Subgroups — C₁₉×#20618 #18026577

Order 4864.

3690 conjugacy classes of subgroups.

The subgroup lattice has 618 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
2	C₂×C₁₉×#421	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#417	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#413	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1793	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1792	C₂	1	4	yes	maximal, complemented
8	C₁₉×#585	—	2	8	no	—
9	C₁₉×#585	—	2	4	no	—
10	C₁₉×#585	C₄	1	8	yes	complemented
11	C₂×C₁₉×2₋¹⁺⁴	—	2	2	no	—
12	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	2	yes	—
13	C₂×C₁₉×H(5,𝔽₂)	—	2	2	no	—
14	C₂×C₁₉×H(5,𝔽₂)	—	2	2	no	—
15	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	2	yes	—
16	C₂²×#41×C₁₉	—	2	4	no	—
17	C₂²×#41×C₁₉	—	2	2	no	—
18	C₂²×#41×C₁₉	C₂²	1	2	yes	—
19	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	complemented
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#421	—	2	8	no	—
24	C₂×C₁₉×#104	C₂²	1	8	yes	complemented
25	C₁₉×#417	—	2	4	no	—
26	C₁₉×#417	C₂²	1	8	yes	complemented
27	C₂×C₁₉×#103	—	2	2	no	—
28	C₂×C₁₉×#102	—	2	2	no	—
29	C₁₉×#413	—	2	4	no	—
30	C₂×C₁₉×#101	C₂²	1	2	yes	complemented
31	C₂×C₁₉×#100	C₂²	1	2	yes	complemented
32	C₁₉×#391	C₂²	1	2	yes	complemented
33	C₁₉×#390	C₂²	1	2	yes	complemented
34	C₁₉×#386	—	2	2	no	—
35	C₁₉×#380	—	2	2	no	—
36	C₁₉×2₋¹⁺⁴	—	2	16	no	—
37	C₁₉×2₋¹⁺⁴	—	2	8	no	—
38	C₁₉×2₋¹⁺⁴	—	2	16	no	—
39	C₁₉×2₋¹⁺⁴	—	2	4	no	—
40	C₁₉×2₋¹⁺⁴	C₂×C₄	1	8	yes	complemented
41	C₁₉×H(5,𝔽₂)	—	2	16	no	—
42	C₁₉×H(5,𝔽₂)	—	2	16	no	—
43	C₁₉×H(5,𝔽₂)	—	2	8	no	—
44	C₁₉×H(5,𝔽₂)	—	2	16	no	—
45	C₁₉×H(5,𝔽₂)	—	2	16	no	—
46	C₁₉×H(5,𝔽₂)	—	2	4	no	—
47	C₁₉×H(5,𝔽₂)	C₂×C₄	1	8	yes	complemented
48	C₂×#41×C₁₉	—	2	4	no	—
49	C₂×#41×C₁₉	—	2	8	no	—
50	C₂×#41×C₁₉	—	2	4	no	—
51	C₂×#41×C₁₉	—	2	32	no	—
52	C₂×#41×C₁₉	—	2	16	no	—
53	C₂×#41×C₁₉	—	2	32	no	—
54	C₂×#41×C₁₉	—	2	4	no	—
55	C₂×#41×C₁₉	—	2	4	no	—
56	C₂×#41×C₁₉	—	2	16	no	—
57	C₂×#41×C₁₉	—	2	2	no	—
58	C₂×#41×C₁₉	—	2	2	no	—
59	C₂×#41×C₁₉	—	2	4	no	—
60	C₂×#41×C₁₉	—	2	2	no	—
61	C₂×#41×C₁₉	—	2	2	no	—
62	C₂×#41×C₁₉	—	2	4	no	—
63	C₂×#41×C₁₉	—	2	4	no	—
64	C₂×#41×C₁₉	—	2	4	no	—
65	C₂×#41×C₁₉	C₂×C₄	1	8	yes	—
66	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
67	C₂×#41×C₁₉	D₄	1	8	yes	—
68	C₂×#41×C₁₉	D₄	1	4	yes	—
69	C₂×#41×C₁₉	D₄	1	4	yes	—
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	—
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	D₄	1	2	yes	—
81	C₂²×D₄×C₁₉	D₄	1	2	yes	—
82	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₉	—	2	4	no	—
84	C₂³×C₄×C₁₉	—	2	2	no	—
85	C₂³×C₄×C₁₉	—	2	1	no	—
86	C₂³×C₄×C₁₉	D₄	1	2	yes	—
87	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₁₉	—	2	2	no	—
89	C₂×M₁₆×C₁₉	—	2	4	no	—
90	C₂×M₁₆×C₁₉	—	2	4	no	—
91	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
