Subgroups — C₁₉×#33373 #18039332

Order 4864.

1312 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3498	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2888	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2134	C₂	1	6	yes	maximal, complemented
4	C₁₉×#2132	C₂	1	6	yes	maximal, complemented
5	C₂×C₁₉×H(5,𝔽₂)	C₄	1	1	yes	characteristic
6	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
7	C₁₉×#568	—	2	2	no	—
8	C₁₉×#550	—	2	2	no	—
9	D₄²×C₁₉	—	2	6	no	—
10	C₁₉×#535	C₄	1	3	yes	—
11	C₁₉×#535	C₂²	1	3	yes	—
12	C₁₉×#532	C₂²	1	3	yes	—
13	C₂×C₁₉×#127	C₄	1	3	yes	—
14	C₄×#41×C₁₉	C₄	1	1	yes	characteristic
15	C₁₉×#413	C₂²	1	12	yes	complemented
16	C₂×C₁₉×#100	—	2	6	no	—
17	C₁₉×#356	C₂²	1	4	yes	complemented
18	C₁₉×#355	C₂²	1	12	yes	complemented
19	C₁₉×H(5,𝔽₂)	—	4	4	no	—
20	C₁₉×H(5,𝔽₂)	—	4	4	no	—
21	C₂×#41×C₁₉	—	2	1	no	—
22	C₂×#41×C₁₉	C₂×C₄	1	3	yes	—
23	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×#41×C₁₉	D₄	1	2	yes	—
25	C₂×#41×C₁₉	C₂³	1	3	yes	—
26	C₂²×D₄×C₁₉	—	2	6	no	—
27	C₂²×D₄×C₁₉	—	2	3	no	—
28	C₂²×D₄×C₁₉	C₂×C₄	1	3	yes	—
29	C₂²×D₄×C₁₉	C₂×C₄	1	3	yes	—
30	C₂²×D₄×C₁₉	D₄	1	6	yes	—
31	C₁₉×#131	—	4	8	no	—
32	C₂×M₁₆×C₁₉	—	2	12	no	—
33	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
34	C₁₉×#127	—	2	6	no	—
35	C₁₉×#127	C₂×C₄	1	3	yes	—
36	C₁₉×#127	C₂×C₄	1	6	yes	—
37	C₁₉×#124	C₂×C₄	1	3	yes	—
38	C₁₉×#124	C₂³	1	3	yes	—
39	C₁₉×#121	—	2	6	no	—
40	C₁₉×#121	—	2	6	no	—
41	C₁₉×#121	—	2	6	no	—
42	C₁₉×#120	—	2	6	no	—
43	C₁₉×#120	—	2	6	no	—
44	C₄×Q₈×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	—	2	3	no	—
46	C₄×D₄×C₁₉	—	2	6	no	—
47	C₁₉×#117	C₂×C₄	1	3	yes	—
48	C₂×C₄²×C₁₉	C₂×C₄	1	3	yes	—
49	C₁₉×#101	C₂³	1	8	yes	—
50	C₁₉×#100	—	2	12	no	—
51	C₂⁴×C₁₉	—	2	3	no	—
52	C₂⁴×C₁₉	C₂²⋊C₄	1	6	yes	—
53	#41×C₁₉	—	2	8	no	—
54	#41×C₁₉	—	2	4	no	—
55	#41×C₁₉	—	4	6	no	—
56	#41×C₁₉	—	4	6	no	—
57	#41×C₁₉	—	4	4	no	—
58	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
61	C₂×D₄×C₁₉	—	2	6	no	—
62	C₂×D₄×C₁₉	—	2	3	no	—
63	C₂×D₄×C₁₉	—	2	12	no	—
64	C₂×D₄×C₁₉	—	2	3	no	—
65	C₂×D₄×C₁₉	—	4	6	no	—
66	C₂×D₄×C₁₉	—	4	12	no	—
67	C₂×D₄×C₁₉	—	4	6	no	—
68	C₂×D₄×C₁₉	—	4	12	no	—
69	C₂×D₄×C₁₉	—	8	12	no	—
70	C₂×D₄×C₁₉	C₂²⋊C₄	1	3	yes	—
71	C₂×D₄×C₁₉	C₂²⋊C₄	1	6	yes	—
72	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
