Subgroups — C₁₉×#26270 #18032229

Order 4864.

776 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3154	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3097	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3096	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2952	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2052	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2051	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2038	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2037	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1977	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1974	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1951	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1883	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1882	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1772	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#536	C₂²	1	1	yes	characteristic
21	C₁₉×#535	C₂²	1	1	yes	characteristic
22	C₁₉×#520	C₂²	1	1	yes	characteristic
23	C₁₉×#520	C₂²	1	1	yes	characteristic
24	C₁₉×#497	—	2	1	no	—
25	C₁₉×#496	—	2	1	no	—
26	C₁₉×#495	—	2	1	no	—
27	C₁₉×#492	—	2	1	no	—
28	C₁₉×#485	—	2	1	no	—
29	C₁₉×#485	—	2	1	no	—
30	C₁₉×#484	—	2	1	no	—
31	C₁₉×#483	—	2	1	no	—
32	C₁₉×#482	—	2	1	no	—
33	C₁₉×#482	—	2	1	no	—
34	C₁₉×#481	—	2	1	no	—
35	C₁₉×#480	—	2	1	no	—
36	C₁₉×#442	—	2	1	no	—
37	C₁₉×#441	—	2	1	no	—
38	C₄×SD₁₆×C₁₉	—	2	1	no	—
39	C₄×SD₁₆×C₁₉	—	2	1	no	—
40	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
42	C₁₉×#428	C₂²	1	1	yes	characteristic
43	C₁₉×#428	C₂²	1	1	yes	characteristic
44	C₁₉×#427	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
48	C₁₉×#419	C₂²	1	1	yes	characteristic
49	C₁₉×#418	C₂²	1	1	yes	characteristic
50	C₁₉×#417	C₂²	1	1	yes	characteristic
51	C₁₉×#417	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
56	C₁₉×#408	C₂²	1	1	yes	characteristic
57	C₁₉×#408	C₂²	1	1	yes	characteristic
58	C₁₉×#405	C₂²	1	1	yes	characteristic
59	C₁₉×#405	C₂²	1	1	yes	characteristic
60	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
61	C₁₉×#391	C₂²	1	1	yes	characteristic
62	C₁₉×#390	C₂²	1	1	yes	characteristic
63	C₁₉×#343	C₂²	1	1	yes	characteristic
64	C₁₉×#343	C₂²	1	1	yes	characteristic
65	C₁₉×#339	C₂²	1	1	yes	characteristic
66	C₁₉×#339	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₁₉×#137	—	2	2	no	—
72	C₁₉×#137	—	4	1	no	—
73	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
74	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
75	C₁₉×#135	—	2	2	no	—
76	C₁₉×#135	—	2	2	no	—
77	C₂×Q₁₆×C₁₉	—	2	1	no	—
