Subgroups — C₁₉×#18756 #18024715

Order 4864.

1224 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3036	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1647	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1625	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1486	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₉	—	2	1	no	—
11	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
12	C₁₉×#547	—	2	2	no	—
13	C₁₉×#547	—	2	2	no	—
14	C₁₉×#547	—	2	2	no	—
15	C₁₉×#547	C₂²	1	4	yes	—
16	C₁₉×#532	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#123	—	2	2	no	—
19	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₁₉×#121	—	2	1	no	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
24	C₁₉×#500	C₂²	1	2	yes	complemented
25	C₁₉×#486	C₂²	1	2	yes	complemented
26	C₁₉×#480	—	2	2	no	—
27	C₁₉×#480	—	2	1	no	—
28	C₁₉×#474	—	2	2	no	—
29	C₁₉×#474	C₂²	1	2	yes	complemented
30	C₁₉×#463	—	2	2	no	—
31	C₁₉×#461	C₂²	1	2	yes	complemented
32	C₁₉×#459	C₂²	1	2	yes	complemented
33	C₁₉×#459	C₂²	1	2	yes	complemented
34	C₁₉×#447	—	2	1	no	—
35	C₄×D₈×C₁₉	—	2	2	no	—
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₁₉×#423	C₂²	1	1	yes	characteristic
39	C₁₉×#417	—	2	1	no	—
40	C₁₉×#332	C₂²	1	4	yes	complemented
41	C₁₉×D₄⋊C₈	C₂²	1	4	yes	complemented
42	C₁₉×D₄⋊C₈	C₂²	1	4	yes	complemented
43	C₂×#41×C₁₉	—	2	4	no	—
44	C₂×#41×C₁₉	—	2	4	no	—
45	C₂×#41×C₁₉	—	2	1	no	—
46	C₂×#41×C₁₉	—	4	4	no	—
47	C₂×#41×C₁₉	—	4	4	no	—
48	C₂²×Q₈×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	2	no	—
50	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	—	2	2	no	—
53	C₂³×C₄×C₁₉	—	2	1	no	—
54	C₂³×C₄×C₁₉	—	2	1	no	—
55	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
56	C₂×SD₁₆×C₁₉	—	2	2	no	—
57	C₂×D₈×C₁₉	—	2	2	no	—
58	C₂×D₈×C₁₉	—	2	2	no	—
59	C₂×M₁₆×C₁₉	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
63	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₁₉×#127	C₂³	1	1	yes	characteristic
66	C₁₉×#124	—	2	1	no	—
67	C₁₉×#123	—	2	8	no	—
68	C₁₉×#123	—	2	8	no	—
69	C₁₉×C₂²⋊Q₈	—	2	4	no	—
70	C₁₉×C₂²⋊Q₈	—	2	4	no	—
71	C₁₉×#121	—	2	4	no	—
72	C₁₉×#121	—	2	4	no	—
73	C₁₉×#121	—	2	1	no	—
74	C₁₉×#121	—	2	1	no	—
75	C₄×D₄×C₁₉	—	2	1	no	—
76	C₄×D₄×C₁₉	—	2	1	no	—
77	C₄×D₄×C₁₉	—	2	1	no	—
78	C₄×D₄×C₁₉	—	2	1	no	—
79	C₄×D₄×C₁₉	—	2	1	no	—
80	C₄×D₄×C₁₉	—	2	1	no	—
81	C₄×D₄×C₁₉	D₄	1	2	yes	—
82	C₄×D₄×C₁₉	D₄	1	2	yes	—
83	C₄×D₄×C₁₉	C₂³	1	2	yes	—
84	C₄×D₄×C₁₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
89	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
96	C₁₉×#107	—	2	2	no	—
97	C₁₉×#107	—	2	4	no	—
98	C₁₉×C₄⋊C₈	—	2	1	no	—
99	C₁₉×C₄⋊C₈	—	2	1	no	—
100	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
101	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
102	C₁₉×#103	—	2	2	no	—
103	C₁₉×#102	—	2	2	no	—
104	C₁₉×#102	—	2	2	no	—
105	C₁₉×#102	—	2	2	no	—
106	C₁₉×#102	—	2	4	no	—
107	C₁₉×C₂²⋊C₈	—	2	1	no	—
108	C₁₉×C₂²⋊C₈	—	2	1	no	—
109	C₄×C₈×C₁₉	—	2	1	no	—
110	C₄×C₈×C₁₉	C₂³	1	2	yes	—
111	C₂⁴×C₁₉	—	2	1	no	—
112	C₂⁴×C₁₉	—	2	1	no	—
113	#41×C₁₉	—	4	8	no	—
114	#41×C₁₉	—	4	16	no	—
115	#41×C₁₉	—	4	8	no	—
116	#41×C₁₉	—	4	2	no	—
117	#41×C₁₉	—	4	2	no	—
118	C₂×Q₈×C₁₉	—	2	2	no	—
119	C₂×Q₈×C₁₉	—	2	2	no	—
120	C₂×Q₈×C₁₉	—	2	1	no	—
121	C₂×Q₈×C₁₉	—	4	2	no	—
122	C₂×Q₈×C₁₉	—	4	2	no	—
123	C₂×D₄×C₁₉	—	2	8	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	2	1	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	2	1	no	—
129	C₂×D₄×C₁₉	—	2	1	no	—
130	C₂×D₄×C₁₉	—	4	2	no	—
131	C₂×D₄×C₁₉	—	4	8	no	—
132	C₂×D₄×C₁₉	—	4	1	no	—
133	C₂×D₄×C₁₉	D₈	1	4	yes	complemented
134	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₉	—	2	8	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	4	4	no	—
