Subgroups — C₂×C₁₉×#2054 #18029495

Order 4864.

1918 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	C₂³×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×#102	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#390	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2054	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
8	C₂²×D₈×C₁₉	—	2	8	no	—
9	C₂²×D₈×C₁₉	—	2	4	no	—
10	C₂²×D₈×C₁₉	C₂²	1	4	yes	—
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
15	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊C₈	—	2	4	no	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	complemented
19	C₂×C₁₉×#102	—	2	8	no	—
20	C₂×C₁₉×#102	C₂²	1	8	yes	complemented
21	C₁₉×#390	—	2	4	no	—
22	C₁₉×#390	C₂²	1	8	yes	complemented
23	C₁₉×#340	C₂²	1	4	yes	complemented
24	C₂⁵×C₁₉	—	2	2	no	—
25	C₂²×D₄×C₁₉	—	2	4	no	—
26	C₂²×D₄×C₁₉	—	2	4	no	—
27	C₂²×D₄×C₁₉	—	2	2	no	—
28	C₂²×D₄×C₁₉	—	2	4	no	—
29	C₂²×D₄×C₁₉	—	2	4	no	—
30	C₂²×D₄×C₁₉	—	2	4	no	—
31	C₂²×D₄×C₁₉	D₄	1	8	yes	—
32	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
33	C₂³×C₄×C₁₉	—	2	2	no	—
34	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×D₈×C₁₉	—	2	32	no	—
38	C₂×D₈×C₁₉	—	2	16	no	—
39	C₂×D₈×C₁₉	—	2	8	no	—
40	C₂²×C₈×C₁₉	—	2	4	no	—
41	C₂²×C₈×C₁₉	—	2	4	no	—
42	C₂²×C₈×C₁₉	—	2	2	no	—
43	C₂²×C₈×C₁₉	D₄	1	4	yes	—
44	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
46	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
54	C₂×C₄²×C₁₉	—	2	2	no	—
55	C₂×C₄²×C₁₉	—	2	2	no	—
56	C₂×C₄²×C₁₉	D₄	1	2	yes	—
57	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
58	C₁₉×C₄⋊C₈	—	2	8	no	—
59	C₁₉×#102	—	2	16	no	—
60	C₂⁴×C₁₉	—	2	8	no	—
61	C₂⁴×C₁₉	—	2	4	no	—
62	C₂⁴×C₁₉	—	4	4	no	—
63	C₂⁴×C₁₉	—	4	4	no	—
64	C₂⁴×C₁₉	—	4	4	no	—
65	C₂⁴×C₁₉	—	4	4	no	—
66	C₂⁴×C₁₉	—	4	4	no	—
67	C₂⁴×C₁₉	—	4	4	no	—
68	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂×D₄×C₁₉	—	2	16	no	—
70	C₂×D₄×C₁₉	—	2	8	no	—
71	C₂×D₄×C₁₉	—	2	16	no	—
72	C₂×D₄×C₁₉	—	2	4	no	—
73	C₂×D₄×C₁₉	—	2	4	no	—
74	C₂×D₄×C₁₉	—	2	4	no	—
75	C₂×D₄×C₁₉	—	2	4	no	—
76	C₂×D₄×C₁₉	—	2	4	no	—
77	C₂×D₄×C₁₉	—	4	4	no	—
78	C₂×D₄×C₁₉	—	4	4	no	—
79	C₂×D₄×C₁₉	—	4	8	no	—
80	C₂×D₄×C₁₉	—	4	8	no	—
81	C₂×D₄×C₁₉	C₂×D₄	1	8	yes	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	4	no	—
87	C₂²×C₄×C₁₉	—	4	4	no	—
88	C₂²×C₄×C₁₉	—	4	4	no	—
89	C₂²×C₄×C₁₉	—	4	4	no	—
90	C₂²×C₄×C₁₉	D₈	1	4	yes	complemented
91	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂×D₄	1	4	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	4	yes	—
98	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
99	D₈×C₁₉	—	2	32	no	—
100	C₂×C₈×C₁₉	—	2	8	no	—
101	C₂×C₈×C₁₉	—	2	4	no	—
102	C₂×C₈×C₁₉	—	2	4	no	—
103	C₂×C₈×C₁₉	—	2	2	no	—
104	C₂×C₈×C₁₉	—	4	4	no	—
105	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
106	C₄⋊C₄×C₁₉	—	2	4	no	—
107	C₄⋊C₄×C₁₉	—	2	4	no	—
108	C₄⋊C₄×C₁₉	—	4	4	no	—
109	C₂²⋊C₄×C₁₉	—	4	16	no	—
110	C₂²⋊C₄×C₁₉	—	4	16	no	—
111	C₄²×C₁₉	—	2	4	no	—
112	C₄²×C₁₉	—	2	2	no	—
113	C₄²×C₁₉	—	2	2	no	—
114	C₂×#2054	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₁₉	—	2	8	no	—
