Subgroups — #18078364

Order 4864.

508 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572670	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563460	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562246	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562130	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561533	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561492	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3109	C₂	1	1	yes	maximal, characteristic
8	#11926622	—	2	1	no	—
9	#11926616	—	2	2	no	—
10	D₄×C₁₉⋊C₈	—	2	1	no	—
11	#11926601	C₂²	1	1	yes	characteristic
12	#11926597	C₂²	1	1	yes	characteristic
13	C₂×#10597289	—	2	1	no	—
14	#11926508	—	2	1	no	—
15	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
16	C₂×#10597260	C₂²	1	1	yes	characteristic
17	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
18	#11926306	—	2	1	no	—
19	#11926284	—	2	2	no	—
20	#11926278	—	2	1	no	—
21	#11926278	—	2	1	no	—
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#481	—	2	1	no	—
25	C₁₉×#476	C₄	1	1	yes	characteristic, complemented
26	C₁₉×#476	C₄	1	1	yes	characteristic, complemented
27	C₁₉×#459	C₄	1	1	yes	characteristic, complemented
28	C₁₉×#459	C₄	1	1	yes	characteristic, complemented
29	C₁₉×#447	—	2	1	no	—
30	C₁₉×#442	—	2	1	no	—
31	C₁₉×#442	—	2	1	no	—
32	C₁₉×#432	C₂²	1	1	yes	characteristic
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	—	2	1	no	—
36	C₂×D₈×C₁₉	—	2	1	no	—
37	C₂×D₈×C₁₉	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
39	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
40	C₁₉×#124	—	2	1	no	—
41	C₁₉×#121	—	2	1	no	—
42	C₁₉×#121	—	2	1	no	—
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	—	2	1	no	—
46	C₄×D₄×C₁₉	—	2	1	no	—
47	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊Dic₁₉	—	2	1	no	—
55	C₂×C₄×Dic₁₉	—	2	1	no	—
56	C₂×#64520	—	2	2	no	—
57	C₂²×C₁₉⋊C₈	—	2	1	no	—
58	C₂²×C₁₉⋊C₈	—	2	2	no	—
59	C₁₉×#106	—	2	1	no	—
60	C₁₉×#106	—	2	1	no	—
61	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
62	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
63	C₁₉×#102	—	2	1	no	—
64	C₁₉×#102	—	2	1	no	—
65	C₁₉×#102	—	2	1	no	—
66	C₁₉×#102	—	2	1	no	—
67	C₁₉×C₂²⋊C₈	—	2	1	no	—
68	C₁₉×#97	—	2	1	no	—
69	#10597289	—	2	4	no	—
70	C₁₉⋊#95	—	2	1	no	—
71	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
72	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
73	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
74	C₂²⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
75	C₂²⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
76	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
78	#10597260	—	2	1	no	—
79	#10597260	—	2	1	no	—
80	#10597260	D₄	1	2	yes	—
81	C₄×C₁₉⋊C₈	—	2	1	no	—
82	C₂⁴×C₁₉	—	2	1	no	—
83	#41×C₁₉	—	8	1	no	—
84	#41×C₁₉	—	8	1	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	2	1	no	—
88	C₂×D₄×C₁₉	—	2	1	no	—
89	C₂×D₄×C₁₉	—	2	1	no	—
90	C₂×D₄×C₁₉	—	2	1	no	—
91	C₂×D₄×C₁₉	—	4	1	no	—
92	C₂×D₄×C₁₉	—	4	1	no	—
93	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	8	2	no	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
105	C₂²×Dic₁₉	—	4	1	no	—
106	D₈×C₁₉	—	4	2	no	—
107	D₈×C₁₉	—	4	2	no	—
108	C₂×C₈×C₁₉	—	2	1	no	—
109	C₂×C₈×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂²⋊C₄×C₁₉	—	2	1	no	—
117	C₂²⋊C₄×C₁₉	—	2	1	no	—
118	C₂²⋊C₄×C₁₉	—	2	1	no	—
119	C₂²⋊C₄×C₁₉	—	4	1	no	—
120	C₂²⋊C₄×C₁₉	—	4	1	no	—
121	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₁₉	#41	1	1	yes	characteristic
125	C₄⋊Dic₁₉	—	2	2	no	—
126	C₄⋊Dic₁₉	—	4	1	no	—
127	C₄×Dic₁₉	—	8	1	no	—
128	#64520	—	8	2	no	—
129	C₂×C₁₉⋊C₈	—	2	2	no	—
130	C₂×C₁₉⋊C₈	—	2	1	no	—
131	C₂×C₁₉⋊C₈	—	2	1	no	—
132	C₂×C₁₉⋊C₈	—	2	2	no	—
133	C₂×C₁₉⋊C₈	—	4	1	no	—
134	C₂×C₁₉⋊C₈	—	4	1	no	—
135	C₂×C₁₉⋊C₈	—	8	2	no	—
136	#9163	—	19	1	no	maximal, Sylow
