Subgroups — C₁₉×#12780 #18018739

Order 4864.

756 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3551	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2129	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2128	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2126	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1910	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1909	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1884	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#568	C₂²	1	1	yes	characteristic
9	C₁₉×#563	C₄	1	2	yes	complemented
10	C₁₉×#560	—	2	1	no	—
11	C₁₉×#555	C₄	1	2	yes	complemented
12	C₁₉×#553	—	2	1	no	—
13	C₁₉×#552	—	2	1	no	—
14	C₁₉×#551	—	2	1	no	—
15	C₁₉×#548	—	2	1	no	—
16	C₁₉×#546	—	2	1	no	—
17	C₁₉×#540	—	2	2	no	—
18	C₁₉×#538	—	2	2	no	—
19	C₁₉×#537	—	2	1	no	—
20	C₁₉×#536	C₂²	1	1	yes	characteristic
21	C₁₉×#535	C₂²	1	1	yes	characteristic
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₁₉×#529	—	2	1	no	—
24	C₁₉×#421	—	2	1	no	—
25	C₁₉×#419	—	2	1	no	—
26	C₁₉×#418	—	2	1	no	—
27	C₁₉×#410	C₂²	1	1	yes	characteristic
28	C₁₉×#410	C₂²	1	1	yes	characteristic
29	C₁₉×#410	C₂²	1	1	yes	characteristic
30	C₁₉×#354	—	2	1	no	—
31	C₁₉×#354	—	2	2	no	—
32	C₁₉×#353	—	2	1	no	—
33	C₁₉×#353	—	2	2	no	—
34	C₁₉×#339	—	2	1	no	—
35	C₁₉×H(3,ℤ/4)	—	2	1	no	—
36	C₁₉×H(3,ℤ/4)	—	2	1	no	—
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
39	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
42	C₁₉×#131	—	4	2	no	—
43	C₂×M₁₆×C₁₉	—	2	1	no	—
44	C₂×M₁₆×C₁₉	—	2	1	no	—
45	C₂×M₁₆×C₁₉	—	2	1	no	—
46	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
47	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
48	C₁₉×#127	D₄	1	1	yes	characteristic
49	C₁₉×#127	D₄	1	2	yes	—
50	C₁₉×#126	—	2	2	no	—
51	C₁₉×#126	—	2	2	no	—
52	C₁₉×#126	—	2	2	no	—
53	C₁₉×#125	—	2	1	no	—
54	C₁₉×#125	—	2	2	no	—
55	C₁₉×#124	—	2	1	no	—
56	C₁₉×#124	—	2	2	no	—
57	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
58	C₁₉×#124	C₂×C₄	1	2	yes	—
59	C₁₉×#124	D₄	1	1	yes	characteristic
60	C₁₉×#124	D₄	1	2	yes	—
61	C₁₉×#123	—	2	2	no	—
62	C₁₉×#123	—	2	2	no	—
63	C₁₉×#123	—	2	2	no	—
64	C₁₉×#123	—	2	2	no	—
65	C₁₉×#123	—	2	1	no	—
66	C₁₉×#123	—	2	1	no	—
67	C₁₉×C₂²⋊Q₈	—	2	1	no	—
68	C₁₉×C₂²⋊Q₈	—	2	2	no	—
69	C₁₉×C₂²⋊Q₈	—	2	2	no	—
70	C₁₉×C₂²⋊Q₈	—	2	1	no	—
71	C₁₉×C₂²⋊Q₈	—	2	1	no	—
72	C₁₉×#121	—	2	2	no	—
73	C₁₉×#121	—	2	2	no	—
74	C₁₉×#121	—	2	1	no	—
75	C₁₉×#121	—	2	2	no	—
76	C₁₉×#121	—	2	2	no	—
77	C₁₉×#121	—	2	2	no	—
78	C₁₉×#121	—	2	2	no	—
79	C₁₉×#121	—	2	1	no	—
80	C₁₉×#121	—	2	1	no	—
81	C₁₉×#121	—	2	1	no	—
82	C₁₉×#121	—	2	1	no	—
83	C₁₉×#120	—	2	2	no	—
84	C₁₉×#120	—	2	1	no	—
85	C₁₉×#120	—	2	1	no	—
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×D₄×C₁₉	—	2	2	no	—
88	C₄×D₄×C₁₉	—	2	1	no	—
