Subgroups — #18076645

Order 4864.

464 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572683	C₂	1	1	yes	maximal, characteristic
2	#14563938	C₂	1	1	yes	maximal, characteristic
3	#14563842	C₂	1	1	yes	maximal, characteristic, complemented
4	#14563820	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561521	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561481	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1501	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	#11926622	—	2	1	no	—
10	#11926616	—	2	1	no	—
11	#11926616	—	2	1	no	—
12	D₄×C₁₉⋊C₈	—	2	1	no	—
13	#11926605	—	2	1	no	—
14	C₂×#10597276	—	2	1	no	—
15	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
16	C₂×#10597294	—	2	1	no	—
17	#11926511	—	2	1	no	—
18	#11926508	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₄×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
21	#11926309	—	2	1	no	—
22	#11926303	—	2	1	no	—
23	#11926299	—	2	1	no	—
24	C₁₉×#525	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#328	C₄	1	1	yes	characteristic, complemented
28	C₁₉×#328	C₄	1	1	yes	characteristic, complemented
29	C₁₉×#327	C₄	1	1	yes	characteristic, complemented
30	C₁₉×#327	C₄	1	1	yes	characteristic, complemented
31	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₁₉×#123	—	2	1	no	—
35	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
36	C₁₉×C₂²⋊Q₈	Q₈	1	1	yes	characteristic
37	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
38	C₁₉×#121	Q₈	1	1	yes	characteristic
39	C₁₉×#120	—	2	1	no	—
40	C₄×D₄×C₁₉	—	2	1	no	—
41	C₄×D₄×C₁₉	—	2	1	no	—
42	C₁₉×#117	D₄	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	—	2	1	no	—
45	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
46	C₂×C₄×Dic₁₉	—	2	1	no	—
47	C₂×#64520	—	2	1	no	—
48	C₂×#64520	—	2	1	no	—
49	C₂×#64520	—	2	1	no	—
50	C₂×#64520	—	4	2	no	—
51	C₂×#64520	D₄	1	1	yes	characteristic
52	C₂×#64520	D₄	1	1	yes	characteristic
53	C₂²×C₁₉⋊C₈	—	2	1	no	—
54	C₂²×C₁₉⋊C₈	—	2	1	no	—
55	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
56	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
57	C₁₉×C₂²⋊C₈	—	2	1	no	—
58	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
59	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
60	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
61	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
62	#10597294	—	4	2	no	—
63	C₁₉⋊#95	—	2	1	no	—
64	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
70	#10597276	—	4	2	no	—
71	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
73	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
74	#10597260	—	2	1	no	—
75	C₄×C₁₉⋊C₈	—	2	1	no	—
76	C₂⁴×C₁₉	#41	1	1	yes	characteristic
77	#41×C₁₉	—	4	1	no	—
78	#41×C₁₉	—	4	1	no	—
79	C₂×Q₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
80	C₂×D₄×C₁₉	—	2	1	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
95	C₂²×Dic₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	2	1	no	—
97	C₂×C₈×C₁₉	—	2	1	no	—
98	C₂×C₈×C₁₉	—	4	1	no	—
99	C₂×C₈×C₁₉	—	4	1	no	—
100	C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₄⋊C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
103	C₄⋊C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
104	C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂²⋊C₄×C₁₉	—	2	1	no	—
109	C₂²⋊C₄×C₁₉	—	4	2	no	—
110	C₄²×C₁₉	—	2	1	no	—
111	C₄²×C₁₉	—	4	1	no	—
112	C₄²×C₁₉	—	4	1	no	—
113	C₂²⋊Dic₁₉	—	2	2	no	—
114	C₂²⋊Dic₁₉	—	4	1	no	—
115	C₄×Dic₁₉	—	4	1	no	—
116	C₄×Dic₁₉	—	4	1	no	—
117	#64520	—	2	2	no	—
118	#64520	—	2	2	no	—
119	#64520	—	4	1	no	—
120	#64520	—	4	1	no	—
121	#64520	—	4	1	no	—
122	#64520	—	4	1	no	—
123	#64520	—	8	1	no	—
124	C₂×C₁₉⋊C₈	—	2	2	no	—
125	C₂×C₁₉⋊C₈	—	2	1	no	—
126	C₂×C₁₉⋊C₈	—	2	1	no	—
127	C₂×C₁₉⋊C₈	—	2	1	no	—
128	C₂×C₁₉⋊C₈	—	2	1	no	—
