Subgroups — C₁₉×#19317 #18025276

Order 4864.

598 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3139	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3116	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3079	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2970	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1704	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1700	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1683	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1679	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1569	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1559	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#491	—	2	1	no	—
16	C₁₉×#491	—	2	1	no	—
17	C₁₉×#487	C₂²	1	2	yes	—
18	C₁₉×#487	C₂²	1	2	yes	—
19	C₁₉×#485	—	2	1	no	—
20	C₁₉×#477	—	2	1	no	—
21	C₁₉×#477	C₂²	1	1	yes	characteristic
22	C₁₉×#476	—	2	1	no	—
23	C₁₉×#476	C₂²	1	1	yes	characteristic
24	C₁₉×#475	C₂²	1	2	yes	—
25	C₁₉×#474	C₂²	1	2	yes	—
26	C₁₉×#462	C₂²	1	1	yes	characteristic
27	C₁₉×#461	C₂²	1	1	yes	characteristic
28	C₁₉×#452	—	2	1	no	—
29	C₁₉×#446	C₂²	1	2	yes	—
30	C₁₉×#441	—	2	1	no	—
31	C₁₉×#440	—	2	1	no	—
32	C₁₉×#435	—	2	2	no	—
33	C₈×D₄×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#432	—	2	1	no	—
35	C₁₉×#432	C₂²	1	1	yes	characteristic
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#428	—	2	1	no	—
38	C₁₉×#423	C₂²	1	1	yes	characteristic
39	C₁₉×#419	—	2	2	no	—
40	C₁₉×#417	—	2	1	no	—
41	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#97	—	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×#332	C₂²	1	2	yes	—
47	C₁₉×#332	C₂²	1	2	yes	—
48	C₁₉×#332	C₂²	1	2	yes	—
49	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
50	C₂²×Q₈×C₁₉	—	2	1	no	—
51	C₂×Q₁₆×C₁₉	—	2	1	no	—
52	C₂×SD₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
55	C₂²×C₈×C₁₉	—	2	2	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₉×#125	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×C₂²⋊Q₈	—	2	1	no	—
65	C₄×Q₈×C₁₉	—	2	1	no	—
66	C₄×Q₈×C₁₉	—	2	1	no	—
67	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₁₉	—	2	1	no	—
70	C₄×D₄×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
72	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×#117	—	2	1	no	—
74	C₁₉×#117	—	2	1	no	—
75	C₁₉×#117	D₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄²×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×#107	—	2	2	no	—
81	C₁₉×#107	—	2	1	no	—
82	C₁₉×#106	—	2	2	no	—
83	C₁₉×#106	—	2	1	no	—
84	C₁₉×C₄⋊C₈	—	2	2	no	—
85	C₁₉×C₄⋊C₈	—	2	1	no	—
86	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
87	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
88	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
89	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
90	C₁₉×#103	—	2	2	no	—
91	C₁₉×#103	—	2	1	no	—
92	C₁₉×#103	—	2	2	no	—
93	C₁₉×#103	—	2	2	no	—
94	C₁₉×#103	—	2	2	no	—
95	C₁₉×#103	—	2	2	no	—
96	C₁₉×#103	—	2	1	no	—
97	C₁₉×#103	—	2	1	no	—
98	C₁₉×#102	—	2	2	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	—	2	2	no	—
103	C₁₉×#97	—	2	2	no	—
104	C₁₉×#97	—	2	1	no	—
105	C₁₉×#97	—	2	1	no	—
106	C₁₉×#97	D₄	1	1	yes	characteristic
107	C₁₉×#97	D₄	1	1	yes	characteristic
108	C₄×C₈×C₁₉	C₂³	1	2	yes	—
109	#41×C₁₉	—	2	2	no	—
110	#41×C₁₉	—	4	1	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	4	4	no	—
115	C₂×Q₈×C₁₉	—	4	1	no	—
116	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂×D₄×C₁₉	—	2	1	no	—
118	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	4	1	no	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
126	Q₁₆×C₁₉	—	4	2	no	—
127	SD₁₆×C₁₉	—	4	2	no	—
128	M₁₆×C₁₉	—	4	2	no	—
129	M₁₆×C₁₉	—	4	2	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	1	no	—
133	C₂×C₈×C₁₉	—	2	1	no	—
134	C₂×C₈×C₁₉	—	4	4	no	—
