Subgroups — C₁₉×#18371 #18024330

Order 4864.

924 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3493	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3238	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2621	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1612	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1611	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1610	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1512	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#556	—	2	2	no	—
10	C₁₉×#555	—	2	2	no	—
11	C₁₉×#553	—	2	2	no	—
12	C₁₉×#552	—	2	2	no	—
13	C₁₉×#544	C₂²	1	1	yes	characteristic
14	C₁₉×#538	—	2	1	no	—
15	C₁₉×#538	C₂²	1	2	yes	—
16	C₁₉×#537	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₉×#529	—	2	1	no	—
19	C₁₉×#529	C₂²	1	2	yes	—
20	C₁₉×#525	—	2	1	no	—
21	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
22	C₁₉×#520	—	2	1	no	—
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₁₉×#501	—	2	2	no	—
25	C₁₉×#489	—	2	2	no	—
26	C₁₉×#483	C₂²	1	4	yes	—
27	C₁₉×#480	C₂²	1	4	yes	—
28	C₁₉×#477	—	2	2	no	—
29	C₁₉×#476	—	2	2	no	—
30	C₁₉×#432	C₂²	1	2	yes	—
31	C₁₉×#398	—	2	1	no	—
32	C₁₉×#398	C₂²	1	2	yes	—
33	C₁₉×#397	—	2	1	no	—
34	C₁₉×#397	C₂²	1	2	yes	—
35	C₁₉×#391	—	2	1	no	—
36	C₁₉×#382	C₂²	1	1	yes	characteristic
37	C₁₉×#328	C₂²	1	4	yes	—
38	C₁₉×#327	C₂²	1	4	yes	—
39	C₁₉×#324	C₂²	1	2	yes	—
40	C₁₉×#323	C₂²	1	2	yes	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
44	C₁₉×C₄⋊Q₈	—	2	2	no	—
45	C₁₉×C₄⋊Q₈	—	2	2	no	—
46	C₁₉×C₄⋊Q₈	—	2	2	no	—
47	C₁₉×#126	—	2	2	no	—
48	C₁₉×#126	—	2	2	no	—
49	C₁₉×#126	—	2	2	no	—
50	C₁₉×#126	—	2	2	no	—
51	C₁₉×#125	—	2	1	no	—
52	C₁₉×#125	—	2	2	no	—
53	C₁₉×#125	D₄	1	2	yes	—
54	C₁₉×#124	—	2	1	no	—
55	C₁₉×#124	—	2	2	no	—
56	C₁₉×#124	—	2	2	no	—
57	C₁₉×#124	D₄	1	2	yes	—
58	C₁₉×#123	—	2	2	no	—
59	C₁₉×#123	—	2	2	no	—
60	C₁₉×#123	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	—	2	1	no	—
62	C₁₉×C₂²⋊Q₈	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	4	4	no	—
66	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
67	C₁₉×#121	—	2	1	no	—
68	C₁₉×#121	—	2	1	no	—
69	C₁₉×#121	—	2	2	no	—
70	C₁₉×#121	—	2	2	no	—
71	C₁₉×#121	—	2	2	no	—
72	C₁₉×#121	—	2	1	no	—
73	C₁₉×#121	C₂³	1	2	yes	—
74	C₁₉×#120	—	2	2	no	—
75	C₄×Q₈×C₁₉	—	2	2	no	—
76	C₄×Q₈×C₁₉	—	2	1	no	—
77	C₄×Q₈×C₁₉	D₄	1	2	yes	—
78	C₄×D₄×C₁₉	—	2	2	no	—
79	C₄×D₄×C₁₉	—	2	2	no	—
80	C₄×D₄×C₁₉	—	2	2	no	—
81	C₄×D₄×C₁₉	—	2	1	no	—
82	C₄×D₄×C₁₉	—	2	2	no	—
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	D₄	1	2	yes	—
85	C₁₉×#117	—	2	2	no	—
86	C₁₉×#117	—	2	2	no	—
87	C₁₉×#117	—	2	1	no	—
88	C₁₉×#117	—	2	2	no	—
89	C₁₉×#117	—	2	2	no	—
90	C₁₉×#117	—	2	2	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
103	C₁₉×#107	—	2	4	no	—
104	C₁₉×#106	—	2	4	no	—
105	C₁₉×C₄⋊C₈	—	2	2	no	—
106	C₁₉×#103	—	2	4	no	—
107	C₁₉×#102	—	2	4	no	—
