Subgroups — C₂²×C₁₉×#454 #18066339

Order 4864.

4894 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	C₂²×C₁₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#454	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₁₉×#104	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×2₋¹⁺⁴	—	2	12	no	—
8	C₂×C₁₉×2₋¹⁺⁴	—	2	6	no	—
9	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	12	yes	complemented
10	C₂²×#41×C₁₉	—	2	2	no	—
11	C₂²×#41×C₁₉	—	2	2	no	—
12	C₂²×#41×C₁₉	C₂²	1	2	yes	—
13	C₂³×Q₈×C₁₉	—	2	2	no	—
14	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×AGL(1,ℤ/8)	—	2	12	no	—
17	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	24	yes	complemented
18	C₂²×SD₁₆×C₁₉	—	2	2	no	—
19	C₂²×D₈×C₁₉	—	2	2	no	—
20	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
21	C₂×C₁₉×#124	—	2	6	no	—
22	C₂×C₁₉×#124	C₂²	1	12	yes	complemented
23	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#454	C₂²	1	64	yes	direct product factor
26	C₂×C₁₉×#104	C₂²	1	24	yes	complemented
27	C₂×C₁₉×#101	C₂²	1	12	yes	complemented
28	C₂⁵×C₁₉	—	2	1	no	—
29	C₁₉×2₋¹⁺⁴	—	2	48	no	—
30	C₁₉×2₋¹⁺⁴	—	2	48	no	—
31	C₁₉×2₋¹⁺⁴	—	2	24	no	—
32	C₁₉×2₋¹⁺⁴	C₂³	1	16	yes	complemented
33	C₂×#41×C₁₉	—	2	24	no	—
34	C₂×#41×C₁₉	—	2	24	no	—
35	C₂×#41×C₁₉	—	2	24	no	—
36	C₂×#41×C₁₉	—	2	24	no	—
37	C₂×#41×C₁₉	—	2	6	no	—
38	C₂×#41×C₁₉	—	2	6	no	—
39	C₂×#41×C₁₉	D₄	1	12	yes	—
40	C₂×#41×C₁₉	C₂³	1	12	yes	—
41	C₂²×Q₈×C₁₉	—	2	2	no	—
42	C₂²×Q₈×C₁₉	—	2	24	no	—
43	C₂²×Q₈×C₁₉	—	2	24	no	—
44	C₂²×Q₈×C₁₉	—	2	2	no	—
45	C₂²×Q₈×C₁₉	—	2	6	no	—
46	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
47	C₂²×Q₈×C₁₉	D₄	1	6	yes	—
48	C₂²×Q₈×C₁₉	C₂³	1	6	yes	—
49	C₂²×D₄×C₁₉	—	2	2	no	—
50	C₂²×D₄×C₁₉	—	2	2	no	—
51	C₂²×D₄×C₁₉	—	2	2	no	—
52	C₂²×D₄×C₁₉	—	2	6	no	—
53	C₂²×D₄×C₁₉	—	2	3	no	—
54	C₂²×D₄×C₁₉	D₄	1	2	yes	—
55	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
56	C₂³×C₄×C₁₉	—	2	4	no	—
57	C₂³×C₄×C₁₉	—	2	2	no	—
58	C₂³×C₄×C₁₉	—	2	1	no	—
59	C₂³×C₄×C₁₉	D₄	1	2	yes	—
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₁₉×AGL(1,ℤ/8)	—	2	48	no	—
62	C₁₉×AGL(1,ℤ/8)	C₂³	1	32	yes	complemented
63	C₂×SD₁₆×C₁₉	—	2	24	no	—
64	C₂×D₈×C₁₉	—	2	24	no	—
65	C₂×M₁₆×C₁₉	—	2	6	no	—
66	C₂×M₁₆×C₁₉	C₂³	1	12	yes	—
67	C₂²×C₈×C₁₉	—	2	2	no	—
68	C₁₉×#124	—	2	24	no	—
