Subgroups — C₁₉×#62358 #18068317

Order 4864.

1710 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3507	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3394	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3381	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3364	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3361	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3250	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3249	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3245	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#3168	C₂	1	4	yes	maximal, complemented
10	C₁₉×#3167	C₂	1	2	yes	maximal, complemented
11	C₂×C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#559	C₂²	1	4	yes	—
13	C₁₉×#557	C₂²	1	4	yes	—
14	C₁₉×#556	—	2	4	no	—
15	C₁₉×#556	C₂²	1	4	yes	—
16	C₁₉×#554	C₂²	1	4	yes	—
17	C₁₉×#552	—	2	4	no	—
18	C₁₉×#539	—	2	4	no	—
19	C₁₉×#536	—	2	2	no	—
20	C₁₉×#533	C₂²	1	2	yes	—
21	C₁₉×#532	C₂²	1	2	yes	—
22	C₁₉×#529	C₂²	1	8	yes	—
23	C₁₉×#520	—	2	2	no	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#499	C₂²	1	4	yes	—
26	C₁₉×#498	C₂²	1	2	yes	—
27	C₁₉×#495	C₂²	1	4	yes	—
28	C₁₉×#492	C₂²	1	2	yes	—
29	C₁₉×#488	C₂²	1	8	yes	—
30	C₁₉×#487	C₂²	1	2	yes	—
31	C₁₉×#486	C₂²	1	2	yes	—
32	C₁₉×#479	C₂²	1	8	yes	—
33	C₁₉×#478	C₂²	1	8	yes	—
34	C₁₉×#477	C₂²	1	4	yes	—
35	C₁₉×#474	C₂²	1	4	yes	—
36	C₁₉×#467	C₂²	1	4	yes	—
37	C₁₉×#466	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	C₈×Q₈×C₁₉	C₂²	1	4	yes	—
45	C₈×Q₈×C₁₉	C₂²	1	4	yes	—
46	C₄×Q₁₆×C₁₉	C₂²	1	4	yes	—
47	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
48	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
49	C₄×SD₁₆×C₁₉	C₂²	1	8	yes	—
50	C₄×D₈×C₁₉	C₂²	1	4	yes	—
51	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
53	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
55	C₂×#41×C₁₉	—	2	2	no	—
56	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
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	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
64	C₁₉×C₄⋊Q₈	—	2	4	no	—
65	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
68	C₁₉×#127	C₂³	1	2	yes	—
69	C₁₉×#126	—	2	8	no	—
70	C₁₉×#126	—	2	8	no	—
71	C₁₉×#125	—	2	8	no	—
72	C₁₉×#125	—	2	2	no	—
73	C₁₉×#125	C₂³	1	8	yes	—
74	C₁₉×#124	—	2	4	no	—
75	C₁₉×#124	—	2	2	no	—
76	C₁₉×#124	C₂³	1	8	yes	—
77	C₁₉×#123	—	2	8	no	—
78	C₁₉×#123	—	2	8	no	—
79	C₁₉×C₂²⋊Q₈	—	2	4	no	—
80	C₁₉×C₂²⋊Q₈	—	2	4	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	8	no	—
83	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
84	C₁₉×#121	—	2	2	no	—
85	C₁₉×#121	C₂³	1	4	yes	—
86	C₄×Q₈×C₁₉	—	2	4	no	—
87	C₄×Q₈×C₁₉	—	2	2	no	—
88	C₄×Q₈×C₁₉	D₄	1	4	yes	—
89	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
90	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
91	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
92	C₄×D₄×C₁₉	—	2	8	no	—
93	C₄×D₄×C₁₉	—	2	4	no	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	C₂³	1	8	yes	—
96	C₄×D₄×C₁₉	C₂³	1	4	yes	—
97	C₁₉×#117	—	2	2	no	—
98	C₁₉×#117	—	2	4	no	—
99	C₁₉×#117	—	2	8	no	—
100	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
101	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
103	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₁₉×#107	C₂³	1	4	yes	—
106	C₁₉×#107	C₂³	1	4	yes	—
107	C₁₉×#106	C₂³	1	4	yes	—
108	C₁₉×#106	C₂³	1	4	yes	—
109	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
110	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
