Subgroups — #18075339

Order 4864.

664 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	#127×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	#14563786	C₂	1	1	yes	maximal, characteristic, complemented
3	#14563751	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926288	C₂	1	1	yes	maximal, characteristic
5	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#331	C₂	1	1	yes	maximal, characteristic
8	C₂×D₄×Dic₁₉	—	2	1	no	—
9	C₂×D₄×Dic₁₉	—	2	1	no	—
10	C₂×D₄×Dic₁₉	C₄	1	2	yes	—
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₉⋊C₈	—	2	1	no	—
14	C₂×Dic₁₉⋊C₈	—	2	1	no	—
15	#11926447	—	2	1	no	—
16	#11926447	—	2	1	no	—
17	#11926447	C₄	1	2	yes	—
18	#11926414	C₂²	1	1	yes	characteristic
19	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
20	#11926298	—	2	1	no	—
21	#11926298	—	2	1	no	—
22	#11926288	—	2	2	no	—
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₁₉×#331	—	2	2	no	—
27	C₂²×D₄×C₁₉	—	2	1	no	—
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
30	C₂³×Dic₁₉	—	2	2	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₁₉×#127	—	2	1	no	—
34	C₁₉×#127	—	2	1	no	—
35	C₁₉×#127	D₄	1	2	yes	—
36	C₁₉×#127	Q₈	1	2	yes	—
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
39	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
40	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
41	D₄×Dic₁₉	—	4	2	no	—
42	D₄×Dic₁₉	—	4	2	no	—
43	D₄×Dic₁₉	—	4	4	no	—
44	D₄×Dic₁₉	—	4	2	no	—
45	D₄×Dic₁₉	—	4	2	no	—
46	C₂×C₄⋊Dic₁₉	—	2	1	no	—
47	C₂×C₄⋊Dic₁₉	—	2	1	no	—
48	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
49	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
55	C₂²×C₁₉⋊C₈	—	2	1	no	—
56	C₂²×C₁₉⋊C₈	—	2	1	no	—
57	C₁₉×C₄⋊C₈	—	2	1	no	—
58	C₁₉×C₄⋊C₈	—	2	1	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	—	2	1	no	—
61	Dic₁₉⋊C₈	—	4	2	no	—
62	Dic₁₉⋊C₈	—	4	2	no	—
63	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₂⁴×C₁₉	—	2	2	no	—
68	C₂×D₄×C₁₉	—	2	2	no	—
69	C₂×D₄×C₁₉	—	2	2	no	—
70	C₂×D₄×C₁₉	—	2	2	no	—
71	C₂×D₄×C₁₉	—	2	2	no	—
72	C₂×D₄×C₁₉	—	2	2	no	—
73	C₂×D₄×C₁₉	—	4	2	no	—
74	C₂×D₄×C₁₉	—	4	2	no	—
75	C₂×D₄×C₁₉	—	4	1	no	—
76	C₂×D₄×C₁₉	—	4	1	no	—
77	C₂×D₄×C₁₉	—	4	1	no	—
78	C₂×D₄×C₁₉	—	4	1	no	—
79	C₂×D₄×C₁₉	—	4	1	no	—
80	C₂×D₄×C₁₉	—	4	1	no	—
81	C₂×D₄×C₁₉	—	4	1	no	—
82	C₂×D₄×C₁₉	—	4	1	no	—
83	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
84	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×Dic₁₉	—	2	2	no	—
88	C₂²×Dic₁₉	—	4	4	no	—
89	C₂²×Dic₁₉	—	4	4	no	—
90	C₂²×Dic₁₉	—	4	4	no	—
91	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₂×C₈×C₁₉	—	4	1	no	—
99	C₂×C₈×C₁₉	—	4	1	no	—
100	C₂×C₈×C₁₉	—	4	1	no	—
101	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
103	C₄²×C₁₉	#41	1	1	yes	characteristic
104	C₄²×C₁₉	#41	1	1	yes	characteristic
105	C₂²⋊Dic₁₉	—	4	4	no	—
106	C₂²⋊Dic₁₉	—	4	4	no	—
107	C₂²⋊Dic₁₉	—	4	4	no	—
108	C₄⋊Dic₁₉	—	4	1	no	—
109	C₄⋊Dic₁₉	—	4	1	no	—
110	C₄⋊Dic₁₉	—	4	1	no	—
