Subgroups — #18072164

Order 4864.

622 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926597	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926412	C₂	1	1	yes	maximal, characteristic
3	#14561477	C₂	1	4	yes	maximal
4	C₂×C₁₉×#432	C₂	1	1	yes	maximal, characteristic
5	#11926597	—	2	2	no	—
6	#11926597	C₄	1	4	yes	complemented
7	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
8	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
10	#11926412	—	2	1	no	—
11	#11926412	—	2	1	no	—
12	#11926412	—	2	1	no	—
13	#11926412	—	2	1	no	—
14	C₂×C₁₉⋊#95	C₄	1	2	yes	—
15	C₂×C₁₉⋊#95	C₄	1	2	yes	—
16	C₂×C₁₉⋊#95	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#432	—	2	2	no	—
19	C₁₉×#432	C₄	1	4	yes	complemented
20	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₉×#97	—	2	1	no	—
23	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂³×Dic₁₉	C₂×C₄	1	4	yes	—
27	C₂²×C₈×C₁₉	—	2	2	no	—
28	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₉	D₄	1	2	yes	—
31	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
36	C₂²×C₁₉⋊C₈	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	4	no	—
38	C₁₉×C₂²⋊C₈	—	2	2	no	—
39	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	—
40	C₁₉×#97	—	2	4	no	—
41	C₁₉⋊#95	—	2	2	no	—
42	C₁₉⋊#95	—	2	2	no	—
43	C₁₉⋊#95	—	2	2	no	—
44	C₁₉⋊#95	—	2	2	no	—
45	C₁₉⋊#95	—	2	2	no	—
46	C₁₉⋊#95	—	2	2	no	—
47	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
49	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
50	C₄×C₁₉⋊C₈	—	2	4	no	—
51	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	—	2	4	no	—
53	C₂²×C₄×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	—	4	2	no	—
55	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
56	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
62	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
63	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
69	C₂²×Dic₁₉	—	2	4	no	—
70	C₂²×Dic₁₉	—	2	8	no	—
71	C₂²×Dic₁₉	—	4	4	no	—
72	C₂²×Dic₁₉	—	4	4	no	—
73	C₂×C₈×C₁₉	—	2	4	no	—
74	C₂×C₈×C₁₉	—	4	4	no	—
75	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
76	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
77	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
78	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
79	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
80	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
81	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
82	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
83	C₂×C₁₉⋊C₈	—	2	4	no	—
84	C₂×C₁₉⋊C₈	—	4	4	no	—
85	#7916	—	19	1	no	maximal, Sylow
86	C₂³×C₁₉	—	2	2	no	—
87	C₂³×C₁₉	—	2	2	no	—
88	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
89	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₂³×C₁₉	#131	1	4	yes	—
92	C₂×C₄×C₁₉	—	2	4	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	—	2	2	no	—
97	C₂×C₄×C₁₉	—	2	2	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	2	4	no	—
100	C₂×C₄×C₁₉	—	4	2	no	—
101	C₂×C₄×C₁₉	—	4	2	no	—
102	C₂×C₄×C₁₉	—	4	1	no	—
103	C₂×C₄×C₁₉	—	4	1	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	—	4	1	no	—
106	C₂×C₄×C₁₉	#95	1	2	yes	—
107	C₂×C₄×C₁₉	#95	1	2	yes	—
108	C₂×C₄×C₁₉	#95	1	2	yes	—
109	C₂×C₄×C₁₉	#95	1	2	yes	—
110	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
114	C₂×Dic₁₉	—	4	4	no	—
115	C₂×Dic₁₉	—	4	4	no	—
116	C₂×Dic₁₉	—	4	4	no	—
117	C₂×Dic₁₉	—	8	8	no	—
118	C₈×C₁₉	—	4	4	no	—
119	C₁₉⋊C₈	—	4	4	no	—
120	C₂×#432	D₁₉	1	1	yes	characteristic
121	C₂×#431	—	19	1	no	—
122	C₂×#383	—	19	1	no	—
123	#1280	—	19	4	no	—
124	C₂²×C₁₉	—	2	8	no	—
125	C₂²×C₁₉	—	2	1	no	—
126	C₂²×C₁₉	—	2	1	no	—
127	C₂²×C₁₉	—	2	1	no	—
128	C₂²×C₁₉	—	2	1	no	—
129	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
130	C₂²×C₁₉	#405	1	2	yes	—
131	C₂²×C₁₉	#408	1	2	yes	—
132	C₂²×C₁₉	#410	1	2	yes	—
133	C₂²×C₁₉	#413	1	2	yes	—
134	C₂²×C₁₉	#424	1	2	yes	—
135	C₄×C₁₉	—	2	2	no	—
136	C₄×C₁₉	—	2	2	no	—
137	C₄×C₁₉	—	2	1	no	—
138	C₄×C₁₉	—	2	1	no	—
139	C₄×C₁₉	—	2	1	no	—
140	C₄×C₁₉	—	2	1	no	—
141	C₄×C₁₉	—	2	2	no	—
142	C₄×C₁₉	—	2	2	no	—
143	Dic₁₉	—	8	4	no	—
144	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
145	#432	—	2	2	no	—
146	#432	Dic₁₉	1	4	yes	complemented
147	#431	—	19	4	no	—
148	#431	—	38	2	no	—
149	C₂×C₄⋊C₈	—	2	1	no	—
150	C₂×C₄⋊C₈	—	38	1	no	—
151	C₂×C₂²⋊C₈	—	19	2	no	—
152	C₂×C₂²⋊C₈	C₂×D₁₉	1	2	yes	—
153	C₂×#97	—	2	1	no	—
154	C₂×C₄×C₈	—	38	1	no	—
155	#383	—	38	1	no	—
156	#383	—	38	1	no	—
157	#383	—	38	1	no	—
158	#383	—	38	1	no	—
159	C₂×#95	—	19	2	no	—
160	C₂×#95	—	19	2	no	—
161	C₂×#95	—	19	2	no	—
162	C₂×C₁₉	—	2	2	no	—
163	C₂×C₁₉	—	2	2	no	—
164	C₂×C₁₉	#1473	1	4	yes	—
