Subgroups — C₁₉×#23731 #18029690

Order 4864.

1314 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#428	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₉×#418	C₂	1	2	yes	maximal
3	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2094	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2093	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2092	C₂	1	4	yes	maximal, complemented
8	C₁₉×#1728	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
11	C₂×C₁₉×#117	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#428	—	2	8	no	—
16	C₂×C₁₉×#107	C₂²	1	4	yes	complemented
17	C₂×C₁₉×#106	C₂²	1	4	yes	complemented
18	C₁₉×#418	—	2	8	no	—
19	C₂×C₁₉×#102	C₂²	1	4	yes	—
20	C₂×C₁₉×#102	C₂²	1	4	yes	—
21	C₁₉×#390	—	2	2	no	—
22	C₁₉×#390	C₂²	1	2	yes	—
23	C₁₉×#390	C₂²	1	2	yes	—
24	C₁₉×#384	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#384	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#382	C₂²	1	2	yes	complemented
27	C₁₉×#380	—	2	2	no	—
28	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₁₉×#336	C₂²	1	2	yes	complemented
30	C₁₉×#336	C₂²	1	2	yes	complemented
31	C₂⁵×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	4	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	4	no	—
35	C₂²×D₄×C₁₉	—	2	2	no	—
36	C₂²×D₄×C₁₉	Q₈	1	4	yes	—
37	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₂³×C₄×C₁₉	D₄	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂×M₁₆×C₁₉	—	2	4	no	—
42	C₂×M₁₆×C₁₉	—	2	4	no	—
43	C₂×M₁₆×C₁₉	D₄	1	8	yes	—
44	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
45	C₁₉×#117	—	2	4	no	—
46	C₁₉×#117	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
58	C₂×C₄²×C₁₉	—	2	4	no	—
59	C₂×C₄²×C₁₉	—	2	2	no	—
60	C₂×C₄²×C₁₉	D₄	1	2	yes	—
61	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
63	C₁₉×#107	—	2	8	no	—
64	C₁₉×#106	—	2	8	no	—
65	C₁₉×#102	—	2	8	no	—
66	C₁₉×#102	—	2	8	no	—
67	C₁₉×#95	—	2	4	no	—
68	C₂⁴×C₁₉	—	2	4	no	—
69	C₂⁴×C₁₉	—	2	2	no	—
70	C₂⁴×C₁₉	—	4	4	no	—
71	C₂⁴×C₁₉	—	4	4	no	—
72	C₂⁴×C₁₉	—	4	2	no	—
73	C₂⁴×C₁₉	—	4	2	no	—
74	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂×D₄×C₁₉	—	2	16	no	—
76	C₂×D₄×C₁₉	—	2	4	no	—
77	C₂×D₄×C₁₉	—	2	4	no	—
78	C₂×D₄×C₁₉	—	2	4	no	—
79	C₂×D₄×C₁₉	—	2	2	no	—
80	C₂×D₄×C₁₉	—	4	8	no	—
81	C₂×D₄×C₁₉	—	4	2	no	—
82	C₂×D₄×C₁₉	—	4	2	no	—
83	C₂×D₄×C₁₉	C₂×Q₈	1	4	yes	—
84	C₂²×C₄×C₁₉	—	2	4	no	—
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	4	2	no	—
90	C₂²×C₄×C₁₉	—	4	4	no	—
91	C₂²×C₄×C₁₉	—	4	2	no	—
92	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
97	C₂²×C₄×C₁₉	#41	1	4	yes	—
98	C₂²×C₄×C₁₉	#41	1	2	yes	—
99	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
100	M₁₆×C₁₉	—	2	16	no	—
101	C₂×C₈×C₁₉	—	2	4	no	—
102	C₂×C₈×C₁₉	—	2	4	no	—
103	C₂×C₈×C₁₉	C₂×D₄	1	8	yes	—
104	C₄⋊C₄×C₁₉	—	2	4	no	—
105	C₄⋊C₄×C₁₉	—	2	2	no	—
106	C₄⋊C₄×C₁₉	—	2	2	no	—
107	C₄⋊C₄×C₁₉	—	2	2	no	—
