Subgroups — #18075519

Order 4864.

456 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572330	C₂	1	1	yes	maximal, characteristic
2	#14563671	C₂	1	1	yes	maximal, characteristic, complemented
3	#14563662	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562178	C₂	1	1	yes	maximal, characteristic
5	#14561542	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561541	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1513	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597394	C₄	1	1	yes	characteristic, complemented
9	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	#11926616	—	2	1	no	—
11	#11926616	—	2	1	no	—
12	D₄×C₁₉⋊C₈	—	2	1	no	—
13	D₄×C₁₉⋊C₈	—	2	1	no	—
14	C₂×#10597279	—	2	1	no	—
15	C₂×#10597264	—	2	1	no	—
16	#11926571	C₄	1	1	yes	characteristic, complemented
17	#11926511	C₄	1	1	yes	characteristic, complemented
18	#11926508	C₂²	1	1	yes	characteristic
19	#11926508	C₂²	1	1	yes	characteristic
20	#11926500	C₄	1	1	yes	characteristic, complemented
21	#11926404	C₂²	1	1	yes	characteristic
22	#11926308	—	2	1	no	—
23	#11926306	—	2	1	no	—
24	#11926281	—	2	1	no	—
25	#11926278	—	2	1	no	—
26	C₁₉×#525	C₂²	1	1	yes	characteristic
27	C₁₉×#407	C₂²	1	1	yes	characteristic
28	C₁₉×#380	C₂²	1	1	yes	characteristic
29	C₁₉×#328	—	2	1	no	—
30	C₁₉×#327	—	2	1	no	—
31	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₁₉×#123	—	2	1	no	—
35	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
36	C₁₉×C₂²⋊Q₈	Q₈	1	1	yes	characteristic
37	C₁₉×#121	D₄	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	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
46	#10597394	—	4	2	no	—
47	C₂×C₄⋊Dic₁₉	—	2	1	no	—
48	C₂×#64520	—	2	1	no	—
49	C₂×#64520	—	2	1	no	—
50	C₂×#64520	C₂×C₄	1	1	yes	characteristic
51	C₂×#64520	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₁₉⋊C₈	—	2	1	no	—
53	C₂²×C₁₉⋊C₈	—	4	2	no	—
54	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
57	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
58	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
59	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
60	C₁₉×C₂²⋊C₈	—	2	1	no	—
61	C₁₉×C₂²⋊C₈	—	2	1	no	—
62	C₁₉×#95	—	2	1	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	#10597279	—	4	2	no	—
71	#10597264	—	4	2	no	—
72	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
73	C₄⋊(C₁₉⋊C₈)	—	2	1	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	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	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×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×Dic₁₉	—	4	1	no	—
95	M₁₆×C₁₉	—	4	1	no	—
96	M₁₆×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	4	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	—	8	1	no	—
110	C₄²×C₁₉	—	2	1	no	—
111	C₂²⋊Dic₁₉	—	8	1	no	—
112	C₄⋊Dic₁₉	—	4	1	no	—
113	C₄⋊Dic₁₉	—	4	1	no	—
114	#64520	—	4	2	no	—
115	#64520	—	4	1	no	—
116	#64520	—	4	1	no	—
117	#64520	—	4	1	no	—
118	#64520	—	4	1	no	—
119	C₂×C₁₉⋊C₈	—	2	2	no	—
120	C₂×C₁₉⋊C₈	—	2	2	no	—
121	C₂×C₁₉⋊C₈	—	2	2	no	—
122	C₂×C₁₉⋊C₈	—	2	1	no	—
123	C₂×C₁₉⋊C₈	—	2	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	2	no	—
128	C₂×C₁₉⋊C₈	—	4	1	no	—
129	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
133	#8628	—	19	1	no	maximal, Sylow
134	C₂³×C₁₉	—	2	1	no	—
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	#117	1	1	yes	characteristic
140	C₂³×C₁₉	#121	1	1	yes	characteristic
141	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
142	Q₈×C₁₉	—	4	1	no	—
143	D₄×C₁₉	—	4	1	no	—
