Subgroups — C₁₉×#18438 #18024397

Order 4864.

908 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3561	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3229	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2640	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1612	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1608	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1506	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1500	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1469	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#563	—	2	1	no	—
11	C₁₉×#562	—	2	1	no	—
12	C₁₉×#556	—	2	1	no	—
13	C₁₉×#551	—	2	2	no	—
14	D₄×Q₈×C₁₉	—	2	1	no	—
15	C₁₉×#548	—	2	1	no	—
16	C₁₉×#546	—	2	1	no	—
17	C₁₉×#543	C₂²	1	2	yes	—
18	C₁₉×#542	—	2	1	no	—
19	C₁₉×#542	—	2	2	no	—
20	C₁₉×#538	C₂²	1	2	yes	—
21	C₁₉×#536	—	2	1	no	—
22	C₁₉×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×#529	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
26	C₁₉×#501	—	2	1	no	—
27	C₁₉×#498	—	2	1	no	—
28	C₁₉×#489	—	2	1	no	—
29	C₁₉×#487	—	2	1	no	—
30	C₁₉×#483	C₂²	1	4	yes	—
31	C₁₉×#483	C₂²	1	2	yes	—
32	C₁₉×#480	C₂²	1	2	yes	—
33	C₁₉×#477	—	2	1	no	—
34	C₁₉×#476	—	2	1	no	—
35	C₁₉×#475	—	2	2	no	—
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₁₉×#397	C₂²	1	4	yes	—
39	C₁₉×#393	—	2	2	no	—
40	C₁₉×#391	—	2	1	no	—
41	C₁₉×#390	—	2	1	no	—
42	C₁₉×#376	C₂²	1	1	yes	characteristic
43	C₁₉×#328	C₂²	1	2	yes	—
44	C₁₉×#328	C₂²	1	4	yes	—
45	C₁₉×#327	C₂²	1	2	yes	—
46	C₁₉×#323	C₂²	1	4	yes	—
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	—	2	1	no	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	2	no	—
54	C₁₉×C₄⋊Q₈	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₁₉×#126	—	2	2	no	—
61	C₁₉×#126	—	2	2	no	—
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#126	—	2	1	no	—
64	C₁₉×#125	—	2	1	no	—
65	C₁₉×#125	D₄	1	1	yes	characteristic
66	C₁₉×#124	—	2	1	no	—
67	C₁₉×#124	—	2	2	no	—
68	C₁₉×#124	—	2	2	no	—
69	C₁₉×#124	—	2	1	no	—
70	C₁₉×#124	—	2	1	no	—
71	C₁₉×#124	—	2	1	no	—
72	C₁₉×#124	—	2	1	no	—
73	C₁₉×#124	D₄	1	1	yes	characteristic
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×#123	—	2	2	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×#123	—	2	1	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	1	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	2	no	—
87	C₁₉×C₂²⋊Q₈	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
89	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	C₂³	1	1	yes	characteristic
94	C₁₉×#120	—	2	2	no	—
95	C₄×Q₈×C₁₉	—	2	1	no	—
96	C₄×Q₈×C₁₉	—	2	1	no	—
97	C₄×Q₈×C₁₉	D₄	1	2	yes	—
98	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	2	no	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	2	no	—
103	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
104	C₁₉×#117	—	2	2	no	—
105	C₁₉×#117	—	2	1	no	—
106	C₁₉×#117	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
110	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
111	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
112	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₉	—	2	1	no	—
114	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
115	C₁₉×#107	—	2	2	no	—
116	C₁₉×#106	—	2	4	no	—