92	C₂²×C₈×C₁₉	—	2	2	no	—
93	C₁₉×#117	—	2	4	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
101	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
102	C₁₉×#104	—	2	16	no	—
103	C₁₉×#103	—	2	8	no	—
104	C₁₉×#102	—	2	8	no	—
105	C₁₉×#101	—	2	4	no	—
106	C₁₉×#100	—	2	4	no	—
107	C₁₉×#95	—	2	4	no	—
108	C₂⁴×C₁₉	—	2	4	no	—
109	C₂⁴×C₁₉	—	2	2	no	—
110	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
111	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
112	#41×C₁₉	—	2	32	no	—
113	#41×C₁₉	—	2	16	no	—
114	#41×C₁₉	—	2	64	no	—
115	#41×C₁₉	—	2	16	no	—
116	#41×C₁₉	—	2	16	no	—
117	#41×C₁₉	—	2	32	no	—
118	#41×C₁₉	—	2	16	no	—
119	#41×C₁₉	—	2	16	no	—
120	#41×C₁₉	—	2	8	no	—
121	#41×C₁₉	—	2	8	no	—
122	#41×C₁₉	—	2	16	no	—
123	#41×C₁₉	—	2	8	no	—
124	#41×C₁₉	—	2	8	no	—
125	#41×C₁₉	—	2	8	no	—
126	#41×C₁₉	—	2	8	no	—
127	#41×C₁₉	—	2	8	no	—
128	#41×C₁₉	—	2	8	no	—
129	#41×C₁₉	—	2	8	no	—
130	#41×C₁₉	—	2	4	no	—
131	#41×C₁₉	—	2	4	no	—
132	#41×C₁₉	C₂²⋊C₄	1	16	yes	complemented
133	#41×C₁₉	C₂²×C₄	1	8	yes	—
134	#41×C₁₉	C₂×D₄	1	8	yes	—
135	C₂×Q₈×C₁₉	—	2	4	no	—
136	C₂×Q₈×C₁₉	—	2	16	no	—
137	C₂×Q₈×C₁₉	—	2	16	no	—
138	C₂×Q₈×C₁₉	—	2	16	no	—
139	C₂×Q₈×C₁₉	—	2	2	no	—
140	C₂×Q₈×C₁₉	—	2	4	no	—
141	C₂×Q₈×C₁₉	—	2	2	no	—
142	C₂×Q₈×C₁₉	—	2	2	no	—
143	C₂×Q₈×C₁₉	C₂²⋊C₄	1	8	yes	complemented
144	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
145	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
146	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
147	C₂×D₄×C₁₉	—	2	8	no	—
148	C₂×D₄×C₁₉	—	2	4	no	—
149	C₂×D₄×C₁₉	—	2	16	no	—
150	C₂×D₄×C₁₉	—	2	64	no	—
151	C₂×D₄×C₁₉	—	2	16	no	—
152	C₂×D₄×C₁₉	—	2	16	no	—
153	C₂×D₄×C₁₉	—	2	16	no	—
154	C₂×D₄×C₁₉	—	2	8	no	—
155	C₂×D₄×C₁₉	—	2	4	no	—
156	C₂×D₄×C₁₉	—	2	4	no	—
157	C₂×D₄×C₁₉	—	2	8	no	—
158	C₂×D₄×C₁₉	—	2	4	no	—
159	C₂×D₄×C₁₉	—	2	4	no	—
160	C₂×D₄×C₁₉	—	2	16	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	4	no	—
163	C₂×D₄×C₁₉	—	2	2	no	—
164	C₂×D₄×C₁₉	—	2	2	no	—
165	C₂×D₄×C₁₉	C₂²⋊C₄	1	8	yes	—
166	C₂×D₄×C₁₉	C₂²⋊C₄	1	8	yes	complemented
167	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
168	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
169	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₁₉	—	2	4	no	—
171	C₂²×C₄×C₁₉	—	2	8	no	—
172	C₂²×C₄×C₁₉	—	2	32	no	—
173	C₂²×C₄×C₁₉	—	2	2	no	—
174	C₂²×C₄×C₁₉	—	2	8	no	—
175	C₂²×C₄×C₁₉	—	2	4	no	—
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	8	no	—
178	C₂²×C₄×C₁₉	—	2	2	no	—
179	C₂²×C₄×C₁₉	—	2	4	no	—
180	C₂²×C₄×C₁₉	—	2	4	no	—
181	C₂²×C₄×C₁₉	—	2	2	no	—
182	C₂²×C₄×C₁₉	—	2	2	no	—
183	C₂²×C₄×C₁₉	—	4	2	no	—
184	C₂²×C₄×C₁₉	—	8	2	no	—
185	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
186	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
187	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
