Subgroups — C₁₉×#8378 #18014337

Order 4864.

844 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#553	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1824	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1799	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1519	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1459	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#553	—	2	4	no	—
7	C₁₉×#553	—	2	4	no	—
8	C₂×C₁₉×#126	—	2	1	no	—
9	C₂×C₁₉×#125	C₄	1	1	yes	characteristic, complemented
10	C₂×C₁₉×#123	—	2	1	no	—
11	C₂×C₁₉×#121	—	2	1	no	—
12	C₂×C₁₉×#121	C₄	1	1	yes	characteristic, complemented
13	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₉	—	2	1	no	—
15	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic, complemented
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#117	C₄	1	1	yes	characteristic, complemented
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#99	—	2	1	no	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₁₉×#380	C₂²	1	2	yes	—
22	C₁₉×#342	—	2	1	no	—
23	C₁₉×#340	—	2	4	no	—
24	C₁₉×#327	—	2	4	no	—
25	C₁₉×#324	—	2	1	no	—
26	C₁₉×#323	—	2	1	no	—
27	C₂²×D₄×C₁₉	—	2	1	no	—
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂³×C₄×C₁₉	—	2	1	no	—
33	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂²×C₈×C₁₉	—	2	2	no	—
36	C₁₉×#126	—	2	8	no	—
37	C₁₉×#125	—	2	2	no	—
38	C₁₉×#125	—	2	2	no	—
39	C₁₉×#123	—	2	8	no	—
40	C₁₉×#121	—	2	8	no	—
41	C₁₉×#121	—	2	2	no	—
42	C₁₉×#121	—	2	2	no	—
43	C₁₉×#121	—	2	2	no	—
44	C₁₉×#121	D₄	1	4	yes	—
45	C₄×D₄×C₁₉	—	2	8	no	—
46	C₄×D₄×C₁₉	—	2	2	no	—
47	C₄×D₄×C₁₉	—	2	2	no	—
48	C₄×D₄×C₁₉	—	2	2	no	—
49	C₄×D₄×C₁₉	—	2	2	no	—
50	C₁₉×#117	—	2	2	no	—
51	C₁₉×#117	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₉	—	2	1	no	—
70	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
71	C₁₉×#99	—	4	2	no	—
72	C₁₉×C₂²⋊C₈	—	2	2	no	—
73	C₁₉×C₂²⋊C₈	—	2	2	no	—
74	C₁₉×#95	—	2	2	no	—
75	C₂⁴×C₁₉	—	2	1	no	—
76	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂×D₄×C₁₉	—	2	2	no	—
79	C₂×D₄×C₁₉	—	2	4	no	—
80	C₂×D₄×C₁₉	—	2	2	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	—	2	4	no	—
84	C₂×D₄×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	—	4	2	no	—
86	C₂×D₄×C₁₉	—	4	2	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	8	2	no	—
90	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	—	4	2	no	—
100	C₂²×C₄×C₁₉	—	4	2	no	—
101	C₂²×C₄×C₁₉	—	8	2	no	—
102	C₂²×C₄×C₁₉	—	8	2	no	—
103	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₁₉	—	4	4	no	—
111	C₂×C₈×C₁₉	—	4	2	no	—
112	C₄⋊C₄×C₁₉	—	2	4	no	—
113	C₄⋊C₄×C₁₉	—	2	4	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	2	4	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	4	4	no	—
120	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
121	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
122	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
123	C₂²⋊C₄×C₁₉	—	2	4	no	—
124	C₂²⋊C₄×C₁₉	—	2	4	no	—
125	C₂²⋊C₄×C₁₉	—	2	4	no	—
126	C₂²⋊C₄×C₁₉	—	2	2	no	—
127	C₂²⋊C₄×C₁₉	—	2	4	no	—
128	C₂²⋊C₄×C₁₉	—	2	2	no	—
129	C₂²⋊C₄×C₁₉	—	4	2	no	—
130	C₂²⋊C₄×C₁₉	—	4	2	no	—
131	C₄²×C₁₉	—	2	4	no	—
132	C₄²×C₁₉	—	2	1	no	—
133	C₄²×C₁₉	—	2	1	no	—
134	#8378	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	2	1	no	—
