Subgroups — C₁₉×#14538 #18020497

Order 4864.

1402 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#395	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#391	C₂	1	2	yes	maximal
3	C₂×C₁₉×#387	C₂	1	2	yes	maximal
4	C₁₉×#1443	C₂	1	2	yes	maximal
5	C₁₉×#1441	C₂	1	2	yes	maximal
6	C₁₉×#1441	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1436	C₂	1	2	yes	maximal
8	C₁₉×#1436	C₂	1	2	yes	maximal
9	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#395	C₄	1	8	yes	complemented
19	C₁₉×#391	—	2	8	no	—
20	C₁₉×#387	—	2	8	no	—
21	C₂×C₁₉×#95	C₂²	1	2	yes	—
22	C₂×C₁₉×#95	C₂²	1	2	yes	—
23	C₂×C₁₉×#95	C₂²	1	2	yes	—
24	C₂×C₁₉×#95	C₂²	1	2	yes	—
25	C₂×C₁₉×#95	C₂²	1	2	yes	—
26	C₂×C₁₉×#95	C₂²	1	2	yes	—
27	C₂×C₁₉×#95	C₂²	1	2	yes	—
28	C₂×C₁₉×#95	C₂²	1	2	yes	—
29	C₂×C₁₉×#95	C₂²	1	2	yes	—
30	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#95	C₂²	1	2	yes	—
32	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#95	C₂²	1	2	yes	—
34	C₂²×Q₈×C₁₉	—	2	4	no	—
35	C₂²×Q₈×C₁₉	—	2	4	no	—
36	C₂²×Q₈×C₁₉	—	4	1	no	—
37	C₂²×Q₈×C₁₉	—	4	1	no	—
38	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₉	Q₈	1	4	yes	complemented
62	C₂×C₄²×C₁₉	—	2	4	no	—
63	C₂×C₄²×C₁₉	—	2	4	no	—
64	C₂×C₄²×C₁₉	—	2	2	no	—
65	C₂×C₄²×C₁₉	—	4	2	no	—
66	C₂×C₄²×C₁₉	—	4	1	no	—
67	C₂×C₄²×C₁₉	—	4	1	no	—
68	C₁₉×#95	—	2	4	no	—
69	C₁₉×#95	—	2	4	no	—
70	C₁₉×#95	—	2	4	no	—
71	C₁₉×#95	—	2	4	no	—
72	C₁₉×#95	—	2	4	no	—
73	C₁₉×#95	—	2	4	no	—
74	C₁₉×#95	—	2	4	no	—
75	C₁₉×#95	—	4	2	no	—
76	C₁₉×#95	—	4	2	no	—
77	C₁₉×#95	—	4	1	no	—
78	C₁₉×#95	C₂×C₄	1	4	yes	—
79	C₁₉×#95	C₂×C₄	1	8	yes	—
80	C₁₉×#95	D₄	1	8	yes	—
81	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
82	C₂×Q₈×C₁₉	—	2	16	no	—
83	C₂×Q₈×C₁₉	—	4	4	no	—
84	C₂×Q₈×C₁₉	—	4	4	no	—
85	C₂×Q₈×C₁₉	—	4	8	no	—
86	C₂×Q₈×C₁₉	—	4	4	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	—	2	1	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	1	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	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	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	2	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	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
143	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
144	C₂²×C₄×C₁₉	#41	1	4	yes	—
145	C₂²×C₄×C₁₉	#41	1	2	yes	—
146	C₄⋊C₄×C₁₉	—	2	16	no	—
147	C₄⋊C₄×C₁₉	—	4	4	no	—
148	C₄⋊C₄×C₁₉	—	4	4	no	—
149	C₄⋊C₄×C₁₉	—	4	8	no	—
150	C₄⋊C₄×C₁₉	—	4	4	no	—
151	C₄²×C₁₉	—	4	8	no	—
152	C₄²×C₁₉	—	4	4	no	—
153	#14538	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
155	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
156	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
157	C₂³×C₁₉	C₂×#41	1	2	yes	—
158	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
159	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
160	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
162	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
163	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
164	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
165	Q₈×C₁₉	—	4	16	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	4	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	2	4	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	4	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	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	2	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
224	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
225	C₂×#395	C₂×C₁₉	1	1	yes	characteristic
226	C₂×#391	C₂×C₁₉	1	2	yes	—
227	C₂×#387	C₂×C₁₉	1	2	yes	—
228	#1443	C₂×C₁₉	1	2	yes	—
229	#1441	C₂×C₁₉	1	2	yes	—
230	#1441	C₂×C₁₉	1	1	yes	characteristic
231	#1436	C₂×C₁₉	1	2	yes	—
232	#1436	C₂×C₁₉	1	2	yes	—
