Subgroups — C₁₉×#22448 #18028407

Order 4864.

1506 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2339	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1969	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1877	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1808	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1788	C₂	1	2	yes	maximal, complemented
8	C₈×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₉	C₂²	1	2	yes	—
10	C₂×C₁₉×#135	—	2	8	no	—
11	C₂×C₁₉×#135	C₄	1	8	yes	complemented
12	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
17	C₄×D₈×C₁₉	—	2	8	no	—
18	C₂×C₁₉×#107	C₂²	1	2	yes	—
19	C₂×C₁₉×#103	C₂²	1	4	yes	—
20	C₂×C₁₉×#102	C₂²	1	4	yes	—
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
23	C₁₉×#391	C₂²	1	4	yes	—
24	C₁₉×#386	—	2	4	no	—
25	C₁₉×#381	—	2	2	no	—
26	C₁₉×#380	C₂²	1	2	yes	—
27	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#95	—	2	2	no	—
29	C₁₉×#340	C₂²	1	2	yes	—
30	C₁₉×#336	C₂²	1	2	yes	—
31	C₂×#41×C₁₉	—	2	4	no	—
32	C₂×#41×C₁₉	—	2	8	no	—
33	C₂×#41×C₁₉	—	4	4	no	—
34	C₂×#41×C₁₉	C₂×C₄	1	8	yes	complemented
35	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
36	C₂²×D₄×C₁₉	—	2	2	no	—
37	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₉	—	2	2	no	—
39	C₂³×C₄×C₁₉	—	2	4	no	—
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₁₉×#135	—	2	32	no	—
42	C₂×Q₁₆×C₁₉	—	2	4	no	—
43	C₂×Q₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
44	C₂×SD₁₆×C₁₉	—	2	8	no	—
45	C₂×SD₁₆×C₁₉	C₂×C₄	1	8	yes	complemented
46	C₂×D₈×C₁₉	C₂×C₄	1	4	yes	—
47	C₂×D₈×C₁₉	D₄	1	8	yes	—
48	C₂²×C₈×C₁₉	—	2	4	no	—
49	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	complemented
50	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₄×D₄×C₁₉	—	2	8	no	—
54	C₄×D₄×C₁₉	—	4	4	no	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
59	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
60	C₁₉×#107	—	2	4	no	—
61	C₁₉×#103	—	4	4	no	—
62	C₁₉×#102	—	2	8	no	—
63	C₁₉×C₂²⋊C₈	—	2	2	no	—
64	C₄×C₈×C₁₉	—	2	4	no	—
65	C₁₉×#95	—	2	2	no	—
66	C₁₉×#95	—	2	4	no	—
67	C₁₉×#95	—	2	4	no	—
68	C₁₉×#95	D₄	1	1	yes	characteristic
69	C₁₉×#95	D₄	1	1	yes	characteristic
70	C₂⁴×C₁₉	—	2	2	no	—
71	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
72	#41×C₁₉	—	2	16	no	—
73	#41×C₁₉	—	4	8	no	—
74	#41×C₁₉	—	4	16	no	—
75	C₂×Q₈×C₁₉	—	2	2	no	—
76	C₂×Q₈×C₁₉	—	2	4	no	—
77	C₂×Q₈×C₁₉	—	2	4	no	—
78	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
79	C₂×D₄×C₁₉	—	2	8	no	—
80	C₂×D₄×C₁₉	—	2	2	no	—
81	C₂×D₄×C₁₉	—	2	4	no	—
82	C₂×D₄×C₁₉	—	4	8	no	—
83	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
84	C₂×D₄×C₁₉	C₂×D₄	1	8	yes	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	8	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	4	8	no	—
91	C₂²×C₄×C₁₉	—	4	8	no	—
92	C₂²×C₄×C₁₉	—	4	8	no	—
93	C₂²×C₄×C₁₉	—	8	4	no	—
94	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₉	#41	1	2	yes	—
99	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
100	Q₁₆×C₁₉	—	2	8	no	—
