Subgroups — C₁₉×#18550 #18024509

Order 4864.

1230 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#550	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3138	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3113	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3110	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1642	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1641	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1555	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1491	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1490	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₉	—	2	1	no	—
11	C₁₉×#550	—	2	2	no	—
12	C₁₉×#550	—	2	2	no	—
13	C₁₉×#550	—	2	2	no	—
14	C₁₉×#550	C₂²	1	4	yes	—
15	C₁₉×#533	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#127	—	2	1	no	—
17	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#121	—	2	2	no	—
19	C₂×C₁₉×#121	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	—	2	1	no	—
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#490	—	2	2	no	—
24	C₁₉×#486	C₂²	1	2	yes	complemented
25	C₁₉×#486	C₂²	1	2	yes	complemented
26	C₁₉×#484	—	2	1	no	—
27	C₁₉×#483	—	2	1	no	—
28	C₁₉×#475	C₂²	1	2	yes	complemented
29	C₁₉×#474	C₂²	1	2	yes	complemented
30	C₁₉×#462	C₂²	1	2	yes	complemented
31	C₁₉×#461	C₂²	1	2	yes	complemented
32	C₁₉×#451	—	2	1	no	—
33	C₁₉×#450	—	2	1	no	—
34	C₁₉×#441	—	2	2	no	—
35	C₁₉×#440	—	2	2	no	—
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#432	C₂²	1	1	yes	characteristic
38	C₁₉×#418	—	2	2	no	—
39	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
40	C₁₉×#331	C₂²	1	4	yes	complemented
41	C₁₉×Q₈⋊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	—	4	8	no	—
46	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	—	2	2	no	—
48	C₂²×D₄×C₁₉	—	2	2	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	D₄	1	2	yes	—
52	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₉	—	2	2	no	—
54	C₂³×C₄×C₁₉	—	2	1	no	—
55	C₂×Q₁₆×C₁₉	—	2	2	no	—
56	C₂×SD₁₆×C₁₉	—	2	2	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₉×#127	—	2	4	no	—
61	C₁₉×#127	—	2	4	no	—
62	C₁₉×#127	—	2	1	no	—
63	C₁₉×#127	—	2	1	no	—
64	C₁₉×#127	D₄	1	2	yes	—
65	C₁₉×#127	C₂³	1	2	yes	—
66	C₁₉×#125	—	2	1	no	—
67	C₁₉×C₂²⋊Q₈	—	2	1	no	—
68	C₁₉×C₂²⋊Q₈	—	2	1	no	—
69	C₁₉×#121	—	2	4	no	—
70	C₁₉×#121	—	2	8	no	—
71	C₁₉×#121	—	2	8	no	—
72	C₁₉×#121	—	2	4	no	—
73	C₄×Q₈×C₁₉	—	2	1	no	—
74	C₄×Q₈×C₁₉	—	2	1	no	—
75	C₄×Q₈×C₁₉	—	2	1	no	—
76	C₄×Q₈×C₁₉	—	2	1	no	—
77	C₄×Q₈×C₁₉	D₄	1	2	yes	—
78	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
79	C₄×D₄×C₁₉	—	2	4	no	—
80	C₄×D₄×C₁₉	—	2	4	no	—
81	C₄×D₄×C₁₉	—	2	1	no	—
82	C₄×D₄×C₁₉	—	2	1	no	—
83	C₄×D₄×C₁₉	D₄	1	2	yes	—
84	C₄×D₄×C₁₉	C₂³	1	2	yes	—
85	C₁₉×#117	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	—	2	1	no	—
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₁₉×#107	—	2	2	no	—
94	C₁₉×#106	—	2	2	no	—
95	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
96	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
97	C₁₉×#103	—	2	2	no	—
98	C₁₉×#103	—	2	2	no	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#102	—	2	4	no	—
101	C₁₉×#102	—	2	4	no	—
102	C₁₉×#102	—	2	2	no	—
103	C₁₉×C₂²⋊C₈	—	2	1	no	—
104	C₁₉×C₂²⋊C₈	—	2	1	no	—
105	C₁₉×#97	—	2	1	no	—
106	C₁₉×#97	—	2	1	no	—
107	C₁₉×#97	—	2	1	no	—
108	C₄×C₈×C₁₉	C₂³	1	2	yes	—
109	C₂⁴×C₁₉	—	2	2	no	—
110	C₂⁴×C₁₉	—	2	1	no	—
111	#41×C₁₉	—	4	16	no	—
112	#41×C₁₉	—	4	8	no	—