116	C₂³×C₁₉	—	4	4	no	—
117	C₂³×C₁₉	—	4	4	no	—
118	C₂³×C₁₉	—	4	4	no	—
119	C₂³×C₁₉	—	4	4	no	—
120	C₂³×C₁₉	—	4	4	no	—
121	C₂³×C₁₉	—	4	4	no	—
122	C₂³×C₁₉	—	4	16	no	—
123	C₂³×C₁₉	—	4	16	no	—
124	C₂³×C₁₉	—	4	16	no	—
125	C₂³×C₁₉	—	8	8	no	—
126	C₂³×C₁₉	—	8	8	no	—
127	C₂³×C₁₉	—	8	8	no	—
128	C₂³×C₁₉	—	8	8	no	—
129	C₂³×C₁₉	#121	1	4	yes	—
130	C₂³×C₁₉	#121	1	2	yes	—
131	C₂³×C₁₉	C₂×D₈	1	2	yes	—
132	C₂³×C₁₉	#135	1	2	yes	—
133	C₂³×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
134	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
135	D₄×C₁₉	—	2	8	no	—
136	D₄×C₁₉	—	2	8	no	—
137	D₄×C₁₉	—	4	4	no	—
138	D₄×C₁₉	—	4	4	no	—
139	D₄×C₁₉	—	4	16	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	8	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	4	no	—
145	C₂×C₄×C₁₉	—	4	4	no	—
146	C₂×C₄×C₁₉	—	4	4	no	—
147	C₂×C₄×C₁₉	—	4	4	no	—
148	C₂×C₄×C₁₉	—	4	4	no	—
149	C₂×C₄×C₁₉	—	8	8	no	—
150	C₂×C₄×C₁₉	#120	1	4	yes	—
151	C₂×C₄×C₁₉	#121	1	2	yes	—
152	C₂×C₄×C₁₉	#121	1	4	yes	—
153	C₂×C₄×C₁₉	#123	1	8	yes	—
154	C₂×C₄×C₁₉	#124	1	4	yes	—
155	C₂×C₄×C₁₉	C₂×D₈	1	4	yes	complemented
156	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
157	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
160	C₈×C₁₉	—	2	4	no	—
161	C₈×C₁₉	—	4	2	no	—
162	C₂³×D₈	C₂×C₁₉	1	1	yes	characteristic
163	C₂²×C₄⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
164	C₂²×#102	C₂×C₁₉	1	2	yes	complemented
165	C₂×#390	C₂×C₁₉	1	2	yes	complemented
166	#2054	C₂×C₁₉	1	8	yes	direct product factor
167	C₂×#340	C₂×C₁₉	1	1	yes	characteristic, complemented
168	C₂²×C₁₉	—	4	8	no	—
169	C₂²×C₁₉	—	4	8	no	—
170	C₂²×C₁₉	—	4	8	no	—
171	C₂²×C₁₉	—	8	32	no	—
172	C₂²×C₁₉	—	8	4	no	—
173	C₂²×C₁₉	—	8	4	no	—
174	C₂²×C₁₉	—	8	4	no	—
175	C₂²×C₁₉	—	8	4	no	—
176	C₂²×C₁₉	#394	1	4	yes	—
177	C₂²×C₁₉	#459	1	8	yes	—
178	C₂²×C₁₉	#463	1	8	yes	—
179	C₂²×C₁₉	#466	1	4	yes	—
180	C₂²×C₁₉	#469	1	4	yes	—
181	C₂²×C₁₉	C₂×#121	1	2	yes	—
182	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
183	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
184	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
185	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
186	C₄×C₁₉	—	2	4	no	—
187	C₄×C₁₉	—	4	2	no	—
188	C₄×C₁₉	—	8	4	no	—
189	C₄×C₁₉	#394	1	4	yes	—
190	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
191	C₄×C₁₉	C₂×#123	1	2	yes	—
192	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
193	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
194	C₂²×D₈	—	2	8	no	—
195	C₂²×D₈	—	2	4	no	—
196	C₂²×D₈	C₂²×C₁₉	1	4	yes	—
197	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
198	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
199	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
200	C₂²×C₂²⋊C₄	—	2	2	no	—
201	C₂²×C₂²⋊C₄	—	2	2	no	—
202	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
203	C₂×C₄⋊C₈	—	2	4	no	—
204	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
205	C₂×#102	—	2	8	no	—
206	C₂×#102	C₂²×C₁₉	1	8	yes	complemented
