Subgroups — C₁₉×#22524 #18028483

Order 4864.

1034 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#557	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#446	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1992	C₂	1	2	yes	maximal
5	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1989	C₂	1	2	yes	maximal
7	C₁₉×#1988	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1803	C₂	1	2	yes	maximal
9	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1763	C₂	1	2	yes	maximal
11	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#557	—	2	4	no	—
13	C₁₉×#557	C₄	1	8	yes	complemented
14	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#125	—	2	2	no	—
17	C₂×C₁₉×#125	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#446	—	2	4	no	—
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	2	yes	—
28	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#97	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#389	—	2	1	no	—
32	C₁₉×#389	—	2	2	no	—
33	C₁₉×#384	C₂²	1	1	yes	characteristic
34	C₁₉×#384	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	1	yes	characteristic
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
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	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₁₉×C₄⋊Q₈	—	2	8	no	—
51	C₁₉×C₄⋊Q₈	—	2	2	no	—
52	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
53	C₁₉×#125	—	2	16	no	—
54	C₁₉×#125	—	2	4	no	—
55	C₁₉×#125	C₂×C₄	1	8	yes	—
56	C₄×Q₈×C₁₉	—	2	8	no	—
57	C₄×Q₈×C₁₉	—	2	4	no	—
58	C₄×Q₈×C₁₉	—	2	2	no	—
59	C₄×Q₈×C₁₉	—	4	4	no	—
60	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	—
61	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
62	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
63	C₄×Q₈×C₁₉	D₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
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×C₄²×C₁₉	—	2	2	no	—
81	C₂×C₄²×C₁₉	—	2	1	no	—
82	C₂×C₄²×C₁₉	—	2	2	no	—
83	C₂×C₄²×C₁₉	—	2	1	no	—
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
86	C₁₉×C₄⋊C₈	—	2	4	no	—
87	C₁₉×C₄⋊C₈	—	2	2	no	—
88	C₁₉×#103	—	2	2	no	—
89	C₁₉×#103	—	2	4	no	—
90	C₁₉×#103	Q₈	1	4	yes	complemented
91	C₁₉×#97	—	2	4	no	—
92	C₄×C₈×C₁₉	—	2	2	no	—
93	C₁₉×#95	—	2	2	no	—
94	C₁₉×#95	—	2	1	no	—
95	C₂×Q₈×C₁₉	—	2	4	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	1	no	—
99	C₂×Q₈×C₁₉	—	2	1	no	—
100	C₂×Q₈×C₁₉	—	2	1	no	—
101	C₂×Q₈×C₁₉	—	4	2	no	—
102	C₂×Q₈×C₁₉	—	4	2	no	—
103	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
104	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
105	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
106	C₂×Q₈×C₁₉	#41	1	2	yes	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	1	no	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
118	C₂×C₈×C₁₉	—	2	1	no	—
119	C₂×C₈×C₁₉	—	2	1	no	—
120	C₂×C₈×C₁₉	—	2	1	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	1	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	1	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
127	C₄⋊C₄×C₁₉	—	2	8	no	—
128	C₄⋊C₄×C₁₉	—	2	4	no	—
129	C₄⋊C₄×C₁₉	—	2	8	no	—
130	C₄⋊C₄×C₁₉	—	2	4	no	—
131	C₄⋊C₄×C₁₉	—	2	8	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	4	4	no	—
140	C₄⋊C₄×C₁₉	—	4	2	no	—
141	C₄⋊C₄×C₁₉	—	8	2	no	—
142	C₄⋊C₄×C₁₉	—	8	1	no	—
143	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
144	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
145	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
146	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
147	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
148	C₄²×C₁₉	—	2	8	no	—
149	C₄²×C₁₉	—	2	4	no	—
150	C₄²×C₁₉	—	4	4	no	—
151	C₄²×C₁₉	—	4	2	no	—
152	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
153	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
154	C₄²×C₁₉	C₂×D₄	1	4	yes	—
155	C₄²×C₁₉	C₂×D₄	1	2	yes	—
156	#22524	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₁₉	—	2	2	no	—
