Subgroups — C₁₉×#24503 #18030462

Order 4864.

1054 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#448	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2854	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2066	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2055	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1968	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1933	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂×C₁₉×#123	—	2	1	no	—
15	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#448	—	2	4	no	—
19	C₁₉×#431	—	2	4	no	—
20	C₂×C₁₉×#106	C₂²	1	2	yes	—
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₉×#103	C₂²	1	2	yes	—
23	C₂×C₁₉×#103	C₂²	1	2	yes	—
24	C₂×C₁₉×#103	C₂²	1	2	yes	—
25	C₂×C₁₉×#102	C₂²	1	2	yes	—
26	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
29	C₁₉×#391	—	2	1	no	—
30	C₁₉×#391	—	2	1	no	—
31	C₁₉×#391	C₂²	1	2	yes	—
32	C₁₉×#391	C₂²	1	2	yes	—
33	C₁₉×#390	C₂²	1	1	yes	characteristic
34	C₁₉×#390	C₂²	1	1	yes	characteristic
35	C₁₉×#389	C₂²	1	1	yes	characteristic
36	C₁₉×#389	C₂²	1	1	yes	characteristic
37	C₁₉×#388	—	2	1	no	—
38	C₁₉×#388	—	2	1	no	—
39	C₁₉×#386	—	2	1	no	—
40	C₁₉×#380	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#95	—	2	1	no	—
42	C₂×C₁₉×#95	—	2	1	no	—
43	C₁₉×#340	C₂²	1	2	yes	—
44	C₁₉×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₉	—	2	4	no	—
46	C₂²×Q₈×C₁₉	—	2	1	no	—
47	C₂²×Q₈×C₁₉	—	2	2	no	—
48	C₂²×Q₈×C₁₉	—	2	2	no	—
49	C₂²×Q₈×C₁₉	—	4	2	no	—
50	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₉	—	2	1	no	—
54	C₂³×C₄×C₁₉	—	2	1	no	—
55	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×SD₁₆×C₁₉	—	2	4	no	—
59	C₂×SD₁₆×C₁₉	—	2	4	no	—
60	C₂×SD₁₆×C₁₉	—	4	2	no	—
61	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
63	C₁₉×#123	—	4	4	no	—
64	C₁₉×#121	—	2	2	no	—
65	C₁₉×#121	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄²×C₁₉	—	2	2	no	—
81	C₂×C₄²×C₁₉	—	2	2	no	—
82	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₁₉×#106	—	4	2	no	—
87	C₁₉×C₄⋊C₈	—	2	4	no	—
88	C₁₉×#103	—	2	4	no	—
89	C₁₉×#103	—	2	4	no	—
90	C₁₉×#103	—	4	2	no	—
91	C₁₉×#102	—	4	2	no	—
92	C₁₉×C₂²⋊C₈	—	2	2	no	—
93	C₁₉×C₂²⋊C₈	D₄	1	4	yes	—
94	C₄×C₈×C₁₉	—	2	4	no	—
95	C₁₉×#95	—	2	2	no	—
96	C₁₉×#95	—	2	2	no	—
97	C₁₉×#95	—	2	2	no	—
98	C₁₉×#95	—	2	2	no	—
99	C₁₉×#95	—	2	1	no	—
100	C₁₉×#95	—	2	1	no	—
101	C₁₉×#95	—	2	1	no	—
102	C₂⁴×C₁₉	—	2	1	no	—
103	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂×Q₈×C₁₉	—	2	4	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	2	2	no	—
110	C₂×Q₈×C₁₉	—	4	8	no	—
111	C₂×Q₈×C₁₉	—	4	8	no	—
112	C₂×Q₈×C₁₉	—	4	2	no	—
113	C₂×Q₈×C₁₉	—	4	2	no	—
114	C₂×Q₈×C₁₉	#41	1	4	yes	—
115	C₂×D₄×C₁₉	—	2	1	no	—
116	C₂×D₄×C₁₉	—	2	1	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	4	2	no	—
120	C₂×D₄×C₁₉	—	4	2	no	—
121	C₂×D₄×C₁₉	—	4	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	4	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	4	1	no	—
135	C₂²×C₄×C₁₉	—	4	2	no	—
136	C₂²×C₄×C₁₉	—	4	2	no	—
137	C₂²×C₄×C₁₉	—	4	2	no	—
138	C₂²×C₄×C₁₉	—	4	2	no	—
139	C₂²×C₄×C₁₉	—	4	2	no	—
140	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	complemented
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	#41	1	2	yes	—
