Subgroups — C₁₉×#19804 #18025763

Order 4864.

720 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3362	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3274	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1715	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1691	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1668	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1666	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1642	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1629	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1627	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1623	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1583	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂²×SD₁₆×C₁₉	—	2	1	no	—
18	Q₈²×C₁₉	C₂²	1	1	yes	characteristic, complemented
19	C₁₉×#550	C₂²	1	1	yes	characteristic
20	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	D₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#498	—	2	1	no	—
23	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#493	C₂²	1	1	yes	characteristic
25	C₁₉×#492	C₂²	1	1	yes	characteristic
26	C₁₉×#492	C₂²	1	1	yes	characteristic
27	C₁₉×#486	—	2	1	no	—
28	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#476	—	2	1	no	—
31	C₁₉×#476	—	2	1	no	—
32	C₁₉×#476	C₂²	1	1	yes	characteristic
33	C₁₉×#476	C₂²	1	1	yes	characteristic
34	C₁₉×#475	—	2	1	no	—
35	C₁₉×#475	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#469	—	2	1	no	—
37	C₁₉×#465	—	2	1	no	—
38	C₁₉×#461	C₂²	1	1	yes	characteristic
39	C₁₉×#460	—	2	1	no	—
40	C₁₉×#460	C₂²	1	1	yes	characteristic
41	C₁₉×#460	C₂²	1	1	yes	characteristic
42	C₁₉×#460	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#459	C₂²	1	1	yes	characteristic
44	C₁₉×#450	—	2	1	no	—
45	C₁₉×#449	—	2	1	no	—
46	C₁₉×#448	—	2	1	no	—
47	C₁₉×#447	—	2	1	no	—
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
49	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
50	C₄×SD₁₆×C₁₉	—	2	1	no	—
51	C₄×SD₁₆×C₁₉	—	2	1	no	—
52	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
53	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
54	C₁₉×#436	C₂²	1	1	yes	characteristic
55	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
56	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#333	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#331	C₂²	1	1	yes	characteristic
61	C₁₉×#331	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₉×#322	C₂²	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂²×Q₈×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	—	2	1	no	—
70	C₂²×D₄×C₁₉	—	2	1	no	—
71	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×SD₁₆×C₁₉	—	2	1	no	—
75	C₂×SD₁₆×C₁₉	—	2	1	no	—
76	C₂×SD₁₆×C₁₉	—	2	1	no	—
77	C₂×SD₁₆×C₁₉	—	2	1	no	—
