Subgroups — C₁₉×#61372 #18067331

Order 4864.

1682 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3502	C₂	1	2	yes	maximal
2	C₁₉×#3390	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3387	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3383	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3383	C₂	1	4	yes	maximal, complemented
6	Q₈×Q₁₆×C₁₉	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3164	C₂	1	2	yes	maximal
8	C₁₉×#3160	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#3082	C₂	1	4	yes	maximal
10	C₁₉×#3078	C₂	1	2	yes	maximal
11	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#2950	C₂	1	2	yes	maximal
13	C₂×C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
14	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	Q₈²×C₁₉	—	2	2	no	—
16	Q₈²×C₁₉	C₂²	1	4	yes	—
17	C₁₉×#557	—	2	2	no	—
18	C₁₉×#557	—	2	4	no	—
19	C₁₉×#557	C₂²	1	4	yes	—
20	C₁₉×#557	C₂²	1	8	yes	—
21	C₁₉×#544	—	2	4	no	—
22	C₁₉×#544	C₂²	1	4	yes	—
23	C₁₉×#533	—	2	4	no	—
24	C₁₉×#533	C₂²	1	2	yes	—
25	C₁₉×#533	C₂²	1	1	yes	characteristic
26	C₁₉×#519	C₂²	1	4	yes	—
27	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
28	C₁₉×#501	C₂²	1	8	yes	—
29	C₁₉×#500	C₂²	1	1	yes	characteristic
30	C₁₉×#500	C₂²	1	4	yes	—
31	C₁₉×#500	C₂²	1	1	yes	characteristic
32	C₁₉×#499	C₂²	1	2	yes	—
33	C₁₉×#499	C₂²	1	4	yes	—
34	C₁₉×#499	C₂²	1	2	yes	—
35	C₁₉×#498	C₂²	1	2	yes	—
36	C₁₉×#479	C₂²	1	8	yes	—
37	C₁₉×#479	C₂²	1	8	yes	—
38	C₁₉×#479	C₂²	1	8	yes	—
39	C₁₉×#477	C₂²	1	4	yes	—
40	C₁₉×#477	C₂²	1	8	yes	—
41	C₁₉×#475	C₂²	1	4	yes	—
42	C₁₉×#475	C₂²	1	8	yes	—
43	C₁₉×#446	C₂²	1	2	yes	—
44	C₁₉×#446	C₂²	1	2	yes	—
45	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
46	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
47	C₁₉×#441	C₂²	1	8	yes	—
48	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
49	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
50	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
51	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
52	C₄×Q₁₆×C₁₉	C₂²	1	4	yes	—
53	C₄×Q₁₆×C₁₉	C₂²	1	4	yes	—
54	C₁₉×#428	C₂²	1	4	yes	—
55	C₁₉×#427	C₂²	1	2	yes	—
56	C₁₉×#427	C₂²	1	2	yes	—
57	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
58	C₁₉×#424	C₂²	1	2	yes	—
59	C₁₉×#423	C₂²	1	1	yes	characteristic
60	C₁₉×#419	C₂²	1	4	yes	—
61	C₂×C₁₉×#103	C₂²	1	2	yes	—
62	C₁₉×#405	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
64	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
65	C₂×Q₁₆×C₁₉	Q₈	1	8	yes	complemented
66	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
67	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
68	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₁₉×C₄⋊Q₈	—	2	4	no	—
72	C₁₉×C₄⋊Q₈	—	2	8	no	—
73	C₁₉×C₄⋊Q₈	—	2	4	no	—
74	C₁₉×C₄⋊Q₈	—	2	8	no	—
75	C₁₉×C₄⋊Q₈	—	2	4	no	—
76	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
77	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
78	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
79	C₁₉×C₄⋊Q₈	C₂³	1	8	yes	—
80	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
81	C₁₉×#125	—	2	8	no	—
82	C₁₉×#125	—	2	8	no	—
83	C₁₉×#125	—	2	8	no	—
84	C₁₉×#125	—	2	4	no	—
85	C₁₉×#125	D₄	1	2	yes	—
86	C₁₉×#125	C₂³	1	4	yes	—
87	C₁₉×#125	C₂³	1	8	yes	—
88	C₁₉×C₂²⋊Q₈	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×C₂²⋊Q₈	—	2	8	no	—
91	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
92	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
