Subgroups — C₁₉×#19509 #18025468

Order 4864.

636 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3253	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3245	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3207	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2981	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1703	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1687	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1677	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1665	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1570	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1557	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1551	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#532	C₂²	1	1	yes	characteristic
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₁₉×#532	C₂²	1	1	yes	characteristic
15	C₁₉×#493	C₂²	1	1	yes	characteristic
16	C₁₉×#492	C₂²	1	1	yes	characteristic
17	C₁₉×#487	C₂²	1	1	yes	characteristic
18	C₁₉×#486	C₂²	1	1	yes	characteristic
19	C₁₉×#476	—	2	1	no	—
20	C₁₉×#476	C₂²	1	2	yes	—
21	C₁₉×#474	—	2	1	no	—
22	C₁₉×#474	C₂²	1	2	yes	—
23	C₁₉×#469	—	2	2	no	—
24	C₁₉×#466	—	2	2	no	—
25	C₁₉×#463	—	2	2	no	—
26	C₁₉×#459	—	2	1	no	—
27	C₁₉×#459	—	2	1	no	—
28	C₁₉×#459	C₂²	1	2	yes	—
29	C₁₉×#459	C₂²	1	2	yes	—
30	C₁₉×#449	—	2	2	no	—
31	C₁₉×#436	C₂²	1	2	yes	—
32	C₁₉×#435	—	2	2	no	—
33	C₈×D₄×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#432	C₂²	1	1	yes	characteristic
35	C₁₉×#431	C₂²	1	1	yes	characteristic
36	C₁₉×#423	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₁₉×#408	—	2	2	no	—
39	C₁₉×#334	C₂²	1	2	yes	—
40	C₁₉×#334	C₂²	1	2	yes	—
41	C₁₉×#333	C₂²	1	2	yes	—
42	C₁₉×#332	C₂²	1	2	yes	—
43	C₁₉×#331	C₂²	1	2	yes	—
44	C₁₉×#331	C₂²	1	2	yes	—
45	C₂×#41×C₁₉	—	2	1	no	—
46	C₂×#41×C₁₉	—	2	1	no	—
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×SD₁₆×C₁₉	—	2	2	no	—
49	C₂×D₈×C₁₉	—	2	2	no	—
50	C₂×D₈×C₁₉	—	2	2	no	—
51	C₂×D₈×C₁₉	—	2	2	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	2	no	—
54	C₂²×C₈×C₁₉	—	2	1	no	—
55	C₂²×C₈×C₁₉	—	2	2	no	—
56	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
58	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₁₉×#127	D₄	1	1	yes	characteristic
60	C₁₉×#127	C₂³	1	1	yes	characteristic
61	C₁₉×#127	C₂³	1	1	yes	characteristic
62	C₁₉×#124	—	2	1	no	—
63	C₁₉×#124	—	2	1	no	—
64	C₁₉×#124	—	2	1	no	—
65	C₁₉×#121	—	2	1	no	—
66	C₁₉×#121	—	2	1	no	—
67	C₁₉×#121	—	2	1	no	—
68	C₁₉×#121	—	2	1	no	—
69	C₁₉×#121	—	2	1	no	—
70	C₁₉×#121	D₄	1	2	yes	—
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	—	2	1	no	—
76	C₄×D₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
78	C₁₉×#107	—	2	2	no	—
79	C₁₉×#106	—	2	2	no	—
80	C₁₉×C₄⋊C₈	—	2	1	no	—
81	C₁₉×C₄⋊C₈	—	2	1	no	—
82	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
83	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
85	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
86	C₁₉×#103	—	2	2	no	—
87	C₁₉×#102	—	2	2	no	—
88	C₁₉×#102	—	2	2	no	—
89	C₁₉×#102	—	2	2	no	—
90	C₁₉×#102	—	2	2	no	—
