Subgroups — C₁₉×#18987 #18024946

Order 4864.

904 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3529	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3172	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1664	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1662	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1661	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1659	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1525	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1524	C₂	1	2	yes	maximal, complemented
10	C₁₉×#563	—	2	1	no	—
11	C₁₉×#563	C₂²	1	1	yes	characteristic
12	C₁₉×#562	—	2	2	no	—
13	C₁₉×#562	C₂²	1	2	yes	—
14	C₁₉×H(3,𝔽₄)	C₂²	1	1	yes	characteristic
15	C₁₉×#560	—	2	1	no	—
16	C₁₉×#560	—	2	2	no	—
17	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#532	—	2	1	no	—
19	C₁₉×#532	C₂²	1	1	yes	characteristic
20	C₁₉×#529	—	2	2	no	—
21	C₁₉×#529	C₂²	1	2	yes	—
22	C₁₉×#525	—	2	1	no	—
23	C₁₉×#525	—	2	2	no	—
24	C₁₉×#501	C₂²	1	2	yes	complemented
25	C₁₉×#497	C₂²	1	2	yes	—
26	C₁₉×#491	—	2	1	no	—
27	C₁₉×#491	C₂²	1	2	yes	complemented
28	C₁₉×#490	—	2	1	no	—
29	C₁₉×#489	C₂²	1	2	yes	—
30	C₁₉×#489	C₂²	1	2	yes	—
31	C₁₉×#489	C₂²	1	2	yes	complemented
32	C₁₉×#470	—	2	2	no	—
33	C₁₉×#468	—	2	2	no	—
34	C₄×Q₁₆×C₁₉	—	2	2	no	—
35	C₄×SD₁₆×C₁₉	—	2	2	no	—
36	C₁₉×#416	—	2	1	no	—
37	C₁₉×#416	—	2	1	no	—
38	C₄×M₁₆×C₁₉	C₂²	1	2	yes	complemented
39	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#330	C₂²	1	2	yes	complemented
41	C₁₉×#330	C₂²	1	2	yes	complemented
42	C₁₉×#329	C₂²	1	2	yes	—
43	C₁₉×#329	C₂²	1	2	yes	—
44	C₁₉×#329	C₂²	1	2	yes	—
45	C₁₉×#329	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#329	C₂²	1	1	yes	characteristic, complemented
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
49	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	—	2	1	no	—
51	C₂×Q₁₆×C₁₉	—	2	2	no	—
52	C₂×SD₁₆×C₁₉	—	2	2	no	—
53	C₂×M₁₆×C₁₉	—	2	2	no	—
54	C₂²×C₈×C₁₉	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₁₉×#127	—	2	1	no	—
59	C₁₉×#127	D₄	1	1	yes	characteristic
60	C₁₉×#126	—	2	2	no	—
61	C₁₉×#126	—	2	2	no	—
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#125	—	2	2	no	—
64	C₁₉×#125	—	2	1	no	—
65	C₁₉×#125	C₂³	1	2	yes	—
66	C₁₉×#124	—	2	1	no	—
67	C₁₉×#124	—	2	2	no	—
68	C₁₉×#124	—	2	1	no	—
69	C₁₉×#124	C₂³	1	1	yes	characteristic
70	C₁₉×#124	C₂³	1	2	yes	—
71	C₁₉×#124	C₂³	1	1	yes	characteristic
72	C₁₉×#123	—	2	2	no	—
73	C₁₉×#123	—	2	1	no	—
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×#123	—	2	1	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
85	C₁₉×#121	—	2	2	no	—
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#121	—	2	2	no	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	2	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	D₄	1	2	yes	—
