Subgroups — C₁₉×#19044 #18025003

Order 4864.

956 conjugacy classes of subgroups.

The subgroup lattice has 632 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, complemented
2	C₁₉×#3234	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3180	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3150	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1661	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1660	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1657	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1656	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1532	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1530	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#330	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#135	—	2	2	no	—
13	C₁₉×#563	C₂²	1	2	yes	—
14	C₁₉×#562	C₂²	1	2	yes	—
15	C₁₉×#554	—	2	1	no	—
16	C₁₉×#553	—	2	1	no	—
17	C₁₉×#553	—	2	1	no	—
18	C₁₉×#547	—	2	2	no	—
19	C₁₉×#547	—	2	1	no	—
20	C₁₉×#544	—	2	1	no	—
21	C₁₉×#540	—	2	1	no	—
22	C₁₉×#539	—	2	2	no	—
23	C₁₉×#539	—	2	1	no	—
24	C₁₉×#537	—	2	1	no	—
25	C₁₉×#532	C₂²	1	1	yes	characteristic
26	C₁₉×#532	C₂²	1	1	yes	characteristic
27	C₁₉×#529	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
29	C₁₉×#501	C₂²	1	1	yes	characteristic
30	C₁₉×#501	C₂²	1	2	yes	—
31	C₁₉×#497	—	2	1	no	—
32	C₁₉×#497	C₂²	1	2	yes	—
33	C₁₉×#496	—	2	1	no	—
34	C₁₉×#496	C₂²	1	1	yes	characteristic
35	C₁₉×#496	C₂²	1	2	yes	—
36	C₁₉×#490	C₂²	1	1	yes	characteristic
37	C₁₉×#490	C₂²	1	2	yes	—
38	C₁₉×#489	C₂²	1	1	yes	characteristic
39	C₁₉×#481	—	2	1	no	—
40	C₁₉×#480	—	2	1	no	—
41	C₁₉×#478	—	2	2	no	—
42	C₁₉×#466	—	2	1	no	—
43	C₁₉×#465	—	2	1	no	—
44	C₁₉×#442	—	2	1	no	—
45	C₁₉×#440	—	2	1	no	—
46	C₁₉×#432	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×#97	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	—	2	1	no	—
57	C₂×#41×C₁₉	D₄	1	2	yes	—
58	C₁₉×#135	—	4	8	no	—
59	C₂×Q₁₆×C₁₉	—	2	2	no	—
60	C₂×SD₁₆×C₁₉	—	2	1	no	—
61	C₂×SD₁₆×C₁₉	—	2	2	no	—
62	C₂×SD₁₆×C₁₉	—	2	2	no	—
63	C₂×D₈×C₁₉	—	2	1	no	—
64	C₂×D₈×C₁₉	—	2	2	no	—
65	C₂²×C₈×C₁₉	—	2	1	no	—
66	C₂²×C₈×C₁₉	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	—	2	2	no	—
69	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
70	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₁₉×#127	D₄	1	1	yes	characteristic
72	C₁₉×#127	C₂³	1	1	yes	characteristic
73	C₁₉×#126	—	2	2	no	—
74	C₁₉×#126	—	2	2	no	—
75	C₁₉×#126	—	2	1	no	—
76	C₁₉×#125	—	2	2	no	—
77	C₁₉×#125	—	2	1	no	—
78	C₁₉×#125	—	2	1	no	—
79	C₁₉×#125	—	2	1	no	—
80	C₁₉×#125	D₄	1	2	yes	—
81	C₁₉×#125	C₂³	1	2	yes	—
82	C₁₉×#125	C₂³	1	1	yes	characteristic
83	C₁₉×#124	—	2	1	no	—
84	C₁₉×#124	C₂³	1	1	yes	characteristic
85	C₁₉×#124	C₂³	1	2	yes	—
86	C₁₉×#123	—	2	2	no	—
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×#123	—	2	2	no	—
90	C₁₉×#123	—	2	1	no	—
91	C₁₉×#123	—	2	2	no	—
92	C₁₉×#123	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	—	2	2	no	—
97	C₁₉×C₂²⋊Q₈	—	2	2	no	—
98	C₁₉×C₂²⋊Q₈	—	2	2	no	—
99	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
100	C₁₉×#121	—	2	2	no	—
101	C₁₉×#121	—	2	2	no	—
102	C₁₉×#121	—	2	1	no	—
103	C₁₉×#121	—	2	1	no	—
104	C₁₉×#121	—	2	2	no	—
105	C₁₉×#121	—	2	2	no	—