91	C₁₉×#102	—	2	2	no	—
92	C₁₉×C₂²⋊C₈	—	2	1	no	—
93	C₁₉×C₂²⋊C₈	—	2	2	no	—
94	C₁₉×C₂²⋊C₈	—	2	2	no	—
95	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
96	C₁₉×#97	—	2	1	no	—
97	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
99	#41×C₁₉	—	8	2	no	—
100	#41×C₁₉	—	8	2	no	—
101	#41×C₁₉	—	8	2	no	—
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	4	1	no	—
115	C₂×D₄×C₁₉	—	4	1	no	—
116	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	4	1	no	—
119	C₂²×C₄×C₁₉	—	4	1	no	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
123	SD₁₆×C₁₉	—	8	2	no	—
124	D₈×C₁₉	—	8	2	no	—
125	D₈×C₁₉	—	8	2	no	—
126	D₈×C₁₉	—	8	2	no	—
127	M₁₆×C₁₉	—	8	2	no	—
128	M₁₆×C₁₉	—	8	1	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	8	2	no	—
133	C₂×C₈×C₁₉	—	8	1	no	—
134	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
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	C₂×D₄	1	2	yes	—
142	C₂²⋊C₄×C₁₉	—	2	2	no	—
143	C₂²⋊C₄×C₁₉	—	2	2	no	—
144	C₂²⋊C₄×C₁₉	—	4	1	no	—
145	C₂²⋊C₄×C₁₉	—	4	1	no	—
146	C₂²⋊C₄×C₁₉	—	4	1	no	—
147	C₂²⋊C₄×C₁₉	—	4	1	no	—
148	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₉	#41	1	1	yes	characteristic
151	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
152	#19509	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂³×C₁₉	—	2	2	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	—	4	1	no	—
156	C₂³×C₁₉	#121	1	1	yes	characteristic
157	Q₈×C₁₉	—	4	2	no	—
158	Q₈×C₁₉	—	8	1	no	—
159	Q₈×C₁₉	—	8	1	no	—
160	D₄×C₁₉	—	2	2	no	—
161	D₄×C₁₉	—	2	2	no	—
162	D₄×C₁₉	—	4	2	no	—
163	D₄×C₁₉	—	4	2	no	—
164	D₄×C₁₉	—	4	1	no	—
165	D₄×C₁₉	—	4	1	no	—
166	D₄×C₁₉	—	4	1	no	—
167	D₄×C₁₉	—	4	1	no	—
168	D₄×C₁₉	—	8	1	no	—
169	D₄×C₁₉	—	8	1	no	—
170	D₄×C₁₉	—	8	1	no	—
171	D₄×C₁₉	—	8	1	no	—
172	D₄×C₁₉	—	8	2	no	—
173	D₄×C₁₉	—	8	2	no	—
174	D₄×C₁₉	—	8	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	8	2	no	—
185	C₂×C₄×C₁₉	—	8	2	no	—
186	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
192	C₈×C₁₉	—	2	2	no	—
193	C₈×C₁₉	—	2	2	no	—
194	C₈×C₁₉	—	4	2	no	—
195	C₈×C₁₉	—	4	2	no	—
196	C₈×C₁₉	—	4	2	no	—
197	#3253	C₂×C₁₉	1	1	yes	characteristic, complemented
198	#3245	C₂×C₁₉	1	1	yes	characteristic, complemented
199	#3207	C₂×C₁₉	1	1	yes	characteristic, complemented
200	#2981	C₂×C₁₉	1	1	yes	characteristic, complemented
201	#1703	C₂×C₁₉	1	2	yes	complemented
202	#1687	C₂×C₁₉	1	2	yes	complemented
203	#1677	C₂×C₁₉	1	2	yes	complemented
204	#1665	C₂×C₁₉	1	2	yes	complemented
205	#1570	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#1557	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#1551	C₂×C₁₉	1	1	yes	characteristic, complemented
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	2	1	no	—
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	4	2	no	—
212	C₂²×C₁₉	—	4	2	no	—
213	C₂²×C₁₉	—	4	2	no	—
214	C₂²×C₁₉	—	8	1	no	—
215	C₂²×C₁₉	—	8	1	no	—
216	C₂²×C₁₉	—	8	1	no	—
217	C₂²×C₁₉	—	8	1	no	—
218	C₂²×C₁₉	—	8	1	no	—
219	C₂²×C₁₉	—	8	1	no	—
220	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	1	no	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	8	1	no	—
