Subgroups — C₁₉×#32644 #18038603

Order 4864.

662 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×#2568	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2546	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2068	C₂	1	2	yes	maximal
4	C₁₉×#2043	C₂	1	2	yes	maximal
5	C₁₉×#2024	C₂	1	2	yes	maximal
6	C₁₉×#1985	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1935	C₂	1	2	yes	maximal
8	C₁₉×#1928	C₂	1	2	yes	maximal
9	C₁₉×#1918	C₂	1	2	yes	maximal
10	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
11	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#107	C₂²	1	2	yes	—
15	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#103	C₂²	1	2	yes	—
17	C₂×C₁₉×#103	C₂²	1	2	yes	—
18	C₂×C₁₉×#103	C₂²	1	2	yes	—
19	C₂×C₁₉×#103	C₂²	1	2	yes	—
20	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
21	C₁₉×#400	—	2	1	no	—
22	C₁₉×#400	—	2	1	no	—
23	C₁₉×#398	—	2	1	no	—
24	C₁₉×#398	—	2	1	no	—
25	C₁₉×#391	—	2	1	no	—
26	C₁₉×#391	—	2	1	no	—
27	C₁₉×#391	C₂²	1	2	yes	—
28	C₁₉×#391	C₂²	1	2	yes	—
29	C₁₉×#389	C₂²	1	2	yes	—
30	C₁₉×#389	C₂²	1	2	yes	—
31	C₁₉×#382	—	2	1	no	—
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#340	C₂²	1	2	yes	—
35	C₁₉×#340	C₂²	1	2	yes	—
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₁₉×#336	C₂²	1	2	yes	—
38	C₁₉×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₉	—	2	1	no	—
40	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
44	C₁₉×C₄⋊Q₈	—	4	1	no	—
45	C₁₉×C₄⋊Q₈	—	4	1	no	—
46	C₁₉×C₄⋊Q₈	—	4	1	no	—
47	C₁₉×C₄⋊Q₈	—	4	1	no	—
48	C₁₉×C₄⋊Q₈	—	4	4	no	—
49	C₄×Q₈×C₁₉	—	4	1	no	—
50	C₄×Q₈×C₁₉	—	4	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₄²×C₁₉	—	2	1	no	—
63	C₂×C₄²×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
67	C₁₉×#107	—	2	4	no	—
68	C₁₉×C₄⋊C₈	—	4	1	no	—
69	C₁₉×#103	—	2	4	no	—
70	C₁₉×#103	—	2	4	no	—
71	C₁₉×#103	—	4	2	no	—
72	C₁₉×#103	—	4	2	no	—
73	C₁₉×#97	—	4	1	no	—
74	C₁₉×#95	—	2	1	no	—
75	C₁₉×#95	—	2	1	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₁₉×#95	—	2	2	no	—
81	C₁₉×#95	—	2	2	no	—
82	C₂×Q₈×C₁₉	—	2	2	no	—
83	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	2	2	no	—
87	C₂×Q₈×C₁₉	—	2	2	no	—
88	C₂×Q₈×C₁₉	—	2	2	no	—
89	C₂×Q₈×C₁₉	—	2	2	no	—
90	C₂×Q₈×C₁₉	—	4	1	no	—
91	C₂×Q₈×C₁₉	—	4	2	no	—
92	C₂×Q₈×C₁₉	—	4	2	no	—
93	C₂×Q₈×C₁₉	—	4	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	4	1	no	—
117	C₄⋊C₄×C₁₉	—	4	1	no	—
118	C₄⋊C₄×C₁₉	—	4	1	no	—
119	C₄⋊C₄×C₁₉	—	4	2	no	—
120	C₄⋊C₄×C₁₉	—	4	2	no	—
121	C₄⋊C₄×C₁₉	—	4	2	no	—
122	C₄⋊C₄×C₁₉	—	4	4	no	—
123	C₄⋊C₄×C₁₉	—	4	4	no	—
124	C₄⋊C₄×C₁₉	#41	1	4	yes	—
125	C₄²×C₁₉	—	2	1	no	—
126	C₄²×C₁₉	—	2	1	no	—
127	C₄²×C₁₉	—	2	1	no	—
128	C₄²×C₁₉	—	2	1	no	—
129	C₄²×C₁₉	—	2	1	no	—
130	C₄²×C₁₉	—	2	1	no	—
131	C₄²×C₁₉	—	4	2	no	—
132	C₄²×C₁₉	—	4	2	no	—
133	#32644	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₁₉	—	4	4	no	—
136	Q₈×C₁₉	—	4	2	no	—
137	Q₈×C₁₉	—	4	2	no	—
138	Q₈×C₁₉	—	4	2	no	—
139	Q₈×C₁₉	—	4	2	no	—
140	Q₈×C₁₉	—	8	4	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	2	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	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
167	C₂×C₄×C₁₉	#137	1	2	yes	—
168	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
169	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
172	C₈×C₁₉	—	4	2	no	—
173	C₈×C₁₉	—	4	2	no	—
174	#2568	C₂×C₁₉	1	1	yes	characteristic
175	#2546	C₂×C₁₉	1	1	yes	characteristic
176	#2068	C₂×C₁₉	1	2	yes	—
177	#2043	C₂×C₁₉	1	2	yes	—
178	#2024	C₂×C₁₉	1	2	yes	—
179	#1985	C₂×C₁₉	1	1	yes	characteristic
180	#1935	C₂×C₁₉	1	2	yes	—
181	#1928	C₂×C₁₉	1	2	yes	—
182	#1918	C₂×C₁₉	1	2	yes	—
183	C₂²×C₁₉	#534	1	1	yes	characteristic
184	C₂²×C₁₉	#548	1	2	yes	—
185	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
187	C₂²×C₁₉	#578	1	2	yes	—
188	C₄×C₁₉	—	2	2	no	—
189	C₄×C₁₉	—	2	2	no	—
190	C₄×C₁₉	—	4	4	no	—
191	C₄×C₁₉	—	4	1	no	—
192	C₄×C₁₉	—	4	1	no	—
193	C₄×C₁₉	—	4	1	no	—
194	C₄×C₁₉	—	4	1	no	—
195	C₄×C₁₉	—	8	2	no	—
196	C₄×C₁₉	—	8	2	no	—
197	C₄×C₁₉	—	8	2	no	—
198	C₄×C₁₉	#542	1	2	yes	—
199	C₄×C₁₉	#555	1	1	yes	characteristic
