Subgroups — C₁₉×#19761 #18025720

Order 4864.

694 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3358	C₂	1	1	yes	maximal, characteristic
3	D₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3278	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1722	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1689	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1682	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1674	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1649	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1649	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1641	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1627	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1581	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1579	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#137	—	2	1	no	—
17	C₂²×Q₁₆×C₁₉	—	2	1	no	—
18	C₁₉×#550	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#500	—	2	1	no	—
23	C₁₉×#500	C₂²	1	1	yes	characteristic
24	C₁₉×#500	C₂²	1	1	yes	characteristic
25	C₁₉×#494	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
29	C₁₉×#486	C₂²	1	1	yes	characteristic
30	C₁₉×#474	—	2	1	no	—
31	C₁₉×#474	—	2	1	no	—
32	C₁₉×#474	—	2	1	no	—
33	C₁₉×#474	C₂²	1	1	yes	characteristic
34	C₁₉×#474	C₂²	1	1	yes	characteristic
35	C₁₉×#474	C₂²	1	1	yes	characteristic
36	C₁₉×#468	—	2	1	no	—
37	C₁₉×#467	—	2	1	no	—
38	C₁₉×#462	C₂²	1	1	yes	characteristic
39	C₁₉×#462	C₂²	1	1	yes	characteristic
40	C₁₉×#462	C₂²	1	1	yes	characteristic
41	C₁₉×#460	C₂²	1	1	yes	characteristic
42	C₁₉×#459	—	2	1	no	—
43	C₁₉×#459	C₂²	1	1	yes	characteristic
44	C₁₉×#452	—	2	1	no	—
45	C₁₉×#451	—	2	1	no	—
46	C₁₉×#451	—	2	1	no	—
47	C₁₉×#448	—	2	1	no	—
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
50	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
51	C₄×D₈×C₁₉	—	2	1	no	—
52	C₄×D₈×C₁₉	—	2	1	no	—
53	C₄×D₈×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
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#332	C₂²	1	1	yes	characteristic
59	C₁₉×#332	C₂²	1	1	yes	characteristic
60	C₁₉×#332	C₂²	1	1	yes	characteristic
61	C₁₉×#331	C₂²	1	1	yes	characteristic
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
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
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂²×Q₈×C₁₉	—	2	1	no	—
69	C₂²×Q₈×C₁₉	—	2	1	no	—
70	C₂²×Q₈×C₁₉	—	2	1	no	—
71	C₁₉×#137	—	4	4	no	—
72	C₂×Q₁₆×C₁₉	—	2	1	no	—
73	C₂×Q₁₆×C₁₉	—	2	1	no	—
74	C₂×Q₁₆×C₁₉	—	2	1	no	—
75	C₂×Q₁₆×C₁₉	—	2	1	no	—
76	C₂×Q₁₆×C₁₉	—	2	1	no	—
77	C₂×Q₁₆×C₁₉	—	4	4	no	—
78	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
79	C₂×SD₁₆×C₁₉	—	2	1	no	—
80	C₂×SD₁₆×C₁₉	—	2	1	no	—
81	C₂×SD₁₆×C₁₉	—	2	1	no	—
82	C₂×D₈×C₁₉	—	2	1	no	—
83	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
84	C₂×M₁₆×C₁₉	—	2	1	no	—
85	C₂²×C₈×C₁₉	—	2	1	no	—
86	C₁₉×C₄⋊Q₈	—	2	1	no	—
87	C₁₉×C₄⋊Q₈	—	2	1	no	—
88	C₁₉×C₄⋊Q₈	—	2	1	no	—
89	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₁₉×#127	—	2	1	no	—
93	C₁₉×#127	C₂³	1	1	yes	characteristic
94	C₁₉×C₂²⋊Q₈	—	2	1	no	—
95	C₁₉×C₂²⋊Q₈	—	2	1	no	—
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	—	4	1	no	—
98	C₁₉×C₂²⋊Q₈	—	4	1	no	—
99	C₁₉×C₂²⋊Q₈	—	4	1	no	—
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#121	—	4	1	no	—
102	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
