Subgroups — C₁₉×#13020 #18018979

Order 4864.

460 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2950	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#362	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2141	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1979	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1382	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1379	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#519	—	2	1	no	—
11	C₂×C₁₉×Q₃₂	—	2	2	no	—
12	C₂×C₁₉×Q₃₂	—	2	2	no	—
13	C₂×C₁₉×Q₃₂	C₄	1	4	yes	complemented
14	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
15	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#441	—	2	2	no	—
17	C₄×Q₁₆×C₁₉	—	2	2	no	—
18	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
19	C₁₉×#427	C₂²	1	1	yes	characteristic
20	C₁₉×#419	—	2	1	no	—
21	C₁₉×#419	—	2	1	no	—
22	C₂×C₁₉×#101	—	2	1	no	—
23	C₁₉×#405	C₂²	1	1	yes	characteristic
24	C₁₉×#362	—	2	2	no	—
25	C₁₉×#358	—	2	2	no	—
26	C₂²×Q₈×C₁₉	—	2	1	no	—
27	C₂²×Q₈×C₁₉	—	2	1	no	—
28	C₂×Q₁₆×C₁₉	—	2	1	no	—
29	C₂×Q₁₆×C₁₉	—	2	1	no	—
30	C₂×Q₁₆×C₁₉	—	2	1	no	—
31	C₂×Q₁₆×C₁₉	—	2	1	no	—
32	C₂×Q₁₆×C₁₉	—	2	1	no	—
33	C₂×Q₁₆×C₁₉	—	2	1	no	—
34	C₂×Q₁₆×C₁₉	—	2	1	no	—
35	C₂×Q₁₆×C₁₉	—	2	1	no	—
36	C₂×Q₁₆×C₁₉	C₂×C₄	1	2	yes	—
37	C₂×Q₁₆×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×Q₁₆×C₁₉	D₄	1	2	yes	—
39	C₂×Q₁₆×C₁₉	D₄	1	2	yes	—
40	C₂×M₁₆×C₁₉	—	2	1	no	—
41	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
43	C₄×Q₈×C₁₉	—	2	4	no	—
44	C₄×Q₈×C₁₉	—	4	2	no	—
45	C₁₉×#117	—	2	1	no	—
46	C₁₉×#117	—	4	2	no	—
47	C₁₉×#117	D₄	1	1	yes	characteristic
48	C₁₉×Q₃₂	—	2	8	no	—
49	C₁₉×M₃₂	—	2	1	no	—
50	C₁₉×M₃₂	—	2	1	no	—
51	C₂×C₁₆×C₁₉	—	2	1	no	—
52	C₂×C₁₆×C₁₉	—	2	1	no	—
53	C₂×C₁₆×C₁₉	—	2	1	no	—
54	C₂×C₁₆×C₁₉	C₂×C₄	1	2	yes	—
55	C₁₉×#108	—	2	1	no	—
56	C₁₉×#108	—	2	1	no	—
57	C₁₉×#107	D₄	1	2	yes	—
58	C₁₉×#106	—	2	1	no	—
59	C₁₉×#103	—	2	4	no	—
60	C₁₉×#103	—	4	2	no	—
61	C₁₉×#101	—	4	2	no	—
62	C₁₉×#97	—	2	1	no	—
63	C₄×C₈×C₁₉	—	2	1	no	—
64	C₂×Q₈×C₁₉	—	2	2	no	—
65	C₂×Q₈×C₁₉	—	2	2	no	—
66	C₂×Q₈×C₁₉	—	2	2	no	—
67	C₂×Q₈×C₁₉	—	2	2	no	—
68	C₂×Q₈×C₁₉	—	4	1	no	—
69	C₂×Q₈×C₁₉	—	4	1	no	—
70	C₂×Q₈×C₁₉	—	4	1	no	—
71	C₂×Q₈×C₁₉	—	4	1	no	—
72	C₂×Q₈×C₁₉	—	4	1	no	—
73	C₂×Q₈×C₁₉	—	4	1	no	—
74	C₂×Q₈×C₁₉	—	4	1	no	—
75	C₂×Q₈×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	Q₁₆×C₁₉	—	2	2	no	—
80	Q₁₆×C₁₉	—	2	2	no	—
81	Q₁₆×C₁₉	—	2	2	no	—
82	Q₁₆×C₁₉	—	2	2	no	—
83	Q₁₆×C₁₉	—	2	2	no	—
84	Q₁₆×C₁₉	—	4	1	no	—
