Subgroups — C₁₉×#19314 #18025273

Order 4864.

630 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3116	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3039	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2970	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1694	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1692	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1673	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1671	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1569	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1559	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#137	—	2	1	no	—
13	C₁₉×#533	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#501	—	2	1	no	—
17	C₁₉×#501	—	2	1	no	—
18	C₁₉×#500	C₂²	1	2	yes	—
19	C₁₉×#498	C₂²	1	2	yes	—
20	C₁₉×#485	—	2	1	no	—
21	C₁₉×#477	C₂²	1	1	yes	characteristic
22	C₁₉×#476	C₂²	1	1	yes	characteristic
23	C₁₉×#462	—	2	1	no	—
24	C₁₉×#462	C₂²	1	2	yes	—
25	C₁₉×#462	C₂²	1	1	yes	characteristic
26	C₁₉×#461	—	2	1	no	—
27	C₁₉×#461	C₂²	1	2	yes	—
28	C₁₉×#461	C₂²	1	1	yes	characteristic
29	C₁₉×#452	—	2	1	no	—
30	C₁₉×#446	C₂²	1	2	yes	—
31	C₁₉×#441	—	2	1	no	—
32	C₁₉×#440	—	2	1	no	—
33	C₁₉×#435	—	2	2	no	—
34	C₈×D₄×C₁₉	C₂²	1	2	yes	—
35	C₁₉×#432	—	2	1	no	—
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#428	—	2	2	no	—
39	C₁₉×#423	C₂²	1	1	yes	characteristic
40	C₁₉×#419	—	2	1	no	—
41	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#97	—	2	1	no	—
43	C₁₉×#335	C₂²	1	2	yes	—
44	C₁₉×#334	C₂²	1	2	yes	—
45	C₁₉×#333	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	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×Q₈×C₁₉	—	2	1	no	—
51	C₁₉×#137	—	4	4	no	—
52	C₂×Q₁₆×C₁₉	—	2	1	no	—
53	C₂×Q₁₆×C₁₉	—	2	2	no	—
54	C₂×SD₁₆×C₁₉	—	2	1	no	—
55	C₂×SD₁₆×C₁₉	—	2	2	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
58	C₂²×C₈×C₁₉	—	2	2	no	—
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₁₉×#125	—	2	1	no	—
66	C₁₉×C₂²⋊Q₈	—	2	1	no	—
67	C₁₉×C₂²⋊Q₈	—	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	C₂³	1	1	yes	characteristic
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	—	2	1	no	—
74	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
75	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₁₉×#117	—	2	1	no	—
77	C₁₉×#117	—	2	1	no	—
78	C₁₉×#117	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄²×C₁₉	—	2	1	no	—
82	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
83	C₁₉×#107	—	2	2	no	—
84	C₁₉×#107	—	2	2	no	—
85	C₁₉×#107	—	2	1	no	—
86	C₁₉×#106	—	2	2	no	—
87	C₁₉×#106	—	2	2	no	—
88	C₁₉×#106	—	2	1	no	—
89	C₁₉×C₄⋊C₈	—	2	2	no	—
90	C₁₉×C₄⋊C₈	—	2	1	no	—
91	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
92	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
93	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
94	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₁₉×#103	—	2	1	no	—
96	C₁₉×#103	—	2	2	no	—
97	C₁₉×#103	—	2	2	no	—
98	C₁₉×#103	—	2	1	no	—
99	C₁₉×#103	—	2	1	no	—
100	C₁₉×#102	—	2	1	no	—
101	C₁₉×C₂²⋊C₈	—	2	1	no	—
102	C₁₉×C₂²⋊C₈	—	2	1	no	—
103	C₁₉×C₂²⋊C₈	—	2	2	no	—
104	C₁₉×#97	—	2	2	no	—
105	C₁₉×#97	—	2	1	no	—
106	C₁₉×#97	—	2	1	no	—
107	C₁₉×#97	D₄	1	1	yes	characteristic
108	C₁₉×#97	D₄	1	1	yes	characteristic
109	C₄×C₈×C₁₉	C₂³	1	2	yes	—
110	#41×C₁₉	—	2	2	no	—
111	#41×C₁₉	—	4	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	4	2	no	—
116	C₂×Q₈×C₁₉	—	4	2	no	—
117	C₂×Q₈×C₁₉	—	4	1	no	—
118	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂×D₄×C₁₉	—	2	1	no	—
120	C₂×D₄×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	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	4	1	no	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
128	Q₁₆×C₁₉	—	4	2	no	—
129	Q₁₆×C₁₉	—	4	4	no	—
130	SD₁₆×C₁₉	—	4	2	no	—
131	SD₁₆×C₁₉	—	4	4	no	—
132	M₁₆×C₁₉	—	2	4	no	—
133	M₁₆×C₁₉	—	4	2	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	1	no	—
137	C₂×C₈×C₁₉	—	2	1	no	—
138	C₂×C₈×C₁₉	—	4	4	no	—
139	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
