Subgroups — C₁₉×#33790 #18039749

Order 4864.

606 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3175	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3155	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2250	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2249	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2243	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2240	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2211	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2210	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2207	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2206	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2189	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2187	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2186	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2184	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#2164	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#542	—	2	1	no	—
20	C₁₉×#535	—	2	1	no	—
21	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₉×D₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×D₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×D₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#496	—	2	1	no	—
31	C₁₉×#496	—	2	1	no	—
32	C₁₉×#495	C₂²	1	1	yes	characteristic
33	C₁₉×#495	C₂²	1	1	yes	characteristic
34	C₁₉×#495	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#493	C₂²	1	1	yes	characteristic
36	C₁₉×#493	C₂²	1	1	yes	characteristic
37	C₁₉×#489	—	2	1	no	—
38	C₁₉×#468	—	2	1	no	—
39	C₁₉×#467	C₂²	1	1	yes	characteristic
40	C₁₉×#466	C₂²	1	1	yes	characteristic
41	C₁₉×#440	—	2	1	no	—
42	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
43	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#405	C₂²	1	1	yes	characteristic
45	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#358	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#358	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#357	C₂²	1	1	yes	characteristic
50	C₁₉×#357	C₂²	1	1	yes	characteristic
51	C₁₉×#357	C₂²	1	1	yes	characteristic
52	C₁₉×#357	C₂²	1	1	yes	characteristic
53	C₁₉×#357	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#357	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
56	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₁₉×#346	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
59	C₂×#41×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
62	C₁₉×#135	—	4	1	no	—
63	C₁₉×#135	—	4	1	no	—
64	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×SD₁₆×C₁₉	—	2	1	no	—
67	C₂×SD₁₆×C₁₉	—	2	1	no	—
68	C₂×SD₁₆×C₁₉	—	2	1	no	—
69	C₂×SD₁₆×C₁₉	—	2	1	no	—
70	C₂×D₈×C₁₉	—	2	1	no	—
71	C₂×D₈×C₁₉	—	2	1	no	—
72	C₂×D₈×C₁₉	—	2	1	no	—
73	C₂×D₈×C₁₉	—	4	1	no	—
74	C₂×D₈×C₁₉	—	4	1	no	—
75	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₁₉×C₄⋊Q₈	—	2	1	no	—
82	C₁₉×#127	—	2	1	no	—
83	C₁₉×#127	—	2	1	no	—
84	C₁₉×#126	—	4	1	no	—
85	C₁₉×#124	—	2	1	no	—
86	C₁₉×#124	—	2	1	no	—
87	C₁₉×#124	—	2	1	no	—
88	C₁₉×#124	—	4	1	no	—