145	C₂²×C₄×C₁₉	—	4	8	no	—
146	C₂²×C₄×C₁₉	—	4	2	no	—
147	C₂²×C₄×C₁₉	—	4	2	no	—
148	C₂²×C₄×C₁₉	—	4	1	no	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	SD₁₆×C₁₉	—	4	4	no	—
153	D₈×C₁₉	—	4	4	no	—
154	D₈×C₁₉	—	4	4	no	—
155	M₁₆×C₁₉	—	4	2	no	—
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₂×C₈×C₁₉	—	2	2	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	8	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
168	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
170	C₂²⋊C₄×C₁₉	—	2	8	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	4	1	no	—
176	C₂²⋊C₄×C₁₉	—	4	1	no	—
177	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
181	#18756	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂³×C₁₉	—	2	2	no	—
183	C₂³×C₁₉	—	2	4	no	—
184	C₂³×C₁₉	—	2	2	no	—
185	C₂³×C₁₉	—	4	2	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	4	2	no	—
188	C₂³×C₁₉	—	4	2	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	1	no	—
191	C₂³×C₁₉	#120	1	1	yes	characteristic
192	Q₈×C₁₉	—	4	2	no	—
193	Q₈×C₁₉	—	4	2	no	—
194	Q₈×C₁₉	—	4	4	no	—
195	Q₈×C₁₉	—	4	1	no	—
196	Q₈×C₁₉	—	4	1	no	—
197	D₄×C₁₉	—	2	2	no	—
198	D₄×C₁₉	—	2	2	no	—
199	D₄×C₁₉	—	2	2	no	—
200	D₄×C₁₉	—	2	4	no	—
201	D₄×C₁₉	—	4	2	no	—
202	D₄×C₁₉	—	4	2	no	—
203	D₄×C₁₉	—	4	16	no	—
204	D₄×C₁₉	—	4	1	no	—
205	D₄×C₁₉	—	4	1	no	—
206	D₄×C₁₉	—	4	2	no	—
207	D₄×C₁₉	—	8	2	no	—
208	D₄×C₁₉	C₂×D₈	1	4	yes	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	4	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	16	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	4	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	4	no	—
222	C₂×C₄×C₁₉	—	4	4	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	8	2	no	—
225	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
226	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
229	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
230	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
233	C₈×C₁₉	—	4	2	no	—
234	C₈×C₁₉	—	4	2	no	—
235	C₈×C₁₉	—	4	2	no	—
236	C₂×#547	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#3226	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#3100	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#3036	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#1647	C₂×C₁₉	1	4	yes	complemented
241	#1625	C₂×C₁₉	1	4	yes	complemented
242	#1546	C₂×C₁₉	1	1	yes	characteristic, complemented
243	#1486	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#1478	C₂×C₁₉	1	1	yes	characteristic, complemented
245	C₂²×C₁₉	—	2	1	no	—
246	C₂²×C₁₉	—	2	1	no	—
247	C₂²×C₁₉	—	2	4	no	—
248	C₂²×C₁₉	—	4	8	no	—
249	C₂²×C₁₉	—	4	2	no	—
250	C₂²×C₁₉	—	4	2	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	—	8	4	no	—
255	C₂²×C₁₉	—	8	1	no	—
256	C₂²×C₁₉	—	8	1	no	—
257	C₂²×C₁₉	—	8	1	no	—
258	C₂²×C₁₉	#447	1	2	yes	—
259	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
260	C₄×C₁₉	—	2	1	no	—
261	C₄×C₁₉	—	2	1	no	—
262	C₄×C₁₉	—	2	1	no	—
263	C₄×C₁₉	—	4	2	no	—
264	C₄×C₁₉	—	4	4	no	—
265	C₄×C₁₉	—	4	2	no	—
266	C₄×C₁₉	—	8	1	no	—
267	C₄×C₁₉	#447	1	2	yes	—
268	C₄×C₁₉	C₂²×D₈	1	1	yes	characteristic
269	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
270	C₄×C₁₉	#575	1	2	yes	—
271	C₂²×#41	—	2	1	no	—
272	C₂×AGL(1,ℤ/8)	—	2	1	no	—
273	#547	—	2	2	no	—
274	#547	—	2	2	no	—
275	#547	—	2	2	no	—
276	#547	C₂²×C₁₉	1	4	yes	—
277	#532	C₂²×C₁₉	1	1	yes	characteristic
278	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
279	C₂×#123	—	2	2	no	—
280	C₂×C₂²⋊Q₈	—	2	1	no	—
281	C₂×#121	—	2	1	no	—
282	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
284	C₂²×C₄⋊C₄	—	2	1	no	—
