Subgroups — C₁₉×#24860 #18030819

Order 4864.

704 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3080	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉×#137	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2906	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2089	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2064	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1998	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1908	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1908	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1816	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1815	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
20	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#479	—	2	1	no	—
23	C₁₉×#479	—	2	1	no	—
24	C₁₉×#479	—	2	1	no	—
25	C₁₉×#479	—	2	1	no	—
26	C₁₉×#479	—	2	1	no	—
27	C₁₉×#479	—	2	1	no	—
28	C₁₉×#478	—	2	1	no	—
29	C₁₉×#478	—	2	1	no	—
30	C₁₉×#441	—	2	1	no	—
31	C₁₉×#440	—	2	1	no	—
32	C₄×Q₁₆×C₁₉	—	2	1	no	—
33	C₄×SD₁₆×C₁₉	—	2	1	no	—
34	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
36	C₁₉×#428	C₂²	1	1	yes	characteristic
37	C₁₉×#428	C₂²	1	1	yes	characteristic
38	C₁₉×#428	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
41	C₁₉×#424	—	2	1	no	—
42	C₁₉×#424	—	2	1	no	—
43	C₁₉×#424	C₂²	1	1	yes	characteristic
44	C₁₉×#424	C₂²	1	1	yes	characteristic
45	C₁₉×#423	—	2	1	no	—
46	C₁₉×#423	C₂²	1	1	yes	characteristic
47	C₁₉×#423	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
49	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₁₉×#419	C₂²	1	1	yes	characteristic
51	C₁₉×#417	C₂²	1	1	yes	characteristic
52	C₁₉×#417	C₂²	1	1	yes	characteristic
53	C₁₉×#417	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
56	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
57	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
58	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
59	C₁₉×#343	C₂²	1	1	yes	characteristic
60	C₁₉×#343	C₂²	1	1	yes	characteristic
61	C₁₉×#343	C₂²	1	1	yes	characteristic
62	C₁₉×#343	C₂²	1	1	yes	characteristic
63	C₁₉×#343	C₂²	1	1	yes	characteristic
64	C₁₉×#343	C₂²	1	1	yes	characteristic
65	C₁₉×#341	C₂²	1	1	yes	characteristic
66	C₁₉×#341	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×#137	—	2	2	no	—
70	C₁₉×#137	Q₈	1	4	yes	—
71	C₂×Q₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₁₉×#131	—	2	2	no	—
74	C₁₉×#131	—	2	2	no	—
75	C₁₉×#131	—	4	1	no	—
76	C₁₉×#131	—	4	1	no	—
77	C₂×M₁₆×C₁₉	—	2	1	no	—
78	C₂×M₁₆×C₁₉	—	2	1	no	—
79	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₉	—	2	1	no	—
86	C₂²×C₈×C₁₉	—	2	1	no	—
87	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
89	C₁₉×#125	—	2	1	no	—
90	C₁₉×#125	—	2	1	no	—
91	C₁₉×#125	—	2	1	no	—
92	C₁₉×#125	—	2	1	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
98	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
102	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
103	C₁₉×#117	—	2	1	no	—
104	C₁₉×#117	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₉	—	2	1	no	—
112	C₂×C₄²×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₁₉×#108	—	4	1	no	—
115	C₁₉×#108	—	4	1	no	—
116	C₁₉×#107	—	2	1	no	—
117	C₁₉×#107	—	2	1	no	—
118	C₁₉×#107	—	2	1	no	—
119	C₁₉×#107	—	2	1	no	—
120	C₁₉×#107	—	2	1	no	—
121	C₁₉×#106	—	2	1	no	—
122	C₁₉×#106	—	2	1	no	—
123	C₁₉×#106	—	2	1	no	—
124	C₁₉×#106	—	2	1	no	—
125	C₁₉×#106	—	2	1	no	—
