Subgroups — C₁₉×#18576 #18024535

Order 4864.

980 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×#3508	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3255	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3138	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1642	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1641	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1640	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1640	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1485	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#559	—	2	1	no	—
13	C₁₉×#559	C₂²	1	2	yes	—
14	C₁₉×#550	—	2	1	no	—
15	C₁₉×#550	C₂²	1	2	yes	—
16	C₁₉×#546	—	2	2	no	—
17	C₁₉×#546	—	2	2	no	—
18	C₁₉×#540	—	2	2	no	—
19	C₁₉×#535	—	2	1	no	—
20	C₁₉×#533	C₂²	1	1	yes	characteristic
21	C₁₉×#533	C₂²	1	1	yes	characteristic
22	C₁₉×#532	—	2	1	no	—
23	C₁₉×#532	—	2	1	no	—
24	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
25	C₁₉×#518	—	2	1	no	—
26	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#490	—	2	2	no	—
28	C₁₉×#486	C₂²	1	2	yes	—
29	C₁₉×#486	C₂²	1	2	yes	—
30	C₁₉×#485	—	2	1	no	—
31	C₁₉×#475	—	2	1	no	—
32	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#475	C₂²	1	2	yes	complemented
34	C₁₉×#474	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#470	—	2	2	no	—
36	C₁₉×#462	—	2	1	no	—
37	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#462	C₂²	1	2	yes	complemented
39	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#452	—	2	1	no	—
41	C₄×Q₁₆×C₁₉	—	2	1	no	—
42	C₄×SD₁₆×C₁₉	—	2	1	no	—
43	C₁₉×#431	C₂²	1	1	yes	characteristic
44	C₁₉×#423	C₂²	1	1	yes	characteristic
45	C₁₉×#418	—	2	2	no	—
46	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
47	C₁₉×#331	C₂²	1	2	yes	—
48	C₁₉×#331	C₂²	1	2	yes	—
49	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
50	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
51	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
52	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
53	C₂×#41×C₁₉	—	2	2	no	—
54	C₂×#41×C₁₉	—	2	2	no	—
55	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
56	C₂²×D₄×C₁₉	—	2	1	no	—
57	C₂²×D₄×C₁₉	—	2	1	no	—
58	C₂²×D₄×C₁₉	D₄	1	2	yes	—
59	C₂×Q₁₆×C₁₉	—	2	1	no	—
60	C₂×Q₁₆×C₁₉	—	2	2	no	—
61	C₂×SD₁₆×C₁₉	—	2	1	no	—
62	C₂×M₁₆×C₁₉	—	2	1	no	—
63	C₂×M₁₆×C₁₉	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₁₉×#127	—	2	2	no	—
69	C₁₉×#127	—	2	1	no	—
70	C₁₉×#127	—	2	1	no	—
71	C₁₉×#127	D₄	1	2	yes	—
72	C₁₉×#127	C₂³	1	2	yes	—
73	C₁₉×#125	—	2	1	no	—
74	C₁₉×#125	—	2	1	no	—
75	C₁₉×#124	—	2	2	no	—
76	C₁₉×#124	—	2	2	no	—
77	C₁₉×#124	—	2	2	no	—
78	C₁₉×#123	—	2	4	no	—
79	C₁₉×#123	—	2	4	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	—	2	1	no	—
82	C₁₉×C₂²⋊Q₈	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
84	C₁₉×#121	—	2	2	no	—
85	C₁₉×#121	—	2	2	no	—
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#121	—	2	4	no	—
88	C₁₉×#121	—	2	4	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#120	—	2	4	no	—
91	C₄×Q₈×C₁₉	—	2	1	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	—	2	2	no	—
99	C₄×D₄×C₁₉	—	2	2	no	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	2	no	—
103	C₄×D₄×C₁₉	—	2	2	no	—
104	C₄×D₄×C₁₉	—	2	2	no	—
105	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
106	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₁₉×#117	—	2	1	no	—
108	C₁₉×#117	—	2	1	no	—
109	C₁₉×#117	—	2	1	no	—
110	C₁₉×#117	D₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
112	C₂×C₄²×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₁₉×#107	—	2	1	no	—
115	C₁₉×#106	—	2	1	no	—
116	C₁₉×#106	—	2	2	no	—
117	C₁₉×C₄⋊C₈	—	2	1	no	—
118	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
119	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×#103	—	2	1	no	—
122	C₁₉×#103	—	2	2	no	—