190	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
192	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
194	M₁₆×C₁₉	—	2	4	no	—
195	M₁₆×C₁₉	—	2	4	no	—
196	M₁₆×C₁₉	—	4	4	no	—
197	C₂×C₈×C₁₉	—	2	4	no	—
198	C₂×C₈×C₁₉	—	4	4	no	—
199	C₄⋊C₄×C₁₉	—	2	4	no	—
200	C₄⋊C₄×C₁₉	—	4	1	no	—
201	C₄⋊C₄×C₁₉	—	4	1	no	—
202	C₄⋊C₄×C₁₉	—	4	2	no	—
203	C₂²⋊C₄×C₁₉	—	4	2	no	—
204	C₂²⋊C₄×C₁₉	—	8	4	no	—
205	C₄²×C₁₉	—	2	4	no	—
206	#20618	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₁₉	—	2	16	no	—
208	C₂³×C₁₉	—	2	2	no	—
209	C₂³×C₁₉	—	2	4	no	—
210	C₂³×C₁₉	—	2	2	no	—
211	C₂³×C₁₉	—	2	8	no	—
212	C₂³×C₁₉	—	4	1	no	—
213	C₂³×C₁₉	—	4	1	no	—
214	C₂³×C₁₉	—	4	2	no	—
215	C₂³×C₁₉	—	4	2	no	—
216	C₂³×C₁₉	—	8	2	no	—
217	C₂³×C₁₉	—	8	2	no	—
218	C₂³×C₁₉	—	8	4	no	—
219	C₂³×C₁₉	—	8	4	no	—
220	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
221	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
222	C₂³×C₁₉	#120	1	2	yes	—
223	C₂³×C₁₉	#120	1	2	yes	—
224	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
225	Q₈×C₁₉	—	2	16	no	—
226	Q₈×C₁₉	—	2	4	no	—
227	Q₈×C₁₉	—	2	4	no	—
228	Q₈×C₁₉	—	2	4	no	—
229	Q₈×C₁₉	—	2	8	no	—
230	Q₈×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
231	D₄×C₁₉	—	2	32	no	—
232	D₄×C₁₉	—	2	16	no	—
233	D₄×C₁₉	—	2	8	no	—
234	D₄×C₁₉	—	2	8	no	—
235	D₄×C₁₉	—	2	16	no	—
236	D₄×C₁₉	—	2	16	no	—
237	D₄×C₁₉	—	2	4	no	—
238	D₄×C₁₉	—	2	4	no	—
239	D₄×C₁₉	—	2	4	no	—
240	D₄×C₁₉	—	2	8	no	—
241	D₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
242	C₂×C₄×C₁₉	—	2	16	no	—
243	C₂×C₄×C₁₉	—	2	32	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	2	4	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	8	no	—
248	C₂×C₄×C₁₉	—	2	8	no	—
249	C₂×C₄×C₁₉	—	2	8	no	—
250	C₂×C₄×C₁₉	—	2	16	no	—
251	C₂×C₄×C₁₉	—	2	8	no	—
252	C₂×C₄×C₁₉	—	2	8	no	—
253	C₂×C₄×C₁₉	—	4	2	no	—
254	C₂×C₄×C₁₉	—	4	4	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	4	2	no	—
258	C₂×C₄×C₁₉	—	8	4	no	—
259	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
260	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
261	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
262	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
263	C₂×C₄×C₁₉	#120	1	4	yes	—
264	C₂×C₄×C₁₉	#120	1	4	yes	—
265	C₂×C₄×C₁₉	#120	1	2	yes	—
266	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
267	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
268	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
269	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
272	C₈×C₁₉	—	4	4	no	—
273	C₂×#585	C₂×C₁₉	1	1	yes	characteristic
274	C₂×#421	C₂×C₁₉	1	2	yes	complemented
275	C₂×#417	C₂×C₁₉	1	2	yes	complemented
276	C₂×#413	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#2311	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1793	C₂×C₁₉	1	4	yes	complemented
279	#1792	C₂×C₁₉	1	4	yes	complemented