78	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
79	C₂×SD₁₆×C₁₉	—	2	1	no	—
80	C₂×SD₁₆×C₁₉	—	2	1	no	—
81	C₂×SD₁₆×C₁₉	—	2	1	no	—
82	C₂×SD₁₆×C₁₉	—	2	1	no	—
83	C₂×SD₁₆×C₁₉	—	2	2	no	—
84	C₂×SD₁₆×C₁₉	—	2	2	no	—
85	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
86	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
87	C₂×D₈×C₁₉	—	2	1	no	—
88	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
89	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
95	C₁₉×C₄⋊Q₈	—	2	1	no	—
96	C₁₉×#127	—	2	1	no	—
97	C₁₉×#124	—	2	1	no	—
98	C₁₉×#124	—	2	1	no	—
99	C₁₉×#123	—	4	1	no	—
100	C₁₉×C₂²⋊Q₈	—	2	1	no	—
101	C₁₉×C₂²⋊Q₈	—	2	1	no	—
102	C₁₉×#121	—	2	1	no	—
103	C₁₉×#121	—	2	1	no	—
104	C₁₉×#120	—	4	1	no	—
105	C₄×Q₈×C₁₉	—	2	1	no	—
106	C₄×Q₈×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	—	2	1	no	—
108	C₄×D₄×C₁₉	—	2	1	no	—
109	C₄×D₄×C₁₉	—	4	1	no	—
110	C₄×D₄×C₁₉	—	4	1	no	—
111	C₁₉×#117	—	2	1	no	—
112	C₁₉×#117	—	2	1	no	—
113	C₁₉×#117	C₂³	1	1	yes	characteristic
114	C₁₉×#117	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
120	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
121	C₁₉×#108	—	2	2	no	—
122	C₁₉×#108	—	2	2	no	—
123	C₁₉×#107	—	2	1	no	—
124	C₁₉×#107	—	2	1	no	—
125	C₁₉×#107	D₄	1	1	yes	characteristic
126	C₁₉×#107	D₄	1	1	yes	characteristic
127	C₁₉×#106	—	2	1	no	—
128	C₁₉×#106	—	2	1	no	—
129	C₁₉×#106	—	2	1	no	—
130	C₁₉×#106	—	2	1	no	—
131	C₁₉×#106	D₄	1	1	yes	characteristic
132	C₁₉×#106	D₄	1	1	yes	characteristic
133	C₁₉×#104	—	4	1	no	—
134	C₁₉×#104	—	4	1	no	—
135	C₁₉×#103	—	2	1	no	—
136	C₁₉×#103	—	2	1	no	—
137	C₁₉×#103	—	2	1	no	—
138	C₁₉×#103	—	2	1	no	—
139	C₁₉×#103	—	2	1	no	—
140	C₁₉×#103	—	2	1	no	—
141	C₁₉×#102	—	2	1	no	—
142	C₁₉×#102	—	2	1	no	—
143	C₁₉×#102	—	2	1	no	—
144	C₁₉×#102	—	2	1	no	—
145	C₁₉×#102	—	2	1	no	—
146	C₁₉×#102	—	2	1	no	—
147	C₁₉×#101	—	4	1	no	—
148	C₁₉×#100	—	4	1	no	—
149	C₁₉×C₂²⋊C₈	—	2	1	no	—
150	C₁₉×C₂²⋊C₈	—	2	1	no	—
151	C₁₉×C₂²⋊C₈	—	2	1	no	—
152	C₁₉×C₂²⋊C₈	—	2	1	no	—
153	C₁₉×#97	—	2	1	no	—
154	C₁₉×#97	—	2	1	no	—
155	C₄×C₈×C₁₉	—	2	1	no	—
156	C₄×C₈×C₁₉	—	2	1	no	—
157	C₄×C₈×C₁₉	—	2	2	no	—
158	C₁₉×#95	—	4	1	no	—
159	C₂⁴×C₁₉	—	2	1	no	—
160	#41×C₁₉	—	2	1	no	—
161	#41×C₁₉	—	2	1	no	—
162	#41×C₁₉	—	2	1	no	—
163	#41×C₁₉	—	2	1	no	—
164	#41×C₁₉	—	2	1	no	—
165	#41×C₁₉	—	2	1	no	—
166	#41×C₁₉	—	2	1	no	—
167	#41×C₁₉	—	2	1	no	—
168	C₂×Q₈×C₁₉	—	2	1	no	—
169	C₂×Q₈×C₁₉	—	2	1	no	—
170	C₂×Q₈×C₁₉	—	2	1	no	—
171	C₂×Q₈×C₁₉	—	2	1	no	—
172	C₂×Q₈×C₁₉	—	2	1	no	—
173	C₂×Q₈×C₁₉	—	2	1	no	—
174	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂×D₄×C₁₉	—	2	1	no	—