200	C₄×C₁₉	#563	1	1	yes	characteristic
201	C₂×C₄⋊Q₈	—	2	1	no	—
202	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
203	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
204	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
205	C₂×#107	C₂²×C₁₉	1	2	yes	—
206	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
207	C₂×#103	C₂²×C₁₉	1	2	yes	—
208	C₂×#103	C₂²×C₁₉	1	2	yes	—
209	C₂×#103	C₂²×C₁₉	1	2	yes	—
210	C₂×#103	C₂²×C₁₉	1	2	yes	—
211	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
212	#400	—	2	1	no	—
213	#400	—	2	1	no	—
214	#398	—	2	1	no	—
215	#398	—	2	1	no	—
216	#391	—	2	1	no	—
217	#391	—	2	1	no	—
218	#391	C₂²×C₁₉	1	2	yes	—
219	#391	C₂²×C₁₉	1	2	yes	—
220	#389	C₂²×C₁₉	1	2	yes	—
221	#389	C₂²×C₁₉	1	2	yes	—
222	#382	—	2	1	no	—
223	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
224	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
225	#340	C₂²×C₁₉	1	2	yes	—
226	#340	C₂²×C₁₉	1	2	yes	—
227	#340	C₂²×C₁₉	1	2	yes	—
228	#336	C₂²×C₁₉	1	2	yes	—
229	#336	C₂²×C₁₉	1	2	yes	—
230	C₂×C₁₉	#2731	1	1	yes	characteristic
231	C₂×C₁₉	#3193	1	1	yes	characteristic
232	C₂×C₁₉	#3202	1	1	yes	characteristic
233	C₂×C₁₉	#3367	1	2	yes	—
234	C₂×C₁₉	#3374	1	2	yes	—
235	C₂²×Q₈	—	2	1	no	—
236	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
237	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
238	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
239	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
240	C₄⋊Q₈	—	4	1	no	—
241	C₄⋊Q₈	—	4	1	no	—
242	C₄⋊Q₈	—	4	1	no	—
243	C₄⋊Q₈	—	4	1	no	—
244	C₄⋊Q₈	—	4	4	no	—
245	C₄×Q₈	—	4	1	no	—
246	C₄×Q₈	—	4	1	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
253	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
254	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	—	2	1	no	—
260	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
263	#107	—	2	4	no	—
264	C₄⋊C₈	—	4	1	no	—
265	#103	—	2	4	no	—
266	#103	—	2	4	no	—
267	#103	—	4	2	no	—
268	#103	—	4	2	no	—
269	#97	—	4	1	no	—
270	#95	—	2	1	no	—
271	#95	—	2	1	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	C₁₉	#32644	1	1	yes	characteristic, direct product factor, Sylow
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
301	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	4	4	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	#41×C₁₉	1	4	yes	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	4	2	no	—
329	C₄²	—	4	2	no	—
330	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
331	Q₈	—	4	4	no	—
332	Q₈	—	4	2	no	—
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	2	no	—
336	Q₈	—	8	4	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	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	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
363	C₂×C₄	C₁₉×#137	1	2	yes	—
364	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
365	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
367	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
368	C₈	—	4	2	no	—
369	C₈	—	4	2	no	—
370	C₂²	C₁₉×#534	1	1	yes	characteristic
371	C₂²	C₁₉×#548	1	2	yes	—
372	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
373	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
374	C₂²	C₁₉×#578	1	2	yes	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	1	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	4	no	—
382	C₄	—	8	2	no	—
383	C₄	—	8	2	no	—
384	C₄	—	8	2	no	—
385	C₄	C₁₉×#542	1	2	yes	—
386	C₄	C₁₉×#555	1	1	yes	characteristic
387	C₄	C₁₉×#563	1	1	yes	characteristic
388	C₂	C₁₉×#2731	1	1	yes	characteristic
389	C₂	C₁₉×#3193	1	1	yes	characteristic
390	C₂	C₁₉×#3202	1	1	yes	characteristic
391	C₂	C₁₉×#3367	1	2	yes	—
392	C₂	C₁₉×#3374	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
133. #32644	C₁₉	direct (N × H)
278. C₁₉	#32644	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×#2568	2
C₁₉×#2546	2
C₁₉×#2068	2
C₁₉×#2043	2
C₁₉×#2024	2
C₁₉×#1985	2
C₁₉×#1935	2
C₁₉×#1928	2
C₁₉×#1918	2
#32644	19

Subgroups — C19×#32644 #18038603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32644 #18038603