Subgroups — C₁₉×#10194 #18016153

Order 4864.

640 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3151	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1982	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1502	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1283	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
9	C₁₉×#533	C₂²	1	1	yes	characteristic
10	C₁₉×#532	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
12	C₁₉×#496	—	2	2	no	—
13	C₁₉×#493	—	2	1	no	—
14	C₁₉×#492	—	2	1	no	—
15	C₁₉×#492	—	2	1	no	—
16	C₁₉×#486	—	2	1	no	—
17	C₁₉×#476	—	2	1	no	—
18	C₁₉×#475	—	2	1	no	—
19	C₁₉×#465	—	2	2	no	—
20	C₁₉×#461	—	2	1	no	—
21	C₁₉×#460	—	2	2	no	—
22	C₁₉×#460	—	2	1	no	—
23	C₁₉×#450	—	2	2	no	—
24	C₁₉×#431	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#102	—	2	2	no	—
27	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#339	—	2	2	no	—
30	C₁₉×#327	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
36	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
37	C₂×SD₁₆×C₁₉	—	2	4	no	—
38	C₂×SD₁₆×C₁₉	—	2	4	no	—
39	C₂×SD₁₆×C₁₉	—	2	2	no	—
40	C₂×D₈×C₁₉	—	2	4	no	—
41	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
42	C₂²×C₈×C₁₉	D₄	1	2	yes	—
43	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
44	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
45	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
46	C₁₉×#127	—	2	1	no	—
47	C₁₉×#127	—	2	1	no	—
48	C₁₉×#127	—	2	1	no	—
49	C₁₉×#127	D₄	1	1	yes	characteristic
50	C₁₉×#127	D₄	1	2	yes	—
51	C₁₉×#125	—	2	1	no	—
52	C₁₉×#124	—	2	1	no	—
53	C₁₉×C₂²⋊Q₈	—	2	1	no	—
54	C₁₉×C₂²⋊Q₈	—	2	1	no	—
55	C₁₉×#121	—	2	1	no	—
56	C₁₉×#121	—	2	1	no	—
57	C₄×Q₈×C₁₉	—	2	1	no	—
58	C₄×Q₈×C₁₉	—	2	1	no	—
59	C₄×D₄×C₁₉	—	2	1	no	—
60	C₄×D₄×C₁₉	—	2	1	no	—
61	C₁₉×#117	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄²×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
65	C₁₉×#106	—	2	2	no	—
66	C₁₉×C₄⋊C₈	—	2	1	no	—
67	C₁₉×C₄⋊C₈	—	2	1	no	—
68	C₁₉×C₄⋊C₈	—	2	1	no	—
69	C₁₉×#103	—	2	2	no	—
70	C₁₉×#102	—	2	4	no	—
71	C₁₉×#102	—	2	2	no	—
72	C₁₉×#102	—	4	4	no	—
73	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
74	C₁₉×#97	—	2	1	no	—
75	C₄×C₈×C₁₉	—	2	1	no	—
76	C₄×C₈×C₁₉	—	2	1	no	—
77	C₁₉×#95	—	2	1	no	—
78	C₂⁴×C₁₉	—	4	1	no	—
79	#41×C₁₉	—	4	2	no	—
80	#41×C₁₉	—	4	2	no	—
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×D₄×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	2	2	no	—
89	C₂×D₄×C₁₉	—	2	1	no	—
90	C₂×D₄×C₁₉	—	4	2	no	—
91	C₂×D₄×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	—	4	1	no	—
93	C₂×D₄×C₁₉	—	4	1	no	—
94	C₂×D₄×C₁₉	—	4	1	no	—
95	C₂×D₄×C₁₉	—	4	1	no	—
96	C₂×D₄×C₁₉	—	4	2	no	—
97	C₂×D₄×C₁₉	—	4	2	no	—
98	C₂×D₄×C₁₉	—	8	2	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
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	SD₁₆×C₁₉	—	4	8	no	—
105	SD₁₆×C₁₉	—	8	4	no	—
106	SD₁₆×C₁₉	—	8	2	no	—
107	D₈×C₁₉	—	4	8	no	—
108	M₁₆×C₁₉	—	2	2	no	—
109	M₁₆×C₁₉	SD₁₆	1	4	yes	complemented
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	4	2	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₄⋊C₄×C₁₉	—	4	1	no	—
122	C₄⋊C₄×C₁₉	—	4	1	no	—
123	C₄⋊C₄×C₁₉	—	4	1	no	—
124	C₂²⋊C₄×C₁₉	—	4	1	no	—
125	C₂²⋊C₄×C₁₉	—	4	1	no	—
126	C₂²⋊C₄×C₁₉	—	4	1	no	—
127	C₄²×C₁₉	—	4	1	no	—
128	C₄²×C₁₉	—	4	2	no	—
129	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₉	#41	1	1	yes	characteristic
133	#10194	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	—	8	2	no	—
137	C₂³×C₁₉	—	8	2	no	—
138	C₂³×C₁₉	—	8	1	no	—
139	C₂³×C₁₉	—	8	1	no	—
140	C₂³×C₁₉	#127	1	1	yes	characteristic
