Subgroups — #18070983

Order 4864.

630 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563329	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926299	C₂	1	1	yes	maximal, characteristic, complemented
3	#14561458	C₂	1	2	yes	maximal, complemented
4	#14561456	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2854	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	—	2	1	no	—
7	C₂³×C₁₉⋊C₈	—	2	1	no	—
8	#11926299	—	2	1	no	—
9	#11926299	—	2	1	no	—
10	#11926299	C₂²	1	2	yes	—
11	#11926299	C₂²	1	2	yes	—
12	C₂×C₁₉×#123	—	2	1	no	—
13	C₂×C₁₉×#121	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#390	C₄	1	1	yes	characteristic
16	C₁₉×#390	C₂²	1	1	yes	characteristic
17	C₁₉×#389	C₄	1	1	yes	characteristic
18	C₁₉×#389	C₂²	1	1	yes	characteristic
19	C₁₉×#388	—	2	1	no	—
20	C₁₉×#388	—	2	1	no	—
21	C₁₉×#386	—	2	1	no	—
22	C₁₉×#380	C₄	1	1	yes	characteristic
23	C₂²×D₄×C₁₉	—	2	1	no	—
24	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₁₉×#123	—	4	2	no	—
29	C₁₉×#123	—	4	2	no	—
30	C₁₉×#121	—	4	2	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	—	4	2	no	—
43	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
47	C₂×#64520	—	2	4	no	—
48	C₂×#64520	—	4	2	no	—
49	C₂×#64520	—	4	2	no	—
50	C₂²×C₁₉⋊C₈	—	2	4	no	—
51	C₂²×C₁₉⋊C₈	—	2	2	no	—
52	C₂²×C₁₉⋊C₈	—	2	2	no	—
53	C₂²×C₁₉⋊C₈	—	4	2	no	—
54	C₂²×C₁₉⋊C₈	—	4	2	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉×#95	—	2	1	no	—
57	C₁₉×#95	—	2	1	no	—
58	C₂⁴×C₁₉	—	2	1	no	—
59	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×D₄×C₁₉	—	2	2	no	—
61	C₂×D₄×C₁₉	—	4	1	no	—
62	C₂×D₄×C₁₉	—	4	1	no	—
63	C₂×D₄×C₁₉	—	4	2	no	—
64	C₂×D₄×C₁₉	—	4	2	no	—
65	C₂×D₄×C₁₉	—	4	2	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	D₈	1	2	yes	—
82	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
83	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₄⋊C₄×C₁₉	—	2	2	no	—
87	C₄⋊C₄×C₁₉	—	4	1	no	—
88	C₄⋊C₄×C₁₉	—	4	1	no	—
89	C₄⋊C₄×C₁₉	—	4	2	no	—
90	C₄⋊C₄×C₁₉	—	4	1	no	—
91	C₄⋊C₄×C₁₉	—	4	1	no	—
92	C₂²⋊C₄×C₁₉	—	4	2	no	—
93	C₂²⋊C₄×C₁₉	—	4	2	no	—
94	C₂²⋊C₄×C₁₉	—	4	2	no	—
95	C₂²⋊C₄×C₁₉	—	4	2	no	—
96	C₂²⋊C₄×C₁₉	—	4	1	no	—
97	C₂²⋊C₄×C₁₉	—	4	1	no	—
98	C₂²⋊C₄×C₁₉	—	4	1	no	—
99	C₂²⋊C₄×C₁₉	—	4	1	no	—
100	C₄²×C₁₉	—	4	1	no	—
101	C₄²×C₁₉	—	4	1	no	—
102	C₄²×C₁₉	—	4	1	no	—
103	C₄²×C₁₉	—	4	1	no	—
104	#64520	—	4	8	no	—
105	C₂×C₁₉⋊C₈	—	2	4	no	—
106	C₂×C₁₉⋊C₈	—	2	4	no	—
107	C₂×C₁₉⋊C₈	—	4	8	no	—
108	C₂×C₁₉⋊C₈	—	4	2	no	—
109	C₂×C₁₉⋊C₈	—	4	2	no	—
110	C₂×C₁₉⋊C₈	—	4	2	no	—
111	C₂×C₁₉⋊C₈	—	4	2	no	—
112	#7678	—	19	1	no	maximal, Sylow
113	C₂³×C₁₉	—	2	1	no	—
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	—	2	1	no	—
117	C₂³×C₁₉	—	4	1	no	—
118	C₂³×C₁₉	—	4	1	no	—
119	C₂³×C₁₉	—	4	1	no	—
120	C₂³×C₁₉	—	4	1	no	—
121	C₂³×C₁₉	—	4	1	no	—
122	C₂³×C₁₉	—	4	1	no	—
123	C₂³×C₁₉	—	4	1	no	—
124	C₂³×C₁₉	#99	1	2	yes	—
125	C₂³×C₁₉	#102	1	2	yes	—
126	C₂³×C₁₉	#104	1	2	yes	—
127	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	D₄×C₁₉	—	8	2	no	—
129	D₄×C₁₉	—	8	4	no	—
130	C₂×C₄×C₁₉	—	2	4	no	—
131	C₂×C₄×C₁₉	—	2	4	no	—
132	C₂×C₄×C₁₉	—	2	4	no	—
133	C₂×C₄×C₁₉	—	2	4	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	4	4	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	#102	1	2	yes	—
