Subgroups — C₁₉×#19477 #18025436

Order 4864.

598 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3226	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3112	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#477	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2984	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1698	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1696	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1678	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1676	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1573	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1558	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1551	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#532	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#500	C₂²	1	2	yes	—
16	C₁₉×#486	C₂²	1	2	yes	—
17	C₁₉×#480	—	2	1	no	—
18	C₁₉×#480	—	2	1	no	—
19	C₁₉×#480	—	2	1	no	—
20	C₁₉×#477	—	2	1	no	—
21	C₁₉×#477	—	2	1	no	—
22	C₁₉×#477	C₂²	1	1	yes	characteristic
23	C₁₉×#477	C₂²	1	2	yes	—
24	C₁₉×#477	C₂²	1	1	yes	characteristic
25	C₁₉×#477	C₂²	1	2	yes	—
26	C₁₉×#474	—	2	2	no	—
27	C₁₉×#460	C₂²	1	1	yes	characteristic
28	C₁₉×#460	C₂²	1	1	yes	characteristic
29	C₁₉×#448	—	2	1	no	—
30	C₁₉×#446	—	2	2	no	—
31	C₁₉×#446	C₂²	1	2	yes	—
32	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
33	C₁₉×#440	—	2	1	no	—
34	C₁₉×#440	—	2	1	no	—
35	C₁₉×#432	—	2	1	no	—
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#431	—	2	1	no	—
39	C₁₉×#431	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#107	—	2	1	no	—
41	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#103	—	2	1	no	—
43	C₁₉×#335	C₂²	1	2	yes	—
44	C₁₉×#334	C₂²	1	2	yes	—
45	C₁₉×#333	C₂²	1	2	yes	—
46	C₁₉×#333	C₂²	1	2	yes	—
47	C₁₉×#333	C₂²	1	2	yes	—
48	C₁₉×#331	C₂²	1	2	yes	—
49	C₂×#41×C₁₉	—	2	1	no	—
50	C₂²×Q₈×C₁₉	—	2	1	no	—
51	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
52	C₂×SD₁₆×C₁₉	—	2	1	no	—
53	C₂×SD₁₆×C₁₉	—	2	1	no	—
54	C₂²×C₈×C₁₉	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₉×#127	C₂³	1	1	yes	characteristic
61	C₁₉×#124	—	2	1	no	—
62	C₁₉×#121	—	2	1	no	—
63	C₁₉×#121	—	2	1	no	—
64	C₄×Q₈×C₁₉	—	2	1	no	—
65	C₄×Q₈×C₁₉	—	2	1	no	—
66	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
67	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₄×D₄×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₉	—	2	1	no	—
77	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
78	C₁₉×#107	—	2	2	no	—
79	C₁₉×#107	—	2	2	no	—
80	C₁₉×#107	—	2	2	no	—
81	C₁₉×#107	—	2	2	no	—
82	C₁₉×#107	—	2	1	no	—
83	C₁₉×#107	—	2	1	no	—
84	C₁₉×C₄⋊C₈	—	2	2	no	—
85	C₁₉×C₄⋊C₈	—	2	2	no	—
86	C₁₉×C₄⋊C₈	—	2	1	no	—
87	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
88	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
89	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
90	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
92	C₁₉×#103	—	2	2	no	—
93	C₁₉×#103	—	2	2	no	—
94	C₁₉×#103	—	2	1	no	—
95	C₁₉×#103	—	2	1	no	—
96	C₁₉×#102	—	2	2	no	—
97	C₁₉×#102	—	2	2	no	—
98	C₁₉×#102	—	2	1	no	—
99	C₁₉×#102	—	2	1	no	—
100	C₁₉×C₂²⋊C₈	—	2	1	no	—
101	C₁₉×C₂²⋊C₈	—	2	1	no	—
102	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
103	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
104	C₁₉×#97	—	2	2	no	—
105	C₁₉×#97	—	2	1	no	—
106	C₁₉×#97	—	2	1	no	—
107	C₄×C₈×C₁₉	—	2	2	no	—
108	C₄×C₈×C₁₉	C₂³	1	2	yes	—
109	#41×C₁₉	—	8	2	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×Q₈×C₁₉	—	4	1	no	—
115	C₂×Q₈×C₁₉	—	4	1	no	—
116	C₂×Q₈×C₁₉	—	8	2	no	—
117	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂×D₄×C₁₉	—	2	1	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	4	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	4	1	no	—
126	C₂²×C₄×C₁₉	—	4	1	no	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
130	SD₁₆×C₁₉	—	4	2	no	—
131	SD₁₆×C₁₉	—	4	2	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	—	2	1	no	—
134	C₂×C₈×C₁₉	—	2	1	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	4	2	no	—
