Subgroups — C₂×C₁₉×#1786 #18026553

Order 4864.

6086 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#102	C₂	1	4	yes	maximal, complemented
3	C₂²×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1786	C₂	1	8	yes	maximal, direct product factor
6	C₂⁶×C₁₉	—	2	1	no	—
7	C₂³×D₄×C₁₉	—	2	16	no	—
8	C₂³×D₄×C₁₉	—	2	2	no	—
9	C₂³×D₄×C₁₉	—	2	1	no	—
10	C₂³×D₄×C₁₉	—	2	4	no	—
11	C₂³×D₄×C₁₉	C₄	1	8	yes	complemented
12	C₂³×D₄×C₁₉	C₂²	1	4	yes	—
13	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₉	C₂²	1	2	yes	complemented
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
17	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
18	C₂×C₁₉×#102	—	2	16	no	—
19	C₂×C₁₉×#102	C₂²	1	16	yes	complemented
20	C₂×C₁₉×C₂²⋊C₈	—	2	4	no	—
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	complemented
22	C₁₉×#380	—	2	2	no	—
23	C₁₉×#380	C₂²	1	4	yes	complemented
24	C₂×C₁₉×#95	—	2	1	no	—
25	C₂⁵×C₁₉	—	2	16	no	—
26	C₂⁵×C₁₉	—	2	8	no	—
27	C₂⁵×C₁₉	—	2	4	no	—
28	C₂⁵×C₁₉	—	2	2	no	—
29	C₂⁵×C₁₉	—	4	8	no	—
30	C₂⁵×C₁₉	—	4	4	no	—
31	C₂⁵×C₁₉	—	4	4	no	—
32	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	—	2	16	no	—
34	C₂²×D₄×C₁₉	—	2	32	no	—
35	C₂²×D₄×C₁₉	—	2	64	no	—
36	C₂²×D₄×C₁₉	—	2	64	no	—
37	C₂²×D₄×C₁₉	—	2	32	no	—
38	C₂²×D₄×C₁₉	—	2	16	no	—
39	C₂²×D₄×C₁₉	—	2	8	no	—
40	C₂²×D₄×C₁₉	—	2	4	no	—
41	C₂²×D₄×C₁₉	—	2	8	no	—
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	—	2	8	no	—
44	C₂²×D₄×C₁₉	—	2	4	no	—
45	C₂²×D₄×C₁₉	C₂×C₄	1	8	yes	—
46	C₂²×D₄×C₁₉	C₂×C₄	1	16	yes	complemented
47	C₂²×D₄×C₁₉	D₄	1	16	yes	—
48	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
49	C₂³×C₄×C₁₉	—	2	8	no	—
50	C₂³×C₄×C₁₉	—	2	2	no	—
51	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
52	C₂³×C₄×C₁₉	D₄	1	2	yes	—
53	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	D₄	1	4	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₉	—	2	4	no	—
58	C₂²×C₈×C₁₉	—	2	8	no	—
59	C₂²×C₈×C₁₉	C₂³	1	4	yes	complemented
60	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	complemented
63	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
65	C₁₉×#102	—	2	32	no	—
66	C₁₉×C₂²⋊C₈	—	2	8	no	—
67	C₁₉×#95	—	2	4	no	—
68	C₂⁴×C₁₉	—	2	4	no	—
69	C₂⁴×C₁₉	—	2	4	no	—
70	C₂⁴×C₁₉	—	2	32	no	—
71	C₂⁴×C₁₉	—	2	64	no	—
72	C₂⁴×C₁₉	—	2	8	no	—
73	C₂⁴×C₁₉	—	2	16	no	—
74	C₂⁴×C₁₉	—	2	16	no	—
75	C₂⁴×C₁₉	—	2	4	no	—
76	C₂⁴×C₁₉	—	4	16	no	—
77	C₂⁴×C₁₉	—	4	32	no	—
78	C₂⁴×C₁₉	—	4	64	no	—
79	C₂⁴×C₁₉	—	4	64	no	—
80	C₂⁴×C₁₉	—	4	32	no	—
81	C₂⁴×C₁₉	—	4	8	no	—
82	C₂⁴×C₁₉	—	4	4	no	—
83	C₂⁴×C₁₉	—	4	8	no	—
84	C₂⁴×C₁₉	—	4	4	no	—
85	C₂⁴×C₁₉	—	4	8	no	—
86	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
87	C₂⁴×C₁₉	D₈	1	4	yes	—
88	C₂⁴×C₁₉	SD₁₆	1	4	yes	—
89	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
90	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂×D₄×C₁₉	—	2	32	no	—
92	C₂×D₄×C₁₉	—	2	64	no	—
93	C₂×D₄×C₁₉	—	2	64	no	—
94	C₂×D₄×C₁₉	—	2	128	no	—
95	C₂×D₄×C₁₉	—	2	64	no	—
96	C₂×D₄×C₁₉	—	2	16	no	—
97	C₂×D₄×C₁₉	—	2	8	no	—
98	C₂×D₄×C₁₉	—	2	16	no	—
99	C₂×D₄×C₁₉	—	2	32	no	—