233	C₄⋊#95	C₂×C₁₉	1	1	yes	characteristic
234	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
235	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
236	C₂²×C₁₉	#518	1	1	yes	characteristic
237	C₂²×C₁₉	#519	1	2	yes	—
238	C₂²×C₁₉	#520	1	1	yes	characteristic
239	C₂²×C₁₉	#536	1	2	yes	—
240	C₂²×C₁₉	#537	1	2	yes	—
241	C₂²×C₁₉	#538	1	1	yes	characteristic
242	C₂²×C₁₉	#539	1	1	yes	characteristic
243	C₂²×C₁₉	#541	1	2	yes	—
244	C₂²×C₁₉	#542	1	2	yes	—
245	C₂²×C₁₉	#543	1	1	yes	characteristic
246	C₂²×C₁₉	#544	1	1	yes	characteristic
247	C₂²×C₁₉	D₄²	1	1	yes	characteristic
248	C₂²×C₁₉	#546	1	2	yes	—
249	C₂²×C₁₉	#547	1	2	yes	—
250	C₂²×C₁₉	D₄×Q₈	1	2	yes	—
251	C₂²×C₁₉	#551	1	1	yes	characteristic
252	C₂²×C₁₉	#556	1	2	yes	—
253	C₂²×C₁₉	#557	1	2	yes	—
254	C₂²×C₁₉	#563	1	1	yes	characteristic
255	C₂²×C₁₉	#563	1	1	yes	characteristic
256	C₂²×C₁₉	#563	1	2	yes	—
257	C₄×C₁₉	—	2	4	no	—
258	C₄×C₁₉	—	2	8	no	—
259	C₄×C₁₉	—	4	4	no	—
260	C₄×C₁₉	—	4	2	no	—
261	C₄×C₁₉	—	4	2	no	—
262	C₄×C₁₉	—	4	4	no	—
263	C₄×C₁₉	—	4	4	no	—
264	C₄×C₁₉	—	4	4	no	—
265	C₄×C₁₉	—	8	2	no	—
266	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
268	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
269	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
270	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
271	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
272	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
273	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
274	#395	C₄×C₁₉	1	8	yes	complemented
275	#391	—	2	8	no	—
276	#387	—	2	8	no	—
277	C₂×#95	C₂²×C₁₉	1	2	yes	—
278	C₂×#95	C₂²×C₁₉	1	2	yes	—
279	C₂×#95	C₂²×C₁₉	1	2	yes	—
280	C₂×#95	C₂²×C₁₉	1	2	yes	—
281	C₂×#95	C₂²×C₁₉	1	2	yes	—
282	C₂×#95	C₂²×C₁₉	1	2	yes	—
283	C₂×#95	C₂²×C₁₉	1	2	yes	—
284	C₂×#95	C₂²×C₁₉	1	2	yes	—
285	C₂×#95	C₂²×C₁₉	1	2	yes	—
286	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×#95	C₂²×C₁₉	1	2	yes	—
288	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×#95	C₂²×C₁₉	1	2	yes	—
290	C₂×C₁₉	#2323	1	2	yes	—
291	C₂×C₁₉	#2329	1	1	yes	characteristic
292	C₂×C₁₉	#2358	1	1	yes	characteristic
293	C₂×C₁₉	#2365	1	2	yes	—
294	C₂×C₁₉	#2381	1	1	yes	characteristic
295	C₂×C₁₉	#2680	1	1	yes	characteristic
296	C₂×C₁₉	#2683	1	1	yes	characteristic
297	C₂×C₁₉	#2713	1	2	yes	—
298	C₂×C₁₉	#2715	1	2	yes	—
299	C₂×C₁₉	#2789	1	1	yes	characteristic
300	C₂×C₁₉	#2799	1	1	yes	characteristic
301	C₂²×Q₈	—	2	4	no	—
302	C₂²×Q₈	—	2	4	no	—
303	C₂²×Q₈	—	4	1	no	—
304	C₂²×Q₈	—	4	1	no	—
305	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
306	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
307	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
310	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
311	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
312	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
313	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
314	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
315	C₂×C₄⋊C₄	—	2	4	no	—
316	C₂×C₄⋊C₄	—	2	4	no	—
317	C₂×C₄⋊C₄	—	2	4	no	—
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	—	2	4	no	—
320	C₂×C₄⋊C₄	—	4	1	no	—
321	C₂×C₄⋊C₄	—	4	1	no	—
322	C₂×C₄⋊C₄	—	4	1	no	—
323	C₂×C₄⋊C₄	—	4	1	no	—
324	C₂×C₄⋊C₄	—	4	2	no	—
325	C₂×C₄⋊C₄	—	4	1	no	—
326	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
327	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
328	C₂×C₄⋊C₄	Q₈×C₁₉	1	4	yes	complemented
329	C₂×C₄²	—	2	4	no	—
330	C₂×C₄²	—	2	4	no	—
331	C₂×C₄²	—	2	2	no	—
332	C₂×C₄²	—	4	2	no	—
333	C₂×C₄²	—	4	1	no	—
334	C₂×C₄²	—	4	1	no	—
335	#95	—	2	4	no	—
336	#95	—	2	4	no	—
337	#95	—	2	4	no	—
338	#95	—	2	4	no	—
339	#95	—	2	4	no	—
340	#95	—	2	4	no	—
341	#95	—	2	4	no	—
342	#95	—	4	2	no	—
343	#95	—	4	2	no	—
