Subgroups — C₁₉×#32788 #18038747

Order 4864.

716 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	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2100	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2099	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2077	C₂	1	4	yes	maximal
6	C₁₉×#2058	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2058	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1817	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
12	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
13	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#106	C₂²	1	4	yes	—
15	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₁₉×#391	—	2	1	no	—
17	C₁₉×#391	—	2	1	no	—
18	C₁₉×#389	—	2	1	no	—
19	C₁₉×#389	—	2	1	no	—
20	C₁₉×#389	C₂²	1	2	yes	—
21	C₁₉×#389	C₂²	1	2	yes	—
22	C₁₉×#384	C₂²	1	1	yes	characteristic
23	C₁₉×#384	C₂²	1	1	yes	characteristic
24	C₁₉×#380	—	2	1	no	—
25	C₁₉×#380	—	2	1	no	—
26	C₁₉×#380	C₂²	1	2	yes	—
27	C₁₉×#380	C₂²	1	2	yes	—
28	C₁₉×#340	C₂²	1	4	yes	—
29	C₁₉×#340	C₂²	1	4	yes	—
30	C₁₉×#340	C₂²	1	4	yes	—
31	C₁₉×#336	C₂²	1	2	yes	—
32	C₁₉×#336	C₂²	1	2	yes	—
33	C₂²×Q₈×C₁₉	—	2	1	no	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
39	C₁₉×C₄⋊Q₈	—	4	2	no	—
40	C₁₉×C₄⋊Q₈	—	4	2	no	—
41	C₁₉×C₂²⋊Q₈	—	4	4	no	—
42	C₁₉×C₂²⋊Q₈	—	4	4	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄²×C₁₉	—	4	2	no	—
58	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
62	C₁₉×#106	—	4	4	no	—
63	C₁₉×C₂²⋊C₈	—	4	2	no	—
64	C₁₉×#95	—	2	2	no	—
65	C₁₉×#95	—	2	2	no	—
66	C₁₉×#95	—	2	2	no	—
67	C₁₉×#95	—	2	2	no	—
68	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂×Q₈×C₁₉	—	4	2	no	—
70	C₂×Q₈×C₁₉	—	4	2	no	—
71	C₂×Q₈×C₁₉	—	4	2	no	—
72	C₂×Q₈×C₁₉	—	4	2	no	—
73	C₂×Q₈×C₁₉	—	4	2	no	—
74	C₂×Q₈×C₁₉	—	4	2	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	—
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
94	C₂×C₈×C₁₉	—	2	4	no	—
95	C₂×C₈×C₁₉	—	2	4	no	—
96	C₂×C₈×C₁₉	—	2	4	no	—
97	C₄⋊C₄×C₁₉	—	2	4	no	—
98	C₄⋊C₄×C₁₉	—	2	4	no	—
99	C₄⋊C₄×C₁₉	—	2	4	no	—
100	C₄⋊C₄×C₁₉	—	2	4	no	—
101	C₄⋊C₄×C₁₉	—	4	2	no	—
102	C₄⋊C₄×C₁₉	—	4	2	no	—
103	C₄⋊C₄×C₁₉	—	4	2	no	—
104	C₄⋊C₄×C₁₉	—	4	2	no	—
105	C₄⋊C₄×C₁₉	—	4	2	no	—
106	C₄⋊C₄×C₁₉	—	4	4	no	—
107	C₄⋊C₄×C₁₉	—	4	2	no	—
108	C₄⋊C₄×C₁₉	—	4	4	no	—
109	C₂²⋊C₄×C₁₉	—	4	4	no	—
110	C₂²⋊C₄×C₁₉	—	4	4	no	—
111	C₄²×C₁₉	—	2	2	no	—
112	C₄²×C₁₉	—	2	2	no	—
113	C₄²×C₁₉	—	4	1	no	—
114	C₄²×C₁₉	—	4	1	no	—
115	#32788	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₁₉	—	2	1	no	—
117	C₂³×C₁₉	—	2	1	no	—
118	C₂³×C₁₉	—	2	1	no	—
119	C₂³×C₁₉	—	2	1	no	—
120	C₂³×C₁₉	—	2	1	no	—
121	C₂³×C₁₉	—	2	1	no	—
122	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
123	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
124	Q₈×C₁₉	—	8	4	no	—
125	Q₈×C₁₉	—	8	4	no	—
126	C₂×C₄×C₁₉	—	2	1	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	4	4	no	—
138	C₂×C₄×C₁₉	—	4	4	no	—
139	C₂×C₄×C₁₉	—	4	4	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	—	4	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	2	no	—
