Subgroups — C₁₉×#26852 #18032811

Order 4864.

698 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3137	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3097	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3082	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2947	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2064	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2061	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2052	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#2005	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1938	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1930	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1930	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1886	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1860	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1773	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
17	C₁₉×#544	C₂²	1	1	yes	characteristic
18	C₁₉×#536	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₉×#520	C₂²	1	1	yes	characteristic
21	C₁₉×#519	C₂²	1	1	yes	characteristic
22	C₁₉×#491	—	2	1	no	—
23	C₁₉×#489	—	2	1	no	—
24	C₁₉×#488	—	2	1	no	—
25	C₁₉×#487	—	2	1	no	—
26	C₁₉×#485	—	2	1	no	—
27	C₁₉×#485	—	2	1	no	—
28	C₁₉×#484	—	2	1	no	—
29	C₁₉×#483	—	2	1	no	—
30	C₁₉×#479	—	2	1	no	—
31	C₁₉×#479	—	2	1	no	—
32	C₁₉×#477	—	2	1	no	—
33	C₁₉×#475	—	2	1	no	—
34	C₁₉×#441	—	2	1	no	—
35	C₁₉×#440	—	2	1	no	—
36	C₄×Q₁₆×C₁₉	—	2	1	no	—
37	C₄×SD₁₆×C₁₉	—	2	1	no	—
38	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
39	C₁₉×#428	C₂²	1	1	yes	characteristic
40	C₁₉×#428	C₂²	1	1	yes	characteristic
41	C₁₉×#428	C₂²	1	1	yes	characteristic
42	C₁₉×#427	C₂²	1	1	yes	characteristic
43	C₁₉×#424	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
45	C₁₉×#419	C₂²	1	1	yes	characteristic
46	C₁₉×#419	C₂²	1	1	yes	characteristic
47	C₁₉×#419	C₂²	1	1	yes	characteristic
48	C₁₉×#417	C₂²	1	1	yes	characteristic
49	C₁₉×#416	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
56	C₁₉×#408	C₂²	1	1	yes	characteristic
57	C₁₉×#405	C₂²	1	1	yes	characteristic
58	C₁₉×#405	C₂²	1	1	yes	characteristic
59	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
60	C₁₉×#382	C₂²	1	1	yes	characteristic
61	C₁₉×#343	C₂²	1	1	yes	characteristic
62	C₁₉×#343	C₂²	1	1	yes	characteristic
63	C₁₉×#341	C₂²	1	1	yes	characteristic
64	C₁₉×#339	C₂²	1	1	yes	characteristic
65	C₁₉×#339	C₂²	1	1	yes	characteristic
66	C₁₉×#339	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×#137	—	2	2	no	—
71	C₁₉×#137	—	2	2	no	—
72	C₂×Q₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×C₄⋊Q₈	—	2	1	no	—
81	C₁₉×C₄⋊Q₈	—	2	1	no	—
82	C₁₉×C₄⋊Q₈	—	2	1	no	—
83	C₁₉×C₄⋊Q₈	—	2	2	no	—
84	C₁₉×C₄⋊Q₈	—	2	2	no	—
