Subgroups — #18072734

Order 4864.

740 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#64520	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597372	C₂	1	1	yes	maximal, characteristic
3	#14561527	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2920	C₂	1	1	yes	maximal, characteristic
5	C₂²×#64520	—	2	1	no	—
6	C₂×#10597372	—	2	1	no	—
7	C₄×#64520	—	2	1	no	—
8	C₄×#64520	—	2	1	no	—
9	C₄×#64520	C₄	1	2	yes	complemented
10	C₄×#64520	C₂²	1	2	yes	—
11	C₂×#10597260	C₄	1	2	yes	complemented
12	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
13	C₄×C₄⋊Dic₁₉	—	2	1	no	—
14	C₄×C₄⋊Dic₁₉	C₄	1	2	yes	—
15	C₄×C₂²⋊Dic₁₉	—	2	1	no	—
16	C₄×C₂²⋊Dic₁₉	C₄	1	2	yes	—
17	#11926390	C₂²	1	2	yes	—
18	C₄²×Dic₁₉	—	2	1	no	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#432	—	2	1	no	—
21	C₁₉×#432	C₂²	1	2	yes	—
22	C₁₉×#431	—	2	1	no	—
23	C₁₉×#431	C₄	1	2	yes	complemented
24	C₁₉×#423	C₄	1	2	yes	complemented
25	C₁₉×#407	—	2	1	no	—
26	C₄×M₁₆×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₁₉	—	2	2	no	—
31	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
44	#10597372	—	2	8	no	—
45	C₂×C₄⋊Dic₁₉	—	2	2	no	—
46	C₂×C₄×Dic₁₉	—	2	2	no	—
47	C₂×C₄×Dic₁₉	—	2	2	no	—
48	C₂×C₄×Dic₁₉	—	2	2	no	—
49	C₂×#64520	—	2	8	no	—
50	C₂×#64520	—	2	2	no	—
51	C₂×#64520	—	2	2	no	—
52	C₂²×C₁₉⋊C₈	—	2	2	no	—
53	C₁₉×C₄⋊C₈	—	2	2	no	—
54	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
55	C₁₉×C₂²⋊C₈	—	2	2	no	—
56	C₁₉×C₂²⋊C₈	—	2	2	no	—
57	C₁₉×#97	—	2	2	no	—
58	C₄×C₈×C₁₉	—	2	2	no	—
59	C₁₉⋊#95	—	2	2	no	—
60	C₁₉⋊#95	C₂×C₄	1	4	yes	—
61	#10597260	—	2	2	no	—
62	#10597260	C₂×C₄	1	4	yes	—
63	C₄×C₁₉⋊C₈	—	2	2	no	—
64	C₄×C₁₉⋊C₈	—	2	2	no	—
65	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	—	2	4	no	—
67	C₂²×C₄×C₁₉	—	2	4	no	—
68	C₂²×C₄×C₁₉	—	4	2	no	—
69	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×Dic₁₉	—	2	4	no	—
88	M₁₆×C₁₉	—	4	4	no	—
89	C₂×C₈×C₁₉	—	2	4	no	—
90	C₄²×C₁₉	C₄²	1	1	yes	characteristic
91	C₄²×C₁₉	C₄²	1	1	yes	characteristic
92	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
106	C₂²⋊Dic₁₉	—	2	8	no	—
107	C₄⋊Dic₁₉	—	2	8	no	—
108	C₄×Dic₁₉	—	2	8	no	—
109	C₄×Dic₁₉	—	4	4	no	—
110	C₄×Dic₁₉	—	4	4	no	—
111	#64520	—	2	8	no	—
112	#64520	—	2	8	no	—
113	C₂×C₁₉⋊C₈	—	2	8	no	—
114	C₂×C₁₉⋊C₈	—	2	4	no	—
115	#8068	—	19	1	no	maximal, Sylow
116	C₂³×C₁₉	—	2	2	no	—
117	C₂³×C₁₉	—	2	2	no	—
118	C₂³×C₁₉	—	4	1	no	—
119	C₂³×C₁₉	#95	1	1	yes	characteristic
120	C₂³×C₁₉	#95	1	1	yes	characteristic
121	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₉	—	2	2	no	—
123	C₂×C₄×C₁₉	—	2	2	no	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	2	2	no	—
126	C₂×C₄×C₁₉	—	2	2	no	—
127	C₂×C₄×C₁₉	—	2	2	no	—
128	C₂×C₄×C₁₉	—	2	2	no	—
129	C₂×C₄×C₁₉	—	2	2	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	2	2	no	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	4	1	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	—	4	1	no	—
138	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
140	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#104	1	4	yes	—
145	C₂×C₄×C₁₉	#104	1	4	yes	—
146	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×Dic₁₉	—	2	8	no	—
153	C₂×Dic₁₉	—	4	4	no	—
154	C₂×Dic₁₉	—	4	4	no	—
155	C₈×C₁₉	—	4	4	no	—
156	C₁₉⋊C₈	—	2	8	no	—
157	#2920	D₁₉	1	1	yes	characteristic
158	C₂×C₄×M₁₆	—	19	1	no	—