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	2	1	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	8	1	no	—
144	C₂³×C₁₉	#121	1	1	yes	characteristic
145	Q₈×C₁₉	—	8	1	no	—
146	D₄×C₁₉	—	2	1	no	—
147	D₄×C₁₉	—	2	1	no	—
148	D₄×C₁₉	—	2	1	no	—
149	D₄×C₁₉	—	4	2	no	—
150	D₄×C₁₉	—	4	1	no	—
151	D₄×C₁₉	—	4	1	no	—
152	D₄×C₁₉	—	8	1	no	—
153	D₄×C₁₉	—	8	1	no	—
154	D₄×C₁₉	—	8	1	no	—
155	D₄×C₁₉	—	8	1	no	—
156	D₄×C₁₉	#104	1	2	yes	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	8	1	no	—
168	C₂×C₄×C₁₉	—	8	1	no	—
169	C₂×C₄×C₁₉	—	8	2	no	—
170	C₂×C₄×C₁₉	—	8	1	no	—
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
177	C₂×Dic₁₉	—	4	2	no	—
178	C₂×Dic₁₉	—	8	1	no	—
179	C₂×Dic₁₉	—	8	1	no	—
180	C₈×C₁₉	—	4	1	no	—
181	C₈×C₁₉	—	4	1	no	—
182	C₁₉⋊C₈	—	4	2	no	—
183	C₁₉⋊C₈	—	4	1	no	—
184	C₁₉⋊C₈	—	4	2	no	—
185	C₁₉⋊C₈	—	4	1	no	—
186	#3109	D₁₉	1	1	yes	characteristic
187	#2974	—	19	1	no	—
188	#1762	—	19	1	no	—
189	#1530	—	19	1	no	—
190	#1502	—	19	1	no	—
191	#1302	—	19	1	no	—
192	#1285	—	19	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	2	no	—
196	C₂²×C₁₉	—	4	1	no	—
197	C₂²×C₁₉	—	4	1	no	—
198	C₂²×C₁₉	—	4	1	no	—
199	C₂²×C₁₉	—	4	1	no	—
200	C₂²×C₁₉	—	4	1	no	—
201	C₂²×C₁₉	—	8	2	no	—
202	C₂²×C₁₉	—	8	2	no	—
203	C₂²×C₁₉	—	8	1	no	—
204	C₂²×C₁₉	—	8	1	no	—
205	C₂²×C₁₉	—	8	1	no	—
206	C₂²×C₁₉	#386	1	1	yes	characteristic
207	C₂²×C₁₉	#471	1	1	yes	characteristic
208	C₂²×C₁₉	#472	1	1	yes	characteristic
209	C₄×C₁₉	—	2	1	no	—
210	C₄×C₁₉	—	2	1	no	—
211	C₄×C₁₉	—	2	1	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	2	1	no	—
214	C₄×C₁₉	—	4	1	no	—
215	C₄×C₁₉	—	4	1	no	—
216	C₄×C₁₉	—	8	1	no	—
217	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
218	C₄×C₁₉	#421	1	1	yes	characteristic
219	Dic₁₉	—	8	2	no	—
220	#532	C₂×D₁₉	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
222	#481	—	2	1	no	—
223	#476	Dic₁₉	1	1	yes	characteristic, complemented
224	#476	Dic₁₉	1	1	yes	characteristic, complemented
225	#459	Dic₁₉	1	1	yes	characteristic, complemented
226	#459	Dic₁₉	1	1	yes	characteristic, complemented
227	#447	—	2	1	no	—
228	#442	—	2	1	no	—
229	#442	—	2	1	no	—
230	#436	—	38	1	no	—
231	#435	—	38	2	no	—
232	C₈×D₄	—	38	1	no	—
233	#432	—	19	1	no	—
234	#432	C₂×D₁₉	1	1	yes	characteristic
235	#431	—	19	1	no	—
236	C₂×#102	—	38	1	no	—
237	#407	—	38	1	no	—
238	C₂×C₂²⋊C₈	—	38	1	no	—
239	C₂×#97	—	19	1	no	—
240	C₄×C₄⋊C₄	—	19	1	no	—
241	#340	—	38	1	no	—
242	#329	—	38	2	no	—
243	#327	—	38	1	no	—
244	#327	—	38	1	no	—
245	C₂×C₁₉	—	2	1	no	—
246	C₂×C₁₉	—	2	1	no	—
247	C₂×C₁₉	—	4	2	no	—
248	C₂×C₁₉	—	8	1	no	—
249	C₂×C₁₉	—	16	1	no	—
250	C₂×C₁₉	#1871	1	1	yes	characteristic
251	C₂×C₁₉	#1904	1	1	yes	characteristic
252	C₂×C₁₉	#1907	1	1	yes	characteristic
253	C₂×#41	—	2	1	no	—
254	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
255	C₂³×C₄	—	2	1	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×M₁₆	—	38	2	no	—
259	C₂²×C₈	—	38	1	no	—
260	C₂²×C₈	—	38	2	no	—
261	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
262	#127	C₂×Dic₁₉	1	1	yes	characteristic
263	#124	—	2	1	no	—
264	#121	—	2	1	no	—
265	#121	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	—	2	1	no	—
270	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
271	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
272	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
273	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	—	38	1	no	—
275	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₄²	—	38	1	no	—
278	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
279	#106	—	2	1	no	—
280	#106	—	2	1	no	—
281	C₄⋊C₈	—	38	1	no	—
282	C₄⋊C₈	—	38	1	no	—
283	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
284	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
285	#102	—	2	1	no	—
286	#102	—	2	1	no	—
287	#102	—	2	1	no	—
288	#102	—	2	1	no	—