158	C₂×C₄×C₁₉	#104	1	2	yes	—
159	C₂×C₄×C₁₉	#131	1	2	yes	—
160	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
162	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
164	C₁₉⋊C₈	—	4	4	no	—
165	C₁₉⋊C₈	—	4	4	no	—
166	#2854	D₁₉	1	1	yes	characteristic
167	#1728	—	19	1	no	—
168	C₂×#336	—	19	1	no	—
169	#1271	—	19	2	no	—
170	#1270	—	19	2	no	—
171	C₂²×C₁₉	—	2	2	no	—
172	C₂²×C₁₉	—	2	2	no	—
173	C₂²×C₁₉	—	2	2	no	—
174	C₂²×C₁₉	—	2	2	no	—
175	C₂²×C₁₉	—	2	2	no	—
176	C₂²×C₁₉	—	2	2	no	—
177	C₂²×C₁₉	—	8	1	no	—
178	C₂²×C₁₉	—	8	1	no	—
179	C₂²×C₁₉	—	8	1	no	—
180	C₂²×C₁₉	—	8	1	no	—
181	C₂²×C₁₉	—	8	1	no	—
182	C₂²×C₁₉	—	8	1	no	—
183	C₂²×C₁₉	—	8	1	no	—
184	C₂²×C₁₉	#327	1	4	yes	—
185	C₂²×C₁₉	#408	1	1	yes	characteristic
186	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
187	C₂²×C₁₉	#413	1	1	yes	characteristic
188	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
189	C₂²×C₁₉	#417	1	1	yes	characteristic
190	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
191	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
192	C₄×C₁₉	—	2	2	no	—
193	C₄×C₁₉	—	2	1	no	—
194	C₄×C₁₉	—	2	2	no	—
195	C₄×C₁₉	—	2	1	no	—
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	2	2	no	—
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	4	1	no	—
200	C₄×C₁₉	—	8	1	no	—
201	C₄×C₁₉	—	8	1	no	—
202	C₄×C₁₉	—	8	1	no	—
203	C₂²×M₁₆	—	38	1	no	—
204	C₂³×C₈	—	38	1	no	—
205	C₂×#123	—	2	1	no	—
206	C₂×#121	Dic₁₉	1	1	yes	characteristic
207	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
208	#390	Dic₁₉	1	1	yes	characteristic
209	#390	C₂×D₁₉	1	1	yes	characteristic
210	#389	Dic₁₉	1	1	yes	characteristic
211	#389	C₂×D₁₉	1	1	yes	characteristic
212	#388	—	2	1	no	—
213	#388	—	2	1	no	—
214	#386	—	2	1	no	—
215	#380	Dic₁₉	1	1	yes	characteristic
216	#336	—	19	2	no	—
217	#336	—	19	2	no	—
218	#336	—	38	1	no	—
219	#336	—	38	1	no	—
220	C₂×C₁₉	—	2	4	no	—
221	C₂×C₁₉	—	16	1	no	—
222	C₂×C₁₉	#1468	1	1	yes	characteristic
223	C₂×C₁₉	#1483	1	1	yes	characteristic
224	C₂×C₁₉	#1492	1	1	yes	characteristic
225	C₂×C₁₉	C₂×#327	1	1	yes	characteristic
226	C₂×C₁₉	#1504	1	1	yes	characteristic
227	C₂×C₁₉	#1524	1	1	yes	characteristic
228	C₂×C₁₉	#1547	1	1	yes	characteristic
229	C₂²×D₄	—	2	1	no	—
230	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
231	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
232	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
233	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
234	C₂×M₁₆	—	38	4	no	—
235	C₂×M₁₆	—	76	2	no	—
236	C₂×M₁₆	—	76	2	no	—
237	C₂²×C₈	—	38	4	no	—
238	C₂²×C₈	—	38	2	no	—
239	C₂²×C₈	—	38	2	no	—
240	C₂²×C₈	—	76	2	no	—
241	C₂²×C₈	—	76	2	no	—
242	#123	—	4	2	no	—
243	#123	—	4	2	no	—
244	#121	—	4	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	1	no	—
256	C₂×C₄²	—	4	2	no	—
257	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
258	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
259	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
260	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
261	#95	—	2	1	no	—
262	#95	—	2	1	no	—
263	#95	—	2	1	no	—