93	C₄×Q₈×C₁₉	—	2	4	no	—
94	C₄×Q₈×C₁₉	—	2	4	no	—
95	C₄×Q₈×C₁₉	—	2	4	no	—
96	C₄×Q₈×C₁₉	—	2	8	no	—
97	C₄×Q₈×C₁₉	—	2	4	no	—
98	C₄×Q₈×C₁₉	—	2	2	no	—
99	C₄×Q₈×C₁₉	—	2	2	no	—
100	C₄×Q₈×C₁₉	—	2	2	no	—
101	C₄×Q₈×C₁₉	—	2	2	no	—
102	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
103	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
104	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
105	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
106	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
107	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
108	C₁₉×#117	—	2	8	no	—
109	C₁₉×#117	C₂³	1	4	yes	—
110	C₁₉×#117	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₉	—	2	2	no	—
114	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
115	C₁₉×#107	C₂³	1	2	yes	—
116	C₁₉×#107	C₂³	1	2	yes	—
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×#107	C₂³	1	8	yes	—
122	C₁₉×#106	C₂³	1	4	yes	—
123	C₁₉×#106	C₂³	1	4	yes	—
124	C₁₉×#106	C₂³	1	8	yes	—
125	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
126	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
127	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
128	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
129	C₁₉×#103	C₂³	1	4	yes	—
130	C₁₉×#103	C₂³	1	4	yes	—
131	C₁₉×#103	C₂³	1	8	yes	—
132	C₁₉×#103	C₂³	1	8	yes	—
133	C₁₉×#97	C₂³	1	4	yes	—
134	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
135	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
136	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₁₉	C₂³	1	4	yes	—
139	C₂×Q₈×C₁₉	—	2	2	no	—
140	C₂×Q₈×C₁₉	—	2	2	no	—
141	C₂×Q₈×C₁₉	—	2	2	no	—
142	C₂×Q₈×C₁₉	—	2	8	no	—
143	C₂×Q₈×C₁₉	—	2	4	no	—
144	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
145	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
146	C₂×Q₈×C₁₉	C₂×Q₈	1	8	yes	—
147	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
153	Q₁₆×C₁₉	C₂×Q₈	1	8	yes	—
154	Q₁₆×C₁₉	C₂×Q₈	1	8	yes	—
155	M₁₆×C₁₉	—	2	4	no	—
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₂×C₈×C₁₉	C₂×Q₈	1	4	yes	—
158	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
159	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
160	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
161	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
162	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
163	C₄⋊C₄×C₁₉	—	2	4	no	—
164	C₄⋊C₄×C₁₉	—	2	4	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	8	no	—
167	C₄⋊C₄×C₁₉	—	2	8	no	—
168	C₄⋊C₄×C₁₉	—	2	4	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	8	no	—
172	C₄⋊C₄×C₁₉	—	2	8	no	—
173	C₄⋊C₄×C₁₉	—	2	4	no	—
174	C₄⋊C₄×C₁₉	—	2	8	no	—
175	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
176	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
177	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
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	C₂⁴	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	C₂×D₄	1	4	yes	—
186	C₄²×C₁₉	—	2	4	no	—
187	C₄²×C₁₉	—	2	4	no	—
188	C₄²×C₁₉	—	2	8	no	—
189	C₄²×C₁₉	—	2	8	no	—
190	C₄²×C₁₉	—	2	4	no	—
191	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
194	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
195	C₄²×C₁₉	C₂⁴	1	4	yes	—
196	#61372	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₁₉	—	2	8	no	—
199	Q₈×C₁₉	—	2	4	no	—
200	Q₈×C₁₉	—	2	4	no	—
201	Q₈×C₁₉	—	4	2	no	—
202	Q₈×C₁₉	—	4	4	no	—
