Subgroups — C₁₉×#33526 #18039485

Order 4864.

1150 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#508	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3061	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2189	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2187	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2186	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2184	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2113	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×H(5,𝔽₂)	—	2	1	no	—
13	C₁₉×#576	—	2	4	no	—
14	C₁₉×#576	—	2	4	no	—
15	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
16	C₂×C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
17	C₂×C₁₉×#135	C₂²	1	2	yes	—
18	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₈×C₁₉	C₂²	1	2	yes	—
21	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
23	C₁₉×#537	—	2	1	no	—
24	C₁₉×#509	—	2	4	no	—
25	C₁₉×#508	—	2	4	no	—
26	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₉×SD₃₂	C₂²	1	2	yes	complemented
30	C₂×C₁₉×D₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₉×D₁₆	C₂²	1	2	yes	complemented
32	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#468	—	2	2	no	—
35	C₁₉×#467	C₂²	1	2	yes	complemented
36	C₁₉×#466	C₂²	1	2	yes	complemented
37	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#417	—	2	1	no	—
39	C₁₉×#358	C₂²	1	2	yes	complemented
40	C₁₉×#357	C₂²	1	2	yes	complemented
41	C₁₉×#357	C₂²	1	2	yes	complemented
42	C₁₉×#357	C₂²	1	2	yes	complemented
43	C₁₉×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
44	C₁₉×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
45	C₁₉×H(5,𝔽₂)	—	2	8	no	—
46	C₁₉×H(5,𝔽₂)	—	4	4	no	—
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	—	2	1	no	—
49	C₂×#41×C₁₉	—	2	1	no	—
50	C₂×#41×C₁₉	—	4	1	no	—
51	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₁₉	—	2	2	no	—
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	—	4	2	no	—
55	C₂²×D₄×C₁₉	—	4	1	no	—
56	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
57	C₁₉×AGL(1,ℤ/8)	—	2	16	no	—
58	C₁₉×#135	—	2	4	no	—
59	C₁₉×#135	—	2	4	no	—
60	C₁₉×#135	—	2	2	no	—
61	C₁₉×#135	—	2	2	no	—
62	C₁₉×#135	—	2	2	no	—
63	C₁₉×#135	D₄	1	4	yes	complemented
64	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×SD₁₆×C₁₉	—	2	2	no	—
67	C₂×SD₁₆×C₁₉	—	2	1	no	—
68	C₂×SD₁₆×C₁₉	—	2	1	no	—
69	C₂×D₈×C₁₉	—	2	4	no	—
70	C₂×D₈×C₁₉	—	2	4	no	—
71	C₂×D₈×C₁₉	—	2	2	no	—
72	C₂×D₈×C₁₉	—	2	1	no	—
73	C₂×D₈×C₁₉	—	2	2	no	—
74	C₂×D₈×C₁₉	D₄	1	4	yes	complemented
75	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×D₈×C₁₉	C₂³	1	2	yes	—
78	C₁₉×#131	—	2	2	no	—
79	C₁₉×#131	—	2	2	no	—
80	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
81	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
