Subgroups — C₁₉×#23082 #18029041

Order 4864.

646 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3076	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2925	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1938	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1937	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1929	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1929	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1922	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1922	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1773	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1772	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1768	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1759	C₂	1	1	yes	maximal, characteristic
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#479	C₄	1	1	yes	characteristic, complemented
19	C₁₉×#479	C₄	1	1	yes	characteristic, complemented
20	C₁₉×#478	C₄	1	1	yes	characteristic, complemented
21	C₁₉×#478	C₄	1	1	yes	characteristic, complemented
22	C₁₉×#477	C₄	1	1	yes	characteristic, complemented
23	C₁₉×#476	C₄	1	1	yes	characteristic, complemented
24	C₁₉×#475	C₄	1	1	yes	characteristic, complemented
25	C₁₉×#474	C₄	1	1	yes	characteristic, complemented
26	C₁₉×#446	—	2	1	no	—
27	C₁₉×#446	—	2	1	no	—
28	C₁₉×#446	—	2	1	no	—
29	C₈×Q₈×C₁₉	—	2	1	no	—
30	C₁₉×#433	—	2	1	no	—
31	C₁₉×#433	—	2	1	no	—
32	C₁₉×#432	—	2	1	no	—
33	C₁₉×#431	—	2	1	no	—
34	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
36	C₁₉×#427	C₂²	1	1	yes	characteristic
37	C₁₉×#427	C₂²	1	1	yes	characteristic
38	C₁₉×#424	C₂²	1	1	yes	characteristic
39	C₁₉×#424	C₂²	1	1	yes	characteristic
40	C₁₉×#423	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
45	C₁₉×#416	C₂²	1	1	yes	characteristic
46	C₁₉×#416	C₂²	1	1	yes	characteristic
47	C₁₉×#408	C₂²	1	1	yes	characteristic
48	C₁₉×#408	C₂²	1	1	yes	characteristic
49	C₁₉×#405	C₂²	1	1	yes	characteristic
50	C₁₉×#405	C₂²	1	1	yes	characteristic
51	C₁₉×#405	C₂²	1	1	yes	characteristic
52	C₁₉×#405	C₂²	1	1	yes	characteristic
53	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
56	C₁₉×#376	C₂²	1	1	yes	characteristic
57	C₁₉×#341	C₂²	1	1	yes	characteristic
58	C₁₉×#341	C₂²	1	1	yes	characteristic
59	C₁₉×#339	C₂²	1	1	yes	characteristic
60	C₁₉×#339	C₂²	1	1	yes	characteristic
61	C₁₉×#339	C₂²	1	1	yes	characteristic
62	C₁₉×#339	C₂²	1	1	yes	characteristic
63	C₁₉×#339	C₂²	1	1	yes	characteristic
64	C₁₉×#339	C₂²	1	1	yes	characteristic
65	C₁₉×#336	C₂²	1	1	yes	characteristic
66	C₁₉×#336	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
77	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
78	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
79	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	—	2	1	no	—
82	C₄×Q₈×C₁₉	—	2	1	no	—
83	C₄×Q₈×C₁₉	—	2	1	no	—
84	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
85	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
86	C₄×D₄×C₁₉	—	2	1	no	—
87	C₄×D₄×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
89	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
90	C₁₉×#117	—	2	1	no	—
91	C₁₉×#117	C₂³	1	1	yes	characteristic
92	C₁₉×#117	C₂³	1	1	yes	characteristic
93	C₁₉×#117	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₉	—	2	1	no	—
95	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₁₉×#108	—	2	2	no	—
99	C₁₉×#108	—	2	2	no	—
100	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
101	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
102	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
103	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
104	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
