Subgroups — C₁₉×#19848 #18025807

Order 4864.

556 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3369	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3364	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3363	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3342	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×#1684	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1683	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1674	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1652	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1645	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1638	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic
16	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#557	C₂²	1	1	yes	characteristic
18	C₁₉×#556	C₂²	1	1	yes	characteristic
19	C₁₉×#556	C₂²	1	1	yes	characteristic
20	C₁₉×#500	C₂²	1	1	yes	characteristic
21	C₁₉×#498	C₂²	1	1	yes	characteristic
22	C₁₉×#489	—	2	1	no	—
23	C₁₉×#488	—	2	1	no	—
24	C₁₉×#487	—	2	1	no	—
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×#487	C₂²	1	1	yes	characteristic
29	C₁₉×#485	—	2	1	no	—
30	C₁₉×#485	—	2	1	no	—
31	C₁₉×#479	—	2	1	no	—
32	C₁₉×#477	—	2	1	no	—
33	C₁₉×#477	C₂²	1	1	yes	characteristic
34	C₁₉×#476	C₂²	1	1	yes	characteristic
35	C₁₉×#475	—	2	1	no	—
36	C₁₉×#475	C₂²	1	1	yes	characteristic
37	C₁₉×#475	C₂²	1	1	yes	characteristic
38	C₁₉×#474	C₂²	1	1	yes	characteristic
39	C₁₉×#467	—	2	1	no	—
40	C₁₉×#464	—	2	1	no	—
41	C₁₉×#464	—	2	1	no	—
42	C₁₉×#462	—	2	1	no	—
43	C₁₉×#462	C₂²	1	1	yes	characteristic
44	C₁₉×#462	C₂²	1	1	yes	characteristic
45	C₁₉×#462	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	C₁₉×#441	—	2	1	no	—
50	C₄×Q₁₆×C₁₉	—	2	1	no	—
51	C₄×Q₁₆×C₁₉	—	2	1	no	—
52	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
53	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#427	—	2	1	no	—
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#335	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×Q₈⋊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×Q₁₆×C₁₉	—	2	1	no	—
68	C₂×Q₁₆×C₁₉	—	2	1	no	—
69	C₂×Q₁₆×C₁₉	—	2	1	no	—
70	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
71	C₂×SD₁₆×C₁₉	D₄	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	—	2	1	no	—
73	C₁₉×C₄⋊Q₈	—	2	1	no	—
74	C₁₉×C₄⋊Q₈	—	2	1	no	—
75	C₁₉×C₄⋊Q₈	—	2	1	no	—
76	C₁₉×C₄⋊Q₈	—	4	1	no	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₉×#126	—	4	1	no	—
82	C₁₉×#126	—	4	1	no	—
83	C₁₉×#125	—	2	1	no	—
84	C₁₉×#125	—	4	1	no	—
85	C₁₉×#124	—	2	1	no	—
86	C₁₉×#124	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₄×Q₈×C₁₉	—	2	1	no	—
90	C₄×Q₈×C₁₉	—	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	—	2	1	no	—
95	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₁₉×#117	—	2	1	no	—
100	C₁₉×#117	—	2	1	no	—
101	C₁₉×#107	—	2	1	no	—
102	C₁₉×#107	—	2	1	no	—
103	C₁₉×#107	—	2	1	no	—
104	C₁₉×#107	—	2	1	no	—
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×#106	D₄	1	1	yes	characteristic
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	—	2	1	no	—
127	C₁₉×#103	—	2	1	no	—
128	C₁₉×#103	—	2	1	no	—
129	C₁₉×#103	—	2	1	no	—
130	C₁₉×#103	—	4	1	no	—
131	C₁₉×#103	D₄	1	1	yes	characteristic
132	C₁₉×#103	D₄	1	1	yes	characteristic
133	C₁₉×#103	D₄	1	1	yes	characteristic
134	C₁₉×#102	—	2	1	no	—
135	C₁₉×#102	—	2	1	no	—
136	C₁₉×#102	D₄	1	1	yes	characteristic
137	C₁₉×C₂²⋊C₈	—	2	1	no	—
138	C₁₉×#97	—	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	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	4	1	no	—
