Subgroups — C₁₉×#19901 #18025860

Order 4864.

648 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3360	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3331	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3324	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3294	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1708	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1703	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1701	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1683	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1682	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1654	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1652	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1629	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1622	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1589	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#556	C₂²	1	1	yes	characteristic
17	C₁₉×#554	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#547	C₂²	1	1	yes	characteristic
19	D₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#498	C₂²	1	1	yes	characteristic, complemented
21	C₁₉×#492	C₂²	1	1	yes	characteristic
22	C₁₉×#488	—	2	1	no	—
23	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#487	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#486	C₂²	1	1	yes	characteristic
26	C₁₉×#486	C₂²	1	1	yes	characteristic
27	C₁₉×#483	—	2	1	no	—
28	C₁₉×#482	—	2	1	no	—
29	C₁₉×#480	—	2	1	no	—
30	C₁₉×#479	—	2	1	no	—
31	C₁₉×#476	C₂²	1	1	yes	characteristic
32	C₁₉×#476	C₂²	1	1	yes	characteristic
33	C₁₉×#474	C₂²	1	1	yes	characteristic
34	C₁₉×#474	C₂²	1	1	yes	characteristic
35	C₁₉×#470	—	2	1	no	—
36	C₁₉×#468	—	2	1	no	—
37	C₁₉×#466	—	2	1	no	—
38	C₁₉×#463	—	2	1	no	—
39	C₁₉×#462	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#461	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#460	C₂²	1	1	yes	characteristic
42	C₁₉×#459	C₂²	1	1	yes	characteristic
43	C₁₉×#452	—	2	1	no	—
44	C₁₉×#450	—	2	1	no	—
45	C₁₉×#447	—	2	1	no	—
46	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
47	C₄×SD₁₆×C₁₉	—	2	1	no	—
48	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
49	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
50	C₁₉×#436	C₂²	1	1	yes	characteristic
51	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
52	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
53	C₁₉×#418	—	2	1	no	—
54	C₁₉×#417	—	2	1	no	—
55	C₂×C₁₉×#102	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#334	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#333	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#331	C₂²	1	1	yes	characteristic
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₈²×C₁₉	C₂²	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂²×D₄×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	—	2	1	no	—
70	C₂×Q₁₆×C₁₉	—	2	1	no	—
71	C₂×SD₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	4	1	no	—
74	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
75	C₂×D₈×C₁₉	—	2	1	no	—
76	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
77	C₂×M₁₆×C₁₉	—	2	1	no	—
78	C₂×M₁₆×C₁₉	—	2	1	no	—
79	C₂²×C₈×C₁₉	—	2	1	no	—
80	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₉×#127	C₂³	1	1	yes	characteristic
84	C₁₉×#126	—	4	1	no	—
85	C₁₉×#125	—	2	1	no	—
86	C₁₉×#124	—	2	1	no	—
87	C₁₉×#123	—	4	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	—	4	1	no	—
92	C₁₉×#121	—	2	1	no	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#120	—	4	1	no	—
