Subgroups — #18086367

Order 4864.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926750	C₂	1	1	yes	maximal, characteristic
2	#14564595	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564428	C₂	1	1	yes	maximal, characteristic
4	#14563632	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926294	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926289	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64516	—	2	1	no	—
9	C₂×#10597315	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
11	#11926750	—	2	2	no	—
12	#11926750	—	2	2	no	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#10597273	—	2	1	no	—
15	C₂×#10597266	—	2	1	no	—
16	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
17	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
18	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	#11926306	—	2	1	no	—
20	#11926306	—	2	1	no	—
21	#11926306	—	2	1	no	—
22	#11926294	—	2	2	no	—
23	#11926289	—	2	2	no	—
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₁₉×#384	C₂²	1	1	yes	characteristic
27	C₂²×D₇₆	D₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₉	—	2	1	no	—
29	C₂²×Dic₃₈	—	2	1	no	—
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
37	C₂×C₄⋊Dic₁₉	—	2	1	no	—
38	C₂×C₄⋊Dic₁₉	—	2	1	no	—
39	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
40	C₂²×C₁₉⋊C₈	—	2	1	no	—
41	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
42	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
43	C₂×#64516	—	2	4	no	—
44	C₂×#64516	—	4	2	no	—
45	C₂×#64516	—	4	2	no	—
46	C₄×D₇₆	—	2	1	no	—
47	C₄×D₇₆	—	2	1	no	—
48	C₄×D₇₆	—	2	1	no	—
49	C₄×D₇₆	—	2	1	no	—
50	#10597315	—	2	1	no	—
51	#10597315	—	2	1	no	—
52	#10597315	—	2	1	no	—
53	#10597315	D₄	1	2	yes	—
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₄⋊C₈	—	2	1	no	—
57	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
58	(C₂×D₁₉)⋊C₈	—	4	2	no	—
59	(C₂×D₁₉)⋊C₈	—	4	2	no	—
60	#10597273	—	2	4	no	—
61	#10597266	—	4	2	no	—
62	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
63	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
64	C₄×C₁₉⋊C₈	—	2	1	no	—
65	C₄×C₁₉⋊C₈	—	2	1	no	—
66	C₂³×D₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	4	1	no	—
68	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
71	C₂²×Dic₁₉	—	2	1	no	—
72	C₂²×Dic₁₉	—	4	1	no	—
73	C₂×D₇₆	—	2	1	no	—
74	C₂×D₇₆	—	2	1	no	—
75	C₂×D₇₆	—	2	1	no	—
76	C₂×D₇₆	—	2	1	no	—
77	C₂×D₇₆	—	2	1	no	—
78	C₂×D₇₆	SD₁₆	1	2	yes	—
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×C₄×D₁₉	—	4	1	no	—
84	C₂×C₄×D₁₉	—	4	1	no	—
85	C₂×Dic₃₈	—	2	2	no	—
86	C₂×Dic₃₈	—	4	1	no	—
87	C₂×Dic₃₈	—	4	1	no	—
88	C₂×Dic₃₈	—	4	1	no	—
89	C₂×Dic₃₈	—	4	1	no	—
90	C₂×Dic₃₈	—	4	1	no	—
91	C₂×C₈×C₁₉	—	2	2	no	—
92	C₂×C₈×C₁₉	—	4	1	no	—
93	C₂×C₈×C₁₉	—	4	1	no	—
94	C₂×C₈×C₁₉	—	4	1	no	—
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₄⋊C₄×C₁₉	—	4	1	no	—
98	C₄⋊C₄×C₁₉	—	4	1	no	—
99	C₄⋊C₄×C₁₉	—	4	1	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	8	1	no	—
