Subgroups — C₁₉×#23843 #18029802

Order 4864.

646 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2330	C₂	1	2	yes	maximal
2	C₁₉×#2084	C₂	1	2	yes	maximal
3	C₁₉×#2083	C₂	1	2	yes	maximal
4	C₁₉×#2059	C₂	1	2	yes	maximal
5	C₁₉×#2059	C₂	1	2	yes	maximal
6	C₁₉×#1776	C₂	1	2	yes	maximal
7	C₄×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
8	C₄×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1746	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₉×#125	C₂²	1	2	yes	—
11	C₂×C₁₉×#107	C₂²	1	2	yes	—
12	C₂×C₁₉×#107	C₂²	1	2	yes	—
13	C₂×C₁₉×#106	C₂²	1	2	yes	—
14	C₂×C₁₉×#106	C₂²	1	2	yes	—
15	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#389	—	2	2	no	—
18	C₁₉×#389	—	2	2	no	—
19	C₁₉×#389	C₂²	1	2	yes	—
20	C₁₉×#389	C₂²	1	2	yes	—
21	C₁₉×#387	—	2	2	no	—
22	C₁₉×#387	—	2	2	no	—
23	C₁₉×#384	C₂²	1	2	yes	—
24	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
26	C₁₉×#376	C₂²	1	1	yes	characteristic
27	C₁₉×#340	C₂²	1	1	yes	characteristic
28	C₁₉×#340	C₂²	1	1	yes	characteristic
29	C₁₉×#340	C₂²	1	1	yes	characteristic
30	C₁₉×#340	C₂²	1	1	yes	characteristic
31	C₁₉×#340	C₂²	1	2	yes	—
32	C₁₉×#340	C₂²	1	2	yes	—
33	C₁₉×#336	C₂²	1	2	yes	—
34	C₁₉×#336	C₂²	1	2	yes	—
35	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
38	C₁₉×#125	—	2	4	no	—
39	C₁₉×#125	—	2	4	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₉	—	2	2	no	—
51	C₂×C₄²×C₁₉	—	2	2	no	—
52	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
53	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	C₁₉×#107	—	2	4	no	—
55	C₁₉×#107	—	2	4	no	—
56	C₁₉×#106	—	2	4	no	—
57	C₁₉×#106	—	2	4	no	—
58	C₁₉×#97	Q₈	1	4	yes	—
59	C₄×C₈×C₁₉	Q₈	1	4	yes	—
60	C₁₉×#95	—	2	2	no	—
61	C₁₉×#95	—	2	2	no	—
62	C₁₉×#95	—	2	2	no	—
63	C₁₉×#95	—	2	2	no	—
64	C₁₉×#95	D₄	1	1	yes	characteristic
65	C₁₉×#95	D₄	1	2	yes	—
66	C₁₉×#95	D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
72	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
73	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
76	C₂×C₈×C₁₉	—	2	2	no	—
77	C₂×C₈×C₁₉	—	2	2	no	—
78	C₂×C₈×C₁₉	—	2	2	no	—
79	C₂×C₈×C₁₉	—	2	2	no	—
80	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
81	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
82	C₂×C₈×C₁₉	C₂×Q₈	1	4	yes	—
83	C₄⋊C₄×C₁₉	—	2	8	no	—
84	C₄⋊C₄×C₁₉	—	2	8	no	—
85	C₄⋊C₄×C₁₉	—	2	2	no	—
86	C₄⋊C₄×C₁₉	—	2	2	no	—
87	C₄⋊C₄×C₁₉	—	2	2	no	—
88	C₄⋊C₄×C₁₉	—	2	2	no	—
89	C₄⋊C₄×C₁₉	—	2	2	no	—
90	C₄⋊C₄×C₁₉	—	2	2	no	—
91	C₄⋊C₄×C₁₉	—	8	2	no	—
92	C₄⋊C₄×C₁₉	—	8	2	no	—
93	C₄⋊C₄×C₁₉	—	8	2	no	—
94	C₄⋊C₄×C₁₉	—	8	2	no	—
95	C₄⋊C₄×C₁₉	#41	1	4	yes	—
96	C₄⋊C₄×C₁₉	#41	1	4	yes	—
97	C₄²×C₁₉	—	2	2	no	—
98	C₄²×C₁₉	—	2	2	no	—
99	C₄²×C₁₉	—	8	2	no	—
100	C₄²×C₁₉	—	8	2	no	—
101	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
102	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
103	#23843	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
105	C₂×C₄×C₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	2	2	no	—
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	2	2	no	—
109	C₂×C₄×C₁₉	—	2	2	no	—
110	C₂×C₄×C₁₉	—	2	4	no	—
111	C₂×C₄×C₁₉	—	2	4	no	—
112	C₂×C₄×C₁₉	—	2	2	no	—
113	C₂×C₄×C₁₉	—	2	2	no	—
114	C₂×C₄×C₁₉	—	2	2	no	—
115	C₂×C₄×C₁₉	—	2	2	no	—
116	C₂×C₄×C₁₉	—	4	2	no	—
117	C₂×C₄×C₁₉	—	4	2	no	—
118	C₂×C₄×C₁₉	—	4	2	no	—
119	C₂×C₄×C₁₉	—	4	2	no	—
120	C₂×C₄×C₁₉	—	4	2	no	—
