Subgroups — C₁₉×#3035 #14560892

Order 2432.

496 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#135	C₂	1	2	yes	maximal, complemented
2	C₁₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#464	C₂	1	2	yes	maximal, complemented
5	C₁₉×#463	C₂	1	2	yes	maximal, complemented
6	C₁₉×#462	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#416	C₂	1	2	yes	maximal, complemented
12	C₂×#41×C₁₉	C₂²	1	2	yes	—
13	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#135	—	2	8	no	—
15	C₂×Q₁₆×C₁₉	C₂²	1	2	yes	—
16	C₂×SD₁₆×C₁₉	C₂²	1	2	yes	—
17	C₂×SD₁₆×C₁₉	C₂²	1	2	yes	—
18	C₂×D₈×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
20	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₁₉×#127	C₂²	1	1	yes	characteristic
22	C₁₉×#124	C₂²	1	2	yes	—
23	C₁₉×#121	—	2	1	no	—
24	C₁₉×#121	—	2	1	no	—
25	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₄×D₄×C₁₉	—	2	1	no	—
28	C₄×D₄×C₁₉	—	2	1	no	—
29	C₄×D₄×C₁₉	—	2	1	no	—
30	C₄×D₄×C₁₉	—	2	1	no	—
31	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#117	—	2	1	no	—
34	C₁₉×#117	C₂²	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
40	C₁₉×#103	C₂²	1	2	yes	—
41	C₁₉×#103	C₂²	1	2	yes	—
42	C₁₉×#102	C₂²	1	2	yes	—
43	C₁₉×#102	C₂²	1	2	yes	—
44	#41×C₁₉	—	2	2	no	—
45	#41×C₁₉	—	2	4	no	—
46	#41×C₁₉	—	2	4	no	—
47	#41×C₁₉	D₄	1	4	yes	complemented
48	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
49	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×D₄×C₁₉	—	2	1	no	—
51	C₂×D₄×C₁₉	—	2	2	no	—
52	C₂×D₄×C₁₉	—	2	1	no	—
53	C₂×D₄×C₁₉	—	2	1	no	—
54	C₂×D₄×C₁₉	C₂³	1	2	yes	—
55	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	—	2	1	no	—
57	C₂²×C₄×C₁₉	—	2	1	no	—
58	C₂²×C₄×C₁₉	—	2	1	no	—
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	Q₁₆×C₁₉	—	2	4	no	—
64	SD₁₆×C₁₉	—	2	4	no	—
65	SD₁₆×C₁₉	—	2	4	no	—
66	D₈×C₁₉	—	2	4	no	—
67	C₂×C₈×C₁₉	—	2	4	no	—
68	C₂×C₈×C₁₉	C₂³	1	2	yes	—
69	C₂×C₈×C₁₉	C₂³	1	2	yes	—
70	C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂²⋊C₄×C₁₉	—	2	2	no	—
80	C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₄²×C₁₉	—	2	1	no	—
82	C₄²×C₁₉	—	2	1	no	—
83	C₄²×C₁₉	—	2	1	no	—
84	C₄²×C₁₉	D₄	1	1	yes	characteristic
85	C₄²×C₁₉	D₄	1	1	yes	characteristic
86	C₄²×C₁₉	C₂³	1	1	yes	characteristic
87	C₄²×C₁₉	C₂³	1	1	yes	characteristic
88	C₂³×C₁₉	—	2	1	no	—
89	C₂³×C₁₉	—	2	2	no	—
90	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
91	Q₈×C₁₉	—	2	1	no	—
92	Q₈×C₁₉	—	2	2	no	—
93	Q₈×C₁₉	—	2	2	no	—
94	Q₈×C₁₉	C₂×D₄	1	2	yes	—
95	D₄×C₁₉	—	2	4	no	—
