Subgroups — C₁₉×#18553 #18024512

Order 4864.

1008 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3483	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1646	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1645	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1642	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1641	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1560	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#137	—	2	1	no	—
13	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#555	—	2	2	no	—
15	C₁₉×#555	—	2	1	no	—
16	C₁₉×#555	—	2	1	no	—
17	C₁₉×#555	C₂²	1	1	yes	characteristic
18	C₁₉×#550	—	2	1	no	—
19	C₁₉×#550	—	2	1	no	—
20	C₁₉×#550	C₂²	1	1	yes	characteristic
21	C₁₉×#550	C₂²	1	1	yes	characteristic
22	C₁₉×#532	—	2	2	no	—
23	C₁₉×#532	—	2	1	no	—
24	C₁₉×#532	—	2	1	no	—
25	C₁₉×#532	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₄×#41×C₁₉	—	2	1	no	—
28	C₄×#41×C₁₉	—	2	1	no	—
29	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
30	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#489	—	2	2	no	—
32	C₁₉×#487	C₂²	1	2	yes	—
33	C₁₉×#486	C₂²	1	2	yes	—
34	C₁₉×#477	—	2	1	no	—
35	C₁₉×#476	—	2	1	no	—
36	C₁₉×#475	C₂²	1	2	yes	—
37	C₁₉×#474	C₂²	1	2	yes	—
38	C₁₉×#462	—	2	1	no	—
39	C₁₉×#462	C₂²	1	2	yes	—
40	C₁₉×#461	—	2	1	no	—
41	C₁₉×#461	C₂²	1	2	yes	—
42	C₁₉×#428	—	2	1	no	—
43	C₁₉×#423	C₂²	1	1	yes	characteristic
44	C₁₉×#423	C₂²	1	1	yes	characteristic
45	C₁₉×#419	—	2	1	no	—
46	C₁₉×#417	—	2	1	no	—
47	C₁₉×#417	—	2	2	no	—
48	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#333	C₂²	1	2	yes	—
50	C₁₉×#331	C₂²	1	2	yes	—
51	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
52	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
53	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
54	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
55	C₂×#41×C₁₉	—	2	2	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂×#41×C₁₉	—	2	1	no	—
58	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
59	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
60	C₂×#41×C₁₉	D₄	1	2	yes	—
61	C₂²×Q₈×C₁₉	—	2	1	no	—
62	C₁₉×#137	—	4	4	no	—
63	C₂×Q₁₆×C₁₉	—	2	2	no	—
64	C₂×SD₁₆×C₁₉	—	2	2	no	—
65	C₂×M₁₆×C₁₉	—	2	1	no	—
66	C₂×M₁₆×C₁₉	—	2	1	no	—
67	C₂×M₁₆×C₁₉	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	—	2	2	no	—
69	C₁₉×C₄⋊Q₈	—	2	1	no	—
70	C₁₉×C₄⋊Q₈	—	2	1	no	—
71	C₁₉×C₄⋊Q₈	—	2	1	no	—
72	C₁₉×C₄⋊Q₈	—	2	1	no	—
73	C₁₉×C₄⋊Q₈	—	2	1	no	—
74	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
75	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₁₉×#127	—	2	2	no	—
77	C₁₉×#127	—	2	1	no	—
78	C₁₉×#127	—	2	1	no	—
79	C₁₉×#127	C₂³	1	1	yes	characteristic
80	C₁₉×#124	—	2	2	no	—
81	C₁₉×#124	—	2	2	no	—
82	C₁₉×#124	—	2	2	no	—
83	C₁₉×#124	—	2	2	no	—
84	C₁₉×#124	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	1	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₄×Q₈×C₁₉	—	2	1	no	—
98	C₄×Q₈×C₁₉	—	2	1	no	—
99	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
100	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
