Subgroups — C₁₉×#33881 #18039840

Order 4864.

570 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3338	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3280	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2243	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2236	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2232	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2224	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2220	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2216	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2211	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2189	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2187	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2175	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2139	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#554	—	2	1	no	—
19	C₁₉×#546	—	2	1	no	—
20	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#495	C₂²	1	1	yes	characteristic
27	C₁₉×#484	—	2	1	no	—
28	C₁₉×#484	—	2	1	no	—
29	C₁₉×#477	—	2	1	no	—
30	C₁₉×#467	C₂²	1	1	yes	characteristic
31	C₁₉×#467	C₂²	1	1	yes	characteristic
32	C₁₉×#467	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#466	C₂²	1	1	yes	characteristic
34	C₁₉×#463	—	2	1	no	—
35	C₁₉×#450	—	2	1	no	—
36	C₁₉×#449	—	2	1	no	—
37	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
38	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#366	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#366	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#366	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#358	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#358	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#358	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#358	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#357	C₂²	1	1	yes	characteristic
51	C₁₉×#357	C₂²	1	1	yes	characteristic
52	C₁₉×#357	C₂²	1	1	yes	characteristic
53	C₁₉×#357	C₂²	1	1	yes	characteristic
54	C₁₉×#357	C₂²	1	1	yes	characteristic
55	C₁₉×#357	C₂²	1	1	yes	characteristic
56	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#346	C₂²	1	1	yes	characteristic, complemented
59	C₂×#41×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₁₉×#135	—	2	2	no	—
62	C₁₉×#135	—	4	1	no	—
63	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×SD₁₆×C₁₉	—	2	1	no	—
66	C₂×SD₁₆×C₁₉	—	2	1	no	—
67	C₂×D₈×C₁₉	—	2	2	no	—
68	C₂×D₈×C₁₉	—	2	1	no	—
69	C₂×D₈×C₁₉	—	4	1	no	—
70	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×C₄⋊Q₈	—	2	1	no	—
75	C₁₉×#125	—	4	1	no	—
76	C₁₉×#124	—	2	1	no	—
77	C₁₉×#123	—	4	1	no	—
78	C₁₉×C₂²⋊Q₈	—	2	1	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	—	4	1	no	—
82	C₁₉×C₂²⋊Q₈	—	4	1	no	—
83	C₁₉×#121	—	2	1	no	—
84	C₁₉×#121	—	4	1	no	—
85	C₁₉×#120	—	4	1	no	—
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×D₄×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	—	4	1	no	—
89	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
93	C₁₉×Q₃₂	—	4	1	no	—
94	C₁₉×SD₃₂	—	2	2	no	—
95	C₁₉×SD₃₂	—	4	1	no	—
96	C₁₉×M₃₂	—	4	1	no	—
97	C₂×C₁₆×C₁₉	—	4	1	no	—
98	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×#107	—	2	1	no	—
103	C₁₉×#107	—	2	1	no	—
104	C₁₉×#107	—	2	1	no	—
105	C₁₉×#107	C₂³	1	1	yes	characteristic
106	C₁₉×#107	C₂³	1	1	yes	characteristic
107	C₁₉×#107	C₂³	1	1	yes	characteristic
108	C₁₉×#107	C₂³	1	1	yes	characteristic