108	C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	—	4	4	no	—
110	C₄⋊C₄×C₁₉	—	4	2	no	—
111	C₄⋊C₄×C₁₉	—	4	4	no	—
112	C₂²⋊C₄×C₁₉	—	4	8	no	—
113	C₂²⋊C₄×C₁₉	—	4	4	no	—
114	C₂²⋊C₄×C₁₉	—	4	8	no	—
115	C₄²×C₁₉	—	2	4	no	—
116	C₄²×C₁₉	—	2	2	no	—
117	C₄²×C₁₉	—	2	2	no	—
118	C₄²×C₁₉	—	4	4	no	—
119	#23731	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₁₉	—	2	2	no	—
121	C₂³×C₁₉	—	2	2	no	—
122	C₂³×C₁₉	—	2	4	no	—
123	C₂³×C₁₉	—	4	16	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	—	4	8	no	—
129	C₂³×C₁₉	—	8	8	no	—
130	C₂³×C₁₉	—	8	4	no	—
131	C₂³×C₁₉	—	8	4	no	—
132	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
133	C₂³×C₁₉	#123	1	2	yes	—
134	C₂³×C₁₉	#127	1	2	yes	—
135	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
136	D₄×C₁₉	—	2	8	no	—
137	D₄×C₁₉	—	4	4	no	—
138	D₄×C₁₉	—	4	8	no	—
139	C₂×C₄×C₁₉	—	2	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	—	2	2	no	—
144	C₂×C₄×C₁₉	—	4	8	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	4	no	—
149	C₂×C₄×C₁₉	—	4	4	no	—
150	C₂×C₄×C₁₉	—	4	4	no	—
151	C₂×C₄×C₁₉	—	8	4	no	—
152	C₂×C₄×C₁₉	C₂²⋊Q₈	1	8	yes	—
153	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
154	C₂×C₄×C₁₉	#123	1	8	yes	—
155	C₂×C₄×C₁₉	#123	1	2	yes	—
156	C₂×C₄×C₁₉	#127	1	2	yes	—
157	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
158	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
159	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
161	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
162	C₈×C₁₉	—	2	8	no	—
163	C₂×#428	C₂×C₁₉	1	2	yes	complemented
164	C₂×#418	C₂×C₁₉	1	2	yes	—
165	C₂×#390	C₂×C₁₉	1	1	yes	characteristic
166	#2285	C₂×C₁₉	1	1	yes	characteristic, complemented
167	#2094	C₂×C₁₉	1	2	yes	complemented
168	#2093	C₂×C₁₉	1	2	yes	complemented
169	#2092	C₂×C₁₉	1	4	yes	complemented
170	#1728	C₂×C₁₉	1	1	yes	characteristic, complemented
171	C₂²×C₁₉	—	2	4	no	—
172	C₂²×C₁₉	—	2	4	no	—
173	C₂²×C₁₉	—	2	2	no	—
174	C₂²×C₁₉	—	2	2	no	—
175	C₂²×C₁₉	—	4	8	no	—
176	C₂²×C₁₉	—	4	4	no	—
177	C₂²×C₁₉	—	8	16	no	—
178	C₂²×C₁₉	—	8	4	no	—
179	C₂²×C₁₉	—	8	2	no	—
180	C₂²×C₁₉	—	8	2	no	—
181	C₂²×C₁₉	#399	1	4	yes	—
182	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
183	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
184	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
185	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
186	C₂²×C₁₉	#575	1	2	yes	—
187	C₄×C₁₉	—	2	4	no	—
188	C₄×C₁₉	—	4	2	no	—
189	C₄×C₁₉	—	8	2	no	—
190	C₄×C₁₉	—	8	2	no	—
191	C₄×C₁₉	—	8	2	no	—
192	C₄×C₁₉	#399	1	4	yes	—
193	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
194	C₄×C₁₉	C₂×#123	1	2	yes	—
195	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
196	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
197	C₂×#117	C₂²×C₁₉	1	2	yes	—
198	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
199	C₂²×C₂²⋊C₄	—	2	2	no	—
200	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