105	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
106	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
107	C₁₉×#106	C₂×C₄	1	1	yes	characteristic
108	C₁₉×C₄⋊C₈	—	2	1	no	—
109	C₁₉×C₄⋊C₈	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	2	1	no	—
111	C₁₉×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	—	2	1	no	—
113	C₁₉×C₄⋊C₈	—	2	1	no	—
114	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
115	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
118	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
122	C₁₉×#104	—	2	2	no	—
123	C₁₉×#104	—	2	2	no	—
124	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
125	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
126	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
127	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
128	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
129	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
130	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
131	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
132	C₁₉×C₂²⋊C₈	—	2	1	no	—
133	C₁₉×C₂²⋊C₈	—	2	1	no	—
134	C₁₉×C₂²⋊C₈	—	2	1	no	—
135	C₁₉×C₂²⋊C₈	—	2	1	no	—
136	C₁₉×#97	—	2	1	no	—
137	C₁₉×#97	—	2	1	no	—
138	C₁₉×#97	—	2	1	no	—
139	C₁₉×#97	—	2	1	no	—
140	C₁₉×#97	—	2	1	no	—
141	C₁₉×#97	—	2	2	no	—
142	C₄×C₈×C₁₉	—	2	1	no	—
143	C₄×C₈×C₁₉	—	2	1	no	—
144	C₄×C₈×C₁₉	—	2	1	no	—
145	C₄×C₈×C₁₉	—	2	1	no	—
146	C₄×C₈×C₁₉	—	2	1	no	—
147	C₄×C₈×C₁₉	—	2	2	no	—
148	C₁₉×#95	—	2	1	no	—
149	C₁₉×#95	—	2	1	no	—
150	#41×C₁₉	—	2	1	no	—
151	#41×C₁₉	—	2	1	no	—
152	#41×C₁₉	—	2	1	no	—
153	#41×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	2	1	no	—
156	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	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	#41	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
167	M₁₆×C₁₉	—	2	1	no	—
168	M₁₆×C₁₉	—	2	1	no	—
169	M₁₆×C₁₉	—	2	1	no	—
170	M₁₆×C₁₉	—	2	1	no	—
171	M₁₆×C₁₉	—	2	1	no	—
172	M₁₆×C₁₉	—	2	1	no	—
173	M₁₆×C₁₉	—	2	1	no	—
174	M₁₆×C₁₉	#41	1	2	yes	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×C₁₉	—	2	1	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	1	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₂×C₈×C₁₉	—	2	1	no	—
187	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
204	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
205	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
206	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
207	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
208	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
209	C₂²⋊C₄×C₁₉	—	2	1	no	—
210	C₂²⋊C₄×C₁₉	—	2	1	no	—
211	C₂²⋊C₄×C₁₉	—	2	1	no	—
212	C₂²⋊C₄×C₁₉	—	2	1	no	—
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₄²×C₁₉	—	2	1	no	—
215	C₄²×C₁₉	—	2	1	no	—
216	C₄²×C₁₉	—	2	1	no	—
217	C₄²×C₁₉	—	2	1	no	—
218	C₄²×C₁₉	—	2	1	no	—
219	C₄²×C₁₉	—	2	1	no	—
220	C₄²×C₁₉	—	2	1	no	—
221	C₄²×C₁₉	—	2	1	no	—
222	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
223	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
224	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₁₉	#41	1	2	yes	—
227	#23082	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂³×C₁₉	—	2	1	no	—
229	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
230	Q₈×C₁₉	—	2	1	no	—
231	Q₈×C₁₉	—	2	1	no	—
232	Q₈×C₁₉	—	4	2	no	—
233	Q₈×C₁₉	—	8	1	no	—
234	D₄×C₁₉	—	2	1	no	—
235	D₄×C₁₉	—	2	1	no	—
236	D₄×C₁₉	—	4	1	no	—
237	D₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	2	1	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	1	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	8	1	no	—
257	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
