Subgroups — C₁₉×#19036 #18024995

Order 4864.

880 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3559	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3216	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3172	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3166	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1664	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1661	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1661	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1660	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1529	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1528	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1525	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#563	C₂²	1	2	yes	—
13	C₁₉×#562	C₂²	1	2	yes	—
14	C₁₉×#554	—	2	1	no	—
15	C₁₉×#553	—	2	1	no	—
16	C₁₉×#553	—	2	1	no	—
17	C₁₉×#547	—	2	2	no	—
18	C₁₉×#547	—	2	1	no	—
19	C₁₉×#544	—	2	1	no	—
20	C₁₉×#540	—	2	1	no	—
21	C₁₉×#539	—	2	2	no	—
22	C₁₉×#539	—	2	1	no	—
23	C₁₉×#537	—	2	1	no	—
24	C₁₉×#533	C₂²	1	1	yes	characteristic
25	C₁₉×#532	C₂²	1	1	yes	characteristic
26	C₁₉×#529	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
28	C₁₉×#501	C₂²	1	1	yes	characteristic
29	C₁₉×#501	C₂²	1	2	yes	—
30	C₁₉×#501	C₂²	1	2	yes	—
31	C₁₉×#499	—	2	2	no	—
32	C₁₉×#497	C₂²	1	1	yes	characteristic
33	C₁₉×#497	C₂²	1	2	yes	—
34	C₁₉×#491	C₂²	1	1	yes	characteristic
35	C₁₉×#489	C₂²	1	1	yes	characteristic
36	C₁₉×#489	C₂²	1	2	yes	—
37	C₁₉×#470	—	2	1	no	—
38	C₁₉×#468	—	2	1	no	—
39	C₁₉×#462	—	2	1	no	—
40	C₁₉×#460	—	2	1	no	—
41	C₁₉×#452	—	2	2	no	—
42	C₄×Q₁₆×C₁₉	—	2	1	no	—
43	C₄×SD₁₆×C₁₉	—	2	1	no	—
44	C₁₉×#432	C₂²	1	1	yes	characteristic
45	C₁₉×#428	—	2	1	no	—
46	C₁₉×#428	—	2	1	no	—
47	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#330	C₂²	1	2	yes	—
50	C₁₉×#330	C₂²	1	2	yes	—
51	C₁₉×#330	C₂²	1	2	yes	—
52	C₁₉×#329	C₂²	1	2	yes	—
53	C₁₉×#329	C₂²	1	2	yes	—
54	C₁₉×#329	C₂²	1	2	yes	—
55	C₂×#41×C₁₉	—	2	2	no	—
56	C₂×#41×C₁₉	D₄	1	2	yes	—
57	C₂×Q₁₆×C₁₉	—	2	1	no	—
58	C₂×Q₁₆×C₁₉	—	2	2	no	—
59	C₂×SD₁₆×C₁₉	—	2	1	no	—
60	C₂×SD₁₆×C₁₉	—	2	2	no	—
61	C₂×M₁₆×C₁₉	—	2	1	no	—
62	C₂×M₁₆×C₁₉	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	—	2	2	no	—
65	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₁₉×#127	D₄	1	1	yes	characteristic
69	C₁₉×#126	—	2	2	no	—
70	C₁₉×#126	—	2	2	no	—
71	C₁₉×#126	—	2	1	no	—
72	C₁₉×#125	—	2	2	no	—
73	C₁₉×#125	—	2	1	no	—
74	C₁₉×#125	—	2	1	no	—
75	C₁₉×#125	—	2	1	no	—
76	C₁₉×#125	—	2	1	no	—
77	C₁₉×#125	D₄	1	2	yes	—
78	C₁₉×#125	C₂³	1	1	yes	characteristic
79	C₁₉×#125	C₂³	1	2	yes	—
80	C₁₉×#124	C₂³	1	1	yes	characteristic
81	C₁₉×#124	C₂³	1	2	yes	—
82	C₁₉×#123	—	2	2	no	—
83	C₁₉×#123	—	2	2	no	—
84	C₁₉×#123	—	2	2	no	—
85	C₁₉×#123	—	2	2	no	—
86	C₁₉×#123	—	2	1	no	—
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	—	2	1	no	—
96	C₁₉×C₂²⋊Q₈	—	2	1	no	—