111	C₁₉×#103	C₂³	1	4	yes	—
112	C₁₉×#103	C₂³	1	8	yes	—
113	C₁₉×#103	C₂³	1	4	yes	—
114	C₁₉×#102	C₂³	1	4	yes	—
115	C₁₉×#102	C₂³	1	8	yes	—
116	C₁₉×#102	C₂³	1	4	yes	—
117	C₄×C₈×C₁₉	C₂³	1	4	yes	—
118	C₄×C₈×C₁₉	C₂³	1	2	yes	—
119	C₄×C₈×C₁₉	C₂³	1	2	yes	—
120	C₄×C₈×C₁₉	C₂³	1	4	yes	—
121	#41×C₁₉	—	4	8	no	—
122	C₂×Q₈×C₁₉	—	2	4	no	—
123	C₂×Q₈×C₁₉	—	2	2	no	—
124	C₂×Q₈×C₁₉	—	2	2	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	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
138	Q₁₆×C₁₉	—	4	4	no	—
139	SD₁₆×C₁₉	—	2	8	no	—
140	SD₁₆×C₁₉	—	4	4	no	—
141	D₈×C₁₉	—	4	4	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₂×C₈×C₁₉	—	4	2	no	—
144	C₂×C₈×C₁₉	—	4	1	no	—
145	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
146	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
147	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
148	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	8	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	4	no	—
153	C₄⋊C₄×C₁₉	—	2	8	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	4	no	—
157	C₄⋊C₄×C₁₉	—	2	8	no	—
158	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
159	C₄⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
160	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
161	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
162	C₂²⋊C₄×C₁₉	—	2	4	no	—
163	C₂²⋊C₄×C₁₉	—	2	4	no	—
164	C₂²⋊C₄×C₁₉	—	2	8	no	—
165	C₂²⋊C₄×C₁₉	—	2	8	no	—
166	C₂²⋊C₄×C₁₉	—	2	4	no	—
167	C₂²⋊C₄×C₁₉	—	2	8	no	—
168	C₄²×C₁₉	—	2	8	no	—
169	C₄²×C₁₉	—	2	4	no	—
170	C₄²×C₁₉	C₂×D₄	1	4	yes	—
171	C₄²×C₁₉	C₂×D₄	1	2	yes	—
172	C₄²×C₁₉	C₂⁴	1	4	yes	—
173	C₄²×C₁₉	C₂⁴	1	2	yes	—
174	#62358	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂³×C₁₉	—	2	4	no	—
176	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
177	Q₈×C₁₉	—	2	8	no	—
178	Q₈×C₁₉	—	2	4	no	—
179	Q₈×C₁₉	—	2	4	no	—
180	Q₈×C₁₉	—	4	4	no	—
181	Q₈×C₁₉	—	8	2	no	—
182	D₄×C₁₉	—	2	4	no	—
183	D₄×C₁₉	—	2	4	no	—
184	D₄×C₁₉	—	4	8	no	—
185	D₄×C₁₉	—	4	4	no	—
186	D₄×C₁₉	—	8	2	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	8	no	—
196	C₂×C₄×C₁₉	—	8	8	no	—
197	C₂×C₄×C₁₉	#135	1	4	yes	—
198	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
199	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
204	C₈×C₁₉	—	2	1	no	—
205	C₈×C₁₉	—	2	4	no	—
206	C₈×C₁₉	—	2	2	no	—
207	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
208	#3507	C₂×C₁₉	1	2	yes	complemented
209	#3394	C₂×C₁₉	1	4	yes	complemented
210	#3381	C₂×C₁₉	1	4	yes	complemented
211	#3364	C₂×C₁₉	1	4	yes	complemented
212	#3361	C₂×C₁₉	1	4	yes	complemented
213	#3250	C₂×C₁₉	1	4	yes	complemented
214	#3249	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#3245	C₂×C₁₉	1	1	yes	characteristic
216	#3168	C₂×C₁₉	1	4	yes	complemented
217	#3167	C₂×C₁₉	1	2	yes	complemented
218	C₂×C₈×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	2	1	no	—
221	C₂²×C₁₉	—	4	4	no	—
222	C₂²×C₁₉	—	4	4	no	—
223	C₂²×C₁₉	—	4	4	no	—
224	C₂²×C₁₉	C₂×#135	1	2	yes	—
225	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
226	C₄×C₁₉	—	2	4	no	—
227	C₄×C₁₉	—	2	2	no	—
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	2	4	no	—
230	C₄×C₁₉	—	4	4	no	—
231	C₄×C₁₉	—	4	4	no	—
232	C₄×C₁₉	—	4	4	no	—
233	C₄×C₁₉	C₂×#135	1	4	yes	—
234	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
235	C₄×C₁₉	#585	1	1	yes	characteristic
236	#559	C₂²×C₁₉	1	4	yes	—
237	#557	C₂²×C₁₉	1	4	yes	—
238	#556	—	2	4	no	—
239	#556	C₂²×C₁₉	1	4	yes	—
