Subgroups — C₁₉×#19547 #18025506

Order 4864.

552 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3238	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3233	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2993	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1704	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1703	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1696	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1695	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1684	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1683	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1676	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1675	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1572	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1559	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×#500	C₂²	1	1	yes	characteristic
21	C₁₉×#500	C₂²	1	1	yes	characteristic
22	C₁₉×#499	—	2	1	no	—
23	C₁₉×#489	—	2	1	no	—
24	C₁₉×#488	—	2	1	no	—
25	C₁₉×#487	C₂²	1	1	yes	characteristic
26	C₁₉×#487	C₂²	1	1	yes	characteristic
27	C₁₉×#485	—	2	1	no	—
28	C₁₉×#484	—	2	1	no	—
29	C₁₉×#484	—	2	1	no	—
30	C₁₉×#483	—	2	1	no	—
31	C₁₉×#482	—	2	1	no	—
32	C₁₉×#480	—	2	1	no	—
33	C₁₉×#477	—	2	1	no	—
34	C₁₉×#477	—	2	1	no	—
35	C₁₉×#477	C₂²	1	1	yes	characteristic
36	C₁₉×#477	C₂²	1	1	yes	characteristic
37	C₁₉×#477	C₂²	1	1	yes	characteristic
38	C₁₉×#476	C₂²	1	1	yes	characteristic
39	C₁₉×#476	C₂²	1	1	yes	characteristic
40	C₁₉×#476	C₂²	1	1	yes	characteristic
41	C₁₉×#475	C₂²	1	1	yes	characteristic
42	C₁₉×#474	C₂²	1	1	yes	characteristic
43	C₁₉×#446	C₂²	1	1	yes	characteristic
44	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#436	—	2	1	no	—
46	C₁₉×#436	C₂²	1	1	yes	characteristic
47	C₁₉×#435	—	2	1	no	—
48	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#433	—	2	1	no	—
50	C₁₉×#432	C₂²	1	1	yes	characteristic
51	C₁₉×#431	C₂²	1	1	yes	characteristic
52	C₁₉×#431	C₂²	1	1	yes	characteristic
53	C₁₉×#424	—	2	1	no	—
54	C₁₉×#423	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×M₁₆×C₁₉	—	2	1	no	—
69	C₂×M₁₆×C₁₉	—	2	1	no	—
70	C₂²×C₈×C₁₉	—	2	1	no	—
71	C₁₉×C₄⋊Q₈	—	2	1	no	—
72	C₁₉×C₄⋊Q₈	—	2	1	no	—
73	C₁₉×C₄⋊Q₈	—	2	1	no	—
74	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
75	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₁₉×#126	—	2	1	no	—
79	C₁₉×#125	—	2	1	no	—
80	C₁₉×#125	D₄	1	1	yes	characteristic
81	C₁₉×#124	D₄	1	1	yes	characteristic
82	C₁₉×#123	—	2	1	no	—
83	C₁₉×C₂²⋊Q₈	—	2	1	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
86	C₁₉×#121	D₄	1	1	yes	characteristic
87	C₄×Q₈×C₁₉	—	2	1	no	—
88	C₄×Q₈×C₁₉	—	2	1	no	—
89	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₄×D₄×C₁₉	—	2	1	no	—
91	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₁₉×#117	—	2	1	no	—
93	C₁₉×#117	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
97	C₁₉×#107	—	2	1	no	—
98	C₁₉×#107	—	2	1	no	—
99	C₁₉×#107	—	2	1	no	—
100	C₁₉×#107	—	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×#106	—	2	1	no	—
106	C₁₉×#106	—	2	1	no	—
107	C₁₉×#106	—	2	1	no	—
108	C₁₉×#106	—	2	1	no	—
109	C₁₉×C₄⋊C₈	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	2	1	no	—
111	C₁₉×C₄⋊C₈	—	2	1	no	—
112	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
113	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#102	—	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×C₂²⋊C₈	D₄	1	1	yes	characteristic