201	#428	—	2	8	no	—
202	C₂×#107	C₂²×C₁₉	1	4	yes	complemented
203	C₂×#106	C₂²×C₁₉	1	4	yes	complemented
204	#418	—	2	8	no	—
205	C₂×#102	C₂²×C₁₉	1	4	yes	—
206	C₂×#102	C₂²×C₁₉	1	4	yes	—
207	#390	—	2	2	no	—
208	#390	C₂²×C₁₉	1	2	yes	—
209	#390	C₂²×C₁₉	1	2	yes	—
210	#384	C₂²×C₁₉	1	1	yes	characteristic, complemented
211	#384	C₂²×C₁₉	1	1	yes	characteristic, complemented
212	#382	C₂²×C₁₉	1	2	yes	complemented
213	#380	—	2	2	no	—
214	C₄×C₄⋊C₄	—	2	2	no	—
215	#336	C₂²×C₁₉	1	2	yes	complemented
216	#336	C₂²×C₁₉	1	2	yes	complemented
217	C₂×C₁₉	—	2	4	no	—
218	C₂×C₁₉	—	8	4	no	—
219	C₂×C₁₉	C₂×#399	1	1	yes	characteristic
220	C₂×C₁₉	#3077	1	2	yes	—
221	C₂×C₁₉	#3094	1	2	yes	—
222	C₂×C₁₉	#3151	1	1	yes	characteristic
223	C₂×C₁₉	#3153	1	1	yes	characteristic
224	C₂⁵	—	2	1	no	—
225	C₂²×D₄	—	2	4	no	—
226	C₂²×D₄	—	2	1	no	—
227	C₂²×D₄	—	2	4	no	—
228	C₂²×D₄	—	2	2	no	—
229	C₂²×D₄	Q₈×C₁₉	1	4	yes	—
230	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
231	C₂³×C₄	—	2	1	no	—
232	C₂³×C₄	D₄×C₁₉	1	2	yes	—
233	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
234	C₂×M₁₆	—	2	4	no	—
235	C₂×M₁₆	—	2	4	no	—
236	C₂×M₁₆	D₄×C₁₉	1	8	yes	—
237	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
238	#117	—	2	4	no	—
239	#117	—	2	4	no	—
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	—	2	4	no	—
249	C₂×C₂²⋊C₄	—	2	4	no	—
250	C₂×C₂²⋊C₄	—	4	8	no	—
251	C₂×C₄²	—	2	4	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	D₄×C₁₉	1	2	yes	—
254	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
256	#107	—	2	8	no	—
257	#106	—	2	8	no	—
258	#102	—	2	8	no	—
259	#102	—	2	8	no	—
260	#95	—	2	4	no	—
261	C₁₉	#23731	1	1	yes	characteristic, direct product factor, Sylow
262	C₂⁴	—	2	4	no	—
263	C₂⁴	—	2	2	no	—
264	C₂⁴	—	4	4	no	—
265	C₂⁴	—	4	4	no	—
266	C₂⁴	—	4	2	no	—
267	C₂⁴	—	4	2	no	—
268	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
269	C₂×D₄	—	2	16	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂×D₄	—	4	8	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	C₂×Q₈×C₁₉	1	4	yes	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	4	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
290	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
291	C₂²×C₄	#41×C₁₉	1	4	yes	—
292	C₂²×C₄	#41×C₁₉	1	2	yes	—
293	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
294	M₁₆	—	2	16	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	C₂×D₄×C₁₉	1	8	yes	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	4	4	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	4	4	no	—
306	C₂²⋊C₄	—	4	8	no	—
307	C₂²⋊C₄	—	4	4	no	—
308	C₂²⋊C₄	—	4	8	no	—
309	C₄²	—	2	4	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	4	4	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	4	16	no	—
317	C₂³	—	4	8	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	4	no	—
321	C₂³	—	4	4	no	—
322	C₂³	—	8	8	no	—
323	C₂³	—	8	4	no	—
