Subgroups — C₁₉×#18528 #18024487

Order 4864.

1060 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3481	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3152	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3079	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1632	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1630	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1629	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1560	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1489	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×#137	—	2	2	no	—
10	C₁₉×#559	C₂²	1	1	yes	characteristic
11	C₁₉×#554	C₂²	1	2	yes	—
12	C₁₉×#553	—	2	2	no	—
13	C₁₉×#551	—	2	2	no	—
14	C₁₉×#546	—	2	2	no	—
15	D₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#532	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#529	—	2	2	no	—
19	C₁₉×#525	—	2	2	no	—
20	C₄×#41×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₉	—	2	2	no	—
22	C₁₉×#497	—	2	2	no	—
23	C₁₉×#494	C₂²	1	2	yes	complemented
24	C₁₉×#492	C₂²	1	2	yes	—
25	C₁₉×#477	C₂²	1	4	yes	complemented
26	C₁₉×#476	C₂²	1	4	yes	—
27	C₁₉×#475	—	2	2	no	—
28	C₁₉×#474	—	2	2	no	—
29	C₁₉×#428	—	2	2	no	—
30	C₁₉×#423	C₂²	1	2	yes	complemented
31	C₁₉×#417	—	2	2	no	—
32	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#333	C₂²	1	2	yes	complemented
34	C₁₉×#331	C₂²	1	2	yes	—
35	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	complemented
36	C₁₉×D₄⋊C₈	C₂²	1	4	yes	—
37	C₂×#41×C₁₉	D₄	1	2	yes	—
38	C₂×#41×C₁₉	D₄	1	2	yes	—
39	C₂²×Q₈×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	—	2	2	no	—
41	C₂³×C₄×C₁₉	—	2	2	no	—
42	C₁₉×#137	—	4	8	no	—
43	C₂×Q₁₆×C₁₉	—	2	4	no	—
44	C₂×SD₁₆×C₁₉	—	2	4	no	—
45	C₂×M₁₆×C₁₉	—	2	1	no	—
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₁₉×C₄⋊Q₈	—	2	2	no	—
48	C₁₉×C₄⋊Q₈	—	2	1	no	—
49	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
50	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
51	C₁₉×#127	C₂³	1	1	yes	characteristic
52	C₁₉×#126	—	2	4	no	—
53	C₁₉×#125	—	2	2	no	—
54	C₁₉×#124	—	2	2	no	—
55	C₁₉×#124	D₄	1	2	yes	—
56	C₁₉×#123	—	2	2	no	—
57	C₁₉×#123	—	2	4	no	—
58	C₁₉×#123	—	2	2	no	—
59	C₁₉×C₂²⋊Q₈	—	2	4	no	—
60	C₁₉×C₂²⋊Q₈	—	2	2	no	—
61	C₁₉×#121	—	2	4	no	—
62	C₁₉×#121	—	2	2	no	—
63	C₁₉×#121	—	2	2	no	—
64	C₁₉×#120	—	2	2	no	—
65	C₁₉×#120	—	2	2	no	—
66	C₄×Q₈×C₁₉	D₄	1	2	yes	—
67	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
68	C₄×D₄×C₁₉	—	2	4	no	—
69	C₄×D₄×C₁₉	—	2	4	no	—
70	C₄×D₄×C₁₉	—	2	2	no	—
71	C₄×D₄×C₁₉	—	2	2	no	—
72	C₄×D₄×C₁₉	—	2	2	no	—
73	C₄×D₄×C₁₉	—	2	2	no	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₄×D₄×C₁₉	D₄	1	2	yes	—
76	C₄×D₄×C₁₉	C₂³	1	2	yes	—
77	C₁₉×#117	—	2	2	no	—
78	C₁₉×#117	—	2	2	no	—
79	C₁₉×#117	D₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
83	C₂×C₄²×C₁₉	—	2	2	no	—
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₁₉×#107	—	2	4	no	—
86	C₁₉×#106	—	2	4	no	—