69	C₁₉×#124	C₂³	1	16	yes	complemented
70	C₂×C₂²⋊C₄×C₁₉	—	2	24	no	—
71	C₂×C₄²×C₁₉	—	2	3	no	—
72	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
73	C₁₉×#104	C₂³	1	32	yes	complemented
74	C₁₉×#101	C₂³	1	16	yes	complemented
75	C₂⁴×C₁₉	—	2	2	no	—
76	C₂⁴×C₁₉	—	2	6	no	—
77	C₂⁴×C₁₉	—	4	8	no	—
78	C₂⁴×C₁₉	—	4	3	no	—
79	C₂⁴×C₁₉	—	4	1	no	—
80	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
81	#41×C₁₉	—	2	96	no	—
82	#41×C₁₉	—	2	96	no	—
83	#41×C₁₉	—	2	32	no	—
84	#41×C₁₉	—	2	24	no	—
85	#41×C₁₉	—	2	32	no	—
86	#41×C₁₉	—	2	12	no	—
87	#41×C₁₉	—	2	12	no	—
88	#41×C₁₉	C₂×D₄	1	24	yes	—
89	#41×C₁₉	C₂⁴	1	8	yes	—
90	C₂×Q₈×C₁₉	—	2	24	no	—
91	C₂×Q₈×C₁₉	—	2	96	no	—
92	C₂×Q₈×C₁₉	—	2	32	no	—
93	C₂×Q₈×C₁₉	—	2	6	no	—
94	C₂×Q₈×C₁₉	—	2	12	no	—
95	C₂×Q₈×C₁₉	—	2	12	no	—
96	C₂×Q₈×C₁₉	—	2	12	no	—
97	C₂×Q₈×C₁₉	—	2	12	no	—
98	C₂×Q₈×C₁₉	C₂×D₄	1	12	yes	—
99	C₂×Q₈×C₁₉	C₂×D₄	1	12	yes	—
100	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
101	C₂×D₄×C₁₉	—	2	24	no	—
102	C₂×D₄×C₁₉	—	2	12	no	—
103	C₂×D₄×C₁₉	—	2	12	no	—
104	C₂×D₄×C₁₉	—	2	6	no	—
105	C₂×D₄×C₁₉	—	2	12	no	—
106	C₂×D₄×C₁₉	—	2	12	no	—
107	C₂×D₄×C₁₉	—	2	6	no	—
108	C₂×D₄×C₁₉	—	4	6	no	—
109	C₂×D₄×C₁₉	—	4	6	no	—
110	C₂×D₄×C₁₉	C₂×D₄	1	12	yes	—
111	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
112	C₂²×C₄×C₁₉	—	2	48	no	—
113	C₂²×C₄×C₁₉	—	2	6	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	12	no	—
117	C₂²×C₄×C₁₉	—	2	12	no	—
118	C₂²×C₄×C₁₉	—	2	6	no	—
119	C₂²×C₄×C₁₉	—	4	4	no	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	12	yes	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
125	SD₁₆×C₁₉	—	2	32	no	—
126	D₈×C₁₉	—	2	32	no	—
127	M₁₆×C₁₉	—	2	12	no	—
128	M₁₆×C₁₉	C₂⁴	1	8	yes	—
129	C₂×C₈×C₁₉	—	2	12	no	—
130	C₂²⋊C₄×C₁₉	—	2	32	no	—
131	C₄²×C₁₉	—	2	6	no	—
132	C₄²×C₁₉	C₂⁴	1	4	yes	—
133	C₂²×#454	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₁₉	—	2	4	no	—
135	C₂³×C₁₉	—	2	12	no	—
136	C₂³×C₁₉	—	2	4	no	—
137	C₂³×C₁₉	—	4	24	no	—
138	C₂³×C₁₉	—	4	8	no	—
139	C₂³×C₁₉	—	4	6	no	—
140	C₂³×C₁₉	—	4	6	no	—
141	C₂³×C₁₉	—	8	12	no	—
142	C₂³×C₁₉	—	8	4	no	—
143	C₂³×C₁₉	#120	1	3	yes	—
144	C₂³×C₁₉	#120	1	1	yes	characteristic
145	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
146	Q₈×C₁₉	—	2	32	no	—
147	Q₈×C₁₉	—	2	12	no	—
