Subgroups — C₁₉×#8655 #18014614

Order 4864.

418 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#446	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1834	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1803	C₂	1	2	yes	maximal
4	C₂×C₁₉×#335	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1296	C₂	1	2	yes	maximal
6	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#446	—	2	2	no	—
8	C₁₉×#446	C₄	1	4	yes	complemented
9	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
10	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
11	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#103	—	2	2	no	—
13	C₂×C₁₉×#97	—	2	1	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#384	C₂²	1	2	yes	—
16	C₁₉×#340	—	2	1	no	—
17	C₁₉×#340	—	2	1	no	—
18	C₁₉×#340	—	2	2	no	—
19	C₁₉×#335	—	2	2	no	—
20	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	—	2	1	no	—
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₄×Q₈×C₁₉	—	2	1	no	—
26	C₄×Q₈×C₁₉	—	2	1	no	—
27	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
28	C₄×Q₈×C₁₉	Q₈	1	2	yes	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	—	2	1	no	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₁₉×C₄⋊C₈	—	2	4	no	—
37	C₁₉×C₄⋊C₈	—	2	1	no	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
41	C₁₉×#103	—	4	4	no	—
42	C₁₉×#97	—	2	4	no	—
43	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
44	C₄×C₈×C₁₉	D₄	1	2	yes	—
45	C₂×Q₈×C₁₉	—	2	1	no	—
46	C₂×Q₈×C₁₉	—	2	2	no	—
47	C₂×Q₈×C₁₉	—	2	2	no	—
48	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₉	—	2	1	no	—
50	C₂²×C₄×C₁₉	—	2	1	no	—
51	C₂²×C₄×C₁₉	—	4	2	no	—
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
55	C₂×C₈×C₁₉	—	2	2	no	—
56	C₂×C₈×C₁₉	—	2	2	no	—
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₂×C₈×C₁₉	—	4	2	no	—
59	C₂×C₈×C₁₉	—	4	2	no	—
60	C₂×C₈×C₁₉	—	4	2	no	—
61	C₂×C₈×C₁₉	—	4	2	no	—
62	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
63	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
64	C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₄⋊C₄×C₁₉	—	4	2	no	—
68	C₄⋊C₄×C₁₉	—	4	2	no	—
69	C₄⋊C₄×C₁₉	—	4	2	no	—
70	C₄⋊C₄×C₁₉	—	4	2	no	—
71	C₄⋊C₄×C₁₉	—	8	2	no	—
72	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
73	C₄²×C₁₉	—	2	2	no	—
74	C₄²×C₁₉	—	2	2	no	—
75	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
78	C₄²×C₁₉	#41	1	1	yes	characteristic
79	#8655	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂³×C₁₉	#121	1	1	yes	characteristic
81	Q₈×C₁₉	—	2	4	no	—
82	Q₈×C₁₉	—	4	1	no	—
83	Q₈×C₁₉	—	4	1	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	—	4	1	no	—
90	C₂×C₄×C₁₉	—	4	1	no	—
91	C₂×C₄×C₁₉	—	8	2	no	—
92	C₂×C₄×C₁₉	—	8	2	no	—
93	C₂×C₄×C₁₉	—	8	2	no	—
94	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#135	1	2	yes	—
101	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
102	C₂×C₄×C₁₉	#137	1	2	yes	—
103	C₂×C₄×C₁₉	#137	1	2	yes	—
104	C₈×C₁₉	—	2	2	no	—
105	C₈×C₁₉	—	2	2	no	—
106	C₈×C₁₉	—	4	2	no	—
107	C₈×C₁₉	—	8	2	no	—
108	C₂×#446	C₂×C₁₉	1	1	yes	characteristic
109	#1834	C₂×C₁₉	1	1	yes	characteristic
110	#1803	C₂×C₁₉	1	2	yes	—
111	C₂×#335	C₂×C₁₉	1	1	yes	characteristic
112	#1296	C₂×C₁₉	1	2	yes	—
113	C₂²×C₁₉	#380	1	1	yes	characteristic
114	C₂²×C₁₉	#464	1	2	yes	—
115	C₂²×C₁₉	#468	1	2	yes	—
116	C₂²×C₁₉	#472	1	1	yes	characteristic
117	C₂²×C₁₉	#473	1	1	yes	characteristic
118	C₄×C₁₉	—	2	1	no	—
119	C₄×C₁₉	—	2	1	no	—
120	C₄×C₁₉	—	4	2	no	—
121	C₄×C₁₉	—	4	2	no	—
122	C₄×C₁₉	—	16	2	no	—
123	C₄×C₁₉	#416	1	1	yes	characteristic
124	C₄×C₁₉	#419	1	1	yes	characteristic
125	C₄×C₁₉	#428	1	2	yes	—
126	C₄×C₁₉	#469	1	1	yes	characteristic
127	C₄×C₁₉	#470	1	1	yes	characteristic
128	C₄×C₁₉	#479	1	2	yes	—
129	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
130	#446	—	2	2	no	—
131	#446	C₄×C₁₉	1	4	yes	complemented
132	C₂×C₄⋊C₈	—	2	1	no	—
133	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
134	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
135	C₂×#103	—	2	2	no	—
136	C₂×#97	—	2	1	no	—
137	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
138	#384	C₂²×C₁₉	1	2	yes	—
