Subgroups — C₁₉×#19309 #18025268

Order 4864.

600 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3182	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3112	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1704	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1698	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1696	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1686	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1684	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1678	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1676	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1666	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1569	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1560	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1559	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#532	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#500	C₂²	1	1	yes	characteristic
20	C₁₉×#492	C₂²	1	1	yes	characteristic
21	C₁₉×#487	C₂²	1	1	yes	characteristic
22	C₁₉×#486	C₂²	1	1	yes	characteristic
23	C₁₉×#480	—	2	1	no	—
24	C₁₉×#479	—	2	1	no	—
25	C₁₉×#479	—	2	1	no	—
26	C₁₉×#477	C₂²	1	1	yes	characteristic
27	C₁₉×#477	C₂²	1	1	yes	characteristic
28	C₁₉×#477	C₂²	1	1	yes	characteristic
29	C₁₉×#477	C₂²	1	1	yes	characteristic
30	C₁₉×#475	C₂²	1	1	yes	characteristic
31	C₁₉×#475	C₂²	1	1	yes	characteristic
32	C₁₉×#468	—	2	1	no	—
33	C₁₉×#468	—	2	1	no	—
34	C₁₉×#460	C₂²	1	1	yes	characteristic
35	C₁₉×#460	C₂²	1	1	yes	characteristic
36	C₁₉×#448	—	2	1	no	—
37	C₁₉×#446	—	2	1	no	—
38	C₁₉×#446	—	2	1	no	—
39	C₁₉×#446	C₂²	1	1	yes	characteristic
40	C₁₉×#446	C₂²	1	1	yes	characteristic
41	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
42	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#440	—	2	1	no	—
44	C₁₉×#440	—	2	1	no	—
45	C₁₉×#440	—	2	1	no	—
46	C₁₉×#440	—	2	1	no	—
47	C₁₉×#432	C₂²	1	1	yes	characteristic
48	C₁₉×#428	—	2	1	no	—
49	C₁₉×#423	—	2	1	no	—
50	C₁₉×#423	C₂²	1	1	yes	characteristic
51	C₁₉×#423	C₂²	1	1	yes	characteristic
52	C₁₉×#419	—	2	1	no	—
53	C₄×M₁₆×C₁₉	—	2	1	no	—
54	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#335	C₂²	1	1	yes	characteristic
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#334	C₂²	1	1	yes	characteristic
59	C₁₉×#333	C₂²	1	1	yes	characteristic
60	C₁₉×#333	C₂²	1	1	yes	characteristic
61	C₁₉×#333	C₂²	1	1	yes	characteristic
62	C₁₉×#333	C₂²	1	1	yes	characteristic
63	C₁₉×#332	C₂²	1	1	yes	characteristic
64	C₁₉×#332	C₂²	1	1	yes	characteristic
65	C₁₉×#331	C₂²	1	1	yes	characteristic
66	C₁₉×#331	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
69	C₂×SD₁₆×C₁₉	—	2	1	no	—
70	C₂×SD₁₆×C₁₉	—	2	1	no	—
71	C₂×SD₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×M₁₆×C₁₉	—	2	1	no	—
74	C₂×M₁₆×C₁₉	—	2	1	no	—
75	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
76	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
77	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₉×#127	C₂³	1	1	yes	characteristic
81	C₁₉×#125	—	2	1	no	—
82	C₁₉×#124	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	1	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×#121	—	2	1	no	—
86	C₁₉×#121	—	2	1	no	—
87	C₄×Q₈×C₁₉	—	2	1	no	—
88	C₄×Q₈×C₁₉	—	2	1	no	—
89	C₄×Q₈×C₁₉	—	2	1	no	—
90	C₄×Q₈×C₁₉	—	2	1	no	—
91	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
93	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
94	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₁₉	—	2	1	no	—
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₁₉×#117	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	—	2	1	no	—
101	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×#107	—	2	1	no	—
103	C₁₉×#107	—	2	1	no	—
