Subgroups — C₁₉×#24522 #18030481

Order 4864.

848 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3095	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#451	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2924	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2064	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2047	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1979	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1930	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1901	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1855	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1784	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₁₉×#485	—	2	1	no	—
18	C₁₉×#485	—	2	1	no	—
19	C₁₉×#484	—	2	1	no	—
20	C₁₉×#483	—	2	1	no	—
21	C₁₉×#451	—	2	1	no	—
22	C₁₉×#451	—	2	1	no	—
23	C₁₉×#451	—	2	2	no	—
24	C₁₉×#433	—	2	2	no	—
25	C₁₉×#432	—	2	1	no	—
26	C₁₉×#431	—	2	1	no	—
27	C₂×C₁₉×#108	C₂²	1	2	yes	—
28	C₁₉×#428	C₂²	1	1	yes	characteristic
29	C₁₉×#428	C₂²	1	1	yes	characteristic
30	C₁₉×#424	C₂²	1	2	yes	—
31	C₁₉×#419	—	2	1	no	—
32	C₁₉×#419	—	2	1	no	—
33	C₁₉×#419	C₂²	1	2	yes	—
34	C₁₉×#419	C₂²	1	1	yes	characteristic
35	C₁₉×#419	C₂²	1	1	yes	characteristic
36	C₁₉×#419	C₂²	1	2	yes	—
37	C₂×C₁₉×#103	—	2	1	no	—
38	C₂×C₁₉×#103	—	2	1	no	—
39	C₂×C₁₉×#103	C₂²	1	2	yes	—
40	C₂×C₁₉×#101	C₂²	1	2	yes	—
41	C₂×C₁₉×#101	C₂²	1	2	yes	—
42	C₂×C₁₉×#101	C₂²	1	2	yes	—
43	C₁₉×#407	C₂²	1	1	yes	characteristic
44	C₁₉×#407	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₉×#405	C₂²	1	2	yes	—
47	C₁₉×#343	C₂²	1	2	yes	—
48	C₁₉×#341	C₂²	1	2	yes	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂²×Q₈×C₁₉	—	2	4	no	—
51	C₂²×Q₈×C₁₉	—	2	1	no	—
52	C₂²×Q₈×C₁₉	—	2	1	no	—
53	C₂²×Q₈×C₁₉	—	2	1	no	—
54	C₂²×Q₈×C₁₉	—	2	1	no	—
55	C₂²×Q₈×C₁₉	—	4	2	no	—
56	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₉	—	2	1	no	—
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×Q₁₆×C₁₉	—	2	4	no	—
61	C₂×Q₁₆×C₁₉	—	2	2	no	—
62	C₂×Q₁₆×C₁₉	—	2	2	no	—
63	C₂×Q₁₆×C₁₉	—	4	2	no	—
64	C₂×M₁₆×C₁₉	—	2	1	no	—
65	C₂×M₁₆×C₁₉	—	4	2	no	—
66	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
68	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
69	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₉	—	2	1	no	—
71	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
72	C₁₉×C₂²⋊Q₈	—	2	1	no	—
73	C₁₉×C₂²⋊Q₈	—	2	1	no	—
74	C₁₉×C₂²⋊Q₈	—	2	1	no	—
75	C₁₉×C₂²⋊Q₈	—	2	1	no	—
76	C₁₉×#117	—	2	1	no	—
77	C₁₉×#117	—	2	1	no	—
78	C₁₉×#117	D₄	1	1	yes	characteristic
79	C₁₉×#117	D₄	1	1	yes	characteristic
80	C₁₉×#117	C₂³	1	1	yes	characteristic
81	C₁₉×#117	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₁₉×#108	—	4	2	no	—
90	C₁₉×#107	—	2	1	no	—
