Subgroups — C₁₉×#19019 #18024978

Order 4864.

958 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3171	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3153	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1661	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1660	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1657	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1656	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1529	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1527	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1526	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#137	—	2	1	no	—
13	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
14	C₁₉×#563	C₂²	1	2	yes	—
15	C₁₉×#562	C₂²	1	2	yes	—
16	C₁₉×#556	—	2	1	no	—
17	C₁₉×#551	—	2	2	no	—
18	D₄×Q₈×C₁₉	—	2	1	no	—
19	C₁₉×#548	—	2	1	no	—
20	C₁₉×#546	—	2	1	no	—
21	C₁₉×#543	—	2	1	no	—
22	C₁₉×#542	—	2	1	no	—
23	C₁₉×#542	—	2	2	no	—
24	C₁₉×#538	—	2	1	no	—
25	C₁₉×#536	—	2	1	no	—
26	C₁₉×#533	C₂²	1	1	yes	characteristic
27	C₁₉×#532	C₂²	1	1	yes	characteristic
28	C₁₉×#529	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
30	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#501	C₂²	1	2	yes	complemented
32	C₁₉×#497	C₂²	1	2	yes	—
33	C₁₉×#496	C₂²	1	2	yes	—
34	C₁₉×#496	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#495	—	2	2	no	—
36	C₁₉×#490	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#490	C₂²	1	2	yes	complemented
38	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#482	—	2	2	no	—
40	C₁₉×#476	—	2	1	no	—
41	C₁₉×#474	—	2	1	no	—
42	C₁₉×#469	—	2	1	no	—
43	C₁₉×#468	—	2	1	no	—
44	C₄×SD₁₆×C₁₉	—	2	1	no	—
45	C₄×D₈×C₁₉	—	2	1	no	—
46	C₁₉×#432	C₂²	1	1	yes	characteristic
47	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#330	C₂²	1	2	yes	complemented
50	C₁₉×#330	C₂²	1	2	yes	complemented
51	C₁₉×#330	C₂²	1	2	yes	complemented
52	C₁₉×#329	C₂²	1	2	yes	—
53	C₁₉×#329	C₂²	1	2	yes	—
54	C₁₉×#329	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	—	2	1	no	—
58	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
59	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
60	C₁₉×#137	—	4	4	no	—
61	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
62	C₂×Q₁₆×C₁₉	—	2	2	no	—
63	C₂×SD₁₆×C₁₉	—	2	1	no	—
64	C₂×SD₁₆×C₁₉	—	2	2	no	—
65	C₂×SD₁₆×C₁₉	—	2	2	no	—
66	C₂×D₈×C₁₉	—	2	1	no	—
67	C₂×D₈×C₁₉	—	2	2	no	—
68	C₂×M₁₆×C₁₉	—	2	1	no	—
69	C₂×M₁₆×C₁₉	—	2	1	no	—
70	C₁₉×C₄⋊Q₈	—	2	1	no	—
71	C₁₉×C₄⋊Q₈	—	2	2	no	—
72	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
73	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
74	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
75	C₁₉×#127	C₂³	1	1	yes	characteristic
76	C₁₉×#126	—	2	2	no	—
77	C₁₉×#126	—	2	2	no	—
78	C₁₉×#126	—	2	2	no	—
79	C₁₉×#126	—	2	1	no	—
80	C₁₉×#125	C₂³	1	1	yes	characteristic
81	C₁₉×#125	C₂³	1	2	yes	—
82	C₁₉×#124	—	2	1	no	—
83	C₁₉×#124	—	2	2	no	—
84	C₁₉×#124	—	2	2	no	—
85	C₁₉×#124	—	2	1	no	—
86	C₁₉×#124	—	2	1	no	—
87	C₁₉×#124	—	2	1	no	—
88	C₁₉×#124	D₄	1	2	yes	—