135	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	2	2	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	2	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	4	1	no	—
146	C₄⋊C₄×C₁₉	—	4	1	no	—
147	C₄⋊C₄×C₁₉	—	4	1	no	—
148	C₄⋊C₄×C₁₉	—	4	1	no	—
149	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²⋊C₄×C₁₉	—	2	1	no	—
152	C₂²⋊C₄×C₁₉	—	2	1	no	—
153	C₂²⋊C₄×C₁₉	—	2	1	no	—
154	C₂²⋊C₄×C₁₉	—	4	1	no	—
155	C₄²×C₁₉	—	2	1	no	—
156	C₄²×C₁₉	—	2	1	no	—
157	C₄²×C₁₉	—	2	1	no	—
158	C₄²×C₁₉	—	4	1	no	—
159	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₁₉	#41	1	1	yes	characteristic
162	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
163	#19317	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₁₉	—	2	1	no	—
165	C₂³×C₁₉	#121	1	1	yes	characteristic
166	Q₈×C₁₉	—	2	1	no	—
167	Q₈×C₁₉	—	2	1	no	—
168	Q₈×C₁₉	—	4	1	no	—
169	Q₈×C₁₉	—	4	1	no	—
170	Q₈×C₁₉	—	4	4	no	—
171	Q₈×C₁₉	—	8	1	no	—
172	Q₈×C₁₉	—	8	2	no	—
173	D₄×C₁₉	—	2	1	no	—
174	D₄×C₁₉	—	4	2	no	—
175	D₄×C₁₉	#137	1	2	yes	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	8	1	no	—
189	C₂×C₄×C₁₉	—	8	2	no	—
190	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
196	C₈×C₁₉	—	2	2	no	—
197	C₈×C₁₉	—	2	2	no	—
198	C₈×C₁₉	—	4	1	no	—
199	C₈×C₁₉	—	4	2	no	—
200	C₈×C₁₉	—	4	2	no	—
201	C₈×C₁₉	—	4	1	no	—
202	#3139	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#3116	C₂×C₁₉	1	1	yes	characteristic
204	#3079	C₂×C₁₉	1	1	yes	characteristic
205	#2970	C₂×C₁₉	1	1	yes	characteristic
206	#1704	C₂×C₁₉	1	2	yes	complemented
207	#1700	C₂×C₁₉	1	2	yes	complemented
208	#1683	C₂×C₁₉	1	2	yes	complemented
209	#1679	C₂×C₁₉	1	2	yes	complemented
210	#1569	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#1559	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	2	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	4	1	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	4	1	no	—
225	C₄×C₁₉	—	4	1	no	—
226	C₄×C₁₉	—	4	1	no	—
227	C₄×C₁₉	—	8	2	no	—
228	C₄×C₁₉	—	8	1	no	—
229	C₄×C₁₉	—	8	1	no	—
230	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
231	C₄×C₁₉	#575	1	2	yes	—
232	C₄×C₁₉	#575	1	1	yes	characteristic
233	#533	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
235	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
236	#491	—	2	1	no	—
237	#491	—	2	1	no	—
238	#487	C₂²×C₁₉	1	2	yes	—
239	#487	C₂²×C₁₉	1	2	yes	—
240	#485	—	2	1	no	—
241	#477	—	2	1	no	—
242	#477	C₂²×C₁₉	1	1	yes	characteristic
243	#476	—	2	1	no	—
244	#476	C₂²×C₁₉	1	1	yes	characteristic
245	#475	C₂²×C₁₉	1	2	yes	—
246	#474	C₂²×C₁₉	1	2	yes	—
247	#462	C₂²×C₁₉	1	1	yes	characteristic
248	#461	C₂²×C₁₉	1	1	yes	characteristic
249	#452	—	2	1	no	—
250	#446	C₂²×C₁₉	1	2	yes	—
251	#441	—	2	1	no	—
252	#440	—	2	1	no	—
253	#435	—	2	2	no	—
254	C₈×D₄	C₂²×C₁₉	1	2	yes	—
255	#432	—	2	1	no	—
256	#432	C₂²×C₁₉	1	1	yes	characteristic
257	#432	C₂²×C₁₉	1	1	yes	characteristic
258	#428	—	2	1	no	—
259	#423	C₂²×C₁₉	1	1	yes	characteristic
260	#419	—	2	2	no	—
261	#417	—	2	1	no	—
262	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
263	C₂×#97	—	2	1	no	—
264	#335	C₂²×C₁₉	1	2	yes	—
265	#334	C₂²×C₁₉	1	2	yes	—
266	#333	C₂²×C₁₉	1	2	yes	—
267	#332	C₂²×C₁₉	1	2	yes	—
268	#332	C₂²×C₁₉	1	2	yes	—
269	#332	C₂²×C₁₉	1	2	yes	—
270	C₂×C₁₉	—	4	1	no	—
271	C₂×C₁₉	—	4	2	no	—
272	C₂×C₁₉	#3040	1	1	yes	characteristic
273	C₂×C₁₉	#3056	1	1	yes	characteristic
274	C₂×C₁₉	#3069	1	1	yes	characteristic
275	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
276	C₂²×Q₈	—	2	1	no	—
277	C₂×Q₁₆	—	2	1	no	—
278	C₂×SD₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
281	C₂²×C₈	—	2	2	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
286	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
287	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
288	#125	—	2	1	no	—
289	C₂²⋊Q₈	—	2	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
294	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
298	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
