Subgroups — C₁₉×#19372 #18025331

Order 4864.

588 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3255	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3216	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3182	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1702	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1700	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1694	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1686	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1682	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1680	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1674	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1666	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1569	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1552	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1547	C₂	1	1	yes	maximal, characteristic
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#533	C₂²	1	1	yes	characteristic
18	C₁₉×#532	C₂²	1	1	yes	characteristic
19	C₁₉×#500	C₂²	1	1	yes	characteristic
20	C₁₉×#497	—	2	1	no	—
21	C₁₉×#492	C₂²	1	1	yes	characteristic
22	C₁₉×#489	—	2	1	no	—
23	C₁₉×#487	C₂²	1	1	yes	characteristic
24	C₁₉×#486	C₂²	1	1	yes	characteristic
25	C₁₉×#475	—	2	1	no	—
26	C₁₉×#475	C₂²	1	1	yes	characteristic
27	C₁₉×#475	C₂²	1	1	yes	characteristic
28	C₁₉×#470	—	2	1	no	—
29	C₁₉×#470	—	2	1	no	—
30	C₁₉×#468	—	2	1	no	—
31	C₁₉×#468	—	2	1	no	—
32	C₁₉×#462	—	2	1	no	—
33	C₁₉×#462	C₂²	1	1	yes	characteristic
34	C₁₉×#462	C₂²	1	1	yes	characteristic
35	C₁₉×#462	C₂²	1	1	yes	characteristic
36	C₁₉×#462	C₂²	1	1	yes	characteristic
37	C₁₉×#460	C₂²	1	1	yes	characteristic
38	C₁₉×#460	C₂²	1	1	yes	characteristic
39	C₁₉×#452	—	2	1	no	—
40	C₁₉×#452	—	2	1	no	—
41	C₁₉×#446	—	2	1	no	—
42	C₁₉×#446	—	2	1	no	—
43	C₁₉×#446	C₂²	1	1	yes	characteristic
44	C₁₉×#446	C₂²	1	1	yes	characteristic
45	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
46	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
47	C₁₉×#440	—	2	1	no	—
48	C₁₉×#440	—	2	1	no	—
49	C₁₉×#432	C₂²	1	1	yes	characteristic
50	C₁₉×#424	—	2	1	no	—
51	C₁₉×#423	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
53	C₁₉×#405	—	2	1	no	—
54	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#335	C₂²	1	1	yes	characteristic
56	C₁₉×#335	C₂²	1	1	yes	characteristic
57	C₁₉×#334	C₂²	1	1	yes	characteristic
58	C₁₉×#334	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×#332	C₂²	1	1	yes	characteristic
63	C₁₉×#332	C₂²	1	1	yes	characteristic
64	C₁₉×#332	C₂²	1	1	yes	characteristic
65	C₁₉×#331	C₂²	1	1	yes	characteristic
66	C₁₉×#331	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×Q₁₆×C₁₉	—	2	1	no	—
71	C₂×Q₁₆×C₁₉	—	2	1	no	—
72	C₂×SD₁₆×C₁₉	—	2	1	no	—
73	C₂×SD₁₆×C₁₉	—	2	1	no	—
74	C₂×SD₁₆×C₁₉	—	2	1	no	—
75	C₂×SD₁₆×C₁₉	—	2	1	no	—
76	C₂×M₁₆×C₁₉	—	2	1	no	—
77	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
78	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₁₉	—	2	1	no	—
80	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
81	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
82	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₉×#127	C₂³	1	1	yes	characteristic
86	C₁₉×#125	—	2	1	no	—
87	C₁₉×#125	—	2	1	no	—
88	C₁₉×#124	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
93	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	—	2	1	no	—
98	C₄×Q₈×C₁₉	—	2	1	no	—
99	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
100	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₁₉×#117	—	2	1	no	—
104	C₁₉×#117	—	2	1	no	—
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₁₉×#107	—	2	1	no	—