89	C₁₉×#123	—	4	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	1	no	—
91	C₁₉×C₂²⋊Q₈	—	4	1	no	—
92	C₁₉×#121	—	2	1	no	—
93	C₁₉×#121	—	4	1	no	—
94	C₁₉×#121	—	4	1	no	—
95	C₁₉×#120	—	4	1	no	—
96	C₁₉×#120	—	4	1	no	—
97	C₄×Q₈×C₁₉	—	2	1	no	—
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₁₉×#117	D₄	1	1	yes	characteristic
100	C₁₉×Q₃₂	—	4	1	no	—
101	C₁₉×SD₃₂	—	4	1	no	—
102	C₁₉×SD₃₂	—	4	1	no	—
103	C₁₉×SD₃₂	—	4	1	no	—
104	C₁₉×SD₃₂	—	4	1	no	—
105	C₁₉×D₁₆	—	4	1	no	—
106	C₁₉×D₁₆	—	4	1	no	—
107	C₁₉×D₁₆	—	4	1	no	—
108	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
112	C₁₉×#107	—	2	1	no	—
113	C₁₉×#107	C₂³	1	1	yes	characteristic
114	C₁₉×#107	C₂³	1	1	yes	characteristic
115	C₁₉×#103	—	2	1	no	—
116	C₁₉×#103	—	2	1	no	—
117	C₁₉×#102	—	2	1	no	—
118	C₁₉×#102	—	2	1	no	—
119	C₁₉×#97	D₄	1	1	yes	characteristic
120	C₁₉×#97	D₄	1	1	yes	characteristic
121	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
122	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
123	C₂⁴×C₁₉	—	4	1	no	—
124	#41×C₁₉	—	4	2	no	—
125	#41×C₁₉	—	4	2	no	—
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	2	1	no	—
128	C₂×Q₈×C₁₉	—	4	1	no	—
129	C₂×D₄×C₁₉	—	2	1	no	—
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	4	2	no	—
134	C₂×D₄×C₁₉	—	4	2	no	—
135	C₂×D₄×C₁₉	—	4	1	no	—
136	C₂×D₄×C₁₉	—	4	1	no	—
137	C₂×D₄×C₁₉	—	4	1	no	—
138	C₂×D₄×C₁₉	—	4	1	no	—
139	C₂×D₄×C₁₉	—	4	1	no	—
140	C₂×D₄×C₁₉	—	4	1	no	—
141	C₂×D₄×C₁₉	—	4	1	no	—
142	C₂²×C₄×C₁₉	—	4	1	no	—
143	C₂²×C₄×C₁₉	—	4	1	no	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	Q₁₆×C₁₉	—	2	1	no	—
146	Q₁₆×C₁₉	—	2	1	no	—
147	Q₁₆×C₁₉	—	2	1	no	—
148	Q₁₆×C₁₉	—	2	1	no	—
149	SD₁₆×C₁₉	—	4	2	no	—
150	SD₁₆×C₁₉	—	4	2	no	—
151	SD₁₆×C₁₉	—	4	2	no	—
152	SD₁₆×C₁₉	—	4	2	no	—
153	D₈×C₁₉	—	2	1	no	—
154	D₈×C₁₉	—	2	1	no	—
155	D₈×C₁₉	—	2	1	no	—
156	D₈×C₁₉	—	2	1	no	—
157	D₈×C₁₉	—	2	1	no	—
158	D₈×C₁₉	—	2	1	no	—
159	D₈×C₁₉	—	2	1	no	—
160	D₈×C₁₉	—	2	1	no	—
161	D₈×C₁₉	—	4	2	no	—
162	D₈×C₁₉	—	4	2	no	—
163	D₈×C₁₉	—	4	2	no	—
164	M₁₆×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	—	2	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	C₂⁴	1	1	yes	characteristic
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	4	1	no	—
174	C₄⋊C₄×C₁₉	—	4	1	no	—
175	C₄⋊C₄×C₁₉	—	4	1	no	—
176	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
177	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
178	C₂²⋊C₄×C₁₉	—	4	1	no	—
179	C₂²⋊C₄×C₁₉	—	4	1	no	—
180	C₂²⋊C₄×C₁₉	—	4	1	no	—
181	C₂²⋊C₄×C₁₉	—	4	1	no	—
182	C₂²⋊C₄×C₁₉	—	4	1	no	—
183	C₂²⋊C₄×C₁₉	—	4	1	no	—
184	C₂²⋊C₄×C₁₉	—	4	1	no	—
185	C₂²⋊C₄×C₁₉	—	4	1	no	—
186	C₂²⋊C₄×C₁₉	—	4	1	no	—
187	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
188	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
189	C₄²×C₁₉	—	4	1	no	—
190	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₁₆×C₁₉	—	2	1	no	—
193	C₁₆×C₁₉	—	2	1	no	—
194	C₁₆×C₁₉	—	2	1	no	—
195	C₁₆×C₁₉	—	2	1	no	—
196	#33790	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂³×C₁₉	—	4	1	no	—
198	C₂³×C₁₉	—	4	1	no	—
199	C₂³×C₁₉	—	4	1	no	—
200	C₂³×C₁₉	—	4	1	no	—
