Subgroups — C₁₉×#18061 #18024020

Order 4864.

650 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2991	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉×#135	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1592	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1584	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1581	C₂	1	2	yes	maximal, complemented
7	C₁₉×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1567	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#135	C₄	1	1	yes	characteristic
13	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#446	C₂²	1	2	yes	—
16	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
17	C₄×Q₁₆×C₁₉	C₄	1	1	yes	characteristic
18	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₄×SD₁₆×C₁₉	C₄	1	1	yes	characteristic
20	C₄×SD₁₆×C₁₉	C₄	1	1	yes	characteristic
21	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₄×D₈×C₁₉	C₄	1	1	yes	characteristic
24	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#436	—	2	2	no	—
26	C₁₉×#436	C₂²	1	2	yes	—
27	C₁₉×#435	—	2	2	no	—
28	C₈×D₄×C₁₉	C₂²	1	2	yes	—
29	C₁₉×#432	—	2	1	no	—
30	C₁₉×#431	—	2	1	no	—
31	C₁₉×#431	C₂²	1	1	yes	characteristic
32	C₁₉×#427	C₄	1	1	yes	characteristic
33	C₁₉×#423	—	2	1	no	—
34	C₁₉×#423	C₂²	1	1	yes	characteristic
35	C₁₉×#423	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
37	C₁₉×#416	C₄	1	1	yes	characteristic
38	C₁₉×#416	C₄	1	1	yes	characteristic
39	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#335	C₂²	1	2	yes	—
42	C₁₉×#335	C₂²	1	2	yes	—
43	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
46	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
47	C₁₉×#322	C₂²	1	2	yes	—
48	C₁₉×#322	C₂²	1	2	yes	—
49	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
51	C₁₉×#135	—	2	4	no	—
52	C₂×Q₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
53	C₂×SD₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
54	C₂×SD₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
55	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₂×M₁₆×C₁₉	—	2	2	no	—
60	C₂²×C₈×C₁₉	—	2	2	no	—
61	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
63	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
64	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
65	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₄×D₄×C₁₉	—	2	1	no	—
68	C₄×D₄×C₁₉	—	2	1	no	—
69	C₄×D₄×C₁₉	—	2	1	no	—
70	C₄×D₄×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
72	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
73	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×#117	—	2	1	no	—
76	C₁₉×#117	—	2	1	no	—
77	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
78	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₉	—	2	1	no	—
80	C₂×C₄²×C₁₉	—	2	1	no	—
81	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
82	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
83	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
84	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
85	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
86	C₁₉×C₄⋊C₈	—	2	2	no	—
87	C₁₉×C₄⋊C₈	—	2	2	no	—
88	C₁₉×C₄⋊C₈	—	2	1	no	—
89	C₁₉×C₄⋊C₈	—	2	1	no	—
90	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
91	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
92	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
93	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
94	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
95	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
96	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
97	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
98	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
99	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
100	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
101	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
102	C₁₉×C₂²⋊C₈	—	2	2	no	—
103	C₁₉×C₂²⋊C₈	—	2	2	no	—