96	D₄×C₁₉	—	2	2	no	—
97	D₄×C₁₉	—	2	1	no	—
98	D₄×C₁₉	—	2	2	no	—
99	D₄×C₁₉	—	4	2	no	—
100	D₄×C₁₉	—	4	4	no	—
101	D₄×C₁₉	—	4	2	no	—
102	D₄×C₁₉	C₂×D₄	1	2	yes	—
103	C₂×C₄×C₁₉	—	2	1	no	—
104	C₂×C₄×C₁₉	—	2	4	no	—
105	C₂×C₄×C₁₉	—	2	2	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	2	2	no	—
109	C₂×C₄×C₁₉	—	4	1	no	—
110	C₂×C₄×C₁₉	—	4	2	no	—
111	C₂×C₄×C₁₉	—	4	4	no	—
112	C₂×C₄×C₁₉	—	4	2	no	—
113	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
117	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×C₁₉	#41	1	2	yes	—
120	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
121	C₈×C₁₉	—	2	2	no	—
122	C₈×C₁₉	—	2	2	no	—
123	#3035	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₁₉	—	2	1	no	—
125	C₂²×C₁₉	—	2	1	no	—
126	C₂²×C₁₉	—	2	2	no	—
127	C₂²×C₁₉	—	4	1	no	—
128	C₂²×C₁₉	—	4	1	no	—
129	C₂²×C₁₉	—	4	2	no	—
130	C₂²×C₁₉	—	4	2	no	—
131	C₂²×C₁₉	—	4	2	no	—
132	C₂²×C₁₉	#121	1	2	yes	—
133	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
134	C₄×C₁₉	—	2	2	no	—
135	C₄×C₁₉	—	2	1	no	—
136	C₄×C₁₉	—	2	1	no	—
137	C₄×C₁₉	—	2	1	no	—
138	C₄×C₁₉	—	4	2	no	—
139	C₄×C₁₉	—	4	1	no	—
140	C₄×C₁₉	—	4	1	no	—
141	C₄×C₁₉	#121	1	2	yes	—
142	C₄×C₁₉	#135	1	2	yes	complemented
143	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
144	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
145	C₂×#135	C₂×C₁₉	1	2	yes	complemented
146	#532	C₂×C₁₉	1	1	yes	characteristic, complemented
147	C₄×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
148	#464	C₂×C₁₉	1	2	yes	complemented
149	#463	C₂×C₁₉	1	2	yes	complemented
150	#462	C₂×C₁₉	1	1	yes	characteristic, complemented
151	#461	C₂×C₁₉	1	1	yes	characteristic, complemented
152	#460	C₂×C₁₉	1	1	yes	characteristic, complemented
153	#459	C₂×C₁₉	1	1	yes	characteristic, complemented
154	C₂×C₄⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
155	#416	C₂×C₁₉	1	2	yes	complemented
156	C₂×C₁₉	—	2	2	no	—
157	C₂×C₁₉	—	4	2	no	—
158	C₂×C₁₉	—	8	2	no	—
159	C₂×C₁₉	C₂×#121	1	1	yes	characteristic
160	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
161	C₂×C₁₉	#575	1	1	yes	characteristic
162	C₂×#41	C₂²×C₁₉	1	2	yes	—
163	C₂×#41	C₂²×C₁₉	1	1	yes	characteristic
164	#135	—	2	8	no	—
165	C₂×Q₁₆	C₂²×C₁₉	1	2	yes	—
166	C₂×SD₁₆	C₂²×C₁₉	1	2	yes	—
167	C₂×SD₁₆	C₂²×C₁₉	1	2	yes	—
168	C₂×D₈	C₂²×C₁₉	1	2	yes	—
169	C₂²×C₈	C₂²×C₁₉	1	2	yes	—
170	C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
171	#127	C₂²×C₁₉	1	1	yes	characteristic
172	#124	C₂²×C₁₉	1	2	yes	—
173	#121	—	2	1	no	—