159	Q₈×C₁₉	—	2	2	no	—
160	Q₈×C₁₉	—	2	2	no	—
161	Q₈×C₁₉	—	2	8	no	—
162	Q₈×C₁₉	—	4	8	no	—
163	Q₈×C₁₉	C₄×Q₈	1	4	yes	complemented
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
189	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
190	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
191	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
193	C₂×C₄×C₁₉	#137	1	2	yes	—
194	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
199	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
200	C₈×C₁₉	—	2	2	no	—
201	C₈×C₁₉	—	4	1	no	—
202	C₈×C₁₉	—	4	2	no	—
203	C₂×#557	C₂×C₁₉	1	1	yes	characteristic
204	C₂×#446	C₂×C₁₉	1	1	yes	characteristic
205	Q₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
206	#1992	C₂×C₁₉	1	2	yes	—
207	#1990	C₂×C₁₉	1	1	yes	characteristic
208	#1989	C₂×C₁₉	1	2	yes	—
209	#1988	C₂×C₁₉	1	1	yes	characteristic
210	#1803	C₂×C₁₉	1	1	yes	characteristic
211	#1803	C₂×C₁₉	1	2	yes	—
212	#1763	C₂×C₁₉	1	2	yes	—
213	C₄×#103	C₂×C₁₉	1	1	yes	characteristic
214	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
215	C₂²×C₁₉	#548	1	1	yes	characteristic
216	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
217	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
219	C₂²×C₁₉	#577	1	1	yes	characteristic
220	C₂²×C₁₉	#578	1	1	yes	characteristic
221	C₄×C₁₉	—	2	4	no	—
222	C₄×C₁₉	—	2	4	no	—
223	C₄×C₁₉	—	2	4	no	—
224	C₄×C₁₉	—	2	2	no	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	4	4	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	8	2	no	—
229	C₄×C₁₉	—	8	1	no	—
230	C₄×C₁₉	#417	1	4	yes	—
231	C₄×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
232	C₄×C₁₉	#519	1	1	yes	characteristic
233	C₄×C₁₉	#548	1	1	yes	characteristic
234	C₄×C₁₉	D₄×Q₈	1	1	yes	characteristic
235	#557	—	2	4	no	—
236	#557	C₄×C₁₉	1	8	yes	complemented
237	C₂×C₄⋊Q₈	—	2	1	no	—
238	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×#125	—	2	2	no	—
240	C₂×#125	C₂²×C₁₉	1	2	yes	—
241	C₂×C₄×Q₈	—	2	1	no	—
242	C₂×C₄×Q₈	—	2	1	no	—
243	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
245	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
246	#446	—	2	4	no	—
247	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
249	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×#103	C₂²×C₁₉	1	2	yes	—
251	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×#97	C₂²×C₁₉	1	2	yes	—
253	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
254	#389	—	2	1	no	—
255	#389	—	2	2	no	—
256	#384	C₂²×C₁₉	1	1	yes	characteristic
257	#384	C₂²×C₁₉	1	2	yes	—
258	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
259	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
260	#340	C₂²×C₁₉	1	2	yes	—
261	#340	C₂²×C₁₉	1	2	yes	—
262	#340	C₂²×C₁₉	1	2	yes	—
263	#340	C₂²×C₁₉	1	2	yes	—
264	#340	C₂²×C₁₉	1	1	yes	characteristic
265	#340	C₂²×C₁₉	1	2	yes	—
266	#340	C₂²×C₁₉	1	1	yes	characteristic
267	C₂×C₁₉	Q₈×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₁₉	C₂×#417	1	1	yes	characteristic
269	C₂×C₁₉	#2898	1	1	yes	characteristic
270	C₂×C₁₉	#3368	1	1	yes	characteristic
271	C₂×C₁₉	#3374	1	1	yes	characteristic
272	C₂×C₁₉	#3386	1	1	yes	characteristic
273	C₂×C₁₉	#3387	1	1	yes	characteristic
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
276	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
279	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
280	C₄⋊Q₈	—	2	8	no	—
281	C₄⋊Q₈	—	2	2	no	—
282	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
283	#125	—	2	16	no	—
284	#125	—	2	4	no	—
285	#125	C₂×C₄×C₁₉	1	8	yes	—
286	C₄×Q₈	—	2	8	no	—
287	C₄×Q₈	—	2	4	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	—	4	4	no	—
290	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	—
291	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
292	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
293	C₄×Q₈	D₄×C₁₉	1	4	yes	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
