Subgroups — #18075969

Order 4864.

514 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14566040	C₂	1	1	yes	maximal, characteristic
2	#14563612	C₂	1	1	yes	maximal, characteristic
3	#14563612	C₂	1	1	yes	maximal, characteristic
4	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561518	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597338	—	2	1	no	—
9	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
13	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
14	#11926414	C₂²	1	1	yes	characteristic
15	#11926409	—	2	1	no	—
16	#11926401	—	2	1	no	—
17	#11926401	C₄	1	2	yes	—
18	C₄⋊C₄×Dic₁₉	—	2	1	no	—
19	C₄⋊C₄×Dic₁₉	C₄	1	2	yes	—
20	#11926298	—	2	1	no	—
21	#11926298	—	2	1	no	—
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₁₉×#384	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₉	—	2	1	no	—
29	C₂²×C₈×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
35	C₂×C₄⋊Dic₁₉	—	2	1	no	—
36	C₂×C₄⋊Dic₁₉	—	2	1	no	—
37	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
38	C₂×C₄×Dic₁₉	—	2	2	no	—
39	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
42	C₂²×C₁₉⋊C₈	—	2	1	no	—
43	C₂²×C₁₉⋊C₈	—	2	1	no	—
44	#10597338	—	4	2	no	—
45	#10597338	—	4	2	no	—
46	C₄²×D₁₉	—	2	1	no	—
47	C₄²×D₁₉	—	2	1	no	—
48	C₄²×D₁₉	—	2	1	no	—
49	C₄²×D₁₉	—	2	1	no	—
50	C₁₉×C₄⋊C₈	—	2	1	no	—
51	C₁₉×C₄⋊C₈	—	2	1	no	—
52	C₁₉×C₄⋊C₈	—	2	1	no	—
53	C₁₉×C₄⋊C₈	—	2	1	no	—
54	C₁₉⋊#95	—	2	2	no	—
55	C₁₉⋊#95	—	2	2	no	—
56	(C₂×D₁₉)⋊C₈	—	4	2	no	—
57	(C₂×D₁₉)⋊C₈	—	4	2	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
62	C₂³×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×Dic₁₉	—	2	2	no	—
68	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₄×D₁₉	—	2	1	no	—
72	C₂×C₄×D₁₉	—	2	1	no	—
73	C₂×C₄×D₁₉	—	2	1	no	—
74	C₂×C₄×D₁₉	—	2	1	no	—
75	C₂×C₄×D₁₉	—	2	1	no	—
76	C₂×C₄×D₁₉	—	2	1	no	—
77	C₂×C₄×D₁₉	—	2	1	no	—
78	C₂×C₄×D₁₉	—	2	1	no	—
79	C₂×C₄×D₁₉	—	2	1	no	—
80	C₂×C₄×D₁₉	—	2	1	no	—
81	C₂×C₄×D₁₉	—	2	1	no	—
82	C₂×C₄×D₁₉	—	2	1	no	—
83	C₂×C₄×D₁₉	—	4	1	no	—
84	C₂×C₄×D₁₉	—	4	1	no	—
85	C₂×C₄×D₁₉	SD₁₆	1	2	yes	—
86	C₂×C₄×D₁₉	Q₁₆	1	2	yes	—
87	C₂×C₈×C₁₉	—	4	1	no	—
88	C₂×C₈×C₁₉	—	4	1	no	—
89	C₂×C₈×C₁₉	—	4	1	no	—
90	C₂×C₈×C₁₉	—	4	1	no	—
91	C₂×C₈×C₁₉	—	4	1	no	—
92	C₂×C₈×C₁₉	—	4	1	no	—
93	C₄⋊C₄×C₁₉	—	4	2	no	—
94	C₄⋊C₄×C₁₉	—	4	1	no	—
95	C₄⋊C₄×C₁₉	—	4	1	no	—
96	C₄⋊C₄×C₁₉	—	4	1	no	—
97	C₄⋊C₄×C₁₉	—	4	1	no	—
98	C₄²×C₁₉	#41	1	1	yes	characteristic
99	C₄²×C₁₉	#41	1	1	yes	characteristic
100	C₄²×C₁₉	#41	1	1	yes	characteristic
101	C₄²×C₁₉	#41	1	1	yes	characteristic
102	(C₂×D₁₉)⋊C₄	—	4	4	no	—
103	C₄⋊Dic₁₉	—	4	1	no	—
104	C₄⋊Dic₁₉	—	4	1	no	—
105	C₄⋊Dic₁₉	—	4	1	no	—
106	C₄⋊Dic₁₉	—	4	1	no	—
107	C₄⋊Dic₁₉	—	4	2	no	—
108	C₄×Dic₁₉	—	2	1	no	—
109	C₄×Dic₁₉	—	2	1	no	—
110	C₄×Dic₁₉	—	2	1	no	—
111	C₄×Dic₁₉	—	2	1	no	—
112	C₄×Dic₁₉	—	2	1	no	—
113	C₄×Dic₁₉	—	2	1	no	—
114	C₄×Dic₁₉	—	4	4	no	—
115	C₂×C₁₉⋊C₈	—	4	1	no	—
116	C₂×C₁₉⋊C₈	—	4	1	no	—
117	C₂×C₁₉⋊C₈	—	4	1	no	—