82	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
83	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	4	1	no	—
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#121	—	4	1	no	—
88	C₁₉×#121	—	4	2	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₁₉×Q₃₂	—	2	2	no	—
91	C₁₉×SD₃₂	—	2	2	no	—
92	C₁₉×SD₃₂	—	2	2	no	—
93	C₁₉×SD₃₂	—	2	4	no	—
94	C₁₉×D₁₆	—	2	2	no	—
95	C₁₉×D₁₆	—	2	4	no	—
96	C₁₉×M₃₂	—	2	2	no	—
97	C₂×C₁₆×C₁₉	—	2	2	no	—
98	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₁₆×C₁₉	C₂³	1	2	yes	—
101	C₁₉×#107	—	2	1	no	—
102	C₁₉×#107	C₂³	1	2	yes	—
103	C₁₉×#103	—	2	2	no	—
104	C₁₉×#102	—	2	2	no	—
105	C₂⁴×C₁₉	—	4	2	no	—
106	C₂⁴×C₁₉	—	4	1	no	—
107	#41×C₁₉	—	2	2	no	—
108	#41×C₁₉	—	2	2	no	—
109	#41×C₁₉	—	2	8	no	—
110	#41×C₁₉	—	2	4	no	—
111	#41×C₁₉	—	4	4	no	—
112	#41×C₁₉	—	4	8	no	—
113	#41×C₁₉	—	4	2	no	—
114	#41×C₁₉	—	4	2	no	—
115	#41×C₁₉	—	4	2	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
119	C₂×D₄×C₁₉	—	2	8	no	—
120	C₂×D₄×C₁₉	—	2	4	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	4	4	no	—
125	C₂×D₄×C₁₉	—	4	16	no	—
126	C₂×D₄×C₁₉	—	4	8	no	—
127	C₂×D₄×C₁₉	—	4	2	no	—
128	C₂×D₄×C₁₉	—	4	1	no	—
129	C₂×D₄×C₁₉	—	4	1	no	—
130	C₂×D₄×C₁₉	—	4	2	no	—
131	C₂×D₄×C₁₉	—	4	2	no	—
132	C₂×D₄×C₁₉	—	4	1	no	—
133	C₂×D₄×C₁₉	—	4	2	no	—
134	C₂×D₄×C₁₉	D₈	1	2	yes	—
135	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	—	4	2	no	—
137	C₂²×C₄×C₁₉	—	4	1	no	—
138	C₂²×C₄×C₁₉	—	4	1	no	—
139	C₂²×C₄×C₁₉	—	4	1	no	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	Q₁₆×C₁₉	—	2	1	no	—
143	Q₁₆×C₁₉	—	2	1	no	—
144	Q₁₆×C₁₉	—	2	1	no	—
145	Q₁₆×C₁₉	C₂×D₄	1	2	yes	—
146	SD₁₆×C₁₉	—	2	8	no	—
147	SD₁₆×C₁₉	—	2	4	no	—
148	SD₁₆×C₁₉	—	4	2	no	—
149	D₈×C₁₉	—	2	8	no	—
150	D₈×C₁₉	—	2	4	no	—
151	D₈×C₁₉	—	2	2	no	—
152	D₈×C₁₉	—	2	1	no	—
153	D₈×C₁₉	—	2	1	no	—
154	D₈×C₁₉	—	2	1	no	—
155	D₈×C₁₉	C₂×D₄	1	2	yes	—
156	D₈×C₁₉	C₂×D₄	1	4	yes	—
157	M₁₆×C₁₉	—	2	2	no	—
158	M₁₆×C₁₉	—	2	4	no	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	4	1	no	—
168	C₄⋊C₄×C₁₉	—	4	2	no	—
169	C₂²⋊C₄×C₁₉	—	4	2	no	—
170	C₂²⋊C₄×C₁₉	—	4	2	no	—
171	C₁₆×C₁₉	—	2	1	no	—
172	C₁₆×C₁₉	—	2	1	no	—
173	C₁₆×C₁₉	—	2	2	no	—
174	#33526	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂³×C₁₉	—	4	8	no	—
176	C₂³×C₁₉	—	4	2	no	—
177	C₂³×C₁₉	—	4	1	no	—
178	C₂³×C₁₉	—	4	4	no	—
179	C₂³×C₁₉	—	4	1	no	—
180	C₂³×C₁₉	—	16	1	no	—
181	C₂³×C₁₉	—	16	1	no	—
182	C₂³×C₁₉	—	16	2	no	—
183	C₂³×C₁₉	—	16	2	no	—
184	C₂³×C₁₉	C₂×D₈	1	2	yes	—
185	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
186	Q₈×C₁₉	—	2	2	no	—
187	Q₈×C₁₉	—	2	2	no	—
188	Q₈×C₁₉	—	4	1	no	—
189	Q₈×C₁₉	—	4	1	no	—
190	Q₈×C₁₉	—	4	1	no	—
191	D₄×C₁₉	—	2	4	no	—
192	D₄×C₁₉	—	2	2	no	—
193	D₄×C₁₉	—	2	4	no	—
194	D₄×C₁₉	—	2	2	no	—
195	D₄×C₁₉	—	4	8	no	—
196	D₄×C₁₉	—	4	8	no	—
