Subgroups — C₁₉×#22386 #18028345

Order 4864.

758 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×#2398	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1984	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1924	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1923	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1869	C₂	1	2	yes	maximal
6	C₁₉×#1850	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1840	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1768	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₂²⋊C₄×C₁₉	C₂	1	2	yes	maximal, complemented
10	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
11	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#400	C₄	1	2	yes	—
22	C₁₉×#397	C₄	1	2	yes	—
23	C₁₉×#394	C₄	1	2	yes	—
24	C₁₉×#393	C₄	1	2	yes	—
25	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
26	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
27	C₁₉×#376	C₂²	1	1	yes	characteristic
28	C₁₉×#336	C₂²	1	1	yes	characteristic
29	C₁₉×#336	C₂²	1	2	yes	—
30	C₁₉×#336	C₂²	1	2	yes	—
31	C₁₉×#336	C₂²	1	2	yes	—
32	C₁₉×#336	C₂²	1	2	yes	—
33	C₁₉×#336	C₂²	1	2	yes	—
34	C₁₉×#336	C₂²	1	1	yes	characteristic
35	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₉	—	2	4	no	—
39	C₂²×C₈×C₁₉	—	4	2	no	—
40	C₂²×C₈×C₁₉	—	4	2	no	—
41	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
45	C₄×Q₈×C₁₉	—	4	2	no	—
46	C₄×D₄×C₁₉	—	4	2	no	—
47	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
59	C₁₉×C₄⋊C₈	—	2	4	no	—
60	C₁₉×C₄⋊C₈	—	4	2	no	—
61	C₁₉×C₂²⋊C₈	—	2	4	no	—
62	C₁₉×C₂²⋊C₈	—	4	2	no	—
63	C₁₉×C₂²⋊C₈	—	4	2	no	—
64	C₁₉×#97	—	4	1	no	—
65	C₄×C₈×C₁₉	—	4	2	no	—
66	C₄×C₈×C₁₉	—	4	1	no	—
67	C₁₉×#95	C₂×C₄	1	2	yes	—
68	C₁₉×#95	C₂×C₄	1	2	yes	—
69	C₁₉×#95	C₂×C₄	1	2	yes	—
70	C₁₉×#95	C₂×C₄	1	2	yes	—
71	C₁₉×#95	C₂×C₄	1	2	yes	—
72	C₁₉×#95	C₂×C₄	1	2	yes	—
73	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
74	C₂×Q₈×C₁₉	—	2	4	no	—
75	C₂×Q₈×C₁₉	—	4	1	no	—
76	C₂×D₄×C₁₉	—	2	4	no	—
77	C₂×D₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
92	C₂×C₈×C₁₉	—	2	2	no	—
93	C₂×C₈×C₁₉	—	2	2	no	—
94	C₂×C₈×C₁₉	—	2	2	no	—
95	C₂×C₈×C₁₉	—	2	2	no	—
96	C₂×C₈×C₁₉	—	2	2	no	—
97	C₂×C₈×C₁₉	—	2	2	no	—
98	C₂×C₈×C₁₉	—	2	2	no	—
99	C₂×C₈×C₁₉	—	2	2	no	—
100	C₂×C₈×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	—	2	2	no	—
102	C₂×C₈×C₁₉	—	2	2	no	—
103	C₂×C₈×C₁₉	—	4	8	no	—
104	C₂×C₈×C₁₉	#41	1	4	yes	—
105	C₄⋊C₄×C₁₉	—	4	1	no	—
106	C₄⋊C₄×C₁₉	—	4	2	no	—
107	C₄⋊C₄×C₁₉	—	4	1	no	—
108	C₂²⋊C₄×C₁₉	—	2	4	no	—
109	C₂²⋊C₄×C₁₉	—	2	4	no	—
110	C₂²⋊C₄×C₁₉	—	2	4	no	—
111	C₂²⋊C₄×C₁₉	—	2	4	no	—
112	C₂²⋊C₄×C₁₉	—	4	2	no	—
113	C₄²×C₁₉	—	2	2	no	—
114	C₄²×C₁₉	—	2	2	no	—
115	C₄²×C₁₉	—	2	2	no	—
116	C₄²×C₁₉	—	2	2	no	—
117	C₄²×C₁₉	—	2	1	no	—
118	C₄²×C₁₉	—	2	1	no	—
119	#22386	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	2	no	—
123	C₂³×C₁₉	—	2	2	no	—
124	C₂³×C₁₉	—	2	2	no	—
125	C₂³×C₁₉	—	2	2	no	—
126	C₂³×C₁₉	#131	1	4	yes	—
127	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
128	Q₈×C₁₉	—	4	4	no	—
129	D₄×C₁₉	—	4	4	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	2	2	no	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	2	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	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	#131	1	4	yes	—
153	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
