Subgroups — C₁₉×#34394 #18040353

Order 4864.

1998 conjugacy classes of subgroups.

The subgroup lattice has 478 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×#2378	C₂	1	4	yes	maximal
3	C₁₉×#2369	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2365	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2356	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2351	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2347	C₂	1	2	yes	maximal
8	C₁₉×#2346	C₂	1	2	yes	maximal
9	C₁₉×#2330	C₂	1	4	yes	maximal, complemented
10	C₁₉×#2323	C₂	1	4	yes	maximal
11	C₁₉×#2320	C₂	1	4	yes	maximal, complemented
12	C₁₉×#2285	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#533	C₄	1	16	yes	complemented
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#125	C₂²	1	2	yes	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
23	C₂×C₁₉×#117	C₂²	1	2	yes	—
24	C₂×C₁₉×#117	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#391	C₂²	1	8	yes	—
27	C₁₉×#391	C₂²	1	4	yes	—
28	C₁₉×#389	C₂²	1	8	yes	—
29	C₁₉×#389	C₂²	1	4	yes	—
30	C₁₉×#389	C₂²	1	4	yes	—
31	C₁₉×#389	C₂²	1	4	yes	—
32	C₁₉×#389	C₂²	1	8	yes	—
33	C₁₉×#388	C₂²	1	8	yes	—
34	C₁₉×#388	C₂²	1	8	yes	—
35	C₁₉×#387	C₂²	1	8	yes	—
36	C₁₉×#387	C₂²	1	8	yes	—
37	C₁₉×#387	C₂²	1	8	yes	—
38	C₁₉×#384	C₂²	1	2	yes	—
39	C₁₉×#383	C₂²	1	2	yes	—
40	C₁₉×#383	C₂²	1	4	yes	—
41	C₁₉×#382	C₂²	1	1	yes	characteristic
42	C₁₉×#382	C₂²	1	1	yes	characteristic
43	C₁₉×#382	C₂²	1	2	yes	—
44	C₁₉×#382	C₂²	1	4	yes	—
45	C₁₉×#381	C₂²	1	2	yes	—
46	C₁₉×#380	C₂²	1	2	yes	—
47	C₁₉×#380	C₂²	1	1	yes	characteristic
48	C₁₉×#380	C₂²	1	1	yes	characteristic
49	C₁₉×#380	C₂²	1	2	yes	—
50	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
51	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
52	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
53	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
54	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
55	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
56	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
57	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
58	C₁₉×#376	C₂²	1	2	yes	—
59	C₁₉×#376	C₂²	1	4	yes	—
60	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
61	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	—
66	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	—
67	C₁₉×#125	C₂×C₄	1	16	yes	—
68	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
69	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
70	C₄×Q₈×C₁₉	—	4	8	no	—
71	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	—
72	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	—
73	C₁₉×#117	—	4	4	no	—
74	C₁₉×#117	C₂×C₄	1	16	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	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	4	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
89	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
92	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
93	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	—
94	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
95	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
96	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
97	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
103	C₁₉×#95	C₂³	1	2	yes	—
104	C₁₉×#95	C₂³	1	2	yes	—
105	C₁₉×#95	C₂³	1	4	yes	—
106	C₁₉×#95	C₂³	1	2	yes	—
107	C₁₉×#95	C₂³	1	2	yes	—
108	C₁₉×#95	C₂³	1	8	yes	—
109	C₁₉×#95	C₂³	1	2	yes	—
110	C₁₉×#95	C₂³	1	2	yes	—
111	C₁₉×#95	C₂³	1	4	yes	—
112	C₁₉×#95	C₂³	1	4	yes	—
113	C₁₉×#95	C₂³	1	8	yes	—
114	C₁₉×#95	C₂³	1	8	yes	—
115	C₁₉×#95	C₂³	1	8	yes	—
116	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
117	C₂×Q₈×C₁₉	—	2	4	no	—
118	C₂×Q₈×C₁₉	—	2	4	no	—
119	C₂×Q₈×C₁₉	—	4	4	no	—
120	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
121	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	4	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	4	2	no	—
126	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
127	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
128	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
141	C₄⋊C₄×C₁₉	—	2	4	no	—
142	C₄⋊C₄×C₁₉	—	2	4	no	—
143	C₄⋊C₄×C₁₉	—	2	4	no	—
144	C₄⋊C₄×C₁₉	—	2	4	no	—
145	C₄⋊C₄×C₁₉	—	4	8	no	—
146	C₄⋊C₄×C₁₉	—	4	4	no	—
147	C₄⋊C₄×C₁₉	—	4	4	no	—
148	C₄⋊C₄×C₁₉	—	4	8	no	—
149	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
150	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
151	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
152	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
153	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
154	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
155	C₂²⋊C₄×C₁₉	—	4	4	no	—
156	C₂²⋊C₄×C₁₉	—	4	2	no	—
157	C₂²⋊C₄×C₁₉	—	4	2	no	—
158	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
159	C₄²×C₁₉	—	2	8	no	—
160	C₄²×C₁₉	—	2	8	no	—
161	C₄²×C₁₉	—	4	8	no	—
162	C₄²×C₁₉	—	4	8	no	—
163	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
164	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
165	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
