Subgroups — C₁₉×#9378 #18015337

Order 4864.

498 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3217	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2992	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1982	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1555	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1509	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1290	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1285	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
9	C₁₉×#529	C₂²	1	1	yes	characteristic
10	C₁₉×#496	C₄	1	2	yes	complemented
11	C₁₉×#490	C₄	1	2	yes	complemented
12	C₁₉×#460	—	2	1	no	—
13	C₁₉×#459	—	2	1	no	—
14	C₁₉×#450	—	2	1	no	—
15	C₁₉×#447	—	2	1	no	—
16	C₁₉×#446	—	2	1	no	—
17	C₁₉×#435	—	2	1	no	—
18	C₁₉×#435	—	2	1	no	—
19	C₈×D₄×C₁₉	—	2	1	no	—
20	C₁₉×#433	—	2	1	no	—
21	C₁₉×#432	C₂²	1	1	yes	characteristic
22	C₁₉×#432	C₂²	1	1	yes	characteristic
23	C₁₉×#432	C₂²	1	1	yes	characteristic
24	C₁₉×#424	—	2	1	no	—
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#102	—	2	1	no	—
27	C₂×C₁₉×#102	—	2	1	no	—
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#331	—	2	1	no	—
30	C₁₉×#331	—	2	1	no	—
31	C₁₉×#328	—	2	1	no	—
32	C₁₉×#327	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	—	2	1	no	—
36	C₂×SD₁₆×C₁₉	—	2	2	no	—
37	C₂×D₈×C₁₉	—	2	2	no	—
38	C₂×M₁₆×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₁₉×#127	—	2	1	no	—
43	C₁₉×#127	—	2	1	no	—
44	C₁₉×#127	—	2	1	no	—
45	C₁₉×#127	C₂×C₄	1	2	yes	—
46	C₁₉×#126	—	2	1	no	—
47	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
48	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
49	C₁₉×#123	—	2	1	no	—
50	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
51	C₁₉×#121	D₄	1	1	yes	characteristic
52	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
53	C₄×D₄×C₁₉	—	2	1	no	—
54	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
55	C₁₉×#117	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄²×C₁₉	—	2	1	no	—
58	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	—	2	1	no	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	—	2	1	no	—
63	C₁₉×C₄⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
66	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
67	C₁₉×#102	—	2	2	no	—
68	C₁₉×#102	—	2	2	no	—
69	C₁₉×#102	—	4	2	no	—
70	C₁₉×#102	—	4	2	no	—
71	C₁₉×C₂²⋊C₈	—	2	1	no	—
72	C₁₉×C₂²⋊C₈	—	2	1	no	—
73	C₁₉×C₂²⋊C₈	—	2	1	no	—
74	C₁₉×C₂²⋊C₈	—	2	1	no	—
75	C₁₉×C₂²⋊C₈	—	2	1	no	—
76	C₁₉×#97	—	2	1	no	—
77	C₁₉×#97	—	2	1	no	—
78	C₁₉×#97	—	2	1	no	—
79	C₁₉×#97	C₂×C₄	1	2	yes	—
80	C₄×C₈×C₁₉	—	2	1	no	—
81	C₁₉×#95	—	2	1	no	—
82	C₂⁴×C₁₉	—	4	1	no	—
83	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×D₄×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	—	2	2	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	4	1	no	—
92	C₂×D₄×C₁₉	—	4	1	no	—
93	C₂×D₄×C₁₉	—	4	1	no	—
94	C₂×D₄×C₁₉	—	4	1	no	—
95	C₂×D₄×C₁₉	—	8	1	no	—
96	C₂×D₄×C₁₉	—	8	1	no	—
97	C₂×D₄×C₁₉	—	8	2	no	—
98	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
104	SD₁₆×C₁₉	—	8	2	no	—
105	D₈×C₁₉	—	8	2	no	—
106	M₁₆×C₁₉	—	8	1	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	1	no	—
109	C₂×C₈×C₁₉	—	2	1	no	—
110	C₂×C₈×C₁₉	—	2	1	no	—
111	C₂×C₈×C₁₉	—	2	1	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₂×C₈×C₁₉	—	8	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	4	1	no	—
122	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²⋊C₄×C₁₉	—	2	1	no	—
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	—	2	1	no	—
129	C₄²×C₁₉	—	2	1	no	—
130	C₄²×C₁₉	—	8	1	no	—