227	C₄×C₁₉	—	8	1	no	—
228	C₄×C₁₉	#576	1	2	yes	—
229	C₄×C₁₉	#577	1	1	yes	characteristic
230	C₄×C₁₉	#577	1	1	yes	characteristic
231	#532	C₂²×C₁₉	1	1	yes	characteristic
232	#532	C₂²×C₁₉	1	1	yes	characteristic
233	#532	C₂²×C₁₉	1	1	yes	characteristic
234	#493	C₂²×C₁₉	1	1	yes	characteristic
235	#492	C₂²×C₁₉	1	1	yes	characteristic
236	#487	C₂²×C₁₉	1	1	yes	characteristic
237	#486	C₂²×C₁₉	1	1	yes	characteristic
238	#476	—	2	1	no	—
239	#476	C₂²×C₁₉	1	2	yes	—
240	#474	—	2	1	no	—
241	#474	C₂²×C₁₉	1	2	yes	—
242	#469	—	2	2	no	—
243	#466	—	2	2	no	—
244	#463	—	2	2	no	—
245	#459	—	2	1	no	—
246	#459	—	2	1	no	—
247	#459	C₂²×C₁₉	1	2	yes	—
248	#459	C₂²×C₁₉	1	2	yes	—
249	#449	—	2	2	no	—
250	#436	C₂²×C₁₉	1	2	yes	—
251	#435	—	2	2	no	—
252	C₈×D₄	C₂²×C₁₉	1	2	yes	—
253	#432	C₂²×C₁₉	1	1	yes	characteristic
254	#431	C₂²×C₁₉	1	1	yes	characteristic
255	#423	C₂²×C₁₉	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
257	#408	—	2	2	no	—
258	#334	C₂²×C₁₉	1	2	yes	—
259	#334	C₂²×C₁₉	1	2	yes	—
260	#333	C₂²×C₁₉	1	2	yes	—
261	#332	C₂²×C₁₉	1	2	yes	—
262	#331	C₂²×C₁₉	1	2	yes	—
263	#331	C₂²×C₁₉	1	2	yes	—
264	C₂×C₁₉	—	4	1	no	—
265	C₂×C₁₉	—	8	2	no	—
266	C₂×C₁₉	—	16	1	no	—
267	C₂×C₁₉	—	16	1	no	—
268	C₂×C₁₉	#3041	1	1	yes	characteristic
269	C₂×C₁₉	#3060	1	1	yes	characteristic
270	C₂×C₁₉	#3068	1	1	yes	characteristic
271	C₂×#41	—	2	1	no	—
272	C₂×#41	—	2	1	no	—
273	C₂×#41	—	2	1	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×D₈	—	2	2	no	—
276	C₂×D₈	—	2	2	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
283	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
284	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
285	#127	D₄×C₁₉	1	1	yes	characteristic
286	#127	C₂³×C₁₉	1	1	yes	characteristic
287	#127	C₂³×C₁₉	1	1	yes	characteristic
288	#124	—	2	1	no	—
289	#124	—	2	1	no	—
290	#124	—	2	1	no	—
291	#121	—	2	1	no	—
292	#121	—	2	1	no	—
293	#121	—	2	1	no	—
294	#121	—	2	1	no	—
295	#121	—	2	1	no	—
296	#121	D₄×C₁₉	1	2	yes	—
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	C₂³×C₁₉	1	2	yes	—
303	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
304	#107	—	2	2	no	—
305	#106	—	2	2	no	—
306	C₄⋊C₈	—	2	1	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
309	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
310	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
311	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
312	#103	—	2	2	no	—
313	#102	—	2	2	no	—
314	#102	—	2	2	no	—
315	#102	—	2	2	no	—
316	#102	—	2	2	no	—
317	#102	—	2	2	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₂²⋊C₈	—	2	2	no	—
321	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
322	#97	—	2	1	no	—
323	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
324	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
325	C₁₉	#19509	1	1	yes	characteristic, direct product factor, Sylow
326	#41	—	8	2	no	—
327	#41	—	8	2	no	—
328	#41	—	8	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
349	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