139	C₂³×C₁₉	—	4	1	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	4	1	no	—
147	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂³×C₁₉	#120	1	2	yes	—
149	C₂³×C₁₉	#135	1	2	yes	—
150	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂³×C₁₉	#137	1	1	yes	characteristic
152	D₄×C₁₉	—	4	2	no	—
153	D₄×C₁₉	—	4	2	no	—
154	D₄×C₁₉	—	4	4	no	—
155	D₄×C₁₉	—	4	2	no	—
156	D₄×C₁₉	—	4	4	no	—
157	D₄×C₁₉	—	4	2	no	—
158	D₄×C₁₉	—	8	4	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	8	4	no	—
180	C₂×C₄×C₁₉	—	8	4	no	—
181	C₂×C₄×C₁₉	—	8	2	no	—
182	C₂×C₄×C₁₉	—	8	2	no	—
183	C₂×C₄×C₁₉	—	8	2	no	—
184	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#120	1	2	yes	—
187	C₈×C₁₉	—	8	2	no	—
188	C₂×#553	C₂×C₁₉	1	1	yes	characteristic
189	#1824	C₂×C₁₉	1	2	yes	complemented
190	#1799	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#1519	C₂×C₁₉	1	2	yes	complemented
192	#1459	C₂×C₁₉	1	1	yes	characteristic, complemented
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	2	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	4	2	no	—
198	C₂²×C₁₉	—	4	1	no	—
199	C₂²×C₁₉	—	4	1	no	—
200	C₂²×C₁₉	—	4	2	no	—
201	C₂²×C₁₉	—	4	1	no	—
202	C₂²×C₁₉	—	4	1	no	—
203	C₂²×C₁₉	—	4	2	no	—
204	C₂²×C₁₉	—	4	1	no	—
205	C₂²×C₁₉	—	4	2	no	—
206	C₂²×C₁₉	—	8	1	no	—
207	C₂²×C₁₉	—	8	1	no	—
208	C₂²×C₁₉	—	8	2	no	—
209	C₂²×C₁₉	—	8	2	no	—
210	C₂²×C₁₉	#379	1	1	yes	characteristic
211	C₂²×C₁₉	#416	1	1	yes	characteristic
212	C₂²×C₁₉	#417	1	1	yes	characteristic
213	C₂²×C₁₉	#449	1	2	yes	—
214	C₂²×C₁₉	#452	1	2	yes	—
215	C₄×C₁₉	—	2	2	no	—
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	—	4	2	no	—
218	C₄×C₁₉	—	4	2	no	—
219	C₄×C₁₉	—	4	1	no	—
220	C₄×C₁₉	—	4	1	no	—
221	C₄×C₁₉	—	4	1	no	—
222	C₄×C₁₉	—	4	2	no	—
223	C₄×C₁₉	—	16	2	no	—
224	C₄×C₁₉	#410	1	2	yes	—
225	#553	—	2	4	no	—
226	#553	—	2	4	no	—
227	C₂×#126	—	2	1	no	—
228	C₂×#125	C₄×C₁₉	1	1	yes	characteristic, complemented
229	C₂×#123	—	2	1	no	—
230	C₂×#121	—	2	1	no	—
231	C₂×#121	C₄×C₁₉	1	1	yes	characteristic, complemented
232	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×C₄×D₄	—	2	1	no	—
234	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic, complemented
235	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×#117	C₄×C₁₉	1	1	yes	characteristic, complemented
237	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×#99	—	2	1	no	—
239	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
240	#380	C₂²×C₁₉	1	2	yes	—
241	#342	—	2	1	no	—
242	#340	—	2	4	no	—
243	#327	—	2	4	no	—
244	#324	—	2	1	no	—
245	#323	—	2	1	no	—
246	C₂×C₁₉	—	2	2	no	—
247	C₂×C₁₉	—	2	1	no	—
248	C₂×C₁₉	—	2	1	no	—
249	C₂×C₁₉	—	2	2	no	—
250	C₂×C₁₉	—	8	1	no	—
251	C₂×C₁₉	—	8	2	no	—
252	C₂×C₁₉	#1782	1	1	yes	characteristic
253	C₂×C₁₉	#1788	1	1	yes	characteristic
254	C₂×C₁₉	#1795	1	1	yes	characteristic
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
258	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
262	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
263	C₂²×C₈	—	2	2	no	—
264	#126	—	2	8	no	—
265	#125	—	2	2	no	—
266	#125	—	2	2	no	—
267	#123	—	2	8	no	—
268	#121	—	2	8	no	—
269	#121	—	2	2	no	—
270	#121	—	2	2	no	—
271	#121	—	2	2	no	—
272	#121	D₄×C₁₉	1	4	yes	—
273	C₄×D₄	—	2	8	no	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	—	2	2	no	—
277	C₄×D₄	—	2	2	no	—
278	#117	—	2	2	no	—
