Subgroups — C₁₉×#24527 #18030486

Order 4864.

1182 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#450	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2503	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2073	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2055	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1877	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1823	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1804	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
20	C₁₉×#450	—	2	4	no	—
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
22	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
23	C₂×C₁₉×#102	—	2	4	no	—
24	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×#102	C₂²	1	2	yes	—
28	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₁₉×#400	—	2	2	no	—
30	C₁₉×#391	C₂²	1	2	yes	complemented
31	C₁₉×#390	C₂²	1	2	yes	—
32	C₁₉×#386	—	2	2	no	—
33	C₁₉×#382	C₂²	1	2	yes	complemented
34	C₁₉×#381	—	2	1	no	—
35	C₁₉×#381	—	2	1	no	—
36	C₁₉×#380	C₂²	1	1	yes	characteristic
37	C₁₉×#379	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	complemented
40	C₁₉×#340	C₂²	1	2	yes	complemented
41	C₁₉×#340	C₂²	1	2	yes	complemented
42	C₁₉×#336	C₂²	1	2	yes	complemented
43	C₂⁵×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₉	—	2	4	no	—
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	—	2	2	no	—
48	C₂²×D₄×C₁₉	—	4	2	no	—
49	C₂²×D₄×C₁₉	D₄	1	4	yes	—
50	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂³×C₄×C₁₉	—	2	2	no	—
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂×SD₁₆×C₁₉	—	2	2	no	—
56	C₂×SD₁₆×C₁₉	—	2	2	no	—
57	C₂×SD₁₆×C₁₉	—	2	4	no	—
58	C₂×SD₁₆×C₁₉	—	4	2	no	—
59	C₂²×C₈×C₁₉	—	2	2	no	—
60	C₂²×C₈×C₁₉	—	4	2	no	—
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₄×D₄×C₁₉	—	2	4	no	—
67	C₄×D₄×C₁₉	—	4	2	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	1	no	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
81	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
84	C₁₉×C₄⋊C₈	—	4	2	no	—
85	C₁₉×#103	—	4	2	no	—
86	C₁₉×#102	—	2	4	no	—
87	C₁₉×#102	—	2	4	no	—
88	C₁₉×#102	—	2	2	no	—
89	C₁₉×#102	—	2	2	no	—
90	C₁₉×C₂²⋊C₈	—	2	2	no	—
91	C₁₉×#95	—	2	1	no	—
92	C₁₉×#95	—	2	2	no	—
93	C₁₉×#95	—	2	2	no	—
94	C₁₉×#95	—	2	2	no	—
95	C₁₉×#95	—	2	2	no	—
96	C₁₉×#95	D₄	1	2	yes	—
97	C₂⁴×C₁₉	—	2	1	no	—
98	C₂⁴×C₁₉	—	2	1	no	—
99	C₂⁴×C₁₉	—	2	4	no	—
100	C₂⁴×C₁₉	—	4	4	no	—
101	C₂⁴×C₁₉	—	4	2	no	—
102	C₂⁴×C₁₉	—	4	2	no	—
103	C₂⁴×C₁₉	—	8	2	no	—
104	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂×Q₈×C₁₉	—	2	1	no	—
106	C₂×Q₈×C₁₉	—	2	1	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	8	no	—
110	C₂×D₄×C₁₉	—	2	4	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	4	4	no	—
117	C₂×D₄×C₁₉	—	4	8	no	—
118	C₂×D₄×C₁₉	—	4	4	no	—
119	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₁₉	#41	1	4	yes	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	4	4	no	—
129	C₂²×C₄×C₁₉	—	4	4	no	—
130	C₂²×C₄×C₁₉	—	4	2	no	—
131	C₂²×C₄×C₁₉	—	4	2	no	—
132	C₂²×C₄×C₁₉	—	4	2	no	—
133	C₂²×C₄×C₁₉	—	8	2	no	—
134	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₉	#41	1	2	yes	—
139	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
140	SD₁₆×C₁₉	—	4	4	no	—
141	SD₁₆×C₁₉	—	4	4	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	—	2	1	no	—
145	C₂×C₈×C₁₉	—	2	2	no	—
146	C₂×C₈×C₁₉	—	2	2	no	—
147	C₂×C₈×C₁₉	—	2	2	no	—
148	C₂×C₈×C₁₉	—	2	2	no	—
