Subgroups — C₁₉×#24496 #18030455

Order 4864.

924 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#485	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2434	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2347	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2066	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2043	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1981	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1928	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1894	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1851	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1787	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₁₉×#485	—	2	4	no	—
18	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
21	C₁₉×#419	—	2	4	no	—
22	C₂×C₁₉×#103	C₂²	1	2	yes	—
23	C₂×C₁₉×#103	C₂²	1	2	yes	—
24	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	2	yes	—
27	C₂×C₁₉×#103	C₂²	1	2	yes	—
28	C₂×C₁₉×#103	C₂²	1	2	yes	—
29	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₉×#395	—	2	1	no	—
31	C₁₉×#395	—	2	1	no	—
32	C₁₉×#391	C₂²	1	2	yes	—
33	C₁₉×#389	C₂²	1	2	yes	—
34	C₁₉×#388	—	2	2	no	—
35	C₁₉×#385	—	2	2	no	—
36	C₁₉×#383	—	2	1	no	—
37	C₁₉×#380	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
40	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	—	2	4	no	—
45	C₂²×Q₈×C₁₉	—	2	2	no	—
46	C₂²×Q₈×C₁₉	—	2	2	no	—
47	C₂²×Q₈×C₁₉	—	4	2	no	—
48	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₉	—	2	1	no	—
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₁₉	—	2	2	no	—
53	C₂×M₁₆×C₁₉	—	4	2	no	—
54	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	—	2	4	no	—
58	C₁₉×C₄⋊Q₈	—	4	2	no	—
59	C₁₉×C₂²⋊Q₈	—	2	2	no	—
60	C₁₉×C₂²⋊Q₈	—	2	2	no	—
61	C₁₉×#117	—	2	2	no	—
62	C₁₉×#117	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
75	C₂×C₄²×C₁₉	—	2	1	no	—
76	C₂×C₄²×C₁₉	—	2	2	no	—
77	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
78	C₁₉×#107	—	2	2	no	—
79	C₁₉×#106	—	2	2	no	—
80	C₁₉×C₄⋊C₈	—	4	2	no	—
81	C₁₉×#103	—	2	4	no	—
82	C₁₉×#103	—	2	4	no	—
83	C₁₉×#103	—	2	4	no	—
84	C₁₉×#103	—	2	2	no	—
85	C₁₉×#103	—	2	2	no	—
86	C₁₉×#103	—	4	2	no	—
87	C₁₉×#103	—	4	2	no	—
88	C₁₉×C₂²⋊C₈	—	2	2	no	—
89	C₁₉×#95	—	2	1	no	—
90	C₁₉×#95	—	2	2	no	—
91	C₁₉×#95	—	2	2	no	—
92	C₁₉×#95	—	2	2	no	—
93	C₁₉×#95	—	2	2	no	—
94	C₁₉×#95	D₄	1	1	yes	characteristic
95	C₁₉×#95	D₄	1	1	yes	characteristic
96	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	8	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	1	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	4	4	no	—
108	C₂×Q₈×C₁₉	—	4	8	no	—
109	C₂×Q₈×C₁₉	—	4	4	no	—
110	C₂×Q₈×C₁₉	—	4	2	no	—
111	C₂×Q₈×C₁₉	#41	1	4	yes	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	4	4	no	—
121	C₂²×C₄×C₁₉	—	4	2	no	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	#41	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
128	M₁₆×C₁₉	—	4	4	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	1	no	—
131	C₂×C₈×C₁₉	—	2	1	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	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	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	4	4	no	—
143	C₄⋊C₄×C₁₉	—	4	4	no	—
144	C₄⋊C₄×C₁₉	—	4	2	no	—
145	C₄⋊C₄×C₁₉	—	4	4	no	—
146	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₂²⋊C₄×C₁₉	—	2	4	no	—
149	C₂²⋊C₄×C₁₉	—	2	4	no	—
150	C₂²⋊C₄×C₁₉	—	4	2	no	—
151	C₂²⋊C₄×C₁₉	—	8	1	no	—
152	C₄²×C₁₉	—	2	4	no	—
153	C₄²×C₁₉	—	2	2	no	—
154	C₄²×C₁₉	—	2	2	no	—
155	C₄²×C₁₉	—	8	2	no	—
156	#24496	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	2	1	no	—
