Subgroups — C₁₉×#18993 #18024952

Order 4864.

1012 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#562	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3234	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3213	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3153	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1661	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1656	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1533	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1528	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1527	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#137	—	2	1	no	—
11	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
12	C₁₉×#562	—	2	2	no	—
13	C₁₉×#562	—	2	2	no	—
14	C₁₉×#562	—	2	2	no	—
15	C₁₉×#562	C₂²	1	4	yes	—
16	C₁₉×#532	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#123	—	2	1	no	—
21	C₂×C₁₉×#123	—	2	1	no	—
22	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
23	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₁₉×#121	—	2	1	no	—
25	C₂×C₁₉×#121	—	2	1	no	—
26	C₁₉×#501	C₂²	1	2	yes	complemented
27	C₁₉×#497	C₂²	1	2	yes	complemented
28	C₁₉×#496	C₂²	1	2	yes	complemented
29	C₁₉×#496	C₂²	1	2	yes	complemented
30	C₁₉×#495	—	2	2	no	—
31	C₁₉×#490	C₂²	1	2	yes	complemented
32	C₁₉×#489	C₂²	1	2	yes	complemented
33	C₁₉×#481	—	2	1	no	—
34	C₁₉×#480	—	2	1	no	—
35	C₁₉×#478	—	2	2	no	—
36	C₁₉×#463	—	2	2	no	—
37	C₁₉×#448	—	2	1	no	—
38	C₁₉×#447	—	2	1	no	—
39	C₁₉×#432	C₂²	1	1	yes	characteristic
40	C₁₉×#432	C₂²	1	1	yes	characteristic
41	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
42	C₁₉×#330	C₂²	1	4	yes	complemented
43	C₁₉×#329	C₂²	1	4	yes	complemented
44	C₁₉×#329	C₂²	1	4	yes	complemented
45	C₂×#41×C₁₉	—	2	1	no	—
46	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂³×C₄×C₁₉	—	2	1	no	—
54	C₁₉×#137	—	4	4	no	—
55	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
56	C₂×Q₁₆×C₁₉	—	2	2	no	—
57	C₂×SD₁₆×C₁₉	—	2	2	no	—
58	C₂×SD₁₆×C₁₉	—	2	2	no	—
59	C₂×SD₁₆×C₁₉	—	2	2	no	—
60	C₂×D₈×C₁₉	—	2	2	no	—
61	C₂×D₈×C₁₉	—	2	2	no	—
62	C₂×M₁₆×C₁₉	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₉×#127	C₂³	1	1	yes	characteristic
65	C₁₉×#125	—	2	1	no	—
66	C₁₉×#125	—	2	1	no	—
67	C₁₉×#125	D₄	1	2	yes	—
68	C₁₉×#125	C₂³	1	2	yes	—
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	—	2	1	no	—
74	C₁₉×#124	D₄	1	2	yes	—
75	C₁₉×#124	D₄	1	2	yes	—
76	C₁₉×#124	C₂³	1	2	yes	—
77	C₁₉×#124	C₂³	1	2	yes	—
78	C₁₉×#123	—	2	4	no	—
79	C₁₉×#123	—	2	4	no	—
80	C₁₉×#123	—	2	4	no	—
81	C₁₉×#123	—	2	4	no	—
82	C₁₉×C₂²⋊Q₈	—	2	4	no	—
83	C₁₉×C₂²⋊Q₈	—	2	4	no	—
84	C₁₉×C₂²⋊Q₈	—	2	4	no	—
85	C₁₉×C₂²⋊Q₈	—	2	4	no	—
86	C₁₉×#121	—	2	4	no	—
87	C₁₉×#121	—	2	4	no	—
88	C₁₉×#121	—	2	4	no	—
89	C₁₉×#121	—	2	4	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	1	no	—
92	C₄×D₄×C₁₉	—	2	1	no	—
93	C₄×D₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
107	C₁₉×#107	—	2	2	no	—
108	C₁₉×#106	—	2	2	no	—
109	C₁₉×C₄⋊C₈	—	2	1	no	—
110	C₁₉×C₄⋊C₈	—	2	1	no	—
111	C₁₉×#103	—	2	2	no	—
112	C₁₉×#102	—	2	2	no	—
113	C₁₉×#102	—	2	2	no	—
114	C₁₉×#102	—	2	2	no	—
115	C₁₉×C₂²⋊C₈	—	2	1	no	—
116	C₁₉×C₂²⋊C₈	—	2	1	no	—
117	C₁₉×#97	C₂³	1	2	yes	—
118	C₁₉×#97	C₂³	1	2	yes	—
119	C₁₉×#97	C₂³	1	2	yes	—
120	C₄×C₈×C₁₉	—	2	1	no	—
121	C₂⁴×C₁₉	—	2	1	no	—
122	C₂⁴×C₁₉	—	2	1	no	—
123	#41×C₁₉	—	4	2	no	—
124	#41×C₁₉	—	4	2	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	2	1	no	—
