Subgroups — C₁₉×#19319 #18025278

Order 4864.

652 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3115	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2970	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1702	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1700	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1681	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1679	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1569	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1557	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×#532	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×#489	—	2	1	no	—
17	C₁₉×#489	—	2	1	no	—
18	C₁₉×#487	C₂²	1	2	yes	—
19	C₁₉×#486	C₂²	1	2	yes	—
20	C₁₉×#482	—	2	1	no	—
21	C₁₉×#475	C₂²	1	1	yes	characteristic
22	C₁₉×#474	C₂²	1	1	yes	characteristic
23	C₁₉×#462	—	2	1	no	—
24	C₁₉×#462	C₂²	1	2	yes	—
25	C₁₉×#461	—	2	1	no	—
26	C₁₉×#461	C₂²	1	2	yes	—
27	C₁₉×#460	C₂²	1	1	yes	characteristic
28	C₁₉×#459	C₂²	1	1	yes	characteristic
29	C₁₉×#449	—	2	1	no	—
30	C₁₉×#446	C₂²	1	2	yes	—
31	C₁₉×#442	—	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×#423	C₂²	1	1	yes	characteristic
39	C₁₉×#419	—	2	1	no	—
40	C₁₉×#417	—	2	2	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×#332	C₂²	1	2	yes	—
46	C₁₉×#332	C₂²	1	2	yes	—
47	C₁₉×#332	C₂²	1	2	yes	—
48	C₁₉×#331	C₂²	1	2	yes	—
49	C₂×#41×C₁₉	—	2	1	no	—
50	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
51	C₂²×Q₈×C₁₉	—	2	1	no	—
52	C₁₉×#137	—	4	4	no	—
53	C₂×Q₁₆×C₁₉	—	2	2	no	—
54	C₂×SD₁₆×C₁₉	—	2	1	no	—
55	C₂×SD₁₆×C₁₉	—	2	2	no	—
56	C₂×D₈×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
59	C₂²×C₈×C₁₉	—	2	2	no	—
60	C₁₉×C₄⋊Q₈	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₁₉×#127	C₂³	1	1	yes	characteristic
66	C₁₉×#124	—	2	1	no	—
67	C₁₉×#121	—	2	1	no	—
68	C₁₉×#121	—	2	1	no	—
69	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
70	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	—	2	1	no	—
74	C₄×D₄×C₁₉	—	2	1	no	—
75	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
76	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
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	1	no	—
84	C₁₉×#106	—	2	1	no	—
85	C₁₉×C₄⋊C₈	—	2	2	no	—
86	C₁₉×C₄⋊C₈	—	2	1	no	—
87	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
88	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
89	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
90	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₁₉×#103	—	2	1	no	—
92	C₁₉×#103	—	2	2	no	—
93	C₁₉×#103	—	2	2	no	—
94	C₁₉×#103	—	2	2	no	—
95	C₁₉×#103	—	2	2	no	—
96	C₁₉×#102	—	2	1	no	—
97	C₁₉×#102	—	2	2	no	—
98	C₁₉×#102	—	2	2	no	—
99	C₁₉×#102	—	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	#41×C₁₉	—	4	4	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	2	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	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	4	1	no	—
124	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	4	1	no	—
129	C₂²×C₄×C₁₉	—	4	1	no	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
133	Q₁₆×C₁₉	—	4	4	no	—
134	SD₁₆×C₁₉	—	4	2	no	—
135	SD₁₆×C₁₉	—	4	4	no	—
136	D₈×C₁₉	—	4	2	no	—
137	M₁₆×C₁₉	—	4	2	no	—
138	M₁₆×C₁₉	—	4	2	no	—
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	—	2	2	no	—
141	C₂×C₈×C₁₉	—	2	1	no	—
142	C₂×C₈×C₁₉	—	2	1	no	—
143	C₂×C₈×C₁₉	—	4	4	no	—
144	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	4	1	no	—
153	C₄⋊C₄×C₁₉	—	4	1	no	—
154	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²⋊C₄×C₁₉	—	2	1	no	—
157	C₂²⋊C₄×C₁₉	—	2	1	no	—
158	C₂²⋊C₄×C₁₉	—	2	1	no	—
159	C₂²⋊C₄×C₁₉	—	4	1	no	—
160	C₂²⋊C₄×C₁₉	—	4	1	no	—
161	C₄²×C₁₉	—	2	1	no	—
162	C₄²×C₁₉	—	2	1	no	—
163	C₄²×C₁₉	—	2	1	no	—
164	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₉	#41	1	1	yes	characteristic
167	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
168	#19319	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂³×C₁₉	—	2	1	no	—
170	C₂³×C₁₉	—	4	1	no	—
171	C₂³×C₁₉	#121	1	1	yes	characteristic
172	Q₈×C₁₉	—	2	1	no	—
