Subgroups — C₁₉×#61721 #18067680

Order 4864.

1798 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#555	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3357	C₂	1	8	yes	maximal, complemented
4	C₁₉×#3329	C₂	1	8	yes	maximal, complemented
5	C₁₉×#3230	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3193	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3101	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3095	C₂	1	4	yes	maximal, complemented
9	C₁₉×#2975	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#555	—	2	4	no	—
11	C₁₉×#555	C₂²	1	8	yes	—
12	C₁₉×#554	—	2	4	no	—
13	C₁₉×#554	C₂²	1	4	yes	complemented
14	D₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
15	C₁₉×#544	—	2	1	no	—
16	C₁₉×#543	—	2	2	no	—
17	C₁₉×#533	C₂²	1	2	yes	—
18	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#124	—	2	2	no	—
20	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
21	C₂×C₁₉×#121	—	2	1	no	—
22	C₂×C₁₉×#121	C₂²	1	2	yes	—
23	C₁₉×#518	—	2	1	no	—
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#117	—	2	1	no	—
27	C₂×C₁₉×#117	C₂²	1	2	yes	—
28	C₁₉×#500	C₂²	1	4	yes	complemented
29	C₁₉×#487	C₂²	1	4	yes	complemented
30	C₁₉×#485	C₂²	1	16	yes	complemented
31	C₁₉×#484	C₂²	1	8	yes	—
32	C₁₉×#483	C₂²	1	4	yes	—
33	C₁₉×#480	C₂²	1	8	yes	complemented
34	C₁₉×#477	C₂²	1	8	yes	complemented
35	C₁₉×#476	C₂²	1	4	yes	complemented
36	C₁₉×#468	C₂²	1	16	yes	complemented
37	C₁₉×#461	C₂²	1	4	yes	complemented
38	C₁₉×#450	C₂²	1	4	yes	—
39	C₁₉×#448	C₂²	1	8	yes	complemented
40	C₄×SD₁₆×C₁₉	C₂²	1	8	yes	complemented
41	C₁₉×#436	C₂²	1	8	yes	complemented
42	C₁₉×#431	C₂²	1	2	yes	—
43	C₁₉×#428	C₂²	1	8	yes	complemented
44	C₁₉×#419	C₂²	1	8	yes	complemented
45	C₁₉×#407	C₂²	1	4	yes	—
46	C₂²×Q₈×C₁₉	—	2	1	no	—
47	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
48	C₂²×D₄×C₁₉	—	2	2	no	—
49	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
53	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
54	C₂×M₁₆×C₁₉	C₂³	1	8	yes	—
55	C₁₉×C₄⋊Q₈	—	2	4	no	—
56	C₁₉×C₄⋊Q₈	—	2	2	no	—
57	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
60	C₁₉×#125	—	2	4	no	—
61	C₁₉×#125	—	2	2	no	—
62	C₁₉×#124	—	2	16	no	—
63	C₁₉×C₂²⋊Q₈	—	2	4	no	—
64	C₁₉×C₂²⋊Q₈	—	2	4	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	—	2	8	no	—
67	C₁₉×C₂²⋊Q₈	—	2	8	no	—
68	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
69	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
70	C₁₉×#121	—	2	8	no	—
71	C₁₉×#121	—	2	4	no	—
72	C₁₉×#121	C₂³	1	8	yes	—
73	C₄×Q₈×C₁₉	—	2	2	no	—
74	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
75	C₄×D₄×C₁₉	—	2	4	no	—
76	C₄×D₄×C₁₉	—	2	4	no	—
77	C₄×D₄×C₁₉	—	2	2	no	—
78	C₄×D₄×C₁₉	D₄	1	4	yes	—
79	C₄×D₄×C₁₉	C₂³	1	4	yes	—
80	C₄×D₄×C₁₉	C₂³	1	4	yes	—
81	C₁₉×#117	—	2	4	no	—
82	C₁₉×#117	—	2	2	no	—
83	C₁₉×#117	—	2	8	no	—
84	C₁₉×#117	C₂³	1	8	yes	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
87	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
96	C₂×C₄²×C₁₉	—	2	2	no	—
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₁₉×#107	C₂³	1	16	yes	—
99	C₁₉×#106	C₂³	1	8	yes	—
100	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
101	C₁₉×#103	C₂³	1	8	yes	—
102	C₁₉×#103	C₂³	1	16	yes	—
103	C₁₉×#102	C₂³	1	8	yes	—
104	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
105	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
106	C₄×C₈×C₁₉	C₂³	1	4	yes	—
107	C₂⁴×C₁₉	—	2	1	no	—