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×#117	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₁₉×#107	—	2	1	no	—
106	C₁₉×#107	—	2	1	no	—
107	C₁₉×#107	D₄	1	1	yes	characteristic
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×#106	—	2	1	no	—
110	C₁₉×#106	—	4	1	no	—
111	C₁₉×#106	D₄	1	1	yes	characteristic
112	C₁₉×C₄⋊C₈	—	2	1	no	—
113	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₉×#103	—	2	1	no	—
118	C₁₉×#103	—	2	1	no	—
119	C₁₉×#103	—	2	1	no	—
120	C₁₉×#103	—	2	1	no	—
121	C₁₉×#103	—	2	1	no	—
122	C₁₉×#103	—	2	1	no	—
123	C₁₉×#103	D₄	1	1	yes	characteristic
124	C₁₉×#102	—	2	1	no	—
125	C₁₉×#102	—	2	1	no	—
126	C₁₉×#102	—	2	1	no	—
127	C₁₉×#102	—	2	1	no	—
128	C₁₉×#102	—	2	1	no	—
129	C₁₉×#102	—	2	1	no	—
130	C₁₉×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
134	C₁₉×#102	D₄	1	1	yes	characteristic
135	C₁₉×#102	D₄	1	1	yes	characteristic
136	C₁₉×#102	D₄	1	1	yes	characteristic
137	C₁₉×C₂²⋊C₈	—	2	1	no	—
138	C₁₉×C₂²⋊C₈	—	2	1	no	—
139	C₁₉×C₂²⋊C₈	—	2	1	no	—
140	C₄×C₈×C₁₉	—	2	1	no	—
141	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	C₂⁴×C₁₉	—	4	1	no	—
145	#41×C₁₉	—	4	2	no	—
146	#41×C₁₉	—	8	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	4	1	no	—
155	C₂×D₄×C₁₉	—	4	1	no	—
156	C₂×D₄×C₁₉	—	4	2	no	—
157	C₂×D₄×C₁₉	—	4	2	no	—
158	C₂×D₄×C₁₉	—	4	1	no	—
159	C₂×D₄×C₁₉	—	8	1	no	—
160	C₂×D₄×C₁₉	—	8	1	no	—
161	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	4	1	no	—
168	C₂²×C₄×C₁₉	—	4	1	no	—
169	Q₁₆×C₁₉	—	8	1	no	—
170	SD₁₆×C₁₉	—	2	2	no	—
171	SD₁₆×C₁₉	—	4	2	no	—
172	SD₁₆×C₁₉	—	8	2	no	—
173	SD₁₆×C₁₉	—	8	1	no	—
174	D₈×C₁₉	—	4	1	no	—
175	D₈×C₁₉	—	8	1	no	—
176	M₁₆×C₁₉	—	8	1	no	—
177	M₁₆×C₁₉	—	8	1	no	—
178	C₂×C₈×C₁₉	—	2	1	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	8	1	no	—
184	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	1	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	—	4	1	no	—
196	C₄⋊C₄×C₁₉	—	4	1	no	—
197	C₄⋊C₄×C₁₉	—	4	1	no	—
198	C₄⋊C₄×C₁₉	—	4	1	no	—
199	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₂²⋊C₄×C₁₉	—	2	1	no	—
204	C₂²⋊C₄×C₁₉	—	2	1	no	—
205	C₂²⋊C₄×C₁₉	—	2	1	no	—
206	C₂²⋊C₄×C₁₉	—	4	1	no	—
207	C₂²⋊C₄×C₁₉	—	4	1	no	—
208	C₂²⋊C₄×C₁₉	—	4	1	no	—
209	C₂²⋊C₄×C₁₉	—	4	1	no	—
210	C₂²⋊C₄×C₁₉	—	4	1	no	—
211	C₄²×C₁₉	—	2	1	no	—
212	C₄²×C₁₉	—	4	1	no	—
213	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
214	#19901	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂³×C₁₉	—	2	1	no	—
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	—	2	1	no	—
218	C₂³×C₁₉	—	4	1	no	—
219	C₂³×C₁₉	—	8	2	no	—
220	C₂³×C₁₉	—	8	2	no	—
221	C₂³×C₁₉	—	16	1	no	—
222	Q₈×C₁₉	—	2	1	no	—
223	Q₈×C₁₉	—	2	1	no	—
224	Q₈×C₁₉	—	4	1	no	—
225	Q₈×C₁₉	—	4	1	no	—
226	Q₈×C₁₉	—	4	1	no	—
227	Q₈×C₁₉	—	4	1	no	—
228	Q₈×C₁₉	—	8	1	no	—
229	D₄×C₁₉	—	2	1	no	—
230	D₄×C₁₉	—	2	1	no	—
231	D₄×C₁₉	—	2	1	no	—
232	D₄×C₁₉	—	2	1	no	—
233	D₄×C₁₉	—	2	1	no	—
234	D₄×C₁₉	—	4	1	no	—
235	D₄×C₁₉	—	4	1	no	—
236	D₄×C₁₉	—	4	1	no	—
237	D₄×C₁₉	—	4	1	no	—
238	D₄×C₁₉	—	8	1	no	—
239	D₄×C₁₉	—	8	2	no	—
240	D₄×C₁₉	—	8	2	no	—
241	D₄×C₁₉	—	8	2	no	—
242	D₄×C₁₉	#135	1	2	yes	—
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	—	2	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	—	8	2	no	—
258	C₂×C₄×C₁₉	—	16	1	no	—
259	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
262	C₈×C₁₉	—	2	2	no	—
263	C₈×C₁₉	—	2	1	no	—
264	C₈×C₁₉	—	2	1	no	—
265	C₈×C₁₉	—	2	1	no	—
266	C₈×C₁₉	—	2	1	no	—
267	C₈×C₁₉	—	4	1	no	—
268	C₈×C₁₉	—	4	1	no	—
269	C₈×C₁₉	—	4	1	no	—
270	C₈×C₁₉	—	4	1	no	—
271	#3360	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#3331	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#3324	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#3294	C₂×C₁₉	1	1	yes	characteristic
