Subgroups — C₁₉×#32615 #18038574

Order 4864.

714 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2580	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2097	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2074	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2066	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2055	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2013	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1985	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1973	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1935	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1926	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1921	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1877	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1877	C₂	1	1	yes	maximal, characteristic
16	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
33	C₁₉×#400	—	2	1	no	—
34	C₁₉×#400	—	2	1	no	—
35	C₁₉×#399	—	2	1	no	—
36	C₁₉×#393	—	2	1	no	—
37	C₁₉×#391	—	2	1	no	—
38	C₁₉×#391	C₂²	1	1	yes	characteristic
39	C₁₉×#391	C₂²	1	1	yes	characteristic
40	C₁₉×#391	C₂²	1	1	yes	characteristic
41	C₁₉×#391	C₂²	1	1	yes	characteristic
42	C₁₉×#390	C₂²	1	1	yes	characteristic
43	C₁₉×#390	C₂²	1	1	yes	characteristic
44	C₁₉×#389	C₂²	1	1	yes	characteristic
45	C₁₉×#389	C₂²	1	1	yes	characteristic
46	C₁₉×#385	—	2	1	no	—
47	C₁₉×#385	—	2	1	no	—
48	C₁₉×#382	—	2	1	no	—
49	C₁₉×#382	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#336	C₂²	1	1	yes	characteristic
56	C₁₉×#336	C₂²	1	1	yes	characteristic
57	C₁₉×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
60	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₂×SD₁₆×C₁₉	—	2	2	no	—
65	C₂×SD₁₆×C₁₉	—	2	2	no	—
66	C₂×SD₁₆×C₁₉	—	2	2	no	—
67	C₂×SD₁₆×C₁₉	—	4	1	no	—
68	C₂×SD₁₆×C₁₉	—	4	1	no	—
69	C₂×SD₁₆×C₁₉	—	4	1	no	—
70	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×C₄⋊Q₈	—	4	1	no	—
75	C₁₉×C₄⋊Q₈	—	4	1	no	—
76	C₄×Q₈×C₁₉	—	4	1	no	—
77	C₄×Q₈×C₁₉	—	4	1	no	—
78	C₄×D₄×C₁₉	—	4	1	no	—
79	C₄×D₄×C₁₉	—	4	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₄²×C₁₉	—	2	1	no	—
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#107	—	2	2	no	—
102	C₁₉×#106	—	4	1	no	—
103	C₁₉×C₄⋊C₈	—	4	1	no	—
104	C₁₉×#103	—	2	2	no	—
105	C₁₉×#103	—	4	1	no	—
106	C₁₉×#103	—	4	1	no	—
107	C₁₉×#103	—	4	1	no	—
108	C₁₉×#103	—	4	1	no	—
109	C₁₉×#103	—	4	1	no	—
110	C₁₉×#102	—	2	2	no	—
111	C₁₉×#102	—	4	1	no	—
112	C₁₉×#97	—	4	1	no	—
113	C₁₉×#95	—	2	1	no	—
114	C₁₉×#95	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	—	2	1	no	—
118	C₁₉×#95	—	2	1	no	—
119	C₁₉×#95	—	2	1	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₁₉×#95	—	2	1	no	—
122	C₁₉×#95	—	2	1	no	—
123	C₁₉×#95	—	2	1	no	—
124	C₁₉×#95	—	2	1	no	—
125	C₁₉×#95	—	2	1	no	—
126	C₂⁴×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	2	2	no	—
128	C₂×Q₈×C₁₉	—	2	1	no	—
129	C₂×Q₈×C₁₉	—	2	1	no	—
130	C₂×Q₈×C₁₉	—	2	1	no	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	—	2	1	no	—
134	C₂×Q₈×C₁₉	—	2	1	no	—
135	C₂×Q₈×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	4	1	no	—
141	C₂×Q₈×C₁₉	—	4	1	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	2	1	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	#41	1	2	yes	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	4	2	no	—
156	C₂²×C₄×C₁₉	—	8	1	no	—
157	C₂²×C₄×C₁₉	—	8	1	no	—
