Subgroups — C₁₉×#32890 #18038849

Order 4864.

3688 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#454	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#453	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3006	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2431	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1793	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1792	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1789	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1785	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#585	—	2	8	no	—
11	C₁₉×#585	—	2	8	no	—
12	C₂×C₁₉×2₋¹⁺⁴	—	2	2	no	—
13	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	2	yes	—
14	C₂×C₁₉×H(5,𝔽₂)	—	2	2	no	—
15	C₂×C₁₉×H(5,𝔽₂)	—	2	2	no	—
16	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	2	yes	—
17	C₂²×#41×C₁₉	—	2	4	no	—
18	C₂²×#41×C₁₉	—	2	2	no	—
19	C₂²×#41×C₁₉	C₂²	1	2	yes	—
20	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
22	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#454	—	2	8	no	—
26	C₁₉×#453	—	2	8	no	—
27	C₁₉×#449	—	2	4	no	—
28	C₁₉×#448	—	2	2	no	—
29	C₁₉×#447	—	2	2	no	—
30	C₂×C₁₉×#104	C₂²	1	4	yes	complemented
31	C₂×C₁₉×#104	C₂²	1	4	yes	complemented
32	C₁₉×#417	C₂²	1	4	yes	complemented
33	C₂×C₁₉×#101	C₂²	1	2	yes	complemented
34	C₂×C₁₉×#100	C₂²	1	2	yes	complemented
35	C₁₉×#407	C₂²	1	2	yes	complemented
36	C₁₉×#392	—	2	2	no	—
37	C₁₉×#391	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#386	—	2	2	no	—
40	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×2₋¹⁺⁴	—	2	32	no	—
42	C₁₉×2₋¹⁺⁴	—	2	8	no	—
43	C₁₉×2₋¹⁺⁴	—	2	4	no	—
44	C₁₉×2₋¹⁺⁴	D₄	1	8	yes	complemented
45	C₁₉×H(5,𝔽₂)	—	2	16	no	—
46	C₁₉×H(5,𝔽₂)	—	2	32	no	—
47	C₁₉×H(5,𝔽₂)	—	2	16	no	—
48	C₁₉×H(5,𝔽₂)	—	2	8	no	—
49	C₁₉×H(5,𝔽₂)	—	2	4	no	—
50	C₁₉×H(5,𝔽₂)	D₄	1	8	yes	complemented
51	C₂×#41×C₁₉	—	2	4	no	—
52	C₂×#41×C₁₉	—	2	8	no	—
53	C₂×#41×C₁₉	—	2	4	no	—
54	C₂×#41×C₁₉	—	2	32	no	—
55	C₂×#41×C₁₉	—	2	32	no	—
56	C₂×#41×C₁₉	—	2	16	no	—
57	C₂×#41×C₁₉	—	2	16	no	—
58	C₂×#41×C₁₉	—	2	8	no	—
59	C₂×#41×C₁₉	—	2	8	no	—
60	C₂×#41×C₁₉	—	2	4	no	—
61	C₂×#41×C₁₉	—	2	4	no	—
62	C₂×#41×C₁₉	—	2	4	no	—
63	C₂×#41×C₁₉	—	2	4	no	—
64	C₂×#41×C₁₉	—	2	2	no	—
65	C₂×#41×C₁₉	—	2	2	no	—
66	C₂×#41×C₁₉	—	2	4	no	—
67	C₂×#41×C₁₉	—	2	2	no	—
68	C₂×#41×C₁₉	—	2	2	no	—
69	C₂×#41×C₁₉	D₄	1	4	yes	complemented
70	C₂×#41×C₁₉	C₂³	1	4	yes	—
71	C₂²×Q₈×C₁₉	—	2	2	no	—
72	C₂²×Q₈×C₁₉	—	2	4	no	—
73	C₂²×Q₈×C₁₉	D₄	1	2	yes	complemented
74	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₁₉	—	2	8	no	—
76	C₂²×D₄×C₁₉	—	2	2	no	—
77	C₂²×D₄×C₁₉	—	2	4	no	—
78	C₂²×D₄×C₁₉	—	2	2	no	—
79	C₂²×D₄×C₁₉	—	2	4	no	—
80	C₂²×D₄×C₁₉	—	2	2	no	—
81	C₂²×D₄×C₁₉	—	2	1	no	—
82	C₂²×D₄×C₁₉	D₄	1	2	yes	—
83	C₂²×D₄×C₁₉	D₄	1	2	yes	complemented
84	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₉	—	2	4	no	—