324	C₂³	—	8	4	no	—
325	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
326	C₂³	C₁₉×#123	1	2	yes	—
327	C₂³	C₁₉×#127	1	2	yes	—
328	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
329	D₄	—	2	8	no	—
330	D₄	—	4	8	no	—
331	D₄	—	4	4	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	8	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	8	4	no	—
345	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
346	C₂×C₄	C₁₉×C₂²⋊Q₈	1	8	yes	—
347	C₂×C₄	C₁₉×#123	1	2	yes	—
348	C₂×C₄	C₁₉×#123	1	8	yes	—
349	C₂×C₄	C₁₉×#127	1	2	yes	—
350	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
351	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
352	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
353	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
354	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
355	C₈	—	2	8	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	4	8	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	8	16	no	—
363	C₂²	—	8	4	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	C₁₉×#399	1	4	yes	—
367	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
368	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
369	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
370	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
371	C₂²	C₁₉×#575	1	2	yes	—
372	C₄	—	2	4	no	—
373	C₄	—	4	2	no	—
374	C₄	—	8	2	no	—
375	C₄	—	8	2	no	—
376	C₄	—	8	2	no	—
377	C₄	C₁₉×#399	1	4	yes	—
378	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
379	C₄	C₂×C₁₉×#123	1	2	yes	—
380	C₂	—	2	4	no	—
381	C₂	—	8	4	no	—
382	C₂	C₂×C₁₉×#399	1	1	yes	characteristic
383	C₂	C₁₉×#3077	1	2	yes	—
384	C₂	C₁₉×#3094	1	2	yes	—
385	C₂	C₁₉×#3151	1	1	yes	characteristic
386	C₂	C₁₉×#3153	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#428	C₂	semidirect
4. C₁₉×#2285	C₂	semidirect
5. C₁₉×#2094	C₂	semidirect
6. C₁₉×#2093	C₂	semidirect
7. C₁₉×#2092	C₂	semidirect
8. C₁₉×#1728	C₂	semidirect
16. C₂×C₁₉×#107	C₂²	semidirect
17. C₂×C₁₉×#106	C₂²	semidirect
24. C₁₉×#384	C₂²	semidirect
25. C₁₉×#384	C₂²	semidirect
26. C₁₉×#382	C₂²	semidirect
29. C₁₉×#336	C₂²	semidirect
30. C₁₉×#336	C₂²	semidirect
119. #23731	C₁₉	direct (N × H)
163. C₂×#428	C₂×C₁₉	semidirect
166. #2285	C₂×C₁₉	semidirect
167. #2094	C₂×C₁₉	semidirect
168. #2093	C₂×C₁₉	semidirect
169. #2092	C₂×C₁₉	semidirect
170. #1728	C₂×C₁₉	semidirect
202. C₂×#107	C₂²×C₁₉	semidirect
203. C₂×#106	C₂²×C₁₉	semidirect
210. #384	C₂²×C₁₉	semidirect
211. #384	C₂²×C₁₉	semidirect
212. #382	C₂²×C₁₉	semidirect
215. #336	C₂²×C₁₉	semidirect
216. #336	C₂²×C₁₉	semidirect
261. C₁₉	#23731	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×#428	2
C₂×C₁₉×#418	2
C₂×C₁₉×#390	2
C₁₉×#2285	2
C₁₉×#2094	2
C₁₉×#2093	2
C₁₉×#2092	2
C₁₉×#1728	2
#23731	19

Subgroups — C19×#23731 #18029690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23731 #18029690