Subgroups — C₁₉×#20954 #18026913

Order 4864.

1694 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#536	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2896	C₂	1	2	yes	maximal
4	C₂²×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1888	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1886	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1733	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
11	C₁₉×#536	—	2	4	no	—
12	C₁₉×#536	C₄	1	8	yes	complemented
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₉×#124	C₂²	1	2	yes	—
15	C₂×C₁₉×#123	—	2	2	no	—
16	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
17	C₁₉×#519	—	2	2	no	—
18	C₁₉×#519	—	2	4	no	—
19	C₁₉×#519	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₁₉	—	2	4	no	—
21	C₂×C₁₉×#117	—	2	2	no	—
22	C₂×C₁₉×#117	C₂²	1	2	yes	—
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₁₉×#419	C₂²	1	4	yes	—
25	C₁₉×#418	C₂²	1	4	yes	—
26	C₁₉×#417	—	2	4	no	—
27	C₁₉×#416	—	2	4	no	—
28	C₂×C₁₉×#101	—	2	4	no	—
29	C₂×C₁₉×#101	C₂²	1	4	yes	—
30	C₁₉×#339	C₂²	1	8	yes	—
31	C₂×#41×C₁₉	—	2	2	no	—
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	4	no	—
35	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
36	C₂²×Q₈×C₁₉	—	2	2	no	—
37	C₂²×Q₈×C₁₉	—	2	2	no	—
38	C₂²×Q₈×C₁₉	—	2	4	no	—
39	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
40	C₂²×Q₈×C₁₉	D₄	1	4	yes	—
41	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
42	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₉	—	2	1	no	—
45	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	D₄	1	2	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₁₉	—	2	2	no	—
50	C₂×M₁₆×C₁₉	—	2	4	no	—
51	C₂×M₁₆×C₁₉	—	2	4	no	—
52	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
53	C₂²×C₈×C₁₉	—	2	2	no	—
54	C₁₉×C₄⋊Q₈	—	2	4	no	—
55	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
56	C₁₉×#124	—	2	4	no	—
57	C₁₉×#124	C₂×C₄	1	8	yes	complemented
58	C₁₉×#123	—	2	16	no	—
59	C₁₉×C₂²⋊Q₈	—	2	16	no	—
60	C₄×Q₈×C₁₉	—	2	16	no	—
61	C₄×Q₈×C₁₉	—	2	16	no	—
62	C₁₉×#117	—	2	8	no	—
63	C₁₉×#117	—	2	8	no	—
64	C₁₉×#117	—	2	2	no	—
65	C₁₉×#117	—	2	2	no	—
66	C₁₉×#117	—	2	2	no	—
67	C₁₉×#117	C₂×C₄	1	4	yes	—
68	C₁₉×#117	D₄	1	4	yes	—
69	C₁₉×#117	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
73	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
77	C₂×C₄²×C₁₉	—	2	4	no	—
78	C₂×C₄²×C₁₉	—	2	2	no	—
79	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
80	C₁₉×#103	—	2	8	no	—
81	C₁₉×#102	—	2	8	no	—
82	C₁₉×#101	—	2	8	no	—
83	C₂⁴×C₁₉	—	2	1	no	—
84	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
85	#41×C₁₉	—	2	8	no	—
86	#41×C₁₉	—	2	8	no	—
87	#41×C₁₉	—	4	4	no	—
88	#41×C₁₉	—	4	4	no	—
89	C₂×Q₈×C₁₉	—	2	8	no	—
90	C₂×Q₈×C₁₉	—	2	8	no	—
91	C₂×Q₈×C₁₉	—	2	4	no	—
92	C₂×Q₈×C₁₉	—	2	8	no	—
93	C₂×Q₈×C₁₉	—	2	8	no	—
94	C₂×Q₈×C₁₉	—	2	4	no	—
95	C₂×Q₈×C₁₉	—	2	4	no	—
96	C₂×Q₈×C₁₉	—	2	1	no	—
97	C₂×Q₈×C₁₉	—	2	4	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	C₂²⋊C₄	1	8	yes	—
101	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
102	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
