Subgroups — C₁₉×#24759 #18030718

Order 4864.

1044 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#468	C₂	1	2	yes	maximal
2	C₂×C₁₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2068	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2055	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1894	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₉	—	2	1	no	—
18	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#468	—	2	8	no	—
21	C₁₉×#461	—	2	4	no	—
22	C₂×C₁₉×#107	C₂²	1	2	yes	—
23	C₁₉×#423	—	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×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	2	yes	—
28	C₂×C₁₉×#103	C₂²	1	2	yes	—
29	C₂×C₁₉×#103	C₂²	1	2	yes	—
30	C₂×C₁₉×#102	C₂²	1	2	yes	—
31	C₁₉×#391	C₂²	1	2	yes	—
32	C₁₉×#390	C₂²	1	1	yes	characteristic
33	C₁₉×#389	—	2	1	no	—
34	C₁₉×#389	—	2	1	no	—
35	C₁₉×#389	C₂²	1	1	yes	characteristic
36	C₁₉×#388	—	2	1	no	—
37	C₁₉×#386	—	2	1	no	—
38	C₁₉×#384	C₂²	1	1	yes	characteristic
39	C₁₉×#380	—	2	1	no	—
40	C₁₉×#380	—	2	1	no	—
41	C₁₉×#380	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₁₉×#340	C₂²	1	2	yes	—
45	C₁₉×#340	C₂²	1	2	yes	—
46	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	—	2	1	no	—
50	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂×SD₁₆×C₁₉	—	2	4	no	—
54	C₂×SD₁₆×C₁₉	—	2	4	no	—
55	C₂×SD₁₆×C₁₉	—	4	2	no	—
56	C₂×M₁₆×C₁₉	—	2	4	no	—
57	C₂×M₁₆×C₁₉	—	2	4	no	—
58	C₂×M₁₆×C₁₉	—	4	2	no	—
59	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
61	C₁₉×C₄⋊Q₈	—	2	2	no	—
62	C₁₉×C₄⋊Q₈	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	4	no	—
64	C₁₉×C₂²⋊Q₈	—	2	4	no	—
65	C₁₉×#121	—	2	2	no	—
66	C₁₉×#121	D₄	1	4	yes	—
67	C₄×D₄×C₁₉	—	2	2	no	—
68	C₄×D₄×C₁₉	—	2	2	no	—
69	C₄×D₄×C₁₉	—	4	4	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	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	1	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄²×C₁₉	—	2	2	no	—
87	C₂×C₄²×C₁₉	—	2	2	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₁₉×#107	—	2	4	no	—
94	C₁₉×C₄⋊C₈	—	2	4	no	—
95	C₁₉×C₄⋊C₈	—	2	2	no	—
96	C₁₉×C₄⋊C₈	D₄	1	4	yes	complemented
97	C₁₉×#103	—	2	4	no	—
98	C₁₉×#103	—	2	4	no	—
99	C₁₉×#103	—	4	2	no	—
100	C₁₉×#102	—	2	4	no	—
101	C₁₉×#95	—	2	1	no	—
102	C₁₉×#95	—	2	1	no	—
103	C₁₉×#95	—	2	1	no	—
104	C₁₉×#95	—	2	2	no	—
105	C₁₉×#95	—	2	2	no	—
106	C₂⁴×C₁₉	—	2	1	no	—
107	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	2	2	no	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	2	4	no	—
115	C₂×D₄×C₁₉	—	2	1	no	—
116	C₂×D₄×C₁₉	—	2	1	no	—
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	—	2	1	no	—
119	C₂×D₄×C₁₉	—	2	1	no	—
120	C₂×D₄×C₁₉	—	4	2	no	—
121	C₂×D₄×C₁₉	—	4	2	no	—
122	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	4	1	no	—
138	C₂²×C₄×C₁₉	—	4	2	no	—
139	C₂²×C₄×C₁₉	—	4	2	no	—
140	C₂²×C₄×C₁₉	—	4	2	no	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	#41	1	2	yes	—
148	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
149	SD₁₆×C₁₉	—	4	8	no	—
150	M₁₆×C₁₉	—	4	8	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₂×C₈×C₁₉	—	2	2	no	—
156	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	4	2	no	—
165	C₄⋊C₄×C₁₉	—	4	2	no	—
166	C₄⋊C₄×C₁₉	—	4	4	no	—
167	C₄⋊C₄×C₁₉	—	4	2	no	—
168	C₄⋊C₄×C₁₉	—	4	2	no	—
169	C₄⋊C₄×C₁₉	—	4	2	no	—
