Subgroups — C₁₉×#11041 #18017000

Order 4864.

1374 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#421	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2297	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1728	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₁₉	C₂²	1	2	yes	—
7	C₁₉×#575	—	2	4	no	—
8	C₁₉×#575	—	2	2	no	—
9	C₁₉×#575	C₄	1	4	yes	complemented
10	C₂×C₁₉×#137	—	2	2	no	—
11	C₂×C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
12	C₂×C₁₉×#135	—	2	2	no	—
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#421	—	2	4	no	—
18	C₁₉×#421	—	2	4	no	—
19	C₂×C₁₉×#104	—	2	4	no	—
20	C₁₉×#391	—	2	2	no	—
21	C₁₉×#390	—	2	2	no	—
22	C₁₉×#386	—	2	4	no	—
23	C₄×C₂²⋊C₄×C₁₉	—	2	4	no	—
24	C₁₉×H(3,ℤ/4)	—	2	2	no	—
25	C₁₉×#336	—	2	2	no	—
26	C₂×#41×C₁₉	—	2	2	no	—
27	C₂×#41×C₁₉	—	2	2	no	—
28	C₂×#41×C₁₉	—	2	2	no	—
29	C₂×#41×C₁₉	—	2	2	no	—
30	C₂×#41×C₁₉	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	2	no	—
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	2	no	—
35	C₂×#41×C₁₉	—	2	2	no	—
36	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
37	C₂×#41×C₁₉	D₄	1	4	yes	—
38	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
39	C₂²×D₄×C₁₉	—	2	2	no	—
40	C₂²×D₄×C₁₉	D₄	1	2	yes	—
41	C₂³×C₄×C₁₉	—	2	2	no	—
42	C₂³×C₄×C₁₉	D₄	1	2	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₁₉×#137	—	2	8	no	—
45	C₁₉×#137	—	2	8	no	—
46	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
47	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
48	C₁₉×#135	—	2	8	no	—
49	C₁₉×#135	—	2	8	no	—
50	C₂×Q₁₆×C₁₉	—	2	2	no	—
51	C₂×SD₁₆×C₁₉	—	2	4	no	—
52	C₂×D₈×C₁₉	—	2	2	no	—
53	C₂×M₁₆×C₁₉	—	2	2	no	—
54	C₂×M₁₆×C₁₉	—	2	2	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	2	no	—
57	C₂×M₁₆×C₁₉	—	2	2	no	—
58	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
59	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
60	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
61	C₂²×C₈×C₁₉	—	2	1	no	—
62	C₂²×C₈×C₁₉	D₄	1	2	yes	—
63	C₁₉×#117	—	2	2	no	—
64	C₁₉×#117	—	2	2	no	—
65	C₁₉×#117	—	2	2	no	—
66	C₁₉×#117	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄²×C₁₉	—	2	2	no	—
71	C₂×C₄²×C₁₉	—	2	2	no	—
72	C₂×C₄²×C₁₉	—	2	1	no	—
73	C₂×C₄²×C₁₉	—	2	1	no	—
74	C₂×C₄²×C₁₉	D₄	1	4	yes	—
75	C₁₉×#104	—	2	16	no	—
76	C₁₉×#95	—	2	8	no	—
77	C₂⁴×C₁₉	—	2	2	no	—
78	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
79	#41×C₁₉	—	2	4	no	—
80	#41×C₁₉	—	2	4	no	—
81	#41×C₁₉	—	2	4	no	—
82	#41×C₁₉	—	2	4	no	—
83	#41×C₁₉	—	2	4	no	—
84	#41×C₁₉	—	2	4	no	—
85	#41×C₁₉	—	2	4	no	—
86	#41×C₁₉	—	2	4	no	—
87	#41×C₁₉	—	4	2	no	—
88	#41×C₁₉	—	4	2	no	—
89	#41×C₁₉	—	4	2	no	—
90	#41×C₁₉	—	4	2	no	—
91	#41×C₁₉	—	4	2	no	—
92	#41×C₁₉	—	4	2	no	—
93	#41×C₁₉	—	4	2	no	—
94	#41×C₁₉	—	4	2	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	complemented
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	4	2	no	—
109	C₂×D₄×C₁₉	—	4	2	no	—
110	C₂×D₄×C₁₉	—	4	2	no	—
111	C₂×D₄×C₁₉	—	4	2	no	—
112	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	complemented
113	C₂²×C₄×C₁₉	—	2	4	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	2	4	no	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	4	4	no	—
120	C₂²×C₄×C₁₉	—	4	2	no	—
121	C₂²×C₄×C₁₉	—	4	2	no	—
122	C₂²×C₄×C₁₉	—	4	2	no	—
