Subgroups — C₁₉×#33955 #18039914

Order 4864.

458 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3383	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3380	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2255	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2255	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2253	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2229	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2229	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2228	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#2228	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2226	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#2225	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2183	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2175	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#2175	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₉×SD₃₂	C₂	1	1	yes	maximal, characteristic
16	C₁₉×#557	—	2	1	no	—
17	C₁₉×#554	—	2	1	no	—
18	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
19	C₁₉×#500	C₂²	1	1	yes	characteristic
20	C₁₉×#500	C₂²	1	1	yes	characteristic
21	C₁₉×#499	C₂²	1	1	yes	characteristic
22	C₁₉×#499	C₂²	1	1	yes	characteristic
23	C₁₉×#499	C₂²	1	1	yes	characteristic
24	C₁₉×#499	C₂²	1	1	yes	characteristic
25	C₁₉×#479	—	2	1	no	—
26	C₁₉×#479	—	2	1	no	—
27	C₁₉×#478	—	2	1	no	—
28	C₁₉×#478	—	2	1	no	—
29	C₁₉×#476	—	2	1	no	—
30	C₁₉×#475	—	2	1	no	—
31	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
33	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
34	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
35	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
36	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
37	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
38	C₁₉×#367	C₂²	1	1	yes	characteristic
39	C₁₉×#367	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×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×#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×#346	C₂²	1	1	yes	characteristic
57	C₁₉×#346	C₂²	1	1	yes	characteristic
58	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
59	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	4	1	no	—
64	C₁₉×#125	—	2	1	no	—
65	C₁₉×#125	—	2	1	no	—
66	C₁₉×#125	—	2	1	no	—
67	C₁₉×#125	—	2	1	no	—
68	C₁₉×#125	—	4	1	no	—
69	C₁₉×#125	—	4	1	no	—
70	C₁₉×C₂²⋊Q₈	—	4	1	no	—
71	C₁₉×C₂²⋊Q₈	—	4	1	no	—
72	C₁₉×C₂²⋊Q₈	—	4	1	no	—
73	C₄×Q₈×C₁₉	—	2	1	no	—
74	C₄×Q₈×C₁₉	—	2	1	no	—
75	C₄×Q₈×C₁₉	—	2	1	no	—
76	C₄×Q₈×C₁₉	—	4	1	no	—
77	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
78	C₄×D₄×C₁₉	—	2	1	no	—
79	C₄×D₄×C₁₉	—	2	1	no	—
80	C₄×D₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
82	C₁₉×SD₃₂	Q₈	1	4	yes	complemented
83	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
87	C₁₉×#107	—	2	1	no	—
88	C₁₉×#107	—	2	1	no	—
89	C₁₉×#107	C₂³	1	1	yes	characteristic
90	C₁₉×#107	C₂³	1	1	yes	characteristic
91	C₁₉×#107	C₂³	1	1	yes	characteristic
92	C₁₉×#107	C₂³	1	1	yes	characteristic
93	C₁₉×#107	C₂³	1	1	yes	characteristic
94	C₁₉×#107	C₂³	1	1	yes	characteristic
95	C₁₉×#106	—	2	1	no	—
96	C₁₉×#106	—	2	1	no	—
97	C₁₉×#106	—	2	1	no	—
98	C₁₉×#106	—	2	1	no	—
99	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
100	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