104	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
105	C₁₉×#97	—	2	2	no	—
106	C₁₉×#97	—	2	1	no	—
107	C₄×C₈×C₁₉	—	2	2	no	—
108	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
109	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
110	C₄×C₈×C₁₉	C₂³	1	2	yes	—
111	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
112	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
113	C₄×C₈×C₁₉	C₂³	1	2	yes	—
114	#41×C₁₉	—	2	2	no	—
115	#41×C₁₉	—	2	2	no	—
116	#41×C₁₉	—	4	1	no	—
117	#41×C₁₉	—	4	1	no	—
118	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
119	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
123	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
133	Q₁₆×C₁₉	—	2	2	no	—
134	SD₁₆×C₁₉	—	2	2	no	—
135	SD₁₆×C₁₉	M₁₆	1	4	yes	complemented
136	D₈×C₁₉	—	2	2	no	—
137	M₁₆×C₁₉	—	4	2	no	—
138	M₁₆×C₁₉	—	8	2	no	—
139	M₁₆×C₁₉	—	8	1	no	—
140	M₁₆×C₁₉	—	8	1	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₂×C₈×C₁₉	—	2	2	no	—
144	C₂×C₈×C₁₉	—	2	2	no	—
145	C₂×C₈×C₁₉	—	4	1	no	—
146	C₂×C₈×C₁₉	—	8	2	no	—
147	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
158	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
159	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
160	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
161	C₂²⋊C₄×C₁₉	—	2	1	no	—
162	C₂²⋊C₄×C₁₉	—	2	1	no	—
163	C₂²⋊C₄×C₁₉	—	2	1	no	—
164	C₂²⋊C₄×C₁₉	—	2	1	no	—
165	C₂²⋊C₄×C₁₉	—	2	1	no	—
166	C₂²⋊C₄×C₁₉	—	2	1	no	—
167	C₄²×C₁₉	—	2	1	no	—
168	C₄²×C₁₉	—	2	1	no	—
169	C₄²×C₁₉	—	2	1	no	—
170	C₄²×C₁₉	—	2	1	no	—
171	C₄²×C₁₉	—	2	1	no	—
172	C₄²×C₁₉	—	2	1	no	—
173	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₁₉	#41	1	1	yes	characteristic
176	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
177	#18061	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂³×C₁₉	—	2	1	no	—
179	C₂³×C₁₉	—	2	1	no	—
180	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
181	Q₈×C₁₉	—	2	1	no	—
182	Q₈×C₁₉	—	2	1	no	—
183	Q₈×C₁₉	—	2	1	no	—
184	Q₈×C₁₉	C₂×M₁₆	1	2	yes	—
185	D₄×C₁₉	—	2	1	no	—
186	D₄×C₁₉	—	2	1	no	—
187	D₄×C₁₉	—	2	1	no	—
188	D₄×C₁₉	—	4	2	no	—
189	D₄×C₁₉	—	4	2	no	—
190	D₄×C₁₉	C₂×M₁₆	1	2	yes	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	2	1	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
216	C₈×C₁₉	—	2	1	no	—
217	C₈×C₁₉	—	2	1	no	—
218	C₈×C₁₉	—	2	1	no	—
219	C₈×C₁₉	—	2	2	no	—
220	C₈×C₁₉	—	2	2	no	—
221	C₈×C₁₉	—	4	2	no	—
222	C₈×C₁₉	—	4	2	no	—
223	C₈×C₁₉	—	4	2	no	—
224	C₈×C₁₉	C₂×M₁₆	1	2	yes	—
225	#2991	C₂×C₁₉	1	1	yes	characteristic, complemented
226	#2990	C₂×C₁₉	1	1	yes	characteristic, complemented
227	C₄×#135	C₂×C₁₉	1	1	yes	characteristic
228	#1592	C₂×C₁₉	1	2	yes	complemented
229	#1584	C₂×C₁₉	1	2	yes	complemented
230	#1581	C₂×C₁₉	1	2	yes	complemented
231	SD₁₆⋊C₈	C₂×C₁₉	1	2	yes	complemented
232	#1567	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#1489	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#1489	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#1451	C₂×C₁₉	1	1	yes	characteristic, complemented
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	—	2	1	no	—
239	C₂²×C₁₉	—	2	1	no	—
240	C₂²×C₁₉	—	4	1	no	—
241	C₂²×C₁₉	—	4	1	no	—
242	C₂²×C₁₉	—	4	1	no	—
243	C₂²×C₁₉	—	4	1	no	—
244	C₂²×C₁₉	—	4	1	no	—
245	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
246	C₄×C₁₉	—	2	1	no	—
247	C₄×C₁₉	—	2	2	no	—
248	C₄×C₁₉	—	2	1	no	—
249	C₄×C₁₉	—	2	1	no	—
250	C₄×C₁₉	—	4	1	no	—
251	C₄×C₁₉	—	4	1	no	—
252	C₄×C₁₉	—	4	1	no	—
253	C₄×C₁₉	—	4	1	no	—
254	C₄×C₁₉	—	4	1	no	—
255	C₄×C₁₉	#444	1	2	yes	—
256	C₄×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
257	C₄×C₁₉	#568	1	1	yes	characteristic
258	C₄×C₁₉	#576	1	1	yes	characteristic
259	C₄×C₁₉	#578	1	1	yes	characteristic
260	C₂×#135	C₄×C₁₉	1	1	yes	characteristic
261	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
262	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
263	#446	C₂²×C₁₉	1	2	yes	—
264	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