93	C₁₉×#120	—	2	1	no	—
94	C₁₉×#120	—	2	2	no	—
95	C₁₉×#120	—	2	1	no	—
96	C₁₉×#120	—	2	2	no	—
97	C₄×Q₈×C₁₉	—	2	2	no	—
98	C₄×Q₈×C₁₉	D₄	1	2	yes	—
99	C₄×D₄×C₁₉	—	2	2	no	—
100	C₄×D₄×C₁₉	—	2	2	no	—
101	C₄×D₄×C₁₉	—	2	2	no	—
102	C₄×D₄×C₁₉	—	2	2	no	—
103	C₄×D₄×C₁₉	D₄	1	2	yes	—
104	C₁₉×#117	—	2	1	no	—
105	C₁₉×#117	—	2	2	no	—
106	C₁₉×#117	—	2	1	no	—
107	C₂×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
109	C₁₉×#107	—	2	2	no	—
110	C₁₉×#106	—	2	2	no	—
111	C₁₉×#103	—	2	2	no	—
112	C₁₉×#103	—	2	2	no	—
113	C₁₉×#103	—	2	2	no	—
114	C₁₉×#103	—	2	2	no	—
115	C₁₉×#103	—	2	2	no	—
116	C₁₉×#102	—	2	2	no	—
117	C₁₉×#102	—	2	2	no	—
118	C₁₉×#102	—	2	2	no	—
119	C₁₉×#97	—	2	1	no	—
120	C₁₉×#97	C₂³	1	2	yes	—
121	C₁₉×#97	C₂³	1	2	yes	—
122	C₁₉×#97	C₂³	1	2	yes	—
123	C₄×C₈×C₁₉	—	2	2	no	—
124	C₂⁴×C₁₉	—	2	1	no	—
125	#41×C₁₉	—	4	2	no	—
126	#41×C₁₉	—	4	2	no	—
127	#41×C₁₉	—	8	2	no	—
128	C₂×Q₈×C₁₉	—	2	1	no	—
129	C₂×Q₈×C₁₉	—	2	2	no	—
130	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
131	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	—	2	2	no	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	2	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	2	1	no	—
139	C₂×D₄×C₁₉	—	2	1	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	8	2	no	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
153	Q₁₆×C₁₉	—	4	4	no	—
154	SD₁₆×C₁₉	—	4	4	no	—
155	M₁₆×C₁₉	—	4	4	no	—
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₂×C₈×C₁₉	—	2	2	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	—	4	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	4	2	no	—
171	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
172	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
173	C₂²⋊C₄×C₁₉	—	2	1	no	—
174	C₂²⋊C₄×C₁₉	—	2	1	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂²⋊C₄×C₁₉	—	2	2	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	2	2	no	—
181	C₂²⋊C₄×C₁₉	—	2	2	no	—
182	C₂²⋊C₄×C₁₉	—	2	2	no	—
183	C₂²⋊C₄×C₁₉	—	2	2	no	—
184	C₂²⋊C₄×C₁₉	—	2	2	no	—
185	C₂²⋊C₄×C₁₉	—	2	2	no	—
186	C₂²⋊C₄×C₁₉	—	4	1	no	—
187	C₄²×C₁₉	—	2	1	no	—
188	C₄²×C₁₉	—	2	1	no	—
189	C₄²×C₁₉	—	2	2	no	—
190	C₄²×C₁₉	—	4	1	no	—
191	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₁₉	C₂×D₄	1	2	yes	—
193	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
194	#18987	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂³×C₁₉	—	2	1	no	—
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	2	1	no	—
198	C₂³×C₁₉	—	8	1	no	—
199	C₂³×C₁₉	—	8	2	no	—
200	C₂³×C₁₉	#120	1	1	yes	characteristic
201	Q₈×C₁₉	—	4	2	no	—
202	Q₈×C₁₉	—	4	1	no	—
203	Q₈×C₁₉	—	4	1	no	—
204	Q₈×C₁₉	—	4	2	no	—
205	Q₈×C₁₉	—	4	2	no	—
206	Q₈×C₁₉	—	8	1	no	—
207	D₄×C₁₉	—	4	2	no	—