107	C₁₉×#107	—	2	1	no	—
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×#106	—	2	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	—	2	1	no	—
115	C₁₉×C₄⋊C₈	—	2	1	no	—
116	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×#102	—	2	1	no	—
133	C₁₉×#102	—	2	1	no	—
134	C₁₉×C₂²⋊C₈	—	2	1	no	—
135	C₁₉×#97	—	2	1	no	—
136	C₁₉×#97	—	2	1	no	—
137	C₁₉×#97	—	2	1	no	—
138	C₁₉×#97	D₄	1	1	yes	characteristic
139	C₁₉×#97	D₄	1	1	yes	characteristic
140	C₄×C₈×C₁₉	—	2	1	no	—
141	C₄×C₈×C₁₉	—	2	1	no	—
142	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
144	#41×C₁₉	—	8	1	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	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	4	1	no	—
156	C₂²×C₄×C₁₉	—	4	1	no	—
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
160	Q₁₆×C₁₉	—	8	1	no	—
161	Q₁₆×C₁₉	—	8	1	no	—
162	Q₁₆×C₁₉	—	8	1	no	—
163	Q₁₆×C₁₉	—	8	1	no	—
164	SD₁₆×C₁₉	—	4	2	no	—
165	SD₁₆×C₁₉	—	4	2	no	—
166	SD₁₆×C₁₉	—	8	1	no	—
167	SD₁₆×C₁₉	—	8	1	no	—
168	M₁₆×C₁₉	—	2	2	no	—
169	M₁₆×C₁₉	—	4	1	no	—
170	M₁₆×C₁₉	—	8	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	4	2	no	—
178	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
198	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	2	1	no	—
201	C₂²⋊C₄×C₁₉	—	4	1	no	—
202	C₂²⋊C₄×C₁₉	—	4	1	no	—
203	C₂²⋊C₄×C₁₉	—	4	1	no	—
204	C₄²×C₁₉	—	2	1	no	—
205	C₄²×C₁₉	—	2	1	no	—
206	C₄²×C₁₉	—	4	1	no	—
207	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₉	#41	1	1	yes	characteristic
210	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
211	#19372	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂³×C₁₉	—	4	1	no	—
213	C₂³×C₁₉	#121	1	1	yes	characteristic
214	Q₈×C₁₉	—	2	1	no	—
215	Q₈×C₁₉	—	2	1	no	—
216	Q₈×C₁₉	—	2	1	no	—
217	Q₈×C₁₉	—	2	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	—	4	1	no	—
223	Q₈×C₁₉	—	4	1	no	—
224	Q₈×C₁₉	—	8	1	no	—
225	D₄×C₁₉	—	4	1	no	—
226	D₄×C₁₉	—	4	1	no	—
227	D₄×C₁₉	—	4	1	no	—
228	D₄×C₁₉	—	4	1	no	—
229	D₄×C₁₉	—	8	1	no	—
230	D₄×C₁₉	—	8	2	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	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	8	2	no	—
244	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
250	C₈×C₁₉	—	2	1	no	—
251	C₈×C₁₉	—	2	1	no	—
252	C₈×C₁₉	—	2	1	no	—
253	C₈×C₁₉	—	4	1	no	—
254	C₈×C₁₉	—	4	1	no	—
255	C₈×C₁₉	—	4	1	no	—
256	C₈×C₁₉	—	4	1	no	—
257	C₈×C₁₉	—	4	1	no	—
258	C₈×C₁₉	—	4	1	no	—
259	C₈×C₁₉	#137	1	2	yes	—
260	#3255	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#3216	C₂×C₁₉	1	1	yes	characteristic
262	#3182	C₂×C₁₉	1	1	yes	characteristic
263	#2962	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1702	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1700	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1694	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1686	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#1682	C₂×C₁₉	1	1	yes	characteristic, complemented
269	#1680	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1674	C₂×C₁₉	1	1	yes	characteristic, complemented
271	#1666	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1569	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1552	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1547	C₂×C₁₉	1	1	yes	characteristic
275	C₂²×C₁₉	—	2	1	no	—
276	C₂²×C₁₉	—	2	1	no	—
277	C₂²×C₁₉	—	2	1	no	—
278	C₂²×C₁₉	—	8	1	no	—
279	C₂²×C₁₉	—	8	1	no	—
280	C₂²×C₁₉	—	8	1	no	—
281	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
282	C₄×C₁₉	—	2	1	no	—
283	C₄×C₁₉	—	2	1	no	—
284	C₄×C₁₉	—	2	1	no	—
285	C₄×C₁₉	—	2	1	no	—
286	C₄×C₁₉	—	4	1	no	—
287	C₄×C₁₉	—	4	1	no	—
288	C₄×C₁₉	—	4	1	no	—
289	C₄×C₁₉	—	4	1	no	—