148	Q₈×C₁₉	—	2	24	no	—
149	Q₈×C₁₉	—	2	8	no	—
150	Q₈×C₁₉	C₂²×D₄	1	8	yes	—
151	D₄×C₁₉	—	2	32	no	—
152	D₄×C₁₉	—	2	24	no	—
153	D₄×C₁₉	—	2	8	no	—
154	D₄×C₁₉	—	2	12	no	—
155	D₄×C₁₉	—	2	8	no	—
156	D₄×C₁₉	—	4	12	no	—
157	D₄×C₁₉	C₂²×D₄	1	8	yes	—
158	C₂×C₄×C₁₉	—	2	64	no	—
159	C₂×C₄×C₁₉	—	2	12	no	—
160	C₂×C₄×C₁₉	—	2	12	no	—
161	C₂×C₄×C₁₉	—	2	12	no	—
162	C₂×C₄×C₁₉	—	2	24	no	—
163	C₂×C₄×C₁₉	—	2	8	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	4	12	no	—
166	C₂×C₄×C₁₉	#120	1	6	yes	—
167	C₂×C₄×C₁₉	#120	1	6	yes	—
168	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
169	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
170	C₂×C₄×C₁₉	C₂²×D₄	1	6	yes	—
171	C₂×C₄×C₁₉	C₂²×D₄	1	6	yes	—
172	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
173	C₈×C₁₉	—	2	8	no	—
174	C₂²×2₋¹⁺⁴	C₂×C₁₉	1	1	yes	characteristic, complemented
175	C₂²×AGL(1,ℤ/8)	C₂×C₁₉	1	2	yes	complemented
176	C₂²×#124	C₂×C₁₉	1	1	yes	characteristic, complemented
177	C₂×#454	C₂×C₁₉	1	24	yes	direct product factor
178	C₂²×#104	C₂×C₁₉	1	2	yes	complemented
179	C₂²×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
180	C₂²×C₁₉	—	2	6	no	—
181	C₂²×C₁₉	—	2	6	no	—
182	C₂²×C₁₉	—	2	8	no	—
183	C₂²×C₁₉	—	4	8	no	—
184	C₂²×C₁₉	—	4	24	no	—
185	C₂²×C₁₉	—	4	4	no	—
186	C₂²×C₁₉	—	8	12	no	—
187	C₂²×C₁₉	—	8	12	no	—
188	C₂²×C₁₉	#454	1	4	yes	direct product factor
189	C₂²×C₁₉	C₂×#120	1	3	yes	—
190	C₂²×C₁₉	C₂×#120	1	3	yes	—
191	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
192	C₄×C₁₉	—	2	8	no	—
193	C₄×C₁₉	—	2	8	no	—
194	C₄×C₁₉	—	4	4	no	—
195	C₄×C₁₉	C₂×#120	1	6	yes	—
196	C₄×C₁₉	C₂³×D₄	1	2	yes	—
197	C₂×2₋¹⁺⁴	—	2	12	no	—
198	C₂×2₋¹⁺⁴	—	2	6	no	—
199	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	12	yes	complemented
200	C₂²×#41	—	2	2	no	—
201	C₂²×#41	—	2	2	no	—
202	C₂²×#41	C₂²×C₁₉	1	2	yes	—
203	C₂³×Q₈	—	2	2	no	—
204	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
205	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
206	C₂×AGL(1,ℤ/8)	—	2	12	no	—
207	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	24	yes	complemented
208	C₂²×SD₁₆	—	2	2	no	—
209	C₂²×D₈	—	2	2	no	—
210	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
211	C₂×#124	—	2	6	no	—
212	C₂×#124	C₂²×C₁₉	1	12	yes	complemented
