Subgroups — C₁₉×#11215 #18017174

Order 4864.

710 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2911	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1740	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1733	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
8	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#428	—	2	2	no	—
16	C₁₉×#428	C₄	1	4	yes	complemented
17	C₁₉×#427	—	2	2	no	—
18	C₁₉×#389	—	2	2	no	—
19	C₁₉×#385	—	2	2	no	—
20	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₁₉×#344	—	2	2	no	—
22	C₁₉×#342	—	2	2	no	—
23	C₁₉×#339	—	2	2	no	—
24	C₁₉×#339	—	2	2	no	—
25	C₁₉×#339	—	2	2	no	—
26	C₂³×C₄×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×M₁₆×C₁₉	—	2	1	no	—
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂×M₁₆×C₁₉	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
37	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
38	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
39	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₁₉×#117	—	2	1	no	—
43	C₁₉×#117	—	2	1	no	—
44	C₁₉×#117	—	2	1	no	—
45	C₁₉×#117	—	2	1	no	—
46	C₁₉×#117	—	2	1	no	—
47	C₁₉×#117	—	2	1	no	—
48	C₁₉×#117	—	2	1	no	—
49	C₁₉×#117	—	2	1	no	—
50	C₁₉×#117	—	2	1	no	—
51	C₁₉×#117	—	2	1	no	—
52	C₁₉×#117	—	2	1	no	—
53	C₁₉×#117	—	2	1	no	—
54	C₁₉×#117	—	2	1	no	—
55	C₁₉×#117	C₂×C₄	1	2	yes	—
56	C₁₉×#117	D₄	1	2	yes	—
57	C₁₉×#117	Q₈	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	—	2	1	no	—
70	C₂×C₄²×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	—	2	1	no	—
72	C₂×C₄²×C₁₉	—	2	1	no	—
73	C₂×C₄²×C₁₉	—	2	1	no	—
74	C₂×C₄²×C₁₉	—	2	1	no	—
75	C₂×C₄²×C₁₉	—	2	1	no	—
76	C₂×C₄²×C₁₉	D₄	1	2	yes	—
77	C₁₉×#107	—	2	4	no	—
78	C₁₉×#106	—	2	4	no	—
79	C₁₉×#95	—	2	4	no	—
80	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	4	4	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
103	M₁₆×C₁₉	—	2	2	no	—
104	M₁₆×C₁₉	—	2	2	no	—
105	M₁₆×C₁₉	—	2	2	no	—
106	M₁₆×C₁₉	—	2	2	no	—
107	M₁₆×C₁₉	—	2	2	no	—
108	M₁₆×C₁₉	—	4	1	no	—
109	M₁₆×C₁₉	—	4	1	no	—
110	M₁₆×C₁₉	C₄⋊C₄	1	4	yes	complemented
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	4	1	no	—
116	C₂×C₈×C₁₉	—	4	1	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	4	8	no	—
122	C₄⋊C₄×C₁₉	—	4	1	no	—
123	C₄⋊C₄×C₁₉	—	4	1	no	—
124	C₄⋊C₄×C₁₉	—	4	1	no	—
125	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
126	C₂²⋊C₄×C₁₉	—	2	2	no	—
127	C₂²⋊C₄×C₁₉	—	2	2	no	—
128	C₂²⋊C₄×C₁₉	—	2	2	no	—
129	C₂²⋊C₄×C₁₉	—	2	2	no	—
130	C₂²⋊C₄×C₁₉	—	2	2	no	—
131	C₂²⋊C₄×C₁₉	—	4	1	no	—
132	C₂²⋊C₄×C₁₉	—	4	1	no	—
133	C₂²⋊C₄×C₁₉	—	4	1	no	—
134	C₄²×C₁₉	—	2	2	no	—
135	C₄²×C₁₉	—	2	2	no	—
136	C₄²×C₁₉	—	2	2	no	—
137	C₄²×C₁₉	—	2	2	no	—
138	C₄²×C₁₉	—	2	2	no	—
139	C₄²×C₁₉	—	4	1	no	—
140	C₄²×C₁₉	—	4	1	no	—
141	C₄²×C₁₉	—	4	1	no	—
142	C₄²×C₁₉	—	4	1	no	—
143	C₄²×C₁₉	—	4	1	no	—
144	C₄²×C₁₉	—	4	1	no	—
145	C₄²×C₁₉	—	4	1	no	—
146	#11215	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂³×C₁₉	—	4	2	no	—
148	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
149	C₂³×C₁₉	#120	1	1	yes	characteristic
150	C₂³×C₁₉	#121	1	1	yes	characteristic
151	C₂³×C₁₉	#121	1	1	yes	characteristic
152	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
153	C₂³×C₁₉	#123	1	1	yes	characteristic
154	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	4	4	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	4	no	—
160	C₂×C₄×C₁₉	—	4	4	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	8	2	no	—
167	C₂×C₄×C₁₉	—	8	2	no	—
168	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
196	C₈×C₁₉	—	2	4	no	—
197	C₈×C₁₉	—	4	2	no	—
198	#2911	C₂×C₁₉	1	1	yes	characteristic
199	#2296	C₂×C₁₉	1	1	yes	characteristic
