Subgroups — D₁₉×#555 #14577171

Order 2432.

1240 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927260	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927259	C₂	1	2	yes	maximal, complemented
3	#11927258	C₂	1	4	yes	maximal, complemented
4	#11927257	C₂	1	4	yes	maximal, complemented
5	#11927256	C₂	1	4	yes	maximal, complemented
6	C₄⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#124×D₁₉	C₂	1	4	yes	maximal, complemented
8	#121×D₁₉	C₂	1	4	yes	maximal, complemented
9	C₄×D₄×D₁₉	C₂	1	2	yes	maximal, complemented
10	#117×D₁₉	C₂	1	4	yes	maximal, complemented
11	C₁₉×#555	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×D₁₉	C₂²	1	2	yes	—
13	C₂×D₄×D₁₉	C₂²	1	2	yes	—
14	C₂×D₄×D₁₉	C₂²	1	4	yes	—
15	C₂²×C₄×D₁₉	C₂²	1	4	yes	—
16	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₁₉×#124	C₂²	1	4	yes	complemented
18	C₁₉×#121	C₂²	1	4	yes	complemented
19	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
20	C₁₉×#117	C₂²	1	4	yes	complemented
21	#10597393	C₂²	1	4	yes	complemented
22	#10597390	C₂²	1	2	yes	complemented
23	#10597385	C₂²	1	8	yes	complemented
24	#10597384	C₂²	1	4	yes	complemented
25	#10597382	C₂²	1	4	yes	complemented
26	D₄×Dic₁₉	C₂²	1	2	yes	complemented
27	#10597376	C₂²	1	4	yes	complemented
28	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
29	#10597372	C₂²	1	4	yes	complemented
30	#10597341	C₂²	1	4	yes	complemented
31	#10597339	C₂²	1	2	yes	complemented
32	#10597338	C₂²	1	4	yes	complemented
33	#10597338	C₂²	1	4	yes	complemented
34	C₄⋊C₄×D₁₉	C₂²	1	4	yes	—
35	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
36	#10597334	C₂²	1	4	yes	complemented
37	#10597331	C₂²	1	8	yes	complemented
38	#10597331	C₂²	1	8	yes	complemented
39	#10597330	C₂²	1	8	yes	complemented
40	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
41	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	—
42	C₂²⋊C₄×D₁₉	C₂²	1	8	yes	—
43	#10597323	C₂²	1	8	yes	complemented
44	#10597321	C₂²	1	4	yes	complemented
45	C₄×D₇₆	C₂²	1	2	yes	complemented
46	#10597318	C₂²	1	8	yes	complemented
47	C₄²×D₁₉	C₂²	1	4	yes	—
48	C₄²×D₁₉	C₂²	1	1	yes	characteristic
49	#10597315	C₂²	1	1	yes	characteristic, complemented
50	C₂³×D₁₉	C₂³	1	4	yes	—
51	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
52	C₂×D₄×C₁₉	C₂³	1	2	yes	—
53	C₂×D₄×C₁₉	C₂³	1	4	yes	—
54	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
55	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
56	C₂×C₂²⋊D₁₉	C₂³	1	8	yes	—
57	C₂²×Dic₁₉	C₂³	1	4	yes	—
58	Q₈×D₁₉	—	4	4	no	—
59	D₄×D₁₉	—	2	8	no	—
60	D₄×D₁₉	—	4	8	no	—
61	C₂×D₇₆	C₂³	1	2	yes	—
62	C₂×D₇₆	C₂³	1	4	yes	—
63	C₂×C₄×D₁₉	—	2	16	no	—
64	C₂×C₄×D₁₉	C₂³	1	4	yes	—
65	C₂×C₄×D₁₉	C₂³	1	4	yes	—
66	C₂×C₄×D₁₉	C₂³	1	4	yes	—
67	C₂×C₄×D₁₉	C₂³	1	4	yes	—
68	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₄×D₁₉	C₂³	1	2	yes	—
70	C₂×Dic₃₈	C₂³	1	4	yes	—
71	C₂×Dic₃₈	C₂³	1	2	yes	—
72	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
74	C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
75	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