213	C₂²×C₂²⋊C₄	—	2	2	no	—
214	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
215	#454	C₂²×C₁₉	1	64	yes	direct product factor
216	C₂×#104	C₂²×C₁₉	1	24	yes	complemented
217	C₂×#101	C₂²×C₁₉	1	12	yes	complemented
218	C₂×C₁₉	—	2	1	no	—
219	C₂×C₁₉	—	2	3	no	—
220	C₂×C₁₉	—	4	8	no	—
221	C₂×C₁₉	—	8	4	no	—
222	C₂×C₁₉	C₂×#454	1	6	yes	direct product factor
223	C₂×C₁₉	C₂²×#120	1	1	yes	characteristic
224	C₂⁵	—	2	1	no	—
225	2₋¹⁺⁴	—	2	48	no	—
226	2₋¹⁺⁴	—	2	48	no	—
227	2₋¹⁺⁴	—	2	24	no	—
228	2₋¹⁺⁴	C₂³×C₁₉	1	16	yes	complemented
229	C₂×#41	—	2	24	no	—
230	C₂×#41	—	2	24	no	—
231	C₂×#41	—	2	24	no	—
232	C₂×#41	—	2	24	no	—
233	C₂×#41	—	2	6	no	—
234	C₂×#41	—	2	6	no	—
235	C₂×#41	D₄×C₁₉	1	12	yes	—
236	C₂×#41	C₂³×C₁₉	1	12	yes	—
237	C₂²×Q₈	—	2	2	no	—
238	C₂²×Q₈	—	2	24	no	—
239	C₂²×Q₈	—	2	24	no	—
240	C₂²×Q₈	—	2	2	no	—
241	C₂²×Q₈	—	2	6	no	—
242	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
243	C₂²×Q₈	D₄×C₁₉	1	6	yes	—
244	C₂²×Q₈	C₂³×C₁₉	1	6	yes	—
245	C₂²×D₄	—	2	2	no	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	—	2	2	no	—
248	C₂²×D₄	—	2	6	no	—
249	C₂²×D₄	—	2	3	no	—
250	C₂²×D₄	D₄×C₁₉	1	2	yes	—
251	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
252	C₂³×C₄	—	2	4	no	—
253	C₂³×C₄	—	2	2	no	—
254	C₂³×C₄	—	2	1	no	—
255	C₂³×C₄	D₄×C₁₉	1	2	yes	—
256	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
257	AGL(1,ℤ/8)	—	2	48	no	—
258	AGL(1,ℤ/8)	C₂³×C₁₉	1	32	yes	complemented
259	C₂×SD₁₆	—	2	24	no	—
260	C₂×D₈	—	2	24	no	—
261	C₂×M₁₆	—	2	6	no	—
262	C₂×M₁₆	C₂³×C₁₉	1	12	yes	—
263	C₂²×C₈	—	2	2	no	—
264	#124	—	2	24	no	—
265	#124	C₂³×C₁₉	1	16	yes	complemented
266	C₂×C₂²⋊C₄	—	2	24	no	—
267	C₂×C₄²	—	2	3	no	—
268	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
269	#104	C₂³×C₁₉	1	32	yes	complemented
270	#101	C₂³×C₁₉	1	16	yes	complemented
271	C₁₉	C₂²×#454	1	1	yes	characteristic, direct product factor, Sylow
272	C₂⁴	—	2	2	no	—
273	C₂⁴	—	2	6	no	—
274	C₂⁴	—	4	8	no	—
275	C₂⁴	—	4	3	no	—
276	C₂⁴	—	4	1	no	—
277	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
278	#41	—	2	96	no	—
279	#41	—	2	96	no	—
280	#41	—	2	32	no	—
281	#41	—	2	24	no	—
282	#41	—	2	32	no	—
283	#41	—	2	12	no	—
284	#41	—	2	12	no	—
285	#41	C₂×D₄×C₁₉	1	24	yes	—
286	#41	C₂⁴×C₁₉	1	8	yes	—
287	C₂×Q₈	—	2	24	no	—
288	C₂×Q₈	—	2	96	no	—
