Subgroups — C₁₉×#20615 #18026574

Order 4864.

3718 conjugacy classes of subgroups.

The subgroup lattice has 600 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	C₂²×C₁₉×#104	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2896	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#413	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2297	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×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₉×#104	—	2	8	no	—
24	C₂×C₁₉×#104	C₂²	1	8	yes	complemented
25	C₁₉×#419	—	2	2	no	—
26	C₁₉×#418	—	2	2	no	—
27	C₁₉×#417	C₂²	1	8	yes	complemented
28	C₁₉×#416	—	2	4	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	C₄×C₂²⋊C₄×C₁₉	—	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	2	no	—
94	C₁₉×#117	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄²×C₁₉	—	2	4	no	—
99	C₂×C₄²×C₁₉	—	2	1	no	—
100	C₂×C₄²×C₁₉	—	2	1	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	8	no	—
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	4	no	—
178	C₂²×C₄×C₁₉	—	2	4	no	—
179	C₂²×C₄×C₁₉	—	2	2	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	4	no	—
184	C₂²×C₄×C₁₉	—	4	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	4	yes	—
190	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₁₉	C₂×D₄	1	2	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	C₂²⋊C₄×C₁₉	—	4	8	no	—
201	C₂²⋊C₄×C₁₉	—	4	2	no	—
202	C₄²×C₁₉	—	2	4	no	—
203	C₄²×C₁₉	—	4	2	no	—
204	C₄²×C₁₉	—	4	1	no	—
205	C₄²×C₁₉	—	4	1	no	—
206	#20615	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	2	no	—
213	C₂³×C₁₉	—	4	4	no	—
214	C₂³×C₁₉	—	8	4	no	—
215	C₂³×C₁₉	—	8	8	no	—
216	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
217	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂³×C₁₉	#120	1	2	yes	—
219	C₂³×C₁₉	#120	1	2	yes	—
220	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
221	Q₈×C₁₉	—	2	16	no	—
222	Q₈×C₁₉	—	2	4	no	—
223	Q₈×C₁₉	—	2	4	no	—
224	Q₈×C₁₉	—	2	4	no	—
225	Q₈×C₁₉	—	2	8	no	—
226	Q₈×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
227	D₄×C₁₉	—	2	32	no	—
228	D₄×C₁₉	—	2	16	no	—
229	D₄×C₁₉	—	2	8	no	—
230	D₄×C₁₉	—	2	8	no	—
231	D₄×C₁₉	—	2	16	no	—
232	D₄×C₁₉	—	2	16	no	—
233	D₄×C₁₉	—	2	4	no	—
234	D₄×C₁₉	—	2	4	no	—
235	D₄×C₁₉	—	2	4	no	—
236	D₄×C₁₉	—	2	8	no	—
237	D₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
238	C₂×C₄×C₁₉	—	2	16	no	—
239	C₂×C₄×C₁₉	—	2	32	no	—
240	C₂×C₄×C₁₉	—	2	4	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	8	no	—
244	C₂×C₄×C₁₉	—	2	8	no	—
245	C₂×C₄×C₁₉	—	2	8	no	—
246	C₂×C₄×C₁₉	—	2	16	no	—
247	C₂×C₄×C₁₉	—	2	8	no	—
248	C₂×C₄×C₁₉	—	2	8	no	—
249	C₂×C₄×C₁₉	—	2	4	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
251	C₂×C₄×C₁₉	—	4	8	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	4	4	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
256	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
257	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
258	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
259	C₂×C₄×C₁₉	#120	1	4	yes	—
260	C₂×C₄×C₁₉	#120	1	4	yes	—
261	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#120	1	2	yes	—
263	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
264	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
268	C₈×C₁₉	—	4	4	no	—
269	C₂×#585	C₂×C₁₉	1	1	yes	characteristic
270	C₂²×#104	C₂×C₁₉	1	2	yes	complemented
271	#2896	C₂×C₁₉	1	2	yes	complemented
272	C₂×#413	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#2297	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1793	C₂×C₁₉	1	4	yes	complemented