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
165	SD₁₆×C₁₉	—	4	4	no	—
166	SD₁₆×C₁₉	—	4	4	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×C₁₉	#41	1	2	yes	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	4	1	no	—
190	C₄⋊C₄×C₁₉	—	4	1	no	—
191	C₄⋊C₄×C₁₉	—	4	1	no	—
192	C₄⋊C₄×C₁₉	—	4	2	no	—
193	C₄⋊C₄×C₁₉	—	4	2	no	—
194	C₄⋊C₄×C₁₉	—	8	1	no	—
195	C₄⋊C₄×C₁₉	—	8	1	no	—
196	C₂²⋊C₄×C₁₉	—	4	2	no	—
197	C₂²⋊C₄×C₁₉	—	4	2	no	—
198	C₂²⋊C₄×C₁₉	—	4	2	no	—
199	C₂²⋊C₄×C₁₉	—	8	1	no	—
200	C₂²⋊C₄×C₁₉	—	8	1	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	C₄²×C₁₉	—	2	1	no	—
204	C₄²×C₁₉	—	2	1	no	—
205	C₄²×C₁₉	—	2	1	no	—
206	C₄²×C₁₉	—	2	1	no	—
207	C₄²×C₁₉	—	4	2	no	—
208	#32615	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂³×C₁₉	—	2	2	no	—
210	C₂³×C₁₉	—	4	1	no	—
211	C₂³×C₁₉	—	4	1	no	—
212	C₂³×C₁₉	—	4	1	no	—
213	C₂³×C₁₉	—	4	1	no	—
214	C₂³×C₁₉	—	4	1	no	—
215	C₂³×C₁₉	—	4	1	no	—
216	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₁₉	—	4	4	no	—
218	Q₈×C₁₉	—	4	1	no	—
219	Q₈×C₁₉	—	4	1	no	—
220	Q₈×C₁₉	—	4	1	no	—
221	Q₈×C₁₉	—	4	1	no	—
222	Q₈×C₁₉	—	4	1	no	—
223	Q₈×C₁₉	—	4	1	no	—
224	Q₈×C₁₉	—	4	1	no	—
225	Q₈×C₁₉	—	4	1	no	—
226	D₄×C₁₉	—	2	2	no	—
227	D₄×C₁₉	—	2	2	no	—
228	D₄×C₁₉	—	4	1	no	—
229	D₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	8	4	no	—
269	C₂×C₄×C₁₉	#137	1	2	yes	—
270	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
274	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
275	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
276	C₈×C₁₉	—	2	2	no	—
277	C₈×C₁₉	—	4	1	no	—
278	C₈×C₁₉	—	4	1	no	—
279	C₈×C₁₉	—	4	1	no	—
280	#2580	C₂×C₁₉	1	1	yes	characteristic
281	#2568	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#2097	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#2074	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#2066	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#2055	C₂×C₁₉	1	1	yes	characteristic
286	#2043	C₂×C₁₉	1	1	yes	characteristic, complemented
287	#2013	C₂×C₁₉	1	1	yes	characteristic
288	#1985	C₂×C₁₉	1	1	yes	characteristic, complemented
289	#1973	C₂×C₁₉	1	1	yes	characteristic
290	#1935	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1926	C₂×C₁₉	1	1	yes	characteristic
292	#1921	C₂×C₁₉	1	1	yes	characteristic, complemented
293	#1877	C₂×C₁₉	1	1	yes	characteristic
294	#1877	C₂×C₁₉	1	1	yes	characteristic
295	C₂²×C₁₉	—	4	2	no	—
296	C₂²×C₁₉	—	4	2	no	—
297	C₂²×C₁₉	—	4	2	no	—
298	C₂²×C₁₉	—	8	1	no	—
299	C₂²×C₁₉	—	8	1	no	—
300	C₂²×C₁₉	—	8	1	no	—
301	C₂²×C₁₉	—	8	1	no	—
302	C₂²×C₁₉	#534	1	1	yes	characteristic
303	C₂²×C₁₉	#548	1	1	yes	characteristic
304	C₂²×C₁₉	#550	1	1	yes	characteristic
305	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
306	C₂²×C₁₉	#575	1	1	yes	characteristic
307	C₂²×C₁₉	#577	1	1	yes	characteristic
308	C₂²×C₁₉	#577	1	1	yes	characteristic
309	C₄×C₁₉	—	2	2	no	—
310	C₄×C₁₉	—	4	1	no	—
311	C₄×C₁₉	—	4	1	no	—
312	C₄×C₁₉	—	4	1	no	—
313	C₄×C₁₉	—	4	1	no	—
314	C₄×C₁₉	—	4	1	no	—
315	C₄×C₁₉	—	8	1	no	—
316	C₄×C₁₉	—	8	1	no	—
317	C₄×C₁₉	—	8	1	no	—
318	C₄×C₁₉	—	8	1	no	—
319	C₄×C₁₉	—	8	1	no	—
320	C₄×C₁₉	—	8	1	no	—
321	C₄×C₁₉	—	8	1	no	—
322	C₄×C₁₉	#538	1	1	yes	characteristic
323	C₄×C₁₉	#542	1	1	yes	characteristic
324	C₄×C₁₉	#551	1	1	yes	characteristic
325	C₄×C₁₉	#562	1	1	yes	characteristic
326	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
