Subgroups — C₁₉×#20738 #18026697

Order 4864.

1782 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1824	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1802	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1786	C₂	1	2	yes	maximal
7	C₁₉×#1762	C₂	1	4	yes	maximal, complemented
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₉	—	2	1	no	—
10	C₂×C₄×D₄×C₁₉	—	2	1	no	—
11	C₂×C₄×D₄×C₁₉	—	2	1	no	—
12	C₂×C₄×D₄×C₁₉	—	2	4	no	—
13	C₂×C₄×D₄×C₁₉	C₄	1	8	yes	complemented
14	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
16	C₂×C₁₉×#117	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#432	—	2	4	no	—
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
22	C₂×C₁₉×#102	C₂²	1	8	yes	—
23	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₉×#97	C₂²	1	2	yes	complemented
25	C₁₉×#384	C₂²	1	2	yes	complemented
26	C₁₉×#382	—	2	1	no	—
27	C₁₉×#380	—	2	1	no	—
28	C₁₉×#380	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
31	C₁₉×#340	C₂²	1	8	yes	complemented
32	C₂⁵×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	8	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	—	2	2	no	—
36	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
37	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₂³×C₄×C₁₉	—	2	8	no	—
40	C₂³×C₄×C₁₉	—	2	2	no	—
41	C₂³×C₄×C₁₉	—	2	2	no	—
42	C₂³×C₄×C₁₉	—	4	8	no	—
43	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
47	C₄×D₄×C₁₉	—	2	8	no	—
48	C₄×D₄×C₁₉	—	2	8	no	—
49	C₄×D₄×C₁₉	—	2	4	no	—
50	C₄×D₄×C₁₉	—	2	4	no	—
51	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	—
52	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	—
53	C₁₉×#117	—	4	4	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	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄²×C₁₉	—	2	2	no	—
66	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₉	D₄	1	4	yes	—
70	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
72	C₁₉×C₄⋊C₈	—	2	4	no	—
73	C₁₉×#102	—	2	16	no	—
74	C₁₉×C₂²⋊C₈	—	2	4	no	—
75	C₁₉×#97	—	2	4	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₂⁴×C₁₉	—	2	8	no	—
79	C₂⁴×C₁₉	—	2	4	no	—
80	C₂⁴×C₁₉	—	2	2	no	—
81	C₂⁴×C₁₉	—	4	4	no	—
82	C₂⁴×C₁₉	—	4	2	no	—
83	C₂⁴×C₁₉	—	4	2	no	—
84	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂×D₄×C₁₉	—	2	8	no	—
86	C₂×D₄×C₁₉	—	2	16	no	—
87	C₂×D₄×C₁₉	—	2	16	no	—
88	C₂×D₄×C₁₉	—	2	4	no	—
89	C₂×D₄×C₁₉	—	2	2	no	—
90	C₂×D₄×C₁₉	—	2	4	no	—
91	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
92	C₂×D₄×C₁₉	#41	1	8	yes	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	4	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	8	no	—
100	C₂²×C₄×C₁₉	—	2	8	no	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	—	4	8	no	—
103	C₂²×C₄×C₁₉	—	4	32	no	—
104	C₂²×C₄×C₁₉	—	4	4	no	—
105	C₂²×C₄×C₁₉	—	4	8	no	—
106	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
107	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
108	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₁₉	—	2	4	no	—
117	C₂×C₈×C₁₉	—	2	8	no	—
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	8	no	—
121	C₄⋊C₄×C₁₉	—	4	4	no	—
122	C₄⋊C₄×C₁₉	—	4	4	no	—
123	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
124	C₂²⋊C₄×C₁₉	—	2	8	no	—
125	C₂²⋊C₄×C₁₉	—	2	8	no	—
126	C₂²⋊C₄×C₁₉	—	4	4	no	—
127	C₄²×C₁₉	—	4	4	no	—
128	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
129	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
130	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
131	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
132	C₄²×C₁₉	C₂×D₄	1	2	yes	—
133	C₄²×C₁₉	C₂×D₄	1	2	yes	—
134	#20738	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₁₉	—	2	2	no	—
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	2	16	no	—
138	C₂³×C₁₉	—	2	4	no	—
139	C₂³×C₁₉	—	2	8	no	—
140	C₂³×C₁₉	—	4	8	no	—
141	C₂³×C₁₉	—	4	16	no	—
142	C₂³×C₁₉	—	4	16	no	—
143	C₂³×C₁₉	—	4	4	no	—
144	C₂³×C₁₉	—	4	2	no	—
145	C₂³×C₁₉	—	4	2	no	—
146	C₂³×C₁₉	—	4	8	no	—
147	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
149	C₂³×C₁₉	#137	1	2	yes	—
150	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
151	D₄×C₁₉	—	2	16	no	—
152	D₄×C₁₉	—	2	4	no	—
153	D₄×C₁₉	—	2	8	no	—
154	D₄×C₁₉	#117	1	8	yes	complemented