275	#1792	C₂×C₁₉	1	4	yes	complemented
276	C₂²×C₁₉	—	2	2	no	—
277	C₂²×C₁₉	—	2	4	no	—
278	C₂²×C₁₉	—	2	4	no	—
279	C₂²×C₁₉	—	2	8	no	—
280	C₂²×C₁₉	—	4	2	no	—
281	C₂²×C₁₉	—	4	2	no	—
282	C₂²×C₁₉	—	4	4	no	—
283	C₂²×C₁₉	—	4	4	no	—
284	C₂²×C₁₉	—	4	8	no	—
285	C₂²×C₁₉	—	8	2	no	—
286	C₂²×C₁₉	—	8	8	no	—
287	C₂²×C₁₉	—	8	16	no	—
288	C₂²×C₁₉	#379	1	4	yes	—
289	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
290	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
291	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
292	C₄×C₁₉	—	2	8	no	—
293	C₄×C₁₉	—	2	4	no	—
294	C₄×C₁₉	—	4	4	no	—
295	C₄×C₁₉	—	8	2	no	—
296	C₄×C₁₉	#379	1	2	yes	—
297	C₄×C₁₉	#379	1	2	yes	—
298	C₄×C₁₉	C₂²×C₂²⋊C₄	1	2	yes	—
299	C₄×C₁₉	C₂×#120	1	2	yes	—
300	#585	—	2	8	no	—
301	#585	—	2	4	no	—
302	#585	C₄×C₁₉	1	8	yes	complemented
303	C₂×2₋¹⁺⁴	—	2	2	no	—
304	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	2	yes	—
305	C₂×H(5,𝔽₂)	—	2	2	no	—
306	C₂×H(5,𝔽₂)	—	2	2	no	—
307	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	2	yes	—
308	C₂²×#41	—	2	4	no	—
309	C₂²×#41	—	2	2	no	—
310	C₂²×#41	C₂²×C₁₉	1	2	yes	—
311	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
312	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	complemented
313	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
314	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
315	C₂×#104	—	2	8	no	—
316	C₂×#104	C₂²×C₁₉	1	8	yes	complemented
317	#419	—	2	2	no	—
318	#418	—	2	2	no	—
319	#417	C₂²×C₁₉	1	8	yes	complemented
320	#416	—	2	4	no	—
321	#413	—	2	4	no	—
322	C₂×#101	C₂²×C₁₉	1	2	yes	complemented
323	C₂×#100	C₂²×C₁₉	1	2	yes	complemented
324	#391	C₂²×C₁₉	1	2	yes	complemented
325	#390	C₂²×C₁₉	1	2	yes	complemented
326	#386	—	2	2	no	—
327	C₄×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₁₉	—	2	1	no	—
329	C₂×C₁₉	—	2	1	no	—
330	C₂×C₁₉	—	2	4	no	—
331	C₂×C₁₉	—	4	4	no	—
332	C₂×C₁₉	—	4	8	no	—
333	C₂×C₁₉	C₂×#379	1	1	yes	characteristic
334	C₂×C₁₉	#3018	1	2	yes	—
335	2₋¹⁺⁴	—	2	16	no	—
336	2₋¹⁺⁴	—	2	8	no	—
337	2₋¹⁺⁴	—	2	16	no	—
338	2₋¹⁺⁴	—	2	4	no	—
339	2₋¹⁺⁴	C₂×C₄×C₁₉	1	8	yes	complemented
340	H(5,𝔽₂)	—	2	16	no	—
341	H(5,𝔽₂)	—	2	16	no	—
342	H(5,𝔽₂)	—	2	8	no	—
343	H(5,𝔽₂)	—	2	16	no	—
344	H(5,𝔽₂)	—	2	16	no	—
345	H(5,𝔽₂)	—	2	4	no	—
346	H(5,𝔽₂)	C₂×C₄×C₁₉	1	8	yes	complemented
347	C₂×#41	—	2	4	no	—
348	C₂×#41	—	2	8	no	—
349	C₂×#41	—	2	4	no	—
350	C₂×#41	—	2	32	no	—
351	C₂×#41	—	2	16	no	—
352	C₂×#41	—	2	32	no	—
353	C₂×#41	—	2	4	no	—
354	C₂×#41	—	2	4	no	—
355	C₂×#41	—	2	16	no	—
356	C₂×#41	—	2	2	no	—
357	C₂×#41	—	2	2	no	—
358	C₂×#41	—	2	4	no	—
359	C₂×#41	—	2	2	no	—
360	C₂×#41	—	2	2	no	—
361	C₂×#41	—	2	4	no	—
362	C₂×#41	—	2	4	no	—
363	C₂×#41	—	2	4	no	—
364	C₂×#41	C₂×C₄×C₁₉	1	8	yes	—
365	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
366	C₂×#41	D₄×C₁₉	1	8	yes	—
367	C₂×#41	D₄×C₁₉	1	4	yes	—
368	C₂×#41	D₄×C₁₉	1	4	yes	—
369	C₂×#41	C₂³×C₁₉	1	4	yes	—
370	C₂²×Q₈	—	2	2	no	—
371	C₂²×Q₈	—	2	4	no	—
372	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
373	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
374	C₂²×D₄	—	2	8	no	—
375	C₂²×D₄	—	2	2	no	—
376	C₂²×D₄	—	2	4	no	—
377	C₂²×D₄	—	2	2	no	—
378	C₂²×D₄	—	2	4	no	—
379	C₂²×D₄	D₄×C₁₉	1	2	yes	—
380	C₂²×D₄	D₄×C₁₉	1	2	yes	—
381	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
382	C₂³×C₄	—	2	4	no	—
383	C₂³×C₄	—	2	2	no	—
384	C₂³×C₄	—	2	1	no	—
385	C₂³×C₄	D₄×C₁₉	1	2	yes	—
386	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
387	C₂×M₁₆	—	2	2	no	—
388	C₂×M₁₆	—	2	4	no	—
389	C₂×M₁₆	—	2	4	no	—