149	C₂×C₈×C₁₉	—	4	4	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	4	2	no	—
157	C₄⋊C₄×C₁₉	—	4	2	no	—
158	C₂²⋊C₄×C₁₉	—	2	2	no	—
159	C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₂²⋊C₄×C₁₉	—	4	4	no	—
161	C₂²⋊C₄×C₁₉	—	4	4	no	—
162	C₂²⋊C₄×C₁₉	—	4	2	no	—
163	C₂²⋊C₄×C₁₉	—	4	2	no	—
164	C₂²⋊C₄×C₁₉	—	8	2	no	—
165	C₄²×C₁₉	—	2	2	no	—
166	C₄²×C₁₉	—	2	2	no	—
167	#24527	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	2	2	no	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	4	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	4	8	no	—
174	C₂³×C₁₉	—	4	1	no	—
175	C₂³×C₁₉	—	4	1	no	—
176	C₂³×C₁₉	—	4	2	no	—
177	C₂³×C₁₉	—	4	2	no	—
178	C₂³×C₁₉	—	4	1	no	—
179	C₂³×C₁₉	—	4	1	no	—
180	C₂³×C₁₉	—	4	2	no	—
181	C₂³×C₁₉	—	4	8	no	—
182	C₂³×C₁₉	—	8	4	no	—
183	C₂³×C₁₉	—	8	8	no	—
184	C₂³×C₁₉	—	8	8	no	—
185	C₂³×C₁₉	#121	1	2	yes	—
186	C₂³×C₁₉	#135	1	2	yes	—
187	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
188	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₁₉	—	4	1	no	—
190	Q₈×C₁₉	—	4	1	no	—
191	Q₈×C₁₉	—	4	2	no	—
192	D₄×C₁₉	—	2	2	no	—
193	D₄×C₁₉	—	2	2	no	—
194	D₄×C₁₉	—	2	2	no	—
195	D₄×C₁₉	—	2	4	no	—
196	D₄×C₁₉	—	4	8	no	—
197	D₄×C₁₉	—	4	2	no	—
198	D₄×C₁₉	#123	1	4	yes	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	8	8	no	—
220	C₂×C₄×C₁₉	—	8	4	no	—
221	C₂×C₄×C₁₉	#121	1	2	yes	—
222	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
224	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
226	C₈×C₁₉	—	4	1	no	—
227	C₈×C₁₉	—	4	2	no	—
228	C₈×C₁₉	—	4	1	no	—
229	C₂×#450	C₂×C₁₉	1	1	yes	characteristic
230	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic
231	#2503	C₂×C₁₉	1	1	yes	characteristic, complemented
232	D₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
233	#2073	C₂×C₁₉	1	2	yes	complemented
234	#2055	C₂×C₁₉	1	2	yes	complemented
235	#1892	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#1877	C₂×C₁₉	1	2	yes	complemented
237	#1850	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#1823	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#1804	C₂×C₁₉	1	2	yes	complemented
240	C₂²×C₁₉	—	2	2	no	—
241	C₂²×C₁₉	—	2	4	no	—
242	C₂²×C₁₉	—	2	2	no	—
243	C₂²×C₁₉	—	2	4	no	—
244	C₂²×C₁₉	—	2	4	no	—
245	C₂²×C₁₉	—	4	2	no	—
246	C₂²×C₁₉	—	4	4	no	—
247	C₂²×C₁₉	—	4	2	no	—
248	C₂²×C₁₉	—	4	4	no	—
249	C₂²×C₁₉	—	4	2	no	—
250	C₂²×C₁₉	—	4	2	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	8	16	no	—
253	C₂²×C₁₉	—	8	2	no	—
254	C₂²×C₁₉	—	8	2	no	—
255	C₂²×C₁₉	#463	1	4	yes	—
256	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
257	C₂²×C₁₉	#546	1	2	yes	—
258	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
259	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
260	C₂²×C₁₉	#577	1	2	yes	—
261	C₄×C₁₉	—	2	2	no	—
262	C₄×C₁₉	—	4	2	no	—
263	C₄×C₁₉	—	4	2	no	—
264	C₄×C₁₉	—	8	1	no	—
265	C₄×C₁₉	—	8	2	no	—
266	C₄×C₁₉	—	8	1	no	—
267	C₄×C₁₉	—	8	2	no	—
268	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
269	C₄×C₁₉	#534	1	1	yes	characteristic
270	C₄×C₁₉	#551	1	2	yes	—
271	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
272	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
273	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
274	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
275	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
277	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
278	C₂²×C₂²⋊C₄	—	2	1	no	—
