Subgroups — C₁₉×#9278 #18015237

Order 4864.

564 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3187	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2368	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1964	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1520	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#327	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1294	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1282	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
10	C₁₉×#483	C₄	1	2	yes	complemented
11	C₁₉×#481	—	2	1	no	—
12	C₁₉×#465	—	2	2	no	—
13	C₁₉×#450	C₄	1	2	yes	complemented
14	C₁₉×#448	—	2	1	no	—
15	C₂×C₁₉×#99	—	2	1	no	—
16	C₂×C₁₉×#99	—	2	1	no	—
17	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
19	C₁₉×#391	—	2	1	no	—
20	C₁₉×#387	—	2	1	no	—
21	C₁₉×#387	—	2	1	no	—
22	C₁₉×#385	—	2	1	no	—
23	C₁₉×#380	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
25	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
26	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
28	C₁₉×#328	—	2	2	no	—
29	C₁₉×#327	—	2	1	no	—
30	C₁₉×#327	—	2	1	no	—
31	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	—	2	1	no	—
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×SD₁₆×C₁₉	—	2	2	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₁₉×C₂²⋊Q₈	—	2	1	no	—
40	C₁₉×C₂²⋊Q₈	—	2	1	no	—
41	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
42	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
43	C₁₉×#121	—	2	1	no	—
44	C₁₉×#121	—	2	1	no	—
45	C₁₉×#121	—	2	1	no	—
46	C₁₉×#121	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
53	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₉	—	2	1	no	—
59	C₂×C₄²×C₁₉	—	2	1	no	—
60	C₂×C₄²×C₁₉	—	2	1	no	—
61	C₁₉×#106	—	2	2	no	—
62	C₁₉×#103	—	2	2	no	—
63	C₁₉×#102	—	2	2	no	—
64	C₁₉×#99	—	4	2	no	—
65	C₁₉×#99	—	4	2	no	—
66	C₁₉×C₂²⋊C₈	—	2	1	no	—
67	C₁₉×C₂²⋊C₈	—	2	1	no	—
68	C₁₉×C₂²⋊C₈	—	2	1	no	—
69	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
70	C₁₉×#95	—	2	1	no	—
71	C₁₉×#95	—	2	1	no	—
72	C₁₉×#95	—	2	1	no	—
73	C₁₉×#95	—	2	1	no	—
74	C₁₉×#95	—	2	1	no	—
75	C₁₉×#95	—	2	1	no	—
76	C₁₉×#95	—	2	1	no	—
77	C₁₉×#95	D₄	1	1	yes	characteristic
78	C₁₉×#95	D₄	1	1	yes	characteristic
79	C₂⁴×C₁₉	—	2	1	no	—
80	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	8	1	no	—
83	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
84	C₂×D₄×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	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	—	8	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	4	2	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	8	1	no	—
105	C₂²×C₄×C₁₉	—	8	1	no	—
106	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
112	SD₁₆×C₁₉	—	8	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₂×C₈×C₁₉	—	8	1	no	—
116	C₂×C₈×C₁₉	—	8	1	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₄⋊C₄×C₁₉	—	4	2	no	—
123	C₄⋊C₄×C₁₉	—	8	1	no	—
124	C₄⋊C₄×C₁₉	—	8	1	no	—
125	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
126	C₂²⋊C₄×C₁₉	—	2	2	no	—
127	C₂²⋊C₄×C₁₉	—	2	2	no	—
128	C₂²⋊C₄×C₁₉	—	2	1	no	—
129	C₂²⋊C₄×C₁₉	—	2	1	no	—
130	C₂²⋊C₄×C₁₉	—	2	1	no	—
131	C₂²⋊C₄×C₁₉	—	4	1	no	—
132	C₂²⋊C₄×C₁₉	—	4	1	no	—
133	C₂²⋊C₄×C₁₉	—	4	1	no	—
134	C₂²⋊C₄×C₁₉	—	4	1	no	—
135	C₂²⋊C₄×C₁₉	SD₁₆	1	2	yes	complemented
136	C₄²×C₁₉	—	4	2	no	—
137	C₄²×C₁₉	—	8	1	no	—
138	C₄²×C₁₉	—	8	1	no	—
139	#9278	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	8	1	no	—
146	C₂³×C₁₉	—	8	1	no	—
147	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
148	C₂³×C₁₉	#120	1	1	yes	characteristic
149	C₂³×C₁₉	#121	1	1	yes	characteristic
150	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
151	C₂³×C₁₉	#135	1	1	yes	characteristic
