Subgroups — C₁₉×#19082 #18025041

Order 4864.

864 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3180	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3142	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1664	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1663	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1662	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1658	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1657	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1656	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1524	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₉×#330	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#564	C₂²	1	1	yes	characteristic
13	C₁₉×#563	C₂²	1	2	yes	—
14	C₁₉×#562	C₂²	1	1	yes	characteristic
15	C₁₉×#554	—	2	2	no	—
16	C₁₉×#553	—	2	2	no	—
17	C₁₉×#552	—	2	2	no	—
18	C₁₉×#541	—	2	2	no	—
19	C₁₉×#539	—	2	2	no	—
20	C₁₉×#539	—	2	2	no	—
21	C₁₉×#532	C₂²	1	1	yes	characteristic
22	C₁₉×#529	C₂²	1	2	yes	—
23	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
24	C₁₉×#501	C₂²	1	2	yes	—
25	C₁₉×#496	C₂²	1	2	yes	—
26	C₁₉×#491	C₂²	1	1	yes	characteristic
27	C₁₉×#491	C₂²	1	1	yes	characteristic
28	C₁₉×#490	C₂²	1	2	yes	—
29	C₁₉×#490	C₂²	1	1	yes	characteristic
30	C₁₉×#490	C₂²	1	1	yes	characteristic
31	C₁₉×#489	C₂²	1	2	yes	—
32	C₁₉×#488	—	2	2	no	—
33	C₁₉×#466	—	2	2	no	—
34	C₁₉×#465	—	2	2	no	—
35	C₁₉×#442	—	2	2	no	—
36	C₁₉×#440	—	2	2	no	—
37	C₁₉×#417	—	2	2	no	—
38	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#97	C₂²	1	2	yes	—
40	C₁₉×#330	C₂²	1	1	yes	characteristic
41	C₁₉×#330	C₂²	1	2	yes	—
42	C₁₉×#330	C₂²	1	2	yes	—
43	C₁₉×#330	C₂²	1	1	yes	characteristic
44	C₁₉×#330	C₂²	1	2	yes	—
45	C₁₉×#329	C₂²	1	2	yes	—
46	C₁₉×#329	C₂²	1	2	yes	—
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×SD₁₆×C₁₉	—	2	2	no	—
49	C₂×D₈×C₁₉	—	2	2	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂²×C₈×C₁₉	—	2	2	no	—
52	C₁₉×C₄⋊Q₈	—	2	2	no	—
53	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
54	C₁₉×#127	C₂³	1	1	yes	characteristic
55	C₁₉×#126	—	2	2	no	—
56	C₁₉×#126	—	2	2	no	—
57	C₁₉×#126	—	2	2	no	—
58	C₁₉×#126	—	2	2	no	—
59	C₁₉×#126	—	2	2	no	—
60	C₁₉×#125	—	2	2	no	—
61	C₁₉×#125	—	2	2	no	—
62	C₁₉×#125	—	2	2	no	—
63	C₁₉×#125	—	2	2	no	—
64	C₁₉×#125	—	2	2	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#125	D₄	1	2	yes	—
67	C₁₉×#125	C₂³	1	1	yes	characteristic
68	C₁₉×#125	C₂³	1	1	yes	characteristic
69	C₁₉×#125	C₂³	1	2	yes	—
70	C₁₉×#124	—	2	1	no	—
71	C₁₉×#124	C₂³	1	2	yes	—
72	C₁₉×#123	—	2	2	no	—
73	C₁₉×#123	—	2	2	no	—
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×#123	—	2	2	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×C₂²⋊Q₈	—	2	2	no	—
78	C₁₉×C₂²⋊Q₈	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
84	C₁₉×#121	—	2	2	no	—
85	C₁₉×#121	—	2	2	no	—
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#121	D₄	1	2	yes	—
88	C₄×Q₈×C₁₉	—	2	2	no	—
89	C₄×Q₈×C₁₉	D₄	1	2	yes	—
90	C₄×D₄×C₁₉	—	2	2	no	—
91	C₄×D₄×C₁₉	—	2	2	no	—
92	C₄×D₄×C₁₉	—	2	2	no	—
