Subgroups — C₁₉×#62361 #18068320

Order 4864.

1710 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3507	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3396	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3393	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3383	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3380	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3365	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3360	C₂	1	4	yes	maximal, complemented
8	C₁₉×#3250	C₂	1	4	yes	maximal, complemented
9	C₁₉×#3246	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3170	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3169	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#3168	C₂	1	4	yes	maximal, complemented
13	C₂×C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#559	C₂²	1	4	yes	—
15	C₁₉×#557	C₂²	1	4	yes	—
16	C₁₉×#556	—	2	4	no	—
17	C₁₉×#556	C₂²	1	4	yes	—
18	C₁₉×#554	C₂²	1	4	yes	—
19	C₁₉×#552	—	2	4	no	—
20	C₁₉×#539	—	2	4	no	—
21	C₁₉×#536	—	2	2	no	—
22	C₁₉×#533	C₂²	1	2	yes	—
23	C₁₉×#532	C₂²	1	2	yes	—
24	C₁₉×#529	C₂²	1	8	yes	—
25	C₁₉×#520	—	2	2	no	—
26	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#500	C₂²	1	1	yes	characteristic
28	C₁₉×#500	C₂²	1	1	yes	characteristic
29	C₁₉×#499	C₂²	1	4	yes	—
30	C₁₉×#495	C₂²	1	4	yes	—
31	C₁₉×#494	C₂²	1	1	yes	characteristic
32	C₁₉×#493	C₂²	1	1	yes	characteristic
33	C₁₉×#488	C₂²	1	8	yes	—
34	C₁₉×#487	C₂²	1	2	yes	—
35	C₁₉×#486	C₂²	1	2	yes	—
36	C₁₉×#479	C₂²	1	8	yes	—
37	C₁₉×#478	C₂²	1	8	yes	—
38	C₁₉×#476	C₂²	1	4	yes	—
39	C₁₉×#475	C₂²	1	4	yes	—
40	C₁₉×#467	C₂²	1	2	yes	—
41	C₁₉×#467	C₂²	1	2	yes	—
42	C₁₉×#466	C₂²	1	2	yes	—
43	C₁₉×#466	C₂²	1	2	yes	—
44	C₁₉×#465	C₂²	1	8	yes	—
45	C₁₉×#464	C₂²	1	8	yes	—
46	C₁₉×#463	C₂²	1	8	yes	—
47	C₁₉×#461	C₂²	1	4	yes	—
48	C₁₉×#460	C₂²	1	4	yes	—
49	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
50	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
51	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
52	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
53	C₄×Q₁₆×C₁₉	C₂²	1	4	yes	—
54	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
55	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
56	C₄×SD₁₆×C₁₉	C₂²	1	8	yes	—
57	C₄×D₈×C₁₉	C₂²	1	4	yes	—
58	C₄×D₈×C₁₉	C₂²	1	2	yes	—
59	C₄×D₈×C₁₉	C₂²	1	2	yes	—
60	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
62	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
64	C₂×#41×C₁₉	—	2	2	no	—
65	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
66	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
67	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
68	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
69	C₂×D₈×C₁₉	C₂³	1	2	yes	—
70	C₂×D₈×C₁₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×C₄⋊Q₈	—	2	4	no	—
75	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
76	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
77	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
78	C₁₉×#127	C₂³	1	2	yes	—
79	C₁₉×#126	—	2	8	no	—
80	C₁₉×#126	—	2	8	no	—
81	C₁₉×#125	—	2	8	no	—
82	C₁₉×#125	—	2	2	no	—
83	C₁₉×#125	C₂³	1	8	yes	—
84	C₁₉×#124	—	2	4	no	—
85	C₁₉×#124	—	2	2	no	—
86	C₁₉×#124	C₂³	1	8	yes	—
87	C₁₉×#123	—	2	8	no	—
88	C₁₉×#123	—	2	8	no	—
89	C₁₉×C₂²⋊Q₈	—	2	4	no	—
90	C₁₉×C₂²⋊Q₈	—	2	4	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	8	no	—
93	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
94	C₁₉×#121	—	2	2	no	—
95	C₁₉×#121	C₂³	1	4	yes	—
96	C₄×Q₈×C₁₉	—	2	4	no	—