87	C₁₉×C₄⋊C₈	—	2	2	no	—
88	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
89	C₁₉×#103	—	2	4	no	—
90	C₁₉×#102	—	2	4	no	—
91	C₁₉×#97	—	2	1	no	—
92	C₄×C₈×C₁₉	C₂³	1	2	yes	—
93	C₂⁴×C₁₉	—	2	2	no	—
94	#41×C₁₉	—	2	4	no	—
95	#41×C₁₉	—	4	2	no	—
96	#41×C₁₉	—	4	4	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	4	4	no	—
99	C₂×Q₈×C₁₉	—	4	1	no	—
100	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
101	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	4	4	no	—
107	C₂×D₄×C₁₉	—	4	4	no	—
108	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	—	2	4	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	4	1	no	—
117	C₂²×C₄×C₁₉	—	8	4	no	—
118	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	Q₁₆×C₁₉	—	4	8	no	—
121	SD₁₆×C₁₉	—	4	8	no	—
122	M₁₆×C₁₉	—	2	4	no	—
123	M₁₆×C₁₉	—	4	4	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	4	no	—
126	C₄⋊C₄×C₁₉	—	2	4	no	—
127	C₄⋊C₄×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	4	no	—
132	C₄⋊C₄×C₁₉	—	4	2	no	—
133	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
134	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
135	C₂²⋊C₄×C₁₉	—	2	4	no	—
136	C₂²⋊C₄×C₁₉	—	2	4	no	—
137	C₂²⋊C₄×C₁₉	—	2	2	no	—
138	C₂²⋊C₄×C₁₉	—	2	2	no	—
139	C₂²⋊C₄×C₁₉	—	2	2	no	—
140	C₂²⋊C₄×C₁₉	—	2	2	no	—
141	C₂²⋊C₄×C₁₉	—	2	4	no	—
142	C₂²⋊C₄×C₁₉	—	2	2	no	—
143	C₄²×C₁₉	—	2	2	no	—
144	C₄²×C₁₉	—	2	2	no	—
145	C₄²×C₁₉	—	2	2	no	—
146	C₄²×C₁₉	C₂×D₄	1	2	yes	—
147	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
149	#18528	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₁₉	—	2	2	no	—
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	4	8	no	—
153	C₂³×C₁₉	—	8	2	no	—
154	C₂³×C₁₉	#120	1	1	yes	characteristic
155	Q₈×C₁₉	—	2	2	no	—
156	Q₈×C₁₉	—	2	2	no	—
157	Q₈×C₁₉	—	4	2	no	—
158	Q₈×C₁₉	—	4	4	no	—
159	Q₈×C₁₉	—	8	2	no	—
160	D₄×C₁₉	—	2	2	no	—
161	D₄×C₁₉	—	4	2	no	—
162	D₄×C₁₉	—	4	4	no	—
163	D₄×C₁₉	—	4	8	no	—
164	D₄×C₁₉	—	4	2	no	—
165	D₄×C₁₉	—	4	2	no	—
166	D₄×C₁₉	—	8	2	no	—
167	D₄×C₁₉	#137	1	4	yes	complemented
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	4	no	—
179	C₂×C₄×C₁₉	—	4	4	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	8	2	no	—
182	C₂×C₄×C₁₉	—	8	4	no	—
183	C₂×C₄×C₁₉	—	8	2	no	—
184	C₂×C₄×C₁₉	#120	1	2	yes	—
185	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
188	C₈×C₁₉	—	2	4	no	—
189	C₈×C₁₉	—	4	4	no	—
190	#3481	C₂×C₁₉	1	1	yes	characteristic
191	#3152	C₂×C₁₉	1	1	yes	characteristic, complemented
192	#3079	C₂×C₁₉	1	2	yes	complemented
193	#1632	C₂×C₁₉	1	4	yes	complemented
194	#1630	C₂×C₁₉	1	2	yes	complemented
195	#1629	C₂×C₁₉	1	2	yes	complemented
196	#1560	C₂×C₁₉	1	1	yes	characteristic, complemented
197	#1489	C₂×C₁₉	1	2	yes	complemented
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	4	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	4	2	no	—
202	C₂²×C₁₉	—	4	2	no	—
203	C₂²×C₁₉	—	4	4	no	—
204	C₂²×C₁₉	—	4	2	no	—
205	C₂²×C₁₉	—	8	8	no	—