200	C₂×#344	C₂×C₁₉	1	1	yes	characteristic
201	#1740	C₂×C₁₉	1	1	yes	characteristic
202	#1733	C₂×C₁₉	1	1	yes	characteristic
203	C₂×#339	C₂×C₁₉	1	1	yes	characteristic
204	C₂×#339	C₂×C₁₉	1	1	yes	characteristic
205	C₂²×C₁₉	—	2	2	no	—
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	—	4	1	no	—
210	C₂²×C₁₉	—	4	1	no	—
211	C₂²×C₁₉	—	4	1	no	—
212	C₂²×C₁₉	#386	1	1	yes	characteristic
213	C₂²×C₁₉	#387	1	1	yes	characteristic
214	C₂²×C₁₉	#389	1	1	yes	characteristic
215	C₂²×C₁₉	#394	1	1	yes	characteristic
216	C₂²×C₁₉	#395	1	1	yes	characteristic
217	C₂²×C₁₉	#396	1	1	yes	characteristic
218	C₂²×C₁₉	#398	1	1	yes	characteristic
219	C₄×C₁₉	—	4	4	no	—
220	C₄×C₁₉	—	4	4	no	—
221	C₄×C₁₉	—	8	2	no	—
222	C₄×C₁₉	—	8	2	no	—
223	C₄×C₁₉	—	8	2	no	—
224	C₄×C₁₉	#380	1	1	yes	characteristic
225	C₄×C₁₉	#387	1	1	yes	characteristic
226	C₄×C₁₉	#389	1	1	yes	characteristic
227	C₄×C₁₉	#391	1	1	yes	characteristic
228	C₄×C₁₉	#396	1	1	yes	characteristic
229	C₄×C₁₉	#398	1	1	yes	characteristic
230	C₄×C₁₉	#398	1	1	yes	characteristic
231	C₄×C₁₉	#400	1	1	yes	characteristic
232	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
233	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
237	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
238	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
239	#428	—	2	2	no	—
240	#428	C₄×C₁₉	1	4	yes	complemented
241	#427	—	2	2	no	—
242	#389	—	2	2	no	—
243	#385	—	2	2	no	—
244	C₄×C₄⋊C₄	—	2	2	no	—
245	#344	—	2	2	no	—
246	#342	—	2	2	no	—
247	#339	—	2	2	no	—
248	#339	—	2	2	no	—
249	#339	—	2	2	no	—
250	C₂×C₁₉	—	2	1	no	—
251	C₂×C₁₉	—	2	1	no	—
252	C₂×C₁₉	—	2	1	no	—
253	C₂×C₁₉	—	2	1	no	—
254	C₂×C₁₉	—	2	1	no	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	#1441	1	1	yes	characteristic
257	C₂×C₁₉	#1906	1	2	yes	—
258	C₂³×C₄	—	2	1	no	—
259	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	—	2	1	no	—
263	C₂×M₁₆	—	2	1	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
269	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
270	C₂×M₁₆	Q₈×C₁₉	1	2	yes	—
271	C₂×M₁₆	Q₈×C₁₉	1	2	yes	—
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	—	2	1	no	—
274	#117	—	2	1	no	—
275	#117	—	2	1	no	—
276	#117	—	2	1	no	—
277	#117	—	2	1	no	—
278	#117	—	2	1	no	—
279	#117	—	2	1	no	—
280	#117	—	2	1	no	—
281	#117	—	2	1	no	—
282	#117	—	2	1	no	—
283	#117	—	2	1	no	—
284	#117	—	2	1	no	—
285	#117	—	2	1	no	—
286	#117	—	2	1	no	—
287	#117	C₂×C₄×C₁₉	1	2	yes	—
288	#117	D₄×C₁₉	1	2	yes	—
289	#117	Q₈×C₁₉	1	2	yes	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	4	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
294	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	D₄×C₁₉	1	2	yes	—
309	#107	—	2	4	no	—
310	#106	—	2	4	no	—
311	#95	—	2	4	no	—
312	C₁₉	#11215	1	1	yes	characteristic, direct product factor, Sylow
313	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
327	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
330	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
331	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
333	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
334	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
335	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	2	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	4	1	no	—
342	M₁₆	—	4	1	no	—
343	M₁₆	C₄⋊C₄×C₁₉	1	4	yes	complemented
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	4	8	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	4	1	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	4	1	no	—
373	C₄²	—	4	1	no	—
374	C₄²	—	4	1	no	—
375	C₄²	—	4	1	no	—
376	C₄²	—	4	1	no	—
