Subgroups — C₁₉×#10250 #18016209

Order 4864.

604 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3208	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2548	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1545	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1503	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1303	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#533	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#124	—	2	1	no	—
11	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#492	—	2	1	no	—
13	C₁₉×#486	—	2	1	no	—
14	C₁₉×#479	—	2	2	no	—
15	C₁₉×#477	—	2	1	no	—
16	C₁₉×#475	—	2	1	no	—
17	C₁₉×#460	—	2	2	no	—
18	C₁₉×#450	—	2	2	no	—
19	C₁₉×#431	C₂²	1	1	yes	characteristic
20	C₁₉×#431	C₂²	1	1	yes	characteristic
21	C₁₉×#428	—	2	1	no	—
22	C₁₉×#423	C₂²	1	1	yes	characteristic
23	C₁₉×#419	—	2	1	no	—
24	C₁₉×#394	—	2	2	no	—
25	C₁₉×#390	—	2	2	no	—
26	C₁₉×#390	—	2	1	no	—
27	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#331	—	2	2	no	—
29	C₁₉×#328	—	2	2	no	—
30	C₁₉×Q₈⋊C₈	—	2	2	no	—
31	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	D₄	1	2	yes	—
35	C₂×SD₁₆×C₁₉	—	2	4	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
38	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
39	C₁₉×#127	—	2	1	no	—
40	C₁₉×#127	—	2	1	no	—
41	C₁₉×#127	—	2	1	no	—
42	C₁₉×#127	—	2	1	no	—
43	C₁₉×#125	—	2	1	no	—
44	C₁₉×#124	—	4	2	no	—
45	C₁₉×#124	—	4	2	no	—
46	C₁₉×C₂²⋊Q₈	—	2	1	no	—
47	C₁₉×C₂²⋊Q₈	—	2	1	no	—
48	C₄×Q₈×C₁₉	—	2	1	no	—
49	C₄×Q₈×C₁₉	—	2	1	no	—
50	C₄×Q₈×C₁₉	—	2	1	no	—
51	C₄×Q₈×C₁₉	—	2	1	no	—
52	C₄×Q₈×C₁₉	—	2	1	no	—
53	C₄×Q₈×C₁₉	—	2	1	no	—
54	C₁₉×#117	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
60	C₂×C₄²×C₁₉	—	2	1	no	—
61	C₂×C₄²×C₁₉	—	2	1	no	—
62	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
63	C₁₉×#107	—	2	2	no	—
64	C₁₉×#106	—	2	2	no	—
65	C₁₉×C₄⋊C₈	—	2	1	no	—
66	C₁₉×C₄⋊C₈	—	2	1	no	—
67	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
68	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
69	C₁₉×#103	—	2	2	no	—
70	C₁₉×#103	—	2	2	no	—
71	C₁₉×#102	—	2	4	no	—
72	C₁₉×C₂²⋊C₈	—	2	1	no	—
73	C₁₉×C₂²⋊C₈	—	2	1	no	—
74	C₄×C₈×C₁₉	—	2	1	no	—
75	C₄×C₈×C₁₉	—	2	1	no	—
76	C₁₉×#95	D₄	1	2	yes	—
77	C₂⁴×C₁₉	—	2	2	no	—
78	C₂×Q₈×C₁₉	—	2	1	no	—
79	C₂×Q₈×C₁₉	—	2	1	no	—
80	C₂×Q₈×C₁₉	—	2	1	no	—
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	complemented
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	4	4	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	—	4	1	no	—
96	C₂×D₄×C₁₉	—	4	1	no	—
97	C₂×D₄×C₁₉	—	8	2	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	2	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	C₂×D₄	1	1	yes	characteristic
104	SD₁₆×C₁₉	—	8	4	no	—
105	M₁₆×C₁₉	—	4	1	no	—
106	M₁₆×C₁₉	—	4	1	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	4	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	4	2	no	—
117	C₄⋊C₄×C₁₉	—	4	1	no	—
118	C₄⋊C₄×C₁₉	—	4	1	no	—
119	C₄⋊C₄×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	—	4	1	no	—
121	C₂²⋊C₄×C₁₉	—	4	8	no	—
122	C₂²⋊C₄×C₁₉	—	4	1	no	—
123	C₂²⋊C₄×C₁₉	—	8	4	no	—
124	C₄²×C₁₉	—	4	1	no	—
125	C₄²×C₁₉	—	4	1	no	—
126	C₄²×C₁₉	—	4	1	no	—
127	C₄²×C₁₉	—	4	1	no	—
128	C₄²×C₁₉	—	4	1	no	—
129	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₉	#41	1	1	yes	characteristic
133	#10250	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₁₉	—	4	4	no	—
