Subgroups — #18082259

Order 4864.

510 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563673	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563411	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562155	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562151	C₂	1	1	yes	maximal, characteristic
5	#14561999	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561995	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#465	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597276	—	2	1	no	—
9	#11926508	C₂²	1	1	yes	characteristic
10	#11926508	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×#10597272	—	2	1	no	—
13	C₄×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	#11926309	—	2	1	no	—
15	#11926298	—	2	1	no	—
16	#11926281	—	2	2	no	—
17	#11926278	—	2	2	no	—
18	#11926270	—	2	2	no	—
19	#11926268	—	2	2	no	—
20	C₂²×SD₁₆×C₁₉	C₄	1	1	yes	characteristic, complemented
21	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
24	C₁₉×#465	—	2	1	no	—
25	C₁₉×#465	—	2	1	no	—
26	C₁₉×#465	—	2	1	no	—
27	C₁₉×#465	—	2	1	no	—
28	C₂×C₁₉×#106	C₄	1	1	yes	characteristic, complemented
29	C₂×C₁₉×#103	C₄	1	1	yes	characteristic, complemented
30	C₂×C₁₉×#102	C₄	1	1	yes	characteristic, complemented
31	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×SD₁₆×C₁₉	—	2	1	no	—
36	C₂×SD₁₆×C₁₉	—	2	1	no	—
37	C₂×SD₁₆×C₁₉	—	4	2	no	—
38	C₂²×C₈×C₁₉	—	4	2	no	—
39	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
45	C₁₉×C₂²⋊Q₈	—	2	1	no	—
46	C₁₉×C₂²⋊Q₈	—	2	1	no	—
47	C₁₉×C₂²⋊Q₈	—	2	1	no	—
48	C₁₉×C₂²⋊Q₈	—	2	1	no	—
49	C₁₉×#121	—	2	1	no	—
50	C₁₉×#121	—	2	1	no	—
51	C₁₉×#121	—	2	1	no	—
52	C₁₉×#121	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
59	C₂×C₄×Dic₁₉	—	2	1	no	—
60	C₂×#64520	—	2	1	no	—
61	C₂×#64520	—	2	1	no	—
62	C₂²×C₁₉⋊C₈	—	2	1	no	—
63	C₁₉×#106	—	2	1	no	—
64	C₁₉×#106	—	2	1	no	—
65	C₁₉×#103	—	2	1	no	—
66	C₁₉×#103	—	2	1	no	—
67	C₁₉×#102	—	2	1	no	—
68	C₁₉×#102	—	2	1	no	—
69	C₁₉⋊#95	D₄	1	2	yes	—
70	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
73	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
74	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
75	C₂²⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
76	#10597276	—	4	2	no	—
77	#10597272	—	4	2	no	—
78	C₂⁴×C₁₉	—	2	1	no	—
79	C₂⁴×C₁₉	#41	1	1	yes	characteristic
80	C₂×Q₈×C₁₉	—	2	1	no	—
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	4	1	no	—
83	C₂×Q₈×C₁₉	—	4	1	no	—
84	C₂×D₄×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	8	2	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	C₂²×Dic₁₉	—	2	2	no	—
103	SD₁₆×C₁₉	—	4	2	no	—
104	SD₁₆×C₁₉	—	4	2	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	4	1	no	—
109	C₂×C₈×C₁₉	—	4	1	no	—
110	C₂×C₈×C₁₉	—	4	1	no	—
111	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₄⋊C₄×C₁₉	—	2	1	no	—
119	C₄⋊C₄×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	—	4	1	no	—
121	C₂²⋊C₄×C₁₉	—	4	1	no	—
122	C₂²⋊C₄×C₁₉	—	4	1	no	—
123	C₂²⋊C₄×C₁₉	—	4	1	no	—
124	C₂²⋊C₄×C₁₉	—	4	1	no	—
125	C₂²⋊Dic₁₉	—	4	2	no	—
126	C₄×Dic₁₉	—	4	1	no	—
127	C₄×Dic₁₉	—	4	1	no	—
128	#64520	—	4	1	no	—
129	#64520	—	4	1	no	—
130	#64520	—	4	1	no	—
131	#64520	—	4	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	—	4	1	no	—
136	C₂×C₁₉⋊C₈	—	4	1	no	—
137	#9816	—	19	1	no	maximal, Sylow
138	C₂³×C₁₉	—	2	2	no	—
139	C₂³×C₁₉	—	2	2	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	—	8	1	no	—
144	C₂³×C₁₉	—	8	1	no	—
145	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