106	C₁₉×#121	—	2	1	no	—
107	C₁₉×#121	—	2	1	no	—
108	C₁₉×#121	—	2	1	no	—
109	C₁₉×#121	—	2	1	no	—
110	C₁₉×#121	D₄	1	1	yes	characteristic
111	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
112	C₄×D₄×C₁₉	—	2	2	no	—
113	C₄×D₄×C₁₉	—	2	2	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	—	2	1	no	—
118	C₄×D₄×C₁₉	—	2	1	no	—
119	C₄×D₄×C₁₉	—	2	1	no	—
120	C₄×D₄×C₁₉	—	2	1	no	—
121	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
122	C₁₉×#117	—	2	1	no	—
123	C₁₉×#117	—	2	1	no	—
124	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
130	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
131	C₁₉×#107	—	2	1	no	—
132	C₁₉×#107	—	2	2	no	—
133	C₁₉×#106	—	2	1	no	—
134	C₁₉×#106	—	2	2	no	—
135	C₁₉×C₄⋊C₈	—	2	1	no	—
136	C₁₉×#103	—	2	1	no	—
137	C₁₉×#102	—	2	1	no	—
138	C₁₉×#102	—	2	1	no	—
139	C₁₉×#102	—	2	1	no	—
140	C₁₉×#102	—	2	2	no	—
141	C₁₉×#102	—	2	2	no	—
142	C₁₉×C₂²⋊C₈	—	2	1	no	—
143	C₁₉×#97	—	2	1	no	—
144	C₁₉×#97	—	2	1	no	—
145	C₁₉×#97	C₂³	1	1	yes	characteristic
146	C₁₉×#97	C₂³	1	2	yes	—
147	C₁₉×#97	C₂³	1	1	yes	characteristic
148	C₁₉×#97	C₂³	1	2	yes	—
149	#41×C₁₉	—	4	4	no	—
150	#41×C₁₉	—	4	4	no	—
151	#41×C₁₉	—	8	4	no	—
152	C₂×Q₈×C₁₉	—	2	2	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₁₉	—	2	2	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	2	no	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	1	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	1	no	—
165	C₂×D₄×C₁₉	—	4	1	no	—
166	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₉	—	2	1	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	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	2	no	—
175	C₂²×C₄×C₁₉	—	4	1	no	—
176	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	Q₁₆×C₁₉	—	4	4	no	—
180	SD₁₆×C₁₉	—	4	2	no	—
181	SD₁₆×C₁₉	—	4	4	no	—
182	SD₁₆×C₁₉	—	4	4	no	—
183	D₈×C₁₉	—	4	2	no	—
184	D₈×C₁₉	—	4	4	no	—
185	C₂×C₈×C₁₉	—	2	4	no	—
186	C₂×C₈×C₁₉	—	2	2	no	—
187	C₂×C₈×C₁₉	—	2	1	no	—
188	C₂×C₈×C₁₉	—	2	1	no	—
189	C₂×C₈×C₁₉	—	2	2	no	—
190	C₂×C₈×C₁₉	—	4	2	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	2	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	2	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	—	2	2	no	—
204	C₄⋊C₄×C₁₉	—	2	2	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
210	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
211	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	2	no	—
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	2	no	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	1	no	—
219	C₂²⋊C₄×C₁₉	—	2	1	no	—
220	C₂²⋊C₄×C₁₉	—	2	1	no	—
221	C₂²⋊C₄×C₁₉	—	2	1	no	—
222	C₂²⋊C₄×C₁₉	—	2	2	no	—
223	C₂²⋊C₄×C₁₉	—	2	2	no	—
224	C₂²⋊C₄×C₁₉	—	2	1	no	—
225	C₂²⋊C₄×C₁₉	—	4	1	no	—
226	C₂²⋊C₄×C₁₉	—	4	1	no	—
227	C₄²×C₁₉	—	2	2	no	—
228	C₄²×C₁₉	—	2	1	no	—
229	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
231	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
232	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
233	#19044	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂³×C₁₉	—	2	2	no	—
235	C₂³×C₁₉	—	2	1	no	—
236	C₂³×C₁₉	—	4	1	no	—
237	C₂³×C₁₉	#120	1	1	yes	characteristic
238	Q₈×C₁₉	—	4	2	no	—
239	Q₈×C₁₉	—	4	1	no	—
240	Q₈×C₁₉	—	4	2	no	—
241	Q₈×C₁₉	—	8	2	no	—