166	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
167	C₄²×C₁₉	C₂²×C₄	1	16	yes	—
168	#34394	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂³×C₁₉	—	2	1	no	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
174	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
175	Q₈×C₁₉	—	2	16	no	—
176	Q₈×C₁₉	—	4	8	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	8	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	8	no	—
186	C₂×C₄×C₁₉	—	2	8	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	2	4	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	2	4	no	—
195	C₂×C₄×C₁₉	—	2	4	no	—
196	C₂×C₄×C₁₉	—	2	4	no	—
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	2	4	no	—
199	C₂×C₄×C₁₉	—	4	4	no	—
200	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
201	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
202	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
203	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
204	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
205	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
206	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
207	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
208	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
209	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
210	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
211	C₂×#533	C₂×C₁₉	1	1	yes	characteristic
212	#2378	C₂×C₁₉	1	4	yes	—
213	#2369	C₂×C₁₉	1	2	yes	complemented
214	#2365	C₂×C₁₉	1	2	yes	complemented
215	#2356	C₂×C₁₉	1	2	yes	complemented
216	#2351	C₂×C₁₉	1	2	yes	complemented
217	#2347	C₂×C₁₉	1	2	yes	—
218	#2346	C₂×C₁₉	1	2	yes	—
219	#2330	C₂×C₁₉	1	4	yes	complemented
220	#2323	C₂×C₁₉	1	4	yes	—
221	#2320	C₂×C₁₉	1	4	yes	complemented
222	#2285	C₂×C₁₉	1	1	yes	characteristic
223	#2283	C₂×C₁₉	1	1	yes	characteristic
224	C₂²×C₁₉	—	2	2	no	—
225	C₂²×C₁₉	—	2	2	no	—
226	C₂²×C₁₉	—	2	2	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
230	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
231	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
232	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
233	C₂²×C₁₉	#585	1	2	yes	—
234	C₄×C₁₉	—	2	2	no	—
235	C₄×C₁₉	—	2	2	no	—
236	C₄×C₁₉	—	2	8	no	—
237	C₄×C₁₉	—	2	2	no	—
238	C₄×C₁₉	—	2	2	no	—
239	C₄×C₁₉	—	2	8	no	—
240	C₄×C₁₉	—	4	4	no	—
241	C₄×C₁₉	—	4	4	no	—
242	C₄×C₁₉	—	4	4	no	—
243	C₄×C₁₉	—	4	4	no	—
244	C₄×C₁₉	#519	1	4	yes	—
245	C₄×C₁₉	#520	1	4	yes	—
246	#533	C₄×C₁₉	1	16	yes	complemented
247	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
249	C₂×#125	C₂²×C₁₉	1	2	yes	—
250	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
251	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
252	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
253	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
254	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
255	C₂×#117	C₂²×C₁₉	1	2	yes	—
256	C₂×#117	C₂²×C₁₉	1	2	yes	—
257	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
258	#391	C₂²×C₁₉	1	8	yes	—
259	#391	C₂²×C₁₉	1	4	yes	—
260	#389	C₂²×C₁₉	1	8	yes	—
261	#389	C₂²×C₁₉	1	4	yes	—
262	#389	C₂²×C₁₉	1	4	yes	—
263	#389	C₂²×C₁₉	1	4	yes	—
264	#389	C₂²×C₁₉	1	8	yes	—
265	#388	C₂²×C₁₉	1	8	yes	—
266	#388	C₂²×C₁₉	1	8	yes	—
267	#387	C₂²×C₁₉	1	8	yes	—
268	#387	C₂²×C₁₉	1	8	yes	—
269	#387	C₂²×C₁₉	1	8	yes	—
270	#384	C₂²×C₁₉	1	2	yes	—
271	#383	C₂²×C₁₉	1	2	yes	—
272	#383	C₂²×C₁₉	1	4	yes	—
273	#382	C₂²×C₁₉	1	2	yes	—
274	#382	C₂²×C₁₉	1	4	yes	—
275	#382	C₂²×C₁₉	1	1	yes	characteristic
276	#382	C₂²×C₁₉	1	1	yes	characteristic
277	#381	C₂²×C₁₉	1	2	yes	—
278	#380	C₂²×C₁₉	1	2	yes	—
279	#380	C₂²×C₁₉	1	1	yes	characteristic
280	#380	C₂²×C₁₉	1	1	yes	characteristic
281	#380	C₂²×C₁₉	1	2	yes	—
282	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
283	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
284	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
285	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
286	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
287	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
288	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
289	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
290	#376	C₂²×C₁₉	1	4	yes	—
291	#376	C₂²×C₁₉	1	2	yes	—
292	C₂×C₁₉	—	4	2	no	—
293	C₂×C₁₉	C₂×#519	1	1	yes	characteristic
294	C₂×C₁₉	C₂×#520	1	1	yes	characteristic
295	C₂×C₁₉	#3428	1	1	yes	characteristic
296	C₂×C₁₉	#3547	1	2	yes	—
297	C₂×C₁₉	#3555	1	2	yes	—
298	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
299	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
300	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
301	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
302	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
303	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
304	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
305	#125	C₂×C₄×C₁₉	1	16	yes	—
306	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
307	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
308	C₄×Q₈	—	4	8	no	—
