Subgroups — C₁₉×#11154 #18017113

Order 4864.

870 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#410	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2879	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2311	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1736	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×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	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#410	—	2	4	no	—
12	C₂×C₁₉×#99	—	2	2	no	—
13	C₁₉×#408	—	2	4	no	—
14	C₁₉×#407	—	2	2	no	—
15	C₁₉×#391	C₄	1	2	yes	complemented
16	C₁₉×#390	C₄	1	2	yes	complemented
17	C₁₉×#386	—	2	2	no	—
18	C₁₉×#380	—	2	2	no	—
19	C₁₉×#340	—	2	4	no	—
20	C₁₉×H(3,ℤ/4)	—	2	4	no	—
21	C₂×#41×C₁₉	—	2	2	no	—
22	C₂×#41×C₁₉	—	2	2	no	—
23	C₂×#41×C₁₉	—	2	2	no	—
24	C₂×#41×C₁₉	—	2	2	no	—
25	C₂×#41×C₁₉	—	2	2	no	—
26	C₂×#41×C₁₉	—	2	2	no	—
27	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₉	D₄	1	2	yes	—
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	D₄	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	D₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
55	C₂×C₄²×C₁₉	—	2	2	no	—
56	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
57	C₁₉×#99	—	2	8	no	—
58	C₁₉×C₂²⋊C₈	—	2	8	no	—
59	C₁₉×#95	—	2	4	no	—
60	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
62	#41×C₁₉	—	4	2	no	—
63	#41×C₁₉	—	4	2	no	—
64	#41×C₁₉	—	4	2	no	—
65	#41×C₁₉	—	4	2	no	—
66	#41×C₁₉	—	4	2	no	—
67	#41×C₁₉	—	4	2	no	—
68	#41×C₁₉	—	4	2	no	—
69	#41×C₁₉	—	4	2	no	—
70	C₂×Q₈×C₁₉	—	2	1	no	—
71	C₂×Q₈×C₁₉	—	2	1	no	—
72	C₂×Q₈×C₁₉	—	2	2	no	—
73	C₂×Q₈×C₁₉	—	2	2	no	—
74	C₂×D₄×C₁₉	—	2	2	no	—
75	C₂×D₄×C₁₉	—	2	4	no	—
76	C₂×D₄×C₁₉	—	2	4	no	—
77	C₂×D₄×C₁₉	—	2	2	no	—
78	C₂×D₄×C₁₉	—	2	1	no	—
79	C₂×D₄×C₁₉	—	2	1	no	—
80	C₂×D₄×C₁₉	—	2	2	no	—
81	C₂×D₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	4	no	—
84	C₂²×C₄×C₁₉	—	2	4	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	4	2	no	—
89	C₂²×C₄×C₁₉	—	4	2	no	—
90	C₂²×C₄×C₁₉	—	8	2	no	—
91	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	2	yes	—
97	C₂²×C₄×C₁₉	#41	1	2	yes	—
98	C₂²×C₄×C₁₉	#41	1	2	yes	—
99	C₂²×C₄×C₁₉	#41	1	2	yes	—
100	M₁₆×C₁₉	—	4	2	no	—
101	M₁₆×C₁₉	—	4	2	no	—
102	M₁₆×C₁₉	—	4	2	no	—
103	M₁₆×C₁₉	—	4	2	no	—
104	C₂×C₈×C₁₉	—	2	4	no	—
105	C₂×C₈×C₁₉	—	2	4	no	—
106	C₂×C₈×C₁₉	—	2	4	no	—
107	C₄⋊C₄×C₁₉	—	2	4	no	—
108	C₄⋊C₄×C₁₉	—	2	4	no	—
109	C₄⋊C₄×C₁₉	—	4	1	no	—
110	C₄⋊C₄×C₁₉	—	4	2	no	—
111	C₄⋊C₄×C₁₉	—	4	2	no	—
112	C₄⋊C₄×C₁₉	—	4	1	no	—
113	C₂²⋊C₄×C₁₉	—	2	4	no	—
114	C₂²⋊C₄×C₁₉	—	4	1	no	—
115	C₂²⋊C₄×C₁₉	—	4	1	no	—
116	C₂²⋊C₄×C₁₉	—	4	2	no	—
117	C₂²⋊C₄×C₁₉	—	8	4	no	—
118	C₄²×C₁₉	—	2	4	no	—
119	C₄²×C₁₉	—	2	4	no	—
120	C₄²×C₁₉	—	4	2	no	—
121	#11154	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂³×C₁₉	—	2	2	no	—
123	C₂³×C₁₉	—	2	2	no	—
124	C₂³×C₁₉	—	2	2	no	—
125	C₂³×C₁₉	—	4	1	no	—
126	C₂³×C₁₉	—	4	1	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₁₉	#120	1	1	yes	characteristic
131	C₂³×C₁₉	#121	1	2	yes	—
132	C₂³×C₁₉	#123	1	2	yes	—
133	C₂³×C₁₉	#123	1	1	yes	characteristic
134	Q₈×C₁₉	—	4	2	no	—
135	Q₈×C₁₉	—	4	2	no	—
136	D₄×C₁₉	—	4	4	no	—
137	D₄×C₁₉	—	4	4	no	—
138	D₄×C₁₉	—	4	2	no	—
139	D₄×C₁₉	—	4	2	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	4	4	no	—
