Subgroups — C₁₉×#19379 #18025338

Order 4864.

572 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3252	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3238	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2969	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1696	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1695	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1692	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1691	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1676	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1675	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1672	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1671	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1569	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1554	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1548	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₉×#529	C₂²	1	1	yes	characteristic
19	C₁₉×#501	—	2	1	no	—
20	C₁₉×#501	—	2	1	no	—
21	C₁₉×#501	—	2	1	no	—
22	C₁₉×#500	C₂²	1	1	yes	characteristic
23	C₁₉×#500	C₂²	1	1	yes	characteristic
24	C₁₉×#498	C₂²	1	1	yes	characteristic
25	C₁₉×#498	C₂²	1	1	yes	characteristic
26	C₁₉×#489	—	2	1	no	—
27	C₁₉×#483	—	2	1	no	—
28	C₁₉×#480	—	2	1	no	—
29	C₁₉×#479	—	2	1	no	—
30	C₁₉×#477	C₂²	1	1	yes	characteristic
31	C₁₉×#477	C₂²	1	1	yes	characteristic
32	C₁₉×#477	C₂²	1	1	yes	characteristic
33	C₁₉×#476	C₂²	1	1	yes	characteristic
34	C₁₉×#476	C₂²	1	1	yes	characteristic
35	C₁₉×#476	C₂²	1	1	yes	characteristic
36	C₁₉×#470	—	2	1	no	—
37	C₁₉×#468	—	2	1	no	—
38	C₁₉×#464	—	2	1	no	—
39	C₁₉×#462	C₂²	1	1	yes	characteristic
40	C₁₉×#461	C₂²	1	1	yes	characteristic
41	C₁₉×#446	C₂²	1	1	yes	characteristic
42	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#436	—	2	1	no	—
44	C₁₉×#436	C₂²	1	1	yes	characteristic
45	C₁₉×#435	—	2	1	no	—
46	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₁₉×#433	—	2	1	no	—
48	C₁₉×#432	C₂²	1	1	yes	characteristic
49	C₁₉×#431	C₂²	1	1	yes	characteristic
50	C₁₉×#428	—	2	1	no	—
51	C₁₉×#428	—	2	1	no	—
52	C₁₉×#423	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×#333	C₂²	1	1	yes	characteristic
60	C₁₉×#333	C₂²	1	1	yes	characteristic
61	C₁₉×#333	C₂²	1	1	yes	characteristic
62	C₁₉×#333	C₂²	1	1	yes	characteristic
63	C₁₉×#333	C₂²	1	1	yes	characteristic
64	C₁₉×#333	C₂²	1	1	yes	characteristic
65	C₁₉×#332	C₂²	1	1	yes	characteristic
66	C₁₉×#332	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₁₉	—	2	1	no	—
68	C₂×Q₁₆×C₁₉	—	2	1	no	—
69	C₂×SD₁₆×C₁₉	—	2	1	no	—
70	C₂×M₁₆×C₁₉	—	2	1	no	—
71	C₂×M₁₆×C₁₉	—	2	1	no	—
72	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
73	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	—	2	1	no	—
75	C₁₉×C₄⋊Q₈	—	2	1	no	—
76	C₁₉×C₄⋊Q₈	—	2	1	no	—
77	C₁₉×C₄⋊Q₈	—	2	1	no	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₉×#126	—	2	1	no	—
83	C₁₉×#125	—	2	1	no	—
84	C₁₉×#125	D₄	1	1	yes	characteristic
85	C₁₉×#124	D₄	1	1	yes	characteristic
86	C₁₉×#123	—	2	1	no	—
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
90	C₁₉×#121	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₁₉	—	2	1	no	—
92	C₄×Q₈×C₁₉	—	2	1	no	—
93	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₁₉	—	2	1	no	—
95	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₁₉×#117	—	2	1	no	—
97	C₁₉×#117	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
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×#106	—	2	1	no	—
111	C₁₉×#106	—	2	1	no	—
112	C₁₉×#106	—	2	1	no	—
113	C₁₉×#106	—	2	1	no	—
114	C₁₉×#106	—	2	1	no	—