100	C₂×D₄×C₁₉	—	2	16	no	—
101	C₂×D₄×C₁₉	—	2	8	no	—
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	C₂²⋊C₄	1	32	yes	complemented
104	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
105	C₂×D₄×C₁₉	C₂×D₄	1	16	yes	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	—	2	16	no	—
108	C₂²×C₄×C₁₉	—	2	8	no	—
109	C₂²×C₄×C₁₉	—	2	16	no	—
110	C₂²×C₄×C₁₉	—	2	8	no	—
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	4	4	no	—
113	C₂²×C₄×C₁₉	—	4	4	no	—
114	C₂²×C₄×C₁₉	—	4	4	no	—
115	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
116	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
117	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
125	C₂×C₈×C₁₉	—	2	4	no	—
126	C₂×C₈×C₁₉	—	2	8	no	—
127	C₂×C₈×C₁₉	—	4	8	no	—
128	C₄⋊C₄×C₁₉	—	2	8	no	—
129	C₄⋊C₄×C₁₉	—	4	4	no	—
130	C₂²⋊C₄×C₁₉	—	4	8	no	—
131	C₂×#1786	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₁₉	—	2	4	no	—
133	C₂³×C₁₉	—	2	4	no	—
134	C₂³×C₁₉	—	2	8	no	—
135	C₂³×C₁₉	—	2	8	no	—
136	C₂³×C₁₉	—	2	16	no	—
137	C₂³×C₁₉	—	2	16	no	—
138	C₂³×C₁₉	—	2	64	no	—
139	C₂³×C₁₉	—	2	8	no	—
140	C₂³×C₁₉	—	2	16	no	—
141	C₂³×C₁₉	—	2	32	no	—
142	C₂³×C₁₉	—	4	32	no	—
143	C₂³×C₁₉	—	4	64	no	—
144	C₂³×C₁₉	—	4	64	no	—
145	C₂³×C₁₉	—	4	256	no	—
146	C₂³×C₁₉	—	4	4	no	—
147	C₂³×C₁₉	—	4	4	no	—
148	C₂³×C₁₉	—	4	8	no	—
149	C₂³×C₁₉	—	4	16	no	—
150	C₂³×C₁₉	—	4	32	no	—
151	C₂³×C₁₉	—	4	16	no	—
152	C₂³×C₁₉	—	4	32	no	—
153	C₂³×C₁₉	—	4	32	no	—
154	C₂³×C₁₉	#102	1	16	yes	complemented
155	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
156	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂³×C₁₉	#120	1	4	yes	—
158	C₂³×C₁₉	C₂×D₈	1	4	yes	—
159	C₂³×C₁₉	C₂×D₈	1	2	yes	—
160	C₂³×C₁₉	C₂×SD₁₆	1	4	yes	—
161	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
162	C₂³×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
163	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
164	D₄×C₁₉	—	2	64	no	—
165	D₄×C₁₉	—	2	8	no	—
166	D₄×C₁₉	—	2	16	no	—
167	D₄×C₁₉	—	2	32	no	—
168	D₄×C₁₉	C₂×C₂²⋊C₄	1	16	yes	complemented
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	2	8	no	—
171	C₂×C₄×C₁₉	—	2	8	no	—
172	C₂×C₄×C₁₉	—	2	8	no	—
173	C₂×C₄×C₁₉	—	2	16	no	—
174	C₂×C₄×C₁₉	—	4	4	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	—	4	4	no	—
177	C₂×C₄×C₁₉	—	8	8	no	—
178	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
179	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
180	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂×C₄×C₁₉	#120	1	8	yes	—
182	C₂×C₄×C₁₉	#120	1	4	yes	—
183	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
185	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
186	C₈×C₁₉	—	4	4	no	—
187	C₂⁴×D₄	C₂×C₁₉	1	1	yes	characteristic
188	C₂²×#102	C₂×C₁₉	1	4	yes	complemented
189	C₂²×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
190	C₂×#380	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#1786	C₂×C₁₉	1	8	yes	direct product factor
192	C₂²×C₁₉	—	2	4	no	—
193	C₂²×C₁₉	—	2	8	no	—
194	C₂²×C₁₉	—	2	8	no	—
195	C₂²×C₁₉	—	2	4	no	—
196	C₂²×C₁₉	—	2	32	no	—
