Subgroups — C₁₉×#3224 #14561081

Order 2432.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#489	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#447	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₁₉×#127	C₂²	1	1	yes	characteristic
28	C₁₉×#127	C₂²	1	1	yes	characteristic
29	C₁₉×#126	—	2	1	no	—
30	C₁₉×#124	—	2	1	no	—
31	C₁₉×#124	C₂²	1	1	yes	characteristic
32	C₁₉×#124	C₂²	1	1	yes	characteristic
33	C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#123	—	2	1	no	—
35	C₁₉×C₂²⋊Q₈	—	2	1	no	—
36	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₁₉×#121	—	2	1	no	—
38	C₁₉×#121	—	2	1	no	—
39	C₁₉×#121	C₂²	1	1	yes	characteristic
40	C₁₉×#120	—	2	1	no	—
41	C₁₉×#120	—	2	1	no	—
42	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
43	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#117	C₂²	1	1	yes	characteristic
45	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#102	C₂²	1	1	yes	characteristic
50	C₁₉×#102	C₂²	1	1	yes	characteristic
51	C₁₉×#102	C₂²	1	1	yes	characteristic
52	C₁₉×#102	C₂²	1	1	yes	characteristic
53	C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
56	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
59	C₂⁴×C₁₉	—	2	1	no	—
60	#41×C₁₉	—	4	1	no	—
61	#41×C₁₉	—	4	1	no	—
62	C₂×Q₈×C₁₉	—	2	1	no	—
63	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×D₄×C₁₉	—	2	1	no	—
66	C₂×D₄×C₁₉	—	2	1	no	—
67	C₂×D₄×C₁₉	—	2	1	no	—
68	C₂×D₄×C₁₉	—	2	1	no	—
69	C₂×D₄×C₁₉	—	2	1	no	—
70	C₂×D₄×C₁₉	—	2	1	no	—
71	C₂×D₄×C₁₉	—	2	1	no	—
72	C₂×D₄×C₁₉	—	4	1	no	—
73	C₂×D₄×C₁₉	—	4	1	no	—
74	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	—	2	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
81	Q₁₆×C₁₉	—	4	1	no	—
82	SD₁₆×C₁₉	—	4	1	no	—
83	SD₁₆×C₁₉	—	4	1	no	—
84	SD₁₆×C₁₉	—	4	1	no	—
85	SD₁₆×C₁₉	—	4	1	no	—
86	D₈×C₁₉	—	4	1	no	—
87	D₈×C₁₉	—	4	1	no	—
88	D₈×C₁₉	—	4	1	no	—
89	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
97	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
98	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂²⋊C₄×C₁₉	—	2	1	no	—
109	C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
110	C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
111	C₄²×C₁₉	—	2	1	no	—
112	C₄²×C₁₉	C₂³	1	1	yes	characteristic
113	C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	—	2	1	no	—
117	C₂³×C₁₉	—	2	1	no	—
118	C₂³×C₁₉	—	4	2	no	—
119	C₂³×C₁₉	—	8	1	no	—
120	C₂³×C₁₉	—	8	1	no	—
121	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
122	Q₈×C₁₉	—	2	1	no	—
123	Q₈×C₁₉	—	2	1	no	—
124	Q₈×C₁₉	—	2	1	no	—
125	Q₈×C₁₉	—	2	1	no	—
126	Q₈×C₁₉	—	8	1	no	—
127	D₄×C₁₉	—	2	1	no	—
128	D₄×C₁₉	—	2	1	no	—
129	D₄×C₁₉	—	2	1	no	—
130	D₄×C₁₉	—	2	1	no	—
131	D₄×C₁₉	—	2	1	no	—
132	D₄×C₁₉	—	2	1	no	—
133	D₄×C₁₉	—	2	1	no	—
134	D₄×C₁₉	—	2	1	no	—
135	D₄×C₁₉	—	4	2	no	—
136	D₄×C₁₉	—	4	2	no	—
137	D₄×C₁₉	—	8	1	no	—
138	D₄×C₁₉	—	8	1	no	—
139	D₄×C₁₉	—	8	1	no	—
140	D₄×C₁₉	—	8	1	no	—
141	D₄×C₁₉	—	8	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	8	1	no	—
150	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