89	C₁₉×#124	C₂³	1	1	yes	characteristic
90	C₁₉×#124	C₂³	1	2	yes	—
91	C₁₉×#123	—	2	2	no	—
92	C₁₉×#123	—	2	2	no	—
93	C₁₉×#123	—	2	1	no	—
94	C₁₉×#123	—	2	2	no	—
95	C₁₉×#123	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	—	2	2	no	—
97	C₁₉×C₂²⋊Q₈	—	2	2	no	—
98	C₁₉×C₂²⋊Q₈	—	2	1	no	—
99	C₁₉×C₂²⋊Q₈	—	2	2	no	—
100	C₁₉×C₂²⋊Q₈	—	2	2	no	—
101	C₁₉×C₂²⋊Q₈	—	2	2	no	—
102	C₁₉×C₂²⋊Q₈	—	2	1	no	—
103	C₁₉×C₂²⋊Q₈	—	2	1	no	—
104	C₁₉×C₂²⋊Q₈	—	2	2	no	—
105	C₁₉×C₂²⋊Q₈	—	2	2	no	—
106	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
107	C₁₉×#121	—	2	1	no	—
108	C₁₉×#121	—	2	2	no	—
109	C₁₉×#121	—	2	2	no	—
110	C₁₉×#121	—	2	1	no	—
111	C₁₉×#121	—	2	1	no	—
112	C₁₉×#121	D₄	1	1	yes	characteristic
113	C₁₉×#120	—	2	2	no	—
114	C₄×Q₈×C₁₉	—	2	1	no	—
115	C₄×Q₈×C₁₉	—	2	1	no	—
116	C₄×Q₈×C₁₉	—	2	1	no	—
117	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
118	C₄×D₄×C₁₉	—	2	2	no	—
119	C₄×D₄×C₁₉	—	2	1	no	—
120	C₄×D₄×C₁₉	—	2	2	no	—
121	C₄×D₄×C₁₉	—	2	1	no	—
122	C₄×D₄×C₁₉	—	2	1	no	—
123	C₄×D₄×C₁₉	—	2	1	no	—
124	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
125	C₁₉×#117	—	2	2	no	—
126	C₁₉×#117	—	2	1	no	—
127	C₁₉×#117	D₄	1	2	yes	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
129	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
131	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
132	C₁₉×#107	—	2	1	no	—
133	C₁₉×#107	—	2	2	no	—
134	C₁₉×#106	—	2	1	no	—
135	C₁₉×#106	—	2	2	no	—
136	C₁₉×C₄⋊C₈	—	2	1	no	—
137	C₁₉×#103	—	2	1	no	—
138	C₁₉×#102	—	2	1	no	—
139	C₁₉×#102	—	2	1	no	—
140	C₁₉×#102	—	2	1	no	—
141	C₁₉×#102	—	2	2	no	—
142	C₁₉×#102	—	2	2	no	—
143	C₁₉×C₂²⋊C₈	—	2	1	no	—
144	C₁₉×#97	C₂³	1	1	yes	characteristic
145	C₁₉×#97	C₂³	1	2	yes	—
146	C₁₉×#97	C₂³	1	1	yes	characteristic
147	C₁₉×#97	C₂³	1	2	yes	—
148	C₄×C₈×C₁₉	—	2	1	no	—
149	C₄×C₈×C₁₉	—	2	1	no	—
150	C₂⁴×C₁₉	—	2	1	no	—
151	#41×C₁₉	—	4	2	no	—
152	#41×C₁₉	—	4	2	no	—
153	#41×C₁₉	—	8	2	no	—
154	C₂×Q₈×C₁₉	—	2	2	no	—
155	C₂×Q₈×C₁₉	—	2	1	no	—
156	C₂×Q₈×C₁₉	—	2	1	no	—
157	C₂×Q₈×C₁₉	—	2	1	no	—
158	C₂×Q₈×C₁₉	—	2	1	no	—
159	C₂×Q₈×C₁₉	—	4	2	no	—
160	C₂×Q₈×C₁₉	—	8	2	no	—
161	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	2	no	—
165	C₂×D₄×C₁₉	—	2	2	no	—
166	C₂×D₄×C₁₉	—	2	1	no	—
167	C₂×D₄×C₁₉	—	2	1	no	—
168	C₂×D₄×C₁₉	—	2	1	no	—
169	C₂×D₄×C₁₉	—	2	1	no	—
170	C₂×D₄×C₁₉	—	4	2	no	—
171	C₂×D₄×C₁₉	—	4	1	no	—
172	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₉	—	2	2	no	—
175	C₂²×C₄×C₁₉	—	2	2	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	—	4	1	no	—
180	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
183	Q₁₆×C₁₉	—	4	4	no	—
184	SD₁₆×C₁₉	—	4	2	no	—
185	SD₁₆×C₁₉	—	4	4	no	—
186	SD₁₆×C₁₉	—	4	4	no	—
187	D₈×C₁₉	—	4	2	no	—
188	D₈×C₁₉	—	4	4	no	—
189	M₁₆×C₁₉	—	2	4	no	—
190	M₁₆×C₁₉	—	4	2	no	—
191	C₂×C₈×C₁₉	—	2	2	no	—
192	C₂×C₈×C₁₉	—	2	1	no	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₂×C₈×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	2	no	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	2	no	—
206	C₄⋊C₄×C₁₉	—	2	2	no	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
