Subgroups — C₁₉×#19553 #18025512

Order 4864.

624 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3253	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2979	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1703	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1685	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1683	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1665	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1549	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1543	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#532	C₂²	1	1	yes	characteristic
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₁₉×#500	—	2	1	no	—
16	C₁₉×#492	C₂²	1	2	yes	—
17	C₁₉×#487	C₂²	1	2	yes	—
18	C₁₉×#486	—	2	1	no	—
19	C₁₉×#480	—	2	2	no	—
20	C₁₉×#476	—	2	1	no	—
21	C₁₉×#476	C₂²	1	2	yes	—
22	C₁₉×#474	C₂²	1	2	yes	—
23	C₁₉×#474	C₂²	1	2	yes	—
24	C₁₉×#469	—	2	2	no	—
25	C₁₉×#461	—	2	1	no	—
26	C₁₉×#461	—	2	1	no	—
27	C₁₉×#459	—	2	1	no	—
28	C₁₉×#459	C₂²	1	2	yes	—
29	C₁₉×#448	—	2	2	no	—
30	C₁₉×#436	—	2	1	no	—
31	C₁₉×#436	C₂²	1	2	yes	—
32	C₈×D₄×C₁₉	—	2	1	no	—
33	C₈×D₄×C₁₉	C₂²	1	2	yes	—
34	C₁₉×#431	C₂²	1	1	yes	characteristic
35	C₁₉×#431	C₂²	1	1	yes	characteristic
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#423	C₂²	1	1	yes	characteristic
38	C₁₉×#408	—	2	2	no	—
39	C₁₉×#335	C₂²	1	2	yes	—
40	C₁₉×#334	C₂²	1	2	yes	—
41	C₁₉×#333	C₂²	1	1	yes	characteristic
42	C₁₉×#333	C₂²	1	1	yes	characteristic
43	C₁₉×#332	C₂²	1	2	yes	—
44	C₁₉×#332	C₂²	1	2	yes	—
45	C₁₉×#331	C₂²	1	1	yes	characteristic
46	C₁₉×#331	C₂²	1	1	yes	characteristic
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×#41×C₁₉	—	2	1	no	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂×SD₁₆×C₁₉	—	2	2	no	—
51	C₂×SD₁₆×C₁₉	—	2	2	no	—
52	C₂×D₈×C₁₉	—	2	2	no	—
53	C₂×M₁₆×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	—	2	2	no	—
55	C₂²×C₈×C₁₉	—	2	2	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₉×#127	D₄	1	1	yes	characteristic
63	C₁₉×#127	C₂³	1	1	yes	characteristic
64	C₁₉×#124	—	2	1	no	—
65	C₁₉×#124	—	2	1	no	—
66	C₁₉×#121	—	2	1	no	—
67	C₁₉×#121	—	2	1	no	—
68	C₁₉×#121	—	2	1	no	—
69	C₁₉×#121	D₄	1	2	yes	—
70	C₄×D₄×C₁₉	—	2	1	no	—
71	C₄×D₄×C₁₉	—	2	1	no	—
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
77	C₁₉×#107	—	2	2	no	—
78	C₁₉×#107	—	2	2	no	—
79	C₁₉×#106	—	2	2	no	—
80	C₁₉×C₄⋊C₈	—	2	1	no	—
81	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₁₉×#103	—	2	2	no	—
89	C₁₉×#103	—	2	2	no	—
90	C₁₉×#102	—	2	2	no	—
91	C₁₉×#102	—	2	2	no	—
92	C₁₉×#102	—	2	2	no	—
93	C₁₉×#102	—	2	2	no	—
94	C₁₉×C₂²⋊C₈	—	2	1	no	—
95	C₁₉×C₂²⋊C₈	—	2	1	no	—
96	C₁₉×C₂²⋊C₈	—	2	2	no	—
97	C₁₉×C₂²⋊C₈	—	2	2	no	—
98	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
99	C₄×C₈×C₁₉	—	2	1	no	—
100	C₄×C₈×C₁₉	—	2	1	no	—
101	C₄×C₈×C₁₉	C₂³	1	2	yes	—
102	#41×C₁₉	—	8	1	no	—
103	#41×C₁₉	—	8	1	no	—
