Subgroups — C₁₉×#18662 #18024621

Order 4864.

1260 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3245	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3036	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1647	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1639	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1625	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1619	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1492	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×H(5,𝔽₂)	—	2	1	no	—
13	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
14	C₁₉×#547	—	2	1	no	—
15	C₁₉×#547	C₂²	1	2	yes	—
16	C₁₉×#546	—	2	2	no	—
17	C₁₉×#546	—	2	2	no	—
18	D₄²×C₁₉	—	2	1	no	—
19	D₄²×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#537	—	2	1	no	—
21	C₁₉×#534	—	2	2	no	—
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₁₉×#532	C₂²	1	1	yes	characteristic
24	C₁₉×#532	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₉×#121	—	2	2	no	—
26	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#500	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#493	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#486	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#474	—	2	1	no	—
32	C₁₉×#474	C₂²	1	2	yes	complemented
33	C₁₉×#466	—	2	2	no	—
34	C₁₉×#466	—	2	2	no	—
35	C₁₉×#463	—	2	2	no	—
36	C₁₉×#461	C₂²	1	2	yes	complemented
37	C₁₉×#459	—	2	1	no	—
38	C₁₉×#459	C₂²	1	2	yes	complemented
39	C₁₉×#459	C₂²	1	2	yes	complemented
40	C₄×D₈×C₁₉	—	2	2	no	—
41	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#417	—	2	1	no	—
44	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#332	C₂²	1	2	yes	complemented
46	C₁₉×#331	C₂²	1	2	yes	complemented
47	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
48	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
49	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
50	C₁₉×D₄⋊C₈	C₂²	1	2	yes	complemented
51	C₁₉×H(5,𝔽₂)	—	4	4	no	—
52	C₁₉×H(5,𝔽₂)	—	4	4	no	—
53	C₂×#41×C₁₉	—	2	2	no	—
54	C₂×#41×C₁₉	—	2	2	no	—
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂×#41×C₁₉	—	2	1	no	—
58	C₂²×D₄×C₁₉	—	2	4	no	—
59	C₂²×D₄×C₁₉	—	2	2	no	—
60	C₂²×D₄×C₁₉	—	2	2	no	—
61	C₂²×D₄×C₁₉	—	2	2	no	—
62	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
65	C₂×SD₁₆×C₁₉	—	2	2	no	—
66	C₂×D₈×C₁₉	—	2	2	no	—
67	C₂×D₈×C₁₉	—	2	2	no	—
68	C₂×D₈×C₁₉	—	2	2	no	—
69	C₂×M₁₆×C₁₉	—	2	1	no	—
70	C₂²×C₈×C₁₉	—	2	1	no	—
71	C₂²×C₈×C₁₉	—	2	1	no	—
72	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
73	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
74	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
75	C₁₉×#127	D₄	1	1	yes	characteristic
76	C₁₉×#127	C₂³	1	1	yes	characteristic
77	C₁₉×#127	C₂³	1	1	yes	characteristic
78	C₁₉×#124	—	2	1	no	—
79	C₁₉×#124	—	2	1	no	—
80	C₁₉×#124	—	2	1	no	—
81	C₁₉×#123	—	2	4	no	—
82	C₁₉×#123	—	2	4	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×#121	—	2	4	no	—
86	C₁₉×#121	—	2	4	no	—
87	C₁₉×#121	—	2	2	no	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	—	2	1	no	—
90	C₁₉×#121	—	2	1	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	—	2	1	no	—