101	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
102	C₁₉×#103	—	2	1	no	—
103	C₁₉×#103	—	2	1	no	—
104	C₁₉×#103	—	2	1	no	—
105	C₁₉×#102	—	2	1	no	—
106	C₁₉×#102	—	2	1	no	—
107	C₁₉×#102	—	2	1	no	—
108	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
110	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	4	1	no	—
113	C₂×Q₈×C₁₉	—	4	1	no	—
114	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
115	C₂×D₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	4	1	no	—
117	C₂²×C₄×C₁₉	—	4	1	no	—
118	C₂²×C₄×C₁₉	—	4	1	no	—
119	Q₁₆×C₁₉	—	2	1	no	—
120	Q₁₆×C₁₉	C₂×Q₈	1	2	yes	—
121	D₈×C₁₉	—	2	1	no	—
122	D₈×C₁₉	C₂×Q₈	1	2	yes	—
123	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	4	1	no	—
134	C₄⋊C₄×C₁₉	—	4	1	no	—
135	C₄⋊C₄×C₁₉	—	4	1	no	—
136	C₄⋊C₄×C₁₉	—	4	1	no	—
137	C₄⋊C₄×C₁₉	—	4	1	no	—
138	C₄⋊C₄×C₁₉	—	4	1	no	—
139	C₄⋊C₄×C₁₉	—	4	1	no	—
140	C₄⋊C₄×C₁₉	—	4	1	no	—
141	C₄⋊C₄×C₁₉	—	4	1	no	—
142	C₄⋊C₄×C₁₉	—	4	1	no	—
143	C₄⋊C₄×C₁₉	—	4	1	no	—
144	C₄⋊C₄×C₁₉	—	4	1	no	—
145	C₄⋊C₄×C₁₉	—	4	1	no	—
146	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
147	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
148	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
149	C₂²⋊C₄×C₁₉	—	4	1	no	—
150	C₂²⋊C₄×C₁₉	—	4	1	no	—
151	C₂²⋊C₄×C₁₉	—	4	1	no	—
152	C₄²×C₁₉	—	4	1	no	—
153	C₄²×C₁₉	—	4	1	no	—
154	C₄²×C₁₉	—	4	1	no	—
155	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₁₆×C₁₉	—	2	1	no	—
159	C₁₆×C₁₉	—	2	1	no	—
160	C₁₆×C₁₉	—	2	1	no	—
161	C₁₆×C₁₉	C₂×Q₈	1	2	yes	—
162	#33955	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂³×C₁₉	—	4	1	no	—
164	Q₈×C₁₉	—	2	2	no	—
165	Q₈×C₁₉	—	4	1	no	—
166	Q₈×C₁₉	—	4	1	no	—
167	Q₈×C₁₉	—	8	2	no	—
168	Q₈×C₁₉	—	16	1	no	—
169	D₄×C₁₉	—	2	2	no	—
170	D₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	8	2	no	—
179	C₂×C₄×C₁₉	—	16	1	no	—
180	C₂×C₄×C₁₉	—	16	1	no	—
181	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
188	C₈×C₁₉	—	2	1	no	—
189	C₈×C₁₉	—	2	1	no	—
190	C₈×C₁₉	—	2	1	no	—
191	C₈×C₁₉	C₂²×Q₈	1	1	yes	characteristic
192	C₈×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
193	#3383	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#3380	C₂×C₁₉	1	1	yes	characteristic
195	#2255	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#2255	C₂×C₁₉	1	1	yes	characteristic, complemented
197	#2253	C₂×C₁₉	1	1	yes	characteristic, complemented
198	#2229	C₂×C₁₉	1	1	yes	characteristic, complemented
199	#2229	C₂×C₁₉	1	1	yes	characteristic, complemented
200	#2228	C₂×C₁₉	1	1	yes	characteristic
201	#2228	C₂×C₁₉	1	1	yes	characteristic
202	#2226	C₂×C₁₉	1	1	yes	characteristic
203	#2225	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#2183	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#2175	C₂×C₁₉	1	1	yes	characteristic
206	#2175	C₂×C₁₉	1	1	yes	characteristic
207	C₄×SD₃₂	C₂×C₁₉	1	1	yes	characteristic
208	C₂²×C₁₉	—	4	2	no	—
209	C₂²×C₁₉	—	8	1	no	—
210	C₂²×C₁₉	—	8	1	no	—
211	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	2	1	no	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	4	2	no	—
219	C₄×C₁₉	—	8	1	no	—
220	C₄×C₁₉	—	8	1	no	—
221	C₄×C₁₉	—	8	1	no	—
222	C₄×C₁₉	—	8	1	no	—
223	C₄×C₁₉	—	8	1	no	—
224	C₄×C₁₉	—	8	1	no	—
225	C₄×C₁₉	D₄×Q₈	1	1	yes	characteristic
226	C₄×C₁₉	#578	1	1	yes	characteristic
227	#557	—	2	1	no	—
228	#554	—	2	1	no	—
