Subgroups — #14577270

Order 2432.

1900 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597430	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927188	C₂	1	8	yes	maximal, complemented
3	D₄×C₂²⋊D₁₉	C₂	1	8	yes	maximal, complemented
4	#11927111	C₂	1	2	yes	maximal, complemented
5	#11927103	C₂	1	4	yes	maximal, complemented
6	#11927055	C₂	1	2	yes	maximal, complemented
7	C₂×#10597399	C₂	1	4	yes	maximal, complemented
8	#11927019	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁵×C₁₉	C₂²	1	2	yes	complemented
11	C₂²×D₄×C₁₉	—	2	8	no	—
12	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₁₉	C₂²	1	2	yes	complemented
14	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
15	C₂²×D₄×C₁₉	C₂²	1	8	yes	complemented
16	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
18	C₂²×C₂²⋊D₁₉	C₂²	1	8	yes	complemented
19	#10597430	—	2	8	no	—
20	C₂×#64543	C₂²	1	4	yes	complemented
21	C₂×D₄×D₁₉	C₂²	1	4	yes	complemented
22	C₂×#64541	C₂²	1	2	yes	complemented
23	#10597399	C₂²	1	4	yes	complemented
24	#10597399	C₂²	1	8	yes	complemented
25	#10597399	C₂²	1	16	yes	complemented
26	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	complemented
27	C₂×C₂²⋊Dic₁₉	C₂²	1	8	yes	complemented
28	#10597386	C₂²	1	4	yes	complemented
29	#10597385	C₂²	1	16	yes	complemented
30	#10597384	C₂²	1	8	yes	complemented
31	#10597383	C₂²	1	8	yes	complemented
32	#10597382	C₂²	1	4	yes	complemented
33	#10597381	C₂²	1	8	yes	complemented
34	D₄×Dic₁₉	C₂²	1	8	yes	complemented
35	#10597376	C₂²	1	4	yes	complemented
36	#10597375	C₂²	1	4	yes	complemented
37	C₄×C₂²⋊D₁₉	C₂²	1	8	yes	complemented
38	#10597372	C₂²	1	2	yes	complemented
39	#10597370	C₂²	1	4	yes	complemented
40	C₂⁴×C₁₉	—	2	8	no	—
41	C₂⁴×C₁₉	—	4	8	no	—
42	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
43	C₂⁴×C₁₉	C₂³	1	8	yes	—
44	C₂⁴×C₁₉	C₂³	1	2	yes	—
45	C₂⁴×C₁₉	C₂³	1	2	yes	—
46	C₂³×D₁₉	C₂³	1	4	yes	complemented
47	C₂×D₄×C₁₉	—	2	8	no	—
48	C₂×D₄×C₁₉	—	2	32	no	—
49	C₂×D₄×C₁₉	—	2	4	no	—
50	C₂×D₄×C₁₉	D₄	1	8	yes	complemented
51	C₂×D₄×C₁₉	C₂³	1	8	yes	—
52	C₂×D₄×C₁₉	C₂³	1	4	yes	—
53	C₂×D₄×C₁₉	C₂³	1	4	yes	—
54	C₂²×C₄×C₁₉	—	2	4	no	—
55	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
56	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×C₂²⋊D₁₉	—	2	16	no	—
59	C₂×C₂²⋊D₁₉	—	4	16	no	—
60	C₂×C₂²⋊D₁₉	C₂³	1	8	yes	—
61	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
62	C₂×C₂²⋊D₁₉	C₂³	1	8	yes	complemented
63	C₂×C₂²⋊D₁₉	C₂³	1	16	yes	complemented
64	C₂²×Dic₁₉	C₂³	1	4	yes	complemented
65	C₂²×Dic₁₉	C₂³	1	8	yes	complemented
66	#64543	—	2	16	no	—
67	D₄×D₁₉	—	2	16	no	—
68	#64541	—	2	8	no	—
69	C₂×D₇₆	C₂³	1	2	yes	complemented
70	C₂×C₄×D₁₉	C₂³	1	4	yes	complemented
71	C₂×Dic₃₈	C₂³	1	2	yes	complemented
72	C₂²⋊Dic₁₉	C₂³	1	8	yes	—
73	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