87	C₂³×C₄×C₁₉	—	2	2	no	—
88	C₂³×C₄×C₁₉	D₄	1	2	yes	—
89	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
91	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
92	C₂×SD₁₆×C₁₉	—	2	4	no	—
93	C₂×D₈×C₁₉	—	2	4	no	—
94	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
95	C₁₉×#127	—	2	4	no	—
96	C₁₉×#124	—	2	4	no	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#121	—	2	2	no	—
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₁₉×#104	—	2	8	no	—
107	C₁₉×#104	—	2	8	no	—
108	C₁₉×#103	—	2	4	no	—
109	C₁₉×#102	—	2	4	no	—
110	C₁₉×#101	—	2	4	no	—
111	C₁₉×#100	—	2	4	no	—
112	C₁₉×C₂²⋊C₈	—	2	2	no	—
113	C₁₉×C₂²⋊C₈	—	2	2	no	—
114	C₁₉×#95	—	2	1	no	—
115	C₁₉×#95	—	2	2	no	—
116	C₂⁴×C₁₉	—	2	4	no	—
117	C₂⁴×C₁₉	—	2	2	no	—
118	C₂⁴×C₁₉	—	2	1	no	—
119	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
120	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
121	#41×C₁₉	—	2	32	no	—
122	#41×C₁₉	—	2	8	no	—
123	#41×C₁₉	—	2	8	no	—
124	#41×C₁₉	—	2	16	no	—
125	#41×C₁₉	—	2	64	no	—
126	#41×C₁₉	—	2	32	no	—
127	#41×C₁₉	—	2	16	no	—
128	#41×C₁₉	—	2	16	no	—
129	#41×C₁₉	—	2	16	no	—
130	#41×C₁₉	—	2	16	no	—
131	#41×C₁₉	—	2	16	no	—
132	#41×C₁₉	—	2	8	no	—
133	#41×C₁₉	—	2	16	no	—
134	#41×C₁₉	—	2	8	no	—
135	#41×C₁₉	—	2	16	no	—
136	#41×C₁₉	—	2	16	no	—
137	#41×C₁₉	—	2	4	no	—
138	#41×C₁₉	—	2	4	no	—
139	#41×C₁₉	C₂×D₄	1	8	yes	—
140	#41×C₁₉	C₂×D₄	1	8	yes	—
141	C₂×Q₈×C₁₉	—	2	4	no	—
142	C₂×Q₈×C₁₉	—	2	16	no	—
143	C₂×Q₈×C₁₉	—	2	16	no	—
144	C₂×Q₈×C₁₉	—	2	16	no	—
145	C₂×Q₈×C₁₉	—	2	8	no	—
146	C₂×Q₈×C₁₉	—	2	2	no	—
147	C₂×Q₈×C₁₉	—	2	2	no	—
148	C₂×Q₈×C₁₉	—	2	2	no	—
149	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
150	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
151	C₂×D₄×C₁₉	—	2	8	no	—
152	C₂×D₄×C₁₉	—	2	4	no	—
153	C₂×D₄×C₁₉	—	2	64	no	—
154	C₂×D₄×C₁₉	—	2	16	no	—
155	C₂×D₄×C₁₉	—	2	16	no	—
156	C₂×D₄×C₁₉	—	2	8	no	—
157	C₂×D₄×C₁₉	—	2	8	no	—
158	C₂×D₄×C₁₉	—	2	16	no	—
159	C₂×D₄×C₁₉	—	2	4	no	—
160	C₂×D₄×C₁₉	—	2	4	no	—
161	C₂×D₄×C₁₉	—	2	16	no	—
162	C₂×D₄×C₁₉	—	2	4	no	—
163	C₂×D₄×C₁₉	—	2	4	no	—
164	C₂×D₄×C₁₉	—	2	16	no	—
165	C₂×D₄×C₁₉	—	2	8	no	—
166	C₂×D₄×C₁₉	—	2	2	no	—
167	C₂×D₄×C₁₉	—	2	4	no	—
168	C₂×D₄×C₁₉	—	2	2	no	—
169	C₂×D₄×C₁₉	—	2	2	no	—
170	C₂×D₄×C₁₉	—	2	2	no	—
171	C₂×D₄×C₁₉	—	2	2	no	—
172	C₂×D₄×C₁₉	—	2	2	no	—
173	C₂×D₄×C₁₉	—	4	4	no	—
174	C₂×D₄×C₁₉	—	4	2	no	—
175	C₂×D₄×C₁₉	—	4	4	no	—
176	C₂×D₄×C₁₉	—	8	2	no	—
177	C₂×D₄×C₁₉	—	8	2	no	—
178	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
179	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₁₉	—	2	4	no	—
181	C₂²×C₄×C₁₉	—	2	8	no	—
182	C₂²×C₄×C₁₉	—	2	32	no	—
183	C₂²×C₄×C₁₉	—	2	16	no	—
184	C₂²×C₄×C₁₉	—	2	2	no	—
185	C₂²×C₄×C₁₉	—	2	4	no	—
186	C₂²×C₄×C₁₉	—	2	4	no	—
187	C₂²×C₄×C₁₉	—	2	2	no	—
188	C₂²×C₄×C₁₉	—	2	2	no	—