97	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
98	C₁₉×#121	—	2	2	no	—
99	C₁₉×#121	—	2	2	no	—
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#121	—	2	1	no	—
102	C₁₉×#121	—	2	2	no	—
103	C₁₉×#121	—	2	2	no	—
104	C₁₉×#121	—	2	1	no	—
105	C₁₉×#121	—	2	1	no	—
106	C₁₉×#121	D₄	1	1	yes	characteristic
107	C₄×Q₈×C₁₉	—	2	1	no	—
108	C₄×Q₈×C₁₉	—	2	1	no	—
109	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
110	C₄×D₄×C₁₉	—	2	2	no	—
111	C₄×D₄×C₁₉	—	2	2	no	—
112	C₄×D₄×C₁₉	—	2	1	no	—
113	C₄×D₄×C₁₉	—	2	1	no	—
114	C₄×D₄×C₁₉	—	2	1	no	—
115	C₄×D₄×C₁₉	—	2	1	no	—
116	C₄×D₄×C₁₉	—	2	1	no	—
117	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
118	C₁₉×#117	—	2	1	no	—
119	C₁₉×#117	—	2	1	no	—
120	C₁₉×#117	—	2	1	no	—
121	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
128	C₁₉×#107	—	2	2	no	—
129	C₁₉×#107	—	2	2	no	—
130	C₁₉×#107	—	2	1	no	—
131	C₁₉×#106	—	2	2	no	—
132	C₁₉×#106	—	2	2	no	—
133	C₁₉×#106	—	2	1	no	—
134	C₁₉×C₄⋊C₈	—	2	1	no	—
135	C₁₉×#103	—	2	1	no	—
136	C₁₉×#103	—	2	2	no	—
137	C₁₉×#103	—	2	1	no	—
138	C₁₉×#103	—	2	1	no	—
139	C₁₉×#102	—	2	1	no	—
140	C₁₉×#102	—	2	2	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×#97	C₂³	1	1	yes	characteristic
143	C₁₉×#97	C₂³	1	1	yes	characteristic
144	C₁₉×#97	C₂³	1	2	yes	—
145	C₁₉×#97	C₂³	1	2	yes	—
146	C₄×C₈×C₁₉	—	2	1	no	—
147	C₄×C₈×C₁₉	—	2	1	no	—
148	#41×C₁₉	—	8	4	no	—
149	#41×C₁₉	—	8	2	no	—
150	C₂×Q₈×C₁₉	—	2	2	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
155	C₂×D₄×C₁₉	—	2	2	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₁₉	—	2	1	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	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	Q₁₆×C₁₉	—	4	2	no	—
174	Q₁₆×C₁₉	—	8	2	no	—
175	SD₁₆×C₁₉	—	4	2	no	—
176	SD₁₆×C₁₉	—	8	2	no	—
177	M₁₆×C₁₉	—	2	4	no	—
178	M₁₆×C₁₉	—	4	2	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	2	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	2	no	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	4	1	no	—
204	C₄⋊C₄×C₁₉	—	4	1	no	—
205	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
206	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
207	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₂²⋊C₄×C₁₉	—	2	2	no	—
211	C₂²⋊C₄×C₁₉	—	2	2	no	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	1	no	—
215	C₂²⋊C₄×C₁₉	—	2	1	no	—
216	C₂²⋊C₄×C₁₉	—	2	1	no	—
217	C₂²⋊C₄×C₁₉	—	2	1	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	—	2	1	no	—
221	C₂²⋊C₄×C₁₉	—	4	1	no	—
222	C₄²×C₁₉	—	2	2	no	—
223	C₄²×C₁₉	—	2	1	no	—
224	C₄²×C₁₉	—	4	1	no	—
225	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
227	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
228	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
229	#19036	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂³×C₁₉	—	2	1	no	—
231	C₂³×C₁₉	—	2	2	no	—
232	C₂³×C₁₉	#120	1	1	yes	characteristic
233	Q₈×C₁₉	—	4	1	no	—