229	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
230	#500	C₂²×C₁₉	1	1	yes	characteristic
231	#500	C₂²×C₁₉	1	1	yes	characteristic
232	#499	C₂²×C₁₉	1	1	yes	characteristic
233	#499	C₂²×C₁₉	1	1	yes	characteristic
234	#499	C₂²×C₁₉	1	1	yes	characteristic
235	#499	C₂²×C₁₉	1	1	yes	characteristic
236	#479	—	2	1	no	—
237	#479	—	2	1	no	—
238	#478	—	2	1	no	—
239	#478	—	2	1	no	—
240	#476	—	2	1	no	—
241	#475	—	2	1	no	—
242	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
243	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
244	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
245	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
246	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
247	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
248	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
249	#367	C₂²×C₁₉	1	1	yes	characteristic
250	#367	C₂²×C₁₉	1	1	yes	characteristic
251	#367	C₂²×C₁₉	1	1	yes	characteristic
252	#367	C₂²×C₁₉	1	1	yes	characteristic
253	#367	C₂²×C₁₉	1	1	yes	characteristic
254	#366	C₂²×C₁₉	1	1	yes	characteristic
255	#366	C₂²×C₁₉	1	1	yes	characteristic
256	#366	C₂²×C₁₉	1	1	yes	characteristic
257	#366	C₂²×C₁₉	1	1	yes	characteristic
258	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
259	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
260	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
261	#358	C₂²×C₁₉	1	1	yes	characteristic
262	#358	C₂²×C₁₉	1	1	yes	characteristic
263	#358	C₂²×C₁₉	1	1	yes	characteristic
264	#357	C₂²×C₁₉	1	1	yes	characteristic
265	#357	C₂²×C₁₉	1	1	yes	characteristic
266	#357	C₂²×C₁₉	1	1	yes	characteristic
267	#346	C₂²×C₁₉	1	1	yes	characteristic
268	#346	C₂²×C₁₉	1	1	yes	characteristic
269	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
270	C₂×C₁₉	—	8	2	no	—
271	C₂×C₁₉	Q₈×D₈	1	1	yes	characteristic
272	C₂×C₁₉	#3414	1	1	yes	characteristic
273	C₂×C₁₉	#3416	1	1	yes	characteristic
274	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
275	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	—	4	1	no	—
279	#125	—	2	1	no	—
280	#125	—	2	1	no	—
281	#125	—	2	1	no	—
282	#125	—	2	1	no	—
283	#125	—	4	1	no	—
284	#125	—	4	1	no	—
285	C₂²⋊Q₈	—	4	1	no	—
286	C₂²⋊Q₈	—	4	1	no	—
287	C₂²⋊Q₈	—	4	1	no	—
288	C₄×Q₈	—	2	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	—	4	1	no	—
292	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	4	1	no	—
297	SD₃₂	Q₈×C₁₉	1	4	yes	complemented
298	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
299	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
300	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
301	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
302	#107	—	2	1	no	—
303	#107	—	2	1	no	—
304	#107	C₂³×C₁₉	1	1	yes	characteristic
305	#107	C₂³×C₁₉	1	1	yes	characteristic
306	#107	C₂³×C₁₉	1	1	yes	characteristic
307	#107	C₂³×C₁₉	1	1	yes	characteristic
308	#107	C₂³×C₁₉	1	1	yes	characteristic
309	#107	C₂³×C₁₉	1	1	yes	characteristic
310	#106	—	2	1	no	—
311	#106	—	2	1	no	—
312	#106	—	2	1	no	—
313	#106	—	2	1	no	—
314	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
315	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
316	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
317	#103	—	2	1	no	—
318	#103	—	2	1	no	—
319	#103	—	2	1	no	—
320	#102	—	2	1	no	—
321	#102	—	2	1	no	—
