Subgroups — #18072019

Order 4864.

574 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926601	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926597	C₂	1	1	yes	maximal, characteristic
3	#14561470	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₉×#431	C₂	1	1	yes	maximal, characteristic
5	#11926601	—	2	2	no	—
6	#11926601	C₄	1	4	yes	—
7	#11926597	—	2	2	no	—
8	#11926597	C₄	1	4	yes	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
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×#10597260	—	2	1	no	—
14	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#431	—	2	2	no	—
17	C₁₉×#431	—	2	2	no	—
18	C₂×C₁₉×C₄⋊C₈	C₄	1	2	yes	—
19	C₂×C₁₉×C₂²⋊C₈	C₄	1	2	yes	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
21	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	Q₈	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	D₄	1	2	yes	—
30	C₂×C₄²×C₁₉	D₄	1	2	yes	—
31	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×C₁₉⋊C₈	—	2	2	no	—
34	C₂²×C₁₉⋊C₈	—	2	2	no	—
35	C₁₉×C₄⋊C₈	—	2	4	no	—
36	C₁₉×C₂²⋊C₈	—	2	4	no	—
37	C₄×C₈×C₁₉	—	2	2	no	—
38	C₄×C₈×C₁₉	—	2	2	no	—
39	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
40	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
44	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
45	#10597260	—	2	4	no	—
46	C₄×C₁₉⋊C₈	—	2	4	no	—
47	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	—	2	4	no	—
49	C₂²×C₄×C₁₉	—	2	4	no	—
50	C₂²×C₄×C₁₉	—	4	2	no	—
51	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
52	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
54	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
56	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
63	C₂×C₈×C₁₉	—	2	4	no	—
64	C₂×C₈×C₁₉	—	2	8	no	—
65	C₄²×C₁₉	C₄²	1	2	yes	—
66	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
67	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
68	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
69	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
70	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
71	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
72	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
73	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂×C₁₉⋊C₈	—	2	4	no	—
76	C₂×C₁₉⋊C₈	—	2	4	no	—
77	C₂×C₁₉⋊C₈	—	4	4	no	—
78	C₂×C₁₉⋊C₈	—	4	4	no	—
79	#7878	—	19	1	no	maximal, Sylow
80	C₂³×C₁₉	—	2	2	no	—
81	C₂³×C₁₉	—	2	2	no	—
82	C₂³×C₁₉	—	2	2	no	—
83	C₂³×C₁₉	#95	1	2	yes	—
84	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	4	no	—
90	C₂×C₄×C₁₉	—	2	4	no	—
91	C₂×C₄×C₁₉	—	2	4	no	—
92	C₂×C₄×C₁₉	—	2	4	no	—
93	C₂×C₄×C₁₉	—	4	2	no	—
94	C₂×C₄×C₁₉	—	4	2	no	—
95	C₂×C₄×C₁₉	#95	1	2	yes	—
96	C₂×C₄×C₁₉	#95	1	2	yes	—
97	C₂×C₄×C₁₉	#95	1	2	yes	—
98	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#131	1	4	yes	—
105	C₂×C₄×C₁₉	#135	1	4	yes	—
106	C₈×C₁₉	—	4	4	no	—
107	C₁₉⋊C₈	—	4	4	no	—
108	C₁₉⋊C₈	—	4	4	no	—
109	C₂×#432	—	19	1	no	—
110	C₂×#431	—	19	1	no	—
111	C₂×#431	D₁₉	1	1	yes	characteristic
112	#1277	—	19	4	no	—
113	C₂²×C₁₉	—	2	2	no	—
114	C₂²×C₁₉	—	2	2	no	—
115	C₂²×C₁₉	—	2	2	no	—
116	C₂²×C₁₉	—	4	4	no	—
117	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
118	C₂²×C₁₉	#424	1	2	yes	—
119	C₂²×C₁₉	#427	1	2	yes	—
120	C₂²×C₁₉	#430	1	2	yes	—
121	C₄×C₁₉	—	2	2	no	—
122	C₄×C₁₉	—	2	2	no	—
123	C₄×C₁₉	—	2	2	no	—
124	C₄×C₁₉	—	2	1	no	—
125	C₄×C₁₉	—	2	1	no	—
126	C₄×C₁₉	#405	1	2	yes	—
127	C₄×C₁₉	#408	1	2	yes	—
128	C₄×C₁₉	#416	1	2	yes	—
129	C₄×C₁₉	#416	1	2	yes	—
130	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
131	#432	—	19	4	no	—
132	#432	—	38	2	no	—
133	#431	—	2	2	no	—
134	#431	—	2	2	no	—
135	#431	—	19	4	no	—
136	#431	—	38	2	no	—
137	C₂×C₄⋊C₈	—	19	2	no	—
138	C₂×C₄⋊C₈	—	19	2	no	—
139	C₂×C₄⋊C₈	Dic₁₉	1	2	yes	—
140	C₂×C₂²⋊C₈	—	38	1	no	—
141	C₂×C₂²⋊C₈	—	38	1	no	—
142	C₂×C₂²⋊C₈	Dic₁₉	1	2	yes	—
143	C₂×#97	—	38	1	no	—
144	C₂×C₄×C₈	—	38	1	no	—
145	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
146	C₂×C₁₉	—	4	2	no	—
147	C₂×C₁₉	#1572	1	4	yes	—
148	C₂×C₁₉	#1729	1	1	yes	characteristic
149	C₂×C₁₉	#1735	1	1	yes	characteristic
150	C₂×C₁₉	#1738	1	1	yes	characteristic
151	C₂³×C₄	Dic₃₈	1	1	yes	characteristic
