Subgroups — C₁₉×#19794 #18025753

Order 4864.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3372	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3364	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3335	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#3302	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1718	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1700	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1679	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1672	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1648	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1647	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1644	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1638	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1582	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#557	C₂²	1	1	yes	characteristic
17	C₁₉×#556	C₂²	1	1	yes	characteristic
18	C₁₉×#554	C₂²	1	1	yes	characteristic
19	C₁₉×#547	C₂²	1	1	yes	characteristic
20	C₁₉×#500	C₂²	1	1	yes	characteristic
21	C₁₉×#498	C₂²	1	1	yes	characteristic
22	C₁₉×#491	—	2	1	no	—
23	C₁₉×#488	—	2	1	no	—
24	C₁₉×#487	C₂²	1	1	yes	characteristic
25	C₁₉×#487	C₂²	1	1	yes	characteristic
26	C₁₉×#487	C₂²	1	1	yes	characteristic
27	C₁₉×#487	C₂²	1	1	yes	characteristic
28	C₁₉×#485	—	2	1	no	—
29	C₁₉×#483	—	2	1	no	—
30	C₁₉×#481	—	2	1	no	—
31	C₁₉×#479	—	2	1	no	—
32	C₁₉×#479	—	2	1	no	—
33	C₁₉×#477	C₂²	1	1	yes	characteristic
34	C₁₉×#476	C₂²	1	1	yes	characteristic
35	C₁₉×#475	C₂²	1	1	yes	characteristic
36	C₁₉×#474	C₂²	1	1	yes	characteristic
37	C₁₉×#474	C₂²	1	1	yes	characteristic
38	C₁₉×#467	—	2	1	no	—
39	C₁₉×#465	—	2	1	no	—
40	C₁₉×#464	—	2	1	no	—
41	C₁₉×#462	C₂²	1	1	yes	characteristic
42	C₁₉×#462	C₂²	1	1	yes	characteristic
43	C₁₉×#461	—	2	1	no	—
44	C₁₉×#461	C₂²	1	1	yes	characteristic
45	C₁₉×#452	—	2	1	no	—
46	C₁₉×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
48	C₁₉×#440	—	2	1	no	—
49	C₄×Q₁₆×C₁₉	—	2	1	no	—
50	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
51	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#106	—	2	1	no	—
55	C₁₉×#416	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#333	C₂²	1	1	yes	characteristic
59	C₁₉×#332	C₂²	1	1	yes	characteristic
60	C₁₉×#332	C₂²	1	1	yes	characteristic
61	C₁₉×#332	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×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₉×#322	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂×Q₁₆×C₁₉	—	2	1	no	—
69	C₂×Q₁₆×C₁₉	—	2	1	no	—
70	C₂×SD₁₆×C₁₉	—	2	1	no	—
71	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
72	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	—	2	1	no	—
74	C₂²×C₈×C₁₉	—	2	1	no	—
75	C₁₉×C₄⋊Q₈	—	2	1	no	—
76	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₉×#126	—	4	1	no	—
81	C₁₉×#125	—	2	1	no	—
82	C₁₉×#125	—	2	1	no	—
83	C₁₉×#125	—	4	1	no	—
84	C₁₉×#124	—	2	1	no	—
85	C₁₉×#123	—	4	1	no	—
86	C₁₉×C₂²⋊Q₈	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	—	4	1	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₄×Q₈×C₁₉	—	2	1	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
93	C₄×Q₈×C₁₉	—	2	1	no	—
94	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₁₉×#117	—	2	1	no	—
100	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₁₉×#107	—	2	1	no	—
103	C₁₉×#107	—	2	1	no	—
104	C₁₉×#107	—	2	1	no	—
105	C₁₉×#107	—	4	1	no	—
106	C₁₉×#106	—	2	1	no	—
107	C₁₉×#106	—	2	1	no	—
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×#106	—	2	1	no	—
110	C₁₉×#106	D₄	1	1	yes	characteristic
111	C₁₉×#106	D₄	1	1	yes	characteristic
