Subgroups — C₁₉×#62372 #18068331

Order 4864.

1700 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	C₁₉×#3550	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3394	C₂	1	4	yes	maximal, complemented
3	Q₈×SD₁₆×C₁₉	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3373	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3369	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3263	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3255	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3253	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#3173	C₂	1	4	yes	maximal, complemented
10	C₁₉×#3167	C₂	1	2	yes	maximal, complemented
11	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#563	—	2	4	no	—
13	C₁₉×#559	C₂²	1	4	yes	—
14	Q₈²×C₁₉	C₂²	1	4	yes	—
15	C₁₉×#556	—	2	2	no	—
16	C₁₉×#556	C₂²	1	4	yes	—
17	D₄×Q₈×C₁₉	—	2	2	no	—
18	D₄×Q₈×C₁₉	C₂²	1	4	yes	—
19	C₁₉×#542	—	2	4	no	—
20	C₁₉×#542	C₂²	1	8	yes	—
21	C₁₉×#536	—	2	4	no	—
22	C₁₉×#533	C₂²	1	2	yes	—
23	C₁₉×#533	C₂²	1	1	yes	characteristic
24	C₁₉×#532	C₂²	1	2	yes	—
25	C₁₉×#498	C₂²	1	2	yes	—
26	C₁₉×#498	C₂²	1	4	yes	—
27	C₁₉×#495	C₂²	1	4	yes	—
28	C₁₉×#492	C₂²	1	2	yes	—
29	C₁₉×#489	C₂²	1	8	yes	—
30	C₁₉×#487	C₂²	1	2	yes	—
31	C₁₉×#486	C₂²	1	2	yes	—
32	C₁₉×#476	C₂²	1	4	yes	—
33	C₁₉×#476	C₂²	1	8	yes	—
34	C₁₉×#475	C₂²	1	4	yes	—
35	C₁₉×#475	C₂²	1	8	yes	—
36	C₁₉×#470	C₂²	1	4	yes	—
37	C₁₉×#469	C₂²	1	4	yes	—
38	C₁₉×#465	C₂²	1	4	yes	—
39	C₁₉×#465	C₂²	1	4	yes	—
40	C₁₉×#464	C₂²	1	8	yes	—
41	C₁₉×#463	C₂²	1	8	yes	—
42	C₁₉×#462	C₂²	1	4	yes	—
43	C₁₉×#459	C₂²	1	4	yes	—
44	C₁₉×#446	C₂²	1	4	yes	—
45	C₈×Q₈×C₁₉	C₂²	1	4	yes	—
46	C₁₉×#442	C₂²	1	4	yes	—
47	C₁₉×#441	C₂²	1	4	yes	—
48	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
49	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
50	C₄×SD₁₆×C₁₉	C₂²	1	8	yes	—
51	C₁₉×#424	C₂²	1	2	yes	—
52	C₁₉×#423	C₂²	1	1	yes	characteristic
53	C₁₉×#405	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
55	C₂×#41×C₁₉	—	2	2	no	—
56	C₂²×Q₈×C₁₉	—	2	4	no	—
57	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
58	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
59	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
60	C₂×D₈×C₁₉	C₂³	1	4	yes	—
61	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₁₉×C₄⋊Q₈	—	2	8	no	—
65	C₁₉×C₄⋊Q₈	—	2	4	no	—
66	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
67	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
68	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₉×C₄⋊Q₈	C₂³	1	8	yes	—
70	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
71	C₁₉×#127	C₂³	1	2	yes	—
72	C₁₉×#126	—	2	8	no	—
73	C₁₉×#126	—	2	8	no	—
74	C₁₉×#125	—	2	2	no	—
75	C₁₉×#125	D₄	1	2	yes	—
76	C₁₉×#124	—	2	4	no	—
77	C₁₉×#124	—	2	8	no	—
78	C₁₉×#124	—	2	2	no	—
79	C₁₉×#124	C₂³	1	8	yes	—
80	C₁₉×#123	—	2	8	no	—
81	C₁₉×#123	—	2	8	no	—
82	C₁₉×C₂²⋊Q₈	—	2	4	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	4	no	—
85	C₁₉×C₂²⋊Q₈	—	2	8	no	—
86	C₁₉×C₂²⋊Q₈	—	2	8	no	—
87	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
88	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	C₂³	1	4	yes	—
91	C₄×Q₈×C₁₉	—	2	4	no	—
92	C₄×Q₈×C₁₉	—	2	2	no	—
93	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
94	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
95	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
96	C₄×D₄×C₁₉	—	2	4	no	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	C₂³	1	4	yes	—
99	C₄×D₄×C₁₉	C₂³	1	8	yes	—
100	C₁₉×#117	—	2	2	no	—