264	C₁₉	#7678	1	1	yes	characteristic, complemented, Sylow
265	C₂⁴	—	2	1	no	—
266	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	4	1	no	—
269	C₂×D₄	—	4	1	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	—	4	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	#64525	1	2	yes	—
286	C₂²×C₄	#64526	1	2	yes	—
287	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
288	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
289	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
290	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
293	M₁₆	—	76	8	no	—
294	C₂×C₈	—	38	4	no	—
295	C₂×C₈	—	38	4	no	—
296	C₂×C₈	—	76	8	no	—
297	C₂×C₈	—	76	2	no	—
298	C₂×C₈	—	76	2	no	—
299	C₂×C₈	—	76	2	no	—
300	C₂×C₈	—	76	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	4	1	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₂²⋊C₄	—	4	1	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₄²	—	4	1	no	—
316	C₄²	—	4	1	no	—
317	C₄²	—	4	1	no	—
318	C₄²	—	4	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	4	1	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	4	1	no	—
330	C₂³	#10597289	1	2	yes	—
331	C₂³	#10597291	1	2	yes	—
332	C₂³	#10597294	1	2	yes	—
333	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
334	D₄	—	8	2	no	—
335	D₄	—	8	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	#10597289	1	2	yes	—
364	C₂×C₄	#10597294	1	2	yes	—
365	C₂×C₄	C₂×#64525	1	1	yes	characteristic
366	C₂×C₄	C₂×#64526	1	1	yes	characteristic
367	C₂×C₄	#10597394	1	2	yes	—
368	C₂×C₄	#10597395	1	1	yes	characteristic
369	C₂×C₄	#10597397	1	1	yes	characteristic
370	C₈	—	76	4	no	—
371	C₈	—	76	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	8	1	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	8	1	no	—
385	C₂²	#11926278	1	4	yes	—
386	C₂²	#11926511	1	1	yes	characteristic
387	C₂²	C₂×#10597291	1	1	yes	characteristic
388	C₂²	#11926528	1	1	yes	characteristic
389	C₂²	C₂×#10597289	1	1	yes	characteristic
390	C₂²	#11926545	1	1	yes	characteristic
391	C₂²	C₂×#10597294	1	1	yes	characteristic
392	C₂²	C₂×#10597294	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	4	1	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	1	no	—
404	C₂	—	2	4	no	—
405	C₂	—	16	1	no	—
406	C₂	#14561983	1	1	yes	characteristic
407	C₂	#14562048	1	1	yes	characteristic
408	C₂	#14562086	1	1	yes	characteristic
409	C₂	C₂×#11926278	1	1	yes	characteristic
410	C₂	#14562139	1	1	yes	characteristic
411	C₂	#14562223	1	1	yes	characteristic
412	C₂	#14562312	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2854	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×C₁₉×#121	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2854	D₁₉
hypocenter	C₁₉	#7678
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2854

Complements

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

N	H ≅ G/N	type
1. #14563329	C₂	semidirect
2. C₂×#11926299	C₂	semidirect
3. #14561458	C₂	semidirect
4. #14561456	C₂	semidirect
264. C₁₉	#7678	semidirect

Maximal subgroups

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

subgroup	index
#14563329	2
C₂×#11926299	2
#14561458	2
#14561456	2
C₁₉×#2854	2
#7678	19