173	Q₈×C₁₉	—	2	1	no	—
174	Q₈×C₁₉	—	4	2	no	—
175	Q₈×C₁₉	—	4	2	no	—
176	Q₈×C₁₉	—	4	2	no	—
177	Q₈×C₁₉	—	8	2	no	—
178	D₄×C₁₉	—	2	1	no	—
179	D₄×C₁₉	—	4	2	no	—
180	D₄×C₁₉	—	4	1	no	—
181	D₄×C₁₉	—	4	1	no	—
182	D₄×C₁₉	—	4	2	no	—
183	D₄×C₁₉	—	8	1	no	—
184	D₄×C₁₉	—	8	2	no	—
185	D₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
186	C₂×C₄×C₁₉	—	2	1	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	8	1	no	—
198	C₂×C₄×C₁₉	—	8	2	no	—
199	C₂×C₄×C₁₉	—	8	2	no	—
200	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
201	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₂²×D₄	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	C₈×C₁₉	—	2	2	no	—
207	C₈×C₁₉	—	2	2	no	—
208	C₈×C₁₉	—	4	2	no	—
209	C₈×C₁₉	—	4	1	no	—
210	C₈×C₁₉	—	4	2	no	—
211	C₈×C₁₉	—	4	1	no	—
212	#3141	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#3115	C₂×C₁₉	1	1	yes	characteristic
214	#3039	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#2970	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#1702	C₂×C₁₉	1	2	yes	complemented
217	#1700	C₂×C₁₉	1	2	yes	complemented
218	#1681	C₂×C₁₉	1	2	yes	complemented
219	#1679	C₂×C₁₉	1	2	yes	complemented
220	#1569	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#1557	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	2	no	—
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	—	4	1	no	—
228	C₂²×C₁₉	—	4	1	no	—
229	C₂²×C₁₉	—	8	1	no	—
230	C₂²×C₁₉	—	8	1	no	—
231	C₂²×C₁₉	—	8	1	no	—
232	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
233	C₄×C₁₉	—	2	1	no	—
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	2	1	no	—
236	C₄×C₁₉	—	2	1	no	—
237	C₄×C₁₉	—	4	1	no	—
238	C₄×C₁₉	—	4	1	no	—
239	C₄×C₁₉	—	4	1	no	—
240	C₄×C₁₉	—	8	1	no	—
241	C₄×C₁₉	—	8	2	no	—
242	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₄×C₁₉	#575	1	2	yes	—
244	C₄×C₁₉	#575	1	1	yes	characteristic
245	C₂×#137	—	2	1	no	—
246	#532	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
248	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
249	#489	—	2	1	no	—
250	#489	—	2	1	no	—
251	#487	C₂²×C₁₉	1	2	yes	—
252	#486	C₂²×C₁₉	1	2	yes	—
253	#482	—	2	1	no	—
254	#475	C₂²×C₁₉	1	1	yes	characteristic
255	#474	C₂²×C₁₉	1	1	yes	characteristic
256	#462	—	2	1	no	—
257	#462	C₂²×C₁₉	1	2	yes	—
258	#461	—	2	1	no	—
259	#461	C₂²×C₁₉	1	2	yes	—
260	#460	C₂²×C₁₉	1	1	yes	characteristic
261	#459	C₂²×C₁₉	1	1	yes	characteristic
262	#449	—	2	1	no	—
263	#446	C₂²×C₁₉	1	2	yes	—
264	#442	—	2	1	no	—
265	#440	—	2	1	no	—
266	#435	—	2	2	no	—
267	C₈×D₄	C₂²×C₁₉	1	2	yes	—
268	#432	—	2	1	no	—
269	#432	C₂²×C₁₉	1	1	yes	characteristic
270	#432	C₂²×C₁₉	1	1	yes	characteristic
271	#423	C₂²×C₁₉	1	1	yes	characteristic
272	#419	—	2	1	no	—
273	#417	—	2	2	no	—
274	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
275	C₂×#97	—	2	1	no	—
276	#335	C₂²×C₁₉	1	2	yes	—
277	#334	C₂²×C₁₉	1	2	yes	—
278	#332	C₂²×C₁₉	1	2	yes	—
279	#332	C₂²×C₁₉	1	2	yes	—
280	#332	C₂²×C₁₉	1	2	yes	—
281	#331	C₂²×C₁₉	1	2	yes	—
282	C₂×C₁₉	—	4	1	no	—
283	C₂×C₁₉	—	4	2	no	—
284	C₂×C₁₉	—	16	1	no	—
285	C₂×C₁₉	#3040	1	1	yes	characteristic
286	C₂×C₁₉	#3055	1	1	yes	characteristic
287	C₂×C₁₉	#3069	1	1	yes	characteristic
288	C₂×#41	—	2	1	no	—
289	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
290	C₂²×Q₈	—	2	1	no	—
291	#137	—	4	4	no	—
292	C₂×Q₁₆	—	2	2	no	—
293	C₂×SD₁₆	—	2	1	no	—
294	C₂×SD₁₆	—	2	2	no	—
295	C₂×D₈	—	2	1	no	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
298	C₂²×C₈	—	2	2	no	—
299	C₄⋊Q₈	—	2	1	no	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
303	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
304	#127	C₂³×C₁₉	1	1	yes	characteristic
305	#124	—	2	1	no	—
306	#121	—	2	1	no	—
307	#121	—	2	1	no	—
308	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
309	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
315	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
316	#117	—	2	1	no	—
317	#117	D₄×C₁₉	1	1	yes	characteristic
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
322	#107	—	2	1	no	—
323	#106	—	2	1	no	—
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