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	D₄	1	2	yes	—
96	C₁₉×#117	—	2	2	no	—
97	C₁₉×#117	—	2	2	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
101	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×#107	—	2	2	no	—
103	C₁₉×#106	—	2	2	no	—
104	C₁₉×#103	—	2	2	no	—
105	C₁₉×#103	—	2	2	no	—
106	C₁₉×#103	—	2	2	no	—
107	C₁₉×#102	—	2	2	no	—
108	C₁₉×#102	—	2	2	no	—
109	C₁₉×#102	—	2	2	no	—
110	C₁₉×#102	—	2	2	no	—
111	C₁₉×#102	—	2	2	no	—
112	C₁₉×#97	—	2	2	no	—
113	C₁₉×#97	C₂³	1	2	yes	—
114	C₁₉×#97	C₂³	1	2	yes	—
115	C₁₉×#97	C₂³	1	1	yes	characteristic
116	C₁₉×#97	C₂³	1	1	yes	characteristic
117	C₄×C₈×C₁₉	—	2	1	no	—
118	#41×C₁₉	—	4	4	no	—
119	C₂×Q₈×C₁₉	—	2	2	no	—
120	C₂×Q₈×C₁₉	—	2	1	no	—
121	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	1	no	—
126	C₂×D₄×C₁₉	—	4	1	no	—
127	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	4	1	no	—
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
135	SD₁₆×C₁₉	—	4	4	no	—
136	D₈×C₁₉	—	4	4	no	—
137	M₁₆×C₁₉	—	4	2	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	—	2	1	no	—
141	C₂×C₈×C₁₉	—	2	1	no	—
142	C₂×C₈×C₁₉	—	4	4	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
162	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
163	C₂²⋊C₄×C₁₉	—	2	2	no	—
164	C₂²⋊C₄×C₁₉	—	2	2	no	—
165	C₂²⋊C₄×C₁₉	—	2	2	no	—
166	C₂²⋊C₄×C₁₉	—	2	2	no	—
167	C₂²⋊C₄×C₁₉	—	2	2	no	—
168	C₂²⋊C₄×C₁₉	—	2	2	no	—
169	C₂²⋊C₄×C₁₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	4	2	no	—
173	C₄²×C₁₉	—	2	2	no	—
174	C₄²×C₁₉	—	2	2	no	—
175	C₄²×C₁₉	—	2	2	no	—
176	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₉	C₂×D₄	1	2	yes	—
178	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
179	#19082	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂³×C₁₉	—	2	2	no	—
181	C₂³×C₁₉	—	4	1	no	—
182	C₂³×C₁₉	#120	1	1	yes	characteristic
183	Q₈×C₁₉	—	4	2	no	—
184	Q₈×C₁₉	—	4	2	no	—
185	Q₈×C₁₉	—	8	2	no	—
186	D₄×C₁₉	—	4	2	no	—
187	D₄×C₁₉	—	4	2	no	—
188	D₄×C₁₉	—	4	2	no	—
189	D₄×C₁₉	—	4	2	no	—
190	D₄×C₁₉	—	4	4	no	—
191	D₄×C₁₉	—	8	2	no	—
192	D₄×C₁₉	—	8	2	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	8	2	no	—
202	C₂×C₄×C₁₉	—	8	2	no	—
203	C₂×C₄×C₁₉	—	8	2	no	—
204	C₂×C₄×C₁₉	—	8	2	no	—
205	C₂×C₄×C₁₉	—	8	2	no	—
206	C₂×C₄×C₁₉	#120	1	2	yes	—
207	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
210	C₈×C₁₉	—	2	4	no	—
211	C₈×C₁₉	—	4	2	no	—
212	C₈×C₁₉	—	4	1	no	—
213	C₈×C₁₉	—	4	1	no	—
214	#3553	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#3180	C₂×C₁₉	1	2	yes	complemented
216	#3142	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#1664	C₂×C₁₉	1	2	yes	complemented
218	#1663	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#1662	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#1658	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#1657	C₂×C₁₉	1	2	yes	complemented
222	#1656	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#1524	C₂×C₁₉	1	2	yes	complemented
224	C₂×#330	C₂×C₁₉	1	1	yes	characteristic, complemented
225	C₂²×C₁₉	—	2	2	no	—
226	C₂²×C₁₉	—	4	2	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	—	8	1	no	—
