Subgroups — C₁₉×#22890 #18028849

Order 4864.

1020 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#455	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2947	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2897	C₂	1	2	yes	maximal
4	C₁₉×#1959	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1931	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1908	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1888	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1859	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1765	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#137	C₂²	1	2	yes	—
12	C₂×C₁₉×#131	C₂²	1	2	yes	—
13	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
14	C₁₉×#520	C₂²	1	2	yes	—
15	C₁₉×#519	C₂²	1	1	yes	characteristic, complemented
16	C₁₉×#455	C₄	1	8	yes	complemented
17	C₁₉×#441	—	2	2	no	—
18	C₁₉×#440	—	2	2	no	—
19	C₄×Q₁₆×C₁₉	—	2	2	no	—
20	C₄×SD₁₆×C₁₉	—	2	2	no	—
21	C₁₉×#428	C₂²	1	2	yes	complemented
22	C₂×C₁₉×#104	C₂²	1	2	yes	—
23	C₁₉×#418	—	2	2	no	—
24	C₁₉×#418	C₂²	1	2	yes	—
25	C₁₉×#417	—	2	2	no	—
26	C₁₉×#417	C₂²	1	2	yes	—
27	C₁₉×#416	—	2	2	no	—
28	C₁₉×#416	C₂²	1	2	yes	—
29	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
30	C₂×C₁₉×#102	—	2	2	no	—
31	C₂×C₁₉×#102	C₂²	1	2	yes	—
32	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
34	C₁₉×#405	C₂²	1	2	yes	complemented
35	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#384	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#343	C₂²	1	2	yes	complemented
38	C₁₉×#341	C₂²	1	2	yes	complemented
39	C₁₉×#339	C₂²	1	2	yes	complemented
40	C₁₉×H(5,𝔽₂)	—	2	4	no	—
41	C₁₉×H(5,𝔽₂)	—	4	1	no	—
42	C₁₉×H(5,𝔽₂)	C₂×C₄	1	4	yes	—
43	C₂×#41×C₁₉	—	2	2	no	—
44	C₂×#41×C₁₉	C₂³	1	2	yes	—
45	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	—	2	2	no	—
47	C₂²×D₄×C₁₉	—	4	1	no	—
48	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₁₉×#137	—	2	4	no	—
50	C₁₉×#137	C₂×C₄	1	8	yes	complemented
51	C₂×Q₁₆×C₁₉	—	2	2	no	—
52	C₂×SD₁₆×C₁₉	—	2	2	no	—
53	C₁₉×#131	—	2	4	no	—
54	C₁₉×#131	—	4	2	no	—
55	C₂×M₁₆×C₁₉	—	2	2	no	—
56	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
57	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₉	—	2	2	no	—
59	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
60	C₁₉×#124	—	4	1	no	—
61	C₁₉×#124	C₂×C₄	1	4	yes	complemented
62	C₄×Q₈×C₁₉	—	2	2	no	—
63	C₄×Q₈×C₁₉	—	2	2	no	—
64	C₄×Q₈×C₁₉	—	2	2	no	—
65	C₄×D₄×C₁₉	—	2	2	no	—
66	C₄×D₄×C₁₉	—	4	2	no	—
67	C₁₉×#117	—	2	2	no	—
68	C₁₉×#117	—	4	1	no	—
69	C₁₉×#117	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
74	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×#107	—	2	2	no	—
76	C₁₉×#106	—	2	2	no	—
77	C₁₉×#104	C₂×C₄	1	8	yes	complemented
78	C₁₉×#103	—	2	2	no	—
79	C₁₉×#103	—	2	2	no	—
80	C₁₉×#103	—	2	2	no	—
81	C₁₉×#103	D₄	1	2	yes	—
82	C₁₉×#103	D₄	1	2	yes	—
83	C₁₉×#102	—	2	2	no	—
84	C₁₉×#102	—	2	2	no	—
85	C₁₉×#102	—	2	2	no	—
86	C₁₉×#102	—	2	2	no	—
87	C₁₉×#102	—	2	2	no	—
88	C₁₉×#102	D₄	1	2	yes	—
89	C₁₉×#102	D₄	1	2	yes	—
90	C₁₉×#101	—	4	1	no	—
91	C₁₉×#100	C₂×C₄	1	4	yes	complemented
92	C₁₉×#97	—	2	2	no	—
93	C₁₉×#97	—	4	1	no	—
94	C₄×C₈×C₁₉	—	2	2	no	—
95	C₂⁴×C₁₉	—	2	1	no	—
96	C₂⁴×C₁₉	—	4	1	no	—
97	#41×C₁₉	—	2	2	no	—
98	#41×C₁₉	—	2	2	no	—
99	#41×C₁₉	—	2	8	no	—
100	#41×C₁₉	—	4	4	no	—
101	#41×C₁₉	C₂²×C₄	1	4	yes	—
102	#41×C₁₉	#41	1	4	yes	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