152	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂³×C₁₉	#137	1	1	yes	characteristic
154	Q₈×C₁₉	—	4	2	no	—
155	Q₈×C₁₉	—	8	1	no	—
156	D₄×C₁₉	—	4	2	no	—
157	D₄×C₁₉	—	8	1	no	—
158	D₄×C₁₉	—	8	1	no	—
159	D₄×C₁₉	—	8	1	no	—
160	D₄×C₁₉	—	8	1	no	—
161	D₄×C₁₉	—	8	1	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	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	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	8	2	no	—
190	C₂×C₄×C₁₉	—	8	2	no	—
191	C₂×C₄×C₁₉	—	8	1	no	—
192	C₂×C₄×C₁₉	—	8	1	no	—
193	C₂×C₄×C₁₉	—	8	1	no	—
194	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
198	C₈×C₁₉	—	4	2	no	—
199	C₈×C₁₉	—	8	1	no	—
200	#3187	C₂×C₁₉	1	1	yes	characteristic
201	#2368	C₂×C₁₉	1	1	yes	characteristic, complemented
202	#1964	C₂×C₁₉	1	1	yes	characteristic
203	#1520	C₂×C₁₉	1	1	yes	characteristic, complemented
204	C₂×#327	C₂×C₁₉	1	1	yes	characteristic
205	#1294	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#1282	C₂×C₁₉	1	1	yes	characteristic, complemented
207	C₂²×C₁₉	—	2	1	no	—
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	2	1	no	—
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	—	2	1	no	—
213	C₂²×C₁₉	—	4	1	no	—
214	C₂²×C₁₉	—	4	1	no	—
215	C₂²×C₁₉	—	4	1	no	—
216	C₂²×C₁₉	—	4	1	no	—
217	C₂²×C₁₉	—	8	1	no	—
218	C₂²×C₁₉	—	8	1	no	—
219	C₂²×C₁₉	—	8	1	no	—
220	C₂²×C₁₉	—	16	1	no	—
221	C₂²×C₁₉	—	16	1	no	—
222	C₂²×C₁₉	#386	1	1	yes	characteristic
223	C₂²×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
224	C₂²×C₁₉	#440	1	1	yes	characteristic
225	C₂²×C₁₉	#448	1	1	yes	characteristic
226	C₂²×C₁₉	#449	1	1	yes	characteristic
227	C₂²×C₁₉	#460	1	1	yes	characteristic
228	C₂²×C₁₉	#464	1	1	yes	characteristic
229	C₄×C₁₉	—	2	1	no	—
230	C₄×C₁₉	—	2	1	no	—
231	C₄×C₁₉	—	2	1	no	—
232	C₄×C₁₉	—	2	1	no	—
233	C₄×C₁₉	—	4	2	no	—
234	C₄×C₁₉	—	4	2	no	—
235	C₄×C₁₉	—	4	2	no	—
236	C₄×C₁₉	—	4	2	no	—
237	C₄×C₁₉	—	8	1	no	—
238	C₄×C₁₉	—	8	1	no	—
239	C₄×C₁₉	—	8	1	no	—
240	C₄×C₁₉	—	16	1	no	—
241	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
242	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
243	#483	C₄×C₁₉	1	2	yes	complemented
244	#481	—	2	1	no	—
245	#465	—	2	2	no	—
246	#450	C₄×C₁₉	1	2	yes	complemented
247	#448	—	2	1	no	—
248	C₂×#99	—	2	1	no	—
249	C₂×#99	—	2	1	no	—
250	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
252	#391	—	2	1	no	—
253	#387	—	2	1	no	—
254	#387	—	2	1	no	—
255	#385	—	2	1	no	—
256	#380	C₂²×C₁₉	1	1	yes	characteristic
257	C₄×C₄⋊C₄	—	2	1	no	—
258	C₄×C₂²⋊C₄	—	2	1	no	—
259	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
260	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
261	#328	—	2	2	no	—
262	#327	—	2	1	no	—
263	#327	—	2	1	no	—
264	C₂×C₁₉	—	2	1	no	—
265	C₂×C₁₉	—	2	1	no	—
266	C₂×C₁₉	—	2	1	no	—
267	C₂×C₁₉	—	2	1	no	—
268	C₂×C₁₉	—	2	1	no	—
269	C₂×C₁₉	—	2	1	no	—
270	C₂×C₁₉	—	16	1	no	—
271	C₂×C₁₉	#1880	1	1	yes	characteristic
272	C₂×C₁₉	#1906	1	1	yes	characteristic
273	C₂×C₁₉	#1913	1	1	yes	characteristic
274	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
277	C₂³×C₄	—	2	1	no	—
278	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
279	C₂×SD₁₆	—	2	2	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²⋊Q₈	—	2	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
285	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
286	#121	—	2	1	no	—
287	#121	—	2	1	no	—
288	#121	—	2	1	no	—
289	#121	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
295	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	2	1	no	—
304	#106	—	2	2	no	—
305	#103	—	2	2	no	—
306	#102	—	2	2	no	—
307	#99	—	4	2	no	—
308	#99	—	4	2	no	—
309	C₂²⋊C₈	—	2	1	no	—
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	C₂×C₄×C₁₉	1	2	yes	—
313	#95	—	2	1	no	—