203	Q₈×C₁₉	—	8	2	no	—
204	Q₈×C₁₉	—	8	8	no	—
205	Q₈×C₁₉	C₂²×Q₈	1	8	yes	—
206	C₂×C₄×C₁₉	—	2	8	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	4	no	—
210	C₂×C₄×C₁₉	—	2	4	no	—
211	C₂×C₄×C₁₉	—	2	4	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	8	2	no	—
214	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
216	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
217	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
222	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
223	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
224	C₈×C₁₉	—	2	1	no	—
225	C₈×C₁₉	—	2	1	no	—
226	C₈×C₁₉	—	2	4	no	—
227	C₈×C₁₉	C₂²×Q₈	1	2	yes	—
228	C₈×C₁₉	C₂²×Q₈	1	2	yes	—
229	#3502	C₂×C₁₉	1	2	yes	—
230	#3390	C₂×C₁₉	1	4	yes	complemented
231	#3387	C₂×C₁₉	1	4	yes	complemented
232	#3383	C₂×C₁₉	1	2	yes	complemented
233	#3383	C₂×C₁₉	1	4	yes	complemented
234	Q₈×Q₁₆	C₂×C₁₉	1	2	yes	complemented
235	#3164	C₂×C₁₉	1	2	yes	—
236	#3160	C₂×C₁₉	1	1	yes	characteristic
237	#3082	C₂×C₁₉	1	4	yes	—
238	#3078	C₂×C₁₉	1	2	yes	—
239	#2960	C₂×C₁₉	1	1	yes	characteristic
240	#2950	C₂×C₁₉	1	2	yes	—
241	C₂×C₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic
242	C₂²×C₁₉	—	2	1	no	—
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	D₄×Q₈	1	2	yes	—
245	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
246	C₄×C₁₉	—	2	1	no	—
247	C₄×C₁₉	—	2	1	no	—
248	C₄×C₁₉	—	2	4	no	—
249	C₄×C₁₉	—	2	8	no	—
250	C₄×C₁₉	—	2	1	no	—
251	C₄×C₁₉	—	2	4	no	—
252	C₄×C₁₉	—	4	4	no	—
253	C₄×C₁₉	—	4	4	no	—
254	C₄×C₁₉	—	4	4	no	—
255	C₄×C₁₉	D₄×Q₈	1	2	yes	—
256	C₄×C₁₉	#578	1	2	yes	—
257	C₄×C₁₉	C₂³×Q₈	1	1	yes	characteristic
258	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
259	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
260	Q₈²	—	2	2	no	—
261	Q₈²	C₂²×C₁₉	1	4	yes	—
262	#557	—	2	2	no	—
263	#557	—	2	4	no	—
264	#557	C₂²×C₁₉	1	4	yes	—
265	#557	C₂²×C₁₉	1	8	yes	—
266	#544	—	2	4	no	—
267	#544	C₂²×C₁₉	1	4	yes	—
268	#533	—	2	4	no	—
269	#533	C₂²×C₁₉	1	2	yes	—
270	#533	C₂²×C₁₉	1	1	yes	characteristic
271	#519	C₂²×C₁₉	1	4	yes	—
272	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
273	#501	C₂²×C₁₉	1	8	yes	—
274	#500	C₂²×C₁₉	1	1	yes	characteristic
275	#500	C₂²×C₁₉	1	4	yes	—
276	#500	C₂²×C₁₉	1	1	yes	characteristic
277	#499	C₂²×C₁₉	1	2	yes	—
278	#499	C₂²×C₁₉	1	4	yes	—
279	#499	C₂²×C₁₉	1	2	yes	—
280	#498	C₂²×C₁₉	1	2	yes	—
281	#479	C₂²×C₁₉	1	8	yes	—
282	#479	C₂²×C₁₉	1	8	yes	—
283	#479	C₂²×C₁₉	1	8	yes	—
284	#477	C₂²×C₁₉	1	4	yes	—
285	#477	C₂²×C₁₉	1	8	yes	—
286	#475	C₂²×C₁₉	1	4	yes	—
287	#475	C₂²×C₁₉	1	8	yes	—
288	#446	C₂²×C₁₉	1	2	yes	—
289	#446	C₂²×C₁₉	1	2	yes	—
290	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
291	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
292	#441	C₂²×C₁₉	1	8	yes	—
293	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
294	C₄×Q₁₆	C₂²×C₁₉	1	4	yes	—
295	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
296	C₄×Q₁₆	C₂²×C₁₉	1	4	yes	—
297	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
298	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
299	#428	C₂²×C₁₉	1	4	yes	—
300	#427	C₂²×C₁₉	1	2	yes	—
301	#427	C₂²×C₁₉	1	2	yes	—
302	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
303	#424	C₂²×C₁₉	1	2	yes	—
304	#423	C₂²×C₁₉	1	1	yes	characteristic
305	#419	C₂²×C₁₉	1	4	yes	—
306	C₂×#103	C₂²×C₁₉	1	2	yes	—
307	#405	C₂²×C₁₉	1	2	yes	—
308	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
