Subgroups — C₂×#14561510 #18072483

Order 4864.

690 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×#11926568	C₂	1	2	yes	maximal
2	#14561510	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64520	—	2	2	no	—
5	#11926568	—	2	2	no	—
6	#11926568	—	2	2	no	—
7	#11926568	C₄	1	4	yes	—
8	#11926568	C₂²	1	4	yes	—
9	C₂×C₄⋊(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×C₄⋊C₈	—	2	2	no	—
14	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
15	C₂×C₁₉×C₄⋊C₈	C₄	1	2	yes	—
16	C₂×C₁₉×C₄⋊C₈	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	—	4	4	no	—
23	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
24	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	D₄	1	2	yes	—
29	C₂×C₄²×C₁₉	D₄	1	2	yes	—
30	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×#64520	—	2	4	no	—
33	C₂×#64520	—	2	4	no	—
34	C₂×#64520	—	4	4	no	—
35	C₂×#64520	—	4	4	no	—
36	C₂²×C₁₉⋊C₈	—	2	4	no	—
37	C₁₉×C₄⋊C₈	—	2	4	no	—
38	C₁₉×C₄⋊C₈	—	2	4	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
42	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	8	yes	—
43	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	—	4	2	no	—
47	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
51	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
54	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	D₈	1	2	yes	—
59	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	—
60	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
61	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
64	C₂×C₈×C₁₉	—	2	4	no	—
65	C₂×C₈×C₁₉	—	4	4	no	—
66	C₂×C₈×C₁₉	—	4	4	no	—
67	C₂×C₈×C₁₉	—	4	4	no	—
68	C₄²×C₁₉	C₄²	1	2	yes	—
69	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
70	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
71	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
72	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
73	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
74	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
75	C₄²×C₁₉	C₂×D₄	1	2	yes	—
76	#64520	—	4	8	no	—
77	#64520	—	4	4	no	—
78	#64520	—	4	4	no	—
79	C₂×C₁₉⋊C₈	—	2	8	no	—
80	C₂×C₁₉⋊C₈	—	4	8	no	—
81	C₂×#1292	—	19	1	no	maximal, Sylow
82	C₂³×C₁₉	—	2	2	no	—
83	C₂³×C₁₉	—	2	2	no	—
84	C₂³×C₁₉	#95	1	1	yes	characteristic
85	C₂³×C₁₉	#95	1	1	yes	characteristic
86	C₂³×C₁₉	#106	1	2	yes	—
87	C₂³×C₁₉	#107	1	2	yes	—
88	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₁₉	—	2	4	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	4	1	no	—
99	C₂×C₄×C₁₉	—	4	1	no	—
100	C₂×C₄×C₁₉	#95	1	2	yes	—
101	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#95	1	2	yes	—
103	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#100	1	2	yes	—
105	C₂×C₄×C₁₉	#101	1	2	yes	—
106	C₂×C₄×C₁₉	#102	1	4	yes	—
107	C₂×C₄×C₁₉	#102	1	4	yes	—
108	C₂×C₄×C₁₉	#103	1	4	yes	—
109	C₂×C₄×C₁₉	#103	1	4	yes	—
110	C₂×C₄×C₁₉	#106	1	2	yes	—
111	C₂×C₄×C₁₉	#107	1	2	yes	—
112	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
114	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
115	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
116	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
117	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
118	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
119	C₈×C₁₉	—	4	4	no	—
120	C₁₉⋊C₈	—	4	8	no	—
121	C₂×#423	—	19	2	no	—