117	C₁₉×#106	—	2	2	no	—
118	C₁₉×C₄⋊C₈	—	2	1	no	—
119	C₁₉×C₄⋊C₈	—	2	1	no	—
120	C₁₉×#103	—	2	4	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
124	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
125	C₁₉×#97	—	2	1	no	—
126	C₄×C₈×C₁₉	—	2	1	no	—
127	C₁₉×#95	—	2	1	no	—
128	C₁₉×#95	—	2	4	no	—
129	C₁₉×#95	C₂³	1	2	yes	—
130	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
131	#41×C₁₉	—	8	2	no	—
132	C₂×Q₈×C₁₉	—	2	2	no	—
133	C₂×Q₈×C₁₉	—	2	1	no	—
134	C₂×Q₈×C₁₉	—	2	1	no	—
135	C₂×Q₈×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	4	2	no	—
137	C₂×Q₈×C₁₉	—	4	1	no	—
138	C₂×Q₈×C₁₉	—	4	1	no	—
139	C₂×Q₈×C₁₉	—	8	2	no	—
140	C₂×Q₈×C₁₉	—	8	2	no	—
141	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	4	2	no	—
149	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
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	2	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	4	1	no	—
178	C₄⋊C₄×C₁₉	—	4	1	no	—
179	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
182	C₂²⋊C₄×C₁₉	—	2	2	no	—
183	C₂²⋊C₄×C₁₉	—	2	2	no	—
184	C₂²⋊C₄×C₁₉	—	2	2	no	—
185	C₂²⋊C₄×C₁₉	—	2	2	no	—
186	C₂²⋊C₄×C₁₉	—	2	2	no	—
187	C₂²⋊C₄×C₁₉	—	2	1	no	—
188	C₂²⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	2	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	—	2	2	no	—
195	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	2	1	no	—
197	C₂²⋊C₄×C₁₉	—	8	4	no	—
198	C₄²×C₁₉	—	2	2	no	—
199	C₄²×C₁₉	—	2	2	no	—
200	C₄²×C₁₉	—	2	1	no	—
201	C₄²×C₁₉	—	4	2	no	—
202	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
206	#18438	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₁₉	—	2	2	no	—
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	—	2	4	no	—
210	C₂³×C₁₉	—	4	2	no	—
211	C₂³×C₁₉	—	4	2	no	—
212	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
213	Q₈×C₁₉	—	4	1	no	—
214	Q₈×C₁₉	—	4	2	no	—
215	Q₈×C₁₉	—	4	2	no	—
216	Q₈×C₁₉	—	4	2	no	—
217	Q₈×C₁₉	—	8	1	no	—
218	Q₈×C₁₉	—	8	2	no	—
219	Q₈×C₁₉	—	8	2	no	—
220	Q₈×C₁₉	—	8	2	no	—
221	D₄×C₁₉	—	4	1	no	—
222	D₄×C₁₉	—	4	2	no	—
223	D₄×C₁₉	—	4	2	no	—
224	D₄×C₁₉	—	8	1	no	—
225	D₄×C₁₉	—	8	2	no	—
226	D₄×C₁₉	—	8	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	4	no	—
243	C₂×C₄×C₁₉	—	8	2	no	—
244	C₂×C₄×C₁₉	—	8	2	no	—
245	C₂×C₄×C₁₉	—	8	2	no	—
246	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
249	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
252	C₈×C₁₉	—	4	2	no	—
253	C₈×C₁₉	—	4	2	no	—
254	#3561	C₂×C₁₉	1	1	yes	characteristic
255	#3238	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#3229	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#2640	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1612	C₂×C₁₉	1	4	yes	complemented
259	#1608	C₂×C₁₉	1	4	yes	complemented
260	#1506	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1500	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1469	C₂×C₁₉	1	1	yes	characteristic, complemented
263	C₂²×C₁₉	—	2	1	no	—
264	C₂²×C₁₉	—	2	1	no	—
265	C₂²×C₁₉	—	4	1	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	1	no	—
268	C₂²×C₁₉	—	4	2	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	—	8	4	no	—
272	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
273	C₂²×C₁₉	#577	1	2	yes	—
