Subgroups — C₁₉×#19015 #18024974

Order 4864.

1012 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3558	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3152	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#489	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1661	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1659	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1530	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1527	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1524	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#137	—	2	2	no	—
11	C₁₉×#562	C₂²	1	2	yes	—
12	C₁₉×H(3,𝔽₄)	C₂²	1	2	yes	—
13	C₁₉×#559	—	2	1	no	—
14	C₁₉×#548	—	2	1	no	—
15	C₁₉×#546	—	2	2	no	—
16	C₁₉×#546	—	2	1	no	—
17	D₄²×C₁₉	—	2	1	no	—
18	C₁₉×#542	—	2	1	no	—
19	C₁₉×#538	—	2	2	no	—
20	C₁₉×#538	—	2	1	no	—
21	C₁₉×#535	—	2	1	no	—
22	C₁₉×#534	—	2	1	no	—
23	C₁₉×#532	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#529	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
27	C₁₉×#501	C₂²	1	2	yes	complemented
28	C₁₉×#497	C₂²	1	4	yes	complemented
29	C₁₉×#494	—	2	1	no	—
30	C₁₉×#492	—	2	1	no	—
31	C₁₉×#489	—	2	2	no	—
32	C₁₉×#489	C₂²	1	2	yes	complemented
33	C₁₉×#489	C₂²	1	4	yes	complemented
34	C₁₉×#483	—	2	1	no	—
35	C₁₉×#480	—	2	1	no	—
36	C₁₉×#477	—	2	1	no	—
37	C₁₉×#476	—	2	1	no	—
38	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₉×#103	—	2	1	no	—
40	C₂×C₁₉×#102	—	2	1	no	—
41	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#330	C₂²	1	2	yes	complemented
44	C₁₉×#329	C₂²	1	2	yes	complemented
45	C₁₉×#329	C₂²	1	4	yes	complemented
46	C₁₉×#329	C₂²	1	4	yes	complemented
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×#41×C₁₉	D₄	1	2	yes	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	—	2	2	no	—
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
54	C₁₉×#137	—	4	8	no	—
55	C₂×Q₁₆×C₁₉	—	2	4	no	—
56	C₂×SD₁₆×C₁₉	—	2	4	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂²×C₈×C₁₉	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₉×#127	—	2	1	no	—
65	C₁₉×#127	D₄	1	1	yes	characteristic
66	C₁₉×#126	—	2	2	no	—
67	C₁₉×#126	—	2	1	no	—
68	C₁₉×#125	C₂³	1	1	yes	characteristic
69	C₁₉×#124	—	2	1	no	—
70	C₁₉×#124	—	2	2	no	—
71	C₁₉×#124	—	2	2	no	—
72	C₁₉×#124	—	2	2	no	—
73	C₁₉×#124	—	2	1	no	—
74	C₁₉×#124	—	2	1	no	—
75	C₁₉×#124	D₄	1	2	yes	—
76	C₁₉×#124	C₂³	1	2	yes	—
77	C₁₉×#124	C₂³	1	1	yes	characteristic
78	C₁₉×#124	C₂³	1	2	yes	—
79	C₁₉×#123	—	2	2	no	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×#123	—	2	1	no	—
82	C₁₉×#123	—	2	2	no	—
83	C₁₉×#123	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	2	no	—
87	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	2	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	—	2	2	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	D₄	1	1	yes	characteristic
97	C₁₉×#120	—	2	2	no	—
98	C₁₉×#120	—	2	2	no	—
99	C₁₉×#120	—	2	2	no	—
100	C₁₉×#120	—	2	2	no	—
101	C₁₉×#120	—	2	2	no	—
102	C₄×Q₈×C₁₉	—	2	1	no	—