128	C₂×Q₈×C₁₉	—	4	2	no	—
129	C₂×Q₈×C₁₉	—	8	1	no	—
130	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
131	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
132	C₂×D₄×C₁₉	—	2	4	no	—
133	C₂×D₄×C₁₉	—	2	4	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	—	2	1	no	—
139	C₂×D₄×C₁₉	—	4	2	no	—
140	C₂×D₄×C₁₉	—	4	1	no	—
141	C₂×D₄×C₁₉	—	8	1	no	—
142	C₂×D₄×C₁₉	—	8	2	no	—
143	C₂×D₄×C₁₉	—	8	2	no	—
144	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	4	no	—
151	C₂²×C₄×C₁₉	—	2	4	no	—
152	C₂²×C₄×C₁₉	—	4	1	no	—
153	C₂²×C₄×C₁₉	—	8	2	no	—
154	C₂²×C₄×C₁₉	—	8	2	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	C₂×D₄	1	1	yes	characteristic
158	Q₁₆×C₁₉	—	4	4	no	—
159	SD₁₆×C₁₉	—	4	4	no	—
160	SD₁₆×C₁₉	—	4	4	no	—
161	SD₁₆×C₁₉	—	8	2	no	—
162	D₈×C₁₉	—	4	4	no	—
163	D₈×C₁₉	—	8	2	no	—
164	M₁₆×C₁₉	—	2	4	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₂×C₈×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	4	no	—
169	C₄⋊C₄×C₁₉	—	2	4	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	1	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	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
179	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
180	C₂²⋊C₄×C₁₉	—	2	4	no	—
181	C₂²⋊C₄×C₁₉	—	2	4	no	—
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	2	no	—
188	C₂²⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	4	1	no	—
191	C₂²⋊C₄×C₁₉	—	4	1	no	—
192	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
196	#18993	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂³×C₁₉	—	2	2	no	—
198	C₂³×C₁₉	—	2	2	no	—
199	C₂³×C₁₉	—	4	2	no	—
200	C₂³×C₁₉	—	4	2	no	—
201	C₂³×C₁₉	—	4	2	no	—
202	C₂³×C₁₉	—	4	2	no	—
203	C₂³×C₁₉	—	4	2	no	—
204	C₂³×C₁₉	—	4	2	no	—
205	C₂³×C₁₉	—	4	1	no	—
206	C₂³×C₁₉	#120	1	1	yes	characteristic
207	Q₈×C₁₉	—	4	2	no	—
208	Q₈×C₁₉	—	4	2	no	—
209	Q₈×C₁₉	—	4	1	no	—
210	Q₈×C₁₉	—	4	1	no	—
211	Q₈×C₁₉	—	8	1	no	—
212	Q₈×C₁₉	—	8	1	no	—
213	D₄×C₁₉	—	4	2	no	—
214	D₄×C₁₉	—	4	2	no	—
215	D₄×C₁₉	—	4	1	no	—
216	D₄×C₁₉	—	4	2	no	—
217	D₄×C₁₉	—	4	1	no	—
218	D₄×C₁₉	—	4	2	no	—
219	D₄×C₁₉	—	8	1	no	—
220	D₄×C₁₉	—	8	1	no	—
221	D₄×C₁₉	—	8	4	no	—
222	D₄×C₁₉	—	8	4	no	—
223	D₄×C₁₉	—	8	2	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	8	2	no	—
237	C₂×C₄×C₁₉	—	8	4	no	—
238	C₂×C₄×C₁₉	—	8	4	no	—
239	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
245	C₈×C₁₉	—	2	4	no	—
246	C₈×C₁₉	—	4	2	no	—
247	C₈×C₁₉	—	4	2	no	—
248	C₂×#562	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#3234	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#3213	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#3153	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#1661	C₂×C₁₉	1	4	yes	complemented
253	#1656	C₂×C₁₉	1	4	yes	complemented
254	#1533	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#1528	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#1527	C₂×C₁₉	1	1	yes	characteristic, complemented
257	C₂²×C₁₉	—	2	1	no	—
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	—	4	2	no	—
260	C₂²×C₁₉	—	4	2	no	—
261	C₂²×C₁₉	—	4	2	no	—
262	C₂²×C₁₉	—	4	2	no	—
263	C₂²×C₁₉	—	4	2	no	—
264	C₂²×C₁₉	—	4	2	no	—
265	C₂²×C₁₉	—	8	4	no	—
266	C₂²×C₁₉	—	8	4	no	—
267	C₂²×C₁₉	—	8	1	no	—
268	C₂²×C₁₉	—	8	1	no	—
269	C₂²×C₁₉	—	8	1	no	—
270	C₂²×C₁₉	#453	1	2	yes	—
271	C₂²×C₁₉	C₂×#120	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	—	2	1	no	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	4	2	no	—