150	C₂×C₄×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
153	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
154	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₁₉	#137	1	2	yes	—
156	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
157	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
158	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
159	C₈×C₁₉	—	4	4	no	—
160	#2857	C₂×C₁₉	1	1	yes	characteristic
161	#2857	C₂×C₁₉	1	1	yes	characteristic
162	#2100	C₂×C₁₉	1	2	yes	complemented
163	#2099	C₂×C₁₉	1	2	yes	complemented
164	#2077	C₂×C₁₉	1	4	yes	—
165	#2058	C₂×C₁₉	1	2	yes	complemented
166	#2058	C₂×C₁₉	1	2	yes	complemented
167	#1817	C₂×C₁₉	1	1	yes	characteristic
168	C₂²×C₁₉	—	2	2	no	—
169	C₂²×C₁₉	—	2	2	no	—
170	C₂²×C₁₉	—	2	2	no	—
171	C₂²×C₁₉	—	4	1	no	—
172	C₂²×C₁₉	—	4	1	no	—
173	C₂²×C₁₉	—	4	1	no	—
174	C₂²×C₁₉	—	4	1	no	—
175	C₂²×C₁₉	#534	1	1	yes	characteristic
176	C₂²×C₁₉	#536	1	1	yes	characteristic
177	C₂²×C₁₉	#536	1	1	yes	characteristic
178	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
179	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
181	C₂²×C₁₉	#575	1	1	yes	characteristic
182	C₄×C₁₉	—	2	2	no	—
183	C₄×C₁₉	—	2	2	no	—
184	C₄×C₁₉	—	2	2	no	—
185	C₄×C₁₉	—	2	2	no	—
186	C₄×C₁₉	—	4	1	no	—
187	C₄×C₁₉	—	8	2	no	—
188	C₄×C₁₉	—	8	2	no	—
189	C₄×C₁₉	—	8	2	no	—
190	C₄×C₁₉	—	8	2	no	—
191	C₄×C₁₉	#563	1	4	yes	—
192	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
193	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
194	C₂×C₂²⋊Q₈	—	2	1	no	—
195	C₂×C₂²⋊Q₈	—	2	1	no	—
196	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
197	C₂×#106	C₂²×C₁₉	1	4	yes	—
198	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
199	#391	—	2	1	no	—
200	#391	—	2	1	no	—
201	#389	—	2	1	no	—
202	#389	—	2	1	no	—
203	#389	C₂²×C₁₉	1	2	yes	—
204	#389	C₂²×C₁₉	1	2	yes	—
205	#384	C₂²×C₁₉	1	1	yes	characteristic
206	#384	C₂²×C₁₉	1	1	yes	characteristic
207	#380	—	2	1	no	—
208	#380	—	2	1	no	—
209	#380	C₂²×C₁₉	1	2	yes	—
210	#380	C₂²×C₁₉	1	2	yes	—
211	#340	C₂²×C₁₉	1	4	yes	—
212	#340	C₂²×C₁₉	1	4	yes	—
213	#340	C₂²×C₁₉	1	4	yes	—
214	#336	C₂²×C₁₉	1	2	yes	—
215	#336	C₂²×C₁₉	1	2	yes	—
216	C₂×C₁₉	—	4	2	no	—
217	C₂×C₁₉	#2817	1	1	yes	characteristic
218	C₂×C₁₉	#3187	1	1	yes	characteristic
219	C₂×C₁₉	#3193	1	1	yes	characteristic
220	C₂×C₁₉	#3227	1	1	yes	characteristic
221	C₂×C₁₉	#3229	1	1	yes	characteristic
222	C₂×C₁₉	#3235	1	1	yes	characteristic
223	C₂×C₁₉	#3237	1	1	yes	characteristic
224	C₂²×Q₈	—	2	1	no	—
225	C₂²×Q₈	—	2	1	no	—
226	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
227	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
228	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
230	C₄⋊Q₈	—	4	2	no	—
231	C₄⋊Q₈	—	4	2	no	—
232	C₂²⋊Q₈	—	4	4	no	—
233	C₂²⋊Q₈	—	4	4	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
243	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
