Subgroups — C₂×#14561466 #18071955

Order 4864.

678 conjugacy classes of subgroups.

The subgroup lattice has 272 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	2	yes	maximal
2	#14561466	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
4	#11926597	—	2	2	no	—
5	#11926597	—	2	2	no	—
6	#11926597	C₄	1	4	yes	—
7	#11926597	C₂²	1	4	yes	—
8	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
9	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
10	C₂×C₄×C₁₉⋊C₈	C₄	1	4	yes	—
11	C₂³×C₈×C₁₉	C₄	1	2	yes	—
12	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#97	—	2	2	no	—
14	C₂×C₁₉×#97	—	2	2	no	—
15	C₂×C₁₉×#97	C₄	1	2	yes	—
16	C₂×C₁₉×#97	C₂²	1	2	yes	—
17	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
19	C₂³×C₄×C₁₉	Q₈	1	1	yes	characteristic
20	C₂²×C₈×C₁₉	—	2	2	no	—
21	C₂²×C₈×C₁₉	—	2	2	no	—
22	C₂²×C₈×C₁₉	—	2	4	no	—
23	C₂²×C₈×C₁₉	C₈	1	8	yes	complemented
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	4	no	—
34	C₁₉×#97	—	2	4	no	—
35	C₁₉×#97	—	2	4	no	—
36	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
37	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
40	C₄×C₁₉⋊C₈	—	2	4	no	—
41	C₄×C₁₉⋊C₈	C₂×C₄	1	8	yes	—
42	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	—	4	2	no	—
44	C₂²×C₄×C₁₉	—	4	2	no	—
45	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
52	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂×C₈	1	4	yes	—
57	C₂²×C₄×C₁₉	M₁₆	1	4	yes	—
58	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
61	C₂×C₈×C₁₉	—	2	8	no	—
62	C₂×C₈×C₁₉	—	2	8	no	—
63	C₂×C₈×C₁₉	—	2	4	no	—
64	C₂×C₈×C₁₉	—	2	4	no	—
65	C₂×C₈×C₁₉	C₂×C₈	1	8	yes	complemented
66	C₄²×C₁₉	C₄²	1	2	yes	—
67	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
68	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
69	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
70	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
71	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
72	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
73	C₄²×C₁₉	C₂×D₄	1	2	yes	—
74	C₂×C₁₉⋊C₈	—	2	8	no	—
75	C₂×C₁₉⋊C₈	—	4	8	no	—
76	C₂×#1275	—	19	1	no	maximal, Sylow
77	C₂³×C₁₉	—	2	2	no	—
78	C₂³×C₁₉	—	2	2	no	—
79	C₂³×C₁₉	#95	1	1	yes	characteristic
80	C₂³×C₁₉	#95	1	1	yes	characteristic
81	C₂³×C₁₉	C₄⋊C₈	1	4	yes	—
82	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₉	—	2	4	no	—
84	C₂×C₄×C₁₉	—	2	4	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	—	4	1	no	—
88	C₂×C₄×C₁₉	—	4	1	no	—
89	C₂×C₄×C₁₉	—	4	1	no	—
90	C₂×C₄×C₁₉	—	4	1	no	—
91	C₂×C₄×C₁₉	#95	1	2	yes	—
92	C₂×C₄×C₁₉	#95	1	2	yes	—
93	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₄×C₈	1	2	yes	—
96	C₂×C₄×C₁₉	C₄×C₈	1	2	yes	—
97	C₂×C₄×C₁₉	#97	1	2	yes	—
98	C₂×C₄×C₁₉	#97	1	2	yes	—
99	C₂×C₄×C₁₉	C₂²⋊C₈	1	4	yes	—
100	C₂×C₄×C₁₉	C₂²⋊C₈	1	4	yes	—
101	C₂×C₄×C₁₉	C₄⋊C₈	1	4	yes	—
102	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
105	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
106	C₂×C₄×C₁₉	C₂²×C₈	1	2	yes	—
107	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
108	C₈×C₁₉	—	2	8	no	—
109	C₁₉⋊C₈	—	4	8	no	—
110	C₂×#431	—	19	2	no	—
111	C₂²×#97	D₁₉	1	1	yes	characteristic
112	#1275	—	19	4	no	—
113	C₂²×C₁₉	—	2	1	no	—
114	C₂²×C₁₉	—	2	1	no	—