289	C₂×Q₈	—	2	32	no	—
290	C₂×Q₈	—	2	6	no	—
291	C₂×Q₈	—	2	12	no	—
292	C₂×Q₈	—	2	12	no	—
293	C₂×Q₈	—	2	12	no	—
294	C₂×Q₈	—	2	12	no	—
295	C₂×Q₈	C₂×D₄×C₁₉	1	12	yes	—
296	C₂×Q₈	C₂×D₄×C₁₉	1	12	yes	—
297	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
298	C₂×D₄	—	2	24	no	—
299	C₂×D₄	—	2	12	no	—
300	C₂×D₄	—	2	12	no	—
301	C₂×D₄	—	2	6	no	—
302	C₂×D₄	—	2	12	no	—
303	C₂×D₄	—	2	12	no	—
304	C₂×D₄	—	2	6	no	—
305	C₂×D₄	—	4	6	no	—
306	C₂×D₄	—	4	6	no	—
307	C₂×D₄	C₂×D₄×C₁₉	1	12	yes	—
308	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
309	C₂²×C₄	—	2	48	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	6	no	—
313	C₂²×C₄	—	2	12	no	—
314	C₂²×C₄	—	2	12	no	—
315	C₂²×C₄	—	2	6	no	—
316	C₂²×C₄	—	4	4	no	—
317	C₂²×C₄	C₂×D₄×C₁₉	1	12	yes	—
318	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
319	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
321	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
322	SD₁₆	—	2	32	no	—
323	D₈	—	2	32	no	—
324	M₁₆	—	2	12	no	—
325	M₁₆	C₂⁴×C₁₉	1	8	yes	—
326	C₂×C₈	—	2	12	no	—
327	C₂²⋊C₄	—	2	32	no	—
328	C₄²	—	2	6	no	—
329	C₄²	C₂⁴×C₁₉	1	4	yes	—
330	C₂³	—	2	4	no	—
331	C₂³	—	2	12	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	4	24	no	—
334	C₂³	—	4	8	no	—
335	C₂³	—	4	6	no	—
336	C₂³	—	4	6	no	—
337	C₂³	—	8	12	no	—
338	C₂³	—	8	4	no	—
339	C₂³	C₁₉×#120	1	3	yes	—
340	C₂³	C₁₉×#120	1	1	yes	characteristic
341	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
342	Q₈	—	2	32	no	—
343	Q₈	—	2	12	no	—
344	Q₈	—	2	24	no	—
345	Q₈	—	2	8	no	—
346	Q₈	C₂²×D₄×C₁₉	1	8	yes	—
347	D₄	—	2	32	no	—
348	D₄	—	2	24	no	—
349	D₄	—	2	8	no	—
350	D₄	—	2	12	no	—
351	D₄	—	2	8	no	—
352	D₄	—	4	12	no	—
353	D₄	C₂²×D₄×C₁₉	1	8	yes	—
354	C₂×C₄	—	2	64	no	—
355	C₂×C₄	—	2	12	no	—
356	C₂×C₄	—	2	12	no	—
357	C₂×C₄	—	2	12	no	—
358	C₂×C₄	—	2	24	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	4	12	no	—
362	C₂×C₄	C₁₉×#120	1	6	yes	—
363	C₂×C₄	C₁₉×#120	1	6	yes	—
364	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
365	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
366	C₂×C₄	C₂²×D₄×C₁₉	1	6	yes	—
367	C₂×C₄	C₂²×D₄×C₁₉	1	6	yes	—
368	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
369	C₈	—	2	8	no	—
370	C₂²	—	2	6	no	—
371	C₂²	—	2	6	no	—
372	C₂²	—	2	8	no	—
