Subgroups — C₁₉×#19061 #18025020

Order 4864.

942 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3214	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1662	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1656	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1537	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1530	C₂	1	2	yes	maximal, complemented
8	C₁₉×#562	C₂²	1	4	yes	—
9	C₁₉×#554	—	2	2	no	—
10	C₁₉×#550	—	2	2	no	—
11	C₁₉×#547	—	2	2	no	—
12	C₁₉×#540	—	2	2	no	—
13	C₁₉×#537	—	2	4	no	—
14	C₁₉×#533	C₂²	1	1	yes	characteristic
15	C₁₉×#532	C₂²	1	1	yes	characteristic
16	C₁₉×#532	C₂²	1	2	yes	—
17	C₁₉×#496	C₂²	1	4	yes	—
18	C₁₉×#491	C₂²	1	2	yes	—
19	C₁₉×#490	C₂²	1	2	yes	—
20	C₁₉×#489	—	2	2	no	—
21	C₁₉×#489	C₂²	1	4	yes	—
22	C₁₉×#461	—	2	2	no	—
23	C₁₉×#459	—	2	2	no	—
24	C₁₉×#449	—	2	4	no	—
25	C₁₉×#432	C₂²	1	2	yes	—
26	C₁₉×#416	—	2	2	no	—
27	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
28	C₁₉×#330	C₂²	1	4	yes	—
29	C₁₉×#329	C₂²	1	8	yes	—
30	C₂×#41×C₁₉	—	2	4	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂×#41×C₁₉	D₄	1	4	yes	—
33	C₂×SD₁₆×C₁₉	—	2	4	no	—
34	C₂×D₈×C₁₉	—	2	4	no	—
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
37	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
38	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
39	C₁₉×#127	—	2	2	no	—
40	C₁₉×#127	D₄	1	2	yes	—
41	C₁₉×#127	C₂³	1	1	yes	characteristic
42	C₁₉×#125	—	2	2	no	—
43	C₁₉×#125	C₂³	1	2	yes	—
44	C₁₉×#124	—	2	1	no	—
45	C₁₉×#124	C₂³	1	4	yes	—
46	C₁₉×#123	—	2	8	no	—
47	C₁₉×C₂²⋊Q₈	—	2	4	no	—
48	C₁₉×C₂²⋊Q₈	—	2	8	no	—
49	C₁₉×C₂²⋊Q₈	—	2	2	no	—
50	C₁₉×#121	—	2	8	no	—
51	C₁₉×#121	—	2	4	no	—
52	C₁₉×#121	—	2	8	no	—
53	C₁₉×#121	—	2	2	no	—
54	C₁₉×#121	—	2	2	no	—
55	C₁₉×#121	—	2	2	no	—
56	C₄×Q₈×C₁₉	—	2	2	no	—
57	C₄×D₄×C₁₉	—	2	4	no	—
58	C₄×D₄×C₁₉	—	2	2	no	—
59	C₄×D₄×C₁₉	—	2	2	no	—
60	C₄×D₄×C₁₉	—	2	2	no	—
61	C₁₉×#117	D₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
63	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
64	C₁₉×C₄⋊C₈	—	2	2	no	—
65	C₁₉×#103	—	2	4	no	—
66	C₁₉×#103	—	2	4	no	—
67	C₁₉×#102	—	2	4	no	—
68	C₁₉×#102	—	2	4	no	—
69	C₁₉×C₂²⋊C₈	—	2	2	no	—
70	C₁₉×#97	—	2	1	no	—
71	C₁₉×#97	C₂³	1	2	yes	—
72	C₁₉×#97	C₂³	1	4	yes	—
73	#41×C₁₉	—	4	4	no	—
74	#41×C₁₉	—	8	4	no	—
75	#41×C₁₉	—	8	8	no	—
76	C₂×Q₈×C₁₉	—	2	2	no	—
77	C₂×Q₈×C₁₉	—	2	1	no	—
78	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
79	C₂×D₄×C₁₉	—	2	8	no	—
80	C₂×D₄×C₁₉	—	2	4	no	—