89	C₄×D₄×C₁₉	—	2	2	no	—
90	C₄×D₄×C₁₉	—	2	1	no	—
91	C₄×D₄×C₁₉	—	2	1	no	—
92	C₄×D₄×C₁₉	—	2	2	no	—
93	C₁₉×#117	—	2	2	no	—
94	C₁₉×#117	—	2	2	no	—
95	C₁₉×#117	—	2	1	no	—
96	C₁₉×#117	—	2	1	no	—
97	C₁₉×#117	—	2	1	no	—
98	C₁₉×#117	D₄	1	1	yes	characteristic
99	C₁₉×#117	D₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
102	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
103	C₁₉×#104	—	4	2	no	—
104	C₁₉×#103	—	4	2	no	—
105	C₁₉×#102	—	4	2	no	—
106	C₁₉×#99	—	2	1	no	—
107	C₁₉×#99	—	2	1	no	—
108	C₁₉×#99	—	2	1	no	—
109	C₁₉×#99	—	2	1	no	—
110	C₁₉×#99	—	2	1	no	—
111	C₁₉×#99	—	2	1	no	—
112	C₂⁴×C₁₉	—	2	1	no	—
113	#41×C₁₉	—	4	1	no	—
114	#41×C₁₉	—	4	1	no	—
115	#41×C₁₉	—	4	1	no	—
116	#41×C₁₉	—	4	1	no	—
117	#41×C₁₉	—	8	1	no	—
118	#41×C₁₉	—	8	1	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	4	1	no	—
121	C₂×Q₈×C₁₉	—	4	1	no	—
122	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
124	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	4	1	no	—
134	C₂×D₄×C₁₉	—	4	1	no	—
135	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
136	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
137	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	M₁₆×C₁₉	—	2	2	no	—
150	M₁₆×C₁₉	—	4	1	no	—
151	M₁₆×C₁₉	—	4	1	no	—
152	M₁₆×C₁₉	—	4	1	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₂×C₈×C₁₉	—	4	1	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	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	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	4	1	no	—
168	C₄⋊C₄×C₁₉	—	4	1	no	—
169	C₄⋊C₄×C₁₉	—	4	1	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	1	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂²⋊C₄×C₁₉	—	2	1	no	—
178	C₂²⋊C₄×C₁₉	—	2	1	no	—
179	C₂²⋊C₄×C₁₉	—	2	1	no	—
180	C₂²⋊C₄×C₁₉	—	2	2	no	—
181	C₂²⋊C₄×C₁₉	—	2	1	no	—
182	C₂²⋊C₄×C₁₉	—	2	2	no	—
183	C₂²⋊C₄×C₁₉	—	2	1	no	—
184	C₂²⋊C₄×C₁₉	—	2	2	no	—
185	C₂²⋊C₄×C₁₉	—	4	1	no	—
186	C₂²⋊C₄×C₁₉	—	4	1	no	—
187	C₂²⋊C₄×C₁₉	—	4	1	no	—
188	C₄²×C₁₉	—	2	2	no	—
189	C₄²×C₁₉	—	2	1	no	—
190	C₄²×C₁₉	—	4	1	no	—
191	C₄²×C₁₉	—	4	1	no	—
192	C₄²×C₁₉	—	4	1	no	—
193	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
194	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
195	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
196	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
197	#12780	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂³×C₁₉	—	2	2	no	—
199	C₂³×C₁₉	—	2	1	no	—
200	C₂³×C₁₉	—	8	1	no	—
201	C₂³×C₁₉	—	8	2	no	—
202	C₂³×C₁₉	#120	1	1	yes	characteristic
203	C₂³×C₁₉	#120	1	1	yes	characteristic
204	C₂³×C₁₉	#120	1	1	yes	characteristic
205	Q₈×C₁₉	—	4	1	no	—
206	Q₈×C₁₉	—	4	2	no	—
207	Q₈×C₁₉	—	4	1	no	—
208	Q₈×C₁₉	—	4	1	no	—
209	Q₈×C₁₉	—	4	1	no	—
210	D₄×C₁₉	—	4	1	no	—
211	D₄×C₁₉	—	4	1	no	—
