Subgroups — C₁₉×#33824 #18039783

Order 4864.

476 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3177	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3175	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2229	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2228	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2227	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2225	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2220	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#2219	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2217	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2216	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2211	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2211	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2209	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2208	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#2151	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#542	—	2	1	no	—
17	C₁₉×#541	—	2	1	no	—
18	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
23	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#500	C₂²	1	1	yes	characteristic
25	C₁₉×#499	C₂²	1	1	yes	characteristic
26	C₁₉×#495	C₂²	1	1	yes	characteristic
27	C₁₉×#494	C₂²	1	1	yes	characteristic
28	C₁₉×#491	—	2	1	no	—
29	C₁₉×#489	—	2	1	no	—
30	C₁₉×#470	—	2	1	no	—
31	C₁₉×#468	—	2	1	no	—
32	C₁₉×#467	C₂²	1	1	yes	characteristic
33	C₁₉×#467	C₂²	1	1	yes	characteristic
34	C₁₉×#467	C₂²	1	1	yes	characteristic
35	C₁₉×#466	C₂²	1	1	yes	characteristic
36	C₁₉×#441	—	2	1	no	—
37	C₁₉×#440	—	2	1	no	—
38	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
39	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
40	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
41	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
42	C₁₉×#405	C₂²	1	1	yes	characteristic
43	C₁₉×#367	C₂²	1	1	yes	characteristic
44	C₁₉×#367	C₂²	1	1	yes	characteristic
45	C₁₉×#366	C₂²	1	1	yes	characteristic
46	C₁₉×#366	C₂²	1	1	yes	characteristic
47	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
48	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
49	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
50	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
51	C₁₉×#358	C₂²	1	1	yes	characteristic
52	C₁₉×#358	C₂²	1	1	yes	characteristic
53	C₁₉×#358	C₂²	1	1	yes	characteristic
54	C₁₉×#358	C₂²	1	1	yes	characteristic
55	C₁₉×#358	C₂²	1	1	yes	characteristic
56	C₁₉×#358	C₂²	1	1	yes	characteristic
57	C₁₉×#357	C₂²	1	1	yes	characteristic
58	C₁₉×#357	C₂²	1	1	yes	characteristic
59	C₂×Q₁₆×C₁₉	—	2	1	no	—
60	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×SD₁₆×C₁₉	—	2	1	no	—
64	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
66	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	—	2	1	no	—
69	C₁₉×#126	—	4	1	no	—
70	C₁₉×#126	—	4	1	no	—
71	C₁₉×#126	—	4	1	no	—
72	C₁₉×#125	—	2	1	no	—
73	C₁₉×#125	—	4	1	no	—
74	C₁₉×#125	—	4	1	no	—
75	C₁₉×#124	—	2	1	no	—
76	C₁₉×#124	—	4	1	no	—
77	C₁₉×#123	—	4	1	no	—
78	C₁₉×C₂²⋊Q₈	—	2	1	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	—	4	1	no	—
82	C₁₉×#121	—	2	1	no	—
83	C₄×Q₈×C₁₉	—	2	1	no	—
84	C₄×Q₈×C₁₉	—	2	1	no	—
85	C₄×Q₈×C₁₉	—	2	1	no	—
86	C₄×D₄×C₁₉	—	2	1	no	—
87	C₁₉×#117	D₄	1	1	yes	characteristic
88	C₁₉×Q₃₂	—	4	1	no	—
89	C₁₉×Q₃₂	—	4	1	no	—
90	C₁₉×SD₃₂	—	4	1	no	—
91	C₁₉×SD₃₂	—	4	1	no	—
92	C₁₉×M₃₂	—	4	1	no	—
93	C₂×C₁₆×C₁₉	—	4	1	no	—
94	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
98	C₁₉×#107	—	2	1	no	—
99	C₁₉×#107	C₂³	1	1	yes	characteristic
100	C₁₉×#107	C₂³	1	1	yes	characteristic
101	C₁₉×#107	C₂³	1	1	yes	characteristic
102	C₁₉×#107	C₂³	1	1	yes	characteristic
103	C₁₉×#106	—	2	1	no	—
104	C₁₉×#103	—	2	1	no	—
