Subgroups — C₁₉×#14601 #18020560

Order 4864.

1290 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#395	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1446	C₂	1	2	yes	maximal
3	C₁₉×#1441	C₂	1	3	yes	maximal
4	C₁₉×#1436	C₂	1	6	yes	maximal
5	C₁₉×C₄⋊#95	C₂	1	3	yes	maximal
6	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
9	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
10	C₂²×C₄²×C₁₉	C₂²	1	3	yes	—
11	C₁₉×#395	C₄	1	8	yes	complemented
12	C₂×C₁₉×#95	C₂²	1	6	yes	—
13	C₂×C₁₉×#95	C₂²	1	3	yes	—
14	C₂×C₁₉×#95	C₂²	1	6	yes	—
15	C₂×C₁₉×#95	C₂²	1	6	yes	—
16	C₂×C₁₉×#95	C₂²	1	3	yes	—
17	C₂²×Q₈×C₁₉	—	4	3	no	—
18	C₂²×Q₈×C₁₉	—	4	3	no	—
19	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
20	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
21	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
22	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
24	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
25	C₂×C₄⋊C₄×C₁₉	—	4	3	no	—
26	C₂×C₄⋊C₄×C₁₉	—	4	3	no	—
27	C₂×C₄⋊C₄×C₁₉	—	4	3	no	—
28	C₂×C₄⋊C₄×C₁₉	—	4	3	no	—
29	C₂×C₄⋊C₄×C₁₉	—	4	3	no	—
30	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	12	yes	—
31	C₂×C₄⋊C₄×C₁₉	Q₈	1	12	yes	complemented
32	C₂×C₄²×C₁₉	—	2	6	no	—
33	C₂×C₄²×C₁₉	—	4	3	no	—
34	C₂×C₄²×C₁₉	—	4	3	no	—
35	C₁₉×#95	—	2	12	no	—
36	C₁₉×#95	—	4	6	no	—
37	C₁₉×#95	—	4	6	no	—
38	C₁₉×#95	—	4	3	no	—
39	C₁₉×#95	C₂×C₄	1	12	yes	—
40	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
41	C₂×Q₈×C₁₉	—	4	12	no	—
42	C₂×Q₈×C₁₉	—	4	12	no	—
43	C₂×Q₈×C₁₉	—	4	4	no	—
44	C₂²×C₄×C₁₉	—	2	3	no	—
45	C₂²×C₄×C₁₉	—	2	3	no	—
46	C₂²×C₄×C₁₉	—	2	3	no	—
47	C₂²×C₄×C₁₉	—	2	3	no	—
48	C₂²×C₄×C₁₉	—	2	6	no	—
49	C₂²×C₄×C₁₉	—	2	6	no	—
50	C₂²×C₄×C₁₉	—	2	6	no	—
51	C₂²×C₄×C₁₉	—	2	6	no	—
52	C₂²×C₄×C₁₉	—	2	3	no	—
53	C₂²×C₄×C₁₉	—	2	3	no	—
54	C₂²×C₄×C₁₉	—	2	3	no	—
55	C₂²×C₄×C₁₉	—	2	3	no	—
56	C₂²×C₄×C₁₉	—	2	6	no	—
57	C₂²×C₄×C₁₉	—	2	6	no	—
58	C₂²×C₄×C₁₉	—	2	6	no	—
59	C₂²×C₄×C₁₉	—	2	6	no	—
60	C₂²×C₄×C₁₉	—	2	6	no	—
61	C₂²×C₄×C₁₉	—	2	6	no	—
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
65	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
66	C₂²×C₄×C₁₉	C₂×Q₈	1	12	yes	—
67	C₂²×C₄×C₁₉	C₂×Q₈	1	6	yes	—
68	C₂²×C₄×C₁₉	#41	1	6	yes	—
69	C₄⋊C₄×C₁₉	—	4	12	no	—
70	C₄⋊C₄×C₁₉	—	4	12	no	—
71	C₄⋊C₄×C₁₉	—	4	4	no	—
72	C₄²×C₁₉	—	4	12	no	—
73	#14601	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
75	C₂³×C₁₉	C₂²×Q₈	1	3	yes	—
76	C₂³×C₁₉	C₂×#41	1	3	yes	—
77	C₂³×C₁₉	H(5,𝔽₂)	1	3	yes	—
78	C₂³×C₁₉	H(5,𝔽₂)	1	3	yes	—
79	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
80	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
81	Q₈×C₁₉	—	4	16	no	—
82	C₂×C₄×C₁₉	—	2	6	no	—
83	C₂×C₄×C₁₉	—	2	6	no	—
84	C₂×C₄×C₁₉	—	2	6	no	—
85	C₂×C₄×C₁₉	—	2	6	no	—
86	C₂×C₄×C₁₉	—	2	6	no	—
87	C₂×C₄×C₁₉	—	2	6	no	—
88	C₂×C₄×C₁₉	—	2	6	no	—