144	C₂×C₄×C₁₉	—	4	4	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	4	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	4	no	—
151	C₂×C₄×C₁₉	—	8	2	no	—
152	C₂×C₄×C₁₉	—	8	2	no	—
153	C₂×C₄×C₁₉	—	8	4	no	—
154	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#121	1	2	yes	—
160	C₂×C₄×C₁₉	#121	1	2	yes	—
161	C₂×C₄×C₁₉	#121	1	2	yes	—
162	C₂×C₄×C₁₉	#123	1	2	yes	—
163	C₂×C₄×C₁₉	#123	1	2	yes	—
164	C₂×C₄×C₁₉	#123	1	2	yes	—
165	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#124	1	2	yes	—
167	C₂×C₄×C₁₉	#124	1	2	yes	—
168	C₂×C₄×C₁₉	#126	1	2	yes	—
169	C₂×C₄×C₁₉	#126	1	2	yes	—
170	C₈×C₁₉	—	4	4	no	—
171	C₂×#410	C₂×C₁₉	1	1	yes	characteristic
172	#2879	C₂×C₁₉	1	1	yes	characteristic
173	#2311	C₂×C₁₉	1	1	yes	characteristic
174	#1736	C₂×C₁₉	1	2	yes	complemented
175	C₂×H(3,ℤ/4)	C₂×C₁₉	1	2	yes	complemented
176	C₂²×C₁₉	—	2	1	no	—
177	C₂²×C₁₉	—	2	2	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	2	no	—
180	C₂²×C₁₉	—	4	1	no	—
181	C₂²×C₁₉	—	4	1	no	—
182	C₂²×C₁₉	—	4	2	no	—
183	C₂²×C₁₉	—	4	4	no	—
184	C₂²×C₁₉	—	4	2	no	—
185	C₂²×C₁₉	—	4	2	no	—
186	C₂²×C₁₉	—	4	2	no	—
187	C₂²×C₁₉	—	8	2	no	—
188	C₂²×C₁₉	#381	1	1	yes	characteristic
189	C₂²×C₁₉	#386	1	1	yes	characteristic
190	C₂²×C₁₉	#386	1	1	yes	characteristic
191	C₂²×C₁₉	#394	1	2	yes	—
192	C₂²×C₁₉	#397	1	2	yes	—
193	C₄×C₁₉	—	4	2	no	—
194	C₄×C₁₉	—	8	2	no	—
195	C₄×C₁₉	—	8	4	no	—
196	C₄×C₁₉	—	8	2	no	—
197	C₄×C₁₉	#388	1	2	yes	—
198	C₄×C₁₉	#388	1	2	yes	—
199	C₄×C₁₉	#394	1	2	yes	—
200	C₄×C₁₉	#397	1	2	yes	—
201	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
202	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
203	C₂×#117	C₂²×C₁₉	1	2	yes	—
204	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
205	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
206	#410	—	2	4	no	—
207	C₂×#99	—	2	2	no	—
208	#408	—	2	4	no	—
209	#407	—	2	2	no	—
210	#391	C₄×C₁₉	1	2	yes	complemented
211	#390	C₄×C₁₉	1	2	yes	complemented
212	#386	—	2	2	no	—
213	#380	—	2	2	no	—
214	#340	—	2	4	no	—
215	H(3,ℤ/4)	—	2	4	no	—
216	C₂×C₁₉	—	2	1	no	—
217	C₂×C₁₉	—	2	2	no	—
218	C₂×C₁₉	—	2	1	no	—
219	C₂×C₁₉	—	2	2	no	—
220	C₂×C₁₉	—	8	2	no	—
221	C₂×C₁₉	#1440	1	1	yes	characteristic
222	C₂×C₁₉	#1909	1	1	yes	characteristic
223	C₂×C₁₉	#1910	1	1	yes	characteristic
224	C₂×#41	—	2	2	no	—
225	C₂×#41	—	2	2	no	—
226	C₂×#41	—	2	2	no	—
227	C₂×#41	—	2	2	no	—
228	C₂×#41	—	2	2	no	—
229	C₂×#41	—	2	2	no	—
230	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
231	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
232	C₂²×D₄	D₄×C₁₉	1	2	yes	—
233	C₂³×C₄	—	2	1	no	—
234	C₂³×C₄	D₄×C₁₉	1	2	yes	—
235	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	2	2	no	—
241	C₂×M₁₆	—	2	2	no	—
242	C₂²×C₈	D₄×C₁₉	1	4	yes	—
243	#117	—	2	2	no	—
244	#117	—	2	2	no	—
245	#117	—	2	2	no	—
246	#117	—	2	2	no	—
247	#117	—	2	2	no	—
248	#117	D₄×C₁₉	1	4	yes	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	1	no	—
257	C₂×C₂²⋊C₄	—	2	4	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
260	#99	—	2	8	no	—
261	C₂²⋊C₈	—	2	8	no	—
262	#95	—	2	4	no	—
263	C₁₉	#11154	1	1	yes	characteristic, direct product factor, Sylow
264	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