115	C₂²×C₁₉	—	2	1	no	—
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	—	2	8	no	—
118	C₂²×C₁₉	#336	1	2	yes	—
119	C₂²×C₁₉	#336	1	2	yes	—
120	C₂²×C₁₉	H(3,ℤ/4)	1	2	yes	—
121	C₂²×C₁₉	#338	1	2	yes	—
122	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
123	C₂²×C₁₉	C₂×C₄⋊C₈	1	2	yes	—
124	C₄×C₁₉	—	2	2	no	—
125	C₄×C₁₉	—	2	2	no	—
126	C₄×C₁₉	—	2	2	no	—
127	C₄×C₁₉	—	2	2	no	—
128	C₄×C₁₉	#336	1	2	yes	—
129	C₄×C₁₉	#336	1	2	yes	—
130	C₄×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
131	C₄×C₁₉	C₂×#97	1	1	yes	characteristic
132	C₄×C₁₉	C₂×C₂²⋊C₈	1	2	yes	—
133	C₂³×C₈	Dic₁₉	1	2	yes	—
134	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
135	#431	—	19	4	no	—
136	#431	—	19	4	no	—
137	#431	—	38	2	no	—
138	#431	—	38	2	no	—
139	C₂×C₄⋊C₈	—	38	2	no	—
140	C₂×C₂²⋊C₈	—	38	2	no	—
141	C₂×#97	—	2	2	no	—
142	C₂×#97	—	2	2	no	—
143	C₂×#97	Dic₁₉	1	2	yes	—
144	C₂×#97	C₂×D₁₉	1	2	yes	—
145	C₂×C₄×C₈	—	19	4	no	—
146	C₂×C₁₉	—	2	2	no	—
147	C₂×C₁₉	—	2	2	no	—
148	C₂×C₁₉	#1275	1	4	yes	complemented
149	C₂×C₁₉	C₂×#336	1	1	yes	characteristic
150	C₂×C₁₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
151	C₂×C₁₉	C₂×#338	1	1	yes	characteristic
152	C₂³×C₄	Dic₃₈	1	1	yes	characteristic
153	C₂³×C₄	D₇₆	1	1	yes	characteristic
154	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
155	C₂²×C₈	—	2	4	no	—
156	C₂²×C₈	—	2	2	no	—
157	C₂²×C₈	—	2	2	no	—
158	C₂²×C₈	—	38	4	no	—
159	C₂²×C₈	C₁₉⋊C₈	1	8	yes	complemented
160	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
161	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
162	C₂×C₄²	C₄×D₁₉	1	2	yes	—
163	C₂×C₄²	C₄×D₁₉	1	2	yes	—
164	C₂×C₄²	D₇₆	1	1	yes	characteristic
165	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
166	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
167	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
168	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
169	C₄⋊C₈	—	38	4	no	—
170	C₄⋊C₈	—	38	4	no	—
171	C₂²⋊C₈	—	38	4	no	—
172	C₂²⋊C₈	—	38	4	no	—
173	#97	—	2	4	no	—
174	#97	—	2	4	no	—
175	C₄×C₈	—	19	8	no	—
176	C₄×C₈	—	38	4	no	—
177	C₁₉	C₂×#1275	1	1	yes	characteristic, complemented, Sylow
178	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
179	C₂²×C₄	—	4	2	no	—
180	C₂²×C₄	—	4	2	no	—
181	C₂²×C₄	C₂×C₁₉⋊C₈	1	4	yes	—
182	C₂²×C₄	#64520	1	4	yes	—
183	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
184	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
185	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
186	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
187	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
188	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
189	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
190	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
191	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
192	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
193	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
194	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
195	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
196	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
197	C₂×C₈	—	2	4	no	—
198	C₂×C₈	—	2	8	no	—
199	C₂×C₈	—	2	8	no	—
200	C₂×C₈	—	2	4	no	—