327	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
330	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
331	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
339	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
340	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
341	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
342	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
343	#400	—	2	1	no	—
344	#400	—	2	1	no	—
345	#399	—	2	1	no	—
346	#393	—	2	1	no	—
347	#391	—	2	1	no	—
348	#391	C₂²×C₁₉	1	1	yes	characteristic
349	#391	C₂²×C₁₉	1	1	yes	characteristic
350	#391	C₂²×C₁₉	1	1	yes	characteristic
351	#391	C₂²×C₁₉	1	1	yes	characteristic
352	#390	C₂²×C₁₉	1	1	yes	characteristic
353	#390	C₂²×C₁₉	1	1	yes	characteristic
354	#389	C₂²×C₁₉	1	1	yes	characteristic
355	#389	C₂²×C₁₉	1	1	yes	characteristic
356	#385	—	2	1	no	—
357	#385	—	2	1	no	—
358	#382	—	2	1	no	—
359	#382	C₂²×C₁₉	1	1	yes	characteristic
360	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
361	#340	C₂²×C₁₉	1	1	yes	characteristic
362	#340	C₂²×C₁₉	1	1	yes	characteristic
363	#340	C₂²×C₁₉	1	1	yes	characteristic
364	#340	C₂²×C₁₉	1	1	yes	characteristic
365	#336	C₂²×C₁₉	1	1	yes	characteristic
366	#336	C₂²×C₁₉	1	1	yes	characteristic
367	#336	C₂²×C₁₉	1	1	yes	characteristic
368	#336	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×C₁₉	—	8	2	no	—
370	C₂×C₁₉	#2730	1	1	yes	characteristic
371	C₂×C₁₉	#3196	1	1	yes	characteristic
372	C₂×C₁₉	#3200	1	1	yes	characteristic
373	C₂×C₁₉	#3372	1	1	yes	characteristic
374	C₂×C₁₉	#3376	1	1	yes	characteristic
375	C₂×C₁₉	#3400	1	1	yes	characteristic
376	C₂×C₁₉	#3401	1	1	yes	characteristic
377	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
378	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
379	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
380	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
381	C₂³×C₄	—	2	1	no	—
382	C₂×SD₁₆	—	2	2	no	—
383	C₂×SD₁₆	—	2	2	no	—
384	C₂×SD₁₆	—	2	2	no	—
385	C₂×SD₁₆	—	4	1	no	—
386	C₂×SD₁₆	—	4	1	no	—
387	C₂×SD₁₆	—	4	1	no	—
388	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
390	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
391	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
392	C₄⋊Q₈	—	4	1	no	—
393	C₄⋊Q₈	—	4	1	no	—
394	C₄×Q₈	—	4	1	no	—
395	C₄×Q₈	—	4	1	no	—
396	C₄×D₄	—	4	1	no	—
397	C₄×D₄	—	4	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
403	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
404	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
419	#107	—	2	2	no	—
420	#106	—	4	1	no	—
421	C₄⋊C₈	—	4	1	no	—
422	#103	—	2	2	no	—
423	#103	—	4	1	no	—
424	#103	—	4	1	no	—
425	#103	—	4	1	no	—
426	#103	—	4	1	no	—
427	#103	—	4	1	no	—
428	#102	—	2	2	no	—
429	#102	—	4	1	no	—
430	#97	—	4	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	C₁₉	#32615	1	1	yes	characteristic, direct product factor, Sylow
445	C₂⁴	—	2	1	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	4	1	no	—
460	C₂×Q₈	—	4	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	#41×C₁₉	1	2	yes	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	8	1	no	—
476	C₂²×C₄	—	8	1	no	—
477	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
484	SD₁₆	—	4	4	no	—