121	C₂×C₄×C₁₉	—	4	2	no	—
122	C₂×C₄×C₁₉	—	4	2	no	—
123	C₂×C₄×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	—	4	2	no	—
125	C₂×C₄×C₁₉	—	4	2	no	—
126	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
127	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
128	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
129	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
130	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
131	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
132	C₈×C₁₉	—	2	2	no	—
133	C₈×C₁₉	—	2	4	no	—
134	C₈×C₁₉	—	2	2	no	—
135	#2330	C₂×C₁₉	1	2	yes	—
136	#2084	C₂×C₁₉	1	2	yes	—
137	#2083	C₂×C₁₉	1	2	yes	—
138	#2059	C₂×C₁₉	1	2	yes	—
139	#2059	C₂×C₁₉	1	2	yes	—
140	#1776	C₂×C₁₉	1	2	yes	—
141	C₄×#107	C₂×C₁₉	1	1	yes	characteristic
142	C₄×#106	C₂×C₁₉	1	1	yes	characteristic
143	#1746	C₂×C₁₉	1	1	yes	characteristic
144	C₂²×C₁₉	#525	1	2	yes	—
145	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
146	C₂²×C₁₉	#576	1	1	yes	characteristic
147	C₂²×C₁₉	#577	1	2	yes	—
148	C₂²×C₁₉	#578	1	1	yes	characteristic
149	C₄×C₁₉	—	2	2	no	—
150	C₄×C₁₉	—	2	2	no	—
151	C₄×C₁₉	—	4	2	no	—
152	C₄×C₁₉	—	4	4	no	—
153	C₄×C₁₉	—	4	2	no	—
154	C₄×C₁₉	—	4	4	no	—
155	C₄×C₁₉	—	8	2	no	—
156	C₄×C₁₉	—	8	2	no	—
157	C₄×C₁₉	#533	1	1	yes	characteristic
158	C₄×C₁₉	#533	1	2	yes	—
159	C₄×C₁₉	#533	1	1	yes	characteristic
160	C₂×#125	C₂²×C₁₉	1	2	yes	—
161	C₂×#107	C₂²×C₁₉	1	2	yes	—
162	C₂×#107	C₂²×C₁₉	1	2	yes	—
163	C₂×#106	C₂²×C₁₉	1	2	yes	—
164	C₂×#106	C₂²×C₁₉	1	2	yes	—
165	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
166	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
167	#389	—	2	2	no	—
168	#389	—	2	2	no	—
169	#389	C₂²×C₁₉	1	2	yes	—
170	#389	C₂²×C₁₉	1	2	yes	—
171	#387	—	2	2	no	—
172	#387	—	2	2	no	—
173	#384	C₂²×C₁₉	1	2	yes	—
174	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
175	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
176	#376	C₂²×C₁₉	1	1	yes	characteristic
177	#340	C₂²×C₁₉	1	1	yes	characteristic
178	#340	C₂²×C₁₉	1	1	yes	characteristic
179	#340	C₂²×C₁₉	1	2	yes	—
180	#340	C₂²×C₁₉	1	1	yes	characteristic
181	#340	C₂²×C₁₉	1	2	yes	—
182	#340	C₂²×C₁₉	1	1	yes	characteristic
183	#336	C₂²×C₁₉	1	2	yes	—
184	#336	C₂²×C₁₉	1	2	yes	—
185	C₂×C₁₉	#2399	1	1	yes	characteristic
186	C₂×C₁₉	#3119	1	2	yes	—
187	C₂×C₁₉	#3120	1	2	yes	—
188	C₂×C₁₉	#3163	1	1	yes	characteristic
189	C₂×C₁₉	#3164	1	1	yes	characteristic
190	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
191	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
192	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
193	#125	—	2	4	no	—
194	#125	—	2	4	no	—
195	C₂×C₄⋊C₄	—	2	2	no	—
196	C₂×C₄⋊C₄	—	2	2	no	—
197	C₂×C₄⋊C₄	—	2	2	no	—
198	C₂×C₄⋊C₄	—	2	2	no	—
199	C₂×C₄⋊C₄	—	2	2	no	—
200	C₂×C₄⋊C₄	—	2	2	no	—
201	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
202	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
203	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
204	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
205	C₂×C₄²	—	2	2	no	—
206	C₂×C₄²	—	2	2	no	—
207	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
208	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
209	#107	—	2	4	no	—
210	#107	—	2	4	no	—
211	#106	—	2	4	no	—
212	#106	—	2	4	no	—
213	#97	Q₈×C₁₉	1	4	yes	—
214	C₄×C₈	Q₈×C₁₉	1	4	yes	—
215	#95	—	2	2	no	—