109	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
110	C₁₉×#103	—	2	1	no	—
111	C₁₉×#103	—	2	1	no	—
112	C₁₉×#103	—	2	1	no	—
113	C₁₉×#103	—	2	1	no	—
114	C₁₉×#102	—	2	1	no	—
115	C₁₉×#102	—	2	1	no	—
116	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
117	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
118	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
119	C₂⁴×C₁₉	—	4	1	no	—
120	#41×C₁₉	—	4	2	no	—
121	#41×C₁₉	—	8	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	4	1	no	—
125	C₂×D₄×C₁₉	—	2	1	no	—
126	C₂×D₄×C₁₉	—	2	1	no	—
127	C₂×D₄×C₁₉	—	4	2	no	—
128	C₂×D₄×C₁₉	—	4	1	no	—
129	C₂×D₄×C₁₉	—	4	1	no	—
130	C₂×D₄×C₁₉	—	4	1	no	—
131	C₂×D₄×C₁₉	—	8	1	no	—
132	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	—	4	1	no	—
134	C₂²×C₄×C₁₉	—	4	1	no	—
135	C₂²×C₄×C₁₉	—	4	1	no	—
136	C₂²×C₄×C₁₉	—	4	1	no	—
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	Q₁₆×C₁₉	—	2	1	no	—
140	Q₁₆×C₁₉	—	2	1	no	—
141	Q₁₆×C₁₉	—	2	1	no	—
142	Q₁₆×C₁₉	—	2	1	no	—
143	SD₁₆×C₁₉	—	4	2	no	—
144	SD₁₆×C₁₉	—	8	1	no	—
145	D₈×C₁₉	—	2	1	no	—
146	D₈×C₁₉	—	2	1	no	—
147	D₈×C₁₉	—	2	1	no	—
148	D₈×C₁₉	—	4	2	no	—
149	D₈×C₁₉	#41	1	2	yes	—
150	C₂×C₈×C₁₉	—	2	1	no	—
151	C₂×C₈×C₁₉	—	2	1	no	—
152	C₂×C₈×C₁₉	—	2	1	no	—
153	C₂×C₈×C₁₉	—	2	1	no	—
154	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	4	1	no	—
163	C₄⋊C₄×C₁₉	—	4	1	no	—
164	C₄⋊C₄×C₁₉	—	4	1	no	—
165	C₄⋊C₄×C₁₉	—	4	1	no	—
166	C₄⋊C₄×C₁₉	—	4	1	no	—
167	C₄⋊C₄×C₁₉	—	4	1	no	—
168	C₄⋊C₄×C₁₉	—	4	1	no	—
169	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
170	C₂²⋊C₄×C₁₉	—	4	1	no	—
171	C₂²⋊C₄×C₁₉	—	4	1	no	—
172	C₂²⋊C₄×C₁₉	—	4	1	no	—
173	C₂²⋊C₄×C₁₉	—	4	1	no	—
174	C₂²⋊C₄×C₁₉	—	4	1	no	—
175	C₂²⋊C₄×C₁₉	—	4	1	no	—
176	C₂²⋊C₄×C₁₉	—	4	1	no	—
177	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
178	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
179	C₄²×C₁₉	—	4	1	no	—
180	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₁₆×C₁₉	—	2	1	no	—
182	C₁₆×C₁₉	—	2	1	no	—
183	C₁₆×C₁₉	—	2	1	no	—
184	C₁₆×C₁₉	—	2	1	no	—
185	#33881	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	—	4	1	no	—
188	C₂³×C₁₉	—	8	2	no	—
189	C₂³×C₁₉	—	8	2	no	—
190	C₂³×C₁₉	—	16	1	no	—
191	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
192	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
193	Q₈×C₁₉	—	4	1	no	—
194	Q₈×C₁₉	—	4	1	no	—
195	Q₈×C₁₉	—	4	1	no	—
196	Q₈×C₁₉	—	4	1	no	—
197	Q₈×C₁₉	—	16	1	no	—
198	D₄×C₁₉	—	2	2	no	—
199	D₄×C₁₉	—	2	2	no	—
200	D₄×C₁₉	—	4	1	no	—
201	D₄×C₁₉	—	4	1	no	—
202	D₄×C₁₉	—	4	1	no	—
203	D₄×C₁₉	—	8	2	no	—
204	D₄×C₁₉	—	8	2	no	—
205	D₄×C₁₉	—	16	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	8	2	no	—
217	C₂×C₄×C₁₉	—	16	1	no	—
218	C₂×C₄×C₁₉	—	16	1	no	—
219	C₂×C₄×C₁₉	—	16	1	no	—
220	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
225	C₈×C₁₉	—	2	1	no	—
226	C₈×C₁₉	—	2	1	no	—
227	C₈×C₁₉	—	2	1	no	—
228	C₈×C₁₉	C₂×#41	1	1	yes	characteristic
229	C₈×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
230	#3338	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#3280	C₂×C₁₉	1	1	yes	characteristic
232	#2243	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#2236	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#2232	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#2224	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#2220	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#2216	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#2211	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#2189	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#2187	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#2175	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#2168	C₂×C₁₉	1	1	yes	characteristic, complemented