170	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₂²⋊C₄×C₁₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₉	—	4	2	no	—
173	C₂²⋊C₄×C₁₉	—	4	2	no	—
174	C₂²⋊C₄×C₁₉	—	4	4	no	—
175	C₂²⋊C₄×C₁₉	—	4	2	no	—
176	C₂²⋊C₄×C₁₉	—	4	2	no	—
177	C₄²×C₁₉	—	2	2	no	—
178	C₄²×C₁₉	—	2	2	no	—
179	C₄²×C₁₉	—	2	1	no	—
180	C₄²×C₁₉	—	2	1	no	—
181	C₄²×C₁₉	—	4	2	no	—
182	C₄²×C₁₉	C₂×D₄	1	2	yes	—
183	C₄²×C₁₉	#41	1	2	yes	—
184	#24759	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂³×C₁₉	—	2	1	no	—
186	C₂³×C₁₉	—	2	1	no	—
187	C₂³×C₁₉	—	2	1	no	—
188	C₂³×C₁₉	—	2	1	no	—
189	C₂³×C₁₉	—	2	1	no	—
190	C₂³×C₁₉	—	2	1	no	—
191	C₂³×C₁₉	—	2	2	no	—
192	C₂³×C₁₉	—	4	1	no	—
193	C₂³×C₁₉	—	4	1	no	—
194	C₂³×C₁₉	—	4	1	no	—
195	C₂³×C₁₉	—	4	1	no	—
196	C₂³×C₁₉	—	4	1	no	—
197	C₂³×C₁₉	—	4	1	no	—
198	C₂³×C₁₉	#121	1	2	yes	—
199	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₁₉	—	4	2	no	—
201	Q₈×C₁₉	—	4	2	no	—
202	Q₈×C₁₉	—	4	2	no	—
203	Q₈×C₁₉	—	4	2	no	—
204	D₄×C₁₉	—	2	2	no	—
205	D₄×C₁₉	—	2	2	no	—
206	D₄×C₁₉	—	4	8	no	—
207	D₄×C₁₉	—	4	1	no	—
208	D₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	4	4	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	4	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	8	4	no	—
240	C₂×C₄×C₁₉	#121	1	2	yes	—
241	C₂×C₄×C₁₉	#121	1	2	yes	—
242	C₂×C₄×C₁₉	#121	1	2	yes	—
243	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
244	C₂×C₄×C₁₉	#137	1	2	yes	—
245	C₂×C₄×C₁₉	#137	1	2	yes	—
246	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
251	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
252	C₈×C₁₉	—	2	4	no	—
253	C₈×C₁₉	—	4	2	no	—
254	C₂×#468	C₂×C₁₉	1	2	yes	—
255	C₂×#461	C₂×C₁₉	1	1	yes	characteristic, complemented
256	C₂×#423	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#2857	C₂×C₁₉	1	1	yes	characteristic, complemented
258	C₄×#121	C₂×C₁₉	1	1	yes	characteristic
259	#2068	C₂×C₁₉	1	2	yes	complemented
260	#2055	C₂×C₁₉	1	2	yes	complemented
261	#1981	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1947	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1894	C₂×C₁₉	1	2	yes	complemented
264	#1802	C₂×C₁₉	1	1	yes	characteristic, complemented
265	C₂²×C₁₉	—	2	2	no	—
266	C₂²×C₁₉	—	2	2	no	—
267	C₂²×C₁₉	—	2	2	no	—
268	C₂²×C₁₉	—	4	1	no	—
269	C₂²×C₁₉	—	4	1	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	—	4	2	no	—
273	C₂²×C₁₉	—	4	2	no	—
274	C₂²×C₁₉	—	4	2	no	—
275	C₂²×C₁₉	—	8	1	no	—
276	C₂²×C₁₉	—	8	1	no	—
277	C₂²×C₁₉	—	8	1	no	—
278	C₂²×C₁₉	—	8	1	no	—
279	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
280	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
281	C₂²×C₁₉	#537	1	1	yes	characteristic
282	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
283	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
284	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
285	C₂²×C₁₉	#575	1	1	yes	characteristic
286	C₄×C₁₉	—	2	2	no	—
287	C₄×C₁₉	—	2	2	no	—
288	C₄×C₁₉	—	2	2	no	—
289	C₄×C₁₉	—	4	2	no	—
290	C₄×C₁₉	—	4	1	no	—
291	C₄×C₁₉	—	8	2	no	—
292	C₄×C₁₉	—	8	1	no	—
293	C₄×C₁₉	—	8	2	no	—
294	C₄×C₁₉	—	8	1	no	—
295	C₄×C₁₉	#468	1	4	yes	complemented
296	C₄×C₁₉	D₄²	1	1	yes	characteristic
297	C₄×C₁₉	#547	1	1	yes	characteristic
298	C₄×C₁₉	#548	1	1	yes	characteristic
299	C₄×C₁₉	#553	1	1	yes	characteristic
