Subgroups — C₁₉×#24773 #18030732

Order 4864.

892 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#471	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3038	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2906	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2063	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2046	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1965	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1907	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
15	C₂×C₁₉×#131	C₂²	1	2	yes	—
16	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
17	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#471	—	2	8	no	—
20	C₁₉×#460	—	2	1	no	—
21	C₁₉×#460	—	2	1	no	—
22	C₁₉×#460	—	2	2	no	—
23	C₁₉×#460	—	2	1	no	—
24	C₁₉×#460	—	2	1	no	—
25	C₁₉×#459	—	2	1	no	—
26	C₁₉×#459	—	2	1	no	—
27	C₁₉×#441	—	2	1	no	—
28	C₁₉×#440	—	2	1	no	—
29	C₄×Q₁₆×C₁₉	—	2	1	no	—
30	C₄×SD₁₆×C₁₉	—	2	1	no	—
31	C₂×C₁₉×#108	C₂²	1	2	yes	—
32	C₁₉×#428	C₂²	1	1	yes	characteristic
33	C₁₉×#424	—	2	2	no	—
34	C₁₉×#424	C₂²	1	2	yes	—
35	C₁₉×#423	—	2	1	no	—
36	C₁₉×#423	C₂²	1	1	yes	characteristic
37	C₁₉×#423	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
39	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₉×#419	C₂²	1	1	yes	characteristic
41	C₁₉×#418	C₂²	1	2	yes	—
42	C₁₉×#417	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×#102	C₂²	1	2	yes	—
44	C₂×C₁₉×#101	C₂²	1	2	yes	—
45	C₂×C₁₉×#100	C₂²	1	2	yes	—
46	C₂×C₁₉×#100	C₂²	1	2	yes	—
47	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
48	C₁₉×#343	C₂²	1	2	yes	—
49	C₁₉×#341	C₂²	1	2	yes	—
50	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
55	C₁₉×#137	—	2	2	no	—
56	C₁₉×#137	D₄	1	4	yes	complemented
57	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
58	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
59	C₂×Q₁₆×C₁₉	—	2	1	no	—
60	C₂×SD₁₆×C₁₉	—	2	1	no	—
61	C₂×SD₁₆×C₁₉	—	2	2	no	—
62	C₂×SD₁₆×C₁₉	—	2	4	no	—
63	C₂×SD₁₆×C₁₉	—	2	2	no	—
64	C₂×SD₁₆×C₁₉	—	2	2	no	—
65	C₂×SD₁₆×C₁₉	—	4	2	no	—
66	C₂×D₈×C₁₉	—	2	2	no	—
67	C₁₉×#131	—	2	4	no	—
68	C₁₉×#131	—	4	2	no	—
69	C₂×M₁₆×C₁₉	—	2	2	no	—
70	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
72	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
73	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	—	2	2	no	—
75	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
76	C₁₉×#127	—	2	1	no	—
77	C₁₉×#127	—	2	1	no	—
78	C₁₉×#127	—	2	1	no	—
79	C₁₉×#127	—	2	1	no	—
80	C₄×Q₈×C₁₉	—	2	1	no	—
81	C₄×Q₈×C₁₉	—	2	1	no	—
82	C₄×Q₈×C₁₉	—	2	1	no	—
83	C₄×Q₈×C₁₉	—	2	1	no	—
84	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
85	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
86	C₄×D₄×C₁₉	—	2	1	no	—
87	C₄×D₄×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
89	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
90	C₁₉×#117	—	2	1	no	—
91	C₁₉×#117	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₉	—	2	1	no	—
95	C₂×C₄²×C₁₉	—	2	1	no	—
96	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