174	#121	—	2	1	no	—
175	C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
176	C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
177	C₄×D₄	—	2	1	no	—
178	C₄×D₄	—	2	1	no	—
179	C₄×D₄	—	2	1	no	—
180	C₄×D₄	—	2	1	no	—
181	C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
182	C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
183	#117	—	2	1	no	—
184	#117	C₂²×C₁₉	1	1	yes	characteristic
185	C₂×C₄²	—	2	1	no	—
186	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
187	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
188	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
189	C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
190	#103	C₂²×C₁₉	1	2	yes	—
191	#103	C₂²×C₁₉	1	2	yes	—
192	#102	C₂²×C₁₉	1	2	yes	—
193	#102	C₂²×C₁₉	1	2	yes	—
194	C₁₉	#3035	1	1	yes	characteristic, direct product factor, Sylow
195	#41	—	2	2	no	—
196	#41	—	2	4	no	—
197	#41	—	2	4	no	—
198	#41	D₄×C₁₉	1	4	yes	complemented
199	C₂×Q₈	C₂³×C₁₉	1	2	yes	—
200	C₂×Q₈	C₂³×C₁₉	1	1	yes	characteristic
201	C₂×D₄	—	2	1	no	—
202	C₂×D₄	—	2	2	no	—
203	C₂×D₄	—	2	1	no	—
204	C₂×D₄	—	2	1	no	—
205	C₂×D₄	C₂³×C₁₉	1	2	yes	—
206	C₂×D₄	C₂³×C₁₉	1	1	yes	characteristic
207	C₂²×C₄	—	2	1	no	—
208	C₂²×C₄	—	2	1	no	—
209	C₂²×C₄	—	2	1	no	—
210	C₂²×C₄	—	2	2	no	—
211	C₂²×C₄	D₄×C₁₉	1	1	yes	characteristic
212	C₂²×C₄	D₄×C₁₉	1	1	yes	characteristic
213	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
214	Q₁₆	—	2	4	no	—
215	SD₁₆	—	2	4	no	—
216	SD₁₆	—	2	4	no	—
217	D₈	—	2	4	no	—
218	C₂×C₈	—	2	4	no	—
219	C₂×C₈	C₂³×C₁₉	1	2	yes	—
220	C₂×C₈	C₂³×C₁₉	1	2	yes	—
221	C₄⋊C₄	—	2	1	no	—
222	C₄⋊C₄	—	2	1	no	—
223	C₄⋊C₄	—	2	1	no	—
224	C₄⋊C₄	—	2	1	no	—
225	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
226	C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
227	C₂²⋊C₄	—	2	1	no	—
228	C₂²⋊C₄	—	2	1	no	—
229	C₂²⋊C₄	—	2	1	no	—
230	C₂²⋊C₄	—	2	2	no	—
231	C₂²⋊C₄	—	2	2	no	—
232	C₄²	—	2	1	no	—
233	C₄²	—	2	1	no	—
234	C₄²	—	2	1	no	—
235	C₄²	D₄×C₁₉	1	1	yes	characteristic
236	C₄²	D₄×C₁₉	1	1	yes	characteristic
237	C₄²	C₂³×C₁₉	1	1	yes	characteristic
238	C₄²	C₂³×C₁₉	1	1	yes	characteristic
239	C₂³	—	2	1	no	—
240	C₂³	—	2	2	no	—
241	C₂³	C₂×D₄×C₁₉	1	1	yes	characteristic
242	Q₈	—	2	1	no	—
243	Q₈	—	2	2	no	—
244	Q₈	—	2	2	no	—
245	Q₈	C₂×D₄×C₁₉	1	2	yes	—
246	D₄	—	2	4	no	—
247	D₄	—	2	2	no	—
248	D₄	—	2	1	no	—
249	D₄	—	2	2	no	—
250	D₄	—	4	2	no	—
251	D₄	—	4	4	no	—
252	D₄	—	4	2	no	—
253	D₄	C₂×D₄×C₁₉	1	2	yes	—
254	C₂×C₄	—	2	1	no	—
255	C₂×C₄	—	2	4	no	—