344	#95	—	4	1	no	—
345	#95	C₂×C₄×C₁₉	1	4	yes	—
346	#95	C₂×C₄×C₁₉	1	8	yes	—
347	#95	D₄×C₁₉	1	8	yes	—
348	C₁₉	#14538	1	1	yes	characteristic, direct product factor, Sylow
349	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
350	C₂×Q₈	—	2	16	no	—
351	C₂×Q₈	—	4	4	no	—
352	C₂×Q₈	—	4	4	no	—
353	C₂×Q₈	—	4	8	no	—
354	C₂×Q₈	—	4	4	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	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	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
403	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
404	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
405	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
406	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
408	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
409	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
410	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
411	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
412	C₂²×C₄	#41×C₁₉	1	4	yes	—
413	C₂²×C₄	#41×C₁₉	1	2	yes	—
414	C₄⋊C₄	—	2	16	no	—
415	C₄⋊C₄	—	4	4	no	—
416	C₄⋊C₄	—	4	4	no	—
417	C₄⋊C₄	—	4	8	no	—
418	C₄⋊C₄	—	4	4	no	—
419	C₄²	—	4	8	no	—
420	C₄²	—	4	4	no	—
421	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
422	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
423	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
424	C₂³	C₂×#41×C₁₉	1	2	yes	—
425	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
426	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
428	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
429	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
430	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
431	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
432	Q₈	—	4	16	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
491	C₂×C₄	C₄×Q₈×C₁₉	1	4	yes	—
492	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
493	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
494	C₂²	C₁₉×#518	1	1	yes	characteristic
495	C₂²	C₁₉×#519	1	2	yes	—
496	C₂²	C₁₉×#520	1	1	yes	characteristic
497	C₂²	C₁₉×#536	1	2	yes	—
498	C₂²	C₁₉×#537	1	2	yes	—
499	C₂²	C₁₉×#538	1	1	yes	characteristic
500	C₂²	C₁₉×#539	1	1	yes	characteristic
501	C₂²	C₁₉×#541	1	2	yes	—
502	C₂²	C₁₉×#542	1	2	yes	—
503	C₂²	C₁₉×#543	1	1	yes	characteristic
504	C₂²	C₁₉×#544	1	1	yes	characteristic
505	C₂²	D₄²×C₁₉	1	1	yes	characteristic
506	C₂²	C₁₉×#546	1	2	yes	—
507	C₂²	C₁₉×#547	1	2	yes	—
508	C₂²	D₄×Q₈×C₁₉	1	2	yes	—
509	C₂²	C₁₉×#551	1	1	yes	characteristic
510	C₂²	C₁₉×#556	1	2	yes	—
511	C₂²	C₁₉×#557	1	2	yes	—
512	C₂²	C₁₉×#563	1	1	yes	characteristic
513	C₂²	C₁₉×#563	1	1	yes	characteristic
514	C₂²	C₁₉×#563	1	2	yes	—
515	C₄	—	2	4	no	—
516	C₄	—	2	8	no	—
517	C₄	—	4	4	no	—
518	C₄	—	4	4	no	—
519	C₄	—	4	4	no	—
520	C₄	—	4	4	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	8	2	no	—
524	C₂	C₁₉×#2323	1	2	yes	—
525	C₂	C₁₉×#2329	1	1	yes	characteristic
526	C₂	C₁₉×#2358	1	1	yes	characteristic
527	C₂	C₁₉×#2365	1	2	yes	—
528	C₂	C₁₉×#2381	1	1	yes	characteristic
529	C₂	C₁₉×#2680	1	1	yes	characteristic
530	C₂	C₁₉×#2683	1	1	yes	characteristic
531	C₂	C₁₉×#2713	1	2	yes	—
532	C₂	C₁₉×#2715	1	2	yes	—
533	C₂	C₁₉×#2789	1	1	yes	characteristic
534	C₂	C₁₉×#2799	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
18. C₁₉×#395	C₄	semidirect
61. C₂×C₄⋊C₄×C₁₉	Q₈	semidirect
153. #14538	C₁₉	direct (N × H)
274. #395	C₄×C₁₉	semidirect
328. C₂×C₄⋊C₄	Q₈×C₁₉	semidirect
348. C₁₉	#14538	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×C₁₉×#395	2
C₂×C₁₉×#391	2
C₂×C₁₉×#387	2
C₁₉×#1443	2
C₁₉×#1441	2
C₁₉×#1436	2
C₁₉×C₄⋊#95	2
#14538	19

Subgroups — C19×#14538 #18020497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14538 #18020497