279	C₄×C₁₉	—	4	2	no	—
280	C₄×C₁₉	—	4	2	no	—
281	C₄×C₁₉	—	4	2	no	—
282	C₄×C₁₉	—	8	1	no	—
283	C₂×#137	—	2	1	no	—
284	C₂×AGL(1,ℤ/8)	—	2	1	no	—
285	#562	—	2	2	no	—
286	#562	—	2	2	no	—
287	#562	—	2	2	no	—
288	#562	C₂²×C₁₉	1	4	yes	—
289	#532	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
291	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
292	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×#123	—	2	1	no	—
294	C₂×#123	—	2	1	no	—
295	C₂×C₂²⋊Q₈	—	2	1	no	—
296	C₂×C₂²⋊Q₈	—	2	1	no	—
297	C₂×#121	—	2	1	no	—
298	C₂×#121	—	2	1	no	—
299	#501	C₂²×C₁₉	1	2	yes	complemented
300	#497	C₂²×C₁₉	1	2	yes	complemented
301	#496	C₂²×C₁₉	1	2	yes	complemented
302	#496	C₂²×C₁₉	1	2	yes	complemented
303	#495	—	2	2	no	—
304	#490	C₂²×C₁₉	1	2	yes	complemented
305	#489	C₂²×C₁₉	1	2	yes	complemented
306	#481	—	2	1	no	—
307	#480	—	2	1	no	—
308	#478	—	2	2	no	—
309	#463	—	2	2	no	—
310	#448	—	2	1	no	—
311	#447	—	2	1	no	—
312	#432	C₂²×C₁₉	1	1	yes	characteristic
313	#432	C₂²×C₁₉	1	1	yes	characteristic
314	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
315	#330	C₂²×C₁₉	1	4	yes	complemented
316	#329	C₂²×C₁₉	1	4	yes	complemented
317	#329	C₂²×C₁₉	1	4	yes	complemented
318	C₂×C₁₉	—	2	2	no	—
319	C₂×C₁₉	—	8	2	no	—
320	C₂×C₁₉	—	8	2	no	—
321	C₂×C₁₉	—	16	1	no	—
322	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
323	C₂×C₁₉	#3019	1	1	yes	characteristic
324	C₂×C₁₉	#3020	1	1	yes	characteristic
325	C₂×#41	—	2	1	no	—
326	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
327	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
331	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	—	2	1	no	—
334	#137	—	4	4	no	—
335	AGL(1,ℤ/8)	—	4	4	no	—
336	C₂×Q₁₆	—	2	2	no	—
337	C₂×SD₁₆	—	2	2	no	—
338	C₂×SD₁₆	—	2	2	no	—
339	C₂×SD₁₆	—	2	2	no	—
340	C₂×D₈	—	2	2	no	—
341	C₂×D₈	—	2	2	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
344	#127	C₂³×C₁₉	1	1	yes	characteristic
345	#125	—	2	1	no	—
346	#125	—	2	1	no	—
347	#125	D₄×C₁₉	1	2	yes	—
348	#125	C₂³×C₁₉	1	2	yes	—
349	#124	—	2	1	no	—
350	#124	—	2	1	no	—
351	#124	—	2	1	no	—
352	#124	—	2	1	no	—
353	#124	—	2	1	no	—
354	#124	D₄×C₁₉	1	2	yes	—
355	#124	D₄×C₁₉	1	2	yes	—
356	#124	C₂³×C₁₉	1	2	yes	—
357	#124	C₂³×C₁₉	1	2	yes	—
358	#123	—	2	4	no	—
359	#123	—	2	4	no	—
360	#123	—	2	4	no	—
361	#123	—	2	4	no	—
362	C₂²⋊Q₈	—	2	4	no	—
363	C₂²⋊Q₈	—	2	4	no	—
364	C₂²⋊Q₈	—	2	4	no	—
365	C₂²⋊Q₈	—	2	4	no	—
366	#121	—	2	4	no	—
367	#121	—	2	4	no	—
368	#121	—	2	4	no	—
369	#121	—	2	4	no	—
370	#121	—	2	1	no	—
371	#121	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
379	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
387	#107	—	2	2	no	—
388	#106	—	2	2	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	1	no	—
391	#103	—	2	2	no	—
392	#102	—	2	2	no	—
393	#102	—	2	2	no	—
394	#102	—	2	2	no	—
395	C₂²⋊C₈	—	2	1	no	—
396	C₂²⋊C₈	—	2	1	no	—
397	#97	C₂³×C₁₉	1	2	yes	—
398	#97	C₂³×C₁₉	1	2	yes	—
399	#97	C₂³×C₁₉	1	2	yes	—
400	C₄×C₈	—	2	1	no	—
401	C₁₉	#18993	1	1	yes	characteristic, direct product factor, Sylow
402	C₂⁴	—	2	1	no	—
403	C₂⁴	—	2	1	no	—
404	#41	—	4	2	no	—
405	#41	—	4	2	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	4	2	no	—
410	C₂×Q₈	—	8	1	no	—
411	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
412	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	—	8	1	no	—
423	C₂×D₄	—	8	2	no	—