266	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
267	C₈×C₁₉	—	2	1	no	—
268	C₈×C₁₉	—	2	1	no	—
269	C₈×C₁₉	—	2	1	no	—
270	C₈×C₁₉	—	2	1	no	—
271	C₈×C₁₉	—	2	1	no	—
272	C₈×C₁₉	—	2	1	no	—
273	C₈×C₁₉	—	2	1	no	—
274	C₈×C₁₉	—	2	1	no	—
275	C₈×C₁₉	—	2	2	no	—
276	C₈×C₁₉	—	4	1	no	—
277	C₈×C₁₉	—	4	1	no	—
278	C₈×C₁₉	—	4	1	no	—
279	#3076	C₂×C₁₉	1	1	yes	characteristic
280	#2962	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#2925	C₂×C₁₉	1	1	yes	characteristic
282	#1995	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1950	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1938	C₂×C₁₉	1	1	yes	characteristic
285	#1937	C₂×C₁₉	1	1	yes	characteristic
286	#1929	C₂×C₁₉	1	1	yes	characteristic
287	#1929	C₂×C₁₉	1	1	yes	characteristic
288	#1922	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1922	C₂×C₁₉	1	1	yes	characteristic, complemented
290	#1773	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1772	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1768	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1759	C₂×C₁₉	1	1	yes	characteristic
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	4	1	no	—
297	C₂²×C₁₉	—	4	1	no	—
298	C₂²×C₁₉	—	4	1	no	—
299	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
300	C₂²×C₁₉	#552	1	1	yes	characteristic
301	C₂²×C₁₉	#556	1	1	yes	characteristic
302	C₄×C₁₉	—	2	1	no	—
303	C₄×C₁₉	—	2	1	no	—
304	C₄×C₁₉	—	2	1	no	—
305	C₄×C₁₉	—	2	1	no	—
306	C₄×C₁₉	—	4	2	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	4	1	no	—
309	C₄×C₁₉	—	4	1	no	—
310	C₄×C₁₉	—	4	1	no	—
311	C₄×C₁₉	—	4	1	no	—
312	C₄×C₁₉	—	4	1	no	—
313	C₄×C₁₉	—	4	1	no	—
314	C₄×C₁₉	—	8	1	no	—
315	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
316	C₄×C₁₉	#519	1	1	yes	characteristic
317	C₄×C₁₉	#547	1	1	yes	characteristic
318	C₄×C₁₉	#548	1	1	yes	characteristic
319	#533	C₂²×C₁₉	1	1	yes	characteristic
320	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
321	#479	C₄×C₁₉	1	1	yes	characteristic, complemented
322	#479	C₄×C₁₉	1	1	yes	characteristic, complemented
323	#478	C₄×C₁₉	1	1	yes	characteristic, complemented
324	#478	C₄×C₁₉	1	1	yes	characteristic, complemented
325	#477	C₄×C₁₉	1	1	yes	characteristic, complemented
326	#476	C₄×C₁₉	1	1	yes	characteristic, complemented
327	#475	C₄×C₁₉	1	1	yes	characteristic, complemented
328	#474	C₄×C₁₉	1	1	yes	characteristic, complemented
329	#446	—	2	1	no	—
330	#446	—	2	1	no	—
331	#446	—	2	1	no	—
332	C₈×Q₈	—	2	1	no	—
333	#433	—	2	1	no	—
334	#433	—	2	1	no	—
335	#432	—	2	1	no	—
336	#431	—	2	1	no	—
337	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
339	#427	C₂²×C₁₉	1	1	yes	characteristic
340	#427	C₂²×C₁₉	1	1	yes	characteristic
341	#424	C₂²×C₁₉	1	1	yes	characteristic
342	#424	C₂²×C₁₉	1	1	yes	characteristic
343	#423	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
345	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
346	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
347	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
348	#416	C₂²×C₁₉	1	1	yes	characteristic
349	#416	C₂²×C₁₉	1	1	yes	characteristic
350	#408	C₂²×C₁₉	1	1	yes	characteristic
351	#408	C₂²×C₁₉	1	1	yes	characteristic
352	#405	C₂²×C₁₉	1	1	yes	characteristic
353	#405	C₂²×C₁₉	1	1	yes	characteristic
354	#405	C₂²×C₁₉	1	1	yes	characteristic
355	#405	C₂²×C₁₉	1	1	yes	characteristic
356	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
359	#376	C₂²×C₁₉	1	1	yes	characteristic
360	#341	C₂²×C₁₉	1	1	yes	characteristic
361	#341	C₂²×C₁₉	1	1	yes	characteristic
362	#339	C₂²×C₁₉	1	1	yes	characteristic
363	#339	C₂²×C₁₉	1	1	yes	characteristic
364	#339	C₂²×C₁₉	1	1	yes	characteristic
365	#339	C₂²×C₁₉	1	1	yes	characteristic
366	#339	C₂²×C₁₉	1	1	yes	characteristic