103	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	—	2	1	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	—	2	1	no	—
108	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₁₉×#107	—	2	1	no	—
111	C₁₉×#107	—	2	1	no	—
112	C₁₉×#107	—	2	1	no	—
113	C₁₉×#107	—	2	1	no	—
114	C₁₉×#107	—	2	1	no	—
115	C₁₉×#107	—	4	1	no	—
116	C₁₉×#107	D₄	1	1	yes	characteristic
117	C₁₉×#107	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	—	2	1	no	—
127	C₁₉×#103	D₄	1	1	yes	characteristic
128	C₁₉×#103	D₄	1	1	yes	characteristic
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	#41×C₁₉	—	4	2	no	—
147	#41×C₁₉	—	8	1	no	—
148	C₂×Q₈×C₁₉	—	2	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	1	no	—
154	C₂×Q₈×C₁₉	—	4	2	no	—
155	C₂×Q₈×C₁₉	—	4	2	no	—
156	C₂×Q₈×C₁₉	—	4	2	no	—
157	C₂×Q₈×C₁₉	—	8	1	no	—
158	C₂×Q₈×C₁₉	—	8	1	no	—
159	C₂×Q₈×C₁₉	—	8	1	no	—
160	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	1	no	—
165	C₂×D₄×C₁₉	—	4	1	no	—
166	C₂×D₄×C₁₉	—	4	1	no	—
167	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	4	1	no	—
172	C₂²×C₄×C₁₉	—	4	1	no	—
173	C₂²×C₄×C₁₉	—	4	1	no	—
174	C₂²×C₄×C₁₉	—	4	1	no	—
175	Q₁₆×C₁₉	—	4	2	no	—
176	Q₁₆×C₁₉	—	4	2	no	—
177	Q₁₆×C₁₉	—	4	2	no	—
178	Q₁₆×C₁₉	—	4	2	no	—
179	Q₁₆×C₁₉	—	8	1	no	—
180	Q₁₆×C₁₉	D₈	1	4	yes	complemented
181	SD₁₆×C₁₉	—	4	2	no	—
182	SD₁₆×C₁₉	—	4	2	no	—
183	SD₁₆×C₁₉	—	8	1	no	—
184	D₈×C₁₉	—	2	2	no	—
185	D₈×C₁₉	—	4	2	no	—
186	M₁₆×C₁₉	—	4	2	no	—
187	C₂×C₈×C₁₉	—	2	1	no	—
188	C₂×C₈×C₁₉	—	2	1	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	2	1	no	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	—	4	2	no	—
193	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	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	—	4	1	no	—
206	C₄⋊C₄×C₁₉	—	4	1	no	—
207	C₄⋊C₄×C₁₉	—	4	1	no	—
208	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₁₉	—	2	1	no	—
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₂²⋊C₄×C₁₉	—	4	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	C₂⁴	1	1	yes	characteristic
221	#19761	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂³×C₁₉	—	2	1	no	—
223	C₂³×C₁₉	—	2	1	no	—
224	C₂³×C₁₉	—	4	1	no	—
225	Q₈×C₁₉	—	2	1	no	—
226	Q₈×C₁₉	—	2	1	no	—
227	Q₈×C₁₉	—	4	1	no	—
228	Q₈×C₁₉	—	4	1	no	—
229	Q₈×C₁₉	—	4	1	no	—
230	Q₈×C₁₉	—	4	1	no	—
231	Q₈×C₁₉	—	4	1	no	—
232	Q₈×C₁₉	—	4	1	no	—
233	Q₈×C₁₉	—	8	2	no	—
234	Q₈×C₁₉	—	8	2	no	—
235	Q₈×C₁₉	—	8	2	no	—
236	Q₈×C₁₉	C₂×D₈	1	2	yes	—
237	Q₈×C₁₉	C₂×D₈	1	2	yes	—
238	D₄×C₁₉	—	2	1	no	—
239	D₄×C₁₉	—	2	1	no	—
240	D₄×C₁₉	—	2	1	no	—
241	D₄×C₁₉	—	4	1	no	—
242	D₄×C₁₉	—	4	1	no	—
243	D₄×C₁₉	—	4	1	no	—
244	D₄×C₁₉	—	4	1	no	—
245	D₄×C₁₉	—	8	2	no	—
246	D₄×C₁₉	—	8	1	no	—
247	D₄×C₁₉	—	16	1	no	—
248	D₄×C₁₉	#137	1	2	yes	complemented
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	8	2	no	—
263	C₂×C₄×C₁₉	—	8	2	no	—
264	C₂×C₄×C₁₉	—	8	2	no	—
265	C₂×C₄×C₁₉	—	8	2	no	—
266	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
269	C₈×C₁₉	—	2	1	no	—
270	C₈×C₁₉	—	2	1	no	—
271	C₈×C₁₉	—	2	1	no	—
272	C₈×C₁₉	—	4	1	no	—
273	C₈×C₁₉	—	4	1	no	—
274	C₈×C₁₉	—	4	1	no	—
275	C₈×C₁₉	—	4	1	no	—
276	C₈×C₁₉	—	4	1	no	—
277	C₈×C₁₉	C₂×D₈	1	2	yes	—
278	Q₈×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#3358	C₂×C₁₉	1	1	yes	characteristic