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	—	2	2	no	—
126	C₁₉×#102	—	2	4	no	—
127	C₁₉×#102	—	2	4	no	—
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×C₂²⋊C₈	—	2	1	no	—
130	C₁₉×#97	—	2	1	no	—
131	C₄×C₈×C₁₉	—	2	1	no	—
132	C₄×C₈×C₁₉	C₂³	1	2	yes	—
133	C₂⁴×C₁₉	—	2	2	no	—
134	#41×C₁₉	—	4	1	no	—
135	#41×C₁₉	—	4	1	no	—
136	#41×C₁₉	—	8	2	no	—
137	#41×C₁₉	—	8	2	no	—
138	#41×C₁₉	—	8	4	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	2	4	no	—
146	C₂×D₄×C₁₉	—	2	4	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	2	no	—
151	C₂×D₄×C₁₉	—	2	2	no	—
152	C₂×D₄×C₁₉	—	4	2	no	—
153	C₂×D₄×C₁₉	—	4	2	no	—
154	C₂×D₄×C₁₉	—	4	4	no	—
155	C₂×D₄×C₁₉	—	8	1	no	—
156	C₂×D₄×C₁₉	—	8	1	no	—
157	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₁₉	—	2	4	no	—
160	C₂²×C₄×C₁₉	—	2	4	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	Q₁₆×C₁₉	—	4	2	no	—
168	Q₁₆×C₁₉	—	8	2	no	—
169	SD₁₆×C₁₉	—	4	2	no	—
170	M₁₆×C₁₉	—	4	2	no	—
171	M₁₆×C₁₉	—	8	1	no	—
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	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	2	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	4	1	no	—
188	C₄⋊C₄×C₁₉	—	4	1	no	—
189	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
192	C₂²⋊C₄×C₁₉	—	2	4	no	—
193	C₂²⋊C₄×C₁₉	—	2	4	no	—
194	C₂²⋊C₄×C₁₉	—	2	4	no	—
195	C₂²⋊C₄×C₁₉	—	2	4	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	1	no	—
200	C₂²⋊C₄×C₁₉	—	4	1	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	C₄²×C₁₉	—	2	1	no	—
204	C₄²×C₁₉	—	2	2	no	—
205	C₄²×C₁₉	—	4	1	no	—
206	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
210	#18576	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂³×C₁₉	—	2	4	no	—
212	C₂³×C₁₉	—	2	1	no	—
213	C₂³×C₁₉	—	4	4	no	—
214	C₂³×C₁₉	—	8	2	no	—
215	C₂³×C₁₉	—	8	2	no	—
216	C₂³×C₁₉	#120	1	1	yes	characteristic
217	Q₈×C₁₉	—	2	1	no	—
218	Q₈×C₁₉	—	2	1	no	—
219	Q₈×C₁₉	—	2	2	no	—
220	Q₈×C₁₉	—	2	2	no	—
221	Q₈×C₁₉	—	4	2	no	—
222	Q₈×C₁₉	—	4	1	no	—
223	Q₈×C₁₉	—	4	1	no	—
224	Q₈×C₁₉	—	4	1	no	—
225	Q₈×C₁₉	—	4	1	no	—
226	D₄×C₁₉	—	2	1	no	—
227	D₄×C₁₉	—	2	1	no	—
228	D₄×C₁₉	—	4	4	no	—
229	D₄×C₁₉	—	4	4	no	—
230	D₄×C₁₉	—	4	2	no	—
231	D₄×C₁₉	—	4	2	no	—
232	D₄×C₁₉	—	4	2	no	—
233	D₄×C₁₉	—	4	2	no	—
234	D₄×C₁₉	—	4	2	no	—
235	D₄×C₁₉	—	4	4	no	—
236	D₄×C₁₉	—	8	2	no	—
237	D₄×C₁₉	—	8	4	no	—
238	D₄×C₁₉	—	8	4	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	4	2	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	8	4	no	—
256	C₂×C₄×C₁₉	—	8	4	no	—
257	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
258	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
259	C₂×C₄×C₁₉	#120	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	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
263	C₈×C₁₉	—	4	2	no	—
264	C₈×C₁₉	—	4	1	no	—
265	C₈×C₁₉	—	4	1	no	—
266	C₈×C₁₉	—	4	2	no	—
267	#3508	C₂×C₁₉	1	1	yes	characteristic
268	#3255	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#3138	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#3107	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#1642	C₂×C₁₉	1	2	yes	complemented
272	#1641	C₂×C₁₉	1	2	yes	complemented
273	#1640	C₂×C₁₉	1	2	yes	complemented
274	#1640	C₂×C₁₉	1	2	yes	complemented
275	#1545	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1489	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1485	C₂×C₁₉	1	1	yes	characteristic, complemented
278	C₂²×C₁₉	—	2	1	no	—
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	4	1	no	—
282	C₂²×C₁₉	—	4	4	no	—
283	C₂²×C₁₉	—	4	1	no	—
284	C₂²×C₁₉	—	4	4	no	—
285	C₂²×C₁₉	—	4	1	no	—
286	C₂²×C₁₉	—	4	4	no	—
287	C₂²×C₁₉	—	16	4	no	—
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	—	4	1	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	4	2	no	—
295	C₄×C₁₉	—	4	1	no	—
296	C₄×C₁₉	—	4	2	no	—
297	C₄×C₁₉	—	8	1	no	—
298	C₄×C₁₉	—	8	1	no	—
299	C₄×C₁₉	#455	1	2	yes	—