265	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
266	#41	—	4	2	no	—
267	#41	—	4	2	no	—
268	#41	—	4	2	no	—
269	#41	—	4	2	no	—
270	#41	—	4	2	no	—
271	#41	—	4	2	no	—
272	#41	—	4	2	no	—
273	#41	—	4	2	no	—
274	C₂×Q₈	—	2	1	no	—
275	C₂×Q₈	—	2	1	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	8	2	no	—
295	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
296	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
300	C₂²×C₄	#41×C₁₉	1	2	yes	—
301	C₂²×C₄	#41×C₁₉	1	2	yes	—
302	C₂²×C₄	#41×C₁₉	1	2	yes	—
303	C₂²×C₄	#41×C₁₉	1	2	yes	—
304	M₁₆	—	4	2	no	—
305	M₁₆	—	4	2	no	—
306	M₁₆	—	4	2	no	—
307	M₁₆	—	4	2	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₂²⋊C₄	—	2	4	no	—
318	C₂²⋊C₄	—	4	1	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	8	4	no	—
322	C₄²	—	2	4	no	—
323	C₄²	—	2	4	no	—
324	C₄²	—	4	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	4	1	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
333	C₂³	C₁₉×#120	1	1	yes	characteristic
334	C₂³	C₁₉×#121	1	2	yes	—
335	C₂³	C₁₉×#123	1	2	yes	—
336	C₂³	C₁₉×#123	1	1	yes	characteristic
337	Q₈	—	4	2	no	—
338	Q₈	—	4	2	no	—
339	D₄	—	4	4	no	—
340	D₄	—	4	4	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	8	4	no	—
355	C₂×C₄	—	8	2	no	—
356	C₂×C₄	—	8	2	no	—
357	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
358	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
359	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
360	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
361	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
362	C₂×C₄	C₁₉×#121	1	2	yes	—
363	C₂×C₄	C₁₉×#121	1	2	yes	—
364	C₂×C₄	C₁₉×#121	1	2	yes	—
365	C₂×C₄	C₁₉×#123	1	2	yes	—
366	C₂×C₄	C₁₉×#123	1	2	yes	—
367	C₂×C₄	C₁₉×#123	1	2	yes	—
368	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
369	C₂×C₄	C₁₉×#124	1	2	yes	—
370	C₂×C₄	C₁₉×#124	1	2	yes	—
371	C₂×C₄	C₁₉×#126	1	2	yes	—
372	C₂×C₄	C₁₉×#126	1	2	yes	—
373	C₈	—	4	4	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	C₁₉×#381	1	1	yes	characteristic
387	C₂²	C₁₉×#386	1	1	yes	characteristic
388	C₂²	C₁₉×#386	1	1	yes	characteristic
389	C₂²	C₁₉×#394	1	2	yes	—
390	C₂²	C₁₉×#397	1	2	yes	—
391	C₄	—	4	2	no	—
392	C₄	—	8	2	no	—
393	C₄	—	8	4	no	—
394	C₄	—	8	2	no	—
395	C₄	C₁₉×#388	1	2	yes	—
396	C₄	C₁₉×#388	1	2	yes	—
397	C₄	C₁₉×#394	1	2	yes	—
398	C₄	C₁₉×#397	1	2	yes	—
399	C₂	—	2	1	no	—
400	C₂	—	2	2	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	2	no	—
403	C₂	—	8	2	no	—
404	C₂	C₁₉×#1440	1	1	yes	characteristic
405	C₂	C₁₉×#1909	1	1	yes	characteristic
406	C₂	C₁₉×#1910	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂²×#41×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
4. C₁₉×#1736	C₂	semidirect
5. C₂×C₁₉×H(3,ℤ/4)	C₂	semidirect
15. C₁₉×#391	C₄	semidirect
16. C₁₉×#390	C₄	semidirect
121. #11154	C₁₉	direct (N × H)
174. #1736	C₂×C₁₉	semidirect
175. C₂×H(3,ℤ/4)	C₂×C₁₉	semidirect
210. #391	C₄×C₁₉	semidirect
211. #390	C₄×C₁₉	semidirect
263. C₁₉	#11154	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#410	2
C₁₉×#2879	2
C₁₉×#2311	2
C₁₉×#1736	2
C₂×C₁₉×H(3,ℤ/4)	2
#11154	19

Subgroups — C19×#11154 #18017113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11154 #18017113