108	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₁₉	—	2	2	no	—
110	C₂×Q₈×C₁₉	—	2	4	no	—
111	C₂×Q₈×C₁₉	—	2	4	no	—
112	C₂×Q₈×C₁₉	—	4	8	no	—
113	C₂×Q₈×C₁₉	—	8	2	no	—
114	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
115	C₂×D₄×C₁₉	—	2	8	no	—
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	—	4	2	no	—
119	C₂×D₄×C₁₉	—	8	4	no	—
120	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
121	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	4	no	—
125	C₂²×C₄×C₁₉	—	2	4	no	—
126	C₂²×C₄×C₁₉	—	2	4	no	—
127	C₂²×C₄×C₁₉	—	4	4	no	—
128	C₂²×C₄×C₁₉	—	4	4	no	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
135	SD₁₆×C₁₉	—	4	8	no	—
136	M₁₆×C₁₉	—	4	8	no	—
137	C₂×C₈×C₁₉	C₂⁴	1	8	yes	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	2	4	no	—
140	C₄⋊C₄×C₁₉	—	2	8	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	4	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	4	no	—
148	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
149	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
150	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
151	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
152	C₂²⋊C₄×C₁₉	—	2	4	no	—
153	C₂²⋊C₄×C₁₉	—	2	8	no	—
154	C₂²⋊C₄×C₁₉	—	2	8	no	—
155	C₂²⋊C₄×C₁₉	—	2	8	no	—
156	C₂²⋊C₄×C₁₉	—	2	4	no	—
157	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
158	C₄²×C₁₉	—	2	8	no	—
159	C₄²×C₁₉	—	2	4	no	—
160	C₄²×C₁₉	C₂×D₄	1	2	yes	—
161	C₄²×C₁₉	C₂⁴	1	2	yes	—
162	#61721	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂³×C₁₉	—	2	4	no	—
164	C₂³×C₁₉	—	2	2	no	—
165	C₂³×C₁₉	—	4	2	no	—
166	C₂³×C₁₉	—	4	2	no	—
167	C₂³×C₁₉	—	4	2	no	—
168	C₂³×C₁₉	—	4	2	no	—
169	C₂³×C₁₉	—	4	2	no	—
170	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
171	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₁₉	—	2	8	no	—
173	Q₈×C₁₉	—	8	2	no	—
174	Q₈×C₁₉	—	8	4	no	—
175	Q₈×C₁₉	—	8	4	no	—
176	D₄×C₁₉	—	2	8	no	—
177	D₄×C₁₉	—	2	4	no	—
178	D₄×C₁₉	—	4	2	no	—
179	D₄×C₁₉	—	8	8	no	—
180	C₂×C₄×C₁₉	—	2	8	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	4	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	8	no	—
192	C₂×C₄×C₁₉	—	8	4	no	—
193	C₂×C₄×C₁₉	—	8	4	no	—
194	C₂×C₄×C₁₉	#137	1	4	yes	—
195	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
200	C₈×C₁₉	—	2	8	no	—
201	#3501	C₂×C₁₉	1	1	yes	characteristic, complemented
202	C₂×#555	C₂×C₁₉	1	1	yes	characteristic
203	#3357	C₂×C₁₉	1	8	yes	complemented
204	#3329	C₂×C₁₉	1	8	yes	complemented
205	#3230	C₂×C₁₉	1	2	yes	complemented
206	#3193	C₂×C₁₉	1	4	yes	complemented
207	#3101	C₂×C₁₉	1	2	yes	complemented
208	#3095	C₂×C₁₉	1	4	yes	complemented
209	#2975	C₂×C₁₉	1	1	yes	characteristic, complemented
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	—	2	4	no	—
213	C₂²×C₁₉	—	2	4	no	—
214	C₂²×C₁₉	—	2	4	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	4	2	no	—
217	C₂²×C₁₉	—	4	2	no	—
218	C₂²×C₁₉	—	8	4	no	—
219	C₂²×C₁₉	—	8	4	no	—
220	C₂²×C₁₉	C₂×#137	1	2	yes	—
221	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
222	C₄×C₁₉	—	2	2	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	4	no	—
225	C₄×C₁₉	—	4	4	no	—
226	C₄×C₁₉	—	4	4	no	—
227	C₄×C₁₉	—	4	4	no	—
228	C₄×C₁₉	—	4	2	no	—
229	C₄×C₁₉	C₂×#137	1	4	yes	—
230	C₄×C₁₉	#585	1	2	yes	—
231	#555	—	2	4	no	—
232	#555	C₂²×C₁₉	1	8	yes	—
233	#554	—	2	4	no	—
234	#554	C₂²×C₁₉	1	4	yes	complemented
235	D₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
236	#544	—	2	1	no	—