300	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
301	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
302	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
304	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
305	C₂×C₄×D₄	—	2	1	no	—
306	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
307	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
308	#468	—	2	8	no	—
309	#461	—	2	4	no	—
310	C₂×#107	C₂²×C₁₉	1	2	yes	—
311	#423	—	2	4	no	—
312	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
313	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×#103	C₂²×C₁₉	1	2	yes	—
316	C₂×#103	C₂²×C₁₉	1	2	yes	—
317	C₂×#103	C₂²×C₁₉	1	2	yes	—
318	C₂×#102	C₂²×C₁₉	1	2	yes	—
319	#391	C₂²×C₁₉	1	2	yes	—
320	#390	C₂²×C₁₉	1	1	yes	characteristic
321	#389	—	2	1	no	—
322	#389	—	2	1	no	—
323	#389	C₂²×C₁₉	1	1	yes	characteristic
324	#388	—	2	1	no	—
325	#386	—	2	1	no	—
326	#384	C₂²×C₁₉	1	1	yes	characteristic
327	#380	—	2	1	no	—
328	#380	—	2	1	no	—
329	#380	C₂²×C₁₉	1	1	yes	characteristic
330	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
331	C₄×C₂²⋊C₄	—	2	1	no	—
332	#340	C₂²×C₁₉	1	2	yes	—
333	#340	C₂²×C₁₉	1	2	yes	—
334	C₂×C₁₉	—	4	2	no	—
335	C₂×C₁₉	—	8	2	no	—
336	C₂×C₁₉	#2416	1	1	yes	characteristic
337	C₂×C₁₉	#3036	1	1	yes	characteristic
338	C₂×C₁₉	#3039	1	1	yes	characteristic
339	C₂×C₁₉	C₂×#468	1	1	yes	characteristic
340	C₂×C₁₉	#3056	1	1	yes	characteristic
341	C₂×C₁₉	#3252	1	1	yes	characteristic
342	C₂×C₁₉	#3254	1	1	yes	characteristic
343	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
348	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
349	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
350	C₂×SD₁₆	—	2	4	no	—
351	C₂×SD₁₆	—	2	4	no	—
352	C₂×SD₁₆	—	4	2	no	—
353	C₂×M₁₆	—	2	4	no	—
354	C₂×M₁₆	—	2	4	no	—
355	C₂×M₁₆	—	4	2	no	—
356	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
357	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
358	C₄⋊Q₈	—	2	2	no	—
359	C₄⋊Q₈	—	2	2	no	—
360	C₂²⋊Q₈	—	2	4	no	—
361	C₂²⋊Q₈	—	2	4	no	—
362	#121	—	2	2	no	—
363	#121	D₄×C₁₉	1	4	yes	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	4	4	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₄²	—	2	2	no	—
384	C₂×C₄²	—	2	2	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
387	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
390	#107	—	2	4	no	—
391	C₄⋊C₈	—	2	4	no	—
392	C₄⋊C₈	—	2	2	no	—
393	C₄⋊C₈	D₄×C₁₉	1	4	yes	complemented
394	#103	—	2	4	no	—
395	#103	—	2	4	no	—
396	#103	—	4	2	no	—
397	#102	—	2	4	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	—	2	1	no	—
401	#95	—	2	2	no	—
402	#95	—	2	2	no	—
403	C₁₉	#24759	1	1	yes	characteristic, direct product factor, Sylow
404	C₂⁴	—	2	1	no	—
405	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	4	2	no	—
419	C₂×D₄	—	4	2	no	—
420	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	4	1	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₂²×C₄	#41×C₁₉	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
447	SD₁₆	—	4	8	no	—
448	M₁₆	—	4	8	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	4	2	no	—
463	C₄⋊C₄	—	4	2	no	—
464	C₄⋊C₄	—	4	4	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	—	4	2	no	—
467	C₄⋊C₄	—	4	2	no	—
468	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	4	2	no	—