137	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
138	C₁₉×#97	—	2	1	no	—
139	C₁₉×#97	—	2	1	no	—
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	M₁₆×C₁₉	—	8	1	no	—
159	M₁₆×C₁₉	—	8	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	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	—	8	1	no	—
167	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	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	C₂×D₄	1	1	yes	characteristic
188	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂²⋊C₄×C₁₉	—	2	1	no	—
190	C₂²⋊C₄×C₁₉	—	2	1	no	—
191	C₂²⋊C₄×C₁₉	—	2	1	no	—
192	C₂²⋊C₄×C₁₉	—	2	1	no	—
193	C₂²⋊C₄×C₁₉	—	2	1	no	—
194	C₂²⋊C₄×C₁₉	—	4	1	no	—
195	C₄²×C₁₉	—	2	1	no	—
196	C₄²×C₁₉	—	4	1	no	—
197	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₁₉	#41	1	1	yes	characteristic
200	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
201	#19547	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂³×C₁₉	—	2	1	no	—
203	C₂³×C₁₉	#121	1	1	yes	characteristic
204	Q₈×C₁₉	—	2	1	no	—
205	Q₈×C₁₉	—	2	1	no	—
206	Q₈×C₁₉	—	4	1	no	—
207	Q₈×C₁₉	—	4	1	no	—
208	Q₈×C₁₉	—	8	1	no	—
209	Q₈×C₁₉	—	8	1	no	—
210	Q₈×C₁₉	—	8	1	no	—
211	Q₈×C₁₉	—	8	2	no	—
212	D₄×C₁₉	—	2	1	no	—
213	D₄×C₁₉	—	2	1	no	—
214	D₄×C₁₉	—	8	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	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	—	8	2	no	—
230	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
236	C₈×C₁₉	—	2	1	no	—
237	C₈×C₁₉	—	2	1	no	—
238	C₈×C₁₉	—	2	1	no	—
239	C₈×C₁₉	—	2	1	no	—
240	C₈×C₁₉	—	4	1	no	—
241	C₈×C₁₉	—	4	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	#3238	C₂×C₁₉	1	1	yes	characteristic
247	#3233	C₂×C₁₉	1	1	yes	characteristic
248	#3230	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#2993	C₂×C₁₉	1	1	yes	characteristic
250	#1704	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#1703	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#1696	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#1695	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#1684	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#1683	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1676	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1675	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1572	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1559	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1548	C₂×C₁₉	1	1	yes	characteristic, complemented
261	C₂²×C₁₉	—	2	1	no	—
262	C₂²×C₁₉	—	2	1	no	—
263	C₂²×C₁₉	—	2	1	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	—	4	1	no	—
266	C₂²×C₁₉	—	4	1	no	—
267	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
268	C₄×C₁₉	—	2	1	no	—
269	C₄×C₁₉	—	2	1	no	—
270	C₄×C₁₉	—	2	1	no	—
271	C₄×C₁₉	—	2	1	no	—
272	C₄×C₁₉	—	4	1	no	—
273	C₄×C₁₉	—	4	1	no	—
274	C₄×C₁₉	—	4	1	no	—
275	C₄×C₁₉	—	8	1	no	—
276	C₄×C₁₉	—	8	1	no	—
277	C₄×C₁₉	—	8	1	no	—
278	C₄×C₁₉	—	8	1	no	—
279	C₄×C₁₉	#577	1	1	yes	characteristic
280	C₄×C₁₉	#578	1	1	yes	characteristic
281	C₄×C₁₉	#578	1	1	yes	characteristic
282	C₄×C₁₉	#578	1	1	yes	characteristic
283	#533	C₂²×C₁₉	1	1	yes	characteristic
284	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
285	#529	C₂²×C₁₉	1	1	yes	characteristic
286	#501	—	2	1	no	—
287	#500	C₂²×C₁₉	1	1	yes	characteristic
288	#500	C₂²×C₁₉	1	1	yes	characteristic
289	#499	—	2	1	no	—
290	#489	—	2	1	no	—
291	#488	—	2	1	no	—