197	C₂²×C₁₉	—	2	16	no	—
198	C₂²×C₁₉	—	4	128	no	—
199	C₂²×C₁₉	—	4	8	no	—
200	C₂²×C₁₉	—	4	8	no	—
201	C₂²×C₁₉	—	4	16	no	—
202	C₂²×C₁₉	—	4	16	no	—
203	C₂²×C₁₉	—	4	64	no	—
204	C₂²×C₁₉	#379	1	4	yes	—
205	C₂²×C₁₉	C₂×#102	1	4	yes	—
206	C₂²×C₁₉	C₂×#102	1	8	yes	complemented
207	C₂²×C₁₉	#418	1	4	yes	—
208	C₂²×C₁₉	#447	1	8	yes	—
209	C₂²×C₁₉	#450	1	8	yes	—
210	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₁₉	C₂×#120	1	2	yes	—
212	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
213	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
214	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
215	C₄×C₁₉	—	2	4	no	—
216	C₄×C₁₉	—	8	4	no	—
217	C₄×C₁₉	#379	1	4	yes	—
218	C₄×C₁₉	C₂²×C₂²⋊C₄	1	2	yes	—
219	C₄×C₁₉	C₂×#120	1	2	yes	—
220	C₂⁶	—	2	1	no	—
221	C₂³×D₄	—	2	16	no	—
222	C₂³×D₄	—	2	1	no	—
223	C₂³×D₄	—	2	2	no	—
224	C₂³×D₄	—	2	4	no	—
225	C₂³×D₄	C₄×C₁₉	1	8	yes	complemented
226	C₂³×D₄	C₂²×C₁₉	1	4	yes	—
227	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
228	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
229	C₂³×C₈	C₂²×C₁₉	1	2	yes	complemented
230	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
231	C₂²×C₂²⋊C₄	—	2	1	no	—
232	C₂×#102	—	2	16	no	—
233	C₂×#102	C₂²×C₁₉	1	16	yes	complemented
234	C₂×C₂²⋊C₈	—	2	4	no	—
235	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	complemented
236	#380	—	2	2	no	—
237	#380	C₂²×C₁₉	1	4	yes	complemented
238	C₂×#95	—	2	1	no	—
239	C₂×C₁₉	—	2	8	no	—
240	C₂×C₁₉	—	4	16	no	—
241	C₂×C₁₉	#1786	1	8	yes	direct product factor
242	C₂×C₁₉	C₂×#379	1	1	yes	characteristic
243	C₂×C₁₉	C₂²×#102	1	1	yes	characteristic
244	C₂×C₁₉	C₂×#418	1	1	yes	characteristic
245	C₂×C₁₉	C₂×#447	1	2	yes	—
246	C₂×C₁₉	C₂×#450	1	2	yes	—
247	C₂⁵	—	2	16	no	—
248	C₂⁵	—	2	8	no	—
249	C₂⁵	—	2	4	no	—
250	C₂⁵	—	2	2	no	—
251	C₂⁵	—	4	8	no	—
252	C₂⁵	—	4	4	no	—
253	C₂⁵	—	4	4	no	—
254	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
255	C₂²×D₄	—	2	16	no	—
256	C₂²×D₄	—	2	64	no	—
257	C₂²×D₄	—	2	32	no	—
258	C₂²×D₄	—	2	64	no	—
259	C₂²×D₄	—	2	32	no	—
260	C₂²×D₄	—	2	16	no	—
261	C₂²×D₄	—	2	8	no	—
262	C₂²×D₄	—	2	4	no	—
263	C₂²×D₄	—	2	8	no	—
264	C₂²×D₄	—	2	2	no	—
265	C₂²×D₄	—	2	8	no	—
266	C₂²×D₄	—	2	4	no	—
267	C₂²×D₄	C₂×C₄×C₁₉	1	8	yes	—
268	C₂²×D₄	C₂×C₄×C₁₉	1	16	yes	complemented
269	C₂²×D₄	D₄×C₁₉	1	16	yes	—
270	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
271	C₂³×C₄	—	2	8	no	—
272	C₂³×C₄	—	2	2	no	—
273	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
274	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
275	C₂³×C₄	D₄×C₁₉	1	2	yes	—
276	C₂³×C₄	D₄×C₁₉	1	4	yes	—
277	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
278	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
279	C₂²×C₈	—	2	4	no	—
280	C₂²×C₈	—	2	8	no	—
281	C₂²×C₈	C₂³×C₁₉	1	4	yes	complemented
282	C₂×C₄⋊C₄	—	2	8	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	complemented
285	C₂×C₂²⋊C₄	—	2	4	no	—
286	C₂×C₂²⋊C₄	—	4	4	no	—
287	#102	—	2	32	no	—
288	C₂²⋊C₈	—	2	8	no	—
289	#95	—	2	4	no	—