285	#500	C₂²×C₁₉	1	2	yes	complemented
286	#486	C₂²×C₁₉	1	2	yes	complemented
287	#480	—	2	1	no	—
288	#480	—	2	2	no	—
289	#474	—	2	2	no	—
290	#474	C₂²×C₁₉	1	2	yes	complemented
291	#463	—	2	2	no	—
292	#461	C₂²×C₁₉	1	2	yes	complemented
293	#459	C₂²×C₁₉	1	2	yes	complemented
294	#459	C₂²×C₁₉	1	2	yes	complemented
295	#447	—	2	1	no	—
296	C₄×D₈	—	2	2	no	—
297	#431	C₂²×C₁₉	1	1	yes	characteristic
298	#431	C₂²×C₁₉	1	1	yes	characteristic
299	#423	C₂²×C₁₉	1	1	yes	characteristic
300	#417	—	2	1	no	—
301	#332	C₂²×C₁₉	1	4	yes	complemented
302	D₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
303	D₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
304	C₂×C₁₉	—	2	2	no	—
305	C₂×C₁₉	—	4	4	no	—
306	C₂×C₁₉	—	8	2	no	—
307	C₂×C₁₉	—	16	1	no	—
308	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
309	C₂×C₁₉	#3005	1	1	yes	characteristic
310	C₂×C₁₉	#3020	1	1	yes	characteristic
311	C₂×#41	—	2	4	no	—
312	C₂×#41	—	2	4	no	—
313	C₂×#41	—	2	1	no	—
314	C₂×#41	—	4	4	no	—
315	C₂×#41	—	4	4	no	—
316	C₂²×Q₈	—	2	1	no	—
317	C₂²×D₄	—	2	2	no	—
318	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
319	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
320	C₂³×C₄	—	2	2	no	—
321	C₂³×C₄	—	2	1	no	—
322	C₂³×C₄	—	2	1	no	—
323	AGL(1,ℤ/8)	—	4	4	no	—
324	C₂×SD₁₆	—	2	2	no	—
325	C₂×D₈	—	2	2	no	—
326	C₂×D₈	—	2	2	no	—
327	C₂×M₁₆	—	2	1	no	—
328	C₄⋊Q₈	—	2	1	no	—
329	C₄⋊Q₈	—	2	1	no	—
330	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
331	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
332	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
333	#127	C₂³×C₁₉	1	1	yes	characteristic
334	#124	—	2	1	no	—
335	#123	—	2	8	no	—
336	#123	—	2	8	no	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	#121	—	2	4	no	—
340	#121	—	2	4	no	—
341	#121	—	2	1	no	—
342	#121	—	2	1	no	—
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	2	1	no	—
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	D₄×C₁₉	1	2	yes	—
350	C₄×D₄	D₄×C₁₉	1	2	yes	—
351	C₄×D₄	C₂³×C₁₉	1	2	yes	—
352	C₄×D₄	C₂³×C₁₉	1	2	yes	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	4	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	4	no	—
357	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
358	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
359	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
364	#107	—	2	2	no	—
365	#107	—	2	4	no	—
366	C₄⋊C₈	—	2	1	no	—
367	C₄⋊C₈	—	2	1	no	—
368	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
369	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
370	#103	—	2	2	no	—
371	#102	—	2	2	no	—
372	#102	—	2	2	no	—
373	#102	—	2	2	no	—
374	#102	—	2	4	no	—
375	C₂²⋊C₈	—	2	1	no	—
376	C₂²⋊C₈	—	2	1	no	—
377	C₄×C₈	—	2	1	no	—
378	C₄×C₈	C₂³×C₁₉	1	2	yes	—
379	C₁₉	#18756	1	1	yes	characteristic, direct product factor, Sylow
380	C₂⁴	—	2	1	no	—
381	C₂⁴	—	2	1	no	—
382	#41	—	4	16	no	—
383	#41	—	4	8	no	—
384	#41	—	4	8	no	—
385	#41	—	4	2	no	—
386	#41	—	4	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	4	2	no	—
391	C₂×Q₈	—	4	2	no	—
392	C₂×D₄	—	2	8	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	—	4	8	no	—
401	C₂×D₄	—	4	1	no	—
402	C₂×D₄	D₈×C₁₉	1	4	yes	complemented
403	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
404	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
405	C₂²×C₄	—	2	8	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	4	4	no	—
414	C₂²×C₄	—	4	8	no	—
415	C₂²×C₄	—	4	2	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	—	4	1	no	—
418	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
421	SD₁₆	—	4	4	no	—
422	D₈	—	4	4	no	—
423	D₈	—	4	4	no	—