201	C₂³×C₁₉	—	8	2	no	—
202	C₂³×C₁₉	—	16	1	no	—
203	C₂³×C₁₉	—	16	1	no	—
204	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
205	Q₈×C₁₉	—	4	1	no	—
206	Q₈×C₁₉	—	4	1	no	—
207	Q₈×C₁₉	—	4	1	no	—
208	Q₈×C₁₉	—	4	1	no	—
209	Q₈×C₁₉	—	16	1	no	—
210	D₄×C₁₉	—	4	1	no	—
211	D₄×C₁₉	—	4	1	no	—
212	D₄×C₁₉	—	4	1	no	—
213	D₄×C₁₉	—	4	1	no	—
214	D₄×C₁₉	—	4	1	no	—
215	D₄×C₁₉	—	4	1	no	—
216	D₄×C₁₉	—	4	1	no	—
217	D₄×C₁₉	—	4	1	no	—
218	D₄×C₁₉	—	8	2	no	—
219	D₄×C₁₉	—	8	2	no	—
220	D₄×C₁₉	—	16	1	no	—
221	D₄×C₁₉	—	16	1	no	—
222	D₄×C₁₉	—	16	1	no	—
223	D₄×C₁₉	—	16	1	no	—
224	D₄×C₁₉	—	16	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	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	—	8	2	no	—
232	C₂×C₄×C₁₉	—	16	1	no	—
233	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
239	C₈×C₁₉	—	2	1	no	—
240	C₈×C₁₉	—	2	1	no	—
241	C₈×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
242	C₈×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
243	C₈×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
244	#3175	C₂×C₁₉	1	1	yes	characteristic, complemented
245	#3155	C₂×C₁₉	1	1	yes	characteristic, complemented
246	#2250	C₂×C₁₉	1	1	yes	characteristic, complemented
247	#2249	C₂×C₁₉	1	1	yes	characteristic, complemented
248	#2243	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#2240	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#2211	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#2210	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#2207	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#2206	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#2189	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#2187	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#2186	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#2184	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#2164	C₂×C₁₉	1	1	yes	characteristic, complemented
259	C₂²×C₁₉	—	2	1	no	—
260	C₂²×C₁₉	—	2	1	no	—
261	C₂²×C₁₉	—	2	1	no	—
262	C₂²×C₁₉	—	8	1	no	—
263	C₂²×C₁₉	—	8	1	no	—
264	C₂²×C₁₉	—	8	1	no	—
265	C₂²×C₁₉	—	8	1	no	—
266	C₂²×C₁₉	—	8	1	no	—
267	C₂²×C₁₉	—	8	1	no	—
268	C₂²×C₁₉	—	8	1	no	—
269	C₂²×C₁₉	—	8	1	no	—
270	C₂²×C₁₉	—	8	1	no	—
271	C₂²×C₁₉	—	8	1	no	—
272	C₂²×C₁₉	—	8	1	no	—
273	C₂²×C₁₉	—	8	1	no	—
274	C₂²×C₁₉	—	16	4	no	—
275	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	2	1	no	—
279	C₄×C₁₉	—	2	1	no	—
280	C₄×C₁₉	—	2	1	no	—
281	C₄×C₁₉	—	8	1	no	—
282	C₄×C₁₉	—	8	1	no	—
283	C₄×C₁₉	—	8	1	no	—
284	C₄×C₁₉	—	8	1	no	—
285	C₄×C₁₉	#535	1	1	yes	characteristic
286	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
287	C₂×AGL(1,ℤ/8)	—	2	1	no	—
288	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
289	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
290	#542	—	2	1	no	—
291	#535	—	2	1	no	—
292	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
293	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
296	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
297	C₂×D₁₆	C₂²×C₁₉	1	1	yes	characteristic