177	C₂×D₄×C₁₉	—	2	1	no	—
178	C₂×D₄×C₁₉	—	2	1	no	—
179	C₂×D₄×C₁₉	—	2	1	no	—
180	C₂×D₄×C₁₉	—	2	1	no	—
181	C₂×D₄×C₁₉	—	2	1	no	—
182	C₂×D₄×C₁₉	—	2	1	no	—
183	C₂×D₄×C₁₉	—	2	1	no	—
184	C₂×D₄×C₁₉	—	4	1	no	—
185	C₂×D₄×C₁₉	—	4	1	no	—
186	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	—	2	1	no	—
189	C₂²×C₄×C₁₉	—	2	1	no	—
190	C₂²×C₄×C₁₉	—	2	1	no	—
191	C₂²×C₄×C₁₉	—	2	1	no	—
192	C₂²×C₄×C₁₉	—	2	1	no	—
193	C₂²×C₄×C₁₉	—	2	1	no	—
194	C₂²×C₄×C₁₉	—	4	1	no	—
195	C₂²×C₄×C₁₉	—	4	1	no	—
196	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
197	Q₁₆×C₁₉	—	2	2	no	—
198	Q₁₆×C₁₉	—	4	2	no	—
199	SD₁₆×C₁₉	—	2	2	no	—
200	SD₁₆×C₁₉	—	2	2	no	—
201	SD₁₆×C₁₉	—	4	2	no	—
202	SD₁₆×C₁₉	—	4	2	no	—
203	SD₁₆×C₁₉	—	4	2	no	—
204	SD₁₆×C₁₉	—	4	2	no	—
205	D₈×C₁₉	—	2	2	no	—
206	D₈×C₁₉	—	4	2	no	—
207	M₁₆×C₁₉	—	2	1	no	—
208	M₁₆×C₁₉	—	2	1	no	—
209	M₁₆×C₁₉	—	2	1	no	—
210	M₁₆×C₁₉	—	2	1	no	—
211	M₁₆×C₁₉	—	2	1	no	—
212	M₁₆×C₁₉	—	2	1	no	—
213	M₁₆×C₁₉	—	2	1	no	—
214	M₁₆×C₁₉	#41	1	2	yes	—
215	C₂×C₈×C₁₉	—	2	1	no	—
216	C₂×C₈×C₁₉	—	2	1	no	—
217	C₂×C₈×C₁₉	—	2	1	no	—
218	C₂×C₈×C₁₉	—	2	1	no	—
219	C₂×C₈×C₁₉	—	2	1	no	—
220	C₂×C₈×C₁₉	—	2	1	no	—
221	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
222	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
223	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₂×C₈×C₁₉	#41	1	2	yes	—
226	C₂×C₈×C₁₉	#41	1	2	yes	—
227	C₄⋊C₄×C₁₉	—	2	1	no	—
228	C₄⋊C₄×C₁₉	—	2	1	no	—
229	C₄⋊C₄×C₁₉	—	2	1	no	—
230	C₄⋊C₄×C₁₉	—	2	1	no	—
231	C₄⋊C₄×C₁₉	—	4	1	no	—
232	C₄⋊C₄×C₁₉	—	4	1	no	—
233	C₄⋊C₄×C₁₉	—	4	1	no	—
234	C₄⋊C₄×C₁₉	—	4	1	no	—
235	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
236	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
237	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
238	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
239	C₂²⋊C₄×C₁₉	—	2	1	no	—
240	C₂²⋊C₄×C₁₉	—	2	1	no	—
241	C₂²⋊C₄×C₁₉	—	4	1	no	—
242	C₂²⋊C₄×C₁₉	—	4	1	no	—
243	C₂²⋊C₄×C₁₉	—	4	1	no	—
244	C₂²⋊C₄×C₁₉	—	4	1	no	—
245	C₂²⋊C₄×C₁₉	—	4	1	no	—
246	C₂²⋊C₄×C₁₉	—	4	1	no	—
247	C₂²⋊C₄×C₁₉	—	8	2	no	—
248	C₄²×C₁₉	—	2	1	no	—
249	C₄²×C₁₉	—	2	1	no	—
250	C₄²×C₁₉	—	2	1	no	—
251	C₄²×C₁₉	—	2	1	no	—
252	C₄²×C₁₉	—	4	1	no	—
253	C₄²×C₁₉	—	4	1	no	—
254	#26270	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂³×C₁₉	—	2	1	no	—
256	C₂³×C₁₉	—	2	1	no	—
257	C₂³×C₁₉	—	4	1	no	—
258	C₂³×C₁₉	—	4	1	no	—
259	C₂³×C₁₉	—	4	1	no	—
260	C₂³×C₁₉	—	8	1	no	—
261	C₂³×C₁₉	—	8	1	no	—
262	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
263	Q₈×C₁₉	—	2	1	no	—
264	Q₈×C₁₉	—	2	1	no	—
265	Q₈×C₁₉	—	2	1	no	—
266	Q₈×C₁₉	—	2	1	no	—