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	—	2	1	no	—
127	C₁₉×#103	—	2	1	no	—
128	C₁₉×#103	—	2	1	no	—
129	C₁₉×#103	—	4	1	no	—
130	C₁₉×#103	D₄	1	1	yes	characteristic
131	C₁₉×#103	D₄	1	1	yes	characteristic
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
134	C₁₉×#102	—	2	1	no	—
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×#97	—	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	#41×C₁₉	—	4	2	no	—
145	#41×C₁₉	—	8	1	no	—
146	C₂×Q₈×C₁₉	—	2	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×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₁₉	—	4	1	no	—
153	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	4	1	no	—
158	C₂²×C₄×C₁₉	—	4	1	no	—
159	Q₁₆×C₁₉	—	4	2	no	—
160	Q₁₆×C₁₉	—	8	1	no	—
161	SD₁₆×C₁₉	—	2	2	no	—
162	SD₁₆×C₁₉	—	4	1	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	—	4	2	no	—
170	C₂×C₈×C₁₉	—	8	1	no	—
171	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	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	—	2	1	no	—
197	C₂²⋊C₄×C₁₉	—	2	1	no	—
198	C₂²⋊C₄×C₁₉	—	4	1	no	—
199	C₂²⋊C₄×C₁₉	—	4	1	no	—
200	C₂²⋊C₄×C₁₉	—	4	1	no	—
201	C₂²⋊C₄×C₁₉	—	4	1	no	—
202	C₄²×C₁₉	—	2	1	no	—
203	C₄²×C₁₉	—	2	1	no	—
204	C₄²×C₁₉	—	4	1	no	—
205	C₄²×C₁₉	—	4	1	no	—
206	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
207	#19794	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×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	—	4	1	no	—
215	Q₈×C₁₉	—	4	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	—	8	1	no	—
221	D₄×C₁₉	—	2	1	no	—
222	D₄×C₁₉	—	2	1	no	—
223	D₄×C₁₉	—	2	1	no	—
224	D₄×C₁₉	—	8	2	no	—
225	D₄×C₁₉	#135	1	2	yes	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	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	—	4	1	no	—
240	C₂×C₄×C₁₉	—	8	2	no	—
241	C₂×C₄×C₁₉	—	16	1	no	—
242	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
245	C₈×C₁₉	—	2	1	no	—
246	C₈×C₁₉	—	2	1	no	—
247	C₈×C₁₉	—	2	1	no	—
248	C₈×C₁₉	—	2	1	no	—
249	C₈×C₁₉	—	4	1	no	—
250	C₈×C₁₉	—	4	1	no	—
251	C₈×C₁₉	—	4	1	no	—
252	C₈×C₁₉	—	4	1	no	—
253	C₈×C₁₉	—	4	1	no	—
254	#3372	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#3364	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#3335	C₂×C₁₉	1	1	yes	characteristic
257	#3302	C₂×C₁₉	1	1	yes	characteristic
258	#1718	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1700	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1683	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1679	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1648	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1647	C₂×C₁₉	1	1	yes	characteristic
265	#1644	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1638	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1582	C₂×C₁₉	1	1	yes	characteristic, complemented
268	SD₁₆⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
269	C₂²×C₁₉	—	2	2	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	—	4	1	no	—
273	C₂²×C₁₉	—	4	1	no	—
274	C₂²×C₁₉	—	4	1	no	—
275	C₂²×C₁₉	D₄²	1	1	yes	characteristic
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	4	1	no	—
278	C₄×C₁₉	—	4	1	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	4	1	no	—
282	C₄×C₁₉	—	4	1	no	—
283	C₄×C₁₉	—	8	1	no	—
284	C₄×C₁₉	—	8	1	no	—
285	C₄×C₁₉	—	8	1	no	—
286	C₄×C₁₉	—	8	1	no	—
287	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
288	C₄×C₁₉	#575	1	1	yes	characteristic
289	C₄×C₁₉	#577	1	1	yes	characteristic
290	C₄×C₁₉	#578	1	1	yes	characteristic
291	#557	C₂²×C₁₉	1	1	yes	characteristic
292	#556	C₂²×C₁₉	1	1	yes	characteristic