230	C₂²×C₁₉	—	8	2	no	—
231	C₂²×C₁₉	#454	1	2	yes	—
232	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
233	C₄×C₁₉	—	2	1	no	—
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	2	2	no	—
236	C₄×C₁₉	—	2	2	no	—
237	C₄×C₁₉	—	4	2	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	4	2	no	—
242	C₄×C₁₉	—	8	1	no	—
243	#564	C₂²×C₁₉	1	1	yes	characteristic
244	#563	C₂²×C₁₉	1	2	yes	—
245	#562	C₂²×C₁₉	1	1	yes	characteristic
246	#554	—	2	2	no	—
247	#553	—	2	2	no	—
248	#552	—	2	2	no	—
249	#541	—	2	2	no	—
250	#539	—	2	2	no	—
251	#539	—	2	2	no	—
252	#532	C₂²×C₁₉	1	1	yes	characteristic
253	#529	C₂²×C₁₉	1	2	yes	—
254	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
255	#501	C₂²×C₁₉	1	2	yes	—
256	#496	C₂²×C₁₉	1	2	yes	—
257	#491	C₂²×C₁₉	1	1	yes	characteristic
258	#491	C₂²×C₁₉	1	1	yes	characteristic
259	#490	C₂²×C₁₉	1	1	yes	characteristic
260	#490	C₂²×C₁₉	1	1	yes	characteristic
261	#490	C₂²×C₁₉	1	2	yes	—
262	#489	C₂²×C₁₉	1	2	yes	—
263	#488	—	2	2	no	—
264	#466	—	2	2	no	—
265	#465	—	2	2	no	—
266	#442	—	2	2	no	—
267	#440	—	2	2	no	—
268	#417	—	2	2	no	—
269	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
270	C₂×#97	C₂²×C₁₉	1	2	yes	—
271	#330	C₂²×C₁₉	1	1	yes	characteristic
272	#330	C₂²×C₁₉	1	2	yes	—
273	#330	C₂²×C₁₉	1	2	yes	—
274	#330	C₂²×C₁₉	1	1	yes	characteristic
275	#330	C₂²×C₁₉	1	2	yes	—
276	#329	C₂²×C₁₉	1	2	yes	—
277	#329	C₂²×C₁₉	1	2	yes	—
278	C₂×C₁₉	—	2	2	no	—
279	C₂×C₁₉	—	8	2	no	—
280	C₂×C₁₉	—	16	1	no	—
281	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
282	C₂×C₁₉	#3018	1	2	yes	—
283	C₂×#41	—	2	1	no	—
284	C₂×SD₁₆	—	2	2	no	—
285	C₂×D₈	—	2	2	no	—
286	C₂×M₁₆	—	2	1	no	—
287	C₂²×C₈	—	2	2	no	—
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
290	#127	C₂³×C₁₉	1	1	yes	characteristic
291	#126	—	2	2	no	—
292	#126	—	2	2	no	—
293	#126	—	2	2	no	—
294	#126	—	2	2	no	—
295	#126	—	2	2	no	—
296	#125	—	2	2	no	—
297	#125	—	2	2	no	—
298	#125	—	2	2	no	—
299	#125	—	2	2	no	—
300	#125	—	2	2	no	—
301	#125	—	2	2	no	—
302	#125	D₄×C₁₉	1	2	yes	—
303	#125	C₂³×C₁₉	1	1	yes	characteristic
304	#125	C₂³×C₁₉	1	1	yes	characteristic
305	#125	C₂³×C₁₉	1	2	yes	—
306	#124	—	2	1	no	—
307	#124	C₂³×C₁₉	1	2	yes	—
308	#123	—	2	2	no	—
309	#123	—	2	2	no	—
310	#123	—	2	2	no	—
311	#123	—	2	2	no	—
312	#123	—	2	2	no	—
313	C₂²⋊Q₈	—	2	2	no	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₂²⋊Q₈	—	2	2	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₂²⋊Q₈	—	2	2	no	—
319	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
320	#121	—	2	2	no	—
321	#121	—	2	2	no	—
322	#121	—	2	2	no	—
323	#121	D₄×C₁₉	1	2	yes	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	D₄×C₁₉	1	2	yes	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	—	2	2	no	—
328	C₄×D₄	—	2	2	no	—
329	C₄×D₄	—	2	2	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	D₄×C₁₉	1	2	yes	—
332	#117	—	2	2	no	—
333	#117	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
337	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
338	#107	—	2	2	no	—
339	#106	—	2	2	no	—