101	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
102	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
103	C₄×D₄×C₁₉	—	2	2	no	—
104	C₄×D₄×C₁₉	—	2	2	no	—
105	C₄×D₄×C₁₉	—	2	2	no	—
106	C₄×D₄×C₁₉	—	2	2	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	—	2	1	no	—
111	C₄×D₄×C₁₉	—	2	1	no	—
112	C₄×D₄×C₁₉	—	2	1	no	—
113	C₄×D₄×C₁₉	—	2	1	no	—
114	C₄×D₄×C₁₉	—	2	1	no	—
115	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
116	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
117	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
118	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
119	C₁₉×#117	—	2	2	no	—
120	C₁₉×#117	—	2	2	no	—
121	C₁₉×#117	—	2	1	no	—
122	C₁₉×#117	—	2	1	no	—
123	C₁₉×#117	—	2	1	no	—
124	C₁₉×#117	—	2	1	no	—
125	C₁₉×#117	D₄	1	1	yes	characteristic
126	C₁₉×#117	D₄	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₂×C₄²×C₁₉	—	2	2	no	—
130	C₂×C₄²×C₁₉	—	2	1	no	—
131	C₂×C₄²×C₁₉	—	2	1	no	—
132	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
133	C₁₉×#107	—	2	2	no	—
134	C₁₉×#106	—	2	2	no	—
135	C₁₉×C₄⋊C₈	—	2	1	no	—
136	C₁₉×C₄⋊C₈	—	2	1	no	—
137	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
138	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
139	C₁₉×#103	—	2	2	no	—
140	C₁₉×#103	—	2	4	no	—
141	C₁₉×#103	—	2	2	no	—
142	C₁₉×#103	—	2	2	no	—
143	C₁₉×#102	—	2	2	no	—
144	C₁₉×#102	—	2	4	no	—
145	C₁₉×#97	—	2	1	no	—
146	C₄×C₈×C₁₉	C₂³	1	2	yes	—
147	#41×C₁₉	—	2	2	no	—
148	#41×C₁₉	—	2	2	no	—
149	#41×C₁₉	—	4	1	no	—
150	#41×C₁₉	—	4	1	no	—
151	#41×C₁₉	—	4	4	no	—
152	#41×C₁₉	—	4	2	no	—
153	#41×C₁₉	—	4	2	no	—
154	#41×C₁₉	—	4	2	no	—
155	#41×C₁₉	—	4	2	no	—
156	#41×C₁₉	—	8	4	no	—
157	C₂×Q₈×C₁₉	—	2	2	no	—
158	C₂×Q₈×C₁₉	—	2	2	no	—
159	C₂×Q₈×C₁₉	—	4	2	no	—
160	C₂×Q₈×C₁₉	—	4	2	no	—
161	C₂×Q₈×C₁₉	—	4	1	no	—
162	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
165	C₂×D₄×C₁₉	—	2	2	no	—
166	C₂×D₄×C₁₉	—	2	2	no	—
167	C₂×D₄×C₁₉	—	2	1	no	—
168	C₂×D₄×C₁₉	—	2	1	no	—
169	C₂×D₄×C₁₉	—	2	2	no	—
170	C₂×D₄×C₁₉	—	2	2	no	—
171	C₂×D₄×C₁₉	—	2	2	no	—
172	C₂×D₄×C₁₉	—	2	2	no	—
173	C₂×D₄×C₁₉	—	2	1	no	—
174	C₂×D₄×C₁₉	—	2	1	no	—
175	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₁₉	—	2	2	no	—
179	C₂²×C₄×C₁₉	—	2	2	no	—
180	C₂²×C₄×C₁₉	—	2	1	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	1	no	—
185	C₂²×C₄×C₁₉	—	2	1	no	—
186	C₂²×C₄×C₁₉	—	2	1	no	—
187	C₂²×C₄×C₁₉	—	4	1	no	—
188	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
191	Q₁₆×C₁₉	—	4	4	no	—
192	SD₁₆×C₁₉	—	4	4	no	—
193	M₁₆×C₁₉	—	4	2	no	—
194	M₁₆×C₁₉	—	4	2	no	—
195	M₁₆×C₁₉	—	4	2	no	—
196	C₂×C₈×C₁₉	—	2	2	no	—
197	C₂×C₈×C₁₉	—	2	2	no	—
198	C₂×C₈×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	—	2	2	no	—
200	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	2	no	—
208	C₄⋊C₄×C₁₉	—	2	2	no	—
209	C₄⋊C₄×C₁₉	—	4	1	no	—
210	C₄⋊C₄×C₁₉	—	4	1	no	—
211	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	2	no	—
219	C₂²⋊C₄×C₁₉	—	2	1	no	—
220	C₂²⋊C₄×C₁₉	—	2	1	no	—
221	C₂²⋊C₄×C₁₉	—	2	2	no	—
222	C₂²⋊C₄×C₁₉	—	2	2	no	—
223	C₂²⋊C₄×C₁₉	—	2	1	no	—
224	C₂²⋊C₄×C₁₉	—	2	1	no	—