207	#390	—	2	4	no	—
208	#390	C₂²×C₁₉	1	8	yes	complemented
209	#340	C₂²×C₁₉	1	4	yes	complemented
210	C₂×C₁₉	—	8	8	no	—
211	C₂×C₁₉	#2054	1	8	yes	direct product factor
212	C₂×C₁₉	C₂×#394	1	1	yes	characteristic
213	C₂×C₁₉	C₂×#459	1	2	yes	—
214	C₂×C₁₉	C₂×#463	1	2	yes	—
215	C₂×C₁₉	C₂×#466	1	1	yes	characteristic
216	C₂×C₁₉	C₂×#469	1	1	yes	characteristic
217	C₂⁵	—	2	2	no	—
218	C₂²×D₄	—	2	4	no	—
219	C₂²×D₄	—	2	4	no	—
220	C₂²×D₄	—	2	2	no	—
221	C₂²×D₄	—	2	4	no	—
222	C₂²×D₄	—	2	4	no	—
223	C₂²×D₄	—	2	4	no	—
224	C₂²×D₄	D₄×C₁₉	1	8	yes	—
225	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
226	C₂³×C₄	—	2	2	no	—
227	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
228	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
230	C₂×D₈	—	2	32	no	—
231	C₂×D₈	—	2	16	no	—
232	C₂×D₈	—	2	8	no	—
233	C₂²×C₈	—	2	4	no	—
234	C₂²×C₈	—	2	4	no	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	D₄×C₁₉	1	4	yes	—
237	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
238	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
243	C₂×C₂²⋊C₄	—	2	8	no	—
244	C₂×C₂²⋊C₄	—	2	8	no	—
245	C₂×C₂²⋊C₄	—	4	8	no	—
246	C₂×C₂²⋊C₄	—	4	8	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	—	2	2	no	—
249	C₂×C₄²	D₄×C₁₉	1	2	yes	—
250	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
251	C₄⋊C₈	—	2	8	no	—
252	#102	—	2	16	no	—
253	C₁₉	C₂×#2054	1	1	yes	characteristic, direct product factor, Sylow
254	C₂⁴	—	2	8	no	—
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	4	4	no	—
257	C₂⁴	—	4	4	no	—
258	C₂⁴	—	4	4	no	—
259	C₂⁴	—	4	4	no	—
260	C₂⁴	—	4	4	no	—
261	C₂⁴	—	4	4	no	—
262	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
263	C₂×D₄	—	2	16	no	—
264	C₂×D₄	—	2	8	no	—
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	—	2	4	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	4	4	no	—
272	C₂×D₄	—	4	4	no	—
273	C₂×D₄	—	4	8	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	C₂×D₄×C₁₉	1	8	yes	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	4	4	no	—
282	C₂²×C₄	—	4	4	no	—
283	C₂²×C₄	—	4	4	no	—
284	C₂²×C₄	D₈×C₁₉	1	4	yes	complemented
285	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
288	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
290	C₂²×C₄	#41×C₁₉	1	2	yes	—
291	C₂²×C₄	#41×C₁₉	1	4	yes	—
292	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
293	D₈	—	2	32	no	—
294	C₂×C₈	—	2	8	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	4	4	no	—
299	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	4	4	no	—
303	C₂²⋊C₄	—	4	16	no	—
304	C₂²⋊C₄	—	4	16	no	—
305	C₄²	—	2	4	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₂³	—	2	8	no	—
309	C₂³	—	4	16	no	—
310	C₂³	—	4	16	no	—
311	C₂³	—	4	16	no	—
312	C₂³	—	4	4	no	—
313	C₂³	—	4	4	no	—
314	C₂³	—	4	4	no	—
315	C₂³	—	4	4	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	4	no	—
318	C₂³	—	8	8	no	—
319	C₂³	—	8	8	no	—
320	C₂³	—	8	8	no	—
321	C₂³	—	8	8	no	—
322	C₂³	C₁₉×#121	1	4	yes	—
323	C₂³	C₁₉×#121	1	2	yes	—
324	C₂³	C₂×D₈×C₁₉	1	2	yes	—
