Subgroups — C₁₉×#19048 #18025007

Order 4864.

908 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3213	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3180	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3135	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1664	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1662	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×#1531	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#329	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#563	C₂²	1	2	yes	—
13	C₁₉×#562	C₂²	1	2	yes	—
14	C₁₉×#556	—	2	1	no	—
15	C₁₉×#551	—	2	2	no	—
16	D₄×Q₈×C₁₉	—	2	1	no	—
17	C₁₉×#548	—	2	1	no	—
18	C₁₉×#546	—	2	1	no	—
19	C₁₉×#543	—	2	1	no	—
20	C₁₉×#542	—	2	1	no	—
21	C₁₉×#542	—	2	2	no	—
22	C₁₉×#538	—	2	1	no	—
23	C₁₉×#536	—	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×#124	C₂²	1	1	yes	characteristic
28	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#496	C₂²	1	2	yes	—
30	C₁₉×#496	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#491	C₂²	1	2	yes	complemented
32	C₁₉×#490	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#490	C₂²	1	2	yes	complemented
34	C₁₉×#489	—	2	1	no	—
35	C₁₉×#489	—	2	1	no	—
36	C₁₉×#489	C₂²	1	2	yes	—
37	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#466	—	2	1	no	—
39	C₁₉×#465	—	2	1	no	—
40	C₁₉×#463	—	2	2	no	—
41	C₁₉×#448	—	2	1	no	—
42	C₁₉×#447	—	2	1	no	—
43	C₁₉×#442	—	2	1	no	—
44	C₁₉×#440	—	2	1	no	—
45	C₁₉×#432	C₂²	1	1	yes	characteristic
46	C₁₉×#416	—	2	2	no	—
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	complemented
50	C₁₉×#330	C₂²	1	2	yes	complemented
51	C₁₉×#330	C₂²	1	2	yes	complemented
52	C₁₉×#329	C₂²	1	2	yes	—
53	C₁₉×#329	C₂²	1	2	yes	—
54	C₁₉×#329	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	—	2	1	no	—
58	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
59	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂×SD₁₆×C₁₉	—	2	1	no	—
61	C₂×SD₁₆×C₁₉	—	2	2	no	—
62	C₂×D₈×C₁₉	—	2	1	no	—
63	C₂×D₈×C₁₉	—	2	2	no	—
64	C₂²×C₈×C₁₉	—	2	1	no	—
65	C₂²×C₈×C₁₉	—	2	1	no	—
66	C₁₉×C₄⋊Q₈	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	2	2	no	—
68	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
69	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
70	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₁₉×#127	C₂³	1	1	yes	characteristic
72	C₁₉×#126	—	2	2	no	—
73	C₁₉×#126	—	2	2	no	—
74	C₁₉×#126	—	2	2	no	—
75	C₁₉×#126	—	2	1	no	—
76	C₁₉×#125	C₂³	1	2	yes	—
77	C₁₉×#125	C₂³	1	1	yes	characteristic
78	C₁₉×#124	—	2	1	no	—
79	C₁₉×#124	—	2	2	no	—
80	C₁₉×#124	—	2	2	no	—
81	C₁₉×#124	—	2	1	no	—
82	C₁₉×#124	—	2	1	no	—
83	C₁₉×#124	—	2	1	no	—
84	C₁₉×#124	D₄	1	2	yes	—
85	C₁₉×#124	C₂³	1	2	yes	—
86	C₁₉×#124	C₂³	1	1	yes	characteristic
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×#123	—	2	1	no	—
90	C₁₉×#123	—	2	2	no	—
91	C₁₉×#123	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	1	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	1	no	—
99	C₁₉×C₂²⋊Q₈	—	2	1	no	—
100	C₁₉×C₂²⋊Q₈	—	2	2	no	—
101	C₁₉×C₂²⋊Q₈	—	2	2	no	—
102	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
109	C₁₉×#120	—	2	2	no	—
110	C₄×Q₈×C₁₉	—	2	1	no	—
111	C₄×Q₈×C₁₉	—	2	1	no	—
112	C₄×Q₈×C₁₉	—	2	1	no	—
113	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
114	C₄×D₄×C₁₉	—	2	2	no	—
115	C₄×D₄×C₁₉	—	2	1	no	—