160	C₂³×C₁₉	—	2	1	no	—
161	C₂³×C₁₉	#121	1	2	yes	—
162	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₁₉	—	2	4	no	—
164	Q₈×C₁₉	—	2	4	no	—
165	Q₈×C₁₉	—	4	8	no	—
166	Q₈×C₁₉	—	4	2	no	—
167	Q₈×C₁₉	—	4	2	no	—
168	Q₈×C₁₉	—	4	1	no	—
169	Q₈×C₁₉	—	4	1	no	—
170	Q₈×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	4	8	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	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	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	#121	1	2	yes	—
198	C₂×C₄×C₁₉	#137	1	4	yes	—
199	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
201	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
203	C₈×C₁₉	—	4	1	no	—
204	C₈×C₁₉	—	4	1	no	—
205	C₈×C₁₉	—	4	2	no	—
206	C₂×#485	C₂×C₁₉	1	1	yes	characteristic
207	C₂×#419	C₂×C₁₉	1	1	yes	characteristic
208	#2434	C₂×C₁₉	1	1	yes	characteristic
209	#2347	C₂×C₁₉	1	1	yes	characteristic
210	#2066	C₂×C₁₉	1	2	yes	complemented
211	#2043	C₂×C₁₉	1	2	yes	complemented
212	#1981	C₂×C₁₉	1	2	yes	complemented
213	#1928	C₂×C₁₉	1	2	yes	complemented
214	#1894	C₂×C₁₉	1	1	yes	characteristic
215	#1851	C₂×C₁₉	1	1	yes	characteristic
216	#1787	C₂×C₁₉	1	1	yes	characteristic
217	C₂²×C₁₉	—	2	2	no	—
218	C₂²×C₁₉	—	2	2	no	—
219	C₂²×C₁₉	—	2	2	no	—
220	C₂²×C₁₉	—	4	2	no	—
221	C₂²×C₁₉	—	4	2	no	—
222	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
223	C₂²×C₁₉	#546	1	2	yes	—
224	C₂²×C₁₉	C₂×#137	1	2	yes	—
225	C₂²×C₁₉	#577	1	1	yes	characteristic
226	C₂²×C₁₉	#578	1	1	yes	characteristic
227	C₄×C₁₉	—	2	2	no	—
228	C₄×C₁₉	—	2	4	no	—
229	C₄×C₁₉	—	4	2	no	—
230	C₄×C₁₉	—	4	4	no	—
231	C₄×C₁₉	—	4	2	no	—
232	C₄×C₁₉	—	4	2	no	—
233	C₄×C₁₉	—	8	1	no	—
234	C₄×C₁₉	—	8	1	no	—
235	C₄×C₁₉	—	8	2	no	—
236	C₄×C₁₉	#525	1	1	yes	characteristic
237	C₄×C₁₉	#535	1	1	yes	characteristic
238	C₄×C₁₉	#551	1	2	yes	—
239	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
240	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
241	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
242	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
243	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
244	#485	—	2	4	no	—
245	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
246	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
248	#419	—	2	4	no	—
249	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×#103	C₂²×C₁₉	1	2	yes	—
252	C₂×#103	C₂²×C₁₉	1	2	yes	—
253	C₂×#103	C₂²×C₁₉	1	2	yes	—
254	C₂×#103	C₂²×C₁₉	1	2	yes	—
255	C₂×#103	C₂²×C₁₉	1	2	yes	—
256	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
257	#395	—	2	1	no	—
258	#395	—	2	1	no	—
259	#391	C₂²×C₁₉	1	2	yes	—
260	#389	C₂²×C₁₉	1	2	yes	—
261	#388	—	2	2	no	—
262	#385	—	2	2	no	—
263	#383	—	2	1	no	—
264	#380	C₂²×C₁₉	1	1	yes	characteristic
265	C₄×C₄⋊C₄	—	2	1	no	—
266	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
267	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
268	#340	C₂²×C₁₉	1	2	yes	—
269	#336	C₂²×C₁₉	1	2	yes	—
270	C₂×C₁₉	—	4	2	no	—
271	C₂×C₁₉	#2411	1	1	yes	characteristic
272	C₂×C₁₉	#3039	1	1	yes	characteristic
273	C₂×C₁₉	#3046	1	1	yes	characteristic
274	C₂×C₁₉	#3320	1	2	yes	—
275	C₂×C₁₉	#3328	1	2	yes	—
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×Q₈	—	2	4	no	—
278	C₂²×Q₈	—	2	2	no	—
279	C₂²×Q₈	—	2	2	no	—
280	C₂²×Q₈	—	4	2	no	—
281	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
282	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	4	2	no	—
287	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
288	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
290	C₄⋊Q₈	—	2	4	no	—
291	C₄⋊Q₈	—	4	2	no	—
