Subgroups — C₁₉×#11348 #18017307

Order 4864.

666 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1742	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1740	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#339	C₂	1	2	yes	maximal
5	C₂×C₁₉×H(3,ℤ/4)	C₂	1	2	yes	maximal
6	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
7	C₂×C₁₉×#117	C₂²	1	2	yes	—
8	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#389	—	2	2	no	—
12	C₁₉×#385	—	2	2	no	—
13	C₄×C₄⋊C₄×C₁₉	C₄	1	4	yes	complemented
14	C₁₉×#343	—	2	2	no	—
15	C₁₉×#342	—	2	2	no	—
16	C₁₉×#339	—	2	4	no	—
17	C₁₉×H(3,ℤ/4)	—	2	4	no	—
18	C₂³×C₄×C₁₉	—	2	1	no	—
19	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂×M₁₆×C₁₉	—	2	2	no	—
21	C₂×M₁₆×C₁₉	—	2	2	no	—
22	C₂×M₁₆×C₁₉	—	2	2	no	—
23	C₂×M₁₆×C₁₉	—	2	2	no	—
24	C₂×M₁₆×C₁₉	—	2	2	no	—
25	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
26	C₂²×C₈×C₁₉	—	2	2	no	—
27	C₁₉×#117	—	2	2	no	—
28	C₁₉×#117	—	2	2	no	—
29	C₁₉×#117	—	2	2	no	—
30	C₁₉×#117	—	2	2	no	—
31	C₁₉×#117	—	2	2	no	—
32	C₁₉×#117	—	2	2	no	—
33	C₁₉×#117	—	2	2	no	—
34	C₁₉×#117	Q₈	1	4	yes	—
35	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
42	C₂×C₄²×C₁₉	—	2	2	no	—
43	C₂×C₄²×C₁₉	—	2	2	no	—
44	C₂×C₄²×C₁₉	—	2	2	no	—
45	C₂×C₄²×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
49	C₁₉×#95	—	2	4	no	—
50	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	4	4	no	—
54	C₂²×C₄×C₁₉	—	4	1	no	—
55	C₂²×C₄×C₁₉	—	4	1	no	—
56	C₂²×C₄×C₁₉	—	4	2	no	—
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
58	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
60	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
62	C₂²×C₄×C₁₉	#41	1	2	yes	—
63	C₂²×C₄×C₁₉	#41	1	2	yes	—
64	C₂²×C₄×C₁₉	#41	1	2	yes	—
65	C₂²×C₄×C₁₉	#41	1	2	yes	—
66	M₁₆×C₁₉	—	2	4	no	—
67	M₁₆×C₁₉	—	2	4	no	—
68	M₁₆×C₁₉	—	4	2	no	—
69	M₁₆×C₁₉	—	4	2	no	—
70	C₂×C₈×C₁₉	—	2	4	no	—
71	C₂×C₈×C₁₉	—	4	2	no	—
72	C₂×C₈×C₁₉	—	4	2	no	—
73	C₄⋊C₄×C₁₉	—	2	4	no	—
74	C₄⋊C₄×C₁₉	—	2	4	no	—
75	C₄⋊C₄×C₁₉	—	4	8	no	—
76	C₄⋊C₄×C₁₉	—	4	2	no	—
77	C₄⋊C₄×C₁₉	—	4	2	no	—
78	C₂²⋊C₄×C₁₉	—	2	4	no	—
79	C₂²⋊C₄×C₁₉	—	2	4	no	—
80	C₂²⋊C₄×C₁₉	—	4	1	no	—
81	C₂²⋊C₄×C₁₉	—	4	1	no	—
82	C₂²⋊C₄×C₁₉	—	4	2	no	—
83	C₄²×C₁₉	—	2	2	no	—
84	C₄²×C₁₉	—	2	2	no	—
85	C₄²×C₁₉	—	2	4	no	—
86	C₄²×C₁₉	—	2	4	no	—
87	C₄²×C₁₉	—	2	4	no	—
88	C₄²×C₁₉	—	4	2	no	—
89	C₄²×C₁₉	—	4	2	no	—
90	#11348	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂³×C₁₉	—	4	2	no	—
92	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
94	C₂³×C₁₉	#123	1	2	yes	—
95	C₂³×C₁₉	#124	1	1	yes	characteristic
96	C₂³×C₁₉	#127	1	1	yes	characteristic
97	C₂×C₄×C₁₉	—	2	4	no	—
98	C₂×C₄×C₁₉	—	2	4	no	—
99	C₂×C₄×C₁₉	—	4	2	no	—
100	C₂×C₄×C₁₉	—	4	4	no	—
101	C₂×C₄×C₁₉	—	4	4	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	—	4	4	no	—
104	C₂×C₄×C₁₉	—	4	4	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	4	4	no	—
107	C₂×C₄×C₁₉	—	8	4	no	—
108	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
110	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
111	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
112	C₂×C₄×C₁₉	#121	1	2	yes	—