212	D₄×C₁₉	—	4	1	no	—
213	D₄×C₁₉	—	4	2	no	—
214	D₄×C₁₉	—	4	1	no	—
215	D₄×C₁₉	—	4	1	no	—
216	D₄×C₁₉	—	4	1	no	—
217	D₄×C₁₉	—	8	1	no	—
218	D₄×C₁₉	—	8	2	no	—
219	D₄×C₁₉	—	8	2	no	—
220	D₄×C₁₉	—	8	2	no	—
221	D₄×C₁₉	—	8	1	no	—
222	D₄×C₁₉	—	8	1	no	—
223	D₄×C₁₉	—	8	2	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	8	1	no	—
239	C₂×C₄×C₁₉	—	8	2	no	—
240	C₂×C₄×C₁₉	—	8	1	no	—
241	C₂×C₄×C₁₉	—	8	2	no	—
242	C₂×C₄×C₁₉	—	8	2	no	—
243	C₂×C₄×C₁₉	—	8	1	no	—
244	C₂×C₄×C₁₉	—	8	1	no	—
245	C₂×C₄×C₁₉	—	8	1	no	—
246	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
250	C₈×C₁₉	—	4	2	no	—
251	#3551	C₂×C₁₉	1	1	yes	characteristic
252	#2129	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#2128	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#2126	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#1910	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1909	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1884	C₂×C₁₉	1	1	yes	characteristic, complemented
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	—	2	1	no	—
260	C₂²×C₁₉	—	2	1	no	—
261	C₂²×C₁₉	—	4	1	no	—
262	C₂²×C₁₉	—	4	1	no	—
263	C₂²×C₁₉	—	4	1	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	—	4	2	no	—
266	C₂²×C₁₉	—	4	1	no	—
267	C₂²×C₁₉	—	4	2	no	—
268	C₂²×C₁₉	—	4	1	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	16	2	no	—
271	C₂²×C₁₉	#379	1	1	yes	characteristic
272	C₄×C₁₉	—	2	1	no	—
273	C₄×C₁₉	—	2	1	no	—
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	4	1	no	—
276	C₄×C₁₉	—	4	2	no	—
277	C₄×C₁₉	—	4	2	no	—
278	C₄×C₁₉	—	4	1	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	4	2	no	—
281	C₄×C₁₉	—	16	1	no	—
282	C₄×C₁₉	—	16	1	no	—
283	C₄×C₁₉	—	16	1	no	—
284	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
285	C₄×C₁₉	#458	1	1	yes	characteristic
286	#568	C₂²×C₁₉	1	1	yes	characteristic
287	#563	C₄×C₁₉	1	2	yes	complemented
288	#560	—	2	1	no	—
289	#555	C₄×C₁₉	1	2	yes	complemented
290	#553	—	2	1	no	—
291	#552	—	2	1	no	—
292	#551	—	2	1	no	—
293	#548	—	2	1	no	—
294	#546	—	2	1	no	—
295	#540	—	2	2	no	—
296	#538	—	2	2	no	—
297	#537	—	2	1	no	—
298	#536	C₂²×C₁₉	1	1	yes	characteristic
299	#535	C₂²×C₁₉	1	1	yes	characteristic
300	#532	C₂²×C₁₉	1	1	yes	characteristic
301	#529	—	2	1	no	—
302	#421	—	2	1	no	—
303	#419	—	2	1	no	—
304	#418	—	2	1	no	—
305	#410	C₂²×C₁₉	1	1	yes	characteristic
306	#410	C₂²×C₁₉	1	1	yes	characteristic
307	#410	C₂²×C₁₉	1	1	yes	characteristic
308	#354	—	2	1	no	—
309	#354	—	2	2	no	—
310	#353	—	2	1	no	—
311	#353	—	2	2	no	—
312	#339	—	2	1	no	—
313	H(3,ℤ/4)	—	2	1	no	—
314	H(3,ℤ/4)	—	2	1	no	—
315	C₂×C₁₉	—	2	1	no	—
316	C₂×C₁₉	—	4	1	no	—
317	C₂×C₁₉	—	4	1	no	—
318	C₂×C₁₉	—	4	1	no	—
319	C₂×C₁₉	—	8	1	no	—
320	C₂×C₁₉	—	8	2	no	—
321	C₂×C₁₉	#1790	1	1	yes	characteristic
322	C₂×#41	—	2	1	no	—