97	C₁₉×#108	—	2	4	no	—
98	C₁₉×#107	—	2	1	no	—
99	C₁₉×#106	—	2	1	no	—
100	C₁₉×C₄⋊C₈	—	2	2	no	—
101	C₁₉×C₄⋊C₈	—	2	2	no	—
102	C₁₉×C₄⋊C₈	—	2	1	no	—
103	C₁₉×C₄⋊C₈	—	2	1	no	—
104	C₁₉×C₄⋊C₈	—	2	1	no	—
105	C₁₉×C₄⋊C₈	—	2	1	no	—
106	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
107	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
108	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
109	C₁₉×#103	—	2	1	no	—
110	C₁₉×#103	—	2	1	no	—
111	C₁₉×#103	—	2	1	no	—
112	C₁₉×#102	—	2	1	no	—
113	C₁₉×#102	—	2	2	no	—
114	C₁₉×#102	—	2	2	no	—
115	C₁₉×#102	—	2	2	no	—
116	C₁₉×#102	—	2	2	no	—
117	C₁₉×#101	—	2	4	no	—
118	C₁₉×#100	—	2	4	no	—
119	C₁₉×#100	—	4	2	no	—
120	C₁₉×#97	—	2	1	no	—
121	C₄×C₈×C₁₉	—	2	1	no	—
122	C₂⁴×C₁₉	—	2	2	no	—
123	#41×C₁₉	—	2	1	no	—
124	#41×C₁₉	—	2	1	no	—
125	#41×C₁₉	C₂×D₄	1	2	yes	—
126	#41×C₁₉	#41	1	2	yes	—
127	C₂×Q₈×C₁₉	—	2	1	no	—
128	C₂×Q₈×C₁₉	—	2	1	no	—
129	C₂×Q₈×C₁₉	—	2	1	no	—
130	C₂×Q₈×C₁₉	—	2	1	no	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
133	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	2	no	—
136	C₂×D₄×C₁₉	—	2	2	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	—	4	1	no	—
142	C₂×D₄×C₁₉	—	4	1	no	—
143	C₂×D₄×C₁₉	—	4	1	no	—
144	C₂×D₄×C₁₉	—	4	1	no	—
145	C₂×D₄×C₁₉	—	8	2	no	—
146	C₂×D₄×C₁₉	—	8	2	no	—
147	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
156	Q₁₆×C₁₉	—	2	4	no	—
157	SD₁₆×C₁₉	—	2	4	no	—
158	SD₁₆×C₁₉	—	4	4	no	—
159	SD₁₆×C₁₉	—	4	4	no	—
160	SD₁₆×C₁₉	—	4	4	no	—
161	D₈×C₁₉	—	4	4	no	—
162	M₁₆×C₁₉	—	2	1	no	—
163	M₁₆×C₁₉	—	2	2	no	—
164	M₁₆×C₁₉	—	2	2	no	—
165	M₁₆×C₁₉	—	2	2	no	—
166	M₁₆×C₁₉	—	2	2	no	—
167	M₁₆×C₁₉	—	2	1	no	—
168	M₁₆×C₁₉	—	2	1	no	—
169	M₁₆×C₁₉	—	4	4	no	—
170	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
171	C₂×C₈×C₁₉	—	2	2	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₂×C₈×C₁₉	—	2	2	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	4	4	no	—
178	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
179	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	4	1	no	—
185	C₄⋊C₄×C₁₉	—	4	1	no	—
186	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²⋊C₄×C₁₉	—	2	1	no	—
189	C₂²⋊C₄×C₁₉	—	2	1	no	—
190	C₂²⋊C₄×C₁₉	—	2	1	no	—
191	C₄²×C₁₉	—	2	1	no	—
192	C₄²×C₁₉	—	2	1	no	—
193	C₄²×C₁₉	—	2	1	no	—
194	C₄²×C₁₉	—	4	1	no	—
195	C₄²×C₁₉	—	4	1	no	—
196	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
200	#24773	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂³×C₁₉	—	2	1	no	—
202	C₂³×C₁₉	—	4	2	no	—
203	C₂³×C₁₉	—	4	2	no	—
204	C₂³×C₁₉	—	4	2	no	—
205	C₂³×C₁₉	—	8	2	no	—
206	C₂³×C₁₉	—	8	2	no	—
207	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
208	Q₈×C₁₉	—	2	1	no	—
209	Q₈×C₁₉	—	2	2	no	—
210	Q₈×C₁₉	—	2	2	no	—
211	Q₈×C₁₉	—	4	1	no	—
212	Q₈×C₁₉	—	4	1	no	—
213	Q₈×C₁₉	#121	1	2	yes	—
214	D₄×C₁₉	—	2	2	no	—
215	D₄×C₁₉	—	2	2	no	—
216	D₄×C₁₉	—	2	1	no	—
217	D₄×C₁₉	—	4	2	no	—
218	D₄×C₁₉	—	4	2	no	—
219	D₄×C₁₉	—	4	2	no	—
220	D₄×C₁₉	—	4	2	no	—
221	D₄×C₁₉	—	8	2	no	—
222	D₄×C₁₉	—	8	2	no	—
223	D₄×C₁₉	—	8	2	no	—