78	C₂×SD₁₆×C₁₉	—	4	1	no	—
79	C₂×SD₁₆×C₁₉	—	4	4	no	—
80	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
81	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
82	C₂×D₈×C₁₉	—	2	1	no	—
83	C₂×D₈×C₁₉	—	2	1	no	—
84	C₂×D₈×C₁₉	—	2	1	no	—
85	C₂×M₁₆×C₁₉	—	2	1	no	—
86	C₂²×C₈×C₁₉	—	2	1	no	—
87	C₁₉×C₄⋊Q₈	—	2	1	no	—
88	C₁₉×C₄⋊Q₈	—	2	1	no	—
89	C₁₉×C₄⋊Q₈	—	2	1	no	—
90	C₁₉×C₄⋊Q₈	—	4	1	no	—
91	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
93	C₁₉×#127	—	2	1	no	—
94	C₁₉×#127	C₂³	1	1	yes	characteristic
95	C₁₉×#127	C₂³	1	1	yes	characteristic
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	—	4	1	no	—
98	C₁₉×#121	—	2	1	no	—
99	C₁₉×#121	—	2	1	no	—
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#121	—	4	1	no	—
102	C₁₉×#120	—	4	1	no	—
103	C₄×Q₈×C₁₉	—	2	1	no	—
104	C₄×Q₈×C₁₉	—	2	1	no	—
105	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
106	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
107	C₄×D₄×C₁₉	—	2	1	no	—
108	C₄×D₄×C₁₉	—	2	1	no	—
109	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₁₉×#106	—	2	1	no	—
112	C₁₉×#106	—	2	1	no	—
113	C₁₉×#106	—	2	1	no	—
114	C₁₉×#106	—	2	1	no	—
115	C₁₉×#106	—	2	1	no	—
116	C₁₉×#106	D₄	1	1	yes	characteristic
117	C₁₉×#106	D₄	1	1	yes	characteristic
118	C₁₉×C₄⋊C₈	—	2	1	no	—
119	C₁₉×C₄⋊C₈	—	2	1	no	—
120	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#103	D₄	1	1	yes	characteristic
127	C₁₉×#103	D₄	1	1	yes	characteristic
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×#102	—	2	1	no	—
130	C₁₉×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
134	C₁₉×#102	—	2	1	no	—
135	C₁₉×#102	—	2	1	no	—
136	C₁₉×#102	—	4	1	no	—
137	C₁₉×#102	D₄	1	1	yes	characteristic
138	C₁₉×#102	D₄	1	1	yes	characteristic
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₁₉×C₂²⋊C₈	—	2	1	no	—
141	C₄×C₈×C₁₉	—	2	1	no	—
142	C₄×C₈×C₁₉	—	2	1	no	—
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
146	C₂⁴×C₁₉	—	4	1	no	—
147	#41×C₁₉	—	4	2	no	—
148	#41×C₁₉	—	8	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	4	1	no	—
152	C₂×Q₈×C₁₉	—	4	1	no	—
153	C₂×Q₈×C₁₉	—	4	2	no	—
154	C₂×Q₈×C₁₉	—	8	1	no	—
155	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	4	1	no	—
164	C₂×D₄×C₁₉	—	4	1	no	—
165	C₂×D₄×C₁₉	—	4	1	no	—
166	C₂×D₄×C₁₉	—	4	1	no	—
167	C₂×D₄×C₁₉	—	4	2	no	—
168	C₂×D₄×C₁₉	—	4	2	no	—
169	C₂×D₄×C₁₉	—	8	1	no	—
170	C₂×D₄×C₁₉	—	8	1	no	—
171	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	4	1	no	—
176	C₂²×C₄×C₁₉	—	4	1	no	—
177	SD₁₆×C₁₉	—	2	2	no	—
178	SD₁₆×C₁₉	—	4	2	no	—
179	SD₁₆×C₁₉	—	4	2	no	—
180	SD₁₆×C₁₉	—	4	2	no	—
181	SD₁₆×C₁₉	—	4	2	no	—
182	SD₁₆×C₁₉	—	4	2	no	—
183	SD₁₆×C₁₉	—	8	1	no	—
184	SD₁₆×C₁₉	—	8	2	no	—
185	SD₁₆×C₁₉	SD₁₆	1	4	yes	complemented
186	D₈×C₁₉	—	4	2	no	—
187	D₈×C₁₉	—	4	2	no	—
188	D₈×C₁₉	—	8	1	no	—
189	M₁₆×C₁₉	—	4	2	no	—