113	#41×C₁₉	—	4	8	no	—
114	C₂×Q₈×C₁₉	—	2	4	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₁₉	—	2	8	no	—
120	C₂×D₄×C₁₉	—	2	8	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	4	2	no	—
128	C₂×D₄×C₁₉	—	4	4	no	—
129	C₂×D₄×C₁₉	—	4	8	no	—
130	C₂×D₄×C₁₉	—	4	4	no	—
131	C₂×D₄×C₁₉	—	4	4	no	—
132	C₂×D₄×C₁₉	—	8	4	no	—
133	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
134	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
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	—	4	8	no	—
142	C₂²×C₄×C₁₉	—	4	4	no	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	Q₁₆×C₁₉	—	4	4	no	—
147	SD₁₆×C₁₉	—	4	4	no	—
148	M₁₆×C₁₉	—	4	2	no	—
149	C₂×C₈×C₁₉	—	2	2	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	4	1	no	—
161	C₄⋊C₄×C₁₉	—	4	1	no	—
162	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
164	C₂²⋊C₄×C₁₉	—	2	8	no	—
165	C₂²⋊C₄×C₁₉	—	2	2	no	—
166	C₂²⋊C₄×C₁₉	—	2	2	no	—
167	C₂²⋊C₄×C₁₉	—	4	1	no	—
168	C₄²×C₁₉	—	2	2	no	—
169	C₄²×C₁₉	—	2	2	no	—
170	C₄²×C₁₉	—	4	1	no	—
171	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
175	#18550	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₁₉	—	2	2	no	—
177	C₂³×C₁₉	—	2	4	no	—
178	C₂³×C₁₉	—	4	4	no	—
179	C₂³×C₁₉	—	4	2	no	—
180	C₂³×C₁₉	—	4	2	no	—
181	C₂³×C₁₉	—	4	4	no	—
182	C₂³×C₁₉	—	4	4	no	—
183	C₂³×C₁₉	—	4	2	no	—
184	C₂³×C₁₉	#120	1	1	yes	characteristic
185	Q₈×C₁₉	—	2	4	no	—
186	Q₈×C₁₉	—	2	2	no	—
187	Q₈×C₁₉	—	4	2	no	—
188	Q₈×C₁₉	—	4	2	no	—
189	Q₈×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
190	D₄×C₁₉	—	2	2	no	—
191	D₄×C₁₉	—	2	2	no	—
192	D₄×C₁₉	—	4	4	no	—
193	D₄×C₁₉	—	4	2	no	—
194	D₄×C₁₉	—	4	4	no	—
195	D₄×C₁₉	—	4	16	no	—
196	D₄×C₁₉	—	4	4	no	—
197	D₄×C₁₉	—	4	4	no	—
198	D₄×C₁₉	—	4	4	no	—
199	D₄×C₁₉	—	8	2	no	—
200	D₄×C₁₉	—	8	8	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	4	16	no	—
209	C₂×C₄×C₁₉	—	4	4	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	4	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
216	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
217	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
221	C₈×C₁₉	—	4	2	no	—
222	C₈×C₁₉	—	4	2	no	—
223	C₈×C₁₉	—	4	2	no	—
224	C₂×#550	C₂×C₁₉	1	1	yes	characteristic
225	#3138	C₂×C₁₉	1	1	yes	characteristic, complemented
226	#3113	C₂×C₁₉	1	1	yes	characteristic, complemented
227	#3110	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#1642	C₂×C₁₉	1	4	yes	complemented
229	#1641	C₂×C₁₉	1	4	yes	complemented
230	#1555	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#1491	C₂×C₁₉	1	1	yes	characteristic, complemented
232	#1490	C₂×C₁₉	1	1	yes	characteristic, complemented
233	C₂²×C₁₉	—	2	1	no	—
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	—	4	4	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	—	4	2	no	—
238	C₂²×C₁₉	—	4	4	no	—
239	C₂²×C₁₉	—	4	4	no	—
240	C₂²×C₁₉	—	4	2	no	—
241	C₂²×C₁₉	—	8	8	no	—
242	C₂²×C₁₉	—	8	4	no	—
243	C₂²×C₁₉	#455	1	2	yes	—
244	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
245	C₄×C₁₉	—	2	4	no	—
246	C₄×C₁₉	—	2	1	no	—
247	C₄×C₁₉	—	2	1	no	—
248	C₄×C₁₉	—	2	1	no	—
249	C₄×C₁₉	—	2	1	no	—
250	C₄×C₁₉	—	4	2	no	—
251	C₄×C₁₉	—	4	2	no	—
252	C₄×C₁₉	—	8	1	no	—
253	C₄×C₁₉	—	8	1	no	—
254	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
255	C₄×C₁₉	#575	1	2	yes	—
256	C₂²×#41	—	2	1	no	—
257	#550	—	2	2	no	—
258	#550	—	2	2	no	—
259	#550	—	2	2	no	—
260	#550	C₂²×C₁₉	1	4	yes	—
261	#533	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×#127	—	2	1	no	—
