Subgroups — #18072084

Order 4864.

614 conjugacy classes of subgroups.

The subgroup lattice has 280 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×#11926597	C₂	1	1	yes	maximal, characteristic
3	#14561476	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic
5	#11926597	—	2	2	no	—
6	#11926597	—	2	2	no	—
7	#11926597	C₄	1	4	yes	complemented
8	#11926597	C₄	1	4	yes	complemented
9	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
11	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
12	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
13	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
14	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#383	—	2	1	no	—
17	C₁₉×#382	C₄	1	2	yes	—
18	C₁₉×#381	—	2	1	no	—
19	C₁₉×#380	C₄	1	2	yes	—
20	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
21	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
22	C₁₉×#376	—	2	1	no	—
23	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
27	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄²×C₁₉	—	2	2	no	—
29	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	D₄	1	2	yes	—
35	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂²×C₁₉⋊C₈	—	2	2	no	—
38	C₂²×C₁₉⋊C₈	—	2	2	no	—
39	C₁₉×#95	—	2	2	no	—
40	C₁₉×#95	—	2	2	no	—
41	C₁₉×#95	—	2	2	no	—
42	C₁₉×#95	—	2	2	no	—
43	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
48	C₄×C₁₉⋊C₈	—	2	4	no	—
49	C₄×C₁₉⋊C₈	—	2	2	no	—
50	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
51	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	—	2	4	no	—
53	C₂²×C₄×C₁₉	—	2	4	no	—
54	C₂²×C₄×C₁₉	—	2	4	no	—
55	C₂²×C₄×C₁₉	—	4	2	no	—
56	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
59	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
63	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
65	C₂²×C₄×C₁₉	C₂²×C₄	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	C₄⋊C₄×C₁₉	—	2	8	no	—
69	C₂²⋊C₄×C₁₉	—	4	4	no	—
70	C₄²×C₁₉	—	4	4	no	—
71	C₄²×C₁₉	C₄²	1	2	yes	—
72	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
73	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
74	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
75	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
76	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
77	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
79	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
81	C₂×C₁₉⋊C₈	—	2	4	no	—
82	C₂×C₁₉⋊C₈	—	2	4	no	—
83	C₂×C₁₉⋊C₈	—	4	4	no	—
84	C₂×C₁₉⋊C₈	—	4	4	no	—
85	#7894	—	19	1	no	maximal, Sylow
86	C₂³×C₁₉	—	2	2	no	—
87	C₂³×C₁₉	—	2	2	no	—
88	C₂³×C₁₉	—	2	2	no	—
89	C₂³×C₁₉	#95	1	2	yes	—
90	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	2	4	no	—
96	C₂×C₄×C₁₉	—	2	4	no	—
97	C₂×C₄×C₁₉	—	2	4	no	—
98	C₂×C₄×C₁₉	—	2	4	no	—
99	C₂×C₄×C₁₉	—	4	2	no	—
100	C₂×C₄×C₁₉	—	4	2	no	—
101	C₂×C₄×C₁₉	—	4	4	no	—
102	C₂×C₄×C₁₉	—	4	4	no	—
103	C₂×C₄×C₁₉	—	4	4	no	—
104	C₂×C₄×C₁₉	#95	1	2	yes	—
105	C₂×C₄×C₁₉	#95	1	2	yes	—
106	C₂×C₄×C₁₉	#95	1	2	yes	—
107	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
108	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×C₁₉	#131	1	4	yes	—
114	C₂×C₄×C₁₉	#135	1	4	yes	—
115	C₁₉⋊C₈	—	4	4	no	—
116	C₁₉⋊C₈	—	4	4	no	—
117	C₂×#431	—	19	1	no	—
118	C₂×#431	—	19	1	no	—
119	#2283	D₁₉	1	1	yes	characteristic
120	#1279	—	19	4	no	—
121	C₂²×C₁₉	—	2	2	no	—
122	C₂²×C₁₉	—	2	2	no	—
123	C₂²×C₁₉	—	2	2	no	—
124	C₂²×C₁₉	—	4	4	no	—
125	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
126	C₂²×C₁₉	#408	1	2	yes	—
127	C₂²×C₁₉	#416	1	2	yes	—
128	C₂²×C₁₉	#421	1	2	yes	—
129	C₄×C₁₉	—	2	2	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	2	no	—
132	C₄×C₁₉	—	2	1	no	—
133	C₄×C₁₉	—	2	2	no	—
134	C₄×C₁₉	—	8	4	no	—
135	C₄×C₁₉	#405	1	2	yes	—
136	C₄×C₁₉	#416	1	2	yes	—
137	C₄×C₁₉	#424	1	2	yes	—
138	C₄×C₁₉	#427	1	2	yes	—
139	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
140	#431	—	19	4	no	—
141	#431	—	19	4	no	—
142	#431	—	38	2	no	—
143	#431	—	38	2	no	—
144	C₂×C₄⋊C₈	—	19	2	no	—
145	C₂×C₄⋊C₈	—	38	1	no	—
146	C₂×C₂²⋊C₈	—	38	1	no	—
147	C₂×C₂²⋊C₈	—	38	1	no	—
148	C₂×C₄×C₈	—	19	2	no	—
149	C₂×C₄×C₈	—	38	1	no	—
150	#383	—	2	1	no	—
151	#382	Dic₁₉	1	2	yes	—
152	#381	—	2	1	no	—
153	#380	Dic₁₉	1	2	yes	—
154	C₄×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
155	C₄×C₂²⋊C₄	—	2	1	no	—
156	#376	—	2	1	no	—
157	C₂×C₁₉	—	4	2	no	—
158	C₂×C₁₉	#1482	1	4	yes	—
159	C₂×C₁₉	#1729	1	1	yes	characteristic
160	C₂×C₁₉	#1733	1	1	yes	characteristic