118	C₂×C₁₉⋊C₈	—	4	1	no	—
119	C₂×C₁₉⋊C₈	—	4	1	no	—
120	C₂×C₁₉⋊C₈	—	4	1	no	—
121	#8727	—	19	1	no	maximal, Sylow
122	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×D₁₉	—	2	1	no	—
124	C₂²×D₁₉	—	2	1	no	—
125	C₂²×D₁₉	—	2	1	no	—
126	C₂²×D₁₉	—	2	1	no	—
127	C₂²×D₁₉	—	2	1	no	—
128	C₂²×D₁₉	—	2	1	no	—
129	C₂²×D₁₉	#103	1	2	yes	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	4	2	no	—
133	C₂×C₄×C₁₉	—	4	2	no	—
134	C₂×C₄×C₁₉	—	4	2	no	—
135	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
136	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
137	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
138	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
140	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
141	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
145	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
146	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
149	C₂×Dic₁₉	—	2	1	no	—
150	C₂×Dic₁₉	—	2	1	no	—
151	C₂×Dic₁₉	—	2	1	no	—
152	C₂×Dic₁₉	—	2	1	no	—
153	C₂×Dic₁₉	—	2	1	no	—
154	C₂×Dic₁₉	—	2	1	no	—
155	C₂×Dic₁₉	—	2	1	no	—
156	C₂×Dic₁₉	—	2	1	no	—
157	C₂×Dic₁₉	—	4	2	no	—
158	C₂×Dic₁₉	—	4	2	no	—
159	C₂×Dic₁₉	—	4	2	no	—
160	C₂×Dic₁₉	#103	1	2	yes	—
161	C₄×D₁₉	—	2	2	no	—
162	C₄×D₁₉	—	2	2	no	—
163	C₄×D₁₉	—	2	2	no	—
164	C₄×D₁₉	—	2	2	no	—
165	C₄×D₁₉	—	4	2	no	—
166	C₄×D₁₉	—	4	2	no	—
167	C₄×D₁₉	—	4	1	no	—
168	C₄×D₁₉	—	4	1	no	—
169	C₄×D₁₉	—	4	1	no	—
170	C₄×D₁₉	—	4	1	no	—
171	C₈×C₁₉	—	8	1	no	—
172	C₈×C₁₉	—	8	1	no	—
173	C₁₉⋊C₈	—	8	1	no	—
174	C₁₉⋊C₈	—	8	1	no	—
175	#2285	—	19	1	no	—
176	#1797	—	19	1	no	—
177	#1797	—	19	1	no	—
178	#1296	—	19	1	no	—
179	#1296	—	19	1	no	—
180	#1296	—	19	1	no	—
181	#1296	D₁₉	1	1	yes	characteristic, complemented
182	C₂²×C₁₉	#381	1	1	yes	characteristic
183	C₂²×C₁₉	#413	1	1	yes	characteristic
184	C₂²×C₁₉	#413	1	1	yes	characteristic
185	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
186	C₂²×C₁₉	#416	1	1	yes	characteristic
187	C₂²×C₁₉	#417	1	1	yes	characteristic
188	C₂²×C₁₉	#418	1	1	yes	characteristic
189	C₂×D₁₉	—	2	2	no	—
190	C₂×D₁₉	—	2	2	no	—
191	C₂×D₁₉	—	2	2	no	—
192	C₂×D₁₉	—	4	1	no	—
193	C₂×D₁₉	—	4	1	no	—
194	C₂×D₁₉	—	4	1	no	—
195	C₂×D₁₉	—	4	1	no	—
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	8	2	no	—
199	C₄×C₁₉	#481	1	1	yes	characteristic
200	C₄×C₁₉	#481	1	1	yes	characteristic
201	C₄×C₁₉	#482	1	1	yes	characteristic
202	C₄×C₁₉	#482	1	1	yes	characteristic
203	C₄×C₁₉	#484	1	1	yes	characteristic
204	C₄×C₁₉	#484	1	1	yes	characteristic
205	C₄×C₁₉	#485	1	1	yes	characteristic
206	C₄×C₁₉	#485	1	1	yes	characteristic
207	Dic₁₉	—	2	2	no	—
208	Dic₁₉	—	4	1	no	—
209	Dic₁₉	—	4	1	no	—
210	Dic₁₉	—	8	2	no	—
211	C₂×#117	—	38	1	no	—
212	C₂²×C₄²	—	19	1	no	—
213	C₂×C₄⋊C₈	—	19	1	no	—
214	C₂×C₄⋊C₈	—	19	1	no	—
215	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
217	C₂×C₂²⋊C₈	—	38	1	no	—
218	C₂×C₂²⋊C₈	—	38	1	no	—
219	#384	—	19	1	no	—
