Subgroups — C₁₉×#18539 #18024498

Order 4864.

1178 conjugacy classes of subgroups.

The subgroup lattice has 496 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
2	C₁₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3110	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3110	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1654	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1647	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1490	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×#547	—	2	2	no	—
12	C₁₉×#547	—	2	2	no	—
13	C₁₉×#547	—	2	2	no	—
14	C₁₉×#547	C₂²	1	4	yes	—
15	C₁₉×#533	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#123	—	2	2	no	—
18	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₉×#121	—	2	1	no	—
20	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₁₉×#501	—	2	2	no	—
24	C₁₉×#500	C₂²	1	2	yes	complemented
25	C₁₉×#498	C₂²	1	2	yes	complemented
26	C₁₉×#484	—	2	1	no	—
27	C₁₉×#484	—	2	1	no	—
28	C₁₉×#474	C₂²	1	2	yes	complemented
29	C₁₉×#474	C₂²	1	2	yes	complemented
30	C₁₉×#461	C₂²	1	2	yes	complemented
31	C₁₉×#461	C₂²	1	2	yes	complemented
32	C₁₉×#450	—	2	1	no	—
33	C₁₉×#450	—	2	1	no	—
34	C₁₉×#440	—	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×#428	—	2	2	no	—
39	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
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	—	4	8	no	—
46	C₂²×Q₈×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	—	2	2	no	—
48	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	—	2	2	no	—
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂×SD₁₆×C₁₉	—	2	2	no	—
54	C₂×SD₁₆×C₁₉	—	2	2	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
59	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₁₉×#125	—	2	1	no	—
63	C₁₉×#123	—	2	8	no	—
64	C₁₉×#123	—	2	8	no	—
65	C₁₉×C₂²⋊Q₈	—	2	4	no	—
66	C₁₉×C₂²⋊Q₈	—	2	4	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	4	no	—
71	C₄×Q₈×C₁₉	—	2	1	no	—
72	C₄×Q₈×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	—	2	1	no	—
74	C₄×D₄×C₁₉	—	2	1	no	—
75	C₄×D₄×C₁₉	—	2	1	no	—
76	C₄×D₄×C₁₉	—	2	1	no	—
77	C₄×D₄×C₁₉	D₄	1	2	yes	—
78	C₄×D₄×C₁₉	D₄	1	2	yes	—
79	C₄×D₄×C₁₉	C₂³	1	2	yes	—
80	C₄×D₄×C₁₉	C₂³	1	2	yes	—
81	C₁₉×#117	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
86	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
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×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₁₉×#107	—	2	4	no	—
94	C₁₉×#107	—	2	2	no	—
95	C₁₉×#107	—	2	2	no	—
96	C₁₉×#106	—	2	4	no	—
97	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
98	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#103	—	2	2	no	—
101	C₁₉×#102	—	2	2	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	1	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	2	no	—
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	4	4	no	—
119	C₂×D₄×C₁₉	—	2	4	no	—
120	C₂×D₄×C₁₉	—	2	8	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	4	2	no	—
124	C₂×D₄×C₁₉	—	4	8	no	—
125	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₉	—	2	8	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	4	4	no	—
136	C₂²×C₄×C₁₉	—	4	4	no	—
137	C₂²×C₄×C₁₉	—	4	8	no	—
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	SD₁₆×C₁₉	—	4	4	no	—
142	SD₁₆×C₁₉	—	4	4	no	—
143	M₁₆×C₁₉	—	2	4	no	—
144	C₂×C₈×C₁₉	—	2	2	no	—
145	C₂×C₈×C₁₉	—	2	2	no	—
146	C₂×C₈×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	8	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×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	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	4	1	no	—
158	C₄⋊C₄×C₁₉	—	4	1	no	—
159	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
162	C₂²⋊C₄×C₁₉	—	2	8	no	—
163	C₂²⋊C₄×C₁₉	—	2	2	no	—
164	C₂²⋊C₄×C₁₉	—	2	2	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	—	4	1	no	—
169	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
173	#18539	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂³×C₁₉	—	2	4	no	—
175	C₂³×C₁₉	—	2	2	no	—
176	C₂³×C₁₉	—	2	2	no	—
177	C₂³×C₁₉	—	4	2	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	—	4	2	no	—
180	C₂³×C₁₉	—	4	2	no	—
181	C₂³×C₁₉	—	4	2	no	—