309	C₂×C₁₉	—	2	2	no	—
310	C₂×C₁₉	C₂×D₄×Q₈	1	1	yes	characteristic
311	C₂×C₁₉	C₂×#578	1	1	yes	characteristic
312	C₂×C₁₉	#3584	1	1	yes	characteristic
313	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
314	C₂×Q₁₆	Q₈×C₁₉	1	8	yes	complemented
315	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
316	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
317	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
318	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
320	C₄⋊Q₈	—	2	4	no	—
321	C₄⋊Q₈	—	2	8	no	—
322	C₄⋊Q₈	—	2	4	no	—
323	C₄⋊Q₈	—	2	8	no	—
324	C₄⋊Q₈	—	2	4	no	—
325	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
326	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
327	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
328	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
329	C₄⋊Q₈	C₂³×C₁₉	1	8	yes	—
330	#125	—	2	8	no	—
331	#125	—	2	8	no	—
332	#125	—	2	8	no	—
333	#125	—	2	4	no	—
334	#125	D₄×C₁₉	1	2	yes	—
335	#125	C₂³×C₁₉	1	4	yes	—
336	#125	C₂³×C₁₉	1	8	yes	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	—	2	2	no	—
339	C₂²⋊Q₈	—	2	8	no	—
340	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
341	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
342	C₄×Q₈	—	2	4	no	—
343	C₄×Q₈	—	2	4	no	—
344	C₄×Q₈	—	2	4	no	—
345	C₄×Q₈	—	2	8	no	—
346	C₄×Q₈	—	2	4	no	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	—	2	2	no	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
352	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
353	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
354	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
355	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
356	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
357	#117	—	2	8	no	—
358	#117	C₂³×C₁₉	1	4	yes	—
359	#117	C₂³×C₁₉	1	2	yes	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
362	C₂×C₄²	—	2	2	no	—
363	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
364	#107	C₂³×C₁₉	1	2	yes	—
365	#107	C₂³×C₁₉	1	2	yes	—
366	#107	C₂³×C₁₉	1	2	yes	—
367	#107	C₂³×C₁₉	1	2	yes	—
368	#107	C₂³×C₁₉	1	2	yes	—
369	#107	C₂³×C₁₉	1	2	yes	—
370	#107	C₂³×C₁₉	1	8	yes	—
371	#106	C₂³×C₁₉	1	4	yes	—
372	#106	C₂³×C₁₉	1	4	yes	—
373	#106	C₂³×C₁₉	1	8	yes	—
374	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
375	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
376	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
377	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
378	#103	C₂³×C₁₉	1	4	yes	—
379	#103	C₂³×C₁₉	1	4	yes	—
380	#103	C₂³×C₁₉	1	8	yes	—
381	#103	C₂³×C₁₉	1	8	yes	—
382	#97	C₂³×C₁₉	1	4	yes	—
383	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
384	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
385	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
386	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
387	C₄×C₈	C₂³×C₁₉	1	4	yes	—
388	C₁₉	#61372	1	1	yes	characteristic, direct product factor, Sylow
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	8	no	—
393	C₂×Q₈	—	2	4	no	—
394	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
395	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
396	C₂×Q₈	C₂×Q₈×C₁₉	1	8	yes	—
397	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
402	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
403	Q₁₆	C₂×Q₈×C₁₉	1	8	yes	—
404	Q₁₆	C₂×Q₈×C₁₉	1	8	yes	—