148	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
149	SD₁₆×C₁₉	—	4	8	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	4	2	no	—
163	C₄⋊C₄×C₁₉	—	4	2	no	—
164	C₄⋊C₄×C₁₉	—	4	2	no	—
165	C₂²⋊C₄×C₁₉	—	4	2	no	—
166	C₂²⋊C₄×C₁₉	—	4	2	no	—
167	C₂²⋊C₄×C₁₉	—	4	2	no	—
168	C₂²⋊C₄×C₁₉	—	4	2	no	—
169	C₂²⋊C₄×C₁₉	—	4	2	no	—
170	C₂²⋊C₄×C₁₉	—	4	2	no	—
171	C₄²×C₁₉	—	2	2	no	—
172	C₄²×C₁₉	—	2	2	no	—
173	C₄²×C₁₉	—	2	1	no	—
174	C₄²×C₁₉	—	2	1	no	—
175	C₄²×C₁₉	—	2	1	no	—
176	C₄²×C₁₉	—	2	1	no	—
177	#24503	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	—	2	1	no	—
181	C₂³×C₁₉	—	2	1	no	—
182	C₂³×C₁₉	—	4	1	no	—
183	C₂³×C₁₉	—	4	1	no	—
184	C₂³×C₁₉	—	4	1	no	—
185	C₂³×C₁₉	—	4	1	no	—
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	—	4	1	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	#121	1	2	yes	—
190	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
191	C₂³×C₁₉	#135	1	2	yes	—
192	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₁₉	—	2	4	no	—
194	Q₈×C₁₉	—	2	4	no	—
195	Q₈×C₁₉	—	4	8	no	—
196	Q₈×C₁₉	—	4	2	no	—
197	Q₈×C₁₉	—	4	2	no	—
198	D₄×C₁₉	—	4	2	no	—
199	D₄×C₁₉	—	4	2	no	—
200	D₄×C₁₉	—	8	4	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	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	8	no	—
210	C₂×C₄×C₁₉	—	2	4	no	—
211	C₂×C₄×C₁₉	—	2	4	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	4	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	4	4	no	—
217	C₂×C₄×C₁₉	—	4	8	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	8	4	no	—
233	C₂×C₄×C₁₉	#121	1	2	yes	—
234	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
235	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
236	C₂×C₄×C₁₉	#137	1	2	yes	—
237	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
239	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
241	C₈×C₁₉	—	2	4	no	—
242	C₈×C₁₉	—	4	2	no	—
243	C₂×#448	C₂×C₁₉	1	1	yes	characteristic
244	C₂×#431	C₂×C₁₉	1	1	yes	characteristic, complemented
245	#2854	C₂×C₁₉	1	1	yes	characteristic
246	C₂×#391	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#2066	C₂×C₁₉	1	2	yes	complemented
248	#2055	C₂×C₁₉	1	2	yes	complemented
249	#1968	C₂×C₁₉	1	2	yes	complemented
250	#1933	C₂×C₁₉	1	2	yes	complemented
251	#1874	C₂×C₁₉	1	1	yes	characteristic
252	#1853	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#1787	C₂×C₁₉	1	1	yes	characteristic, complemented
254	C₂²×C₁₉	—	2	2	no	—
255	C₂²×C₁₉	—	2	2	no	—
256	C₂²×C₁₉	—	2	2	no	—
257	C₂²×C₁₉	—	2	2	no	—
258	C₂²×C₁₉	—	2	2	no	—
259	C₂²×C₁₉	—	2	2	no	—
260	C₂²×C₁₉	—	8	1	no	—
261	C₂²×C₁₉	—	8	1	no	—
262	C₂²×C₁₉	—	8	1	no	—
263	C₂²×C₁₉	—	8	1	no	—
264	C₂²×C₁₉	—	8	1	no	—
265	C₂²×C₁₉	—	8	1	no	—
266	C₂²×C₁₉	—	8	1	no	—
267	C₂²×C₁₉	#465	1	4	yes	—
268	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
269	C₂²×C₁₉	#525	1	1	yes	characteristic
270	C₂²×C₁₉	#535	1	1	yes	characteristic
271	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
272	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
273	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
274	C₂²×C₁₉	#575	1	1	yes	characteristic
275	C₄×C₁₉	—	2	2	no	—
276	C₄×C₁₉	—	2	2	no	—
277	C₄×C₁₉	—	2	2	no	—
278	C₄×C₁₉	—	2	2	no	—
