Subgroups — C₁₉×#34221 #18040180

Order 4864.

2138 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2371	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2368	C₂	1	4	yes	maximal
4	C₁₉×#2356	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2343	C₂	1	4	yes	maximal
6	C₁₉×#2331	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2327	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2320	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₉×C₂²⋊Q₈	C₂	1	4	yes	maximal
10	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#2276	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₉×#376	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#533	C₄	1	16	yes	complemented
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#125	C₂²	1	2	yes	—
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
22	C₂×C₁₉×#117	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#391	C₂²	1	4	yes	—
26	C₁₉×#391	C₂²	1	8	yes	—
27	C₁₉×#389	C₂²	1	4	yes	—
28	C₁₉×#387	C₂²	1	8	yes	—
29	C₁₉×#387	C₂²	1	8	yes	—
30	C₁₉×#387	C₂²	1	8	yes	—
31	C₁₉×#387	C₂²	1	8	yes	—
32	C₁₉×#387	C₂²	1	8	yes	—
33	C₁₉×#385	C₂²	1	8	yes	—
34	C₁₉×#383	C₂²	1	2	yes	—
35	C₁₉×#383	C₂²	1	4	yes	—
36	C₁₉×#382	C₂²	1	2	yes	—
37	C₁₉×#382	C₂²	1	4	yes	—
38	C₁₉×#381	C₂²	1	2	yes	—
39	C₁₉×#380	C₂²	1	2	yes	—
40	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
43	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
44	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
45	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
46	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
47	C₁₉×#376	C₂²	1	1	yes	characteristic
48	C₁₉×#376	C₂²	1	1	yes	characteristic
49	C₁₉×#376	C₂²	1	2	yes	—
50	C₁₉×#376	C₂²	1	2	yes	—
51	C₁₉×#376	C₂²	1	2	yes	—
52	C₁₉×#376	C₂²	1	4	yes	—
53	C₁₉×#376	C₂²	1	2	yes	—
54	C₂×C₁₉×#95	C₂²	1	2	yes	—
55	C₂×C₁₉×#95	C₂²	1	2	yes	—
56	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
57	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
63	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
64	C₁₉×#125	C₂×C₄	1	16	yes	complemented
65	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
66	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
67	C₄×Q₈×C₁₉	—	2	16	no	—
68	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	complemented
69	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	complemented
70	C₁₉×#117	C₂×C₄	1	16	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
80	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
81	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
82	C₂×C₄²×C₁₉	—	2	8	no	—
83	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	—
84	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
85	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
87	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
88	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
89	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
94	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
95	C₁₉×#95	C₂³	1	2	yes	—
96	C₁₉×#95	C₂³	1	2	yes	—
97	C₁₉×#95	C₂³	1	2	yes	—
98	C₁₉×#95	C₂³	1	2	yes	—
99	C₁₉×#95	C₂³	1	4	yes	—
100	C₁₉×#95	C₂³	1	4	yes	—
101	C₁₉×#95	C₂³	1	4	yes	—
102	C₁₉×#95	C₂³	1	4	yes	—
103	C₁₉×#95	C₂³	1	8	yes	—
104	C₁₉×#95	C₂³	1	4	yes	—
105	C₁₉×#95	C₂³	1	4	yes	—
106	C₁₉×#95	C₂³	1	8	yes	—
107	C₁₉×#95	C₂³	1	8	yes	—
108	C₁₉×#95	C₂³	1	8	yes	—
109	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
110	C₂×Q₈×C₁₉	—	2	8	no	—
111	C₂×Q₈×C₁₉	—	4	4	no	—
112	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
113	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
114	C₂²×C₄×C₁₉	—	2	4	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	8	no	—
117	C₂²×C₄×C₁₉	—	2	8	no	—
118	C₂²×C₄×C₁₉	—	4	2	no	—
119	C₂²×C₄×C₁₉	—	4	4	no	—
120	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
122	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
123	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
124	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
134	C₄⋊C₄×C₁₉	—	2	16	no	—
135	C₄⋊C₄×C₁₉	—	2	8	no	—
136	C₄⋊C₄×C₁₉	—	4	8	no	—
137	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
138	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
139	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
140	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
141	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
142	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
143	C₂²⋊C₄×C₁₉	—	2	8	no	—
144	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
145	C₄²×C₁₉	—	2	8	no	—
146	C₄²×C₁₉	—	2	4	no	—
147	C₄²×C₁₉	—	2	16	no	—
148	C₄²×C₁₉	—	4	8	no	—
149	C₄²×C₁₉	—	4	4	no	—
150	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
151	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
152	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
153	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
154	C₄²×C₁₉	C₂²×C₄	1	16	yes	—
155	C₄²×C₁₉	#41	1	8	yes	—
156	#34221	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
160	C₂³×C₁₉	2₋¹⁺⁴	1	4	yes	—
161	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
162	Q₈×C₁₉	—	2	16	no	—