290	C₄×C₁₉	—	8	1	no	—
291	C₄×C₁₉	—	8	1	no	—
292	C₄×C₁₉	—	8	1	no	—
293	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
294	C₄×C₁₉	#575	1	1	yes	characteristic
295	C₄×C₁₉	#576	1	1	yes	characteristic
296	C₄×C₁₉	#577	1	1	yes	characteristic
297	#533	C₂²×C₁₉	1	1	yes	characteristic
298	#533	C₂²×C₁₉	1	1	yes	characteristic
299	#532	C₂²×C₁₉	1	1	yes	characteristic
300	#500	C₂²×C₁₉	1	1	yes	characteristic
301	#497	—	2	1	no	—
302	#492	C₂²×C₁₉	1	1	yes	characteristic
303	#489	—	2	1	no	—
304	#487	C₂²×C₁₉	1	1	yes	characteristic
305	#486	C₂²×C₁₉	1	1	yes	characteristic
306	#475	—	2	1	no	—
307	#475	C₂²×C₁₉	1	1	yes	characteristic
308	#475	C₂²×C₁₉	1	1	yes	characteristic
309	#470	—	2	1	no	—
310	#470	—	2	1	no	—
311	#468	—	2	1	no	—
312	#468	—	2	1	no	—
313	#462	—	2	1	no	—
314	#462	C₂²×C₁₉	1	1	yes	characteristic
315	#462	C₂²×C₁₉	1	1	yes	characteristic
316	#462	C₂²×C₁₉	1	1	yes	characteristic
317	#462	C₂²×C₁₉	1	1	yes	characteristic
318	#460	C₂²×C₁₉	1	1	yes	characteristic
319	#460	C₂²×C₁₉	1	1	yes	characteristic
320	#452	—	2	1	no	—
321	#452	—	2	1	no	—
322	#446	—	2	1	no	—
323	#446	—	2	1	no	—
324	#446	C₂²×C₁₉	1	1	yes	characteristic
325	#446	C₂²×C₁₉	1	1	yes	characteristic
326	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
327	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
328	#440	—	2	1	no	—
329	#440	—	2	1	no	—
330	#432	C₂²×C₁₉	1	1	yes	characteristic
331	#424	—	2	1	no	—
332	#423	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
334	#405	—	2	1	no	—
335	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
336	#335	C₂²×C₁₉	1	1	yes	characteristic
337	#335	C₂²×C₁₉	1	1	yes	characteristic
338	#334	C₂²×C₁₉	1	1	yes	characteristic
339	#334	C₂²×C₁₉	1	1	yes	characteristic
340	#332	C₂²×C₁₉	1	1	yes	characteristic
341	#332	C₂²×C₁₉	1	1	yes	characteristic
342	#332	C₂²×C₁₉	1	1	yes	characteristic
343	#332	C₂²×C₁₉	1	1	yes	characteristic
344	#332	C₂²×C₁₉	1	1	yes	characteristic
345	#332	C₂²×C₁₉	1	1	yes	characteristic
346	#331	C₂²×C₁₉	1	1	yes	characteristic
347	#331	C₂²×C₁₉	1	1	yes	characteristic
348	C₂×C₁₉	—	4	1	no	—
349	C₂×C₁₉	—	16	1	no	—
350	C₂×C₁₉	#3037	1	1	yes	characteristic
351	C₂×C₁₉	#3062	1	1	yes	characteristic
352	C₂×C₁₉	#3069	1	1	yes	characteristic
353	C₂×#41	—	2	1	no	—
354	C₂×Q₁₆	—	2	1	no	—
355	C₂×Q₁₆	—	2	1	no	—
356	C₂×Q₁₆	—	2	1	no	—
357	C₂×Q₁₆	—	2	1	no	—
358	C₂×SD₁₆	—	2	1	no	—
359	C₂×SD₁₆	—	2	1	no	—
360	C₂×SD₁₆	—	2	1	no	—
361	C₂×SD₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
364	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
365	C₂²×C₈	—	2	1	no	—
366	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
367	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
368	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
369	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
370	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
371	#127	C₂³×C₁₉	1	1	yes	characteristic
372	#125	—	2	1	no	—
373	#125	—	2	1	no	—
374	#124	—	2	1	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	—	2	1	no	—
377	C₂²⋊Q₈	—	2	1	no	—
378	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
379	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
380	#121	—	2	1	no	—
381	#121	—	2	1	no	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
386	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	#117	—	2	1	no	—
390	#117	—	2	1	no	—
391	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
392	#107	—	2	1	no	—
393	#107	—	2	1	no	—
394	#106	—	2	1	no	—
395	#106	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	—	2	1	no	—
398	C₄⋊C₈	—	2	1	no	—
399	C₄⋊C₈	—	2	1	no	—
400	C₄⋊C₈	—	2	1	no	—
401	C₄⋊C₈	—	2	1	no	—
