Subgroups — C₁₉×#19849 #18025808

Order 4864.

566 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3395	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3374	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3365	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3365	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1720	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1702	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1682	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1680	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1670	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1640	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1626	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1579	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#559	C₂²	1	1	yes	characteristic
17	C₁₉×#557	C₂²	1	1	yes	characteristic
18	C₁₉×#557	C₂²	1	1	yes	characteristic
19	C₁₉×#557	C₂²	1	1	yes	characteristic
20	C₁₉×#498	C₂²	1	1	yes	characteristic
21	C₁₉×#494	—	2	1	no	—
22	C₁₉×#494	C₂²	1	1	yes	characteristic
23	C₁₉×#491	—	2	1	no	—
24	C₁₉×#488	—	2	1	no	—
25	C₁₉×#488	—	2	1	no	—
26	C₁₉×#487	C₂²	1	1	yes	characteristic
27	C₁₉×#486	C₂²	1	1	yes	characteristic
28	C₁₉×#486	C₂²	1	1	yes	characteristic
29	C₁₉×#486	C₂²	1	1	yes	characteristic
30	C₁₉×#479	—	2	1	no	—
31	C₁₉×#478	—	2	1	no	—
32	C₁₉×#478	—	2	1	no	—
33	C₁₉×#475	C₂²	1	1	yes	characteristic
34	C₁₉×#475	C₂²	1	1	yes	characteristic
35	C₁₉×#475	C₂²	1	1	yes	characteristic
36	C₁₉×#464	—	2	1	no	—
37	C₁₉×#464	—	2	1	no	—
38	C₁₉×#462	—	2	1	no	—
39	C₁₉×#462	—	2	1	no	—
40	C₁₉×#462	—	2	1	no	—
41	C₁₉×#462	C₂²	1	1	yes	characteristic
42	C₁₉×#462	C₂²	1	1	yes	characteristic
43	C₁₉×#462	C₂²	1	1	yes	characteristic
44	C₁₉×#460	C₂²	1	1	yes	characteristic
45	C₁₉×#460	C₂²	1	1	yes	characteristic
46	C₁₉×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
50	C₁₉×#441	—	2	1	no	—
51	C₄×Q₁₆×C₁₉	—	2	1	no	—
52	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
53	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
54	C₄×SD₁₆×C₁₉	—	2	1	no	—
55	C₄×SD₁₆×C₁₉	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#332	C₂²	1	1	yes	characteristic
59	C₁₉×#332	C₂²	1	1	yes	characteristic
60	C₁₉×#332	C₂²	1	1	yes	characteristic
61	C₁₉×#331	C₂²	1	1	yes	characteristic
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₉×#322	C₂²	1	1	yes	characteristic
67	C₂×Q₁₆×C₁₉	—	2	1	no	—
68	C₂×Q₁₆×C₁₉	—	2	1	no	—
69	C₂×Q₁₆×C₁₉	—	2	1	no	—
70	C₂×Q₁₆×C₁₉	—	2	1	no	—
71	C₂×Q₁₆×C₁₉	—	2	1	no	—
72	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
73	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
74	C₂×SD₁₆×C₁₉	—	2	1	no	—
75	C₂×SD₁₆×C₁₉	—	2	1	no	—
76	C₁₉×C₄⋊Q₈	—	2	1	no	—
77	C₁₉×C₄⋊Q₈	—	2	1	no	—
78	C₁₉×C₄⋊Q₈	—	2	1	no	—
79	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₉×#127	C₂³	1	1	yes	characteristic
83	C₁₉×#125	—	2	1	no	—
84	C₁₉×#125	—	2	1	no	—
85	C₁₉×#125	—	2	1	no	—
86	C₁₉×#125	—	4	1	no	—
87	C₁₉×#125	—	4	1	no	—
88	C₁₉×#125	—	4	1	no	—
89	C₁₉×#124	—	2	1	no	—
90	C₁₉×#124	—	2	1	no	—
91	C₁₉×#123	—	4	1	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	—	2	1	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	—	2	1	no	—
98	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
99	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
100	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
101	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	—	2	1	no	—
104	C₁₉×#107	D₄	1	1	yes	characteristic
105	C₁₉×#107	D₄	1	1	yes	characteristic
106	C₁₉×#106	—	2	1	no	—