350	SD₁₆	—	8	2	no	—
351	D₈	—	8	2	no	—
352	D₈	—	8	2	no	—
353	D₈	—	8	2	no	—
354	M₁₆	—	8	2	no	—
355	M₁₆	—	8	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	8	2	no	—
360	C₂×C₈	—	8	1	no	—
361	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
362	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
363	C₄⋊C₄	—	2	1	no	—
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	C₂×D₄×C₁₉	1	2	yes	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	4	1	no	—
372	C₂²⋊C₄	—	4	1	no	—
373	C₂²⋊C₄	—	4	1	no	—
374	C₂²⋊C₄	—	4	1	no	—
375	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
376	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
377	C₄²	#41×C₁₉	1	1	yes	characteristic
378	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
379	C₂³	—	2	2	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	C₁₉×#121	1	1	yes	characteristic
383	Q₈	—	4	2	no	—
384	Q₈	—	8	1	no	—
385	Q₈	—	8	1	no	—
386	D₄	—	2	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	1	no	—
391	D₄	—	4	1	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	8	1	no	—
395	D₄	—	8	1	no	—
396	D₄	—	8	1	no	—
397	D₄	—	8	1	no	—
398	D₄	—	8	2	no	—
399	D₄	—	8	2	no	—
400	D₄	—	8	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	8	2	no	—
411	C₂×C₄	—	8	2	no	—
412	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
413	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
414	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	4	2	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	2	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	—	8	1	no	—
434	C₂²	—	8	1	no	—
435	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	4	2	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	C₁₉×#576	1	2	yes	—
444	C₄	C₁₉×#577	1	1	yes	characteristic
445	C₄	C₁₉×#577	1	1	yes	characteristic
446	C₂	—	4	1	no	—
447	C₂	—	8	2	no	—
448	C₂	—	16	1	no	—
449	C₂	—	16	1	no	—
450	C₂	C₁₉×#3041	1	1	yes	characteristic
451	C₂	C₁₉×#3060	1	1	yes	characteristic
452	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
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×#3253	C₂	semidirect
2. C₁₉×#3245	C₂	semidirect
3. C₁₉×#3207	C₂	semidirect
4. C₁₉×#2981	C₂	semidirect
5. C₁₉×#1703	C₂	semidirect
6. C₁₉×#1687	C₂	semidirect
7. C₁₉×#1677	C₂	semidirect
8. C₁₉×#1665	C₂	semidirect
9. C₁₉×#1570	C₂	semidirect
10. C₁₉×#1557	C₂	semidirect
11. C₁₉×#1551	C₂	semidirect
152. #19509	C₁₉	direct (N × H)
197. #3253	C₂×C₁₉	semidirect
198. #3245	C₂×C₁₉	semidirect
199. #3207	C₂×C₁₉	semidirect
200. #2981	C₂×C₁₉	semidirect
201. #1703	C₂×C₁₉	semidirect
202. #1687	C₂×C₁₉	semidirect
203. #1677	C₂×C₁₉	semidirect
204. #1665	C₂×C₁₉	semidirect
205. #1570	C₂×C₁₉	semidirect
206. #1557	C₂×C₁₉	semidirect
207. #1551	C₂×C₁₉	semidirect
325. C₁₉	#19509	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×#3253	2
C₁₉×#3245	2
C₁₉×#3207	2
C₁₉×#2981	2
C₁₉×#1703	2
C₁₉×#1687	2
C₁₉×#1677	2
C₁₉×#1665	2
C₁₉×#1570	2
C₁₉×#1557	2
C₁₉×#1551	2
#19509	19

Subgroups — C19×#19509 #18025468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19509 #18025468