Subgroups — C₁₉×#10341 #18016300

Order 4864.

684 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2659	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1787	C₂	1	2	yes	maximal
3	C₁₉×#1446	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1294	C₂	1	2	yes	maximal
5	C₁₉×#1280	C₂	1	1	yes	maximal, characteristic
6	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
8	C₂×C₁₉×#103	—	2	2	no	—
9	C₂×C₁₉×#103	—	2	2	no	—
10	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
11	C₁₉×#398	—	2	2	no	—
12	C₁₉×#395	—	2	2	no	—
13	C₁₉×#380	—	2	1	no	—
14	C₁₉×#380	C₂²	1	2	yes	—
15	C₂×C₁₉×#95	—	2	1	no	—
16	C₂×C₁₉×#95	—	2	1	no	—
17	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
19	C₂²×Q₈×C₁₉	—	2	1	no	—
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂²×Q₈×C₁₉	—	2	2	no	—
22	C₂²×Q₈×C₁₉	—	2	2	no	—
23	C₂²×Q₈×C₁₉	—	4	2	no	—
24	C₂²×Q₈×C₁₉	—	4	2	no	—
25	C₂²×Q₈×C₁₉	Q₈	1	2	yes	complemented
26	C₂³×C₄×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×C₈×C₁₉	—	2	2	no	—
32	C₁₉×C₂²⋊Q₈	—	4	2	no	—
33	C₁₉×C₂²⋊Q₈	—	4	2	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
39	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
41	C₁₉×#103	—	4	4	no	—
42	C₁₉×#103	—	4	4	no	—
43	C₁₉×C₂²⋊C₈	—	2	2	no	—
44	C₁₉×C₂²⋊C₈	—	2	2	no	—
45	C₁₉×#95	—	2	2	no	—
46	C₁₉×#95	—	2	2	no	—
47	C₁₉×#95	—	2	2	no	—
48	C₁₉×#95	—	2	2	no	—
49	C₁₉×#95	—	4	2	no	—
50	C₁₉×#95	—	4	2	no	—
51	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×Q₈×C₁₉	—	2	4	no	—
53	C₂×Q₈×C₁₉	—	2	4	no	—
54	C₂×Q₈×C₁₉	—	2	4	no	—
55	C₂×Q₈×C₁₉	—	4	4	no	—
56	C₂×Q₈×C₁₉	—	4	2	no	—
57	C₂×Q₈×C₁₉	—	4	2	no	—
58	C₂×Q₈×C₁₉	—	4	4	no	—
59	C₂×Q₈×C₁₉	—	4	2	no	—
60	C₂×Q₈×C₁₉	—	4	8	no	—
61	C₂×Q₈×C₁₉	—	4	2	no	—
62	C₂×Q₈×C₁₉	—	8	1	no	—
63	C₂×Q₈×C₁₉	—	8	1	no	—
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	4	1	no	—
75	C₂²×C₄×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
91	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	#41	1	2	yes	—
95	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
96	C₂×C₈×C₁₉	—	4	2	no	—
97	C₂×C₈×C₁₉	—	4	2	no	—
98	C₂×C₈×C₁₉	—	4	2	no	—
99	C₄⋊C₄×C₁₉	—	4	2	no	—
100	C₄⋊C₄×C₁₉	—	4	2	no	—
101	C₄⋊C₄×C₁₉	—	4	2	no	—
102	C₄⋊C₄×C₁₉	—	4	4	no	—
103	C₄⋊C₄×C₁₉	—	8	1	no	—
104	C₄⋊C₄×C₁₉	—	8	1	no	—
105	C₂²⋊C₄×C₁₉	—	4	2	no	—
106	C₂²⋊C₄×C₁₉	—	4	2	no	—
107	#10341	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂³×C₁₉	—	2	1	no	—
109	C₂³×C₁₉	—	2	1	no	—
110	C₂³×C₁₉	—	2	1	no	—
111	C₂³×C₁₉	—	2	1	no	—
112	C₂³×C₁₉	#120	1	1	yes	characteristic
113	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
114	C₂³×C₁₉	#124	1	1	yes	characteristic
115	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
116	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
117	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
118	C₂³×C₁₉	#137	1	1	yes	characteristic
119	Q₈×C₁₉	—	2	8	no	—
120	Q₈×C₁₉	—	4	4	no	—
121	Q₈×C₁₉	—	4	4	no	—
122	Q₈×C₁₉	—	4	4	no	—
123	Q₈×C₁₉	—	8	4	no	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	2	2	no	—
126	C₂×C₄×C₁₉	—	2	4	no	—
127	C₂×C₄×C₁₉	—	2	2	no	—
128	C₂×C₄×C₁₉	—	2	2	no	—
129	C₂×C₄×C₁₉	—	4	1	no	—
130	C₂×C₄×C₁₉	—	4	1	no	—