111	C₄⋊Dic₁₉	—	4	1	no	—
112	C₄⋊Dic₁₉	—	4	2	no	—
113	C₄×Dic₁₉	—	2	1	no	—
114	C₄×Dic₁₉	—	2	1	no	—
115	C₄×Dic₁₉	—	2	1	no	—
116	C₄×Dic₁₉	—	2	1	no	—
117	C₄×Dic₁₉	—	2	1	no	—
118	C₄×Dic₁₉	—	2	1	no	—
119	C₄×Dic₁₉	—	2	2	no	—
120	C₄×Dic₁₉	—	4	1	no	—
121	C₄×Dic₁₉	D₈	1	2	yes	—
122	C₄×Dic₁₉	SD₁₆	1	2	yes	—
123	C₂×C₁₉⋊C₈	—	4	1	no	—
124	C₂×C₁₉⋊C₈	—	4	1	no	—
125	C₂×C₁₉⋊C₈	—	4	1	no	—
126	C₂×C₁₉⋊C₈	—	4	1	no	—
127	C₂×C₁₉⋊C₈	—	4	1	no	—
128	C₂×C₁₉⋊C₈	—	4	1	no	—
129	#8588	—	19	1	no	maximal, Sylow
130	C₂³×C₁₉	—	2	4	no	—
131	C₂³×C₁₉	—	4	2	no	—
132	C₂³×C₁₉	—	4	2	no	—
133	C₂³×C₁₉	—	4	2	no	—
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	—	4	2	no	—
137	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	D₄×C₁₉	—	4	4	no	—
139	D₄×C₁₉	—	4	4	no	—
140	D₄×C₁₉	—	4	2	no	—
141	D₄×C₁₉	—	4	2	no	—
142	D₄×C₁₉	—	4	2	no	—
143	D₄×C₁₉	—	4	2	no	—
144	D₄×C₁₉	—	4	2	no	—
145	D₄×C₁₉	—	4	2	no	—
146	D₄×C₁₉	—	4	2	no	—
147	D₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
160	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
164	C₂×Dic₁₉	—	2	1	no	—
165	C₂×Dic₁₉	—	2	1	no	—
166	C₂×Dic₁₉	—	2	1	no	—
167	C₂×Dic₁₉	—	2	1	no	—
168	C₂×Dic₁₉	—	2	1	no	—
169	C₂×Dic₁₉	—	2	1	no	—
170	C₂×Dic₁₉	—	2	1	no	—
171	C₂×Dic₁₉	—	2	1	no	—
172	C₂×Dic₁₉	—	2	1	no	—
173	C₂×Dic₁₉	—	4	2	no	—
174	C₂×Dic₁₉	—	4	2	no	—
175	C₂×Dic₁₉	—	4	2	no	—
176	C₂×Dic₁₉	—	8	8	no	—
177	C₂×Dic₁₉	#100	1	2	yes	—
178	C₂×Dic₁₉	#102	1	2	yes	—
179	C₂×Dic₁₉	#102	1	2	yes	—
180	C₈×C₁₉	—	8	1	no	—
181	C₈×C₁₉	—	8	1	no	—
182	C₁₉⋊C₈	—	8	1	no	—
183	C₁₉⋊C₈	—	8	1	no	—
184	C₄×#127	—	19	1	no	—
185	#1842	—	19	1	no	—
186	#1831	—	19	1	no	—
187	C₂×#331	—	19	1	no	—
188	C₂×#331	D₁₉	1	1	yes	characteristic
189	#1296	—	19	1	no	—
190	#1296	—	19	1	no	—
191	C₂²×C₁₉	—	4	4	no	—
192	C₂²×C₁₉	—	4	4	no	—
193	C₂²×C₁₉	—	4	4	no	—
194	C₂²×C₁₉	—	8	2	no	—
195	C₂²×C₁₉	—	8	2	no	—
196	C₂²×C₁₉	—	8	2	no	—
197	C₂²×C₁₉	—	8	2	no	—
198	C₂²×C₁₉	#380	1	1	yes	characteristic
199	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
200	C₂²×C₁₉	#413	1	1	yes	characteristic
201	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
202	C₂²×C₁₉	#416	1	1	yes	characteristic
203	C₂²×C₁₉	#417	1	1	yes	characteristic
204	C₂²×C₁₉	#418	1	1	yes	characteristic
205	C₄×C₁₉	—	2	1	no	—
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	#459	1	1	yes	characteristic
208	C₄×C₁₉	#461	1	1	yes	characteristic
209	C₄×C₁₉	#463	1	1	yes	characteristic
210	C₄×C₁₉	#463	1	1	yes	characteristic
211	C₄×C₁₉	#474	1	1	yes	characteristic
212	C₄×C₁₉	#476	1	1	yes	characteristic
213	C₄×C₁₉	#478	1	1	yes	characteristic
214	C₄×C₁₉	#478	1	1	yes	characteristic
215	Dic₁₉	—	2	2	no	—
216	Dic₁₉	—	2	2	no	—
217	Dic₁₉	—	2	2	no	—
218	Dic₁₉	—	4	1	no	—
219	Dic₁₉	—	8	2	no	—
220	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
221	C₂×C₄×D₄	—	19	2	no	—
222	C₂×C₄×D₄	—	38	1	no	—
223	C₂×C₄×D₄	—	38	1	no	—
224	C₂×C₄⋊C₈	—	19	1	no	—
225	C₂×C₄⋊C₈	—	19	1	no	—
226	C₂×C₄⋊C₈	—	38	1	no	—
227	C₂×C₄⋊C₈	—	38	1	no	—
