Subgroups — C₁₉×#24985 #18030944

Order 4864.

646 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3067	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2080	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2053	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1976	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1945	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1906	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1833	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1827	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1812	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#575	C₂²	1	2	yes	—
13	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
15	C₄×#41×C₁₉	C₂²	1	2	yes	—
16	C₁₉×#473	—	2	1	no	—
17	C₁₉×#472	—	2	1	no	—
18	C₁₉×#471	—	2	2	no	—
19	C₄×Q₁₆×C₁₉	—	2	1	no	—
20	C₄×SD₁₆×C₁₉	—	2	2	no	—
21	C₄×D₈×C₁₉	—	2	1	no	—
22	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
23	C₁₉×#427	C₂²	1	1	yes	characteristic
24	C₁₉×#427	C₂²	1	1	yes	characteristic
25	C₁₉×#424	C₂²	1	2	yes	—
26	C₁₉×#421	C₂²	1	2	yes	—
27	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
28	C₁₉×#416	C₂²	1	2	yes	—
29	C₁₉×#416	C₂²	1	1	yes	characteristic
30	C₁₉×#413	C₂²	1	2	yes	—
31	C₁₉×#410	C₂²	1	2	yes	—
32	C₁₉×#410	C₂²	1	2	yes	—
33	C₁₉×#405	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
35	C₁₉×#344	C₂²	1	2	yes	—
36	C₁₉×#341	C₂²	1	1	yes	characteristic
37	C₁₉×#339	C₂²	1	2	yes	—
38	C₁₉×#339	C₂²	1	1	yes	characteristic
39	C₁₉×H(3,ℤ/4)	C₂²	1	2	yes	—
40	C₁₉×H(3,ℤ/4)	C₂²	1	2	yes	—
41	C₂×#41×C₁₉	C₂³	1	2	yes	—
42	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
43	C₁₉×#137	—	2	2	no	—
44	C₁₉×#137	—	2	2	no	—
45	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
46	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
47	C₁₉×#135	—	2	1	no	—
48	C₁₉×#135	—	2	1	no	—
49	C₁₉×#135	—	2	1	no	—
50	C₁₉×#135	—	2	1	no	—
51	C₁₉×#135	—	4	2	no	—
52	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
53	C₂×SD₁₆×C₁₉	D₄	1	2	yes	—
54	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
55	C₁₉×#131	—	2	1	no	—
56	C₁₉×#131	—	2	1	no	—
57	C₁₉×#131	—	2	1	no	—
58	C₁₉×#131	—	2	1	no	—
59	C₂×M₁₆×C₁₉	—	2	1	no	—
60	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₉	—	2	1	no	—
64	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₄×Q₈×C₁₉	—	2	2	no	—
67	C₄×D₄×C₁₉	—	2	2	no	—
68	C₄×D₄×C₁₉	—	4	2	no	—
69	C₁₉×#117	—	2	2	no	—
70	C₁₉×#117	C₂³	1	2	yes	—
71	C₁₉×#117	C₂³	1	1	yes	characteristic
72	C₁₉×#117	C₂³	1	2	yes	—
73	C₂×C₄²×C₁₉	—	2	2	no	—
74	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×#108	—	2	1	no	—
76	C₁₉×#108	—	2	1	no	—
77	C₁₉×#107	—	2	1	no	—
78	C₁₉×#107	—	2	1	no	—
79	C₁₉×#106	—	2	1	no	—
80	C₁₉×#106	—	2	1	no	—
81	C₁₉×C₄⋊C₈	—	4	2	no	—
82	C₁₉×#104	—	2	1	no	—
83	C₁₉×#104	—	2	1	no	—
84	C₁₉×#104	—	4	2	no	—
85	C₁₉×#103	—	2	2	no	—
86	C₁₉×#103	—	2	1	no	—
87	C₁₉×#102	—	2	2	no	—
88	C₁₉×#102	—	2	1	no	—
89	C₁₉×#101	—	2	2	no	—
90	C₁₉×#100	—	2	2	no	—
91	C₁₉×#99	—	4	2	no	—
92	C₁₉×#99	—	4	2	no	—
93	C₁₉×#97	—	2	1	no	—
94	C₄×C₈×C₁₉	—	2	1	no	—
95	C₄×C₈×C₁₉	—	2	1	no	—
96	C₄×C₈×C₁₉	—	2	1	no	—
97	#41×C₁₉	—	2	1	no	—
98	#41×C₁₉	—	2	1	no	—
99	#41×C₁₉	—	2	2	no	—
100	#41×C₁₉	—	2	2	no	—
101	#41×C₁₉	—	2	2	no	—
102	#41×C₁₉	—	2	1	no	—
103	#41×C₁₉	—	2	1	no	—
