Subgroups — C₁₉×#19525 #18025484

Order 4864.

596 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3207	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1704	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1688	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1678	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1666	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1570	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1557	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1551	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₁₉×#532	C₂²	1	1	yes	characteristic
15	C₁₉×#493	C₂²	1	1	yes	characteristic
16	C₁₉×#492	C₂²	1	1	yes	characteristic
17	C₁₉×#487	C₂²	1	1	yes	characteristic
18	C₁₉×#486	C₂²	1	1	yes	characteristic
19	C₁₉×#477	C₂²	1	2	yes	—
20	C₁₉×#476	—	2	1	no	—
21	C₁₉×#475	C₂²	1	2	yes	—
22	C₁₉×#474	—	2	1	no	—
23	C₁₉×#468	—	2	2	no	—
24	C₁₉×#465	—	2	2	no	—
25	C₁₉×#463	—	2	2	no	—
26	C₁₉×#461	—	2	1	no	—
27	C₁₉×#461	—	2	1	no	—
28	C₁₉×#460	C₂²	1	2	yes	—
29	C₁₉×#460	C₂²	1	2	yes	—
30	C₁₉×#449	—	2	2	no	—
31	C₁₉×#446	—	2	2	no	—
32	C₁₉×#446	C₂²	1	2	yes	—
33	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#433	—	2	2	no	—
35	C₁₉×#432	C₂²	1	1	yes	characteristic
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#423	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₉×#334	C₂²	1	2	yes	—
40	C₁₉×#334	C₂²	1	2	yes	—
41	C₁₉×#333	C₂²	1	2	yes	—
42	C₁₉×#332	C₂²	1	2	yes	—
43	C₁₉×#331	C₂²	1	2	yes	—
44	C₁₉×#331	C₂²	1	2	yes	—
45	C₂×#41×C₁₉	—	2	1	no	—
46	C₂×#41×C₁₉	—	2	1	no	—
47	C₂×SD₁₆×C₁₉	—	2	2	no	—
48	C₂×SD₁₆×C₁₉	—	2	2	no	—
49	C₂×SD₁₆×C₁₉	—	2	2	no	—
50	C₂×D₈×C₁₉	—	2	2	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂²×C₈×C₁₉	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
54	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
55	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
57	C₁₉×#127	C₂³	1	1	yes	characteristic
58	C₁₉×#127	C₂³	1	1	yes	characteristic
59	C₁₉×#125	—	2	1	no	—
60	C₁₉×#124	—	2	1	no	—
61	C₁₉×#124	—	2	1	no	—
62	C₁₉×C₂²⋊Q₈	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
64	C₁₉×#121	—	2	1	no	—
65	C₁₉×#121	—	2	1	no	—
66	C₁₉×#121	—	2	1	no	—
67	C₁₉×#121	—	2	1	no	—
68	C₄×Q₈×C₁₉	—	2	1	no	—
69	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
70	C₄×D₄×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	—	2	1	no	—
74	C₁₉×#117	—	2	1	no	—
75	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
76	C₁₉×#107	—	2	2	no	—
77	C₁₉×#106	—	2	2	no	—
78	C₁₉×C₄⋊C₈	—	2	2	no	—
79	C₁₉×C₄⋊C₈	—	2	2	no	—
80	C₁₉×C₄⋊C₈	—	2	1	no	—
81	C₁₉×C₄⋊C₈	—	2	1	no	—
82	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
83	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
85	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
86	C₁₉×#103	—	2	2	no	—
87	C₁₉×#103	—	2	2	no	—
88	C₁₉×#103	—	2	2	no	—
89	C₁₉×#102	—	2	2	no	—
90	C₁₉×#102	—	2	2	no	—
91	C₁₉×#102	—	2	2	no	—
92	C₁₉×C₂²⋊C₈	—	2	1	no	—
93	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
94	C₁₉×#97	—	2	2	no	—
95	C₁₉×#97	—	2	1	no	—
96	C₄×C₈×C₁₉	—	2	2	no	—
97	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
99	#41×C₁₉	—	8	2	no	—
100	#41×C₁₉	—	8	2	no	—
101	C₂×Q₈×C₁₉	—	2	1	no	—
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
105	C₂×D₄×C₁₉	—	2	1	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	4	1	no	—
112	C₂×D₄×C₁₉	—	4	1	no	—
113	C₂²×C₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	—	4	1	no	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
118	SD₁₆×C₁₉	—	8	2	no	—
119	SD₁₆×C₁₉	—	8	2	no	—
120	SD₁₆×C₁₉	—	8	2	no	—
121	D₈×C₁₉	—	8	2	no	—
122	M₁₆×C₁₉	—	8	1	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	8	1	no	—
127	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
139	C₂²⋊C₄×C₁₉	—	2	2	no	—