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	1	no	—
147	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
156	C₂²⋊C₄×C₁₉	—	2	1	no	—
157	C₂²⋊C₄×C₁₉	—	2	1	no	—
158	C₂²⋊C₄×C₁₉	—	4	1	no	—
159	C₄²×C₁₉	—	2	1	no	—
160	C₄²×C₁₉	—	2	1	no	—
161	C₄²×C₁₉	—	2	1	no	—
162	C₄²×C₁₉	—	4	1	no	—
163	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₉	#41	1	1	yes	characteristic
166	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
167	#19314	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂³×C₁₉	—	2	1	no	—
169	C₂³×C₁₉	#121	1	1	yes	characteristic
170	Q₈×C₁₉	—	2	1	no	—
171	Q₈×C₁₉	—	2	1	no	—
172	Q₈×C₁₉	—	4	2	no	—
173	Q₈×C₁₉	—	4	1	no	—
174	Q₈×C₁₉	—	4	1	no	—
175	Q₈×C₁₉	—	4	2	no	—
176	Q₈×C₁₉	—	8	1	no	—
177	Q₈×C₁₉	—	8	2	no	—
178	D₄×C₁₉	—	2	1	no	—
179	D₄×C₁₉	—	4	2	no	—
180	D₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
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	—	2	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	8	1	no	—
194	C₂×C₄×C₁₉	—	8	2	no	—
195	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
201	C₈×C₁₉	—	2	2	no	—
202	C₈×C₁₉	—	4	2	no	—
203	C₈×C₁₉	—	4	1	no	—
204	C₈×C₁₉	—	4	2	no	—
205	C₈×C₁₉	—	4	1	no	—
206	C₈×C₁₉	#137	1	4	yes	complemented
207	#3165	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#3116	C₂×C₁₉	1	1	yes	characteristic
209	#3039	C₂×C₁₉	1	1	yes	characteristic
210	#2970	C₂×C₁₉	1	1	yes	characteristic
211	#1694	C₂×C₁₉	1	2	yes	complemented
212	#1692	C₂×C₁₉	1	2	yes	complemented
213	#1673	C₂×C₁₉	1	2	yes	complemented
214	#1671	C₂×C₁₉	1	2	yes	complemented
215	#1569	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#1559	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	2	2	no	—
221	C₂²×C₁₉	—	2	1	no	—
222	C₂²×C₁₉	—	4	1	no	—
223	C₂²×C₁₉	—	4	1	no	—
224	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	2	1	no	—
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	4	1	no	—
230	C₄×C₁₉	—	4	1	no	—
231	C₄×C₁₉	—	4	1	no	—
232	C₄×C₁₉	—	8	2	no	—
233	C₄×C₁₉	—	8	1	no	—
234	C₄×C₁₉	—	8	1	no	—
235	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₄×C₁₉	C₂×#137	1	2	yes	—
237	C₄×C₁₉	#575	1	1	yes	characteristic
238	C₂×#137	—	2	1	no	—
239	#533	C₂²×C₁₉	1	1	yes	characteristic
240	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
241	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
242	#501	—	2	1	no	—
243	#501	—	2	1	no	—
244	#500	C₂²×C₁₉	1	2	yes	—
245	#498	C₂²×C₁₉	1	2	yes	—
246	#485	—	2	1	no	—
247	#477	C₂²×C₁₉	1	1	yes	characteristic
248	#476	C₂²×C₁₉	1	1	yes	characteristic
249	#462	—	2	1	no	—
250	#462	C₂²×C₁₉	1	1	yes	characteristic
251	#462	C₂²×C₁₉	1	2	yes	—
252	#461	—	2	1	no	—
253	#461	C₂²×C₁₉	1	1	yes	characteristic
254	#461	C₂²×C₁₉	1	2	yes	—
255	#452	—	2	1	no	—
256	#446	C₂²×C₁₉	1	2	yes	—
257	#441	—	2	1	no	—
258	#440	—	2	1	no	—
259	#435	—	2	2	no	—
260	C₈×D₄	C₂²×C₁₉	1	2	yes	—
261	#432	—	2	1	no	—
262	#432	C₂²×C₁₉	1	1	yes	characteristic
263	#432	C₂²×C₁₉	1	1	yes	characteristic
264	#428	—	2	2	no	—
265	#423	C₂²×C₁₉	1	1	yes	characteristic
266	#419	—	2	1	no	—
267	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
268	C₂×#97	—	2	1	no	—
269	#335	C₂²×C₁₉	1	2	yes	—
270	#334	C₂²×C₁₉	1	2	yes	—
271	#333	C₂²×C₁₉	1	2	yes	—
272	#332	C₂²×C₁₉	1	2	yes	—
273	#332	C₂²×C₁₉	1	2	yes	—
274	#332	C₂²×C₁₉	1	2	yes	—
275	C₂×C₁₉	—	4	1	no	—
276	C₂×C₁₉	—	4	2	no	—
277	C₂×C₁₉	#3039	1	1	yes	characteristic
278	C₂×C₁₉	#3055	1	1	yes	characteristic
279	C₂×C₁₉	#3069	1	1	yes	characteristic
280	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
281	C₂²×Q₈	—	2	1	no	—
282	#137	—	4	4	no	—
283	C₂×Q₁₆	—	2	2	no	—
284	C₂×Q₁₆	—	2	1	no	—
285	C₂×SD₁₆	—	2	2	no	—
286	C₂×SD₁₆	—	2	1	no	—
287	C₂×M₁₆	—	2	1	no	—
288	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
289	C₂²×C₈	—	2	2	no	—
290	C₄⋊Q₈	—	2	1	no	—
291	C₄⋊Q₈	—	2	1	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
294	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
295	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
296	#125	—	2	1	no	—
297	C₂²⋊Q₈	—	2	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