208	D₄×C₁₉	—	4	1	no	—
209	D₄×C₁₉	—	4	1	no	—
210	D₄×C₁₉	—	8	2	no	—
211	D₄×C₁₉	—	8	2	no	—
212	D₄×C₁₉	—	8	1	no	—
213	D₄×C₁₉	—	8	1	no	—
214	D₄×C₁₉	—	8	2	no	—
215	D₄×C₁₉	—	8	2	no	—
216	D₄×C₁₉	—	8	2	no	—
217	D₄×C₁₉	—	8	1	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	4	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	8	2	no	—
230	C₂×C₄×C₁₉	—	8	2	no	—
231	C₂×C₄×C₁₉	—	8	1	no	—
232	C₂×C₄×C₁₉	#120	1	2	yes	—
233	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
236	C₈×C₁₉	—	2	4	no	—
237	C₈×C₁₉	—	4	2	no	—
238	C₈×C₁₉	—	4	2	no	—
239	#3529	C₂×C₁₉	1	1	yes	characteristic
240	#3172	C₂×C₁₉	1	2	yes	complemented
241	#3135	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#1664	C₂×C₁₉	1	2	yes	complemented
243	#1662	C₂×C₁₉	1	2	yes	complemented
244	#1661	C₂×C₁₉	1	2	yes	complemented
245	#1659	C₂×C₁₉	1	2	yes	complemented
246	#1525	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#1524	C₂×C₁₉	1	2	yes	complemented
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	2	2	no	—
250	C₂²×C₁₉	—	4	1	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	4	1	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	—	4	2	no	—
256	C₂²×C₁₉	—	4	2	no	—
257	C₂²×C₁₉	—	8	4	no	—
258	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	2	no	—
261	C₄×C₁₉	—	2	2	no	—
262	C₄×C₁₉	—	4	1	no	—
263	C₄×C₁₉	—	4	2	no	—
264	C₄×C₁₉	—	4	1	no	—
265	C₄×C₁₉	—	4	2	no	—
266	C₄×C₁₉	—	4	2	no	—
267	C₄×C₁₉	—	8	2	no	—
268	C₄×C₁₉	#455	1	2	yes	—
269	#563	—	2	1	no	—
270	#563	C₂²×C₁₉	1	1	yes	characteristic
271	#562	—	2	2	no	—
272	#562	C₂²×C₁₉	1	2	yes	—
273	H(3,𝔽₄)	C₂²×C₁₉	1	1	yes	characteristic
274	#560	—	2	1	no	—
275	#560	—	2	2	no	—
276	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
277	#532	—	2	1	no	—
278	#532	C₂²×C₁₉	1	1	yes	characteristic
279	#529	—	2	2	no	—
280	#529	C₂²×C₁₉	1	2	yes	—
281	#525	—	2	1	no	—
282	#525	—	2	2	no	—
283	#501	C₂²×C₁₉	1	2	yes	complemented
284	#497	C₂²×C₁₉	1	2	yes	—
285	#491	—	2	1	no	—
286	#491	C₂²×C₁₉	1	2	yes	complemented
287	#490	—	2	1	no	—
288	#489	C₂²×C₁₉	1	2	yes	—
289	#489	C₂²×C₁₉	1	2	yes	—
290	#489	C₂²×C₁₉	1	2	yes	complemented
291	#470	—	2	2	no	—
292	#468	—	2	2	no	—
293	C₄×Q₁₆	—	2	2	no	—
294	C₄×SD₁₆	—	2	2	no	—
295	#416	—	2	1	no	—
296	#416	—	2	1	no	—
297	C₄×M₁₆	C₂²×C₁₉	1	2	yes	complemented
298	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
299	#330	C₂²×C₁₉	1	2	yes	complemented
300	#330	C₂²×C₁₉	1	2	yes	complemented
301	#329	C₂²×C₁₉	1	2	yes	—
302	#329	C₂²×C₁₉	1	2	yes	—
303	#329	C₂²×C₁₉	1	2	yes	—
304	#329	C₂²×C₁₉	1	1	yes	characteristic, complemented
305	#329	C₂²×C₁₉	1	1	yes	characteristic, complemented
306	C₂×C₁₉	—	4	1	no	—
307	C₂×C₁₉	—	8	1	no	—
308	C₂×C₁₉	—	8	1	no	—
309	C₂×C₁₉	—	8	2	no	—
310	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