377	C₄²	—	4	1	no	—
378	C₄²	—	4	1	no	—
379	C₂³	—	4	2	no	—
380	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
381	C₂³	C₁₉×#120	1	1	yes	characteristic
382	C₂³	C₁₉×#121	1	1	yes	characteristic
383	C₂³	C₁₉×#121	1	1	yes	characteristic
384	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
385	C₂³	C₁₉×#123	1	1	yes	characteristic
386	C₂³	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	8	2	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
401	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
402	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
403	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
404	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
405	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
406	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
407	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
408	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
409	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
410	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
411	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
412	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
413	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
414	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
415	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
416	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
417	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
418	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
419	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
420	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
421	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
422	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
423	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
424	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
425	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
426	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
427	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
428	C₈	—	2	4	no	—
429	C₈	—	4	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	C₁₉×#386	1	1	yes	characteristic
438	C₂²	C₁₉×#387	1	1	yes	characteristic
439	C₂²	C₁₉×#389	1	1	yes	characteristic
440	C₂²	C₁₉×#394	1	1	yes	characteristic
441	C₂²	C₁₉×#395	1	1	yes	characteristic
442	C₂²	C₁₉×#396	1	1	yes	characteristic
443	C₂²	C₁₉×#398	1	1	yes	characteristic
444	C₄	—	4	4	no	—
445	C₄	—	4	4	no	—
446	C₄	—	8	2	no	—
447	C₄	—	8	2	no	—
448	C₄	—	8	2	no	—
449	C₄	C₁₉×#380	1	1	yes	characteristic
450	C₄	C₁₉×#387	1	1	yes	characteristic
451	C₄	C₁₉×#389	1	1	yes	characteristic
452	C₄	C₁₉×#391	1	1	yes	characteristic
453	C₄	C₁₉×#396	1	1	yes	characteristic
454	C₄	C₁₉×#398	1	1	yes	characteristic
455	C₄	C₁₉×#398	1	1	yes	characteristic
456	C₄	C₁₉×#400	1	1	yes	characteristic
457	C₂	—	2	1	no	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	2	1	no	—
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	C₁₉×#1441	1	1	yes	characteristic
464	C₂	C₁₉×#1906	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#121
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	#386
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₁₉×#428	C₄	semidirect
110. M₁₆×C₁₉	C₄⋊C₄	semidirect
146. #11215	C₁₉	direct (N × H)
240. #428	C₄×C₁₉	semidirect
312. C₁₉	#11215	direct (N × H)
343. M₁₆	C₄⋊C₄×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#2911	2
C₁₉×#2296	2
C₂×C₁₉×#344	2
C₁₉×#1740	2
C₁₉×#1733	2
C₂×C₁₉×#339	2
#11215	19

Subgroups — C19×#11215 #18017174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11215 #18017174