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	2	1	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	4	2	no	—
282	C₄×C₁₉	—	4	2	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	2	no	—
285	C₄×C₁₉	—	8	2	no	—
286	C₄×C₁₉	—	8	2	no	—
287	C₄×C₁₉	#455	1	2	yes	—
288	#563	—	2	1	no	—
289	#562	—	2	1	no	—
290	#556	—	2	1	no	—
291	#551	—	2	2	no	—
292	D₄×Q₈	—	2	1	no	—
293	#548	—	2	1	no	—
294	#546	—	2	1	no	—
295	#543	C₂²×C₁₉	1	2	yes	—
296	#542	—	2	1	no	—
297	#542	—	2	2	no	—
298	#538	C₂²×C₁₉	1	2	yes	—
299	#536	—	2	1	no	—
300	#533	C₂²×C₁₉	1	1	yes	characteristic
301	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
302	#529	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
304	#501	—	2	1	no	—
305	#498	—	2	1	no	—
306	#489	—	2	1	no	—
307	#487	—	2	1	no	—
308	#483	C₂²×C₁₉	1	2	yes	—
309	#483	C₂²×C₁₉	1	4	yes	—
310	#480	C₂²×C₁₉	1	2	yes	—
311	#477	—	2	1	no	—
312	#476	—	2	1	no	—
313	#475	—	2	2	no	—
314	#432	C₂²×C₁₉	1	1	yes	characteristic
315	#431	C₂²×C₁₉	1	1	yes	characteristic
316	#397	C₂²×C₁₉	1	4	yes	—
317	#393	—	2	2	no	—
318	#391	—	2	1	no	—
319	#390	—	2	1	no	—
320	#376	C₂²×C₁₉	1	1	yes	characteristic
321	#328	C₂²×C₁₉	1	2	yes	—
322	#328	C₂²×C₁₉	1	4	yes	—
323	#327	C₂²×C₁₉	1	2	yes	—
324	#323	C₂²×C₁₉	1	4	yes	—
325	C₂×C₁₉	—	2	2	no	—
326	C₂×C₁₉	—	8	1	no	—
327	C₂×C₁₉	—	8	2	no	—
328	C₂×C₁₉	#3010	1	1	yes	characteristic
329	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
330	C₂×C₁₉	#3028	1	1	yes	characteristic
331	C₂×#41	—	2	1	no	—
332	C₂²×Q₈	—	2	1	no	—
333	C₂²×Q₈	—	2	1	no	—
334	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
335	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
336	C₄⋊Q₈	—	2	1	no	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	—	2	1	no	—
339	C₄⋊Q₈	—	2	1	no	—
340	C₄⋊Q₈	—	2	1	no	—
341	C₄⋊Q₈	—	2	1	no	—
342	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
343	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
344	#126	—	2	2	no	—
345	#126	—	2	2	no	—
346	#126	—	2	2	no	—
347	#126	—	2	1	no	—
348	#125	—	2	1	no	—
349	#125	D₄×C₁₉	1	1	yes	characteristic
350	#124	—	2	1	no	—
351	#124	—	2	2	no	—
352	#124	—	2	2	no	—
353	#124	—	2	1	no	—
354	#124	—	2	1	no	—
355	#124	—	2	1	no	—
356	#124	—	2	1	no	—
357	#124	D₄×C₁₉	1	1	yes	characteristic
358	#123	—	2	2	no	—
359	#123	—	2	2	no	—
360	#123	—	2	2	no	—
361	#123	—	2	1	no	—
362	#123	—	2	2	no	—
363	C₂²⋊Q₈	—	2	2	no	—
364	C₂²⋊Q₈	—	2	1	no	—
365	C₂²⋊Q₈	—	2	2	no	—
366	C₂²⋊Q₈	—	2	2	no	—
367	C₂²⋊Q₈	—	2	2	no	—
368	C₂²⋊Q₈	—	2	1	no	—
369	C₂²⋊Q₈	—	2	2	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
373	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
374	#121	—	2	1	no	—
375	#121	—	2	2	no	—
376	#121	—	2	2	no	—
377	#121	C₂³×C₁₉	1	1	yes	characteristic
378	#120	—	2	2	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	—	2	1	no	—
381	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
382	C₄×Q₈	D₄×C₁₉	1	2	yes	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
388	#117	—	2	2	no	—
389	#117	—	2	1	no	—
390	#117	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
393	C₂×C₂²⋊C₄	—	2	2	no	—
394	C₂×C₂²⋊C₄	—	2	4	no	—
395	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
399	#107	—	2	2	no	—
400	#106	—	2	4	no	—
401	#106	—	2	2	no	—
402	C₄⋊C₈	—	2	1	no	—
403	C₄⋊C₈	—	2	1	no	—
404	#103	—	2	4	no	—