101	C₁₉×#117	—	2	4	no	—
102	C₁₉×#117	C₂³	1	2	yes	—
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₁₉×#106	C₂³	1	4	yes	—
105	C₁₉×#106	C₂³	1	4	yes	—
106	C₁₉×#106	C₂³	1	4	yes	—
107	C₁₉×#106	C₂³	1	4	yes	—
108	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
109	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
110	C₁₉×#103	C₂³	1	4	yes	—
111	C₁₉×#103	C₂³	1	8	yes	—
112	C₁₉×#103	C₂³	1	4	yes	—
113	C₁₉×#102	C₂³	1	4	yes	—
114	C₁₉×#102	C₂³	1	8	yes	—
115	C₁₉×#102	C₂³	1	4	yes	—
116	C₁₉×#97	C₂³	1	4	yes	—
117	C₄×C₈×C₁₉	C₂³	1	2	yes	—
118	C₄×C₈×C₁₉	C₂³	1	2	yes	—
119	C₄×C₈×C₁₉	C₂³	1	4	yes	—
120	#41×C₁₉	—	8	4	no	—
121	C₂×Q₈×C₁₉	—	2	2	no	—
122	C₂×Q₈×C₁₉	—	2	8	no	—
123	C₂×Q₈×C₁₉	—	2	2	no	—
124	C₂×Q₈×C₁₉	—	8	8	no	—
125	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
126	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
127	C₂×D₄×C₁₉	—	2	4	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₉	—	2	4	no	—
132	C₂²×C₄×C₁₉	—	2	8	no	—
133	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
135	Q₁₆×C₁₉	—	4	4	no	—
136	SD₁₆×C₁₉	—	2	8	no	—
137	SD₁₆×C₁₉	—	4	4	no	—
138	D₈×C₁₉	—	4	4	no	—
139	M₁₆×C₁₉	—	4	2	no	—
140	C₂×C₈×C₁₉	—	2	2	no	—
141	C₂×C₈×C₁₉	—	4	1	no	—
142	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
143	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
144	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
145	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	4	no	—
151	C₄⋊C₄×C₁₉	—	2	8	no	—
152	C₄⋊C₄×C₁₉	—	2	8	no	—
153	C₄⋊C₄×C₁₉	—	2	4	no	—
154	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
155	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
156	C₄⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
157	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
158	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
159	C₂²⋊C₄×C₁₉	—	2	4	no	—
160	C₂²⋊C₄×C₁₉	—	2	8	no	—
161	C₂²⋊C₄×C₁₉	—	2	4	no	—
162	C₂²⋊C₄×C₁₉	—	2	8	no	—
163	C₂²⋊C₄×C₁₉	—	2	4	no	—
164	C₂²⋊C₄×C₁₉	—	2	8	no	—
165	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
166	C₄²×C₁₉	—	2	4	no	—
167	C₄²×C₁₉	—	2	8	no	—
168	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₉	C₂⁴	1	2	yes	—
171	C₄²×C₁₉	C₂⁴	1	4	yes	—
172	#62372	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂³×C₁₉	—	2	4	no	—
174	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₁₉	—	2	8	no	—
176	Q₈×C₁₉	—	2	4	no	—
177	Q₈×C₁₉	—	2	4	no	—
178	Q₈×C₁₉	—	4	4	no	—
179	Q₈×C₁₉	—	8	8	no	—
180	Q₈×C₁₉	—	8	2	no	—
181	D₄×C₁₉	—	2	4	no	—
182	D₄×C₁₉	—	2	4	no	—
183	D₄×C₁₉	—	4	4	no	—
184	D₄×C₁₉	—	8	2	no	—
185	D₄×C₁₉	—	8	4	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	1	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	—	4	8	no	—
193	C₂×C₄×C₁₉	—	8	8	no	—
194	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
195	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
199	C₈×C₁₉	—	2	1	no	—
200	C₈×C₁₉	—	2	2	no	—
201	C₈×C₁₉	—	2	4	no	—
202	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
203	#3550	C₂×C₁₉	1	2	yes	complemented
204	#3394	C₂×C₁₉	1	4	yes	complemented
205	Q₈×SD₁₆	C₂×C₁₉	1	4	yes	complemented
206	#3373	C₂×C₁₉	1	4	yes	complemented
207	#3369	C₂×C₁₉	1	4	yes	complemented
208	#3263	C₂×C₁₉	1	4	yes	complemented
209	#3255	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#3253	C₂×C₁₉	1	1	yes	characteristic
211	#3173	C₂×C₁₉	1	4	yes	complemented
212	#3167	C₂×C₁₉	1	2	yes	complemented
213	#2960	C₂×C₁₉	1	1	yes	characteristic, complemented
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	2	no	—