159	C₄×#117	—	19	1	no	—
160	#1300	—	19	4	no	—
161	C₂²×C₁₉	—	2	1	no	—
162	C₂²×C₁₉	—	2	1	no	—
163	C₂²×C₁₉	—	2	1	no	—
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	—	2	1	no	—
166	C₂²×C₁₉	—	2	1	no	—
167	C₂²×C₁₉	—	2	1	no	—
168	C₂²×C₁₉	—	4	4	no	—
169	C₂²×C₁₉	#339	1	2	yes	—
170	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
171	C₂²×C₁₉	C₂×#104	1	2	yes	—
172	C₄×C₁₉	—	2	1	no	—
173	C₄×C₁₉	—	2	1	no	—
174	C₄×C₁₉	—	2	1	no	—
175	C₄×C₁₉	—	2	1	no	—
176	C₄×C₁₉	—	2	1	no	—
177	C₄×C₁₉	—	2	1	no	—
178	C₄×C₁₉	—	2	1	no	—
179	C₄×C₁₉	#339	1	2	yes	—
180	C₄×C₁₉	#339	1	2	yes	—
181	C₄×C₁₉	#339	1	2	yes	—
182	C₄×C₁₉	#344	1	2	yes	—
183	C₄×C₁₉	C₂×#104	1	2	yes	—
184	Dic₁₉	—	4	8	no	—
185	C₂²×M₁₆	—	38	1	no	—
186	C₂×#117	—	38	1	no	—
187	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
188	#432	—	2	1	no	—
189	#432	C₂×D₁₉	1	2	yes	—
190	#431	—	2	1	no	—
191	#431	Dic₁₉	1	2	yes	complemented
192	#423	Dic₁₉	1	2	yes	complemented
193	#407	—	2	1	no	—
194	C₄×M₁₆	—	2	1	no	—
195	C₄×M₁₆	—	19	2	no	—
196	C₄×M₁₆	—	19	2	no	—
197	C₄×M₁₆	—	38	1	no	—
198	C₄×M₁₆	—	38	1	no	—
199	C₂×#97	—	19	2	no	—
200	C₂×C₄×C₈	—	38	1	no	—
201	C₄×C₄⋊C₄	—	19	2	no	—
202	C₄×C₄⋊C₄	—	38	1	no	—
203	C₄×C₂²⋊C₄	—	19	2	no	—
204	C₄×C₂²⋊C₄	—	38	1	no	—
205	#376	—	19	2	no	—
206	C₄³	—	38	1	no	—
207	C₂×C₁₉	—	2	2	no	—
208	C₂×C₁₉	—	2	2	no	—
209	C₂×C₁₉	—	4	1	no	—
210	C₂×C₁₉	C₂×#339	1	1	yes	characteristic
211	C₂×C₁₉	C₂×#339	1	1	yes	characteristic
212	C₂×C₁₉	C₂×#344	1	1	yes	characteristic
213	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
214	C₂³×C₄	D₇₆	1	1	yes	characteristic
215	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
216	C₂×M₁₆	—	2	2	no	—
217	C₂×M₁₆	—	38	8	no	—
218	C₂×M₁₆	—	38	2	no	—
219	C₂×M₁₆	—	38	2	no	—
220	C₂²×C₈	—	38	2	no	—
221	#117	—	38	8	no	—
222	C₂×C₄⋊C₄	—	38	2	no	—
223	C₂×C₂²⋊C₄	—	38	2	no	—
224	C₂×C₄²	—	38	2	no	—
225	C₂×C₄²	—	38	2	no	—
226	C₂×C₄²	—	38	2	no	—
227	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
228	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
229	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
230	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
231	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
232	C₂×C₄²	D₇₆	1	1	yes	characteristic
233	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
234	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
235	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
236	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
237	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
238	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
239	C₄⋊C₈	—	2	2	no	—
240	C₄⋊C₈	C₂×Dic₁₉	1	4	yes	—
241	C₂²⋊C₈	—	2	2	no	—
242	C₂²⋊C₈	—	2	2	no	—
243	#97	—	2	2	no	—
244	#97	—	19	4	no	—
245	#97	—	38	2	no	—
246	C₄×C₈	—	2	2	no	—
247	C₄×C₈	—	38	2	no	—
248	C₄×C₈	—	38	2	no	—
249	#95	—	19	4	no	—
250	#95	—	38	2	no	—
251	C₁₉	#8068	1	1	yes	characteristic, complemented, Sylow
252	C₂⁴	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	—	38	4	no	—
257	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
258	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
259	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
264	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
265	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