225	C₂²⋊C₄×C₁₉	—	2	1	no	—
226	C₂²⋊C₄×C₁₉	—	2	1	no	—
227	C₄²×C₁₉	—	2	2	no	—
228	C₄²×C₁₉	—	2	2	no	—
229	C₄²×C₁₉	—	2	1	no	—
230	C₄²×C₁₉	—	2	1	no	—
231	C₄²×C₁₉	—	2	1	no	—
232	C₄²×C₁₉	—	2	1	no	—
233	C₄²×C₁₉	—	2	1	no	—
234	C₄²×C₁₉	—	2	1	no	—
235	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
237	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
238	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
239	#18553	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂³×C₁₉	—	2	1	no	—
241	C₂³×C₁₉	—	2	1	no	—
242	C₂³×C₁₉	—	2	2	no	—
243	C₂³×C₁₉	#120	1	1	yes	characteristic
244	Q₈×C₁₉	—	2	1	no	—
245	Q₈×C₁₉	—	2	1	no	—
246	Q₈×C₁₉	—	4	2	no	—
247	Q₈×C₁₉	—	4	2	no	—
248	Q₈×C₁₉	—	4	2	no	—
249	Q₈×C₁₉	—	8	2	no	—
250	Q₈×C₁₉	—	8	2	no	—
251	Q₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
252	Q₈×C₁₉	#137	1	2	yes	complemented
253	D₄×C₁₉	—	2	1	no	—
254	D₄×C₁₉	—	2	1	no	—
255	D₄×C₁₉	—	2	1	no	—
256	D₄×C₁₉	—	2	1	no	—
257	D₄×C₁₉	—	4	2	no	—
258	D₄×C₁₉	—	4	2	no	—
259	D₄×C₁₉	—	4	2	no	—
260	D₄×C₁₉	—	4	4	no	—
261	D₄×C₁₉	—	4	4	no	—
262	D₄×C₁₉	—	4	1	no	—
263	D₄×C₁₉	—	4	1	no	—
264	D₄×C₁₉	—	4	1	no	—
265	D₄×C₁₉	—	4	1	no	—
266	D₄×C₁₉	—	8	2	no	—
267	D₄×C₁₉	—	8	2	no	—
268	D₄×C₁₉	—	8	2	no	—
269	D₄×C₁₉	—	8	2	no	—
270	C₂×C₄×C₁₉	—	2	1	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	1	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	2	2	no	—
280	C₂×C₄×C₁₉	—	2	1	no	—
281	C₂×C₄×C₁₉	—	2	1	no	—
282	C₂×C₄×C₁₉	—	4	2	no	—
283	C₂×C₄×C₁₉	—	4	2	no	—
284	C₂×C₄×C₁₉	—	4	4	no	—
285	C₂×C₄×C₁₉	—	4	4	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	4	no	—
291	C₂×C₄×C₁₉	—	4	2	no	—
292	C₂×C₄×C₁₉	—	4	2	no	—
293	C₂×C₄×C₁₉	—	4	2	no	—
294	C₂×C₄×C₁₉	—	8	2	no	—
295	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
296	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
297	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
298	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
301	C₈×C₁₉	—	4	2	no	—
302	C₈×C₁₉	—	4	2	no	—
303	C₈×C₁₉	—	4	2	no	—
304	#3483	C₂×C₁₉	1	1	yes	characteristic
305	#3141	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#3079	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#3039	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#1646	C₂×C₁₉	1	2	yes	complemented
309	#1645	C₂×C₁₉	1	2	yes	complemented
310	#1642	C₂×C₁₉	1	2	yes	complemented
311	#1641	C₂×C₁₉	1	2	yes	complemented
312	#1560	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1489	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#1489	C₂×C₁₉	1	1	yes	characteristic, complemented
315	C₂²×C₁₉	—	2	1	no	—
316	C₂²×C₁₉	—	2	1	no	—
317	C₂²×C₁₉	—	2	1	no	—
318	C₂²×C₁₉	—	4	1	no	—
319	C₂²×C₁₉	—	4	2	no	—
320	C₂²×C₁₉	—	4	1	no	—
321	C₂²×C₁₉	—	4	1	no	—
322	C₂²×C₁₉	—	4	2	no	—
323	C₂²×C₁₉	—	4	1	no	—
324	C₂²×C₁₉	—	4	2	no	—
325	C₂²×C₁₉	—	4	1	no	—
326	C₂²×C₁₉	—	4	1	no	—
327	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
328	C₄×C₁₉	—	2	1	no	—
329	C₄×C₁₉	—	2	2	no	—
330	C₄×C₁₉	—	2	1	no	—
331	C₄×C₁₉	—	2	2	no	—
332	C₄×C₁₉	—	2	1	no	—
333	C₄×C₁₉	—	4	1	no	—