424	M₁₆	—	4	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₄⋊C₄	—	2	8	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
437	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
438	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
439	C₂²⋊C₄	—	2	8	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	4	1	no	—
445	C₂²⋊C₄	—	4	1	no	—
446	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
450	C₂³	—	2	4	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	1	no	—
459	C₂³	C₁₉×#120	1	1	yes	characteristic
460	Q₈	—	4	4	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	4	2	no	—
463	Q₈	—	4	1	no	—
464	Q₈	—	4	1	no	—
465	D₄	—	2	4	no	—
466	D₄	—	2	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	16	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	2	no	—
475	D₄	—	8	2	no	—
476	D₄	C₂×D₈×C₁₉	1	4	yes	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	16	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	4	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	8	2	no	—
493	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
494	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
495	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
496	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
497	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
498	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
500	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
501	C₈	—	4	2	no	—
502	C₈	—	4	2	no	—
503	C₈	—	4	2	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	4	8	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	8	4	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	—	8	1	no	—
517	C₂²	C₁₉×#447	1	2	yes	—
518	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	2	no	—
525	C₄	—	8	1	no	—
526	C₄	C₁₉×#447	1	2	yes	—
527	C₄	C₂²×D₈×C₁₉	1	1	yes	characteristic
528	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
529	C₄	C₁₉×#575	1	2	yes	—
530	C₂	—	2	2	no	—
531	C₂	—	4	4	no	—
532	C₂	—	8	2	no	—
533	C₂	—	16	1	no	—
534	C₂	C₂×C₁₉×#447	1	1	yes	characteristic
535	C₂	C₁₉×#3005	1	1	yes	characteristic
536	C₂	C₁₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
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. C₂×C₁₉×#547	C₂	semidirect
2. C₁₉×#3226	C₂	semidirect
3. C₁₉×#3100	C₂	semidirect
4. C₁₉×#3036	C₂	semidirect
5. C₁₉×#1647	C₂	semidirect
6. C₁₉×#1625	C₂	semidirect
7. C₁₉×#1546	C₂	semidirect
8. C₁₉×#1486	C₂	semidirect
9. C₁₉×#1478	C₂	semidirect
24. C₁₉×#500	C₂²	semidirect
25. C₁₉×#486	C₂²	semidirect
29. C₁₉×#474	C₂²	semidirect
31. C₁₉×#461	C₂²	semidirect
32. C₁₉×#459	C₂²	semidirect
33. C₁₉×#459	C₂²	semidirect
40. C₁₉×#332	C₂²	semidirect
41. C₁₉×D₄⋊C₈	C₂²	semidirect
42. C₁₉×D₄⋊C₈	C₂²	semidirect
133. C₂×D₄×C₁₉	D₈	semidirect
181. #18756	C₁₉	direct (N × H)
236. C₂×#547	C₂×C₁₉	semidirect
237. #3226	C₂×C₁₉	semidirect
238. #3100	C₂×C₁₉	semidirect
239. #3036	C₂×C₁₉	semidirect
240. #1647	C₂×C₁₉	semidirect
241. #1625	C₂×C₁₉	semidirect
242. #1546	C₂×C₁₉	semidirect
243. #1486	C₂×C₁₉	semidirect
244. #1478	C₂×C₁₉	semidirect
285. #500	C₂²×C₁₉	semidirect
286. #486	C₂²×C₁₉	semidirect
290. #474	C₂²×C₁₉	semidirect
292. #461	C₂²×C₁₉	semidirect
293. #459	C₂²×C₁₉	semidirect
294. #459	C₂²×C₁₉	semidirect
301. #332	C₂²×C₁₉	semidirect
302. D₄⋊C₈	C₂²×C₁₉	semidirect
303. D₄⋊C₈	C₂²×C₁₉	semidirect
379. C₁₉	#18756	direct (N × H)
402. C₂×D₄	D₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#547	2
C₁₉×#3226	2
C₁₉×#3100	2
C₁₉×#3036	2
C₁₉×#1647	2
C₁₉×#1625	2
C₁₉×#1546	2
C₁₉×#1486	2
C₁₉×#1478	2
#18756	19

Subgroups — C19×#18756 #18024715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18756 #18024715