Subgroups — #18076727

Order 4864.

618 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564398	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563791	C₂	1	1	yes	maximal, characteristic, complemented
3	#14563635	C₂	1	1	yes	maximal, characteristic
4	C₂×D₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
5	#14561518	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597265	—	2	1	no	—
9	C₂×#10597265	—	2	2	no	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×#10597289	—	2	1	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926414	C₂²	1	1	yes	characteristic
15	#11926306	—	2	1	no	—
16	#11926306	—	2	1	no	—
17	D₄⋊(C₁₉⋊C₈)	C₄	1	4	yes	complemented
18	C₂×C₄×D₄×C₁₉	—	2	1	no	—
19	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
21	C₁₉×#389	—	2	1	no	—
22	C₁₉×#385	—	2	2	no	—
23	C₁₉×#384	C₂²	1	1	yes	characteristic
24	C₁₉×#380	—	2	1	no	—
25	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	—	2	2	no	—
29	C₄×D₄×C₁₉	—	2	1	no	—
30	C₄×D₄×C₁₉	—	2	1	no	—
31	C₄×D₄×C₁₉	—	4	2	no	—
32	C₄×D₄×C₁₉	—	4	2	no	—
33	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₄×D₄×C₁₉	Q₈	1	2	yes	—
35	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
39	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
40	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
46	C₂×C₄²×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×C₄⋊Dic₁₉	—	2	1	no	—
49	C₂×C₄⋊Dic₁₉	—	2	1	no	—
50	C₂×C₄⋊Dic₁₉	—	2	1	no	—
51	C₂²×C₁₉⋊C₈	—	2	1	no	—
52	C₂²×C₁₉⋊C₈	—	2	1	no	—
53	C₂²×C₁₉⋊C₈	—	2	1	no	—
54	C₁₉×#95	—	2	2	no	—
55	C₁₉×#95	—	2	1	no	—
56	#10597289	—	4	2	no	—
57	#10597265	—	4	4	no	—
58	#10597265	—	4	2	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
62	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	complemented
63	C₄×C₁₉⋊C₈	—	2	1	no	—
64	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	complemented
65	C₂⁴×C₁₉	—	2	1	no	—
66	C₂×D₄×C₁₉	—	2	1	no	—
67	C₂×D₄×C₁₉	—	2	1	no	—
68	C₂×D₄×C₁₉	—	2	1	no	—
69	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
70	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
71	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	4	4	no	—
79	C₂²×C₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	—	4	4	no	—
84	C₂²×C₄×C₁₉	—	8	2	no	—
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×Dic₁₉	—	4	1	no	—
89	C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₄⋊C₄×C₁₉	—	4	2	no	—
94	C₄⋊C₄×C₁₉	—	4	4	no	—
95	C₄⋊C₄×C₁₉	—	4	1	no	—
96	C₄⋊C₄×C₁₉	—	4	1	no	—
97	C₄⋊C₄×C₁₉	—	4	1	no	—
98	C₄⋊C₄×C₁₉	—	4	1	no	—
99	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
100	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	—
101	C₂²⋊C₄×C₁₉	—	2	2	no	—
102	C₂²⋊C₄×C₁₉	—	2	2	no	—
103	C₂²⋊C₄×C₁₉	—	4	4	no	—
104	C₄²×C₁₉	—	4	1	no	—
105	C₄²×C₁₉	—	4	1	no	—
106	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
108	C₄²×C₁₉	#41	1	1	yes	characteristic
109	C₄²×C₁₉	#41	1	1	yes	characteristic
110	C₄⋊Dic₁₉	—	4	2	no	—
111	C₄⋊Dic₁₉	—	4	1	no	—
112	C₄⋊Dic₁₉	—	4	1	no	—
113	C₄⋊Dic₁₉	—	4	1	no	—
114	C₄⋊Dic₁₉	—	4	1	no	—
115	C₂×C₁₉⋊C₈	—	2	2	no	—
116	C₂×C₁₉⋊C₈	—	2	2	no	—
117	C₂×C₁₉⋊C₈	—	2	2	no	—
118	C₂×C₁₉⋊C₈	—	2	2	no	—
119	C₂×C₁₉⋊C₈	—	4	1	no	—
120	C₂×C₁₉⋊C₈	—	4	1	no	—
121	C₂×C₁₉⋊C₈	—	4	1	no	—
122	C₂×C₁₉⋊C₈	—	4	1	no	—
123	C₂×C₁₉⋊C₈	—	4	1	no	—
124	#8886	—	19	1	no	maximal, Sylow
125	C₂³×C₁₉	—	2	2	no	—
126	C₂³×C₁₉	—	2	2	no	—
127	C₂³×C₁₉	—	2	2	no	—
128	C₂³×C₁₉	—	4	1	no	—
129	C₂³×C₁₉	—	4	1	no	—
130	C₂³×C₁₉	—	4	1	no	—
131	C₂³×C₁₉	—	4	1	no	—
132	C₂³×C₁₉	#120	1	1	yes	characteristic
133	D₄×C₁₉	—	2	2	no	—
134	D₄×C₁₉	—	2	2	no	—
