Subgroups — #18081401

Order 4864.

606 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#64525	C₂	1	1	yes	maximal, characteristic
2	#14564429	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11926296	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926271	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64525	C₄	1	1	yes	characteristic
9	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
10	C₄×#64525	—	2	2	no	—
11	C₄×#64525	—	2	2	no	—
12	C₂×#10597264	C₄	1	1	yes	characteristic
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#10597289	C₄	1	1	yes	characteristic
15	C₂×#10597266	C₄	1	1	yes	characteristic
16	C₂×(C₂×D₁₉)⋊C₈	—	2	2	no	—
17	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	#11926296	—	2	2	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
21	#11926271	—	2	2	no	—
22	C₈×C₁₉⋊C₈	—	2	2	no	—
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
26	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	—	2	1	no	—
29	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	D₄	1	2	yes	—
33	C₄×D₄×C₁₉	—	2	1	no	—
34	C₄×D₄×C₁₉	—	2	1	no	—
35	C₄×D₄×C₁₉	—	2	1	no	—
36	C₄×D₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×#64525	—	2	2	no	—
41	C₂×#64525	—	2	2	no	—
42	C₂×#64525	C₈	1	4	yes	complemented
43	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
44	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₁₉⋊C₈	—	2	1	no	—
46	C₂²×C₁₉⋊C₈	—	2	1	no	—
47	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
49	C₄×D₇₆	—	2	1	no	—
50	C₄×D₇₆	—	2	1	no	—
51	C₄×D₇₆	—	2	1	no	—
52	C₄×D₇₆	—	2	1	no	—
53	C₁₉×C₄⋊C₈	—	2	1	no	—
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₂²⋊C₈	—	4	4	no	—
56	C₄×C₈×C₁₉	—	2	1	no	—
57	C₄×C₈×C₁₉	—	2	1	no	—
58	#10597289	—	2	2	no	—
59	(C₂×D₁₉)⋊C₈	—	4	4	no	—
60	#10597266	—	2	2	no	—
61	#10597264	—	2	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	D₄	1	2	yes	—
66	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
67	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
68	C₂⁴×C₁₉	—	2	1	no	—
69	C₂³×D₁₉	—	2	1	no	—
70	C₂×D₄×C₁₉	—	2	1	no	—
71	C₂×D₄×C₁₉	—	2	1	no	—
72	C₂×D₄×C₁₉	—	2	1	no	—
73	C₂×D₄×C₁₉	—	2	1	no	—
74	C₂×D₄×C₁₉	—	2	1	no	—
75	C₂×D₄×C₁₉	C₂×C₈	1	2	yes	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	2	no	—
80	C₂²×C₄×C₁₉	—	4	2	no	—
81	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
84	C₂²×Dic₁₉	—	2	1	no	—
85	C₂×D₇₆	—	2	1	no	—
86	C₂×D₇₆	—	2	1	no	—
87	C₂×D₇₆	—	2	1	no	—
88	C₂×D₇₆	—	2	1	no	—
89	C₂×D₇₆	—	2	1	no	—
90	C₂×D₇₆	C₂×C₈	1	2	yes	—
91	C₂×C₄×D₁₉	—	4	1	no	—
92	C₂×C₄×D₁₉	—	4	1	no	—
93	C₂×C₄×D₁₉	—	4	2	no	—
94	C₂×C₄×D₁₉	—	4	2	no	—
95	C₂×C₈×C₁₉	—	2	2	no	—
96	C₂×C₈×C₁₉	—	2	2	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₂×C₈×C₁₉	—	4	2	no	—
99	C₂×C₈×C₁₉	D₈	1	4	yes	complemented
100	C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂²⋊C₄×C₁₉	—	4	1	no	—