103	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
104	C₄×D₄×C₁₉	—	2	2	no	—
105	C₄×D₄×C₁₉	—	2	2	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	—	2	1	no	—
108	C₄×D₄×C₁₉	—	2	1	no	—
109	C₄×D₄×C₁₉	—	2	1	no	—
110	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
111	C₁₉×#117	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
118	C₁₉×#107	—	2	2	no	—
119	C₁₉×#106	—	2	2	no	—
120	C₁₉×C₄⋊C₈	—	2	1	no	—
121	C₁₉×#103	—	2	4	no	—
122	C₁₉×#103	—	2	2	no	—
123	C₁₉×#102	—	2	4	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×C₂²⋊C₈	—	2	1	no	—
126	C₁₉×#97	—	2	1	no	—
127	C₁₉×#97	C₂³	1	2	yes	—
128	C₁₉×#97	C₂³	1	2	yes	—
129	C₁₉×#97	C₂³	1	2	yes	—
130	C₄×C₈×C₁₉	—	2	1	no	—
131	C₂⁴×C₁₉	—	2	2	no	—
132	C₂⁴×C₁₉	—	2	1	no	—
133	#41×C₁₉	—	4	4	no	—
134	#41×C₁₉	—	8	2	no	—
135	C₂×Q₈×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	2	no	—
137	C₂×Q₈×C₁₉	—	4	2	no	—
138	C₂×Q₈×C₁₉	—	4	4	no	—
139	C₂×Q₈×C₁₉	—	4	1	no	—
140	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
142	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	2	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	2	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	4	2	no	—
154	C₂×D₄×C₁₉	—	8	2	no	—
155	C₂×D₄×C₁₉	—	8	4	no	—
156	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	2	no	—
164	C₂²×C₄×C₁₉	—	4	1	no	—
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	Q₁₆×C₁₉	—	4	8	no	—
169	SD₁₆×C₁₉	—	4	8	no	—
170	M₁₆×C₁₉	—	2	4	no	—
171	C₂×C₈×C₁₉	—	2	2	no	—
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	4	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	4	1	no	—
186	C₄⋊C₄×C₁₉	—	4	1	no	—
187	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₉	—	2	2	no	—
192	C₂²⋊C₄×C₁₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	1	no	—
195	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	2	1	no	—
197	C₂²⋊C₄×C₁₉	—	2	2	no	—
198	C₂²⋊C₄×C₁₉	—	2	1	no	—
199	C₂²⋊C₄×C₁₉	—	2	2	no	—
200	C₂²⋊C₄×C₁₉	—	2	2	no	—
201	C₂²⋊C₄×C₁₉	—	2	1	no	—
202	C₂²⋊C₄×C₁₉	—	2	1	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₄²×C₁₉	—	2	2	no	—
206	C₄²×C₁₉	—	2	1	no	—
207	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
211	#19015	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂³×C₁₉	—	2	2	no	—
213	C₂³×C₁₉	—	2	1	no	—
214	C₂³×C₁₉	—	2	2	no	—
215	C₂³×C₁₉	—	4	2	no	—
216	C₂³×C₁₉	—	8	1	no	—
217	C₂³×C₁₉	—	8	1	no	—
218	C₂³×C₁₉	—	8	2	no	—
219	C₂³×C₁₉	—	8	2	no	—
220	C₂³×C₁₉	—	8	2	no	—
221	C₂³×C₁₉	#120	1	1	yes	characteristic
222	Q₈×C₁₉	—	4	2	no	—
223	Q₈×C₁₉	—	4	2	no	—
224	Q₈×C₁₉	—	4	1	no	—
225	Q₈×C₁₉	—	4	4	no	—
226	Q₈×C₁₉	—	4	2	no	—
227	Q₈×C₁₉	—	8	2	no	—
228	D₄×C₁₉	—	4	2	no	—
229	D₄×C₁₉	—	4	2	no	—
230	D₄×C₁₉	—	4	1	no	—
231	D₄×C₁₉	—	4	2	no	—
232	D₄×C₁₉	—	4	4	no	—
233	D₄×C₁₉	—	4	2	no	—
234	D₄×C₁₉	—	4	2	no	—
235	D₄×C₁₉	—	8	1	no	—
236	D₄×C₁₉	—	8	2	no	—
237	D₄×C₁₉	—	8	2	no	—
238	D₄×C₁₉	—	8	2	no	—
239	D₄×C₁₉	—	8	2	no	—
240	D₄×C₁₉	—	8	2	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	2	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