267	Q₈×C₁₉	—	4	1	no	—
268	Q₈×C₁₉	—	4	1	no	—
269	Q₈×C₁₉	—	4	1	no	—
270	Q₈×C₁₉	—	4	1	no	—
271	D₄×C₁₉	—	2	1	no	—
272	D₄×C₁₉	—	2	1	no	—
273	D₄×C₁₉	—	2	1	no	—
274	D₄×C₁₉	—	2	1	no	—
275	D₄×C₁₉	—	4	1	no	—
276	D₄×C₁₉	—	4	1	no	—
277	D₄×C₁₉	—	4	1	no	—
278	D₄×C₁₉	—	4	1	no	—
279	D₄×C₁₉	—	4	1	no	—
280	D₄×C₁₉	—	4	1	no	—
281	D₄×C₁₉	—	4	1	no	—
282	D₄×C₁₉	—	4	1	no	—
283	D₄×C₁₉	—	16	1	no	—
284	D₄×C₁₉	—	16	1	no	—
285	C₂×C₄×C₁₉	—	2	2	no	—
286	C₂×C₄×C₁₉	—	2	1	no	—
287	C₂×C₄×C₁₉	—	2	1	no	—
288	C₂×C₄×C₁₉	—	2	1	no	—
289	C₂×C₄×C₁₉	—	2	1	no	—
290	C₂×C₄×C₁₉	—	2	1	no	—
291	C₂×C₄×C₁₉	—	2	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	4	1	no	—
294	C₂×C₄×C₁₉	—	4	1	no	—
295	C₂×C₄×C₁₉	—	4	1	no	—
296	C₂×C₄×C₁₉	—	4	1	no	—
297	C₂×C₄×C₁₉	—	4	1	no	—
298	C₂×C₄×C₁₉	—	4	1	no	—
299	C₂×C₄×C₁₉	—	4	1	no	—
300	C₂×C₄×C₁₉	—	4	1	no	—
301	C₂×C₄×C₁₉	—	4	1	no	—
302	C₂×C₄×C₁₉	—	4	1	no	—
303	C₂×C₄×C₁₉	—	8	1	no	—
304	C₂×C₄×C₁₉	—	8	1	no	—
305	C₂×C₄×C₁₉	—	16	1	no	—
306	C₂×C₄×C₁₉	—	16	1	no	—
307	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
310	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
311	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
312	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
313	C₈×C₁₉	—	2	1	no	—
314	C₈×C₁₉	—	2	1	no	—
315	C₈×C₁₉	—	2	2	no	—
316	C₈×C₁₉	—	4	1	no	—
317	C₈×C₁₉	—	4	1	no	—
318	C₈×C₁₉	—	4	1	no	—
319	C₈×C₁₉	#123	1	2	yes	—
320	C₈×C₁₉	#123	1	2	yes	—
321	#3154	C₂×C₁₉	1	1	yes	characteristic
322	#3097	C₂×C₁₉	1	1	yes	characteristic, complemented
323	#3096	C₂×C₁₉	1	1	yes	characteristic, complemented
324	#2952	C₂×C₁₉	1	1	yes	characteristic, complemented
325	#2052	C₂×C₁₉	1	1	yes	characteristic, complemented
326	#2051	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#2038	C₂×C₁₉	1	1	yes	characteristic, complemented
328	#2037	C₂×C₁₉	1	1	yes	characteristic, complemented
329	#1977	C₂×C₁₉	1	1	yes	characteristic, complemented
330	#1974	C₂×C₁₉	1	1	yes	characteristic, complemented
331	#1968	C₂×C₁₉	1	1	yes	characteristic, complemented
332	#1951	C₂×C₁₉	1	1	yes	characteristic, complemented
333	#1883	C₂×C₁₉	1	1	yes	characteristic, complemented
334	#1882	C₂×C₁₉	1	1	yes	characteristic, complemented
335	#1772	C₂×C₁₉	1	1	yes	characteristic, complemented
336	C₂²×C₁₉	—	2	1	no	—
337	C₂²×C₁₉	—	2	1	no	—
338	C₂²×C₁₉	—	4	1	no	—
339	C₂²×C₁₉	—	4	1	no	—
340	C₂²×C₁₉	—	4	1	no	—
341	C₂²×C₁₉	—	4	1	no	—
342	C₂²×C₁₉	—	4	1	no	—
343	C₂²×C₁₉	—	4	1	no	—
344	C₂²×C₁₉	—	8	2	no	—
345	C₂²×C₁₉	—	8	1	no	—
346	C₂²×C₁₉	—	8	1	no	—
347	C₂²×C₁₉	—	8	1	no	—
348	C₂²×C₁₉	—	16	1	no	—
349	C₂²×C₁₉	#540	1	1	yes	characteristic