210	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
211	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	2	no	—
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	2	no	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	1	no	—
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	—	2	2	no	—
221	C₂²⋊C₄×C₁₉	—	2	2	no	—
222	C₂²⋊C₄×C₁₉	—	2	1	no	—
223	C₂²⋊C₄×C₁₉	—	2	1	no	—
224	C₂²⋊C₄×C₁₉	—	2	2	no	—
225	C₂²⋊C₄×C₁₉	—	2	2	no	—
226	C₂²⋊C₄×C₁₉	—	2	1	no	—
227	C₂²⋊C₄×C₁₉	—	2	1	no	—
228	C₂²⋊C₄×C₁₉	—	4	1	no	—
229	C₂²⋊C₄×C₁₉	—	4	1	no	—
230	C₄²×C₁₉	—	2	2	no	—
231	C₄²×C₁₉	—	2	2	no	—
232	C₄²×C₁₉	—	2	1	no	—
233	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
234	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
237	#19019	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂³×C₁₉	—	2	2	no	—
239	C₂³×C₁₉	—	2	1	no	—
240	C₂³×C₁₉	—	4	2	no	—
241	C₂³×C₁₉	—	4	1	no	—
242	C₂³×C₁₉	—	8	1	no	—
243	C₂³×C₁₉	—	8	1	no	—
244	C₂³×C₁₉	#120	1	1	yes	characteristic
245	Q₈×C₁₉	—	4	2	no	—
246	Q₈×C₁₉	—	4	1	no	—
247	Q₈×C₁₉	—	4	1	no	—
248	Q₈×C₁₉	—	4	1	no	—
249	Q₈×C₁₉	—	4	2	no	—
250	Q₈×C₁₉	—	4	2	no	—
251	Q₈×C₁₉	—	8	1	no	—
252	Q₈×C₁₉	—	8	2	no	—
253	D₄×C₁₉	—	4	2	no	—
254	D₄×C₁₉	—	4	1	no	—
255	D₄×C₁₉	—	4	1	no	—
256	D₄×C₁₉	—	4	1	no	—
257	D₄×C₁₉	—	4	1	no	—
258	D₄×C₁₉	—	4	1	no	—
259	D₄×C₁₉	—	4	2	no	—
260	D₄×C₁₉	—	4	2	no	—
261	D₄×C₁₉	—	4	2	no	—
262	D₄×C₁₉	—	8	2	no	—
263	D₄×C₁₉	—	8	2	no	—
264	D₄×C₁₉	—	8	2	no	—
265	C₂×C₄×C₁₉	—	2	2	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	2	2	no	—
268	C₂×C₄×C₁₉	—	2	1	no	—
269	C₂×C₄×C₁₉	—	2	2	no	—
270	C₂×C₄×C₁₉	—	2	2	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	2	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	8	1	no	—
277	C₂×C₄×C₁₉	—	8	2	no	—
278	C₂×C₄×C₁₉	—	8	2	no	—
279	C₂×C₄×C₁₉	—	8	2	no	—
280	C₂×C₄×C₁₉	—	8	2	no	—
281	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
282	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
283	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
284	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
287	C₈×C₁₉	—	2	4	no	—
288	C₈×C₁₉	—	2	2	no	—
289	C₈×C₁₉	—	4	2	no	—
290	C₈×C₁₉	—	4	1	no	—
291	#3561	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#3235	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#3171	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#3153	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#1661	C₂×C₁₉	1	2	yes	complemented
296	#1660	C₂×C₁₉	1	2	yes	complemented
297	#1657	C₂×C₁₉	1	2	yes	complemented
298	#1656	C₂×C₁₉	1	2	yes	complemented
299	#1529	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#1527	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#1526	C₂×C₁₉	1	1	yes	characteristic, complemented
302	C₂²×C₁₉	—	2	1	no	—
303	C₂²×C₁₉	—	2	1	no	—
304	C₂²×C₁₉	—	2	1	no	—
305	C₂²×C₁₉	—	4	1	no	—
306	C₂²×C₁₉	—	4	2	no	—
307	C₂²×C₁₉	—	4	2	no	—
308	C₂²×C₁₉	—	4	1	no	—
309	C₂²×C₁₉	—	4	1	no	—
310	C₂²×C₁₉	—	4	2	no	—
311	C₂²×C₁₉	—	8	1	no	—
312	C₂²×C₁₉	—	8	1	no	—
313	C₂²×C₁₉	—	8	1	no	—
314	C₂²×C₁₉	—	16	2	no	—
315	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
