Subgroups — C₁₉×#13307 #18019266

Order 4864.

552 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#472	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3061	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#359	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#350	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1387	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
9	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
10	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
12	C₁₉×#537	—	2	1	no	—
13	C₁₉×#509	—	2	2	no	—
14	C₁₉×#509	—	2	2	no	—
15	C₂×C₁₉×SD₃₂	—	2	1	no	—
16	C₂×C₁₉×D₁₆	—	2	1	no	—
17	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
18	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#472	—	2	2	no	—
20	C₁₉×#472	—	2	2	no	—
21	C₁₉×#468	—	2	2	no	—
22	C₁₉×#467	—	2	1	no	—
23	C₁₉×#466	—	2	1	no	—
24	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
26	C₁₉×#417	—	2	1	no	—
27	C₂×C₁₉×#100	—	2	1	no	—
28	C₁₉×#359	—	2	2	no	—
29	C₁₉×#357	—	2	2	no	—
30	C₁₉×#350	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
35	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
36	C₁₉×#135	—	2	1	no	—
37	C₁₉×#135	—	2	1	no	—
38	C₁₉×#135	—	2	1	no	—
39	C₁₉×#135	—	2	1	no	—
40	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
41	C₂×SD₁₆×C₁₉	—	2	1	no	—
42	C₂×SD₁₆×C₁₉	—	4	1	no	—
43	C₂×D₈×C₁₉	—	2	1	no	—
44	C₂×D₈×C₁₉	—	2	1	no	—
45	C₂×D₈×C₁₉	—	2	1	no	—
46	C₂×D₈×C₁₉	—	2	1	no	—
47	C₂×D₈×C₁₉	—	2	1	no	—
48	C₂×D₈×C₁₉	—	4	1	no	—
49	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
50	C₂×D₈×C₁₉	D₄	1	2	yes	complemented
51	C₁₉×#131	—	2	1	no	—
52	C₁₉×#131	—	2	1	no	—
53	C₁₉×#131	—	2	1	no	—
54	C₁₉×#131	—	2	1	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₁₉	—	2	1	no	—
59	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₁₉×C₂²⋊Q₈	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	—	4	1	no	—
62	C₁₉×#121	—	2	2	no	—
63	C₁₉×#121	—	4	2	no	—
64	C₁₉×#121	—	4	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₁₉×SD₃₂	—	2	4	no	—
67	C₁₉×D₁₆	—	2	4	no	—
68	C₁₉×M₃₂	—	2	1	no	—
69	C₁₉×M₃₂	D₄	1	2	yes	complemented
70	C₂×C₁₆×C₁₉	—	2	1	no	—
71	C₂×C₁₆×C₁₉	—	2	1	no	—
72	C₂×C₁₆×C₁₉	—	2	1	no	—
73	C₂×C₁₆×C₁₉	—	2	1	no	—
74	C₁₉×#108	—	2	1	no	—
75	C₁₉×#108	D₄	1	2	yes	complemented
76	C₁₉×#107	—	2	1	no	—
77	C₁₉×#107	D₄	1	2	yes	—
78	C₁₉×#103	—	2	2	no	—
79	C₁₉×#102	—	2	2	no	—
80	C₁₉×#100	—	2	4	no	—
81	C₂⁴×C₁₉	—	4	1	no	—
82	#41×C₁₉	—	2	1	no	—
83	#41×C₁₉	—	2	1	no	—
84	#41×C₁₉	—	2	1	no	—
85	#41×C₁₉	—	2	1	no	—
86	#41×C₁₉	—	4	1	no	—
87	#41×C₁₉	—	4	1	no	—
88	#41×C₁₉	—	4	1	no	—
89	#41×C₁₉	—	4	1	no	—
90	C₂×Q₈×C₁₉	—	2	1	no	—
91	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	—	2	2	no	—
95	C₂×D₄×C₁₉	—	4	1	no	—
96	C₂×D₄×C₁₉	—	4	2	no	—
97	C₂×D₄×C₁₉	—	4	1	no	—
98	C₂×D₄×C₁₉	—	4	1	no	—
99	C₂×D₄×C₁₉	—	4	1	no	—
100	C₂×D₄×C₁₉	—	4	1	no	—
101	C₂×D₄×C₁₉	—	4	1	no	—