280	D₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#3278	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1722	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1689	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1682	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1674	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1665	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1649	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1649	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1641	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1627	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1581	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1579	C₂×C₁₉	1	1	yes	characteristic, complemented
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	4	1	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	—	4	1	no	—
297	C₂²×C₁₉	—	4	1	no	—
298	C₂²×C₁₉	—	4	1	no	—
299	C₂²×C₁₉	—	8	1	no	—
300	C₂²×C₁₉	—	8	1	no	—
301	C₂²×C₁₉	—	8	1	no	—
302	C₂²×C₁₉	D₄²	1	1	yes	characteristic
303	C₄×C₁₉	—	2	2	no	—
304	C₄×C₁₉	—	2	2	no	—
305	C₄×C₁₉	—	2	1	no	—
306	C₄×C₁₉	—	4	1	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	4	1	no	—
309	C₄×C₁₉	—	4	1	no	—
310	C₄×C₁₉	—	8	1	no	—
311	C₄×C₁₉	—	8	1	no	—
312	C₄×C₁₉	—	8	1	no	—
313	C₄×C₁₉	C₂²×D₈	1	1	yes	characteristic
314	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
315	C₄×C₁₉	#576	1	1	yes	characteristic
316	C₄×C₁₉	#578	1	1	yes	characteristic
317	C₂×#137	—	2	1	no	—
318	C₂²×Q₁₆	—	2	1	no	—
319	#550	C₂²×C₁₉	1	1	yes	characteristic
320	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
321	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
322	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
323	#500	—	2	1	no	—
324	#500	C₂²×C₁₉	1	1	yes	characteristic
325	#500	C₂²×C₁₉	1	1	yes	characteristic
326	#494	C₂²×C₁₉	1	1	yes	characteristic
327	#492	C₂²×C₁₉	1	1	yes	characteristic
328	#486	—	2	1	no	—
329	#486	C₂²×C₁₉	1	1	yes	characteristic
330	#486	C₂²×C₁₉	1	1	yes	characteristic
331	#474	—	2	1	no	—
332	#474	—	2	1	no	—
333	#474	—	2	1	no	—
334	#474	C₂²×C₁₉	1	1	yes	characteristic
335	#474	C₂²×C₁₉	1	1	yes	characteristic
336	#474	C₂²×C₁₉	1	1	yes	characteristic
337	#468	—	2	1	no	—
338	#467	—	2	1	no	—
339	#462	C₂²×C₁₉	1	1	yes	characteristic
340	#462	C₂²×C₁₉	1	1	yes	characteristic
341	#462	C₂²×C₁₉	1	1	yes	characteristic
342	#460	C₂²×C₁₉	1	1	yes	characteristic
343	#459	—	2	1	no	—
344	#459	C₂²×C₁₉	1	1	yes	characteristic
345	#452	—	2	1	no	—
346	#451	—	2	1	no	—
347	#451	—	2	1	no	—
348	#448	—	2	1	no	—
349	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
350	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
351	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
352	C₄×D₈	—	2	1	no	—
353	C₄×D₈	—	2	1	no	—
354	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
355	#436	C₂²×C₁₉	1	1	yes	characteristic
356	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
357	#335	C₂²×C₁₉	1	1	yes	characteristic
358	#334	C₂²×C₁₉	1	1	yes	characteristic
359	#332	C₂²×C₁₉	1	1	yes	characteristic
360	#332	C₂²×C₁₉	1	1	yes	characteristic
361	#332	C₂²×C₁₉	1	1	yes	characteristic
362	#331	C₂²×C₁₉	1	1	yes	characteristic
363	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
364	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
365	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
366	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
367	#322	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×C₁₉	—	4	2	no	—
369	C₂×C₁₉	—	8	1	no	—
370	C₂×C₁₉	—	16	1	no	—
371	C₂×C₁₉	#3270	1	1	yes	characteristic