242	D₄×C₁₉	—	4	2	no	—
243	D₄×C₁₉	—	4	1	no	—
244	D₄×C₁₉	—	4	2	no	—
245	D₄×C₁₉	—	4	2	no	—
246	D₄×C₁₉	—	4	1	no	—
247	D₄×C₁₉	—	4	1	no	—
248	D₄×C₁₉	—	4	2	no	—
249	D₄×C₁₉	—	4	4	no	—
250	D₄×C₁₉	—	4	2	no	—
251	D₄×C₁₉	—	8	1	no	—
252	D₄×C₁₉	—	8	2	no	—
253	D₄×C₁₉	—	8	2	no	—
254	D₄×C₁₉	—	8	2	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	1	no	—
258	C₂×C₄×C₁₉	—	2	2	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	2	no	—
265	C₂×C₄×C₁₉	—	4	2	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	8	2	no	—
268	C₂×C₄×C₁₉	—	8	2	no	—
269	C₂×C₄×C₁₉	—	8	1	no	—
270	C₂×C₄×C₁₉	—	8	2	no	—
271	C₂×C₄×C₁₉	—	8	2	no	—
272	C₂×C₄×C₁₉	—	8	2	no	—
273	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
274	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
275	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
276	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
279	C₈×C₁₉	—	2	4	no	—
280	C₈×C₁₉	—	2	2	no	—
281	C₈×C₁₉	—	4	2	no	—
282	C₈×C₁₉	—	4	1	no	—
283	#3559	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#3234	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#3180	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#3150	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#1661	C₂×C₁₉	1	2	yes	complemented
288	#1660	C₂×C₁₉	1	2	yes	complemented
289	#1657	C₂×C₁₉	1	2	yes	complemented
290	#1656	C₂×C₁₉	1	2	yes	complemented
291	#1532	C₂×C₁₉	1	1	yes	characteristic, complemented
292	#1530	C₂×C₁₉	1	1	yes	characteristic, complemented
293	C₂×#330	C₂×C₁₉	1	1	yes	characteristic, complemented
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	4	2	no	—
297	C₂²×C₁₉	—	4	1	no	—
298	C₂²×C₁₉	—	4	2	no	—
299	C₂²×C₁₉	—	4	1	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	4	2	no	—
302	C₂²×C₁₉	—	8	1	no	—
303	C₂²×C₁₉	—	8	1	no	—
304	C₂²×C₁₉	—	8	1	no	—
305	C₂²×C₁₉	#453	1	2	yes	—
306	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
307	C₄×C₁₉	—	2	1	no	—
308	C₄×C₁₉	—	2	1	no	—
309	C₄×C₁₉	—	2	1	no	—
310	C₄×C₁₉	—	2	1	no	—
311	C₄×C₁₉	—	2	1	no	—
312	C₄×C₁₉	—	2	1	no	—
313	C₄×C₁₉	—	4	2	no	—
314	C₄×C₁₉	—	4	2	no	—
315	C₄×C₁₉	—	4	1	no	—
316	C₄×C₁₉	—	4	2	no	—
317	C₄×C₁₉	—	4	1	no	—
318	C₄×C₁₉	—	4	1	no	—
319	C₄×C₁₉	—	8	1	no	—
320	C₂×#135	—	2	2	no	—
321	#563	C₂²×C₁₉	1	2	yes	—
322	#562	C₂²×C₁₉	1	2	yes	—
323	#554	—	2	1	no	—
324	#553	—	2	1	no	—
325	#553	—	2	1	no	—
326	#547	—	2	2	no	—
327	#547	—	2	1	no	—
328	#544	—	2	1	no	—
329	#540	—	2	1	no	—
330	#539	—	2	2	no	—
331	#539	—	2	1	no	—
332	#537	—	2	1	no	—
333	#532	C₂²×C₁₉	1	1	yes	characteristic
334	#532	C₂²×C₁₉	1	1	yes	characteristic
335	#529	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
337	#501	C₂²×C₁₉	1	1	yes	characteristic
338	#501	C₂²×C₁₉	1	2	yes	—
339	#497	—	2	1	no	—
340	#497	C₂²×C₁₉	1	2	yes	—
341	#496	—	2	1	no	—
342	#496	C₂²×C₁₉	1	2	yes	—
343	#496	C₂²×C₁₉	1	1	yes	characteristic
344	#490	C₂²×C₁₉	1	1	yes	characteristic
345	#490	C₂²×C₁₉	1	2	yes	—
346	#489	C₂²×C₁₉	1	1	yes	characteristic
347	#481	—	2	1	no	—
348	#480	—	2	1	no	—
349	#478	—	2	2	no	—
350	#466	—	2	1	no	—
351	#465	—	2	1	no	—
352	#442	—	2	1	no	—
353	#440	—	2	1	no	—
354	#432	C₂²×C₁₉	1	1	yes	characteristic
355	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