94	C₁₉×#121	—	2	1	no	—
95	C₁₉×#121	D₄	1	2	yes	—
96	C₁₉×#121	D₄	1	2	yes	—
97	C₁₉×#120	—	2	4	no	—
98	C₁₉×#120	—	2	4	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	2	1	no	—
101	C₄×D₄×C₁₉	—	2	1	no	—
102	C₄×D₄×C₁₉	—	2	1	no	—
103	C₄×D₄×C₁₉	—	2	1	no	—
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	D₄	1	2	yes	—
106	C₄×D₄×C₁₉	D₄	1	2	yes	—
107	C₄×D₄×C₁₉	C₂³	1	2	yes	—
108	C₄×D₄×C₁₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
110	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₁₉×#107	—	2	2	no	—
115	C₁₉×#107	—	2	2	no	—
116	C₁₉×C₄⋊C₈	—	2	1	no	—
117	C₁₉×C₄⋊C₈	—	2	1	no	—
118	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
119	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
120	C₁₉×#103	—	2	2	no	—
121	C₁₉×#102	—	2	2	no	—
122	C₁₉×#102	—	2	2	no	—
123	C₁₉×#102	—	2	2	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×#102	—	2	2	no	—
126	C₄×C₈×C₁₉	—	2	1	no	—
127	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
128	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
129	C₂⁴×C₁₉	—	2	1	no	—
130	C₂⁴×C₁₉	—	2	4	no	—
131	#41×C₁₉	—	4	4	no	—
132	#41×C₁₉	—	4	8	no	—
133	#41×C₁₉	—	4	4	no	—
134	#41×C₁₉	—	4	2	no	—
135	#41×C₁₉	—	4	2	no	—
136	#41×C₁₉	—	4	2	no	—
137	#41×C₁₉	—	4	2	no	—
138	#41×C₁₉	—	4	2	no	—
139	#41×C₁₉	—	4	2	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	4	no	—
144	C₂×D₄×C₁₉	—	2	4	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	2	no	—
147	C₂×D₄×C₁₉	—	2	4	no	—
148	C₂×D₄×C₁₉	—	2	1	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	2	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	1	no	—
157	C₂×D₄×C₁₉	—	4	4	no	—
158	C₂×D₄×C₁₉	—	4	8	no	—
159	C₂×D₄×C₁₉	—	4	16	no	—
160	C₂×D₄×C₁₉	—	4	4	no	—
161	C₂×D₄×C₁₉	—	4	1	no	—
162	C₂×D₄×C₁₉	—	8	2	no	—
163	C₂×D₄×C₁₉	—	8	2	no	—
164	C₂×D₄×C₁₉	D₈	1	4	yes	complemented
165	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
166	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₉	—	2	4	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	2	no	—
171	C₂²×C₄×C₁₉	—	2	2	no	—
172	C₂²×C₄×C₁₉	—	2	2	no	—
173	C₂²×C₄×C₁₉	—	2	2	no	—
174	C₂²×C₄×C₁₉	—	4	1	no	—
175	C₂²×C₄×C₁₉	—	8	1	no	—
176	C₂²×C₄×C₁₉	—	8	1	no	—
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
180	SD₁₆×C₁₉	—	4	4	no	—
181	D₈×C₁₉	—	4	4	no	—
182	D₈×C₁₉	—	4	4	no	—
183	D₈×C₁₉	—	8	2	no	—
184	M₁₆×C₁₉	—	4	2	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₂×C₈×C₁₉	—	2	2	no	—
187	C₂×C₈×C₁₉	—	2	1	no	—
188	C₂×C₈×C₁₉	—	2	2	no	—
189	C₂×C₈×C₁₉	—	4	2	no	—
190	C₂×C₈×C₁₉	—	8	1	no	—
191	C₄⋊C₄×C₁₉	—	2	4	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
199	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
200	C₂²⋊C₄×C₁₉	—	2	4	no	—
201	C₂²⋊C₄×C₁₉	—	2	4	no	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	4	1	no	—
209	C₂²⋊C₄×C₁₉	—	4	1	no	—
210	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
214	#18662	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂³×C₁₉	—	2	2	no	—
216	C₂³×C₁₉	—	2	4	no	—
217	C₂³×C₁₉	—	2	2	no	—
218	C₂³×C₁₉	—	2	2	no	—
219	C₂³×C₁₉	—	4	8	no	—
220	C₂³×C₁₉	—	4	1	no	—
221	C₂³×C₁₉	—	8	1	no	—
222	C₂³×C₁₉	—	8	1	no	—
223	C₂³×C₁₉	—	8	4	no	—