102	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	—	4	1	no	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	Q₁₆×C₁₉	—	2	1	no	—
108	Q₁₆×C₁₉	—	2	1	no	—
109	SD₁₆×C₁₉	—	4	4	no	—
110	SD₁₆×C₁₉	—	4	1	no	—
111	SD₁₆×C₁₉	—	4	1	no	—
112	D₈×C₁₉	—	2	2	no	—
113	D₈×C₁₉	—	2	1	no	—
114	D₈×C₁₉	—	2	2	no	—
115	D₈×C₁₉	—	2	1	no	—
116	D₈×C₁₉	—	4	4	no	—
117	D₈×C₁₉	—	4	1	no	—
118	D₈×C₁₉	—	4	1	no	—
119	M₁₆×C₁₉	—	2	2	no	—
120	M₁₆×C₁₉	—	2	1	no	—
121	M₁₆×C₁₉	—	2	1	no	—
122	M₁₆×C₁₉	—	4	1	no	—
123	M₁₆×C₁₉	—	4	1	no	—
124	M₁₆×C₁₉	—	4	1	no	—
125	C₂×C₈×C₁₉	—	2	1	no	—
126	C₂×C₈×C₁₉	—	4	1	no	—
127	C₂×C₈×C₁₉	—	4	1	no	—
128	C₂×C₈×C₁₉	—	4	1	no	—
129	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	4	2	no	—
137	C₄⋊C₄×C₁₉	—	4	1	no	—
138	C₂²⋊C₄×C₁₉	—	4	2	no	—
139	C₂²⋊C₄×C₁₉	—	4	2	no	—
140	C₁₆×C₁₉	—	2	2	no	—
141	C₁₆×C₁₉	—	4	1	no	—
142	#13307	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂³×C₁₉	—	2	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	2	no	—
146	C₂³×C₁₉	—	8	1	no	—
147	C₂³×C₁₉	—	8	1	no	—
148	C₂³×C₁₉	—	16	1	no	—
149	C₂³×C₁₉	—	16	1	no	—
150	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
151	Q₈×C₁₉	—	2	1	no	—
152	Q₈×C₁₉	—	2	1	no	—
153	Q₈×C₁₉	—	4	1	no	—
154	Q₈×C₁₉	—	4	1	no	—
155	D₄×C₁₉	—	2	1	no	—
156	D₄×C₁₉	—	2	1	no	—
157	D₄×C₁₉	—	4	1	no	—
158	D₄×C₁₉	—	4	1	no	—
159	D₄×C₁₉	—	4	2	no	—
160	D₄×C₁₉	—	4	1	no	—
161	D₄×C₁₉	—	4	2	no	—
162	D₄×C₁₉	—	4	1	no	—
163	D₄×C₁₉	—	8	1	no	—
164	D₄×C₁₉	—	8	1	no	—
165	D₄×C₁₉	—	8	1	no	—
166	D₄×C₁₉	—	8	1	no	—
167	D₄×C₁₉	—	16	2	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	8	1	no	—
174	C₂×C₄×C₁₉	—	8	1	no	—
175	C₂×C₄×C₁₉	—	16	1	no	—
176	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
181	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₈×C₁₉	—	4	1	no	—
183	C₈×C₁₉	—	4	2	no	—
184	C₈×C₁₉	#120	1	1	yes	characteristic
185	C₈×C₁₉	#121	1	1	yes	characteristic
186	C₈×C₁₉	#121	1	1	yes	characteristic
187	C₈×C₁₉	#127	1	1	yes	characteristic
188	C₂×#509	C₂×C₁₉	1	1	yes	characteristic, complemented
189	C₂×#472	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#3061	C₂×C₁₉	1	1	yes	characteristic, complemented
191	C₂×#359	C₂×C₁₉	1	1	yes	characteristic, complemented
192	C₂×#357	C₂×C₁₉	1	1	yes	characteristic, complemented
193	C₂×#350	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#1387	C₂×C₁₉	1	1	yes	characteristic, complemented
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	4	1	no	—
198	C₂²×C₁₉	—	4	1	no	—
199	C₂²×C₁₉	—	4	1	no	—
200	C₂²×C₁₉	—	8	1	no	—
201	C₂²×C₁₉	—	8	1	no	—
202	C₂²×C₁₉	—	8	1	no	—
203	C₂²×C₁₉	—	8	2	no	—
204	C₂²×C₁₉	—	16	2	no	—
205	C₂²×C₁₉	—	16	2	no	—
206	C₂²×C₁₉	—	16	1	no	—
207	C₂²×C₁₉	—	16	1	no	—
208	C₂²×C₁₉	#447	1	1	yes	characteristic
209	C₂²×C₁₉	#449	1	1	yes	characteristic
210	C₂²×C₁₉	#469	1	1	yes	characteristic
211	C₄×C₁₉	—	4	1	no	—
212	C₄×C₁₉	—	8	2	no	—
213	C₄×C₁₉	—	8	1	no	—
214	C₄×C₁₉	#392	1	1	yes	characteristic
215	C₄×C₁₉	#447	1	1	yes	characteristic
216	C₄×C₁₉	#449	1	1	yes	characteristic
217	C₄×C₁₉	#466	1	1	yes	characteristic
