Subgroups — C₁₉×#22490 #18028449

Order 4864.

1142 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#556	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2354	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1892	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1873	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1825	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1735	C₂	1	2	yes	maximal, complemented
12	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
13	C₁₉×#556	—	2	4	no	—
14	C₁₉×#556	C₄	1	8	yes	complemented
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#126	—	2	2	no	—
17	C₂×C₁₉×#124	—	2	1	no	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	C₂²	1	2	yes	—
23	C₂×C₁₉×#117	C₂²	1	2	yes	—
24	C₈×D₄×C₁₉	—	2	4	no	—
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#103	C₂²	1	2	yes	—
29	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#390	—	2	1	no	—
32	C₁₉×#388	—	2	2	no	—
33	C₁₉×#384	C₂²	1	1	yes	characteristic
34	C₁₉×#380	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	1	yes	characteristic
42	C₁₉×#340	C₂²	1	2	yes	—
43	C₁₉×#340	C₂²	1	1	yes	characteristic
44	C₂²×Q₈×C₁₉	—	2	1	no	—
45	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₉	—	2	4	no	—
49	C₂²×C₈×C₁₉	—	2	4	no	—
50	C₂²×C₈×C₁₉	—	4	2	no	—
51	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
54	C₁₉×C₄⋊Q₈	—	2	2	no	—
55	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
56	C₁₉×#126	—	2	16	no	—
57	C₁₉×#124	—	2	8	no	—
58	C₁₉×C₂²⋊Q₈	—	2	4	no	—
59	C₁₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
60	C₄×Q₈×C₁₉	—	2	8	no	—
61	C₄×Q₈×C₁₉	—	2	2	no	—
62	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
63	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
64	C₄×D₄×C₁₉	D₄	1	4	yes	—
65	C₁₉×#117	—	2	4	no	—
66	C₁₉×#117	—	2	4	no	—
67	C₁₉×#117	—	4	2	no	—
68	C₁₉×#117	C₂×C₄	1	8	yes	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
85	C₂×C₄²×C₁₉	—	2	2	no	—
86	C₂×C₄²×C₁₉	—	2	1	no	—
87	C₂×C₄²×C₁₉	—	2	1	no	—
88	C₂×C₄²×C₁₉	—	2	2	no	—
89	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
90	C₁₉×C₄⋊C₈	—	2	2	no	—
91	C₁₉×#103	—	2	2	no	—
92	C₁₉×#103	—	2	2	no	—
93	C₁₉×#103	—	4	2	no	—
94	C₁₉×C₂²⋊C₈	—	2	4	no	—
95	C₄×C₈×C₁₉	—	2	2	no	—
96	C₁₉×#95	—	2	2	no	—
97	C₁₉×#95	—	2	1	no	—
98	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
99	C₂×Q₈×C₁₉	—	2	4	no	—
100	C₂×Q₈×C₁₉	—	2	1	no	—
101	C₂×Q₈×C₁₉	—	2	1	no	—
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×Q₈×C₁₉	—	4	2	no	—
106	C₂×Q₈×C₁₉	—	4	2	no	—
107	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
127	C₂×C₈×C₁₉	—	2	1	no	—
128	C₂×C₈×C₁₉	—	2	1	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	1	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	1	no	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	2	1	no	—
135	C₂×C₈×C₁₉	—	4	8	no	—
136	C₂×C₈×C₁₉	#41	1	2	yes	—
137	C₄⋊C₄×C₁₉	—	2	8	no	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	2	4	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	4	2	no	—
148	C₄⋊C₄×C₁₉	—	8	1	no	—
149	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
150	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
151	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
152	C₄⋊C₄×C₁₉	#41	1	2	yes	—
153	C₂²⋊C₄×C₁₉	—	2	8	no	—
154	C₂²⋊C₄×C₁₉	—	2	8	no	—
155	C₂²⋊C₄×C₁₉	—	4	4	no	—
156	C₂²⋊C₄×C₁₉	—	8	2	no	—
157	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
158	C₄²×C₁₉	—	2	8	no	—
159	C₄²×C₁₉	—	2	4	no	—
160	C₄²×C₁₉	—	4	4	no	—
161	C₄²×C₁₉	—	4	2	no	—
162	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
163	C₄²×C₁₉	C₂×D₄	1	2	yes	—
164	#22490	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂³×C₁₉	—	2	2	no	—
166	C₂³×C₁₉	—	2	2	no	—
167	C₂³×C₁₉	—	2	2	no	—
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	2	2	no	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
172	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₁₉	—	2	2	no	—
174	Q₈×C₁₉	—	2	2	no	—
175	Q₈×C₁₉	—	4	1	no	—
176	Q₈×C₁₉	—	4	1	no	—
177	Q₈×C₁₉	—	4	8	no	—
178	D₄×C₁₉	—	2	8	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