279	C₄×C₁₉	—	4	4	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	8	1	no	—
282	C₄×C₁₉	—	8	1	no	—
283	C₄×C₁₉	—	8	2	no	—
284	C₄×C₁₉	—	8	1	no	—
285	C₄×C₁₉	#546	1	2	yes	—
286	C₄×C₁₉	#551	1	2	yes	—
287	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
288	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
289	C₂×#123	—	2	1	no	—
290	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
291	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
292	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
293	#448	—	2	4	no	—
294	#431	—	2	4	no	—
295	C₂×#106	C₂²×C₁₉	1	2	yes	—
296	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
297	C₂×#103	C₂²×C₁₉	1	2	yes	—
298	C₂×#103	C₂²×C₁₉	1	2	yes	—
299	C₂×#103	C₂²×C₁₉	1	2	yes	—
300	C₂×#102	C₂²×C₁₉	1	2	yes	—
301	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
304	#391	—	2	1	no	—
305	#391	—	2	1	no	—
306	#391	C₂²×C₁₉	1	2	yes	—
307	#391	C₂²×C₁₉	1	2	yes	—
308	#390	C₂²×C₁₉	1	1	yes	characteristic
309	#390	C₂²×C₁₉	1	1	yes	characteristic
310	#389	C₂²×C₁₉	1	1	yes	characteristic
311	#389	C₂²×C₁₉	1	1	yes	characteristic
312	#388	—	2	1	no	—
313	#388	—	2	1	no	—
314	#386	—	2	1	no	—
315	#380	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×#95	—	2	1	no	—
317	C₂×#95	—	2	1	no	—
318	#340	C₂²×C₁₉	1	2	yes	—
319	#340	C₂²×C₁₉	1	2	yes	—
320	C₂×C₁₉	—	2	4	no	—
321	C₂×C₁₉	—	16	1	no	—
322	C₂×C₁₉	#2411	1	1	yes	characteristic
323	C₂×C₁₉	C₂×#465	1	1	yes	characteristic
324	C₂×C₁₉	#3056	1	1	yes	characteristic
325	C₂×C₁₉	#3103	1	1	yes	characteristic
326	C₂×C₁₉	#3108	1	1	yes	characteristic
327	C₂×C₁₉	#3206	1	1	yes	characteristic
328	C₂×C₁₉	#3211	1	1	yes	characteristic
329	C₂²×Q₈	—	2	4	no	—
330	C₂²×Q₈	—	2	1	no	—
331	C₂²×Q₈	—	2	2	no	—
332	C₂²×Q₈	—	2	2	no	—
333	C₂²×Q₈	—	4	2	no	—
334	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
340	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂×SD₁₆	—	2	4	no	—
343	C₂×SD₁₆	—	2	4	no	—
344	C₂×SD₁₆	—	4	2	no	—
345	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
346	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
347	#123	—	4	4	no	—
348	#121	—	2	2	no	—
349	#121	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	4	2	no	—
354	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
355	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₄²	—	2	2	no	—
365	C₂×C₄²	—	2	2	no	—
366	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
367	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
370	#106	—	4	2	no	—
371	C₄⋊C₈	—	2	4	no	—
372	#103	—	2	4	no	—
373	#103	—	2	4	no	—
374	#103	—	4	2	no	—
375	#102	—	4	2	no	—
376	C₂²⋊C₈	—	2	2	no	—
377	C₂²⋊C₈	D₄×C₁₉	1	4	yes	—
378	C₄×C₈	—	2	4	no	—
379	#95	—	2	2	no	—
380	#95	—	2	2	no	—
381	#95	—	2	2	no	—
382	#95	—	2	2	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	C₁₉	#24503	1	1	yes	characteristic, direct product factor, Sylow
387	C₂⁴	—	2	1	no	—
388	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	4	8	no	—
396	C₂×Q₈	—	4	8	no	—
397	C₂×Q₈	—	4	2	no	—
398	C₂×Q₈	—	4	2	no	—
399	C₂×Q₈	#41×C₁₉	1	4	yes	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	4	1	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	SD₁₆×C₁₉	1	4	yes	complemented