340	#103	—	2	2	no	—
341	#103	—	2	2	no	—
342	#103	—	2	2	no	—
343	#102	—	2	2	no	—
344	#102	—	2	2	no	—
345	#102	—	2	2	no	—
346	#102	—	2	2	no	—
347	#102	—	2	2	no	—
348	#97	—	2	2	no	—
349	#97	C₂³×C₁₉	1	1	yes	characteristic
350	#97	C₂³×C₁₉	1	1	yes	characteristic
351	#97	C₂³×C₁₉	1	2	yes	—
352	#97	C₂³×C₁₉	1	2	yes	—
353	C₄×C₈	—	2	1	no	—
354	C₁₉	#19082	1	1	yes	characteristic, direct product factor, Sylow
355	#41	—	4	4	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	4	1	no	—
364	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	4	1	no	—
370	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
372	SD₁₆	—	4	4	no	—
373	D₈	—	4	4	no	—
374	M₁₆	—	4	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	4	4	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
397	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
398	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
399	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	4	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₄²	C₂×D₄×C₁₉	1	2	yes	—
415	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
416	C₂³	—	2	2	no	—
417	C₂³	—	4	1	no	—
418	C₂³	C₁₉×#120	1	1	yes	characteristic
419	Q₈	—	4	2	no	—
420	Q₈	—	4	2	no	—
421	Q₈	—	8	2	no	—
422	D₄	—	4	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	4	no	—
427	D₄	—	8	2	no	—
428	D₄	—	8	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	8	2	no	—
438	C₂×C₄	—	8	2	no	—
439	C₂×C₄	—	8	2	no	—
440	C₂×C₄	—	8	2	no	—
441	C₂×C₄	—	8	2	no	—
442	C₂×C₄	C₁₉×#120	1	2	yes	—
443	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
446	C₈	—	2	4	no	—
447	C₈	—	4	2	no	—
448	C₈	—	4	1	no	—
449	C₈	—	4	1	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	2	no	—
456	C₂²	C₁₉×#454	1	2	yes	—
457	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	2	no	—
467	C₄	—	8	1	no	—
468	C₂	—	2	2	no	—
469	C₂	—	8	2	no	—
470	C₂	—	16	1	no	—
471	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
472	C₂	C₁₉×#3018	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
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×#3553	C₂	semidirect
2. C₁₉×#3180	C₂	semidirect
3. C₁₉×#3142	C₂	semidirect
4. C₁₉×#1664	C₂	semidirect
5. C₁₉×#1663	C₂	semidirect
6. C₁₉×#1662	C₂	semidirect
7. C₁₉×#1658	C₂	semidirect
8. C₁₉×#1657	C₂	semidirect
9. C₁₉×#1656	C₂	semidirect
10. C₁₉×#1524	C₂	semidirect
11. C₂×C₁₉×#330	C₂	semidirect
179. #19082	C₁₉	direct (N × H)
214. #3553	C₂×C₁₉	semidirect
215. #3180	C₂×C₁₉	semidirect
216. #3142	C₂×C₁₉	semidirect
217. #1664	C₂×C₁₉	semidirect
218. #1663	C₂×C₁₉	semidirect
219. #1662	C₂×C₁₉	semidirect
220. #1658	C₂×C₁₉	semidirect
221. #1657	C₂×C₁₉	semidirect
222. #1656	C₂×C₁₉	semidirect
223. #1524	C₂×C₁₉	semidirect
224. C₂×#330	C₂×C₁₉	semidirect
354. C₁₉	#19082	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×#3553	2
C₁₉×#3180	2
C₁₉×#3142	2
C₁₉×#1664	2
C₁₉×#1663	2
C₁₉×#1662	2
C₁₉×#1658	2
C₁₉×#1657	2
C₁₉×#1656	2
C₁₉×#1524	2
C₂×C₁₉×#330	2
#19082	19

Subgroups — C19×#19082 #18025041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19082 #18025041