156	C₈×C₁₉	—	2	1	no	—
157	C₈×C₁₉	—	2	1	no	—
158	C₈×C₁₉	—	2	1	no	—
159	C₈×C₁₉	—	2	1	no	—
160	#3224	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂²×C₁₉	—	2	1	no	—
162	C₂²×C₁₉	—	2	1	no	—
163	C₂²×C₁₉	—	2	1	no	—
164	C₂²×C₁₉	—	4	1	no	—
165	C₂²×C₁₉	—	4	1	no	—
166	C₂²×C₁₉	—	4	1	no	—
167	C₂²×C₁₉	—	4	1	no	—
168	C₂²×C₁₉	—	4	1	no	—
169	C₂²×C₁₉	—	4	1	no	—
170	C₂²×C₁₉	—	4	1	no	—
171	C₂²×C₁₉	—	4	1	no	—
172	C₂²×C₁₉	—	4	1	no	—
173	C₂²×C₁₉	—	4	1	no	—
174	C₂²×C₁₉	—	4	1	no	—
175	C₂²×C₁₉	—	4	1	no	—
176	C₂²×C₁₉	—	8	4	no	—
177	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
178	C₄×C₁₉	—	2	1	no	—
179	C₄×C₁₉	—	2	1	no	—
180	C₄×C₁₉	—	2	1	no	—
181	C₄×C₁₉	—	2	1	no	—
182	C₄×C₁₉	—	2	1	no	—
183	C₄×C₁₉	—	4	1	no	—
184	C₄×C₁₉	—	4	1	no	—
185	C₄×C₁₉	—	4	1	no	—
186	C₄×C₁₉	—	4	1	no	—
187	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
188	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
189	#542	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#535	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#496	C₂×C₁₉	1	1	yes	characteristic, complemented
192	#495	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#489	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#486	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#464	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#463	C₂×C₁₉	1	1	yes	characteristic, complemented
197	#460	C₂×C₁₉	1	1	yes	characteristic, complemented
198	#459	C₂×C₁₉	1	1	yes	characteristic, complemented
199	#452	C₂×C₁₉	1	1	yes	characteristic, complemented
200	#450	C₂×C₁₉	1	1	yes	characteristic, complemented
201	#449	C₂×C₁₉	1	1	yes	characteristic, complemented
202	#447	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#433	C₂×C₁₉	1	1	yes	characteristic, complemented
204	C₂×C₁₉	—	4	1	no	—
205	C₂×C₁₉	—	8	1	no	—
206	C₂×C₁₉	—	8	1	no	—
207	C₂×C₁₉	—	8	1	no	—
208	C₂×C₁₉	—	8	1	no	—
209	C₂×C₁₉	#535	1	1	yes	characteristic
210	C₂×C₁₉	#576	1	1	yes	characteristic
211	C₂×C₁₉	#577	1	1	yes	characteristic
212	C₂×#41	C₂²×C₁₉	1	1	yes	characteristic
213	C₂²×D₄	C₂²×C₁₉	1	1	yes	characteristic
214	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
215	C₂×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
218	C₂×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
219	C₂×D₈	C₂²×C₁₉	1	1	yes	characteristic
220	C₂×D₈	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
222	C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
223	#127	C₂²×C₁₉	1	1	yes	characteristic
224	#127	C₂²×C₁₉	1	1	yes	characteristic
225	#126	—	2	1	no	—
226	#124	—	2	1	no	—
227	#124	C₂²×C₁₉	1	1	yes	characteristic
228	#124	C₂²×C₁₉	1	1	yes	characteristic
229	#124	C₂²×C₁₉	1	1	yes	characteristic, complemented
230	#123	—	2	1	no	—
231	C₂²⋊Q₈	—	2	1	no	—
232	C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
233	#121	—	2	1	no	—
234	#121	—	2	1	no	—
235	#121	C₂²×C₁₉	1	1	yes	characteristic
236	#120	—	2	1	no	—
237	#120	—	2	1	no	—
238	C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
239	C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
