Subgroups — C₁₉×#32772 #18038731

Order 4864.

774 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2850	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2095	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2094	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2085	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2042	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2035	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2033	C₂	1	2	yes	maximal
9	C₁₉×#2024	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2023	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1817	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#107	C₂²	1	2	yes	—
19	C₂×C₁₉×#106	C₂²	1	2	yes	—
20	C₂×C₁₉×#103	C₂²	1	2	yes	—
21	C₂×C₁₉×#103	C₂²	1	2	yes	—
22	C₂×C₁₉×#102	C₂²	1	2	yes	—
23	C₂×C₁₉×#102	C₂²	1	2	yes	—
24	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₁₉×#391	—	2	1	no	—
26	C₁₉×#391	C₂²	1	1	yes	characteristic
27	C₁₉×#390	C₂²	1	1	yes	characteristic
28	C₁₉×#389	—	2	1	no	—
29	C₁₉×#389	C₂²	1	2	yes	—
30	C₁₉×#388	—	2	1	no	—
31	C₁₉×#388	—	2	1	no	—
32	C₁₉×#386	—	2	1	no	—
33	C₁₉×#386	—	2	1	no	—
34	C₁₉×#384	C₂²	1	1	yes	characteristic
35	C₁₉×#382	C₂²	1	1	yes	characteristic
36	C₁₉×#380	—	2	1	no	—
37	C₁₉×#380	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#336	C₂²	1	1	yes	characteristic
41	C₁₉×#336	C₂²	1	1	yes	characteristic
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
52	C₁₉×C₄⋊Q₈	—	4	2	no	—
53	C₁₉×#124	—	4	2	no	—
54	C₁₉×C₂²⋊Q₈	—	4	2	no	—
55	C₁₉×C₂²⋊Q₈	—	4	4	no	—
56	C₁₉×#121	—	4	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄²×C₁₉	—	4	2	no	—
74	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
78	C₁₉×#107	—	4	2	no	—
79	C₁₉×#106	—	4	2	no	—
80	C₁₉×#103	—	4	2	no	—
81	C₁₉×#103	—	4	2	no	—
82	C₁₉×#102	—	4	2	no	—
83	C₁₉×#102	—	4	2	no	—
84	C₁₉×C₂²⋊C₈	—	4	2	no	—
85	C₁₉×#95	—	2	2	no	—
86	C₁₉×#95	—	2	2	no	—
87	C₁₉×#95	—	2	1	no	—
88	C₁₉×#95	—	2	1	no	—
89	C₁₉×#95	—	2	1	no	—
90	C₁₉×#95	—	2	1	no	—
91	C₂⁴×C₁₉	—	2	1	no	—
92	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂×Q₈×C₁₉	—	2	2	no	—
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	2	1	no	—
96	C₂×Q₈×C₁₉	—	2	1	no	—
97	C₂×Q₈×C₁₉	—	4	2	no	—
98	C₂×Q₈×C₁₉	—	4	2	no	—
99	C₂×Q₈×C₁₉	—	4	2	no	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	2	2	no	—
102	C₂×D₄×C₁₉	—	2	1	no	—
103	C₂×D₄×C₁₉	—	2	1	no	—
104	C₂×D₄×C₁₉	—	4	2	no	—
105	C₂×D₄×C₁₉	—	4	2	no	—
106	C₂×D₄×C₁₉	—	4	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	1	no	—
113	C₂²×C₄×C₁₉	—	2	1	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	—	4	1	no	—
120	C₂²×C₄×C₁₉	—	4	1	no	—
121	C₂²×C₄×C₁₉	—	4	1	no	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₁₉	—	2	2	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	4	2	no	—
141	C₄⋊C₄×C₁₉	—	4	2	no	—
142	C₄⋊C₄×C₁₉	—	4	2	no	—
143	C₄⋊C₄×C₁₉	—	4	4	no	—
144	C₄⋊C₄×C₁₉	—	4	2	no	—
145	C₂²⋊C₄×C₁₉	—	4	2	no	—
146	C₂²⋊C₄×C₁₉	—	4	2	no	—
147	C₂²⋊C₄×C₁₉	—	4	2	no	—
148	C₂²⋊C₄×C₁₉	—	4	2	no	—
149	C₂²⋊C₄×C₁₉	—	4	4	no	—
150	C₂²⋊C₄×C₁₉	—	4	2	no	—
151	C₂²⋊C₄×C₁₉	—	4	2	no	—
152	C₄²×C₁₉	—	2	2	no	—
153	C₄²×C₁₉	—	2	2	no	—
154	C₄²×C₁₉	—	4	1	no	—
155	C₄²×C₁₉	—	4	1	no	—
156	#32772	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	—	2	1	no	—
158	C₂³×C₁₉	—	2	1	no	—
159	C₂³×C₁₉	—	2	1	no	—
160	C₂³×C₁₉	—	2	1	no	—
161	C₂³×C₁₉	—	2	1	no	—
162	C₂³×C₁₉	—	2	1	no	—
163	C₂³×C₁₉	—	4	1	no	—
164	C₂³×C₁₉	—	4	1	no	—
165	C₂³×C₁₉	—	4	1	no	—
166	C₂³×C₁₉	—	4	1	no	—
167	C₂³×C₁₉	—	4	1	no	—
168	C₂³×C₁₉	—	4	1	no	—
169	C₂³×C₁₉	—	4	1	no	—
170	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
171	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₁₉	—	4	2	no	—
173	Q₈×C₁₉	—	4	2	no	—
174	Q₈×C₁₉	—	8	4	no	—
175	D₄×C₁₉	—	4	2	no	—
176	D₄×C₁₉	—	4	2	no	—
177	D₄×C₁₉	—	8	4	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	2	1	no	—