103	C₂²⋊C₄×C₁₉	—	4	1	no	—
104	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₁₉	#41	1	1	yes	characteristic
108	#64525	—	2	8	no	—
109	(C₂×D₁₉)⋊C₄	—	4	1	no	—
110	(C₂×D₁₉)⋊C₄	—	4	1	no	—
111	C₄⋊Dic₁₉	—	2	1	no	—
112	C₄⋊Dic₁₉	—	2	1	no	—
113	C₂×C₁₉⋊C₈	—	2	4	no	—
114	C₂×C₁₉⋊C₈	—	2	2	no	—
115	C₂×C₁₉⋊C₈	—	2	1	no	—
116	C₂×C₁₉⋊C₈	—	2	1	no	—
117	C₂×C₁₉⋊C₈	—	4	1	no	—
118	C₂×C₁₉⋊C₈	—	4	2	no	—
119	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
120	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
121	C₂×C₁₉⋊C₈	C₂×C₈	1	2	yes	—
122	C₂×C₁₉⋊C₈	M₁₆	1	2	yes	—
123	#9657	—	19	1	no	maximal, Sylow
124	C₂³×C₁₉	—	2	2	no	—
125	C₂³×C₁₉	—	4	1	no	—
126	C₂³×C₁₉	—	4	1	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
130	C₂²×D₁₉	—	2	2	no	—
131	C₂²×D₁₉	—	4	1	no	—
132	C₂²×D₁₉	—	4	1	no	—
133	C₂²×D₁₉	—	4	2	no	—
134	C₂²×D₁₉	—	4	2	no	—
135	D₄×C₁₉	—	2	2	no	—
136	D₄×C₁₉	—	2	2	no	—
137	D₄×C₁₉	—	4	1	no	—
138	D₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	8	2	no	—
143	C₂×C₄×C₁₉	—	8	1	no	—
144	C₂×C₄×C₁₉	—	8	1	no	—
145	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
156	C₂×C₄×C₁₉	#135	1	2	yes	—
157	C₂×Dic₁₉	—	4	1	no	—
158	C₂×Dic₁₉	—	4	2	no	—
159	D₇₆	—	2	2	no	—
160	D₇₆	—	2	2	no	—
161	D₇₆	—	4	1	no	—
162	D₇₆	—	4	1	no	—
163	C₄×D₁₉	—	8	2	no	—
164	C₄×D₁₉	—	8	1	no	—
165	C₄×D₁₉	—	8	1	no	—
166	C₈×C₁₉	—	2	4	no	—
167	C₈×C₁₉	—	8	1	no	—
168	C₁₉⋊C₈	—	2	4	no	—
169	C₁₉⋊C₈	—	2	2	no	—
170	C₁₉⋊C₈	—	8	1	no	—
171	C₁₉⋊C₈	C₂²⋊C₈	1	4	yes	complemented
172	C₂×C₄×D₈	—	19	1	no	—
173	#1954	—	19	1	no	—
174	#1954	D₁₉	1	1	yes	characteristic, complemented
175	C₂×#335	—	19	1	no	—
176	C₂×D₄⋊C₈	—	19	1	no	—
177	C₂×D₄⋊C₈	—	19	1	no	—
178	C₂×C₈²	—	19	1	no	—
179	C₂²×C₁₉	—	4	4	no	—
180	C₂²×C₁₉	—	4	2	no	—
181	C₂²×C₁₉	—	8	2	no	—
182	C₂²×C₁₉	—	8	1	no	—
183	C₂²×C₁₉	—	8	1	no	—
184	C₂²×C₁₉	#390	1	1	yes	characteristic
185	C₂²×C₁₉	C₈×D₄	1	1	yes	characteristic
186	C₂²×C₁₉	#436	1	1	yes	characteristic
187	C₂²×C₁₉	C₄×D₈	1	2	yes	—
188	C₂²×C₁₉	#443	1	2	yes	—
189	C₂×D₁₉	—	4	4	no	—
190	C₂×D₁₉	—	4	2	no	—
191	C₂×D₁₉	—	8	2	no	—
192	C₂×D₁₉	—	8	1	no	—
193	C₂×D₁₉	—	8	1	no	—
194	C₄×C₁₉	—	2	1	no	—
195	C₄×C₁₉	—	2	1	no	—
196	C₄×C₁₉	—	8	1	no	—
197	C₄×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
198	C₄×C₁₉	#408	1	1	yes	characteristic
199	C₄×C₁₉	C₈×D₄	1	1	yes	characteristic
200	C₄×C₁₉	#436	1	1	yes	characteristic
201	C₄×C₁₉	#466	1	2	yes	—
202	C₄×C₁₉	#493	1	1	yes	characteristic
203	C₄×C₁₉	#495	1	1	yes	characteristic
204	Dic₁₉	—	8	1	no	—
205	C₂²×D₈	—	19	1	no	—
206	C₂×C₄×D₄	—	19	1	no	—
207	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
208	C₄×D₈	—	38	2	no	—
209	C₄×D₈	—	38	2	no	—
210	C₂×#107	—	19	1	no	—
211	C₂×C₄⋊C₈	—	19	1	no	—
212	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
213	C₂×#102	—	19	1	no	—
214	C₂×#102	—	19	1	no	—
215	C₂×C₂²⋊C₈	—	2	2	no	—
216	C₂×C₂²⋊C₈	—	38	2	no	—
217	C₂×C₄×C₈	—	19	1	no	—
