Subgroups — C₁₉×#32945 #18038904

Order 4864.

1346 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#472	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#469	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3006	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1907	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1900	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1815	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1811	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	—
11	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
12	C₁₉×#568	—	2	8	no	—
13	C₂×C₁₉×#131	—	2	2	no	—
14	C₂×C₁₉×#131	C₂²	1	2	yes	—
15	C₂×C₁₉×#131	C₂²	1	2	yes	—
16	C₂²×M₁₆×C₁₉	—	2	2	no	—
17	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#121	C₂²	1	2	yes	—
20	C₁₉×#472	—	2	8	no	—
21	C₁₉×#469	—	2	2	no	—
22	C₁₉×#469	—	2	2	no	—
23	C₁₉×#449	—	2	4	no	—
24	C₁₉×#448	—	2	2	no	—
25	C₁₉×#447	—	2	2	no	—
26	C₂×C₁₉×#108	C₂²	1	2	yes	complemented
27	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#417	C₂²	1	4	yes	—
29	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
30	C₂×C₁₉×#100	C₂²	1	4	yes	complemented
31	C₁₉×#407	C₂²	1	2	yes	—
32	C₁₉×#343	C₂²	1	4	yes	complemented
33	C₁₉×#341	C₂²	1	2	yes	complemented
34	C₂×#41×C₁₉	—	2	4	no	—
35	C₂×#41×C₁₉	—	2	4	no	—
36	C₂×#41×C₁₉	—	2	1	no	—
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	D₄	1	2	yes	—
39	C₂×#41×C₁₉	C₂³	1	2	yes	—
40	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
48	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
49	C₂×SD₁₆×C₁₉	—	2	4	no	—
50	C₂×D₈×C₁₉	—	2	4	no	—
51	C₂×D₈×C₁₉	—	2	2	no	—
52	C₂×D₈×C₁₉	—	2	4	no	—
53	C₁₉×#131	—	2	16	no	—
54	C₁₉×#131	—	2	4	no	—
55	C₁₉×#131	—	2	4	no	—
56	C₁₉×#131	—	2	4	no	—
57	C₁₉×#131	D₄	1	8	yes	complemented
58	C₂×M₁₆×C₁₉	—	2	16	no	—
59	C₂×M₁₆×C₁₉	—	2	1	no	—
60	C₂×M₁₆×C₁₉	—	2	4	no	—
61	C₂×M₁₆×C₁₉	—	2	2	no	—
62	C₂×M₁₆×C₁₉	—	2	2	no	—
63	C₂×M₁₆×C₁₉	—	2	4	no	—
64	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
65	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
66	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
67	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₉	—	2	1	no	—
69	C₂²×C₈×C₁₉	—	2	2	no	—
70	C₂²×C₈×C₁₉	—	2	2	no	—
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×#121	—	2	2	no	—
74	C₁₉×#121	—	2	2	no	—
75	C₁₉×#121	—	2	2	no	—
76	C₁₉×#121	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
79	C₁₉×#108	—	2	4	no	—
80	C₁₉×#106	—	2	2	no	—
81	C₁₉×#103	—	2	4	no	—
82	C₁₉×#102	—	2	4	no	—
83	C₁₉×#102	—	2	4	no	—
84	C₁₉×#100	—	2	8	no	—
85	C₁₉×C₂²⋊C₈	—	2	2	no	—
86	C₁₉×C₂²⋊C₈	—	2	2	no	—
87	C₂⁴×C₁₉	—	2	1	no	—
88	C₂⁴×C₁₉	—	2	2	no	—
89	C₂⁴×C₁₉	#41	1	1	yes	characteristic
90	#41×C₁₉	—	2	4	no	—
91	#41×C₁₉	—	2	8	no	—
92	#41×C₁₉	—	2	4	no	—
93	#41×C₁₉	—	2	4	no	—
94	#41×C₁₉	—	2	4	no	—
95	#41×C₁₉	—	2	2	no	—
96	#41×C₁₉	—	2	2	no	—
97	#41×C₁₉	C₂×D₄	1	4	yes	—
98	#41×C₁₉	#41	1	4	yes	—
99	C₂×Q₈×C₁₉	—	2	4	no	—
100	C₂×Q₈×C₁₉	—	2	1	no	—