165	C₂×C₁₉	#1729	1	1	yes	characteristic
166	C₂×C₁₉	#1740	1	1	yes	characteristic
167	C₂×C₁₉	#1742	1	1	yes	characteristic
168	C₂³×C₄	—	19	4	no	—
169	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
170	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
171	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
172	C₂²×C₈	—	2	2	no	—
173	C₂²×C₈	—	38	2	no	—
174	C₂×C₄²	Dic₃₈	1	2	yes	—
175	C₂×C₄²	C₄×D₁₉	1	2	yes	—
176	C₂×C₄²	D₇₆	1	1	yes	characteristic
177	C₂×C₄²	D₇₆	1	1	yes	characteristic
178	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
179	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
180	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
181	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
182	C₄⋊C₈	—	2	4	no	—
183	C₄⋊C₈	—	38	4	no	—
184	C₂²⋊C₈	—	2	2	no	—
185	C₂²⋊C₈	—	19	4	no	—
186	C₂²⋊C₈	—	38	2	no	—
187	C₂²⋊C₈	C₂×Dic₁₉	1	4	yes	—
188	#97	—	2	4	no	—
189	C₄×C₈	—	38	4	no	—
190	#95	—	38	2	no	—
191	#95	—	38	2	no	—
192	#95	—	38	2	no	—
193	#95	—	38	2	no	—
194	#95	—	38	2	no	—
195	#95	—	38	2	no	—
196	C₁₉	#7916	1	1	yes	characteristic, complemented, Sylow
197	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
198	C₂²×C₄	—	2	4	no	—
199	C₂²×C₄	—	4	2	no	—
200	C₂²×C₄	—	4	2	no	—
201	C₂²×C₄	—	38	4	no	—
202	C₂²×C₄	—	38	8	no	—
203	C₂²×C₄	—	76	4	no	—
204	C₂²×C₄	—	76	4	no	—
205	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
206	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
207	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
208	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
209	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
210	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
211	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
212	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
213	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
214	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
215	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
216	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
217	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
218	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
219	C₂×C₈	—	2	4	no	—
220	C₂×C₈	—	4	4	no	—
221	C₂×C₈	—	38	4	no	—
222	C₂×C₈	—	76	4	no	—
223	C₄²	Dic₁₉⋊C₄	1	2	yes	—
224	C₄²	Dic₁₉⋊C₄	1	2	yes	—
225	C₄²	C₄⋊Dic₁₉	1	2	yes	—
226	C₄²	C₄⋊Dic₁₉	1	2	yes	—
227	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
228	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
229	C₄²	C₂²⋊Dic₁₉	1	2	yes	—
230	C₄²	C₂²⋊Dic₁₉	1	2	yes	—
231	C₂³	—	2	2	no	—
232	C₂³	—	2	2	no	—
233	C₂³	#10597353	1	4	yes	—
234	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
235	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
236	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
237	C₂×C₄	—	2	4	no	—
238	C₂×C₄	—	2	4	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	4	2	no	—
246	C₂×C₄	—	4	2	no	—
247	C₂×C₄	—	4	1	no	—
248	C₂×C₄	—	4	1	no	—
249	C₂×C₄	—	4	1	no	—
250	C₂×C₄	—	4	1	no	—
251	C₂×C₄	—	76	4	no	—
252	C₂×C₄	—	76	4	no	—
253	C₂×C₄	—	76	4	no	—
254	C₂×C₄	—	152	8	no	—
255	C₂×C₄	C₁₉⋊#95	1	2	yes	—
256	C₂×C₄	C₁₉⋊#95	1	2	yes	—
257	C₂×C₄	C₁₉⋊#95	1	2	yes	—
258	C₂×C₄	C₁₉⋊#95	1	2	yes	—
259	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
260	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
261	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
262	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
263	C₈	—	4	4	no	—
264	C₈	—	76	4	no	—
265	C₂²	—	2	1	no	—
266	C₂²	—	2	1	no	—
267	C₂²	—	2	1	no	—
268	C₂²	—	2	1	no	—
269	C₂²	—	2	8	no	—
270	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
271	C₂²	#11926502	1	2	yes	—
272	C₂²	#11926512	1	2	yes	—
273	C₂²	#11926517	1	2	yes	—
274	C₂²	#11926526	1	2	yes	—
275	C₂²	#11926572	1	2	yes	—
276	C₄	—	2	2	no	—
277	C₄	—	2	2	no	—
278	C₄	—	2	1	no	—
279	C₄	—	2	1	no	—
280	C₄	—	2	1	no	—
281	C₄	—	2	1	no	—
282	C₄	—	2	2	no	—
283	C₄	—	2	2	no	—
284	C₄	—	152	4	no	—
285	C₂	—	2	2	no	—
286	C₂	—	2	2	no	—
287	C₂	#14562005	1	4	yes	—
288	C₂	#14563333	1	1	yes	characteristic
289	C₂	#14563367	1	1	yes	characteristic
290	C₂	#14563373	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#432	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#432	D₁₉
hypocenter	C₁₉	#7916
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#432

Complements

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

N	H ≅ G/N	type
6. #11926597	C₄	semidirect
19. C₁₉×#432	C₄	semidirect
146. #432	Dic₁₉	semidirect
196. C₁₉	#7916	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926597	2
C₂×#11926412	2
#14561477	2
C₂×C₁₉×#432	2
#7916	19