115	C₁₉×C₄⋊C₈	—	2	1	no	—
116	C₁₉×C₄⋊C₈	—	2	1	no	—
117	C₁₉×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#102	—	2	1	no	—
130	C₁₉×#102	—	2	1	no	—
131	C₁₉×#102	—	2	1	no	—
132	C₁₉×C₂²⋊C₈	—	2	1	no	—
133	C₁₉×C₂²⋊C₈	—	2	1	no	—
134	C₁₉×C₂²⋊C₈	—	2	1	no	—
135	C₁₉×C₂²⋊C₈	—	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	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	—	8	2	no	—
150	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	4	1	no	—
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
158	Q₁₆×C₁₉	—	8	1	no	—
159	SD₁₆×C₁₉	—	8	1	no	—
160	M₁₆×C₁₉	—	2	2	no	—
161	M₁₆×C₁₉	—	2	2	no	—
162	M₁₆×C₁₉	—	4	2	no	—
163	M₁₆×C₁₉	—	8	1	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	—	2	1	no	—
170	C₂×C₈×C₁₉	—	4	2	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	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	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	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₁₉	—	2	1	no	—
194	C₂²⋊C₄×C₁₉	—	2	1	no	—
195	C₂²⋊C₄×C₁₉	—	2	1	no	—
196	C₂²⋊C₄×C₁₉	—	2	1	no	—
197	C₂²⋊C₄×C₁₉	—	2	1	no	—
198	C₂²⋊C₄×C₁₉	—	4	1	no	—
199	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	4	1	no	—
201	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₉	#41	1	1	yes	characteristic
204	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
205	#19379	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂³×C₁₉	—	2	1	no	—
207	C₂³×C₁₉	#121	1	1	yes	characteristic
208	Q₈×C₁₉	—	2	1	no	—
209	Q₈×C₁₉	—	2	1	no	—
210	Q₈×C₁₉	—	4	1	no	—
211	Q₈×C₁₉	—	4	1	no	—
212	Q₈×C₁₉	—	8	1	no	—
213	Q₈×C₁₉	—	8	1	no	—
214	Q₈×C₁₉	—	8	1	no	—
215	Q₈×C₁₉	—	8	2	no	—
216	D₄×C₁₉	—	2	1	no	—
217	D₄×C₁₉	—	2	1	no	—
218	D₄×C₁₉	—	8	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×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	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	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	—	8	2	no	—
234	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
236	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
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	C₈×C₁₉	—	4	1	no	—
248	C₈×C₁₉	#137	1	2	yes	—
249	C₈×C₁₉	#137	1	2	yes	—
250	#3252	C₂×C₁₉	1	1	yes	characteristic
251	#3238	C₂×C₁₉	1	1	yes	characteristic
252	#3165	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#2969	C₂×C₁₉	1	1	yes	characteristic
254	#1696	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#1695	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1692	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1691	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1676	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1675	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1672	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1671	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1569	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#1554	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1548	C₂×C₁₉	1	1	yes	characteristic, complemented
265	C₂²×C₁₉	—	2	1	no	—
266	C₂²×C₁₉	—	2	1	no	—
267	C₂²×C₁₉	—	2	1	no	—
268	C₂²×C₁₉	—	4	1	no	—
269	C₂²×C₁₉	—	4	1	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
272	C₄×C₁₉	—	2	1	no	—
273	C₄×C₁₉	—	2	1	no	—
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	4	1	no	—
277	C₄×C₁₉	—	4	1	no	—
278	C₄×C₁₉	—	4	1	no	—
279	C₄×C₁₉	—	8	1	no	—
280	C₄×C₁₉	—	8	1	no	—
281	C₄×C₁₉	—	8	1	no	—
282	C₄×C₁₉	—	8	1	no	—
283	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
284	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