101	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
102	C₂×D₄×C₁₉	—	2	8	no	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	4	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	4	no	—
110	C₂×D₄×C₁₉	—	2	4	no	—
111	C₂×D₄×C₁₉	—	4	2	no	—
112	C₂×D₄×C₁₉	—	4	2	no	—
113	C₂×D₄×C₁₉	—	8	4	no	—
114	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
129	SD₁₆×C₁₉	—	4	8	no	—
130	D₈×C₁₉	—	4	8	no	—
131	D₈×C₁₉	—	4	4	no	—
132	M₁₆×C₁₉	—	2	4	no	—
133	M₁₆×C₁₉	—	2	8	no	—
134	M₁₆×C₁₉	—	2	2	no	—
135	M₁₆×C₁₉	—	2	4	no	—
136	M₁₆×C₁₉	—	2	8	no	—
137	M₁₆×C₁₉	—	2	4	no	—
138	M₁₆×C₁₉	—	2	4	no	—
139	M₁₆×C₁₉	—	2	4	no	—
140	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
141	C₂×C₈×C₁₉	—	2	4	no	—
142	C₂×C₈×C₁₉	—	2	8	no	—
143	C₂×C₈×C₁₉	—	2	2	no	—
144	C₂×C₈×C₁₉	—	2	2	no	—
145	C₂×C₈×C₁₉	—	2	8	no	—
146	C₂×C₈×C₁₉	—	2	4	no	—
147	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₂²⋊C₄×C₁₉	—	4	2	no	—
153	C₂²⋊C₄×C₁₉	—	4	2	no	—
154	#32945	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₁₉	—	2	4	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	4	4	no	—
161	C₂³×C₁₉	—	8	2	no	—
162	C₂³×C₁₉	—	8	2	no	—
163	C₂³×C₁₉	—	8	2	no	—
164	C₂³×C₁₉	#121	1	1	yes	characteristic
165	C₂³×C₁₉	#121	1	1	yes	characteristic
166	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
167	Q₈×C₁₉	—	2	4	no	—
168	Q₈×C₁₉	—	2	2	no	—
169	Q₈×C₁₉	#121	1	4	yes	—
170	D₄×C₁₉	—	2	8	no	—
171	D₄×C₁₉	—	2	4	no	—
172	D₄×C₁₉	—	2	4	no	—
173	D₄×C₁₉	—	2	4	no	—
174	D₄×C₁₉	—	2	2	no	—
175	D₄×C₁₉	—	4	2	no	—
176	D₄×C₁₉	—	4	4	no	—
177	D₄×C₁₉	—	4	2	no	—
178	D₄×C₁₉	—	8	4	no	—
179	D₄×C₁₉	—	8	4	no	—
180	D₄×C₁₉	#121	1	4	yes	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	8	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	1	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	8	2	no	—
195	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
201	C₈×C₁₉	—	2	4	no	—
202	C₈×C₁₉	—	2	2	no	—
203	C₈×C₁₉	—	4	4	no	—
204	C₈×C₁₉	#120	1	4	yes	—
205	C₂×#568	C₂×C₁₉	1	1	yes	characteristic, complemented
206	C₂×#472	C₂×C₁₉	1	2	yes	complemented
207	C₂×#469	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#3006	C₂×C₁₉	1	2	yes	complemented
209	#1907	C₂×C₁₉	1	4	yes	complemented
210	#1900	C₂×C₁₉	1	2	yes	complemented
211	#1815	C₂×C₁₉	1	2	yes	complemented
212	#1811	C₂×C₁₉	1	1	yes	characteristic, complemented
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	4	no	—
217	C₂²×C₁₉	—	2	2	no	—
218	C₂²×C₁₉	—	2	2	no	—
219	C₂²×C₁₉	—	4	4	no	—
220	C₂²×C₁₉	—	8	2	no	—
221	C₂²×C₁₉	—	8	4	no	—
222	C₂²×C₁₉	—	8	2	no	—
223	C₂²×C₁₉	—	8	2	no	—
224	C₂²×C₁₉	—	8	2	no	—
225	C₂²×C₁₉	—	16	4	no	—
226	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
227	C₂²×C₁₉	#525	1	2	yes	—
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	2	4	no	—
230	C₄×C₁₉	—	2	1	no	—
231	C₄×C₁₉	—	8	2	no	—
232	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
233	C₄×C₁₉	C₂×#121	1	2	yes	—
234	C₄×C₁₉	#525	1	1	yes	characteristic
235	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	—