316	C₄×C₁₉	—	2	1	no	—
317	C₄×C₁₉	—	2	1	no	—
318	C₄×C₁₉	—	2	1	no	—
319	C₄×C₁₉	—	2	1	no	—
320	C₄×C₁₉	—	2	1	no	—
321	C₄×C₁₉	—	4	1	no	—
322	C₄×C₁₉	—	4	2	no	—
323	C₄×C₁₉	—	4	2	no	—
324	C₄×C₁₉	—	4	1	no	—
325	C₄×C₁₉	—	4	2	no	—
326	C₄×C₁₉	—	4	1	no	—
327	C₄×C₁₉	—	8	1	no	—
328	C₄×C₁₉	#453	1	2	yes	—
329	C₂×#137	—	2	1	no	—
330	C₂×AGL(1,ℤ/8)	—	2	1	no	—
331	#563	C₂²×C₁₉	1	2	yes	—
332	#562	C₂²×C₁₉	1	2	yes	—
333	#556	—	2	1	no	—
334	#551	—	2	2	no	—
335	D₄×Q₈	—	2	1	no	—
336	#548	—	2	1	no	—
337	#546	—	2	1	no	—
338	#543	—	2	1	no	—
339	#542	—	2	1	no	—
340	#542	—	2	2	no	—
341	#538	—	2	1	no	—
342	#536	—	2	1	no	—
343	#533	C₂²×C₁₉	1	1	yes	characteristic
344	#532	C₂²×C₁₉	1	1	yes	characteristic
345	#529	C₂²×C₁₉	1	1	yes	characteristic
346	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
347	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
348	#501	C₂²×C₁₉	1	2	yes	complemented
349	#497	C₂²×C₁₉	1	2	yes	—
350	#496	C₂²×C₁₉	1	2	yes	—
351	#496	C₂²×C₁₉	1	1	yes	characteristic, complemented
352	#495	—	2	2	no	—
353	#490	C₂²×C₁₉	1	1	yes	characteristic, complemented
354	#490	C₂²×C₁₉	1	2	yes	complemented
355	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
356	#482	—	2	2	no	—
357	#476	—	2	1	no	—
358	#474	—	2	1	no	—
359	#469	—	2	1	no	—
360	#468	—	2	1	no	—
361	C₄×SD₁₆	—	2	1	no	—
362	C₄×D₈	—	2	1	no	—
363	#432	C₂²×C₁₉	1	1	yes	characteristic
364	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
365	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
366	#330	C₂²×C₁₉	1	2	yes	complemented
367	#330	C₂²×C₁₉	1	2	yes	complemented
368	#330	C₂²×C₁₉	1	2	yes	complemented
369	#329	C₂²×C₁₉	1	2	yes	—
370	#329	C₂²×C₁₉	1	2	yes	—
371	#329	C₂²×C₁₉	1	2	yes	complemented
372	C₂×C₁₉	—	4	1	no	—
373	C₂×C₁₉	—	8	1	no	—
374	C₂×C₁₉	—	8	2	no	—
375	C₂×C₁₉	—	16	1	no	—
376	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
377	C₂×C₁₉	#3018	1	1	yes	characteristic
378	C₂×C₁₉	#3020	1	1	yes	characteristic
379	C₂×#41	—	2	1	no	—
380	C₂×#41	—	2	1	no	—
381	C₂²×Q₈	—	2	1	no	—
382	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
383	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
384	#137	—	4	4	no	—
385	AGL(1,ℤ/8)	—	4	4	no	—
386	C₂×Q₁₆	—	2	2	no	—
387	C₂×SD₁₆	—	2	2	no	—
388	C₂×SD₁₆	—	2	1	no	—
389	C₂×SD₁₆	—	2	2	no	—
390	C₂×D₈	—	2	2	no	—
391	C₂×D₈	—	2	1	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₄⋊Q₈	—	2	1	no	—
395	C₄⋊Q₈	—	2	2	no	—
396	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
397	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
398	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
399	#127	C₂³×C₁₉	1	1	yes	characteristic
400	#126	—	2	2	no	—
401	#126	—	2	2	no	—
402	#126	—	2	2	no	—
403	#126	—	2	1	no	—
404	#125	C₂³×C₁₉	1	1	yes	characteristic
405	#125	C₂³×C₁₉	1	2	yes	—
406	#124	—	2	1	no	—
407	#124	—	2	2	no	—
408	#124	—	2	2	no	—
409	#124	—	2	1	no	—
410	#124	—	2	1	no	—
411	#124	—	2	1	no	—
412	#124	D₄×C₁₉	1	2	yes	—
413	#124	C₂³×C₁₉	1	2	yes	—
414	#124	C₂³×C₁₉	1	1	yes	characteristic
415	#123	—	2	2	no	—
416	#123	—	2	2	no	—
417	#123	—	2	1	no	—