126	C₁₉×C₄⋊C₈	—	2	1	no	—
127	C₁₉×C₄⋊C₈	—	2	1	no	—
128	C₁₉×C₄⋊C₈	—	2	1	no	—
129	C₁₉×C₄⋊C₈	—	2	1	no	—
130	C₁₉×C₄⋊C₈	—	2	1	no	—
131	C₁₉×C₄⋊C₈	—	2	1	no	—
132	C₁₉×C₄⋊C₈	—	2	1	no	—
133	C₁₉×C₄⋊C₈	—	2	1	no	—
134	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
135	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
136	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
137	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
138	C₁₉×#103	—	2	1	no	—
139	C₁₉×#103	—	2	1	no	—
140	C₁₉×#103	—	2	1	no	—
141	C₁₉×#103	—	2	1	no	—
142	C₁₉×#103	—	2	1	no	—
143	C₁₉×#103	—	2	1	no	—
144	C₁₉×#103	—	2	1	no	—
145	C₁₉×#103	—	2	1	no	—
146	C₁₉×#103	—	2	1	no	—
147	C₁₉×#102	—	2	1	no	—
148	C₁₉×#102	—	2	1	no	—
149	C₁₉×#102	—	2	1	no	—
150	C₁₉×#101	—	4	1	no	—
151	C₁₉×#101	—	4	1	no	—
152	C₁₉×#97	—	2	1	no	—
153	C₄×C₈×C₁₉	—	2	1	no	—
154	#41×C₁₉	—	2	1	no	—
155	#41×C₁₉	—	2	1	no	—
156	#41×C₁₉	C₂×Q₈	1	2	yes	—
157	#41×C₁₉	#41	1	2	yes	—
158	C₂×Q₈×C₁₉	—	2	1	no	—
159	C₂×Q₈×C₁₉	—	2	1	no	—
160	C₂×Q₈×C₁₉	—	2	1	no	—
161	C₂×Q₈×C₁₉	—	2	1	no	—
162	C₂×Q₈×C₁₉	—	2	1	no	—
163	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
165	C₂×D₄×C₁₉	—	2	1	no	—
166	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
177	Q₁₆×C₁₉	—	2	4	no	—
178	SD₁₆×C₁₉	—	2	4	no	—
179	M₁₆×C₁₉	—	2	1	no	—
180	M₁₆×C₁₉	—	2	1	no	—
181	M₁₆×C₁₉	—	2	1	no	—
182	M₁₆×C₁₉	—	2	1	no	—
183	M₁₆×C₁₉	—	2	1	no	—
184	M₁₆×C₁₉	—	2	1	no	—
185	M₁₆×C₁₉	—	2	1	no	—
186	M₁₆×C₁₉	—	2	1	no	—
187	M₁₆×C₁₉	—	2	1	no	—
188	M₁₆×C₁₉	—	2	1	no	—
189	M₁₆×C₁₉	—	2	1	no	—
190	M₁₆×C₁₉	—	4	2	no	—
191	M₁₆×C₁₉	—	4	2	no	—
192	M₁₆×C₁₉	C₂×Q₈	1	2	yes	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₂×C₈×C₁₉	—	2	1	no	—
195	C₂×C₈×C₁₉	—	2	1	no	—
196	C₂×C₈×C₁₉	—	2	1	no	—
197	C₂×C₈×C₁₉	—	2	1	no	—
198	C₂×C₈×C₁₉	—	2	1	no	—
199	C₂×C₈×C₁₉	—	2	1	no	—
200	C₂×C₈×C₁₉	—	2	1	no	—
201	C₂×C₈×C₁₉	—	2	1	no	—
202	C₂×C₈×C₁₉	—	2	1	no	—
203	C₂×C₈×C₁₉	—	4	2	no	—
204	C₂×C₈×C₁₉	—	4	2	no	—
205	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄⋊C₄×C₁₉	—	2	1	no	—
210	C₄⋊C₄×C₁₉	—	2	1	no	—
211	C₄⋊C₄×C₁₉	—	2	1	no	—
212	C₄⋊C₄×C₁₉	—	2	1	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	2	1	no	—
215	C₄⋊C₄×C₁₉	—	2	1	no	—
216	C₄⋊C₄×C₁₉	—	2	1	no	—
217	C₄⋊C₄×C₁₉	—	4	1	no	—
218	C₄⋊C₄×C₁₉	—	4	1	no	—
219	C₄⋊C₄×C₁₉	—	4	1	no	—
220	C₄⋊C₄×C₁₉	—	4	1	no	—
221	C₄⋊C₄×C₁₉	—	4	1	no	—
222	C₄⋊C₄×C₁₉	—	4	1	no	—
223	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₂²⋊C₄×C₁₉	—	2	1	no	—
226	C₂²⋊C₄×C₁₉	—	2	1	no	—
227	C₂²⋊C₄×C₁₉	—	2	1	no	—
228	C₄²×C₁₉	—	2	1	no	—
229	C₄²×C₁₉	—	2	1	no	—
230	C₄²×C₁₉	—	2	1	no	—
231	C₄²×C₁₉	—	4	1	no	—
232	C₄²×C₁₉	—	4	1	no	—
233	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
234	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
237	#24860	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂³×C₁₉	—	2	1	no	—
239	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
240	Q₈×C₁₉	—	2	1	no	—
241	Q₈×C₁₉	—	2	2	no	—
242	Q₈×C₁₉	—	2	2	no	—
243	Q₈×C₁₉	—	4	1	no	—
244	Q₈×C₁₉	—	4	1	no	—
245	Q₈×C₁₉	C₂²⋊Q₈	1	2	yes	—
246	D₄×C₁₉	—	2	2	no	—
247	D₄×C₁₉	—	2	2	no	—
248	D₄×C₁₉	—	2	1	no	—
249	D₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	8	1	no	—
265	C₂×C₄×C₁₉	—	8	1	no	—
266	C₂×C₄×C₁₉	—	8	1	no	—
267	C₂×C₄×C₁₉	—	8	1	no	—
268	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
269	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
270	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