73	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
74	C₂×D₄×C₁₉	C₂×D₄	1	6	yes	—
75	C₂²×C₄×C₁₉	—	2	3	no	—
76	C₂²×C₄×C₁₉	—	2	3	no	—
77	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
78	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
79	M₁₆×C₁₉	—	2	8	no	—
80	M₁₆×C₁₉	—	4	12	no	—
81	C₂×C₈×C₁₉	—	4	12	no	—
82	C₄⋊C₄×C₁₉	—	2	3	no	—
83	C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂²⋊C₄×C₁₉	—	2	3	no	—
85	C₂²⋊C₄×C₁₉	—	2	6	no	—
86	C₂²⋊C₄×C₁₉	—	2	6	no	—
87	C₄²×C₁₉	—	2	3	no	—
88	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
90	#33373	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂³×C₁₉	—	2	3	no	—
92	C₂³×C₁₉	—	4	6	no	—
93	C₂³×C₁₉	—	4	6	no	—
94	C₂³×C₁₉	—	8	6	no	—
95	C₂³×C₁₉	—	8	6	no	—
96	C₂³×C₁₉	C₂×C₂²⋊C₄	1	3	yes	—
97	C₂³×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
98	Q₈×C₁₉	—	4	1	no	—
99	Q₈×C₁₉	—	4	1	no	—
100	Q₈×C₁₉	#99	1	4	yes	—
101	D₄×C₁₉	—	2	6	no	—
102	D₄×C₁₉	—	2	12	no	—
103	D₄×C₁₉	—	4	3	no	—
104	D₄×C₁₉	—	4	6	no	—
105	D₄×C₁₉	—	4	3	no	—
106	D₄×C₁₉	—	4	12	no	—
107	D₄×C₁₉	—	4	6	no	—
108	D₄×C₁₉	—	4	6	no	—
109	D₄×C₁₉	—	8	12	no	—
110	C₂×C₄×C₁₉	—	2	1	no	—
111	C₂×C₄×C₁₉	—	2	12	no	—
112	C₂×C₄×C₁₉	—	2	6	no	—
113	C₂×C₄×C₁₉	—	2	3	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	4	6	no	—
116	C₂×C₄×C₁₉	—	4	6	no	—
117	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	3	yes	—
118	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
119	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
120	C₈×C₁₉	—	4	8	no	—
121	#3498	C₂×C₁₉	1	1	yes	characteristic
122	#2888	C₂×C₁₉	1	2	yes	complemented
123	#2134	C₂×C₁₉	1	6	yes	complemented
124	#2132	C₂×C₁₉	1	6	yes	complemented
125	C₂²×C₁₉	—	2	3	no	—
126	C₂²×C₁₉	—	2	6	no	—
127	C₂²×C₁₉	—	4	3	no	—
128	C₂²×C₁₉	—	4	6	no	—
129	C₂²×C₁₉	—	4	6	no	—
130	C₂²×C₁₉	—	4	3	no	—
131	C₂²×C₁₉	—	16	6	no	—
132	C₂²×C₁₉	—	16	6	no	—
133	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
134	C₄×C₁₉	—	2	2	no	—
135	C₄×C₁₉	—	2	2	no	—
136	C₄×C₁₉	—	2	1	no	—
137	C₄×C₁₉	—	4	3	no	—
138	C₄×C₁₉	—	4	1	no	—
139	C₄×C₁₉	C₂×#99	1	6	yes	—
140	C₂×H(5,𝔽₂)	C₄×C₁₉	1	1	yes	characteristic
141	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
142	#568	—	2	2	no	—
143	#550	—	2	2	no	—
144	D₄²	—	2	6	no	—
145	#535	C₄×C₁₉	1	3	yes	—
146	#535	C₂²×C₁₉	1	3	yes	—
147	#532	C₂²×C₁₉	1	3	yes	—