309	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	—
310	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	—
311	#117	—	4	4	no	—
312	#117	C₂×C₄×C₁₉	1	16	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
331	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	—
332	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
333	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
334	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
335	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
336	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
337	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
341	#95	C₂³×C₁₉	1	2	yes	—
342	#95	C₂³×C₁₉	1	2	yes	—
343	#95	C₂³×C₁₉	1	4	yes	—
344	#95	C₂³×C₁₉	1	2	yes	—
345	#95	C₂³×C₁₉	1	2	yes	—
346	#95	C₂³×C₁₉	1	8	yes	—
347	#95	C₂³×C₁₉	1	2	yes	—
348	#95	C₂³×C₁₉	1	2	yes	—
349	#95	C₂³×C₁₉	1	4	yes	—
350	#95	C₂³×C₁₉	1	4	yes	—
351	#95	C₂³×C₁₉	1	8	yes	—
352	#95	C₂³×C₁₉	1	8	yes	—
353	#95	C₂³×C₁₉	1	8	yes	—
354	C₁₉	#34394	1	1	yes	characteristic, direct product factor, Sylow
355	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	—	2	4	no	—
358	C₂×Q₈	—	4	4	no	—
359	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
360	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
366	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
367	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
368	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
370	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
371	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
372	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
373	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
374	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
375	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
376	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
378	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	4	8	no	—
385	C₄⋊C₄	—	4	4	no	—
386	C₄⋊C₄	—	4	4	no	—
387	C₄⋊C₄	—	4	8	no	—
388	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
389	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
390	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
391	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
392	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
393	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
394	C₂²⋊C₄	—	4	4	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
398	C₄²	—	2	8	no	—
399	C₄²	—	2	8	no	—
400	C₄²	—	4	8	no	—
401	C₄²	—	4	8	no	—
402	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
403	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
404	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
405	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
406	C₄²	C₂²×C₄×C₁₉	1	16	yes	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	2	no	—
411	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
412	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
413	Q₈	—	2	16	no	—
414	Q₈	—	4	8	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
439	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
440	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
441	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
442	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
443	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
444	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
445	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
446	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
447	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	—
448	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
455	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
456	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
457	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
458	C₂²	C₁₉×#585	1	2	yes	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	8	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	8	no	—
465	C₄	—	4	4	no	—
466	C₄	—	4	4	no	—
467	C₄	—	4	4	no	—
468	C₄	—	4	4	no	—
469	C₄	C₁₉×#519	1	4	yes	—
470	C₄	C₁₉×#520	1	4	yes	—
471	C₂	—	4	2	no	—
472	C₂	C₂×C₁₉×#519	1	1	yes	characteristic
473	C₂	C₂×C₁₉×#520	1	1	yes	characteristic
474	C₂	C₁₉×#3428	1	1	yes	characteristic
475	C₂	C₁₉×#3547	1	2	yes	—
476	C₂	C₁₉×#3555	1	2	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
3. C₁₉×#2369	C₂	semidirect
4. C₁₉×#2365	C₂	semidirect
5. C₁₉×#2356	C₂	semidirect
6. C₁₉×#2351	C₂	semidirect
9. C₁₉×#2330	C₂	semidirect
11. C₁₉×#2320	C₂	semidirect
14. C₁₉×#533	C₄	semidirect
168. #34394	C₁₉	direct (N × H)
213. #2369	C₂×C₁₉	semidirect
214. #2365	C₂×C₁₉	semidirect
215. #2356	C₂×C₁₉	semidirect
216. #2351	C₂×C₁₉	semidirect
219. #2330	C₂×C₁₉	semidirect
221. #2320	C₂×C₁₉	semidirect
246. #533	C₄×C₁₉	semidirect
354. C₁₉	#34394	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×#2378	2
C₁₉×#2369	2
C₁₉×#2365	2
C₁₉×#2356	2
C₁₉×#2351	2
C₁₉×#2347	2
C₁₉×#2346	2
C₁₉×#2330	2
C₁₉×#2323	2
C₁₉×#2320	2
C₁₉×#2285	2
C₁₉×#2283	2
#34394	19

Subgroups — C19×#34394 #18040353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34394 #18040353