372	C₂×C₁₉	D₄×D₈	1	1	yes	characteristic
373	C₂×C₁₉	#3289	1	1	yes	characteristic
374	C₂×#41	—	2	1	no	—
375	C₂²×Q₈	—	2	1	no	—
376	C₂²×Q₈	—	2	1	no	—
377	C₂²×Q₈	—	2	1	no	—
378	#137	—	4	4	no	—
379	C₂×Q₁₆	—	2	1	no	—
380	C₂×Q₁₆	—	2	1	no	—
381	C₂×Q₁₆	—	2	1	no	—
382	C₂×Q₁₆	—	2	1	no	—
383	C₂×Q₁₆	—	2	1	no	—
384	C₂×Q₁₆	—	4	4	no	—
385	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
386	C₂×SD₁₆	—	2	1	no	—
387	C₂×SD₁₆	—	2	1	no	—
388	C₂×SD₁₆	—	2	1	no	—
389	C₂×D₈	—	2	1	no	—
390	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
391	C₂×M₁₆	—	2	1	no	—
392	C₂²×C₈	—	2	1	no	—
393	C₄⋊Q₈	—	2	1	no	—
394	C₄⋊Q₈	—	2	1	no	—
395	C₄⋊Q₈	—	2	1	no	—
396	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
397	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
398	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
399	#127	—	2	1	no	—
400	#127	C₂³×C₁₉	1	1	yes	characteristic
401	C₂²⋊Q₈	—	2	1	no	—
402	C₂²⋊Q₈	—	2	1	no	—
403	C₂²⋊Q₈	—	2	1	no	—
404	C₂²⋊Q₈	—	4	1	no	—
405	C₂²⋊Q₈	—	4	1	no	—
406	C₂²⋊Q₈	—	4	1	no	—
407	#121	—	2	1	no	—
408	#121	—	4	1	no	—
409	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
410	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	—	2	1	no	—
415	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
416	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
417	#107	—	2	1	no	—
418	#107	—	2	1	no	—
419	#107	—	2	1	no	—
420	#107	—	2	1	no	—
421	#107	—	2	1	no	—
422	#107	—	4	1	no	—
423	#107	D₄×C₁₉	1	1	yes	characteristic
424	#107	D₄×C₁₉	1	1	yes	characteristic
425	C₄⋊C₈	—	2	1	no	—
426	C₄⋊C₈	—	2	1	no	—
427	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
428	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
429	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
430	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
431	#103	—	2	1	no	—
432	#103	—	2	1	no	—
433	#103	—	2	1	no	—
434	#103	D₄×C₁₉	1	1	yes	characteristic
435	#103	D₄×C₁₉	1	1	yes	characteristic
436	#102	—	2	1	no	—
437	#102	—	2	1	no	—
438	#102	—	2	1	no	—
439	#102	—	2	1	no	—
440	#102	—	2	1	no	—
441	#102	—	2	1	no	—
442	#102	—	2	1	no	—
443	#102	—	4	1	no	—
444	#102	D₄×C₁₉	1	1	yes	characteristic
445	#102	D₄×C₁₉	1	1	yes	characteristic
446	C₂²⋊C₈	—	2	1	no	—
447	C₂²⋊C₈	—	2	1	no	—
448	C₄×C₈	—	2	1	no	—
449	C₄×C₈	—	2	1	no	—
450	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
451	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
452	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
453	C₁₉	#19761	1	1	yes	characteristic, direct product factor, Sylow
454	#41	—	4	2	no	—
455	#41	—	8	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	4	1	no	—
460	C₂×Q₈	—	4	1	no	—
461	C₂×Q₈	—	4	1	no	—
462	C₂×Q₈	—	4	2	no	—
463	C₂×Q₈	—	4	2	no	—
464	C₂×Q₈	—	4	2	no	—
465	C₂×Q₈	—	8	1	no	—
466	C₂×Q₈	—	8	1	no	—
467	C₂×Q₈	—	8	1	no	—
468	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	4	1	no	—
474	C₂×D₄	—	4	1	no	—
475	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	4	1	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	—	4	1	no	—
482	C₂²×C₄	—	4	1	no	—
483	Q₁₆	—	4	2	no	—
484	Q₁₆	—	4	2	no	—
485	Q₁₆	—	4	2	no	—
486	Q₁₆	—	4	2	no	—
487	Q₁₆	—	8	1	no	—
488	Q₁₆	D₈×C₁₉	1	4	yes	complemented
489	SD₁₆	—	4	2	no	—
490	SD₁₆	—	4	2	no	—
491	SD₁₆	—	8	1	no	—
492	D₈	—	2	2	no	—
493	D₈	—	4	2	no	—
494	M₁₆	—	4	2	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	4	2	no	—
501	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