116	C₄×D₄×C₁₉	—	2	2	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	D₄	1	1	yes	characteristic
121	C₁₉×#117	—	2	2	no	—
122	C₁₉×#117	—	2	1	no	—
123	C₁₉×#117	D₄	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
125	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
128	C₁₉×#107	—	2	1	no	—
129	C₁₉×#106	—	2	1	no	—
130	C₁₉×C₄⋊C₈	—	2	1	no	—
131	C₁₉×#103	—	2	1	no	—
132	C₁₉×#103	—	2	2	no	—
133	C₁₉×#103	—	2	2	no	—
134	C₁₉×#103	—	2	2	no	—
135	C₁₉×#102	—	2	1	no	—
136	C₁₉×#102	—	2	2	no	—
137	C₁₉×#102	—	2	2	no	—
138	C₁₉×#102	—	2	2	no	—
139	C₁₉×#102	—	2	1	no	—
140	C₁₉×#102	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×#97	—	2	1	no	—
143	C₁₉×#97	—	2	1	no	—
144	C₁₉×#97	C₂³	1	1	yes	characteristic
145	C₁₉×#97	C₂³	1	2	yes	—
146	C₁₉×#97	C₂³	1	1	yes	characteristic
147	C₁₉×#97	C₂³	1	2	yes	—
148	C₂⁴×C₁₉	—	2	1	no	—
149	#41×C₁₉	—	4	4	no	—
150	#41×C₁₉	—	8	2	no	—
151	C₂×Q₈×C₁₉	—	2	2	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	2	1	no	—
156	C₂×Q₈×C₁₉	—	8	2	no	—
157	C₂×Q₈×C₁₉	—	8	1	no	—
158	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	1	no	—
165	C₂×D₄×C₁₉	—	2	1	no	—
166	C₂×D₄×C₁₉	—	2	1	no	—
167	C₂×D₄×C₁₉	—	4	1	no	—
168	C₂×D₄×C₁₉	—	8	1	no	—
169	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
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	1	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	4	1	no	—
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
180	SD₁₆×C₁₉	—	4	2	no	—
181	SD₁₆×C₁₉	—	8	2	no	—
182	D₈×C₁₉	—	4	2	no	—
183	D₈×C₁₉	—	8	2	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₂×C₈×C₁₉	—	2	2	no	—
187	C₂×C₈×C₁₉	—	2	2	no	—
188	C₂×C₈×C₁₉	—	4	2	no	—
189	C₂×C₈×C₁₉	—	4	2	no	—
190	C₄⋊C₄×C₁₉	—	2	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	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	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	1	no	—
200	C₄⋊C₄×C₁₉	—	2	2	no	—
201	C₄⋊C₄×C₁₉	—	2	2	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
205	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
206	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
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	1	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	1	no	—
218	C₂²⋊C₄×C₁₉	—	2	1	no	—
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	—	2	2	no	—
221	C₂²⋊C₄×C₁₉	—	2	1	no	—
222	C₂²⋊C₄×C₁₉	—	2	1	no	—
223	C₂²⋊C₄×C₁₉	—	4	1	no	—
224	C₂²⋊C₄×C₁₉	—	4	1	no	—
225	C₄²×C₁₉	—	2	2	no	—
226	C₄²×C₁₉	—	2	2	no	—
227	C₄²×C₁₉	—	2	1	no	—
228	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
231	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
232	#19048	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂³×C₁₉	—	2	2	no	—
234	C₂³×C₁₉	—	2	1	no	—
235	C₂³×C₁₉	—	4	2	no	—
236	C₂³×C₁₉	—	4	1	no	—
237	C₂³×C₁₉	—	8	1	no	—
238	C₂³×C₁₉	—	8	1	no	—
239	C₂³×C₁₉	#120	1	1	yes	characteristic
240	Q₈×C₁₉	—	4	1	no	—
241	Q₈×C₁₉	—	4	2	no	—
242	Q₈×C₁₉	—	4	2	no	—
243	Q₈×C₁₉	—	4	2	no	—
244	Q₈×C₁₉	—	4	2	no	—
245	Q₈×C₁₉	—	8	1	no	—
246	Q₈×C₁₉	—	8	2	no	—
247	D₄×C₁₉	—	4	1	no	—
248	D₄×C₁₉	—	4	2	no	—
249	D₄×C₁₉	—	4	2	no	—
250	D₄×C₁₉	—	4	1	no	—
251	D₄×C₁₉	—	4	2	no	—
252	D₄×C₁₉	—	4	1	no	—
253	D₄×C₁₉	—	4	2	no	—
254	D₄×C₁₉	—	4	2	no	—
255	D₄×C₁₉	—	8	2	no	—
256	D₄×C₁₉	—	8	2	no	—
257	D₄×C₁₉	—	8	2	no	—
258	C₂×C₄×C₁₉	—	2	2	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	2	no	—