163	Q₈×C₁₉	—	4	8	no	—
164	C₂×C₄×C₁₉	—	2	8	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	8	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	8	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	2	8	no	—
178	C₂×C₄×C₁₉	—	2	8	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	8	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	4	4	no	—
183	C₂×C₄×C₁₉	—	4	16	no	—
184	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
185	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
186	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
187	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
188	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
189	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
190	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
191	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
192	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
193	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
194	C₂×#533	C₂×C₁₉	1	1	yes	characteristic
195	#2371	C₂×C₁₉	1	4	yes	complemented
196	#2368	C₂×C₁₉	1	4	yes	—
197	#2356	C₂×C₁₉	1	4	yes	complemented
198	#2343	C₂×C₁₉	1	4	yes	—
199	#2331	C₂×C₁₉	1	2	yes	complemented
200	#2327	C₂×C₁₉	1	2	yes	complemented
201	#2320	C₂×C₁₉	1	2	yes	complemented
202	C₄×C₂²⋊Q₈	C₂×C₁₉	1	4	yes	—
203	#2283	C₂×C₁₉	1	1	yes	characteristic
204	#2276	C₂×C₁₉	1	2	yes	complemented
205	C₂×#376	C₂×C₁₉	1	1	yes	characteristic
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	2	8	no	—
209	C₂²×C₁₉	#519	1	4	yes	—
210	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
211	C₂²×C₁₉	C₂²×#41	1	2	yes	—
212	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
213	C₂²×C₁₉	#585	1	2	yes	—
214	C₄×C₁₉	—	2	2	no	—
215	C₄×C₁₉	—	2	8	no	—
216	C₄×C₁₉	—	2	2	no	—
217	C₄×C₁₉	—	2	2	no	—
218	C₄×C₁₉	—	2	2	no	—
219	C₄×C₁₉	—	2	2	no	—
220	C₄×C₁₉	—	2	8	no	—
221	C₄×C₁₉	—	2	8	no	—
222	C₄×C₁₉	—	4	8	no	—
223	C₄×C₁₉	—	4	4	no	—
224	C₄×C₁₉	C₄×#41	1	4	yes	—
225	#533	C₄×C₁₉	1	16	yes	complemented
226	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×#125	C₂²×C₁₉	1	2	yes	—
229	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
230	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
231	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
232	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
233	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
234	C₂×#117	C₂²×C₁₉	1	2	yes	—
235	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
236	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
237	#391	C₂²×C₁₉	1	4	yes	—
238	#391	C₂²×C₁₉	1	8	yes	—
239	#389	C₂²×C₁₉	1	4	yes	—
240	#387	C₂²×C₁₉	1	8	yes	—
241	#387	C₂²×C₁₉	1	8	yes	—
242	#387	C₂²×C₁₉	1	8	yes	—
243	#387	C₂²×C₁₉	1	8	yes	—
244	#387	C₂²×C₁₉	1	8	yes	—
245	#385	C₂²×C₁₉	1	8	yes	—
246	#383	C₂²×C₁₉	1	4	yes	—
247	#383	C₂²×C₁₉	1	2	yes	—
248	#382	C₂²×C₁₉	1	4	yes	—
249	#382	C₂²×C₁₉	1	2	yes	—
250	#381	C₂²×C₁₉	1	2	yes	—
251	#380	C₂²×C₁₉	1	2	yes	—
252	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
253	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
254	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
255	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
256	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
257	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
258	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
259	#376	C₂²×C₁₉	1	1	yes	characteristic
260	#376	C₂²×C₁₉	1	2	yes	—
261	#376	C₂²×C₁₉	1	4	yes	—
262	#376	C₂²×C₁₉	1	2	yes	—
263	#376	C₂²×C₁₉	1	2	yes	—
264	#376	C₂²×C₁₉	1	2	yes	—
265	#376	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×#95	C₂²×C₁₉	1	2	yes	—
267	C₂×#95	C₂²×C₁₉	1	2	yes	—
268	C₂×C₁₉	—	2	4	no	—
269	C₂×C₁₉	C₂×C₄×#41	1	1	yes	characteristic
270	C₂×C₁₉	C₂×#519	1	1	yes	characteristic
271	C₂×C₁₉	#3428	1	1	yes	characteristic
272	C₂×C₁₉	#3495	1	4	yes	—
273	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
274	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
275	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
276	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
277	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
279	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
280	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
281	#125	C₂×C₄×C₁₉	1	16	yes	complemented
282	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
283	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
284	C₄×Q₈	—	2	16	no	—
285	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	complemented
286	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	complemented
287	#117	C₂×C₄×C₁₉	1	16	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
299	C₂×C₄²	—	2	8	no	—
300	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	—
301	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
302	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
303	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
304	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
305	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
306	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