91	C₁₉×#107	—	2	1	no	—
92	C₁₉×#106	—	2	1	no	—
93	C₁₉×#106	—	2	1	no	—
94	C₁₉×C₄⋊C₈	—	2	2	no	—
95	C₁₉×C₄⋊C₈	—	2	2	no	—
96	C₁₉×#103	—	2	2	no	—
97	C₁₉×#103	—	2	2	no	—
98	C₁₉×#103	—	2	2	no	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#103	—	2	2	no	—
101	C₁₉×#103	—	2	2	no	—
102	C₁₉×#103	—	2	1	no	—
103	C₁₉×#103	—	2	1	no	—
104	C₁₉×#103	—	2	1	no	—
105	C₁₉×#103	—	2	1	no	—
106	C₁₉×#101	—	2	4	no	—
107	C₁₉×#101	—	4	2	no	—
108	C₁₉×#101	—	4	2	no	—
109	C₁₉×C₂²⋊C₈	—	2	1	no	—
110	C₁₉×C₂²⋊C₈	—	2	1	no	—
111	C₁₉×C₂²⋊C₈	—	2	1	no	—
112	C₁₉×C₂²⋊C₈	—	2	1	no	—
113	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
114	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
115	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
116	C₁₉×#97	—	2	2	no	—
117	C₄×C₈×C₁₉	—	2	2	no	—
118	C₂⁴×C₁₉	#41	1	1	yes	characteristic
119	C₂×Q₈×C₁₉	—	2	2	no	—
120	C₂×Q₈×C₁₉	—	2	4	no	—
121	C₂×Q₈×C₁₉	—	2	4	no	—
122	C₂×Q₈×C₁₉	—	2	2	no	—
123	C₂×Q₈×C₁₉	—	2	2	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	2	no	—
127	C₂×Q₈×C₁₉	—	2	2	no	—
128	C₂×Q₈×C₁₉	—	2	2	no	—
129	C₂×Q₈×C₁₉	—	2	2	no	—
130	C₂×Q₈×C₁₉	—	4	4	no	—
131	C₂×Q₈×C₁₉	—	4	4	no	—
132	C₂×Q₈×C₁₉	—	4	4	no	—
133	C₂×Q₈×C₁₉	—	4	2	no	—
134	C₂×Q₈×C₁₉	—	4	2	no	—
135	C₂×Q₈×C₁₉	—	4	1	no	—
136	C₂×Q₈×C₁₉	—	4	1	no	—
137	C₂×Q₈×C₁₉	#41	1	4	yes	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	4	4	no	—
146	C₂²×C₄×C₁₉	—	4	1	no	—
147	C₂²×C₄×C₁₉	—	4	1	no	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
154	Q₁₆×C₁₉	—	4	4	no	—
155	Q₁₆×C₁₉	—	4	4	no	—
156	M₁₆×C₁₉	—	2	2	no	—
157	M₁₆×C₁₉	—	2	2	no	—
158	M₁₆×C₁₉	—	2	2	no	—
159	M₁₆×C₁₉	—	2	2	no	—
160	M₁₆×C₁₉	—	2	2	no	—
161	M₁₆×C₁₉	—	2	2	no	—
162	M₁₆×C₁₉	—	4	2	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	—	4	2	no	—
170	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
171	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	4	1	no	—
177	C₄⋊C₄×C₁₉	—	4	1	no	—
178	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂²⋊C₄×C₁₉	—	2	1	no	—
183	C₂²⋊C₄×C₁₉	—	2	1	no	—
184	C₂²⋊C₄×C₁₉	—	2	1	no	—
185	C₂²⋊C₄×C₁₉	—	2	1	no	—
186	C₂²⋊C₄×C₁₉	—	4	1	no	—
187	C₂²⋊C₄×C₁₉	—	4	1	no	—
188	C₄²×C₁₉	—	2	1	no	—
189	C₄²×C₁₉	—	2	1	no	—
190	C₄²×C₁₉	—	2	1	no	—
191	C₄²×C₁₉	—	2	1	no	—
192	#24522	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂³×C₁₉	—	2	2	no	—
194	C₂³×C₁₉	—	2	2	no	—
195	C₂³×C₁₉	—	4	1	no	—
196	C₂³×C₁₉	#121	1	1	yes	characteristic
197	C₂³×C₁₉	#121	1	1	yes	characteristic
198	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
199	Q₈×C₁₉	—	2	4	no	—
200	Q₈×C₁₉	—	2	4	no	—
201	Q₈×C₁₉	—	4	4	no	—
202	Q₈×C₁₉	—	4	4	no	—
203	Q₈×C₁₉	—	4	2	no	—
204	Q₈×C₁₉	—	4	2	no	—
205	Q₈×C₁₉	—	4	1	no	—
206	Q₈×C₁₉	—	4	1	no	—