471	C₂²⋊C₄	—	4	2	no	—
472	C₂²⋊C₄	—	4	4	no	—
473	C₂²⋊C₄	—	4	2	no	—
474	C₂²⋊C₄	—	4	2	no	—
475	C₄²	—	2	2	no	—
476	C₄²	—	2	2	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	4	2	no	—
480	C₄²	C₂×D₄×C₁₉	1	2	yes	—
481	C₄²	#41×C₁₉	1	2	yes	—
482	C₂³	—	2	1	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	C₁₉×#121	1	2	yes	—
496	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
497	Q₈	—	4	2	no	—
498	Q₈	—	4	2	no	—
499	Q₈	—	4	2	no	—
500	Q₈	—	4	2	no	—
501	D₄	—	2	2	no	—
502	D₄	—	2	2	no	—
503	D₄	—	4	8	no	—
504	D₄	—	4	1	no	—
505	D₄	—	4	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	8	4	no	—
537	C₂×C₄	C₁₉×#121	1	2	yes	—
538	C₂×C₄	C₁₉×#121	1	2	yes	—
539	C₂×C₄	C₁₉×#121	1	2	yes	—
540	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
541	C₂×C₄	C₁₉×#137	1	2	yes	—
542	C₂×C₄	C₁₉×#137	1	2	yes	—
543	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
545	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
546	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
547	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
549	C₈	—	2	4	no	—
550	C₈	—	4	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	—	8	1	no	—
565	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
566	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
567	C₂²	C₁₉×#537	1	1	yes	characteristic
568	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
569	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
570	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
571	C₂²	C₁₉×#575	1	1	yes	characteristic
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	1	no	—
577	C₄	—	8	2	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	2	no	—
580	C₄	—	8	1	no	—
581	C₄	C₁₉×#468	1	4	yes	complemented
582	C₄	D₄²×C₁₉	1	1	yes	characteristic
583	C₄	C₁₉×#547	1	1	yes	characteristic
584	C₄	C₁₉×#548	1	1	yes	characteristic
585	C₄	C₁₉×#553	1	1	yes	characteristic
586	C₂	—	4	2	no	—
587	C₂	—	8	2	no	—
588	C₂	C₁₉×#2416	1	1	yes	characteristic
589	C₂	C₁₉×#3036	1	1	yes	characteristic
590	C₂	C₁₉×#3039	1	1	yes	characteristic
591	C₂	C₂×C₁₉×#468	1	1	yes	characteristic
592	C₂	C₁₉×#3056	1	1	yes	characteristic
593	C₂	C₁₉×#3252	1	1	yes	characteristic
594	C₂	C₁₉×#3254	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#461	C₂	semidirect
3. C₂×C₁₉×#423	C₂	semidirect
4. C₁₉×#2857	C₂	semidirect
6. C₁₉×#2068	C₂	semidirect
7. C₁₉×#2055	C₂	semidirect
8. C₁₉×#1981	C₂	semidirect
9. C₁₉×#1947	C₂	semidirect
10. C₁₉×#1894	C₂	semidirect
11. C₁₉×#1802	C₂	semidirect
96. C₁₉×C₄⋊C₈	D₄	semidirect
184. #24759	C₁₉	direct (N × H)
255. C₂×#461	C₂×C₁₉	semidirect
256. C₂×#423	C₂×C₁₉	semidirect
257. #2857	C₂×C₁₉	semidirect
259. #2068	C₂×C₁₉	semidirect
260. #2055	C₂×C₁₉	semidirect
261. #1981	C₂×C₁₉	semidirect
262. #1947	C₂×C₁₉	semidirect
263. #1894	C₂×C₁₉	semidirect
264. #1802	C₂×C₁₉	semidirect
295. C₄×C₁₉	#468	semidirect
393. C₄⋊C₈	D₄×C₁₉	semidirect
403. C₁₉	#24759	direct (N × H)
581. C₄	C₁₉×#468	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#468	2
C₂×C₁₉×#461	2
C₂×C₁₉×#423	2
C₁₉×#2857	2
C₄×C₁₉×#121	2
C₁₉×#2068	2
C₁₉×#2055	2
C₁₉×#1981	2
C₁₉×#1947	2
C₁₉×#1894	2
C₁₉×#1802	2
#24759	19

Subgroups — C19×#24759 #18030718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24759 #18030718