240	#117	C₂²×C₁₉	1	1	yes	characteristic
241	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
242	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
243	#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
244	#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
245	#102	C₂²×C₁₉	1	1	yes	characteristic
246	#102	C₂²×C₁₉	1	1	yes	characteristic
247	#102	C₂²×C₁₉	1	1	yes	characteristic
248	#102	C₂²×C₁₉	1	1	yes	characteristic
249	#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
250	#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
251	C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
252	C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
253	#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
254	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
255	C₁₉	#3224	1	1	yes	characteristic, direct product factor, Sylow
256	C₂⁴	—	2	1	no	—
257	#41	—	4	1	no	—
258	#41	—	4	1	no	—
259	C₂×Q₈	—	2	1	no	—
260	C₂×Q₈	C₂³×C₁₉	1	1	yes	characteristic
261	C₂×Q₈	C₂³×C₁₉	1	1	yes	characteristic
262	C₂×D₄	—	2	1	no	—
263	C₂×D₄	—	2	1	no	—
264	C₂×D₄	—	2	1	no	—
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	—	2	1	no	—
267	C₂×D₄	—	2	1	no	—
268	C₂×D₄	—	2	1	no	—
269	C₂×D₄	—	4	1	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	C₂³×C₁₉	1	1	yes	characteristic
272	C₂×D₄	C₂³×C₁₉	1	1	yes	characteristic
273	C₂×D₄	C₂³×C₁₉	1	1	yes	characteristic
274	C₂×D₄	C₂³×C₁₉	1	1	yes	characteristic
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
278	Q₁₆	—	4	1	no	—
279	SD₁₆	—	4	1	no	—
280	SD₁₆	—	4	1	no	—
281	SD₁₆	—	4	1	no	—
282	SD₁₆	—	4	1	no	—
283	D₈	—	4	1	no	—
284	D₈	—	4	1	no	—
285	D₈	—	4	1	no	—
286	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
287	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
288	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
289	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
294	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
295	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
296	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
297	C₂²⋊C₄	—	2	1	no	—
298	C₂²⋊C₄	—	2	1	no	—
299	C₂²⋊C₄	—	2	1	no	—
300	C₂²⋊C₄	—	2	1	no	—
301	C₂²⋊C₄	—	2	1	no	—
302	C₂²⋊C₄	—	2	1	no	—
303	C₂²⋊C₄	—	2	1	no	—
304	C₂²⋊C₄	—	2	1	no	—
305	C₂²⋊C₄	—	2	1	no	—
306	C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
307	C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
308	C₄²	—	2	1	no	—
309	C₄²	C₂³×C₁₉	1	1	yes	characteristic
310	C₄²	C₂³×C₁₉	1	1	yes	characteristic
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	8	1	no	—
317	C₂³	—	8	1	no	—
318	C₂³	C₂×D₄×C₁₉	1	1	yes	characteristic
319	Q₈	—	2	1	no	—
320	Q₈	—	2	1	no	—
321	Q₈	—	2	1	no	—
322	Q₈	—	2	1	no	—
323	Q₈	—	8	1	no	—
324	D₄	—	2	1	no	—
325	D₄	—	2	1	no	—
326	D₄	—	2	1	no	—
327	D₄	—	2	1	no	—
328	D₄	—	2	1	no	—
329	D₄	—	2	1	no	—
330	D₄	—	2	1	no	—
331	D₄	—	2	1	no	—
332	D₄	—	4	2	no	—
333	D₄	—	4	2	no	—
334	D₄	—	8	1	no	—
335	D₄	—	8	1	no	—
336	D₄	—	8	1	no	—
337	D₄	—	8	1	no	—
