Subgroups — #18076451

Order 4864.

552 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926609	C₂	1	1	yes	maximal, characteristic
2	#14564354	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#10597266	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926296	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926273	C₂	1	1	yes	maximal, characteristic
6	C₁₉⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₁₉	—	2	1	no	—
9	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
10	#11926609	—	2	2	no	—
11	#11926609	—	2	2	no	—
12	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#10597266	C₄	1	1	yes	characteristic
15	C₂×#10597266	C₄	1	1	yes	characteristic
16	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
17	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	#11926306	C₄	1	1	yes	characteristic
20	#11926306	C₄	1	1	yes	characteristic
21	#11926299	—	2	1	no	—
22	#11926296	—	2	2	no	—
23	#11926273	—	2	2	no	—
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₉	—	2	1	no	—
29	C₂²×C₈×C₁₉	—	2	1	no	—
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	—	2	1	no	—
34	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
36	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₁₉⋊C₈	—	2	1	no	—
38	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
41	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
42	C₂×C₈×D₁₉	—	2	4	no	—
43	C₂×C₈×D₁₉	—	4	2	no	—
44	C₂×C₈×D₁₉	—	4	2	no	—
45	C₄×D₇₆	—	2	1	no	—
46	C₄×D₇₆	—	2	1	no	—
47	C₄×D₇₆	D₄	1	2	yes	—
48	C₄×D₇₆	Q₈	1	2	yes	—
49	C₁₉×C₄⋊C₈	—	2	1	no	—
50	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
51	C₄×C₈×C₁₉	—	2	1	no	—
52	C₄×C₈×C₁₉	—	2	1	no	—
53	C₁₉×#95	—	2	1	no	—
54	(C₂×D₁₉)⋊C₈	—	2	4	no	—
55	#10597266	—	2	2	no	—
56	#10597266	C₈	1	4	yes	complemented
57	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
59	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
60	C₄×C₁₉⋊C₈	—	2	1	no	—
61	C₄×C₁₉⋊C₈	—	2	1	no	—
62	C₄×C₁₉⋊C₈	—	2	1	no	—
63	C₄×C₁₉⋊C₈	—	2	1	no	—
64	C₂³×D₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
70	C₂²×Dic₁₉	—	2	1	no	—
71	C₂×D₇₆	—	2	1	no	—
72	C₂×D₇₆	—	2	1	no	—
73	C₂×D₇₆	—	2	1	no	—
74	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
75	C₂×D₇₆	C₂×C₈	1	2	yes	—
76	C₂×D₇₆	M₁₆	1	2	yes	—
77	C₂×C₄×D₁₉	—	2	2	no	—
78	C₂×C₄×D₁₉	—	2	2	no	—
79	C₂×C₄×D₁₉	—	4	1	no	—
80	C₂×C₄×D₁₉	—	4	1	no	—
81	C₂×C₄×D₁₉	—	4	1	no	—
82	C₂×C₄×D₁₉	—	4	1	no	—
83	C₂×C₈×C₁₉	—	2	2	no	—
84	C₂×C₈×C₁₉	—	2	2	no	—
85	C₂×C₈×C₁₉	—	4	1	no	—
86	C₂×C₈×C₁₉	—	4	1	no	—
87	C₂×C₈×C₁₉	—	4	1	no	—
88	C₂×C₈×C₁₉	—	4	1	no	—
89	C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₄⋊C₄×C₁₉	C₂×C₈	1	2	yes	complemented
93	C₄²×C₁₉	—	4	1	no	—
94	C₄²×C₁₉	—	4	1	no	—
95	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
98	C₄²×C₁₉	#41	1	1	yes	characteristic
99	(C₂×D₁₉)⋊C₄	—	2	2	no	—
100	(C₂×D₁₉)⋊C₄	—	2	2	no	—
101	C₄⋊Dic₁₉	—	2	1	no	—
102	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
103	C₂×C₁₉⋊C₈	—	2	1	no	—