367	#339	C₂²×C₁₉	1	1	yes	characteristic
368	#336	C₂²×C₁₉	1	1	yes	characteristic
369	#336	C₂²×C₁₉	1	1	yes	characteristic
370	C₂×C₁₉	—	2	1	no	—
371	C₂×C₁₉	—	2	1	no	—
372	C₂×C₁₉	—	8	1	no	—
373	C₂×C₁₉	#2362	1	1	yes	characteristic
374	C₂×C₁₉	#2955	1	1	yes	characteristic
375	C₂×C₁₉	#2957	1	1	yes	characteristic
376	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
377	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
378	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
379	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
380	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
385	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
386	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
387	#125	C₂×C₄×C₁₉	1	1	yes	characteristic
388	#125	C₂×C₄×C₁₉	1	1	yes	characteristic
389	C₂²⋊Q₈	—	2	1	no	—
390	C₂²⋊Q₈	—	2	1	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	—	2	1	no	—
393	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
394	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
398	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
399	#117	—	2	1	no	—
400	#117	C₂³×C₁₉	1	1	yes	characteristic
401	#117	C₂³×C₁₉	1	1	yes	characteristic
402	#117	C₂³×C₁₉	1	1	yes	characteristic
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
407	#108	—	2	2	no	—
408	#108	—	2	2	no	—
409	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
410	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
411	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
412	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
413	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
414	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
415	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
416	#106	C₂×C₄×C₁₉	1	1	yes	characteristic
417	C₄⋊C₈	—	2	1	no	—
418	C₄⋊C₈	—	2	1	no	—
419	C₄⋊C₈	—	2	1	no	—
420	C₄⋊C₈	—	2	1	no	—
421	C₄⋊C₈	—	2	1	no	—
422	C₄⋊C₈	—	2	1	no	—
423	C₄⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
424	C₄⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
425	C₄⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
426	C₄⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
427	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
428	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
429	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
430	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
431	#104	—	2	2	no	—
432	#104	—	2	2	no	—
433	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
434	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
435	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
436	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
437	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
438	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
439	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
440	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
441	C₂²⋊C₈	—	2	1	no	—
442	C₂²⋊C₈	—	2	1	no	—
443	C₂²⋊C₈	—	2	1	no	—
444	C₂²⋊C₈	—	2	1	no	—
445	#97	—	2	1	no	—
446	#97	—	2	1	no	—
447	#97	—	2	1	no	—
448	#97	—	2	1	no	—
449	#97	—	2	1	no	—
450	#97	—	2	2	no	—
451	C₄×C₈	—	2	1	no	—
452	C₄×C₈	—	2	1	no	—
453	C₄×C₈	—	2	1	no	—
454	C₄×C₈	—	2	1	no	—
455	C₄×C₈	—	2	1	no	—
456	C₄×C₈	—	2	2	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	C₁₉	#23082	1	1	yes	characteristic, direct product factor, Sylow
460	#41	—	2	1	no	—
461	#41	—	2	1	no	—
462	#41	—	2	1	no	—
463	#41	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
475	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
476	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
477	M₁₆	—	2	1	no	—
478	M₁₆	—	2	1	no	—