290	C₁₉	C₂×#1786	1	1	yes	characteristic, direct product factor, Sylow
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	2	4	no	—
293	C₂⁴	—	2	64	no	—
294	C₂⁴	—	2	32	no	—
295	C₂⁴	—	2	8	no	—
296	C₂⁴	—	2	16	no	—
297	C₂⁴	—	2	16	no	—
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	4	32	no	—
300	C₂⁴	—	4	64	no	—
301	C₂⁴	—	4	64	no	—
302	C₂⁴	—	4	16	no	—
303	C₂⁴	—	4	8	no	—
304	C₂⁴	—	4	4	no	—
305	C₂⁴	—	4	8	no	—
306	C₂⁴	—	4	4	no	—
307	C₂⁴	—	4	8	no	—
308	C₂⁴	—	4	32	no	—
309	C₂⁴	C₂²⋊C₄×C₁₉	1	4	yes	—
310	C₂⁴	D₈×C₁₉	1	4	yes	—
311	C₂⁴	SD₁₆×C₁₉	1	4	yes	—
312	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
313	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
314	C₂×D₄	—	2	64	no	—
315	C₂×D₄	—	2	32	no	—
316	C₂×D₄	—	2	128	no	—
317	C₂×D₄	—	2	64	no	—
318	C₂×D₄	—	2	64	no	—
319	C₂×D₄	—	2	8	no	—
320	C₂×D₄	—	2	16	no	—
321	C₂×D₄	—	2	16	no	—
322	C₂×D₄	—	2	16	no	—
323	C₂×D₄	—	2	32	no	—
324	C₂×D₄	—	2	8	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	C₂²⋊C₄×C₁₉	1	32	yes	complemented
327	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
328	C₂×D₄	C₂×D₄×C₁₉	1	16	yes	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	16	no	—
331	C₂²×C₄	—	2	16	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
339	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
340	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
341	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
344	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
346	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
347	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	8	no	—
350	C₂×C₈	—	4	8	no	—
351	C₄⋊C₄	—	2	8	no	—
352	C₄⋊C₄	—	4	4	no	—
353	C₂²⋊C₄	—	4	8	no	—
354	C₂³	—	2	8	no	—
355	C₂³	—	2	8	no	—
356	C₂³	—	2	16	no	—
357	C₂³	—	2	16	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	64	no	—
361	C₂³	—	2	32	no	—
362	C₂³	—	2	8	no	—
363	C₂³	—	2	16	no	—
364	C₂³	—	4	64	no	—
365	C₂³	—	4	64	no	—
366	C₂³	—	4	256	no	—
367	C₂³	—	4	32	no	—
368	C₂³	—	4	16	no	—
369	C₂³	—	4	32	no	—
370	C₂³	—	4	16	no	—
371	C₂³	—	4	32	no	—
372	C₂³	—	4	32	no	—
373	C₂³	—	4	4	no	—
374	C₂³	—	4	4	no	—
375	C₂³	—	4	8	no	—
376	C₂³	C₁₉×#102	1	16	yes	complemented
377	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
378	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
379	C₂³	C₁₉×#120	1	4	yes	—
380	C₂³	C₂×D₈×C₁₉	1	4	yes	—
381	C₂³	C₂×D₈×C₁₉	1	2	yes	—
382	C₂³	C₂×SD₁₆×C₁₉	1	4	yes	—
383	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
384	C₂³	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
385	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
386	D₄	—	2	64	no	—
387	D₄	—	2	32	no	—
388	D₄	—	2	8	no	—
389	D₄	—	2	16	no	—
390	D₄	C₂×C₂²⋊C₄×C₁₉	1	16	yes	complemented
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	16	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	8	8	no	—
400	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
401	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
402	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
