Subgroups — C₁₉×#34966 #18040925

Order 4864.

1878 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2606	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2605	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2570	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2550	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2442	C₂	1	2	yes	maximal
6	C₁₉×#2440	C₂	1	2	yes	maximal
7	C₁₉×#2438	C₂	1	4	yes	maximal
8	C₁₉×#2402	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2399	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₉×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×#125	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₉×C₂²⋊Q₈	C₂	1	4	yes	maximal
13	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic
14	C₄×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
15	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₉×#125	C₂²	1	2	yes	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
19	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
20	C₂×C₁₉×#117	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
22	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#400	C₂²	1	4	yes	—
25	C₁₉×#400	C₂²	1	4	yes	—
26	C₁₉×#398	C₂²	1	4	yes	—
27	C₁₉×#398	C₂²	1	4	yes	—
28	C₁₉×#398	C₂²	1	4	yes	—
29	C₁₉×#398	C₂²	1	4	yes	—
30	C₁₉×#395	C₂²	1	4	yes	—
31	C₁₉×#395	C₂²	1	4	yes	—
32	C₁₉×#391	C₂²	1	4	yes	—
33	C₁₉×#391	C₂²	1	4	yes	—
34	C₁₉×#389	C₂²	1	4	yes	—
35	C₁₉×#389	C₂²	1	2	yes	—
36	C₁₉×#389	C₂²	1	2	yes	—
37	C₁₉×#389	C₂²	1	2	yes	—
38	C₁₉×#389	C₂²	1	2	yes	—
39	C₁₉×#389	C₂²	1	4	yes	—
40	C₁₉×#387	C₂²	1	4	yes	—
41	C₁₉×#387	C₂²	1	4	yes	—
42	C₁₉×#387	C₂²	1	4	yes	—
43	C₁₉×#387	C₂²	1	4	yes	—
44	C₁₉×#385	C₂²	1	4	yes	—
45	C₁₉×#385	C₂²	1	4	yes	—
46	C₁₉×#384	C₂²	1	2	yes	—
47	C₁₉×#383	C₂²	1	2	yes	—
48	C₁₉×#382	C₂²	1	2	yes	—
49	C₁₉×#382	C₂²	1	2	yes	—
50	C₁₉×#381	C₂²	1	2	yes	—
51	C₁₉×#380	C₂²	1	4	yes	—
52	C₁₉×#380	C₂²	1	2	yes	—
53	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
55	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
56	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
58	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
59	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
60	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
62	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
65	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
69	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
70	C₁₉×#376	C₂²	1	2	yes	—
71	C₁₉×#376	C₂²	1	1	yes	characteristic
72	C₁₉×#376	C₂²	1	1	yes	characteristic
73	C₂×C₁₉×#95	C₂²	1	2	yes	—
74	C₄³×C₁₉	C₂²	1	2	yes	—
75	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
76	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
77	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×C₄⋊Q₈	—	2	8	no	—
81	C₁₉×#125	—	2	8	no	—
82	C₁₉×C₂²⋊Q₈	—	2	16	no	—
83	C₄×Q₈×C₁₉	—	4	8	no	—
84	C₁₉×#117	—	2	8	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
102	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
103	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
105	C₂×C₄²×C₁₉	—	4	4	no	—
106	C₂×C₄²×C₁₉	Q₈	1	8	yes	complemented
107	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
108	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
109	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
110	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
111	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
114	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
116	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