424	C₂×D₄	—	8	2	no	—
425	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
426	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	4	1	no	—
434	C₂²×C₄	—	8	2	no	—
435	C₂²×C₄	—	8	2	no	—
436	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	Q₁₆	—	4	4	no	—
440	SD₁₆	—	4	4	no	—
441	SD₁₆	—	4	4	no	—
442	SD₁₆	—	8	2	no	—
443	D₈	—	4	4	no	—
444	D₈	—	8	2	no	—
445	M₁₆	—	2	4	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
460	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
461	C₂²⋊C₄	—	2	4	no	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
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	—	4	1	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	1	no	—
486	C₂³	C₁₉×#120	1	1	yes	characteristic
487	Q₈	—	4	2	no	—
488	Q₈	—	4	2	no	—
489	Q₈	—	4	1	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	8	1	no	—
492	Q₈	—	8	1	no	—
493	D₄	—	4	2	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	1	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	1	no	—
498	D₄	—	4	2	no	—
499	D₄	—	8	1	no	—
500	D₄	—	8	1	no	—
501	D₄	—	8	4	no	—
502	D₄	—	8	4	no	—
503	D₄	—	8	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	8	2	no	—
517	C₂×C₄	—	8	4	no	—
518	C₂×C₄	—	8	4	no	—
519	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
520	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
521	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
525	C₈	—	2	4	no	—
526	C₈	—	4	2	no	—
527	C₈	—	4	2	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	8	4	no	—
537	C₂²	—	8	4	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	—	8	1	no	—
541	C₂²	C₁₉×#453	1	2	yes	—
542	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	2	no	—
552	C₄	—	4	2	no	—
553	C₄	—	8	1	no	—
554	C₂	—	2	2	no	—
555	C₂	—	8	2	no	—
556	C₂	—	8	2	no	—
557	C₂	—	16	1	no	—
558	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
559	C₂	C₁₉×#3019	1	1	yes	characteristic
560	C₂	C₁₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
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. C₂×C₁₉×#562	C₂	semidirect
2. C₁₉×#3234	C₂	semidirect
3. C₁₉×#3213	C₂	semidirect
4. C₁₉×#3153	C₂	semidirect
5. C₁₉×#1661	C₂	semidirect
6. C₁₉×#1656	C₂	semidirect
7. C₁₉×#1533	C₂	semidirect
8. C₁₉×#1528	C₂	semidirect
9. C₁₉×#1527	C₂	semidirect
26. C₁₉×#501	C₂²	semidirect
27. C₁₉×#497	C₂²	semidirect
28. C₁₉×#496	C₂²	semidirect
29. C₁₉×#496	C₂²	semidirect
31. C₁₉×#490	C₂²	semidirect
32. C₁₉×#489	C₂²	semidirect
42. C₁₉×#330	C₂²	semidirect
43. C₁₉×#329	C₂²	semidirect
44. C₁₉×#329	C₂²	semidirect
196. #18993	C₁₉	direct (N × H)
248. C₂×#562	C₂×C₁₉	semidirect
249. #3234	C₂×C₁₉	semidirect
250. #3213	C₂×C₁₉	semidirect
251. #3153	C₂×C₁₉	semidirect
252. #1661	C₂×C₁₉	semidirect
253. #1656	C₂×C₁₉	semidirect
254. #1533	C₂×C₁₉	semidirect
255. #1528	C₂×C₁₉	semidirect
256. #1527	C₂×C₁₉	semidirect
299. #501	C₂²×C₁₉	semidirect
300. #497	C₂²×C₁₉	semidirect
301. #496	C₂²×C₁₉	semidirect
302. #496	C₂²×C₁₉	semidirect
304. #490	C₂²×C₁₉	semidirect
305. #489	C₂²×C₁₉	semidirect
315. #330	C₂²×C₁₉	semidirect
316. #329	C₂²×C₁₉	semidirect
317. #329	C₂²×C₁₉	semidirect
401. C₁₉	#18993	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#562	2
C₁₉×#3234	2
C₁₉×#3213	2
C₁₉×#3153	2
C₁₉×#1661	2
C₁₉×#1656	2
C₁₉×#1533	2
C₁₉×#1528	2
C₁₉×#1527	2
#18993	19

Subgroups — C19×#18993 #18024952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18993 #18024952