185	C₂×C₄×C₁₉	—	2	1	no	—
186	C₂×C₄×C₁₉	—	2	1	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	4	4	no	—
192	C₂×C₄×C₁₉	—	4	4	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	2	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	#135	1	2	yes	—
211	C₂×C₄×C₁₉	#137	1	2	yes	—
212	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
213	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
214	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
215	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
216	C₈×C₁₉	—	4	2	no	—
217	C₈×C₁₉	—	4	2	no	—
218	#2857	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#2850	C₂×C₁₉	1	1	yes	characteristic
220	#2095	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#2094	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#2085	C₂×C₁₉	1	2	yes	complemented
223	#2042	C₂×C₁₉	1	2	yes	complemented
224	#2035	C₂×C₁₉	1	2	yes	complemented
225	#2033	C₂×C₁₉	1	2	yes	—
226	#2024	C₂×C₁₉	1	1	yes	characteristic, complemented
227	#2023	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#1817	C₂×C₁₉	1	1	yes	characteristic, complemented
229	C₂²×C₁₉	—	2	2	no	—
230	C₂²×C₁₉	—	2	2	no	—
231	C₂²×C₁₉	—	2	2	no	—
232	C₂²×C₁₉	—	4	1	no	—
233	C₂²×C₁₉	—	4	1	no	—
234	C₂²×C₁₉	—	4	1	no	—
235	C₂²×C₁₉	—	4	1	no	—
236	C₂²×C₁₉	—	8	1	no	—
237	C₂²×C₁₉	—	8	1	no	—
238	C₂²×C₁₉	—	8	1	no	—
239	C₂²×C₁₉	—	8	1	no	—
240	C₂²×C₁₉	—	8	1	no	—
241	C₂²×C₁₉	—	8	1	no	—
242	C₂²×C₁₉	—	8	1	no	—
243	C₂²×C₁₉	#534	1	1	yes	characteristic
244	C₂²×C₁₉	#535	1	1	yes	characteristic
245	C₂²×C₁₉	#536	1	1	yes	characteristic
246	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
247	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
248	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
249	C₂²×C₁₉	#575	1	1	yes	characteristic
250	C₄×C₁₉	—	2	2	no	—
251	C₄×C₁₉	—	2	2	no	—
252	C₄×C₁₉	—	4	1	no	—
253	C₄×C₁₉	—	4	1	no	—
254	C₄×C₁₉	—	4	1	no	—
255	C₄×C₁₉	—	8	1	no	—
256	C₄×C₁₉	—	8	2	no	—
257	C₄×C₁₉	—	8	1	no	—
258	C₄×C₁₉	—	8	2	no	—
259	C₄×C₁₉	—	8	1	no	—
260	C₄×C₁₉	#562	1	2	yes	—
261	C₄×C₁₉	#562	1	2	yes	—
262	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
263	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
264	C₂×C₂²⋊Q₈	—	2	1	no	—
265	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
267	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
268	C₂×#107	C₂²×C₁₉	1	2	yes	—
269	C₂×#106	C₂²×C₁₉	1	2	yes	—
270	C₂×#103	C₂²×C₁₉	1	2	yes	—
271	C₂×#103	C₂²×C₁₉	1	2	yes	—
272	C₂×#102	C₂²×C₁₉	1	2	yes	—
273	C₂×#102	C₂²×C₁₉	1	2	yes	—
274	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
275	#391	—	2	1	no	—
276	#391	C₂²×C₁₉	1	1	yes	characteristic
277	#390	C₂²×C₁₉	1	1	yes	characteristic
278	#389	—	2	1	no	—
279	#389	C₂²×C₁₉	1	2	yes	—
280	#388	—	2	1	no	—
281	#388	—	2	1	no	—
282	#386	—	2	1	no	—
283	#386	—	2	1	no	—
284	#384	C₂²×C₁₉	1	1	yes	characteristic
285	#382	C₂²×C₁₉	1	1	yes	characteristic
286	#380	—	2	1	no	—
287	#380	C₂²×C₁₉	1	2	yes	—
288	#340	C₂²×C₁₉	1	2	yes	—
289	#340	C₂²×C₁₉	1	2	yes	—
290	#336	C₂²×C₁₉	1	2	yes	—
291	#336	C₂²×C₁₉	1	1	yes	characteristic
292	#336	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×C₁₉	—	4	2	no	—
294	C₂×C₁₉	—	16	1	no	—
295	C₂×C₁₉	#2816	1	1	yes	characteristic
296	C₂×C₁₉	#3188	1	1	yes	characteristic
297	C₂×C₁₉	#3196	1	1	yes	characteristic
298	C₂×C₁₉	#3210	1	1	yes	characteristic
299	C₂×C₁₉	#3213	1	1	yes	characteristic
300	C₂×C₁₉	#3233	1	1	yes	characteristic
301	C₂×C₁₉	#3238	1	1	yes	characteristic
302	C₂²×Q₈	—	2	1	no	—
303	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
304	C₂²×D₄	—	2	1	no	—
305	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
306	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
307	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
310	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