154	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
155	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
156	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
157	C₈×C₁₉	—	2	4	no	—
158	C₈×C₁₉	—	4	2	no	—
159	C₈×C₁₉	—	4	2	no	—
160	C₈×C₁₉	—	4	2	no	—
161	#2398	C₂×C₁₉	1	1	yes	characteristic
162	#1984	C₂×C₁₉	1	2	yes	complemented
163	#1924	C₂×C₁₉	1	2	yes	complemented
164	#1923	C₂×C₁₉	1	2	yes	complemented
165	#1869	C₂×C₁₉	1	2	yes	—
166	#1850	C₂×C₁₉	1	2	yes	complemented
167	#1840	C₂×C₁₉	1	1	yes	characteristic, complemented
168	#1768	C₂×C₁₉	1	1	yes	characteristic, complemented
169	C₈×C₂²⋊C₄	C₂×C₁₉	1	2	yes	complemented
170	C₂²×C₁₉	—	2	4	no	—
171	C₂²×C₁₉	—	2	4	no	—
172	C₂²×C₁₉	—	2	4	no	—
173	C₂²×C₁₉	—	4	2	no	—
174	C₂²×C₁₉	—	4	2	no	—
175	C₂²×C₁₉	—	4	2	no	—
176	C₂²×C₁₉	—	4	2	no	—
177	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
178	C₂²×C₁₉	#518	1	1	yes	characteristic
179	C₂²×C₁₉	#520	1	1	yes	characteristic
180	C₂²×C₁₉	C₂×#131	1	2	yes	—
181	C₂²×C₁₉	C₂×#131	1	2	yes	—
182	C₄×C₁₉	—	2	4	no	—
183	C₄×C₁₉	—	4	2	no	—
184	C₄×C₁₉	—	4	2	no	—
185	C₄×C₁₉	—	4	2	no	—
186	C₄×C₁₉	—	4	1	no	—
187	C₄×C₁₉	—	4	1	no	—
188	C₄×C₁₉	—	4	2	no	—
189	C₄×C₁₉	#538	1	2	yes	—
190	C₄×C₁₉	#542	1	2	yes	—
191	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
192	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
193	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
194	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
195	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
196	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
197	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
198	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
199	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
200	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
201	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
202	#400	C₄×C₁₉	1	2	yes	—
203	#397	C₄×C₁₉	1	2	yes	—
204	#394	C₄×C₁₉	1	2	yes	—
205	#393	C₄×C₁₉	1	2	yes	—
206	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
207	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
208	#376	C₂²×C₁₉	1	1	yes	characteristic
209	#336	C₂²×C₁₉	1	1	yes	characteristic
210	#336	C₂²×C₁₉	1	2	yes	—
211	#336	C₂²×C₁₉	1	1	yes	characteristic
212	#336	C₂²×C₁₉	1	2	yes	—
213	#336	C₂²×C₁₉	1	2	yes	—
214	#336	C₂²×C₁₉	1	2	yes	—
215	#336	C₂²×C₁₉	1	2	yes	—
216	C₂×C₁₉	—	4	4	no	—
217	C₂×C₁₉	#2337	1	1	yes	characteristic
218	C₂×C₁₉	#2966	1	2	yes	—
219	C₂×C₁₉	#2977	1	1	yes	characteristic
220	C₂×C₁₉	#2977	1	1	yes	characteristic
221	C₂×C₁₉	#2994	1	2	yes	—
222	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
223	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
224	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
225	C₂²×C₈	—	2	4	no	—
226	C₂²×C₈	—	4	2	no	—
227	C₂²×C₈	—	4	2	no	—
228	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
229	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
230	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
231	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
232	C₄×Q₈	—	4	2	no	—
233	C₄×D₄	—	4	2	no	—
234	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
236	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
237	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
238	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