402	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
403	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
405	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
406	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
407	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#103	—	2	1	no	—
412	#103	—	2	1	no	—
413	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	#102	—	2	1	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	#97	—	2	1	no	—
422	#97	—	2	1	no	—
423	#97	—	2	1	no	—
424	#97	D₄×C₁₉	1	1	yes	characteristic
425	#97	D₄×C₁₉	1	1	yes	characteristic
426	C₄×C₈	—	2	1	no	—
427	C₄×C₈	—	2	1	no	—
428	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
429	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
430	C₁₉	#19372	1	1	yes	characteristic, direct product factor, Sylow
431	#41	—	8	1	no	—
432	#41	—	8	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
447	Q₁₆	—	8	1	no	—
448	Q₁₆	—	8	1	no	—
449	Q₁₆	—	8	1	no	—
450	Q₁₆	—	8	1	no	—
451	SD₁₆	—	4	2	no	—
452	SD₁₆	—	4	2	no	—
453	SD₁₆	—	8	1	no	—
454	SD₁₆	—	8	1	no	—
455	M₁₆	—	2	2	no	—
456	M₁₆	—	4	1	no	—
457	M₁₆	—	8	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	4	2	no	—
465	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
485	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	4	1	no	—
494	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₄²	#41×C₁₉	1	1	yes	characteristic
497	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
498	C₂³	—	4	1	no	—
499	C₂³	C₁₉×#121	1	1	yes	characteristic
500	Q₈	—	2	1	no	—
501	Q₈	—	2	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	8	1	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	1	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	1	no	—
515	D₄	—	8	1	no	—
516	D₄	—	8	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	8	2	no	—
530	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
531	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
532	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
535	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	C₁₉×#137	1	2	yes	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	8	1	no	—
562	C₄	—	8	1	no	—
563	C₄	—	8	1	no	—
564	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
565	C₄	C₁₉×#575	1	1	yes	characteristic
566	C₄	C₁₉×#576	1	1	yes	characteristic
567	C₄	C₁₉×#577	1	1	yes	characteristic
568	C₂	—	4	1	no	—
569	C₂	—	16	1	no	—
570	C₂	C₁₉×#3037	1	1	yes	characteristic
571	C₂	C₁₉×#3062	1	1	yes	characteristic
572	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3255	C₂	semidirect
4. C₁₉×#2962	C₂	semidirect
5. C₁₉×#1702	C₂	semidirect
6. C₁₉×#1700	C₂	semidirect
7. C₁₉×#1694	C₂	semidirect
8. C₁₉×#1686	C₂	semidirect
9. C₁₉×#1682	C₂	semidirect
10. C₁₉×#1680	C₂	semidirect
11. C₁₉×#1674	C₂	semidirect
12. C₁₉×#1666	C₂	semidirect
13. C₁₉×#1569	C₂	semidirect
14. C₁₉×#1552	C₂	semidirect
211. #19372	C₁₉	direct (N × H)
260. #3255	C₂×C₁₉	semidirect
263. #2962	C₂×C₁₉	semidirect
264. #1702	C₂×C₁₉	semidirect
265. #1700	C₂×C₁₉	semidirect
266. #1694	C₂×C₁₉	semidirect
267. #1686	C₂×C₁₉	semidirect
268. #1682	C₂×C₁₉	semidirect
269. #1680	C₂×C₁₉	semidirect
270. #1674	C₂×C₁₉	semidirect
271. #1666	C₂×C₁₉	semidirect
272. #1569	C₂×C₁₉	semidirect
273. #1552	C₂×C₁₉	semidirect
430. C₁₉	#19372	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×#3255	2
C₁₉×#3216	2
C₁₉×#3182	2
C₁₉×#2962	2
C₁₉×#1702	2
C₁₉×#1700	2
C₁₉×#1694	2
C₁₉×#1686	2
C₁₉×#1682	2
C₁₉×#1680	2
C₁₉×#1674	2
C₁₉×#1666	2
C₁₉×#1569	2
C₁₉×#1552	2
C₁₉×#1547	2
#19372	19

Subgroups — C19×#19372 #18025331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19372 #18025331