104	#41×C₁₉	—	8	2	no	—
105	C₂×Q₈×C₁₉	—	2	1	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	2	1	no	—
108	C₂×Q₈×C₁₉	—	4	1	no	—
109	C₂×Q₈×C₁₉	—	8	1	no	—
110	C₂×Q₈×C₁₉	—	8	1	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	2	1	no	—
115	C₂×D₄×C₁₉	—	2	1	no	—
116	C₂×D₄×C₁₉	—	2	1	no	—
117	C₂×D₄×C₁₉	—	4	1	no	—
118	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	4	1	no	—
121	C₂²×C₄×C₁₉	—	4	1	no	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
125	SD₁₆×C₁₉	—	8	2	no	—
126	SD₁₆×C₁₉	—	8	2	no	—
127	D₈×C₁₉	—	8	2	no	—
128	M₁₆×C₁₉	—	8	2	no	—
129	M₁₆×C₁₉	—	8	1	no	—
130	C₂×C₈×C₁₉	—	2	1	no	—
131	C₂×C₈×C₁₉	—	2	1	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	—	2	1	no	—
134	C₂×C₈×C₁₉	—	2	1	no	—
135	C₂×C₈×C₁₉	—	8	2	no	—
136	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	4	1	no	—
144	C₄⋊C₄×C₁₉	—	4	1	no	—
145	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₂²⋊C₄×C₁₉	—	2	2	no	—
147	C₂²⋊C₄×C₁₉	—	2	2	no	—
148	C₂²⋊C₄×C₁₉	—	4	1	no	—
149	C₂²⋊C₄×C₁₉	—	4	1	no	—
150	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₁₉	#41	1	1	yes	characteristic
153	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
154	#19553	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	4	1	no	—
157	C₂³×C₁₉	#121	1	1	yes	characteristic
158	Q₈×C₁₉	—	4	2	no	—
159	Q₈×C₁₉	—	4	2	no	—
160	Q₈×C₁₉	—	8	1	no	—
161	Q₈×C₁₉	—	8	1	no	—
162	Q₈×C₁₉	—	8	2	no	—
163	D₄×C₁₉	—	2	2	no	—
164	D₄×C₁₉	—	2	2	no	—
165	D₄×C₁₉	—	4	1	no	—
166	D₄×C₁₉	—	4	1	no	—
167	D₄×C₁₉	—	4	1	no	—
168	D₄×C₁₉	—	4	1	no	—
169	D₄×C₁₉	—	4	2	no	—
170	D₄×C₁₉	—	8	1	no	—
171	D₄×C₁₉	—	8	1	no	—
172	D₄×C₁₉	—	8	2	no	—
173	D₄×C₁₉	—	8	2	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	8	2	no	—
185	C₂×C₄×C₁₉	—	8	2	no	—
186	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
192	C₈×C₁₉	—	2	2	no	—
193	C₈×C₁₉	—	2	2	no	—
194	C₈×C₁₉	—	4	1	no	—
195	C₈×C₁₉	—	4	1	no	—
196	C₈×C₁₉	—	4	1	no	—
197	C₈×C₁₉	—	4	2	no	—
198	C₈×C₁₉	—	4	1	no	—
199	#3253	C₂×C₁₉	1	1	yes	characteristic
200	#3226	C₂×C₁₉	1	1	yes	characteristic, complemented
201	#3206	C₂×C₁₉	1	1	yes	characteristic, complemented
202	#2979	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#1703	C₂×C₁₉	1	2	yes	complemented
204	#1685	C₂×C₁₉	1	2	yes	complemented
205	#1683	C₂×C₁₉	1	2	yes	complemented
206	#1665	C₂×C₁₉	1	2	yes	complemented
207	#1574	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#1549	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#1543	C₂×C₁₉	1	1	yes	characteristic, complemented
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	—	2	1	no	—
213	C₂²×C₁₉	—	4	2	no	—
214	C₂²×C₁₉	—	4	2	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	8	1	no	—
217	C₂²×C₁₉	—	8	1	no	—
218	C₂²×C₁₉	—	8	1	no	—
219	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	—	8	2	no	—
225	C₄×C₁₉	—	8	1	no	—
226	C₄×C₁₉	#471	1	2	yes	—
227	C₄×C₁₉	#576	1	1	yes	characteristic