76	C₄²×C₁₉	C₂³	1	4	yes	—
77	C₄²×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
79	C₂²⋊Dic₁₉	C₂³	1	8	yes	—
80	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
81	(C₂×D₁₉)⋊C₄	C₂³	1	8	yes	—
82	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
83	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
84	C₄⋊Dic₁₉	C₂³	1	4	yes	—
85	C₄⋊Dic₁₉	C₂³	1	2	yes	—
86	Dic₁₉⋊C₄	C₂³	1	8	yes	—
87	Dic₁₉⋊C₄	C₂³	1	4	yes	—
88	C₄×Dic₁₉	C₂³	1	2	yes	—
89	C₄×Dic₁₉	C₂³	1	4	yes	—
90	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
91	C₄×Dic₁₉	C₂³	1	8	yes	—
92	C₂³×C₁₉	C₂⁴	1	4	yes	—
93	C₂²×D₁₉	—	2	8	no	—
94	C₂²×D₁₉	—	2	8	no	—
95	C₂²×D₁₉	—	2	8	no	—
96	C₂²×D₁₉	C₂⁴	1	4	yes	—
97	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
98	Q₈×C₁₉	—	4	2	no	—
99	D₄×C₁₉	—	2	4	no	—
100	D₄×C₁₉	—	4	4	no	—
101	C₂×C₄×C₁₉	—	2	8	no	—
102	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
103	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
104	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
105	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
106	C₂²⋊D₁₉	—	2	8	no	—
107	C₂²⋊D₁₉	—	4	8	no	—
108	C₂×Dic₁₉	—	2	8	no	—
109	C₂×Dic₁₉	C₂⁴	1	4	yes	—
110	C₂×Dic₁₉	C₂⁴	1	4	yes	—
111	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
112	C₂×Dic₁₉	C₂⁴	1	2	yes	—
113	D₇₆	—	2	4	no	—
114	D₇₆	—	4	4	no	—
115	C₄×D₁₉	—	2	8	no	—
116	C₄×D₁₉	—	2	8	no	—
117	C₄×D₁₉	—	2	2	no	—
118	C₄×D₁₉	—	2	8	no	—
119	C₄×D₁₉	—	2	8	no	—
120	C₄×D₁₉	#41	1	8	yes	—
121	Dic₃₈	—	4	4	no	—
122	Dic₃₈	—	4	2	no	—
123	C₂×#555	—	19	1	no	maximal, Sylow
124	C₂²×C₁₉	—	2	4	no	—
125	C₂²×C₁₉	—	2	4	no	—
126	C₂²×C₁₉	—	2	4	no	—
127	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
128	C₂×D₁₉	—	2	4	no	—
129	C₂×D₁₉	—	2	4	no	—
130	C₂×D₁₉	—	2	4	no	—
131	C₂×D₁₉	—	4	16	no	—
132	C₂×D₁₉	C₂×#41	1	4	yes	—
133	C₂×D₁₉	H(5,𝔽₂)	1	2	yes	—
134	C₄×C₁₉	—	2	4	no	—
135	C₄×C₁₉	—	2	1	no	—
136	C₄×C₁₉	—	2	4	no	—
137	C₄×C₁₉	C₂×#41	1	4	yes	—
138	Dic₁₉	—	2	4	no	—
139	Dic₁₉	—	2	1	no	—
140	Dic₁₉	—	2	4	no	—
141	Dic₁₉	C₂×#41	1	4	yes	—
142	#555	—	19	1	no	—
143	#555	—	19	4	no	—
144	#555	—	19	4	no	—
145	#555	—	19	2	no	—
146	#555	—	19	4	no	—
147	#555	D₁₉	1	1	yes	characteristic, direct product factor
148	C₂×C₄⋊Q₈	—	19	1	no	—
149	C₂×#124	—	19	4	no	—
150	C₂×#121	—	19	4	no	—
151	C₂×C₄×D₄	—	19	2	no	—
152	C₂×#117	—	19	4	no	—
153	C₂×C₁₉	—	4	4	no	—
154	C₂×C₁₉	C₂²×#41	1	2	yes	—
155	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
156	D₁₉	—	4	4	no	—
157	D₁₉	#555	1	4	yes	direct product factor
158	C₂²×Q₈	—	19	2	no	—
159	C₂²×D₄	—	19	2	no	—
160	C₂²×D₄	—	19	4	no	—
161	C₂³×C₄	—	19	4	no	—
162	C₄⋊Q₈	—	19	2	no	—
163	C₄⋊Q₈	—	19	4	no	—
164	C₄⋊Q₈	—	19	1	no	—
165	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
166	#124	—	19	4	no	—
167	#124	—	19	4	no	—
168	#124	—	19	8	no	—
169	#124	—	19	8	no	—
170	#124	—	19	4	no	—
171	#124	C₂×D₁₉	1	4	yes	complemented
172	#121	—	19	4	no	—
173	#121	—	19	8	no	—
174	#121	—	19	4	no	—
175	#121	—	19	4	no	—
176	#121	—	19	8	no	—
177	#121	C₂×D₁₉	1	4	yes	complemented
178	C₄×D₄	—	19	2	no	—
179	C₄×D₄	—	19	4	no	—