131	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₉	#41	1	1	yes	characteristic
135	#9378	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	8	1	no	—
139	C₂³×C₁₉	—	8	1	no	—
140	C₂³×C₁₉	—	8	1	no	—
141	C₂³×C₁₉	—	8	1	no	—
142	C₂³×C₁₉	—	8	1	no	—
143	C₂³×C₁₉	—	8	1	no	—
144	C₂³×C₁₉	#121	1	1	yes	characteristic
145	Q₈×C₁₉	—	4	1	no	—
146	D₄×C₁₉	—	4	1	no	—
147	D₄×C₁₉	—	4	2	no	—
148	D₄×C₁₉	—	4	2	no	—
149	D₄×C₁₉	—	4	2	no	—
150	D₄×C₁₉	—	4	2	no	—
151	D₄×C₁₉	—	4	1	no	—
152	D₄×C₁₉	—	4	1	no	—
153	D₄×C₁₉	—	8	2	no	—
154	D₄×C₁₉	—	8	2	no	—
155	D₄×C₁₉	—	8	2	no	—
156	D₄×C₁₉	—	8	1	no	—
157	D₄×C₁₉	—	8	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	8	1	no	—
170	C₂×C₄×C₁₉	—	8	1	no	—
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
177	C₈×C₁₉	—	4	2	no	—
178	C₈×C₁₉	—	4	1	no	—
179	C₈×C₁₉	—	4	1	no	—
180	C₈×C₁₉	—	4	1	no	—
181	C₈×C₁₉	—	4	1	no	—
182	C₈×C₁₉	—	8	1	no	—
183	#3217	C₂×C₁₉	1	1	yes	characteristic
184	#2992	C₂×C₁₉	1	1	yes	characteristic, complemented
185	#1982	C₂×C₁₉	1	1	yes	characteristic, complemented
186	#1555	C₂×C₁₉	1	1	yes	characteristic, complemented
187	#1509	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#1290	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#1285	C₂×C₁₉	1	1	yes	characteristic, complemented
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	—	4	1	no	—
194	C₂²×C₁₉	—	4	1	no	—
195	C₂²×C₁₉	—	8	2	no	—
196	C₂²×C₁₉	—	8	2	no	—
197	C₂²×C₁₉	—	8	2	no	—
198	C₂²×C₁₉	—	16	1	no	—
199	C₂²×C₁₉	—	16	1	no	—
200	C₂²×C₁₉	—	16	1	no	—
201	C₂²×C₁₉	—	16	1	no	—
202	C₂²×C₁₉	#386	1	1	yes	characteristic
203	C₂²×C₁₉	#471	1	1	yes	characteristic
204	C₂²×C₁₉	#472	1	1	yes	characteristic
205	C₄×C₁₉	—	2	1	no	—
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	1	no	—
209	C₄×C₁₉	—	2	1	no	—
210	C₄×C₁₉	—	4	1	no	—
211	C₄×C₁₉	—	4	1	no	—
212	C₄×C₁₉	—	4	1	no	—
213	C₄×C₁₉	—	8	2	no	—
214	C₄×C₁₉	#453	1	1	yes	characteristic
215	C₄×C₁₉	#454	1	1	yes	characteristic
216	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
217	#529	C₂²×C₁₉	1	1	yes	characteristic
218	#496	C₄×C₁₉	1	2	yes	complemented
219	#490	C₄×C₁₉	1	2	yes	complemented
220	#460	—	2	1	no	—
221	#459	—	2	1	no	—
222	#450	—	2	1	no	—
223	#447	—	2	1	no	—
224	#446	—	2	1	no	—
225	#435	—	2	1	no	—
226	#435	—	2	1	no	—
227	C₈×D₄	—	2	1	no	—
228	#433	—	2	1	no	—
229	#432	C₂²×C₁₉	1	1	yes	characteristic
230	#432	C₂²×C₁₉	1	1	yes	characteristic
231	#432	C₂²×C₁₉	1	1	yes	characteristic
232	#424	—	2	1	no	—
233	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×#102	—	2	1	no	—
235	C₂×#102	—	2	1	no	—
236	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
237	#331	—	2	1	no	—
238	#331	—	2	1	no	—
239	#328	—	2	1	no	—
240	#327	—	2	1	no	—
241	C₂×C₁₉	—	2	1	no	—
242	C₂×C₁₉	—	2	1	no	—
243	C₂×C₁₉	—	8	1	no	—
244	C₂×C₁₉	—	16	2	no	—
245	C₂×C₁₉	#1883	1	1	yes	characteristic
246	C₂×C₁₉	#1907	1	1	yes	characteristic
247	C₂×C₁₉	#1910	1	1	yes	characteristic
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂×SD₁₆	—	2	2	no	—
252	C₂×D₈	—	2	2	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
256	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
257	#127	—	2	1	no	—
258	#127	—	2	1	no	—
259	#127	—	2	1	no	—
260	#127	C₂×C₄×C₁₉	1	2	yes	—
261	#126	—	2	1	no	—
262	#125	C₂×C₄×C₁₉	1	1	yes	characteristic
263	#124	C₂×C₄×C₁₉	1	1	yes	characteristic
264	#123	—	2	1	no	—
265	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
266	#121	D₄×C₁₉	1	1	yes	characteristic
267	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
270	#117	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