122	C₂²×C₄⋊C₈	D₁₉	1	1	yes	characteristic
123	#1292	—	19	4	no	—
124	C₂²×C₁₉	—	2	4	no	—
125	C₂²×C₁₉	—	2	4	no	—
126	C₂²×C₁₉	—	2	1	no	—
127	C₂²×C₁₉	—	2	1	no	—
128	C₂²×C₁₉	—	2	1	no	—
129	C₂²×C₁₉	—	2	1	no	—
130	C₂²×C₁₉	#338	1	2	yes	—
131	C₂²×C₁₉	#340	1	2	yes	—
132	C₂²×C₁₉	#340	1	2	yes	—
133	C₂²×C₁₉	#343	1	2	yes	—
134	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
135	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
136	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
137	C₄×C₁₉	—	2	2	no	—
138	C₄×C₁₉	—	2	2	no	—
139	C₄×C₁₉	—	2	1	no	—
140	C₄×C₁₉	—	2	1	no	—
141	C₄×C₁₉	#340	1	4	yes	—
142	C₄×C₁₉	#343	1	2	yes	—
143	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
144	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
145	C₄×C₁₉	C₂×#102	1	2	yes	—
146	C₄×C₁₉	C₂×#103	1	2	yes	—
147	C₂²×M₁₆	—	38	2	no	—
148	C₂³×C₈	Dic₁₉	1	2	yes	—
149	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
150	#423	—	19	4	no	—
151	#423	—	19	4	no	—
152	#423	—	38	2	no	—
153	#423	—	38	2	no	—
154	C₂×C₄⋊C₈	—	2	2	no	—
155	C₂×C₄⋊C₈	—	2	2	no	—
156	C₂×C₄⋊C₈	—	19	4	no	—
157	C₂×C₄⋊C₈	—	38	2	no	—
158	C₂×C₄⋊C₈	Dic₁₉	1	2	yes	—
159	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
160	C₂×C₁₉	—	2	2	no	—
161	C₂×C₁₉	—	2	1	no	—
162	C₂×C₁₉	—	2	1	no	—
163	C₂×C₁₉	#1292	1	4	yes	complemented
164	C₂×C₁₉	C₂×#338	1	1	yes	characteristic
165	C₂×C₁₉	C₂×#340	1	1	yes	characteristic
166	C₂×C₁₉	C₂×#343	1	1	yes	characteristic
167	C₂³×C₄	Dic₃₈	1	1	yes	characteristic
168	C₂³×C₄	D₇₆	1	1	yes	characteristic
169	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
170	C₂×M₁₆	—	38	4	no	—
171	C₂×M₁₆	—	38	4	no	—
172	C₂×M₁₆	—	76	4	no	—
173	C₂×M₁₆	—	76	4	no	—
174	C₂²×C₈	—	2	2	no	—
175	C₂²×C₈	—	2	2	no	—
176	C₂²×C₈	—	4	4	no	—
177	C₂²×C₈	—	38	4	no	—
178	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
179	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
180	C₂×C₄²	C₄×D₁₉	1	2	yes	—
181	C₂×C₄²	C₄×D₁₉	1	2	yes	—
182	C₂×C₄²	D₇₆	1	1	yes	characteristic
183	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
184	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
185	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
186	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
187	C₄⋊C₈	—	2	4	no	—
188	C₄⋊C₈	—	2	4	no	—
189	C₄⋊C₈	—	19	8	no	—
190	C₄⋊C₈	—	38	4	no	—
191	C₄⋊C₈	—	38	4	no	—
192	C₄⋊C₈	—	38	4	no	—
193	C₁₉	C₂×#1292	1	1	yes	characteristic, complemented, Sylow
194	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
195	C₂²×C₄	—	2	2	no	—
196	C₂²×C₄	—	2	2	no	—
197	C₂²×C₄	—	4	2	no	—
198	C₂²×C₄	#64516	1	4	yes	—
199	C₂²×C₄	D₁₅₂	1	2	yes	—
200	C₂²×C₄	Dic₇₆	1	2	yes	—
201	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
202	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
203	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
204	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
205	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
206	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
207	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
208	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
209	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
210	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
211	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
212	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