85	Q₁₆×C₁₉	—	4	1	no	—
86	Q₁₆×C₁₉	C₂²⋊C₄	1	4	yes	—
87	M₁₆×C₁₉	—	2	1	no	—
88	M₁₆×C₁₉	—	2	1	no	—
89	M₁₆×C₁₉	—	4	1	no	—
90	M₁₆×C₁₉	—	4	1	no	—
91	C₂×C₈×C₁₉	—	2	1	no	—
92	C₂×C₈×C₁₉	—	4	1	no	—
93	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
98	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
99	C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₄⋊C₄×C₁₉	—	4	4	no	—
101	C₄⋊C₄×C₁₉	D₈	1	2	yes	—
102	C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂²⋊C₄×C₁₉	—	4	1	no	—
104	C₄²×C₁₉	—	2	1	no	—
105	C₄²×C₁₉	—	4	4	no	—
106	C₄²×C₁₉	—	4	1	no	—
107	C₁₆×C₁₉	—	2	2	no	—
108	C₁₆×C₁₉	—	4	1	no	—
109	#13020	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
111	Q₈×C₁₉	—	2	4	no	—
112	Q₈×C₁₉	—	4	2	no	—
113	Q₈×C₁₉	—	4	2	no	—
114	Q₈×C₁₉	—	4	2	no	—
115	Q₈×C₁₉	—	4	2	no	—
116	Q₈×C₁₉	—	4	2	no	—
117	Q₈×C₁₉	—	8	1	no	—
118	Q₈×C₁₉	—	8	1	no	—
119	C₂×C₄×C₁₉	—	2	2	no	—
120	C₂×C₄×C₁₉	—	4	2	no	—
121	C₂×C₄×C₁₉	—	4	2	no	—
122	C₂×C₄×C₁₉	—	4	2	no	—
123	C₂×C₄×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	—	4	2	no	—
125	C₂×C₄×C₁₉	—	8	1	no	—
126	C₂×C₄×C₁₉	—	8	1	no	—
127	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
128	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
129	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
130	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
131	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
132	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
133	C₈×C₁₉	—	4	1	no	—
134	C₈×C₁₉	—	8	1	no	—
135	C₈×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₈×C₁₉	C₄×D₄	1	1	yes	characteristic
137	C₈×C₁₉	#121	1	1	yes	characteristic
138	C₈×C₁₉	#123	1	1	yes	characteristic
139	C₂²×Q₃₂	C₂×C₁₉	1	1	yes	characteristic
140	#2950	C₂×C₁₉	1	1	yes	characteristic
141	C₂×#362	C₂×C₁₉	1	1	yes	characteristic
142	#2141	C₂×C₁₉	1	1	yes	characteristic
143	#1979	C₂×C₁₉	1	1	yes	characteristic
144	#1382	C₂×C₁₉	1	1	yes	characteristic
145	#1379	C₂×C₁₉	1	1	yes	characteristic
146	C₂²×C₁₉	—	2	2	no	—
147	C₂²×C₁₉	#442	1	1	yes	characteristic
148	C₂²×C₁₉	#447	1	1	yes	characteristic
149	C₂²×C₁₉	#463	1	1	yes	characteristic
150	C₄×C₁₉	—	4	4	no	—
151	C₄×C₁₉	—	4	2	no	—
152	C₄×C₁₉	—	8	2	no	—
153	C₄×C₁₉	—	8	2	no	—
154	C₄×C₁₉	#386	1	1	yes	characteristic
155	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
156	C₄×C₁₉	#449	1	1	yes	characteristic
157	C₄×C₁₉	#459	1	1	yes	characteristic
158	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