144	D₄×C₁₉	—	4	2	no	—
145	D₄×C₁₉	—	4	2	no	—
146	D₄×C₁₉	—	4	1	no	—
147	D₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	2	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	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	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	—	8	1	no	—
163	C₂×C₄×C₁₉	—	8	1	no	—
164	C₂×C₄×C₁₉	—	8	1	no	—
165	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂×Dic₁₉	—	8	1	no	—
170	C₂×Dic₁₉	—	8	1	no	—
171	C₂×Dic₁₉	—	8	1	no	—
172	C₈×C₁₉	—	8	1	no	—
173	C₁₉⋊C₈	—	2	1	no	—
174	C₁₉⋊C₈	—	2	1	no	—
175	C₁₉⋊C₈	—	2	1	no	—
176	C₁₉⋊C₈	—	4	1	no	—
177	C₁₉⋊C₈	—	4	1	no	—
178	C₁₉⋊C₈	—	8	1	no	—
179	C₁₉⋊C₈	#99	1	2	yes	—
180	#2929	—	19	1	no	—
181	#1810	—	19	1	no	—
182	#1808	—	19	1	no	—
183	#1513	—	19	1	no	—
184	#1513	D₁₉	1	1	yes	characteristic
185	#1305	—	19	1	no	—
186	#1305	—	19	1	no	—
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	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	—	4	2	no	—
196	C₂²×C₁₉	—	4	2	no	—
197	C₂²×C₁₉	—	4	1	no	—
198	C₂²×C₁₉	—	4	1	no	—
199	C₂²×C₁₉	—	4	1	no	—
200	C₂²×C₁₉	#380	1	1	yes	characteristic
201	C₂²×C₁₉	#472	1	1	yes	characteristic
202	C₂²×C₁₉	#473	1	1	yes	characteristic
203	C₄×C₁₉	—	2	1	no	—
204	C₄×C₁₉	—	2	1	no	—
205	C₄×C₁₉	—	2	1	no	—
206	C₄×C₁₉	—	4	1	no	—
207	C₄×C₁₉	—	4	1	no	—
208	C₄×C₁₉	—	4	1	no	—
209	C₄×C₁₉	—	16	1	no	—
210	C₄×C₁₉	C₂×#99	1	1	yes	characteristic
211	C₄×C₁₉	#410	1	1	yes	characteristic
212	Dic₁₉	—	16	1	no	—
213	C₂×#131	—	19	1	no	—
214	C₂³×C₈	—	19	1	no	—
215	#525	C₂×D₁₉	1	1	yes	characteristic
216	#435	—	38	1	no	—
217	#435	—	38	1	no	—
218	C₈×D₄	—	38	1	no	—
219	C₈×D₄	—	38	1	no	—
220	C₂×#108	—	38	1	no	—
221	C₂×#107	—	38	1	no	—
222	#424	—	19	1	no	—
223	#408	—	19	1	no	—
224	#407	—	19	1	no	—
225	#407	—	19	1	no	—
226	#407	C₂×D₁₉	1	1	yes	characteristic
227	#405	—	19	1	no	—
228	#380	—	19	1	no	—
229	#380	C₂×D₁₉	1	1	yes	characteristic
230	#341	—	38	1	no	—
231	#340	—	38	1	no	—
232	#328	—	2	1	no	—
233	#328	—	38	1	no	—
234	#327	—	2	1	no	—
235	#327	—	38	1	no	—
236	C₂×C₁₉	—	2	1	no	—
237	C₂×C₁₉	—	2	1	no	—
238	C₂×C₁₉	—	4	1	no	—
239	C₂×C₁₉	—	4	1	no	—
240	C₂×C₁₉	—	8	1	no	—
241	C₂×C₁₉	#1799	1	1	yes	characteristic
242	C₂×C₁₉	#1814	1	1	yes	characteristic
243	C₂×C₁₉	#1816	1	1	yes	characteristic
244	C₂×#41	C₄×D₁₉	1	1	yes	characteristic
245	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
246	#131	—	76	2	no	—
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	19	1	no	—
249	C₂×M₁₆	—	19	1	no	—
250	C₂×M₁₆	—	38	1	no	—
251	C₂×M₁₆	—	38	1	no	—
252	C₂²×C₈	—	19	1	no	—
253	C₂²×C₈	—	19	1	no	—
254	C₂²×C₈	—	19	1	no	—
255	C₂²×C₈	—	19	1	no	—
256	C₂²×C₈	—	19	1	no	—
257	C₂²×C₈	—	19	1	no	—
258	C₂²×C₈	—	38	1	no	—
259	C₂²×C₈	—	76	2	no	—
260	#123	—	2	1	no	—
261	C₂²⋊Q₈	Dic₃₈	1	1	yes	characteristic
262	C₂²⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
263	#121	Dic₃₈	1	1	yes	characteristic
264	#121	C₂²⋊D₁₉	1	1	yes	characteristic
265	#120	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	#117	C₄×D₁₉	1	1	yes	characteristic
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	38	1	no	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	38	1	no	—
273	#108	—	76	2	no	—
274	#107	—	76	2	no	—
275	C₄⋊C₈	—	38	1	no	—
276	C₄⋊C₈	—	38	1	no	—
277	C₂²⋊C₈	—	2	1	no	—
278	C₂²⋊C₈	—	2	1	no	—
279	C₂²⋊C₈	—	38	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	#97	—	38	1	no	—
286	C₄×C₈	—	38	1	no	—
287	#95	—	2	1	no	—
288	#95	—	38	1	no	—
289	C₁₉	#8628	1	1	yes	characteristic, complemented, Sylow
290	C₂⁴	#64543	1	1	yes	characteristic
