Subgroups — C₁₉×#22843 #18028802

Order 4864.

1186 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₁₉	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₉×#408	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2388	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1923	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1870	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1869	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1850	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1753	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
12	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₈×D₄×C₁₉	—	2	8	no	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₁₉×#408	—	2	8	no	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
28	C₁₉×#395	C₄	1	1	yes	characteristic
29	C₁₉×#394	C₄	1	2	yes	—
30	C₁₉×#394	C₄	1	1	yes	characteristic
31	C₁₉×#393	C₄	1	1	yes	characteristic
32	C₁₉×#392	C₄	1	1	yes	characteristic
33	C₁₉×#392	C₄	1	2	yes	—
34	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
36	C₁₉×#336	C₂²	1	2	yes	—
37	C₁₉×#336	C₂²	1	2	yes	—
38	C₁₉×#336	C₂²	1	2	yes	—
39	C₂×#41×C₁₉	—	2	4	no	—
40	C₂×#41×C₁₉	—	2	4	no	—
41	C₂×#41×C₁₉	—	4	1	no	—
42	C₂×#41×C₁₉	—	4	1	no	—
43	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
47	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
51	C₂×M₁₆×C₁₉	—	2	4	no	—
52	C₂×M₁₆×C₁₉	—	2	4	no	—
53	C₂×M₁₆×C₁₉	—	4	2	no	—
54	C₂²×C₈×C₁₉	—	2	4	no	—
55	C₂²×C₈×C₁₉	—	2	4	no	—
56	C₂²×C₈×C₁₉	—	2	4	no	—
57	C₂²×C₈×C₁₉	—	4	1	no	—
58	C₂²×C₈×C₁₉	—	4	2	no	—
59	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
63	C₄×D₄×C₁₉	—	2	4	no	—
64	C₄×D₄×C₁₉	—	2	4	no	—
65	C₄×D₄×C₁₉	—	4	1	no	—
66	C₄×D₄×C₁₉	—	4	1	no	—
67	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
70	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
72	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
73	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
74	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
77	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
78	C₁₉×C₄⋊C₈	—	2	4	no	—
79	C₁₉×C₄⋊C₈	—	4	1	no	—
80	C₁₉×C₂²⋊C₈	—	2	4	no	—
81	C₁₉×C₂²⋊C₈	—	2	4	no	—
82	C₁₉×C₂²⋊C₈	—	2	4	no	—
83	C₁₉×C₂²⋊C₈	—	2	4	no	—
84	C₁₉×C₂²⋊C₈	—	4	1	no	—
85	C₁₉×C₂²⋊C₈	D₄	1	8	yes	complemented
86	C₁₉×#97	—	4	1	no	—
87	C₄×C₈×C₁₉	—	2	4	no	—
88	C₁₉×#95	C₂×C₄	1	2	yes	—
89	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
90	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
91	C₁₉×#95	C₂×C₄	1	2	yes	—
92	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
93	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
94	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	#41×C₁₉	—	4	4	no	—
96	#41×C₁₉	—	4	8	no	—
97	#41×C₁₉	—	4	4	no	—
98	C₂×Q₈×C₁₉	—	2	4	no	—
99	C₂×Q₈×C₁₉	—	4	1	no	—
100	C₂×D₄×C₁₉	—	2	4	no	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	4	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	4	no	—
106	C₂×D₄×C₁₉	—	2	4	no	—
107	C₂×D₄×C₁₉	—	4	1	no	—
108	C₂×D₄×C₁₉	—	4	1	no	—
109	C₂×D₄×C₁₉	—	4	2	no	—
110	C₂×D₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₉	#41	1	4	yes	—
132	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
133	M₁₆×C₁₉	—	4	8	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	—	2	2	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	—	4	4	no	—
145	C₂×C₈×C₁₉	—	4	8	no	—
146	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
147	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
148	C₄⋊C₄×C₁₉	—	2	4	no	—
149	C₄⋊C₄×C₁₉	—	4	1	no	—
150	C₂²⋊C₄×C₁₉	—	2	4	no	—
151	C₂²⋊C₄×C₁₉	—	2	4	no	—
152	C₂²⋊C₄×C₁₉	—	2	4	no	—
153	C₂²⋊C₄×C₁₉	—	2	4	no	—
154	C₂²⋊C₄×C₁₉	—	4	2	no	—
155	C₂²⋊C₄×C₁₉	—	4	1	no	—
156	C₂²⋊C₄×C₁₉	—	4	1	no	—
157	C₄²×C₁₉	—	2	2	no	—
158	C₄²×C₁₉	—	2	2	no	—
159	C₄²×C₁₉	—	2	1	no	—
160	C₄²×C₁₉	—	2	1	no	—
161	#22843	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂³×C₁₉	—	2	2	no	—
163	C₂³×C₁₉	—	2	2	no	—
164	C₂³×C₁₉	—	2	1	no	—
165	C₂³×C₁₉	—	2	2	no	—
166	C₂³×C₁₉	—	2	2	no	—
167	C₂³×C₁₉	—	2	2	no	—
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	2	2	no	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	2	1	no	—
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	2	1	no	—
176	C₂³×C₁₉	—	2	1	no	—
177	C₂³×C₁₉	C₄×D₄	1	4	yes	—
178	C₂³×C₁₉	#131	1	2	yes	—
179	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
180	Q₈×C₁₉	—	4	4	no	—
181	D₄×C₁₉	—	2	16	no	—