237	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
238	#568	—	2	8	no	—
239	C₂×#131	—	2	2	no	—
240	C₂×#131	C₂²×C₁₉	1	2	yes	—
241	C₂×#131	C₂²×C₁₉	1	2	yes	—
242	C₂²×M₁₆	—	2	2	no	—
243	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
244	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
245	C₂×#121	C₂²×C₁₉	1	2	yes	—
246	#472	—	2	8	no	—
247	#469	—	2	2	no	—
248	#469	—	2	2	no	—
249	#449	—	2	4	no	—
250	#448	—	2	2	no	—
251	#447	—	2	2	no	—
252	C₂×#108	C₂²×C₁₉	1	2	yes	complemented
253	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic, complemented
254	#417	C₂²×C₁₉	1	4	yes	—
255	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
256	C₂×#100	C₂²×C₁₉	1	4	yes	complemented
257	#407	C₂²×C₁₉	1	2	yes	—
258	#343	C₂²×C₁₉	1	4	yes	complemented
259	#341	C₂²×C₁₉	1	2	yes	complemented
260	C₂×C₁₉	—	2	2	no	—
261	C₂×C₁₉	—	4	1	no	—
262	C₂×C₁₉	—	4	1	no	—
263	C₂×C₁₉	—	4	4	no	—
264	C₂×C₁₉	—	16	2	no	—
265	C₂×C₁₉	#2847	1	1	yes	characteristic
266	C₂×C₁₉	#3068	1	2	yes	—
267	C₂×#41	—	2	4	no	—
268	C₂×#41	—	2	4	no	—
269	C₂×#41	—	2	1	no	—
270	C₂×#41	—	2	1	no	—
271	C₂×#41	D₄×C₁₉	1	2	yes	—
272	C₂×#41	C₂³×C₁₉	1	2	yes	—
273	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
277	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
280	AGL(1,ℤ/8)	—	2	8	no	—
281	AGL(1,ℤ/8)	—	2	8	no	—
282	C₂×SD₁₆	—	2	4	no	—
283	C₂×D₈	—	2	4	no	—
284	C₂×D₈	—	2	2	no	—
285	C₂×D₈	—	2	4	no	—
286	#131	—	2	16	no	—
287	#131	—	2	4	no	—
288	#131	—	2	4	no	—
289	#131	—	2	4	no	—
290	#131	D₄×C₁₉	1	8	yes	complemented
291	C₂×M₁₆	—	2	16	no	—
292	C₂×M₁₆	—	2	1	no	—
293	C₂×M₁₆	—	2	4	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	4	no	—
297	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
298	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
299	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
300	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
301	C₂²×C₈	—	2	1	no	—
302	C₂²×C₈	—	2	2	no	—
303	C₂²×C₈	—	2	2	no	—
304	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
306	#121	—	2	2	no	—
307	#121	—	2	2	no	—
308	#121	—	2	2	no	—
309	#121	—	2	2	no	—
310	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	#108	—	2	4	no	—
313	#106	—	2	2	no	—
314	#103	—	2	4	no	—
315	#102	—	2	4	no	—
316	#102	—	2	4	no	—
317	#100	—	2	8	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₁₉	#32945	1	1	yes	characteristic, direct product factor, Sylow
321	C₂⁴	—	2	1	no	—
322	C₂⁴	—	2	2	no	—
323	C₂⁴	#41×C₁₉	1	1	yes	characteristic
324	#41	—	2	4	no	—
325	#41	—	2	8	no	—
326	#41	—	2	4	no	—
327	#41	—	2	4	no	—
328	#41	—	2	4	no	—
329	#41	—	2	2	no	—
330	#41	—	2	2	no	—
331	#41	C₂×D₄×C₁₉	1	4	yes	—
332	#41	#41×C₁₉	1	4	yes	—
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
336	C₂×D₄	—	2	8	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	8	4	no	—
348	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
363	SD₁₆	—	4	8	no	—
364	D₈	—	4	8	no	—
365	D₈	—	4	4	no	—
366	M₁₆	—	2	4	no	—
367	M₁₆	—	2	8	no	—