189	C₂²×C₄×C₁₉	—	2	4	no	—
190	C₂²×C₄×C₁₉	—	2	4	no	—
191	C₂²×C₄×C₁₉	—	2	2	no	—
192	C₂²×C₄×C₁₉	—	2	2	no	—
193	C₂²×C₄×C₁₉	—	2	1	no	—
194	C₂²×C₄×C₁₉	—	2	1	no	—
195	C₂²×C₄×C₁₉	—	2	1	no	—
196	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
199	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
200	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
201	SD₁₆×C₁₉	—	4	8	no	—
202	D₈×C₁₉	—	4	8	no	—
203	M₁₆×C₁₉	—	2	4	no	—
204	M₁₆×C₁₉	—	2	4	no	—
205	C₂×C₈×C₁₉	—	2	4	no	—
206	C₄⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	4	2	no	—
208	C₂²⋊C₄×C₁₉	—	4	1	no	—
209	C₂²⋊C₄×C₁₉	—	4	1	no	—
210	C₂²⋊C₄×C₁₉	—	4	4	no	—
211	C₂²⋊C₄×C₁₉	—	8	2	no	—
212	C₄²×C₁₉	—	2	2	no	—
213	C₄²×C₁₉	—	2	2	no	—
214	#32890	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂³×C₁₉	—	2	8	no	—
216	C₂³×C₁₉	—	2	16	no	—
217	C₂³×C₁₉	—	2	2	no	—
218	C₂³×C₁₉	—	2	4	no	—
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	2	2	no	—
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	4	1	no	—
223	C₂³×C₁₉	—	4	1	no	—
224	C₂³×C₁₉	—	4	2	no	—
225	C₂³×C₁₉	—	4	2	no	—
226	C₂³×C₁₉	—	4	2	no	—
227	C₂³×C₁₉	—	4	2	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	—	8	2	no	—
232	C₂³×C₁₉	—	8	2	no	—
233	C₂³×C₁₉	—	8	4	no	—
234	C₂³×C₁₉	—	8	4	no	—
235	C₂³×C₁₉	#120	1	2	yes	—
236	C₂³×C₁₉	#120	1	4	yes	—
237	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
238	Q₈×C₁₉	—	2	16	no	—
239	Q₈×C₁₉	—	2	8	no	—
240	Q₈×C₁₉	—	2	4	no	—
241	Q₈×C₁₉	—	2	8	no	—
242	Q₈×C₁₉	#120	1	8	yes	—
243	D₄×C₁₉	—	2	32	no	—
244	D₄×C₁₉	—	2	16	no	—
245	D₄×C₁₉	—	2	16	no	—
246	D₄×C₁₉	—	2	16	no	—
247	D₄×C₁₉	—	2	8	no	—
248	D₄×C₁₉	—	2	8	no	—
249	D₄×C₁₉	—	2	8	no	—
250	D₄×C₁₉	—	2	8	no	—
251	D₄×C₁₉	—	2	4	no	—
252	D₄×C₁₉	—	4	4	no	—
253	D₄×C₁₉	—	8	8	no	—
254	D₄×C₁₉	—	8	4	no	—
255	D₄×C₁₉	#120	1	8	yes	—
256	C₂×C₄×C₁₉	—	2	16	no	—
257	C₂×C₄×C₁₉	—	2	8	no	—
258	C₂×C₄×C₁₉	—	2	16	no	—
259	C₂×C₄×C₁₉	—	2	8	no	—
260	C₂×C₄×C₁₉	—	2	32	no	—
261	C₂×C₄×C₁₉	—	2	8	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	2	no	—
265	C₂×C₄×C₁₉	—	2	4	no	—
266	C₂×C₄×C₁₉	—	2	2	no	—
267	C₂×C₄×C₁₉	—	2	4	no	—
268	C₂×C₄×C₁₉	—	2	8	no	—
269	C₂×C₄×C₁₉	—	2	8	no	—
270	C₂×C₄×C₁₉	—	2	4	no	—
271	C₂×C₄×C₁₉	—	2	2	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	2	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	#120	1	4	yes	—
280	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
281	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
282	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
283	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
284	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
285	C₈×C₁₉	—	4	4	no	—
286	C₂×#585	C₂×C₁₉	1	1	yes	characteristic, complemented
287	C₂×#454	C₂×C₁₉	1	2	yes	complemented
288	C₂×#453	C₂×C₁₉	1	2	yes	complemented
289	#3006	C₂×C₁₉	1	2	yes	complemented