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	2	2	no	—
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	—	2	2	no	—
284	C₂²×C₁₉	—	2	4	no	—
285	C₂²×C₁₉	—	2	8	no	—
286	C₂²×C₁₉	—	4	2	no	—
287	C₂²×C₁₉	—	4	2	no	—
288	C₂²×C₁₉	—	4	4	no	—
289	C₂²×C₁₉	—	4	2	no	—
290	C₂²×C₁₉	—	4	4	no	—
291	C₂²×C₁₉	—	4	2	no	—
292	C₂²×C₁₉	—	4	4	no	—
293	C₂²×C₁₉	—	8	2	no	—
294	C₂²×C₁₉	—	8	8	no	—
295	C₂²×C₁₉	—	8	16	no	—
296	C₂²×C₁₉	#379	1	4	yes	—
297	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
298	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
299	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
300	C₄×C₁₉	—	2	8	no	—
301	C₄×C₁₉	—	2	4	no	—
302	C₄×C₁₉	—	8	2	no	—
303	C₄×C₁₉	—	8	2	no	—
304	C₄×C₁₉	#379	1	2	yes	—
305	C₄×C₁₉	#379	1	2	yes	—
306	C₄×C₁₉	C₂²×C₂²⋊C₄	1	2	yes	—
307	C₄×C₁₉	C₂×#120	1	2	yes	—
308	#585	—	2	8	no	—
309	#585	—	2	4	no	—
310	#585	C₄×C₁₉	1	8	yes	complemented
311	C₂×2₋¹⁺⁴	—	2	2	no	—
312	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	2	yes	—
313	C₂×H(5,𝔽₂)	—	2	2	no	—
314	C₂×H(5,𝔽₂)	—	2	2	no	—
315	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	2	yes	—
316	C₂²×#41	—	2	4	no	—
317	C₂²×#41	—	2	2	no	—
318	C₂²×#41	C₂²×C₁₉	1	2	yes	—
319	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
320	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	complemented
321	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
322	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
323	#421	—	2	8	no	—
324	C₂×#104	C₂²×C₁₉	1	8	yes	complemented
325	#417	—	2	4	no	—
326	#417	C₂²×C₁₉	1	8	yes	complemented
327	C₂×#103	—	2	2	no	—
328	C₂×#102	—	2	2	no	—
329	#413	—	2	4	no	—
330	C₂×#101	C₂²×C₁₉	1	2	yes	complemented
331	C₂×#100	C₂²×C₁₉	1	2	yes	complemented
332	#391	C₂²×C₁₉	1	2	yes	complemented
333	#390	C₂²×C₁₉	1	2	yes	complemented
334	#386	—	2	2	no	—
335	#380	—	2	2	no	—
336	C₂×C₁₉	—	2	1	no	—
337	C₂×C₁₉	—	2	1	no	—
338	C₂×C₁₉	—	2	4	no	—
339	C₂×C₁₉	—	4	4	no	—
340	C₂×C₁₉	—	4	8	no	—
341	C₂×C₁₉	C₂×#379	1	1	yes	characteristic
342	C₂×C₁₉	#3021	1	1	yes	characteristic
343	C₂×C₁₉	#3022	1	1	yes	characteristic
344	2₋¹⁺⁴	—	2	16	no	—
345	2₋¹⁺⁴	—	2	8	no	—
346	2₋¹⁺⁴	—	2	16	no	—
347	2₋¹⁺⁴	—	2	4	no	—
348	2₋¹⁺⁴	C₂×C₄×C₁₉	1	8	yes	complemented
349	H(5,𝔽₂)	—	2	16	no	—
350	H(5,𝔽₂)	—	2	16	no	—
351	H(5,𝔽₂)	—	2	8	no	—
352	H(5,𝔽₂)	—	2	16	no	—
353	H(5,𝔽₂)	—	2	16	no	—
354	H(5,𝔽₂)	—	2	4	no	—
355	H(5,𝔽₂)	C₂×C₄×C₁₉	1	8	yes	complemented
356	C₂×#41	—	2	4	no	—
357	C₂×#41	—	2	8	no	—
358	C₂×#41	—	2	4	no	—
359	C₂×#41	—	2	32	no	—
360	C₂×#41	—	2	16	no	—
361	C₂×#41	—	2	32	no	—
362	C₂×#41	—	2	4	no	—
363	C₂×#41	—	2	4	no	—
364	C₂×#41	—	2	16	no	—
365	C₂×#41	—	2	2	no	—
366	C₂×#41	—	2	2	no	—
367	C₂×#41	—	2	4	no	—
368	C₂×#41	—	2	2	no	—
369	C₂×#41	—	2	2	no	—
370	C₂×#41	—	2	4	no	—
371	C₂×#41	—	2	4	no	—
372	C₂×#41	—	2	4	no	—
373	C₂×#41	C₂×C₄×C₁₉	1	8	yes	—