104	C₁₉×#107	—	2	1	no	—
105	C₁₉×#107	—	2	1	no	—
106	C₁₉×#107	—	2	1	no	—
107	C₁₉×#107	—	2	1	no	—
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×#106	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	2	1	no	—
111	C₁₉×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	—	2	1	no	—
113	C₁₉×C₄⋊C₈	—	2	1	no	—
114	C₁₉×C₄⋊C₈	—	2	1	no	—
115	C₁₉×C₄⋊C₈	—	2	1	no	—
116	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₉×#103	—	2	1	no	—
123	C₁₉×#103	—	2	1	no	—
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#103	—	2	1	no	—
127	C₁₉×#103	—	2	1	no	—
128	C₁₉×#103	—	2	1	no	—
129	C₁₉×#103	—	2	1	no	—
130	C₁₉×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
134	C₁₉×C₂²⋊C₈	—	2	1	no	—
135	C₁₉×#97	—	2	1	no	—
136	C₁₉×#97	—	2	1	no	—
137	C₁₉×#97	—	2	1	no	—
138	C₁₉×#97	D₄	1	1	yes	characteristic
139	C₁₉×#97	D₄	1	1	yes	characteristic
140	C₄×C₈×C₁₉	—	2	1	no	—
141	C₄×C₈×C₁₉	—	2	1	no	—
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	#41×C₁₉	—	8	2	no	—
145	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	—	2	2	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	4	1	no	—
151	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	4	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	4	1	no	—
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
163	SD₁₆×C₁₉	—	4	2	no	—
164	SD₁₆×C₁₉	—	4	2	no	—
165	SD₁₆×C₁₉	—	4	2	no	—
166	SD₁₆×C₁₉	—	4	2	no	—
167	M₁₆×C₁₉	—	2	2	no	—
168	M₁₆×C₁₉	—	4	1	no	—
169	M₁₆×C₁₉	—	4	2	no	—
170	M₁₆×C₁₉	—	4	2	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	4	1	no	—
193	C₄⋊C₄×C₁₉	—	4	1	no	—
194	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂²⋊C₄×C₁₉	—	4	1	no	—
197	C₂²⋊C₄×C₁₉	—	4	1	no	—
198	C₂²⋊C₄×C₁₉	—	4	1	no	—
199	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	2	1	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	C₄²×C₁₉	—	4	1	no	—
204	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₁₉	#41	1	1	yes	characteristic
207	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
208	#19309	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂³×C₁₉	—	4	1	no	—
210	C₂³×C₁₉	#121	1	1	yes	characteristic
211	Q₈×C₁₉	—	2	1	no	—
212	Q₈×C₁₉	—	2	1	no	—
213	Q₈×C₁₉	—	2	1	no	—
214	Q₈×C₁₉	—	4	2	no	—
215	Q₈×C₁₉	—	4	1	no	—
216	Q₈×C₁₉	—	4	1	no	—
217	Q₈×C₁₉	—	8	1	no	—
218	Q₈×C₁₉	—	8	1	no	—
219	Q₈×C₁₉	#137	1	2	yes	—
220	D₄×C₁₉	—	4	1	no	—
221	D₄×C₁₉	—	4	1	no	—
222	D₄×C₁₉	—	4	1	no	—
223	D₄×C₁₉	—	4	1	no	—
224	D₄×C₁₉	—	8	1	no	—
225	D₄×C₁₉	—	8	2	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	8	2	no	—
240	C₂×C₄×C₁₉	—	8	1	no	—
241	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
247	C₈×C₁₉	—	2	1	no	—
248	C₈×C₁₉	—	2	1	no	—
249	C₈×C₁₉	—	2	1	no	—
250	C₈×C₁₉	—	4	1	no	—
251	C₈×C₁₉	—	4	1	no	—
252	C₈×C₁₉	—	4	1	no	—
253	C₈×C₁₉	—	4	1	no	—
254	C₈×C₁₉	—	4	1	no	—
255	C₈×C₁₉	—	4	1	no	—
256	C₈×C₁₉	#137	1	2	yes	—
257	#3182	C₂×C₁₉	1	1	yes	characteristic
258	#3112	C₂×C₁₉	1	1	yes	characteristic
259	#3078	C₂×C₁₉	1	1	yes	characteristic, complemented
260	Q₈×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1704	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1698	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1696	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1686	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1684	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1678	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1676	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#1666	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1569	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1560	C₂×C₁₉	1	1	yes	characteristic
271	#1559	C₂×C₁₉	1	1	yes	characteristic, complemented
272	C₂²×C₁₉	—	2	1	no	—
273	C₂²×C₁₉	—	2	1	no	—