117	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
122	C₁₉×#95	C₂³	1	4	yes	—
123	C₁₉×#95	C₂³	1	2	yes	—
124	C₁₉×#95	C₂³	1	2	yes	—
125	C₁₉×#95	C₂³	1	2	yes	—
126	C₁₉×#95	C₂³	1	2	yes	—
127	C₁₉×#95	C₂³	1	1	yes	characteristic
128	C₁₉×#95	C₂³	1	1	yes	characteristic
129	C₁₉×#95	C₂³	1	1	yes	characteristic
130	C₁₉×#95	C₂³	1	1	yes	characteristic
131	C₁₉×#95	C₂³	1	4	yes	—
132	C₁₉×#95	C₂³	1	4	yes	—
133	C₁₉×#95	C₂³	1	4	yes	—
134	C₁₉×#95	C₂³	1	4	yes	—
135	C₁₉×#95	C₂³	1	4	yes	—
136	C₁₉×#95	C₂³	1	2	yes	—
137	C₁₉×#95	C₂³	1	2	yes	—
138	C₁₉×#95	C₂³	1	4	yes	—
139	C₁₉×#95	C₂³	1	4	yes	—
140	C₁₉×#95	C₂³	1	4	yes	—
141	C₁₉×#95	C₂³	1	4	yes	—
142	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
143	C₂×Q₈×C₁₉	—	2	8	no	—
144	C₂×Q₈×C₁₉	—	2	8	no	—
145	C₂×Q₈×C₁₉	—	4	4	no	—
146	C₂²×C₄×C₁₉	—	2	4	no	—
147	C₂²×C₄×C₁₉	—	2	4	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	8	no	—
151	C₂²×C₄×C₁₉	—	2	8	no	—
152	C₂²×C₄×C₁₉	—	4	4	no	—
153	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
154	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
155	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
156	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
170	C₄⋊C₄×C₁₉	—	2	8	no	—
171	C₄⋊C₄×C₁₉	—	2	4	no	—
172	C₄⋊C₄×C₁₉	—	2	4	no	—
173	C₄⋊C₄×C₁₉	—	2	4	no	—
174	C₄⋊C₄×C₁₉	—	2	8	no	—
175	C₄⋊C₄×C₁₉	—	2	8	no	—
176	C₄⋊C₄×C₁₉	—	2	8	no	—
177	C₄⋊C₄×C₁₉	—	2	8	no	—
178	C₄⋊C₄×C₁₉	—	2	8	no	—
179	C₄⋊C₄×C₁₉	—	2	4	no	—
180	C₄⋊C₄×C₁₉	—	2	8	no	—
181	C₄⋊C₄×C₁₉	—	2	4	no	—
182	C₄⋊C₄×C₁₉	—	4	4	no	—
183	C₄⋊C₄×C₁₉	—	4	4	no	—
184	C₄⋊C₄×C₁₉	—	4	4	no	—
185	C₄⋊C₄×C₁₉	#41	1	8	yes	—
186	C₂²⋊C₄×C₁₉	—	2	4	no	—
187	C₂²⋊C₄×C₁₉	—	2	8	no	—
188	C₂²⋊C₄×C₁₉	#41	1	8	yes	—
189	C₄²×C₁₉	—	2	4	no	—
190	C₄²×C₁₉	—	2	4	no	—
191	C₄²×C₁₉	—	2	4	no	—
192	C₄²×C₁₉	—	2	4	no	—
193	C₄²×C₁₉	—	2	8	no	—
194	C₄²×C₁₉	—	2	4	no	—
195	C₄²×C₁₉	—	2	4	no	—
196	C₄²×C₁₉	—	2	4	no	—
197	C₄²×C₁₉	—	2	4	no	—
198	C₄²×C₁₉	—	4	2	no	—
199	C₄²×C₁₉	—	4	2	no	—
200	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
201	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
202	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
203	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
204	#34966	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	—	2	1	no	—
207	C₂³×C₁₉	—	2	1	no	—
208	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
209	C₂³×C₁₉	C₂×#41	1	4	yes	—
210	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
211	Q₈×C₁₉	—	4	16	no	—
212	C₂×C₄×C₁₉	—	2	8	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	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	4	no	—
219	C₂×C₄×C₁₉	—	2	4	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	8	no	—
225	C₂×C₄×C₁₉	—	2	8	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	4	no	—
231	C₂×C₄×C₁₉	—	2	4	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	4	no	—
235	C₂×C₄×C₁₉	—	2	4	no	—
236	C₂×C₄×C₁₉	—	2	4	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	4	no	—
241	C₂×C₄×C₁₉	—	4	16	no	—
242	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
243	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
244	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
245	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
246	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
247	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
248	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
249	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
250	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