322	#102	—	2	1	no	—
323	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
324	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
325	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
326	C₁₉	#33955	1	1	yes	characteristic, direct product factor, Sylow
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	4	1	no	—
329	C₂×Q₈	—	4	1	no	—
330	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
331	C₂×D₄	—	2	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	4	1	no	—
335	Q₁₆	—	2	1	no	—
336	Q₁₆	C₂×Q₈×C₁₉	1	2	yes	—
337	D₈	—	2	1	no	—
338	D₈	C₂×Q₈×C₁₉	1	2	yes	—
339	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
340	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
341	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
363	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
364	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	4	1	no	—
368	C₄²	—	4	1	no	—
369	C₄²	—	4	1	no	—
370	C₄²	—	4	1	no	—
371	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
373	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
374	C₁₆	—	2	1	no	—
375	C₁₆	—	2	1	no	—
376	C₁₆	—	2	1	no	—
377	C₁₆	C₂×Q₈×C₁₉	1	2	yes	—
378	C₂³	—	4	1	no	—
379	Q₈	—	2	2	no	—
380	Q₈	—	4	1	no	—
381	Q₈	—	4	1	no	—
382	Q₈	—	8	2	no	—
383	Q₈	—	16	1	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	8	2	no	—
394	C₂×C₄	—	16	1	no	—
395	C₂×C₄	—	16	1	no	—
396	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
397	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
398	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
399	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
400	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
401	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
402	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	C₂²×Q₈×C₁₉	1	1	yes	characteristic
407	C₈	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
408	C₂²	—	4	2	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	4	2	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	1	no	—
422	C₄	—	8	1	no	—
423	C₄	—	8	1	no	—
424	C₄	—	8	1	no	—
425	C₄	D₄×Q₈×C₁₉	1	1	yes	characteristic
426	C₄	C₁₉×#578	1	1	yes	characteristic
427	C₂	—	8	2	no	—
428	C₂	Q₈×D₈×C₁₉	1	1	yes	characteristic
429	C₂	C₁₉×#3414	1	1	yes	characteristic
430	C₂	C₁₉×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₂×D₈×C₁₉	C₂³
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×Q₈×C₁₉ ◁ C₈×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3383	C₂	semidirect
3. C₁₉×#2255	C₂	semidirect
4. C₁₉×#2255	C₂	semidirect
5. C₁₉×#2253	C₂	semidirect
6. C₁₉×#2229	C₂	semidirect
7. C₁₉×#2229	C₂	semidirect
11. C₁₉×#2225	C₂	semidirect
12. C₁₉×#2183	C₂	semidirect
82. C₁₉×SD₃₂	Q₈	semidirect
162. #33955	C₁₉	direct (N × H)
193. #3383	C₂×C₁₉	semidirect
195. #2255	C₂×C₁₉	semidirect
196. #2255	C₂×C₁₉	semidirect
197. #2253	C₂×C₁₉	semidirect
198. #2229	C₂×C₁₉	semidirect
199. #2229	C₂×C₁₉	semidirect
203. #2225	C₂×C₁₉	semidirect
204. #2183	C₂×C₁₉	semidirect
297. SD₃₂	Q₈×C₁₉	semidirect
326. C₁₉	#33955	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×#3383	2
C₁₉×#3380	2
C₁₉×#2255	2
C₁₉×#2253	2
C₁₉×#2229	2
C₁₉×#2228	2
C₁₉×#2226	2
C₁₉×#2225	2
C₁₉×#2183	2
C₁₉×#2175	2
C₄×C₁₉×SD₃₂	2
#33955	19

Subgroups — C19×#33955 #18039914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33955 #18039914