146	C₂³×C₁₉	#121	1	1	yes	characteristic
147	C₂³×C₁₉	#124	1	1	yes	characteristic
148	Q₈×C₁₉	—	4	1	no	—
149	Q₈×C₁₉	—	4	1	no	—
150	Q₈×C₁₉	—	8	1	no	—
151	D₄×C₁₉	—	4	1	no	—
152	D₄×C₁₉	—	4	1	no	—
153	D₄×C₁₉	—	8	1	no	—
154	D₄×C₁₉	—	8	2	no	—
155	D₄×C₁₉	—	8	2	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	8	1	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	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
175	C₂×Dic₁₉	—	4	2	no	—
176	C₂×Dic₁₉	—	4	2	no	—
177	C₂×Dic₁₉	—	4	2	no	—
178	C₈×C₁₉	—	2	1	no	—
179	C₈×C₁₉	—	2	1	no	—
180	C₈×C₁₉	—	2	1	no	—
181	C₈×C₁₉	#99	1	2	yes	—
182	C₁₉⋊C₈	—	4	2	no	—
183	C₁₉⋊C₈	—	8	1	no	—
184	C₁₉⋊C₈	—	8	1	no	—
185	C₂×#465	D₁₉	1	1	yes	characteristic
186	#1810	—	19	1	no	—
187	#1752	—	19	1	no	—
188	#1508	—	19	1	no	—
189	#1507	—	19	1	no	—
190	#1472	—	19	1	no	—
191	#1471	—	19	1	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	4	4	no	—
200	C₂²×C₁₉	—	8	1	no	—
201	C₂²×C₁₉	—	8	1	no	—
202	C₂²×C₁₉	—	8	1	no	—
203	C₂²×C₁₉	—	16	2	no	—
204	C₂²×C₁₉	#390	1	1	yes	characteristic
205	C₂²×C₁₉	#444	1	2	yes	—
206	C₂²×C₁₉	#471	1	2	yes	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	1	no	—
209	C₄×C₁₉	—	2	1	no	—
210	C₄×C₁₉	—	8	1	no	—
211	C₄×C₁₉	—	8	1	no	—
212	C₄×C₁₉	—	8	1	no	—
213	C₄×C₁₉	C₂×#99	1	1	yes	characteristic
214	C₄×C₁₉	#410	1	1	yes	characteristic
215	Dic₁₉	—	8	2	no	—
216	C₂²×SD₁₆	Dic₁₉	1	1	yes	characteristic, complemented
217	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
218	C₂×C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
219	C₂×#121	C₂×D₁₉	1	1	yes	characteristic
220	#465	—	2	1	no	—
221	#465	—	2	1	no	—
222	#465	—	2	1	no	—
223	#465	—	2	1	no	—
224	C₂×#108	—	38	1	no	—
225	C₂×#106	Dic₁₉	1	1	yes	characteristic, complemented
226	C₂×#103	Dic₁₉	1	1	yes	characteristic, complemented
227	C₂×#102	Dic₁₉	1	1	yes	characteristic, complemented
228	#407	—	19	1	no	—
229	#407	—	19	1	no	—
230	C₂×C₂²⋊C₈	—	19	1	no	—
231	C₂×#97	—	38	1	no	—
232	C₄×C₂²⋊C₄	—	19	1	no	—
233	#341	—	38	1	no	—
234	#336	—	38	1	no	—
235	#328	—	38	2	no	—
236	#327	—	38	2	no	—
237	#324	—	38	2	no	—
238	#323	—	38	2	no	—
239	C₂×C₁₉	—	2	2	no	—
240	C₂×C₁₉	—	2	2	no	—
241	C₂×C₁₉	—	4	1	no	—
242	C₂×C₁₉	—	16	1	no	—
243	C₂×C₁₉	#1964	1	1	yes	characteristic
244	C₂×C₁₉	#1975	1	1	yes	characteristic
245	C₂×C₁₉	#1977	1	1	yes	characteristic
246	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
249	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
250	C₂×SD₁₆	—	2	1	no	—
251	C₂×SD₁₆	—	2	1	no	—
252	C₂×SD₁₆	—	4	2	no	—
253	C₂×M₁₆	—	38	1	no	—
254	C₂×M₁₆	—	38	1	no	—
255	C₂²×C₈	—	4	2	no	—
256	C₂²×C₈	—	38	1	no	—
257	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
258	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
259	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
260	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
261	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
262	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
263	C₂²⋊Q₈	—	2	1	no	—
264	C₂²⋊Q₈	—	2	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	—	2	1	no	—
267	#121	—	2	1	no	—
268	#121	—	2	1	no	—
269	#121	—	2	1	no	—
270	#121	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	38	1	no	—
277	C₂×C₄²	—	38	1	no	—
278	#108	—	76	2	no	—
279	#106	—	2	1	no	—
280	#106	—	2	1	no	—
281	#103	—	2	1	no	—
282	#103	—	2	1	no	—
283	#102	—	2	1	no	—
284	#102	—	2	1	no	—
285	C₂²⋊C₈	—	19	2	no	—
286	C₂²⋊C₈	—	38	1	no	—
287	C₂²⋊C₈	—	38	1	no	—