107	C₁₉×#106	—	2	1	no	—
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×#106	—	4	1	no	—
110	C₁₉×C₄⋊C₈	—	2	1	no	—
111	C₁₉×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	—	2	1	no	—
113	C₁₉×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
124	C₁₉×#103	—	2	1	no	—
125	C₁₉×#103	—	2	1	no	—
126	C₁₉×#103	D₄	1	1	yes	characteristic
127	C₁₉×#103	D₄	1	1	yes	characteristic
128	C₁₉×#103	D₄	1	1	yes	characteristic
129	C₁₉×#103	D₄	1	1	yes	characteristic
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	—	2	1	no	—
135	C₁₉×#102	—	2	1	no	—
136	C₁₉×#102	—	4	1	no	—
137	C₁₉×#97	—	2	1	no	—
138	C₄×C₈×C₁₉	—	2	1	no	—
139	C₄×C₈×C₁₉	—	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	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄×C₁₉	—	4	1	no	—
155	Q₁₆×C₁₉	—	2	2	no	—
156	Q₁₆×C₁₉	—	4	1	no	—
157	Q₁₆×C₁₉	—	4	2	no	—
158	Q₁₆×C₁₉	—	4	2	no	—
159	Q₁₆×C₁₉	—	8	1	no	—
160	Q₁₆×C₁₉	—	8	1	no	—
161	Q₁₆×C₁₉	—	8	1	no	—
162	SD₁₆×C₁₉	—	4	2	no	—
163	SD₁₆×C₁₉	—	4	2	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
184	C₄⋊C₄×C₁₉	—	4	1	no	—
185	C₄⋊C₄×C₁₉	—	4	1	no	—
186	C₄⋊C₄×C₁₉	—	4	1	no	—
187	C₄⋊C₄×C₁₉	—	4	1	no	—
188	C₄⋊C₄×C₁₉	—	4	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	C₂×D₄	1	1	yes	characteristic
193	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂²⋊C₄×C₁₉	—	4	1	no	—
197	C₂²⋊C₄×C₁₉	—	4	1	no	—
198	C₂²⋊C₄×C₁₉	—	4	1	no	—
199	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	2	1	no	—
201	C₄²×C₁₉	—	2	1	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	C₄²×C₁₉	—	4	1	no	—
204	C₄²×C₁₉	—	4	1	no	—
205	C₄²×C₁₉	—	4	1	no	—
206	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
207	#19849	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂³×C₁₉	—	4	1	no	—
209	Q₈×C₁₉	—	2	1	no	—
210	Q₈×C₁₉	—	2	1	no	—
211	Q₈×C₁₉	—	2	1	no	—
212	Q₈×C₁₉	—	2	1	no	—
213	Q₈×C₁₉	—	2	1	no	—
214	Q₈×C₁₉	—	2	1	no	—
215	Q₈×C₁₉	—	2	1	no	—
216	Q₈×C₁₉	—	4	1	no	—
217	Q₈×C₁₉	—	4	1	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	#135	1	2	yes	—
223	D₄×C₁₉	—	4	1	no	—
224	D₄×C₁₉	—	4	1	no	—
225	D₄×C₁₉	—	4	1	no	—
226	D₄×C₁₉	—	4	1	no	—
227	D₄×C₁₉	—	8	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	16	1	no	—
240	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
243	C₈×C₁₉	—	2	1	no	—
244	C₈×C₁₉	—	2	1	no	—
245	C₈×C₁₉	—	2	1	no	—
246	C₈×C₁₉	—	2	1	no	—
247	C₈×C₁₉	—	4	1	no	—
248	C₈×C₁₉	—	4	1	no	—
249	C₈×C₁₉	—	4	1	no	—
250	C₈×C₁₉	—	4	1	no	—
251	C₈×C₁₉	—	4	1	no	—
252	#3395	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#3374	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#3365	C₂×C₁₉	1	1	yes	characteristic
255	#3365	C₂×C₁₉	1	1	yes	characteristic
256	#1720	C₂×C₁₉	1	1	yes	characteristic
257	#1702	C₂×C₁₉	1	1	yes	characteristic
258	#1682	C₂×C₁₉	1	1	yes	characteristic
259	#1680	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1670	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1653	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1653	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1640	C₂×C₁₉	1	1	yes	characteristic
264	#1626	C₂×C₁₉	1	1	yes	characteristic
265	#1584	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1579	C₂×C₁₉	1	1	yes	characteristic, complemented
267	C₂²×C₁₉	—	8	1	no	—
268	C₂²×C₁₉	—	8	1	no	—
269	C₂²×C₁₉	—	8	1	no	—
270	C₂²×C₁₉	D₄²	1	1	yes	characteristic
271	C₄×C₁₉	—	2	2	no	—
272	C₄×C₁₉	—	2	1	no	—
273	C₄×C₁₉	—	4	1	no	—
274	C₄×C₁₉	—	4	1	no	—
275	C₄×C₁₉	—	4	1	no	—
276	C₄×C₁₉	—	4	1	no	—
277	C₄×C₁₉	—	4	1	no	—
278	C₄×C₁₉	—	4	1	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	8	1	no	—