285	C₄×C₁₉	#577	1	1	yes	characteristic
286	C₄×C₁₉	#578	1	1	yes	characteristic
287	#533	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
289	#529	C₂²×C₁₉	1	1	yes	characteristic
290	#501	—	2	1	no	—
291	#501	—	2	1	no	—
292	#501	—	2	1	no	—
293	#500	C₂²×C₁₉	1	1	yes	characteristic
294	#500	C₂²×C₁₉	1	1	yes	characteristic
295	#498	C₂²×C₁₉	1	1	yes	characteristic
296	#498	C₂²×C₁₉	1	1	yes	characteristic
297	#489	—	2	1	no	—
298	#483	—	2	1	no	—
299	#480	—	2	1	no	—
300	#479	—	2	1	no	—
301	#477	C₂²×C₁₉	1	1	yes	characteristic
302	#477	C₂²×C₁₉	1	1	yes	characteristic
303	#477	C₂²×C₁₉	1	1	yes	characteristic
304	#476	C₂²×C₁₉	1	1	yes	characteristic
305	#476	C₂²×C₁₉	1	1	yes	characteristic
306	#476	C₂²×C₁₉	1	1	yes	characteristic
307	#470	—	2	1	no	—
308	#468	—	2	1	no	—
309	#464	—	2	1	no	—
310	#462	C₂²×C₁₉	1	1	yes	characteristic
311	#461	C₂²×C₁₉	1	1	yes	characteristic
312	#446	C₂²×C₁₉	1	1	yes	characteristic
313	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
314	#436	—	2	1	no	—
315	#436	C₂²×C₁₉	1	1	yes	characteristic
316	#435	—	2	1	no	—
317	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
318	#433	—	2	1	no	—
319	#432	C₂²×C₁₉	1	1	yes	characteristic
320	#431	C₂²×C₁₉	1	1	yes	characteristic
321	#428	—	2	1	no	—
322	#428	—	2	1	no	—
323	#423	C₂²×C₁₉	1	1	yes	characteristic
324	#405	—	2	1	no	—
325	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
326	#335	C₂²×C₁₉	1	1	yes	characteristic
327	#335	C₂²×C₁₉	1	1	yes	characteristic
328	#334	C₂²×C₁₉	1	1	yes	characteristic
329	#334	C₂²×C₁₉	1	1	yes	characteristic
330	#333	C₂²×C₁₉	1	1	yes	characteristic
331	#333	C₂²×C₁₉	1	1	yes	characteristic
332	#333	C₂²×C₁₉	1	1	yes	characteristic
333	#333	C₂²×C₁₉	1	1	yes	characteristic
334	#333	C₂²×C₁₉	1	1	yes	characteristic
335	#333	C₂²×C₁₉	1	1	yes	characteristic
336	#332	C₂²×C₁₉	1	1	yes	characteristic
337	#332	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×C₁₉	—	4	1	no	—
339	C₂×C₁₉	—	8	1	no	—
340	C₂×C₁₉	#3039	1	1	yes	characteristic
341	C₂×C₁₉	#3063	1	1	yes	characteristic
342	C₂×C₁₉	#3068	1	1	yes	characteristic
343	C₂²×Q₈	—	2	1	no	—
344	C₂×Q₁₆	—	2	1	no	—
345	C₂×SD₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
349	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
350	C₂²×C₈	—	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	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
358	#126	—	2	1	no	—
359	#125	—	2	1	no	—
360	#125	D₄×C₁₉	1	1	yes	characteristic
361	#124	D₄×C₁₉	1	1	yes	characteristic
362	#123	—	2	1	no	—
363	C₂²⋊Q₈	—	2	1	no	—
364	C₂²⋊Q₈	—	2	1	no	—
365	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
366	#121	D₄×C₁₉	1	1	yes	characteristic
367	C₄×Q₈	—	2	1	no	—
368	C₄×Q₈	—	2	1	no	—
369	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
377	#107	—	2	1	no	—
378	#107	—	2	1	no	—
379	#107	—	2	1	no	—
380	#107	—	2	1	no	—
381	#107	—	2	1	no	—
382	#107	—	2	1	no	—
383	#107	—	2	1	no	—
384	#106	—	2	1	no	—
385	#106	—	2	1	no	—
386	#106	—	2	1	no	—
387	#106	—	2	1	no	—
388	#106	—	2	1	no	—
389	#106	—	2	1	no	—
390	#106	—	2	1	no	—
391	C₄⋊C₈	—	2	1	no	—
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	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
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	#102	—	2	1	no	—
406	#102	—	2	1	no	—
407	#102	—	2	1	no	—
408	C₂²⋊C₈	—	2	1	no	—
409	C₂²⋊C₈	—	2	1	no	—
410	C₂²⋊C₈	—	2	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	#97	—	2	1	no	—
413	#97	—	2	1	no	—
414	#97	D₄×C₁₉	1	1	yes	characteristic
415	#97	D₄×C₁₉	1	1	yes	characteristic
