Subgroups — C₁₉×#19340 #18025299

Order 4864.

582 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3237	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3216	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3167	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1700	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1698	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1672	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1666	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1559	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1557	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#533	C₂²	1	1	yes	characteristic
14	C₁₉×#532	C₂²	1	1	yes	characteristic
15	C₁₉×#501	—	2	1	no	—
16	C₁₉×#498	C₂²	1	1	yes	characteristic
17	C₁₉×#497	—	2	1	no	—
18	C₁₉×#492	C₂²	1	1	yes	characteristic
19	C₁₉×#491	—	2	1	no	—
20	C₁₉×#489	—	2	1	no	—
21	C₁₉×#487	C₂²	1	1	yes	characteristic
22	C₁₉×#486	C₂²	1	1	yes	characteristic
23	C₁₉×#485	—	2	2	no	—
24	C₁₉×#477	C₂²	1	2	yes	—
25	C₁₉×#475	C₂²	1	2	yes	—
26	C₁₉×#465	—	2	1	no	—
27	C₁₉×#465	—	2	1	no	—
28	C₁₉×#462	C₂²	1	2	yes	—
29	C₁₉×#460	C₂²	1	2	yes	—
30	C₁₉×#452	—	2	2	no	—
31	C₁₉×#446	—	2	1	no	—
32	C₁₉×#446	C₂²	1	2	yes	—
33	C₈×Q₈×C₁₉	—	2	1	no	—
34	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
35	C₄×SD₁₆×C₁₉	—	2	1	no	—
36	C₄×SD₁₆×C₁₉	—	2	1	no	—
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#432	C₂²	1	1	yes	characteristic
39	C₁₉×#424	—	2	1	no	—
40	C₁₉×#423	C₂²	1	1	yes	characteristic
41	C₁₉×#405	—	2	1	no	—
42	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
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×#331	C₂²	1	2	yes	—
49	C₂×#41×C₁₉	—	2	1	no	—
50	C₂×Q₁₆×C₁₉	—	2	2	no	—
51	C₂×SD₁₆×C₁₉	—	2	2	no	—
52	C₂×SD₁₆×C₁₉	—	2	1	no	—
53	C₂×SD₁₆×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
58	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₉×#127	C₂³	1	1	yes	characteristic
63	C₁₉×#125	—	2	1	no	—
64	C₁₉×#125	—	2	1	no	—
65	C₁₉×#124	—	2	1	no	—
66	C₁₉×C₂²⋊Q₈	—	2	1	no	—
67	C₁₉×C₂²⋊Q₈	—	2	1	no	—
68	C₁₉×C₂²⋊Q₈	—	2	1	no	—
69	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
70	C₁₉×#121	—	2	1	no	—
71	C₁₉×#121	—	2	1	no	—
72	C₄×Q₈×C₁₉	—	2	1	no	—
73	C₄×Q₈×C₁₉	—	2	1	no	—
74	C₄×Q₈×C₁₉	—	2	1	no	—
75	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
76	C₄×D₄×C₁₉	—	2	1	no	—
77	C₄×D₄×C₁₉	—	2	1	no	—
78	C₁₉×#117	—	2	1	no	—
79	C₁₉×#117	—	2	1	no	—
80	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
81	C₁₉×#107	—	2	2	no	—
82	C₁₉×#106	—	2	1	no	—
83	C₁₉×#106	—	2	1	no	—
84	C₁₉×#106	—	2	2	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	C₂³	1	2	yes	—
89	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
90	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
91	C₁₉×#103	—	2	2	no	—
92	C₁₉×#103	—	2	2	no	—
93	C₁₉×#103	—	2	1	no	—
94	C₁₉×#103	—	2	1	no	—
95	C₁₉×#103	—	2	2	no	—
96	C₁₉×#102	—	2	1	no	—
97	C₁₉×#102	—	2	1	no	—
98	C₁₉×#102	—	2	2	no	—
99	C₁₉×C₂²⋊C₈	—	2	1	no	—
100	C₁₉×C₂²⋊C₈	—	2	1	no	—
101	C₁₉×#97	—	2	2	no	—
102	C₁₉×#97	—	2	1	no	—
103	C₁₉×#97	—	2	1	no	—
104	C₄×C₈×C₁₉	—	2	2	no	—
105	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
106	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
109	#41×C₁₉	—	8	2	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
115	C₂×D₄×C₁₉	—	2	1	no	—
116	C₂×D₄×C₁₉	—	2	1	no	—
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×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	Q₁₆×C₁₉	—	8	2	no	—
124	SD₁₆×C₁₉	—	4	2	no	—
125	SD₁₆×C₁₉	—	4	2	no	—
126	SD₁₆×C₁₉	—	8	2	no	—
127	M₁₆×C₁₉	—	4	2	no	—
128	C₂×C₈×C₁₉	—	2	2	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	—	4	1	no	—
133	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	2	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	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	1	no	—
148	C₄⋊C₄×C₁₉	—	4	1	no	—
149	C₄⋊C₄×C₁₉	—	4	1	no	—
150	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂²⋊C₄×C₁₉	—	2	2	no	—