182	D₄×C₁₉	—	4	8	no	—
183	D₄×C₁₉	—	4	4	no	—
184	D₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	1	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	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
212	C₂×C₄×C₁₉	#131	1	4	yes	—
213	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
215	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
217	C₈×C₁₉	—	2	4	no	—
218	C₈×C₁₉	—	2	4	no	—
219	C₈×C₁₉	—	4	2	no	—
220	C₈×C₁₉	—	4	2	no	—
221	C₂×C₈×D₄	C₂×C₁₉	1	2	yes	complemented
222	C₂×#408	C₂×C₁₉	1	2	yes	complemented
223	#2388	C₂×C₁₉	1	1	yes	characteristic
224	#1955	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#1923	C₂×C₁₉	1	2	yes	complemented
226	#1870	C₂×C₁₉	1	2	yes	complemented
227	#1869	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#1850	C₂×C₁₉	1	2	yes	complemented
229	#1753	C₂×C₁₉	1	2	yes	complemented
230	C₂²×C₁₉	—	2	4	no	—
231	C₂²×C₁₉	—	2	4	no	—
232	C₂²×C₁₉	—	2	4	no	—
233	C₂²×C₁₉	—	2	4	no	—
234	C₂²×C₁₉	—	2	2	no	—
235	C₂²×C₁₉	—	4	1	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	—	4	2	no	—
238	C₂²×C₁₉	—	4	2	no	—
239	C₂²×C₁₉	—	4	2	no	—
240	C₂²×C₁₉	—	4	1	no	—
241	C₂²×C₁₉	—	4	2	no	—
242	C₂²×C₁₉	—	4	1	no	—
243	C₂²×C₁₉	—	4	2	no	—
244	C₂²×C₁₉	—	4	2	no	—
245	C₂²×C₁₉	—	4	1	no	—
246	C₂²×C₁₉	—	4	1	no	—
247	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
248	C₂²×C₁₉	#518	1	1	yes	characteristic
249	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
250	C₂²×C₁₉	C₂×#131	1	2	yes	—
251	C₂²×C₁₉	#568	1	1	yes	characteristic
252	C₄×C₁₉	—	2	4	no	—
253	C₄×C₁₉	—	2	4	no	—
254	C₄×C₁₉	—	4	1	no	—
255	C₄×C₁₉	—	4	1	no	—
256	C₄×C₁₉	—	4	2	no	—
257	C₄×C₁₉	—	4	1	no	—
258	C₄×C₁₉	—	4	1	no	—
259	C₄×C₁₉	D₄²	1	1	yes	characteristic
260	C₄×C₁₉	#546	1	2	yes	—
261	C₄×C₁₉	#551	1	1	yes	characteristic
262	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
263	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
264	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
265	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
267	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
268	C₈×D₄	—	2	8	no	—
269	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
270	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
271	#408	—	2	8	no	—
272	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
273	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
274	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
275	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
276	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
278	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
279	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
280	#395	C₄×C₁₉	1	1	yes	characteristic
281	#394	C₄×C₁₉	1	1	yes	characteristic
282	#394	C₄×C₁₉	1	2	yes	—
283	#393	C₄×C₁₉	1	1	yes	characteristic
284	#392	C₄×C₁₉	1	2	yes	—
285	#392	C₄×C₁₉	1	1	yes	characteristic
286	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
287	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
288	#336	C₂²×C₁₉	1	2	yes	—
289	#336	C₂²×C₁₉	1	2	yes	—
290	#336	C₂²×C₁₉	1	2	yes	—
291	C₂×C₁₉	—	4	4	no	—
292	C₂×C₁₉	—	4	2	no	—
293	C₂×C₁₉	—	8	1	no	—
294	C₂×C₁₉	#2358	1	1	yes	characteristic
295	C₂×C₁₉	#2929	1	2	yes	—
296	C₂×C₁₉	#2935	1	2	yes	—
297	C₂×C₁₉	#2976	1	1	yes	characteristic
298	C₂×C₁₉	#2979	1	1	yes	characteristic
299	C₂×#41	—	2	4	no	—
300	C₂×#41	—	2	4	no	—
301	C₂×#41	—	4	1	no	—
302	C₂×#41	—	4	1	no	—
303	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
304	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
305	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
306	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
307	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
311	C₂×M₁₆	—	2	4	no	—
312	C₂×M₁₆	—	2	4	no	—
313	C₂×M₁₆	—	4	2	no	—
314	C₂²×C₈	—	2	4	no	—
315	C₂²×C₈	—	2	4	no	—
316	C₂²×C₈	—	2	4	no	—
317	C₂²×C₈	—	4	1	no	—
318	C₂²×C₈	—	4	2	no	—
319	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
320	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
321	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
322	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
323	C₄×D₄	—	2	4	no	—
324	C₄×D₄	—	2	4	no	—
325	C₄×D₄	—	4	1	no	—
326	C₄×D₄	—	4	1	no	—
327	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
328	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
330	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