108	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
109	C₁₉×#97	—	2	2	no	—
110	C₁₉×#95	—	2	1	no	—
111	C₁₉×#95	—	2	2	no	—
112	C₁₉×#95	—	2	2	no	—
113	C₁₉×#95	C₂³	1	2	yes	—
114	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
115	#41×C₁₉	—	4	2	no	—
116	#41×C₁₉	—	4	2	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	4	2	no	—
120	C₂×Q₈×C₁₉	—	4	2	no	—
121	C₂×Q₈×C₁₉	—	4	1	no	—
122	C₂×Q₈×C₁₉	—	4	1	no	—
123	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	1	no	—
129	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	4	1	no	—
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
145	C₂×C₈×C₁₉	—	2	4	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	4	no	—
159	C₄⋊C₄×C₁₉	—	4	2	no	—
160	C₄⋊C₄×C₁₉	—	4	2	no	—
161	C₄⋊C₄×C₁₉	—	4	4	no	—
162	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
168	C₂²⋊C₄×C₁₉	—	2	2	no	—
169	C₂²⋊C₄×C₁₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	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	4	no	—
176	C₄²×C₁₉	—	2	2	no	—
177	C₄²×C₁₉	—	2	2	no	—
178	C₄²×C₁₉	—	2	1	no	—
179	C₄²×C₁₉	—	2	1	no	—
180	C₄²×C₁₉	—	2	2	no	—
181	C₄²×C₁₉	C₂×D₄	1	2	yes	—
182	C₄²×C₁₉	C₂×D₄	1	2	yes	—
183	#18371	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂³×C₁₉	—	2	1	no	—
185	C₂³×C₁₉	—	2	2	no	—
186	C₂³×C₁₉	—	2	1	no	—
187	C₂³×C₁₉	—	2	1	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	—	4	1	no	—
190	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₁₉	—	4	2	no	—
192	Q₈×C₁₉	—	4	2	no	—
193	Q₈×C₁₉	—	8	2	no	—
194	Q₈×C₁₉	—	8	2	no	—
195	Q₈×C₁₉	—	8	1	no	—
196	D₄×C₁₉	—	4	2	no	—
197	D₄×C₁₉	—	4	2	no	—
198	D₄×C₁₉	—	4	2	no	—
199	D₄×C₁₉	—	4	2	no	—
200	D₄×C₁₉	—	8	2	no	—
201	D₄×C₁₉	—	8	1	no	—
202	D₄×C₁₉	—	8	2	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	4	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	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	—	8	2	no	—
226	C₂×C₄×C₁₉	—	8	2	no	—
227	C₂×C₄×C₁₉	#120	1	2	yes	—
228	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
230	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
231	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
232	C₈×C₁₉	—	4	4	no	—
233	#3493	C₂×C₁₉	1	1	yes	characteristic
234	#3238	C₂×C₁₉	1	2	yes	complemented
235	#2621	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#1612	C₂×C₁₉	1	4	yes	complemented
237	#1611	C₂×C₁₉	1	2	yes	complemented
238	#1610	C₂×C₁₉	1	2	yes	complemented
239	#1512	C₂×C₁₉	1	2	yes	complemented
240	#1464	C₂×C₁₉	1	1	yes	characteristic, complemented
241	C₂²×C₁₉	—	2	1	no	—
242	C₂²×C₁₉	—	2	1	no	—
243	C₂²×C₁₉	—	4	2	no	—
244	C₂²×C₁₉	—	4	1	no	—
245	C₂²×C₁₉	—	4	2	no	—
246	C₂²×C₁₉	—	4	2	no	—
247	C₂²×C₁₉	—	4	1	no	—
248	C₂²×C₁₉	—	4	2	no	—
249	C₂²×C₁₉	—	4	1	no	—
250	C₂²×C₁₉	—	8	1	no	—
251	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
252	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₂²×C₁₉	#575	1	1	yes	characteristic
254	C₄×C₁₉	—	2	2	no	—