85	C₁₉×#125	—	2	1	no	—
86	C₁₉×#125	—	2	1	no	—
87	C₁₉×#124	—	2	1	no	—
88	C₁₉×#123	—	4	1	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	—	4	1	no	—
92	C₄×Q₈×C₁₉	—	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×D₄×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	—	4	1	no	—
99	C₁₉×#117	—	2	1	no	—
100	C₁₉×#117	—	4	1	no	—
101	C₁₉×#117	C₂³	1	1	yes	characteristic
102	C₁₉×#117	C₂³	1	1	yes	characteristic
103	C₁₉×#117	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
109	C₁₉×#108	—	2	2	no	—
110	C₁₉×#107	—	2	1	no	—
111	C₁₉×#107	—	2	1	no	—
112	C₁₉×#107	—	2	1	no	—
113	C₁₉×#107	D₄	1	1	yes	characteristic
114	C₁₉×#107	D₄	1	1	yes	characteristic
115	C₁₉×#106	—	2	1	no	—
116	C₁₉×#106	—	2	1	no	—
117	C₁₉×#106	—	2	1	no	—
118	C₁₉×#106	D₄	1	1	yes	characteristic
119	C₁₉×#106	D₄	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	—	2	1	no	—
121	C₁₉×C₄⋊C₈	—	2	1	no	—
122	C₁₉×#104	—	2	2	no	—
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#103	—	2	1	no	—
127	C₁₉×#103	—	2	1	no	—
128	C₁₉×#103	—	2	1	no	—
129	C₁₉×#103	—	2	1	no	—
130	C₁₉×#103	—	2	1	no	—
131	C₁₉×#103	—	2	1	no	—
132	C₁₉×#103	—	2	1	no	—
133	C₁₉×#103	—	2	1	no	—
134	C₁₉×#103	—	2	1	no	—
135	C₁₉×#103	—	2	1	no	—
136	C₁₉×#103	—	2	1	no	—
137	C₁₉×#103	—	2	1	no	—
138	C₁₉×#103	D₄	1	1	yes	characteristic
139	C₁₉×#103	D₄	1	1	yes	characteristic
140	C₁₉×#102	—	2	1	no	—
141	C₁₉×#102	D₄	1	1	yes	characteristic
142	C₁₉×#102	D₄	1	1	yes	characteristic
143	C₁₉×#101	—	2	2	no	—
144	C₁₉×#101	—	2	2	no	—
145	C₁₉×C₂²⋊C₈	—	2	1	no	—
146	C₁₉×C₂²⋊C₈	—	2	1	no	—
147	C₁₉×#97	—	2	1	no	—
148	C₁₉×#97	—	2	1	no	—
149	C₁₉×#97	—	2	2	no	—
150	C₄×C₈×C₁₉	—	2	1	no	—
151	C₄×C₈×C₁₉	—	2	1	no	—
152	C₁₉×#95	—	4	1	no	—
153	#41×C₁₉	—	2	1	no	—
154	#41×C₁₉	—	2	1	no	—
155	#41×C₁₉	—	2	1	no	—
156	#41×C₁₉	—	2	1	no	—
157	C₂×Q₈×C₁₉	—	2	1	no	—
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	—	2	1	no	—
164	C₂×Q₈×C₁₉	—	2	1	no	—
165	C₂×Q₈×C₁₉	—	2	1	no	—
166	C₂×Q₈×C₁₉	—	2	1	no	—
167	C₂×Q₈×C₁₉	—	2	1	no	—
168	C₂×Q₈×C₁₉	—	4	1	no	—
169	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂×Q₈×C₁₉	#41	1	2	yes	—
171	C₂×D₄×C₁₉	—	2	1	no	—
172	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	4	1	no	—
180	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
181	Q₁₆×C₁₉	—	2	4	no	—
182	SD₁₆×C₁₉	—	2	4	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	#41	1	2	yes	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	4	1	no	—
208	C₄⋊C₄×C₁₉	—	4	4	no	—
209	C₄⋊C₄×C₁₉	—	4	1	no	—
210	C₄⋊C₄×C₁₉	—	4	1	no	—
211	C₄⋊C₄×C₁₉	—	4	1	no	—
212	C₄⋊C₄×C₁₉	—	4	1	no	—
213	C₄⋊C₄×C₁₉	—	4	1	no	—
214	C₄⋊C₄×C₁₉	—	4	1	no	—
215	C₄⋊C₄×C₁₉	—	4	1	no	—
216	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
220	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