314	#95	—	2	1	no	—
315	#95	—	2	1	no	—
316	#95	—	2	1	no	—
317	#95	—	2	1	no	—
318	#95	—	2	1	no	—
319	#95	—	2	1	no	—
320	#95	D₄×C₁₉	1	1	yes	characteristic
321	#95	D₄×C₁₉	1	1	yes	characteristic
322	C₁₉	#9278	1	1	yes	characteristic, direct product factor, Sylow
323	C₂⁴	—	2	1	no	—
324	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	8	1	no	—
327	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	4	1	no	—
336	C₂×D₄	—	8	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
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	—	4	2	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	—	8	1	no	—
349	C₂²×C₄	—	8	1	no	—
350	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
355	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
356	SD₁₆	—	8	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	4	1	no	—
359	C₂×C₈	—	8	1	no	—
360	C₂×C₈	—	8	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	8	1	no	—
368	C₄⋊C₄	—	8	1	no	—
369	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	2	1	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	4	1	no	—
378	C₂²⋊C₄	—	4	1	no	—
379	C₂²⋊C₄	SD₁₆×C₁₉	1	2	yes	complemented
380	C₄²	—	4	2	no	—
381	C₄²	—	8	1	no	—
382	C₄²	—	8	1	no	—
383	C₂³	—	4	1	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	8	1	no	—
389	C₂³	—	8	1	no	—
390	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
391	C₂³	C₁₉×#120	1	1	yes	characteristic
392	C₂³	C₁₉×#121	1	1	yes	characteristic
393	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
394	C₂³	C₁₉×#135	1	1	yes	characteristic
395	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
396	C₂³	C₁₉×#137	1	1	yes	characteristic
397	Q₈	—	4	2	no	—
398	Q₈	—	8	1	no	—
399	D₄	—	4	2	no	—
400	D₄	—	8	1	no	—
401	D₄	—	8	1	no	—
402	D₄	—	8	1	no	—
403	D₄	—	8	1	no	—
404	D₄	—	8	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	8	2	no	—
433	C₂×C₄	—	8	2	no	—
434	C₂×C₄	—	8	1	no	—
435	C₂×C₄	—	8	1	no	—
436	C₂×C₄	—	8	1	no	—
437	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
438	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
439	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
440	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
441	C₈	—	4	2	no	—
442	C₈	—	8	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	16	1	no	—
457	C₂²	—	16	1	no	—
458	C₂²	C₁₉×#386	1	1	yes	characteristic
459	C₂²	C₄×SD₁₆×C₁₉	1	1	yes	characteristic
460	C₂²	C₁₉×#440	1	1	yes	characteristic
461	C₂²	C₁₉×#448	1	1	yes	characteristic
462	C₂²	C₁₉×#449	1	1	yes	characteristic
463	C₂²	C₁₉×#460	1	1	yes	characteristic
464	C₂²	C₁₉×#464	1	1	yes	characteristic
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	8	1	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	1	no	—
476	C₄	—	16	1	no	—
477	C₂	—	2	1	no	—
478	C₂	—	2	1	no	—
479	C₂	—	2	1	no	—
480	C₂	—	2	1	no	—
481	C₂	—	2	1	no	—
482	C₂	—	2	1	no	—
483	C₂	—	16	1	no	—
484	C₂	C₁₉×#1880	1	1	yes	characteristic
485	C₂	C₁₉×#1906	1	1	yes	characteristic
486	C₂	C₁₉×#1913	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2368	C₂	semidirect
4. C₁₉×#1520	C₂	semidirect
6. C₁₉×#1294	C₂	semidirect
7. C₁₉×#1282	C₂	semidirect
10. C₁₉×#483	C₄	semidirect
13. C₁₉×#450	C₄	semidirect
135. C₂²⋊C₄×C₁₉	SD₁₆	semidirect
139. #9278	C₁₉	direct (N × H)
201. #2368	C₂×C₁₉	semidirect
203. #1520	C₂×C₁₉	semidirect
205. #1294	C₂×C₁₉	semidirect
206. #1282	C₂×C₁₉	semidirect
243. #483	C₄×C₁₉	semidirect
246. #450	C₄×C₁₉	semidirect
322. C₁₉	#9278	direct (N × H)
379. C₂²⋊C₄	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×#3187	2
C₁₉×#2368	2
C₁₉×#1964	2
C₁₉×#1520	2
C₂×C₁₉×#327	2
C₁₉×#1294	2
C₁₉×#1282	2
#9278	19

Subgroups — C19×#9278 #18015237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9278 #18015237