350	C₂²×C₁₉	D₄²	1	1	yes	characteristic
351	C₂²×C₁₉	#559	1	1	yes	characteristic
352	C₄×C₁₉	—	4	2	no	—
353	C₄×C₁₉	—	4	1	no	—
354	C₄×C₁₉	—	4	1	no	—
355	C₄×C₁₉	—	4	1	no	—
356	C₄×C₁₉	—	4	1	no	—
357	C₄×C₁₉	—	4	1	no	—
358	C₄×C₁₉	—	4	1	no	—
359	C₄×C₁₉	—	8	1	no	—
360	C₄×C₁₉	—	8	1	no	—
361	C₄×C₁₉	—	8	1	no	—
362	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
363	C₄×C₁₉	#532	1	1	yes	characteristic
364	C₄×C₁₉	#546	1	1	yes	characteristic
365	C₄×C₁₉	#550	1	1	yes	characteristic
366	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
369	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
370	#536	C₂²×C₁₉	1	1	yes	characteristic
371	#535	C₂²×C₁₉	1	1	yes	characteristic
372	#520	C₂²×C₁₉	1	1	yes	characteristic
373	#520	C₂²×C₁₉	1	1	yes	characteristic
374	#497	—	2	1	no	—
375	#496	—	2	1	no	—
376	#495	—	2	1	no	—
377	#492	—	2	1	no	—
378	#485	—	2	1	no	—
379	#485	—	2	1	no	—
380	#484	—	2	1	no	—
381	#483	—	2	1	no	—
382	#482	—	2	1	no	—
383	#482	—	2	1	no	—
384	#481	—	2	1	no	—
385	#480	—	2	1	no	—
386	#442	—	2	1	no	—
387	#441	—	2	1	no	—
388	C₄×SD₁₆	—	2	1	no	—
389	C₄×SD₁₆	—	2	1	no	—
390	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
391	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
392	#428	C₂²×C₁₉	1	1	yes	characteristic
393	#428	C₂²×C₁₉	1	1	yes	characteristic
394	#427	C₂²×C₁₉	1	1	yes	characteristic
395	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
396	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
397	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
398	#419	C₂²×C₁₉	1	1	yes	characteristic
399	#418	C₂²×C₁₉	1	1	yes	characteristic
400	#417	C₂²×C₁₉	1	1	yes	characteristic
401	#417	C₂²×C₁₉	1	1	yes	characteristic
402	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
403	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
404	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
405	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
406	#408	C₂²×C₁₉	1	1	yes	characteristic
407	#408	C₂²×C₁₉	1	1	yes	characteristic
408	#405	C₂²×C₁₉	1	1	yes	characteristic
409	#405	C₂²×C₁₉	1	1	yes	characteristic
410	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
411	#391	C₂²×C₁₉	1	1	yes	characteristic
412	#390	C₂²×C₁₉	1	1	yes	characteristic
413	#343	C₂²×C₁₉	1	1	yes	characteristic
414	#343	C₂²×C₁₉	1	1	yes	characteristic
415	#339	C₂²×C₁₉	1	1	yes	characteristic
416	#339	C₂²×C₁₉	1	1	yes	characteristic
417	C₂×C₁₉	—	2	1	no	—
418	C₂×C₁₉	—	2	1	no	—
419	C₂×C₁₉	—	8	1	no	—
420	C₂×C₁₉	—	8	1	no	—
421	C₂×C₁₉	—	16	1	no	—
422	C₂×C₁₉	#2445	1	1	yes	characteristic
423	C₂×C₁₉	#3290	1	1	yes	characteristic