218	C₂×C₄×C₈	—	19	1	no	—
219	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
220	#335	—	38	2	no	—
221	D₄⋊C₈	—	38	2	no	—
222	D₄⋊C₈	—	38	2	no	—
223	C₈²	—	38	2	no	—
224	C₂×C₁₉	—	8	2	no	—
225	C₂×C₁₉	C₈×D₈	1	2	yes	—
226	C₂×C₁₉	#1589	1	2	yes	—
227	C₂×C₁₉	#1954	1	1	yes	characteristic
228	C₂×C₁₉	#1970	1	1	yes	characteristic
229	C₂×C₁₉	#1974	1	1	yes	characteristic
230	D₁₉	—	8	2	no	—
231	C₂²×D₄	—	19	1	no	—
232	C₂²×D₄	C₄×D₁₉	1	1	yes	characteristic
233	C₂³×C₄	—	2	1	no	—
234	C₂³×C₄	—	38	1	no	—
235	C₂×D₈	—	19	4	no	—
236	C₂×D₈	—	38	2	no	—
237	C₂×D₈	—	38	2	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	—	19	1	no	—
240	C₂²×C₈	—	19	1	no	—
241	C₂²×C₈	—	38	1	no	—
242	C₂²×C₈	—	38	1	no	—
243	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	38	1	no	—
249	C₄×D₄	—	38	1	no	—
250	C₄×D₄	—	38	1	no	—
251	C₄×D₄	—	38	1	no	—
252	C₂×C₄⋊C₄	—	19	1	no	—
253	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	38	1	no	—
256	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
257	#107	—	38	2	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	38	1	no	—
261	C₄⋊C₈	—	38	1	no	—
262	#102	—	38	2	no	—
263	#102	—	38	2	no	—
264	C₂²⋊C₈	—	4	4	no	—
265	C₂²⋊C₈	—	76	4	no	—
266	C₄×C₈	—	2	1	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	—	19	2	no	—
269	C₄×C₈	—	19	2	no	—
270	C₄×C₈	—	19	2	no	—
271	C₄×C₈	—	38	1	no	—
272	C₁₉	#9657	1	1	yes	characteristic, complemented, Sylow
273	C₂⁴	—	2	1	no	—
274	C₂⁴	—	38	1	no	—
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	19	2	no	—
281	C₂×D₄	—	38	1	no	—
282	C₂×D₄	—	38	1	no	—
283	C₂×D₄	—	38	1	no	—
284	C₂×D₄	—	38	1	no	—
285	C₂×D₄	—	38	1	no	—
286	C₂×D₄	C₈×D₁₉	1	2	yes	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	38	1	no	—
293	C₂²×C₄	—	76	2	no	—
294	C₂²×C₄	—	76	1	no	—
295	C₂²×C₄	—	76	1	no	—
296	C₂²×C₄	—	76	2	no	—
297	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
298	C₂²×C₄	#64541	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
300	D₈	—	38	8	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	4	2	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	19	2	no	—
306	C₂×C₈	—	19	2	no	—
307	C₂×C₈	—	19	2	no	—
308	C₂×C₈	—	19	2	no	—
309	C₂×C₈	—	38	4	no	—
310	C₂×C₈	—	38	2	no	—
311	C₂×C₈	—	38	1	no	—
312	C₂×C₈	—	38	1	no	—
313	C₂×C₈	—	76	2	no	—
314	C₂×C₈	—	76	1	no	—
315	C₂×C₈	#64525	1	4	yes	complemented
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	38	1	no	—
319	C₄⋊C₄	—	38	1	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	76	1	no	—
323	C₂²⋊C₄	—	76	1	no	—
324	C₄²	D₄×D₁₉	1	1	yes	characteristic
325	C₄²	D₄×D₁₉	1	1	yes	characteristic
326	C₄²	D₄×D₁₉	1	1	yes	characteristic
327	C₄²	#64543	1	1	yes	characteristic
328	C₂³	—	2	2	no	—
329	C₂³	—	4	1	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	1	no	—
333	C₂³	—	38	2	no	—
334	C₂³	—	76	1	no	—
335	C₂³	—	76	2	no	—
336	C₂³	—	76	2	no	—
