Subgroups — C₁₉×#22896 #18028855

Order 4864.

1016 conjugacy classes of subgroups.

The subgroup lattice has 446 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×#1958	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×#1860	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1764	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×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#382	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	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
73	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×#107	—	2	2	no	—
75	C₁₉×#106	—	2	2	no	—
76	C₁₉×#104	C₂×C₄	1	8	yes	complemented
77	C₁₉×#103	—	2	2	no	—
78	C₁₉×#103	—	2	2	no	—
79	C₁₉×#103	—	2	2	no	—
80	C₁₉×#103	D₄	1	2	yes	—
81	C₁₉×#103	D₄	1	2	yes	—
82	C₁₉×#102	—	2	2	no	—
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	D₄	1	2	yes	—
88	C₁₉×#102	D₄	1	2	yes	—
89	C₁₉×#101	—	4	1	no	—
90	C₁₉×#100	C₂×C₄	1	4	yes	complemented
91	C₁₉×#97	—	2	2	no	—
92	C₄×C₈×C₁₉	—	2	2	no	—
93	C₄×C₈×C₁₉	—	4	1	no	—
94	C₁₉×#95	—	4	1	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	2	no	—
144	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²⋊C₄×C₁₉	—	2	2	no	—
147	C₂²⋊C₄×C₁₉	—	4	4	no	—
148	C₂²⋊C₄×C₁₉	—	4	2	no	—
149	C₄²×C₁₉	—	2	2	no	—
150	C₄²×C₁₉	—	2	1	no	—
151	C₄²×C₁₉	—	4	2	no	—
152	C₄²×C₁₉	—	4	1	no	—
153	C₄²×C₁₉	—	4	1	no	—
154	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
155	#22896	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	4	4	no	—
159	C₂³×C₁₉	—	4	1	no	—
160	C₂³×C₁₉	—	4	1	no	—
161	C₂³×C₁₉	—	8	2	no	—
162	C₂³×C₁₉	—	16	2	no	—
163	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
164	Q₈×C₁₉	—	2	2	no	—
165	Q₈×C₁₉	—	2	4	no	—
166	Q₈×C₁₉	—	4	2	no	—
167	Q₈×C₁₉	C₄×D₄	1	4	yes	—
168	D₄×C₁₉	—	2	4	no	—
169	D₄×C₁₉	—	2	4	no	—
170	D₄×C₁₉	—	2	4	no	—
171	D₄×C₁₉	—	2	2	no	—
172	D₄×C₁₉	—	4	8	no	—
173	D₄×C₁₉	—	4	2	no	—
174	D₄×C₁₉	C₄×D₄	1	4	yes	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	4	4	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	8	2	no	—
188	C₂×C₄×C₁₉	—	16	2	no	—
189	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
191	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
192	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
193	C₈×C₁₉	—	2	4	no	—
194	C₈×C₁₉	—	2	2	no	—
195	C₈×C₁₉	—	2	2	no	—
196	C₈×C₁₉	—	4	2	no	—
197	C₂×#455	C₂×C₁₉	1	1	yes	characteristic
198	#2947	C₂×C₁₉	1	2	yes	complemented
199	#2897	C₂×C₁₉	1	2	yes	—
200	#1958	C₂×C₁₉	1	1	yes	characteristic, complemented
201	#1931	C₂×C₁₉	1	2	yes	complemented
202	#1908	C₂×C₁₉	1	2	yes	complemented
203	#1888	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#1860	C₂×C₁₉	1	2	yes	complemented
205	#1764	C₂×C₁₉	1	2	yes	complemented
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	2	4	no	—
208	C₂²×C₁₉	—	4	2	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	8	2	no	—
212	C₂²×C₁₉	—	8	2	no	—
213	C₂²×C₁₉	—	16	1	no	—
214	C₂²×C₁₉	—	16	4	no	—
215	C₂²×C₁₉	#518	1	1	yes	characteristic
216	C₂²×C₁₉	D₄²	1	1	yes	characteristic
217	C₂²×C₁₉	#551	1	1	yes	characteristic
218	C₄×C₁₉	—	2	4	no	—
219	C₄×C₁₉	—	4	2	no	—
220	C₄×C₁₉	—	4	2	no	—
221	C₄×C₁₉	—	4	2	no	—
222	C₄×C₁₉	—	4	2	no	—
223	C₄×C₁₉	—	8	2	no	—
224	C₄×C₁₉	C₂×C₄×D₄	1	2	yes	—
225	C₄×C₁₉	#546	1	2	yes	—
226	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×#137	C₂²×C₁₉	1	2	yes	—
228	C₂×#131	C₂²×C₁₉	1	2	yes	—
229	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
230	#520	C₂²×C₁₉	1	2	yes	—
231	#519	C₂²×C₁₉	1	1	yes	characteristic, complemented
232	#455	C₄×C₁₉	1	8	yes	complemented
233	#441	—	2	2	no	—
234	#440	—	2	2	no	—
235	C₄×Q₁₆	—	2	2	no	—
236	C₄×SD₁₆	—	2	2	no	—
237	#428	C₂²×C₁₉	1	2	yes	complemented
238	C₂×#104	C₂²×C₁₉	1	2	yes	—
239	#418	—	2	2	no	—
240	#418	C₂²×C₁₉	1	2	yes	—
241	#417	—	2	2	no	—
242	#417	C₂²×C₁₉	1	2	yes	—
243	#416	—	2	2	no	—
244	#416	C₂²×C₁₉	1	2	yes	—
245	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
246	C₂×#102	—	2	2	no	—
247	C₂×#102	C₂²×C₁₉	1	2	yes	—
248	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic, complemented
249	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
250	#405	C₂²×C₁₉	1	2	yes	complemented
