Subgroups — C₁₉×#13335 #18019294

Order 4864.

536 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3414	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3156	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2145	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2141	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1976	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1378	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#137	—	2	1	no	—
9	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
11	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#536	—	2	1	no	—
13	C₁₉×#510	—	2	2	no	—
14	C₁₉×#510	—	2	2	no	—
15	C₁₉×#510	—	2	1	no	—
16	C₁₉×#510	—	2	1	no	—
17	C₁₉×#509	—	2	1	no	—
18	C₁₉×#509	—	2	1	no	—
19	C₁₉×#508	—	2	2	no	—
20	C₂×C₁₉×Q₃₂	—	2	1	no	—
21	C₂×C₁₉×SD₃₂	—	2	1	no	—
22	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
24	C₁₉×#497	—	2	2	no	—
25	C₁₉×#495	—	2	1	no	—
26	C₁₉×#494	—	2	1	no	—
27	C₁₉×#427	C₂²	1	1	yes	characteristic
28	C₁₉×#421	—	2	1	no	—
29	C₁₉×#410	—	2	1	no	—
30	C₁₉×#405	C₂²	1	1	yes	characteristic
31	C₁₉×#360	—	2	2	no	—
32	C₁₉×#358	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂×#41×C₁₉	—	2	1	no	—
35	C₂²×Q₈×C₁₉	—	2	1	no	—
36	C₁₉×#137	—	4	2	no	—
37	C₁₉×#137	—	4	2	no	—
38	C₁₉×#135	—	2	1	no	—
39	C₁₉×#135	—	2	1	no	—
40	C₁₉×#135	—	2	1	no	—
41	C₁₉×#135	—	2	1	no	—
42	C₁₉×#135	—	2	1	no	—
43	C₁₉×#135	—	2	1	no	—
44	C₁₉×#135	—	2	1	no	—
45	C₁₉×#135	—	2	1	no	—
46	C₂×Q₁₆×C₁₉	—	2	2	no	—
47	C₂×Q₁₆×C₁₉	—	2	1	no	—
48	C₂×Q₁₆×C₁₉	—	2	1	no	—
49	C₂×Q₁₆×C₁₉	—	2	1	no	—
50	C₂×Q₁₆×C₁₉	—	2	1	no	—
51	C₂×Q₁₆×C₁₉	—	2	1	no	—
52	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
53	C₂×Q₁₆×C₁₉	D₄	1	2	yes	—
54	C₂×Q₁₆×C₁₉	D₄	1	1	yes	characteristic
55	C₂×SD₁₆×C₁₉	—	2	2	no	—
56	C₂×SD₁₆×C₁₉	—	2	1	no	—
57	C₂×SD₁₆×C₁₉	—	2	1	no	—
58	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
59	C₂×D₈×C₁₉	D₄	1	1	yes	characteristic
60	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₁₉×C₄⋊Q₈	—	2	2	no	—
63	C₁₉×#124	—	2	2	no	—
64	C₁₉×#123	—	4	2	no	—
65	C₁₉×C₂²⋊Q₈	—	4	2	no	—
66	C₁₉×#117	—	2	1	no	—
67	C₁₉×#117	D₄	1	1	yes	characteristic
68	C₁₉×Q₃₂	—	2	4	no	—
69	C₁₉×Q₃₂	—	2	2	no	—
70	C₁₉×SD₃₂	—	2	4	no	—
71	C₁₉×SD₃₂	—	2	2	no	—
72	C₁₉×SD₃₂	—	2	2	no	—
73	C₁₉×D₁₆	—	2	2	no	—
74	C₁₉×M₃₂	—	2	1	no	—
75	C₁₉×M₃₂	—	2	1	no	—
76	C₁₉×M₃₂	—	2	1	no	—
77	C₁₉×M₃₂	D₄	1	2	yes	—
78	C₂×C₁₆×C₁₉	—	2	1	no	—
79	C₂×C₁₆×C₁₉	D₄	1	2	yes	—
80	C₁₉×#107	—	2	1	no	—
81	C₁₉×#106	—	2	1	no	—
82	C₁₉×#104	—	4	2	no	—
83	C₁₉×#99	—	4	2	no	—
84	C₁₉×#97	—	2	1	no	—
85	C₄×C₈×C₁₉	—	2	1	no	—
86	#41×C₁₉	—	4	1	no	—
87	#41×C₁₉	—	4	1	no	—
88	#41×C₁₉	—	4	1	no	—
89	#41×C₁₉	—	4	1	no	—
90	#41×C₁₉	—	4	1	no	—
91	#41×C₁₉	—	4	1	no	—
92	#41×C₁₉	—	4	1	no	—
93	#41×C₁₉	—	4	1	no	—
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	2	1	no	—
96	C₂×Q₈×C₁₉	—	2	1	no	—
97	C₂×Q₈×C₁₉	—	4	1	no	—
98	C₂×Q₈×C₁₉	—	4	1	no	—
99	C₂×Q₈×C₁₉	—	4	1	no	—
100	C₂×Q₈×C₁₉	—	4	1	no	—