251	C₂×C₄×C₁₉	—	8	2	no	—
252	C₂×C₄×C₁₉	—	8	1	no	—
253	C₂×C₄×C₁₉	—	8	2	no	—
254	C₂×C₄×C₁₉	—	8	2	no	—
255	C₂×C₄×C₁₉	—	8	2	no	—
256	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
257	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
258	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
262	C₈×C₁₉	—	2	4	no	—
263	C₈×C₁₉	—	4	2	no	—
264	C₈×C₁₉	—	4	2	no	—
265	#3558	C₂×C₁₉	1	1	yes	characteristic
266	#3238	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#3152	C₂×C₁₉	1	1	yes	characteristic, complemented
268	C₂×#489	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1661	C₂×C₁₉	1	4	yes	complemented
270	#1659	C₂×C₁₉	1	4	yes	complemented
271	#1530	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1527	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1524	C₂×C₁₉	1	1	yes	characteristic, complemented
274	C₂²×C₁₉	—	2	1	no	—
275	C₂²×C₁₉	—	2	1	no	—
276	C₂²×C₁₉	—	4	2	no	—
277	C₂²×C₁₉	—	4	2	no	—
278	C₂²×C₁₉	—	4	1	no	—
279	C₂²×C₁₉	—	4	1	no	—
280	C₂²×C₁₉	—	4	2	no	—
281	C₂²×C₁₉	—	4	2	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	2	no	—
284	C₂²×C₁₉	—	4	2	no	—
285	C₂²×C₁₉	—	16	2	no	—
286	C₂²×C₁₉	—	16	4	no	—
287	C₂²×C₁₉	#453	1	2	yes	—
288	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
289	C₄×C₁₉	—	2	1	no	—
290	C₄×C₁₉	—	2	1	no	—
291	C₄×C₁₉	—	2	1	no	—
292	C₄×C₁₉	—	2	1	no	—
293	C₄×C₁₉	—	2	1	no	—
294	C₄×C₁₉	—	4	1	no	—
295	C₄×C₁₉	—	4	2	no	—
296	C₄×C₁₉	—	4	1	no	—
297	C₄×C₁₉	—	4	2	no	—
298	C₄×C₁₉	—	4	1	no	—
299	C₄×C₁₉	—	8	2	no	—
300	C₄×C₁₉	#455	1	2	yes	—
301	C₂×#137	—	2	2	no	—
302	#562	C₂²×C₁₉	1	2	yes	—
303	H(3,𝔽₄)	C₂²×C₁₉	1	2	yes	—
304	#559	—	2	1	no	—
305	#548	—	2	1	no	—
306	#546	—	2	2	no	—
307	#546	—	2	1	no	—
308	D₄²	—	2	1	no	—
309	#542	—	2	1	no	—
310	#538	—	2	2	no	—
311	#538	—	2	1	no	—
312	#535	—	2	1	no	—
313	#534	—	2	1	no	—
314	#532	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
316	#529	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
318	#501	C₂²×C₁₉	1	2	yes	complemented
319	#497	C₂²×C₁₉	1	4	yes	complemented
320	#494	—	2	1	no	—
321	#492	—	2	1	no	—
322	#489	—	2	2	no	—
323	#489	C₂²×C₁₉	1	4	yes	complemented
324	#489	C₂²×C₁₉	1	2	yes	complemented
325	#483	—	2	1	no	—
326	#480	—	2	1	no	—
327	#477	—	2	1	no	—
328	#476	—	2	1	no	—
329	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
330	C₂×#103	—	2	1	no	—
331	C₂×#102	—	2	1	no	—
332	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
333	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
334	#330	C₂²×C₁₉	1	2	yes	complemented
335	#329	C₂²×C₁₉	1	2	yes	complemented
336	#329	C₂²×C₁₉	1	4	yes	complemented
337	#329	C₂²×C₁₉	1	4	yes	complemented
338	C₂×C₁₉	—	2	2	no	—
339	C₂×C₁₉	—	8	2	no	—
340	C₂×C₁₉	—	8	2	no	—
341	C₂×C₁₉	—	8	1	no	—
342	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
343	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
344	C₂×C₁₉	#3022	1	1	yes	characteristic
345	C₂×#41	—	2	1	no	—