218	C₂×AGL(1,ℤ/8)	—	2	1	no	—
219	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
220	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
222	#537	—	2	1	no	—
223	#509	—	2	2	no	—
224	#509	—	2	2	no	—
225	C₂×SD₃₂	—	2	1	no	—
226	C₂×D₁₆	—	2	1	no	—
227	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
228	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
229	#472	—	2	2	no	—
230	#472	—	2	2	no	—
231	#468	—	2	2	no	—
232	#467	—	2	1	no	—
233	#466	—	2	1	no	—
234	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
236	#417	—	2	1	no	—
237	C₂×#100	—	2	1	no	—
238	#359	—	2	2	no	—
239	#357	—	2	2	no	—
240	#350	—	2	2	no	—
241	C₂×C₁₉	—	2	1	no	—
242	C₂×C₁₉	—	2	1	no	—
243	C₂×C₁₉	—	8	1	no	—
244	C₂×C₁₉	—	16	1	no	—
245	C₂×C₁₉	—	16	2	no	—
246	C₂×C₁₉	#1999	1	1	yes	characteristic
247	C₂×C₁₉	#2192	1	1	yes	characteristic
248	C₂×C₁₉	#2193	1	1	yes	characteristic
249	C₂×#41	—	2	1	no	—
250	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
251	C₂²×D₄	—	2	1	no	—
252	AGL(1,ℤ/8)	—	2	4	no	—
253	AGL(1,ℤ/8)	—	4	2	no	—
254	#135	—	2	1	no	—
255	#135	—	2	1	no	—
256	#135	—	2	1	no	—
257	#135	—	2	1	no	—
258	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
259	C₂×SD₁₆	—	2	1	no	—
260	C₂×SD₁₆	—	4	1	no	—
261	C₂×D₈	—	2	1	no	—
262	C₂×D₈	—	2	1	no	—
263	C₂×D₈	—	2	1	no	—
264	C₂×D₈	—	2	1	no	—
265	C₂×D₈	—	2	1	no	—
266	C₂×D₈	—	4	1	no	—
267	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
268	C₂×D₈	D₄×C₁₉	1	2	yes	complemented
269	#131	—	2	1	no	—
270	#131	—	2	1	no	—
271	#131	—	2	1	no	—
272	#131	—	2	1	no	—
273	C₂×M₁₆	—	2	1	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
278	C₂²⋊Q₈	—	2	2	no	—
279	C₂²⋊Q₈	—	4	1	no	—
280	#121	—	2	2	no	—
281	#121	—	4	2	no	—
282	#121	—	4	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	SD₃₂	—	2	4	no	—
285	D₁₆	—	2	4	no	—
286	M₃₂	—	2	1	no	—
287	M₃₂	D₄×C₁₉	1	2	yes	complemented
288	C₂×C₁₆	—	2	1	no	—
289	C₂×C₁₆	—	2	1	no	—
290	C₂×C₁₆	—	2	1	no	—
291	C₂×C₁₆	—	2	1	no	—
292	#108	—	2	1	no	—
293	#108	D₄×C₁₉	1	2	yes	complemented
294	#107	—	2	1	no	—
295	#107	D₄×C₁₉	1	2	yes	—
296	#103	—	2	2	no	—
297	#102	—	2	2	no	—
298	#100	—	2	4	no	—
299	C₁₉	#13307	1	1	yes	characteristic, direct product factor, Sylow
300	C₂⁴	—	4	1	no	—
301	#41	—	2	1	no	—
302	#41	—	2	1	no	—
303	#41	—	2	1	no	—
304	#41	—	2	1	no	—
305	#41	—	4	1	no	—
306	#41	—	4	1	no	—
307	#41	—	4	1	no	—
308	#41	—	4	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
326	Q₁₆	—	2	1	no	—
327	Q₁₆	—	2	1	no	—
328	SD₁₆	—	4	4	no	—
329	SD₁₆	—	4	1	no	—
330	SD₁₆	—	4	1	no	—
331	D₈	—	2	1	no	—
332	D₈	—	2	2	no	—
333	D₈	—	2	2	no	—
334	D₈	—	2	1	no	—
335	D₈	—	4	4	no	—
336	D₈	—	4	1	no	—
337	D₈	—	4	1	no	—
338	M₁₆	—	2	1	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	2	1	no	—
341	M₁₆	—	4	1	no	—
342	M₁₆	—	4	1	no	—
343	M₁₆	—	4	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
349	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
350	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