102	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₁₉	#41	1	1	yes	characteristic
105	C₄²×C₁₉	#41	1	1	yes	characteristic
106	(C₂×D₁₉)⋊C₄	—	4	1	no	—
107	(C₂×D₁₉)⋊C₄	—	4	1	no	—
108	C₄⋊Dic₁₉	—	2	1	no	—
109	C₄⋊Dic₁₉	—	2	2	no	—
110	C₄⋊Dic₁₉	—	2	2	no	—
111	C₄⋊Dic₁₉	—	2	1	no	—
112	C₄⋊Dic₁₉	—	4	1	no	—
113	C₄⋊Dic₁₉	—	4	1	no	—
114	C₂×C₁₉⋊C₈	—	2	1	no	—
115	C₂×C₁₉⋊C₈	—	2	1	no	—
116	C₂×C₁₉⋊C₈	—	2	1	no	—
117	C₂×C₁₉⋊C₈	—	2	1	no	—
118	C₂×C₁₉⋊C₈	—	2	1	no	—
119	C₂×C₁₉⋊C₈	—	4	1	no	—
120	C₂×C₁₉⋊C₈	—	4	1	no	—
121	C₂×C₁₉⋊C₈	—	4	1	no	—
122	C₂×C₁₉⋊C₈	SD₁₆	1	2	yes	complemented
123	#64516	—	4	8	no	—
124	#10477	—	19	1	no	maximal, Sylow
125	C₂³×C₁₉	#121	1	1	yes	characteristic
126	C₂²×D₁₉	—	2	2	no	—
127	C₂²×D₁₉	—	4	1	no	—
128	C₂²×D₁₉	—	4	1	no	—
129	C₂²×D₁₉	—	4	1	no	—
130	C₂²×D₁₉	—	4	1	no	—
131	C₂²×D₁₉	—	4	1	no	—
132	C₂²×D₁₉	—	4	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	8	1	no	—
136	C₂×C₄×C₁₉	—	8	1	no	—
137	C₂×C₄×C₁₉	—	8	1	no	—
138	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
140	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#135	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	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
152	C₂×Dic₁₉	—	4	2	no	—
153	C₂×Dic₁₉	—	4	1	no	—
154	C₂×Dic₁₉	—	4	1	no	—
155	C₂×Dic₁₉	—	4	1	no	—
156	C₂×Dic₁₉	—	8	1	no	—
157	C₂×Dic₁₉	—	8	1	no	—
158	D₇₆	—	2	2	no	—
159	D₇₆	—	2	2	no	—
160	D₇₆	—	4	1	no	—
161	D₇₆	—	4	1	no	—
162	C₄×D₁₉	—	8	1	no	—
163	C₄×D₁₉	—	8	1	no	—
164	C₄×D₁₉	—	8	1	no	—
165	C₄×D₁₉	—	8	1	no	—
166	Dic₃₈	—	4	2	no	—
167	Dic₃₈	—	4	2	no	—
168	Dic₃₈	—	8	1	no	—
169	Dic₃₈	—	8	1	no	—
170	C₈×C₁₉	—	4	2	no	—
171	C₈×C₁₉	—	8	1	no	—
172	C₁₉⋊C₈	—	2	2	no	—
173	C₁₉⋊C₈	—	4	1	no	—
174	C₁₉⋊C₈	—	8	1	no	—
175	C₂×#461	—	19	1	no	—
176	#1990	—	19	1	no	—
177	#1954	—	19	1	no	—
178	#1802	—	19	1	no	—
179	C₂×#334	—	19	1	no	—
180	C₂×#332	—	19	1	no	—
181	#1296	D₁₉	1	1	yes	characteristic, complemented
182	C₂²×C₁₉	#394	1	1	yes	characteristic
183	C₂²×C₁₉	#461	1	1	yes	characteristic
184	C₂²×C₁₉	#463	1	1	yes	characteristic
185	C₂²×C₁₉	#465	1	1	yes	characteristic
186	C₂²×C₁₉	#469	1	1	yes	characteristic
187	C₂²×C₁₉	#471	1	1	yes	characteristic
188	C₂²×C₁₉	#473	1	1	yes	characteristic
189	C₂×D₁₉	—	4	2	no	—
190	C₂×D₁₉	—	4	2	no	—
191	C₂×D₁₉	—	4	2	no	—
192	C₂×D₁₉	—	8	1	no	—
193	C₂×D₁₉	—	8	1	no	—
194	C₂×D₁₉	—	8	1	no	—
195	C₂×D₁₉	—	8	1	no	—
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	16	1	no	—
199	C₄×C₁₉	#449	1	1	yes	characteristic
200	C₄×C₁₉	#450	1	1	yes	characteristic
201	C₄×C₁₉	#460	1	1	yes	characteristic
202	C₄×C₁₉	#464	1	1	yes	characteristic
203	C₄×C₁₉	#465	1	1	yes	characteristic
204	C₄×C₁₉	#468	1	1	yes	characteristic
205	C₄×C₁₉	#481	1	1	yes	characteristic
206	C₄×C₁₉	#482	1	1	yes	characteristic
207	Dic₁₉	—	8	1	no	—
208	Dic₁₉	—	8	2	no	—
209	C₂²×SD₁₆	—	38	1	no	—
210	C₂×C₄⋊Q₈	—	19	1	no	—
211	C₂×C₄×D₄	—	19	1	no	—
212	#461	—	38	2	no	—
213	#461	—	38	2	no	—
214	C₂×C₄⋊C₈	—	19	1	no	—
215	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
217	C₂×#103	—	38	1	no	—