279	#450	—	2	4	no	—
280	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
281	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
282	C₂×#102	—	2	4	no	—
283	C₂×#102	C₂²×C₁₉	1	2	yes	—
284	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
285	C₂×#102	C₂²×C₁₉	1	2	yes	—
286	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
288	#400	—	2	2	no	—
289	#391	C₂²×C₁₉	1	2	yes	complemented
290	#390	C₂²×C₁₉	1	2	yes	—
291	#386	—	2	2	no	—
292	#382	C₂²×C₁₉	1	2	yes	complemented
293	#381	—	2	1	no	—
294	#381	—	2	1	no	—
295	#380	C₂²×C₁₉	1	1	yes	characteristic
296	#379	—	2	1	no	—
297	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
298	#340	C₂²×C₁₉	1	2	yes	complemented
299	#340	C₂²×C₁₉	1	2	yes	complemented
300	#340	C₂²×C₁₉	1	2	yes	complemented
301	#336	C₂²×C₁₉	1	2	yes	complemented
302	C₂×C₁₉	—	2	4	no	—
303	C₂×C₁₉	—	4	4	no	—
304	C₂×C₁₉	—	8	2	no	—
305	C₂×C₁₉	#2412	1	1	yes	characteristic
306	C₂×C₁₉	C₂×#463	1	1	yes	characteristic
307	C₂×C₁₉	#3042	1	1	yes	characteristic
308	C₂×C₁₉	#3296	1	2	yes	—
309	C₂×C₁₉	#3310	1	2	yes	—
310	C₂⁵	—	2	1	no	—
311	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
312	C₂²×D₄	—	2	4	no	—
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	—	2	2	no	—
315	C₂²×D₄	—	4	2	no	—
316	C₂²×D₄	D₄×C₁₉	1	4	yes	—
317	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
318	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
319	C₂³×C₄	—	2	1	no	—
320	C₂³×C₄	—	2	2	no	—
321	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
322	C₂×SD₁₆	—	2	2	no	—
323	C₂×SD₁₆	—	2	2	no	—
324	C₂×SD₁₆	—	2	4	no	—
325	C₂×SD₁₆	—	4	2	no	—
326	C₂²×C₈	—	2	2	no	—
327	C₂²×C₈	—	4	2	no	—
328	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
329	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
331	C₂²⋊Q₈	—	2	2	no	—
332	C₂²⋊Q₈	—	2	2	no	—
333	C₄×D₄	—	2	4	no	—
334	C₄×D₄	—	4	2	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	4	4	no	—
348	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
349	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
351	C₄⋊C₈	—	4	2	no	—
352	#103	—	4	2	no	—
353	#102	—	2	4	no	—
354	#102	—	2	4	no	—
355	#102	—	2	2	no	—
356	#102	—	2	2	no	—
357	C₂²⋊C₈	—	2	2	no	—
358	#95	—	2	1	no	—
359	#95	—	2	2	no	—
360	#95	—	2	2	no	—
361	#95	—	2	2	no	—
362	#95	—	2	2	no	—
363	#95	D₄×C₁₉	1	2	yes	—
364	C₁₉	#24527	1	1	yes	characteristic, direct product factor, Sylow
365	C₂⁴	—	2	1	no	—
366	C₂⁴	—	2	1	no	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	4	4	no	—
369	C₂⁴	—	4	2	no	—
370	C₂⁴	—	4	2	no	—
371	C₂⁴	—	8	2	no	—
372	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×D₄	—	2	8	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	4	8	no	—
386	C₂×D₄	—	4	4	no	—
387	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
388	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
389	C₂×D₄	#41×C₁₉	1	4	yes	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	4	4	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	8	2	no	—
402	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
403	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
404	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
406	C₂²×C₄	#41×C₁₉	1	2	yes	—
407	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
408	SD₁₆	—	4	4	no	—
409	SD₁₆	—	4	4	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	4	4	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	4	4	no	—
429	C₂²⋊C₄	—	4	4	no	—