182	C₂³×C₁₉	#120	1	1	yes	characteristic
183	Q₈×C₁₉	—	4	4	no	—
184	Q₈×C₁₉	—	4	4	no	—
185	Q₈×C₁₉	—	4	2	no	—
186	Q₈×C₁₉	—	4	2	no	—
187	D₄×C₁₉	—	2	4	no	—
188	D₄×C₁₉	—	2	2	no	—
189	D₄×C₁₉	—	2	2	no	—
190	D₄×C₁₉	—	2	2	no	—
191	D₄×C₁₉	—	4	2	no	—
192	D₄×C₁₉	—	4	16	no	—
193	D₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	4	4	no	—
201	C₂×C₄×C₁₉	—	4	4	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	4	no	—
205	C₂×C₄×C₁₉	—	4	16	no	—
206	C₂×C₄×C₁₉	—	4	4	no	—
207	C₂×C₄×C₁₉	—	4	4	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
211	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
212	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
216	C₈×C₁₉	—	2	4	no	—
217	C₈×C₁₉	—	4	2	no	—
218	C₈×C₁₉	—	4	2	no	—
219	C₂×#547	C₂×C₁₉	1	1	yes	characteristic
220	#3165	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#3110	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#3110	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#1654	C₂×C₁₉	1	4	yes	complemented
224	#1647	C₂×C₁₉	1	4	yes	complemented
225	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
226	#1490	C₂×C₁₉	1	1	yes	characteristic, complemented
227	#1490	C₂×C₁₉	1	1	yes	characteristic, complemented
228	C₂²×C₁₉	—	2	1	no	—
229	C₂²×C₁₉	—	2	1	no	—
230	C₂²×C₁₉	—	2	4	no	—
231	C₂²×C₁₉	—	4	8	no	—
232	C₂²×C₁₉	—	4	2	no	—
233	C₂²×C₁₉	—	4	2	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	—	4	2	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	—	8	4	no	—
238	C₂²×C₁₉	#456	1	2	yes	—
239	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
240	C₄×C₁₉	—	2	1	no	—
241	C₄×C₁₉	—	2	1	no	—
242	C₄×C₁₉	—	2	1	no	—
243	C₄×C₁₉	—	2	1	no	—
244	C₄×C₁₉	—	4	2	no	—
245	C₄×C₁₉	—	4	4	no	—
246	C₄×C₁₉	—	4	2	no	—
247	C₄×C₁₉	—	8	1	no	—
248	C₄×C₁₉	—	8	1	no	—
249	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
250	C₄×C₁₉	#575	1	2	yes	—
251	C₂²×#41	—	2	1	no	—
252	#547	—	2	2	no	—
253	#547	—	2	2	no	—
254	#547	—	2	2	no	—
255	#547	C₂²×C₁₉	1	4	yes	—
256	#533	C₂²×C₁₉	1	1	yes	characteristic
257	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×#123	—	2	2	no	—
259	C₂×C₂²⋊Q₈	—	2	1	no	—
260	C₂×#121	—	2	1	no	—
261	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
263	C₂²×C₄⋊C₄	—	2	1	no	—
264	#501	—	2	2	no	—
265	#500	C₂²×C₁₉	1	2	yes	complemented
266	#498	C₂²×C₁₉	1	2	yes	complemented
267	#484	—	2	1	no	—
268	#484	—	2	1	no	—
269	#474	C₂²×C₁₉	1	2	yes	complemented
270	#474	C₂²×C₁₉	1	2	yes	complemented
271	#461	C₂²×C₁₉	1	2	yes	complemented
272	#461	C₂²×C₁₉	1	2	yes	complemented
273	#450	—	2	1	no	—
274	#450	—	2	1	no	—
275	#440	—	2	2	no	—
276	#440	—	2	2	no	—
277	#432	C₂²×C₁₉	1	1	yes	characteristic
278	#432	C₂²×C₁₉	1	1	yes	characteristic
279	#428	—	2	2	no	—
280	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
281	#332	C₂²×C₁₉	1	4	yes	complemented
282	D₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
283	D₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
284	C₂×C₁₉	—	2	2	no	—
285	C₂×C₁₉	—	4	4	no	—
286	C₂×C₁₉	—	8	2	no	—
287	C₂×C₁₉	#3003	1	1	yes	characteristic
288	C₂×C₁₉	#3005	1	1	yes	characteristic
289	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
290	C₂×#41	—	2	4	no	—
291	C₂×#41	—	2	4	no	—
292	C₂×#41	—	4	8	no	—
293	C₂²×Q₈	—	2	1	no	—
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
296	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
297	C₂³×C₄	—	2	2	no	—
298	C₂³×C₄	—	2	1	no	—
299	C₂³×C₄	—	2	1	no	—
300	C₂×SD₁₆	—	2	2	no	—
301	C₂×SD₁₆	—	2	2	no	—
302	C₂×M₁₆	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
306	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
307	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
308	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
309	#125	—	2	1	no	—
310	#123	—	2	8	no	—
311	#123	—	2	8	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	C₂²⋊Q₈	—	2	1	no	—
315	C₂²⋊Q₈	—	2	1	no	—
316	#121	—	2	4	no	—
317	#121	—	2	4	no	—
318	C₄×Q₈	—	2	1	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	—	2	1	no	—
324	C₄×D₄	D₄×C₁₉	1	2	yes	—
325	C₄×D₄	D₄×C₁₉	1	2	yes	—
326	C₄×D₄	C₂³×C₁₉	1	2	yes	—
327	C₄×D₄	C₂³×C₁₉	1	2	yes	—
328	#117	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	4	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	4	no	—