105	C₁₉×#103	—	2	1	no	—
106	C₁₉×#103	—	2	1	no	—
107	C₁₉×#103	—	2	1	no	—
108	C₁₉×#103	—	2	1	no	—
109	C₁₉×#103	—	2	1	no	—
110	C₁₉×#102	—	2	1	no	—
111	C₁₉×#102	—	2	1	no	—
112	C₁₉×#97	D₄	1	1	yes	characteristic
113	C₁₉×#97	D₄	1	1	yes	characteristic
114	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
115	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	4	1	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	4	1	no	—
122	C₂²×C₄×C₁₉	—	4	1	no	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	Q₁₆×C₁₉	—	2	1	no	—
125	Q₁₆×C₁₉	—	2	1	no	—
126	Q₁₆×C₁₉	—	2	1	no	—
127	Q₁₆×C₁₉	—	2	1	no	—
128	Q₁₆×C₁₉	—	2	1	no	—
129	Q₁₆×C₁₉	—	2	1	no	—
130	Q₁₆×C₁₉	—	4	2	no	—
131	SD₁₆×C₁₉	—	4	2	no	—
132	D₈×C₁₉	—	2	1	no	—
133	D₈×C₁₉	—	2	1	no	—
134	M₁₆×C₁₉	—	4	1	no	—
135	C₂×C₈×C₁₉	—	2	1	no	—
136	C₂×C₈×C₁₉	—	2	1	no	—
137	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	4	1	no	—
146	C₄⋊C₄×C₁₉	—	4	1	no	—
147	C₄⋊C₄×C₁₉	—	4	1	no	—
148	C₄⋊C₄×C₁₉	—	4	1	no	—
149	C₄⋊C₄×C₁₉	—	4	1	no	—
150	C₄⋊C₄×C₁₉	—	4	1	no	—
151	C₄⋊C₄×C₁₉	—	4	1	no	—
152	C₄⋊C₄×C₁₉	—	4	1	no	—
153	C₄⋊C₄×C₁₉	—	4	1	no	—
154	C₄⋊C₄×C₁₉	—	4	1	no	—
155	C₄⋊C₄×C₁₉	—	4	1	no	—
156	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
157	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
158	C₂²⋊C₄×C₁₉	—	4	1	no	—
159	C₂²⋊C₄×C₁₉	—	4	1	no	—
160	C₂²⋊C₄×C₁₉	—	4	1	no	—
161	C₂²⋊C₄×C₁₉	—	4	1	no	—
162	C₂²⋊C₄×C₁₉	—	4	1	no	—
163	C₂²⋊C₄×C₁₉	—	4	1	no	—
164	C₂²⋊C₄×C₁₉	—	4	1	no	—
165	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
166	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
167	C₄²×C₁₉	—	4	1	no	—
168	C₄²×C₁₉	—	4	1	no	—
169	C₄²×C₁₉	—	4	1	no	—
170	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₁₆×C₁₉	—	2	1	no	—
173	C₁₆×C₁₉	—	2	1	no	—
174	C₁₆×C₁₉	—	2	1	no	—
175	C₁₆×C₁₉	—	2	1	no	—
176	#33824	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂³×C₁₉	—	4	1	no	—
178	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
179	Q₈×C₁₉	—	4	1	no	—
180	Q₈×C₁₉	—	4	1	no	—
181	Q₈×C₁₉	—	4	1	no	—
182	Q₈×C₁₉	—	4	1	no	—
183	Q₈×C₁₉	—	4	1	no	—
184	Q₈×C₁₉	—	4	1	no	—
185	Q₈×C₁₉	—	16	1	no	—
186	D₄×C₁₉	—	4	1	no	—
187	D₄×C₁₉	—	4	1	no	—
188	D₄×C₁₉	—	16	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	16	1	no	—
199	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
205	C₈×C₁₉	—	2	1	no	—
206	C₈×C₁₉	—	2	1	no	—
207	C₈×C₁₉	—	2	1	no	—
208	C₈×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
209	C₈×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
210	#3177	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#3175	C₂×C₁₉	1	1	yes	characteristic
212	#2229	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#2228	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#2227	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#2225	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#2220	C₂×C₁₉	1	1	yes	characteristic
217	#2219	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#2217	C₂×C₁₉	1	1	yes	characteristic
219	#2216	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#2211	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#2211	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#2209	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#2208	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#2151	C₂×C₁₉	1	1	yes	characteristic, complemented
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	—	2	1	no	—
228	C₂²×C₁₉	—	8	1	no	—
229	C₂²×C₁₉	—	8	1	no	—
230	C₂²×C₁₉	—	8	1	no	—
231	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
232	C₄×C₁₉	—	2	1	no	—
233	C₄×C₁₉	—	2	1	no	—
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	2	1	no	—
236	C₄×C₁₉	—	2	1	no	—
237	C₄×C₁₉	—	8	1	no	—
238	C₄×C₁₉	—	8	1	no	—
239	C₄×C₁₉	—	8	1	no	—
240	C₄×C₁₉	—	8	1	no	—