298	C₂×D₁₆	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×D₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
300	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
301	#496	—	2	1	no	—
302	#496	—	2	1	no	—
303	#495	C₂²×C₁₉	1	1	yes	characteristic
304	#495	C₂²×C₁₉	1	1	yes	characteristic
305	#495	C₂²×C₁₉	1	1	yes	characteristic, complemented
306	#493	C₂²×C₁₉	1	1	yes	characteristic
307	#493	C₂²×C₁₉	1	1	yes	characteristic
308	#489	—	2	1	no	—
309	#468	—	2	1	no	—
310	#467	C₂²×C₁₉	1	1	yes	characteristic
311	#466	C₂²×C₁₉	1	1	yes	characteristic
312	#440	—	2	1	no	—
313	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
314	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
315	#405	C₂²×C₁₉	1	1	yes	characteristic
316	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
317	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
318	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
319	#358	C₂²×C₁₉	1	1	yes	characteristic, complemented
320	#357	C₂²×C₁₉	1	1	yes	characteristic
321	#357	C₂²×C₁₉	1	1	yes	characteristic
322	#357	C₂²×C₁₉	1	1	yes	characteristic
323	#357	C₂²×C₁₉	1	1	yes	characteristic
324	#357	C₂²×C₁₉	1	1	yes	characteristic, complemented
325	#357	C₂²×C₁₉	1	1	yes	characteristic, complemented
326	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
327	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
328	#346	C₂²×C₁₉	1	1	yes	characteristic, complemented
329	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
330	C₂×C₁₉	—	4	1	no	—
331	C₂×C₁₉	—	16	1	no	—
332	C₂×C₁₉	—	16	1	no	—
333	C₂×C₁₉	—	16	1	no	—
334	C₂×C₁₉	—	16	1	no	—
335	C₂×C₁₉	#3205	1	1	yes	characteristic
336	C₂×C₁₉	#3415	1	1	yes	characteristic
337	C₂×C₁₉	#3416	1	1	yes	characteristic
338	C₂×#41	—	2	1	no	—
339	C₂²×D₄	—	2	1	no	—
340	AGL(1,ℤ/8)	—	4	4	no	—
341	#135	—	4	1	no	—
342	#135	—	4	1	no	—
343	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
344	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
345	C₂×SD₁₆	—	2	1	no	—
346	C₂×SD₁₆	—	2	1	no	—
347	C₂×SD₁₆	—	2	1	no	—
348	C₂×SD₁₆	—	2	1	no	—
349	C₂×D₈	—	2	1	no	—
350	C₂×D₈	—	2	1	no	—
351	C₂×D₈	—	2	1	no	—
352	C₂×D₈	—	4	1	no	—
353	C₂×D₈	—	4	1	no	—
354	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
355	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
356	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
357	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
358	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
359	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
360	C₄⋊Q₈	—	2	1	no	—
361	#127	—	2	1	no	—
362	#127	—	2	1	no	—
363	#126	—	4	1	no	—
364	#124	—	2	1	no	—
365	#124	—	2	1	no	—
366	#124	—	2	1	no	—
367	#124	—	4	1	no	—
368	#123	—	4	1	no	—
369	C₂²⋊Q₈	—	2	1	no	—
370	C₂²⋊Q₈	—	4	1	no	—
371	#121	—	2	1	no	—
372	#121	—	4	1	no	—
373	#121	—	4	1	no	—
374	#120	—	4	1	no	—
375	#120	—	4	1	no	—
376	C₄×Q₈	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	#117	D₄×C₁₉	1	1	yes	characteristic
379	Q₃₂	—	4	1	no	—
380	SD₃₂	—	4	1	no	—
381	SD₃₂	—	4	1	no	—
382	SD₃₂	—	4	1	no	—
383	SD₃₂	—	4	1	no	—
384	D₁₆	—	4	1	no	—
385	D₁₆	—	4	1	no	—