213	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
214	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
215	M₁₆	—	76	8	no	—
216	M₁₆	—	76	4	no	—
217	M₁₆	—	76	4	no	—
218	C₂×C₈	—	2	4	no	—
219	C₂×C₈	—	4	4	no	—
220	C₂×C₈	—	4	4	no	—
221	C₂×C₈	—	4	4	no	—
222	C₂×C₈	—	38	8	no	—
223	C₂×C₈	—	76	8	no	—
224	C₄²	C₄×Dic₁₉	1	2	yes	—
225	C₄²	Dic₁₉⋊C₄	1	2	yes	—
226	C₄²	Dic₁₉⋊C₄	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	C₂×C₄×D₁₉	1	2	yes	—
231	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
232	C₂³	—	2	2	no	—
233	C₂³	—	2	2	no	—
234	C₂³	#10597274	1	2	yes	—
235	C₂³	#10597275	1	2	yes	—
236	C₂³	C₁₉⋊#95	1	1	yes	characteristic
237	C₂³	C₁₉⋊#95	1	1	yes	characteristic
238	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
239	C₂×C₄	—	2	4	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	1	no	—
244	C₂×C₄	—	2	1	no	—
245	C₂×C₄	—	2	1	no	—
246	C₂×C₄	—	2	1	no	—
247	C₂×C₄	—	4	2	no	—
248	C₂×C₄	—	4	1	no	—
249	C₂×C₄	—	4	1	no	—
250	C₂×C₄	#10597273	1	4	yes	—
251	C₂×C₄	#10597273	1	4	yes	—
252	C₂×C₄	#10597274	1	2	yes	—
253	C₂×C₄	#10597275	1	2	yes	—
254	C₂×C₄	#10597278	1	4	yes	—
255	C₂×C₄	#10597278	1	4	yes	—
256	C₂×C₄	C₁₉⋊#95	1	2	yes	—
257	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
258	C₂×C₄	C₁₉⋊#95	1	2	yes	—
259	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
260	C₂×C₄	#10597290	1	2	yes	—
261	C₂×C₄	#10597293	1	2	yes	—
262	C₂×C₄	C₂×#64516	1	2	yes	—
263	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
264	C₂×C₄	C₂×Dic₇₆	1	1	yes	characteristic
265	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
266	C₂×C₄	C₂×Dic₁₉⋊C₄	1	2	yes	—
267	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
268	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
269	C₈	—	4	4	no	—
270	C₈	—	76	8	no	—
271	C₂²	—	2	1	no	—
272	C₂²	—	2	1	no	—
273	C₂²	—	2	1	no	—
274	C₂²	—	2	1	no	—
275	C₂²	—	2	4	no	—
276	C₂²	—	2	4	no	—
277	C₂²	C₁₉⋊#338	1	2	yes	—
278	C₂²	#11926307	1	2	yes	—
279	C₂²	#11926307	1	2	yes	—
280	C₂²	#11926313	1	2	yes	—
281	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
282	C₂²	C₂×#10597274	1	1	yes	characteristic
283	C₂²	C₂×#10597275	1	1	yes	characteristic
284	C₄	—	2	2	no	—
285	C₄	—	2	2	no	—
286	C₄	—	2	1	no	—
287	C₄	—	2	1	no	—
288	C₄	#11926307	1	4	yes	—
289	C₄	#11926313	1	2	yes	—
290	C₄	C₂×#10597290	1	1	yes	characteristic
291	C₄	C₂×#10597293	1	1	yes	characteristic
292	C₄	C₂×#10597278	1	2	yes	—
293	C₄	C₂×#10597273	1	2	yes	—
294	C₂	—	2	2	no	—
295	C₂	—	2	1	no	—
296	C₂	—	2	1	no	—
297	C₂	#14561510	1	4	yes	direct product factor
298	C₂	C₂×C₁₉⋊#338	1	1	yes	characteristic
299	C₂	C₂×#11926307	1	1	yes	characteristic
300	C₂	C₂×#11926313	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₁₉⋊#95
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂²×C₁₉×C₄⋊C₈	C₂
socle	C₂³×C₁₉	#95
prime radical	C₂⁴×C₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂²×C₄⋊C₈	D₁₉
hypocenter	C₁₉	C₂×#1292
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. #14561510	C₂	direct (N × H)
163. C₂×C₁₉	#1292	semidirect
193. C₁₉	C₂×#1292	semidirect
297. C₂	#14561510	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×#11926568	2
#14561510	2
C₂²×C₁₉×C₄⋊C₈	2
C₂×#1292	19

Subgroups — C2×#14561510 #18072483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14561510 #18072483