279	#117	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
288	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
289	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
299	#99	—	4	2	no	—
300	C₂²⋊C₈	—	2	2	no	—
301	C₂²⋊C₈	—	2	2	no	—
302	#95	—	2	2	no	—
303	C₁₉	#8378	1	1	yes	characteristic, direct product factor, Sylow
304	C₂⁴	—	2	1	no	—
305	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
306	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	8	2	no	—
319	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	8	2	no	—
331	C₂²×C₄	—	8	2	no	—
332	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
333	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
334	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
339	C₂×C₈	—	4	4	no	—
340	C₂×C₈	—	4	2	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	4	4	no	—
349	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
350	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
351	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
352	C₂²⋊C₄	—	2	4	no	—
353	C₂²⋊C₄	—	2	4	no	—
354	C₂²⋊C₄	—	2	4	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₄²	—	2	4	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
376	C₂³	C₁₉×#120	1	2	yes	—
377	C₂³	C₁₉×#135	1	2	yes	—
378	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
379	C₂³	C₁₉×#137	1	1	yes	characteristic
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	4	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	2	no	—
386	D₄	—	8	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	8	4	no	—
408	C₂×C₄	—	8	4	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	—	8	2	no	—
411	C₂×C₄	—	8	2	no	—
412	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
413	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
414	C₂×C₄	C₁₉×#120	1	2	yes	—
415	C₈	—	8	2	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	C₁₉×#379	1	1	yes	characteristic
434	C₂²	C₁₉×#416	1	1	yes	characteristic
435	C₂²	C₁₉×#417	1	1	yes	characteristic
436	C₂²	C₁₉×#449	1	2	yes	—
437	C₂²	C₁₉×#452	1	2	yes	—
438	C₄	—	2	2	no	—
439	C₄	—	2	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	1	no	—
446	C₄	—	16	2	no	—
447	C₄	C₁₉×#410	1	2	yes	—
448	C₂	—	2	2	no	—
449	C₂	—	2	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	2	2	no	—
452	C₂	—	8	2	no	—
453	C₂	—	8	1	no	—
454	C₂	C₁₉×#1782	1	1	yes	characteristic
455	C₂	C₁₉×#1788	1	1	yes	characteristic
456	C₂	C₁₉×#1795	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#553	C₂
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×#1824	C₂	semidirect
3. C₁₉×#1799	C₂	semidirect
4. C₁₉×#1519	C₂	semidirect
5. C₁₉×#1459	C₂	semidirect
9. C₂×C₁₉×#125	C₄	semidirect
12. C₂×C₁₉×#121	C₄	semidirect
15. C₂×C₄×D₄×C₁₉	C₄	semidirect
17. C₂×C₁₉×#117	C₄	semidirect
134. #8378	C₁₉	direct (N × H)
189. #1824	C₂×C₁₉	semidirect
190. #1799	C₂×C₁₉	semidirect
191. #1519	C₂×C₁₉	semidirect
192. #1459	C₂×C₁₉	semidirect
228. C₂×#125	C₄×C₁₉	semidirect
231. C₂×#121	C₄×C₁₉	semidirect
234. C₂×C₄×D₄	C₄×C₁₉	semidirect
236. C₂×#117	C₄×C₁₉	semidirect
303. C₁₉	#8378	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×#553	2
C₁₉×#1824	2
C₁₉×#1799	2
C₁₉×#1519	2
C₁₉×#1459	2
#8378	19

Subgroups — C19×#8378 #18014337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8378 #18014337