220	#384	C₂×D₁₉	1	1	yes	characteristic
221	#382	—	38	1	no	—
222	#380	—	19	2	no	—
223	#380	—	38	1	no	—
224	C₄×C₄⋊C₄	—	19	2	no	—
225	C₄×C₄⋊C₄	—	38	1	no	—
226	#336	—	38	1	no	—
227	#336	—	38	1	no	—
228	C₂×C₁₉	#1542	1	1	yes	characteristic
229	C₂×C₁₉	#1550	1	1	yes	characteristic
230	C₂×C₁₉	#1553	1	1	yes	characteristic
231	C₂×C₁₉	#1557	1	1	yes	characteristic
232	C₂×C₁₉	#1822	1	1	yes	characteristic
233	C₂×C₁₉	#1824	1	1	yes	characteristic
234	C₂×C₁₉	#1825	1	1	yes	characteristic
235	D₁₉	—	4	2	no	—
236	C₂³×C₄	—	19	1	no	—
237	C₂³×C₄	—	19	1	no	—
238	C₂³×C₄	—	19	1	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	38	1	no	—
242	C₂²×C₈	—	38	1	no	—
243	#117	—	76	2	no	—
244	#117	—	76	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	19	2	no	—
248	C₂×C₄⋊C₄	—	38	1	no	—
249	C₂×C₄⋊C₄	—	38	1	no	—
250	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
251	C₂×C₂²⋊C₄	—	38	2	no	—
252	C₂×C₄²	—	19	1	no	—
253	C₂×C₄²	—	19	1	no	—
254	C₂×C₄²	—	19	1	no	—
255	C₂×C₄²	—	38	1	no	—
256	C₂×C₄²	—	38	1	no	—
257	C₂×C₄²	—	38	1	no	—
258	C₂×C₄²	—	38	1	no	—
259	C₂×C₄²	—	38	2	no	—
260	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	38	1	no	—
266	C₄⋊C₈	—	38	1	no	—
267	C₄⋊C₈	—	38	1	no	—
268	C₄⋊C₈	—	38	1	no	—
269	C₂²⋊C₈	—	76	2	no	—
270	C₂²⋊C₈	—	76	2	no	—
271	#95	—	38	2	no	—
272	#95	—	38	2	no	—
273	C₁₉	#8727	1	1	yes	characteristic, complemented, Sylow
274	C₂⁴	—	19	1	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	19	1	no	—
277	C₂²×C₄	—	19	2	no	—
278	C₂²×C₄	—	19	2	no	—
279	C₂²×C₄	—	19	1	no	—
280	C₂²×C₄	—	19	1	no	—
281	C₂²×C₄	—	38	1	no	—
282	C₂²×C₄	—	38	1	no	—
283	C₂²×C₄	—	38	1	no	—
284	C₂²×C₄	—	38	1	no	—
285	C₂²×C₄	—	38	1	no	—
286	C₂²×C₄	—	38	1	no	—
287	C₂²×C₄	—	38	1	no	—
288	C₂²×C₄	—	38	1	no	—
289	C₂²×C₄	—	38	1	no	—
290	C₂²×C₄	—	38	1	no	—
291	C₂²×C₄	—	38	1	no	—
292	C₂²×C₄	—	38	1	no	—
293	C₂²×C₄	—	38	2	no	—
294	C₂²×C₄	—	76	1	no	—
295	C₂²×C₄	—	76	1	no	—
296	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
297	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
298	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	76	1	no	—
306	C₂×C₈	—	76	1	no	—
307	C₂×C₈	—	76	1	no	—
308	C₂×C₈	—	76	1	no	—
309	C₂×C₈	—	76	1	no	—
310	C₂×C₈	—	76	1	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	76	2	no	—
317	C₄⋊C₄	—	76	1	no	—
318	C₄⋊C₄	—	76	1	no	—
319	C₄⋊C₄	—	76	1	no	—
320	C₄⋊C₄	—	76	1	no	—
321	C₂²⋊C₄	—	76	4	no	—
322	C₄²	—	38	1	no	—
323	C₄²	—	38	1	no	—
324	C₄²	—	38	1	no	—
325	C₄²	—	38	1	no	—
326	C₄²	—	38	1	no	—
327	C₄²	—	38	1	no	—
328	C₄²	—	76	4	no	—
329	C₄²	#64541	1	1	yes	characteristic
330	C₄²	#64541	1	1	yes	characteristic
331	C₄²	#64543	1	1	yes	characteristic
332	C₄²	#64545	1	1	yes	characteristic
333	C₂³	—	19	2	no	—
334	C₂³	—	38	1	no	—
335	C₂³	—	38	1	no	—
336	C₂³	—	38	1	no	—
337	C₂³	—	38	1	no	—
338	C₂³	—	38	1	no	—
339	C₂³	—	38	1	no	—
340	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	19	2	no	—
