Subgroups — C₁₉×#3335 #14561192

Order 2432.

388 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#547	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#483	C₂	1	2	yes	maximal, complemented
5	C₁₉×#481	C₂	1	2	yes	maximal, complemented
6	C₁₉×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#465	C₂	1	2	yes	maximal, complemented
9	C₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#106	C₂	1	2	yes	maximal, complemented
12	C₂×#41×C₁₉	—	2	1	no	—
13	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
15	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₁₉×#125	—	2	1	no	—
18	C₁₉×#123	—	2	2	no	—
19	C₁₉×C₂²⋊Q₈	—	2	1	no	—
20	C₁₉×C₂²⋊Q₈	—	2	2	no	—
21	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₁₉×#121	C₂²	1	2	yes	—
23	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₄×D₄×C₁₉	—	2	1	no	—
25	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
28	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
29	C₁₉×#106	C₂²	1	1	yes	characteristic
30	C₁₉×#106	C₂²	1	2	yes	—
31	C₁₉×#106	C₂²	1	2	yes	—
32	C₁₉×#106	C₂²	1	2	yes	—
33	C₁₉×#106	C₂²	1	2	yes	—
34	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₁₉×#103	C₂²	1	1	yes	characteristic
36	C₁₉×#103	C₂²	1	2	yes	—
37	C₁₉×#102	C₂²	1	1	yes	characteristic
38	C₁₉×#102	C₂²	1	2	yes	—
39	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
40	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
41	#41×C₁₉	—	4	4	no	—
42	C₂×Q₈×C₁₉	—	2	1	no	—
43	C₂×Q₈×C₁₉	—	2	1	no	—
44	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂×D₄×C₁₉	—	2	2	no	—
46	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	2	1	no	—
51	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
52	SD₁₆×C₁₉	—	2	2	no	—
53	C₂×C₈×C₁₉	—	2	4	no	—
54	C₂×C₈×C₁₉	C₂³	1	2	yes	—
55	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
67	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
68	C₂²⋊C₄×C₁₉	—	2	2	no	—
69	C₂²⋊C₄×C₁₉	—	2	1	no	—
70	C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
72	C₄²×C₁₉	—	2	1	no	—
73	C₄²×C₁₉	C₂³	1	1	yes	characteristic
74	C₂³×C₁₉	—	2	1	no	—
75	C₂³×C₁₉	C₂×D₄	1	2	yes	—
76	Q₈×C₁₉	—	2	1	no	—
77	Q₈×C₁₉	—	2	1	no	—
78	Q₈×C₁₉	—	4	2	no	—
79	Q₈×C₁₉	—	8	1	no	—
80	D₄×C₁₉	—	2	1	no	—
81	D₄×C₁₉	—	2	1	no	—
82	D₄×C₁₉	—	4	4	no	—
83	D₄×C₁₉	SD₁₆	1	4	yes	complemented
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	4	4	no	—
92	C₂×C₄×C₁₉	—	4	2	no	—
93	C₂×C₄×C₁₉	—	8	2	no	—
94	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
96	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
98	C₈×C₁₉	—	2	2	no	—
99	C₈×C₁₉	—	2	1	no	—
100	C₈×C₁₉	#41	1	2	yes	complemented
101	#3335	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂²×C₁₉	—	2	2	no	—
103	C₂²×C₁₉	—	2	2	no	—
104	C₂²×C₁₉	—	4	1	no	—
105	C₂²×C₁₉	—	4	1	no	—
106	C₂²×C₁₉	—	4	1	no	—
107	C₂²×C₁₉	C₂×SD₁₆	1	4	yes	—
108	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
109	C₄×C₁₉	—	2	2	no	—
110	C₄×C₁₉	—	2	1	no	—
111	C₄×C₁₉	—	4	1	no	—
112	C₄×C₁₉	—	4	1	no	—
113	C₄×C₁₉	—	4	2	no	—
114	C₄×C₁₉	—	4	1	no	—
115	C₄×C₁₉	—	4	2	no	—
116	C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
117	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
118	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
119	#554	C₂×C₁₉	1	1	yes	characteristic, complemented
120	#547	C₂×C₁₉	1	1	yes	characteristic
121	#498	C₂×C₁₉	1	1	yes	characteristic, complemented
122	#483	C₂×C₁₉	1	2	yes	complemented
123	#481	C₂×C₁₉	1	2	yes	complemented
124	#476	C₂×C₁₉	1	1	yes	characteristic, complemented
125	#475	C₂×C₁₉	1	1	yes	characteristic, complemented
126	#465	C₂×C₁₉	1	2	yes	complemented
127	C₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
128	C₈×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
129	C₂×#106	C₂×C₁₉	1	2	yes	complemented
130	C₂×C₁₉	—	2	4	no	—
131	C₂×C₁₉	—	8	1	no	—
132	C₂×C₁₉	#547	1	1	yes	characteristic
133	C₂×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
134	C₂×C₁₉	#577	1	1	yes	characteristic
135	C₂×#41	—	2	1	no	—
136	C₂×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
137	C₂²×C₈	C₂²×C₁₉	1	2	yes	—
138	C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
139	C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
140	#125	—	2	1	no	—
141	#123	—	2	2	no	—
142	C₂²⋊Q₈	—	2	1	no	—
143	C₂²⋊Q₈	—	2	2	no	—
144	C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
145	#121	C₂²×C₁₉	1	2	yes	—