479	M₁₆	—	2	1	no	—
480	M₁₆	—	2	1	no	—
481	M₁₆	—	2	1	no	—
482	M₁₆	—	2	1	no	—
483	M₁₆	—	2	1	no	—
484	M₁₆	#41×C₁₉	1	2	yes	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
498	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
499	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
500	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
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	C₂²×C₄×C₁₉	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
533	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
534	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
535	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
536	C₄²	#41×C₁₉	1	2	yes	—
537	C₂³	—	2	1	no	—
538	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
539	Q₈	—	2	1	no	—
540	Q₈	—	2	1	no	—
541	Q₈	—	4	2	no	—
542	Q₈	—	8	1	no	—
543	D₄	—	2	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	8	1	no	—
566	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
567	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
568	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
569	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
570	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
571	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
572	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
573	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
574	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
575	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
576	C₈	—	2	1	no	—
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	2	1	no	—
580	C₈	—	2	1	no	—
581	C₈	—	2	1	no	—
582	C₈	—	2	1	no	—
583	C₈	—	2	1	no	—
584	C₈	—	2	2	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
594	C₂²	C₁₉×#552	1	1	yes	characteristic
595	C₂²	C₁₉×#556	1	1	yes	characteristic
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	8	1	no	—
609	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
610	C₄	C₁₉×#519	1	1	yes	characteristic
611	C₄	C₁₉×#547	1	1	yes	characteristic
612	C₄	C₁₉×#548	1	1	yes	characteristic
613	C₂	—	2	1	no	—
614	C₂	—	2	1	no	—
615	C₂	—	8	1	no	—
616	C₂	C₁₉×#2362	1	1	yes	characteristic
617	C₂	C₁₉×#2955	1	1	yes	characteristic
618	C₂	C₁₉×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×C₄×D₄
prime radical	C₂×#41×C₁₉	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₁₉×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2962	C₂	semidirect
4. C₁₉×#1995	C₂	semidirect
5. C₁₉×#1950	C₂	semidirect
10. C₁₉×#1922	C₂	semidirect
11. C₁₉×#1922	C₂	semidirect
12. C₁₉×#1773	C₂	semidirect
13. C₁₉×#1772	C₂	semidirect
14. C₁₉×#1768	C₂	semidirect
18. C₁₉×#479	C₄	semidirect
19. C₁₉×#479	C₄	semidirect
20. C₁₉×#478	C₄	semidirect
21. C₁₉×#478	C₄	semidirect
22. C₁₉×#477	C₄	semidirect
23. C₁₉×#476	C₄	semidirect
24. C₁₉×#475	C₄	semidirect
25. C₁₉×#474	C₄	semidirect
227. #23082	C₁₉	direct (N × H)
280. #2962	C₂×C₁₉	semidirect
282. #1995	C₂×C₁₉	semidirect
283. #1950	C₂×C₁₉	semidirect
288. #1922	C₂×C₁₉	semidirect
289. #1922	C₂×C₁₉	semidirect
290. #1773	C₂×C₁₉	semidirect
291. #1772	C₂×C₁₉	semidirect
292. #1768	C₂×C₁₉	semidirect
321. #479	C₄×C₁₉	semidirect
322. #479	C₄×C₁₉	semidirect
323. #478	C₄×C₁₉	semidirect
324. #478	C₄×C₁₉	semidirect
325. #477	C₄×C₁₉	semidirect
326. #476	C₄×C₁₉	semidirect
327. #475	C₄×C₁₉	semidirect
328. #474	C₄×C₁₉	semidirect
459. C₁₉	#23082	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×#3076	2
C₁₉×#2962	2
C₁₉×#2925	2
C₁₉×#1995	2
C₁₉×#1950	2
C₁₉×#1938	2
C₁₉×#1937	2
C₁₉×#1929	2
C₁₉×#1922	2
C₁₉×#1773	2
C₁₉×#1772	2
C₁₉×#1768	2
C₁₉×#1759	2
#23082	19

Subgroups — C19×#23082 #18029041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23082 #18029041