234	Q₈×C₁₉	—	4	2	no	—
235	Q₈×C₁₉	—	4	1	no	—
236	Q₈×C₁₉	—	4	1	no	—
237	Q₈×C₁₉	—	4	1	no	—
238	Q₈×C₁₉	—	4	1	no	—
239	Q₈×C₁₉	—	8	2	no	—
240	D₄×C₁₉	—	4	1	no	—
241	D₄×C₁₉	—	4	2	no	—
242	D₄×C₁₉	—	4	4	no	—
243	D₄×C₁₉	—	4	2	no	—
244	D₄×C₁₉	—	4	2	no	—
245	D₄×C₁₉	—	8	1	no	—
246	D₄×C₁₉	—	8	2	no	—
247	D₄×C₁₉	—	8	2	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	2	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	8	2	no	—
262	C₂×C₄×C₁₉	—	8	1	no	—
263	C₂×C₄×C₁₉	—	8	2	no	—
264	C₂×C₄×C₁₉	—	8	2	no	—
265	C₂×C₄×C₁₉	—	8	2	no	—
266	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
267	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
268	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
269	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
272	C₈×C₁₉	—	2	4	no	—
273	C₈×C₁₉	—	2	2	no	—
274	C₈×C₁₉	—	4	1	no	—
275	C₈×C₁₉	—	4	2	no	—
276	#3559	C₂×C₁₉	1	1	yes	characteristic
277	#3216	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#3172	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#3166	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1664	C₂×C₁₉	1	2	yes	complemented
281	#1661	C₂×C₁₉	1	2	yes	complemented
282	#1661	C₂×C₁₉	1	2	yes	complemented
283	#1660	C₂×C₁₉	1	2	yes	complemented
284	#1529	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#1528	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1525	C₂×C₁₉	1	1	yes	characteristic, complemented
287	C₂²×C₁₉	—	2	1	no	—
288	C₂²×C₁₉	—	2	1	no	—
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	2	no	—
292	C₂²×C₁₉	—	4	2	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	—	4	2	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
297	C₄×C₁₉	—	2	1	no	—
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	2	1	no	—
301	C₄×C₁₉	—	2	1	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	4	2	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	4	2	no	—
306	C₄×C₁₉	—	4	2	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	8	1	no	—
309	C₄×C₁₉	—	8	1	no	—
310	C₄×C₁₉	#456	1	2	yes	—
311	#563	C₂²×C₁₉	1	2	yes	—
312	#562	C₂²×C₁₉	1	2	yes	—
313	#554	—	2	1	no	—
314	#553	—	2	1	no	—
315	#553	—	2	1	no	—
316	#547	—	2	2	no	—
317	#547	—	2	1	no	—
318	#544	—	2	1	no	—
319	#540	—	2	1	no	—
320	#539	—	2	2	no	—
321	#539	—	2	1	no	—
322	#537	—	2	1	no	—
323	#533	C₂²×C₁₉	1	1	yes	characteristic
324	#532	C₂²×C₁₉	1	1	yes	characteristic
325	#529	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
327	#501	C₂²×C₁₉	1	2	yes	—
328	#501	C₂²×C₁₉	1	2	yes	—
329	#501	C₂²×C₁₉	1	1	yes	characteristic
330	#499	—	2	2	no	—
331	#497	C₂²×C₁₉	1	1	yes	characteristic
332	#497	C₂²×C₁₉	1	2	yes	—
333	#491	C₂²×C₁₉	1	1	yes	characteristic
334	#489	C₂²×C₁₉	1	1	yes	characteristic
335	#489	C₂²×C₁₉	1	2	yes	—
336	#470	—	2	1	no	—
337	#468	—	2	1	no	—
338	#462	—	2	1	no	—
339	#460	—	2	1	no	—
340	#452	—	2	2	no	—
341	C₄×Q₁₆	—	2	1	no	—
342	C₄×SD₁₆	—	2	1	no	—
