4	2	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	1	no	—
428	C₈	—	4	2	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	C₁₉×#473	1	2	yes	—
432	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	2	no	—
443	C₄	—	8	1	no	—
444	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
445	C₄	C₁₉×#575	1	1	yes	characteristic
446	C₄	C₁₉×#578	1	2	yes	—
447	C₂	—	2	2	no	—
448	C₂	C₁₉×#3044	1	1	yes	characteristic
449	C₂	C₁₉×#3055	1	1	yes	characteristic
450	C₂	C₂×C₁₉×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	#121
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₉×#1700	C₂	semidirect
6. C₁₉×#1694	C₂	semidirect
7. C₁₉×#1680	C₂	semidirect
8. C₁₉×#1674	C₂	semidirect
165. #19476	C₁₉	direct (N × H)
208. #1700	C₂×C₁₉	semidirect
209. #1694	C₂×C₁₉	semidirect
210. #1680	C₂×C₁₉	semidirect
211. #1674	C₂×C₁₉	semidirect
335. C₁₉	#19476	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3230	2
C₁₉×#3113	2
C₂×C₁₉×#462	2
C₁₉×#2984	2
C₁₉×#1700	2
C₁₉×#1694	2
C₁₉×#1680	2
C₁₉×#1674	2
C₁₉×#1573	2
C₁₉×#1556	2
C₁₉×#1552	2
#19476	19

Subgroups — C19×#19476 #18025435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19476 #18025435