271	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
275	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
277	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
278	C₈×C₁₉	—	2	2	no	—
279	C₈×C₁₉	—	2	1	no	—
280	C₈×C₁₉	—	2	1	no	—
281	C₈×C₁₉	—	2	1	no	—
282	C₈×C₁₉	—	2	1	no	—
283	C₈×C₁₉	—	4	1	no	—
284	C₈×C₁₉	—	4	1	no	—
285	C₈×C₁₉	—	4	1	no	—
286	C₈×C₁₉	—	4	1	no	—
287	C₈×C₁₉	—	4	1	no	—
288	#3080	C₂×C₁₉	1	1	yes	characteristic
289	C₂×#479	C₂×C₁₉	1	1	yes	characteristic, complemented
290	C₄×#137	C₂×C₁₉	1	1	yes	characteristic
291	#2906	C₂×C₁₉	1	1	yes	characteristic
292	#2090	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#2089	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#2064	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#2064	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1998	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#1950	C₂×C₁₉	1	1	yes	characteristic, complemented
298	#1908	C₂×C₁₉	1	1	yes	characteristic
299	#1908	C₂×C₁₉	1	1	yes	characteristic
300	#1816	C₂×C₁₉	1	1	yes	characteristic
301	#1815	C₂×C₁₉	1	1	yes	characteristic
302	#1801	C₂×C₁₉	1	1	yes	characteristic, complemented
303	C₂²×C₁₉	—	2	1	no	—
304	C₂²×C₁₉	—	2	1	no	—
305	C₂²×C₁₉	—	2	2	no	—
306	C₂²×C₁₉	—	4	1	no	—
307	C₂²×C₁₉	—	4	1	no	—
308	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
309	C₂²×C₁₉	#552	1	1	yes	characteristic
310	C₂²×C₁₉	#554	1	1	yes	characteristic
311	C₄×C₁₉	—	2	2	no	—
312	C₄×C₁₉	—	2	1	no	—
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	—	2	1	no	—
316	C₄×C₁₉	—	4	2	no	—
317	C₄×C₁₉	—	4	1	no	—
318	C₄×C₁₉	—	4	1	no	—
319	C₄×C₁₉	—	8	1	no	—
320	C₄×C₁₉	—	8	1	no	—
321	C₄×C₁₉	—	8	1	no	—
322	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
323	C₄×C₁₉	#537	1	1	yes	characteristic
324	C₄×C₁₉	#546	1	1	yes	characteristic
325	C₄×C₁₉	D₄×Q₈	1	1	yes	characteristic
326	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
327	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
330	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
331	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
332	#479	—	2	1	no	—
333	#479	—	2	1	no	—
334	#479	—	2	1	no	—
335	#479	—	2	1	no	—
336	#479	—	2	1	no	—
337	#479	—	2	1	no	—
338	#478	—	2	1	no	—
339	#478	—	2	1	no	—
340	#441	—	2	1	no	—
341	#440	—	2	1	no	—
342	C₄×Q₁₆	—	2	1	no	—
343	C₄×SD₁₆	—	2	1	no	—
344	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
345	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
346	#428	C₂²×C₁₉	1	1	yes	characteristic
347	#428	C₂²×C₁₉	1	1	yes	characteristic
348	#428	C₂²×C₁₉	1	1	yes	characteristic
349	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
350	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
351	#424	—	2	1	no	—
352	#424	—	2	1	no	—
353	#424	C₂²×C₁₉	1	1	yes	characteristic
354	#424	C₂²×C₁₉	1	1	yes	characteristic
355	#423	—	2	1	no	—
356	#423	C₂²×C₁₉	1	1	yes	characteristic
357	#423	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×C₄⋊C₈	—	2	1	no	—
359	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
360	#419	C₂²×C₁₉	1	1	yes	characteristic
361	#417	C₂²×C₁₉	1	1	yes	characteristic
362	#417	C₂²×C₁₉	1	1	yes	characteristic
363	#417	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
368	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
369	#343	C₂²×C₁₉	1	1	yes	characteristic
370	#343	C₂²×C₁₉	1	1	yes	characteristic
371	#343	C₂²×C₁₉	1	1	yes	characteristic