135	C₂³×C₁₉	—	4	4	no	—
136	C₂³×C₁₉	—	4	2	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	#120	1	1	yes	characteristic
140	Q₈×C₁₉	—	2	2	no	—
141	Q₈×C₁₉	—	2	2	no	—
142	Q₈×C₁₉	—	4	1	no	—
143	Q₈×C₁₉	—	4	1	no	—
144	Q₈×C₁₉	—	4	2	no	—
145	Q₈×C₁₉	—	8	1	no	—
146	D₄×C₁₉	—	4	4	no	—
147	D₄×C₁₉	—	8	2	no	—
148	D₄×C₁₉	—	8	2	no	—
149	D₄×C₁₉	—	8	2	no	—
150	D₄×C₁₉	—	8	1	no	—
151	D₄×C₁₉	—	8	1	no	—
152	D₄×C₁₉	—	8	1	no	—
153	D₄×C₁₉	—	8	1	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
174	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
176	C₈×C₁₉	—	4	2	no	—
177	C₈×C₁₉	—	4	2	no	—
178	C₈×C₁₉	—	8	1	no	—
179	#3208	C₂×C₁₉	1	1	yes	characteristic
180	#3078	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#2548	C₂×C₁₉	1	1	yes	characteristic
182	#1545	C₂×C₁₉	1	1	yes	characteristic
183	#1503	C₂×C₁₉	1	1	yes	characteristic, complemented
184	#1479	C₂×C₁₉	1	1	yes	characteristic, complemented
185	#1303	C₂×C₁₉	1	1	yes	characteristic, complemented
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	8	4	no	—
189	C₂²×C₁₉	—	8	4	no	—
190	C₂²×C₁₉	—	8	2	no	—
191	C₂²×C₁₉	—	8	2	no	—
192	C₂²×C₁₉	—	8	2	no	—
193	C₂²×C₁₉	#392	1	1	yes	characteristic
194	C₂²×C₁₉	#450	1	1	yes	characteristic
195	C₂²×C₁₉	#452	1	1	yes	characteristic
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	4	2	no	—
200	C₄×C₁₉	—	8	2	no	—
201	C₄×C₁₉	—	8	1	no	—
202	C₄×C₁₉	—	8	1	no	—
203	C₄×C₁₉	—	8	1	no	—
204	C₄×C₁₉	#448	1	1	yes	characteristic
205	C₄×C₁₉	#449	1	1	yes	characteristic
206	C₄×C₁₉	#455	1	2	yes	—
207	C₄×C₁₉	#465	1	1	yes	characteristic
208	C₄×C₁₉	#468	1	1	yes	characteristic
209	#533	C₂²×C₁₉	1	1	yes	characteristic
210	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×#124	—	2	1	no	—
212	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
213	#492	—	2	1	no	—
214	#486	—	2	1	no	—
215	#479	—	2	2	no	—
216	#477	—	2	1	no	—
217	#475	—	2	1	no	—
218	#460	—	2	2	no	—
219	#450	—	2	2	no	—
220	#431	C₂²×C₁₉	1	1	yes	characteristic
221	#431	C₂²×C₁₉	1	1	yes	characteristic
222	#428	—	2	1	no	—
223	#423	C₂²×C₁₉	1	1	yes	characteristic
224	#419	—	2	1	no	—
225	#394	—	2	2	no	—
226	#390	—	2	2	no	—
227	#390	—	2	1	no	—
228	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
229	#331	—	2	2	no	—
230	#328	—	2	2	no	—
231	Q₈⋊C₈	—	2	2	no	—
232	C₂×C₁₉	—	2	1	no	—
233	C₂×C₁₉	—	2	1	no	—
234	C₂×C₁₉	—	16	2	no	—
235	C₂×C₁₉	#2000	1	1	yes	characteristic
236	C₂×C₁₉	#2004	1	1	yes	characteristic
237	C₂×C₁₉	#2008	1	1	yes	characteristic
238	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	D₄×C₁₉	1	2	yes	—
242	C₂×SD₁₆	—	2	4	no	—
243	C₂×M₁₆	—	2	1	no	—
244	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
245	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
246	#127	—	2	1	no	—
247	#127	—	2	1	no	—
248	#127	—	2	1	no	—
249	#127	—	2	1	no	—
250	#125	—	2	1	no	—
251	#124	—	4	2	no	—
252	#124	—	4	2	no	—
253	C₂²⋊Q₈	—	2	1	no	—
254	C₂²⋊Q₈	—	2	1	no	—
255	C₄×Q₈	—	2	1	no	—
256	C₄×Q₈	—	2	1	no	—
257	C₄×Q₈	—	2	1	no	—
258	C₄×Q₈	—	2	1	no	—
259	C₄×Q₈	—	2	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	#117	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	2	4	no	—
266	C₂×C₂²⋊C₄	—	2	4	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
270	#107	—	2	2	no	—
271	#106	—	2	2	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
275	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
276	#103	—	2	2	no	—