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	8	no	—
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	8	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	4	16	no	—
167	C₂×C₄×C₁₉	—	4	8	no	—
168	C₂×C₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	4	16	no	—
170	C₂×C₄×C₁₉	—	4	4	no	—
171	C₂×C₄×C₁₉	—	4	4	no	—
172	C₂×C₄×C₁₉	—	4	4	no	—
173	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
179	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
182	C₈×C₁₉	—	4	4	no	—
183	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic
184	C₂×#432	C₂×C₁₉	1	1	yes	characteristic, complemented
185	#2285	C₂×C₁₉	1	1	yes	characteristic, complemented
186	#1824	C₂×C₁₉	1	2	yes	complemented
187	#1802	C₂×C₁₉	1	4	yes	complemented
188	#1786	C₂×C₁₉	1	2	yes	—
189	#1762	C₂×C₁₉	1	4	yes	complemented
190	C₂²×C₁₉	—	2	4	no	—
191	C₂²×C₁₉	—	2	4	no	—
192	C₂²×C₁₉	—	2	2	no	—
193	C₂²×C₁₉	—	2	2	no	—
194	C₂²×C₁₉	—	2	8	no	—
195	C₂²×C₁₉	—	4	32	no	—
196	C₂²×C₁₉	—	4	8	no	—
197	C₂²×C₁₉	—	4	8	no	—
198	C₂²×C₁₉	—	4	4	no	—
199	C₂²×C₁₉	—	4	4	no	—
200	C₂²×C₁₉	#417	1	4	yes	—
201	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
202	C₂²×C₁₉	#525	1	2	yes	—
203	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
205	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
206	C₄×C₁₉	—	2	2	no	—
207	C₄×C₁₉	—	2	2	no	—
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	2	2	no	—
210	C₄×C₁₉	—	4	4	no	—
211	C₄×C₁₉	—	8	4	no	—
212	C₄×C₁₉	#418	1	4	yes	—
213	C₄×C₁₉	C₂×#117	1	2	yes	—
214	C₄×C₁₉	#525	1	2	yes	—
215	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
216	C₂⁴×C₄	—	2	1	no	—
217	C₂×C₄×D₄	—	2	1	no	—
218	C₂×C₄×D₄	—	2	1	no	—
219	C₂×C₄×D₄	—	2	4	no	—
220	C₂×C₄×D₄	C₄×C₁₉	1	8	yes	complemented
221	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
222	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
223	C₂×#117	—	2	1	no	—
224	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
225	C₂²×C₂²⋊C₄	—	2	1	no	—
226	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
227	#432	—	2	4	no	—
228	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
229	C₂×#102	C₂²×C₁₉	1	8	yes	—
230	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
231	C₂×#97	C₂²×C₁₉	1	2	yes	complemented
232	#384	C₂²×C₁₉	1	2	yes	complemented
233	#382	—	2	1	no	—
234	#380	—	2	1	no	—
235	#380	C₂²×C₁₉	1	2	yes	—
236	C₄×C₄⋊C₄	—	2	1	no	—
237	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
238	#340	C₂²×C₁₉	1	8	yes	complemented
239	C₂×C₁₉	—	2	4	no	—
240	C₂×C₁₉	—	4	8	no	—
241	C₂×C₁₉	#2280	1	1	yes	characteristic
242	C₂×C₁₉	C₂×#418	1	1	yes	characteristic
243	C₂×C₁₉	C₂×#417	1	1	yes	characteristic
244	C₂×C₁₉	#3109	1	2	yes	—
245	C₂×C₁₉	#3110	1	2	yes	—
246	C₂⁵	—	2	1	no	—
247	C₂²×D₄	—	2	8	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	2	no	—
250	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
251	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
252	C₂³×C₄	—	2	1	no	—
253	C₂³×C₄	—	2	8	no	—
254	C₂³×C₄	—	2	2	no	—
255	C₂³×C₄	—	2	2	no	—
256	C₂³×C₄	—	4	8	no	—
257	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
258	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
259	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
261	C₄×D₄	—	2	8	no	—
262	C₄×D₄	—	2	8	no	—
263	C₄×D₄	—	2	4	no	—
264	C₄×D₄	—	2	4	no	—
265	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	—
266	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	—
267	#117	—	4	4	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	8	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
281	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
282	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
283	C₂×C₄²	D₄×C₁₉	1	4	yes	—
284	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
286	C₄⋊C₈	—	2	4	no	—
287	#102	—	2	16	no	—
288	C₂²⋊C₈	—	2	4	no	—
289	#97	—	2	4	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	C₁₉	#20738	1	1	yes	characteristic, direct product factor, Sylow
293	C₂⁴	—	2	8	no	—
294	C₂⁴	—	2	4	no	—
295	C₂⁴	—	2	2	no	—
296	C₂⁴	—	4	4	no	—
297	C₂⁴	—	4	2	no	—
298	C₂⁴	—	4	2	no	—
299	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	16	no	—