81	C₂×D₄×C₁₉	—	2	2	no	—
82	C₂×D₄×C₁₉	—	2	2	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
87	C₂²×C₄×C₁₉	—	2	8	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
92	SD₁₆×C₁₉	—	8	4	no	—
93	D₈×C₁₉	—	8	4	no	—
94	C₂×C₈×C₁₉	—	2	2	no	—
95	C₂×C₈×C₁₉	—	2	4	no	—
96	C₂×C₈×C₁₉	—	4	2	no	—
97	C₄⋊C₄×C₁₉	—	2	8	no	—
98	C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₄⋊C₄×C₁₉	—	2	2	no	—
101	C₄⋊C₄×C₁₉	—	2	4	no	—
102	C₄⋊C₄×C₁₉	—	2	2	no	—
103	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
104	C₂²⋊C₄×C₁₉	—	2	8	no	—
105	C₂²⋊C₄×C₁₉	—	2	2	no	—
106	C₂²⋊C₄×C₁₉	—	2	4	no	—
107	C₂²⋊C₄×C₁₉	—	2	4	no	—
108	C₂²⋊C₄×C₁₉	—	4	2	no	—
109	C₄²×C₁₉	—	2	2	no	—
110	C₄²×C₁₉	C₂×D₄	1	2	yes	—
111	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
113	#19061	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂³×C₁₉	—	2	4	no	—
115	C₂³×C₁₉	—	4	1	no	—
116	C₂³×C₁₉	#120	1	1	yes	characteristic
117	Q₈×C₁₉	—	4	4	no	—
118	Q₈×C₁₉	—	4	4	no	—
119	Q₈×C₁₉	—	4	2	no	—
120	D₄×C₁₉	—	4	4	no	—
121	D₄×C₁₉	—	4	4	no	—
122	D₄×C₁₉	—	4	2	no	—
123	D₄×C₁₉	—	4	2	no	—
124	D₄×C₁₉	—	4	2	no	—
125	D₄×C₁₉	—	4	4	no	—
126	D₄×C₁₉	—	8	4	no	—
127	D₄×C₁₉	—	8	8	no	—
128	D₄×C₁₉	—	8	2	no	—
129	C₂×C₄×C₁₉	—	2	2	no	—
130	C₂×C₄×C₁₉	—	2	4	no	—
131	C₂×C₄×C₁₉	—	2	4	no	—
132	C₂×C₄×C₁₉	—	4	2	no	—
133	C₂×C₄×C₁₉	—	4	8	no	—
134	C₂×C₄×C₁₉	—	4	1	no	—
135	C₂×C₄×C₁₉	—	8	8	no	—
136	C₂×C₄×C₁₉	—	8	2	no	—
137	C₂×C₄×C₁₉	#120	1	2	yes	—
138	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
139	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
140	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
141	C₈×C₁₉	—	4	2	no	—
142	C₈×C₁₉	—	4	4	no	—
143	#3548	C₂×C₁₉	1	1	yes	characteristic, complemented
144	#3214	C₂×C₁₉	1	2	yes	complemented
145	#3135	C₂×C₁₉	1	1	yes	characteristic, complemented
146	#1662	C₂×C₁₉	1	4	yes	complemented
147	#1656	C₂×C₁₉	1	4	yes	complemented
148	#1537	C₂×C₁₉	1	1	yes	characteristic, complemented
149	#1530	C₂×C₁₉	1	2	yes	complemented
150	C₂²×C₁₉	—	2	1	no	—
151	C₂²×C₁₉	—	2	2	no	—
152	C₂²×C₁₉	—	4	4	no	—
153	C₂²×C₁₉	—	4	4	no	—
154	C₂²×C₁₉	—	4	4	no	—
155	C₂²×C₁₉	—	8	1	no	—
156	C₂²×C₁₉	—	8	2	no	—
157	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
158	C₄×C₁₉	—	2	1	no	—
159	C₄×C₁₉	—	2	2	no	—
160	C₄×C₁₉	—	2	2	no	—
161	C₄×C₁₉	—	4	4	no	—
162	C₄×C₁₉	—	4	4	no	—
163	C₄×C₁₉	—	8	1	no	—
164	C₄×C₁₉	#454	1	2	yes	—
165	#562	C₂²×C₁₉	1	4	yes	—
166	#554	—	2	2	no	—
167	#550	—	2	2	no	—
168	#547	—	2	2	no	—
169	#540	—	2	2	no	—