148	C₂×#127	C₄×C₁₉	1	3	yes	—
149	C₄×#41	C₄×C₁₉	1	1	yes	characteristic
150	#413	C₂²×C₁₉	1	12	yes	complemented
151	C₂×#100	—	2	6	no	—
152	#356	C₂²×C₁₉	1	4	yes	complemented
153	#355	C₂²×C₁₉	1	12	yes	complemented
154	C₂×C₁₉	—	2	1	no	—
155	C₂×C₁₉	—	4	6	no	—
156	C₂×C₁₉	—	4	3	no	—
157	C₂×C₁₉	—	8	3	no	—
158	C₂×C₁₉	C₂²×#99	1	1	yes	characteristic
159	H(5,𝔽₂)	—	4	4	no	—
160	H(5,𝔽₂)	—	4	4	no	—
161	C₂×#41	—	2	1	no	—
162	C₂×#41	C₂×C₄×C₁₉	1	3	yes	—
163	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
164	C₂×#41	D₄×C₁₉	1	2	yes	—
165	C₂×#41	C₂³×C₁₉	1	3	yes	—
166	C₂²×D₄	—	2	6	no	—
167	C₂²×D₄	—	2	3	no	—
168	C₂²×D₄	C₂×C₄×C₁₉	1	3	yes	—
169	C₂²×D₄	C₂×C₄×C₁₉	1	3	yes	—
170	C₂²×D₄	D₄×C₁₉	1	6	yes	—
171	#131	—	4	8	no	—
172	C₂×M₁₆	—	2	12	no	—
173	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
174	#127	—	2	6	no	—
175	#127	C₂×C₄×C₁₉	1	3	yes	—
176	#127	C₂×C₄×C₁₉	1	6	yes	—
177	#124	C₂×C₄×C₁₉	1	3	yes	—
178	#124	C₂³×C₁₉	1	3	yes	—
179	#121	—	2	6	no	—
180	#121	—	2	6	no	—
181	#121	—	2	6	no	—
182	#120	—	2	6	no	—
183	#120	—	2	6	no	—
184	C₄×Q₈	—	2	1	no	—
185	C₄×D₄	—	2	3	no	—
186	C₄×D₄	—	2	6	no	—
187	#117	C₂×C₄×C₁₉	1	3	yes	—
188	C₂×C₄²	C₂×C₄×C₁₉	1	3	yes	—
189	#101	C₂³×C₁₉	1	8	yes	—
190	#100	—	2	12	no	—
191	C₁₉	#33373	1	1	yes	characteristic, direct product factor, Sylow
192	C₂⁴	—	2	3	no	—
193	C₂⁴	C₂²⋊C₄×C₁₉	1	6	yes	—
194	#41	—	2	8	no	—
195	#41	—	2	4	no	—
196	#41	—	4	6	no	—
197	#41	—	4	6	no	—
198	#41	—	4	4	no	—
199	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
200	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
201	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
202	C₂×D₄	—	2	6	no	—
203	C₂×D₄	—	2	3	no	—
204	C₂×D₄	—	2	12	no	—
205	C₂×D₄	—	2	3	no	—
206	C₂×D₄	—	4	6	no	—
207	C₂×D₄	—	4	12	no	—
208	C₂×D₄	—	4	6	no	—
209	C₂×D₄	—	4	12	no	—
210	C₂×D₄	—	8	12	no	—
211	C₂×D₄	C₂²⋊C₄×C₁₉	1	3	yes	—
212	C₂×D₄	C₂²⋊C₄×C₁₉	1	6	yes	—
213	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
214	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
215	C₂×D₄	C₂×D₄×C₁₉	1	6	yes	—
216	C₂²×C₄	—	2	3	no	—
217	C₂²×C₄	—	2	3	no	—
218	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
219	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
220	M₁₆	—	2	8	no	—
221	M₁₆	—	4	12	no	—
222	C₂×C₈	—	4	12	no	—
223	C₄⋊C₄	—	2	3	no	—
224	C₄⋊C₄	—	2	2	no	—
