Subgroups — C₁₉×#11073 #18017032

Order 4864.

1026 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2905	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#418	C₂	1	2	yes	maximal
3	C₁₉×#2309	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1740	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
6	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂×C₁₉×#117	C₂²	1	2	yes	—
9	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
11	C₁₉×#424	—	2	4	no	—
12	C₁₉×#423	—	2	2	no	—
13	C₁₉×#418	—	2	4	no	—
14	C₁₉×#418	—	2	4	no	—
15	C₂×C₁₉×#102	—	2	4	no	—
16	C₁₉×#390	—	2	2	no	—
17	C₁₉×#390	C₄	1	4	yes	complemented
18	C₁₉×#379	—	2	2	no	—
19	C₁₉×#342	—	2	2	no	—
20	C₁₉×H(3,ℤ/4)	—	2	4	no	—
21	C₂⁵×C₁₉	—	2	1	no	—
22	C₂²×D₄×C₁₉	—	2	2	no	—
23	C₂²×D₄×C₁₉	—	2	2	no	—
24	C₂²×D₄×C₁₉	—	2	1	no	—
25	C₂²×D₄×C₁₉	—	2	2	no	—
26	C₂²×D₄×C₁₉	—	2	2	no	—
27	C₂²×D₄×C₁₉	—	2	1	no	—
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₁₉	D₄	1	2	yes	—
31	C₂²×D₄×C₁₉	Q₈	1	2	yes	—
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂×M₁₆×C₁₉	—	2	2	no	—
34	C₂×M₁₆×C₁₉	—	2	2	no	—
35	C₂×M₁₆×C₁₉	—	2	2	no	—
36	C₂×M₁₆×C₁₉	—	2	2	no	—
37	C₂×M₁₆×C₁₉	—	2	2	no	—
38	C₂×M₁₆×C₁₉	—	2	2	no	—
39	C₂²×C₈×C₁₉	D₄	1	4	yes	—
40	C₁₉×#117	—	2	2	no	—
41	C₁₉×#117	—	2	2	no	—
42	C₁₉×#117	—	2	2	no	—
43	C₁₉×#117	—	2	2	no	—
44	C₁₉×#117	—	2	2	no	—
45	C₁₉×#117	—	2	2	no	—
46	C₁₉×#117	—	2	2	no	—
47	C₁₉×#117	D₄	1	4	yes	—
48	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
54	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
55	C₂×C₄²×C₁₉	—	2	2	no	—
56	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₁₉	D₄	1	2	yes	—
58	C₁₉×C₄⋊C₈	—	2	8	no	—
59	C₁₉×#102	—	2	16	no	—
60	C₂⁴×C₁₉	—	2	2	no	—
61	C₂⁴×C₁₉	—	2	2	no	—
62	C₂⁴×C₁₉	—	2	2	no	—
63	C₂⁴×C₁₉	—	4	2	no	—
64	C₂⁴×C₁₉	—	4	2	no	—
65	C₂⁴×C₁₉	—	8	4	no	—
66	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂×D₄×C₁₉	—	2	2	no	—
68	C₂×D₄×C₁₉	—	2	4	no	—
69	C₂×D₄×C₁₉	—	2	4	no	—
70	C₂×D₄×C₁₉	—	2	4	no	—
71	C₂×D₄×C₁₉	—	2	2	no	—
72	C₂×D₄×C₁₉	—	2	4	no	—
73	C₂×D₄×C₁₉	—	2	4	no	—
74	C₂×D₄×C₁₉	—	2	2	no	—
75	C₂×D₄×C₁₉	—	2	4	no	—
76	C₂×D₄×C₁₉	—	4	1	no	—
77	C₂×D₄×C₁₉	—	4	2	no	—
78	C₂×D₄×C₁₉	—	4	2	no	—
79	C₂×D₄×C₁₉	—	4	1	no	—
80	C₂×D₄×C₁₉	—	4	2	no	—
81	C₂×D₄×C₁₉	—	4	1	no	—
82	C₂×D₄×C₁₉	—	4	2	no	—
83	C₂×D₄×C₁₉	—	4	1	no	—
84	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	4	2	no	—
87	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	2	yes	—
97	C₂²×C₄×C₁₉	#41	1	2	yes	—
98	M₁₆×C₁₉	—	4	2	no	—
99	M₁₆×C₁₉	—	4	2	no	—
100	M₁₆×C₁₉	—	4	2	no	—
101	M₁₆×C₁₉	—	4	2	no	—
102	C₂×C₈×C₁₉	—	2	4	no	—
103	C₂×C₈×C₁₉	—	2	4	no	—
104	C₂×C₈×C₁₉	—	2	4	no	—
105	C₄⋊C₄×C₁₉	—	2	4	no	—
106	C₄⋊C₄×C₁₉	—	2	4	no	—
107	C₄⋊C₄×C₁₉	—	4	1	no	—
108	C₄⋊C₄×C₁₉	—	4	2	no	—
109	C₄⋊C₄×C₁₉	—	4	1	no	—
110	C₂²⋊C₄×C₁₉	—	2	4	no	—
111	C₂²⋊C₄×C₁₉	—	2	4	no	—
112	C₂²⋊C₄×C₁₉	—	4	2	no	—
113	C₂²⋊C₄×C₁₉	—	4	2	no	—
114	C₂²⋊C₄×C₁₉	—	8	8	no	—
115	C₄²×C₁₉	—	2	2	no	—
116	C₄²×C₁₉	—	2	2	no	—
117	C₄²×C₁₉	—	2	4	no	—
118	C₄²×C₁₉	—	2	4	no	—
119	C₄²×C₁₉	—	4	2	no	—
120	#11073	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂³×C₁₉	—	2	4	no	—
122	C₂³×C₁₉	—	4	2	no	—
123	C₂³×C₁₉	—	4	8	no	—
124	C₂³×C₁₉	—	4	2	no	—
125	C₂³×C₁₉	—	4	2	no	—
126	C₂³×C₁₉	—	4	4	no	—
127	C₂³×C₁₉	—	4	4	no	—
128	C₂³×C₁₉	—	8	8	no	—
129	C₂³×C₁₉	—	8	4	no	—
130	C₂³×C₁₉	—	8	4	no	—
131	C₂³×C₁₉	—	8	8	no	—
132	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₁₉	#121	1	2	yes	—
134	C₂³×C₁₉	#121	1	1	yes	characteristic
135	C₂³×C₁₉	#121	1	2	yes	—