346	C₂×#41	D₄×C₁₉	1	2	yes	—
347	C₂²×Q₈	—	2	1	no	—
348	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
349	C₂²×D₄	—	2	2	no	—
350	C₂²×D₄	—	2	1	no	—
351	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
352	#137	—	4	8	no	—
353	C₂×Q₁₆	—	2	4	no	—
354	C₂×SD₁₆	—	2	4	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂²×C₈	—	2	1	no	—
357	C₄⋊Q₈	—	2	1	no	—
358	C₄⋊Q₈	—	2	1	no	—
359	C₄⋊Q₈	—	2	1	no	—
360	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
361	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
362	#127	—	2	1	no	—
363	#127	D₄×C₁₉	1	1	yes	characteristic
364	#126	—	2	2	no	—
365	#126	—	2	1	no	—
366	#125	C₂³×C₁₉	1	1	yes	characteristic
367	#124	—	2	1	no	—
368	#124	—	2	2	no	—
369	#124	—	2	2	no	—
370	#124	—	2	2	no	—
371	#124	—	2	1	no	—
372	#124	—	2	1	no	—
373	#124	D₄×C₁₉	1	2	yes	—
374	#124	C₂³×C₁₉	1	2	yes	—
375	#124	C₂³×C₁₉	1	1	yes	characteristic
376	#124	C₂³×C₁₉	1	2	yes	—
377	#123	—	2	2	no	—
378	#123	—	2	2	no	—
379	#123	—	2	1	no	—
380	#123	—	2	2	no	—
381	#123	—	2	2	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	C₂²⋊Q₈	—	2	2	no	—
384	C₂²⋊Q₈	—	2	2	no	—
385	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
386	#121	—	2	2	no	—
387	#121	—	2	2	no	—
388	#121	—	2	2	no	—
389	#121	—	2	1	no	—
390	#121	—	2	2	no	—
391	#121	—	2	2	no	—
392	#121	—	2	1	no	—
393	#121	—	2	1	no	—
394	#121	D₄×C₁₉	1	1	yes	characteristic
395	#120	—	2	2	no	—
396	#120	—	2	2	no	—
397	#120	—	2	2	no	—
398	#120	—	2	2	no	—
399	#120	—	2	2	no	—
400	C₄×Q₈	—	2	1	no	—
401	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
409	#117	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	2	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
416	#107	—	2	2	no	—
417	#106	—	2	2	no	—
418	C₄⋊C₈	—	2	1	no	—
419	#103	—	2	4	no	—
420	#103	—	2	2	no	—
421	#102	—	2	4	no	—
422	#102	—	2	2	no	—
423	C₂²⋊C₈	—	2	1	no	—
424	#97	—	2	1	no	—
425	#97	C₂³×C₁₉	1	2	yes	—
426	#97	C₂³×C₁₉	1	2	yes	—
427	#97	C₂³×C₁₉	1	2	yes	—
428	C₄×C₈	—	2	1	no	—
429	C₁₉	#19015	1	1	yes	characteristic, direct product factor, Sylow
430	C₂⁴	—	2	2	no	—
431	C₂⁴	—	2	1	no	—
432	#41	—	4	4	no	—
433	#41	—	8	2	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	4	2	no	—
437	C₂×Q₈	—	4	4	no	—
438	C₂×Q₈	—	4	1	no	—
439	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
441	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	—	8	2	no	—
454	C₂×D₄	—	8	4	no	—
455	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
457	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
467	Q₁₆	—	4	8	no	—
468	SD₁₆	—	4	8	no	—
469	M₁₆	—	2	4	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	4	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₄²	—	2	2	no	—
505	C₄²	—	2	1	no	—
506	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
507	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
509	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
510	C₂³	—	2	2	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	8	1	no	—
515	C₂³	—	8	1	no	—