240	#554	C₂²×C₁₉	1	4	yes	—
241	#552	—	2	4	no	—
242	#539	—	2	4	no	—
243	#536	—	2	2	no	—
244	#533	C₂²×C₁₉	1	2	yes	—
245	#532	C₂²×C₁₉	1	2	yes	—
246	#529	C₂²×C₁₉	1	8	yes	—
247	#520	—	2	2	no	—
248	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
249	#499	C₂²×C₁₉	1	4	yes	—
250	#498	C₂²×C₁₉	1	2	yes	—
251	#495	C₂²×C₁₉	1	4	yes	—
252	#492	C₂²×C₁₉	1	2	yes	—
253	#488	C₂²×C₁₉	1	8	yes	—
254	#487	C₂²×C₁₉	1	2	yes	—
255	#486	C₂²×C₁₉	1	2	yes	—
256	#479	C₂²×C₁₉	1	8	yes	—
257	#478	C₂²×C₁₉	1	8	yes	—
258	#477	C₂²×C₁₉	1	4	yes	—
259	#474	C₂²×C₁₉	1	4	yes	—
260	#467	C₂²×C₁₉	1	4	yes	—
261	#466	C₂²×C₁₉	1	4	yes	—
262	#465	C₂²×C₁₉	1	4	yes	—
263	#465	C₂²×C₁₉	1	4	yes	—
264	#464	C₂²×C₁₉	1	8	yes	—
265	#463	C₂²×C₁₉	1	8	yes	—
266	#462	C₂²×C₁₉	1	4	yes	—
267	#459	C₂²×C₁₉	1	4	yes	—
268	C₈×Q₈	C₂²×C₁₉	1	4	yes	—
269	C₈×Q₈	C₂²×C₁₉	1	4	yes	—
270	C₄×Q₁₆	C₂²×C₁₉	1	4	yes	—
271	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
272	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
273	C₄×SD₁₆	C₂²×C₁₉	1	8	yes	—
274	C₄×D₈	C₂²×C₁₉	1	4	yes	—
275	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
277	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
278	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
279	C₂×C₁₉	—	2	2	no	—
280	C₂×C₁₉	—	8	4	no	—
281	C₂×C₁₉	#3497	1	1	yes	characteristic
282	C₂×C₁₉	C₂²×#135	1	1	yes	characteristic
283	C₂×C₁₉	#3584	1	1	yes	characteristic
284	C₂×#41	—	2	2	no	—
285	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
286	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
287	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
288	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
289	C₂×D₈	C₂³×C₁₉	1	4	yes	—
290	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
293	C₄⋊Q₈	—	2	4	no	—
294	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
295	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
296	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
297	#127	C₂³×C₁₉	1	2	yes	—
298	#126	—	2	8	no	—
299	#126	—	2	8	no	—
300	#125	—	2	8	no	—
301	#125	—	2	2	no	—
302	#125	C₂³×C₁₉	1	8	yes	—
303	#124	—	2	4	no	—
304	#124	—	2	2	no	—
305	#124	C₂³×C₁₉	1	8	yes	—
306	#123	—	2	8	no	—
307	#123	—	2	8	no	—
308	C₂²⋊Q₈	—	2	4	no	—
309	C₂²⋊Q₈	—	2	4	no	—
310	C₂²⋊Q₈	—	2	2	no	—
311	C₂²⋊Q₈	—	2	8	no	—
312	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
313	#121	—	2	2	no	—
314	#121	C₂³×C₁₉	1	4	yes	—
315	C₄×Q₈	—	2	4	no	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	D₄×C₁₉	1	4	yes	—
318	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
319	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
320	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
321	C₄×D₄	—	2	8	no	—
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	C₂³×C₁₉	1	8	yes	—
325	C₄×D₄	C₂³×C₁₉	1	4	yes	—
326	#117	—	2	2	no	—
327	#117	—	2	4	no	—
328	#117	—	2	8	no	—
329	C₂×C₄⋊C₄	—	2	4	no	—
330	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
331	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
332	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
333	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
334	#107	C₂³×C₁₉	1	4	yes	—
335	#107	C₂³×C₁₉	1	4	yes	—
336	#106	C₂³×C₁₉	1	4	yes	—
337	#106	C₂³×C₁₉	1	4	yes	—
338	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
339	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
340	#103	C₂³×C₁₉	1	4	yes	—
341	#103	C₂³×C₁₉	1	8	yes	—
342	#103	C₂³×C₁₉	1	4	yes	—
343	#102	C₂³×C₁₉	1	4	yes	—
344	#102	C₂³×C₁₉	1	8	yes	—