104	C₂×C₁₉⋊C₈	—	2	1	no	—
105	C₂×C₁₉⋊C₈	—	2	1	no	—
106	C₂×C₁₉⋊C₈	—	2	1	no	—
107	C₂×C₁₉⋊C₈	—	2	1	no	—
108	C₂×C₁₉⋊C₈	—	2	1	no	—
109	C₂×C₁₉⋊C₈	—	2	1	no	—
110	C₂×C₁₉⋊C₈	—	2	1	no	—
111	C₂×C₁₉⋊C₈	—	2	1	no	—
112	C₂×C₁₉⋊C₈	—	2	1	no	—
113	C₂×C₁₉⋊C₈	—	4	1	no	—
114	C₂×C₁₉⋊C₈	—	4	1	no	—
115	C₂×C₁₉⋊C₈	—	4	1	no	—
116	C₂×C₁₉⋊C₈	C₂×C₈	1	2	yes	complemented
117	C₂×C₁₉⋊C₈	D₈	1	2	yes	—
118	C₈×D₁₉	—	4	8	no	—
119	#8843	—	19	1	no	maximal, Sylow
120	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
121	C₂²×D₁₉	—	2	2	no	—
122	C₂²×D₁₉	—	2	2	no	—
123	C₂²×D₁₉	—	2	2	no	—
124	C₂²×D₁₉	—	4	1	no	—
125	C₂²×D₁₉	—	4	1	no	—
126	C₂²×D₁₉	—	4	1	no	—
127	C₂²×D₁₉	—	4	1	no	—
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	4	1	no	—
132	C₂×C₄×C₁₉	—	4	1	no	—
133	C₂×C₄×C₁₉	—	4	1	no	—
134	C₂×C₄×C₁₉	—	4	1	no	—
135	C₂×C₄×C₁₉	—	4	1	no	—
136	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
138	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
139	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
140	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
148	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
150	C₂×Dic₁₉	—	2	2	no	—
151	C₂×Dic₁₉	—	4	1	no	—
152	C₂×Dic₁₉	—	4	1	no	—
153	D₇₆	—	2	2	no	—
154	D₇₆	—	2	2	no	—
155	D₇₆	—	2	2	no	—
156	D₇₆	C₄⋊C₈	1	4	yes	complemented
157	C₄×D₁₉	—	4	2	no	—
158	C₄×D₁₉	—	4	2	no	—
159	C₄×D₁₉	—	4	2	no	—
160	C₄×D₁₉	—	4	2	no	—
161	C₈×C₁₉	—	4	2	no	—
162	C₈×C₁₉	—	4	2	no	—
163	C₁₉⋊C₈	—	2	2	no	—
164	C₁₉⋊C₈	—	2	2	no	—
165	C₁₉⋊C₈	—	4	1	no	—
166	C₁₉⋊C₈	—	4	1	no	—
167	C₁₉⋊C₈	—	8	1	no	—
168	C₂×C₈×D₄	—	19	1	no	—
169	#1939	—	19	1	no	—
170	C₄×#102	—	19	1	no	—
171	C₂×#335	—	19	1	no	—
172	C₂×D₄⋊C₈	—	19	1	no	—
173	#1279	D₁₉	1	1	yes	characteristic, complemented
174	#1273	—	19	1	no	—
175	C₂²×C₁₉	#385	1	1	yes	characteristic
176	C₂²×C₁₉	C₈×D₄	1	1	yes	characteristic
177	C₂²×C₁₉	#435	1	1	yes	characteristic
178	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
179	C₂²×C₁₉	#440	1	1	yes	characteristic
180	C₂²×C₁₉	#443	1	1	yes	characteristic
181	C₂²×C₁₉	#444	1	1	yes	characteristic
182	C₂×D₁₉	—	2	4	no	—
183	C₂×D₁₉	—	4	2	no	—
184	C₂×D₁₉	—	4	2	no	—
185	C₂×D₁₉	—	4	2	no	—
186	C₂×D₁₉	—	4	2	no	—
187	C₂×D₁₉	—	4	2	no	—
188	C₂×D₁₉	—	4	2	no	—
189	C₄×C₁₉	—	2	1	no	—
190	C₄×C₁₉	—	2	1	no	—
191	C₄×C₁₉	—	4	2	no	—
192	C₄×C₁₉	—	8	1	no	—
193	C₄×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
194	C₄×C₁₉	#424	1	1	yes	characteristic
195	C₄×C₁₉	C₈×D₄	1	1	yes	characteristic
196	C₄×C₁₉	#435	1	1	yes	characteristic
197	C₄×C₁₉	#447	1	1	yes	characteristic
198	C₄×C₁₉	#452	1	1	yes	characteristic
199	C₄×C₁₉	#474	1	1	yes	characteristic
200	C₄×C₁₉	#478	1	1	yes	characteristic
201	Dic₁₉	—	4	2	no	—
202	C₂³×C₈	—	38	1	no	—
203	C₂×C₄×D₄	—	19	1	no	—
204	C₈×D₄	—	38	2	no	—
205	C₈×D₄	—	38	2	no	—
206	C₂×C₄⋊C₈	—	19	1	no	—
207	C₂×C₄⋊C₈	—	38	1	no	—
208	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
209	C₂×#102	—	19	1	no	—
210	C₂×#102	—	19	1	no	—
211	C₂×C₂²⋊C₈	—	38	1	no	—
212	C₂×C₄×C₈	—	19	1	no	—