137	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	4	1	no	—
149	C₄⋊C₄×C₁₉	—	4	1	no	—
150	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²⋊C₄×C₁₉	—	4	1	no	—
153	C₂²⋊C₄×C₁₉	—	4	1	no	—
154	C₄²×C₁₉	—	2	1	no	—
155	C₄²×C₁₉	—	2	1	no	—
156	C₄²×C₁₉	—	2	1	no	—
157	C₄²×C₁₉	—	2	1	no	—
158	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₉	#41	1	1	yes	characteristic
161	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
162	#19477	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂³×C₁₉	—	4	1	no	—
164	C₂³×C₁₉	#121	1	1	yes	characteristic
165	Q₈×C₁₉	—	2	1	no	—
166	Q₈×C₁₉	—	2	1	no	—
167	Q₈×C₁₉	—	2	1	no	—
168	Q₈×C₁₉	—	4	2	no	—
169	Q₈×C₁₉	—	8	2	no	—
170	Q₈×C₁₉	—	8	1	no	—
171	Q₈×C₁₉	—	8	2	no	—
172	Q₈×C₁₉	#137	1	2	yes	—
173	D₄×C₁₉	—	4	1	no	—
174	D₄×C₁₉	—	4	1	no	—
175	D₄×C₁₉	—	4	2	no	—
176	D₄×C₁₉	—	8	1	no	—
177	D₄×C₁₉	—	8	2	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	2	1	no	—
185	C₂×C₄×C₁₉	—	2	1	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	8	2	no	—
191	C₂×C₄×C₁₉	—	8	2	no	—
192	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
198	C₈×C₁₉	—	2	2	no	—
199	C₈×C₁₉	—	2	2	no	—
200	C₈×C₁₉	—	4	1	no	—
201	C₈×C₁₉	—	4	2	no	—
202	C₈×C₁₉	—	4	1	no	—
203	C₈×C₁₉	—	4	2	no	—
204	#3226	C₂×C₁₉	1	1	yes	characteristic
205	#3112	C₂×C₁₉	1	1	yes	characteristic
206	C₂×#477	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#2984	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#1698	C₂×C₁₉	1	2	yes	complemented
209	#1696	C₂×C₁₉	1	2	yes	complemented
210	#1678	C₂×C₁₉	1	2	yes	complemented
211	#1676	C₂×C₁₉	1	2	yes	complemented
212	#1573	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#1558	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#1551	C₂×C₁₉	1	1	yes	characteristic
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	8	1	no	—
218	C₂²×C₁₉	—	8	1	no	—
219	C₂²×C₁₉	—	8	1	no	—
220	C₂²×C₁₉	#472	1	2	yes	—
221	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	2	no	—
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	4	1	no	—
228	C₄×C₁₉	—	4	1	no	—
229	C₄×C₁₉	—	4	1	no	—
230	C₄×C₁₉	—	8	1	no	—
231	C₄×C₁₉	—	8	2	no	—
232	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
233	C₄×C₁₉	#575	1	1	yes	characteristic
234	C₄×C₁₉	#578	1	2	yes	—
235	#532	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
238	#500	C₂²×C₁₉	1	2	yes	—
239	#486	C₂²×C₁₉	1	2	yes	—
240	#480	—	2	1	no	—
241	#480	—	2	1	no	—
242	#480	—	2	1	no	—
243	#477	—	2	1	no	—
244	#477	—	2	1	no	—
245	#477	C₂²×C₁₉	1	2	yes	—
246	#477	C₂²×C₁₉	1	2	yes	—
247	#477	C₂²×C₁₉	1	1	yes	characteristic
248	#477	C₂²×C₁₉	1	1	yes	characteristic
249	#474	—	2	2	no	—
250	#460	C₂²×C₁₉	1	1	yes	characteristic
251	#460	C₂²×C₁₉	1	1	yes	characteristic
252	#448	—	2	1	no	—
253	#446	—	2	2	no	—
254	#446	C₂²×C₁₉	1	2	yes	—
255	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
256	#440	—	2	1	no	—
257	#440	—	2	1	no	—
258	#432	—	2	1	no	—
259	#432	C₂²×C₁₉	1	1	yes	characteristic
260	#432	C₂²×C₁₉	1	1	yes	characteristic
261	#431	—	2	1	no	—
262	#431	C₂²×C₁₉	1	1	yes	characteristic
263	C₂×#107	—	2	1	no	—
264	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×#103	—	2	1	no	—
266	#335	C₂²×C₁₉	1	2	yes	—
267	#334	C₂²×C₁₉	1	2	yes	—
268	#333	C₂²×C₁₉	1	2	yes	—
269	#333	C₂²×C₁₉	1	2	yes	—
270	#333	C₂²×C₁₉	1	2	yes	—
271	#331	C₂²×C₁₉	1	2	yes	—
272	C₂×C₁₉	—	2	2	no	—
273	C₂×C₁₉	—	16	1	no	—
274	C₂×C₁₉	#3044	1	1	yes	characteristic
275	C₂×C₁₉	#3056	1	1	yes	characteristic
276	C₂×C₁₉	C₂×#472	1	1	yes	characteristic
277	C₂×#41	—	2	1	no	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
280	C₂×SD₁₆	—	2	1	no	—
281	C₂×SD₁₆	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
287	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
288	#127	C₂³×C₁₉	1	1	yes	characteristic
289	#124	—	2	1	no	—
290	#121	—	2	1	no	—
291	#121	—	2	1	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
295	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
296	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