123	C₂²×C₄×C₁₉	—	4	2	no	—
124	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	#41	1	2	yes	—
133	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
134	Q₁₆×C₁₉	—	2	8	no	—
135	SD₁₆×C₁₉	—	2	16	no	—
136	D₈×C₁₉	—	2	8	no	—
137	M₁₆×C₁₉	—	2	4	no	—
138	M₁₆×C₁₉	—	2	4	no	—
139	M₁₆×C₁₉	—	2	4	no	—
140	M₁₆×C₁₉	—	4	2	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₂×C₈×C₁₉	—	2	2	no	—
144	C₂×C₈×C₁₉	—	4	1	no	—
145	C₂×C₈×C₁₉	—	4	1	no	—
146	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	complemented
147	C₄⋊C₄×C₁₉	—	4	2	no	—
148	C₄⋊C₄×C₁₉	—	4	2	no	—
149	C₂²⋊C₄×C₁₉	—	4	16	no	—
150	C₂²⋊C₄×C₁₉	—	4	2	no	—
151	C₂²⋊C₄×C₁₉	—	4	2	no	—
152	C₄²×C₁₉	—	2	4	no	—
153	C₄²×C₁₉	—	2	4	no	—
154	C₄²×C₁₉	—	4	1	no	—
155	C₄²×C₁₉	—	4	2	no	—
156	C₄²×C₁₉	—	4	1	no	—
157	#11041	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂³×C₁₉	—	2	4	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	4	8	no	—
161	C₂³×C₁₉	—	4	2	no	—
162	C₂³×C₁₉	—	4	2	no	—
163	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
164	C₂³×C₁₉	#120	1	2	yes	—
165	C₂³×C₁₉	#121	1	1	yes	characteristic
166	C₂³×C₁₉	#121	1	2	yes	—
167	C₂³×C₁₉	#127	1	1	yes	characteristic
168	Q₈×C₁₉	—	2	4	no	—
169	Q₈×C₁₉	—	2	4	no	—
170	Q₈×C₁₉	—	4	2	no	—
171	Q₈×C₁₉	—	4	2	no	—
172	D₄×C₁₉	—	2	4	no	—
173	D₄×C₁₉	—	2	4	no	—
174	D₄×C₁₉	—	4	4	no	—
175	D₄×C₁₉	—	4	4	no	—
176	D₄×C₁₉	—	4	4	no	—
177	D₄×C₁₉	—	4	4	no	—
178	D₄×C₁₉	—	4	2	no	—
179	D₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	2	8	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	4	no	—
183	C₂×C₄×C₁₉	—	4	4	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	4	no	—
189	C₂×C₄×C₁₉	—	4	4	no	—
190	C₂×C₄×C₁₉	—	4	4	no	—
191	C₂×C₄×C₁₉	—	4	4	no	—
192	C₂×C₄×C₁₉	—	4	8	no	—
193	C₂×C₄×C₁₉	—	4	4	no	—
194	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
200	C₂×C₄×C₁₉	#120	1	2	yes	—
201	C₂×C₄×C₁₉	#120	1	2	yes	—
202	C₂×C₄×C₁₉	#121	1	2	yes	—
203	C₂×C₄×C₁₉	#121	1	2	yes	—
204	C₂×C₄×C₁₉	#121	1	2	yes	—
205	C₂×C₄×C₁₉	#121	1	2	yes	—
206	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#123	1	2	yes	—
208	C₂×C₄×C₁₉	#123	1	2	yes	—
209	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
210	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
211	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
212	C₈×C₁₉	—	2	4	no	—
213	C₈×C₁₉	—	4	2	no	—
214	C₂×#575	C₂×C₁₉	1	1	yes	characteristic
215	C₂×#421	C₂×C₁₉	1	2	yes	complemented
216	#2297	C₂×C₁₉	1	2	yes	complemented
217	C₂×H(3,ℤ/4)	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#1728	C₂×C₁₉	1	1	yes	characteristic, complemented
219	C₂²×C₁₉	—	2	4	no	—
220	C₂²×C₁₉	—	2	2	no	—
221	C₂²×C₁₉	—	4	1	no	—
222	C₂²×C₁₉	—	4	2	no	—
223	C₂²×C₁₉	—	4	1	no	—
224	C₂²×C₁₉	—	4	8	no	—
225	C₂²×C₁₉	—	4	4	no	—
226	C₂²×C₁₉	—	8	4	no	—
227	C₂²×C₁₉	—	8	4	no	—
228	C₂²×C₁₉	#386	1	2	yes	—
229	C₂²×C₁₉	#390	1	1	yes	characteristic
230	C₂²×C₁₉	#392	1	2	yes	—
231	C₂²×C₁₉	#392	1	1	yes	characteristic
232	C₂²×C₁₉	#394	1	1	yes	characteristic
233	C₄×C₁₉	—	4	4	no	—
234	C₄×C₁₉	—	4	4	no	—
235	C₄×C₁₉	—	8	4	no	—
236	C₄×C₁₉	#379	1	1	yes	characteristic
237	C₄×C₁₉	#386	1	2	yes	—
238	C₄×C₁₉	#390	1	1	yes	characteristic
239	C₄×C₁₉	#392	1	1	yes	characteristic
240	C₄×C₁₉	#394	1	2	yes	—
241	C₄×C₁₉	#394	1	1	yes	characteristic
