Subgroups — C₁₉×#9910 #18015869

Order 4864.

640 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2851	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1294	C₂	1	2	yes	maximal
5	C₁₉×#1294	C₂	1	2	yes	maximal
6	C₂×C₁₉×#125	C₄	1	1	yes	characteristic, complemented
7	C₂²×C₄²×C₁₉	—	2	1	no	—
8	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
10	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
11	C₁₉×#389	C₄	1	1	yes	characteristic, complemented
12	C₁₉×#389	C₄	1	1	yes	characteristic, complemented
13	C₁₉×#387	—	2	1	no	—
14	C₁₉×#387	—	2	1	no	—
15	C₁₉×#385	—	2	1	no	—
16	C₁₉×#385	—	2	1	no	—
17	C₁₉×#382	C₄	1	1	yes	characteristic, complemented
18	C₁₉×#380	C₂²	1	1	yes	characteristic
19	C₁₉×#380	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#95	—	2	1	no	—
21	C₂×C₁₉×#95	C₂²	1	2	yes	—
22	C₁₉×#336	—	2	1	no	—
23	C₂³×C₄×C₁₉	—	2	2	no	—
24	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₁₉	—	2	2	no	—
28	C₁₉×#125	—	4	2	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄²×C₁₉	—	2	4	no	—
40	C₂×C₄²×C₁₉	—	4	2	no	—
41	C₂×C₄²×C₁₉	—	4	2	no	—
42	C₂×C₄²×C₁₉	—	4	2	no	—
43	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
47	C₁₉×C₄⋊C₈	—	4	2	no	—
48	C₁₉×C₂²⋊C₈	—	2	4	no	—
49	C₁₉×#95	—	2	4	no	—
50	C₁₉×#95	—	2	1	no	—
51	C₁₉×#95	—	2	1	no	—
52	C₁₉×#95	—	2	1	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉×#95	—	2	2	no	—
57	C₁₉×#95	Q₈	1	4	yes	—
58	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	—	2	1	no	—
60	C₂²×C₄×C₁₉	—	2	1	no	—
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	—	2	4	no	—
64	C₂²×C₄×C₁₉	—	2	4	no	—
65	C₂²×C₄×C₁₉	—	2	4	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	4	1	no	—
73	C₂²×C₄×C₁₉	—	4	1	no	—
74	C₂²×C₄×C₁₉	—	4	1	no	—
75	C₂²×C₄×C₁₉	—	4	2	no	—
76	C₂²×C₄×C₁₉	—	4	2	no	—
77	C₂²×C₄×C₁₉	—	4	2	no	—
78	C₂²×C₄×C₁₉	—	4	2	no	—
79	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
86	C₂²×C₄×C₁₉	#41	1	2	yes	—
87	C₂×C₈×C₁₉	—	4	2	no	—
88	C₂×C₈×C₁₉	—	4	2	no	—
89	C₂×C₈×C₁₉	—	4	2	no	—
90	C₄⋊C₄×C₁₉	—	4	1	no	—
91	C₄⋊C₄×C₁₉	—	4	1	no	—
92	C₄⋊C₄×C₁₉	—	4	1	no	—
93	C₄⋊C₄×C₁₉	—	4	1	no	—
94	C₄⋊C₄×C₁₉	—	4	2	no	—
95	C₄⋊C₄×C₁₉	—	4	2	no	—
96	C₄⋊C₄×C₁₉	—	4	2	no	—
97	C₄⋊C₄×C₁₉	—	4	2	no	—
98	C₂²⋊C₄×C₁₉	—	4	2	no	—
99	C₂²⋊C₄×C₁₉	—	4	1	no	—
100	C₂²⋊C₄×C₁₉	—	4	1	no	—
101	C₄²×C₁₉	—	2	2	no	—
102	C₄²×C₁₉	—	2	2	no	—
103	C₄²×C₁₉	—	4	1	no	—
104	C₄²×C₁₉	—	4	1	no	—
105	C₄²×C₁₉	—	4	8	no	—
106	#9910	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂³×C₁₉	—	2	1	no	—
108	C₂³×C₁₉	—	2	1	no	—
109	C₂³×C₁₉	—	2	1	no	—
110	C₂³×C₁₉	—	2	1	no	—
111	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
112	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
113	C₂³×C₁₉	#135	1	2	yes	—
114	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
115	C₂³×C₁₉	#137	1	1	yes	characteristic
116	C₂×C₄×C₁₉	—	2	4	no	—
117	C₂×C₄×C₁₉	—	2	4	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	2	1	no	—
120	C₂×C₄×C₁₉	—	2	1	no	—
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	—	2	1	no	—
124	C₂×C₄×C₁₉	—	2	1	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	2	1	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	8	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	4	2	no	—