190	C₂×C₈×C₁₉	—	2	1	no	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	—	2	1	no	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₂×C₈×C₁₉	—	2	1	no	—
195	C₂×C₈×C₁₉	—	4	2	no	—
196	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	no	—
206	C₄⋊C₄×C₁₉	—	4	1	no	—
207	C₄⋊C₄×C₁₉	—	4	1	no	—
208	C₄⋊C₄×C₁₉	—	4	1	no	—
209	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	no	—
214	C₂²⋊C₄×C₁₉	—	2	1	no	—
215	C₂²⋊C₄×C₁₉	—	4	1	no	—
216	C₂²⋊C₄×C₁₉	—	4	1	no	—
217	C₂²⋊C₄×C₁₉	—	4	1	no	—
218	C₄²×C₁₉	—	2	1	no	—
219	C₄²×C₁₉	—	2	1	no	—
220	C₄²×C₁₉	—	4	1	no	—
221	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
222	#19804	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂³×C₁₉	—	2	1	no	—
224	C₂³×C₁₉	—	2	1	no	—
225	C₂³×C₁₉	—	4	1	no	—
226	C₂³×C₁₉	—	4	1	no	—
227	C₂³×C₁₉	—	8	2	no	—
228	C₂³×C₁₉	—	8	2	no	—
229	C₂³×C₁₉	—	16	1	no	—
230	Q₈×C₁₉	—	2	1	no	—
231	Q₈×C₁₉	—	2	1	no	—
232	Q₈×C₁₉	—	4	1	no	—
233	Q₈×C₁₉	—	4	1	no	—
234	Q₈×C₁₉	—	8	2	no	—
235	Q₈×C₁₉	—	8	1	no	—
236	Q₈×C₁₉	—	16	1	no	—
237	Q₈×C₁₉	C₂×SD₁₆	1	2	yes	complemented
238	Q₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	complemented
239	D₄×C₁₉	—	2	1	no	—
240	D₄×C₁₉	—	2	1	no	—
241	D₄×C₁₉	—	2	1	no	—
242	D₄×C₁₉	—	4	1	no	—
243	D₄×C₁₉	—	4	1	no	—
244	D₄×C₁₉	—	4	1	no	—
245	D₄×C₁₉	—	4	1	no	—
246	D₄×C₁₉	—	4	1	no	—
247	D₄×C₁₉	—	4	1	no	—
248	D₄×C₁₉	—	4	1	no	—
249	D₄×C₁₉	—	4	1	no	—
250	D₄×C₁₉	—	8	2	no	—
251	D₄×C₁₉	—	8	1	no	—
252	D₄×C₁₉	—	8	1	no	—
253	D₄×C₁₉	—	8	2	no	—
254	D₄×C₁₉	—	8	2	no	—
255	D₄×C₁₉	—	16	1	no	—
256	D₄×C₁₉	C₂×SD₁₆	1	2	yes	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	8	2	no	—
270	C₂×C₄×C₁₉	—	8	2	no	—
271	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
274	C₈×C₁₉	—	2	1	no	—
275	C₈×C₁₉	—	2	1	no	—
276	C₈×C₁₉	—	2	1	no	—
277	C₈×C₁₉	—	4	1	no	—
278	C₈×C₁₉	—	4	1	no	—
279	C₈×C₁₉	—	4	1	no	—
280	C₈×C₁₉	—	4	1	no	—
281	C₈×C₁₉	—	4	1	no	—
282	C₈×C₁₉	C₂×SD₁₆	1	2	yes	complemented
283	Q₈×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#3362	C₂×C₁₉	1	1	yes	characteristic, complemented
285	D₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#3274	C₂×C₁₉	1	1	yes	characteristic
287	#1715	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1691	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1677	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1668	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1666	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1642	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1629	C₂×C₁₉	1	1	yes	characteristic, complemented
294	#1627	C₂×C₁₉	1	1	yes	characteristic, complemented
295	#1623	C₂×C₁₉	1	1	yes	characteristic, complemented
296	#1583	C₂×C₁₉	1	1	yes	characteristic, complemented
297	SD₁₆⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	4	1	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	1	no	—