327	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
328	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
329	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
330	#103	—	2	1	no	—
331	#103	—	2	2	no	—
332	#103	—	2	2	no	—
333	#103	—	2	2	no	—
334	#103	—	2	2	no	—
335	#102	—	2	1	no	—
336	#102	—	2	2	no	—
337	#102	—	2	2	no	—
338	#102	—	2	1	no	—
339	#102	—	2	1	no	—
340	C₂²⋊C₈	—	2	1	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	2	2	no	—
343	#97	—	2	2	no	—
344	#97	—	2	1	no	—
345	#97	—	2	1	no	—
346	#97	D₄×C₁₉	1	1	yes	characteristic
347	#97	D₄×C₁₉	1	1	yes	characteristic
348	C₄×C₈	C₂³×C₁₉	1	2	yes	—
349	C₁₉	#19319	1	1	yes	characteristic, direct product factor, Sylow
350	#41	—	2	2	no	—
351	#41	—	4	1	no	—
352	#41	—	4	4	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	4	2	no	—
356	C₂×Q₈	—	4	2	no	—
357	C₂×Q₈	—	4	1	no	—
358	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	4	1	no	—
364	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	—	4	1	no	—
370	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
373	Q₁₆	—	4	4	no	—
374	SD₁₆	—	4	2	no	—
375	SD₁₆	—	4	4	no	—
376	D₈	—	4	2	no	—
377	M₁₆	—	4	2	no	—
378	M₁₆	—	4	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	4	4	no	—
384	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
385	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	4	1	no	—
393	C₄⋊C₄	—	4	1	no	—
394	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
395	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
396	C₂²⋊C₄	—	2	1	no	—
397	C₂²⋊C₄	—	2	1	no	—
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	4	1	no	—
400	C₂²⋊C₄	—	4	1	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
405	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
406	C₄²	#41×C₁₉	1	1	yes	characteristic
407	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
408	C₂³	—	2	1	no	—
409	C₂³	—	4	1	no	—
410	C₂³	C₁₉×#121	1	1	yes	characteristic
411	Q₈	—	2	1	no	—
412	Q₈	—	2	1	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	8	2	no	—
417	D₄	—	2	1	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	1	no	—
420	D₄	—	4	1	no	—
421	D₄	—	4	2	no	—
422	D₄	—	8	1	no	—
423	D₄	—	8	2	no	—
424	D₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	8	1	no	—
437	C₂×C₄	—	8	2	no	—
438	C₂×C₄	—	8	2	no	—
439	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
440	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
441	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
442	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
445	C₈	—	2	2	no	—
446	C₈	—	2	2	no	—
447	C₈	—	4	2	no	—
448	C₈	—	4	1	no	—
449	C₈	—	4	2	no	—
450	C₈	—	4	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	1	no	—
468	C₄	—	8	1	no	—
469	C₄	—	8	2	no	—
470	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
471	C₄	C₁₉×#575	1	2	yes	—
472	C₄	C₁₉×#575	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	4	2	no	—
475	C₂	—	16	1	no	—
476	C₂	C₁₉×#3040	1	1	yes	characteristic
477	C₂	C₁₉×#3055	1	1	yes	characteristic
478	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3115	C₂
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×#3141	C₂	semidirect
3. C₁₉×#3039	C₂	semidirect
4. C₁₉×#2970	C₂	semidirect
5. C₁₉×#1702	C₂	semidirect
6. C₁₉×#1700	C₂	semidirect
7. C₁₉×#1681	C₂	semidirect
8. C₁₉×#1679	C₂	semidirect
9. C₁₉×#1569	C₂	semidirect
10. C₁₉×#1557	C₂	semidirect
11. C₁₉×#1556	C₂	semidirect
168. #19319	C₁₉	direct (N × H)
212. #3141	C₂×C₁₉	semidirect
214. #3039	C₂×C₁₉	semidirect
215. #2970	C₂×C₁₉	semidirect
216. #1702	C₂×C₁₉	semidirect
217. #1700	C₂×C₁₉	semidirect
218. #1681	C₂×C₁₉	semidirect
219. #1679	C₂×C₁₉	semidirect
220. #1569	C₂×C₁₉	semidirect
221. #1557	C₂×C₁₉	semidirect
222. #1556	C₂×C₁₉	semidirect
349. C₁₉	#19319	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×#3141	2
C₁₉×#3115	2
C₁₉×#3039	2
C₁₉×#2970	2
C₁₉×#1702	2
C₁₉×#1700	2
C₁₉×#1681	2
C₁₉×#1679	2
C₁₉×#1569	2
C₁₉×#1557	2
C₁₉×#1556	2
#19319	19

Subgroups — C19×#19319 #18025278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19319 #18025278