256	C₂×C₄	—	2	2	no	—
257	C₂×C₄	—	2	1	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	2	2	no	—
260	C₂×C₄	—	4	1	no	—
261	C₂×C₄	—	4	2	no	—
262	C₂×C₄	—	4	4	no	—
263	C₂×C₄	—	4	2	no	—
264	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
265	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
266	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
267	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
268	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
269	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
270	C₂×C₄	#41×C₁₉	1	2	yes	—
271	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
272	C₈	—	2	2	no	—
273	C₈	—	2	2	no	—
274	C₂²	—	2	1	no	—
275	C₂²	—	2	1	no	—
276	C₂²	—	2	2	no	—
277	C₂²	—	4	1	no	—
278	C₂²	—	4	1	no	—
279	C₂²	—	4	2	no	—
280	C₂²	—	4	2	no	—
281	C₂²	—	4	2	no	—
282	C₂²	C₁₉×#121	1	2	yes	—
283	C₂²	C₂²×D₄×C₁₉	1	1	yes	characteristic
284	C₄	—	2	2	no	—
285	C₄	—	2	1	no	—
286	C₄	—	2	1	no	—
287	C₄	—	2	1	no	—
288	C₄	—	4	2	no	—
289	C₄	—	4	1	no	—
290	C₄	—	4	1	no	—
291	C₄	C₁₉×#121	1	2	yes	—
292	C₄	C₁₉×#135	1	2	yes	complemented
293	C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
294	C₄	C₂×#41×C₁₉	1	1	yes	characteristic
295	C₂	—	2	2	no	—
296	C₂	—	4	2	no	—
297	C₂	—	8	2	no	—
298	C₂	C₂×C₁₉×#121	1	1	yes	characteristic
299	C₂	C₂×C₁₉×#135	1	1	yes	characteristic
300	C₂	C₁₉×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#135	C₂	semidirect
2. C₁₉×#532	C₂	semidirect
3. C₄×#41×C₁₉	C₂	semidirect
4. C₁₉×#464	C₂	semidirect
5. C₁₉×#463	C₂	semidirect
6. C₁₉×#462	C₂	semidirect
7. C₁₉×#461	C₂	semidirect
8. C₁₉×#460	C₂	semidirect
9. C₁₉×#459	C₂	semidirect
10. C₂×C₁₉×C₄⋊C₈	C₂	semidirect
11. C₁₉×#416	C₂	semidirect
47. #41×C₁₉	D₄	semidirect
123. #3035	C₁₉	direct (N × H)
142. C₄×C₁₉	#135	semidirect
145. C₂×#135	C₂×C₁₉	semidirect
146. #532	C₂×C₁₉	semidirect
147. C₄×#41	C₂×C₁₉	semidirect
148. #464	C₂×C₁₉	semidirect
149. #463	C₂×C₁₉	semidirect
150. #462	C₂×C₁₉	semidirect
151. #461	C₂×C₁₉	semidirect
152. #460	C₂×C₁₉	semidirect
153. #459	C₂×C₁₉	semidirect
154. C₂×C₄⋊C₈	C₂×C₁₉	semidirect
155. #416	C₂×C₁₉	semidirect
194. C₁₉	#3035	direct (N × H)
198. #41	D₄×C₁₉	semidirect
292. C₄	C₁₉×#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#135	2
C₁₉×#532	2
C₄×#41×C₁₉	2
C₁₉×#464	2
C₁₉×#463	2
C₁₉×#462	2
C₁₉×#461	2
C₁₉×#460	2
C₁₉×#459	2
C₂×C₁₉×C₄⋊C₈	2
C₁₉×#416	2
#3035	19

Subgroups — C19×#3035 #14560892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#3035 #14560892