251	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
252	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
253	#343	C₂²×C₁₉	1	2	yes	complemented
254	#341	C₂²×C₁₉	1	2	yes	complemented
255	#339	C₂²×C₁₉	1	2	yes	complemented
256	C₂×C₁₉	—	2	1	no	—
257	C₂×C₁₉	—	2	1	no	—
258	C₂×C₁₉	—	4	4	no	—
259	C₂×C₁₉	—	8	2	no	—
260	C₂×C₁₉	#2358	1	1	yes	characteristic
261	C₂×C₁₉	#3290	1	2	yes	—
262	H(5,𝔽₂)	—	2	4	no	—
263	H(5,𝔽₂)	—	4	1	no	—
264	H(5,𝔽₂)	C₂×C₄×C₁₉	1	4	yes	—
265	C₂×#41	—	2	2	no	—
266	C₂×#41	C₂³×C₁₉	1	2	yes	—
267	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
268	C₂²×D₄	—	2	2	no	—
269	C₂²×D₄	—	4	1	no	—
270	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
271	#137	—	2	4	no	—
272	#137	C₂×C₄×C₁₉	1	8	yes	complemented
273	C₂×Q₁₆	—	2	2	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	#131	—	2	4	no	—
276	#131	—	4	2	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
279	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
282	#124	—	4	1	no	—
283	#124	C₂×C₄×C₁₉	1	4	yes	complemented
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	—	2	2	no	—
286	C₄×Q₈	—	2	2	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	—	4	2	no	—
289	#117	—	2	2	no	—
290	#117	—	4	1	no	—
291	#117	C₂³×C₁₉	1	2	yes	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
294	C₂×C₂²⋊C₄	—	4	1	no	—
295	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
296	#107	—	2	2	no	—
297	#106	—	2	2	no	—
298	#104	C₂×C₄×C₁₉	1	8	yes	complemented
299	#103	—	2	2	no	—
300	#103	—	2	2	no	—
301	#103	—	2	2	no	—
302	#103	D₄×C₁₉	1	2	yes	—
303	#103	D₄×C₁₉	1	2	yes	—
304	#102	—	2	2	no	—
305	#102	—	2	2	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	D₄×C₁₉	1	2	yes	—
310	#102	D₄×C₁₉	1	2	yes	—
311	#101	—	4	1	no	—
312	#100	C₂×C₄×C₁₉	1	4	yes	complemented
313	#97	—	2	2	no	—
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	—	4	1	no	—
316	#95	—	4	1	no	—
317	C₁₉	#22896	1	1	yes	characteristic, direct product factor, Sylow
318	C₂⁴	—	2	1	no	—
319	C₂⁴	—	4	1	no	—
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	—	2	8	no	—
323	#41	—	4	4	no	—
324	#41	C₂²×C₄×C₁₉	1	4	yes	—
325	#41	#41×C₁₉	1	4	yes	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
330	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	8	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
341	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
349	Q₁₆	—	2	8	no	—
350	SD₁₆	—	2	8	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	2	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	4	4	no	—
355	M₁₆	C₂²×C₄×C₁₉	1	4	yes	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	4	4	no	—
361	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
362	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
368	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	4	4	no	—
371	C₂²⋊C₄	—	4	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	4	2	no	—
375	C₄²	—	4	1	no	—
376	C₄²	—	4	1	no	—
377	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	4	4	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	8	2	no	—
384	C₂³	—	16	2	no	—
385	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
386	Q₈	—	2	2	no	—
387	Q₈	—	2	4	no	—
388	Q₈	—	4	2	no	—
389	Q₈	C₄×D₄×C₁₉	1	4	yes	—
390	D₄	—	2	4	no	—
391	D₄	—	2	4	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	2	no	—
394	D₄	—	4	8	no	—
395	D₄	—	4	2	no	—
396	D₄	C₄×D₄×C₁₉	1	4	yes	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	—	16	2	no	—
411	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
413	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
414	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
415	C₈	—	2	4	no	—
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	4	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	16	1	no	—
427	C₂²	—	16	4	no	—
428	C₂²	C₁₉×#518	1	1	yes	characteristic
429	C₂²	D₄²×C₁₉	1	1	yes	characteristic
430	C₂²	C₁₉×#551	1	1	yes	characteristic
431	C₄	—	2	4	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	8	2	no	—
437	C₄	C₂×C₄×D₄×C₁₉	1	2	yes	—
438	C₄	C₁₉×#546	1	2	yes	—
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	4	4	no	—
442	C₂	—	8	2	no	—
443	C₂	C₁₉×#2358	1	1	yes	characteristic
444	C₂	C₁₉×#3290	1	2	yes	—