323	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
324	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
325	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
326	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
327	#131	—	4	2	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
332	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
333	#127	D₄×C₁₉	1	1	yes	characteristic
334	#127	D₄×C₁₉	1	2	yes	—
335	#126	—	2	2	no	—
336	#126	—	2	2	no	—
337	#126	—	2	2	no	—
338	#125	—	2	1	no	—
339	#125	—	2	2	no	—
340	#124	—	2	1	no	—
341	#124	—	2	2	no	—
342	#124	C₂×C₄×C₁₉	1	1	yes	characteristic
343	#124	C₂×C₄×C₁₉	1	2	yes	—
344	#124	D₄×C₁₉	1	1	yes	characteristic
345	#124	D₄×C₁₉	1	2	yes	—
346	#123	—	2	2	no	—
347	#123	—	2	2	no	—
348	#123	—	2	2	no	—
349	#123	—	2	2	no	—
350	#123	—	2	1	no	—
351	#123	—	2	1	no	—
352	C₂²⋊Q₈	—	2	1	no	—
353	C₂²⋊Q₈	—	2	2	no	—
354	C₂²⋊Q₈	—	2	2	no	—
355	C₂²⋊Q₈	—	2	1	no	—
356	C₂²⋊Q₈	—	2	1	no	—
357	#121	—	2	2	no	—
358	#121	—	2	2	no	—
359	#121	—	2	1	no	—
360	#121	—	2	2	no	—
361	#121	—	2	2	no	—
362	#121	—	2	2	no	—
363	#121	—	2	2	no	—
364	#121	—	2	1	no	—
365	#121	—	2	1	no	—
366	#121	—	2	1	no	—
367	#121	—	2	1	no	—
368	#120	—	2	2	no	—
369	#120	—	2	1	no	—
370	#120	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	2	no	—
378	#117	—	2	2	no	—
379	#117	—	2	2	no	—
380	#117	—	2	1	no	—
381	#117	—	2	1	no	—
382	#117	—	2	1	no	—
383	#117	D₄×C₁₉	1	1	yes	characteristic
384	#117	D₄×C₁₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	2	no	—
387	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
388	#104	—	4	2	no	—
389	#103	—	4	2	no	—
390	#102	—	4	2	no	—
391	#99	—	2	1	no	—
392	#99	—	2	1	no	—
393	#99	—	2	1	no	—
394	#99	—	2	1	no	—
395	#99	—	2	1	no	—
396	#99	—	2	1	no	—
397	C₁₉	#12780	1	1	yes	characteristic, direct product factor, Sylow
398	C₂⁴	—	2	1	no	—
399	#41	—	4	1	no	—
400	#41	—	4	1	no	—
401	#41	—	4	1	no	—
402	#41	—	4	1	no	—
403	#41	—	8	1	no	—
404	#41	—	8	1	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	4	1	no	—
407	C₂×Q₈	—	4	1	no	—
408	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
409	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
410	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
422	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
423	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
425	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
435	M₁₆	—	2	2	no	—
436	M₁₆	—	4	1	no	—
437	M₁₆	—	4	1	no	—
438	M₁₆	—	4	1	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	4	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	4	1	no	—
454	C₄⋊C₄	—	4	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	4	1	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	4	1	no	—
477	C₄²	—	4	1	no	—