244	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₄²	—	4	2	no	—
249	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
250	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
253	#106	—	4	4	no	—
254	C₂²⋊C₈	—	4	2	no	—
255	#95	—	2	2	no	—
256	#95	—	2	2	no	—
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	C₁₉	#32788	1	1	yes	characteristic, direct product factor, Sylow
260	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
261	C₂×Q₈	—	4	2	no	—
262	C₂×Q₈	—	4	2	no	—
263	C₂×Q₈	—	4	2	no	—
264	C₂×Q₈	—	4	2	no	—
265	C₂×Q₈	—	4	2	no	—
266	C₂×Q₈	—	4	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	SD₁₆×C₁₉	1	4	yes	—
280	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	4	2	no	—
294	C₄⋊C₄	—	4	2	no	—
295	C₄⋊C₄	—	4	2	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄⋊C₄	—	4	4	no	—
299	C₄⋊C₄	—	4	2	no	—
300	C₄⋊C₄	—	4	4	no	—
301	C₂²⋊C₄	—	4	4	no	—
302	C₂²⋊C₄	—	4	4	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	4	1	no	—
306	C₄²	—	4	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
314	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
315	Q₈	—	8	4	no	—
316	Q₈	—	8	4	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
344	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
345	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
346	C₂×C₄	C₁₉×#137	1	2	yes	—
347	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
348	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
349	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
350	C₈	—	4	4	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	C₁₉×#534	1	1	yes	characteristic
359	C₂²	C₁₉×#536	1	1	yes	characteristic
360	C₂²	C₁₉×#536	1	1	yes	characteristic
361	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
362	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
363	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
364	C₂²	C₁₉×#575	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	4	1	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	2	no	—
372	C₄	—	8	2	no	—
373	C₄	—	8	2	no	—
374	C₄	C₁₉×#563	1	4	yes	—
375	C₂	—	4	2	no	—
376	C₂	C₁₉×#2817	1	1	yes	characteristic
377	C₂	C₁₉×#3187	1	1	yes	characteristic
378	C₂	C₁₉×#3193	1	1	yes	characteristic
379	C₂	C₁₉×#3227	1	1	yes	characteristic
380	C₂	C₁₉×#3229	1	1	yes	characteristic
381	C₂	C₁₉×#3235	1	1	yes	characteristic
382	C₂	C₁₉×#3237	1	1	yes	characteristic

	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 ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2100	C₂	semidirect
4. C₁₉×#2099	C₂	semidirect
6. C₁₉×#2058	C₂	semidirect
7. C₁₉×#2058	C₂	semidirect
115. #32788	C₁₉	direct (N × H)
162. #2100	C₂×C₁₉	semidirect
163. #2099	C₂×C₁₉	semidirect
165. #2058	C₂×C₁₉	semidirect
166. #2058	C₂×C₁₉	semidirect
259. C₁₉	#32788	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×#2857	2
C₁₉×#2100	2
C₁₉×#2099	2
C₁₉×#2077	2
C₁₉×#2058	2
C₁₉×#1817	2
#32788	19

Subgroups — C19×#32788 #18038747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32788 #18038747