418	#123	—	2	2	no	—
419	#123	—	2	2	no	—
420	C₂²⋊Q₈	—	2	2	no	—
421	C₂²⋊Q₈	—	2	2	no	—
422	C₂²⋊Q₈	—	2	1	no	—
423	C₂²⋊Q₈	—	2	2	no	—
424	C₂²⋊Q₈	—	2	2	no	—
425	C₂²⋊Q₈	—	2	2	no	—
426	C₂²⋊Q₈	—	2	1	no	—
427	C₂²⋊Q₈	—	2	1	no	—
428	C₂²⋊Q₈	—	2	2	no	—
429	C₂²⋊Q₈	—	2	2	no	—
430	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
431	#121	—	2	1	no	—
432	#121	—	2	2	no	—
433	#121	—	2	2	no	—
434	#121	—	2	1	no	—
435	#121	—	2	1	no	—
436	#121	D₄×C₁₉	1	1	yes	characteristic
437	#120	—	2	2	no	—
438	C₄×Q₈	—	2	1	no	—
439	C₄×Q₈	—	2	1	no	—
440	C₄×Q₈	—	2	1	no	—
441	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	2	1	no	—
444	C₄×D₄	—	2	2	no	—
445	C₄×D₄	—	2	1	no	—
446	C₄×D₄	—	2	1	no	—
447	C₄×D₄	—	2	1	no	—
448	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
449	#117	—	2	2	no	—
450	#117	—	2	1	no	—
451	#117	D₄×C₁₉	1	2	yes	—
452	C₂×C₂²⋊C₄	—	2	2	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
456	#107	—	2	1	no	—
457	#107	—	2	2	no	—
458	#106	—	2	1	no	—
459	#106	—	2	2	no	—
460	C₄⋊C₈	—	2	1	no	—
461	#103	—	2	1	no	—
462	#102	—	2	1	no	—
463	#102	—	2	1	no	—
464	#102	—	2	1	no	—
465	#102	—	2	2	no	—
466	#102	—	2	2	no	—
467	C₂²⋊C₈	—	2	1	no	—
468	#97	C₂³×C₁₉	1	2	yes	—
469	#97	C₂³×C₁₉	1	1	yes	characteristic
470	#97	C₂³×C₁₉	1	1	yes	characteristic
471	#97	C₂³×C₁₉	1	2	yes	—
472	C₄×C₈	—	2	1	no	—
473	C₄×C₈	—	2	1	no	—
474	C₁₉	#19019	1	1	yes	characteristic, direct product factor, Sylow
475	C₂⁴	—	2	1	no	—
476	#41	—	4	2	no	—
477	#41	—	4	2	no	—
478	#41	—	8	2	no	—
479	C₂×Q₈	—	2	2	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	4	2	no	—
485	C₂×Q₈	—	8	2	no	—
486	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	—	4	1	no	—
497	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	4	1	no	—
505	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
508	Q₁₆	—	4	4	no	—
509	SD₁₆	—	4	2	no	—
510	SD₁₆	—	4	4	no	—
511	SD₁₆	—	4	4	no	—
512	D₈	—	4	2	no	—
513	D₈	—	4	4	no	—
514	M₁₆	—	2	4	no	—
515	M₁₆	—	4	2	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	2	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
535	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
536	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
537	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	2	1	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	2	2	no	—
546	C₂²⋊C₄	—	2	2	no	—
547	C₂²⋊C₄	—	2	1	no	—
548	C₂²⋊C₄	—	2	1	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	1	no	—
552	C₂²⋊C₄	—	2	1	no	—
553	C₂²⋊C₄	—	4	1	no	—
554	C₂²⋊C₄	—	4	1	no	—
555	C₄²	—	2	2	no	—
556	C₄²	—	2	2	no	—
557	C₄²	—	2	1	no	—
558	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
559	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
560	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
561	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
562	C₂³	—	2	2	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	4	2	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	8	1	no	—
567	C₂³	—	8	1	no	—
568	C₂³	C₁₉×#120	1	1	yes	characteristic
569	Q₈	—	4	2	no	—
570	Q₈	—	4	1	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	2	no	—