89	C₂×C₄×C₁₉	—	2	6	no	—
90	C₂×C₄×C₁₉	—	2	12	no	—
91	C₂×C₄×C₁₉	—	2	12	no	—
92	C₂×C₄×C₁₉	—	2	12	no	—
93	C₂×C₄×C₁₉	—	2	12	no	—
94	C₂×C₄×C₁₉	—	4	6	no	—
95	C₂×C₄×C₁₉	—	4	6	no	—
96	C₂×C₄×C₁₉	—	4	6	no	—
97	C₂×C₄×C₁₉	—	4	3	no	—
98	C₂×C₄×C₁₉	—	4	6	no	—
99	C₂×C₄×C₁₉	—	4	6	no	—
100	C₂×C₄×C₁₉	—	4	3	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	3	no	—
103	C₂×C₄×C₁₉	—	4	6	no	—
104	C₂×C₄×C₁₉	—	4	6	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	C₄×Q₈	1	12	yes	—
107	C₂×#395	C₂×C₁₉	1	1	yes	characteristic
108	#1446	C₂×C₁₉	1	2	yes	—
109	#1441	C₂×C₁₉	1	3	yes	—
110	#1436	C₂×C₁₉	1	6	yes	—
111	C₄⋊#95	C₂×C₁₉	1	3	yes	—
112	C₂²×C₁₉	C₂×C₄×Q₈	1	3	yes	—
113	C₂²×C₁₉	#518	1	3	yes	—
114	C₂²×C₁₉	#520	1	1	yes	characteristic
115	C₂²×C₁₉	#538	1	3	yes	—
116	C₂²×C₁₉	#539	1	3	yes	—
117	C₂²×C₁₉	#543	1	3	yes	—
118	C₂²×C₁₉	#544	1	3	yes	—
119	C₂²×C₁₉	#554	1	6	yes	—
120	C₂²×C₁₉	#555	1	3	yes	—
121	C₂²×C₁₉	Q₈²	1	3	yes	—
122	C₂²×C₁₉	#560	1	3	yes	—
123	C₂²×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
124	C₄×C₁₉	—	2	12	no	—
125	C₄×C₁₉	—	4	2	no	—
126	C₄×C₁₉	—	4	6	no	—
127	C₄×C₁₉	—	4	12	no	—
128	C₄×C₁₉	—	8	2	no	—
129	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
130	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
131	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
132	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
133	C₂²×C₄²	C₂²×C₁₉	1	3	yes	—
134	#395	C₄×C₁₉	1	8	yes	complemented
135	C₂×#95	C₂²×C₁₉	1	6	yes	—
136	C₂×#95	C₂²×C₁₉	1	3	yes	—
137	C₂×#95	C₂²×C₁₉	1	6	yes	—
138	C₂×#95	C₂²×C₁₉	1	6	yes	—
139	C₂×#95	C₂²×C₁₉	1	3	yes	—
140	C₂×C₁₉	#2329	1	3	yes	—
141	C₂×C₁₉	#2369	1	3	yes	—
142	C₂×C₁₉	#2375	1	1	yes	characteristic
143	C₂×C₁₉	#2784	1	3	yes	—
144	C₂×C₁₉	#2785	1	1	yes	characteristic
145	C₂×C₁₉	#2792	1	3	yes	—
146	C₂×C₁₉	#2811	1	1	yes	characteristic
147	C₂²×Q₈	—	4	3	no	—
148	C₂²×Q₈	—	4	3	no	—
149	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
150	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
151	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
152	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
153	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
154	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
155	C₂×C₄⋊C₄	—	4	3	no	—
156	C₂×C₄⋊C₄	—	4	3	no	—
157	C₂×C₄⋊C₄	—	4	3	no	—
158	C₂×C₄⋊C₄	—	4	3	no	—
159	C₂×C₄⋊C₄	—	4	3	no	—
160	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	12	yes	—
161	C₂×C₄⋊C₄	Q₈×C₁₉	1	12	yes	complemented
162	C₂×C₄²	—	2	6	no	—
163	C₂×C₄²	—	4	3	no	—
164	C₂×C₄²	—	4	3	no	—
165	#95	—	2	12	no	—
166	#95	—	4	3	no	—
167	#95	—	4	6	no	—
168	#95	—	4	6	no	—
169	#95	C₂×C₄×C₁₉	1	12	yes	—
170	C₁₉	#14601	1	1	yes	characteristic, direct product factor, Sylow
171	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
172	C₂×Q₈	—	4	12	no	—