213	C₂×C₄×C₈	—	19	1	no	—
214	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
215	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
216	#340	—	19	1	no	—
217	#340	—	19	1	no	—
218	#336	—	38	1	no	—
219	#335	—	38	2	no	—
220	D₄⋊C₈	—	38	2	no	—
221	C₂×C₁₉	C₈×D₈	1	1	yes	characteristic
222	C₂×C₁₉	SD₁₆⋊C₈	1	1	yes	characteristic
223	C₂×C₁₉	#1581	1	1	yes	characteristic
224	C₂×C₁₉	#1585	1	1	yes	characteristic
225	C₂×C₁₉	#1850	1	1	yes	characteristic
226	C₂×C₁₉	#1862	1	1	yes	characteristic
227	C₂×C₁₉	#1866	1	1	yes	characteristic
228	D₁₉	—	4	4	no	—
229	C₂²×D₄	—	19	1	no	—
230	C₂³×C₄	—	38	1	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	19	1	no	—
234	C₂²×C₈	—	19	1	no	—
235	C₂²×C₈	—	19	1	no	—
236	C₂²×C₈	—	19	1	no	—
237	C₂²×C₈	—	38	4	no	—
238	C₂²×C₈	—	38	1	no	—
239	C₂²×C₈	—	76	2	no	—
240	C₂²×C₈	—	76	2	no	—
241	C₄×D₄	—	19	2	no	—
242	C₄×D₄	—	19	2	no	—
243	C₄×D₄	—	38	1	no	—
244	C₄×D₄	—	38	1	no	—
245	C₂×C₄⋊C₄	—	19	1	no	—
246	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	—	38	1	no	—
249	C₂×C₄²	—	2	1	no	—
250	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	—	38	1	no	—
253	C₄⋊C₈	—	38	1	no	—
254	C₄⋊C₈	—	76	2	no	—
255	C₄⋊C₈	D₇₆	1	2	yes	—
256	#102	—	19	4	no	—
257	#102	—	38	2	no	—
258	C₂²⋊C₈	—	38	4	no	—
259	C₄×C₈	—	2	1	no	—
260	C₄×C₈	—	2	1	no	—
261	C₄×C₈	—	38	1	no	—
262	C₄×C₈	—	38	1	no	—
263	C₄×C₈	—	38	1	no	—
264	C₄×C₈	—	38	1	no	—
265	#95	—	2	1	no	—
266	C₁₉	#8843	1	1	yes	characteristic, complemented, Sylow
267	C₂⁴	—	38	1	no	—
268	C₂×D₄	—	19	2	no	—
269	C₂×D₄	—	19	2	no	—
270	C₂×D₄	—	19	2	no	—
271	C₂×D₄	—	38	1	no	—
272	C₂×D₄	—	38	1	no	—
273	C₂×D₄	—	38	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	38	1	no	—
277	C₂²×C₄	—	38	2	no	—
278	C₂²×C₄	—	38	2	no	—
279	C₂²×C₄	—	76	1	no	—
280	C₂²×C₄	—	76	1	no	—
281	C₂²×C₄	—	76	1	no	—
282	C₂²×C₄	—	76	1	no	—
283	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
284	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
285	C₂²×C₄	#64543	1	1	yes	characteristic
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	4	1	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	19	2	no	—
293	C₂×C₈	—	19	2	no	—
294	C₂×C₈	—	38	1	no	—
295	C₂×C₈	—	38	1	no	—
296	C₂×C₈	—	38	1	no	—
297	C₂×C₈	—	38	1	no	—
298	C₂×C₈	—	38	1	no	—
299	C₂×C₈	—	38	1	no	—
300	C₂×C₈	—	38	1	no	—
301	C₂×C₈	—	38	1	no	—
302	C₂×C₈	—	38	1	no	—
303	C₂×C₈	—	38	1	no	—
304	C₂×C₈	—	76	8	no	—
305	C₂×C₈	—	76	1	no	—
306	C₂×C₈	—	76	1	no	—
307	C₂×C₈	—	76	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	19	2	no	—
312	C₄⋊C₄	—	38	1	no	—
313	C₄⋊C₄	C₈×D₁₉	1	2	yes	complemented
314	C₂²⋊C₄	—	38	2	no	—
315	C₂²⋊C₄	—	38	2	no	—
316	C₄²	—	4	1	no	—
317	C₄²	—	4	1	no	—
318	C₄²	C₂×D₇₆	1	1	yes	characteristic
319	C₄²	#64541	1	1	yes	characteristic
320	C₄²	D₄×D₁₉	1	1	yes	characteristic
321	C₄²	Q₈×D₁₉	1	1	yes	characteristic
322	C₂³	—	38	2	no	—
323	C₂³	—	38	2	no	—
324	C₂³	—	38	2	no	—
325	C₂³	—	76	1	no	—
326	C₂³	—	76	1	no	—
327	C₂³	—	76	1	no	—
328	C₂³	—	76	1	no	—