224	C₂³×C₁₉	—	8	4	no	—
225	C₂³×C₁₉	#120	1	1	yes	characteristic
226	Q₈×C₁₉	—	4	1	no	—
227	Q₈×C₁₉	—	4	1	no	—
228	Q₈×C₁₉	—	4	2	no	—
229	Q₈×C₁₉	—	4	1	no	—
230	Q₈×C₁₉	—	4	1	no	—
231	D₄×C₁₉	—	2	2	no	—
232	D₄×C₁₉	—	2	2	no	—
233	D₄×C₁₉	—	2	2	no	—
234	D₄×C₁₉	—	2	4	no	—
235	D₄×C₁₉	—	4	2	no	—
236	D₄×C₁₉	—	4	2	no	—
237	D₄×C₁₉	—	4	8	no	—
238	D₄×C₁₉	—	4	8	no	—
239	D₄×C₁₉	—	4	4	no	—
240	D₄×C₁₉	—	4	4	no	—
241	D₄×C₁₉	—	4	1	no	—
242	D₄×C₁₉	—	4	1	no	—
243	D₄×C₁₉	—	4	1	no	—
244	D₄×C₁₉	—	4	1	no	—
245	D₄×C₁₉	—	4	1	no	—
246	D₄×C₁₉	—	4	1	no	—
247	D₄×C₁₉	—	4	1	no	—
248	D₄×C₁₉	—	4	1	no	—
249	D₄×C₁₉	—	4	2	no	—
250	D₄×C₁₉	—	8	1	no	—
251	D₄×C₁₉	—	8	4	no	—
252	D₄×C₁₉	—	8	2	no	—
253	D₄×C₁₉	C₂×D₈	1	4	yes	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	2	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	8	no	—
261	C₂×C₄×C₁₉	—	4	2	no	—
262	C₂×C₄×C₁₉	—	4	2	no	—
263	C₂×C₄×C₁₉	—	4	2	no	—
264	C₂×C₄×C₁₉	—	4	2	no	—
265	C₂×C₄×C₁₉	—	4	4	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	8	2	no	—
268	C₂×C₄×C₁₉	—	8	1	no	—
269	C₂×C₄×C₁₉	—	8	2	no	—
270	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
271	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
272	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
273	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
274	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
275	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
278	C₈×C₁₉	—	2	2	no	—
279	C₈×C₁₉	—	4	1	no	—
280	C₈×C₁₉	—	4	2	no	—
281	C₈×C₁₉	—	4	2	no	—
282	#3496	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#3245	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#3169	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#3036	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#1647	C₂×C₁₉	1	2	yes	complemented
287	#1639	C₂×C₁₉	1	2	yes	complemented
288	#1625	C₂×C₁₉	1	2	yes	complemented
289	#1619	C₂×C₁₉	1	2	yes	complemented
290	#1547	C₂×C₁₉	1	1	yes	characteristic, complemented
291	#1492	C₂×C₁₉	1	1	yes	characteristic, complemented
292	C₂×D₄⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
293	C₂²×C₁₉	—	2	1	no	—
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	4	no	—
296	C₂²×C₁₉	—	4	2	no	—
297	C₂²×C₁₉	—	4	2	no	—
298	C₂²×C₁₉	—	4	2	no	—
299	C₂²×C₁₉	—	4	2	no	—
300	C₂²×C₁₉	—	4	2	no	—
301	C₂²×C₁₉	—	4	2	no	—
302	C₂²×C₁₉	—	4	2	no	—
303	C₂²×C₁₉	—	4	2	no	—
304	C₂²×C₁₉	—	8	4	no	—
305	C₂²×C₁₉	—	8	1	no	—
306	C₂²×C₁₉	—	8	1	no	—
307	C₂²×C₁₉	—	8	1	no	—
308	C₂²×C₁₉	—	16	8	no	—
309	C₂²×C₁₉	#447	1	2	yes	—
310	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
311	C₄×C₁₉	—	2	1	no	—
312	C₄×C₁₉	—	2	1	no	—
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	4	2	no	—
315	C₄×C₁₉	—	4	2	no	—
316	C₄×C₁₉	—	4	2	no	—
317	C₄×C₁₉	—	8	1	no	—
318	C₄×C₁₉	#447	1	2	yes	—
319	C₄×C₁₉	C₂²×D₈	1	1	yes	characteristic
320	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
321	C₄×C₁₉	#576	1	1	yes	characteristic
322	C₄×C₁₉	#577	1	1	yes	characteristic
323	C₂×H(5,𝔽₂)	—	2	1	no	—
324	C₂×AGL(1,ℤ/8)	—	2	1	no	—
325	#547	—	2	1	no	—
326	#547	C₂²×C₁₉	1	2	yes	—
327	#546	—	2	2	no	—
328	#546	—	2	2	no	—
329	D₄²	—	2	1	no	—