237	#543	—	2	2	no	—
238	#533	C₂²×C₁₉	1	2	yes	—
239	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
240	C₂×#124	—	2	2	no	—
241	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
242	C₂×#121	—	2	1	no	—
243	C₂×#121	C₂²×C₁₉	1	2	yes	—
244	#518	—	2	1	no	—
245	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
246	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×#117	—	2	1	no	—
248	C₂×#117	C₂²×C₁₉	1	2	yes	—
249	#500	C₂²×C₁₉	1	4	yes	complemented
250	#487	C₂²×C₁₉	1	4	yes	complemented
251	#485	C₂²×C₁₉	1	16	yes	complemented
252	#484	C₂²×C₁₉	1	8	yes	—
253	#483	C₂²×C₁₉	1	4	yes	—
254	#480	C₂²×C₁₉	1	8	yes	complemented
255	#477	C₂²×C₁₉	1	8	yes	complemented
256	#476	C₂²×C₁₉	1	4	yes	complemented
257	#468	C₂²×C₁₉	1	16	yes	complemented
258	#461	C₂²×C₁₉	1	4	yes	complemented
259	#450	C₂²×C₁₉	1	4	yes	—
260	#448	C₂²×C₁₉	1	8	yes	complemented
261	C₄×SD₁₆	C₂²×C₁₉	1	8	yes	complemented
262	#436	C₂²×C₁₉	1	8	yes	complemented
263	#431	C₂²×C₁₉	1	2	yes	—
264	#428	C₂²×C₁₉	1	8	yes	complemented
265	#419	C₂²×C₁₉	1	8	yes	complemented
266	#407	C₂²×C₁₉	1	4	yes	—
267	C₂×C₁₉	—	2	2	no	—
268	C₂×C₁₉	—	4	4	no	—
269	C₂×C₁₉	—	8	2	no	—
270	C₂×C₁₉	#3485	1	1	yes	characteristic
271	C₂×C₁₉	C₂²×#137	1	1	yes	characteristic
272	C₂×C₁₉	#3585	1	1	yes	characteristic
273	C₂²×Q₈	—	2	1	no	—
274	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
277	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
280	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
281	C₂×M₁₆	C₂³×C₁₉	1	8	yes	—
282	C₄⋊Q₈	—	2	4	no	—
283	C₄⋊Q₈	—	2	2	no	—
284	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
285	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
286	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
287	#125	—	2	4	no	—
288	#125	—	2	2	no	—
289	#124	—	2	16	no	—
290	C₂²⋊Q₈	—	2	4	no	—
291	C₂²⋊Q₈	—	2	4	no	—
292	C₂²⋊Q₈	—	2	2	no	—
293	C₂²⋊Q₈	—	2	8	no	—
294	C₂²⋊Q₈	—	2	8	no	—
295	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
296	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
297	#121	—	2	8	no	—
298	#121	—	2	4	no	—
299	#121	C₂³×C₁₉	1	8	yes	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
302	C₄×D₄	—	2	4	no	—
303	C₄×D₄	—	2	4	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	D₄×C₁₉	1	4	yes	—
306	C₄×D₄	C₂³×C₁₉	1	4	yes	—
307	C₄×D₄	C₂³×C₁₉	1	4	yes	—
308	#117	—	2	4	no	—
309	#117	—	2	2	no	—
310	#117	—	2	8	no	—
311	#117	C₂³×C₁₉	1	8	yes	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	4	no	—
314	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	4	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
323	C₂×C₄²	—	2	2	no	—
324	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
325	#107	C₂³×C₁₉	1	16	yes	—
326	#106	C₂³×C₁₉	1	8	yes	—
327	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
328	#103	C₂³×C₁₉	1	8	yes	—
329	#103	C₂³×C₁₉	1	16	yes	—
330	#102	C₂³×C₁₉	1	8	yes	—
331	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
332	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
333	C₄×C₈	C₂³×C₁₉	1	4	yes	—
334	C₁₉	#61721	1	1	yes	characteristic, direct product factor, Sylow
335	C₂⁴	—	2	1	no	—
336	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	4	8	no	—
341	C₂×Q₈	—	8	2	no	—
342	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	8	4	no	—
348	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
349	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	—	4	4	no	—