152	C₂²⋊C₄×C₁₉	—	4	1	no	—
153	C₂²⋊C₄×C₁₉	—	4	1	no	—
154	C₂²⋊C₄×C₁₉	—	4	1	no	—
155	C₄²×C₁₉	—	2	2	no	—
156	C₄²×C₁₉	—	4	1	no	—
157	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₉	#41	1	1	yes	characteristic
160	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
161	#19340	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂³×C₁₉	—	4	1	no	—
163	C₂³×C₁₉	#121	1	1	yes	characteristic
164	Q₈×C₁₉	—	2	2	no	—
165	Q₈×C₁₉	—	2	2	no	—
166	Q₈×C₁₉	—	4	2	no	—
167	Q₈×C₁₉	—	4	1	no	—
168	Q₈×C₁₉	—	4	1	no	—
169	Q₈×C₁₉	—	4	2	no	—
170	Q₈×C₁₉	—	8	1	no	—
171	D₄×C₁₉	—	4	1	no	—
172	D₄×C₁₉	—	4	1	no	—
173	D₄×C₁₉	—	4	2	no	—
174	D₄×C₁₉	—	8	1	no	—
175	D₄×C₁₉	—	8	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	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	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	1	no	—
193	C₈×C₁₉	—	2	1	no	—
194	C₈×C₁₉	—	2	1	no	—
195	C₈×C₁₉	—	4	2	no	—
196	C₈×C₁₉	—	4	2	no	—
197	C₈×C₁₉	—	4	2	no	—
198	C₈×C₁₉	#137	1	2	yes	—
199	#3237	C₂×C₁₉	1	1	yes	characteristic, complemented
200	#3216	C₂×C₁₉	1	1	yes	characteristic
201	#3167	C₂×C₁₉	1	1	yes	characteristic
202	#2960	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#1700	C₂×C₁₉	1	2	yes	complemented
204	#1698	C₂×C₁₉	1	2	yes	complemented
205	#1672	C₂×C₁₉	1	2	yes	complemented
206	#1666	C₂×C₁₉	1	2	yes	complemented
207	#1568	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#1559	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#1557	C₂×C₁₉	1	1	yes	characteristic
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	—	2	1	no	—
213	C₂²×C₁₉	—	8	1	no	—
214	C₂²×C₁₉	—	8	1	no	—
215	C₂²×C₁₉	—	8	1	no	—
216	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	4	2	no	—
222	C₄×C₁₉	—	4	2	no	—
223	C₄×C₁₉	—	8	1	no	—
224	C₄×C₁₉	—	8	1	no	—
225	C₄×C₁₉	—	8	1	no	—
226	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
227	C₄×C₁₉	#575	1	1	yes	characteristic
228	C₄×C₁₉	#577	1	2	yes	—
229	#533	C₂²×C₁₉	1	1	yes	characteristic
230	#533	C₂²×C₁₉	1	1	yes	characteristic
231	#532	C₂²×C₁₉	1	1	yes	characteristic
232	#501	—	2	1	no	—
233	#498	C₂²×C₁₉	1	1	yes	characteristic
234	#497	—	2	1	no	—
235	#492	C₂²×C₁₉	1	1	yes	characteristic
236	#491	—	2	1	no	—
237	#489	—	2	1	no	—
238	#487	C₂²×C₁₉	1	1	yes	characteristic
239	#486	C₂²×C₁₉	1	1	yes	characteristic
240	#485	—	2	2	no	—
241	#477	C₂²×C₁₉	1	2	yes	—
242	#475	C₂²×C₁₉	1	2	yes	—
243	#465	—	2	1	no	—
244	#465	—	2	1	no	—
245	#462	C₂²×C₁₉	1	2	yes	—
246	#460	C₂²×C₁₉	1	2	yes	—
247	#452	—	2	2	no	—
248	#446	—	2	1	no	—
249	#446	C₂²×C₁₉	1	2	yes	—
250	C₈×Q₈	—	2	1	no	—
251	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
252	C₄×SD₁₆	—	2	1	no	—
253	C₄×SD₁₆	—	2	1	no	—
254	#432	C₂²×C₁₉	1	1	yes	characteristic
255	#432	C₂²×C₁₉	1	1	yes	characteristic
256	#424	—	2	1	no	—
257	#423	C₂²×C₁₉	1	1	yes	characteristic
258	#405	—	2	1	no	—
259	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
260	#335	C₂²×C₁₉	1	2	yes	—
261	#334	C₂²×C₁₉	1	2	yes	—
262	#333	C₂²×C₁₉	1	2	yes	—
263	#332	C₂²×C₁₉	1	2	yes	—
264	#332	C₂²×C₁₉	1	2	yes	—
265	#331	C₂²×C₁₉	1	2	yes	—
266	C₂×C₁₉	—	4	1	no	—
267	C₂×C₁₉	—	16	1	no	—
268	C₂×C₁₉	#3037	1	1	yes	characteristic
269	C₂×C₁₉	#3057	1	1	yes	characteristic
270	C₂×C₁₉	#3067	1	1	yes	characteristic
271	C₂×#41	—	2	1	no	—
272	C₂×Q₁₆	—	2	2	no	—
273	C₂×SD₁₆	—	2	2	no	—
274	C₂×SD₁₆	—	2	1	no	—
275	C₂×SD₁₆	—	2	1	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
278	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
279	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
280	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
281	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
282	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
283	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
284	#127	C₂³×C₁₉	1	1	yes	characteristic
285	#125	—	2	1	no	—
286	#125	—	2	1	no	—
287	#124	—	2	1	no	—
288	C₂²⋊Q₈	—	2	1	no	—
