Subgroups — C₁₉×#33944 #18039903

Order 4864.

468 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3393	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3383	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2245	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2243	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2242	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2229	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2228	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#2227	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2211	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2211	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#2209	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2183	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2176	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2175	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₉×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#557	—	2	1	no	—
17	C₁₉×#556	—	2	1	no	—
18	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
21	C₁₉×#500	C₂²	1	1	yes	characteristic
22	C₁₉×#499	C₂²	1	1	yes	characteristic
23	C₁₉×#499	C₂²	1	1	yes	characteristic
24	C₁₉×#495	C₂²	1	1	yes	characteristic
25	C₁₉×#495	C₂²	1	1	yes	characteristic
26	C₁₉×#494	C₂²	1	1	yes	characteristic
27	C₁₉×#479	—	2	1	no	—
28	C₁₉×#479	—	2	1	no	—
29	C₁₉×#475	—	2	1	no	—
30	C₁₉×#464	—	2	1	no	—
31	C₁₉×#464	—	2	1	no	—
32	C₁₉×#461	—	2	1	no	—
33	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
34	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
35	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
36	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
37	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
38	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
39	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
40	C₁₉×#367	C₂²	1	1	yes	characteristic
41	C₁₉×#366	C₂²	1	1	yes	characteristic
42	C₁₉×#366	C₂²	1	1	yes	characteristic
43	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
44	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
45	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
46	C₁₉×#358	C₂²	1	1	yes	characteristic
47	C₁₉×#358	C₂²	1	1	yes	characteristic
48	C₁₉×#358	C₂²	1	1	yes	characteristic
49	C₁₉×#358	C₂²	1	1	yes	characteristic
50	C₁₉×#358	C₂²	1	1	yes	characteristic
51	C₁₉×#358	C₂²	1	1	yes	characteristic
52	C₁₉×#358	C₂²	1	1	yes	characteristic
53	C₁₉×#357	C₂²	1	1	yes	characteristic
54	C₁₉×#357	C₂²	1	1	yes	characteristic
55	C₁₉×#357	C₂²	1	1	yes	characteristic
56	C₁₉×#346	C₂²	1	1	yes	characteristic
57	C₁₉×#346	C₂²	1	1	yes	characteristic
58	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
59	C₂×Q₁₆×C₁₉	—	2	1	no	—
60	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×SD₁₆×C₁₉	—	2	1	no	—
64	C₂×SD₁₆×C₁₉	—	2	1	no	—
65	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₁₉×C₄⋊Q₈	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	—	4	1	no	—
69	C₁₉×#126	—	4	1	no	—
70	C₁₉×#126	—	4	1	no	—
71	C₁₉×#125	—	2	1	no	—
72	C₁₉×#125	—	2	1	no	—
73	C₁₉×#125	—	4	1	no	—
74	C₁₉×#125	—	4	1	no	—
75	C₁₉×#124	—	2	1	no	—
76	C₁₉×#124	—	2	1	no	—
77	C₁₉×C₂²⋊Q₈	—	4	1	no	—
78	C₄×Q₈×C₁₉	—	2	1	no	—
79	C₄×Q₈×C₁₉	—	2	1	no	—
80	C₄×Q₈×C₁₉	—	2	1	no	—
81	C₄×Q₈×C₁₉	—	2	1	no	—
82	C₄×Q₈×C₁₉	—	2	1	no	—
83	C₄×Q₈×C₁₉	—	4	1	no	—
84	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
85	C₄×D₄×C₁₉	—	2	1	no	—
86	C₁₉×#117	—	4	1	no	—
87	C₁₉×Q₃₂	—	2	2	no	—
88	C₁₉×Q₃₂	—	2	2	no	—
89	C₁₉×SD₃₂	—	2	2	no	—
90	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
94	C₁₉×#107	—	2	1	no	—
95	C₁₉×#107	C₂³	1	1	yes	characteristic
96	C₁₉×#107	C₂³	1	1	yes	characteristic