374	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
375	C₂×#41	D₄×C₁₉	1	8	yes	—
376	C₂×#41	D₄×C₁₉	1	4	yes	—
377	C₂×#41	D₄×C₁₉	1	4	yes	—
378	C₂×#41	C₂³×C₁₉	1	4	yes	—
379	C₂²×Q₈	—	2	2	no	—
380	C₂²×Q₈	—	2	4	no	—
381	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
382	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
383	C₂²×D₄	—	2	8	no	—
384	C₂²×D₄	—	2	2	no	—
385	C₂²×D₄	—	2	4	no	—
386	C₂²×D₄	—	2	2	no	—
387	C₂²×D₄	—	2	4	no	—
388	C₂²×D₄	D₄×C₁₉	1	2	yes	—
389	C₂²×D₄	D₄×C₁₉	1	2	yes	—
390	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
391	C₂³×C₄	—	2	4	no	—
392	C₂³×C₄	—	2	2	no	—
393	C₂³×C₄	—	2	1	no	—
394	C₂³×C₄	D₄×C₁₉	1	2	yes	—
395	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
396	C₂×M₁₆	—	2	2	no	—
397	C₂×M₁₆	—	2	4	no	—
398	C₂×M₁₆	—	2	4	no	—
399	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
400	C₂²×C₈	—	2	2	no	—
401	#117	—	2	4	no	—
402	C₂×C₄⋊C₄	—	2	2	no	—
403	C₂×C₄⋊C₄	—	2	2	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	4	no	—
409	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
410	#104	—	2	16	no	—
411	#103	—	2	8	no	—
412	#102	—	2	8	no	—
413	#101	—	2	4	no	—
414	#100	—	2	4	no	—
415	#95	—	2	4	no	—
416	C₁₉	#20618	1	1	yes	characteristic, direct product factor, Sylow
417	C₂⁴	—	2	4	no	—
418	C₂⁴	—	2	2	no	—
419	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
420	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
421	#41	—	2	32	no	—
422	#41	—	2	64	no	—
423	#41	—	2	16	no	—
424	#41	—	2	32	no	—
425	#41	—	2	16	no	—
426	#41	—	2	16	no	—
427	#41	—	2	16	no	—
428	#41	—	2	16	no	—
429	#41	—	2	8	no	—
430	#41	—	2	8	no	—
431	#41	—	2	16	no	—
432	#41	—	2	8	no	—
433	#41	—	2	8	no	—
434	#41	—	2	8	no	—
435	#41	—	2	8	no	—
436	#41	—	2	8	no	—
437	#41	—	2	8	no	—
438	#41	—	2	8	no	—
439	#41	—	2	4	no	—
440	#41	—	2	4	no	—
441	#41	C₂²⋊C₄×C₁₉	1	16	yes	complemented
442	#41	C₂²×C₄×C₁₉	1	8	yes	—
443	#41	C₂×D₄×C₁₉	1	8	yes	—
444	C₂×Q₈	—	2	4	no	—
445	C₂×Q₈	—	2	16	no	—
446	C₂×Q₈	—	2	16	no	—
447	C₂×Q₈	—	2	16	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	2	4	no	—
450	C₂×Q₈	—	2	2	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×Q₈	C₂²⋊C₄×C₁₉	1	8	yes	complemented
453	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
454	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
455	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
456	C₂×D₄	—	2	8	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	64	no	—
459	C₂×D₄	—	2	16	no	—
460	C₂×D₄	—	2	16	no	—
461	C₂×D₄	—	2	16	no	—
462	C₂×D₄	—	2	16	no	—
463	C₂×D₄	—	2	8	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	8	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	16	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	4	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	—
475	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	complemented