251	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
252	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
253	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
254	#2606	C₂×C₁₉	1	2	yes	complemented
255	#2605	C₂×C₁₉	1	2	yes	complemented
256	#2570	C₂×C₁₉	1	2	yes	complemented
257	#2550	C₂×C₁₉	1	2	yes	complemented
258	#2442	C₂×C₁₉	1	2	yes	—
259	#2440	C₂×C₁₉	1	2	yes	—
260	#2438	C₂×C₁₉	1	4	yes	—
261	#2402	C₂×C₁₉	1	2	yes	complemented
262	#2399	C₂×C₁₉	1	2	yes	complemented
263	C₄×C₄⋊Q₈	C₂×C₁₉	1	2	yes	complemented
264	C₄×#125	C₂×C₁₉	1	2	yes	complemented
265	C₄×C₂²⋊Q₈	C₂×C₁₉	1	4	yes	—
266	#2283	C₂×C₁₉	1	1	yes	characteristic
267	C₄×#117	C₂×C₁₉	1	1	yes	characteristic
268	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
269	C₂²×C₁₉	—	2	2	no	—
270	C₂²×C₁₉	—	2	2	no	—
271	C₂²×C₁₉	—	2	4	no	—
272	C₂²×C₁₉	—	2	4	no	—
273	C₂²×C₁₉	#533	1	4	yes	—
274	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
275	C₂²×C₁₉	C₂²×#41	1	2	yes	—
276	C₂²×C₁₉	C₂²×#41	1	2	yes	—
277	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
278	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
279	C₄×C₁₉	—	2	2	no	—
280	C₄×C₁₉	—	2	2	no	—
281	C₄×C₁₉	—	2	2	no	—
282	C₄×C₁₉	—	2	2	no	—
283	C₄×C₁₉	—	2	8	no	—
284	C₄×C₁₉	—	2	4	no	—
285	C₄×C₁₉	—	2	4	no	—
286	C₄×C₁₉	—	4	2	no	—
287	C₄×C₁₉	—	4	4	no	—
288	C₄×C₁₉	—	4	4	no	—
289	C₄×C₁₉	—	4	2	no	—
290	C₄×C₁₉	—	4	4	no	—
291	C₄×C₁₉	#533	1	4	yes	—
292	C₄×C₁₉	#544	1	4	yes	—
293	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
294	C₂×#125	C₂²×C₁₉	1	2	yes	—
295	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
296	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
297	C₂×#117	C₂²×C₁₉	1	2	yes	—
298	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
299	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
300	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
301	#400	C₂²×C₁₉	1	4	yes	—
302	#400	C₂²×C₁₉	1	4	yes	—
303	#398	C₂²×C₁₉	1	4	yes	—
304	#398	C₂²×C₁₉	1	4	yes	—
305	#398	C₂²×C₁₉	1	4	yes	—
306	#398	C₂²×C₁₉	1	4	yes	—
307	#395	C₂²×C₁₉	1	4	yes	—
308	#395	C₂²×C₁₉	1	4	yes	—
309	#391	C₂²×C₁₉	1	4	yes	—
310	#391	C₂²×C₁₉	1	4	yes	—
311	#389	C₂²×C₁₉	1	2	yes	—
312	#389	C₂²×C₁₉	1	2	yes	—
313	#389	C₂²×C₁₉	1	2	yes	—
314	#389	C₂²×C₁₉	1	4	yes	—
315	#389	C₂²×C₁₉	1	2	yes	—
316	#389	C₂²×C₁₉	1	4	yes	—
317	#387	C₂²×C₁₉	1	4	yes	—
318	#387	C₂²×C₁₉	1	4	yes	—
319	#387	C₂²×C₁₉	1	4	yes	—
320	#387	C₂²×C₁₉	1	4	yes	—
321	#385	C₂²×C₁₉	1	4	yes	—
322	#385	C₂²×C₁₉	1	4	yes	—
323	#384	C₂²×C₁₉	1	2	yes	—
324	#383	C₂²×C₁₉	1	2	yes	—
325	#382	C₂²×C₁₉	1	2	yes	—
326	#382	C₂²×C₁₉	1	2	yes	—
327	#381	C₂²×C₁₉	1	2	yes	—
328	#380	C₂²×C₁₉	1	4	yes	—
329	#380	C₂²×C₁₉	1	2	yes	—
330	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
331	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
332	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
333	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
334	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
335	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
336	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
337	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
338	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
339	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
340	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
341	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
342	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
343	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