104	#41×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
106	C₂×Q₈×C₁₉	#41	1	1	yes	characteristic
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₁₉	#41	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	—	2	1	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
116	Q₁₆×C₁₉	—	2	1	no	—
117	Q₁₆×C₁₉	—	2	1	no	—
118	Q₁₆×C₁₉	—	4	2	no	—
119	SD₁₆×C₁₉	—	2	2	no	—
120	SD₁₆×C₁₉	—	2	2	no	—
121	SD₁₆×C₁₉	—	4	2	no	—
122	SD₁₆×C₁₉	—	4	2	no	—
123	D₈×C₁₉	—	2	1	no	—
124	D₈×C₁₉	—	2	1	no	—
125	D₈×C₁₉	—	4	2	no	—
126	M₁₆×C₁₉	—	2	1	no	—
127	M₁₆×C₁₉	—	2	2	no	—
128	M₁₆×C₁₉	—	2	1	no	—
129	M₁₆×C₁₉	—	2	2	no	—
130	M₁₆×C₁₉	—	2	1	no	—
131	M₁₆×C₁₉	—	2	1	no	—
132	M₁₆×C₁₉	—	4	1	no	—
133	M₁₆×C₁₉	—	4	1	no	—
134	C₂×C₈×C₁₉	—	2	1	no	—
135	C₂×C₈×C₁₉	—	2	1	no	—
136	C₂×C₈×C₁₉	—	2	1	no	—
137	C₂×C₈×C₁₉	—	2	1	no	—
138	C₂×C₈×C₁₉	—	2	1	no	—
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	—	4	1	no	—
141	C₂×C₈×C₁₉	—	4	1	no	—
142	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
145	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
146	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
147	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	4	2	no	—
152	C₂²⋊C₄×C₁₉	—	2	2	no	—
153	C₂²⋊C₄×C₁₉	—	2	2	no	—
154	C₂²⋊C₄×C₁₉	—	2	1	no	—
155	C₂²⋊C₄×C₁₉	—	4	2	no	—
156	C₄²×C₁₉	—	2	1	no	—
157	C₄²×C₁₉	—	2	2	no	—
158	C₄²×C₁₉	—	2	1	no	—
159	C₄²×C₁₉	—	2	2	no	—
160	C₄²×C₁₉	—	4	2	no	—
161	C₄²×C₁₉	#41	1	1	yes	characteristic
162	C₄²×C₁₉	#41	1	1	yes	characteristic
163	#24985	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₁₉	—	2	2	no	—
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
167	Q₈×C₁₉	—	2	2	no	—
168	Q₈×C₁₉	—	2	1	no	—
169	Q₈×C₁₉	—	2	1	no	—
170	Q₈×C₁₉	—	2	2	no	—
171	D₄×C₁₉	—	2	2	no	—
172	D₄×C₁₉	—	2	1	no	—
173	D₄×C₁₉	—	2	1	no	—
174	D₄×C₁₉	—	2	2	no	—
175	D₄×C₁₉	—	4	2	no	—
176	D₄×C₁₉	—	4	1	no	—
177	D₄×C₁₉	—	4	1	no	—
178	D₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	8	4	no	—
192	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
198	C₈×C₁₉	—	4	1	no	—
199	C₈×C₁₉	—	4	1	no	—
200	C₈×C₁₉	—	4	2	no	—
201	C₈×C₁₉	—	4	1	no	—
202	C₈×C₁₉	#123	1	1	yes	characteristic
203	C₈×C₁₉	#123	1	1	yes	characteristic
204	C₈×C₁₉	#123	1	1	yes	characteristic
205	C₈×C₁₉	#123	1	1	yes	characteristic
206	#3067	C₂×C₁₉	1	1	yes	characteristic
207	C₄×#135	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#2080	C₂×C₁₉	1	2	yes	complemented
209	#2053	C₂×C₁₉	1	2	yes	complemented
210	#1976	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#1945	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#1906	C₂×C₁₉	1	2	yes	complemented
213	#1833	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1827	C₂×C₁₉	1	2	yes	complemented
215	#1812	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#1764	C₂×C₁₉	1	1	yes	characteristic, complemented
217	C₂²×C₁₉	—	4	1	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	—	4	2	no	—
220	C₂²×C₁₉	—	8	2	no	—
221	C₂²×C₁₉	—	8	1	no	—
222	C₂²×C₁₉	#540	1	1	yes	characteristic
223	C₂²×C₁₉	#546	1	1	yes	characteristic
224	C₂²×C₁₉	#553	1	1	yes	characteristic
225	C₄×C₁₉	—	2	2	no	—
226	C₄×C₁₉	—	4	1	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	4	1	no	—
229	C₄×C₁₉	—	8	2	no	—
230	C₄×C₁₉	—	8	1	no	—
231	C₄×C₁₉	—	8	2	no	—
232	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