338	D₄	—	8	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	8	1	no	—
347	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
348	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
349	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
350	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
352	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	8	4	no	—
373	C₂²	C₂²×D₄×C₁₉	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	4	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	1	no	—
383	C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
384	C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
385	C₂	—	4	1	no	—
386	C₂	—	8	1	no	—
387	C₂	—	8	1	no	—
388	C₂	—	8	1	no	—
389	C₂	—	8	1	no	—
390	C₂	C₁₉×#535	1	1	yes	characteristic
391	C₂	C₁₉×#576	1	1	yes	characteristic
392	C₂	C₁₉×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#542	C₂	semidirect
2. C₁₉×#535	C₂	semidirect
3. C₁₉×#496	C₂	semidirect
4. C₁₉×#495	C₂	semidirect
5. C₁₉×#489	C₂	semidirect
6. C₁₉×#486	C₂	semidirect
7. C₁₉×#464	C₂	semidirect
8. C₁₉×#463	C₂	semidirect
9. C₁₉×#460	C₂	semidirect
10. C₁₉×#459	C₂	semidirect
11. C₁₉×#452	C₂	semidirect
12. C₁₉×#450	C₂	semidirect
13. C₁₉×#449	C₂	semidirect
14. C₁₉×#447	C₂	semidirect
15. C₁₉×#433	C₂	semidirect
18. C₂×Q₁₆×C₁₉	C₂²	semidirect
21. C₂×SD₁₆×C₁₉	C₂²	semidirect
22. C₂×SD₁₆×C₁₉	C₂²	semidirect
25. C₂×D₈×C₁₉	C₂²	semidirect
26. C₁₉×C₄⋊Q₈	C₂²	semidirect
33. C₁₉×#124	C₂²	semidirect
42. C₄×Q₈×C₁₉	C₂²	semidirect
43. C₄×D₄×C₁₉	C₂²	semidirect
45. C₁₉×C₄⋊C₈	C₂²	semidirect
46. C₁₉×C₄⋊C₈	C₂²	semidirect
47. C₁₉×#103	C₂²	semidirect
48. C₁₉×#103	C₂²	semidirect
53. C₁₉×#102	C₂²	semidirect
54. C₁₉×#102	C₂²	semidirect
57. C₁₉×#97	C₂²	semidirect
58. C₄×C₈×C₁₉	C₂²	semidirect
160. #3224	C₁₉	direct (N × H)
189. #542	C₂×C₁₉	semidirect
190. #535	C₂×C₁₉	semidirect
191. #496	C₂×C₁₉	semidirect
192. #495	C₂×C₁₉	semidirect
193. #489	C₂×C₁₉	semidirect
194. #486	C₂×C₁₉	semidirect
195. #464	C₂×C₁₉	semidirect
196. #463	C₂×C₁₉	semidirect
197. #460	C₂×C₁₉	semidirect
198. #459	C₂×C₁₉	semidirect
199. #452	C₂×C₁₉	semidirect
200. #450	C₂×C₁₉	semidirect
201. #449	C₂×C₁₉	semidirect
202. #447	C₂×C₁₉	semidirect
203. #433	C₂×C₁₉	semidirect
214. C₂×Q₁₆	C₂²×C₁₉	semidirect
217. C₂×SD₁₆	C₂²×C₁₉	semidirect
218. C₂×SD₁₆	C₂²×C₁₉	semidirect
221. C₂×D₈	C₂²×C₁₉	semidirect
222. C₄⋊Q₈	C₂²×C₁₉	semidirect
229. #124	C₂²×C₁₉	semidirect
238. C₄×Q₈	C₂²×C₁₉	semidirect
239. C₄×D₄	C₂²×C₁₉	semidirect
241. C₄⋊C₈	C₂²×C₁₉	semidirect
242. C₄⋊C₈	C₂²×C₁₉	semidirect
243. #103	C₂²×C₁₉	semidirect
244. #103	C₂²×C₁₉	semidirect
249. #102	C₂²×C₁₉	semidirect
250. #102	C₂²×C₁₉	semidirect
253. #97	C₂²×C₁₉	semidirect
254. C₄×C₈	C₂²×C₁₉	semidirect
255. C₁₉	#3224	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×#542	2
C₁₉×#535	2
C₁₉×#496	2
C₁₉×#495	2
C₁₉×#489	2
C₁₉×#486	2
C₁₉×#464	2
C₁₉×#463	2
C₁₉×#460	2
C₁₉×#459	2
C₁₉×#452	2
C₁₉×#450	2
C₁₉×#449	2
C₁₉×#447	2
C₁₉×#433	2
#3224	19

Subgroups — C19×#3224 #14561081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#3224 #14561081