129	C₂×C₁₉⋊C₈	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	C₂×C₁₉⋊C₈	—	8	1	no	—
134	#8874	—	19	1	no	maximal, Sylow
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	1	no	—
140	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
141	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂³×C₁₉	#123	1	1	yes	characteristic
143	Q₈×C₁₉	—	4	1	no	—
144	D₄×C₁₉	—	4	1	no	—
145	D₄×C₁₉	—	4	1	no	—
146	D₄×C₁₉	—	4	1	no	—
147	D₄×C₁₉	—	8	1	no	—
148	D₄×C₁₉	—	8	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	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	1	no	—
169	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
173	C₂×Dic₁₉	—	4	2	no	—
174	C₂×Dic₁₉	—	8	1	no	—
175	C₂×Dic₁₉	—	8	1	no	—
176	C₈×C₁₉	—	4	1	no	—
177	C₈×C₁₉	—	4	1	no	—
178	C₁₉⋊C₈	—	4	2	no	—
179	C₁₉⋊C₈	—	4	1	no	—
180	C₁₉⋊C₈	—	4	1	no	—
181	C₁₉⋊C₈	—	4	1	no	—
182	C₁₉⋊C₈	—	4	1	no	—
183	#2976	—	19	1	no	—
184	#1871	—	19	1	no	—
185	#1855	—	19	1	no	—
186	#1851	—	19	1	no	—
187	#1501	D₁₉	1	1	yes	characteristic
188	#1297	—	19	1	no	—
189	#1282	—	19	1	no	—
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	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	—	4	1	no	—
199	C₂²×C₁₉	—	4	1	no	—
200	C₂²×C₁₉	—	4	1	no	—
201	C₂²×C₁₉	—	8	1	no	—
202	C₂²×C₁₉	—	8	1	no	—
203	C₂²×C₁₉	#385	1	1	yes	characteristic
204	C₂²×C₁₉	#443	1	1	yes	characteristic
205	C₂²×C₁₉	#444	1	1	yes	characteristic
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	1	no	—
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	—	4	1	no	—
211	C₄×C₁₉	—	4	1	no	—
212	C₄×C₁₉	—	4	1	no	—
213	C₄×C₁₉	—	8	1	no	—
214	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
215	C₄×C₁₉	#458	1	1	yes	characteristic
216	Dic₁₉	—	8	2	no	—
217	C₂²×M₁₆	—	19	1	no	—
218	#525	C₂×D₁₉	1	1	yes	characteristic
219	#436	—	38	1	no	—
220	#435	—	38	1	no	—
221	#435	—	38	1	no	—
222	C₈×D₄	—	38	1	no	—
223	#433	—	38	1	no	—
224	C₂×#108	—	38	1	no	—
225	C₂×C₄⋊C₈	—	38	1	no	—
226	C₂×#104	—	38	1	no	—
227	#408	—	38	1	no	—
228	#407	—	19	1	no	—
229	C₂×C₂²⋊C₈	—	19	1	no	—
230	C₂×C₂²⋊C₈	C₂×D₁₉	1	1	yes	characteristic
231	C₄×C₂²⋊C₄	—	19	1	no	—
232	C₄×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
233	#341	—	38	1	no	—
234	#339	—	38	1	no	—
235	#336	—	38	1	no	—
236	#328	Dic₁₉	1	1	yes	characteristic, complemented
237	#328	Dic₁₉	1	1	yes	characteristic, complemented
238	#327	Dic₁₉	1	1	yes	characteristic, complemented
239	#327	Dic₁₉	1	1	yes	characteristic, complemented
240	C₂×C₁₉	—	2	1	no	—
241	C₂×C₁₉	—	2	1	no	—
242	C₂×C₁₉	—	4	1	no	—
243	C₂×C₁₉	—	4	1	no	—
244	C₂×C₁₉	—	8	1	no	—
245	C₂×C₁₉	#1861	1	1	yes	characteristic
246	C₂×C₁₉	#1866	1	1	yes	characteristic
247	C₂×C₁₉	#1867	1	1	yes	characteristic
248	C₂×#41	D₇₆	1	1	yes	characteristic
249	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
250	C₂×M₁₆	—	19	1	no	—
251	C₂×M₁₆	—	19	1	no	—
252	C₂×M₁₆	—	38	1	no	—
253	C₂×M₁₆	—	38	1	no	—
254	C₂×M₁₆	—	38	1	no	—
255	C₂×M₁₆	—	76	2	no	—
256	C₂²×C₈	—	2	1	no	—
257	C₂²×C₈	—	19	1	no	—
258	C₂²×C₈	—	19	1	no	—
259	C₂²×C₈	—	38	1	no	—
260	C₂²×C₈	—	38	1	no	—
261	#123	—	2	1	no	—
262	C₂²⋊Q₈	Dic₃₈	1	1	yes	characteristic
263	C₂²⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
264	#121	Dic₃₈	1	1	yes	characteristic
265	#121	C₂×Dic₁₉	1	1	yes	characteristic
266	#120	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	—	2	1	no	—
269	#117	D₇₆	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₂²⋊C₄	—	38	1	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	—	38	1	no	—
274	#108	—	76	2	no	—
275	C₄⋊C₈	—	38	1	no	—
276	C₄⋊C₈	—	38	1	no	—
277	C₄⋊C₈	—	76	2	no	—
278	#104	—	76	2	no	—
279	C₂²⋊C₈	—	2	1	no	—
280	C₂²⋊C₈	—	38	1	no	—
281	C₂²⋊C₈	—	38	1	no	—
282	C₂²⋊C₈	—	38	1	no	—
283	C₂²⋊C₈	—	38	1	no	—
284	C₂²⋊C₈	—	38	1	no	—
285	C₂²⋊C₈	—	38	1	no	—
286	C₂²⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
287	C₂²⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