255	C₄×C₁₉	—	2	1	no	—
256	C₄×C₁₉	—	2	1	no	—
257	C₄×C₁₉	—	2	2	no	—
258	C₄×C₁₉	—	2	2	no	—
259	C₄×C₁₉	—	4	2	no	—
260	C₄×C₁₉	—	4	1	no	—
261	C₄×C₁₉	—	4	2	no	—
262	C₄×C₁₉	—	4	1	no	—
263	C₄×C₁₉	—	4	2	no	—
264	C₄×C₁₉	—	8	2	no	—
265	C₄×C₁₉	—	8	2	no	—
266	#556	—	2	2	no	—
267	#555	—	2	2	no	—
268	#553	—	2	2	no	—
269	#552	—	2	2	no	—
270	#544	C₂²×C₁₉	1	1	yes	characteristic
271	#538	—	2	1	no	—
272	#538	C₂²×C₁₉	1	2	yes	—
273	#537	C₂²×C₁₉	1	1	yes	characteristic
274	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
275	#529	—	2	1	no	—
276	#529	C₂²×C₁₉	1	2	yes	—
277	#525	—	2	1	no	—
278	C₂×C₂²⋊Q₈	—	2	1	no	—
279	#520	—	2	1	no	—
280	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
281	#501	—	2	2	no	—
282	#489	—	2	2	no	—
283	#483	C₂²×C₁₉	1	4	yes	—
284	#480	C₂²×C₁₉	1	4	yes	—
285	#477	—	2	2	no	—
286	#476	—	2	2	no	—
287	#432	C₂²×C₁₉	1	2	yes	—
288	#398	—	2	1	no	—
289	#398	C₂²×C₁₉	1	2	yes	—
290	#397	—	2	1	no	—
291	#397	C₂²×C₁₉	1	2	yes	—
292	#391	—	2	1	no	—
293	#382	C₂²×C₁₉	1	1	yes	characteristic
294	#328	C₂²×C₁₉	1	4	yes	—
295	#327	C₂²×C₁₉	1	4	yes	—
296	#324	C₂²×C₁₉	1	2	yes	—
297	#323	C₂²×C₁₉	1	2	yes	—
298	C₂×C₁₉	—	2	1	no	—
299	C₂×C₁₉	—	2	1	no	—
300	C₂×C₁₉	—	8	2	no	—
301	C₂×C₁₉	—	8	1	no	—
302	C₂×C₁₉	#3006	1	1	yes	characteristic
303	C₂×C₁₉	#3022	1	1	yes	characteristic
304	C₂×C₁₉	#3028	1	1	yes	characteristic
305	C₂×#41	—	2	1	no	—
306	C₂²×Q₈	—	2	1	no	—
307	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
308	C₄⋊Q₈	—	2	2	no	—
309	C₄⋊Q₈	—	2	2	no	—
310	C₄⋊Q₈	—	2	2	no	—
311	#126	—	2	2	no	—
312	#126	—	2	2	no	—
313	#126	—	2	2	no	—
314	#126	—	2	2	no	—
315	#125	—	2	1	no	—
316	#125	—	2	2	no	—
317	#125	D₄×C₁₉	1	2	yes	—
318	#124	—	2	1	no	—
319	#124	—	2	2	no	—
320	#124	—	2	2	no	—
321	#124	D₄×C₁₉	1	2	yes	—
322	#123	—	2	2	no	—
323	#123	—	2	2	no	—
324	#123	—	2	2	no	—
325	C₂²⋊Q₈	—	2	1	no	—
326	C₂²⋊Q₈	—	2	1	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	—	2	2	no	—
329	C₂²⋊Q₈	—	4	4	no	—
330	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
331	#121	—	2	1	no	—
332	#121	—	2	1	no	—
333	#121	—	2	2	no	—
334	#121	—	2	2	no	—
335	#121	—	2	2	no	—
336	#121	—	2	1	no	—
337	#121	C₂³×C₁₉	1	2	yes	—
338	#120	—	2	2	no	—
339	C₄×Q₈	—	2	2	no	—
340	C₄×Q₈	—	2	1	no	—
341	C₄×Q₈	D₄×C₁₉	1	2	yes	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	—	2	2	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	D₄×C₁₉	1	2	yes	—
349	#117	—	2	2	no	—
350	#117	—	2	2	no	—
351	#117	—	2	1	no	—
352	#117	—	2	2	no	—
353	#117	—	2	2	no	—
354	#117	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
365	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
367	#107	—	2	4	no	—
368	#106	—	2	4	no	—
369	C₄⋊C₈	—	2	2	no	—
370	#103	—	2	4	no	—
371	#102	—	2	4	no	—
372	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
373	#97	—	2	2	no	—
374	#95	—	2	1	no	—
375	#95	—	2	2	no	—
376	#95	—	2	2	no	—
377	#95	C₂³×C₁₉	1	2	yes	—