343	#432	C₂²×C₁₉	1	1	yes	characteristic
344	#428	—	2	1	no	—
345	#428	—	2	1	no	—
346	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
347	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
348	#330	C₂²×C₁₉	1	2	yes	—
349	#330	C₂²×C₁₉	1	2	yes	—
350	#330	C₂²×C₁₉	1	2	yes	—
351	#329	C₂²×C₁₉	1	2	yes	—
352	#329	C₂²×C₁₉	1	2	yes	—
353	#329	C₂²×C₁₉	1	2	yes	—
354	C₂×C₁₉	—	4	1	no	—
355	C₂×C₁₉	—	8	1	no	—
356	C₂×C₁₉	—	8	2	no	—
357	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
358	C₂×C₁₉	#3018	1	1	yes	characteristic
359	C₂×C₁₉	#3019	1	1	yes	characteristic
360	C₂×#41	—	2	2	no	—
361	C₂×#41	D₄×C₁₉	1	2	yes	—
362	C₂×Q₁₆	—	2	1	no	—
363	C₂×Q₁₆	—	2	2	no	—
364	C₂×SD₁₆	—	2	1	no	—
365	C₂×SD₁₆	—	2	2	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₄⋊Q₈	—	2	1	no	—
369	C₄⋊Q₈	—	2	2	no	—
370	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
371	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
372	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
373	#127	D₄×C₁₉	1	1	yes	characteristic
374	#126	—	2	2	no	—
375	#126	—	2	2	no	—
376	#126	—	2	1	no	—
377	#125	—	2	2	no	—
378	#125	—	2	1	no	—
379	#125	—	2	1	no	—
380	#125	—	2	1	no	—
381	#125	—	2	1	no	—
382	#125	D₄×C₁₉	1	2	yes	—
383	#125	C₂³×C₁₉	1	2	yes	—
384	#125	C₂³×C₁₉	1	1	yes	characteristic
385	#124	C₂³×C₁₉	1	1	yes	characteristic
386	#124	C₂³×C₁₉	1	2	yes	—
387	#123	—	2	2	no	—
388	#123	—	2	2	no	—
389	#123	—	2	2	no	—
390	#123	—	2	2	no	—
391	#123	—	2	1	no	—
392	#123	—	2	2	no	—
393	#123	—	2	2	no	—
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	2	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	2	1	no	—
401	C₂²⋊Q₈	—	2	1	no	—
402	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
403	#121	—	2	2	no	—
404	#121	—	2	2	no	—
405	#121	—	2	1	no	—
406	#121	—	2	1	no	—
407	#121	—	2	2	no	—
408	#121	—	2	2	no	—
409	#121	—	2	1	no	—
410	#121	—	2	1	no	—
411	#121	D₄×C₁₉	1	1	yes	characteristic
412	C₄×Q₈	—	2	1	no	—
413	C₄×Q₈	—	2	1	no	—
414	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
423	#117	—	2	1	no	—
424	#117	—	2	1	no	—
425	#117	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	2	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
431	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
433	#107	—	2	2	no	—
434	#107	—	2	2	no	—
435	#107	—	2	1	no	—
436	#106	—	2	2	no	—
437	#106	—	2	2	no	—
438	#106	—	2	1	no	—
439	C₄⋊C₈	—	2	1	no	—
440	#103	—	2	1	no	—
441	#103	—	2	2	no	—
442	#103	—	2	1	no	—
443	#103	—	2	1	no	—
444	#102	—	2	1	no	—
445	#102	—	2	2	no	—
446	C₂²⋊C₈	—	2	1	no	—
447	#97	C₂³×C₁₉	1	2	yes	—
448	#97	C₂³×C₁₉	1	1	yes	characteristic
449	#97	C₂³×C₁₉	1	1	yes	characteristic
450	#97	C₂³×C₁₉	1	2	yes	—
451	C₄×C₈	—	2	1	no	—
452	C₄×C₈	—	2	1	no	—
453	C₁₉	#19036	1	1	yes	characteristic, direct product factor, Sylow
454	#41	—	8	4	no	—
455	#41	—	8	2	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
479	Q₁₆	—	4	2	no	—
