Subgroups — C₁₉×#17974 #18023933

Order 4864.

592 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3168	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2993	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1594	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1593	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1590	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1580	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1579	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×SD₁₆×C₁₉	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1566	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1495	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#529	C₂²	1	2	yes	—
13	C₁₉×#499	C₄	1	1	yes	characteristic
14	C₁₉×#495	C₄	1	1	yes	characteristic
15	C₁₉×#488	C₄	1	2	yes	—
16	C₁₉×#467	C₄	1	1	yes	characteristic
17	C₁₉×#466	C₄	1	1	yes	characteristic
18	C₁₉×#465	C₄	1	2	yes	—
19	C₁₉×#446	C₂²	1	2	yes	—
20	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
21	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
23	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#436	—	2	2	no	—
25	C₁₉×#436	C₂²	1	2	yes	—
26	C₁₉×#435	—	2	2	no	—
27	C₈×D₄×C₁₉	C₂²	1	2	yes	—
28	C₁₉×#433	—	2	2	no	—
29	C₁₉×#431	C₂²	1	1	yes	characteristic
30	C₁₉×#431	C₂²	1	1	yes	characteristic
31	C₁₉×#424	—	2	2	no	—
32	C₁₉×#423	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#334	C₂²	1	2	yes	—
35	C₁₉×#334	C₂²	1	1	yes	characteristic
36	C₁₉×#334	C₂²	1	1	yes	characteristic
37	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
40	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
41	C₁₉×#322	C₂²	1	1	yes	characteristic
42	C₁₉×#322	C₂²	1	1	yes	characteristic
43	C₈²×C₁₉	C₂²	1	1	yes	characteristic
44	C₈²×C₁₉	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×SD₁₆×C₁₉	C₂×C₄	1	2	yes	—
47	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×M₁₆×C₁₉	—	2	2	no	—
49	C₂×M₁₆×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
53	C₁₉×#126	—	2	2	no	—
54	C₁₉×#125	C₂×C₄	1	2	yes	—
55	C₁₉×#124	C₂×C₄	1	2	yes	—
56	C₁₉×#123	—	2	2	no	—
57	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
58	C₁₉×#121	C₂×C₄	1	2	yes	—
59	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
60	C₄×D₄×C₁₉	—	2	2	no	—
61	C₄×D₄×C₁₉	C₂³	1	2	yes	—
62	C₁₉×#117	—	2	2	no	—
63	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
64	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
65	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
66	C₁₉×#106	C₂×C₄	1	2	yes	—
67	C₁₉×C₄⋊C₈	—	2	2	no	—
68	C₁₉×C₄⋊C₈	—	2	2	no	—
69	C₁₉×C₄⋊C₈	—	2	2	no	—
70	C₁₉×C₄⋊C₈	—	2	1	no	—
71	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
72	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
74	C₁₉×#103	C₂×C₄	1	2	yes	—
75	C₁₉×#103	C₂×C₄	1	2	yes	—
76	C₁₉×#102	C₂×C₄	1	2	yes	—
77	C₁₉×#102	C₂×C₄	1	2	yes	—
78	C₁₉×C₂²⋊C₈	—	2	1	no	—
79	C₁₉×C₂²⋊C₈	—	2	2	no	—
80	C₁₉×C₂²⋊C₈	—	2	2	no	—
81	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
82	C₁₉×#97	—	2	2	no	—
83	C₄×C₈×C₁₉	—	2	2	no	—
84	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
85	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
86	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
93	C₂×D₄×C₁₉	—	2	2	no	—
94	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
99	Q₁₆×C₁₉	—	2	2	no	—
100	SD₁₆×C₁₉	—	2	4	no	—
101	D₈×C₁₉	—	2	2	no	—
102	M₁₆×C₁₉	—	8	2	no	—
103	M₁₆×C₁₉	—	8	2	no	—
104	C₂×C₈×C₁₉	—	2	2	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	1	no	—
109	C₂×C₈×C₁₉	—	2	1	no	—
110	C₂×C₈×C₁₉	—	8	2	no	—
111	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
122	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
123	C₂²⋊C₄×C₁₉	—	2	2	no	—
124	C₂²⋊C₄×C₁₉	—	2	2	no	—
125	C₂²⋊C₄×C₁₉	—	2	2	no	—