159	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
160	#519	—	2	1	no	—
161	C₂×Q₃₂	—	2	2	no	—
162	C₂×Q₃₂	—	2	2	no	—
163	C₂×Q₃₂	C₄×C₁₉	1	4	yes	complemented
164	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
165	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
166	#441	—	2	2	no	—
167	C₄×Q₁₆	—	2	2	no	—
168	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
169	#427	C₂²×C₁₉	1	1	yes	characteristic
170	#419	—	2	1	no	—
171	#419	—	2	1	no	—
172	C₂×#101	—	2	1	no	—
173	#405	C₂²×C₁₉	1	1	yes	characteristic
174	#362	—	2	2	no	—
175	#358	—	2	2	no	—
176	C₂×C₁₉	—	2	1	no	—
177	C₂×C₁₉	—	2	1	no	—
178	C₂×C₁₉	#1879	1	1	yes	characteristic
179	C₂×C₁₉	#2195	1	2	yes	—
180	C₂²×Q₈	—	2	1	no	—
181	C₂²×Q₈	—	2	1	no	—
182	C₂×Q₁₆	—	2	1	no	—
183	C₂×Q₁₆	—	2	1	no	—
184	C₂×Q₁₆	—	2	1	no	—
185	C₂×Q₁₆	—	2	1	no	—
186	C₂×Q₁₆	—	2	1	no	—
187	C₂×Q₁₆	—	2	1	no	—
188	C₂×Q₁₆	—	2	1	no	—
189	C₂×Q₁₆	—	2	1	no	—
190	C₂×Q₁₆	C₂×C₄×C₁₉	1	2	yes	—
191	C₂×Q₁₆	C₂×C₄×C₁₉	1	2	yes	—
192	C₂×Q₁₆	D₄×C₁₉	1	2	yes	—
193	C₂×Q₁₆	D₄×C₁₉	1	2	yes	—
194	C₂×M₁₆	—	2	1	no	—
195	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
196	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
197	C₄×Q₈	—	2	4	no	—
198	C₄×Q₈	—	4	2	no	—
199	#117	—	2	1	no	—
200	#117	—	4	2	no	—
201	#117	D₄×C₁₉	1	1	yes	characteristic
202	Q₃₂	—	2	8	no	—
203	M₃₂	—	2	1	no	—
204	M₃₂	—	2	1	no	—
205	C₂×C₁₆	—	2	1	no	—
206	C₂×C₁₆	—	2	1	no	—
207	C₂×C₁₆	—	2	1	no	—
208	C₂×C₁₆	C₂×C₄×C₁₉	1	2	yes	—
209	#108	—	2	1	no	—
210	#108	—	2	1	no	—
211	#107	D₄×C₁₉	1	2	yes	—
212	#106	—	2	1	no	—
213	#103	—	2	4	no	—
214	#103	—	4	2	no	—
215	#101	—	4	2	no	—
216	#97	—	2	1	no	—
217	C₄×C₈	—	2	1	no	—
218	C₁₉	#13020	1	1	yes	characteristic, direct product factor, Sylow
219	C₂×Q₈	—	2	2	no	—
220	C₂×Q₈	—	2	2	no	—
221	C₂×Q₈	—	2	2	no	—
222	C₂×Q₈	—	2	2	no	—
223	C₂×Q₈	—	4	1	no	—
224	C₂×Q₈	—	4	1	no	—
225	C₂×Q₈	—	4	1	no	—
226	C₂×Q₈	—	4	1	no	—
227	C₂×Q₈	—	4	1	no	—
228	C₂×Q₈	—	4	1	no	—
229	C₂×Q₈	—	4	1	no	—
230	C₂×Q₈	—	4	1	no	—
231	C₂²×C₄	—	4	1	no	—
232	C₂²×C₄	—	4	1	no	—
233	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
234	Q₁₆	—	2	2	no	—
235	Q₁₆	—	2	2	no	—
236	Q₁₆	—	2	2	no	—
237	Q₁₆	—	2	2	no	—
238	Q₁₆	—	2	2	no	—
239	Q₁₆	—	4	1	no	—
240	Q₁₆	—	4	1	no	—
241	Q₁₆	C₂²⋊C₄×C₁₉	1	4	yes	—
242	M₁₆	—	2	1	no	—
243	M₁₆	—	2	1	no	—
244	M₁₆	—	4	1	no	—
245	M₁₆	—	4	1	no	—
246	C₂×C₈	—	2	1	no	—
247	C₂×C₈	—	4	1	no	—
248	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
249	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