311	C₂×C₁₉	#3018	1	2	yes	—
312	C₂×#41	—	2	1	no	—
313	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
314	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
315	C₂³×C₄	—	2	1	no	—
316	C₂×Q₁₆	—	2	2	no	—
317	C₂×SD₁₆	—	2	2	no	—
318	C₂×M₁₆	—	2	2	no	—
319	C₂²×C₈	—	2	1	no	—
320	C₄⋊Q₈	—	2	1	no	—
321	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
322	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
323	#127	—	2	1	no	—
324	#127	D₄×C₁₉	1	1	yes	characteristic
325	#126	—	2	2	no	—
326	#126	—	2	2	no	—
327	#126	—	2	2	no	—
328	#125	—	2	2	no	—
329	#125	—	2	1	no	—
330	#125	C₂³×C₁₉	1	2	yes	—
331	#124	—	2	1	no	—
332	#124	—	2	2	no	—
333	#124	—	2	1	no	—
334	#124	C₂³×C₁₉	1	2	yes	—
335	#124	C₂³×C₁₉	1	1	yes	characteristic
336	#124	C₂³×C₁₉	1	1	yes	characteristic
337	#123	—	2	2	no	—
338	#123	—	2	1	no	—
339	#123	—	2	2	no	—
340	#123	—	2	1	no	—
341	#123	—	2	2	no	—
342	#123	—	2	2	no	—
343	#123	—	2	2	no	—
344	C₂²⋊Q₈	—	2	2	no	—
345	C₂²⋊Q₈	—	2	2	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	2	2	no	—
348	C₂²⋊Q₈	—	2	2	no	—
349	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
350	#121	—	2	2	no	—
351	#121	—	2	2	no	—
352	#121	—	2	2	no	—
353	#121	—	2	2	no	—
354	#121	—	2	2	no	—
355	#121	—	2	2	no	—
356	#121	—	2	2	no	—
357	#121	D₄×C₁₉	1	2	yes	—
358	#120	—	2	1	no	—
359	#120	—	2	2	no	—
360	#120	—	2	1	no	—
361	#120	—	2	2	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	D₄×C₁₉	1	2	yes	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	D₄×C₁₉	1	2	yes	—
369	#117	—	2	1	no	—
370	#117	—	2	2	no	—
371	#117	—	2	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
374	#107	—	2	2	no	—
375	#106	—	2	2	no	—
376	#103	—	2	2	no	—
377	#103	—	2	2	no	—
378	#103	—	2	2	no	—
379	#103	—	2	2	no	—
380	#103	—	2	2	no	—
381	#102	—	2	2	no	—
382	#102	—	2	2	no	—
383	#102	—	2	2	no	—
384	#97	—	2	1	no	—
385	#97	C₂³×C₁₉	1	2	yes	—
386	#97	C₂³×C₁₉	1	2	yes	—
387	#97	C₂³×C₁₉	1	2	yes	—
388	C₄×C₈	—	2	2	no	—
389	C₁₉	#18987	1	1	yes	characteristic, direct product factor, Sylow
390	C₂⁴	—	2	1	no	—
391	#41	—	4	2	no	—
392	#41	—	4	2	no	—
393	#41	—	8	2	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
408	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
409	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	8	2	no	—
417	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
419	Q₁₆	—	4	4	no	—
420	SD₁₆	—	4	4	no	—
421	M₁₆	—	4	4	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	4	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	4	2	no	—
437	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
438	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	4	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	4	1	no	—
457	C₄²	C₂×D₄×C₁₉	1	2	yes	—