136	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
137	D₄×C₁₉	—	2	8	no	—
138	D₄×C₁₉	—	4	4	no	—
139	D₄×C₁₉	—	4	2	no	—
140	D₄×C₁₉	—	4	2	no	—
141	D₄×C₁₉	—	4	2	no	—
142	D₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	2	4	no	—
144	C₂×C₄×C₁₉	—	4	4	no	—
145	C₂×C₄×C₁₉	—	4	4	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	4	no	—
148	C₂×C₄×C₁₉	—	8	4	no	—
149	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₁₉	#120	1	2	yes	—
154	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#121	1	2	yes	—
156	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
158	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
159	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#123	1	2	yes	—
161	C₂×C₄×C₁₉	#123	1	2	yes	—
162	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#124	1	2	yes	—
164	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#126	1	2	yes	—
166	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
167	C₈×C₁₉	—	4	4	no	—
168	#2905	C₂×C₁₉	1	1	yes	characteristic, complemented
169	C₂×#418	C₂×C₁₉	1	2	yes	—
170	#2309	C₂×C₁₉	1	1	yes	characteristic
171	#1740	C₂×C₁₉	1	1	yes	characteristic, complemented
172	C₂×H(3,ℤ/4)	C₂×C₁₉	1	2	yes	complemented
173	C₂²×C₁₉	—	2	2	no	—
174	C₂²×C₁₉	—	2	4	no	—
175	C₂²×C₁₉	—	4	2	no	—
176	C₂²×C₁₉	—	4	1	no	—
177	C₂²×C₁₉	—	4	1	no	—
178	C₂²×C₁₉	—	4	8	no	—
179	C₂²×C₁₉	—	4	4	no	—
180	C₂²×C₁₉	—	8	4	no	—
181	C₂²×C₁₉	—	8	8	no	—
182	C₂²×C₁₉	—	8	8	no	—
183	C₂²×C₁₉	—	8	4	no	—
184	C₂²×C₁₉	#380	1	1	yes	characteristic
185	C₂²×C₁₉	#386	1	1	yes	characteristic
186	C₂²×C₁₉	#390	1	1	yes	characteristic
187	C₂²×C₁₉	#394	1	2	yes	—
188	C₂²×C₁₉	#396	1	2	yes	—
189	C₄×C₁₉	—	4	4	no	—
190	C₄×C₁₉	—	8	2	no	—
191	C₄×C₁₉	—	8	4	no	—
192	C₄×C₁₉	#385	1	2	yes	—
193	C₄×C₁₉	#388	1	2	yes	—
194	C₄×C₁₉	#392	1	1	yes	characteristic
195	C₄×C₁₉	#393	1	1	yes	characteristic
196	C₄×C₁₉	#397	1	1	yes	characteristic
197	C₄×C₁₉	#399	1	1	yes	characteristic
198	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
199	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
200	C₂×#117	C₂²×C₁₉	1	2	yes	—
201	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
202	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
203	#424	—	2	4	no	—
204	#423	—	2	2	no	—
205	#418	—	2	4	no	—
206	#418	—	2	4	no	—
207	C₂×#102	—	2	4	no	—
208	#390	—	2	2	no	—
209	#390	C₄×C₁₉	1	4	yes	complemented
210	#379	—	2	2	no	—
211	#342	—	2	2	no	—
212	H(3,ℤ/4)	—	2	4	no	—
213	C₂×C₁₉	—	2	1	no	—
214	C₂×C₁₉	—	2	2	no	—
215	C₂×C₁₉	—	2	1	no	—
216	C₂×C₁₉	—	2	2	no	—
217	C₂×C₁₉	—	8	4	no	—
218	C₂×C₁₉	#1439	1	1	yes	characteristic
219	C₂×C₁₉	#1910	1	2	yes	—
220	C₂⁵	—	2	1	no	—
221	C₂²×D₄	—	2	2	no	—
222	C₂²×D₄	—	2	2	no	—
223	C₂²×D₄	—	2	1	no	—
224	C₂²×D₄	—	2	2	no	—
225	C₂²×D₄	—	2	2	no	—
226	C₂²×D₄	—	2	1	no	—
227	C₂²×D₄	—	2	1	no	—
228	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
229	C₂²×D₄	D₄×C₁₉	1	2	yes	—
230	C₂²×D₄	Q₈×C₁₉	1	2	yes	—
231	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂²×C₈	D₄×C₁₉	1	4	yes	—
239	#117	—	2	2	no	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	—	2	2	no	—
243	#117	—	2	2	no	—
244	#117	—	2	2	no	—
245	#117	—	2	2	no	—
246	#117	D₄×C₁₉	1	4	yes	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	2	8	no	—
253	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
256	C₂×C₄²	D₄×C₁₉	1	2	yes	—
257	C₄⋊C₈	—	2	8	no	—
258	#102	—	2	16	no	—
259	C₁₉	#11073	1	1	yes	characteristic, direct product factor, Sylow
260	C₂⁴	—	2	2	no	—
261	C₂⁴	—	2	2	no	—
262	C₂⁴	—	2	2	no	—
263	C₂⁴	—	4	2	no	—