480	Q₁₆	—	8	2	no	—
481	SD₁₆	—	4	2	no	—
482	SD₁₆	—	8	2	no	—
483	M₁₆	—	2	4	no	—
484	M₁₆	—	4	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	4	1	no	—
510	C₄⋊C₄	—	4	1	no	—
511	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
514	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	4	1	no	—
528	C₄²	—	2	2	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	4	1	no	—
531	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
532	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
533	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
534	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
535	C₂³	—	2	1	no	—
536	C₂³	—	2	2	no	—
537	C₂³	C₁₉×#120	1	1	yes	characteristic
538	Q₈	—	4	1	no	—
539	Q₈	—	4	2	no	—
540	Q₈	—	4	1	no	—
541	Q₈	—	4	1	no	—
542	Q₈	—	4	1	no	—
543	Q₈	—	4	1	no	—
544	Q₈	—	8	2	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	4	no	—
548	D₄	—	4	2	no	—
549	D₄	—	4	2	no	—
550	D₄	—	8	1	no	—
551	D₄	—	8	2	no	—
552	D₄	—	8	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	8	2	no	—
567	C₂×C₄	—	8	1	no	—
568	C₂×C₄	—	8	2	no	—
569	C₂×C₄	—	8	2	no	—
570	C₂×C₄	—	8	2	no	—
571	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
572	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
573	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
574	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
575	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
577	C₈	—	2	4	no	—
578	C₈	—	2	2	no	—
579	C₈	—	4	1	no	—
580	C₈	—	4	2	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	4	1	no	—
590	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	1	no	—
602	C₄	—	8	1	no	—
603	C₄	—	8	1	no	—
604	C₄	C₁₉×#456	1	2	yes	—
605	C₂	—	4	1	no	—
606	C₂	—	8	1	no	—
607	C₂	—	8	2	no	—
608	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
609	C₂	C₁₉×#3018	1	1	yes	characteristic
610	C₂	C₁₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3559	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×#3216	C₂	semidirect
3. C₁₉×#3172	C₂	semidirect
4. C₁₉×#3166	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1661	C₂	semidirect
7. C₁₉×#1661	C₂	semidirect
8. C₁₉×#1660	C₂	semidirect
9. C₁₉×#1529	C₂	semidirect
10. C₁₉×#1528	C₂	semidirect
11. C₁₉×#1525	C₂	semidirect
229. #19036	C₁₉	direct (N × H)
277. #3216	C₂×C₁₉	semidirect
278. #3172	C₂×C₁₉	semidirect
279. #3166	C₂×C₁₉	semidirect
280. #1664	C₂×C₁₉	semidirect
281. #1661	C₂×C₁₉	semidirect
282. #1661	C₂×C₁₉	semidirect
283. #1660	C₂×C₁₉	semidirect
284. #1529	C₂×C₁₉	semidirect
285. #1528	C₂×C₁₉	semidirect
286. #1525	C₂×C₁₉	semidirect
453. C₁₉	#19036	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×#3559	2
C₁₉×#3216	2
C₁₉×#3172	2
C₁₉×#3166	2
C₁₉×#1664	2
C₁₉×#1661	2
C₁₉×#1660	2
C₁₉×#1529	2
C₁₉×#1528	2
C₁₉×#1525	2
#19036	19

Subgroups — C19×#19036 #18024995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19036 #18024995