263	C₂×C₄×C₁₉	—	2	2	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	2	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	8	2	no	—
270	C₂×C₄×C₁₉	—	8	1	no	—
271	C₂×C₄×C₁₉	—	8	2	no	—
272	C₂×C₄×C₁₉	—	8	2	no	—
273	C₂×C₄×C₁₉	—	8	2	no	—
274	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
275	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
276	C₂×C₄×C₁₉	#120	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	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
280	C₈×C₁₉	—	2	2	no	—
281	C₈×C₁₉	—	4	2	no	—
282	C₈×C₁₉	—	4	1	no	—
283	C₈×C₁₉	—	4	2	no	—
284	#3561	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#3213	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#3180	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#3135	C₂×C₁₉	1	1	yes	characteristic, complemented
288	#1664	C₂×C₁₉	1	2	yes	complemented
289	#1662	C₂×C₁₉	1	2	yes	complemented
290	#1657	C₂×C₁₉	1	2	yes	complemented
291	#1656	C₂×C₁₉	1	2	yes	complemented
292	#1532	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1531	C₂×C₁₉	1	1	yes	characteristic, complemented
294	C₂×#329	C₂×C₁₉	1	1	yes	characteristic, complemented
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	4	1	no	—
298	C₂²×C₁₉	—	4	2	no	—
299	C₂²×C₁₉	—	4	2	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	2	no	—
303	C₂²×C₁₉	—	8	1	no	—
304	C₂²×C₁₉	—	8	1	no	—
305	C₂²×C₁₉	—	8	1	no	—
306	C₂²×C₁₉	—	16	2	no	—
307	C₂²×C₁₉	#454	1	2	yes	—
308	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
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	—	2	1	no	—
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	—	4	1	no	—
316	C₄×C₁₉	—	4	1	no	—
317	C₄×C₁₉	—	4	2	no	—
318	C₄×C₁₉	—	4	1	no	—
319	C₄×C₁₉	—	4	2	no	—
320	C₄×C₁₉	—	4	2	no	—
321	C₄×C₁₉	—	8	1	no	—
322	#563	C₂²×C₁₉	1	2	yes	—
323	#562	C₂²×C₁₉	1	2	yes	—
324	#556	—	2	1	no	—
325	#551	—	2	2	no	—
326	D₄×Q₈	—	2	1	no	—
327	#548	—	2	1	no	—
328	#546	—	2	1	no	—
329	#543	—	2	1	no	—
330	#542	—	2	1	no	—
331	#542	—	2	2	no	—
332	#538	—	2	1	no	—
333	#536	—	2	1	no	—
334	#533	C₂²×C₁₉	1	1	yes	characteristic
335	#532	C₂²×C₁₉	1	1	yes	characteristic
336	#529	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
338	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	#496	C₂²×C₁₉	1	2	yes	—
340	#496	C₂²×C₁₉	1	1	yes	characteristic, complemented
341	#491	C₂²×C₁₉	1	2	yes	complemented
342	#490	C₂²×C₁₉	1	2	yes	complemented
343	#490	C₂²×C₁₉	1	1	yes	characteristic, complemented
344	#489	—	2	1	no	—
345	#489	—	2	1	no	—
346	#489	C₂²×C₁₉	1	2	yes	—
347	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
348	#466	—	2	1	no	—
349	#465	—	2	1	no	—
350	#463	—	2	2	no	—
351	#448	—	2	1	no	—
352	#447	—	2	1	no	—
353	#442	—	2	1	no	—
354	#440	—	2	1	no	—
355	#432	C₂²×C₁₉	1	1	yes	characteristic
356	#416	—	2	2	no	—
357	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
359	#330	C₂²×C₁₉	1	2	yes	complemented
360	#330	C₂²×C₁₉	1	2	yes	complemented
361	#330	C₂²×C₁₉	1	2	yes	complemented
362	#329	C₂²×C₁₉	1	2	yes	—
363	#329	C₂²×C₁₉	1	2	yes	—
364	#329	C₂²×C₁₉	1	2	yes	complemented
365	C₂×C₁₉	—	2	2	no	—
366	C₂×C₁₉	—	8	1	no	—
367	C₂×C₁₉	—	8	2	no	—
368	C₂×C₁₉	—	16	1	no	—
369	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
370	C₂×C₁₉	#3018	1	1	yes	characteristic
371	C₂×C₁₉	#3019	1	1	yes	characteristic
372	C₂×#41	—	2	1	no	—
373	C₂×#41	—	2	1	no	—
374	C₂²×Q₈	—	2	1	no	—
375	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