216	#95	—	2	2	no	—
217	#95	—	2	2	no	—
218	#95	—	2	2	no	—
219	#95	D₄×C₁₉	1	1	yes	characteristic
220	#95	D₄×C₁₉	1	2	yes	—
221	#95	D₄×C₁₉	1	1	yes	characteristic
222	C₁₉	#23843	1	1	yes	characteristic, direct product factor, Sylow
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	2	2	no	—
226	C₂²×C₄	—	2	2	no	—
227	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
228	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
229	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
230	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
231	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
232	C₂×C₈	—	2	2	no	—
233	C₂×C₈	—	2	2	no	—
234	C₂×C₈	—	2	2	no	—
235	C₂×C₈	—	2	2	no	—
236	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
237	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
238	C₂×C₈	C₂×Q₈×C₁₉	1	4	yes	—
239	C₄⋊C₄	—	2	8	no	—
240	C₄⋊C₄	—	2	8	no	—
241	C₄⋊C₄	—	2	2	no	—
242	C₄⋊C₄	—	2	2	no	—
243	C₄⋊C₄	—	2	2	no	—
244	C₄⋊C₄	—	2	2	no	—
245	C₄⋊C₄	—	2	2	no	—
246	C₄⋊C₄	—	2	2	no	—
247	C₄⋊C₄	—	8	2	no	—
248	C₄⋊C₄	—	8	2	no	—
249	C₄⋊C₄	—	8	2	no	—
250	C₄⋊C₄	—	8	2	no	—
251	C₄⋊C₄	#41×C₁₉	1	4	yes	—
252	C₄⋊C₄	#41×C₁₉	1	4	yes	—
253	C₄²	—	2	2	no	—
254	C₄²	—	2	2	no	—
255	C₄²	—	8	2	no	—
256	C₄²	—	8	2	no	—
257	C₄²	C₂×Q₈×C₁₉	1	2	yes	—
258	C₄²	C₂×Q₈×C₁₉	1	2	yes	—
259	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
260	C₂×C₄	—	2	1	no	—
261	C₂×C₄	—	2	2	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	2	2	no	—
264	C₂×C₄	—	2	2	no	—
265	C₂×C₄	—	2	4	no	—
266	C₂×C₄	—	2	4	no	—
267	C₂×C₄	—	2	2	no	—
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	2	no	—
271	C₂×C₄	—	4	2	no	—
272	C₂×C₄	—	4	2	no	—
273	C₂×C₄	—	4	2	no	—
274	C₂×C₄	—	4	2	no	—
275	C₂×C₄	—	4	2	no	—
276	C₂×C₄	—	4	2	no	—
277	C₂×C₄	—	4	2	no	—
278	C₂×C₄	—	4	2	no	—
279	C₂×C₄	—	4	2	no	—
280	C₂×C₄	—	4	2	no	—
281	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
282	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
283	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
284	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
285	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
286	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
287	C₈	—	2	2	no	—
288	C₈	—	2	4	no	—
289	C₈	—	2	2	no	—
290	C₂²	C₁₉×#525	1	2	yes	—
291	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
292	C₂²	C₁₉×#576	1	1	yes	characteristic
293	C₂²	C₁₉×#577	1	2	yes	—
294	C₂²	C₁₉×#578	1	1	yes	characteristic
295	C₄	—	2	2	no	—
296	C₄	—	2	2	no	—
297	C₄	—	4	2	no	—
298	C₄	—	4	4	no	—
299	C₄	—	4	2	no	—
300	C₄	—	4	4	no	—
301	C₄	—	8	2	no	—
302	C₄	—	8	2	no	—
303	C₄	C₁₉×#533	1	1	yes	characteristic
304	C₄	C₁₉×#533	1	2	yes	—
305	C₄	C₁₉×#533	1	1	yes	characteristic
306	C₂	C₁₉×#2399	1	1	yes	characteristic
307	C₂	C₁₉×#3119	1	2	yes	—
308	C₂	C₁₉×#3120	1	2	yes	—
309	C₂	C₁₉×#3163	1	1	yes	characteristic
310	C₂	C₁₉×#3164	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₁₉×#376 ◁ G

Complements

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

N	H ≅ G/N	type
103. #23843	C₁₉	direct (N × H)
222. C₁₉	#23843	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×#2330	2
C₁₉×#2084	2
C₁₉×#2083	2
C₁₉×#2059	2
C₁₉×#1776	2
C₄×C₁₉×#107	2
C₄×C₁₉×#106	2
C₁₉×#1746	2
#23843	19

Subgroups — C19×#23843 #18029802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23843 #18029802