275	#1708	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#1703	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1701	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1683	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1682	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1654	C₂×C₁₉	1	1	yes	characteristic, complemented
281	#1652	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1629	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1622	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1589	C₂×C₁₉	1	1	yes	characteristic, complemented
285	C₈×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
286	C₂²×C₁₉	—	2	2	no	—
287	C₂²×C₁₉	—	4	1	no	—
288	C₂²×C₁₉	—	4	1	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	—	4	1	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	—	4	1	no	—
295	C₂²×C₁₉	—	8	1	no	—
296	C₂²×C₁₉	—	8	1	no	—
297	C₂²×C₁₉	—	8	1	no	—
298	C₂²×C₁₉	—	16	4	no	—
299	C₂²×C₁₉	D₄²	1	1	yes	characteristic
300	C₄×C₁₉	—	2	1	no	—
301	C₄×C₁₉	—	4	1	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	8	1	no	—
307	C₄×C₁₉	—	8	1	no	—
308	C₄×C₁₉	—	8	1	no	—
309	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
310	C₄×C₁₉	#575	1	1	yes	characteristic
311	C₄×C₁₉	#576	1	1	yes	characteristic
312	C₄×C₁₉	#577	1	1	yes	characteristic
313	#556	C₂²×C₁₉	1	1	yes	characteristic
314	#554	C₂²×C₁₉	1	1	yes	characteristic, complemented
315	#547	C₂²×C₁₉	1	1	yes	characteristic
316	D₄²	C₂²×C₁₉	1	1	yes	characteristic
317	#498	C₂²×C₁₉	1	1	yes	characteristic, complemented
318	#492	C₂²×C₁₉	1	1	yes	characteristic
319	#488	—	2	1	no	—
320	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
321	#487	C₂²×C₁₉	1	1	yes	characteristic, complemented
322	#486	C₂²×C₁₉	1	1	yes	characteristic
323	#486	C₂²×C₁₉	1	1	yes	characteristic
324	#483	—	2	1	no	—
325	#482	—	2	1	no	—
326	#480	—	2	1	no	—
327	#479	—	2	1	no	—
328	#476	C₂²×C₁₉	1	1	yes	characteristic
329	#476	C₂²×C₁₉	1	1	yes	characteristic
330	#474	C₂²×C₁₉	1	1	yes	characteristic
331	#474	C₂²×C₁₉	1	1	yes	characteristic
332	#470	—	2	1	no	—
333	#468	—	2	1	no	—
334	#466	—	2	1	no	—
335	#463	—	2	1	no	—
336	#462	C₂²×C₁₉	1	1	yes	characteristic, complemented
337	#461	C₂²×C₁₉	1	1	yes	characteristic, complemented
338	#460	C₂²×C₁₉	1	1	yes	characteristic
339	#459	C₂²×C₁₉	1	1	yes	characteristic
340	#452	—	2	1	no	—
341	#450	—	2	1	no	—
342	#447	—	2	1	no	—
343	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
344	C₄×SD₁₆	—	2	1	no	—
345	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
346	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
347	#436	C₂²×C₁₉	1	1	yes	characteristic
348	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
349	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
350	#418	—	2	1	no	—
351	#417	—	2	1	no	—
352	C₂×#102	—	2	1	no	—
353	#335	C₂²×C₁₉	1	1	yes	characteristic, complemented
354	#334	C₂²×C₁₉	1	1	yes	characteristic, complemented
355	#333	C₂²×C₁₉	1	1	yes	characteristic, complemented
356	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
357	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
358	#331	C₂²×C₁₉	1	1	yes	characteristic
359	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
360	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
361	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
362	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
363	C₈²	C₂²×C₁₉	1	1	yes	characteristic, complemented
364	C₂×C₁₉	—	4	2	no	—
365	C₂×C₁₉	—	8	1	no	—
366	C₂×C₁₉	—	8	1	no	—
367	C₂×C₁₉	—	16	1	no	—