426	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
432	C₂²×C₄	#41×C₁₉	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
434	SD₁₆	—	4	8	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₄⋊C₄	—	4	2	no	—
449	C₄⋊C₄	—	4	2	no	—
450	C₂²⋊C₄	—	4	2	no	—
451	C₂²⋊C₄	—	4	2	no	—
452	C₂²⋊C₄	—	4	2	no	—
453	C₂²⋊C₄	—	4	2	no	—
454	C₂²⋊C₄	—	4	2	no	—
455	C₂²⋊C₄	—	4	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	1	no	—
473	C₂³	C₁₉×#121	1	2	yes	—
474	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
475	C₂³	C₁₉×#135	1	2	yes	—
476	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
477	Q₈	—	2	4	no	—
478	Q₈	—	2	4	no	—
479	Q₈	—	4	8	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	D₄	—	8	4	no	—
485	C₂×C₄	—	2	8	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	8	4	no	—
517	C₂×C₄	C₁₉×#121	1	2	yes	—
518	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
519	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
520	C₂×C₄	C₁₉×#137	1	2	yes	—
521	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
522	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
523	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
524	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
525	C₈	—	2	4	no	—
526	C₈	—	4	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	C₁₉×#465	1	4	yes	—
541	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
542	C₂²	C₁₉×#525	1	1	yes	characteristic
543	C₂²	C₁₉×#535	1	1	yes	characteristic
544	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
545	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
546	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
547	C₂²	C₁₉×#575	1	1	yes	characteristic
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	2	no	—
552	C₄	—	4	4	no	—
553	C₄	—	4	1	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	2	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	C₁₉×#546	1	2	yes	—
559	C₄	C₁₉×#551	1	2	yes	—
560	C₂	—	2	4	no	—
561	C₂	—	16	1	no	—
562	C₂	C₁₉×#2411	1	1	yes	characteristic
563	C₂	C₂×C₁₉×#465	1	1	yes	characteristic
564	C₂	C₁₉×#3056	1	1	yes	characteristic
565	C₂	C₁₉×#3103	1	1	yes	characteristic
566	C₂	C₁₉×#3108	1	1	yes	characteristic
567	C₂	C₁₉×#3206	1	1	yes	characteristic
568	C₂	C₁₉×#3211	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#431	C₂	semidirect
4. C₂×C₁₉×#391	C₂	semidirect
5. C₁₉×#2066	C₂	semidirect
6. C₁₉×#2055	C₂	semidirect
7. C₁₉×#1968	C₂	semidirect
8. C₁₉×#1933	C₂	semidirect
10. C₁₉×#1853	C₂	semidirect
11. C₁₉×#1787	C₂	semidirect
140. C₂²×C₄×C₁₉	SD₁₆	semidirect
177. #24503	C₁₉	direct (N × H)
244. C₂×#431	C₂×C₁₉	semidirect
246. C₂×#391	C₂×C₁₉	semidirect
247. #2066	C₂×C₁₉	semidirect
248. #2055	C₂×C₁₉	semidirect
249. #1968	C₂×C₁₉	semidirect
250. #1933	C₂×C₁₉	semidirect
252. #1853	C₂×C₁₉	semidirect
253. #1787	C₂×C₁₉	semidirect
386. C₁₉	#24503	direct (N × H)
425. C₂²×C₄	SD₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#448	2
C₂×C₁₉×#431	2
C₁₉×#2854	2
C₂×C₁₉×#391	2
C₁₉×#2066	2
C₁₉×#2055	2
C₁₉×#1968	2
C₁₉×#1933	2
C₁₉×#1874	2
C₁₉×#1853	2
C₁₉×#1787	2
#24503	19

Subgroups — C19×#24503 #18030462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24503 #18030462