289	#102	—	38	4	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	—	19	1	no	—
292	C₂²⋊C₈	—	19	1	no	—
293	C₂²⋊C₈	—	38	2	no	—
294	C₂²⋊C₈	—	38	2	no	—
295	C₂²⋊C₈	—	38	1	no	—
296	#97	—	2	1	no	—
297	#97	—	19	2	no	—
298	#97	—	38	1	no	—
299	#97	—	38	1	no	—
300	C₄×C₈	—	38	1	no	—
301	#95	—	38	1	no	—
302	C₁₉	#9163	1	1	yes	characteristic, complemented, Sylow
303	C₂⁴	—	2	1	no	—
304	#41	—	8	1	no	—
305	#41	—	8	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
315	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	8	2	no	—
323	C₂²×C₄	—	76	1	no	—
324	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
325	C₂²×C₄	#64543	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
327	D₈	—	4	2	no	—
328	D₈	—	4	2	no	—
329	M₁₆	—	152	2	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	38	2	no	—
333	C₂×C₈	—	38	1	no	—
334	C₂×C₈	—	38	1	no	—
335	C₂×C₈	—	38	2	no	—
336	C₂×C₈	—	76	1	no	—
337	C₂×C₈	—	76	1	no	—
338	C₂×C₈	—	152	2	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	38	2	no	—
343	C₄⋊C₄	—	76	1	no	—
344	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
345	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	2	1	no	—
348	C₂²⋊C₄	—	2	1	no	—
349	C₂²⋊C₄	—	2	1	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₄²	—	152	1	no	—
353	C₄²	D₄×D₁₉	1	1	yes	characteristic
354	C₄²	#64543	1	1	yes	characteristic
355	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
356	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	8	1	no	—
364	C₂³	#10597385	1	1	yes	characteristic
365	Q₈	—	8	1	no	—
366	D₄	—	2	1	no	—
367	D₄	—	2	1	no	—
368	D₄	—	2	1	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	1	no	—
371	D₄	—	4	1	no	—
372	D₄	—	8	1	no	—
373	D₄	—	8	1	no	—
374	D₄	—	8	1	no	—
375	D₄	—	8	1	no	—
376	D₄	#10597294	1	2	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	8	1	no	—
388	C₂×C₄	—	8	1	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	—	76	2	no	—
392	C₂×C₄	—	152	1	no	—
393	C₂×C₄	—	152	1	no	—
394	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
395	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
396	C₂×C₄	#10597381	1	1	yes	characteristic
397	C₂×C₄	#10597383	1	1	yes	characteristic
398	C₂×C₄	#10597385	1	1	yes	characteristic
399	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
400	C₈	—	4	1	no	—
401	C₈	—	4	1	no	—
402	C₈	—	76	2	no	—
403	C₈	—	76	1	no	—
404	C₈	—	76	2	no	—
405	C₈	—	76	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	#11926424	1	1	yes	characteristic
420	C₂²	#11926805	1	1	yes	characteristic
421	C₂²	#11926812	1	1	yes	characteristic
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	8	1	no	—
430	C₄	—	152	2	no	—
431	C₄	C₂×#10597294	1	1	yes	characteristic
432	C₄	#11926561	1	1	yes	characteristic
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	4	2	no	—
436	C₂	—	8	1	no	—
437	C₂	—	16	1	no	—
438	C₂	#14563938	1	1	yes	characteristic
439	C₂	#14564124	1	1	yes	characteristic
440	C₂	#14564145	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3109	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3109	D₁₉
hypocenter	C₁₉	#9163
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3109

Complements

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

N	H ≅ G/N	type
1. #14572670	C₂	semidirect
2. #14563460	C₂	semidirect
3. #14562246	C₂	semidirect
4. #14562130	C₂	semidirect
5. #14561533	C₂	semidirect
6. #14561492	C₂	semidirect
25. C₁₉×#476	C₄	semidirect
26. C₁₉×#476	C₄	semidirect
27. C₁₉×#459	C₄	semidirect
28. C₁₉×#459	C₄	semidirect
223. #476	Dic₁₉	semidirect
224. #476	Dic₁₉	semidirect
225. #459	Dic₁₉	semidirect
226. #459	Dic₁₉	semidirect
302. C₁₉	#9163	semidirect

Maximal subgroups

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

subgroup	index
#14572670	2
#14563460	2
#14562246	2
#14562130	2
#14561533	2
#14561492	2
C₁₉×#3109	2
#9163	19