103	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
104	C₂×D₄×C₁₉	—	2	4	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	4	1	no	—
109	C₂×D₄×C₁₉	—	4	1	no	—
110	C₂×D₄×C₁₉	—	4	2	no	—
111	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	4	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	4	2	no	—
120	C₂²×C₄×C₁₉	—	4	2	no	—
121	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
122	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	#41	1	4	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
130	M₁₆×C₁₉	—	2	4	no	—
131	M₁₆×C₁₉	—	2	4	no	—
132	M₁₆×C₁₉	—	4	4	no	—
133	C₂×C₈×C₁₉	—	2	4	no	—
134	C₂×C₈×C₁₉	—	4	4	no	—
135	C₄⋊C₄×C₁₉	—	2	16	no	—
136	C₄⋊C₄×C₁₉	—	2	4	no	—
137	C₄⋊C₄×C₁₉	—	2	16	no	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
140	C₂²⋊C₄×C₁₉	—	2	4	no	—
141	C₂²⋊C₄×C₁₉	—	2	4	no	—
142	C₂²⋊C₄×C₁₉	—	2	4	no	—
143	C₂²⋊C₄×C₁₉	—	2	16	no	—
144	C₄²×C₁₉	—	2	16	no	—
145	C₄²×C₁₉	—	2	4	no	—
146	C₄²×C₁₉	—	2	4	no	—
147	C₄²×C₁₉	—	2	2	no	—
148	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
149	#20954	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₁₉	—	2	2	no	—
151	C₂³×C₁₉	—	4	2	no	—
152	C₂³×C₁₉	—	4	4	no	—
153	C₂³×C₁₉	—	4	1	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂³×C₁₉	#120	1	1	yes	characteristic
157	C₂³×C₁₉	#120	1	1	yes	characteristic
158	C₂³×C₁₉	#123	1	2	yes	—
159	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₁₉	—	2	8	no	—
161	Q₈×C₁₉	—	2	8	no	—
162	Q₈×C₁₉	—	2	16	no	—
163	Q₈×C₁₉	—	2	4	no	—
164	Q₈×C₁₉	—	4	2	no	—
165	D₄×C₁₉	—	2	4	no	—
166	D₄×C₁₉	—	4	4	no	—
167	D₄×C₁₉	—	4	4	no	—
168	D₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	8	no	—
172	C₂×C₄×C₁₉	—	2	8	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	—	4	4	no	—
177	C₂×C₄×C₁₉	—	4	8	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	8	no	—
181	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
182	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
184	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
185	C₂×C₄×C₁₉	#120	1	2	yes	—
186	C₂×C₄×C₁₉	#121	1	4	yes	—
187	C₂×C₄×C₁₉	#121	1	4	yes	—
188	C₂×C₄×C₁₉	#123	1	2	yes	—
189	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
191	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
193	C₈×C₁₉	—	4	4	no	—
194	C₂×#536	C₂×C₁₉	1	1	yes	characteristic
195	C₂×#519	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#2896	C₂×C₁₉	1	2	yes	—
197	C₂²×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
198	#1888	C₂×C₁₉	1	4	yes	complemented
199	#1886	C₂×C₁₉	1	4	yes	complemented
200	#1733	C₂×C₁₉	1	2	yes	complemented
201	C₂²×C₁₉	—	2	2	no	—
202	C₂²×C₁₉	—	2	2	no	—
203	C₂²×C₁₉	—	2	2	no	—
204	C₂²×C₁₉	—	4	2	no	—
205	C₂²×C₁₉	—	4	2	no	—
206	C₂²×C₁₉	—	4	4	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	8	2	no	—
209	C₂²×C₁₉	—	8	2	no	—
210	C₂²×C₁₉	#386	1	2	yes	—
211	C₂²×C₁₉	#386	1	2	yes	—
212	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
213	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
214	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
215	C₄×C₁₉	—	2	8	no	—
216	C₄×C₁₉	—	4	4	no	—
217	C₄×C₁₉	—	4	8	no	—
218	C₄×C₁₉	—	4	2	no	—