299	#117	—	2	1	no	—
300	#117	—	2	1	no	—
301	#117	D₄×C₁₉	1	1	yes	characteristic
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
306	#107	—	2	2	no	—
307	#107	—	2	1	no	—
308	#106	—	2	2	no	—
309	#106	—	2	1	no	—
310	C₄⋊C₈	—	2	2	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
313	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
314	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
315	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
316	#103	—	2	2	no	—
317	#103	—	2	1	no	—
318	#103	—	2	2	no	—
319	#103	—	2	2	no	—
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	1	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	C₂²⋊C₈	—	2	2	no	—
329	#97	—	2	2	no	—
330	#97	—	2	1	no	—
331	#97	—	2	1	no	—
332	#97	D₄×C₁₉	1	1	yes	characteristic
333	#97	D₄×C₁₉	1	1	yes	characteristic
334	C₄×C₈	C₂³×C₁₉	1	2	yes	—
335	C₁₉	#19317	1	1	yes	characteristic, direct product factor, Sylow
336	#41	—	2	2	no	—
337	#41	—	4	1	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	4	4	no	—
342	C₂×Q₈	—	4	1	no	—
343	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	4	1	no	—
350	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
352	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
353	Q₁₆	—	4	2	no	—
354	SD₁₆	—	4	2	no	—
355	M₁₆	—	4	2	no	—
356	M₁₆	—	4	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	4	4	no	—
362	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
363	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
377	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	4	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	4	1	no	—
386	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
387	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
388	C₄²	#41×C₁₉	1	1	yes	characteristic
389	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
390	C₂³	—	2	1	no	—
391	C₂³	C₁₉×#121	1	1	yes	characteristic
392	Q₈	—	2	1	no	—
393	Q₈	—	2	1	no	—
394	Q₈	—	4	1	no	—
395	Q₈	—	4	1	no	—
396	Q₈	—	4	4	no	—
397	Q₈	—	8	1	no	—
398	Q₈	—	8	2	no	—
399	D₄	—	2	1	no	—
400	D₄	—	4	2	no	—
401	D₄	C₁₉×#137	1	2	yes	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	8	1	no	—
415	C₂×C₄	—	8	2	no	—
416	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
417	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
418	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
420	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
421	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
422	C₈	—	2	2	no	—
423	C₈	—	2	2	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	2	no	—
426	C₈	—	4	2	no	—
427	C₈	—	4	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	8	2	no	—
443	C₄	—	8	1	no	—
444	C₄	—	8	1	no	—
445	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
446	C₄	C₁₉×#575	1	2	yes	—
447	C₄	C₁₉×#575	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	4	2	no	—
450	C₂	C₁₉×#3040	1	1	yes	characteristic
451	C₂	C₁₉×#3056	1	1	yes	characteristic
452	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	D₄
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×#3139	C₂	semidirect
5. C₁₉×#1704	C₂	semidirect
6. C₁₉×#1700	C₂	semidirect
7. C₁₉×#1683	C₂	semidirect
8. C₁₉×#1679	C₂	semidirect
9. C₁₉×#1569	C₂	semidirect
10. C₁₉×#1559	C₂	semidirect
11. C₁₉×#1556	C₂	semidirect
163. #19317	C₁₉	direct (N × H)
202. #3139	C₂×C₁₉	semidirect
206. #1704	C₂×C₁₉	semidirect
207. #1700	C₂×C₁₉	semidirect
208. #1683	C₂×C₁₉	semidirect
209. #1679	C₂×C₁₉	semidirect
210. #1569	C₂×C₁₉	semidirect
211. #1559	C₂×C₁₉	semidirect
212. #1556	C₂×C₁₉	semidirect
335. C₁₉	#19317	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×#3139	2
C₁₉×#3116	2
C₁₉×#3079	2
C₁₉×#2970	2
C₁₉×#1704	2
C₁₉×#1700	2
C₁₉×#1683	2
C₁₉×#1679	2
C₁₉×#1569	2
C₁₉×#1559	2
C₁₉×#1556	2
#19317	19

Subgroups — C19×#19317 #18025276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19317 #18025276