386	D₁₆	—	4	1	no	—
387	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
388	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
389	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
390	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
391	#107	—	2	1	no	—
392	#107	C₂³×C₁₉	1	1	yes	characteristic
393	#107	C₂³×C₁₉	1	1	yes	characteristic
394	#103	—	2	1	no	—
395	#103	—	2	1	no	—
396	#102	—	2	1	no	—
397	#102	—	2	1	no	—
398	#97	D₄×C₁₉	1	1	yes	characteristic
399	#97	D₄×C₁₉	1	1	yes	characteristic
400	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
401	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
402	C₁₉	#33790	1	1	yes	characteristic, direct product factor, Sylow
403	C₂⁴	—	4	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	—	4	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	4	1	no	—
416	C₂×D₄	—	4	1	no	—
417	C₂×D₄	—	4	1	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂²×C₄	—	4	1	no	—
423	C₂²×C₄	—	4	1	no	—
424	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
425	Q₁₆	—	2	1	no	—
426	Q₁₆	—	2	1	no	—
427	Q₁₆	—	2	1	no	—
428	Q₁₆	—	2	1	no	—
429	SD₁₆	—	4	2	no	—
430	SD₁₆	—	4	2	no	—
431	SD₁₆	—	4	2	no	—
432	SD₁₆	—	4	2	no	—
433	D₈	—	2	1	no	—
434	D₈	—	2	1	no	—
435	D₈	—	2	1	no	—
436	D₈	—	2	1	no	—
437	D₈	—	2	1	no	—
438	D₈	—	2	1	no	—
439	D₈	—	2	1	no	—
440	D₈	—	2	1	no	—
441	D₈	—	4	2	no	—
442	D₈	—	4	2	no	—
443	D₈	—	4	2	no	—
444	M₁₆	—	2	2	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	4	1	no	—
454	C₄⋊C₄	—	4	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
457	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
458	C₂²⋊C₄	—	4	1	no	—
459	C₂²⋊C₄	—	4	1	no	—
460	C₂²⋊C₄	—	4	1	no	—
461	C₂²⋊C₄	—	4	1	no	—
462	C₂²⋊C₄	—	4	1	no	—
463	C₂²⋊C₄	—	4	1	no	—
464	C₂²⋊C₄	—	4	1	no	—
465	C₂²⋊C₄	—	4	1	no	—
466	C₂²⋊C₄	—	4	1	no	—
467	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
468	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
469	C₄²	—	4	1	no	—
470	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
472	C₁₆	—	2	1	no	—
473	C₁₆	—	2	1	no	—
474	C₁₆	—	2	1	no	—
475	C₁₆	—	2	1	no	—
476	C₂³	—	4	1	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	8	2	no	—
481	C₂³	—	16	1	no	—
482	C₂³	—	16	1	no	—
483	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
484	Q₈	—	4	1	no	—
485	Q₈	—	4	1	no	—
486	Q₈	—	4	1	no	—
487	Q₈	—	4	1	no	—
488	Q₈	—	16	1	no	—
489	D₄	—	4	1	no	—
490	D₄	—	4	1	no	—
491	D₄	—	4	1	no	—
492	D₄	—	4	1	no	—
493	D₄	—	4	1	no	—
494	D₄	—	4	1	no	—
495	D₄	—	4	1	no	—
496	D₄	—	4	1	no	—
497	D₄	—	8	2	no	—
498	D₄	—	8	2	no	—
499	D₄	—	16	1	no	—
500	D₄	—	16	1	no	—
501	D₄	—	16	1	no	—
502	D₄	—	16	1	no	—
503	D₄	—	16	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	8	2	no	—
511	C₂×C₄	—	16	1	no	—
512	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
513	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
514	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
515	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
516	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
521	C₈	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