458	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
460	C₂³	—	2	1	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	8	1	no	—
464	C₂³	—	8	2	no	—
465	C₂³	C₁₉×#120	1	1	yes	characteristic
466	Q₈	—	4	2	no	—
467	Q₈	—	4	1	no	—
468	Q₈	—	4	1	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	2	no	—
471	Q₈	—	8	1	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	1	no	—
475	D₄	—	8	2	no	—
476	D₄	—	8	1	no	—
477	D₄	—	8	1	no	—
478	D₄	—	8	2	no	—
479	D₄	—	8	2	no	—
480	D₄	—	8	1	no	—
481	D₄	—	8	2	no	—
482	D₄	—	8	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	8	2	no	—
495	C₂×C₄	—	8	1	no	—
496	C₂×C₄	—	8	2	no	—
497	C₂×C₄	C₁₉×#120	1	2	yes	—
498	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
500	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
501	C₈	—	2	4	no	—
502	C₈	—	4	2	no	—
503	C₈	—	4	2	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	8	4	no	—
514	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
515	C₄	—	2	1	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	8	2	no	—
524	C₄	C₁₉×#455	1	2	yes	—
525	C₂	—	4	1	no	—
526	C₂	—	8	1	no	—
527	C₂	—	8	2	no	—
528	C₂	—	8	1	no	—
529	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
530	C₂	C₁₉×#3018	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#120
prime radical	C₁₉×#3529	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3172	C₂	semidirect
3. C₁₉×#3135	C₂	semidirect
4. C₁₉×#1664	C₂	semidirect
5. C₁₉×#1662	C₂	semidirect
6. C₁₉×#1661	C₂	semidirect
7. C₁₉×#1659	C₂	semidirect
8. C₁₉×#1525	C₂	semidirect
9. C₁₉×#1524	C₂	semidirect
17. C₁₉×#533	C₂²	semidirect
24. C₁₉×#501	C₂²	semidirect
27. C₁₉×#491	C₂²	semidirect
31. C₁₉×#489	C₂²	semidirect
38. C₄×M₁₆×C₁₉	C₂²	semidirect
39. C₂×C₁₉×#97	C₂²	semidirect
40. C₁₉×#330	C₂²	semidirect
41. C₁₉×#330	C₂²	semidirect
45. C₁₉×#329	C₂²	semidirect
46. C₁₉×#329	C₂²	semidirect
194. #18987	C₁₉	direct (N × H)
240. #3172	C₂×C₁₉	semidirect
241. #3135	C₂×C₁₉	semidirect
242. #1664	C₂×C₁₉	semidirect
243. #1662	C₂×C₁₉	semidirect
244. #1661	C₂×C₁₉	semidirect
245. #1659	C₂×C₁₉	semidirect
246. #1525	C₂×C₁₉	semidirect
247. #1524	C₂×C₁₉	semidirect
276. #533	C₂²×C₁₉	semidirect
283. #501	C₂²×C₁₉	semidirect
286. #491	C₂²×C₁₉	semidirect
290. #489	C₂²×C₁₉	semidirect
297. C₄×M₁₆	C₂²×C₁₉	semidirect
298. C₂×#97	C₂²×C₁₉	semidirect
299. #330	C₂²×C₁₉	semidirect
300. #330	C₂²×C₁₉	semidirect
304. #329	C₂²×C₁₉	semidirect
305. #329	C₂²×C₁₉	semidirect
389. C₁₉	#18987	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×#3529	2
C₁₉×#3172	2
C₁₉×#3135	2
C₁₉×#1664	2
C₁₉×#1662	2
C₁₉×#1661	2
C₁₉×#1659	2
C₁₉×#1525	2
C₁₉×#1524	2
#18987	19

Subgroups — C19×#18987 #18024946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18987 #18024946