334	C₄×C₁₉	—	4	1	no	—
335	C₄×C₁₉	—	4	2	no	—
336	C₄×C₁₉	—	4	1	no	—
337	C₄×C₁₉	—	4	1	no	—
338	C₄×C₁₉	—	8	2	no	—
339	C₄×C₁₉	#455	1	2	yes	—
340	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
341	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
342	C₄×C₁₉	#575	1	1	yes	characteristic
343	C₄×C₁₉	#575	1	1	yes	characteristic
344	C₂×#137	—	2	1	no	—
345	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
346	#555	—	2	2	no	—
347	#555	—	2	1	no	—
348	#555	—	2	1	no	—
349	#555	C₂²×C₁₉	1	1	yes	characteristic
350	#550	—	2	1	no	—
351	#550	—	2	1	no	—
352	#550	C₂²×C₁₉	1	1	yes	characteristic
353	#550	C₂²×C₁₉	1	1	yes	characteristic
354	#532	—	2	2	no	—
355	#532	—	2	1	no	—
356	#532	—	2	1	no	—
357	#532	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
359	C₄×#41	—	2	1	no	—
360	C₄×#41	—	2	1	no	—
361	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
362	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
363	#489	—	2	2	no	—
364	#487	C₂²×C₁₉	1	2	yes	—
365	#486	C₂²×C₁₉	1	2	yes	—
366	#477	—	2	1	no	—
367	#476	—	2	1	no	—
368	#475	C₂²×C₁₉	1	2	yes	—
369	#474	C₂²×C₁₉	1	2	yes	—
370	#462	—	2	1	no	—
371	#462	C₂²×C₁₉	1	2	yes	—
372	#461	—	2	1	no	—
373	#461	C₂²×C₁₉	1	2	yes	—
374	#428	—	2	1	no	—
375	#423	C₂²×C₁₉	1	1	yes	characteristic
376	#423	C₂²×C₁₉	1	1	yes	characteristic
377	#419	—	2	1	no	—
378	#417	—	2	1	no	—
379	#417	—	2	2	no	—
380	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
381	#333	C₂²×C₁₉	1	2	yes	—
382	#331	C₂²×C₁₉	1	2	yes	—
383	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
384	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
385	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
386	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
387	C₂×C₁₉	—	4	1	no	—
388	C₂×C₁₉	—	8	1	no	—
389	C₂×C₁₉	—	8	1	no	—
390	C₂×C₁₉	—	8	2	no	—
391	C₂×C₁₉	#3006	1	1	yes	characteristic
392	C₂×C₁₉	#3007	1	1	yes	characteristic
393	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
394	C₂×#41	—	2	2	no	—
395	C₂×#41	—	2	1	no	—
396	C₂×#41	—	2	1	no	—
397	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
398	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
399	C₂×#41	D₄×C₁₉	1	2	yes	—
400	C₂²×Q₈	—	2	1	no	—
401	#137	—	4	4	no	—
402	C₂×Q₁₆	—	2	2	no	—
403	C₂×SD₁₆	—	2	2	no	—
404	C₂×M₁₆	—	2	1	no	—
405	C₂×M₁₆	—	2	1	no	—
406	C₂×M₁₆	—	2	1	no	—
407	C₄⋊Q₈	—	2	2	no	—
408	C₄⋊Q₈	—	2	1	no	—
409	C₄⋊Q₈	—	2	1	no	—
410	C₄⋊Q₈	—	2	1	no	—
411	C₄⋊Q₈	—	2	1	no	—
412	C₄⋊Q₈	—	2	1	no	—
413	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
414	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
415	#127	—	2	2	no	—
416	#127	—	2	1	no	—
417	#127	—	2	1	no	—
418	#127	C₂³×C₁₉	1	1	yes	characteristic
419	#124	—	2	2	no	—
420	#124	—	2	2	no	—
421	#124	—	2	2	no	—
422	#124	—	2	2	no	—
423	#124	D₄×C₁₉	1	2	yes	—
424	#121	—	2	2	no	—
425	#121	—	2	2	no	—
426	#121	—	2	2	no	—
427	#121	—	2	2	no	—
428	#121	—	2	1	no	—
429	#121	—	2	1	no	—
430	#121	—	2	2	no	—
431	#121	—	2	2	no	—
432	#121	—	2	1	no	—
433	#121	—	2	1	no	—
434	#121	—	2	1	no	—
435	#121	—	2	1	no	—
436	C₄×Q₈	—	2	1	no	—