265	C₄×Q₁₆	C₄×C₁₉	1	1	yes	characteristic
266	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
267	C₄×SD₁₆	C₄×C₁₉	1	1	yes	characteristic
268	C₄×SD₁₆	C₄×C₁₉	1	1	yes	characteristic
269	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
270	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
271	C₄×D₈	C₄×C₁₉	1	1	yes	characteristic
272	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
273	#436	—	2	2	no	—
274	#436	C₂²×C₁₉	1	2	yes	—
275	#435	—	2	2	no	—
276	C₈×D₄	C₂²×C₁₉	1	2	yes	—
277	#432	—	2	1	no	—
278	#431	—	2	1	no	—
279	#431	C₂²×C₁₉	1	1	yes	characteristic
280	#427	C₄×C₁₉	1	1	yes	characteristic
281	#423	—	2	1	no	—
282	#423	C₂²×C₁₉	1	1	yes	characteristic
283	#423	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×C₄⋊C₈	—	2	1	no	—
285	#416	C₄×C₁₉	1	1	yes	characteristic
286	#416	C₄×C₁₉	1	1	yes	characteristic
287	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
289	#335	C₂²×C₁₉	1	2	yes	—
290	#335	C₂²×C₁₉	1	2	yes	—
291	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
292	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
293	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
294	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
295	#322	C₂²×C₁₉	1	2	yes	—
296	#322	C₂²×C₁₉	1	2	yes	—
297	C₂×C₁₉	—	4	1	no	—
298	C₂×C₁₉	—	4	2	no	—
299	C₂×C₁₉	—	8	1	no	—
300	C₂×C₁₉	D₄×M₁₆	1	1	yes	characteristic
301	C₂×C₁₉	#2951	1	1	yes	characteristic
302	C₂×C₁₉	C₂×#444	1	1	yes	characteristic
303	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
304	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
305	#135	—	2	4	no	—
306	C₂×Q₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
307	C₂×SD₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
308	C₂×SD₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
309	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
310	C₂×M₁₆	—	2	1	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂×M₁₆	—	2	1	no	—
313	C₂×M₁₆	—	2	2	no	—
314	C₂²×C₈	—	2	2	no	—
315	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
316	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
317	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
318	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
319	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
320	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	—	2	1	no	—
324	C₄×D₄	—	2	1	no	—
325	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
326	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
327	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
328	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
329	#117	—	2	1	no	—
330	#117	—	2	1	no	—
331	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
332	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
336	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
337	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
338	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
339	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
340	C₄⋊C₈	—	2	2	no	—
341	C₄⋊C₈	—	2	2	no	—
342	C₄⋊C₈	—	2	1	no	—
343	C₄⋊C₈	—	2	1	no	—
344	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
345	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
346	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
347	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
348	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
349	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
350	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
351	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
352	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
353	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
354	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
355	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
356	C₂²⋊C₈	—	2	2	no	—
357	C₂²⋊C₈	—	2	2	no	—
358	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
359	#97	—	2	2	no	—
360	#97	—	2	1	no	—