113	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
114	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
115	C₂×C₄×C₁₉	#123	1	2	yes	—
116	C₂×C₄×C₁₉	#123	1	2	yes	—
117	C₂×C₄×C₁₉	#123	1	2	yes	—
118	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
119	C₂×C₄×C₁₉	#125	1	2	yes	—
120	C₂×C₄×C₁₉	#125	1	2	yes	—
121	C₂×C₄×C₁₉	#126	1	2	yes	—
122	C₂×C₄×C₁₉	#126	1	2	yes	—
123	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
124	C₈×C₁₉	—	4	4	no	—
125	#2296	C₂×C₁₉	1	1	yes	characteristic
126	#1742	C₂×C₁₉	1	1	yes	characteristic
127	#1740	C₂×C₁₉	1	1	yes	characteristic
128	C₂×#339	C₂×C₁₉	1	2	yes	—
129	C₂×H(3,ℤ/4)	C₂×C₁₉	1	2	yes	—
130	C₂²×C₁₉	—	2	2	no	—
131	C₂²×C₁₉	—	2	4	no	—
132	C₂²×C₁₉	—	4	1	no	—
133	C₂²×C₁₉	—	4	1	no	—
134	C₂²×C₁₉	—	4	2	no	—
135	C₂²×C₁₉	#381	1	1	yes	characteristic
136	C₂²×C₁₉	#390	1	1	yes	characteristic
137	C₂²×C₁₉	#391	1	1	yes	characteristic
138	C₂²×C₁₉	#399	1	2	yes	—
139	C₂²×C₁₉	#400	1	2	yes	—
140	C₄×C₁₉	—	4	4	no	—
141	C₄×C₁₉	—	4	4	no	—
142	C₄×C₁₉	—	8	2	no	—
143	C₄×C₁₉	—	8	4	no	—
144	C₄×C₁₉	#387	1	2	yes	—
145	C₄×C₁₉	#387	1	2	yes	—
146	C₄×C₁₉	#397	1	2	yes	—
147	C₄×C₁₉	#398	1	2	yes	—
148	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
149	C₂×#117	C₂²×C₁₉	1	2	yes	—
150	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
151	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
152	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
153	#389	—	2	2	no	—
154	#385	—	2	2	no	—
155	C₄×C₄⋊C₄	C₄×C₁₉	1	4	yes	complemented
156	#343	—	2	2	no	—
157	#342	—	2	2	no	—
158	#339	—	2	4	no	—
159	H(3,ℤ/4)	—	2	4	no	—
160	C₂×C₁₉	—	2	1	no	—
161	C₂×C₁₉	—	2	2	no	—
162	C₂×C₁₉	—	2	1	no	—
163	C₂×C₁₉	—	2	2	no	—
164	C₂×C₁₉	#1445	1	1	yes	characteristic
165	C₂×C₁₉	#1827	1	2	yes	—
166	C₂³×C₄	—	2	1	no	—
167	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
168	C₂×M₁₆	—	2	2	no	—
169	C₂×M₁₆	—	2	2	no	—
170	C₂×M₁₆	—	2	2	no	—
171	C₂×M₁₆	—	2	2	no	—
172	C₂×M₁₆	—	2	2	no	—
173	C₂×M₁₆	D₄×C₁₉	1	4	yes	—
174	C₂²×C₈	—	2	2	no	—
175	#117	—	2	2	no	—
176	#117	—	2	2	no	—
177	#117	—	2	2	no	—
178	#117	—	2	2	no	—
179	#117	—	2	2	no	—
180	#117	—	2	2	no	—
181	#117	—	2	2	no	—
182	#117	Q₈×C₁₉	1	4	yes	—
183	C₂×C₄⋊C₄	—	2	2	no	—
184	C₂×C₄⋊C₄	—	2	4	no	—
185	C₂×C₄⋊C₄	—	2	1	no	—
186	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
187	C₂×C₂²⋊C₄	—	2	2	no	—
188	C₂×C₂²⋊C₄	—	2	1	no	—
189	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
190	C₂×C₄²	—	2	2	no	—
191	C₂×C₄²	—	2	2	no	—
192	C₂×C₄²	—	2	2	no	—
193	C₂×C₄²	—	2	1	no	—
194	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
195	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
196	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
197	#95	—	2	4	no	—
198	C₁₉	#11348	1	1	yes	characteristic, direct product factor, Sylow
199	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
200	C₂²×C₄	—	2	2	no	—
201	C₂²×C₄	—	2	2	no	—
202	C₂²×C₄	—	4	4	no	—
203	C₂²×C₄	—	4	1	no	—
204	C₂²×C₄	—	4	1	no	—
205	C₂²×C₄	—	4	2	no	—
206	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
207	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
208	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