101	C₂×Q₈×C₁₉	—	4	1	no	—
102	C₂×D₄×C₁₉	—	2	1	no	—
103	C₂×D₄×C₁₉	—	2	1	no	—
104	C₂×D₄×C₁₉	—	4	1	no	—
105	C₂×D₄×C₁₉	—	4	1	no	—
106	C₂²×C₄×C₁₉	—	4	1	no	—
107	C₂²×C₄×C₁₉	—	4	1	no	—
108	C₂²×C₄×C₁₉	—	4	1	no	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	Q₁₆×C₁₉	—	2	2	no	—
111	Q₁₆×C₁₉	—	2	1	no	—
112	Q₁₆×C₁₉	—	2	1	no	—
113	Q₁₆×C₁₉	—	2	1	no	—
114	Q₁₆×C₁₉	—	2	2	no	—
115	Q₁₆×C₁₉	—	2	1	no	—
116	Q₁₆×C₁₉	—	4	4	no	—
117	Q₁₆×C₁₉	—	4	1	no	—
118	Q₁₆×C₁₉	—	4	1	no	—
119	SD₁₆×C₁₉	—	4	4	no	—
120	SD₁₆×C₁₉	—	4	1	no	—
121	SD₁₆×C₁₉	—	4	1	no	—
122	SD₁₆×C₁₉	—	4	1	no	—
123	SD₁₆×C₁₉	—	4	1	no	—
124	D₈×C₁₉	—	2	1	no	—
125	D₈×C₁₉	—	2	1	no	—
126	D₈×C₁₉	—	2	1	no	—
127	D₈×C₁₉	—	2	1	no	—
128	M₁₆×C₁₉	—	2	1	no	—
129	M₁₆×C₁₉	D₈	1	2	yes	—
130	C₂×C₈×C₁₉	—	2	1	no	—
131	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	4	4	no	—
139	C₄⋊C₄×C₁₉	—	4	1	no	—
140	C₂²⋊C₄×C₁₉	—	4	4	no	—
141	C₂²⋊C₄×C₁₉	—	4	1	no	—
142	C₂²⋊C₄×C₁₉	D₈	1	2	yes	—
143	C₄²×C₁₉	—	2	1	no	—
144	C₄²×C₁₉	—	4	1	no	—
145	C₁₆×C₁₉	—	2	2	no	—
146	C₁₆×C₁₉	—	2	2	no	—
147	#13335	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
151	Q₈×C₁₉	—	4	1	no	—
152	Q₈×C₁₉	—	4	1	no	—
153	Q₈×C₁₉	—	4	2	no	—
154	Q₈×C₁₉	—	4	2	no	—
155	Q₈×C₁₉	—	4	1	no	—
156	Q₈×C₁₉	—	4	1	no	—
157	Q₈×C₁₉	—	8	1	no	—
158	Q₈×C₁₉	—	8	1	no	—
159	D₄×C₁₉	—	4	1	no	—
160	D₄×C₁₉	—	4	1	no	—
161	D₄×C₁₉	—	4	1	no	—
162	D₄×C₁₉	—	4	1	no	—
163	D₄×C₁₉	—	8	1	no	—
164	D₄×C₁₉	—	8	1	no	—
165	D₄×C₁₉	—	8	1	no	—
166	D₄×C₁₉	—	8	1	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	8	1	no	—
172	C₂×C₄×C₁₉	—	8	1	no	—
173	C₂×C₄×C₁₉	—	8	1	no	—
174	C₂×C₄×C₁₉	—	8	1	no	—
175	C₂×C₄×C₁₉	—	8	1	no	—
176	C₂×C₄×C₁₉	—	8	1	no	—
177	C₂×C₄×C₁₉	—	8	1	no	—
178	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
182	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₈×C₁₉	—	2	2	no	—
185	C₈×C₁₉	#120	1	1	yes	characteristic
186	C₈×C₁₉	#120	1	1	yes	characteristic
187	C₈×C₁₉	#121	1	1	yes	characteristic
188	C₈×C₁₉	#121	1	1	yes	characteristic
189	#3414	C₂×C₁₉	1	1	yes	characteristic
190	C₂×#510	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#3156	C₂×C₁₉	1	1	yes	characteristic, complemented
192	#2145	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#2141	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#1976	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#1378	C₂×C₁₉	1	1	yes	characteristic, complemented
196	C₂²×C₁₉	—	4	1	no	—
197	C₂²×C₁₉	—	8	2	no	—
198	C₂²×C₁₉	—	8	1	no	—
199	C₂²×C₁₉	—	8	1	no	—
200	C₂²×C₁₉	—	16	1	no	—
201	C₂²×C₁₉	#447	1	1	yes	characteristic
202	C₂²×C₁₉	#459	1	1	yes	characteristic
203	C₂²×C₁₉	#493	1	1	yes	characteristic
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	—	8	1	no	—
206	C₄×C₁₉	—	8	1	no	—
207	C₄×C₁₉	—	8	2	no	—
208	C₄×C₁₉	—	16	1	no	—
209	C₄×C₁₉	#392	1	1	yes	characteristic
210	C₄×C₁₉	#447	1	1	yes	characteristic
211	C₄×C₁₉	#459	1	1	yes	characteristic
212	C₄×C₁₉	#496	1	1	yes	characteristic
213	C₂×#137	—	2	1	no	—