303	C₂²×C₁₉	—	4	1	no	—
304	C₂²×C₁₉	—	8	1	no	—
305	C₂²×C₁₉	—	8	1	no	—
306	C₂²×C₁₉	—	8	1	no	—
307	C₂²×C₁₉	—	8	1	no	—
308	C₂²×C₁₉	—	8	1	no	—
309	C₂²×C₁₉	—	8	1	no	—
310	C₂²×C₁₉	—	16	4	no	—
311	C₂²×C₁₉	D₄²	1	1	yes	characteristic
312	C₄×C₁₉	—	2	2	no	—
313	C₄×C₁₉	—	2	2	no	—
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	—	4	1	no	—
316	C₄×C₁₉	—	4	1	no	—
317	C₄×C₁₉	—	4	1	no	—
318	C₄×C₁₉	—	4	1	no	—
319	C₄×C₁₉	—	8	1	no	—
320	C₄×C₁₉	—	8	1	no	—
321	C₄×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
322	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
323	C₄×C₁₉	#577	1	1	yes	characteristic
324	C₄×C₁₉	#577	1	1	yes	characteristic
325	C₂×AGL(1,ℤ/8)	—	2	1	no	—
326	C₂²×SD₁₆	—	2	1	no	—
327	Q₈²	C₂²×C₁₉	1	1	yes	characteristic, complemented
328	#550	C₂²×C₁₉	1	1	yes	characteristic
329	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
330	D₄²	C₂²×C₁₉	1	1	yes	characteristic
331	#498	—	2	1	no	—
332	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
333	#493	C₂²×C₁₉	1	1	yes	characteristic
334	#492	C₂²×C₁₉	1	1	yes	characteristic
335	#492	C₂²×C₁₉	1	1	yes	characteristic
336	#486	—	2	1	no	—
337	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
338	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	#476	—	2	1	no	—
340	#476	—	2	1	no	—
341	#476	C₂²×C₁₉	1	1	yes	characteristic
342	#476	C₂²×C₁₉	1	1	yes	characteristic
343	#475	—	2	1	no	—
344	#475	C₂²×C₁₉	1	1	yes	characteristic, complemented
345	#469	—	2	1	no	—
346	#465	—	2	1	no	—
347	#461	C₂²×C₁₉	1	1	yes	characteristic
348	#460	—	2	1	no	—
349	#460	C₂²×C₁₉	1	1	yes	characteristic
350	#460	C₂²×C₁₉	1	1	yes	characteristic
351	#460	C₂²×C₁₉	1	1	yes	characteristic, complemented
352	#459	C₂²×C₁₉	1	1	yes	characteristic
353	#450	—	2	1	no	—
354	#449	—	2	1	no	—
355	#448	—	2	1	no	—
356	#447	—	2	1	no	—
357	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
358	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
359	C₄×SD₁₆	—	2	1	no	—
360	C₄×SD₁₆	—	2	1	no	—
361	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
362	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
363	#436	C₂²×C₁₉	1	1	yes	characteristic
364	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
365	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
366	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
367	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
368	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
369	#331	C₂²×C₁₉	1	1	yes	characteristic
370	#331	C₂²×C₁₉	1	1	yes	characteristic, complemented
371	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
372	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
373	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
