Subgroups — C₁₉×#10180 #18016139

Order 4864.

562 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3036	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1549	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1480	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1460	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1301	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
9	C₁₉×#532	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#492	—	2	1	no	—
13	C₁₉×#487	—	2	1	no	—
14	C₁₉×#476	—	2	2	no	—
15	C₁₉×#476	—	2	2	no	—
16	C₁₉×#463	—	2	2	no	—
17	C₁₉×#461	—	2	2	no	—
18	C₁₉×#461	—	2	1	no	—
19	C₁₉×#459	—	2	1	no	—
20	C₁₉×#448	—	2	2	no	—
21	C₁₉×#431	C₂²	1	1	yes	characteristic
22	C₁₉×#431	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#106	—	2	1	no	—
24	C₁₉×#423	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₁₉×#417	—	2	1	no	—
27	C₂×C₁₉×#102	—	2	1	no	—
28	C₁₉×#332	—	2	2	no	—
29	C₁₉×D₄⋊C₈	—	2	2	no	—
30	C₁₉×#323	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	—	2	1	no	—
35	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
36	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
37	C₂×SD₁₆×C₁₉	—	2	2	no	—
38	C₂×SD₁₆×C₁₉	—	2	4	no	—
39	C₂×D₈×C₁₉	—	2	2	no	—
40	C₂×M₁₆×C₁₉	—	2	1	no	—
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₁₉×C₄⋊Q₈	—	2	1	no	—
43	C₁₉×C₄⋊Q₈	—	2	1	no	—
44	C₁₉×C₄⋊Q₈	—	2	1	no	—
45	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
46	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
47	C₁₉×#127	D₄	1	1	yes	characteristic
48	C₁₉×#124	—	2	1	no	—
49	C₁₉×#121	—	2	1	no	—
50	C₁₉×#121	—	2	1	no	—
51	C₄×D₄×C₁₉	—	2	1	no	—
52	C₄×D₄×C₁₉	—	2	1	no	—
53	C₄×D₄×C₁₉	—	2	1	no	—
54	C₄×D₄×C₁₉	—	2	1	no	—
55	C₄×D₄×C₁₉	—	2	1	no	—
56	C₄×D₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
62	C₁₉×#106	—	2	4	no	—
63	C₁₉×C₄⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	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	4	no	—
71	C₁₉×#102	—	2	4	no	—
72	C₁₉×#102	—	2	2	no	—
73	C₁₉×C₂²⋊C₈	—	2	1	no	—
74	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
75	C₄×C₈×C₁₉	—	2	1	no	—
76	C₄×C₈×C₁₉	—	2	1	no	—
77	C₂⁴×C₁₉	—	2	1	no	—
78	#41×C₁₉	—	4	1	no	—
79	#41×C₁₉	—	4	1	no	—
80	#41×C₁₉	—	4	1	no	—
81	#41×C₁₉	—	4	1	no	—
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	—	4	1	no	—
85	C₂×Q₈×C₁₉	—	8	2	no	—
86	C₂×D₄×C₁₉	—	2	1	no	—
87	C₂×D₄×C₁₉	—	2	1	no	—
88	C₂×D₄×C₁₉	—	2	1	no	—
89	C₂×D₄×C₁₉	—	2	1	no	—
90	C₂×D₄×C₁₉	—	2	1	no	—
91	C₂×D₄×C₁₉	—	2	1	no	—
92	C₂×D₄×C₁₉	—	2	1	no	—
93	C₂×D₄×C₁₉	—	2	1	no	—
94	C₂×D₄×C₁₉	—	4	1	no	—
95	C₂×D₄×C₁₉	SD₁₆	1	2	yes	complemented
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	8	2	no	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
105	SD₁₆×C₁₉	—	4	4	no	—
106	SD₁₆×C₁₉	—	8	4	no	—
107	D₈×C₁₉	—	4	4	no	—
108	M₁₆×C₁₉	—	4	1	no	—
109	M₁₆×C₁₉	—	4	1	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₂×C₈×C₁₉	—	4	1	no	—
116	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
122	C₄⋊C₄×C₁₉	—	4	1	no	—
123	C₄⋊C₄×C₁₉	—	4	1	no	—
124	C₂²⋊C₄×C₁₉	—	4	1	no	—
125	C₂²⋊C₄×C₁₉	—	4	1	no	—
126	C₂²⋊C₄×C₁₉	—	4	1	no	—
127	C₂²⋊C₄×C₁₉	—	4	1	no	—
128	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
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	#10180	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	—	8	1	no	—
138	C₂³×C₁₉	—	8	1	no	—
139	C₂³×C₁₉	#121	1	1	yes	characteristic
140	Q₈×C₁₉	—	4	4	no	—
141	Q₈×C₁₉	—	4	1	no	—