437	C₄×Q₈	—	2	1	no	—
438	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
439	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
440	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
441	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	2	2	no	—
444	C₄×D₄	—	2	2	no	—
445	C₄×D₄	—	2	2	no	—
446	C₄×D₄	—	2	1	no	—
447	C₄×D₄	—	2	1	no	—
448	C₄×D₄	—	2	1	no	—
449	C₄×D₄	—	2	1	no	—
450	C₄×D₄	—	2	1	no	—
451	C₄×D₄	—	2	1	no	—
452	C₄×D₄	—	2	1	no	—
453	C₄×D₄	—	2	1	no	—
454	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
455	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
456	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
457	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
458	#117	—	2	2	no	—
459	#117	—	2	2	no	—
460	#117	—	2	1	no	—
461	#117	—	2	1	no	—
462	#117	—	2	1	no	—
463	#117	—	2	1	no	—
464	#117	D₄×C₁₉	1	1	yes	characteristic
465	#117	D₄×C₁₉	1	1	yes	characteristic
466	C₂×C₄⋊C₄	—	2	1	no	—
467	C₂×C₄⋊C₄	—	2	1	no	—
468	C₂×C₄²	—	2	2	no	—
469	C₂×C₄²	—	2	1	no	—
470	C₂×C₄²	—	2	1	no	—
471	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
472	#107	—	2	2	no	—
473	#106	—	2	2	no	—
474	C₄⋊C₈	—	2	1	no	—
475	C₄⋊C₈	—	2	1	no	—
476	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
477	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
478	#103	—	2	2	no	—
479	#103	—	2	4	no	—
480	#103	—	2	2	no	—
481	#103	—	2	2	no	—
482	#102	—	2	2	no	—
483	#102	—	2	4	no	—
484	#97	—	2	1	no	—
485	C₄×C₈	C₂³×C₁₉	1	2	yes	—
486	C₁₉	#18553	1	1	yes	characteristic, direct product factor, Sylow
487	#41	—	2	2	no	—
488	#41	—	2	2	no	—
489	#41	—	4	1	no	—
490	#41	—	4	1	no	—
491	#41	—	4	4	no	—
492	#41	—	4	2	no	—
493	#41	—	4	2	no	—
494	#41	—	4	2	no	—
495	#41	—	4	2	no	—
496	#41	—	8	4	no	—
497	C₂×Q₈	—	2	2	no	—
498	C₂×Q₈	—	2	2	no	—
499	C₂×Q₈	—	4	2	no	—
500	C₂×Q₈	—	4	2	no	—
501	C₂×Q₈	—	4	1	no	—
502	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
505	C₂×D₄	—	2	2	no	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	4	1	no	—
528	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
531	Q₁₆	—	4	4	no	—
532	SD₁₆	—	4	4	no	—
533	M₁₆	—	4	2	no	—
534	M₁₆	—	4	2	no	—
535	M₁₆	—	4	2	no	—
536	C₂×C₈	—	2	2	no	—
537	C₂×C₈	—	2	2	no	—
538	C₂×C₈	—	2	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	4	1	no	—
550	C₄⋊C₄	—	4	1	no	—
551	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
552	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
553	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
554	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
555	C₂²⋊C₄	—	2	2	no	—
556	C₂²⋊C₄	—	2	2	no	—
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	1	no	—
560	C₂²⋊C₄	—	2	1	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	1	no	—
564	C₂²⋊C₄	—	2	1	no	—
565	C₂²⋊C₄	—	2	1	no	—
566	C₂²⋊C₄	—	2	1	no	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	2	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	2	1	no	—
571	C₄²	—	2	1	no	—
572	C₄²	—	2	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	—	2	1	no	—
575	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