228	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
229	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
230	#390	—	19	2	no	—
231	#390	—	38	1	no	—
232	#390	—	38	1	no	—
233	#384	—	19	1	no	—
234	C₄³	—	19	1	no	—
235	#336	—	38	1	no	—
236	#336	—	38	1	no	—
237	#331	—	2	2	no	—
238	#331	—	38	2	no	—
239	C₂×C₁₉	—	8	4	no	—
240	C₂×C₁₉	#1540	1	1	yes	characteristic
241	C₂×C₁₉	#1545	1	1	yes	characteristic
242	C₂×C₁₉	#1551	1	1	yes	characteristic
243	C₂×C₁₉	#1557	1	1	yes	characteristic
244	C₂×C₁₉	#1800	1	1	yes	characteristic
245	C₂×C₁₉	#1802	1	1	yes	characteristic
246	C₂×C₁₉	#1804	1	1	yes	characteristic
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	C₄×D₁₉	1	2	yes	—
250	C₂³×C₄	—	38	2	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	38	1	no	—
254	C₂²×C₈	—	38	1	no	—
255	#127	—	2	1	no	—
256	#127	—	2	1	no	—
257	#127	Dic₃₈	1	2	yes	—
258	#127	C₂²⋊D₁₉	1	2	yes	—
259	C₄×D₄	—	76	2	no	—
260	C₄×D₄	—	76	2	no	—
261	C₄×D₄	—	76	2	no	—
262	C₄×D₄	—	76	2	no	—
263	C₄×D₄	—	76	4	no	—
264	C₂×C₄⋊C₄	—	19	2	no	—
265	C₂×C₄⋊C₄	—	38	1	no	—
266	C₂×C₄⋊C₄	—	38	1	no	—
267	C₂×C₂²⋊C₄	—	38	2	no	—
268	C₂×C₂²⋊C₄	—	38	2	no	—
269	C₂×C₂²⋊C₄	—	38	2	no	—
270	C₂×C₄²	—	19	1	no	—
271	C₂×C₄²	—	19	1	no	—
272	C₂×C₄²	—	19	1	no	—
273	C₂×C₄²	—	19	1	no	—
274	C₂×C₄²	—	19	1	no	—
275	C₂×C₄²	—	19	1	no	—
276	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	—	38	1	no	—
282	C₄⋊C₈	—	38	1	no	—
283	C₄⋊C₈	—	38	1	no	—
284	C₄⋊C₈	—	38	1	no	—
285	C₄⋊C₈	—	76	2	no	—
286	C₄⋊C₈	—	76	2	no	—
287	C₁₉	#8588	1	1	yes	characteristic, complemented, Sylow
288	C₂⁴	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	Dic₁₉⋊C₄	1	4	yes	—
305	C₂²×C₄	—	19	1	no	—
306	C₂²×C₄	—	19	1	no	—
307	C₂²×C₄	—	19	1	no	—
308	C₂²×C₄	—	19	1	no	—
309	C₂²×C₄	—	38	2	no	—
310	C₂²×C₄	—	76	4	no	—
311	C₂²×C₄	—	76	4	no	—
312	C₂²×C₄	—	76	4	no	—
313	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
314	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
315	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	4	1	no	—
320	C₂×C₈	—	4	1	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	76	1	no	—
323	C₂×C₈	—	76	1	no	—
324	C₂×C₈	—	76	1	no	—
325	C₂×C₈	—	76	1	no	—
326	C₂×C₈	—	76	1	no	—
327	C₂×C₈	—	76	1	no	—
328	C₄⋊C₄	—	76	2	no	—
329	C₄⋊C₄	—	76	1	no	—
330	C₄⋊C₄	—	76	1	no	—
331	C₄⋊C₄	—	76	1	no	—
332	C₄⋊C₄	—	76	1	no	—
333	C₂²⋊C₄	—	76	4	no	—
334	C₂²⋊C₄	—	76	4	no	—
335	C₂²⋊C₄	—	76	4	no	—
336	C₄²	—	19	2	no	—
337	C₄²	—	19	2	no	—
338	C₄²	—	38	2	no	—
339	C₄²	—	38	1	no	—
340	C₄²	—	38	1	no	—
341	C₄²	—	38	1	no	—
342	C₄²	—	38	1	no	—
343	C₄²	—	38	1	no	—
344	C₄²	—	38	1	no	—
345	C₄²	—	76	1	no	—
346	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
347	C₄²	#64543	1	1	yes	characteristic
348	C₄²	#64543	1	1	yes	characteristic
349	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
350	C₂³	—	2	4	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
358	D₄	—	4	4	no	—