374	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
375	#322	C₂²×C₁₉	1	1	yes	characteristic, complemented
376	C₂×C₁₉	—	4	2	no	—
377	C₂×C₁₉	—	8	1	no	—
378	C₂×C₁₉	—	16	1	no	—
379	C₂×C₁₉	—	16	1	no	—
380	C₂×C₁₉	#3265	1	1	yes	characteristic
381	C₂×C₁₉	D₄×SD₁₆	1	1	yes	characteristic
382	C₂×C₁₉	#3288	1	1	yes	characteristic
383	C₂×#41	—	2	1	no	—
384	C₂²×Q₈	—	2	1	no	—
385	C₂²×D₄	—	2	1	no	—
386	C₂²×D₄	—	2	1	no	—
387	AGL(1,ℤ/8)	—	4	4	no	—
388	C₂×SD₁₆	—	2	1	no	—
389	C₂×SD₁₆	—	2	1	no	—
390	C₂×SD₁₆	—	2	1	no	—
391	C₂×SD₁₆	—	2	1	no	—
392	C₂×SD₁₆	—	2	1	no	—
393	C₂×SD₁₆	—	2	1	no	—
394	C₂×SD₁₆	—	4	1	no	—
395	C₂×SD₁₆	—	4	4	no	—
396	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
397	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
398	C₂×D₈	—	2	1	no	—
399	C₂×D₈	—	2	1	no	—
400	C₂×D₈	—	2	1	no	—
401	C₂×M₁₆	—	2	1	no	—
402	C₂²×C₈	—	2	1	no	—
403	C₄⋊Q₈	—	2	1	no	—
404	C₄⋊Q₈	—	2	1	no	—
405	C₄⋊Q₈	—	2	1	no	—
406	C₄⋊Q₈	—	4	1	no	—
407	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
408	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
409	#127	—	2	1	no	—
410	#127	C₂³×C₁₉	1	1	yes	characteristic
411	#127	C₂³×C₁₉	1	1	yes	characteristic
412	C₂²⋊Q₈	—	2	1	no	—
413	C₂²⋊Q₈	—	4	1	no	—
414	#121	—	2	1	no	—
415	#121	—	2	1	no	—
416	#121	—	2	1	no	—
417	#121	—	4	1	no	—
418	#120	—	4	1	no	—
419	C₄×Q₈	—	2	1	no	—
420	C₄×Q₈	—	2	1	no	—
421	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
422	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
423	C₄×D₄	—	2	1	no	—
424	C₄×D₄	—	2	1	no	—
425	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
426	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
427	#106	—	2	1	no	—
428	#106	—	2	1	no	—
429	#106	—	2	1	no	—
430	#106	—	2	1	no	—
431	#106	—	2	1	no	—
432	#106	D₄×C₁₉	1	1	yes	characteristic
433	#106	D₄×C₁₉	1	1	yes	characteristic
434	C₄⋊C₈	—	2	1	no	—
435	C₄⋊C₈	—	2	1	no	—
436	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
437	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
438	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
439	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
440	#103	—	2	1	no	—
441	#103	—	2	1	no	—
442	#103	D₄×C₁₉	1	1	yes	characteristic
443	#103	D₄×C₁₉	1	1	yes	characteristic
444	#102	—	2	1	no	—
445	#102	—	2	1	no	—
446	#102	—	2	1	no	—
447	#102	—	2	1	no	—
448	#102	—	2	1	no	—
449	#102	—	2	1	no	—
450	#102	—	2	1	no	—
451	#102	—	2	1	no	—
452	#102	—	4	1	no	—
453	#102	D₄×C₁₉	1	1	yes	characteristic
454	#102	D₄×C₁₉	1	1	yes	characteristic
455	C₂²⋊C₈	—	2	1	no	—
456	C₂²⋊C₈	—	2	1	no	—
457	C₄×C₈	—	2	1	no	—
458	C₄×C₈	—	2	1	no	—
459	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
460	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
461	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