281	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
282	#102	—	2	2	no	—
283	#102	—	2	2	no	—
284	#102	—	4	2	no	—
285	#102	—	4	2	no	—
286	C₂²⋊C₈	—	2	1	no	—
287	C₂²⋊C₈	—	2	1	no	—
288	C₂²⋊C₈	—	2	1	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	#97	—	2	1	no	—
292	#97	—	2	1	no	—
293	#97	—	2	1	no	—
294	#97	C₂×C₄×C₁₉	1	2	yes	—
295	C₄×C₈	—	2	1	no	—
296	#95	—	2	1	no	—
297	C₁₉	#9378	1	1	yes	characteristic, direct product factor, Sylow
298	C₂⁴	—	4	1	no	—
299	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	8	1	no	—
312	C₂×D₄	—	8	1	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
320	SD₁₆	—	8	2	no	—
321	D₈	—	8	2	no	—
322	M₁₆	—	8	1	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	8	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
339	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	1	no	—
342	C₂²⋊C₄	—	2	1	no	—
343	C₂²⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	8	1	no	—
347	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
348	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
349	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
350	C₄²	#41×C₁₉	1	1	yes	characteristic
351	C₂³	—	2	1	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	8	1	no	—
354	C₂³	—	8	1	no	—
355	C₂³	—	8	1	no	—
356	C₂³	—	8	1	no	—
357	C₂³	—	8	1	no	—
358	C₂³	—	8	1	no	—
359	C₂³	C₁₉×#121	1	1	yes	characteristic
360	Q₈	—	4	1	no	—
361	D₄	—	4	1	no	—
362	D₄	—	4	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	1	no	—
367	D₄	—	4	1	no	—
368	D₄	—	8	2	no	—
369	D₄	—	8	2	no	—
370	D₄	—	8	2	no	—
371	D₄	—	8	1	no	—
372	D₄	—	8	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	1	no	—
385	C₂×C₄	—	8	1	no	—
386	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
387	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
388	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
389	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
390	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
391	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
392	C₈	—	4	2	no	—
393	C₈	—	4	1	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	8	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	16	1	no	—
407	C₂²	—	16	1	no	—
408	C₂²	—	16	1	no	—
409	C₂²	—	16	1	no	—
410	C₂²	C₁₉×#386	1	1	yes	characteristic
411	C₂²	C₁₉×#471	1	1	yes	characteristic
412	C₂²	C₁₉×#472	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	8	2	no	—
422	C₄	C₁₉×#453	1	1	yes	characteristic
423	C₄	C₁₉×#454	1	1	yes	characteristic
424	C₂	—	2	1	no	—
425	C₂	—	2	1	no	—
426	C₂	—	8	1	no	—
427	C₂	—	16	2	no	—
428	C₂	C₁₉×#1883	1	1	yes	characteristic
429	C₂	C₁₉×#1907	1	1	yes	characteristic
430	C₂	C₁₉×#1910	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3217	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
2. C₁₉×#2992	C₂	semidirect
3. C₁₉×#1982	C₂	semidirect
4. C₁₉×#1555	C₂	semidirect
5. C₁₉×#1509	C₂	semidirect
6. C₁₉×#1290	C₂	semidirect
7. C₁₉×#1285	C₂	semidirect
10. C₁₉×#496	C₄	semidirect
11. C₁₉×#490	C₄	semidirect
135. #9378	C₁₉	direct (N × H)
184. #2992	C₂×C₁₉	semidirect
185. #1982	C₂×C₁₉	semidirect
186. #1555	C₂×C₁₉	semidirect
187. #1509	C₂×C₁₉	semidirect
188. #1290	C₂×C₁₉	semidirect
189. #1285	C₂×C₁₉	semidirect
218. #496	C₄×C₁₉	semidirect
219. #490	C₄×C₁₉	semidirect
297. C₁₉	#9378	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×#3217	2
C₁₉×#2992	2
C₁₉×#1982	2
C₁₉×#1555	2
C₁₉×#1509	2
C₁₉×#1290	2
C₁₉×#1285	2
#9378	19

Subgroups — C19×#9378 #18015337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9378 #18015337