239	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
240	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
241	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
242	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
244	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
246	C₄⋊C₈	—	2	4	no	—
247	C₄⋊C₈	—	4	2	no	—
248	C₂²⋊C₈	—	2	4	no	—
249	C₂²⋊C₈	—	4	2	no	—
250	C₂²⋊C₈	—	4	2	no	—
251	#97	—	4	1	no	—
252	C₄×C₈	—	4	1	no	—
253	C₄×C₈	—	4	2	no	—
254	#95	C₂×C₄×C₁₉	1	2	yes	—
255	#95	C₂×C₄×C₁₉	1	2	yes	—
256	#95	C₂×C₄×C₁₉	1	2	yes	—
257	#95	C₂×C₄×C₁₉	1	2	yes	—
258	#95	C₂×C₄×C₁₉	1	2	yes	—
259	#95	C₂×C₄×C₁₉	1	2	yes	—
260	C₁₉	#22386	1	1	yes	characteristic, direct product factor, Sylow
261	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	—	4	1	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	—	4	1	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
274	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
276	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
279	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	4	8	no	—
292	C₂×C₈	#41×C₁₉	1	4	yes	—
293	C₄⋊C₄	—	4	1	no	—
294	C₄⋊C₄	—	4	2	no	—
295	C₄⋊C₄	—	4	1	no	—
296	C₂²⋊C₄	—	2	4	no	—
297	C₂²⋊C₄	—	2	4	no	—
298	C₂²⋊C₄	—	2	4	no	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	4	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	1	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	C₁₉×#131	1	4	yes	—
314	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
315	Q₈	—	4	4	no	—
316	D₄	—	4	4	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	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	—	2	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	C₁₉×#131	1	4	yes	—
340	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
341	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
342	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
343	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
344	C₈	—	2	4	no	—
345	C₈	—	4	2	no	—
346	C₈	—	4	2	no	—
347	C₈	—	4	2	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	4	2	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
356	C₂²	C₁₉×#518	1	1	yes	characteristic
357	C₂²	C₁₉×#520	1	1	yes	characteristic
358	C₂²	C₂×C₁₉×#131	1	2	yes	—
359	C₂²	C₂×C₁₉×#131	1	2	yes	—
360	C₄	—	2	4	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	C₁₉×#538	1	2	yes	—
368	C₄	C₁₉×#542	1	2	yes	—
369	C₂	—	4	4	no	—
370	C₂	C₁₉×#2337	1	1	yes	characteristic
371	C₂	C₁₉×#2966	1	2	yes	—
372	C₂	C₁₉×#2977	1	1	yes	characteristic
373	C₂	C₁₉×#2977	1	1	yes	characteristic
374	C₂	C₁₉×#2994	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1984	C₂	semidirect
3. C₁₉×#1924	C₂	semidirect
4. C₁₉×#1923	C₂	semidirect
6. C₁₉×#1850	C₂	semidirect
7. C₁₉×#1840	C₂	semidirect
8. C₁₉×#1768	C₂	semidirect
9. C₈×C₂²⋊C₄×C₁₉	C₂	semidirect
119. #22386	C₁₉	direct (N × H)
162. #1984	C₂×C₁₉	semidirect
163. #1924	C₂×C₁₉	semidirect
164. #1923	C₂×C₁₉	semidirect
166. #1850	C₂×C₁₉	semidirect
167. #1840	C₂×C₁₉	semidirect
168. #1768	C₂×C₁₉	semidirect
169. C₈×C₂²⋊C₄	C₂×C₁₉	semidirect
260. C₁₉	#22386	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×#2398	2
C₁₉×#1984	2
C₁₉×#1924	2
C₁₉×#1923	2
C₁₉×#1869	2
C₁₉×#1850	2
C₁₉×#1840	2
C₁₉×#1768	2
C₈×C₂²⋊C₄×C₁₉	2
#22386	19

Subgroups — C19×#22386 #18028345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22386 #18028345