330	D₄²	C₂²×C₁₉	1	2	yes	—
331	#537	—	2	1	no	—
332	#534	—	2	2	no	—
333	#532	C₂²×C₁₉	1	1	yes	characteristic
334	#532	C₂²×C₁₉	1	1	yes	characteristic
335	#532	C₂²×C₁₉	1	1	yes	characteristic, complemented
336	C₂×#121	—	2	2	no	—
337	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
338	#500	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	#493	C₂²×C₁₉	1	1	yes	characteristic, complemented
340	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
341	#486	C₂²×C₁₉	1	1	yes	characteristic, complemented
342	#474	—	2	1	no	—
343	#474	C₂²×C₁₉	1	2	yes	complemented
344	#466	—	2	2	no	—
345	#466	—	2	2	no	—
346	#463	—	2	2	no	—
347	#461	C₂²×C₁₉	1	2	yes	complemented
348	#459	—	2	1	no	—
349	#459	C₂²×C₁₉	1	2	yes	complemented
350	#459	C₂²×C₁₉	1	2	yes	complemented
351	C₄×D₈	—	2	2	no	—
352	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
353	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
354	#417	—	2	1	no	—
355	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
356	#332	C₂²×C₁₉	1	2	yes	complemented
357	#331	C₂²×C₁₉	1	2	yes	complemented
358	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
359	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
360	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
361	D₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
362	C₂×C₁₉	—	2	2	no	—
363	C₂×C₁₉	—	4	4	no	—
364	C₂×C₁₉	—	8	2	no	—
365	C₂×C₁₉	—	8	2	no	—
366	C₂×C₁₉	—	16	1	no	—
367	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
368	C₂×C₁₉	#3012	1	1	yes	characteristic
369	C₂×C₁₉	#3018	1	1	yes	characteristic
370	H(5,𝔽₂)	—	4	4	no	—
371	H(5,𝔽₂)	—	4	4	no	—
372	C₂×#41	—	2	2	no	—
373	C₂×#41	—	2	2	no	—
374	C₂×#41	—	2	1	no	—
375	C₂×#41	—	2	1	no	—
376	C₂×#41	—	2	1	no	—
377	C₂²×D₄	—	2	4	no	—
378	C₂²×D₄	—	2	2	no	—
379	C₂²×D₄	—	2	2	no	—
380	C₂²×D₄	—	2	2	no	—
381	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
382	C₂³×C₄	—	2	1	no	—
383	AGL(1,ℤ/8)	—	4	4	no	—
384	C₂×SD₁₆	—	2	2	no	—
385	C₂×D₈	—	2	2	no	—
386	C₂×D₈	—	2	2	no	—
387	C₂×D₈	—	2	2	no	—
388	C₂×M₁₆	—	2	1	no	—
389	C₂²×C₈	—	2	1	no	—
390	C₂²×C₈	—	2	1	no	—
391	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
392	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
393	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
394	#127	D₄×C₁₉	1	1	yes	characteristic
395	#127	C₂³×C₁₉	1	1	yes	characteristic
396	#127	C₂³×C₁₉	1	1	yes	characteristic
397	#124	—	2	1	no	—
398	#124	—	2	1	no	—
399	#124	—	2	1	no	—
400	#123	—	2	4	no	—
401	#123	—	2	4	no	—
402	C₂²⋊Q₈	—	2	2	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	#121	—	2	4	no	—
405	#121	—	2	4	no	—
406	#121	—	2	2	no	—
407	#121	—	2	2	no	—
408	#121	—	2	1	no	—
409	#121	—	2	1	no	—
410	#121	—	2	2	no	—
411	#121	—	2	2	no	—
412	#121	—	2	1	no	—
413	#121	—	2	1	no	—
414	#121	D₄×C₁₉	1	2	yes	—
415	#121	D₄×C₁₉	1	2	yes	—
416	#120	—	2	4	no	—
417	#120	—	2	4	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	—	2	1	no	—
423	C₄×D₄	—	2	1	no	—
424	C₄×D₄	D₄×C₁₉	1	2	yes	—
425	C₄×D₄	D₄×C₁₉	1	2	yes	—
426	C₄×D₄	C₂³×C₁₉	1	2	yes	—
427	C₄×D₄	C₂³×C₁₉	1	2	yes	—
428	C₂×C₄⋊C₄	—	2	2	no	—
