Subgroups — C₁₉×#32784 #18038743

Order 4864.

644 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2629	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2621	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2096	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2095	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2085	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2043	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2036	C₂	1	2	yes	maximal
8	C₁₉×#2035	C₂	1	2	yes	maximal
9	C₁₉×#2026	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2026	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1818	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#107	C₂²	1	2	yes	—
18	C₂×C₁₉×#106	C₂²	1	2	yes	—
19	C₂×C₁₉×#103	C₂²	1	2	yes	—
20	C₂×C₁₉×#103	C₂²	1	2	yes	—
21	C₂×C₁₉×#103	C₂²	1	2	yes	—
22	C₂×C₁₉×#103	C₂²	1	2	yes	—
23	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₁₉×#398	—	2	2	no	—
25	C₁₉×#398	—	2	2	no	—
26	C₁₉×#397	—	2	2	no	—
27	C₁₉×#396	—	2	2	no	—
28	C₁₉×#391	C₂²	1	1	yes	characteristic
29	C₁₉×#391	C₂²	1	1	yes	characteristic
30	C₁₉×#389	C₂²	1	2	yes	—
31	C₁₉×#384	C₂²	1	1	yes	characteristic
32	C₁₉×#382	C₂²	1	1	yes	characteristic
33	C₁₉×#380	C₂²	1	2	yes	—
34	C₁₉×#340	C₂²	1	2	yes	—
35	C₁₉×#340	C₂²	1	2	yes	—
36	C₁₉×#336	C₂²	1	1	yes	characteristic
37	C₁₉×#336	C₂²	1	1	yes	characteristic
38	C₁₉×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
44	C₁₉×C₄⋊Q₈	—	4	2	no	—
45	C₁₉×#125	—	4	2	no	—
46	C₁₉×C₂²⋊Q₈	—	4	2	no	—
47	C₁₉×C₂²⋊Q₈	—	4	2	no	—
48	C₁₉×#117	—	4	2	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
64	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
66	C₁₉×#107	—	4	2	no	—
67	C₁₉×#106	—	4	2	no	—
68	C₁₉×#103	—	4	2	no	—
69	C₁₉×#103	—	4	2	no	—
70	C₁₉×#103	—	4	2	no	—
71	C₁₉×#103	—	4	2	no	—
72	C₁₉×C₂²⋊C₈	—	4	2	no	—
73	C₁₉×#95	—	2	2	no	—
74	C₁₉×#95	—	2	2	no	—
75	C₁₉×#95	—	2	2	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₁₉	—	2	2	no	—
80	C₂×Q₈×C₁₉	—	2	2	no	—
81	C₂×Q₈×C₁₉	—	2	2	no	—
82	C₂×Q₈×C₁₉	—	2	2	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₁₉	—	2	2	no	—
102	C₂×C₈×C₁₉	—	2	2	no	—
103	C₂×C₈×C₁₉	—	2	2	no	—
104	C₂×C₈×C₁₉	—	2	2	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₄⋊C₄×C₁₉	—	2	2	no	—
108	C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	—	2	2	no	—
110	C₄⋊C₄×C₁₉	—	2	2	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	4	2	no	—
114	C₄⋊C₄×C₁₉	—	4	2	no	—
115	C₄⋊C₄×C₁₉	—	4	2	no	—
116	C₄⋊C₄×C₁₉	—	4	4	no	—
117	C₄⋊C₄×C₁₉	—	4	4	no	—
118	C₄⋊C₄×C₁₉	—	8	2	no	—
119	C₄⋊C₄×C₁₉	—	8	2	no	—
120	C₂²⋊C₄×C₁₉	—	4	2	no	—
121	C₂²⋊C₄×C₁₉	—	4	2	no	—
122	C₂²⋊C₄×C₁₉	—	4	2	no	—
123	C₂²⋊C₄×C₁₉	—	8	2	no	—
124	C₄²×C₁₉	—	2	2	no	—
125	C₄²×C₁₉	—	2	2	no	—
126	#32784	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₁₉	—	2	1	no	—
128	C₂³×C₁₉	—	2	1	no	—
129	C₂³×C₁₉	—	2	1	no	—
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	2	2	no	—
