Subgroups — #18076958

Order 4864.

644 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564442	C₂	1	1	yes	maximal, characteristic
2	#14564398	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564393	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926288	C₂	1	1	yes	maximal, characteristic
5	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2366	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597264	—	2	1	no	—
9	C₂×#10597265	—	2	1	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	2	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	#11926288	C₄	1	4	yes	complemented
18	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₉	—	2	1	no	—
20	C₂×C₄×D₄×C₁₉	—	2	1	no	—
21	C₁₉×#390	—	2	1	no	—
22	C₁₉×#390	—	2	1	no	—
23	C₁₉×#386	—	2	2	no	—
24	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×D₄×C₁₉	—	2	1	no	—
27	C₂²×D₄×C₁₉	—	2	1	no	—
28	C₂²×D₄×C₁₉	D₄	1	2	yes	—
29	C₂³×C₄×C₁₉	—	2	2	no	—
30	C₁₉×#127	—	2	1	no	—
31	C₁₉×#127	—	2	1	no	—
32	C₁₉×#127	C₂×C₄	1	2	yes	—
33	C₁₉×#127	Q₈	1	2	yes	—
34	C₄×D₄×C₁₉	—	4	2	no	—
35	C₄×D₄×C₁₉	—	4	2	no	—
36	C₄×D₄×C₁₉	—	4	2	no	—
37	C₄×D₄×C₁₉	—	4	2	no	—
38	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
45	C₂×C₄²×C₁₉	—	2	1	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	1	no	—
55	C₁₉×#95	—	2	1	no	—
56	#10597289	—	4	4	no	—
57	#10597265	—	4	2	no	—
58	#10597264	—	4	2	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
61	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	complemented
62	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	complemented
63	C₄×C₁₉⋊C₈	—	2	1	no	—
64	C₄×C₁₉⋊C₈	—	2	1	no	—
65	C₂⁴×C₁₉	—	2	2	no	—
66	C₂×D₄×C₁₉	—	2	2	no	—
67	C₂×D₄×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	—	4	2	no	—
72	C₂×D₄×C₁₉	—	4	2	no	—
73	C₂×D₄×C₁₉	—	4	1	no	—
74	C₂×D₄×C₁₉	—	4	1	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	C₄⋊C₄	1	4	yes	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	4	4	no	—
87	C₂²×C₄×C₁₉	—	4	4	no	—
88	C₂²×C₄×C₁₉	—	8	2	no	—
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×Dic₁₉	—	4	1	no	—
93	C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₄⋊C₄×C₁₉	D₈	1	2	yes	—
100	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	—
101	C₂²⋊C₄×C₁₉	—	4	4	no	—
102	C₂²⋊C₄×C₁₉	—	4	4	no	—
103	C₂²⋊C₄×C₁₉	—	8	2	no	—
104	C₄²×C₁₉	—	4	1	no	—
105	C₄²×C₁₉	—	4	1	no	—
106	C₄²×C₁₉	—	4	1	no	—
107	C₄²×C₁₉	—	4	1	no	—
108	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
110	C₄²×C₁₉	#41	1	1	yes	characteristic
111	C₄²×C₁₉	#41	1	1	yes	characteristic
112	C₄⋊Dic₁₉	—	4	2	no	—
113	C₄⋊Dic₁₉	—	4	1	no	—
114	C₄⋊Dic₁₉	—	4	1	no	—
115	C₄⋊Dic₁₉	—	4	1	no	—
116	C₄⋊Dic₁₉	—	4	1	no	—
117	C₂×C₁₉⋊C₈	—	2	2	no	—
118	C₂×C₁₉⋊C₈	—	2	2	no	—
119	C₂×C₁₉⋊C₈	—	2	2	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	C₂×C₁₉⋊C₈	—	4	1	no	—
125	C₂×C₁₉⋊C₈	—	4	1	no	—
126	#8921	—	19	1	no	maximal, Sylow
127	C₂³×C₁₉	—	2	4	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	—	4	2	no	—
130	C₂³×C₁₉	—	4	2	no	—
131	C₂³×C₁₉	—	4	2	no	—
132	C₂³×C₁₉	—	4	2	no	—
133	C₂³×C₁₉	—	4	2	no	—
134	C₂³×C₁₉	#120	1	1	yes	characteristic
135	D₄×C₁₉	—	4	4	no	—
136	D₄×C₁₉	—	4	2	no	—
137	D₄×C₁₉	—	4	2	no	—
138	D₄×C₁₉	—	4	2	no	—
139	D₄×C₁₉	—	4	2	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	—	8	2	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	8	8	no	—
160	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