206	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
207	C₄×C₁₉	—	2	2	no	—
208	C₄×C₁₉	—	2	1	no	—
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	—	4	2	no	—
211	C₄×C₁₉	—	4	2	no	—
212	C₄×C₁₉	—	4	2	no	—
213	C₄×C₁₉	—	8	2	no	—
214	C₄×C₁₉	#453	1	2	yes	—
215	C₄×C₁₉	C₂×#137	1	2	yes	—
216	C₄×C₁₉	#575	1	2	yes	—
217	C₂×#137	—	2	2	no	—
218	#559	C₂²×C₁₉	1	1	yes	characteristic
219	#554	C₂²×C₁₉	1	2	yes	—
220	#553	—	2	2	no	—
221	#551	—	2	2	no	—
222	#546	—	2	2	no	—
223	D₄²	C₂²×C₁₉	1	1	yes	characteristic
224	#532	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
226	#529	—	2	2	no	—
227	#525	—	2	2	no	—
228	C₄×#41	C₂²×C₁₉	1	2	yes	—
229	C₂×C₄×D₄	—	2	2	no	—
230	#497	—	2	2	no	—
231	#494	C₂²×C₁₉	1	2	yes	complemented
232	#492	C₂²×C₁₉	1	2	yes	—
233	#477	C₂²×C₁₉	1	4	yes	complemented
234	#476	C₂²×C₁₉	1	4	yes	—
235	#475	—	2	2	no	—
236	#474	—	2	2	no	—
237	#428	—	2	2	no	—
238	#423	C₂²×C₁₉	1	2	yes	complemented
239	#417	—	2	2	no	—
240	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
241	#333	C₂²×C₁₉	1	2	yes	complemented
242	#331	C₂²×C₁₉	1	2	yes	—
243	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	complemented
244	D₄⋊C₈	C₂²×C₁₉	1	4	yes	—
245	C₂×C₁₉	—	4	1	no	—
246	C₂×C₁₉	—	4	4	no	—
247	C₂×C₁₉	—	8	2	no	—
248	C₂×C₁₉	#3007	1	2	yes	—
249	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
250	C₂×#41	D₄×C₁₉	1	2	yes	—
251	C₂×#41	D₄×C₁₉	1	2	yes	—
252	C₂²×Q₈	—	2	1	no	—
253	C₂²×D₄	—	2	2	no	—
254	C₂³×C₄	—	2	2	no	—
255	#137	—	4	8	no	—
256	C₂×Q₁₆	—	2	4	no	—
257	C₂×SD₁₆	—	2	4	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₄⋊Q₈	—	2	2	no	—
261	C₄⋊Q₈	—	2	1	no	—
262	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
263	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
264	#127	C₂³×C₁₉	1	1	yes	characteristic
265	#126	—	2	4	no	—
266	#125	—	2	2	no	—
267	#124	—	2	2	no	—
268	#124	D₄×C₁₉	1	2	yes	—
269	#123	—	2	2	no	—
270	#123	—	2	4	no	—
271	#123	—	2	2	no	—
272	C₂²⋊Q₈	—	2	4	no	—
273	C₂²⋊Q₈	—	2	2	no	—
274	#121	—	2	4	no	—
275	#121	—	2	2	no	—
276	#121	—	2	2	no	—
277	#120	—	2	2	no	—
278	#120	—	2	2	no	—
279	C₄×Q₈	D₄×C₁₉	1	2	yes	—
280	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	—	2	4	no	—
283	C₄×D₄	—	2	2	no	—
284	C₄×D₄	—	2	2	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	D₄×C₁₉	1	2	yes	—
289	C₄×D₄	C₂³×C₁₉	1	2	yes	—
290	#117	—	2	2	no	—
291	#117	—	2	2	no	—
292	#117	D₄×C₁₉	1	2	yes	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	4	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
298	#107	—	2	4	no	—
299	#106	—	2	4	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
302	#103	—	2	4	no	—
303	#102	—	2	4	no	—
304	#97	—	2	1	no	—
305	C₄×C₈	C₂³×C₁₉	1	2	yes	—
306	C₁₉	#18528	1	1	yes	characteristic, direct product factor, Sylow
307	C₂⁴	—	2	2	no	—
308	#41	—	2	4	no	—
309	#41	—	4	2	no	—
310	#41	—	4	4	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	4	4	no	—
313	C₂×Q₈	—	4	1	no	—
314	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