97	C₄×Q₈×C₁₉	—	2	2	no	—
98	C₄×Q₈×C₁₉	D₄	1	2	yes	—
99	C₄×Q₈×C₁₉	D₄	1	2	yes	—
100	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
101	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
102	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
103	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
104	C₄×D₄×C₁₉	—	2	8	no	—
105	C₄×D₄×C₁₉	—	2	4	no	—
106	C₄×D₄×C₁₉	—	2	2	no	—
107	C₄×D₄×C₁₉	C₂³	1	4	yes	—
108	C₄×D₄×C₁₉	C₂³	1	8	yes	—
109	C₁₉×#117	—	2	2	no	—
110	C₁₉×#117	—	2	4	no	—
111	C₁₉×#117	—	2	8	no	—
112	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
113	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
115	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
117	C₁₉×#107	C₂³	1	2	yes	—
118	C₁₉×#107	C₂³	1	2	yes	—
119	C₁₉×#107	C₂³	1	2	yes	—
120	C₁₉×#107	C₂³	1	2	yes	—
121	C₁₉×#106	C₂³	1	8	yes	—
122	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
123	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
124	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
125	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
126	C₁₉×#103	C₂³	1	4	yes	—
127	C₁₉×#103	C₂³	1	8	yes	—
128	C₁₉×#103	C₂³	1	4	yes	—
129	C₁₉×#102	C₂³	1	4	yes	—
130	C₁₉×#102	C₂³	1	8	yes	—
131	C₁₉×#102	C₂³	1	4	yes	—
132	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
133	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
134	C₄×C₈×C₁₉	C₂³	1	4	yes	—
135	C₄×C₈×C₁₉	C₂³	1	4	yes	—
136	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
138	#41×C₁₉	—	4	8	no	—
139	C₂×Q₈×C₁₉	—	2	4	no	—
140	C₂×Q₈×C₁₉	—	2	2	no	—
141	C₂×Q₈×C₁₉	—	2	2	no	—
142	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
144	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
145	C₂×D₄×C₁₉	—	2	4	no	—
146	C₂×D₄×C₁₉	—	2	2	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₉	—	2	4	no	—
150	C₂²×C₄×C₁₉	—	2	8	no	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
156	Q₁₆×C₁₉	—	2	4	no	—
157	Q₁₆×C₁₉	—	4	2	no	—
158	SD₁₆×C₁₉	—	4	8	no	—
159	D₈×C₁₉	—	2	4	no	—
160	D₈×C₁₉	—	4	2	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₂×C₈×C₁₉	—	4	1	no	—
163	C₂×C₈×C₁₉	—	4	2	no	—
164	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
165	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
166	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
167	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
168	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	8	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	4	no	—
173	C₄⋊C₄×C₁₉	—	2	8	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	4	no	—
177	C₄⋊C₄×C₁₉	—	2	8	no	—
178	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
179	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
181	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
182	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
183	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
184	C₂²⋊C₄×C₁₉	—	2	4	no	—
185	C₂²⋊C₄×C₁₉	—	2	4	no	—
186	C₂²⋊C₄×C₁₉	—	2	8	no	—
187	C₂²⋊C₄×C₁₉	—	2	8	no	—
188	C₂²⋊C₄×C₁₉	—	2	4	no	—
189	C₂²⋊C₄×C₁₉	—	2	8	no	—
190	C₄²×C₁₉	—	2	8	no	—
191	C₄²×C₁₉	—	2	4	no	—
192	C₄²×C₁₉	C₂×D₄	1	4	yes	—
193	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
196	C₄²×C₁₉	C₂⁴	1	4	yes	—
197	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
198	#62361	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂³×C₁₉	—	2	4	no	—
200	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₁₉	—	2	4	no	—
202	Q₈×C₁₉	—	2	4	no	—
203	Q₈×C₁₉	—	2	4	no	—
204	Q₈×C₁₉	—	2	4	no	—
205	Q₈×C₁₉	—	4	4	no	—