133	C₂×C₄×C₁₉	—	4	2	no	—
134	C₂×C₄×C₁₉	—	4	4	no	—
135	C₂×C₄×C₁₉	—	4	4	no	—
136	C₂×C₄×C₁₉	—	4	4	no	—
137	C₂×C₄×C₁₉	—	4	4	no	—
138	C₂×C₄×C₁₉	—	4	4	no	—
139	C₂×C₄×C₁₉	—	4	4	no	—
140	C₂×C₄×C₁₉	—	4	4	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	#99	1	2	yes	—
154	C₂×C₄×C₁₉	#104	1	2	yes	—
155	C₂×C₄×C₁₉	#104	1	2	yes	—
156	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
157	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
159	C₈×C₁₉	—	8	2	no	—
160	#2851	C₂×C₁₉	1	1	yes	characteristic
161	#1797	C₂×C₁₉	1	1	yes	characteristic
162	C₄×#95	C₂×C₁₉	1	1	yes	characteristic
163	#1294	C₂×C₁₉	1	2	yes	—
164	#1294	C₂×C₁₉	1	2	yes	—
165	C₂²×C₁₉	—	2	2	no	—
166	C₂²×C₁₉	—	2	2	no	—
167	C₂²×C₁₉	—	2	2	no	—
168	C₂²×C₁₉	—	2	2	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	2	1	no	—
171	C₂²×C₁₉	—	2	1	no	—
172	C₂²×C₁₉	—	2	1	no	—
173	C₂²×C₁₉	#391	1	1	yes	characteristic
174	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
175	C₂²×C₁₉	#410	1	1	yes	characteristic
176	C₂²×C₁₉	#416	1	1	yes	characteristic
177	C₂²×C₁₉	#417	1	1	yes	characteristic
178	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
179	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
180	C₂²×C₁₉	#478	1	2	yes	—
181	C₂²×C₁₉	#479	1	2	yes	—
182	C₄×C₁₉	—	2	1	no	—
183	C₄×C₁₉	—	2	2	no	—
184	C₄×C₁₉	—	2	1	no	—
185	C₄×C₁₉	—	2	2	no	—
186	C₄×C₁₉	—	2	2	no	—
187	C₄×C₁₉	—	2	2	no	—
188	C₄×C₁₉	—	4	8	no	—
189	C₄×C₁₉	—	4	1	no	—
190	C₄×C₁₉	—	8	1	no	—
191	C₄×C₁₉	—	8	1	no	—
192	C₄×C₁₉	—	8	1	no	—
193	C₄×C₁₉	—	8	1	no	—
194	C₂×#125	C₄×C₁₉	1	1	yes	characteristic, complemented
195	C₂²×C₄²	—	2	1	no	—
196	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
197	C₂×C₄⋊C₈	—	2	1	no	—
198	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
199	#389	C₄×C₁₉	1	1	yes	characteristic, complemented
200	#389	C₄×C₁₉	1	1	yes	characteristic, complemented
201	#387	—	2	1	no	—
202	#387	—	2	1	no	—
203	#385	—	2	1	no	—
204	#385	—	2	1	no	—
205	#382	C₄×C₁₉	1	1	yes	characteristic, complemented
206	#380	C₂²×C₁₉	1	1	yes	characteristic
207	#380	C₂²×C₁₉	1	1	yes	characteristic
208	C₂×#95	—	2	1	no	—
209	C₂×#95	C₂²×C₁₉	1	2	yes	—
210	#336	—	2	1	no	—
211	C₂×C₁₉	—	2	2	no	—
212	C₂×C₁₉	—	2	2	no	—
213	C₂×C₁₉	#1500	1	1	yes	characteristic
214	C₂×C₁₉	#1501	1	1	yes	characteristic
215	C₂×C₁₉	#1504	1	1	yes	characteristic
216	C₂×C₁₉	#1509	1	1	yes	characteristic
217	C₂×C₁₉	#1989	1	1	yes	characteristic
218	C₂×C₁₉	#1994	1	1	yes	characteristic
219	C₂×C₁₉	#1996	1	1	yes	characteristic
220	C₂³×C₄	—	2	2	no	—
221	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
222	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
223	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
224	C₂²×C₈	—	2	2	no	—
225	#125	—	4	2	no	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄⋊C₄	—	2	1	no	—
228	C₂×C₄⋊C₄	—	2	1	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
234	C₂×C₂²⋊C₄	—	2	1	no	—
235	C₂×C₂²⋊C₄	—	2	1	no	—
236	C₂×C₄²	—	2	4	no	—
237	C₂×C₄²	—	4	2	no	—
238	C₂×C₄²	—	4	2	no	—
239	C₂×C₄²	—	4	2	no	—
240	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
241	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
