Subgroups — C₁₉×#3553 #14561410

Order 2432.

932 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#564	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#563	C₂	1	2	yes	maximal, complemented
3	C₁₉×#562	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#554	C₂	1	4	yes	maximal, complemented
5	C₁₉×#553	C₂	1	4	yes	maximal, complemented
6	C₁₉×#552	C₂	1	4	yes	maximal, complemented
7	C₁₉×#541	C₂	1	4	yes	maximal, complemented
8	C₁₉×#539	C₂	1	4	yes	maximal, complemented
9	C₁₉×#539	C₂	1	4	yes	maximal, complemented
10	C₁₉×#529	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×C₄⋊Q₈	C₂²	1	4	yes	—
13	C₁₉×#126	C₂²	1	4	yes	—
14	C₁₉×#126	C₂²	1	4	yes	—
15	C₁₉×#126	C₂²	1	4	yes	—
16	C₁₉×#126	C₂²	1	4	yes	—
17	C₁₉×#126	C₂²	1	4	yes	—
18	C₁₉×#125	C₂²	1	4	yes	—
19	C₁₉×#125	C₂²	1	2	yes	—
20	C₁₉×#125	C₂²	1	1	yes	characteristic
21	C₁₉×#125	C₂²	1	1	yes	characteristic
22	C₁₉×#125	C₂²	1	2	yes	—
23	C₁₉×#125	C₂²	1	4	yes	—
24	C₁₉×#125	C₂²	1	4	yes	—
25	C₁₉×#125	C₂²	1	4	yes	—
26	C₁₉×#125	C₂²	1	4	yes	—
27	C₁₉×#125	C₂²	1	4	yes	—
28	C₁₉×#124	C₂²	1	2	yes	—
29	C₁₉×#123	C₂²	1	4	yes	—
30	C₁₉×#123	C₂²	1	4	yes	—
31	C₁₉×#123	C₂²	1	4	yes	—
32	C₁₉×#123	C₂²	1	4	yes	—
33	C₁₉×#123	C₂²	1	4	yes	—
34	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
36	C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
37	C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
38	C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
39	C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
40	C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
41	C₁₉×#121	C₂²	1	2	yes	—
42	C₁₉×#121	C₂²	1	4	yes	—
43	C₁₉×#121	C₂²	1	4	yes	—
44	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
45	C₄×Q₈×C₁₉	C₂²	1	4	yes	—
46	C₄×D₄×C₁₉	C₂²	1	2	yes	—
47	C₄×D₄×C₁₉	C₂²	1	4	yes	—
48	C₄×D₄×C₁₉	C₂²	1	4	yes	—
49	C₄×D₄×C₁₉	C₂²	1	4	yes	—
50	C₄×D₄×C₁₉	C₂²	1	4	yes	—
51	C₁₉×#117	C₂²	1	4	yes	—
52	C₁₉×#117	C₂²	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
56	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
57	C₂×Q₈×C₁₉	C₂³	1	4	yes	—
58	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
59	C₂×D₄×C₁₉	C₂³	1	4	yes	—
60	C₂×D₄×C₁₉	C₂³	1	4	yes	—
61	C₂×D₄×C₁₉	C₂³	1	2	yes	—
62	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
65	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
66	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
67	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
68	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
69	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
70	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
71	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
72	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
73	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
74	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
75	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
76	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
77	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
80	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
81	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
82	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
83	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
84	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
85	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
86	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
87	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
88	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
89	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
90	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
91	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
92	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
93	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
94	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
95	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
96	C₄²×C₁₉	C₂³	1	1	yes	characteristic
97	C₄²×C₁₉	C₂³	1	2	yes	—