140	C₂²⋊C₄×C₁₉	—	4	1	no	—
141	C₂²⋊C₄×C₁₉	—	4	1	no	—
142	C₂²⋊C₄×C₁₉	—	4	1	no	—
143	C₂²⋊C₄×C₁₉	—	4	1	no	—
144	C₄²×C₁₉	—	2	2	no	—
145	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₁₉	#41	1	1	yes	characteristic
148	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
149	#19525	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	#121	1	1	yes	characteristic
153	Q₈×C₁₉	—	2	2	no	—
154	Q₈×C₁₉	—	2	2	no	—
155	Q₈×C₁₉	—	4	2	no	—
156	Q₈×C₁₉	—	8	1	no	—
157	Q₈×C₁₉	—	8	1	no	—
158	D₄×C₁₉	—	4	2	no	—
159	D₄×C₁₉	—	4	2	no	—
160	D₄×C₁₉	—	4	1	no	—
161	D₄×C₁₉	—	4	1	no	—
162	D₄×C₁₉	—	4	1	no	—
163	D₄×C₁₉	—	4	1	no	—
164	D₄×C₁₉	—	8	1	no	—
165	D₄×C₁₉	—	8	1	no	—
166	D₄×C₁₉	—	8	2	no	—
167	D₄×C₁₉	—	8	2	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	1	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	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	8	2	no	—
177	C₂×C₄×C₁₉	—	8	2	no	—
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
184	C₈×C₁₉	—	2	2	no	—
185	C₈×C₁₉	—	2	2	no	—
186	C₈×C₁₉	—	4	2	no	—
187	C₈×C₁₉	—	4	2	no	—
188	C₈×C₁₉	—	4	2	no	—
189	#3254	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#3246	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#3207	C₂×C₁₉	1	1	yes	characteristic
192	#2985	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#1704	C₂×C₁₉	1	2	yes	complemented
194	#1688	C₂×C₁₉	1	2	yes	complemented
195	#1678	C₂×C₁₉	1	2	yes	complemented
196	#1666	C₂×C₁₉	1	2	yes	complemented
197	#1570	C₂×C₁₉	1	1	yes	characteristic, complemented
198	#1557	C₂×C₁₉	1	1	yes	characteristic, complemented
199	#1551	C₂×C₁₉	1	1	yes	characteristic, complemented
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	—	8	1	no	—
204	C₂²×C₁₉	—	8	1	no	—
205	C₂²×C₁₉	—	8	1	no	—
206	C₂²×C₁₉	—	8	1	no	—
207	C₂²×C₁₉	—	8	1	no	—
208	C₂²×C₁₉	—	8	1	no	—
209	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
210	C₄×C₁₉	—	2	1	no	—
211	C₄×C₁₉	—	2	1	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	2	1	no	—
214	C₄×C₁₉	—	4	2	no	—
215	C₄×C₁₉	—	4	2	no	—
216	C₄×C₁₉	—	8	1	no	—
217	C₄×C₁₉	—	8	1	no	—
218	C₄×C₁₉	#577	1	2	yes	—
219	C₄×C₁₉	#577	1	1	yes	characteristic
220	C₄×C₁₉	#577	1	1	yes	characteristic
221	#533	C₂²×C₁₉	1	1	yes	characteristic
222	#532	C₂²×C₁₉	1	1	yes	characteristic
223	#532	C₂²×C₁₉	1	1	yes	characteristic
224	#493	C₂²×C₁₉	1	1	yes	characteristic
225	#492	C₂²×C₁₉	1	1	yes	characteristic
226	#487	C₂²×C₁₉	1	1	yes	characteristic
227	#486	C₂²×C₁₉	1	1	yes	characteristic
228	#477	C₂²×C₁₉	1	2	yes	—
229	#476	—	2	1	no	—
230	#475	C₂²×C₁₉	1	2	yes	—
231	#474	—	2	1	no	—
232	#468	—	2	2	no	—
233	#465	—	2	2	no	—
234	#463	—	2	2	no	—
235	#461	—	2	1	no	—
236	#461	—	2	1	no	—
237	#460	C₂²×C₁₉	1	2	yes	—
238	#460	C₂²×C₁₉	1	2	yes	—
239	#449	—	2	2	no	—
240	#446	—	2	2	no	—
241	#446	C₂²×C₁₉	1	2	yes	—
242	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
243	#433	—	2	2	no	—
244	#432	C₂²×C₁₉	1	1	yes	characteristic
245	#431	C₂²×C₁₉	1	1	yes	characteristic
246	#423	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
248	#334	C₂²×C₁₉	1	2	yes	—
249	#334	C₂²×C₁₉	1	2	yes	—
250	#333	C₂²×C₁₉	1	2	yes	—
251	#332	C₂²×C₁₉	1	2	yes	—
252	#331	C₂²×C₁₉	1	2	yes	—
253	#331	C₂²×C₁₉	1	2	yes	—
254	C₂×C₁₉	—	4	1	no	—
255	C₂×C₁₉	—	16	1	no	—
256	C₂×C₁₉	—	16	1	no	—
257	C₂×C₁₉	#3043	1	1	yes	characteristic
258	C₂×C₁₉	#3060	1	1	yes	characteristic
259	C₂×C₁₉	#3068	1	1	yes	characteristic
260	C₂×#41	—	2	1	no	—
261	C₂×#41	—	2	1	no	—
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×SD₁₆	—	2	2	no	—
265	C₂×D₈	—	2	2	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
269	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
270	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
271	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
272	#127	C₂³×C₁₉	1	1	yes	characteristic