373	C₂²	—	4	8	no	—
374	C₂²	—	4	24	no	—
375	C₂²	—	4	4	no	—
376	C₂²	—	8	12	no	—
377	C₂²	—	8	12	no	—
378	C₂²	C₁₉×#454	1	4	yes	direct product factor
379	C₂²	C₂×C₁₉×#120	1	3	yes	—
380	C₂²	C₂×C₁₉×#120	1	3	yes	—
381	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
382	C₄	—	2	8	no	—
383	C₄	—	2	8	no	—
384	C₄	—	4	4	no	—
385	C₄	C₂×C₁₉×#120	1	6	yes	—
386	C₄	C₂³×D₄×C₁₉	1	2	yes	—
387	C₂	—	2	1	no	—
388	C₂	—	2	3	no	—
389	C₂	—	4	8	no	—
390	C₂	—	8	4	no	—
391	C₂	C₂×C₁₉×#454	1	6	yes	direct product factor
392	C₂	C₂²×C₁₉×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×2₋¹⁺⁴	C₂	semidirect
2. C₂²×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
3. C₂²×C₁₉×#124	C₂	semidirect
4. C₂×C₁₉×#454	C₂	direct (N × H)
5. C₂²×C₁₉×#104	C₂	semidirect
6. C₂²×C₁₉×#101	C₂	semidirect
9. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
17. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₁₉×#124	C₂²	semidirect
25. C₁₉×#454	C₂²	direct (N × H)
26. C₂×C₁₉×#104	C₂²	semidirect
27. C₂×C₁₉×#101	C₂²	semidirect
32. C₁₉×2₋¹⁺⁴	C₂³	semidirect
62. C₁₉×AGL(1,ℤ/8)	C₂³	semidirect
69. C₁₉×#124	C₂³	semidirect
73. C₁₉×#104	C₂³	semidirect
74. C₁₉×#101	C₂³	semidirect
133. C₂²×#454	C₁₉	direct (N × H)
174. C₂²×2₋¹⁺⁴	C₂×C₁₉	semidirect
175. C₂²×AGL(1,ℤ/8)	C₂×C₁₉	semidirect
176. C₂²×#124	C₂×C₁₉	semidirect
177. C₂×#454	C₂×C₁₉	direct (N × H)
178. C₂²×#104	C₂×C₁₉	semidirect
179. C₂²×#101	C₂×C₁₉	semidirect
188. C₂²×C₁₉	#454	direct (N × H)
199. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
207. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
212. C₂×#124	C₂²×C₁₉	semidirect
215. #454	C₂²×C₁₉	direct (N × H)
216. C₂×#104	C₂²×C₁₉	semidirect
217. C₂×#101	C₂²×C₁₉	semidirect
222. C₂×C₁₉	C₂×#454	direct (N × H)
228. 2₋¹⁺⁴	C₂³×C₁₉	semidirect
258. AGL(1,ℤ/8)	C₂³×C₁₉	semidirect
265. #124	C₂³×C₁₉	semidirect
269. #104	C₂³×C₁₉	semidirect
270. #101	C₂³×C₁₉	semidirect
271. C₁₉	C₂²×#454	direct (N × H)
378. C₂²	C₁₉×#454	direct (N × H)
391. C₂	C₂×C₁₉×#454	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×2₋¹⁺⁴	2
C₂²×C₁₉×AGL(1,ℤ/8)	2
C₂²×C₁₉×#124	2
C₂×C₁₉×#454	2
C₂²×C₁₉×#104	2
C₂²×C₁₉×#101	2
C₂²×#454	19

Subgroups — C22×C19×#454 #18066339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₉×#454 #18066339