288	C₂²⋊C₈	—	38	1	no	—
289	C₂²⋊C₈	—	38	1	no	—
290	C₂²⋊C₈	—	38	1	no	—
291	#97	—	76	2	no	—
292	#95	—	19	2	no	—
293	C₁₉	#9816	1	1	yes	characteristic, complemented, Sylow
294	C₂⁴	—	2	1	no	—
295	C₂⁴	#64543	1	1	yes	characteristic
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	8	2	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	38	2	no	—
313	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
314	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
315	C₂²×C₄	#64543	1	1	yes	characteristic
316	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
319	SD₁₆	—	4	2	no	—
320	SD₁₆	—	4	2	no	—
321	M₁₆	—	76	1	no	—
322	M₁₆	—	76	1	no	—
323	M₁₆	—	76	1	no	—
324	M₁₆	—	76	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	38	2	no	—
332	C₂×C₈	—	76	1	no	—
333	C₂×C₈	—	76	1	no	—
334	C₂×C₈	—	76	1	no	—
335	C₂×C₈	—	76	1	no	—
336	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
337	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
338	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
339	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	—	4	1	no	—
350	C₂²⋊C₄	—	76	2	no	—
351	C₄²	—	76	1	no	—
352	C₄²	—	76	1	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	8	1	no	—
359	C₂³	—	8	1	no	—
360	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
361	C₂³	#10597382	1	1	yes	characteristic
362	C₂³	#10597384	1	1	yes	characteristic
363	Q₈	—	4	1	no	—
364	Q₈	—	4	1	no	—
365	Q₈	—	8	1	no	—
366	D₄	—	4	1	no	—
367	D₄	—	4	1	no	—
368	D₄	—	8	1	no	—
369	D₄	—	8	2	no	—
370	D₄	—	8	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	8	1	no	—
385	C₂×C₄	—	8	1	no	—
386	C₂×C₄	—	76	2	no	—
387	C₂×C₄	—	76	2	no	—
388	C₂×C₄	—	76	2	no	—
389	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
390	C₂×C₄	#10597384	1	1	yes	characteristic
391	C₂×C₄	#10597386	1	1	yes	characteristic
392	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	76	2	no	—
397	C₈	—	152	1	no	—
398	C₈	—	152	1	no	—
399	C₈	#10597291	1	2	yes	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	16	2	no	—
412	C₂²	#11926447	1	1	yes	characteristic
413	C₂²	#11926666	1	2	yes	—
414	C₂²	#11926804	1	2	yes	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	1	no	—
421	C₄	—	152	2	no	—
422	C₄	C₂×#10597291	1	1	yes	characteristic
423	C₄	#11926518	1	1	yes	characteristic
424	C₂	—	2	2	no	—
425	C₂	—	2	2	no	—
426	C₂	—	4	1	no	—
427	C₂	—	16	1	no	—
428	C₂	#14564472	1	1	yes	characteristic
429	C₂	#14564529	1	1	yes	characteristic
430	C₂	#14564540	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926447
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#465	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂×C₁₉×#121	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#465	D₁₉
hypocenter	C₁₉	#9816
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#465

Complements

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

N	H ≅ G/N	type
1. #14563673	C₂	semidirect
2. #14563411	C₂	semidirect
3. #14562155	C₂	semidirect
5. #14561999	C₂	semidirect
20. C₂²×SD₁₆×C₁₉	C₄	semidirect
28. C₂×C₁₉×#106	C₄	semidirect
29. C₂×C₁₉×#103	C₄	semidirect
30. C₂×C₁₉×#102	C₄	semidirect
216. C₂²×SD₁₆	Dic₁₉	semidirect
225. C₂×#106	Dic₁₉	semidirect
226. C₂×#103	Dic₁₉	semidirect
227. C₂×#102	Dic₁₉	semidirect
293. C₁₉	#9816	semidirect

Maximal subgroups

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

subgroup	index
#14563673	2
#14563411	2
#14562155	2
#14562151	2
#14561999	2
#14561995	2
C₂×C₁₉×#465	2
#9816	19