170	#537	—	2	4	no	—
171	#533	C₂²×C₁₉	1	1	yes	characteristic
172	#532	C₂²×C₁₉	1	1	yes	characteristic
173	#532	C₂²×C₁₉	1	2	yes	—
174	#496	C₂²×C₁₉	1	4	yes	—
175	#491	C₂²×C₁₉	1	2	yes	—
176	#490	C₂²×C₁₉	1	2	yes	—
177	#489	—	2	2	no	—
178	#489	C₂²×C₁₉	1	4	yes	—
179	#461	—	2	2	no	—
180	#459	—	2	2	no	—
181	#449	—	2	4	no	—
182	#432	C₂²×C₁₉	1	2	yes	—
183	#416	—	2	2	no	—
184	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
185	#330	C₂²×C₁₉	1	4	yes	—
186	#329	C₂²×C₁₉	1	8	yes	—
187	C₂×C₁₉	—	4	1	no	—
188	C₂×C₁₉	—	8	4	no	—
189	C₂×C₁₉	—	16	1	no	—
190	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
191	C₂×C₁₉	#3019	1	2	yes	—
192	C₂×#41	—	2	4	no	—
193	C₂×#41	—	2	1	no	—
194	C₂×#41	D₄×C₁₉	1	4	yes	—
195	C₂×SD₁₆	—	2	4	no	—
196	C₂×D₈	—	2	4	no	—
197	C₂²×C₈	—	2	1	no	—
198	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
199	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
200	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
201	#127	—	2	2	no	—
202	#127	D₄×C₁₉	1	2	yes	—
203	#127	C₂³×C₁₉	1	1	yes	characteristic
204	#125	—	2	2	no	—
205	#125	C₂³×C₁₉	1	2	yes	—
206	#124	—	2	1	no	—
207	#124	C₂³×C₁₉	1	4	yes	—
208	#123	—	2	8	no	—
209	C₂²⋊Q₈	—	2	4	no	—
210	C₂²⋊Q₈	—	2	8	no	—
211	C₂²⋊Q₈	—	2	2	no	—
212	#121	—	2	8	no	—
213	#121	—	2	4	no	—
214	#121	—	2	8	no	—
215	#121	—	2	2	no	—
216	#121	—	2	2	no	—
217	#121	—	2	2	no	—
218	C₄×Q₈	—	2	2	no	—
219	C₄×D₄	—	2	4	no	—
220	C₄×D₄	—	2	2	no	—
221	C₄×D₄	—	2	2	no	—
222	C₄×D₄	—	2	2	no	—
223	#117	D₄×C₁₉	1	2	yes	—
224	C₂×C₄⋊C₄	—	2	4	no	—
225	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
226	C₄⋊C₈	—	2	2	no	—
227	#103	—	2	4	no	—
228	#103	—	2	4	no	—
229	#102	—	2	4	no	—
230	#102	—	2	4	no	—
231	C₂²⋊C₈	—	2	2	no	—
232	#97	—	2	1	no	—
233	#97	C₂³×C₁₉	1	2	yes	—
234	#97	C₂³×C₁₉	1	4	yes	—
235	C₁₉	#19061	1	1	yes	characteristic, direct product factor, Sylow
236	#41	—	4	4	no	—
237	#41	—	8	4	no	—
238	#41	—	8	8	no	—
239	C₂×Q₈	—	2	2	no	—
240	C₂×Q₈	—	2	1	no	—
241	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
242	C₂×D₄	—	2	8	no	—
243	C₂×D₄	—	2	4	no	—
244	C₂×D₄	—	2	2	no	—
245	C₂×D₄	—	2	2	no	—
246	C₂×D₄	—	2	1	no	—
247	C₂×D₄	—	2	2	no	—
248	C₂×D₄	—	4	1	no	—
249	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
250	C₂²×C₄	—	2	8	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	4	1	no	—
253	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
254	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
255	SD₁₆	—	8	4	no	—