462	C₁₉	#19804	1	1	yes	characteristic, direct product factor, Sylow
463	C₂⁴	—	4	1	no	—
464	#41	—	4	2	no	—
465	#41	—	8	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	4	1	no	—
469	C₂×Q₈	—	4	1	no	—
470	C₂×Q₈	—	4	2	no	—
471	C₂×Q₈	—	8	1	no	—
472	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	4	1	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	—	4	1	no	—
483	C₂×D₄	—	4	1	no	—
484	C₂×D₄	—	4	2	no	—
485	C₂×D₄	—	4	2	no	—
486	C₂×D₄	—	8	1	no	—
487	C₂×D₄	—	8	1	no	—
488	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	4	1	no	—
493	C₂²×C₄	—	4	1	no	—
494	SD₁₆	—	2	2	no	—
495	SD₁₆	—	4	2	no	—
496	SD₁₆	—	4	2	no	—
497	SD₁₆	—	4	2	no	—
498	SD₁₆	—	4	2	no	—
499	SD₁₆	—	4	2	no	—
500	SD₁₆	—	8	1	no	—
501	SD₁₆	—	8	2	no	—
502	SD₁₆	SD₁₆×C₁₉	1	4	yes	complemented
503	D₈	—	4	2	no	—
504	D₈	—	4	2	no	—
505	D₈	—	8	1	no	—
506	M₁₆	—	4	2	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	4	2	no	—
513	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
515	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	4	1	no	—
524	C₄⋊C₄	—	4	1	no	—
525	C₄⋊C₄	—	4	1	no	—
526	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	4	1	no	—
533	C₂²⋊C₄	—	4	1	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	4	1	no	—
538	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	8	2	no	—
544	C₂³	—	8	2	no	—
545	C₂³	—	16	1	no	—
546	Q₈	—	2	1	no	—
547	Q₈	—	2	1	no	—
548	Q₈	—	4	1	no	—
549	Q₈	—	4	1	no	—
550	Q₈	—	8	2	no	—
551	Q₈	—	8	1	no	—
552	Q₈	—	16	1	no	—
553	Q₈	C₂×SD₁₆×C₁₉	1	2	yes	complemented
554	Q₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	complemented
555	D₄	—	2	1	no	—
556	D₄	—	2	1	no	—
557	D₄	—	2	1	no	—
558	D₄	—	4	1	no	—
559	D₄	—	4	1	no	—
560	D₄	—	4	1	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	D₄	—	8	2	no	—
567	D₄	—	8	1	no	—
568	D₄	—	8	1	no	—
569	D₄	—	8	2	no	—
570	D₄	—	8	2	no	—
571	D₄	—	16	1	no	—
572	D₄	C₂×SD₁₆×C₁₉	1	2	yes	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	8	2	no	—
586	C₂×C₄	—	8	2	no	—
587	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
589	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
590	C₈	—	2	1	no	—
591	C₈	—	2	1	no	—
592	C₈	—	2	1	no	—
593	C₈	—	4	1	no	—
594	C₈	—	4	1	no	—
595	C₈	—	4	1	no	—
596	C₈	—	4	1	no	—
597	C₈	—	4	1	no	—
598	C₈	C₂×SD₁₆×C₁₉	1	2	yes	complemented
599	C₂²	—	2	2	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	8	1	no	—
606	C₂²	—	8	1	no	—
607	C₂²	—	8	1	no	—
608	C₂²	—	8	1	no	—
609	C₂²	—	8	1	no	—
610	C₂²	—	8	1	no	—
611	C₂²	—	16	4	no	—
612	C₂²	D₄²×C₁₉	1	1	yes	characteristic
613	C₄	—	2	2	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	1	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	8	1	no	—
621	C₄	—	8	1	no	—
622	C₄	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
623	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