429	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	—	2	4	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
433	#107	—	2	2	no	—
434	#107	—	2	2	no	—
435	C₄⋊C₈	—	2	1	no	—
436	C₄⋊C₈	—	2	1	no	—
437	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
438	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
439	#103	—	2	2	no	—
440	#102	—	2	2	no	—
441	#102	—	2	2	no	—
442	#102	—	2	2	no	—
443	#102	—	2	2	no	—
444	#102	—	2	2	no	—
445	C₄×C₈	—	2	1	no	—
446	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
447	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
448	C₁₉	#18662	1	1	yes	characteristic, direct product factor, Sylow
449	C₂⁴	—	2	1	no	—
450	C₂⁴	—	2	4	no	—
451	#41	—	4	8	no	—
452	#41	—	4	4	no	—
453	#41	—	4	4	no	—
454	#41	—	4	2	no	—
455	#41	—	4	2	no	—
456	#41	—	4	2	no	—
457	#41	—	4	2	no	—
458	#41	—	4	2	no	—
459	#41	—	4	2	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	4	8	no	—
478	C₂×D₄	—	4	4	no	—
479	C₂×D₄	—	4	16	no	—
480	C₂×D₄	—	4	4	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	—	8	2	no	—
483	C₂×D₄	—	8	2	no	—
484	C₂×D₄	D₈×C₁₉	1	4	yes	complemented
485	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
486	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
487	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	4	1	no	—
495	C₂²×C₄	—	8	1	no	—
496	C₂²×C₄	—	8	1	no	—
497	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
500	SD₁₆	—	4	4	no	—
501	D₈	—	4	4	no	—
502	D₈	—	4	4	no	—
503	D₈	—	8	2	no	—
504	M₁₆	—	4	2	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	4	2	no	—
510	C₂×C₈	—	8	1	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
518	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
519	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	4	1	no	—
529	C₂²⋊C₄	—	4	1	no	—
530	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
532	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
533	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	4	8	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	8	1	no	—
541	C₂³	—	8	1	no	—
542	C₂³	—	8	4	no	—
543	C₂³	—	8	4	no	—
544	C₂³	C₁₉×#120	1	1	yes	characteristic
545	Q₈	—	4	2	no	—
546	Q₈	—	4	1	no	—
547	Q₈	—	4	1	no	—
548	Q₈	—	4	1	no	—
549	Q₈	—	4	1	no	—
550	D₄	—	2	4	no	—
551	D₄	—	2	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	2	2	no	—
554	D₄	—	4	2	no	—
555	D₄	—	4	2	no	—
556	D₄	—	4	8	no	—
557	D₄	—	4	8	no	—
558	D₄	—	4	4	no	—
559	D₄	—	4	4	no	—
560	D₄	—	4	2	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	D₄	—	4	1	no	—
567	D₄	—	4	1	no	—
568	D₄	—	4	1	no	—
569	D₄	—	8	1	no	—
570	D₄	—	8	4	no	—
571	D₄	—	8	2	no	—
572	D₄	C₂×D₈×C₁₉	1	4	yes	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	8	no	—
580	C₂×C₄	—	4	4	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	8	2	no	—
587	C₂×C₄	—	8	1	no	—
588	C₂×C₄	—	8	2	no	—
589	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
590	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
591	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
592	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
593	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
594	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