368	C₂×C₁₉	#3275	1	1	yes	characteristic
369	C₂×C₁₉	#3280	1	1	yes	characteristic
370	C₂×C₁₉	#3291	1	1	yes	characteristic
371	C₂×#41	—	2	1	no	—
372	C₂²×D₄	—	2	1	no	—
373	C₂²×D₄	—	2	1	no	—
374	C₂×Q₁₆	—	2	1	no	—
375	C₂×SD₁₆	—	2	1	no	—
376	C₂×SD₁₆	—	2	1	no	—
377	C₂×SD₁₆	—	4	1	no	—
378	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
379	C₂×D₈	—	2	1	no	—
380	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂²×C₈	—	2	1	no	—
384	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
385	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
386	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
387	#127	C₂³×C₁₉	1	1	yes	characteristic
388	#126	—	4	1	no	—
389	#125	—	2	1	no	—
390	#124	—	2	1	no	—
391	#123	—	4	1	no	—
392	C₂²⋊Q₈	—	2	1	no	—
393	C₂²⋊Q₈	—	2	1	no	—
394	C₂²⋊Q₈	—	2	1	no	—
395	C₂²⋊Q₈	—	4	1	no	—
396	#121	—	2	1	no	—
397	#121	—	2	1	no	—
398	#121	—	2	1	no	—
399	#120	—	4	1	no	—
400	C₄×Q₈	—	2	1	no	—
401	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
404	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
405	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
406	#117	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	#107	—	2	1	no	—
410	#107	—	2	1	no	—
411	#107	D₄×C₁₉	1	1	yes	characteristic
412	#106	—	2	1	no	—
413	#106	—	2	1	no	—
414	#106	—	4	1	no	—
415	#106	D₄×C₁₉	1	1	yes	characteristic
416	C₄⋊C₈	—	2	1	no	—
417	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
419	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
420	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
421	#103	—	2	1	no	—
422	#103	—	2	1	no	—
423	#103	—	2	1	no	—
424	#103	—	2	1	no	—
425	#103	—	2	1	no	—
426	#103	—	2	1	no	—
427	#103	D₄×C₁₉	1	1	yes	characteristic
428	#102	—	2	1	no	—
429	#102	—	2	1	no	—
430	#102	—	2	1	no	—
431	#102	—	2	1	no	—
432	#102	—	2	1	no	—
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	—	2	1	no	—
437	#102	—	2	1	no	—
438	#102	D₄×C₁₉	1	1	yes	characteristic
439	#102	D₄×C₁₉	1	1	yes	characteristic
440	#102	D₄×C₁₉	1	1	yes	characteristic
441	C₂²⋊C₈	—	2	1	no	—
442	C₂²⋊C₈	—	2	1	no	—
443	C₂²⋊C₈	—	2	1	no	—
444	C₄×C₈	—	2	1	no	—
445	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
446	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
447	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
448	C₁₉	#19901	1	1	yes	characteristic, direct product factor, Sylow
449	C₂⁴	—	4	1	no	—
450	#41	—	4	2	no	—
451	#41	—	8	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂×D₄	—	4	1	no	—
461	C₂×D₄	—	4	2	no	—
462	C₂×D₄	—	4	2	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	—	8	1	no	—
465	C₂×D₄	—	8	1	no	—
466	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	Q₁₆	—	8	1	no	—
475	SD₁₆	—	2	2	no	—
476	SD₁₆	—	4	2	no	—
477	SD₁₆	—	8	2	no	—
478	SD₁₆	—	8	1	no	—
479	D₈	—	4	1	no	—
480	D₈	—	8	1	no	—
481	M₁₆	—	8	1	no	—
482	M₁₆	—	8	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	8	1	no	—
489	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
492	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	—	4	1	no	—
502	C₄⋊C₄	—	4	1	no	—
503	C₄⋊C₄	—	4	1	no	—
504	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
506	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
507	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₂²⋊C₄	—	4	1	no	—
513	C₂²⋊C₄	—	4	1	no	—
514	C₂²⋊C₄	—	4	1	no	—
515	C₂²⋊C₄	—	4	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	4	1	no	—
518	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	8	2	no	—
524	C₂³	—	8	2	no	—
525	C₂³	—	16	1	no	—
526	Q₈	—	2	1	no	—
527	Q₈	—	2	1	no	—
528	Q₈	—	4	1	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	4	1	no	—