292	#487	C₂²×C₁₉	1	1	yes	characteristic
293	#487	C₂²×C₁₉	1	1	yes	characteristic
294	#485	—	2	1	no	—
295	#484	—	2	1	no	—
296	#484	—	2	1	no	—
297	#483	—	2	1	no	—
298	#482	—	2	1	no	—
299	#480	—	2	1	no	—
300	#477	—	2	1	no	—
301	#477	—	2	1	no	—
302	#477	C₂²×C₁₉	1	1	yes	characteristic
303	#477	C₂²×C₁₉	1	1	yes	characteristic
304	#477	C₂²×C₁₉	1	1	yes	characteristic
305	#476	C₂²×C₁₉	1	1	yes	characteristic
306	#476	C₂²×C₁₉	1	1	yes	characteristic
307	#476	C₂²×C₁₉	1	1	yes	characteristic
308	#475	C₂²×C₁₉	1	1	yes	characteristic
309	#474	C₂²×C₁₉	1	1	yes	characteristic
310	#446	C₂²×C₁₉	1	1	yes	characteristic
311	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
312	#436	—	2	1	no	—
313	#436	C₂²×C₁₉	1	1	yes	characteristic
314	#435	—	2	1	no	—
315	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
316	#433	—	2	1	no	—
317	#432	C₂²×C₁₉	1	1	yes	characteristic
318	#431	C₂²×C₁₉	1	1	yes	characteristic
319	#431	C₂²×C₁₉	1	1	yes	characteristic
320	#424	—	2	1	no	—
321	#423	C₂²×C₁₉	1	1	yes	characteristic
322	#335	C₂²×C₁₉	1	1	yes	characteristic
323	#335	C₂²×C₁₉	1	1	yes	characteristic
324	#334	C₂²×C₁₉	1	1	yes	characteristic
325	#334	C₂²×C₁₉	1	1	yes	characteristic
326	#333	C₂²×C₁₉	1	1	yes	characteristic
327	#333	C₂²×C₁₉	1	1	yes	characteristic
328	#333	C₂²×C₁₉	1	1	yes	characteristic
329	#333	C₂²×C₁₉	1	1	yes	characteristic
330	#333	C₂²×C₁₉	1	1	yes	characteristic
331	#333	C₂²×C₁₉	1	1	yes	characteristic
332	#332	C₂²×C₁₉	1	1	yes	characteristic
333	#332	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×C₁₉	—	4	1	no	—
335	C₂×C₁₉	—	8	1	no	—
336	C₂×C₁₉	#3046	1	1	yes	characteristic
337	C₂×C₁₉	#3059	1	1	yes	characteristic
338	C₂×C₁₉	#3068	1	1	yes	characteristic
339	C₂²×Q₈	—	2	1	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	1	no	—
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	C₂³×C₁₉	1	1	yes	characteristic
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	#126	—	2	1	no	—
351	#125	—	2	1	no	—
352	#125	D₄×C₁₉	1	1	yes	characteristic
353	#124	D₄×C₁₉	1	1	yes	characteristic
354	#123	—	2	1	no	—
355	C₂²⋊Q₈	—	2	1	no	—
356	C₂²⋊Q₈	—	2	1	no	—
357	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
358	#121	D₄×C₁₉	1	1	yes	characteristic
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	—	2	1	no	—
361	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
364	#117	—	2	1	no	—
365	#117	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
369	#107	—	2	1	no	—
370	#107	—	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	—	2	1	no	—
376	#107	—	2	1	no	—
377	#106	—	2	1	no	—
378	#106	—	2	1	no	—
379	#106	—	2	1	no	—
380	#106	—	2	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
385	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
386	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
387	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
388	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
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	#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	#102	—	2	1	no	—
401	#102	—	2	1	no	—
402	#102	—	2	1	no	—
403	#102	—	2	1	no	—
404	C₂²⋊C₈	—	2	1	no	—
405	C₂²⋊C₈	—	2	1	no	—
406	C₂²⋊C₈	—	2	1	no	—
407	C₂²⋊C₈	—	2	1	no	—
408	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
409	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
410	#97	—	2	1	no	—
411	#97	—	2	1	no	—
412	C₄×C₈	—	2	1	no	—
413	C₄×C₈	—	2	1	no	—