126	C₂²⋊C₄×C₁₉	—	2	2	no	—
127	C₂²⋊C₄×C₁₉	—	2	2	no	—
128	C₄²×C₁₉	—	2	2	no	—
129	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₉	#41	1	1	yes	characteristic
132	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
133	#17974	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
136	Q₈×C₁₉	—	2	2	no	—
137	Q₈×C₁₉	—	2	2	no	—
138	D₄×C₁₉	—	2	2	no	—
139	D₄×C₁₉	—	2	2	no	—
140	D₄×C₁₉	—	8	2	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
156	C₈×C₁₉	—	2	1	no	—
157	C₈×C₁₉	—	2	1	no	—
158	C₈×C₁₉	—	2	2	no	—
159	C₈×C₁₉	—	2	2	no	—
160	C₈×C₁₉	—	4	1	no	—
161	C₈×C₁₉	—	4	1	no	—
162	C₈×C₁₉	—	4	2	no	—
163	C₈×C₁₉	—	4	2	no	—
164	C₈×C₁₉	#131	1	2	yes	—
165	C₈×C₁₉	#131	1	2	yes	—
166	#3168	C₂×C₁₉	1	1	yes	characteristic
167	#2993	C₂×C₁₉	1	2	yes	complemented
168	#1594	C₂×C₁₉	1	1	yes	characteristic, complemented
169	#1593	C₂×C₁₉	1	1	yes	characteristic, complemented
170	#1590	C₂×C₁₉	1	2	yes	complemented
171	#1580	C₂×C₁₉	1	1	yes	characteristic, complemented
172	#1579	C₂×C₁₉	1	1	yes	characteristic, complemented
173	C₈×SD₁₆	C₂×C₁₉	1	2	yes	complemented
174	#1566	C₂×C₁₉	1	1	yes	characteristic, complemented
175	#1495	C₂×C₁₉	1	2	yes	complemented
176	#1450	C₂×C₁₉	1	1	yes	characteristic, complemented
177	C₂²×C₁₉	—	2	1	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	4	2	no	—
181	C₂²×C₁₉	—	4	2	no	—
182	C₂²×C₁₉	—	4	2	no	—
183	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
184	C₄×C₁₉	—	2	1	no	—
185	C₄×C₁₉	—	2	1	no	—
186	C₄×C₁₉	—	2	1	no	—
187	C₄×C₁₉	—	2	1	no	—
188	C₄×C₁₉	—	4	2	no	—
189	C₄×C₁₉	—	4	2	no	—
190	C₄×C₁₉	—	4	2	no	—
191	C₄×C₁₉	C₂×#131	1	1	yes	characteristic
192	C₄×C₁₉	C₂×#131	1	1	yes	characteristic
193	C₄×C₁₉	#577	1	2	yes	—
194	#529	C₂²×C₁₉	1	2	yes	—
195	#499	C₄×C₁₉	1	1	yes	characteristic
196	#495	C₄×C₁₉	1	1	yes	characteristic
197	#488	C₄×C₁₉	1	2	yes	—
198	#467	C₄×C₁₉	1	1	yes	characteristic
199	#466	C₄×C₁₉	1	1	yes	characteristic
200	#465	C₄×C₁₉	1	2	yes	—
201	#446	C₂²×C₁₉	1	2	yes	—
202	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
203	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
204	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
205	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
206	#436	—	2	2	no	—
207	#436	C₂²×C₁₉	1	2	yes	—
208	#435	—	2	2	no	—
209	C₈×D₄	C₂²×C₁₉	1	2	yes	—
210	#433	—	2	2	no	—
211	#431	C₂²×C₁₉	1	1	yes	characteristic
212	#431	C₂²×C₁₉	1	1	yes	characteristic
213	#424	—	2	2	no	—
214	#423	C₂²×C₁₉	1	2	yes	—
215	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
216	#334	C₂²×C₁₉	1	2	yes	—
217	#334	C₂²×C₁₉	1	1	yes	characteristic
218	#334	C₂²×C₁₉	1	1	yes	characteristic
219	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
220	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
221	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
222	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
223	#322	C₂²×C₁₉	1	1	yes	characteristic
224	#322	C₂²×C₁₉	1	1	yes	characteristic
225	C₈²	C₂²×C₁₉	1	1	yes	characteristic
226	C₈²	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×C₁₉	—	4	1	no	—
228	C₂×C₁₉	—	8	2	no	—
229	C₂×C₁₉	#2931	1	1	yes	characteristic
230	C₂×C₁₉	#2952	1	1	yes	characteristic
231	C₂×C₁₉	#2957	1	1	yes	characteristic
232	C₂×Q₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
233	C₂×SD₁₆	C₂×C₄×C₁₉	1	2	yes	—
234	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
239	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
240	#126	—	2	2	no	—
241	#125	C₂×C₄×C₁₉	1	2	yes	—
242	#124	C₂×C₄×C₁₉	1	2	yes	—
243	#123	—	2	2	no	—
244	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
245	#121	C₂×C₄×C₁₉	1	2	yes	—
246	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	C₂³×C₁₉	1	2	yes	—
249	#117	—	2	2	no	—
250	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