241	C₄×C₁₉	—	8	1	no	—
242	C₄×C₁₉	—	8	1	no	—
243	C₄×C₁₉	—	8	1	no	—
244	C₄×C₁₉	#537	1	1	yes	characteristic
245	C₄×C₁₉	#575	1	1	yes	characteristic
246	#542	—	2	1	no	—
247	#541	—	2	1	no	—
248	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic
249	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
253	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
254	#500	C₂²×C₁₉	1	1	yes	characteristic
255	#499	C₂²×C₁₉	1	1	yes	characteristic
256	#495	C₂²×C₁₉	1	1	yes	characteristic
257	#494	C₂²×C₁₉	1	1	yes	characteristic
258	#491	—	2	1	no	—
259	#489	—	2	1	no	—
260	#470	—	2	1	no	—
261	#468	—	2	1	no	—
262	#467	C₂²×C₁₉	1	1	yes	characteristic
263	#467	C₂²×C₁₉	1	1	yes	characteristic
264	#467	C₂²×C₁₉	1	1	yes	characteristic
265	#466	C₂²×C₁₉	1	1	yes	characteristic
266	#441	—	2	1	no	—
267	#440	—	2	1	no	—
268	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
269	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
270	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
271	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
272	#405	C₂²×C₁₉	1	1	yes	characteristic
273	#367	C₂²×C₁₉	1	1	yes	characteristic
274	#367	C₂²×C₁₉	1	1	yes	characteristic
275	#366	C₂²×C₁₉	1	1	yes	characteristic
276	#366	C₂²×C₁₉	1	1	yes	characteristic
277	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
278	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
279	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
280	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
281	#358	C₂²×C₁₉	1	1	yes	characteristic
282	#358	C₂²×C₁₉	1	1	yes	characteristic
283	#358	C₂²×C₁₉	1	1	yes	characteristic
284	#358	C₂²×C₁₉	1	1	yes	characteristic
285	#358	C₂²×C₁₉	1	1	yes	characteristic
286	#358	C₂²×C₁₉	1	1	yes	characteristic
287	#357	C₂²×C₁₉	1	1	yes	characteristic
288	#357	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×C₁₉	—	4	1	no	—
290	C₂×C₁₉	—	16	1	no	—
291	C₂×C₁₉	#3245	1	1	yes	characteristic
292	C₂×C₁₉	#3416	1	1	yes	characteristic
293	C₂×C₁₉	#3417	1	1	yes	characteristic
294	C₂×Q₁₆	—	2	1	no	—
295	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
296	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
297	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
298	C₂×SD₁₆	—	2	1	no	—
299	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
300	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	#126	—	4	1	no	—
305	#126	—	4	1	no	—
306	#126	—	4	1	no	—
307	#125	—	2	1	no	—
308	#125	—	4	1	no	—
309	#125	—	4	1	no	—
310	#124	—	2	1	no	—
311	#124	—	4	1	no	—
312	#123	—	4	1	no	—
313	C₂²⋊Q₈	—	2	1	no	—
314	C₂²⋊Q₈	—	2	1	no	—
315	C₂²⋊Q₈	—	2	1	no	—
316	C₂²⋊Q₈	—	4	1	no	—
317	#121	—	2	1	no	—
318	C₄×Q₈	—	2	1	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	#117	D₄×C₁₉	1	1	yes	characteristic
323	Q₃₂	—	4	1	no	—
324	Q₃₂	—	4	1	no	—
325	SD₃₂	—	4	1	no	—
326	SD₃₂	—	4	1	no	—
327	M₃₂	—	4	1	no	—
328	C₂×C₁₆	—	4	1	no	—
329	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
330	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
331	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
332	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
333	#107	—	2	1	no	—
334	#107	C₂³×C₁₉	1	1	yes	characteristic
335	#107	C₂³×C₁₉	1	1	yes	characteristic
336	#107	C₂³×C₁₉	1	1	yes	characteristic
337	#107	C₂³×C₁₉	1	1	yes	characteristic
338	#106	—	2	1	no	—
339	#103	—	2	1	no	—
340	#103	—	2	1	no	—
341	#103	—	2	1	no	—
342	#103	—	2	1	no	—
343	#103	—	2	1	no	—
344	#103	—	2	1	no	—
345	#102	—	2	1	no	—
346	#102	—	2	1	no	—
347	#97	D₄×C₁₉	1	1	yes	characteristic
348	#97	D₄×C₁₉	1	1	yes	characteristic
349	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
350	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
351	C₁₉	#33824	1	1	yes	characteristic, direct product factor, Sylow