141	Q₈×C₁₉	—	4	2	no	—
142	Q₈×C₁₉	—	4	2	no	—
143	Q₈×C₁₉	—	4	1	no	—
144	Q₈×C₁₉	—	4	1	no	—
145	D₄×C₁₉	—	4	4	no	—
146	D₄×C₁₉	—	4	4	no	—
147	D₄×C₁₉	—	4	2	no	—
148	D₄×C₁₉	—	4	4	no	—
149	D₄×C₁₉	—	4	1	no	—
150	D₄×C₁₉	—	4	1	no	—
151	D₄×C₁₉	—	8	1	no	—
152	D₄×C₁₉	—	8	2	no	—
153	D₄×C₁₉	—	8	1	no	—
154	D₄×C₁₉	—	8	1	no	—
155	D₄×C₁₉	—	8	1	no	—
156	D₄×C₁₉	—	8	1	no	—
157	D₄×C₁₉	—	8	2	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	8	1	no	—
166	C₂×C₄×C₁₉	—	8	1	no	—
167	C₂×C₄×C₁₉	—	8	2	no	—
168	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
175	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
176	C₈×C₁₉	—	2	4	no	—
177	C₈×C₁₉	—	4	2	no	—
178	C₈×C₁₉	—	4	2	no	—
179	#3246	C₂×C₁₉	1	1	yes	characteristic, complemented
180	#3208	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#3151	C₂×C₁₉	1	1	yes	characteristic
182	#1986	C₂×C₁₉	1	1	yes	characteristic, complemented
183	#1982	C₂×C₁₉	1	1	yes	characteristic, complemented
184	#1502	C₂×C₁₉	1	1	yes	characteristic, complemented
185	#1283	C₂×C₁₉	1	1	yes	characteristic, complemented
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	8	2	no	—
189	C₂²×C₁₉	—	8	1	no	—
190	C₂²×C₁₉	—	8	2	no	—
191	C₂²×C₁₉	—	8	1	no	—
192	C₂²×C₁₉	—	8	1	no	—
193	C₂²×C₁₉	—	8	2	no	—
194	C₂²×C₁₉	—	16	2	no	—
195	C₂²×C₁₉	—	16	2	no	—
196	C₂²×C₁₉	#392	1	1	yes	characteristic
197	C₂²×C₁₉	#492	1	1	yes	characteristic
198	C₂²×C₁₉	#496	1	1	yes	characteristic
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	8	2	no	—
203	C₄×C₁₉	—	8	1	no	—
204	C₄×C₁₉	—	8	1	no	—
205	C₄×C₁₉	—	8	1	no	—
206	C₄×C₁₉	#450	1	2	yes	—
207	C₄×C₁₉	#453	1	1	yes	characteristic
208	C₄×C₁₉	#454	1	1	yes	characteristic
209	C₄×C₁₉	#460	1	2	yes	—
210	C₂×AGL(1,ℤ/8)	—	2	2	no	—
211	#533	C₂²×C₁₉	1	1	yes	characteristic
212	#532	C₂²×C₁₉	1	1	yes	characteristic
213	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
214	#496	—	2	2	no	—
215	#493	—	2	1	no	—
216	#492	—	2	1	no	—
217	#492	—	2	1	no	—
218	#486	—	2	1	no	—
219	#476	—	2	1	no	—
220	#475	—	2	1	no	—
221	#465	—	2	2	no	—
222	#461	—	2	1	no	—
223	#460	—	2	2	no	—
224	#460	—	2	1	no	—
225	#450	—	2	2	no	—
226	#431	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×#102	—	2	2	no	—
229	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
230	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
231	#339	—	2	2	no	—
232	#327	—	2	2	no	—
233	C₂×C₁₉	—	2	1	no	—
234	C₂×C₁₉	—	2	1	no	—
235	C₂×C₁₉	—	16	1	no	—
236	C₂×C₁₉	—	16	2	no	—
237	C₂×C₁₉	#2006	1	1	yes	characteristic
238	C₂×C₁₉	#2008	1	1	yes	characteristic
239	C₂×C₁₉	#2014	1	1	yes	characteristic
240	C₂×#41	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	AGL(1,ℤ/8)	—	4	4	no	—
245	AGL(1,ℤ/8)	—	4	4	no	—
246	C₂×SD₁₆	—	2	4	no	—
247	C₂×SD₁₆	—	2	4	no	—
248	C₂×SD₁₆	—	2	2	no	—
249	C₂×D₈	—	2	4	no	—
250	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
251	C₂²×C₈	D₄×C₁₉	1	2	yes	—
252	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
253	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
254	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
255	#127	—	2	1	no	—
256	#127	—	2	1	no	—
257	#127	—	2	1	no	—
258	#127	D₄×C₁₉	1	2	yes	—
259	#127	D₄×C₁₉	1	1	yes	characteristic
260	#125	—	2	1	no	—
261	#124	—	2	1	no	—
262	C₂²⋊Q₈	—	2	1	no	—
263	C₂²⋊Q₈	—	2	1	no	—
264	#121	—	2	1	no	—
265	#121	—	2	1	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	—	2	1	no	—
270	#117	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
274	#106	—	2	2	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	1	no	—
278	#103	—	2	2	no	—
279	#102	—	2	4	no	—
280	#102	—	2	2	no	—