372	#343	C₂²×C₁₉	1	1	yes	characteristic
373	#343	C₂²×C₁₉	1	1	yes	characteristic
374	#343	C₂²×C₁₉	1	1	yes	characteristic
375	#341	C₂²×C₁₉	1	1	yes	characteristic
376	#341	C₂²×C₁₉	1	1	yes	characteristic
377	C₂×C₁₉	—	2	1	no	—
378	C₂×C₁₉	—	2	1	no	—
379	C₂×C₁₉	—	4	2	no	—
380	C₂×C₁₉	#2417	1	1	yes	characteristic
381	C₂×C₁₉	#3067	1	1	yes	characteristic
382	C₂×C₁₉	#3069	1	1	yes	characteristic
383	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
384	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
385	#137	—	2	2	no	—
386	#137	Q₈×C₁₉	1	4	yes	—
387	C₂×Q₁₆	—	2	1	no	—
388	C₂×SD₁₆	—	2	1	no	—
389	#131	—	2	2	no	—
390	#131	—	2	2	no	—
391	#131	—	4	1	no	—
392	#131	—	4	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	1	no	—
395	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
396	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
397	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
398	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
399	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
400	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
401	C₂²×C₈	—	2	1	no	—
402	C₂²×C₈	—	2	1	no	—
403	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
405	#125	—	2	1	no	—
406	#125	—	2	1	no	—
407	#125	—	2	1	no	—
408	#125	—	2	1	no	—
409	C₄×Q₈	—	2	1	no	—
410	C₄×Q₈	—	2	1	no	—
411	C₄×Q₈	—	2	1	no	—
412	C₄×Q₈	—	2	1	no	—
413	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
414	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	—	2	1	no	—
417	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
418	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
419	#117	—	2	1	no	—
420	#117	C₂³×C₁₉	1	1	yes	characteristic
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
430	#108	—	4	1	no	—
431	#108	—	4	1	no	—
432	#107	—	2	1	no	—
433	#107	—	2	1	no	—
434	#107	—	2	1	no	—
435	#107	—	2	1	no	—
436	#107	—	2	1	no	—
437	#106	—	2	1	no	—
438	#106	—	2	1	no	—
439	#106	—	2	1	no	—
440	#106	—	2	1	no	—
441	#106	—	2	1	no	—
442	C₄⋊C₈	—	2	1	no	—
443	C₄⋊C₈	—	2	1	no	—
444	C₄⋊C₈	—	2	1	no	—
445	C₄⋊C₈	—	2	1	no	—
446	C₄⋊C₈	—	2	1	no	—
447	C₄⋊C₈	—	2	1	no	—
448	C₄⋊C₈	—	2	1	no	—
449	C₄⋊C₈	—	2	1	no	—
450	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
451	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
452	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
453	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
454	#103	—	2	1	no	—
455	#103	—	2	1	no	—
456	#103	—	2	1	no	—
457	#103	—	2	1	no	—
458	#103	—	2	1	no	—
459	#103	—	2	1	no	—
460	#103	—	2	1	no	—
461	#103	—	2	1	no	—
462	#103	—	2	1	no	—
463	#102	—	2	1	no	—
464	#102	—	2	1	no	—
465	#102	—	2	1	no	—
466	#101	—	4	1	no	—
467	#101	—	4	1	no	—
468	#97	—	2	1	no	—
469	C₄×C₈	—	2	1	no	—
470	C₁₉	#24860	1	1	yes	characteristic, direct product factor, Sylow
471	#41	—	2	1	no	—
472	#41	—	2	1	no	—
473	#41	C₂×Q₈×C₁₉	1	2	yes	—
474	#41	#41×C₁₉	1	2	yes	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
492	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
493	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
494	Q₁₆	—	2	4	no	—
495	SD₁₆	—	2	4	no	—
496	M₁₆	—	2	1	no	—
497	M₁₆	—	2	1	no	—
498	M₁₆	—	2	1	no	—
499	M₁₆	—	2	1	no	—
500	M₁₆	—	2	1	no	—
501	M₁₆	—	2	1	no	—
502	M₁₆	—	2	1	no	—
503	M₁₆	—	2	1	no	—
504	M₁₆	—	2	1	no	—
505	M₁₆	—	2	1	no	—
506	M₁₆	—	2	1	no	—
507	M₁₆	—	4	2	no	—
508	M₁₆	—	4	2	no	—