288	#97	—	38	1	no	—
289	C₄×C₈	—	38	1	no	—
290	#95	—	38	1	no	—
291	#95	C₂×Dic₁₉	1	1	yes	characteristic
292	#95	C₂×Dic₁₉	1	1	yes	characteristic
293	C₁₉	#8874	1	1	yes	characteristic, complemented, Sylow
294	C₂⁴	#64543	1	1	yes	characteristic
295	#41	—	4	1	no	—
296	#41	—	4	1	no	—
297	C₂×Q₈	C₄⋊Dic₁₉	1	1	yes	characteristic
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	C₄⋊Dic₁₉	1	1	yes	characteristic
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	76	1	no	—
308	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
310	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
311	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
312	C₂²×C₄	#64543	1	1	yes	characteristic
313	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
314	M₁₆	—	38	2	no	—
315	M₁₆	—	38	2	no	—
316	M₁₆	—	76	1	no	—
317	M₁₆	—	76	1	no	—
318	M₁₆	—	76	1	no	—
319	M₁₆	—	76	1	no	—
320	M₁₆	—	152	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	38	2	no	—
326	C₂×C₈	—	38	1	no	—
327	C₂×C₈	—	38	1	no	—
328	C₂×C₈	—	38	1	no	—
329	C₂×C₈	—	38	1	no	—
330	C₂×C₈	—	76	1	no	—
331	C₂×C₈	—	76	1	no	—
332	C₂×C₈	—	76	1	no	—
333	C₂×C₈	—	76	1	no	—
334	C₂×C₈	—	152	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
338	C₄⋊C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	1	no	—
342	C₂²⋊C₄	—	2	1	no	—
343	C₂²⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	4	2	no	—
345	C₂²⋊C₄	—	38	2	no	—
346	C₂²⋊C₄	—	76	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	4	1	no	—
349	C₄²	—	4	1	no	—
350	C₄²	—	76	1	no	—
351	C₄²	—	76	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	#10597324	1	1	yes	characteristic
358	C₂³	#10597332	1	1	yes	characteristic
359	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
360	Q₈	—	4	1	no	—
361	D₄	—	4	1	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	1	no	—
364	D₄	—	8	1	no	—
365	D₄	—	8	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	76	2	no	—
387	C₂×C₄	—	152	1	no	—
388	C₂×C₄	—	152	1	no	—
389	C₂×C₄	#10597324	1	1	yes	characteristic
390	C₂×C₄	#10597328	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
392	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
393	C₈	—	4	1	no	—
394	C₈	—	4	1	no	—
395	C₈	—	76	2	no	—
396	C₈	—	76	1	no	—
397	C₈	—	76	1	no	—
398	C₈	—	76	1	no	—
399	C₈	—	76	1	no	—
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	—	2	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	#11926419	1	1	yes	characteristic
414	C₂²	#11926661	1	1	yes	characteristic
415	C₂²	#11926666	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	—	8	1	no	—
424	C₄	—	152	2	no	—
425	C₄	#11926732	1	1	yes	characteristic
426	C₄	#11926735	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	4	1	no	—
430	C₂	—	4	1	no	—
431	C₂	—	8	1	no	—
432	C₂	#14563877	1	1	yes	characteristic
433	C₂	#14563912	1	1	yes	characteristic
434	C₂	#14563918	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597328
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1501	C₂
socle	C₂²×C₁₉	#385
prime radical	C₁₉×#525	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1501	D₁₉
hypocenter	C₁₉	#8874
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1501

Complements

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

N	H ≅ G/N	type
3. #14563842	C₂	semidirect
4. #14563820	C₂	semidirect
5. #14561521	C₂	semidirect
6. #14561481	C₂	semidirect
27. C₁₉×#328	C₄	semidirect
28. C₁₉×#328	C₄	semidirect
29. C₁₉×#327	C₄	semidirect
30. C₁₉×#327	C₄	semidirect
236. #328	Dic₁₉	semidirect
237. #328	Dic₁₉	semidirect
238. #327	Dic₁₉	semidirect
239. #327	Dic₁₉	semidirect
293. C₁₉	#8874	semidirect

Maximal subgroups

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

subgroup	index
#14572683	2
#14563938	2
#14563842	2
#14563820	2
#14561521	2
#14561481	2
C₁₉×#1501	2
#8874	19