424	C₂×C₁₉	#3291	1	1	yes	characteristic
425	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
426	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
427	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
428	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
429	#137	—	2	2	no	—
430	#137	—	4	1	no	—
431	AGL(1,ℤ/8)	—	2	2	no	—
432	AGL(1,ℤ/8)	—	4	1	no	—
433	#135	—	2	2	no	—
434	#135	—	2	2	no	—
435	C₂×Q₁₆	—	2	1	no	—
436	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
437	C₂×SD₁₆	—	2	1	no	—
438	C₂×SD₁₆	—	2	1	no	—
439	C₂×SD₁₆	—	2	1	no	—
440	C₂×SD₁₆	—	2	1	no	—
441	C₂×SD₁₆	—	2	2	no	—
442	C₂×SD₁₆	—	2	2	no	—
443	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
444	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
445	C₂×D₈	—	2	1	no	—
446	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
447	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
448	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
449	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
450	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
453	C₄⋊Q₈	—	2	1	no	—
454	#127	—	2	1	no	—
455	#124	—	2	1	no	—
456	#124	—	2	1	no	—
457	#123	—	4	1	no	—
458	C₂²⋊Q₈	—	2	1	no	—
459	C₂²⋊Q₈	—	2	1	no	—
460	#121	—	2	1	no	—
461	#121	—	2	1	no	—
462	#120	—	4	1	no	—
463	C₄×Q₈	—	2	1	no	—
464	C₄×Q₈	—	2	1	no	—
465	C₄×D₄	—	2	1	no	—
466	C₄×D₄	—	2	1	no	—
467	C₄×D₄	—	4	1	no	—
468	C₄×D₄	—	4	1	no	—
469	#117	—	2	1	no	—
470	#117	—	2	1	no	—
471	#117	C₂³×C₁₉	1	1	yes	characteristic
472	#117	C₂³×C₁₉	1	1	yes	characteristic
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	—	4	1	no	—
478	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
479	#108	—	2	2	no	—
480	#108	—	2	2	no	—
481	#107	—	2	1	no	—
482	#107	—	2	1	no	—
483	#107	D₄×C₁₉	1	1	yes	characteristic
484	#107	D₄×C₁₉	1	1	yes	characteristic
485	#106	—	2	1	no	—
486	#106	—	2	1	no	—
487	#106	—	2	1	no	—
488	#106	—	2	1	no	—
489	#106	D₄×C₁₉	1	1	yes	characteristic
490	#106	D₄×C₁₉	1	1	yes	characteristic
491	#104	—	4	1	no	—
492	#104	—	4	1	no	—
493	#103	—	2	1	no	—
494	#103	—	2	1	no	—
495	#103	—	2	1	no	—
496	#103	—	2	1	no	—
497	#103	—	2	1	no	—
498	#103	—	2	1	no	—
499	#102	—	2	1	no	—
500	#102	—	2	1	no	—
501	#102	—	2	1	no	—
502	#102	—	2	1	no	—
503	#102	—	2	1	no	—
504	#102	—	2	1	no	—
505	#101	—	4	1	no	—
506	#100	—	4	1	no	—
507	C₂²⋊C₈	—	2	1	no	—
508	C₂²⋊C₈	—	2	1	no	—
509	C₂²⋊C₈	—	2	1	no	—
510	C₂²⋊C₈	—	2	1	no	—
511	#97	—	2	1	no	—
512	#97	—	2	1	no	—
513	C₄×C₈	—	2	1	no	—
514	C₄×C₈	—	2	1	no	—
515	C₄×C₈	—	2	2	no	—
516	#95	—	4	1	no	—
517	C₁₉	#26270	1	1	yes	characteristic, direct product factor, Sylow