221	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
222	C₂²⋊C₄×C₁₉	—	2	1	no	—
223	C₂²⋊C₄×C₁₉	—	2	1	no	—
224	C₂²⋊C₄×C₁₉	—	2	1	no	—
225	C₂²⋊C₄×C₁₉	—	4	1	no	—
226	C₂²⋊C₄×C₁₉	—	4	1	no	—
227	C₂²⋊C₄×C₁₉	—	4	1	no	—
228	C₄²×C₁₉	—	2	1	no	—
229	C₄²×C₁₉	—	2	1	no	—
230	C₄²×C₁₉	—	2	1	no	—
231	C₄²×C₁₉	—	2	1	no	—
232	C₄²×C₁₉	—	4	1	no	—
233	C₄²×C₁₉	—	4	1	no	—
234	C₄²×C₁₉	—	4	1	no	—
235	C₄²×C₁₉	#41	1	2	yes	—
236	#26852	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂³×C₁₉	—	2	1	no	—
238	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
239	Q₈×C₁₉	—	2	2	no	—
240	Q₈×C₁₉	—	2	1	no	—
241	Q₈×C₁₉	—	2	1	no	—
242	Q₈×C₁₉	—	2	2	no	—
243	Q₈×C₁₉	—	4	1	no	—
244	Q₈×C₁₉	—	4	1	no	—
245	Q₈×C₁₉	—	4	1	no	—
246	Q₈×C₁₉	—	4	1	no	—
247	Q₈×C₁₉	—	4	1	no	—
248	Q₈×C₁₉	—	4	1	no	—
249	Q₈×C₁₉	—	16	1	no	—
250	D₄×C₁₉	—	2	1	no	—
251	D₄×C₁₉	—	2	1	no	—
252	D₄×C₁₉	—	4	1	no	—
253	D₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	2	2	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	8	1	no	—
275	C₂×C₄×C₁₉	—	8	1	no	—
276	C₂×C₄×C₁₉	—	16	1	no	—
277	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
280	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
283	C₈×C₁₉	—	2	2	no	—
284	C₈×C₁₉	—	2	1	no	—
285	C₈×C₁₉	—	2	1	no	—
286	C₈×C₁₉	—	2	1	no	—
287	C₈×C₁₉	—	2	1	no	—
288	C₈×C₁₉	—	4	1	no	—
289	C₈×C₁₉	—	4	1	no	—
290	C₈×C₁₉	—	4	1	no	—
291	#3137	C₂×C₁₉	1	1	yes	characteristic
292	#3097	C₂×C₁₉	1	1	yes	characteristic
293	#3082	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#2947	C₂×C₁₉	1	1	yes	characteristic
295	#2064	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#2061	C₂×C₁₉	1	1	yes	characteristic, complemented
297	#2052	C₂×C₁₉	1	1	yes	characteristic
298	#2005	C₂×C₁₉	1	1	yes	characteristic
299	#1960	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#1938	C₂×C₁₉	1	1	yes	characteristic
301	#1930	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1930	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#1886	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#1860	C₂×C₁₉	1	1	yes	characteristic
305	#1773	C₂×C₁₉	1	1	yes	characteristic, complemented
306	C₂²×C₁₉	—	2	1	no	—
307	C₂²×C₁₉	—	2	1	no	—
308	C₂²×C₁₉	—	4	1	no	—
309	C₂²×C₁₉	—	4	1	no	—
310	C₂²×C₁₉	—	4	1	no	—
311	C₂²×C₁₉	#542	1	1	yes	characteristic
312	C₂²×C₁₉	D₄²	1	1	yes	characteristic
313	C₂²×C₁₉	#551	1	1	yes	characteristic
314	C₄×C₁₉	—	4	2	no	—
315	C₄×C₁₉	—	4	1	no	—
316	C₄×C₁₉	—	4	2	no	—
317	C₄×C₁₉	—	4	1	no	—
318	C₄×C₁₉	—	4	1	no	—
319	C₄×C₁₉	—	4	1	no	—
320	C₄×C₁₉	—	4	1	no	—
321	C₄×C₁₉	—	4	1	no	—
322	C₄×C₁₉	—	4	1	no	—
323	C₄×C₁₉	—	8	1	no	—
324	C₄×C₁₉	—	8	1	no	—
325	C₄×C₁₉	—	8	1	no	—
326	C₄×C₁₉	#525	1	1	yes	characteristic
327	C₄×C₁₉	#532	1	1	yes	characteristic
328	C₄×C₁₉	#547	1	1	yes	characteristic