206	Q₈×C₁₉	—	8	2	no	—
207	D₄×C₁₉	—	2	4	no	—
208	D₄×C₁₉	—	2	4	no	—
209	D₄×C₁₉	—	4	8	no	—
210	D₄×C₁₉	—	4	4	no	—
211	D₄×C₁₉	—	8	2	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	2	4	no	—
217	C₂×C₄×C₁₉	—	2	4	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	8	no	—
221	C₂×C₄×C₁₉	—	8	8	no	—
222	C₂×C₄×C₁₉	#135	1	4	yes	—
223	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
224	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
226	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
231	C₈×C₁₉	—	2	1	no	—
232	C₈×C₁₉	—	2	1	no	—
233	C₈×C₁₉	—	2	4	no	—
234	C₈×C₁₉	—	2	1	no	—
235	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
236	#3507	C₂×C₁₉	1	2	yes	complemented
237	#3396	C₂×C₁₉	1	2	yes	complemented
238	#3393	C₂×C₁₉	1	2	yes	complemented
239	#3383	C₂×C₁₉	1	2	yes	complemented
240	#3380	C₂×C₁₉	1	2	yes	complemented
241	#3365	C₂×C₁₉	1	4	yes	complemented
242	#3360	C₂×C₁₉	1	4	yes	complemented
243	#3250	C₂×C₁₉	1	4	yes	complemented
244	#3246	C₂×C₁₉	1	2	yes	complemented
245	#3170	C₂×C₁₉	1	1	yes	characteristic, complemented
246	#3169	C₂×C₁₉	1	1	yes	characteristic
247	#3168	C₂×C₁₉	1	4	yes	complemented
248	C₂×C₈×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
249	C₂²×C₁₉	—	2	1	no	—
250	C₂²×C₁₉	—	2	1	no	—
251	C₂²×C₁₉	—	4	4	no	—
252	C₂²×C₁₉	—	4	4	no	—
253	C₂²×C₁₉	—	4	4	no	—
254	C₂²×C₁₉	C₂×#135	1	2	yes	—
255	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
256	C₄×C₁₉	—	2	4	no	—
257	C₄×C₁₉	—	2	1	no	—
258	C₄×C₁₉	—	2	1	no	—
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	4	no	—
261	C₄×C₁₉	—	4	4	no	—
262	C₄×C₁₉	—	4	4	no	—
263	C₄×C₁₉	—	4	4	no	—
264	C₄×C₁₉	C₂×#135	1	2	yes	—
265	C₄×C₁₉	C₂×#135	1	2	yes	—
266	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
267	C₄×C₁₉	#585	1	1	yes	characteristic
268	#559	C₂²×C₁₉	1	4	yes	—
269	#557	C₂²×C₁₉	1	4	yes	—
270	#556	—	2	4	no	—
271	#556	C₂²×C₁₉	1	4	yes	—
272	#554	C₂²×C₁₉	1	4	yes	—
273	#552	—	2	4	no	—
274	#539	—	2	4	no	—
275	#536	—	2	2	no	—
276	#533	C₂²×C₁₉	1	2	yes	—
277	#532	C₂²×C₁₉	1	2	yes	—
278	#529	C₂²×C₁₉	1	8	yes	—
279	#520	—	2	2	no	—
280	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
281	#500	C₂²×C₁₉	1	1	yes	characteristic
282	#500	C₂²×C₁₉	1	1	yes	characteristic
283	#499	C₂²×C₁₉	1	4	yes	—
284	#495	C₂²×C₁₉	1	4	yes	—
285	#494	C₂²×C₁₉	1	1	yes	characteristic
286	#493	C₂²×C₁₉	1	1	yes	characteristic
287	#488	C₂²×C₁₉	1	8	yes	—
288	#487	C₂²×C₁₉	1	2	yes	—
289	#486	C₂²×C₁₉	1	2	yes	—
290	#479	C₂²×C₁₉	1	8	yes	—
291	#478	C₂²×C₁₉	1	8	yes	—
292	#476	C₂²×C₁₉	1	4	yes	—
293	#475	C₂²×C₁₉	1	4	yes	—
294	#467	C₂²×C₁₉	1	2	yes	—
295	#467	C₂²×C₁₉	1	2	yes	—
296	#466	C₂²×C₁₉	1	2	yes	—
297	#466	C₂²×C₁₉	1	2	yes	—
298	#465	C₂²×C₁₉	1	8	yes	—
299	#464	C₂²×C₁₉	1	8	yes	—
300	#463	C₂²×C₁₉	1	8	yes	—
301	#461	C₂²×C₁₉	1	4	yes	—
302	#460	C₂²×C₁₉	1	4	yes	—
303	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
304	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
305	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
306	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
307	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
308	C₄×Q₁₆	C₂²×C₁₉	1	4	yes	—
309	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
310	C₄×SD₁₆	C₂²×C₁₉	1	8	yes	—
311	C₄×D₈	C₂²×C₁₉	1	2	yes	—
312	C₄×D₈	C₂²×C₁₉	1	2	yes	—
313	C₄×D₈	C₂²×C₁₉	1	4	yes	—
314	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
316	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
317	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×C₁₉	—	2	2	no	—
319	C₂×C₁₉	—	8	4	no	—