344	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
345	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
346	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
347	#376	C₂²×C₁₉	1	1	yes	characteristic
348	#376	C₂²×C₁₉	1	1	yes	characteristic
349	#376	C₂²×C₁₉	1	2	yes	—
350	C₂×#95	C₂²×C₁₉	1	2	yes	—
351	C₄³	C₂²×C₁₉	1	2	yes	—
352	C₂×C₁₉	—	2	4	no	—
353	C₂×C₁₉	C₂×#533	1	1	yes	characteristic
354	C₂×C₁₉	C₂×#533	1	1	yes	characteristic
355	C₂×C₁₉	C₂×#544	1	1	yes	characteristic
356	C₂×C₁₉	#3481	1	2	yes	—
357	C₂×C₁₉	#3482	1	2	yes	—
358	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
359	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
360	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
361	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
362	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
363	C₄⋊Q₈	—	2	8	no	—
364	#125	—	2	8	no	—
365	C₂²⋊Q₈	—	2	16	no	—
366	C₄×Q₈	—	4	8	no	—
367	#117	—	2	8	no	—
368	C₂×C₄⋊C₄	—	2	8	no	—
369	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
388	C₂×C₄²	—	4	4	no	—
389	C₂×C₄²	Q₈×C₁₉	1	8	yes	complemented
390	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
391	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
392	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
393	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
394	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
395	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
396	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
397	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
398	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
399	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
400	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
401	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
404	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
405	#95	C₂³×C₁₉	1	4	yes	—
406	#95	C₂³×C₁₉	1	2	yes	—
407	#95	C₂³×C₁₉	1	2	yes	—
408	#95	C₂³×C₁₉	1	2	yes	—
409	#95	C₂³×C₁₉	1	2	yes	—
410	#95	C₂³×C₁₉	1	1	yes	characteristic
411	#95	C₂³×C₁₉	1	1	yes	characteristic
412	#95	C₂³×C₁₉	1	1	yes	characteristic
413	#95	C₂³×C₁₉	1	1	yes	characteristic
414	#95	C₂³×C₁₉	1	4	yes	—
415	#95	C₂³×C₁₉	1	4	yes	—
416	#95	C₂³×C₁₉	1	4	yes	—
417	#95	C₂³×C₁₉	1	4	yes	—
418	#95	C₂³×C₁₉	1	4	yes	—
419	#95	C₂³×C₁₉	1	2	yes	—
420	#95	C₂³×C₁₉	1	2	yes	—
421	#95	C₂³×C₁₉	1	4	yes	—
422	#95	C₂³×C₁₉	1	4	yes	—
423	#95	C₂³×C₁₉	1	4	yes	—
424	#95	C₂³×C₁₉	1	4	yes	—
425	C₁₉	#34966	1	1	yes	characteristic, direct product factor, Sylow
426	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
427	C₂×Q₈	—	2	8	no	—
428	C₂×Q₈	—	2	8	no	—
429	C₂×Q₈	—	4	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	8	no	—
435	C₂²×C₄	—	2	8	no	—
436	C₂²×C₄	—	4	4	no	—
437	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
438	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
439	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
440	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
441	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
442	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
444	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
447	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
448	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
453	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
454	C₄⋊C₄	—	2	8	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	8	no	—