329	C₄×C₁₉	#548	1	1	yes	characteristic
330	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
331	#544	C₂²×C₁₉	1	1	yes	characteristic
332	#536	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
334	#520	C₂²×C₁₉	1	1	yes	characteristic
335	#519	C₂²×C₁₉	1	1	yes	characteristic
336	#491	—	2	1	no	—
337	#489	—	2	1	no	—
338	#488	—	2	1	no	—
339	#487	—	2	1	no	—
340	#485	—	2	1	no	—
341	#485	—	2	1	no	—
342	#484	—	2	1	no	—
343	#483	—	2	1	no	—
344	#479	—	2	1	no	—
345	#479	—	2	1	no	—
346	#477	—	2	1	no	—
347	#475	—	2	1	no	—
348	#441	—	2	1	no	—
349	#440	—	2	1	no	—
350	C₄×Q₁₆	—	2	1	no	—
351	C₄×SD₁₆	—	2	1	no	—
352	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
353	#428	C₂²×C₁₉	1	1	yes	characteristic
354	#428	C₂²×C₁₉	1	1	yes	characteristic
355	#428	C₂²×C₁₉	1	1	yes	characteristic
356	#427	C₂²×C₁₉	1	1	yes	characteristic
357	#424	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
359	#419	C₂²×C₁₉	1	1	yes	characteristic
360	#419	C₂²×C₁₉	1	1	yes	characteristic
361	#419	C₂²×C₁₉	1	1	yes	characteristic
362	#417	C₂²×C₁₉	1	1	yes	characteristic
363	#416	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×#103	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
370	#408	C₂²×C₁₉	1	1	yes	characteristic
371	#405	C₂²×C₁₉	1	1	yes	characteristic
372	#405	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
374	#382	C₂²×C₁₉	1	1	yes	characteristic
375	#343	C₂²×C₁₉	1	1	yes	characteristic
376	#343	C₂²×C₁₉	1	1	yes	characteristic
377	#341	C₂²×C₁₉	1	1	yes	characteristic
378	#339	C₂²×C₁₉	1	1	yes	characteristic
379	#339	C₂²×C₁₉	1	1	yes	characteristic
380	#339	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×C₁₉	—	2	1	no	—
382	C₂×C₁₉	—	2	1	no	—
383	C₂×C₁₉	—	8	1	no	—
384	C₂×C₁₉	#2461	1	1	yes	characteristic
385	C₂×C₁₉	#3289	1	1	yes	characteristic
386	C₂×C₁₉	#3289	1	1	yes	characteristic
387	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
388	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
389	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
390	#137	—	2	2	no	—
391	#137	—	2	2	no	—
392	C₂×Q₁₆	—	2	1	no	—
393	C₂×SD₁₆	—	2	1	no	—
394	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
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	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
400	C₄⋊Q₈	—	2	1	no	—
401	C₄⋊Q₈	—	2	1	no	—
402	C₄⋊Q₈	—	2	1	no	—
403	C₄⋊Q₈	—	2	2	no	—
404	C₄⋊Q₈	—	2	2	no	—
405	#125	—	2	1	no	—
406	#125	—	2	1	no	—
407	#124	—	2	1	no	—
408	#123	—	4	1	no	—
409	C₂²⋊Q₈	—	2	1	no	—
410	C₂²⋊Q₈	—	2	1	no	—
411	C₂²⋊Q₈	—	4	1	no	—
412	C₄×Q₈	—	2	1	no	—
413	C₄×Q₈	—	2	1	no	—
414	C₄×Q₈	—	2	1	no	—
415	C₄×Q₈	—	2	1	no	—
416	C₄×Q₈	—	2	1	no	—
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	4	1	no	—
419	#117	—	2	1	no	—