290	#2431	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1793	C₂×C₁₉	1	2	yes	complemented
292	#1792	C₂×C₁₉	1	2	yes	complemented
293	#1789	C₂×C₁₉	1	2	yes	complemented
294	#1785	C₂×C₁₉	1	1	yes	characteristic, complemented
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	2	2	no	—
298	C₂²×C₁₉	—	2	4	no	—
299	C₂²×C₁₉	—	2	8	no	—
300	C₂²×C₁₉	—	2	2	no	—
301	C₂²×C₁₉	—	2	2	no	—
302	C₂²×C₁₉	—	4	4	no	—
303	C₂²×C₁₉	—	4	2	no	—
304	C₂²×C₁₉	—	4	4	no	—
305	C₂²×C₁₉	—	4	2	no	—
306	C₂²×C₁₉	—	4	4	no	—
307	C₂²×C₁₉	—	8	1	no	—
308	C₂²×C₁₉	—	8	1	no	—
309	C₂²×C₁₉	—	8	2	no	—
310	C₂²×C₁₉	—	8	2	no	—
311	C₂²×C₁₉	—	8	2	no	—
312	C₂²×C₁₉	—	8	8	no	—
313	C₂²×C₁₉	—	8	16	no	—
314	C₂²×C₁₉	—	8	1	no	—
315	C₂²×C₁₉	—	8	1	no	—
316	C₂²×C₁₉	—	8	1	no	—
317	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
318	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
319	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
320	C₄×C₁₉	—	2	1	no	—
321	C₄×C₁₉	—	2	8	no	—
322	C₄×C₁₉	—	2	4	no	—
323	C₄×C₁₉	—	2	1	no	—
324	C₄×C₁₉	—	4	2	no	—
325	C₄×C₁₉	—	8	1	no	—
326	C₄×C₁₉	—	8	1	no	—
327	C₄×C₁₉	C₂×#120	1	4	yes	—
328	#585	—	2	8	no	—
329	#585	—	2	8	no	—
330	C₂×2₋¹⁺⁴	—	2	2	no	—
331	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	2	yes	—
332	C₂×H(5,𝔽₂)	—	2	2	no	—
333	C₂×H(5,𝔽₂)	—	2	2	no	—
334	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	2	yes	—
335	C₂²×#41	—	2	4	no	—
336	C₂²×#41	—	2	2	no	—
337	C₂²×#41	C₂²×C₁₉	1	2	yes	—
338	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
339	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	complemented
340	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic, complemented
341	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic, complemented
342	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic, complemented
343	#454	—	2	8	no	—
344	#453	—	2	8	no	—
345	#449	—	2	4	no	—
346	#448	—	2	2	no	—
347	#447	—	2	2	no	—
348	C₂×#104	C₂²×C₁₉	1	4	yes	complemented
349	C₂×#104	C₂²×C₁₉	1	4	yes	complemented
350	#417	C₂²×C₁₉	1	4	yes	complemented
351	C₂×#101	C₂²×C₁₉	1	2	yes	complemented
352	C₂×#100	C₂²×C₁₉	1	2	yes	complemented
353	#407	C₂²×C₁₉	1	2	yes	complemented
354	#392	—	2	2	no	—
355	#391	C₂²×C₁₉	1	1	yes	characteristic, complemented
356	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
357	#386	—	2	2	no	—
358	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
359	C₂×C₁₉	—	2	1	no	—
360	C₂×C₁₉	—	2	1	no	—
361	C₂×C₁₉	—	4	2	no	—
362	C₂×C₁₉	—	4	4	no	—
363	C₂×C₁₉	—	4	8	no	—
364	C₂×C₁₉	—	16	1	no	—
365	C₂×C₁₉	#2846	1	1	yes	characteristic
366	C₂×C₁₉	#3018	1	1	yes	characteristic
367	C₂×C₁₉	#3021	1	1	yes	characteristic
368	2₋¹⁺⁴	—	2	32	no	—
369	2₋¹⁺⁴	—	2	8	no	—
370	2₋¹⁺⁴	—	2	4	no	—
371	2₋¹⁺⁴	D₄×C₁₉	1	8	yes	complemented
372	H(5,𝔽₂)	—	2	16	no	—
373	H(5,𝔽₂)	—	2	32	no	—
374	H(5,𝔽₂)	—	2	16	no	—