135	D₄×C₁₉	—	2	2	no	—
136	D₄×C₁₉	#106	1	4	yes	complemented
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	8	8	no	—
156	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
166	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
170	C₂×Dic₁₉	—	8	1	no	—
171	C₂×Dic₁₉	—	8	1	no	—
172	C₂×Dic₁₉	—	8	1	no	—
173	C₁₉⋊C₈	—	2	4	no	—
174	C₁₉⋊C₈	—	4	2	no	—
175	C₁₉⋊C₈	—	8	1	no	—
176	D₄×C₄⋊C₄	D₁₉	1	1	yes	characteristic
177	#1948	—	19	1	no	—
178	#1844	—	19	1	no	—
179	#1802	—	19	1	no	—
180	C₂×D₄⋊C₈	—	19	1	no	—
181	#1296	—	19	1	no	—
182	#1279	—	19	1	no	—
183	C₂²×C₁₉	—	2	4	no	—
184	C₂²×C₁₉	—	4	2	no	—
185	C₂²×C₁₉	—	4	2	no	—
186	C₂²×C₁₉	—	4	2	no	—
187	C₂²×C₁₉	—	4	2	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	4	2	no	—
190	C₂²×C₁₉	#385	1	1	yes	characteristic
191	C₂²×C₁₉	#448	1	1	yes	characteristic
192	C₂²×C₁₉	#449	1	1	yes	characteristic
193	C₂²×C₁₉	#450	1	1	yes	characteristic
194	C₂²×C₁₉	#450	1	1	yes	characteristic
195	C₂²×C₁₉	#453	1	1	yes	characteristic
196	C₂²×C₁₉	#456	1	1	yes	characteristic
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	4	2	no	—
200	C₄×C₁₉	—	4	2	no	—
201	C₄×C₁₉	—	8	2	no	—
202	C₄×C₁₉	—	8	1	no	—
203	C₄×C₁₉	C₂×#106	1	1	yes	characteristic
204	C₄×C₁₉	#428	1	1	yes	characteristic
205	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
206	C₄×C₁₉	#442	1	1	yes	characteristic
207	C₄×C₁₉	#476	1	1	yes	characteristic
208	C₄×C₁₉	#478	1	1	yes	characteristic
209	C₄×C₁₉	#481	1	1	yes	characteristic
210	C₄×C₁₉	#483	1	1	yes	characteristic
211	Dic₁₉	—	16	1	no	—
212	C₂×C₄×D₄	—	2	1	no	—
213	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
214	C₂²×C₄⋊C₄	—	2	1	no	—
215	C₂×#106	—	38	2	no	—
216	C₂×#106	—	38	1	no	—
217	C₂×C₄⋊C₈	—	19	1	no	—
218	C₂×C₄⋊C₈	—	19	1	no	—
219	C₂×#102	—	38	1	no	—
220	C₂×C₄×C₈	—	19	1	no	—
221	#389	—	2	1	no	—
222	#385	—	2	2	no	—
223	#384	—	19	1	no	—
224	#384	C₂×D₁₉	1	1	yes	characteristic
225	#380	—	2	1	no	—
226	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
227	#340	—	38	1	no	—
228	#340	—	38	1	no	—
229	D₄⋊C₈	—	19	4	no	—
230	C₂×C₁₉	—	4	4	no	—
231	C₂×C₁₉	#1622	1	1	yes	characteristic
232	C₂×C₁₉	#1629	1	1	yes	characteristic
233	C₂×C₁₉	#1651	1	1	yes	characteristic
234	C₂×C₁₉	#1654	1	1	yes	characteristic
235	C₂×C₁₉	#1853	1	1	yes	characteristic
236	C₂×C₁₉	#1859	1	1	yes	characteristic
237	C₂×C₁₉	#1864	1	1	yes	characteristic
238	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
239	C₂³×C₄	—	2	1	no	—
240	C₂³×C₄	—	2	2	no	—
241	C₂²×C₈	—	38	1	no	—
242	C₂²×C₈	—	38	1	no	—
243	C₂²×C₈	—	38	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	4	2	no	—
247	C₄×D₄	—	4	2	no	—
248	C₄×D₄	Dic₃₈	1	2	yes	—
249	C₄×D₄	C₄×D₁₉	1	2	yes	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	4	2	no	—
254	C₂×C₄⋊C₄	—	4	2	no	—
255	C₂×C₄⋊C₄	—	38	1	no	—
256	C₂×C₄⋊C₄	—	38	1	no	—
257	C₂×C₄⋊C₄	—	38	1	no	—
258	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
266	#106	—	76	2	no	—
267	#106	—	76	4	no	—
268	C₄⋊C₈	—	19	2	no	—
269	C₄⋊C₈	—	38	1	no	—
270	C₄⋊C₈	—	38	1	no	—
271	C₄⋊C₈	—	38	1	no	—
272	#102	—	76	2	no	—
273	C₄×C₈	—	19	2	no	—
274	C₄×C₈	—	38	1	no	—
275	#95	—	2	2	no	—
276	#95	—	2	1	no	—
277	C₁₉	#8886	1	1	yes	characteristic, complemented, Sylow
278	C₂⁴	—	2	1	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
283	C₂×D₄	#64526	1	2	yes	—
284	C₂×D₄	#64527	1	2	yes	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	4	no	—
297	C₂²×C₄	—	8	2	no	—
298	C₂²×C₄	—	76	1	no	—
299	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
302	C₂×C₈	—	38	2	no	—
303	C₂×C₈	—	38	2	no	—