264	C₂⁴	—	4	2	no	—
265	C₂⁴	—	8	4	no	—
266	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂×D₄	C₄⋊C₄×C₁₉	1	4	yes	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
288	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
293	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
294	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
295	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
296	C₂²×C₄	#41×C₁₉	1	2	yes	—
297	C₂²×C₄	#41×C₁₉	1	2	yes	—
298	M₁₆	—	4	2	no	—
299	M₁₆	—	4	2	no	—
300	M₁₆	—	4	2	no	—
301	M₁₆	—	4	2	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	4	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	8	8	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	2	4	no	—
319	C₄²	—	4	2	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	8	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	4	no	—
327	C₂³	—	8	8	no	—
328	C₂³	—	8	4	no	—
329	C₂³	—	8	4	no	—
330	C₂³	—	8	8	no	—
331	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
332	C₂³	C₁₉×#121	1	2	yes	—
333	C₂³	C₁₉×#121	1	1	yes	characteristic
334	C₂³	C₁₉×#121	1	2	yes	—
335	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
336	D₄	—	2	8	no	—
337	D₄	—	4	4	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	8	4	no	—
348	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
349	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
350	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
351	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
352	C₂×C₄	C₁₉×#120	1	2	yes	—
353	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
354	C₂×C₄	C₁₉×#121	1	2	yes	—
355	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
356	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
357	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
358	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
359	C₂×C₄	C₁₉×#123	1	2	yes	—
360	C₂×C₄	C₁₉×#123	1	2	yes	—
361	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
362	C₂×C₄	C₁₉×#124	1	2	yes	—
363	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
364	C₂×C₄	C₁₉×#126	1	2	yes	—
365	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
366	C₈	—	4	4	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	4	4	no	—
374	C₂²	—	8	4	no	—
375	C₂²	—	8	8	no	—
376	C₂²	—	8	8	no	—
377	C₂²	—	8	4	no	—
378	C₂²	C₁₉×#380	1	1	yes	characteristic
379	C₂²	C₁₉×#386	1	1	yes	characteristic
380	C₂²	C₁₉×#390	1	1	yes	characteristic
381	C₂²	C₁₉×#394	1	2	yes	—
382	C₂²	C₁₉×#396	1	2	yes	—
383	C₄	—	4	4	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	4	no	—
386	C₄	C₁₉×#385	1	2	yes	—
387	C₄	C₁₉×#388	1	2	yes	—
388	C₄	C₁₉×#392	1	1	yes	characteristic
389	C₄	C₁₉×#393	1	1	yes	characteristic
390	C₄	C₁₉×#397	1	1	yes	characteristic
391	C₄	C₁₉×#399	1	1	yes	characteristic
392	C₂	—	2	1	no	—
393	C₂	—	2	2	no	—
394	C₂	—	2	1	no	—
395	C₂	—	2	2	no	—
396	C₂	—	8	4	no	—
397	C₂	C₁₉×#1439	1	1	yes	characteristic
398	C₂	C₁₉×#1910	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2905	C₂	semidirect
4. C₁₉×#1740	C₂	semidirect
5. C₂×C₁₉×H(3,ℤ/4)	C₂	semidirect
17. C₁₉×#390	C₄	semidirect
120. #11073	C₁₉	direct (N × H)
168. #2905	C₂×C₁₉	semidirect
171. #1740	C₂×C₁₉	semidirect
172. C₂×H(3,ℤ/4)	C₂×C₁₉	semidirect
209. #390	C₄×C₁₉	semidirect
259. C₁₉	#11073	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×#2905	2
C₂×C₁₉×#418	2
C₁₉×#2309	2
C₁₉×#1740	2
C₂×C₁₉×H(3,ℤ/4)	2
#11073	19

Subgroups — C19×#11073 #18017032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11073 #18017032