359	D₄	—	4	4	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	19	2	no	—
371	C₂×C₄	—	19	2	no	—
372	C₂×C₄	—	19	2	no	—
373	C₂×C₄	—	38	1	no	—
374	C₂×C₄	—	38	1	no	—
375	C₂×C₄	—	38	1	no	—
376	C₂×C₄	—	38	1	no	—
377	C₂×C₄	—	38	1	no	—
378	C₂×C₄	—	38	1	no	—
379	C₂×C₄	—	38	1	no	—
380	C₂×C₄	—	38	1	no	—
381	C₂×C₄	—	38	1	no	—
382	C₂×C₄	—	76	2	no	—
383	C₂×C₄	—	76	2	no	—
384	C₂×C₄	—	76	2	no	—
385	C₂×C₄	—	152	8	no	—
386	C₂×C₄	#10597323	1	1	yes	characteristic
387	C₂×C₄	#10597324	1	1	yes	characteristic
388	C₂×C₄	#10597324	1	1	yes	characteristic
389	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
390	C₂×C₄	#10597357	1	1	yes	characteristic
391	C₂×C₄	#10597357	1	1	yes	characteristic
392	C₂×C₄	#10597358	1	1	yes	characteristic
393	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
394	C₂×C₄	#10597360	1	1	yes	characteristic
395	C₂×C₄	#10597361	1	1	yes	characteristic
396	C₂×C₄	#10597362	1	1	yes	characteristic
397	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
398	C₂×C₄	#10597385	1	1	yes	characteristic
399	C₂×C₄	#10597385	1	1	yes	characteristic
400	C₈	—	8	1	no	—
401	C₈	—	8	1	no	—
402	C₈	—	152	1	no	—
403	C₈	—	152	1	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	2	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	#11926402	1	1	yes	characteristic
412	C₂²	#100×D₁₉	1	1	yes	characteristic
413	C₂²	#11926525	1	1	yes	characteristic
414	C₂²	#102×D₁₉	1	1	yes	characteristic
415	C₂²	#11926537	1	1	yes	characteristic
416	C₂²	#11926542	1	1	yes	characteristic
417	C₂²	#11926547	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	38	2	no	—
421	C₄	—	38	2	no	—
422	C₄	—	38	2	no	—
423	C₄	—	76	1	no	—
424	C₄	—	152	2	no	—
425	C₄	#11926737	1	1	yes	characteristic
426	C₄	#11926747	1	1	yes	characteristic
427	C₄	#11926757	1	1	yes	characteristic
428	C₄	#11926761	1	1	yes	characteristic
429	C₄	#11926822	1	1	yes	characteristic
430	C₄	#11926832	1	1	yes	characteristic
431	C₄	#11926842	1	1	yes	characteristic
432	C₄	#11926846	1	1	yes	characteristic
433	C₂	—	8	4	no	—
434	C₂	#14562281	1	1	yes	characteristic
435	C₂	#14562301	1	1	yes	characteristic
436	C₂	#14562327	1	1	yes	characteristic
437	C₂	#14562354	1	1	yes	characteristic
438	C₂	#14563625	1	1	yes	characteristic
439	C₂	#14563633	1	1	yes	characteristic
440	C₂	#14563643	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#331	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×C₁₉×#127	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#331	D₁₉
hypocenter	C₁₉	#8588
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#331

Complements

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

N	H ≅ G/N	type
2. #14563786	C₂	semidirect
3. #14563751	C₂	semidirect
5. #14561519	C₂	semidirect
6. #14561519	C₂	semidirect
287. C₁₉	#8588	semidirect

Maximal subgroups

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

subgroup	index
#127×Dic₁₉	2
#14563786	2
#14563751	2
C₂×#11926288	2
#14561519	2
C₂×C₁₉×#331	2
#8588	19