368	M₁₆	—	2	2	no	—
369	M₁₆	—	2	4	no	—
370	M₁₆	—	2	8	no	—
371	M₁₆	—	2	4	no	—
372	M₁₆	—	2	4	no	—
373	M₁₆	—	2	4	no	—
374	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
375	C₂×C₈	—	2	4	no	—
376	C₂×C₈	—	2	8	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	8	no	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
382	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
383	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	8	2	no	—
395	C₂³	—	8	2	no	—
396	C₂³	—	8	2	no	—
397	C₂³	C₁₉×#121	1	1	yes	characteristic
398	C₂³	C₁₉×#121	1	1	yes	characteristic
399	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
400	Q₈	—	2	4	no	—
401	Q₈	—	2	2	no	—
402	Q₈	C₁₉×#121	1	4	yes	—
403	D₄	—	2	8	no	—
404	D₄	—	2	4	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	2	no	—
411	D₄	—	8	4	no	—
412	D₄	—	8	4	no	—
413	D₄	C₁₉×#121	1	4	yes	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
429	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
434	C₈	—	2	4	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	4	no	—
437	C₈	C₁₉×#120	1	4	yes	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	4	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	16	4	no	—
451	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
452	C₂²	C₁₉×#525	1	2	yes	—
453	C₄	—	2	1	no	—
454	C₄	—	2	4	no	—
455	C₄	—	2	1	no	—
456	C₄	—	8	2	no	—
457	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
458	C₄	C₂×C₁₉×#121	1	2	yes	—
459	C₄	C₁₉×#525	1	1	yes	characteristic
460	C₂	—	2	2	no	—
461	C₂	—	4	1	no	—
462	C₂	—	4	1	no	—
463	C₂	—	4	4	no	—
464	C₂	—	16	2	no	—
465	C₂	C₁₉×#2847	1	1	yes	characteristic
466	C₂	C₁₉×#3068	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#568	C₂	semidirect
2. C₂×C₁₉×#472	C₂	semidirect
3. C₂×C₁₉×#469	C₂	semidirect
4. C₁₉×#3006	C₂	semidirect
5. C₁₉×#1907	C₂	semidirect
6. C₁₉×#1900	C₂	semidirect
7. C₁₉×#1815	C₂	semidirect
8. C₁₉×#1811	C₂	semidirect
11. C₂²×D₈×C₁₉	C₂²	semidirect
26. C₂×C₁₉×#108	C₂²	semidirect
27. C₂×C₁₉×#106	C₂²	semidirect
29. C₂×C₁₉×#102	C₂²	semidirect
30. C₂×C₁₉×#100	C₂²	semidirect
32. C₁₉×#343	C₂²	semidirect
33. C₁₉×#341	C₂²	semidirect
57. C₁₉×#131	D₄	semidirect
154. #32945	C₁₉	direct (N × H)
205. C₂×#568	C₂×C₁₉	semidirect
206. C₂×#472	C₂×C₁₉	semidirect
207. C₂×#469	C₂×C₁₉	semidirect
208. #3006	C₂×C₁₉	semidirect
209. #1907	C₂×C₁₉	semidirect
210. #1900	C₂×C₁₉	semidirect
211. #1815	C₂×C₁₉	semidirect
212. #1811	C₂×C₁₉	semidirect
237. C₂²×D₈	C₂²×C₁₉	semidirect
252. C₂×#108	C₂²×C₁₉	semidirect
253. C₂×#106	C₂²×C₁₉	semidirect
255. C₂×#102	C₂²×C₁₉	semidirect
256. C₂×#100	C₂²×C₁₉	semidirect
258. #343	C₂²×C₁₉	semidirect
259. #341	C₂²×C₁₉	semidirect
290. #131	D₄×C₁₉	semidirect
320. C₁₉	#32945	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#568	2
C₂×C₁₉×#472	2
C₂×C₁₉×#469	2
C₁₉×#3006	2
C₁₉×#1907	2
C₁₉×#1900	2
C₁₉×#1815	2
C₁₉×#1811	2
#32945	19

Subgroups — C19×#32945 #18038904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32945 #18038904