300	C₄×C₁₉	#575	1	1	yes	characteristic
301	C₄×C₁₉	#575	1	1	yes	characteristic
302	C₄×C₁₉	#576	1	1	yes	characteristic
303	C₄×C₁₉	#577	1	1	yes	characteristic
304	#559	—	2	1	no	—
305	#559	C₂²×C₁₉	1	2	yes	—
306	#550	—	2	1	no	—
307	#550	C₂²×C₁₉	1	2	yes	—
308	#546	—	2	2	no	—
309	#546	—	2	2	no	—
310	#540	—	2	2	no	—
311	#535	—	2	1	no	—
312	#533	C₂²×C₁₉	1	1	yes	characteristic
313	#533	C₂²×C₁₉	1	1	yes	characteristic
314	#532	—	2	1	no	—
315	#532	—	2	1	no	—
316	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
317	#518	—	2	1	no	—
318	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
319	#490	—	2	2	no	—
320	#486	C₂²×C₁₉	1	2	yes	—
321	#486	C₂²×C₁₉	1	2	yes	—
322	#485	—	2	1	no	—
323	#475	—	2	1	no	—
324	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
325	#475	C₂²×C₁₉	1	2	yes	complemented
326	#474	C₂²×C₁₉	1	1	yes	characteristic, complemented
327	#470	—	2	2	no	—
328	#462	—	2	1	no	—
329	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
330	#462	C₂²×C₁₉	1	2	yes	complemented
331	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
332	#452	—	2	1	no	—
333	C₄×Q₁₆	—	2	1	no	—
334	C₄×SD₁₆	—	2	1	no	—
335	#431	C₂²×C₁₉	1	1	yes	characteristic
336	#423	C₂²×C₁₉	1	1	yes	characteristic
337	#418	—	2	2	no	—
338	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
339	#331	C₂²×C₁₉	1	2	yes	—
340	#331	C₂²×C₁₉	1	2	yes	—
341	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	complemented
342	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	complemented
343	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	complemented
344	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
345	C₂×C₁₉	—	4	1	no	—
346	C₂×C₁₉	—	8	1	no	—
347	C₂×C₁₉	—	8	4	no	—
348	C₂×C₁₉	#3005	1	1	yes	characteristic
349	C₂×C₁₉	#3012	1	1	yes	characteristic
350	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
351	C₂×#41	—	2	2	no	—
352	C₂×#41	—	2	2	no	—
353	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
354	C₂²×D₄	—	2	1	no	—
355	C₂²×D₄	—	2	1	no	—
356	C₂²×D₄	D₄×C₁₉	1	2	yes	—
357	C₂×Q₁₆	—	2	1	no	—
358	C₂×Q₁₆	—	2	2	no	—
359	C₂×SD₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
363	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
364	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
365	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
366	#127	—	2	2	no	—
367	#127	—	2	1	no	—
368	#127	—	2	1	no	—
369	#127	D₄×C₁₉	1	2	yes	—
370	#127	C₂³×C₁₉	1	2	yes	—
371	#125	—	2	1	no	—
372	#125	—	2	1	no	—
373	#124	—	2	2	no	—
374	#124	—	2	2	no	—
375	#124	—	2	2	no	—
376	#123	—	2	4	no	—
377	#123	—	2	4	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	C₂²⋊Q₈	—	2	1	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
382	#121	—	2	2	no	—
383	#121	—	2	2	no	—
384	#121	—	2	2	no	—
385	#121	—	2	4	no	—
386	#121	—	2	4	no	—
387	#121	—	2	2	no	—
388	#120	—	2	4	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
393	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
394	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
404	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
405	#117	—	2	1	no	—
406	#117	—	2	1	no	—
407	#117	—	2	1	no	—
408	#117	D₄×C₁₉	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	—	2	4	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
412	#107	—	2	1	no	—
413	#106	—	2	1	no	—
414	#106	—	2	2	no	—
415	C₄⋊C₈	—	2	1	no	—
416	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
417	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
419	#103	—	2	1	no	—
420	#103	—	2	2	no	—
421	#103	—	2	1	no	—
422	#103	—	2	1	no	—
423	#103	—	2	2	no	—
424	#102	—	2	4	no	—
425	#102	—	2	4	no	—
426	#102	—	2	1	no	—
427	C₂²⋊C₈	—	2	1	no	—
428	#97	—	2	1	no	—
429	C₄×C₈	—	2	1	no	—
430	C₄×C₈	C₂³×C₁₉	1	2	yes	—
431	C₁₉	#18576	1	1	yes	characteristic, direct product factor, Sylow
432	C₂⁴	—	2	2	no	—