218	C₂×#102	—	38	1	no	—
219	C₂×C₂²⋊C₈	—	38	1	no	—
220	C₂×C₂²⋊C₈	—	38	1	no	—
221	C₂×C₄×C₈	—	19	1	no	—
222	#384	C₂×D₁₉	1	1	yes	characteristic
223	#340	—	38	1	no	—
224	#340	—	38	1	no	—
225	#340	—	38	1	no	—
226	#334	—	38	2	no	—
227	#332	—	38	2	no	—
228	C₂×C₁₉	#1671	1	1	yes	characteristic
229	C₂×C₁₉	#1679	1	1	yes	characteristic
230	C₂×C₁₉	#1693	1	1	yes	characteristic
231	C₂×C₁₉	#1701	1	1	yes	characteristic
232	C₂×C₁₉	#2034	1	1	yes	characteristic
233	C₂×C₁₉	#2052	1	1	yes	characteristic
234	C₂×C₁₉	#2055	1	1	yes	characteristic
235	D₁₉	—	8	2	no	—
236	C₂²×Q₈	—	38	1	no	—
237	C₂²×D₄	—	19	1	no	—
238	C₂³×C₄	—	38	1	no	—
239	C₂×SD₁₆	—	38	4	no	—
240	C₂×SD₁₆	—	76	2	no	—
241	C₂×SD₁₆	—	76	2	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	19	1	no	—
245	C₂²×C₈	—	19	1	no	—
246	C₂²×C₈	—	38	1	no	—
247	C₄⋊Q₈	—	19	2	no	—
248	C₄⋊Q₈	—	38	1	no	—
249	C₄⋊Q₈	—	38	1	no	—
250	C₄⋊Q₈	—	38	1	no	—
251	C₄×D₄	—	38	1	no	—
252	C₄×D₄	—	38	1	no	—
253	C₄×D₄	—	38	1	no	—
254	C₄×D₄	—	38	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	19	1	no	—
259	C₂×C₄⋊C₄	—	38	1	no	—
260	C₂×C₄⋊C₄	—	38	1	no	—
261	C₂×C₂²⋊C₄	—	38	1	no	—
262	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	38	1	no	—
267	C₄⋊C₈	—	38	1	no	—
268	C₄⋊C₈	D₇₆	1	2	yes	—
269	#103	—	38	4	no	—
270	#102	—	76	2	no	—
271	C₂²⋊C₈	—	76	2	no	—
272	C₂²⋊C₈	—	76	2	no	—
273	C₄×C₈	—	38	1	no	—
274	C₄×C₈	—	38	1	no	—
275	C₁₉	#10477	1	1	yes	characteristic, complemented, Sylow
276	C₂⁴	—	38	1	no	—
277	C₂×Q₈	—	38	2	no	—
278	C₂×Q₈	—	76	1	no	—
279	C₂×Q₈	—	76	1	no	—
280	C₂×Q₈	—	76	1	no	—
281	C₂×Q₈	—	76	1	no	—
282	C₂×Q₈	—	76	1	no	—
283	C₂×D₄	—	19	2	no	—
284	C₂×D₄	—	38	1	no	—
285	C₂×D₄	—	38	1	no	—
286	C₂×D₄	—	38	1	no	—
287	C₂×D₄	—	38	1	no	—
288	C₂×D₄	—	38	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	38	1	no	—
291	C₂²×C₄	—	76	1	no	—
292	C₂²×C₄	—	76	1	no	—
293	C₂²×C₄	—	76	1	no	—
294	C₂²×C₄	—	76	1	no	—
295	C₂²×C₄	—	76	1	no	—
296	C₂²×C₄	—	76	1	no	—
297	C₂²×C₄	—	76	1	no	—
298	C₂²×C₄	#64541	1	1	yes	characteristic
299	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
300	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
301	SD₁₆	—	76	8	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	19	2	no	—
309	C₂×C₈	—	38	1	no	—
310	C₂×C₈	—	38	1	no	—
311	C₂×C₈	—	38	1	no	—
312	C₂×C₈	—	38	1	no	—
313	C₂×C₈	—	38	1	no	—
314	C₂×C₈	—	76	1	no	—
315	C₂×C₈	—	76	1	no	—
316	C₂×C₈	—	76	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	8	1	no	—
322	C₄⋊C₄	—	38	1	no	—
323	C₄⋊C₄	—	38	2	no	—
324	C₄⋊C₄	—	38	1	no	—
325	C₄⋊C₄	—	38	2	no	—
326	C₄⋊C₄	—	76	1	no	—
327	C₄⋊C₄	—	76	1	no	—
328	C₂²⋊C₄	—	76	1	no	—
329	C₂²⋊C₄	—	76	1	no	—
330	C₄²	C₂×D₇₆	1	1	yes	characteristic
331	C₄²	#64541	1	1	yes	characteristic
332	C₄²	D₄×D₁₉	1	1	yes	characteristic
333	C₄²	#64545	1	1	yes	characteristic
334	C₂³	—	38	2	no	—
335	C₂³	—	76	1	no	—
336	C₂³	—	76	1	no	—
337	C₂³	—	76	1	no	—
338	C₂³	—	76	1	no	—
339	C₂³	—	76	1	no	—
340	C₂³	—	76	1	no	—
341	C₂³	#10597330	1	1	yes	characteristic
342	Q₈	—	76	2	no	—