74	C₂²⋊Dic₁₉	C₂³	1	8	yes	complemented
75	C₂²⋊Dic₁₉	C₂³	1	16	yes	complemented
76	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	complemented
77	C₄⋊Dic₁₉	C₂³	1	4	yes	complemented
78	Dic₁₉⋊C₄	C₂³	1	8	yes	complemented
79	C₄×Dic₁₉	C₂³	1	4	yes	complemented
80	C₂³×C₁₉	—	2	2	no	—
81	C₂³×C₁₉	—	2	4	no	—
82	C₂³×C₁₉	—	2	16	no	—
83	C₂³×C₁₉	—	2	4	no	—
84	C₂³×C₁₉	—	2	16	no	—
85	C₂³×C₁₉	—	4	4	no	—
86	C₂³×C₁₉	—	4	8	no	—
87	C₂³×C₁₉	—	4	4	no	—
88	C₂³×C₁₉	—	4	32	no	—
89	C₂³×C₁₉	C₂×D₄	1	8	yes	complemented
90	C₂³×C₁₉	C₂⁴	1	4	yes	—
91	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
92	C₂³×C₁₉	C₂⁴	1	4	yes	—
93	C₂³×C₁₉	C₂⁴	1	2	yes	—
94	C₂²×D₁₉	—	2	8	no	—
95	C₂²×D₁₉	—	4	8	no	—
96	C₂²×D₁₉	C₂⁴	1	4	yes	—
97	D₄×C₁₉	—	2	16	no	—
98	D₄×C₁₉	—	2	8	no	—
99	D₄×C₁₉	C₂×D₄	1	16	yes	complemented
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	2	8	no	—
102	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	complemented
103	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
104	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
105	C₂²⋊D₁₉	—	2	8	no	—
106	C₂²⋊D₁₉	—	2	16	no	—
107	C₂²⋊D₁₉	—	2	16	no	—
108	C₂²⋊D₁₉	—	4	16	no	—
109	C₂×Dic₁₉	—	2	8	no	—
110	C₂×Dic₁₉	—	4	8	no	—
111	C₂×Dic₁₉	C₂⁴	1	8	yes	—
112	C₂×Dic₁₉	C₂⁴	1	4	yes	—
113	D₇₆	—	2	4	no	—
114	C₄×D₁₉	—	2	8	no	—
115	Dic₃₈	—	2	4	no	—
116	#3484	—	19	1	no	maximal, Sylow
117	C₂²×C₁₉	—	2	8	no	—
118	C₂²×C₁₉	—	2	2	no	—
119	C₂²×C₁₉	—	2	8	no	—
120	C₂²×C₁₉	—	2	2	no	—
121	C₂²×C₁₉	—	2	2	no	—
122	C₂²×C₁₉	—	2	4	no	—
123	C₂²×C₁₉	—	2	8	no	—
124	C₂²×C₁₉	—	4	8	no	—
125	C₂²×C₁₉	—	4	32	no	—
126	C₂²×C₁₉	—	4	8	no	—
127	C₂²×C₁₉	C₂²×D₄	1	8	yes	—
128	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
129	C₂²×C₁₉	H(5,𝔽₂)	1	4	yes	complemented
130	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
131	C₂×D₁₉	—	2	4	no	—
132	C₂×D₁₉	—	2	8	no	—
133	C₂×D₁₉	—	8	8	no	—
134	C₄×C₁₉	—	2	2	no	—
135	C₄×C₁₉	C₂²×D₄	1	4	yes	—
136	Dic₁₉	—	2	4	no	—
137	Dic₁₉	—	2	8	no	—
138	C₂×H(5,𝔽₂)	—	19	1	no	—
139	C₂³×D₄	D₁₉	1	1	yes	characteristic, complemented
140	#546	—	19	8	no	—
141	D₄²	—	19	8	no	—
142	#535	—	19	2	no	—
143	#534	—	19	4	no	—
144	#525	—	19	2	no	—
145	C₂×#120	—	19	4	no	—
146	#518	—	19	1	no	—
147	C₂×C₁₉	—	2	8	no	—
148	C₂×C₁₉	—	2	2	no	—
149	C₂×C₁₉	—	2	4	no	—
150	C₂×C₁₉	—	4	4	no	—
151	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
152	C₂×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
153	D₁₉	—	4	4	no	—
154	C₂⁵	C₂×D₁₉	1	2	yes	complemented
155	H(5,𝔽₂)	—	38	8	no	—
156	C₂×#41	—	19	4	no	—
157	C₂×#41	—	19	2	no	—
158	C₂²×D₄	—	2	8	no	—
159	C₂²×D₄	—	19	4	no	—
160	C₂²×D₄	—	19	8	no	—
161	C₂²×D₄	—	19	4	no	—
162	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
163	C₂²×D₄	C₂×D₁₉	1	2	yes	complemented
164	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