233	C₄×C₁₉	#529	1	1	yes	characteristic
234	C₄×C₁₉	#546	1	1	yes	characteristic
235	C₄×C₁₉	#555	1	1	yes	characteristic
236	#575	C₂²×C₁₉	1	2	yes	—
237	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
239	C₄×#41	C₂²×C₁₉	1	2	yes	—
240	#473	—	2	1	no	—
241	#472	—	2	1	no	—
242	#471	—	2	2	no	—
243	C₄×Q₁₆	—	2	1	no	—
244	C₄×SD₁₆	—	2	2	no	—
245	C₄×D₈	—	2	1	no	—
246	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
247	#427	C₂²×C₁₉	1	1	yes	characteristic
248	#427	C₂²×C₁₉	1	1	yes	characteristic
249	#424	C₂²×C₁₉	1	2	yes	—
250	#421	C₂²×C₁₉	1	2	yes	—
251	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
252	#416	C₂²×C₁₉	1	1	yes	characteristic
253	#416	C₂²×C₁₉	1	2	yes	—
254	#413	C₂²×C₁₉	1	2	yes	—
255	#410	C₂²×C₁₉	1	2	yes	—
256	#410	C₂²×C₁₉	1	2	yes	—
257	#405	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
259	#344	C₂²×C₁₉	1	2	yes	—
260	#341	C₂²×C₁₉	1	1	yes	characteristic
261	#339	C₂²×C₁₉	1	1	yes	characteristic
262	#339	C₂²×C₁₉	1	2	yes	—
263	H(3,ℤ/4)	C₂²×C₁₉	1	2	yes	—
264	H(3,ℤ/4)	C₂²×C₁₉	1	2	yes	—
265	C₂×C₁₉	—	2	1	no	—
266	C₂×C₁₉	—	2	1	no	—
267	C₂×C₁₉	—	2	1	no	—
268	C₂×C₁₉	—	8	2	no	—
269	C₂×C₁₉	—	8	1	no	—
270	C₂×C₁₉	#2420	1	1	yes	characteristic
271	C₂×#41	C₂³×C₁₉	1	2	yes	—
272	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
273	#137	—	2	2	no	—
274	#137	—	2	2	no	—
275	AGL(1,ℤ/8)	—	2	2	no	—
276	AGL(1,ℤ/8)	—	2	2	no	—
277	#135	—	2	1	no	—
278	#135	—	2	1	no	—
279	#135	—	2	1	no	—
280	#135	—	2	1	no	—
281	#135	—	4	2	no	—
282	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
283	C₂×SD₁₆	D₄×C₁₉	1	2	yes	—
284	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
285	#131	—	2	1	no	—
286	#131	—	2	1	no	—
287	#131	—	2	1	no	—
288	#131	—	2	1	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
291	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
292	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
296	C₄×Q₈	—	2	2	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	—	4	2	no	—
299	#117	—	2	2	no	—
300	#117	C₂³×C₁₉	1	2	yes	—
301	#117	C₂³×C₁₉	1	1	yes	characteristic
302	#117	C₂³×C₁₉	1	2	yes	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
305	#108	—	2	1	no	—
306	#108	—	2	1	no	—
307	#107	—	2	1	no	—
308	#107	—	2	1	no	—
309	#106	—	2	1	no	—
310	#106	—	2	1	no	—
311	C₄⋊C₈	—	4	2	no	—
312	#104	—	2	1	no	—
313	#104	—	2	1	no	—
314	#104	—	4	2	no	—
315	#103	—	2	2	no	—
316	#103	—	2	1	no	—
317	#102	—	2	2	no	—
318	#102	—	2	1	no	—
319	#101	—	2	2	no	—
320	#100	—	2	2	no	—
321	#99	—	4	2	no	—
322	#99	—	4	2	no	—
323	#97	—	2	1	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	—	2	1	no	—
327	C₁₉	#24985	1	1	yes	characteristic, direct product factor, Sylow
328	#41	—	2	1	no	—
329	#41	—	2	1	no	—
330	#41	—	2	1	no	—
331	#41	—	2	2	no	—
332	#41	—	2	2	no	—
333	#41	—	2	2	no	—
334	#41	—	2	2	no	—
335	#41	—	2	1	no	—
336	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
337	C₂×Q₈	#41×C₁₉	1	1	yes	characteristic
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
341	C₂×D₄	#41×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
347	Q₁₆	—	2	1	no	—
348	Q₁₆	—	2	1	no	—
349	Q₁₆	—	4	2	no	—
350	SD₁₆	—	2	2	no	—
351	SD₁₆	—	2	2	no	—
352	SD₁₆	—	4	2	no	—
353	SD₁₆	—	4	2	no	—
354	D₈	—	2	1	no	—
355	D₈	—	2	1	no	—
356	D₈	—	4	2	no	—
357	M₁₆	—	2	1	no	—
358	M₁₆	—	2	2	no	—
359	M₁₆	—	2	1	no	—