518	C₂⁴	—	2	1	no	—
519	#41	—	2	1	no	—
520	#41	—	2	1	no	—
521	#41	—	2	1	no	—
522	#41	—	2	1	no	—
523	#41	—	2	1	no	—
524	#41	—	2	1	no	—
525	#41	—	2	1	no	—
526	#41	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
534	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	4	1	no	—
544	C₂×D₄	—	4	1	no	—
545	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
546	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	4	1	no	—
554	C₂²×C₄	—	4	1	no	—
555	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
556	Q₁₆	—	2	2	no	—
557	Q₁₆	—	4	2	no	—
558	SD₁₆	—	2	2	no	—
559	SD₁₆	—	2	2	no	—
560	SD₁₆	—	4	2	no	—
561	SD₁₆	—	4	2	no	—
562	SD₁₆	—	4	2	no	—
563	SD₁₆	—	4	2	no	—
564	D₈	—	2	2	no	—
565	D₈	—	4	2	no	—
566	M₁₆	—	2	1	no	—
567	M₁₆	—	2	1	no	—
568	M₁₆	—	2	1	no	—
569	M₁₆	—	2	1	no	—
570	M₁₆	—	2	1	no	—
571	M₁₆	—	2	1	no	—
572	M₁₆	—	2	1	no	—
573	M₁₆	#41×C₁₉	1	2	yes	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
581	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
582	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
583	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
584	C₂×C₈	#41×C₁₉	1	2	yes	—
585	C₂×C₈	#41×C₁₉	1	2	yes	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	4	1	no	—
591	C₄⋊C₄	—	4	1	no	—
592	C₄⋊C₄	—	4	1	no	—
593	C₄⋊C₄	—	4	1	no	—
594	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
595	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
596	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
597	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
598	C₂²⋊C₄	—	2	1	no	—
599	C₂²⋊C₄	—	2	1	no	—
600	C₂²⋊C₄	—	4	1	no	—
601	C₂²⋊C₄	—	4	1	no	—
602	C₂²⋊C₄	—	4	1	no	—
603	C₂²⋊C₄	—	4	1	no	—
604	C₂²⋊C₄	—	4	1	no	—
605	C₂²⋊C₄	—	4	1	no	—
606	C₂²⋊C₄	—	8	2	no	—
607	C₄²	—	2	1	no	—
608	C₄²	—	2	1	no	—
609	C₄²	—	2	1	no	—
610	C₄²	—	2	1	no	—
611	C₄²	—	4	1	no	—
612	C₄²	—	4	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	8	1	no	—
619	C₂³	—	8	1	no	—
620	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
621	Q₈	—	2	1	no	—
622	Q₈	—	2	1	no	—
623	Q₈	—	2	1	no	—
624	Q₈	—	2	1	no	—
625	Q₈	—	4	1	no	—
626	Q₈	—	4	1	no	—
627	Q₈	—	4	1	no	—
628	Q₈	—	4	1	no	—
629	D₄	—	2	1	no	—
630	D₄	—	2	1	no	—
631	D₄	—	2	1	no	—
632	D₄	—	2	1	no	—
633	D₄	—	4	1	no	—
634	D₄	—	4	1	no	—
635	D₄	—	4	1	no	—
636	D₄	—	4	1	no	—
637	D₄	—	4	1	no	—
638	D₄	—	4	1	no	—
639	D₄	—	4	1	no	—
640	D₄	—	4	1	no	—
641	D₄	—	16	1	no	—
642	D₄	—	16	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	8	1	no	—
662	C₂×C₄	—	8	1	no	—
663	C₂×C₄	—	16	1	no	—
664	C₂×C₄	—	16	1	no	—