277	#103	—	2	2	no	—
278	#102	—	2	4	no	—
279	C₂²⋊C₈	—	2	1	no	—
280	C₂²⋊C₈	—	2	1	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	—	2	1	no	—
283	#95	D₄×C₁₉	1	2	yes	—
284	C₁₉	#10250	1	1	yes	characteristic, direct product factor, Sylow
285	C₂⁴	—	2	2	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	SD₁₆×C₁₉	1	2	yes	complemented
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	8	2	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
312	SD₁₆	—	8	4	no	—
313	M₁₆	—	4	1	no	—
314	M₁₆	—	4	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	4	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₂²⋊C₄	—	4	8	no	—
330	C₂²⋊C₄	—	4	1	no	—
331	C₂²⋊C₄	—	8	4	no	—
332	C₄²	—	4	1	no	—
333	C₄²	—	4	1	no	—
334	C₄²	—	4	1	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
338	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
340	C₄²	#41×C₁₉	1	1	yes	characteristic
341	C₂³	—	4	4	no	—
342	C₂³	—	4	4	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	C₁₉×#120	1	1	yes	characteristic
347	Q₈	—	2	2	no	—
348	Q₈	—	2	2	no	—
349	Q₈	—	4	1	no	—
350	Q₈	—	4	1	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	8	1	no	—
353	D₄	—	4	4	no	—
354	D₄	—	8	2	no	—
355	D₄	—	8	2	no	—
356	D₄	—	8	2	no	—
357	D₄	—	8	1	no	—
358	D₄	—	8	1	no	—
359	D₄	—	8	1	no	—
360	D₄	—	8	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
374	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
375	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
376	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
377	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
378	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
379	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
380	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
381	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
382	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
383	C₈	—	4	2	no	—
384	C₈	—	4	2	no	—
385	C₈	—	8	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	8	4	no	—
389	C₂²	—	8	4	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	C₁₉×#392	1	1	yes	characteristic
394	C₂²	C₁₉×#450	1	1	yes	characteristic
395	C₂²	C₁₉×#452	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	4	2	no	—
400	C₄	—	8	2	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	1	no	—
404	C₄	C₁₉×#448	1	1	yes	characteristic
405	C₄	C₁₉×#449	1	1	yes	characteristic
406	C₄	C₁₉×#455	1	2	yes	—
407	C₄	C₁₉×#465	1	1	yes	characteristic
408	C₄	C₁₉×#468	1	1	yes	characteristic
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	16	2	no	—
412	C₂	C₁₉×#2000	1	1	yes	characteristic
413	C₂	C₁₉×#2004	1	1	yes	characteristic
414	C₂	C₁₉×#2008	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂×C₁₉×#127	C₂²
LCS	G ▷ C₂×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×#3078	C₂	semidirect
5. C₁₉×#1503	C₂	semidirect
6. C₁₉×#1479	C₂	semidirect
7. C₁₉×#1303	C₂	semidirect
85. C₂×Q₈×C₁₉	SD₁₆	semidirect
133. #10250	C₁₉	direct (N × H)
180. #3078	C₂×C₁₉	semidirect
183. #1503	C₂×C₁₉	semidirect
184. #1479	C₂×C₁₉	semidirect
185. #1303	C₂×C₁₉	semidirect
284. C₁₉	#10250	direct (N × H)
293. C₂×Q₈	SD₁₆×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3208	2
C₁₉×#3078	2
C₁₉×#2548	2
C₁₉×#1545	2
C₁₉×#1503	2
C₁₉×#1479	2
C₁₉×#1303	2
#10250	19

Subgroups — C19×#10250 #18016209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10250 #18016209