	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×#1958	C₂	semidirect
5. C₁₉×#1931	C₂	semidirect
6. C₁₉×#1908	C₂	semidirect
7. C₁₉×#1888	C₂	semidirect
8. C₁₉×#1860	C₂	semidirect
9. C₁₉×#1764	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×C₄×C₈×C₁₉	C₂²	semidirect
36. C₁₉×#382	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
76. C₁₉×#104	C₂×C₄	semidirect
90. C₁₉×#100	C₂×C₄	semidirect
155. #22896	C₁₉	direct (N × H)
198. #2947	C₂×C₁₉	semidirect
200. #1958	C₂×C₁₉	semidirect
201. #1931	C₂×C₁₉	semidirect
202. #1908	C₂×C₁₉	semidirect
203. #1888	C₂×C₁₉	semidirect
204. #1860	C₂×C₁₉	semidirect
205. #1764	C₂×C₁₉	semidirect
231. #519	C₂²×C₁₉	semidirect
232. #455	C₄×C₁₉	semidirect
237. #428	C₂²×C₁₉	semidirect
245. C₂×#103	C₂²×C₁₉	semidirect
248. C₂×#101	C₂²×C₁₉	semidirect
250. #405	C₂²×C₁₉	semidirect
251. C₂×C₄×C₈	C₂²×C₁₉	semidirect
252. #382	C₂²×C₁₉	semidirect
253. #343	C₂²×C₁₉	semidirect
254. #341	C₂²×C₁₉	semidirect
255. #339	C₂²×C₁₉	semidirect
272. #137	C₂×C₄×C₁₉	semidirect
283. #124	C₂×C₄×C₁₉	semidirect
298. #104	C₂×C₄×C₁₉	semidirect
312. #100	C₂×C₄×C₁₉	semidirect
317. C₁₉	#22896	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×#1958	2
C₁₉×#1931	2
C₁₉×#1908	2
C₁₉×#1888	2
C₁₉×#1860	2
C₁₉×#1764	2
#22896	19

Subgroups — C19×#22896 #18028855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22896 #18028855