320	C₂×C₁₉	#3497	1	1	yes	characteristic
321	C₂×C₁₉	C₂²×#135	1	1	yes	characteristic
322	C₂×C₁₉	#3584	1	1	yes	characteristic
323	C₂×#41	—	2	2	no	—
324	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
325	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
326	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
327	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
328	C₂×D₈	C₂³×C₁₉	1	2	yes	—
329	C₂×D₈	C₂³×C₁₉	1	2	yes	—
330	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
332	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
333	C₄⋊Q₈	—	2	4	no	—
334	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
335	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
336	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
337	#127	C₂³×C₁₉	1	2	yes	—
338	#126	—	2	8	no	—
339	#126	—	2	8	no	—
340	#125	—	2	8	no	—
341	#125	—	2	2	no	—
342	#125	C₂³×C₁₉	1	8	yes	—
343	#124	—	2	4	no	—
344	#124	—	2	2	no	—
345	#124	C₂³×C₁₉	1	8	yes	—
346	#123	—	2	8	no	—
347	#123	—	2	8	no	—
348	C₂²⋊Q₈	—	2	4	no	—
349	C₂²⋊Q₈	—	2	4	no	—
350	C₂²⋊Q₈	—	2	2	no	—
351	C₂²⋊Q₈	—	2	8	no	—
352	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
353	#121	—	2	2	no	—
354	#121	C₂³×C₁₉	1	4	yes	—
355	C₄×Q₈	—	2	4	no	—
356	C₄×Q₈	—	2	2	no	—
357	C₄×Q₈	D₄×C₁₉	1	2	yes	—
358	C₄×Q₈	D₄×C₁₉	1	2	yes	—
359	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
360	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
361	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
362	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
363	C₄×D₄	—	2	8	no	—
364	C₄×D₄	—	2	4	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	C₂³×C₁₉	1	8	yes	—
367	C₄×D₄	C₂³×C₁₉	1	4	yes	—
368	#117	—	2	2	no	—
369	#117	—	2	4	no	—
370	#117	—	2	8	no	—
371	C₂×C₄⋊C₄	—	2	4	no	—
372	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
373	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
374	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
375	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
376	#107	C₂³×C₁₉	1	2	yes	—
377	#107	C₂³×C₁₉	1	2	yes	—
378	#107	C₂³×C₁₉	1	2	yes	—
379	#107	C₂³×C₁₉	1	2	yes	—
380	#106	C₂³×C₁₉	1	8	yes	—
381	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
382	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
383	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
384	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
385	#103	C₂³×C₁₉	1	4	yes	—
386	#103	C₂³×C₁₉	1	8	yes	—
387	#103	C₂³×C₁₉	1	4	yes	—
388	#102	C₂³×C₁₉	1	4	yes	—
389	#102	C₂³×C₁₉	1	8	yes	—
390	#102	C₂³×C₁₉	1	4	yes	—
391	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
392	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
393	C₄×C₈	C₂³×C₁₉	1	4	yes	—
394	C₄×C₈	C₂³×C₁₉	1	4	yes	—
395	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
396	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
397	C₁₉	#62361	1	1	yes	characteristic, direct product factor, Sylow
398	#41	—	4	8	no	—
399	C₂×Q₈	—	2	4	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
403	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
404	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	8	no	—
411	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
415	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
416	Q₁₆	—	2	4	no	—
417	Q₁₆	—	4	2	no	—
418	SD₁₆	—	4	8	no	—
419	D₈	—	2	4	no	—
420	D₈	—	4	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	4	1	no	—
423	C₂×C₈	—	4	2	no	—
424	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