311	C₄⋊Q₈	—	4	2	no	—
312	#124	—	4	2	no	—
313	C₂²⋊Q₈	—	4	2	no	—
314	C₂²⋊Q₈	—	4	4	no	—
315	#121	—	4	2	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₄²	—	4	2	no	—
333	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
334	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
337	#107	—	4	2	no	—
338	#106	—	4	2	no	—
339	#103	—	4	2	no	—
340	#103	—	4	2	no	—
341	#102	—	4	2	no	—
342	#102	—	4	2	no	—
343	C₂²⋊C₈	—	4	2	no	—
344	#95	—	2	2	no	—
345	#95	—	2	2	no	—
346	#95	—	2	1	no	—
347	#95	—	2	1	no	—
348	#95	—	2	1	no	—
349	#95	—	2	1	no	—
350	C₁₉	#32772	1	1	yes	characteristic, direct product factor, Sylow
351	C₂⁴	—	2	1	no	—
352	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	4	2	no	—
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₄⋊C₄	—	4	2	no	—
403	C₄⋊C₄	—	4	4	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₂²⋊C₄	—	4	2	no	—
406	C₂²⋊C₄	—	4	2	no	—
407	C₂²⋊C₄	—	4	2	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₂²⋊C₄	—	4	4	no	—
410	C₂²⋊C₄	—	4	2	no	—
411	C₂²⋊C₄	—	4	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	4	1	no	—
415	C₄²	—	4	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
430	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
431	Q₈	—	4	2	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	8	4	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	8	4	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	C₁₉×#135	1	2	yes	—
470	C₂×C₄	C₁₉×#137	1	2	yes	—
471	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
472	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
473	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
474	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
475	C₈	—	4	2	no	—
476	C₈	—	4	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	8	1	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	1	no	—
488	C₂²	—	8	1	no	—
489	C₂²	—	8	1	no	—
490	C₂²	—	8	1	no	—
491	C₂²	C₁₉×#534	1	1	yes	characteristic
492	C₂²	C₁₉×#535	1	1	yes	characteristic
493	C₂²	C₁₉×#536	1	1	yes	characteristic
494	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
495	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
496	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
497	C₂²	C₁₉×#575	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	4	1	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	1	no	—
503	C₄	—	8	2	no	—
504	C₄	—	8	1	no	—
505	C₄	—	8	1	no	—
506	C₄	—	8	2	no	—
507	C₄	—	8	1	no	—
508	C₄	C₁₉×#562	1	2	yes	—
509	C₄	C₁₉×#562	1	2	yes	—
510	C₂	—	4	2	no	—
511	C₂	—	16	1	no	—
512	C₂	C₁₉×#2816	1	1	yes	characteristic
513	C₂	C₁₉×#3188	1	1	yes	characteristic
514	C₂	C₁₉×#3196	1	1	yes	characteristic
515	C₂	C₁₉×#3210	1	1	yes	characteristic
516	C₂	C₁₉×#3213	1	1	yes	characteristic
517	C₂	C₁₉×#3233	1	1	yes	characteristic
518	C₂	C₁₉×#3238	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂²×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
1. C₁₉×#2857	C₂	semidirect
3. C₁₉×#2095	C₂	semidirect
4. C₁₉×#2094	C₂	semidirect
5. C₁₉×#2085	C₂	semidirect
6. C₁₉×#2042	C₂	semidirect
7. C₁₉×#2035	C₂	semidirect
9. C₁₉×#2024	C₂	semidirect
10. C₁₉×#2023	C₂	semidirect
11. C₁₉×#1817	C₂	semidirect
156. #32772	C₁₉	direct (N × H)
218. #2857	C₂×C₁₉	semidirect
220. #2095	C₂×C₁₉	semidirect
221. #2094	C₂×C₁₉	semidirect
222. #2085	C₂×C₁₉	semidirect
223. #2042	C₂×C₁₉	semidirect
224. #2035	C₂×C₁₉	semidirect
226. #2024	C₂×C₁₉	semidirect
227. #2023	C₂×C₁₉	semidirect
228. #1817	C₂×C₁₉	semidirect
350. C₁₉	#32772	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×#2857	2
C₁₉×#2850	2
C₁₉×#2095	2
C₁₉×#2094	2
C₁₉×#2085	2
C₁₉×#2042	2
C₁₉×#2035	2
C₁₉×#2033	2
C₁₉×#2024	2
C₁₉×#2023	2
C₁₉×#1817	2
#32772	19

Subgroups — C19×#32772 #18038731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32772 #18038731