165	C₂²×D₄	C₂×D₁₉	1	8	yes	complemented
166	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
167	#127	—	19	4	no	—
168	#124	—	19	4	no	—
169	#123	—	19	8	no	—
170	#123	—	19	4	no	—
171	C₂²⋊Q₈	—	19	4	no	—
172	#121	—	19	8	no	—
173	#121	—	19	16	no	—
174	#121	—	19	4	no	—
175	#120	—	19	4	no	—
176	#120	—	19	8	no	—
177	#120	—	19	16	no	—
178	#120	—	19	8	no	—
179	C₄×D₄	—	19	8	no	—
180	C₄×D₄	—	19	8	no	—
181	#117	—	19	2	no	—
182	C₂×C₂²⋊C₄	—	19	4	no	—
183	C₂×C₂²⋊C₄	—	19	8	no	—
184	C₁₉	#3484	1	1	yes	characteristic, complemented, Sylow
185	C₂⁴	—	2	8	no	—
186	C₂⁴	—	4	8	no	—
187	C₂⁴	—	19	4	no	—
188	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
189	C₂⁴	C₂²×D₁₉	1	8	yes	—
190	C₂⁴	C₂²×D₁₉	1	2	yes	—
191	C₂⁴	C₂²×D₁₉	1	2	yes	—
192	#41	—	38	16	no	—
193	#41	—	38	8	no	—
194	C₂×Q₈	—	19	2	no	—
195	C₂×D₄	—	2	8	no	—
196	C₂×D₄	—	2	32	no	—
197	C₂×D₄	—	2	4	no	—
198	C₂×D₄	—	19	8	no	—
199	C₂×D₄	—	19	4	no	—
200	C₂×D₄	—	19	8	no	—
201	C₂×D₄	—	19	16	no	—
202	C₂×D₄	—	19	2	no	—
203	C₂×D₄	—	38	16	no	—
204	C₂×D₄	—	38	16	no	—
205	C₂×D₄	—	76	16	no	—
206	C₂×D₄	C₂²⋊D₁₉	1	8	yes	complemented
207	C₂×D₄	C₂²×D₁₉	1	8	yes	—
208	C₂×D₄	C₂²×D₁₉	1	4	yes	—
209	C₂×D₄	C₂²×D₁₉	1	4	yes	—
210	C₂²×C₄	—	2	4	no	—
211	C₂²×C₄	—	19	4	no	—
212	C₂²×C₄	—	19	8	no	—
213	C₂²×C₄	—	19	4	no	—
214	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
215	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
216	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
217	C₄⋊C₄	—	19	8	no	—
218	C₄⋊C₄	—	19	4	no	—
219	C₂²⋊C₄	—	19	4	no	—
220	C₂²⋊C₄	—	19	8	no	—
221	C₂²⋊C₄	—	19	8	no	—
222	C₂²⋊C₄	—	19	16	no	—
223	C₂²⋊C₄	—	19	8	no	—
224	C₄²	—	19	4	no	—
225	C₂³	—	2	4	no	—
226	C₂³	—	2	2	no	—
227	C₂³	—	2	16	no	—
228	C₂³	—	2	16	no	—
229	C₂³	—	2	4	no	—
230	C₂³	—	4	4	no	—
231	C₂³	—	4	8	no	—
232	C₂³	—	4	4	no	—
233	C₂³	—	4	32	no	—
234	C₂³	—	19	4	no	—
235	C₂³	—	38	8	no	—
236	C₂³	—	76	8	no	—
237	C₂³	C₂×C₂²⋊D₁₉	1	8	yes	complemented
238	C₂³	C₂³×D₁₉	1	4	yes	—
239	C₂³	C₂³×D₁₉	1	2	yes	—
240	C₂³	C₂³×D₁₉	1	1	yes	characteristic
241	C₂³	C₂³×D₁₉	1	4	yes	—
242	Q₈	—	38	4	no	—
243	D₄	—	2	16	no	—
244	D₄	—	2	8	no	—
245	D₄	—	38	16	no	—
246	D₄	—	38	8	no	—
247	D₄	—	38	16	no	—
248	D₄	—	38	4	no	—
249	D₄	—	76	16	no	—
250	D₄	C₂×C₂²⋊D₁₉	1	16	yes	complemented
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	8	no	—
253	C₂×C₄	—	19	8	no	—
254	C₂×C₄	—	19	4	no	—
255	C₂×C₄	—	38	8	no	—
256	C₂×C₄	—	38	8	no	—
257	C₂×C₄	—	76	8	no	—
258	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	complemented
259	C₂×C₄	C₂³×D₁₉	1	2	yes	—
260	C₂×C₄	C₂³×D₁₉	1	2	yes	—
261	C₂²	—	2	8	no	—
262	C₂²	—	2	2	no	—
263	C₂²	—	2	8	no	—
264	C₂²	—	2	2	no	—
265	C₂²	—	2	2	no	—
266	C₂²	—	2	4	no	—
267	C₂²	—	2	8	no	—
268	C₂²	—	4	8	no	—
269	C₂²	—	4	32	no	—
270	C₂²	—	4	8	no	—
271	C₂²	—	38	4	no	—
272	C₂²	—	38	8	no	—
273	C₂²	—	152	8	no	—