357	#330	C₂²×C₁₉	1	2	yes	—
358	#330	C₂²×C₁₉	1	2	yes	—
359	#330	C₂²×C₁₉	1	2	yes	—
360	#329	C₂²×C₁₉	1	2	yes	—
361	#329	C₂²×C₁₉	1	2	yes	—
362	#329	C₂²×C₁₉	1	2	yes	—
363	C₂×C₁₉	—	2	2	no	—
364	C₂×C₁₉	—	8	2	no	—
365	C₂×C₁₉	—	8	1	no	—
366	C₂×C₁₉	—	16	1	no	—
367	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
368	C₂×C₁₉	#3018	1	1	yes	characteristic
369	C₂×C₁₉	#3020	1	1	yes	characteristic
370	C₂×#41	—	2	2	no	—
371	C₂×#41	—	2	1	no	—
372	C₂×#41	D₄×C₁₉	1	2	yes	—
373	#135	—	4	8	no	—
374	C₂×Q₁₆	—	2	2	no	—
375	C₂×SD₁₆	—	2	2	no	—
376	C₂×SD₁₆	—	2	1	no	—
377	C₂×SD₁₆	—	2	2	no	—
378	C₂×D₈	—	2	2	no	—
379	C₂×D₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	2	1	no	—
382	C₄⋊Q₈	—	2	1	no	—
383	C₄⋊Q₈	—	2	2	no	—
384	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
385	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
386	#127	D₄×C₁₉	1	1	yes	characteristic
387	#127	C₂³×C₁₉	1	1	yes	characteristic
388	#126	—	2	2	no	—
389	#126	—	2	2	no	—
390	#126	—	2	1	no	—
391	#125	—	2	2	no	—
392	#125	—	2	1	no	—
393	#125	—	2	1	no	—
394	#125	—	2	1	no	—
395	#125	D₄×C₁₉	1	2	yes	—
396	#125	C₂³×C₁₉	1	2	yes	—
397	#125	C₂³×C₁₉	1	1	yes	characteristic
398	#124	—	2	1	no	—
399	#124	C₂³×C₁₉	1	1	yes	characteristic
400	#124	C₂³×C₁₉	1	2	yes	—
401	#123	—	2	2	no	—
402	#123	—	2	2	no	—
403	#123	—	2	2	no	—
404	#123	—	2	2	no	—
405	#123	—	2	1	no	—
406	#123	—	2	2	no	—
407	#123	—	2	2	no	—
408	C₂²⋊Q₈	—	2	2	no	—
409	C₂²⋊Q₈	—	2	2	no	—
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	2	no	—
412	C₂²⋊Q₈	—	2	2	no	—
413	C₂²⋊Q₈	—	2	2	no	—
414	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
415	#121	—	2	2	no	—
416	#121	—	2	2	no	—
417	#121	—	2	1	no	—
418	#121	—	2	1	no	—
419	#121	—	2	2	no	—
420	#121	—	2	2	no	—
421	#121	—	2	1	no	—
422	#121	—	2	1	no	—
423	#121	—	2	1	no	—
424	#121	—	2	1	no	—
425	#121	D₄×C₁₉	1	1	yes	characteristic
426	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
427	C₄×D₄	—	2	2	no	—
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	2	1	no	—
430	C₄×D₄	—	2	1	no	—
431	C₄×D₄	—	2	1	no	—
432	C₄×D₄	—	2	1	no	—
433	C₄×D₄	—	2	1	no	—
434	C₄×D₄	—	2	1	no	—
435	C₄×D₄	—	2	1	no	—
436	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
437	#117	—	2	1	no	—
438	#117	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	2	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
444	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
446	#107	—	2	1	no	—
447	#107	—	2	2	no	—
448	#106	—	2	1	no	—
449	#106	—	2	2	no	—
450	C₄⋊C₈	—	2	1	no	—
451	#103	—	2	1	no	—
452	#102	—	2	1	no	—
453	#102	—	2	1	no	—
454	#102	—	2	1	no	—
455	#102	—	2	2	no	—
456	#102	—	2	2	no	—
457	C₂²⋊C₈	—	2	1	no	—
458	#97	—	2	1	no	—
459	#97	—	2	1	no	—
460	#97	C₂³×C₁₉	1	2	yes	—
461	#97	C₂³×C₁₉	1	1	yes	characteristic
462	#97	C₂³×C₁₉	1	1	yes	characteristic
463	#97	C₂³×C₁₉	1	2	yes	—
464	C₁₉	#19044	1	1	yes	characteristic, direct product factor, Sylow
465	#41	—	4	4	no	—
466	#41	—	4	4	no	—
467	#41	—	8	4	no	—
468	C₂×Q₈	—	2	2	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	4	1	no	—
492	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
495	Q₁₆	—	4	4	no	—
496	SD₁₆	—	4	2	no	—
497	SD₁₆	—	4	4	no	—
498	SD₁₆	—	4	4	no	—
499	D₈	—	4	2	no	—
500	D₈	—	4	4	no	—