291	#41	—	4	1	no	—
292	#41	—	4	1	no	—
293	C₂×Q₈	Dic₁₉⋊C₄	1	1	yes	characteristic
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	Dic₁₉⋊C₄	1	1	yes	characteristic
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	76	1	no	—
303	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
305	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
306	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
307	C₂²×C₄	#64543	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
309	M₁₆	—	4	1	no	—
310	M₁₆	—	4	1	no	—
311	M₁₆	—	76	2	no	—
312	M₁₆	—	76	1	no	—
313	M₁₆	—	76	1	no	—
314	M₁₆	—	76	1	no	—
315	M₁₆	—	76	1	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	19	1	no	—
318	C₂×C₈	—	19	1	no	—
319	C₂×C₈	—	19	1	no	—
320	C₂×C₈	—	19	1	no	—
321	C₂×C₈	—	38	2	no	—
322	C₂×C₈	—	38	2	no	—
323	C₂×C₈	—	38	2	no	—
324	C₂×C₈	—	38	1	no	—
325	C₂×C₈	—	38	1	no	—
326	C₂×C₈	—	76	1	no	—
327	C₂×C₈	—	76	1	no	—
328	C₂×C₈	—	76	1	no	—
329	C₂×C₈	—	76	2	no	—
330	C₂×C₈	—	76	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	76	1	no	—
336	C₄⋊C₄	—	76	1	no	—
337	C₄⋊C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
338	C₄⋊C₄	Dic₁₉⋊C₄	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	—	8	1	no	—
345	C₂²⋊C₄	—	152	1	no	—
346	C₄²	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	1	no	—
352	C₂³	#10597323	1	1	yes	characteristic
353	C₂³	#10597324	1	1	yes	characteristic
354	C₂³	#10597385	1	1	yes	characteristic
355	Q₈	—	4	1	no	—
356	D₄	—	4	1	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	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	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	8	1	no	—
376	C₂×C₄	—	8	1	no	—
377	C₂×C₄	—	8	1	no	—
378	C₂×C₄	—	152	1	no	—
379	C₂×C₄	—	152	1	no	—
380	C₂×C₄	—	152	1	no	—
381	C₂×C₄	#10597324	1	1	yes	characteristic
382	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
383	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
384	C₂×C₄	#10597385	1	1	yes	characteristic
385	C₈	—	8	1	no	—
386	C₈	—	19	2	no	—
387	C₈	—	38	1	no	—
388	C₈	—	38	1	no	—
389	C₈	—	38	1	no	—
390	C₈	—	76	1	no	—
391	C₈	—	76	1	no	—
392	C₈	—	152	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	#11926402	1	1	yes	characteristic
407	C₂²	#11926812	1	1	yes	characteristic
408	C₂²	#11926817	1	1	yes	characteristic
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	1	no	—
415	C₄	—	16	1	no	—
416	C₄	—	304	1	no	—
417	C₄	#99×D₁₉	1	1	yes	characteristic
418	C₄	#11926516	1	1	yes	characteristic
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	—	4	1	no	—
422	C₂	—	4	1	no	—
423	C₂	—	8	1	no	—
424	C₂	#14563621	1	1	yes	characteristic
425	C₂	#14563687	1	1	yes	characteristic
426	C₂	#14563697	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926402
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1513	C₂
socle	C₂²×C₁₉	#380
prime radical	C₁₉×#525	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1513	D₁₉
hypocenter	C₁₉	#8628
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #1513

Complements

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

N	H ≅ G/N	type
2. #14563671	C₂	semidirect
3. #14563662	C₂	semidirect
5. #14561542	C₂	semidirect
6. #14561541	C₂	semidirect
8. C₂×#10597394	C₄	semidirect
16. #11926571	C₄	semidirect
17. #11926511	C₄	semidirect
20. #11926500	C₄	semidirect
289. C₁₉	#8628	semidirect

Maximal subgroups

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

subgroup	index
#14572330	2
#14563671	2
#14563662	2
#14562178	2
#14561542	2
#14561541	2
C₁₉×#1513	2
#8628	19