206	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂×C₄×C₁₉	#135	1	2	yes	—
209	C₂×C₄×C₁₉	#135	1	2	yes	—
210	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
216	C₈×C₁₉	—	2	2	no	—
217	C₈×C₁₉	—	4	2	no	—
218	C₈×C₁₉	—	4	1	no	—
219	C₂×#556	C₂×C₁₉	1	1	yes	characteristic
220	C₂×C₈×D₄	C₂×C₁₉	1	1	yes	characteristic
221	#2354	C₂×C₁₉	1	1	yes	characteristic
222	#1990	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#1988	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#1892	C₂×C₁₉	1	2	yes	complemented
225	#1873	C₂×C₁₉	1	2	yes	complemented
226	#1825	C₂×C₁₉	1	2	yes	complemented
227	#1803	C₂×C₁₉	1	1	yes	characteristic, complemented
228	C₄×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
229	#1735	C₂×C₁₉	1	2	yes	complemented
230	C₂²×C₁₉	—	2	4	no	—
231	C₂²×C₁₉	—	2	4	no	—
232	C₂²×C₁₉	—	2	4	no	—
233	C₂²×C₁₉	—	4	2	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	—	4	2	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
238	C₂²×C₁₉	#546	1	1	yes	characteristic
239	C₂²×C₁₉	#547	1	1	yes	characteristic
240	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
241	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
242	C₂²×C₁₉	#577	1	1	yes	characteristic
243	C₂²×C₁₉	#578	1	1	yes	characteristic
244	C₄×C₁₉	—	2	4	no	—
245	C₄×C₁₉	—	2	2	no	—
246	C₄×C₁₉	—	4	2	no	—
247	C₄×C₁₉	—	4	4	no	—
248	C₄×C₁₉	—	4	2	no	—
249	C₄×C₁₉	—	4	2	no	—
250	C₄×C₁₉	—	8	1	no	—
251	C₄×C₁₉	—	8	2	no	—
252	C₄×C₁₉	#416	1	4	yes	—
253	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
254	C₄×C₁₉	#520	1	1	yes	characteristic
255	C₄×C₁₉	#546	1	1	yes	characteristic
256	C₄×C₁₉	#547	1	1	yes	characteristic
257	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
258	#556	—	2	4	no	—
259	#556	C₄×C₁₉	1	8	yes	complemented
260	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×#126	—	2	2	no	—
262	C₂×#124	—	2	1	no	—
263	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
264	C₂×C₄×Q₈	—	2	1	no	—
265	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
267	C₂×#117	C₂²×C₁₉	1	2	yes	—
268	C₂×#117	C₂²×C₁₉	1	2	yes	—
269	C₈×D₄	—	2	4	no	—
270	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
271	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
272	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
273	C₂×#103	C₂²×C₁₉	1	2	yes	—
274	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
275	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
276	#390	—	2	1	no	—
277	#388	—	2	2	no	—
278	#384	C₂²×C₁₉	1	1	yes	characteristic
279	#380	C₂²×C₁₉	1	2	yes	—
280	C₄×C₄⋊C₄	—	2	1	no	—
281	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
282	#340	C₂²×C₁₉	1	2	yes	—
283	#340	C₂²×C₁₉	1	1	yes	characteristic
284	#340	C₂²×C₁₉	1	2	yes	—
285	#340	C₂²×C₁₉	1	2	yes	—
286	#340	C₂²×C₁₉	1	2	yes	—
287	#340	C₂²×C₁₉	1	2	yes	—
288	#340	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×C₁₉	—	4	4	no	—
290	C₂×C₁₉	#2339	1	1	yes	characteristic
291	C₂×C₁₉	C₂×#416	1	1	yes	characteristic
292	C₂×C₁₉	#2898	1	1	yes	characteristic
293	C₂×C₁₉	#3302	1	1	yes	characteristic
294	C₂×C₁₉	#3304	1	1	yes	characteristic
295	C₂×C₁₉	#3340	1	1	yes	characteristic
296	C₂×C₁₉	#3342	1	1	yes	characteristic
297	C₂²×Q₈	—	2	1	no	—
298	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
299	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
300	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
301	C₂²×C₈	—	2	4	no	—
302	C₂²×C₈	—	2	4	no	—
303	C₂²×C₈	—	4	2	no	—
304	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
305	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
307	C₄⋊Q₈	—	2	2	no	—
308	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
309	#126	—	2	16	no	—
310	#124	—	2	8	no	—
311	C₂²⋊Q₈	—	2	4	no	—
312	C₂²⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
313	C₄×Q₈	—	2	8	no	—
314	C₄×Q₈	—	2	2	no	—
315	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
316	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
317	C₄×D₄	D₄×C₁₉	1	4	yes	—
318	#117	—	2	4	no	—
319	#117	—	2	4	no	—
320	#117	—	4	2	no	—
321	#117	C₂×C₄×C₁₉	1	8	yes	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
338	C₂×C₄²	—	2	2	no	—