161	C₂×C₁₉	#1735	1	1	yes	characteristic
162	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
163	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
164	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
165	C₂²×C₈	—	38	2	no	—
166	C₂²×C₈	—	38	2	no	—
167	C₂×C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
168	C₂×C₂²⋊C₄	—	2	2	no	—
169	C₂×C₄²	—	2	2	no	—
170	C₂×C₄²	Dic₃₈	1	2	yes	—
171	C₂×C₄²	C₄×D₁₉	1	2	yes	—
172	C₂×C₄²	C₄×D₁₉	1	2	yes	—
173	C₂×C₄²	D₇₆	1	2	yes	—
174	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
175	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
176	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
177	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
178	C₄⋊C₈	—	19	4	no	—
179	C₄⋊C₈	—	38	4	no	—
180	C₄⋊C₈	—	38	2	no	—
181	C₂²⋊C₈	—	38	4	no	—
182	C₂²⋊C₈	—	38	4	no	—
183	C₄×C₈	—	19	4	no	—
184	C₄×C₈	—	38	4	no	—
185	C₄×C₈	—	38	2	no	—
186	#95	—	2	2	no	—
187	#95	—	2	2	no	—
188	#95	—	2	2	no	—
189	#95	—	2	2	no	—
190	C₁₉	#7894	1	1	yes	characteristic, complemented, Sylow
191	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
192	C₂²×C₄	—	2	4	no	—
193	C₂²×C₄	—	2	4	no	—
194	C₂²×C₄	—	2	4	no	—
195	C₂²×C₄	—	4	2	no	—
196	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
197	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
198	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
199	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
200	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
201	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
202	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
203	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
204	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
205	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
206	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
207	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
208	C₂×C₈	—	38	4	no	—
209	C₂×C₈	—	38	4	no	—
210	C₂×C₈	—	76	4	no	—
211	C₂×C₈	—	76	4	no	—
212	C₄⋊C₄	—	2	8	no	—
213	C₂²⋊C₄	—	4	4	no	—
214	C₄²	—	4	4	no	—
215	C₄²	C₄×Dic₁₉	1	2	yes	—
216	C₄²	Dic₁₉⋊C₄	1	2	yes	—
217	C₄²	Dic₁₉⋊C₄	1	2	yes	—
218	C₄²	C₄⋊Dic₁₉	1	2	yes	—
219	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
220	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
221	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
222	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
223	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
224	C₄²	C₂×D₇₆	1	1	yes	characteristic
225	C₂³	—	2	2	no	—
226	C₂³	—	2	2	no	—
227	C₂³	—	2	2	no	—
228	C₂³	C₁₉⋊#95	1	2	yes	—
229	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	4	no	—
235	C₂×C₄	—	2	4	no	—
236	C₂×C₄	—	2	4	no	—
237	C₂×C₄	—	2	4	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂×C₄	—	4	4	no	—
241	C₂×C₄	—	4	4	no	—
242	C₂×C₄	—	4	4	no	—
243	C₂×C₄	C₁₉⋊#95	1	2	yes	—
244	C₂×C₄	C₁₉⋊#95	1	2	yes	—
245	C₂×C₄	C₁₉⋊#95	1	2	yes	—
246	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
247	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
248	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
249	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
250	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
251	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
252	C₂×C₄	#10597394	1	4	yes	—
253	C₂×C₄	#10597396	1	4	yes	—
254	C₈	—	76	4	no	—
255	C₈	—	76	4	no	—
256	C₂²	—	2	2	no	—
257	C₂²	—	2	2	no	—
258	C₂²	—	2	2	no	—
259	C₂²	—	4	4	no	—
260	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
261	C₂²	#11926511	1	2	yes	—
262	C₂²	#11926540	1	2	yes	—
263	C₂²	#11926561	1	2	yes	—
264	C₄	—	2	2	no	—
265	C₄	—	2	1	no	—
266	C₄	—	2	2	no	—
267	C₄	—	2	1	no	—
268	C₄	—	2	2	no	—
269	C₄	—	8	4	no	—
270	C₄	#11926500	1	2	yes	—
271	C₄	#11926538	1	2	yes	—
272	C₄	#11926571	1	2	yes	—
273	C₄	#11926580	1	2	yes	—
274	C₂	—	4	2	no	—
275	C₂	#14562043	1	4	yes	—
276	C₂	#14563332	1	1	yes	characteristic
277	C₂	#14563344	1	1	yes	characteristic
278	C₂	#14563351	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2283	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2283	D₁₉
hypocenter	C₁₉	#7894
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ #2283

Complements

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

N	H ≅ G/N	type
3. #14561476	C₂	semidirect
7. #11926597	C₄	semidirect
8. #11926597	C₄	semidirect
190. C₁₉	#7894	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
#14561476	2
C₁₉×#2283	2
#7894	19