574	Q₈	—	4	2	no	—
575	Q₈	—	8	1	no	—
576	Q₈	—	8	2	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	1	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	D₄	—	4	1	no	—
582	D₄	—	4	1	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	8	2	no	—
587	D₄	—	8	2	no	—
588	D₄	—	8	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	8	1	no	—
601	C₂×C₄	—	8	2	no	—
602	C₂×C₄	—	8	2	no	—
603	C₂×C₄	—	8	2	no	—
604	C₂×C₄	—	8	2	no	—
605	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
606	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
607	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
608	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
609	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
610	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
611	C₈	—	2	4	no	—
612	C₈	—	2	2	no	—
613	C₈	—	4	1	no	—
614	C₈	—	4	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	8	1	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	16	2	no	—
628	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	2	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	1	no	—
640	C₄	—	8	1	no	—
641	C₄	C₁₉×#453	1	2	yes	—
642	C₂	—	4	1	no	—
643	C₂	—	8	2	no	—
644	C₂	—	8	1	no	—
645	C₂	—	16	1	no	—
646	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
647	C₂	C₁₉×#3018	1	1	yes	characteristic
648	C₂	C₁₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
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
1. C₁₉×#3561	C₂	semidirect
2. C₁₉×#3235	C₂	semidirect
3. C₁₉×#3171	C₂	semidirect
4. C₁₉×#3153	C₂	semidirect
5. C₁₉×#1661	C₂	semidirect
6. C₁₉×#1660	C₂	semidirect
7. C₁₉×#1657	C₂	semidirect
8. C₁₉×#1656	C₂	semidirect
9. C₁₉×#1529	C₂	semidirect
10. C₁₉×#1527	C₂	semidirect
11. C₁₉×#1526	C₂	semidirect
30. C₁₉×#501	C₂²	semidirect
31. C₁₉×#501	C₂²	semidirect
34. C₁₉×#496	C₂²	semidirect
36. C₁₉×#490	C₂²	semidirect
37. C₁₉×#490	C₂²	semidirect
38. C₁₉×#489	C₂²	semidirect
49. C₁₉×#330	C₂²	semidirect
50. C₁₉×#330	C₂²	semidirect
51. C₁₉×#330	C₂²	semidirect
54. C₁₉×#329	C₂²	semidirect
237. #19019	C₁₉	direct (N × H)
291. #3561	C₂×C₁₉	semidirect
292. #3235	C₂×C₁₉	semidirect
293. #3171	C₂×C₁₉	semidirect
294. #3153	C₂×C₁₉	semidirect
295. #1661	C₂×C₁₉	semidirect
296. #1660	C₂×C₁₉	semidirect
297. #1657	C₂×C₁₉	semidirect
298. #1656	C₂×C₁₉	semidirect
299. #1529	C₂×C₁₉	semidirect
300. #1527	C₂×C₁₉	semidirect
301. #1526	C₂×C₁₉	semidirect
347. #501	C₂²×C₁₉	semidirect
348. #501	C₂²×C₁₉	semidirect
351. #496	C₂²×C₁₉	semidirect
353. #490	C₂²×C₁₉	semidirect
354. #490	C₂²×C₁₉	semidirect
355. #489	C₂²×C₁₉	semidirect
366. #330	C₂²×C₁₉	semidirect
367. #330	C₂²×C₁₉	semidirect
368. #330	C₂²×C₁₉	semidirect
371. #329	C₂²×C₁₉	semidirect
474. C₁₉	#19019	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×#3561	2
C₁₉×#3235	2
C₁₉×#3171	2
C₁₉×#3153	2
C₁₉×#1661	2
C₁₉×#1660	2
C₁₉×#1657	2
C₁₉×#1656	2
C₁₉×#1529	2
C₁₉×#1527	2
C₁₉×#1526	2
#19019	19

Subgroups — C19×#19019 #18024978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19019 #18024978