216	C₂²×C₁₉	—	4	4	no	—
217	C₂²×C₁₉	—	4	4	no	—
218	C₂²×C₁₉	—	4	4	no	—
219	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	2	no	—
222	C₄×C₁₉	—	2	8	no	—
223	C₄×C₁₉	—	4	4	no	—
224	C₄×C₁₉	—	4	4	no	—
225	C₄×C₁₉	—	4	4	no	—
226	C₄×C₁₉	#577	1	4	yes	—
227	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
228	C₄×C₁₉	#585	1	1	yes	characteristic
229	#563	—	2	4	no	—
230	#559	C₂²×C₁₉	1	4	yes	—
231	Q₈²	C₂²×C₁₉	1	4	yes	—
232	#556	—	2	2	no	—
233	#556	C₂²×C₁₉	1	4	yes	—
234	D₄×Q₈	—	2	2	no	—
235	D₄×Q₈	C₂²×C₁₉	1	4	yes	—
236	#542	—	2	4	no	—
237	#542	C₂²×C₁₉	1	8	yes	—
238	#536	—	2	4	no	—
239	#533	C₂²×C₁₉	1	2	yes	—
240	#533	C₂²×C₁₉	1	1	yes	characteristic
241	#532	C₂²×C₁₉	1	2	yes	—
242	#498	C₂²×C₁₉	1	2	yes	—
243	#498	C₂²×C₁₉	1	4	yes	—
244	#495	C₂²×C₁₉	1	4	yes	—
245	#492	C₂²×C₁₉	1	2	yes	—
246	#489	C₂²×C₁₉	1	8	yes	—
247	#487	C₂²×C₁₉	1	2	yes	—
248	#486	C₂²×C₁₉	1	2	yes	—
249	#476	C₂²×C₁₉	1	4	yes	—
250	#476	C₂²×C₁₉	1	8	yes	—
251	#475	C₂²×C₁₉	1	8	yes	—
252	#475	C₂²×C₁₉	1	4	yes	—
253	#470	C₂²×C₁₉	1	4	yes	—
254	#469	C₂²×C₁₉	1	4	yes	—
255	#465	C₂²×C₁₉	1	4	yes	—
256	#465	C₂²×C₁₉	1	4	yes	—
257	#464	C₂²×C₁₉	1	8	yes	—
258	#463	C₂²×C₁₉	1	8	yes	—
259	#462	C₂²×C₁₉	1	4	yes	—
260	#459	C₂²×C₁₉	1	4	yes	—
261	#446	C₂²×C₁₉	1	4	yes	—
262	C₈×Q₈	C₂²×C₁₉	1	4	yes	—
263	#442	C₂²×C₁₉	1	4	yes	—
264	#441	C₂²×C₁₉	1	4	yes	—
265	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
266	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
267	C₄×SD₁₆	C₂²×C₁₉	1	8	yes	—
268	#424	C₂²×C₁₉	1	2	yes	—
269	#423	C₂²×C₁₉	1	1	yes	characteristic
270	#405	C₂²×C₁₉	1	2	yes	—
271	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
272	C₂×C₁₉	—	4	1	no	—
273	C₂×C₁₉	—	8	4	no	—
274	C₂×C₁₉	#3497	1	1	yes	characteristic
275	C₂×C₁₉	C₂×#577	1	2	yes	—
276	C₂×#41	—	2	2	no	—
277	C₂²×Q₈	—	2	4	no	—
278	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
279	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
280	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
281	C₂×D₈	C₂³×C₁₉	1	4	yes	—
282	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
283	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
285	C₄⋊Q₈	—	2	8	no	—
286	C₄⋊Q₈	—	2	4	no	—
287	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
288	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
289	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
290	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
291	C₄⋊Q₈	C₂³×C₁₉	1	8	yes	—
292	#127	C₂³×C₁₉	1	2	yes	—
293	#126	—	2	8	no	—
294	#126	—	2	8	no	—
295	#125	—	2	2	no	—
296	#125	D₄×C₁₉	1	2	yes	—
297	#124	—	2	4	no	—
298	#124	—	2	8	no	—
299	#124	—	2	2	no	—
300	#124	C₂³×C₁₉	1	8	yes	—
301	#123	—	2	8	no	—
302	#123	—	2	8	no	—
303	C₂²⋊Q₈	—	2	4	no	—
304	C₂²⋊Q₈	—	2	2	no	—
305	C₂²⋊Q₈	—	2	4	no	—
306	C₂²⋊Q₈	—	2	8	no	—
307	C₂²⋊Q₈	—	2	8	no	—
308	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
309	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
310	#121	—	2	2	no	—
311	#121	C₂³×C₁₉	1	4	yes	—
312	C₄×Q₈	—	2	4	no	—
313	C₄×Q₈	—	2	2	no	—
314	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
315	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
316	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	2	2	no	—
319	C₄×D₄	C₂³×C₁₉	1	4	yes	—
320	C₄×D₄	C₂³×C₁₉	1	8	yes	—
321	#117	—	2	2	no	—
322	#117	—	2	4	no	—
323	#117	C₂³×C₁₉	1	2	yes	—
324	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
325	#106	C₂³×C₁₉	1	4	yes	—
326	#106	C₂³×C₁₉	1	4	yes	—
327	#106	C₂³×C₁₉	1	4	yes	—