304	C₂×C₈	—	38	2	no	—
305	C₂×C₈	—	38	2	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	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	4	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	76	2	no	—
322	C₄⋊C₄	—	76	1	no	—
323	C₄⋊C₄	—	76	1	no	—
324	C₄⋊C₄	—	76	1	no	—
325	C₄⋊C₄	—	76	1	no	—
326	C₄⋊C₄	Dic₁₉⋊C₄	1	2	yes	—
327	C₄⋊C₄	#64526	1	2	yes	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₄²	—	4	1	no	—
332	C₄²	—	4	1	no	—
333	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
334	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
335	C₄²	#64541	1	1	yes	characteristic
336	C₄²	#64541	1	1	yes	characteristic
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	—	4	1	no	—
344	C₂³	#10597399	1	1	yes	characteristic
345	D₄	—	2	2	no	—
346	D₄	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	#10597265	1	4	yes	complemented
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	8	8	no	—
368	C₂×C₄	—	152	1	no	—
369	C₂×C₄	—	152	1	no	—
370	C₂×C₄	—	152	1	no	—
371	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
372	C₂×C₄	#10597370	1	1	yes	characteristic
373	C₂×C₄	#10597370	1	1	yes	characteristic
374	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
375	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
376	C₂×C₄	#10597375	1	1	yes	characteristic
377	C₂×C₄	#10597378	1	1	yes	characteristic
378	C₂×C₄	#10597378	1	1	yes	characteristic
379	C₂×C₄	C₂×#64526	1	1	yes	characteristic
380	C₂×C₄	C₂×#64526	1	1	yes	characteristic
381	C₂×C₄	C₂×#64527	1	1	yes	characteristic
382	C₂×C₄	#10597388	1	1	yes	characteristic
383	C₂×C₄	#10597395	1	1	yes	characteristic
384	C₂×C₄	#10597396	1	1	yes	characteristic
385	C₈	—	38	4	no	—
386	C₈	—	76	2	no	—
387	C₈	—	152	1	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	#11926417	1	1	yes	characteristic
396	C₂²	#11926683	1	1	yes	characteristic
397	C₂²	#11926689	1	1	yes	characteristic
398	C₂²	#11926695	1	1	yes	characteristic
399	C₂²	#11926695	1	1	yes	characteristic
400	C₂²	#11926712	1	1	yes	characteristic
401	C₂²	#11926727	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	8	1	no	—
407	C₄	—	8	2	no	—
408	C₄	—	304	1	no	—
409	C₄	C₂×#10597265	1	1	yes	characteristic
410	C₄	#11926584	1	1	yes	characteristic
411	C₄	C₄×#64526	1	1	yes	characteristic
412	C₄	#11926654	1	1	yes	characteristic
413	C₄	#11926834	1	1	yes	characteristic
414	C₄	#11926844	1	1	yes	characteristic
415	C₄	#11926862	1	1	yes	characteristic
416	C₄	#11926874	1	1	yes	characteristic
417	C₂	—	4	4	no	—
418	C₂	#14562707	1	1	yes	characteristic
419	C₂	#14562751	1	1	yes	characteristic
420	C₂	#14562898	1	1	yes	characteristic
421	C₂	#14562919	1	1	yes	characteristic
422	C₂	#14563828	1	1	yes	characteristic
423	C₂	#14563861	1	1	yes	characteristic
424	C₂	#14563896	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	D₄×C₄⋊C₄×C₁₉	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	D₄×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#8886
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ D₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. #14564398	C₂	semidirect
2. #14563791	C₂	semidirect
5. #14561518	C₂	semidirect
6. #14561476	C₂	semidirect
17. D₄⋊(C₁₉⋊C₈)	C₄	semidirect
62. C₄⋊(C₁₉⋊C₈)	C₂×C₄	semidirect
64. C₄×C₁₉⋊C₈	C₂×C₄	semidirect
136. D₄×C₁₉	#106	semidirect
277. C₁₉	#8886	semidirect
348. D₄	#10597265	semidirect

Maximal subgroups

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

subgroup	index
#14564398	2
#14563791	2
#14563635	2
C₂×D₄⋊(C₁₉⋊C₈)	2
#14561518	2
#14561476	2
D₄×C₄⋊C₄×C₁₉	2
#8886	19