403	C₂×C₄	C₁₉×#120	1	4	yes	—
404	C₂×C₄	C₁₉×#120	1	8	yes	—
405	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
407	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
408	C₈	—	4	4	no	—
409	C₂²	—	2	8	no	—
410	C₂²	—	2	8	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	32	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	16	no	—
415	C₂²	—	4	128	no	—
416	C₂²	—	4	16	no	—
417	C₂²	—	4	16	no	—
418	C₂²	—	4	64	no	—
419	C₂²	—	4	8	no	—
420	C₂²	—	4	8	no	—
421	C₂²	C₁₉×#379	1	4	yes	—
422	C₂²	C₂×C₁₉×#102	1	4	yes	—
423	C₂²	C₂×C₁₉×#102	1	8	yes	complemented
424	C₂²	C₁₉×#418	1	4	yes	—
425	C₂²	C₁₉×#447	1	8	yes	—
426	C₂²	C₁₉×#450	1	8	yes	—
427	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
428	C₂²	C₂×C₁₉×#120	1	2	yes	—
429	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
430	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
431	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
432	C₄	—	2	4	no	—
433	C₄	—	8	4	no	—
434	C₄	C₁₉×#379	1	4	yes	—
435	C₄	C₂²×C₂²⋊C₄×C₁₉	1	2	yes	—
436	C₄	C₂×C₁₉×#120	1	2	yes	—
437	C₂	—	2	8	no	—
438	C₂	—	4	16	no	—
439	C₂	C₁₉×#1786	1	8	yes	direct product factor
440	C₂	C₂×C₁₉×#379	1	1	yes	characteristic
441	C₂	C₂²×C₁₉×#102	1	1	yes	characteristic
442	C₂	C₂×C₁₉×#418	1	1	yes	characteristic
443	C₂	C₂×C₁₉×#447	1	2	yes	—
444	C₂	C₂×C₁₉×#450	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#102	C₂	semidirect
3. C₂²×C₁₉×C₂²⋊C₈	C₂	semidirect
4. C₂×C₁₉×#380	C₂	semidirect
5. C₁₉×#1786	C₂	direct (N × H)
11. C₂³×D₄×C₁₉	C₄	semidirect
15. C₂³×C₈×C₁₉	C₂²	semidirect
16. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
19. C₂×C₁₉×#102	C₂²	semidirect
21. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
23. C₁₉×#380	C₂²	semidirect
46. C₂²×D₄×C₁₉	C₂×C₄	semidirect
59. C₂²×C₈×C₁₉	C₂³	semidirect
62. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
103. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
131. C₂×#1786	C₁₉	direct (N × H)
154. C₂³×C₁₉	#102	semidirect
168. D₄×C₁₉	C₂×C₂²⋊C₄	semidirect
188. C₂²×#102	C₂×C₁₉	semidirect
189. C₂²×C₂²⋊C₈	C₂×C₁₉	semidirect
190. C₂×#380	C₂×C₁₉	semidirect
191. #1786	C₂×C₁₉	direct (N × H)
206. C₂²×C₁₉	C₂×#102	semidirect
225. C₂³×D₄	C₄×C₁₉	semidirect
229. C₂³×C₈	C₂²×C₁₉	semidirect
230. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
233. C₂×#102	C₂²×C₁₉	semidirect
235. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
237. #380	C₂²×C₁₉	semidirect
241. C₂×C₁₉	#1786	direct (N × H)
268. C₂²×D₄	C₂×C₄×C₁₉	semidirect
281. C₂²×C₈	C₂³×C₁₉	semidirect
284. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
290. C₁₉	C₂×#1786	direct (N × H)
326. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect
376. C₂³	C₁₉×#102	semidirect
390. D₄	C₂×C₂²⋊C₄×C₁₉	semidirect
423. C₂²	C₂×C₁₉×#102	semidirect
439. C₂	C₁₉×#1786	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₁₉	2
C₂²×C₁₉×#102	2
C₂²×C₁₉×C₂²⋊C₈	2
C₂×C₁₉×#380	2
C₁₉×#1786	2
C₂×#1786	19

Subgroups — C2×C19×#1786 #18026553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1786 #18026553