459	C₄⋊C₄	—	2	8	no	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	—	2	8	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	8	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	4	4	no	—
467	C₄⋊C₄	—	4	4	no	—
468	C₄⋊C₄	—	4	4	no	—
469	C₄⋊C₄	#41×C₁₉	1	8	yes	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	8	no	—
472	C₂²⋊C₄	#41×C₁₉	1	8	yes	—
473	C₄²	—	2	4	no	—
474	C₄²	—	2	4	no	—
475	C₄²	—	2	4	no	—
476	C₄²	—	2	4	no	—
477	C₄²	—	2	8	no	—
478	C₄²	—	2	4	no	—
479	C₄²	—	2	4	no	—
480	C₄²	—	2	4	no	—
481	C₄²	—	2	4	no	—
482	C₄²	—	4	2	no	—
483	C₄²	—	4	2	no	—
484	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
485	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
486	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
487	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	2	1	no	—
491	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
492	C₂³	C₂×#41×C₁₉	1	4	yes	—
493	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
494	Q₈	—	4	16	no	—
495	C₂×C₄	—	2	8	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	8	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	4	16	no	—
525	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
526	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
527	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
528	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
529	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
530	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
531	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
532	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
533	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
534	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
535	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
536	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	2	4	no	—
541	C₂²	C₁₉×#533	1	4	yes	—
542	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
543	C₂²	C₂²×#41×C₁₉	1	2	yes	—
544	C₂²	C₂²×#41×C₁₉	1	2	yes	—
545	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
546	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	8	no	—
552	C₄	—	2	4	no	—
553	C₄	—	2	4	no	—
554	C₄	—	4	4	no	—
555	C₄	—	4	4	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	2	no	—
558	C₄	—	4	4	no	—
559	C₄	C₁₉×#533	1	4	yes	—
560	C₄	C₁₉×#544	1	4	yes	—
561	C₂	—	2	4	no	—
562	C₂	C₂×C₁₉×#533	1	1	yes	characteristic
563	C₂	C₂×C₁₉×#533	1	1	yes	characteristic
564	C₂	C₂×C₁₉×#544	1	1	yes	characteristic
565	C₂	C₁₉×#3481	1	2	yes	—
566	C₂	C₁₉×#3482	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂⁵
prime radical	C₂⁴×C₁₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2606	C₂	semidirect
2. C₁₉×#2605	C₂	semidirect
3. C₁₉×#2570	C₂	semidirect
4. C₁₉×#2550	C₂	semidirect
8. C₁₉×#2402	C₂	semidirect
9. C₁₉×#2399	C₂	semidirect
10. C₄×C₁₉×C₄⋊Q₈	C₂	semidirect
11. C₄×C₁₉×#125	C₂	semidirect
106. C₂×C₄²×C₁₉	Q₈	semidirect
204. #34966	C₁₉	direct (N × H)
254. #2606	C₂×C₁₉	semidirect
255. #2605	C₂×C₁₉	semidirect
256. #2570	C₂×C₁₉	semidirect
257. #2550	C₂×C₁₉	semidirect
261. #2402	C₂×C₁₉	semidirect
262. #2399	C₂×C₁₉	semidirect
263. C₄×C₄⋊Q₈	C₂×C₁₉	semidirect
264. C₄×#125	C₂×C₁₉	semidirect
389. C₂×C₄²	Q₈×C₁₉	semidirect
425. C₁₉	#34966	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×#2606	2
C₁₉×#2605	2
C₁₉×#2570	2
C₁₉×#2550	2
C₁₉×#2442	2
C₁₉×#2440	2
C₁₉×#2438	2
C₁₉×#2402	2
C₁₉×#2399	2
C₄×C₁₉×C₄⋊Q₈	2
C₄×C₁₉×#125	2
C₄×C₁₉×C₂²⋊Q₈	2
C₁₉×#2283	2
C₄×C₁₉×#117	2
C₂×C₄×C₄⋊C₄×C₁₉	2
#34966	19

Subgroups — C19×#34966 #18040925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34966 #18040925