243	#2139	C₂×C₁₉	1	1	yes	characteristic, complemented
244	C₂×#357	C₂×C₁₉	1	1	yes	characteristic, complemented
245	C₂²×C₁₉	—	2	1	no	—
246	C₂²×C₁₉	—	2	1	no	—
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	2	1	no	—
250	C₂²×C₁₉	—	4	2	no	—
251	C₂²×C₁₉	—	8	1	no	—
252	C₂²×C₁₉	—	8	1	no	—
253	C₂²×C₁₉	—	8	1	no	—
254	C₂²×C₁₉	—	8	1	no	—
255	C₂²×C₁₉	—	8	1	no	—
256	C₂²×C₁₉	—	16	4	no	—
257	C₂²×C₁₉	#510	1	2	yes	—
258	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	2	1	no	—
263	C₄×C₁₉	—	8	1	no	—
264	C₄×C₁₉	—	8	1	no	—
265	C₄×C₁₉	—	8	1	no	—
266	C₄×C₁₉	—	8	1	no	—
267	C₄×C₁₉	—	8	1	no	—
268	C₄×C₁₉	—	8	1	no	—
269	C₄×C₁₉	#546	1	1	yes	characteristic
270	C₄×C₁₉	#577	1	1	yes	characteristic
271	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
272	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
273	#554	—	2	1	no	—
274	#546	—	2	1	no	—
275	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
276	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
278	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
279	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
280	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
281	#495	C₂²×C₁₉	1	1	yes	characteristic
282	#484	—	2	1	no	—
283	#484	—	2	1	no	—
284	#477	—	2	1	no	—
285	#467	C₂²×C₁₉	1	1	yes	characteristic
286	#467	C₂²×C₁₉	1	1	yes	characteristic
287	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
288	#466	C₂²×C₁₉	1	1	yes	characteristic
289	#463	—	2	1	no	—
290	#450	—	2	1	no	—
291	#449	—	2	1	no	—
292	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
293	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
294	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
296	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
297	#366	C₂²×C₁₉	1	1	yes	characteristic, complemented
298	#366	C₂²×C₁₉	1	1	yes	characteristic, complemented
299	#366	C₂²×C₁₉	1	1	yes	characteristic, complemented
300	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
301	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
302	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
303	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
304	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
305	#357	C₂²×C₁₉	1	1	yes	characteristic
306	#357	C₂²×C₁₉	1	1	yes	characteristic
307	#357	C₂²×C₁₉	1	1	yes	characteristic
308	#357	C₂²×C₁₉	1	1	yes	characteristic
309	#357	C₂²×C₁₉	1	1	yes	characteristic
310	#357	C₂²×C₁₉	1	1	yes	characteristic
311	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
312	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
313	#346	C₂²×C₁₉	1	1	yes	characteristic, complemented
314	C₂×C₁₉	—	2	2	no	—
315	C₂×C₁₉	—	4	1	no	—
316	C₂×C₁₉	—	8	2	no	—
317	C₂×C₁₉	—	16	1	no	—
318	C₂×C₁₉	#3294	1	1	yes	characteristic
319	C₂×C₁₉	C₂×#510	1	1	yes	characteristic
320	C₂×C₁₉	#3415	1	1	yes	characteristic
321	C₂×#41	—	2	1	no	—
322	C₂²×D₄	—	2	1	no	—
323	#135	—	2	2	no	—
324	#135	—	4	1	no	—
325	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
326	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
327	C₂×SD₁₆	—	2	1	no	—
