Subgroups — C₁₉×#33910 #18039869

Order 4864.

504 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3336	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3334	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2255	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2236	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2235	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2234	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2232	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2228	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2227	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2220	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2217	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2175	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2159	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#366	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#552	—	2	1	no	—
17	C₁₉×#547	—	2	1	no	—
18	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
20	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#500	C₂²	1	1	yes	characteristic
22	C₁₉×#499	C₂²	1	1	yes	characteristic
23	C₁₉×#485	—	2	1	no	—
24	C₁₉×#483	—	2	1	no	—
25	C₁₉×#480	—	2	1	no	—
26	C₁₉×#480	—	2	1	no	—
27	C₁₉×#479	—	2	1	no	—
28	C₁₉×#474	—	2	1	no	—
29	C₁₉×#467	C₂²	1	1	yes	characteristic
30	C₁₉×#467	C₂²	1	1	yes	characteristic
31	C₁₉×#466	C₂²	1	1	yes	characteristic
32	C₁₉×#466	C₂²	1	1	yes	characteristic
33	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
34	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
35	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#427	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
40	C₁₉×#367	C₂²	1	1	yes	characteristic
41	C₁₉×#367	C₂²	1	1	yes	characteristic
42	C₁₉×#367	C₂²	1	1	yes	characteristic
43	C₁₉×#366	C₂²	1	1	yes	characteristic
44	C₁₉×#366	C₂²	1	1	yes	characteristic
45	C₁₉×#366	C₂²	1	1	yes	characteristic
46	C₁₉×#366	C₂²	1	1	yes	characteristic
47	C₁₉×#366	C₂²	1	1	yes	characteristic
48	C₁₉×#366	C₂²	1	1	yes	characteristic
49	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
50	C₁₉×#358	C₂²	1	1	yes	characteristic
51	C₁₉×#358	C₂²	1	1	yes	characteristic
52	C₁₉×#358	C₂²	1	1	yes	characteristic
53	C₁₉×#357	C₂²	1	1	yes	characteristic
54	C₁₉×#357	C₂²	1	1	yes	characteristic
55	C₁₉×#357	C₂²	1	1	yes	characteristic
56	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
58	C₁₉×#346	C₂²	1	1	yes	characteristic
59	C₂×#41×C₁₉	—	4	1	no	—
60	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₁₉×C₄⋊Q₈	—	2	1	no	—
65	C₁₉×#126	—	4	1	no	—
66	C₁₉×#125	—	2	1	no	—
67	C₁₉×#125	—	4	1	no	—
68	C₁₉×#123	—	4	1	no	—
69	C₁₉×#123	—	4	1	no	—
70	C₁₉×#123	—	4	1	no	—
71	C₁₉×C₂²⋊Q₈	—	2	1	no	—
72	C₁₉×C₂²⋊Q₈	—	2	1	no	—
73	C₁₉×C₂²⋊Q₈	—	4	1	no	—
74	C₁₉×#121	—	2	1	no	—
75	C₁₉×#121	—	2	1	no	—
76	C₄×Q₈×C₁₉	—	2	1	no	—
77	C₄×D₄×C₁₉	—	2	1	no	—
78	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
79	C₁₉×#117	—	2	1	no	—
80	C₁₉×#117	—	4	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₁₉×SD₃₂	—	2	2	no	—
85	C₁₉×M₃₂	—	2	2	no	—
86	C₂×C₁₆×C₁₉	—	2	2	no	—
87	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
91	C₁₉×#107	—	2	1	no	—
92	C₁₉×#107	—	2	1	no	—
93	C₁₉×#107	—	2	1	no	—
94	C₁₉×#107	—	2	1	no	—
95	C₁₉×#107	C₂³	1	1	yes	characteristic
96	C₁₉×#107	C₂³	1	1	yes	characteristic
97	C₁₉×#107	C₂³	1	1	yes	characteristic
98	C₁₉×#107	C₂³	1	1	yes	characteristic
99	C₁₉×#107	C₂³	1	1	yes	characteristic
100	C₁₉×#107	C₂³	1	1	yes	characteristic
101	C₁₉×#106	—	2	1	no	—