263	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
264	C₂×#121	—	2	2	no	—
265	C₂×#121	—	2	1	no	—
266	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
267	C₂×C₄×D₄	—	2	1	no	—
268	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
269	#490	—	2	2	no	—
270	#486	C₂²×C₁₉	1	2	yes	complemented
271	#486	C₂²×C₁₉	1	2	yes	complemented
272	#484	—	2	1	no	—
273	#483	—	2	1	no	—
274	#475	C₂²×C₁₉	1	2	yes	complemented
275	#474	C₂²×C₁₉	1	2	yes	complemented
276	#462	C₂²×C₁₉	1	2	yes	complemented
277	#461	C₂²×C₁₉	1	2	yes	complemented
278	#451	—	2	1	no	—
279	#450	—	2	1	no	—
280	#441	—	2	2	no	—
281	#440	—	2	2	no	—
282	#432	C₂²×C₁₉	1	1	yes	characteristic
283	#432	C₂²×C₁₉	1	1	yes	characteristic
284	#418	—	2	2	no	—
285	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
286	#331	C₂²×C₁₉	1	4	yes	complemented
287	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	complemented
288	D₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
289	C₂×C₁₉	—	2	2	no	—
290	C₂×C₁₉	—	8	2	no	—
291	C₂×C₁₉	—	8	4	no	—
292	C₂×C₁₉	#3003	1	1	yes	characteristic
293	C₂×C₁₉	#3005	1	1	yes	characteristic
294	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
295	C₂×#41	—	2	4	no	—
296	C₂×#41	—	2	4	no	—
297	C₂×#41	—	4	8	no	—
298	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	—	2	2	no	—
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
304	C₂²×D₄	D₄×C₁₉	1	2	yes	—
305	C₂³×C₄	—	2	2	no	—
306	C₂³×C₄	—	2	1	no	—
307	C₂×Q₁₆	—	2	2	no	—
308	C₂×SD₁₆	—	2	2	no	—
309	C₂×M₁₆	—	2	1	no	—
310	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
311	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
312	#127	—	2	4	no	—
313	#127	—	2	4	no	—
314	#127	—	2	1	no	—
315	#127	—	2	1	no	—
316	#127	D₄×C₁₉	1	2	yes	—
317	#127	C₂³×C₁₉	1	2	yes	—
318	#125	—	2	1	no	—
319	C₂²⋊Q₈	—	2	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	#121	—	2	4	no	—
322	#121	—	2	8	no	—
323	#121	—	2	8	no	—
324	#121	—	2	4	no	—
325	C₄×Q₈	—	2	1	no	—
326	C₄×Q₈	—	2	1	no	—
327	C₄×Q₈	—	2	1	no	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	D₄×C₁₉	1	2	yes	—
330	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
331	C₄×D₄	—	2	4	no	—
332	C₄×D₄	—	2	4	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	D₄×C₁₉	1	2	yes	—
336	C₄×D₄	C₂³×C₁₉	1	2	yes	—
337	#117	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
340	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
345	#107	—	2	2	no	—
346	#106	—	2	2	no	—
347	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
348	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
349	#103	—	2	2	no	—
350	#103	—	2	2	no	—
351	#103	—	2	2	no	—
352	#102	—	2	4	no	—
353	#102	—	2	4	no	—
354	#102	—	2	2	no	—
355	C₂²⋊C₈	—	2	1	no	—
356	C₂²⋊C₈	—	2	1	no	—
357	#97	—	2	1	no	—
358	#97	—	2	1	no	—
359	#97	—	2	1	no	—
360	C₄×C₈	C₂³×C₁₉	1	2	yes	—
361	C₁₉	#18550	1	1	yes	characteristic, direct product factor, Sylow
362	C₂⁴	—	2	2	no	—
363	C₂⁴	—	2	1	no	—
364	#41	—	4	16	no	—
365	#41	—	4	8	no	—
366	#41	—	4	8	no	—
367	C₂×Q₈	—	2	4	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
372	C₂×D₄	—	2	8	no	—
373	C₂×D₄	—	2	8	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	4	no	—
382	C₂×D₄	—	4	8	no	—
383	C₂×D₄	—	4	4	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	8	4	no	—
386	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
387	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	4	8	no	—
395	C₂²×C₄	—	4	4	no	—
396	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