328	C₂×SD₁₆	—	2	1	no	—
329	C₂×D₈	—	2	2	no	—
330	C₂×D₈	—	2	1	no	—
331	C₂×D₈	—	4	1	no	—
332	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
333	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
336	C₄⋊Q₈	—	2	1	no	—
337	#125	—	4	1	no	—
338	#124	—	2	1	no	—
339	#123	—	4	1	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	—	2	1	no	—
342	C₂²⋊Q₈	—	2	1	no	—
343	C₂²⋊Q₈	—	4	1	no	—
344	C₂²⋊Q₈	—	4	1	no	—
345	#121	—	2	1	no	—
346	#121	—	4	1	no	—
347	#120	—	4	1	no	—
348	C₄×Q₈	—	2	1	no	—
349	C₄×D₄	—	2	1	no	—
350	C₄×D₄	—	4	1	no	—
351	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₂²⋊C₄	—	4	1	no	—
355	Q₃₂	—	4	1	no	—
356	SD₃₂	—	2	2	no	—
357	SD₃₂	—	4	1	no	—
358	M₃₂	—	4	1	no	—
359	C₂×C₁₆	—	4	1	no	—
360	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
361	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
362	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
363	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
364	#107	—	2	1	no	—
365	#107	—	2	1	no	—
366	#107	—	2	1	no	—
367	#107	C₂³×C₁₉	1	1	yes	characteristic
368	#107	C₂³×C₁₉	1	1	yes	characteristic
369	#107	C₂³×C₁₉	1	1	yes	characteristic
370	#107	C₂³×C₁₉	1	1	yes	characteristic
371	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
372	#103	—	2	1	no	—
373	#103	—	2	1	no	—
374	#103	—	2	1	no	—
375	#103	—	2	1	no	—
376	#102	—	2	1	no	—
377	#102	—	2	1	no	—
378	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
379	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
380	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
381	C₁₉	#33881	1	1	yes	characteristic, direct product factor, Sylow
382	C₂⁴	—	4	1	no	—
383	#41	—	4	2	no	—
384	#41	—	8	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	4	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	1	no	—
392	C₂×D₄	—	4	1	no	—
393	C₂×D₄	—	4	1	no	—
394	C₂×D₄	—	8	1	no	—
395	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
396	C₂²×C₄	—	4	1	no	—
397	C₂²×C₄	—	4	1	no	—
398	C₂²×C₄	—	4	1	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
402	Q₁₆	—	2	1	no	—
403	Q₁₆	—	2	1	no	—
404	Q₁₆	—	2	1	no	—
405	Q₁₆	—	2	1	no	—
406	SD₁₆	—	4	2	no	—
407	SD₁₆	—	8	1	no	—
408	D₈	—	2	1	no	—
409	D₈	—	2	1	no	—
410	D₈	—	2	1	no	—
411	D₈	—	4	2	no	—
412	D₈	#41×C₁₉	1	2	yes	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	4	1	no	—
426	C₄⋊C₄	—	4	1	no	—
427	C₄⋊C₄	—	4	1	no	—
428	C₄⋊C₄	—	4	1	no	—
429	C₄⋊C₄	—	4	1	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄⋊C₄	—	4	1	no	—
432	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
433	C₂²⋊C₄	—	4	1	no	—
434	C₂²⋊C₄	—	4	1	no	—
435	C₂²⋊C₄	—	4	1	no	—
436	C₂²⋊C₄	—	4	1	no	—
437	C₂²⋊C₄	—	4	1	no	—
438	C₂²⋊C₄	—	4	1	no	—
439	C₂²⋊C₄	—	4	1	no	—
440	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
441	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
442	C₄²	—	4	1	no	—
443	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₁₆	—	2	1	no	—
445	C₁₆	—	2	1	no	—
446	C₁₆	—	2	1	no	—
447	C₁₆	—	2	1	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	8	2	no	—
451	C₂³	—	8	2	no	—
452	C₂³	—	16	1	no	—
453	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
454	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
455	Q₈	—	4	1	no	—
456	Q₈	—	4	1	no	—
457	Q₈	—	4	1	no	—
458	Q₈	—	4	1	no	—
459	Q₈	—	16	1	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	1	no	—
465	D₄	—	8	2	no	—
466	D₄	—	8	2	no	—
467	D₄	—	16	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	8	2	no	—