97	C₁₉×#107	C₂³	1	1	yes	characteristic
98	C₁₉×#107	C₂³	1	1	yes	characteristic
99	C₁₉×#106	—	2	1	no	—
100	C₁₉×#106	—	2	1	no	—
101	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
102	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
103	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
104	C₁₉×#103	—	2	1	no	—
105	C₁₉×#103	—	2	1	no	—
106	C₁₉×#103	—	2	1	no	—
107	C₁₉×#103	—	2	1	no	—
108	C₁₉×#103	—	2	1	no	—
109	C₁₉×#102	—	2	1	no	—
110	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
112	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	4	1	no	—
117	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
118	C₂×D₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	4	1	no	—
120	Q₁₆×C₁₉	—	2	1	no	—
121	Q₁₆×C₁₉	—	2	1	no	—
122	Q₁₆×C₁₉	—	2	1	no	—
123	Q₁₆×C₁₉	—	2	1	no	—
124	Q₁₆×C₁₉	—	2	1	no	—
125	Q₁₆×C₁₉	—	8	1	no	—
126	Q₁₆×C₁₉	#41	1	2	yes	—
127	SD₁₆×C₁₉	—	8	1	no	—
128	SD₁₆×C₁₉	—	8	1	no	—
129	D₈×C₁₉	—	2	1	no	—
130	D₈×C₁₉	—	2	1	no	—
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	C₂⁴	1	1	yes	characteristic
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	4	1	no	—
140	C₄⋊C₄×C₁₉	—	4	1	no	—
141	C₄⋊C₄×C₁₉	—	4	1	no	—
142	C₄⋊C₄×C₁₉	—	4	1	no	—
143	C₄⋊C₄×C₁₉	—	4	1	no	—
144	C₄⋊C₄×C₁₉	—	4	1	no	—
145	C₄⋊C₄×C₁₉	—	4	1	no	—
146	C₄⋊C₄×C₁₉	—	4	1	no	—
147	C₄⋊C₄×C₁₉	—	4	1	no	—
148	C₄⋊C₄×C₁₉	—	4	1	no	—
149	C₄⋊C₄×C₁₉	—	4	1	no	—
150	C₄⋊C₄×C₁₉	—	4	1	no	—
151	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
152	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
153	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
154	C₂²⋊C₄×C₁₉	—	4	1	no	—
155	C₂²⋊C₄×C₁₉	—	4	1	no	—
156	C₂²⋊C₄×C₁₉	—	4	1	no	—
157	C₂²⋊C₄×C₁₉	—	4	1	no	—
158	C₂²⋊C₄×C₁₉	—	4	1	no	—
159	C₄²×C₁₉	—	4	1	no	—
160	C₄²×C₁₉	—	4	1	no	—
161	C₄²×C₁₉	—	4	1	no	—
162	C₄²×C₁₉	—	4	1	no	—
163	C₄²×C₁₉	—	4	1	no	—
164	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₁₆×C₁₉	—	2	1	no	—
168	C₁₆×C₁₉	—	2	1	no	—
169	C₁₆×C₁₉	—	2	1	no	—
170	C₁₆×C₁₉	—	2	1	no	—
171	#33944	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂³×C₁₉	—	4	1	no	—
173	Q₈×C₁₉	—	2	2	no	—
174	Q₈×C₁₉	—	4	1	no	—
175	Q₈×C₁₉	—	4	1	no	—
176	Q₈×C₁₉	—	4	1	no	—
177	Q₈×C₁₉	—	4	1	no	—
178	Q₈×C₁₉	—	4	1	no	—
179	Q₈×C₁₉	—	4	1	no	—
180	Q₈×C₁₉	—	8	2	no	—
181	D₄×C₁₉	—	4	1	no	—
182	D₄×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	—	4	1	no	—
190	C₂×C₄×C₁₉	—	8	2	no	—
191	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
198	C₈×C₁₉	—	2	1	no	—
199	C₈×C₁₉	—	2	1	no	—
200	C₈×C₁₉	—	2	1	no	—
201	C₈×C₁₉	C₂×#41	1	1	yes	characteristic
202	C₈×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
203	#3393	C₂×C₁₉	1	1	yes	characteristic
204	#3383	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#2245	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#2243	C₂×C₁₉	1	1	yes	characteristic
207	#2242	C₂×C₁₉	1	1	yes	characteristic
208	#2229	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#2228	C₂×C₁₉	1	1	yes	characteristic
210	#2227	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#2211	C₂×C₁₉	1	1	yes	characteristic
212	#2211	C₂×C₁₉	1	1	yes	characteristic
213	#2209	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#2183	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#2176	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#2175	C₂×C₁₉	1	1	yes	characteristic
217	C₄×Q₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
218	C₂²×C₁₉	—	8	1	no	—
219	C₂²×C₁₉	—	8	1	no	—
220	C₂²×C₁₉	—	8	1	no	—
221	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	1	no	—
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	2	1	no	—
228	C₄×C₁₉	—	4	2	no	—
229	C₄×C₁₉	—	8	1	no	—
230	C₄×C₁₉	—	8	1	no	—