98	C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₄²×C₁₉	C₂³	1	4	yes	—
100	C₄²×C₁₉	C₂³	1	4	yes	—
101	C₄²×C₁₉	C₂³	1	4	yes	—
102	C₂³×C₁₉	C₂⁴	1	4	yes	—
103	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
104	Q₈×C₁₉	—	4	4	no	—
105	Q₈×C₁₉	—	4	2	no	—
106	D₄×C₁₉	—	2	8	no	—
107	D₄×C₁₉	—	4	4	no	—
108	D₄×C₁₉	—	4	2	no	—
109	C₂×C₄×C₁₉	—	2	2	no	—
110	C₂×C₄×C₁₉	—	4	4	no	—
111	C₂×C₄×C₁₉	—	4	2	no	—
112	C₂×C₄×C₁₉	—	4	4	no	—
113	C₂×C₄×C₁₉	—	4	4	no	—
114	C₂×C₄×C₁₉	—	4	4	no	—
115	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
116	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
117	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
118	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
119	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
120	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
121	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
122	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
123	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
124	#3553	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂²×C₁₉	—	2	2	no	—
126	C₂²×C₁₉	—	2	4	no	—
127	C₂²×C₁₉	—	2	4	no	—
128	C₂²×C₁₉	—	2	4	no	—
129	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
130	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	2	1	no	—
133	C₄×C₁₉	—	2	4	no	—
134	C₄×C₁₉	—	2	2	no	—
135	C₄×C₁₉	—	2	4	no	—
136	C₄×C₁₉	—	2	4	no	—
137	C₄×C₁₉	—	2	4	no	—
138	C₄×C₁₉	—	2	2	no	—
139	C₄×C₁₉	—	2	4	no	—
140	#564	C₂×C₁₉	1	1	yes	characteristic, complemented
141	#563	C₂×C₁₉	1	2	yes	complemented
142	#562	C₂×C₁₉	1	1	yes	characteristic, complemented
143	#554	C₂×C₁₉	1	4	yes	complemented
144	#553	C₂×C₁₉	1	4	yes	complemented
145	#552	C₂×C₁₉	1	4	yes	complemented
146	#541	C₂×C₁₉	1	4	yes	complemented
147	#539	C₂×C₁₉	1	4	yes	complemented
148	#539	C₂×C₁₉	1	4	yes	complemented
149	#529	C₂×C₁₉	1	2	yes	complemented
150	C₂×#125	C₂×C₁₉	1	1	yes	characteristic, complemented
151	C₂×C₁₉	—	2	2	no	—
152	C₂×C₁₉	—	4	4	no	—
153	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
154	C₂×C₁₉	#585	1	2	yes	—
155	C₄⋊Q₈	C₂²×C₁₉	1	4	yes	—
156	#126	C₂²×C₁₉	1	4	yes	—
157	#126	C₂²×C₁₉	1	4	yes	—
158	#126	C₂²×C₁₉	1	4	yes	—
159	#126	C₂²×C₁₉	1	4	yes	—
160	#126	C₂²×C₁₉	1	4	yes	—
161	#125	C₂²×C₁₉	1	4	yes	—
162	#125	C₂²×C₁₉	1	2	yes	—
163	#125	C₂²×C₁₉	1	1	yes	characteristic
164	#125	C₂²×C₁₉	1	1	yes	characteristic
165	#125	C₂²×C₁₉	1	2	yes	—
166	#125	C₂²×C₁₉	1	4	yes	—
167	#125	C₂²×C₁₉	1	4	yes	—
168	#125	C₂²×C₁₉	1	4	yes	—
169	#125	C₂²×C₁₉	1	4	yes	—
170	#125	C₂²×C₁₉	1	4	yes	—
171	#124	C₂²×C₁₉	1	2	yes	—
172	#123	C₂²×C₁₉	1	4	yes	—
173	#123	C₂²×C₁₉	1	4	yes	—
174	#123	C₂²×C₁₉	1	4	yes	—
175	#123	C₂²×C₁₉	1	4	yes	—
176	#123	C₂²×C₁₉	1	4	yes	—
177	C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
178	C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
179	C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
180	C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
181	C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
182	C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
183	C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
184	#121	C₂²×C₁₉	1	2	yes	—
185	#121	C₂²×C₁₉	1	4	yes	—
186	#121	C₂²×C₁₉	1	4	yes	—
187	C₄×Q₈	C₂²×C₁₉	1	2	yes	—
188	C₄×Q₈	C₂²×C₁₉	1	4	yes	—
189	C₄×D₄	C₂²×C₁₉	1	2	yes	—
190	C₄×D₄	C₂²×C₁₉	1	4	yes	—
191	C₄×D₄	C₂²×C₁₉	1	4	yes	—
192	C₄×D₄	C₂²×C₁₉	1	4	yes	—
193	C₄×D₄	C₂²×C₁₉	1	4	yes	—
194	#117	C₂²×C₁₉	1	4	yes	—
195	#117	C₂²×C₁₉	1	4	yes	—
196	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
197	C₂×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
198	C₂×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
199	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
200	C₁₉	#3553	1	1	yes	characteristic, direct product factor, Sylow
201	C₂×Q₈	C₂³×C₁₉	1	4	yes	—
202	C₂×Q₈	C₂³×C₁₉	1	2	yes	—
203	C₂×D₄	C₂³×C₁₉	1	4	yes	—
204	C₂×D₄	C₂³×C₁₉	1	4	yes	—
205	C₂×D₄	C₂³×C₁₉	1	2	yes	—
206	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
207	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