146	C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
147	C₄×D₄	—	2	1	no	—
148	C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
149	C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
150	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
151	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
152	#106	C₂²×C₁₉	1	1	yes	characteristic
153	#106	C₂²×C₁₉	1	2	yes	—
154	#106	C₂²×C₁₉	1	2	yes	—
155	#106	C₂²×C₁₉	1	2	yes	—
156	#106	C₂²×C₁₉	1	2	yes	—
157	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
158	#103	C₂²×C₁₉	1	1	yes	characteristic
159	#103	C₂²×C₁₉	1	2	yes	—
160	#102	C₂²×C₁₉	1	1	yes	characteristic
161	#102	C₂²×C₁₉	1	2	yes	—
162	C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
163	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
164	C₁₉	#3335	1	1	yes	characteristic, direct product factor, Sylow
165	#41	—	4	4	no	—
166	C₂×Q₈	—	2	1	no	—
167	C₂×Q₈	—	2	1	no	—
168	C₂×Q₈	C₂³×C₁₉	1	1	yes	characteristic
169	C₂×D₄	—	2	2	no	—
170	C₂×D₄	D₄×C₁₉	1	1	yes	characteristic
171	C₂×D₄	C₂³×C₁₉	1	1	yes	characteristic
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	1	no	—
175	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
176	SD₁₆	—	2	2	no	—
177	C₂×C₈	—	2	4	no	—
178	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
179	C₂×C₈	C₂³×C₁₉	1	2	yes	—
180	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	2	2	no	—
183	C₄⋊C₄	—	2	1	no	—
184	C₄⋊C₄	—	2	1	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	2	1	no	—
187	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
188	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
189	C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
190	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
191	C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
192	C₂²⋊C₄	—	2	2	no	—
193	C₂²⋊C₄	—	2	1	no	—
194	C₂²⋊C₄	—	2	2	no	—
195	C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
196	C₄²	—	2	1	no	—
197	C₄²	C₂³×C₁₉	1	1	yes	characteristic
198	C₂³	—	2	1	no	—
199	C₂³	C₂×D₄×C₁₉	1	2	yes	—
200	Q₈	—	2	1	no	—
201	Q₈	—	2	1	no	—
202	Q₈	—	4	2	no	—
203	Q₈	—	8	1	no	—
204	D₄	—	2	1	no	—
205	D₄	—	2	1	no	—
206	D₄	—	4	4	no	—
207	D₄	SD₁₆×C₁₉	1	4	yes	complemented
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	4	4	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	8	2	no	—
218	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
219	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
220	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
221	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
222	C₈	—	2	2	no	—
223	C₈	—	2	1	no	—
224	C₈	#41×C₁₉	1	2	yes	complemented
225	C₂²	—	2	2	no	—
226	C₂²	—	2	2	no	—
227	C₂²	—	4	1	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	1	no	—
230	C₂²	C₂×SD₁₆×C₁₉	1	4	yes	—
231	C₂²	C₂²×D₄×C₁₉	1	1	yes	characteristic
232	C₄	—	2	2	no	—
233	C₄	—	2	1	no	—
234	C₄	—	4	1	no	—
235	C₄	—	4	1	no	—
236	C₄	—	4	2	no	—
237	C₄	—	4	1	no	—
238	C₄	—	4	2	no	—
239	C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
240	C₄	C₂×#41×C₁₉	1	1	yes	characteristic
241	C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
242	C₂	—	2	4	no	—
243	C₂	—	8	1	no	—
244	C₂	C₁₉×#547	1	1	yes	characteristic
245	C₂	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
246	C₂	C₁₉×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#547	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#554	C₂	semidirect
3. C₁₉×#498	C₂	semidirect
4. C₁₉×#483	C₂	semidirect
5. C₁₉×#481	C₂	semidirect
6. C₁₉×#476	C₂	semidirect
7. C₁₉×#475	C₂	semidirect
8. C₁₉×#465	C₂	semidirect
9. C₄×SD₁₆×C₁₉	C₂	semidirect
10. C₈×D₄×C₁₉	C₂	semidirect
11. C₂×C₁₉×#106	C₂	semidirect
83. D₄×C₁₉	SD₁₆	semidirect
100. C₈×C₁₉	#41	semidirect
101. #3335	C₁₉	direct (N × H)
119. #554	C₂×C₁₉	semidirect
121. #498	C₂×C₁₉	semidirect
122. #483	C₂×C₁₉	semidirect
123. #481	C₂×C₁₉	semidirect
124. #476	C₂×C₁₉	semidirect
125. #475	C₂×C₁₉	semidirect
126. #465	C₂×C₁₉	semidirect
127. C₄×SD₁₆	C₂×C₁₉	semidirect
128. C₈×D₄	C₂×C₁₉	semidirect
129. C₂×#106	C₂×C₁₉	semidirect
164. C₁₉	#3335	direct (N × H)
207. D₄	SD₁₆×C₁₉	semidirect
224. C₈	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#554	2
C₁₉×#547	2
C₁₉×#498	2
C₁₉×#483	2
C₁₉×#481	2
C₁₉×#476	2
C₁₉×#475	2
C₁₉×#465	2
C₄×SD₁₆×C₁₉	2
C₈×D₄×C₁₉	2
C₂×C₁₉×#106	2
#3335	19

Subgroups — C19×#3335 #14561192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#3335 #14561192