251	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
252	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
253	#106	C₂×C₄×C₁₉	1	2	yes	—
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
259	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
260	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
261	#103	C₂×C₄×C₁₉	1	2	yes	—
262	#103	C₂×C₄×C₁₉	1	2	yes	—
263	#102	C₂×C₄×C₁₉	1	2	yes	—
264	#102	C₂×C₄×C₁₉	1	2	yes	—
265	C₂²⋊C₈	—	2	1	no	—
266	C₂²⋊C₈	—	2	2	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
269	#97	—	2	2	no	—
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
272	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
275	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
276	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
279	C₁₉	#17974	1	1	yes	characteristic, direct product factor, Sylow
280	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
286	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
287	Q₁₆	—	2	2	no	—
288	SD₁₆	—	2	4	no	—
289	D₈	—	2	2	no	—
290	M₁₆	—	8	2	no	—
291	M₁₆	—	8	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	8	2	no	—
299	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
300	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
301	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
302	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
304	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
310	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
318	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
319	C₄²	#41×C₁₉	1	1	yes	characteristic
320	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
321	C₂³	—	2	2	no	—
322	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	Q₈	—	2	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	2	2	no	—
327	D₄	—	8	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
338	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
339	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
340	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
341	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
342	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
343	C₈	—	2	1	no	—
344	C₈	—	2	1	no	—
345	C₈	—	2	2	no	—
346	C₈	—	2	2	no	—
347	C₈	—	4	1	no	—
348	C₈	—	4	1	no	—
349	C₈	—	4	2	no	—
350	C₈	—	4	2	no	—
351	C₈	C₁₉×#131	1	2	yes	—
352	C₈	C₁₉×#131	1	2	yes	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	C₂×C₁₉×#131	1	1	yes	characteristic
368	C₄	C₂×C₁₉×#131	1	1	yes	characteristic
369	C₄	C₁₉×#577	1	2	yes	—
370	C₂	—	4	1	no	—
371	C₂	—	8	2	no	—
372	C₂	C₁₉×#2931	1	1	yes	characteristic
373	C₂	C₁₉×#2952	1	1	yes	characteristic
374	C₂	C₁₉×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×C₄×D₄
prime radical	C₁₉×#466	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2993	C₂	semidirect
3. C₁₉×#1594	C₂	semidirect
4. C₁₉×#1593	C₂	semidirect
5. C₁₉×#1590	C₂	semidirect
6. C₁₉×#1580	C₂	semidirect
7. C₁₉×#1579	C₂	semidirect
8. C₈×SD₁₆×C₁₉	C₂	semidirect
9. C₁₉×#1566	C₂	semidirect
10. C₁₉×#1495	C₂	semidirect
11. C₁₉×#1450	C₂	semidirect
133. #17974	C₁₉	direct (N × H)
167. #2993	C₂×C₁₉	semidirect
168. #1594	C₂×C₁₉	semidirect
169. #1593	C₂×C₁₉	semidirect
170. #1590	C₂×C₁₉	semidirect
171. #1580	C₂×C₁₉	semidirect
172. #1579	C₂×C₁₉	semidirect
173. C₈×SD₁₆	C₂×C₁₉	semidirect
174. #1566	C₂×C₁₉	semidirect
175. #1495	C₂×C₁₉	semidirect
176. #1450	C₂×C₁₉	semidirect
279. C₁₉	#17974	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×#3168	2
C₁₉×#2993	2
C₁₉×#1594	2
C₁₉×#1593	2
C₁₉×#1590	2
C₁₉×#1580	2
C₁₉×#1579	2
C₈×SD₁₆×C₁₉	2
C₁₉×#1566	2
C₁₉×#1495	2
C₁₉×#1450	2
#17974	19

Subgroups — C19×#17974 #18023933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17974 #18023933