414	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
415	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
416	C₁₉	#19547	1	1	yes	characteristic, direct product factor, Sylow
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	4	1	no	—
422	C₂×Q₈	—	8	2	no	—
423	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	4	1	no	—
428	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
431	M₁₆	—	8	1	no	—
432	M₁₆	—	8	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	8	1	no	—
440	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	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	—	4	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	—	4	1	no	—
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	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	4	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	4	1	no	—
470	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
472	C₄²	#41×C₁₉	1	1	yes	characteristic
473	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
474	C₂³	—	2	1	no	—
475	C₂³	C₁₉×#121	1	1	yes	characteristic
476	Q₈	—	2	1	no	—
477	Q₈	—	2	1	no	—
478	Q₈	—	4	1	no	—
479	Q₈	—	4	1	no	—
480	Q₈	—	8	1	no	—
481	Q₈	—	8	1	no	—
482	Q₈	—	8	1	no	—
483	Q₈	—	8	2	no	—
484	D₄	—	2	1	no	—
485	D₄	—	2	1	no	—
486	D₄	—	8	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	8	2	no	—
502	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
503	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
504	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
507	C₂×C₄	C₂×#41×C₁₉	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	C₈	—	4	1	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	4	1	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	4	1	no	—
524	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
525	C₄	—	2	1	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	2	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	1	no	—
532	C₄	—	8	1	no	—
533	C₄	—	8	1	no	—
534	C₄	—	8	1	no	—
535	C₄	—	8	1	no	—
536	C₄	C₁₉×#577	1	1	yes	characteristic
537	C₄	C₁₉×#578	1	1	yes	characteristic
538	C₄	C₁₉×#578	1	1	yes	characteristic
539	C₄	C₁₉×#578	1	1	yes	characteristic
540	C₂	—	4	1	no	—
541	C₂	—	8	1	no	—
542	C₂	C₁₉×#3046	1	1	yes	characteristic
543	C₂	C₁₉×#3059	1	1	yes	characteristic
544	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×#3230	C₂	semidirect
5. C₁₉×#1704	C₂	semidirect
6. C₁₉×#1703	C₂	semidirect
7. C₁₉×#1696	C₂	semidirect
8. C₁₉×#1695	C₂	semidirect
9. C₁₉×#1684	C₂	semidirect
10. C₁₉×#1683	C₂	semidirect
11. C₁₉×#1676	C₂	semidirect
12. C₁₉×#1675	C₂	semidirect
13. C₁₉×#1572	C₂	semidirect
14. C₁₉×#1559	C₂	semidirect
15. C₁₉×#1548	C₂	semidirect
201. #19547	C₁₉	direct (N × H)
248. #3230	C₂×C₁₉	semidirect
250. #1704	C₂×C₁₉	semidirect
251. #1703	C₂×C₁₉	semidirect
252. #1696	C₂×C₁₉	semidirect
253. #1695	C₂×C₁₉	semidirect
254. #1684	C₂×C₁₉	semidirect
255. #1683	C₂×C₁₉	semidirect
256. #1676	C₂×C₁₉	semidirect
257. #1675	C₂×C₁₉	semidirect
258. #1572	C₂×C₁₉	semidirect
259. #1559	C₂×C₁₉	semidirect
260. #1548	C₂×C₁₉	semidirect
416. C₁₉	#19547	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×#3238	2
C₁₉×#3233	2
C₁₉×#3230	2
C₁₉×#2993	2
C₁₉×#1704	2
C₁₉×#1703	2
C₁₉×#1696	2
C₁₉×#1695	2
C₁₉×#1684	2
C₁₉×#1683	2
C₁₉×#1676	2
C₁₉×#1675	2
C₁₉×#1572	2
C₁₉×#1559	2
C₁₉×#1548	2
#19547	19

Subgroups — C19×#19547 #18025506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19547 #18025506