173	C₂×Q₈	—	4	12	no	—
174	C₂×Q₈	—	4	4	no	—
175	C₂²×C₄	—	2	3	no	—
176	C₂²×C₄	—	2	3	no	—
177	C₂²×C₄	—	2	3	no	—
178	C₂²×C₄	—	2	3	no	—
179	C₂²×C₄	—	2	6	no	—
180	C₂²×C₄	—	2	6	no	—
181	C₂²×C₄	—	2	6	no	—
182	C₂²×C₄	—	2	6	no	—
183	C₂²×C₄	—	2	3	no	—
184	C₂²×C₄	—	2	6	no	—
185	C₂²×C₄	—	2	6	no	—
186	C₂²×C₄	—	2	6	no	—
187	C₂²×C₄	—	2	6	no	—
188	C₂²×C₄	—	2	3	no	—
189	C₂²×C₄	—	2	3	no	—
190	C₂²×C₄	—	2	3	no	—
191	C₂²×C₄	—	2	6	no	—
192	C₂²×C₄	—	2	6	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
195	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
196	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
197	C₂²×C₄	C₂×Q₈×C₁₉	1	12	yes	—
198	C₂²×C₄	C₂×Q₈×C₁₉	1	6	yes	—
199	C₂²×C₄	#41×C₁₉	1	6	yes	—
200	C₄⋊C₄	—	4	12	no	—
201	C₄⋊C₄	—	4	12	no	—
202	C₄⋊C₄	—	4	4	no	—
203	C₄²	—	4	12	no	—
204	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
205	C₂³	C₂²×Q₈×C₁₉	1	3	yes	—
206	C₂³	C₂×#41×C₁₉	1	3	yes	—
207	C₂³	C₁₉×H(5,𝔽₂)	1	3	yes	—
208	C₂³	C₁₉×H(5,𝔽₂)	1	3	yes	—
209	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
210	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
211	Q₈	—	4	16	no	—
212	C₂×C₄	—	2	6	no	—
213	C₂×C₄	—	2	6	no	—
214	C₂×C₄	—	2	6	no	—
215	C₂×C₄	—	2	6	no	—
216	C₂×C₄	—	2	6	no	—
217	C₂×C₄	—	2	6	no	—
218	C₂×C₄	—	2	6	no	—
219	C₂×C₄	—	2	6	no	—
220	C₂×C₄	—	2	12	no	—
221	C₂×C₄	—	2	12	no	—
222	C₂×C₄	—	2	12	no	—
223	C₂×C₄	—	2	12	no	—
224	C₂×C₄	—	4	6	no	—
225	C₂×C₄	—	4	6	no	—
226	C₂×C₄	—	4	6	no	—
227	C₂×C₄	—	4	3	no	—
228	C₂×C₄	—	4	6	no	—
229	C₂×C₄	—	4	6	no	—
230	C₂×C₄	—	4	3	no	—
231	C₂×C₄	—	4	1	no	—
232	C₂×C₄	—	4	3	no	—
233	C₂×C₄	—	4	6	no	—
234	C₂×C₄	—	4	6	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	C₄×Q₈×C₁₉	1	12	yes	—
237	C₂²	C₂×C₄×Q₈×C₁₉	1	3	yes	—
238	C₂²	C₁₉×#518	1	3	yes	—
239	C₂²	C₁₉×#520	1	1	yes	characteristic
240	C₂²	C₁₉×#538	1	3	yes	—
241	C₂²	C₁₉×#539	1	3	yes	—
242	C₂²	C₁₉×#543	1	3	yes	—
243	C₂²	C₁₉×#544	1	3	yes	—
244	C₂²	C₁₉×#554	1	6	yes	—
245	C₂²	C₁₉×#555	1	3	yes	—
246	C₂²	Q₈²×C₁₉	1	3	yes	—
247	C₂²	C₁₉×#560	1	3	yes	—
248	C₂²	C₁₉×H(3,𝔽₄)	1	1	yes	characteristic
249	C₄	—	2	12	no	—
250	C₄	—	4	12	no	—
251	C₄	—	4	6	no	—
252	C₄	—	4	2	no	—
253	C₄	—	8	2	no	—
254	C₂	C₁₉×#2329	1	3	yes	—
255	C₂	C₁₉×#2369	1	3	yes	—
256	C₂	C₁₉×#2375	1	1	yes	characteristic
257	C₂	C₁₉×#2784	1	3	yes	—
258	C₂	C₁₉×#2785	1	1	yes	characteristic
259	C₂	C₁₉×#2792	1	3	yes	—
260	C₂	C₁₉×#2811	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₁₉×#395	C₄	semidirect
31. C₂×C₄⋊C₄×C₁₉	Q₈	semidirect
73. #14601	C₁₉	direct (N × H)
134. #395	C₄×C₁₉	semidirect
161. C₂×C₄⋊C₄	Q₈×C₁₉	semidirect
170. C₁₉	#14601	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#395	2
C₁₉×#1446	2
C₁₉×#1441	2
C₁₉×#1436	2
C₁₉×C₄⋊#95	2
#14601	19

Subgroups — C19×#14601 #18020560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14601 #18020560