142	Q₈×C₁₉	—	4	1	no	—
143	Q₈×C₁₉	—	8	2	no	—
144	D₄×C₁₉	—	2	2	no	—
145	D₄×C₁₉	—	2	2	no	—
146	D₄×C₁₉	—	4	2	no	—
147	D₄×C₁₉	—	4	1	no	—
148	D₄×C₁₉	—	4	1	no	—
149	D₄×C₁₉	—	4	1	no	—
150	D₄×C₁₉	—	4	1	no	—
151	D₄×C₁₉	—	4	2	no	—
152	D₄×C₁₉	—	8	1	no	—
153	D₄×C₁₉	—	8	1	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	8	2	no	—
160	C₂×C₄×C₁₉	—	8	2	no	—
161	C₂×C₄×C₁₉	—	8	1	no	—
162	C₂×C₄×C₁₉	—	8	1	no	—
163	C₂×C₄×C₁₉	—	8	2	no	—
164	C₂×C₄×C₁₉	—	8	1	no	—
165	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
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	#127	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
173	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
175	C₈×C₁₉	—	4	2	no	—
176	C₈×C₁₉	—	4	2	no	—
177	C₈×C₁₉	—	4	2	no	—
178	C₈×C₁₉	—	8	1	no	—
179	#3206	C₂×C₁₉	1	1	yes	characteristic, complemented
180	C₂×#476	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#3036	C₂×C₁₉	1	1	yes	characteristic
182	#1549	C₂×C₁₉	1	1	yes	characteristic, complemented
183	#1480	C₂×C₁₉	1	1	yes	characteristic, complemented
184	#1460	C₂×C₁₉	1	1	yes	characteristic, complemented
185	#1301	C₂×C₁₉	1	1	yes	characteristic, complemented
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	8	2	no	—
190	C₂²×C₁₉	—	8	2	no	—
191	C₂²×C₁₉	—	8	1	no	—
192	C₂²×C₁₉	—	8	1	no	—
193	C₂²×C₁₉	—	8	1	no	—
194	C₂²×C₁₉	—	8	1	no	—
195	C₂²×C₁₉	—	8	1	no	—
196	C₂²×C₁₉	#392	1	1	yes	characteristic
197	C₂²×C₁₉	#465	1	1	yes	characteristic
198	C₂²×C₁₉	#468	1	1	yes	characteristic
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	8	1	no	—
203	C₄×C₁₉	—	8	2	no	—
204	C₄×C₁₉	—	8	1	no	—
205	C₄×C₁₉	#448	1	1	yes	characteristic
206	C₄×C₁₉	#449	1	1	yes	characteristic
207	C₄×C₁₉	#450	1	1	yes	characteristic
208	C₄×C₁₉	#452	1	1	yes	characteristic
209	C₄×C₁₉	#471	1	2	yes	—
210	C₂×AGL(1,ℤ/8)	—	2	1	no	—
211	#532	C₂²×C₁₉	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
213	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
214	#492	—	2	1	no	—
215	#487	—	2	1	no	—
216	#476	—	2	2	no	—
217	#476	—	2	2	no	—
218	#463	—	2	2	no	—
219	#461	—	2	2	no	—
220	#461	—	2	1	no	—
221	#459	—	2	1	no	—
222	#448	—	2	2	no	—
223	#431	C₂²×C₁₉	1	1	yes	characteristic
224	#431	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×#106	—	2	1	no	—
226	#423	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
228	#417	—	2	1	no	—
229	C₂×#102	—	2	1	no	—
230	#332	—	2	2	no	—
231	D₄⋊C₈	—	2	2	no	—
232	#323	—	2	2	no	—
233	C₂×C₁₉	—	2	1	no	—
234	C₂×C₁₉	—	2	1	no	—
235	C₂×C₁₉	—	8	2	no	—
236	C₂×C₁₉	—	16	1	no	—
237	C₂×C₁₉	#2000	1	1	yes	characteristic
238	C₂×C₁₉	#2008	1	1	yes	characteristic
239	C₂×C₁₉	#2019	1	1	yes	characteristic
240	C₂×#41	—	2	1	no	—
241	C₂²×Q₈	—	2	1	no	—
242	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
243	C₂³×C₄	—	2	1	no	—
244	AGL(1,ℤ/8)	—	4	2	no	—
245	AGL(1,ℤ/8)	—	4	2	no	—
246	C₂×SD₁₆	—	2	2	no	—
247	C₂×SD₁₆	—	2	4	no	—
248	C₂×D₈	—	2	2	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
255	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
256	#127	D₄×C₁₉	1	1	yes	characteristic
257	#124	—	2	1	no	—
258	#121	—	2	1	no	—
259	#121	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
271	#106	—	2	4	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
277	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
278	#103	—	2	2	no	—
279	#103	—	2	4	no	—
280	#102	—	2	4	no	—
281	#102	—	2	2	no	—
282	C₂²⋊C₈	—	2	1	no	—
283	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	—	2	1	no	—