107	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	8	no	—
110	C₂×D₄×C₁₉	—	2	2	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	4	4	no	—
114	C₂×D₄×C₁₉	—	4	2	no	—
115	C₂×D₄×C₁₉	—	4	4	no	—
116	C₂×D₄×C₁₉	—	4	4	no	—
117	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
118	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	—	4	2	no	—
125	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
126	Q₁₆×C₁₉	—	2	8	no	—
127	SD₁₆×C₁₉	—	2	8	no	—
128	M₁₆×C₁₉	—	2	2	no	—
129	M₁₆×C₁₉	—	2	2	no	—
130	M₁₆×C₁₉	—	2	2	no	—
131	M₁₆×C₁₉	—	4	4	no	—
132	M₁₆×C₁₉	C₂²×C₄	1	4	yes	—
133	C₂×C₈×C₁₉	—	2	2	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	—	4	4	no	—
138	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	4	2	no	—
143	C₄⋊C₄×C₁₉	—	4	1	no	—
144	C₄⋊C₄×C₁₉	—	4	1	no	—
145	C₄⋊C₄×C₁₉	—	8	2	no	—
146	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₂²⋊C₄×C₁₉	—	2	2	no	—
149	C₂²⋊C₄×C₁₉	—	4	4	no	—
150	C₂²⋊C₄×C₁₉	—	4	2	no	—
151	C₄²×C₁₉	—	2	2	no	—
152	C₄²×C₁₉	—	2	1	no	—
153	C₄²×C₁₉	—	4	2	no	—
154	C₄²×C₁₉	—	4	2	no	—
155	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
156	#22890	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	4	4	no	—
160	C₂³×C₁₉	—	4	1	no	—
161	C₂³×C₁₉	—	4	1	no	—
162	C₂³×C₁₉	—	8	1	no	—
163	C₂³×C₁₉	—	8	1	no	—
164	C₂³×C₁₉	—	16	1	no	—
165	C₂³×C₁₉	—	16	1	no	—
166	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
167	Q₈×C₁₉	—	2	2	no	—
168	Q₈×C₁₉	—	2	4	no	—
169	Q₈×C₁₉	—	4	2	no	—
170	Q₈×C₁₉	C₄×D₄	1	4	yes	—
171	D₄×C₁₉	—	2	4	no	—
172	D₄×C₁₉	—	2	4	no	—
173	D₄×C₁₉	—	2	4	no	—
174	D₄×C₁₉	—	2	2	no	—
175	D₄×C₁₉	—	4	8	no	—
176	D₄×C₁₉	—	4	2	no	—
177	D₄×C₁₉	C₄×D₄	1	4	yes	—
178	C₂×C₄×C₁₉	—	2	2	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	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	4	4	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	8	2	no	—
192	C₂×C₄×C₁₉	—	16	2	no	—
193	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
196	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
197	C₈×C₁₉	—	2	4	no	—
198	C₈×C₁₉	—	2	2	no	—
199	C₈×C₁₉	—	2	2	no	—
200	C₈×C₁₉	—	4	2	no	—
201	C₂×#455	C₂×C₁₉	1	1	yes	characteristic
202	#2947	C₂×C₁₉	1	2	yes	complemented
203	#2897	C₂×C₁₉	1	2	yes	—
204	#1959	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#1931	C₂×C₁₉	1	2	yes	complemented
206	#1908	C₂×C₁₉	1	2	yes	complemented
207	#1888	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#1859	C₂×C₁₉	1	2	yes	complemented
209	#1765	C₂×C₁₉	1	2	yes	complemented
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	—	2	4	no	—
213	C₂²×C₁₉	—	4	2	no	—
214	C₂²×C₁₉	—	4	2	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	8	2	no	—
217	C₂²×C₁₉	—	8	1	no	—
218	C₂²×C₁₉	—	8	1	no	—
219	C₂²×C₁₉	—	16	1	no	—
220	C₂²×C₁₉	—	16	4	no	—
221	C₂²×C₁₉	#518	1	1	yes	characteristic
222	C₂²×C₁₉	D₄²	1	1	yes	characteristic
223	C₂²×C₁₉	#551	1	1	yes	characteristic
224	C₄×C₁₉	—	2	4	no	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	4	2	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	4	2	no	—
229	C₄×C₁₉	—	8	2	no	—
230	C₄×C₁₉	C₂×C₄×D₄	1	2	yes	—
231	C₄×C₁₉	#546	1	2	yes	—
232	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×#137	C₂²×C₁₉	1	2	yes	—
234	C₂×#131	C₂²×C₁₉	1	2	yes	—
235	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
236	#520	C₂²×C₁₉	1	2	yes	—
237	#519	C₂²×C₁₉	1	1	yes	characteristic, complemented