274	C₂²	#10597430	1	4	yes	complemented
275	C₂²	C₂²×C₂²⋊D₁₉	1	2	yes	—
276	C₂²	C₂²×C₂²⋊D₁₉	1	8	yes	—
277	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
278	C₄	—	2	2	no	—
279	C₄	—	38	4	no	—
280	C₄	—	38	8	no	—
281	C₄	C₂²×C₂²⋊D₁₉	1	4	yes	—
282	C₂	—	2	4	no	—
283	C₂	—	2	2	no	—
284	C₂	—	2	8	no	—
285	C₂	—	4	4	no	—
286	C₂	—	76	4	no	—
287	C₂	C₂³×C₂²⋊D₁₉	1	1	yes	characteristic
288	C₂	C₂×#10597430	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₂³×D₄×C₁₉	C₂
hypercenter	C₂³×D₄	D₁₉
hypocenter	C₁₉	#3484
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#10597430	C₂	semidirect
2. #11927188	C₂	semidirect
3. D₄×C₂²⋊D₁₉	C₂	semidirect
4. #11927111	C₂	semidirect
5. #11927103	C₂	semidirect
6. #11927055	C₂	semidirect
7. C₂×#10597399	C₂	semidirect
8. #11927019	C₂	semidirect
9. C₂³×D₄×C₁₉	C₂	semidirect
10. C₂⁵×C₁₉	C₂²	semidirect
13. C₂²×D₄×C₁₉	C₂²	semidirect
14. C₂²×D₄×C₁₉	C₂²	semidirect
15. C₂²×D₄×C₁₉	C₂²	semidirect
16. C₂³×C₄×C₁₉	C₂²	semidirect
17. C₂²×C₂²⋊D₁₉	C₂²	semidirect
18. C₂²×C₂²⋊D₁₉	C₂²	semidirect
20. C₂×#64543	C₂²	semidirect
21. C₂×D₄×D₁₉	C₂²	semidirect
22. C₂×#64541	C₂²	semidirect
23. #10597399	C₂²	semidirect
24. #10597399	C₂²	semidirect
25. #10597399	C₂²	semidirect
26. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
27. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
28. #10597386	C₂²	semidirect
29. #10597385	C₂²	semidirect
30. #10597384	C₂²	semidirect
31. #10597383	C₂²	semidirect
32. #10597382	C₂²	semidirect
33. #10597381	C₂²	semidirect
34. D₄×Dic₁₉	C₂²	semidirect
35. #10597376	C₂²	semidirect
36. #10597375	C₂²	semidirect
37. C₄×C₂²⋊D₁₉	C₂²	semidirect
38. #10597372	C₂²	semidirect
39. #10597370	C₂²	semidirect
46. C₂³×D₁₉	C₂³	semidirect
50. C₂×D₄×C₁₉	D₄	semidirect
62. C₂×C₂²⋊D₁₉	C₂³	semidirect
63. C₂×C₂²⋊D₁₉	C₂³	semidirect
64. C₂²×Dic₁₉	C₂³	semidirect
65. C₂²×Dic₁₉	C₂³	semidirect
69. C₂×D₇₆	C₂³	semidirect
70. C₂×C₄×D₁₉	C₂³	semidirect
71. C₂×Dic₃₈	C₂³	semidirect
74. C₂²⋊Dic₁₉	C₂³	semidirect
75. C₂²⋊Dic₁₉	C₂³	semidirect
76. (C₂×D₁₉)⋊C₄	C₂³	semidirect
77. C₄⋊Dic₁₉	C₂³	semidirect
78. Dic₁₉⋊C₄	C₂³	semidirect
79. C₄×Dic₁₉	C₂³	semidirect
89. C₂³×C₁₉	C₂×D₄	semidirect
99. D₄×C₁₉	C₂×D₄	semidirect
102. C₂×C₄×C₁₉	C₂×D₄	semidirect
129. C₂²×C₁₉	H(5,𝔽₂)	semidirect
139. C₂³×D₄	D₁₉	semidirect
154. C₂⁵	C₂×D₁₉	semidirect
163. C₂²×D₄	C₂×D₁₉	semidirect
164. C₂²×D₄	C₂×D₁₉	semidirect
165. C₂²×D₄	C₂×D₁₉	semidirect
166. C₂³×C₄	C₂×D₁₉	semidirect
184. C₁₉	#3484	semidirect
206. C₂×D₄	C₂²⋊D₁₉	semidirect
237. C₂³	C₂×C₂²⋊D₁₉	semidirect
250. D₄	C₂×C₂²⋊D₁₉	semidirect
258. C₂×C₄	C₂×C₂²⋊D₁₉	semidirect
274. C₂²	#10597430	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597430	2
#11927188	2
D₄×C₂²⋊D₁₉	2
#11927111	2
#11927103	2
#11927055	2
C₂×#10597399	2
#11927019	2
C₂³×D₄×C₁₉	2
#3484	19