207	Q₈×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	4	no	—
220	C₂×C₄×C₁₉	—	4	4	no	—
221	C₂×C₄×C₁₉	—	4	4	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	2	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	8	1	no	—
229	C₂×C₄×C₁₉	—	8	1	no	—
230	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
235	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
236	C₈×C₁₉	—	2	2	no	—
237	C₈×C₁₉	—	2	2	no	—
238	C₈×C₁₉	—	4	1	no	—
239	C₈×C₁₉	—	4	2	no	—
240	C₈×C₁₉	—	4	1	no	—
241	C₈×C₁₉	—	4	2	no	—
242	#3095	C₂×C₁₉	1	1	yes	characteristic
243	C₂×#451	C₂×C₁₉	1	1	yes	characteristic
244	#2924	C₂×C₁₉	1	1	yes	characteristic
245	C₂×#419	C₂×C₁₉	1	1	yes	characteristic
246	#2064	C₂×C₁₉	1	2	yes	complemented
247	#2047	C₂×C₁₉	1	2	yes	complemented
248	#1979	C₂×C₁₉	1	2	yes	complemented
249	#1930	C₂×C₁₉	1	2	yes	complemented
250	#1901	C₂×C₁₉	1	1	yes	characteristic
251	#1855	C₂×C₁₉	1	1	yes	characteristic
252	#1784	C₂×C₁₉	1	1	yes	characteristic
253	C₂²×C₁₉	—	2	1	no	—
254	C₂²×C₁₉	—	2	1	no	—
255	C₂²×C₁₉	—	2	1	no	—
256	C₂²×C₁₉	—	2	1	no	—
257	C₂²×C₁₉	—	2	1	no	—
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	—	2	1	no	—
260	C₂²×C₁₉	—	4	4	no	—
261	C₂²×C₁₉	#473	1	2	yes	—
262	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
263	C₂²×C₁₉	#551	1	2	yes	—
264	C₄×C₁₉	—	2	1	no	—
265	C₄×C₁₉	—	2	1	no	—
266	C₄×C₁₉	—	4	4	no	—
267	C₄×C₁₉	—	4	1	no	—
268	C₄×C₁₉	—	4	1	no	—
269	C₄×C₁₉	—	4	1	no	—
270	C₄×C₁₉	—	4	1	no	—
271	C₄×C₁₉	—	8	1	no	—
272	C₄×C₁₉	—	8	1	no	—
273	C₄×C₁₉	#525	1	1	yes	characteristic
274	C₄×C₁₉	#535	1	1	yes	characteristic
275	C₄×C₁₉	#546	1	2	yes	—
276	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
277	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	—
278	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
279	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
280	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
281	#485	—	2	1	no	—
282	#485	—	2	1	no	—
283	#484	—	2	1	no	—
284	#483	—	2	1	no	—
285	#451	—	2	1	no	—
286	#451	—	2	1	no	—
287	#451	—	2	2	no	—
288	#433	—	2	2	no	—
289	#432	—	2	1	no	—
290	#431	—	2	1	no	—
291	C₂×#108	C₂²×C₁₉	1	2	yes	—
292	#428	C₂²×C₁₉	1	1	yes	characteristic
293	#428	C₂²×C₁₉	1	1	yes	characteristic
294	#424	C₂²×C₁₉	1	2	yes	—
295	#419	—	2	1	no	—
296	#419	—	2	1	no	—
297	#419	C₂²×C₁₉	1	2	yes	—
298	#419	C₂²×C₁₉	1	1	yes	characteristic
299	#419	C₂²×C₁₉	1	1	yes	characteristic
300	#419	C₂²×C₁₉	1	2	yes	—
301	C₂×#103	—	2	1	no	—
302	C₂×#103	—	2	1	no	—
303	C₂×#103	C₂²×C₁₉	1	2	yes	—
304	C₂×#101	C₂²×C₁₉	1	2	yes	—
305	C₂×#101	C₂²×C₁₉	1	2	yes	—
306	C₂×#101	C₂²×C₁₉	1	2	yes	—
307	#407	C₂²×C₁₉	1	1	yes	characteristic
308	#407	C₂²×C₁₉	1	1	yes	characteristic
309	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