238	#455	C₄×C₁₉	1	8	yes	complemented
239	#441	—	2	2	no	—
240	#440	—	2	2	no	—
241	C₄×Q₁₆	—	2	2	no	—
242	C₄×SD₁₆	—	2	2	no	—
243	#428	C₂²×C₁₉	1	2	yes	complemented
244	C₂×#104	C₂²×C₁₉	1	2	yes	—
245	#418	—	2	2	no	—
246	#418	C₂²×C₁₉	1	2	yes	—
247	#417	—	2	2	no	—
248	#417	C₂²×C₁₉	1	2	yes	—
249	#416	—	2	2	no	—
250	#416	C₂²×C₁₉	1	2	yes	—
251	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
252	C₂×#102	—	2	2	no	—
253	C₂×#102	C₂²×C₁₉	1	2	yes	—
254	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic, complemented
255	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
256	#405	C₂²×C₁₉	1	2	yes	complemented
257	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
258	#384	C₂²×C₁₉	1	1	yes	characteristic, complemented
259	#343	C₂²×C₁₉	1	2	yes	complemented
260	#341	C₂²×C₁₉	1	2	yes	complemented
261	#339	C₂²×C₁₉	1	2	yes	complemented
262	C₂×C₁₉	—	2	1	no	—
263	C₂×C₁₉	—	2	1	no	—
264	C₂×C₁₉	—	4	4	no	—
265	C₂×C₁₉	—	8	2	no	—
266	C₂×C₁₉	#2358	1	1	yes	characteristic
267	C₂×C₁₉	#3288	1	1	yes	characteristic
268	C₂×C₁₉	#3289	1	1	yes	characteristic
269	H(5,𝔽₂)	—	2	4	no	—
270	H(5,𝔽₂)	—	4	1	no	—
271	H(5,𝔽₂)	C₂×C₄×C₁₉	1	4	yes	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	C₂³×C₁₉	1	2	yes	—
274	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	—	4	1	no	—
277	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
278	#137	—	2	4	no	—
279	#137	C₂×C₄×C₁₉	1	8	yes	complemented
280	C₂×Q₁₆	—	2	2	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	#131	—	2	4	no	—
283	#131	—	4	2	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
286	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
289	#124	—	4	1	no	—
290	#124	C₂×C₄×C₁₉	1	4	yes	complemented
291	C₄×Q₈	—	2	2	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	4	2	no	—
296	#117	—	2	2	no	—
297	#117	—	4	1	no	—
298	#117	C₂³×C₁₉	1	2	yes	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	4	1	no	—
301	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
302	C₂×C₂²⋊C₄	—	4	1	no	—
303	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
304	#107	—	2	2	no	—
305	#106	—	2	2	no	—
306	#104	C₂×C₄×C₁₉	1	8	yes	complemented
307	#103	—	2	2	no	—
308	#103	—	2	2	no	—
309	#103	—	2	2	no	—
310	#103	D₄×C₁₉	1	2	yes	—
311	#103	D₄×C₁₉	1	2	yes	—
312	#102	—	2	2	no	—
313	#102	—	2	2	no	—
314	#102	—	2	2	no	—
315	#102	—	2	2	no	—
316	#102	—	2	2	no	—
317	#102	D₄×C₁₉	1	2	yes	—
318	#102	D₄×C₁₉	1	2	yes	—
319	#101	—	4	1	no	—
320	#100	C₂×C₄×C₁₉	1	4	yes	complemented
321	#97	—	2	2	no	—
322	#97	—	4	1	no	—
323	C₄×C₈	—	2	2	no	—
324	C₁₉	#22890	1	1	yes	characteristic, direct product factor, Sylow
325	C₂⁴	—	2	1	no	—
326	C₂⁴	—	4	1	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	#41	—	2	8	no	—
330	#41	—	4	4	no	—
331	#41	C₂²×C₄×C₁₉	1	4	yes	—
332	#41	#41×C₁₉	1	4	yes	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
337	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	4	4	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	4	no	—
346	C₂×D₄	—	4	4	no	—
347	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
348	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
356	Q₁₆	—	2	8	no	—
357	SD₁₆	—	2	8	no	—
358	M₁₆	—	2	2	no	—
359	M₁₆	—	2	2	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	4	4	no	—
362	M₁₆	C₂²×C₄×C₁₉	1	4	yes	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	4	4	no	—