219	C₄×C₁₉	#386	1	4	yes	—
220	C₄×C₁₉	C₂×C₄×D₄	1	2	yes	—
221	C₄×C₁₉	C₂×#121	1	2	yes	—
222	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
223	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
224	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
225	#536	—	2	4	no	—
226	#536	C₄×C₁₉	1	8	yes	complemented
227	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
228	C₂×#124	C₂²×C₁₉	1	2	yes	—
229	C₂×#123	—	2	2	no	—
230	C₂×C₂²⋊Q₈	—	2	2	no	—
231	#519	—	2	2	no	—
232	#519	—	2	4	no	—
233	#519	C₂²×C₁₉	1	4	yes	—
234	C₂×C₄×Q₈	—	2	4	no	—
235	C₂×#117	—	2	2	no	—
236	C₂×#117	C₂²×C₁₉	1	2	yes	—
237	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
238	#419	C₂²×C₁₉	1	4	yes	—
239	#418	C₂²×C₁₉	1	4	yes	—
240	#417	—	2	4	no	—
241	#416	—	2	4	no	—
242	C₂×#101	—	2	4	no	—
243	C₂×#101	C₂²×C₁₉	1	4	yes	—
244	#339	C₂²×C₁₉	1	8	yes	—
245	C₂×C₁₉	—	2	1	no	—
246	C₂×C₁₉	—	2	1	no	—
247	C₂×C₁₉	—	2	2	no	—
248	C₂×C₁₉	—	2	2	no	—
249	C₂×C₁₉	—	8	2	no	—
250	C₂×C₁₉	C₂×#386	1	1	yes	characteristic
251	C₂×C₁₉	#3020	1	2	yes	—
252	C₂×#41	—	2	2	no	—
253	C₂×#41	—	2	2	no	—
254	C₂×#41	—	2	2	no	—
255	C₂×#41	—	2	4	no	—
256	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
257	C₂²×Q₈	—	2	2	no	—
258	C₂²×Q₈	—	2	2	no	—
259	C₂²×Q₈	—	2	4	no	—
260	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
261	C₂²×Q₈	D₄×C₁₉	1	4	yes	—
262	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
263	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
264	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
267	C₂³×C₄	—	2	1	no	—
268	C₂³×C₄	D₄×C₁₉	1	2	yes	—
269	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	2	4	no	—
272	C₂×M₁₆	—	2	4	no	—
273	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
274	C₂²×C₈	—	2	2	no	—
275	C₄⋊Q₈	—	2	4	no	—
276	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
277	#124	—	2	4	no	—
278	#124	C₂×C₄×C₁₉	1	8	yes	complemented
279	#123	—	2	16	no	—
280	C₂²⋊Q₈	—	2	16	no	—
281	C₄×Q₈	—	2	16	no	—
282	C₄×Q₈	—	2	16	no	—
283	#117	—	2	8	no	—
284	#117	—	2	8	no	—
285	#117	—	2	2	no	—
286	#117	—	2	2	no	—
287	#117	—	2	2	no	—
288	#117	C₂×C₄×C₁₉	1	4	yes	—
289	#117	D₄×C₁₉	1	4	yes	—
290	#117	C₂³×C₁₉	1	4	yes	—
291	C₂×C₄⋊C₄	—	2	4	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	4	no	—
294	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	4	no	—
298	C₂×C₄²	—	2	4	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
301	#103	—	2	8	no	—
302	#102	—	2	8	no	—
303	#101	—	2	8	no	—
304	C₁₉	#20954	1	1	yes	characteristic, direct product factor, Sylow
305	C₂⁴	—	2	1	no	—
306	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
307	#41	—	2	8	no	—
308	#41	—	2	8	no	—
309	#41	—	4	4	no	—
310	#41	—	4	4	no	—
311	C₂×Q₈	—	2	8	no	—
312	C₂×Q₈	—	2	8	no	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	2	8	no	—
315	C₂×Q₈	—	2	8	no	—
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	2	4	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	C₂²⋊C₄×C₁₉	1	8	yes	—
323	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
324	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
325	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