420	#117	—	4	1	no	—
421	#117	C₂³×C₁₉	1	1	yes	characteristic
422	#117	C₂³×C₁₉	1	1	yes	characteristic
423	#117	C₂³×C₁₉	1	1	yes	characteristic
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	4	1	no	—
426	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
429	#108	—	2	2	no	—
430	#107	—	2	1	no	—
431	#107	—	2	1	no	—
432	#107	—	2	1	no	—
433	#107	D₄×C₁₉	1	1	yes	characteristic
434	#107	D₄×C₁₉	1	1	yes	characteristic
435	#106	—	2	1	no	—
436	#106	—	2	1	no	—
437	#106	—	2	1	no	—
438	#106	D₄×C₁₉	1	1	yes	characteristic
439	#106	D₄×C₁₉	1	1	yes	characteristic
440	C₄⋊C₈	—	2	1	no	—
441	C₄⋊C₈	—	2	1	no	—
442	#104	—	2	2	no	—
443	#103	—	2	1	no	—
444	#103	—	2	1	no	—
445	#103	—	2	1	no	—
446	#103	—	2	1	no	—
447	#103	—	2	1	no	—
448	#103	—	2	1	no	—
449	#103	—	2	1	no	—
450	#103	—	2	1	no	—
451	#103	—	2	1	no	—
452	#103	—	2	1	no	—
453	#103	—	2	1	no	—
454	#103	—	2	1	no	—
455	#103	—	2	1	no	—
456	#103	—	2	1	no	—
457	#103	—	2	1	no	—
458	#103	D₄×C₁₉	1	1	yes	characteristic
459	#103	D₄×C₁₉	1	1	yes	characteristic
460	#102	—	2	1	no	—
461	#102	D₄×C₁₉	1	1	yes	characteristic
462	#102	D₄×C₁₉	1	1	yes	characteristic
463	#101	—	2	2	no	—
464	#101	—	2	2	no	—
465	C₂²⋊C₈	—	2	1	no	—
466	C₂²⋊C₈	—	2	1	no	—
467	#97	—	2	1	no	—
468	#97	—	2	1	no	—
469	#97	—	2	2	no	—
470	C₄×C₈	—	2	1	no	—
471	C₄×C₈	—	2	1	no	—
472	#95	—	4	1	no	—
473	C₁₉	#26852	1	1	yes	characteristic, direct product factor, Sylow
474	#41	—	2	1	no	—
475	#41	—	2	1	no	—
476	#41	—	2	1	no	—
477	#41	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	4	1	no	—
490	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₂×Q₈	#41×C₁₉	1	2	yes	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	4	1	no	—
501	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
502	Q₁₆	—	2	4	no	—
503	SD₁₆	—	2	4	no	—
504	M₁₆	—	2	1	no	—
505	M₁₆	—	2	1	no	—
506	M₁₆	—	2	1	no	—
507	M₁₆	—	2	1	no	—
508	M₁₆	—	2	1	no	—
509	M₁₆	—	2	1	no	—
510	M₁₆	—	2	1	no	—
511	M₁₆	#41×C₁₉	1	2	yes	—
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	C₂×D₄×C₁₉	1	1	yes	characteristic
521	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
522	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
523	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	4	1	no	—
529	C₄⋊C₄	—	4	4	no	—
530	C₄⋊C₄	—	4	1	no	—
531	C₄⋊C₄	—	4	1	no	—
532	C₄⋊C₄	—	4	1	no	—
533	C₄⋊C₄	—	4	1	no	—
534	C₄⋊C₄	—	4	1	no	—
535	C₄⋊C₄	—	4	1	no	—
536	C₄⋊C₄	—	4	1	no	—
537	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
538	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
539	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
540	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
541	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
542	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