132	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
133	Q₈×C₁₉	—	4	2	no	—
134	Q₈×C₁₉	—	4	2	no	—
135	Q₈×C₁₉	—	4	2	no	—
136	Q₈×C₁₉	—	4	2	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	2	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	2	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	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	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	2	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
165	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
166	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
167	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
168	C₈×C₁₉	—	4	2	no	—
169	C₈×C₁₉	—	4	2	no	—
170	#2629	C₂×C₁₉	1	1	yes	characteristic
171	#2621	C₂×C₁₉	1	1	yes	characteristic
172	#2096	C₂×C₁₉	1	1	yes	characteristic, complemented
173	#2095	C₂×C₁₉	1	1	yes	characteristic, complemented
174	#2085	C₂×C₁₉	1	2	yes	complemented
175	#2043	C₂×C₁₉	1	2	yes	complemented
176	#2036	C₂×C₁₉	1	2	yes	—
177	#2035	C₂×C₁₉	1	2	yes	—
178	#2026	C₂×C₁₉	1	1	yes	characteristic, complemented
179	#2026	C₂×C₁₉	1	1	yes	characteristic, complemented
180	#1818	C₂×C₁₉	1	1	yes	characteristic
181	C₂²×C₁₉	—	4	1	no	—
182	C₂²×C₁₉	—	4	2	no	—
183	C₂²×C₁₉	—	4	1	no	—
184	C₂²×C₁₉	—	4	1	no	—
185	C₂²×C₁₉	—	4	2	no	—
186	C₂²×C₁₉	#534	1	1	yes	characteristic
187	C₂²×C₁₉	#535	1	1	yes	characteristic
188	C₂²×C₁₉	#536	1	1	yes	characteristic
189	C₂²×C₁₉	#577	1	2	yes	—
190	C₂²×C₁₉	#578	1	2	yes	—
191	C₄×C₁₉	—	4	1	no	—
192	C₄×C₁₉	—	4	2	no	—
193	C₄×C₁₉	—	4	2	no	—
194	C₄×C₁₉	—	8	1	no	—
195	C₄×C₁₉	—	8	1	no	—
196	C₄×C₁₉	—	8	2	no	—
197	C₄×C₁₉	—	8	1	no	—
198	C₄×C₁₉	—	8	2	no	—
199	C₄×C₁₉	—	8	1	no	—
200	C₄×C₁₉	#562	1	2	yes	—
201	C₄×C₁₉	#562	1	2	yes	—
202	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
203	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
204	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
205	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
206	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
207	C₂×#107	C₂²×C₁₉	1	2	yes	—
208	C₂×#106	C₂²×C₁₉	1	2	yes	—
209	C₂×#103	C₂²×C₁₉	1	2	yes	—
210	C₂×#103	C₂²×C₁₉	1	2	yes	—
211	C₂×#103	C₂²×C₁₉	1	2	yes	—
212	C₂×#103	C₂²×C₁₉	1	2	yes	—
213	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
214	#398	—	2	2	no	—
215	#398	—	2	2	no	—
216	#397	—	2	2	no	—
217	#396	—	2	2	no	—
218	#391	C₂²×C₁₉	1	1	yes	characteristic
219	#391	C₂²×C₁₉	1	1	yes	characteristic
220	#389	C₂²×C₁₉	1	2	yes	—
221	#384	C₂²×C₁₉	1	1	yes	characteristic
222	#382	C₂²×C₁₉	1	1	yes	characteristic
223	#380	C₂²×C₁₉	1	2	yes	—
224	#340	C₂²×C₁₉	1	2	yes	—
225	#340	C₂²×C₁₉	1	2	yes	—
226	#336	C₂²×C₁₉	1	2	yes	—
227	#336	C₂²×C₁₉	1	1	yes	characteristic
228	#336	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×C₁₉	—	8	1	no	—
230	C₂×C₁₉	#2816	1	1	yes	characteristic
231	C₂×C₁₉	#3201	1	2	yes	—
232	C₂×C₁₉	#3221	1	1	yes	characteristic