170	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
172	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
174	C₂×Dic₁₉	—	8	1	no	—
175	C₂×Dic₁₉	—	8	1	no	—
176	C₂×Dic₁₉	—	8	1	no	—
177	C₁₉⋊C₈	—	4	2	no	—
178	C₁₉⋊C₈	—	4	2	no	—
179	C₁₉⋊C₈	—	4	2	no	—
180	#2366	D₁₉	1	1	yes	characteristic
181	#1957	—	19	1	no	—
182	#1948	—	19	1	no	—
183	#1947	—	19	1	no	—
184	C₂×#331	—	19	1	no	—
185	#1279	—	19	1	no	—
186	#1279	—	19	1	no	—
187	C₂²×C₁₉	—	4	4	no	—
188	C₂²×C₁₉	—	4	4	no	—
189	C₂²×C₁₉	—	4	4	no	—
190	C₂²×C₁₉	—	8	2	no	—
191	C₂²×C₁₉	—	8	2	no	—
192	C₂²×C₁₉	—	8	2	no	—
193	C₂²×C₁₉	—	8	2	no	—
194	C₂²×C₁₉	#385	1	1	yes	characteristic
195	C₂²×C₁₉	#447	1	1	yes	characteristic
196	C₂²×C₁₉	#449	1	1	yes	characteristic
197	C₂²×C₁₉	#450	1	1	yes	characteristic
198	C₂²×C₁₉	#452	1	1	yes	characteristic
199	C₂²×C₁₉	#453	1	1	yes	characteristic
200	C₂²×C₁₉	#455	1	1	yes	characteristic
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	—	8	1	no	—
206	C₄×C₁₉	—	8	1	no	—
207	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
208	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
209	C₄×C₁₉	#440	1	1	yes	characteristic
210	C₄×C₁₉	#442	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	—	16	1	no	—
216	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
217	C₂×C₄×D₄	—	2	1	no	—
218	C₂×C₄×D₄	—	2	1	no	—
219	C₂×#107	—	38	1	no	—
220	C₂×#106	—	38	1	no	—
221	C₂×C₄⋊C₈	—	19	1	no	—
222	C₂×C₄⋊C₈	—	19	1	no	—
223	C₂×#102	—	38	2	no	—
224	C₂×C₄×C₈	—	19	1	no	—
225	#390	—	2	1	no	—
226	#390	—	2	1	no	—
227	#386	—	2	2	no	—
228	#384	—	19	1	no	—
229	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
230	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
231	#340	—	38	1	no	—
232	#340	—	38	1	no	—
233	#331	—	19	4	no	—
234	C₂×C₁₉	—	8	4	no	—
235	C₂×C₁₉	#1621	1	1	yes	characteristic
236	C₂×C₁₉	#1631	1	1	yes	characteristic
237	C₂×C₁₉	#1639	1	1	yes	characteristic
238	C₂×C₁₉	#1640	1	1	yes	characteristic
239	C₂×C₁₉	#1856	1	1	yes	characteristic
240	C₂×C₁₉	#1862	1	1	yes	characteristic
241	C₂×C₁₉	#1864	1	1	yes	characteristic
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
245	C₂³×C₄	—	2	2	no	—
246	C₂²×C₈	—	38	1	no	—
247	C₂²×C₈	—	38	1	no	—
248	C₂²×C₈	—	38	1	no	—
249	#127	—	2	1	no	—
250	#127	—	2	1	no	—
251	#127	Dic₃₈	1	2	yes	—
252	#127	C₄×D₁₉	1	2	yes	—
253	C₄×D₄	—	4	2	no	—
254	C₄×D₄	—	4	2	no	—
255	C₄×D₄	—	4	2	no	—
256	C₄×D₄	—	4	2	no	—
257	C₂×C₄⋊C₄	—	38	1	no	—
258	C₂×C₄⋊C₄	—	38	1	no	—
259	C₂×C₄⋊C₄	—	38	1	no	—
260	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
270	#107	—	76	2	no	—
271	#106	—	76	2	no	—
272	C₄⋊C₈	—	19	2	no	—
273	C₄⋊C₈	—	19	2	no	—
274	C₄⋊C₈	—	38	1	no	—
275	C₄⋊C₈	—	38	1	no	—
276	#102	—	76	4	no	—
277	C₄×C₈	—	38	1	no	—
278	C₄×C₈	—	38	1	no	—
279	#95	—	2	1	no	—
280	#95	—	2	1	no	—
281	C₁₉	#8921	1	1	yes	characteristic, complemented, Sylow
282	C₂⁴	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	Dic₁₉⋊C₄	1	4	yes	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	4	4	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	8	2	no	—
306	C₂²×C₄	—	76	1	no	—
307	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
310	C₂×C₈	—	38	2	no	—
311	C₂×C₈	—	38	2	no	—
312	C₂×C₈	—	38	2	no	—
313	C₂×C₈	—	76	1	no	—
314	C₂×C₈	—	76	1	no	—
315	C₂×C₈	—	76	1	no	—
316	C₂×C₈	—	76	1	no	—
317	C₂×C₈	—	76	1	no	—
318	C₂×C₈	—	76	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	76	2	no	—