101	SD₁₆×C₁₉	—	2	16	no	—
102	D₈×C₁₉	C₂²⋊C₄	1	16	yes	complemented
103	C₂×C₈×C₁₉	—	2	2	no	—
104	C₂×C₈×C₁₉	—	2	8	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
111	C₄⋊C₄×C₁₉	—	2	4	no	—
112	C₄⋊C₄×C₁₉	—	2	4	no	—
113	C₂²⋊C₄×C₁₉	—	2	4	no	—
114	C₂²⋊C₄×C₁₉	—	4	8	no	—
115	C₂²⋊C₄×C₁₉	—	8	2	no	—
116	C₄²×C₁₉	—	2	2	no	—
117	C₄²×C₁₉	—	2	2	no	—
118	#22448	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂³×C₁₉	—	2	4	no	—
120	C₂³×C₁₉	—	2	8	no	—
121	C₂³×C₁₉	—	2	2	no	—
122	C₂³×C₁₉	—	2	2	no	—
123	C₂³×C₁₉	—	2	1	no	—
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	—	4	4	no	—
126	C₂³×C₁₉	—	4	2	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	C₄×D₄	1	2	yes	—
129	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
130	Q₈×C₁₉	—	2	4	no	—
131	Q₈×C₁₉	—	2	4	no	—
132	Q₈×C₁₉	—	4	4	no	—
133	D₄×C₁₉	—	2	4	no	—
134	D₄×C₁₉	—	2	8	no	—
135	D₄×C₁₉	—	4	16	no	—
136	D₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	2	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	4	no	—
143	C₂×C₄×C₁₉	—	2	4	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	4	16	no	—
148	C₂×C₄×C₁₉	—	4	4	no	—
149	C₂×C₄×C₁₉	—	4	4	no	—
150	C₂×C₄×C₁₉	—	4	4	no	—
151	C₂×C₄×C₁₉	—	4	4	no	—
152	C₂×C₄×C₁₉	—	8	16	no	—
153	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₁₉	#135	1	4	yes	complemented
155	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
157	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
159	C₈×C₁₉	—	2	2	no	—
160	C₈×C₁₉	—	4	2	no	—
161	C₈×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
162	C₂²×#135	C₂×C₁₉	1	1	yes	characteristic
163	C₂×C₄×D₈	C₂×C₁₉	1	2	yes	complemented
164	#2339	C₂×C₁₉	1	2	yes	complemented
165	#1969	C₂×C₁₉	1	2	yes	complemented
166	#1877	C₂×C₁₉	1	4	yes	complemented
167	#1808	C₂×C₁₉	1	1	yes	characteristic, complemented
168	#1788	C₂×C₁₉	1	2	yes	complemented
169	C₈×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
170	C₂²×C₁₉	—	2	2	no	—
171	C₂²×C₁₉	—	2	8	no	—
172	C₂²×C₁₉	—	2	2	no	—
173	C₂²×C₁₉	—	2	2	no	—
174	C₂²×C₁₉	—	4	4	no	—
175	C₂²×C₁₉	—	4	4	no	—
176	C₂²×C₁₉	—	4	8	no	—
177	C₂²×C₁₉	—	4	2	no	—
178	C₂²×C₁₉	—	4	2	no	—
179	C₂²×C₁₉	—	4	8	no	—
180	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
181	C₂²×C₁₉	D₄²	1	2	yes	—
182	C₂²×C₁₉	C₂×#135	1	2	yes	—
183	C₂²×C₁₉	#576	1	1	yes	characteristic
184	C₂²×C₁₉	#578	1	1	yes	characteristic
185	C₄×C₁₉	—	2	2	no	—
186	C₄×C₁₉	—	2	4	no	—
187	C₄×C₁₉	—	4	4	no	—
188	C₄×C₁₉	—	4	2	no	—
189	C₄×C₁₉	—	8	4	no	—
190	C₄×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
191	C₄×C₁₉	#518	1	1	yes	characteristic
192	C₄×C₁₉	#546	1	2	yes	—
193	C₂²×#41	C₂²×C₁₉	1	2	yes	—
194	C₂×#135	—	2	8	no	—
195	C₂×#135	C₄×C₁₉	1	8	yes	complemented
196	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
197	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
198	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
199	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
200	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