149	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	Q₁₆×C₁₉	—	4	1	no	—
155	Q₁₆×C₁₉	—	4	2	no	—
156	Q₁₆×C₁₉	—	4	2	no	—
157	Q₁₆×C₁₉	—	4	2	no	—
158	SD₁₆×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	—	2	1	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₂×C₈×C₁₉	—	2	1	no	—
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	4	2	no	—
165	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
181	C₄⋊C₄×C₁₉	—	4	1	no	—
182	C₄⋊C₄×C₁₉	—	4	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	C₂×D₄	1	1	yes	characteristic
188	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₂²⋊C₄×C₁₉	—	2	1	no	—
192	C₂²⋊C₄×C₁₉	—	4	1	no	—
193	C₂²⋊C₄×C₁₉	—	4	1	no	—
194	C₂²⋊C₄×C₁₉	—	4	1	no	—
195	C₂²⋊C₄×C₁₉	—	4	1	no	—
196	C₄²×C₁₉	—	2	1	no	—
197	C₄²×C₁₉	—	2	1	no	—
198	C₄²×C₁₉	—	2	1	no	—
199	C₄²×C₁₉	—	4	1	no	—
200	C₄²×C₁₉	—	4	1	no	—
201	C₄²×C₁₉	—	4	1	no	—
202	C₄²×C₁₉	—	4	1	no	—
203	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
204	#19848	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂³×C₁₉	—	2	1	no	—
206	Q₈×C₁₉	—	2	1	no	—
207	Q₈×C₁₉	—	2	1	no	—
208	Q₈×C₁₉	—	2	1	no	—
209	Q₈×C₁₉	—	2	1	no	—
210	Q₈×C₁₉	—	2	1	no	—
211	Q₈×C₁₉	—	4	1	no	—
212	Q₈×C₁₉	—	4	1	no	—
213	Q₈×C₁₉	—	4	1	no	—
214	Q₈×C₁₉	—	4	1	no	—
215	Q₈×C₁₉	—	4	1	no	—
216	Q₈×C₁₉	—	4	1	no	—
217	Q₈×C₁₉	—	8	1	no	—
218	Q₈×C₁₉	—	16	1	no	—
219	Q₈×C₁₉	#135	1	2	yes	—
220	D₄×C₁₉	—	2	1	no	—
221	D₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	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	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
238	C₈×C₁₉	—	2	1	no	—
239	C₈×C₁₉	—	2	1	no	—
240	C₈×C₁₉	—	2	1	no	—
241	C₈×C₁₉	—	2	1	no	—
242	C₈×C₁₉	—	4	1	no	—
243	C₈×C₁₉	—	4	1	no	—
244	C₈×C₁₉	—	4	1	no	—
245	C₈×C₁₉	—	4	1	no	—
246	C₈×C₁₉	—	4	1	no	—
247	#3369	C₂×C₁₉	1	1	yes	characteristic
248	#3364	C₂×C₁₉	1	1	yes	characteristic
249	#3363	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#3342	C₂×C₁₉	1	1	yes	characteristic
251	#1718	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#1700	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#1684	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#1683	C₂×C₁₉	1	1	yes	characteristic
255	#1674	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1653	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1652	C₂×C₁₉	1	1	yes	characteristic
258	#1645	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1638	C₂×C₁₉	1	1	yes	characteristic
260	#1584	C₂×C₁₉	1	1	yes	characteristic, complemented
261	SD₁₆⋊C₈	C₂×C₁₉	1	1	yes	characteristic
262	C₂²×C₁₉	—	4	1	no	—
263	C₂²×C₁₉	—	4	1	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	D₄²	1	1	yes	characteristic
266	C₄×C₁₉	—	2	2	no	—
267	C₄×C₁₉	—	2	1	no	—
268	C₄×C₁₉	—	4	1	no	—
269	C₄×C₁₉	—	4	1	no	—
270	C₄×C₁₉	—	4	1	no	—
271	C₄×C₁₉	—	4	1	no	—
272	C₄×C₁₉	—	4	1	no	—
273	C₄×C₁₉	—	4	1	no	—
274	C₄×C₁₉	—	8	1	no	—
275	C₄×C₁₉	—	8	1	no	—
276	C₄×C₁₉	—	8	1	no	—
277	C₄×C₁₉	—	8	1	no	—
278	C₄×C₁₉	C₂×#135	1	1	yes	characteristic
279	C₄×C₁₉	#575	1	1	yes	characteristic
280	C₄×C₁₉	#578	1	1	yes	characteristic
281	C₄×C₁₉	#578	1	1	yes	characteristic
282	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
283	#557	C₂²×C₁₉	1	1	yes	characteristic
284	#556	C₂²×C₁₉	1	1	yes	characteristic
285	#556	C₂²×C₁₉	1	1	yes	characteristic
286	#500	C₂²×C₁₉	1	1	yes	characteristic
287	#498	C₂²×C₁₉	1	1	yes	characteristic
288	#489	—	2	1	no	—
289	#488	—	2	1	no	—
290	#487	—	2	1	no	—
291	#487	C₂²×C₁₉	1	1	yes	characteristic