224	D₄×C₁₉	—	8	2	no	—
225	D₄×C₁₉	#121	1	2	yes	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	8	1	no	—
239	C₂×C₄×C₁₉	—	8	1	no	—
240	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
249	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
250	C₈×C₁₉	—	2	2	no	—
251	C₈×C₁₉	—	2	2	no	—
252	C₈×C₁₉	—	2	2	no	—
253	C₈×C₁₉	—	4	2	no	—
254	C₈×C₁₉	—	4	1	no	—
255	C₈×C₁₉	—	4	2	no	—
256	C₂×#471	C₂×C₁₉	1	2	yes	complemented
257	#3038	C₂×C₁₉	1	1	yes	characteristic
258	C₂×#460	C₂×C₁₉	1	1	yes	characteristic, complemented
259	C₄×#137	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#2906	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#2063	C₂×C₁₉	1	2	yes	complemented
262	#2046	C₂×C₁₉	1	2	yes	complemented
263	#1965	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1950	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1907	C₂×C₁₉	1	2	yes	complemented
266	#1801	C₂×C₁₉	1	1	yes	characteristic, complemented
267	C₂²×C₁₉	—	2	1	no	—
268	C₂²×C₁₉	—	2	1	no	—
269	C₂²×C₁₉	—	2	2	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	—	8	2	no	—
273	C₂²×C₁₉	—	8	2	no	—
274	C₂²×C₁₉	—	8	2	no	—
275	C₂²×C₁₉	—	16	2	no	—
276	C₂²×C₁₉	—	16	2	no	—
277	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
278	C₂²×C₁₉	#547	1	1	yes	characteristic
279	C₂²×C₁₉	#553	1	1	yes	characteristic
280	C₄×C₁₉	—	2	2	no	—
281	C₄×C₁₉	—	2	1	no	—
282	C₄×C₁₉	—	2	1	no	—
283	C₄×C₁₉	—	2	1	no	—
284	C₄×C₁₉	—	4	2	no	—
285	C₄×C₁₉	—	4	1	no	—
286	C₄×C₁₉	—	4	1	no	—
287	C₄×C₁₉	—	8	1	no	—
288	C₄×C₁₉	#471	1	2	yes	complemented
289	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
290	C₄×C₁₉	#537	1	1	yes	characteristic
291	C₄×C₁₉	D₄²	1	1	yes	characteristic
292	C₄×C₁₉	#548	1	1	yes	characteristic
293	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	—
295	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
296	C₂×#131	C₂²×C₁₉	1	2	yes	—
297	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
298	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
300	#471	—	2	8	no	—
301	#460	—	2	1	no	—
302	#460	—	2	1	no	—
303	#460	—	2	1	no	—
304	#460	—	2	1	no	—
305	#460	—	2	2	no	—
306	#459	—	2	1	no	—
307	#459	—	2	1	no	—
308	#441	—	2	1	no	—
309	#440	—	2	1	no	—
310	C₄×Q₁₆	—	2	1	no	—
311	C₄×SD₁₆	—	2	1	no	—
312	C₂×#108	C₂²×C₁₉	1	2	yes	—
313	#428	C₂²×C₁₉	1	1	yes	characteristic
314	#424	—	2	2	no	—
315	#424	C₂²×C₁₉	1	2	yes	—
316	#423	—	2	1	no	—
317	#423	C₂²×C₁₉	1	1	yes	characteristic
318	#423	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×C₄⋊C₈	—	2	1	no	—
320	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
321	#419	C₂²×C₁₉	1	1	yes	characteristic
322	#418	C₂²×C₁₉	1	2	yes	—
323	#417	C₂²×C₁₉	1	1	yes	characteristic
324	C₂×#102	C₂²×C₁₉	1	2	yes	—
325	C₂×#101	C₂²×C₁₉	1	2	yes	—
326	C₂×#100	C₂²×C₁₉	1	2	yes	—
327	C₂×#100	C₂²×C₁₉	1	2	yes	—
328	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
329	#343	C₂²×C₁₉	1	2	yes	—
330	#341	C₂²×C₁₉	1	2	yes	—
331	C₂×C₁₉	—	2	1	no	—
332	C₂×C₁₉	—	2	1	no	—
333	C₂×C₁₉	—	4	2	no	—
334	C₂×C₁₉	—	16	2	no	—