197	D₄×C₁₉	—	4	4	no	—
198	D₄×C₁₉	—	4	1	no	—
199	D₄×C₁₉	—	4	1	no	—
200	D₄×C₁₉	—	4	2	no	—
201	D₄×C₁₉	—	4	1	no	—
202	D₄×C₁₉	—	4	4	no	—
203	D₄×C₁₉	—	8	2	no	—
204	D₄×C₁₉	—	16	2	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	4	8	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	4	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	8	2	no	—
213	C₂×C₄×C₁₉	—	16	1	no	—
214	C₂×C₄×C₁₉	#120	1	2	yes	—
215	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
216	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
217	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
218	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
219	C₈×C₁₉	—	2	2	no	—
220	C₈×C₁₉	#120	1	2	yes	—
221	C₈×C₁₉	C₂²×D₄	1	1	yes	characteristic
222	C₈×C₁₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×#576	C₂×C₁₉	1	1	yes	characteristic, complemented
224	C₂×#509	C₂×C₁₉	1	1	yes	characteristic, complemented
225	C₂×#508	C₂×C₁₉	1	1	yes	characteristic, complemented
226	#3061	C₂×C₁₉	1	1	yes	characteristic, complemented
227	#2189	C₂×C₁₉	1	2	yes	complemented
228	#2187	C₂×C₁₉	1	2	yes	complemented
229	#2186	C₂×C₁₉	1	2	yes	complemented
230	#2184	C₂×C₁₉	1	2	yes	complemented
231	#2139	C₂×C₁₉	1	1	yes	characteristic, complemented
232	C₂×#357	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#2113	C₂×C₁₉	1	1	yes	characteristic, complemented
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	2	2	no	—
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	—	2	2	no	—
239	C₂²×C₁₉	—	4	4	no	—
240	C₂²×C₁₉	—	4	2	no	—
241	C₂²×C₁₉	—	8	2	no	—
242	C₂²×C₁₉	—	8	1	no	—
243	C₂²×C₁₉	—	8	2	no	—
244	C₂²×C₁₉	—	8	1	no	—
245	C₂²×C₁₉	—	8	1	no	—
246	C₂²×C₁₉	—	8	1	no	—
247	C₂²×C₁₉	—	8	1	no	—
248	C₂²×C₁₉	—	16	4	no	—
249	C₂²×C₁₉	—	16	8	no	—
250	C₂²×C₁₉	#447	1	2	yes	—
251	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
252	C₄×C₁₉	—	2	2	no	—
253	C₄×C₁₉	—	4	2	no	—
254	C₄×C₁₉	—	8	2	no	—
255	C₄×C₁₉	—	8	1	no	—
256	C₄×C₁₉	#447	1	2	yes	—
257	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
258	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
259	C₂×H(5,𝔽₂)	—	2	1	no	—
260	#576	—	2	4	no	—
261	#576	—	2	4	no	—
262	C₂×AGL(1,ℤ/8)	—	2	1	no	—
263	C₂×AGL(1,ℤ/8)	—	2	2	no	—
264	C₂×#135	C₂²×C₁₉	1	2	yes	—
265	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic, complemented
267	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
268	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
269	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
270	#537	—	2	1	no	—
271	#509	—	2	4	no	—
272	#508	—	2	4	no	—
273	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
274	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
275	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
276	C₂×SD₃₂	C₂²×C₁₉	1	2	yes	complemented