293	#554	C₂²×C₁₉	1	1	yes	characteristic
294	#547	C₂²×C₁₉	1	1	yes	characteristic
295	#500	C₂²×C₁₉	1	1	yes	characteristic
296	#498	C₂²×C₁₉	1	1	yes	characteristic
297	#491	—	2	1	no	—
298	#488	—	2	1	no	—
299	#487	C₂²×C₁₉	1	1	yes	characteristic
300	#487	C₂²×C₁₉	1	1	yes	characteristic
301	#487	C₂²×C₁₉	1	1	yes	characteristic
302	#487	C₂²×C₁₉	1	1	yes	characteristic
303	#485	—	2	1	no	—
304	#483	—	2	1	no	—
305	#481	—	2	1	no	—
306	#479	—	2	1	no	—
307	#479	—	2	1	no	—
308	#477	C₂²×C₁₉	1	1	yes	characteristic
309	#476	C₂²×C₁₉	1	1	yes	characteristic
310	#475	C₂²×C₁₉	1	1	yes	characteristic
311	#474	C₂²×C₁₉	1	1	yes	characteristic
312	#474	C₂²×C₁₉	1	1	yes	characteristic
313	#467	—	2	1	no	—
314	#465	—	2	1	no	—
315	#464	—	2	1	no	—
316	#462	C₂²×C₁₉	1	1	yes	characteristic
317	#462	C₂²×C₁₉	1	1	yes	characteristic
318	#461	—	2	1	no	—
319	#461	C₂²×C₁₉	1	1	yes	characteristic
320	#452	—	2	1	no	—
321	#446	C₂²×C₁₉	1	1	yes	characteristic
322	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
323	#440	—	2	1	no	—
324	C₄×Q₁₆	—	2	1	no	—
325	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
326	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
327	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
328	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×#106	—	2	1	no	—
330	#416	—	2	1	no	—
331	#335	C₂²×C₁₉	1	1	yes	characteristic
332	#334	C₂²×C₁₉	1	1	yes	characteristic
333	#333	C₂²×C₁₉	1	1	yes	characteristic
334	#332	C₂²×C₁₉	1	1	yes	characteristic
335	#332	C₂²×C₁₉	1	1	yes	characteristic
336	#332	C₂²×C₁₉	1	1	yes	characteristic
337	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
338	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
339	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
340	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
341	#322	C₂²×C₁₉	1	1	yes	characteristic
342	C₂×C₁₉	—	4	2	no	—
343	C₂×C₁₉	—	8	1	no	—
344	C₂×C₁₉	#3269	1	1	yes	characteristic
345	C₂×C₁₉	#3282	1	1	yes	characteristic
346	C₂×C₁₉	#3289	1	1	yes	characteristic
347	C₂×#41	—	2	1	no	—
348	C₂×Q₁₆	—	2	1	no	—
349	C₂×Q₁₆	—	2	1	no	—
350	C₂×SD₁₆	—	2	1	no	—
351	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
352	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
353	C₂²×C₈	—	2	1	no	—
354	C₂²×C₈	—	2	1	no	—
355	C₄⋊Q₈	—	2	1	no	—
356	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
357	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
358	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
359	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
360	#126	—	4	1	no	—
361	#125	—	2	1	no	—
362	#125	—	2	1	no	—
363	#125	—	4	1	no	—
364	#124	—	2	1	no	—
365	#123	—	4	1	no	—
366	C₂²⋊Q₈	—	2	1	no	—
367	C₂²⋊Q₈	—	2	1	no	—
368	C₂²⋊Q₈	—	2	1	no	—
369	C₂²⋊Q₈	—	4	1	no	—
370	#121	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
375	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
378	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
379	#117	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	#107	—	2	1	no	—
383	#107	—	2	1	no	—
384	#107	—	2	1	no	—
385	#107	—	4	1	no	—
386	#106	—	2	1	no	—
387	#106	—	2	1	no	—
388	#106	—	2	1	no	—
389	#106	—	2	1	no	—
390	#106	D₄×C₁₉	1	1	yes	characteristic
391	#106	D₄×C₁₉	1	1	yes	characteristic
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
395	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
396	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
397	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
398	#103	—	2	1	no	—
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#103	—	2	1	no	—