416	C₄×C₈	—	2	1	no	—
417	C₄×C₈	—	2	1	no	—
418	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
419	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
420	C₁₉	#19379	1	1	yes	characteristic, direct product factor, Sylow
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	4	1	no	—
426	C₂×Q₈	—	8	2	no	—
427	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
434	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
435	Q₁₆	—	8	1	no	—
436	SD₁₆	—	8	1	no	—
437	M₁₆	—	2	2	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	4	2	no	—
440	M₁₆	—	8	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	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	4	2	no	—
448	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	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	—	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	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	4	1	no	—
478	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₄²	#41×C₁₉	1	1	yes	characteristic
481	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
482	C₂³	—	2	1	no	—
483	C₂³	C₁₉×#121	1	1	yes	characteristic
484	Q₈	—	2	1	no	—
485	Q₈	—	2	1	no	—
486	Q₈	—	4	1	no	—
487	Q₈	—	4	1	no	—
488	Q₈	—	8	1	no	—
489	Q₈	—	8	1	no	—
490	Q₈	—	8	1	no	—
491	Q₈	—	8	2	no	—
492	D₄	—	2	1	no	—
493	D₄	—	2	1	no	—
494	D₄	—	8	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	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	8	2	no	—
510	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
511	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
512	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
515	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
516	C₈	—	2	1	no	—
517	C₈	—	2	1	no	—
518	C₈	—	4	1	no	—
519	C₈	—	4	1	no	—
520	C₈	—	4	1	no	—
521	C₈	—	4	1	no	—
522	C₈	—	4	1	no	—
523	C₈	—	4	1	no	—
524	C₈	C₁₉×#137	1	2	yes	—
525	C₈	C₁₉×#137	1	2	yes	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	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	—	8	1	no	—
544	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
545	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
546	C₄	C₁₉×#577	1	1	yes	characteristic
547	C₄	C₁₉×#578	1	1	yes	characteristic
548	C₂	—	4	1	no	—
549	C₂	—	8	1	no	—
550	C₂	C₁₉×#3039	1	1	yes	characteristic
551	C₂	C₁₉×#3063	1	1	yes	characteristic
552	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#121	D₄
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
3. C₁₉×#3165	C₂	semidirect
5. C₁₉×#1696	C₂	semidirect
6. C₁₉×#1695	C₂	semidirect
7. C₁₉×#1692	C₂	semidirect
8. C₁₉×#1691	C₂	semidirect
9. C₁₉×#1676	C₂	semidirect
10. C₁₉×#1675	C₂	semidirect
11. C₁₉×#1672	C₂	semidirect
12. C₁₉×#1671	C₂	semidirect
13. C₁₉×#1569	C₂	semidirect
14. C₁₉×#1554	C₂	semidirect
15. C₁₉×#1548	C₂	semidirect
205. #19379	C₁₉	direct (N × H)
252. #3165	C₂×C₁₉	semidirect
254. #1696	C₂×C₁₉	semidirect
255. #1695	C₂×C₁₉	semidirect
256. #1692	C₂×C₁₉	semidirect
257. #1691	C₂×C₁₉	semidirect
258. #1676	C₂×C₁₉	semidirect
259. #1675	C₂×C₁₉	semidirect
260. #1672	C₂×C₁₉	semidirect
261. #1671	C₂×C₁₉	semidirect
262. #1569	C₂×C₁₉	semidirect
263. #1554	C₂×C₁₉	semidirect
264. #1548	C₂×C₁₉	semidirect
420. C₁₉	#19379	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×#3252	2
C₁₉×#3238	2
C₁₉×#3165	2
C₁₉×#2969	2
C₁₉×#1696	2
C₁₉×#1695	2
C₁₉×#1692	2
C₁₉×#1691	2
C₁₉×#1676	2
C₁₉×#1675	2
C₁₉×#1672	2
C₁₉×#1671	2
C₁₉×#1569	2
C₁₉×#1554	2
C₁₉×#1548	2
#19379	19

Subgroups — C19×#19379 #18025338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19379 #18025338