231	C₄×C₁₉	—	8	1	no	—
232	C₄×C₁₉	—	8	1	no	—
233	C₄×C₁₉	—	8	1	no	—
234	C₄×C₁₉	—	8	1	no	—
235	C₄×C₁₉	#548	1	1	yes	characteristic
236	C₄×C₁₉	#577	1	1	yes	characteristic
237	#557	—	2	1	no	—
238	#556	—	2	1	no	—
239	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic
240	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic
241	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
242	#500	C₂²×C₁₉	1	1	yes	characteristic
243	#499	C₂²×C₁₉	1	1	yes	characteristic
244	#499	C₂²×C₁₉	1	1	yes	characteristic
245	#495	C₂²×C₁₉	1	1	yes	characteristic
246	#495	C₂²×C₁₉	1	1	yes	characteristic
247	#494	C₂²×C₁₉	1	1	yes	characteristic
248	#479	—	2	1	no	—
249	#479	—	2	1	no	—
250	#475	—	2	1	no	—
251	#464	—	2	1	no	—
252	#464	—	2	1	no	—
253	#461	—	2	1	no	—
254	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
255	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
256	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
257	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
258	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
259	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
260	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
261	#367	C₂²×C₁₉	1	1	yes	characteristic
262	#366	C₂²×C₁₉	1	1	yes	characteristic
263	#366	C₂²×C₁₉	1	1	yes	characteristic
264	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
265	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
266	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
267	#358	C₂²×C₁₉	1	1	yes	characteristic
268	#358	C₂²×C₁₉	1	1	yes	characteristic
269	#358	C₂²×C₁₉	1	1	yes	characteristic
270	#358	C₂²×C₁₉	1	1	yes	characteristic
271	#358	C₂²×C₁₉	1	1	yes	characteristic
272	#358	C₂²×C₁₉	1	1	yes	characteristic
273	#358	C₂²×C₁₉	1	1	yes	characteristic
274	#357	C₂²×C₁₉	1	1	yes	characteristic
275	#357	C₂²×C₁₉	1	1	yes	characteristic
276	#357	C₂²×C₁₉	1	1	yes	characteristic
277	#346	C₂²×C₁₉	1	1	yes	characteristic
278	#346	C₂²×C₁₉	1	1	yes	characteristic
279	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
280	C₂×C₁₉	—	16	1	no	—
281	C₂×C₁₉	#3358	1	1	yes	characteristic
282	C₂×C₁₉	#3414	1	1	yes	characteristic
283	C₂×C₁₉	#3417	1	1	yes	characteristic
284	C₂×Q₁₆	—	2	1	no	—
285	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
286	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
287	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
288	C₂×SD₁₆	—	2	1	no	—
289	C₂×SD₁₆	—	2	1	no	—
290	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
291	C₄⋊Q₈	—	2	1	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	—	4	1	no	—
294	#126	—	4	1	no	—
295	#126	—	4	1	no	—
296	#125	—	2	1	no	—
297	#125	—	2	1	no	—
298	#125	—	4	1	no	—
299	#125	—	4	1	no	—
300	#124	—	2	1	no	—
301	#124	—	2	1	no	—
302	C₂²⋊Q₈	—	4	1	no	—
303	C₄×Q₈	—	2	1	no	—
304	C₄×Q₈	—	2	1	no	—
305	C₄×Q₈	—	2	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	4	1	no	—
309	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
310	C₄×D₄	—	2	1	no	—
311	#117	—	4	1	no	—
312	Q₃₂	—	2	2	no	—
313	Q₃₂	—	2	2	no	—
314	SD₃₂	—	2	2	no	—
315	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
316	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
317	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
318	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
319	#107	—	2	1	no	—
320	#107	C₂³×C₁₉	1	1	yes	characteristic
321	#107	C₂³×C₁₉	1	1	yes	characteristic
322	#107	C₂³×C₁₉	1	1	yes	characteristic
323	#107	C₂³×C₁₉	1	1	yes	characteristic
324	#106	—	2	1	no	—
325	#106	—	2	1	no	—
326	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
327	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
328	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