281	C₄×C₁₉	—	8	1	no	—
282	C₄×C₁₉	—	8	1	no	—
283	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
284	C₄×C₁₉	#575	1	1	yes	characteristic
285	C₄×C₁₉	#577	1	1	yes	characteristic
286	C₄×C₁₉	#578	1	1	yes	characteristic
287	#559	C₂²×C₁₉	1	1	yes	characteristic
288	#557	C₂²×C₁₉	1	1	yes	characteristic
289	#557	C₂²×C₁₉	1	1	yes	characteristic
290	#557	C₂²×C₁₉	1	1	yes	characteristic
291	#498	C₂²×C₁₉	1	1	yes	characteristic
292	#494	—	2	1	no	—
293	#494	C₂²×C₁₉	1	1	yes	characteristic
294	#491	—	2	1	no	—
295	#488	—	2	1	no	—
296	#488	—	2	1	no	—
297	#487	C₂²×C₁₉	1	1	yes	characteristic
298	#486	C₂²×C₁₉	1	1	yes	characteristic
299	#486	C₂²×C₁₉	1	1	yes	characteristic
300	#486	C₂²×C₁₉	1	1	yes	characteristic
301	#479	—	2	1	no	—
302	#478	—	2	1	no	—
303	#478	—	2	1	no	—
304	#475	C₂²×C₁₉	1	1	yes	characteristic
305	#475	C₂²×C₁₉	1	1	yes	characteristic
306	#475	C₂²×C₁₉	1	1	yes	characteristic
307	#464	—	2	1	no	—
308	#464	—	2	1	no	—
309	#462	—	2	1	no	—
310	#462	—	2	1	no	—
311	#462	—	2	1	no	—
312	#462	C₂²×C₁₉	1	1	yes	characteristic
313	#462	C₂²×C₁₉	1	1	yes	characteristic
314	#462	C₂²×C₁₉	1	1	yes	characteristic
315	#460	C₂²×C₁₉	1	1	yes	characteristic
316	#460	C₂²×C₁₉	1	1	yes	characteristic
317	#446	C₂²×C₁₉	1	1	yes	characteristic
318	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
319	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
320	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
321	#441	—	2	1	no	—
322	C₄×Q₁₆	—	2	1	no	—
323	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
324	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
325	C₄×SD₁₆	—	2	1	no	—
326	C₄×SD₁₆	—	2	1	no	—
327	#335	C₂²×C₁₉	1	1	yes	characteristic
328	#334	C₂²×C₁₉	1	1	yes	characteristic
329	#332	C₂²×C₁₉	1	1	yes	characteristic
330	#332	C₂²×C₁₉	1	1	yes	characteristic
331	#332	C₂²×C₁₉	1	1	yes	characteristic
332	#331	C₂²×C₁₉	1	1	yes	characteristic
333	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
334	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
335	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
336	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
337	#322	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×C₁₉	—	16	1	no	—
339	C₂×C₁₉	#3271	1	1	yes	characteristic
340	C₂×C₁₉	#3285	1	1	yes	characteristic
341	C₂×C₁₉	#3289	1	1	yes	characteristic
342	C₂×Q₁₆	—	2	1	no	—
343	C₂×Q₁₆	—	2	1	no	—
344	C₂×Q₁₆	—	2	1	no	—
345	C₂×Q₁₆	—	2	1	no	—
346	C₂×Q₁₆	—	2	1	no	—
347	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
348	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
349	C₂×SD₁₆	—	2	1	no	—
350	C₂×SD₁₆	—	2	1	no	—
351	C₄⋊Q₈	—	2	1	no	—
352	C₄⋊Q₈	—	2	1	no	—
353	C₄⋊Q₈	—	2	1	no	—
354	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
355	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
356	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
357	#127	C₂³×C₁₉	1	1	yes	characteristic
358	#125	—	2	1	no	—
359	#125	—	2	1	no	—
360	#125	—	2	1	no	—
361	#125	—	4	1	no	—
362	#125	—	4	1	no	—
363	#125	—	4	1	no	—
364	#124	—	2	1	no	—
365	#124	—	2	1	no	—
366	#123	—	4	1	no	—
367	C₄×Q₈	—	2	1	no	—
368	C₄×Q₈	—	2	1	no	—
369	C₄×Q₈	—	2	1	no	—
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
374	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
375	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
376	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	#107	D₄×C₁₉	1	1	yes	characteristic
380	#107	D₄×C₁₉	1	1	yes	characteristic
381	#106	—	2	1	no	—
382	#106	—	2	1	no	—
383	#106	—	2	1	no	—
384	#106	—	4	1	no	—