665	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
666	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
667	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
668	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
669	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
670	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
671	C₈	—	2	1	no	—
672	C₈	—	2	1	no	—
673	C₈	—	2	2	no	—
674	C₈	—	4	1	no	—
675	C₈	—	4	1	no	—
676	C₈	—	4	1	no	—
677	C₈	C₁₉×#123	1	2	yes	—
678	C₈	C₁₉×#123	1	2	yes	—
679	C₂²	—	2	1	no	—
680	C₂²	—	2	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	8	2	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	—	16	1	no	—
692	C₂²	C₁₉×#540	1	1	yes	characteristic
693	C₂²	D₄²×C₁₉	1	1	yes	characteristic
694	C₂²	C₁₉×#559	1	1	yes	characteristic
695	C₄	—	4	2	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	8	1	no	—
703	C₄	—	8	1	no	—
704	C₄	—	8	1	no	—
705	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
706	C₄	C₁₉×#532	1	1	yes	characteristic
707	C₄	C₁₉×#546	1	1	yes	characteristic
708	C₄	C₁₉×#550	1	1	yes	characteristic
709	C₂	—	2	1	no	—
710	C₂	—	2	1	no	—
711	C₂	—	8	1	no	—
712	C₂	—	8	1	no	—
713	C₂	—	16	1	no	—
714	C₂	C₁₉×#2445	1	1	yes	characteristic
715	C₂	C₁₉×#3290	1	1	yes	characteristic
716	C₂	C₁₉×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3154	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3097	C₂	semidirect
3. C₁₉×#3096	C₂	semidirect
4. C₁₉×#2952	C₂	semidirect
5. C₁₉×#2052	C₂	semidirect
6. C₁₉×#2051	C₂	semidirect
7. C₁₉×#2038	C₂	semidirect
8. C₁₉×#2037	C₂	semidirect
9. C₁₉×#1977	C₂	semidirect
10. C₁₉×#1974	C₂	semidirect
11. C₁₉×#1968	C₂	semidirect
12. C₁₉×#1951	C₂	semidirect
13. C₁₉×#1883	C₂	semidirect
14. C₁₉×#1882	C₂	semidirect
15. C₁₉×#1772	C₂	semidirect
254. #26270	C₁₉	direct (N × H)
322. #3097	C₂×C₁₉	semidirect
323. #3096	C₂×C₁₉	semidirect
324. #2952	C₂×C₁₉	semidirect
325. #2052	C₂×C₁₉	semidirect
326. #2051	C₂×C₁₉	semidirect
327. #2038	C₂×C₁₉	semidirect
328. #2037	C₂×C₁₉	semidirect
329. #1977	C₂×C₁₉	semidirect
330. #1974	C₂×C₁₉	semidirect
331. #1968	C₂×C₁₉	semidirect
332. #1951	C₂×C₁₉	semidirect
333. #1883	C₂×C₁₉	semidirect
334. #1882	C₂×C₁₉	semidirect
335. #1772	C₂×C₁₉	semidirect
517. C₁₉	#26270	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×#3154	2
C₁₉×#3097	2
C₁₉×#3096	2
C₁₉×#2952	2
C₁₉×#2052	2
C₁₉×#2051	2
C₁₉×#2038	2
C₁₉×#2037	2
C₁₉×#1977	2
C₁₉×#1974	2
C₁₉×#1968	2
C₁₉×#1951	2
C₁₉×#1883	2
C₁₉×#1882	2
C₁₉×#1772	2
#26270	19

Subgroups — C19×#26270 #18032229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26270 #18032229