297	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
306	#107	—	2	2	no	—
307	#107	—	2	2	no	—
308	#107	—	2	2	no	—
309	#107	—	2	2	no	—
310	#107	—	2	1	no	—
311	#107	—	2	1	no	—
312	C₄⋊C₈	—	2	2	no	—
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
316	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
317	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
318	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
319	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
320	#103	—	2	2	no	—
321	#103	—	2	2	no	—
322	#103	—	2	1	no	—
323	#103	—	2	1	no	—
324	#102	—	2	2	no	—
325	#102	—	2	2	no	—
326	#102	—	2	1	no	—
327	#102	—	2	1	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	—	2	1	no	—
330	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
331	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
332	#97	—	2	2	no	—
333	#97	—	2	1	no	—
334	#97	—	2	1	no	—
335	C₄×C₈	—	2	2	no	—
336	C₄×C₈	C₂³×C₁₉	1	2	yes	—
337	C₁₉	#19477	1	1	yes	characteristic, direct product factor, Sylow
338	#41	—	8	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	4	1	no	—
344	C₂×Q₈	—	4	1	no	—
345	C₂×Q₈	—	8	2	no	—
346	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
347	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	4	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
359	SD₁₆	—	4	2	no	—
360	SD₁₆	—	4	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	4	2	no	—
366	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
367	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
380	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₂²⋊C₄	—	4	1	no	—
382	C₂²⋊C₄	—	4	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
388	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₄²	#41×C₁₉	1	1	yes	characteristic
390	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
391	C₂³	—	4	1	no	—
392	C₂³	C₁₉×#121	1	1	yes	characteristic
393	Q₈	—	2	1	no	—
394	Q₈	—	2	1	no	—
395	Q₈	—	2	1	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	8	2	no	—
398	Q₈	—	8	1	no	—
399	Q₈	—	8	2	no	—
400	Q₈	C₁₉×#137	1	2	yes	—
401	D₄	—	4	1	no	—
402	D₄	—	4	1	no	—
403	D₄	—	4	2	no	—
404	D₄	—	8	1	no	—
405	D₄	—	8	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	—	8	2	no	—
420	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
421	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
422	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	2	2	no	—
428	C₈	—	4	1	no	—
429	C₈	—	4	2	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	2	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	8	1	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	C₁₉×#472	1	2	yes	—
438	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	4	1	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	1	no	—
447	C₄	—	8	1	no	—
448	C₄	—	8	2	no	—
449	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
450	C₄	C₁₉×#575	1	1	yes	characteristic
451	C₄	C₁₉×#578	1	2	yes	—
452	C₂	—	2	2	no	—
453	C₂	—	16	1	no	—
454	C₂	C₁₉×#3044	1	1	yes	characteristic
455	C₂	C₁₉×#3056	1	1	yes	characteristic
456	C₂	C₂×C₁₉×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#532	C₂²
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
3. C₂×C₁₉×#477	C₂	semidirect
4. C₁₉×#2984	C₂	semidirect
5. C₁₉×#1698	C₂	semidirect
6. C₁₉×#1696	C₂	semidirect
7. C₁₉×#1678	C₂	semidirect
8. C₁₉×#1676	C₂	semidirect
9. C₁₉×#1573	C₂	semidirect
10. C₁₉×#1558	C₂	semidirect
162. #19477	C₁₉	direct (N × H)
206. C₂×#477	C₂×C₁₉	semidirect
207. #2984	C₂×C₁₉	semidirect
208. #1698	C₂×C₁₉	semidirect
209. #1696	C₂×C₁₉	semidirect
210. #1678	C₂×C₁₉	semidirect
211. #1676	C₂×C₁₉	semidirect
212. #1573	C₂×C₁₉	semidirect
213. #1558	C₂×C₁₉	semidirect
337. C₁₉	#19477	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×#3226	2
C₁₉×#3112	2
C₂×C₁₉×#477	2
C₁₉×#2984	2
C₁₉×#1698	2
C₁₉×#1696	2
C₁₉×#1678	2
C₁₉×#1676	2
C₁₉×#1573	2
C₁₉×#1558	2
C₁₉×#1551	2
#19477	19

Subgroups — C19×#19477 #18025436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19477 #18025436