277	C₂×D₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
278	C₂×D₁₆	C₂²×C₁₉	1	2	yes	complemented
279	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic, complemented
280	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
281	#468	—	2	2	no	—
282	#467	C₂²×C₁₉	1	2	yes	complemented
283	#466	C₂²×C₁₉	1	2	yes	complemented
284	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
285	#417	—	2	1	no	—
286	#358	C₂²×C₁₉	1	2	yes	complemented
287	#357	C₂²×C₁₉	1	2	yes	complemented
288	#357	C₂²×C₁₉	1	2	yes	complemented
289	#357	C₂²×C₁₉	1	2	yes	complemented
290	C₂²⋊C₁₆	C₂²×C₁₉	1	2	yes	complemented
291	C₂²⋊C₁₆	C₂²×C₁₉	1	2	yes	complemented
292	C₂×C₁₉	—	2	2	no	—
293	C₂×C₁₉	—	4	2	no	—
294	C₂×C₁₉	—	8	4	no	—
295	C₂×C₁₉	—	8	2	no	—
296	C₂×C₁₉	—	16	1	no	—
297	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
298	C₂×C₁₉	#3415	1	1	yes	characteristic
299	C₂×C₁₉	#3416	1	1	yes	characteristic
300	H(5,𝔽₂)	—	2	8	no	—
301	H(5,𝔽₂)	—	4	4	no	—
302	C₂×#41	—	2	2	no	—
303	C₂×#41	—	2	1	no	—
304	C₂×#41	—	2	1	no	—
305	C₂×#41	—	4	1	no	—
306	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
307	C₂²×D₄	—	2	2	no	—
308	C₂²×D₄	—	2	1	no	—
309	C₂²×D₄	—	4	2	no	—
310	C₂²×D₄	—	4	1	no	—
311	AGL(1,ℤ/8)	—	2	8	no	—
312	AGL(1,ℤ/8)	—	2	16	no	—
313	#135	—	2	4	no	—
314	#135	—	2	4	no	—
315	#135	—	2	2	no	—
316	#135	—	2	2	no	—
317	#135	—	2	2	no	—
318	#135	D₄×C₁₉	1	4	yes	complemented
319	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
320	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
321	C₂×SD₁₆	—	2	2	no	—
322	C₂×SD₁₆	—	2	1	no	—
323	C₂×SD₁₆	—	2	1	no	—
324	C₂×D₈	—	2	4	no	—
325	C₂×D₈	—	2	4	no	—
326	C₂×D₈	—	2	2	no	—
327	C₂×D₈	—	2	1	no	—
328	C₂×D₈	—	2	2	no	—
329	C₂×D₈	D₄×C₁₉	1	4	yes	complemented
330	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
331	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
332	C₂×D₈	C₂³×C₁₉	1	2	yes	—
333	#131	—	2	2	no	—
334	#131	—	2	2	no	—
335	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
336	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
337	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
338	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
339	C₂²⋊Q₈	—	2	2	no	—
340	C₂²⋊Q₈	—	4	1	no	—
341	#121	—	2	2	no	—
342	#121	—	4	1	no	—
343	#121	—	4	2	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	Q₃₂	—	2	2	no	—
346	SD₃₂	—	2	2	no	—
347	SD₃₂	—	2	2	no	—
348	SD₃₂	—	2	4	no	—
349	D₁₆	—	2	2	no	—
350	D₁₆	—	2	4	no	—
351	M₃₂	—	2	2	no	—
352	C₂×C₁₆	—	2	2	no	—
353	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
354	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
355	C₂×C₁₆	C₂³×C₁₉	1	2	yes	—
356	#107	—	2	1	no	—
357	#107	C₂³×C₁₉	1	2	yes	—
358	#103	—	2	2	no	—
359	#102	—	2	2	no	—