509	M₁₆	C₂×Q₈×C₁₉	1	2	yes	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	4	2	no	—
521	C₂×C₈	—	4	2	no	—
522	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
523	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	4	1	no	—
535	C₄⋊C₄	—	4	1	no	—
536	C₄⋊C₄	—	4	1	no	—
537	C₄⋊C₄	—	4	1	no	—
538	C₄⋊C₄	—	4	1	no	—
539	C₄⋊C₄	—	4	1	no	—
540	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
541	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	2	1	no	—
544	C₂²⋊C₄	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	4	1	no	—
549	C₄²	—	4	1	no	—
550	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
551	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
552	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
553	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
554	C₂³	—	2	1	no	—
555	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
556	Q₈	—	2	1	no	—
557	Q₈	—	2	2	no	—
558	Q₈	—	2	2	no	—
559	Q₈	—	4	1	no	—
560	Q₈	—	4	1	no	—
561	Q₈	C₁₉×C₂²⋊Q₈	1	2	yes	—
562	D₄	—	2	2	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	1	no	—
565	D₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	8	1	no	—
581	C₂×C₄	—	8	1	no	—
582	C₂×C₄	—	8	1	no	—
583	C₂×C₄	—	8	1	no	—
584	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
585	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
586	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
587	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
589	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
590	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
591	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
592	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
593	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
594	C₈	—	2	2	no	—
595	C₈	—	2	1	no	—
596	C₈	—	2	1	no	—
597	C₈	—	2	1	no	—
598	C₈	—	2	1	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₈	—	4	1	no	—
602	C₈	—	4	1	no	—
603	C₈	—	4	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
610	C₂²	C₁₉×#552	1	1	yes	characteristic
611	C₂²	C₁₉×#554	1	1	yes	characteristic
612	C₄	—	2	2	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	8	1	no	—
621	C₄	—	8	1	no	—
622	C₄	—	8	1	no	—
623	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
624	C₄	C₁₉×#537	1	1	yes	characteristic
625	C₄	C₁₉×#546	1	1	yes	characteristic
626	C₄	D₄×Q₈×C₁₉	1	1	yes	characteristic
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	4	2	no	—
630	C₂	C₁₉×#2417	1	1	yes	characteristic
631	C₂	C₁₉×#3067	1	1	yes	characteristic
632	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#479	C₂	semidirect
5. C₁₉×#2090	C₂	semidirect
6. C₁₉×#2089	C₂	semidirect
7. C₁₉×#2064	C₂	semidirect
8. C₁₉×#2064	C₂	semidirect
9. C₁₉×#1998	C₂	semidirect
10. C₁₉×#1950	C₂	semidirect
15. C₁₉×#1801	C₂	semidirect
237. #24860	C₁₉	direct (N × H)
289. C₂×#479	C₂×C₁₉	semidirect
292. #2090	C₂×C₁₉	semidirect
293. #2089	C₂×C₁₉	semidirect
294. #2064	C₂×C₁₉	semidirect
295. #2064	C₂×C₁₉	semidirect
296. #1998	C₂×C₁₉	semidirect
297. #1950	C₂×C₁₉	semidirect
302. #1801	C₂×C₁₉	semidirect
470. C₁₉	#24860	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×#3080	2
C₂×C₁₉×#479	2
C₄×C₁₉×#137	2
C₁₉×#2906	2
C₁₉×#2090	2
C₁₉×#2089	2
C₁₉×#2064	2
C₁₉×#1998	2
C₁₉×#1950	2
C₁₉×#1908	2
C₁₉×#1816	2
C₁₉×#1815	2
C₁₉×#1801	2
#24860	19

Subgroups — C19×#24860 #18030819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24860 #18030819