289	C₂²⋊Q₈	—	2	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
292	#121	—	2	1	no	—
293	#121	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×Q₈	—	2	1	no	—
297	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	#117	—	2	1	no	—
301	#117	—	2	1	no	—
302	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
303	#107	—	2	2	no	—
304	#106	—	2	1	no	—
305	#106	—	2	1	no	—
306	#106	—	2	2	no	—
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	—	2	2	no	—
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
311	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
312	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
313	#103	—	2	2	no	—
314	#103	—	2	2	no	—
315	#103	—	2	1	no	—
316	#103	—	2	1	no	—
317	#103	—	2	2	no	—
318	#102	—	2	1	no	—
319	#102	—	2	1	no	—
320	#102	—	2	2	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	2	1	no	—
323	#97	—	2	2	no	—
324	#97	—	2	1	no	—
325	#97	—	2	1	no	—
326	C₄×C₈	—	2	2	no	—
327	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
328	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
329	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
330	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
331	C₁₉	#19340	1	1	yes	characteristic, direct product factor, Sylow
332	#41	—	8	2	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
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	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
346	Q₁₆	—	8	2	no	—
347	SD₁₆	—	4	2	no	—
348	SD₁₆	—	4	2	no	—
349	SD₁₆	—	8	2	no	—
350	M₁₆	—	4	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
357	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	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	1	no	—
371	C₄⋊C₄	—	4	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	4	1	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	4	1	no	—
380	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
382	C₄²	#41×C₁₉	1	1	yes	characteristic
383	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
384	C₂³	—	4	1	no	—
385	C₂³	C₁₉×#121	1	1	yes	characteristic
386	Q₈	—	2	2	no	—
387	Q₈	—	2	2	no	—
388	Q₈	—	4	2	no	—
389	Q₈	—	4	1	no	—
390	Q₈	—	4	1	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	8	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	D₄	—	4	2	no	—
396	D₄	—	8	1	no	—
397	D₄	—	8	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	8	2	no	—
408	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
409	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
410	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
414	C₈	—	2	1	no	—
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₈	—	4	2	no	—
420	C₈	C₁₉×#137	1	2	yes	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	8	1	no	—
435	C₄	—	8	1	no	—
436	C₄	—	8	1	no	—
437	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
438	C₄	C₁₉×#575	1	1	yes	characteristic
439	C₄	C₁₉×#577	1	2	yes	—
440	C₂	—	4	1	no	—
441	C₂	—	16	1	no	—
442	C₂	C₁₉×#3037	1	1	yes	characteristic
443	C₂	C₁₉×#3057	1	1	yes	characteristic
444	C₂	C₁₉×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#532	C₂²
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×#3237	C₂	semidirect
4. C₁₉×#2960	C₂	semidirect
5. C₁₉×#1700	C₂	semidirect
6. C₁₉×#1698	C₂	semidirect
7. C₁₉×#1672	C₂	semidirect
8. C₁₉×#1666	C₂	semidirect
9. C₁₉×#1568	C₂	semidirect
10. C₁₉×#1559	C₂	semidirect
161. #19340	C₁₉	direct (N × H)
199. #3237	C₂×C₁₉	semidirect
202. #2960	C₂×C₁₉	semidirect
203. #1700	C₂×C₁₉	semidirect
204. #1698	C₂×C₁₉	semidirect
205. #1672	C₂×C₁₉	semidirect
206. #1666	C₂×C₁₉	semidirect
207. #1568	C₂×C₁₉	semidirect
208. #1559	C₂×C₁₉	semidirect
331. C₁₉	#19340	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×#3237	2
C₁₉×#3216	2
C₁₉×#3167	2
C₁₉×#2960	2
C₁₉×#1700	2
C₁₉×#1698	2
C₁₉×#1672	2
C₁₉×#1666	2
C₁₉×#1568	2
C₁₉×#1559	2
C₁₉×#1557	2
#19340	19

Subgroups — C19×#19340 #18025299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19340 #18025299