214	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
215	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
216	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
217	#536	—	2	1	no	—
218	#510	—	2	2	no	—
219	#510	—	2	1	no	—
220	#510	—	2	1	no	—
221	#510	—	2	2	no	—
222	#509	—	2	1	no	—
223	#509	—	2	1	no	—
224	#508	—	2	2	no	—
225	C₂×Q₃₂	—	2	1	no	—
226	C₂×SD₃₂	—	2	1	no	—
227	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
229	#497	—	2	2	no	—
230	#495	—	2	1	no	—
231	#494	—	2	1	no	—
232	#427	C₂²×C₁₉	1	1	yes	characteristic
233	#421	—	2	1	no	—
234	#410	—	2	1	no	—
235	#405	C₂²×C₁₉	1	1	yes	characteristic
236	#360	—	2	2	no	—
237	#358	—	2	2	no	—
238	C₂×C₁₉	—	2	1	no	—
239	C₂×C₁₉	—	2	1	no	—
240	C₂×C₁₉	—	2	1	no	—
241	C₂×C₁₉	—	16	1	no	—
242	C₂×C₁₉	—	16	1	no	—
243	C₂×C₁₉	#2011	1	1	yes	characteristic
244	C₂×#41	—	2	1	no	—
245	C₂×#41	—	2	1	no	—
246	C₂²×Q₈	—	2	1	no	—
247	#137	—	4	2	no	—
248	#137	—	4	2	no	—
249	#135	—	2	1	no	—
250	#135	—	2	1	no	—
251	#135	—	2	1	no	—
252	#135	—	2	1	no	—
253	#135	—	2	1	no	—
254	#135	—	2	1	no	—
255	#135	—	2	1	no	—
256	#135	—	2	1	no	—
257	C₂×Q₁₆	—	2	2	no	—
258	C₂×Q₁₆	—	2	1	no	—
259	C₂×Q₁₆	—	2	1	no	—
260	C₂×Q₁₆	—	2	1	no	—
261	C₂×Q₁₆	—	2	1	no	—
262	C₂×Q₁₆	—	2	1	no	—
263	C₂×Q₁₆	D₄×C₁₉	1	2	yes	—
264	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
265	C₂×Q₁₆	D₄×C₁₉	1	1	yes	characteristic
266	C₂×SD₁₆	—	2	2	no	—
267	C₂×SD₁₆	—	2	1	no	—
268	C₂×SD₁₆	—	2	1	no	—
269	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
270	C₂×D₈	D₄×C₁₉	1	1	yes	characteristic
271	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
273	C₄⋊Q₈	—	2	2	no	—
274	#124	—	2	2	no	—
275	#123	—	4	2	no	—
276	C₂²⋊Q₈	—	4	2	no	—
277	#117	—	2	1	no	—
278	#117	D₄×C₁₉	1	1	yes	characteristic
279	Q₃₂	—	2	4	no	—
280	Q₃₂	—	2	2	no	—
281	SD₃₂	—	2	4	no	—
282	SD₃₂	—	2	2	no	—
283	SD₃₂	—	2	2	no	—
284	D₁₆	—	2	2	no	—
285	M₃₂	—	2	1	no	—
286	M₃₂	—	2	1	no	—
287	M₃₂	—	2	1	no	—
288	M₃₂	D₄×C₁₉	1	2	yes	—
289	C₂×C₁₆	—	2	1	no	—
290	C₂×C₁₆	D₄×C₁₉	1	2	yes	—
291	#107	—	2	1	no	—
292	#106	—	2	1	no	—
293	#104	—	4	2	no	—
294	#99	—	4	2	no	—
295	#97	—	2	1	no	—
296	C₄×C₈	—	2	1	no	—
297	C₁₉	#13335	1	1	yes	characteristic, direct product factor, Sylow
298	#41	—	4	1	no	—
299	#41	—	4	1	no	—
300	#41	—	4	1	no	—
301	#41	—	4	1	no	—
302	#41	—	4	1	no	—
303	#41	—	4	1	no	—
304	#41	—	4	1	no	—
305	#41	—	4	1	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	4	1	no	—
310	C₂×Q₈	—	4	1	no	—
311	C₂×Q₈	—	4	1	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×Q₈	—	4	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
322	Q₁₆	—	2	2	no	—
323	Q₁₆	—	2	1	no	—
324	Q₁₆	—	2	1	no	—
325	Q₁₆	—	2	1	no	—
326	Q₁₆	—	2	2	no	—
327	Q₁₆	—	2	1	no	—
328	Q₁₆	—	4	4	no	—
329	Q₁₆	—	4	1	no	—
330	Q₁₆	—	4	1	no	—
331	SD₁₆	—	4	4	no	—
332	SD₁₆	—	4	1	no	—
333	SD₁₆	—	4	1	no	—
334	SD₁₆	—	4	1	no	—
335	SD₁₆	—	4	1	no	—
336	D₈	—	2	1	no	—
337	D₈	—	2	1	no	—
338	D₈	—	2	1	no	—
339	D₈	—	2	1	no	—
340	M₁₆	—	2	1	no	—