310	#405	C₂²×C₁₉	1	2	yes	—
311	#343	C₂²×C₁₉	1	2	yes	—
312	#341	C₂²×C₁₉	1	2	yes	—
313	C₂×C₁₉	—	2	2	no	—
314	C₂×C₁₉	—	2	2	no	—
315	C₂×C₁₉	—	4	1	no	—
316	C₂×C₁₉	#2411	1	1	yes	characteristic
317	C₂×C₁₉	C₂×#473	1	1	yes	characteristic
318	C₂×C₁₉	#3069	1	1	yes	characteristic
319	C₂²×Q₈	—	2	1	no	—
320	C₂²×Q₈	—	2	4	no	—
321	C₂²×Q₈	—	2	1	no	—
322	C₂²×Q₈	—	2	1	no	—
323	C₂²×Q₈	—	2	1	no	—
324	C₂²×Q₈	—	2	1	no	—
325	C₂²×Q₈	—	4	2	no	—
326	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
327	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
328	C₂³×C₄	—	2	1	no	—
329	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
330	C₂×Q₁₆	—	2	4	no	—
331	C₂×Q₁₆	—	2	2	no	—
332	C₂×Q₁₆	—	2	2	no	—
333	C₂×Q₁₆	—	4	2	no	—
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	—	4	2	no	—
336	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
337	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
338	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
339	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
340	C₂²×C₈	—	2	1	no	—
341	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
342	C₂²⋊Q₈	—	2	1	no	—
343	C₂²⋊Q₈	—	2	1	no	—
344	C₂²⋊Q₈	—	2	1	no	—
345	C₂²⋊Q₈	—	2	1	no	—
346	#117	—	2	1	no	—
347	#117	—	2	1	no	—
348	#117	D₄×C₁₉	1	1	yes	characteristic
349	#117	D₄×C₁₉	1	1	yes	characteristic
350	#117	C₂³×C₁₉	1	1	yes	characteristic
351	#117	C₂³×C₁₉	1	1	yes	characteristic
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
354	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₄²	—	2	1	no	—
359	#108	—	4	2	no	—
360	#107	—	2	1	no	—
361	#107	—	2	1	no	—
362	#106	—	2	1	no	—
363	#106	—	2	1	no	—
364	C₄⋊C₈	—	2	2	no	—
365	C₄⋊C₈	—	2	2	no	—
366	#103	—	2	2	no	—
367	#103	—	2	2	no	—
368	#103	—	2	2	no	—
369	#103	—	2	2	no	—
370	#103	—	2	2	no	—
371	#103	—	2	2	no	—
372	#103	—	2	1	no	—
373	#103	—	2	1	no	—
374	#103	—	2	1	no	—
375	#103	—	2	1	no	—
376	#101	—	2	4	no	—
377	#101	—	4	2	no	—
378	#101	—	4	2	no	—
379	C₂²⋊C₈	—	2	1	no	—
380	C₂²⋊C₈	—	2	1	no	—
381	C₂²⋊C₈	—	2	1	no	—
382	C₂²⋊C₈	—	2	1	no	—
383	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
384	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
385	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
386	#97	—	2	2	no	—
387	C₄×C₈	—	2	2	no	—
388	C₁₉	#24522	1	1	yes	characteristic, direct product factor, Sylow
389	C₂⁴	#41×C₁₉	1	1	yes	characteristic
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	4	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	4	4	no	—
402	C₂×Q₈	—	4	4	no	—
403	C₂×Q₈	—	4	4	no	—
404	C₂×Q₈	—	4	2	no	—
405	C₂×Q₈	—	4	2	no	—
406	C₂×Q₈	—	4	1	no	—
407	C₂×Q₈	—	4	1	no	—
408	C₂×Q₈	#41×C₁₉	1	4	yes	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	4	4	no	—