595	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
596	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
597	C₈	—	2	2	no	—
598	C₈	—	4	1	no	—
599	C₈	—	4	2	no	—
600	C₈	—	4	2	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	4	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	8	4	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	—	8	1	no	—
616	C₂²	—	16	8	no	—
617	C₂²	C₁₉×#447	1	2	yes	—
618	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	8	1	no	—
626	C₄	C₁₉×#447	1	2	yes	—
627	C₄	C₂²×D₈×C₁₉	1	1	yes	characteristic
628	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
629	C₄	C₁₉×#576	1	1	yes	characteristic
630	C₄	C₁₉×#577	1	1	yes	characteristic
631	C₂	—	2	2	no	—
632	C₂	—	4	4	no	—
633	C₂	—	8	2	no	—
634	C₂	—	8	2	no	—
635	C₂	—	16	1	no	—
636	C₂	C₂×C₁₉×#447	1	1	yes	characteristic
637	C₂	C₁₉×#3012	1	1	yes	characteristic
638	C₂	C₁₉×#3018	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. C₁₉×#3496	C₂	semidirect
2. C₁₉×#3245	C₂	semidirect
3. C₁₉×#3169	C₂	semidirect
4. C₁₉×#3036	C₂	semidirect
5. C₁₉×#1647	C₂	semidirect
6. C₁₉×#1639	C₂	semidirect
7. C₁₉×#1625	C₂	semidirect
8. C₁₉×#1619	C₂	semidirect
9. C₁₉×#1547	C₂	semidirect
10. C₁₉×#1492	C₂	semidirect
11. C₂×C₁₉×D₄⋊C₈	C₂	semidirect
24. C₁₉×#532	C₂²	semidirect
27. C₁₉×#500	C₂²	semidirect
28. C₁₉×#493	C₂²	semidirect
29. C₁₉×#486	C₂²	semidirect
30. C₁₉×#486	C₂²	semidirect
32. C₁₉×#474	C₂²	semidirect
36. C₁₉×#461	C₂²	semidirect
38. C₁₉×#459	C₂²	semidirect
39. C₁₉×#459	C₂²	semidirect
41. C₁₉×#423	C₂²	semidirect
42. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
44. C₂×C₄×C₈×C₁₉	C₂²	semidirect
45. C₁₉×#332	C₂²	semidirect
46. C₁₉×#331	C₂²	semidirect
47. C₁₉×D₄⋊C₈	C₂²	semidirect
48. C₁₉×D₄⋊C₈	C₂²	semidirect
49. C₁₉×D₄⋊C₈	C₂²	semidirect
50. C₁₉×D₄⋊C₈	C₂²	semidirect
164. C₂×D₄×C₁₉	D₈	semidirect
214. #18662	C₁₉	direct (N × H)
282. #3496	C₂×C₁₉	semidirect
283. #3245	C₂×C₁₉	semidirect
284. #3169	C₂×C₁₉	semidirect
285. #3036	C₂×C₁₉	semidirect
286. #1647	C₂×C₁₉	semidirect
287. #1639	C₂×C₁₉	semidirect
288. #1625	C₂×C₁₉	semidirect
289. #1619	C₂×C₁₉	semidirect
290. #1547	C₂×C₁₉	semidirect
291. #1492	C₂×C₁₉	semidirect
292. C₂×D₄⋊C₈	C₂×C₁₉	semidirect
335. #532	C₂²×C₁₉	semidirect
338. #500	C₂²×C₁₉	semidirect
339. #493	C₂²×C₁₉	semidirect
340. #486	C₂²×C₁₉	semidirect
341. #486	C₂²×C₁₉	semidirect
343. #474	C₂²×C₁₉	semidirect
347. #461	C₂²×C₁₉	semidirect
349. #459	C₂²×C₁₉	semidirect
350. #459	C₂²×C₁₉	semidirect
352. #423	C₂²×C₁₉	semidirect
353. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
355. C₂×C₄×C₈	C₂²×C₁₉	semidirect
356. #332	C₂²×C₁₉	semidirect
357. #331	C₂²×C₁₉	semidirect
358. D₄⋊C₈	C₂²×C₁₉	semidirect
359. D₄⋊C₈	C₂²×C₁₉	semidirect
360. D₄⋊C₈	C₂²×C₁₉	semidirect
361. D₄⋊C₈	C₂²×C₁₉	semidirect
448. C₁₉	#18662	direct (N × H)
484. C₂×D₄	D₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3496	2
C₁₉×#3245	2
C₁₉×#3169	2
C₁₉×#3036	2
C₁₉×#1647	2
C₁₉×#1639	2
C₁₉×#1625	2
C₁₉×#1619	2
C₁₉×#1547	2
C₁₉×#1492	2
C₂×C₁₉×D₄⋊C₈	2
#18662	19

Subgroups — C19×#18662 #18024621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18662 #18024621