242	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
243	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
244	C₄⋊C₈	—	4	2	no	—
245	C₂²⋊C₈	—	2	4	no	—
246	#95	—	2	4	no	—
247	#95	—	2	1	no	—
248	#95	—	2	1	no	—
249	#95	—	2	1	no	—
250	#95	—	2	1	no	—
251	#95	—	2	1	no	—
252	#95	—	2	1	no	—
253	#95	—	2	2	no	—
254	#95	Q₈×C₁₉	1	4	yes	—
255	C₁₉	#9910	1	1	yes	characteristic, direct product factor, Sylow
256	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
278	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
279	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
284	C₂²×C₄	#41×C₁₉	1	2	yes	—
285	C₂×C₈	—	4	2	no	—
286	C₂×C₈	—	4	2	no	—
287	C₂×C₈	—	4	2	no	—
288	C₄⋊C₄	—	4	1	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₄⋊C₄	—	4	1	no	—
292	C₄⋊C₄	—	4	2	no	—
293	C₄⋊C₄	—	4	2	no	—
294	C₄⋊C₄	—	4	2	no	—
295	C₄⋊C₄	—	4	2	no	—
296	C₂²⋊C₄	—	4	2	no	—
297	C₂²⋊C₄	—	4	1	no	—
298	C₂²⋊C₄	—	4	1	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	4	1	no	—
302	C₄²	—	4	1	no	—
303	C₄²	—	4	8	no	—
304	C₂³	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
309	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
310	C₂³	C₁₉×#135	1	2	yes	—
311	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
312	C₂³	C₁₉×#137	1	1	yes	characteristic
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	C₁₉×#99	1	2	yes	—
351	C₂×C₄	C₁₉×#104	1	2	yes	—
352	C₂×C₄	C₁₉×#104	1	2	yes	—
353	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
354	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
355	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
356	C₈	—	8	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	C₁₉×#391	1	1	yes	characteristic
366	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
367	C₂²	C₁₉×#410	1	1	yes	characteristic
368	C₂²	C₁₉×#416	1	1	yes	characteristic
369	C₂²	C₁₉×#417	1	1	yes	characteristic
370	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
371	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
372	C₂²	C₁₉×#478	1	2	yes	—
373	C₂²	C₁₉×#479	1	2	yes	—
374	C₄	—	2	1	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	4	8	no	—
381	C₄	—	4	1	no	—
382	C₄	—	8	1	no	—
383	C₄	—	8	1	no	—
384	C₄	—	8	1	no	—
385	C₄	—	8	1	no	—
386	C₂	—	2	2	no	—
387	C₂	—	2	2	no	—
388	C₂	C₁₉×#1500	1	1	yes	characteristic
389	C₂	C₁₉×#1501	1	1	yes	characteristic
390	C₂	C₁₉×#1504	1	1	yes	characteristic
391	C₂	C₁₉×#1509	1	1	yes	characteristic
392	C₂	C₁₉×#1989	1	1	yes	characteristic
393	C₂	C₁₉×#1994	1	1	yes	characteristic
394	C₂	C₁₉×#1996	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ 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
6. C₂×C₁₉×#125	C₄	semidirect
11. C₁₉×#389	C₄	semidirect
12. C₁₉×#389	C₄	semidirect
17. C₁₉×#382	C₄	semidirect
106. #9910	C₁₉	direct (N × H)
194. C₂×#125	C₄×C₁₉	semidirect
199. #389	C₄×C₁₉	semidirect
200. #389	C₄×C₁₉	semidirect
205. #382	C₄×C₁₉	semidirect
255. C₁₉	#9910	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×#2851	2
C₁₉×#1797	2
C₄×C₁₉×#95	2
C₁₉×#1294	2
#9910	19

Subgroups — C19×#9910 #18015869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9910 #18015869