433	#41	—	4	1	no	—
434	#41	—	4	1	no	—
435	#41	—	8	2	no	—
436	#41	—	8	2	no	—
437	#41	—	8	4	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	4	2	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	—	4	4	no	—
454	C₂×D₄	—	8	1	no	—
455	C₂×D₄	—	8	1	no	—
456	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
466	Q₁₆	—	4	2	no	—
467	Q₁₆	—	8	2	no	—
468	SD₁₆	—	4	2	no	—
469	M₁₆	—	4	2	no	—
470	M₁₆	—	8	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
490	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	2	no	—
504	C₄²	—	4	1	no	—
505	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
506	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
507	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
509	C₂³	—	2	4	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	4	4	no	—
512	C₂³	—	8	2	no	—
513	C₂³	—	8	2	no	—
514	C₂³	C₁₉×#120	1	1	yes	characteristic
515	Q₈	—	2	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	2	2	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	4	2	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	4	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	4	4	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	4	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	8	2	no	—
535	D₄	—	8	4	no	—
536	D₄	—	8	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	8	4	no	—
554	C₂×C₄	—	8	4	no	—
555	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
556	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
557	C₂×C₄	C₁₉×#120	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	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
561	C₈	—	4	2	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	2	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	16	4	no	—
575	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	2	no	—
584	C₄	—	8	1	no	—
585	C₄	—	8	1	no	—
586	C₄	C₁₉×#455	1	2	yes	—
587	C₄	C₁₉×#575	1	1	yes	characteristic
588	C₄	C₁₉×#575	1	1	yes	characteristic
589	C₄	C₁₉×#576	1	1	yes	characteristic
590	C₄	C₁₉×#577	1	1	yes	characteristic
591	C₂	—	4	1	no	—
592	C₂	—	8	4	no	—
593	C₂	—	8	1	no	—
594	C₂	C₁₉×#3005	1	1	yes	characteristic
595	C₂	C₁₉×#3012	1	1	yes	characteristic
596	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×#3508	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×#3255	C₂	semidirect
3. C₁₉×#3138	C₂	semidirect
4. C₁₉×#3107	C₂	semidirect
5. C₁₉×#1642	C₂	semidirect
6. C₁₉×#1641	C₂	semidirect
7. C₁₉×#1640	C₂	semidirect
8. C₁₉×#1640	C₂	semidirect
9. C₁₉×#1545	C₂	semidirect
10. C₁₉×#1489	C₂	semidirect
11. C₁₉×#1485	C₂	semidirect
32. C₁₉×#475	C₂²	semidirect
33. C₁₉×#475	C₂²	semidirect
34. C₁₉×#474	C₂²	semidirect
37. C₁₉×#462	C₂²	semidirect
38. C₁₉×#462	C₂²	semidirect
39. C₁₉×#461	C₂²	semidirect
49. C₁₉×Q₈⋊C₈	C₂²	semidirect
50. C₁₉×Q₈⋊C₈	C₂²	semidirect
51. C₁₉×Q₈⋊C₈	C₂²	semidirect
52. C₁₉×D₄⋊C₈	C₂²	semidirect
210. #18576	C₁₉	direct (N × H)
268. #3255	C₂×C₁₉	semidirect
269. #3138	C₂×C₁₉	semidirect
270. #3107	C₂×C₁₉	semidirect
271. #1642	C₂×C₁₉	semidirect
272. #1641	C₂×C₁₉	semidirect
273. #1640	C₂×C₁₉	semidirect
274. #1640	C₂×C₁₉	semidirect
275. #1545	C₂×C₁₉	semidirect
276. #1489	C₂×C₁₉	semidirect
277. #1485	C₂×C₁₉	semidirect
324. #475	C₂²×C₁₉	semidirect
325. #475	C₂²×C₁₉	semidirect
326. #474	C₂²×C₁₉	semidirect
329. #462	C₂²×C₁₉	semidirect
330. #462	C₂²×C₁₉	semidirect
331. #461	C₂²×C₁₉	semidirect
341. Q₈⋊C₈	C₂²×C₁₉	semidirect
342. Q₈⋊C₈	C₂²×C₁₉	semidirect
343. Q₈⋊C₈	C₂²×C₁₉	semidirect
344. D₄⋊C₈	C₂²×C₁₉	semidirect
431. C₁₉	#18576	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×#3508	2
C₁₉×#3255	2
C₁₉×#3138	2
C₁₉×#3107	2
C₁₉×#1642	2
C₁₉×#1641	2
C₁₉×#1640	2
C₁₉×#1545	2
C₁₉×#1489	2
C₁₉×#1485	2
#18576	19

Subgroups — C19×#18576 #18024535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18576 #18024535