425	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
426	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
427	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
428	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	8	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	8	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	8	no	—
438	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
439	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
440	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
441	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
442	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
443	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	—	2	8	no	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	8	no	—
450	C₄²	—	2	8	no	—
451	C₄²	—	2	4	no	—
452	C₄²	C₂×D₄×C₁₉	1	4	yes	—
453	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
456	C₄²	C₂⁴×C₁₉	1	4	yes	—
457	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
458	C₂³	—	2	4	no	—
459	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
460	Q₈	—	2	4	no	—
461	Q₈	—	2	4	no	—
462	Q₈	—	2	4	no	—
463	Q₈	—	2	4	no	—
464	Q₈	—	4	4	no	—
465	Q₈	—	8	2	no	—
466	D₄	—	2	4	no	—
467	D₄	—	2	4	no	—
468	D₄	—	4	8	no	—
469	D₄	—	4	4	no	—
470	D₄	—	8	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	8	no	—
480	C₂×C₄	—	8	8	no	—
481	C₂×C₄	C₁₉×#135	1	4	yes	—
482	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
483	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
485	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
489	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
490	C₈	—	2	1	no	—
491	C₈	—	2	1	no	—
492	C₈	—	2	4	no	—
493	C₈	—	2	1	no	—
494	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	4	no	—
500	C₂²	C₂×C₁₉×#135	1	2	yes	—
501	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
502	C₄	—	2	1	no	—
503	C₄	—	2	4	no	—
504	C₄	—	2	4	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	4	4	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	4	no	—
510	C₄	C₂×C₁₉×#135	1	2	yes	—
511	C₄	C₂×C₁₉×#135	1	2	yes	—
512	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
513	C₄	C₁₉×#585	1	1	yes	characteristic
514	C₂	—	2	2	no	—
515	C₂	—	8	4	no	—
516	C₂	C₁₉×#3497	1	1	yes	characteristic
517	C₂	C₂²×C₁₉×#135	1	1	yes	characteristic
518	C₂	C₁₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3169	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3507	C₂	semidirect
2. C₁₉×#3396	C₂	semidirect
3. C₁₉×#3393	C₂	semidirect
4. C₁₉×#3383	C₂	semidirect
5. C₁₉×#3380	C₂	semidirect
6. C₁₉×#3365	C₂	semidirect
7. C₁₉×#3360	C₂	semidirect
8. C₁₉×#3250	C₂	semidirect
9. C₁₉×#3246	C₂	semidirect
10. C₁₉×#3170	C₂	semidirect
12. C₁₉×#3168	C₂	semidirect
13. C₂×C₈×Q₈×C₁₉	C₂	semidirect
198. #62361	C₁₉	direct (N × H)
236. #3507	C₂×C₁₉	semidirect
237. #3396	C₂×C₁₉	semidirect
238. #3393	C₂×C₁₉	semidirect
239. #3383	C₂×C₁₉	semidirect
240. #3380	C₂×C₁₉	semidirect
241. #3365	C₂×C₁₉	semidirect
242. #3360	C₂×C₁₉	semidirect
243. #3250	C₂×C₁₉	semidirect
244. #3246	C₂×C₁₉	semidirect
245. #3170	C₂×C₁₉	semidirect
247. #3168	C₂×C₁₉	semidirect
248. C₂×C₈×Q₈	C₂×C₁₉	semidirect
397. C₁₉	#62361	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×#3507	2
C₁₉×#3396	2
C₁₉×#3393	2
C₁₉×#3383	2
C₁₉×#3380	2
C₁₉×#3365	2
C₁₉×#3360	2
C₁₉×#3250	2
C₁₉×#3246	2
C₁₉×#3170	2
C₁₉×#3169	2
C₁₉×#3168	2
C₂×C₈×Q₈×C₁₉	2
#62361	19

Subgroups — C19×#62361 #18068320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62361 #18068320