102	C₁₉×#106	—	2	1	no	—
103	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
104	C₁₉×#103	—	2	1	no	—
105	C₁₉×#103	—	2	1	no	—
106	C₁₉×#103	—	2	1	no	—
107	C₁₉×#102	—	2	1	no	—
108	C₁₉×#102	—	2	1	no	—
109	C₁₉×#102	—	2	1	no	—
110	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
111	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
112	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
113	#41×C₁₉	—	8	4	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	4	1	no	—
116	C₂×D₄×C₁₉	—	2	1	no	—
117	C₂×D₄×C₁₉	—	4	1	no	—
118	C₂×D₄×C₁₉	—	4	1	no	—
119	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	—	4	1	no	—
121	C₂²×C₄×C₁₉	—	4	1	no	—
122	C₂²×C₄×C₁₉	—	4	1	no	—
123	C₂²×C₄×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	Q₁₆×C₁₉	—	2	1	no	—
127	Q₁₆×C₁₉	—	2	1	no	—
128	D₈×C₁₉	—	2	1	no	—
129	D₈×C₁₉	—	2	1	no	—
130	C₂×C₈×C₁₉	—	2	1	no	—
131	C₂×C₈×C₁₉	—	2	1	no	—
132	C₂×C₈×C₁₉	—	2	1	no	—
133	C₂×C₈×C₁₉	—	2	1	no	—
134	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	4	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	D₈	1	1	yes	characteristic
154	C₂²⋊C₄×C₁₉	—	4	1	no	—
155	C₂²⋊C₄×C₁₉	—	4	1	no	—
156	C₂²⋊C₄×C₁₉	—	4	1	no	—
157	C₂²⋊C₄×C₁₉	—	4	1	no	—
158	C₂²⋊C₄×C₁₉	—	4	1	no	—
159	C₂²⋊C₄×C₁₉	—	4	1	no	—
160	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
161	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
162	C₄²×C₁₉	—	4	1	no	—
163	C₄²×C₁₉	—	4	1	no	—
164	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₁₆×C₁₉	—	2	1	no	—
166	C₁₆×C₁₉	—	2	1	no	—
167	C₁₆×C₁₉	—	2	1	no	—
168	C₁₆×C₁₉	#41	1	2	yes	complemented
169	#33910	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂³×C₁₉	—	4	1	no	—
171	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
172	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
173	Q₈×C₁₉	—	4	1	no	—
174	Q₈×C₁₉	—	4	1	no	—
175	Q₈×C₁₉	—	8	2	no	—
176	D₄×C₁₉	—	2	2	no	—
177	D₄×C₁₉	—	4	1	no	—
178	D₄×C₁₉	—	4	1	no	—
179	D₄×C₁₉	—	8	2	no	—
180	D₄×C₁₉	—	8	2	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	2	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	8	2	no	—
193	C₂×C₄×C₁₉	—	8	2	no	—
194	C₂×C₄×C₁₉	—	8	2	no	—
195	C₂×C₄×C₁₉	—	8	2	no	—
196	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
201	C₈×C₁₉	—	2	1	no	—
202	C₈×C₁₉	—	2	1	no	—
203	C₈×C₁₉	—	2	1	no	—
204	C₈×C₁₉	C₂×#41	1	1	yes	characteristic
205	C₈×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
206	#3336	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#3334	C₂×C₁₉	1	1	yes	characteristic
208	#2255	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#2236	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#2235	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#2234	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#2232	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	#2220	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#2217	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#2175	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#2168	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#2159	C₂×C₁₉	1	1	yes	characteristic, complemented
220	C₂×#366	C₂×C₁₉	1	1	yes	characteristic, complemented
221	C₂²×C₁₉	—	2	1	no	—
222	C₂²×C₁₉	—	2	1	no	—
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	8	1	no	—
227	C₂²×C₁₉	—	8	1	no	—
228	C₂²×C₁₉	—	8	1	no	—
229	C₂²×C₁₉	#509	1	2	yes	—
230	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
231	C₄×C₁₉	—	2	1	no	—
232	C₄×C₁₉	—	2	1	no	—
233	C₄×C₁₉	—	2	1	no	—
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	8	1	no	—