368	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
369	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	8	2	no	—
376	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
377	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	4	2	no	—
384	C₄²	—	4	2	no	—
385	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	4	4	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	8	1	no	—
392	C₂³	—	8	1	no	—
393	C₂³	—	16	1	no	—
394	C₂³	—	16	1	no	—
395	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
396	Q₈	—	2	2	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	4	2	no	—
399	Q₈	C₄×D₄×C₁₉	1	4	yes	—
400	D₄	—	2	4	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	4	no	—
403	D₄	—	2	2	no	—
404	D₄	—	4	8	no	—
405	D₄	—	4	2	no	—
406	D₄	C₄×D₄×C₁₉	1	4	yes	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	8	2	no	—
421	C₂×C₄	—	16	2	no	—
422	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
424	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
425	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
426	C₈	—	2	4	no	—
427	C₈	—	2	2	no	—
428	C₈	—	2	2	no	—
429	C₈	—	4	2	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	16	1	no	—
440	C₂²	—	16	4	no	—
441	C₂²	C₁₉×#518	1	1	yes	characteristic
442	C₂²	D₄²×C₁₉	1	1	yes	characteristic
443	C₂²	C₁₉×#551	1	1	yes	characteristic
444	C₄	—	2	4	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	8	2	no	—
450	C₄	C₂×C₄×D₄×C₁₉	1	2	yes	—
451	C₄	C₁₉×#546	1	2	yes	—
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	—	4	4	no	—
455	C₂	—	8	2	no	—
456	C₂	C₁₉×#2358	1	1	yes	characteristic
457	C₂	C₁₉×#3288	1	1	yes	characteristic
458	C₂	C₁₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×H(5,𝔽₂)	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2947	C₂	semidirect
4. C₁₉×#1959	C₂	semidirect
5. C₁₉×#1931	C₂	semidirect
6. C₁₉×#1908	C₂	semidirect
7. C₁₉×#1888	C₂	semidirect
8. C₁₉×#1859	C₂	semidirect
9. C₁₉×#1765	C₂	semidirect
15. C₁₉×#519	C₂²	semidirect
16. C₁₉×#455	C₄	semidirect
21. C₁₉×#428	C₂²	semidirect
29. C₂×C₁₉×#103	C₂²	semidirect
32. C₂×C₁₉×#101	C₂²	semidirect
34. C₁₉×#405	C₂²	semidirect
35. C₂×C₁₉×#97	C₂²	semidirect
36. C₁₉×#384	C₂²	semidirect
37. C₁₉×#343	C₂²	semidirect
38. C₁₉×#341	C₂²	semidirect
39. C₁₉×#339	C₂²	semidirect
50. C₁₉×#137	C₂×C₄	semidirect
61. C₁₉×#124	C₂×C₄	semidirect
77. C₁₉×#104	C₂×C₄	semidirect
91. C₁₉×#100	C₂×C₄	semidirect
156. #22890	C₁₉	direct (N × H)
202. #2947	C₂×C₁₉	semidirect
204. #1959	C₂×C₁₉	semidirect
205. #1931	C₂×C₁₉	semidirect
206. #1908	C₂×C₁₉	semidirect
207. #1888	C₂×C₁₉	semidirect
208. #1859	C₂×C₁₉	semidirect
209. #1765	C₂×C₁₉	semidirect
237. #519	C₂²×C₁₉	semidirect
238. #455	C₄×C₁₉	semidirect
243. #428	C₂²×C₁₉	semidirect
251. C₂×#103	C₂²×C₁₉	semidirect
254. C₂×#101	C₂²×C₁₉	semidirect
256. #405	C₂²×C₁₉	semidirect
257. C₂×#97	C₂²×C₁₉	semidirect
258. #384	C₂²×C₁₉	semidirect
259. #343	C₂²×C₁₉	semidirect
260. #341	C₂²×C₁₉	semidirect
261. #339	C₂²×C₁₉	semidirect
279. #137	C₂×C₄×C₁₉	semidirect
290. #124	C₂×C₄×C₁₉	semidirect
306. #104	C₂×C₄×C₁₉	semidirect
320. #100	C₂×C₄×C₁₉	semidirect
324. C₁₉	#22890	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×#455	2
C₁₉×#2947	2
C₁₉×#2897	2
C₁₉×#1959	2
C₁₉×#1931	2
C₁₉×#1908	2
C₁₉×#1888	2
C₁₉×#1859	2
C₁₉×#1765	2
#22890	19

Subgroups — C19×#22890 #18028849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22890 #18028849