375	H(5,𝔽₂)	—	2	8	no	—
376	H(5,𝔽₂)	—	2	4	no	—
377	H(5,𝔽₂)	D₄×C₁₉	1	8	yes	complemented
378	C₂×#41	—	2	4	no	—
379	C₂×#41	—	2	8	no	—
380	C₂×#41	—	2	4	no	—
381	C₂×#41	—	2	32	no	—
382	C₂×#41	—	2	32	no	—
383	C₂×#41	—	2	16	no	—
384	C₂×#41	—	2	16	no	—
385	C₂×#41	—	2	8	no	—
386	C₂×#41	—	2	8	no	—
387	C₂×#41	—	2	4	no	—
388	C₂×#41	—	2	4	no	—
389	C₂×#41	—	2	4	no	—
390	C₂×#41	—	2	4	no	—
391	C₂×#41	—	2	2	no	—
392	C₂×#41	—	2	2	no	—
393	C₂×#41	—	2	4	no	—
394	C₂×#41	—	2	2	no	—
395	C₂×#41	—	2	2	no	—
396	C₂×#41	D₄×C₁₉	1	4	yes	complemented
397	C₂×#41	C₂³×C₁₉	1	4	yes	—
398	C₂²×Q₈	—	2	2	no	—
399	C₂²×Q₈	—	2	4	no	—
400	C₂²×Q₈	D₄×C₁₉	1	2	yes	complemented
401	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
402	C₂²×D₄	—	2	8	no	—
403	C₂²×D₄	—	2	2	no	—
404	C₂²×D₄	—	2	4	no	—
405	C₂²×D₄	—	2	2	no	—
406	C₂²×D₄	—	2	4	no	—
407	C₂²×D₄	—	2	2	no	—
408	C₂²×D₄	—	2	1	no	—
409	C₂²×D₄	D₄×C₁₉	1	2	yes	—
410	C₂²×D₄	D₄×C₁₉	1	2	yes	complemented
411	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
412	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
413	C₂³×C₄	—	2	4	no	—
414	C₂³×C₄	—	2	2	no	—
415	C₂³×C₄	D₄×C₁₉	1	2	yes	—
416	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
417	AGL(1,ℤ/8)	—	2	8	no	—
418	AGL(1,ℤ/8)	—	2	8	no	—
419	C₂×SD₁₆	—	2	4	no	—
420	C₂×D₈	—	2	4	no	—
421	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
422	#127	—	2	4	no	—
423	#124	—	2	4	no	—
424	#121	—	2	2	no	—
425	#121	—	2	2	no	—
426	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	2	no	—
430	C₂×C₂²⋊C₄	—	2	2	no	—
431	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
433	#104	—	2	8	no	—
434	#104	—	2	8	no	—
435	#103	—	2	4	no	—
436	#102	—	2	4	no	—
437	#101	—	2	4	no	—
438	#100	—	2	4	no	—
439	C₂²⋊C₈	—	2	2	no	—
440	C₂²⋊C₈	—	2	2	no	—
441	#95	—	2	1	no	—
442	#95	—	2	2	no	—
443	C₁₉	#32890	1	1	yes	characteristic, direct product factor, Sylow
444	C₂⁴	—	2	4	no	—
445	C₂⁴	—	2	2	no	—
446	C₂⁴	—	2	1	no	—
447	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
448	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
449	#41	—	2	32	no	—
450	#41	—	2	8	no	—
451	#41	—	2	8	no	—
452	#41	—	2	16	no	—
453	#41	—	2	64	no	—
454	#41	—	2	32	no	—
455	#41	—	2	16	no	—
456	#41	—	2	16	no	—
457	#41	—	2	16	no	—
458	#41	—	2	16	no	—
459	#41	—	2	16	no	—
460	#41	—	2	8	no	—
461	#41	—	2	16	no	—
462	#41	—	2	8	no	—
463	#41	—	2	16	no	—
464	#41	—	2	16	no	—
465	#41	—	2	4	no	—
466	#41	—	2	4	no	—
467	#41	C₂×D₄×C₁₉	1	8	yes	—
468	#41	C₂×D₄×C₁₉	1	8	yes	—
469	C₂×Q₈	—	2	4	no	—
470	C₂×Q₈	—	2	16	no	—
471	C₂×Q₈	—	2	16	no	—
472	C₂×Q₈	—	2	16	no	—
473	C₂×Q₈	—	2	8	no	—
474	C₂×Q₈	—	2	2	no	—
475	C₂×Q₈	—	2	2	no	—
476	C₂×Q₈	—	2	2	no	—
477	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
478	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