576	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
577	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
578	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	2	no	—
582	C₂³	C₁₉×#120	1	1	yes	characteristic
583	Q₈	—	2	1	no	—
584	Q₈	—	2	1	no	—
585	Q₈	—	4	2	no	—
586	Q₈	—	4	2	no	—
587	Q₈	—	4	2	no	—
588	Q₈	—	8	2	no	—
589	Q₈	—	8	2	no	—
590	Q₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
591	Q₈	C₁₉×#137	1	2	yes	complemented
592	D₄	—	2	1	no	—
593	D₄	—	2	1	no	—
594	D₄	—	2	1	no	—
595	D₄	—	2	1	no	—
596	D₄	—	4	2	no	—
597	D₄	—	4	2	no	—
598	D₄	—	4	2	no	—
599	D₄	—	4	4	no	—
600	D₄	—	4	4	no	—
601	D₄	—	4	1	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	1	no	—
604	D₄	—	4	1	no	—
605	D₄	—	8	2	no	—
606	D₄	—	8	2	no	—
607	D₄	—	8	2	no	—
608	D₄	—	8	2	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	4	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	4	4	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	2	no	—
633	C₂×C₄	—	8	2	no	—
634	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
635	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
636	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
637	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
638	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
639	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
640	C₈	—	4	2	no	—
641	C₈	—	4	2	no	—
642	C₈	—	4	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	2	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	1	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	8	2	no	—
667	C₄	C₁₉×#455	1	2	yes	—
668	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
669	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
670	C₄	C₁₉×#575	1	1	yes	characteristic
671	C₄	C₁₉×#575	1	1	yes	characteristic
672	C₂	—	4	1	no	—
673	C₂	—	8	1	no	—
674	C₂	—	8	1	no	—
675	C₂	—	8	2	no	—
676	C₂	C₁₉×#3006	1	1	yes	characteristic
677	C₂	C₁₉×#3007	1	1	yes	characteristic
678	C₂	C₂×C₁₉×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3483	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×#3141	C₂	semidirect
3. C₁₉×#3079	C₂	semidirect
4. C₁₉×#3039	C₂	semidirect
5. C₁₉×#1646	C₂	semidirect
6. C₁₉×#1645	C₂	semidirect
7. C₁₉×#1642	C₂	semidirect
8. C₁₉×#1641	C₂	semidirect
9. C₁₉×#1560	C₂	semidirect
10. C₁₉×#1489	C₂	semidirect
11. C₁₉×#1489	C₂	semidirect
239. #18553	C₁₉	direct (N × H)
252. Q₈×C₁₉	#137	semidirect
305. #3141	C₂×C₁₉	semidirect
306. #3079	C₂×C₁₉	semidirect
307. #3039	C₂×C₁₉	semidirect
308. #1646	C₂×C₁₉	semidirect
309. #1645	C₂×C₁₉	semidirect
310. #1642	C₂×C₁₉	semidirect
311. #1641	C₂×C₁₉	semidirect
312. #1560	C₂×C₁₉	semidirect
313. #1489	C₂×C₁₉	semidirect
314. #1489	C₂×C₁₉	semidirect
486. C₁₉	#18553	direct (N × H)
591. Q₈	C₁₉×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3483	2
C₁₉×#3141	2
C₁₉×#3079	2
C₁₉×#3039	2
C₁₉×#1646	2
C₁₉×#1645	2
C₁₉×#1642	2
C₁₉×#1641	2
C₁₉×#1560	2
C₁₉×#1489	2
#18553	19

Subgroups — C19×#18553 #18024512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18553 #18024512