361	C₄×C₈	—	2	2	no	—
362	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
363	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
364	C₄×C₈	C₂³×C₁₉	1	2	yes	—
365	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
366	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
367	C₄×C₈	C₂³×C₁₉	1	2	yes	—
368	C₁₉	#18061	1	1	yes	characteristic, direct product factor, Sylow
369	#41	—	2	2	no	—
370	#41	—	2	2	no	—
371	#41	—	4	1	no	—
372	#41	—	4	1	no	—
373	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
374	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
378	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
387	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
388	Q₁₆	—	2	2	no	—
389	SD₁₆	—	2	2	no	—
390	SD₁₆	M₁₆×C₁₉	1	4	yes	complemented
391	D₈	—	2	2	no	—
392	M₁₆	—	4	2	no	—
393	M₁₆	—	8	2	no	—
394	M₁₆	—	8	1	no	—
395	M₁₆	—	8	1	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	4	1	no	—
401	C₂×C₈	—	8	2	no	—
402	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
403	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
404	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
405	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
406	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
407	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
413	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
414	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
415	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
429	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₄²	#41×C₁₉	1	1	yes	characteristic
431	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	2	1	no	—
437	Q₈	—	2	1	no	—
438	Q₈	C₂×M₁₆×C₁₉	1	2	yes	—
439	D₄	—	2	1	no	—
440	D₄	—	2	1	no	—
441	D₄	—	2	1	no	—
442	D₄	—	4	2	no	—
443	D₄	—	4	2	no	—
444	D₄	C₂×M₁₆×C₁₉	1	2	yes	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
465	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
466	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
467	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
469	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
470	C₈	—	2	1	no	—
471	C₈	—	2	1	no	—
472	C₈	—	2	1	no	—
473	C₈	—	2	2	no	—
474	C₈	—	2	2	no	—
475	C₈	—	4	2	no	—
476	C₈	—	4	2	no	—
477	C₈	—	4	2	no	—
478	C₈	C₂×M₁₆×C₁₉	1	2	yes	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
489	C₄	—	2	1	no	—
490	C₄	—	2	2	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	C₁₉×#444	1	2	yes	—
499	C₄	C₂²×M₁₆×C₁₉	1	1	yes	characteristic
500	C₄	C₁₉×#568	1	1	yes	characteristic
501	C₄	C₁₉×#576	1	1	yes	characteristic
502	C₄	C₁₉×#578	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	4	2	no	—
505	C₂	—	8	1	no	—
506	C₂	D₄×M₁₆×C₁₉	1	1	yes	characteristic
507	C₂	C₁₉×#2951	1	1	yes	characteristic
508	C₂	C₂×C₁₉×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×C₄×D₄
prime radical	C₂×C₁₉×#135	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#431 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2991	C₂	semidirect
2. C₁₉×#2990	C₂	semidirect
4. C₁₉×#1592	C₂	semidirect
5. C₁₉×#1584	C₂	semidirect
6. C₁₉×#1581	C₂	semidirect
7. C₁₉×SD₁₆⋊C₈	C₂	semidirect
8. C₁₉×#1567	C₂	semidirect
9. C₁₉×#1489	C₂	semidirect
10. C₁₉×#1489	C₂	semidirect
11. C₁₉×#1451	C₂	semidirect
135. SD₁₆×C₁₉	M₁₆	semidirect
177. #18061	C₁₉	direct (N × H)
225. #2991	C₂×C₁₉	semidirect
226. #2990	C₂×C₁₉	semidirect
228. #1592	C₂×C₁₉	semidirect
229. #1584	C₂×C₁₉	semidirect
230. #1581	C₂×C₁₉	semidirect
231. SD₁₆⋊C₈	C₂×C₁₉	semidirect
232. #1567	C₂×C₁₉	semidirect
233. #1489	C₂×C₁₉	semidirect
234. #1489	C₂×C₁₉	semidirect
235. #1451	C₂×C₁₉	semidirect
368. C₁₉	#18061	direct (N × H)
390. SD₁₆	M₁₆×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#2991	2
C₁₉×#2990	2
C₄×C₁₉×#135	2
C₁₉×#1592	2
C₁₉×#1584	2
C₁₉×#1581	2
C₁₉×SD₁₆⋊C₈	2
C₁₉×#1567	2
C₁₉×#1489	2
C₁₉×#1451	2
#18061	19

Subgroups — C19×#18061 #18024020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18061 #18024020