333	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
334	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
335	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
340	#107	—	2	4	no	—
341	#107	—	2	2	no	—
342	#107	—	2	2	no	—
343	#106	—	2	4	no	—
344	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
345	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
346	#103	—	2	2	no	—
347	#103	—	2	2	no	—
348	#102	—	2	2	no	—
349	#102	—	2	2	no	—
350	C₂²⋊C₈	—	2	1	no	—
351	C₂²⋊C₈	—	2	1	no	—
352	#97	—	2	1	no	—
353	#97	—	2	1	no	—
354	#97	—	2	1	no	—
355	C₄×C₈	C₂³×C₁₉	1	2	yes	—
356	C₁₉	#18539	1	1	yes	characteristic, direct product factor, Sylow
357	C₂⁴	—	2	1	no	—
358	C₂⁴	—	2	1	no	—
359	#41	—	4	16	no	—
360	#41	—	4	8	no	—
361	#41	—	4	8	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	4	4	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	8	no	—
373	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
374	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
375	C₂²×C₄	—	2	8	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	8	no	—
386	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
389	SD₁₆	—	4	4	no	—
390	SD₁₆	—	4	4	no	—
391	M₁₆	—	2	4	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₄⋊C₄	—	2	8	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	4	1	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
408	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
409	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	4	1	no	—
416	C₄²	—	4	1	no	—
417	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
421	C₂³	—	2	4	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	C₁₉×#120	1	1	yes	characteristic
430	Q₈	—	4	4	no	—
431	Q₈	—	4	4	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	4	2	no	—
434	D₄	—	2	4	no	—
435	D₄	—	2	2	no	—
436	D₄	—	2	2	no	—
437	D₄	—	2	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	16	no	—
440	D₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	16	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
458	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
459	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
463	C₈	—	2	4	no	—
464	C₈	—	4	2	no	—
465	C₈	—	4	2	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	4	8	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	8	4	no	—
476	C₂²	C₁₉×#456	1	2	yes	—
477	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	2	no	—
485	C₄	—	8	1	no	—
486	C₄	—	8	1	no	—
487	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
488	C₄	C₁₉×#575	1	2	yes	—
489	C₂	—	2	2	no	—
490	C₂	—	4	4	no	—
491	C₂	—	8	2	no	—
492	C₂	C₁₉×#3003	1	1	yes	characteristic
493	C₂	C₁₉×#3005	1	1	yes	characteristic
494	C₂	C₂×C₁₉×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#547	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×#3165	C₂	semidirect
3. C₁₉×#3110	C₂	semidirect
4. C₁₉×#3110	C₂	semidirect
5. C₁₉×#1654	C₂	semidirect
6. C₁₉×#1647	C₂	semidirect
7. C₁₉×#1556	C₂	semidirect
8. C₁₉×#1490	C₂	semidirect
9. C₁₉×#1490	C₂	semidirect
24. C₁₉×#500	C₂²	semidirect
25. C₁₉×#498	C₂²	semidirect
28. C₁₉×#474	C₂²	semidirect
29. C₁₉×#474	C₂²	semidirect
30. C₁₉×#461	C₂²	semidirect
31. C₁₉×#461	C₂²	semidirect
40. C₁₉×#332	C₂²	semidirect
41. C₁₉×D₄⋊C₈	C₂²	semidirect
42. C₁₉×D₄⋊C₈	C₂²	semidirect
173. #18539	C₁₉	direct (N × H)
220. #3165	C₂×C₁₉	semidirect
221. #3110	C₂×C₁₉	semidirect
222. #3110	C₂×C₁₉	semidirect
223. #1654	C₂×C₁₉	semidirect
224. #1647	C₂×C₁₉	semidirect
225. #1556	C₂×C₁₉	semidirect
226. #1490	C₂×C₁₉	semidirect
227. #1490	C₂×C₁₉	semidirect
265. #500	C₂²×C₁₉	semidirect
266. #498	C₂²×C₁₉	semidirect
269. #474	C₂²×C₁₉	semidirect
270. #474	C₂²×C₁₉	semidirect
271. #461	C₂²×C₁₉	semidirect
272. #461	C₂²×C₁₉	semidirect
281. #332	C₂²×C₁₉	semidirect
282. D₄⋊C₈	C₂²×C₁₉	semidirect
283. D₄⋊C₈	C₂²×C₁₉	semidirect
356. C₁₉	#18539	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×#547	2
C₁₉×#3165	2
C₁₉×#3110	2
C₁₉×#1654	2
C₁₉×#1647	2
C₁₉×#1556	2
C₁₉×#1490	2
#18539	19

Subgroups — C19×#18539 #18024498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18539 #18024498