479	C₂×D₄	—	2	8	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	64	no	—
482	C₂×D₄	—	2	16	no	—
483	C₂×D₄	—	2	16	no	—
484	C₂×D₄	—	2	8	no	—
485	C₂×D₄	—	2	8	no	—
486	C₂×D₄	—	2	16	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	16	no	—
490	C₂×D₄	—	2	4	no	—
491	C₂×D₄	—	2	4	no	—
492	C₂×D₄	—	2	16	no	—
493	C₂×D₄	—	2	8	no	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	2	4	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	4	4	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	—	4	4	no	—
504	C₂×D₄	—	8	2	no	—
505	C₂×D₄	—	8	2	no	—
506	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
507	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	8	no	—
510	C₂²×C₄	—	2	32	no	—
511	C₂²×C₄	—	2	16	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
526	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
527	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
529	SD₁₆	—	4	8	no	—
530	D₈	—	4	8	no	—
531	M₁₆	—	2	4	no	—
532	M₁₆	—	2	4	no	—
533	C₂×C₈	—	2	4	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₂²⋊C₄	—	4	2	no	—
536	C₂²⋊C₄	—	4	1	no	—
537	C₂²⋊C₄	—	4	1	no	—
538	C₂²⋊C₄	—	4	4	no	—
539	C₂²⋊C₄	—	8	2	no	—
540	C₄²	—	2	2	no	—
541	C₄²	—	2	2	no	—
542	C₂³	—	2	8	no	—
543	C₂³	—	2	16	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	4	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	2	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	2	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	8	2	no	—
559	C₂³	—	8	2	no	—
560	C₂³	—	8	4	no	—
561	C₂³	—	8	4	no	—
562	C₂³	C₁₉×#120	1	2	yes	—
563	C₂³	C₁₉×#120	1	4	yes	—
564	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
565	Q₈	—	2	16	no	—
566	Q₈	—	2	8	no	—
567	Q₈	—	2	4	no	—
568	Q₈	—	2	8	no	—
569	Q₈	C₁₉×#120	1	8	yes	—
570	D₄	—	2	32	no	—
571	D₄	—	2	16	no	—
572	D₄	—	2	16	no	—
573	D₄	—	2	16	no	—
574	D₄	—	2	8	no	—
575	D₄	—	2	8	no	—
576	D₄	—	2	8	no	—
577	D₄	—	2	8	no	—
578	D₄	—	2	4	no	—
579	D₄	—	4	4	no	—
580	D₄	—	8	8	no	—
581	D₄	—	8	4	no	—
582	D₄	C₁₉×#120	1	8	yes	—
583	C₂×C₄	—	2	16	no	—
584	C₂×C₄	—	2	8	no	—
585	C₂×C₄	—	2	16	no	—
586	C₂×C₄	—	2	8	no	—
587	C₂×C₄	—	2	32	no	—
588	C₂×C₄	—	2	8	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	8	no	—
596	C₂×C₄	—	2	8	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
607	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
608	C₂×C₄	C₁₉×#120	1	4	yes	—
609	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
610	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
611	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
612	C₈	—	4	4	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	4	no	—
619	C₂²	—	2	8	no	—
620	C₂²	—	4	4	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	4	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	4	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	8	2	no	—
628	C₂²	—	8	2	no	—