236	C₄×C₁₉	—	8	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	#547	1	1	yes	characteristic
243	C₄×C₁₉	#578	1	1	yes	characteristic
244	#552	—	2	1	no	—
245	#547	—	2	1	no	—
246	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
248	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
249	#500	C₂²×C₁₉	1	1	yes	characteristic
250	#499	C₂²×C₁₉	1	1	yes	characteristic
251	#485	—	2	1	no	—
252	#483	—	2	1	no	—
253	#480	—	2	1	no	—
254	#480	—	2	1	no	—
255	#479	—	2	1	no	—
256	#474	—	2	1	no	—
257	#467	C₂²×C₁₉	1	1	yes	characteristic
258	#467	C₂²×C₁₉	1	1	yes	characteristic
259	#466	C₂²×C₁₉	1	1	yes	characteristic
260	#466	C₂²×C₁₉	1	1	yes	characteristic
261	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
262	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
263	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
264	#427	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
267	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
268	#367	C₂²×C₁₉	1	1	yes	characteristic
269	#367	C₂²×C₁₉	1	1	yes	characteristic
270	#367	C₂²×C₁₉	1	1	yes	characteristic
271	#366	C₂²×C₁₉	1	1	yes	characteristic
272	#366	C₂²×C₁₉	1	1	yes	characteristic
273	#366	C₂²×C₁₉	1	1	yes	characteristic
274	#366	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	#358	C₂²×C₁₉	1	1	yes	characteristic
279	#358	C₂²×C₁₉	1	1	yes	characteristic
280	#358	C₂²×C₁₉	1	1	yes	characteristic
281	#357	C₂²×C₁₉	1	1	yes	characteristic
282	#357	C₂²×C₁₉	1	1	yes	characteristic
283	#357	C₂²×C₁₉	1	1	yes	characteristic
284	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
285	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
286	#346	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×C₁₉	—	2	2	no	—
288	C₂×C₁₉	—	4	1	no	—
289	C₂×C₁₉	—	16	1	no	—
290	C₂×C₁₉	#3334	1	1	yes	characteristic
291	C₂×C₁₉	C₂×#509	1	1	yes	characteristic
292	C₂×C₁₉	#3417	1	1	yes	characteristic
293	C₂×#41	—	4	1	no	—
294	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
295	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
298	C₄⋊Q₈	—	2	1	no	—
299	#126	—	4	1	no	—
300	#125	—	2	1	no	—
301	#125	—	4	1	no	—
302	#123	—	4	1	no	—
303	#123	—	4	1	no	—
304	#123	—	4	1	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	C₂²⋊Q₈	—	4	1	no	—
308	#121	—	2	1	no	—
309	#121	—	2	1	no	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
313	#117	—	2	1	no	—
314	#117	—	4	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	SD₃₂	—	2	2	no	—
319	M₃₂	—	2	2	no	—
320	C₂×C₁₆	—	2	2	no	—
321	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
322	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
323	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
324	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
325	#107	—	2	1	no	—
326	#107	—	2	1	no	—
327	#107	—	2	1	no	—
328	#107	—	2	1	no	—
329	#107	C₂³×C₁₉	1	1	yes	characteristic
330	#107	C₂³×C₁₉	1	1	yes	characteristic
331	#107	C₂³×C₁₉	1	1	yes	characteristic
332	#107	C₂³×C₁₉	1	1	yes	characteristic
333	#107	C₂³×C₁₉	1	1	yes	characteristic
334	#107	C₂³×C₁₉	1	1	yes	characteristic
335	#106	—	2	1	no	—
336	#106	—	2	1	no	—
337	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
338	#103	—	2	1	no	—
339	#103	—	2	1	no	—
340	#103	—	2	1	no	—
341	#102	—	2	1	no	—
342	#102	—	2	1	no	—
343	#102	—	2	1	no	—
344	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
345	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
346	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
347	C₁₉	#33910	1	1	yes	characteristic, direct product factor, Sylow