376	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
377	C₂×SD₁₆	—	2	1	no	—
378	C₂×SD₁₆	—	2	2	no	—
379	C₂×D₈	—	2	1	no	—
380	C₂×D₈	—	2	2	no	—
381	C₂²×C₈	—	2	1	no	—
382	C₂²×C₈	—	2	1	no	—
383	C₄⋊Q₈	—	2	1	no	—
384	C₄⋊Q₈	—	2	2	no	—
385	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
386	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
387	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
388	#127	C₂³×C₁₉	1	1	yes	characteristic
389	#126	—	2	2	no	—
390	#126	—	2	2	no	—
391	#126	—	2	2	no	—
392	#126	—	2	1	no	—
393	#125	C₂³×C₁₉	1	1	yes	characteristic
394	#125	C₂³×C₁₉	1	2	yes	—
395	#124	—	2	1	no	—
396	#124	—	2	2	no	—
397	#124	—	2	2	no	—
398	#124	—	2	1	no	—
399	#124	—	2	1	no	—
400	#124	—	2	1	no	—
401	#124	D₄×C₁₉	1	2	yes	—
402	#124	C₂³×C₁₉	1	2	yes	—
403	#124	C₂³×C₁₉	1	1	yes	characteristic
404	#123	—	2	2	no	—
405	#123	—	2	2	no	—
406	#123	—	2	1	no	—
407	#123	—	2	2	no	—
408	#123	—	2	2	no	—
409	C₂²⋊Q₈	—	2	2	no	—
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	1	no	—
412	C₂²⋊Q₈	—	2	2	no	—
413	C₂²⋊Q₈	—	2	2	no	—
414	C₂²⋊Q₈	—	2	2	no	—
415	C₂²⋊Q₈	—	2	1	no	—
416	C₂²⋊Q₈	—	2	1	no	—
417	C₂²⋊Q₈	—	2	2	no	—
418	C₂²⋊Q₈	—	2	2	no	—
419	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
420	#121	—	2	1	no	—
421	#121	—	2	2	no	—
422	#121	—	2	2	no	—
423	#121	—	2	1	no	—
424	#121	—	2	1	no	—
425	#121	D₄×C₁₉	1	1	yes	characteristic
426	#120	—	2	2	no	—
427	C₄×Q₈	—	2	1	no	—
428	C₄×Q₈	—	2	1	no	—
429	C₄×Q₈	—	2	1	no	—
430	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
431	C₄×D₄	—	2	2	no	—
432	C₄×D₄	—	2	1	no	—
433	C₄×D₄	—	2	2	no	—
434	C₄×D₄	—	2	1	no	—
435	C₄×D₄	—	2	1	no	—
436	C₄×D₄	—	2	1	no	—
437	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
438	#117	—	2	2	no	—
439	#117	—	2	1	no	—
440	#117	D₄×C₁₉	1	2	yes	—
441	C₂×C₂²⋊C₄	—	2	2	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
445	#107	—	2	1	no	—
446	#106	—	2	1	no	—
447	C₄⋊C₈	—	2	1	no	—
448	#103	—	2	1	no	—
449	#103	—	2	2	no	—
450	#103	—	2	2	no	—
451	#103	—	2	2	no	—
452	#102	—	2	1	no	—
453	#102	—	2	2	no	—
454	#102	—	2	2	no	—
455	#102	—	2	2	no	—
456	#102	—	2	1	no	—
457	#102	—	2	1	no	—
458	C₂²⋊C₈	—	2	1	no	—
459	#97	—	2	1	no	—
460	#97	—	2	1	no	—
461	#97	C₂³×C₁₉	1	2	yes	—
462	#97	C₂³×C₁₉	1	1	yes	characteristic
463	#97	C₂³×C₁₉	1	1	yes	characteristic
464	#97	C₂³×C₁₉	1	2	yes	—
465	C₁₉	#19048	1	1	yes	characteristic, direct product factor, Sylow
466	C₂⁴	—	2	1	no	—
467	#41	—	4	4	no	—
468	#41	—	8	2	no	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	8	2	no	—
475	C₂×Q₈	—	8	1	no	—
476	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	4	1	no	—
486	C₂×D₄	—	8	1	no	—
487	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	4	1	no	—
495	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
498	SD₁₆	—	4	2	no	—
499	SD₁₆	—	8	2	no	—
500	D₈	—	4	2	no	—
501	D₈	—	8	2	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	4	2	no	—
507	C₂×C₈	—	4	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	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
523	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
524	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	2	no	—
535	C₂²⋊C₄	—	2	1	no	—
536	C₂²⋊C₄	—	2	1	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	1	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	2	no	—
545	C₄²	—	2	1	no	—
546	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