228	C₄×C₁₉	#576	1	1	yes	characteristic
229	C₄×C₁₉	#577	1	1	yes	characteristic
230	C₄×C₁₉	#578	1	1	yes	characteristic
231	#532	C₂²×C₁₉	1	1	yes	characteristic
232	#532	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
234	#500	—	2	1	no	—
235	#492	C₂²×C₁₉	1	2	yes	—
236	#487	C₂²×C₁₉	1	2	yes	—
237	#486	—	2	1	no	—
238	#480	—	2	2	no	—
239	#476	—	2	1	no	—
240	#476	C₂²×C₁₉	1	2	yes	—
241	#474	C₂²×C₁₉	1	2	yes	—
242	#474	C₂²×C₁₉	1	2	yes	—
243	#469	—	2	2	no	—
244	#461	—	2	1	no	—
245	#461	—	2	1	no	—
246	#459	—	2	1	no	—
247	#459	C₂²×C₁₉	1	2	yes	—
248	#448	—	2	2	no	—
249	#436	—	2	1	no	—
250	#436	C₂²×C₁₉	1	2	yes	—
251	C₈×D₄	—	2	1	no	—
252	C₈×D₄	C₂²×C₁₉	1	2	yes	—
253	#431	C₂²×C₁₉	1	1	yes	characteristic
254	#431	C₂²×C₁₉	1	1	yes	characteristic
255	#431	C₂²×C₁₉	1	1	yes	characteristic
256	#423	C₂²×C₁₉	1	1	yes	characteristic
257	#408	—	2	2	no	—
258	#335	C₂²×C₁₉	1	2	yes	—
259	#334	C₂²×C₁₉	1	2	yes	—
260	#333	C₂²×C₁₉	1	1	yes	characteristic
261	#333	C₂²×C₁₉	1	1	yes	characteristic
262	#332	C₂²×C₁₉	1	2	yes	—
263	#332	C₂²×C₁₉	1	2	yes	—
264	#331	C₂²×C₁₉	1	1	yes	characteristic
265	#331	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×C₁₉	—	4	1	no	—
267	C₂×C₁₉	—	8	2	no	—
268	C₂×C₁₉	—	16	1	no	—
269	C₂×C₁₉	#3041	1	1	yes	characteristic
270	C₂×C₁₉	#3063	1	1	yes	characteristic
271	C₂×C₁₉	C₂×#471	1	1	yes	characteristic
272	C₂×#41	—	2	1	no	—
273	C₂×#41	—	2	1	no	—
274	C₂²×Q₈	—	2	1	no	—
275	C₂×SD₁₆	—	2	2	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
285	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
286	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
287	#127	D₄×C₁₉	1	1	yes	characteristic
288	#127	C₂³×C₁₉	1	1	yes	characteristic
289	#124	—	2	1	no	—
290	#124	—	2	1	no	—
291	#121	—	2	1	no	—
292	#121	—	2	1	no	—
293	#121	—	2	1	no	—
294	#121	D₄×C₁₉	1	2	yes	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	C₂³×C₁₉	1	2	yes	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
302	#107	—	2	2	no	—
303	#107	—	2	2	no	—
304	#106	—	2	2	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
307	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
308	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
309	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
310	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
311	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
312	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
313	#103	—	2	2	no	—
314	#103	—	2	2	no	—
315	#102	—	2	2	no	—
316	#102	—	2	2	no	—
317	#102	—	2	2	no	—
318	#102	—	2	2	no	—
319	C₂²⋊C₈	—	2	1	no	—
320	C₂²⋊C₈	—	2	1	no	—
321	C₂²⋊C₈	—	2	2	no	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	C₂³×C₁₉	1	2	yes	—
327	C₁₉	#19553	1	1	yes	characteristic, direct product factor, Sylow
328	#41	—	8	1	no	—
329	#41	—	8	1	no	—
330	#41	—	8	2	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	4	1	no	—