292	C₂²⋊Q₈	—	2	2	no	—
293	C₂²⋊Q₈	—	2	2	no	—
294	#117	—	2	2	no	—
295	#117	D₄×C₁₉	1	4	yes	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
311	#107	—	2	2	no	—
312	#106	—	2	2	no	—
313	C₄⋊C₈	—	4	2	no	—
314	#103	—	2	4	no	—
315	#103	—	2	4	no	—
316	#103	—	2	4	no	—
317	#103	—	2	2	no	—
318	#103	—	2	2	no	—
319	#103	—	4	2	no	—
320	#103	—	4	2	no	—
321	C₂²⋊C₈	—	2	2	no	—
322	#95	—	2	1	no	—
323	#95	—	2	2	no	—
324	#95	—	2	2	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	D₄×C₁₉	1	1	yes	characteristic
328	#95	D₄×C₁₉	1	1	yes	characteristic
329	C₁₉	#24496	1	1	yes	characteristic, direct product factor, Sylow
330	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	8	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	4	no	—
342	C₂×Q₈	—	4	8	no	—
343	C₂×Q₈	—	4	4	no	—
344	C₂×Q₈	—	4	2	no	—
345	C₂×Q₈	#41×C₁₉	1	4	yes	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	4	4	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
359	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
360	C₂²×C₄	#41×C₁₉	1	2	yes	—
361	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
362	M₁₆	—	4	4	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	4	4	no	—
380	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
381	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	4	2	no	—
385	C₂²⋊C₄	—	8	1	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	8	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	C₁₉×#121	1	2	yes	—
395	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
396	Q₈	—	2	4	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	4	8	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	1	no	—
402	Q₈	—	4	1	no	—
403	Q₈	—	4	2	no	—
404	C₂×C₄	—	2	2	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	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	8	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	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	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	C₁₉×#121	1	2	yes	—
431	C₂×C₄	C₁₉×#137	1	4	yes	—
432	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
434	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
435	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
436	C₈	—	4	1	no	—
437	C₈	—	4	2	no	—
438	C₈	—	4	1	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
445	C₂²	C₁₉×#546	1	2	yes	—
446	C₂²	C₂×C₁₉×#137	1	2	yes	—
447	C₂²	C₁₉×#577	1	1	yes	characteristic
448	C₂²	C₁₉×#578	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	4	no	—
451	C₄	—	4	4	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	1	no	—
457	C₄	—	8	2	no	—
458	C₄	C₁₉×#525	1	1	yes	characteristic
459	C₄	C₁₉×#535	1	1	yes	characteristic
460	C₄	C₁₉×#551	1	2	yes	—
461	C₂	—	4	2	no	—
462	C₂	C₁₉×#2411	1	1	yes	characteristic
463	C₂	C₁₉×#3039	1	1	yes	characteristic
464	C₂	C₁₉×#3046	1	1	yes	characteristic
465	C₂	C₁₉×#3320	1	2	yes	—
466	C₂	C₁₉×#3328	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₂²⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₉×#2066	C₂	semidirect
6. C₁₉×#2043	C₂	semidirect
7. C₁₉×#1981	C₂	semidirect
8. C₁₉×#1928	C₂	semidirect
156. #24496	C₁₉	direct (N × H)
210. #2066	C₂×C₁₉	semidirect
211. #2043	C₂×C₁₉	semidirect
212. #1981	C₂×C₁₉	semidirect
213. #1928	C₂×C₁₉	semidirect
329. C₁₉	#24496	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×#485	2
C₂×C₁₉×#419	2
C₁₉×#2434	2
C₁₉×#2347	2
C₁₉×#2066	2
C₁₉×#2043	2
C₁₉×#1981	2
C₁₉×#1928	2
C₁₉×#1894	2
C₁₉×#1851	2
C₁₉×#1787	2
#24496	19

Subgroups — C19×#24496 #18030455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24496 #18030455