139	#340	—	2	1	no	—
140	#340	—	2	1	no	—
141	#340	—	2	2	no	—
142	#335	—	2	2	no	—
143	C₂×C₁₉	#1698	1	2	yes	—
144	C₂×C₁₉	#1700	1	2	yes	—
145	C₂×C₁₉	#1805	1	1	yes	characteristic
146	C₂×C₁₉	#1809	1	1	yes	characteristic
147	C₂×C₁₉	#1816	1	1	yes	characteristic
148	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
149	C₂²×C₈	—	2	1	no	—
150	C₂²×C₈	—	2	2	no	—
151	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
152	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
153	C₄×Q₈	—	2	1	no	—
154	C₄×Q₈	—	2	1	no	—
155	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
156	C₄×Q₈	Q₈×C₁₉	1	2	yes	—
157	C₂×C₄⋊C₄	—	2	1	no	—
158	C₂×C₄⋊C₄	—	2	2	no	—
159	C₂×C₄⋊C₄	—	2	2	no	—
160	C₂×C₄⋊C₄	—	2	2	no	—
161	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
162	C₂×C₄²	—	2	1	no	—
163	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
164	C₄⋊C₈	—	2	4	no	—
165	C₄⋊C₈	—	2	1	no	—
166	C₄⋊C₈	—	2	2	no	—
167	C₄⋊C₈	—	2	2	no	—
168	C₄⋊C₈	C₂×C₄×C₁₉	1	2	yes	—
169	#103	—	4	4	no	—
170	#97	—	2	4	no	—
171	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
172	C₄×C₈	D₄×C₁₉	1	2	yes	—
173	C₁₉	#8655	1	1	yes	characteristic, direct product factor, Sylow
174	C₂×Q₈	—	2	1	no	—
175	C₂×Q₈	—	2	2	no	—
176	C₂×Q₈	—	2	2	no	—
177	C₂×Q₈	C₄⋊C₄×C₁₉	1	2	yes	—
178	C₂²×C₄	—	2	1	no	—
179	C₂²×C₄	—	2	1	no	—
180	C₂²×C₄	—	4	2	no	—
181	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
182	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
183	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	2	no	—
186	C₂×C₈	—	2	2	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	4	2	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
192	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
193	C₄⋊C₄	—	2	2	no	—
194	C₄⋊C₄	—	2	1	no	—
195	C₄⋊C₄	—	2	2	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₄⋊C₄	—	4	2	no	—
198	C₄⋊C₄	—	4	2	no	—
199	C₄⋊C₄	—	4	2	no	—
200	C₄⋊C₄	—	8	2	no	—
201	C₄⋊C₄	C₄⋊C₄×C₁₉	1	2	yes	—
202	C₄²	—	2	2	no	—
203	C₄²	—	2	2	no	—
204	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
205	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
206	C₄²	C₂×Q₈×C₁₉	1	1	yes	characteristic
207	C₄²	#41×C₁₉	1	1	yes	characteristic
208	C₂³	C₁₉×#121	1	1	yes	characteristic
209	Q₈	—	2	4	no	—
210	Q₈	—	4	1	no	—
211	Q₈	—	4	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	4	1	no	—
218	C₂×C₄	—	4	1	no	—
219	C₂×C₄	—	8	2	no	—
220	C₂×C₄	—	8	2	no	—
221	C₂×C₄	—	8	2	no	—
222	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
223	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
224	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
225	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
226	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
227	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
228	C₂×C₄	C₁₉×#135	1	2	yes	—
229	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
230	C₂×C₄	C₁₉×#137	1	2	yes	—
231	C₂×C₄	C₁₉×#137	1	2	yes	—
232	C₈	—	2	2	no	—
233	C₈	—	2	2	no	—
234	C₈	—	4	2	no	—
235	C₈	—	8	2	no	—
236	C₂²	C₁₉×#380	1	1	yes	characteristic
237	C₂²	C₁₉×#464	1	2	yes	—
238	C₂²	C₁₉×#468	1	2	yes	—
239	C₂²	C₁₉×#472	1	1	yes	characteristic
240	C₂²	C₁₉×#473	1	1	yes	characteristic
241	C₄	—	2	1	no	—
242	C₄	—	2	1	no	—
243	C₄	—	4	2	no	—
244	C₄	—	4	2	no	—
245	C₄	—	16	2	no	—
246	C₄	C₁₉×#416	1	1	yes	characteristic
247	C₄	C₁₉×#419	1	1	yes	characteristic
248	C₄	C₁₉×#428	1	2	yes	—
249	C₄	C₁₉×#469	1	1	yes	characteristic
250	C₄	C₁₉×#470	1	1	yes	characteristic
251	C₄	C₁₉×#479	1	2	yes	—
252	C₂	C₁₉×#1698	1	2	yes	—
253	C₂	C₁₉×#1700	1	2	yes	—
254	C₂	C₁₉×#1805	1	1	yes	characteristic
255	C₂	C₁₉×#1809	1	1	yes	characteristic
256	C₂	C₁₉×#1816	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	#121
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₁₉×#446	C₄	semidirect
79. #8655	C₁₉	direct (N × H)
131. #446	C₄×C₁₉	semidirect
173. C₁₉	#8655	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×#446	2
C₁₉×#1834	2
C₁₉×#1803	2
C₂×C₁₉×#335	2
C₁₉×#1296	2
#8655	19

Subgroups — C19×#8655 #18014614

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8655 #18014614