417	C₂²×C₄	—	4	1	no	—
418	C₂²×C₄	—	4	1	no	—
419	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
425	Q₁₆	—	4	4	no	—
426	Q₁₆	—	4	4	no	—
427	M₁₆	—	2	2	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	2	2	no	—
430	M₁₆	—	2	2	no	—
431	M₁₆	—	2	2	no	—
432	M₁₆	—	2	2	no	—
433	M₁₆	—	4	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	4	2	no	—
441	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
442	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	4	1	no	—
448	C₄⋊C₄	—	4	1	no	—
449	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	4	1	no	—
458	C₂²⋊C₄	—	4	1	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	4	1	no	—
466	C₂³	C₁₉×#121	1	1	yes	characteristic
467	C₂³	C₁₉×#121	1	1	yes	characteristic
468	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
469	Q₈	—	2	4	no	—
470	Q₈	—	2	4	no	—
471	Q₈	—	4	4	no	—
472	Q₈	—	4	4	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	1	no	—
476	Q₈	—	4	1	no	—
477	Q₈	—	4	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	4	4	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	8	1	no	—
499	C₂×C₄	—	8	1	no	—
500	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
501	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
504	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
505	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
506	C₈	—	2	2	no	—
507	C₈	—	2	2	no	—
508	C₈	—	4	1	no	—
509	C₈	—	4	2	no	—
510	C₈	—	4	1	no	—
511	C₈	—	4	2	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	2	1	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	4	4	no	—
520	C₂²	C₁₉×#473	1	2	yes	—
521	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
522	C₂²	C₁₉×#551	1	2	yes	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	8	1	no	—
531	C₄	—	8	1	no	—
532	C₄	C₁₉×#525	1	1	yes	characteristic
533	C₄	C₁₉×#535	1	1	yes	characteristic
534	C₄	C₁₉×#546	1	2	yes	—
535	C₂	—	2	2	no	—
536	C₂	—	2	2	no	—
537	C₂	—	4	1	no	—
538	C₂	C₁₉×#2411	1	1	yes	characteristic
539	C₂	C₂×C₁₉×#473	1	1	yes	characteristic
540	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. C₁₉×#2064	C₂	semidirect
6. C₁₉×#2047	C₂	semidirect
7. C₁₉×#1979	C₂	semidirect
8. C₁₉×#1930	C₂	semidirect
192. #24522	C₁₉	direct (N × H)
246. #2064	C₂×C₁₉	semidirect
247. #2047	C₂×C₁₉	semidirect
248. #1979	C₂×C₁₉	semidirect
249. #1930	C₂×C₁₉	semidirect
388. C₁₉	#24522	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×#3095	2
C₂×C₁₉×#451	2
C₁₉×#2924	2
C₂×C₁₉×#419	2
C₁₉×#2064	2
C₁₉×#2047	2
C₁₉×#1979	2
C₁₉×#1930	2
C₁₉×#1901	2
C₁₉×#1855	2
C₁₉×#1784	2
#24522	19

Subgroups — C19×#24522 #18030481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24522 #18030481