256	D₈	—	8	4	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	4	2	no	—
260	C₄⋊C₄	—	2	8	no	—
261	C₄⋊C₄	—	2	2	no	—
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	2	2	no	—
264	C₄⋊C₄	—	2	4	no	—
265	C₄⋊C₄	—	2	2	no	—
266	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
267	C₂²⋊C₄	—	2	8	no	—
268	C₂²⋊C₄	—	2	2	no	—
269	C₂²⋊C₄	—	2	4	no	—
270	C₂²⋊C₄	—	2	4	no	—
271	C₂²⋊C₄	—	4	2	no	—
272	C₄²	—	2	2	no	—
273	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
274	C₄²	C₂×D₄×C₁₉	1	2	yes	—
275	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
276	C₂³	—	2	4	no	—
277	C₂³	—	4	1	no	—
278	C₂³	C₁₉×#120	1	1	yes	characteristic
279	Q₈	—	4	4	no	—
280	Q₈	—	4	4	no	—
281	Q₈	—	4	2	no	—
282	D₄	—	4	4	no	—
283	D₄	—	4	4	no	—
284	D₄	—	4	2	no	—
285	D₄	—	4	2	no	—
286	D₄	—	4	2	no	—
287	D₄	—	4	4	no	—
288	D₄	—	8	4	no	—
289	D₄	—	8	8	no	—
290	D₄	—	8	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	4	2	no	—
295	C₂×C₄	—	4	8	no	—
296	C₂×C₄	—	4	1	no	—
297	C₂×C₄	—	8	8	no	—
298	C₂×C₄	—	8	2	no	—
299	C₂×C₄	C₁₉×#120	1	2	yes	—
300	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
301	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
302	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
303	C₈	—	4	2	no	—
304	C₈	—	4	4	no	—
305	C₂²	—	2	1	no	—
306	C₂²	—	2	2	no	—
307	C₂²	—	4	4	no	—
308	C₂²	—	4	4	no	—
309	C₂²	—	4	4	no	—
310	C₂²	—	8	1	no	—
311	C₂²	—	8	2	no	—
312	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
313	C₄	—	2	1	no	—
314	C₄	—	2	2	no	—
315	C₄	—	2	2	no	—
316	C₄	—	4	4	no	—
317	C₄	—	4	4	no	—
318	C₄	—	8	1	no	—
319	C₄	C₁₉×#454	1	2	yes	—
320	C₂	—	4	1	no	—
321	C₂	—	8	4	no	—
322	C₂	—	16	1	no	—
323	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
324	C₂	C₁₉×#3019	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3548	C₂	semidirect
2. C₁₉×#3214	C₂	semidirect
3. C₁₉×#3135	C₂	semidirect
4. C₁₉×#1662	C₂	semidirect
5. C₁₉×#1656	C₂	semidirect
6. C₁₉×#1537	C₂	semidirect
7. C₁₉×#1530	C₂	semidirect
113. #19061	C₁₉	direct (N × H)
143. #3548	C₂×C₁₉	semidirect
144. #3214	C₂×C₁₉	semidirect
145. #3135	C₂×C₁₉	semidirect
146. #1662	C₂×C₁₉	semidirect
147. #1656	C₂×C₁₉	semidirect
148. #1537	C₂×C₁₉	semidirect
149. #1530	C₂×C₁₉	semidirect
235. C₁₉	#19061	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×#3548	2
C₁₉×#3214	2
C₁₉×#3135	2
C₁₉×#1662	2
C₁₉×#1656	2
C₁₉×#1537	2
C₁₉×#1530	2
#19061	19

Subgroups — C19×#19061 #18025020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19061 #18025020