209	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
210	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
211	C₂²×C₄	#41×C₁₉	1	2	yes	—
212	C₂²×C₄	#41×C₁₉	1	2	yes	—
213	C₂²×C₄	#41×C₁₉	1	2	yes	—
214	C₂²×C₄	#41×C₁₉	1	2	yes	—
215	M₁₆	—	2	4	no	—
216	M₁₆	—	2	4	no	—
217	M₁₆	—	4	2	no	—
218	M₁₆	—	4	2	no	—
219	C₂×C₈	—	2	4	no	—
220	C₂×C₈	—	4	2	no	—
221	C₂×C₈	—	4	2	no	—
222	C₄⋊C₄	—	2	4	no	—
223	C₄⋊C₄	—	2	4	no	—
224	C₄⋊C₄	—	4	8	no	—
225	C₄⋊C₄	—	4	2	no	—
226	C₄⋊C₄	—	4	2	no	—
227	C₂²⋊C₄	—	2	4	no	—
228	C₂²⋊C₄	—	2	4	no	—
229	C₂²⋊C₄	—	4	1	no	—
230	C₂²⋊C₄	—	4	1	no	—
231	C₂²⋊C₄	—	4	2	no	—
232	C₄²	—	2	2	no	—
233	C₄²	—	2	2	no	—
234	C₄²	—	2	4	no	—
235	C₄²	—	2	4	no	—
236	C₄²	—	2	4	no	—
237	C₄²	—	4	2	no	—
238	C₄²	—	4	2	no	—
239	C₂³	—	4	2	no	—
240	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
241	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
242	C₂³	C₁₉×#123	1	2	yes	—
243	C₂³	C₁₉×#124	1	1	yes	characteristic
244	C₂³	C₁₉×#127	1	1	yes	characteristic
245	C₂×C₄	—	2	4	no	—
246	C₂×C₄	—	2	4	no	—
247	C₂×C₄	—	4	2	no	—
248	C₂×C₄	—	4	4	no	—
249	C₂×C₄	—	4	4	no	—
250	C₂×C₄	—	4	2	no	—
251	C₂×C₄	—	4	4	no	—
252	C₂×C₄	—	4	4	no	—
253	C₂×C₄	—	4	2	no	—
254	C₂×C₄	—	4	4	no	—
255	C₂×C₄	—	8	4	no	—
256	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
257	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
258	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
259	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
260	C₂×C₄	C₁₉×#121	1	2	yes	—
261	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
262	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
263	C₂×C₄	C₁₉×#123	1	2	yes	—
264	C₂×C₄	C₁₉×#123	1	2	yes	—
265	C₂×C₄	C₁₉×#123	1	2	yes	—
266	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
267	C₂×C₄	C₁₉×#125	1	2	yes	—
268	C₂×C₄	C₁₉×#125	1	2	yes	—
269	C₂×C₄	C₁₉×#126	1	2	yes	—
270	C₂×C₄	C₁₉×#126	1	2	yes	—
271	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
272	C₈	—	4	4	no	—
273	C₂²	—	2	2	no	—
274	C₂²	—	2	4	no	—
275	C₂²	—	4	1	no	—
276	C₂²	—	4	1	no	—
277	C₂²	—	4	2	no	—
278	C₂²	C₁₉×#381	1	1	yes	characteristic
279	C₂²	C₁₉×#390	1	1	yes	characteristic
280	C₂²	C₁₉×#391	1	1	yes	characteristic
281	C₂²	C₁₉×#399	1	2	yes	—
282	C₂²	C₁₉×#400	1	2	yes	—
283	C₄	—	4	4	no	—
284	C₄	—	4	4	no	—
285	C₄	—	8	2	no	—
286	C₄	—	8	4	no	—
287	C₄	C₁₉×#387	1	2	yes	—
288	C₄	C₁₉×#387	1	2	yes	—
289	C₄	C₁₉×#397	1	2	yes	—
290	C₄	C₁₉×#398	1	2	yes	—
291	C₂	—	2	1	no	—
292	C₂	—	2	2	no	—
293	C₂	—	2	1	no	—
294	C₂	—	2	2	no	—
295	C₂	C₁₉×#1445	1	1	yes	characteristic
296	C₂	C₁₉×#1827	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#117
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	#381
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
13. C₄×C₄⋊C₄×C₁₉	C₄	semidirect
90. #11348	C₁₉	direct (N × H)
155. C₄×C₄⋊C₄	C₄×C₁₉	semidirect
198. C₁₉	#11348	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2296	2
C₁₉×#1742	2
C₁₉×#1740	2
C₂×C₁₉×#339	2
C₂×C₁₉×H(3,ℤ/4)	2
#11348	19

Subgroups — C19×#11348 #18017307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11348 #18017307