344	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
346	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
350	C₂²×C₄	#41×C₁₉	1	4	yes	—
351	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
352	M₁₆	—	2	4	no	—
353	M₁₆	—	2	4	no	—
354	M₁₆	—	4	4	no	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	—	4	4	no	—
357	C₄⋊C₄	—	2	16	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	16	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	2	16	no	—
366	C₄²	—	2	16	no	—
367	C₄²	—	2	4	no	—
368	C₄²	—	2	4	no	—
369	C₄²	—	2	2	no	—
370	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
371	C₂³	—	2	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	4	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
377	C₂³	C₁₉×#120	1	1	yes	characteristic
378	C₂³	C₁₉×#120	1	1	yes	characteristic
379	C₂³	C₁₉×#123	1	2	yes	—
380	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
381	Q₈	—	2	16	no	—
382	Q₈	—	2	8	no	—
383	Q₈	—	2	8	no	—
384	Q₈	—	2	4	no	—
385	Q₈	—	4	2	no	—
386	D₄	—	2	4	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	2	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	8	no	—
402	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
403	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
404	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
405	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
406	C₂×C₄	C₁₉×#120	1	2	yes	—
407	C₂×C₄	C₁₉×#121	1	4	yes	—
408	C₂×C₄	C₁₉×#121	1	4	yes	—
409	C₂×C₄	C₁₉×#123	1	2	yes	—
410	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
412	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
414	C₈	—	4	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	C₁₉×#386	1	2	yes	—
425	C₂²	C₁₉×#386	1	2	yes	—
426	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
427	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
428	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
429	C₄	—	2	8	no	—
430	C₄	—	4	4	no	—
431	C₄	—	4	8	no	—
432	C₄	—	4	2	no	—
433	C₄	C₁₉×#386	1	4	yes	—
434	C₄	C₂×C₄×D₄×C₁₉	1	2	yes	—
435	C₄	C₂×C₁₉×#121	1	2	yes	—
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	2	2	no	—
439	C₂	—	2	2	no	—
440	C₂	—	8	2	no	—
441	C₂	C₂×C₁₉×#386	1	1	yes	characteristic
442	C₂	C₁₉×#3020	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#519	C₂	semidirect
4. C₂²×C₁₉×#101	C₂	semidirect
5. C₁₉×#1888	C₂	semidirect
6. C₁₉×#1886	C₂	semidirect
7. C₁₉×#1733	C₂	semidirect
12. C₁₉×#536	C₄	semidirect
55. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
57. C₁₉×#124	C₂×C₄	semidirect
149. #20954	C₁₉	direct (N × H)
195. C₂×#519	C₂×C₁₉	semidirect
197. C₂²×#101	C₂×C₁₉	semidirect
198. #1888	C₂×C₁₉	semidirect
199. #1886	C₂×C₁₉	semidirect
200. #1733	C₂×C₁₉	semidirect
226. #536	C₄×C₁₉	semidirect
276. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
278. #124	C₂×C₄×C₁₉	semidirect
304. C₁₉	#20954	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×#536	2
C₂×C₁₉×#519	2
C₁₉×#2896	2
C₂²×C₁₉×#101	2
C₁₉×#1888	2
C₁₉×#1886	2
C₁₉×#1733	2
#20954	19

Subgroups — C19×#20954 #18026913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20954 #18026913