335	C₂×C₁₉	#2416	1	1	yes	characteristic
336	C₂×C₁₉	C₂×#471	1	1	yes	characteristic
337	C₂×C₁₉	#3068	1	1	yes	characteristic
338	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
339	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
343	#137	—	2	2	no	—
344	#137	D₄×C₁₉	1	4	yes	complemented
345	AGL(1,ℤ/8)	—	2	4	no	—
346	AGL(1,ℤ/8)	—	2	4	no	—
347	C₂×Q₁₆	—	2	1	no	—
348	C₂×SD₁₆	—	2	1	no	—
349	C₂×SD₁₆	—	2	4	no	—
350	C₂×SD₁₆	—	2	2	no	—
351	C₂×SD₁₆	—	2	2	no	—
352	C₂×SD₁₆	—	2	2	no	—
353	C₂×SD₁₆	—	4	2	no	—
354	C₂×D₈	—	2	2	no	—
355	#131	—	2	4	no	—
356	#131	—	4	2	no	—
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
359	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
360	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
361	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
362	C₂²×C₈	—	2	2	no	—
363	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
364	#127	—	2	1	no	—
365	#127	—	2	1	no	—
366	#127	—	2	1	no	—
367	#127	—	2	1	no	—
368	C₄×Q₈	—	2	1	no	—
369	C₄×Q₈	—	2	1	no	—
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
373	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
377	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
378	#117	—	2	1	no	—
379	#117	C₂³×C₁₉	1	1	yes	characteristic
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
385	#108	—	2	4	no	—
386	#107	—	2	1	no	—
387	#106	—	2	1	no	—
388	C₄⋊C₈	—	2	2	no	—
389	C₄⋊C₈	—	2	2	no	—
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
395	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
396	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
397	#103	—	2	1	no	—
398	#103	—	2	1	no	—
399	#103	—	2	1	no	—
400	#102	—	2	1	no	—
401	#102	—	2	2	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	#102	—	2	2	no	—
405	#101	—	2	4	no	—
406	#100	—	2	4	no	—
407	#100	—	4	2	no	—
408	#97	—	2	1	no	—
409	C₄×C₈	—	2	1	no	—
410	C₁₉	#24773	1	1	yes	characteristic, direct product factor, Sylow
411	C₂⁴	—	2	2	no	—
412	#41	—	2	1	no	—
413	#41	—	2	1	no	—
414	#41	C₂×D₄×C₁₉	1	2	yes	—
415	#41	#41×C₁₉	1	2	yes	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
422	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	—	4	1	no	—
433	C₂×D₄	—	4	1	no	—
434	C₂×D₄	—	8	2	no	—
435	C₂×D₄	—	8	2	no	—
436	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
445	Q₁₆	—	2	4	no	—
446	SD₁₆	—	2	4	no	—
447	SD₁₆	—	4	4	no	—
448	SD₁₆	—	4	4	no	—
449	SD₁₆	—	4	4	no	—
450	D₈	—	4	4	no	—
451	M₁₆	—	2	1	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	—	2	2	no	—
455	M₁₆	—	2	1	no	—
456	M₁₆	—	2	2	no	—
457	M₁₆	—	2	1	no	—
458	M₁₆	—	4	4	no	—
459	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	4	4	no	—
467	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
468	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	—	4	1	no	—
475	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	4	1	no	—
484	C₄²	—	4	1	no	—
485	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
486	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₂³	—	2	1	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	8	2	no	—