516	C₂³	—	8	2	no	—
517	C₂³	—	8	2	no	—
518	C₂³	—	8	2	no	—
519	C₂³	C₁₉×#120	1	1	yes	characteristic
520	Q₈	—	4	2	no	—
521	Q₈	—	4	2	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	4	4	no	—
524	Q₈	—	4	2	no	—
525	Q₈	—	8	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	4	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	8	1	no	—
534	D₄	—	8	2	no	—
535	D₄	—	8	2	no	—
536	D₄	—	8	2	no	—
537	D₄	—	8	2	no	—
538	D₄	—	8	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	8	2	no	—
550	C₂×C₄	—	8	1	no	—
551	C₂×C₄	—	8	2	no	—
552	C₂×C₄	—	8	2	no	—
553	C₂×C₄	—	8	2	no	—
554	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
555	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
556	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
557	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
560	C₈	—	2	4	no	—
561	C₈	—	4	2	no	—
562	C₈	—	4	2	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	16	2	no	—
575	C₂²	—	16	4	no	—
576	C₂²	C₁₉×#453	1	2	yes	—
577	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	1	no	—
588	C₄	—	8	2	no	—
589	C₄	C₁₉×#455	1	2	yes	—
590	C₂	—	2	2	no	—
591	C₂	—	8	2	no	—
592	C₂	—	8	1	no	—
593	C₂	—	8	2	no	—
594	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
595	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
596	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3558	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3238	C₂	semidirect
3. C₁₉×#3152	C₂	semidirect
4. C₂×C₁₉×#489	C₂	semidirect
5. C₁₉×#1661	C₂	semidirect
6. C₁₉×#1659	C₂	semidirect
7. C₁₉×#1530	C₂	semidirect
8. C₁₉×#1527	C₂	semidirect
9. C₁₉×#1524	C₂	semidirect
24. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
27. C₁₉×#501	C₂²	semidirect
28. C₁₉×#497	C₂²	semidirect
32. C₁₉×#489	C₂²	semidirect
33. C₁₉×#489	C₂²	semidirect
38. C₁₉×#432	C₂²	semidirect
41. C₄×M₁₆×C₁₉	C₂²	semidirect
42. C₂×C₁₉×#97	C₂²	semidirect
43. C₁₉×#330	C₂²	semidirect
44. C₁₉×#329	C₂²	semidirect
45. C₁₉×#329	C₂²	semidirect
46. C₁₉×#329	C₂²	semidirect
211. #19015	C₁₉	direct (N × H)
266. #3238	C₂×C₁₉	semidirect
267. #3152	C₂×C₁₉	semidirect
268. C₂×#489	C₂×C₁₉	semidirect
269. #1661	C₂×C₁₉	semidirect
270. #1659	C₂×C₁₉	semidirect
271. #1530	C₂×C₁₉	semidirect
272. #1527	C₂×C₁₉	semidirect
273. #1524	C₂×C₁₉	semidirect
315. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
318. #501	C₂²×C₁₉	semidirect
319. #497	C₂²×C₁₉	semidirect
323. #489	C₂²×C₁₉	semidirect
324. #489	C₂²×C₁₉	semidirect
329. #432	C₂²×C₁₉	semidirect
332. C₄×M₁₆	C₂²×C₁₉	semidirect
333. C₂×#97	C₂²×C₁₉	semidirect
334. #330	C₂²×C₁₉	semidirect
335. #329	C₂²×C₁₉	semidirect
336. #329	C₂²×C₁₉	semidirect
337. #329	C₂²×C₁₉	semidirect
429. C₁₉	#19015	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×#3558	2
C₁₉×#3238	2
C₁₉×#3152	2
C₂×C₁₉×#489	2
C₁₉×#1661	2
C₁₉×#1659	2
C₁₉×#1530	2
C₁₉×#1527	2
C₁₉×#1524	2
#19015	19

Subgroups — C19×#19015 #18024974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19015 #18024974