335	C₂×Q₈	—	8	1	no	—
336	C₂×Q₈	—	8	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
350	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
351	SD₁₆	—	8	2	no	—
352	SD₁₆	—	8	2	no	—
353	D₈	—	8	2	no	—
354	M₁₆	—	8	2	no	—
355	M₁₆	—	8	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	8	2	no	—
362	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
363	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	4	1	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
377	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
378	C₄²	#41×C₁₉	1	1	yes	characteristic
379	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
380	C₂³	—	2	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	C₁₉×#121	1	1	yes	characteristic
383	Q₈	—	4	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	8	1	no	—
386	Q₈	—	8	1	no	—
387	Q₈	—	8	2	no	—
388	D₄	—	2	2	no	—
389	D₄	—	2	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	1	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	D₄	—	8	1	no	—
396	D₄	—	8	1	no	—
397	D₄	—	8	2	no	—
398	D₄	—	8	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	—	8	2	no	—
411	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
412	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
413	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	4	1	no	—
420	C₈	—	4	1	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	2	no	—
438	C₄	—	8	2	no	—
439	C₄	—	8	1	no	—
440	C₄	C₁₉×#471	1	2	yes	—
441	C₄	C₁₉×#576	1	1	yes	characteristic
442	C₄	C₁₉×#576	1	1	yes	characteristic
443	C₄	C₁₉×#577	1	1	yes	characteristic
444	C₄	C₁₉×#578	1	1	yes	characteristic
445	C₂	—	4	1	no	—
446	C₂	—	8	2	no	—
447	C₂	—	16	1	no	—
448	C₂	C₁₉×#3041	1	1	yes	characteristic
449	C₂	C₁₉×#3063	1	1	yes	characteristic
450	C₂	C₂×C₁₉×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3253	C₂
LCS	G ▷ 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
2. C₁₉×#3226	C₂	semidirect
3. C₁₉×#3206	C₂	semidirect
4. C₁₉×#2979	C₂	semidirect
5. C₁₉×#1703	C₂	semidirect
6. C₁₉×#1685	C₂	semidirect
7. C₁₉×#1683	C₂	semidirect
8. C₁₉×#1665	C₂	semidirect
9. C₁₉×#1574	C₂	semidirect
10. C₁₉×#1549	C₂	semidirect
11. C₁₉×#1543	C₂	semidirect
154. #19553	C₁₉	direct (N × H)
200. #3226	C₂×C₁₉	semidirect
201. #3206	C₂×C₁₉	semidirect
202. #2979	C₂×C₁₉	semidirect
203. #1703	C₂×C₁₉	semidirect
204. #1685	C₂×C₁₉	semidirect
205. #1683	C₂×C₁₉	semidirect
206. #1665	C₂×C₁₉	semidirect
207. #1574	C₂×C₁₉	semidirect
208. #1549	C₂×C₁₉	semidirect
209. #1543	C₂×C₁₉	semidirect
327. C₁₉	#19553	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×#3253	2
C₁₉×#3226	2
C₁₉×#3206	2
C₁₉×#2979	2
C₁₉×#1703	2
C₁₉×#1685	2
C₁₉×#1683	2
C₁₉×#1665	2
C₁₉×#1574	2
C₁₉×#1549	2
C₁₉×#1543	2
#19553	19

Subgroups — C19×#19553 #18025512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19553 #18025512