390	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
391	C₂²×C₈	—	2	2	no	—
392	#117	—	2	2	no	—
393	#117	—	2	2	no	—
394	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	4	no	—
397	C₂×C₄²	—	2	4	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
401	#104	—	2	16	no	—
402	#103	—	2	8	no	—
403	#102	—	2	8	no	—
404	#101	—	2	4	no	—
405	#100	—	2	4	no	—
406	#95	—	2	4	no	—
407	C₁₉	#20615	1	1	yes	characteristic, direct product factor, Sylow
408	C₂⁴	—	2	4	no	—
409	C₂⁴	—	2	2	no	—
410	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
411	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
412	#41	—	2	32	no	—
413	#41	—	2	64	no	—
414	#41	—	2	16	no	—
415	#41	—	2	32	no	—
416	#41	—	2	16	no	—
417	#41	—	2	16	no	—
418	#41	—	2	16	no	—
419	#41	—	2	16	no	—
420	#41	—	2	8	no	—
421	#41	—	2	8	no	—
422	#41	—	2	16	no	—
423	#41	—	2	8	no	—
424	#41	—	2	8	no	—
425	#41	—	2	8	no	—
426	#41	—	2	8	no	—
427	#41	—	2	8	no	—
428	#41	—	2	8	no	—
429	#41	—	2	8	no	—
430	#41	—	2	4	no	—
431	#41	—	2	4	no	—
432	#41	C₂²⋊C₄×C₁₉	1	16	yes	complemented
433	#41	C₂²×C₄×C₁₉	1	8	yes	—
434	#41	C₂×D₄×C₁₉	1	8	yes	—
435	C₂×Q₈	—	2	4	no	—
436	C₂×Q₈	—	2	16	no	—
437	C₂×Q₈	—	2	16	no	—
438	C₂×Q₈	—	2	16	no	—
439	C₂×Q₈	—	2	2	no	—
440	C₂×Q₈	—	2	4	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	C₂²⋊C₄×C₁₉	1	8	yes	complemented
444	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
445	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
446	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
447	C₂×D₄	—	2	8	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	64	no	—
450	C₂×D₄	—	2	16	no	—
451	C₂×D₄	—	2	16	no	—
452	C₂×D₄	—	2	16	no	—
453	C₂×D₄	—	2	16	no	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	8	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	4	no	—
460	C₂×D₄	—	2	16	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	—
466	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	complemented
467	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
468	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
469	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	8	no	—
472	C₂²×C₄	—	2	32	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	8	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	8	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	4	4	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
486	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
487	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
488	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
490	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
491	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
492	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
493	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
494	M₁₆	—	2	4	no	—
495	M₁₆	—	2	4	no	—
496	M₁₆	—	4	4	no	—
497	C₂×C₈	—	2	4	no	—
498	C₂×C₈	—	4	4	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	4	8	no	—
501	C₂²⋊C₄	—	4	2	no	—
502	C₄²	—	2	4	no	—
503	C₄²	—	4	2	no	—
504	C₄²	—	4	1	no	—
505	C₄²	—	4	1	no	—
506	C₂³	—	2	16	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	8	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	4	no	—
513	C₂³	—	8	4	no	—
514	C₂³	—	8	8	no	—
515	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
516	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
517	C₂³	C₁₉×#120	1	2	yes	—
518	C₂³	C₁₉×#120	1	2	yes	—
519	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
520	Q₈	—	2	16	no	—
521	Q₈	—	2	8	no	—
522	Q₈	—	2	4	no	—