304	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
315	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
316	C₄⋊C₈	—	2	2	no	—
317	C₄⋊C₈	—	2	4	no	—
318	#103	—	2	2	no	—
319	#103	—	2	4	no	—
320	#103	Q₈×C₁₉	1	4	yes	complemented
321	#97	—	2	4	no	—
322	C₄×C₈	—	2	2	no	—
323	#95	—	2	2	no	—
324	#95	—	2	1	no	—
325	C₁₉	#22524	1	1	yes	characteristic, direct product factor, Sylow
326	C₂×Q₈	—	2	4	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	—	4	2	no	—
334	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
335	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
336	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
337	C₂×Q₈	#41×C₁₉	1	2	yes	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
348	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	8	2	no	—
373	C₄⋊C₄	—	8	1	no	—
374	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
375	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
376	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
377	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
378	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
379	C₄²	—	2	8	no	—
380	C₄²	—	2	4	no	—
381	C₄²	—	4	4	no	—
382	C₄²	—	4	2	no	—
383	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
384	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
385	C₄²	C₂×D₄×C₁₉	1	2	yes	—
386	C₄²	C₂×D₄×C₁₉	1	4	yes	—
387	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
388	Q₈	—	2	8	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	2	2	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	4	8	no	—
393	Q₈	C₄×Q₈×C₁₉	1	4	yes	complemented
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
419	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
420	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
421	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
422	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
423	C₂×C₄	C₁₉×#137	1	2	yes	—
424	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
425	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
426	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
427	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
428	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
429	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	4	1	no	—
432	C₈	—	4	2	no	—
433	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
434	C₂²	C₁₉×#548	1	1	yes	characteristic
435	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
436	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
437	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
438	C₂²	C₁₉×#577	1	1	yes	characteristic
439	C₂²	C₁₉×#578	1	1	yes	characteristic
440	C₄	—	2	4	no	—
441	C₄	—	2	4	no	—
442	C₄	—	2	4	no	—
443	C₄	—	2	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	4	no	—
446	C₄	—	4	2	no	—
447	C₄	—	8	2	no	—
448	C₄	—	8	1	no	—
449	C₄	C₁₉×#417	1	4	yes	—
450	C₄	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
451	C₄	C₁₉×#519	1	1	yes	characteristic
452	C₄	C₁₉×#548	1	1	yes	characteristic
453	C₄	D₄×Q₈×C₁₉	1	1	yes	characteristic
454	C₂	Q₈×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
455	C₂	C₂×C₁₉×#417	1	1	yes	characteristic
456	C₂	C₁₉×#2898	1	1	yes	characteristic
457	C₂	C₁₉×#3368	1	1	yes	characteristic
458	C₂	C₁₉×#3374	1	1	yes	characteristic
459	C₂	C₁₉×#3386	1	1	yes	characteristic
460	C₂	C₁₉×#3387	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₁₉×#557	C₄	semidirect
90. C₁₉×#103	Q₈	semidirect
156. #22524	C₁₉	direct (N × H)
163. Q₈×C₁₉	C₄×Q₈	semidirect
236. #557	C₄×C₁₉	semidirect
320. #103	Q₈×C₁₉	semidirect
325. C₁₉	#22524	direct (N × H)
393. Q₈	C₄×Q₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#557	2
C₂×C₁₉×#446	2
Q₈×C₄⋊C₄×C₁₉	2
C₁₉×#1992	2
C₁₉×#1990	2
C₁₉×#1989	2
C₁₉×#1988	2
C₁₉×#1803	2
C₁₉×#1763	2
C₄×C₁₉×#103	2
#22524	19

Subgroups — C19×#22524 #18028483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22524 #18028483