476	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
477	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
478	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	8	no	—
481	C₂²×C₄	—	2	32	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	8	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	8	2	no	—
494	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
495	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
496	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
497	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
499	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
500	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
501	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
502	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
503	M₁₆	—	2	4	no	—
504	M₁₆	—	2	4	no	—
505	M₁₆	—	4	4	no	—
506	C₂×C₈	—	2	4	no	—
507	C₂×C₈	—	4	4	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	4	1	no	—
510	C₄⋊C₄	—	4	1	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₂²⋊C₄	—	4	2	no	—
513	C₂²⋊C₄	—	8	4	no	—
514	C₄²	—	2	4	no	—
515	C₂³	—	2	16	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	8	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	2	no	—
523	C₂³	—	4	2	no	—
524	C₂³	—	8	2	no	—
525	C₂³	—	8	2	no	—
526	C₂³	—	8	4	no	—
527	C₂³	—	8	4	no	—
528	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
529	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
530	C₂³	C₁₉×#120	1	2	yes	—
531	C₂³	C₁₉×#120	1	2	yes	—
532	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
533	Q₈	—	2	16	no	—
534	Q₈	—	2	8	no	—
535	Q₈	—	2	4	no	—
536	Q₈	—	2	4	no	—
537	Q₈	—	2	4	no	—
538	Q₈	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
539	D₄	—	2	32	no	—
540	D₄	—	2	16	no	—
541	D₄	—	2	16	no	—
542	D₄	—	2	16	no	—
543	D₄	—	2	8	no	—
544	D₄	—	2	8	no	—
545	D₄	—	2	8	no	—
546	D₄	—	2	4	no	—
547	D₄	—	2	4	no	—
548	D₄	—	2	4	no	—
549	D₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
550	C₂×C₄	—	2	16	no	—
551	C₂×C₄	—	2	32	no	—
552	C₂×C₄	—	2	8	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	16	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	2	8	no	—
560	C₂×C₄	—	2	8	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	8	4	no	—
567	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
568	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
569	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
570	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
571	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
572	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
573	C₂×C₄	C₁₉×#120	1	2	yes	—
574	C₂×C₄	C₁₉×#120	1	4	yes	—
575	C₂×C₄	C₁₉×#120	1	4	yes	—
576	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
577	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