131	C₂×C₄×C₁₉	—	4	2	no	—
132	C₂×C₄×C₁₉	—	4	2	no	—
133	C₂×C₄×C₁₉	—	4	2	no	—
134	C₂×C₄×C₁₉	—	4	2	no	—
135	C₂×C₄×C₁₉	—	4	2	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	—	4	1	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	4	2	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	8	1	no	—
154	C₂×C₄×C₁₉	—	8	1	no	—
155	C₂×C₄×C₁₉	—	8	1	no	—
156	C₂×C₄×C₁₉	—	8	1	no	—
157	C₂×C₄×C₁₉	—	8	1	no	—
158	C₂×C₄×C₁₉	—	8	1	no	—
159	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
160	C₂×C₄×C₁₉	#124	1	2	yes	—
161	C₈×C₁₉	—	8	2	no	—
162	#2659	C₂×C₁₉	1	1	yes	characteristic
163	#1787	C₂×C₁₉	1	2	yes	—
164	#1446	C₂×C₁₉	1	1	yes	characteristic
165	#1294	C₂×C₁₉	1	2	yes	—
166	#1280	C₂×C₁₉	1	1	yes	characteristic
167	C₂²×C₁₉	—	2	1	no	—
168	C₂²×C₁₉	—	2	1	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	2	1	no	—
171	C₂²×C₁₉	—	2	1	no	—
172	C₂²×C₁₉	—	2	1	no	—
173	C₂²×C₁₉	—	2	1	no	—
174	C₂²×C₁₉	—	2	1	no	—
175	C₂²×C₁₉	—	2	1	no	—
176	C₂²×C₁₉	—	2	1	no	—
177	C₂²×C₁₉	—	2	1	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	#393	1	1	yes	characteristic
180	C₂²×C₁₉	#450	1	1	yes	characteristic
181	C₂²×C₁₉	#451	1	1	yes	characteristic
182	C₂²×C₁₉	#455	1	1	yes	characteristic
183	C₂²×C₁₉	#456	1	1	yes	characteristic
184	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
185	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
186	C₂²×C₁₉	#475	1	1	yes	characteristic
187	C₂²×C₁₉	#477	1	1	yes	characteristic
188	C₂²×C₁₉	#487	1	1	yes	characteristic
189	C₂²×C₁₉	#489	1	1	yes	characteristic
190	C₄×C₁₉	—	2	2	no	—
191	C₄×C₁₉	—	2	2	no	—
192	C₄×C₁₉	—	4	2	no	—
193	C₄×C₁₉	—	4	2	no	—
194	C₄×C₁₉	—	4	4	no	—
195	C₄×C₁₉	—	8	2	no	—
196	C₄×C₁₉	—	8	2	no	—
197	C₄×C₁₉	—	8	2	no	—
198	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
199	C₂×C₂²⋊Q₈	—	2	1	no	—
200	C₂×#103	—	2	2	no	—
201	C₂×#103	—	2	2	no	—
202	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
203	#398	—	2	2	no	—
204	#395	—	2	2	no	—
205	#380	—	2	1	no	—
206	#380	C₂²×C₁₉	1	2	yes	—
207	C₂×#95	—	2	1	no	—
208	C₂×#95	—	2	1	no	—
209	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
210	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×C₁₉	—	2	1	no	—
212	C₂×C₁₉	—	2	1	no	—
213	C₂×C₁₉	—	2	1	no	—
214	C₂×C₁₉	—	2	1	no	—
215	C₂×C₁₉	#1601	1	1	yes	characteristic
216	C₂×C₁₉	#1602	1	1	yes	characteristic
217	C₂×C₁₉	#1604	1	1	yes	characteristic
218	C₂×C₁₉	#1605	1	1	yes	characteristic
219	C₂×C₁₉	#2024	1	1	yes	characteristic
220	C₂×C₁₉	#2028	1	1	yes	characteristic
221	C₂×C₁₉	#2029	1	1	yes	characteristic
222	C₂²×Q₈	—	2	1	no	—
223	C₂²×Q₈	—	2	1	no	—
224	C₂²×Q₈	—	2	2	no	—
225	C₂²×Q₈	—	2	2	no	—
226	C₂²×Q₈	—	4	2	no	—
227	C₂²×Q₈	—	4	2	no	—
228	C₂²×Q₈	Q₈×C₁₉	1	2	yes	complemented
229	C₂³×C₄	—	2	1	no	—
230	C₂³×C₄	—	2	1	no	—
231	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
232	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
234	C₂²×C₈	—	2	2	no	—
235	C₂²⋊Q₈	—	4	2	no	—
236	C₂²⋊Q₈	—	4	2	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
242	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	#103	—	4	4	no	—