326	C₄⋊C₄	—	76	1	no	—
327	C₄⋊C₄	—	76	1	no	—
328	C₄⋊C₄	—	76	1	no	—
329	C₄⋊C₄	—	76	1	no	—
330	C₄⋊C₄	#64525	1	2	yes	—
331	C₄⋊C₄	#64526	1	2	yes	—
332	C₂²⋊C₄	—	4	4	no	—
333	C₂²⋊C₄	—	4	4	no	—
334	C₂²⋊C₄	—	8	2	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	—	4	1	no	—
338	C₄²	—	4	1	no	—
339	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
340	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
341	C₄²	#64541	1	1	yes	characteristic
342	C₄²	#64541	1	1	yes	characteristic
343	C₂³	—	2	4	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	#10597399	1	1	yes	characteristic
351	D₄	—	4	4	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	8	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	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	8	no	—
376	C₂×C₄	—	152	1	no	—
377	C₂×C₄	—	152	1	no	—
378	C₂×C₄	—	152	1	no	—
379	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
380	C₂×C₄	#10597370	1	1	yes	characteristic
381	C₂×C₄	#10597370	1	1	yes	characteristic
382	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
383	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
384	C₂×C₄	#10597375	1	1	yes	characteristic
385	C₂×C₄	C₂×#64525	1	1	yes	characteristic
386	C₂×C₄	#10597378	1	1	yes	characteristic
387	C₂×C₄	#10597378	1	1	yes	characteristic
388	C₂×C₄	C₂×#64526	1	1	yes	characteristic
389	C₂×C₄	#10597395	1	1	yes	characteristic
390	C₂×C₄	#10597396	1	1	yes	characteristic
391	C₂×C₄	#10597396	1	1	yes	characteristic
392	C₂×C₄	#10597397	1	1	yes	characteristic
393	C₈	—	76	2	no	—
394	C₈	—	76	2	no	—
395	C₈	—	76	2	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	#11926417	1	1	yes	characteristic
404	C₂²	#11926678	1	1	yes	characteristic
405	C₂²	#11926689	1	1	yes	characteristic
406	C₂²	#11926695	1	1	yes	characteristic
407	C₂²	#11926706	1	1	yes	characteristic
408	C₂²	#11926712	1	1	yes	characteristic
409	C₂²	#11926722	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	1	no	—
415	C₄	—	8	1	no	—
416	C₄	—	304	1	no	—
417	C₄	C₄×#64525	1	1	yes	characteristic
418	C₄	C₄×#64526	1	1	yes	characteristic
419	C₄	#11926644	1	1	yes	characteristic
420	C₄	#11926654	1	1	yes	characteristic
421	C₄	#11926824	1	1	yes	characteristic
422	C₄	#11926834	1	1	yes	characteristic
423	C₄	#11926844	1	1	yes	characteristic
424	C₄	#11926844	1	1	yes	characteristic
425	C₂	—	8	4	no	—
426	C₂	#14562700	1	1	yes	characteristic
427	C₂	#14562762	1	1	yes	characteristic
428	C₂	#14562814	1	1	yes	characteristic
429	C₂	#14562821	1	1	yes	characteristic
430	C₂	#14563845	1	1	yes	characteristic
431	C₂	#14563882	1	1	yes	characteristic
432	C₂	#14563896	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2366	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×C₁₉×#127	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2366	D₁₉
hypocenter	C₁₉	#8921
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2366

Complements

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

N	H ≅ G/N	type
2. #14564398	C₂	semidirect
3. #14564393	C₂	semidirect
5. #14561476	C₂	semidirect
6. #14561476	C₂	semidirect
17. #11926288	C₄	semidirect
61. C₄⋊(C₁₉⋊C₈)	C₂×C₄	semidirect
62. C₄⋊(C₁₉⋊C₈)	C₂×C₄	semidirect
281. C₁₉	#8921	semidirect

Maximal subgroups

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

subgroup	index
#14564442	2
#14564398	2
#14564393	2
C₂×#11926288	2
#14561476	2
C₁₉×#2366	2
#8921	19