523	Q₈	—	2	4	no	—
524	Q₈	—	2	4	no	—
525	Q₈	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
526	D₄	—	2	32	no	—
527	D₄	—	2	16	no	—
528	D₄	—	2	16	no	—
529	D₄	—	2	16	no	—
530	D₄	—	2	8	no	—
531	D₄	—	2	8	no	—
532	D₄	—	2	8	no	—
533	D₄	—	2	4	no	—
534	D₄	—	2	4	no	—
535	D₄	—	2	4	no	—
536	D₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
537	C₂×C₄	—	2	16	no	—
538	C₂×C₄	—	2	32	no	—
539	C₂×C₄	—	2	8	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	16	no	—
544	C₂×C₄	—	2	8	no	—
545	C₂×C₄	—	2	8	no	—
546	C₂×C₄	—	2	8	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	8	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	4	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
555	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
556	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
557	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
558	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
559	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
560	C₂×C₄	C₁₉×#120	1	2	yes	—
561	C₂×C₄	C₁₉×#120	1	4	yes	—
562	C₂×C₄	C₁₉×#120	1	4	yes	—
563	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
564	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
565	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
566	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
567	C₈	—	4	4	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	4	no	—
570	C₂²	—	2	4	no	—
571	C₂²	—	2	8	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	4	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	8	no	—
577	C₂²	—	8	2	no	—
578	C₂²	—	8	8	no	—
579	C₂²	—	8	16	no	—
580	C₂²	C₁₉×#379	1	4	yes	—
581	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
582	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
583	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
584	C₄	—	2	8	no	—
585	C₄	—	2	4	no	—
586	C₄	—	4	4	no	—
587	C₄	—	8	2	no	—
588	C₄	C₁₉×#379	1	2	yes	—
589	C₄	C₁₉×#379	1	2	yes	—
590	C₄	C₂²×C₂²⋊C₄×C₁₉	1	2	yes	—
591	C₄	C₂×C₁₉×#120	1	2	yes	—
592	C₂	—	2	1	no	—
593	C₂	—	2	1	no	—
594	C₂	—	2	4	no	—
595	C₂	—	4	4	no	—
596	C₂	—	4	8	no	—
597	C₂	C₂×C₁₉×#379	1	1	yes	characteristic
598	C₂	C₁₉×#3018	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#120
prime radical	C₂×C₁₉×#585	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#104	C₂	semidirect
3. C₁₉×#2896	C₂	semidirect
4. C₂×C₁₉×#413	C₂	semidirect
5. C₁₉×#2297	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×C₄²×C₁₉	C₂²	semidirect
24. C₂×C₁₉×#104	C₂²	semidirect
27. 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. #20615	C₁₉	direct (N × H)
270. C₂²×#104	C₂×C₁₉	semidirect
271. #2896	C₂×C₁₉	semidirect
272. C₂×#413	C₂×C₁₉	semidirect
273. #2297	C₂×C₁₉	semidirect
274. #1793	C₂×C₁₉	semidirect
275. #1792	C₂×C₁₉	semidirect
302. #585	C₄×C₁₉	semidirect
312. C₂²×M₁₆	C₂²×C₁₉	semidirect
313. C₂×#117	C₂²×C₁₉	semidirect
314. C₂²×C₄²	C₂²×C₁₉	semidirect
316. C₂×#104	C₂²×C₁₉	semidirect
319. #417	C₂²×C₁₉	semidirect
322. C₂×#101	C₂²×C₁₉	semidirect
323. C₂×#100	C₂²×C₁₉	semidirect
324. #391	C₂²×C₁₉	semidirect
325. #390	C₂²×C₁₉	semidirect
339. 2₋¹⁺⁴	C₂×C₄×C₁₉	semidirect
346. H(5,𝔽₂)	C₂×C₄×C₁₉	semidirect
407. C₁₉	#20615	direct (N × H)
432. #41	C₂²⋊C₄×C₁₉	semidirect
443. C₂×Q₈	C₂²⋊C₄×C₁₉	semidirect
466. 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
C₂²×C₁₉×#104	2
C₁₉×#2896	2
C₂×C₁₉×#413	2
C₁₉×#2297	2
C₁₉×#1793	2
C₁₉×#1792	2
#20615	19

Subgroups — C19×#20615 #18026574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20615 #18026574