347	C₂×C₄	—	38	1	no	—
348	C₂×C₄	—	38	1	no	—
349	C₂×C₄	—	38	2	no	—
350	C₂×C₄	—	38	2	no	—
351	C₂×C₄	—	38	2	no	—
352	C₂×C₄	—	38	2	no	—
353	C₂×C₄	—	38	1	no	—
354	C₂×C₄	—	38	1	no	—
355	C₂×C₄	—	38	1	no	—
356	C₂×C₄	—	38	1	no	—
357	C₂×C₄	—	38	1	no	—
358	C₂×C₄	—	38	1	no	—
359	C₂×C₄	—	76	2	no	—
360	C₂×C₄	—	76	2	no	—
361	C₂×C₄	—	76	1	no	—
362	C₂×C₄	—	76	1	no	—
363	C₂×C₄	—	76	1	no	—
364	C₂×C₄	—	76	1	no	—
365	C₂×C₄	—	76	2	no	—
366	C₂×C₄	—	76	2	no	—
367	C₂×C₄	—	76	2	no	—
368	C₂×C₄	#10597318	1	1	yes	characteristic
369	C₂×C₄	#10597329	1	1	yes	characteristic
370	C₂×C₄	#10597329	1	1	yes	characteristic
371	C₂×C₄	#10597338	1	1	yes	characteristic
372	C₂×C₄	#10597340	1	1	yes	characteristic
373	C₂×C₄	#10597340	1	1	yes	characteristic
374	C₂×C₄	#10597357	1	1	yes	characteristic
375	C₂×C₄	#10597357	1	1	yes	characteristic
376	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
377	C₂×C₄	#10597360	1	1	yes	characteristic
378	C₂×C₄	#10597361	1	1	yes	characteristic
379	C₂×C₄	#10597362	1	1	yes	characteristic
380	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
381	C₂×C₄	#10597365	1	1	yes	characteristic
382	C₈	—	8	1	no	—
383	C₈	—	8	1	no	—
384	C₈	—	152	1	no	—
385	C₈	—	152	1	no	—
386	C₂²	—	38	2	no	—
387	C₂²	—	38	2	no	—
388	C₂²	—	38	2	no	—
389	C₂²	—	76	1	no	—
390	C₂²	—	76	1	no	—
391	C₂²	—	76	1	no	—
392	C₂²	—	76	1	no	—
393	C₂²	#11926406	1	1	yes	characteristic
394	C₂²	#11926525	1	1	yes	characteristic
395	C₂²	#11926527	1	1	yes	characteristic
396	C₂²	#103×D₁₉	1	1	yes	characteristic
397	C₂²	#11926539	1	1	yes	characteristic
398	C₂²	#11926542	1	1	yes	characteristic
399	C₂²	#11926547	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	8	2	no	—
403	C₄	—	38	2	no	—
404	C₄	—	76	1	no	—
405	C₄	—	76	1	no	—
406	C₄	—	152	2	no	—
407	C₄	#11926861	1	1	yes	characteristic
408	C₄	#11926864	1	1	yes	characteristic
409	C₄	#11926867	1	1	yes	characteristic
410	C₄	#11926871	1	1	yes	characteristic
411	C₄	#11926878	1	1	yes	characteristic
412	C₄	#11926881	1	1	yes	characteristic
413	C₄	#11926884	1	1	yes	characteristic
414	C₄	#11926888	1	1	yes	characteristic
415	C₂	—	76	2	no	—
416	C₂	#14562289	1	1	yes	characteristic
417	C₂	#14562324	1	1	yes	characteristic
418	C₂	#14562339	1	1	yes	characteristic
419	C₂	#14562354	1	1	yes	characteristic
420	C₂	#14563717	1	1	yes	characteristic
421	C₂	#14563724	1	1	yes	characteristic
422	C₂	#14563729	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1296	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1296	D₁₉
hypocenter	C₁₉	#8727
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
4. #14561519	C₂	semidirect
5. #14561519	C₂	semidirect
6. #14561518	C₂	semidirect
7. C₁₉×#1296	C₂	semidirect
181. #1296	D₁₉	semidirect
273. C₁₉	#8727	semidirect

Maximal subgroups

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

subgroup	index
#14566040	2
#14563612	2
#14561519	2
#14561518	2
C₁₉×#1296	2
#8727	19