522	C₈	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	8	1	no	—
527	C₂²	—	8	1	no	—
528	C₂²	—	8	1	no	—
529	C₂²	—	8	1	no	—
530	C₂²	—	8	1	no	—
531	C₂²	—	8	1	no	—
532	C₂²	—	8	1	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	16	4	no	—
539	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	8	1	no	—
546	C₄	—	8	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	1	no	—
549	C₄	C₁₉×#535	1	1	yes	characteristic
550	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
551	C₂	—	4	1	no	—
552	C₂	—	16	1	no	—
553	C₂	—	16	1	no	—
554	C₂	—	16	1	no	—
555	C₂	—	16	1	no	—
556	C₂	C₁₉×#3205	1	1	yes	characteristic
557	C₂	C₁₉×#3415	1	1	yes	characteristic
558	C₂	C₁₉×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#117 ◁ C₁₉×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3175	C₂	semidirect
2. C₁₉×#3155	C₂	semidirect
3. C₁₉×#2250	C₂	semidirect
4. C₁₉×#2249	C₂	semidirect
5. C₁₉×#2243	C₂	semidirect
6. C₁₉×#2240	C₂	semidirect
7. C₁₉×#2211	C₂	semidirect
8. C₁₉×#2210	C₂	semidirect
9. C₁₉×#2207	C₂	semidirect
10. C₁₉×#2206	C₂	semidirect
11. C₁₉×#2189	C₂	semidirect
12. C₁₉×#2187	C₂	semidirect
13. C₁₉×#2186	C₂	semidirect
14. C₁₉×#2184	C₂	semidirect
15. C₁₉×#2164	C₂	semidirect
21. C₂×C₁₉×Q₃₂	C₂²	semidirect
24. C₂×C₁₉×SD₃₂	C₂²	semidirect
25. C₂×C₁₉×SD₃₂	C₂²	semidirect
28. C₂×C₁₉×D₁₆	C₂²	semidirect
29. C₁₉×#500	C₂²	semidirect
34. C₁₉×#495	C₂²	semidirect
42. C₄×Q₁₆×C₁₉	C₂²	semidirect
43. C₄×D₈×C₁₉	C₂²	semidirect
45. C₁₉×C₄⋊C₁₆	C₂²	semidirect
46. C₁₉×C₄⋊C₁₆	C₂²	semidirect
47. C₁₉×#358	C₂²	semidirect
48. C₁₉×#358	C₂²	semidirect
53. C₁₉×#357	C₂²	semidirect
54. C₁₉×#357	C₂²	semidirect
57. C₁₉×#346	C₂²	semidirect
58. C₄×C₁₆×C₁₉	C₂²	semidirect
196. #33790	C₁₉	direct (N × H)
244. #3175	C₂×C₁₉	semidirect
245. #3155	C₂×C₁₉	semidirect
246. #2250	C₂×C₁₉	semidirect
247. #2249	C₂×C₁₉	semidirect
248. #2243	C₂×C₁₉	semidirect
249. #2240	C₂×C₁₉	semidirect
250. #2211	C₂×C₁₉	semidirect
251. #2210	C₂×C₁₉	semidirect
252. #2207	C₂×C₁₉	semidirect
253. #2206	C₂×C₁₉	semidirect
254. #2189	C₂×C₁₉	semidirect
255. #2187	C₂×C₁₉	semidirect
256. #2186	C₂×C₁₉	semidirect
257. #2184	C₂×C₁₉	semidirect
258. #2164	C₂×C₁₉	semidirect
292. C₂×Q₃₂	C₂²×C₁₉	semidirect
295. C₂×SD₃₂	C₂²×C₁₉	semidirect
296. C₂×SD₃₂	C₂²×C₁₉	semidirect
299. C₂×D₁₆	C₂²×C₁₉	semidirect
300. #500	C₂²×C₁₉	semidirect
305. #495	C₂²×C₁₉	semidirect
313. C₄×Q₁₆	C₂²×C₁₉	semidirect
314. C₄×D₈	C₂²×C₁₉	semidirect
316. C₄⋊C₁₆	C₂²×C₁₉	semidirect
317. C₄⋊C₁₆	C₂²×C₁₉	semidirect
318. #358	C₂²×C₁₉	semidirect
319. #358	C₂²×C₁₉	semidirect
324. #357	C₂²×C₁₉	semidirect
325. #357	C₂²×C₁₉	semidirect
328. #346	C₂²×C₁₉	semidirect
329. C₄×C₁₆	C₂²×C₁₉	semidirect
402. C₁₉	#33790	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×#3175	2
C₁₉×#3155	2
C₁₉×#2250	2
C₁₉×#2249	2
C₁₉×#2243	2
C₁₉×#2240	2
C₁₉×#2211	2
C₁₉×#2210	2
C₁₉×#2207	2
C₁₉×#2206	2
C₁₉×#2189	2
C₁₉×#2187	2
C₁₉×#2186	2
C₁₉×#2184	2
C₁₉×#2164	2
#33790	19

Subgroups — C19×#33790 #18039749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33790 #18039749