245	#103	—	4	4	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	2	2	no	—
248	#95	—	2	2	no	—
249	#95	—	2	2	no	—
250	#95	—	2	2	no	—
251	#95	—	2	2	no	—
252	#95	—	4	2	no	—
253	#95	—	4	2	no	—
254	C₁₉	#10341	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
256	C₂×Q₈	—	2	4	no	—
257	C₂×Q₈	—	2	4	no	—
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	—	4	4	no	—
260	C₂×Q₈	—	4	2	no	—
261	C₂×Q₈	—	4	2	no	—
262	C₂×Q₈	—	4	4	no	—
263	C₂×Q₈	—	4	2	no	—
264	C₂×Q₈	—	4	8	no	—
265	C₂×Q₈	—	4	2	no	—
266	C₂×Q₈	—	8	1	no	—
267	C₂×Q₈	—	8	1	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	—
295	C₂²×C₄	Q₁₆×C₁₉	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
297	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
298	C₂²×C₄	#41×C₁₉	1	2	yes	—
299	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	—	4	2	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₄⋊C₄	—	4	4	no	—
307	C₄⋊C₄	—	8	1	no	—
308	C₄⋊C₄	—	8	1	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	C₁₉×#120	1	1	yes	characteristic
316	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
317	C₂³	C₁₉×#124	1	1	yes	characteristic
318	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
319	C₂³	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
320	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
321	C₂³	C₁₉×#137	1	1	yes	characteristic
322	Q₈	—	2	8	no	—
323	Q₈	—	4	4	no	—
324	Q₈	—	4	4	no	—
325	Q₈	—	4	4	no	—
326	Q₈	—	8	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	8	1	no	—
357	C₂×C₄	—	8	1	no	—
358	C₂×C₄	—	8	1	no	—
359	C₂×C₄	—	8	1	no	—
360	C₂×C₄	—	8	1	no	—
361	C₂×C₄	—	8	1	no	—
362	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
363	C₂×C₄	C₁₉×#124	1	2	yes	—
364	C₈	—	8	2	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	C₁₉×#393	1	1	yes	characteristic
378	C₂²	C₁₉×#450	1	1	yes	characteristic
379	C₂²	C₁₉×#451	1	1	yes	characteristic
380	C₂²	C₁₉×#455	1	1	yes	characteristic
381	C₂²	C₁₉×#456	1	1	yes	characteristic
382	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
383	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
384	C₂²	C₁₉×#475	1	1	yes	characteristic
385	C₂²	C₁₉×#477	1	1	yes	characteristic
386	C₂²	C₁₉×#487	1	1	yes	characteristic
387	C₂²	C₁₉×#489	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	4	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	8	2	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	2	no	—
396	C₂	—	2	1	no	—
397	C₂	—	2	1	no	—
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	C₁₉×#1601	1	1	yes	characteristic
401	C₂	C₁₉×#1602	1	1	yes	characteristic
402	C₂	C₁₉×#1604	1	1	yes	characteristic
403	C₂	C₁₉×#1605	1	1	yes	characteristic
404	C₂	C₁₉×#2024	1	1	yes	characteristic
405	C₂	C₁₉×#2028	1	1	yes	characteristic
406	C₂	C₁₉×#2029	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
25. C₂²×Q₈×C₁₉	Q₈	semidirect
107. #10341	C₁₉	direct (N × H)
228. C₂²×Q₈	Q₈×C₁₉	semidirect
254. C₁₉	#10341	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2659	2
C₁₉×#1787	2
C₁₉×#1446	2
C₁₉×#1294	2
C₁₉×#1280	2
#10341	19

Subgroups — C19×#10341 #18016300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10341 #18016300