478	C₄²	—	4	1	no	—
479	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
480	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
481	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
482	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	8	1	no	—
486	C₂³	—	8	2	no	—
487	C₂³	C₁₉×#120	1	1	yes	characteristic
488	C₂³	C₁₉×#120	1	1	yes	characteristic
489	C₂³	C₁₉×#120	1	1	yes	characteristic
490	Q₈	—	4	1	no	—
491	Q₈	—	4	2	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	1	no	—
494	Q₈	—	4	1	no	—
495	D₄	—	4	1	no	—
496	D₄	—	4	1	no	—
497	D₄	—	4	1	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	1	no	—
500	D₄	—	4	1	no	—
501	D₄	—	4	1	no	—
502	D₄	—	8	1	no	—
503	D₄	—	8	2	no	—
504	D₄	—	8	2	no	—
505	D₄	—	8	2	no	—
506	D₄	—	8	2	no	—
507	D₄	—	8	1	no	—
508	D₄	—	8	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	8	1	no	—
524	C₂×C₄	—	8	2	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	—	8	1	no	—
527	C₂×C₄	—	8	2	no	—
528	C₂×C₄	—	8	1	no	—
529	C₂×C₄	—	8	1	no	—
530	C₂×C₄	—	8	1	no	—
531	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
532	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
533	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
534	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
535	C₈	—	4	2	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	16	2	no	—
549	C₂²	C₁₉×#379	1	1	yes	characteristic
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	2	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	2	no	—
559	C₄	—	16	1	no	—
560	C₄	—	16	1	no	—
561	C₄	—	16	1	no	—
562	C₄	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
563	C₄	C₁₉×#458	1	1	yes	characteristic
564	C₂	—	2	1	no	—
565	C₂	—	4	1	no	—
566	C₂	—	4	1	no	—
567	C₂	—	4	1	no	—
568	C₂	—	8	2	no	—
569	C₂	—	8	1	no	—
570	C₂	C₁₉×#1790	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#1790
commutator	C₂×Q₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×#41	C₂³×C₁₉
prime radical	C₁₉×#3551	C₂
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2129	C₂	semidirect
3. C₁₉×#2128	C₂	semidirect
4. C₁₉×#2126	C₂	semidirect
5. C₁₉×#1910	C₂	semidirect
6. C₁₉×#1909	C₂	semidirect
7. C₁₉×#1884	C₂	semidirect
9. C₁₉×#563	C₄	semidirect
11. C₁₉×#555	C₄	semidirect
197. #12780	C₁₉	direct (N × H)
252. #2129	C₂×C₁₉	semidirect
253. #2128	C₂×C₁₉	semidirect
254. #2126	C₂×C₁₉	semidirect
255. #1910	C₂×C₁₉	semidirect
256. #1909	C₂×C₁₉	semidirect
257. #1884	C₂×C₁₉	semidirect
287. #563	C₄×C₁₉	semidirect
289. #555	C₄×C₁₉	semidirect
397. C₁₉	#12780	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×#3551	2
C₁₉×#2129	2
C₁₉×#2128	2
C₁₉×#2126	2
C₁₉×#1910	2
C₁₉×#1909	2
C₁₉×#1884	2
#12780	19

Subgroups — C19×#12780 #18018739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12780 #18018739