502	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	4	1	no	—
514	C₄⋊C₄	—	4	1	no	—
515	C₄⋊C₄	—	4	1	no	—
516	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
519	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	4	1	no	—
523	C₂²⋊C₄	—	4	1	no	—
524	C₂²⋊C₄	—	4	1	no	—
525	C₂²⋊C₄	—	4	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	4	1	no	—
532	Q₈	—	2	1	no	—
533	Q₈	—	2	1	no	—
534	Q₈	—	4	1	no	—
535	Q₈	—	4	1	no	—
536	Q₈	—	4	1	no	—
537	Q₈	—	4	1	no	—
538	Q₈	—	4	1	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	8	2	no	—
541	Q₈	—	8	2	no	—
542	Q₈	—	8	2	no	—
543	Q₈	C₂×D₈×C₁₉	1	2	yes	—
544	Q₈	C₂×D₈×C₁₉	1	2	yes	—
545	D₄	—	2	1	no	—
546	D₄	—	2	1	no	—
547	D₄	—	2	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	1	no	—
552	D₄	—	8	2	no	—
553	D₄	—	8	1	no	—
554	D₄	—	16	1	no	—
555	D₄	C₁₉×#137	1	2	yes	complemented
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	8	2	no	—
570	C₂×C₄	—	8	2	no	—
571	C₂×C₄	—	8	2	no	—
572	C₂×C₄	—	8	2	no	—
573	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
574	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
575	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
576	C₈	—	2	1	no	—
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	4	1	no	—
580	C₈	—	4	1	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₈	—	4	1	no	—
584	C₈	C₂×D₈×C₁₉	1	2	yes	—
585	C₂²	—	2	2	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	D₄²×C₁₉	1	1	yes	characteristic
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	8	1	no	—
603	C₄	—	8	1	no	—
604	C₄	—	8	1	no	—
605	C₄	C₂²×D₈×C₁₉	1	1	yes	characteristic
606	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
607	C₄	C₁₉×#576	1	1	yes	characteristic
608	C₄	C₁₉×#578	1	1	yes	characteristic
609	C₂	—	4	2	no	—
610	C₂	—	8	1	no	—
611	C₂	—	16	1	no	—
612	C₂	C₁₉×#3270	1	1	yes	characteristic
613	C₂	D₄×D₈×C₁₉	1	1	yes	characteristic
614	C₂	C₁₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3358	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×D₈×C₁₉	C₂	semidirect
3. D₄×Q₁₆×C₁₉	C₂	semidirect
4. C₁₉×#3278	C₂	semidirect
5. C₁₉×#1722	C₂	semidirect
6. C₁₉×#1689	C₂	semidirect
7. C₁₉×#1682	C₂	semidirect
8. C₁₉×#1674	C₂	semidirect
9. C₁₉×#1665	C₂	semidirect
10. C₁₉×#1649	C₂	semidirect
11. C₁₉×#1649	C₂	semidirect
12. C₁₉×#1641	C₂	semidirect
13. C₁₉×#1627	C₂	semidirect
14. C₁₉×#1581	C₂	semidirect
15. C₁₉×#1579	C₂	semidirect
180. Q₁₆×C₁₉	D₈	semidirect
221. #19761	C₁₉	direct (N × H)
248. D₄×C₁₉	#137	semidirect
278. Q₈×D₈	C₂×C₁₉	semidirect
280. D₄×Q₁₆	C₂×C₁₉	semidirect
281. #3278	C₂×C₁₉	semidirect
282. #1722	C₂×C₁₉	semidirect
283. #1689	C₂×C₁₉	semidirect
284. #1682	C₂×C₁₉	semidirect
285. #1674	C₂×C₁₉	semidirect
286. #1665	C₂×C₁₉	semidirect
287. #1649	C₂×C₁₉	semidirect
288. #1649	C₂×C₁₉	semidirect
289. #1641	C₂×C₁₉	semidirect
290. #1627	C₂×C₁₉	semidirect
291. #1581	C₂×C₁₉	semidirect
292. #1579	C₂×C₁₉	semidirect
453. C₁₉	#19761	direct (N × H)
488. Q₁₆	D₈×C₁₉	semidirect
555. D₄	C₁₉×#137	semidirect

Maximal subgroups

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

subgroup	index
Q₈×D₈×C₁₉	2
C₁₉×#3358	2
D₄×Q₁₆×C₁₉	2
C₁₉×#3278	2
C₁₉×#1722	2
C₁₉×#1689	2
C₁₉×#1682	2
C₁₉×#1674	2
C₁₉×#1665	2
C₁₉×#1649	2
C₁₉×#1641	2
C₁₉×#1627	2
C₁₉×#1581	2
C₁₉×#1579	2
#19761	19

Subgroups — C19×#19761 #18025720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19761 #18025720