250	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
251	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
252	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
253	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
254	C₄⋊C₄	—	2	2	no	—
255	C₄⋊C₄	—	4	4	no	—
256	C₄⋊C₄	D₈×C₁₉	1	2	yes	—
257	C₂²⋊C₄	—	2	1	no	—
258	C₂²⋊C₄	—	4	1	no	—
259	C₄²	—	2	1	no	—
260	C₄²	—	4	4	no	—
261	C₄²	—	4	1	no	—
262	C₁₆	—	2	2	no	—
263	C₁₆	—	4	1	no	—
264	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
265	Q₈	—	2	4	no	—
266	Q₈	—	4	2	no	—
267	Q₈	—	4	2	no	—
268	Q₈	—	4	2	no	—
269	Q₈	—	4	2	no	—
270	Q₈	—	4	2	no	—
271	Q₈	—	8	1	no	—
272	Q₈	—	8	1	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	4	2	no	—
275	C₂×C₄	—	4	2	no	—
276	C₂×C₄	—	4	2	no	—
277	C₂×C₄	—	4	2	no	—
278	C₂×C₄	—	4	2	no	—
279	C₂×C₄	—	8	1	no	—
280	C₂×C₄	—	8	1	no	—
281	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
282	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
283	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
284	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
285	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
286	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
287	C₈	—	4	1	no	—
288	C₈	—	8	1	no	—
289	C₈	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
290	C₈	C₄×D₄×C₁₉	1	1	yes	characteristic
291	C₈	C₁₉×#121	1	1	yes	characteristic
292	C₈	C₁₉×#123	1	1	yes	characteristic
293	C₂²	—	2	2	no	—
294	C₂²	C₁₉×#442	1	1	yes	characteristic
295	C₂²	C₁₉×#447	1	1	yes	characteristic
296	C₂²	C₁₉×#463	1	1	yes	characteristic
297	C₄	—	4	2	no	—
298	C₄	—	4	4	no	—
299	C₄	—	8	2	no	—
300	C₄	—	8	2	no	—
301	C₄	C₁₉×#386	1	1	yes	characteristic
302	C₄	C₄×D₈×C₁₉	1	1	yes	characteristic
303	C₄	C₁₉×#449	1	1	yes	characteristic
304	C₄	C₁₉×#459	1	1	yes	characteristic
305	C₂	—	2	1	no	—
306	C₂	—	2	1	no	—
307	C₂	C₁₉×#1879	1	1	yes	characteristic
308	C₂	C₁₉×#2195	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	AGL(1,ℤ/8)
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#405 ◁ G

Complements

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

N	H ≅ G/N	type
13. C₂×C₁₉×Q₃₂	C₄	semidirect
109. #13020	C₁₉	direct (N × H)
163. C₂×Q₃₂	C₄×C₁₉	semidirect
218. C₁₉	#13020	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×Q₃₂	2
C₁₉×#2950	2
C₂×C₁₉×#362	2
C₁₉×#2141	2
C₁₉×#1979	2
C₁₉×#1382	2
C₁₉×#1379	2
#13020	19

Subgroups — C19×#13020 #18018979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13020 #18018979