479	C₂×C₄	—	16	1	no	—
480	C₂×C₄	—	16	1	no	—
481	C₂×C₄	—	16	1	no	—
482	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
483	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
484	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
485	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
487	C₈	—	2	1	no	—
488	C₈	—	2	1	no	—
489	C₈	—	2	1	no	—
490	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
491	C₈	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	8	1	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	16	4	no	—
504	C₂²	C₁₉×#510	1	2	yes	—
505	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	8	1	no	—
511	C₄	—	8	1	no	—
512	C₄	—	8	1	no	—
513	C₄	—	8	1	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	1	no	—
516	C₄	C₁₉×#546	1	1	yes	characteristic
517	C₄	C₁₉×#577	1	1	yes	characteristic
518	C₂	—	2	2	no	—
519	C₂	—	4	1	no	—
520	C₂	—	8	2	no	—
521	C₂	—	16	1	no	—
522	C₂	C₁₉×#3294	1	1	yes	characteristic
523	C₂	C₂×C₁₉×#510	1	1	yes	characteristic
524	C₂	C₁₉×#3415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₁₉×#3280	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×D₄×C₁₉ ◁ C₈×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3338	C₂	semidirect
3. C₁₉×#2243	C₂	semidirect
4. C₁₉×#2236	C₂	semidirect
5. C₁₉×#2232	C₂	semidirect
6. C₁₉×#2224	C₂	semidirect
7. C₁₉×#2220	C₂	semidirect
8. C₁₉×#2216	C₂	semidirect
9. C₁₉×#2211	C₂	semidirect
10. C₁₉×#2189	C₂	semidirect
11. C₁₉×#2187	C₂	semidirect
12. C₁₉×#2175	C₂	semidirect
13. C₁₉×#2168	C₂	semidirect
14. C₁₉×#2139	C₂	semidirect
15. C₂×C₁₉×#357	C₂	semidirect
20. C₂×C₁₉×Q₃₂	C₂²	semidirect
23. C₂×C₁₉×M₃₂	C₂²	semidirect
25. C₁₉×#500	C₂²	semidirect
32. C₁₉×#467	C₂²	semidirect
37. C₄×Q₁₆×C₁₉	C₂²	semidirect
41. C₂×C₁₉×#107	C₂²	semidirect
42. C₁₉×#366	C₂²	semidirect
43. C₁₉×#366	C₂²	semidirect
44. C₁₉×#366	C₂²	semidirect
45. C₁₉×C₄⋊C₁₆	C₂²	semidirect
46. C₁₉×#358	C₂²	semidirect
47. C₁₉×#358	C₂²	semidirect
48. C₁₉×#358	C₂²	semidirect
49. C₁₉×#358	C₂²	semidirect
57. C₁₉×C₂²⋊C₁₆	C₂²	semidirect
58. C₁₉×#346	C₂²	semidirect
185. #33881	C₁₉	direct (N × H)
230. #3338	C₂×C₁₉	semidirect
232. #2243	C₂×C₁₉	semidirect
233. #2236	C₂×C₁₉	semidirect
234. #2232	C₂×C₁₉	semidirect
235. #2224	C₂×C₁₉	semidirect
236. #2220	C₂×C₁₉	semidirect
237. #2216	C₂×C₁₉	semidirect
238. #2211	C₂×C₁₉	semidirect
239. #2189	C₂×C₁₉	semidirect
240. #2187	C₂×C₁₉	semidirect
241. #2175	C₂×C₁₉	semidirect
242. #2168	C₂×C₁₉	semidirect
243. #2139	C₂×C₁₉	semidirect
244. C₂×#357	C₂×C₁₉	semidirect
275. C₂×Q₃₂	C₂²×C₁₉	semidirect
278. C₂×M₃₂	C₂²×C₁₉	semidirect
280. #500	C₂²×C₁₉	semidirect
287. #467	C₂²×C₁₉	semidirect
292. C₄×Q₁₆	C₂²×C₁₉	semidirect
296. C₂×#107	C₂²×C₁₉	semidirect
297. #366	C₂²×C₁₉	semidirect
298. #366	C₂²×C₁₉	semidirect
299. #366	C₂²×C₁₉	semidirect
300. C₄⋊C₁₆	C₂²×C₁₉	semidirect
301. #358	C₂²×C₁₉	semidirect
302. #358	C₂²×C₁₉	semidirect
303. #358	C₂²×C₁₉	semidirect
304. #358	C₂²×C₁₉	semidirect
312. C₂²⋊C₁₆	C₂²×C₁₉	semidirect
313. #346	C₂²×C₁₉	semidirect
381. C₁₉	#33881	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×#3338	2
C₁₉×#3280	2
C₁₉×#2243	2
C₁₉×#2236	2
C₁₉×#2232	2
C₁₉×#2224	2
C₁₉×#2220	2
C₁₉×#2216	2
C₁₉×#2211	2
C₁₉×#2189	2
C₁₉×#2187	2
C₁₉×#2175	2
C₁₉×#2168	2
C₁₉×#2139	2
C₂×C₁₉×#357	2
#33881	19

Subgroups — C19×#33881 #18039840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33881 #18039840