201	C₄×D₈	—	2	8	no	—
202	C₂×#107	C₂²×C₁₉	1	2	yes	—
203	C₂×#103	C₂²×C₁₉	1	4	yes	—
204	C₂×#102	C₂²×C₁₉	1	4	yes	—
205	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
207	#391	C₂²×C₁₉	1	4	yes	—
208	#386	—	2	4	no	—
209	#381	—	2	2	no	—
210	#380	C₂²×C₁₉	1	2	yes	—
211	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
212	C₂×#95	—	2	2	no	—
213	#340	C₂²×C₁₉	1	2	yes	—
214	#336	C₂²×C₁₉	1	2	yes	—
215	C₂×C₁₉	—	4	2	no	—
216	C₂×C₁₉	—	4	8	no	—
217	C₂×C₁₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₁₉	C₄×#135	1	1	yes	characteristic
219	C₂×C₁₉	#2951	1	1	yes	characteristic
220	C₂×C₁₉	#3280	1	2	yes	—
221	C₂×C₁₉	#3283	1	2	yes	—
222	C₂×#41	—	2	4	no	—
223	C₂×#41	—	2	8	no	—
224	C₂×#41	—	4	4	no	—
225	C₂×#41	C₂×C₄×C₁₉	1	8	yes	complemented
226	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
227	C₂²×D₄	—	2	2	no	—
228	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
229	C₂³×C₄	—	2	2	no	—
230	C₂³×C₄	—	2	4	no	—
231	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
232	#135	—	2	32	no	—
233	C₂×Q₁₆	—	2	4	no	—
234	C₂×Q₁₆	C₂×C₄×C₁₉	1	4	yes	complemented
235	C₂×SD₁₆	—	2	8	no	—
236	C₂×SD₁₆	C₂×C₄×C₁₉	1	8	yes	complemented
237	C₂×D₈	C₂×C₄×C₁₉	1	4	yes	—
238	C₂×D₈	D₄×C₁₉	1	8	yes	—
239	C₂²×C₈	—	2	4	no	—
240	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	complemented
241	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
242	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
244	C₄×D₄	—	2	8	no	—
245	C₄×D₄	—	4	4	no	—
246	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
247	C₂×C₂²⋊C₄	—	2	4	no	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
250	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
251	#107	—	2	4	no	—
252	#103	—	4	4	no	—
253	#102	—	2	8	no	—
254	C₂²⋊C₈	—	2	2	no	—
255	C₄×C₈	—	2	4	no	—
256	#95	—	2	2	no	—
257	#95	—	2	4	no	—
258	#95	—	2	4	no	—
259	#95	D₄×C₁₉	1	1	yes	characteristic
260	#95	D₄×C₁₉	1	1	yes	characteristic
261	C₁₉	#22448	1	1	yes	characteristic, direct product factor, Sylow
262	C₂⁴	—	2	2	no	—
263	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
264	#41	—	2	16	no	—
265	#41	—	4	8	no	—
266	#41	—	4	16	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
271	C₂×D₄	—	2	8	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
276	C₂×D₄	C₂×D₄×C₁₉	1	8	yes	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	8	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	4	8	no	—
283	C₂²×C₄	—	4	8	no	—
284	C₂²×C₄	—	4	8	no	—
285	C₂²×C₄	—	8	4	no	—
286	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
290	C₂²×C₄	#41×C₁₉	1	2	yes	—
291	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
292	Q₁₆	—	2	8	no	—
293	SD₁₆	—	2	16	no	—
294	D₈	C₂²⋊C₄×C₁₉	1	16	yes	complemented
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	8	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
301	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
302	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₂²⋊C₄	—	2	4	no	—
306	C₂²⋊C₄	—	4	8	no	—