201	C₂×C₈	—	38	8	no	—
202	C₂×C₈	—	76	8	no	—
203	C₂×C₈	C₂×C₁₉⋊C₈	1	8	yes	complemented
204	C₄²	C₄×Dic₁₉	1	2	yes	—
205	C₄²	Dic₁₉⋊C₄	1	2	yes	—
206	C₄²	Dic₁₉⋊C₄	1	2	yes	—
207	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
208	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
209	C₄²	C₂²⋊Dic₁₉	1	2	yes	—
210	C₄²	C₂×C₄×D₁₉	1	2	yes	—
211	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
212	C₂³	—	2	2	no	—
213	C₂³	—	2	2	no	—
214	C₂³	C₄⋊(C₁₉⋊C₈)	1	4	yes	—
215	C₂³	C₁₉⋊#95	1	1	yes	characteristic
216	C₂³	C₁₉⋊#95	1	1	yes	characteristic
217	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
218	C₂×C₄	—	2	4	no	—
219	C₂×C₄	—	2	4	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	—	4	1	no	—
222	C₂×C₄	—	4	1	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	1	no	—
225	C₂×C₄	—	4	1	no	—
226	C₂×C₄	C₄×C₁₉⋊C₈	1	2	yes	—
227	C₂×C₄	C₄×C₁₉⋊C₈	1	2	yes	—
228	C₂×C₄	#10597260	1	2	yes	—
229	C₂×C₄	#10597260	1	2	yes	—
230	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	4	yes	—
231	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	4	yes	—
232	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	4	yes	—
233	C₂×C₄	C₁₉⋊#95	1	2	yes	—
234	C₂×C₄	C₁₉⋊#95	1	2	yes	—
235	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
236	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
237	C₂×C₄	C₂²×C₁₉⋊C₈	1	2	yes	—
238	C₂×C₄	C₂×#64520	1	2	yes	—
239	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
240	C₂×C₄	C₂×Dic₁₉⋊C₄	1	2	yes	—
241	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
242	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
243	C₈	—	2	8	no	—
244	C₈	—	76	8	no	—
245	C₂²	—	2	1	no	—
246	C₂²	—	2	1	no	—
247	C₂²	—	2	1	no	—
248	C₂²	—	2	1	no	—
249	C₂²	—	2	8	no	—
250	C₂²	#11926299	1	2	yes	—
251	C₂²	#11926299	1	2	yes	—
252	C₂²	#11926301	1	2	yes	—
253	C₂²	C₁₉⋊#338	1	2	yes	—
254	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
255	C₂²	C₂×C₄⋊(C₁₉⋊C₈)	1	2	yes	—
256	C₄	—	2	2	no	—
257	C₄	—	2	2	no	—
258	C₄	—	2	2	no	—
259	C₄	—	2	2	no	—
260	C₄	#11926299	1	2	yes	—
261	C₄	#11926299	1	2	yes	—
262	C₄	C₂×C₄×C₁₉⋊C₈	1	1	yes	characteristic
263	C₄	C₂×#10597260	1	1	yes	characteristic
264	C₄	C₂×C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
265	C₂	—	2	2	no	—
266	C₂	—	2	2	no	—
267	C₂	#14561466	1	4	yes	direct product factor
268	C₂	C₂×#11926299	1	1	yes	characteristic
269	C₂	C₂×#11926301	1	1	yes	characteristic
270	C₂	C₂×C₁₉⋊#338	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₄×Dic₁₉
commutator	C₄×C₁₉	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂²×C₁₉×#97	C₂
socle	C₂³×C₁₉	#95
prime radical	C₂⁴×C₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂²×#97	D₁₉
hypocenter	C₁₉	C₂×#1275
LCS	G ▷ C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
2. #14561466	C₂	direct (N × H)
23. C₂²×C₈×C₁₉	C₈	semidirect
65. C₂×C₈×C₁₉	C₂×C₈	semidirect
148. C₂×C₁₉	#1275	semidirect
159. C₂²×C₈	C₁₉⋊C₈	semidirect
177. C₁₉	C₂×#1275	semidirect
203. C₂×C₈	C₂×C₁₉⋊C₈	semidirect
267. C₂	#14561466	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11926597	2
#14561466	2
C₂²×C₁₉×#97	2
C₂×#1275	19

Subgroups — C2×#14561466 #18071955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14561466 #18071955