345	#102	C₂³×C₁₉	1	4	yes	—
346	C₄×C₈	C₂³×C₁₉	1	4	yes	—
347	C₄×C₈	C₂³×C₁₉	1	2	yes	—
348	C₄×C₈	C₂³×C₁₉	1	2	yes	—
349	C₄×C₈	C₂³×C₁₉	1	4	yes	—
350	C₁₉	#62358	1	1	yes	characteristic, direct product factor, Sylow
351	#41	—	4	8	no	—
352	C₂×Q₈	—	2	4	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
356	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
368	Q₁₆	—	4	4	no	—
369	SD₁₆	—	2	8	no	—
370	SD₁₆	—	4	4	no	—
371	D₈	—	4	4	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	4	2	no	—
374	C₂×C₈	—	4	1	no	—
375	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
376	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
377	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
378	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
389	C₄⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
390	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
391	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	2	8	no	—
395	C₂²⋊C₄	—	2	8	no	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	2	8	no	—
398	C₄²	—	2	8	no	—
399	C₄²	—	2	4	no	—
400	C₄²	C₂×D₄×C₁₉	1	4	yes	—
401	C₄²	C₂×D₄×C₁₉	1	2	yes	—
402	C₄²	C₂⁴×C₁₉	1	4	yes	—
403	C₄²	C₂⁴×C₁₉	1	2	yes	—
404	C₂³	—	2	4	no	—
405	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
406	Q₈	—	2	8	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	2	4	no	—
409	Q₈	—	4	4	no	—
410	Q₈	—	8	2	no	—
411	D₄	—	2	4	no	—
412	D₄	—	2	4	no	—
413	D₄	—	4	8	no	—
414	D₄	—	4	4	no	—
415	D₄	—	8	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	—	8	8	no	—
426	C₂×C₄	C₁₉×#135	1	4	yes	—
427	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
428	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
430	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
432	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
433	C₈	—	2	1	no	—
434	C₈	—	2	4	no	—
435	C₈	—	2	2	no	—
436	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	4	no	—
442	C₂²	C₂×C₁₉×#135	1	2	yes	—
443	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
444	C₄	—	2	1	no	—
445	C₄	—	2	4	no	—
446	C₄	—	2	4	no	—
447	C₄	—	2	2	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	4	no	—
451	C₄	C₂×C₁₉×#135	1	4	yes	—
452	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
453	C₄	C₁₉×#585	1	1	yes	characteristic
454	C₂	—	2	2	no	—
455	C₂	—	8	4	no	—
456	C₂	C₁₉×#3497	1	1	yes	characteristic
457	C₂	C₂²×C₁₉×#135	1	1	yes	characteristic
458	C₂	C₁₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3245	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3507	C₂	semidirect
2. C₁₉×#3394	C₂	semidirect
3. C₁₉×#3381	C₂	semidirect
4. C₁₉×#3364	C₂	semidirect
5. C₁₉×#3361	C₂	semidirect
6. C₁₉×#3250	C₂	semidirect
7. C₁₉×#3249	C₂	semidirect
9. C₁₉×#3168	C₂	semidirect
10. C₁₉×#3167	C₂	semidirect
11. C₂×C₈×Q₈×C₁₉	C₂	semidirect
174. #62358	C₁₉	direct (N × H)
208. #3507	C₂×C₁₉	semidirect
209. #3394	C₂×C₁₉	semidirect
210. #3381	C₂×C₁₉	semidirect
211. #3364	C₂×C₁₉	semidirect
212. #3361	C₂×C₁₉	semidirect
213. #3250	C₂×C₁₉	semidirect
214. #3249	C₂×C₁₉	semidirect
216. #3168	C₂×C₁₉	semidirect
217. #3167	C₂×C₁₉	semidirect
218. C₂×C₈×Q₈	C₂×C₁₉	semidirect
350. C₁₉	#62358	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×#3507	2
C₁₉×#3394	2
C₁₉×#3381	2
C₁₉×#3364	2
C₁₉×#3361	2
C₁₉×#3250	2
C₁₉×#3249	2
C₁₉×#3245	2
C₁₉×#3168	2
C₁₉×#3167	2
C₂×C₈×Q₈×C₁₉	2
#62358	19

Subgroups — C19×#62358 #18068317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62358 #18068317