233	C₂×C₁₉	#3223	1	1	yes	characteristic
234	C₂×C₁₉	#3242	1	2	yes	—
235	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
236	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
239	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
240	C₄⋊Q₈	—	4	2	no	—
241	#125	—	4	2	no	—
242	C₂²⋊Q₈	—	4	2	no	—
243	C₂²⋊Q₈	—	4	2	no	—
244	#117	—	4	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
256	C₂×C₂²⋊C₄	—	2	1	no	—
257	C₂×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
260	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
262	#107	—	4	2	no	—
263	#106	—	4	2	no	—
264	#103	—	4	2	no	—
265	#103	—	4	2	no	—
266	#103	—	4	2	no	—
267	#103	—	4	2	no	—
268	C₂²⋊C₈	—	4	2	no	—
269	#95	—	2	2	no	—
270	#95	—	2	2	no	—
271	#95	—	2	2	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	C₁₉	#32784	1	1	yes	characteristic, direct product factor, Sylow
275	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
297	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	4	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	8	2	no	—
316	C₄⋊C₄	—	8	2	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	8	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
329	Q₈	—	4	2	no	—
330	Q₈	—	4	2	no	—
331	Q₈	—	4	2	no	—
332	Q₈	—	4	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
361	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
362	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
363	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
364	C₈	—	4	2	no	—
365	C₈	—	4	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	1	no	—
371	C₂²	C₁₉×#534	1	1	yes	characteristic
372	C₂²	C₁₉×#535	1	1	yes	characteristic
373	C₂²	C₁₉×#536	1	1	yes	characteristic
374	C₂²	C₁₉×#577	1	2	yes	—
375	C₂²	C₁₉×#578	1	2	yes	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	1	no	—
379	C₄	—	8	2	no	—
380	C₄	—	8	1	no	—
381	C₄	—	8	2	no	—
382	C₄	—	8	1	no	—
383	C₄	—	8	1	no	—
384	C₄	—	8	1	no	—
385	C₄	C₁₉×#562	1	2	yes	—
386	C₄	C₁₉×#562	1	2	yes	—
387	C₂	—	8	1	no	—
388	C₂	C₁₉×#2816	1	1	yes	characteristic
389	C₂	C₁₉×#3201	1	2	yes	—
390	C₂	C₁₉×#3221	1	1	yes	characteristic
391	C₂	C₁₉×#3223	1	1	yes	characteristic
392	C₂	C₁₉×#3242	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2096	C₂	semidirect
4. C₁₉×#2095	C₂	semidirect
5. C₁₉×#2085	C₂	semidirect
6. C₁₉×#2043	C₂	semidirect
9. C₁₉×#2026	C₂	semidirect
10. C₁₉×#2026	C₂	semidirect
126. #32784	C₁₉	direct (N × H)
172. #2096	C₂×C₁₉	semidirect
173. #2095	C₂×C₁₉	semidirect
174. #2085	C₂×C₁₉	semidirect
175. #2043	C₂×C₁₉	semidirect
178. #2026	C₂×C₁₉	semidirect
179. #2026	C₂×C₁₉	semidirect
274. C₁₉	#32784	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×#2629	2
C₁₉×#2621	2
C₁₉×#2096	2
C₁₉×#2095	2
C₁₉×#2085	2
C₁₉×#2043	2
C₁₉×#2036	2
C₁₉×#2035	2
C₁₉×#2026	2
C₁₉×#1818	2
#32784	19

Subgroups — C19×#32784 #18038743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32784 #18038743