225	C₂²⋊C₄	—	2	3	no	—
226	C₂²⋊C₄	—	2	6	no	—
227	C₂²⋊C₄	—	2	6	no	—
228	C₄²	—	2	3	no	—
229	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
230	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
231	C₂³	—	2	3	no	—
232	C₂³	—	4	6	no	—
233	C₂³	—	4	6	no	—
234	C₂³	—	8	6	no	—
235	C₂³	—	8	6	no	—
236	C₂³	C₂×C₂²⋊C₄×C₁₉	1	3	yes	—
237	C₂³	C₂×C₂²⋊C₄×C₁₉	1	6	yes	—
238	Q₈	—	4	1	no	—
239	Q₈	—	4	1	no	—
240	Q₈	C₁₉×#99	1	4	yes	—
241	D₄	—	2	6	no	—
242	D₄	—	2	12	no	—
243	D₄	—	4	3	no	—
244	D₄	—	4	6	no	—
245	D₄	—	4	3	no	—
246	D₄	—	4	12	no	—
247	D₄	—	4	6	no	—
248	D₄	—	4	6	no	—
249	D₄	—	8	12	no	—
250	C₂×C₄	—	2	1	no	—
251	C₂×C₄	—	2	12	no	—
252	C₂×C₄	—	2	6	no	—
253	C₂×C₄	—	2	3	no	—
254	C₂×C₄	—	2	1	no	—
255	C₂×C₄	—	4	6	no	—
256	C₂×C₄	—	4	6	no	—
257	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	3	yes	—
258	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
259	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
260	C₈	—	4	8	no	—
261	C₂²	—	2	3	no	—
262	C₂²	—	2	6	no	—
263	C₂²	—	4	3	no	—
264	C₂²	—	4	6	no	—
265	C₂²	—	4	6	no	—
266	C₂²	—	4	3	no	—
267	C₂²	—	16	6	no	—
268	C₂²	—	16	6	no	—
269	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
270	C₄	—	2	2	no	—
271	C₄	—	2	2	no	—
272	C₄	—	2	1	no	—
273	C₄	—	4	3	no	—
274	C₄	—	4	1	no	—
275	C₄	C₂×C₁₉×#99	1	6	yes	—
276	C₂	—	2	1	no	—
277	C₂	—	4	3	no	—
278	C₂	—	4	6	no	—
279	C₂	—	8	3	no	—
280	C₂	C₂²×C₁₉×#99	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	C₂²×#99
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×Q₈	C₂⁴×C₁₉
prime radical	C₁₉×#3498	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×Q₈×C₁₉ ◁ C₂×C₁₉×H(5,𝔽₂) ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2888	C₂	semidirect
3. C₁₉×#2134	C₂	semidirect
4. C₁₉×#2132	C₂	semidirect
15. C₁₉×#413	C₂²	semidirect
17. C₁₉×#356	C₂²	semidirect
18. C₁₉×#355	C₂²	semidirect
90. #33373	C₁₉	direct (N × H)
122. #2888	C₂×C₁₉	semidirect
123. #2134	C₂×C₁₉	semidirect
124. #2132	C₂×C₁₉	semidirect
150. #413	C₂²×C₁₉	semidirect
152. #356	C₂²×C₁₉	semidirect
153. #355	C₂²×C₁₉	semidirect
191. C₁₉	#33373	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×#3498	2
C₁₉×#2888	2
C₁₉×#2134	2
C₁₉×#2132	2
#33373	19

Subgroups — C19×#33373 #18039332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33373 #18039332