180	C₄×D₄	—	19	2	no	—
181	C₄×D₄	—	19	4	no	—
182	C₄×D₄	—	19	2	no	—
183	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
184	#117	—	19	4	no	—
185	#117	—	19	4	no	—
186	#117	—	19	4	no	—
187	#117	—	19	8	no	—
188	#117	—	19	8	no	—
189	#117	C₂×D₁₉	1	4	yes	complemented
190	C₂×C₄⋊C₄	—	19	2	no	—
191	C₂×C₄⋊C₄	—	19	4	no	—
192	C₂×C₂²⋊C₄	—	19	8	no	—
193	C₂×C₂²⋊C₄	—	19	4	no	—
194	C₂×C₄²	—	19	4	no	—
195	C₂×C₄²	—	19	1	no	—
196	C₁₉	C₂×#555	1	1	yes	characteristic, complemented, Sylow
197	C₂⁴	—	19	4	no	—
198	C₂×Q₈	—	19	4	no	—
199	C₂×Q₈	—	19	2	no	—
200	C₂×Q₈	—	76	4	no	—
201	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
202	C₂×D₄	—	19	4	no	—
203	C₂×D₄	—	19	8	no	—
204	C₂×D₄	—	19	2	no	—
205	C₂×D₄	—	19	4	no	—
206	C₂×D₄	—	38	8	no	—
207	C₂×D₄	—	76	8	no	—
208	C₂×D₄	C₂²×D₁₉	1	2	yes	—
209	C₂×D₄	C₂²×D₁₉	1	4	yes	—
210	C₂²×C₄	—	19	2	no	—
211	C₂²×C₄	—	19	4	no	—
212	C₂²×C₄	—	19	4	no	—
213	C₂²×C₄	—	19	1	no	—
214	C₂²×C₄	—	19	4	no	—
215	C₂²×C₄	—	19	4	no	—
216	C₂²×C₄	—	19	4	no	—
217	C₂²×C₄	—	38	16	no	—
218	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
219	C₄⋊C₄	—	19	4	no	—
220	C₄⋊C₄	—	19	8	no	—
221	C₄⋊C₄	—	19	2	no	—
222	C₄⋊C₄	—	19	4	no	—
223	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
224	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
225	C₂²⋊C₄	—	19	8	no	—
226	C₂²⋊C₄	—	19	4	no	—
227	C₂²⋊C₄	—	19	8	no	—
228	C₂²⋊C₄	—	19	8	no	—
229	C₂²⋊C₄	—	19	4	no	—
230	C₂²⋊C₄	—	19	4	no	—
231	C₂²⋊C₄	C₂²×D₁₉	1	8	yes	—
232	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
233	C₄²	—	19	4	no	—
234	C₄²	—	19	8	no	—
235	C₄²	—	19	1	no	—
236	C₄²	—	19	2	no	—
237	C₄²	C₂²×D₁₉	1	4	yes	—
238	C₄²	C₂²×D₁₉	1	1	yes	characteristic
239	C₂³	—	19	1	no	—
240	C₂³	—	19	4	no	—
241	C₂³	—	38	8	no	—
242	C₂³	—	38	8	no	—
243	C₂³	—	38	8	no	—
244	C₂³	C₂³×D₁₉	1	4	yes	—
245	Q₈	—	4	2	no	—
246	Q₈	—	76	4	no	—
247	Q₈	—	76	2	no	—
248	D₄	—	2	4	no	—
249	D₄	—	4	4	no	—
250	D₄	—	38	8	no	—
251	D₄	—	38	4	no	—
252	D₄	—	76	4	no	—
253	D₄	—	76	8	no	—
254	C₂×C₄	—	2	8	no	—
255	C₂×C₄	—	19	2	no	—
256	C₂×C₄	—	19	8	no	—
257	C₂×C₄	—	19	4	no	—
258	C₂×C₄	—	19	1	no	—
259	C₂×C₄	—	19	4	no	—
260	C₂×C₄	—	38	8	no	—
261	C₂×C₄	—	38	8	no	—
262	C₂×C₄	—	38	8	no	—
263	C₂×C₄	—	38	2	no	—
264	C₂×C₄	—	38	8	no	—
265	C₂×C₄	—	38	8	no	—
266	C₂×C₄	C₂³×D₁₉	1	4	yes	—
267	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
268	C₂×C₄	C₂³×D₁₉	1	4	yes	—
269	C₂×C₄	C₂³×D₁₉	1	2	yes	—
270	C₂²	—	2	4	no	—
271	C₂²	—	2	4	no	—
272	C₂²	—	2	4	no	—
273	C₂²	—	19	4	no	—
274	C₂²	—	19	2	no	—
275	C₂²	—	38	4	no	—
276	C₂²	—	38	4	no	—
277	C₂²	—	38	4	no	—
278	C₂²	—	76	16	no	—
279	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
280	C₄	—	2	4	no	—
281	C₄	—	2	4	no	—
282	C₄	—	2	1	no	—
283	C₄	—	19	4	no	—
284	C₄	—	38	4	no	—
285	C₄	—	38	4	no	—
286	C₄	—	38	1	no	—
287	C₄	#41×D₁₉	1	4	yes	—
288	C₂	—	4	4	no	—
289	C₂	—	19	4	no	—
290	C₂	—	76	4	no	—
291	C₂	C₂×#41×D₁₉	1	2	yes	—
292	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#555	C₂
hypercenter	#555	D₁₉
hypocenter	C₁₉	C₂×#555
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #555