302	C₂×D₄	—	2	16	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
307	C₂×D₄	#41×C₁₉	1	8	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	—	2	8	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	4	8	no	—
318	C₂²×C₄	—	4	32	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	4	8	no	—
321	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
322	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
323	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
330	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
331	C₂×C₈	—	2	4	no	—
332	C₂×C₈	—	2	8	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	8	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
339	C₂²⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₄²	—	4	4	no	—
343	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
344	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
345	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
346	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
347	C₄²	C₂×D₄×C₁₉	1	2	yes	—
348	C₄²	C₂×D₄×C₁₉	1	2	yes	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	16	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	8	no	—
354	C₂³	—	4	8	no	—
355	C₂³	—	4	16	no	—
356	C₂³	—	4	16	no	—
357	C₂³	—	4	8	no	—
358	C₂³	—	4	4	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	2	no	—
361	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
362	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
363	C₂³	C₁₉×#137	1	2	yes	—
364	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
365	D₄	—	2	16	no	—
366	D₄	—	2	4	no	—
367	D₄	—	2	8	no	—
368	D₄	C₁₉×#117	1	8	yes	complemented
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	4	16	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	16	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
388	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
389	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
390	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
391	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
392	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
393	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
395	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
396	C₈	—	4	4	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	8	no	—
402	C₂²	—	4	32	no	—
403	C₂²	—	4	8	no	—
404	C₂²	—	4	8	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	C₁₉×#417	1	4	yes	—
408	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
409	C₂²	C₁₉×#525	1	2	yes	—
410	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
411	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
412	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	4	no	—
418	C₄	—	8	4	no	—
419	C₄	C₁₉×#418	1	4	yes	—
420	C₄	C₂×C₁₉×#117	1	2	yes	—
421	C₄	C₁₉×#525	1	2	yes	—
422	C₂	—	2	4	no	—
423	C₂	—	4	8	no	—
424	C₂	C₁₉×#2280	1	1	yes	characteristic
425	C₂	C₂×C₁₉×#418	1	1	yes	characteristic
426	C₂	C₂×C₁₉×#417	1	1	yes	characteristic
427	C₂	C₁₉×#3109	1	2	yes	—
428	C₂	C₁₉×#3110	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#432	C₂	semidirect
3. C₁₉×#2285	C₂	semidirect
4. C₁₉×#1824	C₂	semidirect
5. C₁₉×#1802	C₂	semidirect
7. C₁₉×#1762	C₂	semidirect
13. C₂×C₄×D₄×C₁₉	C₄	semidirect
21. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
24. C₂×C₁₉×#97	C₂²	semidirect
25. C₁₉×#384	C₂²	semidirect
30. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
31. C₁₉×#340	C₂²	semidirect
134. #20738	C₁₉	direct (N × H)
154. D₄×C₁₉	#117	semidirect
184. C₂×#432	C₂×C₁₉	semidirect
185. #2285	C₂×C₁₉	semidirect
186. #1824	C₂×C₁₉	semidirect
187. #1802	C₂×C₁₉	semidirect
189. #1762	C₂×C₁₉	semidirect
220. C₂×C₄×D₄	C₄×C₁₉	semidirect
228. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
231. C₂×#97	C₂²×C₁₉	semidirect
232. #384	C₂²×C₁₉	semidirect
237. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
238. #340	C₂²×C₁₉	semidirect
292. C₁₉	#20738	direct (N × H)
368. D₄	C₁₉×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₉	2
C₂×C₁₉×#432	2
C₁₉×#2285	2
C₁₉×#1824	2
C₁₉×#1802	2
C₁₉×#1786	2
C₁₉×#1762	2
#20738	19

Subgroups — C19×#20738 #18026697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20738 #18026697