501	C₂×C₈	—	2	4	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	4	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
526	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
527	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
528	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	2	1	no	—
536	C₂²⋊C₄	—	2	1	no	—
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₂²⋊C₄	—	4	1	no	—
542	C₂²⋊C₄	—	4	1	no	—
543	C₄²	—	2	2	no	—
544	C₄²	—	2	1	no	—
545	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
546	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
547	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
548	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
549	C₂³	—	2	2	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	4	1	no	—
552	C₂³	C₁₉×#120	1	1	yes	characteristic
553	Q₈	—	4	2	no	—
554	Q₈	—	4	1	no	—
555	Q₈	—	4	2	no	—
556	Q₈	—	8	2	no	—
557	D₄	—	4	2	no	—
558	D₄	—	4	1	no	—
559	D₄	—	4	2	no	—
560	D₄	—	4	2	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	2	no	—
564	D₄	—	4	4	no	—
565	D₄	—	4	2	no	—
566	D₄	—	8	1	no	—
567	D₄	—	8	2	no	—
568	D₄	—	8	2	no	—
569	D₄	—	8	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	8	2	no	—
583	C₂×C₄	—	8	2	no	—
584	C₂×C₄	—	8	1	no	—
585	C₂×C₄	—	8	2	no	—
586	C₂×C₄	—	8	2	no	—
587	C₂×C₄	—	8	2	no	—
588	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
589	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
590	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
591	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
592	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
593	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
594	C₈	—	2	4	no	—
595	C₈	—	2	2	no	—
596	C₈	—	4	1	no	—
597	C₈	—	4	2	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	8	1	no	—
607	C₂²	—	8	1	no	—
608	C₂²	—	8	1	no	—
609	C₂²	C₁₉×#453	1	2	yes	—
610	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	8	1	no	—
624	C₂	—	2	2	no	—
625	C₂	—	8	2	no	—
626	C₂	—	8	1	no	—
627	C₂	—	16	1	no	—
628	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
629	C₂	C₁₉×#3018	1	1	yes	characteristic
630	C₂	C₁₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
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
1. C₁₉×#3559	C₂	semidirect
2. C₁₉×#3234	C₂	semidirect
3. C₁₉×#3180	C₂	semidirect
4. C₁₉×#3150	C₂	semidirect
5. C₁₉×#1661	C₂	semidirect
6. C₁₉×#1660	C₂	semidirect
7. C₁₉×#1657	C₂	semidirect
8. C₁₉×#1656	C₂	semidirect
9. C₁₉×#1532	C₂	semidirect
10. C₁₉×#1530	C₂	semidirect
11. C₂×C₁₉×#330	C₂	semidirect
233. #19044	C₁₉	direct (N × H)
283. #3559	C₂×C₁₉	semidirect
284. #3234	C₂×C₁₉	semidirect
285. #3180	C₂×C₁₉	semidirect
286. #3150	C₂×C₁₉	semidirect
287. #1661	C₂×C₁₉	semidirect
288. #1660	C₂×C₁₉	semidirect
289. #1657	C₂×C₁₉	semidirect
290. #1656	C₂×C₁₉	semidirect
291. #1532	C₂×C₁₉	semidirect
292. #1530	C₂×C₁₉	semidirect
293. C₂×#330	C₂×C₁₉	semidirect
464. C₁₉	#19044	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×#3234	2
C₁₉×#3180	2
C₁₉×#3150	2
C₁₉×#1661	2
C₁₉×#1660	2
C₁₉×#1657	2
C₁₉×#1656	2
C₁₉×#1532	2
C₁₉×#1530	2
C₂×C₁₉×#330	2
#19044	19

Subgroups — C19×#19044 #18025003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19044 #18025003