485	SD₁₆	—	4	4	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	#41×C₁₉	1	2	yes	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	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	—	4	1	no	—
509	C₄⋊C₄	—	4	1	no	—
510	C₄⋊C₄	—	4	1	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	—	4	2	no	—
513	C₄⋊C₄	—	8	1	no	—
514	C₄⋊C₄	—	8	1	no	—
515	C₂²⋊C₄	—	4	2	no	—
516	C₂²⋊C₄	—	4	2	no	—
517	C₂²⋊C₄	—	4	2	no	—
518	C₂²⋊C₄	—	8	1	no	—
519	C₂²⋊C₄	—	8	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	4	2	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	4	1	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	4	1	no	—
534	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
535	Q₈	—	4	4	no	—
536	Q₈	—	4	1	no	—
537	Q₈	—	4	1	no	—
538	Q₈	—	4	1	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	1	no	—
541	Q₈	—	4	1	no	—
542	Q₈	—	4	1	no	—
543	Q₈	—	4	1	no	—
544	D₄	—	2	2	no	—
545	D₄	—	2	2	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	8	4	no	—
587	C₂×C₄	C₁₉×#137	1	2	yes	—
588	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
589	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
590	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
591	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
592	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
593	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
594	C₈	—	2	2	no	—
595	C₈	—	4	1	no	—
596	C₈	—	4	1	no	—
597	C₈	—	4	1	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	8	1	no	—
602	C₂²	—	8	1	no	—
603	C₂²	—	8	1	no	—
604	C₂²	—	8	1	no	—
605	C₂²	C₁₉×#534	1	1	yes	characteristic
606	C₂²	C₁₉×#548	1	1	yes	characteristic
607	C₂²	C₁₉×#550	1	1	yes	characteristic
608	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
609	C₂²	C₁₉×#575	1	1	yes	characteristic
610	C₂²	C₁₉×#577	1	1	yes	characteristic
611	C₂²	C₁₉×#577	1	1	yes	characteristic
612	C₄	—	2	2	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	1	no	—
618	C₄	—	8	1	no	—
619	C₄	—	8	1	no	—
620	C₄	—	8	1	no	—
621	C₄	—	8	1	no	—
622	C₄	—	8	1	no	—
623	C₄	—	8	1	no	—
624	C₄	—	8	1	no	—
625	C₄	C₁₉×#538	1	1	yes	characteristic
626	C₄	C₁₉×#542	1	1	yes	characteristic
627	C₄	C₁₉×#551	1	1	yes	characteristic
628	C₄	C₁₉×#562	1	1	yes	characteristic
629	C₂	—	8	2	no	—
630	C₂	C₁₉×#2730	1	1	yes	characteristic
631	C₂	C₁₉×#3196	1	1	yes	characteristic
632	C₂	C₁₉×#3200	1	1	yes	characteristic
633	C₂	C₁₉×#3372	1	1	yes	characteristic
634	C₂	C₁₉×#3376	1	1	yes	characteristic
635	C₂	C₁₉×#3400	1	1	yes	characteristic
636	C₂	C₁₉×#3401	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2568	C₂	semidirect
3. C₁₉×#2097	C₂	semidirect
4. C₁₉×#2074	C₂	semidirect
5. C₁₉×#2066	C₂	semidirect
7. C₁₉×#2043	C₂	semidirect
9. C₁₉×#1985	C₂	semidirect
11. C₁₉×#1935	C₂	semidirect
13. C₁₉×#1921	C₂	semidirect
208. #32615	C₁₉	direct (N × H)
281. #2568	C₂×C₁₉	semidirect
282. #2097	C₂×C₁₉	semidirect
283. #2074	C₂×C₁₉	semidirect
284. #2066	C₂×C₁₉	semidirect
286. #2043	C₂×C₁₉	semidirect
288. #1985	C₂×C₁₉	semidirect
290. #1935	C₂×C₁₉	semidirect
292. #1921	C₂×C₁₉	semidirect
444. C₁₉	#32615	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×#2580	2
C₁₉×#2568	2
C₁₉×#2097	2
C₁₉×#2074	2
C₁₉×#2066	2
C₁₉×#2055	2
C₁₉×#2043	2
C₁₉×#2013	2
C₁₉×#1985	2
C₁₉×#1973	2
C₁₉×#1935	2
C₁₉×#1926	2
C₁₉×#1921	2
C₁₉×#1877	2
#32615	19

Subgroups — C19×#32615 #18038574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32615 #18038574