286	C₁₉	#10180	1	1	yes	characteristic, direct product factor, Sylow
287	C₂⁴	—	2	1	no	—
288	#41	—	4	1	no	—
289	#41	—	4	1	no	—
290	#41	—	4	1	no	—
291	#41	—	4	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	—	8	2	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	SD₁₆×C₁₉	1	2	yes	complemented
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	8	2	no	—
312	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
314	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
315	SD₁₆	—	4	4	no	—
316	SD₁₆	—	8	4	no	—
317	D₈	—	4	4	no	—
318	M₁₆	—	4	1	no	—
319	M₁₆	—	4	1	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
341	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₂³	—	2	2	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	8	1	no	—
347	C₂³	—	8	1	no	—
348	C₂³	C₁₉×#121	1	1	yes	characteristic
349	Q₈	—	4	4	no	—
350	Q₈	—	4	1	no	—
351	Q₈	—	4	1	no	—
352	Q₈	—	8	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	1	no	—
357	D₄	—	4	1	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	2	no	—
361	D₄	—	8	1	no	—
362	D₄	—	8	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	2	no	—
369	C₂×C₄	—	8	2	no	—
370	C₂×C₄	—	8	1	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	—	8	2	no	—
373	C₂×C₄	—	8	1	no	—
374	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
375	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
376	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
377	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
378	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
379	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
380	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
381	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
382	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
383	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₈	—	8	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	8	1	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	8	1	no	—
397	C₂²	—	8	1	no	—
398	C₂²	C₁₉×#392	1	1	yes	characteristic
399	C₂²	C₁₉×#465	1	1	yes	characteristic
400	C₂²	C₁₉×#468	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	8	1	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	1	no	—
407	C₄	C₁₉×#448	1	1	yes	characteristic
408	C₄	C₁₉×#449	1	1	yes	characteristic
409	C₄	C₁₉×#450	1	1	yes	characteristic
410	C₄	C₁₉×#452	1	1	yes	characteristic
411	C₄	C₁₉×#471	1	2	yes	—
412	C₂	—	2	1	no	—
413	C₂	—	2	1	no	—
414	C₂	—	8	2	no	—
415	C₂	—	16	1	no	—
416	C₂	C₁₉×#2000	1	1	yes	characteristic
417	C₂	C₁₉×#2008	1	1	yes	characteristic
418	C₂	C₁₉×#2019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3036	C₂
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
1. C₁₉×#3206	C₂	semidirect
2. C₂×C₁₉×#476	C₂	semidirect
4. C₁₉×#1549	C₂	semidirect
5. C₁₉×#1480	C₂	semidirect
6. C₁₉×#1460	C₂	semidirect
7. C₁₉×#1301	C₂	semidirect
95. C₂×D₄×C₁₉	SD₁₆	semidirect
132. #10180	C₁₉	direct (N × H)
179. #3206	C₂×C₁₉	semidirect
180. C₂×#476	C₂×C₁₉	semidirect
182. #1549	C₂×C₁₉	semidirect
183. #1480	C₂×C₁₉	semidirect
184. #1460	C₂×C₁₉	semidirect
185. #1301	C₂×C₁₉	semidirect
286. C₁₉	#10180	direct (N × H)
305. C₂×D₄	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×#3206	2
C₂×C₁₉×#476	2
C₁₉×#3036	2
C₁₉×#1549	2
C₁₉×#1480	2
C₁₉×#1460	2
C₁₉×#1301	2
#10180	19

Subgroups — C19×#10180 #18016139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10180 #18016139