281	#102	—	4	4	no	—
282	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
283	#97	—	2	1	no	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	—	2	1	no	—
286	#95	—	2	1	no	—
287	C₁₉	#10194	1	1	yes	characteristic, direct product factor, Sylow
288	C₂⁴	—	4	1	no	—
289	#41	—	4	2	no	—
290	#41	—	4	2	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	8	2	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
314	SD₁₆	—	4	8	no	—
315	SD₁₆	—	8	4	no	—
316	SD₁₆	—	8	2	no	—
317	D₈	—	4	8	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	SD₁₆×C₁₉	1	4	yes	complemented
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	4	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₄²	—	4	1	no	—
338	C₄²	—	4	2	no	—
339	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
341	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₄²	#41×C₁₉	1	1	yes	characteristic
343	C₂³	—	4	1	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	8	2	no	—
346	C₂³	—	8	2	no	—
347	C₂³	—	8	1	no	—
348	C₂³	—	8	1	no	—
349	C₂³	C₁₉×#127	1	1	yes	characteristic
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	1	no	—
353	Q₈	—	4	1	no	—
354	D₄	—	4	4	no	—
355	D₄	—	4	4	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	4	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	1	no	—
360	D₄	—	8	1	no	—
361	D₄	—	8	2	no	—
362	D₄	—	8	1	no	—
363	D₄	—	8	1	no	—
364	D₄	—	8	1	no	—
365	D₄	—	8	1	no	—
366	D₄	—	8	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	8	1	no	—
375	C₂×C₄	—	8	1	no	—
376	C₂×C₄	—	8	2	no	—
377	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
378	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
379	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
380	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
381	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
382	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
383	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
384	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
385	C₈	—	2	4	no	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	1	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	8	1	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	16	2	no	—
397	C₂²	—	16	2	no	—
398	C₂²	C₁₉×#392	1	1	yes	characteristic
399	C₂²	C₁₉×#492	1	1	yes	characteristic
400	C₂²	C₁₉×#496	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	8	2	no	—
405	C₄	—	8	1	no	—
406	C₄	—	8	1	no	—
407	C₄	—	8	1	no	—
408	C₄	C₁₉×#450	1	2	yes	—
409	C₄	C₁₉×#453	1	1	yes	characteristic
410	C₄	C₁₉×#454	1	1	yes	characteristic
411	C₄	C₁₉×#460	1	2	yes	—
412	C₂	—	2	1	no	—
413	C₂	—	2	1	no	—
414	C₂	—	16	2	no	—
415	C₂	—	16	1	no	—
416	C₂	C₁₉×#2006	1	1	yes	characteristic
417	C₂	C₁₉×#2008	1	1	yes	characteristic
418	C₂	C₁₉×#2014	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3151	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3246	C₂	semidirect
2. C₁₉×#3208	C₂	semidirect
4. C₁₉×#1986	C₂	semidirect
5. C₁₉×#1982	C₂	semidirect
6. C₁₉×#1502	C₂	semidirect
7. C₁₉×#1283	C₂	semidirect
109. M₁₆×C₁₉	SD₁₆	semidirect
133. #10194	C₁₉	direct (N × H)
179. #3246	C₂×C₁₉	semidirect
180. #3208	C₂×C₁₉	semidirect
182. #1986	C₂×C₁₉	semidirect
183. #1982	C₂×C₁₉	semidirect
184. #1502	C₂×C₁₉	semidirect
185. #1283	C₂×C₁₉	semidirect
287. C₁₉	#10194	direct (N × H)
319. M₁₆	SD₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3246	2
C₁₉×#3208	2
C₁₉×#3151	2
C₁₉×#1986	2
C₁₉×#1982	2
C₁₉×#1502	2
C₁₉×#1283	2
#10194	19

Subgroups — C19×#10194 #18016153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10194 #18016153