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
390	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
391	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
392	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
393	#103	—	2	1	no	—
394	#103	—	2	1	no	—
395	#103	—	2	1	no	—
396	#103	—	2	1	no	—
397	#103	—	2	1	no	—
398	#103	—	2	1	no	—
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#103	D₄×C₁₉	1	1	yes	characteristic
402	#103	D₄×C₁₉	1	1	yes	characteristic
403	#103	D₄×C₁₉	1	1	yes	characteristic
404	#103	D₄×C₁₉	1	1	yes	characteristic
405	#102	—	2	1	no	—
406	#102	—	2	1	no	—
407	#102	—	2	1	no	—
408	#102	—	2	1	no	—
409	#102	—	2	1	no	—
410	#102	—	2	1	no	—
411	#102	—	4	1	no	—
412	#97	—	2	1	no	—
413	C₄×C₈	—	2	1	no	—
414	C₄×C₈	—	2	1	no	—
415	C₄×C₈	—	2	1	no	—
416	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
419	C₁₉	#19849	1	1	yes	characteristic, direct product factor, Sylow
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
425	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	Q₁₆	—	2	2	no	—
432	Q₁₆	—	4	1	no	—
433	Q₁₆	—	4	2	no	—
434	Q₁₆	—	4	2	no	—
435	Q₁₆	—	8	1	no	—
436	Q₁₆	—	8	1	no	—
437	Q₁₆	—	8	1	no	—
438	SD₁₆	—	4	2	no	—
439	SD₁₆	—	4	2	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
472	C₂²⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	4	1	no	—
480	C₄²	—	4	1	no	—
481	C₄²	—	4	1	no	—
482	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
483	C₂³	—	4	1	no	—
484	Q₈	—	2	1	no	—
485	Q₈	—	2	1	no	—
486	Q₈	—	2	1	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	2	1	no	—
489	Q₈	—	2	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	1	no	—
494	Q₈	—	4	1	no	—
495	Q₈	—	4	1	no	—
496	Q₈	—	4	1	no	—
497	Q₈	C₁₉×#135	1	2	yes	—
498	D₄	—	4	1	no	—
499	D₄	—	4	1	no	—
500	D₄	—	4	1	no	—
501	D₄	—	4	1	no	—
502	D₄	—	8	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	16	1	no	—
515	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
517	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	4	1	no	—
523	C₈	—	4	1	no	—
524	C₈	—	4	1	no	—
525	C₈	—	4	1	no	—
526	C₈	—	4	1	no	—
527	C₂²	—	8	1	no	—
528	C₂²	—	8	1	no	—
529	C₂²	—	8	1	no	—
530	C₂²	D₄²×C₁₉	1	1	yes	characteristic
531	C₄	—	2	2	no	—
532	C₄	—	2	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	8	1	no	—
541	C₄	—	8	1	no	—
542	C₄	—	8	1	no	—
543	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
544	C₄	C₁₉×#575	1	1	yes	characteristic
545	C₄	C₁₉×#577	1	1	yes	characteristic
546	C₄	C₁₉×#578	1	1	yes	characteristic
547	C₂	—	16	1	no	—
548	C₂	C₁₉×#3271	1	1	yes	characteristic
549	C₂	C₁₉×#3285	1	1	yes	characteristic
550	C₂	C₁₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#127	C₂³
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×#3395	C₂	semidirect
2. C₁₉×#3374	C₂	semidirect
8. C₁₉×#1680	C₂	semidirect
9. C₁₉×#1670	C₂	semidirect
10. C₁₉×#1653	C₂	semidirect
11. C₁₉×#1653	C₂	semidirect
14. C₁₉×#1584	C₂	semidirect
15. C₁₉×#1579	C₂	semidirect
207. #19849	C₁₉	direct (N × H)
252. #3395	C₂×C₁₉	semidirect
253. #3374	C₂×C₁₉	semidirect
259. #1680	C₂×C₁₉	semidirect
260. #1670	C₂×C₁₉	semidirect
261. #1653	C₂×C₁₉	semidirect
262. #1653	C₂×C₁₉	semidirect
265. #1584	C₂×C₁₉	semidirect
266. #1579	C₂×C₁₉	semidirect
419. C₁₉	#19849	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×#3395	2
C₁₉×#3374	2
C₁₉×#3365	2
C₁₉×#1720	2
C₁₉×#1702	2
C₁₉×#1682	2
C₁₉×#1680	2
C₁₉×#1670	2
C₁₉×#1653	2
C₁₉×#1640	2
C₁₉×#1626	2
C₁₉×#1584	2
C₁₉×#1579	2
#19849	19

Subgroups — C19×#19849 #18025808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19849 #18025808