152	C₂³×C₄	D₇₆	1	1	yes	characteristic
153	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
154	C₂²×C₈	—	38	2	no	—
155	C₂²×C₈	—	38	2	no	—
156	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
157	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
158	C₂×C₄²	C₄×D₁₉	1	2	yes	—
159	C₂×C₄²	C₄×D₁₉	1	2	yes	—
160	C₂×C₄²	D₇₆	1	1	yes	characteristic
161	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
162	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
163	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
164	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
165	C₄⋊C₈	—	2	4	no	—
166	C₄⋊C₈	—	19	4	no	—
167	C₄⋊C₈	—	19	4	no	—
168	C₄⋊C₈	—	38	2	no	—
169	C₄⋊C₈	—	38	2	no	—
170	C₂²⋊C₈	—	2	4	no	—
171	C₂²⋊C₈	—	38	4	no	—
172	C₂²⋊C₈	—	38	4	no	—
173	#97	—	38	4	no	—
174	C₄×C₈	—	2	2	no	—
175	C₄×C₈	—	2	2	no	—
176	C₄×C₈	—	38	4	no	—
177	C₁₉	#7878	1	1	yes	characteristic, complemented, Sylow
178	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
179	C₂²×C₄	—	2	4	no	—
180	C₂²×C₄	—	2	4	no	—
181	C₂²×C₄	—	4	2	no	—
182	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
183	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
184	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
185	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
186	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
187	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
188	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
189	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
190	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
191	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
192	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
193	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
194	C₂×C₈	—	2	8	no	—
195	C₂×C₈	—	2	4	no	—
196	C₂×C₈	—	38	4	no	—
197	C₂×C₈	—	38	4	no	—
198	C₂×C₈	—	76	4	no	—
199	C₂×C₈	—	76	4	no	—
200	C₄²	C₄×Dic₁₉	1	2	yes	—
201	C₄²	Dic₁₉⋊C₄	1	2	yes	—
202	C₄²	Dic₁₉⋊C₄	1	2	yes	—
203	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
204	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
205	C₄²	C₂²⋊Dic₁₉	1	2	yes	—
206	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
207	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
208	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
209	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
210	C₂³	—	2	2	no	—
211	C₂³	—	2	2	no	—
212	C₂³	—	2	2	no	—
213	C₂³	C₁₉⋊#95	1	2	yes	—
214	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	4	no	—
220	C₂×C₄	—	2	4	no	—
221	C₂×C₄	—	2	4	no	—
222	C₂×C₄	—	2	4	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	C₁₉⋊#95	1	2	yes	—
226	C₂×C₄	C₁₉⋊#95	1	2	yes	—
227	C₂×C₄	C₁₉⋊#95	1	2	yes	—
228	C₂×C₄	#10597350	1	4	yes	—
229	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
230	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
231	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
232	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
233	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
234	C₂×C₄	#10597394	1	4	yes	—
235	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
236	C₈	—	4	4	no	—
237	C₈	—	76	4	no	—
238	C₈	—	76	4	no	—
239	C₂²	—	2	2	no	—
240	C₂²	—	2	2	no	—
241	C₂²	—	2	2	no	—
242	C₂²	—	4	4	no	—
243	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
244	C₂²	#11926571	1	2	yes	—
245	C₂²	#11926582	1	2	yes	—
246	C₂²	#11926593	1	2	yes	—
247	C₄	—	2	2	no	—
248	C₄	—	2	2	no	—
249	C₄	—	2	2	no	—
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	#11926500	1	2	yes	—
253	C₄	#11926511	1	2	yes	—
254	C₄	#11926541	1	2	yes	—
255	C₄	#11926541	1	2	yes	—
256	C₂	—	4	2	no	—
257	C₂	#14562415	1	4	yes	—
258	C₂	#14563332	1	1	yes	characteristic
259	C₂	#14563352	1	1	yes	characteristic
260	C₂	#14563362	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#431	C₂
socle	C₂³×C₁₉	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#431	D₁₉
hypocenter	C₁₉	#7878
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #14561470	C₂	semidirect
177. C₁₉	#7878	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926601	2
C₂×#11926597	2
#14561470	2
C₂×C₁₉×#431	2
#7878	19