360	M₁₆	—	2	1	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	1	no	—
363	M₁₆	—	4	1	no	—
364	M₁₆	—	4	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	4	1	no	—
372	C₂×C₈	—	4	1	no	—
373	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
374	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
375	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
376	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
377	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
378	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	4	2	no	—
392	C₄²	#41×C₁₉	1	1	yes	characteristic
393	C₄²	#41×C₁₉	1	1	yes	characteristic
394	C₂³	—	2	2	no	—
395	C₂³	—	2	1	no	—
396	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
397	Q₈	—	2	2	no	—
398	Q₈	—	2	1	no	—
399	Q₈	—	2	1	no	—
400	Q₈	—	2	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	2	1	no	—
403	D₄	—	2	1	no	—
404	D₄	—	2	2	no	—
405	D₄	—	4	1	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	1	no	—
408	D₄	—	4	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	8	4	no	—
422	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
423	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
424	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
427	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
428	C₈	—	4	1	no	—
429	C₈	—	4	1	no	—
430	C₈	—	4	2	no	—
431	C₈	—	4	1	no	—
432	C₈	C₁₉×#123	1	1	yes	characteristic
433	C₈	C₁₉×#123	1	1	yes	characteristic
434	C₈	C₁₉×#123	1	1	yes	characteristic
435	C₈	C₁₉×#123	1	1	yes	characteristic
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	1	no	—
441	C₂²	C₁₉×#540	1	1	yes	characteristic
442	C₂²	C₁₉×#546	1	1	yes	characteristic
443	C₂²	C₁₉×#553	1	1	yes	characteristic
444	C₄	—	2	2	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	1	no	—
448	C₄	—	8	2	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	1	no	—
451	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
452	C₄	C₁₉×#529	1	1	yes	characteristic
453	C₄	C₁₉×#546	1	1	yes	characteristic
454	C₄	C₁₉×#555	1	1	yes	characteristic
455	C₂	—	2	1	no	—
456	C₂	—	2	1	no	—
457	C₂	—	2	1	no	—
458	C₂	—	8	2	no	—
459	C₂	—	8	1	no	—
460	C₂	C₁₉×#2420	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	#555
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂×C₁₉	#2420
prime radical	C₁₉×#3067	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₉×#135	C₂	semidirect
3. C₁₉×#2080	C₂	semidirect
4. C₁₉×#2053	C₂	semidirect
5. C₁₉×#1976	C₂	semidirect
6. C₁₉×#1945	C₂	semidirect
7. C₁₉×#1906	C₂	semidirect
8. C₁₉×#1833	C₂	semidirect
9. C₁₉×#1827	C₂	semidirect
10. C₁₉×#1812	C₂	semidirect
11. C₁₉×#1764	C₂	semidirect
163. #24985	C₁₉	direct (N × H)
207. C₄×#135	C₂×C₁₉	semidirect
208. #2080	C₂×C₁₉	semidirect
209. #2053	C₂×C₁₉	semidirect
210. #1976	C₂×C₁₉	semidirect
211. #1945	C₂×C₁₉	semidirect
212. #1906	C₂×C₁₉	semidirect
213. #1833	C₂×C₁₉	semidirect
214. #1827	C₂×C₁₉	semidirect
215. #1812	C₂×C₁₉	semidirect
216. #1764	C₂×C₁₉	semidirect
327. C₁₉	#24985	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3067	2
C₄×C₁₉×#135	2
C₁₉×#2080	2
C₁₉×#2053	2
C₁₉×#1976	2
C₁₉×#1945	2
C₁₉×#1906	2
C₁₉×#1833	2
C₁₉×#1827	2
C₁₉×#1812	2
C₁₉×#1764	2
#24985	19

Subgroups — C19×#24985 #18030944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24985 #18030944