274	C₂²×C₁₉	—	2	1	no	—
275	C₂²×C₁₉	—	8	1	no	—
276	C₂²×C₁₉	—	8	1	no	—
277	C₂²×C₁₉	—	8	1	no	—
278	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
279	C₄×C₁₉	—	2	1	no	—
280	C₄×C₁₉	—	2	1	no	—
281	C₄×C₁₉	—	2	2	no	—
282	C₄×C₁₉	—	2	1	no	—
283	C₄×C₁₉	—	2	1	no	—
284	C₄×C₁₉	—	4	1	no	—
285	C₄×C₁₉	—	4	1	no	—
286	C₄×C₁₉	—	4	1	no	—
287	C₄×C₁₉	—	8	1	no	—
288	C₄×C₁₉	—	8	1	no	—
289	C₄×C₁₉	—	8	1	no	—
290	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
291	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
292	C₄×C₁₉	#575	1	1	yes	characteristic
293	C₄×C₁₉	#575	1	1	yes	characteristic
294	#533	C₂²×C₁₉	1	1	yes	characteristic
295	#532	C₂²×C₁₉	1	1	yes	characteristic
296	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
297	#500	C₂²×C₁₉	1	1	yes	characteristic
298	#492	C₂²×C₁₉	1	1	yes	characteristic
299	#487	C₂²×C₁₉	1	1	yes	characteristic
300	#486	C₂²×C₁₉	1	1	yes	characteristic
301	#480	—	2	1	no	—
302	#479	—	2	1	no	—
303	#479	—	2	1	no	—
304	#477	C₂²×C₁₉	1	1	yes	characteristic
305	#477	C₂²×C₁₉	1	1	yes	characteristic
306	#477	C₂²×C₁₉	1	1	yes	characteristic
307	#477	C₂²×C₁₉	1	1	yes	characteristic
308	#475	C₂²×C₁₉	1	1	yes	characteristic
309	#475	C₂²×C₁₉	1	1	yes	characteristic
310	#468	—	2	1	no	—
311	#468	—	2	1	no	—
312	#460	C₂²×C₁₉	1	1	yes	characteristic
313	#460	C₂²×C₁₉	1	1	yes	characteristic
314	#448	—	2	1	no	—
315	#446	—	2	1	no	—
316	#446	—	2	1	no	—
317	#446	C₂²×C₁₉	1	1	yes	characteristic
318	#446	C₂²×C₁₉	1	1	yes	characteristic
319	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
320	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
321	#440	—	2	1	no	—
322	#440	—	2	1	no	—
323	#440	—	2	1	no	—
324	#440	—	2	1	no	—
325	#432	C₂²×C₁₉	1	1	yes	characteristic
326	#428	—	2	1	no	—
327	#423	—	2	1	no	—
328	#423	C₂²×C₁₉	1	1	yes	characteristic
329	#423	C₂²×C₁₉	1	1	yes	characteristic
330	#419	—	2	1	no	—
331	C₄×M₁₆	—	2	1	no	—
332	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
333	#335	C₂²×C₁₉	1	1	yes	characteristic
334	#335	C₂²×C₁₉	1	1	yes	characteristic
335	#334	C₂²×C₁₉	1	1	yes	characteristic
336	#334	C₂²×C₁₉	1	1	yes	characteristic
337	#333	C₂²×C₁₉	1	1	yes	characteristic
338	#333	C₂²×C₁₉	1	1	yes	characteristic
339	#333	C₂²×C₁₉	1	1	yes	characteristic
340	#333	C₂²×C₁₉	1	1	yes	characteristic
341	#332	C₂²×C₁₉	1	1	yes	characteristic
342	#332	C₂²×C₁₉	1	1	yes	characteristic
343	#331	C₂²×C₁₉	1	1	yes	characteristic
344	#331	C₂²×C₁₉	1	1	yes	characteristic
345	C₂×C₁₉	—	4	1	no	—
346	C₂×C₁₉	—	16	1	no	—
347	C₂×C₁₉	#3037	1	1	yes	characteristic
348	C₂×C₁₉	#3056	1	1	yes	characteristic
349	C₂×C₁₉	#3068	1	1	yes	characteristic
350	C₂×#41	—	2	1	no	—
351	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
352	C₂×SD₁₆	—	2	1	no	—
353	C₂×SD₁₆	—	2	1	no	—
354	C₂×SD₁₆	—	2	1	no	—
355	C₂×SD₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
359	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
360	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
361	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
362	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
363	#127	C₂³×C₁₉	1	1	yes	characteristic
364	#125	—	2	1	no	—
365	#124	—	2	1	no	—
366	C₂²⋊Q₈	—	2	1	no	—
367	C₂²⋊Q₈	—	2	1	no	—
368	#121	—	2	1	no	—
369	#121	—	2	1	no	—
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
375	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
376	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
377	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	#117	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
385	#107	—	2	1	no	—
386	#107	—	2	1	no	—
387	#107	—	2	1	no	—
388	#107	—	2	1	no	—
389	#107	—	2	1	no	—
390	#107	—	2	1	no	—
391	#106	—	2	1	no	—
392	#106	—	2	1	no	—