360	C₁₉	#33526	1	1	yes	characteristic, direct product factor, Sylow
361	C₂⁴	—	4	2	no	—
362	C₂⁴	—	4	1	no	—
363	#41	—	2	2	no	—
364	#41	—	2	2	no	—
365	#41	—	2	8	no	—
366	#41	—	2	4	no	—
367	#41	—	4	4	no	—
368	#41	—	4	8	no	—
369	#41	—	4	2	no	—
370	#41	—	4	2	no	—
371	#41	—	4	2	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	4	4	no	—
381	C₂×D₄	—	4	16	no	—
382	C₂×D₄	—	4	8	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	1	no	—
385	C₂×D₄	—	4	1	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	—	4	1	no	—
389	C₂×D₄	—	4	2	no	—
390	C₂×D₄	D₈×C₁₉	1	2	yes	—
391	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	—	4	1	no	—
396	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
398	Q₁₆	—	2	1	no	—
399	Q₁₆	—	2	1	no	—
400	Q₁₆	—	2	1	no	—
401	Q₁₆	C₂×D₄×C₁₉	1	2	yes	—
402	SD₁₆	—	2	8	no	—
403	SD₁₆	—	2	4	no	—
404	SD₁₆	—	4	2	no	—
405	D₈	—	2	8	no	—
406	D₈	—	2	4	no	—
407	D₈	—	2	2	no	—
408	D₈	—	2	1	no	—
409	D₈	—	2	1	no	—
410	D₈	—	2	1	no	—
411	D₈	C₂×D₄×C₁₉	1	2	yes	—
412	D₈	C₂×D₄×C₁₉	1	4	yes	—
413	M₁₆	—	2	2	no	—
414	M₁₆	—	2	4	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
418	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
420	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
421	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	4	1	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₂²⋊C₄	—	4	2	no	—
426	C₂²⋊C₄	—	4	2	no	—
427	C₁₆	—	2	1	no	—
428	C₁₆	—	2	1	no	—
429	C₁₆	—	2	2	no	—
430	C₂³	—	4	8	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	4	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	16	1	no	—
436	C₂³	—	16	1	no	—
437	C₂³	—	16	2	no	—
438	C₂³	—	16	2	no	—
439	C₂³	C₂×D₈×C₁₉	1	2	yes	—
440	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
441	Q₈	—	2	2	no	—
442	Q₈	—	2	2	no	—
443	Q₈	—	4	1	no	—
444	Q₈	—	4	1	no	—
445	Q₈	—	4	1	no	—
446	D₄	—	2	4	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	2	4	no	—
450	D₄	—	4	8	no	—
451	D₄	—	4	8	no	—
452	D₄	—	4	4	no	—
453	D₄	—	4	4	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	1	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	1	no	—
458	D₄	—	8	2	no	—
459	D₄	—	16	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	8	2	no	—
468	C₂×C₄	—	16	1	no	—
469	C₂×C₄	C₁₉×#120	1	2	yes	—
470	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
471	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
472	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	C₁₉×#120	1	2	yes	—
476	C₈	C₂²×D₄×C₁₉	1	1	yes	characteristic
477	C₈	C₂²×D₄×C₁₉	1	1	yes	characteristic
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	1	no	—
489	C₂²	—	8	1	no	—
490	C₂²	—	8	1	no	—
491	C₂²	—	8	1	no	—
492	C₂²	—	16	4	no	—
493	C₂²	—	16	8	no	—
494	C₂²	C₁₉×#447	1	2	yes	—
495	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