337	C₂³	—	76	1	no	—
338	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
339	D₄	—	2	2	no	—
340	D₄	—	2	2	no	—
341	D₄	—	4	1	no	—
342	D₄	—	4	1	no	—
343	D₄	—	38	2	no	—
344	D₄	—	38	2	no	—
345	D₄	—	76	1	no	—
346	D₄	—	76	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	—	8	1	no	—
352	C₂×C₄	—	8	2	no	—
353	C₂×C₄	—	76	2	no	—
354	C₂×C₄	—	76	1	no	—
355	C₂×C₄	—	152	1	no	—
356	C₂×C₄	—	152	1	no	—
357	C₂×C₄	—	152	2	no	—
358	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
359	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
360	C₂×C₄	#10597330	1	1	yes	characteristic
361	C₂×C₄	#10597331	1	1	yes	characteristic
362	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
363	C₂×C₄	#10597347	1	1	yes	characteristic
364	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
365	C₂×C₄	#10597353	1	1	yes	characteristic
366	C₂×C₄	C₂×#64525	1	2	yes	—
367	C₂×C₄	#10597385	1	1	yes	characteristic
368	C₂×C₄	#10597386	1	1	yes	characteristic
369	C₂×C₄	#10597396	1	2	yes	—
370	C₈	—	2	4	no	—
371	C₈	—	8	1	no	—
372	C₈	—	19	4	no	—
373	C₈	—	38	4	no	—
374	C₈	—	38	2	no	—
375	C₈	—	152	1	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	76	2	no	—
382	C₂²	—	76	4	no	—
383	C₂²	—	152	1	no	—
384	C₂²	—	152	1	no	—
385	C₂²	—	152	2	no	—
386	C₂²	#11926444	1	1	yes	characteristic
387	C₂²	C₈×C₂²⋊D₁₉	1	1	yes	characteristic
388	C₂²	#11926620	1	1	yes	characteristic
389	C₂²	C₄×#64525	1	2	yes	—
390	C₂²	#11926659	1	2	yes	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	8	1	no	—
394	C₄	—	152	1	no	—
395	C₄	C₂²⋊C₈×D₁₉	1	1	yes	characteristic
396	C₄	#11926509	1	1	yes	characteristic
397	C₄	(C₂²⋊D₁₉)⋊C₈	1	1	yes	characteristic
398	C₄	#11926619	1	1	yes	characteristic
399	C₄	#11926778	1	2	yes	—
400	C₄	#11926920	1	1	yes	characteristic
401	C₄	#11926926	1	1	yes	characteristic
402	C₂	—	8	2	no	—
403	C₂	—	152	2	no	—
404	C₂	C₈×#64525	1	2	yes	—
405	C₂	#14562518	1	2	yes	—
406	C₂	#14564427	1	1	yes	characteristic
407	C₂	#14564500	1	1	yes	characteristic
408	C₂	#14564522	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1954	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂²×#64525	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1954	D₁₉
hypocenter	C₁₉	#9657
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1954

Complements

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

N	H ≅ G/N	type
2. #14564429	C₂	semidirect
3. C₂×#11926296	C₂	semidirect
4. C₂×D₄⋊(C₁₉⋊C₈)	C₂	semidirect
5. C₂×#11926271	C₂	semidirect
6. C₂×C₈×C₁₉⋊C₈	C₂	semidirect
7. C₁₉×#1954	C₂	semidirect
42. C₂×#64525	C₈	semidirect
99. C₂×C₈×C₁₉	D₈	semidirect
171. C₁₉⋊C₈	C₂²⋊C₈	semidirect
174. #1954	D₁₉	semidirect
272. C₁₉	#9657	semidirect
315. C₂×C₈	#64525	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#64525	2
#14564429	2
C₂×#11926296	2
C₂×D₄⋊(C₁₉⋊C₈)	2
C₂×#11926271	2
C₂×C₈×C₁₉⋊C₈	2
C₁₉×#1954	2
#9657	19