242	C₂²×#41	C₂²×C₁₉	1	2	yes	—
243	#575	—	2	4	no	—
244	#575	—	2	2	no	—
245	#575	C₄×C₁₉	1	4	yes	complemented
246	C₂×#137	—	2	2	no	—
247	C₂×AGL(1,ℤ/8)	—	2	2	no	—
248	C₂×#135	—	2	2	no	—
249	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
250	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×#117	C₂²×C₁₉	1	2	yes	—
252	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
253	#421	—	2	4	no	—
254	#421	—	2	4	no	—
255	C₂×#104	—	2	4	no	—
256	#391	—	2	2	no	—
257	#390	—	2	2	no	—
258	#386	—	2	4	no	—
259	C₄×C₂²⋊C₄	—	2	4	no	—
260	H(3,ℤ/4)	—	2	2	no	—
261	#336	—	2	2	no	—
262	C₂×C₁₉	—	2	2	no	—
263	C₂×C₁₉	—	2	2	no	—
264	C₂×C₁₉	—	2	1	no	—
265	C₂×C₁₉	—	2	1	no	—
266	C₂×C₁₉	—	8	4	no	—
267	C₂×C₁₉	#1438	1	1	yes	characteristic
268	C₂×C₁₉	#2010	1	2	yes	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	2	2	no	—
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	—	2	2	no	—
279	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
280	C₂×#41	D₄×C₁₉	1	4	yes	—
281	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	D₄×C₁₉	1	2	yes	—
284	C₂³×C₄	—	2	2	no	—
285	C₂³×C₄	D₄×C₁₉	1	2	yes	—
286	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
287	#137	—	2	8	no	—
288	#137	—	2	8	no	—
289	AGL(1,ℤ/8)	—	2	8	no	—
290	AGL(1,ℤ/8)	—	2	8	no	—
291	#135	—	2	8	no	—
292	#135	—	2	8	no	—
293	C₂×Q₁₆	—	2	2	no	—
294	C₂×SD₁₆	—	2	4	no	—
295	C₂×D₈	—	2	2	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
302	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
303	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	D₄×C₁₉	1	2	yes	—
306	#117	—	2	2	no	—
307	#117	—	2	2	no	—
308	#117	—	2	2	no	—
309	#117	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	8	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	2	2	no	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	D₄×C₁₉	1	4	yes	—
318	#104	—	2	16	no	—
319	#95	—	2	8	no	—
320	C₁₉	#11041	1	1	yes	characteristic, direct product factor, Sylow
321	C₂⁴	—	2	2	no	—
322	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
323	#41	—	2	4	no	—
324	#41	—	2	4	no	—
325	#41	—	2	4	no	—
326	#41	—	2	4	no	—
327	#41	—	2	4	no	—
328	#41	—	2	4	no	—
329	#41	—	2	4	no	—
330	#41	—	2	4	no	—
331	#41	—	4	2	no	—
332	#41	—	4	2	no	—
333	#41	—	4	2	no	—
334	#41	—	4	2	no	—
335	#41	—	4	2	no	—
336	#41	—	4	2	no	—
337	#41	—	4	2	no	—
338	#41	—	4	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	complemented
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	4	2	no	—
355	C₂×D₄	—	4	2	no	—
356	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	complemented
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	4	4	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
375	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
376	C₂²×C₄	#41×C₁₉	1	2	yes	—
377	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
378	Q₁₆	—	2	8	no	—
379	SD₁₆	—	2	16	no	—
380	D₈	—	2	8	no	—
381	M₁₆	—	2	4	no	—
382	M₁₆	—	2	4	no	—
383	M₁₆	—	2	4	no	—
384	M₁₆	—	4	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	4	1	no	—
389	C₂×C₈	—	4	1	no	—
390	C₂×C₈	C₂²⋊C₄×C₁₉	1	4	yes	complemented
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₂²⋊C₄	—	4	16	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₄²	—	2	4	no	—
397	C₄²	—	2	4	no	—
398	C₄²	—	4	1	no	—