341	M₁₆	D₈×C₁₉	1	2	yes	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
344	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
347	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
348	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	4	4	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₂²⋊C₄	—	4	4	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	D₈×C₁₉	1	2	yes	—
355	C₄²	—	2	1	no	—
356	C₄²	—	4	1	no	—
357	C₁₆	—	2	2	no	—
358	C₁₆	—	2	2	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	1	no	—
361	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
362	Q₈	—	4	1	no	—
363	Q₈	—	4	1	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	1	no	—
367	Q₈	—	4	1	no	—
368	Q₈	—	8	1	no	—
369	Q₈	—	8	1	no	—
370	D₄	—	4	1	no	—
371	D₄	—	4	1	no	—
372	D₄	—	4	1	no	—
373	D₄	—	4	1	no	—
374	D₄	—	8	1	no	—
375	D₄	—	8	1	no	—
376	D₄	—	8	1	no	—
377	D₄	—	8	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	8	1	no	—
383	C₂×C₄	—	8	1	no	—
384	C₂×C₄	—	8	1	no	—
385	C₂×C₄	—	8	1	no	—
386	C₂×C₄	—	8	1	no	—
387	C₂×C₄	—	8	1	no	—
388	C₂×C₄	—	8	1	no	—
389	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
390	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
391	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
392	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
393	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	C₁₉×#120	1	1	yes	characteristic
397	C₈	C₁₉×#120	1	1	yes	characteristic
398	C₈	C₁₉×#121	1	1	yes	characteristic
399	C₈	C₁₉×#121	1	1	yes	characteristic
400	C₂²	—	4	1	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	16	1	no	—
405	C₂²	C₁₉×#447	1	1	yes	characteristic
406	C₂²	C₁₉×#459	1	1	yes	characteristic
407	C₂²	C₁₉×#493	1	1	yes	characteristic
408	C₄	—	4	2	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	2	no	—
412	C₄	—	16	1	no	—
413	C₄	C₁₉×#392	1	1	yes	characteristic
414	C₄	C₁₉×#447	1	1	yes	characteristic
415	C₄	C₁₉×#459	1	1	yes	characteristic
416	C₄	C₁₉×#496	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	16	1	no	—
421	C₂	—	16	1	no	—
422	C₂	C₁₉×#2011	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2011
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₁₉×#3414	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#405 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#510	C₂	semidirect
3. C₁₉×#3156	C₂	semidirect
4. C₁₉×#2145	C₂	semidirect
5. C₁₉×#2141	C₂	semidirect
6. C₁₉×#1976	C₂	semidirect
7. C₁₉×#1378	C₂	semidirect
147. #13335	C₁₉	direct (N × H)
190. C₂×#510	C₂×C₁₉	semidirect
191. #3156	C₂×C₁₉	semidirect
192. #2145	C₂×C₁₉	semidirect
193. #2141	C₂×C₁₉	semidirect
194. #1976	C₂×C₁₉	semidirect
195. #1378	C₂×C₁₉	semidirect
297. C₁₉	#13335	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×#3414	2
C₂×C₁₉×#510	2
C₁₉×#3156	2
C₁₉×#2145	2
C₁₉×#2141	2
C₁₉×#1976	2
C₁₉×#1378	2
#13335	19

Subgroups — C19×#13335 #18019294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13335 #18019294