292	#487	C₂²×C₁₉	1	1	yes	characteristic
293	#487	C₂²×C₁₉	1	1	yes	characteristic
294	#487	C₂²×C₁₉	1	1	yes	characteristic
295	#485	—	2	1	no	—
296	#485	—	2	1	no	—
297	#479	—	2	1	no	—
298	#477	—	2	1	no	—
299	#477	C₂²×C₁₉	1	1	yes	characteristic
300	#476	C₂²×C₁₉	1	1	yes	characteristic
301	#475	—	2	1	no	—
302	#475	C₂²×C₁₉	1	1	yes	characteristic
303	#475	C₂²×C₁₉	1	1	yes	characteristic
304	#474	C₂²×C₁₉	1	1	yes	characteristic
305	#467	—	2	1	no	—
306	#464	—	2	1	no	—
307	#464	—	2	1	no	—
308	#462	—	2	1	no	—
309	#462	C₂²×C₁₉	1	1	yes	characteristic
310	#462	C₂²×C₁₉	1	1	yes	characteristic
311	#462	C₂²×C₁₉	1	1	yes	characteristic
312	#446	C₂²×C₁₉	1	1	yes	characteristic
313	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
314	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
315	#441	—	2	1	no	—
316	C₄×Q₁₆	—	2	1	no	—
317	C₄×Q₁₆	—	2	1	no	—
318	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
319	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
320	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
321	#427	—	2	1	no	—
322	#335	C₂²×C₁₉	1	1	yes	characteristic
323	#335	C₂²×C₁₉	1	1	yes	characteristic
324	#333	C₂²×C₁₉	1	1	yes	characteristic
325	#332	C₂²×C₁₉	1	1	yes	characteristic
326	#332	C₂²×C₁₉	1	1	yes	characteristic
327	#332	C₂²×C₁₉	1	1	yes	characteristic
328	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
329	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
330	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
331	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
332	#322	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×C₁₉	—	8	1	no	—
334	C₂×C₁₉	#3269	1	1	yes	characteristic
335	C₂×C₁₉	#3285	1	1	yes	characteristic
336	C₂×C₁₉	#3289	1	1	yes	characteristic
337	C₂×Q₁₆	—	2	1	no	—
338	C₂×Q₁₆	—	2	1	no	—
339	C₂×Q₁₆	—	2	1	no	—
340	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
341	C₂×SD₁₆	D₄×C₁₉	1	1	yes	characteristic
342	C₂²×C₈	—	2	1	no	—
343	C₄⋊Q₈	—	2	1	no	—
344	C₄⋊Q₈	—	2	1	no	—
345	C₄⋊Q₈	—	2	1	no	—
346	C₄⋊Q₈	—	4	1	no	—
347	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
348	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
349	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
350	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
351	#126	—	4	1	no	—
352	#126	—	4	1	no	—
353	#125	—	2	1	no	—
354	#125	—	4	1	no	—
355	#124	—	2	1	no	—
356	#124	—	2	1	no	—
357	C₂²⋊Q₈	—	2	1	no	—
358	C₂²⋊Q₈	—	2	1	no	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	—	2	1	no	—
361	C₄×Q₈	—	2	1	no	—
362	C₄×Q₈	—	2	1	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
366	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
367	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
368	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
369	#117	—	2	1	no	—
370	#117	—	2	1	no	—
371	#107	—	2	1	no	—
372	#107	—	2	1	no	—
373	#107	—	2	1	no	—
374	#107	—	2	1	no	—
375	#107	D₄×C₁₉	1	1	yes	characteristic
376	#106	—	2	1	no	—
377	#106	—	2	1	no	—
378	#106	—	2	1	no	—
379	#106	—	4	1	no	—
380	#106	D₄×C₁₉	1	1	yes	characteristic
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
385	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
386	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
387	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
388	#103	—	2	1	no	—
389	#103	—	2	1	no	—
390	#103	—	2	1	no	—
391	#103	—	2	1	no	—
392	#103	—	2	1	no	—
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	—	4	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	#102	—	2	1	no	—