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	—	2	1	no	—
398	C₄⋊C₈	—	2	1	no	—
399	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
400	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
401	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
402	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
403	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#103	—	2	1	no	—
412	#103	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	—	2	1	no	—
415	#102	—	2	1	no	—
416	#102	—	2	1	no	—
417	C₂²⋊C₈	—	2	1	no	—
418	#97	—	2	1	no	—
419	#97	—	2	1	no	—
420	#97	—	2	1	no	—
421	#97	D₄×C₁₉	1	1	yes	characteristic
422	#97	D₄×C₁₉	1	1	yes	characteristic
423	C₄×C₈	—	2	1	no	—
424	C₄×C₈	—	2	1	no	—
425	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
426	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
427	C₁₉	#19309	1	1	yes	characteristic, direct product factor, Sylow
428	#41	—	8	2	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	4	1	no	—
435	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
436	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
447	SD₁₆	—	4	2	no	—
448	SD₁₆	—	4	2	no	—
449	SD₁₆	—	4	2	no	—
450	SD₁₆	—	4	2	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	4	1	no	—
453	M₁₆	—	4	2	no	—
454	M₁₆	—	4	2	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	4	1	no	—
488	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₄²	#41×C₁₉	1	1	yes	characteristic
491	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
492	C₂³	—	4	1	no	—
493	C₂³	C₁₉×#121	1	1	yes	characteristic
494	Q₈	—	2	1	no	—
495	Q₈	—	2	1	no	—
496	Q₈	—	2	1	no	—
497	Q₈	—	4	2	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	8	1	no	—
501	Q₈	—	8	1	no	—
502	Q₈	C₁₉×#137	1	2	yes	—
503	D₄	—	4	1	no	—
504	D₄	—	4	1	no	—
505	D₄	—	4	1	no	—
506	D₄	—	4	1	no	—
507	D₄	—	8	1	no	—
508	D₄	—	8	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	8	2	no	—
523	C₂×C₄	—	8	1	no	—
524	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
525	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
526	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
529	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₈	C₁₉×#137	1	2	yes	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
559	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
560	C₄	C₁₉×#575	1	1	yes	characteristic
561	C₄	C₁₉×#575	1	1	yes	characteristic
562	C₂	—	4	1	no	—
563	C₂	—	16	1	no	—
564	C₂	C₁₉×#3037	1	1	yes	characteristic
565	C₂	C₁₉×#3056	1	1	yes	characteristic
566	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×#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. C₁₉×#3078	C₂	semidirect
4. Q₈×M₁₆×C₁₉	C₂	semidirect
5. C₁₉×#1704	C₂	semidirect
6. C₁₉×#1698	C₂	semidirect
7. C₁₉×#1696	C₂	semidirect
8. C₁₉×#1686	C₂	semidirect
9. C₁₉×#1684	C₂	semidirect
10. C₁₉×#1678	C₂	semidirect
11. C₁₉×#1676	C₂	semidirect
12. C₁₉×#1666	C₂	semidirect
13. C₁₉×#1569	C₂	semidirect
15. C₁₉×#1559	C₂	semidirect
208. #19309	C₁₉	direct (N × H)
259. #3078	C₂×C₁₉	semidirect
260. Q₈×M₁₆	C₂×C₁₉	semidirect
261. #1704	C₂×C₁₉	semidirect
262. #1698	C₂×C₁₉	semidirect
263. #1696	C₂×C₁₉	semidirect
264. #1686	C₂×C₁₉	semidirect
265. #1684	C₂×C₁₉	semidirect
266. #1678	C₂×C₁₉	semidirect
267. #1676	C₂×C₁₉	semidirect
268. #1666	C₂×C₁₉	semidirect
269. #1569	C₂×C₁₉	semidirect
271. #1559	C₂×C₁₉	semidirect
427. C₁₉	#19309	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×#3182	2
C₁₉×#3112	2
C₁₉×#3078	2
Q₈×M₁₆×C₁₉	2
C₁₉×#1704	2
C₁₉×#1698	2
C₁₉×#1696	2
C₁₉×#1686	2
C₁₉×#1684	2
C₁₉×#1678	2
C₁₉×#1676	2
C₁₉×#1666	2
C₁₉×#1569	2
C₁₉×#1560	2
C₁₉×#1559	2
#19309	19

Subgroups — C19×#19309 #18025268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19309 #18025268