405	M₁₆	—	2	4	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	C₂×Q₈×C₁₉	1	4	yes	—
408	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
409	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
410	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
411	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
412	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	8	no	—
422	C₄⋊C₄	—	2	8	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	8	no	—
425	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
426	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
427	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
428	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
429	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
430	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
431	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
432	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
433	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
436	C₄²	—	2	4	no	—
437	C₄²	—	2	4	no	—
438	C₄²	—	2	8	no	—
439	C₄²	—	2	8	no	—
440	C₄²	—	2	4	no	—
441	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
444	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
445	C₄²	C₂⁴×C₁₉	1	4	yes	—
446	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
447	Q₈	—	2	8	no	—
448	Q₈	—	2	4	no	—
449	Q₈	—	2	4	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	4	4	no	—
452	Q₈	—	8	2	no	—
453	Q₈	—	8	8	no	—
454	Q₈	C₂²×Q₈×C₁₉	1	8	yes	—
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	8	2	no	—
463	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
465	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
466	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
470	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
471	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
472	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
473	C₈	—	2	1	no	—
474	C₈	—	2	1	no	—
475	C₈	—	2	4	no	—
476	C₈	C₂²×Q₈×C₁₉	1	2	yes	—
477	C₈	C₂²×Q₈×C₁₉	1	2	yes	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	D₄×Q₈×C₁₉	1	2	yes	—
481	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
482	C₄	—	2	8	no	—
483	C₄	—	2	1	no	—
484	C₄	—	2	4	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	4	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	4	no	—
491	C₄	D₄×Q₈×C₁₉	1	2	yes	—
492	C₄	C₁₉×#578	1	2	yes	—
493	C₄	C₂³×Q₈×C₁₉	1	1	yes	characteristic
494	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
495	C₂	—	2	2	no	—
496	C₂	C₂×D₄×Q₈×C₁₉	1	1	yes	characteristic
497	C₂	C₂×C₁₉×#578	1	1	yes	characteristic
498	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	C₂³×C₁₉	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3390	C₂	semidirect
3. C₁₉×#3387	C₂	semidirect
4. C₁₉×#3383	C₂	semidirect
5. C₁₉×#3383	C₂	semidirect
6. Q₈×Q₁₆×C₁₉	C₂	semidirect
65. C₂×Q₁₆×C₁₉	Q₈	semidirect
196. #61372	C₁₉	direct (N × H)
230. #3390	C₂×C₁₉	semidirect
231. #3387	C₂×C₁₉	semidirect
232. #3383	C₂×C₁₉	semidirect
233. #3383	C₂×C₁₉	semidirect
234. Q₈×Q₁₆	C₂×C₁₉	semidirect
314. C₂×Q₁₆	Q₈×C₁₉	semidirect
388. C₁₉	#61372	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×#3502	2
C₁₉×#3390	2
C₁₉×#3387	2
C₁₉×#3383	2
Q₈×Q₁₆×C₁₉	2
C₁₉×#3164	2
C₁₉×#3160	2
C₁₉×#3082	2
C₁₉×#3078	2
C₁₉×#2960	2
C₁₉×#2950	2
C₂×C₄×Q₁₆×C₁₉	2
#61372	19

Subgroups — C19×#61372 #18067331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61372 #18067331