208	C₂²×C₄	C₂³×C₁₉	1	4	yes	—
209	C₂²×C₄	C₂³×C₁₉	1	4	yes	—
210	C₂²×C₄	C₂³×C₁₉	1	4	yes	—
211	C₂²×C₄	C₂³×C₁₉	1	4	yes	—
212	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
213	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
214	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
215	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
216	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
217	C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
218	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
219	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
220	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
221	C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
222	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
223	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
224	C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
225	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
226	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
227	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
228	C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
229	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
230	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
231	C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
232	C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
233	C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
234	C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
235	C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
236	C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
237	C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
238	C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
239	C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
240	C₄²	C₂³×C₁₉	1	1	yes	characteristic
241	C₄²	C₂³×C₁₉	1	2	yes	—
242	C₄²	C₂³×C₁₉	1	1	yes	characteristic
243	C₄²	C₂³×C₁₉	1	4	yes	—
244	C₄²	C₂³×C₁₉	1	4	yes	—
245	C₄²	C₂³×C₁₉	1	4	yes	—
246	C₂³	C₂⁴×C₁₉	1	4	yes	—
247	C₂³	C₂⁴×C₁₉	1	1	yes	characteristic
248	Q₈	—	4	4	no	—
249	Q₈	—	4	2	no	—
250	D₄	—	2	8	no	—
251	D₄	—	4	4	no	—
252	D₄	—	4	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	4	4	no	—
255	C₂×C₄	—	4	2	no	—
256	C₂×C₄	—	4	4	no	—
257	C₂×C₄	—	4	4	no	—
258	C₂×C₄	—	4	4	no	—
259	C₂×C₄	C₂⁴×C₁₉	1	2	yes	—
260	C₂×C₄	C₂⁴×C₁₉	1	4	yes	—
261	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
262	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
263	C₂×C₄	C₂⁴×C₁₉	1	4	yes	—
264	C₂×C₄	C₂⁴×C₁₉	1	2	yes	—
265	C₂×C₄	C₂⁴×C₁₉	1	4	yes	—
266	C₂×C₄	C₂⁴×C₁₉	1	4	yes	—
267	C₂×C₄	C₂⁴×C₁₉	1	4	yes	—
268	C₂²	—	2	2	no	—
269	C₂²	—	2	4	no	—
270	C₂²	—	2	4	no	—
271	C₂²	—	2	4	no	—
272	C₂²	C₁₉×2₋¹⁺⁴	1	2	yes	—
273	C₂²	C₂⁵×C₁₉	1	1	yes	characteristic
274	C₄	—	2	1	no	—
275	C₄	—	2	1	no	—
276	C₄	—	2	4	no	—
277	C₄	—	2	2	no	—
278	C₄	—	2	4	no	—
279	C₄	—	2	4	no	—
280	C₄	—	2	4	no	—
281	C₄	—	2	2	no	—
282	C₄	—	2	4	no	—
283	C₂	—	2	2	no	—
284	C₂	—	4	4	no	—
285	C₂	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
286	C₂	C₁₉×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#564	C₂	semidirect
2. C₁₉×#563	C₂	semidirect
3. C₁₉×#562	C₂	semidirect
4. C₁₉×#554	C₂	semidirect
5. C₁₉×#553	C₂	semidirect
6. C₁₉×#552	C₂	semidirect
7. C₁₉×#541	C₂	semidirect
8. C₁₉×#539	C₂	semidirect
9. C₁₉×#539	C₂	semidirect
10. C₁₉×#529	C₂	semidirect
11. C₂×C₁₉×#125	C₂	semidirect
124. #3553	C₁₉	direct (N × H)
140. #564	C₂×C₁₉	semidirect
141. #563	C₂×C₁₉	semidirect
142. #562	C₂×C₁₉	semidirect
143. #554	C₂×C₁₉	semidirect
144. #553	C₂×C₁₉	semidirect
145. #552	C₂×C₁₉	semidirect
146. #541	C₂×C₁₉	semidirect
147. #539	C₂×C₁₉	semidirect
148. #539	C₂×C₁₉	semidirect
149. #529	C₂×C₁₉	semidirect
150. C₂×#125	C₂×C₁₉	semidirect
200. C₁₉	#3553	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×#564	2
C₁₉×#563	2
C₁₉×#562	2
C₁₉×#554	2
C₁₉×#553	2
C₁₉×#552	2
C₁₉×#541	2
C₁₉×#539	2
C₁₉×#529	2
C₂×C₁₉×#125	2
#3553	19

Subgroups — C19×#3553 #14561410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#3553 #14561410