343	Q₈	—	76	2	no	—
344	Q₈	—	152	1	no	—
345	Q₈	—	152	1	no	—
346	D₄	—	38	2	no	—
347	D₄	—	38	2	no	—
348	D₄	—	76	1	no	—
349	D₄	—	76	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	8	1	no	—
353	C₂×C₄	—	8	1	no	—
354	C₂×C₄	—	8	1	no	—
355	C₂×C₄	—	76	1	no	—
356	C₂×C₄	—	76	2	no	—
357	C₂×C₄	—	76	1	no	—
358	C₂×C₄	—	76	1	no	—
359	C₂×C₄	—	152	1	no	—
360	C₂×C₄	—	152	1	no	—
361	C₂×C₄	—	152	1	no	—
362	C₂×C₄	—	152	1	no	—
363	C₂×C₄	—	152	1	no	—
364	C₂×C₄	—	152	1	no	—
365	C₂×C₄	#10597321	1	1	yes	characteristic
366	C₂×C₄	#10597328	1	1	yes	characteristic
367	C₂×C₄	#10597330	1	1	yes	characteristic
368	C₂×C₄	#10597340	1	1	yes	characteristic
369	C₂×C₄	#10597340	1	1	yes	characteristic
370	C₂×C₄	#10597341	1	1	yes	characteristic
371	C₂×C₄	#10597357	1	1	yes	characteristic
372	C₂×C₄	#10597357	1	1	yes	characteristic
373	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
374	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
375	C₂×C₄	#10597360	1	1	yes	characteristic
376	C₂×C₄	#10597362	1	1	yes	characteristic
377	C₂×C₄	#10597364	1	1	yes	characteristic
378	C₂×C₄	#10597365	1	1	yes	characteristic
379	C₈	—	4	2	no	—
380	C₈	—	8	1	no	—
381	C₈	—	38	2	no	—
382	C₈	—	76	1	no	—
383	C₈	—	152	1	no	—
384	C₂²	—	76	2	no	—
385	C₂²	—	76	2	no	—
386	C₂²	—	76	2	no	—
387	C₂²	—	152	1	no	—
388	C₂²	—	152	1	no	—
389	C₂²	—	152	1	no	—
390	C₂²	—	152	1	no	—
391	C₂²	#11926462	1	1	yes	characteristic
392	C₂²	#11926748	1	1	yes	characteristic
393	C₂²	#11926758	1	1	yes	characteristic
394	C₂²	#11926776	1	1	yes	characteristic
395	C₂²	#11926796	1	1	yes	characteristic
396	C₂²	#11926806	1	1	yes	characteristic
397	C₂²	#11926818	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	16	1	no	—
401	C₄	—	152	1	no	—
402	C₄	—	152	2	no	—
403	C₄	#11926692	1	1	yes	characteristic
404	C₄	#11926696	1	1	yes	characteristic
405	C₄	#11926743	1	1	yes	characteristic
406	C₄	#11926769	1	1	yes	characteristic
407	C₄	#11926774	1	1	yes	characteristic
408	C₄	#11926791	1	1	yes	characteristic
409	C₄	#11926864	1	1	yes	characteristic
410	C₄	#11926871	1	1	yes	characteristic
411	C₂	—	152	2	no	—
412	C₂	#14563013	1	1	yes	characteristic
413	C₂	#14563057	1	1	yes	characteristic
414	C₂	#14563147	1	1	yes	characteristic
415	C₂	#14563195	1	1	yes	characteristic
416	C₂	#14564827	1	1	yes	characteristic
417	C₂	#14564937	1	1	yes	characteristic
418	C₂	#14564954	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597330
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1296	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×D₇₆	D₄
hypercenter	#1296	D₁₉
hypocenter	C₁₉	#10477
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
2. #14564595	C₂	semidirect
5. C₂×#11926294	C₂	semidirect
6. C₂×#11926289	C₂	semidirect
7. C₁₉×#1296	C₂	semidirect
122. C₂×C₁₉⋊C₈	SD₁₆	semidirect
181. #1296	D₁₉	semidirect
275. C₁₉	#10477	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926750	2
#14564595	2
#14564428	2
#14563632	2
C₂×#11926294	2
C₂×#11926289	2
C₁₉×#1296	2
#10477	19