271	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
275	M₁₆	—	4	4	no	—
276	M₁₆	—	38	8	no	—
277	M₁₆	—	38	8	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	38	8	no	—
280	C₂×C₈	—	38	4	no	—
281	C₄⋊C₄	—	38	8	no	—
282	C₂²⋊C₄	—	38	8	no	—
283	C₄²	—	38	8	no	—
284	C₄²	—	76	4	no	—
285	C₄²	—	76	4	no	—
286	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
287	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
288	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
289	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
290	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
291	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
292	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
293	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
294	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
295	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
296	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
297	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
298	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
299	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
300	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
301	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	4	1	no	—
305	C₂³	C₁₉⋊#95	1	1	yes	characteristic
306	C₂³	C₁₉⋊#95	1	1	yes	characteristic
307	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	38	8	no	—
325	C₂×C₄	—	76	4	no	—
326	C₂×C₄	—	76	4	no	—
327	C₂×C₄	#10597282	1	4	yes	—
328	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
329	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
330	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
331	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
332	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
333	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
334	C₂×C₄	#10597294	1	4	yes	—
335	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
336	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
338	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
339	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
340	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
341	C₈	—	4	4	no	—
342	C₈	—	38	8	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	4	4	no	—
351	C₂²	#11926303	1	2	yes	—
352	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
353	C₂²	C₂×#10597282	1	2	yes	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	76	8	no	—
362	C₄	#11926303	1	2	yes	—
363	C₄	#11926305	1	2	yes	—
364	C₄	#11926305	1	2	yes	—
365	C₄	#11926315	1	2	yes	—
366	C₄	C₂×#10597294	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	2	no	—
369	C₂	—	4	1	no	—
370	C₂	C₂×#11926303	1	1	yes	characteristic
371	C₂	C₂×#11926305	1	1	yes	characteristic
372	C₂	C₂×#11926315	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2920	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2920	D₁₉
hypocenter	C₁₉	#8068
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #14561527	C₂	semidirect
9. C₄×#64520	C₄	semidirect
11. C₂×#10597260	C₄	semidirect
23. C₁₉×#431	C₄	semidirect
24. C₁₉×#423	C₄	semidirect
191. #431	Dic₁₉	semidirect
192. #423	Dic₁₉	semidirect
251. C₁₉	#8068	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#64520	2
C₄×#10597372	2
#14561527	2
C₁₉×#2920	2
#8068	19