307	C₂²⋊C₄	—	8	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	8	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	C₄×D₄×C₁₉	1	2	yes	—
320	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
321	Q₈	—	2	4	no	—
322	Q₈	—	2	4	no	—
323	Q₈	—	4	4	no	—
324	D₄	—	2	4	no	—
325	D₄	—	2	8	no	—
326	D₄	—	4	16	no	—
327	D₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	16	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	8	16	no	—
344	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
345	C₂×C₄	C₁₉×#135	1	4	yes	complemented
346	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
347	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
348	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
349	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
350	C₈	—	2	2	no	—
351	C₈	—	4	2	no	—
352	C₈	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	8	no	—
357	C₂²	—	4	4	no	—
358	C₂²	—	4	4	no	—
359	C₂²	—	4	8	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	8	no	—
363	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
364	C₂²	D₄²×C₁₉	1	2	yes	—
365	C₂²	C₂×C₁₉×#135	1	2	yes	—
366	C₂²	C₁₉×#576	1	1	yes	characteristic
367	C₂²	C₁₉×#578	1	1	yes	characteristic
368	C₄	—	2	4	no	—
369	C₄	—	2	2	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	4	no	—
372	C₄	—	8	4	no	—
373	C₄	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
374	C₄	C₁₉×#518	1	1	yes	characteristic
375	C₄	C₁₉×#546	1	2	yes	—
376	C₂	—	4	2	no	—
377	C₂	—	4	8	no	—
378	C₂	D₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
379	C₂	C₄×C₁₉×#135	1	1	yes	characteristic
380	C₂	C₁₉×#2951	1	1	yes	characteristic
381	C₂	C₁₉×#3280	1	2	yes	—
382	C₂	C₁₉×#3283	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₂²⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₈×C₁₉	C₂	semidirect
3. C₁₉×#2339	C₂	semidirect
4. C₁₉×#1969	C₂	semidirect
5. C₁₉×#1877	C₂	semidirect
6. C₁₉×#1808	C₂	semidirect
7. C₁₉×#1788	C₂	semidirect
8. C₈×C₂²⋊C₄×C₁₉	C₂	semidirect
11. C₂×C₁₉×#135	C₄	semidirect
34. C₂×#41×C₁₉	C₂×C₄	semidirect
43. C₂×Q₁₆×C₁₉	C₂×C₄	semidirect
45. C₂×SD₁₆×C₁₉	C₂×C₄	semidirect
49. C₂²×C₈×C₁₉	C₂×C₄	semidirect
102. D₈×C₁₉	C₂²⋊C₄	semidirect
118. #22448	C₁₉	direct (N × H)
154. C₂×C₄×C₁₉	#135	semidirect
163. C₂×C₄×D₈	C₂×C₁₉	semidirect
164. #2339	C₂×C₁₉	semidirect
165. #1969	C₂×C₁₉	semidirect
166. #1877	C₂×C₁₉	semidirect
167. #1808	C₂×C₁₉	semidirect
168. #1788	C₂×C₁₉	semidirect
169. C₈×C₂²⋊C₄	C₂×C₁₉	semidirect
195. C₂×#135	C₄×C₁₉	semidirect
225. C₂×#41	C₂×C₄×C₁₉	semidirect
234. C₂×Q₁₆	C₂×C₄×C₁₉	semidirect
236. C₂×SD₁₆	C₂×C₄×C₁₉	semidirect
240. C₂²×C₈	C₂×C₄×C₁₉	semidirect
261. C₁₉	#22448	direct (N × H)
294. D₈	C₂²⋊C₄×C₁₉	semidirect
345. C₂×C₄	C₁₉×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#135	2
C₂×C₄×D₈×C₁₉	2
C₁₉×#2339	2
C₁₉×#1969	2
C₁₉×#1877	2
C₁₉×#1808	2
C₁₉×#1788	2
C₈×C₂²⋊C₄×C₁₉	2
#22448	19

Subgroups — C19×#22448 #18028407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22448 #18028407