399	Q₁₆	—	4	4	no	—
400	SD₁₆	—	4	4	no	—
401	M₁₆	—	4	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	4	1	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
416	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
417	C₂²⋊C₄	—	2	8	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	4	1	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	4	1	no	—
424	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
425	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
428	C₂³	—	2	2	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	4	4	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	4	no	—
434	C₂³	—	4	4	no	—
435	C₂³	—	4	2	no	—
436	C₂³	C₁₉×#120	1	1	yes	characteristic
437	Q₈	—	2	4	no	—
438	Q₈	—	2	2	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	4	2	no	—
441	Q₈	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
442	D₄	—	2	2	no	—
443	D₄	—	2	2	no	—
444	D₄	—	4	4	no	—
445	D₄	—	4	16	no	—
446	D₄	—	4	4	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	4	no	—
449	D₄	—	4	4	no	—
450	D₄	—	4	4	no	—
451	D₄	—	8	2	no	—
452	D₄	—	8	8	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	4	16	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
468	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
469	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
472	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
473	C₈	—	4	2	no	—
474	C₈	—	4	2	no	—
475	C₈	—	4	2	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	4	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	8	8	no	—
485	C₂²	—	8	4	no	—
486	C₂²	C₁₉×#455	1	2	yes	—
487	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
488	C₄	—	2	4	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	8	1	no	—
496	C₄	—	8	1	no	—
497	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
498	C₄	C₁₉×#575	1	2	yes	—
499	C₂	—	2	2	no	—
500	C₂	—	8	2	no	—
501	C₂	—	8	4	no	—
502	C₂	C₁₉×#3003	1	1	yes	characteristic
503	C₂	C₁₉×#3005	1	1	yes	characteristic
504	C₂	C₂×C₁₉×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#550	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
2. C₁₉×#3138	C₂	semidirect
3. C₁₉×#3113	C₂	semidirect
4. C₁₉×#3110	C₂	semidirect
5. C₁₉×#1642	C₂	semidirect
6. C₁₉×#1641	C₂	semidirect
7. C₁₉×#1555	C₂	semidirect
8. C₁₉×#1491	C₂	semidirect
9. C₁₉×#1490	C₂	semidirect
24. C₁₉×#486	C₂²	semidirect
25. C₁₉×#486	C₂²	semidirect
28. C₁₉×#475	C₂²	semidirect
29. C₁₉×#474	C₂²	semidirect
30. C₁₉×#462	C₂²	semidirect
31. C₁₉×#461	C₂²	semidirect
40. C₁₉×#331	C₂²	semidirect
41. C₁₉×Q₈⋊C₈	C₂²	semidirect
42. C₁₉×D₄⋊C₈	C₂²	semidirect
175. #18550	C₁₉	direct (N × H)
225. #3138	C₂×C₁₉	semidirect
226. #3113	C₂×C₁₉	semidirect
227. #3110	C₂×C₁₉	semidirect
228. #1642	C₂×C₁₉	semidirect
229. #1641	C₂×C₁₉	semidirect
230. #1555	C₂×C₁₉	semidirect
231. #1491	C₂×C₁₉	semidirect
232. #1490	C₂×C₁₉	semidirect
270. #486	C₂²×C₁₉	semidirect
271. #486	C₂²×C₁₉	semidirect
274. #475	C₂²×C₁₉	semidirect
275. #474	C₂²×C₁₉	semidirect
276. #462	C₂²×C₁₉	semidirect
277. #461	C₂²×C₁₉	semidirect
286. #331	C₂²×C₁₉	semidirect
287. Q₈⋊C₈	C₂²×C₁₉	semidirect
288. D₄⋊C₈	C₂²×C₁₉	semidirect
361. C₁₉	#18550	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#550	2
C₁₉×#3138	2
C₁₉×#3113	2
C₁₉×#3110	2
C₁₉×#1642	2
C₁₉×#1641	2
C₁₉×#1555	2
C₁₉×#1491	2
C₁₉×#1490	2
#18550	19

Subgroups — C19×#18550 #18024509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18550 #18024509