543	C₂²⋊C₄	—	2	1	no	—
544	C₂²⋊C₄	—	2	1	no	—
545	C₂²⋊C₄	—	2	1	no	—
546	C₂²⋊C₄	—	4	1	no	—
547	C₂²⋊C₄	—	4	1	no	—
548	C₂²⋊C₄	—	4	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	4	1	no	—
554	C₄²	—	4	1	no	—
555	C₄²	—	4	1	no	—
556	C₄²	#41×C₁₉	1	2	yes	—
557	C₂³	—	2	1	no	—
558	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
559	Q₈	—	2	2	no	—
560	Q₈	—	2	1	no	—
561	Q₈	—	2	1	no	—
562	Q₈	—	2	2	no	—
563	Q₈	—	4	1	no	—
564	Q₈	—	4	1	no	—
565	Q₈	—	4	1	no	—
566	Q₈	—	4	1	no	—
567	Q₈	—	4	1	no	—
568	Q₈	—	4	1	no	—
569	Q₈	—	16	1	no	—
570	D₄	—	2	1	no	—
571	D₄	—	2	1	no	—
572	D₄	—	4	1	no	—
573	D₄	—	4	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	8	1	no	—
595	C₂×C₄	—	8	1	no	—
596	C₂×C₄	—	16	1	no	—
597	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
598	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
599	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
600	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
601	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
602	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
603	C₈	—	2	2	no	—
604	C₈	—	2	1	no	—
605	C₈	—	2	1	no	—
606	C₈	—	2	1	no	—
607	C₈	—	2	1	no	—
608	C₈	—	4	1	no	—
609	C₈	—	4	1	no	—
610	C₈	—	4	1	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	C₁₉×#542	1	1	yes	characteristic
617	C₂²	D₄²×C₁₉	1	1	yes	characteristic
618	C₂²	C₁₉×#551	1	1	yes	characteristic
619	C₄	—	4	2	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	1	no	—
628	C₄	—	8	1	no	—
629	C₄	—	8	1	no	—
630	C₄	—	8	1	no	—
631	C₄	C₁₉×#525	1	1	yes	characteristic
632	C₄	C₁₉×#532	1	1	yes	characteristic
633	C₄	C₁₉×#547	1	1	yes	characteristic
634	C₄	C₁₉×#548	1	1	yes	characteristic
635	C₂	—	2	1	no	—
636	C₂	—	2	1	no	—
637	C₂	—	8	1	no	—
638	C₂	C₁₉×#2461	1	1	yes	characteristic
639	C₂	C₁₉×#3289	1	1	yes	characteristic
640	C₂	C₁₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#3082	C₂	semidirect
5. C₁₉×#2064	C₂	semidirect
6. C₁₉×#2061	C₂	semidirect
9. C₁₉×#1960	C₂	semidirect
11. C₁₉×#1930	C₂	semidirect
12. C₁₉×#1930	C₂	semidirect
13. C₁₉×#1886	C₂	semidirect
15. C₁₉×#1773	C₂	semidirect
236. #26852	C₁₉	direct (N × H)
293. #3082	C₂×C₁₉	semidirect
295. #2064	C₂×C₁₉	semidirect
296. #2061	C₂×C₁₉	semidirect
299. #1960	C₂×C₁₉	semidirect
301. #1930	C₂×C₁₉	semidirect
302. #1930	C₂×C₁₉	semidirect
303. #1886	C₂×C₁₉	semidirect
305. #1773	C₂×C₁₉	semidirect
473. C₁₉	#26852	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×#3137	2
C₁₉×#3097	2
C₁₉×#3082	2
C₁₉×#2947	2
C₁₉×#2064	2
C₁₉×#2061	2
C₁₉×#2052	2
C₁₉×#2005	2
C₁₉×#1960	2
C₁₉×#1938	2
C₁₉×#1930	2
C₁₉×#1886	2
C₁₉×#1860	2
C₁₉×#1773	2
#26852	19

Subgroups — C19×#26852 #18032811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26852 #18032811