405	#103	—	2	2	no	—
406	#102	—	2	2	no	—
407	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
408	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
409	#97	—	2	1	no	—
410	C₄×C₈	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	4	no	—
413	#95	C₂³×C₁₉	1	2	yes	—
414	C₁₉	#18438	1	1	yes	characteristic, direct product factor, Sylow
415	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
416	#41	—	8	2	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	4	2	no	—
422	C₂×Q₈	—	4	1	no	—
423	C₂×Q₈	—	4	1	no	—
424	C₂×Q₈	—	8	2	no	—
425	C₂×Q₈	—	8	2	no	—
426	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	4	2	no	—
434	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	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	—	2	1	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
466	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	8	4	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	2	2	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	4	2	no	—
487	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₂³	—	2	2	no	—
492	C₂³	—	2	1	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
497	Q₈	—	4	1	no	—
498	Q₈	—	4	2	no	—
499	Q₈	—	4	2	no	—
500	Q₈	—	4	2	no	—
501	Q₈	—	8	1	no	—
502	Q₈	—	8	2	no	—
503	Q₈	—	8	2	no	—
504	Q₈	—	8	2	no	—
505	D₄	—	4	1	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	8	1	no	—
509	D₄	—	8	2	no	—
510	D₄	—	8	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	4	no	—
527	C₂×C₄	—	8	2	no	—
528	C₂×C₄	—	8	2	no	—
529	C₂×C₄	—	8	2	no	—
530	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
531	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
532	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
533	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
536	C₈	—	4	2	no	—
537	C₈	—	4	2	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	8	4	no	—
547	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
548	C₂²	C₁₉×#577	1	2	yes	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	2	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	2	no	—
560	C₄	—	8	2	no	—
561	C₄	—	8	2	no	—
562	C₄	C₁₉×#455	1	2	yes	—
563	C₂	—	2	2	no	—
564	C₂	—	8	2	no	—
565	C₂	—	8	1	no	—
566	C₂	C₁₉×#3010	1	1	yes	characteristic
567	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
568	C₂	C₁₉×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3561	C₂
LCS	G ▷ C₂²×C₄ ▷ 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
2. C₁₉×#3238	C₂	semidirect
3. C₁₉×#3229	C₂	semidirect
4. C₁₉×#2640	C₂	semidirect
5. C₁₉×#1612	C₂	semidirect
6. C₁₉×#1608	C₂	semidirect
7. C₁₉×#1506	C₂	semidirect
8. C₁₉×#1500	C₂	semidirect
9. C₁₉×#1469	C₂	semidirect
206. #18438	C₁₉	direct (N × H)
255. #3238	C₂×C₁₉	semidirect
256. #3229	C₂×C₁₉	semidirect
257. #2640	C₂×C₁₉	semidirect
258. #1612	C₂×C₁₉	semidirect
259. #1608	C₂×C₁₉	semidirect
260. #1506	C₂×C₁₉	semidirect
261. #1500	C₂×C₁₉	semidirect
262. #1469	C₂×C₁₉	semidirect
414. C₁₉	#18438	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×#3561	2
C₁₉×#3238	2
C₁₉×#3229	2
C₁₉×#2640	2
C₁₉×#1612	2
C₁₉×#1608	2
C₁₉×#1506	2
C₁₉×#1500	2
C₁₉×#1469	2
#18438	19

Subgroups — C19×#18438 #18024397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18438 #18024397