624	C₄	C₁₉×#577	1	1	yes	characteristic
625	C₄	C₁₉×#577	1	1	yes	characteristic
626	C₂	—	4	2	no	—
627	C₂	—	8	1	no	—
628	C₂	—	16	1	no	—
629	C₂	—	16	1	no	—
630	C₂	C₁₉×#3265	1	1	yes	characteristic
631	C₂	D₄×SD₁₆×C₁₉	1	1	yes	characteristic
632	C₂	C₁₉×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3274	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×SD₁₆×C₁₉	C₂	semidirect
2. C₁₉×#3362	C₂	semidirect
3. D₄×SD₁₆×C₁₉	C₂	semidirect
5. C₁₉×#1715	C₂	semidirect
6. C₁₉×#1691	C₂	semidirect
7. C₁₉×#1677	C₂	semidirect
8. C₁₉×#1668	C₂	semidirect
9. C₁₉×#1666	C₂	semidirect
10. C₁₉×#1642	C₂	semidirect
11. C₁₉×#1629	C₂	semidirect
12. C₁₉×#1627	C₂	semidirect
13. C₁₉×#1623	C₂	semidirect
14. C₁₉×#1583	C₂	semidirect
15. C₁₉×SD₁₆⋊C₈	C₂	semidirect
18. Q₈²×C₁₉	C₂²	semidirect
23. C₁₉×#498	C₂²	semidirect
28. C₁₉×#486	C₂²	semidirect
29. C₁₉×#486	C₂²	semidirect
35. C₁₉×#475	C₂²	semidirect
42. C₁₉×#460	C₂²	semidirect
48. C₈×Q₈×C₁₉	C₂²	semidirect
49. C₈×Q₈×C₁₉	C₂²	semidirect
56. C₁₉×#335	C₂²	semidirect
57. C₁₉×#334	C₂²	semidirect
58. C₁₉×#333	C₂²	semidirect
59. C₁₉×#332	C₂²	semidirect
61. C₁₉×#331	C₂²	semidirect
62. C₁₉×Q₈⋊C₈	C₂²	semidirect
63. C₁₉×Q₈⋊C₈	C₂²	semidirect
66. C₁₉×#322	C₂²	semidirect
185. SD₁₆×C₁₉	SD₁₆	semidirect
222. #19804	C₁₉	direct (N × H)
237. Q₈×C₁₉	C₂×SD₁₆	semidirect
238. Q₈×C₁₉	AGL(1,ℤ/8)	semidirect
282. C₈×C₁₉	C₂×SD₁₆	semidirect
283. Q₈×SD₁₆	C₂×C₁₉	semidirect
284. #3362	C₂×C₁₉	semidirect
285. D₄×SD₁₆	C₂×C₁₉	semidirect
287. #1715	C₂×C₁₉	semidirect
288. #1691	C₂×C₁₉	semidirect
289. #1677	C₂×C₁₉	semidirect
290. #1668	C₂×C₁₉	semidirect
291. #1666	C₂×C₁₉	semidirect
292. #1642	C₂×C₁₉	semidirect
293. #1629	C₂×C₁₉	semidirect
294. #1627	C₂×C₁₉	semidirect
295. #1623	C₂×C₁₉	semidirect
296. #1583	C₂×C₁₉	semidirect
297. SD₁₆⋊C₈	C₂×C₁₉	semidirect
327. Q₈²	C₂²×C₁₉	semidirect
332. #498	C₂²×C₁₉	semidirect
337. #486	C₂²×C₁₉	semidirect
338. #486	C₂²×C₁₉	semidirect
344. #475	C₂²×C₁₉	semidirect
351. #460	C₂²×C₁₉	semidirect
357. C₈×Q₈	C₂²×C₁₉	semidirect
358. C₈×Q₈	C₂²×C₁₉	semidirect
365. #335	C₂²×C₁₉	semidirect
366. #334	C₂²×C₁₉	semidirect
367. #333	C₂²×C₁₉	semidirect
368. #332	C₂²×C₁₉	semidirect
370. #331	C₂²×C₁₉	semidirect
371. Q₈⋊C₈	C₂²×C₁₉	semidirect
372. Q₈⋊C₈	C₂²×C₁₉	semidirect
375. #322	C₂²×C₁₉	semidirect
462. C₁₉	#19804	direct (N × H)
502. SD₁₆	SD₁₆×C₁₉	semidirect
553. Q₈	C₂×SD₁₆×C₁₉	semidirect
554. Q₈	C₁₉×AGL(1,ℤ/8)	semidirect
598. C₈	C₂×SD₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
Q₈×SD₁₆×C₁₉	2
C₁₉×#3362	2
D₄×SD₁₆×C₁₉	2
C₁₉×#3274	2
C₁₉×#1715	2
C₁₉×#1691	2
C₁₉×#1677	2
C₁₉×#1668	2
C₁₉×#1666	2
C₁₉×#1642	2
C₁₉×#1629	2
C₁₉×#1627	2
C₁₉×#1623	2
C₁₉×#1583	2
C₁₉×SD₁₆⋊C₈	2
#19804	19

Subgroups — C19×#19804 #18025763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19804 #18025763