405	#102	—	2	1	no	—
406	#102	D₄×C₁₉	1	1	yes	characteristic
407	C₂²⋊C₈	—	2	1	no	—
408	#97	—	2	1	no	—
409	C₄×C₈	—	2	1	no	—
410	C₄×C₈	—	2	1	no	—
411	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
412	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
413	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
414	C₁₉	#19848	1	1	yes	characteristic, direct product factor, Sylow
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	4	1	no	—
420	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
421	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
422	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₂²×C₄	—	2	1	no	—
425	Q₁₆	—	4	1	no	—
426	Q₁₆	—	4	2	no	—
427	Q₁₆	—	4	2	no	—
428	Q₁₆	—	4	2	no	—
429	SD₁₆	—	2	2	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	4	2	no	—
436	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	4	1	no	—
452	C₄⋊C₄	—	4	1	no	—
453	C₄⋊C₄	—	4	1	no	—
454	C₄⋊C₄	—	4	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₄⋊C₄	—	4	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	4	1	no	—
464	C₂²⋊C₄	—	4	1	no	—
465	C₂²⋊C₄	—	4	1	no	—
466	C₂²⋊C₄	—	4	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	4	1	no	—
471	C₄²	—	4	1	no	—
472	C₄²	—	4	1	no	—
473	C₄²	—	4	1	no	—
474	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
475	C₂³	—	2	1	no	—
476	Q₈	—	2	1	no	—
477	Q₈	—	2	1	no	—
478	Q₈	—	2	1	no	—
479	Q₈	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	4	1	no	—
482	Q₈	—	4	1	no	—
483	Q₈	—	4	1	no	—
484	Q₈	—	4	1	no	—
485	Q₈	—	4	1	no	—
486	Q₈	—	4	1	no	—
487	Q₈	—	8	1	no	—
488	Q₈	—	16	1	no	—
489	Q₈	C₁₉×#135	1	2	yes	—
490	D₄	—	2	1	no	—
491	D₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
507	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
508	C₈	—	2	1	no	—
509	C₈	—	2	1	no	—
510	C₈	—	2	1	no	—
511	C₈	—	2	1	no	—
512	C₈	—	4	1	no	—
513	C₈	—	4	1	no	—
514	C₈	—	4	1	no	—
515	C₈	—	4	1	no	—
516	C₈	—	4	1	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	1	no	—
519	C₂²	—	4	1	no	—
520	C₂²	D₄²×C₁₉	1	1	yes	characteristic
521	C₄	—	2	2	no	—
522	C₄	—	2	1	no	—
523	C₄	—	4	1	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	8	1	no	—
530	C₄	—	8	1	no	—
531	C₄	—	8	1	no	—
532	C₄	—	8	1	no	—
533	C₄	C₂×C₁₉×#135	1	1	yes	characteristic
534	C₄	C₁₉×#575	1	1	yes	characteristic
535	C₄	C₁₉×#578	1	1	yes	characteristic
536	C₄	C₁₉×#578	1	1	yes	characteristic
537	C₂	—	8	1	no	—
538	C₂	C₁₉×#3269	1	1	yes	characteristic
539	C₂	C₁₉×#3285	1	1	yes	characteristic
540	C₂	C₁₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂×D₄×C₁₉	C₂×D₄
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
3. C₁₉×#3363	C₂	semidirect
5. C₁₉×#1718	C₂	semidirect
6. C₁₉×#1700	C₂	semidirect
7. C₁₉×#1684	C₂	semidirect
9. C₁₉×#1674	C₂	semidirect
10. C₁₉×#1653	C₂	semidirect
12. C₁₉×#1645	C₂	semidirect
14. C₁₉×#1584	C₂	semidirect
204. #19848	C₁₉	direct (N × H)
249. #3363	C₂×C₁₉	semidirect
251. #1718	C₂×C₁₉	semidirect
252. #1700	C₂×C₁₉	semidirect
253. #1684	C₂×C₁₉	semidirect
255. #1674	C₂×C₁₉	semidirect
256. #1653	C₂×C₁₉	semidirect
258. #1645	C₂×C₁₉	semidirect
260. #1584	C₂×C₁₉	semidirect
414. C₁₉	#19848	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×#3369	2
C₁₉×#3364	2
C₁₉×#3363	2
C₁₉×#3342	2
C₁₉×#1718	2
C₁₉×#1700	2
C₁₉×#1684	2
C₁₉×#1683	2
C₁₉×#1674	2
C₁₉×#1653	2
C₁₉×#1652	2
C₁₉×#1645	2
C₁₉×#1638	2
C₁₉×#1584	2
C₁₉×SD₁₆⋊C₈	2
#19848	19

Subgroups — C19×#19848 #18025807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19848 #18025807