329	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
330	D₄	—	19	4	no	—
331	D₄	—	38	2	no	—
332	D₄	—	38	2	no	—
333	D₄	—	38	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	38	2	no	—
343	C₂×C₄	—	76	1	no	—
344	C₂×C₄	—	76	1	no	—
345	C₂×C₄	—	76	2	no	—
346	C₂×C₄	—	76	2	no	—
347	C₂×C₄	—	76	2	no	—
348	C₂×C₄	—	76	2	no	—
349	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
350	C₂×C₄	#10597328	1	1	yes	characteristic
351	C₂×C₄	#10597329	1	1	yes	characteristic
352	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
353	C₂×C₄	#10597342	1	1	yes	characteristic
354	C₂×C₄	#10597343	1	1	yes	characteristic
355	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
356	C₂×C₄	#10597347	1	1	yes	characteristic
357	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
358	C₂×C₄	#10597353	1	1	yes	characteristic
359	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
360	C₂×C₄	#10597360	1	1	yes	characteristic
361	C₂×C₄	#10597362	1	1	yes	characteristic
362	C₂×C₄	#10597364	1	1	yes	characteristic
363	C₈	—	4	2	no	—
364	C₈	—	4	2	no	—
365	C₈	—	38	2	no	—
366	C₈	—	38	2	no	—
367	C₈	—	76	1	no	—
368	C₈	—	76	1	no	—
369	C₈	—	152	1	no	—
370	C₂²	—	38	4	no	—
371	C₂²	—	76	2	no	—
372	C₂²	—	76	2	no	—
373	C₂²	—	76	2	no	—
374	C₂²	—	76	2	no	—
375	C₂²	—	76	2	no	—
376	C₂²	—	76	2	no	—
377	C₂²	#11926418	1	1	yes	characteristic
378	C₂²	(C₂²⋊D₁₉)⋊C₈	1	1	yes	characteristic
379	C₂²	#11926618	1	1	yes	characteristic
380	C₂²	#11926624	1	1	yes	characteristic
381	C₂²	#11926647	1	1	yes	characteristic
382	C₂²	#11926658	1	1	yes	characteristic
383	C₂²	#11926663	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	8	1	no	—
388	C₄	—	76	2	no	—
389	C₄	C₄⋊C₈×D₁₉	1	1	yes	characteristic
390	C₄	#11926569	1	1	yes	characteristic
391	C₄	C₈×D₇₆	1	1	yes	characteristic
392	C₄	#11926617	1	1	yes	characteristic
393	C₄	#11926679	1	1	yes	characteristic
394	C₄	#11926709	1	1	yes	characteristic
395	C₄	#11926823	1	1	yes	characteristic
396	C₄	#11926843	1	1	yes	characteristic
397	C₂	—	76	4	no	—
398	C₂	#14562427	1	1	yes	characteristic
399	C₂	#14562450	1	1	yes	characteristic
400	C₂	#14562467	1	1	yes	characteristic
401	C₂	#14562495	1	1	yes	characteristic
402	C₂	#14563814	1	1	yes	characteristic
403	C₂	#14563883	1	1	yes	characteristic
404	C₂	#14563911	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1279	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂²×D₇₆	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1279	D₁₉
hypocenter	C₁₉	#8843
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
2. #14564354	C₂	semidirect
4. C₂×#11926296	C₂	semidirect
6. C₁₉⋊#1273	C₂	semidirect
7. C₁₉×#1279	C₂	semidirect
56. #10597266	C₈	semidirect
92. C₄⋊C₄×C₁₉	C₂×C₈	semidirect
116. C₂×C₁₉⋊C₈	C₂×C₈	semidirect
156. D₇₆	C₄⋊C₈	semidirect
173. #1279	D₁₉	semidirect
266. C₁₉	#8843	semidirect
313. C₄⋊C₄	C₈×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926609	2
#14564354	2
C₄×#10597266	2
C₂×#11926296	2
C₂×#11926273	2
C₁₉⋊#1273	2
C₁₉×#1279	2
#8843	19