496	C₄	—	2	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	8	1	no	—
499	C₄	—	8	2	no	—
500	C₄	C₁₉×#447	1	2	yes	—
501	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
502	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
503	C₂	—	2	2	no	—
504	C₂	—	4	2	no	—
505	C₂	—	8	4	no	—
506	C₂	—	8	2	no	—
507	C₂	—	16	1	no	—
508	C₂	C₂×C₁₉×#447	1	1	yes	characteristic
509	C₂	C₁₉×#3415	1	1	yes	characteristic
510	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 ◁ C₂×#41×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#576	C₂	semidirect
2. C₂×C₁₉×#509	C₂	semidirect
3. C₂×C₁₉×#508	C₂	semidirect
4. C₁₉×#3061	C₂	semidirect
5. C₁₉×#2189	C₂	semidirect
6. C₁₉×#2187	C₂	semidirect
7. C₁₉×#2186	C₂	semidirect
8. C₁₉×#2184	C₂	semidirect
9. C₁₉×#2139	C₂	semidirect
10. C₂×C₁₉×#357	C₂	semidirect
11. C₁₉×#2113	C₂	semidirect
19. C₂×C₁₉×#135	C₂²	semidirect
26. C₂×C₁₉×Q₃₂	C₂²	semidirect
27. C₂×C₁₉×SD₃₂	C₂²	semidirect
28. C₂×C₁₉×SD₃₂	C₂²	semidirect
29. C₂×C₁₉×SD₃₂	C₂²	semidirect
30. C₂×C₁₉×D₁₆	C₂²	semidirect
31. C₂×C₁₉×D₁₆	C₂²	semidirect
32. C₂×C₁₉×M₃₂	C₂²	semidirect
33. C₂²×C₁₆×C₁₉	C₂²	semidirect
35. C₁₉×#467	C₂²	semidirect
36. C₁₉×#466	C₂²	semidirect
37. C₂×C₁₉×#107	C₂²	semidirect
39. C₁₉×#358	C₂²	semidirect
40. C₁₉×#357	C₂²	semidirect
41. C₁₉×#357	C₂²	semidirect
42. C₁₉×#357	C₂²	semidirect
43. C₁₉×C₂²⋊C₁₆	C₂²	semidirect
44. C₁₉×C₂²⋊C₁₆	C₂²	semidirect
63. C₁₉×#135	D₄	semidirect
74. C₂×D₈×C₁₉	D₄	semidirect
174. #33526	C₁₉	direct (N × H)
223. C₂×#576	C₂×C₁₉	semidirect
224. C₂×#509	C₂×C₁₉	semidirect
225. C₂×#508	C₂×C₁₉	semidirect
226. #3061	C₂×C₁₉	semidirect
227. #2189	C₂×C₁₉	semidirect
228. #2187	C₂×C₁₉	semidirect
229. #2186	C₂×C₁₉	semidirect
230. #2184	C₂×C₁₉	semidirect
231. #2139	C₂×C₁₉	semidirect
232. C₂×#357	C₂×C₁₉	semidirect
233. #2113	C₂×C₁₉	semidirect
266. C₂×#135	C₂²×C₁₉	semidirect
273. C₂×Q₃₂	C₂²×C₁₉	semidirect
274. C₂×SD₃₂	C₂²×C₁₉	semidirect
275. C₂×SD₃₂	C₂²×C₁₉	semidirect
276. C₂×SD₃₂	C₂²×C₁₉	semidirect
277. C₂×D₁₆	C₂²×C₁₉	semidirect
278. C₂×D₁₆	C₂²×C₁₉	semidirect
279. C₂×M₃₂	C₂²×C₁₉	semidirect
280. C₂²×C₁₆	C₂²×C₁₉	semidirect
282. #467	C₂²×C₁₉	semidirect
283. #466	C₂²×C₁₉	semidirect
284. C₂×#107	C₂²×C₁₉	semidirect
286. #358	C₂²×C₁₉	semidirect
287. #357	C₂²×C₁₉	semidirect
288. #357	C₂²×C₁₉	semidirect
289. #357	C₂²×C₁₉	semidirect
290. C₂²⋊C₁₆	C₂²×C₁₉	semidirect
291. C₂²⋊C₁₆	C₂²×C₁₉	semidirect
318. #135	D₄×C₁₉	semidirect
329. C₂×D₈	D₄×C₁₉	semidirect
360. C₁₉	#33526	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×#576	2
C₂×C₁₉×#509	2
C₂×C₁₉×#508	2
C₁₉×#3061	2
C₁₉×#2189	2
C₁₉×#2187	2
C₁₉×#2186	2
C₁₉×#2184	2
C₁₉×#2139	2
C₂×C₁₉×#357	2
C₁₉×#2113	2
#33526	19

Subgroups — C19×#33526 #18039485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33526 #18039485