307	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
310	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
312	#95	C₂³×C₁₉	1	2	yes	—
313	#95	C₂³×C₁₉	1	2	yes	—
314	#95	C₂³×C₁₉	1	2	yes	—
315	#95	C₂³×C₁₉	1	2	yes	—
316	#95	C₂³×C₁₉	1	4	yes	—
317	#95	C₂³×C₁₉	1	4	yes	—
318	#95	C₂³×C₁₉	1	4	yes	—
319	#95	C₂³×C₁₉	1	4	yes	—
320	#95	C₂³×C₁₉	1	8	yes	—
321	#95	C₂³×C₁₉	1	4	yes	—
322	#95	C₂³×C₁₉	1	4	yes	—
323	#95	C₂³×C₁₉	1	8	yes	—
324	#95	C₂³×C₁₉	1	8	yes	—
325	#95	C₂³×C₁₉	1	8	yes	—
326	C₁₉	#34221	1	1	yes	characteristic, direct product factor, Sylow
327	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
328	C₂×Q₈	—	2	8	no	—
329	C₂×Q₈	—	4	4	no	—
330	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
331	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	2	8	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
339	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
340	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
341	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
342	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
343	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
345	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
346	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
347	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
348	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
349	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
350	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
351	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
352	C₄⋊C₄	—	2	16	no	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	4	8	no	—
355	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
356	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
357	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
358	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
359	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
360	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
361	C₂²⋊C₄	—	2	8	no	—
362	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
363	C₄²	—	2	8	no	—
364	C₄²	—	2	4	no	—
365	C₄²	—	2	16	no	—
366	C₄²	—	4	8	no	—
367	C₄²	—	4	4	no	—
368	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
369	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
370	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
371	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
372	C₄²	C₂²×C₄×C₁₉	1	16	yes	—
373	C₄²	#41×C₁₉	1	8	yes	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
377	C₂³	C₁₉×2₋¹⁺⁴	1	4	yes	—
378	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
379	Q₈	—	2	16	no	—
380	Q₈	—	4	8	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	16	no	—
401	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
402	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
403	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
404	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
405	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
406	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
407	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
408	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
409	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
410	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	8	no	—
414	C₂²	C₁₉×#519	1	4	yes	—
415	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
416	C₂²	C₂²×#41×C₁₉	1	2	yes	—
417	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
418	C₂²	C₁₉×#585	1	2	yes	—
419	C₄	—	2	2	no	—
420	C₄	—	2	8	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	8	no	—
426	C₄	—	2	8	no	—
427	C₄	—	4	4	no	—
428	C₄	—	4	8	no	—
429	C₄	C₄×#41×C₁₉	1	4	yes	—
430	C₂	—	2	4	no	—
431	C₂	C₂×C₄×#41×C₁₉	1	1	yes	characteristic
432	C₂	C₂×C₁₉×#519	1	1	yes	characteristic
433	C₂	C₁₉×#3428	1	1	yes	characteristic
434	C₂	C₁₉×#3495	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2371	C₂	semidirect
4. C₁₉×#2356	C₂	semidirect
6. C₁₉×#2331	C₂	semidirect
7. C₁₉×#2327	C₂	semidirect
8. C₁₉×#2320	C₂	semidirect
11. C₁₉×#2276	C₂	semidirect
13. C₁₉×#533	C₄	semidirect
62. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
63. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
64. C₁₉×#125	C₂×C₄	semidirect
68. C₄×Q₈×C₁₉	C₂×C₄	semidirect
69. C₄×Q₈×C₁₉	C₂×C₄	semidirect
156. #34221	C₁₉	direct (N × H)
195. #2371	C₂×C₁₉	semidirect
197. #2356	C₂×C₁₉	semidirect
199. #2331	C₂×C₁₉	semidirect
200. #2327	C₂×C₁₉	semidirect
201. #2320	C₂×C₁₉	semidirect
204. #2276	C₂×C₁₉	semidirect
225. #533	C₄×C₁₉	semidirect
279. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
280. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
281. #125	C₂×C₄×C₁₉	semidirect
285. C₄×Q₈	C₂×C₄×C₁₉	semidirect
286. C₄×Q₈	C₂×C₄×C₁₉	semidirect
326. C₁₉	#34221	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×#533	2
C₁₉×#2371	2
C₁₉×#2368	2
C₁₉×#2356	2
C₁₉×#2343	2
C₁₉×#2331	2
C₁₉×#2327	2
C₁₉×#2320	2
C₄×C₁₉×C₂²⋊Q₈	2
C₁₉×#2283	2
C₁₉×#2276	2
C₂×C₁₉×#376	2
#34221	19

Subgroups — C19×#34221 #18040180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34221 #18040180