494	C₂³	—	8	2	no	—
495	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
496	Q₈	—	2	1	no	—
497	Q₈	—	2	2	no	—
498	Q₈	—	2	2	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	C₁₉×#121	1	2	yes	—
502	D₄	—	2	2	no	—
503	D₄	—	2	2	no	—
504	D₄	—	2	1	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	8	2	no	—
510	D₄	—	8	2	no	—
511	D₄	—	8	2	no	—
512	D₄	—	8	2	no	—
513	D₄	C₁₉×#121	1	2	yes	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	8	1	no	—
527	C₂×C₄	—	8	1	no	—
528	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
529	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
530	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
531	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
535	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
536	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
537	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
538	C₈	—	2	2	no	—
539	C₈	—	2	2	no	—
540	C₈	—	2	2	no	—
541	C₈	—	4	2	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	2	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	8	2	no	—
550	C₂²	—	8	2	no	—
551	C₂²	—	8	2	no	—
552	C₂²	—	16	2	no	—
553	C₂²	—	16	2	no	—
554	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
555	C₂²	C₁₉×#547	1	1	yes	characteristic
556	C₂²	C₁₉×#553	1	1	yes	characteristic
557	C₄	—	2	2	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	8	1	no	—
565	C₄	C₁₉×#471	1	2	yes	complemented
566	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
567	C₄	C₁₉×#537	1	1	yes	characteristic
568	C₄	D₄²×C₁₉	1	1	yes	characteristic
569	C₄	C₁₉×#548	1	1	yes	characteristic
570	C₂	—	2	1	no	—
571	C₂	—	2	1	no	—
572	C₂	—	4	2	no	—
573	C₂	—	16	2	no	—
574	C₂	C₁₉×#2416	1	1	yes	characteristic
575	C₂	C₂×C₁₉×#471	1	1	yes	characteristic
576	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3038	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#471	C₂	semidirect
3. C₂×C₁₉×#460	C₂	semidirect
4. C₄×C₁₉×#137	C₂	semidirect
5. C₁₉×#2906	C₂	semidirect
6. C₁₉×#2063	C₂	semidirect
7. C₁₉×#2046	C₂	semidirect
8. C₁₉×#1965	C₂	semidirect
9. C₁₉×#1950	C₂	semidirect
10. C₁₉×#1907	C₂	semidirect
11. C₁₉×#1801	C₂	semidirect
56. C₁₉×#137	D₄	semidirect
200. #24773	C₁₉	direct (N × H)
256. C₂×#471	C₂×C₁₉	semidirect
258. C₂×#460	C₂×C₁₉	semidirect
259. C₄×#137	C₂×C₁₉	semidirect
260. #2906	C₂×C₁₉	semidirect
261. #2063	C₂×C₁₉	semidirect
262. #2046	C₂×C₁₉	semidirect
263. #1965	C₂×C₁₉	semidirect
264. #1950	C₂×C₁₉	semidirect
265. #1907	C₂×C₁₉	semidirect
266. #1801	C₂×C₁₉	semidirect
288. C₄×C₁₉	#471	semidirect
344. #137	D₄×C₁₉	semidirect
410. C₁₉	#24773	direct (N × H)
565. C₄	C₁₉×#471	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#471	2
C₁₉×#3038	2
C₂×C₁₉×#460	2
C₄×C₁₉×#137	2
C₁₉×#2906	2
C₁₉×#2063	2
C₁₉×#2046	2
C₁₉×#1965	2
C₁₉×#1950	2
C₁₉×#1907	2
C₁₉×#1801	2
#24773	19

Subgroups — C19×#24773 #18030732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24773 #18030732