399	C₄²	—	4	2	no	—
400	C₄²	—	4	1	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	8	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
407	C₂³	C₁₉×#120	1	2	yes	—
408	C₂³	C₁₉×#121	1	1	yes	characteristic
409	C₂³	C₁₉×#121	1	2	yes	—
410	C₂³	C₁₉×#127	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	2	4	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	D₄	—	2	4	no	—
416	D₄	—	2	4	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	4	no	—
419	D₄	—	4	4	no	—
420	D₄	—	4	4	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	2	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	4	8	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
438	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
439	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
440	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
441	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
442	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
443	C₂×C₄	C₁₉×#120	1	2	yes	—
444	C₂×C₄	C₁₉×#120	1	2	yes	—
445	C₂×C₄	C₁₉×#121	1	2	yes	—
446	C₂×C₄	C₁₉×#121	1	2	yes	—
447	C₂×C₄	C₁₉×#121	1	2	yes	—
448	C₂×C₄	C₁₉×#121	1	2	yes	—
449	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
450	C₂×C₄	C₁₉×#123	1	2	yes	—
451	C₂×C₄	C₁₉×#123	1	2	yes	—
452	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
453	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
454	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
455	C₈	—	2	4	no	—
456	C₈	—	4	2	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	8	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	8	4	no	—
465	C₂²	—	8	4	no	—
466	C₂²	C₁₉×#386	1	2	yes	—
467	C₂²	C₁₉×#390	1	1	yes	characteristic
468	C₂²	C₁₉×#392	1	2	yes	—
469	C₂²	C₁₉×#392	1	1	yes	characteristic
470	C₂²	C₁₉×#394	1	1	yes	characteristic
471	C₄	—	4	4	no	—
472	C₄	—	4	4	no	—
473	C₄	—	8	4	no	—
474	C₄	C₁₉×#379	1	1	yes	characteristic
475	C₄	C₁₉×#386	1	2	yes	—
476	C₄	C₁₉×#390	1	1	yes	characteristic
477	C₄	C₁₉×#392	1	1	yes	characteristic
478	C₄	C₁₉×#394	1	2	yes	—
479	C₄	C₁₉×#394	1	1	yes	characteristic
480	C₂	—	2	2	no	—
481	C₂	—	2	2	no	—
482	C₂	—	2	1	no	—
483	C₂	—	2	1	no	—
484	C₂	—	8	4	no	—
485	C₂	C₁₉×#1438	1	1	yes	characteristic
486	C₂	C₁₉×#2010	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#127
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	#392
prime radical	C₂×C₁₉×#575	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#421	C₂	semidirect
3. C₁₉×#2297	C₂	semidirect
4. C₂×C₁₉×H(3,ℤ/4)	C₂	semidirect
5. C₁₉×#1728	C₂	semidirect
9. C₁₉×#575	C₄	semidirect
100. C₂×Q₈×C₁₉	C₂²⋊C₄	semidirect
112. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
146. C₂×C₈×C₁₉	C₂²⋊C₄	semidirect
157. #11041	C₁₉	direct (N × H)
215. C₂×#421	C₂×C₁₉	semidirect
216. #2297	C₂×C₁₉	semidirect
217. C₂×H(3,ℤ/4)	C₂×C₁₉	semidirect
218. #1728	C₂×C₁₉	semidirect
245. #575	C₄×C₁₉	semidirect
320. C₁₉	#11041	direct (N × H)
344. C₂×Q₈	C₂²⋊C₄×C₁₉	semidirect
356. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect
390. C₂×C₈	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#575	2
C₂×C₁₉×#421	2
C₁₉×#2297	2
C₂×C₁₉×H(3,ℤ/4)	2
C₁₉×#1728	2
#11041	19

Subgroups — C19×#11041 #18017000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11041 #18017000