325	C₂³	C₁₉×#135	1	2	yes	—
326	C₂³	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
327	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
328	D₄	—	2	8	no	—
329	D₄	—	2	8	no	—
330	D₄	—	4	16	no	—
331	D₄	—	4	4	no	—
332	D₄	—	4	4	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	8	8	no	—
343	C₂×C₄	C₁₉×#120	1	4	yes	—
344	C₂×C₄	C₁₉×#121	1	2	yes	—
345	C₂×C₄	C₁₉×#121	1	4	yes	—
346	C₂×C₄	C₁₉×#123	1	8	yes	—
347	C₂×C₄	C₁₉×#124	1	4	yes	—
348	C₂×C₄	C₂×D₈×C₁₉	1	4	yes	complemented
349	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
350	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
351	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
352	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
353	C₈	—	2	4	no	—
354	C₈	—	4	2	no	—
355	C₂²	—	4	8	no	—
356	C₂²	—	4	8	no	—
357	C₂²	—	4	8	no	—
358	C₂²	—	8	4	no	—
359	C₂²	—	8	4	no	—
360	C₂²	—	8	4	no	—
361	C₂²	—	8	4	no	—
362	C₂²	—	8	32	no	—
363	C₂²	C₁₉×#394	1	4	yes	—
364	C₂²	C₁₉×#459	1	8	yes	—
365	C₂²	C₁₉×#463	1	8	yes	—
366	C₂²	C₁₉×#466	1	4	yes	—
367	C₂²	C₁₉×#469	1	4	yes	—
368	C₂²	C₂×C₁₉×#121	1	2	yes	—
369	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
370	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
371	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
372	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
373	C₄	—	2	4	no	—
374	C₄	—	4	2	no	—
375	C₄	—	8	4	no	—
376	C₄	C₁₉×#394	1	4	yes	—
377	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
378	C₄	C₂×C₁₉×#123	1	2	yes	—
379	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
380	C₂	—	8	8	no	—
381	C₂	C₁₉×#2054	1	8	yes	direct product factor
382	C₂	C₂×C₁₉×#394	1	1	yes	characteristic
383	C₂	C₂×C₁₉×#459	1	2	yes	—
384	C₂	C₂×C₁₉×#463	1	2	yes	—
385	C₂	C₂×C₁₉×#466	1	1	yes	characteristic
386	C₂	C₂×C₁₉×#469	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₈×C₁₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×C₄⋊C₈	C₂	semidirect
3. C₂²×C₁₉×#102	C₂	semidirect
4. C₂×C₁₉×#390	C₂	semidirect
5. C₁₉×#2054	C₂	direct (N × H)
6. C₂×C₁₉×#340	C₂	semidirect
18. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
20. C₂×C₁₉×#102	C₂²	semidirect
22. C₁₉×#390	C₂²	semidirect
23. C₁₉×#340	C₂²	semidirect
90. C₂²×C₄×C₁₉	D₈	semidirect
114. C₂×#2054	C₁₉	direct (N × H)
155. C₂×C₄×C₁₉	C₂×D₈	semidirect
163. C₂²×C₄⋊C₈	C₂×C₁₉	semidirect
164. C₂²×#102	C₂×C₁₉	semidirect
165. C₂×#390	C₂×C₁₉	semidirect
166. #2054	C₂×C₁₉	direct (N × H)
167. C₂×#340	C₂×C₁₉	semidirect
204. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
206. C₂×#102	C₂²×C₁₉	semidirect
208. #390	C₂²×C₁₉	semidirect
209. #340	C₂²×C₁₉	semidirect
211. C₂×C₁₉	#2054	direct (N × H)
253. C₁₉	C₂×#2054	direct (N × H)
284. C₂²×C₄	D₈×C₁₉	semidirect
348. C₂×C₄	C₂×D₈×C₁₉	semidirect
381. C₂	C₁₉×#2054	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₁₉	2
C₂²×C₁₉×C₄⋊C₈	2
C₂²×C₁₉×#102	2
C₂×C₁₉×#390	2
C₁₉×#2054	2
C₂×C₁₉×#340	2
C₂×#2054	19

Subgroups — C2×C19×#2054 #18029495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2054 #18029495