328	#106	C₂³×C₁₉	1	4	yes	—
329	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
330	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
331	#103	C₂³×C₁₉	1	4	yes	—
332	#103	C₂³×C₁₉	1	8	yes	—
333	#103	C₂³×C₁₉	1	4	yes	—
334	#102	C₂³×C₁₉	1	4	yes	—
335	#102	C₂³×C₁₉	1	8	yes	—
336	#102	C₂³×C₁₉	1	4	yes	—
337	#97	C₂³×C₁₉	1	4	yes	—
338	C₄×C₈	C₂³×C₁₉	1	2	yes	—
339	C₄×C₈	C₂³×C₁₉	1	2	yes	—
340	C₄×C₈	C₂³×C₁₉	1	4	yes	—
341	C₁₉	#62372	1	1	yes	characteristic, direct product factor, Sylow
342	#41	—	8	4	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	8	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	8	8	no	—
347	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
348	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
357	Q₁₆	—	4	4	no	—
358	SD₁₆	—	2	8	no	—
359	SD₁₆	—	4	4	no	—
360	D₈	—	4	4	no	—
361	M₁₆	—	4	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
365	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
366	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
367	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
377	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
378	C₄⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
379	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
380	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
388	C₄²	—	2	4	no	—
389	C₄²	—	2	8	no	—
390	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
392	C₄²	C₂⁴×C₁₉	1	2	yes	—
393	C₄²	C₂⁴×C₁₉	1	4	yes	—
394	C₂³	—	2	4	no	—
395	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
396	Q₈	—	2	8	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	2	4	no	—
399	Q₈	—	4	4	no	—
400	Q₈	—	8	8	no	—
401	Q₈	—	8	2	no	—
402	D₄	—	2	4	no	—
403	D₄	—	2	4	no	—
404	D₄	—	4	4	no	—
405	D₄	—	8	2	no	—
406	D₄	—	8	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	—	8	8	no	—
415	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
416	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
419	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
420	C₈	—	2	1	no	—
421	C₈	—	2	2	no	—
422	C₈	—	2	4	no	—
423	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	2	no	—
432	C₄	—	2	8	no	—
433	C₄	—	4	4	no	—
434	C₄	—	4	4	no	—
435	C₄	—	4	4	no	—
436	C₄	C₁₉×#577	1	4	yes	—
437	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
438	C₄	C₁₉×#585	1	1	yes	characteristic
439	C₂	—	4	1	no	—
440	C₂	—	8	4	no	—
441	C₂	C₁₉×#3497	1	1	yes	characteristic
442	C₂	C₂×C₁₉×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3253	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3550	C₂	semidirect
2. C₁₉×#3394	C₂	semidirect
3. Q₈×SD₁₆×C₁₉	C₂	semidirect
4. C₁₉×#3373	C₂	semidirect
5. C₁₉×#3369	C₂	semidirect
6. C₁₉×#3263	C₂	semidirect
7. C₁₉×#3255	C₂	semidirect
9. C₁₉×#3173	C₂	semidirect
10. C₁₉×#3167	C₂	semidirect
11. C₁₉×#2960	C₂	semidirect
172. #62372	C₁₉	direct (N × H)
203. #3550	C₂×C₁₉	semidirect
204. #3394	C₂×C₁₉	semidirect
205. Q₈×SD₁₆	C₂×C₁₉	semidirect
206. #3373	C₂×C₁₉	semidirect
207. #3369	C₂×C₁₉	semidirect
208. #3263	C₂×C₁₉	semidirect
209. #3255	C₂×C₁₉	semidirect
211. #3173	C₂×C₁₉	semidirect
212. #3167	C₂×C₁₉	semidirect
213. #2960	C₂×C₁₉	semidirect
341. C₁₉	#62372	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×#3550	2
C₁₉×#3394	2
Q₈×SD₁₆×C₁₉	2
C₁₉×#3373	2
C₁₉×#3369	2
C₁₉×#3263	2
C₁₉×#3255	2
C₁₉×#3253	2
C₁₉×#3173	2
C₁₉×#3167	2
C₁₉×#2960	2
#62372	19

Subgroups — C19×#62372 #18068331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62372 #18068331