357	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
360	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
363	SD₁₆	—	4	8	no	—
364	M₁₆	—	4	8	no	—
365	C₂×C₈	C₂⁴×C₁₉	1	8	yes	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
377	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
378	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
379	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
386	C₄²	—	2	8	no	—
387	C₄²	—	2	4	no	—
388	C₄²	C₂×D₄×C₁₉	1	2	yes	—
389	C₄²	C₂⁴×C₁₉	1	2	yes	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
398	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
399	Q₈	—	2	8	no	—
400	Q₈	—	8	4	no	—
401	Q₈	—	8	4	no	—
402	Q₈	—	8	2	no	—
403	D₄	—	2	8	no	—
404	D₄	—	2	4	no	—
405	D₄	—	4	2	no	—
406	D₄	—	8	8	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	8	no	—
419	C₂×C₄	—	8	4	no	—
420	C₂×C₄	—	8	4	no	—
421	C₂×C₄	C₁₉×#137	1	4	yes	—
422	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
423	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
425	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
426	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
427	C₈	—	2	8	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	8	4	no	—
437	C₂²	—	8	4	no	—
438	C₂²	C₂×C₁₉×#137	1	2	yes	—
439	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	4	no	—
442	C₄	—	2	2	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	4	no	—
446	C₄	—	4	4	no	—
447	C₄	C₂×C₁₉×#137	1	4	yes	—
448	C₄	C₁₉×#585	1	2	yes	—
449	C₂	—	2	2	no	—
450	C₂	—	4	4	no	—
451	C₂	—	8	2	no	—
452	C₂	C₁₉×#3485	1	1	yes	characteristic
453	C₂	C₂²×C₁₉×#137	1	1	yes	characteristic
454	C₂	C₁₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₂×C₁₉×#555	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3501	C₂	semidirect
3. C₁₉×#3357	C₂	semidirect
4. C₁₉×#3329	C₂	semidirect
5. C₁₉×#3230	C₂	semidirect
6. C₁₉×#3193	C₂	semidirect
7. C₁₉×#3101	C₂	semidirect
8. C₁₉×#3095	C₂	semidirect
9. C₁₉×#2975	C₂	semidirect
13. C₁₉×#554	C₂²	semidirect
14. D₄×Q₈×C₁₉	C₂²	semidirect
28. C₁₉×#500	C₂²	semidirect
29. C₁₉×#487	C₂²	semidirect
30. C₁₉×#485	C₂²	semidirect
33. C₁₉×#480	C₂²	semidirect
34. C₁₉×#477	C₂²	semidirect
35. C₁₉×#476	C₂²	semidirect
36. C₁₉×#468	C₂²	semidirect
37. C₁₉×#461	C₂²	semidirect
39. C₁₉×#448	C₂²	semidirect
40. C₄×SD₁₆×C₁₉	C₂²	semidirect
41. C₁₉×#436	C₂²	semidirect
43. C₁₉×#428	C₂²	semidirect
44. C₁₉×#419	C₂²	semidirect
162. #61721	C₁₉	direct (N × H)
201. #3501	C₂×C₁₉	semidirect
203. #3357	C₂×C₁₉	semidirect
204. #3329	C₂×C₁₉	semidirect
205. #3230	C₂×C₁₉	semidirect
206. #3193	C₂×C₁₉	semidirect
207. #3101	C₂×C₁₉	semidirect
208. #3095	C₂×C₁₉	semidirect
209. #2975	C₂×C₁₉	semidirect
234. #554	C₂²×C₁₉	semidirect
235. D₄×Q₈	C₂²×C₁₉	semidirect
249. #500	C₂²×C₁₉	semidirect
250. #487	C₂²×C₁₉	semidirect
251. #485	C₂²×C₁₉	semidirect
254. #480	C₂²×C₁₉	semidirect
255. #477	C₂²×C₁₉	semidirect
256. #476	C₂²×C₁₉	semidirect
257. #468	C₂²×C₁₉	semidirect
258. #461	C₂²×C₁₉	semidirect
260. #448	C₂²×C₁₉	semidirect
261. C₄×SD₁₆	C₂²×C₁₉	semidirect
262. #436	C₂²×C₁₉	semidirect
264. #428	C₂²×C₁₉	semidirect
265. #419	C₂²×C₁₉	semidirect
334. C₁₉	#61721	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×#3501	2
C₂×C₁₉×#555	2
C₁₉×#3357	2
C₁₉×#3329	2
C₁₉×#3230	2
C₁₉×#3193	2
C₁₉×#3101	2
C₁₉×#3095	2
C₁₉×#2975	2
#61721	19

Subgroups — C19×#61721 #18067680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61721 #18067680