578	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
579	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
580	C₈	—	4	4	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	4	no	—
586	C₂²	—	2	8	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	4	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	4	no	—
594	C₂²	—	8	2	no	—
595	C₂²	—	8	8	no	—
596	C₂²	—	8	16	no	—
597	C₂²	C₁₉×#379	1	4	yes	—
598	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
599	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
600	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
601	C₄	—	2	8	no	—
602	C₄	—	2	4	no	—
603	C₄	—	8	2	no	—
604	C₄	—	8	2	no	—
605	C₄	C₁₉×#379	1	2	yes	—
606	C₄	C₁₉×#379	1	2	yes	—
607	C₄	C₂²×C₂²⋊C₄×C₁₉	1	2	yes	—
608	C₄	C₂×C₁₉×#120	1	2	yes	—
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	4	no	—
612	C₂	—	4	4	no	—
613	C₂	—	4	8	no	—
614	C₂	C₂×C₁₉×#379	1	1	yes	characteristic
615	C₂	C₁₉×#3021	1	1	yes	characteristic
616	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#585	C₂
LCS	G ▷ C₂×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
2. C₂×C₁₉×#421	C₂	semidirect
3. C₂×C₁₉×#417	C₂	semidirect
4. C₂×C₁₉×#413	C₂	semidirect
5. C₁₉×#2311	C₂	semidirect
6. C₁₉×#1793	C₂	semidirect
7. C₁₉×#1792	C₂	semidirect
10. C₁₉×#585	C₄	semidirect
20. C₂²×M₁₆×C₁₉	C₂²	semidirect
21. C₂×C₁₉×#117	C₂²	semidirect
22. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
24. C₂×C₁₉×#104	C₂²	semidirect
26. C₁₉×#417	C₂²	semidirect
30. C₂×C₁₉×#101	C₂²	semidirect
31. C₂×C₁₉×#100	C₂²	semidirect
32. C₁₉×#391	C₂²	semidirect
33. C₁₉×#390	C₂²	semidirect
40. C₁₉×2₋¹⁺⁴	C₂×C₄	semidirect
47. C₁₉×H(5,𝔽₂)	C₂×C₄	semidirect
132. #41×C₁₉	C₂²⋊C₄	semidirect
143. C₂×Q₈×C₁₉	C₂²⋊C₄	semidirect
166. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
206. #20618	C₁₉	direct (N × H)
274. C₂×#421	C₂×C₁₉	semidirect
275. C₂×#417	C₂×C₁₉	semidirect
276. C₂×#413	C₂×C₁₉	semidirect
277. #2311	C₂×C₁₉	semidirect
278. #1793	C₂×C₁₉	semidirect
279. #1792	C₂×C₁₉	semidirect
310. #585	C₄×C₁₉	semidirect
320. C₂²×M₁₆	C₂²×C₁₉	semidirect
321. C₂×#117	C₂²×C₁₉	semidirect
322. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
324. C₂×#104	C₂²×C₁₉	semidirect
326. #417	C₂²×C₁₉	semidirect
330. C₂×#101	C₂²×C₁₉	semidirect
331. C₂×#100	C₂²×C₁₉	semidirect
332. #391	C₂²×C₁₉	semidirect
333. #390	C₂²×C₁₉	semidirect
348. 2₋¹⁺⁴	C₂×C₄×C₁₉	semidirect
355. H(5,𝔽₂)	C₂×C₄×C₁₉	semidirect
416. C₁₉	#20618	direct (N × H)
441. #41	C₂²⋊C₄×C₁₉	semidirect
452. C₂×Q₈	C₂²⋊C₄×C₁₉	semidirect
475. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect

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×#421	2
C₂×C₁₉×#417	2
C₂×C₁₉×#413	2
C₁₉×#2311	2
C₁₉×#1793	2
C₁₉×#1792	2
#20618	19

Subgroups — C19×#20618 #18026577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20618 #18026577