329	#103	—	2	1	no	—
330	#103	—	2	1	no	—
331	#103	—	2	1	no	—
332	#103	—	2	1	no	—
333	#103	—	2	1	no	—
334	#102	—	2	1	no	—
335	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
336	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
337	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
338	C₁₉	#33944	1	1	yes	characteristic, direct product factor, Sylow
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	4	1	no	—
343	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
344	C₂×D₄	—	2	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	Q₁₆	—	2	1	no	—
347	Q₁₆	—	2	1	no	—
348	Q₁₆	—	2	1	no	—
349	Q₁₆	—	2	1	no	—
350	Q₁₆	—	2	1	no	—
351	Q₁₆	—	8	1	no	—
352	Q₁₆	#41×C₁₉	1	2	yes	—
353	SD₁₆	—	8	1	no	—
354	SD₁₆	—	8	1	no	—
355	D₈	—	2	1	no	—
356	D₈	—	2	1	no	—
357	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
360	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	—	4	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
378	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
379	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
380	C₂²⋊C₄	—	4	1	no	—
381	C₂²⋊C₄	—	4	1	no	—
382	C₂²⋊C₄	—	4	1	no	—
383	C₂²⋊C₄	—	4	1	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₄²	—	4	1	no	—
386	C₄²	—	4	1	no	—
387	C₄²	—	4	1	no	—
388	C₄²	—	4	1	no	—
389	C₄²	—	4	1	no	—
390	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
392	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₁₆	—	2	1	no	—
394	C₁₆	—	2	1	no	—
395	C₁₆	—	2	1	no	—
396	C₁₆	—	2	1	no	—
397	C₂³	—	4	1	no	—
398	Q₈	—	2	2	no	—
399	Q₈	—	4	1	no	—
400	Q₈	—	4	1	no	—
401	Q₈	—	4	1	no	—
402	Q₈	—	4	1	no	—
403	Q₈	—	4	1	no	—
404	Q₈	—	4	1	no	—
405	Q₈	—	8	2	no	—
406	D₄	—	4	1	no	—
407	D₄	—	4	1	no	—
408	C₂×C₄	—	4	1	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	—	8	2	no	—
416	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
418	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
419	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
420	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
421	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
422	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
423	C₈	—	2	1	no	—
424	C₈	—	2	1	no	—
425	C₈	—	2	1	no	—
426	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
427	C₈	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	8	1	no	—
440	C₄	—	8	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	1	no	—
444	C₄	—	8	1	no	—
445	C₄	C₁₉×#548	1	1	yes	characteristic
446	C₄	C₁₉×#577	1	1	yes	characteristic
447	C₂	—	16	1	no	—
448	C₂	C₁₉×#3358	1	1	yes	characteristic
449	C₂	C₁₉×#3414	1	1	yes	characteristic
450	C₂	C₁₉×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₂×D₈×C₁₉	C₂³
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×Q₈×C₁₉ ◁ C₈×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3383	C₂	semidirect
3. C₁₉×#2245	C₂	semidirect
6. C₁₉×#2229	C₂	semidirect
8. C₁₉×#2227	C₂	semidirect
11. C₁₉×#2209	C₂	semidirect
12. C₁₉×#2183	C₂	semidirect
13. C₁₉×#2176	C₂	semidirect
15. C₄×C₁₉×Q₃₂	C₂	semidirect
171. #33944	C₁₉	direct (N × H)
204. #3383	C₂×C₁₉	semidirect
205. #2245	C₂×C₁₉	semidirect
208. #2229	C₂×C₁₉	semidirect
210. #2227	C₂×C₁₉	semidirect
213. #2209	C₂×C₁₉	semidirect
214. #2183	C₂×C₁₉	semidirect
215. #2176	C₂×C₁₉	semidirect
217. C₄×Q₃₂	C₂×C₁₉	semidirect
338. C₁₉	#33944	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3393	2
C₁₉×#3383	2
C₁₉×#2245	2
C₁₉×#2243	2
C₁₉×#2242	2
C₁₉×#2229	2
C₁₉×#2228	2
C₁₉×#2227	2
C₁₉×#2211	2
C₁₉×#2209	2
C₁₉×#2183	2
C₁₉×#2176	2
C₁₉×#2175	2
C₄×C₁₉×Q₃₂	2
#33944	19

Subgroups — C19×#33944 #18039903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33944 #18039903