Complements

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

N	H ≅ G/N	type
1. #11927260	C₂	semidirect
2. #11927259	C₂	semidirect
3. #11927258	C₂	semidirect
4. #11927257	C₂	semidirect
5. #11927256	C₂	semidirect
6. C₄⋊Q₈×D₁₉	C₂	semidirect
7. #124×D₁₉	C₂	semidirect
8. #121×D₁₉	C₂	semidirect
9. C₄×D₄×D₁₉	C₂	semidirect
10. #117×D₁₉	C₂	semidirect
11. C₁₉×#555	C₂	semidirect
16. C₁₉×C₄⋊Q₈	C₂²	semidirect
17. C₁₉×#124	C₂²	semidirect
18. C₁₉×#121	C₂²	semidirect
19. C₄×D₄×C₁₉	C₂²	semidirect
20. C₁₉×#117	C₂²	semidirect
21. #10597393	C₂²	semidirect
22. #10597390	C₂²	semidirect
23. #10597385	C₂²	semidirect
24. #10597384	C₂²	semidirect
25. #10597382	C₂²	semidirect
26. D₄×Dic₁₉	C₂²	semidirect
27. #10597376	C₂²	semidirect
28. C₄×C₂²⋊D₁₉	C₂²	semidirect
29. #10597372	C₂²	semidirect
30. #10597341	C₂²	semidirect
31. #10597339	C₂²	semidirect
32. #10597338	C₂²	semidirect
33. #10597338	C₂²	semidirect
36. #10597334	C₂²	semidirect
37. #10597331	C₂²	semidirect
38. #10597331	C₂²	semidirect
39. #10597330	C₂²	semidirect
40. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
43. #10597323	C₂²	semidirect
44. #10597321	C₂²	semidirect
45. C₄×D₇₆	C₂²	semidirect
46. #10597318	C₂²	semidirect
49. #10597315	C₂²	semidirect
147. #555	D₁₉	direct (N × H)
157. D₁₉	#555	direct (N × H)
165. C₄⋊Q₈	C₂×D₁₉	semidirect
171. #124	C₂×D₁₉	semidirect
177. #121	C₂×D₁₉	semidirect
183. C₄×D₄	C₂×D₁₉	semidirect
189. #117	C₂×D₁₉	semidirect
196. C₁₉	C₂×#555	semidirect

Maximal subgroups

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

subgroup	index
#11927260	2
#11927259	2
#11927258	2
#11927257	2
#11927256	2
C₄⋊Q₈×D₁₉	2
#124×D₁₉	2
#121×D₁₉	2
C₄×D₄×D₁₉	2
#117×D₁₉	2
C₁₉×#555	2
C₂×#555	19

Subgroups — D19×#555 #14577171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉×#555 #14577171