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	4	1	no	—
410	#103	D₄×C₁₉	1	1	yes	characteristic
411	#103	D₄×C₁₉	1	1	yes	characteristic
412	#102	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	—	2	1	no	—
415	#102	D₄×C₁₉	1	1	yes	characteristic
416	#102	D₄×C₁₉	1	1	yes	characteristic
417	C₂²⋊C₈	—	2	1	no	—
418	C₂²⋊C₈	—	2	1	no	—
419	#97	—	2	1	no	—
420	C₄×C₈	—	2	1	no	—
421	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
422	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
423	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
424	C₁₉	#19794	1	1	yes	characteristic, direct product factor, Sylow
425	#41	—	4	2	no	—
426	#41	—	8	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
432	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
433	C₂×D₄	—	4	1	no	—
434	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
435	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	4	1	no	—
439	C₂²×C₄	—	4	1	no	—
440	Q₁₆	—	4	2	no	—
441	Q₁₆	—	8	1	no	—
442	SD₁₆	—	2	2	no	—
443	SD₁₆	—	4	1	no	—
444	SD₁₆	—	4	2	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	4	2	no	—
451	C₂×C₈	—	8	1	no	—
452	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	4	1	no	—
486	C₄²	—	4	1	no	—
487	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
488	C₂³	—	2	1	no	—
489	C₂³	—	2	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	4	1	no	—
495	Q₈	—	4	1	no	—
496	Q₈	—	4	1	no	—
497	Q₈	—	4	1	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	8	1	no	—
501	D₄	—	2	1	no	—
502	D₄	—	2	1	no	—
503	D₄	—	2	1	no	—
504	D₄	—	8	2	no	—
505	D₄	C₁₉×#135	1	2	yes	—
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	—	2	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	8	2	no	—
521	C₂×C₄	—	16	1	no	—
522	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
524	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	1	no	—
533	C₈	—	4	1	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	D₄²×C₁₉	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	8	1	no	—
549	C₄	—	8	1	no	—
550	C₄	—	8	1	no	—
551	C₄	—	8	1	no	—
552	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
553	C₄	C₁₉×#575	1	1	yes	characteristic
554	C₄	C₁₉×#577	1	1	yes	characteristic
555	C₄	C₁₉×#578	1	1	yes	characteristic
556	C₂	—	4	2	no	—
557	C₂	—	8	1	no	—
558	C₂	C₁₉×#3269	1	1	yes	characteristic
559	C₂	C₁₉×#3282	1	1	yes	characteristic
560	C₂	C₁₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#547	C₂²
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×#3372	C₂	semidirect
2. C₁₉×#3364	C₂	semidirect
5. C₁₉×#1718	C₂	semidirect
6. C₁₉×#1700	C₂	semidirect
7. C₁₉×#1683	C₂	semidirect
8. C₁₉×#1679	C₂	semidirect
9. C₁₉×#1672	C₂	semidirect
10. C₁₉×#1648	C₂	semidirect
12. C₁₉×#1644	C₂	semidirect
13. C₁₉×#1638	C₂	semidirect
14. C₁₉×#1582	C₂	semidirect
15. C₁₉×SD₁₆⋊C₈	C₂	semidirect
207. #19794	C₁₉	direct (N × H)
254. #3372	C₂×C₁₉	semidirect
255. #3364	C₂×C₁₉	semidirect
258. #1718	C₂×C₁₉	semidirect
259. #1700	C₂×C₁₉	semidirect
260. #1683	C₂×C₁₉	semidirect
261. #1679	C₂×C₁₉	semidirect
262. #1672	C₂×C₁₉	semidirect
263. #1648	C₂×C₁₉	semidirect
265. #1644	C₂×C₁₉	semidirect
266. #1638	C₂×C₁₉	semidirect
267. #1582	C₂×C₁₉	semidirect
268. SD₁₆⋊C₈	C₂×C₁₉	semidirect
424. C₁₉	#19794	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×#3372	2
C₁₉×#3364	2
C₁₉×#3335	2
C₁₉×#3302	2
C₁₉×#1718	2
C₁₉×#1700	2
C₁₉×#1683	2
C₁₉×#1679	2
C₁₉×#1672	2
C₁₉×#1648	2
C₁₉×#1647	2
C₁₉×#1644	2
C₁₉×#1638	2
C₁₉×#1582	2
C₁₉×SD₁₆⋊C₈	2
#19794	19

Subgroups — C19×#19794 #18025753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19794 #18025753