302	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
306	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
307	#117	—	2	1	no	—
308	#117	—	2	1	no	—
309	#117	D₄×C₁₉	1	1	yes	characteristic
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
314	#107	—	2	2	no	—
315	#107	—	2	2	no	—
316	#107	—	2	1	no	—
317	#106	—	2	2	no	—
318	#106	—	2	2	no	—
319	#106	—	2	1	no	—
320	C₄⋊C₈	—	2	2	no	—
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
323	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
324	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
325	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
326	#103	—	2	1	no	—
327	#103	—	2	2	no	—
328	#103	—	2	2	no	—
329	#103	—	2	1	no	—
330	#103	—	2	1	no	—
331	#102	—	2	1	no	—
332	C₂²⋊C₈	—	2	1	no	—
333	C₂²⋊C₈	—	2	1	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	#97	—	2	2	no	—
336	#97	—	2	1	no	—
337	#97	—	2	1	no	—
338	#97	D₄×C₁₉	1	1	yes	characteristic
339	#97	D₄×C₁₉	1	1	yes	characteristic
340	C₄×C₈	C₂³×C₁₉	1	2	yes	—
341	C₁₉	#19314	1	1	yes	characteristic, direct product factor, Sylow
342	#41	—	2	2	no	—
343	#41	—	4	1	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	4	2	no	—
348	C₂×Q₈	—	4	2	no	—
349	C₂×Q₈	—	4	1	no	—
350	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
360	Q₁₆	—	4	2	no	—
361	Q₁₆	—	4	4	no	—
362	SD₁₆	—	4	2	no	—
363	SD₁₆	—	4	4	no	—
364	M₁₆	—	2	4	no	—
365	M₁₆	—	4	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	4	4	no	—
371	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
372	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄⋊C₄	—	4	1	no	—
385	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
386	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
387	C₂²⋊C₄	—	2	1	no	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	4	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	4	1	no	—
395	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
396	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₄²	#41×C₁₉	1	1	yes	characteristic
398	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
399	C₂³	—	2	1	no	—
400	C₂³	C₁₉×#121	1	1	yes	characteristic
401	Q₈	—	2	1	no	—
402	Q₈	—	2	1	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	4	1	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	4	2	no	—
407	Q₈	—	8	1	no	—
408	Q₈	—	8	2	no	—
409	D₄	—	2	1	no	—
410	D₄	—	4	2	no	—
411	D₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	8	1	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
427	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
428	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	1	no	—
435	C₈	—	4	2	no	—
436	C₈	—	4	1	no	—
437	C₈	C₁₉×#137	1	4	yes	complemented
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	8	2	no	—
453	C₄	—	8	1	no	—
454	C₄	—	8	1	no	—
455	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
456	C₄	C₂×C₁₉×#137	1	2	yes	—
457	C₄	C₁₉×#575	1	1	yes	characteristic
458	C₂	—	4	1	no	—
459	C₂	—	4	2	no	—
460	C₂	C₁₉×#3039	1	1	yes	characteristic
461	C₂	C₁₉×#3055	1	1	yes	characteristic
462	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	D₄
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
1. C₁₉×#3165	C₂	semidirect
5. C₁₉×#1694	C₂	semidirect
6. C₁₉×#1692	C₂	semidirect
7. C₁₉×#1673	C₂	semidirect
8. C₁₉×#1671	C₂	semidirect
9. C₁₉×#1569	C₂	semidirect
10. C₁₉×#1559	C₂	semidirect
11. C₁₉×#1556	C₂	semidirect
167. #19314	C₁₉	direct (N × H)
206. C₈×C₁₉	#137	semidirect
207. #3165	C₂×C₁₉	semidirect
211. #1694	C₂×C₁₉	semidirect
212. #1692	C₂×C₁₉	semidirect
213. #1673	C₂×C₁₉	semidirect
214. #1671	C₂×C₁₉	semidirect
215. #1569	C₂×C₁₉	semidirect
216. #1559	C₂×C₁₉	semidirect
217. #1556	C₂×C₁₉	semidirect
341. C₁₉	#19314	direct (N × H)
437. C₈	C₁₉×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3165	2
C₁₉×#3116	2
C₁₉×#3039	2
C₁₉×#2970	2
C₁₉×#1694	2
C₁₉×#1692	2
C₁₉×#1673	2
C₁₉×#1671	2
C₁₉×#1569	2
C₁₉×#1559	2
C₁₉×#1556	2
#19314	19

Subgroups — C19×#19314 #18025273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19314 #18025273