273	#127	C₂³×C₁₉	1	1	yes	characteristic
274	#125	—	2	1	no	—
275	#124	—	2	1	no	—
276	#124	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
279	#121	—	2	1	no	—
280	#121	—	2	1	no	—
281	#121	—	2	1	no	—
282	#121	—	2	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	—	2	1	no	—
289	#117	—	2	1	no	—
290	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
291	#107	—	2	2	no	—
292	#106	—	2	2	no	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
298	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
299	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
300	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
301	#103	—	2	2	no	—
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	#102	—	2	2	no	—
305	#102	—	2	2	no	—
306	#102	—	2	2	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
309	#97	—	2	2	no	—
310	#97	—	2	1	no	—
311	C₄×C₈	—	2	2	no	—
312	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
313	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
314	C₁₉	#19525	1	1	yes	characteristic, direct product factor, Sylow
315	#41	—	8	2	no	—
316	#41	—	8	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
333	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
334	SD₁₆	—	8	2	no	—
335	SD₁₆	—	8	2	no	—
336	SD₁₆	—	8	2	no	—
337	D₈	—	8	2	no	—
338	M₁₆	—	8	1	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	8	1	no	—
343	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
344	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	4	1	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₄²	—	2	2	no	—
361	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
362	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
363	C₄²	#41×C₁₉	1	1	yes	characteristic
364	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	C₁₉×#121	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	8	1	no	—
372	Q₈	—	8	1	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	1	no	—
378	D₄	—	4	1	no	—
379	D₄	—	8	1	no	—
380	D₄	—	8	1	no	—
381	D₄	—	8	2	no	—
382	D₄	—	8	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
394	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
395	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
397	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
398	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
399	C₈	—	2	2	no	—
400	C₈	—	2	2	no	—
401	C₈	—	4	2	no	—
402	C₈	—	4	2	no	—
403	C₈	—	4	2	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	1	no	—
422	C₄	C₁₉×#577	1	2	yes	—
423	C₄	C₁₉×#577	1	1	yes	characteristic
424	C₄	C₁₉×#577	1	1	yes	characteristic
425	C₂	—	4	1	no	—
426	C₂	—	16	1	no	—
427	C₂	—	16	1	no	—
428	C₂	C₁₉×#3043	1	1	yes	characteristic
429	C₂	C₁₉×#3060	1	1	yes	characteristic
430	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3207	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
1. C₁₉×#3254	C₂	semidirect
2. C₁₉×#3246	C₂	semidirect
4. C₁₉×#2985	C₂	semidirect
5. C₁₉×#1704	C₂	semidirect
6. C₁₉×#1688	C₂	semidirect
7. C₁₉×#1678	C₂	semidirect
8. C₁₉×#1666	C₂	semidirect
9. C₁₉×#1570	C₂	semidirect
10. C₁₉×#1557	C₂	semidirect
11. C₁₉×#1551	C₂	semidirect
149. #19525	C₁₉	direct (N × H)
189. #3254	C₂×C₁₉	semidirect
190. #3246	C₂×C₁₉	semidirect
192. #2985	C₂×C₁₉	semidirect
193. #1704	C₂×C₁₉	semidirect
194. #1688	C₂×C₁₉	semidirect
195. #1678	C₂×C₁₉	semidirect
196. #1666	C₂×C₁₉	semidirect
197. #1570	C₂×C₁₉	semidirect
198. #1557	C₂×C₁₉	semidirect
199. #1551	C₂×C₁₉	semidirect
314. C₁₉	#19525	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×#3254	2
C₁₉×#3246	2
C₁₉×#3207	2
C₁₉×#2985	2
C₁₉×#1704	2
C₁₉×#1688	2
C₁₉×#1678	2
C₁₉×#1666	2
C₁₉×#1570	2
C₁₉×#1557	2
C₁₉×#1551	2
#19525	19

Subgroups — C19×#19525 #18025484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19525 #18025484