352	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
353	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₁₆	—	2	2	no	—
360	C₁₆	—	4	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	8	1	no	—
365	C₂³	—	8	1	no	—
366	C₂³	—	16	1	no	—
367	C₂³	—	16	1	no	—
368	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
369	Q₈	—	2	1	no	—
370	Q₈	—	2	1	no	—
371	Q₈	—	4	1	no	—
372	Q₈	—	4	1	no	—
373	D₄	—	2	1	no	—
374	D₄	—	2	1	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	1	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	1	no	—
381	D₄	—	8	1	no	—
382	D₄	—	8	1	no	—
383	D₄	—	8	1	no	—
384	D₄	—	8	1	no	—
385	D₄	—	16	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	8	1	no	—
392	C₂×C₄	—	8	1	no	—
393	C₂×C₄	—	16	1	no	—
394	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
395	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
396	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
397	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
398	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
399	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₈	—	4	1	no	—
401	C₈	—	4	2	no	—
402	C₈	C₁₉×#120	1	1	yes	characteristic
403	C₈	C₁₉×#121	1	1	yes	characteristic
404	C₈	C₁₉×#121	1	1	yes	characteristic
405	C₈	C₁₉×#127	1	1	yes	characteristic
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	16	2	no	—
416	C₂²	—	16	2	no	—
417	C₂²	—	16	1	no	—
418	C₂²	—	16	1	no	—
419	C₂²	C₁₉×#447	1	1	yes	characteristic
420	C₂²	C₁₉×#449	1	1	yes	characteristic
421	C₂²	C₁₉×#469	1	1	yes	characteristic
422	C₄	—	4	1	no	—
423	C₄	—	8	2	no	—
424	C₄	—	8	1	no	—
425	C₄	C₁₉×#392	1	1	yes	characteristic
426	C₄	C₁₉×#447	1	1	yes	characteristic
427	C₄	C₁₉×#449	1	1	yes	characteristic
428	C₄	C₁₉×#466	1	1	yes	characteristic
429	C₂	—	2	1	no	—
430	C₂	—	2	1	no	—
431	C₂	—	8	1	no	—
432	C₂	—	16	1	no	—
433	C₂	—	16	2	no	—
434	C₂	C₁₉×#1999	1	1	yes	characteristic
435	C₂	C₁₉×#2192	1	1	yes	characteristic
436	C₂	C₁₉×#2193	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₁₉×#509	C₂	semidirect
2. C₂×C₁₉×#472	C₂	semidirect
3. C₁₉×#3061	C₂	semidirect
4. C₂×C₁₉×#359	C₂	semidirect
5. C₂×C₁₉×#357	C₂	semidirect
6. C₂×C₁₉×#350	C₂	semidirect
7. C₁₉×#1387	C₂	semidirect
50. C₂×D₈×C₁₉	D₄	semidirect
69. C₁₉×M₃₂	D₄	semidirect
75. C₁₉×#108	D₄	semidirect
142. #13307	C₁₉	direct (N × H)
188. C₂×#509	C₂×C₁₉	semidirect
189. C₂×#472	C₂×C₁₉	semidirect
190. #3061	C₂×C₁₉	semidirect
191. C₂×#359	C₂×C₁₉	semidirect
192. C₂×#357	C₂×C₁₉	semidirect
193. C₂×#350	C₂×C₁₉	semidirect
194. #1387	C₂×C₁₉	semidirect
268. C₂×D₈	D₄×C₁₉	semidirect
287. M₃₂	D₄×C₁₉	semidirect
293. #108	D₄×C₁₉	semidirect
299. C₁₉	#13307	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#509	2
C₂×C₁₉×#472	2
C₁₉×#3061	2
C₂×C₁₉×#359	2
C₂×C₁₉×#357	2
C₂×C₁₉×#350	2
C₁₉×#1387	2
#13307	19

Subgroups — C19×#13307 #18019266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13307 #18019266