629	C₂²	—	8	2	no	—
630	C₂²	—	8	8	no	—
631	C₂²	—	8	16	no	—
632	C₂²	—	8	1	no	—
633	C₂²	—	8	1	no	—
634	C₂²	—	8	1	no	—
635	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
636	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
637	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
638	C₄	—	2	1	no	—
639	C₄	—	2	8	no	—
640	C₄	—	2	4	no	—
641	C₄	—	2	1	no	—
642	C₄	—	4	2	no	—
643	C₄	—	8	1	no	—
644	C₄	—	8	1	no	—
645	C₄	C₂×C₁₉×#120	1	4	yes	—
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	4	2	no	—
649	C₂	—	4	4	no	—
650	C₂	—	4	8	no	—
651	C₂	—	16	1	no	—
652	C₂	C₁₉×#2846	1	1	yes	characteristic
653	C₂	C₁₉×#3018	1	1	yes	characteristic
654	C₂	C₁₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#585	C₂	semidirect
2. C₂×C₁₉×#454	C₂	semidirect
3. C₂×C₁₉×#453	C₂	semidirect
4. C₁₉×#3006	C₂	semidirect
5. C₁₉×#2431	C₂	semidirect
6. C₁₉×#1793	C₂	semidirect
7. C₁₉×#1792	C₂	semidirect
8. C₁₉×#1789	C₂	semidirect
9. C₁₉×#1785	C₂	semidirect
21. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₁₉×#127	C₂²	semidirect
23. C₂×C₁₉×#124	C₂²	semidirect
24. C₂×C₁₉×#121	C₂²	semidirect
30. C₂×C₁₉×#104	C₂²	semidirect
31. C₂×C₁₉×#104	C₂²	semidirect
32. C₁₉×#417	C₂²	semidirect
33. C₂×C₁₉×#101	C₂²	semidirect
34. C₂×C₁₉×#100	C₂²	semidirect
35. C₁₉×#407	C₂²	semidirect
37. C₁₉×#391	C₂²	semidirect
38. C₁₉×#390	C₂²	semidirect
40. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
44. C₁₉×2₋¹⁺⁴	D₄	semidirect
50. C₁₉×H(5,𝔽₂)	D₄	semidirect
69. C₂×#41×C₁₉	D₄	semidirect
73. C₂²×Q₈×C₁₉	D₄	semidirect
83. C₂²×D₄×C₁₉	D₄	semidirect
214. #32890	C₁₉	direct (N × H)
286. C₂×#585	C₂×C₁₉	semidirect
287. C₂×#454	C₂×C₁₉	semidirect
288. C₂×#453	C₂×C₁₉	semidirect
289. #3006	C₂×C₁₉	semidirect
290. #2431	C₂×C₁₉	semidirect
291. #1793	C₂×C₁₉	semidirect
292. #1792	C₂×C₁₉	semidirect
293. #1789	C₂×C₁₉	semidirect
294. #1785	C₂×C₁₉	semidirect
339. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
340. C₂×#127	C₂²×C₁₉	semidirect
341. C₂×#124	C₂²×C₁₉	semidirect
342. C₂×#121	C₂²×C₁₉	semidirect
348. C₂×#104	C₂²×C₁₉	semidirect
349. C₂×#104	C₂²×C₁₉	semidirect
350. #417	C₂²×C₁₉	semidirect
351. C₂×#101	C₂²×C₁₉	semidirect
352. C₂×#100	C₂²×C₁₉	semidirect
353. #407	C₂²×C₁₉	semidirect
355. #391	C₂²×C₁₉	semidirect
356. #390	C₂²×C₁₉	semidirect
358. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
371. 2₋¹⁺⁴	D₄×C₁₉	semidirect
377. H(5,𝔽₂)	D₄×C₁₉	semidirect
396. C₂×#41	D₄×C₁₉	semidirect
400. C₂²×Q₈	D₄×C₁₉	semidirect
410. C₂²×D₄	D₄×C₁₉	semidirect
443. C₁₉	#32890	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×#585	2
C₂×C₁₉×#454	2
C₂×C₁₉×#453	2
C₁₉×#3006	2
C₁₉×#2431	2
C₁₉×#1793	2
C₁₉×#1792	2
C₁₉×#1789	2
C₁₉×#1785	2
#32890	19

Subgroups — C19×#32890 #18038849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32890 #18038849