331	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
332	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
333	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
336	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
337	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
338	C₄⋊C₈	—	2	4	no	—
339	C₄⋊C₈	—	4	1	no	—
340	C₂²⋊C₈	—	2	4	no	—
341	C₂²⋊C₈	—	2	4	no	—
342	C₂²⋊C₈	—	2	4	no	—
343	C₂²⋊C₈	—	2	4	no	—
344	C₂²⋊C₈	—	4	1	no	—
345	C₂²⋊C₈	D₄×C₁₉	1	8	yes	complemented
346	#97	—	4	1	no	—
347	C₄×C₈	—	2	4	no	—
348	#95	C₂×C₄×C₁₉	1	2	yes	—
349	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
350	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
351	#95	C₂×C₄×C₁₉	1	2	yes	—
352	C₁₉	#22843	1	1	yes	characteristic, direct product factor, Sylow
353	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
354	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
355	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
356	#41	—	4	4	no	—
357	#41	—	4	8	no	—
358	#41	—	4	4	no	—
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	—	4	1	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	4	1	no	—
369	C₂×D₄	—	4	1	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	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	C₂²×C₄×C₁₉	1	2	yes	—
385	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
387	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
390	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
391	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
392	C₂²×C₄	#41×C₁₉	1	4	yes	—
393	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
394	M₁₆	—	4	8	no	—
395	C₂×C₈	—	2	2	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	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	4	4	no	—
406	C₂×C₈	—	4	8	no	—
407	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
408	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	4	1	no	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	1	no	—
417	C₂²⋊C₄	—	4	1	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	C₄×D₄×C₁₉	1	4	yes	—
438	C₂³	C₁₉×#131	1	2	yes	—
439	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
440	Q₈	—	4	4	no	—
441	D₄	—	2	16	no	—
442	D₄	—	4	8	no	—
443	D₄	—	4	4	no	—
444	D₄	—	4	4	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
472	C₂×C₄	C₁₉×#131	1	4	yes	—
473	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
474	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
475	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
477	C₈	—	2	4	no	—
478	C₈	—	2	4	no	—
479	C₈	—	4	2	no	—
480	C₈	—	4	2	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	1	no	—
498	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
499	C₂²	C₁₉×#518	1	1	yes	characteristic
500	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
501	C₂²	C₂×C₁₉×#131	1	2	yes	—
502	C₂²	C₁₉×#568	1	1	yes	characteristic
503	C₄	—	2	4	no	—
504	C₄	—	2	4	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	1	no	—
507	C₄	—	4	1	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	1	no	—
510	C₄	D₄²×C₁₉	1	1	yes	characteristic
511	C₄	C₁₉×#546	1	2	yes	—
512	C₄	C₁₉×#551	1	1	yes	characteristic
513	C₂	—	4	4	no	—
514	C₂	—	4	2	no	—
515	C₂	—	8	1	no	—
516	C₂	C₁₉×#2358	1	1	yes	characteristic
517	C₂	C₁₉×#2929	1	2	yes	—
518	C₂	C₁₉×#2935	1	2	yes	—
519	C₂	C₁₉×#2976	1	1	yes	characteristic
520	C₂	C₁₉×#2979	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂³×C₄
prime radical	C₁₉×#2388	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×D₄×C₁₉	C₂	semidirect
2. C₂×C₁₉×#408	C₂	semidirect
4. C₁₉×#1955	C₂	semidirect
5. C₁₉×#1923	C₂	semidirect
6. C₁₉×#1870	C₂	semidirect
7. C₁₉×#1869	C₂	semidirect
8. C₁₉×#1850	C₂	semidirect
9. C₁₉×#1753	C₂	semidirect
85. C₁₉×C₂²⋊C₈	D₄	semidirect
161. #22843	C₁₉	direct (N × H)
221. C₂×C₈×D₄	C₂×C₁₉	semidirect
222. C₂×#408	C₂×C₁₉	semidirect
224. #1955	C₂×C₁₉	semidirect
225. #1923	C₂×C₁₉	semidirect
226. #1870	C₂×C₁₉	semidirect
227. #1869	C₂×C₁₉	semidirect
228. #1850	C₂×C₁₉	semidirect
229. #1753	C₂×C₁₉	semidirect
345. C₂²⋊C₈	D₄×C₁₉	semidirect
352. C₁₉	#22843	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄×C₁₉	2
C₂×C₁₉×#408	2
C₁₉×#2388	2
C₁₉×#1955	2
C₁₉×#1923	2
C₁₉×#1870	2
C₁₉×#1869	2
C₁₉×#1850	2
C₁₉×#1753	2
#22843	19

Subgroups — C19×#22843 #18028802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22843 #18028802