430	C₂²⋊C₄	—	4	2	no	—
431	C₂²⋊C₄	—	4	2	no	—
432	C₂²⋊C₄	—	8	2	no	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	4	8	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	8	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	8	4	no	—
450	C₂³	—	8	8	no	—
451	C₂³	—	8	8	no	—
452	C₂³	C₁₉×#121	1	2	yes	—
453	C₂³	C₁₉×#135	1	2	yes	—
454	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
455	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
456	Q₈	—	4	1	no	—
457	Q₈	—	4	1	no	—
458	Q₈	—	4	2	no	—
459	D₄	—	2	2	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	4	no	—
463	D₄	—	4	8	no	—
464	D₄	—	4	2	no	—
465	D₄	C₁₉×#123	1	4	yes	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	8	8	no	—
487	C₂×C₄	—	8	4	no	—
488	C₂×C₄	C₁₉×#121	1	2	yes	—
489	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
490	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
491	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
492	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
493	C₈	—	4	1	no	—
494	C₈	—	4	2	no	—
495	C₈	—	4	1	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	4	no	—
500	C₂²	—	2	4	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	8	16	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	C₁₉×#463	1	4	yes	—
512	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
513	C₂²	C₁₉×#546	1	2	yes	—
514	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
515	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
516	C₂²	C₁₉×#577	1	2	yes	—
517	C₄	—	2	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	8	1	no	—
521	C₄	—	8	2	no	—
522	C₄	—	8	1	no	—
523	C₄	—	8	2	no	—
524	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
525	C₄	C₁₉×#534	1	1	yes	characteristic
526	C₄	C₁₉×#551	1	2	yes	—
527	C₂	—	2	4	no	—
528	C₂	—	4	4	no	—
529	C₂	—	8	2	no	—
530	C₂	C₁₉×#2412	1	1	yes	characteristic
531	C₂	C₂×C₁₉×#463	1	1	yes	characteristic
532	C₂	C₁₉×#3042	1	1	yes	characteristic
533	C₂	C₁₉×#3296	1	2	yes	—
534	C₂	C₁₉×#3310	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2503	C₂	semidirect
5. C₁₉×#2073	C₂	semidirect
6. C₁₉×#2055	C₂	semidirect
7. C₁₉×#1892	C₂	semidirect
8. C₁₉×#1877	C₂	semidirect
9. C₁₉×#1850	C₂	semidirect
10. C₁₉×#1823	C₂	semidirect
11. C₁₉×#1804	C₂	semidirect
21. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
22. C₂×C₁₉×#103	C₂²	semidirect
30. C₁₉×#391	C₂²	semidirect
33. C₁₉×#382	C₂²	semidirect
39. C₁₉×#340	C₂²	semidirect
40. C₁₉×#340	C₂²	semidirect
41. C₁₉×#340	C₂²	semidirect
42. C₁₉×#336	C₂²	semidirect
167. #24527	C₁₉	direct (N × H)
231. #2503	C₂×C₁₉	semidirect
233. #2073	C₂×C₁₉	semidirect
234. #2055	C₂×C₁₉	semidirect
235. #1892	C₂×C₁₉	semidirect
236. #1877	C₂×C₁₉	semidirect
237. #1850	C₂×C₁₉	semidirect
238. #1823	C₂×C₁₉	semidirect
239. #1804	C₂×C₁₉	semidirect
280. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
281. C₂×#103	C₂²×C₁₉	semidirect
289. #391	C₂²×C₁₉	semidirect
292. #382	C₂²×C₁₉	semidirect
298. #340	C₂²×C₁₉	semidirect
299. #340	C₂²×C₁₉	semidirect
300. #340	C₂²×C₁₉	semidirect
301. #336	C₂²×C₁₉	semidirect
364. C₁₉	#24527	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×#450	2
C₂²×C₁₉×#102	2
C₁₉×#2503	2
D₄×C₂²⋊C₄×C₁₉	2
C₁₉×#2073	2
C₁₉×#2055	2
C₁₉×#1892	2
C₁₉×#1877	2
C₁₉×#1850	2
C₁₉×#1823	2
C₁₉×#1804	2
#24527	19

Subgroups — C19×#24527 #18030486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24527 #18030486