315	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	4	4	no	—
322	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
323	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	8	4	no	—
332	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
334	Q₁₆	—	4	8	no	—
335	SD₁₆	—	4	8	no	—
336	M₁₆	—	2	4	no	—
337	M₁₆	—	4	4	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	4	no	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
348	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	2	4	no	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₄²	C₂×D₄×C₁₉	1	2	yes	—
362	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
363	C₂³	—	2	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	4	8	no	—
366	C₂³	—	8	2	no	—
367	C₂³	C₁₉×#120	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	4	no	—
372	Q₈	—	8	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	4	no	—
376	D₄	—	4	8	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	8	2	no	—
380	D₄	C₁₉×#137	1	4	yes	complemented
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	—	8	4	no	—
396	C₂×C₄	—	8	2	no	—
397	C₂×C₄	C₁₉×#120	1	2	yes	—
398	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
401	C₈	—	2	4	no	—
402	C₈	—	4	4	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	8	8	no	—
411	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	8	2	no	—
419	C₄	C₁₉×#453	1	2	yes	—
420	C₄	C₂×C₁₉×#137	1	2	yes	—
421	C₄	C₁₉×#575	1	2	yes	—
422	C₂	—	4	1	no	—
423	C₂	—	4	4	no	—
424	C₂	—	8	2	no	—
425	C₂	C₁₉×#3007	1	2	yes	—
426	C₂	C₂×C₁₉×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3481	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3152	C₂	semidirect
3. C₁₉×#3079	C₂	semidirect
4. C₁₉×#1632	C₂	semidirect
5. C₁₉×#1630	C₂	semidirect
6. C₁₉×#1629	C₂	semidirect
7. C₁₉×#1560	C₂	semidirect
8. C₁₉×#1489	C₂	semidirect
17. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
23. C₁₉×#494	C₂²	semidirect
25. C₁₉×#477	C₂²	semidirect
30. C₁₉×#423	C₂²	semidirect
32. C₄×M₁₆×C₁₉	C₂²	semidirect
33. C₁₉×#333	C₂²	semidirect
35. C₁₉×Q₈⋊C₈	C₂²	semidirect
149. #18528	C₁₉	direct (N × H)
167. D₄×C₁₉	#137	semidirect
191. #3152	C₂×C₁₉	semidirect
192. #3079	C₂×C₁₉	semidirect
193. #1632	C₂×C₁₉	semidirect
194. #1630	C₂×C₁₉	semidirect
195. #1629	C₂×C₁₉	semidirect
196. #1560	C₂×C₁₉	semidirect
197. #1489	C₂×C₁₉	semidirect
225. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
231. #494	C₂²×C₁₉	semidirect
233. #477	C₂²×C₁₉	semidirect
238. #423	C₂²×C₁₉	semidirect
240. C₄×M₁₆	C₂²×C₁₉	semidirect
241. #333	C₂²×C₁₉	semidirect
243. Q₈⋊C₈	C₂²×C₁₉	semidirect
306. C₁₉	#18528	direct (N × H)
380. D₄	C₁₉×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3481	2
C₁₉×#3152	2
C₁₉×#3079	2
C₁₉×#1632	2
C₁₉×#1630	2
C₁₉×#1629	2
C₁₉×#1560	2
C₁₉×#1489	2
#18528	19

Subgroups — C19×#18528 #18024487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18528 #18024487