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	4	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
360	Q₁₆	—	2	1	no	—
361	Q₁₆	—	2	1	no	—
362	Q₁₆	—	2	1	no	—
363	Q₁₆	—	2	1	no	—
364	Q₁₆	—	2	1	no	—
365	Q₁₆	—	2	1	no	—
366	Q₁₆	—	4	2	no	—
367	SD₁₆	—	4	2	no	—
368	D₈	—	2	1	no	—
369	D₈	—	2	1	no	—
370	M₁₆	—	4	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
374	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
375	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
376	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄⋊C₄	—	4	1	no	—
385	C₄⋊C₄	—	4	1	no	—
386	C₄⋊C₄	—	4	1	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	—	4	1	no	—
390	C₄⋊C₄	—	4	1	no	—
391	C₄⋊C₄	—	4	1	no	—
392	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
393	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
394	C₂²⋊C₄	—	4	1	no	—
395	C₂²⋊C₄	—	4	1	no	—
396	C₂²⋊C₄	—	4	1	no	—
397	C₂²⋊C₄	—	4	1	no	—
398	C₂²⋊C₄	—	4	1	no	—
399	C₂²⋊C₄	—	4	1	no	—
400	C₂²⋊C₄	—	4	1	no	—
401	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
402	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
403	C₄²	—	4	1	no	—
404	C₄²	—	4	1	no	—
405	C₄²	—	4	1	no	—
406	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
408	C₁₆	—	2	1	no	—
409	C₁₆	—	2	1	no	—
410	C₁₆	—	2	1	no	—
411	C₁₆	—	2	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
414	Q₈	—	4	1	no	—
415	Q₈	—	4	1	no	—
416	Q₈	—	4	1	no	—
417	Q₈	—	4	1	no	—
418	Q₈	—	4	1	no	—
419	Q₈	—	4	1	no	—
420	Q₈	—	16	1	no	—
421	D₄	—	4	1	no	—
422	D₄	—	4	1	no	—
423	D₄	—	16	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	16	1	no	—
434	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
435	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
436	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
437	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
438	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
440	C₈	—	2	1	no	—
441	C₈	—	2	1	no	—
442	C₈	—	2	1	no	—
443	C₈	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
444	C₈	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	1	no	—
451	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	1	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	1	no	—
462	C₄	—	8	1	no	—
463	C₄	—	8	1	no	—
464	C₄	C₁₉×#537	1	1	yes	characteristic
465	C₄	C₁₉×#575	1	1	yes	characteristic
466	C₂	—	4	1	no	—
467	C₂	—	16	1	no	—
468	C₂	C₁₉×#3245	1	1	yes	characteristic
469	C₂	C₁₉×#3416	1	1	yes	characteristic
470	C₂	C₁₉×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₁₉×#466	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#117 ◁ C₁₉×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3177	C₂	semidirect
3. C₁₉×#2229	C₂	semidirect
4. C₁₉×#2228	C₂	semidirect
5. C₁₉×#2227	C₂	semidirect
6. C₁₉×#2225	C₂	semidirect
8. C₁₉×#2219	C₂	semidirect
10. C₁₉×#2216	C₂	semidirect
11. C₁₉×#2211	C₂	semidirect
12. C₁₉×#2211	C₂	semidirect
13. C₁₉×#2209	C₂	semidirect
14. C₁₉×#2208	C₂	semidirect
15. C₁₉×#2151	C₂	semidirect
176. #33824	C₁₉	direct (N × H)
210. #3177	C₂×C₁₉	semidirect
212. #2229	C₂×C₁₉	semidirect
213. #2228	C₂×C₁₉	semidirect
214. #2227	C₂×C₁₉	semidirect
215. #2225	C₂×C₁₉	semidirect
217. #2219	C₂×C₁₉	semidirect
219. #2216	C₂×C₁₉	semidirect
220. #2211	C₂×C₁₉	semidirect
221. #2211	C₂×C₁₉	semidirect
222. #2209	C₂×C₁₉	semidirect
223. #2208	C₂×C₁₉	semidirect
224. #2151	C₂×C₁₉	semidirect
351. C₁₉	#33824	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×#3177	2
C₁₉×#3175	2
C₁₉×#2229	2
C₁₉×#2228	2
C₁₉×#2227	2
C₁₉×#2225	2
C₁₉×#2220	2
C₁₉×#2219	2
C₁₉×#2217	2
C₁₉×#2216	2
C₁₉×#2211	2
C₁₉×#2209	2
C₁₉×#2208	2
C₁₉×#2151	2
#33824	19

Subgroups — C19×#33824 #18039783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33824 #18039783