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	—	2	2	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
343	C₄⋊C₈	—	2	2	no	—
344	#103	—	2	2	no	—
345	#103	—	2	2	no	—
346	#103	—	4	2	no	—
347	C₂²⋊C₈	—	2	4	no	—
348	C₄×C₈	—	2	2	no	—
349	#95	—	2	2	no	—
350	#95	—	2	1	no	—
351	C₁₉	#22490	1	1	yes	characteristic, direct product factor, Sylow
352	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
353	C₂×Q₈	—	2	4	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	—	4	2	no	—
361	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
376	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
379	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
380	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	4	8	no	—
390	C₂×C₈	#41×C₁₉	1	2	yes	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₄⋊C₄	—	8	1	no	—
403	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
404	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
405	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
406	C₄⋊C₄	#41×C₁₉	1	2	yes	—
407	C₂²⋊C₄	—	2	8	no	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	4	4	no	—
410	C₂²⋊C₄	—	8	2	no	—
411	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
412	C₄²	—	2	8	no	—
413	C₄²	—	2	4	no	—
414	C₄²	—	4	4	no	—
415	C₄²	—	4	2	no	—
416	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
417	C₄²	C₂×D₄×C₁₉	1	2	yes	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
425	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
426	Q₈	—	2	2	no	—
427	Q₈	—	2	2	no	—
428	Q₈	—	4	8	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	4	1	no	—
431	D₄	—	2	8	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
459	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
460	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
461	C₂×C₄	C₁₉×#135	1	2	yes	—
462	C₂×C₄	C₁₉×#135	1	2	yes	—
463	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
465	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
466	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
467	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
469	C₈	—	2	2	no	—
470	C₈	—	4	2	no	—
471	C₈	—	4	1	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	2	4	no	—
474	C₂²	—	2	4	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
480	C₂²	C₁₉×#546	1	1	yes	characteristic
481	C₂²	C₁₉×#547	1	1	yes	characteristic
482	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
483	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
484	C₂²	C₁₉×#577	1	1	yes	characteristic
485	C₂²	C₁₉×#578	1	1	yes	characteristic
486	C₄	—	2	4	no	—
487	C₄	—	2	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	4	no	—
491	C₄	—	4	2	no	—
492	C₄	—	8	2	no	—
493	C₄	—	8	1	no	—
494	C₄	C₁₉×#416	1	4	yes	—
495	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
496	C₄	C₁₉×#520	1	1	yes	characteristic
497	C₄	C₁₉×#546	1	1	yes	characteristic
498	C₄	C₁₉×#547	1	1	yes	characteristic
499	C₂	—	4	4	no	—
500	C₂	C₁₉×#2339	1	1	yes	characteristic
501	C₂	C₂×C₁₉×#416	1	1	yes	characteristic
502	C₂	C₁₉×#2898	1	1	yes	characteristic
503	C₂	C₁₉×#3302	1	1	yes	characteristic
504	C₂	C₁₉×#3304	1	1	yes	characteristic
505	C₂	C₁₉×#3340	1	1	yes	characteristic
506	C₂	C₁₉×#3342	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1990	C₂	semidirect
5. C₁₉×#1988	C₂	semidirect
6. C₁₉×#1892	C₂	semidirect
7. C₁₉×#1873	C₂	semidirect
8. C₁₉×#1825	C₂	semidirect
9. C₁₉×#1803	C₂	semidirect
10. C₄×C₁₉×#103	C₂	semidirect
11. C₁₉×#1735	C₂	semidirect
14. C₁₉×#556	C₄	semidirect
164. #22490	C₁₉	direct (N × H)
222. #1990	C₂×C₁₉	semidirect
223. #1988	C₂×C₁₉	semidirect
224. #1892	C₂×C₁₉	semidirect
225. #1873	C₂×C₁₉	semidirect
226. #1825	C₂×C₁₉	semidirect
227. #1803	C₂×C₁₉	semidirect
228. C₄×#103	C₂×C₁₉	semidirect
229. #1735	C₂×C₁₉	semidirect
259. #556	C₄×C₁₉	semidirect
351. C₁₉	#22490	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#556	2
C₂×C₈×D₄×C₁₉	2
C₁₉×#2354	2
C₁₉×#1990	2
C₁₉×#1988	2
C₁₉×#1892	2
C₁₉×#1873	2
C₁₉×#1825	2
C₁₉×#1803	2
C₄×C₁₉×#103	2
C₁₉×#1735	2
#22490	19

Subgroups — C19×#22490 #18028449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22490 #18028449