378	C₁₉	#18371	1	1	yes	characteristic, direct product factor, Sylow
379	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
380	#41	—	4	2	no	—
381	#41	—	4	2	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	4	2	no	—
385	C₂×Q₈	—	4	2	no	—
386	C₂×Q₈	—	4	1	no	—
387	C₂×Q₈	—	4	1	no	—
388	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	4	1	no	—
404	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
409	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
410	C₂×C₈	—	2	4	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₄⋊C₄	—	4	4	no	—
427	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
428	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	4	4	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	2	no	—
446	C₄²	C₂×D₄×C₁₉	1	2	yes	—
447	C₄²	C₂×D₄×C₁₉	1	2	yes	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	4	1	no	—
454	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
455	Q₈	—	4	2	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	8	2	no	—
458	Q₈	—	8	2	no	—
459	Q₈	—	8	1	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	2	no	—
463	D₄	—	4	2	no	—
464	D₄	—	8	2	no	—
465	D₄	—	8	1	no	—
466	D₄	—	8	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	8	2	no	—
490	C₂×C₄	—	8	2	no	—
491	C₂×C₄	C₁₉×#120	1	2	yes	—
492	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
493	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
494	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
495	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
496	C₈	—	4	4	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	8	1	no	—
507	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
508	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
509	C₂²	C₁₉×#575	1	1	yes	characteristic
510	C₄	—	2	2	no	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	8	2	no	—
521	C₄	—	8	2	no	—
522	C₂	—	2	1	no	—
523	C₂	—	2	1	no	—
524	C₂	—	8	1	no	—
525	C₂	—	8	2	no	—
526	C₂	C₁₉×#3006	1	1	yes	characteristic
527	C₂	C₁₉×#3022	1	1	yes	characteristic
528	C₂	C₁₉×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3493	C₂
LCS	G ▷ C₂²×C₄ ▷ 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×#3238	C₂	semidirect
3. C₁₉×#2621	C₂	semidirect
4. C₁₉×#1612	C₂	semidirect
5. C₁₉×#1611	C₂	semidirect
6. C₁₉×#1610	C₂	semidirect
7. C₁₉×#1512	C₂	semidirect
8. C₁₉×#1464	C₂	semidirect
183. #18371	C₁₉	direct (N × H)
234. #3238	C₂×C₁₉	semidirect
235. #2621	C₂×C₁₉	semidirect
236. #1612	C₂×C₁₉	semidirect
237. #1611	C₂×C₁₉	semidirect
238. #1610	C₂×C₁₉	semidirect
239. #1512	C₂×C₁₉	semidirect
240. #1464	C₂×C₁₉	semidirect
378. C₁₉	#18371	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×#3493	2
C₁₉×#3238	2
C₁₉×#2621	2
C₁₉×#1612	2
C₁₉×#1611	2
C₁₉×#1610	2
C₁₉×#1512	2
C₁₉×#1464	2
#18371	19

Subgroups — C19×#18371 #18024330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18371 #18024330