547	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
548	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
549	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
550	C₂³	—	2	2	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	8	1	no	—
555	C₂³	—	8	1	no	—
556	C₂³	C₁₉×#120	1	1	yes	characteristic
557	Q₈	—	4	1	no	—
558	Q₈	—	4	2	no	—
559	Q₈	—	4	2	no	—
560	Q₈	—	4	2	no	—
561	Q₈	—	4	2	no	—
562	Q₈	—	8	1	no	—
563	Q₈	—	8	2	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	2	no	—
566	D₄	—	4	2	no	—
567	D₄	—	4	1	no	—
568	D₄	—	4	2	no	—
569	D₄	—	4	1	no	—
570	D₄	—	4	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	8	2	no	—
573	D₄	—	8	2	no	—
574	D₄	—	8	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	8	2	no	—
587	C₂×C₄	—	8	1	no	—
588	C₂×C₄	—	8	2	no	—
589	C₂×C₄	—	8	2	no	—
590	C₂×C₄	—	8	2	no	—
591	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
592	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
593	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
594	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
595	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
596	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
597	C₈	—	2	2	no	—
598	C₈	—	4	2	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	2	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	8	1	no	—
610	C₂²	—	8	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	16	2	no	—
613	C₂²	C₁₉×#454	1	2	yes	—
614	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	2	no	—
627	C₄	—	8	1	no	—
628	C₂	—	2	2	no	—
629	C₂	—	8	2	no	—
630	C₂	—	8	1	no	—
631	C₂	—	16	1	no	—
632	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
633	C₂	C₁₉×#3018	1	1	yes	characteristic
634	C₂	C₁₉×#3019	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×#3561	C₂	semidirect
2. C₁₉×#3213	C₂	semidirect
3. C₁₉×#3180	C₂	semidirect
4. C₁₉×#3135	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1662	C₂	semidirect
7. C₁₉×#1657	C₂	semidirect
8. C₁₉×#1656	C₂	semidirect
9. C₁₉×#1532	C₂	semidirect
10. C₁₉×#1531	C₂	semidirect
11. C₂×C₁₉×#329	C₂	semidirect
28. C₁₉×#501	C₂²	semidirect
30. C₁₉×#496	C₂²	semidirect
31. C₁₉×#491	C₂²	semidirect
32. C₁₉×#490	C₂²	semidirect
33. C₁₉×#490	C₂²	semidirect
37. C₁₉×#489	C₂²	semidirect
49. C₁₉×#330	C₂²	semidirect
50. C₁₉×#330	C₂²	semidirect
51. C₁₉×#330	C₂²	semidirect
54. C₁₉×#329	C₂²	semidirect
232. #19048	C₁₉	direct (N × H)
284. #3561	C₂×C₁₉	semidirect
285. #3213	C₂×C₁₉	semidirect
286. #3180	C₂×C₁₉	semidirect
287. #3135	C₂×C₁₉	semidirect
288. #1664	C₂×C₁₉	semidirect
289. #1662	C₂×C₁₉	semidirect
290. #1657	C₂×C₁₉	semidirect
291. #1656	C₂×C₁₉	semidirect
292. #1532	C₂×C₁₉	semidirect
293. #1531	C₂×C₁₉	semidirect
294. C₂×#329	C₂×C₁₉	semidirect
338. #501	C₂²×C₁₉	semidirect
340. #496	C₂²×C₁₉	semidirect
341. #491	C₂²×C₁₉	semidirect
342. #490	C₂²×C₁₉	semidirect
343. #490	C₂²×C₁₉	semidirect
347. #489	C₂²×C₁₉	semidirect
359. #330	C₂²×C₁₉	semidirect
360. #330	C₂²×C₁₉	semidirect
361. #330	C₂²×C₁₉	semidirect
364. #329	C₂²×C₁₉	semidirect
465. C₁₉	#19048	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×#3561	2
C₁₉×#3213	2
C₁₉×#3180	2
C₁₉×#3135	2
C₁₉×#1664	2
C₁₉×#1662	2
C₁₉×#1657	2
C₁₉×#1656	2
C₁₉×#1532	2
C₁₉×#1531	2
C₂×C₁₉×#329	2
#19048	19

Subgroups — C19×#19048 #18025007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19048 #18025007