348	#41	—	8	4	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	4	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	—	4	1	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
361	Q₁₆	—	2	1	no	—
362	Q₁₆	—	2	1	no	—
363	D₈	—	2	1	no	—
364	D₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
370	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	4	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	D₈×C₁₉	1	1	yes	characteristic
389	C₂²⋊C₄	—	4	1	no	—
390	C₂²⋊C₄	—	4	1	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
396	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
397	C₄²	—	4	1	no	—
398	C₄²	—	4	1	no	—
399	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
400	C₁₆	—	2	1	no	—
401	C₁₆	—	2	1	no	—
402	C₁₆	—	2	1	no	—
403	C₁₆	#41×C₁₉	1	2	yes	complemented
404	C₂³	—	4	1	no	—
405	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
406	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
407	Q₈	—	4	1	no	—
408	Q₈	—	4	1	no	—
409	Q₈	—	8	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	1	no	—
413	D₄	—	8	2	no	—
414	D₄	—	8	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	8	2	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	8	2	no	—
430	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
432	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
433	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
434	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
435	C₈	—	2	1	no	—
436	C₈	—	2	1	no	—
437	C₈	—	2	1	no	—
438	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
439	C₈	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	C₁₉×#509	1	2	yes	—
449	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	8	1	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	1	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	1	no	—
460	C₄	—	8	1	no	—
461	C₄	C₁₉×#547	1	1	yes	characteristic
462	C₄	C₁₉×#578	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	1	no	—
465	C₂	—	16	1	no	—
466	C₂	C₁₉×#3334	1	1	yes	characteristic
467	C₂	C₂×C₁₉×#509	1	1	yes	characteristic
468	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×#3334	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×D₄×C₁₉ ◁ C₈×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3336	C₂	semidirect
3. C₁₉×#2255	C₂	semidirect
4. C₁₉×#2236	C₂	semidirect
5. C₁₉×#2235	C₂	semidirect
6. C₁₉×#2234	C₂	semidirect
7. C₁₉×#2232	C₂	semidirect
8. C₁₉×#2228	C₂	semidirect
9. C₁₉×#2227	C₂	semidirect
10. C₁₉×#2220	C₂	semidirect
11. C₁₉×#2217	C₂	semidirect
12. C₁₉×#2175	C₂	semidirect
13. C₁₉×#2168	C₂	semidirect
14. C₁₉×#2159	C₂	semidirect
15. C₂×C₁₉×#366	C₂	semidirect
168. C₁₆×C₁₉	#41	semidirect
169. #33910	C₁₉	direct (N × H)
206. #3336	C₂×C₁₉	semidirect
208. #2255	C₂×C₁₉	semidirect
209. #2236	C₂×C₁₉	semidirect
210. #2235	C₂×C₁₉	semidirect
211. #2234	C₂×C₁₉	semidirect
212. #2232	C₂×C₁₉	semidirect
213. #2228	C₂×C₁₉	semidirect
214. #2227	C₂×C₁₉	semidirect
215. #2220	C₂×C₁₉	semidirect
216. #2217	C₂×C₁₉	semidirect
217. #2175	C₂×C₁₉	semidirect
218. #2168	C₂×C₁₉	semidirect
219. #2159	C₂×C₁₉	semidirect
220. C₂×#366	C₂×C₁₉	semidirect
347. C₁₉	#33910	direct (N × H)
403. C₁₆	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3336	2
C₁₉×#3334	2
C₁₉×#2255	2
C₁₉×#2236	2
C₁₉×#2235	2
C₁₉×#2234	2
C₁₉×#2232	2
C₁₉×#2228	2
C₁₉×#2227	2
C₁₉×#2220	2
C₁₉×#2217	2
C₁₉×#2175	2
C₁₉×#2168	2
C₁₉×#2159	2
C₂×C₁₉×#366	2
#33910	19

Subgroups — C19×#33910 #18039869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33910 #18039869