531	Q₈	—	4	1	no	—
532	Q₈	—	8	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	2	1	no	—
535	D₄	—	2	1	no	—
536	D₄	—	2	1	no	—
537	D₄	—	2	1	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	1	no	—
542	D₄	—	8	1	no	—
543	D₄	—	8	2	no	—
544	D₄	—	8	2	no	—
545	D₄	—	8	2	no	—
546	D₄	C₁₉×#135	1	2	yes	—
547	C₂×C₄	—	2	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	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	8	2	no	—
562	C₂×C₄	—	16	1	no	—
563	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
564	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
565	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
566	C₈	—	2	2	no	—
567	C₈	—	2	1	no	—
568	C₈	—	2	1	no	—
569	C₈	—	2	1	no	—
570	C₈	—	2	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	8	1	no	—
585	C₂²	—	8	1	no	—
586	C₂²	—	8	1	no	—
587	C₂²	—	16	4	no	—
588	C₂²	D₄²×C₁₉	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	8	1	no	—
596	C₄	—	8	1	no	—
597	C₄	—	8	1	no	—
598	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
599	C₄	C₁₉×#575	1	1	yes	characteristic
600	C₄	C₁₉×#576	1	1	yes	characteristic
601	C₄	C₁₉×#577	1	1	yes	characteristic
602	C₂	—	4	2	no	—
603	C₂	—	8	1	no	—
604	C₂	—	8	1	no	—
605	C₂	—	16	1	no	—
606	C₂	C₁₉×#3275	1	1	yes	characteristic
607	C₂	C₁₉×#3280	1	1	yes	characteristic
608	C₂	C₁₉×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3294	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3360	C₂	semidirect
2. C₁₉×#3331	C₂	semidirect
3. C₁₉×#3324	C₂	semidirect
5. C₁₉×#1708	C₂	semidirect
6. C₁₉×#1703	C₂	semidirect
7. C₁₉×#1701	C₂	semidirect
8. C₁₉×#1683	C₂	semidirect
9. C₁₉×#1682	C₂	semidirect
10. C₁₉×#1654	C₂	semidirect
11. C₁₉×#1652	C₂	semidirect
12. C₁₉×#1629	C₂	semidirect
13. C₁₉×#1622	C₂	semidirect
14. C₁₉×#1589	C₂	semidirect
15. C₈×SD₁₆×C₁₉	C₂	semidirect
17. C₁₉×#554	C₂²	semidirect
20. C₁₉×#498	C₂²	semidirect
23. C₁₉×#487	C₂²	semidirect
24. C₁₉×#487	C₂²	semidirect
39. C₁₉×#462	C₂²	semidirect
40. C₁₉×#461	C₂²	semidirect
46. C₈×Q₈×C₁₉	C₂²	semidirect
51. C₁₉×#436	C₂²	semidirect
56. C₁₉×#335	C₂²	semidirect
57. C₁₉×#334	C₂²	semidirect
58. C₁₉×#333	C₂²	semidirect
59. C₁₉×#332	C₂²	semidirect
60. C₁₉×#332	C₂²	semidirect
62. C₁₉×Q₈⋊C₈	C₂²	semidirect
65. C₁₉×D₄⋊C₈	C₂²	semidirect
66. C₈²×C₁₉	C₂²	semidirect
214. #19901	C₁₉	direct (N × H)
271. #3360	C₂×C₁₉	semidirect
272. #3331	C₂×C₁₉	semidirect
273. #3324	C₂×C₁₉	semidirect
275. #1708	C₂×C₁₉	semidirect
276. #1703	C₂×C₁₉	semidirect
277. #1701	C₂×C₁₉	semidirect
278. #1683	C₂×C₁₉	semidirect
279. #1682	C₂×C₁₉	semidirect
280. #1654	C₂×C₁₉	semidirect
281. #1652	C₂×C₁₉	semidirect
282. #1629	C₂×C₁₉	semidirect
283. #1622	C₂×C₁₉	semidirect
284. #1589	C₂×C₁₉	semidirect
285. C₈×SD₁₆	C₂×C₁₉	semidirect
314. #554	C₂²×C₁₉	semidirect
317. #498	C₂²×C₁₉	semidirect
320. #487	C₂²×C₁₉	semidirect
321. #487	C₂²×C₁₉	semidirect
336. #462	C₂²×C₁₉	semidirect
337. #461	C₂²×C₁₉	semidirect
343. C₈×Q₈	C₂²×C₁₉	semidirect
348. #436	C₂²×C₁₉	semidirect
353. #335	C₂²×C₁₉	semidirect
354. #334	C₂²×C₁₉	semidirect
355. #333	C₂²×C₁₉	semidirect
356. #332	C₂²×C₁₉	semidirect
357. #332	C₂²×C₁₉	semidirect
359. Q₈⋊C₈	C₂²×C₁₉	semidirect
362. D₄⋊C₈	C₂²×C₁₉	semidirect
363. C₈²	C₂²×C₁₉	semidirect
448. C₁₉	#19901	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×#3360	2
C₁₉×#3331	2
C₁₉×#3324	2
C₁₉×#3294	2
C₁₉×#1708	2
C₁₉×#1703	2
C₁₉×#1701	2
C₁₉×#1683	2
C₁₉×#1682	2
C₁₉×#1654	2
C₁₉×#1652	2
C₁₉×#1629	2
C₁₉×#1622	2
C₁₉×#1589	2
C₈×SD₁₆×C₁₉	2
#19901	19

Subgroups — C19×#19901 #18025860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19901 #18025860